Identifier
Mp00109:
Permutations
—descent word⟶
Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Images
=>
[1]=>=>[]=>[]
[1,2]=>0=>[1]=>[1]
[2,1]=>1=>[1]=>[1]
[1,2,3]=>00=>[2]=>[2]
[1,3,2]=>01=>[1,1]=>[1,1]
[2,1,3]=>10=>[1,1]=>[1,1]
[2,3,1]=>01=>[1,1]=>[1,1]
[3,1,2]=>10=>[1,1]=>[1,1]
[3,2,1]=>11=>[2]=>[2]
[1,2,3,4]=>000=>[3]=>[3]
[1,2,4,3]=>001=>[2,1]=>[1,2]
[1,3,2,4]=>010=>[1,1,1]=>[1,1,1]
[1,3,4,2]=>001=>[2,1]=>[1,2]
[1,4,2,3]=>010=>[1,1,1]=>[1,1,1]
[1,4,3,2]=>011=>[1,2]=>[2,1]
[2,1,3,4]=>100=>[1,2]=>[2,1]
[2,1,4,3]=>101=>[1,1,1]=>[1,1,1]
[2,3,1,4]=>010=>[1,1,1]=>[1,1,1]
[2,3,4,1]=>001=>[2,1]=>[1,2]
[2,4,1,3]=>010=>[1,1,1]=>[1,1,1]
[2,4,3,1]=>011=>[1,2]=>[2,1]
[3,1,2,4]=>100=>[1,2]=>[2,1]
[3,1,4,2]=>101=>[1,1,1]=>[1,1,1]
[3,2,1,4]=>110=>[2,1]=>[1,2]
[3,2,4,1]=>101=>[1,1,1]=>[1,1,1]
[3,4,1,2]=>010=>[1,1,1]=>[1,1,1]
[3,4,2,1]=>011=>[1,2]=>[2,1]
[4,1,2,3]=>100=>[1,2]=>[2,1]
[4,1,3,2]=>101=>[1,1,1]=>[1,1,1]
[4,2,1,3]=>110=>[2,1]=>[1,2]
[4,2,3,1]=>101=>[1,1,1]=>[1,1,1]
[4,3,1,2]=>110=>[2,1]=>[1,2]
[4,3,2,1]=>111=>[3]=>[3]
[1,2,3,4,5]=>0000=>[4]=>[4]
[1,2,3,5,4]=>0001=>[3,1]=>[1,3]
[1,2,4,3,5]=>0010=>[2,1,1]=>[1,1,2]
[1,2,4,5,3]=>0001=>[3,1]=>[1,3]
[1,2,5,3,4]=>0010=>[2,1,1]=>[1,1,2]
[1,2,5,4,3]=>0011=>[2,2]=>[2,2]
[1,3,2,4,5]=>0100=>[1,1,2]=>[2,1,1]
[1,3,2,5,4]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,3,4,2,5]=>0010=>[2,1,1]=>[1,1,2]
[1,3,4,5,2]=>0001=>[3,1]=>[1,3]
[1,3,5,2,4]=>0010=>[2,1,1]=>[1,1,2]
[1,3,5,4,2]=>0011=>[2,2]=>[2,2]
[1,4,2,3,5]=>0100=>[1,1,2]=>[2,1,1]
[1,4,2,5,3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,4,3,2,5]=>0110=>[1,2,1]=>[1,2,1]
[1,4,3,5,2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,4,5,2,3]=>0010=>[2,1,1]=>[1,1,2]
[1,4,5,3,2]=>0011=>[2,2]=>[2,2]
[1,5,2,3,4]=>0100=>[1,1,2]=>[2,1,1]
[1,5,2,4,3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,5,3,2,4]=>0110=>[1,2,1]=>[1,2,1]
[1,5,3,4,2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[1,5,4,2,3]=>0110=>[1,2,1]=>[1,2,1]
[1,5,4,3,2]=>0111=>[1,3]=>[3,1]
[2,1,3,4,5]=>1000=>[1,3]=>[3,1]
[2,1,3,5,4]=>1001=>[1,2,1]=>[1,2,1]
[2,1,4,3,5]=>1010=>[1,1,1,1]=>[1,1,1,1]
[2,1,4,5,3]=>1001=>[1,2,1]=>[1,2,1]
[2,1,5,3,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[2,1,5,4,3]=>1011=>[1,1,2]=>[2,1,1]
[2,3,1,4,5]=>0100=>[1,1,2]=>[2,1,1]
[2,3,1,5,4]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,3,4,1,5]=>0010=>[2,1,1]=>[1,1,2]
[2,3,4,5,1]=>0001=>[3,1]=>[1,3]
[2,3,5,1,4]=>0010=>[2,1,1]=>[1,1,2]
[2,3,5,4,1]=>0011=>[2,2]=>[2,2]
[2,4,1,3,5]=>0100=>[1,1,2]=>[2,1,1]
[2,4,1,5,3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,4,3,1,5]=>0110=>[1,2,1]=>[1,2,1]
[2,4,3,5,1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,4,5,1,3]=>0010=>[2,1,1]=>[1,1,2]
[2,4,5,3,1]=>0011=>[2,2]=>[2,2]
[2,5,1,3,4]=>0100=>[1,1,2]=>[2,1,1]
[2,5,1,4,3]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,5,3,1,4]=>0110=>[1,2,1]=>[1,2,1]
[2,5,3,4,1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[2,5,4,1,3]=>0110=>[1,2,1]=>[1,2,1]
[2,5,4,3,1]=>0111=>[1,3]=>[3,1]
[3,1,2,4,5]=>1000=>[1,3]=>[3,1]
[3,1,2,5,4]=>1001=>[1,2,1]=>[1,2,1]
[3,1,4,2,5]=>1010=>[1,1,1,1]=>[1,1,1,1]
[3,1,4,5,2]=>1001=>[1,2,1]=>[1,2,1]
[3,1,5,2,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[3,1,5,4,2]=>1011=>[1,1,2]=>[2,1,1]
[3,2,1,4,5]=>1100=>[2,2]=>[2,2]
[3,2,1,5,4]=>1101=>[2,1,1]=>[1,1,2]
[3,2,4,1,5]=>1010=>[1,1,1,1]=>[1,1,1,1]
[3,2,4,5,1]=>1001=>[1,2,1]=>[1,2,1]
[3,2,5,1,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[3,2,5,4,1]=>1011=>[1,1,2]=>[2,1,1]
[3,4,1,2,5]=>0100=>[1,1,2]=>[2,1,1]
[3,4,1,5,2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,4,2,1,5]=>0110=>[1,2,1]=>[1,2,1]
[3,4,2,5,1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,4,5,1,2]=>0010=>[2,1,1]=>[1,1,2]
[3,4,5,2,1]=>0011=>[2,2]=>[2,2]
[3,5,1,2,4]=>0100=>[1,1,2]=>[2,1,1]
[3,5,1,4,2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,5,2,1,4]=>0110=>[1,2,1]=>[1,2,1]
[3,5,2,4,1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[3,5,4,1,2]=>0110=>[1,2,1]=>[1,2,1]
[3,5,4,2,1]=>0111=>[1,3]=>[3,1]
[4,1,2,3,5]=>1000=>[1,3]=>[3,1]
[4,1,2,5,3]=>1001=>[1,2,1]=>[1,2,1]
[4,1,3,2,5]=>1010=>[1,1,1,1]=>[1,1,1,1]
[4,1,3,5,2]=>1001=>[1,2,1]=>[1,2,1]
[4,1,5,2,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[4,1,5,3,2]=>1011=>[1,1,2]=>[2,1,1]
[4,2,1,3,5]=>1100=>[2,2]=>[2,2]
[4,2,1,5,3]=>1101=>[2,1,1]=>[1,1,2]
[4,2,3,1,5]=>1010=>[1,1,1,1]=>[1,1,1,1]
[4,2,3,5,1]=>1001=>[1,2,1]=>[1,2,1]
[4,2,5,1,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[4,2,5,3,1]=>1011=>[1,1,2]=>[2,1,1]
[4,3,1,2,5]=>1100=>[2,2]=>[2,2]
[4,3,1,5,2]=>1101=>[2,1,1]=>[1,1,2]
[4,3,2,1,5]=>1110=>[3,1]=>[1,3]
[4,3,2,5,1]=>1101=>[2,1,1]=>[1,1,2]
[4,3,5,1,2]=>1010=>[1,1,1,1]=>[1,1,1,1]
[4,3,5,2,1]=>1011=>[1,1,2]=>[2,1,1]
[4,5,1,2,3]=>0100=>[1,1,2]=>[2,1,1]
[4,5,1,3,2]=>0101=>[1,1,1,1]=>[1,1,1,1]
[4,5,2,1,3]=>0110=>[1,2,1]=>[1,2,1]
[4,5,2,3,1]=>0101=>[1,1,1,1]=>[1,1,1,1]
[4,5,3,1,2]=>0110=>[1,2,1]=>[1,2,1]
[4,5,3,2,1]=>0111=>[1,3]=>[3,1]
[5,1,2,3,4]=>1000=>[1,3]=>[3,1]
[5,1,2,4,3]=>1001=>[1,2,1]=>[1,2,1]
[5,1,3,2,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[5,1,3,4,2]=>1001=>[1,2,1]=>[1,2,1]
[5,1,4,2,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[5,1,4,3,2]=>1011=>[1,1,2]=>[2,1,1]
[5,2,1,3,4]=>1100=>[2,2]=>[2,2]
[5,2,1,4,3]=>1101=>[2,1,1]=>[1,1,2]
[5,2,3,1,4]=>1010=>[1,1,1,1]=>[1,1,1,1]
[5,2,3,4,1]=>1001=>[1,2,1]=>[1,2,1]
[5,2,4,1,3]=>1010=>[1,1,1,1]=>[1,1,1,1]
[5,2,4,3,1]=>1011=>[1,1,2]=>[2,1,1]
[5,3,1,2,4]=>1100=>[2,2]=>[2,2]
[5,3,1,4,2]=>1101=>[2,1,1]=>[1,1,2]
[5,3,2,1,4]=>1110=>[3,1]=>[1,3]
[5,3,2,4,1]=>1101=>[2,1,1]=>[1,1,2]
[5,3,4,1,2]=>1010=>[1,1,1,1]=>[1,1,1,1]
[5,3,4,2,1]=>1011=>[1,1,2]=>[2,1,1]
[5,4,1,2,3]=>1100=>[2,2]=>[2,2]
[5,4,1,3,2]=>1101=>[2,1,1]=>[1,1,2]
[5,4,2,1,3]=>1110=>[3,1]=>[1,3]
[5,4,2,3,1]=>1101=>[2,1,1]=>[1,1,2]
[5,4,3,1,2]=>1110=>[3,1]=>[1,3]
[5,4,3,2,1]=>1111=>[4]=>[4]
[1,2,3,4,5,6]=>00000=>[5]=>[5]
[1,2,3,4,6,5]=>00001=>[4,1]=>[1,4]
[1,2,3,5,4,6]=>00010=>[3,1,1]=>[1,1,3]
[1,2,3,5,6,4]=>00001=>[4,1]=>[1,4]
[1,2,3,6,4,5]=>00010=>[3,1,1]=>[1,1,3]
[1,2,3,6,5,4]=>00011=>[3,2]=>[2,3]
[1,2,4,3,5,6]=>00100=>[2,1,2]=>[2,1,2]
[1,2,4,3,6,5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,4,5,3,6]=>00010=>[3,1,1]=>[1,1,3]
[1,2,4,5,6,3]=>00001=>[4,1]=>[1,4]
[1,2,4,6,3,5]=>00010=>[3,1,1]=>[1,1,3]
[1,2,4,6,5,3]=>00011=>[3,2]=>[2,3]
[1,2,5,3,4,6]=>00100=>[2,1,2]=>[2,1,2]
[1,2,5,3,6,4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,5,4,3,6]=>00110=>[2,2,1]=>[1,2,2]
[1,2,5,4,6,3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,5,6,3,4]=>00010=>[3,1,1]=>[1,1,3]
[1,2,5,6,4,3]=>00011=>[3,2]=>[2,3]
[1,2,6,3,4,5]=>00100=>[2,1,2]=>[2,1,2]
[1,2,6,3,5,4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,6,4,3,5]=>00110=>[2,2,1]=>[1,2,2]
[1,2,6,4,5,3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,2,6,5,3,4]=>00110=>[2,2,1]=>[1,2,2]
[1,2,6,5,4,3]=>00111=>[2,3]=>[3,2]
[1,3,2,4,5,6]=>01000=>[1,1,3]=>[3,1,1]
[1,3,2,4,6,5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,3,2,5,4,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,3,2,5,6,4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,3,2,6,4,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,3,2,6,5,4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,3,4,2,5,6]=>00100=>[2,1,2]=>[2,1,2]
[1,3,4,2,6,5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,4,5,2,6]=>00010=>[3,1,1]=>[1,1,3]
[1,3,4,5,6,2]=>00001=>[4,1]=>[1,4]
[1,3,4,6,2,5]=>00010=>[3,1,1]=>[1,1,3]
[1,3,4,6,5,2]=>00011=>[3,2]=>[2,3]
[1,3,5,2,4,6]=>00100=>[2,1,2]=>[2,1,2]
[1,3,5,2,6,4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,5,4,2,6]=>00110=>[2,2,1]=>[1,2,2]
[1,3,5,4,6,2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,5,6,2,4]=>00010=>[3,1,1]=>[1,1,3]
[1,3,5,6,4,2]=>00011=>[3,2]=>[2,3]
[1,3,6,2,4,5]=>00100=>[2,1,2]=>[2,1,2]
[1,3,6,2,5,4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,6,4,2,5]=>00110=>[2,2,1]=>[1,2,2]
[1,3,6,4,5,2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,3,6,5,2,4]=>00110=>[2,2,1]=>[1,2,2]
[1,3,6,5,4,2]=>00111=>[2,3]=>[3,2]
[1,4,2,3,5,6]=>01000=>[1,1,3]=>[3,1,1]
[1,4,2,3,6,5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,4,2,5,3,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,4,2,5,6,3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,4,2,6,3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,4,2,6,5,3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,4,3,2,5,6]=>01100=>[1,2,2]=>[2,2,1]
[1,4,3,2,6,5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,4,3,5,2,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,4,3,5,6,2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,4,3,6,2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,4,3,6,5,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,4,5,2,3,6]=>00100=>[2,1,2]=>[2,1,2]
[1,4,5,2,6,3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,5,3,2,6]=>00110=>[2,2,1]=>[1,2,2]
[1,4,5,3,6,2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,5,6,2,3]=>00010=>[3,1,1]=>[1,1,3]
[1,4,5,6,3,2]=>00011=>[3,2]=>[2,3]
[1,4,6,2,3,5]=>00100=>[2,1,2]=>[2,1,2]
[1,4,6,2,5,3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,6,3,2,5]=>00110=>[2,2,1]=>[1,2,2]
[1,4,6,3,5,2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,4,6,5,2,3]=>00110=>[2,2,1]=>[1,2,2]
[1,4,6,5,3,2]=>00111=>[2,3]=>[3,2]
[1,5,2,3,4,6]=>01000=>[1,1,3]=>[3,1,1]
[1,5,2,3,6,4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,5,2,4,3,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,5,2,4,6,3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,5,2,6,3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,5,2,6,4,3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,5,3,2,4,6]=>01100=>[1,2,2]=>[2,2,1]
[1,5,3,2,6,4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,5,3,4,2,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,5,3,4,6,2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,5,3,6,2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,5,3,6,4,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,5,4,2,3,6]=>01100=>[1,2,2]=>[2,2,1]
[1,5,4,2,6,3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,5,4,3,2,6]=>01110=>[1,3,1]=>[1,3,1]
[1,5,4,3,6,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,5,4,6,2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,5,4,6,3,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,5,6,2,3,4]=>00100=>[2,1,2]=>[2,1,2]
[1,5,6,2,4,3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,5,6,3,2,4]=>00110=>[2,2,1]=>[1,2,2]
[1,5,6,3,4,2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[1,5,6,4,2,3]=>00110=>[2,2,1]=>[1,2,2]
[1,5,6,4,3,2]=>00111=>[2,3]=>[3,2]
[1,6,2,3,4,5]=>01000=>[1,1,3]=>[3,1,1]
[1,6,2,3,5,4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,6,2,4,3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,6,2,4,5,3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,6,2,5,3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,6,2,5,4,3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,6,3,2,4,5]=>01100=>[1,2,2]=>[2,2,1]
[1,6,3,2,5,4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,6,3,4,2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,6,3,4,5,2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[1,6,3,5,2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,6,3,5,4,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,6,4,2,3,5]=>01100=>[1,2,2]=>[2,2,1]
[1,6,4,2,5,3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,6,4,3,2,5]=>01110=>[1,3,1]=>[1,3,1]
[1,6,4,3,5,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,6,4,5,2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,6,4,5,3,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[1,6,5,2,3,4]=>01100=>[1,2,2]=>[2,2,1]
[1,6,5,2,4,3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,6,5,3,2,4]=>01110=>[1,3,1]=>[1,3,1]
[1,6,5,3,4,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[1,6,5,4,2,3]=>01110=>[1,3,1]=>[1,3,1]
[1,6,5,4,3,2]=>01111=>[1,4]=>[4,1]
[2,1,3,4,5,6]=>10000=>[1,4]=>[4,1]
[2,1,3,4,6,5]=>10001=>[1,3,1]=>[1,3,1]
[2,1,3,5,4,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[2,1,3,5,6,4]=>10001=>[1,3,1]=>[1,3,1]
[2,1,3,6,4,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[2,1,3,6,5,4]=>10011=>[1,2,2]=>[2,2,1]
[2,1,4,3,5,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[2,1,4,3,6,5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,1,4,5,3,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[2,1,4,5,6,3]=>10001=>[1,3,1]=>[1,3,1]
[2,1,4,6,3,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[2,1,4,6,5,3]=>10011=>[1,2,2]=>[2,2,1]
[2,1,5,3,4,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[2,1,5,3,6,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,1,5,4,3,6]=>10110=>[1,1,2,1]=>[1,2,1,1]
[2,1,5,4,6,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,1,5,6,3,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[2,1,5,6,4,3]=>10011=>[1,2,2]=>[2,2,1]
[2,1,6,3,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[2,1,6,3,5,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,1,6,4,3,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[2,1,6,4,5,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,1,6,5,3,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[2,1,6,5,4,3]=>10111=>[1,1,3]=>[3,1,1]
[2,3,1,4,5,6]=>01000=>[1,1,3]=>[3,1,1]
[2,3,1,4,6,5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,3,1,5,4,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,3,1,5,6,4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,3,1,6,4,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,3,1,6,5,4]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,3,4,1,5,6]=>00100=>[2,1,2]=>[2,1,2]
[2,3,4,1,6,5]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,4,5,1,6]=>00010=>[3,1,1]=>[1,1,3]
[2,3,4,5,6,1]=>00001=>[4,1]=>[1,4]
[2,3,4,6,1,5]=>00010=>[3,1,1]=>[1,1,3]
[2,3,4,6,5,1]=>00011=>[3,2]=>[2,3]
[2,3,5,1,4,6]=>00100=>[2,1,2]=>[2,1,2]
[2,3,5,1,6,4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,5,4,1,6]=>00110=>[2,2,1]=>[1,2,2]
[2,3,5,4,6,1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,5,6,1,4]=>00010=>[3,1,1]=>[1,1,3]
[2,3,5,6,4,1]=>00011=>[3,2]=>[2,3]
[2,3,6,1,4,5]=>00100=>[2,1,2]=>[2,1,2]
[2,3,6,1,5,4]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,6,4,1,5]=>00110=>[2,2,1]=>[1,2,2]
[2,3,6,4,5,1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,3,6,5,1,4]=>00110=>[2,2,1]=>[1,2,2]
[2,3,6,5,4,1]=>00111=>[2,3]=>[3,2]
[2,4,1,3,5,6]=>01000=>[1,1,3]=>[3,1,1]
[2,4,1,3,6,5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,4,1,5,3,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,4,1,5,6,3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,4,1,6,3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,4,1,6,5,3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,4,3,1,5,6]=>01100=>[1,2,2]=>[2,2,1]
[2,4,3,1,6,5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,4,3,5,1,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,4,3,5,6,1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,4,3,6,1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,4,3,6,5,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,4,5,1,3,6]=>00100=>[2,1,2]=>[2,1,2]
[2,4,5,1,6,3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,5,3,1,6]=>00110=>[2,2,1]=>[1,2,2]
[2,4,5,3,6,1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,5,6,1,3]=>00010=>[3,1,1]=>[1,1,3]
[2,4,5,6,3,1]=>00011=>[3,2]=>[2,3]
[2,4,6,1,3,5]=>00100=>[2,1,2]=>[2,1,2]
[2,4,6,1,5,3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,6,3,1,5]=>00110=>[2,2,1]=>[1,2,2]
[2,4,6,3,5,1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,4,6,5,1,3]=>00110=>[2,2,1]=>[1,2,2]
[2,4,6,5,3,1]=>00111=>[2,3]=>[3,2]
[2,5,1,3,4,6]=>01000=>[1,1,3]=>[3,1,1]
[2,5,1,3,6,4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,5,1,4,3,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,5,1,4,6,3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,5,1,6,3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,5,1,6,4,3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,5,3,1,4,6]=>01100=>[1,2,2]=>[2,2,1]
[2,5,3,1,6,4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,5,3,4,1,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,5,3,4,6,1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,5,3,6,1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,5,3,6,4,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,5,4,1,3,6]=>01100=>[1,2,2]=>[2,2,1]
[2,5,4,1,6,3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,5,4,3,1,6]=>01110=>[1,3,1]=>[1,3,1]
[2,5,4,3,6,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,5,4,6,1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,5,4,6,3,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,5,6,1,3,4]=>00100=>[2,1,2]=>[2,1,2]
[2,5,6,1,4,3]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,5,6,3,1,4]=>00110=>[2,2,1]=>[1,2,2]
[2,5,6,3,4,1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[2,5,6,4,1,3]=>00110=>[2,2,1]=>[1,2,2]
[2,5,6,4,3,1]=>00111=>[2,3]=>[3,2]
[2,6,1,3,4,5]=>01000=>[1,1,3]=>[3,1,1]
[2,6,1,3,5,4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,6,1,4,3,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,6,1,4,5,3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,6,1,5,3,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,6,1,5,4,3]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,6,3,1,4,5]=>01100=>[1,2,2]=>[2,2,1]
[2,6,3,1,5,4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,6,3,4,1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,6,3,4,5,1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[2,6,3,5,1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,6,3,5,4,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,6,4,1,3,5]=>01100=>[1,2,2]=>[2,2,1]
[2,6,4,1,5,3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,6,4,3,1,5]=>01110=>[1,3,1]=>[1,3,1]
[2,6,4,3,5,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,6,4,5,1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[2,6,4,5,3,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[2,6,5,1,3,4]=>01100=>[1,2,2]=>[2,2,1]
[2,6,5,1,4,3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,6,5,3,1,4]=>01110=>[1,3,1]=>[1,3,1]
[2,6,5,3,4,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[2,6,5,4,1,3]=>01110=>[1,3,1]=>[1,3,1]
[2,6,5,4,3,1]=>01111=>[1,4]=>[4,1]
[3,1,2,4,5,6]=>10000=>[1,4]=>[4,1]
[3,1,2,4,6,5]=>10001=>[1,3,1]=>[1,3,1]
[3,1,2,5,4,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[3,1,2,5,6,4]=>10001=>[1,3,1]=>[1,3,1]
[3,1,2,6,4,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[3,1,2,6,5,4]=>10011=>[1,2,2]=>[2,2,1]
[3,1,4,2,5,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[3,1,4,2,6,5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,1,4,5,2,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[3,1,4,5,6,2]=>10001=>[1,3,1]=>[1,3,1]
[3,1,4,6,2,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[3,1,4,6,5,2]=>10011=>[1,2,2]=>[2,2,1]
[3,1,5,2,4,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[3,1,5,2,6,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,1,5,4,2,6]=>10110=>[1,1,2,1]=>[1,2,1,1]
[3,1,5,4,6,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,1,5,6,2,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[3,1,5,6,4,2]=>10011=>[1,2,2]=>[2,2,1]
[3,1,6,2,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[3,1,6,2,5,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,1,6,4,2,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[3,1,6,4,5,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,1,6,5,2,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[3,1,6,5,4,2]=>10111=>[1,1,3]=>[3,1,1]
[3,2,1,4,5,6]=>11000=>[2,3]=>[3,2]
[3,2,1,4,6,5]=>11001=>[2,2,1]=>[1,2,2]
[3,2,1,5,4,6]=>11010=>[2,1,1,1]=>[1,1,1,2]
[3,2,1,5,6,4]=>11001=>[2,2,1]=>[1,2,2]
[3,2,1,6,4,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[3,2,1,6,5,4]=>11011=>[2,1,2]=>[2,1,2]
[3,2,4,1,5,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[3,2,4,1,6,5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,2,4,5,1,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[3,2,4,5,6,1]=>10001=>[1,3,1]=>[1,3,1]
[3,2,4,6,1,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[3,2,4,6,5,1]=>10011=>[1,2,2]=>[2,2,1]
[3,2,5,1,4,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[3,2,5,1,6,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,2,5,4,1,6]=>10110=>[1,1,2,1]=>[1,2,1,1]
[3,2,5,4,6,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,2,5,6,1,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[3,2,5,6,4,1]=>10011=>[1,2,2]=>[2,2,1]
[3,2,6,1,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[3,2,6,1,5,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,2,6,4,1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[3,2,6,4,5,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,2,6,5,1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[3,2,6,5,4,1]=>10111=>[1,1,3]=>[3,1,1]
[3,4,1,2,5,6]=>01000=>[1,1,3]=>[3,1,1]
[3,4,1,2,6,5]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,4,1,5,2,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,4,1,5,6,2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,4,1,6,2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,4,1,6,5,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,4,2,1,5,6]=>01100=>[1,2,2]=>[2,2,1]
[3,4,2,1,6,5]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,4,2,5,1,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,4,2,5,6,1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,4,2,6,1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,4,2,6,5,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,4,5,1,2,6]=>00100=>[2,1,2]=>[2,1,2]
[3,4,5,1,6,2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,5,2,1,6]=>00110=>[2,2,1]=>[1,2,2]
[3,4,5,2,6,1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,5,6,1,2]=>00010=>[3,1,1]=>[1,1,3]
[3,4,5,6,2,1]=>00011=>[3,2]=>[2,3]
[3,4,6,1,2,5]=>00100=>[2,1,2]=>[2,1,2]
[3,4,6,1,5,2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,6,2,1,5]=>00110=>[2,2,1]=>[1,2,2]
[3,4,6,2,5,1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,4,6,5,1,2]=>00110=>[2,2,1]=>[1,2,2]
[3,4,6,5,2,1]=>00111=>[2,3]=>[3,2]
[3,5,1,2,4,6]=>01000=>[1,1,3]=>[3,1,1]
[3,5,1,2,6,4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,5,1,4,2,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,5,1,4,6,2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,5,1,6,2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,5,1,6,4,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,5,2,1,4,6]=>01100=>[1,2,2]=>[2,2,1]
[3,5,2,1,6,4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,5,2,4,1,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,5,2,4,6,1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,5,2,6,1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,5,2,6,4,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,5,4,1,2,6]=>01100=>[1,2,2]=>[2,2,1]
[3,5,4,1,6,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,5,4,2,1,6]=>01110=>[1,3,1]=>[1,3,1]
[3,5,4,2,6,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,5,4,6,1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,5,4,6,2,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,5,6,1,2,4]=>00100=>[2,1,2]=>[2,1,2]
[3,5,6,1,4,2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,5,6,2,1,4]=>00110=>[2,2,1]=>[1,2,2]
[3,5,6,2,4,1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[3,5,6,4,1,2]=>00110=>[2,2,1]=>[1,2,2]
[3,5,6,4,2,1]=>00111=>[2,3]=>[3,2]
[3,6,1,2,4,5]=>01000=>[1,1,3]=>[3,1,1]
[3,6,1,2,5,4]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,6,1,4,2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,6,1,4,5,2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,6,1,5,2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,6,1,5,4,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,6,2,1,4,5]=>01100=>[1,2,2]=>[2,2,1]
[3,6,2,1,5,4]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,6,2,4,1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,6,2,4,5,1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[3,6,2,5,1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,6,2,5,4,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,6,4,1,2,5]=>01100=>[1,2,2]=>[2,2,1]
[3,6,4,1,5,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,6,4,2,1,5]=>01110=>[1,3,1]=>[1,3,1]
[3,6,4,2,5,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,6,4,5,1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[3,6,4,5,2,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[3,6,5,1,2,4]=>01100=>[1,2,2]=>[2,2,1]
[3,6,5,1,4,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,6,5,2,1,4]=>01110=>[1,3,1]=>[1,3,1]
[3,6,5,2,4,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[3,6,5,4,1,2]=>01110=>[1,3,1]=>[1,3,1]
[3,6,5,4,2,1]=>01111=>[1,4]=>[4,1]
[4,1,2,3,5,6]=>10000=>[1,4]=>[4,1]
[4,1,2,3,6,5]=>10001=>[1,3,1]=>[1,3,1]
[4,1,2,5,3,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[4,1,2,5,6,3]=>10001=>[1,3,1]=>[1,3,1]
[4,1,2,6,3,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[4,1,2,6,5,3]=>10011=>[1,2,2]=>[2,2,1]
[4,1,3,2,5,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[4,1,3,2,6,5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,1,3,5,2,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[4,1,3,5,6,2]=>10001=>[1,3,1]=>[1,3,1]
[4,1,3,6,2,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[4,1,3,6,5,2]=>10011=>[1,2,2]=>[2,2,1]
[4,1,5,2,3,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[4,1,5,2,6,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,1,5,3,2,6]=>10110=>[1,1,2,1]=>[1,2,1,1]
[4,1,5,3,6,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,1,5,6,2,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[4,1,5,6,3,2]=>10011=>[1,2,2]=>[2,2,1]
[4,1,6,2,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[4,1,6,2,5,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,1,6,3,2,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[4,1,6,3,5,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,1,6,5,2,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[4,1,6,5,3,2]=>10111=>[1,1,3]=>[3,1,1]
[4,2,1,3,5,6]=>11000=>[2,3]=>[3,2]
[4,2,1,3,6,5]=>11001=>[2,2,1]=>[1,2,2]
[4,2,1,5,3,6]=>11010=>[2,1,1,1]=>[1,1,1,2]
[4,2,1,5,6,3]=>11001=>[2,2,1]=>[1,2,2]
[4,2,1,6,3,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[4,2,1,6,5,3]=>11011=>[2,1,2]=>[2,1,2]
[4,2,3,1,5,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[4,2,3,1,6,5]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,2,3,5,1,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[4,2,3,5,6,1]=>10001=>[1,3,1]=>[1,3,1]
[4,2,3,6,1,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[4,2,3,6,5,1]=>10011=>[1,2,2]=>[2,2,1]
[4,2,5,1,3,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[4,2,5,1,6,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,2,5,3,1,6]=>10110=>[1,1,2,1]=>[1,2,1,1]
[4,2,5,3,6,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,2,5,6,1,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[4,2,5,6,3,1]=>10011=>[1,2,2]=>[2,2,1]
[4,2,6,1,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[4,2,6,1,5,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,2,6,3,1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[4,2,6,3,5,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,2,6,5,1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[4,2,6,5,3,1]=>10111=>[1,1,3]=>[3,1,1]
[4,3,1,2,5,6]=>11000=>[2,3]=>[3,2]
[4,3,1,2,6,5]=>11001=>[2,2,1]=>[1,2,2]
[4,3,1,5,2,6]=>11010=>[2,1,1,1]=>[1,1,1,2]
[4,3,1,5,6,2]=>11001=>[2,2,1]=>[1,2,2]
[4,3,1,6,2,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[4,3,1,6,5,2]=>11011=>[2,1,2]=>[2,1,2]
[4,3,2,1,5,6]=>11100=>[3,2]=>[2,3]
[4,3,2,1,6,5]=>11101=>[3,1,1]=>[1,1,3]
[4,3,2,5,1,6]=>11010=>[2,1,1,1]=>[1,1,1,2]
[4,3,2,5,6,1]=>11001=>[2,2,1]=>[1,2,2]
[4,3,2,6,1,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[4,3,2,6,5,1]=>11011=>[2,1,2]=>[2,1,2]
[4,3,5,1,2,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[4,3,5,1,6,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,3,5,2,1,6]=>10110=>[1,1,2,1]=>[1,2,1,1]
[4,3,5,2,6,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,3,5,6,1,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[4,3,5,6,2,1]=>10011=>[1,2,2]=>[2,2,1]
[4,3,6,1,2,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[4,3,6,1,5,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,3,6,2,1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[4,3,6,2,5,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,3,6,5,1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[4,3,6,5,2,1]=>10111=>[1,1,3]=>[3,1,1]
[4,5,1,2,3,6]=>01000=>[1,1,3]=>[3,1,1]
[4,5,1,2,6,3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,5,1,3,2,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,5,1,3,6,2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,5,1,6,2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,5,1,6,3,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,5,2,1,3,6]=>01100=>[1,2,2]=>[2,2,1]
[4,5,2,1,6,3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,5,2,3,1,6]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,5,2,3,6,1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,5,2,6,1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,5,2,6,3,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,5,3,1,2,6]=>01100=>[1,2,2]=>[2,2,1]
[4,5,3,1,6,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,5,3,2,1,6]=>01110=>[1,3,1]=>[1,3,1]
[4,5,3,2,6,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,5,3,6,1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,5,3,6,2,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,5,6,1,2,3]=>00100=>[2,1,2]=>[2,1,2]
[4,5,6,1,3,2]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,5,6,2,1,3]=>00110=>[2,2,1]=>[1,2,2]
[4,5,6,2,3,1]=>00101=>[2,1,1,1]=>[1,1,1,2]
[4,5,6,3,1,2]=>00110=>[2,2,1]=>[1,2,2]
[4,5,6,3,2,1]=>00111=>[2,3]=>[3,2]
[4,6,1,2,3,5]=>01000=>[1,1,3]=>[3,1,1]
[4,6,1,2,5,3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,6,1,3,2,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,6,1,3,5,2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,6,1,5,2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,6,1,5,3,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,6,2,1,3,5]=>01100=>[1,2,2]=>[2,2,1]
[4,6,2,1,5,3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,6,2,3,1,5]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,6,2,3,5,1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[4,6,2,5,1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,6,2,5,3,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,6,3,1,2,5]=>01100=>[1,2,2]=>[2,2,1]
[4,6,3,1,5,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,6,3,2,1,5]=>01110=>[1,3,1]=>[1,3,1]
[4,6,3,2,5,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,6,3,5,1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[4,6,3,5,2,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[4,6,5,1,2,3]=>01100=>[1,2,2]=>[2,2,1]
[4,6,5,1,3,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,6,5,2,1,3]=>01110=>[1,3,1]=>[1,3,1]
[4,6,5,2,3,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[4,6,5,3,1,2]=>01110=>[1,3,1]=>[1,3,1]
[4,6,5,3,2,1]=>01111=>[1,4]=>[4,1]
[5,1,2,3,4,6]=>10000=>[1,4]=>[4,1]
[5,1,2,3,6,4]=>10001=>[1,3,1]=>[1,3,1]
[5,1,2,4,3,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[5,1,2,4,6,3]=>10001=>[1,3,1]=>[1,3,1]
[5,1,2,6,3,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[5,1,2,6,4,3]=>10011=>[1,2,2]=>[2,2,1]
[5,1,3,2,4,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[5,1,3,2,6,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,1,3,4,2,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[5,1,3,4,6,2]=>10001=>[1,3,1]=>[1,3,1]
[5,1,3,6,2,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[5,1,3,6,4,2]=>10011=>[1,2,2]=>[2,2,1]
[5,1,4,2,3,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[5,1,4,2,6,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,1,4,3,2,6]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,1,4,3,6,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,1,4,6,2,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[5,1,4,6,3,2]=>10011=>[1,2,2]=>[2,2,1]
[5,1,6,2,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[5,1,6,2,4,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,1,6,3,2,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,1,6,3,4,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,1,6,4,2,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,1,6,4,3,2]=>10111=>[1,1,3]=>[3,1,1]
[5,2,1,3,4,6]=>11000=>[2,3]=>[3,2]
[5,2,1,3,6,4]=>11001=>[2,2,1]=>[1,2,2]
[5,2,1,4,3,6]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,2,1,4,6,3]=>11001=>[2,2,1]=>[1,2,2]
[5,2,1,6,3,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,2,1,6,4,3]=>11011=>[2,1,2]=>[2,1,2]
[5,2,3,1,4,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[5,2,3,1,6,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,2,3,4,1,6]=>10010=>[1,2,1,1]=>[1,1,2,1]
[5,2,3,4,6,1]=>10001=>[1,3,1]=>[1,3,1]
[5,2,3,6,1,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[5,2,3,6,4,1]=>10011=>[1,2,2]=>[2,2,1]
[5,2,4,1,3,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[5,2,4,1,6,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,2,4,3,1,6]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,2,4,3,6,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,2,4,6,1,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[5,2,4,6,3,1]=>10011=>[1,2,2]=>[2,2,1]
[5,2,6,1,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[5,2,6,1,4,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,2,6,3,1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,2,6,3,4,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,2,6,4,1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,2,6,4,3,1]=>10111=>[1,1,3]=>[3,1,1]
[5,3,1,2,4,6]=>11000=>[2,3]=>[3,2]
[5,3,1,2,6,4]=>11001=>[2,2,1]=>[1,2,2]
[5,3,1,4,2,6]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,3,1,4,6,2]=>11001=>[2,2,1]=>[1,2,2]
[5,3,1,6,2,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,3,1,6,4,2]=>11011=>[2,1,2]=>[2,1,2]
[5,3,2,1,4,6]=>11100=>[3,2]=>[2,3]
[5,3,2,1,6,4]=>11101=>[3,1,1]=>[1,1,3]
[5,3,2,4,1,6]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,3,2,4,6,1]=>11001=>[2,2,1]=>[1,2,2]
[5,3,2,6,1,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,3,2,6,4,1]=>11011=>[2,1,2]=>[2,1,2]
[5,3,4,1,2,6]=>10100=>[1,1,1,2]=>[2,1,1,1]
[5,3,4,1,6,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,3,4,2,1,6]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,3,4,2,6,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,3,4,6,1,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[5,3,4,6,2,1]=>10011=>[1,2,2]=>[2,2,1]
[5,3,6,1,2,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[5,3,6,1,4,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,3,6,2,1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,3,6,2,4,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,3,6,4,1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,3,6,4,2,1]=>10111=>[1,1,3]=>[3,1,1]
[5,4,1,2,3,6]=>11000=>[2,3]=>[3,2]
[5,4,1,2,6,3]=>11001=>[2,2,1]=>[1,2,2]
[5,4,1,3,2,6]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,4,1,3,6,2]=>11001=>[2,2,1]=>[1,2,2]
[5,4,1,6,2,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,4,1,6,3,2]=>11011=>[2,1,2]=>[2,1,2]
[5,4,2,1,3,6]=>11100=>[3,2]=>[2,3]
[5,4,2,1,6,3]=>11101=>[3,1,1]=>[1,1,3]
[5,4,2,3,1,6]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,4,2,3,6,1]=>11001=>[2,2,1]=>[1,2,2]
[5,4,2,6,1,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,4,2,6,3,1]=>11011=>[2,1,2]=>[2,1,2]
[5,4,3,1,2,6]=>11100=>[3,2]=>[2,3]
[5,4,3,1,6,2]=>11101=>[3,1,1]=>[1,1,3]
[5,4,3,2,1,6]=>11110=>[4,1]=>[1,4]
[5,4,3,2,6,1]=>11101=>[3,1,1]=>[1,1,3]
[5,4,3,6,1,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[5,4,3,6,2,1]=>11011=>[2,1,2]=>[2,1,2]
[5,4,6,1,2,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[5,4,6,1,3,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,4,6,2,1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,4,6,2,3,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,4,6,3,1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[5,4,6,3,2,1]=>10111=>[1,1,3]=>[3,1,1]
[5,6,1,2,3,4]=>01000=>[1,1,3]=>[3,1,1]
[5,6,1,2,4,3]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,6,1,3,2,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,6,1,3,4,2]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,6,1,4,2,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,6,1,4,3,2]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,6,2,1,3,4]=>01100=>[1,2,2]=>[2,2,1]
[5,6,2,1,4,3]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,6,2,3,1,4]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,6,2,3,4,1]=>01001=>[1,1,2,1]=>[1,2,1,1]
[5,6,2,4,1,3]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,6,2,4,3,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,6,3,1,2,4]=>01100=>[1,2,2]=>[2,2,1]
[5,6,3,1,4,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,6,3,2,1,4]=>01110=>[1,3,1]=>[1,3,1]
[5,6,3,2,4,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,6,3,4,1,2]=>01010=>[1,1,1,1,1]=>[1,1,1,1,1]
[5,6,3,4,2,1]=>01011=>[1,1,1,2]=>[2,1,1,1]
[5,6,4,1,2,3]=>01100=>[1,2,2]=>[2,2,1]
[5,6,4,1,3,2]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,6,4,2,1,3]=>01110=>[1,3,1]=>[1,3,1]
[5,6,4,2,3,1]=>01101=>[1,2,1,1]=>[1,1,2,1]
[5,6,4,3,1,2]=>01110=>[1,3,1]=>[1,3,1]
[5,6,4,3,2,1]=>01111=>[1,4]=>[4,1]
[6,1,2,3,4,5]=>10000=>[1,4]=>[4,1]
[6,1,2,3,5,4]=>10001=>[1,3,1]=>[1,3,1]
[6,1,2,4,3,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[6,1,2,4,5,3]=>10001=>[1,3,1]=>[1,3,1]
[6,1,2,5,3,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[6,1,2,5,4,3]=>10011=>[1,2,2]=>[2,2,1]
[6,1,3,2,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[6,1,3,2,5,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,1,3,4,2,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[6,1,3,4,5,2]=>10001=>[1,3,1]=>[1,3,1]
[6,1,3,5,2,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[6,1,3,5,4,2]=>10011=>[1,2,2]=>[2,2,1]
[6,1,4,2,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[6,1,4,2,5,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,1,4,3,2,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,1,4,3,5,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,1,4,5,2,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[6,1,4,5,3,2]=>10011=>[1,2,2]=>[2,2,1]
[6,1,5,2,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[6,1,5,2,4,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,1,5,3,2,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,1,5,3,4,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,1,5,4,2,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,1,5,4,3,2]=>10111=>[1,1,3]=>[3,1,1]
[6,2,1,3,4,5]=>11000=>[2,3]=>[3,2]
[6,2,1,3,5,4]=>11001=>[2,2,1]=>[1,2,2]
[6,2,1,4,3,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,2,1,4,5,3]=>11001=>[2,2,1]=>[1,2,2]
[6,2,1,5,3,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,2,1,5,4,3]=>11011=>[2,1,2]=>[2,1,2]
[6,2,3,1,4,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[6,2,3,1,5,4]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,2,3,4,1,5]=>10010=>[1,2,1,1]=>[1,1,2,1]
[6,2,3,4,5,1]=>10001=>[1,3,1]=>[1,3,1]
[6,2,3,5,1,4]=>10010=>[1,2,1,1]=>[1,1,2,1]
[6,2,3,5,4,1]=>10011=>[1,2,2]=>[2,2,1]
[6,2,4,1,3,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[6,2,4,1,5,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,2,4,3,1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,2,4,3,5,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,2,4,5,1,3]=>10010=>[1,2,1,1]=>[1,1,2,1]
[6,2,4,5,3,1]=>10011=>[1,2,2]=>[2,2,1]
[6,2,5,1,3,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[6,2,5,1,4,3]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,2,5,3,1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,2,5,3,4,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,2,5,4,1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,2,5,4,3,1]=>10111=>[1,1,3]=>[3,1,1]
[6,3,1,2,4,5]=>11000=>[2,3]=>[3,2]
[6,3,1,2,5,4]=>11001=>[2,2,1]=>[1,2,2]
[6,3,1,4,2,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,3,1,4,5,2]=>11001=>[2,2,1]=>[1,2,2]
[6,3,1,5,2,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,3,1,5,4,2]=>11011=>[2,1,2]=>[2,1,2]
[6,3,2,1,4,5]=>11100=>[3,2]=>[2,3]
[6,3,2,1,5,4]=>11101=>[3,1,1]=>[1,1,3]
[6,3,2,4,1,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,3,2,4,5,1]=>11001=>[2,2,1]=>[1,2,2]
[6,3,2,5,1,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,3,2,5,4,1]=>11011=>[2,1,2]=>[2,1,2]
[6,3,4,1,2,5]=>10100=>[1,1,1,2]=>[2,1,1,1]
[6,3,4,1,5,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,3,4,2,1,5]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,3,4,2,5,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,3,4,5,1,2]=>10010=>[1,2,1,1]=>[1,1,2,1]
[6,3,4,5,2,1]=>10011=>[1,2,2]=>[2,2,1]
[6,3,5,1,2,4]=>10100=>[1,1,1,2]=>[2,1,1,1]
[6,3,5,1,4,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,3,5,2,1,4]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,3,5,2,4,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,3,5,4,1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,3,5,4,2,1]=>10111=>[1,1,3]=>[3,1,1]
[6,4,1,2,3,5]=>11000=>[2,3]=>[3,2]
[6,4,1,2,5,3]=>11001=>[2,2,1]=>[1,2,2]
[6,4,1,3,2,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,4,1,3,5,2]=>11001=>[2,2,1]=>[1,2,2]
[6,4,1,5,2,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,4,1,5,3,2]=>11011=>[2,1,2]=>[2,1,2]
[6,4,2,1,3,5]=>11100=>[3,2]=>[2,3]
[6,4,2,1,5,3]=>11101=>[3,1,1]=>[1,1,3]
[6,4,2,3,1,5]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,4,2,3,5,1]=>11001=>[2,2,1]=>[1,2,2]
[6,4,2,5,1,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,4,2,5,3,1]=>11011=>[2,1,2]=>[2,1,2]
[6,4,3,1,2,5]=>11100=>[3,2]=>[2,3]
[6,4,3,1,5,2]=>11101=>[3,1,1]=>[1,1,3]
[6,4,3,2,1,5]=>11110=>[4,1]=>[1,4]
[6,4,3,2,5,1]=>11101=>[3,1,1]=>[1,1,3]
[6,4,3,5,1,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,4,3,5,2,1]=>11011=>[2,1,2]=>[2,1,2]
[6,4,5,1,2,3]=>10100=>[1,1,1,2]=>[2,1,1,1]
[6,4,5,1,3,2]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,4,5,2,1,3]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,4,5,2,3,1]=>10101=>[1,1,1,1,1]=>[1,1,1,1,1]
[6,4,5,3,1,2]=>10110=>[1,1,2,1]=>[1,2,1,1]
[6,4,5,3,2,1]=>10111=>[1,1,3]=>[3,1,1]
[6,5,1,2,3,4]=>11000=>[2,3]=>[3,2]
[6,5,1,2,4,3]=>11001=>[2,2,1]=>[1,2,2]
[6,5,1,3,2,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,5,1,3,4,2]=>11001=>[2,2,1]=>[1,2,2]
[6,5,1,4,2,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,5,1,4,3,2]=>11011=>[2,1,2]=>[2,1,2]
[6,5,2,1,3,4]=>11100=>[3,2]=>[2,3]
[6,5,2,1,4,3]=>11101=>[3,1,1]=>[1,1,3]
[6,5,2,3,1,4]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,5,2,3,4,1]=>11001=>[2,2,1]=>[1,2,2]
[6,5,2,4,1,3]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,5,2,4,3,1]=>11011=>[2,1,2]=>[2,1,2]
[6,5,3,1,2,4]=>11100=>[3,2]=>[2,3]
[6,5,3,1,4,2]=>11101=>[3,1,1]=>[1,1,3]
[6,5,3,2,1,4]=>11110=>[4,1]=>[1,4]
[6,5,3,2,4,1]=>11101=>[3,1,1]=>[1,1,3]
[6,5,3,4,1,2]=>11010=>[2,1,1,1]=>[1,1,1,2]
[6,5,3,4,2,1]=>11011=>[2,1,2]=>[2,1,2]
[6,5,4,1,2,3]=>11100=>[3,2]=>[2,3]
[6,5,4,1,3,2]=>11101=>[3,1,1]=>[1,1,3]
[6,5,4,2,1,3]=>11110=>[4,1]=>[1,4]
[6,5,4,2,3,1]=>11101=>[3,1,1]=>[1,1,3]
[6,5,4,3,1,2]=>11110=>[4,1]=>[1,4]
[6,5,4,3,2,1]=>11111=>[5]=>[5]
[1,2,3,4,5,6,7]=>000000=>[6]=>[6]
[1,2,3,4,5,7,6]=>000001=>[5,1]=>[1,5]
[1,2,3,4,6,5,7]=>000010=>[4,1,1]=>[1,1,4]
[1,2,3,4,6,7,5]=>000001=>[5,1]=>[1,5]
[1,2,3,4,7,5,6]=>000010=>[4,1,1]=>[1,1,4]
[1,2,3,4,7,6,5]=>000011=>[4,2]=>[2,4]
[1,2,3,5,4,6,7]=>000100=>[3,1,2]=>[2,1,3]
[1,2,3,5,4,7,6]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,3,5,6,4,7]=>000010=>[4,1,1]=>[1,1,4]
[1,2,3,5,6,7,4]=>000001=>[5,1]=>[1,5]
[1,2,3,5,7,4,6]=>000010=>[4,1,1]=>[1,1,4]
[1,2,3,5,7,6,4]=>000011=>[4,2]=>[2,4]
[1,2,3,6,4,5,7]=>000100=>[3,1,2]=>[2,1,3]
[1,2,3,6,4,7,5]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,3,6,5,4,7]=>000110=>[3,2,1]=>[1,2,3]
[1,2,3,6,5,7,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,3,6,7,4,5]=>000010=>[4,1,1]=>[1,1,4]
[1,2,3,6,7,5,4]=>000011=>[4,2]=>[2,4]
[1,2,3,7,4,5,6]=>000100=>[3,1,2]=>[2,1,3]
[1,2,3,7,4,6,5]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,3,7,5,4,6]=>000110=>[3,2,1]=>[1,2,3]
[1,2,3,7,5,6,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,3,7,6,4,5]=>000110=>[3,2,1]=>[1,2,3]
[1,2,3,7,6,5,4]=>000111=>[3,3]=>[3,3]
[1,2,4,3,5,6,7]=>001000=>[2,1,3]=>[3,1,2]
[1,2,4,3,5,7,6]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,4,3,6,5,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,4,3,6,7,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,4,3,7,5,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,4,3,7,6,5]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,2,4,5,3,6,7]=>000100=>[3,1,2]=>[2,1,3]
[1,2,4,5,3,7,6]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,4,5,6,3,7]=>000010=>[4,1,1]=>[1,1,4]
[1,2,4,5,6,7,3]=>000001=>[5,1]=>[1,5]
[1,2,4,5,7,3,6]=>000010=>[4,1,1]=>[1,1,4]
[1,2,4,5,7,6,3]=>000011=>[4,2]=>[2,4]
[1,2,4,6,3,5,7]=>000100=>[3,1,2]=>[2,1,3]
[1,2,4,6,3,7,5]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,4,6,5,3,7]=>000110=>[3,2,1]=>[1,2,3]
[1,2,4,6,5,7,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,4,6,7,3,5]=>000010=>[4,1,1]=>[1,1,4]
[1,2,4,6,7,5,3]=>000011=>[4,2]=>[2,4]
[1,2,4,7,3,5,6]=>000100=>[3,1,2]=>[2,1,3]
[1,2,4,7,3,6,5]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,4,7,5,3,6]=>000110=>[3,2,1]=>[1,2,3]
[1,2,4,7,5,6,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,4,7,6,3,5]=>000110=>[3,2,1]=>[1,2,3]
[1,2,4,7,6,5,3]=>000111=>[3,3]=>[3,3]
[1,2,5,3,4,6,7]=>001000=>[2,1,3]=>[3,1,2]
[1,2,5,3,4,7,6]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,5,3,6,4,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,5,3,6,7,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,5,3,7,4,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,5,3,7,6,4]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,2,5,4,3,6,7]=>001100=>[2,2,2]=>[2,2,2]
[1,2,5,4,3,7,6]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,2,5,4,6,3,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,5,4,6,7,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,5,4,7,3,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,5,4,7,6,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,2,5,6,3,4,7]=>000100=>[3,1,2]=>[2,1,3]
[1,2,5,6,3,7,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,5,6,4,3,7]=>000110=>[3,2,1]=>[1,2,3]
[1,2,5,6,4,7,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,5,6,7,3,4]=>000010=>[4,1,1]=>[1,1,4]
[1,2,5,6,7,4,3]=>000011=>[4,2]=>[2,4]
[1,2,5,7,3,4,6]=>000100=>[3,1,2]=>[2,1,3]
[1,2,5,7,3,6,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,5,7,4,3,6]=>000110=>[3,2,1]=>[1,2,3]
[1,2,5,7,4,6,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,5,7,6,3,4]=>000110=>[3,2,1]=>[1,2,3]
[1,2,5,7,6,4,3]=>000111=>[3,3]=>[3,3]
[1,2,6,3,4,5,7]=>001000=>[2,1,3]=>[3,1,2]
[1,2,6,3,4,7,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,6,3,5,4,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,6,3,5,7,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,6,3,7,4,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,6,3,7,5,4]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,2,6,4,3,5,7]=>001100=>[2,2,2]=>[2,2,2]
[1,2,6,4,3,7,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,2,6,4,5,3,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,6,4,5,7,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,6,4,7,3,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,6,4,7,5,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,2,6,5,3,4,7]=>001100=>[2,2,2]=>[2,2,2]
[1,2,6,5,3,7,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,2,6,5,4,3,7]=>001110=>[2,3,1]=>[1,3,2]
[1,2,6,5,4,7,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,2,6,5,7,3,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,6,5,7,4,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,2,6,7,3,4,5]=>000100=>[3,1,2]=>[2,1,3]
[1,2,6,7,3,5,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,6,7,4,3,5]=>000110=>[3,2,1]=>[1,2,3]
[1,2,6,7,4,5,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,2,6,7,5,3,4]=>000110=>[3,2,1]=>[1,2,3]
[1,2,6,7,5,4,3]=>000111=>[3,3]=>[3,3]
[1,2,7,3,4,5,6]=>001000=>[2,1,3]=>[3,1,2]
[1,2,7,3,4,6,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,7,3,5,4,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,7,3,5,6,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,7,3,6,4,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,7,3,6,5,4]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,2,7,4,3,5,6]=>001100=>[2,2,2]=>[2,2,2]
[1,2,7,4,3,6,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,2,7,4,5,3,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,7,4,5,6,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,2,7,4,6,3,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,7,4,6,5,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,2,7,5,3,4,6]=>001100=>[2,2,2]=>[2,2,2]
[1,2,7,5,3,6,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,2,7,5,4,3,6]=>001110=>[2,3,1]=>[1,3,2]
[1,2,7,5,4,6,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,2,7,5,6,3,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,2,7,5,6,4,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,2,7,6,3,4,5]=>001100=>[2,2,2]=>[2,2,2]
[1,2,7,6,3,5,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,2,7,6,4,3,5]=>001110=>[2,3,1]=>[1,3,2]
[1,2,7,6,4,5,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,2,7,6,5,3,4]=>001110=>[2,3,1]=>[1,3,2]
[1,2,7,6,5,4,3]=>001111=>[2,4]=>[4,2]
[1,3,2,4,5,6,7]=>010000=>[1,1,4]=>[4,1,1]
[1,3,2,4,5,7,6]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,3,2,4,6,5,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,3,2,4,6,7,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,3,2,4,7,5,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,3,2,4,7,6,5]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,3,2,5,4,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,3,2,5,4,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,3,2,5,6,4,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,3,2,5,6,7,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,3,2,5,7,4,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,3,2,5,7,6,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,3,2,6,4,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,3,2,6,4,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,3,2,6,5,4,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,3,2,6,5,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,3,2,6,7,4,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,3,2,6,7,5,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,3,2,7,4,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,3,2,7,4,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,3,2,7,5,4,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,3,2,7,5,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,3,2,7,6,4,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,3,2,7,6,5,4]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,3,4,2,5,6,7]=>001000=>[2,1,3]=>[3,1,2]
[1,3,4,2,5,7,6]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,4,2,6,5,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,4,2,6,7,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,4,2,7,5,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,4,2,7,6,5]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,3,4,5,2,6,7]=>000100=>[3,1,2]=>[2,1,3]
[1,3,4,5,2,7,6]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,4,5,6,2,7]=>000010=>[4,1,1]=>[1,1,4]
[1,3,4,5,6,7,2]=>000001=>[5,1]=>[1,5]
[1,3,4,5,7,2,6]=>000010=>[4,1,1]=>[1,1,4]
[1,3,4,5,7,6,2]=>000011=>[4,2]=>[2,4]
[1,3,4,6,2,5,7]=>000100=>[3,1,2]=>[2,1,3]
[1,3,4,6,2,7,5]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,4,6,5,2,7]=>000110=>[3,2,1]=>[1,2,3]
[1,3,4,6,5,7,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,4,6,7,2,5]=>000010=>[4,1,1]=>[1,1,4]
[1,3,4,6,7,5,2]=>000011=>[4,2]=>[2,4]
[1,3,4,7,2,5,6]=>000100=>[3,1,2]=>[2,1,3]
[1,3,4,7,2,6,5]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,4,7,5,2,6]=>000110=>[3,2,1]=>[1,2,3]
[1,3,4,7,5,6,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,4,7,6,2,5]=>000110=>[3,2,1]=>[1,2,3]
[1,3,4,7,6,5,2]=>000111=>[3,3]=>[3,3]
[1,3,5,2,4,6,7]=>001000=>[2,1,3]=>[3,1,2]
[1,3,5,2,4,7,6]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,5,2,6,4,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,5,2,6,7,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,5,2,7,4,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,5,2,7,6,4]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,3,5,4,2,6,7]=>001100=>[2,2,2]=>[2,2,2]
[1,3,5,4,2,7,6]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,3,5,4,6,2,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,5,4,6,7,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,5,4,7,2,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,5,4,7,6,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,3,5,6,2,4,7]=>000100=>[3,1,2]=>[2,1,3]
[1,3,5,6,2,7,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,5,6,4,2,7]=>000110=>[3,2,1]=>[1,2,3]
[1,3,5,6,4,7,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,5,6,7,2,4]=>000010=>[4,1,1]=>[1,1,4]
[1,3,5,6,7,4,2]=>000011=>[4,2]=>[2,4]
[1,3,5,7,2,4,6]=>000100=>[3,1,2]=>[2,1,3]
[1,3,5,7,2,6,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,5,7,4,2,6]=>000110=>[3,2,1]=>[1,2,3]
[1,3,5,7,4,6,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,5,7,6,2,4]=>000110=>[3,2,1]=>[1,2,3]
[1,3,5,7,6,4,2]=>000111=>[3,3]=>[3,3]
[1,3,6,2,4,5,7]=>001000=>[2,1,3]=>[3,1,2]
[1,3,6,2,4,7,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,6,2,5,4,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,6,2,5,7,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,6,2,7,4,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,6,2,7,5,4]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,3,6,4,2,5,7]=>001100=>[2,2,2]=>[2,2,2]
[1,3,6,4,2,7,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,3,6,4,5,2,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,6,4,5,7,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,6,4,7,2,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,6,4,7,5,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,3,6,5,2,4,7]=>001100=>[2,2,2]=>[2,2,2]
[1,3,6,5,2,7,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,3,6,5,4,2,7]=>001110=>[2,3,1]=>[1,3,2]
[1,3,6,5,4,7,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,3,6,5,7,2,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,6,5,7,4,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,3,6,7,2,4,5]=>000100=>[3,1,2]=>[2,1,3]
[1,3,6,7,2,5,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,6,7,4,2,5]=>000110=>[3,2,1]=>[1,2,3]
[1,3,6,7,4,5,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,3,6,7,5,2,4]=>000110=>[3,2,1]=>[1,2,3]
[1,3,6,7,5,4,2]=>000111=>[3,3]=>[3,3]
[1,3,7,2,4,5,6]=>001000=>[2,1,3]=>[3,1,2]
[1,3,7,2,4,6,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,7,2,5,4,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,7,2,5,6,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,7,2,6,4,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,7,2,6,5,4]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,3,7,4,2,5,6]=>001100=>[2,2,2]=>[2,2,2]
[1,3,7,4,2,6,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,3,7,4,5,2,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,7,4,5,6,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,3,7,4,6,2,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,7,4,6,5,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,3,7,5,2,4,6]=>001100=>[2,2,2]=>[2,2,2]
[1,3,7,5,2,6,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,3,7,5,4,2,6]=>001110=>[2,3,1]=>[1,3,2]
[1,3,7,5,4,6,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,3,7,5,6,2,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,3,7,5,6,4,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,3,7,6,2,4,5]=>001100=>[2,2,2]=>[2,2,2]
[1,3,7,6,2,5,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,3,7,6,4,2,5]=>001110=>[2,3,1]=>[1,3,2]
[1,3,7,6,4,5,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,3,7,6,5,2,4]=>001110=>[2,3,1]=>[1,3,2]
[1,3,7,6,5,4,2]=>001111=>[2,4]=>[4,2]
[1,4,2,3,5,6,7]=>010000=>[1,1,4]=>[4,1,1]
[1,4,2,3,5,7,6]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,4,2,3,6,5,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,2,3,6,7,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,4,2,3,7,5,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,2,3,7,6,5]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,4,2,5,3,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,4,2,5,3,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,2,5,6,3,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,2,5,6,7,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,4,2,5,7,3,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,2,5,7,6,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,4,2,6,3,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,4,2,6,3,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,2,6,5,3,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,4,2,6,5,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,2,6,7,3,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,2,6,7,5,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,4,2,7,3,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,4,2,7,3,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,2,7,5,3,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,4,2,7,5,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,2,7,6,3,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,4,2,7,6,5,3]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,4,3,2,5,6,7]=>011000=>[1,2,3]=>[3,2,1]
[1,4,3,2,5,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,4,3,2,6,5,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,4,3,2,6,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,4,3,2,7,5,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,4,3,2,7,6,5]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,4,3,5,2,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,4,3,5,2,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,3,5,6,2,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,3,5,6,7,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,4,3,5,7,2,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,3,5,7,6,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,4,3,6,2,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,4,3,6,2,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,3,6,5,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,4,3,6,5,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,3,6,7,2,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,4,3,6,7,5,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,4,3,7,2,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,4,3,7,2,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,3,7,5,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,4,3,7,5,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,4,3,7,6,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,4,3,7,6,5,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,4,5,2,3,6,7]=>001000=>[2,1,3]=>[3,1,2]
[1,4,5,2,3,7,6]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,4,5,2,6,3,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,5,2,6,7,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,4,5,2,7,3,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,5,2,7,6,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,4,5,3,2,6,7]=>001100=>[2,2,2]=>[2,2,2]
[1,4,5,3,2,7,6]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,4,5,3,6,2,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,5,3,6,7,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,4,5,3,7,2,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,5,3,7,6,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,4,5,6,2,3,7]=>000100=>[3,1,2]=>[2,1,3]
[1,4,5,6,2,7,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,4,5,6,3,2,7]=>000110=>[3,2,1]=>[1,2,3]
[1,4,5,6,3,7,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,4,5,6,7,2,3]=>000010=>[4,1,1]=>[1,1,4]
[1,4,5,6,7,3,2]=>000011=>[4,2]=>[2,4]
[1,4,5,7,2,3,6]=>000100=>[3,1,2]=>[2,1,3]
[1,4,5,7,2,6,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,4,5,7,3,2,6]=>000110=>[3,2,1]=>[1,2,3]
[1,4,5,7,3,6,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,4,5,7,6,2,3]=>000110=>[3,2,1]=>[1,2,3]
[1,4,5,7,6,3,2]=>000111=>[3,3]=>[3,3]
[1,4,6,2,3,5,7]=>001000=>[2,1,3]=>[3,1,2]
[1,4,6,2,3,7,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,4,6,2,5,3,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,6,2,5,7,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,4,6,2,7,3,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,6,2,7,5,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,4,6,3,2,5,7]=>001100=>[2,2,2]=>[2,2,2]
[1,4,6,3,2,7,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,4,6,3,5,2,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,6,3,5,7,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,4,6,3,7,2,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,6,3,7,5,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,4,6,5,2,3,7]=>001100=>[2,2,2]=>[2,2,2]
[1,4,6,5,2,7,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,4,6,5,3,2,7]=>001110=>[2,3,1]=>[1,3,2]
[1,4,6,5,3,7,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,4,6,5,7,2,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,6,5,7,3,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,4,6,7,2,3,5]=>000100=>[3,1,2]=>[2,1,3]
[1,4,6,7,2,5,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,4,6,7,3,2,5]=>000110=>[3,2,1]=>[1,2,3]
[1,4,6,7,3,5,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,4,6,7,5,2,3]=>000110=>[3,2,1]=>[1,2,3]
[1,4,6,7,5,3,2]=>000111=>[3,3]=>[3,3]
[1,4,7,2,3,5,6]=>001000=>[2,1,3]=>[3,1,2]
[1,4,7,2,3,6,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,4,7,2,5,3,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,7,2,5,6,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,4,7,2,6,3,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,7,2,6,5,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,4,7,3,2,5,6]=>001100=>[2,2,2]=>[2,2,2]
[1,4,7,3,2,6,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,4,7,3,5,2,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,7,3,5,6,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,4,7,3,6,2,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,7,3,6,5,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,4,7,5,2,3,6]=>001100=>[2,2,2]=>[2,2,2]
[1,4,7,5,2,6,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,4,7,5,3,2,6]=>001110=>[2,3,1]=>[1,3,2]
[1,4,7,5,3,6,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,4,7,5,6,2,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,4,7,5,6,3,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,4,7,6,2,3,5]=>001100=>[2,2,2]=>[2,2,2]
[1,4,7,6,2,5,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,4,7,6,3,2,5]=>001110=>[2,3,1]=>[1,3,2]
[1,4,7,6,3,5,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,4,7,6,5,2,3]=>001110=>[2,3,1]=>[1,3,2]
[1,4,7,6,5,3,2]=>001111=>[2,4]=>[4,2]
[1,5,2,3,4,6,7]=>010000=>[1,1,4]=>[4,1,1]
[1,5,2,3,4,7,6]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,5,2,3,6,4,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,5,2,3,6,7,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,5,2,3,7,4,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,5,2,3,7,6,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,5,2,4,3,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,5,2,4,3,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,2,4,6,3,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,5,2,4,6,7,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,5,2,4,7,3,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,5,2,4,7,6,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,5,2,6,3,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,5,2,6,3,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,2,6,4,3,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,5,2,6,4,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,2,6,7,3,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,5,2,6,7,4,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,5,2,7,3,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,5,2,7,3,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,2,7,4,3,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,5,2,7,4,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,2,7,6,3,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,5,2,7,6,4,3]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,5,3,2,4,6,7]=>011000=>[1,2,3]=>[3,2,1]
[1,5,3,2,4,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,5,3,2,6,4,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,5,3,2,6,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,5,3,2,7,4,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,5,3,2,7,6,4]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,5,3,4,2,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,5,3,4,2,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,3,4,6,2,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,5,3,4,6,7,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,5,3,4,7,2,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,5,3,4,7,6,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,5,3,6,2,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,5,3,6,2,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,3,6,4,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,5,3,6,4,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,3,6,7,2,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,5,3,6,7,4,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,5,3,7,2,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,5,3,7,2,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,3,7,4,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,5,3,7,4,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,3,7,6,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,5,3,7,6,4,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,5,4,2,3,6,7]=>011000=>[1,2,3]=>[3,2,1]
[1,5,4,2,3,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,5,4,2,6,3,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,5,4,2,6,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,5,4,2,7,3,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,5,4,2,7,6,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,5,4,3,2,6,7]=>011100=>[1,3,2]=>[2,3,1]
[1,5,4,3,2,7,6]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,5,4,3,6,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,5,4,3,6,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,5,4,3,7,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,5,4,3,7,6,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,5,4,6,2,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,5,4,6,2,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,4,6,3,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,5,4,6,3,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,4,6,7,2,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,5,4,6,7,3,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,5,4,7,2,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,5,4,7,2,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,4,7,3,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,5,4,7,3,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,5,4,7,6,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,5,4,7,6,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,5,6,2,3,4,7]=>001000=>[2,1,3]=>[3,1,2]
[1,5,6,2,3,7,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,5,6,2,4,3,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,6,2,4,7,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,5,6,2,7,3,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,6,2,7,4,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,5,6,3,2,4,7]=>001100=>[2,2,2]=>[2,2,2]
[1,5,6,3,2,7,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,5,6,3,4,2,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,6,3,4,7,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,5,6,3,7,2,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,6,3,7,4,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,5,6,4,2,3,7]=>001100=>[2,2,2]=>[2,2,2]
[1,5,6,4,2,7,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,5,6,4,3,2,7]=>001110=>[2,3,1]=>[1,3,2]
[1,5,6,4,3,7,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,5,6,4,7,2,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,6,4,7,3,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,5,6,7,2,3,4]=>000100=>[3,1,2]=>[2,1,3]
[1,5,6,7,2,4,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,5,6,7,3,2,4]=>000110=>[3,2,1]=>[1,2,3]
[1,5,6,7,3,4,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[1,5,6,7,4,2,3]=>000110=>[3,2,1]=>[1,2,3]
[1,5,6,7,4,3,2]=>000111=>[3,3]=>[3,3]
[1,5,7,2,3,4,6]=>001000=>[2,1,3]=>[3,1,2]
[1,5,7,2,3,6,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,5,7,2,4,3,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,7,2,4,6,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,5,7,2,6,3,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,7,2,6,4,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,5,7,3,2,4,6]=>001100=>[2,2,2]=>[2,2,2]
[1,5,7,3,2,6,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,5,7,3,4,2,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,7,3,4,6,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,5,7,3,6,2,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,7,3,6,4,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,5,7,4,2,3,6]=>001100=>[2,2,2]=>[2,2,2]
[1,5,7,4,2,6,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,5,7,4,3,2,6]=>001110=>[2,3,1]=>[1,3,2]
[1,5,7,4,3,6,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,5,7,4,6,2,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,5,7,4,6,3,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,5,7,6,2,3,4]=>001100=>[2,2,2]=>[2,2,2]
[1,5,7,6,2,4,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,5,7,6,3,2,4]=>001110=>[2,3,1]=>[1,3,2]
[1,5,7,6,3,4,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,5,7,6,4,2,3]=>001110=>[2,3,1]=>[1,3,2]
[1,5,7,6,4,3,2]=>001111=>[2,4]=>[4,2]
[1,6,2,3,4,5,7]=>010000=>[1,1,4]=>[4,1,1]
[1,6,2,3,4,7,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,6,2,3,5,4,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,2,3,5,7,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,6,2,3,7,4,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,2,3,7,5,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,6,2,4,3,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,6,2,4,3,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,2,4,5,3,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,2,4,5,7,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,6,2,4,7,3,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,2,4,7,5,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,6,2,5,3,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,6,2,5,3,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,2,5,4,3,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,2,5,4,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,2,5,7,3,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,2,5,7,4,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,6,2,7,3,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,6,2,7,3,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,2,7,4,3,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,2,7,4,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,2,7,5,3,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,2,7,5,4,3]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,6,3,2,4,5,7]=>011000=>[1,2,3]=>[3,2,1]
[1,6,3,2,4,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,6,3,2,5,4,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,3,2,5,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,6,3,2,7,4,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,3,2,7,5,4]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,6,3,4,2,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,6,3,4,2,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,3,4,5,2,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,3,4,5,7,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,6,3,4,7,2,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,3,4,7,5,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,6,3,5,2,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,6,3,5,2,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,3,5,4,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,3,5,4,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,3,5,7,2,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,3,5,7,4,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,6,3,7,2,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,6,3,7,2,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,3,7,4,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,3,7,4,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,3,7,5,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,3,7,5,4,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,6,4,2,3,5,7]=>011000=>[1,2,3]=>[3,2,1]
[1,6,4,2,3,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,6,4,2,5,3,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,4,2,5,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,6,4,2,7,3,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,4,2,7,5,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,6,4,3,2,5,7]=>011100=>[1,3,2]=>[2,3,1]
[1,6,4,3,2,7,5]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,6,4,3,5,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,4,3,5,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,6,4,3,7,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,4,3,7,5,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,6,4,5,2,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,6,4,5,2,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,4,5,3,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,4,5,3,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,4,5,7,2,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,6,4,5,7,3,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,6,4,7,2,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,6,4,7,2,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,4,7,3,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,4,7,3,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,4,7,5,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,4,7,5,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,6,5,2,3,4,7]=>011000=>[1,2,3]=>[3,2,1]
[1,6,5,2,3,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,6,5,2,4,3,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,5,2,4,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,6,5,2,7,3,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,5,2,7,4,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,6,5,3,2,4,7]=>011100=>[1,3,2]=>[2,3,1]
[1,6,5,3,2,7,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,6,5,3,4,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,5,3,4,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,6,5,3,7,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,5,3,7,4,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,6,5,4,2,3,7]=>011100=>[1,3,2]=>[2,3,1]
[1,6,5,4,2,7,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,6,5,4,3,2,7]=>011110=>[1,4,1]=>[1,4,1]
[1,6,5,4,3,7,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,6,5,4,7,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,6,5,4,7,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,6,5,7,2,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,6,5,7,2,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,5,7,3,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,5,7,3,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,6,5,7,4,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,6,5,7,4,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,6,7,2,3,4,5]=>001000=>[2,1,3]=>[3,1,2]
[1,6,7,2,3,5,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,6,7,2,4,3,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,6,7,2,4,5,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,6,7,2,5,3,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,6,7,2,5,4,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,6,7,3,2,4,5]=>001100=>[2,2,2]=>[2,2,2]
[1,6,7,3,2,5,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,6,7,3,4,2,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,6,7,3,4,5,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[1,6,7,3,5,2,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,6,7,3,5,4,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,6,7,4,2,3,5]=>001100=>[2,2,2]=>[2,2,2]
[1,6,7,4,2,5,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,6,7,4,3,2,5]=>001110=>[2,3,1]=>[1,3,2]
[1,6,7,4,3,5,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,6,7,4,5,2,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[1,6,7,4,5,3,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[1,6,7,5,2,3,4]=>001100=>[2,2,2]=>[2,2,2]
[1,6,7,5,2,4,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,6,7,5,3,2,4]=>001110=>[2,3,1]=>[1,3,2]
[1,6,7,5,3,4,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[1,6,7,5,4,2,3]=>001110=>[2,3,1]=>[1,3,2]
[1,6,7,5,4,3,2]=>001111=>[2,4]=>[4,2]
[1,7,2,3,4,5,6]=>010000=>[1,1,4]=>[4,1,1]
[1,7,2,3,4,6,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,7,2,3,5,4,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,7,2,3,5,6,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,7,2,3,6,4,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,7,2,3,6,5,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,7,2,4,3,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,7,2,4,3,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,2,4,5,3,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,7,2,4,5,6,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,7,2,4,6,3,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,7,2,4,6,5,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,7,2,5,3,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,7,2,5,3,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,2,5,4,3,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,2,5,4,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,2,5,6,3,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,7,2,5,6,4,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,7,2,6,3,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,7,2,6,3,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,2,6,4,3,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,2,6,4,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,2,6,5,3,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,2,6,5,4,3]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,7,3,2,4,5,6]=>011000=>[1,2,3]=>[3,2,1]
[1,7,3,2,4,6,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,3,2,5,4,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,3,2,5,6,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,3,2,6,4,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,3,2,6,5,4]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,7,3,4,2,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,7,3,4,2,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,3,4,5,2,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,7,3,4,5,6,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[1,7,3,4,6,2,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,7,3,4,6,5,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,7,3,5,2,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,7,3,5,2,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,3,5,4,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,3,5,4,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,3,5,6,2,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,7,3,5,6,4,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,7,3,6,2,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,7,3,6,2,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,3,6,4,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,3,6,4,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,3,6,5,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,3,6,5,4,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,7,4,2,3,5,6]=>011000=>[1,2,3]=>[3,2,1]
[1,7,4,2,3,6,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,4,2,5,3,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,4,2,5,6,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,4,2,6,3,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,4,2,6,5,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,7,4,3,2,5,6]=>011100=>[1,3,2]=>[2,3,1]
[1,7,4,3,2,6,5]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,7,4,3,5,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,4,3,5,6,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,4,3,6,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,4,3,6,5,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,7,4,5,2,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,7,4,5,2,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,4,5,3,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,4,5,3,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,4,5,6,2,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[1,7,4,5,6,3,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[1,7,4,6,2,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,7,4,6,2,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,4,6,3,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,4,6,3,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,4,6,5,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,4,6,5,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,7,5,2,3,4,6]=>011000=>[1,2,3]=>[3,2,1]
[1,7,5,2,3,6,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,5,2,4,3,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,5,2,4,6,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,5,2,6,3,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,5,2,6,4,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,7,5,3,2,4,6]=>011100=>[1,3,2]=>[2,3,1]
[1,7,5,3,2,6,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,7,5,3,4,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,5,3,4,6,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,5,3,6,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,5,3,6,4,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,7,5,4,2,3,6]=>011100=>[1,3,2]=>[2,3,1]
[1,7,5,4,2,6,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,7,5,4,3,2,6]=>011110=>[1,4,1]=>[1,4,1]
[1,7,5,4,3,6,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,7,5,4,6,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,5,4,6,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,7,5,6,2,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,7,5,6,2,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,5,6,3,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,5,6,3,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,7,5,6,4,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[1,7,5,6,4,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[1,7,6,2,3,4,5]=>011000=>[1,2,3]=>[3,2,1]
[1,7,6,2,3,5,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,6,2,4,3,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,6,2,4,5,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,6,2,5,3,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,6,2,5,4,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,7,6,3,2,4,5]=>011100=>[1,3,2]=>[2,3,1]
[1,7,6,3,2,5,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,7,6,3,4,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,6,3,4,5,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[1,7,6,3,5,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,6,3,5,4,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,7,6,4,2,3,5]=>011100=>[1,3,2]=>[2,3,1]
[1,7,6,4,2,5,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,7,6,4,3,2,5]=>011110=>[1,4,1]=>[1,4,1]
[1,7,6,4,3,5,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,7,6,4,5,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[1,7,6,4,5,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[1,7,6,5,2,3,4]=>011100=>[1,3,2]=>[2,3,1]
[1,7,6,5,2,4,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,7,6,5,3,2,4]=>011110=>[1,4,1]=>[1,4,1]
[1,7,6,5,3,4,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[1,7,6,5,4,2,3]=>011110=>[1,4,1]=>[1,4,1]
[1,7,6,5,4,3,2]=>011111=>[1,5]=>[5,1]
[2,1,3,4,5,6,7]=>100000=>[1,5]=>[5,1]
[2,1,3,4,5,7,6]=>100001=>[1,4,1]=>[1,4,1]
[2,1,3,4,6,5,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,1,3,4,6,7,5]=>100001=>[1,4,1]=>[1,4,1]
[2,1,3,4,7,5,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,1,3,4,7,6,5]=>100011=>[1,3,2]=>[2,3,1]
[2,1,3,5,4,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,1,3,5,4,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,3,5,6,4,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,1,3,5,6,7,4]=>100001=>[1,4,1]=>[1,4,1]
[2,1,3,5,7,4,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,1,3,5,7,6,4]=>100011=>[1,3,2]=>[2,3,1]
[2,1,3,6,4,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,1,3,6,4,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,3,6,5,4,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,3,6,5,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,3,6,7,4,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,1,3,6,7,5,4]=>100011=>[1,3,2]=>[2,3,1]
[2,1,3,7,4,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,1,3,7,4,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,3,7,5,4,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,3,7,5,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,3,7,6,4,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,3,7,6,5,4]=>100111=>[1,2,3]=>[3,2,1]
[2,1,4,3,5,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[2,1,4,3,5,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,4,3,6,5,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,4,3,6,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,4,3,7,5,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,4,3,7,6,5]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,1,4,5,3,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,1,4,5,3,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,4,5,6,3,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,1,4,5,6,7,3]=>100001=>[1,4,1]=>[1,4,1]
[2,1,4,5,7,3,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,1,4,5,7,6,3]=>100011=>[1,3,2]=>[2,3,1]
[2,1,4,6,3,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,1,4,6,3,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,4,6,5,3,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,4,6,5,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,4,6,7,3,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,1,4,6,7,5,3]=>100011=>[1,3,2]=>[2,3,1]
[2,1,4,7,3,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,1,4,7,3,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,4,7,5,3,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,4,7,5,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,4,7,6,3,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,4,7,6,5,3]=>100111=>[1,2,3]=>[3,2,1]
[2,1,5,3,4,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[2,1,5,3,4,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,5,3,6,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,5,3,6,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,5,3,7,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,5,3,7,6,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,1,5,4,3,6,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[2,1,5,4,3,7,6]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,1,5,4,6,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,5,4,6,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,5,4,7,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,5,4,7,6,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,1,5,6,3,4,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,1,5,6,3,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,5,6,4,3,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,5,6,4,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,5,6,7,3,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[2,1,5,6,7,4,3]=>100011=>[1,3,2]=>[2,3,1]
[2,1,5,7,3,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,1,5,7,3,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,5,7,4,3,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,5,7,4,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,5,7,6,3,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,5,7,6,4,3]=>100111=>[1,2,3]=>[3,2,1]
[2,1,6,3,4,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[2,1,6,3,4,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,6,3,5,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,6,3,5,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,6,3,7,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,6,3,7,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,1,6,4,3,5,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[2,1,6,4,3,7,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,1,6,4,5,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,6,4,5,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,6,4,7,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,6,4,7,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,1,6,5,3,4,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[2,1,6,5,3,7,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,1,6,5,4,3,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[2,1,6,5,4,7,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,1,6,5,7,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,6,5,7,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,1,6,7,3,4,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[2,1,6,7,3,5,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,6,7,4,3,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,6,7,4,5,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,1,6,7,5,3,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[2,1,6,7,5,4,3]=>100111=>[1,2,3]=>[3,2,1]
[2,1,7,3,4,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[2,1,7,3,4,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,7,3,5,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,7,3,5,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,7,3,6,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,7,3,6,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,1,7,4,3,5,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[2,1,7,4,3,6,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,1,7,4,5,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,7,4,5,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,1,7,4,6,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,7,4,6,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,1,7,5,3,4,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[2,1,7,5,3,6,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,1,7,5,4,3,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[2,1,7,5,4,6,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,1,7,5,6,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,1,7,5,6,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,1,7,6,3,4,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[2,1,7,6,3,5,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,1,7,6,4,3,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[2,1,7,6,4,5,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,1,7,6,5,3,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[2,1,7,6,5,4,3]=>101111=>[1,1,4]=>[4,1,1]
[2,3,1,4,5,6,7]=>010000=>[1,1,4]=>[4,1,1]
[2,3,1,4,5,7,6]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,3,1,4,6,5,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,3,1,4,6,7,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,3,1,4,7,5,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,3,1,4,7,6,5]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,3,1,5,4,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,3,1,5,4,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,3,1,5,6,4,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,3,1,5,6,7,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,3,1,5,7,4,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,3,1,5,7,6,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,3,1,6,4,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,3,1,6,4,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,3,1,6,5,4,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,3,1,6,5,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,3,1,6,7,4,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,3,1,6,7,5,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,3,1,7,4,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,3,1,7,4,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,3,1,7,5,4,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,3,1,7,5,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,3,1,7,6,4,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,3,1,7,6,5,4]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,3,4,1,5,6,7]=>001000=>[2,1,3]=>[3,1,2]
[2,3,4,1,5,7,6]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,4,1,6,5,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,4,1,6,7,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,4,1,7,5,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,4,1,7,6,5]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,3,4,5,1,6,7]=>000100=>[3,1,2]=>[2,1,3]
[2,3,4,5,1,7,6]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,4,5,6,1,7]=>000010=>[4,1,1]=>[1,1,4]
[2,3,4,5,6,7,1]=>000001=>[5,1]=>[1,5]
[2,3,4,5,7,1,6]=>000010=>[4,1,1]=>[1,1,4]
[2,3,4,5,7,6,1]=>000011=>[4,2]=>[2,4]
[2,3,4,6,1,5,7]=>000100=>[3,1,2]=>[2,1,3]
[2,3,4,6,1,7,5]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,4,6,5,1,7]=>000110=>[3,2,1]=>[1,2,3]
[2,3,4,6,5,7,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,4,6,7,1,5]=>000010=>[4,1,1]=>[1,1,4]
[2,3,4,6,7,5,1]=>000011=>[4,2]=>[2,4]
[2,3,4,7,1,5,6]=>000100=>[3,1,2]=>[2,1,3]
[2,3,4,7,1,6,5]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,4,7,5,1,6]=>000110=>[3,2,1]=>[1,2,3]
[2,3,4,7,5,6,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,4,7,6,1,5]=>000110=>[3,2,1]=>[1,2,3]
[2,3,4,7,6,5,1]=>000111=>[3,3]=>[3,3]
[2,3,5,1,4,6,7]=>001000=>[2,1,3]=>[3,1,2]
[2,3,5,1,4,7,6]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,5,1,6,4,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,5,1,6,7,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,5,1,7,4,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,5,1,7,6,4]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,3,5,4,1,6,7]=>001100=>[2,2,2]=>[2,2,2]
[2,3,5,4,1,7,6]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,3,5,4,6,1,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,5,4,6,7,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,5,4,7,1,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,5,4,7,6,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,3,5,6,1,4,7]=>000100=>[3,1,2]=>[2,1,3]
[2,3,5,6,1,7,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,5,6,4,1,7]=>000110=>[3,2,1]=>[1,2,3]
[2,3,5,6,4,7,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,5,6,7,1,4]=>000010=>[4,1,1]=>[1,1,4]
[2,3,5,6,7,4,1]=>000011=>[4,2]=>[2,4]
[2,3,5,7,1,4,6]=>000100=>[3,1,2]=>[2,1,3]
[2,3,5,7,1,6,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,5,7,4,1,6]=>000110=>[3,2,1]=>[1,2,3]
[2,3,5,7,4,6,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,5,7,6,1,4]=>000110=>[3,2,1]=>[1,2,3]
[2,3,5,7,6,4,1]=>000111=>[3,3]=>[3,3]
[2,3,6,1,4,5,7]=>001000=>[2,1,3]=>[3,1,2]
[2,3,6,1,4,7,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,6,1,5,4,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,6,1,5,7,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,6,1,7,4,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,6,1,7,5,4]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,3,6,4,1,5,7]=>001100=>[2,2,2]=>[2,2,2]
[2,3,6,4,1,7,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,3,6,4,5,1,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,6,4,5,7,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,6,4,7,1,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,6,4,7,5,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,3,6,5,1,4,7]=>001100=>[2,2,2]=>[2,2,2]
[2,3,6,5,1,7,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,3,6,5,4,1,7]=>001110=>[2,3,1]=>[1,3,2]
[2,3,6,5,4,7,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,3,6,5,7,1,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,6,5,7,4,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,3,6,7,1,4,5]=>000100=>[3,1,2]=>[2,1,3]
[2,3,6,7,1,5,4]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,6,7,4,1,5]=>000110=>[3,2,1]=>[1,2,3]
[2,3,6,7,4,5,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,3,6,7,5,1,4]=>000110=>[3,2,1]=>[1,2,3]
[2,3,6,7,5,4,1]=>000111=>[3,3]=>[3,3]
[2,3,7,1,4,5,6]=>001000=>[2,1,3]=>[3,1,2]
[2,3,7,1,4,6,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,7,1,5,4,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,7,1,5,6,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,7,1,6,4,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,7,1,6,5,4]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,3,7,4,1,5,6]=>001100=>[2,2,2]=>[2,2,2]
[2,3,7,4,1,6,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,3,7,4,5,1,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,7,4,5,6,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,3,7,4,6,1,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,7,4,6,5,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,3,7,5,1,4,6]=>001100=>[2,2,2]=>[2,2,2]
[2,3,7,5,1,6,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,3,7,5,4,1,6]=>001110=>[2,3,1]=>[1,3,2]
[2,3,7,5,4,6,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,3,7,5,6,1,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,3,7,5,6,4,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,3,7,6,1,4,5]=>001100=>[2,2,2]=>[2,2,2]
[2,3,7,6,1,5,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,3,7,6,4,1,5]=>001110=>[2,3,1]=>[1,3,2]
[2,3,7,6,4,5,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,3,7,6,5,1,4]=>001110=>[2,3,1]=>[1,3,2]
[2,3,7,6,5,4,1]=>001111=>[2,4]=>[4,2]
[2,4,1,3,5,6,7]=>010000=>[1,1,4]=>[4,1,1]
[2,4,1,3,5,7,6]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,4,1,3,6,5,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,4,1,3,6,7,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,4,1,3,7,5,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,4,1,3,7,6,5]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,4,1,5,3,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,4,1,5,3,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,1,5,6,3,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,4,1,5,6,7,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,4,1,5,7,3,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,4,1,5,7,6,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,4,1,6,3,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,4,1,6,3,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,1,6,5,3,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,4,1,6,5,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,1,6,7,3,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,4,1,6,7,5,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,4,1,7,3,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,4,1,7,3,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,1,7,5,3,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,4,1,7,5,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,1,7,6,3,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,4,1,7,6,5,3]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,4,3,1,5,6,7]=>011000=>[1,2,3]=>[3,2,1]
[2,4,3,1,5,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,4,3,1,6,5,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,4,3,1,6,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,4,3,1,7,5,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,4,3,1,7,6,5]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,4,3,5,1,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,4,3,5,1,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,3,5,6,1,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,4,3,5,6,7,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,4,3,5,7,1,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,4,3,5,7,6,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,4,3,6,1,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,4,3,6,1,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,3,6,5,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,4,3,6,5,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,3,6,7,1,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,4,3,6,7,5,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,4,3,7,1,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,4,3,7,1,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,3,7,5,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,4,3,7,5,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,4,3,7,6,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,4,3,7,6,5,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,4,5,1,3,6,7]=>001000=>[2,1,3]=>[3,1,2]
[2,4,5,1,3,7,6]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,4,5,1,6,3,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,5,1,6,7,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,4,5,1,7,3,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,5,1,7,6,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,4,5,3,1,6,7]=>001100=>[2,2,2]=>[2,2,2]
[2,4,5,3,1,7,6]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,4,5,3,6,1,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,5,3,6,7,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,4,5,3,7,1,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,5,3,7,6,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,4,5,6,1,3,7]=>000100=>[3,1,2]=>[2,1,3]
[2,4,5,6,1,7,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,4,5,6,3,1,7]=>000110=>[3,2,1]=>[1,2,3]
[2,4,5,6,3,7,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,4,5,6,7,1,3]=>000010=>[4,1,1]=>[1,1,4]
[2,4,5,6,7,3,1]=>000011=>[4,2]=>[2,4]
[2,4,5,7,1,3,6]=>000100=>[3,1,2]=>[2,1,3]
[2,4,5,7,1,6,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,4,5,7,3,1,6]=>000110=>[3,2,1]=>[1,2,3]
[2,4,5,7,3,6,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,4,5,7,6,1,3]=>000110=>[3,2,1]=>[1,2,3]
[2,4,5,7,6,3,1]=>000111=>[3,3]=>[3,3]
[2,4,6,1,3,5,7]=>001000=>[2,1,3]=>[3,1,2]
[2,4,6,1,3,7,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,4,6,1,5,3,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,6,1,5,7,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,4,6,1,7,3,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,6,1,7,5,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,4,6,3,1,5,7]=>001100=>[2,2,2]=>[2,2,2]
[2,4,6,3,1,7,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,4,6,3,5,1,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,6,3,5,7,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,4,6,3,7,1,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,6,3,7,5,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,4,6,5,1,3,7]=>001100=>[2,2,2]=>[2,2,2]
[2,4,6,5,1,7,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,4,6,5,3,1,7]=>001110=>[2,3,1]=>[1,3,2]
[2,4,6,5,3,7,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,4,6,5,7,1,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,6,5,7,3,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,4,6,7,1,3,5]=>000100=>[3,1,2]=>[2,1,3]
[2,4,6,7,1,5,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,4,6,7,3,1,5]=>000110=>[3,2,1]=>[1,2,3]
[2,4,6,7,3,5,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,4,6,7,5,1,3]=>000110=>[3,2,1]=>[1,2,3]
[2,4,6,7,5,3,1]=>000111=>[3,3]=>[3,3]
[2,4,7,1,3,5,6]=>001000=>[2,1,3]=>[3,1,2]
[2,4,7,1,3,6,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,4,7,1,5,3,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,7,1,5,6,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,4,7,1,6,3,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,7,1,6,5,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,4,7,3,1,5,6]=>001100=>[2,2,2]=>[2,2,2]
[2,4,7,3,1,6,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,4,7,3,5,1,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,7,3,5,6,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,4,7,3,6,1,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,7,3,6,5,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,4,7,5,1,3,6]=>001100=>[2,2,2]=>[2,2,2]
[2,4,7,5,1,6,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,4,7,5,3,1,6]=>001110=>[2,3,1]=>[1,3,2]
[2,4,7,5,3,6,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,4,7,5,6,1,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,4,7,5,6,3,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,4,7,6,1,3,5]=>001100=>[2,2,2]=>[2,2,2]
[2,4,7,6,1,5,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,4,7,6,3,1,5]=>001110=>[2,3,1]=>[1,3,2]
[2,4,7,6,3,5,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,4,7,6,5,1,3]=>001110=>[2,3,1]=>[1,3,2]
[2,4,7,6,5,3,1]=>001111=>[2,4]=>[4,2]
[2,5,1,3,4,6,7]=>010000=>[1,1,4]=>[4,1,1]
[2,5,1,3,4,7,6]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,5,1,3,6,4,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,5,1,3,6,7,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,5,1,3,7,4,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,5,1,3,7,6,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,5,1,4,3,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,5,1,4,3,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,1,4,6,3,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,5,1,4,6,7,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,5,1,4,7,3,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,5,1,4,7,6,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,5,1,6,3,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,5,1,6,3,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,1,6,4,3,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,5,1,6,4,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,1,6,7,3,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,5,1,6,7,4,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,5,1,7,3,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,5,1,7,3,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,1,7,4,3,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,5,1,7,4,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,1,7,6,3,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,5,1,7,6,4,3]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,5,3,1,4,6,7]=>011000=>[1,2,3]=>[3,2,1]
[2,5,3,1,4,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,5,3,1,6,4,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,5,3,1,6,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,5,3,1,7,4,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,5,3,1,7,6,4]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,5,3,4,1,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,5,3,4,1,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,3,4,6,1,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,5,3,4,6,7,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,5,3,4,7,1,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,5,3,4,7,6,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,5,3,6,1,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,5,3,6,1,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,3,6,4,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,5,3,6,4,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,3,6,7,1,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,5,3,6,7,4,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,5,3,7,1,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,5,3,7,1,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,3,7,4,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,5,3,7,4,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,3,7,6,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,5,3,7,6,4,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,5,4,1,3,6,7]=>011000=>[1,2,3]=>[3,2,1]
[2,5,4,1,3,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,5,4,1,6,3,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,5,4,1,6,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,5,4,1,7,3,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,5,4,1,7,6,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,5,4,3,1,6,7]=>011100=>[1,3,2]=>[2,3,1]
[2,5,4,3,1,7,6]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,5,4,3,6,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,5,4,3,6,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,5,4,3,7,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,5,4,3,7,6,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,5,4,6,1,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,5,4,6,1,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,4,6,3,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,5,4,6,3,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,4,6,7,1,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,5,4,6,7,3,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,5,4,7,1,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,5,4,7,1,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,4,7,3,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,5,4,7,3,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,5,4,7,6,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,5,4,7,6,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,5,6,1,3,4,7]=>001000=>[2,1,3]=>[3,1,2]
[2,5,6,1,3,7,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,5,6,1,4,3,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,6,1,4,7,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,5,6,1,7,3,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,6,1,7,4,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,5,6,3,1,4,7]=>001100=>[2,2,2]=>[2,2,2]
[2,5,6,3,1,7,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,5,6,3,4,1,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,6,3,4,7,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,5,6,3,7,1,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,6,3,7,4,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,5,6,4,1,3,7]=>001100=>[2,2,2]=>[2,2,2]
[2,5,6,4,1,7,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,5,6,4,3,1,7]=>001110=>[2,3,1]=>[1,3,2]
[2,5,6,4,3,7,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,5,6,4,7,1,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,6,4,7,3,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,5,6,7,1,3,4]=>000100=>[3,1,2]=>[2,1,3]
[2,5,6,7,1,4,3]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,5,6,7,3,1,4]=>000110=>[3,2,1]=>[1,2,3]
[2,5,6,7,3,4,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[2,5,6,7,4,1,3]=>000110=>[3,2,1]=>[1,2,3]
[2,5,6,7,4,3,1]=>000111=>[3,3]=>[3,3]
[2,5,7,1,3,4,6]=>001000=>[2,1,3]=>[3,1,2]
[2,5,7,1,3,6,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,5,7,1,4,3,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,7,1,4,6,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,5,7,1,6,3,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,7,1,6,4,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,5,7,3,1,4,6]=>001100=>[2,2,2]=>[2,2,2]
[2,5,7,3,1,6,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,5,7,3,4,1,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,7,3,4,6,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,5,7,3,6,1,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,7,3,6,4,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,5,7,4,1,3,6]=>001100=>[2,2,2]=>[2,2,2]
[2,5,7,4,1,6,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,5,7,4,3,1,6]=>001110=>[2,3,1]=>[1,3,2]
[2,5,7,4,3,6,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,5,7,4,6,1,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,5,7,4,6,3,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,5,7,6,1,3,4]=>001100=>[2,2,2]=>[2,2,2]
[2,5,7,6,1,4,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,5,7,6,3,1,4]=>001110=>[2,3,1]=>[1,3,2]
[2,5,7,6,3,4,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,5,7,6,4,1,3]=>001110=>[2,3,1]=>[1,3,2]
[2,5,7,6,4,3,1]=>001111=>[2,4]=>[4,2]
[2,6,1,3,4,5,7]=>010000=>[1,1,4]=>[4,1,1]
[2,6,1,3,4,7,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,6,1,3,5,4,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,6,1,3,5,7,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,6,1,3,7,4,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,6,1,3,7,5,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,6,1,4,3,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,6,1,4,3,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,1,4,5,3,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,6,1,4,5,7,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,6,1,4,7,3,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,6,1,4,7,5,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,6,1,5,3,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,6,1,5,3,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,1,5,4,3,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,1,5,4,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,1,5,7,3,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,6,1,5,7,4,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,6,1,7,3,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,6,1,7,3,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,1,7,4,3,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,1,7,4,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,1,7,5,3,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,1,7,5,4,3]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,6,3,1,4,5,7]=>011000=>[1,2,3]=>[3,2,1]
[2,6,3,1,4,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,6,3,1,5,4,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,3,1,5,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,6,3,1,7,4,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,3,1,7,5,4]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,6,3,4,1,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,6,3,4,1,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,3,4,5,1,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,6,3,4,5,7,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,6,3,4,7,1,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,6,3,4,7,5,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,6,3,5,1,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,6,3,5,1,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,3,5,4,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,3,5,4,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,3,5,7,1,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,6,3,5,7,4,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,6,3,7,1,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,6,3,7,1,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,3,7,4,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,3,7,4,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,3,7,5,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,3,7,5,4,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,6,4,1,3,5,7]=>011000=>[1,2,3]=>[3,2,1]
[2,6,4,1,3,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,6,4,1,5,3,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,4,1,5,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,6,4,1,7,3,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,4,1,7,5,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,6,4,3,1,5,7]=>011100=>[1,3,2]=>[2,3,1]
[2,6,4,3,1,7,5]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,6,4,3,5,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,4,3,5,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,6,4,3,7,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,4,3,7,5,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,6,4,5,1,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,6,4,5,1,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,4,5,3,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,4,5,3,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,4,5,7,1,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,6,4,5,7,3,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,6,4,7,1,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,6,4,7,1,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,4,7,3,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,4,7,3,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,4,7,5,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,4,7,5,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,6,5,1,3,4,7]=>011000=>[1,2,3]=>[3,2,1]
[2,6,5,1,3,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,6,5,1,4,3,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,5,1,4,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,6,5,1,7,3,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,5,1,7,4,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,6,5,3,1,4,7]=>011100=>[1,3,2]=>[2,3,1]
[2,6,5,3,1,7,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,6,5,3,4,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,5,3,4,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,6,5,3,7,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,5,3,7,4,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,6,5,4,1,3,7]=>011100=>[1,3,2]=>[2,3,1]
[2,6,5,4,1,7,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,6,5,4,3,1,7]=>011110=>[1,4,1]=>[1,4,1]
[2,6,5,4,3,7,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,6,5,4,7,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,6,5,4,7,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,6,5,7,1,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,6,5,7,1,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,5,7,3,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,5,7,3,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,6,5,7,4,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,6,5,7,4,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,6,7,1,3,4,5]=>001000=>[2,1,3]=>[3,1,2]
[2,6,7,1,3,5,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,6,7,1,4,3,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,6,7,1,4,5,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,6,7,1,5,3,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,6,7,1,5,4,3]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,6,7,3,1,4,5]=>001100=>[2,2,2]=>[2,2,2]
[2,6,7,3,1,5,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,6,7,3,4,1,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,6,7,3,4,5,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[2,6,7,3,5,1,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,6,7,3,5,4,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,6,7,4,1,3,5]=>001100=>[2,2,2]=>[2,2,2]
[2,6,7,4,1,5,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,6,7,4,3,1,5]=>001110=>[2,3,1]=>[1,3,2]
[2,6,7,4,3,5,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,6,7,4,5,1,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[2,6,7,4,5,3,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[2,6,7,5,1,3,4]=>001100=>[2,2,2]=>[2,2,2]
[2,6,7,5,1,4,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,6,7,5,3,1,4]=>001110=>[2,3,1]=>[1,3,2]
[2,6,7,5,3,4,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[2,6,7,5,4,1,3]=>001110=>[2,3,1]=>[1,3,2]
[2,6,7,5,4,3,1]=>001111=>[2,4]=>[4,2]
[2,7,1,3,4,5,6]=>010000=>[1,1,4]=>[4,1,1]
[2,7,1,3,4,6,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,7,1,3,5,4,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,7,1,3,5,6,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,7,1,3,6,4,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,7,1,3,6,5,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,7,1,4,3,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,7,1,4,3,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,1,4,5,3,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,7,1,4,5,6,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,7,1,4,6,3,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,7,1,4,6,5,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,7,1,5,3,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,7,1,5,3,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,1,5,4,3,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,1,5,4,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,1,5,6,3,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,7,1,5,6,4,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,7,1,6,3,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,7,1,6,3,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,1,6,4,3,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,1,6,4,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,1,6,5,3,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,1,6,5,4,3]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,7,3,1,4,5,6]=>011000=>[1,2,3]=>[3,2,1]
[2,7,3,1,4,6,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,3,1,5,4,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,3,1,5,6,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,3,1,6,4,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,3,1,6,5,4]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,7,3,4,1,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,7,3,4,1,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,3,4,5,1,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,7,3,4,5,6,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[2,7,3,4,6,1,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,7,3,4,6,5,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,7,3,5,1,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,7,3,5,1,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,3,5,4,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,3,5,4,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,3,5,6,1,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,7,3,5,6,4,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,7,3,6,1,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,7,3,6,1,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,3,6,4,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,3,6,4,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,3,6,5,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,3,6,5,4,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,7,4,1,3,5,6]=>011000=>[1,2,3]=>[3,2,1]
[2,7,4,1,3,6,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,4,1,5,3,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,4,1,5,6,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,4,1,6,3,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,4,1,6,5,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,7,4,3,1,5,6]=>011100=>[1,3,2]=>[2,3,1]
[2,7,4,3,1,6,5]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,7,4,3,5,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,4,3,5,6,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,4,3,6,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,4,3,6,5,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,7,4,5,1,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,7,4,5,1,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,4,5,3,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,4,5,3,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,4,5,6,1,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[2,7,4,5,6,3,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[2,7,4,6,1,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,7,4,6,1,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,4,6,3,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,4,6,3,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,4,6,5,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,4,6,5,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,7,5,1,3,4,6]=>011000=>[1,2,3]=>[3,2,1]
[2,7,5,1,3,6,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,5,1,4,3,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,5,1,4,6,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,5,1,6,3,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,5,1,6,4,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,7,5,3,1,4,6]=>011100=>[1,3,2]=>[2,3,1]
[2,7,5,3,1,6,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,7,5,3,4,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,5,3,4,6,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,5,3,6,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,5,3,6,4,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,7,5,4,1,3,6]=>011100=>[1,3,2]=>[2,3,1]
[2,7,5,4,1,6,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,7,5,4,3,1,6]=>011110=>[1,4,1]=>[1,4,1]
[2,7,5,4,3,6,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,7,5,4,6,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,5,4,6,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,7,5,6,1,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[2,7,5,6,1,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,5,6,3,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,5,6,3,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[2,7,5,6,4,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[2,7,5,6,4,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[2,7,6,1,3,4,5]=>011000=>[1,2,3]=>[3,2,1]
[2,7,6,1,3,5,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,6,1,4,3,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,6,1,4,5,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,6,1,5,3,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,6,1,5,4,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,7,6,3,1,4,5]=>011100=>[1,3,2]=>[2,3,1]
[2,7,6,3,1,5,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,7,6,3,4,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,6,3,4,5,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[2,7,6,3,5,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,6,3,5,4,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,7,6,4,1,3,5]=>011100=>[1,3,2]=>[2,3,1]
[2,7,6,4,1,5,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,7,6,4,3,1,5]=>011110=>[1,4,1]=>[1,4,1]
[2,7,6,4,3,5,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,7,6,4,5,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[2,7,6,4,5,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[2,7,6,5,1,3,4]=>011100=>[1,3,2]=>[2,3,1]
[2,7,6,5,1,4,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,7,6,5,3,1,4]=>011110=>[1,4,1]=>[1,4,1]
[2,7,6,5,3,4,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[2,7,6,5,4,1,3]=>011110=>[1,4,1]=>[1,4,1]
[2,7,6,5,4,3,1]=>011111=>[1,5]=>[5,1]
[3,1,2,4,5,6,7]=>100000=>[1,5]=>[5,1]
[3,1,2,4,5,7,6]=>100001=>[1,4,1]=>[1,4,1]
[3,1,2,4,6,5,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,2,4,6,7,5]=>100001=>[1,4,1]=>[1,4,1]
[3,1,2,4,7,5,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,2,4,7,6,5]=>100011=>[1,3,2]=>[2,3,1]
[3,1,2,5,4,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,1,2,5,4,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,2,5,6,4,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,2,5,6,7,4]=>100001=>[1,4,1]=>[1,4,1]
[3,1,2,5,7,4,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,2,5,7,6,4]=>100011=>[1,3,2]=>[2,3,1]
[3,1,2,6,4,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,1,2,6,4,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,2,6,5,4,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,2,6,5,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,2,6,7,4,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,2,6,7,5,4]=>100011=>[1,3,2]=>[2,3,1]
[3,1,2,7,4,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,1,2,7,4,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,2,7,5,4,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,2,7,5,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,2,7,6,4,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,2,7,6,5,4]=>100111=>[1,2,3]=>[3,2,1]
[3,1,4,2,5,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,1,4,2,5,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,4,2,6,5,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,4,2,6,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,4,2,7,5,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,4,2,7,6,5]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,1,4,5,2,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,1,4,5,2,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,4,5,6,2,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,4,5,6,7,2]=>100001=>[1,4,1]=>[1,4,1]
[3,1,4,5,7,2,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,4,5,7,6,2]=>100011=>[1,3,2]=>[2,3,1]
[3,1,4,6,2,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,1,4,6,2,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,4,6,5,2,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,4,6,5,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,4,6,7,2,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,4,6,7,5,2]=>100011=>[1,3,2]=>[2,3,1]
[3,1,4,7,2,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,1,4,7,2,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,4,7,5,2,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,4,7,5,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,4,7,6,2,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,4,7,6,5,2]=>100111=>[1,2,3]=>[3,2,1]
[3,1,5,2,4,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,1,5,2,4,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,5,2,6,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,5,2,6,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,5,2,7,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,5,2,7,6,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,1,5,4,2,6,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,1,5,4,2,7,6]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,1,5,4,6,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,5,4,6,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,5,4,7,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,5,4,7,6,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,1,5,6,2,4,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,1,5,6,2,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,5,6,4,2,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,5,6,4,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,5,6,7,2,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,1,5,6,7,4,2]=>100011=>[1,3,2]=>[2,3,1]
[3,1,5,7,2,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,1,5,7,2,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,5,7,4,2,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,5,7,4,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,5,7,6,2,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,5,7,6,4,2]=>100111=>[1,2,3]=>[3,2,1]
[3,1,6,2,4,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,1,6,2,4,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,6,2,5,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,6,2,5,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,6,2,7,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,6,2,7,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,1,6,4,2,5,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,1,6,4,2,7,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,1,6,4,5,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,6,4,5,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,6,4,7,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,6,4,7,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,1,6,5,2,4,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,1,6,5,2,7,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,1,6,5,4,2,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,1,6,5,4,7,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,1,6,5,7,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,6,5,7,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,1,6,7,2,4,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,1,6,7,2,5,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,6,7,4,2,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,6,7,4,5,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,1,6,7,5,2,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,1,6,7,5,4,2]=>100111=>[1,2,3]=>[3,2,1]
[3,1,7,2,4,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,1,7,2,4,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,7,2,5,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,7,2,5,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,7,2,6,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,7,2,6,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,1,7,4,2,5,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,1,7,4,2,6,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,1,7,4,5,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,7,4,5,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,1,7,4,6,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,7,4,6,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,1,7,5,2,4,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,1,7,5,2,6,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,1,7,5,4,2,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,1,7,5,4,6,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,1,7,5,6,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,1,7,5,6,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,1,7,6,2,4,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,1,7,6,2,5,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,1,7,6,4,2,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,1,7,6,4,5,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,1,7,6,5,2,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,1,7,6,5,4,2]=>101111=>[1,1,4]=>[4,1,1]
[3,2,1,4,5,6,7]=>110000=>[2,4]=>[4,2]
[3,2,1,4,5,7,6]=>110001=>[2,3,1]=>[1,3,2]
[3,2,1,4,6,5,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[3,2,1,4,6,7,5]=>110001=>[2,3,1]=>[1,3,2]
[3,2,1,4,7,5,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[3,2,1,4,7,6,5]=>110011=>[2,2,2]=>[2,2,2]
[3,2,1,5,4,6,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[3,2,1,5,4,7,6]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,2,1,5,6,4,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[3,2,1,5,6,7,4]=>110001=>[2,3,1]=>[1,3,2]
[3,2,1,5,7,4,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[3,2,1,5,7,6,4]=>110011=>[2,2,2]=>[2,2,2]
[3,2,1,6,4,5,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[3,2,1,6,4,7,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,2,1,6,5,4,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[3,2,1,6,5,7,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,2,1,6,7,4,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[3,2,1,6,7,5,4]=>110011=>[2,2,2]=>[2,2,2]
[3,2,1,7,4,5,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[3,2,1,7,4,6,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,2,1,7,5,4,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[3,2,1,7,5,6,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,2,1,7,6,4,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[3,2,1,7,6,5,4]=>110111=>[2,1,3]=>[3,1,2]
[3,2,4,1,5,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,2,4,1,5,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,4,1,6,5,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,4,1,6,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,4,1,7,5,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,4,1,7,6,5]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,2,4,5,1,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,2,4,5,1,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,4,5,6,1,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,2,4,5,6,7,1]=>100001=>[1,4,1]=>[1,4,1]
[3,2,4,5,7,1,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,2,4,5,7,6,1]=>100011=>[1,3,2]=>[2,3,1]
[3,2,4,6,1,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,2,4,6,1,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,4,6,5,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,2,4,6,5,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,4,6,7,1,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,2,4,6,7,5,1]=>100011=>[1,3,2]=>[2,3,1]
[3,2,4,7,1,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,2,4,7,1,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,4,7,5,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,2,4,7,5,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,4,7,6,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,2,4,7,6,5,1]=>100111=>[1,2,3]=>[3,2,1]
[3,2,5,1,4,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,2,5,1,4,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,5,1,6,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,5,1,6,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,5,1,7,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,5,1,7,6,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,2,5,4,1,6,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,2,5,4,1,7,6]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,2,5,4,6,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,5,4,6,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,5,4,7,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,5,4,7,6,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,2,5,6,1,4,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,2,5,6,1,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,5,6,4,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,2,5,6,4,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,5,6,7,1,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[3,2,5,6,7,4,1]=>100011=>[1,3,2]=>[2,3,1]
[3,2,5,7,1,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,2,5,7,1,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,5,7,4,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,2,5,7,4,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,5,7,6,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,2,5,7,6,4,1]=>100111=>[1,2,3]=>[3,2,1]
[3,2,6,1,4,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,2,6,1,4,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,6,1,5,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,6,1,5,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,6,1,7,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,6,1,7,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,2,6,4,1,5,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,2,6,4,1,7,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,2,6,4,5,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,6,4,5,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,6,4,7,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,6,4,7,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,2,6,5,1,4,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,2,6,5,1,7,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,2,6,5,4,1,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,2,6,5,4,7,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,2,6,5,7,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,6,5,7,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,2,6,7,1,4,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[3,2,6,7,1,5,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,6,7,4,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,2,6,7,4,5,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,2,6,7,5,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[3,2,6,7,5,4,1]=>100111=>[1,2,3]=>[3,2,1]
[3,2,7,1,4,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[3,2,7,1,4,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,7,1,5,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,7,1,5,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,7,1,6,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,7,1,6,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,2,7,4,1,5,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,2,7,4,1,6,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,2,7,4,5,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,7,4,5,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,2,7,4,6,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,7,4,6,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,2,7,5,1,4,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,2,7,5,1,6,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,2,7,5,4,1,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,2,7,5,4,6,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,2,7,5,6,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,2,7,5,6,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,2,7,6,1,4,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[3,2,7,6,1,5,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,2,7,6,4,1,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,2,7,6,4,5,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,2,7,6,5,1,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[3,2,7,6,5,4,1]=>101111=>[1,1,4]=>[4,1,1]
[3,4,1,2,5,6,7]=>010000=>[1,1,4]=>[4,1,1]
[3,4,1,2,5,7,6]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,4,1,2,6,5,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,1,2,6,7,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,4,1,2,7,5,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,1,2,7,6,5]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,4,1,5,2,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,4,1,5,2,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,1,5,6,2,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,1,5,6,7,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,4,1,5,7,2,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,1,5,7,6,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,4,1,6,2,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,4,1,6,2,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,1,6,5,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,4,1,6,5,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,1,6,7,2,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,1,6,7,5,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,4,1,7,2,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,4,1,7,2,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,1,7,5,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,4,1,7,5,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,1,7,6,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,4,1,7,6,5,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,4,2,1,5,6,7]=>011000=>[1,2,3]=>[3,2,1]
[3,4,2,1,5,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,4,2,1,6,5,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,4,2,1,6,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,4,2,1,7,5,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,4,2,1,7,6,5]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,4,2,5,1,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,4,2,5,1,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,2,5,6,1,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,2,5,6,7,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,4,2,5,7,1,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,2,5,7,6,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,4,2,6,1,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,4,2,6,1,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,2,6,5,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,4,2,6,5,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,2,6,7,1,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,4,2,6,7,5,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,4,2,7,1,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,4,2,7,1,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,2,7,5,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,4,2,7,5,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,4,2,7,6,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,4,2,7,6,5,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,4,5,1,2,6,7]=>001000=>[2,1,3]=>[3,1,2]
[3,4,5,1,2,7,6]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,4,5,1,6,2,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,5,1,6,7,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,4,5,1,7,2,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,5,1,7,6,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,4,5,2,1,6,7]=>001100=>[2,2,2]=>[2,2,2]
[3,4,5,2,1,7,6]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,4,5,2,6,1,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,5,2,6,7,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,4,5,2,7,1,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,5,2,7,6,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,4,5,6,1,2,7]=>000100=>[3,1,2]=>[2,1,3]
[3,4,5,6,1,7,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[3,4,5,6,2,1,7]=>000110=>[3,2,1]=>[1,2,3]
[3,4,5,6,2,7,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[3,4,5,6,7,1,2]=>000010=>[4,1,1]=>[1,1,4]
[3,4,5,6,7,2,1]=>000011=>[4,2]=>[2,4]
[3,4,5,7,1,2,6]=>000100=>[3,1,2]=>[2,1,3]
[3,4,5,7,1,6,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[3,4,5,7,2,1,6]=>000110=>[3,2,1]=>[1,2,3]
[3,4,5,7,2,6,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[3,4,5,7,6,1,2]=>000110=>[3,2,1]=>[1,2,3]
[3,4,5,7,6,2,1]=>000111=>[3,3]=>[3,3]
[3,4,6,1,2,5,7]=>001000=>[2,1,3]=>[3,1,2]
[3,4,6,1,2,7,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,4,6,1,5,2,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,6,1,5,7,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,4,6,1,7,2,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,6,1,7,5,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,4,6,2,1,5,7]=>001100=>[2,2,2]=>[2,2,2]
[3,4,6,2,1,7,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,4,6,2,5,1,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,6,2,5,7,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,4,6,2,7,1,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,6,2,7,5,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,4,6,5,1,2,7]=>001100=>[2,2,2]=>[2,2,2]
[3,4,6,5,1,7,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,4,6,5,2,1,7]=>001110=>[2,3,1]=>[1,3,2]
[3,4,6,5,2,7,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,4,6,5,7,1,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,6,5,7,2,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,4,6,7,1,2,5]=>000100=>[3,1,2]=>[2,1,3]
[3,4,6,7,1,5,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[3,4,6,7,2,1,5]=>000110=>[3,2,1]=>[1,2,3]
[3,4,6,7,2,5,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[3,4,6,7,5,1,2]=>000110=>[3,2,1]=>[1,2,3]
[3,4,6,7,5,2,1]=>000111=>[3,3]=>[3,3]
[3,4,7,1,2,5,6]=>001000=>[2,1,3]=>[3,1,2]
[3,4,7,1,2,6,5]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,4,7,1,5,2,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,7,1,5,6,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,4,7,1,6,2,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,7,1,6,5,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,4,7,2,1,5,6]=>001100=>[2,2,2]=>[2,2,2]
[3,4,7,2,1,6,5]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,4,7,2,5,1,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,7,2,5,6,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,4,7,2,6,1,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,7,2,6,5,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,4,7,5,1,2,6]=>001100=>[2,2,2]=>[2,2,2]
[3,4,7,5,1,6,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,4,7,5,2,1,6]=>001110=>[2,3,1]=>[1,3,2]
[3,4,7,5,2,6,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,4,7,5,6,1,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,4,7,5,6,2,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,4,7,6,1,2,5]=>001100=>[2,2,2]=>[2,2,2]
[3,4,7,6,1,5,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,4,7,6,2,1,5]=>001110=>[2,3,1]=>[1,3,2]
[3,4,7,6,2,5,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,4,7,6,5,1,2]=>001110=>[2,3,1]=>[1,3,2]
[3,4,7,6,5,2,1]=>001111=>[2,4]=>[4,2]
[3,5,1,2,4,6,7]=>010000=>[1,1,4]=>[4,1,1]
[3,5,1,2,4,7,6]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,5,1,2,6,4,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,5,1,2,6,7,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,5,1,2,7,4,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,5,1,2,7,6,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,5,1,4,2,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,5,1,4,2,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,1,4,6,2,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,5,1,4,6,7,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,5,1,4,7,2,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,5,1,4,7,6,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,5,1,6,2,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,5,1,6,2,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,1,6,4,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,5,1,6,4,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,1,6,7,2,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,5,1,6,7,4,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,5,1,7,2,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,5,1,7,2,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,1,7,4,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,5,1,7,4,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,1,7,6,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,5,1,7,6,4,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,5,2,1,4,6,7]=>011000=>[1,2,3]=>[3,2,1]
[3,5,2,1,4,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,5,2,1,6,4,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,5,2,1,6,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,5,2,1,7,4,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,5,2,1,7,6,4]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,5,2,4,1,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,5,2,4,1,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,2,4,6,1,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,5,2,4,6,7,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,5,2,4,7,1,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,5,2,4,7,6,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,5,2,6,1,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,5,2,6,1,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,2,6,4,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,5,2,6,4,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,2,6,7,1,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,5,2,6,7,4,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,5,2,7,1,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,5,2,7,1,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,2,7,4,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,5,2,7,4,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,2,7,6,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,5,2,7,6,4,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,5,4,1,2,6,7]=>011000=>[1,2,3]=>[3,2,1]
[3,5,4,1,2,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,5,4,1,6,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,5,4,1,6,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,5,4,1,7,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,5,4,1,7,6,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,5,4,2,1,6,7]=>011100=>[1,3,2]=>[2,3,1]
[3,5,4,2,1,7,6]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,5,4,2,6,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,5,4,2,6,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,5,4,2,7,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,5,4,2,7,6,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,5,4,6,1,2,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,5,4,6,1,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,4,6,2,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,5,4,6,2,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,4,6,7,1,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,5,4,6,7,2,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,5,4,7,1,2,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,5,4,7,1,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,4,7,2,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,5,4,7,2,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,5,4,7,6,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,5,4,7,6,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,5,6,1,2,4,7]=>001000=>[2,1,3]=>[3,1,2]
[3,5,6,1,2,7,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,5,6,1,4,2,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,6,1,4,7,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,5,6,1,7,2,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,6,1,7,4,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,5,6,2,1,4,7]=>001100=>[2,2,2]=>[2,2,2]
[3,5,6,2,1,7,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,5,6,2,4,1,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,6,2,4,7,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,5,6,2,7,1,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,6,2,7,4,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,5,6,4,1,2,7]=>001100=>[2,2,2]=>[2,2,2]
[3,5,6,4,1,7,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,5,6,4,2,1,7]=>001110=>[2,3,1]=>[1,3,2]
[3,5,6,4,2,7,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,5,6,4,7,1,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,6,4,7,2,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,5,6,7,1,2,4]=>000100=>[3,1,2]=>[2,1,3]
[3,5,6,7,1,4,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[3,5,6,7,2,1,4]=>000110=>[3,2,1]=>[1,2,3]
[3,5,6,7,2,4,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[3,5,6,7,4,1,2]=>000110=>[3,2,1]=>[1,2,3]
[3,5,6,7,4,2,1]=>000111=>[3,3]=>[3,3]
[3,5,7,1,2,4,6]=>001000=>[2,1,3]=>[3,1,2]
[3,5,7,1,2,6,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,5,7,1,4,2,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,7,1,4,6,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,5,7,1,6,2,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,7,1,6,4,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,5,7,2,1,4,6]=>001100=>[2,2,2]=>[2,2,2]
[3,5,7,2,1,6,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,5,7,2,4,1,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,7,2,4,6,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,5,7,2,6,1,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,7,2,6,4,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,5,7,4,1,2,6]=>001100=>[2,2,2]=>[2,2,2]
[3,5,7,4,1,6,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,5,7,4,2,1,6]=>001110=>[2,3,1]=>[1,3,2]
[3,5,7,4,2,6,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,5,7,4,6,1,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,5,7,4,6,2,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,5,7,6,1,2,4]=>001100=>[2,2,2]=>[2,2,2]
[3,5,7,6,1,4,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,5,7,6,2,1,4]=>001110=>[2,3,1]=>[1,3,2]
[3,5,7,6,2,4,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,5,7,6,4,1,2]=>001110=>[2,3,1]=>[1,3,2]
[3,5,7,6,4,2,1]=>001111=>[2,4]=>[4,2]
[3,6,1,2,4,5,7]=>010000=>[1,1,4]=>[4,1,1]
[3,6,1,2,4,7,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,6,1,2,5,4,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,1,2,5,7,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,6,1,2,7,4,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,1,2,7,5,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,6,1,4,2,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,6,1,4,2,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,1,4,5,2,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,1,4,5,7,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,6,1,4,7,2,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,1,4,7,5,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,6,1,5,2,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,6,1,5,2,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,1,5,4,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,1,5,4,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,1,5,7,2,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,1,5,7,4,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,6,1,7,2,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,6,1,7,2,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,1,7,4,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,1,7,4,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,1,7,5,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,1,7,5,4,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,6,2,1,4,5,7]=>011000=>[1,2,3]=>[3,2,1]
[3,6,2,1,4,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,6,2,1,5,4,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,2,1,5,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,6,2,1,7,4,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,2,1,7,5,4]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,6,2,4,1,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,6,2,4,1,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,2,4,5,1,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,2,4,5,7,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,6,2,4,7,1,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,2,4,7,5,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,6,2,5,1,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,6,2,5,1,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,2,5,4,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,2,5,4,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,2,5,7,1,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,2,5,7,4,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,6,2,7,1,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,6,2,7,1,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,2,7,4,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,2,7,4,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,2,7,5,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,2,7,5,4,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,6,4,1,2,5,7]=>011000=>[1,2,3]=>[3,2,1]
[3,6,4,1,2,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,6,4,1,5,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,4,1,5,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,6,4,1,7,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,4,1,7,5,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,6,4,2,1,5,7]=>011100=>[1,3,2]=>[2,3,1]
[3,6,4,2,1,7,5]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,6,4,2,5,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,4,2,5,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,6,4,2,7,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,4,2,7,5,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,6,4,5,1,2,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,6,4,5,1,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,4,5,2,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,4,5,2,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,4,5,7,1,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,6,4,5,7,2,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,6,4,7,1,2,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,6,4,7,1,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,4,7,2,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,4,7,2,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,4,7,5,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,4,7,5,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,6,5,1,2,4,7]=>011000=>[1,2,3]=>[3,2,1]
[3,6,5,1,2,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,6,5,1,4,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,5,1,4,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,6,5,1,7,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,5,1,7,4,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,6,5,2,1,4,7]=>011100=>[1,3,2]=>[2,3,1]
[3,6,5,2,1,7,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,6,5,2,4,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,5,2,4,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,6,5,2,7,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,5,2,7,4,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,6,5,4,1,2,7]=>011100=>[1,3,2]=>[2,3,1]
[3,6,5,4,1,7,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,6,5,4,2,1,7]=>011110=>[1,4,1]=>[1,4,1]
[3,6,5,4,2,7,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,6,5,4,7,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,6,5,4,7,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,6,5,7,1,2,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,6,5,7,1,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,5,7,2,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,5,7,2,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,6,5,7,4,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,6,5,7,4,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,6,7,1,2,4,5]=>001000=>[2,1,3]=>[3,1,2]
[3,6,7,1,2,5,4]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,6,7,1,4,2,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,6,7,1,4,5,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,6,7,1,5,2,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,6,7,1,5,4,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,6,7,2,1,4,5]=>001100=>[2,2,2]=>[2,2,2]
[3,6,7,2,1,5,4]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,6,7,2,4,1,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,6,7,2,4,5,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[3,6,7,2,5,1,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,6,7,2,5,4,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,6,7,4,1,2,5]=>001100=>[2,2,2]=>[2,2,2]
[3,6,7,4,1,5,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,6,7,4,2,1,5]=>001110=>[2,3,1]=>[1,3,2]
[3,6,7,4,2,5,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,6,7,4,5,1,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[3,6,7,4,5,2,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[3,6,7,5,1,2,4]=>001100=>[2,2,2]=>[2,2,2]
[3,6,7,5,1,4,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,6,7,5,2,1,4]=>001110=>[2,3,1]=>[1,3,2]
[3,6,7,5,2,4,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[3,6,7,5,4,1,2]=>001110=>[2,3,1]=>[1,3,2]
[3,6,7,5,4,2,1]=>001111=>[2,4]=>[4,2]
[3,7,1,2,4,5,6]=>010000=>[1,1,4]=>[4,1,1]
[3,7,1,2,4,6,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,7,1,2,5,4,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,7,1,2,5,6,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,7,1,2,6,4,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,7,1,2,6,5,4]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,7,1,4,2,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,7,1,4,2,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,1,4,5,2,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,7,1,4,5,6,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,7,1,4,6,2,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,7,1,4,6,5,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,7,1,5,2,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,7,1,5,2,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,1,5,4,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,1,5,4,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,1,5,6,2,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,7,1,5,6,4,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,7,1,6,2,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,7,1,6,2,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,1,6,4,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,1,6,4,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,1,6,5,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,1,6,5,4,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,7,2,1,4,5,6]=>011000=>[1,2,3]=>[3,2,1]
[3,7,2,1,4,6,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,2,1,5,4,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,2,1,5,6,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,2,1,6,4,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,2,1,6,5,4]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,7,2,4,1,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,7,2,4,1,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,2,4,5,1,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,7,2,4,5,6,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[3,7,2,4,6,1,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,7,2,4,6,5,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,7,2,5,1,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,7,2,5,1,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,2,5,4,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,2,5,4,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,2,5,6,1,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,7,2,5,6,4,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,7,2,6,1,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,7,2,6,1,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,2,6,4,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,2,6,4,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,2,6,5,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,2,6,5,4,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,7,4,1,2,5,6]=>011000=>[1,2,3]=>[3,2,1]
[3,7,4,1,2,6,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,4,1,5,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,4,1,5,6,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,4,1,6,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,4,1,6,5,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,7,4,2,1,5,6]=>011100=>[1,3,2]=>[2,3,1]
[3,7,4,2,1,6,5]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,7,4,2,5,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,4,2,5,6,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,4,2,6,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,4,2,6,5,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,7,4,5,1,2,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,7,4,5,1,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,4,5,2,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,4,5,2,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,4,5,6,1,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[3,7,4,5,6,2,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[3,7,4,6,1,2,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,7,4,6,1,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,4,6,2,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,4,6,2,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,4,6,5,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,4,6,5,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,7,5,1,2,4,6]=>011000=>[1,2,3]=>[3,2,1]
[3,7,5,1,2,6,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,5,1,4,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,5,1,4,6,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,5,1,6,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,5,1,6,4,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,7,5,2,1,4,6]=>011100=>[1,3,2]=>[2,3,1]
[3,7,5,2,1,6,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,7,5,2,4,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,5,2,4,6,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,5,2,6,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,5,2,6,4,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,7,5,4,1,2,6]=>011100=>[1,3,2]=>[2,3,1]
[3,7,5,4,1,6,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,7,5,4,2,1,6]=>011110=>[1,4,1]=>[1,4,1]
[3,7,5,4,2,6,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,7,5,4,6,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,5,4,6,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,7,5,6,1,2,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[3,7,5,6,1,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,5,6,2,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,5,6,2,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[3,7,5,6,4,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[3,7,5,6,4,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[3,7,6,1,2,4,5]=>011000=>[1,2,3]=>[3,2,1]
[3,7,6,1,2,5,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,6,1,4,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,6,1,4,5,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,6,1,5,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,6,1,5,4,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,7,6,2,1,4,5]=>011100=>[1,3,2]=>[2,3,1]
[3,7,6,2,1,5,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,7,6,2,4,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,6,2,4,5,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[3,7,6,2,5,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,6,2,5,4,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,7,6,4,1,2,5]=>011100=>[1,3,2]=>[2,3,1]
[3,7,6,4,1,5,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,7,6,4,2,1,5]=>011110=>[1,4,1]=>[1,4,1]
[3,7,6,4,2,5,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,7,6,4,5,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[3,7,6,4,5,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[3,7,6,5,1,2,4]=>011100=>[1,3,2]=>[2,3,1]
[3,7,6,5,1,4,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,7,6,5,2,1,4]=>011110=>[1,4,1]=>[1,4,1]
[3,7,6,5,2,4,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[3,7,6,5,4,1,2]=>011110=>[1,4,1]=>[1,4,1]
[3,7,6,5,4,2,1]=>011111=>[1,5]=>[5,1]
[4,1,2,3,5,6,7]=>100000=>[1,5]=>[5,1]
[4,1,2,3,5,7,6]=>100001=>[1,4,1]=>[1,4,1]
[4,1,2,3,6,5,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,1,2,3,6,7,5]=>100001=>[1,4,1]=>[1,4,1]
[4,1,2,3,7,5,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,1,2,3,7,6,5]=>100011=>[1,3,2]=>[2,3,1]
[4,1,2,5,3,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,2,5,3,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,2,5,6,3,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,1,2,5,6,7,3]=>100001=>[1,4,1]=>[1,4,1]
[4,1,2,5,7,3,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,1,2,5,7,6,3]=>100011=>[1,3,2]=>[2,3,1]
[4,1,2,6,3,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,2,6,3,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,2,6,5,3,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,2,6,5,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,2,6,7,3,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,1,2,6,7,5,3]=>100011=>[1,3,2]=>[2,3,1]
[4,1,2,7,3,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,2,7,3,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,2,7,5,3,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,2,7,5,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,2,7,6,3,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,2,7,6,5,3]=>100111=>[1,2,3]=>[3,2,1]
[4,1,3,2,5,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,1,3,2,5,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,3,2,6,5,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,3,2,6,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,3,2,7,5,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,3,2,7,6,5]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,1,3,5,2,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,3,5,2,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,3,5,6,2,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,1,3,5,6,7,2]=>100001=>[1,4,1]=>[1,4,1]
[4,1,3,5,7,2,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,1,3,5,7,6,2]=>100011=>[1,3,2]=>[2,3,1]
[4,1,3,6,2,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,3,6,2,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,3,6,5,2,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,3,6,5,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,3,6,7,2,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,1,3,6,7,5,2]=>100011=>[1,3,2]=>[2,3,1]
[4,1,3,7,2,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,3,7,2,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,3,7,5,2,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,3,7,5,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,3,7,6,2,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,3,7,6,5,2]=>100111=>[1,2,3]=>[3,2,1]
[4,1,5,2,3,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,1,5,2,3,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,5,2,6,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,5,2,6,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,5,2,7,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,5,2,7,6,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,1,5,3,2,6,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,1,5,3,2,7,6]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,1,5,3,6,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,5,3,6,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,5,3,7,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,5,3,7,6,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,1,5,6,2,3,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,5,6,2,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,5,6,3,2,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,5,6,3,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,5,6,7,2,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,1,5,6,7,3,2]=>100011=>[1,3,2]=>[2,3,1]
[4,1,5,7,2,3,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,5,7,2,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,5,7,3,2,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,5,7,3,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,5,7,6,2,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,5,7,6,3,2]=>100111=>[1,2,3]=>[3,2,1]
[4,1,6,2,3,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,1,6,2,3,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,6,2,5,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,6,2,5,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,6,2,7,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,6,2,7,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,1,6,3,2,5,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,1,6,3,2,7,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,1,6,3,5,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,6,3,5,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,6,3,7,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,6,3,7,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,1,6,5,2,3,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,1,6,5,2,7,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,1,6,5,3,2,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,1,6,5,3,7,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,1,6,5,7,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,6,5,7,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,1,6,7,2,3,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,1,6,7,2,5,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,6,7,3,2,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,6,7,3,5,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,1,6,7,5,2,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,1,6,7,5,3,2]=>100111=>[1,2,3]=>[3,2,1]
[4,1,7,2,3,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,1,7,2,3,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,7,2,5,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,7,2,5,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,7,2,6,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,7,2,6,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,1,7,3,2,5,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,1,7,3,2,6,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,1,7,3,5,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,7,3,5,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,1,7,3,6,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,7,3,6,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,1,7,5,2,3,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,1,7,5,2,6,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,1,7,5,3,2,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,1,7,5,3,6,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,1,7,5,6,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,1,7,5,6,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,1,7,6,2,3,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,1,7,6,2,5,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,1,7,6,3,2,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,1,7,6,3,5,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,1,7,6,5,2,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,1,7,6,5,3,2]=>101111=>[1,1,4]=>[4,1,1]
[4,2,1,3,5,6,7]=>110000=>[2,4]=>[4,2]
[4,2,1,3,5,7,6]=>110001=>[2,3,1]=>[1,3,2]
[4,2,1,3,6,5,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,2,1,3,6,7,5]=>110001=>[2,3,1]=>[1,3,2]
[4,2,1,3,7,5,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,2,1,3,7,6,5]=>110011=>[2,2,2]=>[2,2,2]
[4,2,1,5,3,6,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,2,1,5,3,7,6]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,2,1,5,6,3,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,2,1,5,6,7,3]=>110001=>[2,3,1]=>[1,3,2]
[4,2,1,5,7,3,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,2,1,5,7,6,3]=>110011=>[2,2,2]=>[2,2,2]
[4,2,1,6,3,5,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,2,1,6,3,7,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,2,1,6,5,3,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,2,1,6,5,7,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,2,1,6,7,3,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,2,1,6,7,5,3]=>110011=>[2,2,2]=>[2,2,2]
[4,2,1,7,3,5,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,2,1,7,3,6,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,2,1,7,5,3,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,2,1,7,5,6,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,2,1,7,6,3,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,2,1,7,6,5,3]=>110111=>[2,1,3]=>[3,1,2]
[4,2,3,1,5,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,2,3,1,5,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,3,1,6,5,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,3,1,6,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,3,1,7,5,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,3,1,7,6,5]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,3,5,1,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,2,3,5,1,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,3,5,6,1,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,2,3,5,6,7,1]=>100001=>[1,4,1]=>[1,4,1]
[4,2,3,5,7,1,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,2,3,5,7,6,1]=>100011=>[1,3,2]=>[2,3,1]
[4,2,3,6,1,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,2,3,6,1,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,3,6,5,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,2,3,6,5,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,3,6,7,1,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,2,3,6,7,5,1]=>100011=>[1,3,2]=>[2,3,1]
[4,2,3,7,1,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,2,3,7,1,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,3,7,5,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,2,3,7,5,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,3,7,6,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,2,3,7,6,5,1]=>100111=>[1,2,3]=>[3,2,1]
[4,2,5,1,3,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,2,5,1,3,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,5,1,6,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,5,1,6,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,5,1,7,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,5,1,7,6,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,5,3,1,6,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,2,5,3,1,7,6]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,5,3,6,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,5,3,6,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,5,3,7,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,5,3,7,6,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,5,6,1,3,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,2,5,6,1,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,5,6,3,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,2,5,6,3,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,5,6,7,1,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,2,5,6,7,3,1]=>100011=>[1,3,2]=>[2,3,1]
[4,2,5,7,1,3,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,2,5,7,1,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,5,7,3,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,2,5,7,3,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,5,7,6,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,2,5,7,6,3,1]=>100111=>[1,2,3]=>[3,2,1]
[4,2,6,1,3,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,2,6,1,3,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,6,1,5,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,6,1,5,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,6,1,7,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,6,1,7,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,6,3,1,5,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,2,6,3,1,7,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,6,3,5,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,6,3,5,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,6,3,7,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,6,3,7,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,6,5,1,3,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,2,6,5,1,7,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,6,5,3,1,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,2,6,5,3,7,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,6,5,7,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,6,5,7,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,6,7,1,3,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,2,6,7,1,5,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,6,7,3,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,2,6,7,3,5,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,2,6,7,5,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,2,6,7,5,3,1]=>100111=>[1,2,3]=>[3,2,1]
[4,2,7,1,3,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,2,7,1,3,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,7,1,5,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,7,1,5,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,7,1,6,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,7,1,6,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,7,3,1,5,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,2,7,3,1,6,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,7,3,5,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,7,3,5,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,2,7,3,6,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,7,3,6,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,7,5,1,3,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,2,7,5,1,6,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,7,5,3,1,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,2,7,5,3,6,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,7,5,6,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,2,7,5,6,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,2,7,6,1,3,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,2,7,6,1,5,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,7,6,3,1,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,2,7,6,3,5,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,2,7,6,5,1,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,2,7,6,5,3,1]=>101111=>[1,1,4]=>[4,1,1]
[4,3,1,2,5,6,7]=>110000=>[2,4]=>[4,2]
[4,3,1,2,5,7,6]=>110001=>[2,3,1]=>[1,3,2]
[4,3,1,2,6,5,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,3,1,2,6,7,5]=>110001=>[2,3,1]=>[1,3,2]
[4,3,1,2,7,5,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,3,1,2,7,6,5]=>110011=>[2,2,2]=>[2,2,2]
[4,3,1,5,2,6,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,3,1,5,2,7,6]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,1,5,6,2,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,3,1,5,6,7,2]=>110001=>[2,3,1]=>[1,3,2]
[4,3,1,5,7,2,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,3,1,5,7,6,2]=>110011=>[2,2,2]=>[2,2,2]
[4,3,1,6,2,5,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,3,1,6,2,7,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,1,6,5,2,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,3,1,6,5,7,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,1,6,7,2,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,3,1,6,7,5,2]=>110011=>[2,2,2]=>[2,2,2]
[4,3,1,7,2,5,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,3,1,7,2,6,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,1,7,5,2,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,3,1,7,5,6,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,1,7,6,2,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,3,1,7,6,5,2]=>110111=>[2,1,3]=>[3,1,2]
[4,3,2,1,5,6,7]=>111000=>[3,3]=>[3,3]
[4,3,2,1,5,7,6]=>111001=>[3,2,1]=>[1,2,3]
[4,3,2,1,6,5,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[4,3,2,1,6,7,5]=>111001=>[3,2,1]=>[1,2,3]
[4,3,2,1,7,5,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[4,3,2,1,7,6,5]=>111011=>[3,1,2]=>[2,1,3]
[4,3,2,5,1,6,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,3,2,5,1,7,6]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,2,5,6,1,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,3,2,5,6,7,1]=>110001=>[2,3,1]=>[1,3,2]
[4,3,2,5,7,1,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,3,2,5,7,6,1]=>110011=>[2,2,2]=>[2,2,2]
[4,3,2,6,1,5,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,3,2,6,1,7,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,2,6,5,1,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,3,2,6,5,7,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,2,6,7,1,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[4,3,2,6,7,5,1]=>110011=>[2,2,2]=>[2,2,2]
[4,3,2,7,1,5,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[4,3,2,7,1,6,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,2,7,5,1,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,3,2,7,5,6,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,3,2,7,6,1,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[4,3,2,7,6,5,1]=>110111=>[2,1,3]=>[3,1,2]
[4,3,5,1,2,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,3,5,1,2,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,5,1,6,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,5,1,6,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,5,1,7,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,5,1,7,6,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,3,5,2,1,6,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,3,5,2,1,7,6]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,3,5,2,6,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,5,2,6,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,5,2,7,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,5,2,7,6,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,3,5,6,1,2,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,3,5,6,1,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,3,5,6,2,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,3,5,6,2,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,3,5,6,7,1,2]=>100010=>[1,3,1,1]=>[1,1,3,1]
[4,3,5,6,7,2,1]=>100011=>[1,3,2]=>[2,3,1]
[4,3,5,7,1,2,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,3,5,7,1,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,3,5,7,2,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,3,5,7,2,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,3,5,7,6,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,3,5,7,6,2,1]=>100111=>[1,2,3]=>[3,2,1]
[4,3,6,1,2,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,3,6,1,2,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,6,1,5,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,6,1,5,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,6,1,7,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,6,1,7,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,3,6,2,1,5,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,3,6,2,1,7,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,3,6,2,5,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,6,2,5,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,6,2,7,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,6,2,7,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,3,6,5,1,2,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,3,6,5,1,7,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,3,6,5,2,1,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,3,6,5,2,7,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,3,6,5,7,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,6,5,7,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,3,6,7,1,2,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[4,3,6,7,1,5,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,3,6,7,2,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,3,6,7,2,5,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,3,6,7,5,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[4,3,6,7,5,2,1]=>100111=>[1,2,3]=>[3,2,1]
[4,3,7,1,2,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[4,3,7,1,2,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,7,1,5,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,7,1,5,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,7,1,6,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,7,1,6,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,3,7,2,1,5,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,3,7,2,1,6,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,3,7,2,5,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,7,2,5,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,3,7,2,6,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,7,2,6,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,3,7,5,1,2,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,3,7,5,1,6,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,3,7,5,2,1,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,3,7,5,2,6,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,3,7,5,6,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,3,7,5,6,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,3,7,6,1,2,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[4,3,7,6,1,5,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,3,7,6,2,1,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,3,7,6,2,5,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,3,7,6,5,1,2]=>101110=>[1,1,3,1]=>[1,3,1,1]
[4,3,7,6,5,2,1]=>101111=>[1,1,4]=>[4,1,1]
[4,5,1,2,3,6,7]=>010000=>[1,1,4]=>[4,1,1]
[4,5,1,2,3,7,6]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,5,1,2,6,3,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,1,2,6,7,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,5,1,2,7,3,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,1,2,7,6,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,5,1,3,2,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,5,1,3,2,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,1,3,6,2,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,1,3,6,7,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,5,1,3,7,2,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,1,3,7,6,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,5,1,6,2,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,5,1,6,2,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,1,6,3,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,5,1,6,3,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,1,6,7,2,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,1,6,7,3,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,5,1,7,2,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,5,1,7,2,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,1,7,3,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,5,1,7,3,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,1,7,6,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,5,1,7,6,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,5,2,1,3,6,7]=>011000=>[1,2,3]=>[3,2,1]
[4,5,2,1,3,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,5,2,1,6,3,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,5,2,1,6,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,5,2,1,7,3,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,5,2,1,7,6,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,5,2,3,1,6,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,5,2,3,1,7,6]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,2,3,6,1,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,2,3,6,7,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,5,2,3,7,1,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,2,3,7,6,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,5,2,6,1,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,5,2,6,1,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,2,6,3,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,5,2,6,3,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,2,6,7,1,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,2,6,7,3,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,5,2,7,1,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,5,2,7,1,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,2,7,3,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,5,2,7,3,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,2,7,6,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,5,2,7,6,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,5,3,1,2,6,7]=>011000=>[1,2,3]=>[3,2,1]
[4,5,3,1,2,7,6]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,5,3,1,6,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,5,3,1,6,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,5,3,1,7,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,5,3,1,7,6,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,5,3,2,1,6,7]=>011100=>[1,3,2]=>[2,3,1]
[4,5,3,2,1,7,6]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,5,3,2,6,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,5,3,2,6,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,5,3,2,7,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,5,3,2,7,6,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,5,3,6,1,2,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,5,3,6,1,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,3,6,2,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,5,3,6,2,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,3,6,7,1,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,5,3,6,7,2,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,5,3,7,1,2,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,5,3,7,1,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,3,7,2,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,5,3,7,2,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,5,3,7,6,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,5,3,7,6,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,5,6,1,2,3,7]=>001000=>[2,1,3]=>[3,1,2]
[4,5,6,1,2,7,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[4,5,6,1,3,2,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,6,1,3,7,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[4,5,6,1,7,2,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,6,1,7,3,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[4,5,6,2,1,3,7]=>001100=>[2,2,2]=>[2,2,2]
[4,5,6,2,1,7,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,5,6,2,3,1,7]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,6,2,3,7,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[4,5,6,2,7,1,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,6,2,7,3,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[4,5,6,3,1,2,7]=>001100=>[2,2,2]=>[2,2,2]
[4,5,6,3,1,7,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,5,6,3,2,1,7]=>001110=>[2,3,1]=>[1,3,2]
[4,5,6,3,2,7,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,5,6,3,7,1,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,6,3,7,2,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[4,5,6,7,1,2,3]=>000100=>[3,1,2]=>[2,1,3]
[4,5,6,7,1,3,2]=>000101=>[3,1,1,1]=>[1,1,1,3]
[4,5,6,7,2,1,3]=>000110=>[3,2,1]=>[1,2,3]
[4,5,6,7,2,3,1]=>000101=>[3,1,1,1]=>[1,1,1,3]
[4,5,6,7,3,1,2]=>000110=>[3,2,1]=>[1,2,3]
[4,5,6,7,3,2,1]=>000111=>[3,3]=>[3,3]
[4,5,7,1,2,3,6]=>001000=>[2,1,3]=>[3,1,2]
[4,5,7,1,2,6,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[4,5,7,1,3,2,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,7,1,3,6,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[4,5,7,1,6,2,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,7,1,6,3,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[4,5,7,2,1,3,6]=>001100=>[2,2,2]=>[2,2,2]
[4,5,7,2,1,6,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,5,7,2,3,1,6]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,7,2,3,6,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[4,5,7,2,6,1,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,7,2,6,3,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[4,5,7,3,1,2,6]=>001100=>[2,2,2]=>[2,2,2]
[4,5,7,3,1,6,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,5,7,3,2,1,6]=>001110=>[2,3,1]=>[1,3,2]
[4,5,7,3,2,6,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,5,7,3,6,1,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,5,7,3,6,2,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[4,5,7,6,1,2,3]=>001100=>[2,2,2]=>[2,2,2]
[4,5,7,6,1,3,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,5,7,6,2,1,3]=>001110=>[2,3,1]=>[1,3,2]
[4,5,7,6,2,3,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,5,7,6,3,1,2]=>001110=>[2,3,1]=>[1,3,2]
[4,5,7,6,3,2,1]=>001111=>[2,4]=>[4,2]
[4,6,1,2,3,5,7]=>010000=>[1,1,4]=>[4,1,1]
[4,6,1,2,3,7,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,6,1,2,5,3,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,6,1,2,5,7,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,6,1,2,7,3,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,6,1,2,7,5,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,6,1,3,2,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,6,1,3,2,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,1,3,5,2,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,6,1,3,5,7,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,6,1,3,7,2,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,6,1,3,7,5,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,6,1,5,2,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,6,1,5,2,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,1,5,3,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,1,5,3,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,1,5,7,2,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,6,1,5,7,3,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,6,1,7,2,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,6,1,7,2,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,1,7,3,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,1,7,3,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,1,7,5,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,1,7,5,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,6,2,1,3,5,7]=>011000=>[1,2,3]=>[3,2,1]
[4,6,2,1,3,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,6,2,1,5,3,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,2,1,5,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,6,2,1,7,3,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,2,1,7,5,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,6,2,3,1,5,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,6,2,3,1,7,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,2,3,5,1,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,6,2,3,5,7,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,6,2,3,7,1,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,6,2,3,7,5,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,6,2,5,1,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,6,2,5,1,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,2,5,3,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,2,5,3,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,2,5,7,1,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,6,2,5,7,3,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,6,2,7,1,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,6,2,7,1,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,2,7,3,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,2,7,3,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,2,7,5,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,2,7,5,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,6,3,1,2,5,7]=>011000=>[1,2,3]=>[3,2,1]
[4,6,3,1,2,7,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,6,3,1,5,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,3,1,5,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,6,3,1,7,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,3,1,7,5,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,6,3,2,1,5,7]=>011100=>[1,3,2]=>[2,3,1]
[4,6,3,2,1,7,5]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,6,3,2,5,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,3,2,5,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,6,3,2,7,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,3,2,7,5,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,6,3,5,1,2,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,6,3,5,1,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,3,5,2,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,3,5,2,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,3,5,7,1,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,6,3,5,7,2,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,6,3,7,1,2,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,6,3,7,1,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,3,7,2,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,3,7,2,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,3,7,5,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,3,7,5,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,6,5,1,2,3,7]=>011000=>[1,2,3]=>[3,2,1]
[4,6,5,1,2,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,6,5,1,3,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,5,1,3,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,6,5,1,7,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,5,1,7,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,6,5,2,1,3,7]=>011100=>[1,3,2]=>[2,3,1]
[4,6,5,2,1,7,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,6,5,2,3,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,5,2,3,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,6,5,2,7,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,5,2,7,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,6,5,3,1,2,7]=>011100=>[1,3,2]=>[2,3,1]
[4,6,5,3,1,7,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,6,5,3,2,1,7]=>011110=>[1,4,1]=>[1,4,1]
[4,6,5,3,2,7,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,6,5,3,7,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,6,5,3,7,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,6,5,7,1,2,3]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,6,5,7,1,3,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,5,7,2,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,5,7,2,3,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,6,5,7,3,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,6,5,7,3,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,6,7,1,2,3,5]=>001000=>[2,1,3]=>[3,1,2]
[4,6,7,1,2,5,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[4,6,7,1,3,2,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,6,7,1,3,5,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[4,6,7,1,5,2,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,6,7,1,5,3,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[4,6,7,2,1,3,5]=>001100=>[2,2,2]=>[2,2,2]
[4,6,7,2,1,5,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,6,7,2,3,1,5]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,6,7,2,3,5,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[4,6,7,2,5,1,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,6,7,2,5,3,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[4,6,7,3,1,2,5]=>001100=>[2,2,2]=>[2,2,2]
[4,6,7,3,1,5,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,6,7,3,2,1,5]=>001110=>[2,3,1]=>[1,3,2]
[4,6,7,3,2,5,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,6,7,3,5,1,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[4,6,7,3,5,2,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[4,6,7,5,1,2,3]=>001100=>[2,2,2]=>[2,2,2]
[4,6,7,5,1,3,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,6,7,5,2,1,3]=>001110=>[2,3,1]=>[1,3,2]
[4,6,7,5,2,3,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[4,6,7,5,3,1,2]=>001110=>[2,3,1]=>[1,3,2]
[4,6,7,5,3,2,1]=>001111=>[2,4]=>[4,2]
[4,7,1,2,3,5,6]=>010000=>[1,1,4]=>[4,1,1]
[4,7,1,2,3,6,5]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,7,1,2,5,3,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,7,1,2,5,6,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,7,1,2,6,3,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,7,1,2,6,5,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,7,1,3,2,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,7,1,3,2,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,1,3,5,2,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,7,1,3,5,6,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,7,1,3,6,2,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,7,1,3,6,5,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,7,1,5,2,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,7,1,5,2,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,1,5,3,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,1,5,3,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,1,5,6,2,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,7,1,5,6,3,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,7,1,6,2,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,7,1,6,2,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,1,6,3,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,1,6,3,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,1,6,5,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,1,6,5,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,7,2,1,3,5,6]=>011000=>[1,2,3]=>[3,2,1]
[4,7,2,1,3,6,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,2,1,5,3,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,2,1,5,6,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,2,1,6,3,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,2,1,6,5,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,7,2,3,1,5,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,7,2,3,1,6,5]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,2,3,5,1,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,7,2,3,5,6,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[4,7,2,3,6,1,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,7,2,3,6,5,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,7,2,5,1,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,7,2,5,1,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,2,5,3,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,2,5,3,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,2,5,6,1,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,7,2,5,6,3,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,7,2,6,1,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,7,2,6,1,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,2,6,3,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,2,6,3,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,2,6,5,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,2,6,5,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,7,3,1,2,5,6]=>011000=>[1,2,3]=>[3,2,1]
[4,7,3,1,2,6,5]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,3,1,5,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,3,1,5,6,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,3,1,6,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,3,1,6,5,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,7,3,2,1,5,6]=>011100=>[1,3,2]=>[2,3,1]
[4,7,3,2,1,6,5]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,7,3,2,5,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,3,2,5,6,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,3,2,6,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,3,2,6,5,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,7,3,5,1,2,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,7,3,5,1,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,3,5,2,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,3,5,2,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,3,5,6,1,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[4,7,3,5,6,2,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[4,7,3,6,1,2,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,7,3,6,1,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,3,6,2,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,3,6,2,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,3,6,5,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,3,6,5,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,7,5,1,2,3,6]=>011000=>[1,2,3]=>[3,2,1]
[4,7,5,1,2,6,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,5,1,3,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,5,1,3,6,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,5,1,6,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,5,1,6,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,7,5,2,1,3,6]=>011100=>[1,3,2]=>[2,3,1]
[4,7,5,2,1,6,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,7,5,2,3,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,5,2,3,6,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,5,2,6,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,5,2,6,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,7,5,3,1,2,6]=>011100=>[1,3,2]=>[2,3,1]
[4,7,5,3,1,6,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,7,5,3,2,1,6]=>011110=>[1,4,1]=>[1,4,1]
[4,7,5,3,2,6,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,7,5,3,6,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,5,3,6,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,7,5,6,1,2,3]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[4,7,5,6,1,3,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,5,6,2,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,5,6,2,3,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[4,7,5,6,3,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[4,7,5,6,3,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[4,7,6,1,2,3,5]=>011000=>[1,2,3]=>[3,2,1]
[4,7,6,1,2,5,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,6,1,3,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,6,1,3,5,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,6,1,5,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,6,1,5,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,7,6,2,1,3,5]=>011100=>[1,3,2]=>[2,3,1]
[4,7,6,2,1,5,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,7,6,2,3,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,6,2,3,5,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[4,7,6,2,5,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,6,2,5,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,7,6,3,1,2,5]=>011100=>[1,3,2]=>[2,3,1]
[4,7,6,3,1,5,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,7,6,3,2,1,5]=>011110=>[1,4,1]=>[1,4,1]
[4,7,6,3,2,5,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,7,6,3,5,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[4,7,6,3,5,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[4,7,6,5,1,2,3]=>011100=>[1,3,2]=>[2,3,1]
[4,7,6,5,1,3,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,7,6,5,2,1,3]=>011110=>[1,4,1]=>[1,4,1]
[4,7,6,5,2,3,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[4,7,6,5,3,1,2]=>011110=>[1,4,1]=>[1,4,1]
[4,7,6,5,3,2,1]=>011111=>[1,5]=>[5,1]
[5,1,2,3,4,6,7]=>100000=>[1,5]=>[5,1]
[5,1,2,3,4,7,6]=>100001=>[1,4,1]=>[1,4,1]
[5,1,2,3,6,4,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,1,2,3,6,7,4]=>100001=>[1,4,1]=>[1,4,1]
[5,1,2,3,7,4,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,1,2,3,7,6,4]=>100011=>[1,3,2]=>[2,3,1]
[5,1,2,4,3,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,1,2,4,3,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,2,4,6,3,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,1,2,4,6,7,3]=>100001=>[1,4,1]=>[1,4,1]
[5,1,2,4,7,3,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,1,2,4,7,6,3]=>100011=>[1,3,2]=>[2,3,1]
[5,1,2,6,3,4,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,1,2,6,3,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,2,6,4,3,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,2,6,4,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,2,6,7,3,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,1,2,6,7,4,3]=>100011=>[1,3,2]=>[2,3,1]
[5,1,2,7,3,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,1,2,7,3,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,2,7,4,3,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,2,7,4,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,2,7,6,3,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,2,7,6,4,3]=>100111=>[1,2,3]=>[3,2,1]
[5,1,3,2,4,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,1,3,2,4,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,3,2,6,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,3,2,6,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,3,2,7,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,3,2,7,6,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,1,3,4,2,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,1,3,4,2,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,3,4,6,2,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,1,3,4,6,7,2]=>100001=>[1,4,1]=>[1,4,1]
[5,1,3,4,7,2,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,1,3,4,7,6,2]=>100011=>[1,3,2]=>[2,3,1]
[5,1,3,6,2,4,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,1,3,6,2,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,3,6,4,2,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,3,6,4,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,3,6,7,2,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,1,3,6,7,4,2]=>100011=>[1,3,2]=>[2,3,1]
[5,1,3,7,2,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,1,3,7,2,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,3,7,4,2,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,3,7,4,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,3,7,6,2,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,3,7,6,4,2]=>100111=>[1,2,3]=>[3,2,1]
[5,1,4,2,3,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,1,4,2,3,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,4,2,6,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,4,2,6,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,4,2,7,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,4,2,7,6,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,1,4,3,2,6,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,1,4,3,2,7,6]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,1,4,3,6,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,4,3,6,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,4,3,7,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,4,3,7,6,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,1,4,6,2,3,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,1,4,6,2,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,4,6,3,2,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,4,6,3,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,4,6,7,2,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,1,4,6,7,3,2]=>100011=>[1,3,2]=>[2,3,1]
[5,1,4,7,2,3,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,1,4,7,2,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,4,7,3,2,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,4,7,3,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,4,7,6,2,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,4,7,6,3,2]=>100111=>[1,2,3]=>[3,2,1]
[5,1,6,2,3,4,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,1,6,2,3,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,6,2,4,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,6,2,4,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,6,2,7,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,6,2,7,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,1,6,3,2,4,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,1,6,3,2,7,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,1,6,3,4,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,6,3,4,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,6,3,7,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,6,3,7,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,1,6,4,2,3,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,1,6,4,2,7,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,1,6,4,3,2,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,1,6,4,3,7,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,1,6,4,7,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,6,4,7,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,1,6,7,2,3,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,1,6,7,2,4,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,6,7,3,2,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,6,7,3,4,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,1,6,7,4,2,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,1,6,7,4,3,2]=>100111=>[1,2,3]=>[3,2,1]
[5,1,7,2,3,4,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,1,7,2,3,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,7,2,4,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,7,2,4,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,7,2,6,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,7,2,6,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,1,7,3,2,4,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,1,7,3,2,6,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,1,7,3,4,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,7,3,4,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,1,7,3,6,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,7,3,6,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,1,7,4,2,3,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,1,7,4,2,6,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,1,7,4,3,2,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,1,7,4,3,6,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,1,7,4,6,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,1,7,4,6,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,1,7,6,2,3,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,1,7,6,2,4,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,1,7,6,3,2,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,1,7,6,3,4,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,1,7,6,4,2,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,1,7,6,4,3,2]=>101111=>[1,1,4]=>[4,1,1]
[5,2,1,3,4,6,7]=>110000=>[2,4]=>[4,2]
[5,2,1,3,4,7,6]=>110001=>[2,3,1]=>[1,3,2]
[5,2,1,3,6,4,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,2,1,3,6,7,4]=>110001=>[2,3,1]=>[1,3,2]
[5,2,1,3,7,4,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,2,1,3,7,6,4]=>110011=>[2,2,2]=>[2,2,2]
[5,2,1,4,3,6,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,2,1,4,3,7,6]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,2,1,4,6,3,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,2,1,4,6,7,3]=>110001=>[2,3,1]=>[1,3,2]
[5,2,1,4,7,3,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,2,1,4,7,6,3]=>110011=>[2,2,2]=>[2,2,2]
[5,2,1,6,3,4,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,2,1,6,3,7,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,2,1,6,4,3,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,2,1,6,4,7,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,2,1,6,7,3,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,2,1,6,7,4,3]=>110011=>[2,2,2]=>[2,2,2]
[5,2,1,7,3,4,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,2,1,7,3,6,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,2,1,7,4,3,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,2,1,7,4,6,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,2,1,7,6,3,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,2,1,7,6,4,3]=>110111=>[2,1,3]=>[3,1,2]
[5,2,3,1,4,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,2,3,1,4,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,3,1,6,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,3,1,6,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,3,1,7,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,3,1,7,6,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,2,3,4,1,6,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,2,3,4,1,7,6]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,3,4,6,1,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,2,3,4,6,7,1]=>100001=>[1,4,1]=>[1,4,1]
[5,2,3,4,7,1,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,2,3,4,7,6,1]=>100011=>[1,3,2]=>[2,3,1]
[5,2,3,6,1,4,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,2,3,6,1,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,3,6,4,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,2,3,6,4,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,3,6,7,1,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,2,3,6,7,4,1]=>100011=>[1,3,2]=>[2,3,1]
[5,2,3,7,1,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,2,3,7,1,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,3,7,4,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,2,3,7,4,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,3,7,6,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,2,3,7,6,4,1]=>100111=>[1,2,3]=>[3,2,1]
[5,2,4,1,3,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,2,4,1,3,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,4,1,6,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,4,1,6,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,4,1,7,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,4,1,7,6,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,2,4,3,1,6,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,2,4,3,1,7,6]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,2,4,3,6,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,4,3,6,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,4,3,7,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,4,3,7,6,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,2,4,6,1,3,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,2,4,6,1,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,4,6,3,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,2,4,6,3,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,4,6,7,1,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,2,4,6,7,3,1]=>100011=>[1,3,2]=>[2,3,1]
[5,2,4,7,1,3,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,2,4,7,1,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,4,7,3,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,2,4,7,3,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,4,7,6,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,2,4,7,6,3,1]=>100111=>[1,2,3]=>[3,2,1]
[5,2,6,1,3,4,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,2,6,1,3,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,6,1,4,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,6,1,4,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,6,1,7,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,6,1,7,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,2,6,3,1,4,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,2,6,3,1,7,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,2,6,3,4,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,6,3,4,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,6,3,7,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,6,3,7,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,2,6,4,1,3,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,2,6,4,1,7,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,2,6,4,3,1,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,2,6,4,3,7,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,2,6,4,7,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,6,4,7,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,2,6,7,1,3,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,2,6,7,1,4,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,6,7,3,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,2,6,7,3,4,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,2,6,7,4,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,2,6,7,4,3,1]=>100111=>[1,2,3]=>[3,2,1]
[5,2,7,1,3,4,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,2,7,1,3,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,7,1,4,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,7,1,4,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,7,1,6,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,7,1,6,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,2,7,3,1,4,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,2,7,3,1,6,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,2,7,3,4,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,7,3,4,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,2,7,3,6,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,7,3,6,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,2,7,4,1,3,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,2,7,4,1,6,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,2,7,4,3,1,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,2,7,4,3,6,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,2,7,4,6,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,2,7,4,6,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,2,7,6,1,3,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,2,7,6,1,4,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,2,7,6,3,1,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,2,7,6,3,4,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,2,7,6,4,1,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,2,7,6,4,3,1]=>101111=>[1,1,4]=>[4,1,1]
[5,3,1,2,4,6,7]=>110000=>[2,4]=>[4,2]
[5,3,1,2,4,7,6]=>110001=>[2,3,1]=>[1,3,2]
[5,3,1,2,6,4,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,3,1,2,6,7,4]=>110001=>[2,3,1]=>[1,3,2]
[5,3,1,2,7,4,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,3,1,2,7,6,4]=>110011=>[2,2,2]=>[2,2,2]
[5,3,1,4,2,6,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,3,1,4,2,7,6]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,1,4,6,2,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,3,1,4,6,7,2]=>110001=>[2,3,1]=>[1,3,2]
[5,3,1,4,7,2,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,3,1,4,7,6,2]=>110011=>[2,2,2]=>[2,2,2]
[5,3,1,6,2,4,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,3,1,6,2,7,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,1,6,4,2,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,3,1,6,4,7,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,1,6,7,2,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,3,1,6,7,4,2]=>110011=>[2,2,2]=>[2,2,2]
[5,3,1,7,2,4,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,3,1,7,2,6,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,1,7,4,2,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,3,1,7,4,6,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,1,7,6,2,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,3,1,7,6,4,2]=>110111=>[2,1,3]=>[3,1,2]
[5,3,2,1,4,6,7]=>111000=>[3,3]=>[3,3]
[5,3,2,1,4,7,6]=>111001=>[3,2,1]=>[1,2,3]
[5,3,2,1,6,4,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[5,3,2,1,6,7,4]=>111001=>[3,2,1]=>[1,2,3]
[5,3,2,1,7,4,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[5,3,2,1,7,6,4]=>111011=>[3,1,2]=>[2,1,3]
[5,3,2,4,1,6,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,3,2,4,1,7,6]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,2,4,6,1,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,3,2,4,6,7,1]=>110001=>[2,3,1]=>[1,3,2]
[5,3,2,4,7,1,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,3,2,4,7,6,1]=>110011=>[2,2,2]=>[2,2,2]
[5,3,2,6,1,4,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,3,2,6,1,7,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,2,6,4,1,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,3,2,6,4,7,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,2,6,7,1,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,3,2,6,7,4,1]=>110011=>[2,2,2]=>[2,2,2]
[5,3,2,7,1,4,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,3,2,7,1,6,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,2,7,4,1,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,3,2,7,4,6,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,3,2,7,6,1,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,3,2,7,6,4,1]=>110111=>[2,1,3]=>[3,1,2]
[5,3,4,1,2,6,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,3,4,1,2,7,6]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,3,4,1,6,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,4,1,6,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,3,4,1,7,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,4,1,7,6,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,3,4,2,1,6,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,3,4,2,1,7,6]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,3,4,2,6,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,4,2,6,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,3,4,2,7,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,4,2,7,6,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,3,4,6,1,2,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,3,4,6,1,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,3,4,6,2,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,3,4,6,2,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,3,4,6,7,1,2]=>100010=>[1,3,1,1]=>[1,1,3,1]
[5,3,4,6,7,2,1]=>100011=>[1,3,2]=>[2,3,1]
[5,3,4,7,1,2,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,3,4,7,1,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,3,4,7,2,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,3,4,7,2,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,3,4,7,6,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,3,4,7,6,2,1]=>100111=>[1,2,3]=>[3,2,1]
[5,3,6,1,2,4,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,3,6,1,2,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,3,6,1,4,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,6,1,4,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,3,6,1,7,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,6,1,7,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,3,6,2,1,4,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,3,6,2,1,7,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,3,6,2,4,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,6,2,4,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,3,6,2,7,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,6,2,7,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,3,6,4,1,2,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,3,6,4,1,7,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,3,6,4,2,1,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,3,6,4,2,7,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,3,6,4,7,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,6,4,7,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,3,6,7,1,2,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,3,6,7,1,4,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,3,6,7,2,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,3,6,7,2,4,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,3,6,7,4,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,3,6,7,4,2,1]=>100111=>[1,2,3]=>[3,2,1]
[5,3,7,1,2,4,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,3,7,1,2,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,3,7,1,4,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,7,1,4,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,3,7,1,6,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,7,1,6,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,3,7,2,1,4,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,3,7,2,1,6,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,3,7,2,4,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,7,2,4,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,3,7,2,6,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,7,2,6,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,3,7,4,1,2,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,3,7,4,1,6,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,3,7,4,2,1,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,3,7,4,2,6,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,3,7,4,6,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,3,7,4,6,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,3,7,6,1,2,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,3,7,6,1,4,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,3,7,6,2,1,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,3,7,6,2,4,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,3,7,6,4,1,2]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,3,7,6,4,2,1]=>101111=>[1,1,4]=>[4,1,1]
[5,4,1,2,3,6,7]=>110000=>[2,4]=>[4,2]
[5,4,1,2,3,7,6]=>110001=>[2,3,1]=>[1,3,2]
[5,4,1,2,6,3,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,4,1,2,6,7,3]=>110001=>[2,3,1]=>[1,3,2]
[5,4,1,2,7,3,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,4,1,2,7,6,3]=>110011=>[2,2,2]=>[2,2,2]
[5,4,1,3,2,6,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,4,1,3,2,7,6]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,1,3,6,2,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,4,1,3,6,7,2]=>110001=>[2,3,1]=>[1,3,2]
[5,4,1,3,7,2,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,4,1,3,7,6,2]=>110011=>[2,2,2]=>[2,2,2]
[5,4,1,6,2,3,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,4,1,6,2,7,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,1,6,3,2,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,4,1,6,3,7,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,1,6,7,2,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,4,1,6,7,3,2]=>110011=>[2,2,2]=>[2,2,2]
[5,4,1,7,2,3,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,4,1,7,2,6,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,1,7,3,2,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,4,1,7,3,6,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,1,7,6,2,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,4,1,7,6,3,2]=>110111=>[2,1,3]=>[3,1,2]
[5,4,2,1,3,6,7]=>111000=>[3,3]=>[3,3]
[5,4,2,1,3,7,6]=>111001=>[3,2,1]=>[1,2,3]
[5,4,2,1,6,3,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[5,4,2,1,6,7,3]=>111001=>[3,2,1]=>[1,2,3]
[5,4,2,1,7,3,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[5,4,2,1,7,6,3]=>111011=>[3,1,2]=>[2,1,3]
[5,4,2,3,1,6,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,4,2,3,1,7,6]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,2,3,6,1,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,4,2,3,6,7,1]=>110001=>[2,3,1]=>[1,3,2]
[5,4,2,3,7,1,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,4,2,3,7,6,1]=>110011=>[2,2,2]=>[2,2,2]
[5,4,2,6,1,3,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,4,2,6,1,7,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,2,6,3,1,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,4,2,6,3,7,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,2,6,7,1,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,4,2,6,7,3,1]=>110011=>[2,2,2]=>[2,2,2]
[5,4,2,7,1,3,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,4,2,7,1,6,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,2,7,3,1,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,4,2,7,3,6,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,2,7,6,1,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,4,2,7,6,3,1]=>110111=>[2,1,3]=>[3,1,2]
[5,4,3,1,2,6,7]=>111000=>[3,3]=>[3,3]
[5,4,3,1,2,7,6]=>111001=>[3,2,1]=>[1,2,3]
[5,4,3,1,6,2,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[5,4,3,1,6,7,2]=>111001=>[3,2,1]=>[1,2,3]
[5,4,3,1,7,2,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[5,4,3,1,7,6,2]=>111011=>[3,1,2]=>[2,1,3]
[5,4,3,2,1,6,7]=>111100=>[4,2]=>[2,4]
[5,4,3,2,1,7,6]=>111101=>[4,1,1]=>[1,1,4]
[5,4,3,2,6,1,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[5,4,3,2,6,7,1]=>111001=>[3,2,1]=>[1,2,3]
[5,4,3,2,7,1,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[5,4,3,2,7,6,1]=>111011=>[3,1,2]=>[2,1,3]
[5,4,3,6,1,2,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,4,3,6,1,7,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,3,6,2,1,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,4,3,6,2,7,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,3,6,7,1,2]=>110010=>[2,2,1,1]=>[1,1,2,2]
[5,4,3,6,7,2,1]=>110011=>[2,2,2]=>[2,2,2]
[5,4,3,7,1,2,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[5,4,3,7,1,6,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,3,7,2,1,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,4,3,7,2,6,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,4,3,7,6,1,2]=>110110=>[2,1,2,1]=>[1,2,1,2]
[5,4,3,7,6,2,1]=>110111=>[2,1,3]=>[3,1,2]
[5,4,6,1,2,3,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,4,6,1,2,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,4,6,1,3,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,6,1,3,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,4,6,1,7,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,6,1,7,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,4,6,2,1,3,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,4,6,2,1,7,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,4,6,2,3,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,6,2,3,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,4,6,2,7,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,6,2,7,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,4,6,3,1,2,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,4,6,3,1,7,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,4,6,3,2,1,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,4,6,3,2,7,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,4,6,3,7,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,6,3,7,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,4,6,7,1,2,3]=>100100=>[1,2,1,2]=>[2,1,2,1]
[5,4,6,7,1,3,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,4,6,7,2,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,4,6,7,2,3,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,4,6,7,3,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[5,4,6,7,3,2,1]=>100111=>[1,2,3]=>[3,2,1]
[5,4,7,1,2,3,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[5,4,7,1,2,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,4,7,1,3,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,7,1,3,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,4,7,1,6,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,7,1,6,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,4,7,2,1,3,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,4,7,2,1,6,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,4,7,2,3,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,7,2,3,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,4,7,2,6,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,7,2,6,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,4,7,3,1,2,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,4,7,3,1,6,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,4,7,3,2,1,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,4,7,3,2,6,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,4,7,3,6,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,4,7,3,6,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,4,7,6,1,2,3]=>101100=>[1,1,2,2]=>[2,2,1,1]
[5,4,7,6,1,3,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,4,7,6,2,1,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,4,7,6,2,3,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,4,7,6,3,1,2]=>101110=>[1,1,3,1]=>[1,3,1,1]
[5,4,7,6,3,2,1]=>101111=>[1,1,4]=>[4,1,1]
[5,6,1,2,3,4,7]=>010000=>[1,1,4]=>[4,1,1]
[5,6,1,2,3,7,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[5,6,1,2,4,3,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,1,2,4,7,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[5,6,1,2,7,3,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,1,2,7,4,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,6,1,3,2,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,6,1,3,2,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,1,3,4,2,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,1,3,4,7,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[5,6,1,3,7,2,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,1,3,7,4,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,6,1,4,2,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,6,1,4,2,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,1,4,3,2,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,1,4,3,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,1,4,7,2,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,1,4,7,3,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,6,1,7,2,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,6,1,7,2,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,1,7,3,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,1,7,3,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,1,7,4,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,1,7,4,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[5,6,2,1,3,4,7]=>011000=>[1,2,3]=>[3,2,1]
[5,6,2,1,3,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,6,2,1,4,3,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,2,1,4,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,6,2,1,7,3,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,2,1,7,4,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,6,2,3,1,4,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,6,2,3,1,7,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,2,3,4,1,7]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,2,3,4,7,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[5,6,2,3,7,1,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,2,3,7,4,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,6,2,4,1,3,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,6,2,4,1,7,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,2,4,3,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,2,4,3,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,2,4,7,1,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,2,4,7,3,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,6,2,7,1,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,6,2,7,1,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,2,7,3,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,2,7,3,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,2,7,4,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,2,7,4,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[5,6,3,1,2,4,7]=>011000=>[1,2,3]=>[3,2,1]
[5,6,3,1,2,7,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,6,3,1,4,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,3,1,4,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,6,3,1,7,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,3,1,7,4,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,6,3,2,1,4,7]=>011100=>[1,3,2]=>[2,3,1]
[5,6,3,2,1,7,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,6,3,2,4,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,3,2,4,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,6,3,2,7,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,3,2,7,4,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,6,3,4,1,2,7]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,6,3,4,1,7,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,3,4,2,1,7]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,3,4,2,7,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,3,4,7,1,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,6,3,4,7,2,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,6,3,7,1,2,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,6,3,7,1,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,3,7,2,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,3,7,2,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,3,7,4,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,3,7,4,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[5,6,4,1,2,3,7]=>011000=>[1,2,3]=>[3,2,1]
[5,6,4,1,2,7,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,6,4,1,3,2,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,4,1,3,7,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,6,4,1,7,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,4,1,7,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,6,4,2,1,3,7]=>011100=>[1,3,2]=>[2,3,1]
[5,6,4,2,1,7,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,6,4,2,3,1,7]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,4,2,3,7,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,6,4,2,7,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,4,2,7,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,6,4,3,1,2,7]=>011100=>[1,3,2]=>[2,3,1]
[5,6,4,3,1,7,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,6,4,3,2,1,7]=>011110=>[1,4,1]=>[1,4,1]
[5,6,4,3,2,7,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,6,4,3,7,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,6,4,3,7,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,6,4,7,1,2,3]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,6,4,7,1,3,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,4,7,2,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,4,7,2,3,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,6,4,7,3,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,6,4,7,3,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[5,6,7,1,2,3,4]=>001000=>[2,1,3]=>[3,1,2]
[5,6,7,1,2,4,3]=>001001=>[2,1,2,1]=>[1,2,1,2]
[5,6,7,1,3,2,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,6,7,1,3,4,2]=>001001=>[2,1,2,1]=>[1,2,1,2]
[5,6,7,1,4,2,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,6,7,1,4,3,2]=>001011=>[2,1,1,2]=>[2,1,1,2]
[5,6,7,2,1,3,4]=>001100=>[2,2,2]=>[2,2,2]
[5,6,7,2,1,4,3]=>001101=>[2,2,1,1]=>[1,1,2,2]
[5,6,7,2,3,1,4]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,6,7,2,3,4,1]=>001001=>[2,1,2,1]=>[1,2,1,2]
[5,6,7,2,4,1,3]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,6,7,2,4,3,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[5,6,7,3,1,2,4]=>001100=>[2,2,2]=>[2,2,2]
[5,6,7,3,1,4,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[5,6,7,3,2,1,4]=>001110=>[2,3,1]=>[1,3,2]
[5,6,7,3,2,4,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[5,6,7,3,4,1,2]=>001010=>[2,1,1,1,1]=>[1,1,1,1,2]
[5,6,7,3,4,2,1]=>001011=>[2,1,1,2]=>[2,1,1,2]
[5,6,7,4,1,2,3]=>001100=>[2,2,2]=>[2,2,2]
[5,6,7,4,1,3,2]=>001101=>[2,2,1,1]=>[1,1,2,2]
[5,6,7,4,2,1,3]=>001110=>[2,3,1]=>[1,3,2]
[5,6,7,4,2,3,1]=>001101=>[2,2,1,1]=>[1,1,2,2]
[5,6,7,4,3,1,2]=>001110=>[2,3,1]=>[1,3,2]
[5,6,7,4,3,2,1]=>001111=>[2,4]=>[4,2]
[5,7,1,2,3,4,6]=>010000=>[1,1,4]=>[4,1,1]
[5,7,1,2,3,6,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[5,7,1,2,4,3,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,7,1,2,4,6,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[5,7,1,2,6,3,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,7,1,2,6,4,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,7,1,3,2,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,7,1,3,2,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,1,3,4,2,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,7,1,3,4,6,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[5,7,1,3,6,2,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,7,1,3,6,4,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,7,1,4,2,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,7,1,4,2,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,1,4,3,2,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,1,4,3,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,1,4,6,2,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,7,1,4,6,3,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,7,1,6,2,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,7,1,6,2,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,1,6,3,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,1,6,3,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,1,6,4,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,1,6,4,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[5,7,2,1,3,4,6]=>011000=>[1,2,3]=>[3,2,1]
[5,7,2,1,3,6,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,2,1,4,3,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,2,1,4,6,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,2,1,6,3,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,2,1,6,4,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,7,2,3,1,4,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,7,2,3,1,6,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,2,3,4,1,6]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,7,2,3,4,6,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[5,7,2,3,6,1,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,7,2,3,6,4,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,7,2,4,1,3,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,7,2,4,1,6,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,2,4,3,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,2,4,3,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,2,4,6,1,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,7,2,4,6,3,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,7,2,6,1,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,7,2,6,1,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,2,6,3,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,2,6,3,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,2,6,4,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,2,6,4,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[5,7,3,1,2,4,6]=>011000=>[1,2,3]=>[3,2,1]
[5,7,3,1,2,6,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,3,1,4,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,3,1,4,6,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,3,1,6,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,3,1,6,4,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,7,3,2,1,4,6]=>011100=>[1,3,2]=>[2,3,1]
[5,7,3,2,1,6,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,7,3,2,4,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,3,2,4,6,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,3,2,6,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,3,2,6,4,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,7,3,4,1,2,6]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,7,3,4,1,6,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,3,4,2,1,6]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,3,4,2,6,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,3,4,6,1,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[5,7,3,4,6,2,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[5,7,3,6,1,2,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,7,3,6,1,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,3,6,2,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,3,6,2,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,3,6,4,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,3,6,4,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[5,7,4,1,2,3,6]=>011000=>[1,2,3]=>[3,2,1]
[5,7,4,1,2,6,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,4,1,3,2,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,4,1,3,6,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,4,1,6,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,4,1,6,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,7,4,2,1,3,6]=>011100=>[1,3,2]=>[2,3,1]
[5,7,4,2,1,6,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,7,4,2,3,1,6]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,4,2,3,6,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,4,2,6,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,4,2,6,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,7,4,3,1,2,6]=>011100=>[1,3,2]=>[2,3,1]
[5,7,4,3,1,6,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,7,4,3,2,1,6]=>011110=>[1,4,1]=>[1,4,1]
[5,7,4,3,2,6,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,7,4,3,6,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,4,3,6,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,7,4,6,1,2,3]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[5,7,4,6,1,3,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,4,6,2,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,4,6,2,3,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[5,7,4,6,3,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[5,7,4,6,3,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[5,7,6,1,2,3,4]=>011000=>[1,2,3]=>[3,2,1]
[5,7,6,1,2,4,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,6,1,3,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,6,1,3,4,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,6,1,4,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,6,1,4,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,7,6,2,1,3,4]=>011100=>[1,3,2]=>[2,3,1]
[5,7,6,2,1,4,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,7,6,2,3,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,6,2,3,4,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[5,7,6,2,4,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,6,2,4,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,7,6,3,1,2,4]=>011100=>[1,3,2]=>[2,3,1]
[5,7,6,3,1,4,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,7,6,3,2,1,4]=>011110=>[1,4,1]=>[1,4,1]
[5,7,6,3,2,4,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,7,6,3,4,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[5,7,6,3,4,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[5,7,6,4,1,2,3]=>011100=>[1,3,2]=>[2,3,1]
[5,7,6,4,1,3,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,7,6,4,2,1,3]=>011110=>[1,4,1]=>[1,4,1]
[5,7,6,4,2,3,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[5,7,6,4,3,1,2]=>011110=>[1,4,1]=>[1,4,1]
[5,7,6,4,3,2,1]=>011111=>[1,5]=>[5,1]
[6,1,2,3,4,5,7]=>100000=>[1,5]=>[5,1]
[6,1,2,3,4,7,5]=>100001=>[1,4,1]=>[1,4,1]
[6,1,2,3,5,4,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,1,2,3,5,7,4]=>100001=>[1,4,1]=>[1,4,1]
[6,1,2,3,7,4,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,1,2,3,7,5,4]=>100011=>[1,3,2]=>[2,3,1]
[6,1,2,4,3,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,1,2,4,3,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,2,4,5,3,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,1,2,4,5,7,3]=>100001=>[1,4,1]=>[1,4,1]
[6,1,2,4,7,3,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,1,2,4,7,5,3]=>100011=>[1,3,2]=>[2,3,1]
[6,1,2,5,3,4,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,1,2,5,3,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,2,5,4,3,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,2,5,4,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,2,5,7,3,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,1,2,5,7,4,3]=>100011=>[1,3,2]=>[2,3,1]
[6,1,2,7,3,4,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,1,2,7,3,5,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,2,7,4,3,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,2,7,4,5,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,2,7,5,3,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,2,7,5,4,3]=>100111=>[1,2,3]=>[3,2,1]
[6,1,3,2,4,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,1,3,2,4,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,3,2,5,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,3,2,5,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,3,2,7,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,3,2,7,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,1,3,4,2,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,1,3,4,2,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,3,4,5,2,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,1,3,4,5,7,2]=>100001=>[1,4,1]=>[1,4,1]
[6,1,3,4,7,2,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,1,3,4,7,5,2]=>100011=>[1,3,2]=>[2,3,1]
[6,1,3,5,2,4,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,1,3,5,2,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,3,5,4,2,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,3,5,4,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,3,5,7,2,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,1,3,5,7,4,2]=>100011=>[1,3,2]=>[2,3,1]
[6,1,3,7,2,4,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,1,3,7,2,5,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,3,7,4,2,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,3,7,4,5,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,3,7,5,2,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,3,7,5,4,2]=>100111=>[1,2,3]=>[3,2,1]
[6,1,4,2,3,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,1,4,2,3,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,4,2,5,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,4,2,5,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,4,2,7,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,4,2,7,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,1,4,3,2,5,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,1,4,3,2,7,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,1,4,3,5,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,4,3,5,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,4,3,7,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,4,3,7,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,1,4,5,2,3,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,1,4,5,2,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,4,5,3,2,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,4,5,3,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,4,5,7,2,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,1,4,5,7,3,2]=>100011=>[1,3,2]=>[2,3,1]
[6,1,4,7,2,3,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,1,4,7,2,5,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,4,7,3,2,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,4,7,3,5,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,4,7,5,2,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,4,7,5,3,2]=>100111=>[1,2,3]=>[3,2,1]
[6,1,5,2,3,4,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,1,5,2,3,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,5,2,4,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,5,2,4,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,5,2,7,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,5,2,7,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,1,5,3,2,4,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,1,5,3,2,7,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,1,5,3,4,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,5,3,4,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,5,3,7,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,5,3,7,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,1,5,4,2,3,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,1,5,4,2,7,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,1,5,4,3,2,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,1,5,4,3,7,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,1,5,4,7,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,5,4,7,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,1,5,7,2,3,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,1,5,7,2,4,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,5,7,3,2,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,5,7,3,4,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,1,5,7,4,2,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,1,5,7,4,3,2]=>100111=>[1,2,3]=>[3,2,1]
[6,1,7,2,3,4,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,1,7,2,3,5,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,7,2,4,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,7,2,4,5,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,7,2,5,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,7,2,5,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,1,7,3,2,4,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,1,7,3,2,5,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,1,7,3,4,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,7,3,4,5,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,1,7,3,5,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,7,3,5,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,1,7,4,2,3,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,1,7,4,2,5,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,1,7,4,3,2,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,1,7,4,3,5,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,1,7,4,5,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,1,7,4,5,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,1,7,5,2,3,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,1,7,5,2,4,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,1,7,5,3,2,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,1,7,5,3,4,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,1,7,5,4,2,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,1,7,5,4,3,2]=>101111=>[1,1,4]=>[4,1,1]
[6,2,1,3,4,5,7]=>110000=>[2,4]=>[4,2]
[6,2,1,3,4,7,5]=>110001=>[2,3,1]=>[1,3,2]
[6,2,1,3,5,4,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,2,1,3,5,7,4]=>110001=>[2,3,1]=>[1,3,2]
[6,2,1,3,7,4,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,2,1,3,7,5,4]=>110011=>[2,2,2]=>[2,2,2]
[6,2,1,4,3,5,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,2,1,4,3,7,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,2,1,4,5,3,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,2,1,4,5,7,3]=>110001=>[2,3,1]=>[1,3,2]
[6,2,1,4,7,3,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,2,1,4,7,5,3]=>110011=>[2,2,2]=>[2,2,2]
[6,2,1,5,3,4,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,2,1,5,3,7,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,2,1,5,4,3,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,2,1,5,4,7,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,2,1,5,7,3,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,2,1,5,7,4,3]=>110011=>[2,2,2]=>[2,2,2]
[6,2,1,7,3,4,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,2,1,7,3,5,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,2,1,7,4,3,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,2,1,7,4,5,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,2,1,7,5,3,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,2,1,7,5,4,3]=>110111=>[2,1,3]=>[3,1,2]
[6,2,3,1,4,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,2,3,1,4,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,3,1,5,4,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,3,1,5,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,3,1,7,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,3,1,7,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,2,3,4,1,5,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,2,3,4,1,7,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,3,4,5,1,7]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,2,3,4,5,7,1]=>100001=>[1,4,1]=>[1,4,1]
[6,2,3,4,7,1,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,2,3,4,7,5,1]=>100011=>[1,3,2]=>[2,3,1]
[6,2,3,5,1,4,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,2,3,5,1,7,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,3,5,4,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,2,3,5,4,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,3,5,7,1,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,2,3,5,7,4,1]=>100011=>[1,3,2]=>[2,3,1]
[6,2,3,7,1,4,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,2,3,7,1,5,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,3,7,4,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,2,3,7,4,5,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,3,7,5,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,2,3,7,5,4,1]=>100111=>[1,2,3]=>[3,2,1]
[6,2,4,1,3,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,2,4,1,3,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,4,1,5,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,4,1,5,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,4,1,7,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,4,1,7,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,2,4,3,1,5,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,2,4,3,1,7,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,4,3,5,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,4,3,5,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,4,3,7,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,4,3,7,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,2,4,5,1,3,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,2,4,5,1,7,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,4,5,3,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,2,4,5,3,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,4,5,7,1,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,2,4,5,7,3,1]=>100011=>[1,3,2]=>[2,3,1]
[6,2,4,7,1,3,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,2,4,7,1,5,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,4,7,3,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,2,4,7,3,5,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,4,7,5,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,2,4,7,5,3,1]=>100111=>[1,2,3]=>[3,2,1]
[6,2,5,1,3,4,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,2,5,1,3,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,5,1,4,3,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,5,1,4,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,5,1,7,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,5,1,7,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,2,5,3,1,4,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,2,5,3,1,7,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,5,3,4,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,5,3,4,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,5,3,7,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,5,3,7,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,2,5,4,1,3,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,2,5,4,1,7,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,5,4,3,1,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,2,5,4,3,7,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,5,4,7,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,5,4,7,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,2,5,7,1,3,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,2,5,7,1,4,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,5,7,3,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,2,5,7,3,4,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,2,5,7,4,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,2,5,7,4,3,1]=>100111=>[1,2,3]=>[3,2,1]
[6,2,7,1,3,4,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,2,7,1,3,5,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,7,1,4,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,7,1,4,5,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,7,1,5,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,7,1,5,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,2,7,3,1,4,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,2,7,3,1,5,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,7,3,4,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,7,3,4,5,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,2,7,3,5,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,7,3,5,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,2,7,4,1,3,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,2,7,4,1,5,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,7,4,3,1,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,2,7,4,3,5,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,7,4,5,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,2,7,4,5,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,2,7,5,1,3,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,2,7,5,1,4,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,7,5,3,1,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,2,7,5,3,4,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,2,7,5,4,1,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,2,7,5,4,3,1]=>101111=>[1,1,4]=>[4,1,1]
[6,3,1,2,4,5,7]=>110000=>[2,4]=>[4,2]
[6,3,1,2,4,7,5]=>110001=>[2,3,1]=>[1,3,2]
[6,3,1,2,5,4,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,3,1,2,5,7,4]=>110001=>[2,3,1]=>[1,3,2]
[6,3,1,2,7,4,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,3,1,2,7,5,4]=>110011=>[2,2,2]=>[2,2,2]
[6,3,1,4,2,5,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,3,1,4,2,7,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,1,4,5,2,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,3,1,4,5,7,2]=>110001=>[2,3,1]=>[1,3,2]
[6,3,1,4,7,2,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,3,1,4,7,5,2]=>110011=>[2,2,2]=>[2,2,2]
[6,3,1,5,2,4,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,3,1,5,2,7,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,1,5,4,2,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,3,1,5,4,7,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,1,5,7,2,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,3,1,5,7,4,2]=>110011=>[2,2,2]=>[2,2,2]
[6,3,1,7,2,4,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,3,1,7,2,5,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,1,7,4,2,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,3,1,7,4,5,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,1,7,5,2,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,3,1,7,5,4,2]=>110111=>[2,1,3]=>[3,1,2]
[6,3,2,1,4,5,7]=>111000=>[3,3]=>[3,3]
[6,3,2,1,4,7,5]=>111001=>[3,2,1]=>[1,2,3]
[6,3,2,1,5,4,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,3,2,1,5,7,4]=>111001=>[3,2,1]=>[1,2,3]
[6,3,2,1,7,4,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,3,2,1,7,5,4]=>111011=>[3,1,2]=>[2,1,3]
[6,3,2,4,1,5,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,3,2,4,1,7,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,2,4,5,1,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,3,2,4,5,7,1]=>110001=>[2,3,1]=>[1,3,2]
[6,3,2,4,7,1,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,3,2,4,7,5,1]=>110011=>[2,2,2]=>[2,2,2]
[6,3,2,5,1,4,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,3,2,5,1,7,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,2,5,4,1,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,3,2,5,4,7,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,2,5,7,1,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,3,2,5,7,4,1]=>110011=>[2,2,2]=>[2,2,2]
[6,3,2,7,1,4,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,3,2,7,1,5,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,2,7,4,1,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,3,2,7,4,5,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,3,2,7,5,1,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,3,2,7,5,4,1]=>110111=>[2,1,3]=>[3,1,2]
[6,3,4,1,2,5,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,3,4,1,2,7,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,3,4,1,5,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,4,1,5,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,3,4,1,7,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,4,1,7,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,3,4,2,1,5,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,3,4,2,1,7,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,3,4,2,5,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,4,2,5,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,3,4,2,7,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,4,2,7,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,3,4,5,1,2,7]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,3,4,5,1,7,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,3,4,5,2,1,7]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,3,4,5,2,7,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,3,4,5,7,1,2]=>100010=>[1,3,1,1]=>[1,1,3,1]
[6,3,4,5,7,2,1]=>100011=>[1,3,2]=>[2,3,1]
[6,3,4,7,1,2,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,3,4,7,1,5,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,3,4,7,2,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,3,4,7,2,5,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,3,4,7,5,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,3,4,7,5,2,1]=>100111=>[1,2,3]=>[3,2,1]
[6,3,5,1,2,4,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,3,5,1,2,7,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,3,5,1,4,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,5,1,4,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,3,5,1,7,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,5,1,7,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,3,5,2,1,4,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,3,5,2,1,7,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,3,5,2,4,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,5,2,4,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,3,5,2,7,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,5,2,7,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,3,5,4,1,2,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,3,5,4,1,7,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,3,5,4,2,1,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,3,5,4,2,7,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,3,5,4,7,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,5,4,7,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,3,5,7,1,2,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,3,5,7,1,4,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,3,5,7,2,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,3,5,7,2,4,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,3,5,7,4,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,3,5,7,4,2,1]=>100111=>[1,2,3]=>[3,2,1]
[6,3,7,1,2,4,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,3,7,1,2,5,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,3,7,1,4,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,7,1,4,5,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,3,7,1,5,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,7,1,5,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,3,7,2,1,4,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,3,7,2,1,5,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,3,7,2,4,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,7,2,4,5,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,3,7,2,5,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,7,2,5,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,3,7,4,1,2,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,3,7,4,1,5,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,3,7,4,2,1,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,3,7,4,2,5,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,3,7,4,5,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,3,7,4,5,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,3,7,5,1,2,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,3,7,5,1,4,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,3,7,5,2,1,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,3,7,5,2,4,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,3,7,5,4,1,2]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,3,7,5,4,2,1]=>101111=>[1,1,4]=>[4,1,1]
[6,4,1,2,3,5,7]=>110000=>[2,4]=>[4,2]
[6,4,1,2,3,7,5]=>110001=>[2,3,1]=>[1,3,2]
[6,4,1,2,5,3,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,4,1,2,5,7,3]=>110001=>[2,3,1]=>[1,3,2]
[6,4,1,2,7,3,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,4,1,2,7,5,3]=>110011=>[2,2,2]=>[2,2,2]
[6,4,1,3,2,5,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,4,1,3,2,7,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,1,3,5,2,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,4,1,3,5,7,2]=>110001=>[2,3,1]=>[1,3,2]
[6,4,1,3,7,2,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,4,1,3,7,5,2]=>110011=>[2,2,2]=>[2,2,2]
[6,4,1,5,2,3,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,4,1,5,2,7,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,1,5,3,2,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,4,1,5,3,7,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,1,5,7,2,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,4,1,5,7,3,2]=>110011=>[2,2,2]=>[2,2,2]
[6,4,1,7,2,3,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,4,1,7,2,5,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,1,7,3,2,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,4,1,7,3,5,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,1,7,5,2,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,4,1,7,5,3,2]=>110111=>[2,1,3]=>[3,1,2]
[6,4,2,1,3,5,7]=>111000=>[3,3]=>[3,3]
[6,4,2,1,3,7,5]=>111001=>[3,2,1]=>[1,2,3]
[6,4,2,1,5,3,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,4,2,1,5,7,3]=>111001=>[3,2,1]=>[1,2,3]
[6,4,2,1,7,3,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,4,2,1,7,5,3]=>111011=>[3,1,2]=>[2,1,3]
[6,4,2,3,1,5,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,4,2,3,1,7,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,2,3,5,1,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,4,2,3,5,7,1]=>110001=>[2,3,1]=>[1,3,2]
[6,4,2,3,7,1,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,4,2,3,7,5,1]=>110011=>[2,2,2]=>[2,2,2]
[6,4,2,5,1,3,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,4,2,5,1,7,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,2,5,3,1,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,4,2,5,3,7,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,2,5,7,1,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,4,2,5,7,3,1]=>110011=>[2,2,2]=>[2,2,2]
[6,4,2,7,1,3,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,4,2,7,1,5,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,2,7,3,1,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,4,2,7,3,5,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,2,7,5,1,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,4,2,7,5,3,1]=>110111=>[2,1,3]=>[3,1,2]
[6,4,3,1,2,5,7]=>111000=>[3,3]=>[3,3]
[6,4,3,1,2,7,5]=>111001=>[3,2,1]=>[1,2,3]
[6,4,3,1,5,2,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,4,3,1,5,7,2]=>111001=>[3,2,1]=>[1,2,3]
[6,4,3,1,7,2,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,4,3,1,7,5,2]=>111011=>[3,1,2]=>[2,1,3]
[6,4,3,2,1,5,7]=>111100=>[4,2]=>[2,4]
[6,4,3,2,1,7,5]=>111101=>[4,1,1]=>[1,1,4]
[6,4,3,2,5,1,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,4,3,2,5,7,1]=>111001=>[3,2,1]=>[1,2,3]
[6,4,3,2,7,1,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,4,3,2,7,5,1]=>111011=>[3,1,2]=>[2,1,3]
[6,4,3,5,1,2,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,4,3,5,1,7,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,3,5,2,1,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,4,3,5,2,7,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,3,5,7,1,2]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,4,3,5,7,2,1]=>110011=>[2,2,2]=>[2,2,2]
[6,4,3,7,1,2,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,4,3,7,1,5,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,3,7,2,1,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,4,3,7,2,5,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,4,3,7,5,1,2]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,4,3,7,5,2,1]=>110111=>[2,1,3]=>[3,1,2]
[6,4,5,1,2,3,7]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,4,5,1,2,7,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,4,5,1,3,2,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,5,1,3,7,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,4,5,1,7,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,5,1,7,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,4,5,2,1,3,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,4,5,2,1,7,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,4,5,2,3,1,7]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,5,2,3,7,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,4,5,2,7,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,5,2,7,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,4,5,3,1,2,7]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,4,5,3,1,7,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,4,5,3,2,1,7]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,4,5,3,2,7,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,4,5,3,7,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,5,3,7,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,4,5,7,1,2,3]=>100100=>[1,2,1,2]=>[2,1,2,1]
[6,4,5,7,1,3,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,4,5,7,2,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,4,5,7,2,3,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,4,5,7,3,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[6,4,5,7,3,2,1]=>100111=>[1,2,3]=>[3,2,1]
[6,4,7,1,2,3,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,4,7,1,2,5,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,4,7,1,3,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,7,1,3,5,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,4,7,1,5,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,7,1,5,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,4,7,2,1,3,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,4,7,2,1,5,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,4,7,2,3,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,7,2,3,5,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,4,7,2,5,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,7,2,5,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,4,7,3,1,2,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,4,7,3,1,5,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,4,7,3,2,1,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,4,7,3,2,5,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,4,7,3,5,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,4,7,3,5,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,4,7,5,1,2,3]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,4,7,5,1,3,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,4,7,5,2,1,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,4,7,5,2,3,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,4,7,5,3,1,2]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,4,7,5,3,2,1]=>101111=>[1,1,4]=>[4,1,1]
[6,5,1,2,3,4,7]=>110000=>[2,4]=>[4,2]
[6,5,1,2,3,7,4]=>110001=>[2,3,1]=>[1,3,2]
[6,5,1,2,4,3,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,5,1,2,4,7,3]=>110001=>[2,3,1]=>[1,3,2]
[6,5,1,2,7,3,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,5,1,2,7,4,3]=>110011=>[2,2,2]=>[2,2,2]
[6,5,1,3,2,4,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,5,1,3,2,7,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,1,3,4,2,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,5,1,3,4,7,2]=>110001=>[2,3,1]=>[1,3,2]
[6,5,1,3,7,2,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,5,1,3,7,4,2]=>110011=>[2,2,2]=>[2,2,2]
[6,5,1,4,2,3,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,5,1,4,2,7,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,1,4,3,2,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,1,4,3,7,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,1,4,7,2,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,5,1,4,7,3,2]=>110011=>[2,2,2]=>[2,2,2]
[6,5,1,7,2,3,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,5,1,7,2,4,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,1,7,3,2,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,1,7,3,4,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,1,7,4,2,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,1,7,4,3,2]=>110111=>[2,1,3]=>[3,1,2]
[6,5,2,1,3,4,7]=>111000=>[3,3]=>[3,3]
[6,5,2,1,3,7,4]=>111001=>[3,2,1]=>[1,2,3]
[6,5,2,1,4,3,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,2,1,4,7,3]=>111001=>[3,2,1]=>[1,2,3]
[6,5,2,1,7,3,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,2,1,7,4,3]=>111011=>[3,1,2]=>[2,1,3]
[6,5,2,3,1,4,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,5,2,3,1,7,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,2,3,4,1,7]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,5,2,3,4,7,1]=>110001=>[2,3,1]=>[1,3,2]
[6,5,2,3,7,1,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,5,2,3,7,4,1]=>110011=>[2,2,2]=>[2,2,2]
[6,5,2,4,1,3,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,5,2,4,1,7,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,2,4,3,1,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,2,4,3,7,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,2,4,7,1,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,5,2,4,7,3,1]=>110011=>[2,2,2]=>[2,2,2]
[6,5,2,7,1,3,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,5,2,7,1,4,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,2,7,3,1,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,2,7,3,4,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,2,7,4,1,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,2,7,4,3,1]=>110111=>[2,1,3]=>[3,1,2]
[6,5,3,1,2,4,7]=>111000=>[3,3]=>[3,3]
[6,5,3,1,2,7,4]=>111001=>[3,2,1]=>[1,2,3]
[6,5,3,1,4,2,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,3,1,4,7,2]=>111001=>[3,2,1]=>[1,2,3]
[6,5,3,1,7,2,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,3,1,7,4,2]=>111011=>[3,1,2]=>[2,1,3]
[6,5,3,2,1,4,7]=>111100=>[4,2]=>[2,4]
[6,5,3,2,1,7,4]=>111101=>[4,1,1]=>[1,1,4]
[6,5,3,2,4,1,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,3,2,4,7,1]=>111001=>[3,2,1]=>[1,2,3]
[6,5,3,2,7,1,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,3,2,7,4,1]=>111011=>[3,1,2]=>[2,1,3]
[6,5,3,4,1,2,7]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,5,3,4,1,7,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,3,4,2,1,7]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,3,4,2,7,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,3,4,7,1,2]=>110010=>[2,2,1,1]=>[1,1,2,2]
[6,5,3,4,7,2,1]=>110011=>[2,2,2]=>[2,2,2]
[6,5,3,7,1,2,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,5,3,7,1,4,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,3,7,2,1,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,3,7,2,4,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,3,7,4,1,2]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,3,7,4,2,1]=>110111=>[2,1,3]=>[3,1,2]
[6,5,4,1,2,3,7]=>111000=>[3,3]=>[3,3]
[6,5,4,1,2,7,3]=>111001=>[3,2,1]=>[1,2,3]
[6,5,4,1,3,2,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,4,1,3,7,2]=>111001=>[3,2,1]=>[1,2,3]
[6,5,4,1,7,2,3]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,4,1,7,3,2]=>111011=>[3,1,2]=>[2,1,3]
[6,5,4,2,1,3,7]=>111100=>[4,2]=>[2,4]
[6,5,4,2,1,7,3]=>111101=>[4,1,1]=>[1,1,4]
[6,5,4,2,3,1,7]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,4,2,3,7,1]=>111001=>[3,2,1]=>[1,2,3]
[6,5,4,2,7,1,3]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,4,2,7,3,1]=>111011=>[3,1,2]=>[2,1,3]
[6,5,4,3,1,2,7]=>111100=>[4,2]=>[2,4]
[6,5,4,3,1,7,2]=>111101=>[4,1,1]=>[1,1,4]
[6,5,4,3,2,1,7]=>111110=>[5,1]=>[1,5]
[6,5,4,3,2,7,1]=>111101=>[4,1,1]=>[1,1,4]
[6,5,4,3,7,1,2]=>111010=>[3,1,1,1]=>[1,1,1,3]
[6,5,4,3,7,2,1]=>111011=>[3,1,2]=>[2,1,3]
[6,5,4,7,1,2,3]=>110100=>[2,1,1,2]=>[2,1,1,2]
[6,5,4,7,1,3,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,4,7,2,1,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,4,7,2,3,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[6,5,4,7,3,1,2]=>110110=>[2,1,2,1]=>[1,2,1,2]
[6,5,4,7,3,2,1]=>110111=>[2,1,3]=>[3,1,2]
[6,5,7,1,2,3,4]=>101000=>[1,1,1,3]=>[3,1,1,1]
[6,5,7,1,2,4,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,5,7,1,3,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,5,7,1,3,4,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,5,7,1,4,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,5,7,1,4,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,5,7,2,1,3,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,5,7,2,1,4,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,5,7,2,3,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,5,7,2,3,4,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,5,7,2,4,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,5,7,2,4,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,5,7,3,1,2,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,5,7,3,1,4,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,5,7,3,2,1,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,5,7,3,2,4,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,5,7,3,4,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,5,7,3,4,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,5,7,4,1,2,3]=>101100=>[1,1,2,2]=>[2,2,1,1]
[6,5,7,4,1,3,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,5,7,4,2,1,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,5,7,4,2,3,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,5,7,4,3,1,2]=>101110=>[1,1,3,1]=>[1,3,1,1]
[6,5,7,4,3,2,1]=>101111=>[1,1,4]=>[4,1,1]
[6,7,1,2,3,4,5]=>010000=>[1,1,4]=>[4,1,1]
[6,7,1,2,3,5,4]=>010001=>[1,1,3,1]=>[1,3,1,1]
[6,7,1,2,4,3,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,7,1,2,4,5,3]=>010001=>[1,1,3,1]=>[1,3,1,1]
[6,7,1,2,5,3,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,7,1,2,5,4,3]=>010011=>[1,1,2,2]=>[2,2,1,1]
[6,7,1,3,2,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,7,1,3,2,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,1,3,4,2,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,7,1,3,4,5,2]=>010001=>[1,1,3,1]=>[1,3,1,1]
[6,7,1,3,5,2,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,7,1,3,5,4,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[6,7,1,4,2,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,7,1,4,2,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,1,4,3,2,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,1,4,3,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,1,4,5,2,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,7,1,4,5,3,2]=>010011=>[1,1,2,2]=>[2,2,1,1]
[6,7,1,5,2,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,7,1,5,2,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,1,5,3,2,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,1,5,3,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,1,5,4,2,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,1,5,4,3,2]=>010111=>[1,1,1,3]=>[3,1,1,1]
[6,7,2,1,3,4,5]=>011000=>[1,2,3]=>[3,2,1]
[6,7,2,1,3,5,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,2,1,4,3,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,2,1,4,5,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,2,1,5,3,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,2,1,5,4,3]=>011011=>[1,2,1,2]=>[2,1,2,1]
[6,7,2,3,1,4,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,7,2,3,1,5,4]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,2,3,4,1,5]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,7,2,3,4,5,1]=>010001=>[1,1,3,1]=>[1,3,1,1]
[6,7,2,3,5,1,4]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,7,2,3,5,4,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[6,7,2,4,1,3,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,7,2,4,1,5,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,2,4,3,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,2,4,3,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,2,4,5,1,3]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,7,2,4,5,3,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[6,7,2,5,1,3,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,7,2,5,1,4,3]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,2,5,3,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,2,5,3,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,2,5,4,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,2,5,4,3,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[6,7,3,1,2,4,5]=>011000=>[1,2,3]=>[3,2,1]
[6,7,3,1,2,5,4]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,3,1,4,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,3,1,4,5,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,3,1,5,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,3,1,5,4,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[6,7,3,2,1,4,5]=>011100=>[1,3,2]=>[2,3,1]
[6,7,3,2,1,5,4]=>011101=>[1,3,1,1]=>[1,1,3,1]
[6,7,3,2,4,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,3,2,4,5,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,3,2,5,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,3,2,5,4,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[6,7,3,4,1,2,5]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,7,3,4,1,5,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,3,4,2,1,5]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,3,4,2,5,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,3,4,5,1,2]=>010010=>[1,1,2,1,1]=>[1,1,2,1,1]
[6,7,3,4,5,2,1]=>010011=>[1,1,2,2]=>[2,2,1,1]
[6,7,3,5,1,2,4]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,7,3,5,1,4,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,3,5,2,1,4]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,3,5,2,4,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,3,5,4,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,3,5,4,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[6,7,4,1,2,3,5]=>011000=>[1,2,3]=>[3,2,1]
[6,7,4,1,2,5,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,4,1,3,2,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,4,1,3,5,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,4,1,5,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,4,1,5,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[6,7,4,2,1,3,5]=>011100=>[1,3,2]=>[2,3,1]
[6,7,4,2,1,5,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[6,7,4,2,3,1,5]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,4,2,3,5,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,4,2,5,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,4,2,5,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[6,7,4,3,1,2,5]=>011100=>[1,3,2]=>[2,3,1]
[6,7,4,3,1,5,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[6,7,4,3,2,1,5]=>011110=>[1,4,1]=>[1,4,1]
[6,7,4,3,2,5,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[6,7,4,3,5,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,4,3,5,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[6,7,4,5,1,2,3]=>010100=>[1,1,1,1,2]=>[2,1,1,1,1]
[6,7,4,5,1,3,2]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,4,5,2,1,3]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,4,5,2,3,1]=>010101=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[6,7,4,5,3,1,2]=>010110=>[1,1,1,2,1]=>[1,2,1,1,1]
[6,7,4,5,3,2,1]=>010111=>[1,1,1,3]=>[3,1,1,1]
[6,7,5,1,2,3,4]=>011000=>[1,2,3]=>[3,2,1]
[6,7,5,1,2,4,3]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,5,1,3,2,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,5,1,3,4,2]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,5,1,4,2,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,5,1,4,3,2]=>011011=>[1,2,1,2]=>[2,1,2,1]
[6,7,5,2,1,3,4]=>011100=>[1,3,2]=>[2,3,1]
[6,7,5,2,1,4,3]=>011101=>[1,3,1,1]=>[1,1,3,1]
[6,7,5,2,3,1,4]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,5,2,3,4,1]=>011001=>[1,2,2,1]=>[1,2,2,1]
[6,7,5,2,4,1,3]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,5,2,4,3,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[6,7,5,3,1,2,4]=>011100=>[1,3,2]=>[2,3,1]
[6,7,5,3,1,4,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[6,7,5,3,2,1,4]=>011110=>[1,4,1]=>[1,4,1]
[6,7,5,3,2,4,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[6,7,5,3,4,1,2]=>011010=>[1,2,1,1,1]=>[1,1,1,2,1]
[6,7,5,3,4,2,1]=>011011=>[1,2,1,2]=>[2,1,2,1]
[6,7,5,4,1,2,3]=>011100=>[1,3,2]=>[2,3,1]
[6,7,5,4,1,3,2]=>011101=>[1,3,1,1]=>[1,1,3,1]
[6,7,5,4,2,1,3]=>011110=>[1,4,1]=>[1,4,1]
[6,7,5,4,2,3,1]=>011101=>[1,3,1,1]=>[1,1,3,1]
[6,7,5,4,3,1,2]=>011110=>[1,4,1]=>[1,4,1]
[6,7,5,4,3,2,1]=>011111=>[1,5]=>[5,1]
[7,1,2,3,4,5,6]=>100000=>[1,5]=>[5,1]
[7,1,2,3,4,6,5]=>100001=>[1,4,1]=>[1,4,1]
[7,1,2,3,5,4,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,1,2,3,5,6,4]=>100001=>[1,4,1]=>[1,4,1]
[7,1,2,3,6,4,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,1,2,3,6,5,4]=>100011=>[1,3,2]=>[2,3,1]
[7,1,2,4,3,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,1,2,4,3,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,2,4,5,3,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,1,2,4,5,6,3]=>100001=>[1,4,1]=>[1,4,1]
[7,1,2,4,6,3,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,1,2,4,6,5,3]=>100011=>[1,3,2]=>[2,3,1]
[7,1,2,5,3,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,1,2,5,3,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,2,5,4,3,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,2,5,4,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,2,5,6,3,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,1,2,5,6,4,3]=>100011=>[1,3,2]=>[2,3,1]
[7,1,2,6,3,4,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,1,2,6,3,5,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,2,6,4,3,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,2,6,4,5,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,2,6,5,3,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,2,6,5,4,3]=>100111=>[1,2,3]=>[3,2,1]
[7,1,3,2,4,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,1,3,2,4,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,3,2,5,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,3,2,5,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,3,2,6,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,3,2,6,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,1,3,4,2,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,1,3,4,2,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,3,4,5,2,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,1,3,4,5,6,2]=>100001=>[1,4,1]=>[1,4,1]
[7,1,3,4,6,2,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,1,3,4,6,5,2]=>100011=>[1,3,2]=>[2,3,1]
[7,1,3,5,2,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,1,3,5,2,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,3,5,4,2,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,3,5,4,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,3,5,6,2,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,1,3,5,6,4,2]=>100011=>[1,3,2]=>[2,3,1]
[7,1,3,6,2,4,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,1,3,6,2,5,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,3,6,4,2,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,3,6,4,5,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,3,6,5,2,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,3,6,5,4,2]=>100111=>[1,2,3]=>[3,2,1]
[7,1,4,2,3,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,1,4,2,3,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,4,2,5,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,4,2,5,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,4,2,6,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,4,2,6,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,1,4,3,2,5,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,1,4,3,2,6,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,1,4,3,5,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,4,3,5,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,4,3,6,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,4,3,6,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,1,4,5,2,3,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,1,4,5,2,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,4,5,3,2,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,4,5,3,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,4,5,6,2,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,1,4,5,6,3,2]=>100011=>[1,3,2]=>[2,3,1]
[7,1,4,6,2,3,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,1,4,6,2,5,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,4,6,3,2,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,4,6,3,5,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,4,6,5,2,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,4,6,5,3,2]=>100111=>[1,2,3]=>[3,2,1]
[7,1,5,2,3,4,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,1,5,2,3,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,5,2,4,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,5,2,4,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,5,2,6,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,5,2,6,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,1,5,3,2,4,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,1,5,3,2,6,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,1,5,3,4,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,5,3,4,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,5,3,6,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,5,3,6,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,1,5,4,2,3,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,1,5,4,2,6,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,1,5,4,3,2,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,1,5,4,3,6,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,1,5,4,6,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,5,4,6,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,1,5,6,2,3,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,1,5,6,2,4,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,5,6,3,2,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,5,6,3,4,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,1,5,6,4,2,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,1,5,6,4,3,2]=>100111=>[1,2,3]=>[3,2,1]
[7,1,6,2,3,4,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,1,6,2,3,5,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,6,2,4,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,6,2,4,5,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,6,2,5,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,6,2,5,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,1,6,3,2,4,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,1,6,3,2,5,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,1,6,3,4,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,6,3,4,5,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,1,6,3,5,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,6,3,5,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,1,6,4,2,3,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,1,6,4,2,5,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,1,6,4,3,2,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,1,6,4,3,5,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,1,6,4,5,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,1,6,4,5,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,1,6,5,2,3,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,1,6,5,2,4,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,1,6,5,3,2,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,1,6,5,3,4,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,1,6,5,4,2,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,1,6,5,4,3,2]=>101111=>[1,1,4]=>[4,1,1]
[7,2,1,3,4,5,6]=>110000=>[2,4]=>[4,2]
[7,2,1,3,4,6,5]=>110001=>[2,3,1]=>[1,3,2]
[7,2,1,3,5,4,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,2,1,3,5,6,4]=>110001=>[2,3,1]=>[1,3,2]
[7,2,1,3,6,4,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,2,1,3,6,5,4]=>110011=>[2,2,2]=>[2,2,2]
[7,2,1,4,3,5,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,2,1,4,3,6,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,2,1,4,5,3,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,2,1,4,5,6,3]=>110001=>[2,3,1]=>[1,3,2]
[7,2,1,4,6,3,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,2,1,4,6,5,3]=>110011=>[2,2,2]=>[2,2,2]
[7,2,1,5,3,4,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,2,1,5,3,6,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,2,1,5,4,3,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,2,1,5,4,6,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,2,1,5,6,3,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,2,1,5,6,4,3]=>110011=>[2,2,2]=>[2,2,2]
[7,2,1,6,3,4,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,2,1,6,3,5,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,2,1,6,4,3,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,2,1,6,4,5,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,2,1,6,5,3,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,2,1,6,5,4,3]=>110111=>[2,1,3]=>[3,1,2]
[7,2,3,1,4,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,2,3,1,4,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,3,1,5,4,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,3,1,5,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,3,1,6,4,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,3,1,6,5,4]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,2,3,4,1,5,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,2,3,4,1,6,5]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,3,4,5,1,6]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,2,3,4,5,6,1]=>100001=>[1,4,1]=>[1,4,1]
[7,2,3,4,6,1,5]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,2,3,4,6,5,1]=>100011=>[1,3,2]=>[2,3,1]
[7,2,3,5,1,4,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,2,3,5,1,6,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,3,5,4,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,2,3,5,4,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,3,5,6,1,4]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,2,3,5,6,4,1]=>100011=>[1,3,2]=>[2,3,1]
[7,2,3,6,1,4,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,2,3,6,1,5,4]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,3,6,4,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,2,3,6,4,5,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,3,6,5,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,2,3,6,5,4,1]=>100111=>[1,2,3]=>[3,2,1]
[7,2,4,1,3,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,2,4,1,3,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,4,1,5,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,4,1,5,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,4,1,6,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,4,1,6,5,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,2,4,3,1,5,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,2,4,3,1,6,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,2,4,3,5,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,4,3,5,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,4,3,6,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,4,3,6,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,2,4,5,1,3,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,2,4,5,1,6,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,4,5,3,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,2,4,5,3,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,4,5,6,1,3]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,2,4,5,6,3,1]=>100011=>[1,3,2]=>[2,3,1]
[7,2,4,6,1,3,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,2,4,6,1,5,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,4,6,3,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,2,4,6,3,5,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,4,6,5,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,2,4,6,5,3,1]=>100111=>[1,2,3]=>[3,2,1]
[7,2,5,1,3,4,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,2,5,1,3,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,5,1,4,3,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,5,1,4,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,5,1,6,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,5,1,6,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,2,5,3,1,4,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,2,5,3,1,6,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,2,5,3,4,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,5,3,4,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,5,3,6,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,5,3,6,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,2,5,4,1,3,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,2,5,4,1,6,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,2,5,4,3,1,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,2,5,4,3,6,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,2,5,4,6,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,5,4,6,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,2,5,6,1,3,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,2,5,6,1,4,3]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,5,6,3,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,2,5,6,3,4,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,2,5,6,4,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,2,5,6,4,3,1]=>100111=>[1,2,3]=>[3,2,1]
[7,2,6,1,3,4,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,2,6,1,3,5,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,6,1,4,3,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,6,1,4,5,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,6,1,5,3,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,6,1,5,4,3]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,2,6,3,1,4,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,2,6,3,1,5,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,2,6,3,4,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,6,3,4,5,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,2,6,3,5,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,6,3,5,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,2,6,4,1,3,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,2,6,4,1,5,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,2,6,4,3,1,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,2,6,4,3,5,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,2,6,4,5,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,2,6,4,5,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,2,6,5,1,3,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,2,6,5,1,4,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,2,6,5,3,1,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,2,6,5,3,4,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,2,6,5,4,1,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,2,6,5,4,3,1]=>101111=>[1,1,4]=>[4,1,1]
[7,3,1,2,4,5,6]=>110000=>[2,4]=>[4,2]
[7,3,1,2,4,6,5]=>110001=>[2,3,1]=>[1,3,2]
[7,3,1,2,5,4,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,3,1,2,5,6,4]=>110001=>[2,3,1]=>[1,3,2]
[7,3,1,2,6,4,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,3,1,2,6,5,4]=>110011=>[2,2,2]=>[2,2,2]
[7,3,1,4,2,5,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,3,1,4,2,6,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,1,4,5,2,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,3,1,4,5,6,2]=>110001=>[2,3,1]=>[1,3,2]
[7,3,1,4,6,2,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,3,1,4,6,5,2]=>110011=>[2,2,2]=>[2,2,2]
[7,3,1,5,2,4,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,3,1,5,2,6,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,1,5,4,2,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,3,1,5,4,6,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,1,5,6,2,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,3,1,5,6,4,2]=>110011=>[2,2,2]=>[2,2,2]
[7,3,1,6,2,4,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,3,1,6,2,5,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,1,6,4,2,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,3,1,6,4,5,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,1,6,5,2,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,3,1,6,5,4,2]=>110111=>[2,1,3]=>[3,1,2]
[7,3,2,1,4,5,6]=>111000=>[3,3]=>[3,3]
[7,3,2,1,4,6,5]=>111001=>[3,2,1]=>[1,2,3]
[7,3,2,1,5,4,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,3,2,1,5,6,4]=>111001=>[3,2,1]=>[1,2,3]
[7,3,2,1,6,4,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,3,2,1,6,5,4]=>111011=>[3,1,2]=>[2,1,3]
[7,3,2,4,1,5,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,3,2,4,1,6,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,2,4,5,1,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,3,2,4,5,6,1]=>110001=>[2,3,1]=>[1,3,2]
[7,3,2,4,6,1,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,3,2,4,6,5,1]=>110011=>[2,2,2]=>[2,2,2]
[7,3,2,5,1,4,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,3,2,5,1,6,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,2,5,4,1,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,3,2,5,4,6,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,2,5,6,1,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,3,2,5,6,4,1]=>110011=>[2,2,2]=>[2,2,2]
[7,3,2,6,1,4,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,3,2,6,1,5,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,2,6,4,1,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,3,2,6,4,5,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,3,2,6,5,1,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,3,2,6,5,4,1]=>110111=>[2,1,3]=>[3,1,2]
[7,3,4,1,2,5,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,3,4,1,2,6,5]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,3,4,1,5,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,4,1,5,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,3,4,1,6,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,4,1,6,5,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,3,4,2,1,5,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,3,4,2,1,6,5]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,3,4,2,5,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,4,2,5,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,3,4,2,6,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,4,2,6,5,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,3,4,5,1,2,6]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,3,4,5,1,6,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,3,4,5,2,1,6]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,3,4,5,2,6,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,3,4,5,6,1,2]=>100010=>[1,3,1,1]=>[1,1,3,1]
[7,3,4,5,6,2,1]=>100011=>[1,3,2]=>[2,3,1]
[7,3,4,6,1,2,5]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,3,4,6,1,5,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,3,4,6,2,1,5]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,3,4,6,2,5,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,3,4,6,5,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,3,4,6,5,2,1]=>100111=>[1,2,3]=>[3,2,1]
[7,3,5,1,2,4,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,3,5,1,2,6,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,3,5,1,4,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,5,1,4,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,3,5,1,6,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,5,1,6,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,3,5,2,1,4,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,3,5,2,1,6,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,3,5,2,4,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,5,2,4,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,3,5,2,6,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,5,2,6,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,3,5,4,1,2,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,3,5,4,1,6,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,3,5,4,2,1,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,3,5,4,2,6,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,3,5,4,6,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,5,4,6,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,3,5,6,1,2,4]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,3,5,6,1,4,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,3,5,6,2,1,4]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,3,5,6,2,4,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,3,5,6,4,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,3,5,6,4,2,1]=>100111=>[1,2,3]=>[3,2,1]
[7,3,6,1,2,4,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,3,6,1,2,5,4]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,3,6,1,4,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,6,1,4,5,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,3,6,1,5,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,6,1,5,4,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,3,6,2,1,4,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,3,6,2,1,5,4]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,3,6,2,4,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,6,2,4,5,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,3,6,2,5,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,6,2,5,4,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,3,6,4,1,2,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,3,6,4,1,5,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,3,6,4,2,1,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,3,6,4,2,5,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,3,6,4,5,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,3,6,4,5,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,3,6,5,1,2,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,3,6,5,1,4,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,3,6,5,2,1,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,3,6,5,2,4,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,3,6,5,4,1,2]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,3,6,5,4,2,1]=>101111=>[1,1,4]=>[4,1,1]
[7,4,1,2,3,5,6]=>110000=>[2,4]=>[4,2]
[7,4,1,2,3,6,5]=>110001=>[2,3,1]=>[1,3,2]
[7,4,1,2,5,3,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,4,1,2,5,6,3]=>110001=>[2,3,1]=>[1,3,2]
[7,4,1,2,6,3,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,4,1,2,6,5,3]=>110011=>[2,2,2]=>[2,2,2]
[7,4,1,3,2,5,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,4,1,3,2,6,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,1,3,5,2,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,4,1,3,5,6,2]=>110001=>[2,3,1]=>[1,3,2]
[7,4,1,3,6,2,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,4,1,3,6,5,2]=>110011=>[2,2,2]=>[2,2,2]
[7,4,1,5,2,3,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,4,1,5,2,6,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,1,5,3,2,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,4,1,5,3,6,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,1,5,6,2,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,4,1,5,6,3,2]=>110011=>[2,2,2]=>[2,2,2]
[7,4,1,6,2,3,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,4,1,6,2,5,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,1,6,3,2,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,4,1,6,3,5,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,1,6,5,2,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,4,1,6,5,3,2]=>110111=>[2,1,3]=>[3,1,2]
[7,4,2,1,3,5,6]=>111000=>[3,3]=>[3,3]
[7,4,2,1,3,6,5]=>111001=>[3,2,1]=>[1,2,3]
[7,4,2,1,5,3,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,4,2,1,5,6,3]=>111001=>[3,2,1]=>[1,2,3]
[7,4,2,1,6,3,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,4,2,1,6,5,3]=>111011=>[3,1,2]=>[2,1,3]
[7,4,2,3,1,5,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,4,2,3,1,6,5]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,2,3,5,1,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,4,2,3,5,6,1]=>110001=>[2,3,1]=>[1,3,2]
[7,4,2,3,6,1,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,4,2,3,6,5,1]=>110011=>[2,2,2]=>[2,2,2]
[7,4,2,5,1,3,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,4,2,5,1,6,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,2,5,3,1,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,4,2,5,3,6,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,2,5,6,1,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,4,2,5,6,3,1]=>110011=>[2,2,2]=>[2,2,2]
[7,4,2,6,1,3,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,4,2,6,1,5,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,2,6,3,1,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,4,2,6,3,5,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,2,6,5,1,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,4,2,6,5,3,1]=>110111=>[2,1,3]=>[3,1,2]
[7,4,3,1,2,5,6]=>111000=>[3,3]=>[3,3]
[7,4,3,1,2,6,5]=>111001=>[3,2,1]=>[1,2,3]
[7,4,3,1,5,2,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,4,3,1,5,6,2]=>111001=>[3,2,1]=>[1,2,3]
[7,4,3,1,6,2,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,4,3,1,6,5,2]=>111011=>[3,1,2]=>[2,1,3]
[7,4,3,2,1,5,6]=>111100=>[4,2]=>[2,4]
[7,4,3,2,1,6,5]=>111101=>[4,1,1]=>[1,1,4]
[7,4,3,2,5,1,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,4,3,2,5,6,1]=>111001=>[3,2,1]=>[1,2,3]
[7,4,3,2,6,1,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,4,3,2,6,5,1]=>111011=>[3,1,2]=>[2,1,3]
[7,4,3,5,1,2,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,4,3,5,1,6,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,3,5,2,1,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,4,3,5,2,6,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,3,5,6,1,2]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,4,3,5,6,2,1]=>110011=>[2,2,2]=>[2,2,2]
[7,4,3,6,1,2,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,4,3,6,1,5,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,3,6,2,1,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,4,3,6,2,5,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,4,3,6,5,1,2]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,4,3,6,5,2,1]=>110111=>[2,1,3]=>[3,1,2]
[7,4,5,1,2,3,6]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,4,5,1,2,6,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,4,5,1,3,2,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,5,1,3,6,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,4,5,1,6,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,5,1,6,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,4,5,2,1,3,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,4,5,2,1,6,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,4,5,2,3,1,6]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,5,2,3,6,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,4,5,2,6,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,5,2,6,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,4,5,3,1,2,6]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,4,5,3,1,6,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,4,5,3,2,1,6]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,4,5,3,2,6,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,4,5,3,6,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,5,3,6,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,4,5,6,1,2,3]=>100100=>[1,2,1,2]=>[2,1,2,1]
[7,4,5,6,1,3,2]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,4,5,6,2,1,3]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,4,5,6,2,3,1]=>100101=>[1,2,1,1,1]=>[1,1,1,2,1]
[7,4,5,6,3,1,2]=>100110=>[1,2,2,1]=>[1,2,2,1]
[7,4,5,6,3,2,1]=>100111=>[1,2,3]=>[3,2,1]
[7,4,6,1,2,3,5]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,4,6,1,2,5,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,4,6,1,3,2,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,6,1,3,5,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,4,6,1,5,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,6,1,5,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,4,6,2,1,3,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,4,6,2,1,5,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,4,6,2,3,1,5]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,6,2,3,5,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,4,6,2,5,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,6,2,5,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,4,6,3,1,2,5]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,4,6,3,1,5,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,4,6,3,2,1,5]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,4,6,3,2,5,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,4,6,3,5,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,4,6,3,5,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,4,6,5,1,2,3]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,4,6,5,1,3,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,4,6,5,2,1,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,4,6,5,2,3,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,4,6,5,3,1,2]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,4,6,5,3,2,1]=>101111=>[1,1,4]=>[4,1,1]
[7,5,1,2,3,4,6]=>110000=>[2,4]=>[4,2]
[7,5,1,2,3,6,4]=>110001=>[2,3,1]=>[1,3,2]
[7,5,1,2,4,3,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,5,1,2,4,6,3]=>110001=>[2,3,1]=>[1,3,2]
[7,5,1,2,6,3,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,5,1,2,6,4,3]=>110011=>[2,2,2]=>[2,2,2]
[7,5,1,3,2,4,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,5,1,3,2,6,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,1,3,4,2,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,5,1,3,4,6,2]=>110001=>[2,3,1]=>[1,3,2]
[7,5,1,3,6,2,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,5,1,3,6,4,2]=>110011=>[2,2,2]=>[2,2,2]
[7,5,1,4,2,3,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,5,1,4,2,6,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,1,4,3,2,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,1,4,3,6,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,1,4,6,2,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,5,1,4,6,3,2]=>110011=>[2,2,2]=>[2,2,2]
[7,5,1,6,2,3,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,5,1,6,2,4,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,1,6,3,2,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,1,6,3,4,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,1,6,4,2,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,1,6,4,3,2]=>110111=>[2,1,3]=>[3,1,2]
[7,5,2,1,3,4,6]=>111000=>[3,3]=>[3,3]
[7,5,2,1,3,6,4]=>111001=>[3,2,1]=>[1,2,3]
[7,5,2,1,4,3,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,2,1,4,6,3]=>111001=>[3,2,1]=>[1,2,3]
[7,5,2,1,6,3,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,2,1,6,4,3]=>111011=>[3,1,2]=>[2,1,3]
[7,5,2,3,1,4,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,5,2,3,1,6,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,2,3,4,1,6]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,5,2,3,4,6,1]=>110001=>[2,3,1]=>[1,3,2]
[7,5,2,3,6,1,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,5,2,3,6,4,1]=>110011=>[2,2,2]=>[2,2,2]
[7,5,2,4,1,3,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,5,2,4,1,6,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,2,4,3,1,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,2,4,3,6,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,2,4,6,1,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,5,2,4,6,3,1]=>110011=>[2,2,2]=>[2,2,2]
[7,5,2,6,1,3,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,5,2,6,1,4,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,2,6,3,1,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,2,6,3,4,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,2,6,4,1,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,2,6,4,3,1]=>110111=>[2,1,3]=>[3,1,2]
[7,5,3,1,2,4,6]=>111000=>[3,3]=>[3,3]
[7,5,3,1,2,6,4]=>111001=>[3,2,1]=>[1,2,3]
[7,5,3,1,4,2,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,3,1,4,6,2]=>111001=>[3,2,1]=>[1,2,3]
[7,5,3,1,6,2,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,3,1,6,4,2]=>111011=>[3,1,2]=>[2,1,3]
[7,5,3,2,1,4,6]=>111100=>[4,2]=>[2,4]
[7,5,3,2,1,6,4]=>111101=>[4,1,1]=>[1,1,4]
[7,5,3,2,4,1,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,3,2,4,6,1]=>111001=>[3,2,1]=>[1,2,3]
[7,5,3,2,6,1,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,3,2,6,4,1]=>111011=>[3,1,2]=>[2,1,3]
[7,5,3,4,1,2,6]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,5,3,4,1,6,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,3,4,2,1,6]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,3,4,2,6,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,3,4,6,1,2]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,5,3,4,6,2,1]=>110011=>[2,2,2]=>[2,2,2]
[7,5,3,6,1,2,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,5,3,6,1,4,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,3,6,2,1,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,3,6,2,4,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,3,6,4,1,2]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,3,6,4,2,1]=>110111=>[2,1,3]=>[3,1,2]
[7,5,4,1,2,3,6]=>111000=>[3,3]=>[3,3]
[7,5,4,1,2,6,3]=>111001=>[3,2,1]=>[1,2,3]
[7,5,4,1,3,2,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,4,1,3,6,2]=>111001=>[3,2,1]=>[1,2,3]
[7,5,4,1,6,2,3]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,4,1,6,3,2]=>111011=>[3,1,2]=>[2,1,3]
[7,5,4,2,1,3,6]=>111100=>[4,2]=>[2,4]
[7,5,4,2,1,6,3]=>111101=>[4,1,1]=>[1,1,4]
[7,5,4,2,3,1,6]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,4,2,3,6,1]=>111001=>[3,2,1]=>[1,2,3]
[7,5,4,2,6,1,3]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,4,2,6,3,1]=>111011=>[3,1,2]=>[2,1,3]
[7,5,4,3,1,2,6]=>111100=>[4,2]=>[2,4]
[7,5,4,3,1,6,2]=>111101=>[4,1,1]=>[1,1,4]
[7,5,4,3,2,1,6]=>111110=>[5,1]=>[1,5]
[7,5,4,3,2,6,1]=>111101=>[4,1,1]=>[1,1,4]
[7,5,4,3,6,1,2]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,5,4,3,6,2,1]=>111011=>[3,1,2]=>[2,1,3]
[7,5,4,6,1,2,3]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,5,4,6,1,3,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,4,6,2,1,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,4,6,2,3,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,5,4,6,3,1,2]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,5,4,6,3,2,1]=>110111=>[2,1,3]=>[3,1,2]
[7,5,6,1,2,3,4]=>101000=>[1,1,1,3]=>[3,1,1,1]
[7,5,6,1,2,4,3]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,5,6,1,3,2,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,5,6,1,3,4,2]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,5,6,1,4,2,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,5,6,1,4,3,2]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,5,6,2,1,3,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,5,6,2,1,4,3]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,5,6,2,3,1,4]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,5,6,2,3,4,1]=>101001=>[1,1,1,2,1]=>[1,2,1,1,1]
[7,5,6,2,4,1,3]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,5,6,2,4,3,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,5,6,3,1,2,4]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,5,6,3,1,4,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,5,6,3,2,1,4]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,5,6,3,2,4,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,5,6,3,4,1,2]=>101010=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[7,5,6,3,4,2,1]=>101011=>[1,1,1,1,2]=>[2,1,1,1,1]
[7,5,6,4,1,2,3]=>101100=>[1,1,2,2]=>[2,2,1,1]
[7,5,6,4,1,3,2]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,5,6,4,2,1,3]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,5,6,4,2,3,1]=>101101=>[1,1,2,1,1]=>[1,1,2,1,1]
[7,5,6,4,3,1,2]=>101110=>[1,1,3,1]=>[1,3,1,1]
[7,5,6,4,3,2,1]=>101111=>[1,1,4]=>[4,1,1]
[7,6,1,2,3,4,5]=>110000=>[2,4]=>[4,2]
[7,6,1,2,3,5,4]=>110001=>[2,3,1]=>[1,3,2]
[7,6,1,2,4,3,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,6,1,2,4,5,3]=>110001=>[2,3,1]=>[1,3,2]
[7,6,1,2,5,3,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,6,1,2,5,4,3]=>110011=>[2,2,2]=>[2,2,2]
[7,6,1,3,2,4,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,6,1,3,2,5,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,1,3,4,2,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,6,1,3,4,5,2]=>110001=>[2,3,1]=>[1,3,2]
[7,6,1,3,5,2,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,6,1,3,5,4,2]=>110011=>[2,2,2]=>[2,2,2]
[7,6,1,4,2,3,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,6,1,4,2,5,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,1,4,3,2,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,1,4,3,5,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,1,4,5,2,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,6,1,4,5,3,2]=>110011=>[2,2,2]=>[2,2,2]
[7,6,1,5,2,3,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,6,1,5,2,4,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,1,5,3,2,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,1,5,3,4,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,1,5,4,2,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,1,5,4,3,2]=>110111=>[2,1,3]=>[3,1,2]
[7,6,2,1,3,4,5]=>111000=>[3,3]=>[3,3]
[7,6,2,1,3,5,4]=>111001=>[3,2,1]=>[1,2,3]
[7,6,2,1,4,3,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,2,1,4,5,3]=>111001=>[3,2,1]=>[1,2,3]
[7,6,2,1,5,3,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,2,1,5,4,3]=>111011=>[3,1,2]=>[2,1,3]
[7,6,2,3,1,4,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,6,2,3,1,5,4]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,2,3,4,1,5]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,6,2,3,4,5,1]=>110001=>[2,3,1]=>[1,3,2]
[7,6,2,3,5,1,4]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,6,2,3,5,4,1]=>110011=>[2,2,2]=>[2,2,2]
[7,6,2,4,1,3,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,6,2,4,1,5,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,2,4,3,1,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,2,4,3,5,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,2,4,5,1,3]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,6,2,4,5,3,1]=>110011=>[2,2,2]=>[2,2,2]
[7,6,2,5,1,3,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,6,2,5,1,4,3]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,2,5,3,1,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,2,5,3,4,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,2,5,4,1,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,2,5,4,3,1]=>110111=>[2,1,3]=>[3,1,2]
[7,6,3,1,2,4,5]=>111000=>[3,3]=>[3,3]
[7,6,3,1,2,5,4]=>111001=>[3,2,1]=>[1,2,3]
[7,6,3,1,4,2,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,3,1,4,5,2]=>111001=>[3,2,1]=>[1,2,3]
[7,6,3,1,5,2,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,3,1,5,4,2]=>111011=>[3,1,2]=>[2,1,3]
[7,6,3,2,1,4,5]=>111100=>[4,2]=>[2,4]
[7,6,3,2,1,5,4]=>111101=>[4,1,1]=>[1,1,4]
[7,6,3,2,4,1,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,3,2,4,5,1]=>111001=>[3,2,1]=>[1,2,3]
[7,6,3,2,5,1,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,3,2,5,4,1]=>111011=>[3,1,2]=>[2,1,3]
[7,6,3,4,1,2,5]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,6,3,4,1,5,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,3,4,2,1,5]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,3,4,2,5,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,3,4,5,1,2]=>110010=>[2,2,1,1]=>[1,1,2,2]
[7,6,3,4,5,2,1]=>110011=>[2,2,2]=>[2,2,2]
[7,6,3,5,1,2,4]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,6,3,5,1,4,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,3,5,2,1,4]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,3,5,2,4,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,3,5,4,1,2]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,3,5,4,2,1]=>110111=>[2,1,3]=>[3,1,2]
[7,6,4,1,2,3,5]=>111000=>[3,3]=>[3,3]
[7,6,4,1,2,5,3]=>111001=>[3,2,1]=>[1,2,3]
[7,6,4,1,3,2,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,4,1,3,5,2]=>111001=>[3,2,1]=>[1,2,3]
[7,6,4,1,5,2,3]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,4,1,5,3,2]=>111011=>[3,1,2]=>[2,1,3]
[7,6,4,2,1,3,5]=>111100=>[4,2]=>[2,4]
[7,6,4,2,1,5,3]=>111101=>[4,1,1]=>[1,1,4]
[7,6,4,2,3,1,5]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,4,2,3,5,1]=>111001=>[3,2,1]=>[1,2,3]
[7,6,4,2,5,1,3]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,4,2,5,3,1]=>111011=>[3,1,2]=>[2,1,3]
[7,6,4,3,1,2,5]=>111100=>[4,2]=>[2,4]
[7,6,4,3,1,5,2]=>111101=>[4,1,1]=>[1,1,4]
[7,6,4,3,2,1,5]=>111110=>[5,1]=>[1,5]
[7,6,4,3,2,5,1]=>111101=>[4,1,1]=>[1,1,4]
[7,6,4,3,5,1,2]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,4,3,5,2,1]=>111011=>[3,1,2]=>[2,1,3]
[7,6,4,5,1,2,3]=>110100=>[2,1,1,2]=>[2,1,1,2]
[7,6,4,5,1,3,2]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,4,5,2,1,3]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,4,5,2,3,1]=>110101=>[2,1,1,1,1]=>[1,1,1,1,2]
[7,6,4,5,3,1,2]=>110110=>[2,1,2,1]=>[1,2,1,2]
[7,6,4,5,3,2,1]=>110111=>[2,1,3]=>[3,1,2]
[7,6,5,1,2,3,4]=>111000=>[3,3]=>[3,3]
[7,6,5,1,2,4,3]=>111001=>[3,2,1]=>[1,2,3]
[7,6,5,1,3,2,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,5,1,3,4,2]=>111001=>[3,2,1]=>[1,2,3]
[7,6,5,1,4,2,3]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,5,1,4,3,2]=>111011=>[3,1,2]=>[2,1,3]
[7,6,5,2,1,3,4]=>111100=>[4,2]=>[2,4]
[7,6,5,2,1,4,3]=>111101=>[4,1,1]=>[1,1,4]
[7,6,5,2,3,1,4]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,5,2,3,4,1]=>111001=>[3,2,1]=>[1,2,3]
[7,6,5,2,4,1,3]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,5,2,4,3,1]=>111011=>[3,1,2]=>[2,1,3]
[7,6,5,3,1,2,4]=>111100=>[4,2]=>[2,4]
[7,6,5,3,1,4,2]=>111101=>[4,1,1]=>[1,1,4]
[7,6,5,3,2,1,4]=>111110=>[5,1]=>[1,5]
[7,6,5,3,2,4,1]=>111101=>[4,1,1]=>[1,1,4]
[7,6,5,3,4,1,2]=>111010=>[3,1,1,1]=>[1,1,1,3]
[7,6,5,3,4,2,1]=>111011=>[3,1,2]=>[2,1,3]
[7,6,5,4,1,2,3]=>111100=>[4,2]=>[2,4]
[7,6,5,4,1,3,2]=>111101=>[4,1,1]=>[1,1,4]
[7,6,5,4,2,1,3]=>111110=>[5,1]=>[1,5]
[7,6,5,4,2,3,1]=>111101=>[4,1,1]=>[1,1,4]
[7,6,5,4,3,1,2]=>111110=>[5,1]=>[1,5]
[7,6,5,4,3,2,1]=>111111=>[6]=>[6]
[8,7,6,5,4,3,2,1]=>1111111=>[7]=>[7]
[7,8,6,5,4,3,2,1]=>0111111=>[1,6]=>[6,1]
[8,6,7,5,4,3,2,1]=>1011111=>[1,1,5]=>[5,1,1]
[7,6,8,5,4,3,2,1]=>1011111=>[1,1,5]=>[5,1,1]
[6,7,8,5,4,3,2,1]=>0011111=>[2,5]=>[5,2]
[8,7,5,6,4,3,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[7,8,5,6,4,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[8,6,5,7,4,3,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[8,5,6,7,4,3,2,1]=>1001111=>[1,2,4]=>[4,2,1]
[7,6,5,8,4,3,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[6,7,5,8,4,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[7,5,6,8,4,3,2,1]=>1001111=>[1,2,4]=>[4,2,1]
[6,5,7,8,4,3,2,1]=>1001111=>[1,2,4]=>[4,2,1]
[5,6,7,8,4,3,2,1]=>0001111=>[3,4]=>[4,3]
[8,7,6,4,5,3,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[7,8,6,4,5,3,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[8,6,7,4,5,3,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,6,8,4,5,3,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,7,5,4,6,3,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,7,4,5,6,3,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[8,6,5,4,7,3,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,5,6,4,7,3,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,6,4,5,7,3,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[8,5,4,6,7,3,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[8,4,5,6,7,3,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[7,6,5,4,8,3,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[6,7,5,4,8,3,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[7,5,6,4,8,3,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,5,7,4,8,3,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,6,7,4,8,3,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[7,6,4,5,8,3,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[6,7,4,5,8,3,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[7,5,4,6,8,3,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[7,4,5,6,8,3,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[6,5,4,7,8,3,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[5,6,4,7,8,3,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[6,4,5,7,8,3,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[5,4,6,7,8,3,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[4,5,6,7,8,3,2,1]=>0000111=>[4,3]=>[3,4]
[8,7,6,5,3,4,2,1]=>1111011=>[4,1,2]=>[2,1,4]
[7,8,6,5,3,4,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[8,6,7,5,3,4,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,6,8,5,3,4,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,7,5,6,3,4,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,8,5,6,3,4,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,6,7,3,4,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,6,5,8,3,4,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,7,5,8,3,4,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,5,7,8,3,4,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,6,7,8,3,4,2,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[8,7,6,4,3,5,2,1]=>1111011=>[4,1,2]=>[2,1,4]
[7,8,6,4,3,5,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[8,6,7,4,3,5,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,6,8,4,3,5,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,7,8,4,3,5,2,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[8,7,6,3,4,5,2,1]=>1110011=>[3,2,2]=>[2,2,3]
[7,8,6,3,4,5,2,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[8,6,7,3,4,5,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,6,8,3,4,5,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,7,8,3,4,5,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[8,7,5,4,3,6,2,1]=>1111011=>[4,1,2]=>[2,1,4]
[7,8,5,4,3,6,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[8,7,4,5,3,6,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,7,5,3,4,6,2,1]=>1110011=>[3,2,2]=>[2,2,3]
[7,8,5,3,4,6,2,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[8,7,4,3,5,6,2,1]=>1110011=>[3,2,2]=>[2,2,3]
[8,7,3,4,5,6,2,1]=>1100011=>[2,3,2]=>[2,3,2]
[7,8,3,4,5,6,2,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[8,6,5,4,3,7,2,1]=>1111011=>[4,1,2]=>[2,1,4]
[8,6,4,5,3,7,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,6,4,3,5,7,2,1]=>1110011=>[3,2,2]=>[2,2,3]
[8,5,4,3,6,7,2,1]=>1110011=>[3,2,2]=>[2,2,3]
[8,5,3,4,6,7,2,1]=>1100011=>[2,3,2]=>[2,3,2]
[8,4,3,5,6,7,2,1]=>1100011=>[2,3,2]=>[2,3,2]
[8,3,4,5,6,7,2,1]=>1000011=>[1,4,2]=>[2,4,1]
[7,6,5,4,3,8,2,1]=>1111011=>[4,1,2]=>[2,1,4]
[6,7,5,4,3,8,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[7,5,6,4,3,8,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,5,7,4,3,8,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,6,7,4,3,8,2,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,7,4,5,3,8,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,5,4,6,3,8,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,4,5,6,3,8,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,5,4,7,3,8,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,4,5,7,3,8,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,4,6,7,3,8,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,5,6,7,3,8,2,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[7,6,5,3,4,8,2,1]=>1110011=>[3,2,2]=>[2,2,3]
[7,6,4,3,5,8,2,1]=>1110011=>[3,2,2]=>[2,2,3]
[7,6,3,4,5,8,2,1]=>1100011=>[2,3,2]=>[2,3,2]
[7,5,4,3,6,8,2,1]=>1110011=>[3,2,2]=>[2,2,3]
[7,5,3,4,6,8,2,1]=>1100011=>[2,3,2]=>[2,3,2]
[7,3,4,5,6,8,2,1]=>1000011=>[1,4,2]=>[2,4,1]
[6,5,4,3,7,8,2,1]=>1110011=>[3,2,2]=>[2,2,3]
[4,5,6,3,7,8,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,5,3,4,7,8,2,1]=>1100011=>[2,3,2]=>[2,3,2]
[6,3,4,5,7,8,2,1]=>1000011=>[1,4,2]=>[2,4,1]
[5,4,3,6,7,8,2,1]=>1100011=>[2,3,2]=>[2,3,2]
[5,3,4,6,7,8,2,1]=>1000011=>[1,4,2]=>[2,4,1]
[4,3,5,6,7,8,2,1]=>1000011=>[1,4,2]=>[2,4,1]
[3,4,5,6,7,8,2,1]=>0000011=>[5,2]=>[2,5]
[8,7,6,5,4,2,3,1]=>1111101=>[5,1,1]=>[1,1,5]
[7,8,6,5,4,2,3,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[8,6,7,5,4,2,3,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,6,8,5,4,2,3,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,7,5,6,4,2,3,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,6,5,7,4,2,3,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,5,6,7,4,2,3,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,6,5,8,4,2,3,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,5,8,4,2,3,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,5,6,8,4,2,3,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,6,7,8,4,2,3,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[8,7,6,4,5,2,3,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,6,7,4,5,2,3,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,8,4,5,2,3,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,7,5,4,6,2,3,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,4,5,6,2,3,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,8,4,5,6,2,3,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,6,5,4,7,2,3,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,5,6,4,7,2,3,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,4,5,7,2,3,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,4,5,6,7,2,3,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,6,5,4,8,2,3,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,6,4,8,2,3,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,7,4,8,2,3,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,4,5,8,2,3,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,5,6,7,8,2,3,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[8,7,6,5,3,2,4,1]=>1111101=>[5,1,1]=>[1,1,5]
[7,8,6,5,3,2,4,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[8,6,7,5,3,2,4,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,6,8,5,3,2,4,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,7,8,5,3,2,4,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[8,7,5,6,3,2,4,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,6,5,7,3,2,4,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,5,6,7,3,2,4,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,6,5,8,3,2,4,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,5,8,3,2,4,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,7,8,3,2,4,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[8,7,6,5,2,3,4,1]=>1111001=>[4,2,1]=>[1,2,4]
[8,6,7,5,2,3,4,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,6,8,5,2,3,4,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,7,8,5,2,3,4,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[8,7,5,6,2,3,4,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,8,5,6,2,3,4,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,6,5,7,2,3,4,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,5,6,7,2,3,4,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,6,5,8,2,3,4,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,7,5,8,2,3,4,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,7,8,2,3,4,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,6,7,8,2,3,4,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[8,7,6,4,3,2,5,1]=>1111101=>[5,1,1]=>[1,1,5]
[7,8,6,4,3,2,5,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[8,6,7,4,3,2,5,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,6,8,4,3,2,5,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,7,8,4,3,2,5,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[8,7,6,3,4,2,5,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,8,6,3,4,2,5,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,6,7,3,4,2,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,8,3,4,2,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,8,3,4,2,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,7,6,4,2,3,5,1]=>1111001=>[4,2,1]=>[1,2,4]
[8,6,7,4,2,3,5,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,6,8,4,2,3,5,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,7,8,4,2,3,5,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[8,7,6,3,2,4,5,1]=>1111001=>[4,2,1]=>[1,2,4]
[7,8,6,3,2,4,5,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,6,7,3,2,4,5,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,7,8,3,2,4,5,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[8,7,6,2,3,4,5,1]=>1110001=>[3,3,1]=>[1,3,3]
[7,8,6,2,3,4,5,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[8,6,7,2,3,4,5,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,6,8,2,3,4,5,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,7,8,2,3,4,5,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[8,7,5,4,3,2,6,1]=>1111101=>[5,1,1]=>[1,1,5]
[7,8,5,4,3,2,6,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[8,7,5,3,4,2,6,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,8,5,3,4,2,6,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,7,4,3,5,2,6,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,5,3,2,4,6,1]=>1111001=>[4,2,1]=>[1,2,4]
[8,7,4,3,2,5,6,1]=>1111001=>[4,2,1]=>[1,2,4]
[7,8,4,3,2,5,6,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,8,3,4,2,5,6,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,8,4,2,3,5,6,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,8,3,2,4,5,6,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[8,7,2,3,4,5,6,1]=>1100001=>[2,4,1]=>[1,4,2]
[7,8,2,3,4,5,6,1]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[8,6,5,4,3,2,7,1]=>1111101=>[5,1,1]=>[1,1,5]
[8,5,6,4,3,2,7,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,6,4,5,3,2,7,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,5,4,6,3,2,7,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,6,5,3,4,2,7,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,5,6,3,4,2,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,4,3,5,2,7,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,6,3,4,5,2,7,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,5,4,3,6,2,7,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,4,5,3,6,2,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,3,5,6,2,7,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,3,4,5,6,2,7,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,6,5,4,2,3,7,1]=>1111001=>[4,2,1]=>[1,2,4]
[8,5,6,4,2,3,7,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,6,4,5,2,3,7,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,6,5,3,2,4,7,1]=>1111001=>[4,2,1]=>[1,2,4]
[8,6,4,3,2,5,7,1]=>1111001=>[4,2,1]=>[1,2,4]
[8,6,4,2,3,5,7,1]=>1110001=>[3,3,1]=>[1,3,3]
[8,6,2,3,4,5,7,1]=>1100001=>[2,4,1]=>[1,4,2]
[8,5,4,3,2,6,7,1]=>1111001=>[4,2,1]=>[1,2,4]
[8,4,5,3,2,6,7,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,5,3,4,2,6,7,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,3,4,5,2,6,7,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,5,4,2,3,6,7,1]=>1110001=>[3,3,1]=>[1,3,3]
[8,4,5,2,3,6,7,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,5,2,3,4,6,7,1]=>1100001=>[2,4,1]=>[1,4,2]
[8,4,3,2,5,6,7,1]=>1110001=>[3,3,1]=>[1,3,3]
[8,3,4,2,5,6,7,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,4,2,3,5,6,7,1]=>1100001=>[2,4,1]=>[1,4,2]
[8,3,2,4,5,6,7,1]=>1100001=>[2,4,1]=>[1,4,2]
[8,2,3,4,5,6,7,1]=>1000001=>[1,5,1]=>[1,5,1]
[7,6,5,4,3,2,8,1]=>1111101=>[5,1,1]=>[1,1,5]
[6,7,5,4,3,2,8,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[7,5,6,4,3,2,8,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,5,7,4,3,2,8,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,6,7,4,3,2,8,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[7,6,4,5,3,2,8,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,4,5,3,2,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,4,5,6,3,2,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,5,4,7,3,2,8,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,5,7,3,2,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,5,6,7,3,2,8,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[7,6,5,3,4,2,8,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,6,3,4,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,7,3,4,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,7,3,4,2,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,4,3,5,2,8,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,6,3,4,5,2,8,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,4,3,6,2,8,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,4,5,3,6,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,3,4,6,2,8,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,3,4,5,6,2,8,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,5,4,3,7,2,8,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,5,3,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,3,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,6,3,7,2,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,3,4,7,2,8,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,6,3,4,7,2,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,4,3,5,7,2,8,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,3,4,5,7,2,8,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,4,3,6,7,2,8,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,5,3,6,7,2,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,3,5,6,7,2,8,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,4,5,6,7,2,8,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[7,6,5,4,2,3,8,1]=>1111001=>[4,2,1]=>[1,2,4]
[6,7,5,4,2,3,8,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,5,6,4,2,3,8,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,5,7,4,2,3,8,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,6,7,4,2,3,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[7,6,4,5,2,3,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,7,4,5,2,3,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,5,4,6,2,3,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,4,5,6,2,3,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,5,4,7,2,3,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,6,4,7,2,3,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,4,5,7,2,3,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,4,6,7,2,3,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,5,6,7,2,3,8,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[7,6,5,3,2,4,8,1]=>1111001=>[4,2,1]=>[1,2,4]
[6,7,5,3,2,4,8,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[6,5,7,3,2,4,8,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,6,5,2,3,4,8,1]=>1110001=>[3,3,1]=>[1,3,3]
[7,5,6,2,3,4,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,6,7,2,3,4,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[6,7,4,3,2,5,8,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,6,4,2,3,5,8,1]=>1110001=>[3,3,1]=>[1,3,3]
[7,6,3,2,4,5,8,1]=>1110001=>[3,3,1]=>[1,3,3]
[6,7,3,2,4,5,8,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,6,2,3,4,5,8,1]=>1100001=>[2,4,1]=>[1,4,2]
[6,7,2,3,4,5,8,1]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[7,5,4,3,2,6,8,1]=>1111001=>[4,2,1]=>[1,2,4]
[7,4,3,5,2,6,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,4,2,3,6,8,1]=>1110001=>[3,3,1]=>[1,3,3]
[7,4,5,2,3,6,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,5,3,2,4,6,8,1]=>1110001=>[3,3,1]=>[1,3,3]
[7,5,2,3,4,6,8,1]=>1100001=>[2,4,1]=>[1,4,2]
[7,4,3,2,5,6,8,1]=>1110001=>[3,3,1]=>[1,3,3]
[7,4,2,3,5,6,8,1]=>1100001=>[2,4,1]=>[1,4,2]
[7,3,2,4,5,6,8,1]=>1100001=>[2,4,1]=>[1,4,2]
[7,2,3,4,5,6,8,1]=>1000001=>[1,5,1]=>[1,5,1]
[6,5,4,3,2,7,8,1]=>1111001=>[4,2,1]=>[1,2,4]
[5,4,6,3,2,7,8,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,5,6,3,2,7,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[6,5,3,4,2,7,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,4,5,2,7,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,4,3,6,2,7,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,3,5,6,2,7,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,4,5,6,2,7,8,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[6,5,4,2,3,7,8,1]=>1110001=>[3,3,1]=>[1,3,3]
[5,6,4,2,3,7,8,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[6,4,5,2,3,7,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,4,6,2,3,7,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,5,6,2,3,7,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[6,5,3,2,4,7,8,1]=>1110001=>[3,3,1]=>[1,3,3]
[6,5,2,3,4,7,8,1]=>1100001=>[2,4,1]=>[1,4,2]
[6,2,3,4,5,7,8,1]=>1000001=>[1,5,1]=>[1,5,1]
[5,4,3,2,6,7,8,1]=>1110001=>[3,3,1]=>[1,3,3]
[4,5,3,2,6,7,8,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[5,3,4,2,6,7,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,3,5,2,6,7,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,4,5,2,6,7,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[5,4,2,3,6,7,8,1]=>1100001=>[2,4,1]=>[1,4,2]
[4,5,2,3,6,7,8,1]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[5,3,2,4,6,7,8,1]=>1100001=>[2,4,1]=>[1,4,2]
[5,2,3,4,6,7,8,1]=>1000001=>[1,5,1]=>[1,5,1]
[4,3,2,5,6,7,8,1]=>1100001=>[2,4,1]=>[1,4,2]
[3,4,2,5,6,7,8,1]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[4,2,3,5,6,7,8,1]=>1000001=>[1,5,1]=>[1,5,1]
[3,2,4,5,6,7,8,1]=>1000001=>[1,5,1]=>[1,5,1]
[2,3,4,5,6,7,8,1]=>0000001=>[6,1]=>[1,6]
[8,7,6,5,4,3,1,2]=>1111110=>[6,1]=>[1,6]
[7,8,6,5,4,3,1,2]=>0111110=>[1,5,1]=>[1,5,1]
[8,6,7,5,4,3,1,2]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,6,8,5,4,3,1,2]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[6,7,8,5,4,3,1,2]=>0011110=>[2,4,1]=>[1,4,2]
[8,7,5,6,4,3,1,2]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,8,5,6,4,3,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,6,5,7,4,3,1,2]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,6,5,8,4,3,1,2]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,7,5,8,4,3,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,5,6,8,4,3,1,2]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,5,7,8,4,3,1,2]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,6,7,8,4,3,1,2]=>0001110=>[3,3,1]=>[1,3,3]
[8,7,6,4,5,3,1,2]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,8,6,4,5,3,1,2]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,6,7,4,5,3,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,7,8,4,5,3,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,7,5,4,6,3,1,2]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,5,6,4,7,3,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,6,4,5,7,3,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,5,4,6,7,3,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,6,5,4,8,3,1,2]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,5,6,4,8,3,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,7,4,8,3,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,6,4,5,8,3,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,7,4,5,8,3,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,5,4,7,8,3,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,6,4,7,8,3,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,4,6,7,8,3,1,2]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,5,6,7,8,3,1,2]=>0000110=>[4,2,1]=>[1,2,4]
[8,7,6,5,3,4,1,2]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,8,6,5,3,4,1,2]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,6,8,5,3,4,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,7,8,5,3,4,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,7,5,6,3,4,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,8,5,6,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,5,7,3,4,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,6,7,3,4,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,6,5,8,3,4,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,7,5,8,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,6,8,3,4,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,5,7,8,3,4,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,6,7,8,3,4,1,2]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,7,8,4,3,5,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,7,6,3,4,5,1,2]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,6,7,3,4,5,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,8,5,4,3,6,1,2]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,7,4,5,3,6,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,8,4,5,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,5,3,4,6,1,2]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,7,4,3,5,6,1,2]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,8,4,3,5,6,1,2]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,7,3,4,5,6,1,2]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,8,3,4,5,6,1,2]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,6,5,4,3,7,1,2]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,5,4,3,6,7,1,2]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,5,3,4,6,7,1,2]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,4,3,5,6,7,1,2]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,3,4,5,6,7,1,2]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[7,6,5,4,3,8,1,2]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,5,6,4,3,8,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,5,7,4,3,8,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,6,7,4,3,8,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,7,4,5,3,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,4,7,3,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,7,3,8,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,6,7,3,8,1,2]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,6,5,3,4,8,1,2]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,5,6,3,4,8,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,7,3,4,8,1,2]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,6,4,3,5,8,1,2]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,6,3,4,5,8,1,2]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,5,4,3,6,8,1,2]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,5,3,4,6,8,1,2]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,3,4,5,6,8,1,2]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[6,5,4,3,7,8,1,2]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[5,6,4,3,7,8,1,2]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,4,6,3,7,8,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,6,3,7,8,1,2]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,5,3,4,7,8,1,2]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,6,3,4,7,8,1,2]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,4,3,5,7,8,1,2]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[6,3,4,5,7,8,1,2]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[5,4,3,6,7,8,1,2]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,5,3,6,7,8,1,2]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,3,4,6,7,8,1,2]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[4,3,5,6,7,8,1,2]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[3,4,5,6,7,8,1,2]=>0000010=>[5,1,1]=>[1,1,5]
[8,7,6,5,4,2,1,3]=>1111110=>[6,1]=>[1,6]
[7,8,6,5,4,2,1,3]=>0111110=>[1,5,1]=>[1,5,1]
[8,6,7,5,4,2,1,3]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,6,8,5,4,2,1,3]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[6,7,8,5,4,2,1,3]=>0011110=>[2,4,1]=>[1,4,2]
[8,7,5,6,4,2,1,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,8,5,6,4,2,1,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,6,5,7,4,2,1,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,6,5,8,4,2,1,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,7,5,8,4,2,1,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,5,6,8,4,2,1,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,5,7,8,4,2,1,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,6,7,8,4,2,1,3]=>0001110=>[3,3,1]=>[1,3,3]
[8,7,6,4,5,2,1,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,6,7,4,5,2,1,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,6,8,4,5,2,1,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,7,4,5,6,2,1,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,6,5,4,7,2,1,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,6,4,5,7,2,1,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,4,5,6,7,2,1,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,6,5,4,8,2,1,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[6,7,5,4,8,2,1,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,5,6,4,8,2,1,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,7,4,8,2,1,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,6,7,4,8,2,1,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,6,4,5,8,2,1,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,4,5,6,8,2,1,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,4,6,7,8,2,1,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,5,6,7,8,2,1,3]=>0000110=>[4,2,1]=>[1,2,4]
[8,7,6,5,4,1,2,3]=>1111100=>[5,2]=>[2,5]
[7,8,6,5,4,1,2,3]=>0111100=>[1,4,2]=>[2,4,1]
[7,6,8,5,4,1,2,3]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,7,8,5,4,1,2,3]=>0011100=>[2,3,2]=>[2,3,2]
[7,8,5,6,4,1,2,3]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,6,5,7,4,1,2,3]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,5,6,7,4,1,2,3]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[7,6,5,8,4,1,2,3]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,7,5,8,4,1,2,3]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,5,6,8,4,1,2,3]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,5,7,8,4,1,2,3]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,6,7,8,4,1,2,3]=>0001100=>[3,2,2]=>[2,2,3]
[8,7,6,4,5,1,2,3]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,6,7,4,5,1,2,3]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,8,4,5,1,2,3]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,7,5,4,6,1,2,3]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,8,5,4,6,1,2,3]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,7,4,5,6,1,2,3]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,8,4,5,6,1,2,3]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,5,6,4,7,1,2,3]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,4,5,7,1,2,3]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,5,4,6,7,1,2,3]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,4,5,6,7,1,2,3]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[7,6,5,4,8,1,2,3]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,7,5,4,8,1,2,3]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,5,6,4,8,1,2,3]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,5,7,4,8,1,2,3]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,7,4,8,1,2,3]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,6,4,5,8,1,2,3]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,7,4,5,8,1,2,3]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,5,4,6,8,1,2,3]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,4,5,6,8,1,2,3]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[6,5,4,7,8,1,2,3]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,6,4,7,8,1,2,3]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,4,5,7,8,1,2,3]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[5,4,6,7,8,1,2,3]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,5,6,7,8,1,2,3]=>0000100=>[4,1,2]=>[2,1,4]
[8,7,6,5,3,2,1,4]=>1111110=>[6,1]=>[1,6]
[7,8,6,5,3,2,1,4]=>0111110=>[1,5,1]=>[1,5,1]
[8,6,7,5,3,2,1,4]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,6,8,5,3,2,1,4]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[6,7,8,5,3,2,1,4]=>0011110=>[2,4,1]=>[1,4,2]
[8,7,5,6,3,2,1,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,8,5,6,3,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,6,5,7,3,2,1,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,5,6,7,3,2,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,6,5,8,3,2,1,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,7,5,8,3,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,5,6,8,3,2,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,5,7,8,3,2,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,6,7,8,3,2,1,4]=>0001110=>[3,3,1]=>[1,3,3]
[8,7,6,5,2,3,1,4]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,8,6,5,2,3,1,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,6,7,5,2,3,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,6,8,5,2,3,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,7,8,5,2,3,1,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,7,5,6,2,3,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,8,5,6,2,3,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,5,7,2,3,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,6,7,2,3,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,6,5,8,2,3,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,7,5,8,2,3,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,6,8,2,3,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,5,7,8,2,3,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,6,7,8,2,3,1,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,6,5,3,1,2,4]=>1111100=>[5,2]=>[2,5]
[7,8,6,5,3,1,2,4]=>0111100=>[1,4,2]=>[2,4,1]
[8,6,7,5,3,1,2,4]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,6,8,5,3,1,2,4]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,7,5,6,3,1,2,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,8,5,6,3,1,2,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,6,5,8,3,1,2,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,7,5,8,3,1,2,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,5,6,8,3,1,2,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,5,7,8,3,1,2,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,6,7,8,3,1,2,4]=>0001100=>[3,2,2]=>[2,2,3]
[8,7,6,5,2,1,3,4]=>1111100=>[5,2]=>[2,5]
[7,8,6,5,2,1,3,4]=>0111100=>[1,4,2]=>[2,4,1]
[7,6,8,5,2,1,3,4]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,7,8,5,2,1,3,4]=>0011100=>[2,3,2]=>[2,3,2]
[8,7,5,6,2,1,3,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,8,5,6,2,1,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,6,5,7,2,1,3,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,5,6,7,2,1,3,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[7,6,5,8,2,1,3,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,7,5,8,2,1,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,5,6,8,2,1,3,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,5,7,8,2,1,3,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,6,7,8,2,1,3,4]=>0001100=>[3,2,2]=>[2,2,3]
[8,7,6,5,1,2,3,4]=>1111000=>[4,3]=>[3,4]
[7,8,6,5,1,2,3,4]=>0111000=>[1,3,3]=>[3,3,1]
[8,6,7,5,1,2,3,4]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,6,8,5,1,2,3,4]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,7,8,5,1,2,3,4]=>0011000=>[2,2,3]=>[3,2,2]
[8,7,5,6,1,2,3,4]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,8,5,6,1,2,3,4]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,6,5,7,1,2,3,4]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,5,6,7,1,2,3,4]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,6,5,8,1,2,3,4]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,7,5,8,1,2,3,4]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,5,6,8,1,2,3,4]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,5,7,8,1,2,3,4]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,6,7,8,1,2,3,4]=>0001000=>[3,1,3]=>[3,1,3]
[8,7,6,4,3,2,1,5]=>1111110=>[6,1]=>[1,6]
[7,8,6,4,3,2,1,5]=>0111110=>[1,5,1]=>[1,5,1]
[8,6,7,4,3,2,1,5]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,6,8,4,3,2,1,5]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[6,7,8,4,3,2,1,5]=>0011110=>[2,4,1]=>[1,4,2]
[8,7,6,3,4,2,1,5]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,8,6,3,4,2,1,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,7,8,3,4,2,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,7,6,4,2,3,1,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,7,4,2,3,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,6,8,4,2,3,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,7,8,4,2,3,1,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,7,6,3,2,4,1,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,7,3,2,4,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,7,8,3,2,4,1,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,7,6,2,3,4,1,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,6,7,2,3,4,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,6,8,2,3,4,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,7,8,2,3,4,1,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,7,6,4,3,1,2,5]=>1111100=>[5,2]=>[2,5]
[6,7,8,4,3,1,2,5]=>0011100=>[2,3,2]=>[2,3,2]
[8,7,6,3,4,1,2,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,8,6,3,4,1,2,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,6,7,3,4,1,2,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,8,3,4,1,2,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,7,6,4,2,1,3,5]=>1111100=>[5,2]=>[2,5]
[7,8,6,4,2,1,3,5]=>0111100=>[1,4,2]=>[2,4,1]
[8,6,7,4,2,1,3,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,7,8,4,2,1,3,5]=>0011100=>[2,3,2]=>[2,3,2]
[8,7,6,4,1,2,3,5]=>1111000=>[4,3]=>[3,4]
[7,8,6,4,1,2,3,5]=>0111000=>[1,3,3]=>[3,3,1]
[7,6,8,4,1,2,3,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,7,8,4,1,2,3,5]=>0011000=>[2,2,3]=>[3,2,2]
[8,7,6,3,2,1,4,5]=>1111100=>[5,2]=>[2,5]
[7,8,6,3,2,1,4,5]=>0111100=>[1,4,2]=>[2,4,1]
[8,6,7,3,2,1,4,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,6,8,3,2,1,4,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,7,8,3,2,1,4,5]=>0011100=>[2,3,2]=>[2,3,2]
[8,7,6,2,3,1,4,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,8,6,2,3,1,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,6,7,2,3,1,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,6,8,2,3,1,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,8,2,3,1,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,7,6,3,1,2,4,5]=>1111000=>[4,3]=>[3,4]
[7,8,6,3,1,2,4,5]=>0111000=>[1,3,3]=>[3,3,1]
[8,6,7,3,1,2,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,6,8,3,1,2,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,7,8,3,1,2,4,5]=>0011000=>[2,2,3]=>[3,2,2]
[8,7,6,2,1,3,4,5]=>1111000=>[4,3]=>[3,4]
[7,8,6,2,1,3,4,5]=>0111000=>[1,3,3]=>[3,3,1]
[8,6,7,2,1,3,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,7,8,2,1,3,4,5]=>0011000=>[2,2,3]=>[3,2,2]
[8,7,6,1,2,3,4,5]=>1110000=>[3,4]=>[4,3]
[7,8,6,1,2,3,4,5]=>0110000=>[1,2,4]=>[4,2,1]
[8,6,7,1,2,3,4,5]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,6,8,1,2,3,4,5]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,7,8,1,2,3,4,5]=>0010000=>[2,1,4]=>[4,1,2]
[8,7,5,4,3,2,1,6]=>1111110=>[6,1]=>[1,6]
[7,8,5,4,3,2,1,6]=>0111110=>[1,5,1]=>[1,5,1]
[8,7,4,5,3,2,1,6]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,8,4,5,3,2,1,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,7,5,3,4,2,1,6]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,7,4,3,5,2,1,6]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,7,3,4,5,2,1,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,8,3,4,5,2,1,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,7,4,5,2,3,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,8,4,5,2,3,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,7,5,3,2,4,1,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,8,5,2,3,4,1,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,7,4,3,2,5,1,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,8,4,3,2,5,1,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,7,3,4,2,5,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,8,3,4,2,5,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,7,2,3,4,5,1,6]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,8,2,3,4,5,1,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,7,5,4,3,1,2,6]=>1111100=>[5,2]=>[2,5]
[7,8,5,4,3,1,2,6]=>0111100=>[1,4,2]=>[2,4,1]
[8,7,5,3,4,1,2,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,8,5,3,4,1,2,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,7,3,4,5,1,2,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,8,3,4,5,1,2,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,8,5,4,2,1,3,6]=>0111100=>[1,4,2]=>[2,4,1]
[8,7,5,4,1,2,3,6]=>1111000=>[4,3]=>[3,4]
[7,8,5,4,1,2,3,6]=>0111000=>[1,3,3]=>[3,3,1]
[8,7,4,5,1,2,3,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,8,4,5,1,2,3,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,7,5,3,2,1,4,6]=>1111100=>[5,2]=>[2,5]
[7,8,5,3,2,1,4,6]=>0111100=>[1,4,2]=>[2,4,1]
[8,7,5,2,3,1,4,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,5,3,1,2,4,6]=>1111000=>[4,3]=>[3,4]
[7,8,5,3,1,2,4,6]=>0111000=>[1,3,3]=>[3,3,1]
[8,7,5,2,1,3,4,6]=>1111000=>[4,3]=>[3,4]
[7,8,5,2,1,3,4,6]=>0111000=>[1,3,3]=>[3,3,1]
[8,7,5,1,2,3,4,6]=>1110000=>[3,4]=>[4,3]
[7,8,5,1,2,3,4,6]=>0110000=>[1,2,4]=>[4,2,1]
[8,7,4,3,2,1,5,6]=>1111100=>[5,2]=>[2,5]
[7,8,4,3,2,1,5,6]=>0111100=>[1,4,2]=>[2,4,1]
[8,7,3,4,2,1,5,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,8,3,4,2,1,5,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,8,4,2,3,1,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,7,3,2,4,1,5,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,8,3,2,4,1,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,7,2,3,4,1,5,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,8,2,3,4,1,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,8,4,3,1,2,5,6]=>0111000=>[1,3,3]=>[3,3,1]
[8,7,3,4,1,2,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,8,3,4,1,2,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,7,4,2,1,3,5,6]=>1111000=>[4,3]=>[3,4]
[7,8,4,2,1,3,5,6]=>0111000=>[1,3,3]=>[3,3,1]
[8,7,4,1,2,3,5,6]=>1110000=>[3,4]=>[4,3]
[7,8,4,1,2,3,5,6]=>0110000=>[1,2,4]=>[4,2,1]
[8,7,3,2,1,4,5,6]=>1111000=>[4,3]=>[3,4]
[7,8,3,2,1,4,5,6]=>0111000=>[1,3,3]=>[3,3,1]
[8,7,2,3,1,4,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,8,2,3,1,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,8,3,1,2,4,5,6]=>0110000=>[1,2,4]=>[4,2,1]
[8,7,2,1,3,4,5,6]=>1110000=>[3,4]=>[4,3]
[7,8,2,1,3,4,5,6]=>0110000=>[1,2,4]=>[4,2,1]
[8,7,1,2,3,4,5,6]=>1100000=>[2,5]=>[5,2]
[7,8,1,2,3,4,5,6]=>0100000=>[1,1,5]=>[5,1,1]
[8,6,5,4,3,2,1,7]=>1111110=>[6,1]=>[1,6]
[8,5,6,4,3,2,1,7]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[8,6,4,5,3,2,1,7]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,5,4,6,3,2,1,7]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,4,5,6,3,2,1,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[8,6,5,3,4,2,1,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,5,6,3,4,2,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,6,4,3,5,2,1,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,4,5,3,6,2,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,4,3,5,6,2,1,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,3,4,5,6,2,1,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[8,6,5,4,2,3,1,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,5,6,4,2,3,1,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,6,4,5,2,3,1,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,5,6,2,3,1,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,6,5,3,2,4,1,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,5,2,3,4,1,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,5,6,2,3,4,1,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,6,4,3,2,5,1,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,4,2,3,5,1,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,6,3,2,4,5,1,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,5,4,3,2,6,1,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,4,3,5,2,6,1,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,4,2,3,6,1,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,4,5,2,3,6,1,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,5,3,2,4,6,1,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,5,2,3,4,6,1,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,3,4,2,5,6,1,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,3,2,4,5,6,1,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,2,3,4,5,6,1,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[8,6,5,4,3,1,2,7]=>1111100=>[5,2]=>[2,5]
[8,6,4,5,3,1,2,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,6,5,3,4,1,2,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,5,6,3,4,1,2,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,3,4,5,1,2,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,5,4,3,6,1,2,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,4,5,3,6,1,2,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,3,4,6,1,2,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,4,3,5,6,1,2,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,3,4,5,6,1,2,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[8,6,5,4,2,1,3,7]=>1111100=>[5,2]=>[2,5]
[8,5,6,4,2,1,3,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,6,4,5,2,1,3,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,4,5,6,2,1,3,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,6,5,4,1,2,3,7]=>1111000=>[4,3]=>[3,4]
[8,5,6,4,1,2,3,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,6,4,5,1,2,3,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,4,5,6,1,2,3,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,6,5,3,2,1,4,7]=>1111100=>[5,2]=>[2,5]
[8,5,6,3,2,1,4,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,6,5,2,3,1,4,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,5,6,2,3,1,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,6,3,1,2,4,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,6,5,2,1,3,4,7]=>1111000=>[4,3]=>[3,4]
[8,5,6,2,1,3,4,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,6,5,1,2,3,4,7]=>1110000=>[3,4]=>[4,3]
[8,5,6,1,2,3,4,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,6,4,3,2,1,5,7]=>1111100=>[5,2]=>[2,5]
[8,6,3,4,2,1,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,6,4,2,3,1,5,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,6,3,2,4,1,5,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,6,2,3,4,1,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,6,4,3,1,2,5,7]=>1111000=>[4,3]=>[3,4]
[8,6,3,4,1,2,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,6,4,2,1,3,5,7]=>1111000=>[4,3]=>[3,4]
[8,6,4,1,2,3,5,7]=>1110000=>[3,4]=>[4,3]
[8,6,1,2,3,4,5,7]=>1100000=>[2,5]=>[5,2]
[8,5,4,3,2,1,6,7]=>1111100=>[5,2]=>[2,5]
[8,4,5,3,2,1,6,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,4,3,5,2,1,6,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,3,4,5,2,1,6,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,4,5,2,3,1,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,2,3,4,1,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,4,2,3,5,1,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,2,3,4,5,1,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[8,5,3,4,1,2,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,3,4,5,1,2,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,5,4,2,1,3,6,7]=>1111000=>[4,3]=>[3,4]
[8,5,4,1,2,3,6,7]=>1110000=>[3,4]=>[4,3]
[8,4,5,1,2,3,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,5,3,2,1,4,6,7]=>1111000=>[4,3]=>[3,4]
[8,5,3,1,2,4,6,7]=>1110000=>[3,4]=>[4,3]
[8,5,2,1,3,4,6,7]=>1110000=>[3,4]=>[4,3]
[8,5,1,2,3,4,6,7]=>1100000=>[2,5]=>[5,2]
[8,4,3,2,1,5,6,7]=>1111000=>[4,3]=>[3,4]
[8,3,4,2,1,5,6,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,4,2,3,1,5,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,2,3,4,1,5,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,3,4,1,2,5,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,4,2,1,3,5,6,7]=>1110000=>[3,4]=>[4,3]
[8,4,1,2,3,5,6,7]=>1100000=>[2,5]=>[5,2]
[8,3,2,1,4,5,6,7]=>1110000=>[3,4]=>[4,3]
[8,2,3,1,4,5,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,3,1,2,4,5,6,7]=>1100000=>[2,5]=>[5,2]
[8,2,1,3,4,5,6,7]=>1100000=>[2,5]=>[5,2]
[8,1,2,3,4,5,6,7]=>1000000=>[1,6]=>[6,1]
[7,6,5,4,3,2,1,8]=>1111110=>[6,1]=>[1,6]
[6,7,5,4,3,2,1,8]=>0111110=>[1,5,1]=>[1,5,1]
[7,5,6,4,3,2,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[6,5,7,4,3,2,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[5,6,7,4,3,2,1,8]=>0011110=>[2,4,1]=>[1,4,2]
[7,6,4,5,3,2,1,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,7,4,5,3,2,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,5,4,6,3,2,1,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,4,5,6,3,2,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,5,4,7,3,2,1,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[5,6,4,7,3,2,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,4,6,7,3,2,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[4,5,6,7,3,2,1,8]=>0001110=>[3,3,1]=>[1,3,3]
[7,6,5,3,4,2,1,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[6,7,5,3,4,2,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,5,6,3,4,2,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,7,3,4,2,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,6,7,3,4,2,1,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,6,4,3,5,2,1,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[6,7,4,3,5,2,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,6,3,4,5,2,1,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,5,4,3,6,2,1,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,4,5,3,6,2,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,4,5,6,2,1,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,5,4,3,7,2,1,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[5,6,4,3,7,2,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,4,6,3,7,2,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,4,3,6,7,2,1,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,4,5,6,7,2,1,8]=>0000110=>[4,2,1]=>[1,2,4]
[7,6,5,4,2,3,1,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[6,7,5,4,2,3,1,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,5,6,4,2,3,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,6,7,4,2,3,1,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,6,4,5,2,3,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,7,4,5,2,3,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,4,6,2,3,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,5,6,2,3,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,5,4,7,2,3,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,6,4,7,2,3,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,7,2,3,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,6,7,2,3,1,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,6,5,3,2,4,1,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[6,5,7,3,2,4,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,6,7,3,2,4,1,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,6,5,2,3,4,1,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,7,5,2,3,4,1,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,5,6,2,3,4,1,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,5,7,2,3,4,1,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,7,2,3,4,1,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,6,4,3,2,5,1,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[6,7,4,3,2,5,1,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,7,3,4,2,5,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,4,2,3,5,1,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,7,4,2,3,5,1,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,6,3,2,4,5,1,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,7,3,2,4,5,1,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,6,2,3,4,5,1,8]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[6,7,2,3,4,5,1,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,5,4,3,2,6,1,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,4,5,3,2,6,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,5,3,4,2,6,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,3,5,2,6,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,4,2,3,6,1,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,4,5,2,3,6,1,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,5,3,2,4,6,1,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,4,2,3,5,6,1,8]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,2,3,4,5,6,1,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[6,5,4,3,2,7,1,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[5,6,4,3,2,7,1,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,4,6,3,2,7,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,6,3,4,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,4,5,2,7,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,4,3,6,2,7,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,5,3,6,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,4,6,2,7,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,5,6,2,7,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,5,6,2,7,1,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,4,6,2,3,7,1,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,5,3,2,4,7,1,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,4,2,3,5,7,1,8]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[6,3,2,4,5,7,1,8]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[6,2,3,4,5,7,1,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[5,4,3,2,6,7,1,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,4,5,2,6,7,1,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,4,2,3,6,7,1,8]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,5,2,3,6,7,1,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,2,3,4,6,7,1,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[4,3,2,5,6,7,1,8]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[3,4,2,5,6,7,1,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,2,3,5,6,7,1,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[3,2,4,5,6,7,1,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[2,3,4,5,6,7,1,8]=>0000010=>[5,1,1]=>[1,1,5]
[7,6,5,4,3,1,2,8]=>1111100=>[5,2]=>[2,5]
[6,7,5,4,3,1,2,8]=>0111100=>[1,4,2]=>[2,4,1]
[7,5,6,4,3,1,2,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,6,4,5,3,1,2,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,4,5,6,3,1,2,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,4,6,7,3,1,2,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,5,6,7,3,1,2,8]=>0001100=>[3,2,2]=>[2,2,3]
[7,6,5,3,4,1,2,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,6,3,4,1,2,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,3,4,5,1,2,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,5,3,4,6,1,2,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,5,4,3,7,1,2,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[5,6,3,4,7,1,2,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,4,3,5,7,1,2,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,3,4,5,7,1,2,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,3,5,6,7,1,2,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,4,5,6,7,1,2,8]=>0000100=>[4,1,2]=>[2,1,4]
[7,6,5,4,2,1,3,8]=>1111100=>[5,2]=>[2,5]
[6,5,7,4,2,1,3,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,6,4,5,2,1,3,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,5,4,6,2,1,3,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,4,5,6,2,1,3,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,4,6,7,2,1,3,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,5,6,7,2,1,3,8]=>0001100=>[3,2,2]=>[2,2,3]
[7,6,5,4,1,2,3,8]=>1111000=>[4,3]=>[3,4]
[7,5,6,4,1,2,3,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,6,7,4,1,2,3,8]=>0011000=>[2,2,3]=>[3,2,2]
[7,6,4,5,1,2,3,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,5,4,6,1,2,3,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,5,6,1,2,3,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,4,6,7,1,2,3,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,5,6,7,1,2,3,8]=>0001000=>[3,1,3]=>[3,1,3]
[7,6,5,3,2,1,4,8]=>1111100=>[5,2]=>[2,5]
[7,6,5,2,3,1,4,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,7,5,2,3,1,4,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,5,6,2,3,1,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,5,7,2,3,1,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,7,2,3,1,4,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,5,6,3,1,2,4,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,6,5,2,1,3,4,8]=>1111000=>[4,3]=>[3,4]
[6,7,5,2,1,3,4,8]=>0111000=>[1,3,3]=>[3,3,1]
[7,5,6,2,1,3,4,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,6,7,2,1,3,4,8]=>0011000=>[2,2,3]=>[3,2,2]
[7,6,5,1,2,3,4,8]=>1110000=>[3,4]=>[4,3]
[6,7,5,1,2,3,4,8]=>0110000=>[1,2,4]=>[4,2,1]
[7,5,6,1,2,3,4,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,5,7,1,2,3,4,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,6,7,1,2,3,4,8]=>0010000=>[2,1,4]=>[4,1,2]
[7,6,4,3,2,1,5,8]=>1111100=>[5,2]=>[2,5]
[6,7,4,3,2,1,5,8]=>0111100=>[1,4,2]=>[2,4,1]
[7,6,3,4,2,1,5,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,6,3,2,4,1,5,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,7,3,2,4,1,5,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,6,2,3,4,1,5,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,7,2,3,4,1,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,6,4,3,1,2,5,8]=>1111000=>[4,3]=>[3,4]
[6,7,3,4,1,2,5,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,6,4,2,1,3,5,8]=>1111000=>[4,3]=>[3,4]
[7,6,3,2,1,4,5,8]=>1111000=>[4,3]=>[3,4]
[6,7,3,2,1,4,5,8]=>0111000=>[1,3,3]=>[3,3,1]
[7,6,2,3,1,4,5,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,7,2,3,1,4,5,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,7,3,1,2,4,5,8]=>0110000=>[1,2,4]=>[4,2,1]
[7,6,1,2,3,4,5,8]=>1100000=>[2,5]=>[5,2]
[6,7,1,2,3,4,5,8]=>0100000=>[1,1,5]=>[5,1,1]
[7,5,4,3,2,1,6,8]=>1111100=>[5,2]=>[2,5]
[7,4,5,3,2,1,6,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,4,3,5,2,1,6,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,3,4,5,2,1,6,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[7,5,4,2,3,1,6,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,3,2,4,1,6,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,2,3,4,1,6,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,4,2,3,5,1,6,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,2,3,4,5,1,6,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[7,5,4,3,1,2,6,8]=>1111000=>[4,3]=>[3,4]
[7,5,3,4,1,2,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,5,2,1,3,6,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,4,5,1,2,3,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,5,3,2,1,4,6,8]=>1111000=>[4,3]=>[3,4]
[7,5,2,3,1,4,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,5,3,1,2,4,6,8]=>1110000=>[3,4]=>[4,3]
[7,5,1,2,3,4,6,8]=>1100000=>[2,5]=>[5,2]
[7,4,3,2,1,5,6,8]=>1111000=>[4,3]=>[3,4]
[7,2,3,4,1,5,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,4,3,1,2,5,6,8]=>1110000=>[3,4]=>[4,3]
[7,3,4,1,2,5,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,4,1,2,3,5,6,8]=>1100000=>[2,5]=>[5,2]
[7,3,2,1,4,5,6,8]=>1110000=>[3,4]=>[4,3]
[7,2,3,1,4,5,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,3,1,2,4,5,6,8]=>1100000=>[2,5]=>[5,2]
[7,2,1,3,4,5,6,8]=>1100000=>[2,5]=>[5,2]
[7,1,2,3,4,5,6,8]=>1000000=>[1,6]=>[6,1]
[6,5,4,3,2,1,7,8]=>1111100=>[5,2]=>[2,5]
[5,6,4,3,2,1,7,8]=>0111100=>[1,4,2]=>[2,4,1]
[5,4,6,3,2,1,7,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,5,6,3,2,1,7,8]=>0011100=>[2,3,2]=>[2,3,2]
[6,5,3,4,2,1,7,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,6,3,4,2,1,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,4,3,6,2,1,7,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,4,5,6,2,1,7,8]=>0001100=>[3,2,2]=>[2,2,3]
[5,4,6,2,3,1,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,3,2,4,1,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,5,2,3,4,1,7,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,6,2,3,4,1,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,4,3,2,5,1,7,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,2,3,4,5,1,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[5,4,3,2,6,1,7,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[4,5,3,2,6,1,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,3,5,2,6,1,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,4,5,2,6,1,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,3,2,4,6,1,7,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,2,3,4,6,1,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,3,2,5,6,1,7,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,4,2,5,6,1,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,2,3,5,6,1,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,2,4,5,6,1,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,3,4,5,6,1,7,8]=>0000100=>[4,1,2]=>[2,1,4]
[6,5,4,3,1,2,7,8]=>1111000=>[4,3]=>[3,4]
[6,4,5,3,1,2,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,4,6,3,1,2,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,6,3,4,1,2,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,4,3,6,1,2,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[4,3,5,6,1,2,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,4,5,6,1,2,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[6,5,4,2,1,3,7,8]=>1111000=>[4,3]=>[3,4]
[5,6,4,2,1,3,7,8]=>0111000=>[1,3,3]=>[3,3,1]
[6,4,5,2,1,3,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,5,6,2,1,3,7,8]=>0011000=>[2,2,3]=>[3,2,2]
[6,5,4,1,2,3,7,8]=>1110000=>[3,4]=>[4,3]
[4,5,6,1,2,3,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[6,5,3,2,1,4,7,8]=>1111000=>[4,3]=>[3,4]
[5,6,3,2,1,4,7,8]=>0111000=>[1,3,3]=>[3,3,1]
[5,6,2,1,3,4,7,8]=>0110000=>[1,2,4]=>[4,2,1]
[6,4,3,2,1,5,7,8]=>1111000=>[4,3]=>[3,4]
[6,3,4,2,1,5,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,4,3,1,2,5,7,8]=>1110000=>[3,4]=>[4,3]
[6,4,2,1,3,5,7,8]=>1110000=>[3,4]=>[4,3]
[6,4,1,2,3,5,7,8]=>1100000=>[2,5]=>[5,2]
[6,3,2,1,4,5,7,8]=>1110000=>[3,4]=>[4,3]
[6,2,3,1,4,5,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,3,1,2,4,5,7,8]=>1100000=>[2,5]=>[5,2]
[6,2,1,3,4,5,7,8]=>1100000=>[2,5]=>[5,2]
[6,1,2,3,4,5,7,8]=>1000000=>[1,6]=>[6,1]
[5,4,3,2,1,6,7,8]=>1111000=>[4,3]=>[3,4]
[4,5,3,2,1,6,7,8]=>0111000=>[1,3,3]=>[3,3,1]
[5,3,4,2,1,6,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,3,5,2,1,6,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[3,4,5,2,1,6,7,8]=>0011000=>[2,2,3]=>[3,2,2]
[5,4,2,3,1,6,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[4,5,2,3,1,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,3,2,4,1,6,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[5,2,3,4,1,6,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,3,2,5,1,6,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[3,4,2,5,1,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,2,3,5,1,6,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,2,4,5,1,6,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,3,4,5,1,6,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[5,4,3,1,2,6,7,8]=>1110000=>[3,4]=>[4,3]
[5,3,4,1,2,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[4,3,5,1,2,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,4,5,1,2,6,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[5,4,2,1,3,6,7,8]=>1110000=>[3,4]=>[4,3]
[4,5,2,1,3,6,7,8]=>0110000=>[1,2,4]=>[4,2,1]
[5,4,1,2,3,6,7,8]=>1100000=>[2,5]=>[5,2]
[4,5,1,2,3,6,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[5,3,2,1,4,6,7,8]=>1110000=>[3,4]=>[4,3]
[5,2,3,1,4,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,3,1,2,4,6,7,8]=>1100000=>[2,5]=>[5,2]
[5,2,1,3,4,6,7,8]=>1100000=>[2,5]=>[5,2]
[5,1,2,3,4,6,7,8]=>1000000=>[1,6]=>[6,1]
[4,3,2,1,5,6,7,8]=>1110000=>[3,4]=>[4,3]
[3,4,2,1,5,6,7,8]=>0110000=>[1,2,4]=>[4,2,1]
[4,2,3,1,5,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,2,4,1,5,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[2,3,4,1,5,6,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[4,3,1,2,5,6,7,8]=>1100000=>[2,5]=>[5,2]
[3,4,1,2,5,6,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[4,2,1,3,5,6,7,8]=>1100000=>[2,5]=>[5,2]
[4,1,2,3,5,6,7,8]=>1000000=>[1,6]=>[6,1]
[3,2,1,4,5,6,7,8]=>1100000=>[2,5]=>[5,2]
[2,3,1,4,5,6,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[3,1,2,4,5,6,7,8]=>1000000=>[1,6]=>[6,1]
[2,1,3,4,5,6,7,8]=>1000000=>[1,6]=>[6,1]
[1,2,3,4,5,6,7,8]=>0000000=>[7]=>[7]
[6,8,7,5,4,3,2,1]=>0111111=>[1,6]=>[6,1]
[5,8,7,6,4,3,2,1]=>0111111=>[1,6]=>[6,1]
[5,7,8,6,4,3,2,1]=>0011111=>[2,5]=>[5,2]
[6,5,8,7,4,3,2,1]=>1011111=>[1,1,5]=>[5,1,1]
[5,6,8,7,4,3,2,1]=>0011111=>[2,5]=>[5,2]
[5,7,6,8,4,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[4,8,7,6,5,3,2,1]=>0111111=>[1,6]=>[6,1]
[4,7,8,6,5,3,2,1]=>0011111=>[2,5]=>[5,2]
[4,6,8,7,5,3,2,1]=>0011111=>[2,5]=>[5,2]
[4,7,6,8,5,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[4,6,7,8,5,3,2,1]=>0001111=>[3,4]=>[4,3]
[5,4,7,8,6,3,2,1]=>1001111=>[1,2,4]=>[4,2,1]
[4,5,8,7,6,3,2,1]=>0011111=>[2,5]=>[5,2]
[4,5,7,8,6,3,2,1]=>0001111=>[3,4]=>[4,3]
[6,5,4,8,7,3,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[5,6,4,8,7,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[4,6,5,8,7,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[4,5,6,8,7,3,2,1]=>0001111=>[3,4]=>[4,3]
[5,7,6,4,8,3,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,7,6,5,8,3,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,6,7,5,8,3,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[5,4,7,6,8,3,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,5,7,6,8,3,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[4,6,5,7,8,3,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,8,7,6,5,4,2,1]=>0111111=>[1,6]=>[6,1]
[3,7,8,6,5,4,2,1]=>0011111=>[2,5]=>[5,2]
[3,6,8,7,5,4,2,1]=>0011111=>[2,5]=>[5,2]
[3,7,6,8,5,4,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[3,5,8,7,6,4,2,1]=>0011111=>[2,5]=>[5,2]
[3,5,7,8,6,4,2,1]=>0001111=>[3,4]=>[4,3]
[3,5,6,8,7,4,2,1]=>0001111=>[3,4]=>[4,3]
[3,7,6,5,8,4,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[3,6,7,5,8,4,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[3,5,7,6,8,4,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[3,5,6,7,8,4,2,1]=>0000111=>[4,3]=>[3,4]
[4,3,8,7,6,5,2,1]=>1011111=>[1,1,5]=>[5,1,1]
[4,3,7,8,6,5,2,1]=>1001111=>[1,2,4]=>[4,2,1]
[4,3,6,7,8,5,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[3,4,8,7,6,5,2,1]=>0011111=>[2,5]=>[5,2]
[3,4,6,7,8,5,2,1]=>0000111=>[4,3]=>[3,4]
[5,4,3,8,7,6,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[5,4,3,7,8,6,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[3,5,4,7,8,6,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,4,5,8,7,6,2,1]=>0001111=>[3,4]=>[4,3]
[3,4,5,7,8,6,2,1]=>0000111=>[4,3]=>[3,4]
[6,5,4,3,8,7,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[5,6,4,3,8,7,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,5,6,3,8,7,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[4,3,6,5,8,7,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,4,3,6,8,7,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[4,5,3,6,8,7,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,4,5,6,8,7,2,1]=>0000111=>[4,3]=>[3,4]
[5,7,6,4,3,8,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,7,6,5,3,8,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,4,7,6,3,8,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,7,6,5,4,8,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[3,5,7,6,4,8,2,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,5,6,7,4,8,2,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,3,7,6,5,8,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,7,6,5,8,2,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,4,6,7,5,8,2,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,5,3,7,6,8,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,5,4,7,6,8,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,5,7,6,8,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,4,5,7,6,8,2,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,6,5,4,7,8,2,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,5,6,4,7,8,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,3,6,5,7,8,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,4,6,5,7,8,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,5,4,6,7,8,2,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,8,7,6,5,4,3,1]=>0111111=>[1,6]=>[6,1]
[2,7,8,6,5,4,3,1]=>0011111=>[2,5]=>[5,2]
[2,6,8,7,5,4,3,1]=>0011111=>[2,5]=>[5,2]
[2,7,6,8,5,4,3,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[2,6,7,8,5,4,3,1]=>0001111=>[3,4]=>[4,3]
[2,5,8,7,6,4,3,1]=>0011111=>[2,5]=>[5,2]
[2,6,7,5,8,4,3,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,6,5,7,8,4,3,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,5,6,7,8,4,3,1]=>0000111=>[4,3]=>[3,4]
[2,4,8,7,6,5,3,1]=>0011111=>[2,5]=>[5,2]
[2,4,7,8,6,5,3,1]=>0001111=>[3,4]=>[4,3]
[2,4,6,8,7,5,3,1]=>0001111=>[3,4]=>[4,3]
[2,4,6,7,8,5,3,1]=>0000111=>[4,3]=>[3,4]
[2,5,4,8,7,6,3,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[2,5,4,7,8,6,3,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,4,5,7,8,6,3,1]=>0000111=>[4,3]=>[3,4]
[2,6,5,4,8,7,3,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,5,6,4,8,7,3,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,4,6,5,8,7,3,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,4,5,6,8,7,3,1]=>0000111=>[4,3]=>[3,4]
[2,7,6,5,4,8,3,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,6,7,5,4,8,3,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,5,6,7,4,8,3,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,4,7,6,5,8,3,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,4,6,7,5,8,3,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,5,4,7,6,8,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,5,4,7,8,3,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,5,6,4,7,8,3,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,4,6,5,7,8,3,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,5,4,6,7,8,3,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,4,5,6,7,8,3,1]=>0000011=>[5,2]=>[2,5]
[3,2,8,7,6,5,4,1]=>1011111=>[1,1,5]=>[5,1,1]
[3,2,6,8,7,5,4,1]=>1001111=>[1,2,4]=>[4,2,1]
[3,2,5,7,8,6,4,1]=>1000111=>[1,3,3]=>[3,3,1]
[3,2,6,5,8,7,4,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,2,5,7,6,8,4,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,5,6,7,8,4,1]=>1000011=>[1,4,2]=>[2,4,1]
[2,3,8,7,6,5,4,1]=>0011111=>[2,5]=>[5,2]
[2,3,6,7,8,5,4,1]=>0000111=>[4,3]=>[3,4]
[2,3,5,7,8,6,4,1]=>0000111=>[4,3]=>[3,4]
[2,3,6,5,8,7,4,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,3,5,6,8,7,4,1]=>0000111=>[4,3]=>[3,4]
[2,3,7,6,5,8,4,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,3,5,7,6,8,4,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,3,5,6,7,8,4,1]=>0000011=>[5,2]=>[2,5]
[4,3,2,8,7,6,5,1]=>1101111=>[2,1,4]=>[4,1,2]
[4,3,2,7,8,6,5,1]=>1100111=>[2,2,3]=>[3,2,2]
[3,4,2,8,7,6,5,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[3,4,2,7,8,6,5,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,4,3,8,7,6,5,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[2,4,3,6,8,7,5,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,4,3,6,7,8,5,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,2,4,8,7,6,5,1]=>1001111=>[1,2,4]=>[4,2,1]
[3,2,4,7,8,6,5,1]=>1000111=>[1,3,3]=>[3,3,1]
[2,3,4,8,7,6,5,1]=>0001111=>[3,4]=>[4,3]
[2,3,4,7,8,6,5,1]=>0000111=>[4,3]=>[3,4]
[2,3,4,6,8,7,5,1]=>0000111=>[4,3]=>[3,4]
[2,3,4,7,6,8,5,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,3,4,6,7,8,5,1]=>0000011=>[5,2]=>[2,5]
[5,4,3,2,8,7,6,1]=>1110111=>[3,1,3]=>[3,1,3]
[5,4,3,2,7,8,6,1]=>1110011=>[3,2,2]=>[2,2,3]
[3,5,4,2,7,8,6,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,4,5,2,7,8,6,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,5,4,3,8,7,6,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,5,4,3,7,8,6,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,4,5,3,8,7,6,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,4,5,3,7,8,6,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,2,5,4,7,8,6,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,3,5,4,8,7,6,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,3,5,4,7,8,6,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,3,2,5,8,7,6,1]=>1100111=>[2,2,3]=>[3,2,2]
[4,3,2,5,7,8,6,1]=>1100011=>[2,3,2]=>[2,3,2]
[3,4,2,5,8,7,6,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,4,2,5,7,8,6,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,4,3,5,8,7,6,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,2,4,5,7,8,6,1]=>1000011=>[1,4,2]=>[2,4,1]
[2,3,4,5,8,7,6,1]=>0000111=>[4,3]=>[3,4]
[2,3,4,5,7,8,6,1]=>0000011=>[5,2]=>[2,5]
[6,5,4,3,2,8,7,1]=>1111011=>[4,1,2]=>[2,1,4]
[4,6,5,3,2,8,7,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,4,6,3,2,8,7,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,5,6,3,2,8,7,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,6,5,4,2,8,7,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[3,5,6,4,2,8,7,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,3,6,5,2,8,7,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,4,3,6,2,8,7,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,5,3,6,2,8,7,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,5,4,6,2,8,7,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,4,5,6,2,8,7,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,6,5,4,3,8,7,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,4,6,5,3,8,7,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,4,5,6,3,8,7,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,2,6,5,4,8,7,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,3,5,6,4,8,7,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,3,2,6,5,8,7,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,3,6,5,8,7,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,4,6,5,8,7,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,3,4,6,5,8,7,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[5,4,3,2,6,8,7,1]=>1110011=>[3,2,2]=>[2,2,3]
[4,5,3,2,6,8,7,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,5,4,3,6,8,7,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,4,5,3,6,8,7,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,2,5,4,6,8,7,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,3,2,5,6,8,7,1]=>1100011=>[2,3,2]=>[2,3,2]
[3,4,2,5,6,8,7,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,4,3,5,6,8,7,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,2,4,5,6,8,7,1]=>1000011=>[1,4,2]=>[2,4,1]
[2,3,4,5,6,8,7,1]=>0000011=>[5,2]=>[2,5]
[5,7,6,4,3,2,8,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[4,7,6,5,3,2,8,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[4,6,7,5,3,2,8,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[4,6,5,7,3,2,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,7,6,4,2,8,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[3,5,6,7,4,2,8,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,3,7,6,5,2,8,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,3,6,7,5,2,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,4,7,6,5,2,8,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[3,4,6,7,5,2,8,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[5,4,3,7,6,2,8,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,5,3,7,6,2,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,4,7,6,2,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,5,7,6,2,8,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,6,5,3,7,2,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,5,4,7,2,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,5,6,4,7,2,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,6,5,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,6,5,7,2,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,4,6,7,2,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,7,6,5,4,3,8,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[2,6,5,7,4,3,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,5,6,7,4,3,8,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,4,6,7,5,3,8,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,5,4,7,6,3,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,6,5,7,3,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,5,4,6,7,3,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,5,6,7,3,8,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[3,2,7,6,5,4,8,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,2,6,7,5,4,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,2,5,7,6,4,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,2,6,5,7,4,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,5,6,7,4,8,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,3,7,6,5,4,8,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,3,5,7,6,4,8,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,3,5,6,7,4,8,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[4,3,2,7,6,5,8,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,3,2,6,7,5,8,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,4,2,7,6,5,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,2,6,7,5,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,3,7,6,5,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,3,6,7,5,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,2,4,7,6,5,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,3,4,7,6,5,8,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,3,4,6,7,5,8,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[5,4,3,2,7,6,8,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,5,4,2,7,6,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,5,2,7,6,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,5,2,7,6,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,5,4,3,7,6,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,2,5,4,7,6,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,5,4,7,6,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,2,5,7,6,8,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,4,2,5,7,6,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,3,5,7,6,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,2,4,5,7,6,8,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,3,4,5,7,6,8,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[3,6,5,4,2,7,8,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[3,5,6,4,2,7,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,4,6,5,2,7,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,5,4,6,2,7,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,5,4,3,7,8,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,5,6,4,3,7,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,4,6,5,3,7,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,5,4,6,3,7,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,5,6,3,7,8,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,2,5,6,4,7,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,3,6,5,4,7,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,3,5,6,4,7,8,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,3,2,6,5,7,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,4,2,6,5,7,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,3,6,5,7,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,3,4,6,5,7,8,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,5,4,2,6,7,8,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,5,4,3,6,7,8,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,4,5,3,6,7,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,2,5,4,6,7,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,3,5,4,6,7,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,4,3,5,6,7,8,1]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,8,7,6,5,4,3,2]=>0111111=>[1,6]=>[6,1]
[1,7,8,6,5,4,3,2]=>0011111=>[2,5]=>[5,2]
[1,6,8,7,5,4,3,2]=>0011111=>[2,5]=>[5,2]
[1,7,6,8,5,4,3,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[1,6,7,8,5,4,3,2]=>0001111=>[3,4]=>[4,3]
[1,5,8,7,6,4,3,2]=>0011111=>[2,5]=>[5,2]
[1,6,5,8,7,4,3,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[1,7,6,5,8,4,3,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,6,7,5,8,4,3,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,5,7,6,8,4,3,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,6,5,7,8,4,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,5,6,7,8,4,3,2]=>0000111=>[4,3]=>[3,4]
[1,4,8,7,6,5,3,2]=>0011111=>[2,5]=>[5,2]
[1,4,7,8,6,5,3,2]=>0001111=>[3,4]=>[4,3]
[1,4,6,8,7,5,3,2]=>0001111=>[3,4]=>[4,3]
[1,4,6,7,8,5,3,2]=>0000111=>[4,3]=>[3,4]
[1,5,4,7,8,6,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,4,5,8,7,6,3,2]=>0001111=>[3,4]=>[4,3]
[1,4,5,7,8,6,3,2]=>0000111=>[4,3]=>[3,4]
[1,6,5,4,8,7,3,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,4,6,5,8,7,3,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,7,6,5,4,8,3,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,4,7,6,5,8,3,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,4,6,7,5,8,3,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,6,5,4,7,8,3,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,5,6,4,7,8,3,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,5,4,6,7,8,3,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,4,5,6,7,8,3,2]=>0000011=>[5,2]=>[2,5]
[1,3,8,7,6,5,4,2]=>0011111=>[2,5]=>[5,2]
[1,3,7,8,6,5,4,2]=>0001111=>[3,4]=>[4,3]
[1,3,6,8,7,5,4,2]=>0001111=>[3,4]=>[4,3]
[1,3,6,7,8,5,4,2]=>0000111=>[4,3]=>[3,4]
[1,3,5,8,7,6,4,2]=>0001111=>[3,4]=>[4,3]
[1,3,5,7,8,6,4,2]=>0000111=>[4,3]=>[3,4]
[1,3,5,6,8,7,4,2]=>0000111=>[4,3]=>[3,4]
[1,3,6,7,5,8,4,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,3,5,7,6,8,4,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,3,6,5,7,8,4,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,5,6,7,8,4,2]=>0000011=>[5,2]=>[2,5]
[1,4,3,8,7,6,5,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[1,4,3,7,8,6,5,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,4,3,6,8,7,5,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,4,3,7,6,8,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,4,3,6,7,8,5,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,3,4,8,7,6,5,2]=>0001111=>[3,4]=>[4,3]
[1,3,4,7,6,8,5,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,3,4,6,7,8,5,2]=>0000011=>[5,2]=>[2,5]
[1,5,4,3,8,7,6,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,4,5,3,8,7,6,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,4,5,3,7,8,6,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,5,4,8,7,6,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,3,5,4,7,8,6,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,4,3,5,8,7,6,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,4,3,5,7,8,6,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,3,4,5,8,7,6,2]=>0000111=>[4,3]=>[3,4]
[1,3,4,5,7,8,6,2]=>0000011=>[5,2]=>[2,5]
[1,6,5,4,3,8,7,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,5,6,4,3,8,7,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,4,6,5,3,8,7,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,4,5,6,3,8,7,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,3,6,5,4,8,7,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,4,3,6,5,8,7,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,5,4,3,6,8,7,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,4,5,3,6,8,7,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,4,5,6,8,7,2]=>0000011=>[5,2]=>[2,5]
[1,7,6,5,4,3,8,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[1,6,7,5,4,3,8,2]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,6,5,7,4,3,8,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,4,6,7,5,3,8,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,5,6,4,7,3,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,6,5,7,3,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,5,4,6,7,3,8,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,4,5,6,7,3,8,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,3,5,7,6,4,8,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,3,6,5,7,4,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,5,6,7,4,8,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,4,3,6,7,5,8,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,4,7,6,5,8,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,3,4,6,7,5,8,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,3,5,4,7,6,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,4,5,7,6,8,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,6,5,4,3,7,8,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[1,5,4,6,3,7,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,5,6,4,7,8,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,4,3,6,5,7,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,4,6,5,7,8,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,5,4,3,6,7,8,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[1,4,5,3,6,7,8,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,3,5,4,6,7,8,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,4,3,5,6,7,8,2]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,3,4,5,6,7,8,2]=>0000001=>[6,1]=>[1,6]
[2,1,8,7,6,5,4,3]=>1011111=>[1,1,5]=>[5,1,1]
[2,1,7,8,6,5,4,3]=>1001111=>[1,2,4]=>[4,2,1]
[2,1,6,8,7,5,4,3]=>1001111=>[1,2,4]=>[4,2,1]
[2,1,7,6,8,5,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,1,6,7,8,5,4,3]=>1000111=>[1,3,3]=>[3,3,1]
[2,1,5,8,7,6,4,3]=>1001111=>[1,2,4]=>[4,2,1]
[2,1,5,7,8,6,4,3]=>1000111=>[1,3,3]=>[3,3,1]
[2,1,6,5,8,7,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,1,5,6,8,7,4,3]=>1000111=>[1,3,3]=>[3,3,1]
[2,1,7,6,5,8,4,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,6,7,5,8,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,5,7,6,8,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,6,5,7,8,4,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,5,6,7,8,4,3]=>1000011=>[1,4,2]=>[2,4,1]
[2,1,4,8,7,6,5,3]=>1001111=>[1,2,4]=>[4,2,1]
[2,1,4,7,8,6,5,3]=>1000111=>[1,3,3]=>[3,3,1]
[2,1,4,6,8,7,5,3]=>1000111=>[1,3,3]=>[3,3,1]
[2,1,4,7,6,8,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,4,6,7,8,5,3]=>1000011=>[1,4,2]=>[2,4,1]
[2,1,5,4,8,7,6,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,1,5,4,7,8,6,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,4,5,8,7,6,3]=>1000111=>[1,3,3]=>[3,3,1]
[2,1,4,5,7,8,6,3]=>1000011=>[1,4,2]=>[2,4,1]
[2,1,6,5,4,8,7,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,5,6,4,8,7,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,4,6,5,8,7,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,5,4,6,8,7,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,4,5,6,8,7,3]=>1000011=>[1,4,2]=>[2,4,1]
[2,1,7,6,5,4,8,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,6,7,5,4,8,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,5,7,6,4,8,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,6,5,7,4,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,5,6,7,4,8,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,4,7,6,5,8,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,4,6,7,5,8,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,5,4,7,6,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,5,6,4,7,8,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,1,5,4,6,7,8,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,1,4,5,6,7,8,3]=>1000001=>[1,5,1]=>[1,5,1]
[1,2,8,7,6,5,4,3]=>0011111=>[2,5]=>[5,2]
[1,2,7,8,6,5,4,3]=>0001111=>[3,4]=>[4,3]
[1,2,7,6,8,5,4,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,2,6,7,8,5,4,3]=>0000111=>[4,3]=>[3,4]
[1,2,5,8,7,6,4,3]=>0001111=>[3,4]=>[4,3]
[1,2,6,5,8,7,4,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,2,5,6,8,7,4,3]=>0000111=>[4,3]=>[3,4]
[1,2,7,6,5,8,4,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,2,5,7,6,8,4,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,6,5,7,8,4,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,5,6,7,8,4,3]=>0000011=>[5,2]=>[2,5]
[1,2,4,8,7,6,5,3]=>0001111=>[3,4]=>[4,3]
[1,2,4,7,8,6,5,3]=>0000111=>[4,3]=>[3,4]
[1,2,4,6,8,7,5,3]=>0000111=>[4,3]=>[3,4]
[1,2,4,7,6,8,5,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,4,6,7,8,5,3]=>0000011=>[5,2]=>[2,5]
[1,2,5,4,8,7,6,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,2,4,5,8,7,6,3]=>0000111=>[4,3]=>[3,4]
[1,2,4,5,7,8,6,3]=>0000011=>[5,2]=>[2,5]
[1,2,6,5,4,8,7,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,2,5,4,6,8,7,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,4,5,6,8,7,3]=>0000011=>[5,2]=>[2,5]
[1,2,7,6,5,4,8,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,2,5,7,6,4,8,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,5,6,7,4,8,3]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,4,7,6,5,8,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,5,4,7,6,8,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,6,5,4,7,8,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,2,5,6,4,7,8,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,4,6,5,7,8,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,5,4,6,7,8,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,4,5,6,7,8,3]=>0000001=>[6,1]=>[1,6]
[3,2,1,8,7,6,5,4]=>1101111=>[2,1,4]=>[4,1,2]
[3,2,1,7,8,6,5,4]=>1100111=>[2,2,3]=>[3,2,2]
[3,2,1,6,8,7,5,4]=>1100111=>[2,2,3]=>[3,2,2]
[3,2,1,7,6,8,5,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,2,1,6,7,8,5,4]=>1100011=>[2,3,2]=>[2,3,2]
[3,2,1,5,8,7,6,4]=>1100111=>[2,2,3]=>[3,2,2]
[3,2,1,5,7,8,6,4]=>1100011=>[2,3,2]=>[2,3,2]
[3,2,1,6,5,8,7,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,2,1,5,6,8,7,4]=>1100011=>[2,3,2]=>[2,3,2]
[3,2,1,7,6,5,8,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,2,1,6,7,5,8,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,1,5,7,6,8,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,1,6,5,7,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,2,1,5,6,7,8,4]=>1100001=>[2,4,1]=>[1,4,2]
[2,3,1,8,7,6,5,4]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[2,3,1,7,8,6,5,4]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,3,1,6,8,7,5,4]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,3,1,7,6,8,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,3,1,6,7,8,5,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,3,1,5,7,8,6,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,3,1,6,5,8,7,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,3,1,7,6,5,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,3,1,6,7,5,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,3,1,5,7,6,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,3,1,5,6,7,8,4]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,3,2,8,7,6,5,4]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[1,3,2,6,8,7,5,4]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,3,2,7,6,8,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,3,2,6,7,8,5,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,3,2,5,8,7,6,4]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,3,2,5,7,8,6,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,3,2,6,5,8,7,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,3,2,5,6,8,7,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,3,2,7,6,5,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,3,2,6,7,5,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,2,5,7,6,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,2,6,5,7,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,2,5,6,7,8,4]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,1,3,8,7,6,5,4]=>1001111=>[1,2,4]=>[4,2,1]
[2,1,3,7,8,6,5,4]=>1000111=>[1,3,3]=>[3,3,1]
[2,1,3,6,8,7,5,4]=>1000111=>[1,3,3]=>[3,3,1]
[2,1,3,6,7,8,5,4]=>1000011=>[1,4,2]=>[2,4,1]
[2,1,3,6,5,8,7,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,3,5,7,6,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,3,5,6,7,8,4]=>1000001=>[1,5,1]=>[1,5,1]
[1,2,3,8,7,6,5,4]=>0001111=>[3,4]=>[4,3]
[1,2,3,7,8,6,5,4]=>0000111=>[4,3]=>[3,4]
[1,2,3,6,8,7,5,4]=>0000111=>[4,3]=>[3,4]
[1,2,3,7,6,8,5,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,3,6,7,8,5,4]=>0000011=>[5,2]=>[2,5]
[1,2,3,5,8,7,6,4]=>0000111=>[4,3]=>[3,4]
[1,2,3,5,7,8,6,4]=>0000011=>[5,2]=>[2,5]
[1,2,3,6,5,8,7,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,3,5,6,8,7,4]=>0000011=>[5,2]=>[2,5]
[1,2,3,7,6,5,8,4]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,3,6,7,5,8,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,5,7,6,8,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,6,5,7,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,3,5,6,7,8,4]=>0000001=>[6,1]=>[1,6]
[4,3,2,1,8,7,6,5]=>1110111=>[3,1,3]=>[3,1,3]
[4,3,2,1,7,8,6,5]=>1110011=>[3,2,2]=>[2,2,3]
[4,3,2,1,6,8,7,5]=>1110011=>[3,2,2]=>[2,2,3]
[4,3,2,1,7,6,8,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,3,2,1,6,7,8,5]=>1110001=>[3,3,1]=>[1,3,3]
[3,4,2,1,8,7,6,5]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[3,4,2,1,7,8,6,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,4,2,1,6,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,4,2,1,7,6,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,2,1,6,7,8,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,4,3,1,8,7,6,5]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,4,3,1,7,8,6,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,4,3,1,6,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,4,3,1,7,6,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,4,3,1,6,7,8,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,2,4,1,8,7,6,5]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,2,4,1,7,8,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,2,4,1,6,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,2,4,1,7,6,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,4,1,6,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,3,4,1,8,7,6,5]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,3,4,1,7,8,6,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,3,4,1,6,8,7,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,3,4,1,7,6,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,4,1,6,7,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,4,3,2,8,7,6,5]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,4,3,2,6,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,4,3,2,7,6,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,3,2,6,7,8,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[1,3,4,2,8,7,6,5]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,3,4,2,7,8,6,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,4,2,6,8,7,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,4,2,7,6,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,4,2,6,7,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,4,3,8,7,6,5]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,1,4,3,7,8,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,4,3,6,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,4,3,7,6,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,4,3,6,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,2,4,3,8,7,6,5]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,2,4,3,7,8,6,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,4,3,6,8,7,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,4,3,7,6,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,4,3,6,7,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,2,1,4,8,7,6,5]=>1100111=>[2,2,3]=>[3,2,2]
[3,2,1,4,7,8,6,5]=>1100011=>[2,3,2]=>[2,3,2]
[3,2,1,4,6,8,7,5]=>1100011=>[2,3,2]=>[2,3,2]
[3,2,1,4,7,6,8,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,1,4,6,7,8,5]=>1100001=>[2,4,1]=>[1,4,2]
[2,3,1,4,8,7,6,5]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,3,1,4,7,8,6,5]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,3,1,4,7,6,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,3,1,4,6,7,8,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,3,2,4,8,7,6,5]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,3,2,4,6,8,7,5]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,3,2,4,7,6,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,2,4,6,7,8,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,1,3,4,8,7,6,5]=>1000111=>[1,3,3]=>[3,3,1]
[2,1,3,4,7,8,6,5]=>1000011=>[1,4,2]=>[2,4,1]
[2,1,3,4,7,6,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,3,4,6,7,8,5]=>1000001=>[1,5,1]=>[1,5,1]
[1,2,3,4,8,7,6,5]=>0000111=>[4,3]=>[3,4]
[1,2,3,4,7,8,6,5]=>0000011=>[5,2]=>[2,5]
[1,2,3,4,6,8,7,5]=>0000011=>[5,2]=>[2,5]
[1,2,3,4,7,6,8,5]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,4,6,7,8,5]=>0000001=>[6,1]=>[1,6]
[5,4,3,2,1,8,7,6]=>1111011=>[4,1,2]=>[2,1,4]
[5,4,3,2,1,7,8,6]=>1111001=>[4,2,1]=>[1,2,4]
[4,5,3,2,1,8,7,6]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[3,5,4,2,1,8,7,6]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[3,5,4,2,1,7,8,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[4,3,5,2,1,8,7,6]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,5,2,1,8,7,6]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,4,5,2,1,7,8,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,5,4,3,1,8,7,6]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,5,4,3,1,7,8,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,4,5,3,1,8,7,6]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,4,5,3,1,7,8,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,2,5,4,1,8,7,6]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,2,5,4,1,7,8,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,3,5,4,1,8,7,6]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,3,2,5,1,8,7,6]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,3,2,5,1,7,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,4,2,5,1,8,7,6]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,4,2,5,1,7,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,3,5,1,8,7,6]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,4,3,5,1,7,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,4,5,1,8,7,6]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,3,4,5,1,8,7,6]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,3,4,5,1,7,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,5,4,3,2,8,7,6]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,5,4,3,2,7,8,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[1,4,5,3,2,8,7,6]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,4,5,3,2,7,8,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,3,5,4,2,7,8,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,4,3,5,2,8,7,6]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,4,3,5,2,7,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,4,5,2,8,7,6]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,3,4,5,2,7,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,1,5,4,3,8,7,6]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,4,5,3,8,7,6]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,2,5,4,3,8,7,6]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,2,5,4,3,7,8,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,2,4,5,3,8,7,6]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,4,5,3,7,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,3,2,5,4,8,7,6]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,3,2,5,4,7,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,1,3,5,4,8,7,6]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,3,5,4,7,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,2,3,5,4,8,7,6]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,3,5,4,7,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,3,2,1,5,8,7,6]=>1110011=>[3,2,2]=>[2,2,3]
[4,3,2,1,5,7,8,6]=>1110001=>[3,3,1]=>[1,3,3]
[2,4,3,1,5,8,7,6]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,2,4,1,5,8,7,6]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,2,4,1,5,7,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,3,4,1,5,8,7,6]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,3,4,1,5,7,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,4,3,2,5,8,7,6]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,4,3,2,5,7,8,6]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[1,3,4,2,5,8,7,6]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,4,2,5,7,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,4,3,5,8,7,6]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,4,3,5,7,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,2,4,3,5,8,7,6]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,4,3,5,7,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,2,1,4,5,8,7,6]=>1100011=>[2,3,2]=>[2,3,2]
[3,2,1,4,5,7,8,6]=>1100001=>[2,4,1]=>[1,4,2]
[2,3,1,4,5,7,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,3,2,4,5,8,7,6]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,3,2,4,5,7,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,1,3,4,5,8,7,6]=>1000011=>[1,4,2]=>[2,4,1]
[2,1,3,4,5,7,8,6]=>1000001=>[1,5,1]=>[1,5,1]
[1,2,3,4,5,8,7,6]=>0000011=>[5,2]=>[2,5]
[1,2,3,4,5,7,8,6]=>0000001=>[6,1]=>[1,6]
[6,5,4,3,2,1,8,7]=>1111101=>[5,1,1]=>[1,1,5]
[5,6,4,3,2,1,8,7]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[4,6,5,3,2,1,8,7]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,4,6,3,2,1,8,7]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,5,6,3,2,1,8,7]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[3,6,5,4,2,1,8,7]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[3,5,6,4,2,1,8,7]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[4,3,6,5,2,1,8,7]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,4,6,5,2,1,8,7]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,4,3,6,2,1,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,5,3,6,2,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,3,5,6,2,1,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,4,5,6,2,1,8,7]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,6,5,4,3,1,8,7]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[2,5,6,4,3,1,8,7]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,4,6,5,3,1,8,7]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[3,2,6,5,4,1,8,7]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,2,5,6,4,1,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,3,6,5,4,1,8,7]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,3,5,6,4,1,8,7]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,3,2,6,5,1,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,2,6,5,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,3,6,5,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,4,3,2,6,1,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,5,3,2,6,1,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,5,4,2,6,1,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,5,2,6,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,5,2,6,1,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,5,4,3,6,1,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,4,5,3,6,1,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,2,5,4,6,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,2,5,6,1,8,7]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,4,2,5,6,1,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,3,5,6,1,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,3,4,5,6,1,8,7]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,6,5,4,3,2,8,7]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[1,5,6,4,3,2,8,7]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,5,4,6,3,2,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,3,6,5,4,2,8,7]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,3,4,5,6,2,8,7]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[2,1,6,5,4,3,8,7]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,5,6,4,3,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,4,6,5,3,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,5,4,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,4,5,6,3,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,2,4,5,6,3,8,7]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[3,2,1,6,5,4,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,1,6,5,4,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,3,2,6,5,4,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,3,2,5,6,4,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,3,5,6,4,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,2,3,6,5,4,8,7]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,3,5,6,4,8,7]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[4,3,2,1,6,5,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,2,1,6,5,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,4,3,1,6,5,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,2,4,1,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,4,1,6,5,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,4,2,6,5,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,1,4,3,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,2,4,3,6,5,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,1,4,6,5,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,2,4,6,5,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,3,4,6,5,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,2,3,4,6,5,8,7]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[5,4,3,2,1,6,8,7]=>1111001=>[4,2,1]=>[1,2,4]
[4,5,3,2,1,6,8,7]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[3,5,4,2,1,6,8,7]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[4,3,5,2,1,6,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,4,5,2,1,6,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,5,4,3,1,6,8,7]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,4,5,3,1,6,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,2,5,4,1,6,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,3,5,4,1,6,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,4,3,5,1,6,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,3,4,5,1,6,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,4,5,3,2,6,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,3,5,4,2,6,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,3,4,5,2,6,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,1,4,5,3,6,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,2,5,4,3,6,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,1,3,5,4,6,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,2,3,5,4,6,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,3,2,1,5,6,8,7]=>1110001=>[3,3,1]=>[1,3,3]
[3,2,4,1,5,6,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,3,4,1,5,6,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,4,3,2,5,6,8,7]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[1,3,4,2,5,6,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,4,3,5,6,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,2,4,3,5,6,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,2,1,4,5,6,8,7]=>1100001=>[2,4,1]=>[1,4,2]
[2,3,1,4,5,6,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,3,2,4,5,6,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,1,3,4,5,6,8,7]=>1000001=>[1,5,1]=>[1,5,1]
[1,2,3,4,5,6,8,7]=>0000001=>[6,1]=>[1,6]
[5,7,6,4,3,2,1,8]=>0111110=>[1,5,1]=>[1,5,1]
[4,7,6,5,3,2,1,8]=>0111110=>[1,5,1]=>[1,5,1]
[4,6,7,5,3,2,1,8]=>0011110=>[2,4,1]=>[1,4,2]
[5,4,7,6,3,2,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[4,5,7,6,3,2,1,8]=>0011110=>[2,4,1]=>[1,4,2]
[4,6,5,7,3,2,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,5,7,6,4,2,1,8]=>0011110=>[2,4,1]=>[1,4,2]
[3,5,6,7,4,2,1,8]=>0001110=>[3,3,1]=>[1,3,3]
[4,3,7,6,5,2,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[3,4,7,6,5,2,1,8]=>0011110=>[2,4,1]=>[1,4,2]
[5,4,3,7,6,2,1,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[4,5,3,7,6,2,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,5,4,7,6,2,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,3,5,7,6,2,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,6,5,4,7,2,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,5,6,4,7,2,1,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,3,6,5,7,2,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,7,6,5,4,3,1,8]=>0111110=>[1,5,1]=>[1,5,1]
[2,6,7,5,4,3,1,8]=>0011110=>[2,4,1]=>[1,4,2]
[2,5,7,6,4,3,1,8]=>0011110=>[2,4,1]=>[1,4,2]
[2,5,6,7,4,3,1,8]=>0001110=>[3,3,1]=>[1,3,3]
[2,4,6,7,5,3,1,8]=>0001110=>[3,3,1]=>[1,3,3]
[2,5,4,7,6,3,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,5,6,4,7,3,1,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,5,4,6,7,3,1,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,4,5,6,7,3,1,8]=>0000110=>[4,2,1]=>[1,2,4]
[3,2,7,6,5,4,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[3,2,6,7,5,4,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,2,5,7,6,4,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,2,6,5,7,4,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,5,6,7,4,1,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,3,7,6,5,4,1,8]=>0011110=>[2,4,1]=>[1,4,2]
[2,3,6,7,5,4,1,8]=>0001110=>[3,3,1]=>[1,3,3]
[2,3,5,7,6,4,1,8]=>0001110=>[3,3,1]=>[1,3,3]
[2,3,6,5,7,4,1,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,3,5,6,7,4,1,8]=>0000110=>[4,2,1]=>[1,2,4]
[4,3,2,6,7,5,1,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,4,2,7,6,5,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,4,2,6,7,5,1,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,2,4,6,7,5,1,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,3,4,7,6,5,1,8]=>0001110=>[3,3,1]=>[1,3,3]
[2,3,4,6,7,5,1,8]=>0000110=>[4,2,1]=>[1,2,4]
[5,4,3,2,7,6,1,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[4,5,3,2,7,6,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,5,4,2,7,6,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,3,5,2,7,6,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,5,2,7,6,1,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,2,5,4,7,6,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,3,2,5,7,6,1,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,4,2,5,7,6,1,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,3,4,5,7,6,1,8]=>0000110=>[4,2,1]=>[1,2,4]
[3,6,5,4,2,7,1,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,5,6,4,2,7,1,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,4,6,5,2,7,1,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,5,4,6,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,4,6,3,7,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,5,4,7,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,3,5,6,4,7,1,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,3,2,6,5,7,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,2,6,5,7,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,3,6,5,7,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,4,6,5,7,1,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,5,4,2,6,7,1,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,5,4,3,6,7,1,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,4,5,3,6,7,1,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,5,4,6,7,1,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,7,6,5,4,3,2,8]=>0111110=>[1,5,1]=>[1,5,1]
[1,6,7,5,4,3,2,8]=>0011110=>[2,4,1]=>[1,4,2]
[1,6,5,7,4,3,2,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,5,6,7,4,3,2,8]=>0001110=>[3,3,1]=>[1,3,3]
[1,4,7,6,5,3,2,8]=>0011110=>[2,4,1]=>[1,4,2]
[1,4,6,7,5,3,2,8]=>0001110=>[3,3,1]=>[1,3,3]
[1,5,4,7,6,3,2,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,5,6,4,7,3,2,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,4,6,5,7,3,2,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,5,4,6,7,3,2,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,4,5,6,7,3,2,8]=>0000110=>[4,2,1]=>[1,2,4]
[1,3,7,6,5,4,2,8]=>0011110=>[2,4,1]=>[1,4,2]
[1,3,6,7,5,4,2,8]=>0001110=>[3,3,1]=>[1,3,3]
[1,3,5,7,6,4,2,8]=>0001110=>[3,3,1]=>[1,3,3]
[1,3,6,5,7,4,2,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,3,5,6,7,4,2,8]=>0000110=>[4,2,1]=>[1,2,4]
[1,3,4,6,7,5,2,8]=>0000110=>[4,2,1]=>[1,2,4]
[1,3,5,4,7,6,2,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,4,3,5,7,6,2,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,3,4,5,7,6,2,8]=>0000110=>[4,2,1]=>[1,2,4]
[1,5,4,6,3,7,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,5,6,3,7,2,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,6,5,4,7,2,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,3,5,6,4,7,2,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,4,3,6,5,7,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,4,6,5,7,2,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,5,4,3,6,7,2,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,4,5,3,6,7,2,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,5,4,6,7,2,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,4,5,6,7,2,8]=>0000010=>[5,1,1]=>[1,1,5]
[2,1,7,6,5,4,3,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[2,1,6,7,5,4,3,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[2,1,5,6,7,4,3,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,1,4,6,7,5,3,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,1,4,5,6,7,3,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,2,7,6,5,4,3,8]=>0011110=>[2,4,1]=>[1,4,2]
[1,2,6,7,5,4,3,8]=>0001110=>[3,3,1]=>[1,3,3]
[1,2,5,7,6,4,3,8]=>0001110=>[3,3,1]=>[1,3,3]
[1,2,5,6,7,4,3,8]=>0000110=>[4,2,1]=>[1,2,4]
[1,2,4,6,7,5,3,8]=>0000110=>[4,2,1]=>[1,2,4]
[1,2,5,6,4,7,3,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,5,4,6,7,3,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,4,5,6,7,3,8]=>0000010=>[5,1,1]=>[1,1,5]
[3,2,1,7,6,5,4,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[3,2,1,6,7,5,4,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,2,1,5,7,6,4,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,2,1,5,6,7,4,8]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[2,3,1,6,7,5,4,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,3,1,6,5,7,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,1,5,6,7,4,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,2,7,6,5,4,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,3,2,6,7,5,4,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,3,2,5,7,6,4,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,3,2,6,5,7,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,2,5,6,7,4,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,3,6,7,5,4,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,2,3,7,6,5,4,8]=>0001110=>[3,3,1]=>[1,3,3]
[1,2,3,6,7,5,4,8]=>0000110=>[4,2,1]=>[1,2,4]
[1,2,3,5,7,6,4,8]=>0000110=>[4,2,1]=>[1,2,4]
[1,2,3,6,5,7,4,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,3,5,6,7,4,8]=>0000010=>[5,1,1]=>[1,1,5]
[4,3,2,1,7,6,5,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[4,3,2,1,6,7,5,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,2,4,1,7,6,5,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,4,1,6,7,5,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,3,4,1,7,6,5,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,3,4,1,6,7,5,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,4,3,2,7,6,5,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,4,3,2,6,7,5,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,3,4,2,6,7,5,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,4,3,6,7,5,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,2,1,4,7,6,5,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[2,3,1,4,6,7,5,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,2,4,7,6,5,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,1,3,4,6,7,5,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,2,3,4,7,6,5,8]=>0000110=>[4,2,1]=>[1,2,4]
[1,2,3,4,6,7,5,8]=>0000010=>[5,1,1]=>[1,1,5]
[5,4,3,2,1,7,6,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[4,5,3,2,1,7,6,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,5,4,2,1,7,6,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,4,5,2,1,7,6,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,5,4,3,1,7,6,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,4,5,3,1,7,6,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,5,4,1,7,6,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,3,5,4,1,7,6,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,4,2,5,1,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,3,5,1,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,4,5,1,7,6,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,5,4,3,2,7,6,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,5,3,2,7,6,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,3,5,4,2,7,6,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,4,3,5,2,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,4,5,2,7,6,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,1,5,4,3,7,6,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,4,5,3,7,6,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,2,1,5,4,7,6,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,1,5,4,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,2,5,4,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,2,3,5,4,7,6,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,3,2,1,5,7,6,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,2,4,1,5,7,6,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,3,4,1,5,7,6,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,4,3,2,5,7,6,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,3,4,2,5,7,6,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,4,3,5,7,6,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,1,4,5,7,6,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,2,4,5,7,6,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,3,4,5,7,6,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,2,3,4,5,7,6,8]=>0000010=>[5,1,1]=>[1,1,5]
[3,6,5,4,2,1,7,8]=>0111100=>[1,4,2]=>[2,4,1]
[4,3,6,5,2,1,7,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[2,4,6,5,3,1,7,8]=>0011100=>[2,3,2]=>[2,3,2]
[2,4,5,6,3,1,7,8]=>0001100=>[3,2,2]=>[2,2,3]
[2,3,6,5,4,1,7,8]=>0011100=>[2,3,2]=>[2,3,2]
[2,3,5,6,4,1,7,8]=>0001100=>[3,2,2]=>[2,2,3]
[4,3,2,6,5,1,7,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[2,4,3,6,5,1,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,3,4,6,5,1,7,8]=>0001100=>[3,2,2]=>[2,2,3]
[3,5,4,2,6,1,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,3,5,4,6,1,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,6,5,4,3,2,7,8]=>0111100=>[1,4,2]=>[2,4,1]
[1,5,6,4,3,2,7,8]=>0011100=>[2,3,2]=>[2,3,2]
[1,4,6,5,3,2,7,8]=>0011100=>[2,3,2]=>[2,3,2]
[1,5,4,6,3,2,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,4,5,6,3,2,7,8]=>0001100=>[3,2,2]=>[2,2,3]
[1,3,5,6,4,2,7,8]=>0001100=>[3,2,2]=>[2,2,3]
[1,4,3,6,5,2,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,5,4,3,6,2,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,4,5,3,6,2,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,5,4,6,2,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,4,3,5,6,2,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,3,4,5,6,2,7,8]=>0000100=>[4,1,2]=>[2,1,4]
[2,1,5,6,4,3,7,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[2,1,4,6,5,3,7,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[1,2,6,5,4,3,7,8]=>0011100=>[2,3,2]=>[2,3,2]
[1,2,5,6,4,3,7,8]=>0001100=>[3,2,2]=>[2,2,3]
[1,2,4,6,5,3,7,8]=>0001100=>[3,2,2]=>[2,2,3]
[1,2,4,5,6,3,7,8]=>0000100=>[4,1,2]=>[2,1,4]
[3,2,1,6,5,4,7,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,2,1,5,6,4,7,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[2,3,1,6,5,4,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,3,1,5,6,4,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,3,2,6,5,4,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,3,2,5,6,4,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,3,6,5,4,7,8]=>0001100=>[3,2,2]=>[2,2,3]
[1,2,3,5,6,4,7,8]=>0000100=>[4,1,2]=>[2,1,4]
[4,3,2,1,6,5,7,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[2,4,3,1,6,5,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,4,1,6,5,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,3,4,1,6,5,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,1,4,3,6,5,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,2,4,3,6,5,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,2,4,6,5,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,3,4,6,5,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,2,3,4,6,5,7,8]=>0000100=>[4,1,2]=>[2,1,4]
[3,5,4,2,1,6,7,8]=>0111000=>[1,3,3]=>[3,3,1]
[2,5,4,3,1,6,7,8]=>0111000=>[1,3,3]=>[3,3,1]
[2,4,5,3,1,6,7,8]=>0011000=>[2,2,3]=>[3,2,2]
[3,2,5,4,1,6,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[2,3,5,4,1,6,7,8]=>0011000=>[2,2,3]=>[3,2,2]
[2,4,3,5,1,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,5,4,3,2,6,7,8]=>0111000=>[1,3,3]=>[3,3,1]
[1,4,5,3,2,6,7,8]=>0011000=>[2,2,3]=>[3,2,2]
[1,3,5,4,2,6,7,8]=>0011000=>[2,2,3]=>[3,2,2]
[1,3,4,5,2,6,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[2,1,5,4,3,6,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[2,1,4,5,3,6,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,2,5,4,3,6,7,8]=>0011000=>[2,2,3]=>[3,2,2]
[3,2,1,5,4,6,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[2,3,1,5,4,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,3,2,5,4,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,2,3,5,4,6,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[2,4,3,1,5,6,7,8]=>0110000=>[1,2,4]=>[4,2,1]
[1,4,3,2,5,6,7,8]=>0110000=>[1,2,4]=>[4,2,1]
[1,3,4,2,5,6,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[2,1,4,3,5,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[1,2,4,3,5,6,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[1,3,2,4,5,6,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[1,2,3,4,8,6,7,5]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,5,8,6,7,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,7,5,6,4,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,3,7,5,6,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,3,8,5,6,7,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,3,8,5,7,6,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,3,8,6,5,7,4]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,3,8,6,7,5,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,4,5,8,6,7,3]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,4,7,5,6,8,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,4,8,5,6,7,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,4,8,6,5,7,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,5,4,8,6,7,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,6,4,5,3,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,6,4,5,7,8,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,6,4,5,8,7,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,7,4,5,6,8,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,8,4,5,6,7,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,8,4,6,7,5,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,8,4,7,6,5,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,2,7,5,4,6,3,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,2,7,5,4,6,8,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,2,8,5,4,6,7,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,2,8,5,4,7,6,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,2,8,5,6,4,7,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,8,5,6,7,4,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,8,6,5,4,7,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,2,8,6,5,7,4,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,2,8,7,5,6,4,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,3,2,4,8,6,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,2,7,5,6,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,2,8,5,7,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,3,2,8,6,5,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,3,2,8,6,7,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,3,4,2,8,6,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,4,5,8,6,7,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,3,4,8,5,6,7,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,3,4,8,6,5,7,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,3,4,8,6,7,5,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,3,6,4,5,2,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,6,4,5,7,2,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,6,4,5,7,8,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,3,6,4,5,8,7,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,7,4,5,6,2,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,7,4,5,6,8,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,3,8,4,5,6,7,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,3,8,4,6,5,7,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,8,5,4,6,7,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,3,8,5,4,7,6,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,3,8,5,6,7,4,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,8,5,7,6,4,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,3,8,6,5,7,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,3,8,7,5,6,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,4,3,5,8,6,7,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,4,3,8,5,6,7,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,4,3,8,5,7,6,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,4,3,8,6,5,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,4,3,8,6,7,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,5,3,4,2,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,5,3,4,2,7,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,3,4,2,8,7,6]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,5,3,4,6,2,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,5,3,4,6,2,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,5,3,4,6,7,2,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,5,3,4,6,7,8,2]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,5,3,4,7,6,2,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,5,3,4,8,6,7,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,3,4,5,2,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,6,3,4,5,8,7,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,7,3,4,5,6,2,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,7,3,4,5,6,8,2]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,8,3,4,5,6,7,2]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,8,3,4,6,7,5,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,6,3,5,4,2,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,6,3,5,4,8,7,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,7,3,5,4,6,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,3,5,4,6,7,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,8,3,5,4,7,6,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,3,5,6,4,7,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,8,3,5,6,7,4,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,8,3,5,7,6,4,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,7,3,6,5,4,2,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,7,3,6,5,4,8,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,3,6,5,4,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,3,7,5,6,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,3,7,6,5,4,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[1,6,4,3,5,2,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,6,4,3,5,8,7,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,8,4,3,5,6,7,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[1,8,4,3,5,7,6,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,7,4,3,6,5,8,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,4,3,6,5,7,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,4,3,6,7,5,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,6,4,5,3,2,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,6,4,5,3,2,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,4,5,3,8,7,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,7,4,5,3,6,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,8,4,5,3,6,7,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,7,4,5,6,3,2,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,7,4,5,6,3,8,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,8,4,5,6,3,7,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,8,4,5,6,7,3,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,7,4,6,5,3,2,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,8,4,6,5,3,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,4,6,5,7,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,4,7,6,5,3,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[1,7,5,4,3,6,2,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,7,5,4,3,6,8,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[1,8,5,4,3,6,7,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[1,8,5,4,3,7,6,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,8,5,4,6,3,7,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,5,4,6,7,3,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,8,5,4,7,6,3,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,7,6,4,5,3,2,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,8,6,4,5,3,7,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,6,4,5,7,3,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,8,7,4,5,6,3,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,8,7,4,6,5,3,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,8,6,5,4,3,7,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[1,8,6,5,4,7,3,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,8,7,5,4,6,3,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,8,7,5,6,4,3,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,1,3,4,8,6,7,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,3,5,8,6,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,3,8,5,6,7,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,1,3,8,5,7,6,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,3,8,6,5,7,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,3,8,6,7,5,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,4,3,8,6,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,4,5,8,6,7,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,4,8,5,6,7,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,1,4,8,5,7,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,4,8,6,5,7,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,4,8,6,7,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,5,4,8,6,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,4,5,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,4,5,7,8,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,1,6,4,5,8,7,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,8,4,5,6,7,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,1,8,4,5,7,6,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,7,4,6,5,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,4,6,5,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,4,6,7,5,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,8,4,7,6,5,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,1,7,5,4,6,8,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,1,8,5,4,6,7,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,1,8,5,4,7,6,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,7,5,6,4,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,5,6,4,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,5,6,7,4,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,8,5,7,6,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,1,8,6,5,4,7,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,8,6,5,7,4,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,8,7,5,6,4,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,3,1,7,5,6,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,1,8,5,6,7,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,3,1,8,6,7,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,3,4,1,8,6,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,4,5,8,6,7,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[2,3,4,7,5,6,1,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,4,7,5,6,8,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,3,4,8,5,6,7,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,3,4,8,5,7,6,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,3,4,8,6,5,7,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,3,4,8,6,7,5,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,3,5,4,8,6,7,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,6,4,5,1,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,6,4,5,1,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,6,4,5,7,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,3,6,4,5,8,7,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,3,7,4,5,6,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,3,8,4,5,6,7,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,3,7,4,6,5,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,8,4,6,7,5,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,3,7,5,4,6,1,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,3,7,5,4,6,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,3,8,5,4,6,7,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,3,7,5,6,4,1,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,3,7,5,6,4,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,8,5,6,4,7,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,8,5,6,7,4,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,3,8,5,7,6,4,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,3,8,6,5,4,7,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,4,3,1,8,6,7,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,4,3,5,8,6,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,3,7,5,6,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,3,8,5,6,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,3,8,5,7,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,4,3,8,6,5,7,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,3,8,6,7,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,5,3,4,1,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,5,3,4,1,8,7,6]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,5,3,4,6,7,1,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,5,3,4,6,7,8,1]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,5,3,4,6,8,7,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,5,3,4,7,6,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,3,4,8,6,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,3,4,8,7,6,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,6,3,4,5,1,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,6,3,4,5,7,8,1]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,6,3,4,5,8,7,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,7,3,4,5,6,1,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,8,3,4,5,6,7,1]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,8,3,4,5,7,6,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,6,3,5,4,1,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,6,3,5,4,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,3,5,4,7,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,3,5,4,8,7,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,7,3,5,4,6,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,3,5,4,7,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,7,3,5,6,4,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,8,3,5,6,7,4,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,8,3,5,7,6,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,7,3,6,5,4,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,8,3,7,5,6,4,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,8,3,7,6,5,4,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[2,5,4,3,8,6,7,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,6,4,3,5,1,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,6,4,3,5,7,8,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,6,4,3,5,8,7,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,7,4,3,5,6,8,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,8,4,3,5,6,7,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,8,4,3,5,7,6,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,7,4,3,6,5,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,4,3,6,5,7,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,4,3,6,7,5,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,8,4,3,7,6,5,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,6,4,5,3,1,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,6,4,5,3,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,4,5,3,7,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,4,5,3,8,7,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,8,4,5,3,6,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,7,4,5,6,3,1,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,7,4,5,6,3,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,8,4,5,6,3,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,8,4,5,6,7,3,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,7,4,6,5,3,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,7,4,6,5,3,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,4,6,5,3,7,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,4,7,6,5,3,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[2,7,5,4,3,6,8,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,8,5,4,3,6,7,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,8,5,4,3,7,6,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,7,5,4,6,3,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,5,4,6,7,3,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,8,5,4,7,6,3,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,7,6,4,5,3,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,7,4,5,6,3,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,8,7,4,6,5,3,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,8,7,5,4,6,3,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,8,7,5,6,4,3,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[3,2,1,4,8,6,7,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,1,5,8,6,7,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,1,7,5,6,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,2,1,8,5,6,7,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,2,1,8,5,7,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,2,1,8,6,5,7,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,2,1,8,6,7,5,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,2,4,1,8,6,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,4,5,8,6,7,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,2,4,7,5,6,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,2,4,8,5,6,7,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,2,4,8,6,7,5,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,5,4,8,6,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,4,5,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,4,5,7,1,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,2,7,4,5,6,1,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,2,8,4,5,6,7,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,2,7,4,6,5,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,7,4,6,5,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,8,4,6,5,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,7,5,4,6,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,2,8,5,4,6,7,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,2,8,5,4,7,6,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,2,7,5,6,4,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,7,5,6,4,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,8,5,6,4,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,8,5,7,6,4,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,2,8,6,5,7,4,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,2,8,7,5,6,4,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,2,3,1,5,7,6,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,3,1,5,7,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,2,3,1,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,3,1,6,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,2,3,1,6,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,2,3,1,7,6,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,3,1,8,6,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,3,1,8,7,6,5]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,2,3,5,1,6,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,3,5,1,7,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,3,5,1,8,7,6]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,3,5,6,1,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,2,3,5,6,8,7,1]=>1000011=>[1,4,2]=>[2,4,1]
[4,2,3,5,7,6,1,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,2,3,5,8,7,6,1]=>1000111=>[1,3,3]=>[3,3,1]
[4,2,3,6,5,1,7,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,2,3,6,5,1,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,2,3,6,5,8,7,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,3,7,5,6,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,2,3,7,5,6,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,3,8,5,6,7,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,3,8,5,7,6,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,3,7,6,5,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,2,3,8,6,7,5,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,3,8,7,6,5,1]=>1001111=>[1,2,4]=>[4,2,1]
[5,2,3,4,1,6,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,2,3,4,1,7,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,2,3,4,1,8,7,6]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,2,3,4,6,1,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,2,3,4,7,6,1,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,2,3,4,8,6,7,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,2,3,4,8,7,6,1]=>1000111=>[1,3,3]=>[3,3,1]
[6,2,3,4,5,1,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,2,3,4,5,8,7,1]=>1000011=>[1,4,2]=>[2,4,1]
[8,2,3,4,5,7,6,1]=>1000011=>[1,4,2]=>[2,4,1]
[7,2,3,4,6,5,1,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[8,2,3,4,7,6,5,1]=>1000111=>[1,3,3]=>[3,3,1]
[6,2,3,5,4,1,7,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,2,3,5,4,1,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,2,3,5,4,7,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,2,3,5,4,7,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,2,3,5,4,6,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,2,3,5,4,6,7,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,2,3,5,4,7,6,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,2,3,5,6,4,1,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[8,2,3,5,6,7,4,1]=>1000011=>[1,4,2]=>[2,4,1]
[8,2,3,5,7,6,4,1]=>1000111=>[1,3,3]=>[3,3,1]
[7,2,3,6,5,4,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[8,2,3,6,5,4,7,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,2,3,7,5,6,4,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,2,3,7,6,5,4,1]=>1001111=>[1,2,4]=>[4,2,1]
[5,2,4,3,1,6,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,2,4,3,1,6,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,2,4,3,1,7,6,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,2,4,3,1,8,7,6]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,2,4,3,6,1,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,2,4,3,6,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,4,3,6,7,1,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,2,4,3,7,6,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,2,4,3,7,6,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,4,3,8,7,6,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,2,4,3,5,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,4,3,6,5,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,4,3,6,5,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,4,3,6,5,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,4,3,6,7,5,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,2,4,3,7,6,5,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,2,4,5,3,1,7,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,2,4,5,3,1,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,2,4,5,3,8,7,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,2,4,5,3,6,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,2,4,5,3,6,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,2,4,5,3,7,6,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,2,4,5,6,3,7,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,2,4,5,6,7,3,1]=>1000011=>[1,4,2]=>[2,4,1]
[8,2,4,5,7,6,3,1]=>1000111=>[1,3,3]=>[3,3,1]
[7,2,4,6,5,3,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,2,4,6,5,3,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,2,4,7,5,6,3,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,2,4,7,6,5,3,1]=>1001111=>[1,2,4]=>[4,2,1]
[6,2,5,4,3,1,7,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,2,5,4,3,1,8,7]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,2,5,4,3,7,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,2,5,4,3,7,8,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,2,5,4,3,6,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,2,5,4,3,6,7,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,2,5,4,3,7,6,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,2,5,4,6,3,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,5,4,7,6,3,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,2,6,4,5,3,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,6,4,5,3,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,6,4,5,3,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,6,4,5,7,3,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,2,7,4,5,6,3,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,2,7,4,6,5,3,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,2,6,5,4,3,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,2,6,5,4,3,8,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,2,6,5,4,3,7,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,2,6,5,4,7,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,2,7,5,4,6,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,2,7,5,6,4,3,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,2,7,6,5,4,3,1]=>1011111=>[1,1,5]=>[5,1,1]
[4,3,2,1,8,6,7,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,3,2,7,5,6,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,3,2,8,5,6,7,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,3,2,8,5,7,6,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,3,2,8,6,7,5,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,3,2,4,1,6,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,3,2,4,1,7,6,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,2,4,1,8,7,6]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,3,2,4,6,1,8,7]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,3,2,4,7,6,1,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,3,2,4,6,5,7,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,3,2,4,6,7,5,1]=>1100011=>[2,3,2]=>[2,3,2]
[8,3,2,4,7,6,5,1]=>1100111=>[2,2,3]=>[3,2,2]
[6,3,2,5,4,1,7,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,3,2,5,4,1,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,3,2,5,4,7,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,2,5,4,7,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,2,5,4,8,7,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,3,2,5,4,6,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,3,2,5,4,7,6,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,3,2,5,6,4,8,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,3,2,5,6,4,7,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,3,2,5,6,7,4,1]=>1100011=>[2,3,2]=>[2,3,2]
[8,3,2,5,7,6,4,1]=>1100111=>[2,2,3]=>[3,2,2]
[8,3,2,6,5,7,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,3,2,7,5,6,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,3,2,7,6,5,4,1]=>1101111=>[2,1,4]=>[4,1,2]
[5,3,4,2,1,6,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,3,4,2,1,7,8,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,3,4,2,1,8,7,6]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,3,4,2,6,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,4,2,7,6,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,3,4,2,7,6,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,4,2,8,6,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,4,2,5,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,4,2,6,5,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,4,2,6,5,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,4,2,6,5,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,4,5,2,1,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,3,4,5,2,8,7,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,3,4,5,2,7,6,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,3,4,5,7,6,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[7,3,4,6,5,2,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[8,3,4,7,6,5,2,1]=>1001111=>[1,2,4]=>[4,2,1]
[6,3,5,4,2,1,8,7]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,3,5,4,2,7,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,3,5,4,2,7,8,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,5,4,2,8,7,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,3,5,4,2,6,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,5,4,2,6,7,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,3,5,4,2,7,6,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,3,5,4,6,2,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,5,4,6,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,5,4,6,7,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,3,5,4,7,6,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,3,6,4,5,2,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,6,4,5,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,6,4,5,2,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,6,4,5,7,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,3,7,4,5,6,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,3,7,4,6,5,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,3,6,5,4,2,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,3,6,5,4,2,8,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,6,5,4,2,7,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,6,5,4,7,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,3,7,5,4,6,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,3,7,5,6,4,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,3,7,6,5,4,2,1]=>1011111=>[1,1,5]=>[5,1,1]
[5,4,3,2,8,6,7,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,3,2,5,1,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,3,2,5,8,7,1]=>1110011=>[3,2,2]=>[2,2,3]
[8,4,3,2,5,7,6,1]=>1110011=>[3,2,2]=>[2,2,3]
[7,4,3,2,6,5,1,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,4,3,2,6,5,8,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,4,3,2,6,5,7,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,4,3,2,6,7,5,1]=>1110011=>[3,2,2]=>[2,2,3]
[8,4,3,2,7,6,5,1]=>1110111=>[3,1,3]=>[3,1,3]
[6,4,3,5,2,1,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,4,3,5,2,7,6,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,4,3,5,7,6,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[7,4,3,6,5,2,1,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,4,3,6,5,2,8,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,4,3,7,5,6,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,4,3,7,6,5,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[6,5,3,4,2,1,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,5,3,4,2,7,6,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,5,3,4,7,6,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[8,7,3,4,6,5,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[7,6,3,5,4,2,1,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,6,3,5,4,2,8,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,6,3,5,4,2,7,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,6,3,5,4,7,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,7,3,5,4,6,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,7,3,5,6,4,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[8,7,3,6,5,4,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[8,5,4,3,2,7,6,1]=>1111011=>[4,1,2]=>[2,1,4]
[8,5,4,3,7,6,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,7,4,3,6,5,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,7,4,6,5,3,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[2,4,1,3,6,5,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,4,6,3,5,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,4,1,6,3,5,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,6,1,3,5,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,4,3,6,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,1,3,6,8,5,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,4,6,3,8,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,4,1,6,3,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,6,1,3,8,5,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,1,4,6,8,3,5,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,4,1,6,8,3,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,4,6,1,8,3,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,6,8,1,3,5,7]=>0001000=>[3,1,3]=>[3,1,3]
[2,4,1,3,6,5,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,4,6,3,5,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,4,1,6,3,5,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,4,6,1,3,5,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[2,1,4,6,3,7,5,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,4,1,6,3,7,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,6,1,3,7,5,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,6,7,1,3,5,8]=>0001000=>[3,1,3]=>[3,1,3]
[2,4,1,3,6,7,8,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,1,4,6,3,7,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,4,1,6,3,7,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,6,1,3,7,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,4,6,7,3,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,4,1,6,7,3,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,6,1,7,3,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,6,7,1,3,8,5]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,1,4,6,7,8,3,5]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[2,4,1,6,7,8,3,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,4,6,1,7,8,3,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,6,7,1,8,3,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,4,6,7,8,1,3,5]=>0000100=>[4,1,2]=>[2,1,4]
[2,1,4,3,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,1,3,7,5,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,4,7,3,5,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,4,1,7,3,5,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,7,1,3,5,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,4,3,7,8,5,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,1,3,7,8,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,4,1,7,3,8,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,4,7,8,3,5,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,4,1,7,8,3,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,4,7,1,8,3,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,7,8,1,3,5,6]=>0001000=>[3,1,3]=>[3,1,3]
[2,4,1,5,3,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,5,1,3,7,6,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,5,1,7,3,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,1,3,5,7,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,4,1,5,3,7,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,5,1,3,7,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,4,5,7,3,8,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,4,1,5,7,3,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,5,1,7,3,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,5,7,1,3,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,1,4,5,7,8,3,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[2,4,5,1,7,8,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,5,7,1,8,3,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,4,5,7,8,1,3,6]=>0000100=>[4,1,2]=>[2,1,4]
[2,1,4,3,8,5,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,4,1,3,8,5,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,4,8,3,5,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,4,1,8,3,5,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,4,8,1,3,5,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[2,1,4,3,5,8,6,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,1,5,3,8,6,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,4,5,8,3,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,4,1,5,8,3,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,4,5,1,8,3,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,5,8,1,3,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[2,4,1,5,3,6,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,1,5,6,3,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,5,1,6,3,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,5,6,1,3,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,1,4,5,6,8,3,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[2,4,1,5,6,8,3,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,4,5,1,6,8,3,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,5,6,1,8,3,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,4,5,6,8,1,3,7]=>0000100=>[4,1,2]=>[2,1,4]
[2,4,1,3,5,6,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[2,4,1,5,3,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,4,5,1,3,6,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[2,4,1,5,6,3,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,4,5,1,6,3,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,5,6,1,3,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[2,4,1,5,6,7,3,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,4,5,6,1,7,3,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,4,5,6,7,1,3,8]=>0000100=>[4,1,2]=>[2,1,4]
[2,4,1,5,6,7,8,3]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,4,5,1,6,7,8,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,4,5,6,1,7,8,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,4,5,6,7,1,8,3]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[2,4,5,6,7,8,1,3]=>0000010=>[5,1,1]=>[1,1,5]
[2,1,5,3,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,1,3,6,4,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,5,6,3,4,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,5,1,6,3,4,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,5,6,1,3,4,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,5,3,6,8,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,5,1,3,6,8,4,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,5,1,6,3,8,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,6,1,3,8,4,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,1,5,6,8,3,4,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,5,1,6,8,3,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,5,6,8,1,3,4,7]=>0001000=>[3,1,3]=>[3,1,3]
[2,5,1,3,6,4,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,5,6,3,4,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,5,1,6,3,4,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,1,5,3,6,7,4,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,1,5,6,3,7,4,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,5,1,6,3,7,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,6,1,3,7,4,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,1,5,6,7,3,4,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,5,1,6,7,3,4,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,5,6,1,7,3,4,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,1,5,3,6,7,8,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,5,1,3,6,7,8,4]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,1,5,6,3,7,8,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,5,1,6,3,7,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,5,6,1,3,7,8,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,5,6,7,3,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,5,1,6,7,3,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,6,7,1,3,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,1,5,6,7,8,3,4]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[2,5,1,6,7,8,3,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,5,6,1,7,8,3,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,5,6,7,1,8,3,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,5,6,7,8,1,3,4]=>0000100=>[4,1,2]=>[2,1,4]
[2,1,5,3,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,1,3,7,4,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,5,7,3,4,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,5,1,7,3,4,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,5,7,1,3,4,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,5,3,7,8,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,5,1,3,7,8,4,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,5,7,3,8,4,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,1,5,7,8,3,4,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,5,1,7,8,3,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,5,7,1,8,3,4,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,5,7,8,1,3,4,6]=>0001000=>[3,1,3]=>[3,1,3]
[2,5,1,3,7,4,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,5,7,3,4,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,3,5,1,4,7,6,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,5,7,1,4,6,8]=>0001000=>[3,1,3]=>[3,1,3]
[2,3,5,1,7,4,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,5,7,1,4,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,3,1,5,7,8,4,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,3,5,7,1,8,4,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,5,7,8,1,4,6]=>0000100=>[4,1,2]=>[2,1,4]
[2,1,5,3,8,4,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,5,1,3,8,4,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,5,8,3,4,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,5,1,8,3,4,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,5,8,1,3,4,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[2,3,5,1,4,8,6,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,1,3,5,8,4,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,3,5,1,8,4,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,5,8,1,4,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[2,1,5,3,4,6,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,3,5,1,6,4,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,5,6,1,4,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,3,1,5,6,8,4,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,3,5,1,6,8,4,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,5,6,1,8,4,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,5,6,8,1,4,7]=>0000100=>[4,1,2]=>[2,1,4]
[2,1,5,3,4,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[2,5,1,3,4,6,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[2,3,5,1,4,6,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[2,3,5,1,6,4,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,5,6,1,4,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[2,3,5,6,1,7,4,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,5,6,7,1,4,8]=>0000100=>[4,1,2]=>[2,1,4]
[2,3,5,1,6,7,8,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,3,5,6,1,7,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,3,5,6,7,1,8,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[2,3,5,6,7,8,1,4]=>0000010=>[5,1,1]=>[1,1,5]
[2,1,6,3,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,1,3,7,4,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,6,7,3,4,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,6,1,7,3,4,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,7,1,3,4,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,6,3,7,8,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,1,3,7,8,4,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,6,7,3,8,4,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,6,1,7,3,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,7,8,3,4,5]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,6,1,7,8,3,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,6,7,1,8,3,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,6,7,8,1,3,4,5]=>0001000=>[3,1,3]=>[3,1,3]
[2,1,6,3,7,4,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,1,7,3,4,5,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,6,7,1,3,4,5,8]=>0010000=>[2,1,4]=>[4,1,2]
[2,6,1,3,4,7,5,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,3,1,6,4,7,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,6,1,4,7,5,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,6,7,1,4,5,8]=>0001000=>[3,1,3]=>[3,1,3]
[2,1,6,3,4,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,6,1,3,4,7,8,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,3,6,1,4,7,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,3,6,7,4,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,3,6,7,1,4,8,5]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,1,3,6,7,8,4,5]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[2,3,1,6,7,8,4,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,3,6,1,7,8,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,6,7,1,8,4,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,6,7,8,1,4,5]=>0000100=>[4,1,2]=>[2,1,4]
[2,1,6,3,8,4,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,1,3,8,4,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,6,8,3,4,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,6,1,8,3,4,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,6,8,1,3,4,5,7]=>0010000=>[2,1,4]=>[4,1,2]
[2,1,6,3,4,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,1,3,4,8,5,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,3,1,6,4,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,6,1,4,8,5,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,1,6,8,4,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,3,6,1,8,4,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,6,8,1,4,5,7]=>0001000=>[3,1,3]=>[3,1,3]
[2,1,6,3,4,5,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,6,1,3,4,5,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,1,3,6,4,5,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,3,6,1,4,5,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,3,4,1,6,8,5,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,4,6,1,8,5,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,4,6,8,1,5,7]=>0000100=>[4,1,2]=>[2,1,4]
[2,6,1,3,4,5,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[2,1,3,6,4,5,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,3,1,6,4,5,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,3,6,1,4,5,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[2,3,4,6,1,5,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[2,3,4,6,1,7,5,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,4,6,7,1,5,8]=>0000100=>[4,1,2]=>[2,1,4]
[2,3,4,6,1,7,8,5]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,3,4,6,7,8,1,5]=>0000010=>[5,1,1]=>[1,1,5]
[2,1,7,3,8,4,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,7,1,3,8,4,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,7,8,3,4,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,7,1,8,3,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,7,8,1,3,4,5,6]=>0010000=>[2,1,4]=>[4,1,2]
[2,1,7,3,4,8,5,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,7,1,3,4,8,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,3,7,4,8,5,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,3,1,7,4,8,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,7,1,4,8,5,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,1,3,7,8,4,5,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,3,1,7,8,4,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,3,7,8,1,4,5,6]=>0001000=>[3,1,3]=>[3,1,3]
[2,1,7,3,4,5,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,7,1,3,4,5,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,3,1,7,4,5,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,3,7,1,4,5,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,1,3,4,7,5,8,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,3,4,1,7,5,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,4,7,1,5,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,1,3,4,7,8,5,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[2,3,1,4,7,8,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,3,4,1,7,8,5,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,4,7,1,8,5,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,4,7,8,1,5,6]=>0000100=>[4,1,2]=>[2,1,4]
[2,1,7,3,4,5,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[2,7,1,3,4,5,6,8]=>0100000=>[1,1,5]=>[5,1,1]
[2,3,7,1,4,5,6,8]=>0010000=>[2,1,4]=>[4,1,2]
[2,1,3,4,7,5,6,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,3,1,4,7,5,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,3,4,1,7,5,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,4,7,1,5,6,8]=>0001000=>[3,1,3]=>[3,1,3]
[2,3,4,5,7,1,6,8]=>0000100=>[4,1,2]=>[2,1,4]
[2,3,4,5,7,1,8,6]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[2,3,4,5,7,8,1,6]=>0000010=>[5,1,1]=>[1,1,5]
[2,1,8,3,4,5,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[2,8,1,3,4,5,6,7]=>0100000=>[1,1,5]=>[5,1,1]
[2,1,3,8,4,5,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,3,1,8,4,5,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,3,8,1,4,5,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[2,1,3,4,8,5,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,3,1,4,8,5,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,3,4,1,8,5,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,4,8,1,5,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[2,1,3,4,5,8,6,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[2,3,1,4,5,8,6,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,3,4,1,5,8,6,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,4,5,1,8,6,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,4,5,8,1,6,7]=>0000100=>[4,1,2]=>[2,1,4]
[2,3,4,5,6,8,1,7]=>0000010=>[5,1,1]=>[1,1,5]
[3,1,4,2,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,1,2,6,5,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,4,6,2,5,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,4,1,6,2,5,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,6,1,2,5,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,4,2,6,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,1,2,6,8,5,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,1,4,6,2,8,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,1,6,2,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,4,6,8,2,5,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,4,1,6,8,2,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,6,8,1,2,5,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,4,2,6,5,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,4,1,2,6,5,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,1,4,2,6,7,5,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,1,2,6,7,5,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,4,1,6,2,7,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,6,1,2,7,5,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,1,6,7,2,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,6,7,1,2,5,8]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,4,2,6,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,4,1,2,6,7,8,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,1,4,6,2,7,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,4,1,6,2,7,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,6,1,2,7,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,4,6,7,2,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,4,1,6,7,2,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,4,6,1,7,2,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,6,7,1,2,8,5]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,1,4,6,7,8,2,5]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[3,4,1,6,7,8,2,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,4,6,1,7,8,2,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,6,7,1,8,2,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,6,7,8,1,2,5]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,4,2,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,1,2,7,5,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,4,7,2,5,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,4,1,7,2,5,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,7,1,2,5,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,4,2,7,8,5,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,1,2,7,8,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,1,4,7,2,8,5,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,7,1,8,2,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,4,7,8,1,2,5,6]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,4,2,7,5,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,4,1,2,7,5,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,1,2,5,7,6,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,1,4,5,2,7,6,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,1,5,2,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,1,5,7,2,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,5,7,1,2,6,8]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,4,2,5,7,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,4,1,2,5,7,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,1,4,5,2,7,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,4,5,1,2,7,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,4,5,7,2,8,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,4,1,5,7,2,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,4,5,7,1,2,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,1,4,5,7,8,2,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[3,4,1,5,7,8,2,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,4,5,1,7,8,2,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,5,7,1,8,2,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,5,7,8,1,2,6]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,4,2,8,5,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,4,1,2,8,5,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,1,4,8,2,5,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,4,1,8,2,5,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,4,8,1,2,5,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[3,1,4,2,5,8,6,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,1,2,5,8,6,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,4,1,5,2,8,6,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,5,1,2,8,6,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,1,4,5,8,2,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,4,1,5,8,2,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,5,8,1,2,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,4,1,2,5,6,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,4,5,1,2,6,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,4,5,6,2,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,4,1,5,6,2,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,4,5,1,6,2,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,5,6,1,2,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,1,4,5,6,8,2,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[3,4,1,5,6,8,2,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,4,5,6,1,8,2,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,5,6,8,1,2,7]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,4,2,5,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,1,4,5,2,6,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,4,1,5,2,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,1,4,5,6,2,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,4,1,5,6,2,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,5,1,6,2,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,1,4,5,6,7,2,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[3,4,1,5,6,7,2,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,4,5,1,6,7,2,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,5,6,1,7,2,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,1,4,5,6,7,8,2]=>1000001=>[1,5,1]=>[1,5,1]
[3,4,1,5,6,7,8,2]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,4,5,1,6,7,8,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,4,5,6,1,7,8,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,4,5,6,7,1,8,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[3,1,5,2,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,1,2,6,4,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,5,6,2,4,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,5,1,6,2,4,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,5,6,1,2,4,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,5,2,6,8,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,1,2,6,8,4,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,1,5,6,2,8,4,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,5,6,1,2,8,4,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,1,5,6,8,2,4,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,5,1,6,8,2,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,5,6,1,8,2,4,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,5,6,8,1,2,4,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,5,6,2,4,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,5,1,6,2,4,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,5,6,1,2,4,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[3,5,1,2,6,7,4,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,5,1,6,2,7,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,6,1,2,7,4,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,5,1,6,7,2,4,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,5,6,1,7,2,4,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,5,6,7,1,2,4,8]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,5,2,6,7,8,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,5,1,2,6,7,8,4]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,1,5,6,2,7,8,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,5,1,6,2,7,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,5,6,1,2,7,8,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,5,6,7,2,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,5,1,6,7,2,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,5,6,1,7,2,8,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,6,7,1,2,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,1,5,6,7,8,2,4]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[3,5,1,6,7,8,2,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,5,6,1,7,8,2,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,5,6,7,1,8,2,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,5,6,7,8,1,2,4]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,5,2,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,1,2,7,4,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,5,7,2,4,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,5,1,7,2,4,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,5,7,1,2,4,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,5,2,7,8,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,1,2,7,8,4,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,1,5,7,2,8,4,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,5,1,7,2,8,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,7,8,2,4,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,5,1,7,8,2,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,5,7,8,1,2,4,6]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,5,2,7,4,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,5,1,2,7,4,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,1,5,7,2,4,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,5,1,7,2,4,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,5,7,1,2,4,6,8]=>0010000=>[2,1,4]=>[4,1,2]
[3,1,5,2,4,7,6,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,1,2,4,7,6,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,1,2,5,4,7,6,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,3,5,2,4,7,6,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,1,2,5,7,4,6,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,3,2,5,7,4,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,3,5,2,7,4,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,5,7,2,4,6,8]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,5,2,4,7,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,5,1,2,4,7,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,3,5,2,4,7,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,2,5,7,4,8,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,3,2,5,7,4,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,5,2,7,4,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,5,7,2,4,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,1,2,5,7,8,4,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,3,2,5,7,8,4,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,5,2,7,8,4,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,5,7,2,8,4,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,5,7,8,2,4,6]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,5,2,8,4,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,5,1,2,8,4,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,1,5,8,2,4,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,5,1,8,2,4,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,1,5,2,4,8,6,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,1,2,4,8,6,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,2,5,4,8,6,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,5,2,4,8,6,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,1,2,5,8,4,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,3,2,5,8,4,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,3,5,2,8,4,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,5,8,2,4,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,5,2,4,6,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,5,1,2,4,6,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,1,2,5,4,6,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,3,5,2,4,6,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,3,5,6,2,4,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,1,2,5,6,8,4,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,3,5,2,6,8,4,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,5,6,2,8,4,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,5,6,8,2,4,7]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,5,2,4,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,5,1,2,4,6,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[1,3,5,2,4,6,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[3,1,2,5,6,4,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,3,5,2,6,4,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,5,6,2,4,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,2,5,6,7,4,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,3,5,2,6,7,4,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,5,6,2,7,4,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,5,6,7,2,4,8]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,2,5,6,7,8,4]=>1000001=>[1,5,1]=>[1,5,1]
[1,3,5,2,6,7,8,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,3,5,6,2,7,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,3,5,6,7,2,8,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,3,5,6,7,8,2,4]=>0000010=>[5,1,1]=>[1,1,5]
[3,1,6,2,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,1,2,7,4,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,6,1,7,2,4,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,7,1,2,4,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,6,1,2,7,8,4,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,1,6,7,2,8,4,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,1,7,2,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,7,1,2,8,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,6,1,7,8,2,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,6,7,8,1,2,4,5]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,6,2,7,4,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,1,6,7,2,4,5,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,6,7,1,2,4,5,8]=>0010000=>[2,1,4]=>[4,1,2]
[3,1,6,2,4,7,5,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,6,1,2,4,7,5,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,1,2,6,4,7,5,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,3,2,6,4,7,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,6,2,4,7,5,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,2,6,7,4,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,3,6,2,7,4,5,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,1,6,2,4,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,6,1,2,4,7,8,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,1,2,6,4,7,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,3,2,6,4,7,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,6,2,4,7,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,2,6,7,4,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,3,2,6,7,4,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,6,2,7,4,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,1,2,6,7,8,4,5]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,3,2,6,7,8,4,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,6,2,7,8,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,6,7,8,2,4,5]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,6,2,8,4,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,1,6,8,2,4,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,6,1,8,2,4,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,6,8,1,2,4,5,7]=>0010000=>[2,1,4]=>[4,1,2]
[3,1,6,2,4,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,6,1,2,4,8,5,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,2,6,4,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,6,2,4,8,5,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,1,2,6,8,4,5,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,3,2,6,8,4,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,1,6,2,4,5,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,6,1,2,4,5,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,1,2,6,4,5,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,3,6,2,4,5,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,2,4,6,5,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,3,4,6,2,5,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,1,2,4,6,8,5,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,3,2,4,6,8,5,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,4,6,8,2,5,7]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,6,2,4,5,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,6,1,2,4,5,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[1,3,2,6,4,5,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,3,6,2,4,5,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[1,3,4,6,2,5,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,2,4,6,7,5,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,3,4,6,2,7,5,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,4,6,7,2,5,8]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,2,4,6,7,8,5]=>1000001=>[1,5,1]=>[1,5,1]
[1,3,4,6,7,2,8,5]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,3,4,6,7,8,2,5]=>0000010=>[5,1,1]=>[1,1,5]
[3,1,7,2,8,4,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,7,1,2,8,4,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,1,7,8,2,4,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,7,1,8,2,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,7,8,1,2,4,5,6]=>0010000=>[2,1,4]=>[4,1,2]
[3,7,1,2,4,8,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,1,2,7,4,8,5,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,3,2,7,4,8,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,7,2,4,8,5,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,1,2,7,8,4,5,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,3,7,2,8,4,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,7,8,2,4,5,6]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,7,2,4,5,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,7,1,2,4,5,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,3,7,2,4,5,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,2,4,7,5,8,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,3,2,4,7,5,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,4,2,7,5,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,1,2,4,7,8,5,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,3,2,4,7,8,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,4,2,7,8,5,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,4,7,8,2,5,6]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,7,2,4,5,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,7,1,2,4,5,6,8]=>0100000=>[1,1,5]=>[5,1,1]
[1,3,2,7,4,5,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,3,7,2,4,5,6,8]=>0010000=>[2,1,4]=>[4,1,2]
[3,1,2,4,7,5,6,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,3,4,7,2,5,6,8]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,2,4,5,7,6,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,3,4,5,7,2,6,8]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,2,4,5,7,8,6]=>1000001=>[1,5,1]=>[1,5,1]
[1,3,4,5,7,2,8,6]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,3,4,5,7,8,2,6]=>0000010=>[5,1,1]=>[1,1,5]
[3,1,8,2,4,5,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,8,1,2,4,5,6,7]=>0100000=>[1,1,5]=>[5,1,1]
[3,1,2,8,4,5,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,3,2,8,4,5,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,3,8,2,4,5,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[3,1,2,4,8,5,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,3,2,4,8,5,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,3,4,2,8,5,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,4,8,2,5,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[3,1,2,4,5,8,6,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,3,2,4,5,8,6,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,4,2,5,8,6,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,4,5,2,8,6,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,4,5,8,2,6,7]=>0000100=>[4,1,2]=>[2,1,4]
[3,1,2,4,5,6,8,7]=>1000001=>[1,5,1]=>[1,5,1]
[1,3,4,5,6,8,2,7]=>0000010=>[5,1,1]=>[1,1,5]
[4,1,5,2,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,1,2,6,3,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,5,6,2,3,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,5,1,6,2,3,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,5,6,1,2,3,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,1,5,2,6,8,3,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,1,2,6,8,3,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,1,5,6,2,8,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,1,6,2,8,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,6,1,2,8,3,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,1,5,6,8,2,3,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,5,1,6,8,2,3,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,5,6,1,8,2,3,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,5,6,8,1,2,3,7]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,5,2,6,3,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,1,5,6,2,3,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,5,1,6,2,3,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,5,1,2,6,7,3,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,5,1,6,2,7,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,6,1,2,7,3,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,1,5,6,7,2,3,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,5,1,6,7,2,3,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,5,6,1,7,2,3,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,1,5,2,6,7,8,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,5,1,2,6,7,8,3]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[4,5,1,6,2,7,8,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,5,6,1,2,7,8,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,1,5,6,7,2,8,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,5,1,6,7,2,8,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,5,6,1,7,2,8,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,5,6,7,1,2,8,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,1,5,6,7,8,2,3]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[4,5,1,6,7,8,2,3]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,5,6,1,7,8,2,3]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,5,6,7,1,8,2,3]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,1,5,2,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,1,7,2,3,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,5,7,1,2,3,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,1,5,2,7,8,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,1,2,7,8,3,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,1,5,7,2,8,3,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,1,7,2,8,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,7,1,2,8,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,5,1,7,8,2,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,5,7,8,1,2,3,6]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,5,2,7,3,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,5,1,2,7,3,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,5,7,2,3,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,5,1,7,2,3,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,1,5,2,3,7,6,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,1,2,3,7,6,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,1,2,5,3,7,6,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,2,5,3,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,5,2,3,7,6,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,1,2,5,7,3,6,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,4,2,5,7,3,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,4,5,2,7,3,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,4,5,7,2,3,6,8]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,5,2,3,7,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,1,2,5,3,7,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,4,2,5,3,7,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,4,5,2,3,7,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,1,2,5,7,3,8,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,2,5,7,3,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,4,5,2,7,3,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,5,7,2,3,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,1,2,5,7,8,3,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,4,2,5,7,8,3,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,4,5,2,7,8,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,4,5,7,8,2,3,6]=>0000100=>[4,1,2]=>[2,1,4]
[4,1,5,2,8,3,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,5,1,2,8,3,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,5,8,2,3,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,5,1,8,2,3,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,5,8,1,2,3,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[4,1,5,2,3,8,6,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,1,2,3,8,6,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,1,2,5,3,8,6,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,2,5,3,8,6,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,5,2,3,8,6,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,1,2,5,8,3,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,4,2,5,8,3,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,4,5,2,8,3,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,4,5,8,2,3,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[1,4,2,5,3,6,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,1,2,5,6,3,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,5,2,6,3,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,5,6,2,3,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,1,2,5,6,8,3,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,4,2,5,6,8,3,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,4,5,2,6,8,3,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,4,5,6,2,8,3,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,4,5,6,8,2,3,7]=>0000100=>[4,1,2]=>[2,1,4]
[4,1,5,2,3,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[4,1,2,5,3,6,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,4,2,5,3,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,4,5,2,3,6,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[4,1,2,5,6,3,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,4,5,2,6,3,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,4,5,6,2,3,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,2,5,6,7,3,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,4,2,5,6,7,3,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,4,5,2,6,7,3,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,4,5,6,2,7,3,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,4,5,6,7,2,3,8]=>0000100=>[4,1,2]=>[2,1,4]
[4,1,2,5,6,7,8,3]=>1000001=>[1,5,1]=>[1,5,1]
[1,4,2,5,6,7,8,3]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,4,5,2,6,7,8,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,4,5,6,2,7,8,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,4,5,6,7,2,8,3]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,4,5,6,7,8,2,3]=>0000010=>[5,1,1]=>[1,1,5]
[4,1,6,2,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,7,2,3,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,6,7,1,2,3,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,6,1,2,7,8,3,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,6,1,7,2,8,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,7,1,2,8,3,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,1,6,7,8,2,3,5]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,6,1,7,8,2,3,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,6,7,1,8,2,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,6,7,8,1,2,3,5]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,6,2,7,3,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,6,1,2,7,3,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,6,7,2,3,5,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,6,1,7,2,3,5,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,6,7,1,2,3,5,8]=>0010000=>[2,1,4]=>[4,1,2]
[4,1,6,2,3,7,5,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,1,2,3,7,5,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,1,2,6,3,7,5,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,2,6,3,7,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,2,6,7,3,5,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,4,2,6,7,3,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,4,6,2,7,3,5,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,4,6,7,2,3,5,8]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,6,2,3,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,1,2,6,3,7,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,4,6,2,3,7,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,1,2,6,7,3,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,6,2,7,3,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,6,7,2,3,8,5]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,4,2,6,7,8,3,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,4,6,2,7,8,3,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,4,6,7,2,8,3,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,4,6,7,8,2,3,5]=>0000100=>[4,1,2]=>[2,1,4]
[4,1,6,2,8,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,6,1,2,8,3,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,6,8,2,3,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,6,1,8,2,3,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,6,8,1,2,3,5,7]=>0010000=>[2,1,4]=>[4,1,2]
[4,1,6,2,3,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,1,2,3,8,5,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,1,2,6,3,8,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,2,6,3,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,6,2,3,8,5,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,4,2,6,8,3,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,4,6,2,8,3,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,4,6,8,2,3,5,7]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,6,2,3,5,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,6,1,2,3,5,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[4,1,2,6,3,5,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,4,2,6,3,5,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,4,6,2,3,5,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,1,2,3,6,5,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,2,3,6,5,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,4,6,3,5,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,1,2,3,6,8,5,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,2,4,3,6,8,5,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,4,6,8,3,5,7]=>0000100=>[4,1,2]=>[2,1,4]
[4,1,6,2,3,5,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[4,6,1,2,3,5,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[1,4,2,6,3,5,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,4,6,2,3,5,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[4,1,2,3,6,5,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,4,2,3,6,5,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,4,6,3,5,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,2,3,6,7,5,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,4,2,3,6,7,5,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,4,6,7,3,5,8]=>0000100=>[4,1,2]=>[2,1,4]
[4,1,2,3,6,7,8,5]=>1000001=>[1,5,1]=>[1,5,1]
[1,4,2,3,6,7,8,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,4,6,7,3,8,5]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,4,6,7,8,3,5]=>0000010=>[5,1,1]=>[1,1,5]
[4,1,7,2,8,3,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,1,2,8,3,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,7,8,2,3,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,7,1,8,2,3,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,7,8,1,2,3,5,6]=>0010000=>[2,1,4]=>[4,1,2]
[4,7,1,2,3,8,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,4,2,7,3,8,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,7,2,3,8,5,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,1,2,7,8,3,5,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,4,2,7,8,3,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,4,7,2,8,3,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,4,7,8,2,3,5,6]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,7,2,3,5,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,7,1,2,3,5,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[4,1,2,7,3,5,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,4,2,7,3,5,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,4,7,2,3,5,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,1,2,3,7,5,8,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,2,3,7,5,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,4,3,7,5,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,4,7,3,5,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,1,2,3,7,8,5,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,4,2,3,7,8,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,4,3,7,8,5,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,4,7,3,8,5,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,4,7,8,3,5,6]=>0000100=>[4,1,2]=>[2,1,4]
[4,1,7,2,3,5,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[4,7,1,2,3,5,6,8]=>0100000=>[1,1,5]=>[5,1,1]
[4,1,2,7,3,5,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,4,2,7,3,5,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,4,7,2,3,5,6,8]=>0010000=>[2,1,4]=>[4,1,2]
[4,1,2,3,7,5,6,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,4,2,3,7,5,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,4,3,7,5,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,4,7,3,5,6,8]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,2,3,5,7,6,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,4,2,3,5,7,6,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,4,5,7,3,6,8]=>0000100=>[4,1,2]=>[2,1,4]
[4,1,2,3,5,7,8,6]=>1000001=>[1,5,1]=>[1,5,1]
[1,4,2,3,5,7,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,4,5,7,3,8,6]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,4,5,7,8,3,6]=>0000010=>[5,1,1]=>[1,1,5]
[4,1,8,2,3,5,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[4,8,1,2,3,5,6,7]=>0100000=>[1,1,5]=>[5,1,1]
[4,1,2,8,3,5,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,4,2,8,3,5,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,4,8,2,3,5,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[4,1,2,3,8,5,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,4,2,3,8,5,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,4,3,8,5,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,4,8,3,5,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[4,1,2,3,5,8,6,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,4,2,3,5,8,6,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,4,3,5,8,6,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,4,5,3,8,6,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,4,5,8,3,6,7]=>0000100=>[4,1,2]=>[2,1,4]
[4,1,2,3,5,6,8,7]=>1000001=>[1,5,1]=>[1,5,1]
[1,4,2,3,5,6,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,4,5,6,8,3,7]=>0000010=>[5,1,1]=>[1,1,5]
[1,4,2,3,5,6,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[5,1,6,2,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,1,2,7,3,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,1,6,7,2,3,8,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,6,1,7,2,3,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,6,7,1,2,3,8,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[5,6,1,2,7,8,3,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,1,6,7,2,8,3,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,6,7,1,2,8,3,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,1,6,7,8,2,3,4]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[5,6,1,7,8,2,3,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,6,7,1,8,2,3,4]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,1,6,2,7,3,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,1,2,7,3,4,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,6,1,7,2,3,4,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,1,6,2,3,7,4,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,2,6,3,7,4,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,5,2,6,3,7,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,2,6,7,3,4,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,5,2,6,7,3,4,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,5,6,2,7,3,4,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,5,6,7,2,3,4,8]=>0001000=>[3,1,3]=>[3,1,3]
[5,1,6,2,3,7,8,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,6,1,2,3,7,8,4]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[5,1,2,6,3,7,8,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,5,2,6,3,7,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,6,2,3,7,8,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[5,1,2,6,7,3,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,5,6,7,2,3,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[5,1,2,6,7,8,3,4]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,5,2,6,7,8,3,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,5,6,2,7,8,3,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,5,6,7,2,8,3,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,5,6,7,8,2,3,4]=>0000100=>[4,1,2]=>[2,1,4]
[5,1,6,2,8,3,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,1,2,8,3,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,6,1,8,2,3,4,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,6,8,1,2,3,4,7]=>0010000=>[2,1,4]=>[4,1,2]
[5,1,6,2,3,8,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,1,2,3,8,4,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,1,2,6,3,8,4,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,5,2,6,3,8,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,6,2,3,8,4,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,1,2,6,8,3,4,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,5,2,6,8,3,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,5,6,2,8,3,4,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,5,6,8,2,3,4,7]=>0001000=>[3,1,3]=>[3,1,3]
[5,1,6,2,3,4,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,6,1,2,3,4,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[5,1,2,6,3,4,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,5,2,6,3,4,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,6,2,3,4,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,5,2,3,6,4,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,5,3,6,4,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,5,6,3,4,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[5,1,2,3,6,8,4,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,5,2,3,6,8,4,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,5,6,3,8,4,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,1,6,2,3,4,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,1,2,6,3,4,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,5,2,6,3,4,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,5,6,2,3,4,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[5,1,2,3,6,4,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,5,2,3,6,4,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,5,3,6,4,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,5,6,3,4,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[5,1,2,3,6,7,4,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,5,2,3,6,7,4,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,5,3,6,7,4,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,5,6,3,7,4,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,1,2,3,6,7,8,4]=>1000001=>[1,5,1]=>[1,5,1]
[1,5,2,3,6,7,8,4]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,5,3,6,7,8,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,5,6,3,7,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,5,6,7,3,8,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,5,6,7,8,3,4]=>0000010=>[5,1,1]=>[1,1,5]
[5,1,7,2,8,3,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,7,1,2,8,3,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,1,7,8,2,3,4,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,7,1,8,2,3,4,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,7,8,1,2,3,4,6]=>0010000=>[2,1,4]=>[4,1,2]
[5,1,7,2,3,8,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,7,1,2,3,8,4,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,1,2,7,3,8,4,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,5,2,7,3,8,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,7,2,3,8,4,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,1,2,7,8,3,4,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,5,2,7,8,3,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,5,7,2,8,3,4,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,5,7,8,2,3,4,6]=>0001000=>[3,1,3]=>[3,1,3]
[5,1,7,2,3,4,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,7,1,2,3,4,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[5,1,2,7,3,4,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,5,2,7,3,4,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,7,2,3,4,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[5,1,2,3,7,4,8,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,5,2,3,7,4,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,5,3,7,4,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,5,7,3,4,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[5,1,2,3,7,8,4,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,5,2,3,7,8,4,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,5,7,3,8,4,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,5,7,8,3,4,6]=>0000100=>[4,1,2]=>[2,1,4]
[5,7,1,2,3,4,6,8]=>0100000=>[1,1,5]=>[5,1,1]
[5,1,2,7,3,4,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,5,2,7,3,4,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,5,7,2,3,4,6,8]=>0010000=>[2,1,4]=>[4,1,2]
[1,5,2,3,7,4,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,5,3,7,4,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,5,7,3,4,6,8]=>0001000=>[3,1,3]=>[3,1,3]
[1,5,2,3,4,7,6,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,5,3,4,7,6,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,3,5,7,4,6,8]=>0000100=>[4,1,2]=>[2,1,4]
[5,1,2,3,4,7,8,6]=>1000001=>[1,5,1]=>[1,5,1]
[1,5,2,3,4,7,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,5,3,4,7,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,3,5,7,4,8,6]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,5,7,8,4,6]=>0000010=>[5,1,1]=>[1,1,5]
[5,1,8,2,3,4,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,8,1,2,3,4,6,7]=>0100000=>[1,1,5]=>[5,1,1]
[5,1,2,8,3,4,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,5,2,8,3,4,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,5,8,2,3,4,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[5,1,2,3,8,4,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,5,2,3,8,4,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,5,3,8,4,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,5,8,3,4,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[5,1,2,3,4,8,6,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,5,2,3,4,8,6,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,5,3,4,8,6,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,3,5,4,8,6,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,3,5,8,4,6,7]=>0000100=>[4,1,2]=>[2,1,4]
[5,1,2,3,4,6,8,7]=>1000001=>[1,5,1]=>[1,5,1]
[1,5,2,3,4,6,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,5,3,4,6,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,3,5,6,8,4,7]=>0000010=>[5,1,1]=>[1,1,5]
[1,5,2,3,4,6,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[1,2,5,3,4,6,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[6,1,7,2,8,3,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,1,2,8,3,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,1,7,8,2,3,4,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,7,1,8,2,3,4,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,1,7,2,3,8,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,7,1,2,3,8,4,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,1,2,7,3,8,4,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,6,2,7,3,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,7,2,3,8,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,1,2,7,8,3,4,5]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,6,2,7,8,3,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,6,7,2,8,3,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,6,7,8,2,3,4,5]=>0001000=>[3,1,3]=>[3,1,3]
[6,1,7,2,3,4,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,7,1,2,3,4,8,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[6,1,2,7,3,4,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,6,2,7,3,4,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,6,7,2,3,4,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[6,1,2,3,7,4,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,6,2,3,7,4,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,6,3,7,4,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,1,2,3,7,8,4,5]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,6,2,3,7,8,4,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,6,3,7,8,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,6,7,3,8,4,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,6,7,8,3,4,5]=>0000100=>[4,1,2]=>[2,1,4]
[6,1,7,2,3,4,5,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,1,2,7,3,4,5,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,6,2,7,3,4,5,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,6,7,2,3,4,5,8]=>0010000=>[2,1,4]=>[4,1,2]
[6,1,2,3,7,4,5,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,6,2,3,7,4,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,6,3,7,4,5,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,6,7,3,4,5,8]=>0001000=>[3,1,3]=>[3,1,3]
[6,1,2,3,4,7,5,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,6,2,3,4,7,5,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,6,3,4,7,5,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,3,6,4,7,5,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,3,6,7,4,5,8]=>0000100=>[4,1,2]=>[2,1,4]
[6,1,2,3,4,7,8,5]=>1000001=>[1,5,1]=>[1,5,1]
[1,6,2,3,4,7,8,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,6,3,4,7,8,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,3,6,4,7,8,5]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,3,6,7,4,8,5]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,6,7,8,4,5]=>0000010=>[5,1,1]=>[1,1,5]
[6,1,8,2,3,4,5,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,8,1,2,3,4,5,7]=>0100000=>[1,1,5]=>[5,1,1]
[6,1,2,8,3,4,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,6,2,8,3,4,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,6,8,2,3,4,5,7]=>0010000=>[2,1,4]=>[4,1,2]
[6,1,2,3,8,4,5,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,6,2,3,8,4,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,6,3,8,4,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,6,8,3,4,5,7]=>0001000=>[3,1,3]=>[3,1,3]
[6,1,2,3,4,8,5,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,6,2,3,4,8,5,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,6,3,4,8,5,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,3,6,4,8,5,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,3,6,8,4,5,7]=>0000100=>[4,1,2]=>[2,1,4]
[6,1,2,3,4,5,8,7]=>1000001=>[1,5,1]=>[1,5,1]
[1,6,2,3,4,5,8,7]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,6,3,4,5,8,7]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,3,6,4,5,8,7]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,3,4,6,8,5,7]=>0000010=>[5,1,1]=>[1,1,5]
[1,6,2,3,4,5,7,8]=>0100000=>[1,1,5]=>[5,1,1]
[1,2,6,3,4,5,7,8]=>0010000=>[2,1,4]=>[4,1,2]
[1,2,3,6,4,5,7,8]=>0001000=>[3,1,3]=>[3,1,3]
[7,1,8,2,3,4,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,1,2,8,3,4,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[1,7,2,8,3,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,7,8,2,3,4,5,6]=>0010000=>[2,1,4]=>[4,1,2]
[7,1,2,3,8,4,5,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,7,2,3,8,4,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,7,3,8,4,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,7,8,3,4,5,6]=>0001000=>[3,1,3]=>[3,1,3]
[7,1,2,3,4,8,5,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,7,2,3,4,8,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,2,7,3,4,8,5,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,3,7,4,8,5,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,3,7,8,4,5,6]=>0000100=>[4,1,2]=>[2,1,4]
[7,1,2,3,4,5,8,6]=>1000001=>[1,5,1]=>[1,5,1]
[1,7,2,3,4,5,8,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,7,3,4,5,8,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,3,7,4,5,8,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,3,4,7,5,8,6]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,4,7,8,5,6]=>0000010=>[5,1,1]=>[1,1,5]
[1,7,2,3,4,5,6,8]=>0100000=>[1,1,5]=>[5,1,1]
[1,2,7,3,4,5,6,8]=>0010000=>[2,1,4]=>[4,1,2]
[1,2,3,7,4,5,6,8]=>0001000=>[3,1,3]=>[3,1,3]
[1,2,3,4,7,5,6,8]=>0000100=>[4,1,2]=>[2,1,4]
[1,8,2,3,4,5,6,7]=>0100000=>[1,1,5]=>[5,1,1]
[1,2,8,3,4,5,6,7]=>0010000=>[2,1,4]=>[4,1,2]
[1,2,3,8,4,5,6,7]=>0001000=>[3,1,3]=>[3,1,3]
[1,2,3,4,8,5,6,7]=>0000100=>[4,1,2]=>[2,1,4]
[1,2,3,4,5,8,6,7]=>0000010=>[5,1,1]=>[1,1,5]
[5,3,2,6,1,4,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,3,2,5,4,8,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,5,2,3,7,6,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,4,5,2,3,8,1,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,5,2,3,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,2,1,3,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,1,5,4,2,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,5,1,3,2,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,6,4,3,1,2,8,7]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,5,4,3,2,8,1,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,4,3,7,2,5,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,6,4,3,8,2,1,5]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[6,7,4,3,8,1,2,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,7,4,3,1,8,2,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,7,5,1,3,8,2,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,7,1,5,4,8,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,5,4,8,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,8,1,5,4,7,6,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,8,5,1,3,7,6,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,8,4,3,1,7,6,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[6,8,4,3,7,1,5,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,8,4,3,6,5,1,2]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,8,5,7,3,1,4,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,6,7,1,3,4,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,6,1,7,3,5,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,8,1,6,7,4,5,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,8,6,7,4,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,6,8,4,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,1,6,8,4,2,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,7,6,1,8,3,2,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,7,6,8,1,3,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,7,2,1,8,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,4,7,2,8,1,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,4,6,2,8,3,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,4,6,2,7,3,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,2,6,7,4,5,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,3,2,6,8,4,1,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,3,2,7,8,1,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,3,2,7,1,8,4,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,2,1,7,8,5,6]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,4,1,2,8,7,6,5]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[5,3,2,8,1,7,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,3,2,8,7,1,5,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,3,2,8,6,5,1,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,4,7,2,6,5,3,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,4,8,2,6,5,1,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,4,8,2,7,1,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,8,2,1,7,6,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,5,8,1,2,7,6,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,5,1,8,2,7,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,5,8,3,7,6,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,6,8,7,3,5,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,6,1,8,7,2,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,8,1,7,2,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,6,8,7,1,2,4,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[6,5,8,7,2,1,4,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,5,8,6,2,4,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,5,7,6,2,4,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,7,8,6,1,4,2,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,7,8,1,6,5,2,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,7,1,8,6,5,2,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,1,7,8,6,5,3,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,8,1,7,6,5,4,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[4,8,7,1,6,5,3,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[5,8,7,6,1,4,3,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[6,8,7,5,4,1,3,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[2,1,4,3,6,5,8,7,10,9]=>101010101=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[3,4,1,2,6,5,8,7,10,9]=>010010101=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1]
[4,3,2,1,6,5,8,7,10,9]=>111010101=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3]
[6,3,2,5,4,1,8,7,10,9]=>110110101=>[2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2]
[8,3,2,5,4,7,6,1,10,9]=>110101101=>[2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2]
[10,3,2,5,4,7,6,9,8,1]=>110101011=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2]
[4,5,6,1,2,3,8,7,10,9]=>001000101=>[2,1,3,1,1,1]=>[1,1,1,3,1,2]
[3,5,1,6,2,4,8,7,10,9]=>010100101=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]
[2,1,5,6,3,4,8,7,10,9]=>100100101=>[1,2,1,2,1,1,1]=>[1,1,1,2,1,2,1]
[2,1,6,5,4,3,8,7,10,9]=>101110101=>[1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1]
[6,5,4,3,2,1,8,7,10,9]=>111110101=>[5,1,1,1,1]=>[1,1,1,1,5]
[8,5,4,3,2,7,6,1,10,9]=>111101101=>[4,1,2,1,1]=>[1,1,2,1,4]
[10,5,4,3,2,7,6,9,8,1]=>111101011=>[4,1,1,1,2]=>[2,1,1,1,4]
[2,1,8,5,4,7,6,3,10,9]=>101101101=>[1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1]
[8,7,4,3,6,5,2,1,10,9]=>111011101=>[3,1,3,1,1]=>[1,1,3,1,3]
[10,7,4,3,6,5,2,9,8,1]=>111011011=>[3,1,2,1,2]=>[2,1,2,1,3]
[2,1,10,5,4,7,6,9,8,3]=>101101011=>[1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1]
[10,9,4,3,6,5,8,7,2,1]=>111010111=>[3,1,1,1,3]=>[3,1,1,1,3]
[8,9,5,6,3,4,10,1,2,7]=>010100100=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]
[5,6,7,8,1,2,3,4,10,9]=>000100001=>[3,1,4,1]=>[1,4,1,3]
[4,6,7,1,8,2,3,5,10,9]=>001010001=>[2,1,1,1,3,1]=>[1,3,1,1,1,2]
[3,6,1,7,8,2,4,5,10,9]=>010010001=>[1,1,2,1,3,1]=>[1,3,1,2,1,1]
[2,1,6,7,8,3,4,5,10,9]=>100010001=>[1,3,1,3,1]=>[1,3,1,3,1]
[2,1,5,7,3,8,4,6,10,9]=>100101001=>[1,2,1,1,1,2,1]=>[1,2,1,1,1,2,1]
[3,5,1,7,2,8,4,6,10,9]=>010101001=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]
[4,5,7,1,2,8,3,6,10,9]=>001001001=>[2,1,2,1,2,1]=>[1,2,1,2,1,2]
[3,4,1,2,7,8,5,6,10,9]=>010001001=>[1,1,3,1,2,1]=>[1,2,1,3,1,1]
[2,1,4,3,7,8,5,6,10,9]=>101001001=>[1,1,1,2,1,2,1]=>[1,2,1,2,1,1,1]
[2,1,4,3,8,7,6,5,10,9]=>101011101=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1]
[4,3,2,1,8,7,6,5,10,9]=>111011101=>[3,1,3,1,1]=>[1,1,3,1,3]
[8,3,2,7,6,5,4,1,10,9]=>110111101=>[2,1,4,1,1]=>[1,1,4,1,2]
[10,3,2,7,6,5,4,9,8,1]=>110111011=>[2,1,3,1,2]=>[2,1,3,1,2]
[2,1,8,7,6,5,4,3,10,9]=>101111101=>[1,1,5,1,1]=>[1,1,5,1,1]
[8,7,6,5,4,3,2,1,10,9]=>111111101=>[7,1,1]=>[1,1,7]
[9,7,6,5,4,3,2,10,1,8]=>111111010=>[6,1,1,1]=>[1,1,1,6]
[10,7,6,5,4,3,2,9,8,1]=>111111011=>[6,1,2]=>[2,1,6]
[2,1,10,7,6,5,4,9,8,3]=>101111011=>[1,1,4,1,2]=>[2,1,4,1,1]
[10,9,6,5,4,3,8,7,2,1]=>111110111=>[5,1,3]=>[3,1,5]
[2,1,4,3,10,7,6,9,8,5]=>101011011=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]
[4,3,2,1,10,7,6,9,8,5]=>111011011=>[3,1,2,1,2]=>[2,1,2,1,3]
[10,3,2,9,6,5,8,7,4,1]=>110110111=>[2,1,2,1,3]=>[3,1,2,1,2]
[2,1,10,9,6,5,8,7,4,3]=>101110111=>[1,1,3,1,3]=>[3,1,3,1,1]
[10,9,8,5,4,7,6,3,2,1]=>111101111=>[4,1,4]=>[4,1,4]
[10,8,9,6,7,4,5,2,3,1]=>101010101=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[2,1,7,8,9,10,3,4,5,6]=>100001000=>[1,4,1,3]=>[3,1,4,1]
[3,7,1,8,9,10,2,4,5,6]=>010001000=>[1,1,3,1,3]=>[3,1,3,1,1]
[4,7,8,1,9,10,2,3,5,6]=>001001000=>[2,1,2,1,3]=>[3,1,2,1,2]
[5,7,8,9,1,10,2,3,4,6]=>000101000=>[3,1,1,1,3]=>[3,1,1,1,3]
[6,7,8,9,10,1,2,3,4,5]=>000010000=>[4,1,4]=>[4,1,4]
[5,6,8,9,1,2,10,3,4,7]=>000100100=>[3,1,2,1,2]=>[2,1,2,1,3]
[4,6,8,1,9,2,10,3,5,7]=>001010100=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2]
[3,6,1,8,9,2,10,4,5,7]=>010010100=>[1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1]
[2,1,6,8,9,3,10,4,5,7]=>100010100=>[1,3,1,1,1,2]=>[2,1,1,1,3,1]
[2,1,5,8,3,9,10,4,6,7]=>100100100=>[1,2,1,2,1,2]=>[2,1,2,1,2,1]
[3,5,1,8,2,9,10,4,6,7]=>010100100=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]
[4,5,8,1,2,9,10,3,6,7]=>001000100=>[2,1,3,1,2]=>[2,1,3,1,2]
[7,3,2,8,9,10,1,4,5,6]=>110001000=>[2,3,1,3]=>[3,1,3,2]
[3,4,1,2,8,9,10,5,6,7]=>010000100=>[1,1,4,1,2]=>[2,1,4,1,1]
[2,1,4,3,8,9,10,5,6,7]=>101000100=>[1,1,1,3,1,2]=>[2,1,3,1,1,1]
[2,1,4,3,7,9,5,10,6,8]=>101001010=>[1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1]
[3,4,1,2,7,9,5,10,6,8]=>010001010=>[1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1]
[4,5,7,1,2,9,3,10,6,8]=>001001010=>[2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2]
[3,5,1,7,2,9,4,10,6,8]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[2,1,5,7,3,9,4,10,6,8]=>100101010=>[1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1]
[2,1,6,7,9,3,4,10,5,8]=>100010010=>[1,3,1,2,1,1]=>[1,1,2,1,3,1]
[3,6,1,7,9,2,4,10,5,8]=>010010010=>[1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1]
[4,6,7,1,9,2,3,10,5,8]=>001010010=>[2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2]
[5,6,7,9,1,2,3,10,4,8]=>000100010=>[3,1,3,1,1]=>[1,1,3,1,3]
[8,5,4,3,2,9,10,1,6,7]=>111100100=>[4,2,1,2]=>[2,1,2,4]
[2,1,5,6,3,4,9,10,7,8]=>100100010=>[1,2,1,3,1,1]=>[1,1,3,1,2,1]
[3,5,1,6,2,4,9,10,7,8]=>010100010=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1]
[4,5,6,1,2,3,9,10,7,8]=>001000010=>[2,1,4,1,1]=>[1,1,4,1,2]
[3,4,1,2,6,5,9,10,7,8]=>010010010=>[1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1]
[2,1,4,3,6,5,9,10,7,8]=>101010010=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1]
[2,1,4,3,6,5,10,9,8,7]=>101010111=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[4,3,2,1,6,5,10,9,8,7]=>111010111=>[3,1,1,1,3]=>[3,1,1,1,3]
[6,3,2,5,4,1,10,9,8,7]=>110110111=>[2,1,2,1,3]=>[3,1,2,1,2]
[10,3,2,5,4,9,8,7,6,1]=>110101111=>[2,1,1,1,4]=>[4,1,1,1,2]
[2,1,6,5,4,3,10,9,8,7]=>101110111=>[1,1,3,1,3]=>[3,1,3,1,1]
[6,5,4,3,2,1,10,9,8,7]=>111110111=>[5,1,3]=>[3,1,5]
[10,5,4,3,2,9,8,7,6,1]=>111101111=>[4,1,4]=>[4,1,4]
[2,1,10,5,4,9,8,7,6,3]=>101101111=>[1,1,2,1,4]=>[4,1,2,1,1]
[10,9,4,3,8,7,6,5,2,1]=>111011111=>[3,1,5]=>[5,1,3]
[9,7,5,10,3,8,2,6,1,4]=>110101010=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]
[2,1,4,3,10,9,8,7,6,5]=>101011111=>[1,1,1,1,5]=>[5,1,1,1,1]
[4,3,2,1,10,9,8,7,6,5]=>111011111=>[3,1,5]=>[5,1,3]
[10,3,2,9,8,7,6,5,4,1]=>110111111=>[2,1,6]=>[6,1,2]
[2,1,10,9,8,7,6,5,4,3]=>101111111=>[1,1,7]=>[7,1,1]
[9,10,8,7,6,5,4,3,1,2]=>011111110=>[1,7,1]=>[1,7,1]
[10,9,8,7,6,5,4,3,2,1]=>111111111=>[9]=>[9]
[3,2,5,1,4,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[4,2,5,1,3,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,2,4,1,3,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,2,6,1,4,5,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[4,2,6,1,3,5,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,3,6,1,2,4,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,2,4,1,3,5,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,3,5,1,2,4,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,2,7,1,3,4,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,3,7,1,2,4,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,4,7,1,2,3,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,2,7,1,3,4,5,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,3,7,1,2,4,5,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,4,7,1,2,3,5,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,3,5,1,2,4,6,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,3,6,1,2,4,5,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,4,6,1,2,3,5,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,2,8,1,4,5,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[4,2,8,1,3,5,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,2,8,1,3,4,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,4,8,1,2,3,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,2,8,1,3,4,5,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,3,8,1,2,4,5,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,4,8,1,2,3,5,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,5,8,1,2,3,4,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,2,8,1,3,4,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,3,8,1,2,4,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,4,8,1,2,3,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,5,8,1,2,3,4,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,2,4,1,3,5,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,3,5,1,2,4,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,3,6,1,2,4,5,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,3,7,1,2,4,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,4,7,1,2,3,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,5,7,1,2,3,4,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[3,2,5,7,1,4,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,2,5,7,1,3,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,3,5,7,1,2,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,2,4,7,1,3,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,3,4,7,1,2,6,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,2,6,7,1,3,5,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,2,6,7,1,3,4,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,3,6,7,1,2,4,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,2,5,7,1,3,4,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,3,5,7,1,2,4,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,2,4,6,1,3,5,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,3,4,6,1,2,5,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,3,5,6,1,2,4,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,2,5,8,1,4,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,2,5,8,1,3,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,3,5,8,1,2,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,2,4,8,1,3,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,2,6,8,1,4,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,2,6,8,1,3,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,3,6,8,1,2,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,2,6,8,1,3,4,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,2,4,8,1,3,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,3,4,8,1,2,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,2,5,8,1,3,4,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,3,5,8,1,2,4,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,4,5,8,1,2,3,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,2,7,8,1,4,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,3,7,8,1,2,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,3,7,8,1,2,4,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,2,7,8,1,3,4,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,3,7,8,1,2,4,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,4,7,8,1,2,3,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,2,4,8,1,3,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,3,4,8,1,2,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,3,5,8,1,2,4,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,4,5,8,1,2,3,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,4,6,8,1,2,3,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,2,4,6,1,3,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,3,4,6,1,2,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,2,5,6,1,3,4,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,3,5,6,1,2,4,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,2,4,7,1,3,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,2,5,7,1,3,4,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,3,5,7,1,2,4,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,2,6,7,1,3,4,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[8,4,6,7,1,2,3,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,6,2,5,1,4,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,6,2,5,1,3,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,6,3,5,1,2,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,7,2,5,1,4,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,7,3,5,1,2,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,7,2,4,1,3,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,7,3,4,1,2,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,7,2,6,1,4,5,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,7,3,6,1,2,5,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,7,2,6,1,3,4,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,7,3,6,1,2,4,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,7,2,5,1,3,4,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,2,5,1,3,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,8,2,4,1,3,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,8,3,4,1,2,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,8,2,6,1,4,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,2,6,1,3,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,8,3,6,1,2,4,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,8,4,6,1,2,3,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,2,4,1,3,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,3,4,1,2,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,3,5,1,2,4,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,4,5,1,2,3,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,8,2,7,1,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,2,7,1,3,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,3,7,1,2,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,8,2,7,1,3,4,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,8,3,7,1,2,4,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,8,4,7,1,2,3,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,2,7,1,3,4,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,3,7,1,2,4,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,5,7,1,2,3,4]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,8,2,4,1,3,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,8,2,5,1,3,4,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,8,3,5,1,2,4,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,8,4,6,1,2,3,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,3,2,6,1,5,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[5,3,2,6,1,4,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,3,2,5,1,4,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,4,2,5,1,3,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,5,2,4,1,3,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[4,3,2,7,1,5,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[5,3,2,7,1,4,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[5,4,3,7,1,2,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,3,2,7,1,4,5,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,4,2,7,1,3,5,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,4,3,7,1,2,5,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,5,3,7,1,2,4,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,3,2,5,1,4,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,2,5,1,3,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,3,2,6,1,4,5,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,2,6,1,3,5,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,3,6,1,2,5,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,5,2,6,1,3,4,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,5,3,6,1,2,4,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,6,3,5,1,2,4,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[4,3,2,8,1,5,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[5,3,2,8,1,4,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[5,4,3,8,1,2,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,3,2,8,1,4,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,4,2,8,1,3,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,4,3,8,1,2,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,5,2,8,1,3,4,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,5,3,8,1,2,4,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,5,4,8,1,2,3,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,3,2,8,1,4,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,2,8,1,3,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,3,8,1,2,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,5,3,8,1,2,4,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,5,4,8,1,2,3,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,6,2,8,1,3,4,5]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,3,2,5,1,4,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,4,2,5,1,3,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,3,2,6,1,4,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,4,2,6,1,3,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,5,3,6,1,2,4,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,6,2,4,1,3,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,6,2,5,1,3,4,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,3,2,7,1,4,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,4,2,7,1,3,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,4,3,7,1,2,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,5,2,7,1,3,4,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,5,3,7,1,2,4,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,5,4,7,1,2,3,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,6,3,7,1,2,4,5]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,7,2,4,1,3,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,7,2,5,1,3,4,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,7,3,5,1,2,4,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,7,2,6,1,3,4,5]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,7,3,6,1,2,4,5]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,7,4,6,1,2,3,5]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[3,6,2,5,8,1,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,6,3,5,8,1,2,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,6,2,4,8,1,3,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,7,2,5,8,1,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,7,3,5,8,1,2,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,7,2,4,8,1,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,7,3,4,8,1,2,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,7,2,6,8,1,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,7,3,6,8,1,2,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,7,2,6,8,1,3,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,7,4,6,8,1,2,3]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,7,3,4,8,1,2,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,7,3,5,8,1,2,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,8,2,5,7,1,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,8,2,5,7,1,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,8,3,5,7,1,2,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,8,2,4,7,1,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,8,2,6,7,1,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,8,3,6,7,1,2,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,8,2,6,7,1,3,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,8,3,6,7,1,2,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,8,2,5,7,1,3,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,8,3,5,7,1,2,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,8,4,5,7,1,2,3]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,8,2,4,6,1,3,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,8,2,5,6,1,3,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,8,3,5,6,1,2,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,3,2,6,8,1,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,3,2,6,8,1,4,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,4,2,6,8,1,3,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,4,3,6,8,1,2,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,3,2,5,8,1,4,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,4,3,5,8,1,2,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,5,2,4,8,1,3,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,3,2,7,8,1,5,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,3,2,7,8,1,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,4,2,7,8,1,3,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,4,3,7,8,1,2,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,4,2,7,8,1,3,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,4,3,7,8,1,2,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,5,2,7,8,1,3,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,4,2,5,8,1,3,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,4,3,5,8,1,2,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,5,3,4,8,1,2,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,3,2,6,8,1,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,5,2,6,8,1,3,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,5,3,6,8,1,2,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,6,2,4,8,1,3,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,6,3,5,8,1,2,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,3,2,5,7,1,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,4,2,5,7,1,3,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,5,2,4,7,1,3,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,3,2,6,7,1,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,4,2,6,7,1,3,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,5,2,6,7,1,3,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,5,3,6,7,1,2,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,6,2,4,7,1,3,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,6,3,5,7,1,2,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,7,2,4,6,1,3,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,7,3,4,6,1,2,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,7,2,5,6,1,3,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,7,3,5,6,1,2,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,3,7,2,6,1,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,7,2,6,1,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,7,2,6,1,3,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,7,2,5,1,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,7,2,5,1,3,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,7,3,5,1,2,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,6,2,5,1,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,8,2,6,1,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,8,2,6,1,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,8,2,6,1,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,8,3,6,1,2,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,8,2,5,1,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,8,3,5,1,2,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,5,8,2,4,1,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,5,8,3,4,1,2,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,8,2,7,1,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,8,2,7,1,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,8,2,7,1,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,8,3,7,1,2,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,8,2,7,1,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,8,2,7,1,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,8,3,7,1,2,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,8,2,5,1,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,4,8,3,5,1,2,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,5,8,2,4,1,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,5,8,3,4,1,2,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,8,2,6,1,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,4,8,2,6,1,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,5,8,2,6,1,3,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,5,8,3,6,1,2,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,5,8,4,6,1,2,3]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,6,8,2,5,1,3,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,6,8,3,5,1,2,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,3,6,2,5,1,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,6,2,4,1,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,3,7,2,5,1,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,7,2,4,1,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,3,7,2,6,1,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,4,7,2,6,1,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,4,7,3,6,1,2,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,7,2,6,1,3,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,7,2,4,1,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,7,2,5,1,3,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,7,3,5,1,2,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,3,2,7,1,6,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,4,3,2,7,1,5,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,5,3,2,7,1,4,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,5,4,2,7,1,3,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,3,2,6,1,4,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,4,2,6,1,3,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,6,3,2,5,1,4,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[5,4,3,2,8,1,6,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,5,3,2,8,1,4,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,5,4,2,8,1,3,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,5,4,3,8,1,2,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,3,2,8,1,4,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,4,2,8,1,3,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,6,3,2,8,1,4,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,6,4,3,8,1,2,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,6,5,2,8,1,3,4]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,5,3,2,6,1,4,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,5,4,2,6,1,3,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,6,4,2,5,1,3,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,6,5,2,4,1,3,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,5,3,2,7,1,4,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,6,3,2,7,1,4,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,6,4,2,7,1,3,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,6,4,3,7,1,2,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,3,2,6,1,4,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,4,2,6,1,3,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,4,3,6,1,2,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,5,2,6,1,3,4]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,6,2,4,1,3,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,6,2,5,1,3,4]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,6,3,5,1,2,4]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[4,8,3,7,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,7,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,7,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,7,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,7,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,4,7,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,4,7,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,5,7,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,5,7,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,6,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,4,6,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,4,6,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,5,6,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,3,8,2,7,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,4,3,8,2,7,1,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,3,8,2,7,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,4,8,2,7,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,4,8,3,7,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,3,8,2,6,1,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,3,8,2,6,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,4,8,2,6,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,3,8,2,5,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,4,8,2,5,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,5,8,2,4,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,3,7,2,6,1,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,3,7,2,6,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,4,7,2,6,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,4,7,3,6,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,6,3,7,2,5,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,6,4,7,2,5,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,6,5,7,2,4,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,7,3,6,2,5,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,7,4,6,2,5,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,7,4,6,3,5,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,7,5,6,2,4,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,4,3,2,8,1,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,6,4,3,2,8,1,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,6,5,4,2,8,1,3]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,5,4,3,2,7,1,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,4,3,2,7,1,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,5,3,2,7,1,4]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,5,4,2,7,1,3]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,7,4,3,2,6,1,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,7,5,3,2,6,1,4]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,7,5,4,2,6,1,3]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,7,6,3,2,5,1,4]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,7,6,4,2,5,1,3]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,7,6,5,2,4,1,3]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,1,2,3,4,7,5,6]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[8,1,2,3,6,4,5,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[8,1,2,3,7,4,5,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[7,1,2,3,6,4,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,1,2,3,8,7,4,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[8,1,2,3,6,7,4,5]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[4,1,2,8,3,7,5,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,2,5,3,4,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,1,2,5,3,4,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,2,6,3,4,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,1,2,6,3,4,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,1,2,5,3,8,4,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,2,5,3,7,4,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,2,6,3,7,4,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,2,5,3,7,8,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,1,2,8,6,3,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,1,2,8,7,3,5,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,1,2,7,6,3,8,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,1,2,5,6,3,4,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[8,1,2,5,7,3,4,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[8,1,2,7,6,3,4,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[7,1,2,5,6,3,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,1,2,5,8,7,3,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,1,2,8,6,7,3,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,2,5,6,7,3,4]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[3,1,8,2,4,7,5,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,1,8,2,6,4,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,1,8,2,7,4,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,1,7,2,6,4,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,2,8,7,4,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,8,2,6,7,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,1,4,2,3,5,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,1,4,2,3,5,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,1,4,2,3,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,1,4,2,3,7,5,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,1,4,2,3,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,1,5,2,3,4,6,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[7,1,5,2,3,4,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,1,7,2,3,4,5,6]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[6,1,5,2,3,8,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,1,5,2,3,7,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,1,8,2,3,7,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,1,5,2,3,7,8,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,1,4,2,8,3,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,4,2,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,4,2,6,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,1,4,2,7,3,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,4,2,6,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,5,2,6,3,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,1,5,2,7,3,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,8,2,6,3,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,5,2,6,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,4,2,6,8,3,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,4,2,8,7,3,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,1,4,2,6,7,3,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,1,5,2,6,7,3,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,4,2,6,7,8,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,1,4,8,2,7,5,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,1,8,5,2,4,6,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[3,1,7,5,2,4,8,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,1,8,6,2,4,5,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[3,1,7,6,2,4,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,1,6,5,2,8,4,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,8,5,2,7,4,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,8,6,2,7,4,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,6,5,2,7,8,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,1,4,5,2,3,6,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,1,4,5,2,3,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,4,6,2,3,5,7]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,1,4,8,2,3,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,1,4,6,2,3,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,6,5,2,3,4,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,1,8,5,2,3,4,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,1,8,6,2,3,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,1,6,5,2,3,8,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,1,4,5,2,8,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,4,5,2,7,3,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,4,6,2,7,3,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,6,5,2,7,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,1,4,5,2,7,8,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,1,4,8,6,2,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,1,4,8,7,2,5,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,1,4,7,6,2,8,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,1,8,5,6,2,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,1,8,5,7,2,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,1,8,7,6,2,4,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[3,1,7,5,6,2,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,4,5,6,2,3,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[8,1,4,5,7,2,3,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[8,1,4,7,6,2,3,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,1,7,5,6,2,3,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,4,5,6,2,8,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,1,4,5,8,7,2,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,1,4,8,6,7,2,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,1,8,5,6,7,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,1,4,5,6,7,2,3]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[2,8,1,3,4,7,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,8,1,3,6,4,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,8,1,3,7,4,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,7,1,3,6,4,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,1,3,8,7,4,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,8,1,3,6,7,4,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,4,1,8,3,7,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,1,5,3,4,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,7,1,5,3,4,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,1,6,3,4,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,7,1,6,3,4,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,1,5,3,8,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,1,5,3,7,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,1,5,3,7,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,1,8,6,3,5,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,4,1,8,7,3,5,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,4,1,7,6,3,8,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,1,5,6,3,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,8,1,5,7,3,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,8,1,7,6,3,4,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,7,1,5,6,3,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,1,5,8,7,3,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,4,1,8,6,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,1,5,6,7,3,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,3,1,2,4,5,8,6]=>1100001=>[2,4,1]=>[1,4,2]
[6,3,1,2,4,8,5,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,3,1,2,4,7,5,6]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[6,3,1,2,4,7,8,5]=>1100001=>[2,4,1]=>[1,4,2]
[5,3,1,2,8,4,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,3,1,2,7,4,8,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,3,1,2,6,4,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,3,1,2,7,4,5,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,3,1,2,6,4,8,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,3,1,2,6,8,4,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,3,1,2,8,7,4,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,3,1,2,6,7,4,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,3,1,2,6,7,8,4]=>1100001=>[2,4,1]=>[1,4,2]
[7,4,1,2,3,5,8,6]=>1100001=>[2,4,1]=>[1,4,2]
[6,4,1,2,3,8,5,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,4,1,2,3,7,5,6]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[6,4,1,2,3,7,8,5]=>1100001=>[2,4,1]=>[1,4,2]
[7,6,1,2,3,4,8,5]=>1100001=>[2,4,1]=>[1,4,2]
[5,8,1,2,3,7,4,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,6,1,2,3,7,4,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,4,1,2,8,3,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,4,1,2,7,3,8,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,4,1,2,6,3,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,4,1,2,7,3,5,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,4,1,2,6,3,8,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,8,1,2,6,3,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,8,1,2,7,3,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,7,1,2,6,3,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,7,1,2,6,3,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,4,1,2,6,8,3,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,4,1,2,8,7,3,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,4,1,2,6,7,3,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,8,1,2,6,7,3,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,4,1,2,6,7,8,3]=>1100001=>[2,4,1]=>[1,4,2]
[4,3,1,8,2,5,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[4,3,1,7,2,5,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,3,1,6,2,8,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,1,8,2,7,5,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,1,6,2,7,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,3,1,5,2,4,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,3,1,5,2,4,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,3,1,6,2,4,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,3,1,8,2,4,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,3,1,6,2,4,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,1,5,2,8,4,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,3,1,5,2,7,4,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,3,1,6,2,7,4,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,1,5,2,7,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,4,1,5,2,3,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,1,5,2,3,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,4,1,6,2,3,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,1,8,2,3,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,1,6,2,3,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,8,1,5,2,3,4,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,7,1,5,2,3,4,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,7,1,6,2,3,4,5]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,7,1,5,2,3,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,4,1,5,2,8,3,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,1,5,2,7,3,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,1,6,2,7,3,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,8,1,5,2,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,1,5,2,7,8,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,3,1,5,8,2,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,3,1,5,7,2,8,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,3,1,8,6,2,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[4,3,1,8,7,2,5,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[4,3,1,7,6,2,8,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,3,1,5,6,2,4,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,3,1,5,7,2,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,3,1,7,6,2,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,3,1,5,6,2,8,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,4,1,5,6,2,3,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,4,1,5,7,2,3,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,4,1,7,6,2,3,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,8,1,5,6,2,3,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,4,1,5,6,2,8,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,3,1,5,6,8,2,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,3,1,5,8,7,2,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,3,1,8,6,7,2,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,3,1,5,6,7,2,4]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,4,1,5,6,7,2,3]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,3,1,5,6,7,8,2]=>1100001=>[2,4,1]=>[1,4,2]
[2,3,8,1,4,7,5,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,8,1,6,4,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,8,1,7,4,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,7,1,6,4,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,5,1,8,7,4,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,3,8,1,6,7,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,8,4,1,3,5,6,7]=>0110000=>[1,2,4]=>[4,2,1]
[2,7,4,1,3,5,8,6]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,6,4,1,3,8,5,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,4,1,3,7,5,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,6,4,1,3,7,8,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,8,5,1,3,4,6,7]=>0110000=>[1,2,4]=>[4,2,1]
[2,7,5,1,3,4,8,6]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,8,7,1,3,4,5,6]=>0110000=>[1,2,4]=>[4,2,1]
[2,6,5,1,3,8,4,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,5,1,3,7,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,6,8,1,3,7,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,6,5,1,3,7,8,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,5,4,1,8,3,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,5,4,1,7,3,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,4,1,6,3,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,8,4,1,7,3,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,7,4,1,6,3,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,5,1,6,3,4,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,8,5,1,7,3,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,7,8,1,6,3,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,7,5,1,6,3,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,5,4,1,6,8,3,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,5,4,1,8,7,3,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,8,4,1,6,7,3,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,5,1,6,7,3,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,5,4,1,6,7,8,3]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,3,4,1,2,5,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,3,4,1,2,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,3,4,1,2,7,5,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,4,1,2,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,3,5,1,2,4,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,3,7,1,2,4,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,3,5,1,2,8,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,3,5,1,2,7,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,8,1,2,7,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,5,1,2,7,8,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,5,4,1,2,3,8,6]=>1110001=>[3,3,1]=>[1,3,3]
[6,8,4,1,2,3,5,7]=>0110000=>[1,2,4]=>[4,2,1]
[6,7,4,1,2,3,8,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[6,8,5,1,2,3,4,7]=>0110000=>[1,2,4]=>[4,2,1]
[6,7,5,1,2,3,8,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[6,5,4,1,2,8,3,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,5,4,1,2,7,3,6]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,8,4,1,2,7,3,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,8,5,1,2,7,3,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,5,4,1,2,7,8,3]=>1110001=>[3,3,1]=>[1,3,3]
[5,3,4,1,8,2,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,4,1,7,2,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,4,1,6,2,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,3,4,1,7,2,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,4,1,6,2,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,5,1,6,2,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,3,5,1,7,2,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,8,1,6,2,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,5,1,6,2,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,4,1,6,2,3,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,5,4,1,7,2,3,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,8,4,1,6,2,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,8,5,1,6,2,3,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,5,4,1,6,2,8,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,3,4,1,6,8,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,3,4,1,8,7,2,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,3,4,1,6,7,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,3,5,1,6,7,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,5,4,1,6,7,2,3]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[5,3,4,1,6,7,8,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,3,4,8,1,7,5,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,8,5,1,4,6,7]=>0011000=>[2,2,3]=>[3,2,2]
[2,3,7,5,1,4,8,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,3,8,6,1,4,5,7]=>0011000=>[2,2,3]=>[3,2,2]
[2,3,7,6,1,4,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,3,6,5,1,8,4,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,3,8,5,1,7,4,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,3,8,6,1,7,4,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,3,6,5,1,7,8,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,8,4,5,1,3,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,7,4,5,1,3,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,4,6,1,3,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,7,4,8,1,3,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,7,4,6,1,3,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,6,5,1,3,4,7]=>0111000=>[1,3,3]=>[3,3,1]
[2,7,8,5,1,3,4,6]=>0011000=>[2,2,3]=>[3,2,2]
[2,7,8,6,1,3,4,5]=>0011000=>[2,2,3]=>[3,2,2]
[2,7,6,5,1,3,8,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,6,4,5,1,8,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,4,5,1,7,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,4,6,1,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,6,5,1,7,3,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,6,4,5,1,7,8,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,4,5,1,2,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,3,4,6,1,2,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,3,6,5,1,2,4,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,3,8,5,1,2,4,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,3,8,6,1,2,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,3,6,5,1,2,8,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,6,4,5,1,2,8,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,4,5,1,8,2,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,3,4,5,1,7,2,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,3,4,6,1,7,2,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,3,6,5,1,7,2,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,6,4,5,1,7,2,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,4,5,1,7,8,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,3,4,8,6,1,5,7]=>0001100=>[3,2,2]=>[2,2,3]
[2,3,4,8,7,1,5,6]=>0001100=>[3,2,2]=>[2,2,3]
[2,3,4,7,6,1,8,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,3,8,5,6,1,4,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,8,5,7,1,4,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,8,7,6,1,4,5]=>0011100=>[2,3,2]=>[2,3,2]
[2,3,7,5,6,1,8,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,8,4,5,6,1,3,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,8,4,5,7,1,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,8,4,7,6,1,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,8,7,5,6,1,3,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,7,4,5,6,1,8,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,4,5,7,1,2,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[8,3,4,7,6,1,2,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,3,7,5,6,1,2,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,4,5,6,1,8,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,3,4,5,8,7,1,6]=>0000110=>[4,2,1]=>[1,2,4]
[2,3,4,8,6,7,1,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,8,5,6,7,1,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,8,4,5,6,7,1,3]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[9,1,2,3,4,5,6,7,8]=>10000000=>[1,7]=>[7,1]
[8,1,2,3,4,5,6,9,7]=>10000001=>[1,6,1]=>[1,6,1]
[7,1,2,3,4,5,9,6,8]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[9,1,2,3,4,5,8,6,7]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[7,1,2,3,4,5,8,9,6]=>10000001=>[1,6,1]=>[1,6,1]
[6,1,2,3,4,9,5,7,8]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[6,1,2,3,4,8,5,9,7]=>10000101=>[1,4,1,1,1]=>[1,1,1,4,1]
[9,1,2,3,4,7,5,6,8]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[9,1,2,3,4,8,5,6,7]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[8,1,2,3,4,7,5,9,6]=>10000101=>[1,4,1,1,1]=>[1,1,1,4,1]
[6,1,2,3,4,7,9,5,8]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[6,1,2,3,4,9,8,5,7]=>10000110=>[1,4,2,1]=>[1,2,4,1]
[9,1,2,3,4,7,8,5,6]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[6,1,2,3,4,7,8,9,5]=>10000001=>[1,6,1]=>[1,6,1]
[5,1,2,3,8,4,6,9,7]=>10001001=>[1,3,1,2,1]=>[1,2,1,3,1]
[9,1,2,3,6,4,5,7,8]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[8,1,2,3,9,4,5,6,7]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[5,1,2,3,9,8,4,6,7]=>10001100=>[1,3,2,2]=>[2,2,3,1]
[9,1,2,3,6,8,4,5,7]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[5,1,2,3,6,9,8,4,7]=>10000110=>[1,4,2,1]=>[1,2,4,1]
[5,1,2,3,6,7,8,9,4]=>10000001=>[1,6,1]=>[1,6,1]
[4,1,2,8,3,5,6,9,7]=>10010001=>[1,2,1,3,1]=>[1,3,1,2,1]
[4,1,2,9,3,5,8,6,7]=>10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[4,1,2,9,3,8,5,6,7]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[9,1,2,5,3,4,6,7,8]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[9,1,2,8,3,4,5,6,7]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[7,1,2,8,3,4,5,9,6]=>10010001=>[1,2,1,3,1]=>[1,3,1,2,1]
[4,1,2,5,9,3,6,7,8]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[4,1,2,8,9,3,5,6,7]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[8,1,2,5,9,3,4,6,7]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[8,1,2,9,6,3,4,5,7]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[4,1,2,5,9,8,3,6,7]=>10001100=>[1,3,2,2]=>[2,2,3,1]
[9,1,2,8,6,7,3,4,5]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[4,1,2,5,6,7,9,3,8]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[4,1,2,9,6,7,8,3,5]=>10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[9,1,2,5,6,7,8,3,4]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[4,1,2,5,6,7,8,9,3]=>10000001=>[1,6,1]=>[1,6,1]
[3,1,9,2,4,5,6,7,8]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[3,1,8,2,4,5,6,9,7]=>10100001=>[1,1,1,4,1]=>[1,4,1,1,1]
[3,1,9,2,4,5,8,6,7]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[3,1,5,2,7,4,9,6,8]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[8,1,4,2,3,5,6,9,7]=>10100001=>[1,1,1,4,1]=>[1,4,1,1,1]
[9,1,4,2,3,5,8,6,7]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[6,1,4,2,3,7,8,9,5]=>10100001=>[1,1,1,4,1]=>[1,4,1,1,1]
[9,1,8,2,3,4,5,6,7]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[8,1,7,2,3,4,5,9,6]=>10100001=>[1,1,1,4,1]=>[1,4,1,1,1]
[3,1,4,9,2,5,6,7,8]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[3,1,4,9,2,5,8,6,7]=>10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[3,1,9,8,2,4,5,6,7]=>10110000=>[1,1,2,4]=>[4,2,1,1]
[9,1,4,5,2,3,6,7,8]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[7,1,4,5,2,3,8,9,6]=>10010001=>[1,2,1,3,1]=>[1,3,1,2,1]
[7,1,4,9,2,3,5,6,8]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[9,1,4,8,2,3,5,6,7]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[9,1,6,5,2,3,4,7,8]=>10110000=>[1,1,2,4]=>[4,2,1,1]
[7,1,9,6,2,3,4,5,8]=>10110000=>[1,1,2,4]=>[4,2,1,1]
[9,1,8,6,2,3,4,5,7]=>10110000=>[1,1,2,4]=>[4,2,1,1]
[7,1,8,9,2,3,4,5,6]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[3,1,4,8,9,2,5,6,7]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[3,1,8,9,7,2,4,5,6]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[8,1,4,5,6,2,3,9,7]=>10001001=>[1,3,1,2,1]=>[1,2,1,3,1]
[8,1,4,9,7,2,3,5,6]=>10011000=>[1,2,2,3]=>[3,2,2,1]
[8,1,9,5,6,2,3,4,7]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[8,1,9,7,6,2,3,4,5]=>10111000=>[1,1,3,3]=>[3,3,1,1]
[7,1,4,5,6,2,8,9,3]=>10001001=>[1,3,1,2,1]=>[1,2,1,3,1]
[3,1,4,5,6,9,2,7,8]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[3,1,4,5,6,8,2,9,7]=>10000101=>[1,4,1,1,1]=>[1,1,1,4,1]
[3,1,4,9,8,7,2,5,6]=>10011100=>[1,2,3,2]=>[2,3,2,1]
[3,1,9,8,6,7,2,4,5]=>10110100=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]
[9,1,4,5,6,7,2,3,8]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[9,1,4,8,6,7,2,3,5]=>10010100=>[1,2,1,1,1,2]=>[2,1,1,1,2,1]
[9,1,8,5,6,7,2,3,4]=>10100100=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
[8,1,4,5,6,7,2,9,3]=>10000101=>[1,4,1,1,1]=>[1,1,1,4,1]
[3,1,4,5,6,7,9,2,8]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[3,1,4,9,6,7,8,2,5]=>10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[3,1,9,5,6,7,8,2,4]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[9,1,4,5,6,7,8,2,3]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[3,1,4,5,6,7,8,9,2]=>10000001=>[1,6,1]=>[1,6,1]
[2,9,1,3,4,5,6,7,8]=>01000000=>[1,1,6]=>[6,1,1]
[2,8,1,3,4,5,6,9,7]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[2,7,1,3,4,5,9,6,8]=>01000010=>[1,1,4,1,1]=>[1,1,4,1,1]
[2,9,1,3,4,5,8,6,7]=>01000010=>[1,1,4,1,1]=>[1,1,4,1,1]
[2,7,1,3,4,5,8,9,6]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[2,6,1,3,4,9,5,7,8]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[2,9,1,3,4,8,5,6,7]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[2,8,1,3,9,4,5,6,7]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[2,9,1,3,8,7,4,5,6]=>01001100=>[1,1,2,2,2]=>[2,2,2,1,1]
[2,9,1,3,6,7,8,4,5]=>01000010=>[1,1,4,1,1]=>[1,1,4,1,1]
[2,5,1,3,6,7,8,9,4]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[2,4,1,6,3,8,5,9,7]=>01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[2,9,1,8,3,4,5,6,7]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[2,7,1,6,3,4,8,9,5]=>01010001=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
[2,6,1,5,3,7,8,9,4]=>01010001=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
[2,4,1,5,9,3,6,7,8]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[2,4,1,8,9,3,5,6,7]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[2,8,1,9,7,3,4,5,6]=>01011000=>[1,1,1,2,3]=>[3,2,1,1,1]
[2,9,1,8,6,7,3,4,5]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[2,4,1,5,6,7,9,3,8]=>01000010=>[1,1,4,1,1]=>[1,1,4,1,1]
[2,4,1,5,6,9,8,3,7]=>01000110=>[1,1,3,2,1]=>[1,2,3,1,1]
[2,9,1,5,6,7,8,3,4]=>01000010=>[1,1,4,1,1]=>[1,1,4,1,1]
[2,4,1,5,6,7,8,9,3]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[9,3,1,2,4,5,6,7,8]=>11000000=>[2,6]=>[6,2]
[8,3,1,2,4,5,6,9,7]=>11000001=>[2,5,1]=>[1,5,2]
[9,3,1,2,4,5,8,6,7]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[6,3,1,2,4,7,8,9,5]=>11000001=>[2,5,1]=>[1,5,2]
[9,3,1,2,6,7,8,4,5]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[5,3,1,2,6,7,8,9,4]=>11000001=>[2,5,1]=>[1,5,2]
[9,4,1,2,3,5,6,7,8]=>11000000=>[2,6]=>[6,2]
[7,4,1,2,3,5,8,9,6]=>11000001=>[2,5,1]=>[1,5,2]
[6,4,1,2,3,7,8,9,5]=>11000001=>[2,5,1]=>[1,5,2]
[5,9,1,2,3,4,6,7,8]=>01000000=>[1,1,6]=>[6,1,1]
[5,8,1,2,3,4,6,9,7]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[5,7,1,2,3,4,8,9,6]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[9,6,1,2,3,4,5,7,8]=>11000000=>[2,6]=>[6,2]
[8,6,1,2,3,4,5,9,7]=>11000001=>[2,5,1]=>[1,5,2]
[9,7,1,2,3,4,5,6,8]=>11000000=>[2,6]=>[6,2]
[8,9,1,2,3,4,5,6,7]=>01000000=>[1,1,6]=>[6,1,1]
[8,7,1,2,3,4,5,9,6]=>11000001=>[2,5,1]=>[1,5,2]
[7,6,1,2,3,4,9,5,8]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[9,6,1,2,3,4,8,5,7]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[9,7,1,2,3,4,8,5,6]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[7,6,1,2,3,4,8,9,5]=>11000001=>[2,5,1]=>[1,5,2]
[5,6,1,2,3,9,4,7,8]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[5,9,1,2,3,8,4,6,7]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[9,6,1,2,3,7,4,5,8]=>11000100=>[2,3,1,2]=>[2,1,3,2]
[9,8,1,2,3,7,4,5,6]=>11000100=>[2,3,1,2]=>[2,1,3,2]
[8,6,1,2,3,7,4,9,5]=>11000101=>[2,3,1,1,1]=>[1,1,1,3,2]
[5,6,1,2,3,7,9,4,8]=>01000010=>[1,1,4,1,1]=>[1,1,4,1,1]
[9,6,1,2,3,7,8,4,5]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[5,6,1,2,3,7,8,9,4]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[5,4,1,2,9,3,6,7,8]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[8,4,1,2,9,3,5,6,7]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[5,9,1,2,6,3,4,7,8]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[9,7,1,2,6,3,8,4,5]=>11001010=>[2,2,1,1,1,1]=>[1,1,1,1,2,2]
[5,4,1,2,6,9,3,7,8]=>11000100=>[2,3,1,2]=>[2,1,3,2]
[9,8,1,2,6,7,3,4,5]=>11000100=>[2,3,1,2]=>[2,1,3,2]
[5,4,1,2,6,7,9,3,8]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[5,4,1,2,6,7,8,9,3]=>11000001=>[2,5,1]=>[1,5,2]
[4,3,1,9,2,5,6,7,8]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[9,3,1,8,2,4,5,6,7]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[9,4,1,5,2,3,6,7,8]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[9,4,1,8,2,3,5,6,7]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[6,9,1,5,2,3,4,7,8]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[9,7,1,6,2,3,4,5,8]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[8,7,1,9,2,3,4,5,6]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[8,7,1,6,2,3,4,9,5]=>11010001=>[2,1,1,3,1]=>[1,3,1,1,2]
[9,4,1,6,2,8,3,5,7]=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[9,8,1,6,2,7,3,4,5]=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[4,3,1,5,9,2,6,7,8]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[9,8,1,7,6,2,3,4,5]=>11011000=>[2,1,2,3]=>[3,2,1,2]
[4,3,1,5,6,8,2,9,7]=>11000101=>[2,3,1,1,1]=>[1,1,1,3,2]
[4,3,1,5,9,8,2,6,7]=>11001100=>[2,2,2,2]=>[2,2,2,2]
[4,3,1,5,8,7,2,9,6]=>11001101=>[2,2,2,1,1]=>[1,1,2,2,2]
[8,9,1,5,6,7,2,3,4]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[4,3,1,5,6,7,9,2,8]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[4,3,1,5,6,9,8,2,7]=>11000110=>[2,3,2,1]=>[1,2,3,2]
[9,3,1,5,6,7,8,2,4]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[9,4,1,5,6,7,8,2,3]=>11000010=>[2,4,1,1]=>[1,1,4,2]
[4,3,1,5,6,7,8,9,2]=>11000001=>[2,5,1]=>[1,5,2]
[2,3,9,1,4,5,6,7,8]=>00100000=>[2,1,5]=>[5,1,2]
[2,3,8,1,4,5,6,9,7]=>00100001=>[2,1,4,1]=>[1,4,1,2]
[2,3,9,1,4,5,8,6,7]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[2,3,9,1,4,7,8,5,6]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[2,3,9,1,8,7,4,5,6]=>00101100=>[2,1,1,2,2]=>[2,2,1,1,2]
[2,3,8,1,6,7,4,9,5]=>00100101=>[2,1,2,1,1,1]=>[1,1,1,2,1,2]
[2,3,5,1,6,7,9,4,8]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[2,3,9,1,6,7,8,4,5]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[2,3,5,1,6,7,8,9,4]=>00100001=>[2,1,4,1]=>[1,4,1,2]
[2,9,4,1,3,5,6,7,8]=>01100000=>[1,2,5]=>[5,2,1]
[2,6,4,1,3,7,8,9,5]=>01100001=>[1,2,4,1]=>[1,4,2,1]
[2,9,5,1,3,4,6,7,8]=>01100000=>[1,2,5]=>[5,2,1]
[2,6,9,1,3,4,5,7,8]=>00100000=>[2,1,5]=>[5,1,2]
[2,9,7,1,3,4,5,6,8]=>01100000=>[1,2,5]=>[5,2,1]
[2,9,8,1,3,4,5,6,7]=>01100000=>[1,2,5]=>[5,2,1]
[2,6,7,1,3,4,8,9,5]=>00100001=>[2,1,4,1]=>[1,4,1,2]
[2,9,4,1,6,3,5,7,8]=>01101000=>[1,2,1,1,3]=>[3,1,1,2,1]
[2,8,4,1,9,3,5,6,7]=>01101000=>[1,2,1,1,3]=>[3,1,1,2,1]
[2,9,4,1,6,3,8,5,7]=>01101010=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]
[2,9,8,1,7,3,4,5,6]=>01101000=>[1,2,1,1,3]=>[3,1,1,2,1]
[2,9,5,1,6,7,8,3,4]=>01100010=>[1,2,3,1,1]=>[1,1,3,2,1]
[9,3,4,1,2,5,6,7,8]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[6,3,4,1,2,7,8,9,5]=>10100001=>[1,1,1,4,1]=>[1,4,1,1,1]
[9,3,7,1,2,4,5,6,8]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[9,3,8,1,2,4,5,6,7]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[9,5,4,1,2,3,6,7,8]=>11100000=>[3,5]=>[5,3]
[8,5,4,1,2,3,6,9,7]=>11100001=>[3,4,1]=>[1,4,3]
[6,9,4,1,2,3,5,7,8]=>01100000=>[1,2,5]=>[5,2,1]
[6,8,4,1,2,3,5,9,7]=>01100001=>[1,2,4,1]=>[1,4,2,1]
[9,7,4,1,2,3,5,6,8]=>11100000=>[3,5]=>[5,3]
[9,8,4,1,2,3,5,6,7]=>11100000=>[3,5]=>[5,3]
[6,9,5,1,2,3,4,7,8]=>01100000=>[1,2,5]=>[5,2,1]
[6,8,5,1,2,3,4,9,7]=>01100001=>[1,2,4,1]=>[1,4,2,1]
[8,7,5,1,2,3,4,9,6]=>11100001=>[3,4,1]=>[1,4,3]
[6,7,9,1,2,3,4,5,8]=>00100000=>[2,1,5]=>[5,1,2]
[6,9,8,1,2,3,4,5,7]=>01100000=>[1,2,5]=>[5,2,1]
[9,7,8,1,2,3,4,5,6]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[6,7,8,1,2,3,4,9,5]=>00100001=>[2,1,4,1]=>[1,4,1,2]
[6,5,4,1,2,8,3,9,7]=>11100101=>[3,2,1,1,1]=>[1,1,1,2,3]
[9,8,5,1,7,2,3,4,6]=>11101000=>[3,1,1,3]=>[3,1,1,3]
[7,8,9,1,6,2,3,4,5]=>00101000=>[2,1,1,1,3]=>[3,1,1,1,2]
[7,8,5,1,6,2,3,9,4]=>01101001=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]
[5,3,4,1,6,8,2,9,7]=>10100101=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]
[9,3,4,1,8,7,2,5,6]=>10101100=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[8,3,4,1,6,7,2,9,5]=>10100101=>[1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1]
[9,5,4,1,8,7,2,3,6]=>11101100=>[3,1,2,2]=>[2,2,1,3]
[8,5,4,1,6,7,2,9,3]=>11100101=>[3,2,1,1,1]=>[1,1,1,2,3]
[5,3,4,1,9,7,8,2,6]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[9,3,5,1,6,7,8,2,4]=>10100010=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[9,5,4,1,6,7,8,2,3]=>11100010=>[3,3,1,1]=>[1,1,3,3]
[5,3,4,1,6,7,8,9,2]=>10100001=>[1,1,1,4,1]=>[1,4,1,1,1]
[2,3,4,9,1,5,6,7,8]=>00010000=>[3,1,4]=>[4,1,3]
[2,3,4,9,1,5,8,6,7]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[2,3,4,9,1,7,8,5,6]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[2,3,4,6,1,7,8,9,5]=>00010001=>[3,1,3,1]=>[1,3,1,3]
[2,3,9,5,1,4,6,7,8]=>00110000=>[2,2,4]=>[4,2,2]
[2,3,9,6,1,4,5,7,8]=>00110000=>[2,2,4]=>[4,2,2]
[2,3,7,9,1,4,5,6,8]=>00010000=>[3,1,4]=>[4,1,3]
[2,3,9,8,1,4,5,6,7]=>00110000=>[2,2,4]=>[4,2,2]
[2,3,9,5,1,7,4,6,8]=>00110100=>[2,2,1,1,2]=>[2,1,1,2,2]
[2,3,9,6,1,7,8,4,5]=>00110010=>[2,2,2,1,1]=>[1,1,2,2,2]
[2,9,4,5,1,3,6,7,8]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[2,7,4,5,1,3,8,9,6]=>01010001=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
[2,9,8,6,1,3,4,5,7]=>01110000=>[1,3,4]=>[4,3,1]
[2,7,8,9,1,3,4,5,6]=>00010000=>[3,1,4]=>[4,1,3]
[2,8,9,6,1,7,3,4,5]=>00110100=>[2,2,1,1,2]=>[2,1,1,2,2]
[2,9,6,5,1,7,8,3,4]=>01110010=>[1,3,2,1,1]=>[1,1,2,3,1]
[7,3,4,5,1,2,8,9,6]=>10010001=>[1,2,1,3,1]=>[1,3,1,2,1]
[9,3,4,8,1,2,5,6,7]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[7,3,4,8,1,2,5,9,6]=>10010001=>[1,2,1,3,1]=>[1,3,1,2,1]
[7,3,8,9,1,2,4,5,6]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[9,8,4,5,1,2,3,6,7]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[7,8,4,6,1,2,3,9,5]=>01010001=>[1,1,1,1,3,1]=>[1,3,1,1,1,1]
[9,8,6,5,1,2,3,4,7]=>11110000=>[4,4]=>[4,4]
[7,8,9,6,1,2,3,4,5]=>00110000=>[2,2,4]=>[4,2,2]
[7,8,6,5,1,2,3,9,4]=>01110001=>[1,3,3,1]=>[1,3,3,1]
[8,3,9,6,1,7,2,4,5]=>10110100=>[1,1,2,1,1,2]=>[2,1,1,2,1,1]
[8,3,6,5,1,7,2,9,4]=>10110101=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]
[8,6,4,5,1,7,2,9,3]=>11010101=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]
[6,3,4,5,1,7,9,2,8]=>10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[6,3,4,5,1,9,8,2,7]=>10010110=>[1,2,1,1,2,1]=>[1,2,1,1,2,1]
[9,3,4,6,1,7,8,2,5]=>10010010=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[6,3,4,5,1,7,8,9,2]=>10010001=>[1,2,1,3,1]=>[1,3,1,2,1]
[2,3,4,5,9,1,6,7,8]=>00001000=>[4,1,3]=>[3,1,4]
[2,3,4,5,8,1,6,9,7]=>00001001=>[4,1,2,1]=>[1,2,1,4]
[2,3,4,5,9,1,8,6,7]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[2,3,4,5,7,1,8,9,6]=>00001001=>[4,1,2,1]=>[1,2,1,4]
[2,3,4,9,6,1,5,7,8]=>00011000=>[3,2,3]=>[3,2,3]
[2,3,4,9,7,1,5,6,8]=>00011000=>[3,2,3]=>[3,2,3]
[2,3,4,9,6,1,8,5,7]=>00011010=>[3,2,1,1,1]=>[1,1,1,2,3]
[2,3,4,9,7,1,8,5,6]=>00011010=>[3,2,1,1,1]=>[1,1,1,2,3]
[2,3,9,5,6,1,4,7,8]=>00101000=>[2,1,1,1,3]=>[3,1,1,1,2]
[2,3,8,5,6,1,4,9,7]=>00101001=>[2,1,1,1,2,1]=>[1,2,1,1,1,2]
[2,3,9,5,6,1,8,4,7]=>00101010=>[2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2]
[2,8,4,5,6,1,3,9,7]=>01001001=>[1,1,2,1,2,1]=>[1,2,1,2,1,1]
[2,8,9,5,7,1,3,4,6]=>00101000=>[2,1,1,1,3]=>[3,1,1,1,2]
[2,8,9,7,6,1,3,4,5]=>00111000=>[2,3,3]=>[3,3,2]
[2,9,7,5,6,1,8,3,4]=>01101010=>[1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1]
[8,3,4,5,6,1,2,9,7]=>10001001=>[1,3,1,2,1]=>[1,2,1,3,1]
[8,3,4,7,6,1,2,9,5]=>10011001=>[1,2,2,2,1]=>[1,2,2,2,1]
[8,3,9,7,6,1,2,4,5]=>10111000=>[1,1,3,3]=>[3,3,1,1]
[8,3,7,5,6,1,2,9,4]=>10101001=>[1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1]
[9,7,4,5,6,1,2,3,8]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[8,9,4,5,6,1,2,3,7]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[8,9,7,5,6,1,2,3,4]=>01101000=>[1,2,1,1,3]=>[3,1,1,2,1]
[8,7,4,5,6,1,2,9,3]=>11001001=>[2,2,1,2,1]=>[1,2,1,2,2]
[7,3,4,5,6,1,9,2,8]=>10001010=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]
[9,3,4,5,6,1,8,2,7]=>10001010=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]
[9,3,7,5,6,1,8,2,4]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[7,3,4,5,6,1,8,9,2]=>10001001=>[1,3,1,2,1]=>[1,2,1,3,1]
[2,3,4,5,6,9,1,7,8]=>00000100=>[5,1,2]=>[2,1,5]
[2,3,4,5,6,8,1,9,7]=>00000101=>[5,1,1,1]=>[1,1,1,5]
[2,3,4,5,9,7,1,6,8]=>00001100=>[4,2,2]=>[2,2,4]
[2,3,4,5,9,8,1,6,7]=>00001100=>[4,2,2]=>[2,2,4]
[2,3,4,9,6,7,1,5,8]=>00010100=>[3,1,1,1,2]=>[2,1,1,1,3]
[2,3,9,5,6,7,1,4,8]=>00100100=>[2,1,2,1,2]=>[2,1,2,1,2]
[2,3,9,5,6,8,1,4,7]=>00100100=>[2,1,2,1,2]=>[2,1,2,1,2]
[2,9,4,5,6,7,1,3,8]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[2,9,4,5,6,8,1,3,7]=>01000100=>[1,1,3,1,2]=>[2,1,3,1,1]
[2,9,4,5,8,7,1,3,6]=>01001100=>[1,1,2,2,2]=>[2,2,2,1,1]
[2,9,4,8,6,7,1,3,5]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[2,9,8,5,6,7,1,3,4]=>01100100=>[1,2,2,1,2]=>[2,1,2,2,1]
[2,8,4,5,6,7,1,9,3]=>01000101=>[1,1,3,1,1,1]=>[1,1,1,3,1,1]
[9,3,4,5,6,7,1,2,8]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[9,3,4,5,6,8,1,2,7]=>10000100=>[1,4,1,2]=>[2,1,4,1]
[9,8,4,5,6,7,1,2,3]=>11000100=>[2,3,1,2]=>[2,1,3,2]
[8,3,4,5,6,7,1,9,2]=>10000101=>[1,4,1,1,1]=>[1,1,1,4,1]
[2,3,4,5,6,7,9,1,8]=>00000010=>[6,1,1]=>[1,1,6]
[2,3,4,5,6,9,8,1,7]=>00000110=>[5,2,1]=>[1,2,5]
[2,3,4,5,9,7,8,1,6]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[2,3,4,9,6,7,8,1,5]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[2,3,9,5,6,7,8,1,4]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[2,9,4,5,6,7,8,1,3]=>01000010=>[1,1,4,1,1]=>[1,1,4,1,1]
[9,3,4,5,6,7,8,1,2]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[2,3,4,5,6,7,8,9,1]=>00000001=>[7,1]=>[1,7]
[3,5,2,6,1,4,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,5,2,6,4,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,2,7,4,8,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,2,7,4,8,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,5,7,2,3,8,6,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,5,7,2,3,8,1,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,5,6,2,3,1,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,5,6,2,1,3,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,5,1,6,4,2,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,6,1,3,2,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,5,6,3,1,2,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[4,5,7,3,2,8,1,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,5,7,3,2,8,6,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,6,7,3,8,2,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,7,3,8,2,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,6,7,3,8,1,2,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,5,7,3,1,8,2,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,5,7,1,3,8,2,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,5,1,7,4,8,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,5,7,4,8,3,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,1,5,7,4,8,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,5,1,7,4,8,6,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,5,7,1,3,8,6,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,5,7,3,1,8,6,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,6,7,3,8,1,5,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,7,3,8,5,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,6,7,3,8,5,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[5,6,7,8,3,1,4,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[5,6,7,8,1,3,4,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,6,7,1,8,3,5,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,6,1,7,8,4,5,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,6,7,8,4,5,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,6,7,8,4,3,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,6,1,7,8,4,2,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,6,7,1,8,3,2,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,6,7,8,1,3,2,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,5,7,2,1,8,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,6,7,2,8,1,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,6,7,2,8,3,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,6,7,2,8,3,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,6,2,7,8,4,5,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,6,2,7,8,4,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,2,7,8,1,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,5,2,7,1,8,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,2,1,7,8,5,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,4,1,2,7,8,6,5]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,5,2,7,1,8,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,6,2,7,8,1,5,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,6,2,7,8,5,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,2,7,8,5,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,6,7,2,8,5,3,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[4,6,7,2,8,5,1,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,6,7,2,8,1,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,5,7,2,1,8,6,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,5,7,1,2,8,6,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,5,1,7,2,8,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,5,7,3,8,6,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,6,7,8,3,5,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,6,1,7,8,2,5,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,7,1,8,2,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,6,7,8,1,2,4,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[5,6,7,8,2,1,4,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[5,6,7,8,2,4,1,3]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,6,7,8,2,4,3,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[5,6,7,8,1,4,2,3]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,6,7,1,8,5,2,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,6,1,7,8,5,2,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,1,6,7,8,5,3,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,6,1,7,8,5,4,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,6,7,1,8,5,3,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[5,6,7,8,1,4,3,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[5,6,7,8,4,1,3,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[3,4,2,1,6,5,8,7,10,9]=>011010101=>[1,2,1,1,1,1,1,1]=>[1,1,1,1,1,1,2,1]
[3,5,2,6,4,1,8,7,10,9]=>010110101=>[1,1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1,1]
[3,5,2,7,4,8,6,1,10,9]=>010101101=>[1,1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1,1]
[3,5,2,7,4,9,6,10,8,1]=>010101011=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[2,1,5,6,4,3,8,7,10,9]=>100110101=>[1,2,2,1,1,1,1]=>[1,1,1,1,2,2,1]
[4,5,6,3,2,1,8,7,10,9]=>001110101=>[2,3,1,1,1,1]=>[1,1,1,1,3,2]
[4,5,7,3,2,8,6,1,10,9]=>001101101=>[2,2,1,2,1,1]=>[1,1,2,1,2,2]
[4,5,7,3,2,9,6,10,8,1]=>001101011=>[2,2,1,1,1,2]=>[2,1,1,1,2,2]
[2,1,5,7,4,8,6,3,10,9]=>100101101=>[1,2,1,1,2,1,1]=>[1,1,2,1,1,2,1]
[4,6,7,3,8,5,2,1,10,9]=>001011101=>[2,1,1,3,1,1]=>[1,1,3,1,1,2]
[4,6,7,3,9,5,2,10,8,1]=>001011011=>[2,1,1,2,1,2]=>[2,1,2,1,1,2]
[2,1,5,7,4,9,6,10,8,3]=>100101011=>[1,2,1,1,1,1,2]=>[2,1,1,1,1,2,1]
[4,6,8,3,9,5,10,7,2,1]=>001010111=>[2,1,1,1,1,3]=>[3,1,1,1,1,2]
[2,1,4,3,7,8,6,5,10,9]=>101001101=>[1,1,1,2,2,1,1]=>[1,1,2,2,1,1,1]
[3,4,2,1,7,8,6,5,10,9]=>011001101=>[1,2,2,2,1,1]=>[1,1,2,2,2,1]
[3,6,2,7,8,5,4,1,10,9]=>010011101=>[1,1,2,3,1,1]=>[1,1,3,2,1,1]
[3,6,2,7,9,5,4,10,8,1]=>010011011=>[1,1,2,2,1,2]=>[2,1,2,2,1,1]
[2,1,6,7,8,5,4,3,10,9]=>100011101=>[1,3,3,1,1]=>[1,1,3,3,1]
[5,6,7,8,4,3,2,1,10,9]=>000111101=>[3,4,1,1]=>[1,1,4,3]
[5,6,7,9,4,3,2,10,8,1]=>000111011=>[3,3,1,2]=>[2,1,3,3]
[2,1,6,7,9,5,4,10,8,3]=>100011011=>[1,3,2,1,2]=>[2,1,2,3,1]
[5,6,8,9,4,3,10,7,2,1]=>000110111=>[3,2,1,3]=>[3,1,2,3]
[2,1,4,3,7,9,6,10,8,5]=>101001011=>[1,1,1,2,1,1,2]=>[2,1,1,2,1,1,1]
[3,4,2,1,7,9,6,10,8,5]=>011001011=>[1,2,2,1,1,2]=>[2,1,1,2,2,1]
[3,6,2,8,9,5,10,7,4,1]=>010010111=>[1,1,2,1,1,3]=>[3,1,1,2,1,1]
[2,1,6,8,9,5,10,7,4,3]=>100010111=>[1,3,1,1,3]=>[3,1,1,3,1]
[5,7,8,9,4,10,6,3,2,1]=>000101111=>[3,1,1,4]=>[4,1,1,3]
[6,7,8,9,10,1,4,5,3,2]=>000010011=>[4,1,2,2]=>[2,2,1,4]
[6,7,8,9,10,1,4,5,2,3]=>000010010=>[4,1,2,1,1]=>[1,1,2,1,4]
[6,7,8,9,10,4,3,2,1,5]=>000011110=>[4,4,1]=>[1,4,4]
[6,7,8,9,10,1,3,4,5,2]=>000010001=>[4,1,3,1]=>[1,3,1,4]
[6,7,8,9,10,3,4,1,2,5]=>000010100=>[4,1,1,1,2]=>[2,1,1,1,4]
[6,7,8,9,10,3,4,2,1,5]=>000010110=>[4,1,1,2,1]=>[1,2,1,1,4]
[6,7,8,9,10,2,3,4,1,5]=>000010010=>[4,1,2,1,1]=>[1,1,2,1,4]
[2,1,4,3,6,5,9,10,8,7]=>101010011=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]
[3,4,2,1,6,5,9,10,8,7]=>011010011=>[1,2,1,1,2,2]=>[2,2,1,1,2,1]
[3,5,2,6,4,1,9,10,8,7]=>010110011=>[1,1,1,2,2,2]=>[2,2,2,1,1,1]
[3,5,2,8,4,9,10,7,6,1]=>010100111=>[1,1,1,1,2,3]=>[3,2,1,1,1,1]
[2,1,5,6,4,3,9,10,8,7]=>100110011=>[1,2,2,2,2]=>[2,2,2,2,1]
[4,5,6,3,2,1,9,10,8,7]=>001110011=>[2,3,2,2]=>[2,2,3,2]
[4,5,8,3,2,9,10,7,6,1]=>001100111=>[2,2,2,3]=>[3,2,2,2]
[2,1,5,8,4,9,10,7,6,3]=>100100111=>[1,2,1,2,3]=>[3,2,1,2,1]
[4,7,8,3,9,10,6,5,2,1]=>001001111=>[2,1,2,4]=>[4,2,1,2]
[2,1,4,3,8,9,10,7,6,5]=>101000111=>[1,1,1,3,3]=>[3,3,1,1,1]
[3,4,2,1,8,9,10,7,6,5]=>011000111=>[1,2,3,3]=>[3,3,2,1]
[3,7,2,8,9,10,6,5,4,1]=>010001111=>[1,1,3,4]=>[4,3,1,1]
[2,1,7,8,9,10,6,5,4,3]=>100001111=>[1,4,4]=>[4,4,1]
[6,7,8,9,10,1,5,4,3,2]=>000010111=>[4,1,1,3]=>[3,1,1,4]
[6,7,8,9,10,5,4,3,2,1]=>000011111=>[4,5]=>[5,4]
[6,5,8,7,3,4,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,6,7,4,5,8,1,2]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,6,7,4,5,1,8,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,6,7,4,5,2,3,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,5,4,7,6,2,3,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,5,4,7,6,1,8,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,4,7,6,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,3,7,8,6,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,4,3,8,7,6,1,2]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,4,8,3,7,5,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,8,4,5,7,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,3,4,8,6,7,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,5,6,8,7,1,2]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,2,5,6,1,8,7,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,5,6,8,1,7,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,2,4,8,6,1,7,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,2,8,4,5,1,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,4,5,1,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,8,1,4,5,2,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,1,8,4,5,2,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,4,8,6,2,3,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,1,3,2,8,6,5,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,1,3,8,2,6,4,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,8,3,2,5,4,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,8,1,3,2,5,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,3,1,5,6,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,2,8,3,1,5,7,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,2,3,8,1,6,7,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,3,8,2,1,7,5,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,8,3,2,1,6,5,4]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[7,8,4,2,6,1,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,4,2,8,7,1,6,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,5,2,7,8,1,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,3,7,1,6,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,3,7,2,6,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,7,3,2,5,4,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,6,7,3,1,5,8,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,6,7,2,1,8,5,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[7,8,5,6,2,1,4,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,5,8,7,1,2,3,4]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,4,1,8,7,2,3,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,4,8,1,7,2,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,8,3,1,2,6,4,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,3,1,8,2,7,4,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,1,2,8,7,5,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,2,1,3,8,5,7,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,2,1,8,3,4,7,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,2,8,1,3,4,7,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,8,2,1,3,4,6,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[4,3,1,2,6,5,8,7]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,3,1,6,2,4,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,1,5,2,4,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,3,1,5,2,8,4,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,5,1,2,7,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,4,5,1,2,8,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,5,1,2,3,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,4,6,1,2,3,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,1,6,5,3,4,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,1,5,2,4,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,6,5,1,2,3,8,7]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[5,6,4,1,2,3,8,7]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[6,5,4,1,2,3,8,7]=>1110001=>[3,3,1]=>[1,3,3]
[7,5,4,1,2,8,3,6]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,6,4,1,7,2,3,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,6,4,1,8,2,3,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,7,4,1,8,2,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,7,4,1,2,8,3,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,7,5,1,2,8,3,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,7,1,5,2,8,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,5,3,8,4,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,8,5,3,7,4,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,8,1,5,2,7,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,5,1,2,7,3,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,8,4,1,2,7,3,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,8,4,1,7,2,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,7,4,1,6,2,3,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[5,8,6,7,1,2,3,4]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,6,1,7,2,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,8,1,6,7,2,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,8,6,7,3,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,7,6,8,3,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,7,1,6,8,2,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,7,6,1,8,2,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,7,6,8,1,2,3,4]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,4,7,1,2,8,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,7,1,8,2,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,4,6,1,8,2,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,4,6,1,7,2,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,3,1,6,7,2,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,3,1,6,8,2,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,3,1,7,8,2,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,3,1,7,2,8,4,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,1,2,7,8,5,6]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[2,1,4,3,8,7,5,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,1,2,8,7,5,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,1,8,7,2,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,3,1,8,6,2,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,4,7,1,6,2,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,4,8,1,6,2,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,8,1,2,7,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,8,1,2,7,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,5,1,8,2,7,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,5,8,3,7,4,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,1,6,8,7,3,4,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,6,1,8,7,2,4,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,6,8,1,7,2,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,6,8,7,1,2,3,4]=>0011000=>[2,2,3]=>[3,2,2]
[7,5,8,6,1,2,3,4]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,5,7,6,1,2,3,4]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,7,8,6,1,2,3,4]=>0011000=>[2,2,3]=>[3,2,2]
[4,7,8,1,6,2,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,7,1,8,6,2,4,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,7,8,6,3,4,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[2,1,8,7,6,3,4,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[3,8,1,7,6,2,4,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,8,7,1,6,2,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,8,7,6,1,2,3,4]=>0111000=>[1,3,3]=>[3,3,1]
[6,8,7,5,1,2,3,4]=>0111000=>[1,3,3]=>[3,3,1]
[6,4,7,3,8,5,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,4,7,3,5,8,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,7,2,5,1,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,2,7,6,1,3,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,4,2,7,6,1,8,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,4,3,7,6,8,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,4,3,7,8,6,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,4,8,3,5,7,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,4,3,8,6,7,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,4,3,6,8,7,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,4,2,6,7,1,8,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,4,2,6,7,1,3,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,3,2,6,1,7,4,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,2,6,1,7,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,3,2,6,1,8,7,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,4,2,6,8,1,7,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,4,2,8,6,1,7,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,8,2,5,1,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,4,2,5,1,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,8,4,2,5,1,3,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,4,2,8,6,1,3,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,3,2,6,1,8,4,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,2,1,6,8,5,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[4,3,2,1,8,6,5,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[5,3,2,8,1,6,4,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,8,2,1,5,4,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,8,3,2,1,5,4,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,8,3,2,1,5,6,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[6,3,8,2,1,5,7,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,3,2,8,1,6,7,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,4,2,7,8,1,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,3,2,7,1,8,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,3,2,7,1,6,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,3,2,7,1,6,4,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,7,2,1,5,4,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,3,7,2,1,5,8,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,7,2,1,8,5,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,4,7,2,8,1,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,7,8,2,1,4,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,5,8,7,2,1,3,4]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,3,7,2,1,8,4,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,3,7,2,1,4,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,7,2,1,4,5,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,3,2,7,1,4,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,4,2,8,7,1,3,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,8,4,2,6,1,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,8,3,2,1,6,4,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,3,8,2,1,7,4,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,3,2,8,1,7,4,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,2,1,8,7,5,6]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[4,3,2,1,7,5,8,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,3,2,1,7,5,6,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[4,3,2,1,8,5,7,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,3,2,8,1,4,7,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,8,2,1,4,7,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,8,3,2,1,4,6,5]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[6,3,8,2,1,4,5,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,3,2,1,8,5,6,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[4,3,2,1,5,8,6,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,8,5,6,1,2,4,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,8,4,1,6,2,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,8,1,4,6,2,5,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,1,8,4,7,2,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,8,4,7,2,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,6,8,3,2,7,5,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,1,8,3,2,7,5,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,8,1,3,2,6,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,8,3,1,2,6,5,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,8,3,4,6,5,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,8,2,4,6,1,5,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,8,2,3,1,6,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,8,2,1,3,6,5,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,8,1,2,3,6,5,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[6,1,8,2,3,7,5,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,6,8,2,3,7,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,5,2,8,3,7,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,2,8,3,7,6,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,2,1,8,3,7,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,2,8,1,3,7,5,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,2,8,3,1,7,5,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,2,8,4,7,1,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,8,4,7,5,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,8,4,7,5,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,6,8,4,7,1,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,6,8,3,1,7,5,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,6,8,1,3,7,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,5,1,8,3,7,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,2,5,8,3,7,6,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,4,1,3,8,7,6,5]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,5,3,8,1,7,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,5,4,8,7,1,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,4,8,7,6,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,3,4,8,7,6,1,2]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,2,4,8,7,1,6,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,2,3,8,1,7,6,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,1,3,8,7,6,5]=>1100111=>[2,2,3]=>[3,2,2]
[4,1,2,3,8,7,6,5]=>1000111=>[1,3,3]=>[3,3,1]
[1,4,2,3,8,7,6,5]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,1,3,2,8,7,6,5]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,3,1,2,8,7,6,5]=>1100111=>[2,2,3]=>[3,2,2]
[6,3,8,1,2,7,5,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,3,1,8,2,7,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,1,3,8,2,7,6,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,5,3,8,2,7,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,5,4,8,7,2,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,4,8,7,2,6,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,4,1,8,7,2,6,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,8,1,7,2,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,8,7,1,2,4,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,6,8,7,3,4,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,6,8,7,2,1,4,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[4,5,1,8,7,2,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,1,5,8,7,2,6,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,4,5,8,7,2,6,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,3,5,8,2,7,6,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,1,5,8,2,7,6,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,6,8,1,2,7,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,6,8,2,1,7,5,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,6,8,2,7,1,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,8,3,7,5,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,5,3,8,7,6,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,5,2,8,7,1,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,2,8,1,7,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,1,4,2,8,7,6,5]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,1,2,4,8,7,6,5]=>1000111=>[1,3,3]=>[3,3,1]
[3,2,5,8,1,7,6,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,5,8,7,1,6,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,3,5,8,7,6,1,2]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,4,5,8,7,6,1,2]=>0001110=>[3,3,1]=>[1,3,3]
[2,4,5,8,7,1,6,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,3,5,8,1,7,6,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,1,3,2,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,3,2,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,3,2,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,3,2,5,4,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,3,2,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,4,2,5,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,4,2,5,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,4,2,5,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,4,2,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,3,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,6,2,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,2,5,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,5,1,4,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,1,4,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,7,1,4,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,8,1,4,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,8,1,4,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,1,4,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,6,1,4,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,5,1,4,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,2,5,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,7,2,5,4,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,3,5,4,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,3,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,8,2,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,8,2,5,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,5,1,4,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,6,1,4,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,4,3,8,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,4,3,7,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,5,3,7,2,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,5,3,8,2,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,6,1,5,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,8,2,6,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,8,2,6,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,8,2,6,4,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,3,6,4,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,3,6,4,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,2,6,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,7,2,6,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,6,1,5,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,1,5,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,8,1,5,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,5,2,6,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,5,2,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,4,2,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,4,2,6,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,3,2,6,4,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,3,2,6,4,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,3,2,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,3,2,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,3,2,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,4,3,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,4,2,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,3,2,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,3,2,8,4,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,3,2,8,4,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,1,3,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,4,8,1,3,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,8,1,4,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,1,4,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,4,2,8,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,4,2,8,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,5,2,8,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,2,8,4,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,5,3,8,4,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,3,8,4,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,6,2,8,4,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,2,8,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,6,2,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,5,2,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,1,5,2,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,8,1,5,2,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,3,8,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,8,3,7,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,2,6,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,8,3,7,2,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,8,3,7,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,8,4,7,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,4,7,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,4,8,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,7,4,8,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,3,8,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,7,3,8,2,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,8,2,6,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,6,3,7,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,6,3,8,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,2,6,8,1,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,3,6,2,8,1,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,6,2,4,8,1,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,7,3,8,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,3,8,2,4,6,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,4,2,5,8,3,6,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,4,2,5,8,3,1,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,5,2,6,3,8,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,2,1,6,8,3,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,3,1,6,8,2,4,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,6,2,8,1,3,4,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,5,6,1,4,8,2,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,1,5,6,3,8,2,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,1,6,3,8,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,6,3,2,8,1,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,4,5,3,8,2,1,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,4,5,3,8,2,6,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,4,8,3,2,5,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,7,4,8,3,2,1,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,7,4,1,8,3,2,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,4,5,3,1,8,2,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,7,1,5,8,3,2,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,3,7,8,1,4,2,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,5,8,2,4,6,1,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,3,5,8,1,4,6,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,5,1,7,8,3,6,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,4,1,5,8,3,6,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,7,4,3,8,1,5,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,4,8,3,1,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,7,4,8,3,5,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,7,3,8,4,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[5,6,7,3,1,8,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,6,1,7,3,8,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,6,7,3,8,4,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,4,7,1,8,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,8,3,1,4,5,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[6,7,2,8,4,5,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,2,8,4,1,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,1,7,4,8,3,2,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,1,6,7,3,2,8,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,6,1,7,3,2,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,7,3,2,1,8,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,6,7,3,2,8,4,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,6,2,7,3,8,4,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,2,7,3,1,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,2,1,7,3,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,7,4,2,8,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,7,2,1,8,3,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,5,8,2,1,3,4,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,7,3,1,8,2,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,7,1,5,2,8,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,4,2,5,1,8,3,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,7,4,2,1,8,3,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,7,4,2,8,3,1,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,7,4,2,8,3,5,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,7,2,8,4,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,6,7,2,8,4,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,6,7,2,1,8,4,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,7,3,8,2,1,4,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,4,7,8,2,1,5,6]=>0001100=>[3,2,2]=>[2,2,3]
[3,7,8,1,4,6,2,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,7,8,2,6,1,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,7,3,8,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,7,2,8,5,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,6,7,8,5,2,1,4]=>0001110=>[3,3,1]=>[1,3,3]
[3,6,7,8,5,2,4,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[6,4,7,8,2,5,3,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,4,7,8,2,1,5,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,1,5,7,8,2,6,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,3,7,8,1,6,2,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,2,8,5,1,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,4,1,7,8,2,5,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,1,6,2,7,8,4,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,6,2,1,7,8,4,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,6,2,7,1,8,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,2,7,8,4,3,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[5,6,7,2,8,4,3,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[5,6,7,2,1,8,4,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,6,1,7,2,8,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,6,7,2,8,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,4,7,1,8,2,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,7,1,8,5,2,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,7,8,5,2,4,1,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,7,8,3,5,1,4,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,7,8,1,5,3,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[5,1,6,7,8,4,3,2]=>1000111=>[1,3,3]=>[3,3,1]
[5,6,1,7,8,4,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[5,6,7,1,8,4,3,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[8,6,1,3,4,2,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,3,2,5,1,6,4,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,3,6,2,4,1,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,2,7,4,1,8,6]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,5,3,8,2,4,6,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,2,4,5,8,3,6,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,4,5,3,7,1,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,2,4,5,6,3,1,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[8,2,4,5,6,1,3,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[8,1,2,4,5,6,3,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[8,2,5,1,3,6,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,5,6,2,1,4,3,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,5,3,6,4,1,2,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,4,1,5,6,3,2,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,1,4,5,6,3,2,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,5,3,7,2,1,8,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,4,5,8,3,2,6,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,3,6,7,2,8,5,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,3,6,7,2,8,1,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,3,6,7,2,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,5,3,7,1,8,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,5,3,7,2,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,4,7,1,2,8,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,5,8,2,1,4,6,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,5,3,8,4,1,6,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,4,5,8,3,6,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,6,7,8,1,5,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,6,4,7,8,3,5,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,4,7,8,3,5,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,5,6,7,8,4,1,2]=>0000110=>[4,2,1]=>[1,2,4]
[3,1,5,6,7,8,4,2]=>1000011=>[1,4,2]=>[2,4,1]
[4,6,1,7,8,3,5,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,6,7,1,4,8,5,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,2,4,1,7,8,5,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,6,7,1,4,8,3,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,3,6,7,8,1,2,5]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,5,3,6,7,8,2,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,5,6,7,8,2,1,4]=>0000110=>[4,2,1]=>[1,2,4]
[3,5,6,7,8,2,4,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[5,2,7,1,3,8,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,3,1,7,8,2,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,5,2,7,8,1,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,2,6,7,8,3,1,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,2,6,7,8,3,5,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,6,2,7,4,8,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,6,2,7,4,8,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,1,6,4,7,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,7,4,2,1,5,8,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[1,7,3,4,2,5,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,7,2,1,3,5,8,6]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,8,4,2,1,3,6,5]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,8,1,3,4,2,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,8,3,4,2,1,6,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,2,7,1,8,5,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,6,2,7,1,8,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,3,8,2,5,4,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,7,8,5,2,3,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,6,4,7,8,1,5,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,2,7,8,1,5,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,4,5,8,6,2,1,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,4,1,5,8,6,2,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,5,3,8,6,1,2,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,5,8,2,1,6,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,2,7,1,3,8,5,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,3,1,7,8,2,5,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,6,1,7,8,5,2,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,1,2,6,7,8,4,3]=>1000011=>[1,4,2]=>[2,4,1]
[5,2,6,7,8,4,1,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,2,6,7,8,4,3,1]=>1000111=>[1,3,3]=>[3,3,1]
[2,5,6,7,8,4,1,3]=>0000110=>[4,2,1]=>[1,2,4]
[1,5,2,6,7,8,4,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,6,4,7,8,5,2,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,6,7,1,3,8,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,7,8,2,1,5,4,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,7,3,8,5,1,4,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,7,8,5,3,1,2]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[4,5,2,3,7,6,1,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,4,3,7,2,5,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,3,6,5,1,2,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[1,5,6,3,4,8,7,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,6,2,7,3,5,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,7,4,5,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,7,2,6,5,3,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,7,6,2,4,3,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,7,5,4,8,3,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,7,5,4,1,3,2,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[6,8,5,4,2,1,3,7]=>0111100=>[1,4,2]=>[2,4,1]
[5,8,6,2,4,1,3,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,8,2,6,5,1,3,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,2,8,6,5,1,4,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,1,2,6,5,8,7,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,1,6,2,4,8,7,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,1,5,4,2,8,7,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,1,5,4,8,2,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,5,4,7,6,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,8,6,7,4,5,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,1,6,7,4,5,2,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,1,6,8,4,2,5,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,1,7,8,2,4,5,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,1,7,2,8,4,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,2,7,8,5,6,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,2,1,7,8,5,6,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,8,7,1,5,4,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,8,2,7,1,5,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,7,2,1,4,3,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,8,7,1,2,4,3,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,8,6,1,4,2,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,7,6,1,4,3,2,5]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[1,7,6,8,4,3,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,7,8,3,4,5,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[8,6,7,1,3,4,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,6,8,1,3,2,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,7,8,2,1,3,4,6]=>0011000=>[2,2,3]=>[3,2,2]
[4,7,2,8,1,3,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,2,6,8,4,1,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,6,2,8,3,1,5,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,6,8,2,3,1,4,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,5,8,3,2,1,4,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,5,8,3,1,2,4,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,5,7,3,1,4,2,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,5,7,3,8,4,6,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,3,7,8,5,6,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,4,3,7,1,5,2,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,4,3,8,2,1,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[4,5,2,3,8,1,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,2,5,4,8,1,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,5,2,3,1,8,7,6]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,3,1,2,8,7,5]=>1110011=>[3,2,2]=>[2,2,3]
[7,4,3,1,8,2,6,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,4,3,1,7,6,2,5]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[1,5,8,3,7,6,4,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[8,5,1,3,7,6,2,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,5,1,3,8,2,6,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,1,3,2,8,7,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,6,1,2,3,8,7,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,6,2,1,3,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,2,6,1,4,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,2,7,1,8,4,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,2,1,8,3,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,7,1,2,8,3,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,7,1,8,2,3,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,6,1,8,3,2,5,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,6,1,7,3,5,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,6,8,7,3,5,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,7,8,6,5,3,4,2]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[8,7,1,6,5,3,2,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,8,1,6,5,2,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,8,1,7,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,1,2,7,6,3,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,8,2,1,7,6,3,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,2,8,1,7,6,4,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,1,2,8,7,6,5,3]=>1001111=>[1,2,4]=>[4,2,1]
[5,1,8,2,7,6,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,1,8,7,2,5,4,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,1,8,6,5,2,4,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,1,7,6,5,4,2,3]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[3,1,2,6,5,8,7,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,1,6,2,4,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,1,5,2,4,8,7,6]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,5,1,2,3,8,7,6]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,6,1,2,3,8,7,5]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,6,5,3,4,8,7,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[6,1,5,2,4,8,7,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,5,1,2,3,8,7,4]=>1100011=>[2,3,2]=>[2,3,2]
[6,4,1,2,3,8,7,5]=>1100011=>[2,3,2]=>[2,3,2]
[5,4,1,2,3,8,7,6]=>1100011=>[2,3,2]=>[2,3,2]
[5,4,1,2,7,3,6,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,4,1,7,2,3,5,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,4,1,8,2,3,5,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,1,2,8,3,6,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,1,2,8,3,6,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,1,5,2,8,4,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,5,3,8,4,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,5,3,7,4,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,5,2,7,4,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,1,2,7,3,6,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,4,1,2,7,3,6,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,4,1,7,2,3,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,1,6,2,3,5,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,6,1,7,2,3,5,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,1,6,7,2,4,5,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,8,6,7,3,4,5,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,7,6,8,3,4,5,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,1,6,8,2,4,5,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,6,1,8,2,3,5,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,7,1,2,8,3,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,7,2,8,4,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,2,7,8,5,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,3,8,7,5,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,1,2,8,7,5,6,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,1,2,8,7,5,6,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,1,8,2,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,8,7,2,4,5,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[3,1,7,6,2,4,5,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,7,1,6,2,3,5,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,1,6,2,3,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,1,7,2,3,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,1,2,7,3,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,1,2,7,3,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,1,8,2,7,4,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,8,3,7,4,6,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,6,8,7,3,4,5,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[6,1,8,7,2,4,5,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,8,1,7,2,3,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,8,7,1,2,3,4,5]=>0110000=>[1,2,4]=>[4,2,1]
[5,8,7,1,2,3,4,6]=>0110000=>[1,2,4]=>[4,2,1]
[5,8,6,1,2,3,4,7]=>0110000=>[1,2,4]=>[4,2,1]
[5,7,6,1,2,3,4,8]=>0110000=>[1,2,4]=>[4,2,1]
[7,8,1,6,2,3,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,1,8,6,2,4,5,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,7,8,6,3,4,5,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,8,7,6,3,4,5,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,1,7,6,2,4,5,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,7,1,6,2,3,5,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,2,5,1,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,5,4,7,1,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,5,3,7,6,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,5,3,7,1,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,5,3,6,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,5,1,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,4,6,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,5,3,6,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,5,1,6,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,5,2,7,1,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,6,2,7,5,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,6,2,7,1,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,6,1,7,2,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,5,1,7,2,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,4,7,2,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,5,4,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,4,7,6,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,5,3,7,6,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,5,1,7,6,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,6,1,7,5,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,6,5,7,1,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,6,4,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,6,4,7,1,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,6,1,7,4,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,6,3,7,4,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,3,7,5,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,6,4,7,5,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,4,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,4,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,6,4,7,2,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,3,7,2,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,6,3,7,2,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,6,1,7,2,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,6,2,7,1,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,6,2,7,4,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,3,7,4,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,3,7,1,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,1,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,5,1,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,1,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,3,7,1,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,3,7,5,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,4,7,5,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,4,7,1,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,1,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,5,1,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,4,1,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,4,2,7,6,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,5,1,7,6,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,1,7,5,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,5,7,1,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,5,7,3,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,5,7,1,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,1,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,5,1,7,6,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,5,2,7,6,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,2,7,6,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,5,3,7,6,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,3,7,5,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,6,2,7,5,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,2,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,6,2,7,4,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,1,7,4,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,4,7,1,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,4,7,3,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,2,7,3,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,2,7,1,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,1,7,2,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,6,4,7,2,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,5,7,2,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,6,5,7,2,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,5,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,6,5,7,4,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,5,7,3,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,6,4,7,3,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,1,7,3,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,3,7,1,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,5,2,1,6,4,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,6,3,5,2,4,1,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,7,5,2,4,1,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,3,7,5,2,4,6,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,2,4,5,7,3,6,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,4,5,7,3,1,8,6]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[8,2,4,6,5,3,1,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[8,2,5,4,6,1,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,3,5,1,4,2,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,6,1,4,5,3,2,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,1,5,6,4,3,2,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,7,4,3,2,1,8,6]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[8,5,7,4,3,2,6,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,6,8,3,2,7,5,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,7,6,3,2,8,1,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,6,7,3,2,8,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[5,4,7,3,1,8,2,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,7,4,5,3,2,8,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,7,5,1,4,2,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,7,4,2,1,3,8,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,5,7,4,2,1,6,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,7,5,1,4,6,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,4,1,7,5,3,6,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,6,3,8,7,1,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,7,4,8,6,3,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,4,7,6,3,5,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,6,5,8,7,4,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,1,5,8,6,7,4,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,8,1,6,7,3,5,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,6,4,1,8,7,5,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[8,2,6,1,4,7,5,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,7,6,8,1,4,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,1,6,4,8,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,3,5,6,8,2,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,3,6,7,5,8,2,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,7,6,5,8,2,1,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,6,8,5,7,2,4,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,5,7,6,8,1,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,1,6,5,7,8,3,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,7,6,8,3,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,2,6,8,7,3,5,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,8,2,4,6,7,5,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,7,2,6,4,8,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,1,4,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,3,7,2,1,8,4,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,7,3,2,1,5,8,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,7,6,1,3,4,2,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,5,7,3,2,1,6,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,6,7,2,1,5,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,7,8,6,2,1,5,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[8,7,6,3,5,2,4,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,7,4,8,1,6,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,6,8,2,1,7,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[8,4,1,5,7,2,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,5,3,7,1,6,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,7,2,1,3,6,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,2,6,7,1,3,5,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,3,6,1,7,5,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,6,1,8,7,2,5,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,1,2,5,6,7,4,3]=>1000011=>[1,4,2]=>[2,4,1]
[8,2,6,5,7,4,1,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,1,7,8,5,6,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,2,5,7,6,4,3,1]=>1001111=>[1,2,4]=>[4,2,1]
[2,7,6,8,5,4,1,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,7,2,5,8,6,4,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,7,4,8,2,6,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,7,8,1,6,5,2,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,7,8,6,1,3,5,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[8,7,6,3,5,1,4,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,4,7,6,5,1,3,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,7,1,5,6,4,3,2]=>1100111=>[2,2,3]=>[3,2,2]
[8,1,6,7,5,4,3,2]=>1001111=>[1,2,4]=>[4,2,1]
[6,5,3,1,2,4,8,7]=>1110001=>[3,3,1]=>[1,3,3]
[4,6,3,5,1,2,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,5,3,7,2,1,4,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,8,1,4,5,7,3,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[8,7,2,4,5,1,3,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,6,2,4,5,1,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,6,1,4,5,3,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,1,2,4,5,3,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,6,3,2,1,4,8,7]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[5,4,3,6,1,2,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,1,4,5,2,8,7]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,1,6,4,5,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,4,5,1,2,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,7,4,2,6,3,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,8,7,4,1,6,3,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,7,4,2,6,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,7,8,4,5,1,2,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,1,8,7,5,3,4,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[2,1,6,8,5,7,3,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,6,3,8,1,7,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,1,4,5,8,3,2]=>1100011=>[2,3,2]=>[2,3,2]
[3,7,6,4,5,8,2,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[8,5,7,4,1,6,3,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,1,8,4,7,6,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,5,8,4,7,6,1,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,4,8,3,5,6,7,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,1,8,3,5,6,7,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,8,4,2,5,6,7,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[8,4,1,3,5,6,7,2]=>1100001=>[2,4,1]=>[1,4,2]
[7,5,8,4,3,6,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,5,3,8,4,1,7,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,1,5,8,4,6,7,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,1,4,8,3,6,7,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,4,3,8,2,1,7,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,3,8,4,2,6,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,1,2,5,6,7,4]=>1100001=>[2,4,1]=>[1,4,2]
[3,1,8,2,5,6,7,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,3,8,1,5,6,7,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,3,8,2,5,6,7,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,8,2,3,5,6,7,1]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,8,2,1,5,6,7,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,8,1,3,5,6,7,4]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[8,1,2,3,5,6,7,4]=>1000001=>[1,5,1]=>[1,5,1]
[7,8,2,4,3,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,2,4,1,7,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,1,8,3,4,6,7,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,1,7,8,5,4,3,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,7,3,8,1,4,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,8,4,5,3,2,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,7,8,4,5,3,1,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,7,1,4,3,6,2,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,8,7,4,2,6,1,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,7,8,4,3,6,2,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,6,3,8,4,2,7,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,8,3,6,2,1,7,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,6,3,1,4,2,7,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,3,8,2,4,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,3,1,8,5,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,1,3,2,6,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,5,3,6,2,8,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,6,3,5,1,2,7,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,8,3,2,6,1,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,3,8,6,2,7,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,8,4,7,6,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[5,8,2,4,7,6,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,7,5,4,1,6,2,3]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[2,7,6,4,5,8,1,3]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,1,6,4,5,8,2,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,7,3,6,1,8,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,6,5,8,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,8,5,3,6,7,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,8,3,5,2,1,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,8,5,4,2,6,1,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,4,2,5,6,7,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,8,4,1,5,6,7,3]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[4,8,1,2,5,6,7,3]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,4,8,1,5,6,7,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,4,2,8,5,6,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,1,8,5,6,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,1,2,8,5,6,7,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,4,2,1,5,6,7,3]=>1110001=>[3,3,1]=>[1,3,3]
[7,5,2,4,8,6,1,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,5,3,2,8,1,7,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,1,5,3,8,6,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,3,5,8,1,7,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,3,5,4,8,6,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,3,4,1,5,6,7,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,3,1,8,5,6,7,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,1,4,8,5,6,7,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,5,3,7,2,8,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,3,7,4,5,8,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,7,2,4,5,8,3,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[5,1,7,4,8,6,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,5,7,4,8,6,3,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[5,6,3,7,1,8,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,8,7,4,5,2,1,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,7,5,4,8,6,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[5,7,1,4,8,6,2,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,6,3,1,8,2,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,6,3,5,8,2,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,3,8,1,2,7,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,8,4,1,6,2,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,5,1,6,8,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,6,2,5,4,8,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,2,4,7,1,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,5,8,2,4,7,6,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,2,5,8,3,7,6,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,6,5,3,8,1,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,4,2,1,6,8,3,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,3,5,1,4,8,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,1,5,3,8,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,6,4,3,8,2,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,4,3,2,7,1,8,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,4,3,8,2,7,6,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,3,6,2,8,7,5,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,3,7,6,2,1,8,5]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,4,3,1,7,2,8,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,4,3,1,8,2,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[1,4,7,5,8,3,2,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,1,3,5,8,4,2,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,2,5,8,4,1,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[2,8,5,7,4,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,8,7,1,4,6,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,4,5,8,7,3,6,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,5,4,8,7,3,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,3,8,1,7,5,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,3,7,1,8,6,5,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,3,7,6,5,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[5,3,8,7,6,4,2,1]=>1011111=>[1,1,5]=>[5,1,1]
[7,5,3,1,8,6,4,2]=>1110111=>[3,1,3]=>[3,1,3]
[1,8,6,5,3,7,4,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,5,8,6,3,7,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,6,1,8,7,3,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,8,7,3,1,4,5,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[6,2,8,7,4,5,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,6,2,8,4,1,3,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,3,1,6,8,4,2,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[1,7,6,4,8,3,2,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,7,1,6,3,2,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,1,7,5,3,2,8,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,6,5,3,2,1,8,4]=>1111101=>[5,1,1]=>[1,1,5]
[6,5,3,2,8,7,4,1]=>1110111=>[3,1,3]=>[3,1,3]
[5,2,6,3,8,7,4,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,2,7,6,3,1,8,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,5,2,1,7,3,8,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,2,7,4,1,8,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,7,2,6,3,1,8,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,8,6,3,7,5,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,8,6,2,4,7,5,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,3,6,2,4,1,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,7,2,1,4,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[4,3,7,8,2,1,5,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,3,7,1,4,6,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,8,2,5,7,1,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,6,2,7,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,6,2,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,7,3,6,2,5,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,7,8,2,1,6,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,2,6,8,1,7,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,4,8,2,7,1,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,1,5,7,2,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,3,7,1,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,7,2,6,1,3,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,6,2,7,5,1,3,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,6,8,1,7,5,2,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,1,6,8,2,7,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,5,2,8,1,7,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,2,7,1,8,6,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,8,2,7,6,4,3,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[6,2,8,7,5,4,3,1]=>1011111=>[1,1,5]=>[5,1,1]
[7,6,2,1,8,5,4,3]=>1110111=>[3,1,3]=>[3,1,3]
[6,1,7,2,8,5,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,5,1,8,2,6,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,7,1,8,6,2,5,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,8,3,1,6,5,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,7,4,6,1,5,3,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,5,7,1,6,4,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,1,7,5,4,3,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[7,1,8,6,5,4,3,2]=>1011111=>[1,1,5]=>[5,1,1]
[5,4,2,3,7,6,1,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,4,2,7,3,5,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,2,6,3,5,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,2,6,3,1,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,2,7,6,4,5,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,7,2,6,3,5,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,6,2,3,4,1,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,6,5,2,3,8,4,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,7,5,2,8,3,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,5,2,3,1,4,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,8,6,2,3,1,4,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,8,2,6,3,1,5,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,2,8,6,4,1,5,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[3,2,1,6,4,8,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,1,5,2,8,3,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,5,2,7,3,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,8,6,7,2,3,4,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,1,6,7,2,3,4,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[7,1,6,8,2,3,4,5]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,2,1,7,8,4,5,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,2,8,7,1,4,5,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,8,7,2,1,3,4,6]=>0111000=>[1,3,3]=>[3,3,1]
[1,7,6,8,2,3,4,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,5,8,2,3,1,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,7,2,1,3,4,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,4,2,8,3,1,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,4,2,3,8,1,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,2,5,4,1,8,6,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,5,2,3,1,8,6,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,2,3,1,8,6,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,4,2,1,3,8,5,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,4,2,1,8,3,5,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,4,2,1,7,3,5,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[1,4,2,8,7,3,5,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,5,8,2,7,3,4,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,5,1,2,7,3,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,5,1,2,8,3,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,5,1,2,3,8,4,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,6,2,1,3,8,5,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,2,6,1,4,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,2,7,1,8,4,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,2,1,8,3,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,6,1,8,2,3,4,5]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,6,1,7,2,3,4,5]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[1,6,8,7,2,3,4,5]=>0011000=>[2,2,3]=>[3,2,2]
[1,7,8,6,2,3,4,5]=>0011000=>[2,2,3]=>[3,2,2]
[7,8,1,6,2,3,4,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,1,7,2,3,4,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,2,1,7,3,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,8,1,7,4,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,1,8,7,4,5,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,1,8,2,7,3,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,1,8,7,2,3,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,1,7,6,2,3,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[1,8,7,6,2,3,4,5]=>0111000=>[1,3,3]=>[3,3,1]
[6,3,5,1,2,4,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,3,5,6,1,2,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,3,7,5,2,1,4,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,3,7,5,1,8,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,5,2,7,1,8,3,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,2,7,4,1,3,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[2,6,1,5,4,3,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,3,5,1,2,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,3,1,4,6,2,8,7]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,1,4,6,5,2,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,7,4,6,2,8,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,1,4,7,2,6,3,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,7,8,5,2,1,6]=>0001110=>[3,3,1]=>[1,3,3]
[2,1,8,5,7,3,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,3,5,1,7,4,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,8,2,4,6,7,3,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,4,8,6,5,7,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,4,8,1,6,3,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,1,4,6,8,2,7,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,5,4,6,7,1,8,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,6,3,7,5,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,1,6,3,8,5,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,4,2,8,6,5,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[7,4,1,3,5,8,6,2]=>1100011=>[2,3,2]=>[2,3,2]
[6,5,8,4,1,7,3,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,5,3,7,4,1,6,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,1,4,8,3,7,6,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,4,3,8,2,1,6,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,3,7,4,1,8,2,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,1,2,5,7,6,4]=>1100011=>[2,3,2]=>[2,3,2]
[3,1,8,2,7,6,5,4]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,3,8,1,6,7,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,3,7,2,6,8,5,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,7,2,3,8,5,6,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,8,2,1,7,5,6,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,1,3,6,5,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,7,8,5,4,3,1,6]=>0011110=>[2,4,1]=>[1,4,2]
[8,7,1,6,3,4,2,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,8,6,7,2,4,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,8,7,4,2,6,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,3,8,7,2,1,6,5]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,6,1,4,2,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,5,8,2,4,1,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,3,4,1,8,5,7,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,1,3,2,6,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,3,5,6,2,7,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,6,1,8,7,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,6,2,8,7,4,1,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,8,5,6,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,6,5,4,7,1,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,6,4,5,7,2,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,3,6,1,7,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,6,5,7,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,7,5,3,6,8,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,7,3,5,2,1,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,1,4,2,5,6,8,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,7,4,1,6,5,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,6,1,2,8,7,3,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,4,1,5,8,7,6,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,1,2,5,8,6,7,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,4,2,1,5,8,7,3]=>1110011=>[3,2,2]=>[2,2,3]
[8,5,2,4,6,1,7,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,3,2,6,8,1,4]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[2,1,5,3,6,8,7,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,3,5,4,6,1,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,4,1,5,7,8,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,3,1,5,7,6,8,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,1,4,5,6,8,7,2]=>1000011=>[1,4,2]=>[2,4,1]
[4,5,2,6,3,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,5,2,1,4,3,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,5,2,7,4,8,3,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,5,2,7,4,1,6,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,3,7,5,2,1,6,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,3,7,5,2,8,4,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,1,6,5,4,2,8,7]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,6,3,2,4,1,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,2,4,1,5,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,1,3,5,4,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,7,2,3,4,8,5,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[8,7,2,3,4,1,6,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,1,7,3,8,4,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,7,3,8,6,4,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[7,6,1,3,5,8,4,2]=>1100011=>[2,3,2]=>[2,3,2]
[3,6,7,4,1,8,5,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,6,3,7,4,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,7,4,8,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,8,7,4,3,6,5]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,8,3,7,4,2,6,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,8,7,4,1,2,6,5]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,8,1,3,5,2,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,7,3,2,6,1,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,8,6,3,1,5,7,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,1,6,3,2,5,4,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,8,4,1,6,3,7,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,1,2,7,6,3,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,8,4,2,5,7,1,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,8,3,5,2,7,4,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,5,3,8,7,6,4]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,5,3,2,8,7,1,4]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,5,2,4,8,1,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,4,2,8,5,7,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,4,1,8,7,6,5,3]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[8,4,2,1,7,5,3,6]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[4,3,1,8,6,7,5,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,1,4,8,6,5,7,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,1,6,5,4,8,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,7,5,6,8,4,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[5,7,1,6,8,2,4,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,6,2,5,1,7,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,6,2,1,8,7,3,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,6,2,5,8,3,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,5,2,6,3,8,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,1,2,3,6,8,7,5]=>1000011=>[1,4,2]=>[2,4,1]
[2,4,3,1,8,5,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,5,2,8,3,4,6,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,6,2,8,4,3,1,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,7,2,8,1,5,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,7,2,1,4,5,6,3]=>1110001=>[3,3,1]=>[1,3,3]
[3,6,8,7,1,5,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,7,8,6,3,4,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,1,8,5,4,3,6,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,7,8,4,5,3,6,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,7,3,8,1,4,6,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,1,7,8,5,4,6,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,5,8,4,6,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,5,3,8,4,1,2,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,5,8,4,3,6,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,4,8,3,5,6,1,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,1,8,3,6,5,2,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,8,1,7,2,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,4,1,3,7,2,6,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,1,8,2,4,7,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,3,8,1,4,6,7,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,3,8,2,5,1,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,8,4,2,5,7,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,4,3,8,2,5,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,1,4,8,3,5,7,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,8,2,4,3,5,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,2,3,5,1,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,8,2,1,4,6,5,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,1,3,4,5,7,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[2,8,4,1,6,5,3,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,8,4,1,6,5,7,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,7,6,1,4,3,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,8,5,6,7,4,3,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[7,5,8,6,1,4,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,5,7,6,1,4,2,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,5,7,2,4,1,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,5,8,2,4,1,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,5,3,4,7,6,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,8,5,3,4,1,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,5,3,4,1,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,8,7,6,1,4,5,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,8,5,3,6,1,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,5,6,7,4,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,8,5,3,4,7,1,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,5,3,4,6,1,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,5,3,4,6,7,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,5,7,2,4,6,1,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,5,2,7,3,1,4,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,5,2,8,3,1,7,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,5,2,8,3,1,4,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,5,8,2,4,6,3,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,5,8,6,1,4,3,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,5,8,2,1,3,7,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,5,6,2,1,8,7,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,5,7,6,1,4,8,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,5,7,2,4,1,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,7,2,4,6,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[6,5,2,7,3,1,8,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,5,2,6,3,1,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,1,2,3,7,6,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,5,2,7,3,4,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,1,6,7,4,3,8,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,1,2,6,4,8,7,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,1,2,8,6,4,7,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,1,6,8,7,3,4,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,5,2,8,3,7,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,1,2,3,8,7,5,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,1,2,3,8,6,5,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,1,2,3,8,6,7,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,1,2,3,7,6,5,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,1,2,3,8,5,7,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,1,6,8,4,3,5,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,1,2,8,4,5,7,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,6,8,2,3,1,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,8,2,4,3,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,8,2,4,3,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,2,8,3,4,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,2,8,3,7,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,2,7,3,4,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,1,6,7,4,3,2,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,1,6,8,7,3,2,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,1,6,8,4,3,2,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,7,8,6,3,4,2,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,1,8,3,6,5,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,8,3,6,2,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,4,8,6,2,7,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,1,4,8,6,5,2,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,1,6,5,8,3,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,1,6,7,8,3,2,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,1,6,5,7,3,2,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,5,2,6,3,7,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,2,7,3,8,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,6,2,4,8,7,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,5,6,2,4,8,1,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,7,5,6,8,4,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,5,2,8,1,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,2,5,8,4,7,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,1,6,5,8,3,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,2,6,3,8,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,1,2,3,5,8,7,6]=>1000011=>[1,4,2]=>[2,4,1]
[4,1,2,3,7,8,6,5]=>1000011=>[1,4,2]=>[2,4,1]
[4,5,2,7,3,8,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,1,6,7,8,3,5,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,1,2,6,8,5,7,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,1,2,5,6,8,7,3]=>1000011=>[1,4,2]=>[2,4,1]
[4,5,2,6,3,7,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,8,5,6,1,4,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,8,4,2,1,5,3,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,8,2,1,6,5,3,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,4,1,2,5,7,3,8]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[2,4,8,1,5,7,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,3,8,1,7,2,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,1,4,7,2,5,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,8,3,4,5,1,6,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,8,3,5,4,2,1,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,8,4,1,2,3,6,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,8,3,6,5,4,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,8,2,1,5,3,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,8,2,6,4,1,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,8,2,5,6,4,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,8,1,6,5,4,3,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[6,2,1,7,5,4,3,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[2,1,8,7,5,4,3,6]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[1,3,8,2,6,4,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,7,1,6,4,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,6,2,7,4,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,1,2,5,8,7,4,3]=>1000111=>[1,3,3]=>[3,3,1]
[6,3,1,8,4,2,7,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,2,1,5,3,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,3,7,5,8,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,8,7,5,6,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,7,1,5,3,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,7,6,4,2,8,5]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,1,7,5,6,8,4,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,7,2,8,6,4,1,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,8,1,7,6,4,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,5,7,3,6,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,7,5,8,3,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,6,8,2,4,7,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,6,8,5,3,1,4,7]=>0011100=>[2,3,2]=>[2,3,2]
[2,6,1,4,7,3,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,6,7,3,8,4,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,2,8,1,4,7,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,7,5,2,1,3,8]=>0011100=>[2,3,2]=>[2,3,2]
[4,5,6,7,2,8,1,3]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,5,7,6,1,8,3,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,5,8,6,2,7,3,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,6,5,8,3,2,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,5,7,1,2,8,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,7,5,6,3,1,8,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,6,3,4,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,1,4,2,3,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,7,6,4,3,8,1,2]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,3,4,5,8,7,1,2]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,2,4,1,8,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,3,5,4,8,1,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,3,4,5,8,7,2]=>1000011=>[1,4,2]=>[2,4,1]
[5,1,4,2,7,6,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,4,7,8,3,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,7,2,4,1,6,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,4,2,8,5,3,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,7,5,8,1,4,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,7,6,3,4,1,2]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,8,7,6,2,3,1,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,1,7,2,6,5,3,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,2,1,5,6,3,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,2,7,8,1,6,3,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,1,8,7,6,5,3,4]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[3,1,4,7,8,2,6,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,1,7,4,5,6,8,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,2,7,1,6,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,7,5,6,8,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,8,6,3,5,7,1,2]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,8,1,2,5,3,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,8,6,5,2,4,1,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,8,5,6,1,4,7,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,3,7,8,2,1,6,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,2,8,7,1,6,4,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,6,8,7,5,2,4,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[3,6,7,8,5,1,4,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[3,7,6,8,5,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,7,8,5,1,2,4,6]=>0011000=>[2,2,3]=>[3,2,2]
[3,7,1,6,4,2,5,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,1,8,6,2,3,5,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,7,8,6,3,5,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,8,7,6,5,4,1,2]=>0111110=>[1,5,1]=>[1,5,1]
[2,1,7,6,5,3,4,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[2,8,1,6,4,5,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,7,5,1,4,3,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,8,6,7,5,1,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,7,8,6,5,4,1,3]=>0011110=>[2,4,1]=>[1,4,2]
[6,4,2,7,1,3,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,4,2,5,1,3,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,3,6,1,8,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,3,6,1,7,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,3,6,2,4,8,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,3,7,1,2,5,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,6,2,7,1,4,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,3,6,7,1,2,8,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,3,7,4,1,2,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,7,1,5,2,3,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,5,1,2,4,8,6]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,6,4,2,3,8,1,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,6,4,2,3,7,1,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[4,7,6,3,8,1,2,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,7,4,2,3,8,1,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,7,6,1,4,8,2,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,4,7,5,2,8,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,4,8,5,2,6,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,2,6,3,7,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,6,2,4,7,1,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,8,5,7,1,2,4,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,8,5,7,1,3,4,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,6,2,7,1,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,6,5,8,1,3,4,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,6,5,8,1,2,4,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,5,7,4,8,1,3,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,4,6,7,2,8,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,5,7,1,4,8,2,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,3,7,2,4,8,1,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,4,7,3,8,1,2,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,4,6,3,8,1,2,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,4,6,3,7,1,2,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,4,1,6,7,2,3,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,4,1,6,8,2,3,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,5,3,7,1,8,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,1,2,7,8,3,4]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,3,6,4,7,8,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,7,4,8,5,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,7,1,5,8,6,2,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,5,1,2,8,6,3,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,5,3,8,1,6,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,1,8,5,2,3,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,6,1,7,5,2,3,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,7,2,8,1,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,7,8,5,1,2,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,6,8,2,7,1,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,8,7,1,3,5,6]=>0011000=>[2,2,3]=>[3,2,2]
[4,3,8,7,1,2,5,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,3,8,7,1,2,4,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,3,7,6,1,2,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,4,7,6,1,2,3,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,4,8,7,1,2,3,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[3,5,8,7,1,2,4,6]=>0011000=>[2,2,3]=>[3,2,2]
[2,5,8,7,1,3,4,6]=>0011000=>[2,2,3]=>[3,2,2]
[4,6,8,2,7,1,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,8,4,7,5,1,2,3]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,8,7,1,6,2,3,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,8,7,6,1,3,4,5]=>0111000=>[1,3,3]=>[3,3,1]
[3,8,7,6,1,2,4,5]=>0111000=>[1,3,3]=>[3,3,1]
[4,8,7,6,1,2,3,5]=>0111000=>[1,3,3]=>[3,3,1]
[5,6,3,1,4,2,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,5,3,8,2,1,6,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,8,7,4,5,1,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,1,4,5,8,2,3]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,7,8,5,3,6,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,7,3,8,1,2,6,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,7,1,4,5,3,2,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[2,7,8,4,1,6,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[7,1,8,4,2,6,5,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,5,1,4,8,6,3,2]=>1100111=>[2,2,3]=>[3,2,2]
[6,5,3,1,8,4,7,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,3,8,1,5,7,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,6,3,1,2,5,7,4]=>1110001=>[3,3,1]=>[1,3,3]
[8,7,1,4,2,6,5,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,3,8,4,1,6,5,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,3,4,5,6,7,8,1,9]=>00000010=>[6,1,1]=>[1,1,6]
[2,3,4,5,6,8,9,1,7]=>00000010=>[6,1,1]=>[1,1,6]
[2,3,4,5,7,8,9,1,6]=>00000010=>[6,1,1]=>[1,1,6]
[2,3,4,6,7,8,9,1,5]=>00000010=>[6,1,1]=>[1,1,6]
[2,3,5,6,7,8,9,1,4]=>00000010=>[6,1,1]=>[1,1,6]
[2,4,5,6,7,8,9,1,3]=>00000010=>[6,1,1]=>[1,1,6]
[3,4,5,6,7,8,9,1,2]=>00000010=>[6,1,1]=>[1,1,6]
[2,3,4,5,6,7,8,9,10,1]=>000000001=>[8,1]=>[1,8]
[2,3,4,5,6,7,8,9,1,10]=>000000010=>[7,1,1]=>[1,1,7]
[2,3,4,5,6,7,1,8,9]=>00000100=>[5,1,2]=>[2,1,5]
[2,3,4,5,6,7,8,10,1,9]=>000000010=>[7,1,1]=>[1,1,7]
[2,3,4,5,6,1,9,7,8]=>00001010=>[4,1,1,1,1]=>[1,1,1,1,4]
[2,3,4,5,6,7,9,10,1,8]=>000000010=>[7,1,1]=>[1,1,7]
[2,3,4,5,1,8,9,6,7]=>00010010=>[3,1,2,1,1]=>[1,1,2,1,3]
[2,3,4,5,6,8,9,10,1,7]=>000000010=>[7,1,1]=>[1,1,7]
[2,3,4,1,7,8,9,5,6]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[2,3,4,5,7,8,9,10,1,6]=>000000010=>[7,1,1]=>[1,1,7]
[2,3,1,6,7,8,9,4,5]=>01000010=>[1,1,4,1,1]=>[1,1,4,1,1]
[2,3,4,6,7,8,9,10,1,5]=>000000010=>[7,1,1]=>[1,1,7]
[2,1,5,6,7,8,9,3,4]=>10000010=>[1,5,1,1]=>[1,1,5,1]
[2,3,5,6,7,8,9,10,1,4]=>000000010=>[7,1,1]=>[1,1,7]
[1,4,5,6,7,8,9,2,3]=>00000010=>[6,1,1]=>[1,1,6]
[2,4,5,6,7,8,9,10,1,3]=>000000010=>[7,1,1]=>[1,1,7]
[3,4,5,6,7,8,9,10,1,2]=>000000010=>[7,1,1]=>[1,1,7]
[3,6,4,5,7,2,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,3,2,7,4,6,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,3,6,2,4,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,2,5,1,8,4,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,3,6,2,7,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,2,6,3,4,7,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,2,6,3,4,5,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,2,7,3,4,5,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,2,5,7,3,6,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,4,7,6,2,3,8,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,7,3,5,2,4,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,6,2,4,5,8,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,7,6,3,4,5,8,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[6,5,3,1,2,8,4,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,6,5,2,3,7,1,4]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,5,2,1,7,3,4,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,2,1,8,3,4,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[1,6,3,2,8,4,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,6,2,3,1,8,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,5,1,8,3,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,4,8,6,2,7,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,8,3,5,2,7,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,5,2,3,6,1,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,8,2,1,7,3,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,8,6,3,7,2,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,8,2,7,3,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,8,1,7,3,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,8,6,1,7,2,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,8,1,5,7,2,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,2,8,3,7,1,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,1,2,7,3,4,5,6]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,6,2,7,1,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,7,1,2,8,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,2,6,1,8,3,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,1,5,8,2,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,2,1,5,8,4,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,4,1,3,6,8,2,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[1,5,3,4,6,8,2,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,3,5,1,6,8,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,4,6,3,8,7,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,4,5,8,7,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,5,3,4,8,7,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,3,2,8,7,1,4,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,3,1,8,7,2,4,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,5,3,7,6,1,2,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,1,8,3,7,2,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,8,1,7,2,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,6,8,2,3,5,1,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,7,8,2,4,6,1,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,3,8,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,7,8,2,6,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,2,5,8,7,1,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[2,3,8,7,1,4,5,6]=>0011000=>[2,2,3]=>[3,2,2]
[7,2,8,6,1,3,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[2,1,8,7,3,4,5,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,2,7,6,1,3,4,5]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[1,2,8,7,3,4,5,6]=>0011000=>[2,2,3]=>[3,2,2]
[1,3,8,7,2,4,5,6]=>0011000=>[2,2,3]=>[3,2,2]
[1,7,8,3,6,2,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,1,5,8,7,2,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,4,8,7,6,1,2,3]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,8,3,7,5,1,2,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,8,6,2,5,1,3,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,1,6,7,3,2,5,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,1,6,7,3,2,4,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,1,5,3,7,2,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,1,5,3,6,2,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,5,1,3,6,2,4,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,5,8,3,6,2,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,4,8,3,2,6,5,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,4,1,3,2,6,5,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,1,4,3,2,6,5,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,1,4,3,2,7,5,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,1,4,3,2,7,6,5]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,1,5,4,6,7,2,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,1,5,3,6,2,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,4,3,2,6,7,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,1,4,3,2,5,7,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,1,4,3,2,5,6,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,4,1,3,2,5,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,4,8,3,2,5,6,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,4,3,8,2,5,7,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,4,3,1,2,5,8,7]=>1110001=>[3,3,1]=>[1,3,3]
[7,4,1,3,2,5,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,4,1,3,2,6,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,1,3,6,2,8,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,1,4,6,8,2,3]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,5,8,3,6,2,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,4,8,3,2,6,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,4,8,3,2,5,1,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,4,3,8,2,5,1,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,4,3,7,2,5,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,4,3,2,8,6,1,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[5,4,3,2,8,7,1,6]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[6,5,3,8,7,2,1,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,5,4,8,7,1,2,3]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,5,4,1,7,8,2,3]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,5,3,1,7,2,8,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,3,1,2,7,8,5]=>1110001=>[3,3,1]=>[1,3,3]
[5,4,3,2,1,8,6,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[6,5,3,1,8,2,7,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,5,4,1,8,7,2,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,5,1,4,8,6,2,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,4,1,3,2,8,6,5]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,4,1,3,2,8,5,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,4,3,1,2,8,5,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,4,3,1,2,7,5,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,4,3,8,2,7,5,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,5,3,8,7,2,4,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,5,3,1,7,2,4,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,5,3,1,8,2,4,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,1,3,8,2,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,6,1,8,3,2,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,6,1,8,4,5,2,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,8,1,4,5,2,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,6,8,1,3,2,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,3,7,8,2,4,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,4,3,7,2,8,5,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,4,3,7,2,1,5,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,4,8,3,2,1,5,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,4,8,3,2,1,6,5]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,5,8,3,1,2,6,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,5,8,4,1,6,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,5,4,8,1,7,2,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,3,8,1,2,7,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,4,3,2,8,1,7,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,3,7,2,1,8,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,5,3,7,1,2,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,5,4,7,1,8,2,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,3,7,8,2,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,4,3,7,2,8,1,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,4,3,2,7,8,1,6]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[5,4,3,2,6,8,1,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[5,6,2,1,3,4,8,7]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[5,8,2,7,4,1,3,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,3,7,8,2,1,4,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[7,6,1,2,5,8,3,4]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[2,1,7,8,4,3,5,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,3,7,4,1,5,6,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,8,1,2,5,4,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,6,8,3,1,4,7,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[6,1,8,3,2,4,5,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,4,1,3,7,6,2,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,8,7,4,2,1,6,3]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[7,5,1,6,8,3,4,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,2,1,8,7,4,3]=>1110111=>[3,1,3]=>[3,1,3]
[4,7,2,8,1,3,6,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,8,6,1,2,5,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,4,7,1,8,2,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,8,2,4,3,5,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,7,2,4,3,5,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,6,2,4,3,5,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,5,2,4,3,6,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,6,2,5,3,4,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,7,2,5,3,4,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,8,2,5,3,4,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,8,2,6,3,4,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,7,2,6,3,4,5,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,8,2,7,3,5,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,8,3,5,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,8,3,5,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,2,8,3,6,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,2,8,3,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,2,8,4,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,2,3,8,4,6,5,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,3,7,4,6,5,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,2,7,4,6,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,2,7,3,6,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,2,7,3,6,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,7,3,5,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,6,3,5,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,6,3,5,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,5,3,6,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,5,3,6,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,5,3,7,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,2,4,3,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,4,3,7,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,4,3,6,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,4,3,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,3,4,6,5,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,7,2,3,4,6,5,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,8,2,3,4,7,5,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,8,2,4,3,7,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,4,3,8,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,4,3,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,2,4,3,8,6,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,5,3,8,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,5,3,8,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,5,3,7,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,6,3,7,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,6,3,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,2,3,8,4,7,5,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,2,8,4,7,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,2,8,3,7,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,2,8,3,7,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,8,3,7,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,8,3,6,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,7,3,6,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,3,7,2,5,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,3,7,5,2,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,6,3,8,5,1,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,3,8,5,1,2,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,6,8,3,4,1,2,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,6,8,3,4,1,7,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,2,7,5,3,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,6,7,2,4,3,1,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,6,8,4,3,1,7,2]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,6,8,4,3,1,2,7]=>0011100=>[2,3,2]=>[2,3,2]
[5,7,8,4,1,6,2,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,7,8,4,1,6,3,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,7,8,4,1,3,6,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[5,6,8,4,2,1,7,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,6,8,2,4,1,7,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,2,8,5,1,7,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,2,6,8,5,1,7,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,2,6,8,5,1,4,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,6,2,8,5,1,3,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,6,8,2,4,1,3,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,6,8,4,2,1,3,7]=>0011100=>[2,3,2]=>[2,3,2]
[5,7,8,4,1,3,2,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,7,8,4,1,2,6,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[5,7,8,4,1,2,3,6]=>0011000=>[2,2,3]=>[3,2,2]
[6,7,8,1,5,2,3,4]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,7,8,1,5,2,4,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,7,8,1,5,3,2,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,7,8,1,3,5,2,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,7,8,2,1,6,3,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,7,2,8,1,6,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,7,8,1,6,4,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,2,7,8,1,6,5,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,7,2,8,1,6,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,7,8,2,1,6,4,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,7,8,1,3,5,4,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,7,8,1,5,3,4,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,7,8,1,5,4,3,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[6,7,8,1,5,4,2,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,7,8,1,4,5,2,3]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,8,1,4,5,3,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,7,8,1,4,3,5,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,7,8,1,3,4,5,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[5,7,8,2,1,4,6,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[4,7,2,8,1,5,6,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,7,8,1,5,6,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,2,6,8,4,1,7,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,6,2,8,3,1,7,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,8,3,2,1,7,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,7,8,3,1,4,6,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[5,7,8,3,1,6,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,7,8,3,1,6,2,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,7,3,8,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,8,1,6,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,3,8,1,5,6,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,6,3,8,2,1,7,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,3,2,8,1,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,2,3,8,1,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,2,5,4,8,1,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,3,2,8,1,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,6,3,8,2,1,5,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,7,3,8,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,8,1,2,6,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,7,3,8,1,2,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,7,8,3,1,2,4,6]=>0011000=>[2,2,3]=>[3,2,2]
[5,7,8,3,1,2,6,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[5,7,8,3,1,4,2,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,6,8,3,2,1,4,7]=>0011100=>[2,3,2]=>[2,3,2]
[3,2,7,8,1,5,4,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,7,8,2,1,4,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,7,8,1,3,4,2,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,8,1,4,3,2,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,7,8,1,4,2,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,7,8,1,4,2,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,7,8,1,2,5,3,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,8,1,2,5,4,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,7,8,1,2,4,5,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[6,7,8,1,3,2,5,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,7,8,2,1,3,6,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,2,7,8,1,4,6,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,7,8,1,3,2,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,7,8,1,2,4,3,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,8,1,2,3,5,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[7,2,8,5,1,6,4,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,3,7,5,2,6,4,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,3,7,5,4,2,6,8]=>0011100=>[2,3,2]=>[2,3,2]
[7,2,8,5,4,1,6,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,8,5,4,3,1,7,6]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[2,8,4,5,6,1,7,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,8,6,5,7,3,1,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,8,4,5,3,7,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,4,3,5,6,1,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,2,8,4,5,6,1,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,3,7,5,2,4,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,2,3,8,5,1,7,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,3,2,8,5,1,4,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,4,8,2,5,6,3,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,4,8,5,2,1,3,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,4,8,5,1,3,7,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,7,5,2,1,8,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,3,7,5,1,2,8,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,7,1,5,6,8,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,6,1,7,5,2,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,1,2,7,6,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,4,2,1,7,5,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,5,7,1,4,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,2,7,4,1,8,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,5,2,6,4,8,7,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,1,8,6,4,7,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,6,1,8,7,2,4,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,5,8,2,7,4,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,5,8,4,2,3,7,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,2,5,8,3,7,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,6,5,7,3,4,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,2,7,4,6,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,1,8,7,6,3,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,1,3,8,4,6,2,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,3,4,8,6,1,7,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,3,4,8,6,5,1,7]=>0001110=>[3,3,1]=>[1,3,3]
[2,7,3,5,8,6,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,2,4,7,8,6,1,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,5,4,6,2,7,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,4,7,1,8,3,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,6,4,1,8,7,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,3,6,1,4,8,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,3,5,6,8,4,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[6,3,5,1,8,2,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,1,5,8,4,7,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,7,6,5,8,3,4,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,7,1,6,3,8,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,4,1,7,8,5,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,1,4,2,7,8,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,1,4,7,2,8,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,6,4,7,8,2,5,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,4,6,8,5,7,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,3,4,5,7,1,8,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,5,4,6,1,7,8,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,1,4,3,6,5,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,3,4,1,2,6,5,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,4,3,2,1,6,5,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,6,3,2,5,4,1,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[6,7,3,2,5,4,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,3,2,5,4,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,4,5,2,3,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,5,1,6,2,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,2,1,5,6,3,4,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,2,1,6,5,4,3,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,3,6,1,5,4,2,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,4,6,5,1,3,2,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,8,5,4,3,2,7,6]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[1,8,6,4,3,7,2,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,5,7,4,3,1,8,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,4,7,5,1,3,8,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,7,1,5,4,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,1,7,5,4,8,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,2,1,8,5,4,7,6]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,8,1,5,4,7,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,8,5,1,3,7,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,5,8,4,3,1,7,6]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,6,8,4,3,7,1,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,7,8,4,3,6,5,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,8,7,4,3,6,5,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,8,7,5,6,3,4,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,7,8,5,6,3,4,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,6,8,5,7,3,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,5,8,6,7,1,3,4]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,8,6,1,7,3,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,1,8,6,7,4,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,2,1,7,6,8,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,3,7,1,6,8,4,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,4,7,6,1,8,3,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,5,7,6,8,1,3,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,7,5,8,3,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,8,6,5,7,3,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,8,5,6,7,2,3,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,7,5,6,8,2,3,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,5,7,8,2,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,4,6,7,1,8,2,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,6,1,7,8,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,2,1,6,7,8,3,4]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[6,2,1,5,7,3,8,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,3,5,1,7,2,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,5,7,1,2,8,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,5,4,7,2,1,8,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,6,4,7,2,8,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,4,6,2,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,3,2,6,7,4,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,7,3,2,6,8,4,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,6,3,2,7,8,1,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,5,3,2,7,1,8,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,3,2,1,7,8,5]=>1111001=>[4,2,1]=>[1,2,4]
[6,2,1,4,3,7,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,2,1,4,3,8,7,6]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,3,4,1,2,8,7,6]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,6,3,2,8,7,1,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,7,3,2,8,6,5,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,8,3,2,7,6,5,4]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,8,4,7,2,6,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,7,4,8,2,6,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,6,4,8,2,7,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,4,8,2,1,7,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,5,8,1,2,7,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,3,5,1,8,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,1,5,8,3,7,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,2,1,6,8,7,3,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,3,6,1,8,7,2,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,6,8,1,7,2,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,5,6,8,7,1,2,4]=>0001100=>[3,2,2]=>[2,2,3]
[3,6,5,8,7,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,7,5,8,6,2,4,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,5,7,6,2,4,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,6,7,5,4,2,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,6,7,8,5,4,1,2]=>0001110=>[3,3,1]=>[1,3,3]
[3,5,7,8,6,1,4,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[3,4,7,8,1,6,5,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,2,1,7,8,6,5,3]=>1100111=>[2,2,3]=>[3,2,2]
[2,3,8,1,7,6,5,4]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,4,8,7,1,6,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,5,8,7,6,1,4,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,6,8,7,5,4,1,3]=>0011110=>[2,4,1]=>[1,4,2]
[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[2,1,10,9,8,7,6,5,4,3,12,11]=>10111111101=>[1,1,7,1,1]=>[1,1,7,1,1]
[2,1,12,11,10,9,8,7,6,5,4,3]=>10111111111=>[1,1,9]=>[9,1,1]
[10,9,8,7,6,5,4,3,2,1,12,11]=>11111111101=>[9,1,1]=>[1,1,9]
[12,11,10,9,8,7,6,5,4,3,2,1]=>11111111111=>[11]=>[11]
[7,4,6,1,8,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,5,1,7,4,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,4,1,7,5,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,1,7,5,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,6,2,1,7,5,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,6,2,7,5,8,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,7,5,2,6,8,4,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,5,2,1,6,8,4,3]=>1110011=>[3,2,2]=>[2,2,3]
[6,8,4,3,1,7,5,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[3,6,8,4,1,7,5,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,6,7,5,1,8,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[7,5,6,1,8,3,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,6,5,7,1,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,7,5,6,1,8,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,5,1,8,4,3,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,8,4,1,7,5,3,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,7,5,3,1,8,4,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[8,4,2,1,6,7,5,3]=>1110011=>[3,2,2]=>[2,2,3]
[1,8,4,2,6,7,5,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,5,3,2,7,6,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,2,1,7,6,8,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,5,3,1,7,6,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,4,1,6,7,5,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,7,5,1,6,8,4,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,4,6,1,7,5,8,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,7,1,6,5,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,2,6,5,7,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,1,2,7,5,8,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,5,1,2,6,8,4,3]=>1100011=>[2,3,2]=>[2,3,2]
[8,4,1,2,6,7,5,3]=>1100011=>[2,3,2]=>[2,3,2]
[5,3,1,2,7,6,8,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,2,5,3,7,6,8,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,1,2,7,6,8,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,5,1,2,7,6,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,7,1,5,8,2,3,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,7,6,1,5,8,3,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,3,5,1,7,6,8,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,1,5,8,3,2,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,6,7,1,5,8,2,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,1,6,5,8,2,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,1,6,8,4,2,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,4,1,6,7,5,2,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,2,3,1,7,6,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,2,1,7,6,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,3,5,2,7,6,8,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,7,6,2,5,8,3,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,6,2,1,5,8,3,4]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,3,1,5,7,6,2,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,2,4,1,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,5,1,7,4,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,6,4,8,2,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,6,4,7,1,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,5,2,7,4,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,2,5,8,3,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,3,5,7,6,2,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[1,8,3,5,7,6,2,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,5,2,3,7,6,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,2,1,3,7,6,8,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,2,6,8,4,1,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,4,2,6,7,5,1,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,1,4,2,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,6,5,7,1,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,8,2,5,7,1,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,3,2,5,7,6,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,1,3,2,7,6,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,3,2,7,6,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,1,3,7,6,8,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,4,2,3,7,6,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,1,3,7,6,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,1,3,7,6,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,8,3,5,7,6,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,8,2,3,5,7,1,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,7,1,3,5,8,2,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,5,7,6,1,2,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,1,2,3,7,6,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,1,2,4,7,6,8,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[10,8,9,5,6,7,1,2,3,4]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[10,8,9,4,5,6,1,2,3,7]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[10,7,8,5,6,9,1,2,3,4]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[10,7,8,4,5,9,1,2,3,6]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[10,6,7,4,5,8,1,2,3,9]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[10,7,8,3,4,9,1,2,5,6]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[10,6,7,3,4,8,1,2,5,9]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,8,10,5,6,7,1,2,3,4]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,8,10,4,5,6,1,2,3,7]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,7,10,5,6,8,1,2,3,4]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,7,10,4,5,8,1,2,3,6]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,6,10,4,5,7,1,2,3,8]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,7,10,3,4,8,1,2,5,6]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,6,10,3,4,7,1,2,5,8]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,7,9,5,6,10,1,2,3,4]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,7,9,4,5,10,1,2,3,6]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,6,9,4,5,10,1,2,3,7]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[7,6,8,4,5,9,1,2,3,10]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,7,9,3,4,10,1,2,5,6]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,6,9,3,4,10,1,2,5,7]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[7,6,8,3,4,9,1,2,5,10]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,6,10,5,7,8,1,2,3,4]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,6,10,4,7,8,1,2,3,5]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,5,10,4,6,7,1,2,3,8]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,6,10,3,7,8,1,2,4,5]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,5,10,3,6,7,1,2,4,8]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,6,9,5,7,10,1,2,3,4]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,6,9,4,7,10,1,2,3,5]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,5,9,4,6,10,1,2,3,7]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[7,5,8,4,6,9,1,2,3,10]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,6,9,3,7,10,1,2,4,5]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,5,9,3,6,10,1,2,4,7]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[7,5,8,3,6,9,1,2,4,10]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,4,9,3,5,10,1,2,6,7]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[7,4,8,3,5,9,1,2,6,10]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,6,10,2,7,8,1,3,4,5]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[9,5,10,2,6,7,1,3,4,8]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,6,9,2,7,10,1,3,4,5]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,5,9,2,6,10,1,3,4,7]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[7,5,8,2,6,9,1,3,4,10]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,4,9,2,5,10,1,3,6,7]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[7,4,8,2,5,9,1,3,6,10]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[8,1,2,4,3,6,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,3,5,6,2,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,3,4,2,6,7,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,3,2,4,5,7,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,7,8,3,4,5,6,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,6,3,8,4,5,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,2,1,4,5,8,7]=>1110001=>[3,3,1]=>[1,3,3]
[7,3,1,4,2,6,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,4,1,5,6,8,2,3]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,7,8,5,6,1,2,3]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,7,8,5,6,2,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,7,8,4,2,6,1,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,7,8,2,4,5,1,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,6,2,8,4,5,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,6,7,4,5,8,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,5,2,4,8,6,1,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,5,4,2,8,7,1,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,6,5,8,7,1,2,3]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,4,5,1,7,8,2,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,4,1,2,3,8,5,6]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[6,2,4,1,3,7,5,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,4,8,3,7,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,5,8,7,3,4,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,2,5,1,7,3,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,5,2,1,8,3,4,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[2,5,6,7,8,3,4,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[2,4,6,7,3,8,5,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,2,6,7,3,1,5,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,7,8,2,3,1,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,7,8,3,2,1,6,5]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,6,4,8,1,7,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,3,8,1,2,7,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,2,5,3,7,1,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,6,7,2,1,8,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,4,6,7,2,8,1,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,5,2,7,8,1,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,2,5,6,8,1,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,2,7,8,6,4,1,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,1,2,7,8,6,4,3]=>1000111=>[1,3,3]=>[3,3,1]
[4,7,1,8,6,5,2,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,7,1,2,8,6,5,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,6,8,1,2,7,5,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,8,7,1,5,3,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,8,7,3,5,1,2,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,8,1,6,3,5,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,3,6,5,2,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,8,3,6,5,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,7,2,8,6,1,5,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,7,3,4,8,6,5,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,2,7,1,8,6,5,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,8,2,3,6,5,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,5,7,1,6,2,3,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,7,1,2,6,3,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,8,2,7,1,3,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,8,7,2,5,3,1,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,2,4,8,7,1,5,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,6,8,3,7,4,5,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,6,8,3,4,7,5,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,2,4,8,1,7,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,7,2,3,5,1,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,8,2,1,7,3,5,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,5,7,2,1,6,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,5,7,1,2,3,6,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,7,6,2,1,4,3,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,5,7,2,3,1,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,2,7,1,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,7,5,3,4,6,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[1,8,7,3,5,4,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,2,5,4,7,1,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,2,7,3,1,6,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,7,6,2,4,3,1,5]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,7,6,1,2,4,3,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,7,6,1,4,2,3,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,6,4,1,3,2,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[5,8,4,7,2,1,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,7,5,4,3,6,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[1,6,8,4,3,7,5,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,8,7,3,2,5,1,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,8,1,7,3,2,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,5,7,3,1,6,2,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,5,7,1,3,2,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,3,1,2,6,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,8,4,7,1,2,6,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,4,1,7,2,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,8,4,7,1,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,2,6,5,7,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,2,5,6,7,4,1,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,8,5,7,1,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,5,7,1,2,6,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,5,1,7,2,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,5,3,1,7,2,6,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,5,3,7,1,2,6,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,8,1,3,7,2,5,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,2,8,1,7,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,6,4,8,3,7,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,7,4,5,3,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,5,7,2,1,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,5,3,7,2,1,6,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,7,6,3,1,4,2,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,7,6,1,3,2,4,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,5,3,2,7,1,6,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,8,5,2,7,1,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,7,4,3,5,6,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[1,8,7,3,4,5,6,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[8,2,4,5,7,1,6,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,5,2,3,7,1,6,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,3,1,5,4,2,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,3,1,5,2,7,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,5,4,2,1,7,3,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,5,4,2,1,7,6,3]=>1111011=>[4,1,2]=>[2,1,4]
[6,5,4,2,1,3,8,7]=>1111001=>[4,2,1]=>[1,2,4]
[6,5,4,2,3,1,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,3,2,5,1,4,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,5,4,3,1,2,8,7]=>1111001=>[4,2,1]=>[1,2,4]
[6,5,4,1,3,2,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,5,4,1,2,7,6,3]=>1110011=>[3,2,2]=>[2,2,3]
[8,7,4,1,6,3,2,5]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,7,4,1,6,3,5,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,4,1,6,5,3,2]=>1110111=>[3,1,3]=>[3,1,3]
[8,5,4,1,3,7,6,2]=>1110011=>[3,2,2]=>[2,2,3]
[8,5,4,3,1,7,6,2]=>1111011=>[4,1,2]=>[2,1,4]
[8,3,2,5,1,7,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,1,8,5,3,7,6,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,3,2,5,1,7,4,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,4,3,1,7,2,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,5,4,1,3,7,2,6]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,7,4,1,6,5,2,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,7,4,1,6,2,5,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,6,5,2,1,4,3]=>1111101=>[5,1,1]=>[1,1,5]
[8,7,4,3,6,2,1,5]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,3,2,7,6,4,1,5]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[2,1,8,7,6,4,3,5]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[2,1,8,7,6,4,5,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,2,7,6,4,5,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,7,4,3,6,2,5,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,6,5,2,4,3,1]=>1111011=>[4,1,2]=>[2,1,4]
[8,5,4,2,3,7,6,1]=>1110011=>[3,2,2]=>[2,2,3]
[8,7,4,2,6,5,3,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,7,4,2,6,3,5,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,4,2,6,3,1,5]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,3,1,7,6,4,2,5]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,3,1,7,6,4,5,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,3,1,7,6,5,4,2]=>1101111=>[2,1,4]=>[4,1,2]
[8,3,1,5,4,7,6,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,3,1,5,4,7,2,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,3,1,7,6,5,2,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,3,1,7,6,2,5,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,7,4,2,6,1,5,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,4,2,6,5,1,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,5,4,2,3,7,1,6]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,3,2,5,4,7,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,1,8,5,4,7,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,2,7,6,5,1,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,7,4,3,6,5,1,2]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,7,6,5,3,1,4,2]=>1111101=>[5,1,1]=>[1,1,5]
[8,7,6,5,1,3,2,4]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,7,6,5,1,3,4,2]=>1111001=>[4,2,1]=>[1,2,4]
[8,7,6,5,1,4,3,2]=>1111011=>[4,1,2]=>[2,1,4]
[8,7,6,5,4,1,3,2]=>1111101=>[5,1,1]=>[1,1,5]
[8,7,4,3,6,1,5,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,3,2,7,6,1,5,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,1,8,7,6,3,5,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,2,7,6,1,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,7,6,5,1,4,2,3]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,7,6,5,1,2,4,3]=>1111001=>[4,2,1]=>[1,2,4]
[7,3,5,1,8,4,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,4,1,8,5,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,6,2,1,8,7,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,6,5,2,7,4,3,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,4,3,1,8,6,5,2]=>1110111=>[3,1,3]=>[3,1,3]
[7,6,5,1,8,4,3,2]=>1110111=>[3,1,3]=>[3,1,3]
[7,6,4,1,8,5,3,2]=>1110111=>[3,1,3]=>[3,1,3]
[6,4,2,1,8,7,5,3]=>1110111=>[3,1,3]=>[3,1,3]
[1,6,4,2,7,5,3,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,5,3,2,7,6,4,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,3,2,1,8,7,6,4]=>1110111=>[3,1,3]=>[3,1,3]
[2,5,3,1,7,8,6,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,6,4,1,7,8,5,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,6,5,1,7,8,4,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[4,5,7,1,6,8,2,3]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,5,1,2,8,4,3,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,4,1,2,8,5,3,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,3,1,2,8,6,4,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,3,1,2,8,6,5,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,1,2,5,8,3,4,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[7,1,3,4,8,2,5,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[7,1,5,6,8,2,3,4]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,6,1,5,7,8,3,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,4,1,6,8,5,2,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,2,3,1,8,6,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,2,1,6,8,7,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,6,2,5,7,3,4,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,2,1,5,8,7,3,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,3,1,5,8,6,2,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,2,4,1,8,5,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,5,1,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,1,4,8,6,2,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,2,1,4,8,7,3,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[1,6,2,4,7,3,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,2,1,3,8,7,4,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,4,1,3,8,5,2,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,5,1,3,8,4,2,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,6,7,1,4,8,2,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,6,1,4,8,3,2,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,2,1,3,8,7,5,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[2,6,1,4,7,8,3,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,1,4,6,8,2,3,5]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[7,1,3,5,8,2,4,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[6,1,2,4,8,3,5,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[5,2,3,1,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,4,5,2,3,1,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,3,5,2,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,5,2,4,1,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,5,2,4,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,4,1,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,3,5,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,4,1,5,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,3,4,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,7,3,4,1,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,8,6,7,3,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,8,5,7,3,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,3,4,1,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,4,1,5,2,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,3,5,2,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,7,4,5,2,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,4,5,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,8,6,7,4,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,8,6,7,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,3,4,1,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,3,4,1,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,6,2,7,3,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,3,5,1,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,8,4,7,3,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,8,5,7,3,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,8,5,7,4,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,5,7,4,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,4,6,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,7,4,6,2,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,3,6,2,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,7,3,6,2,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,3,5,1,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,8,4,7,3,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,3,6,2,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,6,2,5,1,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,5,1,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,4,1,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,4,1,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,3,6,2,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,4,6,2,3,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,4,6,2,3,1,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,3,1,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,3,1,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,3,1,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,4,2,8,6,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,3,1,8,5,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,6,2,3,1,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,4,8,5,6,2,3,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,8,5,6,2,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,6,2,4,1,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,4,1,8,6,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,5,2,8,6,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,2,8,6,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,3,8,5,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,6,2,8,5,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,6,2,8,5,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,6,2,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,6,2,5,1,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,8,4,6,2,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,3,8,4,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,5,1,6,2,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,8,4,6,2,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,8,5,6,2,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,8,5,6,2,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,5,6,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,4,8,5,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,7,4,8,5,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,3,8,5,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,8,4,5,1,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,5,1,7,3,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,6,2,8,4,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,5,6,1,3,4,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,8,1,3,6,2,5,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,8,4,7,2,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,6,1,4,7,2,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,6,1,2,5,7,3,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,4,8,2,5,7,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,8,2,4,5,6,1,3]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,8,1,5,4,6,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,8,2,1,6,3,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,8,3,5,6,4,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,8,1,4,2,3,6,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,8,5,1,4,2,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,8,4,5,3,1,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,5,8,4,3,2,7,6]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,6,1,4,3,2,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,6,4,8,3,7,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,6,8,3,7,5,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,4,8,5,3,1,6,7]=>0011100=>[2,3,2]=>[2,3,2]
[2,5,8,1,4,7,6,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,5,8,4,7,6,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,6,2,4,7,3,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,6,2,1,4,7,8,3]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[4,6,2,5,3,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,7,5,1,3,6,8,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,5,3,6,2,4,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,7,3,6,1,4,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,3,6,7,2,1,8,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,1,7,5,2,4,8,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,1,2,4,5,8,7]=>1100001=>[2,4,1]=>[1,4,2]
[1,4,7,2,5,3,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,7,8,3,5,1,2]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,6,1,8,4,2,5,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,6,7,5,8,2,4,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,6,7,8,1,4,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[3,6,5,7,8,2,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,2,7,6,1,4,3,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,7,6,8,1,3,4]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,7,5,6,8,4,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,1,6,8,4,5,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,7,1,8,5,3,4,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,7,6,8,5,4,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,3,8,5,6,7,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,8,1,6,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,8,5,4,6,7,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,2,8,4,5,6,1,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,2,8,6,1,7,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,7,1,5,2,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,3,7,8,1,2,6,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,7,3,8,5,2,6,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,1,8,3,6,2,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,7,8,6,3,2,1,4]=>0011110=>[2,4,1]=>[1,4,2]
[5,7,8,6,1,3,4,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[7,6,5,8,1,3,4,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,6,4,3,8,2,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,1,3,4,8,2,6,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,6,5,4,1,2,7,8]=>0111000=>[1,3,3]=>[3,3,1]
[2,4,5,1,7,8,6,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,6,3,4,5,8,1,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,6,4,1,8,3,7,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,3,6,4,8,5,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,1,4,8,3,5,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,1,6,5,3,8,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,2,5,6,3,8,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,5,2,7,1,8,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,6,2,7,3,1,4,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,6,7,4,2,8,1,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,7,6,4,1,8,3,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[6,7,1,5,2,8,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,5,2,4,8,3,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,1,5,2,8,3,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,5,3,8,4,1,2]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,6,5,4,2,3,8,7]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,1,5,3,4,2,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,1,5,3,2,8,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,5,6,4,1,2,8,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,7,5,4,3,1,8,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[7,5,2,4,3,1,6,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,4,6,1,2,5,3,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,1,4,2,5,3,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,8,1,4,2,5,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,6,4,2,5,7,3,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,6,3,7,5,4,2,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,8,1,3,7,5,4,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[7,1,3,5,6,4,2,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,3,1,6,4,5,2,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,2,6,5,1,3,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,4,6,3,1,5,2,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,2,4,1,5,3,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,2,3,5,4,1,6,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,8,1,2,3,4,7,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,5,7,2,3,8,6,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[5,1,8,2,3,6,7,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,8,2,3,7,6,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[6,2,8,1,3,7,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,8,2,3,5,4,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,8,2,4,1,5,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,8,3,1,2,4,7,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,6,4,1,5,7,3,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,6,3,5,7,1,4,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,5,1,7,8,3,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,3,6,8,4,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,4,7,8,5,6,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,4,7,6,8,5,1,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,5,3,7,6,1,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,5,7,8,1,4,6,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,5,7,4,1,6,2,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,3,4,1,8,6,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,8,4,6,1,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,1,8,6,3,7,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,2,8,6,5,3,7,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,2,8,5,7,6,3,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,4,2,7,5,8,6,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,1,8,6,7,5,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,3,8,7,6,2,4,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,8,4,7,6,2,1,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,8,7,4,3,6,1,2]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,4,8,3,1,7,2,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,4,2,8,7,1,3,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,3,8,7,2,5,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,3,7,1,6,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,3,8,6,7,2,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,5,3,7,8,6,2,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,5,7,6,4,2,8,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,8,7,4,1,6,2,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,4,8,1,2,7,3,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,8,5,1,2,3,7,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[6,8,5,2,4,3,7,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,8,5,3,1,2,7,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[4,5,1,2,7,6,3,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,5,1,2,6,8,7,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,5,6,1,8,4,7,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,7,1,2,8,6,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,6,2,7,5,1,4,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,2,6,1,7,3,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,6,3,1,2,7,5,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,5,3,1,7,6,2,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,5,7,1,6,3,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,5,2,7,8,1,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,4,7,5,6,2,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,6,5,8,7,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,1,4,5,8,6,7,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,4,6,8,5,2,7,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[3,5,6,2,8,4,7,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,2,5,6,1,8,7,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,5,3,1,6,8,7,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,1,7,5,8,6,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,2,7,5,3,8,6,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,1,2,7,3,8,6,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,4,1,7,5,2,3,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,1,3,7,5,2,4,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,1,2,6,8,5,4,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,7,1,2,5,4,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,7,2,4,8,6,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,4,1,7,8,6,5,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,4,7,5,1,8,6,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,7,4,1,5,8,6,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,3,7,1,5,8,6,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[5,2,8,1,3,7,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,1,6,8,3,4,7,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,6,8,3,1,5,7,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,8,6,4,1,5,7,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[3,6,4,8,5,1,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,7,4,5,1,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,3,7,5,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,1,7,8,3,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,7,2,3,6,8,1,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,2,7,3,6,8,1,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,7,4,6,2,8,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,3,4,6,1,8,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,3,8,4,6,1,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,2,4,1,6,7,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,2,3,5,1,6,7,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,8,3,6,7,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,8,1,7,3,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,4,1,3,6,2,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,8,3,1,7,2,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,2,8,4,7,1,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,7,3,1,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,8,3,1,7,5,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,3,8,2,7,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,1,8,2,4,7,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,3,8,1,2,6,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,7,4,1,6,2,3,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,5,4,1,2,6,3,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[5,1,8,4,2,7,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,2,8,5,3,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,8,5,3,1,7,4,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[8,4,5,1,2,6,3,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,3,7,1,2,4,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,6,3,7,2,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,2,7,8,5,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,5,7,8,3,1,6,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,7,2,5,8,1,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,1,3,4,6,2,5,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,8,2,4,6,7,1,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,5,6,8,2,7,1,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,4,5,6,8,1,7,3]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[4,8,3,5,6,1,7,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,6,2,3,7,8,1,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,8,7,3,4,1,2,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,7,3,4,1,2,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,4,7,1,5,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,8,4,7,2,5,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,8,7,2,6,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,4,8,7,1,6,3,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,3,8,7,6,1,2,4]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,3,8,7,6,1,2,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,8,3,7,5,1,2,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,3,4,6,5,1,2,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,8,4,7,5,1,2,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,4,8,7,6,1,2,5]=>0011100=>[2,3,2]=>[2,3,2]
[3,5,8,7,6,1,2,4]=>0011100=>[2,3,2]=>[2,3,2]
[4,5,8,7,6,1,2,3]=>0011100=>[2,3,2]=>[2,3,2]
[4,5,8,7,1,6,3,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,5,8,7,2,6,3,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,5,8,2,7,6,4,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[3,5,8,1,7,6,4,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,5,8,1,7,6,4,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,5,8,7,1,6,3,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,4,8,7,1,6,3,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,8,4,7,1,5,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,4,6,1,5,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,4,6,2,5,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,4,7,2,5,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,8,7,2,6,3,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,5,8,7,2,6,3,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,5,8,2,7,6,4,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,5,8,3,7,6,4,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,4,2,8,7,6,5,3]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[1,3,8,2,7,6,4,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,8,3,2,7,5,4,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,3,2,6,5,4,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,2,3,1,6,5,4,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,3,1,7,5,4,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,3,8,1,7,6,4,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,4,1,8,7,6,5,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[4,3,1,8,7,6,5,2]=>1101111=>[2,1,4]=>[4,1,2]
[4,2,1,8,7,6,5,3]=>1101111=>[2,1,4]=>[4,1,2]
[3,8,2,1,7,5,4,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,3,2,1,6,5,4,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,4,2,6,1,5,3,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,2,8,7,1,6,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,2,8,7,1,6,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,2,8,1,7,6,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,3,8,1,7,6,4,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,3,8,2,7,6,4,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,3,2,7,5,4,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,8,3,1,7,5,4,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,8,2,1,7,5,4,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,8,2,7,1,5,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,7,2,1,4,3,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,5,6,1,2,4,3,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,7,1,2,4,3,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,8,1,2,7,5,4,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[6,8,2,3,7,5,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[5,2,8,3,7,6,4,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,1,8,3,7,6,4,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,1,8,7,2,6,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,8,7,2,6,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,8,1,7,2,5,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,1,6,2,5,3,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,3,1,2,6,5,4,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,8,1,2,7,5,4,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,1,8,2,7,6,4,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,2,8,7,6,5,4]=>1001111=>[1,2,4]=>[4,2,1]
[4,1,3,8,7,6,5,2]=>1001111=>[1,2,4]=>[4,2,1]
[3,1,4,8,7,6,5,2]=>1001111=>[1,2,4]=>[4,2,1]
[2,1,8,3,7,6,4,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,1,3,7,5,4,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,2,1,3,6,5,4,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,1,2,3,6,5,4,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,8,2,3,7,5,4,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,2,8,3,7,6,4,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,4,3,6,8,2,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,1,6,2,5,8,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,1,8,2,4,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,4,5,2,8,3,7,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,2,6,5,8,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,4,2,6,8,3,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,1,6,5,8,2,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,6,4,2,5,8,3,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,5,2,6,4,8,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,2,6,5,4,8,3,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,2,5,4,7,3,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,1,2,6,3,8,7,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,1,5,4,2,8,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,4,7,5,2,8,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,1,3,5,2,8,4,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,2,5,1,8,3,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,4,5,2,8,7,3,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,6,4,2,8,3,7,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,2,8,3,7,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,2,5,3,8,7,6,4]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,2,8,6,5,3,7,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,5,2,8,6,3,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,4,2,8,7,3,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,2,1,8,7,3,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,6,2,1,8,3,4,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,3,1,6,2,8,4,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,7,6,4,2,8,3,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,7,5,2,6,3,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,6,2,7,5,3,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,2,7,6,5,3,8,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,2,6,5,3,8,7,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,5,2,6,3,8,7,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,5,2,7,6,3,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,5,2,7,3,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,5,7,4,2,8,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,1,2,8,6,3,7,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,1,8,6,2,4,7,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,7,1,8,2,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,3,1,6,2,4,7,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,1,8,3,2,4,6,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,8,7,3,2,4,6,5]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[1,4,2,8,7,3,6,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,7,4,2,8,3,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,5,4,2,7,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,4,8,5,2,7,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,5,3,1,7,2,4,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,6,2,1,7,3,4,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[1,8,6,4,2,7,3,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,8,5,2,6,3,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,5,2,7,3,8,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,2,8,5,3,7,6,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,2,6,3,8,7,5,4]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,2,7,6,3,8,5,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,6,2,7,3,8,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,7,2,8,5,3,6,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,7,4,2,8,6,3,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,1,8,3,2,6,4,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,2,1,8,6,3,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[1,8,7,3,2,6,4,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,2,8,7,6,3,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,2,8,7,5,3,6,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,2,8,6,3,7,5,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,2,7,3,8,6,5,4]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[4,1,7,3,6,5,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,8,7,6,2,4,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,1,7,6,3,4,5,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,7,8,6,2,4,1,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,7,1,6,2,4,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,1,5,2,7,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,1,4,5,3,7,6,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,1,4,5,3,8,7,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,1,4,5,3,7,8,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,1,7,8,6,2,4,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,1,4,8,3,5,7,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,1,8,6,3,4,5,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,1,4,5,3,8,6,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,1,4,5,3,6,8,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,4,5,3,6,7,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,4,1,5,2,6,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,5,7,2,1,4,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,3,5,8,2,1,7,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,3,5,7,2,1,8,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,4,5,7,3,6,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,4,5,8,3,7,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,8,7,6,2,4,1,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,4,8,6,3,1,7,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,4,1,8,2,3,7,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,8,1,6,2,4,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,1,5,2,6,3,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,5,8,2,1,4,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[2,3,4,1,8,6,5,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,3,5,6,2,1,4,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[2,3,8,5,1,4,7,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,3,8,6,1,5,7,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,8,6,7,1,3,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,3,5,7,2,1,6,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,3,8,5,6,1,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,5,6,3,1,8,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,4,5,6,3,1,7,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,3,5,6,2,8,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,3,5,8,2,1,6,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,3,5,6,2,1,4,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[2,7,6,5,1,3,4,8]=>0111000=>[1,3,3]=>[3,3,1]
[2,7,6,8,1,3,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,7,6,5,8,3,1,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,7,5,6,1,4,2,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,6,4,1,8,5,7,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,6,1,3,8,5,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,7,1,3,6,5,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,7,6,8,4,3,1,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,7,6,1,8,3,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,7,6,1,4,3,5,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,3,5,1,2,8,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,4,1,5,2,3,7,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,8,1,6,3,4,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,1,8,3,2,7,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,8,6,4,1,7,5]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,8,6,7,4,3,1,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,3,5,7,2,4,1,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,3,4,1,8,7,5,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,8,6,1,7,3,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,3,8,1,6,4,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,8,1,4,5,7,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,8,6,1,4,3,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,2,3,4,5,6,7,9,8]=>00000001=>[7,1]=>[1,7]
[2,1,3,4,5,6,7,8,9]=>10000000=>[1,7]=>[7,1]
[1,2,3,4,5,6,7,8,10,9]=>000000001=>[8,1]=>[1,8]
[2,1,3,4,5,6,7,8,9,10]=>100000000=>[1,8]=>[8,1]
[1,2,3,4,5,6,7,8,9,11,10]=>0000000001=>[9,1]=>[1,9]
[9,1,2,3,4,5,6,7,10,8]=>100000001=>[1,7,1]=>[1,7,1]
[1,8,2,3,4,5,6,9,7]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[7,1,2,3,4,5,6,9,8]=>10000001=>[1,6,1]=>[1,6,1]
[2,1,9,3,4,5,6,7,8]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[2,8,1,3,4,5,6,7,9]=>01000000=>[1,1,6]=>[6,1,1]
[2,10,1,3,4,5,6,7,8,9]=>010000000=>[1,1,7]=>[7,1,1]
[2,1,3,4,5,6,7,8,9,10,11]=>1000000000=>[1,9]=>[9,1]
[8,4,3,6,5,1,7,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,5,6,3,4,1,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,5,4,3,1,7,2]=>1111101=>[5,1,1]=>[1,1,5]
[1,7,6,5,4,2,3,8]=>0111100=>[1,4,2]=>[2,4,1]
[1,8,6,5,2,7,3,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,7,5,4,1,6,3,2]=>1111011=>[4,1,2]=>[2,1,4]
[7,8,5,4,1,3,6,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[6,8,5,4,2,1,7,3]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,8,6,2,4,1,7,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,2,6,5,1,7,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,2,8,6,5,1,7,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,2,1,7,6,4,5,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[4,1,3,7,6,2,5,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,1,7,3,6,2,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,1,7,5,3,2,4,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,1,6,5,2,4,3,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,1,6,5,2,3,7,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,2,7,6,3,4,5,8]=>0011000=>[2,2,3]=>[3,2,2]
[1,2,8,3,7,4,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,1,7,2,6,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,8,2,6,4,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,1,8,2,4,7,3,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,8,3,2,7,4,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,3,8,2,7,5,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,2,1,8,4,7,5,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,2,8,7,1,6,5,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,8,2,7,1,6,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,7,2,1,6,4,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[6,8,7,1,3,5,4,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,8,6,1,5,3,4,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,7,6,1,5,4,3,2]=>1110111=>[3,1,3]=>[3,1,3]
[1,8,7,2,6,5,3,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,7,8,2,5,6,3,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,6,7,1,4,5,3,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,6,8,1,4,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,8,3,2,1,7,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,5,8,3,1,4,6,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,5,7,3,1,6,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,6,8,4,2,7,3,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,5,4,8,2,7,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,3,7,1,6,5,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,4,3,8,1,5,6,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,4,3,1,5,2,7,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,4,3,1,2,6,5,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,4,3,1,2,5,7,6]=>1110001=>[3,3,1]=>[1,3,3]
[1,5,4,2,3,6,7,8]=>0110000=>[1,2,4]=>[4,2,1]
[8,5,1,4,2,3,7,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,1,4,2,6,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,1,4,3,2,7,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,6,1,3,4,2,7,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,6,2,1,5,3,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,6,1,5,4,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,7,1,4,6,5,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,7,2,1,3,6,5,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,7,1,3,2,6,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,1,2,4,5,3,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,6,1,2,5,4,3,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,6,1,2,5,3,7,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,7,2,3,6,4,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,7,1,2,3,6,5,4]=>1100011=>[2,3,2]=>[2,3,2]
[7,8,1,2,3,5,6,4]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[6,8,1,2,4,3,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,1,3,2,4,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,2,1,3,5,7,6]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,2,8,1,4,5,7,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,1,3,2,5,6,7,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[5,1,2,4,3,6,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[6,1,2,3,5,4,7,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[7,1,2,3,4,6,5,8]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[8,1,2,3,4,5,7,6]=>1000001=>[1,5,1]=>[1,5,1]
[6,7,3,8,5,1,2,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,7,4,5,1,8,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,7,6,8,1,2,3]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,7,8,6,1,2,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,8,4,5,7,1,2,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,8,6,7,1,2,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,5,6,7,1,8,3,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,5,6,2,7,4,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,6,1,7,8,4,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,5,6,1,8,7,4,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,5,6,8,1,7,3,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,2,4,5,1,6,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,8,6,2,3,7,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,5,6,8,2,3,7,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,5,6,2,8,4,7,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,5,6,3,4,7,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,4,2,6,8,5,7,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,1,3,2,5,4,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,2,3,1,5,6,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,3,1,5,7,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,4,1,6,8,7,5,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,4,1,6,7,8,5,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,3,1,7,6,8,5,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,2,7,8,1,6,3,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,7,2,6,4,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,3,1,5,8,4,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[6,7,2,1,8,5,4,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,7,2,8,1,5,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,8,2,1,4,3,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,7,1,2,8,4,5,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,7,1,3,4,8,5,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[5,2,7,3,4,6,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,1,7,3,4,8,6,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,1,7,8,2,3,6,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,1,8,7,2,3,6,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,8,1,2,7,4,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,3,7,5,8,6,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,1,4,5,7,8,6,2]=>1000011=>[1,4,2]=>[2,4,1]
[2,1,8,3,4,7,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,2,1,3,4,6,5,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[1,8,2,3,4,5,7,6]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,2,8,3,4,6,7,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,2,1,6,5,8,7,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,2,6,1,4,8,7,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,2,6,4,1,8,7,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,2,7,4,8,1,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,7,4,8,6,1,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,7,2,3,8,6,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,7,2,3,8,1,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,6,2,3,1,8,7,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,2,1,3,8,7,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,1,6,4,2,8,7,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,6,1,3,2,8,7,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,3,1,2,8,7,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,6,3,2,1,8,7,4]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,7,3,2,8,1,6,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,7,3,2,8,6,1,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,7,3,8,2,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,7,3,8,1,2,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,7,3,1,8,2,6,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,7,1,3,8,2,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,1,7,4,8,2,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,7,4,8,3,6,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,5,7,4,8,6,3,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[5,1,7,4,8,6,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,7,1,3,8,6,2,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,7,3,1,8,6,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,7,3,8,1,5,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,3,8,5,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,7,8,3,1,4,2,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,7,1,8,3,5,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,7,8,4,5,2,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,6,7,8,4,5,3,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,6,7,8,4,3,5,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[6,1,7,8,4,2,5,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,7,1,8,3,2,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,7,2,1,8,3,6,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,2,8,1,3,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,7,2,8,3,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,7,2,8,3,5,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,8,4,5,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,2,7,8,4,1,5,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,2,7,8,1,4,5,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,2,7,1,8,4,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,1,7,8,5,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,1,2,7,8,6,5,3]=>1000111=>[1,3,3]=>[3,3,1]
[6,2,7,8,1,5,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,2,7,8,5,1,4,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,2,7,8,5,4,1,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,7,2,8,5,3,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,7,2,1,8,6,3,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,7,1,2,8,6,3,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,1,7,2,8,6,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,5,7,3,8,6,4,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,6,7,8,3,5,4,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[6,1,7,8,2,5,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,7,1,8,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,8,2,4,1,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,7,8,2,4,3,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,7,1,8,5,2,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,1,7,8,5,2,4,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,6,7,8,5,3,4,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[6,1,7,8,5,4,2,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,7,1,8,5,3,2,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,7,8,4,1,3,2,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,3,8,5,2,7,4,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,5,2,8,4,7,3,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,3,4,5,8,7,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[3,8,4,7,5,2,1,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,8,1,4,7,2,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,6,1,4,8,7,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,6,4,8,5,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,4,8,6,3,7,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,4,7,1,8,6,5,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[6,3,8,4,2,7,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,6,8,7,1,4,2,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,3,7,1,6,8,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,3,8,5,6,7,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,8,1,7,6,2,4,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,1,2,7,8,5,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,6,4,2,8,7,5,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,3,7,5,2,8,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,5,2,7,4,8,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,7,1,4,8,3,2,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,8,3,5,1,4,6,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,1,4,6,7,2,3]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,5,8,4,3,7,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,3,7,4,2,8,5,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,7,1,6,2,4,5,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,8,6,7,1,4,5,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,3,8,7,4,1,2,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,3,8,7,1,5,6,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,3,6,1,2,5,7,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,6,1,8,7,3,2,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,4,2,7,3,6,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,3,6,4,2,8,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,1,5,3,8,2,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,2,6,3,4,7,5,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,2,6,3,5,4,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,4,3,5,8,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,7,6,4,5,2,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,7,6,5,3,4,8,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[6,5,4,3,1,8,2,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,5,4,2,7,3,1]=>1111011=>[4,1,2]=>[2,1,4]
[8,5,4,1,7,2,6,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,4,1,8,3,2,6]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[1,6,5,2,8,3,4,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,6,5,3,4,8,2,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,4,6,3,1,8,2,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,5,8,4,2,7,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,8,2,6,4,7,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,8,5,3,2,6,4,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[6,8,3,1,7,2,5,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,6,3,7,5,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,7,5,2,6,4,3,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,7,1,6,2,5,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,8,1,7,3,5,6,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,1,3,7,2,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,2,8,5,7,3,6,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,7,6,8,3,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,7,3,1,8,4,2,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,7,3,8,4,5,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,8,5,3,4,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,6,1,8,4,3,2,5]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,6,1,7,4,2,5,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,1,2,7,3,4,6,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,1,2,8,3,5,4,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,2,6,1,7,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,1,4,7,5,6,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,2,1,5,8,3,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,4,3,1,6,8,2,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[4,7,5,6,8,3,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[6,5,4,8,2,7,3,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,5,1,8,7,4,2,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,6,4,7,5,3,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[5,1,8,3,7,6,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,4,8,1,7,2,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,8,2,4,7,5,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[5,7,3,8,2,6,4,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,2,8,6,3,5,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,3,8,7,4,5,6,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[7,2,8,6,4,3,5,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,8,7,5,6,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,2,7,6,3,5,4,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,1,7,6,5,2,4,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,1,8,6,5,3,2,4]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[1,2,8,7,6,3,4,5]=>0011100=>[2,3,2]=>[2,3,2]
[1,3,8,7,4,6,2,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,1,6,8,7,4,2,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,8,4,7,5,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[6,8,7,2,5,4,3,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[3,8,7,6,4,5,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,8,7,6,5,3,4,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[1,8,7,6,5,4,2,3]=>0111110=>[1,5,1]=>[1,5,1]
[5,8,6,7,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,6,7,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,6,7,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,6,7,4,5,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,6,7,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,5,7,4,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,5,7,4,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,5,7,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,6,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,7,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,7,4,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,4,8,5,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,8,5,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,2,8,5,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,1,8,5,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,1,8,5,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,2,8,5,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,3,8,5,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,4,8,5,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,2,7,4,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,2,7,4,5,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,6,4,5,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,6,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,1,7,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,1,7,4,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,4,8,5,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,3,8,5,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,5,6,1,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,5,6,2,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,3,8,4,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,1,7,3,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,1,7,3,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,1,7,3,5,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,6,3,5,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,2,7,3,5,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,2,7,3,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,2,7,3,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,3,8,4,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,2,8,4,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,1,8,4,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,4,7,3,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,4,7,3,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,4,7,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,5,7,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,5,7,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,5,7,3,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,5,7,3,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,6,7,3,5,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,6,7,3,5,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,6,7,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,6,7,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,6,7,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,5,7,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,6,7,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,6,7,1,5,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,6,7,1,5,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,2,8,6,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,1,8,6,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,1,8,5,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,8,5,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,5,7,1,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,4,7,1,5,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,4,6,1,5,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,6,1,5,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,7,1,5,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,7,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,4,7,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,8,4,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,1,8,4,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,2,6,1,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,1,6,2,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,1,6,2,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,1,6,2,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,5,2,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,5,1,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,2,5,1,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,2,6,1,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,2,6,1,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,3,6,2,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,3,6,1,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,9]=>00000000=>[8]=>[8]
[1,2,3,4,5,6,8,9,7]=>00000001=>[7,1]=>[1,7]
[1,2,3,4,5,7,8,9,6]=>00000001=>[7,1]=>[1,7]
[1,2,3,4,6,7,8,9,5]=>00000001=>[7,1]=>[1,7]
[1,2,3,5,6,7,8,9,4]=>00000001=>[7,1]=>[1,7]
[1,2,4,5,6,7,8,9,3]=>00000001=>[7,1]=>[1,7]
[1,3,4,5,6,7,8,9,2]=>00000001=>[7,1]=>[1,7]
[1,2,3,4,5,6,7,8,9,10]=>000000000=>[9]=>[9]
[1,2,3,4,5,6,9,8,7]=>00000011=>[6,2]=>[2,6]
[1,2,3,4,5,6,7,9,10,8]=>000000001=>[8,1]=>[1,8]
[1,2,3,4,5,8,7,9,6]=>00000101=>[5,1,1,1]=>[1,1,1,5]
[1,2,3,4,5,6,8,9,10,7]=>000000001=>[8,1]=>[1,8]
[1,2,3,4,7,6,8,9,5]=>00001001=>[4,1,2,1]=>[1,2,1,4]
[1,2,3,4,5,7,8,9,10,6]=>000000001=>[8,1]=>[1,8]
[1,2,3,6,5,7,8,9,4]=>00010001=>[3,1,3,1]=>[1,3,1,3]
[1,2,3,4,6,7,8,9,10,5]=>000000001=>[8,1]=>[1,8]
[1,2,5,4,6,7,8,9,3]=>00100001=>[2,1,4,1]=>[1,4,1,2]
[1,2,3,5,6,7,8,9,10,4]=>000000001=>[8,1]=>[1,8]
[1,4,3,5,6,7,8,9,2]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[1,2,4,5,6,7,8,9,10,3]=>000000001=>[8,1]=>[1,8]
[3,2,4,5,6,7,8,9,1]=>10000001=>[1,6,1]=>[1,6,1]
[1,3,4,5,6,7,8,9,10,2]=>000000001=>[8,1]=>[1,8]
[6,7,4,8,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,4,5,2,8,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,4,6,2,3,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,4,6,3,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,4,8,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,4,5,3,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,6,3,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,4,8,3,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,3,7,2,4,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,3,7,2,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,3,8,2,7,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,4,8,2,7,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,6,2,7,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,4,5,2,7,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,4,5,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,4,5,2,3,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,6,2,3,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,4,8,2,3,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,3,8,2,4,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,3,4,2,8,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,3,5,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,3,5,2,8,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,3,8,2,5,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,6,2,5,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,6,2,4,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,5,2,4,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,5,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,5,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,6,2,7,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,6,2,7,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,3,8,2,7,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,3,7,2,8,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,6,2,5,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,6,2,8,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,8,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,4,8,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,3,6,2,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,3,6,2,4,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,3,5,2,4,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,3,5,2,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,4,8,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,5,8,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,5,7,2,3,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,4,8,2,3,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,3,8,2,4,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,3,4,2,8,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,3,4,2,6,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,3,4,2,8,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,4,8,2,3,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,7,2,3,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,4,7,2,3,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,4,6,2,3,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,6,2,4,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,7,2,4,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,7,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,7,2,5,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,8,2,5,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,5,2,8,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,5,2,6,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,3,7,2,6,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,3,7,2,8,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,3,8,2,7,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,5,2,7,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,4,2,7,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,4,2,7,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,4,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,4,2,5,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,4,2,6,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,5,2,6,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,3,8,2,6,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,3,6,2,8,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,5,2,1,8,3,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,8,5,2,1,7,6,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,6,5,2,1,3,8,7]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[5,6,4,2,3,1,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,4,5,3,1,2,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,4,6,1,3,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,8,1,7,3,2,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,7,8,1,6,3,5,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,8,1,6,5,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,4,8,1,3,7,6,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,4,5,3,1,7,6,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,4,7,1,3,8,2,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,8,1,7,5,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,6,8,7,2,1,3,4]=>0011100=>[2,3,2]=>[2,3,2]
[8,5,7,6,4,2,1,3]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[8,4,6,3,7,2,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,2,8,7,4,1,5]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[2,1,6,8,7,4,3,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[2,1,7,8,6,4,5,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,3,2,8,6,4,5,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,6,8,5,2,4,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,7,8,6,2,3,1,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,8,7,6,3,2,1,4]=>0111110=>[1,5,1]=>[1,5,1]
[6,8,7,5,3,2,4,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,8,4,2,3,7,6,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,8,4,2,6,5,3,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,8,7,2,6,3,5,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,6,2,7,3,1,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,6,1,8,7,4,2,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,7,1,8,6,4,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,8,1,6,7,5,2,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,7,1,6,8,2,5,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,7,6,2,8,1,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,7,4,2,8,1,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,8,4,2,7,5,1,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,1,8,6,7,5,3,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,3,2,6,7,5,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,6,4,3,7,5,1,2]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[5,8,6,7,3,1,2,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,7,5,8,1,3,4,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,6,5,8,1,4,3,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,6,5,7,4,1,3,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,6,4,3,8,1,5,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,3,2,6,8,1,5,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,1,7,6,8,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,6,8,1,4,2,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,5,7,8,1,2,4,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,3,7,4,6,5,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,2,8,7,4,6,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,2,5,4,7,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,5,4,8,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,1,3,5,4,7,6,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,1,5,4,3,8,7,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,1,8,3,4,5,7,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,1,5,3,4,8,6,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,1,4,3,5,6,8,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,1,3,4,5,6,7,2]=>1000001=>[1,5,1]=>[1,5,1]
[1,7,2,4,5,6,3,8]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,3,2,7,5,1,8,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,4,7,2,5,6,1,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,5,8,2,4,7,3,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,5,2,1,4,3,7,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,5,2,8,4,1,3,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,6,2,1,4,8,3,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,6,1,8,5,2,4,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,2,6,3,5,4,7,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,4,1,2,8,6,5,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,1,2,6,8,5,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,8,1,6,3,2,4,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,3,8,5,2,1,4,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,3,1,5,2,4,7,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,8,2,6,1,5,7,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,8,6,7,2,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,5,6,4,2,1,7,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,2,5,8,3,1,6,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,7,5,6,3,2,4,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,1,2,3,8,5,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,1,2,3,6,5,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,2,1,3,8,6,4,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[1,5,7,3,2,4,6,8]=>0011000=>[2,2,3]=>[3,2,2]
[5,2,7,3,1,8,4,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,2,4,1,3,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,7,2,6,3,4,1,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,8,1,6,3,2,7,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,1,8,6,4,2,7,5]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,1,6,7,4,3,2,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,5,8,7,2,4,1,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,2,1,3,7,8,5,6]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[2,4,1,3,8,7,5,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,5,8,3,1,7,4,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,6,1,3,7,2,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[2,8,1,3,6,4,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,8,2,3,4,1,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,1,8,3,2,4,6,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[9,8,7,6,5,4,3,2,1]=>11111111=>[8]=>[8]
[8,9,7,6,5,4,3,2,1]=>01111111=>[1,7]=>[7,1]
[8,7,9,6,5,4,3,2,1]=>10111111=>[1,1,6]=>[6,1,1]
[8,7,6,9,5,4,3,2,1]=>11011111=>[2,1,5]=>[5,1,2]
[8,7,6,5,9,4,3,2,1]=>11101111=>[3,1,4]=>[4,1,3]
[8,7,6,5,4,9,3,2,1]=>11110111=>[4,1,3]=>[3,1,4]
[8,7,6,5,4,3,9,2,1]=>11111011=>[5,1,2]=>[2,1,5]
[8,7,6,5,4,3,2,9,1]=>11111101=>[6,1,1]=>[1,1,6]
[8,7,6,5,4,3,2,1,9]=>11111110=>[7,1]=>[1,7]
[9,10,8,7,6,5,4,3,2,1]=>011111111=>[1,8]=>[8,1]
[7,8,9,6,5,4,3,2,1]=>00111111=>[2,6]=>[6,2]
[9,8,10,7,6,5,4,3,2,1]=>101111111=>[1,1,7]=>[7,1,1]
[8,6,7,9,5,4,3,2,1]=>10011111=>[1,2,5]=>[5,2,1]
[9,8,7,10,6,5,4,3,2,1]=>110111111=>[2,1,6]=>[6,1,2]
[8,7,5,6,9,4,3,2,1]=>11001111=>[2,2,4]=>[4,2,2]
[9,8,7,6,10,5,4,3,2,1]=>111011111=>[3,1,5]=>[5,1,3]
[8,7,6,4,5,9,3,2,1]=>11100111=>[3,2,3]=>[3,2,3]
[9,8,7,6,5,10,4,3,2,1]=>111101111=>[4,1,4]=>[4,1,4]
[8,7,6,5,3,4,9,2,1]=>11110011=>[4,2,2]=>[2,2,4]
[9,8,7,6,5,4,10,3,2,1]=>111110111=>[5,1,3]=>[3,1,5]
[8,7,6,5,4,2,3,9,1]=>11111001=>[5,2,1]=>[1,2,5]
[9,8,7,6,5,4,3,10,2,1]=>111111011=>[6,1,2]=>[2,1,6]
[8,7,6,5,4,3,1,2,9]=>11111100=>[6,2]=>[2,6]
[9,8,7,6,5,4,3,2,10,1]=>111111101=>[7,1,1]=>[1,1,7]
[9,8,7,6,5,4,3,2,1,10]=>111111110=>[8,1]=>[1,8]
[1,4,2,7,8,6,3,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,6,2,4,8,5,3,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,6,2,4,7,5,3,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,7,3,8,5,2,4,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,7,3,2,8,6,4,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,5,7,8,6,1,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,2,3,1,8,5,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,5,1,7,3,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,2,1,8,3,4,7,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,2,8,3,5,1,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,4,8,5,7,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,3,6,4,8,5,7,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,6,4,7,5,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,2,4,7,5,8,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,2,1,3,7,8,4,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,8,2,1,4,3,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,6,4,2,3,1,8,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,7,2,3,1,6,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,5,4,2,6,8,1,3]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[1,7,5,3,4,6,8,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[8,2,5,4,6,7,1,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,2,6,3,1,8,7,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,2,6,4,3,1,7,5]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,2,7,4,1,3,5,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[1,2,8,4,3,5,6,7]=>0011000=>[2,2,3]=>[3,2,2]
[1,7,4,2,3,5,6,8]=>0110000=>[1,2,4]=>[4,2,1]
[6,8,4,1,3,2,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,8,7,4,3,2,5,6]=>0111100=>[1,4,2]=>[2,4,1]
[1,6,3,8,2,4,7,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,3,8,1,2,7,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,8,3,2,6,4,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,7,3,1,2,6,4,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,7,5,4,2,6,3,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,5,8,2,4,6,3,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,5,8,4,2,7,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,4,6,2,8,3,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,1,6,7,2,4,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,3,6,1,2,8,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,3,2,7,8,4,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,7,4,5,3,8,6,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,4,1,2,5,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,3,1,4,2,7,5,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,8,3,2,4,5,6,7]=>0110000=>[1,2,4]=>[4,2,1]
[8,6,3,2,4,1,7,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,5,3,2,6,7,1,4]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[4,5,2,6,8,1,7,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,2,5,6,7,8,1,3]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[5,2,3,6,7,1,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,2,3,4,1,7,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,2,3,1,4,5,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,6,1,4,3,2,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,3,1,6,5,2,4,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,7,5,1,8,2,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,1,5,2,8,7,3,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,1,2,4,6,5,3,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[8,1,2,5,4,6,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,2,6,5,1,3,4,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,3,1,6,2,5,4,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,1,2,6,4,5,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,2,5,6,4,3,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[8,1,2,6,5,4,3,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[1,7,5,4,2,8,3,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,1,4,8,2,7,3,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,6,8,2,7,3,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,4,7,6,2,8,3,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,1,4,7,2,8,3,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,7,4,5,2,8,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,5,1,2,8,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,7,2,8,1,3,4,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,2,8,7,1,3,4,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,1,5,8,2,7,3,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,6,2,8,7,3,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,4,2,8,6,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,2,6,4,8,7,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,7,6,3,4,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,1,2,7,4,6,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,4,7,2,6,8,3,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,3,6,8,5,7,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[5,1,4,2,7,8,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,4,2,7,6,8,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,2,6,8,7,3,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,1,2,8,4,6,7,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,1,2,7,6,4,8,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,3,7,1,8,2,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,7,4,3,2,5,8,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[4,8,7,2,1,3,5,6]=>0111000=>[1,3,3]=>[3,3,1]
[1,8,7,3,4,2,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,1,7,8,2,6,4,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,2,7,8,3,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,2,8,1,3,4,7,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,1,8,6,3,4,7,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,4,2,6,8,3,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,3,7,8,5,6,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,7,5,8,6,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,4,2,7,3,8,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,1,7,2,8,6,4,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,1,7,8,3,4,6,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,2,3,8,7,5,6,4]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[10,1,2,3,4,5,6,7,8,9]=>100000000=>[1,8]=>[8,1]
[10,1,2,3,4,5,6,9,7,8]=>100000010=>[1,6,1,1]=>[1,1,6,1]
[10,1,2,3,4,5,9,6,7,8]=>100000100=>[1,5,1,2]=>[2,1,5,1]
[9,1,2,3,4,10,5,6,7,8]=>100001000=>[1,4,1,3]=>[3,1,4,1]
[10,1,2,3,9,4,5,6,7,8]=>100010000=>[1,3,1,4]=>[4,1,3,1]
[10,1,2,9,3,4,5,6,7,8]=>100100000=>[1,2,1,5]=>[5,1,2,1]
[9,1,10,2,3,4,5,6,7,8]=>101000000=>[1,1,1,6]=>[6,1,1,1]
[10,9,1,2,3,4,5,6,7,8]=>110000000=>[2,7]=>[7,2]
[11,1,2,3,4,5,6,7,8,9,10]=>1000000000=>[1,9]=>[9,1]
[10,1,2,3,4,5,6,7,8,11,9]=>1000000001=>[1,8,1]=>[1,8,1]
[8,1,2,3,4,5,6,9,10,7]=>100000001=>[1,7,1]=>[1,7,1]
[11,1,2,3,4,5,6,7,10,8,9]=>1000000010=>[1,7,1,1]=>[1,1,7,1]
[7,1,2,3,4,5,10,9,6,8]=>100000110=>[1,5,2,1]=>[1,2,5,1]
[11,1,2,3,4,5,6,10,7,8,9]=>1000000100=>[1,6,1,2]=>[2,1,6,1]
[6,1,2,3,4,10,9,5,7,8]=>100001100=>[1,4,2,2]=>[2,2,4,1]
[5,1,2,3,9,10,4,6,7,8]=>100001000=>[1,4,1,3]=>[3,1,4,1]
[4,1,2,10,9,3,5,6,7,8]=>100110000=>[1,2,2,4]=>[4,2,2,1]
[3,1,10,9,2,4,5,6,7,8]=>101100000=>[1,1,2,5]=>[5,2,1,1]
[10,1,2,11,3,4,5,6,7,8,9]=>1001000000=>[1,2,1,6]=>[6,1,2,1]
[2,9,10,1,3,4,5,6,7,8]=>001000000=>[2,1,6]=>[6,1,2]
[11,1,10,2,3,4,5,6,7,8,9]=>1010000000=>[1,1,1,7]=>[7,1,1,1]
[11,10,1,2,3,4,5,6,7,8,9]=>1100000000=>[2,8]=>[8,2]
[4,7,8,5,6,2,1,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,7,8,4,2,6,1,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,7,8,4,2,5,1,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,6,3,7,2,1,5,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,6,3,8,2,1,5,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,8,3,2,1,5,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,7,8,3,2,1,6,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,7,8,4,3,5,6,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,7,8,4,2,5,1,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,7,8,3,2,1,5,6]=>0011100=>[2,3,2]=>[2,3,2]
[5,7,8,3,2,1,4,6]=>0011100=>[2,3,2]=>[2,3,2]
[7,6,3,8,2,1,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,6,3,7,2,1,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,6,3,8,2,1,4,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,6,4,8,2,5,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,4,8,3,5,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,4,7,3,5,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,4,7,2,5,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,3,7,2,1,5,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,6,3,7,2,1,4,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,4,3,2,1,6,5,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[6,4,3,2,1,7,5,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[4,5,3,2,7,1,6,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,5,4,2,8,6,1,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,4,3,2,1,8,5,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,4,3,2,1,8,5,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,4,3,2,1,7,5,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,4,3,2,1,7,6,5]=>1111011=>[4,1,2]=>[2,1,4]
[7,4,3,2,1,8,6,5]=>1111011=>[4,1,2]=>[2,1,4]
[6,4,3,2,1,8,7,5]=>1111011=>[4,1,2]=>[2,1,4]
[5,6,3,8,2,1,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,5,3,2,8,1,6,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,5,4,2,7,6,1,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,5,4,2,8,6,1,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[6,5,4,2,8,7,1,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[4,6,5,8,7,2,1,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,6,5,7,8,3,4,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,5,4,2,7,8,1,3]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,5,4,2,6,7,1,3]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,5,3,2,6,1,7,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,3,2,6,1,8,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,6,3,7,2,1,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,6,3,7,2,1,8,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,6,4,7,2,8,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,4,7,3,8,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,5,4,2,7,8,1,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,5,3,2,7,1,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,4,3,2,1,6,8,5]=>1111001=>[4,2,1]=>[1,2,4]
[8,4,3,2,1,6,7,5]=>1111001=>[4,2,1]=>[1,2,4]
[8,4,3,2,1,5,7,6]=>1111001=>[4,2,1]=>[1,2,4]
[7,4,3,2,1,5,8,6]=>1111001=>[4,2,1]=>[1,2,4]
[6,4,3,2,1,5,8,7]=>1111001=>[4,2,1]=>[1,2,4]
[3,5,4,2,6,8,1,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,6,3,4,1,2,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,5,3,7,2,6,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,5,7,4,2,6,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,5,8,4,2,6,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,7,8,5,6,3,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,8,3,7,5,1,4,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,7,3,8,1,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,4,8,5,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,5,2,4,1,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,5,8,3,1,6,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,1,5,4,2,8,6,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,5,8,3,2,6,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,3,8,5,2,1,6,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,7,3,5,2,1,6,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,3,2,7,5,1,6,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[4,3,6,2,5,1,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,6,3,2,5,1,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,5,1,7,3,2,6,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,2,1,4,3,7,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,3,1,5,7,2,6,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,3,6,1,5,2,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,6,3,1,5,2,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,3,6,4,1,2,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,3,6,1,7,2,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,2,4,1,3,7,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,6,4,1,2,7,5,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,6,3,1,7,2,5,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,6,2,7,1,3,4,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,5,2,7,3,1,6,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,6,2,1,7,3,5,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,6,1,4,7,5,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,2,7,4,6,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,2,4,8,5,1,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,3,1,4,6,8,2,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[3,2,6,1,5,7,4,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,2,1,5,7,4,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,4,2,1,5,3,7,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[4,2,6,1,5,3,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,1,7,5,3,6,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,4,1,5,6,2,3,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,3,1,5,2,6,4,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,5,1,2,7,4,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,2,6,4,1,3,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[3,6,5,1,2,7,4,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,5,2,1,4,7,8,3]=>1110001=>[3,3,1]=>[1,3,3]
[6,5,3,1,4,7,2,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[2,3,1,8,5,4,7,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,1,5,8,3,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,1,5,3,8,7,6]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,4,5,1,2,8,7,6]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,4,5,1,8,2,7,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,8,4,5,3,2,7,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,8,5,3,1,7,6]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[3,4,5,8,2,1,7,6]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[3,4,5,2,8,1,7,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,6,2,1,7,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,4,6,2,1,7,5,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,5,6,2,7,1,4,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,5,6,2,7,1,8,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,6,2,7,8,1,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,6,2,8,7,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,4,6,8,2,7,1,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,4,8,6,3,7,1,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,8,4,6,3,7,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,4,6,3,7,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,4,6,8,2,7,5,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,4,6,2,8,7,5,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[3,5,6,2,7,8,4,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,5,6,2,7,4,1,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,5,6,7,2,8,3,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,5,6,8,7,2,4,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,5,8,6,7,3,4,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,8,5,6,7,3,4,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,8,5,6,7,3,2,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,5,8,6,7,3,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,5,6,8,7,2,1,4]=>0001110=>[3,3,1]=>[1,3,3]
[4,5,6,7,2,1,8,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[3,4,6,1,8,7,2,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,4,1,6,8,7,3,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,3,1,8,6,7,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,3,2,6,7,5,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,5,1,6,7,8,4,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,5,1,6,7,4,8,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,1,6,7,4,3,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,5,6,1,7,4,2,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,5,6,1,7,4,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,6,1,8,7,5,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[3,4,6,8,1,7,5,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,4,8,6,1,7,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,8,4,6,2,7,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,5,6,7,2,4,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,8,6,7,1,4,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,6,8,7,1,4,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,5,6,7,8,1,3,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[4,5,6,7,1,3,8,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[4,5,6,7,1,3,2,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,5,6,7,3,1,8,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[3,5,6,8,7,4,1,2]=>0001110=>[3,3,1]=>[1,3,3]
[2,5,8,6,7,4,1,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,8,5,6,7,4,2,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,8,5,6,7,4,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,5,8,6,7,4,3,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[8,2,5,3,7,1,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,4,3,7,1,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,2,4,3,7,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,5,6,1,8,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,2,5,6,1,7,3,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,5,7,3,2,4,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,1,5,8,3,2,4,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,8,2,4,7,1,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,6,8,2,4,7,1,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,3,5,6,7,1,8,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,7,1,5,6,8,2,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,7,1,5,8,2,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,3,2,4,6,1,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,3,2,4,6,1,5,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,2,5,1,7,4,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,5,1,8,4,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,5,1,7,8,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,8,3,2,4,6,1,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,1,5,7,8,3,2,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,2,5,6,1,7,8,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,7,6,1,8,3,4,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,8,6,1,7,3,4,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,5,8,7,3,2,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[8,7,3,2,4,6,1,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,2,5,1,8,7,4,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,5,1,6,4,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,4,1,8,7,5,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,5,1,6,8,7,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,8,6,5,1,7,4,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[3,7,6,5,1,8,4,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[6,5,1,7,8,4,2,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,2,5,1,6,7,8,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,2,4,1,8,5,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,4,1,7,5,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,4,1,6,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,2,4,1,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,2,4,7,6,1,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,2,5,1,8,4,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,5,1,6,7,4,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,5,1,7,4,2,3,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,5,1,8,4,2,3,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,4,2,3,7,5,1,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,2,6,1,8,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,1,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,6,1,7,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,1,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,4,2,3,8,5,1,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,5,1,6,4,2,3,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,5,1,6,4,2,3,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,2,5,1,7,6,4,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,5,1,8,6,4,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,2,4,8,6,1,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,6,1,5,7,3,2,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,2,6,1,8,5,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,6,1,7,3,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,8,5,1,7,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[8,5,1,6,7,4,2,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,2,5,1,8,6,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,4,1,8,6,5,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,4,1,5,8,6,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,2,5,1,7,8,6,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,8,5,1,6,4,2,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,8,5,1,7,6,4,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[3,7,5,1,8,6,4,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[8,7,5,1,6,4,2,3]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[3,2,5,1,8,7,6,4]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,5,7,3,1,8,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,6,3,7,1,8,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,6,3,7,5,1,8,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,6,1,7,5,3,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,5,7,4,1,6,3,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,5,7,4,1,6,8,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[5,4,7,3,6,1,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,7,8,3,1,6,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,3,7,5,1,8,6,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,4,3,8,5,1,7,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,8,4,3,6,1,7,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,4,8,3,6,1,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,3,6,7,1,8,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,5,4,6,1,7,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,5,8,1,6,7,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,5,4,6,8,1,7,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,2,8,4,1,6,7,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,6,2,1,8,5,7,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,4,1,7,5,8,6,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,4,1,7,5,3,8,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,4,1,8,5,3,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,4,8,2,1,6,3,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,8,4,1,6,3,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,5,6,1,8,4,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,3,2,6,1,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,5,2,8,1,6,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,1,6,8,5,4,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,2,7,1,5,4,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,7,1,5,8,6,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,8,2,5,1,6,7,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,3,2,6,7,1,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,3,8,2,6,7,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,3,2,6,7,8,1,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,3,2,6,7,1,5,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,3,7,2,6,8,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,3,7,8,2,6,1,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,5,7,4,8,1,6,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,2,5,7,8,1,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,2,5,7,1,6,8,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,2,5,7,1,6,4,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,3,2,7,1,5,4,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,2,7,1,5,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,2,7,8,1,5,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,2,6,1,7,8,5,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,5,2,1,7,8,4,3]=>1110011=>[3,2,2]=>[2,2,3]
[2,1,7,5,3,8,6,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,2,1,8,5,3,7,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,3,2,7,1,4,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,2,1,4,7,8,5]=>1110001=>[3,3,1]=>[1,3,3]
[6,3,2,1,4,7,5,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,5,2,1,7,4,6,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,5,2,1,7,8,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,8,4,2,1,7,3,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,6,2,1,8,3,7,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,4,1,7,3,8,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,7,1,4,8,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,5,8,2,1,7,4,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,8,3,7,2,1,5,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,3,7,2,8,1,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,7,2,1,5,6,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,8,3,2,7,1,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,5,2,8,1,7,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,2,8,1,4,7,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,2,1,4,7,5,8,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,3,2,1,8,4,6,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[4,8,3,2,1,5,6,7]=>0111000=>[1,3,3]=>[3,3,1]
[4,3,8,2,1,5,6,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[1,9,8,7,6,5,4,3,2]=>01111111=>[1,7]=>[7,1]
[8,7,6,4,5,3,2,1,9]=>11101110=>[3,1,3,1]=>[1,3,1,3]
[1,9,8,7,5,6,4,3,2]=>01110111=>[1,3,1,3]=>[3,1,3,1]
[1,10,9,8,7,6,5,4,3,2]=>011111111=>[1,8]=>[8,1]
[10,9,8,7,6,5,4,3,2,1,11]=>1111111110=>[9,1]=>[1,9]
[9,8,7,5,6,4,3,2,1,10]=>111011110=>[3,1,4,1]=>[1,4,1,3]
[8,7,5,4,6,3,2,1,9]=>11101110=>[3,1,3,1]=>[1,3,1,3]
[8,7,4,6,5,3,2,1,9]=>11011110=>[2,1,4,1]=>[1,4,1,2]
[1,9,8,6,5,7,4,3,2]=>01110111=>[1,3,1,3]=>[3,1,3,1]
[1,9,8,5,7,6,4,3,2]=>01101111=>[1,2,1,4]=>[4,1,2,1]
[1,10,9,8,6,7,5,4,3,2]=>011101111=>[1,3,1,4]=>[4,1,3,1]
[1,11,10,9,8,7,6,5,4,3,2]=>0111111111=>[1,9]=>[9,1]
[6,2,3,1,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,5,2,3,1,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,2,5,3,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,5,3,4,1,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,5,3,4,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,5,2,4,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,5,1,3,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,5,3,4,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,5,1,4,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,5,2,4,1,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,5,6,2,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,2,4,1,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,5,1,4,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,5,3,4,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,5,1,3,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,4,5,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,4,5,1,3,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,1,5,3,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,3,5,1,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,5,6,1,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,3,6,1,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,4,6,2,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,4,6,1,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,1,6,4,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,3,6,4,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,5,6,3,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,5,6,1,3,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,4,7,5,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,3,4,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,3,6,2,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,1,6,2,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,7,2,6,4,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,3,6,4,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,3,6,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,1,6,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,2,4,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,3,2,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,3,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,5,2,4,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,1,4,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,3,4,1,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,5,6,3,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,5,6,2,3,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,2,3,1,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,3,1,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,3,1,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,3,1,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,3,2,8,6,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,2,3,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,3,1,7,5,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,2,6,3,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,2,6,1,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,5,6,1,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,2,5,1,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,1,5,2,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,1,3,2,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,6,7,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,3,7,5,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,3,2,7,5,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,5,6,2,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,2,6,4,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,1,6,4,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,4,6,1,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,4,6,3,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,2,6,3,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,2,6,1,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,1,6,2,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,4,6,2,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,1,6,2,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,5,7,3,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,4,6,1,3,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,7,1,6,3,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,4,6,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,1,6,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,7,3,6,1,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,8,3,6,1,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,8,1,3,2,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,8,6,3,2,7,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[6,5,8,7,3,1,2,4]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[1,5,8,7,3,6,2,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,7,2,8,4,6,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,2,8,4,1,5,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,6,2,8,4,5,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,1,8,4,5,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,4,6,1,5,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,1,8,4,5,7,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,1,6,8,4,5,7,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,3,6,8,4,5,7,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[6,3,7,8,4,1,5,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,3,7,8,4,6,5,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,5,7,8,2,4,6,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[5,1,7,8,2,4,6,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,6,7,8,4,2,5,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[7,6,1,8,4,2,5,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,6,8,7,3,2,1,4]=>0011110=>[2,4,1]=>[1,4,2]
[2,8,3,7,1,6,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,2,8,7,3,6,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,2,1,8,4,6,5,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,2,7,8,4,6,5,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,2,7,8,1,4,6,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,2,7,8,5,4,6,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,2,1,3,8,5,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,2,5,8,3,4,6,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,2,8,5,4,3,1,7]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[2,8,3,5,4,1,6,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,8,4,5,3,1,6,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,4,8,5,2,3,1,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,3,5,8,2,4,6,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,3,1,2,8,5,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,4,2,1,8,5,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,7,6,8,4,3,5,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,7,1,8,3,4,6,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,5,8,1,4,6,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,7,5,8,3,4,6,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,6,8,5,4,3,2,7]=>0011110=>[2,4,1]=>[1,4,2]
[4,6,8,5,1,3,2,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,6,8,1,4,3,2,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,8,6,3,4,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,4,8,3,6,5,1,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,8,4,1,5,6,3,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,1,8,3,5,6,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,8,4,1,3,2,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,6,8,1,5,3,2,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,6,8,4,5,3,2,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,7,3,8,5,4,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,7,1,8,5,4,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,7,3,8,4,6,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,3,8,4,6,5,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,7,8,4,3,6,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,8,7,4,1,6,5,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,8,5,4,3,1,6,7]=>0111100=>[1,4,2]=>[2,4,1]
[6,5,8,4,2,3,1,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,3,2,8,5,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,4,3,2,8,5,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,3,2,8,5,4,6,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,8,2,5,3,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,4,3,5,1,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,8,3,4,5,1,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,2,8,4,5,3,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,3,8,5,4,6,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,2,3,1,8,5,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,1,4,8,5,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,1,3,2,4,8,6,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,1,5,3,4,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,2,8,4,5,3,7,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,2,8,5,3,6,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,8,4,2,5,3,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,1,5,3,2,4,6,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[3,8,1,5,2,4,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,5,1,4,8,2,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,5,2,8,4,3,6,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,2,8,5,4,3,6,7]=>0011100=>[2,3,2]=>[2,3,2]
[1,2,5,4,3,8,6,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,2,4,8,5,3,7,6]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,7,4,8,5,3,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,5,2,7,8,4,3,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,1,2,7,4,8,3,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,3,5,1,4,7,2,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,1,5,4,7,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,2,8,5,7,4,3,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,4,8,7,5,3,6]=>0001110=>[3,3,1]=>[1,3,3]
[2,8,1,4,3,7,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,1,2,8,7,4,3,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,4,1,2,8,7,3,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,6,4,8,1,7,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,1,4,2,8,3,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,1,6,2,8,4,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,6,7,2,8,4,3,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,7,1,4,2,8,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,7,1,4,8,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,7,8,1,5,2,4,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,1,2,8,5,3,4,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[1,7,2,8,4,5,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,2,7,8,5,3,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,1,2,8,4,3,7,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,4,1,2,8,3,7,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,6,1,3,2,4,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,7,1,3,2,4,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,2,7,3,5,8,4,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,7,5,8,3,4,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,8,1,3,7,2,4,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,5,8,7,3,4,6]=>0001100=>[3,2,2]=>[2,2,3]
[1,2,5,8,3,7,4,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,8,1,7,3,5,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,1,3,2,4,7,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,2,8,1,7,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,1,7,4,3,6,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,1,2,8,4,3,6,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,2,8,4,7,5,3,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,8,7,4,5,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,8,1,7,5,3,4,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,3,7,1,5,2,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,8,6,1,4,7,2,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,6,1,4,2,7,3,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,1,6,2,7,4,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,1,2,8,6,4,3,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,4,1,2,8,6,3,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,7,4,8,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,8,7,1,6,2,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,2,8,1,7,6,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,1,7,6,4,3,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,8,3,4,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,4,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,4,1,7,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,3,4,1,8,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,3,4,1,8,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,4,1,7,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,4,1,6,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,4,1,5,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,3,4,1,5,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,3,4,1,6,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,8,3,4,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,7,3,4,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,2,8,3,5,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,5,1,6,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,5,1,6,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,5,1,7,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,5,1,8,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,3,1,7,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,4,1,8,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,4,1,7,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,2,5,1,7,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,2,5,1,8,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,1,8,3,7,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,1,7,3,8,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,2,7,3,8,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,7,3,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,7,4,8,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,3,8,4,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,8,4,7,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,8,3,7,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,2,8,3,7,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,1,7,3,6,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,1,8,3,6,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[9,2,1,3,4,5,6,7,8]=>11000000=>[2,6]=>[6,2]
[10,2,1,3,4,5,6,7,8,9]=>110000000=>[2,7]=>[7,2]
[9,2,3,1,4,5,6,7,8]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[4,2,3,5,6,7,8,9,1]=>10000001=>[1,6,1]=>[1,6,1]
[3,4,2,5,6,7,8,9,1]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[3,2,4,5,6,7,8,9,10,1]=>100000001=>[1,7,1]=>[1,7,1]
[2,3,4,5,6,7,8,9,10,11,1]=>0000000001=>[9,1]=>[1,9]
[6,5,3,2,1,4,8,7]=>1111001=>[4,2,1]=>[1,2,4]
[4,6,3,5,2,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,7,3,5,2,4,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,8,2,4,5,7,3,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[8,7,2,4,5,3,1,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,6,1,4,5,2,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,7,4,5,2,1,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,8,4,5,7,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,8,7,4,3,6,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,8,7,4,3,6,1,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,7,4,3,6,2,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,7,3,5,1,4,2,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,1,6,8,5,7,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,3,5,1,7,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,8,4,7,6,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,5,8,4,7,6,3,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[4,3,8,1,5,6,7,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,8,1,3,5,6,7,2]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[5,8,7,4,1,6,3,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,8,3,6,1,4,7,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,3,6,1,2,7,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,8,7,4,1,6,2,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,8,1,2,5,6,7,4]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[8,7,1,4,2,6,3,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,6,3,1,2,4,7,5]=>1110001=>[3,3,1]=>[1,3,3]
[8,1,7,4,5,2,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,8,7,4,5,1,3,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,7,2,4,1,6,3,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,8,3,6,2,4,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,6,3,2,1,4,7,5]=>1111001=>[4,2,1]=>[1,2,4]
[8,7,3,5,2,1,4,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,8,3,6,2,1,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,7,4,2,6,1,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,6,8,4,5,7,1,3]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,1,8,4,5,7,2,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,8,3,5,1,7,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,5,8,3,6,7,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,8,3,6,1,2,7,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,1,8,2,5,6,7,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,4,8,1,5,6,7,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,8,2,1,5,6,7,3]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,4,8,2,5,6,7,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[5,8,1,4,7,6,2,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,8,3,1,6,2,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,3,8,6,1,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,1,8,5,6,7,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,6,8,10,1,3,5,7,9]=>000010000=>[4,1,4]=>[4,1,4]
[2,4,6,9,10,1,3,5,7,8]=>000010000=>[4,1,4]=>[4,1,4]
[2,4,7,8,10,1,3,5,6,9]=>000010000=>[4,1,4]=>[4,1,4]
[2,4,7,9,10,1,3,5,6,8]=>000010000=>[4,1,4]=>[4,1,4]
[2,4,8,9,10,1,3,5,6,7]=>000010000=>[4,1,4]=>[4,1,4]
[2,5,6,8,10,1,3,4,7,9]=>000010000=>[4,1,4]=>[4,1,4]
[2,5,6,9,10,1,3,4,7,8]=>000010000=>[4,1,4]=>[4,1,4]
[2,5,7,8,10,1,3,4,6,9]=>000010000=>[4,1,4]=>[4,1,4]
[2,5,7,9,10,1,3,4,6,8]=>000010000=>[4,1,4]=>[4,1,4]
[2,5,8,9,10,1,3,4,6,7]=>000010000=>[4,1,4]=>[4,1,4]
[2,6,7,8,10,1,3,4,5,9]=>000010000=>[4,1,4]=>[4,1,4]
[2,6,7,9,10,1,3,4,5,8]=>000010000=>[4,1,4]=>[4,1,4]
[2,6,8,9,10,1,3,4,5,7]=>000010000=>[4,1,4]=>[4,1,4]
[2,7,8,9,10,1,3,4,5,6]=>000010000=>[4,1,4]=>[4,1,4]
[3,4,6,8,10,1,2,5,7,9]=>000010000=>[4,1,4]=>[4,1,4]
[3,4,6,9,10,1,2,5,7,8]=>000010000=>[4,1,4]=>[4,1,4]
[3,4,7,8,10,1,2,5,6,9]=>000010000=>[4,1,4]=>[4,1,4]
[3,4,7,9,10,1,2,5,6,8]=>000010000=>[4,1,4]=>[4,1,4]
[3,4,8,9,10,1,2,5,6,7]=>000010000=>[4,1,4]=>[4,1,4]
[3,5,6,8,10,1,2,4,7,9]=>000010000=>[4,1,4]=>[4,1,4]
[3,5,6,9,10,1,2,4,7,8]=>000010000=>[4,1,4]=>[4,1,4]
[3,5,7,8,10,1,2,4,6,9]=>000010000=>[4,1,4]=>[4,1,4]
[3,5,7,9,10,1,2,4,6,8]=>000010000=>[4,1,4]=>[4,1,4]
[3,5,8,9,10,1,2,4,6,7]=>000010000=>[4,1,4]=>[4,1,4]
[3,6,7,8,10,1,2,4,5,9]=>000010000=>[4,1,4]=>[4,1,4]
[3,6,7,9,10,1,2,4,5,8]=>000010000=>[4,1,4]=>[4,1,4]
[3,6,8,9,10,1,2,4,5,7]=>000010000=>[4,1,4]=>[4,1,4]
[3,7,8,9,10,1,2,4,5,6]=>000010000=>[4,1,4]=>[4,1,4]
[4,5,6,8,10,1,2,3,7,9]=>000010000=>[4,1,4]=>[4,1,4]
[4,5,6,9,10,1,2,3,7,8]=>000010000=>[4,1,4]=>[4,1,4]
[4,5,7,8,10,1,2,3,6,9]=>000010000=>[4,1,4]=>[4,1,4]
[4,5,7,9,10,1,2,3,6,8]=>000010000=>[4,1,4]=>[4,1,4]
[4,5,8,9,10,1,2,3,6,7]=>000010000=>[4,1,4]=>[4,1,4]
[4,6,7,8,10,1,2,3,5,9]=>000010000=>[4,1,4]=>[4,1,4]
[4,6,7,9,10,1,2,3,5,8]=>000010000=>[4,1,4]=>[4,1,4]
[4,6,8,9,10,1,2,3,5,7]=>000010000=>[4,1,4]=>[4,1,4]
[4,7,8,9,10,1,2,3,5,6]=>000010000=>[4,1,4]=>[4,1,4]
[5,6,7,8,10,1,2,3,4,9]=>000010000=>[4,1,4]=>[4,1,4]
[5,6,7,9,10,1,2,3,4,8]=>000010000=>[4,1,4]=>[4,1,4]
[5,6,8,9,10,1,2,3,4,7]=>000010000=>[4,1,4]=>[4,1,4]
[5,7,8,9,10,1,2,3,4,6]=>000010000=>[4,1,4]=>[4,1,4]
[2,4,6,8,10,12,1,3,5,7,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,6,8,11,12,1,3,5,7,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,6,9,10,12,1,3,5,7,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,6,9,11,12,1,3,5,7,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,6,10,11,12,1,3,5,7,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,7,8,10,12,1,3,5,6,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,7,8,11,12,1,3,5,6,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,7,9,10,12,1,3,5,6,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,7,9,11,12,1,3,5,6,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,7,10,11,12,1,3,5,6,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,8,9,10,12,1,3,5,6,7,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,8,9,11,12,1,3,5,6,7,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,8,10,11,12,1,3,5,6,7,9]=>00000100000=>[5,1,5]=>[5,1,5]
[2,4,9,10,11,12,1,3,5,6,7,8]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,6,8,10,12,1,3,4,7,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,6,8,11,12,1,3,4,7,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,6,9,10,12,1,3,4,7,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,6,9,11,12,1,3,4,7,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,6,10,11,12,1,3,4,7,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,7,8,10,12,1,3,4,6,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,7,8,11,12,1,3,4,6,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,7,9,10,12,1,3,4,6,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,7,9,11,12,1,3,4,6,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,7,10,11,12,1,3,4,6,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,8,9,10,12,1,3,4,6,7,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,8,9,11,12,1,3,4,6,7,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,8,10,11,12,1,3,4,6,7,9]=>00000100000=>[5,1,5]=>[5,1,5]
[2,5,9,10,11,12,1,3,4,6,7,8]=>00000100000=>[5,1,5]=>[5,1,5]
[2,6,7,8,10,12,1,3,4,5,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,6,7,8,11,12,1,3,4,5,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,6,7,9,10,12,1,3,4,5,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,6,7,9,11,12,1,3,4,5,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,6,7,10,11,12,1,3,4,5,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[2,6,8,9,10,12,1,3,4,5,7,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,6,8,9,11,12,1,3,4,5,7,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,6,8,10,11,12,1,3,4,5,7,9]=>00000100000=>[5,1,5]=>[5,1,5]
[2,6,9,10,11,12,1,3,4,5,7,8]=>00000100000=>[5,1,5]=>[5,1,5]
[2,7,8,9,10,12,1,3,4,5,6,11]=>00000100000=>[5,1,5]=>[5,1,5]
[2,7,8,9,11,12,1,3,4,5,6,10]=>00000100000=>[5,1,5]=>[5,1,5]
[2,7,8,10,11,12,1,3,4,5,6,9]=>00000100000=>[5,1,5]=>[5,1,5]
[2,7,9,10,11,12,1,3,4,5,6,8]=>00000100000=>[5,1,5]=>[5,1,5]
[2,8,9,10,11,12,1,3,4,5,6,7]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,6,8,10,12,1,2,5,7,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,6,8,11,12,1,2,5,7,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,6,9,10,12,1,2,5,7,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,6,9,11,12,1,2,5,7,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,6,10,11,12,1,2,5,7,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,7,8,10,12,1,2,5,6,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,7,8,11,12,1,2,5,6,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,7,9,10,12,1,2,5,6,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,7,9,11,12,1,2,5,6,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,7,10,11,12,1,2,5,6,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,8,9,10,12,1,2,5,6,7,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,8,9,11,12,1,2,5,6,7,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,8,10,11,12,1,2,5,6,7,9]=>00000100000=>[5,1,5]=>[5,1,5]
[3,4,9,10,11,12,1,2,5,6,7,8]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,6,8,10,12,1,2,4,7,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,6,8,11,12,1,2,4,7,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,6,9,10,12,1,2,4,7,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,6,9,11,12,1,2,4,7,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,6,10,11,12,1,2,4,7,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,7,8,10,12,1,2,4,6,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,7,8,11,12,1,2,4,6,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,7,9,10,12,1,2,4,6,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,7,9,11,12,1,2,4,6,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,7,10,11,12,1,2,4,6,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,8,9,10,12,1,2,4,6,7,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,8,9,11,12,1,2,4,6,7,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,8,10,11,12,1,2,4,6,7,9]=>00000100000=>[5,1,5]=>[5,1,5]
[3,5,9,10,11,12,1,2,4,6,7,8]=>00000100000=>[5,1,5]=>[5,1,5]
[3,6,7,8,10,12,1,2,4,5,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,6,7,8,11,12,1,2,4,5,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,6,7,9,10,12,1,2,4,5,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,6,7,9,11,12,1,2,4,5,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,6,7,10,11,12,1,2,4,5,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[3,6,8,9,10,12,1,2,4,5,7,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,6,8,9,11,12,1,2,4,5,7,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,6,8,10,11,12,1,2,4,5,7,9]=>00000100000=>[5,1,5]=>[5,1,5]
[3,6,9,10,11,12,1,2,4,5,7,8]=>00000100000=>[5,1,5]=>[5,1,5]
[3,7,8,9,10,12,1,2,4,5,6,11]=>00000100000=>[5,1,5]=>[5,1,5]
[3,7,8,9,11,12,1,2,4,5,6,10]=>00000100000=>[5,1,5]=>[5,1,5]
[3,7,8,10,11,12,1,2,4,5,6,9]=>00000100000=>[5,1,5]=>[5,1,5]
[3,7,9,10,11,12,1,2,4,5,6,8]=>00000100000=>[5,1,5]=>[5,1,5]
[3,8,9,10,11,12,1,2,4,5,6,7]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,6,8,10,12,1,2,3,7,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,6,8,11,12,1,2,3,7,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,6,9,10,12,1,2,3,7,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,6,9,11,12,1,2,3,7,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,6,10,11,12,1,2,3,7,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,7,8,10,12,1,2,3,6,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,7,8,11,12,1,2,3,6,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,7,9,10,12,1,2,3,6,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,7,9,11,12,1,2,3,6,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,7,10,11,12,1,2,3,6,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,8,9,10,12,1,2,3,6,7,11]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,8,9,11,12,1,2,3,6,7,10]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,8,10,11,12,1,2,3,6,7,9]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,9,10,11,12,1,2,3,6,7,8]=>00000100000=>[5,1,5]=>[5,1,5]
[4,6,7,8,10,12,1,2,3,5,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[4,6,7,8,11,12,1,2,3,5,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[4,6,7,9,10,12,1,2,3,5,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[4,6,7,9,11,12,1,2,3,5,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[4,6,7,10,11,12,1,2,3,5,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[4,6,8,9,10,12,1,2,3,5,7,11]=>00000100000=>[5,1,5]=>[5,1,5]
[4,6,8,9,11,12,1,2,3,5,7,10]=>00000100000=>[5,1,5]=>[5,1,5]
[4,6,8,10,11,12,1,2,3,5,7,9]=>00000100000=>[5,1,5]=>[5,1,5]
[4,6,9,10,11,12,1,2,3,5,7,8]=>00000100000=>[5,1,5]=>[5,1,5]
[4,7,8,9,10,12,1,2,3,5,6,11]=>00000100000=>[5,1,5]=>[5,1,5]
[4,7,8,9,11,12,1,2,3,5,6,10]=>00000100000=>[5,1,5]=>[5,1,5]
[4,7,8,10,11,12,1,2,3,5,6,9]=>00000100000=>[5,1,5]=>[5,1,5]
[4,7,9,10,11,12,1,2,3,5,6,8]=>00000100000=>[5,1,5]=>[5,1,5]
[4,8,9,10,11,12,1,2,3,5,6,7]=>00000100000=>[5,1,5]=>[5,1,5]
[5,6,7,8,10,12,1,2,3,4,9,11]=>00000100000=>[5,1,5]=>[5,1,5]
[5,6,7,8,11,12,1,2,3,4,9,10]=>00000100000=>[5,1,5]=>[5,1,5]
[5,6,7,9,10,12,1,2,3,4,8,11]=>00000100000=>[5,1,5]=>[5,1,5]
[5,6,7,9,11,12,1,2,3,4,8,10]=>00000100000=>[5,1,5]=>[5,1,5]
[5,6,7,10,11,12,1,2,3,4,8,9]=>00000100000=>[5,1,5]=>[5,1,5]
[5,6,8,9,10,12,1,2,3,4,7,11]=>00000100000=>[5,1,5]=>[5,1,5]
[5,6,8,9,11,12,1,2,3,4,7,10]=>00000100000=>[5,1,5]=>[5,1,5]
[5,6,8,10,11,12,1,2,3,4,7,9]=>00000100000=>[5,1,5]=>[5,1,5]
[5,6,9,10,11,12,1,2,3,4,7,8]=>00000100000=>[5,1,5]=>[5,1,5]
[5,7,8,9,10,12,1,2,3,4,6,11]=>00000100000=>[5,1,5]=>[5,1,5]
[5,7,8,9,11,12,1,2,3,4,6,10]=>00000100000=>[5,1,5]=>[5,1,5]
[5,7,8,10,11,12,1,2,3,4,6,9]=>00000100000=>[5,1,5]=>[5,1,5]
[5,7,9,10,11,12,1,2,3,4,6,8]=>00000100000=>[5,1,5]=>[5,1,5]
[5,8,9,10,11,12,1,2,3,4,6,7]=>00000100000=>[5,1,5]=>[5,1,5]
[6,7,8,9,10,12,1,2,3,4,5,11]=>00000100000=>[5,1,5]=>[5,1,5]
[6,7,8,9,11,12,1,2,3,4,5,10]=>00000100000=>[5,1,5]=>[5,1,5]
[6,7,8,10,11,12,1,2,3,4,5,9]=>00000100000=>[5,1,5]=>[5,1,5]
[6,7,9,10,11,12,1,2,3,4,5,8]=>00000100000=>[5,1,5]=>[5,1,5]
[6,8,9,10,11,12,1,2,3,4,5,7]=>00000100000=>[5,1,5]=>[5,1,5]
[7,8,9,10,11,12,1,2,3,4,5,6]=>00000100000=>[5,1,5]=>[5,1,5]
[4,5,7,6,2,3,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,5,7,2,6,4,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,5,7,3,6,4,8,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,5,7,3,6,8,4,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[8,4,3,7,6,1,5,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,7,2,3,5,4,8,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,2,7,3,6,4,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,4,7,6,1,5,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,2,4,7,1,6,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,1,4,7,6,8,5,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,1,3,7,6,8,5,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,1,7,3,6,8,4,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,7,1,3,5,8,4,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[5,8,7,3,6,1,4,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,3,7,6,1,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,8,4,7,6,1,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,4,7,1,6,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,1,4,7,2,6,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,1,3,2,7,6,5,4]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,8,3,1,7,6,5,4]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[3,8,2,1,7,6,5,4]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,7,1,2,8,5,4,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[8,2,3,1,7,6,5,4]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,3,2,1,7,6,5,4]=>1110111=>[3,1,3]=>[3,1,3]
[3,4,1,7,6,8,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,4,2,7,8,6,5,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[8,4,2,7,1,6,5,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,5,7,2,1,6,4,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,5,7,2,8,6,4,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,5,7,1,8,6,4,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[3,5,7,1,6,8,4,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,7,4,5,8,1,3,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,4,7,6,8,1,3,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,7,8,1,6,4,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,5,7,8,2,6,4,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[8,5,7,1,2,6,4,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,4,1,7,2,6,5,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,4,8,7,2,6,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,4,8,7,6,1,5,2]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[4,3,8,7,6,1,5,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,3,7,8,6,1,4,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,7,2,8,1,5,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,2,7,8,1,6,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,8,7,1,6,5,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,2,8,1,7,6,5,4]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,3,8,2,7,6,5,4]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[8,3,1,2,7,6,5,4]=>1100111=>[2,2,3]=>[3,2,2]
[8,2,1,3,7,6,5,4]=>1100111=>[2,2,3]=>[3,2,2]
[1,2,8,3,7,6,5,4]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[2,1,8,3,7,6,5,4]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,1,8,7,2,6,5,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,1,7,8,2,6,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,7,1,8,2,5,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,7,1,2,6,4,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[4,8,1,7,2,6,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,8,1,2,7,6,5,4]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,8,1,3,7,6,5,4]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,8,2,3,7,6,5,4]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[8,1,2,3,7,6,5,4]=>1000111=>[1,3,3]=>[3,3,1]
[3,1,4,5,6,7,8,9,10,2]=>100000001=>[1,7,1]=>[1,7,1]
[2,3,4,5,6,7,8,9,11,1,10]=>0000000010=>[8,1,1]=>[1,1,8]
[10,3,4,5,6,7,8,1,2,9]=>100000100=>[1,5,1,2]=>[2,1,5,1]
[10,1,4,5,6,7,8,9,2,3]=>100000010=>[1,6,1,1]=>[1,1,6,1]
[3,1,4,5,6,7,8,9,10,11,2]=>1000000001=>[1,8,1]=>[1,8,1]
[2,3,4,5,6,7,8,9,10,12,1,11]=>00000000010=>[9,1,1]=>[1,1,9]
[11,3,4,5,6,7,8,9,1,2,10]=>1000000100=>[1,6,1,2]=>[2,1,6,1]
[2,10,4,5,6,7,8,1,3,9]=>010000100=>[1,1,4,1,2]=>[2,1,4,1,1]
[8,3,4,5,6,7,1,10,2,9]=>100001010=>[1,4,1,1,1,1]=>[1,1,1,1,4,1]
[3,1,10,5,6,7,8,9,2,4]=>101000010=>[1,1,1,4,1,1]=>[1,1,4,1,1,1]
[9,1,4,5,6,7,8,2,10,3]=>100000101=>[1,5,1,1,1]=>[1,1,1,5,1]
[11,1,4,5,6,7,8,9,10,2,3]=>1000000010=>[1,7,1,1]=>[1,1,7,1]
[3,1,4,5,6,7,8,9,10,11,12,2]=>10000000001=>[1,9,1]=>[1,9,1]
[6,7,1,8,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,1,5,8,2,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,7,1,5,8,3,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,6,5,1,8,3,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,5,1,8,2,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,6,5,1,8,7,2,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,6,4,1,8,7,2,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,4,5,7,6,2,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,4,5,1,8,7,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,4,6,1,8,7,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,5,6,1,8,7,2,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,5,6,1,8,2,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,5,6,1,8,3,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,6,1,3,8,7,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,4,6,1,2,8,7,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,3,6,1,2,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,3,6,1,8,2,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,1,5,8,2,6,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,1,3,5,7,2,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,2,5,7,3,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,2,1,5,8,3,6,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,2,5,1,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,1,3,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,3,6,1,4,8,7,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,2,5,3,1,8,7,6]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,2,4,1,3,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,2,1,4,3,8,6,5]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,1,2,4,3,7,6,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,1,3,4,2,7,6,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,3,1,4,2,8,6,5]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,3,4,1,2,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,6,3,1,2,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,6,4,1,2,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,6,4,1,3,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,7,1,4,3,8,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,7,1,4,2,8,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,1,3,2,8,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,1,6,7,2,3,5,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,7,1,2,3,8,6,5]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,7,1,2,4,8,6,5]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,7,1,3,4,8,6,5]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,6,3,1,4,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,6,2,1,4,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,6,2,1,8,3,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,5,2,1,8,3,7,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,1,5,2,7,3,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,4,2,3,7,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,4,1,2,3,8,6,5]=>1100011=>[2,3,2]=>[2,3,2]
[6,4,2,1,3,8,7,5]=>1110011=>[3,2,2]=>[2,2,3]
[5,4,2,3,1,8,7,6]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,5,2,4,1,8,7,6]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,2,1,4,8,7,5]=>1110011=>[3,2,2]=>[2,2,3]
[7,3,1,2,4,8,6,5]=>1100011=>[2,3,2]=>[2,3,2]
[8,1,3,2,4,7,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,1,2,3,4,7,6,5]=>1000011=>[1,4,2]=>[2,4,1]
[7,2,1,3,4,8,6,5]=>1100011=>[2,3,2]=>[2,3,2]
[6,2,3,1,4,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,4,3,6,1,5,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,3,6,5,8,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,6,3,5,8,7,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,4,6,3,5,8,1,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,6,3,5,1,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,6,3,1,5,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,4,1,6,5,3,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,6,1,5,3,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,2,6,5,3,1,8,7]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,2,6,5,1,3,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,2,6,5,1,8,7,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,2,6,5,8,1,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,5,8,1,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,6,5,8,3,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,6,1,5,8,3,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,1,6,5,8,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,4,6,5,8,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,4,1,6,5,8,7,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,4,6,1,5,8,7,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,2,6,5,3,8,7,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,2,6,5,8,3,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,4,3,8,7,1,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,6,4,3,8,7,5,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,2,6,8,5,3,7,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,4,6,8,1,5,7,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,4,6,1,8,5,7,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,1,6,8,5,7,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,4,6,8,5,7,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,4,6,8,5,3,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,4,1,6,8,5,3,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,4,6,1,8,5,3,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,4,6,8,1,5,3,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,2,6,8,5,3,1,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[4,2,6,8,5,1,3,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,2,6,8,5,1,7,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,4,6,8,3,5,7,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,4,6,8,3,5,1,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,4,6,8,3,1,5,7]=>0001100=>[3,2,2]=>[2,2,3]
[2,4,6,3,1,8,5,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,4,6,3,8,1,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,6,3,8,5,1,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,4,6,3,8,5,7,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,3,6,8,5,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,3,6,8,5,1,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,4,3,6,8,1,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,4,3,6,1,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,3,1,6,8,5,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,4,1,3,6,8,7,5]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,4,3,6,1,8,7,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,4,3,6,8,1,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,5,2,8,7,3,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,6,5,2,8,7,1,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,6,2,5,8,7,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,6,2,5,8,7,3,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,4,6,3,8,1,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,6,3,1,8,7,5]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,4,1,6,3,8,7,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,4,6,3,8,7,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,4,6,8,3,7,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,4,1,6,8,3,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,6,1,8,3,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,6,8,1,3,7,5]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,4,6,8,3,1,7,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,6,2,8,5,7,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,6,2,8,5,7,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,4,8,7,1,3,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,4,2,8,7,5,3,1]=>1101111=>[2,1,4]=>[4,1,2]
[2,6,4,8,1,7,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,4,1,8,7,5,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,6,1,4,8,7,5,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,1,6,4,8,7,5,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,1,6,4,8,7,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,1,4,8,7,3,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,6,4,1,8,7,3,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,6,4,8,1,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,2,8,7,5,1,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,2,4,8,7,3,5,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,2,4,8,7,3,1,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[1,6,4,7,3,8,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,7,4,5,8,2,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,2,4,7,3,6,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,7,6,3,4,8,2,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,1,6,3,7,2,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,6,3,8,2,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,2,7,4,8,3,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,1,7,3,4,8,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,1,7,4,5,8,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,4,7,3,8,2,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,1,7,5,8,2,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,8,6,3,7,1,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,1,3,7,2,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,8,2,1,7,3,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,7,2,1,8,3,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,7,1,3,8,2,4,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,1,2,4,8,3,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,3,6,1,5,8,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,1,4,5,8,3,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,5,1,3,4,8,2,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[1,6,2,4,8,3,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,5,1,3,7,2,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[1,5,3,2,8,4,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,4,2,1,5,8,3,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[2,5,3,4,1,8,6,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,5,2,1,8,6,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,6,4,8,7,1,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,6,4,8,7,2,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,7,8,3,6,1,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,3,2,8,7,1,5,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,2,4,8,7,1,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,2,8,3,7,1,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,4,8,7,2,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,8,2,5,1,3,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,7,2,5,1,3,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,2,1,5,4,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,8,2,1,5,4,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,3,2,1,5,4,6,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,3,2,1,6,4,5,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,4,2,5,1,6,3,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,3,2,1,5,6,4,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,3,2,1,4,6,5,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,8,2,1,4,5,7,6]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,7,2,1,4,5,8,6]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,2,7,1,4,6,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,2,8,1,4,6,7,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,2,8,1,4,7,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,8,2,1,4,7,5,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,8,2,1,5,7,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,8,2,5,1,7,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,2,5,1,8,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,2,1,5,8,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,7,2,1,4,8,5,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,2,1,7,5,8,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,2,7,1,6,8,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,7,6,1,8,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,3,7,6,8,1,2,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,8,6,7,1,2,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,8,6,1,7,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,2,8,1,6,7,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,2,1,8,7,5,6,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,8,2,1,7,4,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,8,1,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,8,1,6,4,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,7,1,6,4,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,7,6,1,3,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,2,8,6,1,3,7,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,2,8,7,1,3,6,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,7,8,3,4,1,2,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,2,7,8,1,3,6,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,6,8,1,3,7,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,6,7,1,3,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,2,6,1,8,4,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,2,1,8,4,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,7,2,1,8,5,4,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,7,3,8,5,1,2,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,3,7,8,6,1,2,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,2,7,1,8,6,4,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,2,1,6,8,5,7,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,6,1,8,7,4,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,2,6,8,1,7,3,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,6,8,7,1,2,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,2,6,7,1,8,3,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,2,6,1,7,8,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,6,8,7,5,1,2]=>0001110=>[3,3,1]=>[1,3,3]
[5,3,6,4,8,7,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,4,6,2,7,8,5,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,1,8,5,4,2,6,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[1,2,7,5,4,8,6,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,3,7,5,4,8,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,3,8,5,4,6,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,8,7,5,4,6,1,2]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,3,6,7,8,5,1,2]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,5,6,3,8,7,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,6,8,5,4,7,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,8,3,5,4,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,3,5,4,8,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,6,2,5,4,8,7,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,2,5,8,3,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,8,2,5,7,3,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,2,1,5,4,8,7,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,1,6,2,8,7,5,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,8,1,2,4,6,5,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[7,8,3,1,4,2,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,6,1,8,2,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,8,5,4,1,6,7]=>0011100=>[2,3,2]=>[2,3,2]
[4,8,1,5,2,3,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,5,1,6,4,3,2,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[5,8,1,6,4,3,2,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,1,5,7,4,3,2,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[1,5,8,6,4,3,2,7]=>0011110=>[2,4,1]=>[1,4,2]
[3,4,6,1,5,8,2,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,8,4,1,5,3,2,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,8,5,1,6,3,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,6,1,5,7,3,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,8,7,4,3,2,5]=>0011110=>[2,4,1]=>[1,4,2]
[6,8,1,7,4,3,2,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,6,1,7,4,3,2,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,1,7,6,4,3,2,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[6,1,7,8,4,3,2,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,1,8,6,4,3,2,5]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[1,8,7,6,4,3,2,5]=>0111110=>[1,5,1]=>[1,5,1]
[2,1,7,5,6,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,6,7,5,8,2,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,8,1,6,5,3,2,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,8,2,1,4,5,6,3]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,8,1,5,4,6,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,1,5,4,6,8,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,8,5,6,3,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,1,2,5,7,3,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,2,1,5,6,3,7,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,3,6,1,5,7,2,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,6,3,7,8,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,3,6,8,5,7,2,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,4,6,3,7,1,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,6,4,8,7,2,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,1,6,7,3,8,2,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,4,6,1,3,7,2,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,1,5,2,3,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[4,1,7,5,2,3,8,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,2,4,5,8,3,7,6]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[7,2,3,5,4,1,8,6]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,3,5,4,1,7,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,6,3,8,1,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,3,4,1,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,8,1,4,6,3,2,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,1,6,4,7,8,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,5,7,4,3,2,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,1,5,8,4,3,2,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,1,8,7,4,3,2,6]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[6,5,1,8,4,3,2,7]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,5,7,1,4,3,2,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,5,8,1,4,3,2,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,7,1,4,3,2,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,5,7,8,4,3,2,6]=>0001110=>[3,3,1]=>[1,3,3]
[2,4,7,5,1,3,8,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[7,8,4,6,1,3,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,5,4,1,3,2,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,5,6,4,1,8,2,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,6,4,5,1,3,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,6,5,8,4,3,2,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,8,5,1,4,3,2,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,6,5,1,4,3,2,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[1,2,3,4,5,6,9,7,8]=>00000010=>[6,1,1]=>[1,1,6]
[1,2,3,4,5,8,6,9,7]=>00000101=>[5,1,1,1]=>[1,1,1,5]
[1,2,3,4,7,5,8,9,6]=>00001001=>[4,1,2,1]=>[1,2,1,4]
[1,2,3,6,4,7,8,9,5]=>00010001=>[3,1,3,1]=>[1,3,1,3]
[1,2,5,3,6,7,8,9,4]=>00100001=>[2,1,4,1]=>[1,4,1,2]
[1,4,2,5,6,7,8,9,3]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[9,8,1,2,3,4,5,6,7]=>11000000=>[2,6]=>[6,2]
[7,8,9,1,2,3,4,5,6]=>00100000=>[2,1,5]=>[5,1,2]
[9,8,7,1,2,3,4,5,6]=>11100000=>[3,5]=>[5,3]
[6,7,8,9,1,2,3,4,5]=>00010000=>[3,1,4]=>[4,1,3]
[9,6,7,8,1,2,3,4,5]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[8,9,6,7,1,2,3,4,5]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[9,8,6,7,1,2,3,4,5]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[9,8,7,6,1,2,3,4,5]=>11110000=>[4,4]=>[4,4]
[9,5,6,7,8,1,2,3,4]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[8,9,5,6,7,1,2,3,4]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[9,8,5,6,7,1,2,3,4]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[9,7,8,5,6,1,2,3,4]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[9,8,7,5,6,1,2,3,4]=>11101000=>[3,1,1,3]=>[3,1,1,3]
[9,8,7,6,5,1,2,3,4]=>11111000=>[5,3]=>[3,5]
[7,8,9,4,5,6,1,2,3]=>00100100=>[2,1,2,1,2]=>[2,1,2,1,2]
[9,7,8,4,5,6,1,2,3]=>10100100=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
[9,8,7,4,5,6,1,2,3]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[8,9,6,7,4,5,1,2,3]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[9,8,6,7,4,5,1,2,3]=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[9,8,7,6,4,5,1,2,3]=>11110100=>[4,1,1,2]=>[2,1,1,4]
[9,8,7,6,5,4,1,2,3]=>11111100=>[6,2]=>[2,6]
[9,7,8,5,6,3,4,1,2]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[9,8,7,5,6,3,4,1,2]=>11101010=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]
[9,8,7,6,5,3,4,1,2]=>11111010=>[5,1,1,1]=>[1,1,1,5]
[9,8,7,6,5,4,3,1,2]=>11111110=>[7,1]=>[1,7]
[9,10,1,2,3,4,5,6,7,8]=>010000000=>[1,1,7]=>[7,1,1]
[8,9,10,1,2,3,4,5,6,7]=>001000000=>[2,1,6]=>[6,1,2]
[10,8,9,1,2,3,4,5,6,7]=>101000000=>[1,1,1,6]=>[6,1,1,1]
[10,9,8,1,2,3,4,5,6,7]=>111000000=>[3,6]=>[6,3]
[7,8,9,10,1,2,3,4,5,6]=>000100000=>[3,1,5]=>[5,1,3]
[10,7,8,9,1,2,3,4,5,6]=>100100000=>[1,2,1,5]=>[5,1,2,1]
[9,10,7,8,1,2,3,4,5,6]=>010100000=>[1,1,1,1,5]=>[5,1,1,1,1]
[10,9,7,8,1,2,3,4,5,6]=>110100000=>[2,1,1,5]=>[5,1,1,2]
[10,9,8,7,1,2,3,4,5,6]=>111100000=>[4,5]=>[5,4]
[10,6,7,8,9,1,2,3,4,5]=>100010000=>[1,3,1,4]=>[4,1,3,1]
[9,10,6,7,8,1,2,3,4,5]=>010010000=>[1,1,2,1,4]=>[4,1,2,1,1]
[10,9,6,7,8,1,2,3,4,5]=>110010000=>[2,2,1,4]=>[4,1,2,2]
[10,8,9,6,7,1,2,3,4,5]=>101010000=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]
[10,9,8,6,7,1,2,3,4,5]=>111010000=>[3,1,1,4]=>[4,1,1,3]
[10,9,8,7,6,1,2,3,4,5]=>111110000=>[5,4]=>[4,5]
[9,10,5,6,7,8,1,2,3,4]=>010001000=>[1,1,3,1,3]=>[3,1,3,1,1]
[10,9,5,6,7,8,1,2,3,4]=>110001000=>[2,3,1,3]=>[3,1,3,2]
[8,9,10,5,6,7,1,2,3,4]=>001001000=>[2,1,2,1,3]=>[3,1,2,1,2]
[10,9,8,5,6,7,1,2,3,4]=>111001000=>[3,2,1,3]=>[3,1,2,3]
[9,10,7,8,5,6,1,2,3,4]=>010101000=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[10,9,7,8,5,6,1,2,3,4]=>110101000=>[2,1,1,1,1,3]=>[3,1,1,1,1,2]
[10,9,8,7,5,6,1,2,3,4]=>111101000=>[4,1,1,3]=>[3,1,1,4]
[10,9,8,7,6,5,1,2,3,4]=>111111000=>[6,3]=>[3,6]
[10,7,8,9,4,5,6,1,2,3]=>100100100=>[1,2,1,2,1,2]=>[2,1,2,1,2,1]
[9,10,7,8,4,5,6,1,2,3]=>010100100=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]
[10,9,7,8,4,5,6,1,2,3]=>110100100=>[2,1,1,2,1,2]=>[2,1,2,1,1,2]
[10,9,8,7,4,5,6,1,2,3]=>111100100=>[4,2,1,2]=>[2,1,2,4]
[10,8,9,6,7,4,5,1,2,3]=>101010100=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[10,9,8,6,7,4,5,1,2,3]=>111010100=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]
[10,9,8,7,6,4,5,1,2,3]=>111110100=>[5,1,1,2]=>[2,1,1,5]
[10,9,8,7,6,5,4,1,2,3]=>111111100=>[7,2]=>[2,7]
[9,10,7,8,5,6,3,4,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[10,9,7,8,5,6,3,4,1,2]=>110101010=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]
[10,9,8,7,5,6,3,4,1,2]=>111101010=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]
[10,9,8,7,6,5,3,4,1,2]=>111111010=>[6,1,1,1]=>[1,1,1,6]
[10,9,8,7,6,5,4,3,1,2]=>111111110=>[8,1]=>[1,8]
[3,4,6,2,7,1,5,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,6,2,5,4,1,7,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,2,7,5,4,1,6,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,3,6,2,8,1,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,1,2,5,4,7,8,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,2,4,5,1,3,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[4,2,8,5,1,3,7,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,6,8,1,7,2,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,6,4,1,7,2,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,2,1,5,8,3,7,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,6,7,4,8,3,5,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,6,3,7,5,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,7,2,5,8,1,3]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,6,1,7,5,3,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,7,5,4,1,6,3,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,5,4,6,2,8,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,7,5,4,3,8,6,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,4,6,3,5,8,7,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,5,8,4,3,6,7,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[5,4,6,2,7,8,1,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,5,4,1,6,7,3,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,6,3,2,7,1,4,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,6,3,2,7,1,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,5,6,3,2,7,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,4,6,2,8,1,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,1,7,8,5,3,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,5,4,1,6,3,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,6,3,2,1,8,4,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,5,2,1,6,4,7,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,4,3,2,1,5,7]=>0111100=>[1,4,2]=>[2,4,1]
[5,3,8,2,1,6,4,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,7,5,8,2,1,4,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,3,2,8,5,1,6,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,4,6,3,2,1,7,5]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,6,4,3,2,1,7,5]=>1111101=>[5,1,1]=>[1,1,5]
[7,6,4,3,2,1,8,5]=>1111101=>[5,1,1]=>[1,1,5]
[7,8,4,3,2,1,6,5]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,4,7,2,1,8,6,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,5,8,3,2,6,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,7,3,2,1,6,8,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[5,7,3,2,1,6,4,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,3,7,2,5,1,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,8,3,5,2,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,2,5,7,8,4,1,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,1,5,7,8,6,3,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,6,7,2,8,1,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,3,7,2,8,1,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,6,1,7,4,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,5,2,1,4,7,6,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,3,5,2,1,8,4,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,4,1,3,7,8,6]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,5,8,4,1,3,7,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,4,1,7,8,3,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,7,2,8,6,1,4,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,6,8,2,1,7,4,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,3,8,2,1,4,7,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,8,7,3,2,1,5,6]=>0111100=>[1,4,2]=>[2,4,1]
[4,7,3,2,1,5,6,8]=>0111000=>[1,3,3]=>[3,3,1]
[8,4,7,3,2,1,5,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,3,5,2,1,4,7,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,3,2,8,6,1,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,5,2,1,4,6,8,7]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,8,6,5,4,3,2,1,9]=>01111110=>[1,6,1]=>[1,6,1]
[1,8,9,7,6,5,4,3,2]=>00111111=>[2,6]=>[6,2]
[8,9,7,6,5,4,3,2,1,10]=>011111110=>[1,7,1]=>[1,7,1]
[7,6,8,5,4,3,2,1,9]=>10111110=>[1,1,5,1]=>[1,5,1,1]
[6,8,7,5,4,3,2,1,9]=>01111110=>[1,6,1]=>[1,6,1]
[1,8,7,9,6,5,4,3,2]=>01011111=>[1,1,1,5]=>[5,1,1,1]
[1,7,9,8,6,5,4,3,2]=>00111111=>[2,6]=>[6,2]
[1,9,10,8,7,6,5,4,3,2]=>001111111=>[2,7]=>[7,2]
[7,8,3,5,4,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,3,7,5,2,4,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,4,1,6,3,2,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,4,1,6,2,3,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,7,1,6,2,8,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,1,6,2,8,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,7,6,5,1,8,3,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,7,6,5,1,8,4,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,3,6,5,1,4,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,3,6,4,1,5,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,3,6,1,5,4,8,7]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,7,6,1,4,8,5,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,7,6,1,4,8,3,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,3,5,1,8,4,2,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,5,1,8,6,4,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,7,6,1,5,8,4,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,7,6,4,1,8,5,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,1,7,6,3,8,5,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,7,6,3,8,4,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,7,3,6,2,8,4,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,7,6,4,1,8,3,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,3,5,1,8,6,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,5,1,8,2,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,3,4,8,7,6,1,5]=>0001110=>[3,3,1]=>[1,3,3]
[2,3,4,8,5,7,1,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,3,5,4,8,1,2,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,3,5,8,7,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[2,1,4,5,8,7,3,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,4,3,5,8,7,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,3,5,4,8,1,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,4,8,7,5,6,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,3,4,8,7,5,1,6]=>0001110=>[3,3,1]=>[1,3,3]
[2,7,6,5,4,8,1,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,3,5,6,8,4,1,2]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,3,5,6,8,1,4,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,3,5,6,8,1,2,4]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[6,4,1,5,8,7,2,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,4,1,5,8,7,3,2]=>1100111=>[2,2,3]=>[3,2,2]
[6,4,1,5,8,3,7,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,7,1,6,3,8,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,1,5,8,3,2,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,4,1,5,8,2,3,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,4,1,5,8,2,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,3,5,7,8,2,1,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,3,5,7,8,2,4,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,7,6,4,5,8,3,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,7,3,6,1,8,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,4,5,8,6,3,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,3,5,4,8,6,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,3,4,8,5,6,1,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,4,8,7,1,6,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,3,4,8,1,7,6,5]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,3,4,8,1,6,7,5]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,3,4,8,5,1,7,6]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[6,3,5,4,8,2,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,4,3,5,8,2,1,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[2,1,4,5,8,3,7,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,4,3,5,8,2,6,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,3,5,4,8,2,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,3,4,8,5,1,6,7]=>0001100=>[3,2,2]=>[2,2,3]
[2,3,4,8,1,6,5,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,3,4,8,1,5,7,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[7,8,2,6,1,5,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,6,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,6,7,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,5,7,2,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,1,7,2,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,2,7,1,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,6,7,1,5,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,5,7,1,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,1,7,5,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,7,5,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,7,4,6,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,1,7,4,6,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,4,7,1,6,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,2,7,1,6,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,1,7,2,6,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,4,7,2,6,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,1,7,5,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,4,7,5,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,3,7,5,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,1,7,5,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,1,7,4,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,3,7,4,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,3,7,2,6,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,1,7,2,6,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,2,7,1,6,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,2,7,4,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,2,7,5,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,2,7,5,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,7,5,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,4,7,5,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,4,7,5,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,3,7,5,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,3,7,4,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,3,7,1,6,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,1,7,3,6,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,2,8,6,4,1,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,5,1,8,6,2,3,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,4,8,6,1,5,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,1,8,4,5,2,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,1,7,4,2,5,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,7,4,2,8,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,6,7,3,8,5,2,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,1,8,3,5,6,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,3,8,6,2,5,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,4,2,8,6,1,3,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,3,1,8,4,2,5,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,2,8,4,1,5,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,2,8,3,5,1,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,8,3,4,6,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,5,7,8,2,6,3,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,2,3,8,5,7,4,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,2,4,8,5,3,1,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,3,1,4,8,5,2,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[2,6,3,7,8,5,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[2,6,3,7,8,4,5,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,7,3,5,6,8,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,4,7,3,6,8,5,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,5,3,7,8,1,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,5,4,7,8,2,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,3,1,4,8,2,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,2,4,8,6,1,3,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,2,3,8,4,6,7,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,8,2,3,6,1,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,8,2,3,5,7,1,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,4,7,8,3,6,2,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,8,1,3,6,7,2,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,3,8,2,4,7,1,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,4,3,8,1,2,7,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,4,2,8,1,3,7,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,8,2,5,1,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,8,1,4,7,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,1,3,6,2,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,5,7,4,2,6,8,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[5,8,1,4,2,6,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,1,2,7,6,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[6,5,1,2,8,7,3,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,5,3,1,4,2,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,3,1,6,4,2,7,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,2,6,4,1,7,3,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,1,7,5,2,8,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,1,7,2,6,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,6,1,2,8,7,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,5,7,1,8,6,2,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,6,2,7,5,1,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,5,7,1,8,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,4,7,2,8,6,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,4,5,8,2,7,1,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,6,2,8,1,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,5,2,6,8,1,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,2,5,6,1,3,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,3,1,2,5,6,8,7]=>1100001=>[2,4,1]=>[1,4,2]
[5,3,6,8,4,7,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,7,2,5,4,8,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,4,2,5,7,3,6,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,1,6,5,4,8,2,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,6,5,8,3,2,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,1,6,8,4,3,2,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[8,5,4,7,6,3,2,1]=>1101111=>[2,1,4]=>[4,1,2]
[2,7,1,5,4,3,8,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,2,1,5,4,3,7,6]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,4,1,5,7,3,2,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,4,6,1,7,3,2,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,3,6,1,4,7,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,7,6,1,4,3,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,8,5,1,3,2,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,7,2,8,4,3,6,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,7,8,2,4,3,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,7,6,2,8,3,5,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,3,6,2,4,7,5,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,7,6,2,4,8,5,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,7,3,8,4,6,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,3,5,8,6,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[8,7,2,1,4,3,6,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,3,1,4,6,2,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,7,6,3,2,5,4,1]=>1111011=>[4,1,2]=>[2,1,4]
[8,7,3,5,1,6,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,7,2,5,1,3,6,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,4,6,5,7,1,2,3]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,6,5,8,1,2,3]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,7,6,5,1,8,2,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,2,3,4,5,6,7,9]=>10000000=>[1,7]=>[7,1]
[1,9,2,3,4,5,6,7,8]=>01000000=>[1,1,6]=>[6,1,1]
[9,1,2,3,4,5,6,7,8,10]=>100000000=>[1,8]=>[8,1]
[7,8,1,2,3,4,5,6,9]=>01000000=>[1,1,6]=>[6,1,1]
[1,8,9,2,3,4,5,6,7]=>00100000=>[2,1,5]=>[5,1,2]
[1,10,2,3,4,5,6,7,8,9]=>010000000=>[1,1,7]=>[7,1,1]
[10,1,2,3,4,5,6,7,8,9,11]=>1000000000=>[1,9]=>[9,1]
[8,9,1,2,3,4,5,6,7,10]=>010000000=>[1,1,7]=>[7,1,1]
[7,1,8,2,3,4,5,6,9]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[6,8,1,2,3,4,5,7,9]=>01000000=>[1,1,6]=>[6,1,1]
[1,8,2,9,3,4,5,6,7]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,7,9,2,3,4,5,6,8]=>00100000=>[2,1,5]=>[5,1,2]
[1,9,10,2,3,4,5,6,7,8]=>001000000=>[2,1,6]=>[6,1,2]
[1,11,2,3,4,5,6,7,8,9,10]=>0100000000=>[1,1,8]=>[8,1,1]
[3,6,4,8,7,5,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,6,4,3,8,7,1,2]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,6,2,4,7,8,5,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,6,2,4,8,1,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,7,2,8,1,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,7,2,5,8,6,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[7,3,8,4,5,6,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,6,4,8,7,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,6,8,5,3,7,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,8,5,3,4,7,1,2]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,6,5,4,2,8,7,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,8,5,2,7,3,6,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,2,7,5,1,8,6,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,8,1,4,2,6,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,3,6,4,8,2,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,1,7,5,3,2,6,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,5,1,3,4,2,8,7]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,8,5,3,1,7,2,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,4,5,3,2,8,1,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,3,6,1,4,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,8,6,4,1,3,7]=>0011100=>[2,3,2]=>[2,3,2]
[1,4,6,2,5,8,3,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,6,2,5,8,1,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,8,7,4,2,3,5]=>0011100=>[2,3,2]=>[2,3,2]
[6,1,7,8,2,4,3,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,1,8,6,3,4,2,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,2,1,4,5,6,8,3]=>1100001=>[2,4,1]=>[1,4,2]
[1,2,8,3,6,5,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,1,3,2,7,5,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,3,8,5,7,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,4,1,7,5,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,6,5,8,1,4,2,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,8,6,7,3,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,6,4,3,7,2,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,6,3,4,8,7,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,1,3,4,5,2,8,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,8,3,5,4,2,7,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,1,6,3,8,2,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,4,6,3,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,2,6,4,7,8,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,5,7,4,3,1,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,2,5,8,3,4,1,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,8,7,1,2,6,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,5,3,8,2,1,7,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,5,8,4,1,2,3,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,8,7,4,1,3,2,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,5,7,8,4,1,2,6]=>0001100=>[3,2,2]=>[2,2,3]
[1,4,7,5,3,8,2,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,4,6,7,3,1,8,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[7,8,4,6,3,1,2,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,6,4,5,3,8,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,5,8,4,2,1,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,6,8,4,2,3,1,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,8,5,4,3,1,2,7]=>0111100=>[1,4,2]=>[2,4,1]
[6,1,4,2,8,5,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,6,5,3,2,7,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[8,6,5,1,2,4,7,3]=>1110001=>[3,3,1]=>[1,3,3]
[6,7,5,8,2,1,4,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,7,5,8,2,6,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,3,8,5,7,6,2,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,8,5,7,1,2,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,3,1,5,6,2,7,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,8,5,2,1,4,7,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[3,8,2,5,6,1,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,8,1,5,6,3,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,1,2,5,6,3,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,8,2,5,7,6,3,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,1,8,6,2,7,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,8,6,1,7,3,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,6,1,5,7,2,3,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,8,6,5,7,1,2,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,6,5,8,1,2,4,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,1,7,6,8,4,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,1,3,7,8,6,2,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,2,5,8,1,6,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,8,5,7,6,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,2,1,5,7,6,3,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,2,8,6,1,7,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,8,6,5,7,3,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,2,1,3,6,7,8,5]=>1100001=>[2,4,1]=>[1,4,2]
[8,2,5,6,3,7,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,2,6,5,4,1,8,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,1,3,5,4,7,8,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,1,5,3,4,7,8,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,5,6,2,4,1,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,2,6,3,7,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,1,2,6,7,8,5]=>1100001=>[2,4,1]=>[1,4,2]
[8,1,6,5,7,3,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,5,8,6,2,7,1,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,8,1,6,3,7,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,5,6,3,7,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,6,5,4,2,8,3]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,7,6,1,4,2,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,1,4,2,6,5,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,3,5,6,8,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,7,4,1,5,6,8,3]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[5,7,6,4,1,2,8,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[4,7,6,1,5,2,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,7,6,4,5,2,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,3,6,5,7,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,1,6,5,7,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,3,5,7,6,2,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,8,5,4,1,6,2,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,1,5,4,3,7,8,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,5,6,4,2,1,8,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,2,6,5,7,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,6,2,5,1,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,4,3,5,7,8,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,1,3,4,5,7,8,2]=>1000001=>[1,5,1]=>[1,5,1]
[7,2,6,4,5,1,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,3,6,5,7,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,4,7,3,6,8,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,7,8,5,6,1,2]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,7,2,5,1,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,4,7,2,5,8,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,6,2,4,7,1,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,8,3,4,5,7,1,2]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,3,6,7,5,8,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,3,7,5,8,4,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,8,6,4,5,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,2,7,6,5,1,4,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[1,2,7,6,5,8,3,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,8,2,6,1,5,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,8,6,4,1,5,7]=>0011100=>[2,3,2]=>[2,3,2]
[4,3,6,2,5,1,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,2,5,1,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,8,1,2,5,6,3,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,1,6,2,5,7,3,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,1,2,5,8,7,3,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,1,8,6,4,7,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,1,3,6,8,4,2,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,8,3,6,7,4,5,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,1,5,8,3,6,2,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,1,8,7,2,3,6,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,1,5,7,4,2,8,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,1,6,4,7,2,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,4,7,5,1,8,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,7,1,4,2,3,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,8,1,3,2,4,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,8,5,1,3,4,2,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,3,4,5,1,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,2,4,3,1,5,7,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,2,8,3,1,7,5,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,7,4,8,2,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,3,7,4,1,6,2,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,7,3,6,1,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,8,7,6,3,1,2,4]=>0111100=>[1,4,2]=>[2,4,1]
[7,5,6,8,1,4,3,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,4,7,1,6,5,3,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,7,8,5,4,3,6]=>0001110=>[3,3,1]=>[1,3,3]
[6,3,1,2,8,4,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,2,1,3,6,5,8,7]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,8,1,4,5,6,3,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,2,1,5,4,6,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,2,6,1,8,5,3,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,8,2,1,4,5,3,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,8,4,1,5,3,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,6,1,5,8,7,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[7,5,1,6,4,3,8,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,8,1,6,3,4,7,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,1,8,2,7,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,8,1,7,5,2,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,6,1,8,5,3,2,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[5,6,1,7,4,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,1,5,7,4,2,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,5,6,1,7,4,8,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,1,7,5,6,4,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,7,6,4,8,3,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,1,7,8,5,3,4,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,1,8,6,5,4,2,3]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[2,6,5,7,3,4,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,6,4,7,5,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,5,3,6,2,7,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,7,4,6,8,2,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,7,5,6,3,2,8,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,7,6,5,4,8,2,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,6,5,7,2,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,2,7,6,8,3,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,1,7,5,3,8,2,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,7,5,6,8,3,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,4,1,7,6,8,2,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,8,5,6,2,7,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,8,6,4,2,7,5,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[7,8,5,2,4,6,3,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,8,6,3,7,4,5,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,8,1,6,2,4,5,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,8,1,4,7,2,5,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,8,4,1,7,2,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,4,7,1,8,3,2,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,4,1,8,5,2,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,7,1,4,8,3,2,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,7,1,8,4,5,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,2,8,4,3,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,5,1,4,3,8,2,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,6,2,5,8,3,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,5,1,3,7,2,6,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,4,2,1,7,3,6,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,4,2,1,8,5,3,6]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[1,5,4,2,8,3,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,4,3,1,5,8,2,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,7,6,8,4,5,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,7,6,8,5,3,4,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,7,6,8,5,4,2,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,4,8,6,7,5,2,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,4,8,6,7,3,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,3,8,5,4,6,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,8,5,6,7,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,3,5,8,4,7,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,4,3,8,6,7,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,4,2,8,7,3,6,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,2,5,8,7,3,4,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,2,8,5,7,4,6,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,8,7,5,6,2,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,1,8,7,4,6,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,8,5,7,6,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,1,5,8,7,4,2,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,4,1,8,7,6,2,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[5,8,6,7,4,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[4,8,7,5,6,3,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,2,1,6,3,5,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,2,1,4,3,5,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,2,1,4,3,8,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,2,1,4,3,6,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,2,4,1,3,6,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,2,4,1,3,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,2,4,1,3,5,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,2,6,1,3,5,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,1,6,4,3,5,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,6,1,4,3,5,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,4,1,3,5,8,7]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[4,6,2,1,3,5,8,7]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[6,4,2,1,3,5,8,7]=>1110001=>[3,3,1]=>[1,3,3]
[8,4,2,1,3,6,5,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,4,2,1,6,3,5,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,4,2,1,8,3,5,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[4,6,2,1,8,3,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,6,1,4,3,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,4,3,8,5,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,8,4,3,6,5,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,8,1,4,3,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,4,1,3,6,5,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,8,2,1,3,6,5,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,8,2,1,6,3,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,2,1,4,3,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,6,2,1,4,3,5,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[2,8,1,4,6,3,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,8,4,6,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,6,4,8,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,1,4,8,3,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,6,4,1,8,3,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,6,4,8,1,3,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,6,2,8,1,3,5,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,2,6,1,3,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,6,1,8,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,2,4,1,8,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,2,4,1,6,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,2,1,4,6,3,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,2,1,4,8,3,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,2,1,6,8,3,5,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,2,1,6,3,8,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,2,1,3,6,8,5,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[2,1,4,3,8,6,5,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,1,3,8,6,5,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,2,1,3,8,6,5,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,2,1,8,3,6,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,2,1,8,6,3,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,2,1,8,4,3,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,2,1,6,4,3,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,2,6,1,4,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,2,8,1,4,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,8,1,6,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,8,1,3,6,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,8,1,3,6,5,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,1,8,3,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,4,8,3,6,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,1,4,8,6,3,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[2,4,8,1,6,3,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,8,6,1,3,5,7]=>0011000=>[2,2,3]=>[3,2,2]
[4,2,8,6,1,3,5,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,2,8,4,1,3,5,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,2,6,4,1,3,5,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,4,6,2,1,3,5,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,4,8,2,1,3,5,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,6,8,2,1,3,5,7]=>0011000=>[2,2,3]=>[3,2,2]
[2,6,8,4,1,3,5,7]=>0011000=>[2,2,3]=>[3,2,2]
[2,6,8,1,4,3,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,6,1,8,4,3,5,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,6,8,4,3,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[2,1,8,6,4,3,5,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[2,8,1,6,4,3,5,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,8,6,4,1,3,5,7]=>0111000=>[1,3,3]=>[3,3,1]
[4,8,6,2,1,3,5,7]=>0111000=>[1,3,3]=>[3,3,1]
[6,8,4,2,1,3,5,7]=>0111000=>[1,3,3]=>[3,3,1]
[3,2,6,1,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,4,3,8,1,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,4,1,5,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,6,1,5,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,5,2,8,1,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,7,2,6,5,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,8,2,6,1,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,8,1,7,2,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,8,1,5,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,8,3,4,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,8,1,3,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,5,4,8,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,7,6,8,3,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,7,6,8,1,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,7,1,8,5,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,6,5,8,1,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,5,4,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,5,4,8,1,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,6,3,8,4,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,4,6,5,8,1,3,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,8,4,6,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,4,6,1,3,2,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,6,3,4,2,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,6,3,7,2,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,5,1,7,2,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,5,2,6,1,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,5,2,6,4,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,6,3,5,1,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,7,1,5,3,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,4,1,5,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,4,1,7,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,4,3,6,1,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,8,4,6,1,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,8,1,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,7,6,8,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,7,1,8,5,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,5,8,1,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,7,2,4,3,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,8,2,4,1,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,4,1,8,5,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,8,2,4,1,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,8,1,5,2,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,3,8,5,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,3,2,8,5,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,8,5,6,2,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,8,2,6,4,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,8,1,5,4,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,4,5,3,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,7,2,6,3,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,8,2,6,1,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,8,1,7,2,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,5,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,7,4,8,1,3,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,7,1,8,3,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,7,4,8,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,7,1,8,3,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,3,8,1,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,2,1,6,5,8,7,10,9,12,11]=>01101010101=>[1,2,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,2,1]
[5,7,8,9,4,10,6,3,2,1,12,11]=>00010111101=>[3,1,1,4,1,1]=>[1,1,4,1,1,3]
[2,8,3,1,5,4,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,5,3,4,7,1,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,8,3,5,7,6,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,2,5,3,1,8,6,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,2,1,8,5,3,6,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,4,1,3,8,2,6,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,1,4,8,3,2,6,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[1,5,8,4,3,2,6,7]=>0011100=>[2,3,2]=>[2,3,2]
[1,8,5,4,3,2,6,7]=>0111100=>[1,4,2]=>[2,4,1]
[1,7,4,3,8,5,2,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,5,7,3,8,4,2,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,1,4,7,8,3,2,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,8,1,5,7,3,6,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,1,5,3,7,4,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,4,7,6,5,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[1,6,8,5,3,7,4,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,8,1,7,4,3,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,8,1,7,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,8,7,1,5,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,6,4,1,3,8,2,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[1,7,5,6,3,2,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,1,7,8,5,3,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[2,7,4,6,3,1,8,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,8,4,3,7,5,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,2,4,8,3,7,5,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,2,6,3,4,1,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,7,3,1,4,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,7,1,8,3,5,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,3,5,8,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,7,1,3,6,2,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,2,1,7,3,5,6,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,8,2,6,3,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,7,2,6,3,5,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,8,7,4,5,6,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[8,3,7,1,5,6,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,6,1,2,7,5,3,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,1,6,2,7,4,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,5,2,6,7,4,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,2,1,8,6,7,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,8,5,7,6,4,3,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[1,7,8,5,2,6,4,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[7,8,1,6,4,2,5,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,8,6,1,5,3,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,3,8,6,1,5,2,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,7,6,1,5,3,4,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,1,6,4,5,3,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,1,7,5,6,4,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,8,6,7,5,4,3,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[6,3,5,2,1,4,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,5,7,2,8,4,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,5,2,7,4,3,1,6]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[4,5,3,6,1,2,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,5,1,4,6,2,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,4,5,7,2,1,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,7,4,6,3,8,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,8,4,6,3,7,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,4,7,3,6,2,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,3,4,7,5,1,2,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,5,1,4,7,3,2,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,5,3,7,1,4,2,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,1,8,5,7,4,3,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,3,7,1,8,4,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,5,1,4,7,8,3,2]=>1100011=>[2,3,2]=>[2,3,2]
[6,3,4,7,5,8,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,1,4,6,8,3,7,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,7,1,3,5,8,6,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,8,3,7,1,2,6,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,8,6,4,1,7,2,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,8,1,2,5,7,6,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[2,8,7,5,4,1,3,6]=>0111100=>[1,4,2]=>[2,4,1]
[8,7,2,6,4,1,3,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,8,6,7,4,2,1,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,7,6,8,4,2,3,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,3,7,8,2,4,6,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,3,6,2,1,4,7,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,3,7,6,2,1,8,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,3,6,2,8,7,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,7,8,6,4,2,1,3]=>0011110=>[2,4,1]=>[1,4,2]
[2,6,7,5,4,8,1,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,1,7,4,5,8,2,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,7,3,5,1,8,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,7,5,8,3,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,1,5,7,3,6,8,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,7,3,6,1,2,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,1,7,2,5,6,8,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,4,7,1,6,5,8,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,2,1,8,7,5,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[3,4,6,2,7,8,5,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,6,1,2,5,8,7,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[5,6,1,4,8,2,7,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,6,3,1,8,7,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,5,6,4,7,1,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,6,1,5,7,8,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,4,1,5,7,6,8,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,8,2,7,1,6,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,8,2,7,6,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,8,2,7,6,5,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,8,2,7,6,5,4,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[4,8,7,2,6,5,3,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,8,7,2,6,5,1,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,8,7,2,6,1,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,7,2,1,6,5,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,8,7,3,1,6,5,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,8,7,3,2,1,6,5]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[4,8,7,3,2,6,1,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,8,7,3,2,6,5,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,8,7,3,6,2,5,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,7,3,6,2,1,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,8,7,3,6,1,5,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,7,3,6,5,1,2]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,8,7,3,6,5,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[5,8,7,6,3,4,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,8,7,6,3,1,4,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,8,7,6,3,2,4,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,8,7,6,2,4,3,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,8,7,6,2,1,4,3]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,8,7,6,4,2,3,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,8,7,6,4,2,1,3]=>0111110=>[1,5,1]=>[1,5,1]
[5,8,7,6,4,1,3,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,8,7,6,4,3,1,2]=>0111110=>[1,5,1]=>[1,5,1]
[7,3,4,2,1,6,5,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,3,5,2,6,1,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,5,2,6,4,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,5,2,7,4,8,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,1,5,6,4,3,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,3,5,1,6,4,2,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,4,5,6,1,3,2,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,5,7,3,2,8,6]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,4,6,7,3,8,2,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,5,7,3,1,8,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,4,5,7,1,3,8,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,3,5,1,7,4,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,1,5,7,4,8,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,2,1,5,7,4,8,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,4,6,7,3,8,1,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,4,6,7,3,8,5,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,5,6,7,8,3,4,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[2,5,6,7,8,3,1,4]=>0000110=>[4,2,1]=>[1,2,4]
[3,2,1,6,7,8,4,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,2,1,6,7,8,4,3]=>1100011=>[2,3,2]=>[2,3,2]
[5,3,6,1,7,8,4,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,4,6,7,1,8,3,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,5,6,7,8,3,2,4]=>0000110=>[4,2,1]=>[1,2,4]
[6,4,5,7,2,1,8,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,4,6,7,2,8,3,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,3,6,2,7,8,4,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,3,6,2,7,8,1,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,5,2,7,1,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,4,2,1,7,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,3,4,1,2,7,8,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,3,6,2,7,8,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,3,6,2,7,8,5,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,3,6,2,7,8,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,4,6,7,2,8,5,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,4,6,7,2,8,5,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,4,5,7,2,1,8,6]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,2,1,5,7,3,8,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,2,1,6,7,8,3,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[4,3,6,1,7,8,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,5,6,7,8,2,4,3]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,5,6,7,8,4,2,3]=>0000110=>[4,2,1]=>[1,2,4]
[3,4,6,7,1,8,5,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,3,6,1,7,8,5,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,2,1,6,7,8,5,3]=>1100011=>[2,3,2]=>[2,3,2]
[2,3,6,1,7,8,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,4,6,7,1,8,5,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,5,6,7,8,1,4,3]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[2,1,4,3,6,5,8,7,9]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[2,4,1,3,6,5,8,7,9]=>01001010=>[1,1,2,1,1,1,1]=>[1,1,1,1,2,1,1]
[2,4,1,6,3,5,8,7,9]=>01010010=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]
[2,4,1,6,3,8,5,7,9]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[2,4,1,6,3,7,5,9,8]=>01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[2,4,1,5,3,7,6,9,8]=>01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[2,3,1,5,4,7,6,9,8]=>01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[1,3,2,5,4,7,6,9,8]=>01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[2,4,1,3,6,5,8,7,10,9]=>010010101=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1]
[2,4,6,1,3,5,8,7,9]=>00100010=>[2,1,3,1,1]=>[1,1,3,1,2]
[2,4,1,6,3,5,8,7,10,9]=>010100101=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]
[2,4,1,6,8,3,5,7,9]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[2,4,1,6,3,8,5,7,10,9]=>010101001=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]
[2,4,1,6,3,8,9,5,7]=>01010010=>[1,1,1,1,2,1,1]=>[1,1,2,1,1,1,1]
[2,4,1,6,3,8,5,10,7,9]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[2,4,1,6,3,7,5,8,9]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[2,4,1,6,3,8,5,9,7,10]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[2,4,1,5,3,8,6,9,7]=>01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[2,4,1,6,3,7,5,9,8,10]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[2,3,1,6,4,7,5,9,8]=>01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[2,4,1,5,3,7,6,9,8,10]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[1,4,2,5,3,7,6,9,8]=>01010101=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[2,3,1,5,4,7,6,9,8,10]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[1,3,2,5,4,7,6,9,8,10]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,1,2,3,4,5,6,8,9]=>10000000=>[1,7]=>[7,1]
[1,4,3,6,2,5,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,4,3,7,2,5,6,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,4,3,7,6,8,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,3,7,5,8,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,3,7,2,6,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,3,7,4,8,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,2,6,5,8,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,4,8,2,6,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,4,8,3,7,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,2,3,6,5,8,4,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,8,2,4,5,7,1,3]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,7,8,4,5,2,6,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,8,1,4,5,3,6,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,8,7,4,1,6,5,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,8,3,6,1,5,7,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,3,1,6,4,7,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,8,1,4,7,6,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[7,5,1,8,6,2,4,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,4,1,8,2,6,3,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,1,8,4,2,6,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,3,8,5,2,4,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,1,3,8,5,2,4,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[7,1,8,3,6,2,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,1,8,4,2,6,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,2,8,4,1,6,5,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,2,8,3,6,5,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,8,3,6,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,8,2,3,6,5,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,1,2,8,3,5,4,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,5,2,3,8,4,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,1,2,3,8,4,7,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,2,3,8,1,4,7,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,2,8,1,3,5,4,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,2,4,1,8,7,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,1,4,2,8,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,1,6,4,2,8,5,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,6,3,8,7,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,3,8,5,1,4,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,5,1,8,3,4,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,5,1,3,8,4,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,5,3,8,4,7,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,4,8,3,7,6,5]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,4,8,1,3,7,6,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,4,8,3,7,1,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,8,3,7,6,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,5,3,8,1,7,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,4,1,3,8,7,6]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,1,5,4,8,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,1,4,8,2,7,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,2,3,8,4,7,1,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,2,3,7,6,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,8,2,3,7,1,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,8,1,2,3,7,6,5]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,4,8,2,3,7,6,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,4,8,3,7,2,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,8,1,5,2,4,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,8,1,2,4,7,6]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,1,3,8,2,4,7,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,5,3,8,2,4,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,4,8,2,7,6,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,4,8,2,7,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,4,8,1,2,7,6,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,5,1,2,8,7,4,3]=>1100111=>[2,2,3]=>[3,2,2]
[5,3,1,6,4,2,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,1,6,2,8,7,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,1,5,8,2,7,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,1,2,5,8,7,6,3]=>1000111=>[1,3,3]=>[3,3,1]
[1,4,2,5,8,7,6,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,3,5,2,8,7,4,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,5,1,2,8,7,4,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,2,8,7,5,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,2,6,1,8,7,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,3,1,5,8,2,7,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,5,2,8,7,1,4,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,4,8,7,2,6,1,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,4,8,7,1,2,6,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,4,8,1,7,2,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,4,8,7,2,6,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,3,4,8,2,7,6,5]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,4,8,1,2,7,6,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,4,8,2,7,1,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,8,2,7,6,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,2,5,8,1,7,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,3,1,2,5,8,7,6]=>1100011=>[2,3,2]=>[2,3,2]
[3,1,4,2,5,8,7,6]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,3,5,1,8,7,6,4]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[7,8,2,1,5,3,6,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,4,1,2,7,3,5,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[2,3,7,5,4,1,8,6]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[6,3,1,5,4,2,7,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,8,1,5,4,2,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,8,3,5,4,1,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,8,2,5,4,1,3,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,8,2,5,4,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,1,5,4,7,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,6,1,4,7,8,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,3,6,2,4,7,1,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,2,1,7,3,8,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,3,7,5,8,6,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,2,7,1,8,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,7,4,8,1,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,1,6,7,4,8,5,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,7,6,5,3,8,4,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,7,6,5,3,8,1,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,7,6,5,2,4,8,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,7,6,5,3,1,4,8]=>0111100=>[1,4,2]=>[2,4,1]
[2,7,1,4,8,3,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,7,6,4,8,5,1,2]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,7,6,3,8,4,1,2]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,1,6,2,4,8,3,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,7,6,5,2,1,3,8]=>0111100=>[1,4,2]=>[2,4,1]
[4,7,6,5,2,8,1,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,7,6,5,1,8,3,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,7,6,5,2,8,3,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,7,6,5,3,2,8,4]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[4,7,6,5,1,2,8,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[4,7,6,5,3,1,8,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[6,1,3,5,4,8,7,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,2,6,3,4,1,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,6,2,4,7,8,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,2,6,3,4,8,7,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,7,2,4,8,3,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,1,4,2,8,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,1,8,2,6,3,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,2,1,5,3,6,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,7,1,6,2,3,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,7,2,6,8,3,5,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,6,7,4,8,5,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,1,6,7,4,2,8,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,2,8,5,4,6,1,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,7,6,3,5,8,1,2]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,7,1,2,5,3,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,7,6,5,2,4,1,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,7,6,5,1,4,8,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[3,7,6,5,2,1,8,4]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[1,7,6,5,8,2,4,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,7,6,5,8,1,4,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,7,6,5,1,2,4,8]=>0111000=>[1,3,3]=>[3,3,1]
[3,1,6,8,4,2,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,7,6,8,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,6,5,1,4,3,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,7,6,5,8,1,3,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,7,6,5,8,4,1,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,3,2,1,7,4,8,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,2,1,7,3,5,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,3,1,5,4,2,8,6]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,4,1,5,2,7,6,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,2,5,1,3,7,6,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,3,7,2,1,5,8,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,7,2,5,3,1,8,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,7,5,4,1,3,8,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,5,4,3,2,1,8,6]=>1111101=>[5,1,1]=>[1,1,5]
[6,5,2,1,8,4,3,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[4,6,3,2,8,1,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,7,4,3,2,8,1,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,7,6,2,4,8,3,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,7,3,6,4,8,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,7,5,3,8,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,1,8,5,3,6,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,8,3,2,7,1,6,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,7,3,1,6,5,4,2]=>1110111=>[3,1,3]=>[3,1,3]
[8,7,2,6,1,5,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,8,5,7,4,3,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,5,7,2,4,6,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,8,6,1,7,2,5,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,2,8,5,6,1,4,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,7,5,8,2,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,2,6,8,4,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,5,8,1,4,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,5,8,4,1,3,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,5,4,8,3,2,1,7]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,4,3,7,2,1,6,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,2,4,7,1,3,6,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,2,5,8,1,4,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,6,8,2,1,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,3,5,1,8,4,2,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,4,1,5,7,3,6,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,4,2,5,8,3,1,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,4,1,6,8,2,3,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[6,3,7,4,8,5,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,7,2,5,8,6,3,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[6,3,1,8,4,7,5,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,5,3,8,7,4,1,2]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[5,4,8,1,7,6,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,2,8,1,7,3,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,3,8,1,6,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,7,8,1,5,3,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,5,8,7,1,3,6,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[5,3,8,7,2,1,6,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,7,6,1,5,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,2,7,6,5,1,4,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,3,8,7,6,2,1,5]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[2,4,8,7,6,1,3,5]=>0011100=>[2,3,2]=>[2,3,2]
[3,5,8,7,2,6,1,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,7,3,8,6,5,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,5,8,6,4,3,2,1]=>1011111=>[1,1,5]=>[5,1,1]
[5,8,7,3,6,4,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,8,7,6,2,5,3,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[3,8,7,6,5,1,4,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[2,8,7,6,5,4,1,3]=>0111110=>[1,5,1]=>[1,5,1]
[3,4,1,2,5,6,7,8,9]=>01000000=>[1,1,6]=>[6,1,1]
[3,2,1,4,5,6,7,8,9]=>11000000=>[2,6]=>[6,2]
[4,5,6,1,2,3,7,8,9]=>00100000=>[2,1,5]=>[5,1,2]
[4,2,5,1,3,6,7,8,9]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[4,3,2,1,5,6,7,8,9]=>11100000=>[3,5]=>[5,3]
[5,6,7,8,1,2,3,4,9]=>00010000=>[3,1,4]=>[4,1,3]
[5,2,6,7,1,3,4,8,9]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[5,6,3,4,1,2,7,8,9]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[5,3,2,6,1,4,7,8,9]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[5,4,3,2,1,6,7,8,9]=>11110000=>[4,4]=>[4,4]
[6,2,7,8,9,1,3,4,5]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[6,7,3,4,8,1,2,5,9]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[6,3,2,7,8,1,4,5,9]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[6,4,7,2,5,1,3,8,9]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[6,4,3,2,7,1,5,8,9]=>11101000=>[3,1,1,3]=>[3,1,1,3]
[6,5,4,3,2,1,7,8,9]=>11111000=>[5,3]=>[3,5]
[7,4,8,2,5,9,1,3,6]=>10100100=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
[7,4,3,2,8,9,1,5,6]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[7,8,5,6,3,4,1,2,9]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[7,5,3,8,2,6,1,4,9]=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[7,5,4,3,2,8,1,6,9]=>11110100=>[4,1,1,2]=>[2,1,1,4]
[7,6,5,4,3,2,1,8,9]=>11111100=>[6,2]=>[2,6]
[8,6,9,4,7,2,5,1,3]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[8,6,4,3,9,2,7,1,5]=>11101010=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]
[8,6,5,4,3,2,9,1,7]=>11111010=>[5,1,1,1]=>[1,1,1,5]
[3,4,1,2,5,6,7,8,9,10]=>010000000=>[1,1,7]=>[7,1,1]
[3,2,1,4,5,6,7,8,9,10]=>110000000=>[2,7]=>[7,2]
[4,5,6,1,2,3,7,8,9,10]=>001000000=>[2,1,6]=>[6,1,2]
[4,2,5,1,3,6,7,8,9,10]=>101000000=>[1,1,1,6]=>[6,1,1,1]
[4,3,2,1,5,6,7,8,9,10]=>111000000=>[3,6]=>[6,3]
[5,6,7,8,1,2,3,4,9,10]=>000100000=>[3,1,5]=>[5,1,3]
[5,2,6,7,1,3,4,8,9,10]=>100100000=>[1,2,1,5]=>[5,1,2,1]
[5,6,3,4,1,2,7,8,9,10]=>010100000=>[1,1,1,1,5]=>[5,1,1,1,1]
[5,3,2,6,1,4,7,8,9,10]=>110100000=>[2,1,1,5]=>[5,1,1,2]
[5,4,3,2,1,6,7,8,9,10]=>111100000=>[4,5]=>[5,4]
[6,2,7,8,9,1,3,4,5,10]=>100010000=>[1,3,1,4]=>[4,1,3,1]
[6,7,3,4,8,1,2,5,9,10]=>010010000=>[1,1,2,1,4]=>[4,1,2,1,1]
[6,3,2,7,8,1,4,5,9,10]=>110010000=>[2,2,1,4]=>[4,1,2,2]
[6,4,7,2,5,1,3,8,9,10]=>101010000=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]
[6,4,3,2,7,1,5,8,9,10]=>111010000=>[3,1,1,4]=>[4,1,1,3]
[6,5,4,3,2,1,7,8,9,10]=>111110000=>[5,4]=>[4,5]
[7,8,3,4,9,10,1,2,5,6]=>010001000=>[1,1,3,1,3]=>[3,1,3,1,1]
[7,8,9,4,5,6,1,2,3,10]=>001001000=>[2,1,2,1,3]=>[3,1,2,1,2]
[7,4,3,2,8,9,1,5,6,10]=>111001000=>[3,2,1,3]=>[3,1,2,3]
[7,8,5,6,3,4,1,2,9,10]=>010101000=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[7,5,3,8,2,6,1,4,9,10]=>110101000=>[2,1,1,1,1,3]=>[3,1,1,1,1,2]
[7,5,4,3,2,8,1,6,9,10]=>111101000=>[4,1,1,3]=>[3,1,1,4]
[7,6,5,4,3,2,1,8,9,10]=>111111000=>[6,3]=>[3,6]
[8,5,9,10,2,6,7,1,3,4]=>100100100=>[1,2,1,2,1,2]=>[2,1,2,1,2,1]
[8,5,3,9,2,6,10,1,4,7]=>110100100=>[2,1,1,2,1,2]=>[2,1,2,1,1,2]
[8,6,9,4,7,2,5,1,3,10]=>101010100=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[8,6,4,3,9,2,7,1,5,10]=>111010100=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]
[8,6,5,4,3,2,9,1,7,10]=>111110100=>[5,1,1,2]=>[2,1,1,5]
[8,7,6,5,4,3,2,1,9,10]=>111111100=>[7,2]=>[2,7]
[9,7,5,4,3,10,2,8,1,6]=>111101010=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]
[3,6,5,1,2,4,8,7]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,7,5,8,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,5,7,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,7,8,4,3,2,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,1,2,6,4,3,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,1,2,5,4,3,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,1,2,4,6,3,8,7]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,1,2,6,5,3,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,1,5,7,8,3,2,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,1,5,8,7,3,2,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[4,7,1,8,3,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,8,5,2,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,1,7,4,8,2,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,5,3,8,1,4,2,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,1,5,8,7,3,4,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,1,8,4,7,2,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,1,8,7,5,2,3,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,7,1,6,3,2,8,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,1,2,3,7,5,8,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,1,2,3,8,6,5,4]=>1000111=>[1,3,3]=>[3,3,1]
[7,1,2,3,5,8,6,4]=>1000011=>[1,4,2]=>[2,4,1]
[6,8,1,4,3,7,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,7,3,2,4,1,6,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,1,7,3,4,8,6,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,8,3,2,4,1,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,1,4,3,8,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,2,3,5,7,6,4]=>1000011=>[1,4,2]=>[2,4,1]
[8,1,2,3,6,7,5,4]=>1000011=>[1,4,2]=>[2,4,1]
[7,1,2,3,6,8,5,4]=>1000011=>[1,4,2]=>[2,4,1]
[7,1,2,3,8,5,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,2,3,7,5,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,2,3,6,5,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,1,8,5,4,3,2,6]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,8,2,6,3,4,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,2,7,3,4,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,2,8,3,4,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,7,1,4,2,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,7,8,1,4,2,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,6,8,1,4,2,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,7,8,2,4,1,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,6,7,1,4,2,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,2,8,3,1,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,6,2,7,3,1,4,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,1,7,5,4,3,2,6]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[8,1,7,4,5,3,2,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,3,7,1,4,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,7,3,4,6,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,7,3,2,4,1,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,7,2,4,3,6,1,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,1,2,3,5,6,8,4]=>1000001=>[1,5,1]=>[1,5,1]
[6,1,2,3,8,7,4,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,1,2,3,7,8,6,4]=>1000011=>[1,4,2]=>[2,4,1]
[5,1,2,3,8,7,6,4]=>1000111=>[1,3,3]=>[3,3,1]
[5,1,2,3,8,6,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,1,2,3,5,8,7,4]=>1000011=>[1,4,2]=>[2,4,1]
[8,6,2,4,3,1,7,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,6,3,2,4,8,1,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[2,1,6,3,4,8,7,5]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,6,3,2,4,7,1,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,6,2,4,3,1,8,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,1,2,3,5,7,8,4]=>1000001=>[1,5,1]=>[1,5,1]
[5,1,2,3,6,8,7,4]=>1000011=>[1,4,2]=>[2,4,1]
[7,8,1,2,6,3,5,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,4,8,2,7,3,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,8,5,4,7,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,3,8,5,4,2,7,6]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,3,6,8,4,7,1,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,6,8,4,7,5,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,4,8,1,7,3,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,8,5,7,6,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,6,8,4,5,7,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[7,5,1,2,4,3,6,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,4,6,1,5,2,3,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,4,2,6,3,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,8,1,4,7,2,3,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,6,4,2,8,3,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,6,3,8,5,4,2,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,8,1,7,3,5,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,3,6,5,4,2,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,3,1,6,5,4,2,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,2,1,4,6,3,5,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[7,2,3,6,5,1,4,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[7,1,2,3,6,5,4,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,8,1,2,7,3,5,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,2,3,8,5,4,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,5,8,2,7,6,3,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,1,8,2,7,6,3,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,2,7,6,3,4,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,2,8,1,7,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,2,1,7,4,3,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,6,4,1,2,8,5,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,6,3,8,5,4,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,5,1,8,7,6,3,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,5,3,8,7,4,6,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,2,5,3,8,7,4,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,4,8,7,6,5,1,3]=>0011110=>[2,4,1]=>[1,4,2]
[2,5,3,8,7,1,6,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,5,8,4,1,7,6,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,5,8,7,1,4,2,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,3,8,4,1,7,6,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,2,8,7,6,3,5,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,2,8,7,6,5,3,1]=>1011111=>[1,1,5]=>[5,1,1]
[4,1,8,7,6,5,3,2]=>1011111=>[1,1,5]=>[5,1,1]
[4,3,8,7,6,5,1,2]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[6,3,1,8,7,2,5,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,8,3,7,6,1,4,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,3,8,7,6,2,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[1,5,3,8,7,6,2,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,5,8,4,7,2,6,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,1,8,4,7,2,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,7,4,6,1,2,3]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,5,1,2,4,7,3]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[5,6,3,1,2,4,8,7]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[5,6,2,4,3,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,1,2,4,3,8,7]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,5,8,1,7,2,3,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,5,8,1,7,2,6,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,2,5,8,7,4,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,5,1,8,7,4,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,1,8,7,2,6,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,3,6,1,2,8,5,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,8,3,1,7,2,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,5,2,8,7,1,3,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,2,5,8,7,1,6,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,4,8,7,6,2,1,5]=>0011110=>[2,4,1]=>[1,4,2]
[3,1,4,8,7,6,2,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,4,8,7,6,5,1,2]=>0011110=>[2,4,1]=>[1,4,2]
[1,3,4,8,7,6,2,5]=>0001110=>[3,3,1]=>[1,3,3]
[3,4,8,7,6,2,5,1]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[3,2,5,8,7,4,6,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,5,8,3,1,7,6,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,1,3,5,8,7,4,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,2,7,5,8,6,4,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[7,1,4,8,2,6,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,8,1,3,7,5,2,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,7,8,1,2,6,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,7,8,2,6,5,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,3,7,8,1,6,5,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[2,7,8,1,3,6,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[8,1,2,6,7,3,5,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,1,2,6,7,5,3,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[8,2,5,7,1,3,6,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,8,1,6,7,3,5,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,6,8,3,7,1,5,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,8,6,4,7,1,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,8,3,4,1,7,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,8,3,7,4,1,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,8,3,7,5,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,8,1,6,7,5,3,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,2,5,7,1,6,3,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,4,7,2,3,6,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,5,7,4,2,6,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,5,7,4,1,6,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,5,2,4,7,1,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,2,3,5,7,1,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,2,4,7,3,6,1,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,2,7,1,4,6,3,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,7,1,2,4,6,3,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,7,1,4,6,2,3,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,4,7,1,3,6,2,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,8,3,7,2,5,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,3,5,7,1,2,6,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,8,7,1,3,6,2,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,5,4,7,1,6,2,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,5,4,7,1,2,6,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,5,1,4,7,2,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,4,6,8,2,7,5,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,6,5,8,2,7,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,6,3,1,7,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,6,2,8,1,7,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,4,5,7,2,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,7,3,6,1,2,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,3,5,7,1,6,2,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,6,8,3,7,5,2,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,3,8,2,7,5,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,8,4,2,7,1,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,6,4,7,3,1,5,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,4,5,7,3,1,6,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,4,2,5,7,1,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,3,4,7,2,6,1,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,7,1,3,4,6,2,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,3,7,2,4,6,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,4,5,7,1,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,7,3,4,5,1,6,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,7,4,5,2,6,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,8,7,2,3,6,1,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,7,2,3,4,6,1,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,7,2,3,6,1,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[1,3,2,8,5,4,7,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,8,5,3,7,1,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,2,1,8,4,3,7,6]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,2,8,4,3,7,5,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,2,8,4,3,1,6,5]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,3,4,8,2,1,6,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,3,4,8,2,7,5,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,3,4,1,8,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,4,5,2,3,7,6]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,5,4,3,2,7,6]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,5,4,2,8,1,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,3,2,8,7,1,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,4,3,2,8,7,5,1]=>1110111=>[3,1,3]=>[3,1,3]
[6,5,3,2,1,7,8,4]=>1111001=>[4,2,1]=>[1,2,4]
[5,6,3,2,7,8,4,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[4,1,6,3,2,7,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,4,2,7,8,1,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,1,6,4,3,7,2,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,1,7,4,3,6,5,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,7,4,1,3,6,5,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,7,4,2,6,1,5,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,1,7,3,2,6,5,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,7,3,2,6,4,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,3,2,5,4,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,6,3,2,1,5,4,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[4,7,5,6,2,3,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,7,5,6,2,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,7,5,6,1,3,4,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,6,5,7,1,3,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,6,5,7,2,8,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,4,7,2,8,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,5,4,1,7,2,8,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,4,6,2,1,8,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,5,7,1,8,2,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,4,6,1,7,8,2,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,1,5,6,7,2,3,4]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,1,4,6,8,7,3,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,4,6,8,7,1,2,5]=>0001100=>[3,2,2]=>[2,2,3]
[4,3,1,6,8,7,2,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,3,6,8,7,2,4,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,3,5,1,8,7,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,5,8,6,2,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,2,8,5,6,3,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,2,8,5,1,7,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,2,1,8,6,7,3,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,2,8,6,7,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,8,6,7,1,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,1,3,2,6,7,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,3,8,7,1,6,5,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,2,8,7,6,1,5,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,2,8,7,6,4,1,3]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,2,1,8,6,5,4,3]=>1101111=>[2,1,4]=>[4,1,2]
[7,3,6,1,8,5,4,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,3,7,8,5,4,2,1]=>1001111=>[1,2,4]=>[4,2,1]
[5,3,7,8,6,4,1,2]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[4,3,1,7,8,6,5,2]=>1100111=>[2,2,3]=>[3,2,2]
[3,4,7,8,6,1,5,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[8,1,5,7,6,2,4,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,5,7,6,8,1,4,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,5,7,6,8,3,1,2]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,4,1,7,6,8,3,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,4,7,5,8,3,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,4,6,5,1,8,3,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,5,6,4,3,1,8,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,5,1,7,4,3,8,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,6,7,5,3,8,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,6,7,5,1,4,8,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[8,1,6,7,5,4,2,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[8,1,7,6,5,4,3,2]=>1011111=>[1,1,5]=>[5,1,1]
[2,7,6,1,5,4,3,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,7,6,5,1,4,2,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,7,6,5,3,1,2,8]=>0111100=>[1,4,2]=>[2,4,1]
[8,6,4,3,1,5,7,2]=>1111001=>[4,2,1]=>[1,2,4]
[8,6,4,1,5,2,7,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,6,5,1,3,2,7,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,6,3,1,7,2,4,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,7,3,1,5,2,4,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[5,3,1,7,2,4,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,7,1,2,4,5,3,6]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,6,1,2,4,7,3,5]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,5,1,2,6,7,3,4]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,5,1,6,4,2,7,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,5,1,3,6,4,7,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,6,1,5,3,4,7,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,6,1,5,2,4,7,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,6,1,2,5,7,3,4]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,6,1,2,7,4,3,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,7,1,2,5,4,3,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,1,4,2,3,8,6,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,4,2,7,3,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,5,8,2,6,3,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,7,8,1,2,4,6,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[5,7,8,1,3,4,6,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[5,8,1,7,3,4,6,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,1,5,7,2,4,6,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,4,1,2,7,6,3,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[1,4,2,3,8,7,5,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,4,2,7,6,3,5,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,1,2,8,7,5,3,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,1,2,4,8,7,5,3]=>1000111=>[1,3,3]=>[3,3,1]
[3,1,8,4,6,7,5,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,1,7,6,4,8,5,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,1,2,4,6,8,5,3]=>1000011=>[1,4,2]=>[2,4,1]
[7,1,2,6,8,5,3,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,1,2,7,8,5,3,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,1,2,7,4,8,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,1,6,4,7,8,5,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,7,1,3,8,4,6,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,7,1,8,4,2,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,1,5,3,2,8,6,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,1,4,5,2,8,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,7,3,1,5,8,6,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[4,8,7,3,1,5,6,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,1,7,4,5,2,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,5,3,2,6,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,7,1,2,6,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,1,2,8,4,7,5,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,1,2,8,6,4,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,1,7,2,6,4,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,4,2,3,8,6,5,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,4,2,3,8,5,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,1,7,2,4,6,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,1,3,4,7,6,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,1,8,6,4,7,5,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,1,2,6,7,4,5,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,1,2,8,7,3,5,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,2,3,5,8,4,7,6]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[1,2,3,5,8,6,4,7]=>0000110=>[4,2,1]=>[1,2,4]
[7,1,2,8,3,6,5,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,1,2,8,6,4,5,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,1,7,8,4,6,5,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,1,8,7,6,4,5,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,1,2,7,4,6,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,1,2,7,3,6,5,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,2,3,5,8,7,4,6]=>0000110=>[4,2,1]=>[1,2,4]
[1,2,3,6,8,5,4,7]=>0000110=>[4,2,1]=>[1,2,4]
[7,8,5,6,3,1,4,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,8,5,3,6,1,2,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,5,6,3,1,4,2,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,5,8,3,1,4,2,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,8,5,3,1,4,2,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,8,5,3,1,6,2,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,8,5,3,1,6,4,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[7,8,5,3,6,1,4,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,8,5,3,6,4,1,2]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,8,5,3,4,1,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,8,5,3,1,4,6,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,8,5,3,1,2,6,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,5,3,8,1,2,6,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,8,3,4,1,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,8,3,4,6,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,5,6,3,4,1,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,6,3,1,4,8,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,5,6,3,1,2,8,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,5,3,6,1,2,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,3,4,1,2,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,3,1,4,2,6,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,3,1,4,2,8,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,3,1,6,2,8,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,3,1,6,4,8,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,3,6,1,4,8,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,3,6,4,1,8,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,5,3,6,4,8,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,3,8,4,6,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,3,8,1,4,6,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,3,1,8,4,6,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,3,1,8,2,6,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,5,3,1,8,2,4,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,3,1,6,2,4,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,5,3,1,6,4,2,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,5,3,1,8,4,2,6]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,5,3,1,8,6,2,4]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,5,3,8,1,6,4,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,5,3,8,6,1,4,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,5,3,8,6,4,1,2]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,5,8,3,6,4,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,5,8,3,6,1,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,8,3,1,6,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,5,8,3,1,6,2,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,5,3,6,1,4,2,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,3,6,4,1,2,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,5,3,8,4,1,2,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,5,8,6,3,1,2,4]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,5,8,6,3,1,4,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,5,8,6,3,4,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,5,6,8,3,1,4,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,5,6,3,8,1,2,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,5,3,4,1,6,2,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,3,4,1,8,2,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,6,3,1,8,2,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,5,6,3,1,8,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,5,6,3,8,1,4,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,6,3,8,4,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,5,3,6,8,4,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,5,3,6,8,1,4,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,3,6,1,8,4,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,5,3,1,6,8,4,2]=>1110011=>[3,2,2]=>[2,2,3]
[7,5,3,1,6,8,2,4]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,5,3,1,4,8,2,6]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,5,3,1,4,6,2,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,5,3,1,2,6,4,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,5,3,1,2,8,4,6]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,5,3,1,2,8,6,4]=>1110011=>[3,2,2]=>[2,2,3]
[7,5,3,1,4,8,6,2]=>1110011=>[3,2,2]=>[2,2,3]
[7,5,3,4,1,8,6,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,5,3,4,8,1,6,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,3,4,8,6,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,5,3,4,6,1,8,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,3,4,1,6,8,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,3,1,4,6,8,2]=>1110001=>[3,3,1]=>[1,3,3]
[7,5,3,1,2,6,8,4]=>1110001=>[3,3,1]=>[1,3,3]
[7,5,3,1,2,4,8,6]=>1110001=>[3,3,1]=>[1,3,3]
[3,6,2,5,4,1,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,5,2,8,4,7,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,7,3,2,8,6,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,4,8,3,2,7,6,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,4,5,3,2,1,8,7]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,3,2,6,4,1,8,7]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,5,8,3,2,7,6,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,7,6,3,8,5,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,8,6,3,7,5,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,8,5,3,2,7,6,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,8,4,3,2,7,6,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,3,2,8,4,7,6,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,1,5,8,4,7,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,3,2,7,4,8,6,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,7,4,3,2,8,6,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,7,5,3,2,8,6,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,7,8,3,6,5,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[4,6,8,3,7,5,2,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[7,6,4,3,8,5,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[7,3,2,6,8,5,4,1]=>1100111=>[2,2,3]=>[3,2,2]
[2,1,8,6,7,5,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,3,2,6,7,5,4,1]=>1100111=>[2,2,3]=>[3,2,2]
[8,6,4,3,7,5,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,5,7,6,4,3,2,1]=>1011111=>[1,1,5]=>[5,1,1]
[8,4,5,3,2,7,6,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,4,7,3,6,5,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,4,6,3,7,5,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,4,6,3,8,5,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,7,2,6,8,5,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,8,2,6,7,5,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,8,2,5,4,7,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,7,2,8,6,5,4,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[3,6,2,8,7,5,4,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[6,4,7,3,8,5,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,4,8,3,7,5,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,4,8,3,6,5,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,4,5,3,2,8,6,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,5,4,3,2,8,6,1]=>1111011=>[4,1,2]=>[2,1,4]
[7,3,2,5,4,8,6,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,1,7,5,4,8,6,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,3,2,8,6,5,4,1]=>1101111=>[2,1,4]=>[4,1,2]
[7,8,4,3,6,5,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,8,5,7,4,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[6,8,4,3,7,5,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,3,2,8,7,5,4,1]=>1101111=>[2,1,4]=>[4,1,2]
[6,3,2,7,8,5,4,1]=>1100111=>[2,2,3]=>[3,2,2]
[6,7,4,3,8,5,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,3,1,4,5,6,7,8,9]=>01000000=>[1,1,6]=>[6,1,1]
[2,3,4,1,5,6,7,8,9]=>00100000=>[2,1,5]=>[5,1,2]
[2,3,4,5,1,6,7,8,9]=>00010000=>[3,1,4]=>[4,1,3]
[2,3,4,5,6,1,7,8,9]=>00001000=>[4,1,3]=>[3,1,4]
[2,3,1,4,5,6,7,8,9,10]=>010000000=>[1,1,7]=>[7,1,1]
[2,4,3,1,5,6,7,8,9]=>01100000=>[1,2,5]=>[5,2,1]
[2,3,4,1,5,6,7,8,9,10]=>001000000=>[2,1,6]=>[6,1,2]
[2,3,5,4,1,6,7,8,9]=>00110000=>[2,2,4]=>[4,2,2]
[2,3,4,5,1,6,7,8,9,10]=>000100000=>[3,1,5]=>[5,1,3]
[2,3,4,6,5,1,7,8,9]=>00011000=>[3,2,3]=>[3,2,3]
[2,3,4,5,6,1,7,8,9,10]=>000010000=>[4,1,4]=>[4,1,4]
[2,3,4,5,7,6,1,8,9]=>00001100=>[4,2,2]=>[2,2,4]
[2,3,4,5,6,7,1,8,9,10]=>000001000=>[5,1,3]=>[3,1,5]
[2,3,4,5,6,8,7,1,9]=>00000110=>[5,2,1]=>[1,2,5]
[2,3,4,5,6,7,8,1,9,10]=>000000100=>[6,1,2]=>[2,1,6]
[2,3,4,5,6,7,9,8,1]=>00000011=>[6,2]=>[2,6]
[4,6,8,3,5,7,1,2]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,8,1,2,4,5,7,3]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,5,8,2,4,7,1,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,3,5,2,4,1,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,5,7,3,6,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,2,8,3,1,6,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,2,5,8,3,7,1,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,1,6,8,4,7,3,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,2,5,8,3,6,7,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[5,3,6,8,4,7,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,6,5,8,2,4,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,2,6,8,5,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,4,3,8,2,6,7,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,4,8,3,2,1,6,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[5,4,3,7,2,6,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,6,2,7,5,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,6,3,2,1,8,5,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,1,7,3,2,5,8,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,1,7,8,2,6,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,5,1,2,7,8,6,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[7,5,1,4,8,2,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,4,7,3,8,6,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,4,7,6,3,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,8,7,1,4,2,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,3,5,1,2,7,6,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,8,3,1,7,2,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,4,3,5,2,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,6,3,1,5,2,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,7,3,6,5,2,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,3,7,6,4,2,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[1,6,3,4,2,8,7,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,3,6,2,7,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,6,8,7,4,2,5,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[6,4,8,7,5,3,1,2]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,6,4,3,8,5,1,2]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[1,7,6,2,8,4,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,1,3,2,6,8,5,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,5,3,2,7,4,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,3,2,1,8,5,4,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[6,5,3,2,7,4,1,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[5,2,6,3,7,4,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,5,3,1,6,4,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,1,7,3,8,5,4,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,6,2,3,7,8,5,4]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,6,7,2,8,4,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,7,1,8,2,4,6,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,1,2,7,8,3,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,4,1,7,8,6,3,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,2,1,7,3,8,5,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,2,8,4,3,1,5,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,3,2,1,8,4,5,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[7,8,3,2,5,6,1,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,1,8,2,4,5,6,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,7,6,1,2,4,5,3]=>1110001=>[3,3,1]=>[1,3,3]
[8,3,7,6,2,1,4,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[3,2,8,7,5,1,4,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,3,6,5,2,1,4,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,6,3,5,2,4,1,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,6,2,5,3,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,2,4,1,6,5,3,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,2,8,1,7,5,3,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,2,4,1,7,6,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,7,1,5,6,2,4,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,5,7,3,6,4,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,8,3,7,5,4,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,1,6,7,5,2,4,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,1,2,6,4,3,7,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,1,7,5,4,3,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,5,1,8,6,4,3,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,7,2,6,4,3,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,2,7,5,4,3,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[2,1,8,6,5,4,3,7]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[1,2,7,5,4,3,8,6]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,7,2,4,3,8,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,7,2,8,3,6,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,7,8,6,5,2,4,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[7,3,8,6,5,4,1,2]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[1,8,7,6,5,2,4,3]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[8,1,7,3,2,6,5,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,1,4,3,2,8,7,6]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,6,5,3,2,1,7,4]=>1111101=>[5,1,1]=>[1,1,5]
[8,6,3,2,1,7,4,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,5,4,1,7,2,3]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,6,5,1,7,3,2,4]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,6,1,7,4,3,2,5]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[4,6,3,2,7,5,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,4,3,7,2,5,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,4,8,3,1,6,2,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,1,5,8,3,2,6,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,7,4,1,8,2,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,7,4,3,1,8,6,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,8,7,2,5,4,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,5,3,7,2,6,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,1,8,7,5,2,6]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[1,4,8,6,3,5,2,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,4,6,3,5,2,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,5,6,8,4,2,7]=>0000110=>[4,2,1]=>[1,2,4]
[3,5,4,8,7,1,2,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,1,4,6,8,7,2,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,6,3,8,7,2,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,2,4,8,7,5,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[8,4,1,6,7,5,3,2]=>1100111=>[2,2,3]=>[3,2,2]
[7,1,6,4,8,5,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,6,8,5,1,2,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[1,3,7,2,6,8,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,6,5,2,8,1,4,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,6,5,7,2,4,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,2,6,3,8,1,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,6,7,3,5,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,2,4,7,5,1,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,2,4,1,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,8,2,1,6,4,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,3,5,2,1,8,6,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,7,6,4,3,1,5,2]=>1111101=>[5,1,1]=>[1,1,5]
[8,7,6,4,1,5,2,3]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[3,8,7,2,1,4,6,5]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[3,8,2,7,1,5,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,8,2,1,5,4,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,4,8,1,6,5,3,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,2,8,1,5,7,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,5,7,6,1,4,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,6,1,7,3,5,4,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,6,1,7,5,4,2,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[1,6,2,8,7,3,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,2,4,6,7,3,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,8,5,4,7,1,3,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,5,8,6,4,3,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,2,5,6,4,3,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[1,2,5,7,8,4,3,6]=>0000110=>[4,2,1]=>[1,2,4]
[1,2,7,4,8,6,3,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,7,8,3,6,5,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[7,1,8,6,3,5,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,8,7,6,3,5,2,4]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,8,7,4,6,3,2,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,1,5,8,3,4,6,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,1,6,4,2,3,5,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,6,2,4,7,3,5,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,6,2,4,5,7,3,1]=>1100011=>[2,3,2]=>[2,3,2]
[2,7,1,4,5,8,3,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,1,6,4,5,2,3,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,4,5,6,8,2,3]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[7,1,4,6,5,8,3,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,1,2,3,8,5,4,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,1,5,4,3,8,2,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,1,3,4,2,6,8,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,1,5,4,6,2,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,5,6,4,3,8,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,1,6,5,4,3,2,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[8,6,2,5,4,3,7,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,5,1,7,4,3,6,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,5,1,4,7,8,6,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,5,1,4,8,6,2,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,2,4,7,8,1,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,6,2,4,8,7,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,8,2,4,7,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,5,8,7,2,3,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,5,7,8,2,4,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,3,4,2,8,5,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,7,2,5,8,1,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,6,8,1,3,5,2,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,3,8,1,2,7,5,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,6,4,1,7,2,5,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,8,3,1,5,6,4,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,8,7,1,5,4,2,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,3,1,7,6,8,2,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,1,7,5,6,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,1,5,7,6,2,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,7,4,1,6,2,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,4,7,2,5,3,6,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,8,1,2,3,6,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[2,8,6,1,5,3,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,6,5,1,3,8,2,4]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,6,5,1,3,4,8,2]=>1110001=>[3,3,1]=>[1,3,3]
[7,2,6,4,1,3,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,7,5,2,1,3,8,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,4,5,3,7,2,6,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,5,2,8,1,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,6,4,3,1,5,7,8]=>0111000=>[1,3,3]=>[3,3,1]
[7,3,8,4,1,5,2,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,2,3,4,1,6,5,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,2,8,3,6,1,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,8,5,7,2,1,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,8,5,2,7,1,3,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,3,5,2,1,7,4,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,8,5,3,1,4,2,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,6,5,4,2,8,1,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,6,4,7,2,5,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,4,8,2,5,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,5,8,2,4,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,8,2,4,3,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,6,2,4,3,7,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,6,2,4,7,3,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,5,6,2,4,7,8,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,5,8,2,4,7,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,5,7,2,4,8,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,6,5,7,2,4,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,7,2,4,3,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,5,6,7,2,4,8,3]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,5,8,2,4,6,7,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,5,7,2,4,6,8,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,5,7,8,3,2,4,6]=>0001100=>[3,2,2]=>[2,2,3]
[1,5,8,3,2,4,6,7]=>0011000=>[2,2,3]=>[3,2,2]
[1,5,6,2,4,8,3,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,7,6,2,8,3,4,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,7,3,4,2,8,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,6,2,4,3,8,7,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,5,6,2,4,8,7,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,5,8,7,3,2,4,6]=>0011100=>[2,3,2]=>[2,3,2]
[1,4,2,3,5,8,7,6]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,5,2,3,4,8,7,6]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,6,5,2,3,8,7,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,7,4,2,8,6,5,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,7,6,5,2,8,4,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,6,7,5,2,3,8,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,7,5,2,8,4,3,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,7,5,6,2,8,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,7,6,2,4,8,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,5,8,3,2,4,7,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,6,5,2,3,7,4,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,6,5,2,3,7,8,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[1,6,8,4,2,3,7,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,7,4,6,2,8,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,3,5,2,8,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,8,5,2,3,7,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,6,4,2,3,7,8,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[1,6,4,2,3,7,5,8]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,5,8,6,2,4,7,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,5,7,3,2,4,8,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,7,3,4,2,8,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,4,2,8,5,3,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,6,7,4,2,3,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,6,4,2,3,8,5,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,7,6,4,2,8,5,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,7,5,2,8,6,4,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[1,6,4,2,3,8,7,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,3,5,6,1,4,8,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,7,5,6,1,4,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,2,4,1,6,7,5,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,6,1,4,2,7,5,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,6,1,4,2,8,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,7,4,3,5,8,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[6,7,1,4,3,5,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,6,1,4,3,5,8,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,5,4,1,6,7,8,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[4,7,1,6,3,5,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,4,7,6,5,8,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,1,7,4,3,5,8,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,1,6,4,3,5,8,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,7,6,4,3,5,8,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,1,6,4,2,7,5,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,4,1,3,7,2,5,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,7,1,3,8,2,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,4,1,3,8,2,5,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[1,3,6,4,2,8,5,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,7,3,1,2,8,5,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,7,8,1,2,6,5,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[6,8,1,4,2,7,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,6,4,2,7,5,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,8,1,3,7,2,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,7,1,3,6,2,5,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,8,5,7,3,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,8,4,3,7,2,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,8,3,4,7,6,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,7,8,4,6,2,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,7,4,6,8,2,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,4,3,7,8,6,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,4,7,3,8,2,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,7,6,8,3,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,5,3,4,8,6,1,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,7,5,4,8,2,1,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,1,3,4,2,8,5,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,4,3,8,2,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,1,7,3,8,2,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,1,4,3,7,2,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,2,3,4,7,6,1,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,2,3,7,8,6,1,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,2,3,4,8,6,1,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,7,5,6,3,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,2,6,3,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,2,6,8,4,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,2,5,6,8,4,1,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,2,3,8,5,6,1,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,2,3,8,7,6,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[8,2,3,7,5,6,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,8,3,7,2,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,8,4,2,6,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,7,1,8,2,5,6,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,4,8,5,2,1,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,4,3,8,5,6,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,8,3,6,2,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,5,8,6,3,2,1,4]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[6,5,8,7,3,2,1,4]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[8,5,7,6,3,2,1,4]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[2,5,3,8,7,6,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,7,5,8,6,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,7,8,6,5,2,1,4]=>0011110=>[2,4,1]=>[1,4,2]
[1,8,7,3,6,2,5,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,8,7,5,3,2,1,4]=>0111110=>[1,5,1]=>[1,5,1]
[5,7,6,8,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,6,8,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,4,7,6,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,4,6,5,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,4,6,5,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,4,8,6,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,4,6,5,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,4,7,5,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,2,7,5,8,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,4,8,5,7,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,4,6,5,7,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,4,8,6,7,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,5,4,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,5,2,4,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,6,5,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,8,5,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,6,5,8,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,2,7,6,8,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,6,8,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,6,8,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,6,8,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,5,6,1,3,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,6,7,1,3,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,2,7,6,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,6,8,2,4,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,3,2,6,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,6,2,4,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,6,7,2,4,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,4,2,6,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,4,2,5,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,1,4,3,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,8,1,2,4,3,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,3,6,5,8,7,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,6,5,7,8,1,2]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,1,5,6,7,8,9,2]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[3,4,5,1,6,7,8,9,2]=>00100001=>[2,1,4,1]=>[1,4,1,2]
[3,4,5,6,1,7,8,9,2]=>00010001=>[3,1,3,1]=>[1,3,1,3]
[3,4,5,6,7,1,8,9,2]=>00001001=>[4,1,2,1]=>[1,2,1,4]
[3,4,5,6,7,8,1,9,2]=>00000101=>[5,1,1,1]=>[1,1,1,5]
[3,1,2,5,6,7,8,9,4]=>10000001=>[1,6,1]=>[1,6,1]
[3,4,1,5,6,7,8,9,10,2]=>010000001=>[1,1,6,1]=>[1,6,1,1]
[3,4,1,2,6,7,8,9,5]=>01000001=>[1,1,5,1]=>[1,5,1,1]
[3,4,5,1,6,7,8,9,10,2]=>001000001=>[2,1,5,1]=>[1,5,1,2]
[3,4,5,1,2,7,8,9,6]=>00100001=>[2,1,4,1]=>[1,4,1,2]
[3,4,5,6,1,7,8,9,10,2]=>000100001=>[3,1,4,1]=>[1,4,1,3]
[3,4,5,6,1,2,8,9,7]=>00010001=>[3,1,3,1]=>[1,3,1,3]
[3,4,5,6,7,1,8,9,10,2]=>000010001=>[4,1,3,1]=>[1,3,1,4]
[3,4,5,6,7,1,2,9,8]=>00001001=>[4,1,2,1]=>[1,2,1,4]
[3,4,5,6,7,8,1,9,10,2]=>000001001=>[5,1,2,1]=>[1,2,1,5]
[3,4,5,6,7,8,1,2,9]=>00000100=>[5,1,2]=>[2,1,5]
[3,4,5,6,7,8,9,1,10,2]=>000000101=>[6,1,1,1]=>[1,1,1,6]
[1,6,2,3,8,7,4,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,7,4,3,2,8,6,5]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,4,7,6,2,5,8,3]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,2,6,5,3,7,4,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,2,6,5,3,7,8,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,3,7,5,2,6,8,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,3,7,4,2,6,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,2,6,4,3,7,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,2,6,4,3,7,5,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,4,7,3,2,5,8,6]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,4,3,2,5,8,6,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,5,3,2,4,8,6,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,7,5,3,2,8,6,4]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[1,5,3,2,4,8,7,6]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,6,5,4,3,1,8,2]=>1111101=>[5,1,1]=>[1,1,5]
[6,8,5,4,3,2,1,7]=>0111110=>[1,5,1]=>[1,5,1]
[8,7,6,5,4,3,1,9,2]=>11111101=>[6,1,1]=>[1,1,6]
[7,9,6,5,4,3,2,1,8]=>01111110=>[1,6,1]=>[1,6,1]
[9,8,7,6,5,4,3,1,10,2]=>111111101=>[7,1,1]=>[1,1,7]
[1,7,6,5,4,3,9,8,2]=>01111011=>[1,4,1,2]=>[2,1,4,1]
[7,1,5,4,3,8,6,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,6,5,4,8,1,7,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,8,1,4,3,2,7,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,5,4,3,7,1,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,9,6,5,4,3,2,8,7]=>01111101=>[1,5,1,1]=>[1,1,5,1]
[8,10,7,6,5,4,3,2,1,9]=>011111110=>[1,7,1]=>[1,7,1]
[10,9,8,7,6,5,4,3,1,11,2]=>1111111101=>[8,1,1]=>[1,1,8]
[1,8,7,6,5,4,3,10,9,2]=>011111011=>[1,5,1,2]=>[2,1,5,1]
[8,1,6,5,4,3,9,7,2]=>10111011=>[1,1,3,1,2]=>[2,1,3,1,1]
[3,7,6,5,4,9,1,8,2]=>01110101=>[1,3,1,1,1,1]=>[1,1,1,1,3,1]
[7,6,1,4,3,8,5,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,6,5,8,3,1,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,8,5,1,3,2,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,2,4,3,7,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,9,1,5,4,3,2,8,6]=>01011101=>[1,1,1,3,1,1]=>[1,1,3,1,1,1]
[3,8,5,4,7,2,1,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,9,6,5,4,3,8,1,7]=>01111010=>[1,4,1,1,1]=>[1,1,1,4,1]
[1,10,7,6,5,4,3,2,9,8]=>011111101=>[1,6,1,1]=>[1,1,6,1]
[9,11,8,7,6,5,4,3,2,1,10]=>0111111110=>[1,8,1]=>[1,8,1]
[11,10,9,8,7,6,5,4,3,1,12,2]=>11111111101=>[9,1,1]=>[1,1,9]
[1,9,8,7,6,5,4,3,11,10,2]=>0111111011=>[1,6,1,2]=>[2,1,6,1]
[9,1,7,6,5,4,3,10,8,2]=>101111011=>[1,1,4,1,2]=>[2,1,4,1,1]
[3,8,7,6,5,4,10,1,9,2]=>011110101=>[1,4,1,1,1,1]=>[1,1,1,1,4,1]
[8,7,1,5,4,3,9,6,2]=>11011011=>[2,1,2,1,2]=>[2,1,2,1,2]
[1,3,6,5,4,9,8,7,2]=>00110111=>[2,2,1,3]=>[3,1,2,2]
[4,7,6,5,9,3,1,8,2]=>01101101=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[7,6,5,1,3,8,4,2]=>1110011=>[3,2,2]=>[2,2,3]
[1,6,3,4,8,7,5,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,4,5,8,3,7,6,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[6,8,5,4,1,2,7,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[1,8,5,2,3,7,6,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,9,6,1,4,3,2,8,5]=>01101101=>[1,2,1,2,1,1]=>[1,1,2,1,2,1]
[6,8,2,4,3,7,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,3,4,7,2,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,9,2,5,4,3,8,7,6]=>01011011=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
[8,10,1,6,5,4,3,2,9,7]=>010111101=>[1,1,1,4,1,1]=>[1,1,4,1,1,1]
[7,5,8,4,3,2,1,6]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[4,8,5,7,3,2,1,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,9,6,5,4,8,2,1,7]=>01110110=>[1,3,1,2,1]=>[1,2,1,3,1]
[2,10,7,6,5,4,3,9,1,8]=>011111010=>[1,5,1,1,1]=>[1,1,1,5,1]
[1,11,8,7,6,5,4,3,2,10,9]=>0111111101=>[1,7,1,1]=>[1,1,7,1]
[10,12,9,8,7,6,5,4,3,2,1,11]=>01111111110=>[1,9,1]=>[1,9,1]
[5,1,7,6,8,4,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,4,8,5,2,7,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,1,8,6,7,4,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,4,7,5,2,6,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,4,6,8,2,1,7,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,4,5,8,1,2,7,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,4,6,5,2,1,8,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,4,6,5,2,1,7,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,8,7,5,6,1,3,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,7,5,1,8,4,3,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,1,8,7,4,2,3,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[2,8,6,7,4,3,5,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,6,5,2,4,1,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,2,3,6,4,1,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,1,4,5,3,2,8,7]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,8,7,1,4,6,5,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,7,1,2,4,3,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,3,7,6,8,2,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,6,8,1,7,2,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,2,6,8,5,7,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,3,7,2,4,8,5,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,4,8,6,5,2,1,3]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,1,8,2,5,4,3,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,5,3,7,4,1,8,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,6,4,7,5,1,8,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,4,7,6,2,3,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,4,7,1,2,5,6,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,2,8,7,3,5,6,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,1,7,4,2,5,6,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,4,3,8,2,5,6,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,4,1,5,8,2,7,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,5,8,7,3,6,1,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,1,5,8,7,4,6,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,3,5,6,7,4,1,2]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,4,3,2,8,5,6,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,2,7,1,8,5,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,2,8,5,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,8,7,3,5,6,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[4,7,8,3,1,5,6,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,4,7,2,8,5,6,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,7,1,4,8,5,6,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,2,3,4,8,5,6,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,1,8,5,2,7,4,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,1,7,4,5,8,6,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,8,3,6,7,5,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,2,1,6,4,7,5,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,8,2,6,4,1,5,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,3,5,8,7,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,6,2,1,5,8,4,3]=>1110011=>[3,2,2]=>[2,2,3]
[4,5,2,7,6,1,8,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,6,8,4,7,2,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,8,7,5,2,1,4]=>0011110=>[2,4,1]=>[1,4,2]
[7,4,8,6,5,2,3,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,1,6,4,7,3,2,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,6,4,1,2,3,8,5]=>1110001=>[3,3,1]=>[1,3,3]
[2,6,4,8,5,3,7,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,3,5,8,4,2,1,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,2,5,8,4,1,7,6]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,4,7,1,5,2,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,8,7,5,6,1,2,3]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,1,4,8,7,3,5,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,2,8,4,3,5,6,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,7,8,1,3,5,6,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[8,7,3,4,1,5,6,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,8,2,7,3,5,6,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,8,7,2,5,6,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,8,1,7,2,5,6,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,2,3,7,1,5,6,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,4,8,7,1,3,2,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,8,4,6,7,3,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,8,2,7,6,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,8,4,2,1,3,7,5]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,8,2,4,3,5,6,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,3,7,1,5,6,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,1,2,7,3,5,6,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,4,1,3,2,8,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,8,6,2,1,4,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,6,5,2,8,3,1,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,3,7,5,1,8,2,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,8,5,2,7,4,3,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[7,2,5,4,3,8,1,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,6,8,1,4,5,2,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,8,1,2,4,5,3,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,1,6,2,4,5,3,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,8,6,1,2,5,4,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,8,1,6,2,3,4,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,1,6,5,8,2,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,8,6,2,5,1,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,6,1,4,5,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,3,6,8,4,5,1,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,7,5,4,3,8,1,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,3,8,7,4,2,5,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,8,4,3,7,6,1,2]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,7,4,3,1,6,2,5]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[1,7,4,3,8,6,2,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,1,5,3,4,8,2,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,6,1,7,4,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,6,5,7,2,1,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,7,6,8,2,1,5,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,1,8,7,4,3,5,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,5,4,3,1,6,7,2]=>1111001=>[4,2,1]=>[1,2,4]
[1,5,8,6,3,4,7,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,5,8,6,3,4,7,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[4,1,3,8,5,6,7,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,5,8,4,3,1,7,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,6,5,2,8,1,7,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,2,8,1,3,6,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,5,2,3,6,7,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[1,8,3,2,5,6,7,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,8,3,1,5,6,7,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[4,8,3,2,5,6,7,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[8,2,3,1,5,6,7,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,1,8,3,5,6,7,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,4,8,2,3,6,7,5]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,1,2,7,8,6,4,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,5,1,8,2,4,3,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,8,1,2,4,7,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,5,8,1,2,3,7,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,2,7,1,8,6,3,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,8,4,1,2,6,7,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[5,4,8,2,3,6,7,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,8,3,6,7,4,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,3,1,6,8,4,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,3,7,1,8,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,7,3,2,8,5,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,7,1,4,3,8,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,1,8,6,3,7,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,4,1,3,6,2,7,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,8,5,1,7,2,3,4]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,3,6,5,8,2,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,6,3,5,8,2,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,5,8,7,3,6,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,5,2,8,6,1,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,2,5,6,1,4,7,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,6,5,4,1,2,7,3]=>1111001=>[4,2,1]=>[1,2,4]
[2,6,1,8,3,7,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,1,6,2,8,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,1,5,3,8,7,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,6,3,7,1,5,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,6,1,5,8,2,3,4]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,6,8,5,1,2,7,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[6,5,2,4,8,1,7,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,1,4,8,2,6,7,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,8,2,5,1,6,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,8,5,2,6,7,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[4,2,1,8,5,6,7,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,5,4,8,2,6,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,1,5,8,6,3,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[2,8,4,5,1,6,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,4,8,3,7,6,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,5,8,6,2,7,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,3,4,8,5,1,7,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,3,4,8,1,6,7,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,6,1,2,8,3,5,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,5,8,4,1,2,6,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,5,8,4,6,1,3,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,4,8,7,1,3,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,5,4,8,1,2,7,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,1,6,2,3,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,5,1,6,8,2,4,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,4,1,8,2,7,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,5,4,7,1,2,8,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,5,4,7,8,1,3,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,3,7,1,4,2,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,3,1,8,4,2,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,5,1,4,8,3,2,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,1,6,4,7,3,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,1,4,8,3,6,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,3,7,1,4,8,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,4,3,1,5,8,7,2]=>1110011=>[3,2,2]=>[2,2,3]
[7,4,1,5,3,8,6,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,1,5,4,3,7,6,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,1,5,4,3,7,2,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,4,1,5,3,8,2,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,1,5,3,2,6,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,1,5,4,3,2,6,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,1,6,4,2,5,3,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,5,3,1,2,7,4,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,5,3,8,1,4,2,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,8,1,4,3,2,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,1,7,2,5,4,3,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,1,7,2,5,4,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,1,2,5,4,8,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,3,8,1,4,7,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,5,3,1,2,7,8,4]=>1110001=>[3,3,1]=>[1,3,3]
[7,5,1,4,2,6,8,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,1,6,4,2,5,7,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,4,1,5,3,2,8,6]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,3,1,5,2,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,4,3,1,5,7,2,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,4,1,5,3,6,2,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,1,5,4,3,6,2,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,1,5,4,3,6,7,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,4,1,5,3,6,8,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,4,3,1,5,7,8,2]=>1110001=>[3,3,1]=>[1,3,3]
[6,7,3,8,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,4,5,1,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,5,6,2,3,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,5,6,1,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,5,6,3,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,5,8,4,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,3,8,6,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,6,5,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,4,7,1,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,1,7,3,8,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,1,8,2,7,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,1,8,4,7,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,1,6,5,7,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,1,8,6,7,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,4,5,1,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,2,3,1,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,8,1,4,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,3,4,1,8,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,4,5,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,4,5,1,8,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,4,8,1,5,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,3,6,1,5,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,3,4,1,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,5,3,4,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,5,3,6,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,3,8,6,7,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,3,6,2,7,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,6,4,8,2,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,4,7,3,5,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,3,6,4,5,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,3,6,4,8,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,2,8,4,6,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,5,8,4,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,5,8,2,6,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,7,5,6,3,8,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,5,6,3,4,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,2,5,3,4,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,1,5,3,8,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,5,8,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,6,7,2,3,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,2,3,1,8,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,2,8,1,4,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,2,7,5,6,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,1,7,5,8,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,5,8,1,4,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,1,7,5,8,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,1,8,4,7,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,3,1,6,4,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,6,1,4,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,6,7,1,4,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,1,4,3,7,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,2,5,4,6,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,2,7,3,6,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,1,8,2,7,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,1,8,2,7,5,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,1,8,6,7,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,2,5,1,8,6,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,2,8,1,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,2,5,1,6,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,2,8,1,6,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,3,6,1,8,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,7,1,4,2,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,6,3,7,5,1,2,4]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,6,1,8,3,5,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,2,8,3,5,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,2,3,8,5,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,7,1,5,2,6,3,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,7,1,5,2,3,6,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,5,2,3,1,7,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,6,2,3,7,1,5,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,6,2,7,3,1,5,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,7,2,5,1,6,3,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,2,1,7,6,3,5]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,5,7,2,1,4,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,7,3,1,4,2,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,8,7,3,1,4,6,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,5,7,2,1,4,6,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,4,2,1,3,7,6,5]=>1110011=>[3,2,2]=>[2,2,3]
[8,4,3,1,7,2,6,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,6,1,3,7,2,5,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,5,1,3,2,7,6,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,1,5,8,4,2,7,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,2,8,6,4,1,3,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,4,7,5,1,6,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,4,7,5,1,2,3,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,7,3,5,1,2,6,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,3,2,6,5,1,4,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[4,8,6,3,5,1,2,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,8,7,3,1,5,2,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,4,7,2,1,5,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,7,3,1,4,2,6,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,3,1,2,6,4,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,7,3,1,2,4,6,5]=>1110001=>[3,3,1]=>[1,3,3]
[8,3,2,1,4,7,6,5]=>1110011=>[3,2,2]=>[2,2,3]
[8,3,2,1,7,4,6,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,3,2,7,1,5,6,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,4,7,2,1,5,6,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,7,2,1,6,3,4,5]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[3,6,5,4,1,2,8,7]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[3,8,5,6,7,4,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,7,5,8,6,2,1,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,5,7,8,6,3,4,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,8,5,7,6,3,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,6,3,2,1,5,8,7]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[6,2,1,5,3,4,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,8,1,3,7,6,4,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,7,2,3,6,1,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,7,4,2,8,1,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,6,8,5,7,3,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,4,2,7,3,8,5,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,1,6,7,5,3,4,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,5,8,7,6,3,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[2,1,4,7,6,3,8,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,4,7,8,5,3,2,1]=>1001111=>[1,2,4]=>[4,2,1]
[4,1,3,7,6,2,8,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,5,1,6,3,2,7,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,3,7,1,5,2,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,6,8,4,7,5,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,4,6,1,3,2,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,8,6,7,3,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,4,3,8,2,1,5,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[4,7,5,8,1,6,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,3,2,7,8,1,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[4,2,5,1,6,7,8,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,4,8,5,7,1,3,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,7,1,4,6,8,5,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[7,8,2,5,6,1,4,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,3,8,7,5,6,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,6,7,3,5,1,8,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,8,4,2,5,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,5,7,1,6,3,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,7,2,8,4,3,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,4,8,6,5,2,1,7]=>0011110=>[2,4,1]=>[1,4,2]
[2,7,6,1,4,5,8,3]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[6,5,8,2,1,7,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,4,3,5,1,6,8,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,1,6,3,5,8,7,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,2,5,8,4,3,7,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,6,7,1,5,4,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,1,6,5,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,6,8,5,4,3,7]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[4,1,8,5,6,2,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,4,8,7,3,5,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,2,8,4,3,5,1,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,8,2,7,6,1,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,1,8,2,7,5,4,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,8,1,2,6,7,4,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,8,4,3,2,7,1,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,4,8,6,3,2,5,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,8,4,7,2,1,3,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,8,4,3,7,5,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,3,8,2,4,5,7,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,8,4,2,3,6,1,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,8,2,4,3,1,6,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,8,3,1,6,4,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,2,1,3,4,7,5,6]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[1,4,8,2,6,3,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,7,3,5,4,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,3,8,4,5,7,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,2,8,3,4,5,7,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,3,8,2,6,4,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,5,7,2,3,6,4,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,7,2,3,5,4,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,8,2,4,5,7,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,2,3,8,4,6,7,5]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,8,2,3,5,4,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,7,8,2,3,6,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,6,7,8,2,3,5,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,7,8,2,5,3,6,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,7,8,2,4,5,3,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,2,8,3,6,4,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,8,2,3,6,4,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,8,3,5,4,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,7,8,3,6,4,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,5,2,7,8,3,6,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,2,8,4,6,7,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,8,2,3,4,6,7,5]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,7,8,2,4,3,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,3,1,5,2,4,8]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,7,3,1,5,2,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,8,3,1,5,2,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,8,4,5,1,2,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,7,4,5,1,2,8,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,1,6,5,3,4,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,3,6,1,5,2,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,4,6,5,1,2,3,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,7,5,4,1,2,8,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[5,8,6,4,1,7,2,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,7,6,4,1,8,2,3]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,6,7,4,1,8,2,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,7,4,1,2,8,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,4,7,5,1,2,8,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,2,1,7,5,3,8,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,3,8,1,5,2,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,8,5,1,2,7,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,5,8,4,1,2,7,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,6,8,4,1,7,2,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,6,8,5,7,1,2,3]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,5,8,6,7,1,2,3]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,4,8,6,1,7,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,3,8,1,6,7,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,2,1,8,6,7,3,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,2,1,7,6,8,3,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,4,7,6,1,8,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,5,7,6,8,1,2,3]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,6,7,5,8,1,2,3]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,8,6,5,7,1,2,3]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,8,5,6,7,1,2,3]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,7,5,6,8,1,2,3]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,6,5,7,8,1,2,3]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,7,4,6,1,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,6,1,7,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,1,6,7,2,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,7,3,1,6,8,2,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,6,3,1,7,8,2,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,2,1,4,3,8,7,5]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,8,3,1,7,6,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,7,4,8,1,6,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,1,6,8,7,3,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,4,6,8,1,7,2,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,6,8,7,1,2,3]=>0001100=>[3,2,2]=>[2,2,3]
[4,7,5,8,6,1,2,3]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,8,5,7,6,1,2,3]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,8,6,7,5,1,2,3]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,7,6,8,5,1,2,3]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,6,7,8,5,1,2,3]=>0001100=>[3,2,2]=>[2,2,3]
[4,5,7,8,6,1,2,3]=>0001100=>[3,2,2]=>[2,2,3]
[5,4,7,8,1,6,2,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,7,1,8,6,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,2,1,7,8,6,3,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,3,8,1,7,6,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,4,8,7,1,6,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,8,7,5,1,2,3]=>0011100=>[2,3,2]=>[2,3,2]
[4,7,8,6,5,1,2,3]=>0011100=>[2,3,2]=>[2,3,2]
[4,8,7,6,5,1,2,3]=>0111100=>[1,4,2]=>[2,4,1]
[2,5,4,7,3,6,1,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,6,3,7,5,1,8]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,2,7,3,6,5,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,2,6,3,1,5,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,5,3,1,6,4,8,7]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,5,3,7,6,4,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,6,5,3,7,4,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,7,6,3,5,1,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,7,5,3,6,4,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,6,3,7,5,4,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,7,5,2,3,8,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,1,3,7,5,4,8,6]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,3,1,8,6,5,4,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,5,3,1,8,6,4,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,8,3,1,6,5,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,3,2,6,4,1,5,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,6,8,2,1,4,5,7]=>0011000=>[2,2,3]=>[3,2,2]
[1,5,2,8,3,4,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,2,6,3,8,7,4,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,8,3,6,4,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,7,6,3,4,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,1,3,8,7,5,4,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[1,2,3,8,6,4,7,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,3,7,4,8,6,5]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,7,6,3,8,4,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,2,3,6,4,8,7,5]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,3,7,6,4,8,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,6,3,1,8,5,4,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,1,3,8,5,4,7,6]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,1,8,4,2,3,5,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[2,1,8,4,3,5,7,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,2,6,3,1,8,5,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,4,2,8,3,1,6,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[3,5,8,2,4,1,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,5,4,8,3,1,6,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,2,1,8,3,5,7,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,8,7,4,2,3,5,6]=>0111000=>[1,3,3]=>[3,3,1]
[1,5,2,8,7,3,4,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,2,7,3,6,4,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,8,6,3,7,4,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,2,7,3,8,6,4,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,3,8,4,7,6,5]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,7,3,4,8,6,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,6,3,8,4,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,5,2,3,8,7,4,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,2,1,8,3,7,5,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,3,2,1,7,4,5,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[1,8,4,2,7,3,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,2,8,6,3,4,7,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,2,7,3,8,4,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,3,8,7,4,6,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,3,8,7,6,4,5]=>0001110=>[3,3,1]=>[1,3,3]
[2,5,3,8,1,6,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,4,7,1,5,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,5,7,1,4,3,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,5,7,1,2,6,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,8,5,7,2,6,4,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,4,8,6,2,5,7,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,4,8,6,1,2,5,7]=>0011000=>[2,2,3]=>[3,2,2]
[2,5,7,1,4,8,6,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,4,8,1,5,7,6,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,4,3,8,1,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,8,1,7,5,6,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,3,8,1,6,5,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,8,1,3,5,7,6]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,5,7,6,1,2,4,8]=>0011000=>[2,2,3]=>[3,2,2]
[3,5,7,6,2,4,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[4,8,6,7,2,3,5,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,6,7,1,2,3,5]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,8,6,7,1,3,5,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,4,8,6,1,5,7,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,8,5,7,1,6,4,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,8,5,6,1,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,5,7,2,1,6,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,8,6,2,1,5,7]=>0011100=>[2,3,2]=>[2,3,2]
[3,5,7,6,2,1,4,8]=>0011100=>[2,3,2]=>[2,3,2]
[4,8,6,7,2,1,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,8,6,7,3,5,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,6,7,3,4,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,6,7,2,1,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,8,6,7,2,1,4,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,8,6,7,2,1,5,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,3,1,7,5,2,8,6]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,3,2,8,5,1,7,6]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,3,8,5,1,6,7,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,8,6,7,1,5,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,6,7,1,4,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,6,7,2,3,4,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,6,7,2,4,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,6,7,1,2,4,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,2,3,8,5,1,6,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,2,8,5,1,7,6,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,4,2,8,5,6,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,2,4,8,6,1,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,2,5,7,6,1,4,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,8,6,7,1,3,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,6,7,1,2,5,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,6,7,2,5,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,8,5,2,6,7,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,8,5,1,2,6,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,2,6,7,5,1,3,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,8,5,7,1,4,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,4,7,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,2,8,4,6,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,5,1,7,4,6,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,4,7,2,5,1,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,3,8,5,2,6,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,1,2,6,7,5,3,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,2,6,7,5,3,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,8,6,7,3,2,5,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,8,6,7,3,1,2,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,1,5,7,6,2,4,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,4,1,7,5,6,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,5,2,8,6,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,6,7,5,2,3,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,8,6,7,2,3,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,6,7,3,2,4,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,6,7,4,2,3,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,6,7,4,1,2,3]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,8,6,7,4,1,3,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,6,7,3,1,4,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,8,6,7,3,1,5,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,1,6,7,5,3,8,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,1,7,5,3,2,8,6]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,2,8,5,3,1,7,6]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,2,1,6,7,5,3,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,8,6,7,3,2,1,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,8,6,7,4,2,1,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,8,6,7,4,3,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,3,5,8,1,4,2,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,8,7,6,1,4,2,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,1,8,3,6,7,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,4,7,8,5,6,2,3]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,7,1,5,8,6,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,6,1,4,7,8,5,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[1,6,8,4,7,5,2,3]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,8,1,3,5,7,2,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,6,1,4,3,8,2,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,8,1,6,5,4,2,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,1,3,7,5,8,2,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,7,3,8,4,2,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,1,8,6,3,5,2,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,7,6,5,8,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,2,7,6,5,3,4,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,4,2,6,7,5,3,1]=>1100111=>[2,2,3]=>[3,2,2]
[4,8,1,6,7,5,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[7,4,1,6,8,2,5,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,3,8,6,2,7,5,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[6,1,3,2,7,8,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,6,2,5,3,4,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,7,2,6,8,1,5,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,7,3,6,4,5,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,7,8,6,2,1,4,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,7,4,1,6,8,3,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,7,2,4,5,1,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,8,6,4,5,2,3,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,8,4,6,5,1,3,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,4,1,7,5,2,6,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,5,8,6,1,2,4,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,6,8,7,3,1,4,2]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,5,4,3,6,8,1,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,8,5,4,6,2,1,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,8,2,1,3,7,5,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,4,1,2,7,5,8,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,1,8,3,6,7,5,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,3,7,4,5,2,6,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,7,8,5,1,6,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,4,8,2,7,6,1,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,2,7,3,6,5,8,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,8,7,6,3,4,1,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,8,2,6,3,4,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,5,8,6,2,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,1,7,8,4,3,6,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,2,7,5,4,3,6,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,3,8,1,4,7,5,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,8,4,5,6,1,2,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,4,3,5,7,8,2,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,5,8,7,1,3,4,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,6,7,2,4,8,1,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,5,2,7,4,3,8,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,5,6,4,3,1,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,8,6,5,4,3,2,7]=>0111110=>[1,5,1]=>[1,5,1]
[6,1,5,2,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,1,8,5,7,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,1,2,8,5,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,4,7,2,8,5,6,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,7,3,5,8,6,2,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,3,5,8,6,1,2,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,6,8,1,5,7,2,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,4,6,5,8,1,7,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,8,1,5,7,2,3,4]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,1,2,5,8,6,3,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,7,2,5,8,6,3,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,7,6,8,2,3,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,6,8,1,2,3,5,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[2,7,1,5,8,6,3,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,4,7,1,8,5,6,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,7,5,8,3,1,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,7,2,1,8,5,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,6,8,2,1,3,5,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,2,7,6,8,3,5,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,7,6,8,2,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,4,2,1,6,8,5,3]=>1110011=>[3,2,2]=>[2,2,3]
[6,7,4,1,8,5,3,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,7,4,3,1,8,5,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[2,7,4,1,6,8,5,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,3,7,6,8,1,5,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,2,6,8,5,1,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[7,3,2,5,8,6,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,1,7,6,8,2,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,6,8,1,2,5,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,7,6,8,2,5,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,7,4,2,6,8,5,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,4,1,2,6,8,5,3]=>1100011=>[2,3,2]=>[2,3,2]
[7,1,4,2,8,5,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,8,2,5,4,6,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,8,4,6,1,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,8,1,6,4,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,6,8,5,4,2,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,1,2,6,8,5,4,3]=>1000111=>[1,3,3]=>[3,3,1]
[1,7,2,6,8,5,4,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,7,6,8,3,2,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,6,8,3,1,2,5,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,1,5,8,6,3,2,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,2,5,8,6,3,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,6,7,1,8,5,4,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[7,2,6,8,5,4,1,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,6,8,2,3,1,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,6,8,3,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,7,1,6,8,5,4,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[6,7,3,1,8,5,4,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[6,7,1,8,5,4,3,2]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[7,2,1,6,8,5,4,3]=>1100111=>[2,2,3]=>[3,2,2]
[7,6,8,3,2,1,5,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,7,8,5,6,1,3,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,5,8,7,1,3,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,6,4,8,1,2,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,1,5,6,7,2,4,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,4,5,1,8,2,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,7,1,2,8,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,3,6,7,2,1,5,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,3,6,7,1,4,2,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,1,4,6,7,3,2,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[8,1,3,6,7,4,5,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,2,1,6,8,4,5,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,2,6,7,1,4,8,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,6,7,3,1,8,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,2,4,1,5,8,7,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,2,1,5,4,8,6,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,1,4,5,3,7,2,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,3,1,5,4,8,2,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,4,1,5,8,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,3,4,2,1,8,6,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,3,5,2,7,1,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,3,8,1,4,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,2,4,5,6,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,6,1,2,4,5,8,3]=>1100001=>[2,4,1]=>[1,4,2]
[4,7,8,2,3,1,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,6,2,8,1,4,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,2,1,3,7,8,4]=>1110001=>[3,3,1]=>[1,3,3]
[7,5,1,3,2,6,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,1,6,3,2,5,7,4]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,4,1,3,5,2,8,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,4,2,3,1,6,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,3,1,4,5,6,2,8]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[8,1,4,3,5,6,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,2,3,1,5,7,8,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,8,4,2,1,6,5,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[7,8,4,2,1,5,6,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[6,2,3,4,8,7,1,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,2,3,4,7,8,1,5]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[7,8,3,4,6,2,1,5]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,8,3,6,4,2,1,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,8,3,5,6,2,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,2,3,8,7,5,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,2,3,7,8,5,1,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,2,6,3,8,1,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,2,5,8,7,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,3,2,8,4,7,1,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,4,3,8,7,5,1,2]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,4,3,7,8,5,1,2]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,2,4,1,7,3,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,2,7,4,8,1,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,2,5,7,8,1,4]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,7,2,3,6,1,8,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,2,3,6,1,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,7,5,8,3,2,1,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,5,6,8,3,2,1,7]=>0001110=>[3,3,1]=>[1,3,3]
[4,6,8,5,3,2,1,7]=>0011110=>[2,4,1]=>[1,4,2]
[5,6,1,4,2,3,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,6,8,4,3,7,1,2]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,6,1,4,2,3,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,2,8,3,4,1,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,5,8,6,3,2,1,7]=>0011110=>[2,4,1]=>[1,4,2]
[4,6,5,8,3,2,1,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,7,5,6,3,2,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,2,3,4,5,8,1,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[5,1,4,3,6,2,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,4,3,7,2,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,4,3,8,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,2,4,1,7,8,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,6,2,4,1,8,7,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,7,2,4,1,8,6,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,1,4,2,8,7,5,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,1,4,2,7,8,5,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,8,2,4,1,7,6,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,2,7,4,1,6,8,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,4,1,3,7,2,6,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,1,4,3,6,2,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,8,6,4,3,7,1,2]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,8,1,4,2,3,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,1,6,3,4,2,7,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,8,6,5,3,2,1,7]=>0111110=>[1,5,1]=>[1,5,1]
[4,8,5,6,3,2,1,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,4,7,8,3,2,1,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[5,4,8,7,3,2,1,6]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[4,6,8,7,3,2,1,5]=>0011110=>[2,4,1]=>[1,4,2]
[4,6,7,8,3,2,1,5]=>0001110=>[3,3,1]=>[1,3,3]
[4,7,6,8,3,2,1,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,7,8,5,3,2,1,6]=>0011110=>[2,4,1]=>[1,4,2]
[5,7,1,3,4,2,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,1,8,4,2,3,6,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,1,7,4,2,3,6,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[5,8,1,3,4,2,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,8,7,5,3,2,1,6]=>0111110=>[1,5,1]=>[1,5,1]
[4,7,8,6,3,2,1,5]=>0011110=>[2,4,1]=>[1,4,2]
[4,8,7,6,3,2,1,5]=>0111110=>[1,5,1]=>[1,5,1]
[4,8,2,6,3,7,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,8,2,3,6,7,5,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,8,3,1,6,7,5,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[4,3,8,1,6,2,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,4,8,7,3,5,2,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,3,8,7,2,5,1,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,4,3,7,1,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,8,1,4,7,2,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,8,1,7,4,2,3,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,8,1,2,4,3,5,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,8,7,1,3,4,2,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,8,7,6,3,1,2,5]=>0111100=>[1,4,2]=>[2,4,1]
[5,8,4,7,3,1,2,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,3,8,2,7,5,6,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,4,8,3,7,5,6,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,3,8,2,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,3,2,8,1,6,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,1,3,8,2,6,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,1,8,3,7,5,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,8,7,3,5,2,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,7,8,1,5,4,2,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,3,8,1,5,4,6,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,8,1,6,2,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,4,8,7,2,5,1,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,4,8,2,7,5,6,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,4,8,3,6,5,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,4,3,8,6,5,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,4,2,1,8,6,5,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,4,1,8,2,6,5,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,7,8,4,1,2,5]=>0001100=>[3,2,2]=>[2,2,3]
[4,1,7,8,5,3,2,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[4,1,2,8,3,6,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,3,2,8,6,5,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,2,3,1,8,6,5,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,6,8,4,2,1,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,7,1,8,5,2,3,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,6,8,7,4,3,1,5]=>0011110=>[2,4,1]=>[1,4,2]
[3,7,8,6,2,4,1,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,7,8,2,6,4,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,2,3,8,1,6,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,1,8,2,6,5,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,7,8,5,3,2,6]=>0001110=>[3,3,1]=>[1,3,3]
[4,3,7,8,5,2,1,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,7,2,8,4,6,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,8,6,3,1,5,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[2,6,8,4,7,3,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,4,8,6,3,1,5,7]=>0011100=>[2,3,2]=>[2,3,2]
[7,3,6,8,4,2,1,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,6,2,8,3,5,4,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,7,3,8,4,6,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,3,4,8,2,6,5,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,2,4,8,1,6,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,3,8,6,2,4,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,3,8,2,6,4,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,8,3,6,1,5,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,2,8,7,4,3,5,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,4,1,8,5,2,6,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,3,2,8,4,6,5,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,4,3,1,8,6,5,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,3,4,2,8,6,5,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,3,2,4,8,6,5,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,2,1,4,8,6,5,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[3,1,2,4,8,6,5,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,1,4,2,8,6,5,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,4,8,2,6,5,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,3,4,8,5,1,6,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,7,4,8,5,1,2,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,7,2,8,3,5,4,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,3,1,4,8,6,5,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,1,3,4,8,6,5,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,2,3,4,8,6,5,7]=>0000110=>[4,2,1]=>[1,2,4]
[4,8,3,6,2,1,5,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,5,8,2,6,1,4,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,6,5,8,2,4,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,8,7,2,4,6,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,8,4,5,7,3,6,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,4,5,7,3,8,1,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,2,4,5,8,3,1,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,8,1,2,5,6,3,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,1,3,5,2,6,4,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,2,1,6,3,8,4,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,2,5,1,8,4,3,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,1,5,8,4,2,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,1,4,5,8,3,2,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,6,4,8,1,3,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,5,4,3,8,2,1,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[5,4,3,7,2,8,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,8,4,3,7,2,6,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,6,8,3,7,2,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,6,3,2,8,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,4,3,6,2,7,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,4,3,7,2,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,7,8,5,3,1,2,6]=>0011100=>[2,3,2]=>[2,3,2]
[5,7,3,4,1,2,8,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,5,4,7,6,2,1,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,5,7,4,3,6,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,3,8,1,6,7,5,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,7,8,3,6,1,5,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,8,6,7,4,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,8,6,4,7,5,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[8,6,2,7,4,1,5,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,6,2,1,4,3,8,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,6,1,3,4,2,8,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,5,7,3,2,6,8,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,6,7,3,2,5,8,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[3,2,6,8,5,7,4,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,8,2,3,6,7,4,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[7,5,2,3,1,6,8,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,6,4,7,2,3,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,1,7,5,2,8,4,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,5,7,4,1,8,3,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,2,6,1,7,8,3,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,2,7,6,3,8,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,4,8,7,2,3,5,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,2,6,8,7,4,5,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,2,7,4,1,6,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,2,1,7,8,4,5]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,7,1,8,4,2,5,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,2,1,3,7,5,8,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,1,3,7,4,2,6,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,4,3,7,6,2,1,5]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[8,3,5,2,7,6,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,2,8,7,1,5,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,3,2,8,1,6,5,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,8,7,2,6,5,4,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,2,7,8,6,1,5,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,8,2,4,7,1,5,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,2,1,8,7,3,6,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,2,1,6,3,7,5,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,8,3,1,7,5,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,8,1,6,7,2,4,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,2,8,1,5,7,4,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,7,8,2,6,1,4,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,7,2,5,6,4,3,1]=>1100111=>[2,2,3]=>[3,2,2]
[8,6,7,5,2,4,3,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,2,6,8,1,5,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,2,7,8,5,6,4,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[7,4,8,1,6,2,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,1,8,2,6,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,7,3,8,6,5,4]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,2,1,7,6,5,4,3]=>1101111=>[2,1,4]=>[4,1,2]
[8,1,4,7,6,5,3,2]=>1001111=>[1,2,4]=>[4,2,1]
[8,6,7,5,1,4,3,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,8,6,5,4,1,3,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,8,4,3,2,1,6,7]=>0111100=>[1,4,2]=>[2,4,1]
[6,4,7,3,2,1,8,5]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,4,7,3,2,1,6,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,5,3,7,2,1,4,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,8,3,6,2,1,4,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,3,7,8,2,1,4,5]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,3,7,6,2,1,4,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[3,8,7,6,2,1,4,5]=>0111100=>[1,4,2]=>[2,4,1]
[5,8,4,2,6,1,3,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,8,7,2,5,1,3,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,8,3,2,6,1,4,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,8,3,2,5,1,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,7,2,5,1,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,7,2,5,1,4,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,4,2,7,5,1,3,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,3,2,7,5,1,4,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[5,3,2,6,7,1,4,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[3,8,2,6,5,1,4,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,2,7,8,5,1,3,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,2,7,6,8,1,3,4]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,7,6,5,1,3,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[2,8,7,6,5,1,3,4]=>0111100=>[1,4,2]=>[2,4,1]
[6,5,4,3,1,7,8,2]=>1111001=>[4,2,1]=>[1,2,4]
[6,4,7,3,1,5,8,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,4,7,3,1,8,6,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,4,3,7,1,5,8,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,4,3,6,1,8,7,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,3,7,8,1,4,5,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,3,7,6,1,4,8,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,7,6,1,5,8,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,8,7,6,1,4,5,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[6,5,4,2,1,7,3,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[6,4,7,2,1,5,3,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,8,7,2,1,5,3,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,8,3,2,1,4,7,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[4,8,3,2,1,5,7,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[5,3,7,2,1,4,8,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,8,7,2,1,4,5,6]=>0111000=>[1,3,3]=>[3,3,1]
[6,5,2,7,1,4,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,8,2,6,1,4,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,4,2,7,1,5,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,4,2,6,1,8,3,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,3,2,6,1,5,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,2,7,8,1,4,3,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,2,7,6,1,5,3,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,2,7,6,1,4,5,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,5,4,1,8,7,3,2]=>1110111=>[3,1,3]=>[3,1,3]
[5,8,4,1,6,7,3,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[6,4,7,1,5,8,3,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,4,7,1,6,8,3,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,8,7,1,5,6,3,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,4,3,1,6,8,7,2]=>1110011=>[3,2,2]=>[2,2,3]
[4,8,3,1,5,6,7,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,8,7,1,5,4,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,8,2,1,6,4,3,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,3,2,1,5,4,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,3,2,1,6,4,8,7]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,8,2,1,5,4,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,2,7,1,5,4,3,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,2,7,1,6,4,3,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,2,7,1,5,6,3,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,2,7,1,5,4,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,8,7,1,5,4,3,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,5,1,7,8,4,3,2]=>1100111=>[2,2,3]=>[3,2,2]
[5,8,1,6,7,4,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[6,4,1,7,5,8,3,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,4,1,6,7,8,3,2]=>1100011=>[2,3,2]=>[2,3,2]
[4,8,1,6,5,7,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,1,7,5,4,8,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,3,1,6,7,4,8,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,3,1,6,5,7,8,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,8,1,6,5,4,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,2,1,6,7,4,3,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,2,1,6,5,7,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,8,1,6,5,4,3,7]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,1,7,8,5,4,3,2]=>1001111=>[1,2,4]=>[4,2,1]
[4,1,7,6,5,8,3,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,1,7,6,5,4,8,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[4,5,8,1,2,6,3,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,4,5,7,2,6,3,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,7,3,5,6,2,4,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,1,3,5,7,2,4,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,6,8,1,7,2,4,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,4,5,6,8,1,7,2]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[4,5,8,2,6,7,1,3]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,2,3,5,6,7,1,4]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,7,2,3,5,4,6,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,1,2,3,5,4,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,7,8,1,3,5,4,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,7,8,3,5,6,1,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,4,5,7,8,1,6,3]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[4,5,8,1,7,6,3,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[4,5,8,7,2,1,6,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[8,7,3,5,6,2,1,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,7,2,1,3,5,4,6]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[3,6,8,7,2,1,5,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[8,6,4,1,7,5,3,2]=>1110111=>[3,1,3]=>[3,1,3]
[7,6,4,3,1,8,5,2]=>1111011=>[4,1,2]=>[2,1,4]
[2,3,6,7,8,1,5,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[3,6,8,1,2,5,4,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,3,6,7,2,5,4,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,4,1,8,5,2,3,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,1,4,2,8,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,8,2,5,3,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,5,4,2,3,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[1,7,2,6,5,4,3,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,7,6,3,2,5,4,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,6,3,1,2,5,4,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[8,1,7,6,3,2,4,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,2,5,7,6,3,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[3,6,8,1,7,5,4,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[8,2,6,7,5,4,1,3]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[2,7,8,6,3,1,5,4]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[2,7,8,1,6,5,4,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[7,3,1,8,6,5,4,2]=>1101111=>[2,1,4]=>[4,1,2]
[8,7,2,1,6,5,4,3]=>1110111=>[3,1,3]=>[3,1,3]
[8,7,6,3,2,1,5,4]=>1111101=>[5,1,1]=>[1,1,5]
[2,1,8,6,3,7,4,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,6,1,5,2,7,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,5,1,7,4,2,6,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,1,7,5,4,3,8,6]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,1,7,8,3,6,5,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,1,4,8,5,7,3,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,5,3,1,6,2,4,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[6,4,1,5,2,3,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,3,7,5,2,6,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,3,7,4,6,8,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,3,7,6,2,1,4]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,2,6,3,8,5,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,8,2,1,7,6,4,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[8,3,2,4,1,7,5,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,8,3,1,5,4,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,2,8,1,4,6,5,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,2,3,1,4,5,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,8,1,4,5,3,2,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,2,6,1,4,7,3,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,3,5,6,1,7,4,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,3,5,4,1,2,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,7,3,6,5,1,4,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,7,4,3,6,1,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,7,2,8,1,5,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,2,3,5,8,1,6,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,8,4,7,1,6,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,2,4,6,1,5,8,7]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,3,4,5,7,6,1,2]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,2,4,5,6,8,1,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[5,6,8,1,4,2,7,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,5,7,8,4,6,2,3]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,5,7,8,6,2,4]=>0000110=>[4,2,1]=>[1,2,4]
[3,5,7,8,6,1,2,4]=>0001100=>[3,2,2]=>[2,2,3]
[3,5,1,6,8,2,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,5,6,8,2,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,3,5,6,8,1,7,4]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[5,6,4,8,2,1,7,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,6,3,8,4,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,1,6,8,3,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,1,2,6,8,3,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,7,1,8,6,2,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,5,2,7,8,6,3,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,6,7,5,2,8,3,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,1,7,5,2,8,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,6,7,5,1,8,3,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,7,2,8,6,1,3,4]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,5,7,8,6,2,1,4]=>0001110=>[3,3,1]=>[1,3,3]
[5,1,7,8,6,3,4,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,1,3,7,8,6,4,2]=>1000111=>[1,3,3]=>[3,3,1]
[5,2,7,8,4,6,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,2,5,7,8,6,1,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,2,7,5,1,8,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,6,7,5,8,3,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,2,7,5,4,1,8,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,7,5,2,4,1,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,2,5,3,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,7,4,5,2,1,8,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,7,8,6,4,3,2]=>1001111=>[1,2,4]=>[4,2,1]
[2,5,7,8,6,3,1,4]=>0001110=>[3,3,1]=>[1,3,3]
[5,1,7,8,6,3,2,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,3,7,5,1,8,2,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,7,5,3,8,2,4]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,6,7,5,4,2,8,3]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[6,7,5,1,4,2,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,7,8,6,4,1,2,3]=>0011100=>[2,3,2]=>[2,3,2]
[4,1,7,2,6,5,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,4,7,1,5,6,8,3]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[6,7,4,1,5,2,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,6,7,4,5,2,8,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,6,3,7,5,8,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,1,7,5,8,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,5,3,7,8,6,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,7,5,4,2,1,8,3]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[6,3,2,7,5,8,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,7,4,2,5,1,8,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,2,7,4,5,1,8,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,3,7,5,8,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,1,6,3,2,8,7]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,5,1,6,3,8,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,1,6,3,8,4,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,7,6,1,3,8,4,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,7,6,1,3,8,5,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,3,5,1,8,2,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,5,1,8,2,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,7,5,1,8,6,2,4]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,6,7,1,5,8,3,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,6,7,4,1,8,3,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,1,6,7,3,8,5,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,6,7,4,1,8,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[2,6,7,1,5,8,4,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,6,5,1,8,4,7,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,5,1,8,4,2,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,7,5,4,8,1,6,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,7,5,4,8,1,2,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,6,1,5,8,7,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,6,1,5,8,7,2,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,6,1,5,8,2,7,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,5,1,6,2,8,3,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,1,6,2,8,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,6,1,5,8,2,3,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,7,1,5,8,3,6,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,3,4,7,8,1,6,5]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[6,8,5,4,3,2,7,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[10,11,9,8,7,6,5,4,3,2,1]=>0111111111=>[1,9]=>[9,1]
[7,9,6,5,4,3,2,8,1]=>01111101=>[1,5,1,1]=>[1,1,5,1]
[8,9,6,5,4,3,2,1,7]=>01111110=>[1,6,1]=>[1,6,1]
[6,8,5,4,3,7,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,8,4,3,2,1,7,6]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[6,5,4,3,1,8,7,2]=>1111011=>[4,1,2]=>[2,1,4]
[8,7,6,5,4,3,9,1,2]=>11111010=>[5,1,1,1]=>[1,1,1,5]
[8,7,5,4,3,1,6,2]=>1111101=>[5,1,1]=>[1,1,5]
[9,7,6,5,4,3,1,8,2]=>11111101=>[6,1,1]=>[1,1,6]
[11,10,9,8,7,6,5,4,3,1,2]=>1111111110=>[9,1]=>[1,9]
[8,3,4,6,2,1,5,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,5,6,2,1,8,4,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,5,2,6,8,4,1,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,5,3,2,8,4,1,6]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,5,3,2,8,4,6,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,4,5,7,3,8,6,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,2,5,6,8,3,1,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,2,8,1,5,6,3,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,5,6,1,8,4,3,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,3,6,8,1,4,2,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,6,8,1,3,2,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,4,5,6,8,3,2,7]=>0000110=>[4,2,1]=>[1,2,4]
[4,5,6,3,8,2,1,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,5,3,7,2,8,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,4,7,3,2,8,5,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,1,4,7,3,2,8,5]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,7,8,4,5,3,2,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,1,7,3,8,4,2,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,5,1,7,4,3,8,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,5,7,4,1,8,6,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,3,7,1,4,8,6,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,4,3,1,7,8,5,2]=>1110011=>[3,2,2]=>[2,2,3]
[6,4,1,7,3,8,5,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,6,3,7,8,4,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[5,1,6,3,7,8,4,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,6,1,3,7,8,4,2]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[5,6,1,7,8,3,4,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,3,7,4,8,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,2,4,1,8,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,2,1,4,3,8,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,4,7,3,1,2,8,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,6,3,1,2,7,8,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[5,6,1,3,2,7,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,6,3,2,1,7,8,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,5,6,3,7,8,4,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,5,6,3,1,7,8,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,6,4,7,3,1,8,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,7,2,8,4,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,7,2,8,4,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,2,7,1,8,4,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,3,2,1,8,4,6]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,3,8,4,2,1,5,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[4,7,2,1,3,8,6,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[1,3,7,8,6,4,2,5]=>0001110=>[3,3,1]=>[1,3,3]
[7,3,8,4,6,2,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,7,3,8,2,1,6,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,3,7,8,5,2,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[4,6,2,7,8,5,3,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,6,2,1,7,8,5,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,4,5,8,1,2,6,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,5,1,7,3,8,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,2,1,3,8,5,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,1,6,7,8,2,4,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,3,7,1,8,5,2,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,2,1,7,3,8,5,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,2,7,1,8,5,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,3,1,7,8,5,4,2]=>1100111=>[2,2,3]=>[3,2,2]
[4,1,3,6,8,2,5,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,2,3,6,8,1,5,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[5,3,2,1,8,4,7,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,6,5,8,2,1,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,2,1,3,8,7,6]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,2,6,4,5,8,1,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,4,6,5,8,1,3,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,6,2,4,5,8,3,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[5,3,2,1,6,8,4,7]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,2,4,5,8,1,3,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,3,4,6,5,8,2,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,6,3,4,5,8,2,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,4,1,8,5,2,7,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,8,4,1,7,6,3,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,1,4,2,7,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,3,2,8,7,4,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,2,1,7,5,3,4,6]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[1,7,6,4,5,8,3,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,8,7,4,1,2,6,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[5,8,7,4,6,2,1,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,4,2,5,8,6,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,3,5,6,8,7,2]=>1000011=>[1,4,2]=>[2,4,1]
[2,4,8,6,7,1,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,3,6,2,8,1,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,4,8,2,1,6,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,3,5,8,6,7,1,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,2,5,6,8,7,1,4]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,1,8,5,6,7,3,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,2,8,3,5,6,7,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[4,2,3,7,1,8,6,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,6,4,8,1,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,2,1,6,7,3,4,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[2,7,8,5,4,1,3,6]=>0011100=>[2,3,2]=>[2,3,2]
[1,7,5,3,8,4,2,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,7,5,3,1,2,8,6]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,2,4,8,5,3,1,6]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[4,8,3,1,2,7,6,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,5,2,7,4,1,8,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,4,2,3,7,1,5,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[2,8,4,7,1,3,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,2,4,6,7,1,3,5]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,8,2,3,6,7,1,5]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,5,2,7,6,1,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,6,3,2,5,8,7,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,8,3,2,1,6,7,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[5,8,7,3,4,6,2,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,8,2,7,4,1,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,4,2,8,7,6,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,7,6,5,8,2,1,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,3,7,1,6,2,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,8,7,1,3,4]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,3,2,1,8,5,7,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,7,5,4,1,8,6,3]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,2,5,6,8,7,1,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,8,4,2,5,6,7,3]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,8,4,1,5,6,7,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[4,2,8,5,6,7,1,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,2,4,7,1,8,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,3,4,7,1,8,6,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,6,4,1,3,2,5,7]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[8,1,3,6,5,2,4,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,1,4,3,6,5,2,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,5,2,1,8,7,4]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[8,3,2,4,6,5,1,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,4,2,1,6,5,3,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,4,1,2,6,5,3,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,6,4,2,1,5,3,7]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[8,3,6,4,1,5,2,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,2,6,3,4,5,1,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,3,4,8,5,7,2,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,8,4,7,6,2,3,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,3,4,7,5,8,2,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,5,2,4,8,7,6]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,6,5,1,3,8,7,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[4,7,1,6,5,8,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,8,7,6,3,1,2]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[2,8,5,1,4,7,6,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[4,3,1,5,8,6,7,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,1,3,5,8,6,7,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[6,5,3,8,4,7,1,2]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,4,2,1,6,8,7,3]=>1110011=>[3,2,2]=>[2,2,3]
[6,8,4,3,2,7,1,5]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[3,4,7,8,2,1,6,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[5,1,3,2,8,6,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,3,1,2,8,6,7,4]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,2,3,1,6,8,7,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,3,2,1,8,6,7,4]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[5,2,1,3,6,8,7,4]=>1100011=>[2,3,2]=>[2,3,2]
[2,4,7,3,8,1,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,3,8,2,7,4,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,2,1,3,6,4,7,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,5,1,7,8,4,2,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,7,4,5,8,3,1,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,8,4,3,7,2,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,8,7,2,1,6,5]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[5,4,7,8,3,6,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,4,3,8,7,2,1,5]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,3,8,7,4,1,2,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[3,5,7,2,4,8,1,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,4,7,2,3,1,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,4,7,1,3,2,5,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,4,7,2,1,3,5,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[8,6,4,2,1,3,7,5]=>1111001=>[4,2,1]=>[1,2,4]
[8,6,4,1,3,2,7,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,6,4,2,3,1,7,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,5,7,2,6,1,8,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,1,3,8,5,7,2,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,8,3,2,6,7,1,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,8,5,3,6,2,7,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,1,5,4,7,6,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,5,8,7,4,6,2,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,1,7,6,4,5,8,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,7,2,4,6,5,8,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,5,1,7,6,8,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,2,6,1,3,7,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,5,8,7,2,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[2,5,7,8,4,1,6,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,2,8,1,5,6,7,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,1,5,2,6,8,7,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,4,5,1,6,8,7,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,2,8,5,1,6,7,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,1,8,5,2,6,7,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,7,1,8,5,4,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,8,6,2,1,3,7,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[8,2,4,1,5,6,7,3]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,6,3,5,8,1,7,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,7,8,3,5,4,6,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,5,1,8,6,7,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,8,1,4,5,6,7,2]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[3,4,5,6,8,2,1,7]=>0000110=>[4,2,1]=>[1,2,4]
[3,4,5,7,1,8,6,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,4,5,7,8,2,6,1]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[3,4,6,2,8,5,1,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,4,6,8,1,5,2,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,4,7,2,1,8,6,5]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,4,7,8,1,5,6,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[3,4,8,2,1,5,6,7]=>0011000=>[2,2,3]=>[3,2,2]
[3,5,2,6,7,8,1,4]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,5,2,7,8,4,6,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,5,2,8,4,1,6,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,5,6,2,8,4,1,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[3,5,6,8,4,1,2,7]=>0001100=>[3,2,2]=>[2,2,3]
[3,5,7,2,4,8,6,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,5,7,2,8,4,6,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,7,8,4,1,6,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[3,6,2,1,7,8,5,4]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,6,2,1,8,5,4,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,6,7,2,4,8,5,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,6,7,2,8,5,4,1]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[3,6,7,8,4,5,1,2]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,6,8,2,4,5,1,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,7,2,1,4,8,6,5]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,7,2,1,8,5,6,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,7,2,8,4,5,6,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,7,8,2,4,5,6,1]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,8,2,1,4,5,6,7]=>0110000=>[1,2,4]=>[4,2,1]
[4,1,5,6,7,8,3,2]=>1000011=>[1,4,2]=>[2,4,1]
[4,1,5,7,3,8,6,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,1,6,3,7,8,5,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,1,6,3,8,5,2,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,1,6,7,3,8,5,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,1,6,7,8,5,2,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[4,1,6,8,3,5,2,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,1,7,3,2,8,6,5]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,7,8,3,5,6,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,1,8,3,2,5,6,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,5,2,6,7,8,3,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,5,2,6,8,1,3,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,5,6,3,8,1,2,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,5,6,8,3,1,2,7]=>0001100=>[3,2,2]=>[2,2,3]
[4,5,7,3,8,1,6,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,5,8,3,2,1,6,7]=>0011100=>[2,3,2]=>[2,3,2]
[4,6,2,3,7,8,5,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,6,2,3,8,5,1,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,6,2,7,3,8,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,6,2,7,8,5,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,6,7,3,2,8,5,1]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[4,6,8,3,2,5,1,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,7,2,3,1,8,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,2,8,3,5,6,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,7,8,3,2,5,6,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[4,8,2,3,1,5,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,1,2,6,8,4,3,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,1,2,7,4,8,6,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,1,2,7,8,4,6,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,1,2,8,4,3,6,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,1,6,3,8,4,2,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,1,6,7,4,8,2,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,1,6,7,8,4,2,3]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,1,8,3,4,2,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,6,2,3,8,4,1,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,6,2,7,8,4,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,6,8,3,4,2,1,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,7,2,3,4,8,6,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[5,7,2,3,8,4,6,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,7,8,3,4,2,6,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,8,2,3,4,1,6,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,1,2,3,7,8,5,4]=>1000011=>[1,4,2]=>[2,4,1]
[6,1,2,3,8,5,4,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,1,2,7,8,5,4,3]=>1000111=>[1,3,3]=>[3,3,1]
[6,1,2,8,4,5,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,7,3,4,8,5,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,1,7,3,8,5,4,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,1,7,8,4,5,3,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,1,8,3,4,5,2,7]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,7,2,3,8,5,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[6,7,2,8,4,5,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,8,2,3,4,5,1,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,1,2,3,4,8,6,5]=>1000011=>[1,4,2]=>[2,4,1]
[7,1,2,8,4,5,6,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,1,8,3,4,5,6,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,4,1,8,2,3,7,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,8,1,2,4,3,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,5,7,2,6,4,8]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,5,8,6,1,2,4,7]=>0011000=>[2,2,3]=>[3,2,2]
[3,1,6,8,2,4,7,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,6,2,8,1,5,7,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,1,3,8,4,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,7,5,2,3,4,6,8]=>0110000=>[1,2,4]=>[4,2,1]
[2,7,5,1,3,8,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,2,5,7,4,6,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,2,1,3,7,6,4,5]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,2,5,1,3,7,4,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,2,7,5,3,1,6,4]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,2,6,5,4,7,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,6,5,2,4,8,1,3]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[7,8,2,5,3,1,6,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,1,8,6,3,2,4,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,8,1,5,3,2,4,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,6,7,5,3,2,4,8]=>0011100=>[2,3,2]=>[2,3,2]
[6,5,1,2,4,8,3,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,8,1,6,4,2,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,4,1,2,5,6,3,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[1,7,3,6,5,2,4,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,1,3,7,2,6,4,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,3,2,6,5,1,8,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,8,4,2,5,6,1,3]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,2,7,4,5,6,1,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,2,3,6,5,1,7,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,9,8,6,5,4,3,2,1]=>01111111=>[1,7]=>[7,1]
[6,9,8,7,5,4,3,2,1]=>01111111=>[1,7]=>[7,1]
[5,9,8,7,6,4,3,2,1]=>01111111=>[1,7]=>[7,1]
[4,9,8,7,6,5,3,2,1]=>01111111=>[1,7]=>[7,1]
[3,9,8,7,6,5,4,2,1]=>01111111=>[1,7]=>[7,1]
[2,9,8,7,6,5,4,3,1]=>01111111=>[1,7]=>[7,1]
[8,10,9,7,6,5,4,3,2,1]=>011111111=>[1,8]=>[8,1]
[6,9,7,8,5,4,3,2,1]=>01011111=>[1,1,1,5]=>[5,1,1,1]
[7,10,9,8,6,5,4,3,2,1]=>011111111=>[1,8]=>[8,1]
[4,8,6,5,7,3,2,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[5,9,8,6,7,4,3,2,1]=>01101111=>[1,2,1,4]=>[4,1,2,1]
[6,10,9,8,7,5,4,3,2,1]=>011111111=>[1,8]=>[8,1]
[3,8,7,5,4,6,2,1]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[4,8,5,6,7,3,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,9,8,7,5,6,3,2,1]=>01110111=>[1,3,1,3]=>[3,1,3,1]
[5,10,9,8,7,6,4,3,2,1]=>011111111=>[1,8]=>[8,1]
[2,8,7,6,4,3,5,1]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[3,8,7,4,5,6,2,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,9,8,7,6,4,5,2,1]=>01111011=>[1,4,1,2]=>[2,1,4,1]
[4,10,9,8,7,6,5,3,2,1]=>011111111=>[1,8]=>[8,1]
[1,8,7,6,5,3,2,4]=>0111110=>[1,5,1]=>[1,5,1]
[2,8,7,6,3,4,5,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[2,9,8,7,6,5,3,4,1]=>01111101=>[1,5,1,1]=>[1,1,5,1]
[3,10,9,8,7,6,5,4,2,1]=>011111111=>[1,8]=>[8,1]
[1,8,7,6,5,2,3,4]=>0111100=>[1,4,2]=>[2,4,1]
[1,9,8,7,6,5,4,2,3]=>01111110=>[1,6,1]=>[1,6,1]
[2,10,9,8,7,6,5,4,3,1]=>011111111=>[1,8]=>[8,1]
[7,2,8,6,5,4,1,3]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[7,2,8,5,4,6,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,3,2,8,5,1,7,4]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,4,7,2,5,6,3,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,8,5,4,3,1,7,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[5,8,6,4,1,3,7,2]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[4,8,6,1,5,3,7,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,1,8,5,2,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,1,2,8,6,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,8,3,5,4,1,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,2,5,8,3,6,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,7,5,6,3,4,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,6,8,5,3,1,4]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[7,6,3,8,5,2,1,4]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,2,6,4,8,3,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,7,4,2,6,3,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,2,3,1,7,8,5,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,2,8,4,1,7,6,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,6,3,4,7,2,5,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,8,3,4,5,1,7,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,3,2,5,8,4,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[8,3,2,1,5,4,7,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,3,7,1,5,8,4,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,5,1,8,4,3,7,6]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,2,5,4,8,1,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,1,6,5,8,2,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,3,5,4,6,8,2,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,1,3,4,5,8,2,7]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[8,3,4,1,5,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,5,4,2,6,8,3,1]=>1110011=>[3,2,2]=>[2,2,3]
[8,2,6,4,1,7,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,3,8,4,5,2,1,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,5,1,8,4,3,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,7,3,2,5,4,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,7,2,1,5,3,4,6]=>1110100=>[3,1,1,2]=>[2,1,1,3]
[3,6,1,5,8,7,4,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[8,3,6,4,5,1,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,4,6,8,1,2,7,3]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,4,7,2,3,5,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,8,4,1,3,5,7,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,4,7,8,6,2,5,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,1,3,5,7,8,6,2]=>1000011=>[1,4,2]=>[2,4,1]
[6,5,1,8,4,7,3,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[5,3,1,8,4,7,6,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,2,7,4,6,1,3,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,7,3,2,8,1,6,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,3,1,4,7,2,8,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,7,3,6,1,5,2,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,4,3,6,8,2,5,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,4,7,3,8,5,6,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,8,6,1,5,7,3,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,8,2,5,4,3,1,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,8,3,4,2,7,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,5,3,7,4,2,6,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,7,3,2,4,1,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,8,3,4,7,1,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,3,6,7,8,2,5]=>1000010=>[1,4,1,1]=>[1,1,4,1]
[1,7,6,3,2,5,8,4]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[3,8,1,5,6,2,7,4]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,2,5,6,1,7,4,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,1,5,2,8,6,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,5,4,8,7,2,1,3]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[1,8,6,4,5,2,7,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,5,3,6,2,7,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,2,1,7,5,8,4]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,5,4,1,8,7,6,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,7,2,6,5,8,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,1,4,2,7,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,4,7,1,8,2,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,4,7,8,2,5,6,1]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,8,2,4,5,6,7,3]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[5,2,4,1,6,8,7,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,2,5,7,6,1,8,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,3,5,6,1,8,7,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,3,4,1,7,6,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,4,6,5,7,8,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,4,7,3,5,6,8,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,3,2,7,5,8,6,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,4,2,5,8,3,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,2,6,8,5,3,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,5,2,4,8,7,6,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[1,2,6,4,8,7,5,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,2,7,4,8,6,5,3]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[1,3,2,7,5,8,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,2,8,5,7,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,2,4,8,7,3,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,2,6,4,8,7,3,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,7,8,5,6,3,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,8,2,6,7,4,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,6,7,8,2,5,3,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,5,7,8,2,3,6,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,5,2,7,8,4,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,6,2,4,8,7,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,6,7,3,4,8,5,2]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,5,3,7,4,8,6,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,8,4,1,5,3,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,8,4,1,5,7,2,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,3,8,4,2,7,6,5]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,2,8,4,7,3,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,7,4,8,3,6,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,6,4,8,3,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,5,2,4,8,3,7,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,8,3,5,2,7,4,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,3,8,6,2,7,4,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,4,8,6,7,2,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,6,8,5,3,7,4]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,7,8,6,3,5,4]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,6,7,8,5,2,3,4]=>0001100=>[3,2,2]=>[2,2,3]
[1,5,7,8,6,2,3,4]=>0001100=>[3,2,2]=>[2,2,3]
[1,4,7,6,8,2,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,3,7,6,2,8,4,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,3,8,7,4,1,6,5]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,2,5,8,7,6,3,4]=>0001110=>[3,3,1]=>[1,3,3]
[1,2,6,8,7,5,3,4]=>0001110=>[3,3,1]=>[1,3,3]
[1,2,7,8,6,5,3,4]=>0001110=>[3,3,1]=>[1,3,3]
[5,2,6,7,3,4,8,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,2,4,7,6,3,8,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,6,2,1,7,8,3,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,6,2,1,4,8,7,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,6,1,4,5,8,7,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[5,4,2,7,6,3,8,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,7,6,4,5,8,1]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[2,6,1,7,5,8,3,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,1,7,4,8,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,2,7,8,4,3,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,6,1,7,4,8,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,4,1,7,8,2,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,4,6,1,3,8,7,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,6,4,1,5,8,7,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[2,6,1,5,4,8,7,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,1,4,7,8,5,3]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[5,1,2,4,8,6,7,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,1,2,4,8,7,3,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,1,2,4,8,7,6,3]=>1000111=>[1,3,3]=>[3,3,1]
[1,2,3,8,5,4,7,6]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,3,1,2,8,5,7,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,1,5,3,8,6,4,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,2,3,8,5,6,4,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,3,8,6,4,5,7]=>0001100=>[3,2,2]=>[2,2,3]
[1,2,3,8,6,5,4,7]=>0001110=>[3,3,1]=>[1,3,3]
[1,2,3,8,5,4,6,7]=>0001100=>[3,2,2]=>[2,2,3]
[2,6,1,5,4,8,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,2,4,8,6,3,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,1,2,4,8,3,7,6]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,6,3,1,4,8,2,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,5,4,3,1,8,6,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,4,6,3,1,8,7,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,6,4,5,1,8,7,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,6,5,4,1,8,7,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[5,2,6,1,7,8,4,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,1,6,2,8,7,3,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,1,3,7,8,6,4,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[2,1,3,7,8,5,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,2,4,1,7,8,6,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,3,1,2,8,6,7,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,1,4,2,8,6,7,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,1,3,6,8,5,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,2,3,8,6,7,4,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,3,8,7,5,4,6]=>0001110=>[3,3,1]=>[1,3,3]
[1,2,3,8,7,4,5,6]=>0001100=>[3,2,2]=>[2,2,3]
[1,2,3,8,5,7,4,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[2,1,3,6,8,7,4,5]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,4,1,2,8,7,6,3]=>1100111=>[2,2,3]=>[3,2,2]
[3,1,6,2,8,7,5,4]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,2,3,4,5,9,6,7,8]=>00000100=>[5,1,2]=>[2,1,5]
[1,2,3,4,9,5,6,7,8]=>00001000=>[4,1,3]=>[3,1,4]
[1,2,3,9,4,5,6,7,8]=>00010000=>[3,1,4]=>[4,1,3]
[1,2,9,3,4,5,6,7,8]=>00100000=>[2,1,5]=>[5,1,2]
[1,2,3,4,5,6,7,10,8,9]=>000000010=>[7,1,1]=>[1,1,7]
[1,2,3,4,5,9,7,6,8]=>00000110=>[5,2,1]=>[1,2,5]
[1,2,3,4,5,6,10,7,8,9]=>000000100=>[6,1,2]=>[2,1,6]
[1,2,3,4,9,6,5,7,8]=>00001100=>[4,2,2]=>[2,2,4]
[1,2,3,4,5,10,6,7,8,9]=>000001000=>[5,1,3]=>[3,1,5]
[1,2,8,4,5,3,6,7]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,2,3,9,5,4,6,7,8]=>00011000=>[3,2,3]=>[3,2,3]
[1,2,3,4,10,5,6,7,8,9]=>000010000=>[4,1,4]=>[4,1,4]
[1,8,3,4,2,5,6,7]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,2,9,4,3,5,6,7,8]=>00110000=>[2,2,4]=>[4,2,2]
[1,2,3,10,4,5,6,7,8,9]=>000100000=>[3,1,5]=>[5,1,3]
[1,8,4,3,2,5,6,7]=>0111000=>[1,3,3]=>[3,3,1]
[1,9,3,2,4,5,6,7,8]=>01100000=>[1,2,5]=>[5,2,1]
[1,2,10,3,4,5,6,7,8,9]=>001000000=>[2,1,6]=>[6,1,2]
[8,4,7,6,5,3,2,1]=>1011111=>[1,1,5]=>[5,1,1]
[8,4,7,5,6,3,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,5,7,4,6,3,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,7,6,3,5,4,2,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,6,7,3,5,4,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,5,7,3,6,4,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,1,7,4,6,5,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,1,7,3,6,5,4,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,2,7,3,6,5,4,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,3,7,2,6,5,4,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,5,7,2,6,4,3,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,6,7,2,5,4,3,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,7,6,2,5,4,3,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,4,7,1,6,5,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,3,7,1,6,5,4,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,2,7,1,6,5,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,1,7,2,6,5,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[8,7,6,2,5,3,4,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,1,7,6,5,3,4,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,7,6,5,2,4,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,4,7,6,5,2,3,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,5,7,6,4,2,3,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,6,7,5,4,1,3,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,5,7,6,4,1,3,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,3,7,6,5,1,4,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,7,6,4,5,1,3,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,6,2,5,1,4,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,6,1,5,2,4,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,8,1,3,2,5,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,1,4,2,5,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,3,6,1,4,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,5,3,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,2,5,1,4,3,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,1,4,3,6,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,1,4,3,7,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,2,5,1,4,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,2,5,3,7,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,2,5,4,7,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,4,7,6,8,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,3,7,6,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,5,1,4,3,7,6,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,1,4,3,7,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,5,8,1,4,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,1,5,3,7,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,3,7,4,8,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,4,7,5,8,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,3,6,4,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,2,6,4,7,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,2,6,3,7,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,1,5,3,7,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,1,5,2,6,3,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,8,3,7,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,3,7,1,4,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,1,3,2,6,4,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,4,7,1,3,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,4,7,1,3,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,5,7,1,3,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,6,8,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,6,8,1,3,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,5,8,1,3,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,1,3,2,6,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,1,4,2,6,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,5,8,1,4,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,6,8,1,4,2,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,6,8,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,6,8,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,5,8,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,5,8,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,5,8,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,4,8,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,4,8,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,1,5,2,6,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,2,6,1,5,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,7,2,6,5,8,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,3,6,5,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,6,5,8,4,7,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,5,8,4,7,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,5,8,3,7,1,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,6,3,7,1,5,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,4,2,8,5,3,1]=>1110111=>[3,1,3]=>[3,1,3]
[7,6,4,3,8,2,5,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,6,4,8,5,2,3,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,8,4,3,7,2,1,5]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,7,4,3,5,1,8,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,3,5,4,8,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,8,3,7,5,2,4,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,6,8,3,5,2,4,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,6,3,5,8,2,4,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,6,3,5,2,4,8,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,6,4,2,5,1,8,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[7,6,2,8,4,1,5,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[7,6,3,8,2,4,1,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,3,4,8,2,5,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,8,3,7,4,5,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,7,3,5,8,4,2,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[5,7,8,3,6,2,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,8,3,6,7,2,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,4,8,7,2,5,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,3,8,4,7,2,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,2,8,4,1,7,5,3]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,2,7,4,1,5,3,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,3,4,7,5,8,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,3,5,7,8,4,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[5,7,3,6,8,2,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,6,8,3,7,2,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,6,7,3,4,1,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,6,7,8,3,5,2,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,6,8,3,5,7,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,7,3,5,6,8,2,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,7,3,5,8,2,6,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,3,4,7,8,2,1,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,3,8,2,4,1,6,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,4,8,2,6,1,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,3,6,2,5,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,8,3,5,7,2,6,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,8,3,5,6,7,2,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,7,8,3,5,6,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,7,8,3,6,2,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,8,3,6,7,2,5,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,8,3,7,2,5,6,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,3,4,8,2,7,6,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,3,8,2,4,1,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,8,4,1,7,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,4,2,5,1,8,7,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,4,3,5,8,2,1,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,3,5,8,7,2,4,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,8,3,7,2,6,4,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,7,3,4,8,2,1,6]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,8,4,2,3,1,6,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,8,4,2,3,1,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,4,5,3,8,2,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,4,8,5,3,7,2,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[6,4,3,8,5,7,2,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,4,2,8,5,3,1,7]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,4,2,7,3,1,8,5]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,3,7,8,5,2,1]=>1100111=>[2,2,3]=>[3,2,2]
[6,4,5,3,7,1,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,7,4,2,3,1,6,8]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,6,3,7,1,8,2,4]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,6,3,4,7,1,8,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,6,3,4,8,2,1,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,5,7,4,8,2,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,3,5,4,7,8,2,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,4,3,5,7,1,8,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,4,2,5,1,7,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,7,2,4,1,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,3,4,7,2,6,1,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,7,3,6,2,5,8,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,7,3,6,8,2,5,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,7,3,5,8,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,5,7,8,3,6,2,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[4,5,8,3,6,7,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,5,8,3,7,2,6,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,3,4,6,8,2,1,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,3,6,8,2,1,4,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,3,6,7,1,8,2,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,4,6,7,1,8,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,6,3,5,7,8,2,1]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[4,5,7,3,6,8,2,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,5,6,8,3,7,2,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[5,7,4,8,6,3,2,1]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[3,2,6,5,1,8,7,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[3,5,6,7,2,8,4,1]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[7,6,9,8,5,4,3,2,1]=>10111111=>[1,1,6]=>[6,1,1]
[6,5,4,9,8,7,3,2,1]=>11011111=>[2,1,5]=>[5,1,2]
[6,8,5,9,7,4,3,2,1]=>01011111=>[1,1,1,5]=>[5,1,1,1]
[6,7,8,9,5,4,3,2,1]=>00011111=>[3,5]=>[5,3]
[5,4,3,2,9,8,7,6,1]=>11101111=>[3,1,4]=>[4,1,3]
[5,8,4,3,9,7,6,2,1]=>01101111=>[1,2,1,4]=>[4,1,2,1]
[5,4,7,6,9,8,3,2,1]=>10101111=>[1,1,1,1,4]=>[4,1,1,1,1]
[5,7,8,4,9,6,3,2,1]=>00101111=>[2,1,1,4]=>[4,1,1,2]
[5,6,7,8,9,4,3,2,1]=>00001111=>[4,4]=>[4,4]
[4,8,3,2,1,9,7,6,5]=>01110111=>[1,3,1,3]=>[3,1,3,1]
[4,3,7,6,2,9,8,5,1]=>10110111=>[1,1,2,1,3]=>[3,1,2,1,1]
[4,7,8,3,2,9,6,5,1]=>00110111=>[2,2,1,3]=>[3,1,2,2]
[4,6,3,8,5,9,7,2,1]=>01010111=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[4,6,7,8,3,9,5,2,1]=>00010111=>[3,1,1,3]=>[3,1,1,3]
[4,5,6,7,8,9,3,2,1]=>00000111=>[5,3]=>[3,5]
[3,2,1,6,5,4,9,8,7]=>11011011=>[2,1,2,1,2]=>[2,1,2,1,2]
[3,6,2,8,5,1,9,7,4]=>01011011=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
[3,6,7,8,2,1,9,5,4]=>00011011=>[3,2,1,2]=>[2,1,2,3]
[3,2,5,4,7,6,9,8,1]=>10101011=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[3,5,7,2,8,4,9,6,1]=>00101011=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[3,5,6,7,8,2,9,4,1]=>00001011=>[4,1,1,2]=>[2,1,1,4]
[3,4,5,6,7,8,9,2,1]=>00000011=>[6,2]=>[2,6]
[2,4,6,7,1,8,3,9,5]=>00010101=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]
[2,4,5,6,7,8,1,9,3]=>00000101=>[5,1,1,1]=>[1,1,1,5]
[8,7,10,9,6,5,4,3,2,1]=>101111111=>[1,1,7]=>[7,1,1]
[8,9,10,7,6,5,4,3,2,1]=>001111111=>[2,7]=>[7,2]
[7,6,5,10,9,8,4,3,2,1]=>110111111=>[2,1,6]=>[6,1,2]
[7,9,6,10,8,5,4,3,2,1]=>010111111=>[1,1,1,6]=>[6,1,1,1]
[7,8,9,10,6,5,4,3,2,1]=>000111111=>[3,6]=>[6,3]
[6,5,4,3,10,9,8,7,2,1]=>111011111=>[3,1,5]=>[5,1,3]
[6,9,5,4,10,8,7,3,2,1]=>011011111=>[1,2,1,5]=>[5,1,2,1]
[6,5,8,7,10,9,4,3,2,1]=>101011111=>[1,1,1,1,5]=>[5,1,1,1,1]
[6,8,9,5,10,7,4,3,2,1]=>001011111=>[2,1,1,5]=>[5,1,1,2]
[5,4,3,2,1,10,9,8,7,6]=>111101111=>[4,1,4]=>[4,1,4]
[5,9,4,3,2,10,8,7,6,1]=>011101111=>[1,3,1,4]=>[4,1,3,1]
[5,4,8,7,3,10,9,6,2,1]=>101101111=>[1,1,2,1,4]=>[4,1,2,1,1]
[5,8,9,4,3,10,7,6,2,1]=>001101111=>[2,2,1,4]=>[4,1,2,2]
[5,7,4,9,6,10,8,3,2,1]=>010101111=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]
[5,6,7,8,9,10,4,3,2,1]=>000001111=>[5,4]=>[4,5]
[4,3,8,7,2,1,10,9,6,5]=>101110111=>[1,1,3,1,3]=>[3,1,3,1,1]
[4,8,9,3,2,1,10,7,6,5]=>001110111=>[2,3,1,3]=>[3,1,3,2]
[4,3,2,7,6,5,10,9,8,1]=>110110111=>[2,1,2,1,3]=>[3,1,2,1,2]
[4,7,3,9,6,2,10,8,5,1]=>010110111=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[4,7,8,9,3,2,10,6,5,1]=>000110111=>[3,2,1,3]=>[3,1,2,3]
[4,3,6,5,8,7,10,9,2,1]=>101010111=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[4,6,7,8,9,3,10,5,2,1]=>000010111=>[4,1,1,3]=>[3,1,1,4]
[4,5,6,7,8,9,10,3,2,1]=>000000111=>[6,3]=>[3,6]
[3,6,2,1,9,5,4,10,8,7]=>011011011=>[1,2,1,2,1,2]=>[2,1,2,1,2,1]
[3,2,6,5,8,7,1,10,9,4]=>101011011=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]
[3,6,8,2,9,5,1,10,7,4]=>001011011=>[2,1,1,2,1,2]=>[2,1,2,1,1,2]
[3,6,7,8,9,2,1,10,5,4]=>000011011=>[4,2,1,2]=>[2,1,2,4]
[3,5,7,8,2,9,4,10,6,1]=>000101011=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]
[3,5,6,7,8,9,2,10,4,1]=>000001011=>[5,1,1,2]=>[2,1,1,5]
[3,4,5,6,7,8,9,10,2,1]=>000000011=>[7,2]=>[2,7]
[2,4,6,1,8,3,9,5,10,7]=>001010101=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]
[2,4,6,7,8,1,9,3,10,5]=>000010101=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]
[2,4,5,6,7,8,9,1,10,3]=>000000101=>[6,1,1,1]=>[1,1,1,6]
[1,6,2,5,3,4,8,7]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,3,8,2,4,6,5,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,7,2,3,6,4,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,8,2,5,3,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,8,2,5,3,4,7,6]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,8,2,3,6,4,7,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,3,5,2,8,4,7,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,2,7,3,5,4,6,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[1,8,2,7,3,4,6,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,8,2,3,7,4,6]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,6,8,2,3,5,4,7]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,3,6,1,2,4,8,7]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,1,5,8,4,2,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,1,5,7,4,2,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[7,1,4,5,8,2,3,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[7,4,1,6,2,8,3,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,4,1,7,2,6,3,5]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,1,4,7,5,2,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[8,1,5,4,7,2,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,7,5,8,3,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,5,4,8,2,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,4,8,5,2,3,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[6,4,1,7,2,3,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,8,3,1,2,4,6,5]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[8,7,1,6,4,2,3,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[8,6,1,7,4,2,3,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,6,1,8,4,2,3,5]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,3,8,1,2,4,6,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,3,7,1,2,4,6,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,3,6,1,2,4,7,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,3,7,5,1,2,4,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,3,6,1,2,4,8,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[6,7,1,8,4,2,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,8,1,7,4,2,3,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,1,8,5,4,2,3,6]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,1,8,4,5,2,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,1,7,8,5,3,4,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[7,6,3,1,2,4,8,5]=>1110001=>[3,3,1]=>[1,3,3]
[6,1,2,3,8,7,5,4]=>1000111=>[1,3,3]=>[3,3,1]
[6,8,1,4,2,3,7,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,8,3,1,2,7,4,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,7,3,1,2,8,4,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[6,7,1,4,2,3,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,3,6,8,5,7,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,1,2,5,4,8,3,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,2,8,5,4,1,7,6]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[7,8,2,1,4,6,3,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,2,1,5,8,3,4,6]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[2,4,8,5,1,3,6,7]=>0011000=>[2,2,3]=>[3,2,2]
[3,5,6,1,8,4,2,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,3,6,8,7,4,2,5]=>0001110=>[3,3,1]=>[1,3,3]
[1,2,8,5,7,3,4,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,6,1,5,8,3,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,7,1,6,8,4,3,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,8,1,2,5,7,3,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,4,6,2,5,7,3,1]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,3,6,4,7,2,5,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,8,1,4,7,2,5,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,7,8,4,6,2,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,7,4,8,5,1,6,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,7,1,6,5,4,8,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,7,3,1,5,8,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,7,4,6,8,1,3,5]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,7,5,8,6,4,1,3]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,2,6,7,5,4,3,1]=>1001111=>[1,2,4]=>[4,2,1]
[3,8,7,1,6,4,5,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,8,2,7,4,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,5,2,8,7,4,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,2,7,8,1,6,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,3,7,5,6,8,2]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,3,8,1,7,4,2,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,5,8,7,1,4,2,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,7,3,8,5,2,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,1,4,5,8,2,7]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,6,7,4,5,3,8,2]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,1,7,3,5,4,8,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,3,1,2,5,8,4,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[1,4,7,2,8,5,3,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,6,8,7,2,4,1,3]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,8,5,7,1,2,4,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,4,1,7,5,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,2,4,3,7,5,6,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,8,2,1,5,7,3,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,2,8,4,1,6,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,4,8,6,5,3,7]=>0001110=>[3,3,1]=>[1,3,3]
[7,1,5,6,8,4,3,2]=>1000111=>[1,3,3]=>[3,3,1]
[2,7,8,1,4,6,3,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,8,2,5,7,1,6,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,6,8,5,3,7,2]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,2,6,4,8,3,1,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,7,1,3,4,5,8,2]=>0100001=>[1,1,4,1]=>[1,4,1,1]
[1,7,3,2,4,8,5,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[1,3,6,5,2,8,4,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,1,6,5,3,4,8,2]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,3,4,2,8,7,5,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,3,8,7,5,2,6,1]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[6,8,7,4,2,3,5,1]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[3,6,4,5,2,8,7,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,1,3,5,4,2,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,3,8,6,1,2,4,7]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[2,5,6,3,4,8,7,1]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,5,3,6,8,7,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[4,8,7,3,5,2,6,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,8,7,2,6,4,5,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,3,5,4,8,7,2,1]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,3,8,6,1,5,2,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,7,6,2,5,3,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,5,2,6,8,1,4,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,5,2,7,1,4,3,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,8,5,3,6,2,4,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,1,7,2,4,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,5,3,4,8,6,2,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,4,1,3,8,6,2,7]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,1,8,6,3,4,2,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,5,2,8,3,7,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,2,3,7,6,4,5,1]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,8,2,4,7,6,3,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[6,8,2,5,3,4,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,5,6,4,8,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,6,7,4,8,2,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,1,3,5,8,2,6,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[8,2,1,3,5,6,7,4]=>1100001=>[2,4,1]=>[1,4,2]
[6,3,1,4,7,5,8,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,1,3,8,2,6,7,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,8,3,6,7,5,4,1]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,1,7,2,8,5,4,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,1,4,7,2,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,5,8,4,7,2,3,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,1,3,6,2,8,4,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,2,7,4,5,8,1,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,1,8,4,5,7,3,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,5,7,3,2,4,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,1,8,5,4,3,6,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[2,7,4,1,5,3,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,4,8,6,2,3,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,7,1,4,6,3,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,7,5,6,8,1,3,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,1,3,2,8,5,4,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,5,4,1,3,6,7]=>0111000=>[1,3,3]=>[3,3,1]
[5,1,7,4,2,3,8,6]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,8,6,5,1,4,2,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,3,4,8,6,5,2,7]=>0001110=>[3,3,1]=>[1,3,3]
[4,1,8,6,5,3,2,7]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[4,8,5,2,7,3,6,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[7,2,8,5,3,6,4,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,2,8,4,3,7,6,1]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,4,7,5,2,3,6,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,5,2,8,4,6,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,7,4,3,6,2,8,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,7,5,1,2,8,3,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,2,6,8,3,4,7,1]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,6,2,4,5,8,3,1]=>1100011=>[2,3,2]=>[2,3,2]
[3,6,8,4,7,2,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,3,8,4,2,5,1]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,6,3,8,4,7,5,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,2,3,6,5,8,4,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[6,2,7,5,8,3,1,4]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,8,3,6,4,5,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,1,5,6,8,3,7,4]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,8,1,2,6,4,7,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,8,3,2,7,4,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,7,2,8,4,1,3]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,5,1,2,8,4,6,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,4,8,3,6,2,7,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,8,2,7,4,3,6,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[6,4,5,8,2,7,3,1]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,7,3,6,4,8,2,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,5,6,4,8,2,7,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,1,5,6,4,8,7,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,3,6,2,5,7,8,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,4,6,3,5,7,8,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[3,5,1,6,4,7,8,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,6,1,4,2,7,8,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,4,6,3,1,7,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,3,6,5,2,7,8,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,2,6,4,3,8,5,7]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[1,2,6,3,5,8,7,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,3,5,1,8,4,7,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,3,6,1,8,5,4,7]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,7,4,6,8,3,5]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,7,5,1,8,4,6]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[4,7,2,5,3,8,6,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,1,7,5,4,8,6,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,7,6,4,8,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[1,2,7,3,6,8,5,4]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,3,6,1,8,5,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,1,5,4,8,7,6,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,2,5,8,4,7,3,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,6,8,5,4,7,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,3,6,8,5,2,7,4]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[3,5,7,4,8,2,1,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,4,7,6,8,3,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,4,6,8,3,5,2,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,6,8,5,2,4,7]=>0001100=>[3,2,2]=>[2,2,3]
[1,2,6,8,5,4,3,7]=>0001110=>[3,3,1]=>[1,3,3]
[1,2,5,8,4,3,7,6]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,3,5,8,2,4,7,6]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,3,6,8,2,5,4,7]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,4,6,8,3,2,5,7]=>0001100=>[3,2,2]=>[2,2,3]
[3,5,7,4,8,1,2,6]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,6,1,7,5,8,2,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,3,6,7,5,8,1,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,7,5,6,8,2,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,3,6,5,8,1,7,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,6,2,8,1,7,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,5,4,6,8,2,1,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,5,4,6,8,1,2,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,4,7,5,8,3,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,6,7,4,8,3,5]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,6,4,7,1,8,5,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,2,6,7,3,8,5,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,5,7,3,8,6,4]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,1,5,7,6,8,4,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,5,4,6,8,2,7,1]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,2,6,1,8,7,5,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,1,6,5,8,7,4,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,3,6,5,8,7,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[1,2,7,4,6,8,5,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,2,7,5,6,8,4,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,1,6,7,5,8,4,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,6,2,7,5,8,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,5,7,4,8,2,6,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,4,7,6,8,3,5,1]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,4,6,8,3,5,7,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,3,6,8,2,5,7,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,3,5,8,2,7,4,6]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,2,5,8,4,7,6,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,4,8,7,3,6,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,5,8,7,4,3,6]=>0001110=>[3,3,1]=>[1,3,3]
[1,3,5,8,7,2,4,6]=>0001100=>[3,2,2]=>[2,2,3]
[2,3,7,6,8,5,1,4]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,7,1,2,8,6,4,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,1,7,6,8,5,4,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,2,6,8,5,7,4,3]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[1,2,5,8,7,4,6,3]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[1,2,4,8,7,6,3,5]=>0001110=>[3,3,1]=>[1,3,3]
[6,4,5,7,2,8,1,3]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,3,4,7,2,8,1,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,2,7,4,6,8,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,3,6,2,7,1,4,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,3,4,7,1,5,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,7,3,4,5,8,1,6]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,7,4,5,6,8,1,2]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[2,5,7,3,6,8,1,4]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[4,7,6,2,3,8,1,5]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,3,5,2,4,8,1,6]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,6,2,4,5,8,1,3]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[6,5,2,3,4,8,1,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[5,3,1,2,8,4,7,6]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,5,2,3,7,1,4,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,2,1,7,3,4,6,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[5,2,1,8,3,4,6,7]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,3,2,8,4,5,7,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,3,1,2,8,4,6,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,4,1,3,8,5,7,2]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,2,3,1,8,4,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,3,5,2,7,1,4,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,2,4,7,1,5,3]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[8,5,2,3,6,1,4,7]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[8,2,1,7,3,4,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[8,6,3,7,2,4,5,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,1,6,2,3,4,5,8]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,2,7,3,4,5,6,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,1,6,2,3,4,5,7]=>1010000=>[1,1,1,4]=>[4,1,1,1]
[8,1,7,3,4,5,6,2]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[8,6,1,7,2,4,5,3]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[8,1,5,7,2,3,6,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,7,5,8,2,3,6,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,2,1,8,3,4,5,6]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,3,8,2,4,5,6,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,2,8,3,4,5,6,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[1,7,8,3,4,5,6,2]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[1,4,5,8,3,6,7,2]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,5,7,1,8,3,6,4]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,2,7,1,8,4,5,3]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,7,1,3,8,5,6,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,6,2,8,4,5,7,3]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,1,3,6,8,2,7,5]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[5,3,4,6,8,2,7,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,6,3,8,7,1,2,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[6,4,5,8,7,1,2,3]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[5,3,4,8,7,1,2,6]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[3,2,8,7,1,4,6,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,1,8,7,2,4,6,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[5,3,7,6,1,2,4,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[1,8,3,7,2,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,8,1,7,2,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,8,2,3,5,1,4,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,7,8,2,6,1,3,5]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,2,8,7,1,4,5,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[3,8,7,1,4,5,6,2]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[2,8,6,1,3,4,5,7]=>0110000=>[1,2,4]=>[4,2,1]
[2,7,6,1,3,4,5,8]=>0110000=>[1,2,4]=>[4,2,1]
[1,7,6,2,3,4,5,8]=>0110000=>[1,2,4]=>[4,2,1]
[1,8,6,2,3,4,5,7]=>0110000=>[1,2,4]=>[4,2,1]
[2,8,7,3,4,5,6,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[3,8,7,2,4,5,6,1]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,8,3,6,2,4,5,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,8,7,2,3,6,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[8,7,6,1,3,4,5,2]=>1110001=>[3,3,1]=>[1,3,3]
[3,6,2,4,7,1,8,5]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,4,7,2,5,1,8,6]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,1,6,4,8,5,3,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,1,8,5,3,2,7,6]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,6,2,5,7,1,4,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,2,8,3,7,5,4,6]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,1,3,2,8,5,4,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,6,1,2,8,4,3,7]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,6,3,8,7,4,2,5]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,3,8,1,2,6,7,5]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,8,10,9,5,6,3,4,1,2]=>001101010=>[2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2]
[9,10,5,6,8,7,3,4,1,2]=>010011010=>[1,1,2,2,1,1,1]=>[1,1,1,2,2,1,1]
[5,8,10,6,9,7,3,4,1,2]=>001011010=>[2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2]
[5,6,7,10,9,8,3,4,1,2]=>000111010=>[3,3,1,1,1]=>[1,1,1,3,3]
[9,10,7,8,3,4,6,5,1,2]=>010100110=>[1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1]
[7,8,10,9,3,4,6,5,1,2]=>001100110=>[2,2,2,2,1]=>[1,2,2,2,2]
[9,10,3,6,8,4,7,5,1,2]=>010010110=>[1,1,2,1,1,2,1]=>[1,2,1,1,2,1,1]
[3,8,10,6,9,4,7,5,1,2]=>001010110=>[2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2]
[3,6,7,10,9,4,8,5,1,2]=>000110110=>[3,2,1,2,1]=>[1,2,1,2,3]
[9,10,3,4,5,8,7,6,1,2]=>010001110=>[1,1,3,3,1]=>[1,3,3,1,1]
[3,8,10,4,5,9,7,6,1,2]=>001001110=>[2,1,2,3,1]=>[1,3,2,1,2]
[3,4,7,10,5,9,8,6,1,2]=>000101110=>[3,1,1,3,1]=>[1,3,1,1,3]
[3,4,5,6,10,9,8,7,1,2]=>000011110=>[4,4,1]=>[1,4,4]
[9,10,7,8,5,6,1,2,4,3]=>010101001=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]
[7,8,10,9,5,6,1,2,4,3]=>001101001=>[2,2,1,1,2,1]=>[1,2,1,1,2,2]
[9,10,5,6,8,7,1,2,4,3]=>010011001=>[1,1,2,2,2,1]=>[1,2,2,2,1,1]
[5,8,10,6,9,7,1,2,4,3]=>001011001=>[2,1,1,2,2,1]=>[1,2,2,1,1,2]
[5,6,7,10,9,8,1,2,4,3]=>000111001=>[3,3,2,1]=>[1,2,3,3]
[9,10,7,8,1,4,6,2,5,3]=>010100101=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]
[7,8,10,9,1,4,6,2,5,3]=>001100101=>[2,2,2,1,1,1]=>[1,1,1,2,2,2]
[9,10,1,6,8,4,7,2,5,3]=>010010101=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1]
[1,8,10,6,9,4,7,2,5,3]=>001010101=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]
[1,6,7,10,9,4,8,2,5,3]=>000110101=>[3,2,1,1,1,1]=>[1,1,1,1,2,3]
[9,10,1,4,5,8,7,2,6,3]=>010001101=>[1,1,3,2,1,1]=>[1,1,2,3,1,1]
[1,8,10,4,5,9,7,2,6,3]=>001001101=>[2,1,2,2,1,1]=>[1,1,2,2,1,2]
[1,4,7,10,5,9,8,2,6,3]=>000101101=>[3,1,1,2,1,1]=>[1,1,2,1,1,3]
[1,4,5,6,10,9,8,2,7,3]=>000011101=>[4,3,1,1]=>[1,1,3,4]
[9,10,7,8,1,2,3,6,5,4]=>010100011=>[1,1,1,1,3,2]=>[2,3,1,1,1,1]
[7,8,10,9,1,2,3,6,5,4]=>001100011=>[2,2,3,2]=>[2,3,2,2]
[9,10,1,6,8,2,3,7,5,4]=>010010011=>[1,1,2,1,2,2]=>[2,2,1,2,1,1]
[1,8,10,6,9,2,3,7,5,4]=>001010011=>[2,1,1,1,2,2]=>[2,2,1,1,1,2]
[1,6,7,10,9,2,3,8,5,4]=>000110011=>[3,2,2,2]=>[2,2,2,3]
[9,10,1,2,5,8,3,7,6,4]=>010001011=>[1,1,3,1,1,2]=>[2,1,1,3,1,1]
[1,8,10,2,5,9,3,7,6,4]=>001001011=>[2,1,2,1,1,2]=>[2,1,1,2,1,2]
[1,2,7,10,5,9,3,8,6,4]=>000101011=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]
[1,2,5,6,10,9,3,8,7,4]=>000011011=>[4,2,1,2]=>[2,1,2,4]
[9,10,1,2,3,4,8,7,6,5]=>010000111=>[1,1,4,3]=>[3,4,1,1]
[1,8,10,2,3,4,9,7,6,5]=>001000111=>[2,1,3,3]=>[3,3,1,2]
[1,2,7,10,3,4,9,8,6,5]=>000100111=>[3,1,2,3]=>[3,2,1,3]
[1,2,3,6,10,4,9,8,7,5]=>000010111=>[4,1,1,3]=>[3,1,1,4]
[1,2,3,4,5,10,9,8,7,6]=>000001111=>[5,4]=>[4,5]
[11,12,9,10,7,8,5,6,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[3,4,5,6,7,12,11,10,9,8,1,2]=>00000111110=>[5,5,1]=>[1,5,5]
[11,12,9,10,7,8,5,6,1,2,4,3]=>01010101001=>[1,1,1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1,1,1]
[11,12,9,10,7,8,1,4,6,2,5,3]=>01010100101=>[1,1,1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1,1,1]
[11,12,9,10,1,6,8,4,7,2,5,3]=>01010010101=>[1,1,1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1,1,1]
[11,12,1,8,10,6,9,4,7,2,5,3]=>01001010101=>[1,1,2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2,1,1]
[1,4,5,8,12,6,11,10,9,2,7,3]=>00001011101=>[4,1,1,3,1,1]=>[1,1,3,1,1,4]
[3,1,2,4,5,6,7,8,9]=>10000000=>[1,7]=>[7,1]
[2,4,1,3,5,6,7,8,9]=>01000000=>[1,1,6]=>[6,1,1]
[2,3,5,1,4,6,7,8,9]=>00100000=>[2,1,5]=>[5,1,2]
[2,3,4,6,1,5,7,8,9]=>00010000=>[3,1,4]=>[4,1,3]
[2,3,4,5,7,1,6,8,9]=>00001000=>[4,1,3]=>[3,1,4]
[2,3,4,5,6,8,1,7,9]=>00000100=>[5,1,2]=>[2,1,5]
[3,6,8,7,1,2,5,4]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[6,2,8,5,4,7,1,3]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,5,7,2,4,8,1,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,4,1,6,5,8,7,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,5,1,2,4,8,7,6]=>0100011=>[1,1,3,2]=>[2,3,1,1]
[3,7,5,2,1,4,6,8]=>0111000=>[1,3,3]=>[3,3,1]
[3,8,5,2,7,4,1,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,2,8,4,7,3,1,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,2,7,4,1,3,6,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,3,5,1,2,8,7,6]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[3,1,4,6,2,8,7,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,4,6,5,2,8,7,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[3,4,5,6,1,8,7,2]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[3,4,5,8,7,2,1,6]=>0001110=>[3,3,1]=>[1,3,3]
[1,4,7,2,6,3,5,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,4,7,5,2,1,6,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,1,4,7,2,3,6,5]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,8,5,7,3,4,6,2]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,5,1,7,4,2,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,1,4,8,7,3,2,5]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[6,4,8,5,7,1,2,3]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,4,8,1,6,3,2,7]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,4,8,6,3,7,2,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,4,7,6,3,8,1,2]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,6,3,7,5,8,1,2]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,3,5,8,6,2,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[5,7,4,3,8,1,2,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,4,8,3,7,6,5,2]=>0010111=>[2,1,1,3]=>[3,1,1,2]
[4,3,8,2,1,6,5,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,8,4,2,7,1,5,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,1,2,5,7,6,4,8]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[1,8,2,7,6,5,4,3]=>0101111=>[1,1,1,4]=>[4,1,1,1]
[3,8,1,6,7,5,4,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,7,2,6,8,5,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,2,3,8,5,6,1,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,2,1,7,5,6,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[8,1,3,6,5,7,4,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,2,4,3,6,1,5,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,7,8,5,4,3,6,2]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[1,8,4,5,3,2,6,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,8,5,4,3,1,6,2]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[7,1,6,3,4,2,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,8,7,1,4,2,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[3,6,1,4,2,7,5,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,1,8,5,7,6,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,6,5,1,2,8,4,7]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,8,5,6,7,2,1,4]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[8,1,7,6,2,4,3,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[8,5,6,1,4,2,3,7]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,6,5,4,7,1,3,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,6,4,5,7,2,3,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[8,3,6,1,7,2,4,5]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,8,6,5,7,3,4,2]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,7,5,3,6,8,4,2]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[7,4,1,6,5,8,3,2]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,1,5,8,7,6,3,2]=>1001111=>[1,2,4]=>[4,2,1]
[1,2,5,8,6,7,3,4]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[4,2,1,5,8,7,3,6]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[5,2,4,6,1,7,3,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,5,3,6,8,7,4,2]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,5,4,6,1,8,2,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,7,6,8,2,4]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,4,5,6,8,7,2,3]=>0000110=>[4,2,1]=>[1,2,4]
[1,4,6,3,7,2,8,5]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,7,3,6,5,2,8,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[8,6,2,5,4,1,7,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,7,2,6,5,4,1,8]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[7,6,2,5,4,3,1,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[4,7,5,2,6,3,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[3,2,6,4,7,5,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,2,3,7,5,4,1,8]=>1001110=>[1,2,3,1]=>[1,3,2,1]
[1,3,4,7,6,2,8,5]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,8,3,6,1,7,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[8,7,2,5,1,6,4,3]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,8,2,6,5,1,7,4]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,8,2,5,4,1,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,8,5,2,6,1,7,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,5,1,3,7,2,8,6]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,1,3,7,5,2,8,4]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,1,3,6,2,8,5,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[8,1,3,6,2,7,5,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,2,4,7,3,8,6,5]=>0001011=>[3,1,1,2]=>[2,1,1,3]
[7,1,8,2,6,5,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[3,1,8,6,2,7,5,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,1,7,8,2,6,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,6,1,8,2,7,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,7,8,1,6,5,3]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,2,8,6,1,7,5,4]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[7,2,8,1,6,5,4,3]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[1,8,7,2,6,5,4,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[2,8,7,1,6,5,4,3]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[3,8,7,1,6,5,4,2]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[4,8,7,5,1,6,3,2]=>0111011=>[1,3,1,2]=>[2,1,3,1]
[6,7,8,5,1,4,3,2]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,6,3,8,4,1,7,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,3,8,5,4,1,6,2]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[3,4,8,6,5,1,7,2]=>0011101=>[2,3,1,1]=>[1,1,3,2]
[8,3,7,5,1,6,4,2]=>1011011=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,4,8,6,2,7,5,3]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[8,4,6,7,1,5,3,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[5,6,4,7,8,1,3,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,4,6,5,1,2,8,7]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[7,3,5,1,2,8,6,4]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,4,6,2,3,8,7,5]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[1,3,2,7,4,8,6,5]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,2,1,6,3,8,5,4]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[2,3,1,7,6,4,8,5]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,5,2,1,7,3,8,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,6,7,1,2,8,4,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[4,7,5,1,2,8,6,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[3,7,1,6,2,8,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,6,1,2,8,5,4,3]=>1100111=>[2,2,3]=>[3,2,2]
[2,7,1,3,8,6,5,4]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[8,6,1,2,7,5,4,3]=>1100111=>[2,2,3]=>[3,2,2]
[1,7,2,3,8,6,5,4]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[8,7,1,2,6,5,4,3]=>1100111=>[2,2,3]=>[3,2,2]
[7,8,1,2,6,5,4,3]=>0100111=>[1,1,2,3]=>[3,2,1,1]
[3,8,1,6,2,7,5,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,8,5,1,2,7,6,3]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,6,8,1,2,7,4,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[2,1,3,7,4,8,6,5]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[4,2,7,3,6,8,1,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,3,6,4,2,8,1,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,1,5,3,8,2,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,2,6,4,7,3,1,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,3,4,7,5,1,8]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[2,6,3,5,4,8,1,7]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,4,3,5,8,1,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,3,6,4,2,8,1,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,6,4,5,2,8,1,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,4,3,1,8,2,7,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,5,4,2,7,3,1,8]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[5,4,1,7,2,6,3,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,4,1,8,3,2,6,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[6,5,2,8,3,4,7,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,4,2,1,8,3,6,5]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,5,3,4,8,2,7,1]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[6,1,5,3,8,2,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,6,3,1,8,2,7,5]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,8,4,2,7,3,1,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[8,2,6,4,7,3,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,6,2,5,7,4,1,3]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[8,5,3,2,6,4,1,7]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[8,3,1,7,2,5,4,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,5,2,6,4,3,1,8]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[7,1,6,2,5,4,3,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,1,7,3,5,6,4,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[8,6,1,7,4,5,2,3]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[8,1,3,7,2,6,5,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,7,6,8,3,2,4,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,1,5,8,4,2,6,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[7,3,8,4,5,2,6,1]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,2,8,5,3,4,6,1]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[6,1,8,4,3,2,5,7]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[6,1,7,4,2,5,3,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,2,7,3,4,6,5,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[1,7,8,4,3,5,6,2]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,6,2,8,3,5,7,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[2,6,1,7,3,5,4,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,1,5,8,4,2,6,7]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,3,1,6,8,2,7,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[5,7,4,8,3,2,1,6]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,4,8,2,7,3,1,6]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,2,8,7,3,4,1,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,4,7,5,3,2,1,8]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[1,8,3,7,6,2,4,5]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,8,3,2,6,4,1,7]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[6,8,2,4,7,5,1,3]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[7,3,8,2,6,4,1,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[4,6,8,2,7,3,1,5]=>0010110=>[2,1,1,2,1]=>[1,2,1,1,2]
[2,6,8,7,3,4,1,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,2,8,6,3,5,1,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,8,1,7,2,5,4,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[3,8,7,4,5,6,1,2]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[2,8,6,4,3,5,1,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,7,6,3,5,4,1,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[1,7,6,5,2,4,3,8]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,8,6,5,3,2,4,7]=>0111100=>[1,4,2]=>[2,4,1]
[3,8,7,4,6,2,5,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,8,3,7,6,2,4,1]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,1,8,6,5,2,3,4]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[8,4,7,5,3,2,1,6]=>1011110=>[1,1,4,1]=>[1,4,1,1]
[8,7,2,5,4,3,1,6]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[6,8,3,2,5,4,7,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,8,4,5,2,3,7,1]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[1,5,7,8,4,3,6,2]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[6,3,8,1,5,4,7,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,2,1,8,5,4,7,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[2,6,3,1,7,5,4,8]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[2,6,5,7,4,1,3,8]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[2,5,6,8,4,3,7,1]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[2,4,7,5,8,1,6,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[2,5,4,7,1,8,6,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,2,1,8,7,6,4,3]=>1101111=>[2,1,4]=>[4,1,2]
[4,8,5,7,6,1,3,2]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[4,8,6,7,5,3,1,2]=>0101110=>[1,1,1,3,1]=>[1,3,1,1,1]
[4,8,7,5,6,2,3,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,5,4,8,2,1,7,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[5,8,4,7,2,6,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,5,7,4,8,2,6,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[1,5,7,3,2,8,6,4]=>0011011=>[2,2,1,2]=>[2,1,2,2]
[5,8,3,2,7,6,4,1]=>0110111=>[1,2,1,3]=>[3,1,2,1]
[5,2,1,4,3,6,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[3,5,7,4,2,6,1,8]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[3,6,4,5,1,2,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[4,2,1,6,5,3,7,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[4,2,1,5,7,6,3,8]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[4,3,5,1,7,6,2,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[3,5,4,7,1,6,2,8]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[3,4,7,5,6,1,2,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[3,4,5,8,6,7,1,2]=>0001010=>[3,1,1,1,1]=>[1,1,1,1,3]
[3,5,4,6,1,8,7,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,5,1,6,8,7,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[4,2,1,5,6,8,7,3]=>1100011=>[2,3,2]=>[2,3,2]
[4,3,2,1,7,6,5,9,8,10]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,3,2,1,6,5,4,9,8,10]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[4,3,2,1,9,6,5,8,7,10]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[6,3,2,1,9,5,4,8,7,10]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[9,3,2,1,8,5,4,7,6,10]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[6,5,2,1,9,4,3,8,7,10]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[9,5,2,1,8,4,3,7,6,10]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[4,3,2,1,7,6,5,10,8,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,3,2,1,6,5,4,10,8,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[4,3,2,1,8,6,5,10,7,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[6,3,2,1,8,5,4,10,7,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[8,3,2,1,7,5,4,10,6,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[6,5,2,1,8,4,3,10,7,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[8,5,2,1,7,4,3,10,6,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[4,3,2,1,10,6,5,9,7,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[6,3,2,1,10,5,4,9,7,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,3,2,1,10,5,4,9,6,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[10,3,2,1,9,5,4,8,6,7]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[6,5,2,1,10,4,3,9,7,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,5,2,1,10,4,3,9,6,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[10,5,2,1,9,4,3,8,6,7]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[4,3,2,1,8,7,5,10,6,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[5,3,2,1,8,7,4,10,6,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[8,3,2,1,7,6,4,10,5,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[5,4,2,1,8,7,3,10,6,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[8,4,2,1,7,6,3,10,5,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[4,3,2,1,10,7,5,9,6,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[5,3,2,1,10,7,4,9,6,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,3,2,1,10,6,4,9,5,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[10,3,2,1,9,6,4,8,5,7]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[5,4,2,1,10,7,3,9,6,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,4,2,1,10,6,3,9,5,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[10,4,2,1,9,6,3,8,5,7]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,6,2,1,10,5,3,9,4,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[10,6,2,1,9,5,3,8,4,7]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[5,4,3,1,8,7,2,10,6,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[8,4,3,1,7,6,2,10,5,9]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[5,4,3,1,10,7,2,9,6,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,4,3,1,10,6,2,9,5,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[10,4,3,1,9,6,2,8,5,7]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,6,3,1,10,5,2,9,4,8]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[10,6,3,1,9,5,2,8,4,7]=>111011010=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[2,1,4,3,6,5,10,9,7,8]=>101010110=>[1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1]
[2,1,4,3,8,7,5,6,10,9]=>101011001=>[1,1,1,1,2,2,1]=>[1,2,2,1,1,1,1]
[2,1,4,3,10,7,5,9,6,8]=>101011010=>[1,1,1,1,2,1,1,1]=>[1,1,1,2,1,1,1,1]
[2,1,4,3,10,9,8,5,6,7]=>101011100=>[1,1,1,1,3,2]=>[2,3,1,1,1,1]
[2,1,6,5,3,4,8,7,10,9]=>101100101=>[1,1,2,2,1,1,1]=>[1,1,1,2,2,1,1]
[2,1,6,5,3,4,10,9,7,8]=>101100110=>[1,1,2,2,2,1]=>[1,2,2,2,1,1]
[2,1,8,5,3,7,4,6,10,9]=>101101001=>[1,1,2,1,1,2,1]=>[1,2,1,1,2,1,1]
[2,1,10,5,3,7,4,9,6,8]=>101101010=>[1,1,2,1,1,1,1,1]=>[1,1,1,1,1,2,1,1]
[2,1,10,5,3,9,8,4,6,7]=>101101100=>[1,1,2,1,2,2]=>[2,2,1,2,1,1]
[2,1,8,7,6,3,4,5,10,9]=>101110001=>[1,1,3,3,1]=>[1,3,3,1,1]
[2,1,10,7,6,3,4,9,5,8]=>101110010=>[1,1,3,2,1,1]=>[1,1,2,3,1,1]
[2,1,10,9,6,3,8,4,5,7]=>101110100=>[1,1,3,1,1,2]=>[2,1,1,3,1,1]
[2,1,10,9,8,7,3,4,5,6]=>101111000=>[1,1,4,3]=>[3,4,1,1]
[4,3,1,2,6,5,8,7,10,9]=>110010101=>[2,2,1,1,1,1,1]=>[1,1,1,1,1,2,2]
[4,3,1,2,6,5,10,9,7,8]=>110010110=>[2,2,1,1,2,1]=>[1,2,1,1,2,2]
[4,3,1,2,8,7,5,6,10,9]=>110011001=>[2,2,2,2,1]=>[1,2,2,2,2]
[4,3,1,2,10,7,5,9,6,8]=>110011010=>[2,2,2,1,1,1]=>[1,1,1,2,2,2]
[4,3,1,2,10,9,8,5,6,7]=>110011100=>[2,2,3,2]=>[2,3,2,2]
[6,3,1,5,2,4,8,7,10,9]=>110100101=>[2,1,1,2,1,1,1]=>[1,1,1,2,1,1,2]
[6,3,1,5,2,4,10,9,7,8]=>110100110=>[2,1,1,2,2,1]=>[1,2,2,1,1,2]
[8,3,1,5,2,7,4,6,10,9]=>110101001=>[2,1,1,1,1,2,1]=>[1,2,1,1,1,1,2]
[10,3,1,5,2,7,4,9,6,8]=>110101010=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]
[10,3,1,5,2,9,8,4,6,7]=>110101100=>[2,1,1,1,2,2]=>[2,2,1,1,1,2]
[8,3,1,7,6,2,4,5,10,9]=>110110001=>[2,1,2,3,1]=>[1,3,2,1,2]
[10,3,1,7,6,2,4,9,5,8]=>110110010=>[2,1,2,2,1,1]=>[1,1,2,2,1,2]
[10,3,1,9,6,2,8,4,5,7]=>110110100=>[2,1,2,1,1,2]=>[2,1,1,2,1,2]
[10,3,1,9,8,7,2,4,5,6]=>110111000=>[2,1,3,3]=>[3,3,1,2]
[6,5,4,1,2,3,8,7,10,9]=>111000101=>[3,3,1,1,1]=>[1,1,1,3,3]
[6,5,4,1,2,3,10,9,7,8]=>111000110=>[3,3,2,1]=>[1,2,3,3]
[8,5,4,1,2,7,3,6,10,9]=>111001001=>[3,2,1,2,1]=>[1,2,1,2,3]
[10,5,4,1,2,7,3,9,6,8]=>111001010=>[3,2,1,1,1,1]=>[1,1,1,1,2,3]
[10,5,4,1,2,9,8,3,6,7]=>111001100=>[3,2,2,2]=>[2,2,2,3]
[8,7,4,1,6,2,3,5,10,9]=>111010001=>[3,1,1,3,1]=>[1,3,1,1,3]
[10,7,4,1,6,2,3,9,5,8]=>111010010=>[3,1,1,2,1,1]=>[1,1,2,1,1,3]
[10,9,4,1,6,2,8,3,5,7]=>111010100=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]
[10,9,4,1,8,7,2,3,5,6]=>111011000=>[3,1,2,3]=>[3,2,1,3]
[8,7,6,5,1,2,3,4,10,9]=>111100001=>[4,4,1]=>[1,4,4]
[10,7,6,5,1,2,3,9,4,8]=>111100010=>[4,3,1,1]=>[1,1,3,4]
[10,9,6,5,1,2,8,3,4,7]=>111100100=>[4,2,1,2]=>[2,1,2,4]
[10,9,8,5,1,7,2,3,4,6]=>111101000=>[4,1,1,3]=>[3,1,1,4]
[10,3,1,5,2,7,4,9,6,8,12,11]=>11010101001=>[2,1,1,1,1,1,1,2,1]=>[1,2,1,1,1,1,1,1,2]
[10,9,8,7,6,1,2,3,4,5,12,11]=>11111000001=>[5,5,1]=>[1,5,5]
[7,6,5,4,3,2,9,1,8]=>11111010=>[5,1,1,1]=>[1,1,1,5]
[6,5,4,3,9,2,8,1,7]=>11101010=>[3,1,1,1,1,1]=>[1,1,1,1,1,3]
[6,5,4,3,2,8,1,7,9]=>11110100=>[4,1,1,2]=>[2,1,1,4]
[5,4,9,3,8,2,7,1,6]=>10101010=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[5,4,3,8,2,7,1,6,9]=>11010100=>[2,1,1,1,1,2]=>[2,1,1,1,1,2]
[5,4,3,2,7,9,1,6,8]=>11100100=>[3,2,1,2]=>[2,1,2,3]
[5,4,3,2,7,1,6,8,9]=>11101000=>[3,1,1,3]=>[3,1,1,3]
[4,8,3,7,2,6,1,5,9]=>01010100=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[4,3,7,2,6,9,1,5,8]=>10100100=>[1,1,1,2,1,2]=>[2,1,2,1,1,1]
[4,3,7,2,6,1,5,8,9]=>10101000=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[4,3,2,6,8,1,5,7,9]=>11001000=>[2,2,1,3]=>[3,1,2,2]
[4,3,2,6,1,5,7,8,9]=>11010000=>[2,1,1,4]=>[4,1,1,2]
[3,6,9,2,5,8,1,4,7]=>00100100=>[2,1,2,1,2]=>[2,1,2,1,2]
[3,6,2,5,8,1,4,7,9]=>01001000=>[1,1,2,1,3]=>[3,1,2,1,1]
[3,6,2,5,1,4,7,8,9]=>01010000=>[1,1,1,1,4]=>[4,1,1,1,1]
[3,2,5,7,9,1,4,6,8]=>10001000=>[1,3,1,3]=>[3,1,3,1]
[3,2,5,7,1,4,6,8,9]=>10010000=>[1,2,1,4]=>[4,1,2,1]
[3,2,5,1,4,6,7,8,9]=>10100000=>[1,1,1,5]=>[5,1,1,1]
[2,4,6,8,1,3,5,7,9]=>00010000=>[3,1,4]=>[4,1,3]
[2,4,6,1,3,5,7,8,9]=>00100000=>[2,1,5]=>[5,1,2]
[8,7,6,5,4,3,2,10,1,9]=>111111010=>[6,1,1,1]=>[1,1,1,6]
[7,6,5,4,3,10,2,9,1,8]=>111101010=>[4,1,1,1,1,1]=>[1,1,1,1,1,4]
[7,6,5,4,3,2,9,1,8,10]=>111110100=>[5,1,1,2]=>[2,1,1,5]
[6,5,4,10,3,9,2,8,1,7]=>110101010=>[2,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,2]
[6,5,4,3,9,2,8,1,7,10]=>111010100=>[3,1,1,1,1,2]=>[2,1,1,1,1,3]
[6,5,4,3,2,8,10,1,7,9]=>111100100=>[4,2,1,2]=>[2,1,2,4]
[6,5,4,3,2,8,1,7,9,10]=>111101000=>[4,1,1,3]=>[3,1,1,4]
[5,10,4,9,3,8,2,7,1,6]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[5,4,9,3,8,2,7,1,6,10]=>101010100=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]
[5,4,3,8,2,7,10,1,6,9]=>110100100=>[2,1,1,2,1,2]=>[2,1,2,1,1,2]
[5,4,3,8,2,7,1,6,9,10]=>110101000=>[2,1,1,1,1,3]=>[3,1,1,1,1,2]
[5,4,3,2,7,9,1,6,8,10]=>111001000=>[3,2,1,3]=>[3,1,2,3]
[5,4,3,2,7,1,6,8,9,10]=>111010000=>[3,1,1,4]=>[4,1,1,3]
[4,8,3,7,2,6,10,1,5,9]=>010100100=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]
[4,8,3,7,2,6,1,5,9,10]=>010101000=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[4,3,7,10,2,6,9,1,5,8]=>100100100=>[1,2,1,2,1,2]=>[2,1,2,1,2,1]
[4,3,7,2,6,9,1,5,8,10]=>101001000=>[1,1,1,2,1,3]=>[3,1,2,1,1,1]
[4,3,7,2,6,1,5,8,9,10]=>101010000=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]
[4,3,2,6,8,10,1,5,7,9]=>110001000=>[2,3,1,3]=>[3,1,3,2]
[4,3,2,6,8,1,5,7,9,10]=>110010000=>[2,2,1,4]=>[4,1,2,2]
[4,3,2,6,1,5,7,8,9,10]=>110100000=>[2,1,1,5]=>[5,1,1,2]
[3,6,9,2,5,8,1,4,7,10]=>001001000=>[2,1,2,1,3]=>[3,1,2,1,2]
[3,6,2,5,8,10,1,4,7,9]=>010001000=>[1,1,3,1,3]=>[3,1,3,1,1]
[3,6,2,5,8,1,4,7,9,10]=>010010000=>[1,1,2,1,4]=>[4,1,2,1,1]
[3,6,2,5,1,4,7,8,9,10]=>010100000=>[1,1,1,1,5]=>[5,1,1,1,1]
[3,2,5,7,9,1,4,6,8,10]=>100010000=>[1,3,1,4]=>[4,1,3,1]
[3,2,5,7,1,4,6,8,9,10]=>100100000=>[1,2,1,5]=>[5,1,2,1]
[3,2,5,1,4,6,7,8,9,10]=>101000000=>[1,1,1,6]=>[6,1,1,1]
[2,4,6,8,1,3,5,7,9,10]=>000100000=>[3,1,5]=>[5,1,3]
[2,4,6,1,3,5,7,8,9,10]=>001000000=>[2,1,6]=>[6,1,2]
[2,4,1,3,5,6,7,8,9,10]=>010000000=>[1,1,7]=>[7,1,1]
[2,1,7,3,8,4,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,8,2,7,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[4,1,7,2,8,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,3,2,8,4,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,8,2,4,3,6,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,7,2,5,3,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,5,2,8,3,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,7,2,8,3,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,8,2,7,3,6,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,8,2,4,3,7,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,6,2,4,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,8,2,4,3,7,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,8,2,5,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,6,2,5,3,7,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[8,1,6,2,7,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,8,2,7,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,7,2,8,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,7,2,5,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[6,1,7,2,4,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[5,1,6,2,4,3,8,7]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,5,2,4,3,8,6]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,6,2,4,3,8,5]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,6,2,5,3,8,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,6,2,8,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,1,8,2,6,3,5,4]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[1,8,2,7,5,4,6,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,8,2,7,4,3,5,6]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[1,8,6,4,7,2,3,5]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[1,8,4,2,6,3,5,7]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[7,4,8,1,5,2,3,6]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,1,7,2,6,3,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[5,1,7,4,3,6,2,8]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[7,5,8,3,2,4,1,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[1,8,5,4,3,6,2,7]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,8,5,4,3,7,2,6]=>0111010=>[1,3,1,1,1]=>[1,1,1,3,1]
[1,8,5,4,7,2,6,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,4,2,5,3,7,6]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[1,8,5,4,2,6,7,3]=>0111001=>[1,3,2,1]=>[1,2,3,1]
[7,4,8,2,1,3,5,6]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[4,1,7,3,2,5,6,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[7,5,4,8,2,3,6,1]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[7,3,8,1,5,6,2,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[3,1,7,2,6,8,4,5]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,1,7,4,2,6,8,3]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,1,6,3,2,5,8,7]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,1,6,2,5,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,5,4,3,7,1,8,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,3,2,8,5,7,1,4]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[6,5,4,3,8,2,7,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[6,5,4,3,8,7,1,2]=>1110110=>[3,1,2,1]=>[1,2,1,3]
[7,6,3,8,5,4,1,2]=>1101110=>[2,1,3,1]=>[1,3,1,2]
[5,4,8,2,1,7,3,6]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,4,2,8,5,1,3,7]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,6,4,8,5,1,2,3]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,2,8,6,3,1,4,5]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,2,8,6,1,5,3,4]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[2,1,7,8,3,6,4,5]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[6,4,1,7,8,2,3,5]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,2,1,6,7,3,5,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[4,3,1,5,2,7,6,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[5,4,2,7,3,8,1,6]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[4,1,5,3,2,8,6,7]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,1,6,2,8,7,4,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[6,3,1,7,8,5,2,4]=>1100110=>[2,2,2,1]=>[1,2,2,2]
[6,5,4,1,7,8,3,2]=>1110011=>[3,2,2]=>[2,2,3]
[5,4,3,1,6,7,2,8]=>1110010=>[3,2,1,1]=>[1,1,2,3]
[6,5,4,2,7,8,3,1]=>1110011=>[3,2,2]=>[2,2,3]
[5,4,2,6,3,8,7,1]=>1101011=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,3,1,5,2,6,8,7]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,4,2,1,6,7,8,3]=>1110001=>[3,3,1]=>[1,3,3]
[5,4,3,1,6,7,8,2]=>1110001=>[3,3,1]=>[1,3,3]
[6,3,8,1,2,5,7,4]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[3,6,7,1,2,5,8,4]=>0010001=>[2,1,3,1]=>[1,3,1,2]
[7,8,3,1,2,5,6,4]=>0110001=>[1,2,3,1]=>[1,3,2,1]
[7,8,1,3,2,4,6,5]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,8,2,1,3,5,4,6]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[5,2,3,7,1,8,6,4]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[2,5,3,6,1,8,7,4]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,6,7,3,1,8,4,5]=>0011010=>[2,2,1,1,1]=>[1,1,1,2,2]
[2,6,7,1,3,5,4,8]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,2,8,3,1,7,4,5]=>1011010=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[3,2,5,7,1,8,4,6]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,3,1,2,7,8,6,5]=>1100011=>[2,3,2]=>[2,3,2]
[5,1,2,7,3,6,4,8]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[5,1,4,7,8,2,3,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[5,3,4,7,8,6,1,2]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[3,5,4,6,8,7,1,2]=>0100110=>[1,1,2,2,1]=>[1,2,2,1,1]
[1,5,4,6,8,2,3,7]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,6,7,3,2,4,8,5]=>0011001=>[2,2,2,1]=>[1,2,2,2]
[1,5,3,6,2,7,8,4]=>0101001=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[5,1,3,7,2,6,8,4]=>1001001=>[1,2,1,2,1]=>[1,2,1,2,1]
[5,2,4,7,8,1,6,3]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,2,5,7,6,1,8,3]=>1001101=>[1,2,2,1,1]=>[1,1,2,2,1]
[4,5,2,8,6,1,7,3]=>0101101=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,3,1,8,2,6,7,4]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[6,1,8,3,2,4,7,5]=>1011001=>[1,1,2,2,1]=>[1,2,2,1,1]
[4,3,5,7,6,8,1,2]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,1,5,7,6,2,3,8]=>1001100=>[1,2,2,2]=>[2,2,2,1]
[4,5,1,8,6,2,3,7]=>0101100=>[1,1,1,2,2]=>[2,2,1,1,1]
[5,2,1,8,3,6,4,7]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[3,4,2,1,8,7,5,6]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[7,6,5,4,2,1,8,3]=>1111101=>[5,1,1]=>[1,1,5]
[7,6,5,4,8,1,3,2]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,6,5,4,2,1,9,3]=>11111101=>[6,1,1]=>[1,1,6]
[7,6,5,8,2,1,4,3]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,7,6,5,3,2,1,9,4]=>11111101=>[6,1,1]=>[1,1,6]
[8,7,6,4,3,2,1,9,5]=>11111101=>[6,1,1]=>[1,1,6]
[8,7,5,4,3,2,1,9,6]=>11111101=>[6,1,1]=>[1,1,6]
[8,5,4,3,2,1,7,6]=>1111101=>[5,1,1]=>[1,1,5]
[8,6,5,4,3,2,1,9,7]=>11111101=>[6,1,1]=>[1,1,6]
[7,6,5,4,3,2,1,9,8]=>11111101=>[6,1,1]=>[1,1,6]
[7,6,5,4,1,8,3,2]=>1111011=>[4,1,2]=>[2,1,4]
[8,7,6,5,4,9,1,3,2]=>11110101=>[4,1,1,1,1]=>[1,1,1,1,4]
[9,8,7,6,5,4,2,1,10,3]=>111111101=>[7,1,1]=>[1,1,7]
[7,6,5,2,8,1,4,3]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,7,6,5,9,2,1,4,3]=>11101101=>[3,1,2,1,1]=>[1,1,2,1,3]
[9,8,7,6,5,3,2,1,10,4]=>111111101=>[7,1,1]=>[1,1,7]
[7,6,5,8,4,1,3,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[8,7,6,9,3,2,1,5,4]=>11011101=>[2,1,3,1,1]=>[1,1,3,1,2]
[9,8,7,6,4,3,2,1,10,5]=>111111101=>[7,1,1]=>[1,1,7]
[7,6,8,5,2,1,4,3]=>1011101=>[1,1,3,1,1]=>[1,1,3,1,1]
[8,7,9,4,3,2,1,6,5]=>10111101=>[1,1,4,1,1]=>[1,1,4,1,1]
[9,8,7,5,4,3,2,1,10,6]=>111111101=>[7,1,1]=>[1,1,7]
[7,8,6,3,2,1,5,4]=>0111101=>[1,4,1,1]=>[1,1,4,1]
[8,9,5,4,3,2,1,7,6]=>01111101=>[1,5,1,1]=>[1,1,5,1]
[9,8,6,5,4,3,2,1,10,7]=>111111101=>[7,1,1]=>[1,1,7]
[8,7,4,3,2,1,6,5]=>1111101=>[5,1,1]=>[1,1,5]
[9,6,5,4,3,2,1,8,7]=>11111101=>[6,1,1]=>[1,1,6]
[9,7,6,5,4,3,2,1,10,8]=>111111101=>[7,1,1]=>[1,1,7]
[7,8,9,10,4,5,6,2,3,1]=>000100101=>[3,1,2,1,1,1]=>[1,1,1,2,1,3]
[7,8,9,4,5,6,10,2,3,1]=>001000101=>[2,1,3,1,1,1]=>[1,1,1,3,1,2]
[7,8,9,10,4,5,2,3,6,1]=>000101001=>[3,1,1,1,2,1]=>[1,2,1,1,1,3]
[7,8,9,4,5,10,2,3,6,1]=>001001001=>[2,1,2,1,2,1]=>[1,2,1,2,1,2]
[7,8,9,4,5,2,3,6,10,1]=>001010001=>[2,1,1,1,3,1]=>[1,3,1,1,1,2]
[7,8,4,5,9,10,2,3,6,1]=>010001001=>[1,1,3,1,2,1]=>[1,2,1,3,1,1]
[7,8,4,5,9,2,3,6,10,1]=>010010001=>[1,1,2,1,3,1]=>[1,3,1,2,1,1]
[7,8,9,10,4,5,6,2,1,3]=>000100110=>[3,1,2,2,1]=>[1,2,2,1,3]
[7,8,9,4,5,6,10,2,1,3]=>001000110=>[2,1,3,2,1]=>[1,2,3,1,2]
[7,8,9,10,4,5,2,6,1,3]=>000101010=>[3,1,1,1,1,1,1]=>[1,1,1,1,1,1,3]
[7,8,9,4,5,10,2,6,1,3]=>001001010=>[2,1,2,1,1,1,1]=>[1,1,1,1,2,1,2]
[7,8,9,4,5,2,6,10,1,3]=>001010010=>[2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2]
[7,8,4,5,9,10,2,6,1,3]=>010001010=>[1,1,3,1,1,1,1]=>[1,1,1,1,3,1,1]
[7,8,4,5,9,2,6,10,1,3]=>010010010=>[1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1]
[7,8,9,10,4,5,2,1,3,6]=>000101100=>[3,1,1,2,2]=>[2,2,1,1,3]
[7,8,9,4,5,10,2,1,3,6]=>001001100=>[2,1,2,2,2]=>[2,2,2,1,2]
[7,8,9,4,5,2,10,1,3,6]=>001010100=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2]
[7,8,9,4,5,2,1,3,6,10]=>001011000=>[2,1,1,2,3]=>[3,2,1,1,2]
[7,8,4,5,9,10,2,1,3,6]=>010001100=>[1,1,3,2,2]=>[2,2,3,1,1]
[7,8,4,5,9,2,10,1,3,6]=>010010100=>[1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1]
[7,8,4,5,9,2,1,3,6,10]=>010011000=>[1,1,2,2,3]=>[3,2,2,1,1]
[7,8,9,10,4,2,5,6,1,3]=>000110010=>[3,2,2,1,1]=>[1,1,2,2,3]
[7,8,9,4,10,2,5,6,1,3]=>001010010=>[2,1,1,1,2,1,1]=>[1,1,2,1,1,1,2]
[7,8,9,4,2,5,6,10,1,3]=>001100010=>[2,2,3,1,1]=>[1,1,3,2,2]
[7,8,4,9,10,2,5,6,1,3]=>010010010=>[1,1,2,1,2,1,1]=>[1,1,2,1,2,1,1]
[7,8,4,9,2,5,6,10,1,3]=>010100010=>[1,1,1,1,3,1,1]=>[1,1,3,1,1,1,1]
[7,8,9,10,4,2,5,1,3,6]=>000110100=>[3,2,1,1,2]=>[2,1,1,2,3]
[7,8,9,4,10,2,5,1,3,6]=>001010100=>[2,1,1,1,1,1,2]=>[2,1,1,1,1,1,2]
[7,8,9,4,2,5,10,1,3,6]=>001100100=>[2,2,2,1,2]=>[2,1,2,2,2]
[7,8,9,4,2,5,1,3,6,10]=>001101000=>[2,2,1,1,3]=>[3,1,1,2,2]
[7,8,4,9,10,2,5,1,3,6]=>010010100=>[1,1,2,1,1,1,2]=>[2,1,1,1,2,1,1]
[7,8,4,9,2,5,10,1,3,6]=>010100100=>[1,1,1,1,2,1,2]=>[2,1,2,1,1,1,1]
[7,8,4,9,2,5,1,3,6,10]=>010101000=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]
[7,8,4,2,5,9,10,1,3,6]=>011000100=>[1,2,3,1,2]=>[2,1,3,2,1]
[7,8,4,2,5,9,1,3,6,10]=>011001000=>[1,2,2,1,3]=>[3,1,2,2,1]
[7,4,8,9,10,2,5,6,1,3]=>100010010=>[1,3,1,2,1,1]=>[1,1,2,1,3,1]
[7,4,8,9,2,5,6,10,1,3]=>100100010=>[1,2,1,3,1,1]=>[1,1,3,1,2,1]
[7,4,8,9,10,2,5,1,3,6]=>100010100=>[1,3,1,1,1,2]=>[2,1,1,1,3,1]
[7,4,8,9,2,5,10,1,3,6]=>100100100=>[1,2,1,2,1,2]=>[2,1,2,1,2,1]
[7,4,8,9,2,5,1,3,6,10]=>100101000=>[1,2,1,1,1,3]=>[3,1,1,1,2,1]
[7,4,8,2,5,9,10,1,3,6]=>101000100=>[1,1,1,3,1,2]=>[2,1,3,1,1,1]
[7,8,2,4,5,1,3,6]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[4,6,7,2,5,1,3,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[7,8,1,3,2,4,5,6]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[7,8,4,1,5,2,3,6]=>0110100=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,6,7,2,1,4,5,8]=>0011000=>[2,2,3]=>[3,2,2]
[5,2,3,6,1,4,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[2,5,3,6,1,4,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[2,6,7,3,1,4,5,8]=>0011000=>[2,2,3]=>[3,2,2]
[4,6,7,1,5,2,3,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[4,6,7,3,5,8,1,2]=>0010010=>[2,1,2,1,1]=>[1,1,2,1,2]
[6,4,7,1,5,2,3,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,2,7,3,1,4,5,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[3,2,5,6,1,4,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[3,5,2,6,1,4,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,1,4,6,7,2,3,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[3,5,4,6,7,8,1,2]=>0100010=>[1,1,3,1,1]=>[1,1,3,1,1]
[1,5,4,6,7,2,3,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[1,6,7,3,2,4,5,8]=>0011000=>[2,2,3]=>[3,2,2]
[1,5,3,6,2,4,7,8]=>0101000=>[1,1,1,1,3]=>[3,1,1,1,1]
[5,1,3,6,2,4,7,8]=>1001000=>[1,2,1,3]=>[3,1,2,1]
[5,2,4,6,7,1,3,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[2,5,4,6,7,1,3,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[2,6,7,4,5,1,3,8]=>0010100=>[2,1,1,1,2]=>[2,1,1,1,2]
[6,2,7,4,5,1,3,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,2,5,6,7,1,3,8]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[4,5,2,6,7,1,3,8]=>0100100=>[1,1,2,1,2]=>[2,1,2,1,1]
[5,3,1,6,2,4,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[6,1,7,3,2,4,5,8]=>1011000=>[1,1,2,3]=>[3,2,1,1]
[6,1,7,4,5,2,3,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,7,4,5,8,1,2]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[5,4,1,6,7,2,3,8]=>1100100=>[2,2,1,2]=>[2,1,2,2]
[5,2,1,6,3,4,7,8]=>1101000=>[2,1,1,3]=>[3,1,1,2]
[7,3,2,5,4,1,6,8]=>1101100=>[2,1,2,2]=>[2,2,1,2]
[7,3,5,4,2,1,6,8]=>1011100=>[1,1,3,2]=>[2,3,1,1]
[7,3,5,2,4,1,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,6,5,2,1,4,3,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[1,3,6,7,5,2,8,4]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[7,3,4,1,6,2,5,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,3,4,1,6,5,2,8]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,3,4,1,5,6,2,8]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[7,3,2,5,1,6,4,8]=>1101010=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,5,4,1,3,2,8]=>1111010=>[4,1,1,1]=>[1,1,1,4]
[7,3,4,1,5,2,6,8]=>1010100=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[1,3,6,7,2,5,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[1,7,4,6,2,8,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[4,3,1,7,2,6,8,5]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,6,1,4,7,3,8,2]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[5,3,2,1,7,4,8,6]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[1,3,4,5,8,7,2,6]=>0000110=>[4,2,1]=>[1,2,4]
[6,3,4,5,8,1,7,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[2,4,5,1,6,8,7,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,1,2,5,6,8,7,4]=>1000011=>[1,4,2]=>[2,4,1]
[4,3,2,5,6,8,1,7]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[3,7,5,4,6,8,1,2]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,1,4,6,5,8,2,7]=>1001010=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[2,3,4,5,8,6,1,7]=>0000110=>[4,2,1]=>[1,2,4]
[2,3,4,5,8,1,7,6]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[3,1,4,6,5,8,7,2]=>1001011=>[1,2,1,1,2]=>[2,1,1,2,1]
[3,7,5,4,6,8,2,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,6,1,4,7,2,8,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[4,3,1,7,5,6,8,2]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[4,3,1,7,6,5,8,2]=>1101101=>[2,1,2,1,1]=>[1,1,2,1,2]
[3,1,4,6,7,8,5,2]=>1000011=>[1,4,2]=>[2,4,1]
[1,4,5,2,6,8,7,3]=>0010011=>[2,1,2,2]=>[2,2,1,2]
[3,7,5,2,6,8,1,4]=>0110010=>[1,2,2,1,1]=>[1,1,2,2,1]
[3,7,5,2,6,8,4,1]=>0110011=>[1,2,2,2]=>[2,2,2,1]
[5,6,1,2,7,4,8,3]=>0100101=>[1,1,2,1,1,1]=>[1,1,1,2,1,1]
[6,3,5,2,4,7,8,1]=>1010001=>[1,1,1,3,1]=>[1,3,1,1,1]
[5,3,2,1,4,7,8,6]=>1110001=>[3,3,1]=>[1,3,3]
[5,3,1,4,2,7,8,6]=>1101001=>[2,1,1,2,1]=>[1,2,1,1,2]
[5,3,1,2,4,7,8,6]=>1100001=>[2,4,1]=>[1,4,2]
[7,1,5,2,6,8,4,3]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,1,5,2,6,8,3,4]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[1,7,4,6,5,8,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,7,4,6,1,8,3,5]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[2,7,4,6,1,8,5,3]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[2,3,6,7,1,5,8,4]=>0001001=>[3,1,2,1]=>[1,2,1,3]
[2,3,6,7,5,1,8,4]=>0001101=>[3,2,1,1]=>[1,1,2,3]
[4,3,2,6,7,1,8,5]=>1100101=>[2,2,1,1,1]=>[1,1,1,2,2]
[7,3,2,5,6,8,1,4]=>1100010=>[2,3,1,1]=>[1,1,3,2]
[7,1,5,4,6,8,2,3]=>1010010=>[1,1,1,2,1,1]=>[1,1,2,1,1,1]
[2,7,4,6,5,8,1,3]=>0101010=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,3,4,5,8,6,1,2]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,3,4,5,8,1,6,2]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,3,4,5,8,1,2,6]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[1,3,4,5,8,6,2,7]=>0000110=>[4,2,1]=>[1,2,4]
[1,3,4,5,8,2,7,6]=>0000101=>[4,1,1,1]=>[1,1,1,4]
[6,3,4,5,8,2,1,7]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[6,3,4,5,8,2,7,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[7,3,4,5,8,6,2,1]=>1000111=>[1,3,3]=>[3,3,1]
[2,7,4,6,5,8,3,1]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[7,1,5,4,6,8,3,2]=>1010011=>[1,1,1,2,2]=>[2,2,1,1,1]
[7,3,2,5,6,8,4,1]=>1100011=>[2,3,2]=>[2,3,2]
[5,7,4,6,1,8,3,2]=>0101011=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]
[6,3,4,5,8,1,2,7]=>1000100=>[1,3,1,2]=>[2,1,3,1]
[7,3,4,5,8,2,1,6]=>1000110=>[1,3,2,1]=>[1,2,3,1]
[7,3,4,5,8,2,6,1]=>1000101=>[1,3,1,1,1]=>[1,1,1,3,1]
[4,7,6,1,8,2,5,3]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[4,8,6,1,7,5,2,3]=>0110110=>[1,2,1,2,1]=>[1,2,1,2,1]
[4,7,8,2,6,1,5,3]=>0010101=>[2,1,1,1,1,1]=>[1,1,1,1,1,2]
[7,6,4,2,8,3,5,1]=>1110101=>[3,1,1,1,1]=>[1,1,1,1,3]
[8,6,4,2,7,5,3,1]=>1110111=>[3,1,3]=>[3,1,3]
[8,4,7,3,6,5,1,2]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[8,4,6,1,7,5,3,2]=>1010111=>[1,1,1,1,3]=>[3,1,1,1,1]
[6,4,7,1,8,3,2,5]=>1010110=>[1,1,1,1,2,1]=>[1,2,1,1,1,1]
[7,4,8,3,6,1,5,2]=>1010101=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]
[7,8,4,3,6,2,5,1]=>0110101=>[1,2,1,1,1,1]=>[1,1,1,1,2,1]
[8,10,7,9,5,6,3,4,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,6,8,5,7,3,4,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,6,9,5,7,3,4,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,10,6,9,5,8,3,4,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,7,8,4,6,3,5,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,7,9,4,6,3,5,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,6,8,4,7,3,5,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,6,9,4,7,3,5,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,10,6,9,4,8,3,5,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,5,8,4,7,3,6,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,5,9,4,7,3,6,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,10,5,9,4,8,3,6,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[6,10,5,9,4,8,3,7,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,7,8,5,6,2,4,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,7,9,5,6,2,4,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,6,8,5,7,2,4,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,6,9,5,7,2,4,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,10,6,9,5,8,2,4,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,7,8,4,6,2,5,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,7,9,4,6,2,5,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,6,8,4,7,2,5,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,6,9,4,7,2,5,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,10,6,9,4,8,2,5,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,5,8,4,7,2,6,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,5,9,4,7,2,6,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,10,5,9,4,8,2,6,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[6,10,5,9,4,8,2,7,1,3]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,7,8,3,6,2,5,1,4]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,7,9,3,6,2,5,1,4]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,6,8,3,7,2,5,1,4]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,6,9,3,7,2,5,1,4]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,10,6,9,3,8,2,5,1,4]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,5,8,3,7,2,6,1,4]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,5,9,3,7,2,6,1,4]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,10,5,9,3,8,2,6,1,4]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[6,10,5,9,3,8,2,7,1,4]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[9,10,4,8,3,7,2,6,1,5]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[8,10,4,9,3,7,2,6,1,5]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[7,10,4,9,3,8,2,6,1,5]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[6,10,4,9,3,8,2,7,1,5]=>010101010=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]
[10,12,9,11,7,8,5,6,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,7,9,5,6,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,7,9,5,6,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,7,10,5,6,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,6,8,5,7,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,6,8,5,7,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,6,9,5,7,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,6,9,5,7,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,6,10,5,7,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,7,10,6,9,5,8,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,7,11,6,9,5,8,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,7,11,6,10,5,8,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[8,12,7,11,6,10,5,9,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,7,8,4,6,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,7,8,4,6,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,7,9,4,6,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,7,9,4,6,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,7,10,4,6,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,6,8,4,7,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,6,8,4,7,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,6,9,4,7,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,6,9,4,7,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,6,10,4,7,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,7,10,6,9,4,8,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,7,11,6,9,4,8,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,7,11,6,10,4,8,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[8,12,7,11,6,10,4,9,3,5,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,5,8,4,7,3,6,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,5,8,4,7,3,6,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,5,9,4,7,3,6,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,5,9,4,7,3,6,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,5,10,4,7,3,6,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,7,10,5,9,4,8,3,6,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,7,11,5,9,4,8,3,6,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,7,11,5,10,4,8,3,6,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[8,12,7,11,5,10,4,9,3,6,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,6,10,5,9,4,8,3,7,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,6,11,5,9,4,8,3,7,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,6,11,5,10,4,8,3,7,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[8,12,6,11,5,10,4,9,3,7,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[7,12,6,11,5,10,4,9,3,8,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,7,8,5,6,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,7,8,5,6,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,7,9,5,6,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,7,9,5,6,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,7,10,5,6,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,6,8,5,7,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,6,8,5,7,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,6,9,5,7,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,6,9,5,7,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,6,10,5,7,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,7,10,6,9,5,8,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,7,11,6,9,5,8,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,7,11,6,10,5,8,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[8,12,7,11,6,10,5,9,2,4,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,7,8,4,6,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,7,8,4,6,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,7,9,4,6,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,7,9,4,6,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,7,10,4,6,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,6,8,4,7,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,6,8,4,7,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,6,9,4,7,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,6,9,4,7,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,6,10,4,7,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,7,10,6,9,4,8,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,7,11,6,9,4,8,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,7,11,6,10,4,8,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[8,12,7,11,6,10,4,9,2,5,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,5,8,4,7,2,6,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,5,8,4,7,2,6,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,5,9,4,7,2,6,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,5,9,4,7,2,6,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,5,10,4,7,2,6,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,7,10,5,9,4,8,2,6,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,7,11,5,9,4,8,2,6,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,7,11,5,10,4,8,2,6,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[8,12,7,11,5,10,4,9,2,6,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,6,10,5,9,4,8,2,7,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,6,11,5,9,4,8,2,7,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,6,11,5,10,4,8,2,7,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[8,12,6,11,5,10,4,9,2,7,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[7,12,6,11,5,10,4,9,2,8,1,3]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,7,8,3,6,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,7,8,3,6,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,7,9,3,6,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,7,9,3,6,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,7,10,3,6,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,6,8,3,7,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,6,8,3,7,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,6,9,3,7,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,6,9,3,7,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,6,10,3,7,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,7,10,6,9,3,8,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,7,11,6,9,3,8,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,7,11,6,10,3,8,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[8,12,7,11,6,10,3,9,2,5,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,9,10,5,8,3,7,2,6,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,9,11,5,8,3,7,2,6,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,8,10,5,9,3,7,2,6,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,8,11,5,9,3,7,2,6,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[9,12,8,11,5,10,3,7,2,6,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[11,12,7,10,5,9,3,8,2,6,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[10,12,7,11,5,9,3,8,2,6,1,4]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,