Identifier
Mp00109:
Permutations
—descent word⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00104: Binary words —reverse⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Images
=>
[1,2]=>0=>0=>[2]
[2,1]=>1=>1=>[1,1]
[1,2,3]=>00=>00=>[3]
[1,3,2]=>01=>10=>[1,2]
[2,1,3]=>10=>01=>[2,1]
[2,3,1]=>01=>10=>[1,2]
[3,1,2]=>10=>01=>[2,1]
[3,2,1]=>11=>11=>[1,1,1]
[1,2,3,4]=>000=>000=>[4]
[1,2,4,3]=>001=>100=>[1,3]
[1,3,2,4]=>010=>010=>[2,2]
[1,3,4,2]=>001=>100=>[1,3]
[1,4,2,3]=>010=>010=>[2,2]
[1,4,3,2]=>011=>110=>[1,1,2]
[2,1,3,4]=>100=>001=>[3,1]
[2,1,4,3]=>101=>101=>[1,2,1]
[2,3,1,4]=>010=>010=>[2,2]
[2,3,4,1]=>001=>100=>[1,3]
[2,4,1,3]=>010=>010=>[2,2]
[2,4,3,1]=>011=>110=>[1,1,2]
[3,1,2,4]=>100=>001=>[3,1]
[3,1,4,2]=>101=>101=>[1,2,1]
[3,2,1,4]=>110=>011=>[2,1,1]
[3,2,4,1]=>101=>101=>[1,2,1]
[3,4,1,2]=>010=>010=>[2,2]
[3,4,2,1]=>011=>110=>[1,1,2]
[4,1,2,3]=>100=>001=>[3,1]
[4,1,3,2]=>101=>101=>[1,2,1]
[4,2,1,3]=>110=>011=>[2,1,1]
[4,2,3,1]=>101=>101=>[1,2,1]
[4,3,1,2]=>110=>011=>[2,1,1]
[4,3,2,1]=>111=>111=>[1,1,1,1]
[1,2,3,4,5]=>0000=>0000=>[5]
[1,2,3,5,4]=>0001=>1000=>[1,4]
[1,2,4,3,5]=>0010=>0100=>[2,3]
[1,2,4,5,3]=>0001=>1000=>[1,4]
[1,2,5,3,4]=>0010=>0100=>[2,3]
[1,2,5,4,3]=>0011=>1100=>[1,1,3]
[1,3,2,4,5]=>0100=>0010=>[3,2]
[1,3,2,5,4]=>0101=>1010=>[1,2,2]
[1,3,4,2,5]=>0010=>0100=>[2,3]
[1,3,4,5,2]=>0001=>1000=>[1,4]
[1,3,5,2,4]=>0010=>0100=>[2,3]
[1,3,5,4,2]=>0011=>1100=>[1,1,3]
[1,4,2,3,5]=>0100=>0010=>[3,2]
[1,4,2,5,3]=>0101=>1010=>[1,2,2]
[1,4,3,2,5]=>0110=>0110=>[2,1,2]
[1,4,3,5,2]=>0101=>1010=>[1,2,2]
[1,4,5,2,3]=>0010=>0100=>[2,3]
[1,4,5,3,2]=>0011=>1100=>[1,1,3]
[1,5,2,3,4]=>0100=>0010=>[3,2]
[1,5,2,4,3]=>0101=>1010=>[1,2,2]
[1,5,3,2,4]=>0110=>0110=>[2,1,2]
[1,5,3,4,2]=>0101=>1010=>[1,2,2]
[1,5,4,2,3]=>0110=>0110=>[2,1,2]
[1,5,4,3,2]=>0111=>1110=>[1,1,1,2]
[2,1,3,4,5]=>1000=>0001=>[4,1]
[2,1,3,5,4]=>1001=>1001=>[1,3,1]
[2,1,4,3,5]=>1010=>0101=>[2,2,1]
[2,1,4,5,3]=>1001=>1001=>[1,3,1]
[2,1,5,3,4]=>1010=>0101=>[2,2,1]
[2,1,5,4,3]=>1011=>1101=>[1,1,2,1]
[2,3,1,4,5]=>0100=>0010=>[3,2]
[2,3,1,5,4]=>0101=>1010=>[1,2,2]
[2,3,4,1,5]=>0010=>0100=>[2,3]
[2,3,4,5,1]=>0001=>1000=>[1,4]
[2,3,5,1,4]=>0010=>0100=>[2,3]
[2,3,5,4,1]=>0011=>1100=>[1,1,3]
[2,4,1,3,5]=>0100=>0010=>[3,2]
[2,4,1,5,3]=>0101=>1010=>[1,2,2]
[2,4,3,1,5]=>0110=>0110=>[2,1,2]
[2,4,3,5,1]=>0101=>1010=>[1,2,2]
[2,4,5,1,3]=>0010=>0100=>[2,3]
[2,4,5,3,1]=>0011=>1100=>[1,1,3]
[2,5,1,3,4]=>0100=>0010=>[3,2]
[2,5,1,4,3]=>0101=>1010=>[1,2,2]
[2,5,3,1,4]=>0110=>0110=>[2,1,2]
[2,5,3,4,1]=>0101=>1010=>[1,2,2]
[2,5,4,1,3]=>0110=>0110=>[2,1,2]
[2,5,4,3,1]=>0111=>1110=>[1,1,1,2]
[3,1,2,4,5]=>1000=>0001=>[4,1]
[3,1,2,5,4]=>1001=>1001=>[1,3,1]
[3,1,4,2,5]=>1010=>0101=>[2,2,1]
[3,1,4,5,2]=>1001=>1001=>[1,3,1]
[3,1,5,2,4]=>1010=>0101=>[2,2,1]
[3,1,5,4,2]=>1011=>1101=>[1,1,2,1]
[3,2,1,4,5]=>1100=>0011=>[3,1,1]
[3,2,1,5,4]=>1101=>1011=>[1,2,1,1]
[3,2,4,1,5]=>1010=>0101=>[2,2,1]
[3,2,4,5,1]=>1001=>1001=>[1,3,1]
[3,2,5,1,4]=>1010=>0101=>[2,2,1]
[3,2,5,4,1]=>1011=>1101=>[1,1,2,1]
[3,4,1,2,5]=>0100=>0010=>[3,2]
[3,4,1,5,2]=>0101=>1010=>[1,2,2]
[3,4,2,1,5]=>0110=>0110=>[2,1,2]
[3,4,2,5,1]=>0101=>1010=>[1,2,2]
[3,4,5,1,2]=>0010=>0100=>[2,3]
[3,4,5,2,1]=>0011=>1100=>[1,1,3]
[3,5,1,2,4]=>0100=>0010=>[3,2]
[3,5,1,4,2]=>0101=>1010=>[1,2,2]
[3,5,2,1,4]=>0110=>0110=>[2,1,2]
[3,5,2,4,1]=>0101=>1010=>[1,2,2]
[3,5,4,1,2]=>0110=>0110=>[2,1,2]
[3,5,4,2,1]=>0111=>1110=>[1,1,1,2]
[4,1,2,3,5]=>1000=>0001=>[4,1]
[4,1,2,5,3]=>1001=>1001=>[1,3,1]
[4,1,3,2,5]=>1010=>0101=>[2,2,1]
[4,1,3,5,2]=>1001=>1001=>[1,3,1]
[4,1,5,2,3]=>1010=>0101=>[2,2,1]
[4,1,5,3,2]=>1011=>1101=>[1,1,2,1]
[4,2,1,3,5]=>1100=>0011=>[3,1,1]
[4,2,1,5,3]=>1101=>1011=>[1,2,1,1]
[4,2,3,1,5]=>1010=>0101=>[2,2,1]
[4,2,3,5,1]=>1001=>1001=>[1,3,1]
[4,2,5,1,3]=>1010=>0101=>[2,2,1]
[4,2,5,3,1]=>1011=>1101=>[1,1,2,1]
[4,3,1,2,5]=>1100=>0011=>[3,1,1]
[4,3,1,5,2]=>1101=>1011=>[1,2,1,1]
[4,3,2,1,5]=>1110=>0111=>[2,1,1,1]
[4,3,2,5,1]=>1101=>1011=>[1,2,1,1]
[4,3,5,1,2]=>1010=>0101=>[2,2,1]
[4,3,5,2,1]=>1011=>1101=>[1,1,2,1]
[4,5,1,2,3]=>0100=>0010=>[3,2]
[4,5,1,3,2]=>0101=>1010=>[1,2,2]
[4,5,2,1,3]=>0110=>0110=>[2,1,2]
[4,5,2,3,1]=>0101=>1010=>[1,2,2]
[4,5,3,1,2]=>0110=>0110=>[2,1,2]
[4,5,3,2,1]=>0111=>1110=>[1,1,1,2]
[5,1,2,3,4]=>1000=>0001=>[4,1]
[5,1,2,4,3]=>1001=>1001=>[1,3,1]
[5,1,3,2,4]=>1010=>0101=>[2,2,1]
[5,1,3,4,2]=>1001=>1001=>[1,3,1]
[5,1,4,2,3]=>1010=>0101=>[2,2,1]
[5,1,4,3,2]=>1011=>1101=>[1,1,2,1]
[5,2,1,3,4]=>1100=>0011=>[3,1,1]
[5,2,1,4,3]=>1101=>1011=>[1,2,1,1]
[5,2,3,1,4]=>1010=>0101=>[2,2,1]
[5,2,3,4,1]=>1001=>1001=>[1,3,1]
[5,2,4,1,3]=>1010=>0101=>[2,2,1]
[5,2,4,3,1]=>1011=>1101=>[1,1,2,1]
[5,3,1,2,4]=>1100=>0011=>[3,1,1]
[5,3,1,4,2]=>1101=>1011=>[1,2,1,1]
[5,3,2,1,4]=>1110=>0111=>[2,1,1,1]
[5,3,2,4,1]=>1101=>1011=>[1,2,1,1]
[5,3,4,1,2]=>1010=>0101=>[2,2,1]
[5,3,4,2,1]=>1011=>1101=>[1,1,2,1]
[5,4,1,2,3]=>1100=>0011=>[3,1,1]
[5,4,1,3,2]=>1101=>1011=>[1,2,1,1]
[5,4,2,1,3]=>1110=>0111=>[2,1,1,1]
[5,4,2,3,1]=>1101=>1011=>[1,2,1,1]
[5,4,3,1,2]=>1110=>0111=>[2,1,1,1]
[5,4,3,2,1]=>1111=>1111=>[1,1,1,1,1]
[1,2,3,4,5,6]=>00000=>00000=>[6]
[1,2,3,4,6,5]=>00001=>10000=>[1,5]
[1,2,3,5,4,6]=>00010=>01000=>[2,4]
[1,2,3,5,6,4]=>00001=>10000=>[1,5]
[1,2,3,6,4,5]=>00010=>01000=>[2,4]
[1,2,3,6,5,4]=>00011=>11000=>[1,1,4]
[1,2,4,3,5,6]=>00100=>00100=>[3,3]
[1,2,4,3,6,5]=>00101=>10100=>[1,2,3]
[1,2,4,5,3,6]=>00010=>01000=>[2,4]
[1,2,4,5,6,3]=>00001=>10000=>[1,5]
[1,2,4,6,3,5]=>00010=>01000=>[2,4]
[1,2,4,6,5,3]=>00011=>11000=>[1,1,4]
[1,2,5,3,4,6]=>00100=>00100=>[3,3]
[1,2,5,3,6,4]=>00101=>10100=>[1,2,3]
[1,2,5,4,3,6]=>00110=>01100=>[2,1,3]
[1,2,5,4,6,3]=>00101=>10100=>[1,2,3]
[1,2,5,6,3,4]=>00010=>01000=>[2,4]
[1,2,5,6,4,3]=>00011=>11000=>[1,1,4]
[1,2,6,3,4,5]=>00100=>00100=>[3,3]
[1,2,6,3,5,4]=>00101=>10100=>[1,2,3]
[1,2,6,4,3,5]=>00110=>01100=>[2,1,3]
[1,2,6,4,5,3]=>00101=>10100=>[1,2,3]
[1,2,6,5,3,4]=>00110=>01100=>[2,1,3]
[1,2,6,5,4,3]=>00111=>11100=>[1,1,1,3]
[1,3,2,4,5,6]=>01000=>00010=>[4,2]
[1,3,2,4,6,5]=>01001=>10010=>[1,3,2]
[1,3,2,5,4,6]=>01010=>01010=>[2,2,2]
[1,3,2,5,6,4]=>01001=>10010=>[1,3,2]
[1,3,2,6,4,5]=>01010=>01010=>[2,2,2]
[1,3,2,6,5,4]=>01011=>11010=>[1,1,2,2]
[1,3,4,2,5,6]=>00100=>00100=>[3,3]
[1,3,4,2,6,5]=>00101=>10100=>[1,2,3]
[1,3,4,5,2,6]=>00010=>01000=>[2,4]
[1,3,4,5,6,2]=>00001=>10000=>[1,5]
[1,3,4,6,2,5]=>00010=>01000=>[2,4]
[1,3,4,6,5,2]=>00011=>11000=>[1,1,4]
[1,3,5,2,4,6]=>00100=>00100=>[3,3]
[1,3,5,2,6,4]=>00101=>10100=>[1,2,3]
[1,3,5,4,2,6]=>00110=>01100=>[2,1,3]
[1,3,5,4,6,2]=>00101=>10100=>[1,2,3]
[1,3,5,6,2,4]=>00010=>01000=>[2,4]
[1,3,5,6,4,2]=>00011=>11000=>[1,1,4]
[1,3,6,2,4,5]=>00100=>00100=>[3,3]
[1,3,6,2,5,4]=>00101=>10100=>[1,2,3]
[1,3,6,4,2,5]=>00110=>01100=>[2,1,3]
[1,3,6,4,5,2]=>00101=>10100=>[1,2,3]
[1,3,6,5,2,4]=>00110=>01100=>[2,1,3]
[1,3,6,5,4,2]=>00111=>11100=>[1,1,1,3]
[1,4,2,3,5,6]=>01000=>00010=>[4,2]
[1,4,2,3,6,5]=>01001=>10010=>[1,3,2]
[1,4,2,5,3,6]=>01010=>01010=>[2,2,2]
[1,4,2,5,6,3]=>01001=>10010=>[1,3,2]
[1,4,2,6,3,5]=>01010=>01010=>[2,2,2]
[1,4,2,6,5,3]=>01011=>11010=>[1,1,2,2]
[1,4,3,2,5,6]=>01100=>00110=>[3,1,2]
[1,4,3,2,6,5]=>01101=>10110=>[1,2,1,2]
[1,4,3,5,2,6]=>01010=>01010=>[2,2,2]
[1,4,3,5,6,2]=>01001=>10010=>[1,3,2]
[1,4,3,6,2,5]=>01010=>01010=>[2,2,2]
[1,4,3,6,5,2]=>01011=>11010=>[1,1,2,2]
[1,4,5,2,3,6]=>00100=>00100=>[3,3]
[1,4,5,2,6,3]=>00101=>10100=>[1,2,3]
[1,4,5,3,2,6]=>00110=>01100=>[2,1,3]
[1,4,5,3,6,2]=>00101=>10100=>[1,2,3]
[1,4,5,6,2,3]=>00010=>01000=>[2,4]
[1,4,5,6,3,2]=>00011=>11000=>[1,1,4]
[1,4,6,2,3,5]=>00100=>00100=>[3,3]
[1,4,6,2,5,3]=>00101=>10100=>[1,2,3]
[1,4,6,3,2,5]=>00110=>01100=>[2,1,3]
[1,4,6,3,5,2]=>00101=>10100=>[1,2,3]
[1,4,6,5,2,3]=>00110=>01100=>[2,1,3]
[1,4,6,5,3,2]=>00111=>11100=>[1,1,1,3]
[1,5,2,3,4,6]=>01000=>00010=>[4,2]
[1,5,2,3,6,4]=>01001=>10010=>[1,3,2]
[1,5,2,4,3,6]=>01010=>01010=>[2,2,2]
[1,5,2,4,6,3]=>01001=>10010=>[1,3,2]
[1,5,2,6,3,4]=>01010=>01010=>[2,2,2]
[1,5,2,6,4,3]=>01011=>11010=>[1,1,2,2]
[1,5,3,2,4,6]=>01100=>00110=>[3,1,2]
[1,5,3,2,6,4]=>01101=>10110=>[1,2,1,2]
[1,5,3,4,2,6]=>01010=>01010=>[2,2,2]
[1,5,3,4,6,2]=>01001=>10010=>[1,3,2]
[1,5,3,6,2,4]=>01010=>01010=>[2,2,2]
[1,5,3,6,4,2]=>01011=>11010=>[1,1,2,2]
[1,5,4,2,3,6]=>01100=>00110=>[3,1,2]
[1,5,4,2,6,3]=>01101=>10110=>[1,2,1,2]
[1,5,4,3,2,6]=>01110=>01110=>[2,1,1,2]
[1,5,4,3,6,2]=>01101=>10110=>[1,2,1,2]
[1,5,4,6,2,3]=>01010=>01010=>[2,2,2]
[1,5,4,6,3,2]=>01011=>11010=>[1,1,2,2]
[1,5,6,2,3,4]=>00100=>00100=>[3,3]
[1,5,6,2,4,3]=>00101=>10100=>[1,2,3]
[1,5,6,3,2,4]=>00110=>01100=>[2,1,3]
[1,5,6,3,4,2]=>00101=>10100=>[1,2,3]
[1,5,6,4,2,3]=>00110=>01100=>[2,1,3]
[1,5,6,4,3,2]=>00111=>11100=>[1,1,1,3]
[1,6,2,3,4,5]=>01000=>00010=>[4,2]
[1,6,2,3,5,4]=>01001=>10010=>[1,3,2]
[1,6,2,4,3,5]=>01010=>01010=>[2,2,2]
[1,6,2,4,5,3]=>01001=>10010=>[1,3,2]
[1,6,2,5,3,4]=>01010=>01010=>[2,2,2]
[1,6,2,5,4,3]=>01011=>11010=>[1,1,2,2]
[1,6,3,2,4,5]=>01100=>00110=>[3,1,2]
[1,6,3,2,5,4]=>01101=>10110=>[1,2,1,2]
[1,6,3,4,2,5]=>01010=>01010=>[2,2,2]
[1,6,3,4,5,2]=>01001=>10010=>[1,3,2]
[1,6,3,5,2,4]=>01010=>01010=>[2,2,2]
[1,6,3,5,4,2]=>01011=>11010=>[1,1,2,2]
[1,6,4,2,3,5]=>01100=>00110=>[3,1,2]
[1,6,4,2,5,3]=>01101=>10110=>[1,2,1,2]
[1,6,4,3,2,5]=>01110=>01110=>[2,1,1,2]
[1,6,4,3,5,2]=>01101=>10110=>[1,2,1,2]
[1,6,4,5,2,3]=>01010=>01010=>[2,2,2]
[1,6,4,5,3,2]=>01011=>11010=>[1,1,2,2]
[1,6,5,2,3,4]=>01100=>00110=>[3,1,2]
[1,6,5,2,4,3]=>01101=>10110=>[1,2,1,2]
[1,6,5,3,2,4]=>01110=>01110=>[2,1,1,2]
[1,6,5,3,4,2]=>01101=>10110=>[1,2,1,2]
[1,6,5,4,2,3]=>01110=>01110=>[2,1,1,2]
[1,6,5,4,3,2]=>01111=>11110=>[1,1,1,1,2]
[2,1,3,4,5,6]=>10000=>00001=>[5,1]
[2,1,3,4,6,5]=>10001=>10001=>[1,4,1]
[2,1,3,5,4,6]=>10010=>01001=>[2,3,1]
[2,1,3,5,6,4]=>10001=>10001=>[1,4,1]
[2,1,3,6,4,5]=>10010=>01001=>[2,3,1]
[2,1,3,6,5,4]=>10011=>11001=>[1,1,3,1]
[2,1,4,3,5,6]=>10100=>00101=>[3,2,1]
[2,1,4,3,6,5]=>10101=>10101=>[1,2,2,1]
[2,1,4,5,3,6]=>10010=>01001=>[2,3,1]
[2,1,4,5,6,3]=>10001=>10001=>[1,4,1]
[2,1,4,6,3,5]=>10010=>01001=>[2,3,1]
[2,1,4,6,5,3]=>10011=>11001=>[1,1,3,1]
[2,1,5,3,4,6]=>10100=>00101=>[3,2,1]
[2,1,5,3,6,4]=>10101=>10101=>[1,2,2,1]
[2,1,5,4,3,6]=>10110=>01101=>[2,1,2,1]
[2,1,5,4,6,3]=>10101=>10101=>[1,2,2,1]
[2,1,5,6,3,4]=>10010=>01001=>[2,3,1]
[2,1,5,6,4,3]=>10011=>11001=>[1,1,3,1]
[2,1,6,3,4,5]=>10100=>00101=>[3,2,1]
[2,1,6,3,5,4]=>10101=>10101=>[1,2,2,1]
[2,1,6,4,3,5]=>10110=>01101=>[2,1,2,1]
[2,1,6,4,5,3]=>10101=>10101=>[1,2,2,1]
[2,1,6,5,3,4]=>10110=>01101=>[2,1,2,1]
[2,1,6,5,4,3]=>10111=>11101=>[1,1,1,2,1]
[2,3,1,4,5,6]=>01000=>00010=>[4,2]
[2,3,1,4,6,5]=>01001=>10010=>[1,3,2]
[2,3,1,5,4,6]=>01010=>01010=>[2,2,2]
[2,3,1,5,6,4]=>01001=>10010=>[1,3,2]
[2,3,1,6,4,5]=>01010=>01010=>[2,2,2]
[2,3,1,6,5,4]=>01011=>11010=>[1,1,2,2]
[2,3,4,1,5,6]=>00100=>00100=>[3,3]
[2,3,4,1,6,5]=>00101=>10100=>[1,2,3]
[2,3,4,5,1,6]=>00010=>01000=>[2,4]
[2,3,4,5,6,1]=>00001=>10000=>[1,5]
[2,3,4,6,1,5]=>00010=>01000=>[2,4]
[2,3,4,6,5,1]=>00011=>11000=>[1,1,4]
[2,3,5,1,4,6]=>00100=>00100=>[3,3]
[2,3,5,1,6,4]=>00101=>10100=>[1,2,3]
[2,3,5,4,1,6]=>00110=>01100=>[2,1,3]
[2,3,5,4,6,1]=>00101=>10100=>[1,2,3]
[2,3,5,6,1,4]=>00010=>01000=>[2,4]
[2,3,5,6,4,1]=>00011=>11000=>[1,1,4]
[2,3,6,1,4,5]=>00100=>00100=>[3,3]
[2,3,6,1,5,4]=>00101=>10100=>[1,2,3]
[2,3,6,4,1,5]=>00110=>01100=>[2,1,3]
[2,3,6,4,5,1]=>00101=>10100=>[1,2,3]
[2,3,6,5,1,4]=>00110=>01100=>[2,1,3]
[2,3,6,5,4,1]=>00111=>11100=>[1,1,1,3]
[2,4,1,3,5,6]=>01000=>00010=>[4,2]
[2,4,1,3,6,5]=>01001=>10010=>[1,3,2]
[2,4,1,5,3,6]=>01010=>01010=>[2,2,2]
[2,4,1,5,6,3]=>01001=>10010=>[1,3,2]
[2,4,1,6,3,5]=>01010=>01010=>[2,2,2]
[2,4,1,6,5,3]=>01011=>11010=>[1,1,2,2]
[2,4,3,1,5,6]=>01100=>00110=>[3,1,2]
[2,4,3,1,6,5]=>01101=>10110=>[1,2,1,2]
[2,4,3,5,1,6]=>01010=>01010=>[2,2,2]
[2,4,3,5,6,1]=>01001=>10010=>[1,3,2]
[2,4,3,6,1,5]=>01010=>01010=>[2,2,2]
[2,4,3,6,5,1]=>01011=>11010=>[1,1,2,2]
[2,4,5,1,3,6]=>00100=>00100=>[3,3]
[2,4,5,1,6,3]=>00101=>10100=>[1,2,3]
[2,4,5,3,1,6]=>00110=>01100=>[2,1,3]
[2,4,5,3,6,1]=>00101=>10100=>[1,2,3]
[2,4,5,6,1,3]=>00010=>01000=>[2,4]
[2,4,5,6,3,1]=>00011=>11000=>[1,1,4]
[2,4,6,1,3,5]=>00100=>00100=>[3,3]
[2,4,6,1,5,3]=>00101=>10100=>[1,2,3]
[2,4,6,3,1,5]=>00110=>01100=>[2,1,3]
[2,4,6,3,5,1]=>00101=>10100=>[1,2,3]
[2,4,6,5,1,3]=>00110=>01100=>[2,1,3]
[2,4,6,5,3,1]=>00111=>11100=>[1,1,1,3]
[2,5,1,3,4,6]=>01000=>00010=>[4,2]
[2,5,1,3,6,4]=>01001=>10010=>[1,3,2]
[2,5,1,4,3,6]=>01010=>01010=>[2,2,2]
[2,5,1,4,6,3]=>01001=>10010=>[1,3,2]
[2,5,1,6,3,4]=>01010=>01010=>[2,2,2]
[2,5,1,6,4,3]=>01011=>11010=>[1,1,2,2]
[2,5,3,1,4,6]=>01100=>00110=>[3,1,2]
[2,5,3,1,6,4]=>01101=>10110=>[1,2,1,2]
[2,5,3,4,1,6]=>01010=>01010=>[2,2,2]
[2,5,3,4,6,1]=>01001=>10010=>[1,3,2]
[2,5,3,6,1,4]=>01010=>01010=>[2,2,2]
[2,5,3,6,4,1]=>01011=>11010=>[1,1,2,2]
[2,5,4,1,3,6]=>01100=>00110=>[3,1,2]
[2,5,4,1,6,3]=>01101=>10110=>[1,2,1,2]
[2,5,4,3,1,6]=>01110=>01110=>[2,1,1,2]
[2,5,4,3,6,1]=>01101=>10110=>[1,2,1,2]
[2,5,4,6,1,3]=>01010=>01010=>[2,2,2]
[2,5,4,6,3,1]=>01011=>11010=>[1,1,2,2]
[2,5,6,1,3,4]=>00100=>00100=>[3,3]
[2,5,6,1,4,3]=>00101=>10100=>[1,2,3]
[2,5,6,3,1,4]=>00110=>01100=>[2,1,3]
[2,5,6,3,4,1]=>00101=>10100=>[1,2,3]
[2,5,6,4,1,3]=>00110=>01100=>[2,1,3]
[2,5,6,4,3,1]=>00111=>11100=>[1,1,1,3]
[2,6,1,3,4,5]=>01000=>00010=>[4,2]
[2,6,1,3,5,4]=>01001=>10010=>[1,3,2]
[2,6,1,4,3,5]=>01010=>01010=>[2,2,2]
[2,6,1,4,5,3]=>01001=>10010=>[1,3,2]
[2,6,1,5,3,4]=>01010=>01010=>[2,2,2]
[2,6,1,5,4,3]=>01011=>11010=>[1,1,2,2]
[2,6,3,1,4,5]=>01100=>00110=>[3,1,2]
[2,6,3,1,5,4]=>01101=>10110=>[1,2,1,2]
[2,6,3,4,1,5]=>01010=>01010=>[2,2,2]
[2,6,3,4,5,1]=>01001=>10010=>[1,3,2]
[2,6,3,5,1,4]=>01010=>01010=>[2,2,2]
[2,6,3,5,4,1]=>01011=>11010=>[1,1,2,2]
[2,6,4,1,3,5]=>01100=>00110=>[3,1,2]
[2,6,4,1,5,3]=>01101=>10110=>[1,2,1,2]
[2,6,4,3,1,5]=>01110=>01110=>[2,1,1,2]
[2,6,4,3,5,1]=>01101=>10110=>[1,2,1,2]
[2,6,4,5,1,3]=>01010=>01010=>[2,2,2]
[2,6,4,5,3,1]=>01011=>11010=>[1,1,2,2]
[2,6,5,1,3,4]=>01100=>00110=>[3,1,2]
[2,6,5,1,4,3]=>01101=>10110=>[1,2,1,2]
[2,6,5,3,1,4]=>01110=>01110=>[2,1,1,2]
[2,6,5,3,4,1]=>01101=>10110=>[1,2,1,2]
[2,6,5,4,1,3]=>01110=>01110=>[2,1,1,2]
[2,6,5,4,3,1]=>01111=>11110=>[1,1,1,1,2]
[3,1,2,4,5,6]=>10000=>00001=>[5,1]
[3,1,2,4,6,5]=>10001=>10001=>[1,4,1]
[3,1,2,5,4,6]=>10010=>01001=>[2,3,1]
[3,1,2,5,6,4]=>10001=>10001=>[1,4,1]
[3,1,2,6,4,5]=>10010=>01001=>[2,3,1]
[3,1,2,6,5,4]=>10011=>11001=>[1,1,3,1]
[3,1,4,2,5,6]=>10100=>00101=>[3,2,1]
[3,1,4,2,6,5]=>10101=>10101=>[1,2,2,1]
[3,1,4,5,2,6]=>10010=>01001=>[2,3,1]
[3,1,4,5,6,2]=>10001=>10001=>[1,4,1]
[3,1,4,6,2,5]=>10010=>01001=>[2,3,1]
[3,1,4,6,5,2]=>10011=>11001=>[1,1,3,1]
[3,1,5,2,4,6]=>10100=>00101=>[3,2,1]
[3,1,5,2,6,4]=>10101=>10101=>[1,2,2,1]
[3,1,5,4,2,6]=>10110=>01101=>[2,1,2,1]
[3,1,5,4,6,2]=>10101=>10101=>[1,2,2,1]
[3,1,5,6,2,4]=>10010=>01001=>[2,3,1]
[3,1,5,6,4,2]=>10011=>11001=>[1,1,3,1]
[3,1,6,2,4,5]=>10100=>00101=>[3,2,1]
[3,1,6,2,5,4]=>10101=>10101=>[1,2,2,1]
[3,1,6,4,2,5]=>10110=>01101=>[2,1,2,1]
[3,1,6,4,5,2]=>10101=>10101=>[1,2,2,1]
[3,1,6,5,2,4]=>10110=>01101=>[2,1,2,1]
[3,1,6,5,4,2]=>10111=>11101=>[1,1,1,2,1]
[3,2,1,4,5,6]=>11000=>00011=>[4,1,1]
[3,2,1,4,6,5]=>11001=>10011=>[1,3,1,1]
[3,2,1,5,4,6]=>11010=>01011=>[2,2,1,1]
[3,2,1,5,6,4]=>11001=>10011=>[1,3,1,1]
[3,2,1,6,4,5]=>11010=>01011=>[2,2,1,1]
[3,2,1,6,5,4]=>11011=>11011=>[1,1,2,1,1]
[3,2,4,1,5,6]=>10100=>00101=>[3,2,1]
[3,2,4,1,6,5]=>10101=>10101=>[1,2,2,1]
[3,2,4,5,1,6]=>10010=>01001=>[2,3,1]
[3,2,4,5,6,1]=>10001=>10001=>[1,4,1]
[3,2,4,6,1,5]=>10010=>01001=>[2,3,1]
[3,2,4,6,5,1]=>10011=>11001=>[1,1,3,1]
[3,2,5,1,4,6]=>10100=>00101=>[3,2,1]
[3,2,5,1,6,4]=>10101=>10101=>[1,2,2,1]
[3,2,5,4,1,6]=>10110=>01101=>[2,1,2,1]
[3,2,5,4,6,1]=>10101=>10101=>[1,2,2,1]
[3,2,5,6,1,4]=>10010=>01001=>[2,3,1]
[3,2,5,6,4,1]=>10011=>11001=>[1,1,3,1]
[3,2,6,1,4,5]=>10100=>00101=>[3,2,1]
[3,2,6,1,5,4]=>10101=>10101=>[1,2,2,1]
[3,2,6,4,1,5]=>10110=>01101=>[2,1,2,1]
[3,2,6,4,5,1]=>10101=>10101=>[1,2,2,1]
[3,2,6,5,1,4]=>10110=>01101=>[2,1,2,1]
[3,2,6,5,4,1]=>10111=>11101=>[1,1,1,2,1]
[3,4,1,2,5,6]=>01000=>00010=>[4,2]
[3,4,1,2,6,5]=>01001=>10010=>[1,3,2]
[3,4,1,5,2,6]=>01010=>01010=>[2,2,2]
[3,4,1,5,6,2]=>01001=>10010=>[1,3,2]
[3,4,1,6,2,5]=>01010=>01010=>[2,2,2]
[3,4,1,6,5,2]=>01011=>11010=>[1,1,2,2]
[3,4,2,1,5,6]=>01100=>00110=>[3,1,2]
[3,4,2,1,6,5]=>01101=>10110=>[1,2,1,2]
[3,4,2,5,1,6]=>01010=>01010=>[2,2,2]
[3,4,2,5,6,1]=>01001=>10010=>[1,3,2]
[3,4,2,6,1,5]=>01010=>01010=>[2,2,2]
[3,4,2,6,5,1]=>01011=>11010=>[1,1,2,2]
[3,4,5,1,2,6]=>00100=>00100=>[3,3]
[3,4,5,1,6,2]=>00101=>10100=>[1,2,3]
[3,4,5,2,1,6]=>00110=>01100=>[2,1,3]
[3,4,5,2,6,1]=>00101=>10100=>[1,2,3]
[3,4,5,6,1,2]=>00010=>01000=>[2,4]
[3,4,5,6,2,1]=>00011=>11000=>[1,1,4]
[3,4,6,1,2,5]=>00100=>00100=>[3,3]
[3,4,6,1,5,2]=>00101=>10100=>[1,2,3]
[3,4,6,2,1,5]=>00110=>01100=>[2,1,3]
[3,4,6,2,5,1]=>00101=>10100=>[1,2,3]
[3,4,6,5,1,2]=>00110=>01100=>[2,1,3]
[3,4,6,5,2,1]=>00111=>11100=>[1,1,1,3]
[3,5,1,2,4,6]=>01000=>00010=>[4,2]
[3,5,1,2,6,4]=>01001=>10010=>[1,3,2]
[3,5,1,4,2,6]=>01010=>01010=>[2,2,2]
[3,5,1,4,6,2]=>01001=>10010=>[1,3,2]
[3,5,1,6,2,4]=>01010=>01010=>[2,2,2]
[3,5,1,6,4,2]=>01011=>11010=>[1,1,2,2]
[3,5,2,1,4,6]=>01100=>00110=>[3,1,2]
[3,5,2,1,6,4]=>01101=>10110=>[1,2,1,2]
[3,5,2,4,1,6]=>01010=>01010=>[2,2,2]
[3,5,2,4,6,1]=>01001=>10010=>[1,3,2]
[3,5,2,6,1,4]=>01010=>01010=>[2,2,2]
[3,5,2,6,4,1]=>01011=>11010=>[1,1,2,2]
[3,5,4,1,2,6]=>01100=>00110=>[3,1,2]
[3,5,4,1,6,2]=>01101=>10110=>[1,2,1,2]
[3,5,4,2,1,6]=>01110=>01110=>[2,1,1,2]
[3,5,4,2,6,1]=>01101=>10110=>[1,2,1,2]
[3,5,4,6,1,2]=>01010=>01010=>[2,2,2]
[3,5,4,6,2,1]=>01011=>11010=>[1,1,2,2]
[3,5,6,1,2,4]=>00100=>00100=>[3,3]
[3,5,6,1,4,2]=>00101=>10100=>[1,2,3]
[3,5,6,2,1,4]=>00110=>01100=>[2,1,3]
[3,5,6,2,4,1]=>00101=>10100=>[1,2,3]
[3,5,6,4,1,2]=>00110=>01100=>[2,1,3]
[3,5,6,4,2,1]=>00111=>11100=>[1,1,1,3]
[3,6,1,2,4,5]=>01000=>00010=>[4,2]
[3,6,1,2,5,4]=>01001=>10010=>[1,3,2]
[3,6,1,4,2,5]=>01010=>01010=>[2,2,2]
[3,6,1,4,5,2]=>01001=>10010=>[1,3,2]
[3,6,1,5,2,4]=>01010=>01010=>[2,2,2]
[3,6,1,5,4,2]=>01011=>11010=>[1,1,2,2]
[3,6,2,1,4,5]=>01100=>00110=>[3,1,2]
[3,6,2,1,5,4]=>01101=>10110=>[1,2,1,2]
[3,6,2,4,1,5]=>01010=>01010=>[2,2,2]
[3,6,2,4,5,1]=>01001=>10010=>[1,3,2]
[3,6,2,5,1,4]=>01010=>01010=>[2,2,2]
[3,6,2,5,4,1]=>01011=>11010=>[1,1,2,2]
[3,6,4,1,2,5]=>01100=>00110=>[3,1,2]
[3,6,4,1,5,2]=>01101=>10110=>[1,2,1,2]
[3,6,4,2,1,5]=>01110=>01110=>[2,1,1,2]
[3,6,4,2,5,1]=>01101=>10110=>[1,2,1,2]
[3,6,4,5,1,2]=>01010=>01010=>[2,2,2]
[3,6,4,5,2,1]=>01011=>11010=>[1,1,2,2]
[3,6,5,1,2,4]=>01100=>00110=>[3,1,2]
[3,6,5,1,4,2]=>01101=>10110=>[1,2,1,2]
[3,6,5,2,1,4]=>01110=>01110=>[2,1,1,2]
[3,6,5,2,4,1]=>01101=>10110=>[1,2,1,2]
[3,6,5,4,1,2]=>01110=>01110=>[2,1,1,2]
[3,6,5,4,2,1]=>01111=>11110=>[1,1,1,1,2]
[4,1,2,3,5,6]=>10000=>00001=>[5,1]
[4,1,2,3,6,5]=>10001=>10001=>[1,4,1]
[4,1,2,5,3,6]=>10010=>01001=>[2,3,1]
[4,1,2,5,6,3]=>10001=>10001=>[1,4,1]
[4,1,2,6,3,5]=>10010=>01001=>[2,3,1]
[4,1,2,6,5,3]=>10011=>11001=>[1,1,3,1]
[4,1,3,2,5,6]=>10100=>00101=>[3,2,1]
[4,1,3,2,6,5]=>10101=>10101=>[1,2,2,1]
[4,1,3,5,2,6]=>10010=>01001=>[2,3,1]
[4,1,3,5,6,2]=>10001=>10001=>[1,4,1]
[4,1,3,6,2,5]=>10010=>01001=>[2,3,1]
[4,1,3,6,5,2]=>10011=>11001=>[1,1,3,1]
[4,1,5,2,3,6]=>10100=>00101=>[3,2,1]
[4,1,5,2,6,3]=>10101=>10101=>[1,2,2,1]
[4,1,5,3,2,6]=>10110=>01101=>[2,1,2,1]
[4,1,5,3,6,2]=>10101=>10101=>[1,2,2,1]
[4,1,5,6,2,3]=>10010=>01001=>[2,3,1]
[4,1,5,6,3,2]=>10011=>11001=>[1,1,3,1]
[4,1,6,2,3,5]=>10100=>00101=>[3,2,1]
[4,1,6,2,5,3]=>10101=>10101=>[1,2,2,1]
[4,1,6,3,2,5]=>10110=>01101=>[2,1,2,1]
[4,1,6,3,5,2]=>10101=>10101=>[1,2,2,1]
[4,1,6,5,2,3]=>10110=>01101=>[2,1,2,1]
[4,1,6,5,3,2]=>10111=>11101=>[1,1,1,2,1]
[4,2,1,3,5,6]=>11000=>00011=>[4,1,1]
[4,2,1,3,6,5]=>11001=>10011=>[1,3,1,1]
[4,2,1,5,3,6]=>11010=>01011=>[2,2,1,1]
[4,2,1,5,6,3]=>11001=>10011=>[1,3,1,1]
[4,2,1,6,3,5]=>11010=>01011=>[2,2,1,1]
[4,2,1,6,5,3]=>11011=>11011=>[1,1,2,1,1]
[4,2,3,1,5,6]=>10100=>00101=>[3,2,1]
[4,2,3,1,6,5]=>10101=>10101=>[1,2,2,1]
[4,2,3,5,1,6]=>10010=>01001=>[2,3,1]
[4,2,3,5,6,1]=>10001=>10001=>[1,4,1]
[4,2,3,6,1,5]=>10010=>01001=>[2,3,1]
[4,2,3,6,5,1]=>10011=>11001=>[1,1,3,1]
[4,2,5,1,3,6]=>10100=>00101=>[3,2,1]
[4,2,5,1,6,3]=>10101=>10101=>[1,2,2,1]
[4,2,5,3,1,6]=>10110=>01101=>[2,1,2,1]
[4,2,5,3,6,1]=>10101=>10101=>[1,2,2,1]
[4,2,5,6,1,3]=>10010=>01001=>[2,3,1]
[4,2,5,6,3,1]=>10011=>11001=>[1,1,3,1]
[4,2,6,1,3,5]=>10100=>00101=>[3,2,1]
[4,2,6,1,5,3]=>10101=>10101=>[1,2,2,1]
[4,2,6,3,1,5]=>10110=>01101=>[2,1,2,1]
[4,2,6,3,5,1]=>10101=>10101=>[1,2,2,1]
[4,2,6,5,1,3]=>10110=>01101=>[2,1,2,1]
[4,2,6,5,3,1]=>10111=>11101=>[1,1,1,2,1]
[4,3,1,2,5,6]=>11000=>00011=>[4,1,1]
[4,3,1,2,6,5]=>11001=>10011=>[1,3,1,1]
[4,3,1,5,2,6]=>11010=>01011=>[2,2,1,1]
[4,3,1,5,6,2]=>11001=>10011=>[1,3,1,1]
[4,3,1,6,2,5]=>11010=>01011=>[2,2,1,1]
[4,3,1,6,5,2]=>11011=>11011=>[1,1,2,1,1]
[4,3,2,1,5,6]=>11100=>00111=>[3,1,1,1]
[4,3,2,1,6,5]=>11101=>10111=>[1,2,1,1,1]
[4,3,2,5,1,6]=>11010=>01011=>[2,2,1,1]
[4,3,2,5,6,1]=>11001=>10011=>[1,3,1,1]
[4,3,2,6,1,5]=>11010=>01011=>[2,2,1,1]
[4,3,2,6,5,1]=>11011=>11011=>[1,1,2,1,1]
[4,3,5,1,2,6]=>10100=>00101=>[3,2,1]
[4,3,5,1,6,2]=>10101=>10101=>[1,2,2,1]
[4,3,5,2,1,6]=>10110=>01101=>[2,1,2,1]
[4,3,5,2,6,1]=>10101=>10101=>[1,2,2,1]
[4,3,5,6,1,2]=>10010=>01001=>[2,3,1]
[4,3,5,6,2,1]=>10011=>11001=>[1,1,3,1]
[4,3,6,1,2,5]=>10100=>00101=>[3,2,1]
[4,3,6,1,5,2]=>10101=>10101=>[1,2,2,1]
[4,3,6,2,1,5]=>10110=>01101=>[2,1,2,1]
[4,3,6,2,5,1]=>10101=>10101=>[1,2,2,1]
[4,3,6,5,1,2]=>10110=>01101=>[2,1,2,1]
[4,3,6,5,2,1]=>10111=>11101=>[1,1,1,2,1]
[4,5,1,2,3,6]=>01000=>00010=>[4,2]
[4,5,1,2,6,3]=>01001=>10010=>[1,3,2]
[4,5,1,3,2,6]=>01010=>01010=>[2,2,2]
[4,5,1,3,6,2]=>01001=>10010=>[1,3,2]
[4,5,1,6,2,3]=>01010=>01010=>[2,2,2]
[4,5,1,6,3,2]=>01011=>11010=>[1,1,2,2]
[4,5,2,1,3,6]=>01100=>00110=>[3,1,2]
[4,5,2,1,6,3]=>01101=>10110=>[1,2,1,2]
[4,5,2,3,1,6]=>01010=>01010=>[2,2,2]
[4,5,2,3,6,1]=>01001=>10010=>[1,3,2]
[4,5,2,6,1,3]=>01010=>01010=>[2,2,2]
[4,5,2,6,3,1]=>01011=>11010=>[1,1,2,2]
[4,5,3,1,2,6]=>01100=>00110=>[3,1,2]
[4,5,3,1,6,2]=>01101=>10110=>[1,2,1,2]
[4,5,3,2,1,6]=>01110=>01110=>[2,1,1,2]
[4,5,3,2,6,1]=>01101=>10110=>[1,2,1,2]
[4,5,3,6,1,2]=>01010=>01010=>[2,2,2]
[4,5,3,6,2,1]=>01011=>11010=>[1,1,2,2]
[4,5,6,1,2,3]=>00100=>00100=>[3,3]
[4,5,6,1,3,2]=>00101=>10100=>[1,2,3]
[4,5,6,2,1,3]=>00110=>01100=>[2,1,3]
[4,5,6,2,3,1]=>00101=>10100=>[1,2,3]
[4,5,6,3,1,2]=>00110=>01100=>[2,1,3]
[4,5,6,3,2,1]=>00111=>11100=>[1,1,1,3]
[4,6,1,2,3,5]=>01000=>00010=>[4,2]
[4,6,1,2,5,3]=>01001=>10010=>[1,3,2]
[4,6,1,3,2,5]=>01010=>01010=>[2,2,2]
[4,6,1,3,5,2]=>01001=>10010=>[1,3,2]
[4,6,1,5,2,3]=>01010=>01010=>[2,2,2]
[4,6,1,5,3,2]=>01011=>11010=>[1,1,2,2]
[4,6,2,1,3,5]=>01100=>00110=>[3,1,2]
[4,6,2,1,5,3]=>01101=>10110=>[1,2,1,2]
[4,6,2,3,1,5]=>01010=>01010=>[2,2,2]
[4,6,2,3,5,1]=>01001=>10010=>[1,3,2]
[4,6,2,5,1,3]=>01010=>01010=>[2,2,2]
[4,6,2,5,3,1]=>01011=>11010=>[1,1,2,2]
[4,6,3,1,2,5]=>01100=>00110=>[3,1,2]
[4,6,3,1,5,2]=>01101=>10110=>[1,2,1,2]
[4,6,3,2,1,5]=>01110=>01110=>[2,1,1,2]
[4,6,3,2,5,1]=>01101=>10110=>[1,2,1,2]
[4,6,3,5,1,2]=>01010=>01010=>[2,2,2]
[4,6,3,5,2,1]=>01011=>11010=>[1,1,2,2]
[4,6,5,1,2,3]=>01100=>00110=>[3,1,2]
[4,6,5,1,3,2]=>01101=>10110=>[1,2,1,2]
[4,6,5,2,1,3]=>01110=>01110=>[2,1,1,2]
[4,6,5,2,3,1]=>01101=>10110=>[1,2,1,2]
[4,6,5,3,1,2]=>01110=>01110=>[2,1,1,2]
[4,6,5,3,2,1]=>01111=>11110=>[1,1,1,1,2]
[5,1,2,3,4,6]=>10000=>00001=>[5,1]
[5,1,2,3,6,4]=>10001=>10001=>[1,4,1]
[5,1,2,4,3,6]=>10010=>01001=>[2,3,1]
[5,1,2,4,6,3]=>10001=>10001=>[1,4,1]
[5,1,2,6,3,4]=>10010=>01001=>[2,3,1]
[5,1,2,6,4,3]=>10011=>11001=>[1,1,3,1]
[5,1,3,2,4,6]=>10100=>00101=>[3,2,1]
[5,1,3,2,6,4]=>10101=>10101=>[1,2,2,1]
[5,1,3,4,2,6]=>10010=>01001=>[2,3,1]
[5,1,3,4,6,2]=>10001=>10001=>[1,4,1]
[5,1,3,6,2,4]=>10010=>01001=>[2,3,1]
[5,1,3,6,4,2]=>10011=>11001=>[1,1,3,1]
[5,1,4,2,3,6]=>10100=>00101=>[3,2,1]
[5,1,4,2,6,3]=>10101=>10101=>[1,2,2,1]
[5,1,4,3,2,6]=>10110=>01101=>[2,1,2,1]
[5,1,4,3,6,2]=>10101=>10101=>[1,2,2,1]
[5,1,4,6,2,3]=>10010=>01001=>[2,3,1]
[5,1,4,6,3,2]=>10011=>11001=>[1,1,3,1]
[5,1,6,2,3,4]=>10100=>00101=>[3,2,1]
[5,1,6,2,4,3]=>10101=>10101=>[1,2,2,1]
[5,1,6,3,2,4]=>10110=>01101=>[2,1,2,1]
[5,1,6,3,4,2]=>10101=>10101=>[1,2,2,1]
[5,1,6,4,2,3]=>10110=>01101=>[2,1,2,1]
[5,1,6,4,3,2]=>10111=>11101=>[1,1,1,2,1]
[5,2,1,3,4,6]=>11000=>00011=>[4,1,1]
[5,2,1,3,6,4]=>11001=>10011=>[1,3,1,1]
[5,2,1,4,3,6]=>11010=>01011=>[2,2,1,1]
[5,2,1,4,6,3]=>11001=>10011=>[1,3,1,1]
[5,2,1,6,3,4]=>11010=>01011=>[2,2,1,1]
[5,2,1,6,4,3]=>11011=>11011=>[1,1,2,1,1]
[5,2,3,1,4,6]=>10100=>00101=>[3,2,1]
[5,2,3,1,6,4]=>10101=>10101=>[1,2,2,1]
[5,2,3,4,1,6]=>10010=>01001=>[2,3,1]
[5,2,3,4,6,1]=>10001=>10001=>[1,4,1]
[5,2,3,6,1,4]=>10010=>01001=>[2,3,1]
[5,2,3,6,4,1]=>10011=>11001=>[1,1,3,1]
[5,2,4,1,3,6]=>10100=>00101=>[3,2,1]
[5,2,4,1,6,3]=>10101=>10101=>[1,2,2,1]
[5,2,4,3,1,6]=>10110=>01101=>[2,1,2,1]
[5,2,4,3,6,1]=>10101=>10101=>[1,2,2,1]
[5,2,4,6,1,3]=>10010=>01001=>[2,3,1]
[5,2,4,6,3,1]=>10011=>11001=>[1,1,3,1]
[5,2,6,1,3,4]=>10100=>00101=>[3,2,1]
[5,2,6,1,4,3]=>10101=>10101=>[1,2,2,1]
[5,2,6,3,1,4]=>10110=>01101=>[2,1,2,1]
[5,2,6,3,4,1]=>10101=>10101=>[1,2,2,1]
[5,2,6,4,1,3]=>10110=>01101=>[2,1,2,1]
[5,2,6,4,3,1]=>10111=>11101=>[1,1,1,2,1]
[5,3,1,2,4,6]=>11000=>00011=>[4,1,1]
[5,3,1,2,6,4]=>11001=>10011=>[1,3,1,1]
[5,3,1,4,2,6]=>11010=>01011=>[2,2,1,1]
[5,3,1,4,6,2]=>11001=>10011=>[1,3,1,1]
[5,3,1,6,2,4]=>11010=>01011=>[2,2,1,1]
[5,3,1,6,4,2]=>11011=>11011=>[1,1,2,1,1]
[5,3,2,1,4,6]=>11100=>00111=>[3,1,1,1]
[5,3,2,1,6,4]=>11101=>10111=>[1,2,1,1,1]
[5,3,2,4,1,6]=>11010=>01011=>[2,2,1,1]
[5,3,2,4,6,1]=>11001=>10011=>[1,3,1,1]
[5,3,2,6,1,4]=>11010=>01011=>[2,2,1,1]
[5,3,2,6,4,1]=>11011=>11011=>[1,1,2,1,1]
[5,3,4,1,2,6]=>10100=>00101=>[3,2,1]
[5,3,4,1,6,2]=>10101=>10101=>[1,2,2,1]
[5,3,4,2,1,6]=>10110=>01101=>[2,1,2,1]
[5,3,4,2,6,1]=>10101=>10101=>[1,2,2,1]
[5,3,4,6,1,2]=>10010=>01001=>[2,3,1]
[5,3,4,6,2,1]=>10011=>11001=>[1,1,3,1]
[5,3,6,1,2,4]=>10100=>00101=>[3,2,1]
[5,3,6,1,4,2]=>10101=>10101=>[1,2,2,1]
[5,3,6,2,1,4]=>10110=>01101=>[2,1,2,1]
[5,3,6,2,4,1]=>10101=>10101=>[1,2,2,1]
[5,3,6,4,1,2]=>10110=>01101=>[2,1,2,1]
[5,3,6,4,2,1]=>10111=>11101=>[1,1,1,2,1]
[5,4,1,2,3,6]=>11000=>00011=>[4,1,1]
[5,4,1,2,6,3]=>11001=>10011=>[1,3,1,1]
[5,4,1,3,2,6]=>11010=>01011=>[2,2,1,1]
[5,4,1,3,6,2]=>11001=>10011=>[1,3,1,1]
[5,4,1,6,2,3]=>11010=>01011=>[2,2,1,1]
[5,4,1,6,3,2]=>11011=>11011=>[1,1,2,1,1]
[5,4,2,1,3,6]=>11100=>00111=>[3,1,1,1]
[5,4,2,1,6,3]=>11101=>10111=>[1,2,1,1,1]
[5,4,2,3,1,6]=>11010=>01011=>[2,2,1,1]
[5,4,2,3,6,1]=>11001=>10011=>[1,3,1,1]
[5,4,2,6,1,3]=>11010=>01011=>[2,2,1,1]
[5,4,2,6,3,1]=>11011=>11011=>[1,1,2,1,1]
[5,4,3,1,2,6]=>11100=>00111=>[3,1,1,1]
[5,4,3,1,6,2]=>11101=>10111=>[1,2,1,1,1]
[5,4,3,2,1,6]=>11110=>01111=>[2,1,1,1,1]
[5,4,3,2,6,1]=>11101=>10111=>[1,2,1,1,1]
[5,4,3,6,1,2]=>11010=>01011=>[2,2,1,1]
[5,4,3,6,2,1]=>11011=>11011=>[1,1,2,1,1]
[5,4,6,1,2,3]=>10100=>00101=>[3,2,1]
[5,4,6,1,3,2]=>10101=>10101=>[1,2,2,1]
[5,4,6,2,1,3]=>10110=>01101=>[2,1,2,1]
[5,4,6,2,3,1]=>10101=>10101=>[1,2,2,1]
[5,4,6,3,1,2]=>10110=>01101=>[2,1,2,1]
[5,4,6,3,2,1]=>10111=>11101=>[1,1,1,2,1]
[5,6,1,2,3,4]=>01000=>00010=>[4,2]
[5,6,1,2,4,3]=>01001=>10010=>[1,3,2]
[5,6,1,3,2,4]=>01010=>01010=>[2,2,2]
[5,6,1,3,4,2]=>01001=>10010=>[1,3,2]
[5,6,1,4,2,3]=>01010=>01010=>[2,2,2]
[5,6,1,4,3,2]=>01011=>11010=>[1,1,2,2]
[5,6,2,1,3,4]=>01100=>00110=>[3,1,2]
[5,6,2,1,4,3]=>01101=>10110=>[1,2,1,2]
[5,6,2,3,1,4]=>01010=>01010=>[2,2,2]
[5,6,2,3,4,1]=>01001=>10010=>[1,3,2]
[5,6,2,4,1,3]=>01010=>01010=>[2,2,2]
[5,6,2,4,3,1]=>01011=>11010=>[1,1,2,2]
[5,6,3,1,2,4]=>01100=>00110=>[3,1,2]
[5,6,3,1,4,2]=>01101=>10110=>[1,2,1,2]
[5,6,3,2,1,4]=>01110=>01110=>[2,1,1,2]
[5,6,3,2,4,1]=>01101=>10110=>[1,2,1,2]
[5,6,3,4,1,2]=>01010=>01010=>[2,2,2]
[5,6,3,4,2,1]=>01011=>11010=>[1,1,2,2]
[5,6,4,1,2,3]=>01100=>00110=>[3,1,2]
[5,6,4,1,3,2]=>01101=>10110=>[1,2,1,2]
[5,6,4,2,1,3]=>01110=>01110=>[2,1,1,2]
[5,6,4,2,3,1]=>01101=>10110=>[1,2,1,2]
[5,6,4,3,1,2]=>01110=>01110=>[2,1,1,2]
[5,6,4,3,2,1]=>01111=>11110=>[1,1,1,1,2]
[6,1,2,3,4,5]=>10000=>00001=>[5,1]
[6,1,2,3,5,4]=>10001=>10001=>[1,4,1]
[6,1,2,4,3,5]=>10010=>01001=>[2,3,1]
[6,1,2,4,5,3]=>10001=>10001=>[1,4,1]
[6,1,2,5,3,4]=>10010=>01001=>[2,3,1]
[6,1,2,5,4,3]=>10011=>11001=>[1,1,3,1]
[6,1,3,2,4,5]=>10100=>00101=>[3,2,1]
[6,1,3,2,5,4]=>10101=>10101=>[1,2,2,1]
[6,1,3,4,2,5]=>10010=>01001=>[2,3,1]
[6,1,3,4,5,2]=>10001=>10001=>[1,4,1]
[6,1,3,5,2,4]=>10010=>01001=>[2,3,1]
[6,1,3,5,4,2]=>10011=>11001=>[1,1,3,1]
[6,1,4,2,3,5]=>10100=>00101=>[3,2,1]
[6,1,4,2,5,3]=>10101=>10101=>[1,2,2,1]
[6,1,4,3,2,5]=>10110=>01101=>[2,1,2,1]
[6,1,4,3,5,2]=>10101=>10101=>[1,2,2,1]
[6,1,4,5,2,3]=>10010=>01001=>[2,3,1]
[6,1,4,5,3,2]=>10011=>11001=>[1,1,3,1]
[6,1,5,2,3,4]=>10100=>00101=>[3,2,1]
[6,1,5,2,4,3]=>10101=>10101=>[1,2,2,1]
[6,1,5,3,2,4]=>10110=>01101=>[2,1,2,1]
[6,1,5,3,4,2]=>10101=>10101=>[1,2,2,1]
[6,1,5,4,2,3]=>10110=>01101=>[2,1,2,1]
[6,1,5,4,3,2]=>10111=>11101=>[1,1,1,2,1]
[6,2,1,3,4,5]=>11000=>00011=>[4,1,1]
[6,2,1,3,5,4]=>11001=>10011=>[1,3,1,1]
[6,2,1,4,3,5]=>11010=>01011=>[2,2,1,1]
[6,2,1,4,5,3]=>11001=>10011=>[1,3,1,1]
[6,2,1,5,3,4]=>11010=>01011=>[2,2,1,1]
[6,2,1,5,4,3]=>11011=>11011=>[1,1,2,1,1]
[6,2,3,1,4,5]=>10100=>00101=>[3,2,1]
[6,2,3,1,5,4]=>10101=>10101=>[1,2,2,1]
[6,2,3,4,1,5]=>10010=>01001=>[2,3,1]
[6,2,3,4,5,1]=>10001=>10001=>[1,4,1]
[6,2,3,5,1,4]=>10010=>01001=>[2,3,1]
[6,2,3,5,4,1]=>10011=>11001=>[1,1,3,1]
[6,2,4,1,3,5]=>10100=>00101=>[3,2,1]
[6,2,4,1,5,3]=>10101=>10101=>[1,2,2,1]
[6,2,4,3,1,5]=>10110=>01101=>[2,1,2,1]
[6,2,4,3,5,1]=>10101=>10101=>[1,2,2,1]
[6,2,4,5,1,3]=>10010=>01001=>[2,3,1]
[6,2,4,5,3,1]=>10011=>11001=>[1,1,3,1]
[6,2,5,1,3,4]=>10100=>00101=>[3,2,1]
[6,2,5,1,4,3]=>10101=>10101=>[1,2,2,1]
[6,2,5,3,1,4]=>10110=>01101=>[2,1,2,1]
[6,2,5,3,4,1]=>10101=>10101=>[1,2,2,1]
[6,2,5,4,1,3]=>10110=>01101=>[2,1,2,1]
[6,2,5,4,3,1]=>10111=>11101=>[1,1,1,2,1]
[6,3,1,2,4,5]=>11000=>00011=>[4,1,1]
[6,3,1,2,5,4]=>11001=>10011=>[1,3,1,1]
[6,3,1,4,2,5]=>11010=>01011=>[2,2,1,1]
[6,3,1,4,5,2]=>11001=>10011=>[1,3,1,1]
[6,3,1,5,2,4]=>11010=>01011=>[2,2,1,1]
[6,3,1,5,4,2]=>11011=>11011=>[1,1,2,1,1]
[6,3,2,1,4,5]=>11100=>00111=>[3,1,1,1]
[6,3,2,1,5,4]=>11101=>10111=>[1,2,1,1,1]
[6,3,2,4,1,5]=>11010=>01011=>[2,2,1,1]
[6,3,2,4,5,1]=>11001=>10011=>[1,3,1,1]
[6,3,2,5,1,4]=>11010=>01011=>[2,2,1,1]
[6,3,2,5,4,1]=>11011=>11011=>[1,1,2,1,1]
[6,3,4,1,2,5]=>10100=>00101=>[3,2,1]
[6,3,4,1,5,2]=>10101=>10101=>[1,2,2,1]
[6,3,4,2,1,5]=>10110=>01101=>[2,1,2,1]
[6,3,4,2,5,1]=>10101=>10101=>[1,2,2,1]
[6,3,4,5,1,2]=>10010=>01001=>[2,3,1]
[6,3,4,5,2,1]=>10011=>11001=>[1,1,3,1]
[6,3,5,1,2,4]=>10100=>00101=>[3,2,1]
[6,3,5,1,4,2]=>10101=>10101=>[1,2,2,1]
[6,3,5,2,1,4]=>10110=>01101=>[2,1,2,1]
[6,3,5,2,4,1]=>10101=>10101=>[1,2,2,1]
[6,3,5,4,1,2]=>10110=>01101=>[2,1,2,1]
[6,3,5,4,2,1]=>10111=>11101=>[1,1,1,2,1]
[6,4,1,2,3,5]=>11000=>00011=>[4,1,1]
[6,4,1,2,5,3]=>11001=>10011=>[1,3,1,1]
[6,4,1,3,2,5]=>11010=>01011=>[2,2,1,1]
[6,4,1,3,5,2]=>11001=>10011=>[1,3,1,1]
[6,4,1,5,2,3]=>11010=>01011=>[2,2,1,1]
[6,4,1,5,3,2]=>11011=>11011=>[1,1,2,1,1]
[6,4,2,1,3,5]=>11100=>00111=>[3,1,1,1]
[6,4,2,1,5,3]=>11101=>10111=>[1,2,1,1,1]
[6,4,2,3,1,5]=>11010=>01011=>[2,2,1,1]
[6,4,2,3,5,1]=>11001=>10011=>[1,3,1,1]
[6,4,2,5,1,3]=>11010=>01011=>[2,2,1,1]
[6,4,2,5,3,1]=>11011=>11011=>[1,1,2,1,1]
[6,4,3,1,2,5]=>11100=>00111=>[3,1,1,1]
[6,4,3,1,5,2]=>11101=>10111=>[1,2,1,1,1]
[6,4,3,2,1,5]=>11110=>01111=>[2,1,1,1,1]
[6,4,3,2,5,1]=>11101=>10111=>[1,2,1,1,1]
[6,4,3,5,1,2]=>11010=>01011=>[2,2,1,1]
[6,4,3,5,2,1]=>11011=>11011=>[1,1,2,1,1]
[6,4,5,1,2,3]=>10100=>00101=>[3,2,1]
[6,4,5,1,3,2]=>10101=>10101=>[1,2,2,1]
[6,4,5,2,1,3]=>10110=>01101=>[2,1,2,1]
[6,4,5,2,3,1]=>10101=>10101=>[1,2,2,1]
[6,4,5,3,1,2]=>10110=>01101=>[2,1,2,1]
[6,4,5,3,2,1]=>10111=>11101=>[1,1,1,2,1]
[6,5,1,2,3,4]=>11000=>00011=>[4,1,1]
[6,5,1,2,4,3]=>11001=>10011=>[1,3,1,1]
[6,5,1,3,2,4]=>11010=>01011=>[2,2,1,1]
[6,5,1,3,4,2]=>11001=>10011=>[1,3,1,1]
[6,5,1,4,2,3]=>11010=>01011=>[2,2,1,1]
[6,5,1,4,3,2]=>11011=>11011=>[1,1,2,1,1]
[6,5,2,1,3,4]=>11100=>00111=>[3,1,1,1]
[6,5,2,1,4,3]=>11101=>10111=>[1,2,1,1,1]
[6,5,2,3,1,4]=>11010=>01011=>[2,2,1,1]
[6,5,2,3,4,1]=>11001=>10011=>[1,3,1,1]
[6,5,2,4,1,3]=>11010=>01011=>[2,2,1,1]
[6,5,2,4,3,1]=>11011=>11011=>[1,1,2,1,1]
[6,5,3,1,2,4]=>11100=>00111=>[3,1,1,1]
[6,5,3,1,4,2]=>11101=>10111=>[1,2,1,1,1]
[6,5,3,2,1,4]=>11110=>01111=>[2,1,1,1,1]
[6,5,3,2,4,1]=>11101=>10111=>[1,2,1,1,1]
[6,5,3,4,1,2]=>11010=>01011=>[2,2,1,1]
[6,5,3,4,2,1]=>11011=>11011=>[1,1,2,1,1]
[6,5,4,1,2,3]=>11100=>00111=>[3,1,1,1]
[6,5,4,1,3,2]=>11101=>10111=>[1,2,1,1,1]
[6,5,4,2,1,3]=>11110=>01111=>[2,1,1,1,1]
[6,5,4,2,3,1]=>11101=>10111=>[1,2,1,1,1]
[6,5,4,3,1,2]=>11110=>01111=>[2,1,1,1,1]
[6,5,4,3,2,1]=>11111=>11111=>[1,1,1,1,1,1]
[1,2,3,4,5,6,7]=>000000=>000000=>[7]
[1,2,3,4,5,7,6]=>000001=>100000=>[1,6]
[1,2,3,4,6,5,7]=>000010=>010000=>[2,5]
[1,2,3,4,6,7,5]=>000001=>100000=>[1,6]
[1,2,3,4,7,5,6]=>000010=>010000=>[2,5]
[1,2,3,4,7,6,5]=>000011=>110000=>[1,1,5]
[1,2,3,5,4,6,7]=>000100=>001000=>[3,4]
[1,2,3,5,4,7,6]=>000101=>101000=>[1,2,4]
[1,2,3,5,6,4,7]=>000010=>010000=>[2,5]
[1,2,3,5,6,7,4]=>000001=>100000=>[1,6]
[1,2,3,5,7,4,6]=>000010=>010000=>[2,5]
[1,2,3,5,7,6,4]=>000011=>110000=>[1,1,5]
[1,2,3,6,4,5,7]=>000100=>001000=>[3,4]
[1,2,3,6,4,7,5]=>000101=>101000=>[1,2,4]
[1,2,3,6,5,4,7]=>000110=>011000=>[2,1,4]
[1,2,3,6,5,7,4]=>000101=>101000=>[1,2,4]
[1,2,3,6,7,4,5]=>000010=>010000=>[2,5]
[1,2,3,6,7,5,4]=>000011=>110000=>[1,1,5]
[1,2,3,7,4,5,6]=>000100=>001000=>[3,4]
[1,2,3,7,4,6,5]=>000101=>101000=>[1,2,4]
[1,2,3,7,5,4,6]=>000110=>011000=>[2,1,4]
[1,2,3,7,5,6,4]=>000101=>101000=>[1,2,4]
[1,2,3,7,6,4,5]=>000110=>011000=>[2,1,4]
[1,2,3,7,6,5,4]=>000111=>111000=>[1,1,1,4]
[1,2,4,3,5,6,7]=>001000=>000100=>[4,3]
[1,2,4,3,5,7,6]=>001001=>100100=>[1,3,3]
[1,2,4,3,6,5,7]=>001010=>010100=>[2,2,3]
[1,2,4,3,6,7,5]=>001001=>100100=>[1,3,3]
[1,2,4,3,7,5,6]=>001010=>010100=>[2,2,3]
[1,2,4,3,7,6,5]=>001011=>110100=>[1,1,2,3]
[1,2,4,5,3,6,7]=>000100=>001000=>[3,4]
[1,2,4,5,3,7,6]=>000101=>101000=>[1,2,4]
[1,2,4,5,6,3,7]=>000010=>010000=>[2,5]
[1,2,4,5,6,7,3]=>000001=>100000=>[1,6]
[1,2,4,5,7,3,6]=>000010=>010000=>[2,5]
[1,2,4,5,7,6,3]=>000011=>110000=>[1,1,5]
[1,2,4,6,3,5,7]=>000100=>001000=>[3,4]
[1,2,4,6,3,7,5]=>000101=>101000=>[1,2,4]
[1,2,4,6,5,3,7]=>000110=>011000=>[2,1,4]
[1,2,4,6,5,7,3]=>000101=>101000=>[1,2,4]
[1,2,4,6,7,3,5]=>000010=>010000=>[2,5]
[1,2,4,6,7,5,3]=>000011=>110000=>[1,1,5]
[1,2,4,7,3,5,6]=>000100=>001000=>[3,4]
[1,2,4,7,3,6,5]=>000101=>101000=>[1,2,4]
[1,2,4,7,5,3,6]=>000110=>011000=>[2,1,4]
[1,2,4,7,5,6,3]=>000101=>101000=>[1,2,4]
[1,2,4,7,6,3,5]=>000110=>011000=>[2,1,4]
[1,2,4,7,6,5,3]=>000111=>111000=>[1,1,1,4]
[1,2,5,3,4,6,7]=>001000=>000100=>[4,3]
[1,2,5,3,4,7,6]=>001001=>100100=>[1,3,3]
[1,2,5,3,6,4,7]=>001010=>010100=>[2,2,3]
[1,2,5,3,6,7,4]=>001001=>100100=>[1,3,3]
[1,2,5,3,7,4,6]=>001010=>010100=>[2,2,3]
[1,2,5,3,7,6,4]=>001011=>110100=>[1,1,2,3]
[1,2,5,4,3,6,7]=>001100=>001100=>[3,1,3]
[1,2,5,4,3,7,6]=>001101=>101100=>[1,2,1,3]
[1,2,5,4,6,3,7]=>001010=>010100=>[2,2,3]
[1,2,5,4,6,7,3]=>001001=>100100=>[1,3,3]
[1,2,5,4,7,3,6]=>001010=>010100=>[2,2,3]
[1,2,5,4,7,6,3]=>001011=>110100=>[1,1,2,3]
[1,2,5,6,3,4,7]=>000100=>001000=>[3,4]
[1,2,5,6,3,7,4]=>000101=>101000=>[1,2,4]
[1,2,5,6,4,3,7]=>000110=>011000=>[2,1,4]
[1,2,5,6,4,7,3]=>000101=>101000=>[1,2,4]
[1,2,5,6,7,3,4]=>000010=>010000=>[2,5]
[1,2,5,6,7,4,3]=>000011=>110000=>[1,1,5]
[1,2,5,7,3,4,6]=>000100=>001000=>[3,4]
[1,2,5,7,3,6,4]=>000101=>101000=>[1,2,4]
[1,2,5,7,4,3,6]=>000110=>011000=>[2,1,4]
[1,2,5,7,4,6,3]=>000101=>101000=>[1,2,4]
[1,2,5,7,6,3,4]=>000110=>011000=>[2,1,4]
[1,2,5,7,6,4,3]=>000111=>111000=>[1,1,1,4]
[1,2,6,3,4,5,7]=>001000=>000100=>[4,3]
[1,2,6,3,4,7,5]=>001001=>100100=>[1,3,3]
[1,2,6,3,5,4,7]=>001010=>010100=>[2,2,3]
[1,2,6,3,5,7,4]=>001001=>100100=>[1,3,3]
[1,2,6,3,7,4,5]=>001010=>010100=>[2,2,3]
[1,2,6,3,7,5,4]=>001011=>110100=>[1,1,2,3]
[1,2,6,4,3,5,7]=>001100=>001100=>[3,1,3]
[1,2,6,4,3,7,5]=>001101=>101100=>[1,2,1,3]
[1,2,6,4,5,3,7]=>001010=>010100=>[2,2,3]
[1,2,6,4,5,7,3]=>001001=>100100=>[1,3,3]
[1,2,6,4,7,3,5]=>001010=>010100=>[2,2,3]
[1,2,6,4,7,5,3]=>001011=>110100=>[1,1,2,3]
[1,2,6,5,3,4,7]=>001100=>001100=>[3,1,3]
[1,2,6,5,3,7,4]=>001101=>101100=>[1,2,1,3]
[1,2,6,5,4,3,7]=>001110=>011100=>[2,1,1,3]
[1,2,6,5,4,7,3]=>001101=>101100=>[1,2,1,3]
[1,2,6,5,7,3,4]=>001010=>010100=>[2,2,3]
[1,2,6,5,7,4,3]=>001011=>110100=>[1,1,2,3]
[1,2,6,7,3,4,5]=>000100=>001000=>[3,4]
[1,2,6,7,3,5,4]=>000101=>101000=>[1,2,4]
[1,2,6,7,4,3,5]=>000110=>011000=>[2,1,4]
[1,2,6,7,4,5,3]=>000101=>101000=>[1,2,4]
[1,2,6,7,5,3,4]=>000110=>011000=>[2,1,4]
[1,2,6,7,5,4,3]=>000111=>111000=>[1,1,1,4]
[1,2,7,3,4,5,6]=>001000=>000100=>[4,3]
[1,2,7,3,4,6,5]=>001001=>100100=>[1,3,3]
[1,2,7,3,5,4,6]=>001010=>010100=>[2,2,3]
[1,2,7,3,5,6,4]=>001001=>100100=>[1,3,3]
[1,2,7,3,6,4,5]=>001010=>010100=>[2,2,3]
[1,2,7,3,6,5,4]=>001011=>110100=>[1,1,2,3]
[1,2,7,4,3,5,6]=>001100=>001100=>[3,1,3]
[1,2,7,4,3,6,5]=>001101=>101100=>[1,2,1,3]
[1,2,7,4,5,3,6]=>001010=>010100=>[2,2,3]
[1,2,7,4,5,6,3]=>001001=>100100=>[1,3,3]
[1,2,7,4,6,3,5]=>001010=>010100=>[2,2,3]
[1,2,7,4,6,5,3]=>001011=>110100=>[1,1,2,3]
[1,2,7,5,3,4,6]=>001100=>001100=>[3,1,3]
[1,2,7,5,3,6,4]=>001101=>101100=>[1,2,1,3]
[1,2,7,5,4,3,6]=>001110=>011100=>[2,1,1,3]
[1,2,7,5,4,6,3]=>001101=>101100=>[1,2,1,3]
[1,2,7,5,6,3,4]=>001010=>010100=>[2,2,3]
[1,2,7,5,6,4,3]=>001011=>110100=>[1,1,2,3]
[1,2,7,6,3,4,5]=>001100=>001100=>[3,1,3]
[1,2,7,6,3,5,4]=>001101=>101100=>[1,2,1,3]
[1,2,7,6,4,3,5]=>001110=>011100=>[2,1,1,3]
[1,2,7,6,4,5,3]=>001101=>101100=>[1,2,1,3]
[1,2,7,6,5,3,4]=>001110=>011100=>[2,1,1,3]
[1,2,7,6,5,4,3]=>001111=>111100=>[1,1,1,1,3]
[1,3,2,4,5,6,7]=>010000=>000010=>[5,2]
[1,3,2,4,5,7,6]=>010001=>100010=>[1,4,2]
[1,3,2,4,6,5,7]=>010010=>010010=>[2,3,2]
[1,3,2,4,6,7,5]=>010001=>100010=>[1,4,2]
[1,3,2,4,7,5,6]=>010010=>010010=>[2,3,2]
[1,3,2,4,7,6,5]=>010011=>110010=>[1,1,3,2]
[1,3,2,5,4,6,7]=>010100=>001010=>[3,2,2]
[1,3,2,5,4,7,6]=>010101=>101010=>[1,2,2,2]
[1,3,2,5,6,4,7]=>010010=>010010=>[2,3,2]
[1,3,2,5,6,7,4]=>010001=>100010=>[1,4,2]
[1,3,2,5,7,4,6]=>010010=>010010=>[2,3,2]
[1,3,2,5,7,6,4]=>010011=>110010=>[1,1,3,2]
[1,3,2,6,4,5,7]=>010100=>001010=>[3,2,2]
[1,3,2,6,4,7,5]=>010101=>101010=>[1,2,2,2]
[1,3,2,6,5,4,7]=>010110=>011010=>[2,1,2,2]
[1,3,2,6,5,7,4]=>010101=>101010=>[1,2,2,2]
[1,3,2,6,7,4,5]=>010010=>010010=>[2,3,2]
[1,3,2,6,7,5,4]=>010011=>110010=>[1,1,3,2]
[1,3,2,7,4,5,6]=>010100=>001010=>[3,2,2]
[1,3,2,7,4,6,5]=>010101=>101010=>[1,2,2,2]
[1,3,2,7,5,4,6]=>010110=>011010=>[2,1,2,2]
[1,3,2,7,5,6,4]=>010101=>101010=>[1,2,2,2]
[1,3,2,7,6,4,5]=>010110=>011010=>[2,1,2,2]
[1,3,2,7,6,5,4]=>010111=>111010=>[1,1,1,2,2]
[1,3,4,2,5,6,7]=>001000=>000100=>[4,3]
[1,3,4,2,5,7,6]=>001001=>100100=>[1,3,3]
[1,3,4,2,6,5,7]=>001010=>010100=>[2,2,3]
[1,3,4,2,6,7,5]=>001001=>100100=>[1,3,3]
[1,3,4,2,7,5,6]=>001010=>010100=>[2,2,3]
[1,3,4,2,7,6,5]=>001011=>110100=>[1,1,2,3]
[1,3,4,5,2,6,7]=>000100=>001000=>[3,4]
[1,3,4,5,2,7,6]=>000101=>101000=>[1,2,4]
[1,3,4,5,6,2,7]=>000010=>010000=>[2,5]
[1,3,4,5,6,7,2]=>000001=>100000=>[1,6]
[1,3,4,5,7,2,6]=>000010=>010000=>[2,5]
[1,3,4,5,7,6,2]=>000011=>110000=>[1,1,5]
[1,3,4,6,2,5,7]=>000100=>001000=>[3,4]
[1,3,4,6,2,7,5]=>000101=>101000=>[1,2,4]
[1,3,4,6,5,2,7]=>000110=>011000=>[2,1,4]
[1,3,4,6,5,7,2]=>000101=>101000=>[1,2,4]
[1,3,4,6,7,2,5]=>000010=>010000=>[2,5]
[1,3,4,6,7,5,2]=>000011=>110000=>[1,1,5]
[1,3,4,7,2,5,6]=>000100=>001000=>[3,4]
[1,3,4,7,2,6,5]=>000101=>101000=>[1,2,4]
[1,3,4,7,5,2,6]=>000110=>011000=>[2,1,4]
[1,3,4,7,5,6,2]=>000101=>101000=>[1,2,4]
[1,3,4,7,6,2,5]=>000110=>011000=>[2,1,4]
[1,3,4,7,6,5,2]=>000111=>111000=>[1,1,1,4]
[1,3,5,2,4,6,7]=>001000=>000100=>[4,3]
[1,3,5,2,4,7,6]=>001001=>100100=>[1,3,3]
[1,3,5,2,6,4,7]=>001010=>010100=>[2,2,3]
[1,3,5,2,6,7,4]=>001001=>100100=>[1,3,3]
[1,3,5,2,7,4,6]=>001010=>010100=>[2,2,3]
[1,3,5,2,7,6,4]=>001011=>110100=>[1,1,2,3]
[1,3,5,4,2,6,7]=>001100=>001100=>[3,1,3]
[1,3,5,4,2,7,6]=>001101=>101100=>[1,2,1,3]
[1,3,5,4,6,2,7]=>001010=>010100=>[2,2,3]
[1,3,5,4,6,7,2]=>001001=>100100=>[1,3,3]
[1,3,5,4,7,2,6]=>001010=>010100=>[2,2,3]
[1,3,5,4,7,6,2]=>001011=>110100=>[1,1,2,3]
[1,3,5,6,2,4,7]=>000100=>001000=>[3,4]
[1,3,5,6,2,7,4]=>000101=>101000=>[1,2,4]
[1,3,5,6,4,2,7]=>000110=>011000=>[2,1,4]
[1,3,5,6,4,7,2]=>000101=>101000=>[1,2,4]
[1,3,5,6,7,2,4]=>000010=>010000=>[2,5]
[1,3,5,6,7,4,2]=>000011=>110000=>[1,1,5]
[1,3,5,7,2,4,6]=>000100=>001000=>[3,4]
[1,3,5,7,2,6,4]=>000101=>101000=>[1,2,4]
[1,3,5,7,4,2,6]=>000110=>011000=>[2,1,4]
[1,3,5,7,4,6,2]=>000101=>101000=>[1,2,4]
[1,3,5,7,6,2,4]=>000110=>011000=>[2,1,4]
[1,3,5,7,6,4,2]=>000111=>111000=>[1,1,1,4]
[1,3,6,2,4,5,7]=>001000=>000100=>[4,3]
[1,3,6,2,4,7,5]=>001001=>100100=>[1,3,3]
[1,3,6,2,5,4,7]=>001010=>010100=>[2,2,3]
[1,3,6,2,5,7,4]=>001001=>100100=>[1,3,3]
[1,3,6,2,7,4,5]=>001010=>010100=>[2,2,3]
[1,3,6,2,7,5,4]=>001011=>110100=>[1,1,2,3]
[1,3,6,4,2,5,7]=>001100=>001100=>[3,1,3]
[1,3,6,4,2,7,5]=>001101=>101100=>[1,2,1,3]
[1,3,6,4,5,2,7]=>001010=>010100=>[2,2,3]
[1,3,6,4,5,7,2]=>001001=>100100=>[1,3,3]
[1,3,6,4,7,2,5]=>001010=>010100=>[2,2,3]
[1,3,6,4,7,5,2]=>001011=>110100=>[1,1,2,3]
[1,3,6,5,2,4,7]=>001100=>001100=>[3,1,3]
[1,3,6,5,2,7,4]=>001101=>101100=>[1,2,1,3]
[1,3,6,5,4,2,7]=>001110=>011100=>[2,1,1,3]
[1,3,6,5,4,7,2]=>001101=>101100=>[1,2,1,3]
[1,3,6,5,7,2,4]=>001010=>010100=>[2,2,3]
[1,3,6,5,7,4,2]=>001011=>110100=>[1,1,2,3]
[1,3,6,7,2,4,5]=>000100=>001000=>[3,4]
[1,3,6,7,2,5,4]=>000101=>101000=>[1,2,4]
[1,3,6,7,4,2,5]=>000110=>011000=>[2,1,4]
[1,3,6,7,4,5,2]=>000101=>101000=>[1,2,4]
[1,3,6,7,5,2,4]=>000110=>011000=>[2,1,4]
[1,3,6,7,5,4,2]=>000111=>111000=>[1,1,1,4]
[1,3,7,2,4,5,6]=>001000=>000100=>[4,3]
[1,3,7,2,4,6,5]=>001001=>100100=>[1,3,3]
[1,3,7,2,5,4,6]=>001010=>010100=>[2,2,3]
[1,3,7,2,5,6,4]=>001001=>100100=>[1,3,3]
[1,3,7,2,6,4,5]=>001010=>010100=>[2,2,3]
[1,3,7,2,6,5,4]=>001011=>110100=>[1,1,2,3]
[1,3,7,4,2,5,6]=>001100=>001100=>[3,1,3]
[1,3,7,4,2,6,5]=>001101=>101100=>[1,2,1,3]
[1,3,7,4,5,2,6]=>001010=>010100=>[2,2,3]
[1,3,7,4,5,6,2]=>001001=>100100=>[1,3,3]
[1,3,7,4,6,2,5]=>001010=>010100=>[2,2,3]
[1,3,7,4,6,5,2]=>001011=>110100=>[1,1,2,3]
[1,3,7,5,2,4,6]=>001100=>001100=>[3,1,3]
[1,3,7,5,2,6,4]=>001101=>101100=>[1,2,1,3]
[1,3,7,5,4,2,6]=>001110=>011100=>[2,1,1,3]
[1,3,7,5,4,6,2]=>001101=>101100=>[1,2,1,3]
[1,3,7,5,6,2,4]=>001010=>010100=>[2,2,3]
[1,3,7,5,6,4,2]=>001011=>110100=>[1,1,2,3]
[1,3,7,6,2,4,5]=>001100=>001100=>[3,1,3]
[1,3,7,6,2,5,4]=>001101=>101100=>[1,2,1,3]
[1,3,7,6,4,2,5]=>001110=>011100=>[2,1,1,3]
[1,3,7,6,4,5,2]=>001101=>101100=>[1,2,1,3]
[1,3,7,6,5,2,4]=>001110=>011100=>[2,1,1,3]
[1,3,7,6,5,4,2]=>001111=>111100=>[1,1,1,1,3]
[1,4,2,3,5,6,7]=>010000=>000010=>[5,2]
[1,4,2,3,5,7,6]=>010001=>100010=>[1,4,2]
[1,4,2,3,6,5,7]=>010010=>010010=>[2,3,2]
[1,4,2,3,6,7,5]=>010001=>100010=>[1,4,2]
[1,4,2,3,7,5,6]=>010010=>010010=>[2,3,2]
[1,4,2,3,7,6,5]=>010011=>110010=>[1,1,3,2]
[1,4,2,5,3,6,7]=>010100=>001010=>[3,2,2]
[1,4,2,5,3,7,6]=>010101=>101010=>[1,2,2,2]
[1,4,2,5,6,3,7]=>010010=>010010=>[2,3,2]
[1,4,2,5,6,7,3]=>010001=>100010=>[1,4,2]
[1,4,2,5,7,3,6]=>010010=>010010=>[2,3,2]
[1,4,2,5,7,6,3]=>010011=>110010=>[1,1,3,2]
[1,4,2,6,3,5,7]=>010100=>001010=>[3,2,2]
[1,4,2,6,3,7,5]=>010101=>101010=>[1,2,2,2]
[1,4,2,6,5,3,7]=>010110=>011010=>[2,1,2,2]
[1,4,2,6,5,7,3]=>010101=>101010=>[1,2,2,2]
[1,4,2,6,7,3,5]=>010010=>010010=>[2,3,2]
[1,4,2,6,7,5,3]=>010011=>110010=>[1,1,3,2]
[1,4,2,7,3,5,6]=>010100=>001010=>[3,2,2]
[1,4,2,7,3,6,5]=>010101=>101010=>[1,2,2,2]
[1,4,2,7,5,3,6]=>010110=>011010=>[2,1,2,2]
[1,4,2,7,5,6,3]=>010101=>101010=>[1,2,2,2]
[1,4,2,7,6,3,5]=>010110=>011010=>[2,1,2,2]
[1,4,2,7,6,5,3]=>010111=>111010=>[1,1,1,2,2]
[1,4,3,2,5,6,7]=>011000=>000110=>[4,1,2]
[1,4,3,2,5,7,6]=>011001=>100110=>[1,3,1,2]
[1,4,3,2,6,5,7]=>011010=>010110=>[2,2,1,2]
[1,4,3,2,6,7,5]=>011001=>100110=>[1,3,1,2]
[1,4,3,2,7,5,6]=>011010=>010110=>[2,2,1,2]
[1,4,3,2,7,6,5]=>011011=>110110=>[1,1,2,1,2]
[1,4,3,5,2,6,7]=>010100=>001010=>[3,2,2]
[1,4,3,5,2,7,6]=>010101=>101010=>[1,2,2,2]
[1,4,3,5,6,2,7]=>010010=>010010=>[2,3,2]
[1,4,3,5,6,7,2]=>010001=>100010=>[1,4,2]
[1,4,3,5,7,2,6]=>010010=>010010=>[2,3,2]
[1,4,3,5,7,6,2]=>010011=>110010=>[1,1,3,2]
[1,4,3,6,2,5,7]=>010100=>001010=>[3,2,2]
[1,4,3,6,2,7,5]=>010101=>101010=>[1,2,2,2]
[1,4,3,6,5,2,7]=>010110=>011010=>[2,1,2,2]
[1,4,3,6,5,7,2]=>010101=>101010=>[1,2,2,2]
[1,4,3,6,7,2,5]=>010010=>010010=>[2,3,2]
[1,4,3,6,7,5,2]=>010011=>110010=>[1,1,3,2]
[1,4,3,7,2,5,6]=>010100=>001010=>[3,2,2]
[1,4,3,7,2,6,5]=>010101=>101010=>[1,2,2,2]
[1,4,3,7,5,2,6]=>010110=>011010=>[2,1,2,2]
[1,4,3,7,5,6,2]=>010101=>101010=>[1,2,2,2]
[1,4,3,7,6,2,5]=>010110=>011010=>[2,1,2,2]
[1,4,3,7,6,5,2]=>010111=>111010=>[1,1,1,2,2]
[1,4,5,2,3,6,7]=>001000=>000100=>[4,3]
[1,4,5,2,3,7,6]=>001001=>100100=>[1,3,3]
[1,4,5,2,6,3,7]=>001010=>010100=>[2,2,3]
[1,4,5,2,6,7,3]=>001001=>100100=>[1,3,3]
[1,4,5,2,7,3,6]=>001010=>010100=>[2,2,3]
[1,4,5,2,7,6,3]=>001011=>110100=>[1,1,2,3]
[1,4,5,3,2,6,7]=>001100=>001100=>[3,1,3]
[1,4,5,3,2,7,6]=>001101=>101100=>[1,2,1,3]
[1,4,5,3,6,2,7]=>001010=>010100=>[2,2,3]
[1,4,5,3,6,7,2]=>001001=>100100=>[1,3,3]
[1,4,5,3,7,2,6]=>001010=>010100=>[2,2,3]
[1,4,5,3,7,6,2]=>001011=>110100=>[1,1,2,3]
[1,4,5,6,2,3,7]=>000100=>001000=>[3,4]
[1,4,5,6,2,7,3]=>000101=>101000=>[1,2,4]
[1,4,5,6,3,2,7]=>000110=>011000=>[2,1,4]
[1,4,5,6,3,7,2]=>000101=>101000=>[1,2,4]
[1,4,5,6,7,2,3]=>000010=>010000=>[2,5]
[1,4,5,6,7,3,2]=>000011=>110000=>[1,1,5]
[1,4,5,7,2,3,6]=>000100=>001000=>[3,4]
[1,4,5,7,2,6,3]=>000101=>101000=>[1,2,4]
[1,4,5,7,3,2,6]=>000110=>011000=>[2,1,4]
[1,4,5,7,3,6,2]=>000101=>101000=>[1,2,4]
[1,4,5,7,6,2,3]=>000110=>011000=>[2,1,4]
[1,4,5,7,6,3,2]=>000111=>111000=>[1,1,1,4]
[1,4,6,2,3,5,7]=>001000=>000100=>[4,3]
[1,4,6,2,3,7,5]=>001001=>100100=>[1,3,3]
[1,4,6,2,5,3,7]=>001010=>010100=>[2,2,3]
[1,4,6,2,5,7,3]=>001001=>100100=>[1,3,3]
[1,4,6,2,7,3,5]=>001010=>010100=>[2,2,3]
[1,4,6,2,7,5,3]=>001011=>110100=>[1,1,2,3]
[1,4,6,3,2,5,7]=>001100=>001100=>[3,1,3]
[1,4,6,3,2,7,5]=>001101=>101100=>[1,2,1,3]
[1,4,6,3,5,2,7]=>001010=>010100=>[2,2,3]
[1,4,6,3,5,7,2]=>001001=>100100=>[1,3,3]
[1,4,6,3,7,2,5]=>001010=>010100=>[2,2,3]
[1,4,6,3,7,5,2]=>001011=>110100=>[1,1,2,3]
[1,4,6,5,2,3,7]=>001100=>001100=>[3,1,3]
[1,4,6,5,2,7,3]=>001101=>101100=>[1,2,1,3]
[1,4,6,5,3,2,7]=>001110=>011100=>[2,1,1,3]
[1,4,6,5,3,7,2]=>001101=>101100=>[1,2,1,3]
[1,4,6,5,7,2,3]=>001010=>010100=>[2,2,3]
[1,4,6,5,7,3,2]=>001011=>110100=>[1,1,2,3]
[1,4,6,7,2,3,5]=>000100=>001000=>[3,4]
[1,4,6,7,2,5,3]=>000101=>101000=>[1,2,4]
[1,4,6,7,3,2,5]=>000110=>011000=>[2,1,4]
[1,4,6,7,3,5,2]=>000101=>101000=>[1,2,4]
[1,4,6,7,5,2,3]=>000110=>011000=>[2,1,4]
[1,4,6,7,5,3,2]=>000111=>111000=>[1,1,1,4]
[1,4,7,2,3,5,6]=>001000=>000100=>[4,3]
[1,4,7,2,3,6,5]=>001001=>100100=>[1,3,3]
[1,4,7,2,5,3,6]=>001010=>010100=>[2,2,3]
[1,4,7,2,5,6,3]=>001001=>100100=>[1,3,3]
[1,4,7,2,6,3,5]=>001010=>010100=>[2,2,3]
[1,4,7,2,6,5,3]=>001011=>110100=>[1,1,2,3]
[1,4,7,3,2,5,6]=>001100=>001100=>[3,1,3]
[1,4,7,3,2,6,5]=>001101=>101100=>[1,2,1,3]
[1,4,7,3,5,2,6]=>001010=>010100=>[2,2,3]
[1,4,7,3,5,6,2]=>001001=>100100=>[1,3,3]
[1,4,7,3,6,2,5]=>001010=>010100=>[2,2,3]
[1,4,7,3,6,5,2]=>001011=>110100=>[1,1,2,3]
[1,4,7,5,2,3,6]=>001100=>001100=>[3,1,3]
[1,4,7,5,2,6,3]=>001101=>101100=>[1,2,1,3]
[1,4,7,5,3,2,6]=>001110=>011100=>[2,1,1,3]
[1,4,7,5,3,6,2]=>001101=>101100=>[1,2,1,3]
[1,4,7,5,6,2,3]=>001010=>010100=>[2,2,3]
[1,4,7,5,6,3,2]=>001011=>110100=>[1,1,2,3]
[1,4,7,6,2,3,5]=>001100=>001100=>[3,1,3]
[1,4,7,6,2,5,3]=>001101=>101100=>[1,2,1,3]
[1,4,7,6,3,2,5]=>001110=>011100=>[2,1,1,3]
[1,4,7,6,3,5,2]=>001101=>101100=>[1,2,1,3]
[1,4,7,6,5,2,3]=>001110=>011100=>[2,1,1,3]
[1,4,7,6,5,3,2]=>001111=>111100=>[1,1,1,1,3]
[1,5,2,3,4,6,7]=>010000=>000010=>[5,2]
[1,5,2,3,4,7,6]=>010001=>100010=>[1,4,2]
[1,5,2,3,6,4,7]=>010010=>010010=>[2,3,2]
[1,5,2,3,6,7,4]=>010001=>100010=>[1,4,2]
[1,5,2,3,7,4,6]=>010010=>010010=>[2,3,2]
[1,5,2,3,7,6,4]=>010011=>110010=>[1,1,3,2]
[1,5,2,4,3,6,7]=>010100=>001010=>[3,2,2]
[1,5,2,4,3,7,6]=>010101=>101010=>[1,2,2,2]
[1,5,2,4,6,3,7]=>010010=>010010=>[2,3,2]
[1,5,2,4,6,7,3]=>010001=>100010=>[1,4,2]
[1,5,2,4,7,3,6]=>010010=>010010=>[2,3,2]
[1,5,2,4,7,6,3]=>010011=>110010=>[1,1,3,2]
[1,5,2,6,3,4,7]=>010100=>001010=>[3,2,2]
[1,5,2,6,3,7,4]=>010101=>101010=>[1,2,2,2]
[1,5,2,6,4,3,7]=>010110=>011010=>[2,1,2,2]
[1,5,2,6,4,7,3]=>010101=>101010=>[1,2,2,2]
[1,5,2,6,7,3,4]=>010010=>010010=>[2,3,2]
[1,5,2,6,7,4,3]=>010011=>110010=>[1,1,3,2]
[1,5,2,7,3,4,6]=>010100=>001010=>[3,2,2]
[1,5,2,7,3,6,4]=>010101=>101010=>[1,2,2,2]
[1,5,2,7,4,3,6]=>010110=>011010=>[2,1,2,2]
[1,5,2,7,4,6,3]=>010101=>101010=>[1,2,2,2]
[1,5,2,7,6,3,4]=>010110=>011010=>[2,1,2,2]
[1,5,2,7,6,4,3]=>010111=>111010=>[1,1,1,2,2]
[1,5,3,2,4,6,7]=>011000=>000110=>[4,1,2]
[1,5,3,2,4,7,6]=>011001=>100110=>[1,3,1,2]
[1,5,3,2,6,4,7]=>011010=>010110=>[2,2,1,2]
[1,5,3,2,6,7,4]=>011001=>100110=>[1,3,1,2]
[1,5,3,2,7,4,6]=>011010=>010110=>[2,2,1,2]
[1,5,3,2,7,6,4]=>011011=>110110=>[1,1,2,1,2]
[1,5,3,4,2,6,7]=>010100=>001010=>[3,2,2]
[1,5,3,4,2,7,6]=>010101=>101010=>[1,2,2,2]
[1,5,3,4,6,2,7]=>010010=>010010=>[2,3,2]
[1,5,3,4,6,7,2]=>010001=>100010=>[1,4,2]
[1,5,3,4,7,2,6]=>010010=>010010=>[2,3,2]
[1,5,3,4,7,6,2]=>010011=>110010=>[1,1,3,2]
[1,5,3,6,2,4,7]=>010100=>001010=>[3,2,2]
[1,5,3,6,2,7,4]=>010101=>101010=>[1,2,2,2]
[1,5,3,6,4,2,7]=>010110=>011010=>[2,1,2,2]
[1,5,3,6,4,7,2]=>010101=>101010=>[1,2,2,2]
[1,5,3,6,7,2,4]=>010010=>010010=>[2,3,2]
[1,5,3,6,7,4,2]=>010011=>110010=>[1,1,3,2]
[1,5,3,7,2,4,6]=>010100=>001010=>[3,2,2]
[1,5,3,7,2,6,4]=>010101=>101010=>[1,2,2,2]
[1,5,3,7,4,2,6]=>010110=>011010=>[2,1,2,2]
[1,5,3,7,4,6,2]=>010101=>101010=>[1,2,2,2]
[1,5,3,7,6,2,4]=>010110=>011010=>[2,1,2,2]
[1,5,3,7,6,4,2]=>010111=>111010=>[1,1,1,2,2]
[1,5,4,2,3,6,7]=>011000=>000110=>[4,1,2]
[1,5,4,2,3,7,6]=>011001=>100110=>[1,3,1,2]
[1,5,4,2,6,3,7]=>011010=>010110=>[2,2,1,2]
[1,5,4,2,6,7,3]=>011001=>100110=>[1,3,1,2]
[1,5,4,2,7,3,6]=>011010=>010110=>[2,2,1,2]
[1,5,4,2,7,6,3]=>011011=>110110=>[1,1,2,1,2]
[1,5,4,3,2,6,7]=>011100=>001110=>[3,1,1,2]
[1,5,4,3,2,7,6]=>011101=>101110=>[1,2,1,1,2]
[1,5,4,3,6,2,7]=>011010=>010110=>[2,2,1,2]
[1,5,4,3,6,7,2]=>011001=>100110=>[1,3,1,2]
[1,5,4,3,7,2,6]=>011010=>010110=>[2,2,1,2]
[1,5,4,3,7,6,2]=>011011=>110110=>[1,1,2,1,2]
[1,5,4,6,2,3,7]=>010100=>001010=>[3,2,2]
[1,5,4,6,2,7,3]=>010101=>101010=>[1,2,2,2]
[1,5,4,6,3,2,7]=>010110=>011010=>[2,1,2,2]
[1,5,4,6,3,7,2]=>010101=>101010=>[1,2,2,2]
[1,5,4,6,7,2,3]=>010010=>010010=>[2,3,2]
[1,5,4,6,7,3,2]=>010011=>110010=>[1,1,3,2]
[1,5,4,7,2,3,6]=>010100=>001010=>[3,2,2]
[1,5,4,7,2,6,3]=>010101=>101010=>[1,2,2,2]
[1,5,4,7,3,2,6]=>010110=>011010=>[2,1,2,2]
[1,5,4,7,3,6,2]=>010101=>101010=>[1,2,2,2]
[1,5,4,7,6,2,3]=>010110=>011010=>[2,1,2,2]
[1,5,4,7,6,3,2]=>010111=>111010=>[1,1,1,2,2]
[1,5,6,2,3,4,7]=>001000=>000100=>[4,3]
[1,5,6,2,3,7,4]=>001001=>100100=>[1,3,3]
[1,5,6,2,4,3,7]=>001010=>010100=>[2,2,3]
[1,5,6,2,4,7,3]=>001001=>100100=>[1,3,3]
[1,5,6,2,7,3,4]=>001010=>010100=>[2,2,3]
[1,5,6,2,7,4,3]=>001011=>110100=>[1,1,2,3]
[1,5,6,3,2,4,7]=>001100=>001100=>[3,1,3]
[1,5,6,3,2,7,4]=>001101=>101100=>[1,2,1,3]
[1,5,6,3,4,2,7]=>001010=>010100=>[2,2,3]
[1,5,6,3,4,7,2]=>001001=>100100=>[1,3,3]
[1,5,6,3,7,2,4]=>001010=>010100=>[2,2,3]
[1,5,6,3,7,4,2]=>001011=>110100=>[1,1,2,3]
[1,5,6,4,2,3,7]=>001100=>001100=>[3,1,3]
[1,5,6,4,2,7,3]=>001101=>101100=>[1,2,1,3]
[1,5,6,4,3,2,7]=>001110=>011100=>[2,1,1,3]
[1,5,6,4,3,7,2]=>001101=>101100=>[1,2,1,3]
[1,5,6,4,7,2,3]=>001010=>010100=>[2,2,3]
[1,5,6,4,7,3,2]=>001011=>110100=>[1,1,2,3]
[1,5,6,7,2,3,4]=>000100=>001000=>[3,4]
[1,5,6,7,2,4,3]=>000101=>101000=>[1,2,4]
[1,5,6,7,3,2,4]=>000110=>011000=>[2,1,4]
[1,5,6,7,3,4,2]=>000101=>101000=>[1,2,4]
[1,5,6,7,4,2,3]=>000110=>011000=>[2,1,4]
[1,5,6,7,4,3,2]=>000111=>111000=>[1,1,1,4]
[1,5,7,2,3,4,6]=>001000=>000100=>[4,3]
[1,5,7,2,3,6,4]=>001001=>100100=>[1,3,3]
[1,5,7,2,4,3,6]=>001010=>010100=>[2,2,3]
[1,5,7,2,4,6,3]=>001001=>100100=>[1,3,3]
[1,5,7,2,6,3,4]=>001010=>010100=>[2,2,3]
[1,5,7,2,6,4,3]=>001011=>110100=>[1,1,2,3]
[1,5,7,3,2,4,6]=>001100=>001100=>[3,1,3]
[1,5,7,3,2,6,4]=>001101=>101100=>[1,2,1,3]
[1,5,7,3,4,2,6]=>001010=>010100=>[2,2,3]
[1,5,7,3,4,6,2]=>001001=>100100=>[1,3,3]
[1,5,7,3,6,2,4]=>001010=>010100=>[2,2,3]
[1,5,7,3,6,4,2]=>001011=>110100=>[1,1,2,3]
[1,5,7,4,2,3,6]=>001100=>001100=>[3,1,3]
[1,5,7,4,2,6,3]=>001101=>101100=>[1,2,1,3]
[1,5,7,4,3,2,6]=>001110=>011100=>[2,1,1,3]
[1,5,7,4,3,6,2]=>001101=>101100=>[1,2,1,3]
[1,5,7,4,6,2,3]=>001010=>010100=>[2,2,3]
[1,5,7,4,6,3,2]=>001011=>110100=>[1,1,2,3]
[1,5,7,6,2,3,4]=>001100=>001100=>[3,1,3]
[1,5,7,6,2,4,3]=>001101=>101100=>[1,2,1,3]
[1,5,7,6,3,2,4]=>001110=>011100=>[2,1,1,3]
[1,5,7,6,3,4,2]=>001101=>101100=>[1,2,1,3]
[1,5,7,6,4,2,3]=>001110=>011100=>[2,1,1,3]
[1,5,7,6,4,3,2]=>001111=>111100=>[1,1,1,1,3]
[1,6,2,3,4,5,7]=>010000=>000010=>[5,2]
[1,6,2,3,4,7,5]=>010001=>100010=>[1,4,2]
[1,6,2,3,5,4,7]=>010010=>010010=>[2,3,2]
[1,6,2,3,5,7,4]=>010001=>100010=>[1,4,2]
[1,6,2,3,7,4,5]=>010010=>010010=>[2,3,2]
[1,6,2,3,7,5,4]=>010011=>110010=>[1,1,3,2]
[1,6,2,4,3,5,7]=>010100=>001010=>[3,2,2]
[1,6,2,4,3,7,5]=>010101=>101010=>[1,2,2,2]
[1,6,2,4,5,3,7]=>010010=>010010=>[2,3,2]
[1,6,2,4,5,7,3]=>010001=>100010=>[1,4,2]
[1,6,2,4,7,3,5]=>010010=>010010=>[2,3,2]
[1,6,2,4,7,5,3]=>010011=>110010=>[1,1,3,2]
[1,6,2,5,3,4,7]=>010100=>001010=>[3,2,2]
[1,6,2,5,3,7,4]=>010101=>101010=>[1,2,2,2]
[1,6,2,5,4,3,7]=>010110=>011010=>[2,1,2,2]
[1,6,2,5,4,7,3]=>010101=>101010=>[1,2,2,2]
[1,6,2,5,7,3,4]=>010010=>010010=>[2,3,2]
[1,6,2,5,7,4,3]=>010011=>110010=>[1,1,3,2]
[1,6,2,7,3,4,5]=>010100=>001010=>[3,2,2]
[1,6,2,7,3,5,4]=>010101=>101010=>[1,2,2,2]
[1,6,2,7,4,3,5]=>010110=>011010=>[2,1,2,2]
[1,6,2,7,4,5,3]=>010101=>101010=>[1,2,2,2]
[1,6,2,7,5,3,4]=>010110=>011010=>[2,1,2,2]
[1,6,2,7,5,4,3]=>010111=>111010=>[1,1,1,2,2]
[1,6,3,2,4,5,7]=>011000=>000110=>[4,1,2]
[1,6,3,2,4,7,5]=>011001=>100110=>[1,3,1,2]
[1,6,3,2,5,4,7]=>011010=>010110=>[2,2,1,2]
[1,6,3,2,5,7,4]=>011001=>100110=>[1,3,1,2]
[1,6,3,2,7,4,5]=>011010=>010110=>[2,2,1,2]
[1,6,3,2,7,5,4]=>011011=>110110=>[1,1,2,1,2]
[1,6,3,4,2,5,7]=>010100=>001010=>[3,2,2]
[1,6,3,4,2,7,5]=>010101=>101010=>[1,2,2,2]
[1,6,3,4,5,2,7]=>010010=>010010=>[2,3,2]
[1,6,3,4,5,7,2]=>010001=>100010=>[1,4,2]
[1,6,3,4,7,2,5]=>010010=>010010=>[2,3,2]
[1,6,3,4,7,5,2]=>010011=>110010=>[1,1,3,2]
[1,6,3,5,2,4,7]=>010100=>001010=>[3,2,2]
[1,6,3,5,2,7,4]=>010101=>101010=>[1,2,2,2]
[1,6,3,5,4,2,7]=>010110=>011010=>[2,1,2,2]
[1,6,3,5,4,7,2]=>010101=>101010=>[1,2,2,2]
[1,6,3,5,7,2,4]=>010010=>010010=>[2,3,2]
[1,6,3,5,7,4,2]=>010011=>110010=>[1,1,3,2]
[1,6,3,7,2,4,5]=>010100=>001010=>[3,2,2]
[1,6,3,7,2,5,4]=>010101=>101010=>[1,2,2,2]
[1,6,3,7,4,2,5]=>010110=>011010=>[2,1,2,2]
[1,6,3,7,4,5,2]=>010101=>101010=>[1,2,2,2]
[1,6,3,7,5,2,4]=>010110=>011010=>[2,1,2,2]
[1,6,3,7,5,4,2]=>010111=>111010=>[1,1,1,2,2]
[1,6,4,2,3,5,7]=>011000=>000110=>[4,1,2]
[1,6,4,2,3,7,5]=>011001=>100110=>[1,3,1,2]
[1,6,4,2,5,3,7]=>011010=>010110=>[2,2,1,2]
[1,6,4,2,5,7,3]=>011001=>100110=>[1,3,1,2]
[1,6,4,2,7,3,5]=>011010=>010110=>[2,2,1,2]
[1,6,4,2,7,5,3]=>011011=>110110=>[1,1,2,1,2]
[1,6,4,3,2,5,7]=>011100=>001110=>[3,1,1,2]
[1,6,4,3,2,7,5]=>011101=>101110=>[1,2,1,1,2]
[1,6,4,3,5,2,7]=>011010=>010110=>[2,2,1,2]
[1,6,4,3,5,7,2]=>011001=>100110=>[1,3,1,2]
[1,6,4,3,7,2,5]=>011010=>010110=>[2,2,1,2]
[1,6,4,3,7,5,2]=>011011=>110110=>[1,1,2,1,2]
[1,6,4,5,2,3,7]=>010100=>001010=>[3,2,2]
[1,6,4,5,2,7,3]=>010101=>101010=>[1,2,2,2]
[1,6,4,5,3,2,7]=>010110=>011010=>[2,1,2,2]
[1,6,4,5,3,7,2]=>010101=>101010=>[1,2,2,2]
[1,6,4,5,7,2,3]=>010010=>010010=>[2,3,2]
[1,6,4,5,7,3,2]=>010011=>110010=>[1,1,3,2]
[1,6,4,7,2,3,5]=>010100=>001010=>[3,2,2]
[1,6,4,7,2,5,3]=>010101=>101010=>[1,2,2,2]
[1,6,4,7,3,2,5]=>010110=>011010=>[2,1,2,2]
[1,6,4,7,3,5,2]=>010101=>101010=>[1,2,2,2]
[1,6,4,7,5,2,3]=>010110=>011010=>[2,1,2,2]
[1,6,4,7,5,3,2]=>010111=>111010=>[1,1,1,2,2]
[1,6,5,2,3,4,7]=>011000=>000110=>[4,1,2]
[1,6,5,2,3,7,4]=>011001=>100110=>[1,3,1,2]
[1,6,5,2,4,3,7]=>011010=>010110=>[2,2,1,2]
[1,6,5,2,4,7,3]=>011001=>100110=>[1,3,1,2]
[1,6,5,2,7,3,4]=>011010=>010110=>[2,2,1,2]
[1,6,5,2,7,4,3]=>011011=>110110=>[1,1,2,1,2]
[1,6,5,3,2,4,7]=>011100=>001110=>[3,1,1,2]
[1,6,5,3,2,7,4]=>011101=>101110=>[1,2,1,1,2]
[1,6,5,3,4,2,7]=>011010=>010110=>[2,2,1,2]
[1,6,5,3,4,7,2]=>011001=>100110=>[1,3,1,2]
[1,6,5,3,7,2,4]=>011010=>010110=>[2,2,1,2]
[1,6,5,3,7,4,2]=>011011=>110110=>[1,1,2,1,2]
[1,6,5,4,2,3,7]=>011100=>001110=>[3,1,1,2]
[1,6,5,4,2,7,3]=>011101=>101110=>[1,2,1,1,2]
[1,6,5,4,3,2,7]=>011110=>011110=>[2,1,1,1,2]
[1,6,5,4,3,7,2]=>011101=>101110=>[1,2,1,1,2]
[1,6,5,4,7,2,3]=>011010=>010110=>[2,2,1,2]
[1,6,5,4,7,3,2]=>011011=>110110=>[1,1,2,1,2]
[1,6,5,7,2,3,4]=>010100=>001010=>[3,2,2]
[1,6,5,7,2,4,3]=>010101=>101010=>[1,2,2,2]
[1,6,5,7,3,2,4]=>010110=>011010=>[2,1,2,2]
[1,6,5,7,3,4,2]=>010101=>101010=>[1,2,2,2]
[1,6,5,7,4,2,3]=>010110=>011010=>[2,1,2,2]
[1,6,5,7,4,3,2]=>010111=>111010=>[1,1,1,2,2]
[1,6,7,2,3,4,5]=>001000=>000100=>[4,3]
[1,6,7,2,3,5,4]=>001001=>100100=>[1,3,3]
[1,6,7,2,4,3,5]=>001010=>010100=>[2,2,3]
[1,6,7,2,4,5,3]=>001001=>100100=>[1,3,3]
[1,6,7,2,5,3,4]=>001010=>010100=>[2,2,3]
[1,6,7,2,5,4,3]=>001011=>110100=>[1,1,2,3]
[1,6,7,3,2,4,5]=>001100=>001100=>[3,1,3]
[1,6,7,3,2,5,4]=>001101=>101100=>[1,2,1,3]
[1,6,7,3,4,2,5]=>001010=>010100=>[2,2,3]
[1,6,7,3,4,5,2]=>001001=>100100=>[1,3,3]
[1,6,7,3,5,2,4]=>001010=>010100=>[2,2,3]
[1,6,7,3,5,4,2]=>001011=>110100=>[1,1,2,3]
[1,6,7,4,2,3,5]=>001100=>001100=>[3,1,3]
[1,6,7,4,2,5,3]=>001101=>101100=>[1,2,1,3]
[1,6,7,4,3,2,5]=>001110=>011100=>[2,1,1,3]
[1,6,7,4,3,5,2]=>001101=>101100=>[1,2,1,3]
[1,6,7,4,5,2,3]=>001010=>010100=>[2,2,3]
[1,6,7,4,5,3,2]=>001011=>110100=>[1,1,2,3]
[1,6,7,5,2,3,4]=>001100=>001100=>[3,1,3]
[1,6,7,5,2,4,3]=>001101=>101100=>[1,2,1,3]
[1,6,7,5,3,2,4]=>001110=>011100=>[2,1,1,3]
[1,6,7,5,3,4,2]=>001101=>101100=>[1,2,1,3]
[1,6,7,5,4,2,3]=>001110=>011100=>[2,1,1,3]
[1,6,7,5,4,3,2]=>001111=>111100=>[1,1,1,1,3]
[1,7,2,3,4,5,6]=>010000=>000010=>[5,2]
[1,7,2,3,4,6,5]=>010001=>100010=>[1,4,2]
[1,7,2,3,5,4,6]=>010010=>010010=>[2,3,2]
[1,7,2,3,5,6,4]=>010001=>100010=>[1,4,2]
[1,7,2,3,6,4,5]=>010010=>010010=>[2,3,2]
[1,7,2,3,6,5,4]=>010011=>110010=>[1,1,3,2]
[1,7,2,4,3,5,6]=>010100=>001010=>[3,2,2]
[1,7,2,4,3,6,5]=>010101=>101010=>[1,2,2,2]
[1,7,2,4,5,3,6]=>010010=>010010=>[2,3,2]
[1,7,2,4,5,6,3]=>010001=>100010=>[1,4,2]
[1,7,2,4,6,3,5]=>010010=>010010=>[2,3,2]
[1,7,2,4,6,5,3]=>010011=>110010=>[1,1,3,2]
[1,7,2,5,3,4,6]=>010100=>001010=>[3,2,2]
[1,7,2,5,3,6,4]=>010101=>101010=>[1,2,2,2]
[1,7,2,5,4,3,6]=>010110=>011010=>[2,1,2,2]
[1,7,2,5,4,6,3]=>010101=>101010=>[1,2,2,2]
[1,7,2,5,6,3,4]=>010010=>010010=>[2,3,2]
[1,7,2,5,6,4,3]=>010011=>110010=>[1,1,3,2]
[1,7,2,6,3,4,5]=>010100=>001010=>[3,2,2]
[1,7,2,6,3,5,4]=>010101=>101010=>[1,2,2,2]
[1,7,2,6,4,3,5]=>010110=>011010=>[2,1,2,2]
[1,7,2,6,4,5,3]=>010101=>101010=>[1,2,2,2]
[1,7,2,6,5,3,4]=>010110=>011010=>[2,1,2,2]
[1,7,2,6,5,4,3]=>010111=>111010=>[1,1,1,2,2]
[1,7,3,2,4,5,6]=>011000=>000110=>[4,1,2]
[1,7,3,2,4,6,5]=>011001=>100110=>[1,3,1,2]
[1,7,3,2,5,4,6]=>011010=>010110=>[2,2,1,2]
[1,7,3,2,5,6,4]=>011001=>100110=>[1,3,1,2]
[1,7,3,2,6,4,5]=>011010=>010110=>[2,2,1,2]
[1,7,3,2,6,5,4]=>011011=>110110=>[1,1,2,1,2]
[1,7,3,4,2,5,6]=>010100=>001010=>[3,2,2]
[1,7,3,4,2,6,5]=>010101=>101010=>[1,2,2,2]
[1,7,3,4,5,2,6]=>010010=>010010=>[2,3,2]
[1,7,3,4,5,6,2]=>010001=>100010=>[1,4,2]
[1,7,3,4,6,2,5]=>010010=>010010=>[2,3,2]
[1,7,3,4,6,5,2]=>010011=>110010=>[1,1,3,2]
[1,7,3,5,2,4,6]=>010100=>001010=>[3,2,2]
[1,7,3,5,2,6,4]=>010101=>101010=>[1,2,2,2]
[1,7,3,5,4,2,6]=>010110=>011010=>[2,1,2,2]
[1,7,3,5,4,6,2]=>010101=>101010=>[1,2,2,2]
[1,7,3,5,6,2,4]=>010010=>010010=>[2,3,2]
[1,7,3,5,6,4,2]=>010011=>110010=>[1,1,3,2]
[1,7,3,6,2,4,5]=>010100=>001010=>[3,2,2]
[1,7,3,6,2,5,4]=>010101=>101010=>[1,2,2,2]
[1,7,3,6,4,2,5]=>010110=>011010=>[2,1,2,2]
[1,7,3,6,4,5,2]=>010101=>101010=>[1,2,2,2]
[1,7,3,6,5,2,4]=>010110=>011010=>[2,1,2,2]
[1,7,3,6,5,4,2]=>010111=>111010=>[1,1,1,2,2]
[1,7,4,2,3,5,6]=>011000=>000110=>[4,1,2]
[1,7,4,2,3,6,5]=>011001=>100110=>[1,3,1,2]
[1,7,4,2,5,3,6]=>011010=>010110=>[2,2,1,2]
[1,7,4,2,5,6,3]=>011001=>100110=>[1,3,1,2]
[1,7,4,2,6,3,5]=>011010=>010110=>[2,2,1,2]
[1,7,4,2,6,5,3]=>011011=>110110=>[1,1,2,1,2]
[1,7,4,3,2,5,6]=>011100=>001110=>[3,1,1,2]
[1,7,4,3,2,6,5]=>011101=>101110=>[1,2,1,1,2]
[1,7,4,3,5,2,6]=>011010=>010110=>[2,2,1,2]
[1,7,4,3,5,6,2]=>011001=>100110=>[1,3,1,2]
[1,7,4,3,6,2,5]=>011010=>010110=>[2,2,1,2]
[1,7,4,3,6,5,2]=>011011=>110110=>[1,1,2,1,2]
[1,7,4,5,2,3,6]=>010100=>001010=>[3,2,2]
[1,7,4,5,2,6,3]=>010101=>101010=>[1,2,2,2]
[1,7,4,5,3,2,6]=>010110=>011010=>[2,1,2,2]
[1,7,4,5,3,6,2]=>010101=>101010=>[1,2,2,2]
[1,7,4,5,6,2,3]=>010010=>010010=>[2,3,2]
[1,7,4,5,6,3,2]=>010011=>110010=>[1,1,3,2]
[1,7,4,6,2,3,5]=>010100=>001010=>[3,2,2]
[1,7,4,6,2,5,3]=>010101=>101010=>[1,2,2,2]
[1,7,4,6,3,2,5]=>010110=>011010=>[2,1,2,2]
[1,7,4,6,3,5,2]=>010101=>101010=>[1,2,2,2]
[1,7,4,6,5,2,3]=>010110=>011010=>[2,1,2,2]
[1,7,4,6,5,3,2]=>010111=>111010=>[1,1,1,2,2]
[1,7,5,2,3,4,6]=>011000=>000110=>[4,1,2]
[1,7,5,2,3,6,4]=>011001=>100110=>[1,3,1,2]
[1,7,5,2,4,3,6]=>011010=>010110=>[2,2,1,2]
[1,7,5,2,4,6,3]=>011001=>100110=>[1,3,1,2]
[1,7,5,2,6,3,4]=>011010=>010110=>[2,2,1,2]
[1,7,5,2,6,4,3]=>011011=>110110=>[1,1,2,1,2]
[1,7,5,3,2,4,6]=>011100=>001110=>[3,1,1,2]
[1,7,5,3,2,6,4]=>011101=>101110=>[1,2,1,1,2]
[1,7,5,3,4,2,6]=>011010=>010110=>[2,2,1,2]
[1,7,5,3,4,6,2]=>011001=>100110=>[1,3,1,2]
[1,7,5,3,6,2,4]=>011010=>010110=>[2,2,1,2]
[1,7,5,3,6,4,2]=>011011=>110110=>[1,1,2,1,2]
[1,7,5,4,2,3,6]=>011100=>001110=>[3,1,1,2]
[1,7,5,4,2,6,3]=>011101=>101110=>[1,2,1,1,2]
[1,7,5,4,3,2,6]=>011110=>011110=>[2,1,1,1,2]
[1,7,5,4,3,6,2]=>011101=>101110=>[1,2,1,1,2]
[1,7,5,4,6,2,3]=>011010=>010110=>[2,2,1,2]
[1,7,5,4,6,3,2]=>011011=>110110=>[1,1,2,1,2]
[1,7,5,6,2,3,4]=>010100=>001010=>[3,2,2]
[1,7,5,6,2,4,3]=>010101=>101010=>[1,2,2,2]
[1,7,5,6,3,2,4]=>010110=>011010=>[2,1,2,2]
[1,7,5,6,3,4,2]=>010101=>101010=>[1,2,2,2]
[1,7,5,6,4,2,3]=>010110=>011010=>[2,1,2,2]
[1,7,5,6,4,3,2]=>010111=>111010=>[1,1,1,2,2]
[1,7,6,2,3,4,5]=>011000=>000110=>[4,1,2]
[1,7,6,2,3,5,4]=>011001=>100110=>[1,3,1,2]
[1,7,6,2,4,3,5]=>011010=>010110=>[2,2,1,2]
[1,7,6,2,4,5,3]=>011001=>100110=>[1,3,1,2]
[1,7,6,2,5,3,4]=>011010=>010110=>[2,2,1,2]
[1,7,6,2,5,4,3]=>011011=>110110=>[1,1,2,1,2]
[1,7,6,3,2,4,5]=>011100=>001110=>[3,1,1,2]
[1,7,6,3,2,5,4]=>011101=>101110=>[1,2,1,1,2]
[1,7,6,3,4,2,5]=>011010=>010110=>[2,2,1,2]
[1,7,6,3,4,5,2]=>011001=>100110=>[1,3,1,2]
[1,7,6,3,5,2,4]=>011010=>010110=>[2,2,1,2]
[1,7,6,3,5,4,2]=>011011=>110110=>[1,1,2,1,2]
[1,7,6,4,2,3,5]=>011100=>001110=>[3,1,1,2]
[1,7,6,4,2,5,3]=>011101=>101110=>[1,2,1,1,2]
[1,7,6,4,3,2,5]=>011110=>011110=>[2,1,1,1,2]
[1,7,6,4,3,5,2]=>011101=>101110=>[1,2,1,1,2]
[1,7,6,4,5,2,3]=>011010=>010110=>[2,2,1,2]
[1,7,6,4,5,3,2]=>011011=>110110=>[1,1,2,1,2]
[1,7,6,5,2,3,4]=>011100=>001110=>[3,1,1,2]
[1,7,6,5,2,4,3]=>011101=>101110=>[1,2,1,1,2]
[1,7,6,5,3,2,4]=>011110=>011110=>[2,1,1,1,2]
[1,7,6,5,3,4,2]=>011101=>101110=>[1,2,1,1,2]
[1,7,6,5,4,2,3]=>011110=>011110=>[2,1,1,1,2]
[1,7,6,5,4,3,2]=>011111=>111110=>[1,1,1,1,1,2]
[2,1,3,4,5,6,7]=>100000=>000001=>[6,1]
[2,1,3,4,5,7,6]=>100001=>100001=>[1,5,1]
[2,1,3,4,6,5,7]=>100010=>010001=>[2,4,1]
[2,1,3,4,6,7,5]=>100001=>100001=>[1,5,1]
[2,1,3,4,7,5,6]=>100010=>010001=>[2,4,1]
[2,1,3,4,7,6,5]=>100011=>110001=>[1,1,4,1]
[2,1,3,5,4,6,7]=>100100=>001001=>[3,3,1]
[2,1,3,5,4,7,6]=>100101=>101001=>[1,2,3,1]
[2,1,3,5,6,4,7]=>100010=>010001=>[2,4,1]
[2,1,3,5,6,7,4]=>100001=>100001=>[1,5,1]
[2,1,3,5,7,4,6]=>100010=>010001=>[2,4,1]
[2,1,3,5,7,6,4]=>100011=>110001=>[1,1,4,1]
[2,1,3,6,4,5,7]=>100100=>001001=>[3,3,1]
[2,1,3,6,4,7,5]=>100101=>101001=>[1,2,3,1]
[2,1,3,6,5,4,7]=>100110=>011001=>[2,1,3,1]
[2,1,3,6,5,7,4]=>100101=>101001=>[1,2,3,1]
[2,1,3,6,7,4,5]=>100010=>010001=>[2,4,1]
[2,1,3,6,7,5,4]=>100011=>110001=>[1,1,4,1]
[2,1,3,7,4,5,6]=>100100=>001001=>[3,3,1]
[2,1,3,7,4,6,5]=>100101=>101001=>[1,2,3,1]
[2,1,3,7,5,4,6]=>100110=>011001=>[2,1,3,1]
[2,1,3,7,5,6,4]=>100101=>101001=>[1,2,3,1]
[2,1,3,7,6,4,5]=>100110=>011001=>[2,1,3,1]
[2,1,3,7,6,5,4]=>100111=>111001=>[1,1,1,3,1]
[2,1,4,3,5,6,7]=>101000=>000101=>[4,2,1]
[2,1,4,3,5,7,6]=>101001=>100101=>[1,3,2,1]
[2,1,4,3,6,5,7]=>101010=>010101=>[2,2,2,1]
[2,1,4,3,6,7,5]=>101001=>100101=>[1,3,2,1]
[2,1,4,3,7,5,6]=>101010=>010101=>[2,2,2,1]
[2,1,4,3,7,6,5]=>101011=>110101=>[1,1,2,2,1]
[2,1,4,5,3,6,7]=>100100=>001001=>[3,3,1]
[2,1,4,5,3,7,6]=>100101=>101001=>[1,2,3,1]
[2,1,4,5,6,3,7]=>100010=>010001=>[2,4,1]
[2,1,4,5,6,7,3]=>100001=>100001=>[1,5,1]
[2,1,4,5,7,3,6]=>100010=>010001=>[2,4,1]
[2,1,4,5,7,6,3]=>100011=>110001=>[1,1,4,1]
[2,1,4,6,3,5,7]=>100100=>001001=>[3,3,1]
[2,1,4,6,3,7,5]=>100101=>101001=>[1,2,3,1]
[2,1,4,6,5,3,7]=>100110=>011001=>[2,1,3,1]
[2,1,4,6,5,7,3]=>100101=>101001=>[1,2,3,1]
[2,1,4,6,7,3,5]=>100010=>010001=>[2,4,1]
[2,1,4,6,7,5,3]=>100011=>110001=>[1,1,4,1]
[2,1,4,7,3,5,6]=>100100=>001001=>[3,3,1]
[2,1,4,7,3,6,5]=>100101=>101001=>[1,2,3,1]
[2,1,4,7,5,3,6]=>100110=>011001=>[2,1,3,1]
[2,1,4,7,5,6,3]=>100101=>101001=>[1,2,3,1]
[2,1,4,7,6,3,5]=>100110=>011001=>[2,1,3,1]
[2,1,4,7,6,5,3]=>100111=>111001=>[1,1,1,3,1]
[2,1,5,3,4,6,7]=>101000=>000101=>[4,2,1]
[2,1,5,3,4,7,6]=>101001=>100101=>[1,3,2,1]
[2,1,5,3,6,4,7]=>101010=>010101=>[2,2,2,1]
[2,1,5,3,6,7,4]=>101001=>100101=>[1,3,2,1]
[2,1,5,3,7,4,6]=>101010=>010101=>[2,2,2,1]
[2,1,5,3,7,6,4]=>101011=>110101=>[1,1,2,2,1]
[2,1,5,4,3,6,7]=>101100=>001101=>[3,1,2,1]
[2,1,5,4,3,7,6]=>101101=>101101=>[1,2,1,2,1]
[2,1,5,4,6,3,7]=>101010=>010101=>[2,2,2,1]
[2,1,5,4,6,7,3]=>101001=>100101=>[1,3,2,1]
[2,1,5,4,7,3,6]=>101010=>010101=>[2,2,2,1]
[2,1,5,4,7,6,3]=>101011=>110101=>[1,1,2,2,1]
[2,1,5,6,3,4,7]=>100100=>001001=>[3,3,1]
[2,1,5,6,3,7,4]=>100101=>101001=>[1,2,3,1]
[2,1,5,6,4,3,7]=>100110=>011001=>[2,1,3,1]
[2,1,5,6,4,7,3]=>100101=>101001=>[1,2,3,1]
[2,1,5,6,7,3,4]=>100010=>010001=>[2,4,1]
[2,1,5,6,7,4,3]=>100011=>110001=>[1,1,4,1]
[2,1,5,7,3,4,6]=>100100=>001001=>[3,3,1]
[2,1,5,7,3,6,4]=>100101=>101001=>[1,2,3,1]
[2,1,5,7,4,3,6]=>100110=>011001=>[2,1,3,1]
[2,1,5,7,4,6,3]=>100101=>101001=>[1,2,3,1]
[2,1,5,7,6,3,4]=>100110=>011001=>[2,1,3,1]
[2,1,5,7,6,4,3]=>100111=>111001=>[1,1,1,3,1]
[2,1,6,3,4,5,7]=>101000=>000101=>[4,2,1]
[2,1,6,3,4,7,5]=>101001=>100101=>[1,3,2,1]
[2,1,6,3,5,4,7]=>101010=>010101=>[2,2,2,1]
[2,1,6,3,5,7,4]=>101001=>100101=>[1,3,2,1]
[2,1,6,3,7,4,5]=>101010=>010101=>[2,2,2,1]
[2,1,6,3,7,5,4]=>101011=>110101=>[1,1,2,2,1]
[2,1,6,4,3,5,7]=>101100=>001101=>[3,1,2,1]
[2,1,6,4,3,7,5]=>101101=>101101=>[1,2,1,2,1]
[2,1,6,4,5,3,7]=>101010=>010101=>[2,2,2,1]
[2,1,6,4,5,7,3]=>101001=>100101=>[1,3,2,1]
[2,1,6,4,7,3,5]=>101010=>010101=>[2,2,2,1]
[2,1,6,4,7,5,3]=>101011=>110101=>[1,1,2,2,1]
[2,1,6,5,3,4,7]=>101100=>001101=>[3,1,2,1]
[2,1,6,5,3,7,4]=>101101=>101101=>[1,2,1,2,1]
[2,1,6,5,4,3,7]=>101110=>011101=>[2,1,1,2,1]
[2,1,6,5,4,7,3]=>101101=>101101=>[1,2,1,2,1]
[2,1,6,5,7,3,4]=>101010=>010101=>[2,2,2,1]
[2,1,6,5,7,4,3]=>101011=>110101=>[1,1,2,2,1]
[2,1,6,7,3,4,5]=>100100=>001001=>[3,3,1]
[2,1,6,7,3,5,4]=>100101=>101001=>[1,2,3,1]
[2,1,6,7,4,3,5]=>100110=>011001=>[2,1,3,1]
[2,1,6,7,4,5,3]=>100101=>101001=>[1,2,3,1]
[2,1,6,7,5,3,4]=>100110=>011001=>[2,1,3,1]
[2,1,6,7,5,4,3]=>100111=>111001=>[1,1,1,3,1]
[2,1,7,3,4,5,6]=>101000=>000101=>[4,2,1]
[2,1,7,3,4,6,5]=>101001=>100101=>[1,3,2,1]
[2,1,7,3,5,4,6]=>101010=>010101=>[2,2,2,1]
[2,1,7,3,5,6,4]=>101001=>100101=>[1,3,2,1]
[2,1,7,3,6,4,5]=>101010=>010101=>[2,2,2,1]
[2,1,7,3,6,5,4]=>101011=>110101=>[1,1,2,2,1]
[2,1,7,4,3,5,6]=>101100=>001101=>[3,1,2,1]
[2,1,7,4,3,6,5]=>101101=>101101=>[1,2,1,2,1]
[2,1,7,4,5,3,6]=>101010=>010101=>[2,2,2,1]
[2,1,7,4,5,6,3]=>101001=>100101=>[1,3,2,1]
[2,1,7,4,6,3,5]=>101010=>010101=>[2,2,2,1]
[2,1,7,4,6,5,3]=>101011=>110101=>[1,1,2,2,1]
[2,1,7,5,3,4,6]=>101100=>001101=>[3,1,2,1]
[2,1,7,5,3,6,4]=>101101=>101101=>[1,2,1,2,1]
[2,1,7,5,4,3,6]=>101110=>011101=>[2,1,1,2,1]
[2,1,7,5,4,6,3]=>101101=>101101=>[1,2,1,2,1]
[2,1,7,5,6,3,4]=>101010=>010101=>[2,2,2,1]
[2,1,7,5,6,4,3]=>101011=>110101=>[1,1,2,2,1]
[2,1,7,6,3,4,5]=>101100=>001101=>[3,1,2,1]
[2,1,7,6,3,5,4]=>101101=>101101=>[1,2,1,2,1]
[2,1,7,6,4,3,5]=>101110=>011101=>[2,1,1,2,1]
[2,1,7,6,4,5,3]=>101101=>101101=>[1,2,1,2,1]
[2,1,7,6,5,3,4]=>101110=>011101=>[2,1,1,2,1]
[2,1,7,6,5,4,3]=>101111=>111101=>[1,1,1,1,2,1]
[2,3,1,4,5,6,7]=>010000=>000010=>[5,2]
[2,3,1,4,5,7,6]=>010001=>100010=>[1,4,2]
[2,3,1,4,6,5,7]=>010010=>010010=>[2,3,2]
[2,3,1,4,6,7,5]=>010001=>100010=>[1,4,2]
[2,3,1,4,7,5,6]=>010010=>010010=>[2,3,2]
[2,3,1,4,7,6,5]=>010011=>110010=>[1,1,3,2]
[2,3,1,5,4,6,7]=>010100=>001010=>[3,2,2]
[2,3,1,5,4,7,6]=>010101=>101010=>[1,2,2,2]
[2,3,1,5,6,4,7]=>010010=>010010=>[2,3,2]
[2,3,1,5,6,7,4]=>010001=>100010=>[1,4,2]
[2,3,1,5,7,4,6]=>010010=>010010=>[2,3,2]
[2,3,1,5,7,6,4]=>010011=>110010=>[1,1,3,2]
[2,3,1,6,4,5,7]=>010100=>001010=>[3,2,2]
[2,3,1,6,4,7,5]=>010101=>101010=>[1,2,2,2]
[2,3,1,6,5,4,7]=>010110=>011010=>[2,1,2,2]
[2,3,1,6,5,7,4]=>010101=>101010=>[1,2,2,2]
[2,3,1,6,7,4,5]=>010010=>010010=>[2,3,2]
[2,3,1,6,7,5,4]=>010011=>110010=>[1,1,3,2]
[2,3,1,7,4,5,6]=>010100=>001010=>[3,2,2]
[2,3,1,7,4,6,5]=>010101=>101010=>[1,2,2,2]
[2,3,1,7,5,4,6]=>010110=>011010=>[2,1,2,2]
[2,3,1,7,5,6,4]=>010101=>101010=>[1,2,2,2]
[2,3,1,7,6,4,5]=>010110=>011010=>[2,1,2,2]
[2,3,1,7,6,5,4]=>010111=>111010=>[1,1,1,2,2]
[2,3,4,1,5,6,7]=>001000=>000100=>[4,3]
[2,3,4,1,5,7,6]=>001001=>100100=>[1,3,3]
[2,3,4,1,6,5,7]=>001010=>010100=>[2,2,3]
[2,3,4,1,6,7,5]=>001001=>100100=>[1,3,3]
[2,3,4,1,7,5,6]=>001010=>010100=>[2,2,3]
[2,3,4,1,7,6,5]=>001011=>110100=>[1,1,2,3]
[2,3,4,5,1,6,7]=>000100=>001000=>[3,4]
[2,3,4,5,1,7,6]=>000101=>101000=>[1,2,4]
[2,3,4,5,6,1,7]=>000010=>010000=>[2,5]
[2,3,4,5,6,7,1]=>000001=>100000=>[1,6]
[2,3,4,5,7,1,6]=>000010=>010000=>[2,5]
[2,3,4,5,7,6,1]=>000011=>110000=>[1,1,5]
[2,3,4,6,1,5,7]=>000100=>001000=>[3,4]
[2,3,4,6,1,7,5]=>000101=>101000=>[1,2,4]
[2,3,4,6,5,1,7]=>000110=>011000=>[2,1,4]
[2,3,4,6,5,7,1]=>000101=>101000=>[1,2,4]
[2,3,4,6,7,1,5]=>000010=>010000=>[2,5]
[2,3,4,6,7,5,1]=>000011=>110000=>[1,1,5]
[2,3,4,7,1,5,6]=>000100=>001000=>[3,4]
[2,3,4,7,1,6,5]=>000101=>101000=>[1,2,4]
[2,3,4,7,5,1,6]=>000110=>011000=>[2,1,4]
[2,3,4,7,5,6,1]=>000101=>101000=>[1,2,4]
[2,3,4,7,6,1,5]=>000110=>011000=>[2,1,4]
[2,3,4,7,6,5,1]=>000111=>111000=>[1,1,1,4]
[2,3,5,1,4,6,7]=>001000=>000100=>[4,3]
[2,3,5,1,4,7,6]=>001001=>100100=>[1,3,3]
[2,3,5,1,6,4,7]=>001010=>010100=>[2,2,3]
[2,3,5,1,6,7,4]=>001001=>100100=>[1,3,3]
[2,3,5,1,7,4,6]=>001010=>010100=>[2,2,3]
[2,3,5,1,7,6,4]=>001011=>110100=>[1,1,2,3]
[2,3,5,4,1,6,7]=>001100=>001100=>[3,1,3]
[2,3,5,4,1,7,6]=>001101=>101100=>[1,2,1,3]
[2,3,5,4,6,1,7]=>001010=>010100=>[2,2,3]
[2,3,5,4,6,7,1]=>001001=>100100=>[1,3,3]
[2,3,5,4,7,1,6]=>001010=>010100=>[2,2,3]
[2,3,5,4,7,6,1]=>001011=>110100=>[1,1,2,3]
[2,3,5,6,1,4,7]=>000100=>001000=>[3,4]
[2,3,5,6,1,7,4]=>000101=>101000=>[1,2,4]
[2,3,5,6,4,1,7]=>000110=>011000=>[2,1,4]
[2,3,5,6,4,7,1]=>000101=>101000=>[1,2,4]
[2,3,5,6,7,1,4]=>000010=>010000=>[2,5]
[2,3,5,6,7,4,1]=>000011=>110000=>[1,1,5]
[2,3,5,7,1,4,6]=>000100=>001000=>[3,4]
[2,3,5,7,1,6,4]=>000101=>101000=>[1,2,4]
[2,3,5,7,4,1,6]=>000110=>011000=>[2,1,4]
[2,3,5,7,4,6,1]=>000101=>101000=>[1,2,4]
[2,3,5,7,6,1,4]=>000110=>011000=>[2,1,4]
[2,3,5,7,6,4,1]=>000111=>111000=>[1,1,1,4]
[2,3,6,1,4,5,7]=>001000=>000100=>[4,3]
[2,3,6,1,4,7,5]=>001001=>100100=>[1,3,3]
[2,3,6,1,5,4,7]=>001010=>010100=>[2,2,3]
[2,3,6,1,5,7,4]=>001001=>100100=>[1,3,3]
[2,3,6,1,7,4,5]=>001010=>010100=>[2,2,3]
[2,3,6,1,7,5,4]=>001011=>110100=>[1,1,2,3]
[2,3,6,4,1,5,7]=>001100=>001100=>[3,1,3]
[2,3,6,4,1,7,5]=>001101=>101100=>[1,2,1,3]
[2,3,6,4,5,1,7]=>001010=>010100=>[2,2,3]
[2,3,6,4,5,7,1]=>001001=>100100=>[1,3,3]
[2,3,6,4,7,1,5]=>001010=>010100=>[2,2,3]
[2,3,6,4,7,5,1]=>001011=>110100=>[1,1,2,3]
[2,3,6,5,1,4,7]=>001100=>001100=>[3,1,3]
[2,3,6,5,1,7,4]=>001101=>101100=>[1,2,1,3]
[2,3,6,5,4,1,7]=>001110=>011100=>[2,1,1,3]
[2,3,6,5,4,7,1]=>001101=>101100=>[1,2,1,3]
[2,3,6,5,7,1,4]=>001010=>010100=>[2,2,3]
[2,3,6,5,7,4,1]=>001011=>110100=>[1,1,2,3]
[2,3,6,7,1,4,5]=>000100=>001000=>[3,4]
[2,3,6,7,1,5,4]=>000101=>101000=>[1,2,4]
[2,3,6,7,4,1,5]=>000110=>011000=>[2,1,4]
[2,3,6,7,4,5,1]=>000101=>101000=>[1,2,4]
[2,3,6,7,5,1,4]=>000110=>011000=>[2,1,4]
[2,3,6,7,5,4,1]=>000111=>111000=>[1,1,1,4]
[2,3,7,1,4,5,6]=>001000=>000100=>[4,3]
[2,3,7,1,4,6,5]=>001001=>100100=>[1,3,3]
[2,3,7,1,5,4,6]=>001010=>010100=>[2,2,3]
[2,3,7,1,5,6,4]=>001001=>100100=>[1,3,3]
[2,3,7,1,6,4,5]=>001010=>010100=>[2,2,3]
[2,3,7,1,6,5,4]=>001011=>110100=>[1,1,2,3]
[2,3,7,4,1,5,6]=>001100=>001100=>[3,1,3]
[2,3,7,4,1,6,5]=>001101=>101100=>[1,2,1,3]
[2,3,7,4,5,1,6]=>001010=>010100=>[2,2,3]
[2,3,7,4,5,6,1]=>001001=>100100=>[1,3,3]
[2,3,7,4,6,1,5]=>001010=>010100=>[2,2,3]
[2,3,7,4,6,5,1]=>001011=>110100=>[1,1,2,3]
[2,3,7,5,1,4,6]=>001100=>001100=>[3,1,3]
[2,3,7,5,1,6,4]=>001101=>101100=>[1,2,1,3]
[2,3,7,5,4,1,6]=>001110=>011100=>[2,1,1,3]
[2,3,7,5,4,6,1]=>001101=>101100=>[1,2,1,3]
[2,3,7,5,6,1,4]=>001010=>010100=>[2,2,3]
[2,3,7,5,6,4,1]=>001011=>110100=>[1,1,2,3]
[2,3,7,6,1,4,5]=>001100=>001100=>[3,1,3]
[2,3,7,6,1,5,4]=>001101=>101100=>[1,2,1,3]
[2,3,7,6,4,1,5]=>001110=>011100=>[2,1,1,3]
[2,3,7,6,4,5,1]=>001101=>101100=>[1,2,1,3]
[2,3,7,6,5,1,4]=>001110=>011100=>[2,1,1,3]
[2,3,7,6,5,4,1]=>001111=>111100=>[1,1,1,1,3]
[2,4,1,3,5,6,7]=>010000=>000010=>[5,2]
[2,4,1,3,5,7,6]=>010001=>100010=>[1,4,2]
[2,4,1,3,6,5,7]=>010010=>010010=>[2,3,2]
[2,4,1,3,6,7,5]=>010001=>100010=>[1,4,2]
[2,4,1,3,7,5,6]=>010010=>010010=>[2,3,2]
[2,4,1,3,7,6,5]=>010011=>110010=>[1,1,3,2]
[2,4,1,5,3,6,7]=>010100=>001010=>[3,2,2]
[2,4,1,5,3,7,6]=>010101=>101010=>[1,2,2,2]
[2,4,1,5,6,3,7]=>010010=>010010=>[2,3,2]
[2,4,1,5,6,7,3]=>010001=>100010=>[1,4,2]
[2,4,1,5,7,3,6]=>010010=>010010=>[2,3,2]
[2,4,1,5,7,6,3]=>010011=>110010=>[1,1,3,2]
[2,4,1,6,3,5,7]=>010100=>001010=>[3,2,2]
[2,4,1,6,3,7,5]=>010101=>101010=>[1,2,2,2]
[2,4,1,6,5,3,7]=>010110=>011010=>[2,1,2,2]
[2,4,1,6,5,7,3]=>010101=>101010=>[1,2,2,2]
[2,4,1,6,7,3,5]=>010010=>010010=>[2,3,2]
[2,4,1,6,7,5,3]=>010011=>110010=>[1,1,3,2]
[2,4,1,7,3,5,6]=>010100=>001010=>[3,2,2]
[2,4,1,7,3,6,5]=>010101=>101010=>[1,2,2,2]
[2,4,1,7,5,3,6]=>010110=>011010=>[2,1,2,2]
[2,4,1,7,5,6,3]=>010101=>101010=>[1,2,2,2]
[2,4,1,7,6,3,5]=>010110=>011010=>[2,1,2,2]
[2,4,1,7,6,5,3]=>010111=>111010=>[1,1,1,2,2]
[2,4,3,1,5,6,7]=>011000=>000110=>[4,1,2]
[2,4,3,1,5,7,6]=>011001=>100110=>[1,3,1,2]
[2,4,3,1,6,5,7]=>011010=>010110=>[2,2,1,2]
[2,4,3,1,6,7,5]=>011001=>100110=>[1,3,1,2]
[2,4,3,1,7,5,6]=>011010=>010110=>[2,2,1,2]
[2,4,3,1,7,6,5]=>011011=>110110=>[1,1,2,1,2]
[2,4,3,5,1,6,7]=>010100=>001010=>[3,2,2]
[2,4,3,5,1,7,6]=>010101=>101010=>[1,2,2,2]
[2,4,3,5,6,1,7]=>010010=>010010=>[2,3,2]
[2,4,3,5,6,7,1]=>010001=>100010=>[1,4,2]
[2,4,3,5,7,1,6]=>010010=>010010=>[2,3,2]
[2,4,3,5,7,6,1]=>010011=>110010=>[1,1,3,2]
[2,4,3,6,1,5,7]=>010100=>001010=>[3,2,2]
[2,4,3,6,1,7,5]=>010101=>101010=>[1,2,2,2]
[2,4,3,6,5,1,7]=>010110=>011010=>[2,1,2,2]
[2,4,3,6,5,7,1]=>010101=>101010=>[1,2,2,2]
[2,4,3,6,7,1,5]=>010010=>010010=>[2,3,2]
[2,4,3,6,7,5,1]=>010011=>110010=>[1,1,3,2]
[2,4,3,7,1,5,6]=>010100=>001010=>[3,2,2]
[2,4,3,7,1,6,5]=>010101=>101010=>[1,2,2,2]
[2,4,3,7,5,1,6]=>010110=>011010=>[2,1,2,2]
[2,4,3,7,5,6,1]=>010101=>101010=>[1,2,2,2]
[2,4,3,7,6,1,5]=>010110=>011010=>[2,1,2,2]
[2,4,3,7,6,5,1]=>010111=>111010=>[1,1,1,2,2]
[2,4,5,1,3,6,7]=>001000=>000100=>[4,3]
[2,4,5,1,3,7,6]=>001001=>100100=>[1,3,3]
[2,4,5,1,6,3,7]=>001010=>010100=>[2,2,3]
[2,4,5,1,6,7,3]=>001001=>100100=>[1,3,3]
[2,4,5,1,7,3,6]=>001010=>010100=>[2,2,3]
[2,4,5,1,7,6,3]=>001011=>110100=>[1,1,2,3]
[2,4,5,3,1,6,7]=>001100=>001100=>[3,1,3]
[2,4,5,3,1,7,6]=>001101=>101100=>[1,2,1,3]
[2,4,5,3,6,1,7]=>001010=>010100=>[2,2,3]
[2,4,5,3,6,7,1]=>001001=>100100=>[1,3,3]
[2,4,5,3,7,1,6]=>001010=>010100=>[2,2,3]
[2,4,5,3,7,6,1]=>001011=>110100=>[1,1,2,3]
[2,4,5,6,1,3,7]=>000100=>001000=>[3,4]
[2,4,5,6,1,7,3]=>000101=>101000=>[1,2,4]
[2,4,5,6,3,1,7]=>000110=>011000=>[2,1,4]
[2,4,5,6,3,7,1]=>000101=>101000=>[1,2,4]
[2,4,5,6,7,1,3]=>000010=>010000=>[2,5]
[2,4,5,6,7,3,1]=>000011=>110000=>[1,1,5]
[2,4,5,7,1,3,6]=>000100=>001000=>[3,4]
[2,4,5,7,1,6,3]=>000101=>101000=>[1,2,4]
[2,4,5,7,3,1,6]=>000110=>011000=>[2,1,4]
[2,4,5,7,3,6,1]=>000101=>101000=>[1,2,4]
[2,4,5,7,6,1,3]=>000110=>011000=>[2,1,4]
[2,4,5,7,6,3,1]=>000111=>111000=>[1,1,1,4]
[2,4,6,1,3,5,7]=>001000=>000100=>[4,3]
[2,4,6,1,3,7,5]=>001001=>100100=>[1,3,3]
[2,4,6,1,5,3,7]=>001010=>010100=>[2,2,3]
[2,4,6,1,5,7,3]=>001001=>100100=>[1,3,3]
[2,4,6,1,7,3,5]=>001010=>010100=>[2,2,3]
[2,4,6,1,7,5,3]=>001011=>110100=>[1,1,2,3]
[2,4,6,3,1,5,7]=>001100=>001100=>[3,1,3]
[2,4,6,3,1,7,5]=>001101=>101100=>[1,2,1,3]
[2,4,6,3,5,1,7]=>001010=>010100=>[2,2,3]
[2,4,6,3,5,7,1]=>001001=>100100=>[1,3,3]
[2,4,6,3,7,1,5]=>001010=>010100=>[2,2,3]
[2,4,6,3,7,5,1]=>001011=>110100=>[1,1,2,3]
[2,4,6,5,1,3,7]=>001100=>001100=>[3,1,3]
[2,4,6,5,1,7,3]=>001101=>101100=>[1,2,1,3]
[2,4,6,5,3,1,7]=>001110=>011100=>[2,1,1,3]
[2,4,6,5,3,7,1]=>001101=>101100=>[1,2,1,3]
[2,4,6,5,7,1,3]=>001010=>010100=>[2,2,3]
[2,4,6,5,7,3,1]=>001011=>110100=>[1,1,2,3]
[2,4,6,7,1,3,5]=>000100=>001000=>[3,4]
[2,4,6,7,1,5,3]=>000101=>101000=>[1,2,4]
[2,4,6,7,3,1,5]=>000110=>011000=>[2,1,4]
[2,4,6,7,3,5,1]=>000101=>101000=>[1,2,4]
[2,4,6,7,5,1,3]=>000110=>011000=>[2,1,4]
[2,4,6,7,5,3,1]=>000111=>111000=>[1,1,1,4]
[2,4,7,1,3,5,6]=>001000=>000100=>[4,3]
[2,4,7,1,3,6,5]=>001001=>100100=>[1,3,3]
[2,4,7,1,5,3,6]=>001010=>010100=>[2,2,3]
[2,4,7,1,5,6,3]=>001001=>100100=>[1,3,3]
[2,4,7,1,6,3,5]=>001010=>010100=>[2,2,3]
[2,4,7,1,6,5,3]=>001011=>110100=>[1,1,2,3]
[2,4,7,3,1,5,6]=>001100=>001100=>[3,1,3]
[2,4,7,3,1,6,5]=>001101=>101100=>[1,2,1,3]
[2,4,7,3,5,1,6]=>001010=>010100=>[2,2,3]
[2,4,7,3,5,6,1]=>001001=>100100=>[1,3,3]
[2,4,7,3,6,1,5]=>001010=>010100=>[2,2,3]
[2,4,7,3,6,5,1]=>001011=>110100=>[1,1,2,3]
[2,4,7,5,1,3,6]=>001100=>001100=>[3,1,3]
[2,4,7,5,1,6,3]=>001101=>101100=>[1,2,1,3]
[2,4,7,5,3,1,6]=>001110=>011100=>[2,1,1,3]
[2,4,7,5,3,6,1]=>001101=>101100=>[1,2,1,3]
[2,4,7,5,6,1,3]=>001010=>010100=>[2,2,3]
[2,4,7,5,6,3,1]=>001011=>110100=>[1,1,2,3]
[2,4,7,6,1,3,5]=>001100=>001100=>[3,1,3]
[2,4,7,6,1,5,3]=>001101=>101100=>[1,2,1,3]
[2,4,7,6,3,1,5]=>001110=>011100=>[2,1,1,3]
[2,4,7,6,3,5,1]=>001101=>101100=>[1,2,1,3]
[2,4,7,6,5,1,3]=>001110=>011100=>[2,1,1,3]
[2,4,7,6,5,3,1]=>001111=>111100=>[1,1,1,1,3]
[2,5,1,3,4,6,7]=>010000=>000010=>[5,2]
[2,5,1,3,4,7,6]=>010001=>100010=>[1,4,2]
[2,5,1,3,6,4,7]=>010010=>010010=>[2,3,2]
[2,5,1,3,6,7,4]=>010001=>100010=>[1,4,2]
[2,5,1,3,7,4,6]=>010010=>010010=>[2,3,2]
[2,5,1,3,7,6,4]=>010011=>110010=>[1,1,3,2]
[2,5,1,4,3,6,7]=>010100=>001010=>[3,2,2]
[2,5,1,4,3,7,6]=>010101=>101010=>[1,2,2,2]
[2,5,1,4,6,3,7]=>010010=>010010=>[2,3,2]
[2,5,1,4,6,7,3]=>010001=>100010=>[1,4,2]
[2,5,1,4,7,3,6]=>010010=>010010=>[2,3,2]
[2,5,1,4,7,6,3]=>010011=>110010=>[1,1,3,2]
[2,5,1,6,3,4,7]=>010100=>001010=>[3,2,2]
[2,5,1,6,3,7,4]=>010101=>101010=>[1,2,2,2]
[2,5,1,6,4,3,7]=>010110=>011010=>[2,1,2,2]
[2,5,1,6,4,7,3]=>010101=>101010=>[1,2,2,2]
[2,5,1,6,7,3,4]=>010010=>010010=>[2,3,2]
[2,5,1,6,7,4,3]=>010011=>110010=>[1,1,3,2]
[2,5,1,7,3,4,6]=>010100=>001010=>[3,2,2]
[2,5,1,7,3,6,4]=>010101=>101010=>[1,2,2,2]
[2,5,1,7,4,3,6]=>010110=>011010=>[2,1,2,2]
[2,5,1,7,4,6,3]=>010101=>101010=>[1,2,2,2]
[2,5,1,7,6,3,4]=>010110=>011010=>[2,1,2,2]
[2,5,1,7,6,4,3]=>010111=>111010=>[1,1,1,2,2]
[2,5,3,1,4,6,7]=>011000=>000110=>[4,1,2]
[2,5,3,1,4,7,6]=>011001=>100110=>[1,3,1,2]
[2,5,3,1,6,4,7]=>011010=>010110=>[2,2,1,2]
[2,5,3,1,6,7,4]=>011001=>100110=>[1,3,1,2]
[2,5,3,1,7,4,6]=>011010=>010110=>[2,2,1,2]
[2,5,3,1,7,6,4]=>011011=>110110=>[1,1,2,1,2]
[2,5,3,4,1,6,7]=>010100=>001010=>[3,2,2]
[2,5,3,4,1,7,6]=>010101=>101010=>[1,2,2,2]
[2,5,3,4,6,1,7]=>010010=>010010=>[2,3,2]
[2,5,3,4,6,7,1]=>010001=>100010=>[1,4,2]
[2,5,3,4,7,1,6]=>010010=>010010=>[2,3,2]
[2,5,3,4,7,6,1]=>010011=>110010=>[1,1,3,2]
[2,5,3,6,1,4,7]=>010100=>001010=>[3,2,2]
[2,5,3,6,1,7,4]=>010101=>101010=>[1,2,2,2]
[2,5,3,6,4,1,7]=>010110=>011010=>[2,1,2,2]
[2,5,3,6,4,7,1]=>010101=>101010=>[1,2,2,2]
[2,5,3,6,7,1,4]=>010010=>010010=>[2,3,2]
[2,5,3,6,7,4,1]=>010011=>110010=>[1,1,3,2]
[2,5,3,7,1,4,6]=>010100=>001010=>[3,2,2]
[2,5,3,7,1,6,4]=>010101=>101010=>[1,2,2,2]
[2,5,3,7,4,1,6]=>010110=>011010=>[2,1,2,2]
[2,5,3,7,4,6,1]=>010101=>101010=>[1,2,2,2]
[2,5,3,7,6,1,4]=>010110=>011010=>[2,1,2,2]
[2,5,3,7,6,4,1]=>010111=>111010=>[1,1,1,2,2]
[2,5,4,1,3,6,7]=>011000=>000110=>[4,1,2]
[2,5,4,1,3,7,6]=>011001=>100110=>[1,3,1,2]
[2,5,4,1,6,3,7]=>011010=>010110=>[2,2,1,2]
[2,5,4,1,6,7,3]=>011001=>100110=>[1,3,1,2]
[2,5,4,1,7,3,6]=>011010=>010110=>[2,2,1,2]
[2,5,4,1,7,6,3]=>011011=>110110=>[1,1,2,1,2]
[2,5,4,3,1,6,7]=>011100=>001110=>[3,1,1,2]
[2,5,4,3,1,7,6]=>011101=>101110=>[1,2,1,1,2]
[2,5,4,3,6,1,7]=>011010=>010110=>[2,2,1,2]
[2,5,4,3,6,7,1]=>011001=>100110=>[1,3,1,2]
[2,5,4,3,7,1,6]=>011010=>010110=>[2,2,1,2]
[2,5,4,3,7,6,1]=>011011=>110110=>[1,1,2,1,2]
[2,5,4,6,1,3,7]=>010100=>001010=>[3,2,2]
[2,5,4,6,1,7,3]=>010101=>101010=>[1,2,2,2]
[2,5,4,6,3,1,7]=>010110=>011010=>[2,1,2,2]
[2,5,4,6,3,7,1]=>010101=>101010=>[1,2,2,2]
[2,5,4,6,7,1,3]=>010010=>010010=>[2,3,2]
[2,5,4,6,7,3,1]=>010011=>110010=>[1,1,3,2]
[2,5,4,7,1,3,6]=>010100=>001010=>[3,2,2]
[2,5,4,7,1,6,3]=>010101=>101010=>[1,2,2,2]
[2,5,4,7,3,1,6]=>010110=>011010=>[2,1,2,2]
[2,5,4,7,3,6,1]=>010101=>101010=>[1,2,2,2]
[2,5,4,7,6,1,3]=>010110=>011010=>[2,1,2,2]
[2,5,4,7,6,3,1]=>010111=>111010=>[1,1,1,2,2]
[2,5,6,1,3,4,7]=>001000=>000100=>[4,3]
[2,5,6,1,3,7,4]=>001001=>100100=>[1,3,3]
[2,5,6,1,4,3,7]=>001010=>010100=>[2,2,3]
[2,5,6,1,4,7,3]=>001001=>100100=>[1,3,3]
[2,5,6,1,7,3,4]=>001010=>010100=>[2,2,3]
[2,5,6,1,7,4,3]=>001011=>110100=>[1,1,2,3]
[2,5,6,3,1,4,7]=>001100=>001100=>[3,1,3]
[2,5,6,3,1,7,4]=>001101=>101100=>[1,2,1,3]
[2,5,6,3,4,1,7]=>001010=>010100=>[2,2,3]
[2,5,6,3,4,7,1]=>001001=>100100=>[1,3,3]
[2,5,6,3,7,1,4]=>001010=>010100=>[2,2,3]
[2,5,6,3,7,4,1]=>001011=>110100=>[1,1,2,3]
[2,5,6,4,1,3,7]=>001100=>001100=>[3,1,3]
[2,5,6,4,1,7,3]=>001101=>101100=>[1,2,1,3]
[2,5,6,4,3,1,7]=>001110=>011100=>[2,1,1,3]
[2,5,6,4,3,7,1]=>001101=>101100=>[1,2,1,3]
[2,5,6,4,7,1,3]=>001010=>010100=>[2,2,3]
[2,5,6,4,7,3,1]=>001011=>110100=>[1,1,2,3]
[2,5,6,7,1,3,4]=>000100=>001000=>[3,4]
[2,5,6,7,1,4,3]=>000101=>101000=>[1,2,4]
[2,5,6,7,3,1,4]=>000110=>011000=>[2,1,4]
[2,5,6,7,3,4,1]=>000101=>101000=>[1,2,4]
[2,5,6,7,4,1,3]=>000110=>011000=>[2,1,4]
[2,5,6,7,4,3,1]=>000111=>111000=>[1,1,1,4]
[2,5,7,1,3,4,6]=>001000=>000100=>[4,3]
[2,5,7,1,3,6,4]=>001001=>100100=>[1,3,3]
[2,5,7,1,4,3,6]=>001010=>010100=>[2,2,3]
[2,5,7,1,4,6,3]=>001001=>100100=>[1,3,3]
[2,5,7,1,6,3,4]=>001010=>010100=>[2,2,3]
[2,5,7,1,6,4,3]=>001011=>110100=>[1,1,2,3]
[2,5,7,3,1,4,6]=>001100=>001100=>[3,1,3]
[2,5,7,3,1,6,4]=>001101=>101100=>[1,2,1,3]
[2,5,7,3,4,1,6]=>001010=>010100=>[2,2,3]
[2,5,7,3,4,6,1]=>001001=>100100=>[1,3,3]
[2,5,7,3,6,1,4]=>001010=>010100=>[2,2,3]
[2,5,7,3,6,4,1]=>001011=>110100=>[1,1,2,3]
[2,5,7,4,1,3,6]=>001100=>001100=>[3,1,3]
[2,5,7,4,1,6,3]=>001101=>101100=>[1,2,1,3]
[2,5,7,4,3,1,6]=>001110=>011100=>[2,1,1,3]
[2,5,7,4,3,6,1]=>001101=>101100=>[1,2,1,3]
[2,5,7,4,6,1,3]=>001010=>010100=>[2,2,3]
[2,5,7,4,6,3,1]=>001011=>110100=>[1,1,2,3]
[2,5,7,6,1,3,4]=>001100=>001100=>[3,1,3]
[2,5,7,6,1,4,3]=>001101=>101100=>[1,2,1,3]
[2,5,7,6,3,1,4]=>001110=>011100=>[2,1,1,3]
[2,5,7,6,3,4,1]=>001101=>101100=>[1,2,1,3]
[2,5,7,6,4,1,3]=>001110=>011100=>[2,1,1,3]
[2,5,7,6,4,3,1]=>001111=>111100=>[1,1,1,1,3]
[2,6,1,3,4,5,7]=>010000=>000010=>[5,2]
[2,6,1,3,4,7,5]=>010001=>100010=>[1,4,2]
[2,6,1,3,5,4,7]=>010010=>010010=>[2,3,2]
[2,6,1,3,5,7,4]=>010001=>100010=>[1,4,2]
[2,6,1,3,7,4,5]=>010010=>010010=>[2,3,2]
[2,6,1,3,7,5,4]=>010011=>110010=>[1,1,3,2]
[2,6,1,4,3,5,7]=>010100=>001010=>[3,2,2]
[2,6,1,4,3,7,5]=>010101=>101010=>[1,2,2,2]
[2,6,1,4,5,3,7]=>010010=>010010=>[2,3,2]
[2,6,1,4,5,7,3]=>010001=>100010=>[1,4,2]
[2,6,1,4,7,3,5]=>010010=>010010=>[2,3,2]
[2,6,1,4,7,5,3]=>010011=>110010=>[1,1,3,2]
[2,6,1,5,3,4,7]=>010100=>001010=>[3,2,2]
[2,6,1,5,3,7,4]=>010101=>101010=>[1,2,2,2]
[2,6,1,5,4,3,7]=>010110=>011010=>[2,1,2,2]
[2,6,1,5,4,7,3]=>010101=>101010=>[1,2,2,2]
[2,6,1,5,7,3,4]=>010010=>010010=>[2,3,2]
[2,6,1,5,7,4,3]=>010011=>110010=>[1,1,3,2]
[2,6,1,7,3,4,5]=>010100=>001010=>[3,2,2]
[2,6,1,7,3,5,4]=>010101=>101010=>[1,2,2,2]
[2,6,1,7,4,3,5]=>010110=>011010=>[2,1,2,2]
[2,6,1,7,4,5,3]=>010101=>101010=>[1,2,2,2]
[2,6,1,7,5,3,4]=>010110=>011010=>[2,1,2,2]
[2,6,1,7,5,4,3]=>010111=>111010=>[1,1,1,2,2]
[2,6,3,1,4,5,7]=>011000=>000110=>[4,1,2]
[2,6,3,1,4,7,5]=>011001=>100110=>[1,3,1,2]
[2,6,3,1,5,4,7]=>011010=>010110=>[2,2,1,2]
[2,6,3,1,5,7,4]=>011001=>100110=>[1,3,1,2]
[2,6,3,1,7,4,5]=>011010=>010110=>[2,2,1,2]
[2,6,3,1,7,5,4]=>011011=>110110=>[1,1,2,1,2]
[2,6,3,4,1,5,7]=>010100=>001010=>[3,2,2]
[2,6,3,4,1,7,5]=>010101=>101010=>[1,2,2,2]
[2,6,3,4,5,1,7]=>010010=>010010=>[2,3,2]
[2,6,3,4,5,7,1]=>010001=>100010=>[1,4,2]
[2,6,3,4,7,1,5]=>010010=>010010=>[2,3,2]
[2,6,3,4,7,5,1]=>010011=>110010=>[1,1,3,2]
[2,6,3,5,1,4,7]=>010100=>001010=>[3,2,2]
[2,6,3,5,1,7,4]=>010101=>101010=>[1,2,2,2]
[2,6,3,5,4,1,7]=>010110=>011010=>[2,1,2,2]
[2,6,3,5,4,7,1]=>010101=>101010=>[1,2,2,2]
[2,6,3,5,7,1,4]=>010010=>010010=>[2,3,2]
[2,6,3,5,7,4,1]=>010011=>110010=>[1,1,3,2]
[2,6,3,7,1,4,5]=>010100=>001010=>[3,2,2]
[2,6,3,7,1,5,4]=>010101=>101010=>[1,2,2,2]
[2,6,3,7,4,1,5]=>010110=>011010=>[2,1,2,2]
[2,6,3,7,4,5,1]=>010101=>101010=>[1,2,2,2]
[2,6,3,7,5,1,4]=>010110=>011010=>[2,1,2,2]
[2,6,3,7,5,4,1]=>010111=>111010=>[1,1,1,2,2]
[2,6,4,1,3,5,7]=>011000=>000110=>[4,1,2]
[2,6,4,1,3,7,5]=>011001=>100110=>[1,3,1,2]
[2,6,4,1,5,3,7]=>011010=>010110=>[2,2,1,2]
[2,6,4,1,5,7,3]=>011001=>100110=>[1,3,1,2]
[2,6,4,1,7,3,5]=>011010=>010110=>[2,2,1,2]
[2,6,4,1,7,5,3]=>011011=>110110=>[1,1,2,1,2]
[2,6,4,3,1,5,7]=>011100=>001110=>[3,1,1,2]
[2,6,4,3,1,7,5]=>011101=>101110=>[1,2,1,1,2]
[2,6,4,3,5,1,7]=>011010=>010110=>[2,2,1,2]
[2,6,4,3,5,7,1]=>011001=>100110=>[1,3,1,2]
[2,6,4,3,7,1,5]=>011010=>010110=>[2,2,1,2]
[2,6,4,3,7,5,1]=>011011=>110110=>[1,1,2,1,2]
[2,6,4,5,1,3,7]=>010100=>001010=>[3,2,2]
[2,6,4,5,1,7,3]=>010101=>101010=>[1,2,2,2]
[2,6,4,5,3,1,7]=>010110=>011010=>[2,1,2,2]
[2,6,4,5,3,7,1]=>010101=>101010=>[1,2,2,2]
[2,6,4,5,7,1,3]=>010010=>010010=>[2,3,2]
[2,6,4,5,7,3,1]=>010011=>110010=>[1,1,3,2]
[2,6,4,7,1,3,5]=>010100=>001010=>[3,2,2]
[2,6,4,7,1,5,3]=>010101=>101010=>[1,2,2,2]
[2,6,4,7,3,1,5]=>010110=>011010=>[2,1,2,2]
[2,6,4,7,3,5,1]=>010101=>101010=>[1,2,2,2]
[2,6,4,7,5,1,3]=>010110=>011010=>[2,1,2,2]
[2,6,4,7,5,3,1]=>010111=>111010=>[1,1,1,2,2]
[2,6,5,1,3,4,7]=>011000=>000110=>[4,1,2]
[2,6,5,1,3,7,4]=>011001=>100110=>[1,3,1,2]
[2,6,5,1,4,3,7]=>011010=>010110=>[2,2,1,2]
[2,6,5,1,4,7,3]=>011001=>100110=>[1,3,1,2]
[2,6,5,1,7,3,4]=>011010=>010110=>[2,2,1,2]
[2,6,5,1,7,4,3]=>011011=>110110=>[1,1,2,1,2]
[2,6,5,3,1,4,7]=>011100=>001110=>[3,1,1,2]
[2,6,5,3,1,7,4]=>011101=>101110=>[1,2,1,1,2]
[2,6,5,3,4,1,7]=>011010=>010110=>[2,2,1,2]
[2,6,5,3,4,7,1]=>011001=>100110=>[1,3,1,2]
[2,6,5,3,7,1,4]=>011010=>010110=>[2,2,1,2]
[2,6,5,3,7,4,1]=>011011=>110110=>[1,1,2,1,2]
[2,6,5,4,1,3,7]=>011100=>001110=>[3,1,1,2]
[2,6,5,4,1,7,3]=>011101=>101110=>[1,2,1,1,2]
[2,6,5,4,3,1,7]=>011110=>011110=>[2,1,1,1,2]
[2,6,5,4,3,7,1]=>011101=>101110=>[1,2,1,1,2]
[2,6,5,4,7,1,3]=>011010=>010110=>[2,2,1,2]
[2,6,5,4,7,3,1]=>011011=>110110=>[1,1,2,1,2]
[2,6,5,7,1,3,4]=>010100=>001010=>[3,2,2]
[2,6,5,7,1,4,3]=>010101=>101010=>[1,2,2,2]
[2,6,5,7,3,1,4]=>010110=>011010=>[2,1,2,2]
[2,6,5,7,3,4,1]=>010101=>101010=>[1,2,2,2]
[2,6,5,7,4,1,3]=>010110=>011010=>[2,1,2,2]
[2,6,5,7,4,3,1]=>010111=>111010=>[1,1,1,2,2]
[2,6,7,1,3,4,5]=>001000=>000100=>[4,3]
[2,6,7,1,3,5,4]=>001001=>100100=>[1,3,3]
[2,6,7,1,4,3,5]=>001010=>010100=>[2,2,3]
[2,6,7,1,4,5,3]=>001001=>100100=>[1,3,3]
[2,6,7,1,5,3,4]=>001010=>010100=>[2,2,3]
[2,6,7,1,5,4,3]=>001011=>110100=>[1,1,2,3]
[2,6,7,3,1,4,5]=>001100=>001100=>[3,1,3]
[2,6,7,3,1,5,4]=>001101=>101100=>[1,2,1,3]
[2,6,7,3,4,1,5]=>001010=>010100=>[2,2,3]
[2,6,7,3,4,5,1]=>001001=>100100=>[1,3,3]
[2,6,7,3,5,1,4]=>001010=>010100=>[2,2,3]
[2,6,7,3,5,4,1]=>001011=>110100=>[1,1,2,3]
[2,6,7,4,1,3,5]=>001100=>001100=>[3,1,3]
[2,6,7,4,1,5,3]=>001101=>101100=>[1,2,1,3]
[2,6,7,4,3,1,5]=>001110=>011100=>[2,1,1,3]
[2,6,7,4,3,5,1]=>001101=>101100=>[1,2,1,3]
[2,6,7,4,5,1,3]=>001010=>010100=>[2,2,3]
[2,6,7,4,5,3,1]=>001011=>110100=>[1,1,2,3]
[2,6,7,5,1,3,4]=>001100=>001100=>[3,1,3]
[2,6,7,5,1,4,3]=>001101=>101100=>[1,2,1,3]
[2,6,7,5,3,1,4]=>001110=>011100=>[2,1,1,3]
[2,6,7,5,3,4,1]=>001101=>101100=>[1,2,1,3]
[2,6,7,5,4,1,3]=>001110=>011100=>[2,1,1,3]
[2,6,7,5,4,3,1]=>001111=>111100=>[1,1,1,1,3]
[2,7,1,3,4,5,6]=>010000=>000010=>[5,2]
[2,7,1,3,4,6,5]=>010001=>100010=>[1,4,2]
[2,7,1,3,5,4,6]=>010010=>010010=>[2,3,2]
[2,7,1,3,5,6,4]=>010001=>100010=>[1,4,2]
[2,7,1,3,6,4,5]=>010010=>010010=>[2,3,2]
[2,7,1,3,6,5,4]=>010011=>110010=>[1,1,3,2]
[2,7,1,4,3,5,6]=>010100=>001010=>[3,2,2]
[2,7,1,4,3,6,5]=>010101=>101010=>[1,2,2,2]
[2,7,1,4,5,3,6]=>010010=>010010=>[2,3,2]
[2,7,1,4,5,6,3]=>010001=>100010=>[1,4,2]
[2,7,1,4,6,3,5]=>010010=>010010=>[2,3,2]
[2,7,1,4,6,5,3]=>010011=>110010=>[1,1,3,2]
[2,7,1,5,3,4,6]=>010100=>001010=>[3,2,2]
[2,7,1,5,3,6,4]=>010101=>101010=>[1,2,2,2]
[2,7,1,5,4,3,6]=>010110=>011010=>[2,1,2,2]
[2,7,1,5,4,6,3]=>010101=>101010=>[1,2,2,2]
[2,7,1,5,6,3,4]=>010010=>010010=>[2,3,2]
[2,7,1,5,6,4,3]=>010011=>110010=>[1,1,3,2]
[2,7,1,6,3,4,5]=>010100=>001010=>[3,2,2]
[2,7,1,6,3,5,4]=>010101=>101010=>[1,2,2,2]
[2,7,1,6,4,3,5]=>010110=>011010=>[2,1,2,2]
[2,7,1,6,4,5,3]=>010101=>101010=>[1,2,2,2]
[2,7,1,6,5,3,4]=>010110=>011010=>[2,1,2,2]
[2,7,1,6,5,4,3]=>010111=>111010=>[1,1,1,2,2]
[2,7,3,1,4,5,6]=>011000=>000110=>[4,1,2]
[2,7,3,1,4,6,5]=>011001=>100110=>[1,3,1,2]
[2,7,3,1,5,4,6]=>011010=>010110=>[2,2,1,2]
[2,7,3,1,5,6,4]=>011001=>100110=>[1,3,1,2]
[2,7,3,1,6,4,5]=>011010=>010110=>[2,2,1,2]
[2,7,3,1,6,5,4]=>011011=>110110=>[1,1,2,1,2]
[2,7,3,4,1,5,6]=>010100=>001010=>[3,2,2]
[2,7,3,4,1,6,5]=>010101=>101010=>[1,2,2,2]
[2,7,3,4,5,1,6]=>010010=>010010=>[2,3,2]
[2,7,3,4,5,6,1]=>010001=>100010=>[1,4,2]
[2,7,3,4,6,1,5]=>010010=>010010=>[2,3,2]
[2,7,3,4,6,5,1]=>010011=>110010=>[1,1,3,2]
[2,7,3,5,1,4,6]=>010100=>001010=>[3,2,2]
[2,7,3,5,1,6,4]=>010101=>101010=>[1,2,2,2]
[2,7,3,5,4,1,6]=>010110=>011010=>[2,1,2,2]
[2,7,3,5,4,6,1]=>010101=>101010=>[1,2,2,2]
[2,7,3,5,6,1,4]=>010010=>010010=>[2,3,2]
[2,7,3,5,6,4,1]=>010011=>110010=>[1,1,3,2]
[2,7,3,6,1,4,5]=>010100=>001010=>[3,2,2]
[2,7,3,6,1,5,4]=>010101=>101010=>[1,2,2,2]
[2,7,3,6,4,1,5]=>010110=>011010=>[2,1,2,2]
[2,7,3,6,4,5,1]=>010101=>101010=>[1,2,2,2]
[2,7,3,6,5,1,4]=>010110=>011010=>[2,1,2,2]
[2,7,3,6,5,4,1]=>010111=>111010=>[1,1,1,2,2]
[2,7,4,1,3,5,6]=>011000=>000110=>[4,1,2]
[2,7,4,1,3,6,5]=>011001=>100110=>[1,3,1,2]
[2,7,4,1,5,3,6]=>011010=>010110=>[2,2,1,2]
[2,7,4,1,5,6,3]=>011001=>100110=>[1,3,1,2]
[2,7,4,1,6,3,5]=>011010=>010110=>[2,2,1,2]
[2,7,4,1,6,5,3]=>011011=>110110=>[1,1,2,1,2]
[2,7,4,3,1,5,6]=>011100=>001110=>[3,1,1,2]
[2,7,4,3,1,6,5]=>011101=>101110=>[1,2,1,1,2]
[2,7,4,3,5,1,6]=>011010=>010110=>[2,2,1,2]
[2,7,4,3,5,6,1]=>011001=>100110=>[1,3,1,2]
[2,7,4,3,6,1,5]=>011010=>010110=>[2,2,1,2]
[2,7,4,3,6,5,1]=>011011=>110110=>[1,1,2,1,2]
[2,7,4,5,1,3,6]=>010100=>001010=>[3,2,2]
[2,7,4,5,1,6,3]=>010101=>101010=>[1,2,2,2]
[2,7,4,5,3,1,6]=>010110=>011010=>[2,1,2,2]
[2,7,4,5,3,6,1]=>010101=>101010=>[1,2,2,2]
[2,7,4,5,6,1,3]=>010010=>010010=>[2,3,2]
[2,7,4,5,6,3,1]=>010011=>110010=>[1,1,3,2]
[2,7,4,6,1,3,5]=>010100=>001010=>[3,2,2]
[2,7,4,6,1,5,3]=>010101=>101010=>[1,2,2,2]
[2,7,4,6,3,1,5]=>010110=>011010=>[2,1,2,2]
[2,7,4,6,3,5,1]=>010101=>101010=>[1,2,2,2]
[2,7,4,6,5,1,3]=>010110=>011010=>[2,1,2,2]
[2,7,4,6,5,3,1]=>010111=>111010=>[1,1,1,2,2]
[2,7,5,1,3,4,6]=>011000=>000110=>[4,1,2]
[2,7,5,1,3,6,4]=>011001=>100110=>[1,3,1,2]
[2,7,5,1,4,3,6]=>011010=>010110=>[2,2,1,2]
[2,7,5,1,4,6,3]=>011001=>100110=>[1,3,1,2]
[2,7,5,1,6,3,4]=>011010=>010110=>[2,2,1,2]
[2,7,5,1,6,4,3]=>011011=>110110=>[1,1,2,1,2]
[2,7,5,3,1,4,6]=>011100=>001110=>[3,1,1,2]
[2,7,5,3,1,6,4]=>011101=>101110=>[1,2,1,1,2]
[2,7,5,3,4,1,6]=>011010=>010110=>[2,2,1,2]
[2,7,5,3,4,6,1]=>011001=>100110=>[1,3,1,2]
[2,7,5,3,6,1,4]=>011010=>010110=>[2,2,1,2]
[2,7,5,3,6,4,1]=>011011=>110110=>[1,1,2,1,2]
[2,7,5,4,1,3,6]=>011100=>001110=>[3,1,1,2]
[2,7,5,4,1,6,3]=>011101=>101110=>[1,2,1,1,2]
[2,7,5,4,3,1,6]=>011110=>011110=>[2,1,1,1,2]
[2,7,5,4,3,6,1]=>011101=>101110=>[1,2,1,1,2]
[2,7,5,4,6,1,3]=>011010=>010110=>[2,2,1,2]
[2,7,5,4,6,3,1]=>011011=>110110=>[1,1,2,1,2]
[2,7,5,6,1,3,4]=>010100=>001010=>[3,2,2]
[2,7,5,6,1,4,3]=>010101=>101010=>[1,2,2,2]
[2,7,5,6,3,1,4]=>010110=>011010=>[2,1,2,2]
[2,7,5,6,3,4,1]=>010101=>101010=>[1,2,2,2]
[2,7,5,6,4,1,3]=>010110=>011010=>[2,1,2,2]
[2,7,5,6,4,3,1]=>010111=>111010=>[1,1,1,2,2]
[2,7,6,1,3,4,5]=>011000=>000110=>[4,1,2]
[2,7,6,1,3,5,4]=>011001=>100110=>[1,3,1,2]
[2,7,6,1,4,3,5]=>011010=>010110=>[2,2,1,2]
[2,7,6,1,4,5,3]=>011001=>100110=>[1,3,1,2]
[2,7,6,1,5,3,4]=>011010=>010110=>[2,2,1,2]
[2,7,6,1,5,4,3]=>011011=>110110=>[1,1,2,1,2]
[2,7,6,3,1,4,5]=>011100=>001110=>[3,1,1,2]
[2,7,6,3,1,5,4]=>011101=>101110=>[1,2,1,1,2]
[2,7,6,3,4,1,5]=>011010=>010110=>[2,2,1,2]
[2,7,6,3,4,5,1]=>011001=>100110=>[1,3,1,2]
[2,7,6,3,5,1,4]=>011010=>010110=>[2,2,1,2]
[2,7,6,3,5,4,1]=>011011=>110110=>[1,1,2,1,2]
[2,7,6,4,1,3,5]=>011100=>001110=>[3,1,1,2]
[2,7,6,4,1,5,3]=>011101=>101110=>[1,2,1,1,2]
[2,7,6,4,3,1,5]=>011110=>011110=>[2,1,1,1,2]
[2,7,6,4,3,5,1]=>011101=>101110=>[1,2,1,1,2]
[2,7,6,4,5,1,3]=>011010=>010110=>[2,2,1,2]
[2,7,6,4,5,3,1]=>011011=>110110=>[1,1,2,1,2]
[2,7,6,5,1,3,4]=>011100=>001110=>[3,1,1,2]
[2,7,6,5,1,4,3]=>011101=>101110=>[1,2,1,1,2]
[2,7,6,5,3,1,4]=>011110=>011110=>[2,1,1,1,2]
[2,7,6,5,3,4,1]=>011101=>101110=>[1,2,1,1,2]
[2,7,6,5,4,1,3]=>011110=>011110=>[2,1,1,1,2]
[2,7,6,5,4,3,1]=>011111=>111110=>[1,1,1,1,1,2]
[3,1,2,4,5,6,7]=>100000=>000001=>[6,1]
[3,1,2,4,5,7,6]=>100001=>100001=>[1,5,1]
[3,1,2,4,6,5,7]=>100010=>010001=>[2,4,1]
[3,1,2,4,6,7,5]=>100001=>100001=>[1,5,1]
[3,1,2,4,7,5,6]=>100010=>010001=>[2,4,1]
[3,1,2,4,7,6,5]=>100011=>110001=>[1,1,4,1]
[3,1,2,5,4,6,7]=>100100=>001001=>[3,3,1]
[3,1,2,5,4,7,6]=>100101=>101001=>[1,2,3,1]
[3,1,2,5,6,4,7]=>100010=>010001=>[2,4,1]
[3,1,2,5,6,7,4]=>100001=>100001=>[1,5,1]
[3,1,2,5,7,4,6]=>100010=>010001=>[2,4,1]
[3,1,2,5,7,6,4]=>100011=>110001=>[1,1,4,1]
[3,1,2,6,4,5,7]=>100100=>001001=>[3,3,1]
[3,1,2,6,4,7,5]=>100101=>101001=>[1,2,3,1]
[3,1,2,6,5,4,7]=>100110=>011001=>[2,1,3,1]
[3,1,2,6,5,7,4]=>100101=>101001=>[1,2,3,1]
[3,1,2,6,7,4,5]=>100010=>010001=>[2,4,1]
[3,1,2,6,7,5,4]=>100011=>110001=>[1,1,4,1]
[3,1,2,7,4,5,6]=>100100=>001001=>[3,3,1]
[3,1,2,7,4,6,5]=>100101=>101001=>[1,2,3,1]
[3,1,2,7,5,4,6]=>100110=>011001=>[2,1,3,1]
[3,1,2,7,5,6,4]=>100101=>101001=>[1,2,3,1]
[3,1,2,7,6,4,5]=>100110=>011001=>[2,1,3,1]
[3,1,2,7,6,5,4]=>100111=>111001=>[1,1,1,3,1]
[3,1,4,2,5,6,7]=>101000=>000101=>[4,2,1]
[3,1,4,2,5,7,6]=>101001=>100101=>[1,3,2,1]
[3,1,4,2,6,5,7]=>101010=>010101=>[2,2,2,1]
[3,1,4,2,6,7,5]=>101001=>100101=>[1,3,2,1]
[3,1,4,2,7,5,6]=>101010=>010101=>[2,2,2,1]
[3,1,4,2,7,6,5]=>101011=>110101=>[1,1,2,2,1]
[3,1,4,5,2,6,7]=>100100=>001001=>[3,3,1]
[3,1,4,5,2,7,6]=>100101=>101001=>[1,2,3,1]
[3,1,4,5,6,2,7]=>100010=>010001=>[2,4,1]
[3,1,4,5,6,7,2]=>100001=>100001=>[1,5,1]
[3,1,4,5,7,2,6]=>100010=>010001=>[2,4,1]
[3,1,4,5,7,6,2]=>100011=>110001=>[1,1,4,1]
[3,1,4,6,2,5,7]=>100100=>001001=>[3,3,1]
[3,1,4,6,2,7,5]=>100101=>101001=>[1,2,3,1]
[3,1,4,6,5,2,7]=>100110=>011001=>[2,1,3,1]
[3,1,4,6,5,7,2]=>100101=>101001=>[1,2,3,1]
[3,1,4,6,7,2,5]=>100010=>010001=>[2,4,1]
[3,1,4,6,7,5,2]=>100011=>110001=>[1,1,4,1]
[3,1,4,7,2,5,6]=>100100=>001001=>[3,3,1]
[3,1,4,7,2,6,5]=>100101=>101001=>[1,2,3,1]
[3,1,4,7,5,2,6]=>100110=>011001=>[2,1,3,1]
[3,1,4,7,5,6,2]=>100101=>101001=>[1,2,3,1]
[3,1,4,7,6,2,5]=>100110=>011001=>[2,1,3,1]
[3,1,4,7,6,5,2]=>100111=>111001=>[1,1,1,3,1]
[3,1,5,2,4,6,7]=>101000=>000101=>[4,2,1]
[3,1,5,2,4,7,6]=>101001=>100101=>[1,3,2,1]
[3,1,5,2,6,4,7]=>101010=>010101=>[2,2,2,1]
[3,1,5,2,6,7,4]=>101001=>100101=>[1,3,2,1]
[3,1,5,2,7,4,6]=>101010=>010101=>[2,2,2,1]
[3,1,5,2,7,6,4]=>101011=>110101=>[1,1,2,2,1]
[3,1,5,4,2,6,7]=>101100=>001101=>[3,1,2,1]
[3,1,5,4,2,7,6]=>101101=>101101=>[1,2,1,2,1]
[3,1,5,4,6,2,7]=>101010=>010101=>[2,2,2,1]
[3,1,5,4,6,7,2]=>101001=>100101=>[1,3,2,1]
[3,1,5,4,7,2,6]=>101010=>010101=>[2,2,2,1]
[3,1,5,4,7,6,2]=>101011=>110101=>[1,1,2,2,1]
[3,1,5,6,2,4,7]=>100100=>001001=>[3,3,1]
[3,1,5,6,2,7,4]=>100101=>101001=>[1,2,3,1]
[3,1,5,6,4,2,7]=>100110=>011001=>[2,1,3,1]
[3,1,5,6,4,7,2]=>100101=>101001=>[1,2,3,1]
[3,1,5,6,7,2,4]=>100010=>010001=>[2,4,1]
[3,1,5,6,7,4,2]=>100011=>110001=>[1,1,4,1]
[3,1,5,7,2,4,6]=>100100=>001001=>[3,3,1]
[3,1,5,7,2,6,4]=>100101=>101001=>[1,2,3,1]
[3,1,5,7,4,2,6]=>100110=>011001=>[2,1,3,1]
[3,1,5,7,4,6,2]=>100101=>101001=>[1,2,3,1]
[3,1,5,7,6,2,4]=>100110=>011001=>[2,1,3,1]
[3,1,5,7,6,4,2]=>100111=>111001=>[1,1,1,3,1]
[3,1,6,2,4,5,7]=>101000=>000101=>[4,2,1]
[3,1,6,2,4,7,5]=>101001=>100101=>[1,3,2,1]
[3,1,6,2,5,4,7]=>101010=>010101=>[2,2,2,1]
[3,1,6,2,5,7,4]=>101001=>100101=>[1,3,2,1]
[3,1,6,2,7,4,5]=>101010=>010101=>[2,2,2,1]
[3,1,6,2,7,5,4]=>101011=>110101=>[1,1,2,2,1]
[3,1,6,4,2,5,7]=>101100=>001101=>[3,1,2,1]
[3,1,6,4,2,7,5]=>101101=>101101=>[1,2,1,2,1]
[3,1,6,4,5,2,7]=>101010=>010101=>[2,2,2,1]
[3,1,6,4,5,7,2]=>101001=>100101=>[1,3,2,1]
[3,1,6,4,7,2,5]=>101010=>010101=>[2,2,2,1]
[3,1,6,4,7,5,2]=>101011=>110101=>[1,1,2,2,1]
[3,1,6,5,2,4,7]=>101100=>001101=>[3,1,2,1]
[3,1,6,5,2,7,4]=>101101=>101101=>[1,2,1,2,1]
[3,1,6,5,4,2,7]=>101110=>011101=>[2,1,1,2,1]
[3,1,6,5,4,7,2]=>101101=>101101=>[1,2,1,2,1]
[3,1,6,5,7,2,4]=>101010=>010101=>[2,2,2,1]
[3,1,6,5,7,4,2]=>101011=>110101=>[1,1,2,2,1]
[3,1,6,7,2,4,5]=>100100=>001001=>[3,3,1]
[3,1,6,7,2,5,4]=>100101=>101001=>[1,2,3,1]
[3,1,6,7,4,2,5]=>100110=>011001=>[2,1,3,1]
[3,1,6,7,4,5,2]=>100101=>101001=>[1,2,3,1]
[3,1,6,7,5,2,4]=>100110=>011001=>[2,1,3,1]
[3,1,6,7,5,4,2]=>100111=>111001=>[1,1,1,3,1]
[3,1,7,2,4,5,6]=>101000=>000101=>[4,2,1]
[3,1,7,2,4,6,5]=>101001=>100101=>[1,3,2,1]
[3,1,7,2,5,4,6]=>101010=>010101=>[2,2,2,1]
[3,1,7,2,5,6,4]=>101001=>100101=>[1,3,2,1]
[3,1,7,2,6,4,5]=>101010=>010101=>[2,2,2,1]
[3,1,7,2,6,5,4]=>101011=>110101=>[1,1,2,2,1]
[3,1,7,4,2,5,6]=>101100=>001101=>[3,1,2,1]
[3,1,7,4,2,6,5]=>101101=>101101=>[1,2,1,2,1]
[3,1,7,4,5,2,6]=>101010=>010101=>[2,2,2,1]
[3,1,7,4,5,6,2]=>101001=>100101=>[1,3,2,1]
[3,1,7,4,6,2,5]=>101010=>010101=>[2,2,2,1]
[3,1,7,4,6,5,2]=>101011=>110101=>[1,1,2,2,1]
[3,1,7,5,2,4,6]=>101100=>001101=>[3,1,2,1]
[3,1,7,5,2,6,4]=>101101=>101101=>[1,2,1,2,1]
[3,1,7,5,4,2,6]=>101110=>011101=>[2,1,1,2,1]
[3,1,7,5,4,6,2]=>101101=>101101=>[1,2,1,2,1]
[3,1,7,5,6,2,4]=>101010=>010101=>[2,2,2,1]
[3,1,7,5,6,4,2]=>101011=>110101=>[1,1,2,2,1]
[3,1,7,6,2,4,5]=>101100=>001101=>[3,1,2,1]
[3,1,7,6,2,5,4]=>101101=>101101=>[1,2,1,2,1]
[3,1,7,6,4,2,5]=>101110=>011101=>[2,1,1,2,1]
[3,1,7,6,4,5,2]=>101101=>101101=>[1,2,1,2,1]
[3,1,7,6,5,2,4]=>101110=>011101=>[2,1,1,2,1]
[3,1,7,6,5,4,2]=>101111=>111101=>[1,1,1,1,2,1]
[3,2,1,4,5,6,7]=>110000=>000011=>[5,1,1]
[3,2,1,4,5,7,6]=>110001=>100011=>[1,4,1,1]
[3,2,1,4,6,5,7]=>110010=>010011=>[2,3,1,1]
[3,2,1,4,6,7,5]=>110001=>100011=>[1,4,1,1]
[3,2,1,4,7,5,6]=>110010=>010011=>[2,3,1,1]
[3,2,1,4,7,6,5]=>110011=>110011=>[1,1,3,1,1]
[3,2,1,5,4,6,7]=>110100=>001011=>[3,2,1,1]
[3,2,1,5,4,7,6]=>110101=>101011=>[1,2,2,1,1]
[3,2,1,5,6,4,7]=>110010=>010011=>[2,3,1,1]
[3,2,1,5,6,7,4]=>110001=>100011=>[1,4,1,1]
[3,2,1,5,7,4,6]=>110010=>010011=>[2,3,1,1]
[3,2,1,5,7,6,4]=>110011=>110011=>[1,1,3,1,1]
[3,2,1,6,4,5,7]=>110100=>001011=>[3,2,1,1]
[3,2,1,6,4,7,5]=>110101=>101011=>[1,2,2,1,1]
[3,2,1,6,5,4,7]=>110110=>011011=>[2,1,2,1,1]
[3,2,1,6,5,7,4]=>110101=>101011=>[1,2,2,1,1]
[3,2,1,6,7,4,5]=>110010=>010011=>[2,3,1,1]
[3,2,1,6,7,5,4]=>110011=>110011=>[1,1,3,1,1]
[3,2,1,7,4,5,6]=>110100=>001011=>[3,2,1,1]
[3,2,1,7,4,6,5]=>110101=>101011=>[1,2,2,1,1]
[3,2,1,7,5,4,6]=>110110=>011011=>[2,1,2,1,1]
[3,2,1,7,5,6,4]=>110101=>101011=>[1,2,2,1,1]
[3,2,1,7,6,4,5]=>110110=>011011=>[2,1,2,1,1]
[3,2,1,7,6,5,4]=>110111=>111011=>[1,1,1,2,1,1]
[3,2,4,1,5,6,7]=>101000=>000101=>[4,2,1]
[3,2,4,1,5,7,6]=>101001=>100101=>[1,3,2,1]
[3,2,4,1,6,5,7]=>101010=>010101=>[2,2,2,1]
[3,2,4,1,6,7,5]=>101001=>100101=>[1,3,2,1]
[3,2,4,1,7,5,6]=>101010=>010101=>[2,2,2,1]
[3,2,4,1,7,6,5]=>101011=>110101=>[1,1,2,2,1]
[3,2,4,5,1,6,7]=>100100=>001001=>[3,3,1]
[3,2,4,5,1,7,6]=>100101=>101001=>[1,2,3,1]
[3,2,4,5,6,1,7]=>100010=>010001=>[2,4,1]
[3,2,4,5,6,7,1]=>100001=>100001=>[1,5,1]
[3,2,4,5,7,1,6]=>100010=>010001=>[2,4,1]
[3,2,4,5,7,6,1]=>100011=>110001=>[1,1,4,1]
[3,2,4,6,1,5,7]=>100100=>001001=>[3,3,1]
[3,2,4,6,1,7,5]=>100101=>101001=>[1,2,3,1]
[3,2,4,6,5,1,7]=>100110=>011001=>[2,1,3,1]
[3,2,4,6,5,7,1]=>100101=>101001=>[1,2,3,1]
[3,2,4,6,7,1,5]=>100010=>010001=>[2,4,1]
[3,2,4,6,7,5,1]=>100011=>110001=>[1,1,4,1]
[3,2,4,7,1,5,6]=>100100=>001001=>[3,3,1]
[3,2,4,7,1,6,5]=>100101=>101001=>[1,2,3,1]
[3,2,4,7,5,1,6]=>100110=>011001=>[2,1,3,1]
[3,2,4,7,5,6,1]=>100101=>101001=>[1,2,3,1]
[3,2,4,7,6,1,5]=>100110=>011001=>[2,1,3,1]
[3,2,4,7,6,5,1]=>100111=>111001=>[1,1,1,3,1]
[3,2,5,1,4,6,7]=>101000=>000101=>[4,2,1]
[3,2,5,1,4,7,6]=>101001=>100101=>[1,3,2,1]
[3,2,5,1,6,4,7]=>101010=>010101=>[2,2,2,1]
[3,2,5,1,6,7,4]=>101001=>100101=>[1,3,2,1]
[3,2,5,1,7,4,6]=>101010=>010101=>[2,2,2,1]
[3,2,5,1,7,6,4]=>101011=>110101=>[1,1,2,2,1]
[3,2,5,4,1,6,7]=>101100=>001101=>[3,1,2,1]
[3,2,5,4,1,7,6]=>101101=>101101=>[1,2,1,2,1]
[3,2,5,4,6,1,7]=>101010=>010101=>[2,2,2,1]
[3,2,5,4,6,7,1]=>101001=>100101=>[1,3,2,1]
[3,2,5,4,7,1,6]=>101010=>010101=>[2,2,2,1]
[3,2,5,4,7,6,1]=>101011=>110101=>[1,1,2,2,1]
[3,2,5,6,1,4,7]=>100100=>001001=>[3,3,1]
[3,2,5,6,1,7,4]=>100101=>101001=>[1,2,3,1]
[3,2,5,6,4,1,7]=>100110=>011001=>[2,1,3,1]
[3,2,5,6,4,7,1]=>100101=>101001=>[1,2,3,1]
[3,2,5,6,7,1,4]=>100010=>010001=>[2,4,1]
[3,2,5,6,7,4,1]=>100011=>110001=>[1,1,4,1]
[3,2,5,7,1,4,6]=>100100=>001001=>[3,3,1]
[3,2,5,7,1,6,4]=>100101=>101001=>[1,2,3,1]
[3,2,5,7,4,1,6]=>100110=>011001=>[2,1,3,1]
[3,2,5,7,4,6,1]=>100101=>101001=>[1,2,3,1]
[3,2,5,7,6,1,4]=>100110=>011001=>[2,1,3,1]
[3,2,5,7,6,4,1]=>100111=>111001=>[1,1,1,3,1]
[3,2,6,1,4,5,7]=>101000=>000101=>[4,2,1]
[3,2,6,1,4,7,5]=>101001=>100101=>[1,3,2,1]
[3,2,6,1,5,4,7]=>101010=>010101=>[2,2,2,1]
[3,2,6,1,5,7,4]=>101001=>100101=>[1,3,2,1]
[3,2,6,1,7,4,5]=>101010=>010101=>[2,2,2,1]
[3,2,6,1,7,5,4]=>101011=>110101=>[1,1,2,2,1]
[3,2,6,4,1,5,7]=>101100=>001101=>[3,1,2,1]
[3,2,6,4,1,7,5]=>101101=>101101=>[1,2,1,2,1]
[3,2,6,4,5,1,7]=>101010=>010101=>[2,2,2,1]
[3,2,6,4,5,7,1]=>101001=>100101=>[1,3,2,1]
[3,2,6,4,7,1,5]=>101010=>010101=>[2,2,2,1]
[3,2,6,4,7,5,1]=>101011=>110101=>[1,1,2,2,1]
[3,2,6,5,1,4,7]=>101100=>001101=>[3,1,2,1]
[3,2,6,5,1,7,4]=>101101=>101101=>[1,2,1,2,1]
[3,2,6,5,4,1,7]=>101110=>011101=>[2,1,1,2,1]
[3,2,6,5,4,7,1]=>101101=>101101=>[1,2,1,2,1]
[3,2,6,5,7,1,4]=>101010=>010101=>[2,2,2,1]
[3,2,6,5,7,4,1]=>101011=>110101=>[1,1,2,2,1]
[3,2,6,7,1,4,5]=>100100=>001001=>[3,3,1]
[3,2,6,7,1,5,4]=>100101=>101001=>[1,2,3,1]
[3,2,6,7,4,1,5]=>100110=>011001=>[2,1,3,1]
[3,2,6,7,4,5,1]=>100101=>101001=>[1,2,3,1]
[3,2,6,7,5,1,4]=>100110=>011001=>[2,1,3,1]
[3,2,6,7,5,4,1]=>100111=>111001=>[1,1,1,3,1]
[3,2,7,1,4,5,6]=>101000=>000101=>[4,2,1]
[3,2,7,1,4,6,5]=>101001=>100101=>[1,3,2,1]
[3,2,7,1,5,4,6]=>101010=>010101=>[2,2,2,1]
[3,2,7,1,5,6,4]=>101001=>100101=>[1,3,2,1]
[3,2,7,1,6,4,5]=>101010=>010101=>[2,2,2,1]
[3,2,7,1,6,5,4]=>101011=>110101=>[1,1,2,2,1]
[3,2,7,4,1,5,6]=>101100=>001101=>[3,1,2,1]
[3,2,7,4,1,6,5]=>101101=>101101=>[1,2,1,2,1]
[3,2,7,4,5,1,6]=>101010=>010101=>[2,2,2,1]
[3,2,7,4,5,6,1]=>101001=>100101=>[1,3,2,1]
[3,2,7,4,6,1,5]=>101010=>010101=>[2,2,2,1]
[3,2,7,4,6,5,1]=>101011=>110101=>[1,1,2,2,1]
[3,2,7,5,1,4,6]=>101100=>001101=>[3,1,2,1]
[3,2,7,5,1,6,4]=>101101=>101101=>[1,2,1,2,1]
[3,2,7,5,4,1,6]=>101110=>011101=>[2,1,1,2,1]
[3,2,7,5,4,6,1]=>101101=>101101=>[1,2,1,2,1]
[3,2,7,5,6,1,4]=>101010=>010101=>[2,2,2,1]
[3,2,7,5,6,4,1]=>101011=>110101=>[1,1,2,2,1]
[3,2,7,6,1,4,5]=>101100=>001101=>[3,1,2,1]
[3,2,7,6,1,5,4]=>101101=>101101=>[1,2,1,2,1]
[3,2,7,6,4,1,5]=>101110=>011101=>[2,1,1,2,1]
[3,2,7,6,4,5,1]=>101101=>101101=>[1,2,1,2,1]
[3,2,7,6,5,1,4]=>101110=>011101=>[2,1,1,2,1]
[3,2,7,6,5,4,1]=>101111=>111101=>[1,1,1,1,2,1]
[3,4,1,2,5,6,7]=>010000=>000010=>[5,2]
[3,4,1,2,5,7,6]=>010001=>100010=>[1,4,2]
[3,4,1,2,6,5,7]=>010010=>010010=>[2,3,2]
[3,4,1,2,6,7,5]=>010001=>100010=>[1,4,2]
[3,4,1,2,7,5,6]=>010010=>010010=>[2,3,2]
[3,4,1,2,7,6,5]=>010011=>110010=>[1,1,3,2]
[3,4,1,5,2,6,7]=>010100=>001010=>[3,2,2]
[3,4,1,5,2,7,6]=>010101=>101010=>[1,2,2,2]
[3,4,1,5,6,2,7]=>010010=>010010=>[2,3,2]
[3,4,1,5,6,7,2]=>010001=>100010=>[1,4,2]
[3,4,1,5,7,2,6]=>010010=>010010=>[2,3,2]
[3,4,1,5,7,6,2]=>010011=>110010=>[1,1,3,2]
[3,4,1,6,2,5,7]=>010100=>001010=>[3,2,2]
[3,4,1,6,2,7,5]=>010101=>101010=>[1,2,2,2]
[3,4,1,6,5,2,7]=>010110=>011010=>[2,1,2,2]
[3,4,1,6,5,7,2]=>010101=>101010=>[1,2,2,2]
[3,4,1,6,7,2,5]=>010010=>010010=>[2,3,2]
[3,4,1,6,7,5,2]=>010011=>110010=>[1,1,3,2]
[3,4,1,7,2,5,6]=>010100=>001010=>[3,2,2]
[3,4,1,7,2,6,5]=>010101=>101010=>[1,2,2,2]
[3,4,1,7,5,2,6]=>010110=>011010=>[2,1,2,2]
[3,4,1,7,5,6,2]=>010101=>101010=>[1,2,2,2]
[3,4,1,7,6,2,5]=>010110=>011010=>[2,1,2,2]
[3,4,1,7,6,5,2]=>010111=>111010=>[1,1,1,2,2]
[3,4,2,1,5,6,7]=>011000=>000110=>[4,1,2]
[3,4,2,1,5,7,6]=>011001=>100110=>[1,3,1,2]
[3,4,2,1,6,5,7]=>011010=>010110=>[2,2,1,2]
[3,4,2,1,6,7,5]=>011001=>100110=>[1,3,1,2]
[3,4,2,1,7,5,6]=>011010=>010110=>[2,2,1,2]
[3,4,2,1,7,6,5]=>011011=>110110=>[1,1,2,1,2]
[3,4,2,5,1,6,7]=>010100=>001010=>[3,2,2]
[3,4,2,5,1,7,6]=>010101=>101010=>[1,2,2,2]
[3,4,2,5,6,1,7]=>010010=>010010=>[2,3,2]
[3,4,2,5,6,7,1]=>010001=>100010=>[1,4,2]
[3,4,2,5,7,1,6]=>010010=>010010=>[2,3,2]
[3,4,2,5,7,6,1]=>010011=>110010=>[1,1,3,2]
[3,4,2,6,1,5,7]=>010100=>001010=>[3,2,2]
[3,4,2,6,1,7,5]=>010101=>101010=>[1,2,2,2]
[3,4,2,6,5,1,7]=>010110=>011010=>[2,1,2,2]
[3,4,2,6,5,7,1]=>010101=>101010=>[1,2,2,2]
[3,4,2,6,7,1,5]=>010010=>010010=>[2,3,2]
[3,4,2,6,7,5,1]=>010011=>110010=>[1,1,3,2]
[3,4,2,7,1,5,6]=>010100=>001010=>[3,2,2]
[3,4,2,7,1,6,5]=>010101=>101010=>[1,2,2,2]
[3,4,2,7,5,1,6]=>010110=>011010=>[2,1,2,2]
[3,4,2,7,5,6,1]=>010101=>101010=>[1,2,2,2]
[3,4,2,7,6,1,5]=>010110=>011010=>[2,1,2,2]
[3,4,2,7,6,5,1]=>010111=>111010=>[1,1,1,2,2]
[3,4,5,1,2,6,7]=>001000=>000100=>[4,3]
[3,4,5,1,2,7,6]=>001001=>100100=>[1,3,3]
[3,4,5,1,6,2,7]=>001010=>010100=>[2,2,3]
[3,4,5,1,6,7,2]=>001001=>100100=>[1,3,3]
[3,4,5,1,7,2,6]=>001010=>010100=>[2,2,3]
[3,4,5,1,7,6,2]=>001011=>110100=>[1,1,2,3]
[3,4,5,2,1,6,7]=>001100=>001100=>[3,1,3]
[3,4,5,2,1,7,6]=>001101=>101100=>[1,2,1,3]
[3,4,5,2,6,1,7]=>001010=>010100=>[2,2,3]
[3,4,5,2,6,7,1]=>001001=>100100=>[1,3,3]
[3,4,5,2,7,1,6]=>001010=>010100=>[2,2,3]
[3,4,5,2,7,6,1]=>001011=>110100=>[1,1,2,3]
[3,4,5,6,1,2,7]=>000100=>001000=>[3,4]
[3,4,5,6,1,7,2]=>000101=>101000=>[1,2,4]
[3,4,5,6,2,1,7]=>000110=>011000=>[2,1,4]
[3,4,5,6,2,7,1]=>000101=>101000=>[1,2,4]
[3,4,5,6,7,1,2]=>000010=>010000=>[2,5]
[3,4,5,6,7,2,1]=>000011=>110000=>[1,1,5]
[3,4,5,7,1,2,6]=>000100=>001000=>[3,4]
[3,4,5,7,1,6,2]=>000101=>101000=>[1,2,4]
[3,4,5,7,2,1,6]=>000110=>011000=>[2,1,4]
[3,4,5,7,2,6,1]=>000101=>101000=>[1,2,4]
[3,4,5,7,6,1,2]=>000110=>011000=>[2,1,4]
[3,4,5,7,6,2,1]=>000111=>111000=>[1,1,1,4]
[3,4,6,1,2,5,7]=>001000=>000100=>[4,3]
[3,4,6,1,2,7,5]=>001001=>100100=>[1,3,3]
[3,4,6,1,5,2,7]=>001010=>010100=>[2,2,3]
[3,4,6,1,5,7,2]=>001001=>100100=>[1,3,3]
[3,4,6,1,7,2,5]=>001010=>010100=>[2,2,3]
[3,4,6,1,7,5,2]=>001011=>110100=>[1,1,2,3]
[3,4,6,2,1,5,7]=>001100=>001100=>[3,1,3]
[3,4,6,2,1,7,5]=>001101=>101100=>[1,2,1,3]
[3,4,6,2,5,1,7]=>001010=>010100=>[2,2,3]
[3,4,6,2,5,7,1]=>001001=>100100=>[1,3,3]
[3,4,6,2,7,1,5]=>001010=>010100=>[2,2,3]
[3,4,6,2,7,5,1]=>001011=>110100=>[1,1,2,3]
[3,4,6,5,1,2,7]=>001100=>001100=>[3,1,3]
[3,4,6,5,1,7,2]=>001101=>101100=>[1,2,1,3]
[3,4,6,5,2,1,7]=>001110=>011100=>[2,1,1,3]
[3,4,6,5,2,7,1]=>001101=>101100=>[1,2,1,3]
[3,4,6,5,7,1,2]=>001010=>010100=>[2,2,3]
[3,4,6,5,7,2,1]=>001011=>110100=>[1,1,2,3]
[3,4,6,7,1,2,5]=>000100=>001000=>[3,4]
[3,4,6,7,1,5,2]=>000101=>101000=>[1,2,4]
[3,4,6,7,2,1,5]=>000110=>011000=>[2,1,4]
[3,4,6,7,2,5,1]=>000101=>101000=>[1,2,4]
[3,4,6,7,5,1,2]=>000110=>011000=>[2,1,4]
[3,4,6,7,5,2,1]=>000111=>111000=>[1,1,1,4]
[3,4,7,1,2,5,6]=>001000=>000100=>[4,3]
[3,4,7,1,2,6,5]=>001001=>100100=>[1,3,3]
[3,4,7,1,5,2,6]=>001010=>010100=>[2,2,3]
[3,4,7,1,5,6,2]=>001001=>100100=>[1,3,3]
[3,4,7,1,6,2,5]=>001010=>010100=>[2,2,3]
[3,4,7,1,6,5,2]=>001011=>110100=>[1,1,2,3]
[3,4,7,2,1,5,6]=>001100=>001100=>[3,1,3]
[3,4,7,2,1,6,5]=>001101=>101100=>[1,2,1,3]
[3,4,7,2,5,1,6]=>001010=>010100=>[2,2,3]
[3,4,7,2,5,6,1]=>001001=>100100=>[1,3,3]
[3,4,7,2,6,1,5]=>001010=>010100=>[2,2,3]
[3,4,7,2,6,5,1]=>001011=>110100=>[1,1,2,3]
[3,4,7,5,1,2,6]=>001100=>001100=>[3,1,3]
[3,4,7,5,1,6,2]=>001101=>101100=>[1,2,1,3]
[3,4,7,5,2,1,6]=>001110=>011100=>[2,1,1,3]
[3,4,7,5,2,6,1]=>001101=>101100=>[1,2,1,3]
[3,4,7,5,6,1,2]=>001010=>010100=>[2,2,3]
[3,4,7,5,6,2,1]=>001011=>110100=>[1,1,2,3]
[3,4,7,6,1,2,5]=>001100=>001100=>[3,1,3]
[3,4,7,6,1,5,2]=>001101=>101100=>[1,2,1,3]
[3,4,7,6,2,1,5]=>001110=>011100=>[2,1,1,3]
[3,4,7,6,2,5,1]=>001101=>101100=>[1,2,1,3]
[3,4,7,6,5,1,2]=>001110=>011100=>[2,1,1,3]
[3,4,7,6,5,2,1]=>001111=>111100=>[1,1,1,1,3]
[3,5,1,2,4,6,7]=>010000=>000010=>[5,2]
[3,5,1,2,4,7,6]=>010001=>100010=>[1,4,2]
[3,5,1,2,6,4,7]=>010010=>010010=>[2,3,2]
[3,5,1,2,6,7,4]=>010001=>100010=>[1,4,2]
[3,5,1,2,7,4,6]=>010010=>010010=>[2,3,2]
[3,5,1,2,7,6,4]=>010011=>110010=>[1,1,3,2]
[3,5,1,4,2,6,7]=>010100=>001010=>[3,2,2]
[3,5,1,4,2,7,6]=>010101=>101010=>[1,2,2,2]
[3,5,1,4,6,2,7]=>010010=>010010=>[2,3,2]
[3,5,1,4,6,7,2]=>010001=>100010=>[1,4,2]
[3,5,1,4,7,2,6]=>010010=>010010=>[2,3,2]
[3,5,1,4,7,6,2]=>010011=>110010=>[1,1,3,2]
[3,5,1,6,2,4,7]=>010100=>001010=>[3,2,2]
[3,5,1,6,2,7,4]=>010101=>101010=>[1,2,2,2]
[3,5,1,6,4,2,7]=>010110=>011010=>[2,1,2,2]
[3,5,1,6,4,7,2]=>010101=>101010=>[1,2,2,2]
[3,5,1,6,7,2,4]=>010010=>010010=>[2,3,2]
[3,5,1,6,7,4,2]=>010011=>110010=>[1,1,3,2]
[3,5,1,7,2,4,6]=>010100=>001010=>[3,2,2]
[3,5,1,7,2,6,4]=>010101=>101010=>[1,2,2,2]
[3,5,1,7,4,2,6]=>010110=>011010=>[2,1,2,2]
[3,5,1,7,4,6,2]=>010101=>101010=>[1,2,2,2]
[3,5,1,7,6,2,4]=>010110=>011010=>[2,1,2,2]
[3,5,1,7,6,4,2]=>010111=>111010=>[1,1,1,2,2]
[3,5,2,1,4,6,7]=>011000=>000110=>[4,1,2]
[3,5,2,1,4,7,6]=>011001=>100110=>[1,3,1,2]
[3,5,2,1,6,4,7]=>011010=>010110=>[2,2,1,2]
[3,5,2,1,6,7,4]=>011001=>100110=>[1,3,1,2]
[3,5,2,1,7,4,6]=>011010=>010110=>[2,2,1,2]
[3,5,2,1,7,6,4]=>011011=>110110=>[1,1,2,1,2]
[3,5,2,4,1,6,7]=>010100=>001010=>[3,2,2]
[3,5,2,4,1,7,6]=>010101=>101010=>[1,2,2,2]
[3,5,2,4,6,1,7]=>010010=>010010=>[2,3,2]
[3,5,2,4,6,7,1]=>010001=>100010=>[1,4,2]
[3,5,2,4,7,1,6]=>010010=>010010=>[2,3,2]
[3,5,2,4,7,6,1]=>010011=>110010=>[1,1,3,2]
[3,5,2,6,1,4,7]=>010100=>001010=>[3,2,2]
[3,5,2,6,1,7,4]=>010101=>101010=>[1,2,2,2]
[3,5,2,6,4,1,7]=>010110=>011010=>[2,1,2,2]
[3,5,2,6,4,7,1]=>010101=>101010=>[1,2,2,2]
[3,5,2,6,7,1,4]=>010010=>010010=>[2,3,2]
[3,5,2,6,7,4,1]=>010011=>110010=>[1,1,3,2]
[3,5,2,7,1,4,6]=>010100=>001010=>[3,2,2]
[3,5,2,7,1,6,4]=>010101=>101010=>[1,2,2,2]
[3,5,2,7,4,1,6]=>010110=>011010=>[2,1,2,2]
[3,5,2,7,4,6,1]=>010101=>101010=>[1,2,2,2]
[3,5,2,7,6,1,4]=>010110=>011010=>[2,1,2,2]
[3,5,2,7,6,4,1]=>010111=>111010=>[1,1,1,2,2]
[3,5,4,1,2,6,7]=>011000=>000110=>[4,1,2]
[3,5,4,1,2,7,6]=>011001=>100110=>[1,3,1,2]
[3,5,4,1,6,2,7]=>011010=>010110=>[2,2,1,2]
[3,5,4,1,6,7,2]=>011001=>100110=>[1,3,1,2]
[3,5,4,1,7,2,6]=>011010=>010110=>[2,2,1,2]
[3,5,4,1,7,6,2]=>011011=>110110=>[1,1,2,1,2]
[3,5,4,2,1,6,7]=>011100=>001110=>[3,1,1,2]
[3,5,4,2,1,7,6]=>011101=>101110=>[1,2,1,1,2]
[3,5,4,2,6,1,7]=>011010=>010110=>[2,2,1,2]
[3,5,4,2,6,7,1]=>011001=>100110=>[1,3,1,2]
[3,5,4,2,7,1,6]=>011010=>010110=>[2,2,1,2]
[3,5,4,2,7,6,1]=>011011=>110110=>[1,1,2,1,2]
[3,5,4,6,1,2,7]=>010100=>001010=>[3,2,2]
[3,5,4,6,1,7,2]=>010101=>101010=>[1,2,2,2]
[3,5,4,6,2,1,7]=>010110=>011010=>[2,1,2,2]
[3,5,4,6,2,7,1]=>010101=>101010=>[1,2,2,2]
[3,5,4,6,7,1,2]=>010010=>010010=>[2,3,2]
[3,5,4,6,7,2,1]=>010011=>110010=>[1,1,3,2]
[3,5,4,7,1,2,6]=>010100=>001010=>[3,2,2]
[3,5,4,7,1,6,2]=>010101=>101010=>[1,2,2,2]
[3,5,4,7,2,1,6]=>010110=>011010=>[2,1,2,2]
[3,5,4,7,2,6,1]=>010101=>101010=>[1,2,2,2]
[3,5,4,7,6,1,2]=>010110=>011010=>[2,1,2,2]
[3,5,4,7,6,2,1]=>010111=>111010=>[1,1,1,2,2]
[3,5,6,1,2,4,7]=>001000=>000100=>[4,3]
[3,5,6,1,2,7,4]=>001001=>100100=>[1,3,3]
[3,5,6,1,4,2,7]=>001010=>010100=>[2,2,3]
[3,5,6,1,4,7,2]=>001001=>100100=>[1,3,3]
[3,5,6,1,7,2,4]=>001010=>010100=>[2,2,3]
[3,5,6,1,7,4,2]=>001011=>110100=>[1,1,2,3]
[3,5,6,2,1,4,7]=>001100=>001100=>[3,1,3]
[3,5,6,2,1,7,4]=>001101=>101100=>[1,2,1,3]
[3,5,6,2,4,1,7]=>001010=>010100=>[2,2,3]
[3,5,6,2,4,7,1]=>001001=>100100=>[1,3,3]
[3,5,6,2,7,1,4]=>001010=>010100=>[2,2,3]
[3,5,6,2,7,4,1]=>001011=>110100=>[1,1,2,3]
[3,5,6,4,1,2,7]=>001100=>001100=>[3,1,3]
[3,5,6,4,1,7,2]=>001101=>101100=>[1,2,1,3]
[3,5,6,4,2,1,7]=>001110=>011100=>[2,1,1,3]
[3,5,6,4,2,7,1]=>001101=>101100=>[1,2,1,3]
[3,5,6,4,7,1,2]=>001010=>010100=>[2,2,3]
[3,5,6,4,7,2,1]=>001011=>110100=>[1,1,2,3]
[3,5,6,7,1,2,4]=>000100=>001000=>[3,4]
[3,5,6,7,1,4,2]=>000101=>101000=>[1,2,4]
[3,5,6,7,2,1,4]=>000110=>011000=>[2,1,4]
[3,5,6,7,2,4,1]=>000101=>101000=>[1,2,4]
[3,5,6,7,4,1,2]=>000110=>011000=>[2,1,4]
[3,5,6,7,4,2,1]=>000111=>111000=>[1,1,1,4]
[3,5,7,1,2,4,6]=>001000=>000100=>[4,3]
[3,5,7,1,2,6,4]=>001001=>100100=>[1,3,3]
[3,5,7,1,4,2,6]=>001010=>010100=>[2,2,3]
[3,5,7,1,4,6,2]=>001001=>100100=>[1,3,3]
[3,5,7,1,6,2,4]=>001010=>010100=>[2,2,3]
[3,5,7,1,6,4,2]=>001011=>110100=>[1,1,2,3]
[3,5,7,2,1,4,6]=>001100=>001100=>[3,1,3]
[3,5,7,2,1,6,4]=>001101=>101100=>[1,2,1,3]
[3,5,7,2,4,1,6]=>001010=>010100=>[2,2,3]
[3,5,7,2,4,6,1]=>001001=>100100=>[1,3,3]
[3,5,7,2,6,1,4]=>001010=>010100=>[2,2,3]
[3,5,7,2,6,4,1]=>001011=>110100=>[1,1,2,3]
[3,5,7,4,1,2,6]=>001100=>001100=>[3,1,3]
[3,5,7,4,1,6,2]=>001101=>101100=>[1,2,1,3]
[3,5,7,4,2,1,6]=>001110=>011100=>[2,1,1,3]
[3,5,7,4,2,6,1]=>001101=>101100=>[1,2,1,3]
[3,5,7,4,6,1,2]=>001010=>010100=>[2,2,3]
[3,5,7,4,6,2,1]=>001011=>110100=>[1,1,2,3]
[3,5,7,6,1,2,4]=>001100=>001100=>[3,1,3]
[3,5,7,6,1,4,2]=>001101=>101100=>[1,2,1,3]
[3,5,7,6,2,1,4]=>001110=>011100=>[2,1,1,3]
[3,5,7,6,2,4,1]=>001101=>101100=>[1,2,1,3]
[3,5,7,6,4,1,2]=>001110=>011100=>[2,1,1,3]
[3,5,7,6,4,2,1]=>001111=>111100=>[1,1,1,1,3]
[3,6,1,2,4,5,7]=>010000=>000010=>[5,2]
[3,6,1,2,4,7,5]=>010001=>100010=>[1,4,2]
[3,6,1,2,5,4,7]=>010010=>010010=>[2,3,2]
[3,6,1,2,5,7,4]=>010001=>100010=>[1,4,2]
[3,6,1,2,7,4,5]=>010010=>010010=>[2,3,2]
[3,6,1,2,7,5,4]=>010011=>110010=>[1,1,3,2]
[3,6,1,4,2,5,7]=>010100=>001010=>[3,2,2]
[3,6,1,4,2,7,5]=>010101=>101010=>[1,2,2,2]
[3,6,1,4,5,2,7]=>010010=>010010=>[2,3,2]
[3,6,1,4,5,7,2]=>010001=>100010=>[1,4,2]
[3,6,1,4,7,2,5]=>010010=>010010=>[2,3,2]
[3,6,1,4,7,5,2]=>010011=>110010=>[1,1,3,2]
[3,6,1,5,2,4,7]=>010100=>001010=>[3,2,2]
[3,6,1,5,2,7,4]=>010101=>101010=>[1,2,2,2]
[3,6,1,5,4,2,7]=>010110=>011010=>[2,1,2,2]
[3,6,1,5,4,7,2]=>010101=>101010=>[1,2,2,2]
[3,6,1,5,7,2,4]=>010010=>010010=>[2,3,2]
[3,6,1,5,7,4,2]=>010011=>110010=>[1,1,3,2]
[3,6,1,7,2,4,5]=>010100=>001010=>[3,2,2]
[3,6,1,7,2,5,4]=>010101=>101010=>[1,2,2,2]
[3,6,1,7,4,2,5]=>010110=>011010=>[2,1,2,2]
[3,6,1,7,4,5,2]=>010101=>101010=>[1,2,2,2]
[3,6,1,7,5,2,4]=>010110=>011010=>[2,1,2,2]
[3,6,1,7,5,4,2]=>010111=>111010=>[1,1,1,2,2]
[3,6,2,1,4,5,7]=>011000=>000110=>[4,1,2]
[3,6,2,1,4,7,5]=>011001=>100110=>[1,3,1,2]
[3,6,2,1,5,4,7]=>011010=>010110=>[2,2,1,2]
[3,6,2,1,5,7,4]=>011001=>100110=>[1,3,1,2]
[3,6,2,1,7,4,5]=>011010=>010110=>[2,2,1,2]
[3,6,2,1,7,5,4]=>011011=>110110=>[1,1,2,1,2]
[3,6,2,4,1,5,7]=>010100=>001010=>[3,2,2]
[3,6,2,4,1,7,5]=>010101=>101010=>[1,2,2,2]
[3,6,2,4,5,1,7]=>010010=>010010=>[2,3,2]
[3,6,2,4,5,7,1]=>010001=>100010=>[1,4,2]
[3,6,2,4,7,1,5]=>010010=>010010=>[2,3,2]
[3,6,2,4,7,5,1]=>010011=>110010=>[1,1,3,2]
[3,6,2,5,1,4,7]=>010100=>001010=>[3,2,2]
[3,6,2,5,1,7,4]=>010101=>101010=>[1,2,2,2]
[3,6,2,5,4,1,7]=>010110=>011010=>[2,1,2,2]
[3,6,2,5,4,7,1]=>010101=>101010=>[1,2,2,2]
[3,6,2,5,7,1,4]=>010010=>010010=>[2,3,2]
[3,6,2,5,7,4,1]=>010011=>110010=>[1,1,3,2]
[3,6,2,7,1,4,5]=>010100=>001010=>[3,2,2]
[3,6,2,7,1,5,4]=>010101=>101010=>[1,2,2,2]
[3,6,2,7,4,1,5]=>010110=>011010=>[2,1,2,2]
[3,6,2,7,4,5,1]=>010101=>101010=>[1,2,2,2]
[3,6,2,7,5,1,4]=>010110=>011010=>[2,1,2,2]
[3,6,2,7,5,4,1]=>010111=>111010=>[1,1,1,2,2]
[3,6,4,1,2,5,7]=>011000=>000110=>[4,1,2]
[3,6,4,1,2,7,5]=>011001=>100110=>[1,3,1,2]
[3,6,4,1,5,2,7]=>011010=>010110=>[2,2,1,2]
[3,6,4,1,5,7,2]=>011001=>100110=>[1,3,1,2]
[3,6,4,1,7,2,5]=>011010=>010110=>[2,2,1,2]
[3,6,4,1,7,5,2]=>011011=>110110=>[1,1,2,1,2]
[3,6,4,2,1,5,7]=>011100=>001110=>[3,1,1,2]
[3,6,4,2,1,7,5]=>011101=>101110=>[1,2,1,1,2]
[3,6,4,2,5,1,7]=>011010=>010110=>[2,2,1,2]
[3,6,4,2,5,7,1]=>011001=>100110=>[1,3,1,2]
[3,6,4,2,7,1,5]=>011010=>010110=>[2,2,1,2]
[3,6,4,2,7,5,1]=>011011=>110110=>[1,1,2,1,2]
[3,6,4,5,1,2,7]=>010100=>001010=>[3,2,2]
[3,6,4,5,1,7,2]=>010101=>101010=>[1,2,2,2]
[3,6,4,5,2,1,7]=>010110=>011010=>[2,1,2,2]
[3,6,4,5,2,7,1]=>010101=>101010=>[1,2,2,2]
[3,6,4,5,7,1,2]=>010010=>010010=>[2,3,2]
[3,6,4,5,7,2,1]=>010011=>110010=>[1,1,3,2]
[3,6,4,7,1,2,5]=>010100=>001010=>[3,2,2]
[3,6,4,7,1,5,2]=>010101=>101010=>[1,2,2,2]
[3,6,4,7,2,1,5]=>010110=>011010=>[2,1,2,2]
[3,6,4,7,2,5,1]=>010101=>101010=>[1,2,2,2]
[3,6,4,7,5,1,2]=>010110=>011010=>[2,1,2,2]
[3,6,4,7,5,2,1]=>010111=>111010=>[1,1,1,2,2]
[3,6,5,1,2,4,7]=>011000=>000110=>[4,1,2]
[3,6,5,1,2,7,4]=>011001=>100110=>[1,3,1,2]
[3,6,5,1,4,2,7]=>011010=>010110=>[2,2,1,2]
[3,6,5,1,4,7,2]=>011001=>100110=>[1,3,1,2]
[3,6,5,1,7,2,4]=>011010=>010110=>[2,2,1,2]
[3,6,5,1,7,4,2]=>011011=>110110=>[1,1,2,1,2]
[3,6,5,2,1,4,7]=>011100=>001110=>[3,1,1,2]
[3,6,5,2,1,7,4]=>011101=>101110=>[1,2,1,1,2]
[3,6,5,2,4,1,7]=>011010=>010110=>[2,2,1,2]
[3,6,5,2,4,7,1]=>011001=>100110=>[1,3,1,2]
[3,6,5,2,7,1,4]=>011010=>010110=>[2,2,1,2]
[3,6,5,2,7,4,1]=>011011=>110110=>[1,1,2,1,2]
[3,6,5,4,1,2,7]=>011100=>001110=>[3,1,1,2]
[3,6,5,4,1,7,2]=>011101=>101110=>[1,2,1,1,2]
[3,6,5,4,2,1,7]=>011110=>011110=>[2,1,1,1,2]
[3,6,5,4,2,7,1]=>011101=>101110=>[1,2,1,1,2]
[3,6,5,4,7,1,2]=>011010=>010110=>[2,2,1,2]
[3,6,5,4,7,2,1]=>011011=>110110=>[1,1,2,1,2]
[3,6,5,7,1,2,4]=>010100=>001010=>[3,2,2]
[3,6,5,7,1,4,2]=>010101=>101010=>[1,2,2,2]
[3,6,5,7,2,1,4]=>010110=>011010=>[2,1,2,2]
[3,6,5,7,2,4,1]=>010101=>101010=>[1,2,2,2]
[3,6,5,7,4,1,2]=>010110=>011010=>[2,1,2,2]
[3,6,5,7,4,2,1]=>010111=>111010=>[1,1,1,2,2]
[3,6,7,1,2,4,5]=>001000=>000100=>[4,3]
[3,6,7,1,2,5,4]=>001001=>100100=>[1,3,3]
[3,6,7,1,4,2,5]=>001010=>010100=>[2,2,3]
[3,6,7,1,4,5,2]=>001001=>100100=>[1,3,3]
[3,6,7,1,5,2,4]=>001010=>010100=>[2,2,3]
[3,6,7,1,5,4,2]=>001011=>110100=>[1,1,2,3]
[3,6,7,2,1,4,5]=>001100=>001100=>[3,1,3]
[3,6,7,2,1,5,4]=>001101=>101100=>[1,2,1,3]
[3,6,7,2,4,1,5]=>001010=>010100=>[2,2,3]
[3,6,7,2,4,5,1]=>001001=>100100=>[1,3,3]
[3,6,7,2,5,1,4]=>001010=>010100=>[2,2,3]
[3,6,7,2,5,4,1]=>001011=>110100=>[1,1,2,3]
[3,6,7,4,1,2,5]=>001100=>001100=>[3,1,3]
[3,6,7,4,1,5,2]=>001101=>101100=>[1,2,1,3]
[3,6,7,4,2,1,5]=>001110=>011100=>[2,1,1,3]
[3,6,7,4,2,5,1]=>001101=>101100=>[1,2,1,3]
[3,6,7,4,5,1,2]=>001010=>010100=>[2,2,3]
[3,6,7,4,5,2,1]=>001011=>110100=>[1,1,2,3]
[3,6,7,5,1,2,4]=>001100=>001100=>[3,1,3]
[3,6,7,5,1,4,2]=>001101=>101100=>[1,2,1,3]
[3,6,7,5,2,1,4]=>001110=>011100=>[2,1,1,3]
[3,6,7,5,2,4,1]=>001101=>101100=>[1,2,1,3]
[3,6,7,5,4,1,2]=>001110=>011100=>[2,1,1,3]
[3,6,7,5,4,2,1]=>001111=>111100=>[1,1,1,1,3]
[3,7,1,2,4,5,6]=>010000=>000010=>[5,2]
[3,7,1,2,4,6,5]=>010001=>100010=>[1,4,2]
[3,7,1,2,5,4,6]=>010010=>010010=>[2,3,2]
[3,7,1,2,5,6,4]=>010001=>100010=>[1,4,2]
[3,7,1,2,6,4,5]=>010010=>010010=>[2,3,2]
[3,7,1,2,6,5,4]=>010011=>110010=>[1,1,3,2]
[3,7,1,4,2,5,6]=>010100=>001010=>[3,2,2]
[3,7,1,4,2,6,5]=>010101=>101010=>[1,2,2,2]
[3,7,1,4,5,2,6]=>010010=>010010=>[2,3,2]
[3,7,1,4,5,6,2]=>010001=>100010=>[1,4,2]
[3,7,1,4,6,2,5]=>010010=>010010=>[2,3,2]
[3,7,1,4,6,5,2]=>010011=>110010=>[1,1,3,2]
[3,7,1,5,2,4,6]=>010100=>001010=>[3,2,2]
[3,7,1,5,2,6,4]=>010101=>101010=>[1,2,2,2]
[3,7,1,5,4,2,6]=>010110=>011010=>[2,1,2,2]
[3,7,1,5,4,6,2]=>010101=>101010=>[1,2,2,2]
[3,7,1,5,6,2,4]=>010010=>010010=>[2,3,2]
[3,7,1,5,6,4,2]=>010011=>110010=>[1,1,3,2]
[3,7,1,6,2,4,5]=>010100=>001010=>[3,2,2]
[3,7,1,6,2,5,4]=>010101=>101010=>[1,2,2,2]
[3,7,1,6,4,2,5]=>010110=>011010=>[2,1,2,2]
[3,7,1,6,4,5,2]=>010101=>101010=>[1,2,2,2]
[3,7,1,6,5,2,4]=>010110=>011010=>[2,1,2,2]
[3,7,1,6,5,4,2]=>010111=>111010=>[1,1,1,2,2]
[3,7,2,1,4,5,6]=>011000=>000110=>[4,1,2]
[3,7,2,1,4,6,5]=>011001=>100110=>[1,3,1,2]
[3,7,2,1,5,4,6]=>011010=>010110=>[2,2,1,2]
[3,7,2,1,5,6,4]=>011001=>100110=>[1,3,1,2]
[3,7,2,1,6,4,5]=>011010=>010110=>[2,2,1,2]
[3,7,2,1,6,5,4]=>011011=>110110=>[1,1,2,1,2]
[3,7,2,4,1,5,6]=>010100=>001010=>[3,2,2]
[3,7,2,4,1,6,5]=>010101=>101010=>[1,2,2,2]
[3,7,2,4,5,1,6]=>010010=>010010=>[2,3,2]
[3,7,2,4,5,6,1]=>010001=>100010=>[1,4,2]
[3,7,2,4,6,1,5]=>010010=>010010=>[2,3,2]
[3,7,2,4,6,5,1]=>010011=>110010=>[1,1,3,2]
[3,7,2,5,1,4,6]=>010100=>001010=>[3,2,2]
[3,7,2,5,1,6,4]=>010101=>101010=>[1,2,2,2]
[3,7,2,5,4,1,6]=>010110=>011010=>[2,1,2,2]
[3,7,2,5,4,6,1]=>010101=>101010=>[1,2,2,2]
[3,7,2,5,6,1,4]=>010010=>010010=>[2,3,2]
[3,7,2,5,6,4,1]=>010011=>110010=>[1,1,3,2]
[3,7,2,6,1,4,5]=>010100=>001010=>[3,2,2]
[3,7,2,6,1,5,4]=>010101=>101010=>[1,2,2,2]
[3,7,2,6,4,1,5]=>010110=>011010=>[2,1,2,2]
[3,7,2,6,4,5,1]=>010101=>101010=>[1,2,2,2]
[3,7,2,6,5,1,4]=>010110=>011010=>[2,1,2,2]
[3,7,2,6,5,4,1]=>010111=>111010=>[1,1,1,2,2]
[3,7,4,1,2,5,6]=>011000=>000110=>[4,1,2]
[3,7,4,1,2,6,5]=>011001=>100110=>[1,3,1,2]
[3,7,4,1,5,2,6]=>011010=>010110=>[2,2,1,2]
[3,7,4,1,5,6,2]=>011001=>100110=>[1,3,1,2]
[3,7,4,1,6,2,5]=>011010=>010110=>[2,2,1,2]
[3,7,4,1,6,5,2]=>011011=>110110=>[1,1,2,1,2]
[3,7,4,2,1,5,6]=>011100=>001110=>[3,1,1,2]
[3,7,4,2,1,6,5]=>011101=>101110=>[1,2,1,1,2]
[3,7,4,2,5,1,6]=>011010=>010110=>[2,2,1,2]
[3,7,4,2,5,6,1]=>011001=>100110=>[1,3,1,2]
[3,7,4,2,6,1,5]=>011010=>010110=>[2,2,1,2]
[3,7,4,2,6,5,1]=>011011=>110110=>[1,1,2,1,2]
[3,7,4,5,1,2,6]=>010100=>001010=>[3,2,2]
[3,7,4,5,1,6,2]=>010101=>101010=>[1,2,2,2]
[3,7,4,5,2,1,6]=>010110=>011010=>[2,1,2,2]
[3,7,4,5,2,6,1]=>010101=>101010=>[1,2,2,2]
[3,7,4,5,6,1,2]=>010010=>010010=>[2,3,2]
[3,7,4,5,6,2,1]=>010011=>110010=>[1,1,3,2]
[3,7,4,6,1,2,5]=>010100=>001010=>[3,2,2]
[3,7,4,6,1,5,2]=>010101=>101010=>[1,2,2,2]
[3,7,4,6,2,1,5]=>010110=>011010=>[2,1,2,2]
[3,7,4,6,2,5,1]=>010101=>101010=>[1,2,2,2]
[3,7,4,6,5,1,2]=>010110=>011010=>[2,1,2,2]
[3,7,4,6,5,2,1]=>010111=>111010=>[1,1,1,2,2]
[3,7,5,1,2,4,6]=>011000=>000110=>[4,1,2]
[3,7,5,1,2,6,4]=>011001=>100110=>[1,3,1,2]
[3,7,5,1,4,2,6]=>011010=>010110=>[2,2,1,2]
[3,7,5,1,4,6,2]=>011001=>100110=>[1,3,1,2]
[3,7,5,1,6,2,4]=>011010=>010110=>[2,2,1,2]
[3,7,5,1,6,4,2]=>011011=>110110=>[1,1,2,1,2]
[3,7,5,2,1,4,6]=>011100=>001110=>[3,1,1,2]
[3,7,5,2,1,6,4]=>011101=>101110=>[1,2,1,1,2]
[3,7,5,2,4,1,6]=>011010=>010110=>[2,2,1,2]
[3,7,5,2,4,6,1]=>011001=>100110=>[1,3,1,2]
[3,7,5,2,6,1,4]=>011010=>010110=>[2,2,1,2]
[3,7,5,2,6,4,1]=>011011=>110110=>[1,1,2,1,2]
[3,7,5,4,1,2,6]=>011100=>001110=>[3,1,1,2]
[3,7,5,4,1,6,2]=>011101=>101110=>[1,2,1,1,2]
[3,7,5,4,2,1,6]=>011110=>011110=>[2,1,1,1,2]
[3,7,5,4,2,6,1]=>011101=>101110=>[1,2,1,1,2]
[3,7,5,4,6,1,2]=>011010=>010110=>[2,2,1,2]
[3,7,5,4,6,2,1]=>011011=>110110=>[1,1,2,1,2]
[3,7,5,6,1,2,4]=>010100=>001010=>[3,2,2]
[3,7,5,6,1,4,2]=>010101=>101010=>[1,2,2,2]
[3,7,5,6,2,1,4]=>010110=>011010=>[2,1,2,2]
[3,7,5,6,2,4,1]=>010101=>101010=>[1,2,2,2]
[3,7,5,6,4,1,2]=>010110=>011010=>[2,1,2,2]
[3,7,5,6,4,2,1]=>010111=>111010=>[1,1,1,2,2]
[3,7,6,1,2,4,5]=>011000=>000110=>[4,1,2]
[3,7,6,1,2,5,4]=>011001=>100110=>[1,3,1,2]
[3,7,6,1,4,2,5]=>011010=>010110=>[2,2,1,2]
[3,7,6,1,4,5,2]=>011001=>100110=>[1,3,1,2]
[3,7,6,1,5,2,4]=>011010=>010110=>[2,2,1,2]
[3,7,6,1,5,4,2]=>011011=>110110=>[1,1,2,1,2]
[3,7,6,2,1,4,5]=>011100=>001110=>[3,1,1,2]
[3,7,6,2,1,5,4]=>011101=>101110=>[1,2,1,1,2]
[3,7,6,2,4,1,5]=>011010=>010110=>[2,2,1,2]
[3,7,6,2,4,5,1]=>011001=>100110=>[1,3,1,2]
[3,7,6,2,5,1,4]=>011010=>010110=>[2,2,1,2]
[3,7,6,2,5,4,1]=>011011=>110110=>[1,1,2,1,2]
[3,7,6,4,1,2,5]=>011100=>001110=>[3,1,1,2]
[3,7,6,4,1,5,2]=>011101=>101110=>[1,2,1,1,2]
[3,7,6,4,2,1,5]=>011110=>011110=>[2,1,1,1,2]
[3,7,6,4,2,5,1]=>011101=>101110=>[1,2,1,1,2]
[3,7,6,4,5,1,2]=>011010=>010110=>[2,2,1,2]
[3,7,6,4,5,2,1]=>011011=>110110=>[1,1,2,1,2]
[3,7,6,5,1,2,4]=>011100=>001110=>[3,1,1,2]
[3,7,6,5,1,4,2]=>011101=>101110=>[1,2,1,1,2]
[3,7,6,5,2,1,4]=>011110=>011110=>[2,1,1,1,2]
[3,7,6,5,2,4,1]=>011101=>101110=>[1,2,1,1,2]
[3,7,6,5,4,1,2]=>011110=>011110=>[2,1,1,1,2]
[3,7,6,5,4,2,1]=>011111=>111110=>[1,1,1,1,1,2]
[4,1,2,3,5,6,7]=>100000=>000001=>[6,1]
[4,1,2,3,5,7,6]=>100001=>100001=>[1,5,1]
[4,1,2,3,6,5,7]=>100010=>010001=>[2,4,1]
[4,1,2,3,6,7,5]=>100001=>100001=>[1,5,1]
[4,1,2,3,7,5,6]=>100010=>010001=>[2,4,1]
[4,1,2,3,7,6,5]=>100011=>110001=>[1,1,4,1]
[4,1,2,5,3,6,7]=>100100=>001001=>[3,3,1]
[4,1,2,5,3,7,6]=>100101=>101001=>[1,2,3,1]
[4,1,2,5,6,3,7]=>100010=>010001=>[2,4,1]
[4,1,2,5,6,7,3]=>100001=>100001=>[1,5,1]
[4,1,2,5,7,3,6]=>100010=>010001=>[2,4,1]
[4,1,2,5,7,6,3]=>100011=>110001=>[1,1,4,1]
[4,1,2,6,3,5,7]=>100100=>001001=>[3,3,1]
[4,1,2,6,3,7,5]=>100101=>101001=>[1,2,3,1]
[4,1,2,6,5,3,7]=>100110=>011001=>[2,1,3,1]
[4,1,2,6,5,7,3]=>100101=>101001=>[1,2,3,1]
[4,1,2,6,7,3,5]=>100010=>010001=>[2,4,1]
[4,1,2,6,7,5,3]=>100011=>110001=>[1,1,4,1]
[4,1,2,7,3,5,6]=>100100=>001001=>[3,3,1]
[4,1,2,7,3,6,5]=>100101=>101001=>[1,2,3,1]
[4,1,2,7,5,3,6]=>100110=>011001=>[2,1,3,1]
[4,1,2,7,5,6,3]=>100101=>101001=>[1,2,3,1]
[4,1,2,7,6,3,5]=>100110=>011001=>[2,1,3,1]
[4,1,2,7,6,5,3]=>100111=>111001=>[1,1,1,3,1]
[4,1,3,2,5,6,7]=>101000=>000101=>[4,2,1]
[4,1,3,2,5,7,6]=>101001=>100101=>[1,3,2,1]
[4,1,3,2,6,5,7]=>101010=>010101=>[2,2,2,1]
[4,1,3,2,6,7,5]=>101001=>100101=>[1,3,2,1]
[4,1,3,2,7,5,6]=>101010=>010101=>[2,2,2,1]
[4,1,3,2,7,6,5]=>101011=>110101=>[1,1,2,2,1]
[4,1,3,5,2,6,7]=>100100=>001001=>[3,3,1]
[4,1,3,5,2,7,6]=>100101=>101001=>[1,2,3,1]
[4,1,3,5,6,2,7]=>100010=>010001=>[2,4,1]
[4,1,3,5,6,7,2]=>100001=>100001=>[1,5,1]
[4,1,3,5,7,2,6]=>100010=>010001=>[2,4,1]
[4,1,3,5,7,6,2]=>100011=>110001=>[1,1,4,1]
[4,1,3,6,2,5,7]=>100100=>001001=>[3,3,1]
[4,1,3,6,2,7,5]=>100101=>101001=>[1,2,3,1]
[4,1,3,6,5,2,7]=>100110=>011001=>[2,1,3,1]
[4,1,3,6,5,7,2]=>100101=>101001=>[1,2,3,1]
[4,1,3,6,7,2,5]=>100010=>010001=>[2,4,1]
[4,1,3,6,7,5,2]=>100011=>110001=>[1,1,4,1]
[4,1,3,7,2,5,6]=>100100=>001001=>[3,3,1]
[4,1,3,7,2,6,5]=>100101=>101001=>[1,2,3,1]
[4,1,3,7,5,2,6]=>100110=>011001=>[2,1,3,1]
[4,1,3,7,5,6,2]=>100101=>101001=>[1,2,3,1]
[4,1,3,7,6,2,5]=>100110=>011001=>[2,1,3,1]
[4,1,3,7,6,5,2]=>100111=>111001=>[1,1,1,3,1]
[4,1,5,2,3,6,7]=>101000=>000101=>[4,2,1]
[4,1,5,2,3,7,6]=>101001=>100101=>[1,3,2,1]
[4,1,5,2,6,3,7]=>101010=>010101=>[2,2,2,1]
[4,1,5,2,6,7,3]=>101001=>100101=>[1,3,2,1]
[4,1,5,2,7,3,6]=>101010=>010101=>[2,2,2,1]
[4,1,5,2,7,6,3]=>101011=>110101=>[1,1,2,2,1]
[4,1,5,3,2,6,7]=>101100=>001101=>[3,1,2,1]
[4,1,5,3,2,7,6]=>101101=>101101=>[1,2,1,2,1]
[4,1,5,3,6,2,7]=>101010=>010101=>[2,2,2,1]
[4,1,5,3,6,7,2]=>101001=>100101=>[1,3,2,1]
[4,1,5,3,7,2,6]=>101010=>010101=>[2,2,2,1]
[4,1,5,3,7,6,2]=>101011=>110101=>[1,1,2,2,1]
[4,1,5,6,2,3,7]=>100100=>001001=>[3,3,1]
[4,1,5,6,2,7,3]=>100101=>101001=>[1,2,3,1]
[4,1,5,6,3,2,7]=>100110=>011001=>[2,1,3,1]
[4,1,5,6,3,7,2]=>100101=>101001=>[1,2,3,1]
[4,1,5,6,7,2,3]=>100010=>010001=>[2,4,1]
[4,1,5,6,7,3,2]=>100011=>110001=>[1,1,4,1]
[4,1,5,7,2,3,6]=>100100=>001001=>[3,3,1]
[4,1,5,7,2,6,3]=>100101=>101001=>[1,2,3,1]
[4,1,5,7,3,2,6]=>100110=>011001=>[2,1,3,1]
[4,1,5,7,3,6,2]=>100101=>101001=>[1,2,3,1]
[4,1,5,7,6,2,3]=>100110=>011001=>[2,1,3,1]
[4,1,5,7,6,3,2]=>100111=>111001=>[1,1,1,3,1]
[4,1,6,2,3,5,7]=>101000=>000101=>[4,2,1]
[4,1,6,2,3,7,5]=>101001=>100101=>[1,3,2,1]
[4,1,6,2,5,3,7]=>101010=>010101=>[2,2,2,1]
[4,1,6,2,5,7,3]=>101001=>100101=>[1,3,2,1]
[4,1,6,2,7,3,5]=>101010=>010101=>[2,2,2,1]
[4,1,6,2,7,5,3]=>101011=>110101=>[1,1,2,2,1]
[4,1,6,3,2,5,7]=>101100=>001101=>[3,1,2,1]
[4,1,6,3,2,7,5]=>101101=>101101=>[1,2,1,2,1]
[4,1,6,3,5,2,7]=>101010=>010101=>[2,2,2,1]
[4,1,6,3,5,7,2]=>101001=>100101=>[1,3,2,1]
[4,1,6,3,7,2,5]=>101010=>010101=>[2,2,2,1]
[4,1,6,3,7,5,2]=>101011=>110101=>[1,1,2,2,1]
[4,1,6,5,2,3,7]=>101100=>001101=>[3,1,2,1]
[4,1,6,5,2,7,3]=>101101=>101101=>[1,2,1,2,1]
[4,1,6,5,3,2,7]=>101110=>011101=>[2,1,1,2,1]
[4,1,6,5,3,7,2]=>101101=>101101=>[1,2,1,2,1]
[4,1,6,5,7,2,3]=>101010=>010101=>[2,2,2,1]
[4,1,6,5,7,3,2]=>101011=>110101=>[1,1,2,2,1]
[4,1,6,7,2,3,5]=>100100=>001001=>[3,3,1]
[4,1,6,7,2,5,3]=>100101=>101001=>[1,2,3,1]
[4,1,6,7,3,2,5]=>100110=>011001=>[2,1,3,1]
[4,1,6,7,3,5,2]=>100101=>101001=>[1,2,3,1]
[4,1,6,7,5,2,3]=>100110=>011001=>[2,1,3,1]
[4,1,6,7,5,3,2]=>100111=>111001=>[1,1,1,3,1]
[4,1,7,2,3,5,6]=>101000=>000101=>[4,2,1]
[4,1,7,2,3,6,5]=>101001=>100101=>[1,3,2,1]
[4,1,7,2,5,3,6]=>101010=>010101=>[2,2,2,1]
[4,1,7,2,5,6,3]=>101001=>100101=>[1,3,2,1]
[4,1,7,2,6,3,5]=>101010=>010101=>[2,2,2,1]
[4,1,7,2,6,5,3]=>101011=>110101=>[1,1,2,2,1]
[4,1,7,3,2,5,6]=>101100=>001101=>[3,1,2,1]
[4,1,7,3,2,6,5]=>101101=>101101=>[1,2,1,2,1]
[4,1,7,3,5,2,6]=>101010=>010101=>[2,2,2,1]
[4,1,7,3,5,6,2]=>101001=>100101=>[1,3,2,1]
[4,1,7,3,6,2,5]=>101010=>010101=>[2,2,2,1]
[4,1,7,3,6,5,2]=>101011=>110101=>[1,1,2,2,1]
[4,1,7,5,2,3,6]=>101100=>001101=>[3,1,2,1]
[4,1,7,5,2,6,3]=>101101=>101101=>[1,2,1,2,1]
[4,1,7,5,3,2,6]=>101110=>011101=>[2,1,1,2,1]
[4,1,7,5,3,6,2]=>101101=>101101=>[1,2,1,2,1]
[4,1,7,5,6,2,3]=>101010=>010101=>[2,2,2,1]
[4,1,7,5,6,3,2]=>101011=>110101=>[1,1,2,2,1]
[4,1,7,6,2,3,5]=>101100=>001101=>[3,1,2,1]
[4,1,7,6,2,5,3]=>101101=>101101=>[1,2,1,2,1]
[4,1,7,6,3,2,5]=>101110=>011101=>[2,1,1,2,1]
[4,1,7,6,3,5,2]=>101101=>101101=>[1,2,1,2,1]
[4,1,7,6,5,2,3]=>101110=>011101=>[2,1,1,2,1]
[4,1,7,6,5,3,2]=>101111=>111101=>[1,1,1,1,2,1]
[4,2,1,3,5,6,7]=>110000=>000011=>[5,1,1]
[4,2,1,3,5,7,6]=>110001=>100011=>[1,4,1,1]
[4,2,1,3,6,5,7]=>110010=>010011=>[2,3,1,1]
[4,2,1,3,6,7,5]=>110001=>100011=>[1,4,1,1]
[4,2,1,3,7,5,6]=>110010=>010011=>[2,3,1,1]
[4,2,1,3,7,6,5]=>110011=>110011=>[1,1,3,1,1]
[4,2,1,5,3,6,7]=>110100=>001011=>[3,2,1,1]
[4,2,1,5,3,7,6]=>110101=>101011=>[1,2,2,1,1]
[4,2,1,5,6,3,7]=>110010=>010011=>[2,3,1,1]
[4,2,1,5,6,7,3]=>110001=>100011=>[1,4,1,1]
[4,2,1,5,7,3,6]=>110010=>010011=>[2,3,1,1]
[4,2,1,5,7,6,3]=>110011=>110011=>[1,1,3,1,1]
[4,2,1,6,3,5,7]=>110100=>001011=>[3,2,1,1]
[4,2,1,6,3,7,5]=>110101=>101011=>[1,2,2,1,1]
[4,2,1,6,5,3,7]=>110110=>011011=>[2,1,2,1,1]
[4,2,1,6,5,7,3]=>110101=>101011=>[1,2,2,1,1]
[4,2,1,6,7,3,5]=>110010=>010011=>[2,3,1,1]
[4,2,1,6,7,5,3]=>110011=>110011=>[1,1,3,1,1]
[4,2,1,7,3,5,6]=>110100=>001011=>[3,2,1,1]
[4,2,1,7,3,6,5]=>110101=>101011=>[1,2,2,1,1]
[4,2,1,7,5,3,6]=>110110=>011011=>[2,1,2,1,1]
[4,2,1,7,5,6,3]=>110101=>101011=>[1,2,2,1,1]
[4,2,1,7,6,3,5]=>110110=>011011=>[2,1,2,1,1]
[4,2,1,7,6,5,3]=>110111=>111011=>[1,1,1,2,1,1]
[4,2,3,1,5,6,7]=>101000=>000101=>[4,2,1]
[4,2,3,1,5,7,6]=>101001=>100101=>[1,3,2,1]
[4,2,3,1,6,5,7]=>101010=>010101=>[2,2,2,1]
[4,2,3,1,6,7,5]=>101001=>100101=>[1,3,2,1]
[4,2,3,1,7,5,6]=>101010=>010101=>[2,2,2,1]
[4,2,3,1,7,6,5]=>101011=>110101=>[1,1,2,2,1]
[4,2,3,5,1,6,7]=>100100=>001001=>[3,3,1]
[4,2,3,5,1,7,6]=>100101=>101001=>[1,2,3,1]
[4,2,3,5,6,1,7]=>100010=>010001=>[2,4,1]
[4,2,3,5,6,7,1]=>100001=>100001=>[1,5,1]
[4,2,3,5,7,1,6]=>100010=>010001=>[2,4,1]
[4,2,3,5,7,6,1]=>100011=>110001=>[1,1,4,1]
[4,2,3,6,1,5,7]=>100100=>001001=>[3,3,1]
[4,2,3,6,1,7,5]=>100101=>101001=>[1,2,3,1]
[4,2,3,6,5,1,7]=>100110=>011001=>[2,1,3,1]
[4,2,3,6,5,7,1]=>100101=>101001=>[1,2,3,1]
[4,2,3,6,7,1,5]=>100010=>010001=>[2,4,1]
[4,2,3,6,7,5,1]=>100011=>110001=>[1,1,4,1]
[4,2,3,7,1,5,6]=>100100=>001001=>[3,3,1]
[4,2,3,7,1,6,5]=>100101=>101001=>[1,2,3,1]
[4,2,3,7,5,1,6]=>100110=>011001=>[2,1,3,1]
[4,2,3,7,5,6,1]=>100101=>101001=>[1,2,3,1]
[4,2,3,7,6,1,5]=>100110=>011001=>[2,1,3,1]
[4,2,3,7,6,5,1]=>100111=>111001=>[1,1,1,3,1]
[4,2,5,1,3,6,7]=>101000=>000101=>[4,2,1]
[4,2,5,1,3,7,6]=>101001=>100101=>[1,3,2,1]
[4,2,5,1,6,3,7]=>101010=>010101=>[2,2,2,1]
[4,2,5,1,6,7,3]=>101001=>100101=>[1,3,2,1]
[4,2,5,1,7,3,6]=>101010=>010101=>[2,2,2,1]
[4,2,5,1,7,6,3]=>101011=>110101=>[1,1,2,2,1]
[4,2,5,3,1,6,7]=>101100=>001101=>[3,1,2,1]
[4,2,5,3,1,7,6]=>101101=>101101=>[1,2,1,2,1]
[4,2,5,3,6,1,7]=>101010=>010101=>[2,2,2,1]
[4,2,5,3,6,7,1]=>101001=>100101=>[1,3,2,1]
[4,2,5,3,7,1,6]=>101010=>010101=>[2,2,2,1]
[4,2,5,3,7,6,1]=>101011=>110101=>[1,1,2,2,1]
[4,2,5,6,1,3,7]=>100100=>001001=>[3,3,1]
[4,2,5,6,1,7,3]=>100101=>101001=>[1,2,3,1]
[4,2,5,6,3,1,7]=>100110=>011001=>[2,1,3,1]
[4,2,5,6,3,7,1]=>100101=>101001=>[1,2,3,1]
[4,2,5,6,7,1,3]=>100010=>010001=>[2,4,1]
[4,2,5,6,7,3,1]=>100011=>110001=>[1,1,4,1]
[4,2,5,7,1,3,6]=>100100=>001001=>[3,3,1]
[4,2,5,7,1,6,3]=>100101=>101001=>[1,2,3,1]
[4,2,5,7,3,1,6]=>100110=>011001=>[2,1,3,1]
[4,2,5,7,3,6,1]=>100101=>101001=>[1,2,3,1]
[4,2,5,7,6,1,3]=>100110=>011001=>[2,1,3,1]
[4,2,5,7,6,3,1]=>100111=>111001=>[1,1,1,3,1]
[4,2,6,1,3,5,7]=>101000=>000101=>[4,2,1]
[4,2,6,1,3,7,5]=>101001=>100101=>[1,3,2,1]
[4,2,6,1,5,3,7]=>101010=>010101=>[2,2,2,1]
[4,2,6,1,5,7,3]=>101001=>100101=>[1,3,2,1]
[4,2,6,1,7,3,5]=>101010=>010101=>[2,2,2,1]
[4,2,6,1,7,5,3]=>101011=>110101=>[1,1,2,2,1]
[4,2,6,3,1,5,7]=>101100=>001101=>[3,1,2,1]
[4,2,6,3,1,7,5]=>101101=>101101=>[1,2,1,2,1]
[4,2,6,3,5,1,7]=>101010=>010101=>[2,2,2,1]
[4,2,6,3,5,7,1]=>101001=>100101=>[1,3,2,1]
[4,2,6,3,7,1,5]=>101010=>010101=>[2,2,2,1]
[4,2,6,3,7,5,1]=>101011=>110101=>[1,1,2,2,1]
[4,2,6,5,1,3,7]=>101100=>001101=>[3,1,2,1]
[4,2,6,5,1,7,3]=>101101=>101101=>[1,2,1,2,1]
[4,2,6,5,3,1,7]=>101110=>011101=>[2,1,1,2,1]
[4,2,6,5,3,7,1]=>101101=>101101=>[1,2,1,2,1]
[4,2,6,5,7,1,3]=>101010=>010101=>[2,2,2,1]
[4,2,6,5,7,3,1]=>101011=>110101=>[1,1,2,2,1]
[4,2,6,7,1,3,5]=>100100=>001001=>[3,3,1]
[4,2,6,7,1,5,3]=>100101=>101001=>[1,2,3,1]
[4,2,6,7,3,1,5]=>100110=>011001=>[2,1,3,1]
[4,2,6,7,3,5,1]=>100101=>101001=>[1,2,3,1]
[4,2,6,7,5,1,3]=>100110=>011001=>[2,1,3,1]
[4,2,6,7,5,3,1]=>100111=>111001=>[1,1,1,3,1]
[4,2,7,1,3,5,6]=>101000=>000101=>[4,2,1]
[4,2,7,1,3,6,5]=>101001=>100101=>[1,3,2,1]
[4,2,7,1,5,3,6]=>101010=>010101=>[2,2,2,1]
[4,2,7,1,5,6,3]=>101001=>100101=>[1,3,2,1]
[4,2,7,1,6,3,5]=>101010=>010101=>[2,2,2,1]
[4,2,7,1,6,5,3]=>101011=>110101=>[1,1,2,2,1]
[4,2,7,3,1,5,6]=>101100=>001101=>[3,1,2,1]
[4,2,7,3,1,6,5]=>101101=>101101=>[1,2,1,2,1]
[4,2,7,3,5,1,6]=>101010=>010101=>[2,2,2,1]
[4,2,7,3,5,6,1]=>101001=>100101=>[1,3,2,1]
[4,2,7,3,6,1,5]=>101010=>010101=>[2,2,2,1]
[4,2,7,3,6,5,1]=>101011=>110101=>[1,1,2,2,1]
[4,2,7,5,1,3,6]=>101100=>001101=>[3,1,2,1]
[4,2,7,5,1,6,3]=>101101=>101101=>[1,2,1,2,1]
[4,2,7,5,3,1,6]=>101110=>011101=>[2,1,1,2,1]
[4,2,7,5,3,6,1]=>101101=>101101=>[1,2,1,2,1]
[4,2,7,5,6,1,3]=>101010=>010101=>[2,2,2,1]
[4,2,7,5,6,3,1]=>101011=>110101=>[1,1,2,2,1]
[4,2,7,6,1,3,5]=>101100=>001101=>[3,1,2,1]
[4,2,7,6,1,5,3]=>101101=>101101=>[1,2,1,2,1]
[4,2,7,6,3,1,5]=>101110=>011101=>[2,1,1,2,1]
[4,2,7,6,3,5,1]=>101101=>101101=>[1,2,1,2,1]
[4,2,7,6,5,1,3]=>101110=>011101=>[2,1,1,2,1]
[4,2,7,6,5,3,1]=>101111=>111101=>[1,1,1,1,2,1]
[4,3,1,2,5,6,7]=>110000=>000011=>[5,1,1]
[4,3,1,2,5,7,6]=>110001=>100011=>[1,4,1,1]
[4,3,1,2,6,5,7]=>110010=>010011=>[2,3,1,1]
[4,3,1,2,6,7,5]=>110001=>100011=>[1,4,1,1]
[4,3,1,2,7,5,6]=>110010=>010011=>[2,3,1,1]
[4,3,1,2,7,6,5]=>110011=>110011=>[1,1,3,1,1]
[4,3,1,5,2,6,7]=>110100=>001011=>[3,2,1,1]
[4,3,1,5,2,7,6]=>110101=>101011=>[1,2,2,1,1]
[4,3,1,5,6,2,7]=>110010=>010011=>[2,3,1,1]
[4,3,1,5,6,7,2]=>110001=>100011=>[1,4,1,1]
[4,3,1,5,7,2,6]=>110010=>010011=>[2,3,1,1]
[4,3,1,5,7,6,2]=>110011=>110011=>[1,1,3,1,1]
[4,3,1,6,2,5,7]=>110100=>001011=>[3,2,1,1]
[4,3,1,6,2,7,5]=>110101=>101011=>[1,2,2,1,1]
[4,3,1,6,5,2,7]=>110110=>011011=>[2,1,2,1,1]
[4,3,1,6,5,7,2]=>110101=>101011=>[1,2,2,1,1]
[4,3,1,6,7,2,5]=>110010=>010011=>[2,3,1,1]
[4,3,1,6,7,5,2]=>110011=>110011=>[1,1,3,1,1]
[4,3,1,7,2,5,6]=>110100=>001011=>[3,2,1,1]
[4,3,1,7,2,6,5]=>110101=>101011=>[1,2,2,1,1]
[4,3,1,7,5,2,6]=>110110=>011011=>[2,1,2,1,1]
[4,3,1,7,5,6,2]=>110101=>101011=>[1,2,2,1,1]
[4,3,1,7,6,2,5]=>110110=>011011=>[2,1,2,1,1]
[4,3,1,7,6,5,2]=>110111=>111011=>[1,1,1,2,1,1]
[4,3,2,1,5,6,7]=>111000=>000111=>[4,1,1,1]
[4,3,2,1,5,7,6]=>111001=>100111=>[1,3,1,1,1]
[4,3,2,1,6,5,7]=>111010=>010111=>[2,2,1,1,1]
[4,3,2,1,6,7,5]=>111001=>100111=>[1,3,1,1,1]
[4,3,2,1,7,5,6]=>111010=>010111=>[2,2,1,1,1]
[4,3,2,1,7,6,5]=>111011=>110111=>[1,1,2,1,1,1]
[4,3,2,5,1,6,7]=>110100=>001011=>[3,2,1,1]
[4,3,2,5,1,7,6]=>110101=>101011=>[1,2,2,1,1]
[4,3,2,5,6,1,7]=>110010=>010011=>[2,3,1,1]
[4,3,2,5,6,7,1]=>110001=>100011=>[1,4,1,1]
[4,3,2,5,7,1,6]=>110010=>010011=>[2,3,1,1]
[4,3,2,5,7,6,1]=>110011=>110011=>[1,1,3,1,1]
[4,3,2,6,1,5,7]=>110100=>001011=>[3,2,1,1]
[4,3,2,6,1,7,5]=>110101=>101011=>[1,2,2,1,1]
[4,3,2,6,5,1,7]=>110110=>011011=>[2,1,2,1,1]
[4,3,2,6,5,7,1]=>110101=>101011=>[1,2,2,1,1]
[4,3,2,6,7,1,5]=>110010=>010011=>[2,3,1,1]
[4,3,2,6,7,5,1]=>110011=>110011=>[1,1,3,1,1]
[4,3,2,7,1,5,6]=>110100=>001011=>[3,2,1,1]
[4,3,2,7,1,6,5]=>110101=>101011=>[1,2,2,1,1]
[4,3,2,7,5,1,6]=>110110=>011011=>[2,1,2,1,1]
[4,3,2,7,5,6,1]=>110101=>101011=>[1,2,2,1,1]
[4,3,2,7,6,1,5]=>110110=>011011=>[2,1,2,1,1]
[4,3,2,7,6,5,1]=>110111=>111011=>[1,1,1,2,1,1]
[4,3,5,1,2,6,7]=>101000=>000101=>[4,2,1]
[4,3,5,1,2,7,6]=>101001=>100101=>[1,3,2,1]
[4,3,5,1,6,2,7]=>101010=>010101=>[2,2,2,1]
[4,3,5,1,6,7,2]=>101001=>100101=>[1,3,2,1]
[4,3,5,1,7,2,6]=>101010=>010101=>[2,2,2,1]
[4,3,5,1,7,6,2]=>101011=>110101=>[1,1,2,2,1]
[4,3,5,2,1,6,7]=>101100=>001101=>[3,1,2,1]
[4,3,5,2,1,7,6]=>101101=>101101=>[1,2,1,2,1]
[4,3,5,2,6,1,7]=>101010=>010101=>[2,2,2,1]
[4,3,5,2,6,7,1]=>101001=>100101=>[1,3,2,1]
[4,3,5,2,7,1,6]=>101010=>010101=>[2,2,2,1]
[4,3,5,2,7,6,1]=>101011=>110101=>[1,1,2,2,1]
[4,3,5,6,1,2,7]=>100100=>001001=>[3,3,1]
[4,3,5,6,1,7,2]=>100101=>101001=>[1,2,3,1]
[4,3,5,6,2,1,7]=>100110=>011001=>[2,1,3,1]
[4,3,5,6,2,7,1]=>100101=>101001=>[1,2,3,1]
[4,3,5,6,7,1,2]=>100010=>010001=>[2,4,1]
[4,3,5,6,7,2,1]=>100011=>110001=>[1,1,4,1]
[4,3,5,7,1,2,6]=>100100=>001001=>[3,3,1]
[4,3,5,7,1,6,2]=>100101=>101001=>[1,2,3,1]
[4,3,5,7,2,1,6]=>100110=>011001=>[2,1,3,1]
[4,3,5,7,2,6,1]=>100101=>101001=>[1,2,3,1]
[4,3,5,7,6,1,2]=>100110=>011001=>[2,1,3,1]
[4,3,5,7,6,2,1]=>100111=>111001=>[1,1,1,3,1]
[4,3,6,1,2,5,7]=>101000=>000101=>[4,2,1]
[4,3,6,1,2,7,5]=>101001=>100101=>[1,3,2,1]
[4,3,6,1,5,2,7]=>101010=>010101=>[2,2,2,1]
[4,3,6,1,5,7,2]=>101001=>100101=>[1,3,2,1]
[4,3,6,1,7,2,5]=>101010=>010101=>[2,2,2,1]
[4,3,6,1,7,5,2]=>101011=>110101=>[1,1,2,2,1]
[4,3,6,2,1,5,7]=>101100=>001101=>[3,1,2,1]
[4,3,6,2,1,7,5]=>101101=>101101=>[1,2,1,2,1]
[4,3,6,2,5,1,7]=>101010=>010101=>[2,2,2,1]
[4,3,6,2,5,7,1]=>101001=>100101=>[1,3,2,1]
[4,3,6,2,7,1,5]=>101010=>010101=>[2,2,2,1]
[4,3,6,2,7,5,1]=>101011=>110101=>[1,1,2,2,1]
[4,3,6,5,1,2,7]=>101100=>001101=>[3,1,2,1]
[4,3,6,5,1,7,2]=>101101=>101101=>[1,2,1,2,1]
[4,3,6,5,2,1,7]=>101110=>011101=>[2,1,1,2,1]
[4,3,6,5,2,7,1]=>101101=>101101=>[1,2,1,2,1]
[4,3,6,5,7,1,2]=>101010=>010101=>[2,2,2,1]
[4,3,6,5,7,2,1]=>101011=>110101=>[1,1,2,2,1]
[4,3,6,7,1,2,5]=>100100=>001001=>[3,3,1]
[4,3,6,7,1,5,2]=>100101=>101001=>[1,2,3,1]
[4,3,6,7,2,1,5]=>100110=>011001=>[2,1,3,1]
[4,3,6,7,2,5,1]=>100101=>101001=>[1,2,3,1]
[4,3,6,7,5,1,2]=>100110=>011001=>[2,1,3,1]
[4,3,6,7,5,2,1]=>100111=>111001=>[1,1,1,3,1]
[4,3,7,1,2,5,6]=>101000=>000101=>[4,2,1]
[4,3,7,1,2,6,5]=>101001=>100101=>[1,3,2,1]
[4,3,7,1,5,2,6]=>101010=>010101=>[2,2,2,1]
[4,3,7,1,5,6,2]=>101001=>100101=>[1,3,2,1]
[4,3,7,1,6,2,5]=>101010=>010101=>[2,2,2,1]
[4,3,7,1,6,5,2]=>101011=>110101=>[1,1,2,2,1]
[4,3,7,2,1,5,6]=>101100=>001101=>[3,1,2,1]
[4,3,7,2,1,6,5]=>101101=>101101=>[1,2,1,2,1]
[4,3,7,2,5,1,6]=>101010=>010101=>[2,2,2,1]
[4,3,7,2,5,6,1]=>101001=>100101=>[1,3,2,1]
[4,3,7,2,6,1,5]=>101010=>010101=>[2,2,2,1]
[4,3,7,2,6,5,1]=>101011=>110101=>[1,1,2,2,1]
[4,3,7,5,1,2,6]=>101100=>001101=>[3,1,2,1]
[4,3,7,5,1,6,2]=>101101=>101101=>[1,2,1,2,1]
[4,3,7,5,2,1,6]=>101110=>011101=>[2,1,1,2,1]
[4,3,7,5,2,6,1]=>101101=>101101=>[1,2,1,2,1]
[4,3,7,5,6,1,2]=>101010=>010101=>[2,2,2,1]
[4,3,7,5,6,2,1]=>101011=>110101=>[1,1,2,2,1]
[4,3,7,6,1,2,5]=>101100=>001101=>[3,1,2,1]
[4,3,7,6,1,5,2]=>101101=>101101=>[1,2,1,2,1]
[4,3,7,6,2,1,5]=>101110=>011101=>[2,1,1,2,1]
[4,3,7,6,2,5,1]=>101101=>101101=>[1,2,1,2,1]
[4,3,7,6,5,1,2]=>101110=>011101=>[2,1,1,2,1]
[4,3,7,6,5,2,1]=>101111=>111101=>[1,1,1,1,2,1]
[4,5,1,2,3,6,7]=>010000=>000010=>[5,2]
[4,5,1,2,3,7,6]=>010001=>100010=>[1,4,2]
[4,5,1,2,6,3,7]=>010010=>010010=>[2,3,2]
[4,5,1,2,6,7,3]=>010001=>100010=>[1,4,2]
[4,5,1,2,7,3,6]=>010010=>010010=>[2,3,2]
[4,5,1,2,7,6,3]=>010011=>110010=>[1,1,3,2]
[4,5,1,3,2,6,7]=>010100=>001010=>[3,2,2]
[4,5,1,3,2,7,6]=>010101=>101010=>[1,2,2,2]
[4,5,1,3,6,2,7]=>010010=>010010=>[2,3,2]
[4,5,1,3,6,7,2]=>010001=>100010=>[1,4,2]
[4,5,1,3,7,2,6]=>010010=>010010=>[2,3,2]
[4,5,1,3,7,6,2]=>010011=>110010=>[1,1,3,2]
[4,5,1,6,2,3,7]=>010100=>001010=>[3,2,2]
[4,5,1,6,2,7,3]=>010101=>101010=>[1,2,2,2]
[4,5,1,6,3,2,7]=>010110=>011010=>[2,1,2,2]
[4,5,1,6,3,7,2]=>010101=>101010=>[1,2,2,2]
[4,5,1,6,7,2,3]=>010010=>010010=>[2,3,2]
[4,5,1,6,7,3,2]=>010011=>110010=>[1,1,3,2]
[4,5,1,7,2,3,6]=>010100=>001010=>[3,2,2]
[4,5,1,7,2,6,3]=>010101=>101010=>[1,2,2,2]
[4,5,1,7,3,2,6]=>010110=>011010=>[2,1,2,2]
[4,5,1,7,3,6,2]=>010101=>101010=>[1,2,2,2]
[4,5,1,7,6,2,3]=>010110=>011010=>[2,1,2,2]
[4,5,1,7,6,3,2]=>010111=>111010=>[1,1,1,2,2]
[4,5,2,1,3,6,7]=>011000=>000110=>[4,1,2]
[4,5,2,1,3,7,6]=>011001=>100110=>[1,3,1,2]
[4,5,2,1,6,3,7]=>011010=>010110=>[2,2,1,2]
[4,5,2,1,6,7,3]=>011001=>100110=>[1,3,1,2]
[4,5,2,1,7,3,6]=>011010=>010110=>[2,2,1,2]
[4,5,2,1,7,6,3]=>011011=>110110=>[1,1,2,1,2]
[4,5,2,3,1,6,7]=>010100=>001010=>[3,2,2]
[4,5,2,3,1,7,6]=>010101=>101010=>[1,2,2,2]
[4,5,2,3,6,1,7]=>010010=>010010=>[2,3,2]
[4,5,2,3,6,7,1]=>010001=>100010=>[1,4,2]
[4,5,2,3,7,1,6]=>010010=>010010=>[2,3,2]
[4,5,2,3,7,6,1]=>010011=>110010=>[1,1,3,2]
[4,5,2,6,1,3,7]=>010100=>001010=>[3,2,2]
[4,5,2,6,1,7,3]=>010101=>101010=>[1,2,2,2]
[4,5,2,6,3,1,7]=>010110=>011010=>[2,1,2,2]
[4,5,2,6,3,7,1]=>010101=>101010=>[1,2,2,2]
[4,5,2,6,7,1,3]=>010010=>010010=>[2,3,2]
[4,5,2,6,7,3,1]=>010011=>110010=>[1,1,3,2]
[4,5,2,7,1,3,6]=>010100=>001010=>[3,2,2]
[4,5,2,7,1,6,3]=>010101=>101010=>[1,2,2,2]
[4,5,2,7,3,1,6]=>010110=>011010=>[2,1,2,2]
[4,5,2,7,3,6,1]=>010101=>101010=>[1,2,2,2]
[4,5,2,7,6,1,3]=>010110=>011010=>[2,1,2,2]
[4,5,2,7,6,3,1]=>010111=>111010=>[1,1,1,2,2]
[4,5,3,1,2,6,7]=>011000=>000110=>[4,1,2]
[4,5,3,1,2,7,6]=>011001=>100110=>[1,3,1,2]
[4,5,3,1,6,2,7]=>011010=>010110=>[2,2,1,2]
[4,5,3,1,6,7,2]=>011001=>100110=>[1,3,1,2]
[4,5,3,1,7,2,6]=>011010=>010110=>[2,2,1,2]
[4,5,3,1,7,6,2]=>011011=>110110=>[1,1,2,1,2]
[4,5,3,2,1,6,7]=>011100=>001110=>[3,1,1,2]
[4,5,3,2,1,7,6]=>011101=>101110=>[1,2,1,1,2]
[4,5,3,2,6,1,7]=>011010=>010110=>[2,2,1,2]
[4,5,3,2,6,7,1]=>011001=>100110=>[1,3,1,2]
[4,5,3,2,7,1,6]=>011010=>010110=>[2,2,1,2]
[4,5,3,2,7,6,1]=>011011=>110110=>[1,1,2,1,2]
[4,5,3,6,1,2,7]=>010100=>001010=>[3,2,2]
[4,5,3,6,1,7,2]=>010101=>101010=>[1,2,2,2]
[4,5,3,6,2,1,7]=>010110=>011010=>[2,1,2,2]
[4,5,3,6,2,7,1]=>010101=>101010=>[1,2,2,2]
[4,5,3,6,7,1,2]=>010010=>010010=>[2,3,2]
[4,5,3,6,7,2,1]=>010011=>110010=>[1,1,3,2]
[4,5,3,7,1,2,6]=>010100=>001010=>[3,2,2]
[4,5,3,7,1,6,2]=>010101=>101010=>[1,2,2,2]
[4,5,3,7,2,1,6]=>010110=>011010=>[2,1,2,2]
[4,5,3,7,2,6,1]=>010101=>101010=>[1,2,2,2]
[4,5,3,7,6,1,2]=>010110=>011010=>[2,1,2,2]
[4,5,3,7,6,2,1]=>010111=>111010=>[1,1,1,2,2]
[4,5,6,1,2,3,7]=>001000=>000100=>[4,3]
[4,5,6,1,2,7,3]=>001001=>100100=>[1,3,3]
[4,5,6,1,3,2,7]=>001010=>010100=>[2,2,3]
[4,5,6,1,3,7,2]=>001001=>100100=>[1,3,3]
[4,5,6,1,7,2,3]=>001010=>010100=>[2,2,3]
[4,5,6,1,7,3,2]=>001011=>110100=>[1,1,2,3]
[4,5,6,2,1,3,7]=>001100=>001100=>[3,1,3]
[4,5,6,2,1,7,3]=>001101=>101100=>[1,2,1,3]
[4,5,6,2,3,1,7]=>001010=>010100=>[2,2,3]
[4,5,6,2,3,7,1]=>001001=>100100=>[1,3,3]
[4,5,6,2,7,1,3]=>001010=>010100=>[2,2,3]
[4,5,6,2,7,3,1]=>001011=>110100=>[1,1,2,3]
[4,5,6,3,1,2,7]=>001100=>001100=>[3,1,3]
[4,5,6,3,1,7,2]=>001101=>101100=>[1,2,1,3]
[4,5,6,3,2,1,7]=>001110=>011100=>[2,1,1,3]
[4,5,6,3,2,7,1]=>001101=>101100=>[1,2,1,3]
[4,5,6,3,7,1,2]=>001010=>010100=>[2,2,3]
[4,5,6,3,7,2,1]=>001011=>110100=>[1,1,2,3]
[4,5,6,7,1,2,3]=>000100=>001000=>[3,4]
[4,5,6,7,1,3,2]=>000101=>101000=>[1,2,4]
[4,5,6,7,2,1,3]=>000110=>011000=>[2,1,4]
[4,5,6,7,2,3,1]=>000101=>101000=>[1,2,4]
[4,5,6,7,3,1,2]=>000110=>011000=>[2,1,4]
[4,5,6,7,3,2,1]=>000111=>111000=>[1,1,1,4]
[4,5,7,1,2,3,6]=>001000=>000100=>[4,3]
[4,5,7,1,2,6,3]=>001001=>100100=>[1,3,3]
[4,5,7,1,3,2,6]=>001010=>010100=>[2,2,3]
[4,5,7,1,3,6,2]=>001001=>100100=>[1,3,3]
[4,5,7,1,6,2,3]=>001010=>010100=>[2,2,3]
[4,5,7,1,6,3,2]=>001011=>110100=>[1,1,2,3]
[4,5,7,2,1,3,6]=>001100=>001100=>[3,1,3]
[4,5,7,2,1,6,3]=>001101=>101100=>[1,2,1,3]
[4,5,7,2,3,1,6]=>001010=>010100=>[2,2,3]
[4,5,7,2,3,6,1]=>001001=>100100=>[1,3,3]
[4,5,7,2,6,1,3]=>001010=>010100=>[2,2,3]
[4,5,7,2,6,3,1]=>001011=>110100=>[1,1,2,3]
[4,5,7,3,1,2,6]=>001100=>001100=>[3,1,3]
[4,5,7,3,1,6,2]=>001101=>101100=>[1,2,1,3]
[4,5,7,3,2,1,6]=>001110=>011100=>[2,1,1,3]
[4,5,7,3,2,6,1]=>001101=>101100=>[1,2,1,3]
[4,5,7,3,6,1,2]=>001010=>010100=>[2,2,3]
[4,5,7,3,6,2,1]=>001011=>110100=>[1,1,2,3]
[4,5,7,6,1,2,3]=>001100=>001100=>[3,1,3]
[4,5,7,6,1,3,2]=>001101=>101100=>[1,2,1,3]
[4,5,7,6,2,1,3]=>001110=>011100=>[2,1,1,3]
[4,5,7,6,2,3,1]=>001101=>101100=>[1,2,1,3]
[4,5,7,6,3,1,2]=>001110=>011100=>[2,1,1,3]
[4,5,7,6,3,2,1]=>001111=>111100=>[1,1,1,1,3]
[4,6,1,2,3,5,7]=>010000=>000010=>[5,2]
[4,6,1,2,3,7,5]=>010001=>100010=>[1,4,2]
[4,6,1,2,5,3,7]=>010010=>010010=>[2,3,2]
[4,6,1,2,5,7,3]=>010001=>100010=>[1,4,2]
[4,6,1,2,7,3,5]=>010010=>010010=>[2,3,2]
[4,6,1,2,7,5,3]=>010011=>110010=>[1,1,3,2]
[4,6,1,3,2,5,7]=>010100=>001010=>[3,2,2]
[4,6,1,3,2,7,5]=>010101=>101010=>[1,2,2,2]
[4,6,1,3,5,2,7]=>010010=>010010=>[2,3,2]
[4,6,1,3,5,7,2]=>010001=>100010=>[1,4,2]
[4,6,1,3,7,2,5]=>010010=>010010=>[2,3,2]
[4,6,1,3,7,5,2]=>010011=>110010=>[1,1,3,2]
[4,6,1,5,2,3,7]=>010100=>001010=>[3,2,2]
[4,6,1,5,2,7,3]=>010101=>101010=>[1,2,2,2]
[4,6,1,5,3,2,7]=>010110=>011010=>[2,1,2,2]
[4,6,1,5,3,7,2]=>010101=>101010=>[1,2,2,2]
[4,6,1,5,7,2,3]=>010010=>010010=>[2,3,2]
[4,6,1,5,7,3,2]=>010011=>110010=>[1,1,3,2]
[4,6,1,7,2,3,5]=>010100=>001010=>[3,2,2]
[4,6,1,7,2,5,3]=>010101=>101010=>[1,2,2,2]
[4,6,1,7,3,2,5]=>010110=>011010=>[2,1,2,2]
[4,6,1,7,3,5,2]=>010101=>101010=>[1,2,2,2]
[4,6,1,7,5,2,3]=>010110=>011010=>[2,1,2,2]
[4,6,1,7,5,3,2]=>010111=>111010=>[1,1,1,2,2]
[4,6,2,1,3,5,7]=>011000=>000110=>[4,1,2]
[4,6,2,1,3,7,5]=>011001=>100110=>[1,3,1,2]
[4,6,2,1,5,3,7]=>011010=>010110=>[2,2,1,2]
[4,6,2,1,5,7,3]=>011001=>100110=>[1,3,1,2]
[4,6,2,1,7,3,5]=>011010=>010110=>[2,2,1,2]
[4,6,2,1,7,5,3]=>011011=>110110=>[1,1,2,1,2]
[4,6,2,3,1,5,7]=>010100=>001010=>[3,2,2]
[4,6,2,3,1,7,5]=>010101=>101010=>[1,2,2,2]
[4,6,2,3,5,1,7]=>010010=>010010=>[2,3,2]
[4,6,2,3,5,7,1]=>010001=>100010=>[1,4,2]
[4,6,2,3,7,1,5]=>010010=>010010=>[2,3,2]
[4,6,2,3,7,5,1]=>010011=>110010=>[1,1,3,2]
[4,6,2,5,1,3,7]=>010100=>001010=>[3,2,2]
[4,6,2,5,1,7,3]=>010101=>101010=>[1,2,2,2]
[4,6,2,5,3,1,7]=>010110=>011010=>[2,1,2,2]
[4,6,2,5,3,7,1]=>010101=>101010=>[1,2,2,2]
[4,6,2,5,7,1,3]=>010010=>010010=>[2,3,2]
[4,6,2,5,7,3,1]=>010011=>110010=>[1,1,3,2]
[4,6,2,7,1,3,5]=>010100=>001010=>[3,2,2]
[4,6,2,7,1,5,3]=>010101=>101010=>[1,2,2,2]
[4,6,2,7,3,1,5]=>010110=>011010=>[2,1,2,2]
[4,6,2,7,3,5,1]=>010101=>101010=>[1,2,2,2]
[4,6,2,7,5,1,3]=>010110=>011010=>[2,1,2,2]
[4,6,2,7,5,3,1]=>010111=>111010=>[1,1,1,2,2]
[4,6,3,1,2,5,7]=>011000=>000110=>[4,1,2]
[4,6,3,1,2,7,5]=>011001=>100110=>[1,3,1,2]
[4,6,3,1,5,2,7]=>011010=>010110=>[2,2,1,2]
[4,6,3,1,5,7,2]=>011001=>100110=>[1,3,1,2]
[4,6,3,1,7,2,5]=>011010=>010110=>[2,2,1,2]
[4,6,3,1,7,5,2]=>011011=>110110=>[1,1,2,1,2]
[4,6,3,2,1,5,7]=>011100=>001110=>[3,1,1,2]
[4,6,3,2,1,7,5]=>011101=>101110=>[1,2,1,1,2]
[4,6,3,2,5,1,7]=>011010=>010110=>[2,2,1,2]
[4,6,3,2,5,7,1]=>011001=>100110=>[1,3,1,2]
[4,6,3,2,7,1,5]=>011010=>010110=>[2,2,1,2]
[4,6,3,2,7,5,1]=>011011=>110110=>[1,1,2,1,2]
[4,6,3,5,1,2,7]=>010100=>001010=>[3,2,2]
[4,6,3,5,1,7,2]=>010101=>101010=>[1,2,2,2]
[4,6,3,5,2,1,7]=>010110=>011010=>[2,1,2,2]
[4,6,3,5,2,7,1]=>010101=>101010=>[1,2,2,2]
[4,6,3,5,7,1,2]=>010010=>010010=>[2,3,2]
[4,6,3,5,7,2,1]=>010011=>110010=>[1,1,3,2]
[4,6,3,7,1,2,5]=>010100=>001010=>[3,2,2]
[4,6,3,7,1,5,2]=>010101=>101010=>[1,2,2,2]
[4,6,3,7,2,1,5]=>010110=>011010=>[2,1,2,2]
[4,6,3,7,2,5,1]=>010101=>101010=>[1,2,2,2]
[4,6,3,7,5,1,2]=>010110=>011010=>[2,1,2,2]
[4,6,3,7,5,2,1]=>010111=>111010=>[1,1,1,2,2]
[4,6,5,1,2,3,7]=>011000=>000110=>[4,1,2]
[4,6,5,1,2,7,3]=>011001=>100110=>[1,3,1,2]
[4,6,5,1,3,2,7]=>011010=>010110=>[2,2,1,2]
[4,6,5,1,3,7,2]=>011001=>100110=>[1,3,1,2]
[4,6,5,1,7,2,3]=>011010=>010110=>[2,2,1,2]
[4,6,5,1,7,3,2]=>011011=>110110=>[1,1,2,1,2]
[4,6,5,2,1,3,7]=>011100=>001110=>[3,1,1,2]
[4,6,5,2,1,7,3]=>011101=>101110=>[1,2,1,1,2]
[4,6,5,2,3,1,7]=>011010=>010110=>[2,2,1,2]
[4,6,5,2,3,7,1]=>011001=>100110=>[1,3,1,2]
[4,6,5,2,7,1,3]=>011010=>010110=>[2,2,1,2]
[4,6,5,2,7,3,1]=>011011=>110110=>[1,1,2,1,2]
[4,6,5,3,1,2,7]=>011100=>001110=>[3,1,1,2]
[4,6,5,3,1,7,2]=>011101=>101110=>[1,2,1,1,2]
[4,6,5,3,2,1,7]=>011110=>011110=>[2,1,1,1,2]
[4,6,5,3,2,7,1]=>011101=>101110=>[1,2,1,1,2]
[4,6,5,3,7,1,2]=>011010=>010110=>[2,2,1,2]
[4,6,5,3,7,2,1]=>011011=>110110=>[1,1,2,1,2]
[4,6,5,7,1,2,3]=>010100=>001010=>[3,2,2]
[4,6,5,7,1,3,2]=>010101=>101010=>[1,2,2,2]
[4,6,5,7,2,1,3]=>010110=>011010=>[2,1,2,2]
[4,6,5,7,2,3,1]=>010101=>101010=>[1,2,2,2]
[4,6,5,7,3,1,2]=>010110=>011010=>[2,1,2,2]
[4,6,5,7,3,2,1]=>010111=>111010=>[1,1,1,2,2]
[4,6,7,1,2,3,5]=>001000=>000100=>[4,3]
[4,6,7,1,2,5,3]=>001001=>100100=>[1,3,3]
[4,6,7,1,3,2,5]=>001010=>010100=>[2,2,3]
[4,6,7,1,3,5,2]=>001001=>100100=>[1,3,3]
[4,6,7,1,5,2,3]=>001010=>010100=>[2,2,3]
[4,6,7,1,5,3,2]=>001011=>110100=>[1,1,2,3]
[4,6,7,2,1,3,5]=>001100=>001100=>[3,1,3]
[4,6,7,2,1,5,3]=>001101=>101100=>[1,2,1,3]
[4,6,7,2,3,1,5]=>001010=>010100=>[2,2,3]
[4,6,7,2,3,5,1]=>001001=>100100=>[1,3,3]
[4,6,7,2,5,1,3]=>001010=>010100=>[2,2,3]
[4,6,7,2,5,3,1]=>001011=>110100=>[1,1,2,3]
[4,6,7,3,1,2,5]=>001100=>001100=>[3,1,3]
[4,6,7,3,1,5,2]=>001101=>101100=>[1,2,1,3]
[4,6,7,3,2,1,5]=>001110=>011100=>[2,1,1,3]
[4,6,7,3,2,5,1]=>001101=>101100=>[1,2,1,3]
[4,6,7,3,5,1,2]=>001010=>010100=>[2,2,3]
[4,6,7,3,5,2,1]=>001011=>110100=>[1,1,2,3]
[4,6,7,5,1,2,3]=>001100=>001100=>[3,1,3]
[4,6,7,5,1,3,2]=>001101=>101100=>[1,2,1,3]
[4,6,7,5,2,1,3]=>001110=>011100=>[2,1,1,3]
[4,6,7,5,2,3,1]=>001101=>101100=>[1,2,1,3]
[4,6,7,5,3,1,2]=>001110=>011100=>[2,1,1,3]
[4,6,7,5,3,2,1]=>001111=>111100=>[1,1,1,1,3]
[4,7,1,2,3,5,6]=>010000=>000010=>[5,2]
[4,7,1,2,3,6,5]=>010001=>100010=>[1,4,2]
[4,7,1,2,5,3,6]=>010010=>010010=>[2,3,2]
[4,7,1,2,5,6,3]=>010001=>100010=>[1,4,2]
[4,7,1,2,6,3,5]=>010010=>010010=>[2,3,2]
[4,7,1,2,6,5,3]=>010011=>110010=>[1,1,3,2]
[4,7,1,3,2,5,6]=>010100=>001010=>[3,2,2]
[4,7,1,3,2,6,5]=>010101=>101010=>[1,2,2,2]
[4,7,1,3,5,2,6]=>010010=>010010=>[2,3,2]
[4,7,1,3,5,6,2]=>010001=>100010=>[1,4,2]
[4,7,1,3,6,2,5]=>010010=>010010=>[2,3,2]
[4,7,1,3,6,5,2]=>010011=>110010=>[1,1,3,2]
[4,7,1,5,2,3,6]=>010100=>001010=>[3,2,2]
[4,7,1,5,2,6,3]=>010101=>101010=>[1,2,2,2]
[4,7,1,5,3,2,6]=>010110=>011010=>[2,1,2,2]
[4,7,1,5,3,6,2]=>010101=>101010=>[1,2,2,2]
[4,7,1,5,6,2,3]=>010010=>010010=>[2,3,2]
[4,7,1,5,6,3,2]=>010011=>110010=>[1,1,3,2]
[4,7,1,6,2,3,5]=>010100=>001010=>[3,2,2]
[4,7,1,6,2,5,3]=>010101=>101010=>[1,2,2,2]
[4,7,1,6,3,2,5]=>010110=>011010=>[2,1,2,2]
[4,7,1,6,3,5,2]=>010101=>101010=>[1,2,2,2]
[4,7,1,6,5,2,3]=>010110=>011010=>[2,1,2,2]
[4,7,1,6,5,3,2]=>010111=>111010=>[1,1,1,2,2]
[4,7,2,1,3,5,6]=>011000=>000110=>[4,1,2]
[4,7,2,1,3,6,5]=>011001=>100110=>[1,3,1,2]
[4,7,2,1,5,3,6]=>011010=>010110=>[2,2,1,2]
[4,7,2,1,5,6,3]=>011001=>100110=>[1,3,1,2]
[4,7,2,1,6,3,5]=>011010=>010110=>[2,2,1,2]
[4,7,2,1,6,5,3]=>011011=>110110=>[1,1,2,1,2]
[4,7,2,3,1,5,6]=>010100=>001010=>[3,2,2]
[4,7,2,3,1,6,5]=>010101=>101010=>[1,2,2,2]
[4,7,2,3,5,1,6]=>010010=>010010=>[2,3,2]
[4,7,2,3,5,6,1]=>010001=>100010=>[1,4,2]
[4,7,2,3,6,1,5]=>010010=>010010=>[2,3,2]
[4,7,2,3,6,5,1]=>010011=>110010=>[1,1,3,2]
[4,7,2,5,1,3,6]=>010100=>001010=>[3,2,2]
[4,7,2,5,1,6,3]=>010101=>101010=>[1,2,2,2]
[4,7,2,5,3,1,6]=>010110=>011010=>[2,1,2,2]
[4,7,2,5,3,6,1]=>010101=>101010=>[1,2,2,2]
[4,7,2,5,6,1,3]=>010010=>010010=>[2,3,2]
[4,7,2,5,6,3,1]=>010011=>110010=>[1,1,3,2]
[4,7,2,6,1,3,5]=>010100=>001010=>[3,2,2]
[4,7,2,6,1,5,3]=>010101=>101010=>[1,2,2,2]
[4,7,2,6,3,1,5]=>010110=>011010=>[2,1,2,2]
[4,7,2,6,3,5,1]=>010101=>101010=>[1,2,2,2]
[4,7,2,6,5,1,3]=>010110=>011010=>[2,1,2,2]
[4,7,2,6,5,3,1]=>010111=>111010=>[1,1,1,2,2]
[4,7,3,1,2,5,6]=>011000=>000110=>[4,1,2]
[4,7,3,1,2,6,5]=>011001=>100110=>[1,3,1,2]
[4,7,3,1,5,2,6]=>011010=>010110=>[2,2,1,2]
[4,7,3,1,5,6,2]=>011001=>100110=>[1,3,1,2]
[4,7,3,1,6,2,5]=>011010=>010110=>[2,2,1,2]
[4,7,3,1,6,5,2]=>011011=>110110=>[1,1,2,1,2]
[4,7,3,2,1,5,6]=>011100=>001110=>[3,1,1,2]
[4,7,3,2,1,6,5]=>011101=>101110=>[1,2,1,1,2]
[4,7,3,2,5,1,6]=>011010=>010110=>[2,2,1,2]
[4,7,3,2,5,6,1]=>011001=>100110=>[1,3,1,2]
[4,7,3,2,6,1,5]=>011010=>010110=>[2,2,1,2]
[4,7,3,2,6,5,1]=>011011=>110110=>[1,1,2,1,2]
[4,7,3,5,1,2,6]=>010100=>001010=>[3,2,2]
[4,7,3,5,1,6,2]=>010101=>101010=>[1,2,2,2]
[4,7,3,5,2,1,6]=>010110=>011010=>[2,1,2,2]
[4,7,3,5,2,6,1]=>010101=>101010=>[1,2,2,2]
[4,7,3,5,6,1,2]=>010010=>010010=>[2,3,2]
[4,7,3,5,6,2,1]=>010011=>110010=>[1,1,3,2]
[4,7,3,6,1,2,5]=>010100=>001010=>[3,2,2]
[4,7,3,6,1,5,2]=>010101=>101010=>[1,2,2,2]
[4,7,3,6,2,1,5]=>010110=>011010=>[2,1,2,2]
[4,7,3,6,2,5,1]=>010101=>101010=>[1,2,2,2]
[4,7,3,6,5,1,2]=>010110=>011010=>[2,1,2,2]
[4,7,3,6,5,2,1]=>010111=>111010=>[1,1,1,2,2]
[4,7,5,1,2,3,6]=>011000=>000110=>[4,1,2]
[4,7,5,1,2,6,3]=>011001=>100110=>[1,3,1,2]
[4,7,5,1,3,2,6]=>011010=>010110=>[2,2,1,2]
[4,7,5,1,3,6,2]=>011001=>100110=>[1,3,1,2]
[4,7,5,1,6,2,3]=>011010=>010110=>[2,2,1,2]
[4,7,5,1,6,3,2]=>011011=>110110=>[1,1,2,1,2]
[4,7,5,2,1,3,6]=>011100=>001110=>[3,1,1,2]
[4,7,5,2,1,6,3]=>011101=>101110=>[1,2,1,1,2]
[4,7,5,2,3,1,6]=>011010=>010110=>[2,2,1,2]
[4,7,5,2,3,6,1]=>011001=>100110=>[1,3,1,2]
[4,7,5,2,6,1,3]=>011010=>010110=>[2,2,1,2]
[4,7,5,2,6,3,1]=>011011=>110110=>[1,1,2,1,2]
[4,7,5,3,1,2,6]=>011100=>001110=>[3,1,1,2]
[4,7,5,3,1,6,2]=>011101=>101110=>[1,2,1,1,2]
[4,7,5,3,2,1,6]=>011110=>011110=>[2,1,1,1,2]
[4,7,5,3,2,6,1]=>011101=>101110=>[1,2,1,1,2]
[4,7,5,3,6,1,2]=>011010=>010110=>[2,2,1,2]
[4,7,5,3,6,2,1]=>011011=>110110=>[1,1,2,1,2]
[4,7,5,6,1,2,3]=>010100=>001010=>[3,2,2]
[4,7,5,6,1,3,2]=>010101=>101010=>[1,2,2,2]
[4,7,5,6,2,1,3]=>010110=>011010=>[2,1,2,2]
[4,7,5,6,2,3,1]=>010101=>101010=>[1,2,2,2]
[4,7,5,6,3,1,2]=>010110=>011010=>[2,1,2,2]
[4,7,5,6,3,2,1]=>010111=>111010=>[1,1,1,2,2]
[4,7,6,1,2,3,5]=>011000=>000110=>[4,1,2]
[4,7,6,1,2,5,3]=>011001=>100110=>[1,3,1,2]
[4,7,6,1,3,2,5]=>011010=>010110=>[2,2,1,2]
[4,7,6,1,3,5,2]=>011001=>100110=>[1,3,1,2]
[4,7,6,1,5,2,3]=>011010=>010110=>[2,2,1,2]
[4,7,6,1,5,3,2]=>011011=>110110=>[1,1,2,1,2]
[4,7,6,2,1,3,5]=>011100=>001110=>[3,1,1,2]
[4,7,6,2,1,5,3]=>011101=>101110=>[1,2,1,1,2]
[4,7,6,2,3,1,5]=>011010=>010110=>[2,2,1,2]
[4,7,6,2,3,5,1]=>011001=>100110=>[1,3,1,2]
[4,7,6,2,5,1,3]=>011010=>010110=>[2,2,1,2]
[4,7,6,2,5,3,1]=>011011=>110110=>[1,1,2,1,2]
[4,7,6,3,1,2,5]=>011100=>001110=>[3,1,1,2]
[4,7,6,3,1,5,2]=>011101=>101110=>[1,2,1,1,2]
[4,7,6,3,2,1,5]=>011110=>011110=>[2,1,1,1,2]
[4,7,6,3,2,5,1]=>011101=>101110=>[1,2,1,1,2]
[4,7,6,3,5,1,2]=>011010=>010110=>[2,2,1,2]
[4,7,6,3,5,2,1]=>011011=>110110=>[1,1,2,1,2]
[4,7,6,5,1,2,3]=>011100=>001110=>[3,1,1,2]
[4,7,6,5,1,3,2]=>011101=>101110=>[1,2,1,1,2]
[4,7,6,5,2,1,3]=>011110=>011110=>[2,1,1,1,2]
[4,7,6,5,2,3,1]=>011101=>101110=>[1,2,1,1,2]
[4,7,6,5,3,1,2]=>011110=>011110=>[2,1,1,1,2]
[4,7,6,5,3,2,1]=>011111=>111110=>[1,1,1,1,1,2]
[5,1,2,3,4,6,7]=>100000=>000001=>[6,1]
[5,1,2,3,4,7,6]=>100001=>100001=>[1,5,1]
[5,1,2,3,6,4,7]=>100010=>010001=>[2,4,1]
[5,1,2,3,6,7,4]=>100001=>100001=>[1,5,1]
[5,1,2,3,7,4,6]=>100010=>010001=>[2,4,1]
[5,1,2,3,7,6,4]=>100011=>110001=>[1,1,4,1]
[5,1,2,4,3,6,7]=>100100=>001001=>[3,3,1]
[5,1,2,4,3,7,6]=>100101=>101001=>[1,2,3,1]
[5,1,2,4,6,3,7]=>100010=>010001=>[2,4,1]
[5,1,2,4,6,7,3]=>100001=>100001=>[1,5,1]
[5,1,2,4,7,3,6]=>100010=>010001=>[2,4,1]
[5,1,2,4,7,6,3]=>100011=>110001=>[1,1,4,1]
[5,1,2,6,3,4,7]=>100100=>001001=>[3,3,1]
[5,1,2,6,3,7,4]=>100101=>101001=>[1,2,3,1]
[5,1,2,6,4,3,7]=>100110=>011001=>[2,1,3,1]
[5,1,2,6,4,7,3]=>100101=>101001=>[1,2,3,1]
[5,1,2,6,7,3,4]=>100010=>010001=>[2,4,1]
[5,1,2,6,7,4,3]=>100011=>110001=>[1,1,4,1]
[5,1,2,7,3,4,6]=>100100=>001001=>[3,3,1]
[5,1,2,7,3,6,4]=>100101=>101001=>[1,2,3,1]
[5,1,2,7,4,3,6]=>100110=>011001=>[2,1,3,1]
[5,1,2,7,4,6,3]=>100101=>101001=>[1,2,3,1]
[5,1,2,7,6,3,4]=>100110=>011001=>[2,1,3,1]
[5,1,2,7,6,4,3]=>100111=>111001=>[1,1,1,3,1]
[5,1,3,2,4,6,7]=>101000=>000101=>[4,2,1]
[5,1,3,2,4,7,6]=>101001=>100101=>[1,3,2,1]
[5,1,3,2,6,4,7]=>101010=>010101=>[2,2,2,1]
[5,1,3,2,6,7,4]=>101001=>100101=>[1,3,2,1]
[5,1,3,2,7,4,6]=>101010=>010101=>[2,2,2,1]
[5,1,3,2,7,6,4]=>101011=>110101=>[1,1,2,2,1]
[5,1,3,4,2,6,7]=>100100=>001001=>[3,3,1]
[5,1,3,4,2,7,6]=>100101=>101001=>[1,2,3,1]
[5,1,3,4,6,2,7]=>100010=>010001=>[2,4,1]
[5,1,3,4,6,7,2]=>100001=>100001=>[1,5,1]
[5,1,3,4,7,2,6]=>100010=>010001=>[2,4,1]
[5,1,3,4,7,6,2]=>100011=>110001=>[1,1,4,1]
[5,1,3,6,2,4,7]=>100100=>001001=>[3,3,1]
[5,1,3,6,2,7,4]=>100101=>101001=>[1,2,3,1]
[5,1,3,6,4,2,7]=>100110=>011001=>[2,1,3,1]
[5,1,3,6,4,7,2]=>100101=>101001=>[1,2,3,1]
[5,1,3,6,7,2,4]=>100010=>010001=>[2,4,1]
[5,1,3,6,7,4,2]=>100011=>110001=>[1,1,4,1]
[5,1,3,7,2,4,6]=>100100=>001001=>[3,3,1]
[5,1,3,7,2,6,4]=>100101=>101001=>[1,2,3,1]
[5,1,3,7,4,2,6]=>100110=>011001=>[2,1,3,1]
[5,1,3,7,4,6,2]=>100101=>101001=>[1,2,3,1]
[5,1,3,7,6,2,4]=>100110=>011001=>[2,1,3,1]
[5,1,3,7,6,4,2]=>100111=>111001=>[1,1,1,3,1]
[5,1,4,2,3,6,7]=>101000=>000101=>[4,2,1]
[5,1,4,2,3,7,6]=>101001=>100101=>[1,3,2,1]
[5,1,4,2,6,3,7]=>101010=>010101=>[2,2,2,1]
[5,1,4,2,6,7,3]=>101001=>100101=>[1,3,2,1]
[5,1,4,2,7,3,6]=>101010=>010101=>[2,2,2,1]
[5,1,4,2,7,6,3]=>101011=>110101=>[1,1,2,2,1]
[5,1,4,3,2,6,7]=>101100=>001101=>[3,1,2,1]
[5,1,4,3,2,7,6]=>101101=>101101=>[1,2,1,2,1]
[5,1,4,3,6,2,7]=>101010=>010101=>[2,2,2,1]
[5,1,4,3,6,7,2]=>101001=>100101=>[1,3,2,1]
[5,1,4,3,7,2,6]=>101010=>010101=>[2,2,2,1]
[5,1,4,3,7,6,2]=>101011=>110101=>[1,1,2,2,1]
[5,1,4,6,2,3,7]=>100100=>001001=>[3,3,1]
[5,1,4,6,2,7,3]=>100101=>101001=>[1,2,3,1]
[5,1,4,6,3,2,7]=>100110=>011001=>[2,1,3,1]
[5,1,4,6,3,7,2]=>100101=>101001=>[1,2,3,1]
[5,1,4,6,7,2,3]=>100010=>010001=>[2,4,1]
[5,1,4,6,7,3,2]=>100011=>110001=>[1,1,4,1]
[5,1,4,7,2,3,6]=>100100=>001001=>[3,3,1]
[5,1,4,7,2,6,3]=>100101=>101001=>[1,2,3,1]
[5,1,4,7,3,2,6]=>100110=>011001=>[2,1,3,1]
[5,1,4,7,3,6,2]=>100101=>101001=>[1,2,3,1]
[5,1,4,7,6,2,3]=>100110=>011001=>[2,1,3,1]
[5,1,4,7,6,3,2]=>100111=>111001=>[1,1,1,3,1]
[5,1,6,2,3,4,7]=>101000=>000101=>[4,2,1]
[5,1,6,2,3,7,4]=>101001=>100101=>[1,3,2,1]
[5,1,6,2,4,3,7]=>101010=>010101=>[2,2,2,1]
[5,1,6,2,4,7,3]=>101001=>100101=>[1,3,2,1]
[5,1,6,2,7,3,4]=>101010=>010101=>[2,2,2,1]
[5,1,6,2,7,4,3]=>101011=>110101=>[1,1,2,2,1]
[5,1,6,3,2,4,7]=>101100=>001101=>[3,1,2,1]
[5,1,6,3,2,7,4]=>101101=>101101=>[1,2,1,2,1]
[5,1,6,3,4,2,7]=>101010=>010101=>[2,2,2,1]
[5,1,6,3,4,7,2]=>101001=>100101=>[1,3,2,1]
[5,1,6,3,7,2,4]=>101010=>010101=>[2,2,2,1]
[5,1,6,3,7,4,2]=>101011=>110101=>[1,1,2,2,1]
[5,1,6,4,2,3,7]=>101100=>001101=>[3,1,2,1]
[5,1,6,4,2,7,3]=>101101=>101101=>[1,2,1,2,1]
[5,1,6,4,3,2,7]=>101110=>011101=>[2,1,1,2,1]
[5,1,6,4,3,7,2]=>101101=>101101=>[1,2,1,2,1]
[5,1,6,4,7,2,3]=>101010=>010101=>[2,2,2,1]
[5,1,6,4,7,3,2]=>101011=>110101=>[1,1,2,2,1]
[5,1,6,7,2,3,4]=>100100=>001001=>[3,3,1]
[5,1,6,7,2,4,3]=>100101=>101001=>[1,2,3,1]
[5,1,6,7,3,2,4]=>100110=>011001=>[2,1,3,1]
[5,1,6,7,3,4,2]=>100101=>101001=>[1,2,3,1]
[5,1,6,7,4,2,3]=>100110=>011001=>[2,1,3,1]
[5,1,6,7,4,3,2]=>100111=>111001=>[1,1,1,3,1]
[5,1,7,2,3,4,6]=>101000=>000101=>[4,2,1]
[5,1,7,2,3,6,4]=>101001=>100101=>[1,3,2,1]
[5,1,7,2,4,3,6]=>101010=>010101=>[2,2,2,1]
[5,1,7,2,4,6,3]=>101001=>100101=>[1,3,2,1]
[5,1,7,2,6,3,4]=>101010=>010101=>[2,2,2,1]
[5,1,7,2,6,4,3]=>101011=>110101=>[1,1,2,2,1]
[5,1,7,3,2,4,6]=>101100=>001101=>[3,1,2,1]
[5,1,7,3,2,6,4]=>101101=>101101=>[1,2,1,2,1]
[5,1,7,3,4,2,6]=>101010=>010101=>[2,2,2,1]
[5,1,7,3,4,6,2]=>101001=>100101=>[1,3,2,1]
[5,1,7,3,6,2,4]=>101010=>010101=>[2,2,2,1]
[5,1,7,3,6,4,2]=>101011=>110101=>[1,1,2,2,1]
[5,1,7,4,2,3,6]=>101100=>001101=>[3,1,2,1]
[5,1,7,4,2,6,3]=>101101=>101101=>[1,2,1,2,1]
[5,1,7,4,3,2,6]=>101110=>011101=>[2,1,1,2,1]
[5,1,7,4,3,6,2]=>101101=>101101=>[1,2,1,2,1]
[5,1,7,4,6,2,3]=>101010=>010101=>[2,2,2,1]
[5,1,7,4,6,3,2]=>101011=>110101=>[1,1,2,2,1]
[5,1,7,6,2,3,4]=>101100=>001101=>[3,1,2,1]
[5,1,7,6,2,4,3]=>101101=>101101=>[1,2,1,2,1]
[5,1,7,6,3,2,4]=>101110=>011101=>[2,1,1,2,1]
[5,1,7,6,3,4,2]=>101101=>101101=>[1,2,1,2,1]
[5,1,7,6,4,2,3]=>101110=>011101=>[2,1,1,2,1]
[5,1,7,6,4,3,2]=>101111=>111101=>[1,1,1,1,2,1]
[5,2,1,3,4,6,7]=>110000=>000011=>[5,1,1]
[5,2,1,3,4,7,6]=>110001=>100011=>[1,4,1,1]
[5,2,1,3,6,4,7]=>110010=>010011=>[2,3,1,1]
[5,2,1,3,6,7,4]=>110001=>100011=>[1,4,1,1]
[5,2,1,3,7,4,6]=>110010=>010011=>[2,3,1,1]
[5,2,1,3,7,6,4]=>110011=>110011=>[1,1,3,1,1]
[5,2,1,4,3,6,7]=>110100=>001011=>[3,2,1,1]
[5,2,1,4,3,7,6]=>110101=>101011=>[1,2,2,1,1]
[5,2,1,4,6,3,7]=>110010=>010011=>[2,3,1,1]
[5,2,1,4,6,7,3]=>110001=>100011=>[1,4,1,1]
[5,2,1,4,7,3,6]=>110010=>010011=>[2,3,1,1]
[5,2,1,4,7,6,3]=>110011=>110011=>[1,1,3,1,1]
[5,2,1,6,3,4,7]=>110100=>001011=>[3,2,1,1]
[5,2,1,6,3,7,4]=>110101=>101011=>[1,2,2,1,1]
[5,2,1,6,4,3,7]=>110110=>011011=>[2,1,2,1,1]
[5,2,1,6,4,7,3]=>110101=>101011=>[1,2,2,1,1]
[5,2,1,6,7,3,4]=>110010=>010011=>[2,3,1,1]
[5,2,1,6,7,4,3]=>110011=>110011=>[1,1,3,1,1]
[5,2,1,7,3,4,6]=>110100=>001011=>[3,2,1,1]
[5,2,1,7,3,6,4]=>110101=>101011=>[1,2,2,1,1]
[5,2,1,7,4,3,6]=>110110=>011011=>[2,1,2,1,1]
[5,2,1,7,4,6,3]=>110101=>101011=>[1,2,2,1,1]
[5,2,1,7,6,3,4]=>110110=>011011=>[2,1,2,1,1]
[5,2,1,7,6,4,3]=>110111=>111011=>[1,1,1,2,1,1]
[5,2,3,1,4,6,7]=>101000=>000101=>[4,2,1]
[5,2,3,1,4,7,6]=>101001=>100101=>[1,3,2,1]
[5,2,3,1,6,4,7]=>101010=>010101=>[2,2,2,1]
[5,2,3,1,6,7,4]=>101001=>100101=>[1,3,2,1]
[5,2,3,1,7,4,6]=>101010=>010101=>[2,2,2,1]
[5,2,3,1,7,6,4]=>101011=>110101=>[1,1,2,2,1]
[5,2,3,4,1,6,7]=>100100=>001001=>[3,3,1]
[5,2,3,4,1,7,6]=>100101=>101001=>[1,2,3,1]
[5,2,3,4,6,1,7]=>100010=>010001=>[2,4,1]
[5,2,3,4,6,7,1]=>100001=>100001=>[1,5,1]
[5,2,3,4,7,1,6]=>100010=>010001=>[2,4,1]
[5,2,3,4,7,6,1]=>100011=>110001=>[1,1,4,1]
[5,2,3,6,1,4,7]=>100100=>001001=>[3,3,1]
[5,2,3,6,1,7,4]=>100101=>101001=>[1,2,3,1]
[5,2,3,6,4,1,7]=>100110=>011001=>[2,1,3,1]
[5,2,3,6,4,7,1]=>100101=>101001=>[1,2,3,1]
[5,2,3,6,7,1,4]=>100010=>010001=>[2,4,1]
[5,2,3,6,7,4,1]=>100011=>110001=>[1,1,4,1]
[5,2,3,7,1,4,6]=>100100=>001001=>[3,3,1]
[5,2,3,7,1,6,4]=>100101=>101001=>[1,2,3,1]
[5,2,3,7,4,1,6]=>100110=>011001=>[2,1,3,1]
[5,2,3,7,4,6,1]=>100101=>101001=>[1,2,3,1]
[5,2,3,7,6,1,4]=>100110=>011001=>[2,1,3,1]
[5,2,3,7,6,4,1]=>100111=>111001=>[1,1,1,3,1]
[5,2,4,1,3,6,7]=>101000=>000101=>[4,2,1]
[5,2,4,1,3,7,6]=>101001=>100101=>[1,3,2,1]
[5,2,4,1,6,3,7]=>101010=>010101=>[2,2,2,1]
[5,2,4,1,6,7,3]=>101001=>100101=>[1,3,2,1]
[5,2,4,1,7,3,6]=>101010=>010101=>[2,2,2,1]
[5,2,4,1,7,6,3]=>101011=>110101=>[1,1,2,2,1]
[5,2,4,3,1,6,7]=>101100=>001101=>[3,1,2,1]
[5,2,4,3,1,7,6]=>101101=>101101=>[1,2,1,2,1]
[5,2,4,3,6,1,7]=>101010=>010101=>[2,2,2,1]
[5,2,4,3,6,7,1]=>101001=>100101=>[1,3,2,1]
[5,2,4,3,7,1,6]=>101010=>010101=>[2,2,2,1]
[5,2,4,3,7,6,1]=>101011=>110101=>[1,1,2,2,1]
[5,2,4,6,1,3,7]=>100100=>001001=>[3,3,1]
[5,2,4,6,1,7,3]=>100101=>101001=>[1,2,3,1]
[5,2,4,6,3,1,7]=>100110=>011001=>[2,1,3,1]
[5,2,4,6,3,7,1]=>100101=>101001=>[1,2,3,1]
[5,2,4,6,7,1,3]=>100010=>010001=>[2,4,1]
[5,2,4,6,7,3,1]=>100011=>110001=>[1,1,4,1]
[5,2,4,7,1,3,6]=>100100=>001001=>[3,3,1]
[5,2,4,7,1,6,3]=>100101=>101001=>[1,2,3,1]
[5,2,4,7,3,1,6]=>100110=>011001=>[2,1,3,1]
[5,2,4,7,3,6,1]=>100101=>101001=>[1,2,3,1]
[5,2,4,7,6,1,3]=>100110=>011001=>[2,1,3,1]
[5,2,4,7,6,3,1]=>100111=>111001=>[1,1,1,3,1]
[5,2,6,1,3,4,7]=>101000=>000101=>[4,2,1]
[5,2,6,1,3,7,4]=>101001=>100101=>[1,3,2,1]
[5,2,6,1,4,3,7]=>101010=>010101=>[2,2,2,1]
[5,2,6,1,4,7,3]=>101001=>100101=>[1,3,2,1]
[5,2,6,1,7,3,4]=>101010=>010101=>[2,2,2,1]
[5,2,6,1,7,4,3]=>101011=>110101=>[1,1,2,2,1]
[5,2,6,3,1,4,7]=>101100=>001101=>[3,1,2,1]
[5,2,6,3,1,7,4]=>101101=>101101=>[1,2,1,2,1]
[5,2,6,3,4,1,7]=>101010=>010101=>[2,2,2,1]
[5,2,6,3,4,7,1]=>101001=>100101=>[1,3,2,1]
[5,2,6,3,7,1,4]=>101010=>010101=>[2,2,2,1]
[5,2,6,3,7,4,1]=>101011=>110101=>[1,1,2,2,1]
[5,2,6,4,1,3,7]=>101100=>001101=>[3,1,2,1]
[5,2,6,4,1,7,3]=>101101=>101101=>[1,2,1,2,1]
[5,2,6,4,3,1,7]=>101110=>011101=>[2,1,1,2,1]
[5,2,6,4,3,7,1]=>101101=>101101=>[1,2,1,2,1]
[5,2,6,4,7,1,3]=>101010=>010101=>[2,2,2,1]
[5,2,6,4,7,3,1]=>101011=>110101=>[1,1,2,2,1]
[5,2,6,7,1,3,4]=>100100=>001001=>[3,3,1]
[5,2,6,7,1,4,3]=>100101=>101001=>[1,2,3,1]
[5,2,6,7,3,1,4]=>100110=>011001=>[2,1,3,1]
[5,2,6,7,3,4,1]=>100101=>101001=>[1,2,3,1]
[5,2,6,7,4,1,3]=>100110=>011001=>[2,1,3,1]
[5,2,6,7,4,3,1]=>100111=>111001=>[1,1,1,3,1]
[5,2,7,1,3,4,6]=>101000=>000101=>[4,2,1]
[5,2,7,1,3,6,4]=>101001=>100101=>[1,3,2,1]
[5,2,7,1,4,3,6]=>101010=>010101=>[2,2,2,1]
[5,2,7,1,4,6,3]=>101001=>100101=>[1,3,2,1]
[5,2,7,1,6,3,4]=>101010=>010101=>[2,2,2,1]
[5,2,7,1,6,4,3]=>101011=>110101=>[1,1,2,2,1]
[5,2,7,3,1,4,6]=>101100=>001101=>[3,1,2,1]
[5,2,7,3,1,6,4]=>101101=>101101=>[1,2,1,2,1]
[5,2,7,3,4,1,6]=>101010=>010101=>[2,2,2,1]
[5,2,7,3,4,6,1]=>101001=>100101=>[1,3,2,1]
[5,2,7,3,6,1,4]=>101010=>010101=>[2,2,2,1]
[5,2,7,3,6,4,1]=>101011=>110101=>[1,1,2,2,1]
[5,2,7,4,1,3,6]=>101100=>001101=>[3,1,2,1]
[5,2,7,4,1,6,3]=>101101=>101101=>[1,2,1,2,1]
[5,2,7,4,3,1,6]=>101110=>011101=>[2,1,1,2,1]
[5,2,7,4,3,6,1]=>101101=>101101=>[1,2,1,2,1]
[5,2,7,4,6,1,3]=>101010=>010101=>[2,2,2,1]
[5,2,7,4,6,3,1]=>101011=>110101=>[1,1,2,2,1]
[5,2,7,6,1,3,4]=>101100=>001101=>[3,1,2,1]
[5,2,7,6,1,4,3]=>101101=>101101=>[1,2,1,2,1]
[5,2,7,6,3,1,4]=>101110=>011101=>[2,1,1,2,1]
[5,2,7,6,3,4,1]=>101101=>101101=>[1,2,1,2,1]
[5,2,7,6,4,1,3]=>101110=>011101=>[2,1,1,2,1]
[5,2,7,6,4,3,1]=>101111=>111101=>[1,1,1,1,2,1]
[5,3,1,2,4,6,7]=>110000=>000011=>[5,1,1]
[5,3,1,2,4,7,6]=>110001=>100011=>[1,4,1,1]
[5,3,1,2,6,4,7]=>110010=>010011=>[2,3,1,1]
[5,3,1,2,6,7,4]=>110001=>100011=>[1,4,1,1]
[5,3,1,2,7,4,6]=>110010=>010011=>[2,3,1,1]
[5,3,1,2,7,6,4]=>110011=>110011=>[1,1,3,1,1]
[5,3,1,4,2,6,7]=>110100=>001011=>[3,2,1,1]
[5,3,1,4,2,7,6]=>110101=>101011=>[1,2,2,1,1]
[5,3,1,4,6,2,7]=>110010=>010011=>[2,3,1,1]
[5,3,1,4,6,7,2]=>110001=>100011=>[1,4,1,1]
[5,3,1,4,7,2,6]=>110010=>010011=>[2,3,1,1]
[5,3,1,4,7,6,2]=>110011=>110011=>[1,1,3,1,1]
[5,3,1,6,2,4,7]=>110100=>001011=>[3,2,1,1]
[5,3,1,6,2,7,4]=>110101=>101011=>[1,2,2,1,1]
[5,3,1,6,4,2,7]=>110110=>011011=>[2,1,2,1,1]
[5,3,1,6,4,7,2]=>110101=>101011=>[1,2,2,1,1]
[5,3,1,6,7,2,4]=>110010=>010011=>[2,3,1,1]
[5,3,1,6,7,4,2]=>110011=>110011=>[1,1,3,1,1]
[5,3,1,7,2,4,6]=>110100=>001011=>[3,2,1,1]
[5,3,1,7,2,6,4]=>110101=>101011=>[1,2,2,1,1]
[5,3,1,7,4,2,6]=>110110=>011011=>[2,1,2,1,1]
[5,3,1,7,4,6,2]=>110101=>101011=>[1,2,2,1,1]
[5,3,1,7,6,2,4]=>110110=>011011=>[2,1,2,1,1]
[5,3,1,7,6,4,2]=>110111=>111011=>[1,1,1,2,1,1]
[5,3,2,1,4,6,7]=>111000=>000111=>[4,1,1,1]
[5,3,2,1,4,7,6]=>111001=>100111=>[1,3,1,1,1]
[5,3,2,1,6,4,7]=>111010=>010111=>[2,2,1,1,1]
[5,3,2,1,6,7,4]=>111001=>100111=>[1,3,1,1,1]
[5,3,2,1,7,4,6]=>111010=>010111=>[2,2,1,1,1]
[5,3,2,1,7,6,4]=>111011=>110111=>[1,1,2,1,1,1]
[5,3,2,4,1,6,7]=>110100=>001011=>[3,2,1,1]
[5,3,2,4,1,7,6]=>110101=>101011=>[1,2,2,1,1]
[5,3,2,4,6,1,7]=>110010=>010011=>[2,3,1,1]
[5,3,2,4,6,7,1]=>110001=>100011=>[1,4,1,1]
[5,3,2,4,7,1,6]=>110010=>010011=>[2,3,1,1]
[5,3,2,4,7,6,1]=>110011=>110011=>[1,1,3,1,1]
[5,3,2,6,1,4,7]=>110100=>001011=>[3,2,1,1]
[5,3,2,6,1,7,4]=>110101=>101011=>[1,2,2,1,1]
[5,3,2,6,4,1,7]=>110110=>011011=>[2,1,2,1,1]
[5,3,2,6,4,7,1]=>110101=>101011=>[1,2,2,1,1]
[5,3,2,6,7,1,4]=>110010=>010011=>[2,3,1,1]
[5,3,2,6,7,4,1]=>110011=>110011=>[1,1,3,1,1]
[5,3,2,7,1,4,6]=>110100=>001011=>[3,2,1,1]
[5,3,2,7,1,6,4]=>110101=>101011=>[1,2,2,1,1]
[5,3,2,7,4,1,6]=>110110=>011011=>[2,1,2,1,1]
[5,3,2,7,4,6,1]=>110101=>101011=>[1,2,2,1,1]
[5,3,2,7,6,1,4]=>110110=>011011=>[2,1,2,1,1]
[5,3,2,7,6,4,1]=>110111=>111011=>[1,1,1,2,1,1]
[5,3,4,1,2,6,7]=>101000=>000101=>[4,2,1]
[5,3,4,1,2,7,6]=>101001=>100101=>[1,3,2,1]
[5,3,4,1,6,2,7]=>101010=>010101=>[2,2,2,1]
[5,3,4,1,6,7,2]=>101001=>100101=>[1,3,2,1]
[5,3,4,1,7,2,6]=>101010=>010101=>[2,2,2,1]
[5,3,4,1,7,6,2]=>101011=>110101=>[1,1,2,2,1]
[5,3,4,2,1,6,7]=>101100=>001101=>[3,1,2,1]
[5,3,4,2,1,7,6]=>101101=>101101=>[1,2,1,2,1]
[5,3,4,2,6,1,7]=>101010=>010101=>[2,2,2,1]
[5,3,4,2,6,7,1]=>101001=>100101=>[1,3,2,1]
[5,3,4,2,7,1,6]=>101010=>010101=>[2,2,2,1]
[5,3,4,2,7,6,1]=>101011=>110101=>[1,1,2,2,1]
[5,3,4,6,1,2,7]=>100100=>001001=>[3,3,1]
[5,3,4,6,1,7,2]=>100101=>101001=>[1,2,3,1]
[5,3,4,6,2,1,7]=>100110=>011001=>[2,1,3,1]
[5,3,4,6,2,7,1]=>100101=>101001=>[1,2,3,1]
[5,3,4,6,7,1,2]=>100010=>010001=>[2,4,1]
[5,3,4,6,7,2,1]=>100011=>110001=>[1,1,4,1]
[5,3,4,7,1,2,6]=>100100=>001001=>[3,3,1]
[5,3,4,7,1,6,2]=>100101=>101001=>[1,2,3,1]
[5,3,4,7,2,1,6]=>100110=>011001=>[2,1,3,1]
[5,3,4,7,2,6,1]=>100101=>101001=>[1,2,3,1]
[5,3,4,7,6,1,2]=>100110=>011001=>[2,1,3,1]
[5,3,4,7,6,2,1]=>100111=>111001=>[1,1,1,3,1]
[5,3,6,1,2,4,7]=>101000=>000101=>[4,2,1]
[5,3,6,1,2,7,4]=>101001=>100101=>[1,3,2,1]
[5,3,6,1,4,2,7]=>101010=>010101=>[2,2,2,1]
[5,3,6,1,4,7,2]=>101001=>100101=>[1,3,2,1]
[5,3,6,1,7,2,4]=>101010=>010101=>[2,2,2,1]
[5,3,6,1,7,4,2]=>101011=>110101=>[1,1,2,2,1]
[5,3,6,2,1,4,7]=>101100=>001101=>[3,1,2,1]
[5,3,6,2,1,7,4]=>101101=>101101=>[1,2,1,2,1]
[5,3,6,2,4,1,7]=>101010=>010101=>[2,2,2,1]
[5,3,6,2,4,7,1]=>101001=>100101=>[1,3,2,1]
[5,3,6,2,7,1,4]=>101010=>010101=>[2,2,2,1]
[5,3,6,2,7,4,1]=>101011=>110101=>[1,1,2,2,1]
[5,3,6,4,1,2,7]=>101100=>001101=>[3,1,2,1]
[5,3,6,4,1,7,2]=>101101=>101101=>[1,2,1,2,1]
[5,3,6,4,2,1,7]=>101110=>011101=>[2,1,1,2,1]
[5,3,6,4,2,7,1]=>101101=>101101=>[1,2,1,2,1]
[5,3,6,4,7,1,2]=>101010=>010101=>[2,2,2,1]
[5,3,6,4,7,2,1]=>101011=>110101=>[1,1,2,2,1]
[5,3,6,7,1,2,4]=>100100=>001001=>[3,3,1]
[5,3,6,7,1,4,2]=>100101=>101001=>[1,2,3,1]
[5,3,6,7,2,1,4]=>100110=>011001=>[2,1,3,1]
[5,3,6,7,2,4,1]=>100101=>101001=>[1,2,3,1]
[5,3,6,7,4,1,2]=>100110=>011001=>[2,1,3,1]
[5,3,6,7,4,2,1]=>100111=>111001=>[1,1,1,3,1]
[5,3,7,1,2,4,6]=>101000=>000101=>[4,2,1]
[5,3,7,1,2,6,4]=>101001=>100101=>[1,3,2,1]
[5,3,7,1,4,2,6]=>101010=>010101=>[2,2,2,1]
[5,3,7,1,4,6,2]=>101001=>100101=>[1,3,2,1]
[5,3,7,1,6,2,4]=>101010=>010101=>[2,2,2,1]
[5,3,7,1,6,4,2]=>101011=>110101=>[1,1,2,2,1]
[5,3,7,2,1,4,6]=>101100=>001101=>[3,1,2,1]
[5,3,7,2,1,6,4]=>101101=>101101=>[1,2,1,2,1]
[5,3,7,2,4,1,6]=>101010=>010101=>[2,2,2,1]
[5,3,7,2,4,6,1]=>101001=>100101=>[1,3,2,1]
[5,3,7,2,6,1,4]=>101010=>010101=>[2,2,2,1]
[5,3,7,2,6,4,1]=>101011=>110101=>[1,1,2,2,1]
[5,3,7,4,1,2,6]=>101100=>001101=>[3,1,2,1]
[5,3,7,4,1,6,2]=>101101=>101101=>[1,2,1,2,1]
[5,3,7,4,2,1,6]=>101110=>011101=>[2,1,1,2,1]
[5,3,7,4,2,6,1]=>101101=>101101=>[1,2,1,2,1]
[5,3,7,4,6,1,2]=>101010=>010101=>[2,2,2,1]
[5,3,7,4,6,2,1]=>101011=>110101=>[1,1,2,2,1]
[5,3,7,6,1,2,4]=>101100=>001101=>[3,1,2,1]
[5,3,7,6,1,4,2]=>101101=>101101=>[1,2,1,2,1]
[5,3,7,6,2,1,4]=>101110=>011101=>[2,1,1,2,1]
[5,3,7,6,2,4,1]=>101101=>101101=>[1,2,1,2,1]
[5,3,7,6,4,1,2]=>101110=>011101=>[2,1,1,2,1]
[5,3,7,6,4,2,1]=>101111=>111101=>[1,1,1,1,2,1]
[5,4,1,2,3,6,7]=>110000=>000011=>[5,1,1]
[5,4,1,2,3,7,6]=>110001=>100011=>[1,4,1,1]
[5,4,1,2,6,3,7]=>110010=>010011=>[2,3,1,1]
[5,4,1,2,6,7,3]=>110001=>100011=>[1,4,1,1]
[5,4,1,2,7,3,6]=>110010=>010011=>[2,3,1,1]
[5,4,1,2,7,6,3]=>110011=>110011=>[1,1,3,1,1]
[5,4,1,3,2,6,7]=>110100=>001011=>[3,2,1,1]
[5,4,1,3,2,7,6]=>110101=>101011=>[1,2,2,1,1]
[5,4,1,3,6,2,7]=>110010=>010011=>[2,3,1,1]
[5,4,1,3,6,7,2]=>110001=>100011=>[1,4,1,1]
[5,4,1,3,7,2,6]=>110010=>010011=>[2,3,1,1]
[5,4,1,3,7,6,2]=>110011=>110011=>[1,1,3,1,1]
[5,4,1,6,2,3,7]=>110100=>001011=>[3,2,1,1]
[5,4,1,6,2,7,3]=>110101=>101011=>[1,2,2,1,1]
[5,4,1,6,3,2,7]=>110110=>011011=>[2,1,2,1,1]
[5,4,1,6,3,7,2]=>110101=>101011=>[1,2,2,1,1]
[5,4,1,6,7,2,3]=>110010=>010011=>[2,3,1,1]
[5,4,1,6,7,3,2]=>110011=>110011=>[1,1,3,1,1]
[5,4,1,7,2,3,6]=>110100=>001011=>[3,2,1,1]
[5,4,1,7,2,6,3]=>110101=>101011=>[1,2,2,1,1]
[5,4,1,7,3,2,6]=>110110=>011011=>[2,1,2,1,1]
[5,4,1,7,3,6,2]=>110101=>101011=>[1,2,2,1,1]
[5,4,1,7,6,2,3]=>110110=>011011=>[2,1,2,1,1]
[5,4,1,7,6,3,2]=>110111=>111011=>[1,1,1,2,1,1]
[5,4,2,1,3,6,7]=>111000=>000111=>[4,1,1,1]
[5,4,2,1,3,7,6]=>111001=>100111=>[1,3,1,1,1]
[5,4,2,1,6,3,7]=>111010=>010111=>[2,2,1,1,1]
[5,4,2,1,6,7,3]=>111001=>100111=>[1,3,1,1,1]
[5,4,2,1,7,3,6]=>111010=>010111=>[2,2,1,1,1]
[5,4,2,1,7,6,3]=>111011=>110111=>[1,1,2,1,1,1]
[5,4,2,3,1,6,7]=>110100=>001011=>[3,2,1,1]
[5,4,2,3,1,7,6]=>110101=>101011=>[1,2,2,1,1]
[5,4,2,3,6,1,7]=>110010=>010011=>[2,3,1,1]
[5,4,2,3,6,7,1]=>110001=>100011=>[1,4,1,1]
[5,4,2,3,7,1,6]=>110010=>010011=>[2,3,1,1]
[5,4,2,3,7,6,1]=>110011=>110011=>[1,1,3,1,1]
[5,4,2,6,1,3,7]=>110100=>001011=>[3,2,1,1]
[5,4,2,6,1,7,3]=>110101=>101011=>[1,2,2,1,1]
[5,4,2,6,3,1,7]=>110110=>011011=>[2,1,2,1,1]
[5,4,2,6,3,7,1]=>110101=>101011=>[1,2,2,1,1]
[5,4,2,6,7,1,3]=>110010=>010011=>[2,3,1,1]
[5,4,2,6,7,3,1]=>110011=>110011=>[1,1,3,1,1]
[5,4,2,7,1,3,6]=>110100=>001011=>[3,2,1,1]
[5,4,2,7,1,6,3]=>110101=>101011=>[1,2,2,1,1]
[5,4,2,7,3,1,6]=>110110=>011011=>[2,1,2,1,1]
[5,4,2,7,3,6,1]=>110101=>101011=>[1,2,2,1,1]
[5,4,2,7,6,1,3]=>110110=>011011=>[2,1,2,1,1]
[5,4,2,7,6,3,1]=>110111=>111011=>[1,1,1,2,1,1]
[5,4,3,1,2,6,7]=>111000=>000111=>[4,1,1,1]
[5,4,3,1,2,7,6]=>111001=>100111=>[1,3,1,1,1]
[5,4,3,1,6,2,7]=>111010=>010111=>[2,2,1,1,1]
[5,4,3,1,6,7,2]=>111001=>100111=>[1,3,1,1,1]
[5,4,3,1,7,2,6]=>111010=>010111=>[2,2,1,1,1]
[5,4,3,1,7,6,2]=>111011=>110111=>[1,1,2,1,1,1]
[5,4,3,2,1,6,7]=>111100=>001111=>[3,1,1,1,1]
[5,4,3,2,1,7,6]=>111101=>101111=>[1,2,1,1,1,1]
[5,4,3,2,6,1,7]=>111010=>010111=>[2,2,1,1,1]
[5,4,3,2,6,7,1]=>111001=>100111=>[1,3,1,1,1]
[5,4,3,2,7,1,6]=>111010=>010111=>[2,2,1,1,1]
[5,4,3,2,7,6,1]=>111011=>110111=>[1,1,2,1,1,1]
[5,4,3,6,1,2,7]=>110100=>001011=>[3,2,1,1]
[5,4,3,6,1,7,2]=>110101=>101011=>[1,2,2,1,1]
[5,4,3,6,2,1,7]=>110110=>011011=>[2,1,2,1,1]
[5,4,3,6,2,7,1]=>110101=>101011=>[1,2,2,1,1]
[5,4,3,6,7,1,2]=>110010=>010011=>[2,3,1,1]
[5,4,3,6,7,2,1]=>110011=>110011=>[1,1,3,1,1]
[5,4,3,7,1,2,6]=>110100=>001011=>[3,2,1,1]
[5,4,3,7,1,6,2]=>110101=>101011=>[1,2,2,1,1]
[5,4,3,7,2,1,6]=>110110=>011011=>[2,1,2,1,1]
[5,4,3,7,2,6,1]=>110101=>101011=>[1,2,2,1,1]
[5,4,3,7,6,1,2]=>110110=>011011=>[2,1,2,1,1]
[5,4,3,7,6,2,1]=>110111=>111011=>[1,1,1,2,1,1]
[5,4,6,1,2,3,7]=>101000=>000101=>[4,2,1]
[5,4,6,1,2,7,3]=>101001=>100101=>[1,3,2,1]
[5,4,6,1,3,2,7]=>101010=>010101=>[2,2,2,1]
[5,4,6,1,3,7,2]=>101001=>100101=>[1,3,2,1]
[5,4,6,1,7,2,3]=>101010=>010101=>[2,2,2,1]
[5,4,6,1,7,3,2]=>101011=>110101=>[1,1,2,2,1]
[5,4,6,2,1,3,7]=>101100=>001101=>[3,1,2,1]
[5,4,6,2,1,7,3]=>101101=>101101=>[1,2,1,2,1]
[5,4,6,2,3,1,7]=>101010=>010101=>[2,2,2,1]
[5,4,6,2,3,7,1]=>101001=>100101=>[1,3,2,1]
[5,4,6,2,7,1,3]=>101010=>010101=>[2,2,2,1]
[5,4,6,2,7,3,1]=>101011=>110101=>[1,1,2,2,1]
[5,4,6,3,1,2,7]=>101100=>001101=>[3,1,2,1]
[5,4,6,3,1,7,2]=>101101=>101101=>[1,2,1,2,1]
[5,4,6,3,2,1,7]=>101110=>011101=>[2,1,1,2,1]
[5,4,6,3,2,7,1]=>101101=>101101=>[1,2,1,2,1]
[5,4,6,3,7,1,2]=>101010=>010101=>[2,2,2,1]
[5,4,6,3,7,2,1]=>101011=>110101=>[1,1,2,2,1]
[5,4,6,7,1,2,3]=>100100=>001001=>[3,3,1]
[5,4,6,7,1,3,2]=>100101=>101001=>[1,2,3,1]
[5,4,6,7,2,1,3]=>100110=>011001=>[2,1,3,1]
[5,4,6,7,2,3,1]=>100101=>101001=>[1,2,3,1]
[5,4,6,7,3,1,2]=>100110=>011001=>[2,1,3,1]
[5,4,6,7,3,2,1]=>100111=>111001=>[1,1,1,3,1]
[5,4,7,1,2,3,6]=>101000=>000101=>[4,2,1]
[5,4,7,1,2,6,3]=>101001=>100101=>[1,3,2,1]
[5,4,7,1,3,2,6]=>101010=>010101=>[2,2,2,1]
[5,4,7,1,3,6,2]=>101001=>100101=>[1,3,2,1]
[5,4,7,1,6,2,3]=>101010=>010101=>[2,2,2,1]
[5,4,7,1,6,3,2]=>101011=>110101=>[1,1,2,2,1]
[5,4,7,2,1,3,6]=>101100=>001101=>[3,1,2,1]
[5,4,7,2,1,6,3]=>101101=>101101=>[1,2,1,2,1]
[5,4,7,2,3,1,6]=>101010=>010101=>[2,2,2,1]
[5,4,7,2,3,6,1]=>101001=>100101=>[1,3,2,1]
[5,4,7,2,6,1,3]=>101010=>010101=>[2,2,2,1]
[5,4,7,2,6,3,1]=>101011=>110101=>[1,1,2,2,1]
[5,4,7,3,1,2,6]=>101100=>001101=>[3,1,2,1]
[5,4,7,3,1,6,2]=>101101=>101101=>[1,2,1,2,1]
[5,4,7,3,2,1,6]=>101110=>011101=>[2,1,1,2,1]
[5,4,7,3,2,6,1]=>101101=>101101=>[1,2,1,2,1]
[5,4,7,3,6,1,2]=>101010=>010101=>[2,2,2,1]
[5,4,7,3,6,2,1]=>101011=>110101=>[1,1,2,2,1]
[5,4,7,6,1,2,3]=>101100=>001101=>[3,1,2,1]
[5,4,7,6,1,3,2]=>101101=>101101=>[1,2,1,2,1]
[5,4,7,6,2,1,3]=>101110=>011101=>[2,1,1,2,1]
[5,4,7,6,2,3,1]=>101101=>101101=>[1,2,1,2,1]
[5,4,7,6,3,1,2]=>101110=>011101=>[2,1,1,2,1]
[5,4,7,6,3,2,1]=>101111=>111101=>[1,1,1,1,2,1]
[5,6,1,2,3,4,7]=>010000=>000010=>[5,2]
[5,6,1,2,3,7,4]=>010001=>100010=>[1,4,2]
[5,6,1,2,4,3,7]=>010010=>010010=>[2,3,2]
[5,6,1,2,4,7,3]=>010001=>100010=>[1,4,2]
[5,6,1,2,7,3,4]=>010010=>010010=>[2,3,2]
[5,6,1,2,7,4,3]=>010011=>110010=>[1,1,3,2]
[5,6,1,3,2,4,7]=>010100=>001010=>[3,2,2]
[5,6,1,3,2,7,4]=>010101=>101010=>[1,2,2,2]
[5,6,1,3,4,2,7]=>010010=>010010=>[2,3,2]
[5,6,1,3,4,7,2]=>010001=>100010=>[1,4,2]
[5,6,1,3,7,2,4]=>010010=>010010=>[2,3,2]
[5,6,1,3,7,4,2]=>010011=>110010=>[1,1,3,2]
[5,6,1,4,2,3,7]=>010100=>001010=>[3,2,2]
[5,6,1,4,2,7,3]=>010101=>101010=>[1,2,2,2]
[5,6,1,4,3,2,7]=>010110=>011010=>[2,1,2,2]
[5,6,1,4,3,7,2]=>010101=>101010=>[1,2,2,2]
[5,6,1,4,7,2,3]=>010010=>010010=>[2,3,2]
[5,6,1,4,7,3,2]=>010011=>110010=>[1,1,3,2]
[5,6,1,7,2,3,4]=>010100=>001010=>[3,2,2]
[5,6,1,7,2,4,3]=>010101=>101010=>[1,2,2,2]
[5,6,1,7,3,2,4]=>010110=>011010=>[2,1,2,2]
[5,6,1,7,3,4,2]=>010101=>101010=>[1,2,2,2]
[5,6,1,7,4,2,3]=>010110=>011010=>[2,1,2,2]
[5,6,1,7,4,3,2]=>010111=>111010=>[1,1,1,2,2]
[5,6,2,1,3,4,7]=>011000=>000110=>[4,1,2]
[5,6,2,1,3,7,4]=>011001=>100110=>[1,3,1,2]
[5,6,2,1,4,3,7]=>011010=>010110=>[2,2,1,2]
[5,6,2,1,4,7,3]=>011001=>100110=>[1,3,1,2]
[5,6,2,1,7,3,4]=>011010=>010110=>[2,2,1,2]
[5,6,2,1,7,4,3]=>011011=>110110=>[1,1,2,1,2]
[5,6,2,3,1,4,7]=>010100=>001010=>[3,2,2]
[5,6,2,3,1,7,4]=>010101=>101010=>[1,2,2,2]
[5,6,2,3,4,1,7]=>010010=>010010=>[2,3,2]
[5,6,2,3,4,7,1]=>010001=>100010=>[1,4,2]
[5,6,2,3,7,1,4]=>010010=>010010=>[2,3,2]
[5,6,2,3,7,4,1]=>010011=>110010=>[1,1,3,2]
[5,6,2,4,1,3,7]=>010100=>001010=>[3,2,2]
[5,6,2,4,1,7,3]=>010101=>101010=>[1,2,2,2]
[5,6,2,4,3,1,7]=>010110=>011010=>[2,1,2,2]
[5,6,2,4,3,7,1]=>010101=>101010=>[1,2,2,2]
[5,6,2,4,7,1,3]=>010010=>010010=>[2,3,2]
[5,6,2,4,7,3,1]=>010011=>110010=>[1,1,3,2]
[5,6,2,7,1,3,4]=>010100=>001010=>[3,2,2]
[5,6,2,7,1,4,3]=>010101=>101010=>[1,2,2,2]
[5,6,2,7,3,1,4]=>010110=>011010=>[2,1,2,2]
[5,6,2,7,3,4,1]=>010101=>101010=>[1,2,2,2]
[5,6,2,7,4,1,3]=>010110=>011010=>[2,1,2,2]
[5,6,2,7,4,3,1]=>010111=>111010=>[1,1,1,2,2]
[5,6,3,1,2,4,7]=>011000=>000110=>[4,1,2]
[5,6,3,1,2,7,4]=>011001=>100110=>[1,3,1,2]
[5,6,3,1,4,2,7]=>011010=>010110=>[2,2,1,2]
[5,6,3,1,4,7,2]=>011001=>100110=>[1,3,1,2]
[5,6,3,1,7,2,4]=>011010=>010110=>[2,2,1,2]
[5,6,3,1,7,4,2]=>011011=>110110=>[1,1,2,1,2]
[5,6,3,2,1,4,7]=>011100=>001110=>[3,1,1,2]
[5,6,3,2,1,7,4]=>011101=>101110=>[1,2,1,1,2]
[5,6,3,2,4,1,7]=>011010=>010110=>[2,2,1,2]
[5,6,3,2,4,7,1]=>011001=>100110=>[1,3,1,2]
[5,6,3,2,7,1,4]=>011010=>010110=>[2,2,1,2]
[5,6,3,2,7,4,1]=>011011=>110110=>[1,1,2,1,2]
[5,6,3,4,1,2,7]=>010100=>001010=>[3,2,2]
[5,6,3,4,1,7,2]=>010101=>101010=>[1,2,2,2]
[5,6,3,4,2,1,7]=>010110=>011010=>[2,1,2,2]
[5,6,3,4,2,7,1]=>010101=>101010=>[1,2,2,2]
[5,6,3,4,7,1,2]=>010010=>010010=>[2,3,2]
[5,6,3,4,7,2,1]=>010011=>110010=>[1,1,3,2]
[5,6,3,7,1,2,4]=>010100=>001010=>[3,2,2]
[5,6,3,7,1,4,2]=>010101=>101010=>[1,2,2,2]
[5,6,3,7,2,1,4]=>010110=>011010=>[2,1,2,2]
[5,6,3,7,2,4,1]=>010101=>101010=>[1,2,2,2]
[5,6,3,7,4,1,2]=>010110=>011010=>[2,1,2,2]
[5,6,3,7,4,2,1]=>010111=>111010=>[1,1,1,2,2]
[5,6,4,1,2,3,7]=>011000=>000110=>[4,1,2]
[5,6,4,1,2,7,3]=>011001=>100110=>[1,3,1,2]
[5,6,4,1,3,2,7]=>011010=>010110=>[2,2,1,2]
[5,6,4,1,3,7,2]=>011001=>100110=>[1,3,1,2]
[5,6,4,1,7,2,3]=>011010=>010110=>[2,2,1,2]
[5,6,4,1,7,3,2]=>011011=>110110=>[1,1,2,1,2]
[5,6,4,2,1,3,7]=>011100=>001110=>[3,1,1,2]
[5,6,4,2,1,7,3]=>011101=>101110=>[1,2,1,1,2]
[5,6,4,2,3,1,7]=>011010=>010110=>[2,2,1,2]
[5,6,4,2,3,7,1]=>011001=>100110=>[1,3,1,2]
[5,6,4,2,7,1,3]=>011010=>010110=>[2,2,1,2]
[5,6,4,2,7,3,1]=>011011=>110110=>[1,1,2,1,2]
[5,6,4,3,1,2,7]=>011100=>001110=>[3,1,1,2]
[5,6,4,3,1,7,2]=>011101=>101110=>[1,2,1,1,2]
[5,6,4,3,2,1,7]=>011110=>011110=>[2,1,1,1,2]
[5,6,4,3,2,7,1]=>011101=>101110=>[1,2,1,1,2]
[5,6,4,3,7,1,2]=>011010=>010110=>[2,2,1,2]
[5,6,4,3,7,2,1]=>011011=>110110=>[1,1,2,1,2]
[5,6,4,7,1,2,3]=>010100=>001010=>[3,2,2]
[5,6,4,7,1,3,2]=>010101=>101010=>[1,2,2,2]
[5,6,4,7,2,1,3]=>010110=>011010=>[2,1,2,2]
[5,6,4,7,2,3,1]=>010101=>101010=>[1,2,2,2]
[5,6,4,7,3,1,2]=>010110=>011010=>[2,1,2,2]
[5,6,4,7,3,2,1]=>010111=>111010=>[1,1,1,2,2]
[5,6,7,1,2,3,4]=>001000=>000100=>[4,3]
[5,6,7,1,2,4,3]=>001001=>100100=>[1,3,3]
[5,6,7,1,3,2,4]=>001010=>010100=>[2,2,3]
[5,6,7,1,3,4,2]=>001001=>100100=>[1,3,3]
[5,6,7,1,4,2,3]=>001010=>010100=>[2,2,3]
[5,6,7,1,4,3,2]=>001011=>110100=>[1,1,2,3]
[5,6,7,2,1,3,4]=>001100=>001100=>[3,1,3]
[5,6,7,2,1,4,3]=>001101=>101100=>[1,2,1,3]
[5,6,7,2,3,1,4]=>001010=>010100=>[2,2,3]
[5,6,7,2,3,4,1]=>001001=>100100=>[1,3,3]
[5,6,7,2,4,1,3]=>001010=>010100=>[2,2,3]
[5,6,7,2,4,3,1]=>001011=>110100=>[1,1,2,3]
[5,6,7,3,1,2,4]=>001100=>001100=>[3,1,3]
[5,6,7,3,1,4,2]=>001101=>101100=>[1,2,1,3]
[5,6,7,3,2,1,4]=>001110=>011100=>[2,1,1,3]
[5,6,7,3,2,4,1]=>001101=>101100=>[1,2,1,3]
[5,6,7,3,4,1,2]=>001010=>010100=>[2,2,3]
[5,6,7,3,4,2,1]=>001011=>110100=>[1,1,2,3]
[5,6,7,4,1,2,3]=>001100=>001100=>[3,1,3]
[5,6,7,4,1,3,2]=>001101=>101100=>[1,2,1,3]
[5,6,7,4,2,1,3]=>001110=>011100=>[2,1,1,3]
[5,6,7,4,2,3,1]=>001101=>101100=>[1,2,1,3]
[5,6,7,4,3,1,2]=>001110=>011100=>[2,1,1,3]
[5,6,7,4,3,2,1]=>001111=>111100=>[1,1,1,1,3]
[5,7,1,2,3,4,6]=>010000=>000010=>[5,2]
[5,7,1,2,3,6,4]=>010001=>100010=>[1,4,2]
[5,7,1,2,4,3,6]=>010010=>010010=>[2,3,2]
[5,7,1,2,4,6,3]=>010001=>100010=>[1,4,2]
[5,7,1,2,6,3,4]=>010010=>010010=>[2,3,2]
[5,7,1,2,6,4,3]=>010011=>110010=>[1,1,3,2]
[5,7,1,3,2,4,6]=>010100=>001010=>[3,2,2]
[5,7,1,3,2,6,4]=>010101=>101010=>[1,2,2,2]
[5,7,1,3,4,2,6]=>010010=>010010=>[2,3,2]
[5,7,1,3,4,6,2]=>010001=>100010=>[1,4,2]
[5,7,1,3,6,2,4]=>010010=>010010=>[2,3,2]
[5,7,1,3,6,4,2]=>010011=>110010=>[1,1,3,2]
[5,7,1,4,2,3,6]=>010100=>001010=>[3,2,2]
[5,7,1,4,2,6,3]=>010101=>101010=>[1,2,2,2]
[5,7,1,4,3,2,6]=>010110=>011010=>[2,1,2,2]
[5,7,1,4,3,6,2]=>010101=>101010=>[1,2,2,2]
[5,7,1,4,6,2,3]=>010010=>010010=>[2,3,2]
[5,7,1,4,6,3,2]=>010011=>110010=>[1,1,3,2]
[5,7,1,6,2,3,4]=>010100=>001010=>[3,2,2]
[5,7,1,6,2,4,3]=>010101=>101010=>[1,2,2,2]
[5,7,1,6,3,2,4]=>010110=>011010=>[2,1,2,2]
[5,7,1,6,3,4,2]=>010101=>101010=>[1,2,2,2]
[5,7,1,6,4,2,3]=>010110=>011010=>[2,1,2,2]
[5,7,1,6,4,3,2]=>010111=>111010=>[1,1,1,2,2]
[5,7,2,1,3,4,6]=>011000=>000110=>[4,1,2]
[5,7,2,1,3,6,4]=>011001=>100110=>[1,3,1,2]
[5,7,2,1,4,3,6]=>011010=>010110=>[2,2,1,2]
[5,7,2,1,4,6,3]=>011001=>100110=>[1,3,1,2]
[5,7,2,1,6,3,4]=>011010=>010110=>[2,2,1,2]
[5,7,2,1,6,4,3]=>011011=>110110=>[1,1,2,1,2]
[5,7,2,3,1,4,6]=>010100=>001010=>[3,2,2]
[5,7,2,3,1,6,4]=>010101=>101010=>[1,2,2,2]
[5,7,2,3,4,1,6]=>010010=>010010=>[2,3,2]
[5,7,2,3,4,6,1]=>010001=>100010=>[1,4,2]
[5,7,2,3,6,1,4]=>010010=>010010=>[2,3,2]
[5,7,2,3,6,4,1]=>010011=>110010=>[1,1,3,2]
[5,7,2,4,1,3,6]=>010100=>001010=>[3,2,2]
[5,7,2,4,1,6,3]=>010101=>101010=>[1,2,2,2]
[5,7,2,4,3,1,6]=>010110=>011010=>[2,1,2,2]
[5,7,2,4,3,6,1]=>010101=>101010=>[1,2,2,2]
[5,7,2,4,6,1,3]=>010010=>010010=>[2,3,2]
[5,7,2,4,6,3,1]=>010011=>110010=>[1,1,3,2]
[5,7,2,6,1,3,4]=>010100=>001010=>[3,2,2]
[5,7,2,6,1,4,3]=>010101=>101010=>[1,2,2,2]
[5,7,2,6,3,1,4]=>010110=>011010=>[2,1,2,2]
[5,7,2,6,3,4,1]=>010101=>101010=>[1,2,2,2]
[5,7,2,6,4,1,3]=>010110=>011010=>[2,1,2,2]
[5,7,2,6,4,3,1]=>010111=>111010=>[1,1,1,2,2]
[5,7,3,1,2,4,6]=>011000=>000110=>[4,1,2]
[5,7,3,1,2,6,4]=>011001=>100110=>[1,3,1,2]
[5,7,3,1,4,2,6]=>011010=>010110=>[2,2,1,2]
[5,7,3,1,4,6,2]=>011001=>100110=>[1,3,1,2]
[5,7,3,1,6,2,4]=>011010=>010110=>[2,2,1,2]
[5,7,3,1,6,4,2]=>011011=>110110=>[1,1,2,1,2]
[5,7,3,2,1,4,6]=>011100=>001110=>[3,1,1,2]
[5,7,3,2,1,6,4]=>011101=>101110=>[1,2,1,1,2]
[5,7,3,2,4,1,6]=>011010=>010110=>[2,2,1,2]
[5,7,3,2,4,6,1]=>011001=>100110=>[1,3,1,2]
[5,7,3,2,6,1,4]=>011010=>010110=>[2,2,1,2]
[5,7,3,2,6,4,1]=>011011=>110110=>[1,1,2,1,2]
[5,7,3,4,1,2,6]=>010100=>001010=>[3,2,2]
[5,7,3,4,1,6,2]=>010101=>101010=>[1,2,2,2]
[5,7,3,4,2,1,6]=>010110=>011010=>[2,1,2,2]
[5,7,3,4,2,6,1]=>010101=>101010=>[1,2,2,2]
[5,7,3,4,6,1,2]=>010010=>010010=>[2,3,2]
[5,7,3,4,6,2,1]=>010011=>110010=>[1,1,3,2]
[5,7,3,6,1,2,4]=>010100=>001010=>[3,2,2]
[5,7,3,6,1,4,2]=>010101=>101010=>[1,2,2,2]
[5,7,3,6,2,1,4]=>010110=>011010=>[2,1,2,2]
[5,7,3,6,2,4,1]=>010101=>101010=>[1,2,2,2]
[5,7,3,6,4,1,2]=>010110=>011010=>[2,1,2,2]
[5,7,3,6,4,2,1]=>010111=>111010=>[1,1,1,2,2]
[5,7,4,1,2,3,6]=>011000=>000110=>[4,1,2]
[5,7,4,1,2,6,3]=>011001=>100110=>[1,3,1,2]
[5,7,4,1,3,2,6]=>011010=>010110=>[2,2,1,2]
[5,7,4,1,3,6,2]=>011001=>100110=>[1,3,1,2]
[5,7,4,1,6,2,3]=>011010=>010110=>[2,2,1,2]
[5,7,4,1,6,3,2]=>011011=>110110=>[1,1,2,1,2]
[5,7,4,2,1,3,6]=>011100=>001110=>[3,1,1,2]
[5,7,4,2,1,6,3]=>011101=>101110=>[1,2,1,1,2]
[5,7,4,2,3,1,6]=>011010=>010110=>[2,2,1,2]
[5,7,4,2,3,6,1]=>011001=>100110=>[1,3,1,2]
[5,7,4,2,6,1,3]=>011010=>010110=>[2,2,1,2]
[5,7,4,2,6,3,1]=>011011=>110110=>[1,1,2,1,2]
[5,7,4,3,1,2,6]=>011100=>001110=>[3,1,1,2]
[5,7,4,3,1,6,2]=>011101=>101110=>[1,2,1,1,2]
[5,7,4,3,2,1,6]=>011110=>011110=>[2,1,1,1,2]
[5,7,4,3,2,6,1]=>011101=>101110=>[1,2,1,1,2]
[5,7,4,3,6,1,2]=>011010=>010110=>[2,2,1,2]
[5,7,4,3,6,2,1]=>011011=>110110=>[1,1,2,1,2]
[5,7,4,6,1,2,3]=>010100=>001010=>[3,2,2]
[5,7,4,6,1,3,2]=>010101=>101010=>[1,2,2,2]
[5,7,4,6,2,1,3]=>010110=>011010=>[2,1,2,2]
[5,7,4,6,2,3,1]=>010101=>101010=>[1,2,2,2]
[5,7,4,6,3,1,2]=>010110=>011010=>[2,1,2,2]
[5,7,4,6,3,2,1]=>010111=>111010=>[1,1,1,2,2]
[5,7,6,1,2,3,4]=>011000=>000110=>[4,1,2]
[5,7,6,1,2,4,3]=>011001=>100110=>[1,3,1,2]
[5,7,6,1,3,2,4]=>011010=>010110=>[2,2,1,2]
[5,7,6,1,3,4,2]=>011001=>100110=>[1,3,1,2]
[5,7,6,1,4,2,3]=>011010=>010110=>[2,2,1,2]
[5,7,6,1,4,3,2]=>011011=>110110=>[1,1,2,1,2]
[5,7,6,2,1,3,4]=>011100=>001110=>[3,1,1,2]
[5,7,6,2,1,4,3]=>011101=>101110=>[1,2,1,1,2]
[5,7,6,2,3,1,4]=>011010=>010110=>[2,2,1,2]
[5,7,6,2,3,4,1]=>011001=>100110=>[1,3,1,2]
[5,7,6,2,4,1,3]=>011010=>010110=>[2,2,1,2]
[5,7,6,2,4,3,1]=>011011=>110110=>[1,1,2,1,2]
[5,7,6,3,1,2,4]=>011100=>001110=>[3,1,1,2]
[5,7,6,3,1,4,2]=>011101=>101110=>[1,2,1,1,2]
[5,7,6,3,2,1,4]=>011110=>011110=>[2,1,1,1,2]
[5,7,6,3,2,4,1]=>011101=>101110=>[1,2,1,1,2]
[5,7,6,3,4,1,2]=>011010=>010110=>[2,2,1,2]
[5,7,6,3,4,2,1]=>011011=>110110=>[1,1,2,1,2]
[5,7,6,4,1,2,3]=>011100=>001110=>[3,1,1,2]
[5,7,6,4,1,3,2]=>011101=>101110=>[1,2,1,1,2]
[5,7,6,4,2,1,3]=>011110=>011110=>[2,1,1,1,2]
[5,7,6,4,2,3,1]=>011101=>101110=>[1,2,1,1,2]
[5,7,6,4,3,1,2]=>011110=>011110=>[2,1,1,1,2]
[5,7,6,4,3,2,1]=>011111=>111110=>[1,1,1,1,1,2]
[6,1,2,3,4,5,7]=>100000=>000001=>[6,1]
[6,1,2,3,4,7,5]=>100001=>100001=>[1,5,1]
[6,1,2,3,5,4,7]=>100010=>010001=>[2,4,1]
[6,1,2,3,5,7,4]=>100001=>100001=>[1,5,1]
[6,1,2,3,7,4,5]=>100010=>010001=>[2,4,1]
[6,1,2,3,7,5,4]=>100011=>110001=>[1,1,4,1]
[6,1,2,4,3,5,7]=>100100=>001001=>[3,3,1]
[6,1,2,4,3,7,5]=>100101=>101001=>[1,2,3,1]
[6,1,2,4,5,3,7]=>100010=>010001=>[2,4,1]
[6,1,2,4,5,7,3]=>100001=>100001=>[1,5,1]
[6,1,2,4,7,3,5]=>100010=>010001=>[2,4,1]
[6,1,2,4,7,5,3]=>100011=>110001=>[1,1,4,1]
[6,1,2,5,3,4,7]=>100100=>001001=>[3,3,1]
[6,1,2,5,3,7,4]=>100101=>101001=>[1,2,3,1]
[6,1,2,5,4,3,7]=>100110=>011001=>[2,1,3,1]
[6,1,2,5,4,7,3]=>100101=>101001=>[1,2,3,1]
[6,1,2,5,7,3,4]=>100010=>010001=>[2,4,1]
[6,1,2,5,7,4,3]=>100011=>110001=>[1,1,4,1]
[6,1,2,7,3,4,5]=>100100=>001001=>[3,3,1]
[6,1,2,7,3,5,4]=>100101=>101001=>[1,2,3,1]
[6,1,2,7,4,3,5]=>100110=>011001=>[2,1,3,1]
[6,1,2,7,4,5,3]=>100101=>101001=>[1,2,3,1]
[6,1,2,7,5,3,4]=>100110=>011001=>[2,1,3,1]
[6,1,2,7,5,4,3]=>100111=>111001=>[1,1,1,3,1]
[6,1,3,2,4,5,7]=>101000=>000101=>[4,2,1]
[6,1,3,2,4,7,5]=>101001=>100101=>[1,3,2,1]
[6,1,3,2,5,4,7]=>101010=>010101=>[2,2,2,1]
[6,1,3,2,5,7,4]=>101001=>100101=>[1,3,2,1]
[6,1,3,2,7,4,5]=>101010=>010101=>[2,2,2,1]
[6,1,3,2,7,5,4]=>101011=>110101=>[1,1,2,2,1]
[6,1,3,4,2,5,7]=>100100=>001001=>[3,3,1]
[6,1,3,4,2,7,5]=>100101=>101001=>[1,2,3,1]
[6,1,3,4,5,2,7]=>100010=>010001=>[2,4,1]
[6,1,3,4,5,7,2]=>100001=>100001=>[1,5,1]
[6,1,3,4,7,2,5]=>100010=>010001=>[2,4,1]
[6,1,3,4,7,5,2]=>100011=>110001=>[1,1,4,1]
[6,1,3,5,2,4,7]=>100100=>001001=>[3,3,1]
[6,1,3,5,2,7,4]=>100101=>101001=>[1,2,3,1]
[6,1,3,5,4,2,7]=>100110=>011001=>[2,1,3,1]
[6,1,3,5,4,7,2]=>100101=>101001=>[1,2,3,1]
[6,1,3,5,7,2,4]=>100010=>010001=>[2,4,1]
[6,1,3,5,7,4,2]=>100011=>110001=>[1,1,4,1]
[6,1,3,7,2,4,5]=>100100=>001001=>[3,3,1]
[6,1,3,7,2,5,4]=>100101=>101001=>[1,2,3,1]
[6,1,3,7,4,2,5]=>100110=>011001=>[2,1,3,1]
[6,1,3,7,4,5,2]=>100101=>101001=>[1,2,3,1]
[6,1,3,7,5,2,4]=>100110=>011001=>[2,1,3,1]
[6,1,3,7,5,4,2]=>100111=>111001=>[1,1,1,3,1]
[6,1,4,2,3,5,7]=>101000=>000101=>[4,2,1]
[6,1,4,2,3,7,5]=>101001=>100101=>[1,3,2,1]
[6,1,4,2,5,3,7]=>101010=>010101=>[2,2,2,1]
[6,1,4,2,5,7,3]=>101001=>100101=>[1,3,2,1]
[6,1,4,2,7,3,5]=>101010=>010101=>[2,2,2,1]
[6,1,4,2,7,5,3]=>101011=>110101=>[1,1,2,2,1]
[6,1,4,3,2,5,7]=>101100=>001101=>[3,1,2,1]
[6,1,4,3,2,7,5]=>101101=>101101=>[1,2,1,2,1]
[6,1,4,3,5,2,7]=>101010=>010101=>[2,2,2,1]
[6,1,4,3,5,7,2]=>101001=>100101=>[1,3,2,1]
[6,1,4,3,7,2,5]=>101010=>010101=>[2,2,2,1]
[6,1,4,3,7,5,2]=>101011=>110101=>[1,1,2,2,1]
[6,1,4,5,2,3,7]=>100100=>001001=>[3,3,1]
[6,1,4,5,2,7,3]=>100101=>101001=>[1,2,3,1]
[6,1,4,5,3,2,7]=>100110=>011001=>[2,1,3,1]
[6,1,4,5,3,7,2]=>100101=>101001=>[1,2,3,1]
[6,1,4,5,7,2,3]=>100010=>010001=>[2,4,1]
[6,1,4,5,7,3,2]=>100011=>110001=>[1,1,4,1]
[6,1,4,7,2,3,5]=>100100=>001001=>[3,3,1]
[6,1,4,7,2,5,3]=>100101=>101001=>[1,2,3,1]
[6,1,4,7,3,2,5]=>100110=>011001=>[2,1,3,1]
[6,1,4,7,3,5,2]=>100101=>101001=>[1,2,3,1]
[6,1,4,7,5,2,3]=>100110=>011001=>[2,1,3,1]
[6,1,4,7,5,3,2]=>100111=>111001=>[1,1,1,3,1]
[6,1,5,2,3,4,7]=>101000=>000101=>[4,2,1]
[6,1,5,2,3,7,4]=>101001=>100101=>[1,3,2,1]
[6,1,5,2,4,3,7]=>101010=>010101=>[2,2,2,1]
[6,1,5,2,4,7,3]=>101001=>100101=>[1,3,2,1]
[6,1,5,2,7,3,4]=>101010=>010101=>[2,2,2,1]
[6,1,5,2,7,4,3]=>101011=>110101=>[1,1,2,2,1]
[6,1,5,3,2,4,7]=>101100=>001101=>[3,1,2,1]
[6,1,5,3,2,7,4]=>101101=>101101=>[1,2,1,2,1]
[6,1,5,3,4,2,7]=>101010=>010101=>[2,2,2,1]
[6,1,5,3,4,7,2]=>101001=>100101=>[1,3,2,1]
[6,1,5,3,7,2,4]=>101010=>010101=>[2,2,2,1]
[6,1,5,3,7,4,2]=>101011=>110101=>[1,1,2,2,1]
[6,1,5,4,2,3,7]=>101100=>001101=>[3,1,2,1]
[6,1,5,4,2,7,3]=>101101=>101101=>[1,2,1,2,1]
[6,1,5,4,3,2,7]=>101110=>011101=>[2,1,1,2,1]
[6,1,5,4,3,7,2]=>101101=>101101=>[1,2,1,2,1]
[6,1,5,4,7,2,3]=>101010=>010101=>[2,2,2,1]
[6,1,5,4,7,3,2]=>101011=>110101=>[1,1,2,2,1]
[6,1,5,7,2,3,4]=>100100=>001001=>[3,3,1]
[6,1,5,7,2,4,3]=>100101=>101001=>[1,2,3,1]
[6,1,5,7,3,2,4]=>100110=>011001=>[2,1,3,1]
[6,1,5,7,3,4,2]=>100101=>101001=>[1,2,3,1]
[6,1,5,7,4,2,3]=>100110=>011001=>[2,1,3,1]
[6,1,5,7,4,3,2]=>100111=>111001=>[1,1,1,3,1]
[6,1,7,2,3,4,5]=>101000=>000101=>[4,2,1]
[6,1,7,2,3,5,4]=>101001=>100101=>[1,3,2,1]
[6,1,7,2,4,3,5]=>101010=>010101=>[2,2,2,1]
[6,1,7,2,4,5,3]=>101001=>100101=>[1,3,2,1]
[6,1,7,2,5,3,4]=>101010=>010101=>[2,2,2,1]
[6,1,7,2,5,4,3]=>101011=>110101=>[1,1,2,2,1]
[6,1,7,3,2,4,5]=>101100=>001101=>[3,1,2,1]
[6,1,7,3,2,5,4]=>101101=>101101=>[1,2,1,2,1]
[6,1,7,3,4,2,5]=>101010=>010101=>[2,2,2,1]
[6,1,7,3,4,5,2]=>101001=>100101=>[1,3,2,1]
[6,1,7,3,5,2,4]=>101010=>010101=>[2,2,2,1]
[6,1,7,3,5,4,2]=>101011=>110101=>[1,1,2,2,1]
[6,1,7,4,2,3,5]=>101100=>001101=>[3,1,2,1]
[6,1,7,4,2,5,3]=>101101=>101101=>[1,2,1,2,1]
[6,1,7,4,3,2,5]=>101110=>011101=>[2,1,1,2,1]
[6,1,7,4,3,5,2]=>101101=>101101=>[1,2,1,2,1]
[6,1,7,4,5,2,3]=>101010=>010101=>[2,2,2,1]
[6,1,7,4,5,3,2]=>101011=>110101=>[1,1,2,2,1]
[6,1,7,5,2,3,4]=>101100=>001101=>[3,1,2,1]
[6,1,7,5,2,4,3]=>101101=>101101=>[1,2,1,2,1]
[6,1,7,5,3,2,4]=>101110=>011101=>[2,1,1,2,1]
[6,1,7,5,3,4,2]=>101101=>101101=>[1,2,1,2,1]
[6,1,7,5,4,2,3]=>101110=>011101=>[2,1,1,2,1]
[6,1,7,5,4,3,2]=>101111=>111101=>[1,1,1,1,2,1]
[6,2,1,3,4,5,7]=>110000=>000011=>[5,1,1]
[6,2,1,3,4,7,5]=>110001=>100011=>[1,4,1,1]
[6,2,1,3,5,4,7]=>110010=>010011=>[2,3,1,1]
[6,2,1,3,5,7,4]=>110001=>100011=>[1,4,1,1]
[6,2,1,3,7,4,5]=>110010=>010011=>[2,3,1,1]
[6,2,1,3,7,5,4]=>110011=>110011=>[1,1,3,1,1]
[6,2,1,4,3,5,7]=>110100=>001011=>[3,2,1,1]
[6,2,1,4,3,7,5]=>110101=>101011=>[1,2,2,1,1]
[6,2,1,4,5,3,7]=>110010=>010011=>[2,3,1,1]
[6,2,1,4,5,7,3]=>110001=>100011=>[1,4,1,1]
[6,2,1,4,7,3,5]=>110010=>010011=>[2,3,1,1]
[6,2,1,4,7,5,3]=>110011=>110011=>[1,1,3,1,1]
[6,2,1,5,3,4,7]=>110100=>001011=>[3,2,1,1]
[6,2,1,5,3,7,4]=>110101=>101011=>[1,2,2,1,1]
[6,2,1,5,4,3,7]=>110110=>011011=>[2,1,2,1,1]
[6,2,1,5,4,7,3]=>110101=>101011=>[1,2,2,1,1]
[6,2,1,5,7,3,4]=>110010=>010011=>[2,3,1,1]
[6,2,1,5,7,4,3]=>110011=>110011=>[1,1,3,1,1]
[6,2,1,7,3,4,5]=>110100=>001011=>[3,2,1,1]
[6,2,1,7,3,5,4]=>110101=>101011=>[1,2,2,1,1]
[6,2,1,7,4,3,5]=>110110=>011011=>[2,1,2,1,1]
[6,2,1,7,4,5,3]=>110101=>101011=>[1,2,2,1,1]
[6,2,1,7,5,3,4]=>110110=>011011=>[2,1,2,1,1]
[6,2,1,7,5,4,3]=>110111=>111011=>[1,1,1,2,1,1]
[6,2,3,1,4,5,7]=>101000=>000101=>[4,2,1]
[6,2,3,1,4,7,5]=>101001=>100101=>[1,3,2,1]
[6,2,3,1,5,4,7]=>101010=>010101=>[2,2,2,1]
[6,2,3,1,5,7,4]=>101001=>100101=>[1,3,2,1]
[6,2,3,1,7,4,5]=>101010=>010101=>[2,2,2,1]
[6,2,3,1,7,5,4]=>101011=>110101=>[1,1,2,2,1]
[6,2,3,4,1,5,7]=>100100=>001001=>[3,3,1]
[6,2,3,4,1,7,5]=>100101=>101001=>[1,2,3,1]
[6,2,3,4,5,1,7]=>100010=>010001=>[2,4,1]
[6,2,3,4,5,7,1]=>100001=>100001=>[1,5,1]
[6,2,3,4,7,1,5]=>100010=>010001=>[2,4,1]
[6,2,3,4,7,5,1]=>100011=>110001=>[1,1,4,1]
[6,2,3,5,1,4,7]=>100100=>001001=>[3,3,1]
[6,2,3,5,1,7,4]=>100101=>101001=>[1,2,3,1]
[6,2,3,5,4,1,7]=>100110=>011001=>[2,1,3,1]
[6,2,3,5,4,7,1]=>100101=>101001=>[1,2,3,1]
[6,2,3,5,7,1,4]=>100010=>010001=>[2,4,1]
[6,2,3,5,7,4,1]=>100011=>110001=>[1,1,4,1]
[6,2,3,7,1,4,5]=>100100=>001001=>[3,3,1]
[6,2,3,7,1,5,4]=>100101=>101001=>[1,2,3,1]
[6,2,3,7,4,1,5]=>100110=>011001=>[2,1,3,1]
[6,2,3,7,4,5,1]=>100101=>101001=>[1,2,3,1]
[6,2,3,7,5,1,4]=>100110=>011001=>[2,1,3,1]
[6,2,3,7,5,4,1]=>100111=>111001=>[1,1,1,3,1]
[6,2,4,1,3,5,7]=>101000=>000101=>[4,2,1]
[6,2,4,1,3,7,5]=>101001=>100101=>[1,3,2,1]
[6,2,4,1,5,3,7]=>101010=>010101=>[2,2,2,1]
[6,2,4,1,5,7,3]=>101001=>100101=>[1,3,2,1]
[6,2,4,1,7,3,5]=>101010=>010101=>[2,2,2,1]
[6,2,4,1,7,5,3]=>101011=>110101=>[1,1,2,2,1]
[6,2,4,3,1,5,7]=>101100=>001101=>[3,1,2,1]
[6,2,4,3,1,7,5]=>101101=>101101=>[1,2,1,2,1]
[6,2,4,3,5,1,7]=>101010=>010101=>[2,2,2,1]
[6,2,4,3,5,7,1]=>101001=>100101=>[1,3,2,1]
[6,2,4,3,7,1,5]=>101010=>010101=>[2,2,2,1]
[6,2,4,3,7,5,1]=>101011=>110101=>[1,1,2,2,1]
[6,2,4,5,1,3,7]=>100100=>001001=>[3,3,1]
[6,2,4,5,1,7,3]=>100101=>101001=>[1,2,3,1]
[6,2,4,5,3,1,7]=>100110=>011001=>[2,1,3,1]
[6,2,4,5,3,7,1]=>100101=>101001=>[1,2,3,1]
[6,2,4,5,7,1,3]=>100010=>010001=>[2,4,1]
[6,2,4,5,7,3,1]=>100011=>110001=>[1,1,4,1]
[6,2,4,7,1,3,5]=>100100=>001001=>[3,3,1]
[6,2,4,7,1,5,3]=>100101=>101001=>[1,2,3,1]
[6,2,4,7,3,1,5]=>100110=>011001=>[2,1,3,1]
[6,2,4,7,3,5,1]=>100101=>101001=>[1,2,3,1]
[6,2,4,7,5,1,3]=>100110=>011001=>[2,1,3,1]
[6,2,4,7,5,3,1]=>100111=>111001=>[1,1,1,3,1]
[6,2,5,1,3,4,7]=>101000=>000101=>[4,2,1]
[6,2,5,1,3,7,4]=>101001=>100101=>[1,3,2,1]
[6,2,5,1,4,3,7]=>101010=>010101=>[2,2,2,1]
[6,2,5,1,4,7,3]=>101001=>100101=>[1,3,2,1]
[6,2,5,1,7,3,4]=>101010=>010101=>[2,2,2,1]
[6,2,5,1,7,4,3]=>101011=>110101=>[1,1,2,2,1]
[6,2,5,3,1,4,7]=>101100=>001101=>[3,1,2,1]
[6,2,5,3,1,7,4]=>101101=>101101=>[1,2,1,2,1]
[6,2,5,3,4,1,7]=>101010=>010101=>[2,2,2,1]
[6,2,5,3,4,7,1]=>101001=>100101=>[1,3,2,1]
[6,2,5,3,7,1,4]=>101010=>010101=>[2,2,2,1]
[6,2,5,3,7,4,1]=>101011=>110101=>[1,1,2,2,1]
[6,2,5,4,1,3,7]=>101100=>001101=>[3,1,2,1]
[6,2,5,4,1,7,3]=>101101=>101101=>[1,2,1,2,1]
[6,2,5,4,3,1,7]=>101110=>011101=>[2,1,1,2,1]
[6,2,5,4,3,7,1]=>101101=>101101=>[1,2,1,2,1]
[6,2,5,4,7,1,3]=>101010=>010101=>[2,2,2,1]
[6,2,5,4,7,3,1]=>101011=>110101=>[1,1,2,2,1]
[6,2,5,7,1,3,4]=>100100=>001001=>[3,3,1]
[6,2,5,7,1,4,3]=>100101=>101001=>[1,2,3,1]
[6,2,5,7,3,1,4]=>100110=>011001=>[2,1,3,1]
[6,2,5,7,3,4,1]=>100101=>101001=>[1,2,3,1]
[6,2,5,7,4,1,3]=>100110=>011001=>[2,1,3,1]
[6,2,5,7,4,3,1]=>100111=>111001=>[1,1,1,3,1]
[6,2,7,1,3,4,5]=>101000=>000101=>[4,2,1]
[6,2,7,1,3,5,4]=>101001=>100101=>[1,3,2,1]
[6,2,7,1,4,3,5]=>101010=>010101=>[2,2,2,1]
[6,2,7,1,4,5,3]=>101001=>100101=>[1,3,2,1]
[6,2,7,1,5,3,4]=>101010=>010101=>[2,2,2,1]
[6,2,7,1,5,4,3]=>101011=>110101=>[1,1,2,2,1]
[6,2,7,3,1,4,5]=>101100=>001101=>[3,1,2,1]
[6,2,7,3,1,5,4]=>101101=>101101=>[1,2,1,2,1]
[6,2,7,3,4,1,5]=>101010=>010101=>[2,2,2,1]
[6,2,7,3,4,5,1]=>101001=>100101=>[1,3,2,1]
[6,2,7,3,5,1,4]=>101010=>010101=>[2,2,2,1]
[6,2,7,3,5,4,1]=>101011=>110101=>[1,1,2,2,1]
[6,2,7,4,1,3,5]=>101100=>001101=>[3,1,2,1]
[6,2,7,4,1,5,3]=>101101=>101101=>[1,2,1,2,1]
[6,2,7,4,3,1,5]=>101110=>011101=>[2,1,1,2,1]
[6,2,7,4,3,5,1]=>101101=>101101=>[1,2,1,2,1]
[6,2,7,4,5,1,3]=>101010=>010101=>[2,2,2,1]
[6,2,7,4,5,3,1]=>101011=>110101=>[1,1,2,2,1]
[6,2,7,5,1,3,4]=>101100=>001101=>[3,1,2,1]
[6,2,7,5,1,4,3]=>101101=>101101=>[1,2,1,2,1]
[6,2,7,5,3,1,4]=>101110=>011101=>[2,1,1,2,1]
[6,2,7,5,3,4,1]=>101101=>101101=>[1,2,1,2,1]
[6,2,7,5,4,1,3]=>101110=>011101=>[2,1,1,2,1]
[6,2,7,5,4,3,1]=>101111=>111101=>[1,1,1,1,2,1]
[6,3,1,2,4,5,7]=>110000=>000011=>[5,1,1]
[6,3,1,2,4,7,5]=>110001=>100011=>[1,4,1,1]
[6,3,1,2,5,4,7]=>110010=>010011=>[2,3,1,1]
[6,3,1,2,5,7,4]=>110001=>100011=>[1,4,1,1]
[6,3,1,2,7,4,5]=>110010=>010011=>[2,3,1,1]
[6,3,1,2,7,5,4]=>110011=>110011=>[1,1,3,1,1]
[6,3,1,4,2,5,7]=>110100=>001011=>[3,2,1,1]
[6,3,1,4,2,7,5]=>110101=>101011=>[1,2,2,1,1]
[6,3,1,4,5,2,7]=>110010=>010011=>[2,3,1,1]
[6,3,1,4,5,7,2]=>110001=>100011=>[1,4,1,1]
[6,3,1,4,7,2,5]=>110010=>010011=>[2,3,1,1]
[6,3,1,4,7,5,2]=>110011=>110011=>[1,1,3,1,1]
[6,3,1,5,2,4,7]=>110100=>001011=>[3,2,1,1]
[6,3,1,5,2,7,4]=>110101=>101011=>[1,2,2,1,1]
[6,3,1,5,4,2,7]=>110110=>011011=>[2,1,2,1,1]
[6,3,1,5,4,7,2]=>110101=>101011=>[1,2,2,1,1]
[6,3,1,5,7,2,4]=>110010=>010011=>[2,3,1,1]
[6,3,1,5,7,4,2]=>110011=>110011=>[1,1,3,1,1]
[6,3,1,7,2,4,5]=>110100=>001011=>[3,2,1,1]
[6,3,1,7,2,5,4]=>110101=>101011=>[1,2,2,1,1]
[6,3,1,7,4,2,5]=>110110=>011011=>[2,1,2,1,1]
[6,3,1,7,4,5,2]=>110101=>101011=>[1,2,2,1,1]
[6,3,1,7,5,2,4]=>110110=>011011=>[2,1,2,1,1]
[6,3,1,7,5,4,2]=>110111=>111011=>[1,1,1,2,1,1]
[6,3,2,1,4,5,7]=>111000=>000111=>[4,1,1,1]
[6,3,2,1,4,7,5]=>111001=>100111=>[1,3,1,1,1]
[6,3,2,1,5,4,7]=>111010=>010111=>[2,2,1,1,1]
[6,3,2,1,5,7,4]=>111001=>100111=>[1,3,1,1,1]
[6,3,2,1,7,4,5]=>111010=>010111=>[2,2,1,1,1]
[6,3,2,1,7,5,4]=>111011=>110111=>[1,1,2,1,1,1]
[6,3,2,4,1,5,7]=>110100=>001011=>[3,2,1,1]
[6,3,2,4,1,7,5]=>110101=>101011=>[1,2,2,1,1]
[6,3,2,4,5,1,7]=>110010=>010011=>[2,3,1,1]
[6,3,2,4,5,7,1]=>110001=>100011=>[1,4,1,1]
[6,3,2,4,7,1,5]=>110010=>010011=>[2,3,1,1]
[6,3,2,4,7,5,1]=>110011=>110011=>[1,1,3,1,1]
[6,3,2,5,1,4,7]=>110100=>001011=>[3,2,1,1]
[6,3,2,5,1,7,4]=>110101=>101011=>[1,2,2,1,1]
[6,3,2,5,4,1,7]=>110110=>011011=>[2,1,2,1,1]
[6,3,2,5,4,7,1]=>110101=>101011=>[1,2,2,1,1]
[6,3,2,5,7,1,4]=>110010=>010011=>[2,3,1,1]
[6,3,2,5,7,4,1]=>110011=>110011=>[1,1,3,1,1]
[6,3,2,7,1,4,5]=>110100=>001011=>[3,2,1,1]
[6,3,2,7,1,5,4]=>110101=>101011=>[1,2,2,1,1]
[6,3,2,7,4,1,5]=>110110=>011011=>[2,1,2,1,1]
[6,3,2,7,4,5,1]=>110101=>101011=>[1,2,2,1,1]
[6,3,2,7,5,1,4]=>110110=>011011=>[2,1,2,1,1]
[6,3,2,7,5,4,1]=>110111=>111011=>[1,1,1,2,1,1]
[6,3,4,1,2,5,7]=>101000=>000101=>[4,2,1]
[6,3,4,1,2,7,5]=>101001=>100101=>[1,3,2,1]
[6,3,4,1,5,2,7]=>101010=>010101=>[2,2,2,1]
[6,3,4,1,5,7,2]=>101001=>100101=>[1,3,2,1]
[6,3,4,1,7,2,5]=>101010=>010101=>[2,2,2,1]
[6,3,4,1,7,5,2]=>101011=>110101=>[1,1,2,2,1]
[6,3,4,2,1,5,7]=>101100=>001101=>[3,1,2,1]
[6,3,4,2,1,7,5]=>101101=>101101=>[1,2,1,2,1]
[6,3,4,2,5,1,7]=>101010=>010101=>[2,2,2,1]
[6,3,4,2,5,7,1]=>101001=>100101=>[1,3,2,1]
[6,3,4,2,7,1,5]=>101010=>010101=>[2,2,2,1]
[6,3,4,2,7,5,1]=>101011=>110101=>[1,1,2,2,1]
[6,3,4,5,1,2,7]=>100100=>001001=>[3,3,1]
[6,3,4,5,1,7,2]=>100101=>101001=>[1,2,3,1]
[6,3,4,5,2,1,7]=>100110=>011001=>[2,1,3,1]
[6,3,4,5,2,7,1]=>100101=>101001=>[1,2,3,1]
[6,3,4,5,7,1,2]=>100010=>010001=>[2,4,1]
[6,3,4,5,7,2,1]=>100011=>110001=>[1,1,4,1]
[6,3,4,7,1,2,5]=>100100=>001001=>[3,3,1]
[6,3,4,7,1,5,2]=>100101=>101001=>[1,2,3,1]
[6,3,4,7,2,1,5]=>100110=>011001=>[2,1,3,1]
[6,3,4,7,2,5,1]=>100101=>101001=>[1,2,3,1]
[6,3,4,7,5,1,2]=>100110=>011001=>[2,1,3,1]
[6,3,4,7,5,2,1]=>100111=>111001=>[1,1,1,3,1]
[6,3,5,1,2,4,7]=>101000=>000101=>[4,2,1]
[6,3,5,1,2,7,4]=>101001=>100101=>[1,3,2,1]
[6,3,5,1,4,2,7]=>101010=>010101=>[2,2,2,1]
[6,3,5,1,4,7,2]=>101001=>100101=>[1,3,2,1]
[6,3,5,1,7,2,4]=>101010=>010101=>[2,2,2,1]
[6,3,5,1,7,4,2]=>101011=>110101=>[1,1,2,2,1]
[6,3,5,2,1,4,7]=>101100=>001101=>[3,1,2,1]
[6,3,5,2,1,7,4]=>101101=>101101=>[1,2,1,2,1]
[6,3,5,2,4,1,7]=>101010=>010101=>[2,2,2,1]
[6,3,5,2,4,7,1]=>101001=>100101=>[1,3,2,1]
[6,3,5,2,7,1,4]=>101010=>010101=>[2,2,2,1]
[6,3,5,2,7,4,1]=>101011=>110101=>[1,1,2,2,1]
[6,3,5,4,1,2,7]=>101100=>001101=>[3,1,2,1]
[6,3,5,4,1,7,2]=>101101=>101101=>[1,2,1,2,1]
[6,3,5,4,2,1,7]=>101110=>011101=>[2,1,1,2,1]
[6,3,5,4,2,7,1]=>101101=>101101=>[1,2,1,2,1]
[6,3,5,4,7,1,2]=>101010=>010101=>[2,2,2,1]
[6,3,5,4,7,2,1]=>101011=>110101=>[1,1,2,2,1]
[6,3,5,7,1,2,4]=>100100=>001001=>[3,3,1]
[6,3,5,7,1,4,2]=>100101=>101001=>[1,2,3,1]
[6,3,5,7,2,1,4]=>100110=>011001=>[2,1,3,1]
[6,3,5,7,2,4,1]=>100101=>101001=>[1,2,3,1]
[6,3,5,7,4,1,2]=>100110=>011001=>[2,1,3,1]
[6,3,5,7,4,2,1]=>100111=>111001=>[1,1,1,3,1]
[6,3,7,1,2,4,5]=>101000=>000101=>[4,2,1]
[6,3,7,1,2,5,4]=>101001=>100101=>[1,3,2,1]
[6,3,7,1,4,2,5]=>101010=>010101=>[2,2,2,1]
[6,3,7,1,4,5,2]=>101001=>100101=>[1,3,2,1]
[6,3,7,1,5,2,4]=>101010=>010101=>[2,2,2,1]
[6,3,7,1,5,4,2]=>101011=>110101=>[1,1,2,2,1]
[6,3,7,2,1,4,5]=>101100=>001101=>[3,1,2,1]
[6,3,7,2,1,5,4]=>101101=>101101=>[1,2,1,2,1]
[6,3,7,2,4,1,5]=>101010=>010101=>[2,2,2,1]
[6,3,7,2,4,5,1]=>101001=>100101=>[1,3,2,1]
[6,3,7,2,5,1,4]=>101010=>010101=>[2,2,2,1]
[6,3,7,2,5,4,1]=>101011=>110101=>[1,1,2,2,1]
[6,3,7,4,1,2,5]=>101100=>001101=>[3,1,2,1]
[6,3,7,4,1,5,2]=>101101=>101101=>[1,2,1,2,1]
[6,3,7,4,2,1,5]=>101110=>011101=>[2,1,1,2,1]
[6,3,7,4,2,5,1]=>101101=>101101=>[1,2,1,2,1]
[6,3,7,4,5,1,2]=>101010=>010101=>[2,2,2,1]
[6,3,7,4,5,2,1]=>101011=>110101=>[1,1,2,2,1]
[6,3,7,5,1,2,4]=>101100=>001101=>[3,1,2,1]
[6,3,7,5,1,4,2]=>101101=>101101=>[1,2,1,2,1]
[6,3,7,5,2,1,4]=>101110=>011101=>[2,1,1,2,1]
[6,3,7,5,2,4,1]=>101101=>101101=>[1,2,1,2,1]
[6,3,7,5,4,1,2]=>101110=>011101=>[2,1,1,2,1]
[6,3,7,5,4,2,1]=>101111=>111101=>[1,1,1,1,2,1]
[6,4,1,2,3,5,7]=>110000=>000011=>[5,1,1]
[6,4,1,2,3,7,5]=>110001=>100011=>[1,4,1,1]
[6,4,1,2,5,3,7]=>110010=>010011=>[2,3,1,1]
[6,4,1,2,5,7,3]=>110001=>100011=>[1,4,1,1]
[6,4,1,2,7,3,5]=>110010=>010011=>[2,3,1,1]
[6,4,1,2,7,5,3]=>110011=>110011=>[1,1,3,1,1]
[6,4,1,3,2,5,7]=>110100=>001011=>[3,2,1,1]
[6,4,1,3,2,7,5]=>110101=>101011=>[1,2,2,1,1]
[6,4,1,3,5,2,7]=>110010=>010011=>[2,3,1,1]
[6,4,1,3,5,7,2]=>110001=>100011=>[1,4,1,1]
[6,4,1,3,7,2,5]=>110010=>010011=>[2,3,1,1]
[6,4,1,3,7,5,2]=>110011=>110011=>[1,1,3,1,1]
[6,4,1,5,2,3,7]=>110100=>001011=>[3,2,1,1]
[6,4,1,5,2,7,3]=>110101=>101011=>[1,2,2,1,1]
[6,4,1,5,3,2,7]=>110110=>011011=>[2,1,2,1,1]
[6,4,1,5,3,7,2]=>110101=>101011=>[1,2,2,1,1]
[6,4,1,5,7,2,3]=>110010=>010011=>[2,3,1,1]
[6,4,1,5,7,3,2]=>110011=>110011=>[1,1,3,1,1]
[6,4,1,7,2,3,5]=>110100=>001011=>[3,2,1,1]
[6,4,1,7,2,5,3]=>110101=>101011=>[1,2,2,1,1]
[6,4,1,7,3,2,5]=>110110=>011011=>[2,1,2,1,1]
[6,4,1,7,3,5,2]=>110101=>101011=>[1,2,2,1,1]
[6,4,1,7,5,2,3]=>110110=>011011=>[2,1,2,1,1]
[6,4,1,7,5,3,2]=>110111=>111011=>[1,1,1,2,1,1]
[6,4,2,1,3,5,7]=>111000=>000111=>[4,1,1,1]
[6,4,2,1,3,7,5]=>111001=>100111=>[1,3,1,1,1]
[6,4,2,1,5,3,7]=>111010=>010111=>[2,2,1,1,1]
[6,4,2,1,5,7,3]=>111001=>100111=>[1,3,1,1,1]
[6,4,2,1,7,3,5]=>111010=>010111=>[2,2,1,1,1]
[6,4,2,1,7,5,3]=>111011=>110111=>[1,1,2,1,1,1]
[6,4,2,3,1,5,7]=>110100=>001011=>[3,2,1,1]
[6,4,2,3,1,7,5]=>110101=>101011=>[1,2,2,1,1]
[6,4,2,3,5,1,7]=>110010=>010011=>[2,3,1,1]
[6,4,2,3,5,7,1]=>110001=>100011=>[1,4,1,1]
[6,4,2,3,7,1,5]=>110010=>010011=>[2,3,1,1]
[6,4,2,3,7,5,1]=>110011=>110011=>[1,1,3,1,1]
[6,4,2,5,1,3,7]=>110100=>001011=>[3,2,1,1]
[6,4,2,5,1,7,3]=>110101=>101011=>[1,2,2,1,1]
[6,4,2,5,3,1,7]=>110110=>011011=>[2,1,2,1,1]
[6,4,2,5,3,7,1]=>110101=>101011=>[1,2,2,1,1]
[6,4,2,5,7,1,3]=>110010=>010011=>[2,3,1,1]
[6,4,2,5,7,3,1]=>110011=>110011=>[1,1,3,1,1]
[6,4,2,7,1,3,5]=>110100=>001011=>[3,2,1,1]
[6,4,2,7,1,5,3]=>110101=>101011=>[1,2,2,1,1]
[6,4,2,7,3,1,5]=>110110=>011011=>[2,1,2,1,1]
[6,4,2,7,3,5,1]=>110101=>101011=>[1,2,2,1,1]
[6,4,2,7,5,1,3]=>110110=>011011=>[2,1,2,1,1]
[6,4,2,7,5,3,1]=>110111=>111011=>[1,1,1,2,1,1]
[6,4,3,1,2,5,7]=>111000=>000111=>[4,1,1,1]
[6,4,3,1,2,7,5]=>111001=>100111=>[1,3,1,1,1]
[6,4,3,1,5,2,7]=>111010=>010111=>[2,2,1,1,1]
[6,4,3,1,5,7,2]=>111001=>100111=>[1,3,1,1,1]
[6,4,3,1,7,2,5]=>111010=>010111=>[2,2,1,1,1]
[6,4,3,1,7,5,2]=>111011=>110111=>[1,1,2,1,1,1]
[6,4,3,2,1,5,7]=>111100=>001111=>[3,1,1,1,1]
[6,4,3,2,1,7,5]=>111101=>101111=>[1,2,1,1,1,1]
[6,4,3,2,5,1,7]=>111010=>010111=>[2,2,1,1,1]
[6,4,3,2,5,7,1]=>111001=>100111=>[1,3,1,1,1]
[6,4,3,2,7,1,5]=>111010=>010111=>[2,2,1,1,1]
[6,4,3,2,7,5,1]=>111011=>110111=>[1,1,2,1,1,1]
[6,4,3,5,1,2,7]=>110100=>001011=>[3,2,1,1]
[6,4,3,5,1,7,2]=>110101=>101011=>[1,2,2,1,1]
[6,4,3,5,2,1,7]=>110110=>011011=>[2,1,2,1,1]
[6,4,3,5,2,7,1]=>110101=>101011=>[1,2,2,1,1]
[6,4,3,5,7,1,2]=>110010=>010011=>[2,3,1,1]
[6,4,3,5,7,2,1]=>110011=>110011=>[1,1,3,1,1]
[6,4,3,7,1,2,5]=>110100=>001011=>[3,2,1,1]
[6,4,3,7,1,5,2]=>110101=>101011=>[1,2,2,1,1]
[6,4,3,7,2,1,5]=>110110=>011011=>[2,1,2,1,1]
[6,4,3,7,2,5,1]=>110101=>101011=>[1,2,2,1,1]
[6,4,3,7,5,1,2]=>110110=>011011=>[2,1,2,1,1]
[6,4,3,7,5,2,1]=>110111=>111011=>[1,1,1,2,1,1]
[6,4,5,1,2,3,7]=>101000=>000101=>[4,2,1]
[6,4,5,1,2,7,3]=>101001=>100101=>[1,3,2,1]
[6,4,5,1,3,2,7]=>101010=>010101=>[2,2,2,1]
[6,4,5,1,3,7,2]=>101001=>100101=>[1,3,2,1]
[6,4,5,1,7,2,3]=>101010=>010101=>[2,2,2,1]
[6,4,5,1,7,3,2]=>101011=>110101=>[1,1,2,2,1]
[6,4,5,2,1,3,7]=>101100=>001101=>[3,1,2,1]
[6,4,5,2,1,7,3]=>101101=>101101=>[1,2,1,2,1]
[6,4,5,2,3,1,7]=>101010=>010101=>[2,2,2,1]
[6,4,5,2,3,7,1]=>101001=>100101=>[1,3,2,1]
[6,4,5,2,7,1,3]=>101010=>010101=>[2,2,2,1]
[6,4,5,2,7,3,1]=>101011=>110101=>[1,1,2,2,1]
[6,4,5,3,1,2,7]=>101100=>001101=>[3,1,2,1]
[6,4,5,3,1,7,2]=>101101=>101101=>[1,2,1,2,1]
[6,4,5,3,2,1,7]=>101110=>011101=>[2,1,1,2,1]
[6,4,5,3,2,7,1]=>101101=>101101=>[1,2,1,2,1]
[6,4,5,3,7,1,2]=>101010=>010101=>[2,2,2,1]
[6,4,5,3,7,2,1]=>101011=>110101=>[1,1,2,2,1]
[6,4,5,7,1,2,3]=>100100=>001001=>[3,3,1]
[6,4,5,7,1,3,2]=>100101=>101001=>[1,2,3,1]
[6,4,5,7,2,1,3]=>100110=>011001=>[2,1,3,1]
[6,4,5,7,2,3,1]=>100101=>101001=>[1,2,3,1]
[6,4,5,7,3,1,2]=>100110=>011001=>[2,1,3,1]
[6,4,5,7,3,2,1]=>100111=>111001=>[1,1,1,3,1]
[6,4,7,1,2,3,5]=>101000=>000101=>[4,2,1]
[6,4,7,1,2,5,3]=>101001=>100101=>[1,3,2,1]
[6,4,7,1,3,2,5]=>101010=>010101=>[2,2,2,1]
[6,4,7,1,3,5,2]=>101001=>100101=>[1,3,2,1]
[6,4,7,1,5,2,3]=>101010=>010101=>[2,2,2,1]
[6,4,7,1,5,3,2]=>101011=>110101=>[1,1,2,2,1]
[6,4,7,2,1,3,5]=>101100=>001101=>[3,1,2,1]
[6,4,7,2,1,5,3]=>101101=>101101=>[1,2,1,2,1]
[6,4,7,2,3,1,5]=>101010=>010101=>[2,2,2,1]
[6,4,7,2,3,5,1]=>101001=>100101=>[1,3,2,1]
[6,4,7,2,5,1,3]=>101010=>010101=>[2,2,2,1]
[6,4,7,2,5,3,1]=>101011=>110101=>[1,1,2,2,1]
[6,4,7,3,1,2,5]=>101100=>001101=>[3,1,2,1]
[6,4,7,3,1,5,2]=>101101=>101101=>[1,2,1,2,1]
[6,4,7,3,2,1,5]=>101110=>011101=>[2,1,1,2,1]
[6,4,7,3,2,5,1]=>101101=>101101=>[1,2,1,2,1]
[6,4,7,3,5,1,2]=>101010=>010101=>[2,2,2,1]
[6,4,7,3,5,2,1]=>101011=>110101=>[1,1,2,2,1]
[6,4,7,5,1,2,3]=>101100=>001101=>[3,1,2,1]
[6,4,7,5,1,3,2]=>101101=>101101=>[1,2,1,2,1]
[6,4,7,5,2,1,3]=>101110=>011101=>[2,1,1,2,1]
[6,4,7,5,2,3,1]=>101101=>101101=>[1,2,1,2,1]
[6,4,7,5,3,1,2]=>101110=>011101=>[2,1,1,2,1]
[6,4,7,5,3,2,1]=>101111=>111101=>[1,1,1,1,2,1]
[6,5,1,2,3,4,7]=>110000=>000011=>[5,1,1]
[6,5,1,2,3,7,4]=>110001=>100011=>[1,4,1,1]
[6,5,1,2,4,3,7]=>110010=>010011=>[2,3,1,1]
[6,5,1,2,4,7,3]=>110001=>100011=>[1,4,1,1]
[6,5,1,2,7,3,4]=>110010=>010011=>[2,3,1,1]
[6,5,1,2,7,4,3]=>110011=>110011=>[1,1,3,1,1]
[6,5,1,3,2,4,7]=>110100=>001011=>[3,2,1,1]
[6,5,1,3,2,7,4]=>110101=>101011=>[1,2,2,1,1]
[6,5,1,3,4,2,7]=>110010=>010011=>[2,3,1,1]
[6,5,1,3,4,7,2]=>110001=>100011=>[1,4,1,1]
[6,5,1,3,7,2,4]=>110010=>010011=>[2,3,1,1]
[6,5,1,3,7,4,2]=>110011=>110011=>[1,1,3,1,1]
[6,5,1,4,2,3,7]=>110100=>001011=>[3,2,1,1]
[6,5,1,4,2,7,3]=>110101=>101011=>[1,2,2,1,1]
[6,5,1,4,3,2,7]=>110110=>011011=>[2,1,2,1,1]
[6,5,1,4,3,7,2]=>110101=>101011=>[1,2,2,1,1]
[6,5,1,4,7,2,3]=>110010=>010011=>[2,3,1,1]
[6,5,1,4,7,3,2]=>110011=>110011=>[1,1,3,1,1]
[6,5,1,7,2,3,4]=>110100=>001011=>[3,2,1,1]
[6,5,1,7,2,4,3]=>110101=>101011=>[1,2,2,1,1]
[6,5,1,7,3,2,4]=>110110=>011011=>[2,1,2,1,1]
[6,5,1,7,3,4,2]=>110101=>101011=>[1,2,2,1,1]
[6,5,1,7,4,2,3]=>110110=>011011=>[2,1,2,1,1]
[6,5,1,7,4,3,2]=>110111=>111011=>[1,1,1,2,1,1]
[6,5,2,1,3,4,7]=>111000=>000111=>[4,1,1,1]
[6,5,2,1,3,7,4]=>111001=>100111=>[1,3,1,1,1]
[6,5,2,1,4,3,7]=>111010=>010111=>[2,2,1,1,1]
[6,5,2,1,4,7,3]=>111001=>100111=>[1,3,1,1,1]
[6,5,2,1,7,3,4]=>111010=>010111=>[2,2,1,1,1]
[6,5,2,1,7,4,3]=>111011=>110111=>[1,1,2,1,1,1]
[6,5,2,3,1,4,7]=>110100=>001011=>[3,2,1,1]
[6,5,2,3,1,7,4]=>110101=>101011=>[1,2,2,1,1]
[6,5,2,3,4,1,7]=>110010=>010011=>[2,3,1,1]
[6,5,2,3,4,7,1]=>110001=>100011=>[1,4,1,1]
[6,5,2,3,7,1,4]=>110010=>010011=>[2,3,1,1]
[6,5,2,3,7,4,1]=>110011=>110011=>[1,1,3,1,1]
[6,5,2,4,1,3,7]=>110100=>001011=>[3,2,1,1]
[6,5,2,4,1,7,3]=>110101=>101011=>[1,2,2,1,1]
[6,5,2,4,3,1,7]=>110110=>011011=>[2,1,2,1,1]
[6,5,2,4,3,7,1]=>110101=>101011=>[1,2,2,1,1]
[6,5,2,4,7,1,3]=>110010=>010011=>[2,3,1,1]
[6,5,2,4,7,3,1]=>110011=>110011=>[1,1,3,1,1]
[6,5,2,7,1,3,4]=>110100=>001011=>[3,2,1,1]
[6,5,2,7,1,4,3]=>110101=>101011=>[1,2,2,1,1]
[6,5,2,7,3,1,4]=>110110=>011011=>[2,1,2,1,1]
[6,5,2,7,3,4,1]=>110101=>101011=>[1,2,2,1,1]
[6,5,2,7,4,1,3]=>110110=>011011=>[2,1,2,1,1]
[6,5,2,7,4,3,1]=>110111=>111011=>[1,1,1,2,1,1]
[6,5,3,1,2,4,7]=>111000=>000111=>[4,1,1,1]
[6,5,3,1,2,7,4]=>111001=>100111=>[1,3,1,1,1]
[6,5,3,1,4,2,7]=>111010=>010111=>[2,2,1,1,1]
[6,5,3,1,4,7,2]=>111001=>100111=>[1,3,1,1,1]
[6,5,3,1,7,2,4]=>111010=>010111=>[2,2,1,1,1]
[6,5,3,1,7,4,2]=>111011=>110111=>[1,1,2,1,1,1]
[6,5,3,2,1,4,7]=>111100=>001111=>[3,1,1,1,1]
[6,5,3,2,1,7,4]=>111101=>101111=>[1,2,1,1,1,1]
[6,5,3,2,4,1,7]=>111010=>010111=>[2,2,1,1,1]
[6,5,3,2,4,7,1]=>111001=>100111=>[1,3,1,1,1]
[6,5,3,2,7,1,4]=>111010=>010111=>[2,2,1,1,1]
[6,5,3,2,7,4,1]=>111011=>110111=>[1,1,2,1,1,1]
[6,5,3,4,1,2,7]=>110100=>001011=>[3,2,1,1]
[6,5,3,4,1,7,2]=>110101=>101011=>[1,2,2,1,1]
[6,5,3,4,2,1,7]=>110110=>011011=>[2,1,2,1,1]
[6,5,3,4,2,7,1]=>110101=>101011=>[1,2,2,1,1]
[6,5,3,4,7,1,2]=>110010=>010011=>[2,3,1,1]
[6,5,3,4,7,2,1]=>110011=>110011=>[1,1,3,1,1]
[6,5,3,7,1,2,4]=>110100=>001011=>[3,2,1,1]
[6,5,3,7,1,4,2]=>110101=>101011=>[1,2,2,1,1]
[6,5,3,7,2,1,4]=>110110=>011011=>[2,1,2,1,1]
[6,5,3,7,2,4,1]=>110101=>101011=>[1,2,2,1,1]
[6,5,3,7,4,1,2]=>110110=>011011=>[2,1,2,1,1]
[6,5,3,7,4,2,1]=>110111=>111011=>[1,1,1,2,1,1]
[6,5,4,1,2,3,7]=>111000=>000111=>[4,1,1,1]
[6,5,4,1,2,7,3]=>111001=>100111=>[1,3,1,1,1]
[6,5,4,1,3,2,7]=>111010=>010111=>[2,2,1,1,1]
[6,5,4,1,3,7,2]=>111001=>100111=>[1,3,1,1,1]
[6,5,4,1,7,2,3]=>111010=>010111=>[2,2,1,1,1]
[6,5,4,1,7,3,2]=>111011=>110111=>[1,1,2,1,1,1]
[6,5,4,2,1,3,7]=>111100=>001111=>[3,1,1,1,1]
[6,5,4,2,1,7,3]=>111101=>101111=>[1,2,1,1,1,1]
[6,5,4,2,3,1,7]=>111010=>010111=>[2,2,1,1,1]
[6,5,4,2,3,7,1]=>111001=>100111=>[1,3,1,1,1]
[6,5,4,2,7,1,3]=>111010=>010111=>[2,2,1,1,1]
[6,5,4,2,7,3,1]=>111011=>110111=>[1,1,2,1,1,1]
[6,5,4,3,1,2,7]=>111100=>001111=>[3,1,1,1,1]
[6,5,4,3,1,7,2]=>111101=>101111=>[1,2,1,1,1,1]
[6,5,4,3,2,1,7]=>111110=>011111=>[2,1,1,1,1,1]
[6,5,4,3,2,7,1]=>111101=>101111=>[1,2,1,1,1,1]
[6,5,4,3,7,1,2]=>111010=>010111=>[2,2,1,1,1]
[6,5,4,3,7,2,1]=>111011=>110111=>[1,1,2,1,1,1]
[6,5,4,7,1,2,3]=>110100=>001011=>[3,2,1,1]
[6,5,4,7,1,3,2]=>110101=>101011=>[1,2,2,1,1]
[6,5,4,7,2,1,3]=>110110=>011011=>[2,1,2,1,1]
[6,5,4,7,2,3,1]=>110101=>101011=>[1,2,2,1,1]
[6,5,4,7,3,1,2]=>110110=>011011=>[2,1,2,1,1]
[6,5,4,7,3,2,1]=>110111=>111011=>[1,1,1,2,1,1]
[6,5,7,1,2,3,4]=>101000=>000101=>[4,2,1]
[6,5,7,1,2,4,3]=>101001=>100101=>[1,3,2,1]
[6,5,7,1,3,2,4]=>101010=>010101=>[2,2,2,1]
[6,5,7,1,3,4,2]=>101001=>100101=>[1,3,2,1]
[6,5,7,1,4,2,3]=>101010=>010101=>[2,2,2,1]
[6,5,7,1,4,3,2]=>101011=>110101=>[1,1,2,2,1]
[6,5,7,2,1,3,4]=>101100=>001101=>[3,1,2,1]
[6,5,7,2,1,4,3]=>101101=>101101=>[1,2,1,2,1]
[6,5,7,2,3,1,4]=>101010=>010101=>[2,2,2,1]
[6,5,7,2,3,4,1]=>101001=>100101=>[1,3,2,1]
[6,5,7,2,4,1,3]=>101010=>010101=>[2,2,2,1]
[6,5,7,2,4,3,1]=>101011=>110101=>[1,1,2,2,1]
[6,5,7,3,1,2,4]=>101100=>001101=>[3,1,2,1]
[6,5,7,3,1,4,2]=>101101=>101101=>[1,2,1,2,1]
[6,5,7,3,2,1,4]=>101110=>011101=>[2,1,1,2,1]
[6,5,7,3,2,4,1]=>101101=>101101=>[1,2,1,2,1]
[6,5,7,3,4,1,2]=>101010=>010101=>[2,2,2,1]
[6,5,7,3,4,2,1]=>101011=>110101=>[1,1,2,2,1]
[6,5,7,4,1,2,3]=>101100=>001101=>[3,1,2,1]
[6,5,7,4,1,3,2]=>101101=>101101=>[1,2,1,2,1]
[6,5,7,4,2,1,3]=>101110=>011101=>[2,1,1,2,1]
[6,5,7,4,2,3,1]=>101101=>101101=>[1,2,1,2,1]
[6,5,7,4,3,1,2]=>101110=>011101=>[2,1,1,2,1]
[6,5,7,4,3,2,1]=>101111=>111101=>[1,1,1,1,2,1]
[6,7,1,2,3,4,5]=>010000=>000010=>[5,2]
[6,7,1,2,3,5,4]=>010001=>100010=>[1,4,2]
[6,7,1,2,4,3,5]=>010010=>010010=>[2,3,2]
[6,7,1,2,4,5,3]=>010001=>100010=>[1,4,2]
[6,7,1,2,5,3,4]=>010010=>010010=>[2,3,2]
[6,7,1,2,5,4,3]=>010011=>110010=>[1,1,3,2]
[6,7,1,3,2,4,5]=>010100=>001010=>[3,2,2]
[6,7,1,3,2,5,4]=>010101=>101010=>[1,2,2,2]
[6,7,1,3,4,2,5]=>010010=>010010=>[2,3,2]
[6,7,1,3,4,5,2]=>010001=>100010=>[1,4,2]
[6,7,1,3,5,2,4]=>010010=>010010=>[2,3,2]
[6,7,1,3,5,4,2]=>010011=>110010=>[1,1,3,2]
[6,7,1,4,2,3,5]=>010100=>001010=>[3,2,2]
[6,7,1,4,2,5,3]=>010101=>101010=>[1,2,2,2]
[6,7,1,4,3,2,5]=>010110=>011010=>[2,1,2,2]
[6,7,1,4,3,5,2]=>010101=>101010=>[1,2,2,2]
[6,7,1,4,5,2,3]=>010010=>010010=>[2,3,2]
[6,7,1,4,5,3,2]=>010011=>110010=>[1,1,3,2]
[6,7,1,5,2,3,4]=>010100=>001010=>[3,2,2]
[6,7,1,5,2,4,3]=>010101=>101010=>[1,2,2,2]
[6,7,1,5,3,2,4]=>010110=>011010=>[2,1,2,2]
[6,7,1,5,3,4,2]=>010101=>101010=>[1,2,2,2]
[6,7,1,5,4,2,3]=>010110=>011010=>[2,1,2,2]
[6,7,1,5,4,3,2]=>010111=>111010=>[1,1,1,2,2]
[6,7,2,1,3,4,5]=>011000=>000110=>[4,1,2]
[6,7,2,1,3,5,4]=>011001=>100110=>[1,3,1,2]
[6,7,2,1,4,3,5]=>011010=>010110=>[2,2,1,2]
[6,7,2,1,4,5,3]=>011001=>100110=>[1,3,1,2]
[6,7,2,1,5,3,4]=>011010=>010110=>[2,2,1,2]
[6,7,2,1,5,4,3]=>011011=>110110=>[1,1,2,1,2]
[6,7,2,3,1,4,5]=>010100=>001010=>[3,2,2]
[6,7,2,3,1,5,4]=>010101=>101010=>[1,2,2,2]
[6,7,2,3,4,1,5]=>010010=>010010=>[2,3,2]
[6,7,2,3,4,5,1]=>010001=>100010=>[1,4,2]
[6,7,2,3,5,1,4]=>010010=>010010=>[2,3,2]
[6,7,2,3,5,4,1]=>010011=>110010=>[1,1,3,2]
[6,7,2,4,1,3,5]=>010100=>001010=>[3,2,2]
[6,7,2,4,1,5,3]=>010101=>101010=>[1,2,2,2]
[6,7,2,4,3,1,5]=>010110=>011010=>[2,1,2,2]
[6,7,2,4,3,5,1]=>010101=>101010=>[1,2,2,2]
[6,7,2,4,5,1,3]=>010010=>010010=>[2,3,2]
[6,7,2,4,5,3,1]=>010011=>110010=>[1,1,3,2]
[6,7,2,5,1,3,4]=>010100=>001010=>[3,2,2]
[6,7,2,5,1,4,3]=>010101=>101010=>[1,2,2,2]
[6,7,2,5,3,1,4]=>010110=>011010=>[2,1,2,2]
[6,7,2,5,3,4,1]=>010101=>101010=>[1,2,2,2]
[6,7,2,5,4,1,3]=>010110=>011010=>[2,1,2,2]
[6,7,2,5,4,3,1]=>010111=>111010=>[1,1,1,2,2]
[6,7,3,1,2,4,5]=>011000=>000110=>[4,1,2]
[6,7,3,1,2,5,4]=>011001=>100110=>[1,3,1,2]
[6,7,3,1,4,2,5]=>011010=>010110=>[2,2,1,2]
[6,7,3,1,4,5,2]=>011001=>100110=>[1,3,1,2]
[6,7,3,1,5,2,4]=>011010=>010110=>[2,2,1,2]
[6,7,3,1,5,4,2]=>011011=>110110=>[1,1,2,1,2]
[6,7,3,2,1,4,5]=>011100=>001110=>[3,1,1,2]
[6,7,3,2,1,5,4]=>011101=>101110=>[1,2,1,1,2]
[6,7,3,2,4,1,5]=>011010=>010110=>[2,2,1,2]
[6,7,3,2,4,5,1]=>011001=>100110=>[1,3,1,2]
[6,7,3,2,5,1,4]=>011010=>010110=>[2,2,1,2]
[6,7,3,2,5,4,1]=>011011=>110110=>[1,1,2,1,2]
[6,7,3,4,1,2,5]=>010100=>001010=>[3,2,2]
[6,7,3,4,1,5,2]=>010101=>101010=>[1,2,2,2]
[6,7,3,4,2,1,5]=>010110=>011010=>[2,1,2,2]
[6,7,3,4,2,5,1]=>010101=>101010=>[1,2,2,2]
[6,7,3,4,5,1,2]=>010010=>010010=>[2,3,2]
[6,7,3,4,5,2,1]=>010011=>110010=>[1,1,3,2]
[6,7,3,5,1,2,4]=>010100=>001010=>[3,2,2]
[6,7,3,5,1,4,2]=>010101=>101010=>[1,2,2,2]
[6,7,3,5,2,1,4]=>010110=>011010=>[2,1,2,2]
[6,7,3,5,2,4,1]=>010101=>101010=>[1,2,2,2]
[6,7,3,5,4,1,2]=>010110=>011010=>[2,1,2,2]
[6,7,3,5,4,2,1]=>010111=>111010=>[1,1,1,2,2]
[6,7,4,1,2,3,5]=>011000=>000110=>[4,1,2]
[6,7,4,1,2,5,3]=>011001=>100110=>[1,3,1,2]
[6,7,4,1,3,2,5]=>011010=>010110=>[2,2,1,2]
[6,7,4,1,3,5,2]=>011001=>100110=>[1,3,1,2]
[6,7,4,1,5,2,3]=>011010=>010110=>[2,2,1,2]
[6,7,4,1,5,3,2]=>011011=>110110=>[1,1,2,1,2]
[6,7,4,2,1,3,5]=>011100=>001110=>[3,1,1,2]
[6,7,4,2,1,5,3]=>011101=>101110=>[1,2,1,1,2]
[6,7,4,2,3,1,5]=>011010=>010110=>[2,2,1,2]
[6,7,4,2,3,5,1]=>011001=>100110=>[1,3,1,2]
[6,7,4,2,5,1,3]=>011010=>010110=>[2,2,1,2]
[6,7,4,2,5,3,1]=>011011=>110110=>[1,1,2,1,2]
[6,7,4,3,1,2,5]=>011100=>001110=>[3,1,1,2]
[6,7,4,3,1,5,2]=>011101=>101110=>[1,2,1,1,2]
[6,7,4,3,2,1,5]=>011110=>011110=>[2,1,1,1,2]
[6,7,4,3,2,5,1]=>011101=>101110=>[1,2,1,1,2]
[6,7,4,3,5,1,2]=>011010=>010110=>[2,2,1,2]
[6,7,4,3,5,2,1]=>011011=>110110=>[1,1,2,1,2]
[6,7,4,5,1,2,3]=>010100=>001010=>[3,2,2]
[6,7,4,5,1,3,2]=>010101=>101010=>[1,2,2,2]
[6,7,4,5,2,1,3]=>010110=>011010=>[2,1,2,2]
[6,7,4,5,2,3,1]=>010101=>101010=>[1,2,2,2]
[6,7,4,5,3,1,2]=>010110=>011010=>[2,1,2,2]
[6,7,4,5,3,2,1]=>010111=>111010=>[1,1,1,2,2]
[6,7,5,1,2,3,4]=>011000=>000110=>[4,1,2]
[6,7,5,1,2,4,3]=>011001=>100110=>[1,3,1,2]
[6,7,5,1,3,2,4]=>011010=>010110=>[2,2,1,2]
[6,7,5,1,3,4,2]=>011001=>100110=>[1,3,1,2]
[6,7,5,1,4,2,3]=>011010=>010110=>[2,2,1,2]
[6,7,5,1,4,3,2]=>011011=>110110=>[1,1,2,1,2]
[6,7,5,2,1,3,4]=>011100=>001110=>[3,1,1,2]
[6,7,5,2,1,4,3]=>011101=>101110=>[1,2,1,1,2]
[6,7,5,2,3,1,4]=>011010=>010110=>[2,2,1,2]
[6,7,5,2,3,4,1]=>011001=>100110=>[1,3,1,2]
[6,7,5,2,4,1,3]=>011010=>010110=>[2,2,1,2]
[6,7,5,2,4,3,1]=>011011=>110110=>[1,1,2,1,2]
[6,7,5,3,1,2,4]=>011100=>001110=>[3,1,1,2]
[6,7,5,3,1,4,2]=>011101=>101110=>[1,2,1,1,2]
[6,7,5,3,2,1,4]=>011110=>011110=>[2,1,1,1,2]
[6,7,5,3,2,4,1]=>011101=>101110=>[1,2,1,1,2]
[6,7,5,3,4,1,2]=>011010=>010110=>[2,2,1,2]
[6,7,5,3,4,2,1]=>011011=>110110=>[1,1,2,1,2]
[6,7,5,4,1,2,3]=>011100=>001110=>[3,1,1,2]
[6,7,5,4,1,3,2]=>011101=>101110=>[1,2,1,1,2]
[6,7,5,4,2,1,3]=>011110=>011110=>[2,1,1,1,2]
[6,7,5,4,2,3,1]=>011101=>101110=>[1,2,1,1,2]
[6,7,5,4,3,1,2]=>011110=>011110=>[2,1,1,1,2]
[6,7,5,4,3,2,1]=>011111=>111110=>[1,1,1,1,1,2]
[7,1,2,3,4,5,6]=>100000=>000001=>[6,1]
[7,1,2,3,4,6,5]=>100001=>100001=>[1,5,1]
[7,1,2,3,5,4,6]=>100010=>010001=>[2,4,1]
[7,1,2,3,5,6,4]=>100001=>100001=>[1,5,1]
[7,1,2,3,6,4,5]=>100010=>010001=>[2,4,1]
[7,1,2,3,6,5,4]=>100011=>110001=>[1,1,4,1]
[7,1,2,4,3,5,6]=>100100=>001001=>[3,3,1]
[7,1,2,4,3,6,5]=>100101=>101001=>[1,2,3,1]
[7,1,2,4,5,3,6]=>100010=>010001=>[2,4,1]
[7,1,2,4,5,6,3]=>100001=>100001=>[1,5,1]
[7,1,2,4,6,3,5]=>100010=>010001=>[2,4,1]
[7,1,2,4,6,5,3]=>100011=>110001=>[1,1,4,1]
[7,1,2,5,3,4,6]=>100100=>001001=>[3,3,1]
[7,1,2,5,3,6,4]=>100101=>101001=>[1,2,3,1]
[7,1,2,5,4,3,6]=>100110=>011001=>[2,1,3,1]
[7,1,2,5,4,6,3]=>100101=>101001=>[1,2,3,1]
[7,1,2,5,6,3,4]=>100010=>010001=>[2,4,1]
[7,1,2,5,6,4,3]=>100011=>110001=>[1,1,4,1]
[7,1,2,6,3,4,5]=>100100=>001001=>[3,3,1]
[7,1,2,6,3,5,4]=>100101=>101001=>[1,2,3,1]
[7,1,2,6,4,3,5]=>100110=>011001=>[2,1,3,1]
[7,1,2,6,4,5,3]=>100101=>101001=>[1,2,3,1]
[7,1,2,6,5,3,4]=>100110=>011001=>[2,1,3,1]
[7,1,2,6,5,4,3]=>100111=>111001=>[1,1,1,3,1]
[7,1,3,2,4,5,6]=>101000=>000101=>[4,2,1]
[7,1,3,2,4,6,5]=>101001=>100101=>[1,3,2,1]
[7,1,3,2,5,4,6]=>101010=>010101=>[2,2,2,1]
[7,1,3,2,5,6,4]=>101001=>100101=>[1,3,2,1]
[7,1,3,2,6,4,5]=>101010=>010101=>[2,2,2,1]
[7,1,3,2,6,5,4]=>101011=>110101=>[1,1,2,2,1]
[7,1,3,4,2,5,6]=>100100=>001001=>[3,3,1]
[7,1,3,4,2,6,5]=>100101=>101001=>[1,2,3,1]
[7,1,3,4,5,2,6]=>100010=>010001=>[2,4,1]
[7,1,3,4,5,6,2]=>100001=>100001=>[1,5,1]
[7,1,3,4,6,2,5]=>100010=>010001=>[2,4,1]
[7,1,3,4,6,5,2]=>100011=>110001=>[1,1,4,1]
[7,1,3,5,2,4,6]=>100100=>001001=>[3,3,1]
[7,1,3,5,2,6,4]=>100101=>101001=>[1,2,3,1]
[7,1,3,5,4,2,6]=>100110=>011001=>[2,1,3,1]
[7,1,3,5,4,6,2]=>100101=>101001=>[1,2,3,1]
[7,1,3,5,6,2,4]=>100010=>010001=>[2,4,1]
[7,1,3,5,6,4,2]=>100011=>110001=>[1,1,4,1]
[7,1,3,6,2,4,5]=>100100=>001001=>[3,3,1]
[7,1,3,6,2,5,4]=>100101=>101001=>[1,2,3,1]
[7,1,3,6,4,2,5]=>100110=>011001=>[2,1,3,1]
[7,1,3,6,4,5,2]=>100101=>101001=>[1,2,3,1]
[7,1,3,6,5,2,4]=>100110=>011001=>[2,1,3,1]
[7,1,3,6,5,4,2]=>100111=>111001=>[1,1,1,3,1]
[7,1,4,2,3,5,6]=>101000=>000101=>[4,2,1]
[7,1,4,2,3,6,5]=>101001=>100101=>[1,3,2,1]
[7,1,4,2,5,3,6]=>101010=>010101=>[2,2,2,1]
[7,1,4,2,5,6,3]=>101001=>100101=>[1,3,2,1]
[7,1,4,2,6,3,5]=>101010=>010101=>[2,2,2,1]
[7,1,4,2,6,5,3]=>101011=>110101=>[1,1,2,2,1]
[7,1,4,3,2,5,6]=>101100=>001101=>[3,1,2,1]
[7,1,4,3,2,6,5]=>101101=>101101=>[1,2,1,2,1]
[7,1,4,3,5,2,6]=>101010=>010101=>[2,2,2,1]
[7,1,4,3,5,6,2]=>101001=>100101=>[1,3,2,1]
[7,1,4,3,6,2,5]=>101010=>010101=>[2,2,2,1]
[7,1,4,3,6,5,2]=>101011=>110101=>[1,1,2,2,1]
[7,1,4,5,2,3,6]=>100100=>001001=>[3,3,1]
[7,1,4,5,2,6,3]=>100101=>101001=>[1,2,3,1]
[7,1,4,5,3,2,6]=>100110=>011001=>[2,1,3,1]
[7,1,4,5,3,6,2]=>100101=>101001=>[1,2,3,1]
[7,1,4,5,6,2,3]=>100010=>010001=>[2,4,1]
[7,1,4,5,6,3,2]=>100011=>110001=>[1,1,4,1]
[7,1,4,6,2,3,5]=>100100=>001001=>[3,3,1]
[7,1,4,6,2,5,3]=>100101=>101001=>[1,2,3,1]
[7,1,4,6,3,2,5]=>100110=>011001=>[2,1,3,1]
[7,1,4,6,3,5,2]=>100101=>101001=>[1,2,3,1]
[7,1,4,6,5,2,3]=>100110=>011001=>[2,1,3,1]
[7,1,4,6,5,3,2]=>100111=>111001=>[1,1,1,3,1]
[7,1,5,2,3,4,6]=>101000=>000101=>[4,2,1]
[7,1,5,2,3,6,4]=>101001=>100101=>[1,3,2,1]
[7,1,5,2,4,3,6]=>101010=>010101=>[2,2,2,1]
[7,1,5,2,4,6,3]=>101001=>100101=>[1,3,2,1]
[7,1,5,2,6,3,4]=>101010=>010101=>[2,2,2,1]
[7,1,5,2,6,4,3]=>101011=>110101=>[1,1,2,2,1]
[7,1,5,3,2,4,6]=>101100=>001101=>[3,1,2,1]
[7,1,5,3,2,6,4]=>101101=>101101=>[1,2,1,2,1]
[7,1,5,3,4,2,6]=>101010=>010101=>[2,2,2,1]
[7,1,5,3,4,6,2]=>101001=>100101=>[1,3,2,1]
[7,1,5,3,6,2,4]=>101010=>010101=>[2,2,2,1]
[7,1,5,3,6,4,2]=>101011=>110101=>[1,1,2,2,1]
[7,1,5,4,2,3,6]=>101100=>001101=>[3,1,2,1]
[7,1,5,4,2,6,3]=>101101=>101101=>[1,2,1,2,1]
[7,1,5,4,3,2,6]=>101110=>011101=>[2,1,1,2,1]
[7,1,5,4,3,6,2]=>101101=>101101=>[1,2,1,2,1]
[7,1,5,4,6,2,3]=>101010=>010101=>[2,2,2,1]
[7,1,5,4,6,3,2]=>101011=>110101=>[1,1,2,2,1]
[7,1,5,6,2,3,4]=>100100=>001001=>[3,3,1]
[7,1,5,6,2,4,3]=>100101=>101001=>[1,2,3,1]
[7,1,5,6,3,2,4]=>100110=>011001=>[2,1,3,1]
[7,1,5,6,3,4,2]=>100101=>101001=>[1,2,3,1]
[7,1,5,6,4,2,3]=>100110=>011001=>[2,1,3,1]
[7,1,5,6,4,3,2]=>100111=>111001=>[1,1,1,3,1]
[7,1,6,2,3,4,5]=>101000=>000101=>[4,2,1]
[7,1,6,2,3,5,4]=>101001=>100101=>[1,3,2,1]
[7,1,6,2,4,3,5]=>101010=>010101=>[2,2,2,1]
[7,1,6,2,4,5,3]=>101001=>100101=>[1,3,2,1]
[7,1,6,2,5,3,4]=>101010=>010101=>[2,2,2,1]
[7,1,6,2,5,4,3]=>101011=>110101=>[1,1,2,2,1]
[7,1,6,3,2,4,5]=>101100=>001101=>[3,1,2,1]
[7,1,6,3,2,5,4]=>101101=>101101=>[1,2,1,2,1]
[7,1,6,3,4,2,5]=>101010=>010101=>[2,2,2,1]
[7,1,6,3,4,5,2]=>101001=>100101=>[1,3,2,1]
[7,1,6,3,5,2,4]=>101010=>010101=>[2,2,2,1]
[7,1,6,3,5,4,2]=>101011=>110101=>[1,1,2,2,1]
[7,1,6,4,2,3,5]=>101100=>001101=>[3,1,2,1]
[7,1,6,4,2,5,3]=>101101=>101101=>[1,2,1,2,1]
[7,1,6,4,3,2,5]=>101110=>011101=>[2,1,1,2,1]
[7,1,6,4,3,5,2]=>101101=>101101=>[1,2,1,2,1]
[7,1,6,4,5,2,3]=>101010=>010101=>[2,2,2,1]
[7,1,6,4,5,3,2]=>101011=>110101=>[1,1,2,2,1]
[7,1,6,5,2,3,4]=>101100=>001101=>[3,1,2,1]
[7,1,6,5,2,4,3]=>101101=>101101=>[1,2,1,2,1]
[7,1,6,5,3,2,4]=>101110=>011101=>[2,1,1,2,1]
[7,1,6,5,3,4,2]=>101101=>101101=>[1,2,1,2,1]
[7,1,6,5,4,2,3]=>101110=>011101=>[2,1,1,2,1]
[7,1,6,5,4,3,2]=>101111=>111101=>[1,1,1,1,2,1]
[7,2,1,3,4,5,6]=>110000=>000011=>[5,1,1]
[7,2,1,3,4,6,5]=>110001=>100011=>[1,4,1,1]
[7,2,1,3,5,4,6]=>110010=>010011=>[2,3,1,1]
[7,2,1,3,5,6,4]=>110001=>100011=>[1,4,1,1]
[7,2,1,3,6,4,5]=>110010=>010011=>[2,3,1,1]
[7,2,1,3,6,5,4]=>110011=>110011=>[1,1,3,1,1]
[7,2,1,4,3,5,6]=>110100=>001011=>[3,2,1,1]
[7,2,1,4,3,6,5]=>110101=>101011=>[1,2,2,1,1]
[7,2,1,4,5,3,6]=>110010=>010011=>[2,3,1,1]
[7,2,1,4,5,6,3]=>110001=>100011=>[1,4,1,1]
[7,2,1,4,6,3,5]=>110010=>010011=>[2,3,1,1]
[7,2,1,4,6,5,3]=>110011=>110011=>[1,1,3,1,1]
[7,2,1,5,3,4,6]=>110100=>001011=>[3,2,1,1]
[7,2,1,5,3,6,4]=>110101=>101011=>[1,2,2,1,1]
[7,2,1,5,4,3,6]=>110110=>011011=>[2,1,2,1,1]
[7,2,1,5,4,6,3]=>110101=>101011=>[1,2,2,1,1]
[7,2,1,5,6,3,4]=>110010=>010011=>[2,3,1,1]
[7,2,1,5,6,4,3]=>110011=>110011=>[1,1,3,1,1]
[7,2,1,6,3,4,5]=>110100=>001011=>[3,2,1,1]
[7,2,1,6,3,5,4]=>110101=>101011=>[1,2,2,1,1]
[7,2,1,6,4,3,5]=>110110=>011011=>[2,1,2,1,1]
[7,2,1,6,4,5,3]=>110101=>101011=>[1,2,2,1,1]
[7,2,1,6,5,3,4]=>110110=>011011=>[2,1,2,1,1]
[7,2,1,6,5,4,3]=>110111=>111011=>[1,1,1,2,1,1]
[7,2,3,1,4,5,6]=>101000=>000101=>[4,2,1]
[7,2,3,1,4,6,5]=>101001=>100101=>[1,3,2,1]
[7,2,3,1,5,4,6]=>101010=>010101=>[2,2,2,1]
[7,2,3,1,5,6,4]=>101001=>100101=>[1,3,2,1]
[7,2,3,1,6,4,5]=>101010=>010101=>[2,2,2,1]
[7,2,3,1,6,5,4]=>101011=>110101=>[1,1,2,2,1]
[7,2,3,4,1,5,6]=>100100=>001001=>[3,3,1]
[7,2,3,4,1,6,5]=>100101=>101001=>[1,2,3,1]
[7,2,3,4,5,1,6]=>100010=>010001=>[2,4,1]
[7,2,3,4,5,6,1]=>100001=>100001=>[1,5,1]
[7,2,3,4,6,1,5]=>100010=>010001=>[2,4,1]
[7,2,3,4,6,5,1]=>100011=>110001=>[1,1,4,1]
[7,2,3,5,1,4,6]=>100100=>001001=>[3,3,1]
[7,2,3,5,1,6,4]=>100101=>101001=>[1,2,3,1]
[7,2,3,5,4,1,6]=>100110=>011001=>[2,1,3,1]
[7,2,3,5,4,6,1]=>100101=>101001=>[1,2,3,1]
[7,2,3,5,6,1,4]=>100010=>010001=>[2,4,1]
[7,2,3,5,6,4,1]=>100011=>110001=>[1,1,4,1]
[7,2,3,6,1,4,5]=>100100=>001001=>[3,3,1]
[7,2,3,6,1,5,4]=>100101=>101001=>[1,2,3,1]
[7,2,3,6,4,1,5]=>100110=>011001=>[2,1,3,1]
[7,2,3,6,4,5,1]=>100101=>101001=>[1,2,3,1]
[7,2,3,6,5,1,4]=>100110=>011001=>[2,1,3,1]
[7,2,3,6,5,4,1]=>100111=>111001=>[1,1,1,3,1]
[7,2,4,1,3,5,6]=>101000=>000101=>[4,2,1]
[7,2,4,1,3,6,5]=>101001=>100101=>[1,3,2,1]
[7,2,4,1,5,3,6]=>101010=>010101=>[2,2,2,1]
[7,2,4,1,5,6,3]=>101001=>100101=>[1,3,2,1]
[7,2,4,1,6,3,5]=>101010=>010101=>[2,2,2,1]
[7,2,4,1,6,5,3]=>101011=>110101=>[1,1,2,2,1]
[7,2,4,3,1,5,6]=>101100=>001101=>[3,1,2,1]
[7,2,4,3,1,6,5]=>101101=>101101=>[1,2,1,2,1]
[7,2,4,3,5,1,6]=>101010=>010101=>[2,2,2,1]
[7,2,4,3,5,6,1]=>101001=>100101=>[1,3,2,1]
[7,2,4,3,6,1,5]=>101010=>010101=>[2,2,2,1]
[7,2,4,3,6,5,1]=>101011=>110101=>[1,1,2,2,1]
[7,2,4,5,1,3,6]=>100100=>001001=>[3,3,1]
[7,2,4,5,1,6,3]=>100101=>101001=>[1,2,3,1]
[7,2,4,5,3,1,6]=>100110=>011001=>[2,1,3,1]
[7,2,4,5,3,6,1]=>100101=>101001=>[1,2,3,1]
[7,2,4,5,6,1,3]=>100010=>010001=>[2,4,1]
[7,2,4,5,6,3,1]=>100011=>110001=>[1,1,4,1]
[7,2,4,6,1,3,5]=>100100=>001001=>[3,3,1]
[7,2,4,6,1,5,3]=>100101=>101001=>[1,2,3,1]
[7,2,4,6,3,1,5]=>100110=>011001=>[2,1,3,1]
[7,2,4,6,3,5,1]=>100101=>101001=>[1,2,3,1]
[7,2,4,6,5,1,3]=>100110=>011001=>[2,1,3,1]
[7,2,4,6,5,3,1]=>100111=>111001=>[1,1,1,3,1]
[7,2,5,1,3,4,6]=>101000=>000101=>[4,2,1]
[7,2,5,1,3,6,4]=>101001=>100101=>[1,3,2,1]
[7,2,5,1,4,3,6]=>101010=>010101=>[2,2,2,1]
[7,2,5,1,4,6,3]=>101001=>100101=>[1,3,2,1]
[7,2,5,1,6,3,4]=>101010=>010101=>[2,2,2,1]
[7,2,5,1,6,4,3]=>101011=>110101=>[1,1,2,2,1]
[7,2,5,3,1,4,6]=>101100=>001101=>[3,1,2,1]
[7,2,5,3,1,6,4]=>101101=>101101=>[1,2,1,2,1]
[7,2,5,3,4,1,6]=>101010=>010101=>[2,2,2,1]
[7,2,5,3,4,6,1]=>101001=>100101=>[1,3,2,1]
[7,2,5,3,6,1,4]=>101010=>010101=>[2,2,2,1]
[7,2,5,3,6,4,1]=>101011=>110101=>[1,1,2,2,1]
[7,2,5,4,1,3,6]=>101100=>001101=>[3,1,2,1]
[7,2,5,4,1,6,3]=>101101=>101101=>[1,2,1,2,1]
[7,2,5,4,3,1,6]=>101110=>011101=>[2,1,1,2,1]
[7,2,5,4,3,6,1]=>101101=>101101=>[1,2,1,2,1]
[7,2,5,4,6,1,3]=>101010=>010101=>[2,2,2,1]
[7,2,5,4,6,3,1]=>101011=>110101=>[1,1,2,2,1]
[7,2,5,6,1,3,4]=>100100=>001001=>[3,3,1]
[7,2,5,6,1,4,3]=>100101=>101001=>[1,2,3,1]
[7,2,5,6,3,1,4]=>100110=>011001=>[2,1,3,1]
[7,2,5,6,3,4,1]=>100101=>101001=>[1,2,3,1]
[7,2,5,6,4,1,3]=>100110=>011001=>[2,1,3,1]
[7,2,5,6,4,3,1]=>100111=>111001=>[1,1,1,3,1]
[7,2,6,1,3,4,5]=>101000=>000101=>[4,2,1]
[7,2,6,1,3,5,4]=>101001=>100101=>[1,3,2,1]
[7,2,6,1,4,3,5]=>101010=>010101=>[2,2,2,1]
[7,2,6,1,4,5,3]=>101001=>100101=>[1,3,2,1]
[7,2,6,1,5,3,4]=>101010=>010101=>[2,2,2,1]
[7,2,6,1,5,4,3]=>101011=>110101=>[1,1,2,2,1]
[7,2,6,3,1,4,5]=>101100=>001101=>[3,1,2,1]
[7,2,6,3,1,5,4]=>101101=>101101=>[1,2,1,2,1]
[7,2,6,3,4,1,5]=>101010=>010101=>[2,2,2,1]
[7,2,6,3,4,5,1]=>101001=>100101=>[1,3,2,1]
[7,2,6,3,5,1,4]=>101010=>010101=>[2,2,2,1]
[7,2,6,3,5,4,1]=>101011=>110101=>[1,1,2,2,1]
[7,2,6,4,1,3,5]=>101100=>001101=>[3,1,2,1]
[7,2,6,4,1,5,3]=>101101=>101101=>[1,2,1,2,1]
[7,2,6,4,3,1,5]=>101110=>011101=>[2,1,1,2,1]
[7,2,6,4,3,5,1]=>101101=>101101=>[1,2,1,2,1]
[7,2,6,4,5,1,3]=>101010=>010101=>[2,2,2,1]
[7,2,6,4,5,3,1]=>101011=>110101=>[1,1,2,2,1]
[7,2,6,5,1,3,4]=>101100=>001101=>[3,1,2,1]
[7,2,6,5,1,4,3]=>101101=>101101=>[1,2,1,2,1]
[7,2,6,5,3,1,4]=>101110=>011101=>[2,1,1,2,1]
[7,2,6,5,3,4,1]=>101101=>101101=>[1,2,1,2,1]
[7,2,6,5,4,1,3]=>101110=>011101=>[2,1,1,2,1]
[7,2,6,5,4,3,1]=>101111=>111101=>[1,1,1,1,2,1]
[7,3,1,2,4,5,6]=>110000=>000011=>[5,1,1]
[7,3,1,2,4,6,5]=>110001=>100011=>[1,4,1,1]
[7,3,1,2,5,4,6]=>110010=>010011=>[2,3,1,1]
[7,3,1,2,5,6,4]=>110001=>100011=>[1,4,1,1]
[7,3,1,2,6,4,5]=>110010=>010011=>[2,3,1,1]
[7,3,1,2,6,5,4]=>110011=>110011=>[1,1,3,1,1]
[7,3,1,4,2,5,6]=>110100=>001011=>[3,2,1,1]
[7,3,1,4,2,6,5]=>110101=>101011=>[1,2,2,1,1]
[7,3,1,4,5,2,6]=>110010=>010011=>[2,3,1,1]
[7,3,1,4,5,6,2]=>110001=>100011=>[1,4,1,1]
[7,3,1,4,6,2,5]=>110010=>010011=>[2,3,1,1]
[7,3,1,4,6,5,2]=>110011=>110011=>[1,1,3,1,1]
[7,3,1,5,2,4,6]=>110100=>001011=>[3,2,1,1]
[7,3,1,5,2,6,4]=>110101=>101011=>[1,2,2,1,1]
[7,3,1,5,4,2,6]=>110110=>011011=>[2,1,2,1,1]
[7,3,1,5,4,6,2]=>110101=>101011=>[1,2,2,1,1]
[7,3,1,5,6,2,4]=>110010=>010011=>[2,3,1,1]
[7,3,1,5,6,4,2]=>110011=>110011=>[1,1,3,1,1]
[7,3,1,6,2,4,5]=>110100=>001011=>[3,2,1,1]
[7,3,1,6,2,5,4]=>110101=>101011=>[1,2,2,1,1]
[7,3,1,6,4,2,5]=>110110=>011011=>[2,1,2,1,1]
[7,3,1,6,4,5,2]=>110101=>101011=>[1,2,2,1,1]
[7,3,1,6,5,2,4]=>110110=>011011=>[2,1,2,1,1]
[7,3,1,6,5,4,2]=>110111=>111011=>[1,1,1,2,1,1]
[7,3,2,1,4,5,6]=>111000=>000111=>[4,1,1,1]
[7,3,2,1,4,6,5]=>111001=>100111=>[1,3,1,1,1]
[7,3,2,1,5,4,6]=>111010=>010111=>[2,2,1,1,1]
[7,3,2,1,5,6,4]=>111001=>100111=>[1,3,1,1,1]
[7,3,2,1,6,4,5]=>111010=>010111=>[2,2,1,1,1]
[7,3,2,1,6,5,4]=>111011=>110111=>[1,1,2,1,1,1]
[7,3,2,4,1,5,6]=>110100=>001011=>[3,2,1,1]
[7,3,2,4,1,6,5]=>110101=>101011=>[1,2,2,1,1]
[7,3,2,4,5,1,6]=>110010=>010011=>[2,3,1,1]
[7,3,2,4,5,6,1]=>110001=>100011=>[1,4,1,1]
[7,3,2,4,6,1,5]=>110010=>010011=>[2,3,1,1]
[7,3,2,4,6,5,1]=>110011=>110011=>[1,1,3,1,1]
[7,3,2,5,1,4,6]=>110100=>001011=>[3,2,1,1]
[7,3,2,5,1,6,4]=>110101=>101011=>[1,2,2,1,1]
[7,3,2,5,4,1,6]=>110110=>011011=>[2,1,2,1,1]
[7,3,2,5,4,6,1]=>110101=>101011=>[1,2,2,1,1]
[7,3,2,5,6,1,4]=>110010=>010011=>[2,3,1,1]
[7,3,2,5,6,4,1]=>110011=>110011=>[1,1,3,1,1]
[7,3,2,6,1,4,5]=>110100=>001011=>[3,2,1,1]
[7,3,2,6,1,5,4]=>110101=>101011=>[1,2,2,1,1]
[7,3,2,6,4,1,5]=>110110=>011011=>[2,1,2,1,1]
[7,3,2,6,4,5,1]=>110101=>101011=>[1,2,2,1,1]
[7,3,2,6,5,1,4]=>110110=>011011=>[2,1,2,1,1]
[7,3,2,6,5,4,1]=>110111=>111011=>[1,1,1,2,1,1]
[7,3,4,1,2,5,6]=>101000=>000101=>[4,2,1]
[7,3,4,1,2,6,5]=>101001=>100101=>[1,3,2,1]
[7,3,4,1,5,2,6]=>101010=>010101=>[2,2,2,1]
[7,3,4,1,5,6,2]=>101001=>100101=>[1,3,2,1]
[7,3,4,1,6,2,5]=>101010=>010101=>[2,2,2,1]
[7,3,4,1,6,5,2]=>101011=>110101=>[1,1,2,2,1]
[7,3,4,2,1,5,6]=>101100=>001101=>[3,1,2,1]
[7,3,4,2,1,6,5]=>101101=>101101=>[1,2,1,2,1]
[7,3,4,2,5,1,6]=>101010=>010101=>[2,2,2,1]
[7,3,4,2,5,6,1]=>101001=>100101=>[1,3,2,1]
[7,3,4,2,6,1,5]=>101010=>010101=>[2,2,2,1]
[7,3,4,2,6,5,1]=>101011=>110101=>[1,1,2,2,1]
[7,3,4,5,1,2,6]=>100100=>001001=>[3,3,1]
[7,3,4,5,1,6,2]=>100101=>101001=>[1,2,3,1]
[7,3,4,5,2,1,6]=>100110=>011001=>[2,1,3,1]
[7,3,4,5,2,6,1]=>100101=>101001=>[1,2,3,1]
[7,3,4,5,6,1,2]=>100010=>010001=>[2,4,1]
[7,3,4,5,6,2,1]=>100011=>110001=>[1,1,4,1]
[7,3,4,6,1,2,5]=>100100=>001001=>[3,3,1]
[7,3,4,6,1,5,2]=>100101=>101001=>[1,2,3,1]
[7,3,4,6,2,1,5]=>100110=>011001=>[2,1,3,1]
[7,3,4,6,2,5,1]=>100101=>101001=>[1,2,3,1]
[7,3,4,6,5,1,2]=>100110=>011001=>[2,1,3,1]
[7,3,4,6,5,2,1]=>100111=>111001=>[1,1,1,3,1]
[7,3,5,1,2,4,6]=>101000=>000101=>[4,2,1]
[7,3,5,1,2,6,4]=>101001=>100101=>[1,3,2,1]
[7,3,5,1,4,2,6]=>101010=>010101=>[2,2,2,1]
[7,3,5,1,4,6,2]=>101001=>100101=>[1,3,2,1]
[7,3,5,1,6,2,4]=>101010=>010101=>[2,2,2,1]
[7,3,5,1,6,4,2]=>101011=>110101=>[1,1,2,2,1]
[7,3,5,2,1,4,6]=>101100=>001101=>[3,1,2,1]
[7,3,5,2,1,6,4]=>101101=>101101=>[1,2,1,2,1]
[7,3,5,2,4,1,6]=>101010=>010101=>[2,2,2,1]
[7,3,5,2,4,6,1]=>101001=>100101=>[1,3,2,1]
[7,3,5,2,6,1,4]=>101010=>010101=>[2,2,2,1]
[7,3,5,2,6,4,1]=>101011=>110101=>[1,1,2,2,1]
[7,3,5,4,1,2,6]=>101100=>001101=>[3,1,2,1]
[7,3,5,4,1,6,2]=>101101=>101101=>[1,2,1,2,1]
[7,3,5,4,2,1,6]=>101110=>011101=>[2,1,1,2,1]
[7,3,5,4,2,6,1]=>101101=>101101=>[1,2,1,2,1]
[7,3,5,4,6,1,2]=>101010=>010101=>[2,2,2,1]
[7,3,5,4,6,2,1]=>101011=>110101=>[1,1,2,2,1]
[7,3,5,6,1,2,4]=>100100=>001001=>[3,3,1]
[7,3,5,6,1,4,2]=>100101=>101001=>[1,2,3,1]
[7,3,5,6,2,1,4]=>100110=>011001=>[2,1,3,1]
[7,3,5,6,2,4,1]=>100101=>101001=>[1,2,3,1]
[7,3,5,6,4,1,2]=>100110=>011001=>[2,1,3,1]
[7,3,5,6,4,2,1]=>100111=>111001=>[1,1,1,3,1]
[7,3,6,1,2,4,5]=>101000=>000101=>[4,2,1]
[7,3,6,1,2,5,4]=>101001=>100101=>[1,3,2,1]
[7,3,6,1,4,2,5]=>101010=>010101=>[2,2,2,1]
[7,3,6,1,4,5,2]=>101001=>100101=>[1,3,2,1]
[7,3,6,1,5,2,4]=>101010=>010101=>[2,2,2,1]
[7,3,6,1,5,4,2]=>101011=>110101=>[1,1,2,2,1]
[7,3,6,2,1,4,5]=>101100=>001101=>[3,1,2,1]
[7,3,6,2,1,5,4]=>101101=>101101=>[1,2,1,2,1]
[7,3,6,2,4,1,5]=>101010=>010101=>[2,2,2,1]
[7,3,6,2,4,5,1]=>101001=>100101=>[1,3,2,1]
[7,3,6,2,5,1,4]=>101010=>010101=>[2,2,2,1]
[7,3,6,2,5,4,1]=>101011=>110101=>[1,1,2,2,1]
[7,3,6,4,1,2,5]=>101100=>001101=>[3,1,2,1]
[7,3,6,4,1,5,2]=>101101=>101101=>[1,2,1,2,1]
[7,3,6,4,2,1,5]=>101110=>011101=>[2,1,1,2,1]
[7,3,6,4,2,5,1]=>101101=>101101=>[1,2,1,2,1]
[7,3,6,4,5,1,2]=>101010=>010101=>[2,2,2,1]
[7,3,6,4,5,2,1]=>101011=>110101=>[1,1,2,2,1]
[7,3,6,5,1,2,4]=>101100=>001101=>[3,1,2,1]
[7,3,6,5,1,4,2]=>101101=>101101=>[1,2,1,2,1]
[7,3,6,5,2,1,4]=>101110=>011101=>[2,1,1,2,1]
[7,3,6,5,2,4,1]=>101101=>101101=>[1,2,1,2,1]
[7,3,6,5,4,1,2]=>101110=>011101=>[2,1,1,2,1]
[7,3,6,5,4,2,1]=>101111=>111101=>[1,1,1,1,2,1]
[7,4,1,2,3,5,6]=>110000=>000011=>[5,1,1]
[7,4,1,2,3,6,5]=>110001=>100011=>[1,4,1,1]
[7,4,1,2,5,3,6]=>110010=>010011=>[2,3,1,1]
[7,4,1,2,5,6,3]=>110001=>100011=>[1,4,1,1]
[7,4,1,2,6,3,5]=>110010=>010011=>[2,3,1,1]
[7,4,1,2,6,5,3]=>110011=>110011=>[1,1,3,1,1]
[7,4,1,3,2,5,6]=>110100=>001011=>[3,2,1,1]
[7,4,1,3,2,6,5]=>110101=>101011=>[1,2,2,1,1]
[7,4,1,3,5,2,6]=>110010=>010011=>[2,3,1,1]
[7,4,1,3,5,6,2]=>110001=>100011=>[1,4,1,1]
[7,4,1,3,6,2,5]=>110010=>010011=>[2,3,1,1]
[7,4,1,3,6,5,2]=>110011=>110011=>[1,1,3,1,1]
[7,4,1,5,2,3,6]=>110100=>001011=>[3,2,1,1]
[7,4,1,5,2,6,3]=>110101=>101011=>[1,2,2,1,1]
[7,4,1,5,3,2,6]=>110110=>011011=>[2,1,2,1,1]
[7,4,1,5,3,6,2]=>110101=>101011=>[1,2,2,1,1]
[7,4,1,5,6,2,3]=>110010=>010011=>[2,3,1,1]
[7,4,1,5,6,3,2]=>110011=>110011=>[1,1,3,1,1]
[7,4,1,6,2,3,5]=>110100=>001011=>[3,2,1,1]
[7,4,1,6,2,5,3]=>110101=>101011=>[1,2,2,1,1]
[7,4,1,6,3,2,5]=>110110=>011011=>[2,1,2,1,1]
[7,4,1,6,3,5,2]=>110101=>101011=>[1,2,2,1,1]
[7,4,1,6,5,2,3]=>110110=>011011=>[2,1,2,1,1]
[7,4,1,6,5,3,2]=>110111=>111011=>[1,1,1,2,1,1]
[7,4,2,1,3,5,6]=>111000=>000111=>[4,1,1,1]
[7,4,2,1,3,6,5]=>111001=>100111=>[1,3,1,1,1]
[7,4,2,1,5,3,6]=>111010=>010111=>[2,2,1,1,1]
[7,4,2,1,5,6,3]=>111001=>100111=>[1,3,1,1,1]
[7,4,2,1,6,3,5]=>111010=>010111=>[2,2,1,1,1]
[7,4,2,1,6,5,3]=>111011=>110111=>[1,1,2,1,1,1]
[7,4,2,3,1,5,6]=>110100=>001011=>[3,2,1,1]
[7,4,2,3,1,6,5]=>110101=>101011=>[1,2,2,1,1]
[7,4,2,3,5,1,6]=>110010=>010011=>[2,3,1,1]
[7,4,2,3,5,6,1]=>110001=>100011=>[1,4,1,1]
[7,4,2,3,6,1,5]=>110010=>010011=>[2,3,1,1]
[7,4,2,3,6,5,1]=>110011=>110011=>[1,1,3,1,1]
[7,4,2,5,1,3,6]=>110100=>001011=>[3,2,1,1]
[7,4,2,5,1,6,3]=>110101=>101011=>[1,2,2,1,1]
[7,4,2,5,3,1,6]=>110110=>011011=>[2,1,2,1,1]
[7,4,2,5,3,6,1]=>110101=>101011=>[1,2,2,1,1]
[7,4,2,5,6,1,3]=>110010=>010011=>[2,3,1,1]
[7,4,2,5,6,3,1]=>110011=>110011=>[1,1,3,1,1]
[7,4,2,6,1,3,5]=>110100=>001011=>[3,2,1,1]
[7,4,2,6,1,5,3]=>110101=>101011=>[1,2,2,1,1]
[7,4,2,6,3,1,5]=>110110=>011011=>[2,1,2,1,1]
[7,4,2,6,3,5,1]=>110101=>101011=>[1,2,2,1,1]
[7,4,2,6,5,1,3]=>110110=>011011=>[2,1,2,1,1]
[7,4,2,6,5,3,1]=>110111=>111011=>[1,1,1,2,1,1]
[7,4,3,1,2,5,6]=>111000=>000111=>[4,1,1,1]
[7,4,3,1,2,6,5]=>111001=>100111=>[1,3,1,1,1]
[7,4,3,1,5,2,6]=>111010=>010111=>[2,2,1,1,1]
[7,4,3,1,5,6,2]=>111001=>100111=>[1,3,1,1,1]
[7,4,3,1,6,2,5]=>111010=>010111=>[2,2,1,1,1]
[7,4,3,1,6,5,2]=>111011=>110111=>[1,1,2,1,1,1]
[7,4,3,2,1,5,6]=>111100=>001111=>[3,1,1,1,1]
[7,4,3,2,1,6,5]=>111101=>101111=>[1,2,1,1,1,1]
[7,4,3,2,5,1,6]=>111010=>010111=>[2,2,1,1,1]
[7,4,3,2,5,6,1]=>111001=>100111=>[1,3,1,1,1]
[7,4,3,2,6,1,5]=>111010=>010111=>[2,2,1,1,1]
[7,4,3,2,6,5,1]=>111011=>110111=>[1,1,2,1,1,1]
[7,4,3,5,1,2,6]=>110100=>001011=>[3,2,1,1]
[7,4,3,5,1,6,2]=>110101=>101011=>[1,2,2,1,1]
[7,4,3,5,2,1,6]=>110110=>011011=>[2,1,2,1,1]
[7,4,3,5,2,6,1]=>110101=>101011=>[1,2,2,1,1]
[7,4,3,5,6,1,2]=>110010=>010011=>[2,3,1,1]
[7,4,3,5,6,2,1]=>110011=>110011=>[1,1,3,1,1]
[7,4,3,6,1,2,5]=>110100=>001011=>[3,2,1,1]
[7,4,3,6,1,5,2]=>110101=>101011=>[1,2,2,1,1]
[7,4,3,6,2,1,5]=>110110=>011011=>[2,1,2,1,1]
[7,4,3,6,2,5,1]=>110101=>101011=>[1,2,2,1,1]
[7,4,3,6,5,1,2]=>110110=>011011=>[2,1,2,1,1]
[7,4,3,6,5,2,1]=>110111=>111011=>[1,1,1,2,1,1]
[7,4,5,1,2,3,6]=>101000=>000101=>[4,2,1]
[7,4,5,1,2,6,3]=>101001=>100101=>[1,3,2,1]
[7,4,5,1,3,2,6]=>101010=>010101=>[2,2,2,1]
[7,4,5,1,3,6,2]=>101001=>100101=>[1,3,2,1]
[7,4,5,1,6,2,3]=>101010=>010101=>[2,2,2,1]
[7,4,5,1,6,3,2]=>101011=>110101=>[1,1,2,2,1]
[7,4,5,2,1,3,6]=>101100=>001101=>[3,1,2,1]
[7,4,5,2,1,6,3]=>101101=>101101=>[1,2,1,2,1]
[7,4,5,2,3,1,6]=>101010=>010101=>[2,2,2,1]
[7,4,5,2,3,6,1]=>101001=>100101=>[1,3,2,1]
[7,4,5,2,6,1,3]=>101010=>010101=>[2,2,2,1]
[7,4,5,2,6,3,1]=>101011=>110101=>[1,1,2,2,1]
[7,4,5,3,1,2,6]=>101100=>001101=>[3,1,2,1]
[7,4,5,3,1,6,2]=>101101=>101101=>[1,2,1,2,1]
[7,4,5,3,2,1,6]=>101110=>011101=>[2,1,1,2,1]
[7,4,5,3,2,6,1]=>101101=>101101=>[1,2,1,2,1]
[7,4,5,3,6,1,2]=>101010=>010101=>[2,2,2,1]
[7,4,5,3,6,2,1]=>101011=>110101=>[1,1,2,2,1]
[7,4,5,6,1,2,3]=>100100=>001001=>[3,3,1]
[7,4,5,6,1,3,2]=>100101=>101001=>[1,2,3,1]
[7,4,5,6,2,1,3]=>100110=>011001=>[2,1,3,1]
[7,4,5,6,2,3,1]=>100101=>101001=>[1,2,3,1]
[7,4,5,6,3,1,2]=>100110=>011001=>[2,1,3,1]
[7,4,5,6,3,2,1]=>100111=>111001=>[1,1,1,3,1]
[7,4,6,1,2,3,5]=>101000=>000101=>[4,2,1]
[7,4,6,1,2,5,3]=>101001=>100101=>[1,3,2,1]
[7,4,6,1,3,2,5]=>101010=>010101=>[2,2,2,1]
[7,4,6,1,3,5,2]=>101001=>100101=>[1,3,2,1]
[7,4,6,1,5,2,3]=>101010=>010101=>[2,2,2,1]
[7,4,6,1,5,3,2]=>101011=>110101=>[1,1,2,2,1]
[7,4,6,2,1,3,5]=>101100=>001101=>[3,1,2,1]
[7,4,6,2,1,5,3]=>101101=>101101=>[1,2,1,2,1]
[7,4,6,2,3,1,5]=>101010=>010101=>[2,2,2,1]
[7,4,6,2,3,5,1]=>101001=>100101=>[1,3,2,1]
[7,4,6,2,5,1,3]=>101010=>010101=>[2,2,2,1]
[7,4,6,2,5,3,1]=>101011=>110101=>[1,1,2,2,1]
[7,4,6,3,1,2,5]=>101100=>001101=>[3,1,2,1]
[7,4,6,3,1,5,2]=>101101=>101101=>[1,2,1,2,1]
[7,4,6,3,2,1,5]=>101110=>011101=>[2,1,1,2,1]
[7,4,6,3,2,5,1]=>101101=>101101=>[1,2,1,2,1]
[7,4,6,3,5,1,2]=>101010=>010101=>[2,2,2,1]
[7,4,6,3,5,2,1]=>101011=>110101=>[1,1,2,2,1]
[7,4,6,5,1,2,3]=>101100=>001101=>[3,1,2,1]
[7,4,6,5,1,3,2]=>101101=>101101=>[1,2,1,2,1]
[7,4,6,5,2,1,3]=>101110=>011101=>[2,1,1,2,1]
[7,4,6,5,2,3,1]=>101101=>101101=>[1,2,1,2,1]
[7,4,6,5,3,1,2]=>101110=>011101=>[2,1,1,2,1]
[7,4,6,5,3,2,1]=>101111=>111101=>[1,1,1,1,2,1]
[7,5,1,2,3,4,6]=>110000=>000011=>[5,1,1]
[7,5,1,2,3,6,4]=>110001=>100011=>[1,4,1,1]
[7,5,1,2,4,3,6]=>110010=>010011=>[2,3,1,1]
[7,5,1,2,4,6,3]=>110001=>100011=>[1,4,1,1]
[7,5,1,2,6,3,4]=>110010=>010011=>[2,3,1,1]
[7,5,1,2,6,4,3]=>110011=>110011=>[1,1,3,1,1]
[7,5,1,3,2,4,6]=>110100=>001011=>[3,2,1,1]
[7,5,1,3,2,6,4]=>110101=>101011=>[1,2,2,1,1]
[7,5,1,3,4,2,6]=>110010=>010011=>[2,3,1,1]
[7,5,1,3,4,6,2]=>110001=>100011=>[1,4,1,1]
[7,5,1,3,6,2,4]=>110010=>010011=>[2,3,1,1]
[7,5,1,3,6,4,2]=>110011=>110011=>[1,1,3,1,1]
[7,5,1,4,2,3,6]=>110100=>001011=>[3,2,1,1]
[7,5,1,4,2,6,3]=>110101=>101011=>[1,2,2,1,1]
[7,5,1,4,3,2,6]=>110110=>011011=>[2,1,2,1,1]
[7,5,1,4,3,6,2]=>110101=>101011=>[1,2,2,1,1]
[7,5,1,4,6,2,3]=>110010=>010011=>[2,3,1,1]
[7,5,1,4,6,3,2]=>110011=>110011=>[1,1,3,1,1]
[7,5,1,6,2,3,4]=>110100=>001011=>[3,2,1,1]
[7,5,1,6,2,4,3]=>110101=>101011=>[1,2,2,1,1]
[7,5,1,6,3,2,4]=>110110=>011011=>[2,1,2,1,1]
[7,5,1,6,3,4,2]=>110101=>101011=>[1,2,2,1,1]
[7,5,1,6,4,2,3]=>110110=>011011=>[2,1,2,1,1]
[7,5,1,6,4,3,2]=>110111=>111011=>[1,1,1,2,1,1]
[7,5,2,1,3,4,6]=>111000=>000111=>[4,1,1,1]
[7,5,2,1,3,6,4]=>111001=>100111=>[1,3,1,1,1]
[7,5,2,1,4,3,6]=>111010=>010111=>[2,2,1,1,1]
[7,5,2,1,4,6,3]=>111001=>100111=>[1,3,1,1,1]
[7,5,2,1,6,3,4]=>111010=>010111=>[2,2,1,1,1]
[7,5,2,1,6,4,3]=>111011=>110111=>[1,1,2,1,1,1]
[7,5,2,3,1,4,6]=>110100=>001011=>[3,2,1,1]
[7,5,2,3,1,6,4]=>110101=>101011=>[1,2,2,1,1]
[7,5,2,3,4,1,6]=>110010=>010011=>[2,3,1,1]
[7,5,2,3,4,6,1]=>110001=>100011=>[1,4,1,1]
[7,5,2,3,6,1,4]=>110010=>010011=>[2,3,1,1]
[7,5,2,3,6,4,1]=>110011=>110011=>[1,1,3,1,1]
[7,5,2,4,1,3,6]=>110100=>001011=>[3,2,1,1]
[7,5,2,4,1,6,3]=>110101=>101011=>[1,2,2,1,1]
[7,5,2,4,3,1,6]=>110110=>011011=>[2,1,2,1,1]
[7,5,2,4,3,6,1]=>110101=>101011=>[1,2,2,1,1]
[7,5,2,4,6,1,3]=>110010=>010011=>[2,3,1,1]
[7,5,2,4,6,3,1]=>110011=>110011=>[1,1,3,1,1]
[7,5,2,6,1,3,4]=>110100=>001011=>[3,2,1,1]
[7,5,2,6,1,4,3]=>110101=>101011=>[1,2,2,1,1]
[7,5,2,6,3,1,4]=>110110=>011011=>[2,1,2,1,1]
[7,5,2,6,3,4,1]=>110101=>101011=>[1,2,2,1,1]
[7,5,2,6,4,1,3]=>110110=>011011=>[2,1,2,1,1]
[7,5,2,6,4,3,1]=>110111=>111011=>[1,1,1,2,1,1]
[7,5,3,1,2,4,6]=>111000=>000111=>[4,1,1,1]
[7,5,3,1,2,6,4]=>111001=>100111=>[1,3,1,1,1]
[7,5,3,1,4,2,6]=>111010=>010111=>[2,2,1,1,1]
[7,5,3,1,4,6,2]=>111001=>100111=>[1,3,1,1,1]
[7,5,3,1,6,2,4]=>111010=>010111=>[2,2,1,1,1]
[7,5,3,1,6,4,2]=>111011=>110111=>[1,1,2,1,1,1]
[7,5,3,2,1,4,6]=>111100=>001111=>[3,1,1,1,1]
[7,5,3,2,1,6,4]=>111101=>101111=>[1,2,1,1,1,1]
[7,5,3,2,4,1,6]=>111010=>010111=>[2,2,1,1,1]
[7,5,3,2,4,6,1]=>111001=>100111=>[1,3,1,1,1]
[7,5,3,2,6,1,4]=>111010=>010111=>[2,2,1,1,1]
[7,5,3,2,6,4,1]=>111011=>110111=>[1,1,2,1,1,1]
[7,5,3,4,1,2,6]=>110100=>001011=>[3,2,1,1]
[7,5,3,4,1,6,2]=>110101=>101011=>[1,2,2,1,1]
[7,5,3,4,2,1,6]=>110110=>011011=>[2,1,2,1,1]
[7,5,3,4,2,6,1]=>110101=>101011=>[1,2,2,1,1]
[7,5,3,4,6,1,2]=>110010=>010011=>[2,3,1,1]
[7,5,3,4,6,2,1]=>110011=>110011=>[1,1,3,1,1]
[7,5,3,6,1,2,4]=>110100=>001011=>[3,2,1,1]
[7,5,3,6,1,4,2]=>110101=>101011=>[1,2,2,1,1]
[7,5,3,6,2,1,4]=>110110=>011011=>[2,1,2,1,1]
[7,5,3,6,2,4,1]=>110101=>101011=>[1,2,2,1,1]
[7,5,3,6,4,1,2]=>110110=>011011=>[2,1,2,1,1]
[7,5,3,6,4,2,1]=>110111=>111011=>[1,1,1,2,1,1]
[7,5,4,1,2,3,6]=>111000=>000111=>[4,1,1,1]
[7,5,4,1,2,6,3]=>111001=>100111=>[1,3,1,1,1]
[7,5,4,1,3,2,6]=>111010=>010111=>[2,2,1,1,1]
[7,5,4,1,3,6,2]=>111001=>100111=>[1,3,1,1,1]
[7,5,4,1,6,2,3]=>111010=>010111=>[2,2,1,1,1]
[7,5,4,1,6,3,2]=>111011=>110111=>[1,1,2,1,1,1]
[7,5,4,2,1,3,6]=>111100=>001111=>[3,1,1,1,1]
[7,5,4,2,1,6,3]=>111101=>101111=>[1,2,1,1,1,1]
[7,5,4,2,3,1,6]=>111010=>010111=>[2,2,1,1,1]
[7,5,4,2,3,6,1]=>111001=>100111=>[1,3,1,1,1]
[7,5,4,2,6,1,3]=>111010=>010111=>[2,2,1,1,1]
[7,5,4,2,6,3,1]=>111011=>110111=>[1,1,2,1,1,1]
[7,5,4,3,1,2,6]=>111100=>001111=>[3,1,1,1,1]
[7,5,4,3,1,6,2]=>111101=>101111=>[1,2,1,1,1,1]
[7,5,4,3,2,1,6]=>111110=>011111=>[2,1,1,1,1,1]
[7,5,4,3,2,6,1]=>111101=>101111=>[1,2,1,1,1,1]
[7,5,4,3,6,1,2]=>111010=>010111=>[2,2,1,1,1]
[7,5,4,3,6,2,1]=>111011=>110111=>[1,1,2,1,1,1]
[7,5,4,6,1,2,3]=>110100=>001011=>[3,2,1,1]
[7,5,4,6,1,3,2]=>110101=>101011=>[1,2,2,1,1]
[7,5,4,6,2,1,3]=>110110=>011011=>[2,1,2,1,1]
[7,5,4,6,2,3,1]=>110101=>101011=>[1,2,2,1,1]
[7,5,4,6,3,1,2]=>110110=>011011=>[2,1,2,1,1]
[7,5,4,6,3,2,1]=>110111=>111011=>[1,1,1,2,1,1]
[7,5,6,1,2,3,4]=>101000=>000101=>[4,2,1]
[7,5,6,1,2,4,3]=>101001=>100101=>[1,3,2,1]
[7,5,6,1,3,2,4]=>101010=>010101=>[2,2,2,1]
[7,5,6,1,3,4,2]=>101001=>100101=>[1,3,2,1]
[7,5,6,1,4,2,3]=>101010=>010101=>[2,2,2,1]
[7,5,6,1,4,3,2]=>101011=>110101=>[1,1,2,2,1]
[7,5,6,2,1,3,4]=>101100=>001101=>[3,1,2,1]
[7,5,6,2,1,4,3]=>101101=>101101=>[1,2,1,2,1]
[7,5,6,2,3,1,4]=>101010=>010101=>[2,2,2,1]
[7,5,6,2,3,4,1]=>101001=>100101=>[1,3,2,1]
[7,5,6,2,4,1,3]=>101010=>010101=>[2,2,2,1]
[7,5,6,2,4,3,1]=>101011=>110101=>[1,1,2,2,1]
[7,5,6,3,1,2,4]=>101100=>001101=>[3,1,2,1]
[7,5,6,3,1,4,2]=>101101=>101101=>[1,2,1,2,1]
[7,5,6,3,2,1,4]=>101110=>011101=>[2,1,1,2,1]
[7,5,6,3,2,4,1]=>101101=>101101=>[1,2,1,2,1]
[7,5,6,3,4,1,2]=>101010=>010101=>[2,2,2,1]
[7,5,6,3,4,2,1]=>101011=>110101=>[1,1,2,2,1]
[7,5,6,4,1,2,3]=>101100=>001101=>[3,1,2,1]
[7,5,6,4,1,3,2]=>101101=>101101=>[1,2,1,2,1]
[7,5,6,4,2,1,3]=>101110=>011101=>[2,1,1,2,1]
[7,5,6,4,2,3,1]=>101101=>101101=>[1,2,1,2,1]
[7,5,6,4,3,1,2]=>101110=>011101=>[2,1,1,2,1]
[7,5,6,4,3,2,1]=>101111=>111101=>[1,1,1,1,2,1]
[7,6,1,2,3,4,5]=>110000=>000011=>[5,1,1]
[7,6,1,2,3,5,4]=>110001=>100011=>[1,4,1,1]
[7,6,1,2,4,3,5]=>110010=>010011=>[2,3,1,1]
[7,6,1,2,4,5,3]=>110001=>100011=>[1,4,1,1]
[7,6,1,2,5,3,4]=>110010=>010011=>[2,3,1,1]
[7,6,1,2,5,4,3]=>110011=>110011=>[1,1,3,1,1]
[7,6,1,3,2,4,5]=>110100=>001011=>[3,2,1,1]
[7,6,1,3,2,5,4]=>110101=>101011=>[1,2,2,1,1]
[7,6,1,3,4,2,5]=>110010=>010011=>[2,3,1,1]
[7,6,1,3,4,5,2]=>110001=>100011=>[1,4,1,1]
[7,6,1,3,5,2,4]=>110010=>010011=>[2,3,1,1]
[7,6,1,3,5,4,2]=>110011=>110011=>[1,1,3,1,1]
[7,6,1,4,2,3,5]=>110100=>001011=>[3,2,1,1]
[7,6,1,4,2,5,3]=>110101=>101011=>[1,2,2,1,1]
[7,6,1,4,3,2,5]=>110110=>011011=>[2,1,2,1,1]
[7,6,1,4,3,5,2]=>110101=>101011=>[1,2,2,1,1]
[7,6,1,4,5,2,3]=>110010=>010011=>[2,3,1,1]
[7,6,1,4,5,3,2]=>110011=>110011=>[1,1,3,1,1]
[7,6,1,5,2,3,4]=>110100=>001011=>[3,2,1,1]
[7,6,1,5,2,4,3]=>110101=>101011=>[1,2,2,1,1]
[7,6,1,5,3,2,4]=>110110=>011011=>[2,1,2,1,1]
[7,6,1,5,3,4,2]=>110101=>101011=>[1,2,2,1,1]
[7,6,1,5,4,2,3]=>110110=>011011=>[2,1,2,1,1]
[7,6,1,5,4,3,2]=>110111=>111011=>[1,1,1,2,1,1]
[7,6,2,1,3,4,5]=>111000=>000111=>[4,1,1,1]
[7,6,2,1,3,5,4]=>111001=>100111=>[1,3,1,1,1]
[7,6,2,1,4,3,5]=>111010=>010111=>[2,2,1,1,1]
[7,6,2,1,4,5,3]=>111001=>100111=>[1,3,1,1,1]
[7,6,2,1,5,3,4]=>111010=>010111=>[2,2,1,1,1]
[7,6,2,1,5,4,3]=>111011=>110111=>[1,1,2,1,1,1]
[7,6,2,3,1,4,5]=>110100=>001011=>[3,2,1,1]
[7,6,2,3,1,5,4]=>110101=>101011=>[1,2,2,1,1]
[7,6,2,3,4,1,5]=>110010=>010011=>[2,3,1,1]
[7,6,2,3,4,5,1]=>110001=>100011=>[1,4,1,1]
[7,6,2,3,5,1,4]=>110010=>010011=>[2,3,1,1]
[7,6,2,3,5,4,1]=>110011=>110011=>[1,1,3,1,1]
[7,6,2,4,1,3,5]=>110100=>001011=>[3,2,1,1]
[7,6,2,4,1,5,3]=>110101=>101011=>[1,2,2,1,1]
[7,6,2,4,3,1,5]=>110110=>011011=>[2,1,2,1,1]
[7,6,2,4,3,5,1]=>110101=>101011=>[1,2,2,1,1]
[7,6,2,4,5,1,3]=>110010=>010011=>[2,3,1,1]
[7,6,2,4,5,3,1]=>110011=>110011=>[1,1,3,1,1]
[7,6,2,5,1,3,4]=>110100=>001011=>[3,2,1,1]
[7,6,2,5,1,4,3]=>110101=>101011=>[1,2,2,1,1]
[7,6,2,5,3,1,4]=>110110=>011011=>[2,1,2,1,1]
[7,6,2,5,3,4,1]=>110101=>101011=>[1,2,2,1,1]
[7,6,2,5,4,1,3]=>110110=>011011=>[2,1,2,1,1]
[7,6,2,5,4,3,1]=>110111=>111011=>[1,1,1,2,1,1]
[7,6,3,1,2,4,5]=>111000=>000111=>[4,1,1,1]
[7,6,3,1,2,5,4]=>111001=>100111=>[1,3,1,1,1]
[7,6,3,1,4,2,5]=>111010=>010111=>[2,2,1,1,1]
[7,6,3,1,4,5,2]=>111001=>100111=>[1,3,1,1,1]
[7,6,3,1,5,2,4]=>111010=>010111=>[2,2,1,1,1]
[7,6,3,1,5,4,2]=>111011=>110111=>[1,1,2,1,1,1]
[7,6,3,2,1,4,5]=>111100=>001111=>[3,1,1,1,1]
[7,6,3,2,1,5,4]=>111101=>101111=>[1,2,1,1,1,1]
[7,6,3,2,4,1,5]=>111010=>010111=>[2,2,1,1,1]
[7,6,3,2,4,5,1]=>111001=>100111=>[1,3,1,1,1]
[7,6,3,2,5,1,4]=>111010=>010111=>[2,2,1,1,1]
[7,6,3,2,5,4,1]=>111011=>110111=>[1,1,2,1,1,1]
[7,6,3,4,1,2,5]=>110100=>001011=>[3,2,1,1]
[7,6,3,4,1,5,2]=>110101=>101011=>[1,2,2,1,1]
[7,6,3,4,2,1,5]=>110110=>011011=>[2,1,2,1,1]
[7,6,3,4,2,5,1]=>110101=>101011=>[1,2,2,1,1]
[7,6,3,4,5,1,2]=>110010=>010011=>[2,3,1,1]
[7,6,3,4,5,2,1]=>110011=>110011=>[1,1,3,1,1]
[7,6,3,5,1,2,4]=>110100=>001011=>[3,2,1,1]
[7,6,3,5,1,4,2]=>110101=>101011=>[1,2,2,1,1]
[7,6,3,5,2,1,4]=>110110=>011011=>[2,1,2,1,1]
[7,6,3,5,2,4,1]=>110101=>101011=>[1,2,2,1,1]
[7,6,3,5,4,1,2]=>110110=>011011=>[2,1,2,1,1]
[7,6,3,5,4,2,1]=>110111=>111011=>[1,1,1,2,1,1]
[7,6,4,1,2,3,5]=>111000=>000111=>[4,1,1,1]
[7,6,4,1,2,5,3]=>111001=>100111=>[1,3,1,1,1]
[7,6,4,1,3,2,5]=>111010=>010111=>[2,2,1,1,1]
[7,6,4,1,3,5,2]=>111001=>100111=>[1,3,1,1,1]
[7,6,4,1,5,2,3]=>111010=>010111=>[2,2,1,1,1]
[7,6,4,1,5,3,2]=>111011=>110111=>[1,1,2,1,1,1]
[7,6,4,2,1,3,5]=>111100=>001111=>[3,1,1,1,1]
[7,6,4,2,1,5,3]=>111101=>101111=>[1,2,1,1,1,1]
[7,6,4,2,3,1,5]=>111010=>010111=>[2,2,1,1,1]
[7,6,4,2,3,5,1]=>111001=>100111=>[1,3,1,1,1]
[7,6,4,2,5,1,3]=>111010=>010111=>[2,2,1,1,1]
[7,6,4,2,5,3,1]=>111011=>110111=>[1,1,2,1,1,1]
[7,6,4,3,1,2,5]=>111100=>001111=>[3,1,1,1,1]
[7,6,4,3,1,5,2]=>111101=>101111=>[1,2,1,1,1,1]
[7,6,4,3,2,1,5]=>111110=>011111=>[2,1,1,1,1,1]
[7,6,4,3,2,5,1]=>111101=>101111=>[1,2,1,1,1,1]
[7,6,4,3,5,1,2]=>111010=>010111=>[2,2,1,1,1]
[7,6,4,3,5,2,1]=>111011=>110111=>[1,1,2,1,1,1]
[7,6,4,5,1,2,3]=>110100=>001011=>[3,2,1,1]
[7,6,4,5,1,3,2]=>110101=>101011=>[1,2,2,1,1]
[7,6,4,5,2,1,3]=>110110=>011011=>[2,1,2,1,1]
[7,6,4,5,2,3,1]=>110101=>101011=>[1,2,2,1,1]
[7,6,4,5,3,1,2]=>110110=>011011=>[2,1,2,1,1]
[7,6,4,5,3,2,1]=>110111=>111011=>[1,1,1,2,1,1]
[7,6,5,1,2,3,4]=>111000=>000111=>[4,1,1,1]
[7,6,5,1,2,4,3]=>111001=>100111=>[1,3,1,1,1]
[7,6,5,1,3,2,4]=>111010=>010111=>[2,2,1,1,1]
[7,6,5,1,3,4,2]=>111001=>100111=>[1,3,1,1,1]
[7,6,5,1,4,2,3]=>111010=>010111=>[2,2,1,1,1]
[7,6,5,1,4,3,2]=>111011=>110111=>[1,1,2,1,1,1]
[7,6,5,2,1,3,4]=>111100=>001111=>[3,1,1,1,1]
[7,6,5,2,1,4,3]=>111101=>101111=>[1,2,1,1,1,1]
[7,6,5,2,3,1,4]=>111010=>010111=>[2,2,1,1,1]
[7,6,5,2,3,4,1]=>111001=>100111=>[1,3,1,1,1]
[7,6,5,2,4,1,3]=>111010=>010111=>[2,2,1,1,1]
[7,6,5,2,4,3,1]=>111011=>110111=>[1,1,2,1,1,1]
[7,6,5,3,1,2,4]=>111100=>001111=>[3,1,1,1,1]
[7,6,5,3,1,4,2]=>111101=>101111=>[1,2,1,1,1,1]
[7,6,5,3,2,1,4]=>111110=>011111=>[2,1,1,1,1,1]
[7,6,5,3,2,4,1]=>111101=>101111=>[1,2,1,1,1,1]
[7,6,5,3,4,1,2]=>111010=>010111=>[2,2,1,1,1]
[7,6,5,3,4,2,1]=>111011=>110111=>[1,1,2,1,1,1]
[7,6,5,4,1,2,3]=>111100=>001111=>[3,1,1,1,1]
[7,6,5,4,1,3,2]=>111101=>101111=>[1,2,1,1,1,1]
[7,6,5,4,2,1,3]=>111110=>011111=>[2,1,1,1,1,1]
[7,6,5,4,2,3,1]=>111101=>101111=>[1,2,1,1,1,1]
[7,6,5,4,3,1,2]=>111110=>011111=>[2,1,1,1,1,1]
[7,6,5,4,3,2,1]=>111111=>111111=>[1,1,1,1,1,1,1]
[8,7,6,5,4,3,2,1]=>1111111=>1111111=>[1,1,1,1,1,1,1,1]
[7,8,6,5,4,3,2,1]=>0111111=>1111110=>[1,1,1,1,1,1,2]
[8,6,7,5,4,3,2,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[7,6,8,5,4,3,2,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[6,7,8,5,4,3,2,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[8,7,5,6,4,3,2,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[7,8,5,6,4,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[8,6,5,7,4,3,2,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[8,5,6,7,4,3,2,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[7,6,5,8,4,3,2,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[6,7,5,8,4,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[7,5,6,8,4,3,2,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[6,5,7,8,4,3,2,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[5,6,7,8,4,3,2,1]=>0001111=>1111000=>[1,1,1,1,4]
[8,7,6,4,5,3,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,6,7,4,5,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,6,8,4,5,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,7,5,4,6,3,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,6,5,4,7,3,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,5,6,4,7,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,6,4,5,7,3,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,6,5,4,8,3,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[6,7,5,4,8,3,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[7,5,6,4,8,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,5,7,4,8,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,6,7,4,8,3,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[7,6,4,5,8,3,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,7,4,5,8,3,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[7,5,4,6,8,3,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,4,5,6,8,3,2,1]=>1000111=>1110001=>[1,1,1,4,1]
[6,5,4,7,8,3,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[5,6,4,7,8,3,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[6,4,5,7,8,3,2,1]=>1000111=>1110001=>[1,1,1,4,1]
[5,4,6,7,8,3,2,1]=>1000111=>1110001=>[1,1,1,4,1]
[4,5,6,7,8,3,2,1]=>0000111=>1110000=>[1,1,1,5]
[8,7,6,5,3,4,2,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[7,8,6,5,3,4,2,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,6,8,5,3,4,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,7,5,6,3,4,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,8,5,6,3,4,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[8,5,6,7,3,4,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[7,6,5,8,3,4,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,7,5,8,3,4,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[5,6,7,8,3,4,2,1]=>0001011=>1101000=>[1,1,2,4]
[8,7,6,4,3,5,2,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[7,8,6,4,3,5,2,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,6,8,4,3,5,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,7,8,4,3,5,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[8,7,6,3,4,5,2,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,8,6,3,4,5,2,1]=>0110011=>1100110=>[1,1,3,1,2]
[8,6,7,3,4,5,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[7,6,8,3,4,5,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[6,7,8,3,4,5,2,1]=>0010011=>1100100=>[1,1,3,3]
[8,7,5,4,3,6,2,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[7,8,5,4,3,6,2,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,8,5,3,4,6,2,1]=>0110011=>1100110=>[1,1,3,1,2]
[8,7,4,3,5,6,2,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,7,3,4,5,6,2,1]=>1100011=>1100011=>[1,1,4,1,1]
[7,6,5,4,3,8,2,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[7,5,6,4,3,8,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,4,5,6,3,8,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,4,5,7,3,8,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[5,4,6,7,3,8,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[4,5,6,7,3,8,2,1]=>0001011=>1101000=>[1,1,2,4]
[7,6,3,4,5,8,2,1]=>1100011=>1100011=>[1,1,4,1,1]
[7,5,4,3,6,8,2,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,5,3,4,6,8,2,1]=>1100011=>1100011=>[1,1,4,1,1]
[6,5,4,3,7,8,2,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,7,6,5,4,2,3,1]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[8,6,7,5,4,2,3,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,6,8,5,4,2,3,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,5,6,7,4,2,3,1]=>1001101=>1011001=>[1,2,1,3,1]
[7,6,5,8,4,2,3,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,7,5,8,4,2,3,1]=>0101101=>1011010=>[1,2,1,2,2]
[7,5,6,8,4,2,3,1]=>1001101=>1011001=>[1,2,1,3,1]
[5,6,7,8,4,2,3,1]=>0001101=>1011000=>[1,2,1,4]
[8,7,6,4,5,2,3,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,7,4,5,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,8,4,5,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,7,5,4,6,2,3,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,7,4,5,6,2,3,1]=>1100101=>1010011=>[1,2,3,1,1]
[8,6,5,4,7,2,3,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,5,6,4,7,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,4,5,7,2,3,1]=>1100101=>1010011=>[1,2,3,1,1]
[7,5,6,4,8,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,7,4,8,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,6,7,8,2,3,1]=>0000101=>1010000=>[1,2,5]
[8,7,6,5,3,2,4,1]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[7,8,6,5,3,2,4,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[8,6,7,5,3,2,4,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,6,8,5,3,2,4,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,7,8,5,3,2,4,1]=>0011101=>1011100=>[1,2,1,1,3]
[8,6,5,7,3,2,4,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,6,7,3,2,4,1]=>1001101=>1011001=>[1,2,1,3,1]
[7,6,5,8,3,2,4,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,7,5,8,3,2,4,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,6,7,8,3,2,4,1]=>0001101=>1011000=>[1,2,1,4]
[8,7,6,5,2,3,4,1]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,6,7,5,2,3,4,1]=>1011001=>1001101=>[1,3,1,2,1]
[7,6,8,5,2,3,4,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,7,8,5,2,3,4,1]=>0011001=>1001100=>[1,3,1,3]
[8,7,5,6,2,3,4,1]=>1101001=>1001011=>[1,3,2,1,1]
[7,8,5,6,2,3,4,1]=>0101001=>1001010=>[1,3,2,2]
[8,6,5,7,2,3,4,1]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,6,7,2,3,4,1]=>1001001=>1001001=>[1,3,3,1]
[7,6,5,8,2,3,4,1]=>1101001=>1001011=>[1,3,2,1,1]
[6,7,5,8,2,3,4,1]=>0101001=>1001010=>[1,3,2,2]
[6,5,7,8,2,3,4,1]=>1001001=>1001001=>[1,3,3,1]
[5,6,7,8,2,3,4,1]=>0001001=>1001000=>[1,3,4]
[8,7,6,4,3,2,5,1]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[7,8,6,4,3,2,5,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[8,6,7,4,3,2,5,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,6,8,4,3,2,5,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,7,8,4,3,2,5,1]=>0011101=>1011100=>[1,2,1,1,3]
[8,7,6,3,4,2,5,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,7,3,4,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,8,3,4,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,8,4,2,3,5,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,7,8,4,2,3,5,1]=>0011001=>1001100=>[1,3,1,3]
[8,6,7,3,2,4,5,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,7,8,3,2,4,5,1]=>0011001=>1001100=>[1,3,1,3]
[8,7,6,2,3,4,5,1]=>1110001=>1000111=>[1,4,1,1,1]
[7,8,6,2,3,4,5,1]=>0110001=>1000110=>[1,4,1,2]
[8,6,7,2,3,4,5,1]=>1010001=>1000101=>[1,4,2,1]
[7,6,8,2,3,4,5,1]=>1010001=>1000101=>[1,4,2,1]
[6,7,8,2,3,4,5,1]=>0010001=>1000100=>[1,4,3]
[8,7,5,3,4,2,6,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,8,5,3,4,2,6,1]=>0110101=>1010110=>[1,2,2,1,2]
[8,7,5,3,2,4,6,1]=>1111001=>1001111=>[1,3,1,1,1,1]
[7,8,4,3,2,5,6,1]=>0111001=>1001110=>[1,3,1,1,2]
[7,8,3,4,2,5,6,1]=>0101001=>1001010=>[1,3,2,2]
[7,8,3,2,4,5,6,1]=>0110001=>1000110=>[1,4,1,2]
[8,6,5,4,3,2,7,1]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[8,5,6,3,4,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,4,3,5,2,7,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,3,4,5,2,7,1]=>1100101=>1010011=>[1,2,3,1,1]
[8,4,5,3,6,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,6,4,2,3,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[8,6,4,2,3,5,7,1]=>1110001=>1000111=>[1,4,1,1,1]
[8,5,3,4,2,6,7,1]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,4,2,3,6,7,1]=>1110001=>1000111=>[1,4,1,1,1]
[7,4,5,6,3,2,8,1]=>1001101=>1011001=>[1,2,1,3,1]
[6,4,5,7,3,2,8,1]=>1001101=>1011001=>[1,2,1,3,1]
[4,5,6,7,3,2,8,1]=>0001101=>1011000=>[1,2,1,4]
[7,5,6,3,4,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,7,3,4,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,5,3,6,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,4,3,7,2,8,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,4,5,3,7,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,6,3,7,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,6,3,7,2,8,1]=>0010101=>1010100=>[1,2,2,3]
[6,5,3,4,7,2,8,1]=>1100101=>1010011=>[1,2,3,1,1]
[5,6,3,4,7,2,8,1]=>0100101=>1010010=>[1,2,3,2]
[5,4,3,6,7,2,8,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,7,5,4,2,3,8,1]=>0111001=>1001110=>[1,3,1,1,2]
[7,5,6,4,2,3,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,5,7,4,2,3,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[5,6,7,4,2,3,8,1]=>0011001=>1001100=>[1,3,1,3]
[6,7,4,5,2,3,8,1]=>0101001=>1001010=>[1,3,2,2]
[7,4,5,6,2,3,8,1]=>1001001=>1001001=>[1,3,3,1]
[6,5,4,7,2,3,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[5,6,4,7,2,3,8,1]=>0101001=>1001010=>[1,3,2,2]
[6,4,5,7,2,3,8,1]=>1001001=>1001001=>[1,3,3,1]
[5,4,6,7,2,3,8,1]=>1001001=>1001001=>[1,3,3,1]
[4,5,6,7,2,3,8,1]=>0001001=>1001000=>[1,3,4]
[6,7,5,3,2,4,8,1]=>0111001=>1001110=>[1,3,1,1,2]
[6,5,7,3,2,4,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[7,6,5,2,3,4,8,1]=>1110001=>1000111=>[1,4,1,1,1]
[5,6,7,2,3,4,8,1]=>0010001=>1000100=>[1,4,3]
[6,7,4,3,2,5,8,1]=>0111001=>1001110=>[1,3,1,1,2]
[7,6,4,2,3,5,8,1]=>1110001=>1000111=>[1,4,1,1,1]
[6,7,3,2,4,5,8,1]=>0110001=>1000110=>[1,4,1,2]
[6,7,2,3,4,5,8,1]=>0100001=>1000010=>[1,5,2]
[7,5,2,3,4,6,8,1]=>1100001=>1000011=>[1,5,1,1]
[6,5,4,3,2,7,8,1]=>1111001=>1001111=>[1,3,1,1,1,1]
[5,4,6,3,2,7,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[5,4,3,6,2,7,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[3,4,5,6,2,7,8,1]=>0001001=>1001000=>[1,3,4]
[6,5,4,2,3,7,8,1]=>1110001=>1000111=>[1,4,1,1,1]
[5,6,4,2,3,7,8,1]=>0110001=>1000110=>[1,4,1,2]
[6,4,5,2,3,7,8,1]=>1010001=>1000101=>[1,4,2,1]
[5,4,6,2,3,7,8,1]=>1010001=>1000101=>[1,4,2,1]
[6,5,2,3,4,7,8,1]=>1100001=>1000011=>[1,5,1,1]
[5,4,3,2,6,7,8,1]=>1110001=>1000111=>[1,4,1,1,1]
[4,3,5,2,6,7,8,1]=>1010001=>1000101=>[1,4,2,1]
[5,4,2,3,6,7,8,1]=>1100001=>1000011=>[1,5,1,1]
[4,5,2,3,6,7,8,1]=>0100001=>1000010=>[1,5,2]
[5,2,3,4,6,7,8,1]=>1000001=>1000001=>[1,6,1]
[4,3,2,5,6,7,8,1]=>1100001=>1000011=>[1,5,1,1]
[3,4,2,5,6,7,8,1]=>0100001=>1000010=>[1,5,2]
[3,2,4,5,6,7,8,1]=>1000001=>1000001=>[1,6,1]
[2,3,4,5,6,7,8,1]=>0000001=>1000000=>[1,7]
[8,7,6,5,4,3,1,2]=>1111110=>0111111=>[2,1,1,1,1,1,1]
[7,8,6,5,4,3,1,2]=>0111110=>0111110=>[2,1,1,1,1,2]
[8,7,5,6,4,3,1,2]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,8,5,6,4,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[7,6,5,8,4,3,1,2]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,7,5,8,4,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[7,5,6,8,4,3,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[5,6,7,8,4,3,1,2]=>0001110=>0111000=>[2,1,1,4]
[7,8,6,4,5,3,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[8,6,7,4,5,3,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[8,7,5,4,6,3,1,2]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,5,6,4,7,3,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[6,7,4,5,8,3,1,2]=>0100110=>0110010=>[2,1,3,2]
[5,6,4,7,8,3,1,2]=>0100110=>0110010=>[2,1,3,2]
[4,5,6,7,8,3,1,2]=>0000110=>0110000=>[2,1,5]
[8,7,6,5,3,4,1,2]=>1111010=>0101111=>[2,2,1,1,1,1]
[7,8,6,5,3,4,1,2]=>0111010=>0101110=>[2,2,1,1,2]
[6,7,8,5,3,4,1,2]=>0011010=>0101100=>[2,2,1,3]
[8,7,5,6,3,4,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[7,8,5,6,3,4,1,2]=>0101010=>0101010=>[2,2,2,2]
[8,5,6,7,3,4,1,2]=>1001010=>0101001=>[2,2,3,1]
[7,6,5,8,3,4,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[6,7,5,8,3,4,1,2]=>0101010=>0101010=>[2,2,2,2]
[7,5,6,8,3,4,1,2]=>1001010=>0101001=>[2,2,3,1]
[6,5,7,8,3,4,1,2]=>1001010=>0101001=>[2,2,3,1]
[5,6,7,8,3,4,1,2]=>0001010=>0101000=>[2,2,4]
[7,8,5,4,3,6,1,2]=>0111010=>0101110=>[2,2,1,1,2]
[8,7,4,5,3,6,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[7,8,4,5,3,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[7,8,5,3,4,6,1,2]=>0110010=>0100110=>[2,3,1,2]
[8,7,4,3,5,6,1,2]=>1110010=>0100111=>[2,3,1,1,1]
[7,8,4,3,5,6,1,2]=>0110010=>0100110=>[2,3,1,2]
[7,8,3,4,5,6,1,2]=>0100010=>0100010=>[2,4,2]
[8,5,4,3,6,7,1,2]=>1110010=>0100111=>[2,3,1,1,1]
[8,5,3,4,6,7,1,2]=>1100010=>0100011=>[2,4,1,1]
[8,4,3,5,6,7,1,2]=>1100010=>0100011=>[2,4,1,1]
[7,6,5,4,3,8,1,2]=>1111010=>0101111=>[2,2,1,1,1,1]
[5,6,7,4,3,8,1,2]=>0011010=>0101100=>[2,2,1,3]
[6,7,4,5,3,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,6,4,7,3,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,4,6,7,3,8,1,2]=>1001010=>0101001=>[2,2,3,1]
[4,5,6,7,3,8,1,2]=>0001010=>0101000=>[2,2,4]
[7,5,6,3,4,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[7,6,3,4,5,8,1,2]=>1100010=>0100011=>[2,4,1,1]
[7,5,4,3,6,8,1,2]=>1110010=>0100111=>[2,3,1,1,1]
[7,5,3,4,6,8,1,2]=>1100010=>0100011=>[2,4,1,1]
[6,5,4,3,7,8,1,2]=>1110010=>0100111=>[2,3,1,1,1]
[5,4,6,3,7,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[4,5,6,3,7,8,1,2]=>0010010=>0100100=>[2,3,3]
[5,6,3,4,7,8,1,2]=>0100010=>0100010=>[2,4,2]
[6,4,3,5,7,8,1,2]=>1100010=>0100011=>[2,4,1,1]
[6,3,4,5,7,8,1,2]=>1000010=>0100001=>[2,5,1]
[5,4,3,6,7,8,1,2]=>1100010=>0100011=>[2,4,1,1]
[4,5,3,6,7,8,1,2]=>0100010=>0100010=>[2,4,2]
[5,3,4,6,7,8,1,2]=>1000010=>0100001=>[2,5,1]
[4,3,5,6,7,8,1,2]=>1000010=>0100001=>[2,5,1]
[3,4,5,6,7,8,1,2]=>0000010=>0100000=>[2,6]
[8,7,6,5,4,2,1,3]=>1111110=>0111111=>[2,1,1,1,1,1,1]
[7,6,8,5,4,2,1,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,7,8,5,4,2,1,3]=>0011110=>0111100=>[2,1,1,1,3]
[8,7,5,6,4,2,1,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,8,5,6,4,2,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[7,6,5,8,4,2,1,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,7,5,8,4,2,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[7,5,6,8,4,2,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[6,5,7,8,4,2,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[5,6,7,8,4,2,1,3]=>0001110=>0111000=>[2,1,1,4]
[7,6,8,4,5,2,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[8,7,4,5,6,2,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[6,7,5,4,8,2,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[7,5,6,4,8,2,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[7,6,4,5,8,2,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[4,5,6,7,8,2,1,3]=>0000110=>0110000=>[2,1,5]
[8,7,6,5,4,1,2,3]=>1111100=>0011111=>[3,1,1,1,1,1]
[6,7,8,5,4,1,2,3]=>0011100=>0011100=>[3,1,1,3]
[7,8,5,6,4,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[8,5,6,7,4,1,2,3]=>1001100=>0011001=>[3,1,3,1]
[7,6,5,8,4,1,2,3]=>1101100=>0011011=>[3,1,2,1,1]
[6,7,5,8,4,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[7,5,6,8,4,1,2,3]=>1001100=>0011001=>[3,1,3,1]
[6,5,7,8,4,1,2,3]=>1001100=>0011001=>[3,1,3,1]
[5,6,7,8,4,1,2,3]=>0001100=>0011000=>[3,1,4]
[8,7,5,4,6,1,2,3]=>1110100=>0010111=>[3,2,1,1,1]
[8,5,6,4,7,1,2,3]=>1010100=>0010101=>[3,2,2,1]
[8,6,4,5,7,1,2,3]=>1100100=>0010011=>[3,3,1,1]
[7,6,5,4,8,1,2,3]=>1110100=>0010111=>[3,2,1,1,1]
[6,7,5,4,8,1,2,3]=>0110100=>0010110=>[3,2,1,2]
[7,5,6,4,8,1,2,3]=>1010100=>0010101=>[3,2,2,1]
[6,5,7,4,8,1,2,3]=>1010100=>0010101=>[3,2,2,1]
[5,6,7,4,8,1,2,3]=>0010100=>0010100=>[3,2,3]
[7,6,4,5,8,1,2,3]=>1100100=>0010011=>[3,3,1,1]
[6,7,4,5,8,1,2,3]=>0100100=>0010010=>[3,3,2]
[7,5,4,6,8,1,2,3]=>1100100=>0010011=>[3,3,1,1]
[7,4,5,6,8,1,2,3]=>1000100=>0010001=>[3,4,1]
[6,5,4,7,8,1,2,3]=>1100100=>0010011=>[3,3,1,1]
[5,6,4,7,8,1,2,3]=>0100100=>0010010=>[3,3,2]
[6,4,5,7,8,1,2,3]=>1000100=>0010001=>[3,4,1]
[5,4,6,7,8,1,2,3]=>1000100=>0010001=>[3,4,1]
[4,5,6,7,8,1,2,3]=>0000100=>0010000=>[3,5]
[8,7,6,5,3,2,1,4]=>1111110=>0111111=>[2,1,1,1,1,1,1]
[7,8,6,5,3,2,1,4]=>0111110=>0111110=>[2,1,1,1,1,2]
[8,6,7,5,3,2,1,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,6,8,5,3,2,1,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,7,8,5,3,2,1,4]=>0011110=>0111100=>[2,1,1,1,3]
[8,7,5,6,3,2,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,8,5,6,3,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[8,6,5,7,3,2,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,5,6,7,3,2,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[7,6,5,8,3,2,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,7,5,8,3,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[7,5,6,8,3,2,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[6,5,7,8,3,2,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[5,6,7,8,3,2,1,4]=>0001110=>0111000=>[2,1,1,4]
[8,7,6,5,2,3,1,4]=>1111010=>0101111=>[2,2,1,1,1,1]
[7,8,6,5,2,3,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[8,6,7,5,2,3,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,6,8,5,2,3,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[6,7,8,5,2,3,1,4]=>0011010=>0101100=>[2,2,1,3]
[8,7,5,6,2,3,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,8,5,6,2,3,1,4]=>0101010=>0101010=>[2,2,2,2]
[8,6,5,7,2,3,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,6,7,2,3,1,4]=>1001010=>0101001=>[2,2,3,1]
[7,6,5,8,2,3,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,7,5,8,2,3,1,4]=>0101010=>0101010=>[2,2,2,2]
[7,5,6,8,2,3,1,4]=>1001010=>0101001=>[2,2,3,1]
[6,5,7,8,2,3,1,4]=>1001010=>0101001=>[2,2,3,1]
[5,6,7,8,2,3,1,4]=>0001010=>0101000=>[2,2,4]
[8,7,6,5,3,1,2,4]=>1111100=>0011111=>[3,1,1,1,1,1]
[7,8,6,5,3,1,2,4]=>0111100=>0011110=>[3,1,1,1,2]
[7,8,5,6,3,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[7,6,5,8,3,1,2,4]=>1101100=>0011011=>[3,1,2,1,1]
[6,7,5,8,3,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[7,5,6,8,3,1,2,4]=>1001100=>0011001=>[3,1,3,1]
[6,5,7,8,3,1,2,4]=>1001100=>0011001=>[3,1,3,1]
[5,6,7,8,3,1,2,4]=>0001100=>0011000=>[3,1,4]
[8,7,6,5,2,1,3,4]=>1111100=>0011111=>[3,1,1,1,1,1]
[7,6,8,5,2,1,3,4]=>1011100=>0011101=>[3,1,1,2,1]
[6,7,8,5,2,1,3,4]=>0011100=>0011100=>[3,1,1,3]
[7,8,5,6,2,1,3,4]=>0101100=>0011010=>[3,1,2,2]
[8,6,5,7,2,1,3,4]=>1101100=>0011011=>[3,1,2,1,1]
[8,5,6,7,2,1,3,4]=>1001100=>0011001=>[3,1,3,1]
[7,6,5,8,2,1,3,4]=>1101100=>0011011=>[3,1,2,1,1]
[6,7,5,8,2,1,3,4]=>0101100=>0011010=>[3,1,2,2]
[7,5,6,8,2,1,3,4]=>1001100=>0011001=>[3,1,3,1]
[6,5,7,8,2,1,3,4]=>1001100=>0011001=>[3,1,3,1]
[5,6,7,8,2,1,3,4]=>0001100=>0011000=>[3,1,4]
[8,7,6,5,1,2,3,4]=>1111000=>0001111=>[4,1,1,1,1]
[7,8,6,5,1,2,3,4]=>0111000=>0001110=>[4,1,1,2]
[8,6,7,5,1,2,3,4]=>1011000=>0001101=>[4,1,2,1]
[7,6,8,5,1,2,3,4]=>1011000=>0001101=>[4,1,2,1]
[6,7,8,5,1,2,3,4]=>0011000=>0001100=>[4,1,3]
[8,7,5,6,1,2,3,4]=>1101000=>0001011=>[4,2,1,1]
[7,8,5,6,1,2,3,4]=>0101000=>0001010=>[4,2,2]
[8,6,5,7,1,2,3,4]=>1101000=>0001011=>[4,2,1,1]
[8,5,6,7,1,2,3,4]=>1001000=>0001001=>[4,3,1]
[7,6,5,8,1,2,3,4]=>1101000=>0001011=>[4,2,1,1]
[6,7,5,8,1,2,3,4]=>0101000=>0001010=>[4,2,2]
[7,5,6,8,1,2,3,4]=>1001000=>0001001=>[4,3,1]
[6,5,7,8,1,2,3,4]=>1001000=>0001001=>[4,3,1]
[5,6,7,8,1,2,3,4]=>0001000=>0001000=>[4,4]
[8,7,6,4,3,2,1,5]=>1111110=>0111111=>[2,1,1,1,1,1,1]
[7,8,6,4,3,2,1,5]=>0111110=>0111110=>[2,1,1,1,1,2]
[8,6,7,4,3,2,1,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,6,8,4,3,2,1,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,7,8,4,3,2,1,5]=>0011110=>0111100=>[2,1,1,1,3]
[8,7,6,3,4,2,1,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,8,6,3,4,2,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[6,7,8,3,4,2,1,5]=>0010110=>0110100=>[2,1,2,3]
[8,7,6,4,2,3,1,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[7,6,8,4,2,3,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[6,7,8,4,2,3,1,5]=>0011010=>0101100=>[2,2,1,3]
[8,7,6,3,2,4,1,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,6,7,3,2,4,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[6,7,8,3,2,4,1,5]=>0011010=>0101100=>[2,2,1,3]
[8,7,6,2,3,4,1,5]=>1110010=>0100111=>[2,3,1,1,1]
[6,7,8,2,3,4,1,5]=>0010010=>0100100=>[2,3,3]
[8,7,6,4,3,1,2,5]=>1111100=>0011111=>[3,1,1,1,1,1]
[6,7,8,4,3,1,2,5]=>0011100=>0011100=>[3,1,1,3]
[8,7,6,3,4,1,2,5]=>1110100=>0010111=>[3,2,1,1,1]
[6,7,8,3,4,1,2,5]=>0010100=>0010100=>[3,2,3]
[8,7,6,4,2,1,3,5]=>1111100=>0011111=>[3,1,1,1,1,1]
[7,8,6,4,2,1,3,5]=>0111100=>0011110=>[3,1,1,1,2]
[8,6,7,4,2,1,3,5]=>1011100=>0011101=>[3,1,1,2,1]
[6,7,8,4,2,1,3,5]=>0011100=>0011100=>[3,1,1,3]
[8,7,6,4,1,2,3,5]=>1111000=>0001111=>[4,1,1,1,1]
[7,8,6,4,1,2,3,5]=>0111000=>0001110=>[4,1,1,2]
[7,6,8,4,1,2,3,5]=>1011000=>0001101=>[4,1,2,1]
[6,7,8,4,1,2,3,5]=>0011000=>0001100=>[4,1,3]
[8,7,6,3,2,1,4,5]=>1111100=>0011111=>[3,1,1,1,1,1]
[7,6,8,3,2,1,4,5]=>1011100=>0011101=>[3,1,1,2,1]
[6,7,8,3,2,1,4,5]=>0011100=>0011100=>[3,1,1,3]
[8,7,6,2,3,1,4,5]=>1110100=>0010111=>[3,2,1,1,1]
[7,6,8,2,3,1,4,5]=>1010100=>0010101=>[3,2,2,1]
[6,7,8,2,3,1,4,5]=>0010100=>0010100=>[3,2,3]
[8,7,6,3,1,2,4,5]=>1111000=>0001111=>[4,1,1,1,1]
[7,8,6,3,1,2,4,5]=>0111000=>0001110=>[4,1,1,2]
[6,7,8,3,1,2,4,5]=>0011000=>0001100=>[4,1,3]
[8,7,6,2,1,3,4,5]=>1111000=>0001111=>[4,1,1,1,1]
[7,8,6,2,1,3,4,5]=>0111000=>0001110=>[4,1,1,2]
[6,7,8,2,1,3,4,5]=>0011000=>0001100=>[4,1,3]
[8,7,6,1,2,3,4,5]=>1110000=>0000111=>[5,1,1,1]
[7,8,6,1,2,3,4,5]=>0110000=>0000110=>[5,1,2]
[8,6,7,1,2,3,4,5]=>1010000=>0000101=>[5,2,1]
[7,6,8,1,2,3,4,5]=>1010000=>0000101=>[5,2,1]
[6,7,8,1,2,3,4,5]=>0010000=>0000100=>[5,3]
[8,7,5,4,3,2,1,6]=>1111110=>0111111=>[2,1,1,1,1,1,1]
[7,8,5,4,3,2,1,6]=>0111110=>0111110=>[2,1,1,1,1,2]
[8,7,5,3,4,2,1,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,7,3,4,5,2,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[7,8,3,4,5,2,1,6]=>0100110=>0110010=>[2,1,3,2]
[8,7,4,5,2,3,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[7,8,4,5,2,3,1,6]=>0101010=>0101010=>[2,2,2,2]
[8,7,5,3,2,4,1,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,7,4,3,2,5,1,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[7,8,4,3,2,5,1,6]=>0111010=>0101110=>[2,2,1,1,2]
[8,7,3,4,2,5,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[7,8,3,4,2,5,1,6]=>0101010=>0101010=>[2,2,2,2]
[8,7,5,4,3,1,2,6]=>1111100=>0011111=>[3,1,1,1,1,1]
[7,8,5,4,3,1,2,6]=>0111100=>0011110=>[3,1,1,1,2]
[8,7,5,3,4,1,2,6]=>1110100=>0010111=>[3,2,1,1,1]
[7,8,5,3,4,1,2,6]=>0110100=>0010110=>[3,2,1,2]
[7,8,5,4,2,1,3,6]=>0111100=>0011110=>[3,1,1,1,2]
[7,8,5,4,1,2,3,6]=>0111000=>0001110=>[4,1,1,2]
[8,7,4,5,1,2,3,6]=>1101000=>0001011=>[4,2,1,1]
[8,7,5,3,2,1,4,6]=>1111100=>0011111=>[3,1,1,1,1,1]
[7,8,5,3,2,1,4,6]=>0111100=>0011110=>[3,1,1,1,2]
[8,7,5,2,3,1,4,6]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,5,3,1,2,4,6]=>1111000=>0001111=>[4,1,1,1,1]
[7,8,5,3,1,2,4,6]=>0111000=>0001110=>[4,1,1,2]
[8,7,5,2,1,3,4,6]=>1111000=>0001111=>[4,1,1,1,1]
[7,8,5,2,1,3,4,6]=>0111000=>0001110=>[4,1,1,2]
[8,7,5,1,2,3,4,6]=>1110000=>0000111=>[5,1,1,1]
[7,8,5,1,2,3,4,6]=>0110000=>0000110=>[5,1,2]
[8,7,4,3,2,1,5,6]=>1111100=>0011111=>[3,1,1,1,1,1]
[7,8,4,3,2,1,5,6]=>0111100=>0011110=>[3,1,1,1,2]
[8,7,3,4,2,1,5,6]=>1101100=>0011011=>[3,1,2,1,1]
[7,8,3,4,2,1,5,6]=>0101100=>0011010=>[3,1,2,2]
[7,8,4,2,3,1,5,6]=>0110100=>0010110=>[3,2,1,2]
[8,7,3,2,4,1,5,6]=>1110100=>0010111=>[3,2,1,1,1]
[7,8,3,2,4,1,5,6]=>0110100=>0010110=>[3,2,1,2]
[7,8,2,3,4,1,5,6]=>0100100=>0010010=>[3,3,2]
[7,8,4,3,1,2,5,6]=>0111000=>0001110=>[4,1,1,2]
[8,7,3,4,1,2,5,6]=>1101000=>0001011=>[4,2,1,1]
[7,8,3,4,1,2,5,6]=>0101000=>0001010=>[4,2,2]
[7,8,4,2,1,3,5,6]=>0111000=>0001110=>[4,1,1,2]
[7,8,4,1,2,3,5,6]=>0110000=>0000110=>[5,1,2]
[8,7,3,2,1,4,5,6]=>1111000=>0001111=>[4,1,1,1,1]
[7,8,3,2,1,4,5,6]=>0111000=>0001110=>[4,1,1,2]
[7,8,2,3,1,4,5,6]=>0101000=>0001010=>[4,2,2]
[7,8,3,1,2,4,5,6]=>0110000=>0000110=>[5,1,2]
[7,8,2,1,3,4,5,6]=>0110000=>0000110=>[5,1,2]
[7,8,1,2,3,4,5,6]=>0100000=>0000010=>[6,2]
[8,6,5,4,3,2,1,7]=>1111110=>0111111=>[2,1,1,1,1,1,1]
[8,5,6,4,3,2,1,7]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,4,5,6,3,2,1,7]=>1001110=>0111001=>[2,1,1,3,1]
[8,6,5,3,4,2,1,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,5,6,3,4,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,5,3,6,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,6,5,4,2,3,1,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,5,6,4,2,3,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,6,5,3,2,4,1,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,6,5,2,3,4,1,7]=>1110010=>0100111=>[2,3,1,1,1]
[8,5,6,2,3,4,1,7]=>1010010=>0100101=>[2,3,2,1]
[8,6,4,2,3,5,1,7]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,3,2,4,5,1,7]=>1110010=>0100111=>[2,3,1,1,1]
[8,5,2,3,4,6,1,7]=>1100010=>0100011=>[2,4,1,1]
[8,6,4,5,3,1,2,7]=>1101100=>0011011=>[3,1,2,1,1]
[8,5,6,3,4,1,2,7]=>1010100=>0010101=>[3,2,2,1]
[8,6,3,4,5,1,2,7]=>1100100=>0010011=>[3,3,1,1]
[8,4,5,3,6,1,2,7]=>1010100=>0010101=>[3,2,2,1]
[8,4,3,5,6,1,2,7]=>1100100=>0010011=>[3,3,1,1]
[8,6,5,4,2,1,3,7]=>1111100=>0011111=>[3,1,1,1,1,1]
[8,5,6,4,2,1,3,7]=>1011100=>0011101=>[3,1,1,2,1]
[8,5,6,4,1,2,3,7]=>1011000=>0001101=>[4,1,2,1]
[8,4,5,6,1,2,3,7]=>1001000=>0001001=>[4,3,1]
[8,6,5,3,2,1,4,7]=>1111100=>0011111=>[3,1,1,1,1,1]
[8,5,6,3,2,1,4,7]=>1011100=>0011101=>[3,1,1,2,1]
[8,6,5,2,3,1,4,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,5,6,2,3,1,4,7]=>1010100=>0010101=>[3,2,2,1]
[8,5,6,3,1,2,4,7]=>1011000=>0001101=>[4,1,2,1]
[8,6,5,2,1,3,4,7]=>1111000=>0001111=>[4,1,1,1,1]
[8,5,6,2,1,3,4,7]=>1011000=>0001101=>[4,1,2,1]
[8,6,5,1,2,3,4,7]=>1110000=>0000111=>[5,1,1,1]
[8,5,6,1,2,3,4,7]=>1010000=>0000101=>[5,2,1]
[8,6,4,3,2,1,5,7]=>1111100=>0011111=>[3,1,1,1,1,1]
[8,6,3,4,2,1,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[8,6,4,2,3,1,5,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,6,3,2,4,1,5,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,6,3,4,1,2,5,7]=>1101000=>0001011=>[4,2,1,1]
[8,6,4,2,1,3,5,7]=>1111000=>0001111=>[4,1,1,1,1]
[8,6,4,1,2,3,5,7]=>1110000=>0000111=>[5,1,1,1]
[8,4,5,3,2,1,6,7]=>1011100=>0011101=>[3,1,1,2,1]
[8,4,3,5,2,1,6,7]=>1101100=>0011011=>[3,1,2,1,1]
[8,3,4,5,2,1,6,7]=>1001100=>0011001=>[3,1,3,1]
[8,4,5,2,3,1,6,7]=>1010100=>0010101=>[3,2,2,1]
[8,5,2,3,4,1,6,7]=>1100100=>0010011=>[3,3,1,1]
[8,4,2,3,5,1,6,7]=>1100100=>0010011=>[3,3,1,1]
[8,5,3,4,1,2,6,7]=>1101000=>0001011=>[4,2,1,1]
[8,5,4,2,1,3,6,7]=>1111000=>0001111=>[4,1,1,1,1]
[8,5,3,2,1,4,6,7]=>1111000=>0001111=>[4,1,1,1,1]
[8,5,3,1,2,4,6,7]=>1110000=>0000111=>[5,1,1,1]
[8,4,3,2,1,5,6,7]=>1111000=>0001111=>[4,1,1,1,1]
[8,3,4,1,2,5,6,7]=>1010000=>0000101=>[5,2,1]
[8,4,2,1,3,5,6,7]=>1110000=>0000111=>[5,1,1,1]
[8,3,2,1,4,5,6,7]=>1110000=>0000111=>[5,1,1,1]
[8,3,1,2,4,5,6,7]=>1100000=>0000011=>[6,1,1]
[8,1,2,3,4,5,6,7]=>1000000=>0000001=>[7,1]
[7,6,5,4,3,2,1,8]=>1111110=>0111111=>[2,1,1,1,1,1,1]
[6,7,5,4,3,2,1,8]=>0111110=>0111110=>[2,1,1,1,1,2]
[7,5,6,4,3,2,1,8]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,5,7,4,3,2,1,8]=>1011110=>0111101=>[2,1,1,1,2,1]
[5,6,7,4,3,2,1,8]=>0011110=>0111100=>[2,1,1,1,3]
[7,6,4,5,3,2,1,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,4,5,6,3,2,1,8]=>1001110=>0111001=>[2,1,1,3,1]
[6,5,4,7,3,2,1,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[5,6,4,7,3,2,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[4,5,6,7,3,2,1,8]=>0001110=>0111000=>[2,1,1,4]
[7,6,5,3,4,2,1,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,7,5,3,4,2,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[7,5,6,3,4,2,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[6,5,7,3,4,2,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,6,7,3,4,2,1,8]=>0010110=>0110100=>[2,1,2,3]
[7,6,3,4,5,2,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[7,4,5,3,6,2,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,4,5,6,2,1,8]=>1000110=>0110001=>[2,1,4,1]
[6,5,4,3,7,2,1,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[5,4,6,3,7,2,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,4,3,6,7,2,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[7,5,6,4,2,3,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,6,7,4,2,3,1,8]=>0011010=>0101100=>[2,2,1,3]
[7,6,4,5,2,3,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[6,7,4,5,2,3,1,8]=>0101010=>0101010=>[2,2,2,2]
[7,4,5,6,2,3,1,8]=>1001010=>0101001=>[2,2,3,1]
[6,5,4,7,2,3,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,6,4,7,2,3,1,8]=>0101010=>0101010=>[2,2,2,2]
[5,4,6,7,2,3,1,8]=>1001010=>0101001=>[2,2,3,1]
[4,5,6,7,2,3,1,8]=>0001010=>0101000=>[2,2,4]
[5,6,7,3,2,4,1,8]=>0011010=>0101100=>[2,2,1,3]
[7,6,5,2,3,4,1,8]=>1110010=>0100111=>[2,3,1,1,1]
[6,7,5,2,3,4,1,8]=>0110010=>0100110=>[2,3,1,2]
[7,5,6,2,3,4,1,8]=>1010010=>0100101=>[2,3,2,1]
[6,5,7,2,3,4,1,8]=>1010010=>0100101=>[2,3,2,1]
[5,6,7,2,3,4,1,8]=>0010010=>0100100=>[2,3,3]
[6,7,4,3,2,5,1,8]=>0111010=>0101110=>[2,2,1,1,2]
[6,7,3,4,2,5,1,8]=>0101010=>0101010=>[2,2,2,2]
[7,6,4,2,3,5,1,8]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,3,2,4,5,1,8]=>1110010=>0100111=>[2,3,1,1,1]
[6,7,3,2,4,5,1,8]=>0110010=>0100110=>[2,3,1,2]
[7,6,2,3,4,5,1,8]=>1100010=>0100011=>[2,4,1,1]
[6,7,2,3,4,5,1,8]=>0100010=>0100010=>[2,4,2]
[7,4,5,3,2,6,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,3,4,2,6,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,3,5,2,6,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,5,2,3,6,1,8]=>1010010=>0100101=>[2,3,2,1]
[7,5,3,2,4,6,1,8]=>1110010=>0100111=>[2,3,1,1,1]
[7,4,2,3,5,6,1,8]=>1100010=>0100011=>[2,4,1,1]
[5,4,6,3,2,7,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,6,3,4,2,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[6,3,4,5,2,7,1,8]=>1001010=>0101001=>[2,2,3,1]
[5,4,3,6,2,7,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[4,5,3,6,2,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[3,4,5,6,2,7,1,8]=>0001010=>0101000=>[2,2,4]
[6,5,3,2,4,7,1,8]=>1110010=>0100111=>[2,3,1,1,1]
[6,4,2,3,5,7,1,8]=>1100010=>0100011=>[2,4,1,1]
[6,3,2,4,5,7,1,8]=>1100010=>0100011=>[2,4,1,1]
[6,2,3,4,5,7,1,8]=>1000010=>0100001=>[2,5,1]
[5,4,3,2,6,7,1,8]=>1110010=>0100111=>[2,3,1,1,1]
[4,5,2,3,6,7,1,8]=>0100010=>0100010=>[2,4,2]
[7,4,5,6,3,1,2,8]=>1001100=>0011001=>[3,1,3,1]
[5,4,6,7,3,1,2,8]=>1001100=>0011001=>[3,1,3,1]
[4,5,6,7,3,1,2,8]=>0001100=>0011000=>[3,1,4]
[7,5,6,3,4,1,2,8]=>1010100=>0010101=>[3,2,2,1]
[7,5,3,4,6,1,2,8]=>1100100=>0010011=>[3,3,1,1]
[6,5,4,3,7,1,2,8]=>1110100=>0010111=>[3,2,1,1,1]
[3,4,5,6,7,1,2,8]=>0000100=>0010000=>[3,5]
[7,4,5,6,2,1,3,8]=>1001100=>0011001=>[3,1,3,1]
[4,5,6,7,2,1,3,8]=>0001100=>0011000=>[3,1,4]
[7,6,5,4,1,2,3,8]=>1111000=>0001111=>[4,1,1,1,1]
[7,5,6,4,1,2,3,8]=>1011000=>0001101=>[4,1,2,1]
[7,6,4,5,1,2,3,8]=>1101000=>0001011=>[4,2,1,1]
[7,5,4,6,1,2,3,8]=>1101000=>0001011=>[4,2,1,1]
[7,4,5,6,1,2,3,8]=>1001000=>0001001=>[4,3,1]
[4,5,6,7,1,2,3,8]=>0001000=>0001000=>[4,4]
[7,6,5,2,3,1,4,8]=>1110100=>0010111=>[3,2,1,1,1]
[6,7,5,2,3,1,4,8]=>0110100=>0010110=>[3,2,1,2]
[7,5,6,2,3,1,4,8]=>1010100=>0010101=>[3,2,2,1]
[6,5,7,2,3,1,4,8]=>1010100=>0010101=>[3,2,2,1]
[5,6,7,2,3,1,4,8]=>0010100=>0010100=>[3,2,3]
[7,5,6,3,1,2,4,8]=>1011000=>0001101=>[4,1,2,1]
[7,6,5,2,1,3,4,8]=>1111000=>0001111=>[4,1,1,1,1]
[7,6,5,1,2,3,4,8]=>1110000=>0000111=>[5,1,1,1]
[6,7,5,1,2,3,4,8]=>0110000=>0000110=>[5,1,2]
[7,5,6,1,2,3,4,8]=>1010000=>0000101=>[5,2,1]
[6,5,7,1,2,3,4,8]=>1010000=>0000101=>[5,2,1]
[5,6,7,1,2,3,4,8]=>0010000=>0000100=>[5,3]
[7,6,4,3,2,1,5,8]=>1111100=>0011111=>[3,1,1,1,1,1]
[6,7,4,3,2,1,5,8]=>0111100=>0011110=>[3,1,1,1,2]
[7,6,3,2,4,1,5,8]=>1110100=>0010111=>[3,2,1,1,1]
[7,6,2,3,4,1,5,8]=>1100100=>0010011=>[3,3,1,1]
[6,7,2,3,4,1,5,8]=>0100100=>0010010=>[3,3,2]
[7,6,4,2,1,3,5,8]=>1111000=>0001111=>[4,1,1,1,1]
[7,6,3,2,1,4,5,8]=>1111000=>0001111=>[4,1,1,1,1]
[6,7,3,2,1,4,5,8]=>0111000=>0001110=>[4,1,1,2]
[7,6,2,3,1,4,5,8]=>1101000=>0001011=>[4,2,1,1]
[6,7,3,1,2,4,5,8]=>0110000=>0000110=>[5,1,2]
[6,7,1,2,3,4,5,8]=>0100000=>0000010=>[6,2]
[7,5,2,3,4,1,6,8]=>1100100=>0010011=>[3,3,1,1]
[7,4,2,3,5,1,6,8]=>1100100=>0010011=>[3,3,1,1]
[7,2,3,4,5,1,6,8]=>1000100=>0010001=>[3,4,1]
[7,5,3,4,1,2,6,8]=>1101000=>0001011=>[4,2,1,1]
[7,4,5,1,2,3,6,8]=>1010000=>0000101=>[5,2,1]
[7,5,3,2,1,4,6,8]=>1111000=>0001111=>[4,1,1,1,1]
[7,5,3,1,2,4,6,8]=>1110000=>0000111=>[5,1,1,1]
[7,5,1,2,3,4,6,8]=>1100000=>0000011=>[6,1,1]
[7,4,3,2,1,5,6,8]=>1111000=>0001111=>[4,1,1,1,1]
[7,4,3,1,2,5,6,8]=>1110000=>0000111=>[5,1,1,1]
[7,3,4,1,2,5,6,8]=>1010000=>0000101=>[5,2,1]
[7,3,1,2,4,5,6,8]=>1100000=>0000011=>[6,1,1]
[7,1,2,3,4,5,6,8]=>1000000=>0000001=>[7,1]
[5,6,4,3,2,1,7,8]=>0111100=>0011110=>[3,1,1,1,2]
[5,4,6,3,2,1,7,8]=>1011100=>0011101=>[3,1,1,2,1]
[4,5,6,3,2,1,7,8]=>0011100=>0011100=>[3,1,1,3]
[6,5,3,4,2,1,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[5,4,3,6,2,1,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[3,4,5,6,2,1,7,8]=>0001100=>0011000=>[3,1,4]
[5,4,6,2,3,1,7,8]=>1010100=>0010101=>[3,2,2,1]
[5,6,3,2,4,1,7,8]=>0110100=>0010110=>[3,2,1,2]
[6,5,2,3,4,1,7,8]=>1100100=>0010011=>[3,3,1,1]
[5,6,2,3,4,1,7,8]=>0100100=>0010010=>[3,3,2]
[6,4,3,2,5,1,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[5,4,3,2,6,1,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[4,5,3,2,6,1,7,8]=>0110100=>0010110=>[3,2,1,2]
[5,3,2,4,6,1,7,8]=>1100100=>0010011=>[3,3,1,1]
[6,5,4,3,1,2,7,8]=>1111000=>0001111=>[4,1,1,1,1]
[5,6,4,2,1,3,7,8]=>0111000=>0001110=>[4,1,1,2]
[6,4,5,2,1,3,7,8]=>1011000=>0001101=>[4,1,2,1]
[6,4,3,2,1,5,7,8]=>1111000=>0001111=>[4,1,1,1,1]
[6,3,4,2,1,5,7,8]=>1011000=>0001101=>[4,1,2,1]
[6,4,3,1,2,5,7,8]=>1110000=>0000111=>[5,1,1,1]
[6,4,2,1,3,5,7,8]=>1110000=>0000111=>[5,1,1,1]
[5,4,3,2,1,6,7,8]=>1111000=>0001111=>[4,1,1,1,1]
[4,5,3,2,1,6,7,8]=>0111000=>0001110=>[4,1,1,2]
[5,3,4,2,1,6,7,8]=>1011000=>0001101=>[4,1,2,1]
[4,3,5,2,1,6,7,8]=>1011000=>0001101=>[4,1,2,1]
[3,4,5,2,1,6,7,8]=>0011000=>0001100=>[4,1,3]
[5,4,2,3,1,6,7,8]=>1101000=>0001011=>[4,2,1,1]
[4,5,2,3,1,6,7,8]=>0101000=>0001010=>[4,2,2]
[5,3,2,4,1,6,7,8]=>1101000=>0001011=>[4,2,1,1]
[5,2,3,4,1,6,7,8]=>1001000=>0001001=>[4,3,1]
[4,3,2,5,1,6,7,8]=>1101000=>0001011=>[4,2,1,1]
[3,4,2,5,1,6,7,8]=>0101000=>0001010=>[4,2,2]
[4,2,3,5,1,6,7,8]=>1001000=>0001001=>[4,3,1]
[3,2,4,5,1,6,7,8]=>1001000=>0001001=>[4,3,1]
[2,3,4,5,1,6,7,8]=>0001000=>0001000=>[4,4]
[5,4,3,1,2,6,7,8]=>1110000=>0000111=>[5,1,1,1]
[5,3,4,1,2,6,7,8]=>1010000=>0000101=>[5,2,1]
[5,4,2,1,3,6,7,8]=>1110000=>0000111=>[5,1,1,1]
[5,4,1,2,3,6,7,8]=>1100000=>0000011=>[6,1,1]
[4,5,1,2,3,6,7,8]=>0100000=>0000010=>[6,2]
[5,3,2,1,4,6,7,8]=>1110000=>0000111=>[5,1,1,1]
[5,2,3,1,4,6,7,8]=>1010000=>0000101=>[5,2,1]
[5,3,1,2,4,6,7,8]=>1100000=>0000011=>[6,1,1]
[5,2,1,3,4,6,7,8]=>1100000=>0000011=>[6,1,1]
[5,1,2,3,4,6,7,8]=>1000000=>0000001=>[7,1]
[4,3,2,1,5,6,7,8]=>1110000=>0000111=>[5,1,1,1]
[3,4,2,1,5,6,7,8]=>0110000=>0000110=>[5,1,2]
[4,2,3,1,5,6,7,8]=>1010000=>0000101=>[5,2,1]
[3,2,4,1,5,6,7,8]=>1010000=>0000101=>[5,2,1]
[2,3,4,1,5,6,7,8]=>0010000=>0000100=>[5,3]
[4,3,1,2,5,6,7,8]=>1100000=>0000011=>[6,1,1]
[3,4,1,2,5,6,7,8]=>0100000=>0000010=>[6,2]
[4,2,1,3,5,6,7,8]=>1100000=>0000011=>[6,1,1]
[4,1,2,3,5,6,7,8]=>1000000=>0000001=>[7,1]
[3,2,1,4,5,6,7,8]=>1100000=>0000011=>[6,1,1]
[2,3,1,4,5,6,7,8]=>0100000=>0000010=>[6,2]
[3,1,2,4,5,6,7,8]=>1000000=>0000001=>[7,1]
[2,1,3,4,5,6,7,8]=>1000000=>0000001=>[7,1]
[1,2,3,4,5,6,7,8]=>0000000=>0000000=>[8]
[6,8,7,5,4,3,2,1]=>0111111=>1111110=>[1,1,1,1,1,1,2]
[5,8,7,6,4,3,2,1]=>0111111=>1111110=>[1,1,1,1,1,1,2]
[5,7,8,6,4,3,2,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[6,5,8,7,4,3,2,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[5,6,8,7,4,3,2,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[5,7,6,8,4,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[4,8,7,6,5,3,2,1]=>0111111=>1111110=>[1,1,1,1,1,1,2]
[4,7,8,6,5,3,2,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[4,6,8,7,5,3,2,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[4,7,6,8,5,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[4,6,7,8,5,3,2,1]=>0001111=>1111000=>[1,1,1,1,4]
[4,5,8,7,6,3,2,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[4,5,7,8,6,3,2,1]=>0001111=>1111000=>[1,1,1,1,4]
[4,6,5,8,7,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[4,5,6,8,7,3,2,1]=>0001111=>1111000=>[1,1,1,1,4]
[5,7,6,4,8,3,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,7,6,5,8,3,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,6,7,5,8,3,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[5,4,7,6,8,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,5,7,6,8,3,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,6,5,7,8,3,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,8,7,6,5,4,2,1]=>0111111=>1111110=>[1,1,1,1,1,1,2]
[3,5,8,7,6,4,2,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[3,5,7,8,6,4,2,1]=>0001111=>1111000=>[1,1,1,1,4]
[3,5,6,8,7,4,2,1]=>0001111=>1111000=>[1,1,1,1,4]
[3,7,6,5,8,4,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,6,7,5,8,4,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[3,5,6,7,8,4,2,1]=>0000111=>1110000=>[1,1,1,5]
[3,4,8,7,6,5,2,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[3,4,6,7,8,5,2,1]=>0000111=>1110000=>[1,1,1,5]
[5,4,3,7,8,6,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[3,4,5,7,8,6,2,1]=>0000111=>1110000=>[1,1,1,5]
[4,5,6,3,8,7,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,3,6,5,8,7,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,4,3,6,8,7,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[4,5,3,6,8,7,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[5,7,6,4,3,8,2,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,7,6,5,3,8,2,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,4,7,6,5,8,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,5,3,7,6,8,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,3,5,7,6,8,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[3,4,6,5,7,8,2,1]=>0010011=>1100100=>[1,1,3,3]
[2,8,7,6,5,4,3,1]=>0111111=>1111110=>[1,1,1,1,1,1,2]
[2,7,6,8,5,4,3,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[2,5,6,7,8,4,3,1]=>0000111=>1110000=>[1,1,1,5]
[2,4,8,7,6,5,3,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[2,4,6,8,7,5,3,1]=>0001111=>1111000=>[1,1,1,1,4]
[2,4,6,7,8,5,3,1]=>0000111=>1110000=>[1,1,1,5]
[2,5,4,8,7,6,3,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[2,4,5,7,8,6,3,1]=>0000111=>1110000=>[1,1,1,5]
[2,5,6,4,8,7,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[2,4,6,5,8,7,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[2,7,6,5,4,8,3,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,6,7,5,4,8,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,4,7,6,5,8,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,6,5,4,7,8,3,1]=>0110011=>1100110=>[1,1,3,1,2]
[3,2,8,7,6,5,4,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[3,2,6,8,7,5,4,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[3,2,5,7,6,8,4,1]=>1001011=>1101001=>[1,1,2,3,1]
[3,2,5,6,7,8,4,1]=>1000011=>1100001=>[1,1,5,1]
[2,3,8,7,6,5,4,1]=>0011111=>1111100=>[1,1,1,1,1,3]
[2,3,6,7,8,5,4,1]=>0000111=>1110000=>[1,1,1,5]
[2,3,5,7,8,6,4,1]=>0000111=>1110000=>[1,1,1,5]
[2,3,7,6,5,8,4,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,3,5,6,7,8,4,1]=>0000011=>1100000=>[1,1,6]
[4,3,2,8,7,6,5,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[3,4,2,8,7,6,5,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[3,4,2,7,8,6,5,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,4,3,8,7,6,5,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[2,4,3,6,8,7,5,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,2,4,8,7,6,5,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[2,3,4,8,7,6,5,1]=>0001111=>1111000=>[1,1,1,1,4]
[2,3,4,6,7,8,5,1]=>0000011=>1100000=>[1,1,6]
[5,4,3,2,8,7,6,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[5,4,3,2,7,8,6,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[2,5,4,3,8,7,6,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,5,4,3,7,8,6,1]=>0110011=>1100110=>[1,1,3,1,2]
[2,4,5,3,8,7,6,1]=>0010111=>1110100=>[1,1,1,2,3]
[2,3,5,4,8,7,6,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,3,2,5,8,7,6,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[2,4,3,5,8,7,6,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,3,4,5,8,7,6,1]=>0000111=>1110000=>[1,1,1,5]
[6,5,4,3,2,8,7,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[4,6,5,3,2,8,7,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,4,6,3,2,8,7,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,5,6,3,2,8,7,1]=>0011011=>1101100=>[1,1,2,1,3]
[3,6,5,4,2,8,7,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,5,6,4,2,8,7,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,3,6,5,2,8,7,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,4,3,6,2,8,7,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,6,5,4,3,8,7,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,4,6,5,3,8,7,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,3,2,6,5,8,7,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,4,3,6,5,8,7,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,3,4,6,5,8,7,1]=>0001011=>1101000=>[1,1,2,4]
[5,4,3,2,6,8,7,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[2,5,4,3,6,8,7,1]=>0110011=>1100110=>[1,1,3,1,2]
[4,3,2,5,6,8,7,1]=>1100011=>1100011=>[1,1,4,1,1]
[3,4,2,5,6,8,7,1]=>0100011=>1100010=>[1,1,4,2]
[2,4,3,5,6,8,7,1]=>0100011=>1100010=>[1,1,4,2]
[2,3,4,5,6,8,7,1]=>0000011=>1100000=>[1,1,6]
[4,7,6,5,3,2,8,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[4,6,5,7,3,2,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,7,6,4,2,8,1]=>0011101=>1011100=>[1,2,1,1,3]
[3,5,6,7,4,2,8,1]=>0001101=>1011000=>[1,2,1,4]
[4,3,7,6,5,2,8,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,3,6,7,5,2,8,1]=>1001101=>1011001=>[1,2,1,3,1]
[3,4,7,6,5,2,8,1]=>0011101=>1011100=>[1,2,1,1,3]
[5,4,3,7,6,2,8,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,6,5,3,7,2,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[3,6,5,4,7,2,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[3,5,6,4,7,2,8,1]=>0010101=>1010100=>[1,2,2,3]
[4,3,6,5,7,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,5,4,6,7,2,8,1]=>0100101=>1010010=>[1,2,3,2]
[2,5,4,7,6,3,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[2,4,6,5,7,3,8,1]=>0010101=>1010100=>[1,2,2,3]
[2,4,5,6,7,3,8,1]=>0000101=>1010000=>[1,2,5]
[3,2,6,7,5,4,8,1]=>1001101=>1011001=>[1,2,1,3,1]
[3,2,6,5,7,4,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[2,3,7,6,5,4,8,1]=>0011101=>1011100=>[1,2,1,1,3]
[4,3,2,7,6,5,8,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,3,2,6,7,5,8,1]=>1100101=>1010011=>[1,2,3,1,1]
[3,4,2,7,6,5,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[2,4,3,7,6,5,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,2,4,7,6,5,8,1]=>1001101=>1011001=>[1,2,1,3,1]
[2,3,4,7,6,5,8,1]=>0001101=>1011000=>[1,2,1,4]
[5,4,3,2,7,6,8,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,3,5,2,7,6,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[2,5,4,3,7,6,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[3,2,5,4,7,6,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[2,3,5,4,7,6,8,1]=>0010101=>1010100=>[1,2,2,3]
[4,3,2,5,7,6,8,1]=>1100101=>1010011=>[1,2,3,1,1]
[2,4,3,5,7,6,8,1]=>0100101=>1010010=>[1,2,3,2]
[3,2,4,5,7,6,8,1]=>1000101=>1010001=>[1,2,4,1]
[2,3,4,5,7,6,8,1]=>0000101=>1010000=>[1,2,5]
[3,6,5,4,2,7,8,1]=>0111001=>1001110=>[1,3,1,1,2]
[3,5,6,4,2,7,8,1]=>0011001=>1001100=>[1,3,1,3]
[2,6,5,4,3,7,8,1]=>0111001=>1001110=>[1,3,1,1,2]
[2,5,4,6,3,7,8,1]=>0101001=>1001010=>[1,3,2,2]
[2,3,6,5,4,7,8,1]=>0011001=>1001100=>[1,3,1,3]
[2,3,5,6,4,7,8,1]=>0001001=>1001000=>[1,3,4]
[4,3,2,6,5,7,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[3,4,2,6,5,7,8,1]=>0101001=>1001010=>[1,3,2,2]
[2,4,3,6,5,7,8,1]=>0101001=>1001010=>[1,3,2,2]
[2,3,4,6,5,7,8,1]=>0001001=>1001000=>[1,3,4]
[3,5,4,2,6,7,8,1]=>0110001=>1000110=>[1,4,1,2]
[2,5,4,3,6,7,8,1]=>0110001=>1000110=>[1,4,1,2]
[2,4,5,3,6,7,8,1]=>0010001=>1000100=>[1,4,3]
[3,2,5,4,6,7,8,1]=>1010001=>1000101=>[1,4,2,1]
[2,3,5,4,6,7,8,1]=>0010001=>1000100=>[1,4,3]
[2,4,3,5,6,7,8,1]=>0100001=>1000010=>[1,5,2]
[1,8,7,6,5,4,3,2]=>0111111=>1111110=>[1,1,1,1,1,1,2]
[1,7,8,6,5,4,3,2]=>0011111=>1111100=>[1,1,1,1,1,3]
[1,6,8,7,5,4,3,2]=>0011111=>1111100=>[1,1,1,1,1,3]
[1,7,6,8,5,4,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[1,6,7,8,5,4,3,2]=>0001111=>1111000=>[1,1,1,1,4]
[1,7,6,5,8,4,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,6,7,5,8,4,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[1,5,7,6,8,4,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[1,6,5,7,8,4,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[1,5,6,7,8,4,3,2]=>0000111=>1110000=>[1,1,1,5]
[1,4,8,7,6,5,3,2]=>0011111=>1111100=>[1,1,1,1,1,3]
[1,4,7,8,6,5,3,2]=>0001111=>1111000=>[1,1,1,1,4]
[1,4,6,8,7,5,3,2]=>0001111=>1111000=>[1,1,1,1,4]
[1,4,6,7,8,5,3,2]=>0000111=>1110000=>[1,1,1,5]
[1,4,5,7,8,6,3,2]=>0000111=>1110000=>[1,1,1,5]
[1,4,6,5,8,7,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[1,4,7,6,5,8,3,2]=>0011011=>1101100=>[1,1,2,1,3]
[1,6,5,4,7,8,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[1,3,8,7,6,5,4,2]=>0011111=>1111100=>[1,1,1,1,1,3]
[1,3,6,8,7,5,4,2]=>0001111=>1111000=>[1,1,1,1,4]
[1,3,6,7,8,5,4,2]=>0000111=>1110000=>[1,1,1,5]
[1,3,5,8,7,6,4,2]=>0001111=>1111000=>[1,1,1,1,4]
[1,3,5,7,8,6,4,2]=>0000111=>1110000=>[1,1,1,5]
[1,3,5,7,6,8,4,2]=>0001011=>1101000=>[1,1,2,4]
[1,3,6,5,7,8,4,2]=>0010011=>1100100=>[1,1,3,3]
[1,3,5,6,7,8,4,2]=>0000011=>1100000=>[1,1,6]
[1,4,3,8,7,6,5,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[1,4,3,7,8,6,5,2]=>0100111=>1110010=>[1,1,1,3,2]
[1,4,3,6,8,7,5,2]=>0100111=>1110010=>[1,1,1,3,2]
[1,4,3,7,6,8,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,4,8,7,6,5,2]=>0001111=>1111000=>[1,1,1,1,4]
[1,3,4,7,6,8,5,2]=>0001011=>1101000=>[1,1,2,4]
[1,3,4,6,7,8,5,2]=>0000011=>1100000=>[1,1,6]
[1,5,4,3,8,7,6,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,3,5,4,7,8,6,2]=>0010011=>1100100=>[1,1,3,3]
[1,4,3,5,8,7,6,2]=>0100111=>1110010=>[1,1,1,3,2]
[1,4,3,5,7,8,6,2]=>0100011=>1100010=>[1,1,4,2]
[1,3,4,5,8,7,6,2]=>0000111=>1110000=>[1,1,1,5]
[1,6,5,4,3,8,7,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,5,6,4,3,8,7,2]=>0011011=>1101100=>[1,1,2,1,3]
[1,4,6,5,3,8,7,2]=>0011011=>1101100=>[1,1,2,1,3]
[1,3,6,5,4,8,7,2]=>0011011=>1101100=>[1,1,2,1,3]
[1,4,3,6,5,8,7,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,5,4,3,6,8,7,2]=>0110011=>1100110=>[1,1,3,1,2]
[1,6,7,5,4,3,8,2]=>0011101=>1011100=>[1,2,1,1,3]
[1,3,5,7,6,4,8,2]=>0001101=>1011000=>[1,2,1,4]
[1,3,4,7,6,5,8,2]=>0001101=>1011000=>[1,2,1,4]
[1,3,5,4,7,6,8,2]=>0010101=>1010100=>[1,2,2,3]
[1,4,3,6,5,7,8,2]=>0101001=>1001010=>[1,3,2,2]
[1,5,4,3,6,7,8,2]=>0110001=>1000110=>[1,4,1,2]
[2,1,8,7,6,5,4,3]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[2,1,7,8,6,5,4,3]=>1001111=>1111001=>[1,1,1,1,3,1]
[2,1,6,8,7,5,4,3]=>1001111=>1111001=>[1,1,1,1,3,1]
[2,1,7,6,8,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,1,6,7,8,5,4,3]=>1000111=>1110001=>[1,1,1,4,1]
[2,1,5,7,8,6,4,3]=>1000111=>1110001=>[1,1,1,4,1]
[2,1,6,5,8,7,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,1,7,6,5,8,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,1,6,7,5,8,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,6,5,7,8,4,3]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,5,6,7,8,4,3]=>1000011=>1100001=>[1,1,5,1]
[2,1,4,8,7,6,5,3]=>1001111=>1111001=>[1,1,1,1,3,1]
[2,1,4,7,8,6,5,3]=>1000111=>1110001=>[1,1,1,4,1]
[2,1,4,6,8,7,5,3]=>1000111=>1110001=>[1,1,1,4,1]
[2,1,4,6,7,8,5,3]=>1000011=>1100001=>[1,1,5,1]
[2,1,4,5,8,7,6,3]=>1000111=>1110001=>[1,1,1,4,1]
[2,1,4,5,7,8,6,3]=>1000011=>1100001=>[1,1,5,1]
[2,1,4,6,5,8,7,3]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,4,5,6,8,7,3]=>1000011=>1100001=>[1,1,5,1]
[2,1,5,7,6,4,8,3]=>1001101=>1011001=>[1,2,1,3,1]
[2,1,6,5,7,4,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,5,6,7,4,8,3]=>1000101=>1010001=>[1,2,4,1]
[2,1,4,7,6,5,8,3]=>1001101=>1011001=>[1,2,1,3,1]
[2,1,4,6,7,5,8,3]=>1000101=>1010001=>[1,2,4,1]
[2,1,5,4,7,6,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,5,6,4,7,8,3]=>1001001=>1001001=>[1,3,3,1]
[2,1,4,5,6,7,8,3]=>1000001=>1000001=>[1,6,1]
[1,2,8,7,6,5,4,3]=>0011111=>1111100=>[1,1,1,1,1,3]
[1,2,6,7,8,5,4,3]=>0000111=>1110000=>[1,1,1,5]
[1,2,6,5,8,7,4,3]=>0010111=>1110100=>[1,1,1,2,3]
[1,2,7,6,5,8,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,2,5,7,6,8,4,3]=>0001011=>1101000=>[1,1,2,4]
[1,2,6,5,7,8,4,3]=>0010011=>1100100=>[1,1,3,3]
[1,2,5,6,7,8,4,3]=>0000011=>1100000=>[1,1,6]
[1,2,4,8,7,6,5,3]=>0001111=>1111000=>[1,1,1,1,4]
[1,2,4,7,8,6,5,3]=>0000111=>1110000=>[1,1,1,5]
[1,2,4,6,8,7,5,3]=>0000111=>1110000=>[1,1,1,5]
[1,2,4,6,7,8,5,3]=>0000011=>1100000=>[1,1,6]
[1,2,5,4,8,7,6,3]=>0010111=>1110100=>[1,1,1,2,3]
[1,2,4,5,7,8,6,3]=>0000011=>1100000=>[1,1,6]
[1,2,6,5,4,8,7,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,2,5,7,6,4,8,3]=>0001101=>1011000=>[1,2,1,4]
[1,2,5,6,7,4,8,3]=>0000101=>1010000=>[1,2,5]
[1,2,4,7,6,5,8,3]=>0001101=>1011000=>[1,2,1,4]
[1,2,6,5,4,7,8,3]=>0011001=>1001100=>[1,3,1,3]
[3,2,1,8,7,6,5,4]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[3,2,1,7,8,6,5,4]=>1100111=>1110011=>[1,1,1,3,1,1]
[3,2,1,6,8,7,5,4]=>1100111=>1110011=>[1,1,1,3,1,1]
[3,2,1,7,6,8,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,2,1,6,7,8,5,4]=>1100011=>1100011=>[1,1,4,1,1]
[3,2,1,5,8,7,6,4]=>1100111=>1110011=>[1,1,1,3,1,1]
[3,2,1,5,7,8,6,4]=>1100011=>1100011=>[1,1,4,1,1]
[3,2,1,6,5,8,7,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,2,1,5,6,8,7,4]=>1100011=>1100011=>[1,1,4,1,1]
[3,2,1,7,6,5,8,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,2,1,6,7,5,8,4]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,1,5,7,6,8,4]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,1,6,5,7,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[3,2,1,5,6,7,8,4]=>1100001=>1000011=>[1,5,1,1]
[2,3,1,8,7,6,5,4]=>0101111=>1111010=>[1,1,1,1,2,2]
[2,3,1,6,8,7,5,4]=>0100111=>1110010=>[1,1,1,3,2]
[2,3,1,7,6,8,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[2,3,1,6,7,8,5,4]=>0100011=>1100010=>[1,1,4,2]
[2,3,1,6,5,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[2,3,1,5,6,7,8,4]=>0100001=>1000010=>[1,5,2]
[1,3,2,8,7,6,5,4]=>0101111=>1111010=>[1,1,1,1,2,2]
[1,3,2,6,8,7,5,4]=>0100111=>1110010=>[1,1,1,3,2]
[1,3,2,5,7,8,6,4]=>0100011=>1100010=>[1,1,4,2]
[1,3,2,6,5,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,2,7,6,5,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,3,2,5,7,6,8,4]=>0100101=>1010010=>[1,2,3,2]
[1,3,2,6,5,7,8,4]=>0101001=>1001010=>[1,3,2,2]
[2,1,3,8,7,6,5,4]=>1001111=>1111001=>[1,1,1,1,3,1]
[2,1,3,7,8,6,5,4]=>1000111=>1110001=>[1,1,1,4,1]
[2,1,3,6,8,7,5,4]=>1000111=>1110001=>[1,1,1,4,1]
[1,2,3,8,7,6,5,4]=>0001111=>1111000=>[1,1,1,1,4]
[1,2,3,7,8,6,5,4]=>0000111=>1110000=>[1,1,1,5]
[1,2,3,6,8,7,5,4]=>0000111=>1110000=>[1,1,1,5]
[1,2,3,7,6,8,5,4]=>0001011=>1101000=>[1,1,2,4]
[1,2,3,6,7,8,5,4]=>0000011=>1100000=>[1,1,6]
[1,2,3,5,8,7,6,4]=>0000111=>1110000=>[1,1,1,5]
[1,2,3,5,7,8,6,4]=>0000011=>1100000=>[1,1,6]
[1,2,3,6,5,8,7,4]=>0001011=>1101000=>[1,1,2,4]
[1,2,3,5,6,8,7,4]=>0000011=>1100000=>[1,1,6]
[1,2,3,7,6,5,8,4]=>0001101=>1011000=>[1,2,1,4]
[1,2,3,6,7,5,8,4]=>0000101=>1010000=>[1,2,5]
[1,2,3,5,7,6,8,4]=>0000101=>1010000=>[1,2,5]
[1,2,3,6,5,7,8,4]=>0001001=>1001000=>[1,3,4]
[1,2,3,5,6,7,8,4]=>0000001=>1000000=>[1,7]
[4,3,2,1,8,7,6,5]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[4,3,2,1,7,8,6,5]=>1110011=>1100111=>[1,1,3,1,1,1]
[4,3,2,1,6,8,7,5]=>1110011=>1100111=>[1,1,3,1,1,1]
[4,3,2,1,7,6,8,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,3,2,1,6,7,8,5]=>1110001=>1000111=>[1,4,1,1,1]
[3,4,2,1,8,7,6,5]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,4,2,1,7,8,6,5]=>0110011=>1100110=>[1,1,3,1,2]
[3,4,2,1,6,8,7,5]=>0110011=>1100110=>[1,1,3,1,2]
[3,4,2,1,7,6,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,4,2,1,6,7,8,5]=>0110001=>1000110=>[1,4,1,2]
[2,4,3,1,8,7,6,5]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,4,3,1,6,8,7,5]=>0110011=>1100110=>[1,1,3,1,2]
[2,4,3,1,7,6,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[2,4,3,1,6,7,8,5]=>0110001=>1000110=>[1,4,1,2]
[3,2,4,1,8,7,6,5]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,2,4,1,7,8,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[3,2,4,1,6,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[3,2,4,1,7,6,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,4,1,6,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[2,3,4,1,8,7,6,5]=>0010111=>1110100=>[1,1,1,2,3]
[2,3,4,1,7,8,6,5]=>0010011=>1100100=>[1,1,3,3]
[2,3,4,1,6,8,7,5]=>0010011=>1100100=>[1,1,3,3]
[2,3,4,1,7,6,8,5]=>0010101=>1010100=>[1,2,2,3]
[2,3,4,1,6,7,8,5]=>0010001=>1000100=>[1,4,3]
[1,4,3,2,8,7,6,5]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,4,3,2,7,6,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[1,4,3,2,6,7,8,5]=>0110001=>1000110=>[1,4,1,2]
[1,3,4,2,8,7,6,5]=>0010111=>1110100=>[1,1,1,2,3]
[1,3,4,2,7,8,6,5]=>0010011=>1100100=>[1,1,3,3]
[1,3,4,2,6,8,7,5]=>0010011=>1100100=>[1,1,3,3]
[1,3,4,2,7,6,8,5]=>0010101=>1010100=>[1,2,2,3]
[1,3,4,2,6,7,8,5]=>0010001=>1000100=>[1,4,3]
[2,1,4,3,8,7,6,5]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,1,4,3,7,8,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,4,3,6,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,4,3,7,6,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,4,3,6,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[1,2,4,3,8,7,6,5]=>0010111=>1110100=>[1,1,1,2,3]
[1,2,4,3,7,8,6,5]=>0010011=>1100100=>[1,1,3,3]
[1,2,4,3,6,8,7,5]=>0010011=>1100100=>[1,1,3,3]
[1,2,4,3,7,6,8,5]=>0010101=>1010100=>[1,2,2,3]
[1,2,4,3,6,7,8,5]=>0010001=>1000100=>[1,4,3]
[3,2,1,4,8,7,6,5]=>1100111=>1110011=>[1,1,1,3,1,1]
[3,2,1,4,7,8,6,5]=>1100011=>1100011=>[1,1,4,1,1]
[3,2,1,4,6,8,7,5]=>1100011=>1100011=>[1,1,4,1,1]
[3,2,1,4,7,6,8,5]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,1,4,6,7,8,5]=>1100001=>1000011=>[1,5,1,1]
[2,3,1,4,8,7,6,5]=>0100111=>1110010=>[1,1,1,3,2]
[2,3,1,4,7,8,6,5]=>0100011=>1100010=>[1,1,4,2]
[2,3,1,4,7,6,8,5]=>0100101=>1010010=>[1,2,3,2]
[2,3,1,4,6,7,8,5]=>0100001=>1000010=>[1,5,2]
[1,3,2,4,8,7,6,5]=>0100111=>1110010=>[1,1,1,3,2]
[1,3,2,4,6,8,7,5]=>0100011=>1100010=>[1,1,4,2]
[1,3,2,4,7,6,8,5]=>0100101=>1010010=>[1,2,3,2]
[1,3,2,4,6,7,8,5]=>0100001=>1000010=>[1,5,2]
[2,1,3,4,8,7,6,5]=>1000111=>1110001=>[1,1,1,4,1]
[2,1,3,4,7,6,8,5]=>1000101=>1010001=>[1,2,4,1]
[2,1,3,4,6,7,8,5]=>1000001=>1000001=>[1,6,1]
[1,2,3,4,8,7,6,5]=>0000111=>1110000=>[1,1,1,5]
[1,2,3,4,7,8,6,5]=>0000011=>1100000=>[1,1,6]
[1,2,3,4,6,8,7,5]=>0000011=>1100000=>[1,1,6]
[1,2,3,4,7,6,8,5]=>0000101=>1010000=>[1,2,5]
[1,2,3,4,6,7,8,5]=>0000001=>1000000=>[1,7]
[5,4,3,2,1,8,7,6]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[5,4,3,2,1,7,8,6]=>1111001=>1001111=>[1,3,1,1,1,1]
[4,5,3,2,1,8,7,6]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,5,4,2,1,8,7,6]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,5,4,2,1,7,8,6]=>0111001=>1001110=>[1,3,1,1,2]
[4,3,5,2,1,8,7,6]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,4,5,2,1,8,7,6]=>0011011=>1101100=>[1,1,2,1,3]
[3,4,5,2,1,7,8,6]=>0011001=>1001100=>[1,3,1,3]
[2,5,4,3,1,8,7,6]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,5,4,3,1,7,8,6]=>0111001=>1001110=>[1,3,1,1,2]
[2,4,5,3,1,8,7,6]=>0011011=>1101100=>[1,1,2,1,3]
[3,2,5,4,1,8,7,6]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,2,5,4,1,7,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[2,3,5,4,1,8,7,6]=>0011011=>1101100=>[1,1,2,1,3]
[4,3,2,5,1,8,7,6]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,4,2,5,1,8,7,6]=>0101011=>1101010=>[1,1,2,2,2]
[3,4,2,5,1,7,8,6]=>0101001=>1001010=>[1,3,2,2]
[2,4,3,5,1,8,7,6]=>0101011=>1101010=>[1,1,2,2,2]
[2,4,3,5,1,7,8,6]=>0101001=>1001010=>[1,3,2,2]
[3,2,4,5,1,8,7,6]=>1001011=>1101001=>[1,1,2,3,1]
[2,3,4,5,1,8,7,6]=>0001011=>1101000=>[1,1,2,4]
[1,3,5,4,2,7,8,6]=>0011001=>1001100=>[1,3,1,3]
[1,4,3,5,2,7,8,6]=>0101001=>1001010=>[1,3,2,2]
[1,3,4,5,2,8,7,6]=>0001011=>1101000=>[1,1,2,4]
[1,3,4,5,2,7,8,6]=>0001001=>1001000=>[1,3,4]
[1,2,5,4,3,7,8,6]=>0011001=>1001100=>[1,3,1,3]
[1,2,4,5,3,8,7,6]=>0001011=>1101000=>[1,1,2,4]
[1,2,4,5,3,7,8,6]=>0001001=>1001000=>[1,3,4]
[1,3,2,5,4,7,8,6]=>0101001=>1001010=>[1,3,2,2]
[2,1,3,5,4,8,7,6]=>1001011=>1101001=>[1,1,2,3,1]
[1,2,3,5,4,8,7,6]=>0001011=>1101000=>[1,1,2,4]
[1,2,3,5,4,7,8,6]=>0001001=>1001000=>[1,3,4]
[4,3,2,1,5,8,7,6]=>1110011=>1100111=>[1,1,3,1,1,1]
[4,3,2,1,5,7,8,6]=>1110001=>1000111=>[1,4,1,1,1]
[3,2,4,1,5,8,7,6]=>1010011=>1100101=>[1,1,3,2,1]
[3,2,4,1,5,7,8,6]=>1010001=>1000101=>[1,4,2,1]
[2,3,4,1,5,8,7,6]=>0010011=>1100100=>[1,1,3,3]
[2,3,4,1,5,7,8,6]=>0010001=>1000100=>[1,4,3]
[1,4,3,2,5,8,7,6]=>0110011=>1100110=>[1,1,3,1,2]
[1,4,3,2,5,7,8,6]=>0110001=>1000110=>[1,4,1,2]
[1,3,4,2,5,8,7,6]=>0010011=>1100100=>[1,1,3,3]
[1,3,4,2,5,7,8,6]=>0010001=>1000100=>[1,4,3]
[1,2,4,3,5,7,8,6]=>0010001=>1000100=>[1,4,3]
[3,2,1,4,5,8,7,6]=>1100011=>1100011=>[1,1,4,1,1]
[3,2,1,4,5,7,8,6]=>1100001=>1000011=>[1,5,1,1]
[2,3,1,4,5,7,8,6]=>0100001=>1000010=>[1,5,2]
[1,3,2,4,5,7,8,6]=>0100001=>1000010=>[1,5,2]
[1,2,3,4,5,8,7,6]=>0000011=>1100000=>[1,1,6]
[1,2,3,4,5,7,8,6]=>0000001=>1000000=>[1,7]
[6,5,4,3,2,1,8,7]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[5,6,4,3,2,1,8,7]=>0111101=>1011110=>[1,2,1,1,1,2]
[4,6,5,3,2,1,8,7]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,4,6,3,2,1,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,5,6,3,2,1,8,7]=>0011101=>1011100=>[1,2,1,1,3]
[3,6,5,4,2,1,8,7]=>0111101=>1011110=>[1,2,1,1,1,2]
[3,5,6,4,2,1,8,7]=>0011101=>1011100=>[1,2,1,1,3]
[4,3,6,5,2,1,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,4,3,6,2,1,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,5,3,6,2,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[3,4,5,6,2,1,8,7]=>0001101=>1011000=>[1,2,1,4]
[2,6,5,4,3,1,8,7]=>0111101=>1011110=>[1,2,1,1,1,2]
[2,5,6,4,3,1,8,7]=>0011101=>1011100=>[1,2,1,1,3]
[2,4,6,5,3,1,8,7]=>0011101=>1011100=>[1,2,1,1,3]
[2,3,6,5,4,1,8,7]=>0011101=>1011100=>[1,2,1,1,3]
[2,3,5,6,4,1,8,7]=>0001101=>1011000=>[1,2,1,4]
[2,4,3,6,5,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[5,4,3,2,6,1,8,7]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,5,3,2,6,1,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[3,5,4,2,6,1,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[4,3,5,2,6,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[3,4,5,2,6,1,8,7]=>0010101=>1010100=>[1,2,2,3]
[2,5,4,3,6,1,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[2,4,5,3,6,1,8,7]=>0010101=>1010100=>[1,2,2,3]
[3,2,5,4,6,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[3,4,2,5,6,1,8,7]=>0100101=>1010010=>[1,2,3,2]
[2,3,4,5,6,1,8,7]=>0000101=>1010000=>[1,2,5]
[1,5,4,6,3,2,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[1,3,6,5,4,2,8,7]=>0011101=>1011100=>[1,2,1,1,3]
[2,1,6,5,4,3,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,1,5,6,4,3,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[2,1,4,6,5,3,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[2,1,5,4,6,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,4,5,6,3,8,7]=>1000101=>1010001=>[1,2,4,1]
[2,3,1,6,5,4,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[1,2,3,6,5,4,8,7]=>0001101=>1011000=>[1,2,1,4]
[1,2,3,5,6,4,8,7]=>0000101=>1010000=>[1,2,5]
[4,3,2,1,6,5,8,7]=>1110101=>1010111=>[1,2,2,1,1,1]
[3,4,2,1,6,5,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[2,4,3,1,6,5,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[3,2,4,1,6,5,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[2,3,4,1,6,5,8,7]=>0010101=>1010100=>[1,2,2,3]
[2,1,4,3,6,5,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[1,2,4,3,6,5,8,7]=>0010101=>1010100=>[1,2,2,3]
[1,3,2,4,6,5,8,7]=>0100101=>1010010=>[1,2,3,2]
[2,1,3,4,6,5,8,7]=>1000101=>1010001=>[1,2,4,1]
[1,2,3,4,6,5,8,7]=>0000101=>1010000=>[1,2,5]
[5,4,3,2,1,6,8,7]=>1111001=>1001111=>[1,3,1,1,1,1]
[4,5,3,2,1,6,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[3,5,4,2,1,6,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[2,5,4,3,1,6,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[2,4,5,3,1,6,8,7]=>0011001=>1001100=>[1,3,1,3]
[3,2,5,4,1,6,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[1,3,5,4,2,6,8,7]=>0011001=>1001100=>[1,3,1,3]
[1,3,4,5,2,6,8,7]=>0001001=>1001000=>[1,3,4]
[2,1,4,5,3,6,8,7]=>1001001=>1001001=>[1,3,3,1]
[1,2,5,4,3,6,8,7]=>0011001=>1001100=>[1,3,1,3]
[2,1,3,5,4,6,8,7]=>1001001=>1001001=>[1,3,3,1]
[4,3,2,1,5,6,8,7]=>1110001=>1000111=>[1,4,1,1,1]
[3,2,4,1,5,6,8,7]=>1010001=>1000101=>[1,4,2,1]
[2,3,4,1,5,6,8,7]=>0010001=>1000100=>[1,4,3]
[1,4,3,2,5,6,8,7]=>0110001=>1000110=>[1,4,1,2]
[1,3,4,2,5,6,8,7]=>0010001=>1000100=>[1,4,3]
[2,1,4,3,5,6,8,7]=>1010001=>1000101=>[1,4,2,1]
[1,2,4,3,5,6,8,7]=>0010001=>1000100=>[1,4,3]
[2,1,3,4,5,6,8,7]=>1000001=>1000001=>[1,6,1]
[1,2,3,4,5,6,8,7]=>0000001=>1000000=>[1,7]
[5,7,6,4,3,2,1,8]=>0111110=>0111110=>[2,1,1,1,1,2]
[4,7,6,5,3,2,1,8]=>0111110=>0111110=>[2,1,1,1,1,2]
[4,6,7,5,3,2,1,8]=>0011110=>0111100=>[2,1,1,1,3]
[4,5,7,6,3,2,1,8]=>0011110=>0111100=>[2,1,1,1,3]
[4,6,5,7,3,2,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[3,5,7,6,4,2,1,8]=>0011110=>0111100=>[2,1,1,1,3]
[3,5,6,7,4,2,1,8]=>0001110=>0111000=>[2,1,1,4]
[3,4,7,6,5,2,1,8]=>0011110=>0111100=>[2,1,1,1,3]
[4,5,3,7,6,2,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[3,5,4,7,6,2,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[4,3,5,7,6,2,1,8]=>1001110=>0111001=>[2,1,1,3,1]
[2,5,6,7,4,3,1,8]=>0001110=>0111000=>[2,1,1,4]
[2,4,6,7,5,3,1,8]=>0001110=>0111000=>[2,1,1,4]
[3,2,7,6,5,4,1,8]=>1011110=>0111101=>[2,1,1,1,2,1]
[3,2,6,7,5,4,1,8]=>1001110=>0111001=>[2,1,1,3,1]
[3,2,5,7,6,4,1,8]=>1001110=>0111001=>[2,1,1,3,1]
[2,3,7,6,5,4,1,8]=>0011110=>0111100=>[2,1,1,1,3]
[2,3,6,7,5,4,1,8]=>0001110=>0111000=>[2,1,1,4]
[2,3,5,7,6,4,1,8]=>0001110=>0111000=>[2,1,1,4]
[2,3,6,5,7,4,1,8]=>0010110=>0110100=>[2,1,2,3]
[2,3,5,6,7,4,1,8]=>0000110=>0110000=>[2,1,5]
[3,2,4,6,7,5,1,8]=>1000110=>0110001=>[2,1,4,1]
[2,3,4,7,6,5,1,8]=>0001110=>0111000=>[2,1,1,4]
[5,4,3,2,7,6,1,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[4,5,3,2,7,6,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[3,5,4,2,7,6,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[3,2,5,4,7,6,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,3,2,5,7,6,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[3,6,5,4,2,7,1,8]=>0111010=>0101110=>[2,2,1,1,2]
[3,4,6,5,2,7,1,8]=>0011010=>0101100=>[2,2,1,3]
[3,5,4,6,2,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[2,5,4,6,3,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[3,2,6,5,4,7,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[3,4,2,6,5,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[2,4,3,6,5,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[3,5,4,2,6,7,1,8]=>0110010=>0100110=>[2,3,1,2]
[2,5,4,3,6,7,1,8]=>0110010=>0100110=>[2,3,1,2]
[1,5,6,7,4,3,2,8]=>0001110=>0111000=>[2,1,1,4]
[1,4,6,5,7,3,2,8]=>0010110=>0110100=>[2,1,2,3]
[1,3,5,7,6,4,2,8]=>0001110=>0111000=>[2,1,1,4]
[1,3,5,6,7,4,2,8]=>0000110=>0110000=>[2,1,5]
[1,3,5,4,7,6,2,8]=>0010110=>0110100=>[2,1,2,3]
[1,4,3,5,7,6,2,8]=>0100110=>0110010=>[2,1,3,2]
[1,5,4,6,3,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[1,3,6,5,4,7,2,8]=>0011010=>0101100=>[2,2,1,3]
[1,4,3,6,5,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[1,5,4,3,6,7,2,8]=>0110010=>0100110=>[2,3,1,2]
[1,3,4,5,6,7,2,8]=>0000010=>0100000=>[2,6]
[2,1,4,6,7,5,3,8]=>1000110=>0110001=>[2,1,4,1]
[1,2,5,7,6,4,3,8]=>0001110=>0111000=>[2,1,1,4]
[1,2,5,6,7,4,3,8]=>0000110=>0110000=>[2,1,5]
[1,2,5,6,4,7,3,8]=>0001010=>0101000=>[2,2,4]
[1,2,5,4,6,7,3,8]=>0010010=>0100100=>[2,3,3]
[3,2,1,5,7,6,4,8]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,1,5,6,7,4,8]=>1100010=>0100011=>[2,4,1,1]
[2,3,1,6,7,5,4,8]=>0100110=>0110010=>[2,1,3,2]
[2,3,1,6,5,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[2,3,1,5,6,7,4,8]=>0100010=>0100010=>[2,4,2]
[1,3,2,5,7,6,4,8]=>0100110=>0110010=>[2,1,3,2]
[1,3,2,6,5,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[1,3,2,5,6,7,4,8]=>0100010=>0100010=>[2,4,2]
[2,1,3,6,7,5,4,8]=>1000110=>0110001=>[2,1,4,1]
[1,2,3,7,6,5,4,8]=>0001110=>0111000=>[2,1,1,4]
[1,2,3,6,7,5,4,8]=>0000110=>0110000=>[2,1,5]
[1,2,3,5,7,6,4,8]=>0000110=>0110000=>[2,1,5]
[1,2,3,6,5,7,4,8]=>0001010=>0101000=>[2,2,4]
[1,2,3,5,6,7,4,8]=>0000010=>0100000=>[2,6]
[4,3,2,1,7,6,5,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[4,3,2,1,6,7,5,8]=>1110010=>0100111=>[2,3,1,1,1]
[3,2,4,1,7,6,5,8]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,4,1,6,7,5,8]=>1010010=>0100101=>[2,3,2,1]
[2,3,4,1,7,6,5,8]=>0010110=>0110100=>[2,1,2,3]
[2,3,4,1,6,7,5,8]=>0010010=>0100100=>[2,3,3]
[1,4,3,2,7,6,5,8]=>0110110=>0110110=>[2,1,2,1,2]
[1,4,3,2,6,7,5,8]=>0110010=>0100110=>[2,3,1,2]
[1,3,4,2,6,7,5,8]=>0010010=>0100100=>[2,3,3]
[1,2,4,3,6,7,5,8]=>0010010=>0100100=>[2,3,3]
[2,3,1,4,6,7,5,8]=>0100010=>0100010=>[2,4,2]
[1,3,2,4,7,6,5,8]=>0100110=>0110010=>[2,1,3,2]
[1,2,3,4,7,6,5,8]=>0000110=>0110000=>[2,1,5]
[1,2,3,4,6,7,5,8]=>0000010=>0100000=>[2,6]
[5,4,3,2,1,7,6,8]=>1111010=>0101111=>[2,2,1,1,1,1]
[4,5,3,2,1,7,6,8]=>0111010=>0101110=>[2,2,1,1,2]
[3,5,4,2,1,7,6,8]=>0111010=>0101110=>[2,2,1,1,2]
[2,5,4,3,1,7,6,8]=>0111010=>0101110=>[2,2,1,1,2]
[2,4,5,3,1,7,6,8]=>0011010=>0101100=>[2,2,1,3]
[3,2,5,4,1,7,6,8]=>1011010=>0101101=>[2,2,1,2,1]
[3,4,2,5,1,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[2,4,3,5,1,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[1,3,5,4,2,7,6,8]=>0011010=>0101100=>[2,2,1,3]
[1,4,3,5,2,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[1,3,4,5,2,7,6,8]=>0001010=>0101000=>[2,2,4]
[2,3,1,5,4,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[1,3,2,5,4,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[1,2,3,5,4,7,6,8]=>0001010=>0101000=>[2,2,4]
[4,3,2,1,5,7,6,8]=>1110010=>0100111=>[2,3,1,1,1]
[3,2,4,1,5,7,6,8]=>1010010=>0100101=>[2,3,2,1]
[2,3,4,1,5,7,6,8]=>0010010=>0100100=>[2,3,3]
[1,4,3,2,5,7,6,8]=>0110010=>0100110=>[2,3,1,2]
[1,3,4,2,5,7,6,8]=>0010010=>0100100=>[2,3,3]
[1,3,2,4,5,7,6,8]=>0100010=>0100010=>[2,4,2]
[1,2,3,4,5,7,6,8]=>0000010=>0100000=>[2,6]
[3,6,5,4,2,1,7,8]=>0111100=>0011110=>[3,1,1,1,2]
[4,3,6,5,2,1,7,8]=>1011100=>0011101=>[3,1,1,2,1]
[2,4,6,5,3,1,7,8]=>0011100=>0011100=>[3,1,1,3]
[2,4,5,6,3,1,7,8]=>0001100=>0011000=>[3,1,4]
[4,3,2,6,5,1,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[3,5,4,2,6,1,7,8]=>0110100=>0010110=>[3,2,1,2]
[1,5,6,4,3,2,7,8]=>0011100=>0011100=>[3,1,1,3]
[1,4,6,5,3,2,7,8]=>0011100=>0011100=>[3,1,1,3]
[1,5,4,6,3,2,7,8]=>0101100=>0011010=>[3,1,2,2]
[1,4,5,6,3,2,7,8]=>0001100=>0011000=>[3,1,4]
[1,3,5,6,4,2,7,8]=>0001100=>0011000=>[3,1,4]
[1,4,3,6,5,2,7,8]=>0101100=>0011010=>[3,1,2,2]
[1,5,4,3,6,2,7,8]=>0110100=>0010110=>[3,2,1,2]
[2,1,5,6,4,3,7,8]=>1001100=>0011001=>[3,1,3,1]
[2,1,4,6,5,3,7,8]=>1001100=>0011001=>[3,1,3,1]
[1,2,6,5,4,3,7,8]=>0011100=>0011100=>[3,1,1,3]
[1,2,5,6,4,3,7,8]=>0001100=>0011000=>[3,1,4]
[1,2,4,5,6,3,7,8]=>0000100=>0010000=>[3,5]
[3,2,1,5,6,4,7,8]=>1100100=>0010011=>[3,3,1,1]
[1,3,2,5,6,4,7,8]=>0100100=>0010010=>[3,3,2]
[1,2,3,5,6,4,7,8]=>0000100=>0010000=>[3,5]
[4,3,2,1,6,5,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[3,2,4,1,6,5,7,8]=>1010100=>0010101=>[3,2,2,1]
[2,3,4,1,6,5,7,8]=>0010100=>0010100=>[3,2,3]
[2,1,4,3,6,5,7,8]=>1010100=>0010101=>[3,2,2,1]
[1,2,4,3,6,5,7,8]=>0010100=>0010100=>[3,2,3]
[1,3,2,4,6,5,7,8]=>0100100=>0010010=>[3,3,2]
[2,1,3,4,6,5,7,8]=>1000100=>0010001=>[3,4,1]
[1,2,3,4,6,5,7,8]=>0000100=>0010000=>[3,5]
[3,5,4,2,1,6,7,8]=>0111000=>0001110=>[4,1,1,2]
[2,5,4,3,1,6,7,8]=>0111000=>0001110=>[4,1,1,2]
[2,4,5,3,1,6,7,8]=>0011000=>0001100=>[4,1,3]
[3,2,5,4,1,6,7,8]=>1011000=>0001101=>[4,1,2,1]
[2,3,5,4,1,6,7,8]=>0011000=>0001100=>[4,1,3]
[2,4,3,5,1,6,7,8]=>0101000=>0001010=>[4,2,2]
[1,3,5,4,2,6,7,8]=>0011000=>0001100=>[4,1,3]
[1,3,4,5,2,6,7,8]=>0001000=>0001000=>[4,4]
[1,3,2,5,4,6,7,8]=>0101000=>0001010=>[4,2,2]
[1,2,3,5,4,6,7,8]=>0001000=>0001000=>[4,4]
[2,4,3,1,5,6,7,8]=>0110000=>0000110=>[5,1,2]
[1,4,3,2,5,6,7,8]=>0110000=>0000110=>[5,1,2]
[1,3,4,2,5,6,7,8]=>0010000=>0000100=>[5,3]
[2,1,4,3,5,6,7,8]=>1010000=>0000101=>[5,2,1]
[1,2,4,3,5,6,7,8]=>0010000=>0000100=>[5,3]
[1,3,2,4,5,6,7,8]=>0100000=>0000010=>[6,2]
[1,2,3,4,8,6,7,5]=>0000101=>1010000=>[1,2,5]
[1,2,3,5,8,6,7,4]=>0000101=>1010000=>[1,2,5]
[1,2,3,7,5,6,4,8]=>0001010=>0101000=>[2,2,4]
[1,2,3,7,5,6,8,4]=>0001001=>1001000=>[1,3,4]
[1,2,3,8,5,6,7,4]=>0001001=>1001000=>[1,3,4]
[1,2,3,8,5,7,6,4]=>0001011=>1101000=>[1,1,2,4]
[1,2,3,8,6,5,7,4]=>0001101=>1011000=>[1,2,1,4]
[1,2,3,8,6,7,5,4]=>0001011=>1101000=>[1,1,2,4]
[1,2,4,5,8,6,7,3]=>0000101=>1010000=>[1,2,5]
[1,2,4,8,5,6,7,3]=>0001001=>1001000=>[1,3,4]
[1,2,4,8,6,5,7,3]=>0001101=>1011000=>[1,2,1,4]
[1,2,5,4,8,6,7,3]=>0010101=>1010100=>[1,2,2,3]
[1,2,6,4,5,3,7,8]=>0010100=>0010100=>[3,2,3]
[1,2,6,4,5,8,7,3]=>0010011=>1100100=>[1,1,3,3]
[1,2,8,4,5,6,7,3]=>0010001=>1000100=>[1,4,3]
[1,2,8,4,6,7,5,3]=>0010011=>1100100=>[1,1,3,3]
[1,2,8,4,7,6,5,3]=>0010111=>1110100=>[1,1,1,2,3]
[1,2,7,5,4,6,8,3]=>0011001=>1001100=>[1,3,1,3]
[1,2,8,5,4,6,7,3]=>0011001=>1001100=>[1,3,1,3]
[1,2,8,5,4,7,6,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,2,8,6,5,4,7,3]=>0011101=>1011100=>[1,2,1,1,3]
[1,2,8,7,5,6,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,3,2,7,5,6,8,4]=>0101001=>1001010=>[1,3,2,2]
[1,3,2,8,5,7,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,4,5,8,6,7,2]=>0000101=>1010000=>[1,2,5]
[1,3,4,8,5,6,7,2]=>0001001=>1001000=>[1,3,4]
[1,3,6,4,5,2,8,7]=>0010101=>1010100=>[1,2,2,3]
[1,3,6,4,5,7,2,8]=>0010010=>0100100=>[2,3,3]
[1,3,6,4,5,8,7,2]=>0010011=>1100100=>[1,1,3,3]
[1,3,8,4,5,6,7,2]=>0010001=>1000100=>[1,4,3]
[1,3,8,4,6,5,7,2]=>0010101=>1010100=>[1,2,2,3]
[1,3,8,5,4,6,7,2]=>0011001=>1001100=>[1,3,1,3]
[1,3,8,5,4,7,6,2]=>0011011=>1101100=>[1,1,2,1,3]
[1,3,8,5,6,7,4,2]=>0010011=>1100100=>[1,1,3,3]
[1,3,8,5,7,6,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[1,3,8,6,5,7,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[1,3,8,7,5,6,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[1,4,3,8,5,6,7,2]=>0101001=>1001010=>[1,3,2,2]
[1,4,3,8,5,7,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,4,3,8,6,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,5,3,4,2,7,8,6]=>0101001=>1001010=>[1,3,2,2]
[1,5,3,4,6,2,7,8]=>0100100=>0010010=>[3,3,2]
[1,5,3,4,6,7,2,8]=>0100010=>0100010=>[2,4,2]
[1,5,3,4,7,6,2,8]=>0100110=>0110010=>[2,1,3,2]
[1,5,3,4,8,6,7,2]=>0100101=>1010010=>[1,2,3,2]
[1,8,3,4,6,7,5,2]=>0100011=>1100010=>[1,1,4,2]
[1,6,3,5,4,2,7,8]=>0101100=>0011010=>[3,1,2,2]
[1,6,3,5,4,8,7,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,3,5,4,7,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,3,5,6,4,7,2]=>0100101=>1010010=>[1,2,3,2]
[1,8,3,5,7,6,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[1,8,3,6,5,4,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[1,8,3,7,5,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,3,7,6,5,4,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[1,6,4,3,5,2,7,8]=>0110100=>0010110=>[3,2,1,2]
[1,8,4,3,5,6,7,2]=>0110001=>1000110=>[1,4,1,2]
[1,8,4,3,5,7,6,2]=>0110011=>1100110=>[1,1,3,1,2]
[1,7,4,3,6,5,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[1,8,4,3,6,7,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[1,6,4,5,3,8,7,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,4,5,6,3,7,2]=>0100101=>1010010=>[1,2,3,2]
[1,8,4,5,6,7,3,2]=>0100011=>1100010=>[1,1,4,2]
[1,8,4,6,5,7,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,4,7,6,5,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[1,7,5,4,3,6,8,2]=>0111001=>1001110=>[1,3,1,1,2]
[1,8,5,4,3,6,7,2]=>0111001=>1001110=>[1,3,1,1,2]
[1,8,5,4,3,7,6,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,8,5,4,6,3,7,2]=>0110101=>1010110=>[1,2,2,1,2]
[1,8,5,4,6,7,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[1,8,5,4,7,6,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,8,6,4,5,7,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[1,8,7,4,5,6,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[1,8,7,4,6,5,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,8,6,5,4,7,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,8,7,5,4,6,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,8,7,5,6,4,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,1,3,4,8,6,7,5]=>1000101=>1010001=>[1,2,4,1]
[2,1,4,3,8,6,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,4,5,8,6,7,3]=>1000101=>1010001=>[1,2,4,1]
[2,1,4,8,5,6,7,3]=>1001001=>1001001=>[1,3,3,1]
[2,1,4,8,5,7,6,3]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,4,8,6,5,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[2,1,4,8,6,7,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,5,4,8,6,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,6,4,5,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,6,4,5,7,8,3]=>1010001=>1000101=>[1,4,2,1]
[2,1,6,4,5,8,7,3]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,8,4,5,6,7,3]=>1010001=>1000101=>[1,4,2,1]
[2,1,8,4,5,7,6,3]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,8,4,6,5,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,4,6,7,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,8,4,7,6,5,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,1,7,5,4,6,8,3]=>1011001=>1001101=>[1,3,1,2,1]
[2,1,8,5,4,6,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[2,1,8,5,4,7,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,1,7,5,6,4,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,5,6,4,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,5,7,6,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,1,8,7,5,6,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,3,1,8,5,6,7,4]=>0101001=>1001010=>[1,3,2,2]
[2,3,1,8,6,7,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[2,3,4,1,8,6,7,5]=>0010101=>1010100=>[1,2,2,3]
[2,3,4,5,8,6,7,1]=>0000101=>1010000=>[1,2,5]
[2,3,4,7,5,6,1,8]=>0001010=>0101000=>[2,2,4]
[2,3,4,7,5,6,8,1]=>0001001=>1001000=>[1,3,4]
[2,3,4,8,5,6,7,1]=>0001001=>1001000=>[1,3,4]
[2,3,4,8,5,7,6,1]=>0001011=>1101000=>[1,1,2,4]
[2,3,4,8,6,5,7,1]=>0001101=>1011000=>[1,2,1,4]
[2,3,4,8,6,7,5,1]=>0001011=>1101000=>[1,1,2,4]
[2,3,6,4,5,1,8,7]=>0010101=>1010100=>[1,2,2,3]
[2,3,6,4,5,7,8,1]=>0010001=>1000100=>[1,4,3]
[2,3,7,4,5,6,8,1]=>0010001=>1000100=>[1,4,3]
[2,3,8,4,5,6,7,1]=>0010001=>1000100=>[1,4,3]
[2,3,7,4,6,5,8,1]=>0010101=>1010100=>[1,2,2,3]
[2,3,7,5,4,6,1,8]=>0011010=>0101100=>[2,2,1,3]
[2,3,7,5,4,6,8,1]=>0011001=>1001100=>[1,3,1,3]
[2,3,7,5,6,4,1,8]=>0010110=>0110100=>[2,1,2,3]
[2,3,7,5,6,4,8,1]=>0010101=>1010100=>[1,2,2,3]
[2,3,8,5,7,6,4,1]=>0010111=>1110100=>[1,1,1,2,3]
[2,4,3,1,8,6,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[2,4,3,5,8,6,7,1]=>0100101=>1010010=>[1,2,3,2]
[2,4,3,8,5,6,7,1]=>0101001=>1001010=>[1,3,2,2]
[2,4,3,8,6,7,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,3,4,1,6,7,8]=>0101000=>0001010=>[4,2,2]
[2,5,3,4,1,8,7,6]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,3,4,6,7,1,8]=>0100010=>0100010=>[2,4,2]
[2,5,3,4,8,7,6,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,6,3,4,5,7,8,1]=>0100001=>1000010=>[1,5,2]
[2,6,3,4,5,8,7,1]=>0100011=>1100010=>[1,1,4,2]
[2,6,3,5,4,1,7,8]=>0101100=>0011010=>[3,1,2,2]
[2,6,3,5,4,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,3,5,4,7,8,1]=>0101001=>1001010=>[1,3,2,2]
[2,7,3,5,4,6,8,1]=>0101001=>1001010=>[1,3,2,2]
[2,7,3,5,6,4,8,1]=>0100101=>1010010=>[1,2,3,2]
[2,8,3,5,7,6,4,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,7,3,6,5,4,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[2,8,3,7,5,6,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,4,3,8,6,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[2,6,4,3,5,7,8,1]=>0110001=>1000110=>[1,4,1,2]
[2,8,4,3,7,6,5,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,6,4,5,3,1,7,8]=>0101100=>0011010=>[3,1,2,2]
[2,6,4,5,3,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,4,5,3,7,8,1]=>0101001=>1001010=>[1,3,2,2]
[2,6,4,5,3,8,7,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,7,4,5,6,3,1,8]=>0100110=>0110010=>[2,1,3,2]
[2,7,4,5,6,3,8,1]=>0100101=>1010010=>[1,2,3,2]
[2,7,5,4,3,6,8,1]=>0111001=>1001110=>[1,3,1,1,2]
[2,8,5,4,3,6,7,1]=>0111001=>1001110=>[1,3,1,1,2]
[2,8,5,4,3,7,6,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,7,5,4,6,3,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,5,4,7,6,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,8,7,5,4,6,3,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,8,7,5,6,4,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,2,1,4,8,6,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,1,5,8,6,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,1,7,5,6,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[3,2,1,8,5,6,7,4]=>1101001=>1001011=>[1,3,2,1,1]
[3,2,1,8,5,7,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,2,1,8,6,5,7,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,2,1,8,6,7,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,2,4,1,8,6,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,4,8,5,6,7,1]=>1001001=>1001001=>[1,3,3,1]
[3,2,5,4,8,6,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,6,4,5,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,6,4,5,7,1,8]=>1010010=>0100101=>[2,3,2,1]
[3,2,7,4,6,5,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,7,4,6,5,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,8,5,4,6,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[3,2,7,5,6,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,7,5,6,4,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,8,5,6,4,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,8,5,7,6,4,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,2,3,1,6,5,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,3,1,6,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[4,2,3,1,6,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,3,1,7,6,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,3,1,8,6,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,3,1,8,7,6,5]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,2,3,5,1,7,8,6]=>1001001=>1001001=>[1,3,3,1]
[4,2,3,5,1,8,7,6]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,3,5,6,1,8,7]=>1000101=>1010001=>[1,2,4,1]
[4,2,3,5,6,8,7,1]=>1000011=>1100001=>[1,1,5,1]
[4,2,3,6,5,1,7,8]=>1001100=>0011001=>[3,1,3,1]
[4,2,3,6,5,1,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[4,2,3,6,5,8,7,1]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,3,7,5,6,1,8]=>1001010=>0101001=>[2,2,3,1]
[4,2,3,8,5,6,7,1]=>1001001=>1001001=>[1,3,3,1]
[4,2,3,7,6,5,8,1]=>1001101=>1011001=>[1,2,1,3,1]
[4,2,3,8,6,7,5,1]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,3,8,7,6,5,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[5,2,3,4,1,8,7,6]=>1001011=>1101001=>[1,1,2,3,1]
[5,2,3,4,8,7,6,1]=>1000111=>1110001=>[1,1,1,4,1]
[8,2,3,4,7,6,5,1]=>1000111=>1110001=>[1,1,1,4,1]
[6,2,3,5,4,1,7,8]=>1001100=>0011001=>[3,1,3,1]
[6,2,3,5,4,1,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[6,2,3,5,4,7,1,8]=>1001010=>0101001=>[2,2,3,1]
[8,2,3,5,4,7,6,1]=>1001011=>1101001=>[1,1,2,3,1]
[7,2,3,5,6,4,1,8]=>1000110=>0110001=>[2,1,4,1]
[8,2,3,5,6,7,4,1]=>1000011=>1100001=>[1,1,5,1]
[7,2,3,6,5,4,1,8]=>1001110=>0111001=>[2,1,1,3,1]
[8,2,3,7,5,6,4,1]=>1001011=>1101001=>[1,1,2,3,1]
[8,2,3,7,6,5,4,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[5,2,4,3,1,6,7,8]=>1011000=>0001101=>[4,1,2,1]
[5,2,4,3,1,6,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[5,2,4,3,1,7,6,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,2,4,3,1,8,7,6]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,2,4,3,6,1,7,8]=>1010100=>0010101=>[3,2,2,1]
[5,2,4,3,6,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,4,3,7,6,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,4,3,7,6,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,4,3,5,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,4,3,6,5,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,4,3,6,5,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,4,3,6,5,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,4,3,7,6,5,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,2,4,5,3,1,7,8]=>1001100=>0011001=>[3,1,3,1]
[6,2,4,5,3,1,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[6,2,4,5,3,8,7,1]=>1001011=>1101001=>[1,1,2,3,1]
[7,2,4,5,3,6,1,8]=>1001010=>0101001=>[2,2,3,1]
[7,2,4,5,3,6,8,1]=>1001001=>1001001=>[1,3,3,1]
[8,2,4,7,5,6,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[8,2,4,7,6,5,3,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[6,2,5,4,3,1,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,2,5,4,3,6,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[8,2,5,4,3,7,6,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,2,5,4,7,6,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,2,6,4,5,3,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,6,4,5,7,3,1]=>1010011=>1100101=>[1,1,3,2,1]
[8,2,7,4,5,6,3,1]=>1010011=>1100101=>[1,1,3,2,1]
[8,2,7,4,6,5,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,2,6,5,4,3,1,8]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,2,6,5,4,3,7,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,2,7,5,4,6,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,2,7,5,6,4,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,2,7,6,5,4,3,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[4,3,2,1,8,6,7,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,3,2,7,5,6,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[4,3,2,8,5,6,7,1]=>1101001=>1001011=>[1,3,2,1,1]
[4,3,2,8,6,7,5,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,3,2,4,1,6,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,2,4,1,8,7,6]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,3,2,4,6,1,8,7]=>1100101=>1010011=>[1,2,3,1,1]
[6,3,2,5,4,1,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[6,3,2,5,4,1,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,3,2,5,4,7,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,2,5,4,7,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[8,3,2,5,4,7,6,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,3,2,5,6,4,7,1]=>1100101=>1010011=>[1,2,3,1,1]
[8,3,2,5,7,6,4,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,3,2,7,5,6,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,3,2,7,6,5,4,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[5,3,4,2,1,6,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[5,3,4,2,1,7,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[5,3,4,2,1,8,7,6]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,3,4,2,6,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,4,2,7,6,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,3,4,2,7,6,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,4,2,8,6,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,4,2,5,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,4,2,6,5,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,4,2,6,5,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,4,6,5,2,1,8]=>1001110=>0111001=>[2,1,1,3,1]
[6,3,5,4,2,1,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,3,5,4,2,7,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[6,3,5,4,2,7,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[8,3,5,4,2,6,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[7,3,5,4,6,2,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[8,3,5,4,7,6,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,3,6,4,5,2,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,6,4,5,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,6,4,5,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,4,5,6,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[7,3,6,5,4,2,1,8]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,3,7,5,6,4,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,4,3,2,8,6,7,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,4,3,2,6,5,1,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,4,3,2,6,5,8,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,4,3,2,6,7,5,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,4,3,2,7,6,5,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[6,4,3,5,2,1,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,4,3,5,7,6,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,4,3,6,5,2,1,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,4,3,6,5,2,8,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,4,3,7,5,6,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,5,3,4,2,1,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,3,4,2,7,6,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,3,4,7,6,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,7,3,4,6,5,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,6,3,5,4,2,1,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,6,3,5,4,2,7,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,7,3,5,4,6,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,7,3,5,6,4,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,7,3,6,5,4,2,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[8,5,4,3,2,7,6,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[8,5,4,3,7,6,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,7,4,3,6,5,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[2,4,1,3,6,5,8,7]=>0100101=>1010010=>[1,2,3,2]
[2,1,4,6,3,5,8,7]=>1001001=>1001001=>[1,3,3,1]
[2,4,1,6,3,5,8,7]=>0101001=>1001010=>[1,3,2,2]
[2,4,6,1,3,5,8,7]=>0010001=>1000100=>[1,4,3]
[2,1,4,3,6,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[2,4,1,3,6,8,5,7]=>0100010=>0100010=>[2,4,2]
[2,1,4,6,3,8,5,7]=>1001010=>0101001=>[2,2,3,1]
[2,4,1,6,3,8,5,7]=>0101010=>0101010=>[2,2,2,2]
[2,4,6,1,3,8,5,7]=>0010010=>0100100=>[2,3,3]
[2,1,4,6,8,3,5,7]=>1000100=>0010001=>[3,4,1]
[2,4,1,6,8,3,5,7]=>0100100=>0010010=>[3,3,2]
[2,4,6,1,8,3,5,7]=>0010100=>0010100=>[3,2,3]
[2,4,6,8,1,3,5,7]=>0001000=>0001000=>[4,4]
[2,4,1,3,6,5,7,8]=>0100100=>0010010=>[3,3,2]
[2,4,1,6,3,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[2,4,6,1,3,7,5,8]=>0010010=>0100100=>[2,3,3]
[2,4,6,7,1,3,5,8]=>0001000=>0001000=>[4,4]
[2,4,1,3,6,7,8,5]=>0100001=>1000010=>[1,5,2]
[2,1,4,6,3,7,8,5]=>1001001=>1001001=>[1,3,3,1]
[2,4,1,6,3,7,8,5]=>0101001=>1001010=>[1,3,2,2]
[2,4,6,1,3,7,8,5]=>0010001=>1000100=>[1,4,3]
[2,4,1,6,7,3,8,5]=>0100101=>1010010=>[1,2,3,2]
[2,4,6,1,7,3,8,5]=>0010101=>1010100=>[1,2,2,3]
[2,4,6,7,1,3,8,5]=>0001001=>1001000=>[1,3,4]
[2,4,1,6,7,8,3,5]=>0100010=>0100010=>[2,4,2]
[2,4,6,1,7,8,3,5]=>0010010=>0100100=>[2,3,3]
[2,4,6,7,1,8,3,5]=>0001010=>0101000=>[2,2,4]
[2,4,6,7,8,1,3,5]=>0000100=>0010000=>[3,5]
[2,1,4,3,7,5,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,4,1,3,7,5,8,6]=>0100101=>1010010=>[1,2,3,2]
[2,4,1,7,3,5,8,6]=>0101001=>1001010=>[1,3,2,2]
[2,4,7,1,3,5,8,6]=>0010001=>1000100=>[1,4,3]
[2,1,4,3,7,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[2,4,1,3,7,8,5,6]=>0100010=>0100010=>[2,4,2]
[2,4,1,7,3,8,5,6]=>0101010=>0101010=>[2,2,2,2]
[2,4,1,7,8,3,5,6]=>0100100=>0010010=>[3,3,2]
[2,4,7,1,8,3,5,6]=>0010100=>0010100=>[3,2,3]
[2,4,1,5,3,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[2,4,5,1,7,3,6,8]=>0010100=>0010100=>[3,2,3]
[2,4,1,3,5,7,8,6]=>0100001=>1000010=>[1,5,2]
[2,4,1,5,3,7,8,6]=>0101001=>1001010=>[1,3,2,2]
[2,4,5,1,3,7,8,6]=>0010001=>1000100=>[1,4,3]
[2,1,4,5,7,3,8,6]=>1000101=>1010001=>[1,2,4,1]
[2,4,1,5,7,3,8,6]=>0100101=>1010010=>[1,2,3,2]
[2,4,5,1,7,3,8,6]=>0010101=>1010100=>[1,2,2,3]
[2,4,5,7,1,3,8,6]=>0001001=>1001000=>[1,3,4]
[2,4,5,7,8,1,3,6]=>0000100=>0010000=>[3,5]
[2,1,4,3,8,5,6,7]=>1010100=>0010101=>[3,2,2,1]
[2,4,1,3,8,5,6,7]=>0100100=>0010010=>[3,3,2]
[2,1,4,8,3,5,6,7]=>1001000=>0001001=>[4,3,1]
[2,4,1,8,3,5,6,7]=>0101000=>0001010=>[4,2,2]
[2,4,1,5,3,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[2,1,4,5,8,3,6,7]=>1000100=>0010001=>[3,4,1]
[2,4,1,5,8,3,6,7]=>0100100=>0010010=>[3,3,2]
[2,4,5,8,1,3,6,7]=>0001000=>0001000=>[4,4]
[2,4,1,5,6,3,8,7]=>0100101=>1010010=>[1,2,3,2]
[2,1,4,5,6,8,3,7]=>1000010=>0100001=>[2,5,1]
[2,4,5,1,6,8,3,7]=>0010010=>0100100=>[2,3,3]
[2,4,5,6,1,8,3,7]=>0001010=>0101000=>[2,2,4]
[2,4,5,6,8,1,3,7]=>0000100=>0010000=>[3,5]
[2,4,1,3,5,6,7,8]=>0100000=>0000010=>[6,2]
[2,4,1,5,6,3,7,8]=>0100100=>0010010=>[3,3,2]
[2,4,5,1,6,3,7,8]=>0010100=>0010100=>[3,2,3]
[2,4,5,6,1,3,7,8]=>0001000=>0001000=>[4,4]
[2,4,5,6,7,1,3,8]=>0000100=>0010000=>[3,5]
[2,4,1,5,6,7,8,3]=>0100001=>1000010=>[1,5,2]
[2,4,5,6,7,1,8,3]=>0000101=>1010000=>[1,2,5]
[2,1,5,3,6,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,5,6,3,4,8,7]=>1001001=>1001001=>[1,3,3,1]
[2,1,5,3,6,8,4,7]=>1010010=>0100101=>[2,3,2,1]
[2,5,1,3,6,8,4,7]=>0100010=>0100010=>[2,4,2]
[2,5,1,6,8,3,4,7]=>0100100=>0010010=>[3,3,2]
[2,1,5,6,3,4,7,8]=>1001000=>0001001=>[4,3,1]
[2,5,1,6,3,4,7,8]=>0101000=>0001010=>[4,2,2]
[2,1,5,3,6,7,4,8]=>1010010=>0100101=>[2,3,2,1]
[2,1,5,6,3,7,4,8]=>1001010=>0101001=>[2,2,3,1]
[2,5,1,6,3,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[2,5,6,1,3,7,4,8]=>0010010=>0100100=>[2,3,3]
[2,1,5,6,7,3,4,8]=>1000100=>0010001=>[3,4,1]
[2,5,1,6,7,3,4,8]=>0100100=>0010010=>[3,3,2]
[2,1,5,3,6,7,8,4]=>1010001=>1000101=>[1,4,2,1]
[2,5,1,3,6,7,8,4]=>0100001=>1000010=>[1,5,2]
[2,1,5,6,3,7,8,4]=>1001001=>1001001=>[1,3,3,1]
[2,5,1,6,3,7,8,4]=>0101001=>1001010=>[1,3,2,2]
[2,5,6,1,3,7,8,4]=>0010001=>1000100=>[1,4,3]
[2,1,5,6,7,3,8,4]=>1000101=>1010001=>[1,2,4,1]
[2,5,1,6,7,3,8,4]=>0100101=>1010010=>[1,2,3,2]
[2,1,5,6,7,8,3,4]=>1000010=>0100001=>[2,5,1]
[2,5,1,6,7,8,3,4]=>0100010=>0100010=>[2,4,2]
[2,5,6,1,7,8,3,4]=>0010010=>0100100=>[2,3,3]
[2,5,6,7,8,1,3,4]=>0000100=>0010000=>[3,5]
[2,1,5,3,7,4,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,5,1,3,7,4,8,6]=>0100101=>1010010=>[1,2,3,2]
[2,1,5,7,3,4,8,6]=>1001001=>1001001=>[1,3,3,1]
[2,5,1,7,3,4,8,6]=>0101001=>1001010=>[1,3,2,2]
[2,5,7,1,3,4,8,6]=>0010001=>1000100=>[1,4,3]
[2,1,5,3,7,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[2,5,1,3,7,8,4,6]=>0100010=>0100010=>[2,4,2]
[2,1,5,7,3,8,4,6]=>1001010=>0101001=>[2,2,3,1]
[2,1,5,7,8,3,4,6]=>1000100=>0010001=>[3,4,1]
[2,5,1,7,8,3,4,6]=>0100100=>0010010=>[3,3,2]
[2,5,1,3,7,4,6,8]=>0100100=>0010010=>[3,3,2]
[2,1,5,7,3,4,6,8]=>1001000=>0001001=>[4,3,1]
[2,3,5,7,1,4,6,8]=>0001000=>0001000=>[4,4]
[2,3,5,1,7,4,8,6]=>0010101=>1010100=>[1,2,2,3]
[2,3,5,7,1,4,8,6]=>0001001=>1001000=>[1,3,4]
[2,3,5,7,1,8,4,6]=>0001010=>0101000=>[2,2,4]
[2,1,5,3,8,4,6,7]=>1010100=>0010101=>[3,2,2,1]
[2,1,5,8,3,4,6,7]=>1001000=>0001001=>[4,3,1]
[2,5,1,8,3,4,6,7]=>0101000=>0001010=>[4,2,2]
[2,3,5,1,4,8,6,7]=>0010010=>0100100=>[2,3,3]
[2,3,5,8,1,4,6,7]=>0001000=>0001000=>[4,4]
[2,1,5,3,4,6,8,7]=>1010001=>1000101=>[1,4,2,1]
[2,3,5,1,6,4,8,7]=>0010101=>1010100=>[1,2,2,3]
[2,3,5,6,1,4,8,7]=>0001001=>1001000=>[1,3,4]
[2,3,5,6,1,8,4,7]=>0001010=>0101000=>[2,2,4]
[2,3,5,6,8,1,4,7]=>0000100=>0010000=>[3,5]
[2,3,5,6,1,4,7,8]=>0001000=>0001000=>[4,4]
[2,3,5,6,1,7,4,8]=>0001010=>0101000=>[2,2,4]
[2,3,5,1,6,7,8,4]=>0010001=>1000100=>[1,4,3]
[2,3,5,6,1,7,8,4]=>0001001=>1001000=>[1,3,4]
[2,3,5,6,7,1,8,4]=>0000101=>1010000=>[1,2,5]
[2,3,5,6,7,8,1,4]=>0000010=>0100000=>[2,6]
[2,1,6,3,7,4,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,6,1,3,7,4,8,5]=>0100101=>1010010=>[1,2,3,2]
[2,6,7,1,3,4,8,5]=>0010001=>1000100=>[1,4,3]
[2,1,6,3,7,8,4,5]=>1010010=>0100101=>[2,3,2,1]
[2,1,6,7,3,8,4,5]=>1001010=>0101001=>[2,2,3,1]
[2,6,1,7,3,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[2,1,6,7,8,3,4,5]=>1000100=>0010001=>[3,4,1]
[2,6,1,7,8,3,4,5]=>0100100=>0010010=>[3,3,2]
[2,6,7,8,1,3,4,5]=>0001000=>0001000=>[4,4]
[2,6,1,7,3,4,5,8]=>0101000=>0001010=>[4,2,2]
[2,6,7,1,3,4,5,8]=>0010000=>0000100=>[5,3]
[2,3,1,6,4,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[2,3,6,1,4,7,5,8]=>0010010=>0100100=>[2,3,3]
[2,3,6,7,1,4,5,8]=>0001000=>0001000=>[4,4]
[2,1,6,3,4,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[2,3,6,1,4,7,8,5]=>0010001=>1000100=>[1,4,3]
[2,1,3,6,7,4,8,5]=>1000101=>1010001=>[1,2,4,1]
[2,3,6,7,1,4,8,5]=>0001001=>1001000=>[1,3,4]
[2,3,1,6,7,8,4,5]=>0100010=>0100010=>[2,4,2]
[2,3,6,1,7,8,4,5]=>0010010=>0100100=>[2,3,3]
[2,3,6,7,1,8,4,5]=>0001010=>0101000=>[2,2,4]
[2,3,6,7,8,1,4,5]=>0000100=>0010000=>[3,5]
[2,6,1,8,3,4,5,7]=>0101000=>0001010=>[4,2,2]
[2,6,8,1,3,4,5,7]=>0010000=>0000100=>[5,3]
[2,1,6,3,4,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[2,3,1,6,4,8,5,7]=>0101010=>0101010=>[2,2,2,2]
[2,3,6,1,4,8,5,7]=>0010010=>0100100=>[2,3,3]
[2,3,1,6,8,4,5,7]=>0100100=>0010010=>[3,3,2]
[2,3,6,1,8,4,5,7]=>0010100=>0010100=>[3,2,3]
[2,3,6,8,1,4,5,7]=>0001000=>0001000=>[4,4]
[2,1,6,3,4,5,8,7]=>1010001=>1000101=>[1,4,2,1]
[2,6,1,3,4,5,8,7]=>0100001=>1000010=>[1,5,2]
[2,3,6,1,4,5,8,7]=>0010001=>1000100=>[1,4,3]
[2,3,4,1,6,8,5,7]=>0010010=>0100100=>[2,3,3]
[2,3,4,6,1,8,5,7]=>0001010=>0101000=>[2,2,4]
[2,3,6,1,4,5,7,8]=>0010000=>0000100=>[5,3]
[2,3,4,6,7,8,1,5]=>0000010=>0100000=>[2,6]
[2,7,1,3,8,4,5,6]=>0100100=>0010010=>[3,3,2]
[2,1,7,8,3,4,5,6]=>1001000=>0001001=>[4,3,1]
[2,7,1,8,3,4,5,6]=>0101000=>0001010=>[4,2,2]
[2,7,8,1,3,4,5,6]=>0010000=>0000100=>[5,3]
[2,1,7,3,4,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[2,1,3,7,4,8,5,6]=>1001010=>0101001=>[2,2,3,1]
[2,3,1,7,4,8,5,6]=>0101010=>0101010=>[2,2,2,2]
[2,3,1,7,8,4,5,6]=>0100100=>0010010=>[3,3,2]
[2,3,7,8,1,4,5,6]=>0001000=>0001000=>[4,4]
[2,1,7,3,4,5,8,6]=>1010001=>1000101=>[1,4,2,1]
[2,3,1,7,4,5,8,6]=>0101001=>1001010=>[1,3,2,2]
[2,3,7,1,4,5,8,6]=>0010001=>1000100=>[1,4,3]
[2,3,4,1,7,5,8,6]=>0010101=>1010100=>[1,2,2,3]
[2,3,4,7,1,5,8,6]=>0001001=>1001000=>[1,3,4]
[2,1,3,4,7,8,5,6]=>1000010=>0100001=>[2,5,1]
[2,3,1,4,7,8,5,6]=>0100010=>0100010=>[2,4,2]
[2,3,4,1,7,8,5,6]=>0010010=>0100100=>[2,3,3]
[2,3,4,7,8,1,5,6]=>0000100=>0010000=>[3,5]
[2,3,4,1,7,5,6,8]=>0010100=>0010100=>[3,2,3]
[2,3,4,7,1,5,6,8]=>0001000=>0001000=>[4,4]
[2,1,8,3,4,5,6,7]=>1010000=>0000101=>[5,2,1]
[2,8,1,3,4,5,6,7]=>0100000=>0000010=>[6,2]
[2,3,8,1,4,5,6,7]=>0010000=>0000100=>[5,3]
[2,1,3,4,8,5,6,7]=>1000100=>0010001=>[3,4,1]
[2,3,1,4,8,5,6,7]=>0100100=>0010010=>[3,3,2]
[2,3,4,1,8,5,6,7]=>0010100=>0010100=>[3,2,3]
[2,3,4,8,1,5,6,7]=>0001000=>0001000=>[4,4]
[2,3,4,1,5,8,6,7]=>0010010=>0100100=>[2,3,3]
[2,3,4,5,8,1,6,7]=>0000100=>0010000=>[3,5]
[3,1,4,2,6,5,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[3,4,1,2,6,5,8,7]=>0100101=>1010010=>[1,2,3,2]
[3,1,4,2,6,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[3,4,1,2,6,8,5,7]=>0100010=>0100010=>[2,4,2]
[3,1,4,6,2,8,5,7]=>1001010=>0101001=>[2,2,3,1]
[3,1,4,6,8,2,5,7]=>1000100=>0010001=>[3,4,1]
[3,4,1,6,8,2,5,7]=>0100100=>0010010=>[3,3,2]
[3,1,4,2,6,5,7,8]=>1010100=>0010101=>[3,2,2,1]
[3,4,1,2,6,5,7,8]=>0100100=>0010010=>[3,3,2]
[3,1,4,2,6,7,5,8]=>1010010=>0100101=>[2,3,2,1]
[3,4,1,2,6,7,5,8]=>0100010=>0100010=>[2,4,2]
[3,4,1,6,2,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[3,4,6,1,2,7,5,8]=>0010010=>0100100=>[2,3,3]
[3,1,4,2,6,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[3,4,1,2,6,7,8,5]=>0100001=>1000010=>[1,5,2]
[3,4,6,1,2,7,8,5]=>0010001=>1000100=>[1,4,3]
[3,4,6,1,7,2,8,5]=>0010101=>1010100=>[1,2,2,3]
[3,1,4,6,7,8,2,5]=>1000010=>0100001=>[2,5,1]
[3,4,6,1,7,8,2,5]=>0010010=>0100100=>[2,3,3]
[3,4,6,7,1,8,2,5]=>0001010=>0101000=>[2,2,4]
[3,4,6,7,8,1,2,5]=>0000100=>0010000=>[3,5]
[3,1,4,2,7,5,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,4,1,2,7,5,8,6]=>0100101=>1010010=>[1,2,3,2]
[3,4,7,1,2,5,8,6]=>0010001=>1000100=>[1,4,3]
[3,1,4,2,7,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[3,4,1,2,7,8,5,6]=>0100010=>0100010=>[2,4,2]
[3,4,7,1,8,2,5,6]=>0010100=>0010100=>[3,2,3]
[3,1,4,2,7,5,6,8]=>1010100=>0010101=>[3,2,2,1]
[3,4,1,2,7,5,6,8]=>0100100=>0010010=>[3,3,2]
[3,4,1,2,5,7,6,8]=>0100010=>0100010=>[2,4,2]
[3,1,4,5,2,7,6,8]=>1001010=>0101001=>[2,2,3,1]
[3,4,1,5,2,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[3,4,1,5,7,2,6,8]=>0100100=>0010010=>[3,3,2]
[3,1,4,2,5,7,8,6]=>1010001=>1000101=>[1,4,2,1]
[3,4,1,2,5,7,8,6]=>0100001=>1000010=>[1,5,2]
[3,1,4,5,2,7,8,6]=>1001001=>1001001=>[1,3,3,1]
[3,4,1,5,7,2,8,6]=>0100101=>1010010=>[1,2,3,2]
[3,4,5,7,1,2,8,6]=>0001001=>1001000=>[1,3,4]
[3,1,4,5,7,8,2,6]=>1000010=>0100001=>[2,5,1]
[3,4,1,5,7,8,2,6]=>0100010=>0100010=>[2,4,2]
[3,4,5,1,7,8,2,6]=>0010010=>0100100=>[2,3,3]
[3,1,4,2,8,5,6,7]=>1010100=>0010101=>[3,2,2,1]
[3,4,1,2,8,5,6,7]=>0100100=>0010010=>[3,3,2]
[3,1,4,8,2,5,6,7]=>1001000=>0001001=>[4,3,1]
[3,4,1,8,2,5,6,7]=>0101000=>0001010=>[4,2,2]
[3,4,8,1,2,5,6,7]=>0010000=>0000100=>[5,3]
[3,1,4,2,5,8,6,7]=>1010010=>0100101=>[2,3,2,1]
[3,4,1,2,5,8,6,7]=>0100010=>0100010=>[2,4,2]
[3,4,1,5,2,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[3,4,5,1,2,8,6,7]=>0010010=>0100100=>[2,3,3]
[3,4,1,5,8,2,6,7]=>0100100=>0010010=>[3,3,2]
[3,4,5,8,1,2,6,7]=>0001000=>0001000=>[4,4]
[3,4,1,2,5,6,8,7]=>0100001=>1000010=>[1,5,2]
[3,1,4,5,6,2,8,7]=>1000101=>1010001=>[1,2,4,1]
[3,4,5,1,6,2,8,7]=>0010101=>1010100=>[1,2,2,3]
[3,4,5,6,1,2,8,7]=>0001001=>1001000=>[1,3,4]
[3,4,1,5,6,8,2,7]=>0100010=>0100010=>[2,4,2]
[3,4,5,6,1,8,2,7]=>0001010=>0101000=>[2,2,4]
[3,4,5,6,8,1,2,7]=>0000100=>0010000=>[3,5]
[3,1,4,2,5,6,7,8]=>1010000=>0000101=>[5,2,1]
[3,4,1,5,6,2,7,8]=>0100100=>0010010=>[3,3,2]
[3,4,5,1,6,2,7,8]=>0010100=>0010100=>[3,2,3]
[3,4,1,5,6,7,2,8]=>0100010=>0100010=>[2,4,2]
[3,4,5,6,1,7,2,8]=>0001010=>0101000=>[2,2,4]
[3,1,4,5,6,7,8,2]=>1000001=>1000001=>[1,6,1]
[3,4,5,1,6,7,8,2]=>0010001=>1000100=>[1,4,3]
[3,4,5,6,1,7,8,2]=>0001001=>1001000=>[1,3,4]
[3,1,5,2,6,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,5,6,2,4,8,7]=>1001001=>1001001=>[1,3,3,1]
[3,5,1,6,2,4,8,7]=>0101001=>1001010=>[1,3,2,2]
[3,5,6,1,2,4,8,7]=>0010001=>1000100=>[1,4,3]
[3,5,1,2,6,8,4,7]=>0100010=>0100010=>[2,4,2]
[3,1,5,6,2,8,4,7]=>1001010=>0101001=>[2,2,3,1]
[3,5,6,1,2,8,4,7]=>0010010=>0100100=>[2,3,3]
[3,1,5,6,8,2,4,7]=>1000100=>0010001=>[3,4,1]
[3,5,6,1,8,2,4,7]=>0010100=>0010100=>[3,2,3]
[3,1,5,6,2,4,7,8]=>1001000=>0001001=>[4,3,1]
[3,5,1,6,2,4,7,8]=>0101000=>0001010=>[4,2,2]
[3,5,6,1,2,4,7,8]=>0010000=>0000100=>[5,3]
[3,5,1,6,2,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[3,5,6,1,2,7,4,8]=>0010010=>0100100=>[2,3,3]
[3,5,6,1,7,2,4,8]=>0010100=>0010100=>[3,2,3]
[3,1,5,2,6,7,8,4]=>1010001=>1000101=>[1,4,2,1]
[3,5,1,2,6,7,8,4]=>0100001=>1000010=>[1,5,2]
[3,1,5,6,2,7,8,4]=>1001001=>1001001=>[1,3,3,1]
[3,5,1,6,2,7,8,4]=>0101001=>1001010=>[1,3,2,2]
[3,5,6,1,2,7,8,4]=>0010001=>1000100=>[1,4,3]
[3,1,5,6,7,2,8,4]=>1000101=>1010001=>[1,2,4,1]
[3,5,1,6,7,2,8,4]=>0100101=>1010010=>[1,2,3,2]
[3,5,6,1,7,2,8,4]=>0010101=>1010100=>[1,2,2,3]
[3,1,5,6,7,8,2,4]=>1000010=>0100001=>[2,5,1]
[3,5,1,6,7,8,2,4]=>0100010=>0100010=>[2,4,2]
[3,5,6,1,7,8,2,4]=>0010010=>0100100=>[2,3,3]
[3,5,6,7,8,1,2,4]=>0000100=>0010000=>[3,5]
[3,1,5,2,7,4,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,5,1,2,7,4,8,6]=>0100101=>1010010=>[1,2,3,2]
[3,1,5,7,2,4,8,6]=>1001001=>1001001=>[1,3,3,1]
[3,5,1,7,2,4,8,6]=>0101001=>1001010=>[1,3,2,2]
[3,5,7,1,2,4,8,6]=>0010001=>1000100=>[1,4,3]
[3,1,5,2,7,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[3,5,1,2,7,8,4,6]=>0100010=>0100010=>[2,4,2]
[3,1,5,7,2,8,4,6]=>1001010=>0101001=>[2,2,3,1]
[3,5,1,7,2,8,4,6]=>0101010=>0101010=>[2,2,2,2]
[3,1,5,7,8,2,4,6]=>1000100=>0010001=>[3,4,1]
[3,5,1,7,8,2,4,6]=>0100100=>0010010=>[3,3,2]
[3,5,7,8,1,2,4,6]=>0001000=>0001000=>[4,4]
[3,1,5,2,7,4,6,8]=>1010100=>0010101=>[3,2,2,1]
[3,5,1,2,7,4,6,8]=>0100100=>0010010=>[3,3,2]
[3,1,5,7,2,4,6,8]=>1001000=>0001001=>[4,3,1]
[3,5,1,7,2,4,6,8]=>0101000=>0001010=>[4,2,2]
[3,5,7,1,2,4,6,8]=>0010000=>0000100=>[5,3]
[3,1,5,2,4,7,6,8]=>1010010=>0100101=>[2,3,2,1]
[3,5,1,2,4,7,6,8]=>0100010=>0100010=>[2,4,2]
[3,1,2,5,4,7,6,8]=>1001010=>0101001=>[2,2,3,1]
[1,3,5,2,4,7,6,8]=>0010010=>0100100=>[2,3,3]
[3,1,2,5,7,4,6,8]=>1000100=>0010001=>[3,4,1]
[1,3,2,5,7,4,6,8]=>0100100=>0010010=>[3,3,2]
[1,3,5,2,7,4,6,8]=>0010100=>0010100=>[3,2,3]
[1,3,5,7,2,4,6,8]=>0001000=>0001000=>[4,4]
[3,5,1,2,4,7,8,6]=>0100001=>1000010=>[1,5,2]
[1,3,5,2,4,7,8,6]=>0010001=>1000100=>[1,4,3]
[3,1,2,5,7,4,8,6]=>1000101=>1010001=>[1,2,4,1]
[1,3,2,5,7,4,8,6]=>0100101=>1010010=>[1,2,3,2]
[1,3,5,2,7,4,8,6]=>0010101=>1010100=>[1,2,2,3]
[1,3,5,7,2,4,8,6]=>0001001=>1001000=>[1,3,4]
[1,3,2,5,7,8,4,6]=>0100010=>0100010=>[2,4,2]
[1,3,5,2,7,8,4,6]=>0010010=>0100100=>[2,3,3]
[1,3,5,7,2,8,4,6]=>0001010=>0101000=>[2,2,4]
[1,3,5,7,8,2,4,6]=>0000100=>0010000=>[3,5]
[3,1,5,2,8,4,6,7]=>1010100=>0010101=>[3,2,2,1]
[3,5,1,2,8,4,6,7]=>0100100=>0010010=>[3,3,2]
[3,1,5,8,2,4,6,7]=>1001000=>0001001=>[4,3,1]
[3,5,1,8,2,4,6,7]=>0101000=>0001010=>[4,2,2]
[3,1,5,2,4,8,6,7]=>1010010=>0100101=>[2,3,2,1]
[3,5,1,2,4,8,6,7]=>0100010=>0100010=>[2,4,2]
[1,3,2,5,4,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[1,3,5,2,4,8,6,7]=>0010010=>0100100=>[2,3,3]
[3,1,2,5,8,4,6,7]=>1000100=>0010001=>[3,4,1]
[1,3,2,5,8,4,6,7]=>0100100=>0010010=>[3,3,2]
[1,3,5,2,8,4,6,7]=>0010100=>0010100=>[3,2,3]
[1,3,5,8,2,4,6,7]=>0001000=>0001000=>[4,4]
[3,5,1,2,4,6,8,7]=>0100001=>1000010=>[1,5,2]
[3,1,2,5,4,6,8,7]=>1001001=>1001001=>[1,3,3,1]
[1,3,5,2,4,6,8,7]=>0010001=>1000100=>[1,4,3]
[1,3,5,6,2,4,8,7]=>0001001=>1001000=>[1,3,4]
[3,1,2,5,6,8,4,7]=>1000010=>0100001=>[2,5,1]
[1,3,5,2,6,8,4,7]=>0010010=>0100100=>[2,3,3]
[3,5,1,2,4,6,7,8]=>0100000=>0000010=>[6,2]
[1,3,5,2,4,6,7,8]=>0010000=>0000100=>[5,3]
[1,3,5,2,6,4,7,8]=>0010100=>0010100=>[3,2,3]
[1,3,5,6,2,4,7,8]=>0001000=>0001000=>[4,4]
[3,1,2,5,6,7,4,8]=>1000010=>0100001=>[2,5,1]
[1,3,5,2,6,7,4,8]=>0010010=>0100100=>[2,3,3]
[1,3,5,6,2,7,4,8]=>0001010=>0101000=>[2,2,4]
[1,3,5,6,7,2,4,8]=>0000100=>0010000=>[3,5]
[3,1,2,5,6,7,8,4]=>1000001=>1000001=>[1,6,1]
[1,3,5,6,2,7,8,4]=>0001001=>1001000=>[1,3,4]
[1,3,5,6,7,8,2,4]=>0000010=>0100000=>[2,6]
[3,1,6,2,7,4,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,6,1,2,7,4,8,5]=>0100101=>1010010=>[1,2,3,2]
[3,6,1,7,2,4,8,5]=>0101001=>1001010=>[1,3,2,2]
[3,6,7,1,2,4,8,5]=>0010001=>1000100=>[1,4,3]
[3,1,6,7,2,8,4,5]=>1001010=>0101001=>[2,2,3,1]
[3,6,1,7,2,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[3,6,7,1,2,8,4,5]=>0010010=>0100100=>[2,3,3]
[3,6,1,7,8,2,4,5]=>0100100=>0010010=>[3,3,2]
[3,6,7,8,1,2,4,5]=>0001000=>0001000=>[4,4]
[3,1,6,7,2,4,5,8]=>1001000=>0001001=>[4,3,1]
[3,6,7,1,2,4,5,8]=>0010000=>0000100=>[5,3]
[3,1,6,2,4,7,5,8]=>1010010=>0100101=>[2,3,2,1]
[3,6,1,2,4,7,5,8]=>0100010=>0100010=>[2,4,2]
[3,1,2,6,4,7,5,8]=>1001010=>0101001=>[2,2,3,1]
[1,3,2,6,4,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[1,3,6,2,4,7,5,8]=>0010010=>0100100=>[2,3,3]
[1,3,2,6,7,4,5,8]=>0100100=>0010010=>[3,3,2]
[3,1,6,2,4,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[3,6,1,2,4,7,8,5]=>0100001=>1000010=>[1,5,2]
[3,1,2,6,4,7,8,5]=>1001001=>1001001=>[1,3,3,1]
[1,3,2,6,4,7,8,5]=>0101001=>1001010=>[1,3,2,2]
[1,3,6,2,4,7,8,5]=>0010001=>1000100=>[1,4,3]
[3,1,2,6,7,4,8,5]=>1000101=>1010001=>[1,2,4,1]
[1,3,6,2,7,4,8,5]=>0010101=>1010100=>[1,2,2,3]
[1,3,6,2,7,8,4,5]=>0010010=>0100100=>[2,3,3]
[3,1,6,2,8,4,5,7]=>1010100=>0010101=>[3,2,2,1]
[3,1,6,8,2,4,5,7]=>1001000=>0001001=>[4,3,1]
[3,6,8,1,2,4,5,7]=>0010000=>0000100=>[5,3]
[3,1,6,2,4,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[3,6,1,2,4,8,5,7]=>0100010=>0100010=>[2,4,2]
[1,3,2,6,4,8,5,7]=>0101010=>0101010=>[2,2,2,2]
[1,3,6,2,4,8,5,7]=>0010010=>0100100=>[2,3,3]
[3,1,6,2,4,5,8,7]=>1010001=>1000101=>[1,4,2,1]
[3,1,2,6,4,5,8,7]=>1001001=>1001001=>[1,3,3,1]
[1,3,4,6,2,5,8,7]=>0001001=>1001000=>[1,3,4]
[3,1,2,4,6,8,5,7]=>1000010=>0100001=>[2,5,1]
[1,3,2,4,6,8,5,7]=>0100010=>0100010=>[2,4,2]
[1,3,4,6,8,2,5,7]=>0000100=>0010000=>[3,5]
[3,1,6,2,4,5,7,8]=>1010000=>0000101=>[5,2,1]
[1,3,2,6,4,5,7,8]=>0101000=>0001010=>[4,2,2]
[1,3,6,2,4,5,7,8]=>0010000=>0000100=>[5,3]
[3,1,2,4,6,7,5,8]=>1000010=>0100001=>[2,5,1]
[3,1,2,4,6,7,8,5]=>1000001=>1000001=>[1,6,1]
[1,3,4,6,7,2,8,5]=>0000101=>1010000=>[1,2,5]
[3,7,1,2,8,4,5,6]=>0100100=>0010010=>[3,3,2]
[3,1,7,8,2,4,5,6]=>1001000=>0001001=>[4,3,1]
[3,1,2,7,4,8,5,6]=>1001010=>0101001=>[2,2,3,1]
[1,3,2,7,4,8,5,6]=>0101010=>0101010=>[2,2,2,2]
[1,3,7,2,4,8,5,6]=>0010010=>0100100=>[2,3,3]
[3,1,2,7,8,4,5,6]=>1000100=>0010001=>[3,4,1]
[3,7,1,2,4,5,8,6]=>0100001=>1000010=>[1,5,2]
[1,3,7,2,4,5,8,6]=>0010001=>1000100=>[1,4,3]
[3,1,2,4,7,5,8,6]=>1000101=>1010001=>[1,2,4,1]
[1,3,2,4,7,5,8,6]=>0100101=>1010010=>[1,2,3,2]
[3,1,2,4,7,8,5,6]=>1000010=>0100001=>[2,5,1]
[1,3,2,4,7,8,5,6]=>0100010=>0100010=>[2,4,2]
[1,3,4,2,7,8,5,6]=>0010010=>0100100=>[2,3,3]
[3,7,1,2,4,5,6,8]=>0100000=>0000010=>[6,2]
[1,3,2,7,4,5,6,8]=>0101000=>0001010=>[4,2,2]
[3,1,2,4,7,5,6,8]=>1000100=>0010001=>[3,4,1]
[1,3,4,5,7,2,6,8]=>0000100=>0010000=>[3,5]
[1,3,4,5,7,2,8,6]=>0000101=>1010000=>[1,2,5]
[1,3,4,5,7,8,2,6]=>0000010=>0100000=>[2,6]
[3,1,8,2,4,5,6,7]=>1010000=>0000101=>[5,2,1]
[1,3,2,8,4,5,6,7]=>0101000=>0001010=>[4,2,2]
[1,3,8,2,4,5,6,7]=>0010000=>0000100=>[5,3]
[3,1,2,4,8,5,6,7]=>1000100=>0010001=>[3,4,1]
[1,3,2,4,8,5,6,7]=>0100100=>0010010=>[3,3,2]
[1,3,4,2,8,5,6,7]=>0010100=>0010100=>[3,2,3]
[1,3,4,8,2,5,6,7]=>0001000=>0001000=>[4,4]
[3,1,2,4,5,8,6,7]=>1000010=>0100001=>[2,5,1]
[1,3,2,4,5,8,6,7]=>0100010=>0100010=>[2,4,2]
[1,3,4,2,5,8,6,7]=>0010010=>0100100=>[2,3,3]
[1,3,4,5,2,8,6,7]=>0001010=>0101000=>[2,2,4]
[1,3,4,5,8,2,6,7]=>0000100=>0010000=>[3,5]
[4,1,5,2,6,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,5,6,2,3,8,7]=>1001001=>1001001=>[1,3,3,1]
[4,5,1,6,2,3,8,7]=>0101001=>1001010=>[1,3,2,2]
[4,5,6,1,2,3,8,7]=>0010001=>1000100=>[1,4,3]
[4,1,5,2,6,8,3,7]=>1010010=>0100101=>[2,3,2,1]
[4,5,1,2,6,8,3,7]=>0100010=>0100010=>[2,4,2]
[4,1,5,6,2,8,3,7]=>1001010=>0101001=>[2,2,3,1]
[4,5,1,6,2,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[4,1,5,6,8,2,3,7]=>1000100=>0010001=>[3,4,1]
[4,5,6,8,1,2,3,7]=>0001000=>0001000=>[4,4]
[4,1,5,6,2,3,7,8]=>1001000=>0001001=>[4,3,1]
[4,5,1,6,2,3,7,8]=>0101000=>0001010=>[4,2,2]
[4,5,1,6,2,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[4,1,5,6,7,2,3,8]=>1000100=>0010001=>[3,4,1]
[4,5,1,6,7,2,3,8]=>0100100=>0010010=>[3,3,2]
[4,1,5,2,6,7,8,3]=>1010001=>1000101=>[1,4,2,1]
[4,5,1,2,6,7,8,3]=>0100001=>1000010=>[1,5,2]
[4,5,1,6,2,7,8,3]=>0101001=>1001010=>[1,3,2,2]
[4,1,5,6,7,2,8,3]=>1000101=>1010001=>[1,2,4,1]
[4,5,1,6,7,2,8,3]=>0100101=>1010010=>[1,2,3,2]
[4,5,6,1,7,2,8,3]=>0010101=>1010100=>[1,2,2,3]
[4,5,6,7,1,2,8,3]=>0001001=>1001000=>[1,3,4]
[4,1,5,6,7,8,2,3]=>1000010=>0100001=>[2,5,1]
[4,5,1,6,7,8,2,3]=>0100010=>0100010=>[2,4,2]
[4,5,6,7,1,8,2,3]=>0001010=>0101000=>[2,2,4]
[4,1,5,2,7,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,1,7,2,3,8,6]=>0101001=>1001010=>[1,3,2,2]
[4,1,5,2,7,8,3,6]=>1010010=>0100101=>[2,3,2,1]
[4,5,1,2,7,8,3,6]=>0100010=>0100010=>[2,4,2]
[4,1,5,7,2,8,3,6]=>1001010=>0101001=>[2,2,3,1]
[4,5,1,7,2,8,3,6]=>0101010=>0101010=>[2,2,2,2]
[4,5,7,1,2,8,3,6]=>0010010=>0100100=>[2,3,3]
[4,5,1,7,8,2,3,6]=>0100100=>0010010=>[3,3,2]
[4,1,5,2,7,3,6,8]=>1010100=>0010101=>[3,2,2,1]
[4,5,1,2,7,3,6,8]=>0100100=>0010010=>[3,3,2]
[4,1,5,7,2,3,6,8]=>1001000=>0001001=>[4,3,1]
[4,5,1,7,2,3,6,8]=>0101000=>0001010=>[4,2,2]
[4,5,1,2,3,7,6,8]=>0100010=>0100010=>[2,4,2]
[1,4,2,5,3,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[1,4,5,2,3,7,6,8]=>0010010=>0100100=>[2,3,3]
[4,1,2,5,7,3,6,8]=>1000100=>0010001=>[3,4,1]
[1,4,2,5,7,3,6,8]=>0100100=>0010010=>[3,3,2]
[1,4,5,2,7,3,6,8]=>0010100=>0010100=>[3,2,3]
[1,4,5,7,2,3,6,8]=>0001000=>0001000=>[4,4]
[4,1,5,2,3,7,8,6]=>1010001=>1000101=>[1,4,2,1]
[4,1,2,5,3,7,8,6]=>1001001=>1001001=>[1,3,3,1]
[1,4,2,5,3,7,8,6]=>0101001=>1001010=>[1,3,2,2]
[1,4,5,2,3,7,8,6]=>0010001=>1000100=>[1,4,3]
[4,1,2,5,7,3,8,6]=>1000101=>1010001=>[1,2,4,1]
[1,4,2,5,7,3,8,6]=>0100101=>1010010=>[1,2,3,2]
[1,4,5,2,7,3,8,6]=>0010101=>1010100=>[1,2,2,3]
[1,4,5,7,2,3,8,6]=>0001001=>1001000=>[1,3,4]
[4,1,2,5,7,8,3,6]=>1000010=>0100001=>[2,5,1]
[1,4,2,5,7,8,3,6]=>0100010=>0100010=>[2,4,2]
[1,4,5,2,7,8,3,6]=>0010010=>0100100=>[2,3,3]
[1,4,5,7,8,2,3,6]=>0000100=>0010000=>[3,5]
[4,1,5,2,8,3,6,7]=>1010100=>0010101=>[3,2,2,1]
[4,5,1,2,8,3,6,7]=>0100100=>0010010=>[3,3,2]
[4,1,5,8,2,3,6,7]=>1001000=>0001001=>[4,3,1]
[4,5,1,8,2,3,6,7]=>0101000=>0001010=>[4,2,2]
[4,5,8,1,2,3,6,7]=>0010000=>0000100=>[5,3]
[4,1,5,2,3,8,6,7]=>1010010=>0100101=>[2,3,2,1]
[4,5,1,2,3,8,6,7]=>0100010=>0100010=>[2,4,2]
[4,1,2,5,3,8,6,7]=>1001010=>0101001=>[2,2,3,1]
[1,4,2,5,3,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[1,4,5,2,3,8,6,7]=>0010010=>0100100=>[2,3,3]
[4,1,2,5,8,3,6,7]=>1000100=>0010001=>[3,4,1]
[1,4,2,5,8,3,6,7]=>0100100=>0010010=>[3,3,2]
[1,4,5,2,8,3,6,7]=>0010100=>0010100=>[3,2,3]
[1,4,5,8,2,3,6,7]=>0001000=>0001000=>[4,4]
[1,4,2,5,3,6,8,7]=>0101001=>1001010=>[1,3,2,2]
[4,1,2,5,6,3,8,7]=>1000101=>1010001=>[1,2,4,1]
[1,4,5,2,6,3,8,7]=>0010101=>1010100=>[1,2,2,3]
[4,1,2,5,6,8,3,7]=>1000010=>0100001=>[2,5,1]
[1,4,5,2,6,8,3,7]=>0010010=>0100100=>[2,3,3]
[1,4,5,6,2,8,3,7]=>0001010=>0101000=>[2,2,4]
[1,4,5,6,8,2,3,7]=>0000100=>0010000=>[3,5]
[1,4,2,5,3,6,7,8]=>0101000=>0001010=>[4,2,2]
[1,4,5,2,3,6,7,8]=>0010000=>0000100=>[5,3]
[4,1,2,5,6,3,7,8]=>1000100=>0010001=>[3,4,1]
[1,4,5,2,6,3,7,8]=>0010100=>0010100=>[3,2,3]
[4,1,2,5,6,7,3,8]=>1000010=>0100001=>[2,5,1]
[1,4,2,5,6,7,3,8]=>0100010=>0100010=>[2,4,2]
[1,4,5,6,7,2,3,8]=>0000100=>0010000=>[3,5]
[4,1,2,5,6,7,8,3]=>1000001=>1000001=>[1,6,1]
[1,4,5,2,6,7,8,3]=>0010001=>1000100=>[1,4,3]
[1,4,5,6,7,2,8,3]=>0000101=>1010000=>[1,2,5]
[4,1,6,2,7,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,6,7,2,3,8,5]=>1001001=>1001001=>[1,3,3,1]
[4,6,7,1,2,3,8,5]=>0010001=>1000100=>[1,4,3]
[4,6,7,1,2,8,3,5]=>0010010=>0100100=>[2,3,3]
[4,6,7,1,8,2,3,5]=>0010100=>0010100=>[3,2,3]
[4,6,7,8,1,2,3,5]=>0001000=>0001000=>[4,4]
[4,1,6,2,7,3,5,8]=>1010100=>0010101=>[3,2,2,1]
[4,6,1,2,7,3,5,8]=>0100100=>0010010=>[3,3,2]
[4,1,6,7,2,3,5,8]=>1001000=>0001001=>[4,3,1]
[4,6,1,7,2,3,5,8]=>0101000=>0001010=>[4,2,2]
[4,1,6,2,3,7,5,8]=>1010010=>0100101=>[2,3,2,1]
[4,6,1,2,3,7,5,8]=>0100010=>0100010=>[2,4,2]
[4,1,2,6,3,7,5,8]=>1001010=>0101001=>[2,2,3,1]
[1,4,2,6,3,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[4,1,2,6,7,3,5,8]=>1000100=>0010001=>[3,4,1]
[1,4,2,6,7,3,5,8]=>0100100=>0010010=>[3,3,2]
[1,4,6,2,7,3,5,8]=>0010100=>0010100=>[3,2,3]
[4,1,6,2,3,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[4,1,2,6,3,7,8,5]=>1001001=>1001001=>[1,3,3,1]
[1,4,6,2,3,7,8,5]=>0010001=>1000100=>[1,4,3]
[4,1,2,6,7,3,8,5]=>1000101=>1010001=>[1,2,4,1]
[1,4,6,2,7,3,8,5]=>0010101=>1010100=>[1,2,2,3]
[1,4,2,6,7,8,3,5]=>0100010=>0100010=>[2,4,2]
[1,4,6,2,7,8,3,5]=>0010010=>0100100=>[2,3,3]
[1,4,6,7,2,8,3,5]=>0001010=>0101000=>[2,2,4]
[4,1,6,2,8,3,5,7]=>1010100=>0010101=>[3,2,2,1]
[4,6,1,2,8,3,5,7]=>0100100=>0010010=>[3,3,2]
[4,1,6,8,2,3,5,7]=>1001000=>0001001=>[4,3,1]
[4,6,1,8,2,3,5,7]=>0101000=>0001010=>[4,2,2]
[4,6,8,1,2,3,5,7]=>0010000=>0000100=>[5,3]
[4,6,1,2,3,8,5,7]=>0100010=>0100010=>[2,4,2]
[4,1,2,6,3,8,5,7]=>1001010=>0101001=>[2,2,3,1]
[1,4,2,6,3,8,5,7]=>0101010=>0101010=>[2,2,2,2]
[1,4,6,2,3,8,5,7]=>0010010=>0100100=>[2,3,3]
[1,4,2,6,8,3,5,7]=>0100100=>0010010=>[3,3,2]
[1,4,6,2,8,3,5,7]=>0010100=>0010100=>[3,2,3]
[4,1,2,6,3,5,8,7]=>1001001=>1001001=>[1,3,3,1]
[1,4,2,6,3,5,8,7]=>0101001=>1001010=>[1,3,2,2]
[4,1,2,3,6,5,8,7]=>1000101=>1010001=>[1,2,4,1]
[1,4,2,3,6,5,8,7]=>0100101=>1010010=>[1,2,3,2]
[4,1,2,3,6,8,5,7]=>1000010=>0100001=>[2,5,1]
[1,2,4,3,6,8,5,7]=>0010010=>0100100=>[2,3,3]
[1,2,4,6,8,3,5,7]=>0000100=>0010000=>[3,5]
[1,4,2,6,3,5,7,8]=>0101000=>0001010=>[4,2,2]
[4,1,2,3,6,5,7,8]=>1000100=>0010001=>[3,4,1]
[1,4,2,3,6,5,7,8]=>0100100=>0010010=>[3,3,2]
[1,2,4,6,3,5,7,8]=>0001000=>0001000=>[4,4]
[4,1,2,3,6,7,5,8]=>1000010=>0100001=>[2,5,1]
[4,1,2,3,6,7,8,5]=>1000001=>1000001=>[1,6,1]
[1,4,2,3,6,7,8,5]=>0100001=>1000010=>[1,5,2]
[1,2,4,6,7,3,8,5]=>0000101=>1010000=>[1,2,5]
[4,1,7,2,8,3,5,6]=>1010100=>0010101=>[3,2,2,1]
[4,7,1,2,8,3,5,6]=>0100100=>0010010=>[3,3,2]
[4,7,1,8,2,3,5,6]=>0101000=>0001010=>[4,2,2]
[1,4,2,7,3,8,5,6]=>0101010=>0101010=>[2,2,2,2]
[4,1,2,7,8,3,5,6]=>1000100=>0010001=>[3,4,1]
[1,4,2,7,8,3,5,6]=>0100100=>0010010=>[3,3,2]
[4,1,7,2,3,5,8,6]=>1010001=>1000101=>[1,4,2,1]
[4,1,2,7,3,5,8,6]=>1001001=>1001001=>[1,3,3,1]
[1,4,2,7,3,5,8,6]=>0101001=>1001010=>[1,3,2,2]
[1,4,7,2,3,5,8,6]=>0010001=>1000100=>[1,4,3]
[4,1,2,3,7,5,8,6]=>1000101=>1010001=>[1,2,4,1]
[1,2,4,3,7,5,8,6]=>0010101=>1010100=>[1,2,2,3]
[4,1,2,3,7,8,5,6]=>1000010=>0100001=>[2,5,1]
[1,4,2,3,7,8,5,6]=>0100010=>0100010=>[2,4,2]
[1,2,4,3,7,8,5,6]=>0010010=>0100100=>[2,3,3]
[1,2,4,7,8,3,5,6]=>0000100=>0010000=>[3,5]
[1,4,2,7,3,5,6,8]=>0101000=>0001010=>[4,2,2]
[4,1,2,3,7,5,6,8]=>1000100=>0010001=>[3,4,1]
[1,4,2,3,7,5,6,8]=>0100100=>0010010=>[3,3,2]
[4,1,2,3,5,7,6,8]=>1000010=>0100001=>[2,5,1]
[1,4,2,3,5,7,6,8]=>0100010=>0100010=>[2,4,2]
[4,1,2,3,5,7,8,6]=>1000001=>1000001=>[1,6,1]
[1,4,2,3,5,7,8,6]=>0100001=>1000010=>[1,5,2]
[1,2,4,5,7,3,8,6]=>0000101=>1010000=>[1,2,5]
[4,8,1,2,3,5,6,7]=>0100000=>0000010=>[6,2]
[4,1,2,8,3,5,6,7]=>1001000=>0001001=>[4,3,1]
[1,4,2,8,3,5,6,7]=>0101000=>0001010=>[4,2,2]
[1,4,8,2,3,5,6,7]=>0010000=>0000100=>[5,3]
[4,1,2,3,8,5,6,7]=>1000100=>0010001=>[3,4,1]
[1,4,2,3,8,5,6,7]=>0100100=>0010010=>[3,3,2]
[1,2,4,3,8,5,6,7]=>0010100=>0010100=>[3,2,3]
[1,2,4,8,3,5,6,7]=>0001000=>0001000=>[4,4]
[4,1,2,3,5,8,6,7]=>1000010=>0100001=>[2,5,1]
[1,4,2,3,5,8,6,7]=>0100010=>0100010=>[2,4,2]
[1,2,4,3,5,8,6,7]=>0010010=>0100100=>[2,3,3]
[1,2,4,5,3,8,6,7]=>0001010=>0101000=>[2,2,4]
[1,2,4,5,8,3,6,7]=>0000100=>0010000=>[3,5]
[4,1,2,3,5,6,8,7]=>1000001=>1000001=>[1,6,1]
[1,4,2,3,5,6,8,7]=>0100001=>1000010=>[1,5,2]
[1,2,4,5,6,8,3,7]=>0000010=>0100000=>[2,6]
[1,4,2,3,5,6,7,8]=>0100000=>0000010=>[6,2]
[5,1,6,2,7,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,6,1,2,7,3,8,4]=>0100101=>1010010=>[1,2,3,2]
[5,1,6,7,2,3,8,4]=>1001001=>1001001=>[1,3,3,1]
[5,6,1,7,2,3,8,4]=>0101001=>1001010=>[1,3,2,2]
[5,6,7,1,2,3,8,4]=>0010001=>1000100=>[1,4,3]
[5,1,6,7,2,8,3,4]=>1001010=>0101001=>[2,2,3,1]
[5,6,7,1,2,8,3,4]=>0010010=>0100100=>[2,3,3]
[5,1,6,7,8,2,3,4]=>1000100=>0010001=>[3,4,1]
[5,6,1,7,8,2,3,4]=>0100100=>0010010=>[3,3,2]
[5,6,7,1,8,2,3,4]=>0010100=>0010100=>[3,2,3]
[5,1,6,2,7,3,4,8]=>1010100=>0010101=>[3,2,2,1]
[5,1,6,2,3,7,4,8]=>1010010=>0100101=>[2,3,2,1]
[5,1,2,6,3,7,4,8]=>1001010=>0101001=>[2,2,3,1]
[1,5,2,6,3,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[5,1,2,6,7,3,4,8]=>1000100=>0010001=>[3,4,1]
[1,5,2,6,7,3,4,8]=>0100100=>0010010=>[3,3,2]
[1,5,6,7,2,3,4,8]=>0001000=>0001000=>[4,4]
[5,1,6,2,3,7,8,4]=>1010001=>1000101=>[1,4,2,1]
[5,6,1,2,3,7,8,4]=>0100001=>1000010=>[1,5,2]
[5,1,2,6,3,7,8,4]=>1001001=>1001001=>[1,3,3,1]
[1,5,2,6,3,7,8,4]=>0101001=>1001010=>[1,3,2,2]
[1,5,6,2,3,7,8,4]=>0010001=>1000100=>[1,4,3]
[5,1,2,6,7,3,8,4]=>1000101=>1010001=>[1,2,4,1]
[1,5,6,7,2,3,8,4]=>0001001=>1001000=>[1,3,4]
[5,1,2,6,7,8,3,4]=>1000010=>0100001=>[2,5,1]
[1,5,6,7,8,2,3,4]=>0000100=>0010000=>[3,5]
[5,1,6,2,8,3,4,7]=>1010100=>0010101=>[3,2,2,1]
[5,6,1,2,8,3,4,7]=>0100100=>0010010=>[3,3,2]
[5,6,8,1,2,3,4,7]=>0010000=>0000100=>[5,3]
[5,1,6,2,3,8,4,7]=>1010010=>0100101=>[2,3,2,1]
[5,6,1,2,3,8,4,7]=>0100010=>0100010=>[2,4,2]
[5,1,2,6,3,8,4,7]=>1001010=>0101001=>[2,2,3,1]
[1,5,2,6,3,8,4,7]=>0101010=>0101010=>[2,2,2,2]
[1,5,6,2,3,8,4,7]=>0010010=>0100100=>[2,3,3]
[5,1,2,6,8,3,4,7]=>1000100=>0010001=>[3,4,1]
[1,5,2,6,8,3,4,7]=>0100100=>0010010=>[3,3,2]
[1,5,6,2,8,3,4,7]=>0010100=>0010100=>[3,2,3]
[1,5,6,8,2,3,4,7]=>0001000=>0001000=>[4,4]
[5,1,2,6,3,4,8,7]=>1001001=>1001001=>[1,3,3,1]
[1,5,2,6,3,4,8,7]=>0101001=>1001010=>[1,3,2,2]
[1,5,6,2,3,4,8,7]=>0010001=>1000100=>[1,4,3]
[1,2,5,3,6,4,8,7]=>0010101=>1010100=>[1,2,2,3]
[1,2,5,6,3,4,8,7]=>0001001=>1001000=>[1,3,4]
[5,1,2,3,6,8,4,7]=>1000010=>0100001=>[2,5,1]
[1,5,2,3,6,8,4,7]=>0100010=>0100010=>[2,4,2]
[1,2,5,6,3,8,4,7]=>0001010=>0101000=>[2,2,4]
[5,1,6,2,3,4,7,8]=>1010000=>0000101=>[5,2,1]
[5,1,2,6,3,4,7,8]=>1001000=>0001001=>[4,3,1]
[1,5,2,6,3,4,7,8]=>0101000=>0001010=>[4,2,2]
[1,2,5,6,3,4,7,8]=>0001000=>0001000=>[4,4]
[5,1,2,3,6,7,4,8]=>1000010=>0100001=>[2,5,1]
[1,2,5,6,3,7,4,8]=>0001010=>0101000=>[2,2,4]
[5,1,2,3,6,7,8,4]=>1000001=>1000001=>[1,6,1]
[1,5,2,3,6,7,8,4]=>0100001=>1000010=>[1,5,2]
[1,2,5,3,6,7,8,4]=>0010001=>1000100=>[1,4,3]
[1,2,5,6,3,7,8,4]=>0001001=>1001000=>[1,3,4]
[1,2,5,6,7,8,3,4]=>0000010=>0100000=>[2,6]
[5,1,7,2,8,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[5,7,1,2,8,3,4,6]=>0100100=>0010010=>[3,3,2]
[5,7,8,1,2,3,4,6]=>0010000=>0000100=>[5,3]
[5,1,2,7,3,8,4,6]=>1001010=>0101001=>[2,2,3,1]
[1,5,2,7,3,8,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,5,7,2,3,8,4,6]=>0010010=>0100100=>[2,3,3]
[5,1,2,7,8,3,4,6]=>1000100=>0010001=>[3,4,1]
[1,5,2,7,8,3,4,6]=>0100100=>0010010=>[3,3,2]
[1,5,7,2,8,3,4,6]=>0010100=>0010100=>[3,2,3]
[1,5,7,8,2,3,4,6]=>0001000=>0001000=>[4,4]
[5,1,7,2,3,4,8,6]=>1010001=>1000101=>[1,4,2,1]
[5,1,2,7,3,4,8,6]=>1001001=>1001001=>[1,3,3,1]
[1,5,2,7,3,4,8,6]=>0101001=>1001010=>[1,3,2,2]
[1,5,7,2,3,4,8,6]=>0010001=>1000100=>[1,4,3]
[5,1,2,3,7,4,8,6]=>1000101=>1010001=>[1,2,4,1]
[1,5,2,3,7,4,8,6]=>0100101=>1010010=>[1,2,3,2]
[1,2,5,3,7,4,8,6]=>0010101=>1010100=>[1,2,2,3]
[1,2,5,7,3,4,8,6]=>0001001=>1001000=>[1,3,4]
[5,1,2,3,7,8,4,6]=>1000010=>0100001=>[2,5,1]
[1,5,2,3,7,8,4,6]=>0100010=>0100010=>[2,4,2]
[1,2,5,7,3,8,4,6]=>0001010=>0101000=>[2,2,4]
[5,7,1,2,3,4,6,8]=>0100000=>0000010=>[6,2]
[5,1,2,7,3,4,6,8]=>1001000=>0001001=>[4,3,1]
[1,5,2,7,3,4,6,8]=>0101000=>0001010=>[4,2,2]
[1,2,5,7,3,4,6,8]=>0001000=>0001000=>[4,4]
[1,5,2,3,4,7,6,8]=>0100010=>0100010=>[2,4,2]
[1,2,3,5,7,4,6,8]=>0000100=>0010000=>[3,5]
[1,5,2,3,4,7,8,6]=>0100001=>1000010=>[1,5,2]
[1,2,5,3,4,7,8,6]=>0010001=>1000100=>[1,4,3]
[1,2,3,5,7,4,8,6]=>0000101=>1010000=>[1,2,5]
[1,2,3,5,7,8,4,6]=>0000010=>0100000=>[2,6]
[5,1,2,8,3,4,6,7]=>1001000=>0001001=>[4,3,1]
[1,5,2,8,3,4,6,7]=>0101000=>0001010=>[4,2,2]
[1,5,2,3,8,4,6,7]=>0100100=>0010010=>[3,3,2]
[1,2,5,3,8,4,6,7]=>0010100=>0010100=>[3,2,3]
[1,2,5,8,3,4,6,7]=>0001000=>0001000=>[4,4]
[1,5,2,3,4,8,6,7]=>0100010=>0100010=>[2,4,2]
[1,2,5,3,4,8,6,7]=>0010010=>0100100=>[2,3,3]
[1,2,3,5,4,8,6,7]=>0001010=>0101000=>[2,2,4]
[1,2,3,5,8,4,6,7]=>0000100=>0010000=>[3,5]
[1,5,2,3,4,6,8,7]=>0100001=>1000010=>[1,5,2]
[1,2,3,5,6,8,4,7]=>0000010=>0100000=>[2,6]
[1,5,2,3,4,6,7,8]=>0100000=>0000010=>[6,2]
[6,1,7,2,8,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[6,1,7,8,2,3,4,5]=>1001000=>0001001=>[4,3,1]
[6,7,1,8,2,3,4,5]=>0101000=>0001010=>[4,2,2]
[6,1,7,2,3,8,4,5]=>1010010=>0100101=>[2,3,2,1]
[6,7,1,2,3,8,4,5]=>0100010=>0100010=>[2,4,2]
[6,1,2,7,3,8,4,5]=>1001010=>0101001=>[2,2,3,1]
[1,6,2,7,3,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[1,6,7,2,3,8,4,5]=>0010010=>0100100=>[2,3,3]
[1,6,7,2,8,3,4,5]=>0010100=>0010100=>[3,2,3]
[1,6,7,8,2,3,4,5]=>0001000=>0001000=>[4,4]
[6,1,7,2,3,4,8,5]=>1010001=>1000101=>[1,4,2,1]
[6,7,1,2,3,4,8,5]=>0100001=>1000010=>[1,5,2]
[6,1,2,7,3,4,8,5]=>1001001=>1001001=>[1,3,3,1]
[1,6,2,7,3,4,8,5]=>0101001=>1001010=>[1,3,2,2]
[1,6,7,2,3,4,8,5]=>0010001=>1000100=>[1,4,3]
[1,6,2,3,7,4,8,5]=>0100101=>1010010=>[1,2,3,2]
[1,2,6,3,7,4,8,5]=>0010101=>1010100=>[1,2,2,3]
[6,1,2,3,7,8,4,5]=>1000010=>0100001=>[2,5,1]
[1,2,6,3,7,8,4,5]=>0010010=>0100100=>[2,3,3]
[1,2,6,7,3,8,4,5]=>0001010=>0101000=>[2,2,4]
[6,1,7,2,3,4,5,8]=>1010000=>0000101=>[5,2,1]
[1,6,2,7,3,4,5,8]=>0101000=>0001010=>[4,2,2]
[1,6,7,2,3,4,5,8]=>0010000=>0000100=>[5,3]
[1,6,2,3,4,7,5,8]=>0100010=>0100010=>[2,4,2]
[1,2,6,3,4,7,5,8]=>0010010=>0100100=>[2,3,3]
[1,2,3,6,4,7,5,8]=>0001010=>0101000=>[2,2,4]
[1,2,3,6,7,4,5,8]=>0000100=>0010000=>[3,5]
[6,1,2,3,4,7,8,5]=>1000001=>1000001=>[1,6,1]
[1,6,2,3,4,7,8,5]=>0100001=>1000010=>[1,5,2]
[1,2,6,3,4,7,8,5]=>0010001=>1000100=>[1,4,3]
[1,2,3,6,4,7,8,5]=>0001001=>1001000=>[1,3,4]
[1,2,3,6,7,4,8,5]=>0000101=>1010000=>[1,2,5]
[1,2,3,6,7,8,4,5]=>0000010=>0100000=>[2,6]
[6,1,8,2,3,4,5,7]=>1010000=>0000101=>[5,2,1]
[6,1,2,8,3,4,5,7]=>1001000=>0001001=>[4,3,1]
[1,6,2,8,3,4,5,7]=>0101000=>0001010=>[4,2,2]
[1,6,8,2,3,4,5,7]=>0010000=>0000100=>[5,3]
[1,6,2,3,8,4,5,7]=>0100100=>0010010=>[3,3,2]
[1,2,6,3,8,4,5,7]=>0010100=>0010100=>[3,2,3]
[1,2,6,8,3,4,5,7]=>0001000=>0001000=>[4,4]
[1,6,2,3,4,8,5,7]=>0100010=>0100010=>[2,4,2]
[1,2,6,3,4,8,5,7]=>0010010=>0100100=>[2,3,3]
[1,2,3,6,4,8,5,7]=>0001010=>0101000=>[2,2,4]
[6,1,2,3,4,5,8,7]=>1000001=>1000001=>[1,6,1]
[1,6,2,3,4,5,8,7]=>0100001=>1000010=>[1,5,2]
[1,2,6,3,4,5,8,7]=>0010001=>1000100=>[1,4,3]
[1,2,3,6,4,5,8,7]=>0001001=>1001000=>[1,3,4]
[1,2,3,4,6,8,5,7]=>0000010=>0100000=>[2,6]
[1,6,2,3,4,5,7,8]=>0100000=>0000010=>[6,2]
[1,2,6,3,4,5,7,8]=>0010000=>0000100=>[5,3]
[1,2,3,6,4,5,7,8]=>0001000=>0001000=>[4,4]
[7,1,2,8,3,4,5,6]=>1001000=>0001001=>[4,3,1]
[1,7,2,8,3,4,5,6]=>0101000=>0001010=>[4,2,2]
[1,7,8,2,3,4,5,6]=>0010000=>0000100=>[5,3]
[7,1,2,3,8,4,5,6]=>1000100=>0010001=>[3,4,1]
[1,2,7,8,3,4,5,6]=>0001000=>0001000=>[4,4]
[1,2,7,3,4,8,5,6]=>0010010=>0100100=>[2,3,3]
[1,2,3,7,4,8,5,6]=>0001010=>0101000=>[2,2,4]
[1,2,3,7,8,4,5,6]=>0000100=>0010000=>[3,5]
[1,2,7,3,4,5,8,6]=>0010001=>1000100=>[1,4,3]
[1,2,3,7,4,5,8,6]=>0001001=>1001000=>[1,3,4]
[1,2,3,4,7,5,8,6]=>0000101=>1010000=>[1,2,5]
[1,2,3,4,7,8,5,6]=>0000010=>0100000=>[2,6]
[1,7,2,3,4,5,6,8]=>0100000=>0000010=>[6,2]
[1,2,7,3,4,5,6,8]=>0010000=>0000100=>[5,3]
[1,2,3,7,4,5,6,8]=>0001000=>0001000=>[4,4]
[1,2,3,4,7,5,6,8]=>0000100=>0010000=>[3,5]
[1,8,2,3,4,5,6,7]=>0100000=>0000010=>[6,2]
[1,2,8,3,4,5,6,7]=>0010000=>0000100=>[5,3]
[1,2,3,8,4,5,6,7]=>0001000=>0001000=>[4,4]
[1,2,3,4,8,5,6,7]=>0000100=>0010000=>[3,5]
[1,2,3,4,5,8,6,7]=>0000010=>0100000=>[2,6]
[5,3,2,6,1,4,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[7,3,2,5,4,8,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,5,2,3,7,6,1]=>1010011=>1100101=>[1,1,3,2,1]
[7,4,5,2,3,8,1,6]=>1010010=>0100101=>[2,3,2,1]
[6,4,5,2,3,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,6,2,1,3,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[3,6,1,5,4,2,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,5,1,3,2,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[5,6,4,3,1,2,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[7,5,4,3,2,8,1,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,6,4,3,7,2,5,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,6,4,3,8,2,1,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,7,4,3,8,1,2,5]=>0110100=>0010110=>[3,2,1,2]
[5,7,4,3,1,8,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[4,7,5,1,3,8,2,6]=>0110010=>0100110=>[2,3,1,2]
[3,7,1,5,4,8,2,6]=>0101010=>0101010=>[2,2,2,2]
[2,1,7,5,4,8,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[3,8,1,5,4,7,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,8,5,1,3,7,6,2]=>0110011=>1100110=>[1,1,3,1,2]
[5,8,4,3,1,7,6,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,8,4,3,7,1,5,2]=>0110101=>1010110=>[1,2,2,1,2]
[7,8,4,3,6,5,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[6,8,5,7,3,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,6,7,1,3,4,2]=>0101001=>1001010=>[1,3,2,2]
[4,8,6,1,7,3,5,2]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,1,6,7,4,5,2]=>0100101=>1010010=>[1,2,3,2]
[2,1,8,6,7,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,7,6,8,4,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[3,7,1,6,8,4,2,5]=>0100110=>0110010=>[2,1,3,2]
[4,7,6,1,8,3,2,5]=>0110110=>0110110=>[2,1,2,1,2]
[5,7,6,8,1,3,2,4]=>0101010=>0101010=>[2,2,2,2]
[5,4,7,2,1,8,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,4,7,2,8,1,3,5]=>1010100=>0010101=>[3,2,2,1]
[7,4,6,2,8,3,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,6,2,7,3,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,2,6,7,4,5,1]=>1100101=>1010011=>[1,2,3,1,1]
[7,3,2,6,8,4,1,5]=>1100110=>0110011=>[2,1,3,1,1]
[6,3,2,7,8,1,4,5]=>1100100=>0010011=>[3,3,1,1]
[5,3,2,7,1,8,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,3,2,1,7,8,5,6]=>1110010=>0100111=>[2,3,1,1,1]
[3,4,1,2,8,7,6,5]=>0100111=>1110010=>[1,1,1,3,2]
[5,3,2,8,1,7,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,3,2,8,7,1,5,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,3,2,8,6,5,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,4,7,2,6,5,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,4,8,2,6,5,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[6,4,8,2,7,1,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,8,2,1,7,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,5,8,1,2,7,6,3]=>0010011=>1100100=>[1,1,3,3]
[3,5,1,8,2,7,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,5,8,3,7,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,6,8,7,3,5,4]=>1001101=>1011001=>[1,2,1,3,1]
[3,6,1,8,7,2,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,8,1,7,2,5,3]=>0010101=>1010100=>[1,2,2,3]
[5,6,8,7,1,2,4,3]=>0011001=>1001100=>[1,3,1,3]
[6,5,8,7,2,1,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,5,8,6,2,4,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[8,5,7,6,2,4,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,7,8,6,1,4,2,3]=>0011010=>0101100=>[2,2,1,3]
[4,7,8,1,6,5,2,3]=>0010110=>0110100=>[2,1,2,3]
[3,7,1,8,6,5,2,4]=>0101110=>0111010=>[2,1,1,2,2]
[2,1,7,8,6,5,3,4]=>1001110=>0111001=>[2,1,1,3,1]
[3,8,1,7,6,5,4,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[4,8,7,1,6,5,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,8,7,6,1,4,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,8,7,5,4,1,3,2]=>0111101=>1011110=>[1,2,1,1,1,2]
[2,1,4,3,6,5,8,7,10,9]=>101010101=>101010101=>[1,2,2,2,2,1]
[5,2,4,1,3,6,7,8]=>1010000=>0000101=>[5,2,1]
[3,2,6,1,4,5,7,8]=>1010000=>0000101=>[5,2,1]
[6,3,5,1,2,4,7,8]=>1010000=>0000101=>[5,2,1]
[5,2,7,1,3,4,6,8]=>1010000=>0000101=>[5,2,1]
[5,3,7,1,2,4,6,8]=>1010000=>0000101=>[5,2,1]
[5,4,7,1,2,3,6,8]=>1010000=>0000101=>[5,2,1]
[6,2,7,1,3,4,5,8]=>1010000=>0000101=>[5,2,1]
[6,3,7,1,2,4,5,8]=>1010000=>0000101=>[5,2,1]
[6,4,7,1,2,3,5,8]=>1010000=>0000101=>[5,2,1]
[7,3,5,1,2,4,6,8]=>1010000=>0000101=>[5,2,1]
[7,4,6,1,2,3,5,8]=>1010000=>0000101=>[5,2,1]
[3,2,8,1,4,5,6,7]=>1010000=>0000101=>[5,2,1]
[5,2,8,1,3,4,6,7]=>1010000=>0000101=>[5,2,1]
[5,4,8,1,2,3,6,7]=>1010000=>0000101=>[5,2,1]
[6,2,8,1,3,4,5,7]=>1010000=>0000101=>[5,2,1]
[6,5,8,1,2,3,4,7]=>1010000=>0000101=>[5,2,1]
[7,5,8,1,2,3,4,6]=>1010000=>0000101=>[5,2,1]
[8,3,5,1,2,4,6,7]=>1010000=>0000101=>[5,2,1]
[8,3,6,1,2,4,5,7]=>1010000=>0000101=>[5,2,1]
[8,4,7,1,2,3,5,6]=>1010000=>0000101=>[5,2,1]
[8,5,7,1,2,3,4,6]=>1010000=>0000101=>[5,2,1]
[3,2,5,7,1,4,6,8]=>1001000=>0001001=>[4,3,1]
[4,2,5,7,1,3,6,8]=>1001000=>0001001=>[4,3,1]
[4,3,5,7,1,2,6,8]=>1001000=>0001001=>[4,3,1]
[5,3,4,7,1,2,6,8]=>1001000=>0001001=>[4,3,1]
[4,2,6,7,1,3,5,8]=>1001000=>0001001=>[4,3,1]
[5,2,6,7,1,3,4,8]=>1001000=>0001001=>[4,3,1]
[7,3,5,6,1,2,4,8]=>1001000=>0001001=>[4,3,1]
[3,2,5,8,1,4,6,7]=>1001000=>0001001=>[4,3,1]
[4,2,5,8,1,3,6,7]=>1001000=>0001001=>[4,3,1]
[4,3,5,8,1,2,6,7]=>1001000=>0001001=>[4,3,1]
[5,2,4,8,1,3,6,7]=>1001000=>0001001=>[4,3,1]
[3,2,6,8,1,4,5,7]=>1001000=>0001001=>[4,3,1]
[4,2,6,8,1,3,5,7]=>1001000=>0001001=>[4,3,1]
[4,3,6,8,1,2,5,7]=>1001000=>0001001=>[4,3,1]
[5,2,6,8,1,3,4,7]=>1001000=>0001001=>[4,3,1]
[6,2,4,8,1,3,5,7]=>1001000=>0001001=>[4,3,1]
[6,2,5,8,1,3,4,7]=>1001000=>0001001=>[4,3,1]
[6,3,5,8,1,2,4,7]=>1001000=>0001001=>[4,3,1]
[3,2,7,8,1,4,5,6]=>1001000=>0001001=>[4,3,1]
[4,3,7,8,1,2,5,6]=>1001000=>0001001=>[4,3,1]
[6,2,7,8,1,3,4,5]=>1001000=>0001001=>[4,3,1]
[6,3,7,8,1,2,4,5]=>1001000=>0001001=>[4,3,1]
[6,4,7,8,1,2,3,5]=>1001000=>0001001=>[4,3,1]
[7,2,4,8,1,3,5,6]=>1001000=>0001001=>[4,3,1]
[7,3,5,8,1,2,4,6]=>1001000=>0001001=>[4,3,1]
[7,4,5,8,1,2,3,6]=>1001000=>0001001=>[4,3,1]
[8,2,5,6,1,3,4,7]=>1001000=>0001001=>[4,3,1]
[8,2,4,7,1,3,5,6]=>1001000=>0001001=>[4,3,1]
[8,2,5,7,1,3,4,6]=>1001000=>0001001=>[4,3,1]
[8,3,5,7,1,2,4,6]=>1001000=>0001001=>[4,3,1]
[8,2,6,7,1,3,4,5]=>1001000=>0001001=>[4,3,1]
[8,4,6,7,1,2,3,5]=>1001000=>0001001=>[4,3,1]
[4,6,2,5,1,3,7,8]=>0101000=>0001010=>[4,2,2]
[4,6,3,5,1,2,7,8]=>0101000=>0001010=>[4,2,2]
[4,7,3,5,1,2,6,8]=>0101000=>0001010=>[4,2,2]
[5,7,2,4,1,3,6,8]=>0101000=>0001010=>[4,2,2]
[5,7,3,4,1,2,6,8]=>0101000=>0001010=>[4,2,2]
[3,7,2,6,1,4,5,8]=>0101000=>0001010=>[4,2,2]
[5,7,2,6,1,3,4,8]=>0101000=>0001010=>[4,2,2]
[6,7,2,5,1,3,4,8]=>0101000=>0001010=>[4,2,2]
[4,8,2,5,1,3,6,7]=>0101000=>0001010=>[4,2,2]
[5,8,3,4,1,2,6,7]=>0101000=>0001010=>[4,2,2]
[5,8,3,6,1,2,4,7]=>0101000=>0001010=>[4,2,2]
[6,8,2,4,1,3,5,7]=>0101000=>0001010=>[4,2,2]
[6,8,3,4,1,2,5,7]=>0101000=>0001010=>[4,2,2]
[6,8,3,5,1,2,4,7]=>0101000=>0001010=>[4,2,2]
[6,8,4,5,1,2,3,7]=>0101000=>0001010=>[4,2,2]
[3,8,2,7,1,4,5,6]=>0101000=>0001010=>[4,2,2]
[4,8,2,7,1,3,5,6]=>0101000=>0001010=>[4,2,2]
[5,8,2,7,1,3,4,6]=>0101000=>0001010=>[4,2,2]
[5,8,3,7,1,2,4,6]=>0101000=>0001010=>[4,2,2]
[5,8,4,7,1,2,3,6]=>0101000=>0001010=>[4,2,2]
[6,8,2,7,1,3,4,5]=>0101000=>0001010=>[4,2,2]
[6,8,3,7,1,2,4,5]=>0101000=>0001010=>[4,2,2]
[6,8,5,7,1,2,3,4]=>0101000=>0001010=>[4,2,2]
[7,8,2,4,1,3,5,6]=>0101000=>0001010=>[4,2,2]
[7,8,2,5,1,3,4,6]=>0101000=>0001010=>[4,2,2]
[7,8,3,5,1,2,4,6]=>0101000=>0001010=>[4,2,2]
[7,8,4,6,1,2,3,5]=>0101000=>0001010=>[4,2,2]
[4,3,2,6,1,5,7,8]=>1101000=>0001011=>[4,2,1,1]
[5,3,2,6,1,4,7,8]=>1101000=>0001011=>[4,2,1,1]
[6,4,2,5,1,3,7,8]=>1101000=>0001011=>[4,2,1,1]
[6,5,2,4,1,3,7,8]=>1101000=>0001011=>[4,2,1,1]
[4,3,2,7,1,5,6,8]=>1101000=>0001011=>[4,2,1,1]
[5,3,2,7,1,4,6,8]=>1101000=>0001011=>[4,2,1,1]
[5,4,3,7,1,2,6,8]=>1101000=>0001011=>[4,2,1,1]
[6,3,2,7,1,4,5,8]=>1101000=>0001011=>[4,2,1,1]
[6,4,2,7,1,3,5,8]=>1101000=>0001011=>[4,2,1,1]
[6,4,3,7,1,2,5,8]=>1101000=>0001011=>[4,2,1,1]
[6,5,3,7,1,2,4,8]=>1101000=>0001011=>[4,2,1,1]
[7,3,2,5,1,4,6,8]=>1101000=>0001011=>[4,2,1,1]
[7,4,2,5,1,3,6,8]=>1101000=>0001011=>[4,2,1,1]
[7,3,2,6,1,4,5,8]=>1101000=>0001011=>[4,2,1,1]
[7,4,3,6,1,2,5,8]=>1101000=>0001011=>[4,2,1,1]
[7,5,2,6,1,3,4,8]=>1101000=>0001011=>[4,2,1,1]
[7,5,3,6,1,2,4,8]=>1101000=>0001011=>[4,2,1,1]
[7,6,3,5,1,2,4,8]=>1101000=>0001011=>[4,2,1,1]
[4,3,2,8,1,5,6,7]=>1101000=>0001011=>[4,2,1,1]
[5,3,2,8,1,4,6,7]=>1101000=>0001011=>[4,2,1,1]
[5,4,3,8,1,2,6,7]=>1101000=>0001011=>[4,2,1,1]
[6,3,2,8,1,4,5,7]=>1101000=>0001011=>[4,2,1,1]
[6,4,3,8,1,2,5,7]=>1101000=>0001011=>[4,2,1,1]
[6,5,2,8,1,3,4,7]=>1101000=>0001011=>[4,2,1,1]
[6,5,3,8,1,2,4,7]=>1101000=>0001011=>[4,2,1,1]
[6,5,4,8,1,2,3,7]=>1101000=>0001011=>[4,2,1,1]
[7,3,2,8,1,4,5,6]=>1101000=>0001011=>[4,2,1,1]
[7,4,2,8,1,3,5,6]=>1101000=>0001011=>[4,2,1,1]
[7,5,3,8,1,2,4,6]=>1101000=>0001011=>[4,2,1,1]
[7,6,2,8,1,3,4,5]=>1101000=>0001011=>[4,2,1,1]
[8,4,2,5,1,3,6,7]=>1101000=>0001011=>[4,2,1,1]
[8,3,2,6,1,4,5,7]=>1101000=>0001011=>[4,2,1,1]
[8,4,2,6,1,3,5,7]=>1101000=>0001011=>[4,2,1,1]
[8,5,3,6,1,2,4,7]=>1101000=>0001011=>[4,2,1,1]
[8,6,2,4,1,3,5,7]=>1101000=>0001011=>[4,2,1,1]
[8,6,2,5,1,3,4,7]=>1101000=>0001011=>[4,2,1,1]
[8,3,2,7,1,4,5,6]=>1101000=>0001011=>[4,2,1,1]
[8,4,2,7,1,3,5,6]=>1101000=>0001011=>[4,2,1,1]
[8,4,3,7,1,2,5,6]=>1101000=>0001011=>[4,2,1,1]
[8,5,2,7,1,3,4,6]=>1101000=>0001011=>[4,2,1,1]
[8,5,3,7,1,2,4,6]=>1101000=>0001011=>[4,2,1,1]
[8,5,4,7,1,2,3,6]=>1101000=>0001011=>[4,2,1,1]
[8,6,3,7,1,2,4,5]=>1101000=>0001011=>[4,2,1,1]
[8,7,2,4,1,3,5,6]=>1101000=>0001011=>[4,2,1,1]
[8,7,2,5,1,3,4,6]=>1101000=>0001011=>[4,2,1,1]
[8,7,3,5,1,2,4,6]=>1101000=>0001011=>[4,2,1,1]
[8,7,2,6,1,3,4,5]=>1101000=>0001011=>[4,2,1,1]
[8,7,3,6,1,2,4,5]=>1101000=>0001011=>[4,2,1,1]
[8,7,4,6,1,2,3,5]=>1101000=>0001011=>[4,2,1,1]
[4,6,3,5,8,1,2,7]=>0100100=>0010010=>[3,3,2]
[5,6,2,4,8,1,3,7]=>0100100=>0010010=>[3,3,2]
[4,7,2,5,8,1,3,6]=>0100100=>0010010=>[3,3,2]
[4,7,3,5,8,1,2,6]=>0100100=>0010010=>[3,3,2]
[5,7,3,4,8,1,2,6]=>0100100=>0010010=>[3,3,2]
[3,7,2,6,8,1,4,5]=>0100100=>0010010=>[3,3,2]
[4,7,3,6,8,1,2,5]=>0100100=>0010010=>[3,3,2]
[5,7,4,6,8,1,2,3]=>0100100=>0010010=>[3,3,2]
[6,7,3,5,8,1,2,4]=>0100100=>0010010=>[3,3,2]
[3,8,2,5,7,1,4,6]=>0100100=>0010010=>[3,3,2]
[4,8,2,5,7,1,3,6]=>0100100=>0010010=>[3,3,2]
[4,8,3,5,7,1,2,6]=>0100100=>0010010=>[3,3,2]
[3,8,2,6,7,1,4,5]=>0100100=>0010010=>[3,3,2]
[4,8,3,6,7,1,2,5]=>0100100=>0010010=>[3,3,2]
[6,8,2,5,7,1,3,4]=>0100100=>0010010=>[3,3,2]
[6,8,3,5,7,1,2,4]=>0100100=>0010010=>[3,3,2]
[6,8,4,5,7,1,2,3]=>0100100=>0010010=>[3,3,2]
[7,8,2,4,6,1,3,5]=>0100100=>0010010=>[3,3,2]
[7,8,2,5,6,1,3,4]=>0100100=>0010010=>[3,3,2]
[7,8,3,5,6,1,2,4]=>0100100=>0010010=>[3,3,2]
[4,3,2,6,8,1,5,7]=>1100100=>0010011=>[3,3,1,1]
[5,4,2,6,8,1,3,7]=>1100100=>0010011=>[3,3,1,1]
[5,4,3,6,8,1,2,7]=>1100100=>0010011=>[3,3,1,1]
[6,3,2,5,8,1,4,7]=>1100100=>0010011=>[3,3,1,1]
[6,4,3,5,8,1,2,7]=>1100100=>0010011=>[3,3,1,1]
[6,5,2,4,8,1,3,7]=>1100100=>0010011=>[3,3,1,1]
[4,3,2,7,8,1,5,6]=>1100100=>0010011=>[3,3,1,1]
[5,3,2,7,8,1,4,6]=>1100100=>0010011=>[3,3,1,1]
[5,4,2,7,8,1,3,6]=>1100100=>0010011=>[3,3,1,1]
[5,4,3,7,8,1,2,6]=>1100100=>0010011=>[3,3,1,1]
[6,4,2,7,8,1,3,5]=>1100100=>0010011=>[3,3,1,1]
[6,4,3,7,8,1,2,5]=>1100100=>0010011=>[3,3,1,1]
[6,5,2,7,8,1,3,4]=>1100100=>0010011=>[3,3,1,1]
[7,4,2,5,8,1,3,6]=>1100100=>0010011=>[3,3,1,1]
[7,3,2,6,8,1,4,5]=>1100100=>0010011=>[3,3,1,1]
[7,5,3,6,8,1,2,4]=>1100100=>0010011=>[3,3,1,1]
[7,6,3,5,8,1,2,4]=>1100100=>0010011=>[3,3,1,1]
[8,4,2,5,7,1,3,6]=>1100100=>0010011=>[3,3,1,1]
[8,5,2,6,7,1,3,4]=>1100100=>0010011=>[3,3,1,1]
[8,5,3,6,7,1,2,4]=>1100100=>0010011=>[3,3,1,1]
[8,6,3,5,7,1,2,4]=>1100100=>0010011=>[3,3,1,1]
[8,7,2,4,6,1,3,5]=>1100100=>0010011=>[3,3,1,1]
[8,7,3,4,6,1,2,5]=>1100100=>0010011=>[3,3,1,1]
[8,7,2,5,6,1,3,4]=>1100100=>0010011=>[3,3,1,1]
[8,7,3,5,6,1,2,4]=>1100100=>0010011=>[3,3,1,1]
[4,3,7,2,6,1,5,8]=>1010100=>0010101=>[3,2,2,1]
[5,3,7,2,6,1,4,8]=>1010100=>0010101=>[3,2,2,1]
[5,4,7,2,6,1,3,8]=>1010100=>0010101=>[3,2,2,1]
[6,3,7,2,5,1,4,8]=>1010100=>0010101=>[3,2,2,1]
[6,4,7,2,5,1,3,8]=>1010100=>0010101=>[3,2,2,1]
[7,3,6,2,5,1,4,8]=>1010100=>0010101=>[3,2,2,1]
[4,3,8,2,6,1,5,7]=>1010100=>0010101=>[3,2,2,1]
[5,3,8,2,6,1,4,7]=>1010100=>0010101=>[3,2,2,1]
[5,4,8,2,6,1,3,7]=>1010100=>0010101=>[3,2,2,1]
[6,4,8,2,5,1,3,7]=>1010100=>0010101=>[3,2,2,1]
[6,4,8,3,5,1,2,7]=>1010100=>0010101=>[3,2,2,1]
[6,5,8,3,4,1,2,7]=>1010100=>0010101=>[3,2,2,1]
[4,3,8,2,7,1,5,6]=>1010100=>0010101=>[3,2,2,1]
[5,3,8,2,7,1,4,6]=>1010100=>0010101=>[3,2,2,1]
[5,4,8,2,7,1,3,6]=>1010100=>0010101=>[3,2,2,1]
[6,4,8,2,7,1,3,5]=>1010100=>0010101=>[3,2,2,1]
[7,3,8,2,5,1,4,6]=>1010100=>0010101=>[3,2,2,1]
[7,4,8,3,5,1,2,6]=>1010100=>0010101=>[3,2,2,1]
[7,5,8,2,4,1,3,6]=>1010100=>0010101=>[3,2,2,1]
[7,5,8,3,4,1,2,6]=>1010100=>0010101=>[3,2,2,1]
[7,3,8,2,6,1,4,5]=>1010100=>0010101=>[3,2,2,1]
[7,4,8,2,6,1,3,5]=>1010100=>0010101=>[3,2,2,1]
[7,5,8,2,6,1,3,4]=>1010100=>0010101=>[3,2,2,1]
[7,5,8,3,6,1,2,4]=>1010100=>0010101=>[3,2,2,1]
[7,5,8,4,6,1,2,3]=>1010100=>0010101=>[3,2,2,1]
[8,3,6,2,5,1,4,7]=>1010100=>0010101=>[3,2,2,1]
[8,3,7,2,5,1,4,6]=>1010100=>0010101=>[3,2,2,1]
[8,3,7,2,6,1,4,5]=>1010100=>0010101=>[3,2,2,1]
[8,4,7,2,6,1,3,5]=>1010100=>0010101=>[3,2,2,1]
[8,4,7,3,6,1,2,5]=>1010100=>0010101=>[3,2,2,1]
[8,5,7,2,6,1,3,4]=>1010100=>0010101=>[3,2,2,1]
[8,6,7,2,5,1,3,4]=>1010100=>0010101=>[3,2,2,1]
[8,6,7,3,5,1,2,4]=>1010100=>0010101=>[3,2,2,1]
[5,4,3,2,7,1,6,8]=>1110100=>0010111=>[3,2,1,1,1]
[6,4,3,2,7,1,5,8]=>1110100=>0010111=>[3,2,1,1,1]
[6,5,3,2,7,1,4,8]=>1110100=>0010111=>[3,2,1,1,1]
[6,5,4,2,7,1,3,8]=>1110100=>0010111=>[3,2,1,1,1]
[7,5,3,2,6,1,4,8]=>1110100=>0010111=>[3,2,1,1,1]
[5,4,3,2,8,1,6,7]=>1110100=>0010111=>[3,2,1,1,1]
[6,5,3,2,8,1,4,7]=>1110100=>0010111=>[3,2,1,1,1]
[6,5,4,3,8,1,2,7]=>1110100=>0010111=>[3,2,1,1,1]
[7,5,3,2,8,1,4,6]=>1110100=>0010111=>[3,2,1,1,1]
[7,6,4,3,8,1,2,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,5,3,2,6,1,4,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,5,4,2,6,1,3,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,6,5,2,4,1,3,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,5,3,2,7,1,4,6]=>1110100=>0010111=>[3,2,1,1,1]
[8,6,3,2,7,1,4,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,3,2,6,1,4,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,4,2,6,1,3,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,4,3,6,1,2,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,5,2,6,1,3,4]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,6,2,4,1,3,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,6,2,5,1,3,4]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,6,3,5,1,2,4]=>1110100=>0010111=>[3,2,1,1,1]
[4,8,3,7,2,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,7,2,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,7,2,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,7,3,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,7,2,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,8,4,7,2,5,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,4,7,3,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[6,8,5,7,2,4,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,5,7,3,4,1,2]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,6,2,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[7,8,4,6,2,5,1,3]=>0101010=>0101010=>[2,2,2,2]
[7,8,4,6,3,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[7,8,5,6,2,4,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,4,3,8,2,7,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,3,8,2,7,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,4,8,2,7,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,3,8,2,6,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,3,8,2,6,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,4,8,2,6,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[7,6,3,8,2,5,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,6,4,8,2,5,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[7,6,5,8,2,4,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,3,7,2,6,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,3,7,2,6,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,6,3,7,2,5,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,6,4,7,2,5,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[8,6,5,7,2,4,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,3,6,2,5,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,4,6,3,5,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,5,6,2,4,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,4,3,2,8,1,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[7,6,4,3,2,8,1,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,5,4,3,2,7,1,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,7,4,3,2,6,1,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,7,5,3,2,6,1,4]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,7,5,4,2,6,1,3]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,7,6,3,2,5,1,4]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,7,6,5,2,4,1,3]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,1,2,3,7,4,5,6]=>1000100=>0010001=>[3,4,1]
[8,1,2,5,3,4,6,7]=>1001000=>0001001=>[4,3,1]
[6,1,2,5,3,8,4,7]=>1001010=>0101001=>[2,2,3,1]
[8,1,2,6,3,7,4,5]=>1001010=>0101001=>[2,2,3,1]
[4,1,2,8,7,3,5,6]=>1001100=>0011001=>[3,1,3,1]
[4,1,2,7,6,3,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[8,1,2,5,6,3,4,7]=>1000100=>0010001=>[3,4,1]
[8,1,2,7,6,3,4,5]=>1001100=>0011001=>[3,1,3,1]
[7,1,2,5,6,3,8,4]=>1000101=>1010001=>[1,2,4,1]
[4,1,2,5,8,7,3,6]=>1000110=>0110001=>[2,1,4,1]
[8,1,2,5,6,7,3,4]=>1000010=>0100001=>[2,5,1]
[3,1,7,2,6,4,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,5,2,8,7,4,6]=>1010110=>0110101=>[2,1,2,2,1]
[3,1,8,2,6,7,4,5]=>1010010=>0100101=>[2,3,2,1]
[8,1,4,2,3,5,6,7]=>1010000=>0000101=>[5,2,1]
[7,1,4,2,3,5,8,6]=>1010001=>1000101=>[1,4,2,1]
[6,1,4,2,3,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[7,1,5,2,3,4,8,6]=>1010001=>1000101=>[1,4,2,1]
[6,1,5,2,3,8,4,7]=>1010010=>0100101=>[2,3,2,1]
[6,1,8,2,3,7,4,5]=>1010010=>0100101=>[2,3,2,1]
[6,1,5,2,3,7,8,4]=>1010001=>1000101=>[1,4,2,1]
[5,1,4,2,8,3,6,7]=>1010100=>0010101=>[3,2,2,1]
[5,1,4,2,7,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,4,2,6,3,5,7]=>1010100=>0010101=>[3,2,2,1]
[7,1,4,2,6,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,5,2,6,3,4,7]=>1010100=>0010101=>[3,2,2,1]
[8,1,5,2,7,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[7,1,8,2,6,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[7,1,5,2,6,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,4,2,8,7,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,1,4,2,6,7,3,5]=>1010010=>0100101=>[2,3,2,1]
[8,1,5,2,6,7,3,4]=>1010010=>0100101=>[2,3,2,1]
[5,1,4,2,6,7,8,3]=>1010001=>1000101=>[1,4,2,1]
[3,1,8,6,2,4,5,7]=>1011000=>0001101=>[4,1,2,1]
[3,1,6,5,2,8,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[3,1,8,5,2,7,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[3,1,8,6,2,7,4,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,1,4,5,2,3,6,7]=>1001000=>0001001=>[4,3,1]
[7,1,8,5,2,3,4,6]=>1011000=>0001101=>[4,1,2,1]
[7,1,8,6,2,3,4,5]=>1011000=>0001101=>[4,1,2,1]
[7,1,6,5,2,3,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[3,1,4,8,6,2,5,7]=>1001100=>0011001=>[3,1,3,1]
[3,1,8,5,7,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[3,1,7,5,6,2,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,4,5,7,2,3,6]=>1000100=>0010001=>[3,4,1]
[8,1,4,7,6,2,3,5]=>1001100=>0011001=>[3,1,3,1]
[3,1,4,5,8,7,2,6]=>1000110=>0110001=>[2,1,4,1]
[3,1,8,5,6,7,2,4]=>1010010=>0100101=>[2,3,2,1]
[8,1,4,5,6,7,2,3]=>1000010=>0100001=>[2,5,1]
[2,8,1,3,7,4,5,6]=>0100100=>0010010=>[3,3,2]
[2,8,1,3,6,7,4,5]=>0100010=>0100010=>[2,4,2]
[2,6,1,5,3,8,4,7]=>0101010=>0101010=>[2,2,2,2]
[2,6,1,5,3,7,8,4]=>0101001=>1001010=>[1,3,2,2]
[2,4,1,8,6,3,5,7]=>0101100=>0011010=>[3,1,2,2]
[2,8,1,5,7,3,4,6]=>0100100=>0010010=>[3,3,2]
[2,8,1,7,6,3,4,5]=>0101100=>0011010=>[3,1,2,2]
[2,4,1,5,8,7,3,6]=>0100110=>0110010=>[2,1,3,2]
[7,3,1,2,4,5,8,6]=>1100001=>1000011=>[1,5,1,1]
[6,3,1,2,4,8,5,7]=>1100010=>0100011=>[2,4,1,1]
[6,3,1,2,4,7,8,5]=>1100001=>1000011=>[1,5,1,1]
[5,3,1,2,8,4,6,7]=>1100100=>0010011=>[3,3,1,1]
[8,3,1,2,6,4,5,7]=>1100100=>0010011=>[3,3,1,1]
[8,3,1,2,7,4,5,6]=>1100100=>0010011=>[3,3,1,1]
[7,3,1,2,6,4,8,5]=>1100101=>1010011=>[1,2,3,1,1]
[5,3,1,2,8,7,4,6]=>1100110=>0110011=>[2,1,3,1,1]
[5,3,1,2,6,7,8,4]=>1100001=>1000011=>[1,5,1,1]
[8,4,1,2,3,7,5,6]=>1100010=>0100011=>[2,4,1,1]
[7,6,1,2,3,4,8,5]=>1100001=>1000011=>[1,5,1,1]
[8,6,1,2,3,7,4,5]=>1100010=>0100011=>[2,4,1,1]
[5,4,1,2,8,3,6,7]=>1100100=>0010011=>[3,3,1,1]
[8,4,1,2,7,3,5,6]=>1100100=>0010011=>[3,3,1,1]
[7,4,1,2,6,3,8,5]=>1100101=>1010011=>[1,2,3,1,1]
[5,8,1,2,7,3,4,6]=>0100100=>0010010=>[3,3,2]
[8,7,1,2,6,3,4,5]=>1100100=>0010011=>[3,3,1,1]
[5,7,1,2,6,3,8,4]=>0100101=>1010010=>[1,2,3,2]
[5,8,1,2,6,7,3,4]=>0100010=>0100010=>[2,4,2]
[5,4,1,2,6,7,8,3]=>1100001=>1000011=>[1,5,1,1]
[4,3,1,8,2,5,6,7]=>1101000=>0001011=>[4,2,1,1]
[4,3,1,7,2,5,8,6]=>1101001=>1001011=>[1,3,2,1,1]
[4,3,1,6,2,8,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[4,3,1,6,2,7,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[8,3,1,5,2,4,6,7]=>1101000=>0001011=>[4,2,1,1]
[8,3,1,6,2,4,5,7]=>1101000=>0001011=>[4,2,1,1]
[7,3,1,6,2,4,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[8,3,1,5,2,7,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,3,1,6,2,7,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,1,5,2,7,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[7,4,1,5,2,3,8,6]=>1101001=>1001011=>[1,3,2,1,1]
[8,4,1,6,2,3,5,7]=>1101000=>0001011=>[4,2,1,1]
[7,4,1,8,2,3,5,6]=>1101000=>0001011=>[4,2,1,1]
[7,4,1,6,2,3,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[8,7,1,6,2,3,4,5]=>1101000=>0001011=>[4,2,1,1]
[6,7,1,5,2,3,8,4]=>0101001=>1001010=>[1,3,2,2]
[6,4,1,5,2,8,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,1,6,2,7,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[6,8,1,5,2,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,4,1,5,2,7,8,3]=>1101001=>1001011=>[1,3,2,1,1]
[4,3,1,8,7,2,5,6]=>1101100=>0011011=>[3,1,2,1,1]
[4,3,1,7,6,2,8,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,3,1,5,6,2,4,7]=>1100100=>0010011=>[3,3,1,1]
[8,3,1,5,7,2,4,6]=>1100100=>0010011=>[3,3,1,1]
[8,3,1,7,6,2,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[7,3,1,5,6,2,8,4]=>1100101=>1010011=>[1,2,3,1,1]
[8,4,1,5,6,2,3,7]=>1100100=>0010011=>[3,3,1,1]
[7,8,1,5,6,2,3,4]=>0100100=>0010010=>[3,3,2]
[4,3,1,5,6,8,2,7]=>1100010=>0100011=>[2,4,1,1]
[8,4,1,5,6,7,2,3]=>1100010=>0100011=>[2,4,1,1]
[4,3,1,5,6,7,8,2]=>1100001=>1000011=>[1,5,1,1]
[2,3,7,1,6,4,8,5]=>0010101=>1010100=>[1,2,2,3]
[2,3,5,1,8,7,4,6]=>0010110=>0110100=>[2,1,2,3]
[2,3,8,1,6,7,4,5]=>0010010=>0100100=>[2,3,3]
[2,8,4,1,3,5,6,7]=>0110000=>0000110=>[5,1,2]
[2,6,4,1,3,8,5,7]=>0110010=>0100110=>[2,3,1,2]
[2,6,4,1,3,7,8,5]=>0110001=>1000110=>[1,4,1,2]
[2,8,4,1,7,3,5,6]=>0110100=>0010110=>[3,2,1,2]
[2,7,4,1,6,3,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,5,1,7,3,4,6]=>0110100=>0010110=>[3,2,1,2]
[2,7,5,1,6,3,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,4,1,6,7,3,5]=>0110010=>0100110=>[2,3,1,2]
[2,5,4,1,6,7,8,3]=>0110001=>1000110=>[1,4,1,2]
[6,3,4,1,2,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[7,3,5,1,2,4,8,6]=>1010001=>1000101=>[1,4,2,1]
[6,3,7,1,2,4,8,5]=>1010001=>1000101=>[1,4,2,1]
[8,3,5,1,2,7,4,6]=>1010010=>0100101=>[2,3,2,1]
[6,3,8,1,2,7,4,5]=>1010010=>0100101=>[2,3,2,1]
[6,7,4,1,2,3,8,5]=>0110001=>1000110=>[1,4,1,2]
[6,8,5,1,2,3,4,7]=>0110000=>0000110=>[5,1,2]
[8,5,4,1,2,7,3,6]=>1110010=>0100111=>[2,3,1,1,1]
[6,8,4,1,2,7,3,5]=>0110010=>0100110=>[2,3,1,2]
[6,8,5,1,2,7,3,4]=>0110010=>0100110=>[2,3,1,2]
[8,3,4,1,7,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[7,3,4,1,6,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,5,1,6,2,4,7]=>1010100=>0010101=>[3,2,2,1]
[7,3,8,1,6,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[7,3,5,1,6,2,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,4,1,6,2,3,7]=>1110100=>0010111=>[3,2,1,1,1]
[7,8,4,1,6,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[7,8,5,1,6,2,3,4]=>0110100=>0010110=>[3,2,1,2]
[7,5,4,1,6,2,8,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,3,4,1,6,7,8,2]=>1010001=>1000101=>[1,4,2,1]
[2,3,4,8,1,7,5,6]=>0001010=>0101000=>[2,2,4]
[2,3,7,6,1,4,8,5]=>0011001=>1001100=>[1,3,1,3]
[2,3,6,5,1,8,4,7]=>0011010=>0101100=>[2,2,1,3]
[2,3,6,5,1,7,8,4]=>0011001=>1001100=>[1,3,1,3]
[2,8,4,5,1,3,6,7]=>0101000=>0001010=>[4,2,2]
[2,7,4,8,1,3,5,6]=>0101000=>0001010=>[4,2,2]
[2,7,4,6,1,3,8,5]=>0101001=>1001010=>[1,3,2,2]
[2,8,6,5,1,3,4,7]=>0111000=>0001110=>[4,1,1,2]
[2,7,8,5,1,3,4,6]=>0011000=>0001100=>[4,1,3]
[2,7,6,5,1,3,8,4]=>0111001=>1001110=>[1,3,1,1,2]
[2,6,4,5,1,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[2,8,4,6,1,7,3,5]=>0101010=>0101010=>[2,2,2,2]
[7,3,8,5,1,2,4,6]=>1011000=>0001101=>[4,1,2,1]
[8,6,4,5,1,7,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[2,3,4,8,6,1,5,7]=>0001100=>0011000=>[3,1,4]
[2,3,4,8,7,1,5,6]=>0001100=>0011000=>[3,1,4]
[2,3,4,7,6,1,8,5]=>0001101=>1011000=>[1,2,1,4]
[2,3,8,5,7,1,4,6]=>0010100=>0010100=>[3,2,3]
[2,3,7,5,6,1,8,4]=>0010101=>1010100=>[1,2,2,3]
[2,8,4,7,6,1,3,5]=>0101100=>0011010=>[3,1,2,2]
[2,8,7,5,6,1,3,4]=>0110100=>0010110=>[3,2,1,2]
[8,3,4,7,6,1,2,5]=>1001100=>0011001=>[3,1,3,1]
[8,3,7,5,6,1,2,4]=>1010100=>0010101=>[3,2,2,1]
[2,3,4,5,8,7,1,6]=>0000110=>0110000=>[2,1,5]
[2,3,4,8,6,7,1,5]=>0001010=>0101000=>[2,2,4]
[2,8,4,5,6,7,1,3]=>0100010=>0100010=>[2,4,2]
[6,5,8,7,3,4,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[4,6,7,3,8,5,1,2]=>0010110=>0110100=>[2,1,2,3]
[3,6,7,4,5,8,1,2]=>0010010=>0100100=>[2,3,3]
[2,6,7,4,5,1,8,3]=>0010101=>1010100=>[1,2,2,3]
[1,6,7,4,5,2,3,8]=>0010100=>0010100=>[3,2,3]
[1,5,4,7,6,2,3,8]=>0101100=>0011010=>[3,1,2,2]
[2,5,4,7,6,1,8,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,4,7,6,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[4,5,3,7,8,6,1,2]=>0100110=>0110010=>[2,1,3,2]
[5,4,3,8,7,6,1,2]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,4,8,3,7,5,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[6,3,8,4,5,7,1,2]=>1010010=>0100101=>[2,3,2,1]
[5,3,4,8,6,7,1,2]=>1001010=>0101001=>[2,2,3,1]
[4,3,5,6,8,7,1,2]=>1000110=>0110001=>[2,1,4,1]
[3,2,5,6,1,8,7,4]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,5,6,8,1,7,3]=>1000101=>1010001=>[1,2,4,1]
[5,2,4,8,6,1,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[6,2,8,4,5,1,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,2,4,5,1,6,3]=>0100101=>1010010=>[1,2,3,2]
[7,8,1,4,5,2,3,6]=>0100100=>0010010=>[3,3,2]
[6,1,8,4,5,2,3,7]=>1010100=>0010101=>[3,2,2,1]
[5,1,4,8,6,2,3,7]=>1001100=>0011001=>[3,1,3,1]
[4,1,3,2,8,6,5,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,3,8,2,6,4,7]=>1001010=>0101001=>[2,2,3,1]
[6,1,8,3,2,5,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[7,8,1,3,2,5,4,6]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,3,1,5,6,4]=>0101001=>1001010=>[1,3,2,2]
[6,2,8,3,1,5,7,4]=>1011001=>1001101=>[1,3,1,2,1]
[5,2,3,8,1,6,7,4]=>1001001=>1001001=>[1,3,3,1]
[6,3,8,2,1,7,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,8,3,2,1,6,5,4]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,8,4,2,6,1,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[5,4,2,8,7,1,6,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,5,2,7,8,1,6,3]=>0100101=>1010010=>[1,2,3,2]
[3,5,2,7,1,8,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,3,7,1,6,8,4]=>0101001=>1001010=>[1,3,2,2]
[1,5,3,7,2,6,4,8]=>0101010=>0101010=>[2,2,2,2]
[1,6,7,3,2,5,4,8]=>0011010=>0101100=>[2,2,1,3]
[2,6,7,3,1,5,8,4]=>0011001=>1001100=>[1,3,1,3]
[3,6,7,2,1,8,5,4]=>0011011=>1101100=>[1,1,2,1,3]
[4,6,7,2,8,1,5,3]=>0010101=>1010100=>[1,2,2,3]
[5,6,7,8,2,1,4,3]=>0001101=>1011000=>[1,2,1,4]
[7,8,5,6,2,1,4,3]=>0101101=>1011010=>[1,2,1,2,2]
[6,5,8,7,1,2,3,4]=>1011000=>0001101=>[4,1,2,1]
[5,4,1,8,7,2,3,6]=>1101100=>0011011=>[3,1,2,1,1]
[6,4,8,1,7,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[7,8,3,1,2,6,4,5]=>0110010=>0100110=>[2,3,1,2]
[5,3,1,8,2,7,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,3,1,2,8,7,5,6]=>1100110=>0110011=>[2,1,3,1,1]
[4,2,1,3,8,5,7,6]=>1100101=>1010011=>[1,2,3,1,1]
[5,2,1,8,3,4,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[6,2,8,1,3,4,7,5]=>1010001=>1000101=>[1,4,2,1]
[7,8,2,1,3,4,6,5]=>0110001=>1000110=>[1,4,1,2]
[4,5,2,3,7,6,1,8]=>0100110=>0110010=>[2,1,3,2]
[6,4,3,7,2,5,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,3,6,5,1,2,7]=>1101100=>0011011=>[3,1,2,1,1]
[1,5,6,3,4,8,7,2]=>0010011=>1100100=>[1,1,3,3]
[4,6,2,7,3,5,1,8]=>0101010=>0101010=>[2,2,2,2]
[3,2,6,7,4,5,1,8]=>1001010=>0101001=>[2,2,3,1]
[8,7,5,4,1,3,2,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[5,8,6,2,4,1,3,7]=>0110100=>0010110=>[3,2,1,2]
[4,8,2,6,5,1,3,7]=>0101100=>0011010=>[3,1,2,2]
[4,1,2,6,5,8,7,3]=>1001011=>1101001=>[1,1,2,3,1]
[5,1,6,2,4,8,7,3]=>1010011=>1100101=>[1,1,3,2,1]
[6,1,5,4,2,8,7,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,1,5,4,8,2,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,5,4,7,6,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[1,8,6,7,4,5,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[8,1,6,7,4,5,2,3]=>1001010=>0101001=>[2,2,3,1]
[6,1,7,8,2,4,5,3]=>1001001=>1001001=>[1,3,3,1]
[5,1,7,2,8,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,2,7,8,5,6,3]=>1000101=>1010001=>[1,2,4,1]
[3,2,1,7,8,5,6,4]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,8,7,1,5,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[4,8,2,7,1,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[5,8,7,2,1,4,3,6]=>0111010=>0101110=>[2,2,1,1,2]
[6,8,7,1,2,4,3,5]=>0110010=>0100110=>[2,3,1,2]
[7,8,6,1,4,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[8,7,6,1,4,3,2,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[1,6,7,8,3,4,5,2]=>0001001=>1001000=>[1,3,4]
[8,6,7,1,3,4,2,5]=>1010010=>0100101=>[2,3,2,1]
[7,6,8,1,3,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[5,7,8,2,1,3,4,6]=>0011000=>0001100=>[4,1,3]
[4,7,2,8,1,3,5,6]=>0101000=>0001010=>[4,2,2]
[3,2,6,8,4,1,5,7]=>1001100=>0011001=>[3,1,3,1]
[4,6,2,8,3,1,5,7]=>0101100=>0011010=>[3,1,2,2]
[5,6,8,2,3,1,4,7]=>0010100=>0010100=>[3,2,3]
[7,5,8,3,1,2,4,6]=>1011000=>0001101=>[4,1,2,1]
[8,5,7,3,1,4,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,5,7,3,8,4,6,2]=>0010101=>1010100=>[1,2,2,3]
[1,4,3,7,8,5,6,2]=>0100101=>1010010=>[1,2,3,2]
[6,4,3,8,2,1,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[4,5,2,3,8,1,6,7]=>0100100=>0010010=>[3,3,2]
[3,2,5,4,8,1,6,7]=>1010100=>0010101=>[3,2,2,1]
[4,5,2,3,1,8,7,6]=>0101011=>1101010=>[1,1,2,2,2]
[6,4,3,1,2,8,7,5]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,4,3,1,8,2,6,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[1,5,8,3,7,6,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[7,5,1,3,8,2,6,4]=>1100101=>1010011=>[1,2,3,1,1]
[5,6,1,2,3,8,7,4]=>0100011=>1100010=>[1,1,4,2]
[4,6,2,1,3,8,7,5]=>0110011=>1100110=>[1,1,3,1,2]
[3,2,6,1,4,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[3,2,7,1,8,4,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,1,2,8,3,6,4]=>0100101=>1010010=>[1,2,3,2]
[6,7,1,8,2,3,5,4]=>0101001=>1001010=>[1,3,2,2]
[7,6,1,8,3,2,5,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,7,1,6,5,3,2,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,8,1,6,5,2,3,4]=>0101100=>0011010=>[3,1,2,2]
[6,8,1,7,2,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,1,2,7,6,3,4]=>0100110=>0110010=>[2,1,3,2]
[4,8,2,1,7,6,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[3,2,8,1,7,6,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[4,1,2,8,7,6,5,3]=>1001111=>1111001=>[1,1,1,1,3,1]
[5,1,8,2,7,6,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,1,8,7,2,5,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,1,7,6,5,4,2,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[3,2,5,1,6,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,5,4,7,1,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,5,3,7,6,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,5,3,6,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,5,3,6,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,5,2,7,1,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,5,1,7,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,5,3,7,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,5,4,7,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,6,5,7,1,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,6,4,7,1,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,6,3,7,5,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,6,4,7,5,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,6,4,7,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,4,7,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,6,3,7,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,6,2,7,4,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,6,3,7,4,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,6,3,7,1,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,6,1,7,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,6,1,7,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,6,3,7,1,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,6,3,7,5,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,6,4,7,5,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,6,4,7,1,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,6,1,7,4,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,5,1,7,4,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,4,1,7,5,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,4,2,7,6,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,5,1,7,6,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,6,1,7,5,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,6,1,7,5,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,5,2,7,6,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,5,3,7,6,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,6,3,7,5,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,2,7,5,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,6,2,7,5,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,6,2,7,4,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,6,1,7,4,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,6,2,7,1,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,6,4,7,2,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,5,7,2,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,5,7,4,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,6,5,7,3,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,6,4,7,3,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,1,3,4,2,5,7]=>1100100=>0010011=>[3,3,1,1]
[8,3,5,2,1,6,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,6,3,5,2,4,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,3,7,5,2,4,6,1]=>1011001=>1001101=>[1,3,1,2,1]
[8,2,4,5,7,3,6,1]=>1000101=>1010001=>[1,2,4,1]
[2,4,5,7,3,1,8,6]=>0001101=>1011000=>[1,2,1,4]
[8,2,4,6,5,3,1,7]=>1001110=>0111001=>[2,1,1,3,1]
[8,1,2,4,5,6,3,7]=>1000010=>0100001=>[2,5,1]
[8,2,5,1,3,6,4,7]=>1010010=>0100101=>[2,3,2,1]
[8,6,1,4,5,3,2,7]=>1100110=>0110011=>[2,1,3,1,1]
[8,1,5,6,4,3,2,7]=>1001110=>0111001=>[2,1,1,3,1]
[8,5,7,4,3,2,6,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,5,7,4,2,1,6,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,6,3,8,7,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[1,7,4,8,6,3,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[8,4,7,6,3,5,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,1,5,8,6,7,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[4,8,1,6,7,3,5,2]=>0100101=>1010010=>[1,2,3,2]
[3,6,4,1,8,7,5,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[8,2,6,1,4,7,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[2,7,6,8,1,4,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,7,3,5,6,8,2,4]=>0100010=>0100010=>[2,4,2]
[3,7,6,5,8,2,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[3,6,8,5,7,2,4,1]=>0010101=>1010100=>[1,2,2,3]
[2,3,5,7,6,8,1,4]=>0001010=>0101000=>[2,2,4]
[2,1,6,5,7,8,3,4]=>1010010=>0100101=>[2,3,2,1]
[5,2,7,1,3,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[5,3,1,7,8,2,4,6]=>1100100=>0010011=>[3,3,1,1]
[3,7,2,6,4,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[3,2,6,1,4,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[5,3,7,2,1,8,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[4,7,3,2,1,5,8,6]=>0111001=>1001110=>[1,3,1,1,2]
[1,7,3,4,2,5,8,6]=>0101001=>1001010=>[1,3,2,2]
[4,7,2,1,3,5,8,6]=>0110001=>1000110=>[1,4,1,2]
[8,7,6,1,3,4,2,5]=>1110010=>0100111=>[2,3,1,1,1]
[8,5,7,3,2,1,6,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,7,8,6,2,1,5,4]=>0011101=>1011100=>[1,2,1,1,3]
[8,7,6,3,5,2,4,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,7,4,8,1,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,8,2,1,7,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[8,5,3,7,1,6,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,7,2,1,3,6,4]=>1011001=>1001101=>[1,3,1,2,1]
[4,6,1,8,7,2,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[8,1,2,5,6,7,4,3]=>1000011=>1100001=>[1,1,5,1]
[8,2,6,5,7,4,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[2,1,7,8,5,6,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[2,7,6,8,5,4,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[3,7,8,1,6,5,2,4]=>0010110=>0110100=>[2,1,2,3]
[8,7,6,3,5,1,4,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,4,7,6,5,1,3,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,7,1,5,6,4,3,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,1,6,7,5,4,3,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[3,2,5,1,6,8,4,7]=>1010010=>0100101=>[2,3,2,1]
[3,6,2,5,4,8,1,7]=>0101010=>0101010=>[2,2,2,2]
[3,5,2,4,7,1,8,6]=>0100101=>1010010=>[1,2,3,2]
[3,5,8,2,4,7,6,1]=>0010011=>1100100=>[1,1,3,3]
[4,2,6,5,3,8,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[5,3,1,6,8,2,4,7]=>1100100=>0010011=>[3,3,1,1]
[5,6,2,8,1,3,4,7]=>0101000=>0001010=>[4,2,2]
[5,4,3,2,7,1,8,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,4,3,8,2,7,6,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,3,7,6,2,1,8,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,4,3,1,7,2,8,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[1,4,7,5,8,3,2,6]=>0010110=>0110100=>[2,1,2,3]
[7,2,5,8,4,1,3,6]=>1001100=>0011001=>[3,1,3,1]
[2,8,5,7,4,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[3,5,8,7,1,4,6,2]=>0011001=>1001100=>[1,3,1,3]
[4,3,7,1,8,6,5,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,8,3,7,6,5,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[7,5,3,1,8,6,4,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[1,5,8,6,3,7,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[6,2,8,7,4,5,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[6,1,7,5,3,2,8,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,2,6,3,8,7,4,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,5,2,1,7,3,8,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,1,7,4,2,8,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[6,7,2,1,8,3,4,5]=>0110100=>0010110=>[3,2,1,2]
[7,5,8,2,1,3,4,6]=>1011000=>0001101=>[4,1,2,1]
[5,7,3,1,8,2,4,6]=>0110100=>0010110=>[3,2,1,2]
[4,7,1,5,2,8,3,6]=>0101010=>0101010=>[2,2,2,2]
[2,4,8,6,3,7,5,1]=>0011011=>1101100=>[1,1,2,1,3]
[3,8,6,2,4,7,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[7,3,6,2,4,1,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,5,2,7,1,8,4,6]=>0101010=>0101010=>[2,2,2,2]
[4,3,7,8,2,1,5,6]=>1001100=>0011001=>[3,1,3,1]
[8,3,7,1,4,6,2,5]=>1010010=>0100101=>[2,3,2,1]
[3,8,2,5,7,1,6,4]=>0100101=>1010010=>[1,2,3,2]
[7,8,3,6,2,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[8,7,3,6,2,5,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,2,6,8,1,7,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[5,4,8,2,7,1,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,3,7,1,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,7,2,6,1,3,4]=>0110100=>0010110=>[3,2,1,2]
[6,4,8,1,7,2,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,6,8,2,7,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[6,5,2,8,1,7,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,2,7,1,8,6,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,8,2,7,6,4,3,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[6,2,8,7,5,4,3,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[6,1,7,2,8,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,7,1,8,6,2,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,3,1,6,5,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[8,7,4,6,1,5,3,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,7,1,6,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,8,1,7,5,4,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[7,1,8,6,5,4,3,2]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[4,1,3,2,6,5,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,5,1,2,4,8,7]=>1010001=>1000101=>[1,4,2,1]
[4,3,5,6,1,2,8,7]=>1001001=>1001001=>[1,3,3,1]
[8,3,7,5,2,1,4,6]=>1011100=>0011101=>[3,1,1,2,1]
[6,3,7,5,1,8,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,5,2,7,1,8,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[3,5,2,6,4,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[6,1,2,4,5,3,8,7]=>1000101=>1010001=>[1,2,4,1]
[5,6,3,2,1,4,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[2,1,6,3,5,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,3,5,1,2,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,1,4,6,2,8,7]=>1100101=>1010011=>[1,2,3,1,1]
[5,7,4,6,2,8,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,4,7,8,5,2,1,6]=>0001110=>0111000=>[2,1,1,4]
[2,1,8,5,7,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[8,6,3,5,1,7,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,4,8,6,5,7,1,2]=>0011010=>0101100=>[2,2,1,3]
[5,1,4,6,8,2,7,3]=>1000101=>1010001=>[1,2,4,1]
[2,5,4,6,7,1,8,3]=>0100101=>1010010=>[1,2,3,2]
[2,4,6,3,7,5,8,1]=>0010101=>1010100=>[1,2,2,3]
[4,1,6,3,8,5,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[3,7,4,2,8,6,5,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[8,5,3,7,4,1,6,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,1,5,7,4,8,6,3]=>1001011=>1101001=>[1,1,2,3,1]
[3,1,8,2,7,6,5,4]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,3,8,1,6,7,5,4]=>0010011=>1100100=>[1,1,3,3]
[4,3,7,2,6,8,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[2,8,1,3,6,5,7,4]=>0100101=>1010010=>[1,2,3,2]
[8,1,2,3,5,6,7,4]=>1000001=>1000001=>[1,6,1]
[7,8,2,4,3,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,2,4,1,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[2,1,8,3,4,6,7,5]=>1010001=>1000101=>[1,4,2,1]
[2,1,7,8,5,4,3,6]=>1001110=>0111001=>[2,1,1,3,1]
[5,7,3,8,1,4,2,6]=>0101010=>0101010=>[2,2,2,2]
[7,1,8,4,5,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,7,1,6,3,4,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,3,8,7,4,2,6,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,3,6,1,4,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,5,8,2,4,1,6]=>1001010=>0101001=>[2,2,3,1]
[2,3,4,1,8,5,7,6]=>0010101=>1010100=>[1,2,2,3]
[4,1,3,2,8,5,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,4,3,8,5,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,3,2,6,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[8,3,5,6,2,7,1,4]=>1001010=>0101001=>[2,2,3,1]
[5,3,6,1,8,7,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[5,6,2,8,7,4,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[7,8,5,6,1,4,2,3]=>0101010=>0101010=>[2,2,2,2]
[8,1,6,4,5,7,2,3]=>1010010=>0100101=>[2,3,2,1]
[5,8,3,6,1,7,2,4]=>0101010=>0101010=>[2,2,2,2]
[2,1,8,6,5,7,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[2,1,7,5,3,6,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[7,1,4,2,5,6,8,3]=>1010001=>1000101=>[1,4,2,1]
[2,7,4,1,6,5,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[7,3,5,4,6,1,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,4,1,5,7,8,2]=>1010001=>1000101=>[1,4,2,1]
[3,1,4,5,6,8,7,2]=>1000011=>1100001=>[1,1,5,1]
[4,5,2,6,3,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[6,5,2,1,4,3,8,7]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,5,2,7,4,8,3,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,2,7,4,1,6,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,3,7,5,2,1,6,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,3,7,5,2,8,4,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,3,1,5,2,4,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[3,1,6,5,4,2,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,4,3,6,1,2,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[5,6,3,2,4,1,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[6,7,2,3,4,8,5,1]=>0100011=>1100010=>[1,1,4,2]
[8,7,2,3,4,1,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[5,1,7,3,8,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,5,7,3,8,6,4,1]=>0010111=>1110100=>[1,1,1,2,3]
[3,6,7,4,1,8,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[5,6,3,7,4,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[2,1,6,7,4,8,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,8,7,4,3,6,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,8,3,7,4,2,6,1]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,1,3,5,2,6,4]=>0100101=>1010010=>[1,2,3,2]
[5,8,7,3,2,6,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[2,8,6,3,1,5,7,4]=>0111001=>1001110=>[1,3,1,1,2]
[8,1,6,3,2,5,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[2,8,4,1,6,3,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,1,2,7,6,3,5]=>0100110=>0110010=>[2,1,3,2]
[6,8,3,5,2,7,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,8,5,3,7,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,5,3,2,8,7,1,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[2,4,1,8,7,6,5,3]=>0101111=>1111010=>[1,1,1,1,2,2]
[4,1,2,8,7,5,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[8,4,2,1,7,5,3,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[4,3,1,8,6,7,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,1,4,8,6,5,7,2]=>1001101=>1011001=>[1,2,1,3,1]
[7,3,5,4,8,6,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[6,4,3,5,8,1,7,2]=>1100101=>1010011=>[1,2,3,1,1]
[2,1,7,6,5,8,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[5,7,3,6,1,8,2,4]=>0101010=>0101010=>[2,2,2,2]
[2,7,6,4,5,8,1,3]=>0110010=>0100110=>[2,3,1,2]
[3,7,5,6,8,4,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[5,7,1,6,8,2,4,3]=>0100101=>1010010=>[1,2,3,2]
[8,6,2,5,1,7,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,5,2,6,3,8,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[4,1,2,3,6,8,7,5]=>1000011=>1100001=>[1,1,5,1]
[2,4,3,1,8,5,6,7]=>0110100=>0010110=>[3,2,1,2]
[7,5,2,8,3,4,6,1]=>1101001=>1001011=>[1,3,2,1,1]
[4,7,2,8,1,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[8,7,2,1,4,5,6,3]=>1110001=>1000111=>[1,4,1,1,1]
[3,6,8,7,1,5,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[5,7,8,6,3,4,1,2]=>0011010=>0101100=>[2,2,1,3]
[5,7,3,8,1,4,6,2]=>0101001=>1001010=>[1,3,2,2]
[2,1,7,8,5,4,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[7,5,8,4,3,6,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,4,8,3,5,6,1,7]=>0010010=>0100100=>[2,3,3]
[4,1,8,3,6,5,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,1,3,7,2,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[4,3,8,2,5,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,4,8,3,5,7,6]=>1001001=>1001001=>[1,3,3,1]
[6,8,2,4,3,5,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,8,2,3,5,1,6,7]=>0100100=>0010010=>[3,3,2]
[7,8,5,6,1,4,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[7,8,4,2,1,5,3,6]=>0111010=>0101110=>[2,2,1,1,2]
[7,8,2,1,6,5,3,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,4,1,2,5,7,3,8]=>1100010=>0100011=>[2,4,1,1]
[4,3,8,1,7,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[7,8,1,4,6,2,5,3]=>0100101=>1010010=>[1,2,3,2]
[7,8,3,5,4,2,1,6]=>0101110=>0111010=>[2,1,1,2,2]
[7,8,4,1,2,3,6,5]=>0110001=>1000110=>[1,4,1,2]
[7,8,3,6,5,4,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[7,8,2,6,4,1,3,5]=>0101100=>0011010=>[3,1,2,2]
[7,8,1,6,5,4,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[2,1,8,7,5,4,3,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[1,3,8,2,6,4,7,5]=>0010101=>1010100=>[1,2,2,3]
[5,3,7,1,6,4,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,2,5,8,7,4,3]=>1000111=>1110001=>[1,1,1,4,1]
[6,3,1,8,4,2,7,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,4,2,1,5,3,8,7]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,4,3,7,5,8,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[4,3,8,7,5,6,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[2,4,7,1,5,3,6,8]=>0010100=>0010100=>[3,2,3]
[3,7,2,8,6,4,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[3,8,1,7,6,4,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[1,8,5,7,3,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[2,7,5,8,3,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[1,5,6,8,2,4,7,3]=>0001001=>1001000=>[1,3,4]
[2,6,1,4,7,3,5,8]=>0100100=>0010010=>[3,3,2]
[3,6,8,4,7,5,1,2]=>0010110=>0110100=>[2,1,2,3]
[5,6,7,3,8,4,1,2]=>0010110=>0110100=>[2,1,2,3]
[4,5,6,7,2,8,1,3]=>0001010=>0101000=>[2,2,4]
[4,5,7,6,1,8,3,2]=>0011011=>1101100=>[1,1,2,1,3]
[1,5,8,6,2,7,3,4]=>0011010=>0101100=>[2,2,1,3]
[4,7,5,6,3,1,8,2]=>0101101=>1011010=>[1,2,1,2,2]
[5,1,6,3,4,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,1,4,2,3,8,6]=>0101001=>1001010=>[1,3,2,2]
[5,7,6,4,3,8,1,2]=>0111010=>0101110=>[2,2,1,1,2]
[6,3,4,5,8,7,1,2]=>1000110=>0110001=>[2,1,4,1]
[6,2,4,1,8,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,3,5,4,8,1,7]=>1001010=>0101001=>[2,2,3,1]
[5,1,4,2,7,6,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,6,2,4,7,8,3,5]=>0100010=>0100010=>[2,4,2]
[5,7,2,4,1,6,3,8]=>0101010=>0101010=>[2,2,2,2]
[6,1,4,2,8,5,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,7,5,8,1,4,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[5,8,7,6,3,4,1,2]=>0111010=>0101110=>[2,2,1,1,2]
[5,8,7,6,2,3,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[4,1,7,2,6,5,3,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,8,2,1,5,6,3,7]=>0110010=>0100110=>[2,3,1,2]
[4,2,7,8,1,6,3,5]=>1001010=>0101001=>[2,2,3,1]
[2,1,8,7,6,5,3,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,2,7,1,6,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,7,5,6,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[3,8,6,5,2,4,1,7]=>0111010=>0101110=>[2,2,1,1,2]
[3,8,5,6,1,4,7,2]=>0101001=>1001010=>[1,3,2,2]
[5,3,7,8,2,1,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[5,2,8,7,1,6,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,6,7,8,5,1,4,2]=>0001101=>1011000=>[1,2,1,4]
[3,7,8,5,1,2,4,6]=>0011000=>0001100=>[4,1,3]
[4,1,8,6,2,3,5,7]=>1011000=>0001101=>[4,1,2,1]
[4,7,8,6,3,5,1,2]=>0011010=>0101100=>[2,2,1,3]
[3,8,7,6,5,4,1,2]=>0111110=>0111110=>[2,1,1,1,1,2]
[2,8,6,7,5,1,3,4]=>0101100=>0011010=>[3,1,2,2]
[5,3,7,8,2,1,4,6]=>1001100=>0011001=>[3,1,3,1]
[7,6,1,2,5,8,3,4]=>1100010=>0100011=>[2,4,1,1]
[2,1,7,8,4,3,5,6]=>1001100=>0011001=>[3,1,3,1]
[7,8,1,2,5,4,6,3]=>0100101=>1010010=>[1,2,3,2]
[2,6,8,3,1,4,7,5]=>0011001=>1001100=>[1,3,1,3]
[8,4,1,3,7,6,2,5]=>1100110=>0110011=>[2,1,3,1,1]
[6,5,2,1,8,7,4,3]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[4,7,2,8,1,3,6,5]=>0101001=>1001010=>[1,3,2,2]
[7,3,8,6,1,2,5,4]=>1011001=>1001101=>[1,3,1,2,1]
[3,4,7,1,8,2,6,5]=>0010101=>1010100=>[1,2,2,3]
[1,8,2,4,3,5,6,7]=>0101000=>0001010=>[4,2,2]
[1,7,2,4,3,5,6,8]=>0101000=>0001010=>[4,2,2]
[1,5,2,4,3,6,7,8]=>0101000=>0001010=>[4,2,2]
[1,7,2,5,3,4,6,8]=>0101000=>0001010=>[4,2,2]
[1,8,2,5,3,4,6,7]=>0101000=>0001010=>[4,2,2]
[1,8,2,6,3,4,5,7]=>0101000=>0001010=>[4,2,2]
[1,8,2,7,3,4,5,6]=>0101000=>0001010=>[4,2,2]
[1,8,2,7,3,5,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,8,3,5,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,8,3,5,4,7]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,8,3,6,4,7]=>0101010=>0101010=>[2,2,2,2]
[1,4,2,8,3,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[1,3,2,8,4,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[1,2,3,8,4,6,5,7]=>0001010=>0101000=>[2,2,4]
[1,2,3,7,4,6,5,8]=>0001010=>0101000=>[2,2,4]
[1,3,2,7,4,6,5,8]=>0101010=>0101010=>[2,2,2,2]
[1,4,2,7,3,6,5,8]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,7,3,6,4,8]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,7,3,5,4,8]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,6,3,5,4,8]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,6,3,5,4,7]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,5,3,6,4,7]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,5,3,6,4,8]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,5,3,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,4,3,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,4,3,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,4,3,6,5,8]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,4,3,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,4,3,7,5,6]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,4,3,8,5,6]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,4,3,8,5,7]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,4,3,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,5,3,8,4,7]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,5,3,8,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,5,3,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,6,3,7,4,5]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,6,3,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[1,2,3,8,4,7,5,6]=>0001010=>0101000=>[2,2,4]
[1,3,2,8,4,7,5,6]=>0101010=>0101010=>[2,2,2,2]
[1,4,2,8,3,7,5,6]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,8,3,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,8,3,7,4,5]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,8,3,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,7,3,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[2,8,4,1,6,5,3,7]=>0110110=>0110110=>[2,1,2,1,2]
[2,8,4,1,5,6,7,3]=>0110001=>1000110=>[1,4,1,2]
[2,8,7,4,1,6,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[7,2,8,5,1,6,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,3,7,5,2,6,4,8]=>0011010=>0101100=>[2,2,1,3]
[1,3,7,5,4,2,6,8]=>0011100=>0011100=>[3,1,1,3]
[7,2,8,5,4,1,6,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,8,5,3,4,1,6,7]=>0110100=>0010110=>[3,2,1,2]
[2,8,7,6,1,4,5,3]=>0111001=>1001110=>[1,3,1,1,2]
[2,8,6,5,7,3,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[7,2,8,4,5,6,1,3]=>1010010=>0100101=>[2,3,2,1]
[6,2,3,8,5,1,7,4]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,2,8,5,1,4,7]=>1101100=>0011011=>[3,1,2,1,1]
[7,4,8,5,2,1,3,6]=>1011100=>0011101=>[3,1,1,2,1]
[6,4,8,5,1,3,7,2]=>1011001=>1001101=>[1,3,1,2,1]
[4,3,7,5,1,2,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[4,3,7,1,5,6,8,2]=>1010001=>1000101=>[1,4,2,1]
[3,6,1,7,5,2,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[3,4,1,2,7,6,8,5]=>0100101=>1010010=>[1,2,3,2]
[6,5,2,7,4,1,8,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,5,2,6,4,8,7,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,3,2,1,8,6,5,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[4,2,1,3,8,7,6,5]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,1,6,8,4,3,5,2]=>1001101=>1011001=>[1,2,1,3,1]
[6,1,2,8,4,5,7,3]=>1001001=>1001001=>[1,3,3,1]
[5,6,8,2,3,1,7,4]=>0010101=>1010100=>[1,2,2,3]
[6,5,8,2,4,3,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,5,8,4,2,3,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[7,5,3,8,2,4,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[1,6,5,7,3,4,2,8]=>0101010=>0101010=>[2,2,2,2]
[5,2,1,8,7,6,3,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,1,3,8,4,6,2,5]=>1001010=>0101001=>[2,2,3,1]
[5,7,8,4,3,6,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,1,8,3,5,6,7,2]=>1010001=>1000101=>[1,4,2,1]
[4,1,8,3,6,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,3,4,8,6,1,7,5]=>0001101=>1011000=>[1,2,1,4]
[2,3,4,8,6,5,1,7]=>0001110=>0111000=>[2,1,1,4]
[2,7,3,5,8,6,1,4]=>0100110=>0110010=>[2,1,3,2]
[3,2,4,7,8,6,1,5]=>1000110=>0110001=>[2,1,4,1]
[1,5,4,6,2,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[5,2,4,7,1,8,3,6]=>1001010=>0101001=>[2,2,3,1]
[5,3,6,4,1,8,7,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,3,6,1,4,8,2,7]=>1010010=>0100101=>[2,3,2,1]
[7,3,5,6,8,4,2,1]=>1000111=>1110001=>[1,1,1,4,1]
[6,3,5,1,8,2,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,1,6,3,8,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,2,4,1,7,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[2,5,4,6,1,7,8,3]=>0101001=>1001010=>[1,3,2,2]
[7,2,1,4,3,6,5,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,3,4,1,2,6,5,8]=>1010010=>0100101=>[2,3,2,1]
[7,4,3,2,1,6,5,8]=>1111010=>0101111=>[2,2,1,1,1,1]
[6,7,3,2,5,4,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[1,8,3,2,5,4,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[1,8,4,5,2,3,7,6]=>0101001=>1001010=>[1,3,2,2]
[7,3,5,1,6,2,4,8]=>1010100=>0010101=>[3,2,2,1]
[7,2,1,5,6,3,4,8]=>1100100=>0010011=>[3,3,1,1]
[1,8,5,4,3,2,7,6]=>0111101=>1011110=>[1,2,1,1,1,2]
[6,4,7,5,1,3,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[3,2,1,8,5,4,7,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,3,8,1,5,4,7,6]=>0010101=>1010100=>[1,2,2,3]
[2,4,8,5,1,3,7,6]=>0011001=>1001100=>[1,3,1,3]
[2,6,8,4,3,7,1,5]=>0011010=>0101100=>[2,2,1,3]
[2,7,8,4,3,6,5,1]=>0011011=>1101100=>[1,1,2,1,3]
[1,8,7,5,6,3,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,8,5,6,3,4,1]=>0010101=>1010100=>[1,2,2,3]
[2,5,8,6,7,1,3,4]=>0010100=>0010100=>[3,2,3]
[2,4,8,6,1,7,3,5]=>0011010=>0101100=>[2,2,1,3]
[3,2,1,8,6,7,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,2,1,7,6,8,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,3,7,1,6,8,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,4,7,6,1,8,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,5,7,6,8,1,3,2]=>0010101=>1010100=>[1,2,2,3]
[4,6,7,5,8,3,1,2]=>0010110=>0110100=>[2,1,2,3]
[1,8,5,6,7,2,3,4]=>0100100=>0010010=>[3,3,2]
[4,6,5,7,8,2,1,3]=>0100110=>0110010=>[2,1,3,2]
[5,4,6,7,1,8,2,3]=>1001010=>0101001=>[2,2,3,1]
[5,3,6,1,7,8,2,4]=>1010010=>0100101=>[2,3,2,1]
[5,2,1,6,7,8,3,4]=>1100010=>0100011=>[2,4,1,1]
[6,2,1,5,7,3,8,4]=>1100101=>1010011=>[1,2,3,1,1]
[6,3,5,1,7,2,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,5,7,1,2,8,3]=>1001001=>1001001=>[1,3,3,1]
[5,6,4,7,2,8,1,3]=>0101010=>0101010=>[2,2,2,2]
[1,8,4,6,2,7,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,8,3,2,6,7,4,5]=>0110010=>0100110=>[2,3,1,2]
[5,7,3,2,6,8,4,1]=>0110011=>1100110=>[1,1,3,1,2]
[6,5,3,2,7,1,8,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,4,3,2,1,7,8,5]=>1111001=>1001111=>[1,3,1,1,1,1]
[6,2,1,4,3,7,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[5,2,1,4,3,8,7,6]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,3,4,1,2,8,7,6]=>1010011=>1100101=>[1,1,3,2,1]
[4,5,3,2,8,1,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,3,2,8,7,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[1,8,3,2,7,6,5,4]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,8,4,7,2,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[3,6,4,8,2,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[3,4,5,8,1,2,7,6]=>0001001=>1001000=>[1,3,4]
[4,3,5,1,8,2,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,1,5,8,3,7,6]=>1100101=>1010011=>[1,2,3,1,1]
[4,2,1,6,8,7,3,5]=>1100110=>0110011=>[2,1,3,1,1]
[3,4,6,8,1,7,2,5]=>0001010=>0101000=>[2,2,4]
[3,5,6,8,7,1,2,4]=>0001100=>0011000=>[3,1,4]
[3,6,5,8,7,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[3,6,7,8,5,4,1,2]=>0001110=>0111000=>[2,1,1,4]
[3,5,7,8,6,1,4,2]=>0001101=>1011000=>[1,2,1,4]
[4,2,1,7,8,6,5,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[2,3,8,1,7,6,5,4]=>0010111=>1110100=>[1,1,1,2,3]
[2,4,8,7,1,6,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101=>10101010101=>[1,2,2,2,2,2,1]
[8,1,6,7,3,2,5,4]=>1001101=>1011001=>[1,2,1,3,1]
[8,1,6,7,2,3,4,5]=>1001000=>0001001=>[4,3,1]
[8,1,2,4,3,6,5,7]=>1001010=>0101001=>[2,2,3,1]
[8,1,4,3,2,7,6,5]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,1,5,3,7,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,3,5,6,2,7,4]=>1000101=>1010001=>[1,2,4,1]
[6,3,2,1,4,5,8,7]=>1110001=>1000111=>[1,4,1,1,1]
[4,7,8,5,6,1,2,3]=>0010100=>0010100=>[3,2,3]
[3,7,8,5,6,2,1,4]=>0010110=>0110100=>[2,1,2,3]
[3,7,8,4,2,6,1,5]=>0011010=>0101100=>[2,2,1,3]
[3,7,8,2,4,5,1,6]=>0010010=>0100100=>[2,3,3]
[3,6,2,8,4,5,1,7]=>0101010=>0101010=>[2,2,2,2]
[2,3,6,7,4,5,8,1]=>0001001=>1001000=>[1,3,4]
[3,5,2,4,8,6,1,7]=>0100110=>0110010=>[2,1,3,2]
[3,5,4,2,8,7,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[4,6,5,8,7,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[6,4,5,1,7,8,2,3]=>1010010=>0100101=>[2,3,2,1]
[5,4,2,3,1,8,6,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,3,1,8,2,7,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,5,4,1,8,7,2,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,5,1,4,8,6,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[7,4,1,3,2,8,6,5]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,4,1,2,3,8,5,6]=>1100010=>0100011=>[2,4,1,1]
[6,4,2,1,3,8,5,7]=>1110010=>0100111=>[2,3,1,1,1]
[2,6,4,8,3,7,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,5,8,7,3,4,1]=>0101101=>1011010=>[1,2,1,2,2]
[6,5,2,1,8,3,4,7]=>1110100=>0010111=>[3,2,1,1,1]
[7,5,1,2,8,3,4,6]=>1100100=>0010011=>[3,3,1,1]
[7,6,1,8,2,3,4,5]=>1101000=>0001011=>[4,2,1,1]
[7,6,1,8,4,5,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[6,7,8,1,4,5,2,3]=>0010010=>0100100=>[2,3,3]
[6,7,8,1,3,2,5,4]=>0010101=>1010100=>[1,2,2,3]
[2,5,6,7,8,3,4,1]=>0000101=>1010000=>[1,2,5]
[2,4,6,7,3,8,5,1]=>0001011=>1101000=>[1,1,2,4]
[4,2,6,7,3,1,5,8]=>1001100=>0011001=>[3,1,3,1]
[4,7,8,2,3,1,5,6]=>0010100=>0010100=>[3,2,3]
[4,7,8,3,2,1,6,5]=>0011101=>1011100=>[1,2,1,1,3]
[5,7,8,3,1,2,6,4]=>0011001=>1001100=>[1,3,1,3]
[5,7,8,4,1,6,2,3]=>0011010=>0101100=>[2,2,1,3]
[5,6,4,8,1,7,2,3]=>0101010=>0101010=>[2,2,2,2]
[4,6,3,8,2,1,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[4,2,5,3,7,1,6,8]=>1010100=>0010101=>[3,2,2,1]
[5,3,6,7,1,2,8,4]=>1001001=>1001001=>[1,3,3,1]
[3,5,6,7,8,2,1,4]=>0000110=>0110000=>[2,1,5]
[3,4,6,7,2,8,1,5]=>0001010=>0101000=>[2,2,4]
[7,4,6,1,8,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,5,1,8,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,4,1,8,5,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,7,3,1,8,6,2]=>0011011=>1101100=>[1,1,2,1,3]
[4,5,6,2,1,8,7,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,6,5,2,7,4,3,8]=>0110110=>0110110=>[2,1,2,1,2]
[7,4,3,1,8,6,5,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[3,6,7,5,1,8,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[7,5,6,1,8,3,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,5,1,8,4,3,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[7,6,4,1,8,5,3,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[6,4,2,1,8,7,5,3]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[1,5,3,2,7,6,4,8]=>0110110=>0110110=>[2,1,2,1,2]
[2,6,5,1,7,8,4,3]=>0110011=>1100110=>[1,1,3,1,2]
[4,5,7,1,6,8,2,3]=>0010010=>0100100=>[2,3,3]
[4,5,7,1,3,8,2,6]=>0010010=>0100100=>[2,3,3]
[6,4,1,2,8,5,3,7]=>1100110=>0110011=>[2,1,3,1,1]
[5,3,1,2,8,6,4,7]=>1100110=>0110011=>[2,1,3,1,1]
[4,3,1,2,8,6,5,7]=>1100110=>0110011=>[2,1,3,1,1]
[6,1,2,5,8,3,4,7]=>1000100=>0010001=>[3,4,1]
[7,1,3,4,8,2,5,6]=>1000100=>0010001=>[3,4,1]
[2,6,1,5,7,8,3,4]=>0100010=>0100010=>[2,4,2]
[7,6,1,5,8,3,2,4]=>1100110=>0110011=>[2,1,3,1,1]
[3,6,7,1,5,8,2,4]=>0010010=>0100100=>[2,3,3]
[7,1,6,5,8,2,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,1,6,8,4,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[7,4,1,6,8,5,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[5,2,3,1,8,6,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,1,5,8,6,2,4]=>1100110=>0110011=>[2,1,3,1,1]
[6,2,4,1,8,5,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,5,1,8,4,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,4,8,2,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,5,3,8,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,5,2,8,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,1,4,8,6,2,5]=>1100110=>0110011=>[2,1,3,1,1]
[6,2,1,4,8,7,3,5]=>1100110=>0110011=>[2,1,3,1,1]
[5,2,1,3,8,7,4,6]=>1100110=>0110011=>[2,1,3,1,1]
[7,4,1,3,8,5,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[6,1,4,2,8,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,4,3,8,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,6,7,1,4,8,2,5]=>0010010=>0100100=>[2,3,3]
[7,6,1,4,8,3,2,5]=>1100110=>0110011=>[2,1,3,1,1]
[5,1,3,2,8,4,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,1,3,8,7,5,6]=>1100110=>0110011=>[2,1,3,1,1]
[2,6,1,4,7,8,3,5]=>0100010=>0100010=>[2,4,2]
[7,1,3,5,8,2,4,6]=>1000100=>0010001=>[3,4,1]
[7,8,5,6,1,3,4,2]=>0101001=>1001010=>[1,3,2,2]
[7,8,1,3,6,2,5,4]=>0100101=>1010010=>[1,2,3,2]
[1,3,8,4,7,2,5,6]=>0010100=>0010100=>[3,2,3]
[4,6,1,2,5,7,3,8]=>0100010=>0100010=>[2,4,2]
[1,4,8,2,5,7,3,6]=>0010010=>0100100=>[2,3,3]
[7,8,4,2,5,1,3,6]=>0110100=>0010110=>[3,2,1,2]
[7,8,1,5,4,6,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[7,8,2,1,6,3,4,5]=>0110100=>0010110=>[3,2,1,2]
[7,8,3,5,6,4,1,2]=>0100110=>0110010=>[2,1,3,2]
[7,8,4,5,3,1,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,4,8,3,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[1,4,6,8,3,7,5,2]=>0001011=>1101000=>[1,1,2,4]
[2,4,8,5,3,1,6,7]=>0011100=>0011100=>[3,1,1,3]
[2,5,8,1,4,7,6,3]=>0010011=>1100100=>[1,1,3,3]
[2,1,8,4,7,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,5,8,4,7,6,1,2]=>0010110=>0110100=>[2,1,2,3]
[1,6,2,4,7,3,8,5]=>0100101=>1010010=>[1,2,3,2]
[4,6,2,5,3,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,5,1,3,6,8,2]=>0110001=>1000110=>[1,4,1,2]
[7,5,3,6,2,4,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,7,3,6,1,4,8,2]=>0101001=>1001010=>[1,3,2,2]
[5,3,6,7,2,1,8,4]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,1,2,4,5,8,7]=>1100001=>1000011=>[1,5,1,1]
[1,4,7,2,5,3,8,6]=>0010101=>1010100=>[1,2,2,3]
[6,4,7,3,5,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[3,5,6,7,8,1,4,2]=>0000101=>1010000=>[1,2,5]
[3,6,5,7,8,2,1,4]=>0100110=>0110010=>[2,1,3,2]
[5,2,7,6,1,4,3,8]=>1011010=>0101101=>[2,2,1,2,1]
[2,7,5,6,8,4,1,3]=>0100110=>0110010=>[2,1,3,2]
[2,1,6,8,4,5,3,7]=>1001010=>0101001=>[2,2,3,1]
[2,7,1,8,5,3,4,6]=>0101100=>0011010=>[3,1,2,2]
[3,7,6,8,5,4,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[4,3,8,5,6,7,1,2]=>1010010=>0100101=>[2,3,2,1]
[4,2,8,1,6,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,8,5,4,6,7,2]=>1011001=>1001101=>[1,3,1,2,1]
[3,4,2,8,6,1,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[1,7,3,8,5,2,6,4]=>0101101=>1011010=>[1,2,1,2,2]
[4,1,8,3,6,2,5,7]=>1010100=>0010101=>[3,2,2,1]
[5,7,8,6,3,2,1,4]=>0011110=>0111100=>[2,1,1,1,3]
[5,7,8,6,1,3,4,2]=>0011001=>1001100=>[1,3,1,3]
[7,6,5,8,1,3,4,2]=>1101001=>1001011=>[1,3,2,1,1]
[1,6,4,3,8,2,5,7]=>0110100=>0010110=>[3,2,1,2]
[2,6,3,4,5,8,1,7]=>0100010=>0100010=>[2,4,2]
[2,6,4,1,8,3,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,6,4,5,8,7,1,2]=>0100110=>0110010=>[2,1,3,2]
[7,1,6,5,3,8,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,2,5,6,3,8,1,4]=>1001010=>0101001=>[2,2,3,1]
[5,6,2,7,3,1,4,8]=>0101100=>0011010=>[3,1,2,2]
[5,7,6,4,1,8,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,7,1,5,2,8,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,1,5,2,8,3,4,7]=>1010100=>0010101=>[3,2,2,1]
[7,5,2,4,3,1,6,8]=>1101100=>0011011=>[3,1,2,1,1]
[6,8,1,3,7,5,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[7,4,2,6,5,1,3,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,4,6,3,1,5,2,8]=>1011010=>0101101=>[2,2,1,2,1]
[7,2,3,5,4,1,6,8]=>1001100=>0011001=>[3,1,3,1]
[6,8,1,2,3,4,7,5]=>0100001=>1000010=>[1,5,2]
[2,5,1,7,8,3,6,4]=>0100101=>1010010=>[1,2,3,2]
[2,5,3,6,8,4,7,1]=>0100101=>1010010=>[1,2,3,2]
[2,1,4,7,8,5,6,3]=>1000101=>1010001=>[1,2,4,1]
[2,5,7,8,1,4,6,3]=>0001001=>1001000=>[1,3,4]
[3,5,7,4,1,6,2,8]=>0011010=>0101100=>[2,2,1,3]
[5,2,8,4,6,1,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,8,5,7,6,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,1,2,8,5,6,7,3]=>1001001=>1001001=>[1,3,3,1]
[1,4,2,7,5,8,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[4,1,8,6,7,5,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,3,8,7,6,2,4,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,8,4,7,6,2,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[5,8,7,4,3,6,1,2]=>0111010=>0101110=>[2,2,1,1,2]
[6,4,8,3,1,7,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[6,4,2,8,7,1,3,5]=>1101100=>0011011=>[3,1,2,1,1]
[6,3,8,7,2,5,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[6,3,1,8,7,2,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[5,8,3,7,1,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[5,1,8,4,6,2,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,7,4,1,6,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[6,8,5,2,4,3,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,5,3,1,2,7,4]=>0111001=>1001110=>[1,3,1,1,2]
[4,5,1,2,7,6,3,8]=>0100110=>0110010=>[2,1,3,2]
[4,5,1,2,6,8,7,3]=>0100011=>1100010=>[1,1,4,2]
[3,5,6,1,8,4,7,2]=>0010101=>1010100=>[1,2,2,3]
[3,5,7,1,2,8,6,4]=>0010011=>1100100=>[1,1,3,3]
[4,2,6,1,7,3,5,8]=>1010100=>0010101=>[3,2,2,1]
[4,6,3,1,2,7,5,8]=>0110010=>0100110=>[2,3,1,2]
[3,5,2,7,8,1,6,4]=>0100101=>1010010=>[1,2,3,2]
[3,1,4,7,5,6,2,8]=>1001010=>0101001=>[2,2,3,1]
[4,2,5,6,1,8,7,3]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,7,5,8,6,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,2,7,5,3,8,6,4]=>0011011=>1101100=>[1,1,2,1,3]
[4,1,2,7,3,8,6,5]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,4,2,5,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,3,7,5,2,4,8]=>1001100=>0011001=>[3,1,3,1]
[3,1,2,6,8,5,4,7]=>1000110=>0110001=>[2,1,4,1]
[3,7,1,2,5,4,8,6]=>0100101=>1010010=>[1,2,3,2]
[1,3,7,2,4,8,6,5]=>0010011=>1100100=>[1,1,3,3]
[3,2,7,8,1,6,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[2,4,1,7,8,6,5,3]=>0100111=>1110010=>[1,1,1,3,2]
[2,6,8,3,1,5,7,4]=>0011001=>1001100=>[1,3,1,3]
[3,6,4,8,5,1,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,3,7,4,5,1,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,7,5,2,8,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[2,6,3,7,5,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,2,1,7,8,3,4,6]=>1100100=>0010011=>[3,3,1,1]
[5,7,4,6,2,8,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,7,3,4,6,1,8,2]=>0100101=>1010010=>[1,2,3,2]
[4,2,8,3,6,7,1,5]=>1010010=>0100101=>[2,3,2,1]
[4,8,3,1,7,2,5,6]=>0110100=>0010110=>[3,2,1,2]
[5,2,8,4,7,1,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,4,7,3,1,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,8,3,1,7,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[6,3,8,2,7,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,1,8,2,4,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[3,5,1,8,2,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[7,5,1,3,6,2,4,8]=>1100100=>0010011=>[3,3,1,1]
[8,5,4,1,2,6,3,7]=>1110010=>0100111=>[2,3,1,1,1]
[5,1,8,4,2,7,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[4,1,6,2,8,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[1,6,2,8,5,3,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[6,8,5,3,1,7,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,6,7,3,1,8,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[5,6,2,1,7,8,4,3]=>0110011=>1100110=>[1,1,3,1,2]
[8,4,5,1,2,6,3,7]=>1010010=>0100101=>[2,3,2,1]
[1,6,3,7,2,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[6,3,2,7,8,5,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[6,4,7,2,8,1,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,4,8,3,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,5,7,8,3,1,6,2]=>0001101=>1011000=>[1,2,1,4]
[4,7,2,5,8,1,6,3]=>0100101=>1010010=>[1,2,3,2]
[5,7,3,8,2,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[3,4,7,8,2,6,1,5]=>0001010=>0101000=>[2,2,4]
[8,1,3,4,6,2,5,7]=>1000100=>0010001=>[3,4,1]
[3,8,2,4,6,7,1,5]=>0100010=>0100010=>[2,4,2]
[2,4,5,6,8,1,7,3]=>0000101=>1010000=>[1,2,5]
[4,8,3,5,6,1,7,2]=>0100101=>1010010=>[1,2,3,2]
[8,4,3,6,5,1,7,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,6,5,4,3,1,7,2]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[1,8,6,5,2,7,3,4]=>0111010=>0101110=>[2,2,1,1,2]
[8,7,5,4,1,6,3,2]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[7,8,5,4,1,3,6,2]=>0111001=>1001110=>[1,3,1,1,2]
[6,8,5,4,2,1,7,3]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,8,6,2,4,1,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,2,8,6,5,1,7,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,1,7,3,6,2,4,8]=>1010100=>0010101=>[3,2,2,1]
[8,1,6,5,2,3,7,4]=>1011001=>1001101=>[1,3,1,2,1]
[1,2,8,3,7,4,5,6]=>0010100=>0010100=>[3,2,3]
[8,1,7,2,6,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,8,2,6,4,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,8,3,2,7,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[3,2,1,8,4,7,5,6]=>1101010=>0101011=>[2,2,2,1,1]
[3,2,8,7,1,6,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,8,2,7,1,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,8,7,2,1,6,4,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,7,6,1,5,4,3,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,6,7,1,4,5,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[7,6,8,1,4,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,8,1,3,4,5,2]=>0010001=>1000100=>[1,4,3]
[5,7,8,2,1,4,6,3]=>0011001=>1001100=>[1,3,1,3]
[4,7,2,8,1,5,6,3]=>0101001=>1001010=>[1,3,2,2]
[3,2,7,8,1,5,6,4]=>1001001=>1001001=>[1,3,3,1]
[3,2,6,8,4,1,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[4,6,2,8,3,1,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[6,5,8,3,2,1,7,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,5,8,3,1,4,6,2]=>1011001=>1001101=>[1,3,1,2,1]
[8,4,3,7,1,6,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,4,3,8,2,1,7,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,4,3,2,8,1,7,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,5,2,3,8,1,7,6]=>0100101=>1010010=>[1,2,3,2]
[3,2,5,4,8,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,3,1,5,2,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[7,4,3,1,2,6,5,8]=>1110010=>0100111=>[2,3,1,1,1]
[1,5,4,2,3,6,7,8]=>0110000=>0000110=>[5,1,2]
[8,5,1,4,2,3,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[7,5,1,4,2,6,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[4,6,2,1,5,3,7,8]=>0110100=>0010110=>[3,2,1,2]
[3,2,6,1,5,4,7,8]=>1010100=>0010101=>[3,2,2,1]
[5,7,1,3,2,6,4,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,1,2,4,5,3,8]=>0100010=>0100010=>[2,4,2]
[7,6,1,2,5,4,3,8]=>1100110=>0110011=>[2,1,3,1,1]
[7,8,1,2,3,5,6,4]=>0100001=>1000010=>[1,5,2]
[6,8,1,2,4,3,7,5]=>0100101=>1010010=>[1,2,3,2]
[4,8,2,1,3,5,7,6]=>0110001=>1000110=>[1,4,1,2]
[3,2,8,1,4,5,7,6]=>1010001=>1000101=>[1,4,2,1]
[4,1,3,2,5,6,7,8]=>1010000=>0000101=>[5,2,1]
[5,1,2,4,3,6,7,8]=>1001000=>0001001=>[4,3,1]
[5,8,7,3,4,1,2,6]=>0110100=>0010110=>[3,2,1,2]
[6,7,3,8,5,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[6,7,4,5,1,8,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[5,4,7,6,2,3,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[5,4,7,6,8,1,2,3]=>1010100=>0010101=>[3,2,2,1]
[5,3,7,8,6,1,2,4]=>1001100=>0011001=>[3,1,3,1]
[4,3,8,7,6,1,2,5]=>1011100=>0011101=>[3,1,1,2,1]
[4,8,3,7,5,1,2,6]=>0101100=>0011010=>[3,1,2,2]
[4,5,6,7,1,8,3,2]=>0001011=>1101000=>[1,1,2,4]
[3,5,6,2,7,4,8,1]=>0010101=>1010100=>[1,2,2,3]
[3,5,6,1,7,8,4,2]=>0010011=>1100100=>[1,1,3,3]
[2,5,6,8,1,7,3,4]=>0001010=>0101000=>[2,2,4]
[8,2,4,5,1,6,3,7]=>1001010=>0101001=>[2,2,3,1]
[1,4,8,6,2,3,7,5]=>0011001=>1001100=>[1,3,1,3]
[1,5,6,8,2,3,7,4]=>0001001=>1001000=>[1,3,4]
[1,5,6,2,8,4,7,3]=>0010101=>1010100=>[1,2,2,3]
[1,4,2,6,8,5,7,3]=>0100101=>1010010=>[1,2,3,2]
[8,1,3,2,5,4,6,7]=>1010100=>0010101=>[3,2,2,1]
[2,4,1,6,8,7,5,3]=>0100111=>1110010=>[1,1,1,3,2]
[4,3,1,7,6,8,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,8,2,1,7,5,4,6]=>0110110=>0110110=>[2,1,2,1,2]
[8,3,2,1,6,5,4,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,4,2,6,1,5,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[4,2,8,7,1,6,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[5,2,7,8,1,6,3,4]=>1001010=>0101001=>[2,2,3,1]
[5,3,7,2,6,4,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,3,1,5,8,4,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,7,2,1,8,5,4,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,7,2,8,1,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,8,2,1,4,3,5]=>0011010=>0101100=>[2,2,1,3]
[8,5,6,2,1,4,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[5,8,7,1,2,3,4,6]=>0110000=>0000110=>[5,1,2]
[6,7,1,2,8,4,5,3]=>0100101=>1010010=>[1,2,3,2]
[6,7,1,3,4,8,5,2]=>0100011=>1100010=>[1,1,4,2]
[5,1,7,3,4,8,6,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,1,7,8,2,3,6,4]=>1001001=>1001001=>[1,3,3,1]
[4,8,1,7,2,3,5,6]=>0101000=>0001010=>[4,2,2]
[3,8,1,2,7,4,5,6]=>0100100=>0010010=>[3,3,2]
[3,1,8,2,7,4,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,2,8,7,5,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[4,1,3,7,5,8,6,2]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,8,3,4,7,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[1,8,2,3,4,5,7,6]=>0100001=>1000010=>[1,5,2]
[1,2,8,3,4,6,7,5]=>0010001=>1000100=>[1,4,3]
[6,3,8,5,2,7,4,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,5,2,8,4,7,3,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,3,4,5,8,7,2,1]=>1000111=>1110001=>[1,1,1,4,1]
[5,8,1,4,7,2,3,6]=>0100100=>0010010=>[3,3,2]
[3,6,4,8,5,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,1,4,8,6,3,7,2]=>1001101=>1011001=>[1,2,1,3,1]
[3,4,7,1,8,6,5,2]=>0010111=>1110100=>[1,1,1,2,3]
[6,3,8,4,2,7,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[3,6,8,7,1,4,2,5]=>0011010=>0101100=>[2,2,1,3]
[5,3,7,1,6,8,2,4]=>1010010=>0100101=>[2,3,2,1]
[4,6,1,2,7,8,5,3]=>0100011=>1100010=>[1,1,4,2]
[3,6,4,2,8,7,5,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,3,7,5,2,8,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[6,5,2,7,4,8,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[5,8,1,4,6,7,2,3]=>0100010=>0100010=>[2,4,2]
[6,3,7,4,2,8,5,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,7,1,6,2,4,5,3]=>1101001=>1001011=>[1,3,2,1,1]
[5,6,1,8,7,3,2,4]=>0101110=>0111010=>[2,1,1,2,2]
[3,6,4,5,7,2,8,1]=>0100101=>1010010=>[1,2,3,2]
[5,4,2,7,3,6,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[6,4,1,5,3,8,2,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,2,6,3,4,7,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,5,7,3,6,8,1]=>1001001=>1001001=>[1,3,3,1]
[1,6,5,3,4,8,2,7]=>0110010=>0100110=>[2,3,1,2]
[6,8,3,1,7,2,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[1,8,6,3,7,5,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[8,7,5,2,6,4,3,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,7,1,6,2,5,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,8,1,7,3,5,6,4]=>0101001=>1001010=>[1,3,2,2]
[4,8,1,3,7,2,6,5]=>0100101=>1010010=>[1,2,3,2]
[4,2,8,5,7,3,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,3,1,8,4,2,5]=>0110110=>0110110=>[2,1,2,1,2]
[1,7,3,8,4,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,8,5,3,4,6]=>0101100=>0011010=>[3,1,2,2]
[7,6,1,8,4,3,2,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,1,2,8,3,5,4,6]=>1001010=>0101001=>[2,2,3,1]
[6,3,7,2,1,8,4,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,2,6,1,7,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,1,5,8,3,6,7]=>1100100=>0010011=>[3,3,1,1]
[5,4,3,1,6,8,2,7]=>1110010=>0100111=>[2,3,1,1,1]
[1,5,3,4,6,8,2,7]=>0100010=>0100010=>[2,4,2]
[4,3,5,1,6,8,2,7]=>1010010=>0100101=>[2,3,2,1]
[4,7,5,6,8,3,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[6,5,1,8,7,4,2,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,6,4,7,5,3,2,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[5,7,3,8,2,6,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,3,8,7,4,5,6,1]=>0011001=>1001100=>[1,3,1,3]
[7,2,8,6,4,3,5,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,1,8,7,5,6,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,8,6,5,3,2,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,7,1,8,6,5,2,3]=>0101110=>0111010=>[2,1,1,2,2]
[6,8,7,2,5,4,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,7,4,8,3,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[6,7,4,5,2,8,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,7,4,6,2,3,1,8]=>0101010=>0101010=>[2,2,2,2]
[5,7,4,6,3,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,7,4,8,3,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[6,8,4,5,3,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,6,3,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,6,4,8,3,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,7,2,4,1,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,7,2,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,8,2,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,6,4,8,2,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,6,2,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,4,5,2,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[7,8,4,5,2,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,4,5,2,3,1,7]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,6,2,3,1,7]=>0101010=>0101010=>[2,2,2,2]
[5,6,4,8,2,3,1,7]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,8,2,4,1,7]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,4,2,8,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,6,3,5,2,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[4,6,3,5,2,8,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,6,3,8,2,5,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,8,3,6,2,5,1,7]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,6,2,4,1,7]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,5,2,4,1,7]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,5,2,4,1,6]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,5,2,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,5,2,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,6,2,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[4,8,3,6,2,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,6,3,8,2,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,6,3,7,2,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,6,3,7,2,5,1,8]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,6,2,5,1,8]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,6,2,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,8,2,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[5,7,4,8,2,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,7,3,6,2,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,7,3,6,2,4,1,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,5,2,4,1,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,5,2,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,8,2,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,4,8,2,5,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,7,5,8,2,4,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,5,7,2,3,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,4,8,2,3,1,5]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,8,2,4,1,5]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,4,2,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[5,7,3,4,2,6,1,8]=>0101010=>0101010=>[2,2,2,2]
[5,7,3,4,2,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[5,7,3,8,2,4,1,6]=>0101010=>0101010=>[2,2,2,2]
[5,7,4,8,2,3,1,6]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,7,2,3,1,6]=>0101010=>0101010=>[2,2,2,2]
[6,8,4,7,2,3,1,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,4,6,2,3,1,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,6,2,4,1,5]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,7,2,4,1,5]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,7,2,4,1,6]=>0101010=>0101010=>[2,2,2,2]
[4,8,3,7,2,5,1,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,8,2,5,1,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,5,2,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,5,2,6,1,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,3,7,2,6,1,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,3,7,2,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[4,5,3,8,2,7,1,6]=>0101010=>0101010=>[2,2,2,2]
[4,8,3,5,2,7,1,6]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,4,2,7,1,6]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,4,2,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,4,2,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,4,2,5,1,7]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,4,2,6,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,8,3,5,2,6,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,5,3,8,2,6,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,5,3,6,2,8,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,7,5,2,1,8,3,6]=>0111010=>0101110=>[2,2,1,1,2]
[4,6,5,2,1,3,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[5,6,4,2,3,1,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[6,4,5,3,1,2,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[5,4,6,1,3,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,6,8,1,7,3,2,5]=>0010110=>0110100=>[2,1,2,3]
[4,7,8,1,6,3,5,2]=>0010101=>1010100=>[1,2,2,3]
[7,4,8,1,6,5,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,4,5,3,1,8,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,4,8,1,7,5,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[6,4,7,1,8,2,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,6,4,2,1,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[2,1,6,8,7,4,3,5]=>1001110=>0111001=>[2,1,1,3,1]
[2,1,7,8,6,4,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[8,4,7,3,6,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,8,5,2,4,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,7,8,6,2,3,1,4]=>0011010=>0101100=>[2,2,1,3]
[5,8,7,6,3,2,1,4]=>0111110=>0111110=>[2,1,1,1,1,2]
[6,8,7,5,3,2,4,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[7,8,4,2,6,5,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,8,6,2,7,3,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[3,6,1,8,7,4,2,5]=>0101110=>0111010=>[2,1,1,2,2]
[4,7,6,2,8,1,3,5]=>0110100=>0010110=>[3,2,1,2]
[6,7,4,2,8,1,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,4,2,7,5,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[5,7,4,2,3,8,1,6]=>0110010=>0100110=>[2,3,1,2]
[2,1,8,6,7,5,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[8,6,4,3,7,5,1,2]=>1110110=>0110111=>[2,1,2,1,1,1]
[5,8,6,7,3,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[6,7,5,8,1,3,4,2]=>0101001=>1001010=>[1,3,2,2]
[7,6,5,8,1,4,3,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,6,5,7,4,1,3,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,6,4,3,8,1,5,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,1,7,6,8,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,6,8,1,4,2,3]=>1001010=>0101001=>[2,2,3,1]
[4,1,7,3,6,5,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,8,4,7,6,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[8,1,3,7,4,6,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[6,1,5,4,3,8,7,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,1,4,5,3,7,8,2]=>1001001=>1001001=>[1,3,3,1]
[5,1,7,8,6,2,4,3]=>1001101=>1011001=>[1,2,1,3,1]
[6,1,8,3,4,5,7,2]=>1010001=>1000101=>[1,4,2,1]
[8,5,2,1,4,3,7,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,6,2,1,4,8,3,7]=>0110010=>0100110=>[2,3,1,2]
[3,6,1,8,5,2,4,7]=>0101100=>0011010=>[3,1,2,2]
[3,4,1,2,8,6,5,7]=>0100110=>0110010=>[2,1,3,2]
[6,3,8,5,2,1,4,7]=>1011100=>0011101=>[3,1,1,2,1]
[8,5,2,7,3,1,6,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,3,8,5,6,1,7,4]=>0010101=>1010100=>[1,2,2,3]
[7,4,5,6,3,1,8,2]=>1001101=>1011001=>[1,2,1,3,1]
[8,5,6,4,2,1,7,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,5,3,6,2,8,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[1,7,5,6,3,2,4,8]=>0101100=>0011010=>[3,1,2,2]
[8,7,5,4,1,6,2,3]=>1111010=>0101111=>[2,2,1,1,1,1]
[2,6,4,1,8,5,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,1,2,3,8,5,7,4]=>1000101=>1010001=>[1,2,4,1]
[7,1,2,3,6,5,8,4]=>1000101=>1010001=>[1,2,4,1]
[7,2,1,3,8,6,4,5]=>1100110=>0110011=>[2,1,3,1,1]
[1,5,7,3,2,4,6,8]=>0011000=>0001100=>[4,1,3]
[5,2,7,3,1,8,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[5,8,2,4,1,3,7,6]=>0101001=>1001010=>[1,3,2,2]
[8,7,2,6,3,4,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[4,8,1,6,3,2,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[3,1,8,6,4,2,7,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,1,6,7,4,3,2,5]=>1001110=>0111001=>[2,1,1,3,1]
[3,5,8,7,2,4,1,6]=>0011010=>0101100=>[2,2,1,3]
[4,2,1,3,7,8,5,6]=>1100010=>0100011=>[2,4,1,1]
[8,6,1,3,7,2,4,5]=>1100100=>0010011=>[3,3,1,1]
[5,1,8,3,2,4,6,7]=>1011000=>0001101=>[4,1,2,1]
[5,2,7,8,6,4,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[1,4,2,7,8,6,3,5]=>0100110=>0110010=>[2,1,3,2]
[1,6,2,4,8,5,3,7]=>0100110=>0110010=>[2,1,3,2]
[1,6,2,4,7,5,3,8]=>0100110=>0110010=>[2,1,3,2]
[1,7,3,8,5,2,4,6]=>0101100=>0011010=>[3,1,2,2]
[1,7,3,2,8,6,4,5]=>0110110=>0110110=>[2,1,2,1,2]
[7,8,3,6,5,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[4,7,2,8,6,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,2,5,7,8,6,1,3]=>1000110=>0110001=>[2,1,4,1]
[8,2,5,1,7,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[1,3,6,4,8,5,7,2]=>0010101=>1010100=>[1,2,2,3]
[1,3,6,4,7,5,8,2]=>0010101=>1010100=>[1,2,2,3]
[6,2,4,7,5,8,1,3]=>1001010=>0101001=>[2,2,3,1]
[6,2,7,3,5,1,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,1,3,7,8,4,5]=>1100010=>0100011=>[2,4,1,1]
[7,2,5,1,8,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[7,8,2,1,4,3,5,6]=>0110100=>0010110=>[3,2,1,2]
[7,6,4,2,3,1,8,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,5,4,2,6,8,1,3]=>1110010=>0100111=>[2,3,1,1,1]
[1,7,5,3,4,6,8,2]=>0110001=>1000110=>[1,4,1,2]
[8,2,5,4,6,7,1,3]=>1010010=>0100101=>[2,3,2,1]
[8,2,6,4,3,1,7,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,2,7,4,1,3,5,6]=>1011000=>0001101=>[4,1,2,1]
[1,2,8,4,3,5,6,7]=>0011000=>0001100=>[4,1,3]
[1,8,7,4,3,2,5,6]=>0111100=>0011110=>[3,1,1,1,2]
[5,8,4,7,2,1,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[1,8,7,5,4,3,6,2]=>0111101=>1011110=>[1,2,1,1,1,2]
[1,6,8,4,3,7,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[6,8,7,3,2,5,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[5,3,8,1,2,7,4,6]=>1010010=>0100101=>[2,3,2,1]
[5,1,8,3,2,6,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[5,7,3,1,2,6,4,8]=>0110010=>0100110=>[2,3,1,2]
[1,4,6,2,8,3,7,5]=>0010101=>1010100=>[1,2,2,3]
[5,2,6,7,8,4,1,3]=>1000110=>0110001=>[2,1,4,1]
[5,3,6,1,2,8,4,7]=>1010010=>0100101=>[2,3,2,1]
[1,6,3,2,7,8,4,5]=>0110010=>0100110=>[2,3,1,2]
[6,7,3,8,5,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[4,6,2,7,8,1,5,3]=>0100101=>1010010=>[1,2,3,2]
[1,6,4,7,8,3,5,2]=>0100101=>1010010=>[1,2,3,2]
[4,5,7,2,1,8,6,3]=>0011011=>1101100=>[1,1,2,1,3]
[7,8,3,4,2,1,6,5]=>0101101=>1011010=>[1,2,1,2,2]
[6,3,4,1,2,5,8,7]=>1010001=>1000101=>[1,4,2,1]
[6,3,1,4,2,7,5,8]=>1101010=>0101011=>[2,2,2,1,1]
[1,8,3,2,4,5,6,7]=>0110000=>0000110=>[5,1,2]
[8,6,3,2,4,1,7,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,5,3,2,6,7,1,4]=>1110010=>0100111=>[2,3,1,1,1]
[4,5,2,6,8,1,7,3]=>0100101=>1010010=>[1,2,3,2]
[4,2,5,6,7,8,1,3]=>1000010=>0100001=>[2,5,1]
[7,2,3,1,4,5,8,6]=>1010001=>1000101=>[1,4,2,1]
[2,4,6,8,10,1,3,5,7,9]=>000010000=>000010000=>[5,5]
[10,9,8,7,6,1,2,3,4,5]=>111110000=>000011111=>[5,1,1,1,1,1]
[9,10,7,8,5,6,3,4,1,2]=>010101010=>010101010=>[2,2,2,2,2]
[5,6,3,4,1,2,8,7]=>0101001=>1001010=>[1,3,2,2]
[7,8,3,5,4,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,7,5,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,1,7,8,5,6,3,4]=>1001010=>0101001=>[2,2,3,1]
[5,7,3,8,1,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[7,5,8,4,2,6,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[8,6,3,7,5,2,4,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,3,7,2,6,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,7,4,2,6,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,8,4,6,1,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,6,4,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,1,7,4,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[1,8,6,7,4,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[1,8,6,7,3,5,2,4]=>0101010=>0101010=>[2,2,2,2]
[6,8,1,7,3,5,2,4]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,6,3,5,2,4]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,6,1,5,2,4]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,6,4,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,6,4,5,1,3]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,6,3,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,6,1,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,6,2,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,8,6,7,2,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,8,5,7,2,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,1,7,2,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,2,7,1,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,8,2,7,1,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,8,2,7,3,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,8,2,7,4,5,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,7,4,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[3,8,6,7,4,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[2,8,6,7,4,5,1,3]=>0101010=>0101010=>[2,2,2,2]
[2,8,6,7,3,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[2,8,6,7,1,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[2,8,5,7,1,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[2,8,1,7,5,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,7,5,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,7,4,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[2,8,1,7,4,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[2,8,4,7,1,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[2,8,4,7,3,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[2,8,5,7,3,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[3,8,5,7,4,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,7,4,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,8,2,7,4,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,2,7,3,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[4,8,2,7,3,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,8,2,7,1,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[4,8,1,7,2,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,8,4,7,2,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,8,4,7,3,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[4,8,1,7,3,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[4,8,3,7,1,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,7,1,5,2,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,1,7,3,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[1,8,5,7,3,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[1,8,5,7,4,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,1,7,4,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,7,1,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,4,7,1,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,5,7,1,4,2,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,6,7,3,4,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,8,6,7,2,4,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,6,7,1,4,2,3]=>0101010=>0101010=>[2,2,2,2]
[4,8,6,7,1,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[4,8,5,7,1,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[4,8,1,7,5,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[1,8,4,7,5,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[1,8,3,7,5,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[3,8,1,7,5,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[3,8,5,7,1,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[3,8,6,7,1,5,2,4]=>0101010=>0101010=>[2,2,2,2]
[3,8,6,7,2,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[4,8,6,7,2,5,1,3]=>0101010=>0101010=>[2,2,2,2]
[4,8,6,7,3,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[4,8,5,7,3,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[4,8,5,7,2,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[3,8,5,7,2,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[3,8,4,7,2,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[3,8,4,7,1,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[3,8,1,7,4,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[1,8,3,7,4,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[1,8,3,7,2,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[3,8,1,7,2,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[3,8,2,7,1,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[3,8,2,7,4,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[3,8,2,7,5,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[4,8,2,7,5,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[4,8,3,7,5,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[3,8,4,7,5,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[2,8,4,7,5,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[2,8,3,7,5,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[2,8,3,7,4,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[2,8,3,7,1,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[2,8,1,7,3,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[7,5,2,8,6,4,1,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,4,8,6,1,5,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,8,4,5,2,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,6,7,4,2,8,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,6,7,3,8,5,2,4]=>0010110=>0110100=>[2,1,2,3]
[7,1,8,3,5,6,2,4]=>1010010=>0100101=>[2,3,2,1]
[7,3,8,6,2,5,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,4,2,8,6,1,3,5]=>1101100=>0011011=>[3,1,2,1,1]
[6,8,1,7,2,3,4,5]=>0101000=>0001010=>[4,2,2]
[2,6,3,7,8,5,4,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,5,3,7,8,1,6,4]=>0100101=>1010010=>[1,2,3,2]
[2,5,4,1,3,7,8,6]=>0110001=>1000110=>[1,4,1,2]
[3,1,5,4,7,8,2,6]=>1010010=>0100101=>[2,3,2,1]
[5,2,4,8,6,1,3,7]=>1001100=>0011001=>[3,1,3,1]
[4,8,1,3,6,7,2,5]=>0100010=>0100010=>[2,4,2]
[5,3,8,2,4,7,1,6]=>1010010=>0100101=>[2,3,2,1]
[5,4,3,8,1,2,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[6,4,3,1,2,8,5,7]=>1110010=>0100111=>[2,3,1,1,1]
[6,4,2,8,1,3,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[6,3,8,2,5,1,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,8,1,4,7,2,5]=>1010010=>0100101=>[2,3,2,1]
[1,5,7,3,6,8,4,2]=>0010011=>1100100=>[1,1,3,3]
[1,5,7,4,2,6,8,3]=>0011001=>1001100=>[1,3,1,3]
[5,8,1,4,2,6,3,7]=>0101010=>0101010=>[2,2,2,2]
[6,5,1,2,8,7,3,4]=>1100110=>0110011=>[2,1,3,1,1]
[6,5,3,1,4,2,8,7]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,3,1,6,4,2,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[5,2,6,4,1,7,3,8]=>1011010=>0101101=>[2,2,1,2,1]
[4,6,1,7,5,2,8,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,7,1,8,6,2,4]=>0010110=>0110100=>[2,1,2,3]
[3,6,2,7,5,1,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[3,4,7,2,8,6,1,5]=>0010110=>0110100=>[2,1,2,3]
[3,4,5,8,2,7,1,6]=>0001010=>0101000=>[2,2,4]
[3,4,6,2,8,1,5,7]=>0010100=>0010100=>[3,2,3]
[3,5,2,6,8,1,7,4]=>0100101=>1010010=>[1,2,3,2]
[5,3,6,8,4,7,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[3,7,2,5,4,8,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,2,6,5,8,3,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,6,5,8,3,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,6,8,4,3,2,7]=>1001110=>0111001=>[2,1,1,3,1]
[6,7,8,1,4,3,2,5]=>0010110=>0110100=>[2,1,2,3]
[4,7,1,5,8,3,2,6]=>0100110=>0110010=>[2,1,3,2]
[8,3,1,5,4,7,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,1,5,7,3,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[8,4,6,1,7,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,3,6,1,4,7,2,5]=>1010010=>0100101=>[2,3,2,1]
[8,2,6,1,4,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,7,6,1,4,8,2,5]=>0110010=>0100110=>[2,3,1,2]
[6,7,8,5,1,3,2,4]=>0011010=>0101100=>[2,2,1,3]
[6,7,8,2,4,3,5,1]=>0010101=>1010100=>[1,2,2,3]
[4,7,6,2,8,3,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[3,7,6,2,4,8,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[5,7,3,8,4,6,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[8,7,3,1,4,6,2,5]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,6,3,2,5,4,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[8,7,3,5,1,6,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,2,5,1,3,6,4]=>1101001=>1001011=>[1,3,2,1,1]
[8,4,6,5,7,1,2,3]=>1010100=>0010101=>[3,2,2,1]
[4,7,6,5,8,1,2,3]=>0110100=>0010110=>[3,2,1,2]
[8,7,6,5,2,1,4,3]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[3,6,4,8,7,5,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[5,6,4,3,8,7,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[1,6,2,4,7,8,5,3]=>0100011=>1100010=>[1,1,4,2]
[3,6,2,4,8,1,5,7]=>0100100=>0010010=>[3,3,2]
[3,4,7,2,8,1,6,5]=>0010101=>1010100=>[1,2,2,3]
[1,4,7,2,5,8,6,3]=>0010011=>1100100=>[1,1,3,3]
[3,8,7,5,4,6,1,2]=>0111010=>0101110=>[2,2,1,1,2]
[4,3,6,7,8,5,1,2]=>1000110=>0110001=>[2,1,4,1]
[3,5,6,4,8,7,1,2]=>0010110=>0110100=>[2,1,2,3]
[4,6,8,5,3,7,1,2]=>0011010=>0101100=>[2,2,1,3]
[4,2,7,5,1,8,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,1,6,4,8,7,5,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,8,1,4,2,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[6,5,1,3,4,2,8,7]=>1100101=>1010011=>[1,2,3,1,1]
[4,8,5,3,1,7,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[7,4,5,3,2,8,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[5,8,3,6,1,4,2,7]=>0101010=>0101010=>[2,2,2,2]
[1,4,6,2,5,8,3,7]=>0010010=>0100100=>[2,3,3]
[1,6,8,7,4,2,3,5]=>0011100=>0011100=>[3,1,1,3]
[7,6,1,8,3,2,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[7,1,8,6,3,4,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[1,8,7,6,4,3,2,5]=>0111110=>0111110=>[2,1,1,1,1,2]
[2,1,7,5,6,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,7,5,8,2,4]=>1001010=>0101001=>[2,2,3,1]
[7,8,1,6,5,3,2,4]=>0101110=>0111010=>[2,1,1,2,2]
[7,8,2,1,4,5,6,3]=>0110001=>1000110=>[1,4,1,2]
[4,2,6,1,8,5,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,8,1,5,4,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[1,2,8,3,6,5,7,4]=>0010101=>1010100=>[1,2,2,3]
[6,1,3,2,7,5,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,6,4,1,7,5,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[7,6,5,8,1,4,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[5,8,6,7,3,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[1,6,4,3,7,2,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,3,8,1,2,7,5]=>0101001=>1001010=>[1,3,2,2]
[4,1,6,3,8,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,1,3,4,2,6,5]=>0100101=>1010010=>[1,2,3,2]
[2,8,5,7,4,3,1,6]=>0101110=>0111010=>[2,1,1,2,2]
[7,2,5,8,3,4,1,6]=>1001010=>0101001=>[2,2,3,1]
[5,3,8,7,1,2,6,4]=>1011001=>1001101=>[1,3,1,2,1]
[6,5,3,8,2,1,7,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,5,7,8,4,1,2,6]=>0001100=>0011000=>[3,1,4]
[5,4,7,3,6,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[3,4,7,2,5,1,6,8]=>0010100=>0010100=>[3,2,3]
[1,4,7,2,5,8,3,6]=>0010010=>0100100=>[2,3,3]
[3,6,2,4,7,1,5,8]=>0100100=>0010010=>[3,3,2]
[7,6,3,5,4,8,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[4,5,6,3,8,7,1,2]=>0010110=>0110100=>[2,1,2,3]
[6,3,7,5,8,4,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[4,8,2,6,1,5,3,7]=>0101010=>0101010=>[2,2,2,2]
[4,3,6,2,5,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,1,2,5,6,3,4]=>0100010=>0100010=>[2,4,2]
[4,1,6,2,5,7,3,8]=>1010010=>0100101=>[2,3,2,1]
[2,1,8,6,4,7,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,3,6,8,4,2,5]=>1000110=>0110001=>[2,1,4,1]
[1,8,3,6,7,4,5,2]=>0100101=>1010010=>[1,2,3,2]
[7,1,5,8,3,6,2,4]=>1001010=>0101001=>[2,2,3,1]
[3,1,6,4,7,2,5,8]=>1010100=>0010101=>[3,2,2,1]
[5,8,7,1,2,4,3,6]=>0110010=>0100110=>[2,3,1,2]
[1,5,7,8,2,4,6,3]=>0001001=>1001000=>[1,3,4]
[6,8,5,1,3,4,2,7]=>0110010=>0100110=>[2,3,1,2]
[7,6,5,1,4,3,2,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[2,6,4,5,1,3,8,7]=>0101001=>1001010=>[1,3,2,2]
[3,5,6,4,1,8,2,7]=>0011010=>0101100=>[2,2,1,3]
[7,8,5,4,1,3,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[7,8,2,3,4,1,6,5]=>0100101=>1010010=>[1,2,3,2]
[4,2,6,3,8,1,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,3,5,4,1,8,6]=>1001101=>1011001=>[1,2,1,3,1]
[6,2,4,3,1,5,7,8]=>1011000=>0001101=>[4,1,2,1]
[4,2,8,3,1,7,5,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,3,7,4,8,2,5,6]=>0010100=>0010100=>[3,2,3]
[5,3,7,4,1,6,2,8]=>1011010=>0101101=>[2,2,1,2,1]
[2,4,7,3,6,1,8,5]=>0010101=>1010100=>[1,2,2,3]
[5,8,7,6,3,1,2,4]=>0111100=>0011110=>[3,1,1,1,2]
[7,5,6,8,1,4,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[2,4,7,1,6,5,3,8]=>0010110=>0110100=>[2,1,2,3]
[5,2,7,1,8,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,1,2,8,4,5,7]=>1100100=>0010011=>[3,3,1,1]
[4,2,1,3,6,5,8,7]=>1100101=>1010011=>[1,2,3,1,1]
[4,2,6,1,8,5,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[7,8,2,1,4,5,3,6]=>0110010=>0100110=>[2,3,1,2]
[7,8,4,1,5,3,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[7,5,1,6,4,3,8,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,8,1,6,3,4,7,2]=>0101001=>1001010=>[1,3,2,2]
[6,8,1,7,5,2,3,4]=>0101100=>0011010=>[3,1,2,2]
[5,6,1,7,4,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[7,8,5,1,6,4,2,3]=>0110110=>0110110=>[2,1,2,1,2]
[2,6,5,7,3,4,8,1]=>0101001=>1001010=>[1,3,2,2]
[1,6,4,7,5,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[1,3,7,4,6,8,2,5]=>0010010=>0100100=>[2,3,3]
[5,2,4,7,3,6,8,1]=>1001001=>1001001=>[1,3,3,1]
[8,1,6,5,7,2,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,5,8,3,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[1,2,7,6,8,3,4,5]=>0010100=>0010100=>[3,2,3]
[3,8,6,4,2,7,5,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,8,1,6,2,4,5,3]=>0101001=>1001010=>[1,3,2,2]
[2,8,1,7,4,3,6,5]=>0101101=>1011010=>[1,2,1,2,2]
[3,7,4,1,8,5,2,6]=>0110110=>0110110=>[2,1,2,1,2]
[6,7,1,4,8,3,2,5]=>0100110=>0110010=>[2,1,3,2]
[2,7,1,8,4,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[6,1,2,8,4,3,5,7]=>1001100=>0011001=>[3,1,3,1]
[5,1,2,4,8,3,6,7]=>1000100=>0010001=>[3,4,1]
[4,1,3,2,8,5,6,7]=>1010100=>0010101=>[3,2,2,1]
[3,2,1,4,8,5,6,7]=>1100100=>0010011=>[3,3,1,1]
[4,3,6,1,5,8,2,7]=>1010010=>0100101=>[2,3,2,1]
[2,6,1,4,5,8,3,7]=>0100010=>0100010=>[2,4,2]
[1,6,2,5,8,3,4,7]=>0100100=>0010010=>[3,3,2]
[7,4,2,1,8,5,3,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[1,5,4,2,8,3,6,7]=>0110100=>0010110=>[3,2,1,2]
[6,4,3,1,5,8,2,7]=>1110010=>0100111=>[2,3,1,1,1]
[5,4,3,2,1,8,6,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[2,5,3,4,1,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[4,3,5,2,1,8,6,7]=>1011010=>0101101=>[2,2,1,2,1]
[3,7,6,8,4,5,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[1,7,6,8,5,4,2,3]=>0101110=>0111010=>[2,1,1,2,2]
[2,4,8,6,7,3,5,1]=>0010101=>1010100=>[1,2,2,3]
[3,4,8,5,6,7,2,1]=>0010011=>1100100=>[1,1,3,3]
[6,3,5,8,4,7,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[5,4,3,8,6,7,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,2,8,5,7,4,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,7,4,6,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[3,1,8,5,7,6,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[6,1,5,8,7,4,2,3]=>1001110=>0111001=>[2,1,1,3,1]
[5,8,6,7,4,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[4,8,7,5,6,3,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,2,1,6,3,5,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[6,2,1,4,3,8,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,2,1,4,3,6,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,2,4,1,3,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[2,1,6,4,3,5,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[6,4,2,1,3,5,8,7]=>1110001=>1000111=>[1,4,1,1,1]
[8,4,2,1,3,6,5,7]=>1110010=>0100111=>[2,3,1,1,1]
[8,4,2,1,6,3,5,7]=>1110100=>0010111=>[3,2,1,1,1]
[6,4,2,1,8,3,5,7]=>1110100=>0010111=>[3,2,1,1,1]
[4,6,2,1,3,8,5,7]=>0110010=>0100110=>[2,3,1,2]
[2,6,1,4,3,8,5,7]=>0101010=>0101010=>[2,2,2,2]
[2,1,6,4,3,8,5,7]=>1011010=>0101101=>[2,2,1,2,1]
[4,8,2,1,3,6,5,7]=>0110010=>0100110=>[2,3,1,2]
[6,8,2,1,4,3,5,7]=>0110100=>0010110=>[3,2,1,2]
[8,6,2,1,4,3,5,7]=>1110100=>0010111=>[3,2,1,1,1]
[2,8,1,4,6,3,5,7]=>0100100=>0010010=>[3,3,2]
[2,6,1,4,8,3,5,7]=>0100100=>0010010=>[3,3,2]
[2,6,4,1,8,3,5,7]=>0110100=>0010110=>[3,2,1,2]
[2,6,4,8,1,3,5,7]=>0101000=>0001010=>[4,2,2]
[4,2,6,1,8,3,5,7]=>1010100=>0010101=>[3,2,2,1]
[6,2,4,1,8,3,5,7]=>1010100=>0010101=>[3,2,2,1]
[4,2,1,6,8,3,5,7]=>1100100=>0010011=>[3,3,1,1]
[4,2,1,6,3,8,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[4,2,1,3,6,8,5,7]=>1100010=>0100011=>[2,4,1,1]
[2,1,4,3,8,6,5,7]=>1010110=>0110101=>[2,1,2,2,1]
[2,4,1,3,8,6,5,7]=>0100110=>0110010=>[2,1,3,2]
[4,2,1,3,8,6,5,7]=>1100110=>0110011=>[2,1,3,1,1]
[4,2,1,8,3,6,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[4,2,1,8,6,3,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[8,2,1,6,4,3,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[4,2,8,1,6,3,5,7]=>1010100=>0010101=>[3,2,2,1]
[2,4,1,8,3,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[2,1,4,8,3,6,5,7]=>1001010=>0101001=>[2,2,3,1]
[2,4,8,1,6,3,5,7]=>0010100=>0010100=>[3,2,3]
[2,4,8,6,1,3,5,7]=>0011000=>0001100=>[4,1,3]
[4,2,8,6,1,3,5,7]=>1011000=>0001101=>[4,1,2,1]
[2,1,8,6,4,3,5,7]=>1011100=>0011101=>[3,1,1,2,1]
[2,8,6,1,4,3,5,7]=>0110100=>0010110=>[3,2,1,2]
[2,8,6,4,1,3,5,7]=>0111000=>0001110=>[4,1,1,2]
[4,8,6,2,1,3,5,7]=>0111000=>0001110=>[4,1,1,2]
[3,2,6,1,5,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,5,2,4,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,3,2,5,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,6,1,5,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,5,2,8,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,7,2,6,5,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,8,2,6,1,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,8,1,5,2,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,7,6,8,1,3,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,7,1,8,5,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,6,5,8,1,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,5,4,7,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,5,4,8,1,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,3,8,4,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,5,8,3,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,6,5,8,1,3,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,6,1,3,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,6,3,4,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,5,2,6,1,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,5,2,6,4,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,1,5,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,7,2,4,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,3,2,7,4,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,3,7,4,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,3,5,4,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,3,2,5,4,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,5,2,4,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,4,1,5,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,4,1,7,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,8,4,6,1,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,8,1,7,4,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,8,1,5,4,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,4,1,8,5,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,3,2,7,6,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,7,6,8,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,7,1,8,5,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,6,5,8,1,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,4,1,8,5,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,8,1,5,2,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,8,1,3,2,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,8,5,6,2,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,8,2,6,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,8,1,5,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,7,2,6,3,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,8,2,6,1,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,8,4,7,2,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,8,1,3,2,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,7,4,8,1,3,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,6,3,8,1,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,1,5,8,4,6,7]=>1100100=>0010011=>[3,3,1,1]
[2,4,8,3,5,7,6,1]=>0010011=>1100100=>[1,1,3,3]
[4,2,5,3,1,8,6,7]=>1011010=>0101101=>[2,2,1,2,1]
[1,8,4,2,5,3,6,7]=>0110100=>0010110=>[3,2,1,2]
[8,1,5,3,2,4,6,7]=>1011000=>0001101=>[4,1,2,1]
[3,8,1,5,2,4,6,7]=>0101000=>0001010=>[4,2,2]
[5,4,1,3,8,2,6,7]=>1100100=>0010011=>[3,3,1,1]
[1,5,7,3,8,4,2,6]=>0010110=>0110100=>[2,1,2,3]
[5,1,4,7,8,3,2,6]=>1000110=>0110001=>[2,1,4,1]
[8,1,5,3,7,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[1,4,3,8,7,5,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[1,6,8,5,3,7,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[6,4,8,1,7,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,8,7,1,5,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,6,8,4,3,2,5]=>1001110=>0111001=>[2,1,1,3,1]
[1,6,7,2,8,4,3,5]=>0010110=>0110100=>[2,1,2,3]
[6,7,1,4,2,8,3,5]=>0101010=>0101010=>[2,2,2,2]
[6,3,7,1,4,8,2,5]=>1010010=>0100101=>[2,3,2,1]
[3,7,8,1,5,2,4,6]=>0010100=>0010100=>[3,2,3]
[7,1,2,8,5,3,4,6]=>1001100=>0011001=>[3,1,3,1]
[1,7,2,8,4,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[4,2,1,7,8,5,3,6]=>1100110=>0110011=>[2,1,3,1,1]
[6,2,4,8,3,7,5,1]=>1001011=>1101001=>[1,1,2,3,1]
[7,2,6,3,4,1,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,7,1,8,3,5,4,6]=>0101010=>0101010=>[2,2,2,2]
[2,1,7,3,5,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[1,2,7,5,8,3,4,6]=>0010100=>0010100=>[3,2,3]
[8,7,1,3,6,2,4,5]=>1100100=>0010011=>[3,3,1,1]
[8,2,1,7,3,5,6,4]=>1101001=>1001011=>[1,3,2,1,1]
[2,7,8,4,1,6,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[2,8,4,1,6,7,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,1,8,4,7,5,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,1,5,6,2,4]=>1010010=>0100101=>[2,3,2,1]
[8,6,1,2,7,5,3,4]=>1100110=>0110011=>[2,1,3,1,1]
[8,1,6,2,7,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,8,5,2,6,7,4,3]=>0110011=>1100110=>[1,1,3,1,2]
[5,2,1,8,6,7,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,7,6,5,1,4,2,3]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,7,6,1,5,3,4,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,1,7,5,6,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,8,6,7,5,4,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[6,3,5,2,1,4,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[8,3,5,7,2,4,1,6]=>1001010=>0101001=>[2,2,3,1]
[8,5,2,7,4,3,1,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,5,3,1,2,4,8,7]=>1110001=>1000111=>[1,4,1,1,1]
[4,5,3,6,1,2,8,7]=>0101001=>1001010=>[1,3,2,2]
[3,5,1,4,6,2,8,7]=>0100101=>1010010=>[1,2,3,2]
[8,1,4,7,3,6,2,5]=>1001010=>0101001=>[2,2,3,1]
[8,5,1,4,7,3,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[8,5,3,7,1,4,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,4,7,5,8,1,2]=>1001010=>0101001=>[2,2,3,1]
[5,1,4,6,8,3,7,2]=>1000101=>1010001=>[1,2,4,1]
[4,7,1,3,5,8,6,2]=>0100011=>1100010=>[1,1,4,2]
[4,8,3,7,1,2,6,5]=>0101001=>1001010=>[1,3,2,2]
[8,7,1,4,2,6,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[8,6,3,1,2,4,7,5]=>1110001=>1000111=>[1,4,1,1,1]
[2,1,8,7,5,3,4,6]=>1011100=>0011101=>[3,1,1,2,1]
[8,1,7,4,5,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[2,8,7,5,4,1,3,6]=>0111100=>0011110=>[3,1,1,1,2]
[8,7,2,6,4,1,3,5]=>1101100=>0011011=>[3,1,2,1,1]
[5,3,7,8,2,4,6,1]=>1001001=>1001001=>[1,3,3,1]
[5,3,7,6,2,1,8,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,7,8,6,4,2,1,3]=>0011110=>0111100=>[2,1,1,1,3]
[2,6,7,5,4,8,1,3]=>0011010=>0101100=>[2,2,1,3]
[6,7,3,5,1,8,2,4]=>0101010=>0101010=>[2,2,2,2]
[2,1,6,7,5,8,3,4]=>1001010=>0101001=>[2,2,3,1]
[2,1,5,7,3,6,8,4]=>1001001=>1001001=>[1,3,3,1]
[4,1,7,2,5,6,8,3]=>1010001=>1000101=>[1,4,2,1]
[2,4,7,1,6,5,8,3]=>0010101=>1010100=>[1,2,2,3]
[3,4,6,2,7,8,5,1]=>0010011=>1100100=>[1,1,3,3]
[4,6,1,2,5,8,7,3]=>0100011=>1100010=>[1,1,4,2]
[5,6,3,1,8,7,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[3,5,6,4,7,1,8,2]=>0010101=>1010100=>[1,2,2,3]
[3,4,6,1,5,7,8,2]=>0010001=>1000100=>[1,4,3]
[3,4,1,5,7,6,8,2]=>0100101=>1010010=>[1,2,3,2]
[4,2,1,7,3,5,8,6]=>1101001=>1001011=>[1,3,2,1,1]
[7,3,1,5,4,2,8,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,3,1,4,2,8,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,1,5,2,7,6,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,2,5,1,4,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,6,2,7,1,4,8,5]=>0101001=>1001010=>[1,3,2,2]
[2,7,5,4,1,3,8,6]=>0111001=>1001110=>[1,3,1,1,2]
[6,4,3,2,1,8,5,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[1,7,6,2,4,8,3,5]=>0110010=>0100110=>[2,3,1,2]
[2,7,3,6,4,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[6,2,7,5,3,8,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,8,5,3,6,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,8,3,2,7,1,6,4]=>0110101=>1010110=>[1,2,2,1,2]
[8,7,2,6,1,5,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[1,8,5,7,4,3,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[1,8,5,7,2,4,6,3]=>0101001=>1001010=>[1,3,2,2]
[3,8,6,1,7,2,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[7,2,8,5,6,1,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,6,5,8,1,4,2,7]=>0101010=>0101010=>[2,2,2,2]
[4,3,6,8,2,1,5,7]=>1001100=>0011001=>[3,1,3,1]
[4,3,6,7,8,1,2,5]=>1000100=>0010001=>[3,4,1]
[5,4,6,7,2,8,1,3]=>1001010=>0101001=>[2,2,3,1]
[3,5,7,1,4,8,2,6]=>0010010=>0100100=>[2,3,3]
[8,1,5,2,7,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,1,5,7,3,6,2]=>1100101=>1010011=>[1,2,3,1,1]
[6,4,2,5,8,3,1,7]=>1100110=>0110011=>[2,1,3,1,1]
[5,4,1,6,8,2,3,7]=>1100100=>0010011=>[3,3,1,1]
[5,3,1,7,2,8,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[5,3,6,4,7,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[6,3,7,4,8,5,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,7,2,5,8,6,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[6,3,1,8,4,7,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,4,8,1,7,6,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,8,1,7,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,3,8,1,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,4,7,8,1,5,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[4,6,8,2,7,1,5,3]=>0010101=>1010100=>[1,2,2,3]
[2,5,8,7,1,3,6,4]=>0011001=>1001100=>[1,3,1,3]
[8,3,7,6,1,5,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,2,7,6,5,1,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,3,8,7,6,2,1,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[2,4,8,7,6,1,3,5]=>0011100=>0011100=>[3,1,1,3]
[3,5,8,7,2,6,1,4]=>0011010=>0101100=>[2,2,1,3]
[4,7,3,8,6,5,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[7,5,8,6,4,3,2,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[5,8,7,3,6,4,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,8,7,6,5,1,4,2]=>0111101=>1011110=>[1,2,1,1,1,2]
[2,8,7,6,5,4,1,3]=>0111110=>0111110=>[2,1,1,1,1,2]
[5,4,3,2,1,6,7,8,9,10]=>111100000=>000001111=>[6,1,1,1,1]
[6,4,3,2,7,1,5,8,9,10]=>111010000=>000010111=>[5,2,1,1,1]
[7,5,3,8,2,6,1,4,9,10]=>110101000=>000101011=>[4,2,2,1,1]
[8,6,9,4,7,2,5,1,3,10]=>101010100=>001010101=>[3,2,2,2,1]
[7,8,5,6,3,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,5,3,6,1,2,4]=>0110100=>0010110=>[3,2,1,2]
[7,5,6,3,1,4,2,8]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,8,3,1,4,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[7,8,5,3,1,4,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[7,8,5,3,1,6,2,4]=>0111010=>0101110=>[2,2,1,1,2]
[7,8,5,3,1,6,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,8,5,3,6,1,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[7,8,5,3,6,4,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[7,8,5,3,4,1,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[7,8,5,3,1,4,6,2]=>0111001=>1001110=>[1,3,1,1,2]
[7,5,8,3,1,2,6,4]=>1011001=>1001101=>[1,3,1,2,1]
[7,5,8,3,4,1,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,8,3,4,6,1,2]=>1010010=>0100101=>[2,3,2,1]
[7,5,6,3,4,1,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,6,3,1,4,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[7,5,3,1,6,4,8,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,5,3,6,1,4,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[7,5,3,6,4,1,8,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,5,3,6,4,8,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,3,8,4,6,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,3,8,4,1,6,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,5,3,8,1,4,6,2]=>1101001=>1001011=>[1,3,2,1,1]
[7,5,3,1,8,4,6,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,5,3,1,8,2,6,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,5,3,1,6,2,4,8]=>1110100=>0010111=>[3,2,1,1,1]
[7,5,3,1,6,4,2,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,5,3,1,8,4,2,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,5,3,1,8,6,2,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,5,3,8,1,6,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,5,3,8,6,1,4,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,5,3,8,6,4,1,2]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,5,8,3,6,4,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[7,5,8,3,6,1,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,8,3,1,6,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,5,8,3,1,6,2,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,3,8,1,6,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,3,8,1,4,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,3,6,1,4,2,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,3,6,4,1,2,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,5,3,8,4,1,2,6]=>1101100=>0011011=>[3,1,2,1,1]
[7,5,3,8,6,1,2,4]=>1101100=>0011011=>[3,1,2,1,1]
[7,5,8,6,3,1,2,4]=>1011100=>0011101=>[3,1,1,2,1]
[7,5,8,6,3,1,4,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,5,8,6,3,4,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,6,8,3,1,4,2]=>1001101=>1011001=>[1,2,1,3,1]
[7,5,6,3,8,1,2,4]=>1010100=>0010101=>[3,2,2,1]
[7,5,3,6,1,8,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,6,3,1,8,2,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,6,3,1,8,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,5,6,3,8,1,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,6,3,8,4,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[7,5,3,6,8,4,1,2]=>1100110=>0110011=>[2,1,3,1,1]
[7,5,3,6,8,1,4,2]=>1100101=>1010011=>[1,2,3,1,1]
[7,5,3,6,1,8,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,5,3,1,6,8,4,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,5,3,1,6,8,2,4]=>1110010=>0100111=>[2,3,1,1,1]
[7,5,3,1,2,8,6,4]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,5,3,4,1,6,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[4,6,8,3,5,7,1,2]=>0010010=>0100100=>[2,3,3]
[6,8,1,2,4,5,7,3]=>0100001=>1000010=>[1,5,2]
[3,6,8,2,5,7,1,4]=>0010010=>0100100=>[2,3,3]
[8,3,5,2,4,1,6,7]=>1010100=>0010101=>[3,2,2,1]
[3,5,7,2,4,6,1,8]=>0010010=>0100100=>[2,3,3]
[4,2,5,7,3,6,1,8]=>1001010=>0101001=>[2,2,3,1]
[4,5,2,8,3,1,6,7]=>0101100=>0011010=>[3,1,2,2]
[2,1,6,8,4,7,3,5]=>1001010=>0101001=>[2,2,3,1]
[1,2,5,8,3,6,7,4]=>0001001=>1001000=>[1,3,4]
[5,3,6,8,4,7,1,2]=>1001010=>0101001=>[2,2,3,1]
[3,1,2,6,8,5,7,4]=>1000101=>1010001=>[1,2,4,1]
[4,3,6,2,7,5,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,3,1,7,8,2,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[5,4,7,3,8,6,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[5,8,4,7,6,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[8,3,5,1,2,7,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[4,7,3,6,5,2,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[5,3,7,6,4,2,1,8]=>1011110=>0111101=>[2,1,1,1,2,1]
[5,3,1,6,4,2,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,3,8,5,4,2,7,6]=>0011101=>1011100=>[1,2,1,1,3]
[1,8,3,6,2,7,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,6,8,7,4,2,5,3]=>0011101=>1011100=>[1,2,1,1,3]
[6,4,8,7,5,3,1,2]=>1011110=>0111101=>[2,1,1,1,2,1]
[3,1,2,7,6,4,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[5,2,6,3,7,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[2,8,5,3,1,6,4,7]=>0111010=>0101110=>[2,2,1,1,2]
[2,1,7,3,8,5,4,6]=>1010110=>0110101=>[2,1,2,2,1]
[1,6,2,3,7,8,5,4]=>0100011=>1100010=>[1,1,4,2]
[1,6,7,2,8,4,5,3]=>0010101=>1010100=>[1,2,2,3]
[6,3,7,4,8,5,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[5,7,1,8,2,4,6,3]=>0101001=>1001010=>[1,3,2,2]
[5,1,2,7,8,3,6,4]=>1000101=>1010001=>[1,2,4,1]
[4,2,1,7,3,8,5,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,2,8,4,3,1,5,7]=>1011100=>0011101=>[3,1,1,2,1]
[6,4,2,7,3,5,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,3,2,1,8,4,5,6]=>1110100=>0010111=>[3,2,1,1,1]
[3,7,2,8,6,1,4,5]=>0101100=>0011010=>[3,1,2,2]
[7,8,3,2,5,6,1,4]=>0110010=>0100110=>[2,3,1,2]
[7,1,8,2,4,5,6,3]=>1010001=>1000101=>[1,4,2,1]
[8,7,6,1,2,4,5,3]=>1110001=>1000111=>[1,4,1,1,1]
[8,3,6,5,2,1,4,7]=>1011100=>0011101=>[3,1,1,2,1]
[8,2,4,1,6,5,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,2,4,1,7,6,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,5,1,2,7,3,6,4]=>1100101=>1010011=>[1,2,3,1,1]
[6,1,8,2,3,7,5,4]=>1010011=>1100101=>[1,1,3,2,1]
[2,8,1,7,5,4,3,6]=>0101110=>0111010=>[2,1,1,2,2]
[1,7,2,8,3,6,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[7,3,8,6,5,4,1,2]=>1011110=>0111101=>[2,1,1,1,2,1]
[1,8,7,6,5,2,4,3]=>0111101=>1011110=>[1,2,1,1,1,2]
[8,1,7,3,2,6,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,3,1,2,8,7,6,5]=>1100111=>1110011=>[1,1,1,3,1,1]
[5,1,4,3,2,8,7,6]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,6,4,3,1,5,7,2]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,6,4,1,5,2,7,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,5,3,2,1,7,4]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[8,7,2,4,5,3,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[8,5,1,2,6,7,3,4]=>1100010=>0100011=>[2,4,1,1]
[8,5,1,6,4,2,7,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,1,3,6,4,7,2]=>1100101=>1010011=>[1,2,3,1,1]
[8,6,5,1,7,3,2,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,4,8,3,1,6,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,5,8,3,2,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[5,7,4,1,8,2,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[5,7,4,3,1,8,6,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,5,7,4,6,1,3,2]=>1010101=>1010101=>[1,2,2,2,1]
[1,8,7,2,5,4,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[4,3,1,8,7,5,2,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[1,3,5,6,8,4,2,7]=>0000110=>0110000=>[2,1,5]
[3,1,4,6,8,7,2,5]=>1000110=>0110001=>[2,1,4,1]
[1,6,3,8,7,2,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,6,2,4,8,7,5,3]=>0100111=>1110010=>[1,1,1,3,2]
[8,4,1,6,7,5,3,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,3,6,8,5,1,2,4]=>1001100=>0011001=>[3,1,3,1]
[1,3,7,2,6,8,4,5]=>0010010=>0100100=>[2,3,3]
[3,6,5,2,8,1,4,7]=>0110100=>0010110=>[3,2,1,2]
[6,1,2,7,8,5,3,4]=>1000110=>0110001=>[2,1,4,1]
[6,1,2,7,4,8,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[3,1,6,4,7,8,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,7,1,3,8,4,6,2]=>0100101=>1010010=>[1,2,3,2]
[5,7,1,8,4,2,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[5,7,1,2,8,6,3,4]=>0100110=>0110010=>[2,1,3,2]
[4,2,6,3,8,1,5,7]=>1010100=>0010101=>[3,2,2,1]
[4,2,6,7,3,5,1,8]=>1001010=>0101001=>[2,2,3,1]
[3,6,2,4,7,5,1,8]=>0100110=>0110010=>[2,1,3,2]
[3,6,2,4,1,8,5,7]=>0101010=>0101010=>[2,2,2,2]
[7,1,4,5,2,8,6,3]=>1001011=>1101001=>[1,1,2,3,1]
[4,7,3,1,5,8,6,2]=>0110011=>1100110=>[1,1,3,1,2]
[8,7,6,4,1,5,2,3]=>1111010=>0101111=>[2,2,1,1,1,1]
[3,8,2,7,1,5,4,6]=>0101010=>0101010=>[2,2,2,2]
[3,6,8,2,1,5,4,7]=>0011010=>0101100=>[2,2,1,3]
[2,4,8,1,6,5,3,7]=>0010110=>0110100=>[2,1,2,3]
[4,2,8,1,5,7,3,6]=>1010010=>0100101=>[2,3,2,1]
[8,5,7,6,1,4,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[1,8,2,4,6,7,3,5]=>0100010=>0100010=>[2,4,2]
[2,1,5,8,6,4,3,7]=>1001110=>0111001=>[2,1,1,3,1]
[1,2,5,7,8,4,3,6]=>0000110=>0110000=>[2,1,5]
[1,2,7,4,8,6,3,5]=>0010110=>0110100=>[2,1,2,3]
[1,2,7,8,3,6,5,4]=>0001011=>1101000=>[1,1,2,4]
[1,8,5,7,4,3,2,6]=>0101110=>0111010=>[2,1,1,2,2]
[1,6,8,5,4,3,2,7]=>0011110=>0111100=>[2,1,1,1,3]
[7,1,5,8,3,4,6,2]=>1001001=>1001001=>[1,3,3,1]
[7,1,5,8,4,3,2,6]=>1001110=>0111001=>[2,1,1,3,1]
[7,1,2,5,8,3,6,4]=>1000101=>1010001=>[1,2,4,1]
[7,1,6,4,2,3,5,8]=>1011000=>0001101=>[4,1,2,1]
[2,7,1,4,8,3,5,6]=>0100100=>0010010=>[3,3,2]
[7,1,4,6,5,8,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,2,3,8,5,4,6]=>1000110=>0110001=>[2,1,4,1]
[7,1,5,4,3,8,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,3,4,2,6,8,5]=>1001001=>1001001=>[1,3,3,1]
[3,6,7,1,4,8,5,2]=>0010011=>1100100=>[1,1,3,3]
[3,5,1,4,8,6,2,7]=>0100110=>0110010=>[2,1,3,2]
[3,6,2,4,7,8,1,5]=>0100010=>0100010=>[2,4,2]
[5,6,2,4,8,7,1,3]=>0100110=>0110010=>[2,1,3,2]
[6,5,8,7,2,3,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[3,4,7,2,5,8,1,6]=>0010010=>0100100=>[2,3,3]
[4,3,8,1,2,7,5,6]=>1010010=>0100101=>[2,3,2,1]
[5,6,7,8,1,3,4,2]=>0001001=>1001000=>[1,3,4]
[5,7,8,6,1,2,3,4]=>0011000=>0001100=>[4,1,3]
[2,8,3,1,5,6,4,7]=>0110010=>0100110=>[2,3,1,2]
[3,8,7,1,5,4,2,6]=>0110110=>0110110=>[2,1,2,1,2]
[4,3,1,7,6,8,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[3,4,1,7,5,6,8,2]=>0101001=>1001010=>[1,3,2,2]
[3,4,1,5,7,6,2,8]=>0100110=>0110010=>[2,1,3,2]
[2,4,6,1,7,5,8,3]=>0010101=>1010100=>[1,2,2,3]
[4,7,8,1,2,3,6,5]=>0010001=>1000100=>[1,4,3]
[4,2,1,5,6,3,7,8]=>1100100=>0010011=>[3,3,1,1]
[5,8,1,6,4,3,2,7]=>0101110=>0111010=>[2,1,1,2,2]
[5,8,1,6,3,7,2,4]=>0101010=>0101010=>[2,2,2,2]
[7,6,5,1,3,8,2,4]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,5,1,3,4,8,2]=>1110001=>1000111=>[1,4,1,1,1]
[7,2,6,4,1,3,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[8,4,5,3,7,2,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,7,5,2,8,1,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,3,8,5,1,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,4,3,1,5,7,8]=>0111000=>0001110=>[4,1,1,2]
[3,6,4,8,1,7,2,5]=>0101010=>0101010=>[2,2,2,2]
[7,3,8,4,1,5,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[4,2,8,3,6,1,5,7]=>1010100=>0010101=>[3,2,2,1]
[6,7,5,8,2,1,4,3]=>0101101=>1011010=>[1,2,1,2,2]
[6,8,5,7,2,1,3,4]=>0101100=>0011010=>[3,1,2,2]
[4,8,5,2,7,1,3,6]=>0110100=>0010110=>[3,2,1,2]
[6,3,5,2,1,7,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[3,6,5,4,2,8,1,7]=>0111010=>0101110=>[2,2,1,1,2]
[7,4,5,3,8,2,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[1,6,4,7,2,5,3,8]=>0101010=>0101010=>[2,2,2,2]
[1,4,3,7,2,6,5,8]=>0101010=>0101010=>[2,2,2,2]
[1,5,7,2,4,8,3,6]=>0010010=>0100100=>[2,3,3]
[1,6,5,7,2,4,3,8]=>0101010=>0101010=>[2,2,2,2]
[1,7,6,2,8,3,4,5]=>0110100=>0010110=>[3,2,1,2]
[1,4,2,3,5,8,7,6]=>0100011=>1100010=>[1,1,4,2]
[1,5,2,3,4,8,7,6]=>0100011=>1100010=>[1,1,4,2]
[1,6,5,2,3,8,7,4]=>0110011=>1100110=>[1,1,3,1,2]
[1,7,6,5,2,8,4,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,6,5,2,3,8,4,7]=>0110010=>0100110=>[2,3,1,2]
[1,6,7,5,2,3,8,4]=>0011001=>1001100=>[1,3,1,3]
[1,7,5,2,8,4,3,6]=>0110110=>0110110=>[2,1,2,1,2]
[1,7,5,6,2,8,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,5,7,6,2,4,8,3]=>0011001=>1001100=>[1,3,1,3]
[1,4,7,6,2,5,8,3]=>0011001=>1001100=>[1,3,1,3]
[1,2,6,5,3,7,4,8]=>0011010=>0101100=>[2,2,1,3]
[1,3,7,5,2,6,8,4]=>0011001=>1001100=>[1,3,1,3]
[1,7,4,6,2,8,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,7,3,5,2,8,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,3,7,4,2,6,8,5]=>0011001=>1001100=>[1,3,1,3]
[1,4,7,3,2,5,8,6]=>0011001=>1001100=>[1,3,1,3]
[1,5,7,3,2,4,8,6]=>0011001=>1001100=>[1,3,1,3]
[1,7,3,4,2,8,5,6]=>0101010=>0101010=>[2,2,2,2]
[1,7,4,2,8,5,3,6]=>0110110=>0110110=>[2,1,2,1,2]
[1,6,7,4,2,3,8,5]=>0011001=>1001100=>[1,3,1,3]
[1,4,3,2,5,8,6,7]=>0110010=>0100110=>[2,3,1,2]
[1,5,3,2,4,8,6,7]=>0110010=>0100110=>[2,3,1,2]
[1,6,4,2,3,8,5,7]=>0110010=>0100110=>[2,3,1,2]
[1,7,6,4,2,8,5,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,7,5,3,2,8,6,4]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,6,4,2,3,8,7,5]=>0110011=>1100110=>[1,1,3,1,2]
[1,5,3,2,4,8,7,6]=>0110011=>1100110=>[1,1,3,1,2]
[6,8,5,4,3,2,1,7]=>0111110=>0111110=>[2,1,1,1,1,2]
[2,8,5,4,3,7,1,6]=>0111010=>0101110=>[2,2,1,1,2]
[7,6,1,4,3,8,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,6,5,1,3,8,4,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,3,5,4,8,1,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,6,8,4,3,1,7,2]=>0011101=>1011100=>[1,2,1,1,3]
[6,8,5,4,1,2,7,3]=>0111001=>1001110=>[1,3,1,1,2]
[6,8,2,4,3,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[1,8,3,4,7,2,6,5]=>0100101=>1010010=>[1,2,3,2]
[7,5,8,4,3,2,1,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,8,5,7,3,2,1,6]=>0101110=>0111010=>[2,1,1,2,2]
[7,8,1,2,4,3,5,6]=>0100100=>0010010=>[3,3,2]
[7,8,2,1,4,3,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,4,6,5,7,8,1,2]=>0010010=>0100100=>[2,3,3]
[4,3,6,5,8,7,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,6,1,8,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,3,8,4,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[6,7,4,5,1,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[4,5,3,8,6,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,8,4,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,6,4,7,1,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,7,3,4,1,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,1,8,6,7,2,3]=>0101010=>0101010=>[2,2,2,2]
[7,8,4,5,1,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[4,5,2,3,1,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,3,1,8,4,7]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,4,1,8,2,7]=>0101010=>0101010=>[2,2,2,2]
[3,6,4,5,2,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[3,6,4,5,1,8,2,7]=>0101010=>0101010=>[2,2,2,2]
[2,6,4,8,1,5,3,7]=>0101010=>0101010=>[2,2,2,2]
[2,8,3,6,1,5,4,7]=>0101010=>0101010=>[2,2,2,2]
[2,8,3,4,1,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,5,3,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[1,8,3,6,5,7,2,4]=>0101010=>0101010=>[2,2,2,2]
[1,6,4,7,3,8,2,5]=>0101010=>0101010=>[2,2,2,2]
[1,7,3,6,4,8,2,5]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,8,4,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,7,5,8,2,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,1,5,3,8,2,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,1,8,2,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,1,8,4,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[6,7,5,8,1,4,2,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,6,7,2,3,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,2,3,1,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[6,7,2,8,1,4,3,5]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,4,1,8,2,5]=>0101010=>0101010=>[2,2,2,2]
[3,4,2,7,5,6,1,8]=>0101010=>0101010=>[2,2,2,2]
[2,7,5,8,1,4,3,6]=>0101010=>0101010=>[2,2,2,2]
[2,3,1,8,4,7,5,6]=>0101010=>0101010=>[2,2,2,2]
[2,3,1,8,6,7,4,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,3,1,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[2,8,1,4,3,7,5,6]=>0101010=>0101010=>[2,2,2,2]
[2,8,1,7,3,5,4,6]=>0101010=>0101010=>[2,2,2,2]
[4,5,1,7,3,8,2,6]=>0101010=>0101010=>[2,2,2,2]
[3,8,1,5,2,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[3,4,1,8,6,7,2,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,4,1,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[3,4,2,5,1,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[3,4,2,8,1,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[2,5,4,1,6,3,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[3,6,5,1,2,4,8,7]=>0110001=>1000110=>[1,4,1,2]
[5,2,3,6,4,1,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[6,1,4,5,3,2,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[5,6,7,8,1,4,3,2]=>0001011=>1101000=>[1,1,2,4]
[4,2,6,8,5,7,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,5,8,7,6,3,4]=>1001110=>0111001=>[2,1,1,3,1]
[2,1,4,7,6,3,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,7,1,5,2,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,8,6,7,3,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,3,8,2,1,5,6]=>1101100=>0011011=>[3,1,2,1,1]
[2,4,1,5,8,3,7,6]=>0100101=>1010010=>[1,2,3,2]
[4,7,5,8,1,6,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,5,8,7,3,4,6]=>1001100=>0011001=>[3,1,3,1]
[8,5,7,3,6,1,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,5,1,6,7,8,3]=>1010001=>1000101=>[1,4,2,1]
[7,2,3,4,8,5,6,1]=>1000101=>1010001=>[1,2,4,1]
[6,1,8,5,2,7,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,1,7,4,5,8,6,3]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,8,3,6,7,5,4]=>1010011=>1100101=>[1,1,3,2,1]
[6,8,7,2,5,3,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[8,2,1,6,4,7,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,8,4,2,5,1,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,1,2,3,7,5,8,4]=>1000101=>1010001=>[1,2,4,1]
[7,6,8,4,2,5,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,5,7,1,6,3,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[4,1,2,3,7,6,8,5]=>1000101=>1010001=>[1,2,4,1]
[3,2,4,1,8,5,6,7]=>1010100=>0010101=>[3,2,2,1]
[3,4,8,6,5,2,1,7]=>0011110=>0111100=>[2,1,1,1,3]
[4,1,6,3,5,8,7,2]=>1010011=>1100101=>[1,1,3,2,1]
[8,6,7,1,5,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,1,6,5,8,4,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,5,6,2,3,7]=>1010100=>0010101=>[3,2,2,1]
[2,6,4,8,7,3,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,1,8,2,7,5,4,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,2,3,1,7,4,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,8,6,3,2,5,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,8,4,7,2,1,3,6]=>0101100=>0011010=>[3,1,2,2]
[2,1,8,4,3,7,5,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,3,8,2,4,5,7,1]=>1010001=>1000101=>[1,4,2,1]
[5,8,2,4,3,1,6,7]=>0101100=>0011010=>[3,1,2,2]
[7,3,5,8,1,4,2,6]=>1001010=>0101001=>[2,2,3,1]
[3,8,7,6,1,4,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[5,1,8,3,6,7,2,4]=>1010010=>0100101=>[2,3,2,1]
[3,6,1,4,7,8,5,2]=>0100011=>1100010=>[1,1,4,2]
[1,6,8,4,7,5,2,3]=>0010110=>0110100=>[2,1,2,3]
[6,8,1,3,5,7,2,4]=>0100010=>0100010=>[2,4,2]
[7,6,1,4,3,8,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,2,6,7,5,3,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,4,1,6,8,2,5,3]=>1100101=>1010011=>[1,2,3,1,1]
[1,8,6,2,5,3,4,7]=>0110100=>0010110=>[3,2,1,2]
[4,7,1,2,5,3,8,6]=>0100101=>1010010=>[1,2,3,2]
[8,7,3,6,4,5,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,7,8,6,2,1,4,3]=>0011101=>1011100=>[1,2,1,1,3]
[1,8,6,4,5,2,3,7]=>0110100=>0010110=>[3,2,1,2]
[1,4,7,2,6,8,3,5]=>0010010=>0100100=>[2,3,3]
[2,5,4,3,6,8,1,7]=>0110010=>0100110=>[2,3,1,2]
[3,8,5,4,6,2,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[4,8,2,1,3,7,5,6]=>0110010=>0100110=>[2,3,1,2]
[1,8,3,2,5,6,7,4]=>0110001=>1000110=>[1,4,1,2]
[6,4,1,2,7,5,8,3]=>1100101=>1010011=>[1,2,3,1,1]
[4,3,7,8,5,1,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[1,2,7,3,6,5,8,4]=>0010101=>1010100=>[1,2,2,3]
[2,8,7,6,3,4,1,5]=>0111010=>0101110=>[2,2,1,1,2]
[5,8,2,6,3,4,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,1,7,5,8,6,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[1,2,4,5,8,3,7,6]=>0000101=>1010000=>[1,2,5]
[4,8,1,5,2,3,7,6]=>0101001=>1001010=>[1,3,2,2]
[2,4,6,3,7,1,8,5]=>0010101=>1010100=>[1,2,2,3]
[6,5,8,7,1,3,4,2]=>1011001=>1001101=>[1,3,1,2,1]
[3,6,7,2,4,8,1,5]=>0010010=>0100100=>[2,3,3]
[1,5,2,7,4,3,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[7,6,1,2,8,3,5,4]=>1100101=>1010011=>[1,2,3,1,1]
[6,7,8,1,5,2,4,3]=>0010101=>1010100=>[1,2,2,3]
[5,7,8,4,1,2,6,3]=>0011001=>1001100=>[1,3,1,3]
[4,7,8,5,6,1,3,2]=>0010101=>1010100=>[1,2,2,3]
[5,6,4,8,1,2,7,3]=>0101001=>1001010=>[1,3,2,2]
[6,5,4,1,2,3,8,7]=>1110001=>1000111=>[1,4,1,1,1]
[7,5,1,6,2,3,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[4,5,6,7,8,1,3,2]=>0000101=>1010000=>[1,2,5]
[8,1,3,6,7,4,5,2]=>1000101=>1010001=>[1,2,4,1]
[4,2,6,7,3,1,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[7,3,1,5,4,8,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,5,3,2,8,1,6,7]=>0110100=>0010110=>[3,2,1,2]
[7,4,1,5,3,2,6,8]=>1101100=>0011011=>[3,1,2,1,1]
[8,1,5,4,3,2,6,7]=>1011100=>0011101=>[3,1,1,2,1]
[8,1,6,4,2,5,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[6,5,3,1,2,7,4,8]=>1110010=>0100111=>[2,3,1,1,1]
[5,6,3,8,1,4,2,7]=>0101010=>0101010=>[2,2,2,2]
[4,6,3,8,2,1,5,7]=>0101100=>0011010=>[3,1,2,2]
[4,7,8,3,2,1,5,6]=>0011100=>0011100=>[3,1,1,3]
[5,7,8,3,1,4,2,6]=>0011010=>0101100=>[2,2,1,3]
[8,1,7,2,5,4,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,1,7,2,4,5,6,3]=>1010001=>1000101=>[1,4,2,1]
[7,6,1,2,4,5,8,3]=>1100001=>1000011=>[1,5,1,1]
[4,7,8,2,3,1,6,5]=>0010101=>1010100=>[1,2,2,3]
[7,5,1,3,2,6,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[8,1,6,3,2,5,7,4]=>1011001=>1001101=>[1,3,1,2,1]
[8,1,5,3,4,2,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,2,3,1,6,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[6,3,2,1,5,7,4,8]=>1110010=>0100111=>[2,3,1,1,1]
[8,1,4,3,5,6,2,7]=>1010010=>0100101=>[2,3,2,1]
[3,6,5,8,2,4,1,7]=>0101010=>0101010=>[2,2,2,2]
[6,2,4,5,8,3,1,7]=>1000110=>0110001=>[2,1,4,1]
[4,8,1,2,5,6,3,7]=>0100010=>0100010=>[2,4,2]
[8,1,3,5,2,6,4,7]=>1001010=>0101001=>[2,2,3,1]
[5,2,1,6,3,8,4,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,1,4,5,8,3,2,7]=>1000110=>0110001=>[2,1,4,1]
[6,5,4,3,8,2,1,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[4,6,8,3,7,2,5,1]=>0010101=>1010100=>[1,2,2,3]
[1,4,3,6,2,7,8,5]=>0101001=>1001010=>[1,3,2,2]
[4,7,8,5,3,1,2,6]=>0011100=>0011100=>[3,1,1,3]
[8,5,7,4,3,6,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[4,7,8,3,6,1,5,2]=>0010101=>1010100=>[1,2,2,3]
[8,4,6,1,7,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[1,3,8,6,4,7,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[7,6,2,1,4,3,8,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,6,8,1,4,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[1,5,7,3,2,6,8,4]=>0011001=>1001100=>[1,3,1,3]
[3,2,6,8,5,7,4,1]=>1001011=>1101001=>[1,1,2,3,1]
[7,5,2,3,1,6,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[1,6,4,7,2,3,8,5]=>0101001=>1001010=>[1,3,2,2]
[3,1,7,5,2,8,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,7,4,5,2,8,3,6]=>0101010=>0101010=>[2,2,2,2]
[3,2,6,8,7,4,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,2,1,7,8,4,5]=>1110010=>0100111=>[2,3,1,1,1]
[5,7,3,8,2,1,4,6]=>0101100=>0011010=>[3,1,2,2]
[3,7,1,8,4,2,5,6]=>0101100=>0011010=>[3,1,2,2]
[4,2,1,3,7,5,8,6]=>1100101=>1010011=>[1,2,3,1,1]
[8,4,3,7,6,2,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,6,2,8,7,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[7,3,2,8,1,6,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,8,7,2,6,5,4,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,2,7,8,6,1,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,8,4,2,7,1,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[8,5,3,1,7,2,6,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,2,1,6,3,7,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[1,4,6,8,2,7,5,3]=>0001011=>1101000=>[1,1,2,4]
[2,1,7,3,8,6,5,4]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,2,1,7,6,5,4,3]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[8,6,7,5,1,4,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,4,7,3,2,1,8,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,8,7,3,2,1,6,5]=>0111101=>1011110=>[1,2,1,1,1,2]
[6,5,3,7,2,1,4,8]=>1101100=>0011011=>[3,1,2,1,1]
[5,8,3,6,2,1,4,7]=>0101100=>0011010=>[3,1,2,2]
[6,4,3,7,2,1,8,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,8,3,6,2,1,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[6,3,7,8,2,1,4,5]=>1001100=>0011001=>[3,1,3,1]
[5,3,7,6,2,1,4,8]=>1011100=>0011101=>[3,1,1,2,1]
[3,8,7,6,2,1,4,5]=>0111100=>0011110=>[3,1,1,1,2]
[5,8,4,2,6,1,3,7]=>0110100=>0010110=>[3,2,1,2]
[4,8,7,2,5,1,3,6]=>0110100=>0010110=>[3,2,1,2]
[5,8,3,2,6,1,4,7]=>0110100=>0010110=>[3,2,1,2]
[4,8,3,2,5,1,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[4,3,7,2,5,1,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,2,7,5,1,3,8]=>1101100=>0011011=>[3,1,2,1,1]
[5,4,2,6,7,1,3,8]=>1100100=>0010011=>[3,3,1,1]
[6,2,7,8,5,1,3,4]=>1001100=>0011001=>[3,1,3,1]
[2,8,7,6,5,1,3,4]=>0111100=>0011110=>[3,1,1,1,2]
[6,4,7,3,1,5,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[4,8,7,3,1,5,6,2]=>0111001=>1001110=>[1,3,1,1,2]
[6,5,3,7,1,4,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[5,8,3,6,1,4,7,2]=>0101001=>1001010=>[1,3,2,2]
[6,4,3,7,1,5,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[4,8,3,6,1,5,7,2]=>0101001=>1001010=>[1,3,2,2]
[5,3,7,6,1,4,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[4,3,7,6,1,5,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[3,8,7,6,1,4,5,2]=>0111001=>1001110=>[1,3,1,1,2]
[5,8,4,2,1,7,3,6]=>0111010=>0101110=>[2,2,1,1,2]
[6,4,7,2,1,5,3,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,8,3,2,1,4,7,6]=>0111001=>1001110=>[1,3,1,1,2]
[6,3,7,2,1,4,5,8]=>1011000=>0001101=>[4,1,2,1]
[6,5,2,7,1,4,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,8,2,6,1,4,3,7]=>0101010=>0101010=>[2,2,2,2]
[6,4,2,7,1,5,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[2,8,7,6,1,4,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[6,5,4,1,8,7,3,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[6,4,7,1,5,8,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,8,7,1,5,6,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,5,3,1,8,4,7,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,8,3,1,6,4,7,2]=>0110101=>1010110=>[1,2,2,1,2]
[6,4,3,1,5,8,7,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[5,8,2,1,6,4,3,7]=>0110110=>0110110=>[2,1,2,1,2]
[6,4,2,1,5,8,3,7]=>1110010=>0100111=>[2,3,1,1,1]
[3,8,2,1,5,4,6,7]=>0110100=>0010110=>[3,2,1,2]
[6,2,7,1,5,4,3,8]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,7,1,5,4,6,8]=>1010100=>0010101=>[3,2,2,1]
[2,8,7,1,5,4,3,6]=>0110110=>0110110=>[2,1,2,1,2]
[6,5,1,7,8,4,3,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[5,4,1,6,7,8,3,2]=>1100011=>1100011=>[1,1,4,1,1]
[4,3,1,6,5,7,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[4,2,1,6,5,7,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[2,8,1,6,5,4,3,7]=>0101110=>0111010=>[2,1,1,2,2]
[6,1,7,8,5,4,3,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[5,1,7,6,8,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,1,7,6,5,8,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,5,8,1,7,2,3,6]=>0010100=>0010100=>[3,2,3]
[4,5,8,1,2,6,3,7]=>0010010=>0100100=>[2,3,3]
[8,1,3,5,7,2,4,6]=>1000100=>0010001=>[3,4,1]
[3,6,8,1,7,2,4,5]=>0010100=>0010100=>[3,2,3]
[3,4,5,6,8,1,7,2]=>0000101=>1010000=>[1,2,5]
[8,2,3,5,6,7,1,4]=>1000010=>0100001=>[2,5,1]
[8,1,2,3,5,4,6,7]=>1000100=>0010001=>[3,4,1]
[4,5,8,1,7,6,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[8,7,2,1,6,3,4,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,2,1,3,5,4,6]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,4,1,7,5,3,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[2,3,6,7,8,1,5,4]=>0000101=>1010000=>[1,2,5]
[7,4,2,6,8,5,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[7,3,2,5,8,6,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[7,3,1,8,6,2,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[3,1,7,2,5,4,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,4,2,8,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,8,2,5,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,8,4,5,1,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,4,6,1,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,1,6,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,7,5,4,2,3,6]=>1011100=>0011101=>[3,1,1,2,1]
[8,1,2,6,5,4,3,7]=>1001110=>0111001=>[2,1,1,3,1]
[8,1,7,6,3,2,4,5]=>1011100=>0011101=>[3,1,1,2,1]
[8,2,7,5,6,1,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,6,8,1,7,5,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[8,2,6,7,5,4,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[8,6,7,2,3,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,7,8,6,3,1,5,4]=>0011101=>1011100=>[1,2,1,1,3]
[7,3,1,8,6,5,4,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[8,1,7,6,5,4,3,2]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[2,1,8,6,3,7,4,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,6,1,5,2,7,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,1,7,4,2,6,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,1,7,8,3,6,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,4,8,5,7,3,6]=>1001010=>0101001=>[2,2,3,1]
[7,8,1,5,2,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,4,1,5,2,3,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[4,3,7,8,5,2,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[5,3,7,4,6,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[5,8,3,7,6,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[4,2,6,3,8,5,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,8,2,1,7,6,4,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[8,3,2,4,1,7,5,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,4,2,1,7,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[7,2,8,1,4,6,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[6,8,1,4,5,3,2,7]=>0100110=>0110010=>[2,1,3,2]
[8,2,6,1,4,7,3,5]=>1010010=>0100101=>[2,3,2,1]
[4,2,1,3,6,7,8,5]=>1100001=>1000011=>[1,5,1,1]
[2,3,4,1,8,6,5,7]=>0010110=>0110100=>[2,1,2,3]
[6,3,5,4,1,2,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[8,7,3,6,5,1,4,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,4,7,2,8,1,5,6]=>0010100=>0010100=>[3,2,3]
[3,8,4,7,1,6,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,2,4,6,1,5,8,7]=>1001001=>1001001=>[1,3,3,1]
[6,8,5,4,3,7,2,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,8,4,3,2,1,7,6]=>0111101=>1011110=>[1,2,1,1,1,2]
[6,5,4,3,1,8,7,2]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[8,7,5,4,3,1,6,2]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[3,4,6,2,8,5,1,7]=>0010110=>0110100=>[2,1,2,3]
[3,4,6,7,1,8,5,2]=>0001011=>1101000=>[1,1,2,4]
[3,4,6,8,1,5,2,7]=>0001010=>0101000=>[2,2,4]
[3,4,7,2,8,5,6,1]=>0010101=>1010100=>[1,2,2,3]
[3,4,8,2,1,5,6,7]=>0011000=>0001100=>[4,1,3]
[3,5,2,6,8,4,1,7]=>0100110=>0110010=>[2,1,3,2]
[3,5,2,7,4,8,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,6,2,7,8,1,4]=>0010010=>0100100=>[2,3,3]
[3,5,6,2,8,4,1,7]=>0010110=>0110100=>[2,1,2,3]
[3,5,6,8,4,1,2,7]=>0001100=>0011000=>[3,1,4]
[3,5,7,2,4,8,6,1]=>0010011=>1100100=>[1,1,3,3]
[3,5,7,2,8,4,6,1]=>0010101=>1010100=>[1,2,2,3]
[3,5,7,8,4,1,6,2]=>0001101=>1011000=>[1,2,1,4]
[3,5,8,2,4,1,6,7]=>0010100=>0010100=>[3,2,3]
[3,6,2,1,7,8,5,4]=>0110011=>1100110=>[1,1,3,1,2]
[3,6,2,1,8,5,4,7]=>0110110=>0110110=>[2,1,2,1,2]
[3,6,2,7,4,8,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,6,2,7,8,5,4,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,6,8,2,4,5,1,7]=>0010010=>0100100=>[2,3,3]
[3,7,2,1,4,8,6,5]=>0110011=>1100110=>[1,1,3,1,2]
[3,7,2,8,4,5,6,1]=>0101001=>1001010=>[1,3,2,2]
[3,8,2,1,4,5,6,7]=>0110000=>0000110=>[5,1,2]
[4,1,5,6,7,8,3,2]=>1000011=>1100001=>[1,1,5,1]
[4,1,5,7,3,8,6,2]=>1001011=>1101001=>[1,1,2,3,1]
[4,1,5,7,8,2,6,3]=>1000101=>1010001=>[1,2,4,1]
[4,1,5,8,3,2,6,7]=>1001100=>0011001=>[3,1,3,1]
[4,1,6,3,7,8,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,1,6,3,8,5,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[4,1,6,7,3,8,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[4,1,6,8,3,5,2,7]=>1001010=>0101001=>[2,2,3,1]
[4,1,7,3,8,5,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,3,2,5,6,7]=>1011000=>0001101=>[4,1,2,1]
[4,5,2,7,3,8,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,5,7,3,2,8,6,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,5,8,3,2,1,6,7]=>0011100=>0011100=>[3,1,1,3]
[4,6,2,3,8,5,1,7]=>0100110=>0110010=>[2,1,3,2]
[4,6,2,8,3,5,1,7]=>0101010=>0101010=>[2,2,2,2]
[4,6,7,3,2,8,5,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,7,2,8,3,5,6,1]=>0101001=>1001010=>[1,3,2,2]
[4,7,8,3,2,5,6,1]=>0011001=>1001100=>[1,3,1,3]
[4,8,2,3,1,5,6,7]=>0101000=>0001010=>[4,2,2]
[5,1,2,6,8,4,3,7]=>1000110=>0110001=>[2,1,4,1]
[5,1,2,8,4,3,6,7]=>1001100=>0011001=>[3,1,3,1]
[5,1,6,3,7,8,2,4]=>1010010=>0100101=>[2,3,2,1]
[5,1,6,3,8,4,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,6,7,4,8,2,3]=>1001010=>0101001=>[2,2,3,1]
[5,6,2,3,8,4,1,7]=>0100110=>0110010=>[2,1,3,2]
[5,6,2,7,4,8,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,7,8,4,1,3]=>0100110=>0110010=>[2,1,3,2]
[5,6,8,3,4,2,1,7]=>0010110=>0110100=>[2,1,2,3]
[5,7,8,3,4,2,6,1]=>0010101=>1010100=>[1,2,2,3]
[6,1,2,3,7,8,5,4]=>1000011=>1100001=>[1,1,5,1]
[6,1,2,3,8,5,4,7]=>1000110=>0110001=>[2,1,4,1]
[6,1,2,7,8,5,4,3]=>1000111=>1110001=>[1,1,1,4,1]
[6,1,7,8,4,5,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[6,7,2,8,4,5,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[7,1,2,3,4,8,6,5]=>1000011=>1100001=>[1,1,5,1]
[7,1,2,3,8,5,6,4]=>1000101=>1010001=>[1,2,4,1]
[7,1,2,8,4,5,6,3]=>1001001=>1001001=>[1,3,3,1]
[7,1,8,3,4,5,6,2]=>1010001=>1000101=>[1,4,2,1]
[2,4,6,1,8,5,7,3]=>0010101=>1010100=>[1,2,2,3]
[6,4,1,8,2,3,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[5,8,1,2,4,3,7,6]=>0100101=>1010010=>[1,2,3,2]
[5,8,1,6,2,4,3,7]=>0101010=>0101010=>[2,2,2,2]
[1,3,5,7,2,6,4,8]=>0001010=>0101000=>[2,2,4]
[3,5,8,6,1,2,4,7]=>0011000=>0001100=>[4,1,3]
[3,5,1,8,2,4,7,6]=>0101001=>1001010=>[1,3,2,2]
[3,1,6,8,2,4,7,5]=>1001001=>1001001=>[1,3,3,1]
[2,3,5,6,8,1,7,4]=>0000101=>1010000=>[1,2,5]
[5,6,4,8,2,1,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,1,8,6,3,4,5,2]=>1011001=>1001101=>[1,3,1,2,1]
[7,6,5,2,4,8,1,3]=>1110010=>0100111=>[2,3,1,1,1]
[6,7,4,5,2,1,8,3]=>0101101=>1011010=>[1,2,1,2,2]
[5,1,7,8,6,4,3,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[2,5,7,8,6,3,1,4]=>0001110=>0111000=>[2,1,1,4]
[7,1,8,6,3,2,4,5]=>1011100=>0011101=>[3,1,1,2,1]
[7,8,1,6,4,2,3,5]=>0101100=>0011010=>[3,1,2,2]
[2,4,8,1,5,6,7,3]=>0010001=>1000100=>[1,4,3]
[8,4,1,2,5,6,3,7]=>1100010=>0100011=>[2,4,1,1]
[8,3,1,6,5,2,4,7]=>1101100=>0011011=>[3,1,2,1,1]
[2,5,3,8,7,6,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[5,8,7,4,2,6,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[5,1,8,4,7,6,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,3,2,6,5,1,8,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,2,3,6,5,1,7,4]=>1001101=>1011001=>[1,2,1,3,1]
[4,8,6,5,7,3,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,8,5,6,7,3,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,8,7,4,5,6,2,1]=>0110011=>1100110=>[1,1,3,1,2]
[2,8,7,6,3,4,5,1]=>0111001=>1001110=>[1,3,1,1,2]
[1,8,7,6,5,2,3,4]=>0111100=>0011110=>[3,1,1,1,2]
[7,2,8,6,5,4,1,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,3,2,8,5,1,7,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,4,7,2,5,6,3,1]=>1010011=>1100101=>[1,1,3,2,1]
[6,8,5,4,3,1,7,2]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,8,6,4,1,3,7,2]=>0111001=>1001110=>[1,3,1,1,2]
[3,6,1,8,5,2,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[3,4,1,2,8,6,7,5]=>0100101=>1010010=>[1,2,3,2]
[6,8,3,5,4,1,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[7,6,3,8,5,2,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[5,8,7,4,1,6,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,2,3,1,7,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[8,6,3,4,7,2,5,1]=>1100101=>1010011=>[1,2,3,1,1]
[5,2,8,4,1,6,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[4,1,3,6,8,2,5,7]=>1000100=>0010001=>[3,4,1]
[1,6,3,2,5,8,4,7]=>0110010=>0100110=>[2,3,1,2]
[8,3,2,1,5,4,7,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,3,6,2,4,8,1,7]=>1010010=>0100101=>[2,3,2,1]
[1,6,2,4,5,8,3,7]=>0100010=>0100010=>[2,4,2]
[5,3,2,1,6,8,4,7]=>1110010=>0100111=>[2,3,1,1,1]
[2,6,5,8,1,3,4,7]=>0101000=>0001010=>[4,2,2]
[4,3,1,6,5,8,2,7]=>1101010=>0101011=>[2,2,2,1,1]
[3,4,6,5,7,1,8,2]=>0010101=>1010100=>[1,2,2,3]
[8,2,6,4,1,7,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[5,4,6,8,1,2,7,3]=>1001001=>1001001=>[1,3,3,1]
[3,4,7,8,6,2,5,1]=>0001101=>1011000=>[1,2,1,4]
[7,5,8,2,4,6,1,3]=>1010010=>0100101=>[2,3,2,1]
[8,2,7,4,6,1,3,5]=>1010100=>0010101=>[3,2,2,1]
[4,7,3,2,8,1,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,1,7,2,5,6,4]=>0101001=>1001010=>[1,3,2,2]
[8,3,2,5,7,6,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[2,8,6,1,5,7,3,4]=>0110010=>0100110=>[2,3,1,2]
[1,2,8,3,5,6,7,4]=>0010001=>1000100=>[1,4,3]
[4,2,3,7,1,8,6,5]=>1001011=>1101001=>[1,1,2,3,1]
[3,2,6,4,8,1,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,1,6,7,3,4,5]=>1100100=>0010011=>[3,3,1,1]
[2,7,8,5,4,1,3,6]=>0011100=>0011100=>[3,1,1,3]
[1,7,5,3,8,4,2,6]=>0110110=>0110110=>[2,1,2,1,2]
[4,7,5,3,1,2,8,6]=>0111001=>1001110=>[1,3,1,1,2]
[5,6,7,3,8,4,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[5,7,3,2,4,1,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[8,4,1,3,7,2,5,6]=>1100100=>0010011=>[3,3,1,1]
[2,8,4,7,1,3,5,6]=>0101000=>0001010=>[4,2,2]
[3,5,2,8,6,1,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,7,6,3,2,5,8,4]=>0111001=>1001110=>[1,3,1,1,2]
[3,8,1,5,6,2,7,4]=>0100101=>1010010=>[1,2,3,2]
[4,3,5,6,7,1,8,2]=>1000101=>1010001=>[1,2,4,1]
[7,1,5,2,8,6,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,5,4,8,7,2,1,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[1,8,5,3,6,2,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[6,5,8,7,2,1,3,4]=>1011100=>0011101=>[3,1,1,2,1]
[3,6,2,1,7,5,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[4,7,2,6,5,8,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,1,4,2,7,3,5]=>0101010=>0101010=>[2,2,2,2]
[6,3,4,7,1,8,2,5]=>1001010=>0101001=>[2,2,3,1]
[3,4,7,8,2,5,6,1]=>0001001=>1001000=>[1,3,4]
[1,8,2,4,5,6,7,3]=>0100001=>1000010=>[1,5,2]
[2,1,4,6,8,5,7,3]=>1000101=>1010001=>[1,2,4,1]
[3,2,5,7,6,1,8,4]=>1001101=>1011001=>[1,2,1,3,1]
[3,1,4,6,5,7,8,2]=>1001001=>1001001=>[1,3,3,1]
[1,2,3,4,8,6,5,7]=>0000110=>0110000=>[2,1,5]
[1,2,3,8,5,4,6,7]=>0001100=>0011000=>[3,1,4]
[1,2,3,8,5,6,4,7]=>0001010=>0101000=>[2,2,4]
[1,2,3,8,6,5,4,7]=>0001110=>0111000=>[2,1,1,4]
[1,8,3,4,2,5,6,7]=>0101000=>0001010=>[4,2,2]
[1,2,8,5,4,3,6,7]=>0011100=>0011100=>[3,1,1,3]
[1,8,4,3,2,5,6,7]=>0111000=>0001110=>[4,1,1,2]
[8,5,7,6,4,3,2,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[8,4,7,6,5,3,2,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[8,4,7,5,6,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,5,7,4,6,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,7,6,3,5,4,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,6,7,3,5,4,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,5,7,3,6,4,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,4,7,3,6,5,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,1,7,4,6,5,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,3,7,2,6,5,4,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,5,7,2,6,4,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,6,7,2,5,4,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,7,6,2,5,4,3,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,4,7,1,6,5,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,3,7,1,6,5,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,2,7,1,6,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,1,7,2,6,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,1,7,2,6,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,1,6,4,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,1,6,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,1,6,3,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,7,1,5,3,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,7,6,2,5,3,4,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,7,2,5,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,2,6,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,2,6,3,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,2,6,4,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,3,6,4,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,7,3,6,4,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,7,4,6,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,4,6,3,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,4,6,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,3,6,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,7,3,5,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,4,6,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,5,6,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,5,6,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,5,6,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,7,5,6,3,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,6,5,2,4,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,4,7,6,5,2,3,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,5,7,6,4,2,3,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,7,6,5,4,1,3,2]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[8,6,7,5,4,1,3,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,5,7,6,4,1,3,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,3,7,6,5,1,4,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,1,7,5,6,2,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,5,6,1,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,5,6,1,3,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,7,4,5,1,3,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,7,6,4,5,1,3,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,7,3,5,1,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,3,6,1,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,4,6,1,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,7,4,6,2,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,7,3,6,2,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,3,6,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,2,6,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,2,6,1,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,2,6,1,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,7,2,5,1,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,7,6,2,5,1,4,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,7,6,1,5,2,4,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,7,1,5,2,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,1,6,2,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,1,6,2,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,1,6,2,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,1,6,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,6,7,3,8,5,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[6,7,8,9,10,5,4,3,2,1]=>000011111=>111110000=>[1,1,1,1,1,5]
[5,7,8,9,4,10,6,3,2,1]=>000101111=>111101000=>[1,1,1,1,2,4]
[4,6,8,3,9,5,10,7,2,1]=>001010111=>111010100=>[1,1,1,2,2,3]
[3,5,2,7,4,9,6,10,8,1]=>010101011=>110101010=>[1,1,2,2,2,2]
[1,4,8,2,6,3,5,7]=>0010100=>0010100=>[3,2,3]
[1,6,2,4,8,3,5,7]=>0100100=>0010010=>[3,3,2]
[1,5,2,3,8,4,7,6]=>0100101=>1010010=>[1,2,3,2]
[1,7,2,3,5,4,8,6]=>0100101=>1010010=>[1,2,3,2]
[1,8,2,3,5,4,6,7]=>0100100=>0010010=>[3,3,2]
[1,7,8,2,4,5,3,6]=>0010010=>0100100=>[2,3,3]
[1,2,8,3,6,4,5,7]=>0010100=>0010100=>[3,2,3]
[1,5,8,2,3,7,4,6]=>0010010=>0100100=>[2,3,3]
[1,6,8,2,3,5,4,7]=>0010010=>0100100=>[2,3,3]
[5,7,2,6,3,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,7,1,6,8,4,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[4,8,1,2,5,7,3,6]=>0100010=>0100010=>[2,4,2]
[1,7,8,4,6,2,5,3]=>0010101=>1010100=>[1,2,2,3]
[3,7,4,8,5,1,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[3,7,5,4,8,2,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[4,7,1,3,2,8,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[2,7,3,1,5,8,4,6]=>0110010=>0100110=>[2,3,1,2]
[2,7,5,8,6,4,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[3,4,2,7,8,1,6,5]=>0100101=>1010010=>[1,2,3,2]
[4,3,2,1,5,8,6,7]=>1110010=>0100111=>[2,3,1,1,1]
[4,1,3,7,5,6,8,2]=>1001001=>1001001=>[1,3,3,1]
[3,4,6,1,5,8,2,7]=>0010010=>0100100=>[2,3,3]
[6,5,8,7,1,4,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[4,1,7,3,8,5,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[6,1,7,3,5,4,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,6,8,7,2,4,1,3]=>0011010=>0101100=>[2,2,1,3]
[6,8,5,7,1,2,4,3]=>0101001=>1001010=>[1,3,2,2]
[7,1,3,4,2,8,5,6]=>1001010=>0101001=>[2,2,3,1]
[7,6,1,4,3,5,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[3,5,4,1,6,7,8,2]=>0110001=>1000110=>[1,4,1,2]
[2,5,3,4,8,6,1,7]=>0100110=>0110010=>[2,1,3,2]
[2,4,8,3,6,1,7,5]=>0010101=>1010100=>[1,2,2,3]
[8,2,4,3,7,5,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,8,2,1,5,7,3,4]=>0110010=>0100110=>[2,3,1,2]
[7,2,8,4,1,6,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[1,2,4,8,6,5,3,7]=>0001110=>0111000=>[2,1,1,4]
[7,1,5,6,8,4,3,2]=>1000111=>1110001=>[1,1,1,4,1]
[7,3,5,6,1,4,8,2]=>1001001=>1001001=>[1,3,3,1]
[3,7,6,5,1,4,8,2]=>0111001=>1001110=>[1,3,1,1,2]
[2,7,6,5,3,8,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[2,7,8,1,4,6,3,5]=>0010010=>0100100=>[2,3,3]
[4,8,2,5,7,1,6,3]=>0100101=>1010010=>[1,2,3,2]
[4,1,6,8,5,3,7,2]=>1001101=>1011001=>[1,2,1,3,1]
[5,2,6,4,8,3,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[1,2,6,3,4,8,7,5]=>0010011=>1100100=>[1,1,3,3]
[5,3,6,1,4,7,8,2]=>1010001=>1000101=>[1,4,2,1]
[6,7,1,3,4,5,8,2]=>0100001=>1000010=>[1,5,2]
[1,7,3,2,4,8,5,6]=>0110010=>0100110=>[2,3,1,2]
[6,1,4,2,8,3,5,7]=>1010100=>0010101=>[3,2,2,1]
[5,8,6,7,2,1,4,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,4,1,5,8,2,3,6]=>1100100=>0010011=>[3,3,1,1]
[6,3,4,2,8,7,5,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,3,8,7,5,2,6,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,8,7,4,2,3,5,1]=>0111001=>1001110=>[1,3,1,1,2]
[8,6,1,3,5,4,2,7]=>1100110=>0110011=>[2,1,3,1,1]
[2,7,6,3,4,5,8,1]=>0110001=>1000110=>[1,4,1,2]
[5,3,8,6,1,2,4,7]=>1011000=>0001101=>[4,1,2,1]
[2,4,8,7,3,5,6,1]=>0011001=>1001100=>[1,3,1,3]
[2,5,3,6,8,7,4,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,8,7,2,6,4,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[4,5,8,7,2,6,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[8,5,2,7,1,4,3,6]=>1101010=>0101011=>[2,2,2,1,1]
[5,1,7,2,4,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,2,8,3,7,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[8,2,3,7,6,4,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[3,7,5,8,2,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[1,6,7,4,8,2,3,5]=>0010100=>0010100=>[3,2,3]
[8,2,1,3,5,6,7,4]=>1100001=>1000011=>[1,5,1,1]
[4,1,3,8,2,6,7,5]=>1001001=>1001001=>[1,3,3,1]
[3,6,1,4,7,2,8,5]=>0100101=>1010010=>[1,2,3,2]
[6,2,7,4,5,8,1,3]=>1010010=>0100101=>[2,3,2,1]
[2,1,8,4,5,7,3,6]=>1010010=>0100101=>[2,3,2,1]
[1,8,5,7,3,2,4,6]=>0101100=>0011010=>[3,1,2,2]
[3,2,1,6,4,8,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[2,1,8,5,4,3,6,7]=>1011100=>0011101=>[3,1,1,2,1]
[2,7,4,1,5,3,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[7,4,8,6,2,3,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,3,2,4,8,6,1,5]=>1100110=>0110011=>[2,1,3,1,1]
[7,1,3,2,8,5,4,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,7,4,2,3,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[1,3,4,8,6,5,2,7]=>0001110=>0111000=>[2,1,1,4]
[4,1,8,6,5,3,2,7]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,8,5,3,6,2,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[5,7,4,3,6,2,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,7,5,1,2,8,3,4]=>0110010=>0100110=>[2,3,1,2]
[7,5,1,4,2,6,8,3]=>1101001=>1001011=>[1,3,2,1,1]
[5,2,6,8,3,4,7,1]=>1001001=>1001001=>[1,3,3,1]
[7,6,2,4,5,8,3,1]=>1100011=>1100011=>[1,1,4,1,1]
[2,6,3,8,4,7,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,2,7,5,8,3,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[2,1,5,6,8,3,7,4]=>1000101=>1010001=>[1,2,4,1]
[1,2,7,4,8,3,6,5]=>0010101=>1010100=>[1,2,2,3]
[1,6,8,3,2,7,4,5]=>0011010=>0101100=>[2,2,1,3]
[1,6,7,5,2,8,3,4]=>0011010=>0101100=>[2,2,1,3]
[7,5,1,2,8,4,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[5,4,8,3,6,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,2,7,4,3,6,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,7,3,8,2,4,6,1]=>0101001=>1001010=>[1,3,2,2]
[6,4,5,8,2,7,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[5,7,3,6,4,8,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[1,5,6,4,8,2,7,3]=>0010101=>1010100=>[1,2,2,3]
[3,6,2,4,7,1,8,5]=>0100101=>1010010=>[1,2,3,2]
[4,2,8,5,1,6,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[2,1,6,4,8,5,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[1,2,8,3,7,5,4,6]=>0010110=>0110100=>[2,1,2,3]
[1,6,3,8,7,4,2,5]=>0101110=>0111010=>[2,1,1,2,2]
[4,3,8,1,2,6,7,5]=>1010001=>1000101=>[1,4,2,1]
[6,4,5,8,1,2,7,3]=>1001001=>1001001=>[1,3,3,1]
[7,4,6,5,2,1,8,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,1,8,6,7,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,8,5,7,1,4,2,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,2,5,1,3,8,6]=>0101001=>1001010=>[1,3,2,2]
[5,1,7,4,8,6,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,6,5,2,1,8,7,4]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,2,8,4,7,3,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,7,4,1,3,6,8]=>1011000=>0001101=>[4,1,2,1]
[5,2,6,4,1,8,7,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,3,2,1,4,8,7,5]=>1110011=>1100111=>[1,1,3,1,1,1]
[3,1,4,6,2,8,7,5]=>1001011=>1101001=>[1,1,2,3,1]
[6,3,5,1,7,4,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,6,3,7,5,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,7,4,3,8,1,2,6]=>0110100=>0010110=>[3,2,1,2]
[1,5,7,4,8,6,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[1,8,2,7,6,5,4,3]=>0101111=>1111010=>[1,1,1,1,2,2]
[3,8,1,6,7,5,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[3,7,2,6,8,5,1,4]=>0100110=>0110010=>[2,1,3,2]
[8,2,4,3,6,1,5,7]=>1010100=>0010101=>[3,2,2,1]
[1,7,8,5,4,3,6,2]=>0011101=>1011100=>[1,2,1,1,3]
[7,3,8,1,4,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[1,8,4,5,3,2,6,7]=>0101100=>0011010=>[3,1,2,2]
[3,8,7,4,2,6,1,5]=>0111010=>0101110=>[2,2,1,1,2]
[3,7,8,1,2,6,5,4]=>0010011=>1100100=>[1,1,3,3]
[3,5,6,2,7,1,4,8]=>0010100=>0010100=>[3,2,3]
[3,7,1,6,8,2,4,5]=>0100100=>0010010=>[3,3,2]
[8,1,7,6,2,4,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[1,6,4,5,7,2,3,8]=>0100100=>0010010=>[3,3,2]
[8,3,6,1,7,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[1,7,5,3,6,8,4,2]=>0110011=>1100110=>[1,1,3,1,2]
[7,3,5,2,1,8,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[7,4,1,6,5,8,3,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,4,2,8,7,5,1,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,2,1,5,8,7,3,6]=>1100110=>0110011=>[2,1,3,1,1]
[1,5,3,6,8,7,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[3,5,4,6,1,8,2,7]=>0101010=>0101010=>[2,2,2,2]
[3,1,5,7,6,8,2,4]=>1001010=>0101001=>[2,2,3,1]
[6,4,5,7,2,8,1,3]=>1001010=>0101001=>[2,2,3,1]
[5,3,6,4,2,8,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[4,1,5,3,8,2,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,6,3,5,4,8,1,7]=>0101010=>0101010=>[2,2,2,2]
[3,7,4,5,6,8,1,2]=>0100010=>0100010=>[2,4,2]
[2,5,7,3,6,8,1,4]=>0010010=>0100100=>[2,3,3]
[7,6,4,5,2,8,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,3,1,8,2,7,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,2,6,4,7,3,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,6,1,7,4,5,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[1,2,8,3,5,4,6,7]=>0010100=>0010100=>[3,2,3]
[1,7,8,4,3,5,6,2]=>0011001=>1001100=>[1,3,1,3]
[3,1,6,8,4,5,7,2]=>1001001=>1001001=>[1,3,3,1]
[1,4,5,8,3,6,7,2]=>0001001=>1001000=>[1,3,4]
[2,5,7,1,8,3,6,4]=>0010101=>1010100=>[1,2,2,3]
[6,2,7,1,8,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,7,1,3,8,5,6,2]=>0100101=>1010010=>[1,2,3,2]
[3,7,2,1,8,4,5,6]=>0110100=>0010110=>[3,2,1,2]
[2,1,5,8,3,6,7,4]=>1001001=>1001001=>[1,3,3,1]
[4,2,7,1,8,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,1,6,8,2,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[5,3,4,6,8,2,7,1]=>1000101=>1010001=>[1,2,4,1]
[3,5,1,6,8,2,7,4]=>0100101=>1010010=>[1,2,3,2]
[5,1,8,7,4,2,3,6]=>1011100=>0011101=>[3,1,1,2,1]
[5,8,3,2,6,4,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[6,8,2,4,7,5,1,3]=>0100110=>0110010=>[2,1,3,2]
[7,3,8,2,6,4,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[3,8,7,4,5,6,1,2]=>0110010=>0100110=>[2,3,1,2]
[2,7,6,3,5,4,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[3,8,7,4,6,2,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,3,7,6,2,4,1]=>0101101=>1011010=>[1,2,1,2,2]
[8,7,2,5,4,3,1,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,8,3,2,5,4,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,7,4,3,6,2,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,8,6,4,3,7,1,2]=>0111010=>0101110=>[2,2,1,1,2]
[6,5,8,4,3,1,7,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,6,4,7,1,5,3,8]=>0101010=>0101010=>[2,2,2,2]
[2,5,6,8,4,3,7,1]=>0001101=>1011000=>[1,2,1,4]
[5,3,8,1,7,6,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,4,8,7,1,6,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,8,6,7,5,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[4,8,6,5,7,2,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[4,8,5,6,7,1,2,3]=>0100100=>0010010=>[3,3,2]
[5,4,8,6,1,7,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[5,3,8,1,6,7,2,4]=>1010010=>0100101=>[2,3,2,1]
[5,2,1,8,6,7,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,2,1,5,8,3,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[6,5,4,8,2,1,7,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,8,4,7,2,6,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[5,8,3,2,7,6,4,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,8,3,2,6,7,1,4]=>0110010=>0100110=>[2,3,1,2]
[6,5,3,2,8,1,7,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,4,3,2,1,8,7,5]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[6,3,4,1,2,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[6,2,1,4,3,8,7,5]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,2,1,4,3,6,7,8]=>1101000=>0001011=>[4,2,1,1]
[4,6,3,2,5,1,7,8]=>0110100=>0010110=>[3,2,1,2]
[3,5,7,4,2,6,1,8]=>0011010=>0101100=>[2,2,1,3]
[4,3,6,1,5,2,7,8]=>1010100=>0010101=>[3,2,2,1]
[4,2,1,6,5,3,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[4,2,1,5,7,6,3,8]=>1100110=>0110011=>[2,1,3,1,1]
[3,5,4,7,1,6,2,8]=>0101010=>0101010=>[2,2,2,2]
[3,4,7,5,6,1,2,8]=>0010100=>0010100=>[3,2,3]
[3,4,5,8,6,7,1,2]=>0001010=>0101000=>[2,2,4]
[3,4,6,5,8,1,7,2]=>0010101=>1010100=>[1,2,2,3]
[4,3,5,1,6,8,7,2]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,5,3,8,4,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,8,2,5,4,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,3,2,6,4,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,8,2,6,4,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,3,6,4,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,6,3,8,4,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,7,3,5,4,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,7,3,6,4,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,7,3,8,4,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,4,2,7,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,2,7,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,7,2,8,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,7,2,8,4,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,2,5,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,3,2,5,4,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,3,2,6,4,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,3,2,8,4,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,8,2,4,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,7,2,5,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,5,2,8,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,4,2,5,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,6,2,5,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,7,2,5,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,7,2,6,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,7,2,6,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,7,2,8,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,8,2,7,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,5,2,7,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,5,2,6,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,8,2,6,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,6,2,8,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,2,8,4,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,2,6,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,4,2,6,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,4,2,5,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,2,5,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,5,2,8,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,5,2,8,4,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,4,2,8,5,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,3,2,7,5,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,4,2,8,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,8,2,4,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,6,2,4,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,8,2,4,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,3,2,8,4,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,3,2,7,4,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,3,2,7,4,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,3,2,6,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,4,2,6,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,4,2,7,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,5,2,7,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,8,2,5,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,6,2,5,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,6,2,7,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,8,2,7,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,7,2,8,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,7,2,5,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,7,2,4,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,6,2,4,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,5,2,4,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,2,4,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,2,5,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,2,8,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,8,2,6,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,3,1,2,5,6,4]=>0110001=>1000110=>[1,4,1,2]
[7,8,1,3,2,4,6,5]=>0101001=>1001010=>[1,3,2,2]
[6,2,8,1,3,5,4,7]=>1010010=>0100101=>[2,3,2,1]
[6,2,8,3,1,7,4,5]=>1011010=>0101101=>[2,2,1,2,1]
[3,2,5,7,1,8,4,6]=>1001010=>0101001=>[2,2,3,1]
[3,5,2,8,1,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[4,3,1,2,7,8,6,5]=>1100011=>1100011=>[1,1,4,1,1]
[5,3,4,7,8,6,1,2]=>1000110=>0110001=>[2,1,4,1]
[4,1,3,2,6,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[5,1,3,7,2,6,8,4]=>1001001=>1001001=>[1,3,3,1]
[5,2,4,7,8,1,6,3]=>1000101=>1010001=>[1,2,4,1]
[2,5,4,6,8,1,7,3]=>0100101=>1010010=>[1,2,3,2]
[4,3,5,7,6,8,1,2]=>1001010=>0101001=>[2,2,3,1]
[4,2,1,3,7,6,8,5]=>1100101=>1010011=>[1,2,3,1,1]
[2,4,3,1,8,5,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[3,2,4,1,8,6,5,7]=>1010110=>0110101=>[2,1,2,2,1]
[3,4,2,1,8,7,5,6]=>0110110=>0110110=>[2,1,2,1,2]
[7,6,4,3,2,1,8,5]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[7,6,5,8,2,1,4,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,6,8,3,2,1,5,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,8,4,3,2,1,6,5]=>0111101=>1011110=>[1,2,1,1,1,2]
[8,5,4,3,2,1,7,6]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[7,6,3,8,2,1,5,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,6,5,8,4,1,3,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,4,8,3,2,1,6,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,6,8,5,2,1,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,8,6,1,7,5,2,3]=>0110110=>0110110=>[2,1,2,1,2]
[4,8,7,2,6,5,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[4,7,8,2,6,1,5,3]=>0010101=>1010100=>[1,2,2,3]
[4,6,8,2,7,1,3,5]=>0010100=>0010100=>[3,2,3]
[8,6,4,2,7,5,3,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,4,7,3,6,5,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[6,4,7,1,8,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,8,3,6,1,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,4,3,6,2,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,4,3,7,2,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[6,7,4,2,8,3,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[2,8,7,6,5,1,4,3]=>0111101=>1011110=>[1,2,1,1,1,2]
[7,3,2,5,4,1,6,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,3,5,4,2,1,6,8]=>1011100=>0011101=>[3,1,1,2,1]
[2,7,6,3,1,5,8,4]=>0111001=>1001110=>[1,3,1,1,2]
[1,8,4,3,6,5,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[1,8,4,6,5,3,2,7]=>0101110=>0111010=>[2,1,1,2,2]
[7,1,4,2,6,3,5,8]=>1010100=>0010101=>[3,2,2,1]
[7,3,4,1,5,6,2,8]=>1010010=>0100101=>[2,3,2,1]
[7,3,2,5,1,6,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,1,3,5,2,6,8]=>1100100=>0010011=>[3,3,1,1]
[7,3,1,2,4,6,5,8]=>1100010=>0100011=>[2,4,1,1]
[3,6,2,1,4,8,5,7]=>0110010=>0100110=>[2,3,1,2]
[2,3,6,1,4,8,7,5]=>0010011=>1100100=>[1,1,3,3]
[3,6,7,4,1,5,8,2]=>0011001=>1001100=>[1,3,1,3]
[3,1,2,8,6,5,4,7]=>1001110=>0111001=>[2,1,1,3,1]
[5,4,8,6,1,2,3,7]=>1011000=>0001101=>[4,1,2,1]
[5,6,8,2,4,1,3,7]=>0010100=>0010100=>[3,2,3]
[5,6,8,7,4,3,1,2]=>0011110=>0111100=>[2,1,1,1,3]
[6,4,8,5,3,1,7,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,7,8,6,1,3,2,4]=>0011010=>0101100=>[2,2,1,3]
[2,4,8,1,6,3,7,5]=>0010101=>1010100=>[1,2,2,3]
[1,8,4,5,2,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[3,1,4,6,5,8,7,2]=>1001011=>1101001=>[1,1,2,3,1]
[3,7,5,4,6,8,2,1]=>0110011=>1100110=>[1,1,3,1,2]
[5,3,2,1,7,6,8,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,6,1,4,7,2,8,3]=>0100101=>1010010=>[1,2,3,2]
[4,3,1,7,5,6,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[1,8,4,3,6,2,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[5,6,7,3,2,8,1,4]=>0011010=>0101100=>[2,2,1,3]
[5,3,2,1,4,8,6,7]=>1110010=>0100111=>[2,3,1,1,1]
[3,4,7,8,1,2,6,5]=>0001001=>1001000=>[1,3,4]
[3,6,7,8,1,4,5,2]=>0001001=>1001000=>[1,3,4]
[2,3,6,8,5,1,4,7]=>0001100=>0011000=>[3,1,4]
[3,1,6,4,8,2,5,7]=>1010100=>0010101=>[3,2,2,1]
[7,3,2,6,8,5,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[7,3,5,8,4,6,1,2]=>1001010=>0101001=>[2,2,3,1]
[7,5,2,8,4,1,6,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,8,4,2,3,5,7,6]=>0110001=>1000110=>[1,4,1,2]
[6,3,4,8,2,5,7,1]=>1001001=>1001001=>[1,3,3,1]
[7,5,4,8,3,6,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,3,2,5,8,4,6,1]=>1100101=>1010011=>[1,2,3,1,1]
[5,7,8,3,1,4,6,2]=>0011001=>1001100=>[1,3,1,3]
[7,4,8,3,2,5,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[7,3,8,2,4,5,6,1]=>1010001=>1000101=>[1,4,2,1]
[4,2,7,1,5,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,7,1,3,5,4,8,6]=>0100101=>1010010=>[1,2,3,2]
[1,2,7,3,4,8,6,5]=>0010011=>1100100=>[1,1,3,3]
[4,7,2,1,5,8,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,3,4,8,1,6,5,7]=>0001010=>0101000=>[2,2,4]
[3,1,4,8,2,6,7,5]=>1001001=>1001001=>[1,3,3,1]
[4,8,3,6,5,1,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,4,7,3,5,1,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,4,7,8,2,5]=>1010010=>0100101=>[2,3,2,1]
[7,3,1,6,8,2,4,5]=>1100100=>0010011=>[3,3,1,1]
[7,3,5,1,6,8,2,4]=>1010010=>0100101=>[2,3,2,1]
[4,7,3,5,6,1,8,2]=>0100101=>1010010=>[1,2,3,2]
[4,6,8,2,1,5,7,3]=>0011001=>1001100=>[1,3,1,3]
[1,8,2,3,5,7,4,6]=>0100010=>0100010=>[2,4,2]
[2,7,3,6,1,4,5,8]=>0101000=>0001010=>[4,2,2]
[1,2,5,8,3,7,4,6]=>0001010=>0101000=>[2,2,4]
[8,2,4,1,7,5,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,8,4,7,5,1,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[8,4,3,6,1,7,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,1,8,6,7,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[1,2,8,6,3,4,7,5]=>0011001=>1001100=>[1,3,1,3]
[7,3,2,5,6,1,4,8]=>1100100=>0010011=>[3,3,1,1]
[8,4,1,2,7,5,3,6]=>1100110=>0110011=>[2,1,3,1,1]
[1,5,2,8,6,3,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,6,3,1,7,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,8,1,4,2,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,7,4,8,3,5]=>0101010=>0101010=>[2,2,2,2]
[6,2,1,7,8,5,3,4]=>1100110=>0110011=>[2,1,3,1,1]
[6,7,3,8,4,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,7,1,8,5,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[2,1,7,8,6,3,4,5]=>1001100=>0011001=>[3,1,3,1]
[7,8,6,2,1,3,5,4]=>0111001=>1001110=>[1,3,1,1,2]
[5,2,6,3,4,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,2,6,5,3,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[2,6,5,3,1,4,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[6,1,3,4,2,8,7,5]=>1001011=>1101001=>[1,1,2,3,1]
[8,2,6,4,7,3,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,8,5,1,7,2,4,6]=>0110100=>0010110=>[3,2,1,2]
[2,1,7,4,8,5,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,5,1,8,7,4,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,1,3,8,6,4,5,2]=>1001101=>1011001=>[1,2,1,3,1]
[2,3,5,8,6,7,4,1]=>0001011=>1101000=>[1,1,2,4]
[7,4,2,1,8,6,5,3]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[2,1,6,3,4,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[4,6,7,2,5,8,3,1]=>0010011=>1100100=>[1,1,3,3]
[7,6,2,5,3,8,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,2,1,3,4,8,7,5]=>1100011=>1100011=>[1,1,4,1,1]
[8,1,4,2,5,6,7,3]=>1010001=>1000101=>[1,4,2,1]
[3,4,2,1,8,6,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,6,8,1,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[8,1,3,2,5,6,7,4]=>1010001=>1000101=>[1,4,2,1]
[3,2,8,7,4,5,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,3,8,5,7,4,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,4,6,8,5,1,2,3]=>1001100=>0011001=>[3,1,3,1]
[2,1,4,8,7,5,3,6]=>1001110=>0111001=>[2,1,1,3,1]
[7,1,5,8,2,6,3,4]=>1001010=>0101001=>[2,2,3,1]
[3,6,8,2,4,1,5,7]=>0010100=>0010100=>[3,2,3]
[6,2,8,1,7,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,8,5,3,6,7,1,4]=>0110010=>0100110=>[2,3,1,2]
[3,8,1,4,5,6,2,7]=>0100010=>0100010=>[2,4,2]
[5,8,7,3,6,1,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,3,7,6,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[7,5,8,4,6,1,3,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,8,4,7,1,3,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,4,8,1,3,7,6,5]=>0010011=>1100100=>[1,1,3,3]
[2,5,1,3,8,4,7,6]=>0100101=>1010010=>[1,2,3,2]
[2,8,1,5,4,7,3,6]=>0101010=>0101010=>[2,2,2,2]
[3,1,8,2,5,7,4,6]=>1010010=>0100101=>[2,3,2,1]
[8,3,2,6,1,4,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[2,6,1,3,8,7,5,4]=>0100111=>1110010=>[1,1,1,3,2]
[2,5,7,1,3,8,6,4]=>0010011=>1100100=>[1,1,3,3]
[2,8,1,7,6,5,4,3]=>0101111=>1111010=>[1,1,1,1,2,2]
[8,3,2,7,1,6,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,4,2,8,1,6,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,7,5,3,2,1,6,4]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[7,5,2,6,3,1,4,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,4,6,2,1,8,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,4,5,8,6,2,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[6,8,4,5,2,1,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,8,5,1,7,3,2]=>0011011=>1101100=>[1,1,2,1,3]
[4,7,5,1,3,8,6,2]=>0110011=>1100110=>[1,1,3,1,2]
[5,1,7,6,4,2,8,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,1,8,7,6,4,3,2]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[8,5,2,1,6,3,7,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,1,6,2,8,7,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,5,6,1,8,7,2,3]=>0010110=>0110100=>[2,1,2,3]
[3,5,6,8,7,1,4,2]=>0001101=>1011000=>[1,2,1,4]
[3,6,1,7,4,8,2,5]=>0101010=>0101010=>[2,2,2,2]
[8,4,2,6,3,1,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[4,1,8,5,7,3,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,5,8,7,2,3,6]=>1001100=>0011001=>[3,1,3,1]
[3,4,8,7,1,2,6,5]=>0011001=>1001100=>[1,3,1,3]
[3,4,6,8,5,7,1,2]=>0001010=>0101000=>[2,2,4]
[4,6,8,3,5,7,2,1]=>0010011=>1100100=>[1,1,3,3]
[4,7,3,5,8,2,6,1]=>0100101=>1010010=>[1,2,3,2]
[5,4,8,2,7,3,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,7,2,4,8,1,5]=>1010010=>0100101=>[2,3,2,1]
[5,6,8,3,7,2,1,4]=>0010110=>0110100=>[2,1,2,3]
[6,5,2,7,1,3,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[6,5,4,1,7,2,8,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,4,7,3,1,8,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[6,8,5,7,4,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[7,5,8,4,6,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,6,3,7,4,2,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[6,1,3,8,5,2,4,7]=>1001100=>0011001=>[3,1,3,1]
[7,4,2,6,3,5,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[3,4,7,5,6,2,1,8]=>0010110=>0110100=>[2,1,2,3]
[8,1,3,4,5,2,6,7]=>1000100=>0010001=>[3,4,1]
[1,6,8,4,2,5,3,7]=>0011010=>0101100=>[2,2,1,3]
[3,6,8,4,1,7,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[8,7,2,3,6,1,4,5]=>1100100=>0010011=>[3,3,1,1]
[6,7,4,8,5,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[3,2,8,1,5,4,6,7]=>1010100=>0010101=>[3,2,2,1]
[6,1,4,8,5,3,7,2]=>1001101=>1011001=>[1,2,1,3,1]
[1,4,8,5,2,6,7,3]=>0011001=>1001100=>[1,3,1,3]
[8,1,2,3,6,5,7,4]=>1000101=>1010001=>[1,2,4,1]
[6,1,8,4,3,7,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[3,2,6,4,1,8,7,5]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,6,4,3,1,8,2,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,4,6,5,1,7,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,4,6,1,2,8,3]=>1101001=>1001011=>[1,3,2,1,1]
[3,2,5,6,1,7,8,4]=>1001001=>1001001=>[1,3,3,1]
[3,2,8,7,6,1,4,5]=>1011100=>0011101=>[3,1,1,2,1]
[6,8,4,7,2,1,3,5]=>0101100=>0011010=>[3,1,2,2]
[3,8,7,5,6,1,2,4]=>0110100=>0010110=>[3,2,1,2]
[8,2,7,6,5,1,3,4]=>1011100=>0011101=>[3,1,1,2,1]
[4,8,6,7,1,5,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,6,7,2,3,4,5]=>0101000=>0001010=>[4,2,2]
[7,6,3,2,1,8,5,4]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[3,5,4,2,7,1,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[8,6,3,1,4,5,7,2]=>1110001=>1000111=>[1,4,1,1,1]
[3,2,6,1,5,7,4,8]=>1010010=>0100101=>[2,3,2,1]
[5,2,1,4,7,6,3,8]=>1100110=>0110011=>[2,1,3,1,1]
[4,2,1,3,5,8,7,6]=>1100011=>1100011=>[1,1,4,1,1]
[7,4,1,5,3,6,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[3,1,5,2,7,4,9,6,8,10]=>101010100=>001010101=>[3,2,2,2,1]
[6,8,2,4,5,1,3,7]=>0100100=>0010010=>[3,3,2]
[6,8,3,4,1,5,2,7]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,1,7,2,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,3,1,4,5,7,2]=>0110001=>1000110=>[1,4,1,2]
[5,3,8,4,2,6,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[4,1,8,3,5,7,2,6]=>1010010=>0100101=>[2,3,2,1]
[2,4,6,3,5,8,1,7]=>0010010=>0100100=>[2,3,3]
[4,5,7,2,3,6,8,1]=>0010001=>1000100=>[1,4,3]
[2,6,3,4,7,5,8,1]=>0100101=>1010010=>[1,2,3,2]
[4,5,2,7,1,6,8,3]=>0101001=>1001010=>[1,3,2,2]
[2,3,1,7,6,4,8,5]=>0101101=>1011010=>[1,2,1,2,2]
[3,4,1,6,5,8,2,7]=>0101010=>0101010=>[2,2,2,2]
[7,3,1,4,8,5,6,2]=>1100101=>1010011=>[1,2,3,1,1]
[6,4,2,8,7,1,5,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,1,8,2,7,6,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,8,4,1,7,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,6,4,7,2,5,1,8]=>0101010=>0101010=>[2,2,2,2]
[7,3,2,8,6,1,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[4,3,8,7,1,2,5,6]=>1011000=>0001101=>[4,1,2,1]
[1,2,5,8,4,7,3,6]=>0001010=>0101000=>[2,2,4]
[1,3,6,8,5,2,7,4]=>0001101=>1011000=>[1,2,1,4]
[2,5,7,4,1,8,6,3]=>0011011=>1101100=>[1,1,2,1,3]
[2,4,6,1,8,3,7,5]=>0010101=>1010100=>[1,2,2,3]
[3,5,1,7,2,8,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,3,1,7,8,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[5,3,1,6,7,8,4,2]=>1100011=>1100011=>[1,1,4,1,1]
[4,1,6,2,7,8,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,3,4,8,7,5,6]=>1000110=>0110001=>[2,1,4,1]
[4,8,7,3,6,5,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[6,3,8,7,5,4,1,2]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,3,8,7,6,5,1,2]=>1011110=>0111101=>[2,1,1,1,2,1]
[2,8,7,6,1,5,4,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,2,8,7,6,1,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,2,8,7,5,1,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,8,2,6,5,1,4,3]=>0101101=>1011010=>[1,2,1,2,2]
[6,1,8,7,5,4,3,2]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[4,1,8,7,6,5,3,2]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[3,1,8,7,6,5,4,2]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[7,8,2,6,1,5,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[4,2,8,1,7,6,5,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,2,8,1,7,6,5,4]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,8,7,1,6,5,4,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,8,2,1,7,6,5,4]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,8,2,7,6,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,8,2,7,1,6,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[3,8,7,2,1,6,5,4]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,8,7,2,6,1,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,7,6,2,1,4,3]=>0111101=>1011110=>[1,2,1,1,1,2]
[6,5,8,7,1,4,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,8,7,1,6,5,4,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,8,1,7,6,5,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[5,4,1,8,7,6,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[6,4,8,1,7,5,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,8,4,1,6,5,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[7,8,3,1,6,5,4,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,3,1,8,7,6,4,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[4,3,1,8,7,6,5,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[4,2,1,8,7,6,5,3]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[6,5,3,1,8,7,4,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[7,5,2,1,8,6,4,3]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[5,4,2,1,8,7,6,3]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[7,3,2,1,8,6,5,4]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[6,1,4,2,3,5,8,7]=>1010001=>1000101=>[1,4,2,1]
[8,6,1,4,2,3,5,7]=>1101000=>0001011=>[4,2,1,1]
[6,8,1,4,2,3,5,7]=>0101000=>0001010=>[4,2,2]
[4,6,2,3,8,1,5,7]=>0100100=>0010010=>[3,3,2]
[8,2,3,6,4,1,5,7]=>1001100=>0011001=>[3,1,3,1]
[6,2,3,8,4,1,5,7]=>1001100=>0011001=>[3,1,3,1]
[8,4,2,3,6,1,5,7]=>1100100=>0010011=>[3,3,1,1]
[6,4,2,3,8,1,5,7]=>1100100=>0010011=>[3,3,1,1]
[2,8,4,3,6,1,5,7]=>0110100=>0010110=>[3,2,1,2]
[2,6,3,8,4,1,5,7]=>0101100=>0011010=>[3,1,2,2]
[6,3,8,4,2,1,5,7]=>1011100=>0011101=>[3,1,1,2,1]
[2,4,8,3,6,1,5,7]=>0010100=>0010100=>[3,2,3]
[2,4,6,3,8,1,5,7]=>0010100=>0010100=>[3,2,3]
[8,3,6,2,4,1,5,7]=>1010100=>0010101=>[3,2,2,1]
[8,3,6,2,1,4,5,7]=>1011000=>0001101=>[4,1,2,1]
[2,1,8,3,6,4,5,7]=>1010100=>0010101=>[3,2,2,1]
[6,3,8,2,1,4,5,7]=>1011000=>0001101=>[4,1,2,1]
[6,2,4,3,8,1,5,7]=>1010100=>0010101=>[3,2,2,1]
[3,6,4,7,8,5,1,2]=>0100110=>0110010=>[2,1,3,2]
[1,6,4,2,7,5,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,4,6,8,7,5,1,2]=>0001110=>0111000=>[2,1,1,4]
[5,4,6,3,8,7,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[6,4,8,5,3,7,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[1,8,5,2,6,3,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[1,4,6,2,8,5,7,3]=>0010101=>1010100=>[1,2,2,3]
[7,8,1,4,2,5,6,3]=>0101001=>1001010=>[1,3,2,2]
[3,6,5,2,4,1,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,5,3,1,6,2,7]=>0111010=>0101110=>[2,2,1,1,2]
[5,1,6,2,8,7,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[6,1,8,7,4,2,3,5]=>1011100=>0011101=>[3,1,1,2,1]
[1,2,8,5,7,3,6,4]=>0010101=>1010100=>[1,2,2,3]
[1,3,6,8,7,5,2,4]=>0001110=>0111000=>[2,1,1,4]
[7,8,1,2,4,6,5,3]=>0100011=>1100010=>[1,1,4,2]
[1,2,6,4,8,7,5,3]=>0010111=>1110100=>[1,1,1,2,3]
[1,8,2,5,4,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,2,7,3,5,8,6,4]=>0010011=>1100100=>[1,1,3,3]
[4,6,2,1,7,5,3,8]=>0110110=>0110110=>[2,1,2,1,2]
[4,6,2,3,7,8,1,5]=>0100010=>0100010=>[2,4,2]
[4,2,1,3,5,7,8,6]=>1100001=>1000011=>[1,5,1,1]
[7,3,2,4,5,1,8,6]=>1100101=>1010011=>[1,2,3,1,1]
[7,8,3,2,4,1,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[7,8,4,2,6,3,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[4,2,6,3,8,7,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[5,8,2,7,4,3,1,6]=>0101110=>0111010=>[2,1,1,2,2]
[7,5,2,8,3,4,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,3,6,8,1,2,7,5]=>1001001=>1001001=>[1,3,3,1]
[6,4,3,5,2,8,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,8,4,2,3,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[4,1,3,6,5,8,7,2]=>1001011=>1101001=>[1,1,2,3,1]
[2,4,1,3,8,5,7,6]=>0100101=>1010010=>[1,2,3,2]
[2,4,1,3,5,8,7,6]=>0100011=>1100010=>[1,1,4,2]
[4,6,1,3,5,8,7,2]=>0100011=>1100010=>[1,1,4,2]
[1,4,6,3,5,8,7,2]=>0010011=>1100100=>[1,1,3,3]
[4,2,1,3,6,5,7,8]=>1100100=>0010011=>[3,3,1,1]
[4,2,1,6,3,5,7,8]=>1101000=>0001011=>[4,2,1,1]
[4,2,1,8,3,5,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[6,2,1,8,3,5,7,4]=>1101001=>1001011=>[1,3,2,1,1]
[6,4,1,3,8,5,7,2]=>1100101=>1010011=>[1,2,3,1,1]
[6,1,4,3,8,5,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[1,6,4,3,8,5,7,2]=>0110101=>1010110=>[1,2,2,1,2]
[8,1,4,3,6,5,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,1,3,6,5,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[8,2,1,4,3,5,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[8,1,4,6,3,5,7,2]=>1001001=>1001001=>[1,3,3,1]
[6,1,4,8,3,5,7,2]=>1001001=>1001001=>[1,3,3,1]
[6,4,8,1,3,5,7,2]=>1010001=>1000101=>[1,4,2,1]
[2,4,8,1,3,5,7,6]=>0010001=>1000100=>[1,4,3]
[4,6,8,1,3,5,7,2]=>0010001=>1000100=>[1,4,3]
[4,6,1,8,3,5,7,2]=>0101001=>1001010=>[1,3,2,2]
[4,1,6,8,3,5,7,2]=>1001001=>1001001=>[1,3,3,1]
[1,4,6,8,3,5,7,2]=>0001001=>1001000=>[1,3,4]
[1,4,6,3,8,5,7,2]=>0010101=>1010100=>[1,2,2,3]
[4,6,1,3,8,5,7,2]=>0100101=>1010010=>[1,2,3,2]
[2,6,1,3,8,5,7,4]=>0100101=>1010010=>[1,2,3,2]
[2,1,6,3,8,5,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,3,6,8,5,7,4]=>1000101=>1010001=>[1,2,4,1]
[4,1,3,6,8,5,7,2]=>1000101=>1010001=>[1,2,4,1]
[1,4,3,6,8,5,7,2]=>0100101=>1010010=>[1,2,3,2]
[2,1,8,3,6,5,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,4,3,5,7,6]=>1011001=>1001101=>[1,3,1,2,1]
[4,1,8,3,6,5,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,8,4,1,3,5,7,6]=>0110001=>1000110=>[1,4,1,2]
[6,8,1,4,3,5,7,2]=>0101001=>1001010=>[1,3,2,2]
[1,8,6,4,3,5,7,2]=>0111001=>1001110=>[1,3,1,1,2]
[8,6,1,4,3,5,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[8,6,4,1,3,5,7,2]=>1110001=>1000111=>[1,4,1,1,1]
[8,4,2,1,3,5,7,6]=>1110001=>1000111=>[1,4,1,1,1]
[8,5,7,4,3,2,1,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,7,6,5,1,4,3,2]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[8,7,4,3,6,2,1,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,7,3,6,5,2,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,5,8,4,3,2,1,7]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,4,7,6,3,2,1,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[5,8,7,4,3,2,1,6]=>0111110=>0111110=>[2,1,1,1,1,2]
[4,5,2,7,3,1,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[4,8,2,6,3,5,7,1]=>0101001=>1001010=>[1,3,2,2]
[8,6,1,2,7,4,3,5]=>1100110=>0110011=>[2,1,3,1,1]
[4,6,2,1,7,8,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,3,8,7,4,1,6,5]=>0011101=>1011100=>[1,2,1,1,3]
[1,6,2,5,8,4,3,7]=>0100110=>0110010=>[2,1,3,2]
[1,5,8,6,2,3,7,4]=>0011001=>1001100=>[1,3,1,3]
[5,2,7,1,8,6,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[1,2,8,3,7,6,5,4]=>0010111=>1110100=>[1,1,1,2,3]
[6,5,2,8,1,7,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[2,8,3,5,1,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[2,8,5,6,1,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[5,4,2,8,6,1,7,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,4,3,7,2,6,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,3,7,4,2,6,5,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,8,7,4,1,6,5,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,3,2,8,4,1,7,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,8,3,4,1,7,5,6]=>0101010=>0101010=>[2,2,2,2]
[5,4,2,8,3,1,7,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,8,6,4,1,7,5,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,4,7,6,2,5,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,8,7,6,1,5,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,3,8,5,2,1,6,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,3,8,4,2,1,6,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,5,4,3,8,2,1,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[5,4,2,3,8,1,6,7]=>1100100=>0010011=>[3,3,1,1]
[3,7,8,4,1,2,6,5]=>0011001=>1001100=>[1,3,1,3]
[8,7,4,6,3,5,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,3,4,8,2,1,5,6]=>1001100=>0011001=>[3,1,3,1]
[7,5,8,6,2,1,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,5,8,7,3,1,4,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,4,8,3,1,5,7,6]=>0011001=>1001100=>[1,3,1,3]
[6,3,2,4,8,1,5,7]=>1100100=>0010011=>[3,3,1,1]
[2,4,3,8,1,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[2,3,8,4,1,6,7,5]=>0011001=>1001100=>[1,3,1,3]
[8,3,4,7,2,5,6,1]=>1001001=>1001001=>[1,3,3,1]
[3,4,8,7,1,5,6,2]=>0011001=>1001100=>[1,3,1,3]
[2,5,3,8,1,6,4,7]=>0101010=>0101010=>[2,2,2,2]
[3,7,4,8,1,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[8,4,6,7,2,3,5,1]=>1001001=>1001001=>[1,3,3,1]
[2,6,8,5,1,3,7,4]=>0011001=>1001100=>[1,3,1,3]
[2,6,8,4,1,3,7,5]=>0011001=>1001100=>[1,3,1,3]
[3,7,5,8,1,4,2,6]=>0101010=>0101010=>[2,2,2,2]
[2,6,5,8,1,4,3,7]=>0101010=>0101010=>[2,2,2,2]
[2,5,8,3,1,4,7,6]=>0011001=>1001100=>[1,3,1,3]
[4,7,6,8,1,3,2,5]=>0101010=>0101010=>[2,2,2,2]
[5,6,8,7,1,3,4,2]=>0011001=>1001100=>[1,3,1,3]
[8,7,4,1,6,2,5,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,3,7,4,5,8,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[3,5,7,4,6,8,2,1]=>0010011=>1100100=>[1,1,3,3]
[6,8,4,1,7,2,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,5,4,6,7,2,1]=>0110011=>1100110=>[1,1,3,1,2]
[6,8,3,4,5,7,2,1]=>0100011=>1100010=>[1,1,4,2]
[2,5,7,4,6,3,8,1]=>0010101=>1010100=>[1,2,2,3]
[5,4,2,7,8,3,6,1]=>1100101=>1010011=>[1,2,3,1,1]
[8,1,6,2,4,3,5,7]=>1010100=>0010101=>[3,2,2,1]
[8,7,1,2,4,3,5,6]=>1100100=>0010011=>[3,3,1,1]
[6,8,3,1,4,7,2,5]=>0110010=>0100110=>[2,3,1,2]
[6,4,7,2,8,5,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[5,8,1,4,7,3,2,6]=>0100110=>0110010=>[2,1,3,2]
[8,7,1,4,5,3,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[1,7,6,2,4,3,5,8]=>0110100=>0010110=>[3,2,1,2]
[8,7,4,2,6,5,1,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,7,3,2,4,6,5,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[1,7,2,5,4,3,6,8]=>0101100=>0011010=>[3,1,2,2]
[6,8,4,3,7,5,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,4,7,3,8,5,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,3,7,2,4,8,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[8,1,2,5,4,3,6,7]=>1001100=>0011001=>[3,1,3,1]
[2,6,3,1,4,5,8,7]=>0110001=>1000110=>[1,4,1,2]
[4,7,3,2,5,6,1,8]=>0110010=>0100110=>[2,3,1,2]
[3,6,4,1,2,8,7,5]=>0110011=>1100110=>[1,1,3,1,2]
[3,6,5,1,8,2,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,5,1,8,7,2,3]=>0110110=>0110110=>[2,1,2,1,2]
[5,7,1,4,8,6,2,3]=>0100110=>0110010=>[2,1,3,2]
[5,7,1,3,8,2,6,4]=>0100101=>1010010=>[1,2,3,2]
[6,3,7,2,8,4,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,1,8,3,2,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[8,7,6,1,4,5,2,3]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,6,1,3,2,5,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,7,3,5,1,2,6,4]=>1101001=>1001011=>[1,3,2,1,1]
[8,7,4,5,1,6,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,6,4,1,7,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[8,4,6,2,3,1,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,5,4,2,1,7,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,1,6,8,4,5,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[7,5,1,6,4,2,3,8]=>1101100=>0011011=>[3,1,2,1,1]
[8,1,5,7,4,6,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[1,8,4,6,7,5,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[6,1,8,4,7,5,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,4,1,5,6,7,3,2]=>1100011=>1100011=>[1,1,4,1,1]
[8,2,5,6,1,4,7,3]=>1001001=>1001001=>[1,3,3,1]
[4,8,5,2,1,6,7,3]=>0111001=>1001110=>[1,3,1,1,2]
[1,8,4,6,2,5,3,7]=>0101010=>0101010=>[2,2,2,2]
[8,5,6,1,2,4,3,7]=>1010010=>0100101=>[2,3,2,1]
[2,8,3,1,5,6,7,4]=>0110001=>1000110=>[1,4,1,2]
[8,2,4,3,6,7,1,5]=>1010010=>0100101=>[2,3,2,1]
[8,3,2,7,1,5,6,4]=>1101001=>1001011=>[1,3,2,1,1]
[3,2,8,5,7,1,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,6,2,8,5,1,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[6,2,1,8,4,7,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,8,7,1,4,6,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[8,2,7,1,5,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,1,5,6,2,4,8]=>1100100=>0010011=>[3,3,1,1]
[2,7,3,6,5,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[7,2,8,1,6,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,2,6,4,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[8,7,2,4,1,6,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[1,2,8,6,3,7,5,4]=>0011011=>1101100=>[1,1,2,1,3]
[1,8,7,2,3,6,5,4]=>0110011=>1100110=>[1,1,3,1,2]
[1,7,8,2,6,4,3,5]=>0010110=>0110100=>[2,1,2,3]
[7,2,1,5,8,3,4,6]=>1100100=>0010011=>[3,3,1,1]
[7,1,5,8,3,2,4,6]=>1001100=>0011001=>[3,1,3,1]
[7,8,1,5,2,4,3,6]=>0101010=>0101010=>[2,2,2,2]
[8,7,1,2,5,4,3,6]=>1100110=>0110011=>[2,1,3,1,1]
[1,6,2,8,4,3,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[1,8,3,7,2,5,4,6]=>0101010=>0101010=>[2,2,2,2]
[8,1,4,7,3,2,5,6]=>1001100=>0011001=>[3,1,3,1]
[4,7,8,1,3,2,5,6]=>0010100=>0010100=>[3,2,3]
[2,1,8,3,5,7,4,6]=>1010010=>0100101=>[2,3,2,1]
[1,2,3,4,8,5,7,6]=>0000101=>1010000=>[1,2,5]
[8,3,5,2,4,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,2,5,3,1,7,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,7,2,5,6,4,1,8]=>0100110=>0110010=>[2,1,3,2]
[7,6,2,5,4,3,1,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,7,5,2,6,3,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[5,6,7,2,4,3,1,8]=>0010110=>0110100=>[2,1,2,3]
[1,8,3,4,2,7,5,6]=>0101010=>0101010=>[2,2,2,2]
[2,8,3,4,1,6,7,5]=>0101001=>1001010=>[1,3,2,2]
[7,8,2,4,3,1,6,5]=>0101101=>1011010=>[1,2,1,2,2]
[6,1,3,5,7,2,4,8]=>1000100=>0010001=>[3,4,1]
[8,1,3,6,2,4,7,5]=>1001001=>1001001=>[1,3,3,1]
[2,1,8,3,7,5,4,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,1,8,2,5,6,3,4]=>1010010=>0100101=>[2,3,2,1]
[6,1,5,8,2,7,3,4]=>1001010=>0101001=>[2,2,3,1]
[6,2,5,8,1,4,7,3]=>1001001=>1001001=>[1,3,3,1]
[2,3,8,1,5,6,7,4]=>0010001=>1000100=>[1,4,3]
[1,3,8,2,5,7,4,6]=>0010010=>0100100=>[2,3,3]
[2,8,7,1,6,4,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,7,1,5,6,4,2]=>0110011=>1100110=>[1,1,3,1,2]
[4,8,7,5,1,6,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,8,6,7,1,4,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,8,5,1,4,3,2]=>0011011=>1101100=>[1,1,2,1,3]
[5,6,3,8,4,1,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[7,3,8,5,4,1,6,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,4,8,5,6,1,7,2]=>0010101=>1010100=>[1,2,2,3]
[8,3,7,4,1,6,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,5,6,8,4,1,7,2]=>0001101=>1011000=>[1,2,1,4]
[5,6,4,7,8,1,3,2]=>0100101=>1010010=>[1,2,3,2]
[6,2,3,1,5,4,7,8]=>1010100=>0010101=>[3,2,2,1]
[8,5,1,3,2,4,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[7,5,1,3,2,6,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[3,6,4,1,5,2,7,8]=>0110100=>0010110=>[3,2,1,2]
[4,5,6,1,3,2,7,8]=>0010100=>0010100=>[3,2,3]
[6,7,1,4,2,5,3,8]=>0101010=>0101010=>[2,2,2,2]
[2,7,1,3,5,6,4,8]=>0100010=>0100010=>[2,4,2]
[8,6,1,2,4,3,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[7,8,1,2,5,3,6,4]=>0100101=>1010010=>[1,2,3,2]
[6,8,1,4,2,3,7,5]=>0101001=>1001010=>[1,3,2,2]
[4,5,8,1,2,3,7,6]=>0010001=>1000100=>[1,4,3]
[1,8,2,7,5,4,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[1,8,6,3,7,2,4,5]=>0110100=>0010110=>[3,2,1,2]
[1,8,5,3,4,7,2,6]=>0110010=>0100110=>[2,3,1,2]
[1,8,2,5,4,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[7,4,3,8,2,5,6,1]=>1101001=>1001011=>[1,3,2,1,1]
[7,2,8,4,3,5,6,1]=>1011001=>1001101=>[1,3,1,2,1]
[7,2,8,1,3,6,4,5]=>1010010=>0100101=>[2,3,2,1]
[1,4,7,5,2,6,8,3]=>0011001=>1001100=>[1,3,1,3]
[4,6,5,3,7,1,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,6,2,7,3,1,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,6,3,7,5,8,2,4]=>0101010=>0101010=>[2,2,2,2]
[5,2,4,8,1,3,7,6]=>1001001=>1001001=>[1,3,3,1]
[6,2,5,4,8,3,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,5,2,4,7,1,6,8]=>0100100=>0010010=>[3,3,2]
[6,4,5,3,8,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,5,3,4,8,7,1,2]=>1100110=>0110011=>[2,1,3,1,1]
[7,6,3,8,5,4,1,2]=>1101110=>0111011=>[2,1,1,2,1,1]
[5,4,8,1,2,7,3,6]=>1010010=>0100101=>[2,3,2,1]
[6,2,4,8,5,1,3,7]=>1001100=>0011001=>[3,1,3,1]
[7,6,3,8,5,1,2,4]=>1101100=>0011011=>[3,1,2,1,1]
[6,3,8,1,7,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[7,2,8,6,1,3,4,5]=>1011000=>0001101=>[4,1,2,1]
[7,2,8,6,1,5,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[3,2,4,7,8,1,5,6]=>1000100=>0010001=>[3,4,1]
[1,5,7,4,2,8,6,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,3,7,2,8,6,4,5]=>0010110=>0110100=>[2,1,2,3]
[1,5,3,6,8,2,7,4]=>0100101=>1010010=>[1,2,3,2]
[4,3,6,5,7,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[4,2,3,5,6,8,1,7]=>1000010=>0100001=>[2,5,1]
[4,2,6,7,3,8,5,1]=>1001011=>1101001=>[1,1,2,3,1]
[3,2,5,6,8,1,7,4]=>1000101=>1010001=>[1,2,4,1]
[4,2,3,6,8,1,5,7]=>1000100=>0010001=>[3,4,1]
[2,6,1,5,4,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[3,2,1,8,7,5,6,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,1,6,2,5,8,4,7]=>1010010=>0100101=>[2,3,2,1]
[6,5,1,3,4,8,2,7]=>1100010=>0100011=>[2,4,1,1]
[6,2,4,5,8,1,3,7]=>1000100=>0010001=>[3,4,1]
[2,6,1,5,8,3,4,7]=>0100100=>0010010=>[3,3,2]
[2,3,4,8,1,7,6,5]=>0001011=>1101000=>[1,1,2,4]
[6,3,1,7,8,4,5,2]=>1100101=>1010011=>[1,2,3,1,1]
[6,2,7,8,4,5,1,3]=>1001010=>0101001=>[2,2,3,1]
[3,1,4,8,7,6,2,5]=>1001110=>0111001=>[2,1,1,3,1]
[2,3,6,5,8,7,1,4]=>0010110=>0110100=>[2,1,2,3]
[8,4,1,2,7,6,3,5]=>1100110=>0110011=>[2,1,3,1,1]
[3,4,8,2,7,5,1,6]=>0010110=>0110100=>[2,1,2,3]
[6,3,2,8,5,7,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,2,6,8,5,1,7,4]=>1001101=>1011001=>[1,2,1,3,1]
[5,2,4,1,7,8,6,3]=>1010011=>1100101=>[1,1,3,2,1]
[3,8,4,7,2,5,6,1]=>0101001=>1001010=>[1,3,2,2]
[1,8,7,2,4,5,6,3]=>0110001=>1000110=>[1,4,1,2]
[5,3,4,7,1,8,6,2]=>1001011=>1101001=>[1,1,2,3,1]
[5,3,7,1,6,2,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,7,6,5,8,2,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[7,5,1,2,6,8,4,3]=>1100011=>1100011=>[1,1,4,1,1]
[1,2,5,3,8,7,6,4]=>0010111=>1110100=>[1,1,1,2,3]
[2,8,1,5,6,3,7,4]=>0100101=>1010010=>[1,2,3,2]
[4,8,2,3,6,7,1,5]=>0100010=>0100010=>[2,4,2]
[8,2,4,6,7,1,3,5]=>1000100=>0010001=>[3,4,1]
[3,7,5,1,8,4,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[6,5,3,1,8,4,2,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[5,7,4,3,8,6,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,2,3,8,5,6,1,7]=>1001010=>0101001=>[2,2,3,1]
[3,6,4,2,8,5,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[4,7,3,2,5,1,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[2,4,8,7,1,3,5,6]=>0011000=>0001100=>[4,1,3]
[2,4,3,5,1,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[8,6,1,2,4,3,5,7]=>1100100=>0010011=>[3,3,1,1]
[8,6,2,5,4,1,3,7]=>1101100=>0011011=>[3,1,2,1,1]
[8,3,5,7,6,2,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[6,7,5,3,8,2,4,1]=>0110101=>1010110=>[1,2,2,1,2]
[8,2,6,3,4,5,1,7]=>1010010=>0100101=>[2,3,2,1]
[8,1,5,4,3,6,2,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,6,4,2,1,5,3,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,3,2,4,6,1,5,7]=>1100100=>0010011=>[3,3,1,1]
[8,2,3,4,7,6,1,5]=>1000110=>0110001=>[2,1,4,1]
[5,7,1,8,3,4,6,2]=>0101001=>1001010=>[1,3,2,2]
[1,5,6,7,3,4,8,2]=>0001001=>1001000=>[1,3,4]
[4,8,1,2,7,3,6,5]=>0100101=>1010010=>[1,2,3,2]
[2,5,7,8,4,1,3,6]=>0001100=>0011000=>[3,1,4]
[6,3,5,8,7,2,4,1]=>1001101=>1011001=>[1,2,1,3,1]
[5,2,8,7,1,3,4,6]=>1011000=>0001101=>[4,1,2,1]
[5,2,7,4,8,1,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,4,2,5,6,1]=>1011001=>1001101=>[1,3,1,2,1]
[8,1,7,4,5,2,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,7,8,3,5,4,6,2]=>0010101=>1010100=>[1,2,2,3]
[4,6,3,5,8,1,7,2]=>0100101=>1010010=>[1,2,3,2]
[8,2,4,1,5,6,7,3]=>1010001=>1000101=>[1,4,2,1]
[3,5,1,7,6,8,2,4]=>0101010=>0101010=>[2,2,2,2]
[2,1,7,6,4,5,8,3]=>1011001=>1001101=>[1,3,1,2,1]
[1,7,6,5,2,4,8,3]=>0111001=>1001110=>[1,3,1,1,2]
[5,1,7,6,2,8,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,6,2,5,3,8,7,1]=>0101011=>1101010=>[1,1,2,2,2]
[8,6,4,2,3,1,7,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,4,2,1,3,7,5]=>1111001=>1001111=>[1,3,1,1,1,1]
[4,2,8,3,1,5,6,7]=>1011000=>0001101=>[4,1,2,1]
[2,5,7,3,8,4,6,1]=>0010101=>1010100=>[1,2,2,3]
[4,2,7,1,8,5,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[1,3,7,5,8,6,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[2,7,4,5,8,3,6,1]=>0100101=>1010010=>[1,2,3,2]
[3,5,7,1,4,8,6,2]=>0010011=>1100100=>[1,1,3,3]
[3,4,1,2,8,5,7,6]=>0100101=>1010010=>[1,2,3,2]
[6,2,3,1,4,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[8,4,3,2,5,7,1,6]=>1110010=>0100111=>[2,3,1,1,1]
[5,3,6,8,2,1,4,7]=>1001100=>0011001=>[3,1,3,1]
[3,2,6,8,5,4,1,7]=>1001110=>0111001=>[2,1,1,3,1]
[7,3,8,2,5,4,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,2,5,8,3,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[3,1,2,8,5,6,4,7]=>1001010=>0101001=>[2,2,3,1]
[5,2,1,6,8,3,4,7]=>1100100=>0010011=>[3,3,1,1]
[3,1,8,6,5,4,2,7]=>1011110=>0111101=>[2,1,1,1,2,1]
[5,6,8,1,4,3,2,7]=>0010110=>0110100=>[2,1,2,3]
[6,4,8,3,7,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,7,3,6,2,1,8,5]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,4,1,5,3,2,6]=>0110110=>0110110=>[2,1,2,1,2]
[7,3,8,5,1,4,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,5,4,8,3,7,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,7,8,3,1,6,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[8,7,5,3,6,4,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[4,6,1,3,8,7,5,2]=>0100111=>1110010=>[1,1,1,3,2]
[3,1,2,7,5,6,8,4]=>1001001=>1001001=>[1,3,3,1]
[3,6,1,2,7,5,8,4]=>0100101=>1010010=>[1,2,3,2]
[3,6,2,5,8,7,4,1]=>0100111=>1110010=>[1,1,1,3,2]
[8,5,2,3,6,7,4,1]=>1100011=>1100011=>[1,1,4,1,1]
[6,7,1,3,2,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[6,2,7,1,3,4,8,5]=>1010001=>1000101=>[1,4,2,1]
[5,2,1,7,3,8,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,7,2,6,3,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,8,2,6,3,7,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,7,2,4,6,1,8,5]=>0100101=>1010010=>[1,2,3,2]
[5,3,7,2,8,1,4,6]=>1010100=>0010101=>[3,2,2,1]
[7,1,8,3,4,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[7,2,4,1,8,3,5,6]=>1010100=>0010101=>[3,2,2,1]
[4,8,7,6,3,2,1,5]=>0111110=>0111110=>[2,1,1,1,1,2]
[7,3,8,2,6,5,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,8,2,4,6,1,5,3]=>0100101=>1010010=>[1,2,3,2]
[3,5,1,8,7,2,6,4]=>0101101=>1011010=>[1,2,1,2,2]
[5,2,8,1,7,6,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,1,3,8,7,5,4]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,7,8,1,2,5,4,3]=>0010011=>1100100=>[1,1,3,3]
[5,8,7,1,6,4,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,8,7,5,1,4,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,6,4,3,2,1,7,5]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[6,5,4,3,8,2,7,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,5,4,3,2,8,6,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[8,5,4,3,7,2,1,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,4,3,2,1,7,6,5]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[3,7,5,8,1,4,6,2]=>0101001=>1001010=>[1,3,2,2]
[4,7,5,8,3,2,1,6]=>0101110=>0111010=>[2,1,1,2,2]
[5,7,2,3,6,1,8,4]=>0100101=>1010010=>[1,2,3,2]
[7,3,1,4,8,2,5,6]=>1100100=>0010011=>[3,3,1,1]
[7,4,1,2,5,8,3,6]=>1100010=>0100011=>[2,4,1,1]
[4,7,1,6,5,8,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[2,7,5,4,3,8,1,6]=>0111010=>0101110=>[2,2,1,1,2]
[8,6,4,2,3,7,5,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,6,4,2,3,8,1,5]=>1110010=>0100111=>[2,3,1,1,1]
[6,4,7,1,3,8,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[3,1,2,4,8,7,6,5]=>1000111=>1110001=>[1,1,1,4,1]
[6,5,8,7,3,1,2,4]=>1011100=>0011101=>[3,1,1,2,1]
[5,6,7,8,1,4,2,3]=>0001010=>0101000=>[2,2,4]
[2,6,7,4,5,3,1,8]=>0010110=>0110100=>[2,1,2,3]
[1,3,7,4,2,8,5,6]=>0011010=>0101100=>[2,2,1,3]
[4,6,1,3,7,2,5,8]=>0100100=>0010010=>[3,3,2]
[6,5,7,8,3,1,4,2]=>1001101=>1011001=>[1,2,1,3,1]
[7,5,8,6,2,1,3,4]=>1011100=>0011101=>[3,1,1,2,1]
[2,8,1,3,6,5,4,7]=>0100110=>0110010=>[2,1,3,2]
[2,8,7,3,5,4,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[3,4,2,6,8,7,1,5]=>0100110=>0110010=>[2,1,3,2]
[6,1,4,2,7,8,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[7,3,8,4,1,2,6,5]=>1011001=>1001101=>[1,3,1,2,1]
[6,8,3,2,7,1,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,1,4,3,6,2,7,8]=>1010100=>0010101=>[3,2,2,1]
[4,8,5,6,3,2,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[2,8,5,6,3,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,1,4,2,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,2,6,7,4,8,1,5]=>1001010=>0101001=>[2,2,3,1]
[3,7,1,2,4,6,5,8]=>0100010=>0100010=>[2,4,2]
[4,1,8,2,6,3,5,7]=>1010100=>0010101=>[3,2,2,1]
[7,5,6,8,2,1,4,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,8,6,7,1,2,3,4]=>0101000=>0001010=>[4,2,2]
[4,8,1,5,7,2,3,6]=>0100100=>0010010=>[3,3,2]
[3,5,1,4,7,6,8,2]=>0100101=>1010010=>[1,2,3,2]
[5,3,2,7,1,6,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[8,4,3,7,5,1,6,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,1,7,2,4,6,8,3]=>1010001=>1000101=>[1,4,2,1]
[4,5,7,1,2,6,8,3]=>0010001=>1000100=>[1,4,3]
[5,4,1,7,3,6,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[3,6,4,7,5,2,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,4,7,6,2,5,8,1]=>0011001=>1001100=>[1,3,1,3]
[4,8,3,6,5,2,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[1,8,6,5,4,2,3,7]=>0111100=>0011110=>[3,1,1,1,2]
[8,1,7,4,2,5,6,3]=>1011001=>1001101=>[1,3,1,2,1]
[1,8,7,2,5,3,4,6]=>0110100=>0010110=>[3,2,1,2]
[4,8,1,5,2,6,3,7]=>0101010=>0101010=>[2,2,2,2]
[3,6,8,5,1,2,4,7]=>0011000=>0001100=>[4,1,3]
[1,5,2,7,8,4,6,3]=>0100101=>1010010=>[1,2,3,2]
[6,7,2,8,5,3,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[6,7,2,8,3,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[7,1,2,8,3,5,6,4]=>1001001=>1001001=>[1,3,3,1]
[6,7,5,2,8,1,4,3]=>0110101=>1010110=>[1,2,2,1,2]
[7,1,4,5,8,6,2,3]=>1000110=>0110001=>[2,1,4,1]
[3,1,4,6,7,8,5,2]=>1000011=>1100001=>[1,1,5,1]
[5,7,6,4,2,8,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[7,4,6,1,8,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[3,4,5,1,6,8,7,2]=>0010011=>1100100=>[1,1,3,3]
[5,1,6,8,4,2,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[7,4,8,2,3,6,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[7,5,8,6,3,4,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,7,8,3,1,6,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[7,5,8,3,2,4,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,4,1,8,2,5,7,3]=>1101001=>1001011=>[1,3,2,1,1]
[5,8,2,6,3,1,4,7]=>0101100=>0011010=>[3,1,2,2]
[3,6,5,1,8,4,7,2]=>0110101=>1010110=>[1,2,2,1,2]
[8,2,7,5,4,1,3,6]=>1011100=>0011101=>[3,1,1,2,1]
[6,8,5,2,3,4,1,7]=>0110010=>0100110=>[2,3,1,2]
[2,6,8,7,1,5,3,4]=>0011010=>0101100=>[2,2,1,3]
[7,5,1,6,2,8,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,2,7,3,8,4,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[3,7,2,4,8,5,1,6]=>0100110=>0110010=>[2,1,3,2]
[1,5,2,6,3,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,6,2,4,8,7,5]=>0010011=>1100100=>[1,1,3,3]
[7,3,5,2,4,1,6,8]=>1010100=>0010101=>[3,2,2,1]
[8,3,6,2,5,4,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[3,5,8,2,4,6,1,7]=>0010010=>0100100=>[2,3,3]
[6,4,7,8,2,3,1,5]=>1001010=>0101001=>[2,2,3,1]
[7,4,8,5,3,2,1,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[1,5,3,2,8,4,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,7,3,5,1,4,6]=>0110100=>0010110=>[3,2,1,2]
[3,8,4,7,5,1,2,6]=>0101100=>0011010=>[3,1,2,2]
[6,1,2,7,3,8,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,7,3,4,8,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[8,3,1,6,7,2,5,4]=>1100101=>1010011=>[1,2,3,1,1]
[4,8,3,7,1,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[1,3,5,8,2,4,7,6]=>0001001=>1001000=>[1,3,4]
[5,3,7,2,1,4,6,8]=>1011000=>0001101=>[4,1,2,1]
[6,4,2,8,3,1,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[5,7,2,3,8,1,4,6]=>0100100=>0010010=>[3,3,2]
[6,4,7,5,8,1,2,3]=>1010100=>0010101=>[3,2,2,1]
[8,6,4,2,1,7,5,3]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[7,4,2,1,5,8,6,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,6,4,1,8,5,2,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[1,6,4,8,7,5,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[6,3,1,2,8,4,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[3,6,1,8,2,4,7,5]=>0101001=>1001010=>[1,3,2,2]
[6,4,1,8,3,2,7,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,4,8,7,2,6,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[5,4,1,8,7,3,2,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[5,8,4,1,7,6,2,3]=>0110110=>0110110=>[2,1,2,1,2]
[8,6,1,7,5,4,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[3,1,8,7,6,5,2,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,1,2,4,5,3,6,7]=>1000100=>0010001=>[3,4,1]
[1,8,7,6,4,5,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,6,8,1,3,7,5,4]=>0010011=>1100100=>[1,1,3,3]
[2,4,8,1,5,7,6,3]=>0010011=>1100100=>[1,1,3,3]
[3,2,8,6,1,7,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,2,8,3,1,7,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,4,3,8,5,2,1,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,5,2,8,4,3,1,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,3,8,7,5,1,6,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,2,3,8,5,1,6,7]=>1001100=>0011001=>[3,1,3,1]
[4,2,8,5,1,7,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,4,2,8,5,6,1,7]=>0101010=>0101010=>[2,2,2,2]
[3,2,4,8,6,1,5,7]=>1001100=>0011001=>[3,1,3,1]
[3,2,5,8,6,1,4,7]=>1001100=>0011001=>[3,1,3,1]
[8,4,3,7,5,2,6,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,3,7,8,5,1,2,6]=>1001100=>0011001=>[3,1,3,1]
[4,2,6,8,5,1,3,7]=>1001100=>0011001=>[3,1,3,1]
[3,5,2,8,4,6,1,7]=>0101010=>0101010=>[2,2,2,2]
[5,2,6,8,4,1,3,7]=>1001100=>0011001=>[3,1,3,1]
[5,3,7,8,4,1,2,6]=>1001100=>0011001=>[3,1,3,1]
[5,6,2,8,3,4,1,7]=>0101010=>0101010=>[2,2,2,2]
[5,3,8,7,4,1,6,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,4,2,8,5,3,1,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,7,5,3,6,2,4,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,7,4,3,6,2,5,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,5,3,7,2,4,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,6,4,3,8,2,5,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,4,5,3,8,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,5,3,8,2,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,6,3,8,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,6,3,7,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,6,3,7,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,3,5,2,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,3,4,2,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,8,4,3,2,6,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,5,8,3,4,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,8,3,4,2,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,8,3,5,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,8,4,6,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,8,3,6,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,8,3,6,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,8,3,5,2,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,8,3,5,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,7,3,6,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,8,3,7,2,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,8,3,7,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,8,4,7,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,8,4,7,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,5,7,3,8,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,6,3,8,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,3,7,8,2,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[6,5,4,2,8,7,1,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,4,3,7,5,2,1,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,3,7,8,5,2,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[6,3,7,2,5,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[6,3,2,7,5,4,1,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,8,2,6,3,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,1,2,7,3,6]=>0110010=>0100110=>[2,3,1,2]
[5,4,8,1,2,3,7,6]=>1010001=>1000101=>[1,4,2,1]
[1,4,7,6,3,2,5,8]=>0011100=>0011100=>[3,1,1,3]
[4,8,3,2,7,6,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[5,8,1,7,4,2,3,6]=>0101100=>0011010=>[3,1,2,2]
[4,8,6,7,2,3,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,8,7,3,6,2,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[4,3,8,2,7,1,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,7,3,2,5,6]=>1011100=>0011101=>[3,1,1,2,1]
[4,7,8,1,2,5,3,6]=>0010010=>0100100=>[2,3,3]
[4,7,5,1,2,8,3,6]=>0110010=>0100110=>[2,3,1,2]
[2,3,6,7,4,1,8,5]=>0001101=>1011000=>[1,2,1,4]
[2,6,3,4,7,8,1,5]=>0100010=>0100010=>[2,4,2]
[3,1,7,8,4,2,5,6]=>1001100=>0011001=>[3,1,3,1]
[4,3,1,2,8,5,7,6]=>1100101=>1010011=>[1,2,3,1,1]
[3,7,6,8,4,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[4,7,1,8,5,2,3,6]=>0101100=>0011010=>[3,1,2,2]
[2,6,8,7,4,3,1,5]=>0011110=>0111100=>[2,1,1,1,3]
[3,7,8,6,2,4,1,5]=>0011010=>0101100=>[2,2,1,3]
[3,7,8,2,6,4,1,5]=>0010110=>0110100=>[2,1,2,3]
[4,2,3,8,1,6,7,5]=>1001001=>1001001=>[1,3,3,1]
[3,7,2,8,4,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,2,8,3,6,1,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,8,6,3,1,7,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,6,8,4,7,3,1,5]=>0010110=>0110100=>[2,1,2,3]
[2,4,6,8,3,1,7,5]=>0001101=>1011000=>[1,2,1,4]
[3,7,2,4,8,6,1,5]=>0100110=>0110010=>[2,1,3,2]
[1,3,6,4,7,2,5,8]=>0010100=>0010100=>[3,2,3]
[2,4,6,3,8,1,7,5]=>0010101=>1010100=>[1,2,2,3]
[2,6,4,3,8,7,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[2,4,3,6,1,8,7,5]=>0101011=>1101010=>[1,1,2,2,2]
[3,1,7,4,8,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[2,6,3,7,4,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[1,3,5,7,6,8,2,4]=>0001010=>0101000=>[2,2,4]
[1,3,5,7,6,2,8,4]=>0001101=>1011000=>[1,2,1,4]
[1,3,5,7,2,6,8,4]=>0001001=>1001000=>[1,3,4]
[1,3,5,2,7,6,8,4]=>0010101=>1010100=>[1,2,2,3]
[1,3,5,2,7,6,4,8]=>0010110=>0110100=>[2,1,2,3]
[1,3,5,7,6,2,4,8]=>0001100=>0011000=>[3,1,4]
[1,3,5,7,4,6,8,2]=>0001001=>1001000=>[1,3,4]
[1,3,5,7,4,6,2,8]=>0001010=>0101000=>[2,2,4]
[1,3,5,7,4,2,6,8]=>0001100=>0011000=>[3,1,4]
[1,3,5,4,7,2,6,8]=>0010100=>0010100=>[3,2,3]
[1,3,5,4,7,8,2,6]=>0010010=>0100100=>[2,3,3]
[1,3,5,4,7,2,8,6]=>0010101=>1010100=>[1,2,2,3]
[1,3,5,7,4,2,8,6]=>0001101=>1011000=>[1,2,1,4]
[1,3,5,7,4,8,2,6]=>0001010=>0101000=>[2,2,4]
[1,3,5,7,4,8,6,2]=>0001011=>1101000=>[1,1,2,4]
[1,3,5,7,8,4,6,2]=>0000101=>1010000=>[1,2,5]
[1,3,5,7,8,4,2,6]=>0000110=>0110000=>[2,1,5]
[1,3,5,2,7,8,6,4]=>0010011=>1100100=>[1,1,3,3]
[1,3,5,7,2,8,6,4]=>0001011=>1101000=>[1,1,2,4]
[1,3,5,7,8,2,6,4]=>0000101=>1010000=>[1,2,5]
[1,3,5,7,8,6,2,4]=>0000110=>0110000=>[2,1,5]
[2,3,6,1,7,8,5,4]=>0010011=>1100100=>[1,1,3,3]
[2,3,7,1,4,8,6,5]=>0010011=>1100100=>[1,1,3,3]
[2,6,1,3,7,8,5,4]=>0100011=>1100010=>[1,1,4,2]
[2,3,6,8,4,5,1,7]=>0001010=>0101000=>[2,2,4]
[2,5,7,3,4,8,6,1]=>0010011=>1100100=>[1,1,3,3]
[2,6,7,3,4,8,5,1]=>0010011=>1100100=>[1,1,3,3]
[6,5,2,4,3,7,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[2,5,4,6,7,1,3,8]=>0100100=>0010010=>[3,3,2]
[1,7,6,3,5,4,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[2,4,6,3,7,5,1,8]=>0010110=>0110100=>[2,1,2,3]
[4,7,2,3,5,6,1,8]=>0100010=>0100010=>[2,4,2]
[5,3,2,7,4,6,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[1,6,8,5,7,3,4,2]=>0010101=>1010100=>[1,2,2,3]
[4,1,2,5,8,3,7,6]=>1000101=>1010001=>[1,2,4,1]
[4,6,1,2,5,8,3,7]=>0100010=>0100010=>[2,4,2]
[4,1,7,2,6,5,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,6,7,2,1,4,8,3]=>0011001=>1001100=>[1,3,1,3]
[6,4,5,7,1,3,8,2]=>1001001=>1001001=>[1,3,3,1]
[6,8,5,2,4,1,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[5,7,6,8,1,4,2,3]=>0101010=>0101010=>[2,2,2,2]
[4,1,6,2,8,5,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,4,2,3,6,8,5]=>1010001=>1000101=>[1,4,2,1]
[6,4,2,1,3,8,7,5]=>1110011=>1100111=>[1,1,3,1,1,1]
[1,5,8,3,4,6,7,2]=>0010001=>1000100=>[1,4,3]
[8,1,2,3,4,6,7,5]=>1000001=>1000001=>[1,6,1]
[2,8,1,3,5,4,7,6]=>0100101=>1010010=>[1,2,3,2]
[8,7,1,4,3,5,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,3,2,1,4,5,7,6]=>1110001=>1000111=>[1,4,1,1,1]
[4,3,2,8,1,6,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[3,8,6,4,2,1,5,7]=>0111100=>0011110=>[3,1,1,1,2]
[3,8,2,1,5,6,4,7]=>0110010=>0100110=>[2,3,1,2]
[8,5,2,4,3,1,6,7]=>1101100=>0011011=>[3,1,2,1,1]
[8,3,2,5,4,1,6,7]=>1101100=>0011011=>[3,1,2,1,1]
[6,1,2,7,5,3,8,4]=>1001101=>1011001=>[1,2,1,3,1]
[2,6,1,4,7,3,8,5]=>0100101=>1010010=>[1,2,3,2]
[7,3,2,8,6,4,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,8,2,5,3,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,3,7,5,1,8,2,4]=>1011010=>0101101=>[2,2,1,2,1]
[8,1,6,3,5,7,2,4]=>1010010=>0100101=>[2,3,2,1]
[8,3,2,6,4,7,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,8,4,6,1,7,2,3]=>0101010=>0101010=>[2,2,2,2]
[8,4,2,5,6,7,1,3]=>1100010=>0100011=>[2,4,1,1]
[2,3,8,7,6,5,1,4]=>0011110=>0111100=>[2,1,1,1,3]
[1,5,8,7,2,6,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[2,5,8,7,3,6,1,4]=>0011010=>0101100=>[2,2,1,3]
[4,1,8,7,2,6,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,2,8,7,3,6,5,4]=>0011011=>1101100=>[1,1,2,1,3]
[4,5,8,7,1,2,6,3]=>0011001=>1001100=>[1,3,1,3]
[1,5,8,7,3,2,6,4]=>0011101=>1011100=>[1,2,1,1,3]
[4,5,8,7,3,2,1,6]=>0011110=>0111100=>[2,1,1,1,3]
[2,6,8,1,7,5,4,3]=>0010111=>1110100=>[1,1,1,2,3]
[2,6,8,3,7,5,1,4]=>0010110=>0110100=>[2,1,2,3]
[1,6,8,4,7,2,5,3]=>0010101=>1010100=>[1,2,2,3]
[1,6,8,3,7,2,5,4]=>0010101=>1010100=>[1,2,2,3]
[2,5,8,1,7,6,4,3]=>0010111=>1110100=>[1,1,1,2,3]
[2,5,8,3,7,6,1,4]=>0010110=>0110100=>[2,1,2,3]
[3,2,8,4,7,6,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[1,5,8,4,7,2,6,3]=>0010101=>1010100=>[1,2,2,3]
[1,5,8,3,7,2,6,4]=>0010101=>1010100=>[1,2,2,3]
[3,1,8,4,7,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,6,8,1,2,7,4,3]=>0010011=>1100100=>[1,1,3,3]
[1,6,8,2,3,7,5,4]=>0010011=>1100100=>[1,1,3,3]
[1,5,8,4,2,7,6,3]=>0011011=>1101100=>[1,1,2,1,3]
[5,6,8,4,3,2,1,7]=>0011110=>0111100=>[2,1,1,1,3]
[7,1,4,8,6,2,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[7,3,4,8,6,2,1,5]=>1001110=>0111001=>[2,1,1,3,1]
[7,1,5,8,2,6,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,4,8,2,6,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[7,4,5,8,1,2,6,3]=>1001001=>1001001=>[1,3,3,1]
[3,6,2,8,7,5,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[1,6,4,8,7,2,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,2,4,8,7,6,1,5]=>1001110=>0111001=>[2,1,1,3,1]
[1,4,5,8,7,2,6,3]=>0001101=>1011000=>[1,2,1,4]
[3,1,4,8,7,2,6,5]=>1001101=>1011001=>[1,2,1,3,1]
[1,6,5,8,2,7,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,5,8,3,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[1,6,4,8,2,7,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,1,8,3,7,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,4,5,8,3,2,7,6]=>0001101=>1011000=>[1,2,1,4]
[4,6,5,8,3,2,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[7,6,2,3,8,5,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[7,6,1,4,8,2,5,3]=>1100101=>1010011=>[1,2,3,1,1]
[7,6,3,4,8,2,1,5]=>1100110=>0110011=>[2,1,3,1,1]
[7,2,5,3,8,6,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,1,4,8,6,5,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,2,1,3,8,6,5,4]=>1100111=>1110011=>[1,1,1,3,1,1]
[2,6,5,3,8,7,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[2,6,1,4,8,7,5,3]=>0100111=>1110010=>[1,1,1,3,2]
[1,3,5,4,8,2,7,6]=>0010101=>1010100=>[1,2,2,3]
[7,6,5,1,2,8,4,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,1,5,2,3,8,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[7,1,2,4,3,8,6,5]=>1001011=>1101001=>[1,1,2,3,1]
[7,2,5,4,3,8,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,6,2,4,3,8,7,5]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,5,4,3,8,1,7]=>0111010=>0101110=>[2,2,1,1,2]
[7,6,5,1,3,2,8,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,2,7,6,5,4,1,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,2,8,6,5,4,3,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[3,2,8,7,6,5,1,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,8,7,6,5,3,1,2]=>0111110=>0111110=>[2,1,1,1,1,2]
[7,8,6,1,5,4,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,8,5,7,6,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[3,2,4,6,8,1,5,7]=>1000100=>0010001=>[3,4,1]
[3,5,7,2,4,8,1,6]=>0010010=>0100100=>[2,3,3]
[3,5,7,2,4,6,8,1]=>0010001=>1000100=>[1,4,3]
[4,5,1,3,6,8,2,7]=>0100010=>0100010=>[2,4,2]
[4,3,5,7,2,6,8,1]=>1001001=>1001001=>[1,3,3,1]
[4,3,5,1,7,8,2,6]=>1010010=>0100101=>[2,3,2,1]
[4,6,3,5,1,7,8,2]=>0101001=>1001010=>[1,3,2,2]
[4,6,3,5,7,2,8,1]=>0100101=>1010010=>[1,2,3,2]
[5,1,6,7,3,4,8,2]=>1001001=>1001001=>[1,3,3,1]
[1,6,7,3,4,5,8,2]=>0010001=>1000100=>[1,4,3]
[2,6,7,4,5,8,1,3]=>0010010=>0100100=>[2,3,3]
[2,6,7,4,8,1,3,5]=>0010100=>0010100=>[3,2,3]
[1,4,6,7,3,8,2,5]=>0001010=>0101000=>[2,2,4]
[3,5,2,6,7,4,8,1]=>0100101=>1010010=>[1,2,3,2]
[6,3,1,7,8,2,4,5]=>1100100=>0010011=>[3,3,1,1]
[5,7,2,8,1,3,4,6]=>0101000=>0001010=>[4,2,2]
[6,3,7,2,8,1,4,5]=>1010100=>0010101=>[3,2,2,1]
[6,3,7,2,5,8,1,4]=>1010010=>0100101=>[2,3,2,1]
[6,2,4,5,7,3,8,1]=>1000101=>1010001=>[1,2,4,1]
[2,4,6,7,1,5,8,3]=>0001001=>1001000=>[1,3,4]
[2,4,7,1,5,6,8,3]=>0010001=>1000100=>[1,4,3]
[3,7,1,5,6,8,2,4]=>0100010=>0100010=>[2,4,2]
[4,6,7,1,2,5,8,3]=>0010001=>1000100=>[1,4,3]
[1,5,6,7,2,4,8,3]=>0001001=>1001000=>[1,3,4]
[5,6,2,4,1,7,8,3]=>0101001=>1001010=>[1,3,2,2]
[1,5,4,6,2,7,8,3]=>0101001=>1001010=>[1,3,2,2]
[5,6,4,7,1,3,8,2]=>0101001=>1001010=>[1,3,2,2]
[8,4,5,2,6,1,3,7]=>1010100=>0010101=>[3,2,2,1]
[6,4,3,7,2,5,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[6,4,3,7,2,8,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,5,3,1,6,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[6,4,3,7,5,1,8,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,6,3,7,4,1,8,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,7,4,2,1,5,8,3]=>0111001=>1001110=>[1,3,1,1,2]
[6,7,4,2,1,8,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[5,6,7,3,1,8,2,4]=>0011010=>0101100=>[2,2,1,3]
[5,6,3,7,8,1,2,4]=>0100100=>0010010=>[3,3,2]
[5,6,3,7,2,4,8,1]=>0101001=>1001010=>[1,3,2,2]
[5,6,7,2,3,8,1,4]=>0010010=>0100100=>[2,3,3]
[5,6,7,2,8,1,3,4]=>0010100=>0010100=>[3,2,3]
[6,7,3,8,1,2,4,5]=>0101000=>0001010=>[4,2,2]
[6,7,3,2,8,1,4,5]=>0110100=>0010110=>[3,2,1,2]
[7,6,4,2,1,3,8,5]=>1111001=>1001111=>[1,3,1,1,1,1]
[7,6,3,4,1,2,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[7,6,3,2,4,1,8,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,5,3,2,6,1,8,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,5,3,2,7,8,1,4]=>1110010=>0100111=>[2,3,1,1,1]
[6,4,7,2,5,1,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,7,5,1,2,8,3]=>1011001=>1001101=>[1,3,1,2,1]
[5,6,4,2,7,3,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,5,3,7,1,8,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,7,2,1,4,8,3]=>1011001=>1001101=>[1,3,1,2,1]
[5,4,6,7,3,1,8,2]=>1001101=>1011001=>[1,2,1,3,1]
[5,7,8,3,6,4,1,2]=>0010110=>0110100=>[2,1,2,3]
[3,7,8,5,6,4,1,2]=>0010110=>0110100=>[2,1,2,3]
[3,7,8,5,6,1,4,2]=>0010101=>1010100=>[1,2,2,3]
[1,7,8,5,6,3,4,2]=>0010101=>1010100=>[1,2,2,3]
[1,7,5,8,6,3,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[3,7,5,8,6,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[3,7,5,8,6,4,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[5,7,3,8,6,4,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[7,3,8,5,6,4,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,5,8,6,4,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[3,5,7,8,6,4,1,2]=>0001110=>0111000=>[2,1,1,4]
[1,5,7,8,6,3,4,2]=>0001101=>1011000=>[1,2,1,4]
[1,5,7,8,3,6,4,2]=>0001011=>1101000=>[1,1,2,4]
[5,3,7,8,1,6,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[5,3,7,8,6,1,4,2]=>1001101=>1011001=>[1,2,1,3,1]
[7,3,5,8,6,1,4,2]=>1001101=>1011001=>[1,2,1,3,1]
[7,3,8,5,6,1,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,3,5,6,1,4,2]=>0100101=>1010010=>[1,2,3,2]
[7,8,1,5,6,3,4,2]=>0100101=>1010010=>[1,2,3,2]
[7,1,8,5,6,3,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,5,8,6,3,4,2]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,7,8,6,3,4,2]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,7,8,3,6,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[3,1,7,8,5,6,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[1,3,7,8,5,6,4,2]=>0001011=>1101000=>[1,1,2,4]
[3,1,7,5,8,6,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,1,7,3,8,6,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,1,5,3,8,6,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,1,5,8,3,6,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[7,8,1,5,3,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[7,8,3,5,1,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[7,3,8,5,1,6,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,3,5,8,1,6,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[7,3,5,1,8,6,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,3,7,1,8,6,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,5,7,1,8,6,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[1,5,7,3,8,6,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[1,7,5,3,8,6,4,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,7,5,1,8,6,4,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,7,3,1,8,6,4,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,7,3,8,6,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[3,7,5,8,1,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,7,5,8,3,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,7,8,5,3,6,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[3,7,8,5,1,6,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[5,7,8,3,6,1,4,2]=>0010101=>1010100=>[1,2,2,3]
[5,7,8,6,3,1,4,2]=>0011101=>1011100=>[1,2,1,1,3]
[7,5,8,6,1,3,4,2]=>1011001=>1001101=>[1,3,1,2,1]
[5,7,8,1,6,3,4,2]=>0010101=>1010100=>[1,2,2,3]
[5,7,8,1,3,6,4,2]=>0010011=>1100100=>[1,1,3,3]
[1,7,8,3,5,6,4,2]=>0010011=>1100100=>[1,1,3,3]
[1,7,3,8,5,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,7,1,8,5,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[5,7,1,8,3,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[5,7,1,8,6,3,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[7,5,1,8,6,3,4,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,5,8,1,6,3,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,5,1,6,3,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[7,8,5,1,3,6,4,2]=>0110011=>1100110=>[1,1,3,1,2]
[7,5,8,1,3,6,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[7,5,1,8,3,6,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,5,1,3,8,6,4,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[5,7,1,3,8,6,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[3,7,1,5,8,6,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[1,7,3,5,8,6,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[1,5,3,7,8,6,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[3,5,1,7,8,6,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[5,3,1,7,8,6,4,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,3,1,5,8,6,4,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,3,1,8,5,6,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,8,1,3,5,6,4,2]=>0100011=>1100010=>[1,1,4,2]
[7,1,8,3,5,6,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[7,1,3,8,5,6,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,3,5,8,6,4,2]=>1000111=>1110001=>[1,1,1,4,1]
[5,1,3,7,8,6,4,2]=>1000111=>1110001=>[1,1,1,4,1]
[3,1,5,7,8,6,4,2]=>1000111=>1110001=>[1,1,1,4,1]
[4,3,1,2,6,5,8,7]=>1100101=>1010011=>[1,2,3,1,1]
[6,1,4,3,5,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,6,3,5,1,2,8,7]=>0101001=>1001010=>[1,3,2,2]
[6,2,4,5,1,3,8,7]=>1001001=>1001001=>[1,3,3,1]
[2,3,6,1,5,4,8,7]=>0010101=>1010100=>[1,2,2,3]
[2,1,6,5,3,4,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[3,5,6,2,4,1,8,7]=>0010101=>1010100=>[1,2,2,3]
[8,7,6,1,3,2,4,5]=>1110100=>0010111=>[3,2,1,1,1]
[2,5,3,4,8,1,7,6]=>0100101=>1010010=>[1,2,3,2]
[5,1,8,2,3,4,7,6]=>1010001=>1000101=>[1,4,2,1]
[5,4,7,6,2,8,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[2,1,6,8,5,7,3,4]=>1001010=>0101001=>[2,2,3,1]
[2,1,8,4,6,7,3,5]=>1010010=>0100101=>[2,3,2,1]
[3,1,8,6,2,7,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,8,1,5,6,7,2,4]=>0100010=>0100010=>[2,4,2]
[8,2,3,5,7,1,6,4]=>1000101=>1010001=>[1,2,4,1]
[5,8,4,3,7,1,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,3,6,7,5,1,4]=>0100110=>0110010=>[2,1,3,2]
[8,1,2,7,3,5,6,4]=>1001001=>1001001=>[1,3,3,1]
[6,8,4,2,1,3,7,5]=>0111001=>1001110=>[1,3,1,1,2]
[4,3,8,2,7,6,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[2,1,4,5,8,3,7,6]=>1000101=>1010001=>[1,2,4,1]
[8,4,7,1,5,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[7,3,5,8,4,2,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[2,4,8,3,5,6,7,1]=>0010001=>1000100=>[1,4,3]
[6,4,7,5,2,3,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,4,8,1,7,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[2,1,4,3,8,7,5,6]=>1010110=>0110101=>[2,1,2,2,1]
[4,3,1,2,8,6,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[5,1,6,7,8,4,3,2]=>1000111=>1110001=>[1,1,1,4,1]
[8,7,2,6,4,1,5,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,1,5,7,8,4,6,3]=>1000101=>1010001=>[1,2,4,1]
[6,4,1,5,7,2,8,3]=>1100101=>1010011=>[1,2,3,1,1]
[7,4,8,1,2,5,6,3]=>1010001=>1000101=>[1,4,2,1]
[6,1,7,4,3,2,8,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,8,3,4,2,1,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[4,2,6,1,5,7,8,3]=>1010001=>1000101=>[1,4,2,1]
[7,1,4,8,3,5,6,2]=>1001001=>1001001=>[1,3,3,1]
[3,4,8,2,5,7,6,1]=>0010011=>1100100=>[1,1,3,3]
[3,7,1,4,5,6,8,2]=>0100001=>1000010=>[1,5,2]
[6,5,3,8,4,7,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[8,6,4,7,5,3,1,2]=>1101110=>0111011=>[2,1,1,2,1,1]
[1,6,3,7,5,8,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,7,4,5,8,6,2]=>0010011=>1100100=>[1,1,3,3]
[7,3,8,5,4,6,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[3,4,8,5,6,7,1,2]=>0010010=>0100100=>[2,3,3]
[4,7,3,8,5,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[6,8,4,7,5,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[1,7,6,5,3,8,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,7,6,3,1,4,5,8]=>0111000=>0001110=>[4,1,1,2]
[2,7,6,4,5,1,3,8]=>0110100=>0010110=>[3,2,1,2]
[5,7,2,6,4,1,3,8]=>0101100=>0011010=>[3,1,2,2]
[7,6,1,5,3,8,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[1,8,2,7,3,6,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,3,8,4,7,5,6]=>1001010=>0101001=>[2,2,3,1]
[3,1,2,8,4,6,7,5]=>1001001=>1001001=>[1,3,3,1]
[4,1,7,2,8,5,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,2,4,8,3,7,6]=>1000101=>1010001=>[1,2,4,1]
[2,8,4,1,5,6,3,7]=>0110010=>0100110=>[2,3,1,2]
[1,7,2,8,5,3,6,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,2,3,8,4,5,7,6]=>0001001=>1001000=>[1,3,4]
[2,4,8,3,1,5,6,7]=>0011000=>0001100=>[4,1,3]
[3,2,5,6,1,4,7,8]=>1001000=>0001001=>[4,3,1]
[4,7,3,8,2,1,5,6]=>0101100=>0011010=>[3,1,2,2]
[7,4,8,3,2,1,5,6]=>1011100=>0011101=>[3,1,1,2,1]
[7,6,8,5,1,4,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,5,1,2,8,3,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[6,8,4,1,3,7,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,3,7,1,8,4,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,3,1,7,4,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[4,7,1,2,8,3,6,5]=>0100101=>1010010=>[1,2,3,2]
[3,4,1,8,5,6,7,2]=>0101001=>1001010=>[1,3,2,2]
[1,2,8,7,6,3,5,4]=>0011101=>1011100=>[1,2,1,1,3]
[2,3,1,8,7,4,5,6]=>0101100=>0011010=>[3,1,2,2]
[2,6,1,4,8,7,3,5]=>0100110=>0110010=>[2,1,3,2]
[5,8,2,1,7,6,3,4]=>0110110=>0110110=>[2,1,2,1,2]
[8,7,1,6,5,4,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[3,1,8,7,6,4,5,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[1,2,3,4,8,7,5,6]=>0000110=>0110000=>[2,1,5]
[1,2,3,8,6,4,5,7]=>0001100=>0011000=>[3,1,4]
[1,2,8,5,3,4,6,7]=>0011000=>0001100=>[4,1,3]
[1,8,4,2,3,5,6,7]=>0110000=>0000110=>[5,1,2]
[2,4,7,5,6,8,3,1]=>0010011=>1100100=>[1,1,3,3]
[2,5,3,8,7,4,6,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,1,8,5,7,4,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,3,5,7,4,2,6,1]=>1001101=>1011001=>[1,2,1,3,1]
[8,3,6,2,4,5,7,1]=>1010001=>1000101=>[1,4,2,1]
[2,7,6,4,5,8,3,1]=>0110011=>1100110=>[1,1,3,1,2]
[4,8,1,7,6,3,2,5]=>0101110=>0111010=>[2,1,1,2,2]
[3,7,1,8,6,2,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[7,3,6,4,2,8,5,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,8,7,1,4,3,2,6]=>0110110=>0110110=>[2,1,2,1,2]
[5,6,1,2,4,3,8,7]=>0100101=>1010010=>[1,2,3,2]
[3,6,8,1,2,7,5,4]=>0010011=>1100100=>[1,1,3,3]
[8,4,6,2,1,3,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[4,8,1,5,3,7,2,6]=>0101010=>0101010=>[2,2,2,2]
[5,4,8,7,3,1,2,6]=>1011100=>0011101=>[3,1,1,2,1]
[6,4,3,8,1,5,2,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,8,3,7,2,5,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[5,3,6,8,7,2,4,1]=>1001101=>1011001=>[1,2,1,3,1]
[5,7,4,2,8,3,6,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,4,7,2,1,8,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[5,7,8,2,6,4,1,3]=>0010110=>0110100=>[2,1,2,3]
[2,6,8,4,5,7,1,3]=>0010010=>0100100=>[2,3,3]
[1,7,4,8,6,2,3,5]=>0101100=>0011010=>[3,1,2,2]
[2,7,4,8,5,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,3,7,2,8,5,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[3,6,2,5,7,8,1,4]=>0100010=>0100010=>[2,4,2]
[5,3,6,7,1,8,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,3,6,7,2,4,5]=>1000100=>0010001=>[3,4,1]
[8,1,4,2,7,5,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[6,1,3,8,2,7,4,5]=>1001010=>0101001=>[2,2,3,1]
[4,1,5,3,2,8,6,7]=>1011010=>0101101=>[2,2,1,2,1]
[2,7,1,4,3,8,5,6]=>0101010=>0101010=>[2,2,2,2]
[1,7,5,2,8,6,3,4]=>0110110=>0110110=>[2,1,2,1,2]
[7,4,2,5,1,8,6,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,6,3,2,1,8,7,4]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,5,3,2,7,1,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[5,3,6,2,8,1,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,2,8,5,1,7,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,8,4,7,2,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[1,5,8,4,2,6,3,7]=>0011010=>0101100=>[2,2,1,3]
[3,5,7,4,1,6,8,2]=>0011001=>1001100=>[1,3,1,3]
[4,5,8,3,1,7,6,2]=>0011011=>1101100=>[1,1,2,1,3]
[3,4,7,8,2,1,6,5]=>0001101=>1011000=>[1,2,1,4]
[4,6,3,5,2,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,7,1,2,6,4,8]=>0010010=>0100100=>[2,3,3]
[7,4,1,2,8,6,3,5]=>1100110=>0110011=>[2,1,3,1,1]
[5,2,6,1,3,4,8,7]=>1010001=>1000101=>[1,4,2,1]
[3,8,2,6,5,4,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[3,8,7,2,5,4,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[7,5,1,6,8,4,3,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,4,2,1,5,6,3,8]=>1110010=>0100111=>[2,3,1,1,1]
[7,3,8,1,5,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,8,6,5,1,3,4]=>1011100=>0011101=>[3,1,1,2,1]
[6,2,7,8,5,4,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[5,3,2,6,7,4,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[4,8,2,6,5,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[4,3,7,2,5,6,1,8]=>1010010=>0100101=>[2,3,2,1]
[3,8,7,6,2,4,1,5]=>0111010=>0101110=>[2,2,1,1,2]
[6,7,1,4,3,2,5,8]=>0101100=>0011010=>[3,1,2,2]
[3,5,6,2,4,7,1,8]=>0010010=>0100100=>[2,3,3]
[3,5,8,7,2,4,6,1]=>0011001=>1001100=>[1,3,1,3]
[1,7,8,2,5,4,3,6]=>0010110=>0110100=>[2,1,2,3]
[2,7,1,3,6,5,4,8]=>0100110=>0110010=>[2,1,3,2]
[5,7,1,4,6,3,2,8]=>0100110=>0110010=>[2,1,3,2]
[6,3,7,1,5,4,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,7,1,6,3,5,2,8]=>0101010=>0101010=>[2,2,2,2]
[8,7,3,6,1,5,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,7,8,3,2,1,4,6]=>0011100=>0011100=>[3,1,1,3]
[5,4,2,1,7,8,3,6]=>1110010=>0100111=>[2,3,1,1,1]
[4,7,8,3,5,2,1,6]=>0010110=>0110100=>[2,1,2,3]
[8,3,7,6,4,2,1,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,3,2,1,4,7,6,5]=>1110011=>1100111=>[1,1,3,1,1,1]
[6,4,1,7,3,8,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[1,7,5,3,8,2,6,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,1,7,4,2,8,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,6,3,2,7,5,1,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[2,7,5,1,3,8,6,4]=>0110011=>1100110=>[1,1,3,1,2]
[8,7,4,2,6,1,5,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,2,6,1,8,7,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,7,6,4,3,8,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[1,3,8,2,4,7,6,5]=>0010011=>1100100=>[1,1,3,3]
[3,7,5,1,8,6,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[5,1,4,3,2,7,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[3,7,6,2,4,1,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[5,3,1,7,8,4,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[4,1,7,8,5,3,2,6]=>1001110=>0111001=>[2,1,1,3,1]
[2,7,6,4,1,3,8,5]=>0111001=>1001110=>[1,3,1,1,2]
[8,4,2,7,6,3,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,3,1,7,5,2,8,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,2,7,5,3,1,8,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[1,5,8,2,7,4,6,3]=>0010101=>1010100=>[1,2,2,3]
[8,4,7,3,1,6,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,1,6,8,5,7,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[1,8,6,7,3,4,2,5]=>0101010=>0101010=>[2,2,2,2]
[6,7,1,8,3,4,2,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,6,3,4,2,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,5,1,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,8,5,6,2,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[5,7,1,6,2,8,3,4]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,7,1,8,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,2,5,1,8,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,2,4,3,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[2,5,1,8,6,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[2,6,5,8,1,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,7,4,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[2,4,3,8,5,6,1,7]=>0101010=>0101010=>[2,2,2,2]
[2,3,1,8,5,6,4,7]=>0101010=>0101010=>[2,2,2,2]
[4,6,2,7,1,5,3,8]=>0101010=>0101010=>[2,2,2,2]
[4,7,1,6,2,5,3,8]=>0101010=>0101010=>[2,2,2,2]
[4,6,3,5,1,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,7,1,4,2,8]=>0101010=>0101010=>[2,2,2,2]
[1,8,5,6,3,4,2,7]=>0101010=>0101010=>[2,2,2,2]
[4,7,1,8,5,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[3,4,2,6,5,8,1,7]=>0101010=>0101010=>[2,2,2,2]
[3,5,4,6,2,8,1,7]=>0101010=>0101010=>[2,2,2,2]
[3,7,1,6,2,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[3,5,2,7,4,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,2,3,1,8,5,6]=>0101010=>0101010=>[2,2,2,2]
[2,4,3,8,1,7,5,6]=>0101010=>0101010=>[2,2,2,2]
[6,1,2,7,4,5,8,3]=>1001001=>1001001=>[1,3,3,1]
[2,5,8,3,4,1,6,7]=>0010100=>0010100=>[3,2,3]
[5,6,2,7,4,3,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,1,7,3,4,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,6,7,3,2,5,8,1]=>0011001=>1001100=>[1,3,1,3]
[3,7,2,1,4,5,8,6]=>0110001=>1000110=>[1,4,1,2]
[2,7,1,3,4,8,6,5]=>0100011=>1100010=>[1,1,4,2]
[2,6,7,3,8,5,4,1]=>0010111=>1110100=>[1,1,1,2,3]
[2,6,1,8,4,5,3,7]=>0101010=>0101010=>[2,2,2,2]
[4,2,1,6,5,3,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,2,4,3,1,5,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[4,6,2,1,5,3,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[8,4,2,1,6,5,3,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[2,6,4,5,1,8,7,3]=>0101011=>1101010=>[1,1,2,2,2]
[6,8,7,2,1,4,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[6,8,2,1,7,4,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[6,8,2,1,4,3,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[8,6,2,4,3,1,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[6,8,2,4,3,1,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[2,8,4,6,7,3,1,5]=>0100110=>0110010=>[2,1,3,2]
[2,8,6,7,4,3,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[6,8,7,2,4,3,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[4,6,5,2,8,3,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[2,6,4,5,8,3,7,1]=>0100101=>1010010=>[1,2,3,2]
[6,4,2,8,3,5,7,1]=>1101001=>1001011=>[1,3,2,1,1]
[8,4,2,6,3,5,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[4,2,6,3,8,7,5,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,2,4,3,6,5,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,1,6,8,7,5,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[4,2,1,6,5,8,7,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,2,1,3,6,8,7,5]=>1100011=>1100011=>[1,1,4,1,1]
[2,4,3,1,8,6,5,7]=>0110110=>0110110=>[2,1,2,1,2]
[6,2,1,8,7,4,3,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,6,8,7,5,2,1,3]=>0011110=>0111100=>[2,1,1,1,3]
[4,6,5,8,7,2,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[2,6,8,7,4,5,1,3]=>0011010=>0101100=>[2,2,1,3]
[2,4,8,6,7,5,1,3]=>0010110=>0110100=>[2,1,2,3]
[4,2,8,6,5,7,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[6,4,8,2,1,5,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[2,6,8,4,7,1,5,3]=>0010101=>1010100=>[1,2,2,3]
[4,6,5,8,2,1,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,8,6,7,2,1,3,5]=>0101100=>0011010=>[3,1,2,2]
[6,2,3,5,1,4,8,7]=>1001001=>1001001=>[1,3,3,1]
[7,4,5,2,3,8,6,1]=>1010011=>1100101=>[1,1,3,2,1]
[7,3,2,5,4,8,6,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,5,1,6,4,2,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[3,6,2,4,5,1,8,7]=>0100101=>1010010=>[1,2,3,2]
[7,2,3,4,5,8,6,1]=>1000011=>1100001=>[1,1,5,1]
[8,2,3,4,5,7,1,6]=>1000010=>0100001=>[2,5,1]
[6,7,3,4,8,5,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[5,7,1,3,8,6,2,4]=>0100110=>0110010=>[2,1,3,2]
[4,7,3,2,8,6,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[3,8,2,6,7,4,5,1]=>0100101=>1010010=>[1,2,3,2]
[4,8,1,5,6,7,3,2]=>0100011=>1100010=>[1,1,4,2]
[6,8,2,5,1,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,4,6,2,1,5]=>0100110=>0110010=>[2,1,3,2]
[4,8,2,5,1,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[3,8,2,5,4,7,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,7,6,1,8,5,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[4,7,2,3,8,5,1,6]=>0100110=>0110010=>[2,1,3,2]
[4,6,7,1,8,5,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[3,6,1,7,8,5,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[2,1,5,7,3,8,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[6,4,7,2,8,5,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,6,1,4,8,5,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[4,1,2,3,7,8,6,5]=>1000011=>1100001=>[1,1,5,1]
[3,4,2,1,8,5,6,7]=>0110100=>0010110=>[3,2,1,2]
[8,2,3,5,7,1,4,6]=>1000100=>0010001=>[3,4,1]
[8,1,3,6,4,7,2,5]=>1001010=>0101001=>[2,2,3,1]
[5,4,8,3,6,7,1,2]=>1010010=>0100101=>[2,3,2,1]
[4,5,8,3,6,7,2,1]=>0010011=>1100100=>[1,1,3,3]
[2,1,5,8,4,6,7,3]=>1001001=>1001001=>[1,3,3,1]
[4,6,8,3,5,2,7,1]=>0010101=>1010100=>[1,2,2,3]
[3,8,2,4,5,6,7,1]=>0100001=>1000010=>[1,5,2]
[6,8,2,3,1,4,5,7]=>0101000=>0001010=>[4,2,2]
[4,3,1,6,5,8,7,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,2,7,4,1,3,6,5]=>1011001=>1001101=>[1,3,1,2,1]
[3,7,8,2,1,4,6,5]=>0011001=>1001100=>[1,3,1,3]
[3,7,5,2,8,4,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[3,1,5,2,4,8,7,6]=>1010011=>1100101=>[1,1,3,2,1]
[3,6,4,5,1,8,7,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,3,6,1,2,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[6,1,3,5,4,8,7,2]=>1001011=>1101001=>[1,1,2,3,1]
[1,7,3,8,4,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[1,6,7,4,8,5,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[8,1,2,5,4,6,3,7]=>1001010=>0101001=>[2,2,3,1]
[6,8,3,1,4,7,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[8,4,2,5,7,1,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[1,8,5,3,7,4,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,3,2,8,7,1,4,6]=>1101100=>0011011=>[3,1,2,1,1]
[1,2,8,7,5,6,3,4]=>0011010=>0101100=>[2,2,1,3]
[1,4,8,6,5,7,2,3]=>0011010=>0101100=>[2,2,1,3]
[3,5,4,8,6,1,2,7]=>0101100=>0011010=>[3,1,2,2]
[4,3,5,8,1,7,2,6]=>1001010=>0101001=>[2,2,3,1]
[1,4,5,8,6,7,3,2]=>0001011=>1101000=>[1,1,2,4]
[1,7,6,5,8,3,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[7,3,6,1,8,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[7,6,4,5,8,1,3,2]=>1100101=>1010011=>[1,2,3,1,1]
[1,6,5,4,8,2,3,7]=>0110100=>0010110=>[3,2,1,2]
[5,2,6,3,8,1,4,7]=>1010100=>0010101=>[3,2,2,1]
[4,3,1,6,8,7,5,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[4,3,1,8,5,6,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[6,2,8,4,3,1,7,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,1,6,2,3,4,5,8]=>1010000=>0000101=>[5,2,1]
[3,8,6,1,2,5,4,7]=>0110010=>0100110=>[2,3,1,2]
[1,8,5,4,3,6,2,7]=>0111010=>0101110=>[2,2,1,1,2]
[5,3,8,4,1,2,7,6]=>1011001=>1001101=>[1,3,1,2,1]
[1,8,3,6,5,2,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,1,8,2,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,2,4,7,6,5,3]=>0100111=>1110010=>[1,1,1,3,2]
[1,4,8,3,5,7,6,2]=>0010011=>1100100=>[1,1,3,3]
[8,2,1,4,6,5,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[6,1,5,2,4,7,8,3]=>1010001=>1000101=>[1,4,2,1]
[4,1,8,5,2,7,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,3,8,5,1,2,6,7]=>1011000=>0001101=>[4,1,2,1]
[6,3,5,1,4,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,2,3,7,5,6]=>1010010=>0100101=>[2,3,2,1]
[5,3,8,7,2,1,4,6]=>1011100=>0011101=>[3,1,1,2,1]
[7,6,5,4,1,3,2,8]=>1111010=>0101111=>[2,2,1,1,1,1]
[1,8,7,6,2,5,4,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,2,3,4,5,10,9,8,7,6]=>000001111=>111100000=>[1,1,1,1,6]
[4,6,3,1,5,2,7,8]=>0110100=>0010110=>[3,2,1,2]
[6,2,7,4,5,1,3,8]=>1010100=>0010101=>[3,2,2,1]
[5,2,7,4,1,6,3,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,7,3,4,1,6,2,8]=>0101010=>0101010=>[2,2,2,2]
[4,2,8,1,5,6,7,3]=>1010001=>1000101=>[1,4,2,1]
[1,7,8,4,5,6,2,3]=>0010010=>0100100=>[2,3,3]
[1,6,8,4,5,2,7,3]=>0010101=>1010100=>[1,2,2,3]
[1,5,8,4,2,6,7,3]=>0011001=>1001100=>[1,3,1,3]
[1,5,3,8,2,6,7,4]=>0101001=>1001010=>[1,3,2,2]
[1,6,3,8,5,2,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,7,3,8,5,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[6,2,3,7,5,1,4,8]=>1001100=>0011001=>[3,1,3,1]
[4,2,6,1,5,3,7,8]=>1010100=>0010101=>[3,2,2,1]
[5,2,6,4,1,3,7,8]=>1011000=>0001101=>[4,1,2,1]
[1,2,7,8,5,6,3,4]=>0001010=>0101000=>[2,2,4]
[1,2,6,4,8,3,7,5]=>0010101=>1010100=>[1,2,2,3]
[8,7,3,2,1,6,5,4]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[8,7,4,1,6,2,3,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,5,1,7,2,3,4,6]=>1101000=>0001011=>[4,2,1,1]
[10,9,8,5,1,7,2,3,4,6]=>111101000=>000101111=>[4,2,1,1,1,1]
[10,9,4,1,6,2,8,3,5,7]=>111010100=>001010111=>[3,2,2,1,1,1]
[10,3,1,5,2,7,4,9,6,8]=>110101010=>010101011=>[2,2,2,2,1,1]
[1,8,3,2,6,4,5,7]=>0110100=>0010110=>[3,2,1,2]
[7,3,8,1,5,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[3,1,7,2,6,4,5,8]=>1010100=>0010101=>[3,2,2,1]
[1,8,4,2,3,6,7,5]=>0110001=>1000110=>[1,4,1,2]
[2,5,8,3,4,6,7,1]=>0010001=>1000100=>[1,4,3]
[4,1,7,2,3,6,8,5]=>1010001=>1000101=>[1,4,2,1]
[3,1,7,5,4,2,8,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,6,2,1,5,7,8,3]=>0110001=>1000110=>[1,4,1,2]
[4,5,2,3,1,7,8,6]=>0101001=>1001010=>[1,3,2,2]
[3,2,6,7,4,1,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[5,6,2,7,1,4,8,3]=>0101001=>1001010=>[1,3,2,2]
[6,4,2,8,1,5,7,3]=>1101001=>1001011=>[1,3,2,1,1]
[7,3,6,8,5,2,4,1]=>1001101=>1011001=>[1,2,1,3,1]
[2,7,8,3,6,5,1,4]=>0010110=>0110100=>[2,1,2,3]
[2,7,8,5,4,6,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,6,8,3,4,7,1,5]=>0010010=>0100100=>[2,3,3]
[2,5,6,8,3,4,1,7]=>0001010=>0101000=>[2,2,4]
[2,7,8,3,6,1,4,5]=>0010100=>0010100=>[3,2,3]
[2,1,3,7,8,5,6,4]=>1000101=>1010001=>[1,2,4,1]
[5,1,2,4,8,7,3,6]=>1000110=>0110001=>[2,1,4,1]
[2,3,6,1,8,5,7,4]=>0010101=>1010100=>[1,2,2,3]
[5,2,6,1,7,8,4,3]=>1010011=>1100101=>[1,1,3,2,1]
[3,6,5,4,1,8,7,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,4,2,3,7,8,6,1]=>1100011=>1100011=>[1,1,4,1,1]
[4,1,8,2,5,7,3,6]=>1010010=>0100101=>[2,3,2,1]
[3,1,8,4,7,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[2,6,4,1,5,3,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[1,5,8,2,4,7,3,6]=>0010010=>0100100=>[2,3,3]
[6,2,1,4,7,8,3,5]=>1100010=>0100011=>[2,4,1,1]
[3,8,1,4,2,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[8,3,4,2,1,6,5,7]=>1011010=>0101101=>[2,2,1,2,1]
[5,3,2,8,1,6,4,7]=>1101010=>0101011=>[2,2,2,1,1]
[2,4,5,8,3,6,1,7]=>0001010=>0101000=>[2,2,4]
[3,5,8,1,2,6,4,7]=>0010010=>0100100=>[2,3,3]
[8,6,1,3,5,2,4,7]=>1100100=>0010011=>[3,3,1,1]
[5,7,4,3,6,1,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[2,6,4,3,7,8,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[7,4,1,8,3,2,5,6]=>1101100=>0011011=>[3,1,2,1,1]
[2,4,6,5,1,7,8,3]=>0011001=>1001100=>[1,3,1,3]
[5,6,1,7,4,2,8,3]=>0101101=>1011010=>[1,2,1,2,2]
[1,3,8,6,2,7,4,5]=>0011010=>0101100=>[2,2,1,3]
[6,4,7,8,2,1,3,5]=>1001100=>0011001=>[3,1,3,1]
[6,7,3,8,4,1,2,5]=>0101100=>0011010=>[3,1,2,2]
[2,7,8,3,4,6,1,5]=>0010010=>0100100=>[2,3,3]
[3,7,8,1,5,4,2,6]=>0010110=>0110100=>[2,1,2,3]
[7,5,8,4,1,3,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[4,7,5,8,3,1,2,6]=>0101100=>0011010=>[3,1,2,2]
[5,7,3,1,6,8,4,2]=>0110011=>1100110=>[1,1,3,1,2]
[4,6,7,2,8,3,1,5]=>0010110=>0110100=>[2,1,2,3]
[4,8,1,2,3,5,7,6]=>0100001=>1000010=>[1,5,2]
[4,5,6,7,3,1,8,2]=>0001101=>1011000=>[1,2,1,4]
[8,5,3,2,7,6,1,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,5,4,6,2,8,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[2,5,1,3,6,8,7,4]=>0100011=>1100010=>[1,1,4,2]
[7,5,2,8,4,1,3,6]=>1101100=>0011011=>[3,1,2,1,1]
[7,3,8,5,2,1,4,6]=>1011100=>0011101=>[3,1,1,2,1]
[5,8,3,6,4,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[3,7,8,4,1,5,6,2]=>0011001=>1001100=>[1,3,1,3]
[3,5,8,6,7,4,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[3,7,6,8,1,2,5,4]=>0101001=>1001010=>[1,3,2,2]
[4,1,6,3,2,5,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[8,6,1,7,2,5,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,7,6,1,2,3,5,4]=>1110001=>1000111=>[1,4,1,1,1]
[5,4,1,6,2,3,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[2,6,5,3,4,1,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,7,6,1,2,3,4]=>0111000=>0001110=>[4,1,1,2]
[8,2,7,1,5,4,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[2,1,6,3,8,5,4,7]=>1010110=>0110101=>[2,1,2,2,1]
[2,6,3,1,8,5,4,7]=>0110110=>0110110=>[2,1,2,1,2]
[4,6,2,8,5,1,3,7]=>0101100=>0011010=>[3,1,2,2]
[6,5,2,7,4,3,8,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,6,5,2,7,3,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[3,1,6,2,4,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[8,7,5,1,2,6,4,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[2,1,7,6,3,8,4,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,2,3,4,6,7,1,5]=>1000010=>0100001=>[2,5,1]
[2,8,5,7,4,1,3,6]=>0101100=>0011010=>[3,1,2,2]
[7,8,5,3,6,4,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,1,4,8,7,5,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[7,4,6,8,5,1,3,2]=>1001101=>1011001=>[1,2,1,3,1]
[6,4,8,3,5,7,1,2]=>1010010=>0100101=>[2,3,2,1]
[8,5,7,4,6,2,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[4,1,8,5,6,3,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,8,3,2,4,6,1,7]=>0110010=>0100110=>[2,3,1,2]
[2,8,4,1,5,3,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,7,6,5,2,3,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[2,1,8,6,4,3,7,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,6,7,1,8,5,2,4]=>0010110=>0110100=>[2,1,2,3]
[4,2,3,6,8,7,5,1]=>1000111=>1110001=>[1,1,1,4,1]
[6,5,7,3,1,8,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,4,2,5,6,1,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[6,1,5,7,2,4,8,3]=>1001001=>1001001=>[1,3,3,1]
[8,4,7,6,2,1,5,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,5,7,6,4,1,8,2]=>0011101=>1011100=>[1,2,1,1,3]
[2,4,7,5,6,3,8,1]=>0010101=>1010100=>[1,2,2,3]
[5,4,1,7,6,2,8,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,5,6,7,1,4,8,2]=>0001001=>1001000=>[1,3,4]
[4,7,5,2,1,3,8,6]=>0111001=>1001110=>[1,3,1,1,2]
[5,7,2,3,6,4,8,1]=>0100101=>1010010=>[1,2,3,2]
[7,1,2,3,5,8,4,6]=>1000010=>0100001=>[2,5,1]
[8,6,2,3,7,1,4,5]=>1100100=>0010011=>[3,3,1,1]
[6,1,8,2,7,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[7,8,6,1,3,2,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[8,1,5,7,2,3,6,4]=>1001001=>1001001=>[1,3,3,1]
[1,4,5,2,8,6,7,3]=>0010101=>1010100=>[1,2,2,3]
[2,3,1,7,8,6,4,5]=>0100110=>0110010=>[2,1,3,2]
[2,1,4,6,8,3,7,5]=>1000101=>1010001=>[1,2,4,1]
[3,5,7,6,2,8,1,4]=>0011010=>0101100=>[2,2,1,3]
[5,4,1,6,3,8,7,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,5,6,1,2,8,7,3]=>0010011=>1100100=>[1,1,3,3]
[3,5,6,2,4,8,7,1]=>0010011=>1100100=>[1,1,3,3]
[5,4,1,2,8,7,6,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[5,6,3,7,8,4,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[4,3,2,6,8,1,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[7,1,5,6,3,8,2,4]=>1001010=>0101001=>[2,2,3,1]
[1,5,4,2,7,8,3,6]=>0110010=>0100110=>[2,3,1,2]
[6,1,2,8,7,4,3,5]=>1001110=>0111001=>[2,1,1,3,1]
[5,1,6,8,4,7,2,3]=>1001010=>0101001=>[2,2,3,1]
[5,1,3,8,4,2,7,6]=>1001101=>1011001=>[1,2,1,3,1]
[3,1,6,8,7,4,2,5]=>1001110=>0111001=>[2,1,1,3,1]
[3,6,5,8,4,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[6,5,8,4,3,1,2,7]=>1011100=>0011101=>[3,1,1,2,1]
[8,5,1,3,7,4,6,2]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,8,1,4,7,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[6,4,3,8,2,5,7,1]=>1101001=>1001011=>[1,3,2,1,1]
[3,2,5,8,4,1,7,6]=>1001101=>1011001=>[1,2,1,3,1]
[6,8,2,3,4,7,5,1]=>0100011=>1100010=>[1,1,4,2]
[2,1,7,8,3,4,6,5]=>1001001=>1001001=>[1,3,3,1]
[7,5,1,8,4,2,6,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,6,1,8,2,7,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[3,6,8,5,2,7,4,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,1,6,5,4,8,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[2,1,7,3,5,8,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[7,8,1,2,4,5,6,3]=>0100001=>1000010=>[1,5,2]
[3,6,8,1,5,7,2,4]=>0010010=>0100100=>[2,3,3]
[3,5,7,8,4,6,1,2]=>0001010=>0101000=>[2,2,4]
[7,5,2,8,4,6,3,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,8,2,4,3,1,5,6]=>0101100=>0011010=>[3,1,2,2]
[8,4,3,1,7,5,2,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,6,2,8,5,1,4,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,3,8,7,1,6,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,7,1,8,5,2,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,7,5,8,1,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[3,7,6,4,5,1,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[4,7,5,6,3,8,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,2,7,5,8,3,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,2,7,3,4,6,1]=>0101001=>1001010=>[1,3,2,2]
[5,7,2,1,8,3,6,4]=>0110101=>1010110=>[1,2,2,1,2]
[7,8,1,2,3,4,6,5]=>0100001=>1000010=>[1,5,2]
[5,6,2,4,3,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,2,1,7,8,3,5]=>0110010=>0100110=>[2,3,1,2]
[6,3,2,1,4,8,5,7]=>1110010=>0100111=>[2,3,1,1,1]
[7,1,8,3,5,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,2,4,8,5,6,3]=>1000101=>1010001=>[1,2,4,1]
[8,7,6,5,1,3,2,4]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,7,6,2,4,3,1,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,6,8,1,5,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,6,1,8,5,4,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[6,5,8,1,7,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,3,8,7,6,1,5,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,5,8,7,4,1,3,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,4,8,7,6,3,1,2]=>1011110=>0111101=>[2,1,1,1,2,1]
[1,4,8,6,3,2,5,7]=>0011100=>0011100=>[3,1,1,3]
[7,4,1,6,3,8,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,6,3,1,5,8,4,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[1,6,3,8,5,2,4,7]=>0101100=>0011010=>[3,1,2,2]
[4,6,3,7,5,2,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[3,7,2,6,5,4,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[1,7,4,6,2,8,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[6,2,5,1,7,4,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,5,7,4,8,6,1,2]=>0010110=>0110100=>[2,1,2,3]
[5,2,7,4,1,6,8,3]=>1011001=>1001101=>[1,3,1,2,1]
[4,5,8,2,1,7,6,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,6,4,8,5,2,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,4,1,5,3,8,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[3,4,1,2,7,8,6,5]=>0100011=>1100010=>[1,1,4,2]
[4,1,3,2,8,6,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,2,4,7,6,8,5]=>1000101=>1010001=>[1,2,4,1]
[8,1,3,5,4,7,2,6]=>1001010=>0101001=>[2,2,3,1]
[7,1,4,3,5,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,8,1,6,5,4,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,8,4,1,2,5,3,7]=>0110010=>0100110=>[2,3,1,2]
[8,2,1,5,6,4,3,7]=>1100110=>0110011=>[2,1,3,1,1]
[4,7,1,8,2,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[6,7,8,1,4,5,3,2]=>0010011=>1100100=>[1,1,3,3]
[3,2,5,4,7,8,1,6]=>1010010=>0100101=>[2,3,2,1]
[8,4,7,6,2,3,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[6,1,2,8,7,3,5,4]=>1001101=>1011001=>[1,2,1,3,1]
[1,2,7,5,6,8,3,4]=>0010010=>0100100=>[2,3,3]
[5,7,2,3,8,1,6,4]=>0100101=>1010010=>[1,2,3,2]
[3,5,2,6,1,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[3,2,5,6,7,8,1,4]=>1000010=>0100001=>[2,5,1]
[5,4,2,6,8,7,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[6,4,1,2,8,7,3,5]=>1100110=>0110011=>[2,1,3,1,1]
[4,3,8,5,2,1,6,7]=>1011100=>0011101=>[3,1,1,2,1]
[3,6,4,5,2,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[7,5,4,2,3,8,1,6]=>1110010=>0100111=>[2,3,1,1,1]
[5,6,3,1,8,2,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[6,5,4,3,1,2,8,7]=>1111001=>1001111=>[1,3,1,1,1,1]
[4,5,2,1,6,8,3,7]=>0110010=>0100110=>[2,3,1,2]
[5,6,2,8,1,7,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,4,5,8,6,3,7]=>1000110=>0110001=>[2,1,4,1]
[6,7,1,3,4,8,2,5]=>0100010=>0100010=>[2,4,2]
[6,7,8,2,3,5,4,1]=>0010011=>1100100=>[1,1,3,3]
[5,8,6,2,3,7,4,1]=>0110011=>1100110=>[1,1,3,1,2]
[1,8,3,4,7,6,2,5]=>0100110=>0110010=>[2,1,3,2]
[5,8,6,1,7,2,4,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,1,2,8,6,4,5,7]=>1001100=>0011001=>[3,1,3,1]
[1,3,2,8,5,4,6,7]=>0101100=>0011010=>[3,1,2,2]
[3,2,1,8,6,5,4,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[5,2,7,1,8,4,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[6,7,2,1,8,4,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[6,7,3,1,5,8,2,4]=>0110010=>0100110=>[2,3,1,2]
[2,4,1,6,8,5,3,7]=>0100110=>0110010=>[2,1,3,2]
[2,5,6,1,8,4,3,7]=>0010110=>0110100=>[2,1,2,3]
[5,4,7,6,1,8,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[3,5,6,8,4,7,2,1]=>0001011=>1101000=>[1,1,2,4]
[2,5,6,8,7,3,4,1]=>0001101=>1011000=>[1,2,1,4]
[2,4,8,5,7,3,6,1]=>0010101=>1010100=>[1,2,2,3]
[5,3,7,8,4,6,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,7,3,8,4,5,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,2,8,6,7,3,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,8,7,5,4,6,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,1,8,7,6,4,3,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,3,8,7,5,1,2,4]=>1011100=>0011101=>[3,1,1,2,1]
[2,8,7,4,1,3,5,6]=>0111000=>0001110=>[4,1,1,2]
[2,5,3,7,6,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[2,8,7,1,4,5,3,6]=>0110010=>0100110=>[2,3,1,2]
[4,2,1,8,7,3,5,6]=>1101100=>0011011=>[3,1,2,1,1]
[8,7,4,6,2,3,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,1,6,3,2,8,7,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,7,2,3,5,4,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[3,4,2,8,6,1,5,7]=>0101100=>0011010=>[3,1,2,2]
[8,1,4,2,3,6,7,5]=>1010001=>1000101=>[1,4,2,1]
[6,8,3,5,4,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,5,7,6,3,4]=>0100110=>0110010=>[2,1,3,2]
[4,1,6,8,2,3,7,5]=>1001001=>1001001=>[1,3,3,1]
[1,4,6,3,7,2,8,5]=>0010101=>1010100=>[1,2,2,3]
[6,2,1,8,4,5,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[4,7,3,8,5,2,1,6]=>0101110=>0111010=>[2,1,1,2,2]
[3,1,7,4,8,5,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,1,6,3,2,8,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,8,6,2,7,4,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[7,3,1,4,5,2,8,6]=>1100101=>1010011=>[1,2,3,1,1]
[8,1,2,4,6,7,5,3]=>1000011=>1100001=>[1,1,5,1]
[8,1,3,6,7,5,4,2]=>1000111=>1110001=>[1,1,1,4,1]
[6,4,2,8,5,1,3,7]=>1101100=>0011011=>[3,1,2,1,1]
[8,6,2,4,1,3,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[4,7,5,1,8,6,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,7,5,1,4,2,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,2,4,1,7,5,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,6,5,8,4,1,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[7,3,8,2,5,6,4,1]=>1010011=>1100101=>[1,1,3,2,1]
[5,7,3,1,6,4,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[6,1,3,7,4,8,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[3,2,1,7,4,8,5,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,1,5,2,7,6,3,8]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,7,1,4,8,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[7,5,4,1,3,8,6,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[4,3,2,1,8,5,7,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,2,1,7,3,6,5,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,3,2,8,1,6,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,7,5,3,8,1,4,6]=>0110100=>0010110=>[3,2,1,2]
[1,8,5,3,6,4,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[8,1,6,2,7,4,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,1,6,5,4,2,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,5,7,4,3,6,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,8,5,6,1,4,3,7]=>0101010=>0101010=>[2,2,2,2]
[3,7,5,8,2,1,4,6]=>0101100=>0011010=>[3,1,2,2]
[5,4,8,3,2,1,7,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,4,7,1,3,6,5,8]=>0010010=>0100100=>[2,3,3]
[5,7,4,8,1,3,6,2]=>0101001=>1001010=>[1,3,2,2]
[5,1,7,8,2,4,6,3]=>1001001=>1001001=>[1,3,3,1]
[3,6,7,8,1,2,5,4]=>0001001=>1001000=>[1,3,4]
[4,6,7,2,8,1,3,5]=>0010100=>0010100=>[3,2,3]
[6,3,7,1,8,2,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,1,4,8,2,6,3]=>0100101=>1010010=>[1,2,3,2]
[2,7,4,1,8,3,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[6,1,2,7,8,3,5,4]=>1000101=>1010001=>[1,2,4,1]
[3,6,4,7,8,1,2,5]=>0100100=>0010010=>[3,3,2]
[3,7,4,8,5,2,1,6]=>0101110=>0111010=>[2,1,1,2,2]
[7,2,5,8,6,3,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[4,8,1,7,6,2,3,5]=>0101100=>0011010=>[3,1,2,2]
[4,8,2,1,7,5,3,6]=>0110110=>0110110=>[2,1,2,1,2]
[5,8,7,1,3,6,4,2]=>0110011=>1100110=>[1,1,3,1,2]
[2,8,7,1,6,3,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,6,5,1,4,3,8]=>0111010=>0101110=>[2,2,1,1,2]
[3,8,7,6,2,1,5,4]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,8,7,2,6,1,4,3]=>0110101=>1010110=>[1,2,2,1,2]
[7,3,8,6,5,1,2,4]=>1011100=>0011101=>[3,1,1,2,1]
[5,8,6,4,3,2,1,7]=>0111110=>0111110=>[2,1,1,1,1,2]
[8,7,6,2,5,3,1,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,1,2,3,4,7,6,5]=>1000011=>1100001=>[1,1,5,1]
[3,8,2,7,6,5,4,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[4,2,8,7,6,5,3,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[8,3,1,7,6,5,4,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[5,2,8,7,6,4,3,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[8,3,2,1,7,6,5,4]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,4,1,7,6,5,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[6,4,1,3,2,8,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[2,5,8,6,3,1,4,7]=>0011100=>0011100=>[3,1,1,3]
[3,2,7,4,5,8,1,6]=>1010010=>0100101=>[2,3,2,1]
[8,1,6,2,4,5,3,7]=>1010010=>0100101=>[2,3,2,1]
[5,8,1,6,2,3,4,7]=>0101000=>0001010=>[4,2,2]
[5,4,6,1,3,8,2,7]=>1010010=>0100101=>[2,3,2,1]
[2,4,1,7,5,8,3,6]=>0101010=>0101010=>[2,2,2,2]
[2,4,7,6,8,3,5,1]=>0010101=>1010100=>[1,2,2,3]
[4,8,6,5,7,1,2,3]=>0110100=>0010110=>[3,2,1,2]
[8,5,7,4,3,1,6,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,1,7,4,2,3,6,5]=>1011001=>1001101=>[1,3,1,2,1]
[8,2,3,1,5,7,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[1,4,8,2,3,6,7,5]=>0010001=>1000100=>[1,4,3]
[3,1,2,7,8,6,4,5]=>1000110=>0110001=>[2,1,4,1]
[7,5,1,8,2,4,3,6]=>1101010=>0101011=>[2,2,2,1,1]
[3,5,8,1,2,4,7,6]=>0010001=>1000100=>[1,4,3]
[8,4,1,5,2,3,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[3,8,4,1,2,7,6,5]=>0110011=>1100110=>[1,1,3,1,2]
[2,7,5,8,3,4,1,6]=>0101010=>0101010=>[2,2,2,2]
[1,4,7,3,2,8,5,6]=>0011010=>0101100=>[2,2,1,3]
[6,4,1,3,2,7,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[2,3,7,6,8,1,5,4]=>0010101=>1010100=>[1,2,2,3]
[2,6,3,5,1,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[2,7,1,6,8,3,5,4]=>0100101=>1010010=>[1,2,3,2]
[6,7,5,4,2,1,8,3]=>0111101=>1011110=>[1,2,1,1,1,2]
[4,2,1,5,8,7,6,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,5,3,2,6,1,7,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,2,1,5,3,8,7,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,8,4,1,2,5,3,6]=>0110010=>0100110=>[2,3,1,2]
[7,8,1,2,6,5,3,4]=>0100110=>0110010=>[2,1,3,2]
[6,1,4,2,7,5,3,8]=>1010110=>0110101=>[2,1,2,2,1]
[1,2,8,7,5,4,3,6]=>0011110=>0111100=>[2,1,1,1,3]
[1,2,8,3,6,4,7,5]=>0010101=>1010100=>[1,2,2,3]
[5,1,7,3,6,4,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,3,7,4,1,5,8]=>1001100=>0011001=>[3,1,3,1]
[6,2,4,1,7,3,5,8]=>1010100=>0010101=>[3,2,2,1]
[3,4,8,7,5,6,1,2]=>0011010=>0101100=>[2,2,1,3]
[2,7,3,8,6,4,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[1,8,3,7,6,4,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,8,5,3,1,7,4]=>0011101=>1011100=>[1,2,1,1,3]
[5,6,2,1,7,3,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,3,6,2,4,1,7,8]=>1010100=>0010101=>[3,2,2,1]
[5,7,4,2,1,3,6,8]=>0111000=>0001110=>[4,1,1,2]
[6,4,2,1,5,3,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[5,3,1,4,6,2,7,8]=>1100100=>0010011=>[3,3,1,1]
[5,1,2,4,7,6,8,3]=>1000101=>1010001=>[1,2,4,1]
[1,6,4,2,8,7,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[4,8,1,2,6,7,3,5]=>0100010=>0100010=>[2,4,2]
[3,1,2,4,6,8,7,5]=>1000011=>1100001=>[1,1,5,1]
[4,2,8,1,5,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,8,5,7,6,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[4,8,6,3,7,5,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[3,8,6,5,2,7,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[3,8,5,6,1,7,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,7,8,5,2,1,6,4]=>0011101=>1011100=>[1,2,1,1,3]
[4,2,7,8,1,3,6,5]=>1001001=>1001001=>[1,3,3,1]
[2,1,8,7,6,3,5,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,4,1,6,3,2,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,8,1,5,4,7,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,2,5,1,3,8,7]=>0101001=>1001010=>[1,3,2,2]
[2,6,4,3,1,5,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[5,1,7,2,8,6,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,8,2,7,4,3,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[6,8,2,5,4,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[2,1,7,6,3,8,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,6,2,8,4,3,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[2,6,5,1,8,4,3,7]=>0110110=>0110110=>[2,1,2,1,2]
[4,2,1,6,3,8,7,5]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,8,3,2,7,6,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[2,4,8,3,1,7,5,6]=>0011010=>0101100=>[2,2,1,3]
[4,8,3,2,1,7,6,5]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,5,8,2,7,1,4,6]=>0010100=>0010100=>[3,2,3]
[4,5,8,2,6,1,3,7]=>0010100=>0010100=>[3,2,3]
[2,6,8,3,7,1,4,5]=>0010100=>0010100=>[3,2,3]
[6,8,3,7,2,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,3,1,6,2,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,1,7,3,6,2,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,8,1,6,3,2,7]=>0010110=>0110100=>[2,1,2,3]
[6,8,4,7,1,5,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,3,2,1,6,8,5,7]=>1110010=>0100111=>[2,3,1,1,1]
[2,4,1,3,8,7,6,5]=>0100111=>1110010=>[1,1,1,3,2]
[4,8,6,5,1,7,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,5,3,1,7,2,8,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,1,5,4,8,7,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[3,8,5,4,2,1,7,6]=>0111101=>1011110=>[1,2,1,1,1,2]
[2,3,8,5,4,1,6,7]=>0011100=>0011100=>[3,1,1,3]
[2,1,4,8,6,5,3,7]=>1001110=>0111001=>[2,1,1,3,1]
[4,3,2,8,7,6,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,2,8,7,5,4,1,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[2,8,6,5,4,3,1,7]=>0111110=>0111110=>[2,1,1,1,1,2]
[5,4,2,6,3,1,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,5,2,6,3,8,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,3,6,5,2,8,4,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,6,3,1,2,4,8,7]=>0110001=>1000110=>[1,4,1,2]
[7,1,5,3,8,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,7,5,3,8,6,4,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,7,6,4,2,8,5,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,7,3,6,2,8,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,8,7,4,3,5,6]=>1011100=>0011101=>[3,1,1,2,1]
[2,8,6,3,1,4,7,5]=>0111001=>1001110=>[1,3,1,1,2]
[3,5,7,4,8,6,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,5,3,6,8,2,7,1]=>0100101=>1010010=>[1,2,3,2]
[5,6,3,7,4,8,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,7,4,5,8,3,1]=>0010011=>1100100=>[1,1,3,3]
[6,3,7,5,8,4,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,5,2,6,1,7,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,2,6,8,3,7,1]=>1100101=>1010011=>[1,2,3,1,1]
[7,6,8,5,1,4,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,8,5,4,2,3,6]=>1011100=>0011101=>[3,1,1,2,1]
[5,7,3,8,4,1,2,6]=>0101100=>0011010=>[3,1,2,2]
[2,1,7,8,5,3,4,6]=>1001100=>0011001=>[3,1,3,1]
[2,4,8,1,5,6,3,7]=>0010010=>0100100=>[2,3,3]
[4,1,8,2,6,5,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[4,7,3,8,1,2,6,5]=>0101001=>1001010=>[1,3,2,2]
[4,8,1,2,5,3,6,7]=>0100100=>0010010=>[3,3,2]
[3,8,1,2,4,6,5,7]=>0100010=>0100010=>[2,4,2]
[4,8,7,6,3,5,2,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,8,7,6,5,2,4,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[4,8,7,3,6,5,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,8,7,6,3,2,5,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[3,8,7,6,5,2,1,4]=>0111110=>0111110=>[2,1,1,1,1,2]
[7,5,8,3,6,2,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,5,8,3,2,6,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,8,3,2,1,6,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,3,7,8,4,1,6,5]=>0001101=>1011000=>[1,2,1,4]
[2,1,7,5,8,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,5,6,8,1,7,4,3]=>0001011=>1101000=>[1,1,2,4]
[4,2,8,6,1,7,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,6,4,1,3,2,5,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,1,3,2,6,5,4,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,5,3,6,2,4,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,1,2,6,5,3,7]=>1100110=>0110011=>[2,1,3,1,1]
[8,3,5,6,2,1,4,7]=>1001100=>0011001=>[3,1,3,1]
[8,4,2,1,5,6,3,7]=>1110010=>0100111=>[2,3,1,1,1]
[5,4,7,6,8,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,2,3,7,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[3,7,4,5,8,2,1,6]=>0100110=>0110010=>[2,1,3,2]
[6,3,8,5,7,4,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,1,8,3,5,6,2]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,8,7,4,6,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,8,2,1,4,6,3]=>1011001=>1001101=>[1,3,1,2,1]
[8,7,4,2,1,3,6,5]=>1111001=>1001111=>[1,3,1,1,1,1]
[7,4,8,3,2,6,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[6,8,2,3,1,7,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[7,4,3,2,6,8,5,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[5,1,2,3,6,8,7,4]=>1000011=>1100001=>[1,1,5,1]
[2,4,7,3,8,1,6,5]=>0010101=>1010100=>[1,2,2,3]
[6,3,8,2,7,4,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,2,1,3,6,4,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[5,7,8,2,1,4,3,6]=>0011010=>0101100=>[2,2,1,3]
[3,5,1,7,8,4,2,6]=>0100110=>0110010=>[2,1,3,2]
[1,7,8,4,5,3,2,6]=>0010110=>0110100=>[2,1,2,3]
[3,2,4,8,6,7,1,5]=>1001010=>0101001=>[2,2,3,1]
[8,3,1,6,7,4,2,5]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,5,7,4,8,1,6]=>1001010=>0101001=>[2,2,3,1]
[8,4,7,1,3,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[8,4,7,2,1,3,5,6]=>1011000=>0001101=>[4,1,2,1]
[6,4,2,1,3,7,8,5]=>1110001=>1000111=>[1,4,1,1,1]
[7,1,6,3,5,8,2,4]=>1010010=>0100101=>[2,3,2,1]
[3,8,5,1,6,7,2,4]=>0110010=>0100110=>[2,3,1,2]
[5,3,6,7,8,4,2,1]=>1000111=>1110001=>[1,1,1,4,1]
[1,5,2,7,8,6,4,3]=>0100111=>1110010=>[1,1,1,3,2]
[1,4,2,8,6,5,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,1,7,5,2,6,8,3]=>1011001=>1001101=>[1,3,1,2,1]
[7,6,2,4,5,1,8,3]=>1100101=>1010011=>[1,2,3,1,1]
[8,1,4,5,2,6,7,3]=>1001001=>1001001=>[1,3,3,1]
[8,4,6,5,2,1,7,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,5,7,2,1,6,8,4]=>0011001=>1001100=>[1,3,1,3]
[4,2,1,5,6,7,8,3]=>1100001=>1000011=>[1,5,1,1]
[3,7,5,4,6,8,1,2]=>0110010=>0100110=>[2,3,1,2]
[8,3,4,1,5,6,7,2]=>1010001=>1000101=>[1,4,2,1]
[3,5,2,4,7,6,1,8]=>0100110=>0110010=>[2,1,3,2]
[7,3,5,2,4,6,1,8]=>1010010=>0100101=>[2,3,2,1]
[5,3,7,2,4,6,1,8]=>1010010=>0100101=>[2,3,2,1]
[3,5,2,7,4,6,1,8]=>0101010=>0101010=>[2,2,2,2]
[3,2,5,7,4,6,1,8]=>1001010=>0101001=>[2,2,3,1]
[3,7,5,2,4,6,1,8]=>0110010=>0100110=>[2,3,1,2]
[5,7,3,2,4,6,1,8]=>0110010=>0100110=>[2,3,1,2]
[1,5,3,2,4,7,6,8]=>0110010=>0100110=>[2,3,1,2]
[1,5,3,2,7,4,6,8]=>0110100=>0010110=>[3,2,1,2]
[3,7,2,5,4,1,6,8]=>0101100=>0011010=>[3,1,2,2]
[3,2,7,5,4,1,6,8]=>1011100=>0011101=>[3,1,1,2,1]
[5,1,3,2,4,7,6,8]=>1010010=>0100101=>[2,3,2,1]
[5,1,3,2,7,4,6,8]=>1010100=>0010101=>[3,2,2,1]
[7,1,3,2,5,4,6,8]=>1010100=>0010101=>[3,2,2,1]
[1,7,3,2,5,4,6,8]=>0110100=>0010110=>[3,2,1,2]
[1,7,3,5,2,4,6,8]=>0101000=>0001010=>[4,2,2]
[7,1,3,5,2,4,6,8]=>1001000=>0001001=>[4,3,1]
[5,1,3,7,2,4,6,8]=>1001000=>0001001=>[4,3,1]
[3,7,5,1,2,4,6,8]=>0110000=>0000110=>[5,1,2]
[5,7,3,1,2,4,6,8]=>0110000=>0000110=>[5,1,2]
[1,5,3,7,2,4,6,8]=>0101000=>0001010=>[4,2,2]
[3,5,7,2,1,4,6,8]=>0011000=>0001100=>[4,1,3]
[3,5,2,7,1,4,6,8]=>0101000=>0001010=>[4,2,2]
[3,2,5,7,4,1,6,8]=>1001100=>0011001=>[3,1,3,1]
[3,5,2,7,4,1,6,8]=>0101100=>0011010=>[3,1,2,2]
[3,5,7,2,4,1,6,8]=>0010100=>0010100=>[3,2,3]
[5,3,7,2,4,1,6,8]=>1010100=>0010101=>[3,2,2,1]
[7,3,5,2,1,4,6,8]=>1011000=>0001101=>[4,1,2,1]
[5,3,2,4,7,1,6,8]=>1100100=>0010011=>[3,3,1,1]
[3,2,5,4,7,1,6,8]=>1010100=>0010101=>[3,2,2,1]
[1,3,2,7,5,4,6,8]=>0101100=>0011010=>[3,1,2,2]
[1,3,7,2,5,4,6,8]=>0010100=>0010100=>[3,2,3]
[7,3,1,2,5,4,6,8]=>1100100=>0010011=>[3,3,1,1]
[5,3,1,2,7,4,6,8]=>1100100=>0010011=>[3,3,1,1]
[5,3,1,2,4,7,6,8]=>1100010=>0100011=>[2,4,1,1]
[3,5,2,1,4,7,6,8]=>0110010=>0100110=>[2,3,1,2]
[3,2,5,1,7,4,6,8]=>1010100=>0010101=>[3,2,2,1]
[3,5,2,1,7,4,6,8]=>0110100=>0010110=>[3,2,1,2]
[5,3,1,7,2,4,6,8]=>1101000=>0001011=>[4,2,1,1]
[7,3,1,5,2,4,6,8]=>1101000=>0001011=>[4,2,1,1]
[1,3,7,5,2,4,6,8]=>0011000=>0001100=>[4,1,3]
[7,5,1,3,2,4,6,8]=>1101000=>0001011=>[4,2,1,1]
[5,7,1,3,2,4,6,8]=>0101000=>0001010=>[4,2,2]
[3,7,1,5,2,4,6,8]=>0101000=>0001010=>[4,2,2]
[3,7,1,2,5,4,6,8]=>0100100=>0010010=>[3,3,2]
[3,1,2,7,5,4,6,8]=>1001100=>0011001=>[3,1,3,1]
[3,1,7,2,5,4,6,8]=>1010100=>0010101=>[3,2,2,1]
[3,1,7,5,2,4,6,8]=>1011000=>0001101=>[4,1,2,1]
[5,1,7,3,2,4,6,8]=>1011000=>0001101=>[4,1,2,1]
[7,1,5,3,2,4,6,8]=>1011000=>0001101=>[4,1,2,1]
[1,7,5,3,2,4,6,8]=>0111000=>0001110=>[4,1,1,2]
[5,8,7,1,2,6,4,3]=>0110011=>1100110=>[1,1,3,1,2]
[6,8,2,1,7,5,4,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,8,7,6,3,2,5,4]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,8,7,4,1,2,6,3]=>0111001=>1001110=>[1,3,1,1,2]
[2,8,7,4,3,6,1,5]=>0111010=>0101110=>[2,2,1,1,2]
[1,8,5,4,2,7,6,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,6,4,2,8,5,3,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[7,6,4,8,5,1,2,3]=>1101100=>0011011=>[3,1,2,1,1]
[1,6,7,5,3,8,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[7,6,3,5,2,4,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[7,6,4,2,5,1,8,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,6,2,8,3,1,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[1,6,7,5,8,2,3,4]=>0010100=>0010100=>[3,2,3]
[2,6,5,7,8,3,4,1]=>0100101=>1010010=>[1,2,3,2]
[3,2,5,1,7,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[5,2,3,4,8,6,1,7]=>1000110=>0110001=>[2,1,4,1]
[5,3,4,8,2,7,6,1]=>1001011=>1101001=>[1,1,2,3,1]
[5,3,8,2,4,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,8,4,1,7,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,4,2,5,1,8,7,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,4,3,5,8,2,1,7]=>1100110=>0110011=>[2,1,3,1,1]
[6,3,5,4,8,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,5,8,7,1,2,4]=>1001100=>0011001=>[3,1,3,1]
[1,5,7,3,4,8,6,2]=>0010011=>1100100=>[1,1,3,3]
[5,8,4,1,3,7,6,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,4,3,8,5,7,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,4,2,6,3,1,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[4,6,5,3,7,1,2,8]=>0110100=>0010110=>[3,2,1,2]
[3,5,6,1,4,8,7,2]=>0010011=>1100100=>[1,1,3,3]
[3,5,7,6,1,4,8,2]=>0011001=>1001100=>[1,3,1,3]
[3,6,5,7,4,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[4,2,6,5,1,7,3,8]=>1011010=>0101101=>[2,2,1,2,1]
[4,3,5,7,2,1,6,8]=>1001100=>0011001=>[3,1,3,1]
[3,5,4,7,2,6,1,8]=>0101010=>0101010=>[2,2,2,2]
[3,4,7,6,8,1,2,5]=>0010100=>0010100=>[3,2,3]
[1,8,4,3,7,5,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,2,8,6,4,7,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,8,6,3,7,4,2,5]=>0110110=>0110110=>[2,1,2,1,2]
[1,8,6,5,7,2,3,4]=>0110100=>0010110=>[3,2,1,2]
[4,2,8,3,5,7,1,6]=>1010010=>0100101=>[2,3,2,1]
[4,3,8,6,5,7,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[1,3,7,2,6,5,8,4]=>0010101=>1010100=>[1,2,2,3]
[1,5,7,2,4,6,8,3]=>0010001=>1000100=>[1,4,3]
[1,3,6,4,2,5,8,7]=>0011001=>1001100=>[1,3,1,3]
[5,6,3,4,7,1,8,2]=>0100101=>1010010=>[1,2,3,2]
[3,5,2,7,4,1,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[5,2,3,8,4,1,7,6]=>1001101=>1011001=>[1,2,1,3,1]
[7,5,3,4,8,2,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[7,6,3,8,4,2,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,2,8,5,1,6,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,4,3,8,5,2,6,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,2,8,5,1,3,4,6]=>1011000=>0001101=>[4,1,2,1]
[7,6,8,1,2,5,3,4]=>1010010=>0100101=>[2,3,2,1]
[1,5,3,7,6,8,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,2,6,4,5,8,3,7]=>0010010=>0100100=>[2,3,3]
[1,2,7,4,8,5,3,6]=>0010110=>0110100=>[2,1,2,3]
[1,6,3,7,8,2,4,5]=>0100100=>0010010=>[3,3,2]
[3,2,6,7,8,1,4,5]=>1000100=>0010001=>[3,4,1]
[1,4,7,3,5,2,6,8]=>0010100=>0010100=>[3,2,3]
[3,8,4,7,6,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[5,7,4,2,6,3,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[2,4,5,8,1,6,7,3]=>0001001=>1001000=>[1,3,4]
[6,1,3,7,4,2,5,8]=>1001100=>0011001=>[3,1,3,1]
[2,1,8,3,6,7,4,5]=>1010010=>0100101=>[2,3,2,1]
[5,1,8,6,2,7,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[5,7,1,4,2,6,3,8]=>0101010=>0101010=>[2,2,2,2]
[3,2,6,8,1,5,7,4]=>1001001=>1001001=>[1,3,3,1]
[8,2,6,1,5,4,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,5,4,1,6,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,6,2,7,8,1,5,4]=>0100101=>1010010=>[1,2,3,2]
[2,7,3,8,1,5,6,4]=>0101001=>1001010=>[1,3,2,2]
[2,6,8,4,1,5,7,3]=>0011001=>1001100=>[1,3,1,3]
[5,7,8,4,1,6,3,2]=>0011011=>1101100=>[1,1,2,1,3]
[3,4,8,1,2,5,7,6]=>0010001=>1000100=>[1,4,3]
[6,3,1,7,5,2,4,8]=>1101100=>0011011=>[3,1,2,1,1]
[6,3,1,8,2,7,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,8,1,2,4,3,6,5]=>0100101=>1010010=>[1,2,3,2]
[5,2,8,1,3,4,7,6]=>1010001=>1000101=>[1,4,2,1]
[3,2,1,6,4,7,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[4,1,3,6,5,7,8,2]=>1001001=>1001001=>[1,3,3,1]
[5,1,3,4,2,7,8,6]=>1001001=>1001001=>[1,3,3,1]
[6,1,3,4,2,8,5,7]=>1001010=>0101001=>[2,2,3,1]
[8,1,4,3,5,7,6,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,2,4,1,3,7,8,6]=>1010001=>1000101=>[1,4,2,1]
[3,2,6,1,5,7,8,4]=>1010001=>1000101=>[1,4,2,1]
[1,4,6,3,5,7,8,2]=>0010001=>1000100=>[1,4,3]
[3,5,1,6,4,7,8,2]=>0101001=>1001010=>[1,3,2,2]
[3,6,4,2,1,7,8,5]=>0111001=>1001110=>[1,3,1,1,2]
[3,8,6,1,4,7,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[1,8,3,2,6,7,5,4]=>0110011=>1100110=>[1,1,3,1,2]
[8,7,1,3,6,5,4,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[1,8,5,7,4,2,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,5,3,8,2,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[2,7,6,5,8,3,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[1,4,7,6,8,2,3,5]=>0010100=>0010100=>[3,2,3]
[3,5,7,4,8,1,2,6]=>0010100=>0010100=>[3,2,3]
[4,6,1,7,5,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[2,3,6,7,5,8,1,4]=>0001010=>0101000=>[2,2,4]
[1,3,7,5,6,8,2,4]=>0010010=>0100100=>[2,3,3]
[3,2,7,1,6,8,4,5]=>1010010=>0100101=>[2,3,2,1]
[8,1,5,4,7,2,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,5,3,7,1,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,4,7,5,8,3,6]=>1001010=>0101001=>[2,2,3,1]
[1,2,6,7,4,8,3,5]=>0001010=>0101000=>[2,2,4]
[3,6,4,7,8,5,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,2,5,8,6,7,4,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,3,5,8,7,4,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[8,3,5,7,6,4,2,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[4,1,8,3,7,5,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,7,2,8,5,6,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[1,4,8,7,3,5,6,2]=>0011001=>1001100=>[1,3,1,3]
[3,2,8,7,1,5,6,4]=>1011001=>1001101=>[1,3,1,2,1]
[1,5,8,7,4,6,2,3]=>0011010=>0101100=>[2,2,1,3]
[4,7,6,8,5,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[4,8,6,7,5,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[3,8,7,5,6,4,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[8,1,5,6,3,2,4,7]=>1001100=>0011001=>[3,1,3,1]
[1,7,8,3,5,2,4,6]=>0010100=>0010100=>[3,2,3]
[8,2,5,3,1,6,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,2,1,5,6,4,7]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,5,1,3,4,2,7]=>1110010=>0100111=>[2,3,1,1,1]
[1,7,8,5,4,3,2,6]=>0011110=>0111100=>[2,1,1,1,3]
[2,6,8,7,4,3,5,1]=>0011101=>1011100=>[1,2,1,1,3]
[2,7,6,8,4,3,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[1,2,6,7,8,4,3,5]=>0000110=>0110000=>[2,1,5]
[8,5,7,1,3,4,6,2]=>1010001=>1000101=>[1,4,2,1]
[3,5,8,6,7,4,1,2]=>0010110=>0110100=>[2,1,2,3]
[3,1,6,5,8,7,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,7,6,4,8,1,2,5]=>0110100=>0010110=>[3,2,1,2]
[2,3,6,5,7,1,8,4]=>0010101=>1010100=>[1,2,2,3]
[2,3,6,4,1,7,8,5]=>0011001=>1001100=>[1,3,1,3]
[4,7,2,1,5,3,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[3,1,7,4,5,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,7,5,4,2,1,8,6]=>0111101=>1011110=>[1,2,1,1,1,2]
[1,3,6,7,4,2,8,5]=>0001101=>1011000=>[1,2,1,4]
[4,3,7,2,6,8,1,5]=>1010010=>0100101=>[2,3,2,1]
[5,4,2,1,3,7,8,6]=>1110001=>1000111=>[1,4,1,1,1]
[8,7,1,5,6,3,2,4]=>1100110=>0110011=>[2,1,3,1,1]
[8,7,2,5,4,6,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,1,2,4,5,6,3]=>1100001=>1000011=>[1,5,1,1]
[8,7,2,5,3,1,6,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,7,3,2,1,5,6,4]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,7,6,5,1,3,4,2]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,7,6,1,4,5,3,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,7,5,6,1,4,3,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,8,7,1,5,4,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[8,5,7,6,1,4,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,7,8,1,5,4,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[8,7,4,6,5,1,3,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,6,7,1,4,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[8,7,6,3,5,4,1,2]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,7,4,5,6,1,3,2]=>1100101=>1010011=>[1,2,3,1,1]
[8,7,6,5,2,4,3,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[4,2,8,7,6,5,1,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,5,8,1,6,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,5,8,7,6,2,4,3]=>0011101=>1011100=>[1,2,1,1,3]
[7,5,8,4,1,6,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,8,5,1,7,4,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,6,8,7,2,5,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[7,3,8,4,6,1,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,8,5,7,1,6,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,3,7,6,5,1,8,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,4,3,6,7,1,8,2]=>1100101=>1010011=>[1,2,3,1,1]
[5,4,7,3,6,1,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,8,7,6,3,1,5,2]=>0111101=>1011110=>[1,2,1,1,1,2]
[2,4,6,3,1,7,8,5]=>0011001=>1001100=>[1,3,1,3]
[6,8,5,7,3,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[6,8,5,3,7,2,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,8,5,7,4,2,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[2,1,8,7,6,3,4,5]=>1011100=>0011101=>[3,1,1,2,1]
[5,8,7,6,2,4,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[6,8,2,7,5,1,4,3]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,7,2,6,4,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[6,8,7,5,2,4,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[5,8,7,6,4,2,3,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[2,3,6,1,7,5,8,4]=>0010101=>1010100=>[1,2,2,3]
[2,3,6,1,8,5,4,7]=>0010110=>0110100=>[2,1,2,3]
[2,4,1,6,7,5,8,3]=>0100101=>1010010=>[1,2,3,2]
[2,4,1,7,3,8,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[2,4,5,3,7,1,8,6]=>0010101=>1010100=>[1,2,2,3]
[2,4,5,7,3,8,6,1]=>0001011=>1101000=>[1,1,2,4]
[2,4,6,3,1,8,5,7]=>0011010=>0101100=>[2,2,1,3]
[2,4,6,3,8,5,1,7]=>0010110=>0110100=>[2,1,2,3]
[2,4,6,8,3,5,1,7]=>0001010=>0101000=>[2,2,4]
[2,4,7,3,1,5,8,6]=>0011001=>1001100=>[1,3,1,3]
[2,4,7,3,1,8,6,5]=>0011011=>1101100=>[1,1,2,1,3]
[2,4,7,8,3,5,6,1]=>0001001=>1001000=>[1,3,4]
[2,5,1,6,4,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[2,5,1,6,7,4,8,3]=>0100101=>1010010=>[1,2,3,2]
[2,5,1,7,4,3,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[2,5,6,3,4,8,1,7]=>0010010=>0100100=>[2,3,3]
[2,5,6,3,7,4,8,1]=>0010101=>1010100=>[1,2,2,3]
[2,5,6,3,8,4,1,7]=>0010110=>0110100=>[2,1,2,3]
[2,5,6,7,8,4,1,3]=>0000110=>0110000=>[2,1,5]
[2,5,6,8,4,3,1,7]=>0001110=>0111000=>[2,1,1,4]
[2,6,1,7,4,8,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,4,2,6,3,8,5,10,7,9]=>010101010=>010101010=>[2,2,2,2,2]
[6,8,4,3,2,1,7,5]=>0111101=>1011110=>[1,2,1,1,1,2]
[7,6,5,2,8,4,1,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,6,3,8,2,4,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,1,2,3,4,8,7,6]=>1000011=>1100001=>[1,1,5,1]
[4,1,2,3,7,6,5,8]=>1000110=>0110001=>[2,1,4,1]
[7,6,5,8,2,4,3,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,8,7,4,5,2,3,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,4,7,5,2,3,1]=>0101101=>1011010=>[1,2,1,2,2]
[6,8,4,7,2,5,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,4,8,7,5,2,3,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,8,4,2,7,5,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,8,4,7,2,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[6,8,4,7,3,5,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,4,8,2,7,5,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,8,4,2,7,1,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,4,2,8,7,5,3,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[6,8,4,7,3,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[6,8,4,2,1,7,5,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,8,4,7,3,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[6,8,5,7,1,4,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,7,3,6,2,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,7,2,3,6,1,4]=>0110010=>0100110=>[2,3,1,2]
[6,8,2,7,5,4,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[6,8,3,7,5,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[6,8,1,7,3,5,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,8,4,7,3,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,8,1,7,3,2,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[3,8,2,7,6,5,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[1,8,4,7,6,2,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,8,1,7,6,2,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,8,4,7,3,6,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,8,5,7,1,2,6,3]=>0101001=>1001010=>[1,3,2,2]
[1,8,4,7,3,2,6,5]=>0101101=>1011010=>[1,2,1,2,2]
[6,8,5,2,7,4,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[6,8,3,4,7,1,5,2]=>0100101=>1010010=>[1,2,3,2]
[6,8,1,3,7,2,5,4]=>0100101=>1010010=>[1,2,3,2]
[2,8,1,3,7,6,5,4]=>0100111=>1110010=>[1,1,1,3,2]
[2,8,3,4,7,6,1,5]=>0100110=>0110010=>[2,1,3,2]
[6,8,5,4,2,7,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[6,8,1,4,3,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,8,1,4,2,7,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[6,5,4,3,8,7,1,2]=>1110110=>0110111=>[2,1,2,1,1,1]
[3,1,7,2,8,5,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,7,4,8,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[3,1,5,7,8,4,6,2]=>1000101=>1010001=>[1,2,4,1]
[8,6,5,7,1,4,3,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,6,4,2,7,5,1,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,4,8,2,7,5,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,7,6,2,5,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[3,4,5,6,8,7,1,2]=>0000110=>0110000=>[2,1,5]
[3,4,5,7,8,6,1,2]=>0000110=>0110000=>[2,1,5]
[3,4,5,8,7,6,1,2]=>0001110=>0111000=>[2,1,1,4]
[3,4,6,7,8,5,1,2]=>0000110=>0110000=>[2,1,5]
[6,4,7,3,5,2,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,4,7,3,6,2,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,8,7,3,5,2,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[7,5,3,6,8,2,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[5,8,3,6,7,2,1,4]=>0100110=>0110010=>[2,1,3,2]
[5,8,7,3,2,4,1,6]=>0111010=>0101110=>[2,2,1,1,2]
[6,4,7,3,2,5,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[6,5,3,7,2,4,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,3,8,6,2,4,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[6,3,7,8,2,4,1,5]=>1001010=>0101001=>[2,2,3,1]
[5,3,7,6,2,4,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,8,2,6,4,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,8,2,5,6,1,3]=>1010010=>0100101=>[2,3,2,1]
[5,4,7,2,6,8,1,3]=>1010010=>0100101=>[2,3,2,1]
[4,8,7,2,5,6,1,3]=>0110010=>0100110=>[2,3,1,2]
[5,4,3,2,6,8,1,7]=>1110010=>0100111=>[2,3,1,1,1]
[4,8,3,2,5,6,1,7]=>0110010=>0100110=>[2,3,1,2]
[5,3,7,2,6,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,5,2,6,8,4,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[6,4,2,7,5,8,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,8,4,1,2,6,3]=>1011001=>1001101=>[1,3,1,2,1]
[7,1,8,2,3,6,5,4]=>1010011=>1100101=>[1,1,3,2,1]
[7,3,8,4,6,2,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,1,8,4,2,6,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,1,8,3,6,2,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,3,4,5,1,8,6]=>1000101=>1010001=>[1,2,4,1]
[2,8,3,4,5,1,6,7]=>0100100=>0010010=>[3,3,2]
[2,7,3,4,1,5,6,8]=>0101000=>0001010=>[4,2,2]
[5,3,6,1,2,7,4,8]=>1010010=>0100101=>[2,3,2,1]
[10,8,6,4,2,1,3,5,7,9]=>111110000=>000011111=>[5,1,1,1,1,1]
[2,8,5,3,4,6,7,1]=>0110001=>1000110=>[1,4,1,2]
[6,5,4,3,7,8,9,10,1,2]=>111000010=>010000111=>[2,5,1,1,1]
[3,8,1,4,5,6,7,2]=>0100001=>1000010=>[1,5,2]
[4,5,3,1,2,8,7,6]=>0110011=>1100110=>[1,1,3,1,2]
[5,7,3,4,1,6,8,2]=>0101001=>1001010=>[1,3,2,2]
[4,5,3,1,2,6,8,7]=>0110001=>1000110=>[1,4,1,2]
[3,4,1,2,5,8,7,6]=>0100011=>1100010=>[1,1,4,2]
[6,5,3,2,1,8,7,4]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[4,5,2,1,8,7,6,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,4,1,8,7,6,5,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[8,1,2,4,5,6,7,3]=>1000001=>1000001=>[1,6,1]
[7,1,2,3,4,6,8,5]=>1000001=>1000001=>[1,6,1]
[6,1,2,3,5,8,7,4]=>1000011=>1100001=>[1,1,5,1]
[5,1,2,4,8,6,7,3]=>1000101=>1010001=>[1,2,4,1]
[4,1,3,8,5,6,7,2]=>1001001=>1001001=>[1,3,3,1]
[7,1,2,3,5,8,6,4]=>1000011=>1100001=>[1,1,5,1]
[6,1,2,3,5,7,8,4]=>1000001=>1000001=>[1,6,1]
[10,1,2,3,4,6,7,8,9,5]=>100000001=>100000001=>[1,8,1]
[5,1,3,8,4,6,7,2]=>1001001=>1001001=>[1,3,3,1]
[4,1,3,5,8,6,7,2]=>1000101=>1010001=>[1,2,4,1]
[8,6,3,5,2,7,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,5,2,8,6,3,4,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,2,8,6,7,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,2,3,8,6,4,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[5,2,3,8,6,7,4,1]=>1001011=>1101001=>[1,1,2,3,1]
[8,4,1,7,3,5,6,2]=>1101001=>1001011=>[1,3,2,1,1]
[7,4,1,2,6,8,5,3]=>1100011=>1100011=>[1,1,4,1,1]
[5,3,8,4,1,2,6,7]=>1011000=>0001101=>[4,1,2,1]
[6,3,5,8,4,1,2,7]=>1001100=>0011001=>[3,1,3,1]
[7,3,5,6,8,4,1,2]=>1000110=>0110001=>[2,1,4,1]
[7,4,5,1,2,8,6,3]=>1010011=>1100101=>[1,1,3,2,1]
[6,3,8,4,5,1,2,7]=>1010100=>0010101=>[3,2,2,1]
[8,5,1,7,4,6,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,5,1,8,6,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,5,1,7,3,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,7,5,8,6,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,2,8,5,6,3,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,6,3,1,5,7,4,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,4,2,8,5,6,3,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,2,8,5,6,7,3,1]=>1010011=>1100101=>[1,1,3,2,1]
[7,4,8,5,6,1,2,3]=>1010100=>0010101=>[3,2,2,1]
[7,5,8,6,1,2,3,4]=>1011000=>0001101=>[4,1,2,1]
[7,3,4,8,5,6,1,2]=>1001010=>0101001=>[2,2,3,1]
[7,3,4,5,8,6,1,2]=>1000110=>0110001=>[2,1,4,1]
[6,4,8,5,2,3,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,6,3,1,7,5,2,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,2,8,3,4,5,6,1]=>1010001=>1000101=>[1,4,2,1]
[7,4,5,2,8,6,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,5,2,7,4,6,3,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,2,4,8,6,7,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[7,5,8,6,2,3,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,4,8,5,6,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,1,8,4,5,6,2]=>1101001=>1001011=>[1,3,2,1,1]
[7,2,4,5,6,8,3,1]=>1000011=>1100001=>[1,1,5,1]
[3,4,5,7,6,8,1,2]=>0001010=>0101000=>[2,2,4]
[4,8,2,5,1,3,7,6]=>0101001=>1001010=>[1,3,2,2]
[2,1,8,7,3,4,6,5]=>1011001=>1001101=>[1,3,1,2,1]
[2,7,4,5,6,8,1,3]=>0100010=>0100010=>[2,4,2]
[4,1,2,8,7,5,3,6]=>1001110=>0111001=>[2,1,1,3,1]
[4,1,2,6,8,3,7,5]=>1000101=>1010001=>[1,2,4,1]
[3,1,7,6,8,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[8,2,6,3,1,5,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[2,1,7,8,9,10,6,5,4,3]=>100001111=>111100001=>[1,1,1,1,5,1]
[7,3,5,1,8,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[7,8,3,1,5,2,4,6]=>0110100=>0010110=>[3,2,1,2]
[9,8,7,6,1,2,3,4,5,10]=>111100000=>000001111=>[6,1,1,1,1]
[1,5,6,7,8,3,4,2]=>0000101=>1010000=>[1,2,5]
[1,4,6,7,8,3,5,2]=>0000101=>1010000=>[1,2,5]
[1,5,6,3,7,8,4,2]=>0010011=>1100100=>[1,1,3,3]
[6,1,2,3,4,8,7,5]=>1000011=>1100001=>[1,1,5,1]
[5,1,2,3,8,7,6,4]=>1000111=>1110001=>[1,1,1,4,1]
[5,1,2,3,8,6,7,4]=>1000101=>1010001=>[1,2,4,1]
[2,8,5,3,1,4,6,7]=>0111000=>0001110=>[4,1,1,2]
[2,4,3,5,7,8,1,6]=>0100010=>0100010=>[2,4,2]
[2,6,3,7,8,1,4,5]=>0100100=>0010010=>[3,3,2]
[3,4,6,1,7,8,5,2]=>0010011=>1100100=>[1,1,3,3]
[3,4,6,1,8,5,7,2]=>0010101=>1010100=>[1,2,2,3]
[3,4,8,1,5,6,7,2]=>0010001=>1000100=>[1,4,3]
[3,5,1,7,4,8,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,6,4,8,1,7,2]=>0010101=>1010100=>[1,2,2,3]
[3,5,8,4,1,6,7,2]=>0011001=>1001100=>[1,3,1,3]
[3,6,1,8,5,4,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[3,6,7,4,8,5,1,2]=>0010110=>0110100=>[2,1,2,3]
[3,6,8,4,5,1,7,2]=>0010101=>1010100=>[1,2,2,3]
[4,1,5,6,8,3,7,2]=>1000101=>1010001=>[1,2,4,1]
[4,1,5,7,8,6,3,2]=>1000111=>1110001=>[1,1,1,4,1]
[4,1,7,3,5,8,6,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,1,7,8,5,6,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[4,5,7,3,8,6,1,2]=>0010110=>0110100=>[2,1,2,3]
[4,5,7,8,1,6,3,2]=>0001011=>1101000=>[1,1,2,4]
[4,5,8,3,1,6,7,2]=>0011001=>1001100=>[1,3,1,3]
[4,6,3,1,8,5,7,2]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,7,3,5,8,1,2]=>0010010=>0100100=>[2,3,3]
[4,6,7,8,5,1,3,2]=>0001101=>1011000=>[1,2,1,4]
[4,6,8,3,5,1,7,2]=>0010101=>1010100=>[1,2,2,3]
[4,7,3,1,8,6,5,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,7,8,3,5,6,1,2]=>0010010=>0100100=>[2,3,3]
[5,1,6,7,4,8,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[5,1,6,7,8,3,4,2]=>1000101=>1010001=>[1,2,4,1]
[5,6,3,4,8,1,7,2]=>0100101=>1010010=>[1,2,3,2]
[5,6,7,8,4,1,3,2]=>0001101=>1011000=>[1,2,1,4]
[5,7,3,4,1,8,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[5,7,3,4,8,6,1,2]=>0100110=>0110010=>[2,1,3,2]
[5,7,3,8,4,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[5,7,8,4,3,6,1,2]=>0011010=>0101100=>[2,2,1,3]
[6,1,3,7,8,5,4,2]=>1000111=>1110001=>[1,1,1,4,1]
[6,1,7,4,5,8,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[6,1,8,4,5,3,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,3,8,5,4,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[7,1,3,4,8,6,5,2]=>1000111=>1110001=>[1,1,1,4,1]
[8,4,1,3,2,5,6,7]=>1101000=>0001011=>[4,2,1,1]
[8,5,1,2,4,3,6,7]=>1100100=>0010011=>[3,3,1,1]
[8,6,1,2,3,5,4,7]=>1100010=>0100011=>[2,4,1,1]
[8,7,1,2,3,4,6,5]=>1100001=>1000011=>[1,5,1,1]
[8,5,1,4,2,3,6,7]=>1101000=>0001011=>[4,2,1,1]
[8,6,1,2,5,3,4,7]=>1100100=>0010011=>[3,3,1,1]
[8,7,1,2,3,6,4,5]=>1100010=>0100011=>[2,4,1,1]
[8,6,1,2,5,4,3,7]=>1100110=>0110011=>[2,1,3,1,1]
[2,5,8,6,1,7,3,4]=>0011010=>0101100=>[2,2,1,3]
[4,5,6,8,7,2,1,3]=>0001110=>0111000=>[2,1,1,4]
[5,6,8,7,2,3,1,4]=>0011010=>0101100=>[2,2,1,3]
[4,5,7,6,2,8,1,3]=>0011010=>0101100=>[2,2,1,3]
[4,8,2,5,6,1,3,7]=>0100100=>0010010=>[3,3,2]
[5,2,3,6,7,8,1,4]=>1000010=>0100001=>[2,5,1]
[4,2,8,7,5,3,1,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,2,8,6,7,5,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,3,2,4,8,5,7,6]=>0100101=>1010010=>[1,2,3,2]
[1,6,3,2,5,7,8,4]=>0110001=>1000110=>[1,4,1,2]
[2,5,6,1,8,7,3,4]=>0010110=>0110100=>[2,1,2,3]
[7,6,2,1,4,8,3,5]=>1110010=>0100111=>[2,3,1,1,1]
[2,6,5,1,8,7,3,4]=>0110110=>0110110=>[2,1,2,1,2]
[2,7,3,1,8,4,5,6]=>0110100=>0010110=>[3,2,1,2]
[1,4,2,7,3,8,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[1,2,7,3,8,6,5,4]=>0010111=>1110100=>[1,1,1,2,3]
[3,1,8,4,6,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,4,5,1,8,2,7,6]=>0010101=>1010100=>[1,2,2,3]
[3,8,1,6,5,2,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,5,2,3,8,7,4,6]=>0100110=>0110010=>[2,1,3,2]
[2,8,7,6,3,1,4,5]=>0111100=>0011110=>[3,1,1,1,2]
[8,7,2,5,3,1,4,6]=>1101100=>0011011=>[3,1,2,1,1]
[7,6,2,3,4,8,1,5]=>1100010=>0100011=>[2,4,1,1]
[8,7,6,2,1,4,3,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,2,7,4,1,5,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,7,3,2,4,5,8,6]=>0110001=>1000110=>[1,4,1,2]
[1,3,8,6,2,4,7,5]=>0011001=>1001100=>[1,3,1,3]
[1,2,3,8,4,7,6,5]=>0001011=>1101000=>[1,1,2,4]
[1,6,2,3,7,5,8,4]=>0100101=>1010010=>[1,2,3,2]
[4,5,1,2,8,3,7,6]=>0100101=>1010010=>[1,2,3,2]
[1,4,8,2,6,3,7,5]=>0010101=>1010100=>[1,2,2,3]
[8,4,1,7,3,2,5,6]=>1101100=>0011011=>[3,1,2,1,1]
[1,8,7,3,2,4,6,5]=>0111001=>1001110=>[1,3,1,1,2]
[8,3,1,5,6,2,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[3,4,1,6,5,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[3,5,1,6,2,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[5,4,3,6,1,7,2,8]=>1101010=>0101011=>[2,2,2,1,1]
[4,8,7,2,1,6,5,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,2,1,8,7,5,4,3]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[7,5,8,6,3,2,4,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,8,7,6,3,2,4,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,4,7,2,8,1,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,5,4,6,3,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,5,8,3,7,4,6]=>1001010=>0101001=>[2,2,3,1]
[2,1,7,4,8,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[1,2,3,5,8,7,4,6]=>0000110=>0110000=>[2,1,5]
[6,1,2,7,8,4,3,5]=>1000110=>0110001=>[2,1,4,1]
[5,1,4,8,2,7,3,6]=>1001010=>0101001=>[2,2,3,1]
[3,4,1,2,8,7,5,6]=>0100110=>0110010=>[2,1,3,2]
[1,2,5,7,8,6,3,4]=>0000110=>0110000=>[2,1,5]
[2,1,3,4,8,5,7,6]=>1000101=>1010001=>[1,2,4,1]
[6,2,5,1,7,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[1,5,4,8,6,2,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[2,5,1,8,6,3,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[2,1,3,7,4,8,6,5]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,5,8,1,7,3,6]=>1001010=>0101001=>[2,2,3,1]
[2,6,8,5,1,7,3,4]=>0011010=>0101100=>[2,2,1,3]
[1,3,2,7,8,5,4,6]=>0100110=>0110010=>[2,1,3,2]
[7,1,2,3,6,8,4,5]=>1000010=>0100001=>[2,5,1]
[5,1,2,3,8,4,7,6]=>1000101=>1010001=>[1,2,4,1]
[3,4,5,1,8,7,2,6]=>0010110=>0110100=>[2,1,2,3]
[4,1,2,3,8,7,5,6]=>1000110=>0110001=>[2,1,4,1]
[2,3,1,8,5,4,7,6]=>0101101=>1011010=>[1,2,1,2,2]
[2,3,8,4,1,5,7,6]=>0011001=>1001100=>[1,3,1,3]
[5,3,1,8,7,2,4,6]=>1101100=>0011011=>[3,1,2,1,1]
[3,6,1,8,7,2,4,5]=>0101100=>0011010=>[3,1,2,2]
[1,3,8,4,2,7,6,5]=>0011011=>1101100=>[1,1,2,1,3]
[1,2,3,8,5,7,4,6]=>0001010=>0101000=>[2,2,4]
[6,1,7,2,5,8,3,4]=>1010010=>0100101=>[2,3,2,1]
[4,5,1,8,7,2,3,6]=>0101100=>0011010=>[3,1,2,2]
[1,4,2,8,5,3,7,6]=>0101101=>1011010=>[1,2,1,2,2]
[3,1,5,2,8,6,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,6,5,2,1,4,3]=>0111101=>1011110=>[1,2,1,1,1,2]
[8,6,7,5,2,1,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,7,8,2,1,5,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[8,7,5,6,2,1,4,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,2,8,5,6,7,1,4]=>1010010=>0100101=>[2,3,2,1]
[4,2,5,1,8,7,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,7,8,6,3,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[4,2,6,1,5,8,3,7]=>1010010=>0100101=>[2,3,2,1]
[7,2,4,5,8,3,6,1]=>1000101=>1010001=>[1,2,4,1]
[2,4,7,8,6,1,5,3]=>0001101=>1011000=>[1,2,1,4]
[4,2,7,1,5,6,8,3]=>1010001=>1000101=>[1,4,2,1]
[3,2,5,8,1,6,7,4]=>1001001=>1001001=>[1,3,3,1]
[8,1,4,3,2,5,6,7]=>1011000=>0001101=>[4,1,2,1]
[1,7,3,2,4,5,6,8]=>0110000=>0000110=>[5,1,2]
[1,6,3,2,4,5,7,8]=>0110000=>0000110=>[5,1,2]
[1,3,8,4,2,5,6,7]=>0011000=>0001100=>[4,1,3]
[6,2,5,1,8,3,4,7]=>1010100=>0010101=>[3,2,2,1]
[5,1,8,2,4,3,6,7]=>1010100=>0010101=>[3,2,2,1]
[8,2,3,1,5,6,7,4]=>1010001=>1000101=>[1,4,2,1]
[1,7,2,4,5,8,6,3]=>0100011=>1100010=>[1,1,4,2]
[1,5,7,8,4,6,2,3]=>0001010=>0101000=>[2,2,4]
[6,5,8,3,4,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,5,8,2,3,4,1,7]=>1010010=>0100101=>[2,3,2,1]
[3,2,5,4,7,6,9,8,1,10]=>101010110=>011010101=>[2,1,2,2,2,1]
[1,4,3,6,5,8,7,10,9,2]=>010101011=>110101010=>[1,1,2,2,2,2]
[3,2,5,4,7,6,9,8,11,10,1,12]=>10101010110=>01101010101=>[2,1,2,2,2,2,1]
[4,2,1,3,5,8,6,7]=>1100010=>0100011=>[2,4,1,1]
[1,3,8,2,6,4,5,7]=>0010100=>0010100=>[3,2,3]
[6,1,2,7,4,3,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[5,4,1,2,3,8,6,7]=>1100010=>0100011=>[2,4,1,1]
[7,6,8,5,2,4,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[6,7,8,5,2,4,1,3]=>0011010=>0101100=>[2,2,1,3]
[3,4,5,8,2,1,7,6]=>0001101=>1011000=>[1,2,1,4]
[3,4,6,2,7,1,5,8]=>0010100=>0010100=>[3,2,3]
[3,4,6,2,8,1,7,5]=>0010101=>1010100=>[1,2,2,3]
[3,4,6,8,1,5,7,2]=>0001001=>1001000=>[1,3,4]
[3,4,6,1,5,2,7,8]=>0010100=>0010100=>[3,2,3]
[3,4,7,2,1,6,5,8]=>0011010=>0101100=>[2,2,1,3]
[3,4,7,1,5,6,2,8]=>0010010=>0100100=>[2,3,3]
[3,5,2,6,1,4,7,8]=>0101000=>0001010=>[4,2,2]
[3,5,2,7,1,6,4,8]=>0101010=>0101010=>[2,2,2,2]
[3,5,6,4,8,2,1,7]=>0010110=>0110100=>[2,1,2,3]
[3,5,6,4,1,2,7,8]=>0011000=>0001100=>[4,1,3]
[3,5,6,8,4,2,1,7]=>0001110=>0111000=>[2,1,1,4]
[3,5,6,8,1,2,7,4]=>0001001=>1001000=>[1,3,4]
[3,5,6,1,4,2,7,8]=>0010100=>0010100=>[3,2,3]
[3,5,7,4,2,8,1,6]=>0011010=>0101100=>[2,2,1,3]
[3,5,7,4,2,1,6,8]=>0011100=>0011100=>[3,1,1,3]
[3,5,7,4,8,1,6,2]=>0010101=>1010100=>[1,2,2,3]
[3,5,7,8,1,6,2,4]=>0001010=>0101000=>[2,2,4]
[3,5,7,1,4,6,2,8]=>0010010=>0100100=>[2,3,3]
[3,5,8,4,2,6,1,7]=>0011010=>0101100=>[2,2,1,3]
[3,5,8,1,4,6,7,2]=>0010001=>1000100=>[1,4,3]
[3,6,2,4,8,1,7,5]=>0100101=>1010010=>[1,2,3,2]
[3,6,2,7,8,5,1,4]=>0100110=>0110010=>[2,1,3,2]
[3,6,2,7,8,1,4,5]=>0100100=>0010010=>[3,3,2]
[3,6,2,1,5,4,7,8]=>0110100=>0010110=>[3,2,1,2]
[3,6,7,8,5,1,2,4]=>0001100=>0011000=>[3,1,4]
[3,6,7,8,1,5,2,4]=>0001010=>0101000=>[2,2,4]
[3,7,2,4,5,8,1,6]=>0100010=>0100010=>[2,4,2]
[3,7,2,4,8,1,6,5]=>0100101=>1010010=>[1,2,3,2]
[3,7,2,4,1,6,5,8]=>0101010=>0101010=>[2,2,2,2]
[3,7,2,8,5,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[3,7,8,4,5,1,6,2]=>0010101=>1010100=>[1,2,2,3]
[3,7,8,4,1,6,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[3,8,2,4,1,6,7,5]=>0101001=>1001010=>[1,3,2,2]
[3,8,2,1,5,6,7,4]=>0110001=>1000110=>[1,4,1,2]
[8,1,5,4,3,6,7,2]=>1011001=>1001101=>[1,3,1,2,1]
[8,1,4,5,3,6,7,2]=>1001001=>1001001=>[1,3,3,1]
[4,1,6,3,5,7,8,2]=>1010001=>1000101=>[1,4,2,1]
[4,1,7,3,5,6,8,2]=>1010001=>1000101=>[1,4,2,1]
[4,1,3,6,7,8,5,2]=>1000011=>1100001=>[1,1,5,1]
[4,6,2,3,5,1,7,8]=>0100100=>0010010=>[3,3,2]
[3,5,2,4,1,6,7,8]=>0101000=>0001010=>[4,2,2]
[5,8,2,3,4,6,1,7]=>0100010=>0100010=>[2,4,2]
[4,7,2,3,5,1,6,8]=>0100100=>0010010=>[3,3,2]
[5,7,2,3,4,6,8,1]=>0100001=>1000010=>[1,5,2]
[4,6,2,3,5,7,1,8]=>0100010=>0100010=>[2,4,2]
[2,3,7,8,1,6,5,4]=>0001011=>1101000=>[1,1,2,4]
[2,7,6,1,4,8,3,5]=>0110010=>0100110=>[2,3,1,2]
[2,6,8,1,4,5,7,3]=>0010001=>1000100=>[1,4,3]
[2,6,5,8,1,3,7,4]=>0101001=>1001010=>[1,3,2,2]
[6,4,7,5,8,2,3,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,4,1,8,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[6,7,8,1,4,2,5,3]=>0010101=>1010100=>[1,2,2,3]
[5,2,6,1,4,8,3,7]=>1010010=>0100101=>[2,3,2,1]
[7,2,3,5,8,1,4,6]=>1000100=>0010001=>[3,4,1]
[2,4,7,5,8,1,3,6]=>0010100=>0010100=>[3,2,3]
[2,3,6,5,1,8,7,4]=>0011011=>1101100=>[1,1,2,1,3]
[2,3,4,8,1,5,7,6]=>0001001=>1001000=>[1,3,4]
[2,3,4,7,8,1,6,5]=>0000101=>1010000=>[1,2,5]
[2,7,8,5,1,4,6,3]=>0011001=>1001100=>[1,3,1,3]
[2,3,7,5,8,1,4,6]=>0010100=>0010100=>[3,2,3]
[2,3,6,8,5,1,7,4]=>0001101=>1011000=>[1,2,1,4]
[7,6,4,5,1,8,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,6,8,1,5,2,3]=>1001010=>0101001=>[2,2,3,1]
[2,7,4,6,5,8,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,7,8,5,3,1,4]=>0001110=>0111000=>[2,1,1,4]
[2,5,6,1,4,8,3,7]=>0010010=>0100100=>[2,3,3]
[2,6,4,8,5,7,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,8,1,4,6,7,3]=>0010001=>1000100=>[1,4,3]
[7,2,3,4,8,1,6,5]=>1000101=>1010001=>[1,2,4,1]
[3,2,5,7,8,1,6,4]=>1000101=>1010001=>[1,2,4,1]
[6,4,1,7,8,2,3,5]=>1100100=>0010011=>[3,3,1,1]
[5,7,1,6,2,8,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,6,1,8,2,3,7,4]=>0101001=>1001010=>[1,3,2,2]
[7,3,5,1,6,8,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[6,3,4,5,8,2,1,7]=>1000110=>0110001=>[2,1,4,1]
[5,7,6,1,2,8,3,4]=>0110010=>0100110=>[2,3,1,2]
[5,6,8,1,2,4,7,3]=>0010001=>1000100=>[1,4,3]
[6,2,3,4,5,8,1,7]=>1000010=>0100001=>[2,5,1]
[4,7,1,3,8,2,6,5]=>0100101=>1010010=>[1,2,3,2]
[5,4,1,6,7,8,2,3]=>1100010=>0100011=>[2,4,1,1]
[7,4,1,5,8,2,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[5,7,1,8,6,2,3,4]=>0101100=>0011010=>[3,1,2,2]
[7,3,5,1,8,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,8,1,3,5,6,7,2]=>0100001=>1000010=>[1,5,2]
[8,1,2,3,7,5,6,4]=>1000101=>1010001=>[1,2,4,1]
[2,1,8,3,7,5,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,6,7,3,8,2,1,4]=>0010110=>0110100=>[2,1,2,3]
[5,6,8,3,1,2,7,4]=>0011001=>1001100=>[1,3,1,3]
[5,7,3,2,8,6,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[5,7,8,3,1,6,2,4]=>0011010=>0101100=>[2,2,1,3]
[5,8,3,2,1,6,7,4]=>0111001=>1001110=>[1,3,1,1,2]
[6,2,7,3,8,5,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,3,7,8,5,1,4]=>1000110=>0110001=>[2,1,4,1]
[6,7,3,2,8,5,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,7,8,3,5,1,2,4]=>0010100=>0010100=>[3,2,3]
[1,5,6,7,8,3,2,4]=>0000110=>0110000=>[2,1,5]
[1,5,8,3,2,6,7,4]=>0011001=>1001100=>[1,3,1,3]
[1,6,8,3,5,2,7,4]=>0010101=>1010100=>[1,2,2,3]
[1,7,3,2,8,6,5,4]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,7,8,3,5,6,2,4]=>0010010=>0100100=>[2,3,3]
[1,6,7,8,4,2,3,5]=>0001100=>0011000=>[3,1,4]
[1,2,6,8,4,3,7,5]=>0001101=>1011000=>[1,2,1,4]
[1,8,3,4,2,6,7,5]=>0101001=>1001010=>[1,3,2,2]
[1,2,8,4,3,6,7,5]=>0011001=>1001100=>[1,3,1,3]
[6,2,7,8,4,1,3,5]=>1001100=>0011001=>[3,1,3,1]
[6,2,3,7,8,1,4,5]=>1000100=>0010001=>[3,4,1]
[4,5,7,1,8,6,2,3]=>0010110=>0110100=>[2,1,2,3]
[4,5,7,8,2,6,1,3]=>0001010=>0101000=>[2,2,4]
[4,6,2,8,5,1,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,7,1,8,5,2,3]=>0010110=>0110100=>[2,1,2,3]
[4,7,2,8,5,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[4,8,2,1,5,6,7,3]=>0110001=>1000110=>[1,4,1,2]
[1,2,8,4,5,3,7,6]=>0010101=>1010100=>[1,2,2,3]
[1,2,3,8,5,4,7,6]=>0001101=>1011000=>[1,2,1,4]
[1,7,3,8,5,4,2,6]=>0101110=>0111010=>[2,1,1,2,2]
[5,2,7,4,8,6,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,7,8,4,6,1,3]=>1001010=>0101001=>[2,2,3,1]
[7,2,3,8,5,4,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[5,6,2,7,8,1,4,3]=>0100101=>1010010=>[1,2,3,2]
[5,8,2,4,1,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[6,2,1,7,8,5,4,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,7,2,4,8,5,1,3]=>0100110=>0110010=>[2,1,3,2]
[6,7,2,8,5,4,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[6,8,2,4,5,1,7,3]=>0100101=>1010010=>[1,2,3,2]
[3,2,5,6,8,1,4,7]=>1000100=>0010001=>[3,4,1]
[8,1,2,3,7,5,4,6]=>1000110=>0110001=>[2,1,4,1]
[4,1,8,2,7,5,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,1,8,3,4,5,2,6]=>1010010=>0100101=>[2,3,2,1]
[7,1,6,3,8,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[6,1,5,8,2,3,4,7]=>1001000=>0001001=>[4,3,1]
[8,1,6,7,4,2,3,5]=>1001100=>0011001=>[3,1,3,1]
[6,1,5,8,2,3,7,4]=>1001001=>1001001=>[1,3,3,1]
[4,1,7,2,5,8,3,6]=>1010010=>0100101=>[2,3,2,1]
[8,1,6,3,4,7,2,5]=>1010010=>0100101=>[2,3,2,1]
[7,1,6,8,2,5,3,4]=>1001010=>0101001=>[2,2,3,1]
[4,1,8,2,5,6,3,7]=>1010010=>0100101=>[2,3,2,1]
[4,1,8,2,5,6,7,3]=>1010001=>1000101=>[1,4,2,1]
[3,8,1,2,7,5,4,6]=>0100110=>0110010=>[2,1,3,2]
[3,8,1,7,4,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[5,4,7,1,2,8,3,6]=>1010010=>0100101=>[2,3,2,1]
[8,4,7,1,3,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,3,1,2,6,4]=>1011001=>1001101=>[1,3,1,2,1]
[3,8,1,2,4,5,7,6]=>0100001=>1000010=>[1,5,2]
[7,6,2,1,8,4,3,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,5,2,3,6,1,4,7]=>1100100=>0010011=>[3,3,1,1]
[8,5,7,1,4,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[3,6,1,4,2,8,5,7]=>0101010=>0101010=>[2,2,2,2]
[7,6,8,1,4,5,2,3]=>1010010=>0100101=>[2,3,2,1]
[3,7,1,4,2,8,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[5,4,3,8,2,1,7,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,8,7,3,2,1,6,4]=>0111101=>1011110=>[1,2,1,1,1,2]
[2,3,7,1,6,8,5,4]=>0010011=>1100100=>[1,1,3,3]
[2,6,1,5,7,4,8,3]=>0100101=>1010010=>[1,2,3,2]
[2,3,6,1,8,4,7,5]=>0010101=>1010100=>[1,2,2,3]
[3,5,1,4,6,7,8,2]=>0100001=>1000010=>[1,5,2]
[4,5,6,2,1,7,8,3]=>0011001=>1001100=>[1,3,1,3]
[5,2,4,7,6,3,8,1]=>1001101=>1011001=>[1,2,1,3,1]
[8,7,6,1,4,3,5,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,7,6,1,3,4,5,2]=>1110001=>1000111=>[1,4,1,1,1]
[8,7,1,4,5,6,3,2]=>1100011=>1100011=>[1,1,4,1,1]
[8,1,5,6,7,4,3,2]=>1000111=>1110001=>[1,1,1,4,1]
[5,8,3,4,1,6,2,7]=>0101010=>0101010=>[2,2,2,2]
[4,2,6,1,7,8,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[1,5,2,6,7,8,4,3]=>0100011=>1100010=>[1,1,4,2]
[4,5,2,7,8,6,1,3]=>0100110=>0110010=>[2,1,3,2]
[1,5,6,7,4,8,2,3]=>0001010=>0101000=>[2,2,4]
[4,2,6,8,5,1,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[4,2,7,8,5,6,1,3]=>1001010=>0101001=>[2,2,3,1]
[3,5,2,7,4,6,8,1]=>0101001=>1001010=>[1,3,2,2]
[5,6,2,7,3,8,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,2,8,4,6,7,1]=>0101001=>1001010=>[1,3,2,2]
[3,7,2,8,4,1,5,6]=>0101100=>0011010=>[3,1,2,2]
[3,5,2,4,7,8,6,1]=>0100011=>1100010=>[1,1,4,2]
[3,7,1,5,8,2,4,6]=>0100100=>0010010=>[3,3,2]
[5,1,3,8,2,4,6,7]=>1001000=>0001001=>[4,3,1]
[4,2,1,3,8,5,6,7]=>1100100=>0010011=>[3,3,1,1]
[1,8,7,6,3,4,5,2]=>0111001=>1001110=>[1,3,1,1,2]
[8,5,7,6,3,1,4,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,5,7,6,3,2,1,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,7,5,3,1,6,4,2]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[4,2,8,3,1,6,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[7,8,1,4,5,6,3,2]=>0100011=>1100010=>[1,1,4,2]
[4,2,8,3,5,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,7,8,1,6,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[6,8,1,4,5,3,7,2]=>0100101=>1010010=>[1,2,3,2]
[5,1,3,4,2,6,7,8]=>1001000=>0001001=>[4,3,1]
[4,2,7,3,1,6,5,8]=>1011010=>0101101=>[2,2,1,2,1]
[2,3,4,5,8,1,7,6]=>0000101=>1010000=>[1,2,5]
[4,1,5,3,6,7,8,2]=>1010001=>1000101=>[1,4,2,1]
[2,3,4,8,1,6,7,5]=>0001001=>1001000=>[1,3,4]
[5,1,4,6,3,7,8,2]=>1001001=>1001001=>[1,3,3,1]
[5,1,6,3,4,7,8,2]=>1010001=>1000101=>[1,4,2,1]
[2,1,7,5,3,8,6,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,1,8,7,5,3,6,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,5,3,2,1,8,6,4]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[5,2,3,4,1,8,6,7]=>1001010=>0101001=>[2,2,3,1]
[3,8,1,2,5,4,7,6]=>0100101=>1010010=>[1,2,3,2]
[7,4,6,8,5,3,2,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[7,5,8,6,3,2,1,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,4,8,5,6,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,5,8,6,4,2,1,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,4,2,1,8,5,3,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[5,3,8,7,4,2,1,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,4,2,1,6,8,5,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[5,3,8,4,2,1,6,7]=>1011100=>0011101=>[3,1,1,2,1]
[8,6,3,5,7,4,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,3,5,8,4,2,1,7]=>1001110=>0111001=>[2,1,1,3,1]
[6,4,8,7,5,2,1,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,5,2,1,3,8,6,4]=>1110011=>1100111=>[1,1,3,1,1,1]
[6,3,8,7,4,5,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,4,5,2,1,8,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,5,2,1,7,4,6,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,3,8,4,5,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,6,8,4,5,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[7,3,4,5,8,6,2,1]=>1000111=>1110001=>[1,1,1,4,1]
[7,3,8,4,5,6,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[1,8,7,2,6,5,4,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,8,7,6,2,3,4,5]=>0111000=>0001110=>[4,1,1,2]
[1,8,2,5,7,6,4,3]=>0100111=>1110010=>[1,1,1,3,2]
[1,8,2,5,6,7,4,3]=>0100011=>1100010=>[1,1,4,2]
[1,2,8,3,4,5,7,6]=>0010001=>1000100=>[1,4,3]
[7,6,1,2,3,8,4,5]=>1100010=>0100011=>[2,4,1,1]
[1,6,2,3,4,8,7,5]=>0100011=>1100010=>[1,1,4,2]
[6,4,1,2,8,3,5,7]=>1100100=>0010011=>[3,3,1,1]
[4,8,1,2,3,7,5,6]=>0100010=>0100010=>[2,4,2]
[6,4,1,7,2,3,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[7,1,6,2,3,8,4,5]=>1010010=>0100101=>[2,3,2,1]
[6,5,1,2,3,8,4,7]=>1100010=>0100011=>[2,4,1,1]
[1,8,5,2,3,7,4,6]=>0110010=>0100110=>[2,3,1,2]
[6,5,1,2,7,3,8,4]=>1100101=>1010011=>[1,2,3,1,1]
[7,6,4,1,8,2,3,5]=>1110100=>0010111=>[3,2,1,1,1]
[1,5,2,3,6,8,7,4]=>0100011=>1100010=>[1,1,4,2]
[7,3,1,2,8,4,5,6]=>1100100=>0010011=>[3,3,1,1]
[7,6,3,1,8,2,4,5]=>1110100=>0010111=>[3,2,1,1,1]
[5,3,6,1,2,4,8,7]=>1010001=>1000101=>[1,4,2,1]
[5,8,3,1,7,2,4,6]=>0110100=>0010110=>[3,2,1,2]
[7,5,4,1,8,2,3,6]=>1110100=>0010111=>[3,2,1,1,1]
[7,6,1,4,8,2,3,5]=>1100100=>0010011=>[3,3,1,1]
[1,2,8,5,3,7,4,6]=>0011010=>0101100=>[2,2,1,3]
[1,2,7,3,8,6,4,5]=>0010110=>0110100=>[2,1,2,3]
[7,5,1,6,8,2,3,4]=>1100100=>0010011=>[3,3,1,1]
[4,1,2,8,6,3,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,4,1,7,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,3,1,8,2,4,7]=>1110100=>0010111=>[3,2,1,1,1]
[3,8,1,6,7,2,4,5]=>0100100=>0010010=>[3,3,2]
[6,5,3,7,1,2,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[7,1,4,2,8,5,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[1,2,6,8,3,5,4,7]=>0001010=>0101000=>[2,2,4]
[1,2,3,7,8,6,4,5]=>0000110=>0110000=>[2,1,5]
[1,6,8,5,2,7,3,4]=>0011010=>0101100=>[2,2,1,3]
[7,6,3,4,1,8,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[1,4,8,2,3,7,6,5]=>0010011=>1100100=>[1,1,3,3]
[1,2,8,3,5,7,6,4]=>0010011=>1100100=>[1,1,3,3]
[4,5,1,7,6,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[3,4,8,1,2,6,7,5]=>0010001=>1000100=>[1,4,3]
[3,1,8,2,5,6,7,4]=>1010001=>1000101=>[1,4,2,1]
[1,4,2,5,6,8,7,3]=>0100011=>1100010=>[1,1,4,2]
[4,5,6,3,7,1,8,2]=>0010101=>1010100=>[1,2,2,3]
[4,2,5,6,7,8,3,1]=>1000011=>1100001=>[1,1,5,1]
[8,2,7,3,1,5,6,4]=>1011001=>1001101=>[1,3,1,2,1]
[7,2,1,8,4,5,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[4,2,7,1,3,8,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[8,2,6,3,4,7,1,5]=>1010010=>0100101=>[2,3,2,1]
[7,2,3,4,1,8,6,5]=>1001011=>1101001=>[1,1,2,3,1]
[6,1,8,2,7,5,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,8,1,5,6,3,7]=>1010010=>0100101=>[2,3,2,1]
[8,2,7,3,1,4,5,6]=>1011000=>0001101=>[4,1,2,1]
[5,2,1,3,6,7,8,4]=>1100001=>1000011=>[1,5,1,1]
[6,4,8,7,3,2,1,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,5,3,8,7,2,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[5,4,8,7,3,2,1,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,4,3,8,7,2,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,3,8,7,5,2,1,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[5,6,8,1,4,2,7,3]=>0010101=>1010100=>[1,2,2,3]
[5,6,3,1,4,2,7,8]=>0110100=>0010110=>[3,2,1,2]
[5,7,3,8,4,1,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[5,7,3,1,4,6,2,8]=>0110010=>0100110=>[2,3,1,2]
[5,7,3,4,8,1,6,2]=>0100101=>1010010=>[1,2,3,2]
[5,2,6,1,4,3,7,8]=>1010100=>0010101=>[3,2,2,1]
[5,8,3,1,4,6,7,2]=>0110001=>1000110=>[1,4,1,2]
[6,2,7,4,1,5,3,8]=>1011010=>0101101=>[2,2,1,2,1]
[6,7,3,8,1,5,2,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,4,1,5,2,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,8,1,5,4,2,3]=>0010110=>0110100=>[2,1,2,3]
[4,5,6,7,1,3,2,8]=>0001010=>0101000=>[2,2,4]
[6,7,1,4,5,3,2,8]=>0100110=>0110010=>[2,1,3,2]
[4,5,7,8,2,1,6,3]=>0001101=>1011000=>[1,2,1,4]
[7,2,3,8,1,6,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[7,2,3,8,5,1,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[7,2,3,1,5,6,4,8]=>1010010=>0100101=>[2,3,2,1]
[7,2,8,4,1,6,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,2,8,4,5,1,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,6,3,8,1,5,7,2]=>0101001=>1001010=>[1,3,2,2]
[7,8,3,4,1,6,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,7,3,8,1,2,5]=>0010100=>0010100=>[3,2,3]
[4,6,7,8,1,5,3,2]=>0001011=>1101000=>[1,1,2,4]
[4,6,7,1,5,2,3,8]=>0010100=>0010100=>[3,2,3]
[4,6,8,3,1,5,7,2]=>0011001=>1001100=>[1,3,1,3]
[4,6,1,3,5,2,7,8]=>0100100=>0010010=>[3,3,2]
[4,7,3,8,5,1,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,3,8,1,6,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,7,2,3,4,6,8,5]=>0100001=>1000010=>[1,5,2]
[8,1,2,3,5,6,4,7]=>1000010=>0100001=>[2,5,1]
[4,1,8,2,7,3,5,6]=>1010100=>0010101=>[3,2,2,1]
[1,8,4,2,7,3,5,6]=>0110100=>0010110=>[3,2,1,2]
[7,4,1,2,6,8,3,5]=>1100010=>0100011=>[2,4,1,1]
[8,7,1,2,4,5,3,6]=>1100010=>0100011=>[2,4,1,1]
[4,1,8,2,3,5,7,6]=>1010001=>1000101=>[1,4,2,1]
[6,1,2,8,3,4,7,5]=>1001001=>1001001=>[1,3,3,1]
[5,4,1,2,7,8,3,6]=>1100010=>0100011=>[2,4,1,1]
[1,5,2,8,3,4,7,6]=>0101001=>1001010=>[1,3,2,2]
[7,1,2,5,3,6,8,4]=>1001001=>1001001=>[1,3,3,1]
[1,8,2,5,6,3,7,4]=>0100101=>1010010=>[1,2,3,2]
[1,5,2,4,6,7,8,3]=>0100001=>1000010=>[1,5,2]
[6,8,1,3,4,2,5,7]=>0100100=>0010010=>[3,3,2]
[3,1,8,2,5,4,6,7]=>1010100=>0010101=>[3,2,2,1]
[3,1,7,5,8,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[1,7,3,2,8,4,5,6]=>0110100=>0010110=>[3,2,1,2]
[6,3,5,1,8,2,4,7]=>1010100=>0010101=>[3,2,2,1]
[1,6,4,2,3,5,8,7]=>0110001=>1000110=>[1,4,1,2]
[1,7,4,2,3,5,8,6]=>0110001=>1000110=>[1,4,1,2]
[1,7,4,2,3,6,8,5]=>0110001=>1000110=>[1,4,1,2]
[1,2,7,3,8,4,6,5]=>0010101=>1010100=>[1,2,2,3]
[7,1,3,4,5,8,2,6]=>1000010=>0100001=>[2,5,1]
[7,6,1,3,4,8,2,5]=>1100010=>0100011=>[2,4,1,1]
[1,8,7,6,3,2,4,5]=>0111100=>0011110=>[3,1,1,1,2]
[1,8,2,7,5,3,6,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,7,4,5,2,6,8,3]=>0101001=>1001010=>[1,3,2,2]
[1,4,8,5,6,2,7,3]=>0010101=>1010100=>[1,2,2,3]
[3,2,1,8,7,6,4,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,2,1,8,7,5,4,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,2,1,8,7,4,6,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,2,1,8,7,4,5,6]=>1101100=>0011011=>[3,1,2,1,1]
[3,2,1,8,4,7,6,5]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,2,8,7,6,1,5,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,3,8,7,6,2,1,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,5,8,7,3,2,1,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,4,8,5,6,3,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[4,5,3,8,6,2,7,1]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,2,8,5,3,7,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,3,8,4,6,2,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,6,2,7,1,8,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[4,7,1,6,2,8,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[6,2,5,3,8,4,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,6,5,3,8,2,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,3,7,4,5,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,8,4,3,2,1,6]=>0011110=>0111100=>[2,1,1,1,3]
[4,6,8,7,3,2,1,5]=>0011110=>0111100=>[2,1,1,1,3]
[2,4,8,7,6,5,1,3]=>0011110=>0111100=>[2,1,1,1,3]
[4,7,6,8,3,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[3,6,8,5,7,2,1,4]=>0010110=>0110100=>[2,1,2,3]
[4,6,7,8,3,2,1,5]=>0001110=>0111000=>[2,1,1,4]
[3,5,6,8,7,2,1,4]=>0001110=>0111000=>[2,1,1,4]
[1,4,8,7,6,3,5,2]=>0011101=>1011100=>[1,2,1,1,3]
[2,4,5,8,7,6,1,3]=>0001110=>0111000=>[2,1,1,4]
[2,5,4,7,3,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[2,6,4,7,8,3,1,5]=>0100110=>0110010=>[2,1,3,2]
[2,4,7,1,8,3,6,5]=>0010101=>1010100=>[1,2,2,3]
[2,4,6,1,5,8,3,7]=>0010010=>0100100=>[2,3,3]
[3,4,1,7,6,8,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,6,1,7,8,4,2,5]=>0100110=>0110010=>[2,1,3,2]
[3,5,1,7,2,6,8,4]=>0101001=>1001010=>[1,3,2,2]
[4,3,6,2,8,1,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,4,7,2,8,1,6]=>1001010=>0101001=>[2,2,3,1]
[4,5,7,2,1,8,3,6]=>0011010=>0101100=>[2,2,1,3]
[4,5,7,2,1,6,8,3]=>0011001=>1001100=>[1,3,1,3]
[4,6,5,2,8,7,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,5,8,2,1,6,7,3]=>0011001=>1001100=>[1,3,1,3]
[3,4,1,5,6,8,7,2]=>0100011=>1100010=>[1,1,4,2]
[3,6,1,7,2,5,8,4]=>0101001=>1001010=>[1,3,2,2]
[7,3,4,5,8,2,1,6]=>1000110=>0110001=>[2,1,4,1]
[6,3,7,8,2,5,1,4]=>1001010=>0101001=>[2,2,3,1]
[6,7,4,8,2,5,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,1,4,7,2,8,6]=>0100101=>1010010=>[1,2,3,2]
[4,3,7,5,6,2,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,4,8,6,2,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[4,7,8,5,6,2,1,3]=>0010110=>0110100=>[2,1,2,3]
[3,5,1,4,8,7,2,6]=>0100110=>0110010=>[2,1,3,2]
[4,5,6,3,8,2,1,7]=>0010110=>0110100=>[2,1,2,3]
[4,2,6,3,7,8,1,5]=>1010010=>0100101=>[2,3,2,1]
[4,2,7,3,5,8,1,6]=>1010010=>0100101=>[2,3,2,1]
[4,5,3,7,8,1,6,2]=>0100101=>1010010=>[1,2,3,2]
[4,2,6,8,5,3,1,7]=>1001110=>0111001=>[2,1,1,3,1]
[5,1,2,7,8,6,4,3]=>1000111=>1110001=>[1,1,1,4,1]
[4,1,2,7,8,6,3,5]=>1000110=>0110001=>[2,1,4,1]
[4,1,8,7,2,6,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[4,1,5,8,7,3,2,6]=>1001110=>0111001=>[2,1,1,3,1]
[5,1,8,2,7,6,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,1,6,2,8,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[4,7,8,3,2,5,1,6]=>0011010=>0101100=>[2,2,1,3]
[4,5,2,8,7,3,1,6]=>0101110=>0111010=>[2,1,1,2,2]
[4,5,7,6,8,3,1,2]=>0010110=>0110100=>[2,1,2,3]
[8,2,1,7,4,6,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,2,1,6,8,4,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[4,5,2,8,7,1,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[5,2,7,6,8,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,5,7,3,1,8,6]=>1001101=>1011001=>[1,2,1,3,1]
[4,2,8,7,1,3,6,5]=>1011001=>1001101=>[1,3,1,2,1]
[8,2,1,7,3,5,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[5,2,6,3,8,7,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,8,6,4,1,7,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,2,3,8,7,1,4,6]=>1001100=>0011001=>[3,1,3,1]
[5,1,8,3,7,4,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,1,2,7,5,4,3,6]=>1001110=>0111001=>[2,1,1,3,1]
[6,1,2,8,3,7,4,5]=>1001010=>0101001=>[2,2,3,1]
[5,6,7,3,8,1,2,4]=>0010100=>0010100=>[3,2,3]
[4,1,7,6,8,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,1,7,3,5,4,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,1,6,3,4,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,8,5,2,3,4]=>1001100=>0011001=>[3,1,3,1]
[8,1,7,3,5,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,3,8,7,5,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[3,8,5,7,2,4,1,6]=>0101010=>0101010=>[2,2,2,2]
[3,6,5,8,2,1,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,1,8,3,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[7,6,2,3,4,1,8,5]=>1100101=>1010011=>[1,2,3,1,1]
[4,8,6,7,1,2,3,5]=>0101000=>0001010=>[4,2,2]
[8,5,7,3,1,6,2,4]=>1011010=>0101101=>[2,2,1,2,1]
[3,4,7,2,1,5,8,6]=>0011001=>1001100=>[1,3,1,3]
[3,8,6,1,4,7,2,5]=>0110010=>0100110=>[2,3,1,2]
[3,7,6,8,2,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[8,6,2,3,1,5,7,4]=>1101001=>1001011=>[1,3,2,1,1]
[3,8,7,1,2,5,6,4]=>0110001=>1000110=>[1,4,1,2]
[3,4,8,2,5,6,7,1]=>0010001=>1000100=>[1,4,3]
[4,2,1,3,7,6,5,8]=>1100110=>0110011=>[2,1,3,1,1]
[6,3,4,8,7,5,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[8,3,5,7,6,1,4,2]=>1001101=>1011001=>[1,2,1,3,1]
[2,1,8,5,6,7,3,4]=>1010010=>0100101=>[2,3,2,1]
[6,8,4,5,7,2,3,1]=>0100101=>1010010=>[1,2,3,2]
[8,3,2,5,6,7,1,4]=>1100010=>0100011=>[2,4,1,1]
[7,3,2,6,8,5,4,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[4,8,5,3,2,7,6,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,3,5,6,8,1,4,2]=>1000101=>1010001=>[1,2,4,1]
[7,4,8,3,6,5,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,5,6,3,8,4,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,4,5,2,8,3,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,8,6,7,3,5,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,3,1,2,6,7,8,5]=>1100001=>1000011=>[1,5,1,1]
[7,4,6,5,8,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,8,5,2,6,7,3,1]=>0110011=>1100110=>[1,1,3,1,2]
[2,5,8,6,7,3,1,4]=>0010110=>0110100=>[2,1,2,3]
[1,4,6,5,2,7,3,8]=>0011010=>0101100=>[2,2,1,3]
[3,7,4,8,6,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[2,3,4,1,8,7,5,6]=>0010110=>0110100=>[2,1,2,3]
[4,2,6,5,1,8,7,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,5,4,1,3,2,8,7]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,5,4,2,1,3,8,7]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,7,4,3,6,1,5,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,8,4,2,1,5,6,3]=>0111001=>1001110=>[1,3,1,1,2]
[8,6,7,2,4,5,1,3]=>1010010=>0100101=>[2,3,2,1]
[7,8,2,3,6,1,5,4]=>0100101=>1010010=>[1,2,3,2]
[6,8,2,7,3,5,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,7,8,4,5,6,3]=>1001001=>1001001=>[1,3,3,1]
[7,5,8,3,2,4,6,1]=>1011001=>1001101=>[1,3,1,2,1]
[8,6,7,3,4,1,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,2,7,1,3,5,4]=>1101001=>1001011=>[1,3,2,1,1]
[8,3,2,7,6,4,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,5,4,1,3,7,6,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[5,8,2,3,4,7,6,1]=>0100011=>1100010=>[1,1,4,2]
[6,8,2,7,3,4,1,5]=>0101010=>0101010=>[2,2,2,2]
[5,6,1,4,7,2,3,8]=>0100100=>0010010=>[3,3,2]
[4,5,1,6,3,2,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[3,6,7,4,1,2,5,8]=>0011000=>0001100=>[4,1,3]
[2,5,1,4,3,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[1,4,5,3,7,2,8,6]=>0010101=>1010100=>[1,2,2,3]
[5,1,4,3,7,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[1,6,7,4,3,2,8,5]=>0011101=>1011100=>[1,2,1,1,3]
[2,6,7,3,1,4,5,8]=>0011000=>0001100=>[4,1,3]
[5,1,4,6,7,2,3,8]=>1000100=>0010001=>[3,4,1]
[2,6,4,3,1,8,5,7]=>0111010=>0101110=>[2,2,1,1,2]
[1,6,5,2,3,4,8,7]=>0110001=>1000110=>[1,4,1,2]
[7,8,2,1,5,4,3,6]=>0110110=>0110110=>[2,1,2,1,2]
[7,8,1,2,3,6,4,5]=>0100010=>0100010=>[2,4,2]
[1,4,7,8,5,2,3,6]=>0001100=>0011000=>[3,1,4]
[1,3,2,6,5,8,4,7]=>0101010=>0101010=>[2,2,2,2]
[2,1,5,7,8,4,3,6]=>1000110=>0110001=>[2,1,4,1]
[3,1,7,2,6,5,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[1,3,2,7,5,4,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[1,4,5,8,6,2,3,7]=>0001100=>0011000=>[3,1,4]
[1,6,7,2,3,5,8,4]=>0010001=>1000100=>[1,4,3]
[2,4,1,8,6,5,3,7]=>0101110=>0111010=>[2,1,1,2,2]
[7,1,4,5,8,3,6,2]=>1000101=>1010001=>[1,2,4,1]
[3,7,8,5,4,6,1,2]=>0011010=>0101100=>[2,2,1,3]
[5,1,7,2,6,4,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,3,4,6,8,5,7,1]=>0000101=>1010000=>[1,2,5]
[3,6,2,4,7,5,8,1]=>0100101=>1010010=>[1,2,3,2]
[3,7,2,8,4,6,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,7,5,2,3,6,8,1]=>0110001=>1000110=>[1,4,1,2]
[4,3,5,8,7,2,6,1]=>1001101=>1011001=>[1,2,1,3,1]
[2,3,4,8,7,5,6,1]=>0001101=>1011000=>[1,2,1,4]
[5,1,6,3,7,8,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,6,7,5,1,8,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,7,6,3,4,8,1,2]=>0110010=>0100110=>[2,3,1,2]
[6,4,7,5,8,3,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,6,7,5,8,1,4,2]=>0010101=>1010100=>[1,2,2,3]
[1,8,5,6,7,3,4,2]=>0100101=>1010010=>[1,2,3,2]
[3,2,7,4,6,1,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,8,4,5,6,7,2,1]=>0100011=>1100010=>[1,1,4,2]
[8,2,4,1,6,7,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[3,4,8,7,6,1,5,2]=>0011101=>1011100=>[1,2,1,1,3]
[4,3,8,7,6,2,5,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,7,8,5,6,4,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[3,4,7,5,8,6,1,2]=>0010110=>0110100=>[2,1,2,3]
[5,4,6,2,3,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,1,5,4,2,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,4,5,3,2,1,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,8,3,4,6,5,1,2]=>0100110=>0110010=>[2,1,3,2]
[2,1,7,6,8,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,5,4,8,6,3,7,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,4,7,6,1,8,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,5,3,7,4,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[2,1,8,5,3,7,6,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,5,4,2,7,8,3,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[2,6,8,5,7,4,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[2,1,8,6,7,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,5,3,1,6,4,7,8]=>0110100=>0010110=>[3,2,1,2]
[7,5,4,2,3,1,8,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,3,2,4,5,8,1,7]=>1100010=>0100011=>[2,4,1,1]
[3,5,4,2,8,6,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[5,6,8,7,3,2,1,4]=>0011110=>0111100=>[2,1,1,1,3]
[6,4,5,3,2,8,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[4,2,5,7,3,1,6,8]=>1001100=>0011001=>[3,1,3,1]
[7,4,1,3,2,6,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[6,1,4,3,2,7,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[1,6,4,2,3,7,8,5]=>0110001=>1000110=>[1,4,1,2]
[1,4,5,3,8,2,6,7]=>0010100=>0010100=>[3,2,3]
[2,5,4,3,8,1,6,7]=>0110100=>0010110=>[3,2,1,2]
[6,2,5,1,3,7,4,8]=>1010010=>0100101=>[2,3,2,1]
[7,6,5,8,1,2,4,3]=>1101001=>1001011=>[1,3,2,1,1]
[5,7,4,1,3,6,2,8]=>0110010=>0100110=>[2,3,1,2]
[4,3,8,1,6,7,2,5]=>1010010=>0100101=>[2,3,2,1]
[4,3,8,1,6,5,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,8,2,5,6,7,1]=>1010001=>1000101=>[1,4,2,1]
[5,4,8,2,3,6,7,1]=>1010001=>1000101=>[1,4,2,1]
[3,2,8,1,6,7,4,5]=>1010010=>0100101=>[2,3,2,1]
[5,2,8,1,6,7,3,4]=>1010010=>0100101=>[2,3,2,1]
[7,2,6,3,8,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,4,5,8,2,7,1]=>1000101=>1010001=>[1,2,4,1]
[7,3,8,1,4,5,6,2]=>1010001=>1000101=>[1,4,2,1]
[7,3,4,5,8,1,6,2]=>1000101=>1010001=>[1,2,4,1]
[7,4,8,1,5,6,2,3]=>1010010=>0100101=>[2,3,2,1]
[7,2,8,1,6,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,1,3,4,6,5,2,7]=>1000110=>0110001=>[2,1,4,1]
[8,6,5,7,2,1,4,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,8,6,3,7,4,5,2]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,5,1,7,6,4,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,8,1,3,5,6,7,4]=>0100001=>1000010=>[1,5,2]
[2,4,8,7,5,6,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[3,8,7,5,2,6,4,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,8,7,3,4,6,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[2,8,1,4,5,7,6,3]=>0100011=>1100010=>[1,1,4,2]
[1,2,7,6,8,4,5,3]=>0010101=>1010100=>[1,2,2,3]
[1,2,5,3,7,6,8,4]=>0010101=>1010100=>[1,2,2,3]
[3,7,8,1,5,6,2,4]=>0010010=>0100100=>[2,3,3]
[1,2,4,8,3,6,5,7]=>0001010=>0101000=>[2,2,4]
[4,1,3,7,6,8,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[6,5,7,8,1,4,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[3,1,8,6,7,5,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,8,3,1,7,5,4,6]=>0110110=>0110110=>[2,1,2,1,2]
[2,8,3,7,1,4,5,6]=>0101000=>0001010=>[4,2,2]
[4,8,2,7,5,1,3,6]=>0101100=>0011010=>[3,1,2,2]
[4,1,2,6,7,5,3,8]=>1000110=>0110001=>[2,1,4,1]
[1,2,5,3,8,6,4,7]=>0010110=>0110100=>[2,1,2,3]
[5,8,7,6,2,1,3,4]=>0111100=>0011110=>[3,1,1,1,2]
[6,4,8,3,7,5,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,6,8,2,5,7,4,1]=>0010011=>1100100=>[1,1,3,3]
[4,8,7,5,2,6,3,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,2,8,5,6,1,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,4,8,1,5,7,6,2]=>0010011=>1100100=>[1,1,3,3]
[4,5,6,2,7,3,8,1]=>0010101=>1010100=>[1,2,2,3]
[4,7,5,6,2,3,8,1]=>0101001=>1001010=>[1,3,2,2]
[3,5,7,6,2,4,8,1]=>0011001=>1001100=>[1,3,1,3]
[1,6,8,7,4,5,3,2]=>0011011=>1101100=>[1,1,2,1,3]
[8,3,5,7,6,2,4,1]=>1001101=>1011001=>[1,2,1,3,1]
[6,4,5,2,8,7,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,4,2,7,8,5,3,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[2,4,5,8,6,7,1,3]=>0001010=>0101000=>[2,2,4]
[1,3,5,6,8,7,2,4]=>0000110=>0110000=>[2,1,5]
[5,7,4,1,6,2,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,5,6,7,8,2,4,1]=>0000101=>1010000=>[1,2,5]
[5,2,4,1,6,7,8,3]=>1010001=>1000101=>[1,4,2,1]
[8,5,6,7,2,4,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[7,8,4,5,1,6,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,8,6,4,7,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,5,6,8,3,7,2,1]=>0001011=>1101000=>[1,1,2,4]
[8,4,5,7,6,2,3,1]=>1001101=>1011001=>[1,2,1,3,1]
[4,8,6,7,5,2,3,1]=>0101101=>1011010=>[1,2,1,2,2]
[8,7,4,3,6,5,1,2]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,1,4,3,6,5,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,1,2,5,4,3,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[2,8,6,3,4,7,1,5]=>0110010=>0100110=>[2,3,1,2]
[8,1,2,3,5,7,4,6]=>1000010=>0100001=>[2,5,1]
[8,1,2,3,6,5,4,7]=>1000110=>0110001=>[2,1,4,1]
[8,1,2,3,7,6,5,4]=>1000111=>1110001=>[1,1,1,4,1]
[2,8,1,6,7,5,3,4]=>0100110=>0110010=>[2,1,3,2]
[8,1,2,3,5,4,7,6]=>1000101=>1010001=>[1,2,4,1]
[4,8,5,2,7,1,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,7,8,6,4,2,1,5]=>0011110=>0111100=>[2,1,1,1,3]
[3,7,8,4,6,2,1,5]=>0010110=>0110100=>[2,1,2,3]
[8,3,1,5,7,6,2,4]=>1100110=>0110011=>[2,1,3,1,1]
[4,5,2,8,6,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[8,4,5,1,3,2,6,7]=>1010100=>0010101=>[3,2,2,1]
[8,1,2,3,6,7,5,4]=>1000011=>1100001=>[1,1,5,1]
[8,1,6,7,2,5,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[5,4,1,3,2,8,7,6]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,4,2,1,3,8,7,6]=>1110011=>1100111=>[1,1,3,1,1,1]
[3,2,7,4,1,6,5,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,7,3,2,1,6,4,8]=>0111010=>0101110=>[2,2,1,1,2]
[7,6,5,1,3,4,2,8]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,5,2,1,4,3,8]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,6,2,4,3,5,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[7,6,5,1,4,2,3,8]=>1110100=>0010111=>[3,2,1,1,1]
[1,7,6,3,2,4,5,8]=>0111000=>0001110=>[4,1,1,2]
[8,7,3,2,1,6,4,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[1,5,7,2,4,3,6,8]=>0010100=>0010100=>[3,2,3]
[5,2,8,1,4,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,8,2,4,5,3]=>1001001=>1001001=>[1,3,3,1]
[8,4,6,2,3,7,1,5]=>1010010=>0100101=>[2,3,2,1]
[8,6,1,3,7,5,2,4]=>1100110=>0110011=>[2,1,3,1,1]
[5,8,1,3,4,7,2,6]=>0100010=>0100010=>[2,4,2]
[5,8,6,2,3,1,4,7]=>0110100=>0010110=>[3,2,1,2]
[5,8,7,3,2,4,6,1]=>0111001=>1001110=>[1,3,1,1,2]
[7,6,2,8,3,5,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,7,5,2,6,3,1,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,4,7,3,1,5,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[8,2,6,3,1,4,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[8,3,2,7,6,1,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[3,8,2,7,6,4,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[3,6,7,5,8,2,1,4]=>0010110=>0110100=>[2,1,2,3]
[6,3,5,2,8,7,4,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,8,4,3,2,7,6,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,4,6,8,7,3,5,1]=>0001101=>1011000=>[1,2,1,4]
[6,3,5,7,8,2,4,1]=>1000101=>1010001=>[1,2,4,1]
[4,6,8,7,5,2,3,1]=>0011101=>1011100=>[1,2,1,1,3]
[3,5,6,8,7,2,4,1]=>0001101=>1011000=>[1,2,1,4]
[1,6,8,4,7,5,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[3,8,6,5,1,7,2,4]=>0111010=>0101110=>[2,2,1,1,2]
[8,4,6,7,5,2,3,1]=>1001101=>1011001=>[1,2,1,3,1]
[8,4,5,7,2,6,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,7,4,3,8,5,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,6,8,5,4,7,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,7,4,6,8,5,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[6,4,7,8,3,5,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[5,2,4,1,6,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,5,2,7,4,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,4,2,6,1,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,3,7,4,6,1,8,5]=>0010101=>1010100=>[1,2,2,3]
[2,1,7,4,6,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,4,2,6,3,8,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,4,7,2,6,1,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,7,4,6,1,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,4,1,7,6,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,7,5,6,1,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,7,5,6,3,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,4,3,7,5,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[2,6,4,3,7,5,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,5,4,8,6,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,3,7,5,8,6,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[6,7,4,8,3,5,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,5,8,7,4,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,8,3,4,6,7,2,1]=>0100011=>1100010=>[1,1,4,2]
[6,4,3,8,7,2,5,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,6,8,5,4,7,1,2]=>0011010=>0101100=>[2,2,1,3]
[7,5,3,6,8,4,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,4,3,5,7,2,6,1]=>1100101=>1010011=>[1,2,3,1,1]
[4,7,8,6,3,5,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[6,7,5,8,2,4,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,4,1,7,8,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[4,3,1,5,6,8,7,2]=>1100011=>1100011=>[1,1,4,1,1]
[1,6,3,2,5,8,7,4]=>0110011=>1100110=>[1,1,3,1,2]
[8,1,5,3,2,6,7,4]=>1011001=>1001101=>[1,3,1,2,1]
[1,6,8,3,2,4,7,5]=>0011001=>1001100=>[1,3,1,3]
[1,8,7,6,4,2,3,5]=>0111100=>0011110=>[3,1,1,1,2]
[8,1,7,3,5,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,3,8,4,6,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[3,2,8,1,5,6,7,4]=>1010001=>1000101=>[1,4,2,1]
[8,6,1,2,4,5,7,3]=>1100001=>1000011=>[1,5,1,1]
[1,8,6,7,3,4,5,2]=>0101001=>1001010=>[1,3,2,2]
[1,7,3,8,2,4,6,5]=>0101001=>1001010=>[1,3,2,2]
[8,4,3,1,5,6,7,2]=>1110001=>1000111=>[1,4,1,1,1]
[1,8,7,6,3,4,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[1,8,5,3,7,6,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[3,5,2,6,1,4,8,7]=>0101001=>1001010=>[1,3,2,2]
[4,5,7,2,3,8,6,1]=>0010011=>1100100=>[1,1,3,3]
[4,5,7,2,3,8,1,6]=>0010010=>0100100=>[2,3,3]
[4,5,6,2,3,1,8,7]=>0010101=>1010100=>[1,2,2,3]
[4,5,6,2,1,3,8,7]=>0011001=>1001100=>[1,3,1,3]
[4,5,6,1,3,2,8,7]=>0010101=>1010100=>[1,2,2,3]
[4,5,6,3,1,2,8,7]=>0011001=>1001100=>[1,3,1,3]
[4,5,7,3,2,8,1,6]=>0011010=>0101100=>[2,2,1,3]
[4,6,7,3,8,2,5,1]=>0010101=>1010100=>[1,2,2,3]
[4,6,7,3,8,2,1,5]=>0010110=>0110100=>[2,1,2,3]
[4,5,7,3,1,8,2,6]=>0011010=>0101100=>[2,2,1,3]
[3,5,1,7,4,8,2,6]=>0101010=>0101010=>[2,2,2,2]
[2,1,5,7,4,8,3,6]=>1001010=>0101001=>[2,2,3,1]
[4,5,7,1,3,8,6,2]=>0010011=>1100100=>[1,1,3,3]
[4,6,7,3,8,1,5,2]=>0010101=>1010100=>[1,2,2,3]
[5,6,7,8,3,1,4,2]=>0001101=>1011000=>[1,2,1,4]
[4,6,7,1,8,3,5,2]=>0010101=>1010100=>[1,2,2,3]
[3,6,1,7,8,4,5,2]=>0100101=>1010010=>[1,2,3,2]
[2,1,6,7,8,4,5,3]=>1000101=>1010001=>[1,2,4,1]
[2,1,6,7,8,4,3,5]=>1000110=>0110001=>[2,1,4,1]
[4,6,7,1,8,3,2,5]=>0010110=>0110100=>[2,1,2,3]
[5,6,7,8,1,3,2,4]=>0001010=>0101000=>[2,2,4]
[4,6,7,2,8,3,5,1]=>0010101=>1010100=>[1,2,2,3]
[3,6,2,7,8,4,5,1]=>0100101=>1010010=>[1,2,3,2]
[3,6,2,7,8,4,1,5]=>0100110=>0110010=>[2,1,3,2]
[3,4,2,1,7,8,5,6]=>0110010=>0100110=>[2,3,1,2]
[4,6,7,2,8,5,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,6,7,2,8,5,1,3]=>0010110=>0110100=>[2,1,2,3]
[4,5,7,1,2,8,6,3]=>0010011=>1100100=>[1,1,3,3]
[2,1,6,7,8,3,5,4]=>1000101=>1010001=>[1,2,4,1]
[3,6,1,7,8,2,5,4]=>0100101=>1010010=>[1,2,3,2]
[4,6,7,1,8,2,5,3]=>0010101=>1010100=>[1,2,2,3]
[5,6,7,8,1,2,4,3]=>0001001=>1001000=>[1,3,4]
[5,6,7,8,2,4,1,3]=>0001010=>0101000=>[2,2,4]
[5,6,7,8,2,4,3,1]=>0001011=>1101000=>[1,1,2,4]
[3,6,1,7,8,5,2,4]=>0100110=>0110010=>[2,1,3,2]
[2,1,6,7,8,5,3,4]=>1000110=>0110001=>[2,1,4,1]
[3,4,2,1,6,5,8,7,10,9]=>011010101=>101010110=>[1,2,2,2,1,2]
[3,5,2,6,4,1,8,7,10,9]=>010110101=>101011010=>[1,2,2,1,2,2]
[3,5,2,7,4,8,6,1,10,9]=>010101101=>101101010=>[1,2,1,2,2,2]
[2,1,5,6,4,3,8,7,10,9]=>100110101=>101011001=>[1,2,2,1,3,1]
[4,5,6,3,2,1,8,7,10,9]=>001110101=>101011100=>[1,2,2,1,1,3]
[4,5,7,3,2,8,6,1,10,9]=>001101101=>101101100=>[1,2,1,2,1,3]
[4,5,7,3,2,9,6,10,8,1]=>001101011=>110101100=>[1,1,2,2,1,3]
[2,1,5,7,4,8,6,3,10,9]=>100101101=>101101001=>[1,2,1,2,3,1]
[4,6,7,3,8,5,2,1,10,9]=>001011101=>101110100=>[1,2,1,1,2,3]
[4,6,7,3,9,5,2,10,8,1]=>001011011=>110110100=>[1,1,2,1,2,3]
[2,1,5,7,4,9,6,10,8,3]=>100101011=>110101001=>[1,1,2,2,3,1]
[2,1,4,3,7,8,6,5,10,9]=>101001101=>101100101=>[1,2,1,3,2,1]
[3,4,2,1,7,8,6,5,10,9]=>011001101=>101100110=>[1,2,1,3,1,2]
[3,6,2,7,8,5,4,1,10,9]=>010011101=>101110010=>[1,2,1,1,3,2]
[3,6,2,7,9,5,4,10,8,1]=>010011011=>110110010=>[1,1,2,1,3,2]
[2,1,6,7,8,5,4,3,10,9]=>100011101=>101110001=>[1,2,1,1,4,1]
[5,6,7,8,4,3,2,1,10,9]=>000111101=>101111000=>[1,2,1,1,1,4]
[5,6,7,9,4,3,2,10,8,1]=>000111011=>110111000=>[1,1,2,1,1,4]
[2,1,6,7,9,5,4,10,8,3]=>100011011=>110110001=>[1,1,2,1,4,1]
[5,6,8,9,4,3,10,7,2,1]=>000110111=>111011000=>[1,1,1,2,1,4]
[2,1,4,3,7,9,6,10,8,5]=>101001011=>110100101=>[1,1,2,3,2,1]
[3,4,2,1,7,9,6,10,8,5]=>011001011=>110100110=>[1,1,2,3,1,2]
[3,6,2,8,9,5,10,7,4,1]=>010010111=>111010010=>[1,1,1,2,3,2]
[2,1,6,8,9,5,10,7,4,3]=>100010111=>111010001=>[1,1,1,2,4,1]
[2,1,4,3,6,5,9,10,8,7]=>101010011=>110010101=>[1,1,3,2,2,1]
[3,4,2,1,6,5,9,10,8,7]=>011010011=>110010110=>[1,1,3,2,1,2]
[3,5,2,6,4,1,9,10,8,7]=>010110011=>110011010=>[1,1,3,1,2,2]
[3,5,2,8,4,9,10,7,6,1]=>010100111=>111001010=>[1,1,1,3,2,2]
[2,1,5,6,4,3,9,10,8,7]=>100110011=>110011001=>[1,1,3,1,3,1]
[4,5,6,3,2,1,9,10,8,7]=>001110011=>110011100=>[1,1,3,1,1,3]
[4,5,8,3,2,9,10,7,6,1]=>001100111=>111001100=>[1,1,1,3,1,3]
[2,1,5,8,4,9,10,7,6,3]=>100100111=>111001001=>[1,1,1,3,3,1]
[4,7,8,3,9,10,6,5,2,1]=>001001111=>111100100=>[1,1,1,1,3,3]
[2,1,4,3,8,9,10,7,6,5]=>101000111=>111000101=>[1,1,1,4,2,1]
[3,4,2,1,8,9,10,7,6,5]=>011000111=>111000110=>[1,1,1,4,1,2]
[3,7,2,8,9,10,6,5,4,1]=>010001111=>111100010=>[1,1,1,1,4,2]
[5,3,1,6,2,4,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[7,3,1,5,2,8,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,5,1,2,7,3,6]=>1010010=>0100101=>[2,3,2,1]
[7,4,5,1,2,8,3,6]=>1010010=>0100101=>[2,3,2,1]
[6,4,5,1,2,3,8,7]=>1010001=>1000101=>[1,4,2,1]
[5,4,6,1,2,3,8,7]=>1010001=>1000101=>[1,4,2,1]
[3,6,1,5,2,4,8,7]=>0101001=>1001010=>[1,3,2,2]
[4,6,5,1,2,3,8,7]=>0110001=>1000110=>[1,4,1,2]
[5,6,4,1,2,3,8,7]=>0110001=>1000110=>[1,4,1,2]
[7,5,4,1,2,8,3,6]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,4,1,7,2,3,5]=>1110100=>0010111=>[3,2,1,1,1]
[5,7,4,1,2,8,3,6]=>0110010=>0100110=>[2,3,1,2]
[3,7,1,5,2,8,4,6]=>0101010=>0101010=>[2,2,2,2]
[2,1,7,5,3,8,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[4,8,5,1,2,7,3,6]=>0110010=>0100110=>[2,3,1,2]
[6,8,4,1,7,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[4,8,6,1,7,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[2,1,8,6,7,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[2,1,7,6,8,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[4,7,6,1,8,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[5,7,6,8,1,2,3,4]=>0101000=>0001010=>[4,2,2]
[6,4,7,1,8,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[8,4,6,1,7,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[8,3,1,6,7,2,4,5]=>1100100=>0010011=>[3,3,1,1]
[4,3,1,2,7,8,5,6]=>1100010=>0100011=>[2,4,1,1]
[8,4,7,1,6,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[7,4,8,1,6,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[4,5,8,1,2,7,3,6]=>0010010=>0100100=>[2,3,3]
[2,1,6,8,7,3,4,5]=>1001100=>0011001=>[3,1,3,1]
[4,6,8,1,7,2,3,5]=>0010100=>0010100=>[3,2,3]
[5,6,8,7,1,2,3,4]=>0011000=>0001100=>[4,1,3]
[8,5,7,6,1,2,3,4]=>1011000=>0001101=>[4,1,2,1]
[4,7,8,1,6,2,3,5]=>0010100=>0010100=>[3,2,3]
[3,7,1,8,6,2,4,5]=>0101100=>0011010=>[3,1,2,2]
[3,8,1,7,6,2,4,5]=>0101100=>0011010=>[3,1,2,2]
[4,8,7,1,6,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[6,8,7,5,1,2,3,4]=>0111000=>0001110=>[4,1,1,2]
[6,4,7,3,8,5,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[5,4,2,7,6,1,3,8]=>1101100=>0011011=>[3,1,2,1,1]
[5,4,2,7,6,1,8,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,4,3,7,6,8,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,3,7,8,6,1,2]=>1100110=>0110011=>[2,1,3,1,1]
[5,4,3,8,6,7,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,3,6,8,7,1,2]=>1100110=>0110011=>[2,1,3,1,1]
[5,4,2,6,7,1,8,3]=>1100101=>1010011=>[1,2,3,1,1]
[5,3,2,6,1,7,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,3,2,6,1,7,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,2,6,1,8,7,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,4,2,6,8,1,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[6,4,8,2,5,1,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,2,8,6,1,3,7]=>1101100=>0011011=>[3,1,2,1,1]
[5,3,2,6,1,8,4,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,8,2,1,5,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[7,8,3,2,1,5,4,6]=>0111010=>0101110=>[2,2,1,1,2]
[7,8,3,2,1,5,6,4]=>0111001=>1001110=>[1,3,1,1,2]
[6,3,8,2,1,5,7,4]=>1011001=>1001101=>[1,3,1,2,1]
[5,3,2,8,1,6,7,4]=>1101001=>1001011=>[1,3,2,1,1]
[5,4,2,7,8,1,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[5,3,2,7,1,8,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,3,2,7,1,6,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,7,2,1,5,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[6,3,7,2,1,5,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[6,3,7,2,1,8,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,5,7,8,2,1,4,3]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,7,2,1,4,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[5,3,2,7,1,4,8,6]=>1101001=>1001011=>[1,3,2,1,1]
[5,4,2,8,7,1,3,6]=>1101100=>0011011=>[3,1,2,1,1]
[7,8,4,2,6,1,3,5]=>0110100=>0010110=>[3,2,1,2]
[7,8,3,2,1,6,4,5]=>0111010=>0101110=>[2,2,1,1,2]
[6,3,8,2,1,7,4,5]=>1011010=>0101101=>[2,2,1,2,1]
[5,3,2,8,1,7,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,3,2,1,8,7,5,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[4,3,2,1,7,5,8,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,3,2,1,7,5,6,8]=>1110100=>0010111=>[3,2,1,1,1]
[5,3,2,8,1,4,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[6,3,8,2,1,4,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[7,8,3,2,1,4,6,5]=>0111001=>1001110=>[1,3,1,1,2]
[4,3,2,1,8,5,6,7]=>1110100=>0010111=>[3,2,1,1,1]
[7,8,5,6,1,2,4,3]=>0101001=>1001010=>[1,3,2,2]
[7,8,4,1,6,2,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[1,6,8,3,2,7,5,4]=>0011011=>1101100=>[1,1,2,1,3]
[6,1,8,3,2,7,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,8,1,3,2,6,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[7,8,3,1,2,6,5,4]=>0110011=>1100110=>[1,1,3,1,2]
[7,8,2,3,1,6,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[7,8,2,1,3,6,5,4]=>0110011=>1100110=>[1,1,3,1,2]
[7,8,1,2,3,6,5,4]=>0100011=>1100010=>[1,1,4,2]
[1,5,2,8,3,7,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[5,1,2,8,3,7,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[5,2,1,8,3,7,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,2,8,1,3,7,5,4]=>1010011=>1100101=>[1,1,3,2,1]
[6,2,8,4,7,1,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,8,4,7,5,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[2,6,8,3,1,7,5,4]=>0011011=>1101100=>[1,1,2,1,3]
[2,5,1,8,3,7,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,2,5,8,3,7,6,4]=>0001011=>1101000=>[1,1,2,4]
[2,5,3,8,1,7,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,4,8,7,1,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,4,8,7,6,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[5,3,4,8,7,6,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[5,2,4,8,7,1,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,2,3,8,1,7,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[4,1,2,3,8,7,6,5]=>1000111=>1110001=>[1,1,1,4,1]
[1,4,2,3,8,7,6,5]=>0100111=>1110010=>[1,1,1,3,2]
[4,1,3,2,8,7,6,5]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,3,8,1,2,7,5,4]=>1010011=>1100101=>[1,1,3,2,1]
[5,3,1,8,2,7,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,1,3,8,2,7,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[1,5,3,8,2,7,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,5,4,8,7,2,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[5,1,4,8,7,2,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,4,1,8,7,2,6,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,5,8,7,1,2,4,3]=>1011001=>1001101=>[1,3,1,2,1]
[5,6,8,7,3,4,1,2]=>0011010=>0101100=>[2,2,1,3]
[5,6,8,7,2,1,4,3]=>0011101=>1011100=>[1,2,1,1,3]
[4,5,1,8,7,2,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,1,5,8,7,2,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[1,3,5,8,2,7,6,4]=>0001011=>1101000=>[1,1,2,4]
[3,1,5,8,2,7,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[3,6,8,2,1,7,5,4]=>0011011=>1101100=>[1,1,2,1,3]
[4,6,8,3,7,5,1,2]=>0010110=>0110100=>[2,1,2,3]
[4,5,3,8,7,6,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[3,5,2,8,1,7,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[3,1,4,2,8,7,6,5]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,2,5,8,1,7,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,5,8,7,1,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[4,3,5,8,7,6,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[2,4,5,8,7,1,6,3]=>0001101=>1011000=>[1,2,1,4]
[2,3,5,8,1,7,6,4]=>0001011=>1101000=>[1,1,2,4]
[6,2,5,1,4,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,6,1,4,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,7,1,4,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,8,1,4,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,7,1,4,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,6,1,4,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,5,1,4,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,4,3,7,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,6,1,5,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,6,1,5,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,7,1,5,3,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,8,1,5,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,8,1,3,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,1,4,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,1,5,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,8,1,5,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,7,3,8,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,8,3,7,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,8,3,7,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,3,7,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,7,4,8,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,7,3,8,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,7,3,8,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,8,2,6,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,6,3,7,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,4,2,6,8,1,5,7]=>0100100=>0010010=>[3,3,2]
[5,3,6,2,8,1,4,7]=>1010100=>0010101=>[3,2,2,1]
[7,4,2,5,8,3,6,1]=>1100101=>1010011=>[1,2,3,1,1]
[4,5,2,6,3,8,1,7]=>0101010=>0101010=>[2,2,2,2]
[3,5,6,1,4,8,2,7]=>0010010=>0100100=>[2,3,3]
[4,1,5,6,3,8,2,7]=>1001010=>0101001=>[2,2,3,1]
[4,5,1,6,3,8,2,7]=>0101010=>0101010=>[2,2,2,2]
[4,5,6,3,2,8,1,7]=>0011010=>0101100=>[2,2,1,3]
[6,7,4,8,3,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[6,7,4,8,3,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[6,7,4,1,8,3,2,5]=>0110110=>0110110=>[2,1,2,1,2]
[5,3,7,8,1,4,2,6]=>1001010=>0101001=>[2,2,3,1]
[7,3,5,8,1,4,6,2]=>1001001=>1001001=>[1,3,3,1]
[4,5,1,7,8,3,6,2]=>0100101=>1010010=>[1,2,3,2]
[7,4,1,5,8,3,6,2]=>1100101=>1010011=>[1,2,3,1,1]
[6,7,4,3,8,1,5,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,6,1,7,3,8,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[5,1,6,7,3,8,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[6,4,7,1,8,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,8,3,1,4,5,2]=>0011001=>1001100=>[1,3,1,3]
[6,7,2,8,4,5,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,7,2,8,4,1,3,5]=>0101100=>0011010=>[3,1,2,2]
[6,1,7,4,8,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,6,7,3,2,8,4]=>1001101=>1011001=>[1,2,1,3,1]
[5,6,1,7,3,2,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[5,6,7,3,2,1,8,4]=>0011101=>1011100=>[1,2,1,1,3]
[5,6,7,3,2,8,4,1]=>0011011=>1101100=>[1,1,2,1,3]
[7,4,2,5,1,8,3,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,7,4,2,8,3,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[3,6,7,2,8,4,5,1]=>0010101=>1010100=>[1,2,2,3]
[3,6,7,2,8,4,1,5]=>0010110=>0110100=>[2,1,2,3]
[3,6,7,2,1,8,4,5]=>0011010=>0101100=>[2,2,1,3]
[3,4,7,8,2,1,5,6]=>0001100=>0011000=>[3,1,4]
[3,7,8,1,4,6,2,5]=>0010010=>0100100=>[2,3,3]
[3,6,7,2,8,5,1,4]=>0010110=>0110100=>[2,1,2,3]
[3,6,7,8,5,2,1,4]=>0001110=>0111000=>[2,1,1,4]
[3,6,7,8,5,2,4,1]=>0001101=>1011000=>[1,2,1,4]
[6,4,7,8,2,5,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,4,7,8,2,1,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,3,7,8,1,6,2,4]=>1001010=>0101001=>[2,2,3,1]
[6,7,2,8,5,1,3,4]=>0101100=>0011010=>[3,1,2,2]
[6,4,1,7,8,2,5,3]=>1100101=>1010011=>[1,2,3,1,1]
[5,1,6,2,7,8,4,3]=>1010011=>1100101=>[1,1,3,2,1]
[5,6,2,7,1,8,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,6,2,7,8,4,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[5,6,7,2,8,4,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[5,6,7,2,1,8,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[5,6,1,7,2,8,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,1,6,7,2,8,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[6,7,8,3,5,1,4,2]=>0010101=>1010100=>[1,2,2,3]
[5,6,1,7,8,4,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[5,6,7,1,8,4,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[8,3,2,5,1,6,4,7]=>1101010=>0101011=>[2,2,2,1,1]
[5,3,2,7,4,1,8,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,5,3,8,2,4,6,1]=>1101001=>1001011=>[1,3,2,1,1]
[8,2,4,5,6,3,1,7]=>1000110=>0110001=>[2,1,4,1]
[8,2,4,5,6,1,3,7]=>1000100=>0010001=>[3,4,1]
[8,5,3,6,4,1,2,7]=>1101100=>0011011=>[3,1,2,1,1]
[8,4,1,5,6,3,2,7]=>1100110=>0110011=>[2,1,3,1,1]
[8,1,4,5,6,3,2,7]=>1000110=>0110001=>[2,1,4,1]
[4,5,3,7,2,1,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[7,4,5,8,3,2,6,1]=>1001101=>1011001=>[1,2,1,3,1]
[4,3,6,7,2,8,5,1]=>1001011=>1101001=>[1,1,2,3,1]
[4,3,6,7,2,8,1,5]=>1001010=>0101001=>[2,2,3,1]
[1,4,3,6,7,2,8,5]=>0100101=>1010010=>[1,2,3,2]
[4,5,3,7,1,8,2,6]=>0101010=>0101010=>[2,2,2,2]
[5,3,4,7,1,2,8,6]=>1001001=>1001001=>[1,3,3,1]
[7,4,5,8,3,6,1,2]=>1001010=>0101001=>[2,2,3,1]
[4,3,6,7,8,1,5,2]=>1000101=>1010001=>[1,2,4,1]
[3,5,6,7,8,4,1,2]=>0000110=>0110000=>[2,1,5]
[3,1,5,6,7,8,4,2]=>1000011=>1100001=>[1,1,5,1]
[4,6,1,7,8,3,5,2]=>0100101=>1010010=>[1,2,3,2]
[6,2,4,1,7,8,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[2,6,7,1,4,8,3,5]=>0010010=>0100100=>[2,3,3]
[1,5,3,6,7,8,2,4]=>0100010=>0100010=>[2,4,2]
[4,5,2,7,8,1,3,6]=>0100100=>0010010=>[3,3,2]
[4,2,6,7,8,3,1,5]=>1000110=>0110001=>[2,1,4,1]
[4,2,6,7,8,3,5,1]=>1000101=>1010001=>[1,2,4,1]
[3,6,2,7,4,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[3,7,4,2,1,5,8,6]=>0111001=>1001110=>[1,3,1,1,2]
[7,8,4,2,1,3,6,5]=>0111001=>1001110=>[1,3,1,1,2]
[6,3,2,7,1,8,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,6,2,7,1,8,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,3,8,2,5,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,4,7,8,5,2,3,1]=>1001101=>1011001=>[1,2,1,3,1]
[2,6,4,7,8,1,5,3]=>0100101=>1010010=>[1,2,3,2]
[7,4,1,5,8,6,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[7,5,8,2,1,6,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[6,2,7,1,3,8,5,4]=>1010011=>1100101=>[1,1,3,2,1]
[6,3,1,7,8,2,5,4]=>1100101=>1010011=>[1,2,3,1,1]
[4,6,1,7,8,5,2,3]=>0100110=>0110010=>[2,1,3,2]
[5,1,2,6,7,8,4,3]=>1000011=>1100001=>[1,1,5,1]
[5,2,6,7,8,4,3,1]=>1000111=>1110001=>[1,1,1,4,1]
[1,6,4,7,8,5,2,3]=>0100110=>0110010=>[2,1,3,2]
[2,6,7,1,3,8,5,4]=>0010011=>1100100=>[1,1,3,3]
[6,7,3,8,5,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,4,7,8,5,3,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[3,1,2,6,5,8,7,4]=>1001011=>1101001=>[1,1,2,3,1]
[4,5,1,2,3,8,7,6]=>0100011=>1100010=>[1,1,4,2]
[4,6,1,2,3,8,7,5]=>0100011=>1100010=>[1,1,4,2]
[1,6,5,3,4,8,7,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,1,5,2,4,8,7,3]=>1010011=>1100101=>[1,1,3,2,1]
[6,5,1,2,3,8,7,4]=>1100011=>1100011=>[1,1,4,1,1]
[6,4,1,2,3,8,7,5]=>1100011=>1100011=>[1,1,4,1,1]
[5,4,1,2,3,8,7,6]=>1100011=>1100011=>[1,1,4,1,1]
[5,4,1,2,7,3,6,8]=>1100100=>0010011=>[3,3,1,1]
[6,4,1,7,2,3,5,8]=>1101000=>0001011=>[4,2,1,1]
[6,4,1,8,2,3,5,7]=>1101000=>0001011=>[4,2,1,1]
[7,4,1,2,8,3,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[7,5,1,2,8,3,6,4]=>1100101=>1010011=>[1,2,3,1,1]
[7,1,5,2,8,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,7,5,3,8,4,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[8,4,1,2,7,3,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[8,4,1,7,2,3,5,6]=>1101000=>0001011=>[4,2,1,1]
[7,4,1,6,2,3,5,8]=>1101000=>0001011=>[4,2,1,1]
[8,6,1,7,2,3,5,4]=>1101001=>1001011=>[1,3,2,1,1]
[8,1,6,7,2,4,5,3]=>1001001=>1001001=>[1,3,3,1]
[1,7,6,8,3,4,5,2]=>0101001=>1001010=>[1,3,2,2]
[7,6,1,8,2,3,5,4]=>1101001=>1001011=>[1,3,2,1,1]
[3,1,2,7,8,5,6,4]=>1000101=>1010001=>[1,2,4,1]
[3,1,8,7,2,4,5,6]=>1011000=>0001101=>[4,1,2,1]
[3,1,7,6,2,4,5,8]=>1011000=>0001101=>[4,1,2,1]
[4,7,1,6,2,3,5,8]=>0101000=>0001010=>[4,2,2]
[4,8,1,6,2,3,5,7]=>0101000=>0001010=>[4,2,2]
[5,8,1,2,7,3,6,4]=>0100101=>1010010=>[1,2,3,2]
[5,1,8,2,7,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,5,8,3,7,4,6,2]=>0010101=>1010100=>[1,2,2,3]
[1,6,8,7,3,4,5,2]=>0011001=>1001100=>[1,3,1,3]
[6,1,8,7,2,4,5,3]=>1011001=>1001101=>[1,3,1,2,1]
[6,8,1,7,2,3,5,4]=>0101001=>1001010=>[1,3,2,2]
[6,8,7,1,2,3,4,5]=>0110000=>0000110=>[5,1,2]
[5,8,6,1,2,3,4,7]=>0110000=>0000110=>[5,1,2]
[5,7,6,1,2,3,4,8]=>0110000=>0000110=>[5,1,2]
[7,8,1,6,2,3,5,4]=>0101001=>1001010=>[1,3,2,2]
[7,1,8,6,2,4,5,3]=>1011001=>1001101=>[1,3,1,2,1]
[1,7,8,6,3,4,5,2]=>0011001=>1001100=>[1,3,1,3]
[8,1,7,6,2,4,5,3]=>1011001=>1001101=>[1,3,1,2,1]
[8,7,1,6,2,3,5,4]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,3,7,2,1,4,6]=>1101100=>0011011=>[3,1,2,1,1]
[6,8,1,4,5,7,3,2]=>0100011=>1100010=>[1,1,4,2]
[8,7,2,4,5,1,3,6]=>1100100=>0010011=>[3,3,1,1]
[2,6,1,4,5,3,8,7]=>0100101=>1010010=>[1,2,3,2]
[6,3,1,4,5,2,8,7]=>1100101=>1010011=>[1,2,3,1,1]
[3,1,6,4,5,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,4,5,1,2,6]=>1010100=>0010101=>[3,2,2,1]
[5,8,7,4,2,6,3,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,1,7,4,2,6,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[3,7,8,4,5,1,2,6]=>0010100=>0010100=>[3,2,3]
[5,6,3,8,1,7,2,4]=>0101010=>0101010=>[2,2,2,2]
[7,6,1,4,5,8,3,2]=>1100011=>1100011=>[1,1,4,1,1]
[3,7,6,4,5,8,2,1]=>0110011=>1100110=>[1,1,3,1,2]
[8,5,7,4,1,6,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,5,8,4,7,6,1,3]=>0010110=>0110100=>[2,1,2,3]
[3,8,4,2,5,6,7,1]=>0110001=>1000110=>[1,4,1,2]
[8,4,1,3,5,6,7,2]=>1100001=>1000011=>[1,5,1,1]
[7,5,8,4,3,6,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[6,5,3,8,4,1,7,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,1,4,8,3,6,7,5]=>1001001=>1001001=>[1,3,3,1]
[7,3,8,4,2,6,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,1,2,5,6,7,4]=>1100001=>1000011=>[1,5,1,1]
[4,8,2,3,5,6,7,1]=>0100001=>1000010=>[1,5,2]
[2,7,8,4,5,3,1,6]=>0010110=>0110100=>[2,1,2,3]
[8,7,1,4,3,6,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,6,3,8,4,2,7,1]=>0101101=>1011010=>[1,2,1,2,2]
[8,6,3,1,4,2,7,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,3,5,1,2,7,4]=>1101001=>1001011=>[1,3,2,1,1]
[5,8,3,2,6,1,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[3,5,8,4,7,6,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[5,8,2,4,7,6,1,3]=>0100110=>0110010=>[2,1,3,2]
[7,1,6,4,5,8,2,3]=>1010010=>0100101=>[2,3,2,1]
[2,1,8,5,3,6,7,4]=>1011001=>1001101=>[1,3,1,2,1]
[6,8,3,5,2,1,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,5,4,2,6,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[4,8,1,2,5,6,7,3]=>0100001=>1000010=>[1,5,2]
[3,4,2,8,5,6,7,1]=>0101001=>1001010=>[1,3,2,2]
[2,4,1,8,5,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[8,4,2,1,5,6,7,3]=>1110001=>1000111=>[1,4,1,1,1]
[7,5,2,4,8,6,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[2,1,5,3,8,6,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,4,8,5,6,7,2]=>1001001=>1001001=>[1,3,3,1]
[6,5,3,7,2,8,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,7,2,4,5,8,3,1]=>0100011=>1100010=>[1,1,4,2]
[2,5,7,4,8,6,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[5,6,3,7,1,8,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,8,7,4,5,2,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[3,7,5,4,8,6,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,6,3,5,8,2,7,1]=>0100101=>1010010=>[1,2,3,2]
[3,7,8,4,1,6,2,5]=>0011010=>0101100=>[2,2,1,3]
[5,4,2,3,7,6,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,7,6,4,5,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[4,7,2,6,3,5,1,8]=>0101010=>0101010=>[2,2,2,2]
[5,7,6,2,3,4,1,8]=>0110010=>0100110=>[2,3,1,2]
[1,7,5,2,8,3,4,6]=>0110100=>0010110=>[3,2,1,2]
[6,8,5,2,3,1,4,7]=>0110100=>0010110=>[3,2,1,2]
[4,8,2,6,3,1,5,7]=>0101100=>0011010=>[3,1,2,2]
[3,2,8,6,4,1,5,7]=>1011100=>0011101=>[3,1,1,2,1]
[7,1,5,2,8,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[1,8,5,2,7,3,4,6]=>0110100=>0010110=>[3,2,1,2]
[7,1,6,8,2,3,4,5]=>1001000=>0001001=>[4,3,1]
[3,2,1,7,8,4,5,6]=>1100100=>0010011=>[3,3,1,1]
[3,2,8,7,1,4,5,6]=>1011000=>0001101=>[4,1,2,1]
[5,8,7,2,1,3,4,6]=>0111000=>0001110=>[4,1,1,2]
[1,7,6,8,2,3,4,5]=>0101000=>0001010=>[4,2,2]
[6,5,8,2,3,1,4,7]=>1010100=>0010101=>[3,2,2,1]
[8,5,7,2,1,3,4,6]=>1011000=>0001101=>[4,1,2,1]
[3,2,5,4,1,8,6,7]=>1011010=>0101101=>[2,2,1,2,1]
[7,4,2,1,8,3,5,6]=>1110100=>0010111=>[3,2,1,1,1]
[8,4,2,1,7,3,5,6]=>1110100=>0010111=>[3,2,1,1,1]
[1,4,2,8,7,3,5,6]=>0101100=>0011010=>[3,1,2,2]
[1,5,8,2,7,3,4,6]=>0010100=>0010100=>[3,2,3]
[8,5,1,2,7,3,4,6]=>1100100=>0010011=>[3,3,1,1]
[3,2,6,1,4,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[3,2,7,1,8,4,5,6]=>1010100=>0010101=>[3,2,2,1]
[4,7,2,1,8,3,5,6]=>0110100=>0010110=>[3,2,1,2]
[8,6,1,7,2,3,4,5]=>1101000=>0001011=>[4,2,1,1]
[1,6,8,7,2,3,4,5]=>0011000=>0001100=>[4,1,3]
[1,7,8,6,2,3,4,5]=>0011000=>0001100=>[4,1,3]
[7,8,1,6,2,3,4,5]=>0101000=>0001010=>[4,2,2]
[4,8,2,1,7,3,5,6]=>0110100=>0010110=>[3,2,1,2]
[3,2,8,1,7,4,5,6]=>1010100=>0010101=>[3,2,2,1]
[5,1,8,2,7,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[6,1,8,7,2,3,4,5]=>1011000=>0001101=>[4,1,2,1]
[8,1,7,6,2,3,4,5]=>1011000=>0001101=>[4,1,2,1]
[2,8,4,1,6,5,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,5,6,7,4,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[7,5,8,6,1,4,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[3,5,7,6,1,4,2,8]=>0011010=>0101100=>[2,2,1,3]
[7,5,8,2,4,1,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,8,5,3,4,7,6,1]=>0110011=>1100110=>[1,1,3,1,2]
[2,8,5,3,4,1,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,5,3,6,1,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,5,6,7,4,1,3]=>0100110=>0110010=>[2,1,3,2]
[2,8,5,3,4,7,1,6]=>0110010=>0100110=>[2,3,1,2]
[2,8,5,3,4,6,1,7]=>0110010=>0100110=>[2,3,1,2]
[6,5,2,7,3,1,4,8]=>1101100=>0011011=>[3,1,2,1,1]
[6,5,2,8,3,1,7,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,5,2,8,3,1,4,7]=>1101100=>0011011=>[3,1,2,1,1]
[7,5,8,2,4,6,3,1]=>1010011=>1100101=>[1,1,3,2,1]
[7,5,8,6,1,4,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,5,8,2,1,3,7,4]=>1011001=>1001101=>[1,3,1,2,1]
[3,5,6,2,1,8,7,4]=>0011011=>1101100=>[1,1,2,1,3]
[3,5,7,2,4,1,8,6]=>0010101=>1010100=>[1,2,2,3]
[6,5,2,7,3,1,8,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,5,2,6,3,1,7,8]=>0101100=>0011010=>[3,1,2,2]
[6,5,2,7,3,4,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[5,1,6,7,4,3,8,2]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,2,6,4,8,7,3]=>1001011=>1101001=>[1,1,2,3,1]
[5,1,2,8,6,4,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,6,8,7,3,4,2]=>1001101=>1011001=>[1,2,1,3,1]
[6,5,2,8,3,7,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,1,2,3,8,6,5,7]=>1000110=>0110001=>[2,1,4,1]
[4,1,2,3,8,6,7,5]=>1000101=>1010001=>[1,2,4,1]
[4,1,2,3,8,5,7,6]=>1000101=>1010001=>[1,2,4,1]
[6,5,8,2,4,3,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,2,8,3,7,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,2,7,3,4,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,1,6,7,4,3,2,8]=>1001110=>0111001=>[2,1,1,3,1]
[5,1,6,8,7,3,2,4]=>1001110=>0111001=>[2,1,1,3,1]
[5,7,8,6,3,4,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[3,1,4,8,6,2,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[3,1,4,8,6,5,2,7]=>1001110=>0111001=>[2,1,1,3,1]
[4,1,6,7,8,3,2,5]=>1000110=>0110001=>[2,1,4,1]
[4,1,6,5,7,3,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,5,2,6,3,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,2,7,3,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[3,5,6,2,4,8,1,7]=>0010010=>0100100=>[2,3,3]
[3,7,5,6,8,4,1,2]=>0100110=>0110010=>[2,1,3,2]
[3,6,5,2,8,1,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[6,1,2,5,8,4,7,3]=>1000101=>1010001=>[1,2,4,1]
[4,1,2,3,5,8,7,6]=>1000011=>1100001=>[1,1,5,1]
[4,1,6,7,8,3,5,2]=>1000101=>1010001=>[1,2,4,1]
[4,1,2,6,8,5,7,3]=>1000101=>1010001=>[1,2,4,1]
[4,1,2,5,6,8,7,3]=>1000011=>1100001=>[1,1,5,1]
[4,5,2,6,3,7,8,1]=>0101001=>1001010=>[1,3,2,2]
[6,4,2,7,1,3,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[7,4,2,5,1,3,8,6]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,3,6,1,7,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,3,6,2,4,8,1,5]=>1010010=>0100101=>[2,3,2,1]
[6,3,7,4,1,2,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[3,7,5,1,2,4,8,6]=>0110001=>1000110=>[1,4,1,2]
[7,4,8,5,2,6,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[5,8,2,6,3,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[3,8,6,2,4,7,1,5]=>0110010=>0100110=>[2,3,1,2]
[3,8,5,7,1,2,4,6]=>0101000=>0001010=>[4,2,2]
[2,8,5,7,1,3,4,6]=>0101000=>0001010=>[4,2,2]
[4,8,6,2,7,1,3,5]=>0110100=>0010110=>[3,2,1,2]
[3,6,5,8,1,2,4,7]=>0101000=>0001010=>[4,2,2]
[5,4,7,3,8,1,2,6]=>1010100=>0010101=>[3,2,2,1]
[8,4,1,6,7,2,3,5]=>1100100=>0010011=>[3,3,1,1]
[6,5,1,2,7,8,3,4]=>1100010=>0100011=>[2,4,1,1]
[4,7,1,5,8,6,2,3]=>0100110=>0110010=>[2,1,3,2]
[7,6,1,8,5,2,3,4]=>1101100=>0011011=>[3,1,2,1,1]
[5,7,2,8,1,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[6,3,7,8,5,1,2,4]=>1001100=>0011001=>[3,1,3,1]
[3,6,8,2,7,1,4,5]=>0010100=>0010100=>[3,2,3]
[5,3,8,7,1,2,4,6]=>1011000=>0001101=>[4,1,2,1]
[8,3,7,6,1,2,4,5]=>1011000=>0001101=>[4,1,2,1]
[8,4,7,6,1,2,3,5]=>1011000=>0001101=>[4,1,2,1]
[5,4,8,7,1,2,3,6]=>1011000=>0001101=>[4,1,2,1]
[3,5,8,7,1,2,4,6]=>0011000=>0001100=>[4,1,3]
[2,5,8,7,1,3,4,6]=>0011000=>0001100=>[4,1,3]
[6,8,4,7,5,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[5,8,7,1,6,2,3,4]=>0110100=>0010110=>[3,2,1,2]
[2,8,7,6,1,3,4,5]=>0111000=>0001110=>[4,1,1,2]
[3,8,7,6,1,2,4,5]=>0111000=>0001110=>[4,1,1,2]
[4,8,7,6,1,2,3,5]=>0111000=>0001110=>[4,1,1,2]
[5,6,3,1,4,2,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[7,5,3,8,2,1,6,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,8,7,4,5,1,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[6,7,1,4,5,8,2,3]=>0100010=>0100010=>[2,4,2]
[2,1,7,8,5,3,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[5,7,3,8,1,2,6,4]=>0101001=>1001010=>[1,3,2,2]
[7,5,1,4,8,6,3,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,4,3,8,1,5,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[8,6,3,1,2,5,7,4]=>1110001=>1000111=>[1,4,1,1,1]
[8,7,1,4,2,6,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,3,8,4,1,6,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,3,2,7,4,6,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[7,5,3,6,2,4,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[6,3,2,5,1,8,4,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,3,6,2,7,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,2,6,3,4,5,8,1]=>1010001=>1000101=>[1,4,2,1]
[6,2,7,3,4,5,8,1]=>1010001=>1000101=>[1,4,2,1]
[6,7,3,5,2,4,8,1]=>0101001=>1001010=>[1,3,2,2]
[3,7,6,2,4,5,8,1]=>0110001=>1000110=>[1,4,1,2]
[6,5,3,1,2,8,4,7]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,5,2,3,7,1,4]=>1110010=>0100111=>[2,3,1,1,1]
[8,5,2,1,7,3,4,6]=>1110100=>0010111=>[3,2,1,1,1]
[7,5,2,1,8,3,4,6]=>1110100=>0010111=>[3,2,1,1,1]
[1,6,3,2,8,4,5,7]=>0110100=>0010110=>[3,2,1,2]
[4,2,6,5,1,8,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[5,4,8,6,2,7,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[7,8,5,2,3,6,1,4]=>0110010=>0100110=>[2,3,1,2]
[6,8,2,1,7,3,4,5]=>0110100=>0010110=>[3,2,1,2]
[2,8,1,7,3,4,5,6]=>0101000=>0001010=>[4,2,2]
[3,8,6,1,7,2,4,5]=>0110100=>0010110=>[3,2,1,2]
[4,2,8,3,7,1,5,6]=>1010100=>0010101=>[3,2,2,1]
[8,1,2,7,3,4,5,6]=>1001000=>0001001=>[4,3,1]
[6,3,7,1,2,8,4,5]=>1010010=>0100101=>[2,3,2,1]
[7,2,6,1,8,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[7,3,1,5,8,2,4,6]=>1100100=>0010011=>[3,3,1,1]
[5,4,1,3,6,8,2,7]=>1100010=>0100011=>[2,4,1,1]
[8,5,3,7,6,1,2,4]=>1101100=>0011011=>[3,1,2,1,1]
[6,1,8,3,7,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[7,6,8,2,3,5,1,4]=>1010010=>0100101=>[2,3,2,1]
[3,7,8,2,4,6,1,5]=>0010010=>0100100=>[2,3,3]
[5,4,7,8,2,6,1,3]=>1001010=>0101001=>[2,2,3,1]
[4,2,5,8,7,1,3,6]=>1001100=>0011001=>[3,1,3,1]
[2,3,8,7,1,4,5,6]=>0011000=>0001100=>[4,1,3]
[2,1,8,7,3,4,5,6]=>1011000=>0001101=>[4,1,2,1]
[8,2,7,6,1,3,4,5]=>1011000=>0001101=>[4,1,2,1]
[1,2,8,7,3,4,5,6]=>0011000=>0001100=>[4,1,3]
[1,3,8,7,2,4,5,6]=>0011000=>0001100=>[4,1,3]
[1,7,8,3,6,2,4,5]=>0010100=>0010100=>[3,2,3]
[5,4,8,7,6,1,2,3]=>1011100=>0011101=>[3,1,1,2,1]
[6,8,3,7,5,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[7,8,6,2,5,1,3,4]=>0110100=>0010110=>[3,2,1,2]
[8,1,6,7,3,2,4,5]=>1001100=>0011001=>[3,1,3,1]
[8,1,5,3,7,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[8,1,5,3,6,2,4,7]=>1010100=>0010101=>[3,2,2,1]
[7,4,8,3,2,6,5,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,4,1,3,2,6,5,8]=>1101010=>0101011=>[2,2,2,1,1]
[8,1,4,3,2,6,5,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,1,4,3,2,7,5,6]=>1011010=>0101101=>[2,2,1,2,1]
[8,1,5,4,6,7,2,3]=>1010010=>0100101=>[2,3,2,1]
[8,1,5,3,6,2,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,4,3,2,6,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[8,1,4,3,2,5,7,6]=>1011001=>1001101=>[1,3,1,2,1]
[7,4,1,3,2,5,6,8]=>1101000=>0001011=>[4,2,1,1]
[7,4,8,3,2,5,6,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,4,3,1,2,5,8,7]=>1110001=>1000111=>[1,4,1,1,1]
[7,4,1,3,2,5,8,6]=>1101001=>1001011=>[1,3,2,1,1]
[7,5,1,3,6,2,8,4]=>1100101=>1010011=>[1,2,3,1,1]
[7,5,1,4,6,8,2,3]=>1100010=>0100011=>[2,4,1,1]
[6,4,3,8,2,5,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,3,2,8,6,1,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[5,4,3,2,8,7,1,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,5,4,8,7,1,2,3]=>1101100=>0011011=>[3,1,2,1,1]
[6,5,4,1,7,8,2,3]=>1110010=>0100111=>[2,3,1,1,1]
[6,4,3,1,2,7,8,5]=>1110001=>1000111=>[1,4,1,1,1]
[7,4,1,3,2,8,5,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,4,3,1,2,7,5,8]=>1110010=>0100111=>[2,3,1,1,1]
[6,4,3,8,2,7,5,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,5,3,8,7,2,4,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,5,3,1,7,2,4,8]=>1110100=>0010111=>[3,2,1,1,1]
[7,5,1,3,8,2,4,6]=>1100100=>0010011=>[3,3,1,1]
[6,5,3,7,8,2,4,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,4,3,7,2,8,5,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,4,3,7,2,1,5,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,5,8,4,1,6,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[6,5,4,8,1,7,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,3,8,1,2,7,4]=>1101001=>1001011=>[1,3,2,1,1]
[6,5,4,7,1,8,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,3,2,7,8,1,6]=>1110010=>0100111=>[2,3,1,1,1]
[4,6,3,8,5,1,2,7]=>0101100=>0011010=>[3,1,2,2]
[5,6,8,3,4,1,2,7]=>0010100=>0010100=>[3,2,3]
[5,6,8,3,4,1,7,2]=>0010101=>1010100=>[1,2,2,3]
[4,6,2,7,5,3,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[5,6,8,4,3,1,2,7]=>0011100=>0011100=>[3,1,1,3]
[5,7,8,4,1,3,6,2]=>0011001=>1001100=>[1,3,1,3]
[5,6,8,4,2,1,7,3]=>0011101=>1011100=>[1,2,1,1,3]
[5,6,8,2,4,1,7,3]=>0010101=>1010100=>[1,2,2,3]
[3,2,6,8,5,1,4,7]=>1001100=>0011001=>[3,1,3,1]
[5,6,8,4,2,1,3,7]=>0011100=>0011100=>[3,1,1,3]
[5,7,8,4,1,3,2,6]=>0011010=>0101100=>[2,2,1,3]
[5,7,8,4,1,2,3,6]=>0011000=>0001100=>[4,1,3]
[6,7,8,1,5,2,3,4]=>0010100=>0010100=>[3,2,3]
[6,7,8,1,5,3,2,4]=>0010110=>0110100=>[2,1,2,3]
[6,7,8,1,3,5,2,4]=>0010010=>0100100=>[2,3,3]
[5,7,8,2,1,6,3,4]=>0011010=>0101100=>[2,2,1,3]
[4,7,2,8,1,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[3,2,7,8,1,6,4,5]=>1001010=>0101001=>[2,2,3,1]
[4,7,2,8,1,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,7,8,2,1,6,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[6,7,8,1,3,5,4,2]=>0010011=>1100100=>[1,1,3,3]
[6,7,8,1,5,3,4,2]=>0010101=>1010100=>[1,2,2,3]
[6,7,8,1,4,3,5,2]=>0010101=>1010100=>[1,2,2,3]
[5,6,8,3,2,1,7,4]=>0011101=>1011100=>[1,2,1,1,3]
[4,7,3,8,1,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,8,1,5,6,2]=>0101001=>1001010=>[1,3,2,2]
[4,7,3,8,1,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,8,1,2,5,6]=>0101000=>0001010=>[4,2,2]
[5,7,8,3,1,2,4,6]=>0011000=>0001100=>[4,1,3]
[5,6,8,3,2,1,4,7]=>0011100=>0011100=>[3,1,1,3]
[3,2,7,8,1,5,4,6]=>1001010=>0101001=>[2,2,3,1]
[6,7,8,1,3,4,2,5]=>0010010=>0100100=>[2,3,3]
[6,7,8,1,4,2,3,5]=>0010100=>0010100=>[3,2,3]
[6,7,8,1,2,5,3,4]=>0010010=>0100100=>[2,3,3]
[6,7,8,1,2,4,5,3]=>0010001=>1000100=>[1,4,3]
[5,7,8,2,1,3,6,4]=>0011001=>1001100=>[1,3,1,3]
[3,2,7,8,1,4,6,5]=>1001001=>1001001=>[1,3,3,1]
[6,7,8,1,3,2,4,5]=>0010100=>0010100=>[3,2,3]
[6,7,8,1,2,4,3,5]=>0010010=>0100100=>[2,3,3]
[6,7,8,1,2,3,5,4]=>0010001=>1000100=>[1,4,3]
[8,3,5,1,7,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,4,1,7,5,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,8,3,1,7,5,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,2,1,7,5,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[1,4,6,2,7,5,8,3]=>0010101=>1010100=>[1,2,2,3]
[1,7,5,2,6,8,4,3]=>0110011=>1100110=>[1,1,3,1,2]
[7,5,2,1,6,8,4,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[6,8,4,3,1,7,5,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,7,5,6,1,8,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,5,1,8,4,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,8,4,1,7,5,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,7,5,3,1,8,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,4,2,1,6,7,5,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[1,8,4,2,6,7,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[1,5,3,2,7,6,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[2,5,3,1,7,6,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,5,1,6,8,4,3]=>0110011=>1100110=>[1,1,3,1,2]
[4,7,1,6,5,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[4,6,1,2,7,5,8,3]=>0100101=>1010010=>[1,2,3,2]
[8,4,1,2,6,7,5,3]=>1100011=>1100011=>[1,1,4,1,1]
[5,3,1,2,7,6,8,4]=>1100101=>1010011=>[1,2,3,1,1]
[4,3,1,2,7,6,8,5]=>1100101=>1010011=>[1,2,3,1,1]
[3,5,1,2,7,6,8,4]=>0100101=>1010010=>[1,2,3,2]
[6,7,1,5,8,2,3,4]=>0100100=>0010010=>[3,3,2]
[2,7,6,1,5,8,3,4]=>0110010=>0100110=>[2,3,1,2]
[2,3,5,1,7,6,8,4]=>0010101=>1010100=>[1,2,2,3]
[8,4,1,6,7,5,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[5,2,3,1,7,6,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,5,2,1,7,6,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[1,7,6,2,5,8,3,4]=>0110010=>0100110=>[2,3,1,2]
[7,6,2,1,5,8,3,4]=>1110010=>0100111=>[2,3,1,1,1]
[8,2,6,4,7,1,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,5,2,7,4,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,2,5,8,3,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[1,8,3,5,7,6,2,4]=>0100110=>0110010=>[2,1,3,2]
[1,5,2,3,7,6,8,4]=>0100101=>1010010=>[1,2,3,2]
[5,2,1,3,7,6,8,4]=>1100101=>1010011=>[1,2,3,1,1]
[8,4,2,6,7,5,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[6,1,4,2,7,5,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,6,5,7,1,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,3,2,7,6,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[1,4,2,3,7,6,8,5]=>0100101=>1010010=>[1,2,3,2]
[2,4,1,3,7,6,8,5]=>0100101=>1010010=>[1,2,3,2]
[2,5,1,3,7,6,8,4]=>0100101=>1010010=>[1,2,3,2]
[2,8,3,5,7,6,1,4]=>0100110=>0110010=>[2,1,3,2]
[6,8,2,3,5,7,1,4]=>0100010=>0100010=>[2,4,2]
[6,7,1,3,5,8,2,4]=>0100010=>0100010=>[2,4,2]
[8,3,5,7,6,1,2,4]=>1001100=>0011001=>[3,1,3,1]
[5,1,2,3,7,6,8,4]=>1000101=>1010001=>[1,2,4,1]
[4,7,1,2,8,6,5,3]=>0100111=>1110010=>[1,1,1,3,2]
[4,6,8,1,2,7,5,3]=>0010011=>1100100=>[1,1,3,3]
[6,8,7,1,5,3,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,8,7,3,5,1,2,4]=>0110100=>0010110=>[3,2,1,2]
[7,8,1,3,6,5,2,4]=>0100110=>0110010=>[2,1,3,2]
[1,7,3,4,8,6,5,2]=>0100111=>1110010=>[1,1,1,3,2]
[4,2,7,1,8,6,5,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,8,2,3,6,5,1,4]=>0100110=>0110010=>[2,1,3,2]
[8,5,7,1,6,2,3,4]=>1010100=>0010101=>[3,2,2,1]
[8,5,7,1,2,6,3,4]=>1010010=>0100101=>[2,3,2,1]
[6,8,2,7,1,3,5,4]=>0101001=>1001010=>[1,3,2,2]
[6,2,4,8,7,1,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[1,6,8,3,7,4,5,2]=>0010101=>1010100=>[1,2,2,3]
[1,6,8,3,4,7,5,2]=>0010011=>1100100=>[1,1,3,3]
[6,2,4,8,1,7,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[6,8,7,2,3,5,1,4]=>0110010=>0100110=>[2,3,1,2]
[6,8,2,1,7,3,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[8,5,7,2,1,6,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[8,5,7,1,2,3,6,4]=>1010001=>1000101=>[1,4,2,1]
[8,5,7,2,3,1,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[1,8,7,5,3,4,6,2]=>0111001=>1001110=>[1,3,1,1,2]
[1,8,7,3,5,4,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[8,2,5,4,7,1,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,7,6,1,2,4,3,5]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,6,1,4,2,3,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,6,4,1,3,2,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,5,7,1,3,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,4,7,1,2,6,3]=>0101001=>1001010=>[1,3,2,2]
[8,1,2,6,5,7,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[8,2,5,6,7,4,1,3]=>1000110=>0110001=>[2,1,4,1]
[4,8,5,1,7,2,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[8,5,3,7,1,2,6,4]=>1101001=>1001011=>[1,3,2,1,1]
[4,6,2,8,1,7,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,6,4,8,3,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,7,4,5,3,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,5,7,2,1,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[8,5,3,7,2,1,6,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,7,6,3,1,4,2,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,5,3,2,7,1,6,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[1,8,7,4,3,5,6,2]=>0111001=>1001110=>[1,3,1,1,2]
[1,8,7,3,4,5,6,2]=>0110001=>1000110=>[1,4,1,2]
[8,2,4,5,7,1,6,3]=>1000101=>1010001=>[1,2,4,1]
[8,5,2,3,7,1,6,4]=>1100101=>1010011=>[1,2,3,1,1]
[8,3,1,5,2,7,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,4,2,1,7,3,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,5,4,2,1,7,6,3]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[6,5,4,2,3,1,8,7]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,3,2,5,1,4,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,4,1,2,7,6,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,7,4,1,6,3,2,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,7,4,1,6,3,5,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,7,4,1,6,5,3,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,5,4,3,1,7,6,2]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[8,3,2,5,1,7,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,3,2,5,1,7,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,4,3,1,7,2,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,5,4,1,3,7,2,6]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,4,1,6,5,2,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[2,1,8,7,6,4,5,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,3,2,7,6,4,5,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,4,2,3,7,6,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,7,4,2,6,5,3,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,7,4,2,6,3,5,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,7,4,2,6,3,1,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,3,1,7,6,4,2,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,3,1,7,6,4,5,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,3,1,5,4,7,6,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,3,1,7,6,5,2,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,3,1,7,6,2,5,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,4,2,3,7,1,6]=>1110010=>0100111=>[2,3,1,1,1]
[8,3,2,5,4,7,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[2,1,8,5,4,7,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,2,7,6,5,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,7,6,5,3,1,4,2]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[8,3,2,7,6,1,5,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,7,6,5,1,2,4,3]=>1111001=>1001111=>[1,3,1,1,1,1]
[5,2,3,1,6,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,5,2,3,1,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,5,2,4,1,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,5,2,4,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,6,3,5,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,4,1,5,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,7,3,4,1,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,8,5,7,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,7,3,4,1,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,4,1,5,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,7,3,5,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,7,4,5,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,8,6,7,4,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,6,7,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,3,4,1,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,6,2,7,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,3,5,1,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,8,4,7,3,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,8,5,7,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,5,7,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,7,4,6,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,7,3,6,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,8,4,7,3,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,6,2,5,1,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,4,1,7,3,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,4,1,7,3,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,6,2,3,1,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,3,1,7,4,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,3,1,7,4,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,3,1,7,5,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,4,2,8,6,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,3,1,8,5,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,6,2,3,1,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,8,5,6,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,6,2,4,1,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,4,1,8,6,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,5,2,8,6,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,6,2,8,5,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,6,2,8,4,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,6,2,5,1,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,8,4,6,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,7,3,8,4,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,5,1,6,2,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,5,6,2,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,8,5,6,2,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,5,6,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,1,7,4,8,5,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,6,2,8,4,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,8,7,3,4,1,2,5]=>0110100=>0010110=>[3,2,1,2]
[5,4,8,7,2,6,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,3,8,7,6,1,2,4]=>1011100=>0011101=>[3,1,1,2,1]
[8,3,4,6,5,1,2,7]=>1001100=>0011001=>[3,1,3,1]
[3,4,8,7,6,1,2,5]=>0011100=>0011100=>[3,1,1,3]
[3,5,8,7,6,1,2,4]=>0011100=>0011100=>[3,1,1,3]
[4,5,8,7,6,1,2,3]=>0011100=>0011100=>[3,1,1,3]
[4,5,8,7,1,6,3,2]=>0011011=>1101100=>[1,1,2,1,3]
[3,5,8,2,7,6,4,1]=>0010111=>1110100=>[1,1,1,2,3]
[3,5,8,1,7,6,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[2,5,8,7,1,6,3,4]=>0011010=>0101100=>[2,2,1,3]
[2,4,8,7,1,6,3,5]=>0011010=>0101100=>[2,2,1,3]
[2,8,4,7,1,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[8,2,4,6,1,5,3,7]=>1001010=>0101001=>[2,2,3,1]
[8,1,4,6,2,5,3,7]=>1001010=>0101001=>[2,2,3,1]
[1,4,8,7,2,6,3,5]=>0011010=>0101100=>[2,2,1,3]
[1,5,8,7,2,6,3,4]=>0011010=>0101100=>[2,2,1,3]
[1,5,8,2,7,6,4,3]=>0010111=>1110100=>[1,1,1,2,3]
[2,5,8,3,7,6,4,1]=>0010111=>1110100=>[1,1,1,2,3]
[1,4,2,8,7,6,5,3]=>0101111=>1111010=>[1,1,1,1,2,2]
[1,3,8,2,7,6,4,5]=>0010110=>0110100=>[2,1,2,3]
[1,8,3,2,7,5,4,6]=>0110110=>0110110=>[2,1,2,1,2]
[8,2,3,1,6,5,4,7]=>1010110=>0110101=>[2,1,2,2,1]
[2,3,8,1,7,6,4,5]=>0010110=>0110100=>[2,1,2,3]
[5,2,8,7,1,6,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[5,2,8,1,7,6,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,3,8,2,7,6,4,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,8,3,2,7,5,4,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,8,3,1,7,5,4,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,8,1,2,7,5,4,3]=>0100111=>1110010=>[1,1,1,3,2]
[6,8,2,3,7,5,4,1]=>0100111=>1110010=>[1,1,1,3,2]
[5,2,8,3,7,6,4,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,1,8,3,7,6,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,1,8,7,2,6,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[4,8,1,7,2,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[8,4,1,6,2,5,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,3,1,2,6,5,4,7]=>1100110=>0110011=>[2,1,3,1,1]
[3,1,2,8,7,6,5,4]=>1001111=>1111001=>[1,1,1,1,3,1]
[4,1,3,8,7,6,5,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[3,1,4,8,7,6,5,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[2,1,8,3,7,6,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[2,8,1,3,7,5,4,6]=>0100110=>0110010=>[2,1,3,2]
[8,2,1,3,6,5,4,7]=>1100110=>0110011=>[2,1,3,1,1]
[1,8,2,3,7,5,4,6]=>0100110=>0110010=>[2,1,3,2]
[1,2,8,3,7,6,4,5]=>0010110=>0110100=>[2,1,2,3]
[1,4,3,6,8,2,5,7]=>0100100=>0010010=>[3,3,2]
[1,4,5,2,8,3,7,6]=>0010101=>1010100=>[1,2,2,3]
[1,4,2,6,5,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[1,5,4,2,6,8,3,7]=>0110010=>0100110=>[2,3,1,2]
[3,1,6,5,8,2,4,7]=>1010100=>0010101=>[3,2,2,1]
[1,6,4,2,5,8,3,7]=>0110010=>0100110=>[2,3,1,2]
[1,5,2,6,4,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[1,2,6,5,4,8,3,7]=>0011010=>0101100=>[2,2,1,3]
[1,2,5,4,7,3,8,6]=>0010101=>1010100=>[1,2,2,3]
[4,1,2,6,3,8,7,5]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,5,4,2,8,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,4,7,5,2,8,3,6]=>0011010=>0101100=>[2,2,1,3]
[7,1,3,5,2,8,4,6]=>1001010=>0101001=>[2,2,3,1]
[1,4,5,2,8,7,3,6]=>0010110=>0110100=>[2,1,2,3]
[1,6,4,2,8,3,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[1,4,2,8,3,7,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[1,2,8,6,5,3,7,4]=>0011101=>1011100=>[1,2,1,1,3]
[6,2,1,8,7,3,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[7,6,2,1,8,3,4,5]=>1110100=>0010111=>[3,2,1,1,1]
[7,3,1,6,2,8,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[1,7,6,4,2,8,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[1,7,5,2,6,3,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[1,6,2,7,5,3,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,2,7,6,5,3,8,4]=>0011101=>1011100=>[1,2,1,1,3]
[1,2,6,5,3,8,7,4]=>0011011=>1101100=>[1,1,2,1,3]
[1,5,2,7,6,3,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[1,6,5,2,7,3,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[1,5,7,4,2,8,3,6]=>0011010=>0101100=>[2,2,1,3]
[3,1,8,6,2,4,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[4,3,7,1,8,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[8,3,1,6,2,4,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[7,1,8,3,2,4,6,5]=>1011001=>1001101=>[1,3,1,2,1]
[1,4,2,8,7,3,6,5]=>0101101=>1011010=>[1,2,1,2,2]
[1,7,4,2,8,3,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[8,1,5,4,2,7,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,4,8,5,2,7,3,6]=>0011010=>0101100=>[2,2,1,3]
[8,5,3,1,7,2,4,6]=>1110100=>0010111=>[3,2,1,1,1]
[8,6,2,1,7,3,4,5]=>1110100=>0010111=>[3,2,1,1,1]
[1,8,6,4,2,7,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[1,5,2,7,3,8,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,2,8,5,3,7,6,4]=>0011011=>1101100=>[1,1,2,1,3]
[1,2,6,3,8,7,5,4]=>0010111=>1110100=>[1,1,1,2,3]
[1,2,7,6,3,8,5,4]=>0011011=>1101100=>[1,1,2,1,3]
[1,6,2,7,3,8,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,7,4,2,8,6,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[7,1,8,3,2,6,4,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,2,1,8,6,3,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[1,8,7,3,2,6,4,5]=>0111010=>0101110=>[2,2,1,1,2]
[1,4,2,8,7,6,3,5]=>0101110=>0111010=>[2,1,1,2,2]
[1,2,8,7,5,3,6,4]=>0011101=>1011100=>[1,2,1,1,3]
[5,1,8,7,6,2,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,1,7,6,3,4,5,2]=>1011001=>1001101=>[1,3,1,2,1]
[5,7,8,6,2,4,1,3]=>0011010=>0101100=>[2,2,1,3]
[5,7,1,6,2,4,3,8]=>0101010=>0101010=>[2,2,2,2]
[6,4,1,5,2,7,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[8,1,4,5,3,7,6,2]=>1001011=>1101001=>[1,1,2,3,1]
[6,1,4,5,3,8,7,2]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,4,5,3,8,6,2]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,4,5,3,6,8,2]=>1001001=>1001001=>[1,3,3,1]
[7,4,1,5,2,6,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,5,7,2,1,4,8]=>1001100=>0011001=>[3,1,3,1]
[6,3,5,8,2,1,7,4]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,5,7,2,1,8,4]=>1001101=>1011001=>[1,2,1,3,1]
[8,4,5,7,3,6,1,2]=>1001010=>0101001=>[2,2,3,1]
[6,4,5,8,3,7,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[5,4,8,6,3,1,7,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,4,1,8,2,3,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[8,4,1,5,2,6,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,5,8,2,1,4,7]=>1001100=>0011001=>[3,1,3,1]
[2,3,8,5,1,4,7,6]=>0011001=>1001100=>[1,3,1,3]
[2,3,8,6,1,5,7,4]=>0011001=>1001100=>[1,3,1,3]
[2,8,6,7,1,3,5,4]=>0101001=>1001010=>[1,3,2,2]
[8,3,5,7,2,1,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[8,4,5,6,3,1,7,2]=>1001101=>1011001=>[1,2,1,3,1]
[7,3,5,6,2,8,1,4]=>1001010=>0101001=>[2,2,3,1]
[7,3,5,8,2,1,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[7,3,5,6,2,1,4,8]=>1001100=>0011001=>[3,1,3,1]
[2,7,6,5,1,3,4,8]=>0111000=>0001110=>[4,1,1,2]
[2,7,6,8,1,3,5,4]=>0101001=>1001010=>[1,3,2,2]
[8,7,5,6,1,4,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[2,7,1,3,6,5,8,4]=>0100101=>1010010=>[1,2,3,2]
[2,7,6,1,8,3,4,5]=>0110100=>0010110=>[3,2,1,2]
[2,7,6,1,4,3,5,8]=>0110100=>0010110=>[3,2,1,2]
[7,3,5,1,2,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[2,3,8,6,4,1,7,5]=>0011101=>1011100=>[1,2,1,1,3]
[2,8,6,1,7,3,4,5]=>0110100=>0010110=>[3,2,1,2]
[2,3,8,1,6,4,7,5]=>0010101=>1010100=>[1,2,2,3]
[2,3,8,1,4,5,7,6]=>0010001=>1000100=>[1,4,3]
[5,2,6,1,4,8,7,3]=>1010011=>1100101=>[1,1,3,2,1]
[5,7,2,3,8,6,1,4]=>0100110=>0110010=>[2,1,3,2]
[5,6,2,3,1,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[5,6,2,1,3,8,7,4]=>0110011=>1100110=>[1,1,3,1,2]
[5,1,6,4,2,8,7,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,6,1,3,2,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[5,6,3,1,2,8,7,4]=>0110011=>1100110=>[1,1,3,1,2]
[5,7,3,2,8,1,6,4]=>0110101=>1010110=>[1,2,2,1,2]
[6,7,3,8,2,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[6,7,3,8,1,2,5,4]=>0101001=>1001010=>[1,3,2,2]
[5,7,3,1,8,2,6,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,1,7,4,8,2,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,5,7,4,8,3,6,2]=>0010101=>1010100=>[1,2,2,3]
[5,1,7,4,8,6,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[5,7,3,1,8,6,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,7,8,3,1,4,2,5]=>0011010=>0101100=>[2,2,1,3]
[6,7,1,8,3,5,2,4]=>0101010=>0101010=>[2,2,2,2]
[6,1,7,8,4,5,2,3]=>1001010=>0101001=>[2,2,3,1]
[1,6,7,8,4,5,3,2]=>0001011=>1101000=>[1,1,2,4]
[1,6,7,8,4,3,5,2]=>0001101=>1011000=>[1,2,1,4]
[6,1,7,8,4,2,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[6,7,2,8,1,3,5,4]=>0101001=>1001010=>[1,3,2,2]
[6,7,2,8,3,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[6,2,7,8,4,1,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[6,2,7,8,1,4,5,3]=>1001001=>1001001=>[1,3,3,1]
[4,2,1,7,8,5,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[4,1,2,7,8,6,5,3]=>1000111=>1110001=>[1,1,1,4,1]
[6,2,7,8,1,5,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[6,2,7,8,5,1,4,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,7,2,1,8,6,3,4]=>0110110=>0110110=>[2,1,2,1,2]
[1,6,7,8,3,5,4,2]=>0001011=>1101000=>[1,1,2,4]
[6,1,7,8,2,5,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[6,7,8,2,4,1,3,5]=>0010100=>0010100=>[3,2,3]
[6,7,8,2,4,3,1,5]=>0010110=>0110100=>[2,1,2,3]
[6,7,1,8,5,2,3,4]=>0101100=>0011010=>[3,1,2,2]
[6,1,7,8,5,2,4,3]=>1001101=>1011001=>[1,2,1,3,1]
[1,6,7,8,5,3,4,2]=>0001101=>1011000=>[1,2,1,4]
[6,1,7,8,5,4,2,3]=>1001110=>0111001=>[2,1,1,3,1]
[6,7,1,8,5,3,2,4]=>0101110=>0111010=>[2,1,1,2,2]
[6,7,8,4,1,3,2,5]=>0011010=>0101100=>[2,2,1,3]
[3,7,4,8,5,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[3,7,1,8,5,6,2,4]=>0101010=>0101010=>[2,2,2,2]
[2,7,3,8,5,6,1,4]=>0101010=>0101010=>[2,2,2,2]
[1,7,4,8,5,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[2,7,3,8,4,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[3,7,1,8,4,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,8,6,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[2,6,1,8,5,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,8,5,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,8,4,7,3,5]=>0101010=>0101010=>[2,2,2,2]
[2,6,1,8,4,7,3,5]=>0101010=>0101010=>[2,2,2,2]
[3,7,2,6,1,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[4,8,1,6,2,7,3,5]=>0101010=>0101010=>[2,2,2,2]
[5,8,1,6,2,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,2,6,1,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[4,8,2,6,1,7,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,7,3,6,2,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[2,7,3,6,1,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[8,6,1,4,3,2,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[3,7,5,1,8,2,4,6]=>0110100=>0010110=>[3,2,1,2]
[4,1,5,2,8,7,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,1,2,4,6,5,3,7]=>1000110=>0110001=>[2,1,4,1]
[8,2,6,5,1,3,4,7]=>1011000=>0001101=>[4,1,2,1]
[8,3,1,6,2,5,4,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,1,2,6,4,5,3,7]=>1001010=>0101001=>[2,2,3,1]
[8,1,2,5,6,4,3,7]=>1000110=>0110001=>[2,1,4,1]
[1,7,5,4,2,8,3,6]=>0111010=>0101110=>[2,2,1,1,2]
[1,4,6,8,2,7,3,5]=>0001010=>0101000=>[2,2,4]
[1,4,7,6,2,8,3,5]=>0011010=>0101100=>[2,2,1,3]
[5,1,4,7,2,8,3,6]=>1001010=>0101001=>[2,2,3,1]
[3,7,5,1,2,8,4,6]=>0110010=>0100110=>[2,3,1,2]
[4,1,5,8,2,7,3,6]=>1001010=>0101001=>[2,2,3,1]
[1,4,6,2,8,7,3,5]=>0010110=>0110100=>[2,1,2,3]
[1,4,2,8,6,7,3,5]=>0101010=>0101010=>[2,2,2,2]
[3,1,2,6,4,8,7,5]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,7,6,3,4,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[3,1,2,7,4,6,8,5]=>1001001=>1001001=>[1,3,3,1]
[1,2,3,6,8,5,7,4]=>0000101=>1010000=>[1,2,5]
[5,1,4,2,7,8,3,6]=>1010010=>0100101=>[2,3,2,1]
[1,4,2,7,6,8,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,4,2,6,8,7,3,5]=>0100110=>0110010=>[2,1,3,2]
[5,3,7,1,8,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[1,7,4,3,2,5,8,6]=>0111001=>1001110=>[1,3,1,1,2]
[4,8,7,2,1,3,5,6]=>0111000=>0001110=>[4,1,1,2]
[1,8,7,3,4,2,5,6]=>0110100=>0010110=>[3,2,1,2]
[3,1,7,8,2,6,4,5]=>1001010=>0101001=>[2,2,3,1]
[1,4,2,7,8,3,6,5]=>0100101=>1010010=>[1,2,3,2]
[2,1,8,6,3,4,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[1,4,2,6,8,3,7,5]=>0100101=>1010010=>[1,2,3,2]
[1,2,3,7,8,5,6,4]=>0000101=>1010000=>[1,2,5]
[1,2,3,7,5,8,6,4]=>0001011=>1101000=>[1,1,2,4]
[3,1,7,2,8,6,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[1,2,3,8,7,5,6,4]=>0001101=>1011000=>[1,2,1,4]
[5,7,8,4,2,6,1,3]=>0011010=>0101100=>[2,2,1,3]
[6,7,8,4,2,5,1,3]=>0011010=>0101100=>[2,2,1,3]
[8,6,3,7,2,1,5,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,7,8,3,2,1,5,4]=>0011101=>1011100=>[1,2,1,1,3]
[5,7,8,3,2,1,6,4]=>0011101=>1011100=>[1,2,1,1,3]
[2,7,8,4,3,5,6,1]=>0011001=>1001100=>[1,3,1,3]
[3,7,8,4,2,5,1,6]=>0011010=>0101100=>[2,2,1,3]
[7,6,3,8,2,1,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[8,6,3,7,2,1,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[5,6,3,8,2,1,4,7]=>0101100=>0011010=>[3,1,2,2]
[3,6,4,8,2,5,1,7]=>0101010=>0101010=>[2,2,2,2]
[2,6,4,8,3,5,7,1]=>0101001=>1001010=>[1,3,2,2]
[2,6,4,7,3,5,8,1]=>0101001=>1001010=>[1,3,2,2]
[4,6,3,7,2,1,5,8]=>0101100=>0011010=>[3,1,2,2]
[5,6,3,7,2,1,4,8]=>0101100=>0011010=>[3,1,2,2]
[8,4,3,2,1,6,5,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[6,4,3,2,1,7,5,8]=>1111010=>0101111=>[2,2,1,1,1,1]
[4,5,3,2,7,1,6,8]=>0110100=>0010110=>[3,2,1,2]
[7,4,3,2,1,8,5,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,4,3,2,1,7,5,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[7,4,3,2,1,8,6,5]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[5,6,3,8,2,1,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[7,5,3,2,8,1,6,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,5,4,2,7,6,1,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,5,4,2,8,6,1,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,5,4,2,7,8,1,3]=>1110010=>0100111=>[2,3,1,1,1]
[8,5,4,2,6,7,1,3]=>1110010=>0100111=>[2,3,1,1,1]
[5,6,3,7,2,1,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,3,7,2,1,8,5]=>0101101=>1011010=>[1,2,1,2,2]
[3,6,4,7,2,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[2,6,4,7,3,8,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,4,2,7,8,1,6]=>0110010=>0100110=>[2,3,1,2]
[7,4,3,2,1,6,8,5]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,4,3,2,1,6,7,5]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,4,3,2,1,5,7,6]=>1111001=>1001111=>[1,3,1,1,1,1]
[7,4,3,2,1,5,8,6]=>1111001=>1001111=>[1,3,1,1,1,1]
[6,4,3,2,1,5,8,7]=>1111001=>1001111=>[1,3,1,1,1,1]
[3,5,4,2,6,8,1,7]=>0110010=>0100110=>[2,3,1,2]
[3,2,6,4,8,5,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,5,8,3,1,6,7]=>1001100=>0011001=>[3,1,3,1]
[4,3,2,7,5,1,6,8]=>1101100=>0011011=>[3,1,2,1,1]
[4,3,6,2,5,1,7,8]=>1010100=>0010101=>[3,2,2,1]
[4,5,1,7,3,2,6,8]=>0101100=>0011010=>[3,1,2,2]
[5,2,1,4,3,7,8,6]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,6,4,1,2,7,8]=>1011000=>0001101=>[4,1,2,1]
[4,3,6,1,7,2,5,8]=>1010100=>0010101=>[3,2,2,1]
[6,2,4,1,3,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[3,6,4,1,2,7,5,8]=>0110010=>0100110=>[2,3,1,2]
[4,6,3,1,7,2,5,8]=>0110100=>0010110=>[3,2,1,2]
[4,5,2,7,3,1,6,8]=>0101100=>0011010=>[3,1,2,2]
[4,6,2,1,7,3,5,8]=>0110100=>0010110=>[3,2,1,2]
[3,2,6,1,4,7,5,8]=>1010010=>0100101=>[2,3,2,1]
[7,3,1,4,6,8,2,5]=>1100010=>0100011=>[2,4,1,1]
[7,4,1,5,6,2,3,8]=>1100100=>0010011=>[3,3,1,1]
[7,3,1,5,2,6,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,5,1,2,7,4,8]=>1010010=>0100101=>[2,3,2,1]
[3,6,5,1,2,7,4,8]=>0110010=>0100110=>[2,3,1,2]
[2,4,1,5,3,8,7,6]=>0101011=>1101010=>[1,1,2,2,2]
[3,4,5,1,2,8,7,6]=>0010011=>1100100=>[1,1,3,3]
[1,8,4,5,3,2,7,6]=>0101101=>1011010=>[1,2,1,2,2]
[2,4,8,5,3,1,7,6]=>0011101=>1011100=>[1,2,1,1,3]
[3,4,5,2,8,1,7,6]=>0010101=>1010100=>[1,2,2,3]
[3,4,6,2,1,7,8,5]=>0011001=>1001100=>[1,3,1,3]
[3,4,6,2,1,7,5,8]=>0011010=>0101100=>[2,2,1,3]
[3,5,6,2,7,1,8,4]=>0010101=>1010100=>[1,2,2,3]
[3,4,6,2,8,7,1,5]=>0010110=>0110100=>[2,1,2,3]
[3,4,6,8,2,7,1,5]=>0001010=>0101000=>[2,2,4]
[2,4,8,6,3,7,1,5]=>0011010=>0101100=>[2,2,1,3]
[1,8,4,6,3,7,2,5]=>0101010=>0101010=>[2,2,2,2]
[1,8,4,6,3,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,4,6,8,2,7,5,1]=>0001011=>1101000=>[1,1,2,4]
[3,4,6,2,8,7,5,1]=>0010111=>1110100=>[1,1,1,2,3]
[3,5,6,2,7,8,4,1]=>0010011=>1100100=>[1,1,3,3]
[3,5,6,2,7,4,1,8]=>0010110=>0110100=>[2,1,2,3]
[4,5,6,7,2,8,3,1]=>0001011=>1101000=>[1,1,2,4]
[2,5,8,6,7,3,4,1]=>0010101=>1010100=>[1,2,2,3]
[1,8,5,6,7,3,2,4]=>0100110=>0110010=>[2,1,3,2]
[4,5,6,7,2,1,8,3]=>0001101=>1011000=>[1,2,1,4]
[3,4,6,1,8,7,2,5]=>0010110=>0110100=>[2,1,2,3]
[2,4,1,6,8,7,3,5]=>0100110=>0110010=>[2,1,3,2]
[2,5,1,6,7,8,4,3]=>0100011=>1100010=>[1,1,4,2]
[2,5,1,6,7,4,3,8]=>0100110=>0110010=>[2,1,3,2]
[3,5,6,1,7,4,2,8]=>0010110=>0110100=>[2,1,2,3]
[3,5,6,1,7,4,8,2]=>0010101=>1010100=>[1,2,2,3]
[3,4,6,1,8,7,5,2]=>0010111=>1110100=>[1,1,1,2,3]
[3,4,6,8,1,7,5,2]=>0001011=>1101000=>[1,1,2,4]
[2,4,8,6,1,7,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,8,4,6,2,7,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,5,6,7,2,4,3]=>0100101=>1010010=>[1,2,3,2]
[2,5,8,6,7,1,4,3]=>0010101=>1010100=>[1,2,2,3]
[4,5,6,7,1,3,8,2]=>0001001=>1001000=>[1,3,4]
[3,5,6,8,7,4,1,2]=>0001110=>0111000=>[2,1,1,4]
[2,5,8,6,7,4,1,3]=>0010110=>0110100=>[2,1,2,3]
[1,8,5,6,7,4,2,3]=>0100110=>0110010=>[2,1,3,2]
[1,8,5,6,7,4,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[2,5,8,6,7,4,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[8,2,4,3,7,1,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,2,4,3,7,1,6]=>0101010=>0101010=>[2,2,2,2]
[4,2,5,6,1,8,3,7]=>1001010=>0101001=>[2,2,3,1]
[4,2,5,6,1,7,3,8]=>1001010=>0101001=>[2,2,3,1]
[6,1,5,7,3,2,4,8]=>1001100=>0011001=>[3,1,3,1]
[6,1,5,8,3,2,4,7]=>1001100=>0011001=>[3,1,3,1]
[3,8,2,4,7,1,5,6]=>0100100=>0010010=>[3,3,2]
[3,6,8,2,4,7,1,5]=>0010010=>0100100=>[2,3,3]
[7,3,2,4,6,1,5,8]=>1100100=>0010011=>[3,3,1,1]
[3,2,5,1,8,4,6,7]=>1010100=>0010101=>[3,2,2,1]
[7,8,3,2,4,6,1,5]=>0110010=>0100110=>[2,3,1,2]
[6,1,5,7,8,3,2,4]=>1000110=>0110001=>[2,1,4,1]
[4,2,5,6,1,7,8,3]=>1001001=>1001001=>[1,3,3,1]
[5,7,6,1,8,3,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,6,1,7,3,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[6,1,5,8,7,3,2,4]=>1001110=>0111001=>[2,1,1,3,1]
[8,7,3,2,4,6,1,5]=>1110010=>0100111=>[2,3,1,1,1]
[3,2,5,1,8,7,4,6]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,5,1,6,4,7,8]=>1010100=>0010101=>[3,2,2,1]
[3,2,4,1,8,7,5,6]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,5,1,6,8,7,4]=>1010011=>1100101=>[1,1,3,2,1]
[3,8,6,5,1,7,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,7,6,5,1,8,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,5,1,7,8,4,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,5,1,6,7,8,4]=>1010001=>1000101=>[1,4,2,1]
[3,2,4,1,7,5,6,8]=>1010100=>0010101=>[3,2,2,1]
[3,2,4,1,6,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[8,3,2,4,7,6,1,5]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,5,1,8,4,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,5,1,6,7,4,8]=>1010010=>0100101=>[2,3,2,1]
[6,5,1,7,4,2,3,8]=>1101100=>0011011=>[3,1,2,1,1]
[6,5,1,8,4,2,3,7]=>1101100=>0011011=>[3,1,2,1,1]
[8,4,2,3,7,5,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[5,2,6,1,8,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,6,1,8,4,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,2,3,8,5,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[8,5,1,6,4,2,3,7]=>1101100=>0011011=>[3,1,2,1,1]
[3,2,5,1,7,6,4,8]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,5,1,8,6,4,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,6,1,5,7,3,2,4]=>1100110=>0110011=>[2,1,3,1,1]
[8,5,6,1,7,3,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[3,6,8,5,1,7,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[8,5,1,6,7,4,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,5,1,8,6,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,4,1,5,8,6,7]=>1010010=>0100101=>[2,3,2,1]
[3,2,5,1,7,8,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[8,7,5,1,6,4,2,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[3,2,5,1,8,7,6,4]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,6,3,7,1,8,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,3,7,5,1,8,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,2,6,1,7,5,3,8]=>1010110=>0110101=>[2,1,2,2,1]
[2,5,7,4,1,6,3,8]=>0011010=>0101100=>[2,2,1,3]
[2,5,7,4,1,6,8,3]=>0011001=>1001100=>[1,3,1,3]
[5,4,7,8,3,1,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[4,3,7,5,1,8,6,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,4,3,8,5,1,7,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,8,4,3,6,1,7,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,4,8,3,6,1,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,5,4,6,1,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[4,6,2,1,8,5,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[2,4,1,7,5,8,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,4,1,7,5,3,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,4,1,8,5,3,7]=>0110110=>0110110=>[2,1,2,1,2]
[5,4,8,2,1,6,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[2,5,8,4,1,6,3,7]=>0011010=>0101100=>[2,2,1,3]
[3,2,5,6,1,8,4,7]=>1001010=>0101001=>[2,2,3,1]
[4,8,3,2,6,1,5,7]=>0110100=>0010110=>[3,2,1,2]
[3,5,2,8,1,6,4,7]=>0101010=>0101010=>[2,2,2,2]
[3,2,1,6,8,5,4,7]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,7,1,5,4,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,7,1,5,8,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[3,8,2,5,1,6,7,4]=>0101001=>1001010=>[1,3,2,2]
[4,8,3,2,6,7,1,5]=>0110010=>0100110=>[2,3,1,2]
[4,3,8,2,6,7,1,5]=>1010010=>0100101=>[2,3,2,1]
[4,3,2,6,7,8,1,5]=>1100010=>0100011=>[2,4,1,1]
[4,3,2,6,7,1,5,8]=>1100100=>0010011=>[3,3,1,1]
[4,3,7,8,2,6,1,5]=>1001010=>0101001=>[2,2,3,1]
[2,5,7,4,8,1,6,3]=>0010101=>1010100=>[1,2,2,3]
[3,2,5,7,1,6,8,4]=>1001001=>1001001=>[1,3,3,1]
[3,2,5,7,1,6,4,8]=>1001010=>0101001=>[2,2,3,1]
[6,3,2,7,1,5,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,2,7,1,5,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[6,3,2,7,8,1,5,4]=>1100101=>1010011=>[1,2,3,1,1]
[6,5,2,1,7,8,4,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[6,2,1,8,5,3,7,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,3,2,7,1,4,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[6,3,2,1,4,7,8,5]=>1110001=>1000111=>[1,4,1,1,1]
[6,3,2,1,4,7,5,8]=>1110010=>0100111=>[2,3,1,1,1]
[3,5,2,1,7,8,4,6]=>0110010=>0100110=>[2,3,1,2]
[4,6,2,1,8,3,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,2,7,1,4,8,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[3,5,8,2,1,7,4,6]=>0011010=>0101100=>[2,2,1,3]
[4,8,3,7,2,1,5,6]=>0101100=>0011010=>[3,1,2,2]
[4,3,7,2,8,1,5,6]=>1010100=>0010101=>[3,2,2,1]
[4,3,7,2,1,5,6,8]=>1011000=>0001101=>[4,1,2,1]
[4,8,3,2,7,1,5,6]=>0110100=>0010110=>[3,2,1,2]
[6,3,2,8,1,4,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[3,2,1,4,7,5,8,6]=>1100101=>1010011=>[1,2,3,1,1]
[5,3,2,1,8,4,6,7]=>1110100=>0010111=>[3,2,1,1,1]
[4,8,3,2,1,5,6,7]=>0111000=>0001110=>[4,1,1,2]
[4,3,8,2,1,5,6,7]=>1011000=>0001101=>[4,1,2,1]
[6,2,3,1,5,4,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,5,2,3,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,5,3,4,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,5,3,4,1,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,5,1,3,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,5,3,4,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,2,4,1,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,5,1,4,2,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,5,1,3,2,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,4,5,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,7,3,4,2,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,1,4,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,3,4,1,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,2,3,1,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,3,1,5,4,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,3,1,8,5,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,3,1,7,5,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,7,1,3,2,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,1,3,2,7,5,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,1,8,5,7,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,8,6,3,2,7,1]=>0011101=>1011100=>[1,2,1,1,3]
[1,5,8,7,3,6,2,4]=>0011010=>0101100=>[2,2,1,3]
[1,7,2,8,4,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,2,8,4,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,6,2,8,4,5,7,1]=>0101001=>1001010=>[1,3,2,2]
[2,6,1,8,4,5,7,3]=>0101001=>1001010=>[1,3,2,2]
[2,8,4,6,1,5,7,3]=>0101001=>1001010=>[1,3,2,2]
[6,3,1,8,4,5,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[2,3,6,8,4,5,7,1]=>0001001=>1001000=>[1,3,4]
[6,3,7,8,4,1,5,2]=>1001101=>1011001=>[1,2,1,3,1]
[1,3,7,8,4,6,5,2]=>0001011=>1101000=>[1,1,2,4]
[3,6,7,8,4,2,5,1]=>0001101=>1011000=>[1,2,1,4]
[7,6,1,8,4,2,5,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,8,3,7,1,6,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[5,2,8,7,3,6,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,2,1,8,4,6,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,2,7,8,4,6,5,1]=>1001011=>1101001=>[1,1,2,3,1]
[5,2,7,8,1,4,6,3]=>1001001=>1001001=>[1,3,3,1]
[1,2,7,8,5,4,6,3]=>0001101=>1011000=>[1,2,1,4]
[7,2,5,8,3,4,6,1]=>1001001=>1001001=>[1,3,3,1]
[6,2,8,5,4,3,1,7]=>1011110=>0111101=>[2,1,1,1,2,1]
[2,8,3,5,4,1,6,7]=>0101100=>0011010=>[3,1,2,2]
[2,8,4,5,3,1,6,7]=>0101100=>0011010=>[3,1,2,2]
[7,3,5,8,2,4,6,1]=>1001001=>1001001=>[1,3,3,1]
[4,3,1,2,8,5,6,7]=>1100100=>0010011=>[3,3,1,1]
[2,7,6,8,4,3,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[1,7,5,8,3,4,6,2]=>0101001=>1001010=>[1,3,2,2]
[4,6,8,5,1,3,2,7]=>0011010=>0101100=>[2,2,1,3]
[2,4,8,3,6,5,1,7]=>0010110=>0110100=>[2,1,2,3]
[4,1,8,3,5,6,2,7]=>1010010=>0100101=>[2,3,2,1]
[5,6,8,4,1,3,2,7]=>0011010=>0101100=>[2,2,1,3]
[4,6,8,1,5,3,2,7]=>0010110=>0110100=>[2,1,2,3]
[1,6,8,4,5,3,2,7]=>0010110=>0110100=>[2,1,2,3]
[1,7,3,8,5,4,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[3,7,1,8,5,4,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,7,3,8,4,6,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,8,7,4,1,6,5,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,8,5,4,3,1,6,7]=>0111100=>0011110=>[3,1,1,1,2]
[1,4,3,2,8,5,6,7]=>0110100=>0010110=>[3,2,1,2]
[7,3,2,8,5,4,6,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,4,8,2,5,3,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[2,8,4,3,5,1,6,7]=>0110100=>0010110=>[3,2,1,2]
[6,2,8,4,5,3,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,3,8,5,4,6,1]=>1001101=>1011001=>[1,2,1,3,1]
[4,2,3,1,8,5,6,7]=>1010100=>0010101=>[3,2,2,1]
[5,1,3,2,4,8,6,7]=>1010010=>0100101=>[2,3,2,1]
[2,8,1,5,3,4,7,6]=>0101001=>1001010=>[1,3,2,2]
[1,4,2,8,5,3,6,7]=>0101100=>0011010=>[3,1,2,2]
[3,5,1,4,8,2,6,7]=>0100100=>0010010=>[3,3,2]
[1,5,2,8,4,3,6,7]=>0101100=>0011010=>[3,1,2,2]
[1,2,5,4,3,8,6,7]=>0011010=>0101100=>[2,2,1,3]
[1,2,4,8,5,3,7,6]=>0001101=>1011000=>[1,2,1,4]
[1,5,2,7,8,4,3,6]=>0100110=>0110010=>[2,1,3,2]
[5,1,2,7,4,8,3,6]=>1001010=>0101001=>[2,2,3,1]
[8,3,5,1,4,7,2,6]=>1010010=>0100101=>[2,3,2,1]
[1,2,8,5,7,4,3,6]=>0010110=>0110100=>[2,1,2,3]
[1,2,4,8,7,5,3,6]=>0001110=>0111000=>[2,1,1,4]
[2,8,1,4,3,7,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[7,6,1,4,2,8,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,1,6,2,8,4,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[1,4,2,7,8,5,3,6]=>0100110=>0110010=>[2,1,3,2]
[6,1,2,8,4,3,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[6,4,1,2,8,3,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[7,6,1,3,2,4,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[6,7,1,3,2,4,8,5]=>0101001=>1001010=>[1,3,2,2]
[1,2,7,3,5,8,4,6]=>0010010=>0100100=>[2,3,3]
[5,8,1,3,7,2,4,6]=>0100100=>0010010=>[3,3,2]
[1,2,5,8,7,3,4,6]=>0001100=>0011000=>[3,1,4]
[8,6,1,3,2,4,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[4,2,8,1,7,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,2,8,4,3,6,5]=>1001101=>1011001=>[1,2,1,3,1]
[1,2,8,4,7,5,3,6]=>0010110=>0110100=>[2,1,2,3]
[1,2,8,7,4,5,3,6]=>0011010=>0101100=>[2,2,1,3]
[2,8,1,7,5,3,4,6]=>0101100=>0011010=>[3,1,2,2]
[8,3,7,1,5,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[8,6,1,4,2,7,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,1,2,8,6,4,3,5]=>1001110=>0111001=>[2,1,1,3,1]
[3,7,4,8,1,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[3,4,8,7,1,6,2,5]=>0011010=>0101100=>[2,2,1,3]
[4,2,8,1,7,6,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[2,8,1,7,6,4,3,5]=>0101110=>0111010=>[2,1,1,2,2]
[7,8,3,4,1,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,4,1,7,2,5]=>0101010=>0101010=>[2,2,2,2]
[5,7,3,4,1,8,2,6]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,4,1,7,2,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,5,1,6,2,8]=>0101010=>0101010=>[2,2,2,2]
[4,8,3,5,1,6,2,7]=>0101010=>0101010=>[2,2,2,2]
[4,8,3,5,1,7,2,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,5,1,8,2,6]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,3,1,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,4,1,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,4,1,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[4,6,2,5,1,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[4,6,2,5,1,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[4,5,1,8,3,7,2,6]=>0101010=>0101010=>[2,2,2,2]
[4,6,2,7,3,8,1,5]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,7,3,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,8,4,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,8,3,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[4,6,2,8,3,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,5,1,7,3,6,2,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,1,8,3,6,2,7]=>0101010=>0101010=>[2,2,2,2]
[6,5,3,2,1,4,8,7]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,7,3,5,2,4,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,8,2,4,5,7,3,1]=>0100011=>1100010=>[1,1,4,2]
[3,6,1,4,5,2,8,7]=>0100101=>1010010=>[1,2,3,2]
[8,3,7,4,5,2,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[6,3,8,4,5,7,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[8,1,7,4,3,6,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,7,3,5,1,4,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[2,1,6,8,5,7,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[6,8,3,5,1,7,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,8,4,7,6,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,3,8,1,5,6,7,2]=>1010001=>1000101=>[1,4,2,1]
[4,8,3,6,1,2,7,5]=>0101001=>1001010=>[1,3,2,2]
[3,8,7,4,1,6,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[3,8,1,2,5,6,7,4]=>0100001=>1000010=>[1,5,2]
[2,8,7,4,5,1,3,6]=>0110100=>0010110=>[3,2,1,2]
[8,7,2,4,1,6,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,8,3,6,2,4,7,1]=>0101001=>1001010=>[1,3,2,2]
[8,6,3,2,1,4,7,5]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,7,3,5,2,1,4,6]=>1101100=>0011011=>[3,1,2,1,1]
[5,8,3,6,2,1,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[6,1,8,4,5,7,2,3]=>1010010=>0100101=>[2,3,2,1]
[6,8,3,5,1,7,2,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,6,1,2,7,4]=>0101001=>1001010=>[1,3,2,2]
[5,8,1,4,7,6,2,3]=>0100110=>0110010=>[2,1,3,2]
[4,5,3,8,6,1,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,5,7,6,2,3,8,1]=>0011001=>1001100=>[1,3,1,3]
[3,5,7,2,6,4,8,1]=>0010101=>1010100=>[1,2,2,3]
[2,5,7,3,6,4,8,1]=>0010101=>1010100=>[1,2,2,3]
[8,4,3,7,6,1,5,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,7,2,3,5,4,8,1]=>0100101=>1010010=>[1,2,3,2]
[5,2,7,3,6,4,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,4,7,6,1,5,2]=>1001101=>1011001=>[1,2,1,3,1]
[8,2,4,7,1,6,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[3,1,4,7,6,8,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[5,1,7,3,6,8,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[6,7,1,3,5,8,4,2]=>0100011=>1100010=>[1,1,4,2]
[4,8,3,7,6,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,8,4,7,1,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[8,1,4,7,2,6,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,3,2,7,6,5,4]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,8,3,1,7,6,5,4]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,7,1,2,8,5,4,3]=>0100111=>1110010=>[1,1,1,3,2]
[8,2,3,1,7,6,5,4]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,4,2,7,8,6,5,3]=>0100111=>1110010=>[1,1,1,3,2]
[8,4,2,7,1,6,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,7,2,1,6,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,5,7,2,8,6,4,3]=>0010111=>1110100=>[1,1,1,2,3]
[2,5,7,1,8,6,4,3]=>0010111=>1110100=>[1,1,1,2,3]
[3,5,7,1,6,8,4,2]=>0010011=>1100100=>[1,1,3,3]
[6,7,4,5,8,1,3,2]=>0100101=>1010010=>[1,2,3,2]
[2,5,7,8,1,6,4,3]=>0001011=>1101000=>[1,1,2,4]
[1,5,7,8,2,6,4,3]=>0001011=>1101000=>[1,1,2,4]
[8,5,7,1,2,6,4,3]=>1010011=>1100101=>[1,1,3,2,1]
[8,4,1,7,2,6,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,7,2,8,1,5,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,2,7,8,1,6,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,8,7,1,6,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,3,8,2,7,6,5,4]=>0010111=>1110100=>[1,1,1,2,3]
[8,3,1,2,7,6,5,4]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,2,1,3,7,6,5,4]=>1100111=>1110011=>[1,1,1,3,1,1]
[2,1,8,3,7,6,5,4]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,1,7,8,2,6,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[6,7,1,8,2,5,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[4,8,1,7,2,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[3,8,1,2,7,6,5,4]=>0100111=>1110010=>[1,1,1,3,2]
[1,8,2,3,7,6,5,4]=>0100111=>1110010=>[1,1,1,3,2]
[3,7,1,5,8,2,6,4]=>0100101=>1010010=>[1,2,3,2]
[2,7,1,5,8,3,6,4]=>0100101=>1010010=>[1,2,3,2]
[2,6,5,1,8,3,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,6,4,1,8,7,2,3]=>0110110=>0110110=>[2,1,2,1,2]
[8,1,4,5,7,6,2,3]=>1000110=>0110001=>[2,1,4,1]
[6,4,5,1,8,7,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[5,4,6,1,8,7,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[3,5,6,1,8,2,7,4]=>0010101=>1010100=>[1,2,2,3]
[2,5,6,1,8,3,7,4]=>0010101=>1010100=>[1,2,2,3]
[2,4,6,1,3,8,7,5]=>0010011=>1100100=>[1,1,3,3]
[3,4,6,1,2,8,7,5]=>0010011=>1100100=>[1,1,3,3]
[5,3,6,1,8,2,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,1,5,8,2,6,4]=>1100101=>1010011=>[1,2,3,1,1]
[8,1,3,5,7,2,6,4]=>1000101=>1010001=>[1,2,4,1]
[8,1,2,5,7,3,6,4]=>1000101=>1010001=>[1,2,4,1]
[7,2,1,5,8,3,6,4]=>1100101=>1010011=>[1,2,3,1,1]
[6,2,5,1,8,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,6,1,3,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,5,3,1,8,7,6]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,2,4,1,3,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[7,2,1,4,3,8,6,5]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,1,2,4,3,7,6,5]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,3,4,2,7,6,5]=>1001011=>1101001=>[1,1,2,3,1]
[7,3,1,4,2,8,6,5]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,6,3,1,2,8,7,5]=>0110011=>1100110=>[1,1,3,1,2]
[2,6,4,1,3,8,7,5]=>0110011=>1100110=>[1,1,3,1,2]
[2,7,1,4,3,8,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[8,1,6,7,2,3,5,4]=>1001001=>1001001=>[1,3,3,1]
[4,7,1,2,3,8,6,5]=>0100011=>1100010=>[1,1,4,2]
[3,7,1,2,4,8,6,5]=>0100011=>1100010=>[1,1,4,2]
[2,6,3,1,4,8,7,5]=>0110011=>1100110=>[1,1,3,1,2]
[3,6,2,1,4,8,7,5]=>0110011=>1100110=>[1,1,3,1,2]
[5,6,2,1,8,3,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[6,5,2,1,8,3,7,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,1,4,2,3,7,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[7,4,1,2,3,8,6,5]=>1100011=>1100011=>[1,1,4,1,1]
[5,4,2,3,1,8,7,6]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,5,2,4,1,8,7,6]=>0101011=>1101010=>[1,1,2,2,2]
[7,3,1,2,4,8,6,5]=>1100011=>1100011=>[1,1,4,1,1]
[8,1,3,2,4,7,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[7,2,1,3,4,8,6,5]=>1100011=>1100011=>[1,1,4,1,1]
[2,4,3,6,1,5,8,7]=>0101001=>1001010=>[1,3,2,2]
[2,4,3,6,5,8,1,7]=>0101010=>0101010=>[2,2,2,2]
[2,4,6,3,5,8,7,1]=>0010011=>1100100=>[1,1,3,3]
[2,4,6,3,5,1,8,7]=>0010101=>1010100=>[1,2,2,3]
[2,4,6,3,1,5,8,7]=>0011001=>1001100=>[1,3,1,3]
[2,4,1,6,5,3,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[2,4,6,1,5,3,8,7]=>0010101=>1010100=>[1,2,2,3]
[4,2,6,5,3,1,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,2,6,5,1,3,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[4,2,6,5,8,1,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,6,5,8,1,3,7]=>1010100=>0010101=>[3,2,2,1]
[4,2,6,5,8,3,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[2,4,1,6,5,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[2,1,4,6,5,8,3,7]=>1001010=>0101001=>[2,2,3,1]
[2,4,1,6,5,8,7,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,4,6,1,5,8,7,3]=>0010011=>1100100=>[1,1,3,3]
[4,2,6,5,3,8,7,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,6,4,3,8,7,5,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,2,6,8,5,3,7,1]=>1001101=>1011001=>[1,2,1,3,1]
[2,4,6,8,1,5,7,3]=>0001001=>1001000=>[1,3,4]
[2,4,1,6,8,5,7,3]=>0100101=>1010010=>[1,2,3,2]
[2,1,4,6,8,5,3,7]=>1000110=>0110001=>[2,1,4,1]
[2,4,6,1,8,5,3,7]=>0010110=>0110100=>[2,1,2,3]
[2,4,6,8,1,5,3,7]=>0001010=>0101000=>[2,2,4]
[2,4,6,8,3,5,7,1]=>0001001=>1001000=>[1,3,4]
[2,4,6,8,3,1,5,7]=>0001100=>0011000=>[3,1,4]
[2,4,6,3,8,5,7,1]=>0010101=>1010100=>[1,2,2,3]
[2,4,3,6,8,5,7,1]=>0100101=>1010010=>[1,2,3,2]
[2,4,3,6,8,5,1,7]=>0100110=>0110010=>[2,1,3,2]
[2,4,3,6,8,1,5,7]=>0100100=>0010010=>[3,3,2]
[2,4,3,6,1,8,5,7]=>0101010=>0101010=>[2,2,2,2]
[2,4,3,1,6,8,5,7]=>0110010=>0100110=>[2,3,1,2]
[2,4,1,3,6,8,7,5]=>0100011=>1100010=>[1,1,4,2]
[2,4,3,6,8,1,7,5]=>0100101=>1010010=>[1,2,3,2]
[4,6,5,2,8,7,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[4,6,2,5,8,7,1,3]=>0100110=>0110010=>[2,1,3,2]
[4,6,2,5,8,7,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,4,6,3,1,8,7,5]=>0011011=>1101100=>[1,1,2,1,3]
[2,4,1,6,3,8,7,5]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,4,6,3,8,7,5]=>1001011=>1101001=>[1,1,2,3,1]
[2,4,1,6,8,3,7,5]=>0100101=>1010010=>[1,2,3,2]
[2,4,6,8,1,3,7,5]=>0001001=>1001000=>[1,3,4]
[4,6,2,8,5,7,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,2,8,5,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,2,4,8,7,1,3,5]=>1001100=>0011001=>[3,1,3,1]
[2,6,4,8,1,7,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,4,1,8,7,5,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,1,6,4,8,7,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[2,6,4,1,8,7,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[2,6,4,8,1,7,3,5]=>0101010=>0101010=>[2,2,2,2]
[6,2,4,8,7,3,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[6,2,4,8,7,3,1,5]=>1001110=>0111001=>[2,1,1,3,1]
[1,3,7,4,5,8,2,6]=>0010010=>0100100=>[2,3,3]
[1,7,6,3,4,8,2,5]=>0110010=>0100110=>[2,3,1,2]
[8,1,6,3,7,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[1,2,7,4,8,3,5,6]=>0010100=>0010100=>[3,2,3]
[6,1,7,3,4,8,2,5]=>1010010=>0100101=>[2,3,2,1]
[2,1,7,4,5,8,3,6]=>1010010=>0100101=>[2,3,2,1]
[5,1,4,7,3,8,2,6]=>1001010=>0101001=>[2,2,3,1]
[4,3,1,7,5,8,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[2,8,6,3,7,1,4,5]=>0110100=>0010110=>[3,2,1,2]
[6,8,1,3,7,2,4,5]=>0100100=>0010010=>[3,3,2]
[5,8,2,1,7,3,4,6]=>0110100=>0010110=>[3,2,1,2]
[5,7,2,1,8,3,4,6]=>0110100=>0010110=>[3,2,1,2]
[6,7,1,3,8,2,4,5]=>0100100=>0010010=>[3,3,2]
[8,5,1,3,7,2,4,6]=>1100100=>0010011=>[3,3,1,1]
[1,5,3,2,8,4,6,7]=>0110100=>0010110=>[3,2,1,2]
[2,6,4,8,7,1,3,5]=>0101100=>0011010=>[3,1,2,2]
[1,6,4,8,7,2,3,5]=>0101100=>0011010=>[3,1,2,2]
[4,3,2,8,7,1,5,6]=>1101100=>0011011=>[3,1,2,1,1]
[5,2,4,8,7,1,3,6]=>1001100=>0011001=>[3,1,3,1]
[6,2,8,3,7,1,4,5]=>1010100=>0010101=>[3,2,2,1]
[5,1,4,8,7,2,3,6]=>1001100=>0011001=>[3,1,3,1]
[3,7,2,1,5,4,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,2,1,5,4,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[8,3,2,1,5,4,6,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,3,2,1,6,4,5,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,4,2,5,1,6,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,3,2,1,4,6,5,7]=>1110010=>0100111=>[2,3,1,1,1]
[3,8,2,1,4,5,7,6]=>0110001=>1000110=>[1,4,1,2]
[3,2,7,1,4,6,8,5]=>1010001=>1000101=>[1,4,2,1]
[3,2,8,1,4,6,7,5]=>1010001=>1000101=>[1,4,2,1]
[3,8,2,1,4,7,5,6]=>0110010=>0100110=>[2,3,1,2]
[3,8,2,1,5,7,4,6]=>0110010=>0100110=>[2,3,1,2]
[4,8,2,5,1,7,3,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,2,5,1,8,3,6]=>0101010=>0101010=>[2,2,2,2]
[3,7,2,1,5,8,4,6]=>0110010=>0100110=>[2,3,1,2]
[3,7,2,1,4,8,5,6]=>0110010=>0100110=>[2,3,1,2]
[3,2,1,7,5,8,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,2,7,6,1,8,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[4,3,7,6,8,1,2,5]=>1010100=>0010101=>[3,2,2,1]
[4,3,8,6,7,1,2,5]=>1010100=>0010101=>[3,2,2,1]
[3,8,2,1,7,4,5,6]=>0110100=>0010110=>[3,2,1,2]
[3,2,8,1,6,4,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,7,1,6,4,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,7,6,1,3,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[4,2,8,6,1,3,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[5,7,8,3,4,1,2,6]=>0010100=>0010100=>[3,2,3]
[4,2,6,8,1,3,7,5]=>1001001=>1001001=>[1,3,3,1]
[4,2,6,7,1,3,8,5]=>1001001=>1001001=>[1,3,3,1]
[3,2,6,1,8,4,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[3,7,2,1,8,5,4,6]=>0110110=>0110110=>[2,1,2,1,2]
[4,7,3,8,5,1,2,6]=>0101100=>0011010=>[3,1,2,2]
[4,3,7,8,6,1,2,5]=>1001100=>0011001=>[3,1,3,1]
[3,2,7,1,8,6,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,1,6,8,5,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,6,1,8,7,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,6,8,1,7,3,5]=>1001010=>0101001=>[2,2,3,1]
[4,3,6,8,7,1,2,5]=>1001100=>0011001=>[3,1,3,1]
[4,2,6,7,1,8,3,5]=>1001010=>0101001=>[2,2,3,1]
[3,2,6,1,7,8,4,5]=>1010010=>0100101=>[2,3,2,1]
[5,3,6,4,8,7,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[1,4,6,2,7,8,5,3]=>0010011=>1100100=>[1,1,3,3]
[3,1,8,5,4,2,6,7]=>1011100=>0011101=>[3,1,1,2,1]
[1,2,7,5,4,8,6,3]=>0011011=>1101100=>[1,1,2,1,3]
[6,3,7,5,4,8,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[1,6,2,5,4,8,7,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,2,5,7,3,6,4]=>0100101=>1010010=>[1,2,3,2]
[6,2,1,5,4,8,7,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,1,6,2,8,7,5,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,8,3,1,4,2,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[4,3,6,1,8,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,1,6,4,3,2,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,1,5,7,4,3,2,8]=>1001110=>0111001=>[2,1,1,3,1]
[1,5,8,6,4,3,2,7]=>0011110=>0111100=>[2,1,1,1,3]
[7,8,5,1,6,3,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[2,6,1,5,7,3,8,4]=>0100101=>1010010=>[1,2,3,2]
[1,6,8,7,4,3,2,5]=>0011110=>0111100=>[2,1,1,1,3]
[6,8,1,7,4,3,2,5]=>0101110=>0111010=>[2,1,1,2,2]
[5,6,1,7,4,3,2,8]=>0101110=>0111010=>[2,1,1,2,2]
[5,1,7,6,4,3,2,8]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,1,7,8,4,3,2,5]=>1001110=>0111001=>[2,1,1,3,1]
[7,1,8,6,4,3,2,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,2,1,5,4,6,8,3]=>1101001=>1001011=>[1,3,2,1,1]
[1,2,8,5,6,3,7,4]=>0010101=>1010100=>[1,2,2,3]
[6,1,2,5,7,3,8,4]=>1000101=>1010001=>[1,2,4,1]
[4,3,6,1,5,7,2,8]=>1010010=>0100101=>[2,3,2,1]
[1,3,6,8,5,7,2,4]=>0001010=>0101000=>[2,2,4]
[1,3,6,4,8,7,2,5]=>0010110=>0110100=>[2,1,2,3]
[4,1,6,7,3,8,2,5]=>1001010=>0101001=>[2,2,3,1]
[5,4,6,1,3,7,2,8]=>1010010=>0100101=>[2,3,2,1]
[6,4,1,5,2,3,7,8]=>1101000=>0001011=>[4,2,1,1]
[4,1,7,5,2,3,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[2,8,3,5,4,1,7,6]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,1,4,6,3,2,5]=>0100110=>0110010=>[2,1,3,2]
[5,1,8,7,4,3,2,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,5,1,8,4,3,2,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,5,7,1,4,3,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,5,8,1,4,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[1,5,7,8,4,3,2,6]=>0001110=>0111000=>[2,1,1,4]
[2,4,7,5,1,3,8,6]=>0011001=>1001100=>[1,3,1,3]
[7,8,4,6,1,3,2,5]=>0101010=>0101010=>[2,2,2,2]
[1,6,5,8,4,3,2,7]=>0101110=>0111010=>[2,1,1,2,2]
[6,8,5,1,4,3,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[3,6,2,5,4,1,7,8]=>0101100=>0011010=>[3,1,2,2]
[4,3,6,2,8,1,5,7]=>1010100=>0010101=>[3,2,2,1]
[6,1,2,5,4,7,8,3]=>1001001=>1001001=>[1,3,3,1]
[6,2,4,5,1,3,7,8]=>1001000=>0001001=>[4,3,1]
[4,2,8,5,1,3,7,6]=>1011001=>1001101=>[1,3,1,2,1]
[4,3,6,8,1,7,2,5]=>1001010=>0101001=>[2,2,3,1]
[5,3,6,4,1,7,2,8]=>1011010=>0101101=>[2,2,1,2,1]
[1,6,7,4,8,3,5,2]=>0010101=>1010100=>[1,2,2,3]
[1,4,6,3,7,5,8,2]=>0010101=>1010100=>[1,2,2,3]
[4,6,7,2,5,8,1,3]=>0010010=>0100100=>[2,3,3]
[2,4,6,1,7,5,3,8]=>0010110=>0110100=>[2,1,2,3]
[2,7,5,4,1,6,3,8]=>0111010=>0101110=>[2,2,1,1,2]
[1,7,5,4,3,8,6,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,5,8,4,3,6,7,2]=>0011001=>1001100=>[1,3,1,3]
[5,4,6,2,7,8,1,3]=>1010010=>0100101=>[2,3,2,1]
[2,5,4,1,6,7,3,8]=>0110010=>0100110=>[2,3,1,2]
[5,6,3,2,7,1,4,8]=>0110100=>0010110=>[3,2,1,2]
[5,6,3,2,7,1,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[8,5,6,3,2,7,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[5,4,6,2,8,1,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,4,1,7,8,5,3,6]=>0100110=>0110010=>[2,1,3,2]
[5,6,3,2,1,8,4,7]=>0111010=>0101110=>[2,2,1,1,2]
[3,5,2,1,6,4,7,8]=>0110100=>0010110=>[3,2,1,2]
[6,8,4,3,2,1,5,7]=>0111100=>0011110=>[3,1,1,1,2]
[5,3,8,2,1,6,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[7,3,2,8,5,1,6,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,4,6,3,2,1,7,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,4,7,2,1,8,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,7,3,2,1,6,8,4]=>0111001=>1001110=>[1,3,1,1,2]
[6,3,7,2,5,1,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,8,3,5,2,1,4]=>0010110=>0110100=>[2,1,2,3]
[6,2,5,7,8,4,1,3]=>1000110=>0110001=>[2,1,4,1]
[2,1,5,7,8,6,3,4]=>1000110=>0110001=>[2,1,4,1]
[3,6,7,2,8,1,4,5]=>0010100=>0010100=>[3,2,3]
[3,2,6,1,7,4,5,8]=>1010100=>0010101=>[3,2,2,1]
[2,5,8,4,1,3,7,6]=>0011001=>1001100=>[1,3,1,3]
[2,4,1,7,8,3,6,5]=>0100101=>1010010=>[1,2,3,2]
[3,6,8,2,1,7,4,5]=>0011010=>0101100=>[2,2,1,3]
[5,3,8,2,1,4,7,6]=>1011001=>1001101=>[1,3,1,2,1]
[4,8,7,3,2,1,5,6]=>0111100=>0011110=>[3,1,1,1,2]
[4,7,3,2,1,5,6,8]=>0111000=>0001110=>[4,1,1,2]
[8,4,7,3,2,1,5,6]=>1011100=>0011101=>[3,1,1,2,1]
[8,3,5,2,1,4,7,6]=>1011001=>1001101=>[1,3,1,2,1]
[3,5,2,1,4,6,8,7]=>0110001=>1000110=>[1,4,1,2]
[2,7,6,5,1,8,3,4]=>0111010=>0101110=>[2,2,1,1,2]
[2,7,6,5,1,8,4,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,3,6,5,1,4,8,7]=>0011001=>1001100=>[1,3,1,3]
[2,3,6,4,1,5,8,7]=>0011001=>1001100=>[1,3,1,3]
[2,7,6,1,4,8,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[7,3,5,1,8,4,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[2,7,6,1,5,8,4,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,7,6,4,1,8,5,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,7,6,4,1,8,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[7,3,5,1,8,6,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[2,3,4,8,7,6,1,5]=>0001110=>0111000=>[2,1,1,4]
[2,3,4,8,5,7,1,6]=>0001010=>0101000=>[2,2,4]
[7,3,5,4,8,1,2,6]=>1010100=>0010101=>[3,2,2,1]
[6,4,3,5,8,7,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[2,1,4,5,8,7,3,6]=>1000110=>0110001=>[2,1,4,1]
[6,4,3,5,8,7,1,2]=>1100110=>0110011=>[2,1,3,1,1]
[2,3,4,8,7,5,1,6]=>0001110=>0111000=>[2,1,1,4]
[2,7,6,5,4,8,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[7,3,5,6,8,1,2,4]=>1000100=>0010001=>[3,4,1]
[6,4,1,5,8,7,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[6,4,1,5,8,7,3,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,4,1,5,8,3,7,2]=>1100101=>1010011=>[1,2,3,1,1]
[5,7,1,6,3,8,2,4]=>0101010=>0101010=>[2,2,2,2]
[6,4,1,5,8,3,2,7]=>1100110=>0110011=>[2,1,3,1,1]
[6,3,5,7,8,2,1,4]=>1000110=>0110001=>[2,1,4,1]
[5,7,3,6,1,8,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[7,3,5,4,8,6,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,3,4,8,5,6,1,7]=>0001010=>0101000=>[2,2,4]
[2,3,4,8,7,1,6,5]=>0001101=>1011000=>[1,2,1,4]
[2,3,4,8,5,1,7,6]=>0001101=>1011000=>[1,2,1,4]
[7,4,3,5,8,2,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[7,4,3,5,8,2,6,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,3,5,4,8,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[2,3,4,8,5,1,6,7]=>0001100=>0011000=>[3,1,4]
[6,1,4,2,8,5,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,8,6,5,3,2,7,1]=>0111101=>1011110=>[1,2,1,1,1,2]
[8,6,5,1,2,4,7,3]=>1110001=>1000111=>[1,4,1,1,1]
[1,7,5,8,2,6,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,8,5,7,6,2,4]=>0010110=>0110100=>[2,1,2,3]
[6,3,8,5,7,1,2,4]=>1010100=>0010101=>[3,2,2,1]
[6,8,5,2,1,4,7,3]=>0111001=>1001110=>[1,3,1,1,2]
[3,8,2,5,6,1,7,4]=>0100101=>1010010=>[1,2,3,2]
[8,1,2,5,6,3,7,4]=>1000101=>1010001=>[1,2,4,1]
[8,6,1,5,7,2,3,4]=>1100100=>0010011=>[3,3,1,1]
[3,8,6,5,7,1,2,4]=>0110100=>0010110=>[3,2,1,2]
[5,1,7,6,8,4,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,3,7,8,6,2,4]=>1000110=>0110001=>[2,1,4,1]
[7,2,5,8,1,6,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[3,2,8,5,7,6,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[8,2,1,5,7,6,3,4]=>1100110=>0110011=>[2,1,3,1,1]
[5,2,8,6,1,7,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[1,2,8,6,5,7,3,4]=>0011010=>0101100=>[2,2,1,3]
[8,2,5,6,3,7,1,4]=>1001010=>0101001=>[2,2,3,1]
[7,2,6,5,4,1,8,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,1,3,5,4,7,8,2]=>1001001=>1001001=>[1,3,3,1]
[6,1,5,3,4,7,8,2]=>1010001=>1000101=>[1,4,2,1]
[7,5,6,2,4,1,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,2,6,3,7,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,1,6,5,7,3,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[3,5,8,6,2,7,1,4]=>0011010=>0101100=>[2,2,1,3]
[1,8,5,6,3,7,2,4]=>0101010=>0101010=>[2,2,2,2]
[1,7,6,5,4,2,8,3]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,7,6,1,4,2,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[7,1,4,2,6,5,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[2,7,4,1,5,6,8,3]=>0110001=>1000110=>[1,4,1,2]
[5,7,6,4,1,2,8,3]=>0111001=>1001110=>[1,3,1,1,2]
[4,7,6,1,5,2,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[1,7,6,4,5,2,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,1,6,5,7,2,4]=>0101010=>0101010=>[2,2,2,2]
[8,1,3,5,7,6,2,4]=>1000110=>0110001=>[2,1,4,1]
[7,8,5,4,1,6,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[6,1,5,4,3,7,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[7,5,6,4,2,1,8,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,3,2,6,5,7,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,6,2,5,1,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,4,3,5,7,8,2]=>1010001=>1000101=>[1,4,2,1]
[6,1,3,4,5,7,8,2]=>1000001=>1000001=>[1,6,1]
[7,2,6,4,5,1,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,3,6,5,7,1,4]=>1001010=>0101001=>[2,2,3,1]
[3,8,2,7,6,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[4,8,7,2,6,5,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,8,7,3,1,6,5,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,8,7,3,2,6,1,5]=>0111010=>0101110=>[2,2,1,1,2]
[4,8,7,3,2,6,5,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,8,7,3,6,2,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,7,3,6,1,5,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,7,6,3,4,2,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,8,7,6,3,1,4,2]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,8,7,6,2,4,3,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,8,7,6,4,2,1,3]=>0111110=>0111110=>[2,1,1,1,1,2]
[5,8,7,6,4,1,3,2]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,8,7,6,4,3,1,2]=>0111110=>0111110=>[2,1,1,1,1,2]
[7,3,4,2,1,6,5,8]=>1011010=>0101101=>[2,2,1,2,1]
[7,3,5,2,6,1,4,8]=>1010100=>0010101=>[3,2,2,1]
[7,3,5,2,6,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,1,5,6,4,3,8]=>1100110=>0110011=>[2,1,3,1,1]
[7,3,5,1,6,4,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,5,6,1,3,2,8]=>1001010=>0101001=>[2,2,3,1]
[1,4,5,7,3,2,8,6]=>0001101=>1011000=>[1,2,1,4]
[6,4,5,7,3,1,8,2]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,5,1,7,4,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,1,5,7,4,8,3]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,1,5,7,4,8,6]=>1100101=>1010011=>[1,2,3,1,1]
[2,4,6,7,3,8,1,5]=>0001010=>0101000=>[2,2,4]
[1,4,6,7,3,8,5,2]=>0001011=>1101000=>[1,1,2,4]
[2,5,6,7,8,3,1,4]=>0000110=>0110000=>[2,1,5]
[3,2,1,6,7,8,4,5]=>1100010=>0100011=>[2,4,1,1]
[5,2,1,6,7,8,4,3]=>1100011=>1100011=>[1,1,4,1,1]
[5,3,6,1,7,8,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,4,6,7,1,8,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[6,4,5,7,2,1,8,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,4,6,7,2,8,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[5,3,6,2,7,8,4,1]=>1010011=>1100101=>[1,1,3,2,1]
[5,3,6,2,7,8,1,4]=>1010010=>0100101=>[2,3,2,1]
[6,3,5,2,7,1,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,4,1,2,7,8,6]=>1010001=>1000101=>[1,4,2,1]
[4,3,6,2,7,8,1,5]=>1010010=>0100101=>[2,3,2,1]
[4,3,6,2,7,8,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[1,3,6,2,7,8,5,4]=>0010011=>1100100=>[1,1,3,3]
[1,4,6,7,2,8,5,3]=>0001011=>1101000=>[1,1,2,4]
[3,4,6,7,2,8,5,1]=>0001011=>1101000=>[1,1,2,4]
[3,4,5,7,2,1,8,6]=>0001101=>1011000=>[1,2,1,4]
[4,2,1,5,7,3,8,6]=>1100101=>1010011=>[1,2,3,1,1]
[4,2,1,6,7,8,3,5]=>1100010=>0100011=>[2,4,1,1]
[4,3,6,1,7,8,2,5]=>1010010=>0100101=>[2,3,2,1]
[1,5,6,7,8,2,4,3]=>0000101=>1010000=>[1,2,5]
[1,5,6,7,8,4,2,3]=>0000110=>0110000=>[2,1,5]
[4,3,6,1,7,8,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,1,6,7,8,5,3]=>1100011=>1100011=>[1,1,4,1,1]
[2,4,6,7,1,8,5,3]=>0001011=>1101000=>[1,1,2,4]
[2,5,6,7,8,1,4,3]=>0000101=>1010000=>[1,2,5]
[1,4,3,6,2,5,7,8]=>0101000=>0001010=>[4,2,2]
[1,4,3,7,2,5,6,8]=>0101000=>0001010=>[4,2,2]
[1,4,3,7,6,8,2,5]=>0101010=>0101010=>[2,2,2,2]
[1,4,3,7,5,8,2,6]=>0101010=>0101010=>[2,2,2,2]
[1,5,3,7,4,8,2,6]=>0101010=>0101010=>[2,2,2,2]
[1,5,4,8,2,6,3,7]=>0101010=>0101010=>[2,2,2,2]
[1,5,4,8,3,7,2,6]=>0101010=>0101010=>[2,2,2,2]
[1,2,3,6,5,8,4,7]=>0001010=>0101000=>[2,2,4]
[6,8,2,4,5,7,1,3]=>0100010=>0100010=>[2,4,2]
[3,7,8,4,5,2,6,1]=>0010101=>1010100=>[1,2,2,3]
[7,8,1,4,5,3,6,2]=>0100101=>1010010=>[1,2,3,2]
[5,8,1,4,7,6,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[7,5,1,8,6,2,4,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,4,1,8,2,6,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,1,8,4,2,6,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,3,1,8,4,2,6,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,2,8,3,6,5,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,8,3,6,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,2,8,3,5,4,7]=>1001010=>0101001=>[2,2,3,1]
[5,2,3,8,1,4,7,6]=>1001001=>1001001=>[1,3,3,1]
[6,2,4,1,8,7,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[3,1,6,4,2,8,5,7]=>1011010=>0101101=>[2,2,1,2,1]
[2,6,3,8,7,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,3,8,5,1,4,7]=>0101100=>0011010=>[3,1,2,2]
[2,5,1,8,3,4,7,6]=>0101001=>1001010=>[1,3,2,2]
[1,2,5,3,8,4,7,6]=>0010101=>1010100=>[1,2,2,3]
[1,2,4,8,3,7,6,5]=>0001011=>1101000=>[1,1,2,4]
[2,4,8,3,7,1,6,5]=>0010101=>1010100=>[1,2,2,3]
[2,4,8,3,7,6,1,5]=>0010110=>0110100=>[2,1,2,3]
[2,5,3,8,1,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[2,5,4,1,3,8,7,6]=>0110011=>1100110=>[1,1,3,1,2]
[3,1,5,4,8,2,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,1,4,8,2,7,6]=>1100101=>1010011=>[1,2,3,1,1]
[5,2,3,8,4,7,1,6]=>1001010=>0101001=>[2,2,3,1]
[4,8,2,3,7,6,1,5]=>0100110=>0110010=>[2,1,3,2]
[4,8,2,3,7,1,6,5]=>0100101=>1010010=>[1,2,3,2]
[4,8,1,2,3,7,6,5]=>0100011=>1100010=>[1,1,4,2]
[1,4,8,3,7,2,6,5]=>0010101=>1010100=>[1,2,2,3]
[6,3,8,1,5,2,4,7]=>1010100=>0010101=>[3,2,2,1]
[5,3,8,1,2,4,7,6]=>1010001=>1000101=>[1,4,2,1]
[5,1,3,8,2,4,7,6]=>1001001=>1001001=>[1,3,3,1]
[1,5,3,8,2,4,7,6]=>0101001=>1001010=>[1,3,2,2]
[1,5,4,8,2,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,1,4,8,2,7,6,3]=>1001011=>1101001=>[1,1,2,3,1]
[5,4,8,1,2,7,6,3]=>1010011=>1100101=>[1,1,3,2,1]
[6,5,1,2,8,7,4,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[4,1,5,8,2,7,6,3]=>1001011=>1101001=>[1,1,2,3,1]
[4,1,2,5,8,7,6,3]=>1000111=>1110001=>[1,1,1,4,1]
[1,4,2,5,8,7,6,3]=>0100111=>1110010=>[1,1,1,3,2]
[1,3,5,2,8,7,4,6]=>0010110=>0110100=>[2,1,2,3]
[3,5,1,2,8,7,4,6]=>0100110=>0110010=>[2,1,3,2]
[4,2,6,1,8,7,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[4,3,1,5,8,2,7,6]=>1100101=>1010011=>[1,2,3,1,1]
[3,5,2,8,7,1,4,6]=>0101100=>0011010=>[3,1,2,2]
[3,4,8,7,2,6,1,5]=>0011010=>0101100=>[2,2,1,3]
[3,4,8,1,7,2,6,5]=>0010101=>1010100=>[1,2,2,3]
[1,3,4,8,7,2,6,5]=>0001101=>1011000=>[1,2,1,4]
[1,3,4,8,2,7,6,5]=>0001011=>1101000=>[1,1,2,4]
[3,4,8,1,2,7,6,5]=>0010011=>1100100=>[1,1,3,3]
[3,4,8,2,7,1,6,5]=>0010101=>1010100=>[1,2,2,3]
[3,4,8,2,7,6,1,5]=>0010110=>0110100=>[2,1,2,3]
[4,2,5,8,1,7,6,3]=>1001011=>1101001=>[1,1,2,3,1]
[4,3,1,2,5,8,7,6]=>1100011=>1100011=>[1,1,4,1,1]
[3,1,4,2,5,8,7,6]=>1010011=>1100101=>[1,1,3,2,1]
[2,3,5,1,8,7,6,4]=>0010111=>1110100=>[1,1,1,2,3]
[7,8,2,1,5,3,6,4]=>0110101=>1010110=>[1,2,2,1,2]
[6,4,1,2,7,3,5,8]=>1100100=>0010011=>[3,3,1,1]
[2,3,7,5,4,1,8,6]=>0011101=>1011100=>[1,2,1,1,3]
[6,3,1,5,4,2,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,8,1,5,4,2,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,3,5,4,1,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,2,5,4,1,3,6]=>0101100=>0011010=>[3,1,2,2]
[7,8,2,5,4,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,2,1,5,4,7,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,3,6,2,4,7,1,8]=>1010010=>0100101=>[2,3,2,1]
[6,4,2,1,7,3,8,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,7,6,5,3,1,4,8]=>0111100=>0011110=>[3,1,1,1,2]
[3,7,6,4,8,5,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[5,7,6,3,8,4,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[5,1,6,2,4,8,3,7]=>1010010=>0100101=>[2,3,2,1]
[4,7,6,5,2,1,3,8]=>0111100=>0011110=>[3,1,1,1,2]
[4,7,6,5,2,8,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[4,7,6,5,1,8,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,7,6,5,2,8,3,4]=>0111010=>0101110=>[2,2,1,1,2]
[1,7,6,5,3,2,8,4]=>0111101=>1011110=>[1,2,1,1,1,2]
[4,7,6,5,1,2,8,3]=>0111001=>1001110=>[1,3,1,1,2]
[4,7,6,5,3,1,8,2]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,2,6,3,4,1,7,8]=>1010100=>0010101=>[3,2,2,1]
[5,1,6,2,4,7,8,3]=>1010001=>1000101=>[1,4,2,1]
[1,7,2,4,8,3,6,5]=>0100101=>1010010=>[1,2,3,2]
[4,7,2,1,5,3,6,8]=>0110100=>0010110=>[3,2,1,2]
[4,7,1,6,2,3,8,5]=>0101001=>1001010=>[1,3,2,2]
[1,7,2,6,8,3,5,4]=>0100101=>1010010=>[1,2,3,2]
[1,2,6,7,4,8,5,3]=>0001011=>1101000=>[1,1,2,4]
[3,1,6,7,4,2,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[3,2,8,5,4,6,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[4,7,6,3,5,8,1,2]=>0110010=>0100110=>[2,3,1,2]
[3,7,6,5,2,4,1,8]=>0111010=>0101110=>[2,2,1,1,2]
[3,7,6,5,2,1,8,4]=>0111101=>1011110=>[1,2,1,1,1,2]
[1,7,6,5,8,2,4,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,7,6,5,8,1,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[3,7,6,5,1,2,4,8]=>0111000=>0001110=>[4,1,1,2]
[3,1,6,8,4,2,5,7]=>1001100=>0011001=>[3,1,3,1]
[4,7,6,8,3,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[2,7,6,5,8,1,3,4]=>0110100=>0010110=>[3,2,1,2]
[2,7,6,5,8,4,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[3,7,5,8,2,4,1,6]=>0101010=>0101010=>[2,2,2,2]
[5,1,7,8,4,3,2,6]=>1001110=>0111001=>[2,1,1,3,1]
[5,1,2,6,4,3,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,2,4,6,3,8,7]=>1000101=>1010001=>[1,2,4,1]
[4,1,5,7,8,3,2,6]=>1000110=>0110001=>[2,1,4,1]
[4,7,1,8,3,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[4,1,7,8,5,2,3,6]=>1001100=>0011001=>[3,1,3,1]
[5,1,7,4,8,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[5,1,8,4,7,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[4,1,8,7,5,2,3,6]=>1011100=>0011101=>[3,1,1,2,1]
[4,7,1,6,3,2,8,5]=>0101101=>1011010=>[1,2,1,2,2]
[7,1,2,3,8,6,5,4]=>1000111=>1110001=>[1,1,1,4,1]
[6,8,1,4,3,7,2,5]=>0101010=>0101010=>[2,2,2,2]
[8,7,3,2,4,1,6,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,7,1,4,3,8,2,5]=>0101010=>0101010=>[2,2,2,2]
[8,1,2,3,5,7,6,4]=>1000011=>1100001=>[1,1,5,1]
[7,1,2,3,6,8,5,4]=>1000011=>1100001=>[1,1,5,1]
[7,1,8,5,4,3,2,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,8,2,6,3,4,1,5]=>0101010=>0101010=>[2,2,2,2]
[6,7,2,8,3,4,1,5]=>0101010=>0101010=>[2,2,2,2]
[3,8,7,1,4,2,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,7,8,1,4,2,6,5]=>0010101=>1010100=>[1,2,2,3]
[3,6,8,1,4,2,7,5]=>0010101=>1010100=>[1,2,2,3]
[3,5,7,8,2,4,1,6]=>0001010=>0101000=>[2,2,4]
[3,6,7,1,4,2,8,5]=>0010101=>1010100=>[1,2,2,3]
[8,6,2,7,3,1,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[8,1,7,5,4,3,2,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,1,7,4,5,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,8,3,7,1,4,2,6]=>0101010=>0101010=>[2,2,2,2]
[2,1,7,3,4,6,8,5]=>1010001=>1000101=>[1,4,2,1]
[6,7,3,2,4,1,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[8,7,2,4,3,6,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,1,2,3,5,6,8,4]=>1000001=>1000001=>[1,6,1]
[6,1,2,3,8,7,4,5]=>1000110=>0110001=>[2,1,4,1]
[5,1,2,3,7,8,6,4]=>1000011=>1100001=>[1,1,5,1]
[8,6,2,4,3,1,7,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,6,3,2,4,8,1,5]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,3,2,4,7,1,5]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,2,4,3,1,8,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,8,1,2,6,3,5,4]=>0100101=>1010010=>[1,2,3,2]
[1,4,8,2,7,3,5,6]=>0010100=>0010100=>[3,2,3]
[1,2,8,5,4,7,3,6]=>0011010=>0101100=>[2,2,1,3]
[2,3,6,8,4,7,1,5]=>0001010=>0101000=>[2,2,4]
[1,3,6,8,4,7,5,2]=>0001011=>1101000=>[1,1,2,4]
[2,4,8,1,7,3,6,5]=>0010101=>1010100=>[1,2,2,3]
[3,4,8,5,7,6,1,2]=>0010110=>0110100=>[2,1,2,3]
[1,2,6,8,4,5,7,3]=>0001001=>1001000=>[1,3,4]
[7,5,1,2,4,3,6,8]=>1100100=>0010011=>[3,3,1,1]
[7,4,6,1,5,2,3,8]=>1010100=>0010101=>[3,2,2,1]
[6,8,1,4,7,2,3,5]=>0100100=>0010010=>[3,3,2]
[1,6,4,2,8,3,5,7]=>0110100=>0010110=>[3,2,1,2]
[1,6,3,8,5,4,2,7]=>0101110=>0111010=>[2,1,1,2,2]
[7,1,3,6,5,4,2,8]=>1001110=>0111001=>[2,1,1,3,1]
[7,2,1,4,6,3,5,8]=>1100100=>0010011=>[3,3,1,1]
[7,2,3,6,5,1,4,8]=>1001100=>0011001=>[3,1,3,1]
[7,1,2,3,6,5,4,8]=>1000110=>0110001=>[2,1,4,1]
[6,8,1,2,7,3,5,4]=>0100101=>1010010=>[1,2,3,2]
[1,6,2,3,8,5,4,7]=>0100110=>0110010=>[2,1,3,2]
[1,5,8,2,7,6,3,4]=>0010110=>0110100=>[2,1,2,3]
[5,8,2,7,6,3,4,1]=>0101101=>1011010=>[1,2,1,2,2]
[6,2,8,1,7,3,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,6,4,1,2,8,5,7]=>0110010=>0100110=>[2,3,1,2]
[2,5,1,8,7,6,3,4]=>0101110=>0111010=>[2,1,1,2,2]
[1,2,5,3,8,7,4,6]=>0010110=>0110100=>[2,1,2,3]
[2,5,3,8,7,1,6,4]=>0101101=>1011010=>[1,2,1,2,2]
[2,5,8,4,1,7,6,3]=>0011011=>1101100=>[1,1,2,1,3]
[3,5,8,7,1,4,2,6]=>0011010=>0101100=>[2,2,1,3]
[5,3,8,4,1,7,6,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,2,8,7,6,3,5,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,3,1,8,7,2,5,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,1,3,8,7,6,2,4]=>1001110=>0111001=>[2,1,1,3,1]
[1,5,3,8,7,6,2,4]=>0101110=>0111010=>[2,1,1,2,2]
[5,1,8,4,7,2,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,7,4,6,1,2,3]=>0110100=>0010110=>[3,2,1,2]
[6,8,5,1,2,4,7,3]=>0110001=>1000110=>[1,4,1,2]
[4,5,8,1,7,2,6,3]=>0010101=>1010100=>[1,2,2,3]
[1,3,2,5,8,7,4,6]=>0100110=>0110010=>[2,1,3,2]
[3,5,1,8,7,4,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,3,6,1,2,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[4,5,8,3,1,7,2,6]=>0011010=>0101100=>[2,2,1,3]
[4,5,2,8,7,1,3,6]=>0101100=>0011010=>[3,1,2,2]
[3,2,5,8,7,1,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[3,4,8,7,6,2,1,5]=>0011110=>0111100=>[2,1,1,1,3]
[3,4,8,7,6,5,1,2]=>0011110=>0111100=>[2,1,1,1,3]
[1,3,4,8,7,6,2,5]=>0001110=>0111000=>[2,1,1,4]
[3,4,8,7,6,2,5,1]=>0011101=>1011100=>[1,2,1,1,3]
[3,2,5,8,7,4,6,1]=>1001101=>1011001=>[1,2,1,3,1]
[2,1,3,5,8,7,4,6]=>1000110=>0110001=>[2,1,4,1]
[1,2,7,5,8,6,4,3]=>0010111=>1110100=>[1,1,1,2,3]
[6,8,1,3,7,5,2,4]=>0100110=>0110010=>[2,1,3,2]
[1,3,7,8,2,6,5,4]=>0001011=>1101000=>[1,1,2,4]
[2,7,8,1,3,6,5,4]=>0010011=>1100100=>[1,1,3,3]
[8,1,2,6,7,3,5,4]=>1000101=>1010001=>[1,2,4,1]
[8,1,2,6,7,5,3,4]=>1000110=>0110001=>[2,1,4,1]
[8,2,5,7,1,3,6,4]=>1001001=>1001001=>[1,3,3,1]
[2,8,1,6,7,3,5,4]=>0100101=>1010010=>[1,2,3,2]
[2,6,8,3,7,1,5,4]=>0010101=>1010100=>[1,2,2,3]
[2,8,6,4,7,1,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,3,4,1,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,8,3,7,4,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[8,2,5,7,1,6,3,4]=>1001010=>0101001=>[2,2,3,1]
[8,4,7,2,3,6,1,5]=>1010010=>0100101=>[2,3,2,1]
[8,5,7,4,2,6,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,5,7,4,1,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[8,5,2,4,7,1,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[8,2,4,7,3,6,1,5]=>1001010=>0101001=>[2,2,3,1]
[8,2,7,1,4,6,3,5]=>1010010=>0100101=>[2,3,2,1]
[8,7,1,2,4,6,3,5]=>1100010=>0100011=>[2,4,1,1]
[8,7,1,4,6,2,3,5]=>1100100=>0010011=>[3,3,1,1]
[8,4,7,1,3,6,2,5]=>1010010=>0100101=>[2,3,2,1]
[8,3,5,7,1,2,6,4]=>1001001=>1001001=>[1,3,3,1]
[5,8,7,1,3,6,2,4]=>0110010=>0100110=>[2,3,1,2]
[8,5,4,7,1,6,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,4,7,1,2,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,1,4,7,2,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[8,5,6,3,1,7,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,8,4,5,7,2,6,3]=>0100101=>1010010=>[1,2,3,2]
[5,8,7,3,6,1,2,4]=>0110100=>0010110=>[3,2,1,2]
[8,3,5,7,1,6,2,4]=>1001010=>0101001=>[2,2,3,1]
[1,6,8,3,7,5,2,4]=>0010110=>0110100=>[2,1,2,3]
[6,3,8,2,7,5,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[8,6,4,7,3,1,5,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,4,5,7,3,1,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[8,3,4,7,2,6,1,5]=>1001010=>0101001=>[2,2,3,1]
[8,7,1,3,4,6,2,5]=>1100010=>0100011=>[2,4,1,1]
[8,3,7,2,4,6,1,5]=>1010010=>0100101=>[2,3,2,1]
[2,8,4,5,7,1,6,3]=>0100101=>1010010=>[1,2,3,2]
[8,7,3,4,5,1,6,2]=>1100101=>1010011=>[1,2,3,1,1]
[8,7,4,5,2,6,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,2,3,4,6,1,5]=>1100010=>0100011=>[2,4,1,1]
[8,6,5,1,3,2,7,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,3,1,7,2,4,5]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,3,1,5,2,4,6]=>1110100=>0010111=>[3,2,1,1,1]
[8,6,1,2,4,7,3,5]=>1100010=>0100011=>[2,4,1,1]
[8,6,1,5,3,4,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[8,6,1,5,2,4,7,3]=>1101001=>1001011=>[1,3,2,1,1]
[8,6,1,2,5,7,3,4]=>1100010=>0100011=>[2,4,1,1]
[5,1,4,2,3,8,6,7]=>1010010=>0100101=>[2,3,2,1]
[5,1,4,2,7,3,6,8]=>1010100=>0010101=>[3,2,2,1]
[5,7,8,1,2,4,6,3]=>0010001=>1000100=>[1,4,3]
[5,7,8,1,3,4,6,2]=>0010001=>1000100=>[1,4,3]
[5,8,1,7,3,4,6,2]=>0101001=>1001010=>[1,3,2,2]
[8,1,5,7,2,4,6,3]=>1001001=>1001001=>[1,3,3,1]
[1,4,2,3,8,7,5,6]=>0100110=>0110010=>[2,1,3,2]
[1,4,2,7,6,3,5,8]=>0101100=>0011010=>[3,1,2,2]
[6,1,2,8,7,5,3,4]=>1001110=>0111001=>[2,1,1,3,1]
[6,1,2,4,8,7,5,3]=>1000111=>1110001=>[1,1,1,4,1]
[3,1,8,4,6,7,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[3,1,7,6,4,8,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,1,2,4,6,8,5,3]=>1000011=>1100001=>[1,1,5,1]
[7,1,2,6,8,5,3,4]=>1000110=>0110001=>[2,1,4,1]
[7,1,5,3,2,8,6,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,1,7,5,3,2,6,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,3,7,1,2,6,4,5]=>1010010=>0100101=>[2,3,2,1]
[3,1,2,8,4,7,5,6]=>1001010=>0101001=>[2,2,3,1]
[1,4,2,3,8,6,5,7]=>0100110=>0110010=>[2,1,3,2]
[1,4,2,3,8,5,7,6]=>0100101=>1010010=>[1,2,3,2]
[5,8,1,7,2,4,6,3]=>0101001=>1001010=>[1,3,2,2]
[5,8,1,3,4,7,6,2]=>0100011=>1100010=>[1,1,4,2]
[3,1,8,6,4,7,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,1,2,6,7,4,5,3]=>1000101=>1010001=>[1,2,4,1]
[1,2,3,5,8,4,7,6]=>0000101=>1010000=>[1,2,5]
[1,2,3,5,8,6,4,7]=>0000110=>0110000=>[2,1,5]
[7,1,2,8,3,6,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,2,8,6,4,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[3,1,7,8,4,6,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,2,7,4,6,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,2,7,3,6,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[1,2,3,6,8,5,4,7]=>0000110=>0110000=>[2,1,5]
[3,6,2,5,4,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,2,8,4,7,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[5,4,7,3,2,8,6,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,4,8,3,2,7,6,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,3,2,6,4,1,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,5,8,3,2,7,6,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,7,6,3,8,5,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,8,6,3,7,5,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,3,2,8,4,7,6,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,1,5,8,4,7,6,3]=>1001011=>1101001=>[1,1,2,3,1]
[5,3,2,7,4,8,6,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,7,4,3,2,8,6,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,7,5,3,2,8,6,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,7,8,3,6,5,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,6,8,3,7,5,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[7,6,4,3,8,5,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,3,2,6,7,5,4,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,6,4,3,7,5,2,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,4,5,3,2,7,6,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,4,6,3,7,5,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,4,6,3,8,5,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,7,2,6,8,5,4,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,8,2,6,7,5,4,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,7,2,8,6,5,4,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[3,6,2,8,7,5,4,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[7,4,5,3,2,8,6,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,1,7,5,4,8,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,3,2,8,6,5,4,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[7,8,4,3,6,5,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,3,2,8,7,5,4,1]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[6,3,2,7,8,5,4,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[1,6,4,8,2,5,3,7]=>0101010=>0101010=>[2,2,2,2]
[1,6,5,8,2,4,3,7]=>0101010=>0101010=>[2,2,2,2]
[1,6,8,2,4,3,7,5]=>0010101=>1010100=>[1,2,2,3]
[1,6,2,4,3,7,8,5]=>0101001=>1001010=>[1,3,2,2]
[1,5,6,2,4,7,3,8]=>0010010=>0100100=>[2,3,3]
[1,5,6,2,4,7,8,3]=>0010001=>1000100=>[1,4,3]
[1,6,7,2,4,3,8,5]=>0010101=>1010100=>[1,2,2,3]
[1,5,8,2,4,6,7,3]=>0010001=>1000100=>[1,4,3]
[1,5,7,8,3,2,4,6]=>0001100=>0011000=>[3,1,4]
[1,5,8,3,2,4,6,7]=>0011000=>0001100=>[4,1,3]
[1,5,6,2,4,8,3,7]=>0010010=>0100100=>[2,3,3]
[1,7,3,4,2,8,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[1,5,6,2,4,8,7,3]=>0010011=>1100100=>[1,1,3,3]
[1,5,8,7,3,2,4,6]=>0011100=>0011100=>[3,1,1,3]
[1,7,4,2,8,6,5,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,5,8,3,2,4,7,6]=>0011001=>1001100=>[1,3,1,3]
[1,6,5,2,3,7,4,8]=>0110010=>0100110=>[2,3,1,2]
[1,6,5,2,3,7,8,4]=>0110001=>1000110=>[1,4,1,2]
[1,6,8,4,2,3,7,5]=>0011001=>1001100=>[1,3,1,3]
[1,6,8,5,2,3,7,4]=>0011001=>1001100=>[1,3,1,3]
[1,6,4,2,3,7,5,8]=>0110010=>0100110=>[2,3,1,2]
[1,5,8,6,2,4,7,3]=>0011001=>1001100=>[1,3,1,3]
[1,7,5,2,8,6,4,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,7,5,6,1,4,8,2]=>0101001=>1001010=>[1,3,2,2]
[8,6,1,4,2,7,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[1,6,7,4,3,5,8,2]=>0011001=>1001100=>[1,3,1,3]
[6,7,1,4,3,5,8,2]=>0101001=>1001010=>[1,3,2,2]
[4,7,1,6,3,5,8,2]=>0101001=>1001010=>[1,3,2,2]
[3,1,4,7,6,5,8,2]=>1001101=>1011001=>[1,2,1,3,1]
[6,1,7,4,3,5,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[7,1,6,4,3,5,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[1,7,6,4,3,5,8,2]=>0111001=>1001110=>[1,3,1,1,2]
[8,1,6,4,2,7,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,7,1,3,8,2,5,6]=>0100100=>0010010=>[3,3,2]
[7,4,1,3,8,2,5,6]=>1100100=>0010011=>[3,3,1,1]
[1,3,6,4,2,8,5,7]=>0011010=>0101100=>[2,2,1,3]
[4,7,3,1,2,8,5,6]=>0110010=>0100110=>[2,3,1,2]
[4,7,8,1,2,6,5,3]=>0010011=>1100100=>[1,1,3,3]
[1,8,6,4,2,7,5,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,8,1,3,7,2,5,6]=>0100100=>0010010=>[3,3,2]
[8,7,1,3,6,2,5,4]=>1100101=>1010011=>[1,2,3,1,1]
[1,8,4,3,7,2,5,6]=>0110100=>0010110=>[3,2,1,2]
[3,7,4,6,8,2,1,5]=>0100110=>0110010=>[2,1,3,2]
[2,4,3,7,8,6,1,5]=>0100110=>0110010=>[2,1,3,2]
[1,4,7,3,8,2,5,6]=>0010100=>0010100=>[3,2,3]
[5,7,6,8,3,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[6,1,4,3,8,2,5,7]=>1010100=>0010101=>[3,2,2,1]
[4,1,7,3,8,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[8,1,4,3,7,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[4,2,3,7,8,6,1,5]=>1000110=>0110001=>[2,1,4,1]
[2,7,5,6,3,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,7,2,6,8,4,1,3]=>0100110=>0110010=>[2,1,3,2]
[7,2,5,6,8,4,1,3]=>1000110=>0110001=>[2,1,4,1]
[5,2,3,8,7,6,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[8,2,3,7,5,6,1,4]=>1001010=>0101001=>[2,2,3,1]
[6,1,8,3,7,2,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[1,7,8,4,2,6,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[4,7,1,8,2,5,6,3]=>0101001=>1001010=>[1,3,2,2]
[1,4,8,3,6,2,5,7]=>0010100=>0010100=>[3,2,3]
[3,7,5,8,6,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[3,7,8,6,5,2,1,4]=>0011110=>0111100=>[2,1,1,1,3]
[6,8,7,5,3,2,1,4]=>0111110=>0111110=>[2,1,1,1,1,2]
[5,7,6,8,3,4,1,2]=>0101010=>0101010=>[2,2,2,2]
[3,7,6,8,4,5,1,2]=>0101010=>0101010=>[2,2,2,2]
[1,5,4,7,6,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[1,7,4,6,5,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[3,7,4,6,5,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[3,5,4,8,6,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[3,8,4,6,5,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[3,6,4,7,5,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,7,5,8,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,6,4,8,5,7,2,3]=>0101010=>0101010=>[2,2,2,2]
[1,8,4,6,5,7,2,3]=>0101010=>0101010=>[2,2,2,2]
[1,5,4,8,6,7,2,3]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,5,4,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,6,5,7,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,8,5,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,6,5,8,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,7,6,8,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,7,6,8,2,5,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,7,6,8,4,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[7,8,5,6,1,3,2,4]=>0101010=>0101010=>[2,2,2,2]
[5,8,6,7,1,3,2,4]=>0101010=>0101010=>[2,2,2,2]
[1,3,2,7,6,8,4,5]=>0101010=>0101010=>[2,2,2,2]
[1,7,6,8,2,4,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,3,2,8,6,7,4,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,3,2,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,6,2,4,3,5]=>0101010=>0101010=>[2,2,2,2]
[1,8,6,7,2,4,3,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,4,2,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[6,4,8,5,2,7,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[8,4,7,5,2,6,1,3]=>1011010=>0101101=>[2,2,1,2,1]
[5,4,6,8,2,1,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[4,8,7,5,6,1,3,2]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,5,1,8,4,3,6]=>0110110=>0110110=>[2,1,2,1,2]
[2,8,6,7,4,3,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,8,7,1,4,6,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[5,7,1,2,4,3,8,6]=>0100101=>1010010=>[1,2,3,2]
[4,3,7,6,8,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,6,8,1,7,2,4]=>1001010=>0101001=>[2,2,3,1]
[3,2,6,8,5,7,1,4]=>1001010=>0101001=>[2,2,3,1]
[7,4,8,6,5,2,1,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,1,8,2,5,4,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[2,5,3,7,4,1,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[3,6,4,7,5,1,8,2]=>0101101=>1011010=>[1,2,1,2,2]
[8,4,7,1,2,5,6,3]=>1010001=>1000101=>[1,4,2,1]
[4,2,8,7,3,5,6,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,4,1,5,8,2,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[8,3,5,6,7,4,1,2]=>1000110=>0110001=>[2,1,4,1]
[7,4,3,2,8,5,6,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,2,7,1,8,5,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,7,8,3,1,5,6,2]=>0011001=>1001100=>[1,3,1,3]
[3,7,1,4,8,5,6,2]=>0100101=>1010010=>[1,2,3,2]
[2,6,3,5,8,7,1,4]=>0100110=>0110010=>[2,1,3,2]
[7,6,2,1,5,8,4,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[4,5,2,7,6,1,8,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,6,8,7,5,2,1,4]=>0011110=>0111100=>[2,1,1,1,3]
[7,4,8,6,5,2,3,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,1,6,4,7,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,6,4,1,2,3,8,5]=>1110001=>1000111=>[1,4,1,1,1]
[2,6,4,8,5,3,7,1]=>0101101=>1011010=>[1,2,1,2,2]
[4,8,7,5,6,1,2,3]=>0110100=>0010110=>[3,2,1,2]
[6,1,4,8,7,3,5,2]=>1001101=>1011001=>[1,2,1,3,1]
[4,7,8,1,3,5,6,2]=>0010001=>1000100=>[1,4,3]
[8,7,3,4,1,5,6,2]=>1101001=>1001011=>[1,3,2,1,1]
[4,8,2,7,3,5,6,1]=>0101001=>1001010=>[1,3,2,2]
[3,1,8,7,2,5,6,4]=>1011001=>1001101=>[1,3,1,2,1]
[8,2,3,7,1,5,6,4]=>1001001=>1001001=>[1,3,3,1]
[6,4,8,7,1,3,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,8,2,4,3,5,6,1]=>0101001=>1001010=>[1,3,2,2]
[2,8,3,7,1,5,6,4]=>0101001=>1001010=>[1,3,2,2]
[5,3,8,6,2,1,4,7]=>1011100=>0011101=>[3,1,1,2,1]
[4,6,5,2,8,3,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[4,3,7,5,1,8,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,8,5,2,7,4,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,6,8,1,4,5,2,7]=>0010010=>0100100=>[2,3,3]
[6,8,1,2,4,5,3,7]=>0100010=>0100010=>[2,4,2]
[4,1,6,5,8,2,3,7]=>1010100=>0010101=>[3,2,2,1]
[4,3,8,6,2,5,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,6,1,4,5,2,7]=>1010010=>0100101=>[2,3,2,1]
[6,3,8,7,4,2,5,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,8,4,3,7,6,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[8,7,4,3,1,6,2,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[1,7,4,3,8,6,2,5]=>0110110=>0110110=>[2,1,2,1,2]
[7,1,5,3,4,8,2,6]=>1010010=>0100101=>[2,3,2,1]
[2,8,6,1,7,4,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[4,7,6,8,2,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[6,1,8,7,4,3,5,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,5,4,3,1,6,7,2]=>1111001=>1001111=>[1,3,1,1,1,1]
[1,5,8,6,3,4,7,2]=>0011001=>1001100=>[1,3,1,3]
[2,5,8,6,3,4,7,1]=>0011001=>1001100=>[1,3,1,3]
[4,6,5,2,8,1,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[1,8,5,2,3,6,7,4]=>0110001=>1000110=>[1,4,1,2]
[4,8,3,2,5,6,7,1]=>0110001=>1000110=>[1,4,1,2]
[2,1,8,3,5,6,7,4]=>1010001=>1000101=>[1,4,2,1]
[4,2,7,1,8,6,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[3,8,4,1,2,6,7,5]=>0110001=>1000110=>[1,4,1,2]
[5,8,3,6,7,4,1,2]=>0100110=>0110010=>[2,1,3,2]
[2,3,1,6,8,4,7,5]=>0100101=>1010010=>[1,2,3,2]
[2,4,3,7,1,8,5,6]=>0101010=>0101010=>[2,2,2,2]
[2,4,1,8,6,3,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[8,4,1,3,6,2,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[6,8,5,1,7,2,3,4]=>0110100=>0010110=>[3,2,1,2]
[7,3,6,5,8,2,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,6,3,5,8,2,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[4,5,8,7,3,6,1,2]=>0011010=>0101100=>[2,2,1,3]
[8,6,5,4,1,2,7,3]=>1111001=>1001111=>[1,3,1,1,1,1]
[6,1,5,3,8,7,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[2,8,6,3,7,1,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[7,6,1,5,8,2,3,4]=>1100100=>0010011=>[3,3,1,1]
[3,6,8,5,1,2,7,4]=>0011001=>1001100=>[1,3,1,3]
[6,5,2,4,8,1,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[5,1,4,8,2,6,7,3]=>1001001=>1001001=>[1,3,3,1]
[3,4,8,5,2,6,7,1]=>0011001=>1001100=>[1,3,1,3]
[4,2,1,8,5,6,7,3]=>1101001=>1001011=>[1,3,2,1,1]
[1,5,4,8,2,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[7,2,1,5,8,6,3,4]=>1100110=>0110011=>[2,1,3,1,1]
[2,8,4,5,1,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[5,4,8,3,7,6,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[3,1,5,8,6,2,7,4]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,4,8,5,1,7,2]=>1001101=>1011001=>[1,2,1,3,1]
[5,3,4,8,1,6,7,2]=>1001001=>1001001=>[1,3,3,1]
[6,5,4,8,7,1,3,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,5,4,8,1,2,7,3]=>1101001=>1001011=>[1,3,2,1,1]
[7,5,1,6,8,2,4,3]=>1100101=>1010011=>[1,2,3,1,1]
[6,5,4,1,8,2,7,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,5,4,7,1,2,8,3]=>1101001=>1001011=>[1,3,2,1,1]
[6,5,4,7,8,1,3,2]=>1100101=>1010011=>[1,2,3,1,1]
[6,5,3,7,1,4,2,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,1,4,8,3,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[8,1,6,4,7,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,1,4,8,3,6,2]=>1100101=>1010011=>[1,2,3,1,1]
[7,4,1,5,3,8,6,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,1,5,4,3,7,6,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,1,5,4,3,7,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,5,3,8,1,4,2,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,1,7,2,5,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,1,2,5,4,8,3]=>1100101=>1010011=>[1,2,3,1,1]
[6,5,3,8,1,4,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[6,5,3,1,2,7,8,4]=>1110001=>1000111=>[1,4,1,1,1]
[8,1,6,4,2,5,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[8,1,5,4,3,2,7,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,4,1,5,3,2,8,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,4,3,1,5,2,8,7]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,4,3,1,5,7,2,8]=>1110010=>0100111=>[2,3,1,1,1]
[7,4,1,5,3,6,2,8]=>1101010=>0101011=>[2,2,2,1,1]
[6,4,3,1,5,7,8,2]=>1110001=>1000111=>[1,4,1,1,1]
[8,6,7,1,4,2,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,3,7,5,1,2,4]=>1101100=>0011011=>[3,1,2,1,1]
[7,6,1,8,3,5,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,6,2,8,3,5,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,1,5,2,6,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,1,5,2,3,6,4]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,2,3,1,7,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,6,2,3,7,1,5,4]=>1100101=>1010011=>[1,2,3,1,1]
[8,6,2,7,3,1,5,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,7,2,5,1,6,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,7,2,1,4,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[5,8,7,3,1,4,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[8,5,7,2,1,4,6,3]=>1011001=>1001101=>[1,3,1,2,1]
[8,6,1,3,7,2,5,4]=>1100101=>1010011=>[1,2,3,1,1]
[8,4,7,5,1,6,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[8,4,7,5,1,2,3,6]=>1011000=>0001101=>[4,1,2,1]
[8,3,2,6,5,1,4,7]=>1101100=>0011011=>[3,1,2,1,1]
[4,8,7,3,1,5,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[8,4,7,2,1,5,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[8,7,3,1,2,4,6,5]=>1110001=>1000111=>[1,4,1,1,1]
[8,4,7,2,1,5,6,3]=>1011001=>1001101=>[1,3,1,2,1]
[1,2,7,3,5,4,8,6]=>0010101=>1010100=>[1,2,2,3]
[1,5,7,2,3,6,4,8]=>0010010=>0100100=>[2,3,3]
[1,3,8,2,4,5,7,6]=>0010001=>1000100=>[1,4,3]
[1,2,3,8,4,6,7,5]=>0001001=>1001000=>[1,3,4]
[1,7,8,2,3,6,4,5]=>0010010=>0100100=>[2,3,3]
[1,6,7,8,2,3,5,4]=>0001001=>1001000=>[1,3,4]
[1,7,8,2,5,3,6,4]=>0010101=>1010100=>[1,2,2,3]
[1,8,2,3,6,4,5,7]=>0100100=>0010010=>[3,3,2]
[1,2,7,8,3,6,4,5]=>0001010=>0101000=>[2,2,4]
[1,5,2,7,8,3,6,4]=>0100101=>1010010=>[1,2,3,2]
[1,3,2,8,4,6,7,5]=>0101001=>1001010=>[1,3,2,2]
[1,8,2,3,4,6,7,5]=>0100001=>1000010=>[1,5,2]
[1,7,8,2,4,3,6,5]=>0010101=>1010100=>[1,2,2,3]
[7,6,3,1,5,2,4,8]=>1110100=>0010111=>[3,2,1,1,1]
[6,7,3,1,5,2,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,3,1,5,2,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,4,5,1,2,7,3]=>0101001=>1001010=>[1,3,2,2]
[6,7,4,5,1,2,8,3]=>0101001=>1001010=>[1,3,2,2]
[7,2,1,6,5,3,4,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,3,6,1,5,2,4,8]=>1010100=>0010101=>[3,2,2,1]
[7,4,6,5,1,2,3,8]=>1011000=>0001101=>[4,1,2,1]
[6,7,5,4,1,2,8,3]=>0111001=>1001110=>[1,3,1,1,2]
[5,8,6,4,1,7,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[5,7,6,4,1,8,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[5,6,7,4,1,8,2,3]=>0011010=>0101100=>[2,2,1,3]
[6,5,7,4,1,2,8,3]=>1011001=>1001101=>[1,3,1,2,1]
[6,2,1,7,5,3,8,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,3,8,1,5,2,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,8,5,1,2,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[6,5,8,4,1,2,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[5,6,8,4,1,7,2,3]=>0011010=>0101100=>[2,2,1,3]
[4,6,8,5,7,1,2,3]=>0010100=>0010100=>[3,2,3]
[4,5,8,6,7,1,2,3]=>0010100=>0010100=>[3,2,3]
[5,2,1,7,6,8,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[4,5,7,6,8,1,2,3]=>0010100=>0010100=>[3,2,3]
[4,6,7,5,8,1,2,3]=>0010100=>0010100=>[3,2,3]
[4,7,5,6,8,1,2,3]=>0100100=>0010010=>[3,3,2]
[4,6,5,7,8,1,2,3]=>0100100=>0010010=>[3,3,2]
[5,7,4,6,1,8,2,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,3,1,6,7,2,4]=>0110010=>0100110=>[2,3,1,2]
[5,7,3,1,6,8,2,4]=>0110010=>0100110=>[2,3,1,2]
[5,6,3,1,7,8,2,4]=>0110010=>0100110=>[2,3,1,2]
[5,8,3,1,7,6,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[5,7,4,8,1,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[5,2,1,6,8,7,3,4]=>1100110=>0110011=>[2,1,3,1,1]
[5,4,6,8,1,7,2,3]=>1001010=>0101001=>[2,2,3,1]
[4,5,6,8,7,1,2,3]=>0001100=>0011000=>[3,1,4]
[4,7,5,8,6,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[4,8,5,7,6,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[4,8,6,7,5,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[4,7,6,8,5,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[4,6,7,8,5,1,2,3]=>0001100=>0011000=>[3,1,4]
[4,5,7,8,6,1,2,3]=>0001100=>0011000=>[3,1,4]
[5,4,7,8,1,6,2,3]=>1001010=>0101001=>[2,2,3,1]
[5,3,7,1,8,6,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,1,7,8,6,3,4]=>1100110=>0110011=>[2,1,3,1,1]
[5,3,8,1,7,6,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[5,4,8,7,1,6,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[4,6,8,7,5,1,2,3]=>0011100=>0011100=>[3,1,1,3]
[4,7,8,6,5,1,2,3]=>0011100=>0011100=>[3,1,1,3]
[4,8,7,6,5,1,2,3]=>0111100=>0011110=>[3,1,1,1,2]
[2,5,4,7,3,6,1,8]=>0101010=>0101010=>[2,2,2,2]
[4,2,7,3,6,5,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,6,3,1,5,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[2,5,3,1,6,4,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[2,5,3,7,6,4,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[2,6,5,3,7,4,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[4,2,7,6,3,5,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[2,7,5,3,6,4,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[2,6,3,7,5,4,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[1,7,5,2,3,8,4,6]=>0110010=>0100110=>[2,3,1,2]
[2,1,3,7,5,4,8,6]=>1001101=>1011001=>[1,2,1,3,1]
[2,3,1,8,6,5,4,7]=>0101110=>0111010=>[2,1,1,2,2]
[2,5,3,1,8,6,4,7]=>0110110=>0110110=>[2,1,2,1,2]
[4,2,8,3,1,6,5,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,2,6,4,1,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[3,6,8,2,1,4,5,7]=>0011000=>0001100=>[4,1,3]
[1,2,6,3,8,7,4,5]=>0010110=>0110100=>[2,1,2,3]
[1,2,7,6,3,4,8,5]=>0011001=>1001100=>[1,3,1,3]
[2,1,3,8,7,5,4,6]=>1001110=>0111001=>[2,1,1,3,1]
[1,2,3,8,6,4,7,5]=>0001101=>1011000=>[1,2,1,4]
[1,2,3,7,4,8,6,5]=>0001011=>1101000=>[1,1,2,4]
[1,2,7,6,3,8,4,5]=>0011010=>0101100=>[2,2,1,3]
[1,2,3,6,4,8,7,5]=>0001011=>1101000=>[1,1,2,4]
[1,2,3,7,6,4,8,5]=>0001101=>1011000=>[1,2,1,4]
[2,1,3,8,5,4,7,6]=>1001101=>1011001=>[1,2,1,3,1]
[7,1,8,4,2,3,5,6]=>1011000=>0001101=>[4,1,2,1]
[4,2,6,3,1,8,5,7]=>1011010=>0101101=>[2,2,1,2,1]
[5,4,2,8,3,1,6,7]=>1101100=>0011011=>[3,1,2,1,1]
[2,5,4,8,3,1,6,7]=>0101100=>0011010=>[3,1,2,2]
[1,8,7,4,2,3,5,6]=>0111000=>0001110=>[4,1,1,2]
[1,5,2,8,7,3,4,6]=>0101100=>0011010=>[3,1,2,2]
[1,2,7,3,6,4,8,5]=>0010101=>1010100=>[1,2,2,3]
[1,2,8,6,3,7,4,5]=>0011010=>0101100=>[2,2,1,3]
[1,2,6,3,8,4,7,5]=>0010101=>1010100=>[1,2,2,3]
[4,2,1,8,3,7,5,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,3,2,1,7,4,5,6]=>1110100=>0010111=>[3,2,1,1,1]
[1,2,3,8,7,4,6,5]=>0001101=>1011000=>[1,2,1,4]
[1,2,3,8,7,6,4,5]=>0001110=>0111000=>[2,1,1,4]
[2,6,5,7,1,4,3,8]=>0101010=>0101010=>[2,2,2,2]
[2,6,5,7,1,3,8,4]=>0101001=>1001010=>[1,3,2,2]
[3,8,5,7,1,2,6,4]=>0101001=>1001010=>[1,3,2,2]
[3,8,5,7,2,6,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,4,8,6,2,5,7,1]=>0011001=>1001100=>[1,3,1,3]
[3,4,8,6,1,2,5,7]=>0011000=>0001100=>[4,1,3]
[2,5,7,1,4,8,6,3]=>0010011=>1100100=>[1,1,3,3]
[2,8,1,7,5,6,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,3,8,1,6,5,7,4]=>0010101=>1010100=>[1,2,2,3]
[3,5,7,6,1,2,4,8]=>0011000=>0001100=>[4,1,3]
[4,8,6,7,2,3,5,1]=>0101001=>1001010=>[1,3,2,2]
[4,8,6,7,1,3,5,2]=>0101001=>1001010=>[1,3,2,2]
[3,4,8,6,1,5,7,2]=>0011001=>1001100=>[1,3,1,3]
[3,8,5,7,1,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,8,5,7,2,1,6,4]=>0101101=>1011010=>[1,2,1,2,2]
[3,4,8,6,2,1,5,7]=>0011100=>0011100=>[3,1,1,3]
[3,5,7,6,2,1,4,8]=>0011100=>0011100=>[3,1,1,3]
[5,8,6,7,3,4,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[5,8,6,7,2,1,3,4]=>0101100=>0011010=>[3,1,2,2]
[4,8,6,7,2,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,3,1,7,5,2,8,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,3,2,8,5,1,7,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,3,8,5,1,6,7,2]=>1011001=>1001101=>[1,3,1,2,1]
[5,8,6,7,2,3,4,1]=>0101001=>1001010=>[1,3,2,2]
[5,8,6,7,2,4,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[5,8,6,7,1,2,4,3]=>0101001=>1001010=>[1,3,2,2]
[3,2,5,7,6,1,4,8]=>1001100=>0011001=>[3,1,3,1]
[4,8,6,7,1,3,2,5]=>0101010=>0101010=>[2,2,2,2]
[4,8,6,7,1,2,5,3]=>0101001=>1001010=>[1,3,2,2]
[4,8,6,7,2,5,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,3,8,5,2,6,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[4,2,6,7,5,1,3,8]=>1001100=>0011001=>[3,1,3,1]
[3,8,4,7,1,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[3,5,1,7,4,6,2,8]=>0101010=>0101010=>[2,2,2,2]
[3,8,4,7,2,5,1,6]=>0101010=>0101010=>[2,2,2,2]
[4,1,3,8,5,2,6,7]=>1001100=>0011001=>[3,1,3,1]
[4,2,6,7,5,3,8,1]=>1001101=>1011001=>[1,2,1,3,1]
[4,8,6,7,3,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[4,8,6,7,3,1,2,5]=>0101100=>0011010=>[3,1,2,2]
[3,1,5,7,6,2,4,8]=>1001100=>0011001=>[3,1,3,1]
[3,4,1,7,5,6,2,8]=>0101010=>0101010=>[2,2,2,2]
[4,1,7,5,2,8,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,1,6,7,5,2,3,8]=>1001100=>0011001=>[3,1,3,1]
[5,8,6,7,3,2,4,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,6,7,4,2,3,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,6,7,4,1,2,3]=>0101100=>0011010=>[3,1,2,2]
[5,8,6,7,4,1,3,2]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,6,7,3,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,8,6,7,3,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,1,6,7,5,3,8,2]=>1001101=>1011001=>[1,2,1,3,1]
[4,1,7,5,3,2,8,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,2,8,5,3,1,7,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,2,1,6,7,5,3,8]=>1100110=>0110011=>[2,1,3,1,1]
[4,8,6,7,3,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[5,8,6,7,4,2,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[5,8,6,7,4,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[6,1,5,2,8,4,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,6,1,8,5,7,2,3]=>0101010=>0101010=>[2,2,2,2]
[4,7,1,2,8,5,6,3]=>0100101=>1010010=>[1,2,3,2]
[1,4,7,2,8,5,6,3]=>0010101=>1010100=>[1,2,2,3]
[1,7,3,5,8,6,2,4]=>0100110=>0110010=>[2,1,3,2]
[7,3,5,8,6,1,2,4]=>1001100=>0011001=>[3,1,3,1]
[6,8,1,5,7,2,3,4]=>0100100=>0010010=>[3,3,2]
[7,1,2,5,8,6,3,4]=>1000110=>0110001=>[2,1,4,1]
[1,7,2,5,8,6,3,4]=>0100110=>0110010=>[2,1,3,2]
[1,7,6,8,2,3,5,4]=>0101001=>1001010=>[1,3,2,2]
[7,6,8,1,2,3,5,4]=>1010001=>1000101=>[1,4,2,1]
[2,7,1,5,8,6,3,4]=>0100110=>0110010=>[2,1,3,2]
[2,4,7,1,8,5,6,3]=>0010101=>1010100=>[1,2,2,3]
[4,7,5,8,3,1,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,2,1,8,5,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[7,3,5,8,6,2,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[7,6,8,2,1,3,5,4]=>1011001=>1001101=>[1,3,1,2,1]
[1,2,7,6,8,3,5,4]=>0010101=>1010100=>[1,2,2,3]
[3,7,6,8,2,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[6,7,4,1,8,5,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,7,4,3,1,8,5,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,7,4,1,6,8,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[3,1,7,6,8,2,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[1,3,7,6,8,2,5,4]=>0010101=>1010100=>[1,2,2,3]
[1,7,4,2,6,8,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[7,1,4,2,8,5,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,8,2,5,4,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,8,5,4,2,3]=>1001110=>0111001=>[2,1,1,3,1]
[7,1,2,6,8,5,4,3]=>1000111=>1110001=>[1,1,1,4,1]
[1,7,2,6,8,5,4,3]=>0100111=>1110010=>[1,1,1,3,2]
[1,7,6,8,3,2,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[7,6,8,3,1,2,5,4]=>1011001=>1001101=>[1,3,1,2,1]
[7,1,5,8,6,3,2,4]=>1001110=>0111001=>[2,1,1,3,1]
[3,6,7,1,8,5,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[7,2,6,8,5,4,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[7,6,8,2,3,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[2,7,6,8,3,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[2,7,1,6,8,5,4,3]=>0100111=>1110010=>[1,1,1,3,2]
[6,7,3,1,8,5,4,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,7,1,8,5,4,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[7,2,1,6,8,5,4,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,8,4,2,1,6,5,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,2,3,4,8,7,1,5]=>1000110=>0110001=>[2,1,4,1]
[6,2,3,4,7,8,1,5]=>1000010=>0100001=>[2,5,1]
[7,8,3,6,4,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[7,8,3,5,6,2,1,4]=>0100110=>0110010=>[2,1,3,2]
[5,2,6,3,8,1,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,2,5,8,7,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[6,3,2,8,4,7,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[6,4,3,8,7,5,1,2]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,4,3,7,8,5,1,2]=>1100110=>0110011=>[2,1,3,1,1]
[6,3,2,7,4,8,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,2,5,7,8,1,4]=>1100010=>0100011=>[2,4,1,1]
[5,8,2,3,6,1,7,4]=>0100101=>1010010=>[1,2,3,2]
[4,5,6,8,3,2,1,7]=>0001110=>0111000=>[2,1,1,4]
[4,6,8,5,3,2,1,7]=>0011110=>0111100=>[2,1,1,1,3]
[5,6,1,4,2,3,7,8]=>0101000=>0001010=>[4,2,2]
[5,6,8,4,3,7,1,2]=>0011010=>0101100=>[2,2,1,3]
[5,6,1,4,2,3,8,7]=>0101001=>1001010=>[1,3,2,2]
[5,2,8,3,4,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,8,6,3,2,1,7]=>0011110=>0111100=>[2,1,1,1,3]
[4,7,5,6,3,2,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[5,1,4,3,6,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,4,3,8,2,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,6,2,4,1,8,7,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,7,2,4,1,8,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[6,1,4,2,8,7,5,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,8,2,4,1,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,4,1,3,7,2,6,8]=>1100100=>0010011=>[3,3,1,1]
[5,8,1,4,2,3,7,6]=>0101001=>1001010=>[1,3,2,2]
[5,1,6,3,4,2,7,8]=>1010100=>0010101=>[3,2,2,1]
[4,8,6,5,3,2,1,7]=>0111110=>0111110=>[2,1,1,1,1,2]
[5,4,7,8,3,2,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[4,7,8,5,3,2,1,6]=>0011110=>0111100=>[2,1,1,1,3]
[5,7,1,3,4,2,6,8]=>0100100=>0010010=>[3,3,2]
[5,1,8,4,2,3,6,7]=>1011000=>0001101=>[4,1,2,1]
[5,1,7,4,2,3,6,8]=>1011000=>0001101=>[4,1,2,1]
[5,8,1,3,4,2,6,7]=>0100100=>0010010=>[3,3,2]
[4,8,7,5,3,2,1,6]=>0111110=>0111110=>[2,1,1,1,1,2]
[4,7,8,6,3,2,1,5]=>0011110=>0111100=>[2,1,1,1,3]
[4,8,2,3,6,7,5,1]=>0100011=>1100010=>[1,1,4,2]
[4,8,3,1,6,7,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[4,3,8,1,6,2,5,7]=>1010100=>0010101=>[3,2,2,1]
[1,4,8,7,3,5,2,6]=>0011010=>0101100=>[2,2,1,3]
[4,3,8,7,2,5,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[5,8,1,4,7,2,6,3]=>0100101=>1010010=>[1,2,3,2]
[6,8,1,2,4,3,5,7]=>0100100=>0010010=>[3,3,2]
[5,8,7,1,3,4,2,6]=>0110010=>0100110=>[2,3,1,2]
[4,8,7,6,3,1,2,5]=>0111100=>0011110=>[3,1,1,1,2]
[5,8,4,7,3,1,2,6]=>0101100=>0011010=>[3,1,2,2]
[4,3,8,2,7,5,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[1,4,8,3,7,5,6,2]=>0010101=>1010100=>[1,2,2,3]
[1,4,3,8,2,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[4,1,3,8,2,6,5,7]=>1001010=>0101001=>[2,2,3,1]
[4,1,8,7,3,5,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[3,4,8,1,6,2,5,7]=>0010100=>0010100=>[3,2,3]
[3,4,8,7,2,5,1,6]=>0011010=>0101100=>[2,2,1,3]
[3,4,8,2,7,5,6,1]=>0010101=>1010100=>[1,2,2,3]
[1,2,4,3,8,6,5,7]=>0010110=>0110100=>[2,1,2,3]
[3,4,2,1,8,6,5,7]=>0110110=>0110110=>[2,1,2,1,2]
[3,4,1,8,2,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[3,6,7,8,4,1,2,5]=>0001100=>0011000=>[3,1,4]
[4,1,2,8,3,6,5,7]=>1001010=>0101001=>[2,2,3,1]
[1,4,3,2,8,6,5,7]=>0110110=>0110110=>[2,1,2,1,2]
[4,2,3,1,8,6,5,7]=>1010110=>0110101=>[2,1,2,2,1]
[3,7,8,2,6,4,5,1]=>0010101=>1010100=>[1,2,2,3]
[4,2,3,8,1,6,5,7]=>1001010=>0101001=>[2,2,3,1]
[4,3,1,8,2,6,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[1,4,7,8,5,3,2,6]=>0001110=>0111000=>[2,1,1,4]
[4,2,8,6,3,1,5,7]=>1011100=>0011101=>[3,1,1,2,1]
[2,4,8,6,3,1,5,7]=>0011100=>0011100=>[3,1,1,3]
[7,3,6,8,4,2,1,5]=>1001110=>0111001=>[2,1,1,3,1]
[1,7,3,8,4,6,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,4,8,2,6,5,7]=>0001010=>0101000=>[2,2,4]
[3,2,4,8,1,6,5,7]=>1001010=>0101001=>[2,2,3,1]
[7,3,8,2,6,4,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,8,7,4,3,5,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,4,1,8,5,2,6,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,3,2,8,4,6,5,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[1,3,4,2,8,6,5,7]=>0010110=>0110100=>[2,1,2,3]
[1,3,2,4,8,6,5,7]=>0100110=>0110010=>[2,1,3,2]
[3,2,1,4,8,6,5,7]=>1100110=>0110011=>[2,1,3,1,1]
[3,1,2,4,8,6,5,7]=>1000110=>0110001=>[2,1,4,1]
[3,1,4,2,8,6,5,7]=>1010110=>0110101=>[2,1,2,2,1]
[3,1,4,8,2,6,5,7]=>1001010=>0101001=>[2,2,3,1]
[7,3,4,8,5,1,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[3,7,4,8,5,1,2,6]=>0101100=>0011010=>[3,1,2,2]
[6,7,2,8,3,5,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,3,1,4,8,6,5,7]=>0100110=>0110010=>[2,1,3,2]
[2,1,3,4,8,6,5,7]=>1000110=>0110001=>[2,1,4,1]
[3,5,7,8,6,1,2,4]=>0001100=>0011000=>[3,1,4]
[3,1,5,6,8,2,7,4]=>1000101=>1010001=>[1,2,4,1]
[5,1,6,3,8,4,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,5,1,6,8,3,7,4]=>0100101=>1010010=>[1,2,3,2]
[5,1,2,6,8,3,7,4]=>1000101=>1010001=>[1,2,4,1]
[1,5,2,7,8,6,3,4]=>0100110=>0110010=>[2,1,3,2]
[6,1,7,5,2,8,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[2,6,7,5,1,8,3,4]=>0011010=>0101100=>[2,2,1,3]
[5,7,2,8,6,1,3,4]=>0101100=>0011010=>[3,1,2,2]
[3,5,7,8,6,2,1,4]=>0001110=>0111000=>[2,1,1,4]
[3,2,5,7,8,6,1,4]=>1000110=>0110001=>[2,1,4,1]
[6,2,7,5,1,8,3,4]=>1011010=>0101101=>[2,2,1,2,1]
[1,2,6,7,5,8,3,4]=>0001010=>0101000=>[2,2,4]
[6,2,7,5,4,1,8,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,7,5,2,4,1,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,7,2,5,3,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[5,1,7,8,6,3,2,4]=>1001110=>0111001=>[2,1,1,3,1]
[1,6,7,5,3,8,2,4]=>0011010=>0101100=>[2,2,1,3]
[1,6,7,5,4,2,8,3]=>0011101=>1011100=>[1,2,1,1,3]
[5,7,8,6,4,1,2,3]=>0011100=>0011100=>[3,1,1,3]
[6,7,4,1,5,2,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[1,6,7,4,5,2,8,3]=>0010101=>1010100=>[1,2,2,3]
[6,3,1,7,5,8,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[2,5,3,7,8,6,1,4]=>0100110=>0110010=>[2,1,3,2]
[6,3,2,7,5,8,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,7,4,2,5,1,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,2,7,4,5,1,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,3,7,5,8,1,4]=>1001010=>0101001=>[2,2,3,1]
[7,5,1,6,3,8,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,1,6,3,8,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,7,6,1,3,8,4,5]=>0110010=>0100110=>[2,3,1,2]
[2,7,6,1,3,8,5,4]=>0110011=>1100110=>[1,1,3,1,2]
[2,6,7,1,5,8,3,4]=>0010010=>0100100=>[2,3,3]
[2,6,7,4,1,8,3,5]=>0011010=>0101100=>[2,2,1,3]
[2,1,6,7,3,8,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[2,6,7,4,1,8,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[2,6,7,1,5,8,4,3]=>0010011=>1100100=>[1,1,3,3]
[3,6,5,1,8,4,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[3,7,5,4,8,1,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[3,7,5,4,8,1,2,6]=>0110100=>0010110=>[3,2,1,2]
[4,6,1,5,8,7,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[4,6,1,5,8,7,2,3]=>0100110=>0110010=>[2,1,3,2]
[4,6,1,5,8,2,7,3]=>0100101=>1010010=>[1,2,3,2]
[7,5,1,6,2,8,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[4,6,1,5,8,2,3,7]=>0100100=>0010010=>[3,3,2]
[4,7,1,5,8,3,6,2]=>0100101=>1010010=>[1,2,3,2]
[8,3,4,6,2,1,5,7]=>1001100=>0011001=>[3,1,3,1]
[3,5,6,2,1,8,4,7]=>0011010=>0101100=>[2,2,1,3]
[7,5,3,2,8,4,1,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,5,3,2,8,4,6,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,2,5,6,8,3,1,7]=>1000110=>0110001=>[2,1,4,1]
[5,3,6,8,1,4,2,7]=>1001010=>0101001=>[2,2,3,1]
[4,5,6,8,1,3,2,7]=>0001010=>0101000=>[2,2,4]
[1,4,5,6,8,3,2,7]=>0000110=>0110000=>[2,1,5]
[4,5,3,7,2,8,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,4,7,3,2,8,5,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,1,4,7,3,2,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,7,3,8,4,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,3,7,1,4,8,6,2]=>1010011=>1100101=>[1,1,3,2,1]
[6,4,3,1,7,8,5,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[5,6,1,3,7,8,4,2]=>0100011=>1100010=>[1,1,4,2]
[5,6,1,7,8,3,4,2]=>0100101=>1010010=>[1,2,3,2]
[1,6,3,7,4,8,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,2,4,1,8,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,2,1,4,3,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[6,4,7,3,1,2,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[5,6,3,1,2,7,8,4]=>0110001=>1000110=>[1,4,1,2]
[5,6,1,3,2,7,8,4]=>0101001=>1001010=>[1,3,2,2]
[5,6,3,2,1,7,8,4]=>0111001=>1001110=>[1,3,1,1,2]
[5,6,3,2,7,8,4,1]=>0110011=>1100110=>[1,1,3,1,2]
[2,5,6,3,7,8,4,1]=>0010011=>1100100=>[1,1,3,3]
[2,5,6,3,1,7,8,4]=>0011001=>1001100=>[1,3,1,3]
[2,6,4,7,3,1,8,5]=>0101101=>1011010=>[1,2,1,2,2]
[6,3,7,2,8,4,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[6,3,2,7,1,8,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,3,2,1,8,4,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[7,3,8,4,2,1,5,6]=>1011100=>0011101=>[3,1,1,2,1]
[4,7,2,1,3,8,6,5]=>0110011=>1100110=>[1,1,3,1,2]
[1,3,7,8,6,4,2,5]=>0001110=>0111000=>[2,1,1,4]
[5,7,3,8,2,1,6,4]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,2,7,8,5,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,5,1,7,3,8,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,2,1,3,8,5,4]=>0110011=>1100110=>[1,1,3,1,2]
[5,1,6,7,8,2,4,3]=>1000101=>1010001=>[1,2,4,1]
[6,3,7,1,8,5,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,1,7,3,8,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,2,7,1,8,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,3,1,7,8,5,4,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[5,3,2,1,8,4,7,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,5,2,1,3,8,7,6]=>0110011=>1100110=>[1,1,3,1,2]
[3,2,6,4,5,8,1,7]=>1010010=>0100101=>[2,3,2,1]
[2,4,6,5,8,1,3,7]=>0010100=>0010100=>[3,2,3]
[1,3,4,6,5,8,2,7]=>0001010=>0101000=>[2,2,4]
[1,6,3,4,5,8,2,7]=>0100010=>0100010=>[2,4,2]
[3,4,1,8,5,2,7,6]=>0101101=>1011010=>[1,2,1,2,2]
[2,8,4,1,7,6,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[1,5,3,2,8,7,4,6]=>0110110=>0110110=>[2,1,2,1,2]
[8,2,1,7,5,3,4,6]=>1101100=>0011011=>[3,1,2,1,1]
[1,7,6,4,5,8,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[5,8,7,4,6,2,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[3,4,2,5,8,6,7,1]=>0100101=>1010010=>[1,2,3,2]
[4,1,3,5,6,8,7,2]=>1000011=>1100001=>[1,1,5,1]
[2,4,8,6,7,1,3,5]=>0010100=>0010100=>[3,2,3]
[3,7,4,8,2,1,6,5]=>0101101=>1011010=>[1,2,1,2,2]
[2,3,5,8,6,7,1,4]=>0001010=>0101000=>[2,2,4]
[3,2,5,6,8,7,1,4]=>1000110=>0110001=>[2,1,4,1]
[7,2,4,8,5,3,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[4,8,3,1,2,7,6,5]=>0110011=>1100110=>[1,1,3,1,2]
[8,4,2,3,7,1,5,6]=>1100100=>0010011=>[3,3,1,1]
[3,5,2,7,6,1,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,7,3,4,6,2,1]=>0110011=>1100110=>[1,1,3,1,2]
[5,8,2,7,4,1,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[5,1,4,2,8,7,6,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,2,6,8,7,1,3,4]=>1001100=>0011001=>[3,1,3,1]
[6,3,2,1,8,5,7,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,7,5,4,1,8,6,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,2,5,6,8,7,1,3]=>1000110=>0110001=>[2,1,4,1]
[1,8,4,2,5,6,7,3]=>0110001=>1000110=>[1,4,1,2]
[3,8,4,1,5,6,7,2]=>0110001=>1000110=>[1,4,1,2]
[4,2,8,5,6,7,1,3]=>1010010=>0100101=>[2,3,2,1]
[5,2,4,7,1,8,6,3]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,3,6,5,2,4,7]=>1001100=>0011001=>[3,1,3,1]
[8,3,2,4,6,5,1,7]=>1100110=>0110011=>[2,1,3,1,1]
[8,3,6,4,1,5,2,7]=>1011010=>0101101=>[2,2,1,2,1]
[1,3,4,8,5,7,2,6]=>0001010=>0101000=>[2,2,4]
[5,8,4,7,6,2,3,1]=>0101101=>1011010=>[1,2,1,2,2]
[1,3,4,7,5,8,2,6]=>0001010=>0101000=>[2,2,4]
[1,3,5,2,4,8,7,6]=>0010011=>1100100=>[1,1,3,3]
[2,6,5,1,3,8,7,4]=>0110011=>1100110=>[1,1,3,1,2]
[2,8,5,1,4,7,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[4,3,1,5,8,6,7,2]=>1100101=>1010011=>[1,2,3,1,1]
[5,4,2,1,6,8,7,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[6,8,4,3,2,7,1,5]=>0111010=>0101110=>[2,2,1,1,2]
[5,1,3,2,8,6,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,1,2,8,6,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[5,2,3,1,6,8,7,4]=>1010011=>1100101=>[1,1,3,2,1]
[5,3,2,1,8,6,7,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,2,1,3,6,8,7,4]=>1100011=>1100011=>[1,1,4,1,1]
[2,7,4,5,8,3,1,6]=>0100110=>0110010=>[2,1,3,2]
[1,8,4,3,7,2,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,4,8,7,2,1,6,5]=>0011101=>1011100=>[1,2,1,1,3]
[5,4,7,8,3,6,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,3,8,7,4,1,2,5]=>1011100=>0011101=>[3,1,1,2,1]
[8,4,7,2,3,1,5,6]=>1010100=>0010101=>[3,2,2,1]
[8,6,4,1,3,2,7,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[3,5,7,2,6,1,8,4]=>0010101=>1010100=>[1,2,2,3]
[6,1,3,8,5,7,2,4]=>1001010=>0101001=>[2,2,3,1]
[2,8,1,5,4,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,7,2,4,6,5,8,3]=>0100101=>1010010=>[1,2,3,2]
[5,8,2,6,1,3,7,4]=>0101001=>1001010=>[1,3,2,2]
[6,3,5,8,7,2,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[2,5,7,8,4,1,6,3]=>0001101=>1011000=>[1,2,1,4]
[4,1,5,2,6,8,7,3]=>1010011=>1100101=>[1,1,3,2,1]
[4,1,8,5,2,6,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[2,7,1,8,5,4,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,6,2,1,3,7,4]=>0111001=>1001110=>[1,3,1,1,2]
[3,4,5,1,8,6,7,2]=>0010101=>1010100=>[1,2,2,3]
[1,3,2,7,5,8,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,4,2,5,8,3,7,6]=>0100101=>1010010=>[1,2,3,2]
[4,1,2,6,8,5,3,7]=>1000110=>0110001=>[2,1,4,1]
[1,5,2,4,8,7,6,3]=>0100111=>1110010=>[1,1,1,3,2]
[1,2,7,4,8,6,5,3]=>0010111=>1110100=>[1,1,1,2,3]
[1,3,2,8,5,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,2,6,4,8,7,3,5]=>0010110=>0110100=>[2,1,2,3]
[1,3,8,2,6,7,4,5]=>0010010=>0100100=>[2,3,3]
[1,6,7,8,2,5,3,4]=>0001010=>0101000=>[2,2,4]
[1,5,7,8,2,3,6,4]=>0001001=>1001000=>[1,3,4]
[1,2,8,4,7,3,6,5]=>0010101=>1010100=>[1,2,2,3]
[1,5,2,4,8,3,7,6]=>0100101=>1010010=>[1,2,3,2]
[1,8,3,5,2,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,4,8,6,7,2,3,5]=>0010100=>0010100=>[3,2,3]
[1,5,7,8,6,2,3,4]=>0001100=>0011000=>[3,1,4]
[1,3,7,6,2,8,4,5]=>0011010=>0101100=>[2,2,1,3]
[1,2,5,8,7,6,3,4]=>0001110=>0111000=>[2,1,1,4]
[1,2,6,8,7,5,3,4]=>0001110=>0111000=>[2,1,1,4]
[1,2,7,8,6,5,3,4]=>0001110=>0111000=>[2,1,1,4]
[5,2,6,7,3,4,8,1]=>1001001=>1001001=>[1,3,3,1]
[5,6,2,1,7,8,3,4]=>0110010=>0100110=>[2,3,1,2]
[5,6,2,1,4,8,7,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,6,1,4,5,8,7,3]=>0100011=>1100010=>[1,1,4,2]
[5,4,2,7,6,3,8,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,3,7,6,4,5,8,1]=>0011001=>1001100=>[1,3,1,3]
[2,6,1,7,5,8,3,4]=>0101010=>0101010=>[2,2,2,2]
[5,1,2,7,8,4,3,6]=>1000110=>0110001=>[2,1,4,1]
[2,6,1,7,4,8,3,5]=>0101010=>0101010=>[2,2,2,2]
[3,6,4,1,7,8,2,5]=>0110010=>0100110=>[2,3,1,2]
[5,4,6,1,7,8,2,3]=>1010010=>0100101=>[2,3,2,1]
[5,4,6,1,3,8,7,2]=>1010011=>1100101=>[1,1,3,2,1]
[3,6,4,1,5,8,7,2]=>0110011=>1100110=>[1,1,3,1,2]
[2,6,1,5,4,8,7,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,1,4,7,8,5,3]=>0100011=>1100010=>[1,1,4,2]
[5,1,2,4,8,7,6,3]=>1000111=>1110001=>[1,1,1,4,1]
[2,1,5,3,8,6,4,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,2,4,8,6,3,7]=>1000110=>0110001=>[2,1,4,1]
[5,6,3,1,4,8,2,7]=>0110010=>0100110=>[2,3,1,2]
[2,5,4,3,1,8,6,7]=>0111010=>0101110=>[2,2,1,1,2]
[5,4,6,3,1,8,7,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,1,3,7,8,6,4,5]=>1000110=>0110001=>[2,1,4,1]
[5,1,4,2,8,6,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,2,3,8,6,7,4,5]=>0001010=>0101000=>[2,2,4]
[1,2,3,8,7,5,4,6]=>0001110=>0111000=>[2,1,1,4]
[1,2,3,8,7,4,5,6]=>0001100=>0011000=>[3,1,4]
[2,1,3,6,8,7,4,5]=>1000110=>0110001=>[2,1,4,1]
[3,1,6,2,8,7,5,4]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,8,1,3,2,5,4,7]=>0101010=>0101010=>[2,2,2,2]
[6,8,1,4,2,5,3,7]=>0101010=>0101010=>[2,2,2,2]
[7,8,3,6,1,4,2,5]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,5,1,4,3,6]=>0101010=>0101010=>[2,2,2,2]
[7,8,1,4,3,6,2,5]=>0101010=>0101010=>[2,2,2,2]
[5,8,1,4,3,7,2,6]=>0101010=>0101010=>[2,2,2,2]
[6,8,2,5,1,4,3,7]=>0101010=>0101010=>[2,2,2,2]
[6,8,2,5,3,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[2,5,4,7,6,8,1,3]=>0101010=>0101010=>[2,2,2,2]
[2,6,1,4,3,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[2,6,1,5,3,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[2,6,4,7,5,8,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,8,2,6,4,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,7,1,4,2,5]=>0101010=>0101010=>[2,2,2,2]
[5,8,1,3,2,6,4,7]=>0101010=>0101010=>[2,2,2,2]
[5,8,4,7,1,3,2,6]=>0101010=>0101010=>[2,2,2,2]
[6,8,4,7,1,3,2,5]=>0101010=>0101010=>[2,2,2,2]
[6,8,5,7,1,3,2,4]=>0101010=>0101010=>[2,2,2,2]
[5,7,6,8,2,4,1,3]=>0101010=>0101010=>[2,2,2,2]
[4,7,5,8,1,3,2,6]=>0101010=>0101010=>[2,2,2,2]
[4,7,1,3,2,6,5,8]=>0101010=>0101010=>[2,2,2,2]
[3,7,1,4,2,6,5,8]=>0101010=>0101010=>[2,2,2,2]
[3,7,6,8,1,4,2,5]=>0101010=>0101010=>[2,2,2,2]
[4,7,6,8,2,5,1,3]=>0101010=>0101010=>[2,2,2,2]
[4,7,5,8,3,6,1,2]=>0101010=>0101010=>[2,2,2,2]
[4,7,5,8,2,6,1,3]=>0101010=>0101010=>[2,2,2,2]
[3,7,4,8,2,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[3,7,1,5,2,6,4,8]=>0101010=>0101010=>[2,2,2,2]
[3,7,2,6,1,5,4,8]=>0101010=>0101010=>[2,2,2,2]
[3,7,2,6,5,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,6,5,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[2,6,5,8,4,7,1,3]=>0101010=>0101010=>[2,2,2,2]
[2,6,3,7,1,5,4,8]=>0101010=>0101010=>[2,2,2,2]
[7,6,4,8,5,2,3,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,7,4,3,5,1,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[6,7,3,5,4,8,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,8,3,7,5,2,4,1]=>0101101=>1011010=>[1,2,1,2,2]
[7,6,3,5,8,2,4,1]=>1100101=>1010011=>[1,2,3,1,1]
[7,6,2,8,4,1,5,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,6,3,4,8,2,5,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,8,3,7,4,5,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,3,5,8,4,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[5,7,8,3,6,2,1,4]=>0010110=>0110100=>[2,1,2,3]
[6,3,4,8,7,2,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[6,3,8,4,7,2,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[6,3,4,7,5,8,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,3,5,7,8,4,2,1]=>1000111=>1110001=>[1,1,1,4,1]
[5,7,3,6,8,2,1,4]=>0100110=>0110010=>[2,1,3,2]
[5,6,7,3,4,1,8,2]=>0010101=>1010100=>[1,2,2,3]
[4,6,7,8,3,5,2,1]=>0001011=>1101000=>[1,1,2,4]
[4,7,3,5,6,8,2,1]=>0100011=>1100010=>[1,1,4,2]
[5,3,4,7,8,2,1,6]=>1000110=>0110001=>[2,1,4,1]
[5,3,8,2,4,1,6,7]=>1010100=>0010101=>[3,2,2,1]
[5,3,4,8,2,6,1,7]=>1001010=>0101001=>[2,2,3,1]
[4,8,3,6,2,5,7,1]=>0101001=>1001010=>[1,3,2,2]
[4,8,3,5,7,2,6,1]=>0100101=>1010010=>[1,2,3,2]
[4,8,3,5,6,7,2,1]=>0100011=>1100010=>[1,1,4,2]
[4,7,8,3,5,6,2,1]=>0010011=>1100100=>[1,1,3,3]
[4,7,8,3,6,2,5,1]=>0010101=>1010100=>[1,2,2,3]
[4,8,3,6,7,2,5,1]=>0100101=>1010010=>[1,2,3,2]
[4,8,3,7,2,5,6,1]=>0101001=>1001010=>[1,3,2,2]
[5,8,3,7,2,6,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[5,7,3,4,8,2,1,6]=>0100110=>0110010=>[2,1,3,2]
[5,8,4,2,3,1,6,7]=>0110100=>0010110=>[3,2,1,2]
[5,8,4,2,3,1,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[6,4,8,5,3,7,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,4,2,7,3,1,8,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,4,3,7,8,5,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,4,5,3,7,1,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,4,2,3,1,6,8]=>0110100=>0010110=>[3,2,1,2]
[5,6,3,7,1,8,2,4]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,4,8,2,1,7]=>0100110=>0110010=>[2,1,3,2]
[6,3,5,7,4,8,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,3,5,4,7,8,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[6,4,3,5,7,1,8,2]=>1100101=>1010011=>[1,2,3,1,1]
[6,4,2,5,1,7,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,3,4,7,2,6,1,8]=>1001010=>0101001=>[2,2,3,1]
[4,7,3,6,2,5,8,1]=>0101001=>1001010=>[1,3,2,2]
[4,7,3,6,8,2,5,1]=>0100101=>1010010=>[1,2,3,2]
[4,6,7,3,5,8,2,1]=>0010011=>1100100=>[1,1,3,3]
[4,5,7,8,3,6,2,1]=>0001011=>1101000=>[1,1,2,4]
[4,5,8,3,7,2,6,1]=>0010101=>1010100=>[1,2,2,3]
[5,3,4,6,8,2,1,7]=>1000110=>0110001=>[2,1,4,1]
[5,3,6,7,1,8,2,4]=>1001010=>0101001=>[2,2,3,1]
[5,3,4,6,7,1,8,2]=>1000101=>1010001=>[1,2,4,1]
[4,6,3,5,7,8,2,1]=>0100011=>1100010=>[1,1,4,2]
[4,5,7,3,6,8,2,1]=>0010011=>1100100=>[1,1,3,3]
[7,1,5,8,4,2,3,6]=>1001100=>0011001=>[3,1,3,1]
[8,1,5,7,4,2,3,6]=>1001100=>0011001=>[3,1,3,1]
[7,1,4,5,8,2,3,6]=>1000100=>0010001=>[3,4,1]
[7,4,1,6,2,8,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,1,7,2,6,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[8,1,4,7,5,2,3,6]=>1001100=>0011001=>[3,1,3,1]
[8,1,5,4,7,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[2,1,7,5,8,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[7,1,5,4,8,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[7,1,4,8,5,2,3,6]=>1001100=>0011001=>[3,1,3,1]
[7,8,3,1,2,4,6,5]=>0110001=>1000110=>[1,4,1,2]
[8,7,1,6,4,2,3,5]=>1101100=>0011011=>[3,1,2,1,1]
[8,6,1,7,4,2,3,5]=>1101100=>0011011=>[3,1,2,1,1]
[7,6,1,8,4,2,3,5]=>1101100=>0011011=>[3,1,2,1,1]
[7,3,8,1,2,4,6,5]=>1010001=>1000101=>[1,4,2,1]
[8,3,7,1,2,4,6,5]=>1010001=>1000101=>[1,4,2,1]
[8,3,6,1,2,4,7,5]=>1010001=>1000101=>[1,4,2,1]
[8,3,7,5,1,2,4,6]=>1011000=>0001101=>[4,1,2,1]
[7,3,6,1,2,4,8,5]=>1010001=>1000101=>[1,4,2,1]
[6,7,1,8,4,2,3,5]=>0101100=>0011010=>[3,1,2,2]
[6,8,1,7,4,2,3,5]=>0101100=>0011010=>[3,1,2,2]
[7,1,8,4,5,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[7,6,3,1,2,4,8,5]=>1110001=>1000111=>[1,4,1,1,1]
[6,1,2,3,8,7,5,4]=>1000111=>1110001=>[1,1,1,4,1]
[6,8,3,1,2,7,4,5]=>0110010=>0100110=>[2,3,1,2]
[6,7,3,1,2,8,4,5]=>0110010=>0100110=>[2,3,1,2]
[6,7,1,4,2,3,8,5]=>0101001=>1001010=>[1,3,2,2]
[4,3,6,8,5,7,1,2]=>1001010=>0101001=>[2,2,3,1]
[6,1,2,5,4,8,3,7]=>1001010=>0101001=>[2,2,3,1]
[3,2,8,5,4,1,7,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,8,2,1,4,6,3,5]=>0110010=>0100110=>[2,3,1,2]
[2,4,8,5,1,3,6,7]=>0011000=>0001100=>[4,1,3]
[3,5,6,1,8,4,2,7]=>0010110=>0110100=>[2,1,2,3]
[1,3,6,8,7,4,2,5]=>0001110=>0111000=>[2,1,1,4]
[1,2,8,5,7,3,4,6]=>0010100=>0010100=>[3,2,3]
[3,1,5,6,4,8,7,2]=>1001011=>1101001=>[1,1,2,3,1]
[1,3,6,2,5,7,8,4]=>0010001=>1000100=>[1,4,3]
[3,6,1,4,2,7,8,5]=>0101001=>1001010=>[1,3,2,2]
[1,3,6,5,2,7,8,4]=>0011001=>1001100=>[1,3,1,3]
[1,2,6,4,3,8,5,7]=>0011010=>0101100=>[2,2,1,3]
[1,2,6,3,5,8,7,4]=>0010011=>1100100=>[1,1,3,3]
[2,3,5,1,8,4,7,6]=>0010101=>1010100=>[1,2,2,3]
[1,2,7,4,6,8,3,5]=>0010010=>0100100=>[2,3,3]
[2,3,7,5,1,8,4,6]=>0011010=>0101100=>[2,2,1,3]
[4,7,2,5,3,8,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,1,7,5,4,8,6,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,2,7,6,4,8,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[1,2,7,3,6,8,5,4]=>0010011=>1100100=>[1,1,3,3]
[3,1,5,4,8,7,6,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,2,6,8,5,4,7,3]=>0001101=>1011000=>[1,2,1,4]
[3,5,7,4,8,2,1,6]=>0010110=>0110100=>[2,1,2,3]
[2,4,7,6,8,3,1,5]=>0010110=>0110100=>[2,1,2,3]
[1,4,6,8,3,5,2,7]=>0001010=>0101000=>[2,2,4]
[1,3,6,8,5,2,4,7]=>0001100=>0011000=>[3,1,4]
[1,2,6,8,5,4,3,7]=>0001110=>0111000=>[2,1,1,4]
[1,2,5,8,4,3,7,6]=>0001101=>1011000=>[1,2,1,4]
[1,3,6,8,2,5,4,7]=>0001010=>0101000=>[2,2,4]
[1,4,6,8,3,2,5,7]=>0001100=>0011000=>[3,1,4]
[2,3,6,5,8,1,7,4]=>0010101=>1010100=>[1,2,2,3]
[3,5,4,6,8,2,1,7]=>0100110=>0110010=>[2,1,3,2]
[3,5,4,6,8,1,2,7]=>0100100=>0010010=>[3,3,2]
[1,2,4,7,5,8,3,6]=>0001010=>0101000=>[2,2,4]
[3,6,4,7,1,8,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,2,6,7,3,8,5,4]=>0001011=>1101000=>[1,1,2,4]
[1,2,5,7,3,8,6,4]=>0001011=>1101000=>[1,1,2,4]
[3,1,5,7,6,8,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[3,5,4,6,8,2,7,1]=>0100101=>1010010=>[1,2,3,2]
[4,2,6,1,8,7,5,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,2,7,4,6,8,5,3]=>0010011=>1100100=>[1,1,3,3]
[1,2,7,5,6,8,4,3]=>0010011=>1100100=>[1,1,3,3]
[3,1,6,7,5,8,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[4,6,2,7,5,8,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,7,4,8,2,6,1]=>0010101=>1010100=>[1,2,2,3]
[1,3,6,8,2,5,7,4]=>0001001=>1001000=>[1,3,4]
[1,3,5,8,2,7,4,6]=>0001010=>0101000=>[2,2,4]
[1,2,5,8,4,7,6,3]=>0001011=>1101000=>[1,1,2,4]
[1,2,4,8,7,3,6,5]=>0001101=>1011000=>[1,2,1,4]
[1,2,5,8,7,4,3,6]=>0001110=>0111000=>[2,1,1,4]
[1,3,5,8,7,2,4,6]=>0001100=>0011000=>[3,1,4]
[2,3,7,6,8,5,1,4]=>0010110=>0110100=>[2,1,2,3]
[5,7,1,2,8,6,4,3]=>0100111=>1110010=>[1,1,1,3,2]
[3,1,7,6,8,5,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,2,6,8,5,7,4,3]=>0001011=>1101000=>[1,1,2,4]
[1,2,5,8,7,4,6,3]=>0001101=>1011000=>[1,2,1,4]
[1,2,4,8,7,6,3,5]=>0001110=>0111000=>[2,1,1,4]
[3,2,7,4,6,8,1,5]=>1010010=>0100101=>[2,3,2,1]
[5,3,6,2,7,1,4,8]=>1010100=>0010101=>[3,2,2,1]
[2,6,3,4,7,1,5,8]=>0100100=>0010010=>[3,3,2]
[2,7,3,4,5,8,1,6]=>0100010=>0100010=>[2,4,2]
[4,7,6,2,3,8,1,5]=>0110010=>0100110=>[2,3,1,2]
[7,3,5,2,4,8,1,6]=>1010010=>0100101=>[2,3,2,1]
[7,6,2,4,5,8,1,3]=>1100010=>0100011=>[2,4,1,1]
[6,5,2,3,4,8,1,7]=>1100010=>0100011=>[2,4,1,1]
[5,3,1,2,8,4,7,6]=>1100101=>1010011=>[1,2,3,1,1]
[6,5,2,3,7,1,4,8]=>1100100=>0010011=>[3,3,1,1]
[5,2,1,7,3,4,6,8]=>1101000=>0001011=>[4,2,1,1]
[5,2,1,8,3,4,6,7]=>1101000=>0001011=>[4,2,1,1]
[6,3,2,8,4,5,7,1]=>1101001=>1001011=>[1,3,2,1,1]
[7,3,1,2,8,4,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[6,2,3,1,8,4,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,5,2,7,1,4,6]=>1010100=>0010101=>[3,2,2,1]
[8,6,2,4,7,1,5,3]=>1100101=>1010011=>[1,2,3,1,1]
[8,2,1,7,3,4,5,6]=>1101000=>0001011=>[4,2,1,1]
[8,6,3,7,2,4,5,1]=>1101001=>1001011=>[1,3,2,1,1]
[8,2,7,3,4,5,6,1]=>1010001=>1000101=>[1,4,2,1]
[8,1,6,2,3,4,5,7]=>1010000=>0000101=>[5,2,1]
[8,1,7,3,4,5,6,2]=>1010001=>1000101=>[1,4,2,1]
[8,6,1,7,2,4,5,3]=>1101001=>1001011=>[1,3,2,1,1]
[1,7,5,8,2,3,6,4]=>0101001=>1001010=>[1,3,2,2]
[7,2,1,8,3,4,5,6]=>1101000=>0001011=>[4,2,1,1]
[1,7,8,3,4,5,6,2]=>0010001=>1000100=>[1,4,3]
[1,6,2,8,4,5,7,3]=>0101001=>1001010=>[1,3,2,2]
[4,1,3,6,8,2,7,5]=>1000101=>1010001=>[1,2,4,1]
[4,6,3,8,7,1,2,5]=>0101100=>0011010=>[3,1,2,2]
[6,4,5,8,7,1,2,3]=>1001100=>0011001=>[3,1,3,1]
[5,3,4,8,7,1,2,6]=>1001100=>0011001=>[3,1,3,1]
[3,2,8,7,1,4,6,5]=>1011001=>1001101=>[1,3,1,2,1]
[3,1,8,7,2,4,6,5]=>1011001=>1001101=>[1,3,1,2,1]
[5,3,7,6,1,2,4,8]=>1011000=>0001101=>[4,1,2,1]
[1,8,3,7,2,4,5,6]=>0101000=>0001010=>[4,2,2]
[3,8,1,7,2,4,5,6]=>0101000=>0001010=>[4,2,2]
[6,8,2,3,5,1,4,7]=>0100100=>0010010=>[3,3,2]
[4,7,8,2,6,1,3,5]=>0010100=>0010100=>[3,2,3]
[6,2,8,7,1,4,5,3]=>1011001=>1001101=>[1,3,1,2,1]
[3,8,7,1,4,5,6,2]=>0110001=>1000110=>[1,4,1,2]
[2,8,6,1,3,4,5,7]=>0110000=>0000110=>[5,1,2]
[2,7,6,1,3,4,5,8]=>0110000=>0000110=>[5,1,2]
[1,7,6,2,3,4,5,8]=>0110000=>0000110=>[5,1,2]
[1,8,6,2,3,4,5,7]=>0110000=>0000110=>[5,1,2]
[2,8,7,3,4,5,6,1]=>0110001=>1000110=>[1,4,1,2]
[3,8,7,2,4,5,6,1]=>0110001=>1000110=>[1,4,1,2]
[7,8,3,6,2,4,5,1]=>0101001=>1001010=>[1,3,2,2]
[1,5,8,7,2,3,6,4]=>0011001=>1001100=>[1,3,1,3]
[7,8,10,9,5,6,3,4,1,2]=>001101010=>010101100=>[2,2,2,1,3]
[9,10,5,6,8,7,3,4,1,2]=>010011010=>010110010=>[2,2,1,3,2]
[5,8,10,6,9,7,3,4,1,2]=>001011010=>010110100=>[2,2,1,2,3]
[5,6,7,10,9,8,3,4,1,2]=>000111010=>010111000=>[2,2,1,1,4]
[9,10,7,8,3,4,6,5,1,2]=>010100110=>011001010=>[2,1,3,2,2]
[7,8,10,9,3,4,6,5,1,2]=>001100110=>011001100=>[2,1,3,1,3]
[9,10,3,6,8,4,7,5,1,2]=>010010110=>011010010=>[2,1,2,3,2]
[3,8,10,6,9,4,7,5,1,2]=>001010110=>011010100=>[2,1,2,2,3]
[3,6,7,10,9,4,8,5,1,2]=>000110110=>011011000=>[2,1,2,1,4]
[9,10,3,4,5,8,7,6,1,2]=>010001110=>011100010=>[2,1,1,4,2]
[3,8,10,4,5,9,7,6,1,2]=>001001110=>011100100=>[2,1,1,3,3]
[3,4,7,10,5,9,8,6,1,2]=>000101110=>011101000=>[2,1,1,2,4]
[3,4,5,6,10,9,8,7,1,2]=>000011110=>011110000=>[2,1,1,1,5]
[9,10,7,8,5,6,1,2,4,3]=>010101001=>100101010=>[1,3,2,2,2]
[7,8,10,9,5,6,1,2,4,3]=>001101001=>100101100=>[1,3,2,1,3]
[9,10,5,6,8,7,1,2,4,3]=>010011001=>100110010=>[1,3,1,3,2]
[5,8,10,6,9,7,1,2,4,3]=>001011001=>100110100=>[1,3,1,2,3]
[5,6,7,10,9,8,1,2,4,3]=>000111001=>100111000=>[1,3,1,1,4]
[9,10,7,8,1,4,6,2,5,3]=>010100101=>101001010=>[1,2,3,2,2]
[7,8,10,9,1,4,6,2,5,3]=>001100101=>101001100=>[1,2,3,1,3]
[9,10,1,6,8,4,7,2,5,3]=>010010101=>101010010=>[1,2,2,3,2]
[1,8,10,6,9,4,7,2,5,3]=>001010101=>101010100=>[1,2,2,2,3]
[1,6,7,10,9,4,8,2,5,3]=>000110101=>101011000=>[1,2,2,1,4]
[9,10,1,4,5,8,7,2,6,3]=>010001101=>101100010=>[1,2,1,4,2]
[1,8,10,4,5,9,7,2,6,3]=>001001101=>101100100=>[1,2,1,3,3]
[1,4,7,10,5,9,8,2,6,3]=>000101101=>101101000=>[1,2,1,2,4]
[1,4,5,6,10,9,8,2,7,3]=>000011101=>101110000=>[1,2,1,1,5]
[9,10,7,8,1,2,3,6,5,4]=>010100011=>110001010=>[1,1,4,2,2]
[7,8,10,9,1,2,3,6,5,4]=>001100011=>110001100=>[1,1,4,1,3]
[9,10,1,6,8,2,3,7,5,4]=>010010011=>110010010=>[1,1,3,3,2]
[1,8,10,6,9,2,3,7,5,4]=>001010011=>110010100=>[1,1,3,2,3]
[1,6,7,10,9,2,3,8,5,4]=>000110011=>110011000=>[1,1,3,1,4]
[9,10,1,2,5,8,3,7,6,4]=>010001011=>110100010=>[1,1,2,4,2]
[1,8,10,2,5,9,3,7,6,4]=>001001011=>110100100=>[1,1,2,3,3]
[1,2,7,10,5,9,3,8,6,4]=>000101011=>110101000=>[1,1,2,2,4]
[1,2,5,6,10,9,3,8,7,4]=>000011011=>110110000=>[1,1,2,1,5]
[9,10,1,2,3,4,8,7,6,5]=>010000111=>111000010=>[1,1,1,5,2]
[1,8,10,2,3,4,9,7,6,5]=>001000111=>111000100=>[1,1,1,4,3]
[1,2,7,10,3,4,9,8,6,5]=>000100111=>111001000=>[1,1,1,3,4]
[1,2,3,6,10,4,9,8,7,5]=>000010111=>111010000=>[1,1,1,2,5]
[1,7,3,6,5,2,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[8,6,2,5,4,1,7,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,2,6,4,7,5,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,3,7,5,4,1,8]=>1001110=>0111001=>[2,1,1,3,1]
[1,3,4,7,6,2,8,5]=>0001101=>1011000=>[1,2,1,4]
[2,8,3,6,1,7,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[8,7,2,5,1,6,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,8,2,6,5,1,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,2,5,4,1,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,8,5,2,6,1,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[4,5,1,3,7,2,8,6]=>0100101=>1010010=>[1,2,3,2]
[6,1,3,7,5,2,8,4]=>1001101=>1011001=>[1,2,1,3,1]
[7,1,3,6,2,8,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,3,6,2,7,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[1,2,4,7,3,8,6,5]=>0001011=>1101000=>[1,1,2,4]
[7,1,8,2,6,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,1,7,8,2,6,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[3,4,8,6,5,1,7,2]=>0011101=>1011100=>[1,2,1,1,3]
[8,3,7,5,1,6,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,4,8,6,2,7,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[8,4,6,7,1,5,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[3,4,6,5,1,2,8,7]=>0011001=>1001100=>[1,3,1,3]
[7,3,5,1,2,8,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[1,4,6,2,3,8,7,5]=>0010011=>1100100=>[1,1,3,3]
[1,3,2,7,4,8,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[7,2,1,6,3,8,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,5,2,1,7,3,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[5,6,7,1,2,8,4,3]=>0010011=>1100100=>[1,1,3,3]
[4,7,5,1,2,8,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[3,7,1,6,2,8,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[7,6,1,2,8,5,4,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[2,7,1,3,8,6,5,4]=>0100111=>1110010=>[1,1,1,3,2]
[8,6,1,2,7,5,4,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[1,7,2,3,8,6,5,4]=>0100111=>1110010=>[1,1,1,3,2]
[8,7,1,2,6,5,4,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,8,1,2,6,5,4,3]=>0100111=>1110010=>[1,1,1,3,2]
[3,8,1,6,2,7,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[4,8,5,1,2,7,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,1,4,3,6,5,10,9,7,8]=>101010110=>011010101=>[2,1,2,2,2,1]
[2,1,4,3,8,7,5,6,10,9]=>101011001=>100110101=>[1,3,1,2,2,1]
[2,1,4,3,10,7,5,9,6,8]=>101011010=>010110101=>[2,2,1,2,2,1]
[2,1,4,3,10,9,8,5,6,7]=>101011100=>001110101=>[3,1,1,2,2,1]
[2,1,6,5,3,4,8,7,10,9]=>101100101=>101001101=>[1,2,3,1,2,1]
[2,1,6,5,3,4,10,9,7,8]=>101100110=>011001101=>[2,1,3,1,2,1]
[2,1,8,5,3,7,4,6,10,9]=>101101001=>100101101=>[1,3,2,1,2,1]
[2,1,10,5,3,7,4,9,6,8]=>101101010=>010101101=>[2,2,2,1,2,1]
[2,1,10,5,3,9,8,4,6,7]=>101101100=>001101101=>[3,1,2,1,2,1]
[2,1,8,7,6,3,4,5,10,9]=>101110001=>100011101=>[1,4,1,1,2,1]
[2,1,10,7,6,3,4,9,5,8]=>101110010=>010011101=>[2,3,1,1,2,1]
[2,1,10,9,6,3,8,4,5,7]=>101110100=>001011101=>[3,2,1,1,2,1]
[2,1,10,9,8,7,3,4,5,6]=>101111000=>000111101=>[4,1,1,1,2,1]
[4,3,1,2,6,5,8,7,10,9]=>110010101=>101010011=>[1,2,2,3,1,1]
[4,3,1,2,6,5,10,9,7,8]=>110010110=>011010011=>[2,1,2,3,1,1]
[4,3,1,2,8,7,5,6,10,9]=>110011001=>100110011=>[1,3,1,3,1,1]
[4,3,1,2,10,7,5,9,6,8]=>110011010=>010110011=>[2,2,1,3,1,1]
[4,3,1,2,10,9,8,5,6,7]=>110011100=>001110011=>[3,1,1,3,1,1]
[6,3,1,5,2,4,8,7,10,9]=>110100101=>101001011=>[1,2,3,2,1,1]
[6,3,1,5,2,4,10,9,7,8]=>110100110=>011001011=>[2,1,3,2,1,1]
[8,3,1,5,2,7,4,6,10,9]=>110101001=>100101011=>[1,3,2,2,1,1]
[10,3,1,5,2,9,8,4,6,7]=>110101100=>001101011=>[3,1,2,2,1,1]
[8,3,1,7,6,2,4,5,10,9]=>110110001=>100011011=>[1,4,1,2,1,1]
[10,3,1,7,6,2,4,9,5,8]=>110110010=>010011011=>[2,3,1,2,1,1]
[10,3,1,9,6,2,8,4,5,7]=>110110100=>001011011=>[3,2,1,2,1,1]
[10,3,1,9,8,7,2,4,5,6]=>110111000=>000111011=>[4,1,1,2,1,1]
[6,5,4,1,2,3,8,7,10,9]=>111000101=>101000111=>[1,2,4,1,1,1]
[6,5,4,1,2,3,10,9,7,8]=>111000110=>011000111=>[2,1,4,1,1,1]
[8,5,4,1,2,7,3,6,10,9]=>111001001=>100100111=>[1,3,3,1,1,1]
[10,5,4,1,2,7,3,9,6,8]=>111001010=>010100111=>[2,2,3,1,1,1]
[10,5,4,1,2,9,8,3,6,7]=>111001100=>001100111=>[3,1,3,1,1,1]
[8,7,4,1,6,2,3,5,10,9]=>111010001=>100010111=>[1,4,2,1,1,1]
[10,7,4,1,6,2,3,9,5,8]=>111010010=>010010111=>[2,3,2,1,1,1]
[10,9,4,1,8,7,2,3,5,6]=>111011000=>000110111=>[4,1,2,1,1,1]
[8,7,6,5,1,2,3,4,10,9]=>111100001=>100001111=>[1,5,1,1,1,1]
[10,7,6,5,1,2,3,9,4,8]=>111100010=>010001111=>[2,4,1,1,1,1]
[10,9,6,5,1,2,8,3,4,7]=>111100100=>001001111=>[3,3,1,1,1,1]
[2,1,4,3,6,5,8,7,12,11,9,10]=>10101010110=>01101010101=>[2,1,2,2,2,2,1]
[12,11,6,5,1,2,10,9,3,4,7,8]=>11110011000=>00011001111=>[4,1,3,1,1,1,1]
[12,11,10,5,1,9,8,2,3,4,6,7]=>11110110000=>00001101111=>[5,1,2,1,1,1,1]
[1,8,2,7,4,3,5,6]=>0101100=>0011010=>[3,1,2,2]
[1,8,6,4,7,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[1,8,4,2,6,3,5,7]=>0110100=>0010110=>[3,2,1,2]
[7,4,8,1,5,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[4,1,7,2,6,3,5,8]=>1010100=>0010101=>[3,2,2,1]
[5,1,7,4,3,6,2,8]=>1011010=>0101101=>[2,2,1,2,1]
[1,8,5,4,3,7,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[1,8,4,2,5,3,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[1,8,5,4,2,6,7,3]=>0111001=>1001110=>[1,3,1,1,2]
[7,4,8,2,1,3,5,6]=>1011000=>0001101=>[4,1,2,1]
[4,1,7,3,2,5,6,8]=>1011000=>0001101=>[4,1,2,1]
[7,5,4,8,2,3,6,1]=>1101001=>1001011=>[1,3,2,1,1]
[7,3,8,1,5,6,2,4]=>1010010=>0100101=>[2,3,2,1]
[3,1,7,2,6,8,4,5]=>1010010=>0100101=>[2,3,2,1]
[5,1,7,4,2,6,8,3]=>1011001=>1001101=>[1,3,1,2,1]
[4,3,1,6,2,5,7,8]=>1101000=>0001011=>[4,2,1,1]
[6,5,4,3,7,1,8,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,3,2,8,5,7,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,8,2,1,7,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[7,2,8,6,3,1,4,5]=>1011100=>0011101=>[3,1,1,2,1]
[2,1,7,8,3,6,4,5]=>1001010=>0101001=>[2,2,3,1]
[4,2,1,6,7,3,5,8]=>1100100=>0010011=>[3,3,1,1]
[4,3,1,5,2,7,6,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,2,7,3,8,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[3,1,6,2,8,7,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[6,3,1,7,8,5,2,4]=>1100110=>0110011=>[2,1,3,1,1]
[6,5,4,1,7,8,3,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[5,4,3,1,6,7,2,8]=>1110010=>0100111=>[2,3,1,1,1]
[5,4,2,6,3,8,7,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,3,1,5,2,6,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[5,4,2,1,6,7,8,3]=>1110001=>1000111=>[1,4,1,1,1]
[5,4,3,1,6,7,8,2]=>1110001=>1000111=>[1,4,1,1,1]
[7,8,2,4,5,1,3,6]=>0100100=>0010010=>[3,3,2]
[4,6,7,2,5,1,3,8]=>0010100=>0010100=>[3,2,3]
[7,8,1,3,2,4,5,6]=>0101000=>0001010=>[4,2,2]
[7,8,4,1,5,2,3,6]=>0110100=>0010110=>[3,2,1,2]
[3,6,7,2,1,4,5,8]=>0011000=>0001100=>[4,1,3]
[5,2,3,6,1,4,7,8]=>1001000=>0001001=>[4,3,1]
[2,5,3,6,1,4,7,8]=>0101000=>0001010=>[4,2,2]
[6,4,7,1,5,2,3,8]=>1010100=>0010101=>[3,2,2,1]
[6,2,7,3,1,4,5,8]=>1011000=>0001101=>[4,1,2,1]
[3,5,4,6,7,8,1,2]=>0100010=>0100010=>[2,4,2]
[1,5,4,6,7,2,3,8]=>0100100=>0010010=>[3,3,2]
[1,6,7,3,2,4,5,8]=>0011000=>0001100=>[4,1,3]
[1,5,3,6,2,4,7,8]=>0101000=>0001010=>[4,2,2]
[5,1,3,6,2,4,7,8]=>1001000=>0001001=>[4,3,1]
[5,2,4,6,7,1,3,8]=>1000100=>0010001=>[3,4,1]
[2,6,7,4,5,1,3,8]=>0010100=>0010100=>[3,2,3]
[4,2,5,6,7,1,3,8]=>1000100=>0010001=>[3,4,1]
[4,5,2,6,7,1,3,8]=>0100100=>0010010=>[3,3,2]
[5,3,1,6,2,4,7,8]=>1101000=>0001011=>[4,2,1,1]
[6,1,7,3,2,4,5,8]=>1011000=>0001101=>[4,1,2,1]
[6,1,7,4,5,2,3,8]=>1010100=>0010101=>[3,2,2,1]
[6,3,7,4,5,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[5,4,1,6,7,2,3,8]=>1100100=>0010011=>[3,3,1,1]
[5,2,1,6,3,4,7,8]=>1101000=>0001011=>[4,2,1,1]
[1,3,6,7,5,2,8,4]=>0001101=>1011000=>[1,2,1,4]
[7,3,4,1,6,2,5,8]=>1010100=>0010101=>[3,2,2,1]
[7,3,4,1,6,5,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,4,1,5,2,6,8]=>1010100=>0010101=>[3,2,2,1]
[1,3,6,7,2,5,8,4]=>0001001=>1001000=>[1,3,4]
[4,3,1,7,2,6,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[5,6,1,4,7,3,8,2]=>0100101=>1010010=>[1,2,3,2]
[5,3,2,1,7,4,8,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[1,3,4,5,8,7,2,6]=>0000110=>0110000=>[2,1,5]
[6,3,4,5,8,1,7,2]=>1000101=>1010001=>[1,2,4,1]
[2,4,5,1,6,8,7,3]=>0010011=>1100100=>[1,1,3,3]
[3,1,2,5,6,8,7,4]=>1000011=>1100001=>[1,1,5,1]
[4,3,2,5,6,8,1,7]=>1100010=>0100011=>[2,4,1,1]
[3,1,4,6,5,8,2,7]=>1001010=>0101001=>[2,2,3,1]
[2,3,4,5,8,6,1,7]=>0000110=>0110000=>[2,1,5]
[4,3,1,7,6,5,8,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,4,5,2,6,8,7,3]=>0010011=>1100100=>[1,1,3,3]
[3,7,5,2,6,8,1,4]=>0110010=>0100110=>[2,3,1,2]
[3,7,5,2,6,8,4,1]=>0110011=>1100110=>[1,1,3,1,2]
[5,6,1,2,7,4,8,3]=>0100101=>1010010=>[1,2,3,2]
[6,3,5,2,4,7,8,1]=>1010001=>1000101=>[1,4,2,1]
[5,3,2,1,4,7,8,6]=>1110001=>1000111=>[1,4,1,1,1]
[5,3,1,4,2,7,8,6]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,1,2,4,7,8,6]=>1100001=>1000011=>[1,5,1,1]
[7,1,5,2,6,8,4,3]=>1010011=>1100101=>[1,1,3,2,1]
[7,1,5,2,6,8,3,4]=>1010010=>0100101=>[2,3,2,1]
[1,7,4,6,5,8,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[2,7,4,6,1,8,3,5]=>0101010=>0101010=>[2,2,2,2]
[2,7,4,6,1,8,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,3,6,7,1,5,8,4]=>0001001=>1001000=>[1,3,4]
[2,3,6,7,5,1,8,4]=>0001101=>1011000=>[1,2,1,4]
[4,3,2,6,7,1,8,5]=>1100101=>1010011=>[1,2,3,1,1]
[7,3,2,5,6,8,1,4]=>1100010=>0100011=>[2,4,1,1]
[7,1,5,4,6,8,2,3]=>1010010=>0100101=>[2,3,2,1]
[2,7,4,6,5,8,1,3]=>0101010=>0101010=>[2,2,2,2]
[7,3,4,5,8,1,2,6]=>1000100=>0010001=>[3,4,1]
[1,3,4,5,8,6,2,7]=>0000110=>0110000=>[2,1,5]
[1,3,4,5,8,2,7,6]=>0000101=>1010000=>[1,2,5]
[7,1,5,4,6,8,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[7,3,2,5,6,8,4,1]=>1100011=>1100011=>[1,1,4,1,1]
[5,7,4,6,1,8,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,3,4,5,8,1,2,7]=>1000100=>0010001=>[3,4,1]
[7,3,4,5,8,2,6,1]=>1000101=>1010001=>[1,2,4,1]
[4,2,1,8,3,6,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[6,2,1,7,3,5,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[2,7,3,1,4,8,5,6]=>0110010=>0100110=>[2,3,1,2]
[3,2,1,5,7,8,4,6]=>1100010=>0100011=>[2,4,1,1]
[4,3,6,8,5,1,7,2]=>1001101=>1011001=>[1,2,1,3,1]
[2,1,6,8,3,7,4,5]=>1001010=>0101001=>[2,2,3,1]
[3,2,1,5,6,8,4,7]=>1100010=>0100011=>[2,4,1,1]
[2,4,7,1,8,5,3,6]=>0010110=>0110100=>[2,1,2,3]
[2,4,8,5,1,6,3,7]=>0011010=>0101100=>[2,2,1,3]
[6,2,1,7,3,4,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[6,2,1,7,8,3,5,4]=>1100101=>1010011=>[1,2,3,1,1]
[3,2,1,6,7,4,5,8]=>1100100=>0010011=>[3,3,1,1]
[2,4,8,5,1,6,7,3]=>0011001=>1001100=>[1,3,1,3]
[3,2,1,8,4,5,6,7]=>1101000=>0001011=>[4,2,1,1]
[1,6,8,3,7,2,4,5]=>0010100=>0010100=>[3,2,3]
[3,8,1,5,7,2,4,6]=>0100100=>0010010=>[3,3,2]
[1,2,6,8,4,7,3,5]=>0001010=>0101000=>[2,2,4]
[6,1,5,8,2,4,7,3]=>1001001=>1001001=>[1,3,3,1]
[1,2,4,8,3,6,7,5]=>0001001=>1001000=>[1,3,4]
[4,1,2,7,8,3,6,5]=>1000101=>1010001=>[1,2,4,1]
[5,3,8,4,7,6,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[8,7,1,2,5,4,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[5,8,1,2,3,7,6,4]=>0100011=>1100010=>[1,1,4,2]
[1,2,8,4,3,5,7,6]=>0011001=>1001100=>[1,3,1,3]
[1,2,5,3,7,6,4,8]=>0010110=>0110100=>[2,1,2,3]
[6,1,2,8,7,4,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[7,1,6,2,8,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,2,6,3,8,5,4,7]=>0010110=>0110100=>[2,1,2,3]
[1,2,8,5,3,6,4,7]=>0011010=>0101100=>[2,2,1,3]
[1,2,7,3,8,5,4,6]=>0010110=>0110100=>[2,1,2,3]
[1,6,2,8,4,3,5,7]=>0101100=>0011010=>[3,1,2,2]
[1,6,4,2,7,3,5,8]=>0110100=>0010110=>[3,2,1,2]
[1,8,6,3,2,4,5,7]=>0111000=>0001110=>[4,1,1,2]
[3,1,7,8,6,2,4,5]=>1001100=>0011001=>[3,1,3,1]
[1,8,7,3,5,6,2,4]=>0110010=>0100110=>[2,3,1,2]
[1,3,2,8,7,4,5,6]=>0101100=>0011010=>[3,1,2,2]
[1,2,8,4,3,7,5,6]=>0011010=>0101100=>[2,2,1,3]
[8,5,1,7,2,4,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[3,8,6,4,7,5,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[6,1,8,2,7,4,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[1,2,7,5,3,6,4,8]=>0011010=>0101100=>[2,2,1,3]
[1,2,6,3,7,5,4,8]=>0010110=>0110100=>[2,1,2,3]
[1,2,3,7,5,4,8,6]=>0001101=>1011000=>[1,2,1,4]
[3,7,4,8,6,5,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[1,8,2,7,6,4,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,4,6,3,8,5,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,6,2,7,5,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,5,7,8,4,1,3,2]=>1001101=>1011001=>[1,2,1,3,1]
[7,5,6,8,2,4,1,3]=>1001010=>0101001=>[2,2,3,1]
[7,4,6,2,8,5,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[4,3,2,6,8,5,1,7]=>1100110=>0110011=>[2,1,3,1,1]
[3,5,6,8,2,4,1,7]=>0001010=>0101000=>[2,2,4]
[2,6,7,8,1,4,5,3]=>0001001=>1001000=>[1,3,4]
[3,6,7,8,1,4,2,5]=>0001010=>0101000=>[2,2,4]
[3,5,7,8,2,1,4,6]=>0001100=>0011000=>[3,1,4]
[2,6,7,8,1,4,3,5]=>0001010=>0101000=>[2,2,4]
[2,5,7,8,3,1,4,6]=>0001100=>0011000=>[3,1,4]
[2,4,7,3,8,1,5,6]=>0010100=>0010100=>[3,2,3]
[6,4,7,3,8,1,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,7,3,8,1,2,5]=>1010100=>0010101=>[3,2,2,1]
[7,4,6,3,8,2,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[6,3,2,5,4,8,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,4,5,2,3,8,1,7]=>1010010=>0100101=>[2,3,2,1]
[5,4,6,3,8,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,4,7,3,8,1,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,5,7,8,3,1,6,4]=>0001101=>1011000=>[1,2,1,4]
[4,5,7,8,3,1,2,6]=>0001100=>0011000=>[3,1,4]
[4,5,6,8,2,3,1,7]=>0001010=>0101000=>[2,2,4]
[5,4,6,2,8,3,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,3,2,6,8,4,1,7]=>1100110=>0110011=>[2,1,3,1,1]
[5,4,7,2,8,1,3,6]=>1010100=>0010101=>[3,2,2,1]
[4,5,7,8,2,1,3,6]=>0001100=>0011000=>[3,1,4]
[4,6,7,8,1,3,2,5]=>0001010=>0101000=>[2,2,4]
[4,6,7,8,1,3,5,2]=>0001001=>1001000=>[1,3,4]
[2,6,7,8,1,3,5,4]=>0001001=>1001000=>[1,3,4]
[2,6,7,8,1,5,3,4]=>0001010=>0101000=>[2,2,4]
[4,6,7,8,1,5,2,3]=>0001010=>0101000=>[2,2,4]
[4,6,7,8,1,2,5,3]=>0001001=>1001000=>[1,3,4]
[5,3,2,7,8,1,6,4]=>1100101=>1010011=>[1,2,3,1,1]
[4,3,2,7,8,1,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[3,5,7,8,2,1,6,4]=>0001101=>1011000=>[1,2,1,4]
[3,6,7,8,1,5,4,2]=>0001011=>1101000=>[1,1,2,4]
[2,6,7,8,1,5,4,3]=>0001011=>1101000=>[1,1,2,4]
[4,5,8,3,6,7,1,2]=>0010010=>0100100=>[2,3,3]
[4,5,8,3,7,6,1,2]=>0010110=>0110100=>[2,1,2,3]
[4,2,8,3,7,1,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,3,4,8,1,5,6]=>1000100=>0010001=>[3,4,1]
[7,6,3,4,8,5,1,2]=>1100110=>0110011=>[2,1,3,1,1]
[7,6,3,5,8,4,1,2]=>1100110=>0110011=>[2,1,3,1,1]
[7,6,3,8,4,5,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[7,2,3,8,5,1,4,6]=>1001100=>0011001=>[3,1,3,1]
[2,6,4,8,1,5,7,3]=>0101001=>1001010=>[1,3,2,2]
[7,2,3,8,4,1,5,6]=>1001100=>0011001=>[3,1,3,1]
[7,8,2,3,6,1,4,5]=>0100100=>0010010=>[3,3,2]
[4,2,6,3,7,1,5,8]=>1010100=>0010101=>[3,2,2,1]
[7,2,3,5,8,1,6,4]=>1000101=>1010001=>[1,2,4,1]
[7,2,3,8,4,1,6,5]=>1001101=>1011001=>[1,2,1,3,1]
[2,6,4,8,1,3,7,5]=>0101001=>1001010=>[1,3,2,2]
[3,6,4,8,1,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[7,6,5,1,2,3,8,4]=>1110001=>1000111=>[1,4,1,1,1]
[7,6,5,1,4,2,8,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,8,5,4,1,2,6,3]=>0111001=>1001110=>[1,3,1,1,2]
[3,5,6,4,1,2,8,7]=>0011001=>1001100=>[1,3,1,3]
[7,6,5,1,2,4,3,8]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,5,1,2,4,8,3]=>1110001=>1000111=>[1,4,1,1,1]
[7,6,5,1,3,2,4,8]=>1110100=>0010111=>[3,2,1,1,1]
[2,6,4,3,1,8,7,5]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,5,8,4,1,2,7,6]=>0011001=>1001100=>[1,3,1,3]
[3,5,8,4,1,2,6,7]=>0011000=>0001100=>[4,1,3]
[3,5,8,4,1,6,2,7]=>0011010=>0101100=>[2,2,1,3]
[2,5,8,4,1,7,3,6]=>0011010=>0101100=>[2,2,1,3]
[3,6,4,2,1,7,5,8]=>0111010=>0101110=>[2,2,1,1,2]
[3,5,6,4,1,8,7,2]=>0011011=>1101100=>[1,1,2,1,3]
[2,6,4,5,1,3,7,8]=>0101000=>0001010=>[4,2,2]
[7,6,5,1,4,3,8,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,6,5,1,2,8,3,4]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,5,1,8,2,4,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,6,5,1,8,2,3,4]=>1110100=>0010111=>[3,2,1,1,1]
[7,6,5,1,8,3,2,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,6,5,1,4,8,2,3]=>1110010=>0100111=>[2,3,1,1,1]
[3,6,4,5,1,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[2,5,6,4,1,7,8,3]=>0011001=>1001100=>[1,3,1,3]
[2,5,6,4,1,7,3,8]=>0011010=>0101100=>[2,2,1,3]
[3,6,4,5,1,7,8,2]=>0101001=>1001010=>[1,3,2,2]
[7,6,5,1,4,8,3,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,6,5,1,8,3,4,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,6,5,1,8,4,2,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,7,4,2,5,3,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[7,6,4,8,3,1,5,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,4,8,5,6,1,3,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,2,5,6,3,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[4,2,7,5,6,3,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,7,3,5,6,2,1,8]=>0100110=>0110010=>[2,1,3,2]
[1,6,8,5,2,7,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[6,2,8,5,1,7,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,7,4,8,2,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,2,7,8,6,1,5,4]=>1001101=>1011001=>[1,2,1,3,1]
[6,8,4,1,2,3,7,5]=>0110001=>1000110=>[1,4,1,2]
[1,8,2,5,6,4,3,7]=>0100110=>0110010=>[2,1,3,2]
[6,1,8,5,3,7,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,8,1,5,2,7,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[8,2,1,5,3,7,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,1,6,5,3,7,2,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,4,6,3,2,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[3,2,6,4,1,7,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[7,6,4,3,1,2,8,5]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,6,3,5,1,7,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[4,5,3,1,6,7,8,2]=>0110001=>1000110=>[1,4,1,2]
[3,5,2,1,6,7,8,4]=>0110001=>1000110=>[1,4,1,2]
[5,2,3,1,6,7,8,4]=>1010001=>1000101=>[1,4,2,1]
[1,5,3,2,6,7,8,4]=>0110001=>1000110=>[1,4,1,2]
[8,2,7,5,6,1,3,4]=>1010100=>0010101=>[3,2,2,1]
[1,7,4,6,2,3,8,5]=>0101001=>1001010=>[1,3,2,2]
[7,6,4,2,1,5,8,3]=>1111001=>1001111=>[1,3,1,1,1,1]
[5,7,4,6,1,3,8,2]=>0101001=>1001010=>[1,3,2,2]
[8,6,4,7,3,1,2,5]=>1101100=>0011011=>[3,1,2,1,1]
[5,2,4,3,7,1,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,4,1,3,5,2,7]=>1110010=>0100111=>[2,3,1,1,1]
[6,7,4,1,5,3,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[7,5,4,1,2,6,8,3]=>1110001=>1000111=>[1,4,1,1,1]
[1,8,2,5,3,7,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[3,8,1,5,6,4,2,7]=>0100110=>0110010=>[2,1,3,2]
[7,6,4,1,5,2,8,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,1,5,4,7,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[5,2,1,4,6,7,8,3]=>1100001=>1000011=>[1,5,1,1]
[5,4,1,3,6,7,8,2]=>1100001=>1000011=>[1,5,1,1]
[8,4,1,5,3,7,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[7,5,4,1,3,2,8,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[3,2,5,1,4,7,8,6]=>1010001=>1000101=>[1,4,2,1]
[5,1,3,4,6,7,8,2]=>1000001=>1000001=>[1,6,1]
[3,8,1,7,5,6,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[8,2,5,7,3,6,4,1]=>1001011=>1101001=>[1,1,2,3,1]
[1,8,6,7,5,3,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[8,2,6,7,5,3,4,1]=>1001101=>1011001=>[1,2,1,3,1]
[5,4,8,6,2,3,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[2,7,6,1,3,5,4,8]=>0110010=>0100110=>[2,3,1,2]
[2,8,6,1,3,5,4,7]=>0110010=>0100110=>[2,3,1,2]
[5,7,4,1,8,6,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,6,4,2,8,3,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[5,6,4,2,7,3,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[5,8,1,4,6,3,7,2]=>0100101=>1010010=>[1,2,3,2]
[3,6,7,4,5,8,2,1]=>0010011=>1100100=>[1,1,3,3]
[5,4,6,1,7,8,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,6,4,1,8,7,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,5,8,4,6,7,2,1]=>0010011=>1100100=>[1,1,3,3]
[3,6,8,4,5,7,2,1]=>0010011=>1100100=>[1,1,3,3]
[3,7,8,4,5,6,2,1]=>0010011=>1100100=>[1,1,3,3]
[3,7,1,5,4,6,2,8]=>0101010=>0101010=>[2,2,2,2]
[3,8,1,5,4,6,7,2]=>0101001=>1001010=>[1,3,2,2]
[3,7,1,5,4,6,8,2]=>0101001=>1001010=>[1,3,2,2]
[6,7,1,4,5,3,8,2]=>0100101=>1010010=>[1,2,3,2]
[5,7,1,4,6,3,8,2]=>0100101=>1010010=>[1,2,3,2]
[5,4,7,2,8,3,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,4,7,2,8,3,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,6,4,2,8,3,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[5,8,1,4,6,3,2,7]=>0100110=>0110010=>[2,1,3,2]
[3,8,1,5,4,6,2,7]=>0101010=>0101010=>[2,2,2,2]
[3,6,1,5,4,2,7,8]=>0101100=>0011010=>[3,1,2,2]
[3,6,1,5,4,8,2,7]=>0101010=>0101010=>[2,2,2,2]
[6,8,3,1,4,2,5,7]=>0110100=>0010110=>[3,2,1,2]
[7,3,8,1,4,2,5,6]=>1010100=>0010101=>[3,2,2,1]
[3,6,1,5,4,7,8,2]=>0101001=>1001010=>[1,3,2,2]
[3,4,1,2,7,6,5,8]=>0100110=>0110010=>[2,1,3,2]
[3,4,1,2,6,8,7,5]=>0100011=>1100010=>[1,1,4,2]
[7,8,1,4,5,3,2,6]=>0100110=>0110010=>[2,1,3,2]
[3,8,1,5,4,7,2,6]=>0101010=>0101010=>[2,2,2,2]
[3,6,1,5,4,8,7,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,6,1,5,4,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,1,4,2,5,8]=>0110100=>0010110=>[3,2,1,2]
[6,8,3,1,4,2,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[7,8,3,1,4,6,2,5]=>0110010=>0100110=>[2,3,1,2]
[7,8,4,2,6,5,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[6,5,8,7,3,4,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,8,3,1,4,6,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,7,3,1,4,5,2,8]=>0110010=>0100110=>[2,3,1,2]
[3,7,1,5,4,2,6,8]=>0101100=>0011010=>[3,1,2,2]
[3,8,1,5,4,2,7,6]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,1,4,7,3,6,2]=>0100101=>1010010=>[1,2,3,2]
[6,3,7,1,4,8,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[3,7,1,5,4,8,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,7,1,5,4,2,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[6,7,3,1,4,5,8,2]=>0110001=>1000110=>[1,4,1,2]
[7,3,8,1,4,5,2,6]=>1010010=>0100101=>[2,3,2,1]
[6,8,3,1,4,5,2,7]=>0110010=>0100110=>[2,3,1,2]
[3,8,1,5,4,2,6,7]=>0101100=>0011010=>[3,1,2,2]
[2,3,5,4,1,8,6,7]=>0011010=>0101100=>[2,2,1,3]
[2,3,6,4,8,1,5,7]=>0010100=>0010100=>[3,2,3]
[1,8,4,6,3,5,2,7]=>0101010=>0101010=>[2,2,2,2]
[5,4,8,6,2,1,3,7]=>1011100=>0011101=>[3,1,1,2,1]
[2,3,6,8,1,5,4,7]=>0001010=>0101000=>[2,2,4]
[2,5,6,1,4,7,8,3]=>0010001=>1000100=>[1,4,3]
[2,5,6,1,4,7,3,8]=>0010010=>0100100=>[2,3,3]
[2,7,6,1,8,5,4,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,7,6,8,1,4,5,3]=>0101001=>1001010=>[1,3,2,2]
[5,7,8,6,2,3,4,1]=>0011001=>1001100=>[1,3,1,3]
[2,7,6,1,8,5,3,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,3,5,1,7,2,4,8]=>1010100=>0010101=>[3,2,2,1]
[2,3,4,7,6,1,5,8]=>0001100=>0011000=>[3,1,4]
[7,3,5,8,4,1,2,6]=>1001100=>0011001=>[3,1,3,1]
[1,8,4,5,2,7,3,6]=>0101010=>0101010=>[2,2,2,2]
[1,8,4,5,2,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[7,3,5,8,4,1,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[2,7,6,4,8,5,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[7,3,5,4,6,8,1,2]=>1010010=>0100101=>[2,3,2,1]
[6,3,5,4,7,1,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,5,4,7,1,2,8]=>1010100=>0010101=>[3,2,2,1]
[3,7,1,6,8,5,2,4]=>0100110=>0110010=>[2,1,3,2]
[2,3,1,8,6,4,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[1,8,4,3,6,2,5,7]=>0110100=>0010110=>[3,2,1,2]
[2,3,1,8,6,4,5,7]=>0101100=>0011010=>[3,1,2,2]
[3,7,1,6,8,5,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[6,3,5,4,7,2,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,5,4,6,8,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[2,7,6,4,8,5,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[1,8,4,5,2,6,3,7]=>0101010=>0101010=>[2,2,2,2]
[6,4,8,5,3,1,2,7]=>1011100=>0011101=>[3,1,1,2,1]
[7,3,5,8,4,6,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[2,3,4,6,5,8,1,7]=>0001010=>0101000=>[2,2,4]
[2,3,4,7,5,1,8,6]=>0001101=>1011000=>[1,2,1,4]
[2,3,4,7,5,1,6,8]=>0001100=>0011000=>[3,1,4]
[2,3,4,7,1,6,5,8]=>0001010=>0101000=>[2,2,4]
[2,3,4,7,1,6,8,5]=>0001001=>1001000=>[1,3,4]
[2,3,4,6,1,8,7,5]=>0001011=>1101000=>[1,1,2,4]
[6,3,5,8,4,2,7,1]=>1001101=>1011001=>[1,2,1,3,1]
[1,8,4,5,2,3,6,7]=>0101000=>0001010=>[4,2,2]
[7,4,8,5,3,2,6,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,4,8,7,5,2,6,1]=>0011101=>1011100=>[1,2,1,1,3]
[3,2,8,6,1,5,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,7,3,6,4,2,5,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,8,7,2,5,4,6,1]=>0110101=>1010110=>[1,2,2,1,2]
[8,7,2,4,5,6,3,1]=>1100011=>1100011=>[1,1,4,1,1]
[5,3,6,2,4,8,7,1]=>1010011=>1100101=>[1,1,3,2,1]
[3,5,2,8,6,1,4,7]=>0101100=>0011010=>[3,1,2,2]
[3,7,2,5,1,4,8,6]=>0101001=>1001010=>[1,3,2,2]
[5,1,8,6,2,3,4,7]=>1011000=>0001101=>[4,1,2,1]
[2,5,4,1,8,6,3,7]=>0110110=>0110110=>[2,1,2,1,2]
[3,7,6,1,8,2,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[8,2,3,6,1,4,7,5]=>1001001=>1001001=>[1,3,3,1]
[1,8,2,6,3,4,7,5]=>0101001=>1001010=>[1,3,2,2]
[7,1,3,6,4,8,2,5]=>1001010=>0101001=>[2,2,3,1]
[8,2,1,3,5,7,4,6]=>1100010=>0100011=>[2,4,1,1]
[7,5,4,1,3,8,2,6]=>1110010=>0100111=>[2,3,1,1,1]
[7,3,8,5,4,1,2,6]=>1011100=>0011101=>[3,1,1,2,1]
[7,2,3,6,1,4,8,5]=>1001001=>1001001=>[1,3,3,1]
[1,3,7,2,5,8,4,6]=>0010010=>0100100=>[2,3,3]
[1,7,2,3,5,8,4,6]=>0100010=>0100010=>[2,4,2]
[7,4,8,1,3,6,2,5]=>1010010=>0100101=>[2,3,2,1]
[8,6,1,4,7,3,2,5]=>1100110=>0110011=>[2,1,3,1,1]
[2,6,3,7,1,4,8,5]=>0101001=>1001010=>[1,3,2,2]
[2,6,3,8,1,4,7,5]=>0101001=>1001010=>[1,3,2,2]
[7,5,4,8,1,3,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,4,7,1,3,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[2,3,1,8,5,4,6,7]=>0101100=>0011010=>[3,1,2,2]
[8,5,1,7,6,3,4,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,4,7,6,1,8,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[3,5,2,6,7,1,8,4]=>0100101=>1010010=>[1,2,3,2]
[3,2,8,4,7,5,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,7,5,1,3,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,8,3,1,7,2,4,5]=>0110100=>0010110=>[3,2,1,2]
[3,7,2,5,6,1,8,4]=>0100101=>1010010=>[1,2,3,2]
[6,8,4,2,5,1,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,5,3,8,4,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[8,3,1,4,7,2,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[8,3,2,1,5,7,4,6]=>1110010=>0100111=>[2,3,1,1,1]
[2,8,3,6,4,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[7,3,6,4,8,1,2,5]=>1010100=>0010101=>[3,2,2,1]
[8,3,6,4,7,1,2,5]=>1010100=>0010101=>[3,2,2,1]
[1,2,8,3,5,7,4,6]=>0010010=>0100100=>[2,3,3]
[1,8,3,2,5,7,4,6]=>0110010=>0100110=>[2,3,1,2]
[6,5,1,7,4,2,8,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,3,6,4,8,2,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[4,6,1,7,3,5,2,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,1,7,3,4,2,8]=>0101010=>0101010=>[2,2,2,2]
[6,1,7,3,4,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,8,1,6,5,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[8,3,7,1,6,5,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[2,8,1,7,6,5,3,4]=>0101110=>0111010=>[2,1,1,2,2]
[4,2,8,6,5,1,7,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,6,4,7,1,5,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[7,6,4,8,1,5,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[5,1,6,4,2,3,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[4,2,3,8,7,5,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[3,8,7,1,6,5,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[2,4,3,8,1,6,7,5]=>0101001=>1001010=>[1,3,2,2]
[2,4,3,7,1,6,8,5]=>0101001=>1001010=>[1,3,2,2]
[4,2,3,7,8,5,1,6]=>1000110=>0110001=>[2,1,4,1]
[5,1,6,4,2,3,7,8]=>1011000=>0001101=>[4,1,2,1]
[6,4,7,8,1,5,2,3]=>1001010=>0101001=>[2,2,3,1]
[8,7,4,6,1,5,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,7,8,1,4,2,3]=>1001010=>0101001=>[2,2,3,1]
[4,7,8,6,1,5,2,3]=>0011010=>0101100=>[2,2,1,3]
[3,2,4,8,7,1,5,6]=>1001100=>0011001=>[3,1,3,1]
[4,8,7,6,1,5,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[5,8,7,6,1,4,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[8,6,5,7,1,4,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[5,1,6,7,4,2,3,8]=>1001100=>0011001=>[3,1,3,1]
[6,7,4,8,1,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[8,4,7,6,1,5,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,2,4,7,1,5,6]=>1100100=>0010011=>[3,3,1,1]
[7,3,2,4,8,1,5,6]=>1100100=>0010011=>[3,3,1,1]
[2,5,3,7,1,6,4,8]=>0101010=>0101010=>[2,2,2,2]
[8,4,6,7,1,5,2,3]=>1001010=>0101001=>[2,2,3,1]
[5,1,6,8,4,2,3,7]=>1001100=>0011001=>[3,1,3,1]
[4,2,3,7,5,1,6,8]=>1001100=>0011001=>[3,1,3,1]
[2,4,3,7,1,6,5,8]=>0101010=>0101010=>[2,2,2,2]
[2,4,7,1,5,8,6,3]=>0010011=>1100100=>[1,1,3,3]
[3,2,4,7,6,1,5,8]=>1001100=>0011001=>[3,1,3,1]
[4,7,6,8,1,5,2,3]=>0101010=>0101010=>[2,2,2,2]
[8,5,6,7,1,4,2,3]=>1001010=>0101001=>[2,2,3,1]
[8,6,7,5,1,4,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[6,8,7,5,1,4,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[5,6,8,7,1,4,2,3]=>0011010=>0101100=>[2,2,1,3]
[4,6,8,7,1,5,2,3]=>0011010=>0101100=>[2,2,1,3]
[3,2,4,6,1,5,7,8]=>1001000=>0001001=>[4,3,1]
[6,7,8,5,1,4,2,3]=>0011010=>0101100=>[2,2,1,3]
[7,8,6,5,1,4,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[2,1,8,5,4,6,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[4,1,8,5,2,3,6,7]=>1011000=>0001101=>[4,1,2,1]
[5,4,1,3,6,7,2,8]=>1100010=>0100011=>[2,4,1,1]
[8,4,1,2,6,3,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[8,2,7,1,5,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[3,2,7,1,5,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[7,3,8,1,5,4,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,1,5,3,8,4,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[3,6,8,1,5,4,2,7]=>0010110=>0110100=>[2,1,2,3]
[6,8,3,1,5,4,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[7,6,3,1,5,4,2,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[3,6,2,1,5,8,4,7]=>0110010=>0100110=>[2,3,1,2]
[8,6,2,1,5,3,4,7]=>1110100=>0010111=>[3,2,1,1,1]
[2,3,8,1,5,7,4,6]=>0010010=>0100100=>[2,3,3]
[7,1,3,2,8,6,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[4,7,1,2,6,3,8,5]=>0100101=>1010010=>[1,2,3,2]
[2,7,8,1,5,3,4,6]=>0010100=>0010100=>[3,2,3]
[6,7,2,1,5,3,4,8]=>0110100=>0010110=>[3,2,1,2]
[4,7,2,1,8,5,3,6]=>0110110=>0110110=>[2,1,2,1,2]
[8,7,2,1,4,5,3,6]=>1110010=>0100111=>[2,3,1,1,1]
[5,7,8,6,1,4,3,2]=>0011011=>1101100=>[1,1,2,1,3]
[2,7,4,1,6,5,3,8]=>0110110=>0110110=>[2,1,2,1,2]
[7,1,6,4,5,8,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[2,6,4,1,7,5,3,8]=>0110110=>0110110=>[2,1,2,1,2]
[5,6,8,7,1,4,3,2]=>0011011=>1101100=>[1,1,2,1,3]
[4,2,8,1,6,5,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,4,1,8,5,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,3,1,4,5,6,7,2]=>1100001=>1000011=>[1,5,1,1]
[5,3,1,4,8,6,7,2]=>1100101=>1010011=>[1,2,3,1,1]
[7,5,1,6,3,4,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[7,1,5,8,4,3,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[5,8,1,6,4,3,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[5,3,1,8,4,6,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[8,3,1,5,4,6,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[8,2,6,1,4,5,3,7]=>1010010=>0100101=>[2,3,2,1]
[6,2,8,1,4,5,3,7]=>1010010=>0100101=>[2,3,2,1]
[7,2,6,1,5,3,4,8]=>1010100=>0010101=>[3,2,2,1]
[2,8,6,1,5,3,4,7]=>0110100=>0010110=>[3,2,1,2]
[4,2,1,5,6,3,8,7]=>1100101=>1010011=>[1,2,3,1,1]
[7,1,2,5,8,3,4,6]=>1000100=>0010001=>[3,4,1]
[7,1,4,5,6,8,3,2]=>1000011=>1100001=>[1,1,5,1]
[2,6,7,1,4,5,3,8]=>0010010=>0100100=>[2,3,3]
[3,5,1,7,4,6,8,2]=>0101001=>1001010=>[1,3,2,2]
[7,1,5,6,4,8,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,6,5,4,8,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,7,6,1,4,5,3,8]=>0110010=>0100110=>[2,3,1,2]
[5,7,6,8,1,4,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[7,8,6,5,1,4,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,3,1,2,4,8,7,6]=>1100011=>1100011=>[1,1,4,1,1]
[5,3,6,2,1,8,7,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,3,7,2,8,4,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,4,5,8,3,1,6]=>1000110=>0110001=>[2,1,4,1]
[7,2,4,5,1,3,6,8]=>1001000=>0001001=>[4,3,1]
[6,2,4,5,1,8,7,3]=>1001011=>1101001=>[1,1,2,3,1]
[3,1,4,5,2,8,7,6]=>1001011=>1101001=>[1,1,2,3,1]
[1,6,4,5,2,8,7,3]=>0101011=>1101010=>[1,1,2,2,2]
[3,7,4,5,1,2,6,8]=>0101000=>0001010=>[4,2,2]
[1,7,4,2,6,3,5,8]=>0110100=>0010110=>[3,2,1,2]
[8,7,4,5,2,1,6,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,3,7,1,8,4,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[5,7,4,1,6,3,2,8]=>0110110=>0110110=>[2,1,2,1,2]
[1,7,4,8,6,3,2,5]=>0101110=>0111010=>[2,1,1,2,2]
[5,7,4,8,6,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[4,8,3,5,6,7,1,2]=>0100010=>0100010=>[2,4,2]
[1,8,3,5,6,7,2,4]=>0100010=>0100010=>[2,4,2]
[4,8,1,5,6,7,2,3]=>0100010=>0100010=>[2,4,2]
[4,1,3,5,6,7,2,8]=>1000010=>0100001=>[2,5,1]
[5,8,4,3,6,1,2,7]=>0110100=>0010110=>[3,2,1,2]
[5,3,8,4,1,7,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,5,8,4,6,7,3,2]=>0010011=>1100100=>[1,1,3,3]
[1,4,8,3,6,7,5,2]=>0010011=>1100100=>[1,1,3,3]
[4,3,8,2,1,7,5,6]=>1011010=>0101101=>[2,2,1,2,1]
[3,8,4,2,6,1,5,7]=>0110100=>0010110=>[3,2,1,2]
[3,8,1,5,6,7,4,2]=>0100011=>1100010=>[1,1,4,2]
[3,8,2,5,6,7,1,4]=>0100010=>0100010=>[2,4,2]
[8,2,1,5,6,7,4,3]=>1100011=>1100011=>[1,1,4,1,1]
[8,1,3,5,6,7,4,2]=>1000011=>1100001=>[1,1,5,1]
[7,1,4,3,6,2,5,8]=>1010100=>0010101=>[3,2,2,1]
[7,8,4,3,6,2,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[4,3,1,8,5,7,6,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,3,5,8,2,7,1,4]=>1001010=>0101001=>[2,2,3,1]
[7,5,4,8,6,2,1,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,1,4,8,6,2,3,5]=>1001100=>0011001=>[3,1,3,1]
[7,5,4,1,6,2,3,8]=>1110100=>0010111=>[3,2,1,1,1]
[1,6,4,5,8,2,3,7]=>0100100=>0010010=>[3,3,2]
[1,8,5,3,6,7,4,2]=>0110011=>1100110=>[1,1,3,1,2]
[8,3,5,2,1,7,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[4,1,8,5,6,7,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[1,2,8,5,6,7,3,4]=>0010010=>0100100=>[2,3,3]
[4,2,1,5,6,7,3,8]=>1100010=>0100011=>[2,4,1,1]
[1,5,3,8,6,7,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,4,8,5,6,7,2,3]=>0010010=>0100100=>[2,3,3]
[6,2,4,3,8,7,5,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,3,5,4,1,8,6,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,2,7,1,3,4,8,6]=>1010001=>1000101=>[1,4,2,1]
[2,6,5,7,3,1,4,8]=>0101100=>0011010=>[3,1,2,2]
[2,6,5,7,3,1,8,4]=>0101101=>1011010=>[1,2,1,2,2]
[6,3,1,4,7,8,5,2]=>1100011=>1100011=>[1,1,4,1,1]
[6,8,2,1,3,4,5,7]=>0110000=>0000110=>[5,1,2]
[3,7,1,8,4,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[6,3,2,4,7,5,8,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,3,2,4,7,5,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[4,2,1,6,3,7,5,8]=>1101010=>0101011=>[2,2,2,1,1]
[4,2,1,6,3,7,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[7,4,3,5,8,6,1,2]=>1100110=>0110011=>[2,1,3,1,1]
[2,7,6,8,3,1,4,5]=>0101100=>0011010=>[3,1,2,2]
[7,4,3,5,8,6,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[4,2,1,7,3,8,6,5]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,2,1,3,7,8,6,5]=>1100011=>1100011=>[1,1,4,1,1]
[5,8,1,7,4,3,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,1,7,4,3,2,6]=>0101110=>0111010=>[2,1,1,2,2]
[3,7,8,6,2,1,4,5]=>0011100=>0011100=>[3,1,1,3]
[4,2,1,8,3,5,6,7]=>1101000=>0001011=>[4,2,1,1]
[4,2,1,3,6,7,5,8]=>1100010=>0100011=>[2,4,1,1]
[4,2,1,3,7,5,6,8]=>1100100=>0010011=>[3,3,1,1]
[7,3,2,4,8,6,5,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[4,2,1,7,3,5,6,8]=>1101000=>0001011=>[4,2,1,1]
[3,6,7,5,2,1,4,8]=>0011100=>0011100=>[3,1,1,3]
[3,6,7,5,2,1,8,4]=>0011101=>1011100=>[1,2,1,1,3]
[7,3,4,2,6,8,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[4,8,6,2,7,3,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[7,3,4,2,6,8,1,5]=>1010010=>0100101=>[2,3,2,1]
[3,6,7,5,2,4,8,1]=>0011001=>1001100=>[1,3,1,3]
[3,6,7,5,2,4,1,8]=>0011010=>0101100=>[2,2,1,3]
[4,2,1,7,3,6,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[3,7,6,8,4,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,1,7,4,2,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[3,7,8,6,2,4,5,1]=>0011001=>1001100=>[1,3,1,3]
[4,2,1,3,8,6,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[4,2,1,3,5,7,6,8]=>1100010=>0100011=>[2,4,1,1]
[4,8,1,7,3,6,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,2,1,8,3,7,6,5]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,2,1,3,5,6,8,7]=>1100001=>1000011=>[1,5,1,1]
[7,8,2,4,1,3,6,5]=>0101001=>1001010=>[1,3,2,2]
[2,6,1,5,4,7,8,3]=>0101001=>1001010=>[1,3,2,2]
[4,6,3,5,8,7,1,2]=>0100110=>0110010=>[2,1,3,2]
[2,3,6,8,4,1,5,7]=>0001100=>0011000=>[3,1,4]
[2,7,5,1,8,3,4,6]=>0110100=>0010110=>[3,2,1,2]
[4,7,5,2,1,3,6,8]=>0111000=>0001110=>[4,1,1,2]
[3,5,6,2,4,1,7,8]=>0010100=>0010100=>[3,2,3]
[3,1,8,5,2,7,6,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,3,7,6,1,4,5,2]=>1011001=>1001101=>[1,3,1,2,1]
[3,1,7,8,2,5,6,4]=>1001001=>1001001=>[1,3,3,1]
[4,8,1,5,2,7,3,6]=>0101010=>0101010=>[2,2,2,2]
[4,1,2,5,3,8,7,6]=>1001011=>1101001=>[1,1,2,3,1]
[4,3,6,8,7,5,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[6,4,8,1,2,5,3,7]=>1010010=>0100101=>[2,3,2,1]
[6,7,3,1,4,8,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,5,1,2,3,4,8,7]=>1100001=>1000011=>[1,5,1,1]
[1,2,6,7,5,3,8,4]=>0001101=>1011000=>[1,2,1,4]
[1,7,5,3,2,8,4,6]=>0111010=>0101110=>[2,2,1,1,2]
[1,6,5,7,2,3,8,4]=>0101001=>1001010=>[1,3,2,2]
[1,3,8,2,6,5,7,4]=>0010101=>1010100=>[1,2,2,3]
[1,2,5,7,6,3,4,8]=>0001100=>0011000=>[3,1,4]
[1,3,4,8,2,5,7,6]=>0001001=>1001000=>[1,3,4]
[1,5,7,6,2,3,4,8]=>0011000=>0001100=>[4,1,3]
[1,5,3,8,2,6,4,7]=>0101010=>0101010=>[2,2,2,2]
[1,4,8,3,2,5,7,6]=>0011001=>1001100=>[1,3,1,3]
[1,2,4,8,3,5,7,6]=>0001001=>1001000=>[1,3,4]
[1,3,8,4,2,6,7,5]=>0011001=>1001100=>[1,3,1,3]
[1,4,8,2,3,5,7,6]=>0010001=>1000100=>[1,4,3]
[4,2,6,7,5,8,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,7,5,2,1,8,4,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,4,8,7,5,2,1,6]=>0011110=>0111100=>[2,1,1,1,3]
[1,7,5,2,8,4,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[5,6,8,3,1,7,2,4]=>0011010=>0101100=>[2,2,1,3]
[6,1,4,8,3,2,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[3,4,7,1,8,6,2,5]=>0010110=>0110100=>[2,1,2,3]
[3,4,6,8,2,1,5,7]=>0001100=>0011000=>[3,1,4]
[3,8,2,5,6,1,4,7]=>0100100=>0010010=>[3,3,2]
[3,5,2,8,6,4,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[4,2,5,7,3,8,6,1]=>1001011=>1101001=>[1,1,2,3,1]
[7,4,2,5,3,8,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[1,5,6,8,3,4,2,7]=>0001010=>0101000=>[2,2,4]
[4,5,1,6,8,3,2,7]=>0100110=>0110010=>[2,1,3,2]
[4,5,7,3,8,2,6,1]=>0010101=>1010100=>[1,2,2,3]
[6,4,3,7,8,2,5,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,4,3,1,7,8,2,5]=>1110010=>0100111=>[2,3,1,1,1]
[4,5,3,1,7,8,2,6]=>0110010=>0100110=>[2,3,1,2]
[7,1,3,5,4,8,2,6]=>1001010=>0101001=>[2,2,3,1]
[7,5,2,8,1,4,3,6]=>1101010=>0101011=>[2,2,2,1,1]
[1,4,5,7,3,8,6,2]=>0001011=>1101000=>[1,1,2,4]
[4,6,3,7,8,5,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[1,5,3,6,7,8,4,2]=>0100011=>1100010=>[1,1,4,2]
[4,6,1,7,3,8,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,2,4,8,1,5,3]=>0100101=>1010010=>[1,2,3,2]
[5,2,3,6,7,8,4,1]=>1000011=>1100001=>[1,1,5,1]
[6,4,2,7,1,8,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[4,2,6,3,7,8,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[6,7,3,8,2,4,5,1]=>0101001=>1001010=>[1,3,2,2]
[3,6,2,7,4,1,8,5]=>0101101=>1011010=>[1,2,1,2,2]
[6,7,3,2,1,4,8,5]=>0111001=>1001110=>[1,3,1,1,2]
[7,2,4,8,6,1,3,5]=>1001100=>0011001=>[3,1,3,1]
[3,5,7,2,1,8,6,4]=>0011011=>1101100=>[1,1,2,1,3]
[6,7,8,3,2,5,1,4]=>0011010=>0101100=>[2,2,1,3]
[6,3,7,8,2,5,4,1]=>1001011=>1101001=>[1,1,2,3,1]
[2,6,7,4,8,5,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[6,2,4,7,1,8,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[1,7,4,8,5,2,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[1,3,7,8,5,2,6,4]=>0001101=>1011000=>[1,2,1,4]
[2,5,7,8,1,6,3,4]=>0001010=>0101000=>[2,2,4]
[1,6,4,7,8,2,5,3]=>0100101=>1010010=>[1,2,3,2]
[2,5,6,1,7,8,4,3]=>0010011=>1100100=>[1,1,3,3]
[5,6,1,2,7,8,4,3]=>0100011=>1100010=>[1,1,4,2]
[6,7,2,1,8,5,3,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,4,5,2,3,8,7,1]=>1010011=>1100101=>[1,1,3,2,1]
[4,6,5,2,3,1,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[6,4,2,5,3,1,8,7]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,4,2,5,3,8,7,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,6,4,7,5,2,3,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,6,2,7,4,5,3,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,4,2,5,8,7,3,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[4,6,5,2,3,8,7,1]=>0110011=>1100110=>[1,1,3,1,2]
[6,8,2,7,4,5,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[8,6,4,7,2,5,3,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,6,2,4,7,5,3,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,8,2,4,7,5,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[4,8,2,6,7,5,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,8,4,6,7,5,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,8,6,7,4,5,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,8,7,2,4,5,3,1]=>0110011=>1100110=>[1,1,3,1,2]
[2,6,4,5,8,7,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,6,4,8,7,5,3,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[4,6,2,8,7,5,3,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[8,2,4,6,7,5,3,1]=>1000111=>1110001=>[1,1,1,4,1]
[6,2,4,8,7,5,3,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[4,2,6,8,7,5,3,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[4,2,6,5,8,7,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,2,4,5,8,7,3,1]=>1000111=>1110001=>[1,1,1,4,1]
[8,2,6,7,4,5,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[8,6,7,2,4,5,3,1]=>1010011=>1100101=>[1,1,3,2,1]
[6,4,5,8,7,2,3,1]=>1001101=>1011001=>[1,2,1,3,1]
[8,6,7,4,2,5,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,4,6,7,2,5,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[6,4,8,7,2,5,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,2,8,7,4,5,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,6,5,8,7,2,3,1]=>0101101=>1011010=>[1,2,1,2,2]
[2,1,6,8,7,4,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[2,6,8,7,4,5,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,4,8,6,7,5,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[6,2,8,4,7,5,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,2,6,4,7,5,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,6,8,2,7,5,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[2,6,8,4,7,5,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,6,8,7,2,5,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,6,5,8,2,7,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,6,8,4,7,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[2,1,8,6,4,7,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,8,7,4,2,5,3,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,8,6,4,7,5,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,8,6,2,7,5,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,7,8,5,6,1,2,4]=>0010100=>0010100=>[3,2,3]
[3,6,1,8,4,7,2,5]=>0101010=>0101010=>[2,2,2,2]
[3,1,6,8,4,7,2,5]=>1001010=>0101001=>[2,2,3,1]
[4,1,6,8,3,2,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[4,6,1,8,3,2,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,8,1,3,2,6,5]=>0010101=>1010100=>[1,2,2,3]
[4,7,8,3,1,2,6,5]=>0011001=>1001100=>[1,3,1,3]
[2,7,8,3,4,6,5,1]=>0010011=>1100100=>[1,1,3,3]
[4,7,8,2,1,3,6,5]=>0011001=>1001100=>[1,3,1,3]
[4,6,1,8,2,3,7,5]=>0101001=>1001010=>[1,3,2,2]
[4,5,2,1,8,3,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,2,8,1,3,7,5]=>0101001=>1001010=>[1,3,2,2]
[3,6,2,8,4,7,1,5]=>0101010=>0101010=>[2,2,2,2]
[2,3,6,8,4,7,5,1]=>0001011=>1101000=>[1,1,2,4]
[3,2,6,8,4,7,1,5]=>1001010=>0101001=>[2,2,3,1]
[4,2,6,8,3,1,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[4,2,5,1,8,3,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,2,4,3,8,7,6]=>1001011=>1101001=>[1,1,2,3,1]
[5,2,4,1,3,8,7,6]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,5,3,8,1,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,5,4,8,7,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[3,5,2,4,8,7,1,6]=>0100110=>0110010=>[2,1,3,2]
[5,1,4,2,3,8,7,6]=>1010011=>1100101=>[1,1,3,2,1]
[5,4,3,1,2,8,7,6]=>1110011=>1100111=>[1,1,3,1,1,1]
[4,5,3,1,8,2,7,6]=>0110101=>1010110=>[1,2,2,1,2]
[4,5,1,3,8,2,7,6]=>0100101=>1010010=>[1,2,3,2]
[3,1,5,4,8,7,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[3,5,4,1,8,7,2,6]=>0110110=>0110110=>[2,1,2,1,2]
[3,6,5,8,7,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[3,4,1,5,8,7,2,6]=>0100110=>0110010=>[2,1,3,2]
[4,1,3,5,8,2,7,6]=>1000101=>1010001=>[1,2,4,1]
[4,3,6,8,2,1,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[2,4,6,8,3,7,5,1]=>0001011=>1101000=>[1,1,2,4]
[3,4,5,2,8,7,1,6]=>0010110=>0110100=>[2,1,2,3]
[5,3,1,4,2,8,7,6]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,1,3,4,2,8,7,6]=>1001011=>1101001=>[1,1,2,3,1]
[5,1,3,2,4,8,7,6]=>1010011=>1100101=>[1,1,3,2,1]
[5,3,2,1,4,8,7,6]=>1110011=>1100111=>[1,1,3,1,1,1]
[4,3,2,5,8,1,7,6]=>1100101=>1010011=>[1,2,3,1,1]
[3,4,2,5,8,7,1,6]=>0100110=>0110010=>[2,1,3,2]
[3,2,4,5,8,7,1,6]=>1000110=>0110001=>[2,1,4,1]
[4,2,3,5,8,1,7,6]=>1000101=>1010001=>[1,2,4,1]
[5,2,3,1,4,8,7,6]=>1010011=>1100101=>[1,1,3,2,1]
[5,2,1,3,4,8,7,6]=>1100011=>1100011=>[1,1,4,1,1]
[1,7,2,3,5,6,8,4]=>0100001=>1000010=>[1,5,2]
[3,7,4,2,1,5,6,8]=>0111000=>0001110=>[4,1,1,2]
[3,4,6,2,8,5,7,1]=>0010101=>1010100=>[1,2,2,3]
[4,2,1,7,5,8,3,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,7,2,6,5,1,3,8]=>0101100=>0011010=>[3,1,2,2]
[3,7,4,1,2,5,8,6]=>0110001=>1000110=>[1,4,1,2]
[4,7,1,6,5,2,8,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,3,6,5,1,8,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,3,7,1,6,8,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,1,7,5,6,8,3]=>1101001=>1001011=>[1,3,2,1,1]
[4,2,6,8,7,3,1,5]=>1001110=>0111001=>[2,1,1,3,1]
[3,4,6,1,8,5,2,7]=>0010110=>0110100=>[2,1,2,3]
[4,1,6,7,5,8,2,3]=>1001010=>0101001=>[2,2,3,1]
[4,3,6,7,5,1,2,8]=>1001100=>0011001=>[3,1,3,1]
[4,3,7,1,6,8,2,5]=>1010010=>0100101=>[2,3,2,1]
[4,3,7,5,6,8,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[4,1,7,3,6,5,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[2,8,7,4,5,3,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[2,8,7,4,3,5,1,6]=>0111010=>0101110=>[2,2,1,1,2]
[4,1,7,3,6,2,5,8]=>1010100=>0010101=>[3,2,2,1]
[5,8,7,6,1,2,4,3]=>0111001=>1001110=>[1,3,1,1,2]
[4,1,7,2,6,8,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,7,3,6,1,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,7,3,6,5,8,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,8,5,6,2,4,1,7]=>0101010=>0101010=>[2,2,2,2]
[2,8,6,5,3,7,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[3,8,6,5,1,4,7,2]=>0111001=>1001110=>[1,3,1,1,2]
[3,8,2,1,4,6,7,5]=>0110001=>1000110=>[1,4,1,2]
[3,8,2,5,4,6,7,1]=>0101001=>1001010=>[1,3,2,2]
[4,2,6,7,5,3,1,8]=>1001110=>0111001=>[2,1,1,3,1]
[3,2,6,1,4,5,8,7]=>1010001=>1000101=>[1,4,2,1]
[2,8,7,3,4,5,1,6]=>0110010=>0100110=>[2,3,1,2]
[5,8,7,6,1,3,4,2]=>0111001=>1001110=>[1,3,1,1,2]
[5,8,7,6,2,3,4,1]=>0111001=>1001110=>[1,3,1,1,2]
[4,1,7,5,6,2,3,8]=>1010100=>0010101=>[3,2,2,1]
[3,8,1,5,2,6,4,7]=>0101010=>0101010=>[2,2,2,2]
[2,8,7,5,3,4,1,6]=>0111010=>0101110=>[2,2,1,1,2]
[2,8,7,5,4,3,1,6]=>0111110=>0111110=>[2,1,1,1,1,2]
[4,1,7,5,6,3,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,8,7,6,1,3,2,4]=>0111010=>0101110=>[2,2,1,1,2]
[5,8,7,6,4,1,2,3]=>0111100=>0011110=>[3,1,1,1,2]
[8,1,7,2,4,5,3,6]=>1010010=>0100101=>[2,3,2,1]
[8,1,3,6,2,5,4,7]=>1001010=>0101001=>[2,2,3,1]
[7,2,1,6,3,5,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[2,7,1,6,3,5,4,8]=>0101010=>0101010=>[2,2,2,2]
[2,7,1,5,4,3,6,8]=>0101100=>0011010=>[3,1,2,2]
[7,2,1,5,4,3,6,8]=>1101100=>0011011=>[3,1,2,1,1]
[8,1,3,5,4,2,6,7]=>1001100=>0011001=>[3,1,3,1]
[8,1,5,3,4,2,6,7]=>1010100=>0010101=>[3,2,2,1]
[8,1,5,6,2,3,7,4]=>1001001=>1001001=>[1,3,3,1]
[8,1,4,5,3,2,6,7]=>1001100=>0011001=>[3,1,3,1]
[8,1,4,3,5,2,6,7]=>1010100=>0010101=>[3,2,2,1]
[7,2,1,4,5,3,6,8]=>1100100=>0010011=>[3,3,1,1]
[2,7,1,4,5,3,6,8]=>0100100=>0010010=>[3,3,2]
[2,6,3,1,5,4,7,8]=>0110100=>0010110=>[3,2,1,2]
[6,3,2,1,5,4,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[7,3,1,4,5,2,6,8]=>1100100=>0010011=>[3,3,1,1]
[7,3,1,5,4,2,6,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,3,1,6,2,5,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[3,7,1,6,2,5,4,8]=>0101010=>0101010=>[2,2,2,2]
[3,7,1,4,5,2,6,8]=>0100100=>0010010=>[3,3,2]
[2,3,6,1,5,4,7,8]=>0010100=>0010100=>[3,2,3]
[6,3,4,1,5,2,7,8]=>1010100=>0010101=>[3,2,2,1]
[6,2,4,1,5,3,7,8]=>1010100=>0010101=>[3,2,2,1]
[2,6,4,1,5,3,7,8]=>0110100=>0010110=>[3,2,1,2]
[2,6,5,1,3,7,4,8]=>0110010=>0100110=>[2,3,1,2]
[6,5,2,1,3,7,4,8]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,1,2,4,5,3,8]=>1100010=>0100011=>[2,4,1,1]
[6,7,1,2,8,3,5,4]=>0100101=>1010010=>[1,2,3,2]
[6,7,1,2,5,4,3,8]=>0100110=>0110010=>[2,1,3,2]
[5,6,2,1,3,7,4,8]=>0110010=>0100110=>[2,3,1,2]
[5,2,6,1,3,7,4,8]=>1010010=>0100101=>[2,3,2,1]
[2,4,6,1,5,3,7,8]=>0010100=>0010100=>[3,2,3]
[4,7,1,3,5,2,6,8]=>0100100=>0010010=>[3,3,2]
[4,7,1,5,3,2,6,8]=>0101100=>0011010=>[3,1,2,2]
[5,7,1,6,2,3,8,4]=>0101001=>1001010=>[1,3,2,2]
[5,6,3,1,2,7,4,8]=>0110010=>0100110=>[2,3,1,2]
[4,2,5,3,1,6,7,8]=>1011000=>0001101=>[4,1,2,1]
[8,5,6,2,7,1,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,1,2,7,8,4,3]=>1100011=>1100011=>[1,1,4,1,1]
[4,7,6,1,5,3,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,7,6,4,1,3,8,2]=>0111001=>1001110=>[1,3,1,1,2]
[7,6,2,4,5,3,8,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,1,7,5,3,8,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,6,7,5,3,1,4,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,5,2,7,1,6,4,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,6,2,4,7,8,1,3]=>0100010=>0100010=>[2,4,2]
[3,4,8,6,7,1,5,2]=>0010101=>1010100=>[1,2,2,3]
[4,8,5,6,7,2,3,1]=>0100101=>1010010=>[1,2,3,2]
[5,8,6,4,1,2,7,3]=>0111001=>1001110=>[1,3,1,1,2]
[5,8,7,3,2,6,4,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,8,1,7,2,6,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[8,1,5,7,2,6,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,7,2,5,6,3,4]=>1010010=>0100101=>[2,3,2,1]
[6,8,7,2,5,1,3,4]=>0110100=>0010110=>[3,2,1,2]
[5,8,7,2,1,6,3,4]=>0111010=>0101110=>[2,2,1,1,2]
[4,8,1,5,2,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[3,7,8,5,1,6,2,4]=>0011010=>0101100=>[2,2,1,3]
[6,5,2,7,8,1,4,3]=>1100101=>1010011=>[1,2,3,1,1]
[7,1,2,8,5,6,3,4]=>1001010=>0101001=>[2,2,3,1]
[8,7,2,1,5,6,3,4]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,7,1,5,2,3,4]=>1010100=>0010101=>[3,2,2,1]
[6,1,7,8,5,2,3,4]=>1001100=>0011001=>[3,1,3,1]
[7,5,6,2,1,8,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,7,5,2,1,6,4,3]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[7,1,3,5,8,6,2,4]=>1000110=>0110001=>[2,1,4,1]
[5,1,3,4,6,8,7,2]=>1000011=>1100001=>[1,1,5,1]
[8,4,3,1,2,6,7,5]=>1110001=>1000111=>[1,4,1,1,1]
[8,5,1,6,3,4,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[5,1,8,6,3,4,7,2]=>1011001=>1001101=>[1,3,1,2,1]
[4,6,8,1,5,3,7,2]=>0010101=>1010100=>[1,2,2,3]
[6,4,5,8,3,2,7,1]=>1001101=>1011001=>[1,2,1,3,1]
[3,6,4,8,7,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,5,8,1,3,4,7,2]=>1010001=>1000101=>[1,4,2,1]
[6,1,8,3,5,2,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,6,8,3,5,2,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[8,6,1,3,5,2,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[8,7,1,3,5,6,2,4]=>1100010=>0100011=>[2,4,1,1]
[5,8,2,4,3,6,7,1]=>0101001=>1001010=>[1,3,2,2]
[5,8,2,3,1,6,7,4]=>0101001=>1001010=>[1,3,2,2]
[6,8,2,3,5,1,7,4]=>0100101=>1010010=>[1,2,3,2]
[7,8,2,3,5,6,1,4]=>0100010=>0100010=>[2,4,2]
[8,6,5,1,4,3,7,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,4,8,6,1,3,7,5]=>0011001=>1001100=>[1,3,1,3]
[6,7,1,8,4,3,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,7,8,6,1,4,3,5]=>0011010=>0101100=>[2,2,1,3]
[2,7,3,8,1,6,4,5]=>0101010=>0101010=>[2,2,2,2]
[7,5,1,8,2,4,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[2,7,8,4,1,6,3,5]=>0011010=>0101100=>[2,2,1,3]
[2,6,5,4,1,3,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[4,1,7,6,3,8,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[4,8,2,5,7,6,3,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,4,6,5,1,8,2,7]=>0011010=>0101100=>[2,2,1,3]
[4,6,1,5,2,3,8,7]=>0101001=>1001010=>[1,3,2,2]
[2,6,7,5,1,8,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[7,6,5,2,8,3,4,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,4,7,6,5,8,1,3]=>0011010=>0101100=>[2,2,1,3]
[2,1,4,8,7,6,3,5]=>1001110=>0111001=>[2,1,1,3,1]
[8,1,3,5,7,4,6,2]=>1000101=>1010001=>[1,2,4,1]
[3,2,8,7,5,1,6,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,8,5,1,6,7,2,3]=>0110010=>0100110=>[2,3,1,2]
[7,8,6,1,3,5,2,4]=>0110010=>0100110=>[2,3,1,2]
[2,5,1,8,6,7,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,1,8,6,7,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[8,3,5,4,6,7,1,2]=>1010010=>0100101=>[2,3,2,1]
[5,1,3,8,6,7,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[5,6,3,2,8,1,4,7]=>0110100=>0010110=>[3,2,1,2]
[8,1,6,3,5,2,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[4,7,6,8,3,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[2,7,5,8,1,3,4,6]=>0101000=>0001010=>[4,2,2]
[8,1,3,7,5,2,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[3,4,8,7,5,1,6,2]=>0011101=>1011100=>[1,2,1,1,3]
[6,3,8,1,4,2,5,7]=>1010100=>0010101=>[3,2,2,1]
[3,6,8,2,4,1,7,5]=>0010101=>1010100=>[1,2,2,3]
[4,5,8,2,6,7,3,1]=>0010011=>1100100=>[1,1,3,3]
[2,5,8,4,6,7,3,1]=>0010011=>1100100=>[1,1,3,3]
[8,4,3,2,6,7,1,5]=>1110010=>0100111=>[2,3,1,1,1]
[4,2,8,1,6,7,3,5]=>1010010=>0100101=>[2,3,2,1]
[2,4,8,1,6,7,3,5]=>0010010=>0100100=>[2,3,3]
[5,1,8,2,6,7,3,4]=>1010010=>0100101=>[2,3,2,1]
[3,4,8,7,2,1,5,6]=>0011100=>0011100=>[3,1,1,3]
[5,8,4,1,6,7,2,3]=>0110010=>0100110=>[2,3,1,2]
[3,8,1,4,6,7,2,5]=>0100010=>0100010=>[2,4,2]
[1,6,4,5,2,3,7,8]=>0101000=>0001010=>[4,2,2]
[1,7,4,5,2,3,6,8]=>0101000=>0001010=>[4,2,2]
[1,6,3,5,2,4,7,8]=>0101000=>0001010=>[4,2,2]
[1,6,3,4,2,5,7,8]=>0101000=>0001010=>[4,2,2]
[1,7,3,4,2,5,6,8]=>0101000=>0001010=>[4,2,2]
[1,8,5,7,3,4,2,6]=>0101010=>0101010=>[2,2,2,2]
[1,7,3,4,2,6,5,8]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,8,4,7,3,6]=>0101010=>0101010=>[2,2,2,2]
[1,4,2,8,5,7,3,6]=>0101010=>0101010=>[2,2,2,2]
[1,7,3,5,2,6,4,8]=>0101010=>0101010=>[2,2,2,2]
[1,8,4,7,3,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[1,7,3,6,2,5,4,8]=>0101010=>0101010=>[2,2,2,2]
[1,7,3,6,2,4,5,8]=>0101000=>0001010=>[4,2,2]
[1,7,4,6,2,3,5,8]=>0101000=>0001010=>[4,2,2]
[1,8,5,6,2,3,4,7]=>0101000=>0001010=>[4,2,2]
[1,8,5,6,2,4,3,7]=>0101010=>0101010=>[2,2,2,2]
[1,3,2,8,5,6,4,7]=>0101010=>0101010=>[2,2,2,2]
[1,4,2,8,5,6,3,7]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,8,4,6,3,7]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,8,4,5,3,7]=>0101010=>0101010=>[2,2,2,2]
[8,6,4,7,2,1,3,5]=>1101100=>0011011=>[3,1,2,1,1]
[3,8,6,2,4,5,1,7]=>0110010=>0100110=>[2,3,1,2]
[1,7,6,4,8,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[5,8,7,4,1,2,3,6]=>0111000=>0001110=>[4,1,1,2]
[6,8,3,7,2,1,4,5]=>0101100=>0011010=>[3,1,2,2]
[6,1,3,7,4,8,2,5]=>1001010=>0101001=>[2,2,3,1]
[7,1,6,4,8,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[3,8,7,5,1,2,4,6]=>0111000=>0001110=>[4,1,1,2]
[3,7,6,1,2,4,5,8]=>0110000=>0000110=>[5,1,2]
[4,7,6,1,2,3,5,8]=>0110000=>0000110=>[5,1,2]
[8,5,7,4,1,2,3,6]=>1011000=>0001101=>[4,1,2,1]
[8,6,2,3,1,7,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[1,7,2,8,6,3,4,5]=>0101100=>0011010=>[3,1,2,2]
[7,5,8,1,3,6,2,4]=>1010010=>0100101=>[2,3,2,1]
[5,4,1,8,2,3,6,7]=>1101000=>0001011=>[4,2,1,1]
[1,4,8,7,2,3,5,6]=>0011000=>0001100=>[4,1,3]
[1,5,8,7,2,3,4,6]=>0011000=>0001100=>[4,1,3]
[5,7,1,3,8,2,4,6]=>0100100=>0010010=>[3,3,2]
[7,1,5,8,6,2,3,4]=>1001100=>0011001=>[3,1,3,1]
[5,1,8,7,2,3,4,6]=>1011000=>0001101=>[4,1,2,1]
[7,1,5,8,3,4,2,6]=>1001010=>0101001=>[2,2,3,1]
[7,1,4,3,2,5,6,8]=>1011000=>0001101=>[4,1,2,1]
[6,4,2,3,8,5,7,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,4,2,7,5,8,3,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,1,4,6,5,2,3,8]=>1001100=>0011001=>[3,1,3,1]
[7,1,4,6,5,8,2,3]=>1001010=>0101001=>[2,2,3,1]
[7,1,4,6,3,8,2,5]=>1001010=>0101001=>[2,2,3,1]
[7,1,4,3,2,5,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[7,1,4,6,5,2,8,3]=>1001101=>1011001=>[1,2,1,3,1]
[7,1,4,6,5,3,8,2]=>1001101=>1011001=>[1,2,1,3,1]
[7,1,4,6,5,3,2,8]=>1001110=>0111001=>[2,1,1,3,1]
[6,4,2,7,5,3,8,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,4,7,2,6,8,5,1]=>0010011=>1100100=>[1,1,3,3]
[3,4,7,1,6,8,2,5]=>0010010=>0100100=>[2,3,3]
[3,4,7,1,6,8,5,2]=>0010011=>1100100=>[1,1,3,3]
[2,4,1,7,5,3,6,8]=>0101100=>0011010=>[3,1,2,2]
[3,4,1,7,8,6,2,5]=>0100110=>0110010=>[2,1,3,2]
[6,4,2,3,8,5,1,7]=>1100110=>0110011=>[2,1,3,1,1]
[6,4,2,7,5,3,1,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,4,7,2,6,8,1,5]=>0010010=>0100100=>[2,3,3]
[5,4,7,3,6,8,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[3,4,7,2,6,5,1,8]=>0010110=>0110100=>[2,1,2,3]
[4,8,7,3,5,1,2,6]=>0110100=>0010110=>[3,2,1,2]
[4,8,7,1,3,5,2,6]=>0110010=>0100110=>[2,3,1,2]
[4,8,3,1,2,6,5,7]=>0110010=>0100110=>[2,3,1,2]
[3,4,7,1,6,2,5,8]=>0010100=>0010100=>[3,2,3]
[3,4,7,1,6,2,8,5]=>0010101=>1010100=>[1,2,2,3]
[3,4,7,2,6,5,8,1]=>0010101=>1010100=>[1,2,2,3]
[4,8,3,1,2,6,7,5]=>0110001=>1000110=>[1,4,1,2]
[5,8,1,6,3,4,2,7]=>0101010=>0101010=>[2,2,2,2]
[6,8,5,1,3,7,2,4]=>0110010=>0100110=>[2,3,1,2]
[6,8,5,1,3,4,7,2]=>0110001=>1000110=>[1,4,1,2]
[5,8,3,4,2,6,7,1]=>0101001=>1001010=>[1,3,2,2]
[6,4,3,7,5,1,2,8]=>1101100=>0011011=>[3,1,2,1,1]
[3,8,7,4,1,5,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[2,4,7,3,6,1,5,8]=>0010100=>0010100=>[3,2,3]
[5,8,3,2,1,6,4,7]=>0111010=>0101110=>[2,2,1,1,2]
[5,8,7,4,3,1,2,6]=>0111100=>0011110=>[3,1,1,1,2]
[5,3,6,2,4,7,8,1]=>1010001=>1000101=>[1,4,2,1]
[5,3,6,1,4,8,7,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,3,7,2,4,6,8,1]=>1010001=>1000101=>[1,4,2,1]
[4,2,1,5,8,6,3,7]=>1100110=>0110011=>[2,1,3,1,1]
[4,2,1,5,8,6,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[4,3,1,5,7,8,6,2]=>1100011=>1100011=>[1,1,4,1,1]
[4,3,1,7,5,8,6,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,7,3,1,4,8,2,5]=>0110010=>0100110=>[2,3,1,2]
[5,3,7,1,4,8,2,6]=>1010010=>0100101=>[2,3,2,1]
[4,3,1,5,7,8,2,6]=>1100010=>0100011=>[2,4,1,1]
[3,2,1,8,5,4,6,7]=>1101100=>0011011=>[3,1,2,1,1]
[3,2,1,8,5,7,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,7,2,1,8,4,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,2,1,8,5,6,4,7]=>1101010=>0101011=>[2,2,2,1,1]
[4,3,1,6,7,8,5,2]=>1100011=>1100011=>[1,1,4,1,1]
[4,2,1,6,8,5,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[4,2,1,6,8,5,3,7]=>1100110=>0110011=>[2,1,3,1,1]
[5,2,6,1,8,4,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,6,1,8,7,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,6,1,8,3,4,7]=>1010100=>0010101=>[3,2,2,1]
[4,2,1,6,8,3,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[4,3,1,6,7,8,2,5]=>1100010=>0100011=>[2,4,1,1]
[4,2,1,7,8,6,3,5]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,1,8,6,4,7,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,2,1,8,6,4,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[3,2,1,8,4,6,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[3,2,1,8,4,6,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[4,2,1,7,8,3,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[5,2,7,1,8,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,2,1,8,3,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,2,7,1,8,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[4,2,1,7,8,3,5,6]=>1100100=>0010011=>[3,3,1,1]
[3,2,1,8,4,5,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[7,4,8,6,2,5,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,3,8,6,2,4,5,1]=>1011001=>1001101=>[1,3,1,2,1]
[7,4,3,1,8,2,5,6]=>1110100=>0010111=>[3,2,1,1,1]
[7,4,2,8,5,6,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[7,3,8,5,2,4,6,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,3,8,2,4,5,1,7]=>1010010=>0100101=>[2,3,2,1]
[6,3,8,2,5,7,4,1]=>1010011=>1100101=>[1,1,3,2,1]
[5,6,7,3,8,2,4,1]=>0010101=>1010100=>[1,2,2,3]
[5,3,8,2,4,6,7,1]=>1010001=>1000101=>[1,4,2,1]
[6,3,8,2,4,7,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[5,7,4,2,6,8,1,3]=>0110010=>0100110=>[2,3,1,2]
[6,5,3,1,4,2,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[5,7,4,2,6,1,3,8]=>0110100=>0010110=>[3,2,1,2]
[5,6,4,2,3,8,1,7]=>0110010=>0100110=>[2,3,1,2]
[5,6,3,7,8,2,4,1]=>0100101=>1010010=>[1,2,3,2]
[5,6,3,8,2,4,7,1]=>0101001=>1001010=>[1,3,2,2]
[6,3,7,2,4,5,1,8]=>1010010=>0100101=>[2,3,2,1]
[6,3,7,2,5,8,4,1]=>1010011=>1100101=>[1,1,3,2,1]
[5,3,6,8,2,4,7,1]=>1001001=>1001001=>[1,3,3,1]
[5,4,6,2,3,8,1,7]=>1010010=>0100101=>[2,3,2,1]
[5,3,6,7,8,2,4,1]=>1000101=>1010001=>[1,2,4,1]
[3,6,4,2,1,5,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[3,5,8,6,4,2,1,7]=>0011110=>0111100=>[2,1,1,1,3]
[5,8,6,3,4,2,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[5,6,3,4,2,1,8,7]=>0101101=>1011010=>[1,2,1,2,2]
[6,3,4,2,1,5,8,7]=>1011001=>1001101=>[1,3,1,2,1]
[5,6,4,2,1,3,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[2,7,8,5,4,1,6,3]=>0011101=>1011100=>[1,2,1,1,3]
[2,8,5,4,1,6,3,7]=>0111010=>0101110=>[2,2,1,1,2]
[2,6,3,8,5,4,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[2,8,6,3,5,4,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[5,8,6,4,2,1,3,7]=>0111100=>0011110=>[3,1,1,1,2]
[4,2,1,5,7,8,6,3]=>1100011=>1100011=>[1,1,4,1,1]
[2,7,8,6,3,5,4,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,3,8,5,7,6,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,1,8,5,6,4,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,1,8,5,6,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,4,2,1,8,5,7]=>1011010=>0101101=>[2,2,1,2,1]
[3,8,5,6,4,2,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[3,6,4,2,1,8,5,7]=>0111010=>0101110=>[2,2,1,1,2]
[8,5,3,7,6,2,4,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,6,2,4,1,8,5,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,4,1,7,6,2,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,6,2,3,8,5,4,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[2,1,7,8,6,4,3,5]=>1001110=>0111001=>[2,1,1,3,1]
[2,1,6,4,3,7,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[6,3,7,8,4,2,1,5]=>1001110=>0111001=>[2,1,1,3,1]
[7,8,4,2,1,6,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[5,7,6,2,3,8,4,1]=>0110011=>1100110=>[1,1,3,1,2]
[2,6,1,8,4,3,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,1,7,5,8,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[8,4,2,3,7,5,6,1]=>1100101=>1010011=>[1,2,3,1,1]
[8,5,7,6,2,1,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,8,5,7,6,2,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[4,7,6,2,1,3,8,5]=>0111001=>1001110=>[1,3,1,1,2]
[7,5,6,1,8,4,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[2,7,5,8,4,3,6,1]=>0101101=>1011010=>[1,2,1,2,2]
[2,8,4,3,6,1,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[8,4,2,6,3,1,7,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,5,3,7,4,2,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[1,6,7,3,4,2,8,5]=>0010101=>1010100=>[1,2,2,3]
[8,6,5,2,3,1,7,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[1,7,6,3,4,2,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[1,8,6,3,2,5,7,4]=>0111001=>1001110=>[1,3,1,1,2]
[8,7,5,2,1,4,6,3]=>1111001=>1001111=>[1,3,1,1,1,1]
[7,8,5,2,1,4,6,3]=>0111001=>1001110=>[1,3,1,1,2]
[6,8,5,2,3,1,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,6,2,3,1,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,2,6,3,1,7,5]=>0101101=>1011010=>[1,2,1,2,2]
[3,2,8,6,4,1,7,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,2,1,7,5,4,8,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,1,3,7,5,2,8,6]=>1001101=>1011001=>[1,2,1,3,1]
[7,1,6,3,2,5,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[1,2,7,4,3,6,8,5]=>0011001=>1001100=>[1,3,1,3]
[6,1,8,2,4,5,7,3]=>1010001=>1000101=>[1,4,2,1]
[5,1,8,3,2,6,7,4]=>1011001=>1001101=>[1,3,1,2,1]
[4,8,2,7,1,5,6,3]=>0101001=>1001010=>[1,3,2,2]
[5,8,7,2,1,4,6,3]=>0111001=>1001110=>[1,3,1,1,2]
[6,8,7,1,3,4,5,2]=>0110001=>1000110=>[1,4,1,2]
[7,8,6,1,3,4,5,2]=>0110001=>1000110=>[1,4,1,2]
[1,7,8,2,4,5,6,3]=>0010001=>1000100=>[1,4,3]
[8,6,7,1,3,4,5,2]=>1010001=>1000101=>[1,4,2,1]
[7,6,8,1,3,4,5,2]=>1010001=>1000101=>[1,4,2,1]
[6,5,8,2,3,1,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[1,6,8,3,2,5,7,4]=>0011001=>1001100=>[1,3,1,3]
[8,4,2,7,1,5,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[7,4,2,8,1,5,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[6,4,2,8,3,1,7,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,4,2,3,8,1,7,6]=>1100101=>1010011=>[1,2,3,1,1]
[4,5,2,3,1,6,8,7]=>0101001=>1001010=>[1,3,2,2]
[7,4,2,1,3,6,8,5]=>1110001=>1000111=>[1,4,1,1,1]
[8,4,2,1,3,6,7,5]=>1110001=>1000111=>[1,4,1,1,1]
[1,5,3,2,4,7,8,6]=>0110001=>1000110=>[1,4,1,2]
[8,5,1,3,2,6,7,4]=>1101001=>1001011=>[1,3,2,1,1]
[5,6,1,3,4,2,8,7]=>0100101=>1010010=>[1,2,3,2]
[4,7,2,1,3,6,8,5]=>0110001=>1000110=>[1,4,1,2]
[5,7,1,3,2,6,8,4]=>0101001=>1001010=>[1,3,2,2]
[6,7,1,2,4,5,8,3]=>0100001=>1000010=>[1,5,2]
[1,8,2,3,5,6,7,4]=>0100001=>1000010=>[1,5,2]
[5,8,1,3,2,6,7,4]=>0101001=>1001010=>[1,3,2,2]
[4,8,2,1,3,6,7,5]=>0110001=>1000110=>[1,4,1,2]
[4,1,3,2,5,7,8,6]=>1010001=>1000101=>[1,4,2,1]
[5,1,2,4,3,7,8,6]=>1001001=>1001001=>[1,3,3,1]
[8,7,5,2,6,3,4,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,6,5,2,7,3,4,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[1,2,6,4,7,5,8,3]=>0010101=>1010100=>[1,2,2,3]
[3,1,7,5,4,2,6,8]=>1011100=>0011101=>[3,1,1,2,1]
[6,3,8,5,4,7,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[1,6,2,5,4,7,8,3]=>0101001=>1001010=>[1,3,2,2]
[1,2,6,4,8,5,7,3]=>0010101=>1010100=>[1,2,2,3]
[7,8,3,1,4,2,5,6]=>0110100=>0010110=>[3,2,1,2]
[4,8,1,5,2,3,6,7]=>0101000=>0001010=>[4,2,2]
[7,4,1,5,2,3,6,8]=>1101000=>0001011=>[4,2,1,1]
[5,6,1,8,4,3,2,7]=>0101110=>0111010=>[2,1,1,2,2]
[5,1,8,6,4,3,2,7]=>1011110=>0111101=>[2,1,1,1,2,1]
[5,1,6,3,8,7,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[6,1,2,5,8,3,7,4]=>1000101=>1010001=>[1,2,4,1]
[6,1,8,7,4,3,2,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[7,1,2,5,4,8,6,3]=>1001011=>1101001=>[1,1,2,3,1]
[1,2,7,5,8,3,6,4]=>0010101=>1010100=>[1,2,2,3]
[4,1,6,3,7,5,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[1,3,6,7,8,5,2,4]=>0000110=>0110000=>[2,1,5]
[1,2,6,4,7,8,5,3]=>0010011=>1100100=>[1,1,3,3]
[4,1,6,3,7,8,2,5]=>1010010=>0100101=>[2,3,2,1]
[3,1,6,4,8,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,4,1,6,3,2,5]=>0110110=>0110110=>[2,1,2,1,2]
[4,1,6,3,8,7,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,5,1,8,4,3,2,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,5,1,7,4,3,2,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,1,8,5,2,3,7,6]=>1011001=>1001101=>[1,3,1,2,1]
[4,1,6,8,3,7,2,5]=>1001010=>0101001=>[2,2,3,1]
[6,5,8,1,4,3,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[1,6,3,2,7,4,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[1,3,7,2,5,4,8,6]=>0010101=>1010100=>[1,2,2,3]
[1,3,7,5,2,4,8,6]=>0011001=>1001100=>[1,3,1,3]
[2,5,3,7,4,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[3,2,6,7,8,1,5,4]=>1000101=>1010001=>[1,2,4,1]
[3,5,2,7,8,4,1,6]=>0100110=>0110010=>[2,1,3,2]
[3,5,2,6,8,4,7,1]=>0100101=>1010010=>[1,2,3,2]
[2,5,7,4,3,8,6,1]=>0011011=>1101100=>[1,1,2,1,3]
[1,5,7,2,4,8,6,3]=>0010011=>1100100=>[1,1,3,3]
[4,6,3,7,2,8,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[1,4,7,3,8,6,2,5]=>0010110=>0110100=>[2,1,2,3]
[5,1,6,8,2,4,3,7]=>1001010=>0101001=>[2,2,3,1]
[5,3,7,8,2,4,1,6]=>1001010=>0101001=>[2,2,3,1]
[8,5,3,7,2,4,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,2,4,7,3,1,5,6]=>1001100=>0011001=>[3,1,3,1]
[2,4,7,8,3,1,5,6]=>0001100=>0011000=>[3,1,4]
[6,3,1,5,8,2,4,7]=>1100100=>0010011=>[3,3,1,1]
[6,5,3,4,2,8,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[5,2,4,3,8,1,6,7]=>1010100=>0010101=>[3,2,2,1]
[3,2,4,8,1,5,6,7]=>1001000=>0001001=>[4,3,1]
[8,1,5,7,3,2,4,6]=>1001100=>0011001=>[3,1,3,1]
[8,4,6,7,2,3,1,5]=>1001010=>0101001=>[2,2,3,1]
[4,6,7,8,2,3,1,5]=>0001010=>0101000=>[2,2,4]
[7,4,6,8,2,3,1,5]=>1001010=>0101001=>[2,2,3,1]
[7,2,4,8,3,1,5,6]=>1001100=>0011001=>[3,1,3,1]
[5,3,8,7,2,4,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[2,4,8,7,3,1,5,6]=>0011100=>0011100=>[3,1,1,3]
[4,6,8,7,2,3,1,5]=>0011010=>0101100=>[2,2,1,3]
[6,4,8,7,2,3,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[3,1,7,4,2,8,6,5]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,2,8,4,1,7,6,5]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,6,4,8,2,3,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,7,6,8,2,3,1,4]=>0101010=>0101010=>[2,2,2,2]
[4,7,6,8,2,3,1,5]=>0101010=>0101010=>[2,2,2,2]
[8,6,4,7,2,3,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[8,2,3,7,4,1,6,5]=>1001101=>1011001=>[1,2,1,3,1]
[3,7,4,8,2,5,1,6]=>0101010=>0101010=>[2,2,2,2]
[2,3,7,4,1,6,8,5]=>0011001=>1001100=>[1,3,1,3]
[8,1,6,4,2,3,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[4,7,8,6,2,3,1,5]=>0011010=>0101100=>[2,2,1,3]
[6,3,1,7,4,2,8,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,7,6,2,3,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,6,4,2,3,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[3,1,7,6,4,2,8,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,8,7,6,2,3,1,5]=>0111010=>0101110=>[2,2,1,1,2]
[6,8,7,5,2,3,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[4,3,6,1,5,8,7,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,3,6,5,1,8,7,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,6,3,5,1,8,7,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,3,1,5,8,7,2]=>0110011=>1100110=>[1,1,3,1,2]
[4,1,6,5,3,8,7,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,6,1,5,3,8,7,2]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,5,3,1,8,7,4]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,6,5,8,3,1,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,5,3,8,1,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,1,5,8,3,7,2]=>0100101=>1010010=>[1,2,3,2]
[4,1,6,5,8,3,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[1,4,6,5,8,3,7,2]=>0010101=>1010100=>[1,2,2,3]
[4,1,6,5,8,7,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,4,3,8,7,1,5,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,4,8,3,7,1,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[2,6,8,5,3,7,1,4]=>0011010=>0101100=>[2,2,1,3]
[4,6,8,1,5,7,3,2]=>0010011=>1100100=>[1,1,3,3]
[4,6,1,8,5,7,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,4,6,8,5,7,3,2]=>0001011=>1101000=>[1,1,2,4]
[1,4,6,8,5,3,7,2]=>0001101=>1011000=>[1,2,1,4]
[4,6,1,8,5,3,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,3,8,5,7,1,2]=>0101010=>0101010=>[2,2,2,2]
[4,3,6,8,1,5,7,2]=>1001001=>1001001=>[1,3,3,1]
[4,3,6,1,8,5,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,1,6,8,5,7,2]=>1100101=>1010011=>[1,2,3,1,1]
[4,1,3,6,8,7,5,2]=>1000111=>1110001=>[1,1,1,4,1]
[4,3,6,1,8,7,5,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,3,6,8,1,7,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[6,5,2,8,7,3,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,5,2,8,7,1,3,4]=>1101100=>0011011=>[3,1,2,1,1]
[6,2,5,8,7,1,3,4]=>1001100=>0011001=>[3,1,3,1]
[6,2,5,8,7,3,1,4]=>1001110=>0111001=>[2,1,1,3,1]
[4,6,3,8,1,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,3,1,8,7,5,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,1,6,3,8,7,5,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,4,6,3,8,7,5,2]=>0010111=>1110100=>[1,1,1,2,3]
[4,1,6,8,3,7,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[4,6,1,8,3,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,8,1,3,7,5,2]=>0010011=>1100100=>[1,1,3,3]
[6,2,8,5,7,3,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,8,5,7,1,3,4]=>1010100=>0010101=>[3,2,2,1]
[2,4,8,7,1,5,3,6]=>0011010=>0101100=>[2,2,1,3]
[6,4,1,8,7,5,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[6,1,4,8,7,5,3,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[1,6,4,8,7,3,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,4,1,8,7,3,5,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,2,8,7,5,1,3,6]=>1011100=>0011101=>[3,1,1,2,1]
[2,4,8,7,3,5,1,6]=>0011010=>0101100=>[2,2,1,3]
[1,5,3,2,6,4,7,8]=>0110100=>0010110=>[3,2,1,2]
[1,5,3,2,6,7,4,8]=>0110010=>0100110=>[2,3,1,2]
[1,7,3,2,8,5,4,6]=>0110110=>0110110=>[2,1,2,1,2]
[1,7,3,2,5,8,4,6]=>0110010=>0100110=>[2,3,1,2]
[6,4,2,5,3,7,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,7,6,2,3,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[3,6,4,8,2,1,5,7]=>0101100=>0011010=>[3,1,2,2]
[1,6,2,8,5,3,4,7]=>0101100=>0011010=>[3,1,2,2]
[4,6,2,3,7,5,1,8]=>0100110=>0110010=>[2,1,3,2]
[4,7,2,3,6,5,1,8]=>0100110=>0110010=>[2,1,3,2]
[5,3,2,6,4,7,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[3,5,2,1,6,8,4,7]=>0110010=>0100110=>[2,3,1,2]
[1,5,2,6,8,4,3,7]=>0100110=>0110010=>[2,1,3,2]
[1,5,7,2,8,4,3,6]=>0010110=>0110100=>[2,1,2,3]
[3,5,2,1,8,6,4,7]=>0110110=>0110110=>[2,1,2,1,2]
[3,6,8,4,2,1,5,7]=>0011100=>0011100=>[3,1,1,3]
[4,3,2,6,1,8,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[1,5,8,2,7,4,3,6]=>0010110=>0110100=>[2,1,2,3]
[1,7,2,3,4,8,6,5]=>0100011=>1100010=>[1,1,4,2]
[6,8,2,3,4,1,7,5]=>0100101=>1010010=>[1,2,3,2]
[2,3,1,8,4,5,7,6]=>0101001=>1001010=>[1,3,2,2]
[7,3,2,1,4,5,8,6]=>1110001=>1000111=>[1,4,1,1,1]
[7,8,1,4,3,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[1,8,2,3,4,7,6,5]=>0100011=>1100010=>[1,1,4,2]
[3,8,2,1,6,5,4,7]=>0110110=>0110110=>[2,1,2,1,2]
[1,7,8,3,5,4,2,6]=>0010110=>0110100=>[2,1,2,3]
[7,4,1,8,3,5,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,1,7,3,5,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[3,8,4,6,2,1,5,7]=>0101100=>0011010=>[3,1,2,2]
[8,4,2,5,3,1,6,7]=>1101100=>0011011=>[3,1,2,1,1]
[4,3,2,5,1,8,6,7]=>1101010=>0101011=>[2,2,2,1,1]
[3,5,2,4,1,8,6,7]=>0101010=>0101010=>[2,2,2,2]
[2,4,7,8,1,5,3,6]=>0001010=>0101000=>[2,2,4]
[1,8,7,3,5,4,2,6]=>0110110=>0110110=>[2,1,2,1,2]
[5,1,8,2,7,4,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,7,2,8,4,3,6]=>1010110=>0110101=>[2,1,2,2,1]
[6,1,2,8,5,3,4,7]=>1001100=>0011001=>[3,1,3,1]
[6,3,2,1,8,4,5,7]=>1110100=>0010111=>[3,2,1,1,1]
[7,3,2,8,4,5,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[2,7,8,4,3,5,1,6]=>0011010=>0101100=>[2,2,1,3]
[7,1,8,3,5,4,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,8,2,3,4,6,1,5]=>0100010=>0100010=>[2,4,2]
[6,8,1,3,4,7,2,5]=>0100010=>0100010=>[2,4,2]
[8,6,2,3,4,1,7,5]=>1100101=>1010011=>[1,2,3,1,1]
[8,3,2,7,4,5,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,7,2,3,4,1,8,5]=>0100101=>1010010=>[1,2,3,2]
[8,6,2,3,4,7,1,5]=>1100010=>0100011=>[2,4,1,1]
[4,8,7,3,5,6,1,2]=>0110010=>0100110=>[2,3,1,2]
[4,8,7,5,3,6,1,2]=>0111010=>0101110=>[2,2,1,1,2]
[5,8,7,3,4,6,1,2]=>0110010=>0100110=>[2,3,1,2]
[5,8,4,2,1,6,7,3]=>0111001=>1001110=>[1,3,1,1,2]
[5,8,4,1,2,6,7,3]=>0110001=>1000110=>[1,4,1,2]
[5,3,7,2,6,1,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,8,1,6,3,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,2,1,4,7,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[4,8,2,5,1,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[7,8,4,1,2,6,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[4,8,1,5,2,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[5,8,1,2,4,7,6,3]=>0100011=>1100010=>[1,1,4,2]
[5,2,8,3,6,7,1,4]=>1010010=>0100101=>[2,3,2,1]
[2,8,7,6,4,1,3,5]=>0111100=>0011110=>[3,1,1,1,2]
[7,8,2,6,5,1,3,4]=>0101100=>0011010=>[3,1,2,2]
[1,8,7,6,2,4,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[2,8,1,4,5,6,7,3]=>0100001=>1000010=>[1,5,2]
[2,1,7,3,6,5,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,7,1,6,5,8,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,2,8,5,7,3,4]=>1001010=>0101001=>[2,2,3,1]
[6,2,1,8,5,7,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,1,8,5,7,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,4,2,1,7,5,8,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,1,3,8,5,2,7,4]=>1001101=>1011001=>[1,2,1,3,1]
[1,3,7,2,6,8,5,4]=>0010011=>1100100=>[1,1,3,3]
[7,8,2,6,5,3,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[3,2,6,7,5,8,1,4]=>1001010=>0101001=>[2,2,3,1]
[1,2,7,5,6,3,8,4]=>0010101=>1010100=>[1,2,2,3]
[2,8,7,6,4,3,1,5]=>0111110=>0111110=>[2,1,1,1,1,2]
[3,8,7,6,1,2,5,4]=>0111001=>1001110=>[1,3,1,1,2]
[4,8,7,6,2,1,3,5]=>0111100=>0011110=>[3,1,1,1,2]
[4,8,7,6,1,3,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[3,8,7,6,4,1,2,5]=>0111100=>0011110=>[3,1,1,1,2]
[7,8,3,6,5,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[2,3,7,5,6,8,1,4]=>0010010=>0100100=>[2,3,3]
[3,8,7,6,4,2,1,5]=>0111110=>0111110=>[2,1,1,1,1,2]
[3,4,2,6,7,8,1,5]=>0100010=>0100010=>[2,4,2]
[3,1,4,2,6,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[8,3,4,2,6,1,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[2,6,7,3,5,4,1,8]=>0010110=>0110100=>[2,1,2,3]
[2,7,8,3,5,4,1,6]=>0010110=>0110100=>[2,1,2,3]
[2,6,8,3,5,4,1,7]=>0010110=>0110100=>[2,1,2,3]
[4,7,1,2,8,5,3,6]=>0100110=>0110010=>[2,1,3,2]
[4,8,1,2,7,5,3,6]=>0100110=>0110010=>[2,1,3,2]
[2,1,6,3,7,5,4,8]=>1010110=>0110101=>[2,1,2,2,1]
[2,7,1,3,6,8,4,5]=>0100010=>0100010=>[2,4,2]
[7,4,1,2,8,5,3,6]=>1100110=>0110011=>[2,1,3,1,1]
[8,7,4,2,1,5,3,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[7,4,1,2,6,5,3,8]=>1100110=>0110011=>[2,1,3,1,1]
[7,4,3,1,5,6,8,2]=>1110001=>1000111=>[1,4,1,1,1]
[6,7,4,1,5,8,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[4,7,5,1,6,8,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[4,5,3,1,7,6,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,1,2,7,5,3,8]=>0100110=>0110010=>[2,1,3,2]
[4,6,1,2,8,5,3,7]=>0100110=>0110010=>[2,1,3,2]
[4,5,3,1,8,6,7,2]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,5,6,3,1,7,2]=>0101101=>1011010=>[1,2,1,2,2]
[5,1,3,4,8,6,7,2]=>1000101=>1010001=>[1,2,4,1]
[5,4,3,8,1,6,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,3,4,1,6,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[6,4,8,2,1,5,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[6,7,3,2,5,1,4,8]=>0110100=>0010110=>[3,2,1,2]
[6,8,3,2,5,1,4,7]=>0110100=>0010110=>[3,2,1,2]
[5,7,1,4,6,8,3,2]=>0100011=>1100010=>[1,1,4,2]
[5,1,3,4,7,6,8,2]=>1000101=>1010001=>[1,2,4,1]
[5,4,3,7,1,6,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[6,7,5,4,1,8,3,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[7,6,4,2,1,5,3,8]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,5,6,1,3,2,4,7]=>1010100=>0010101=>[3,2,2,1]
[8,6,1,5,3,2,4,7]=>1101100=>0011011=>[3,1,2,1,1]
[7,8,1,5,3,2,4,6]=>0101100=>0011010=>[3,1,2,2]
[8,1,7,5,3,2,4,6]=>1011100=>0011101=>[3,1,1,2,1]
[8,6,1,4,5,2,3,7]=>1100100=>0010011=>[3,3,1,1]
[8,6,3,1,5,2,4,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,4,6,1,5,2,3,7]=>1010100=>0010101=>[3,2,2,1]
[8,6,2,1,5,4,3,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,5,2,6,1,4,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,2,1,7,4,3,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,2,7,5,1,3,4,6]=>1011000=>0001101=>[4,1,2,1]
[8,4,1,7,5,2,3,6]=>1101100=>0011011=>[3,1,2,1,1]
[8,2,6,1,7,4,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,1,7,4,3,2,6,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,1,5,7,3,2,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[5,7,8,1,3,2,6,4]=>0010101=>1010100=>[1,2,2,3]
[8,2,6,1,5,7,3,4]=>1010010=>0100101=>[2,3,2,1]
[5,8,1,6,7,2,3,4]=>0100100=>0010010=>[3,3,2]
[5,7,6,1,8,2,3,4]=>0110100=>0010110=>[3,2,1,2]
[8,1,5,6,7,2,3,4]=>1000100=>0010001=>[3,4,1]
[6,5,7,1,8,2,3,4]=>1010100=>0010101=>[3,2,2,1]
[8,1,6,4,7,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[7,5,8,1,3,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[7,8,4,1,3,2,5,6]=>0110100=>0010110=>[3,2,1,2]
[8,3,7,4,1,2,5,6]=>1011000=>0001101=>[4,1,2,1]
[8,5,1,7,3,2,4,6]=>1101100=>0011011=>[3,1,2,1,1]
[6,8,1,7,3,2,4,5]=>0101100=>0011010=>[3,1,2,2]
[7,1,8,4,3,6,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,3,1,8,6,4,2,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,3,1,7,4,6,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,5,1,7,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[5,6,8,1,7,2,3,4]=>0010100=>0010100=>[3,2,3]
[6,5,8,1,2,7,3,4]=>1010010=>0100101=>[2,3,2,1]
[7,3,1,8,5,6,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,2,7,8,3,1,5,4]=>1001101=>1011001=>[1,2,1,3,1]
[5,8,1,7,3,2,6,4]=>0101101=>1011010=>[1,2,1,2,2]
[8,4,1,7,3,2,6,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,3,4,7,1,2,6,5]=>1001001=>1001001=>[1,3,3,1]
[7,4,8,2,1,3,6,5]=>1011001=>1001101=>[1,3,1,2,1]
[7,4,3,8,1,2,6,5]=>1101001=>1001011=>[1,3,2,1,1]
[8,2,3,6,7,1,5,4]=>1000101=>1010001=>[1,2,4,1]
[2,6,8,7,1,5,4,3]=>0011011=>1101100=>[1,1,2,1,3]
[7,8,5,2,3,6,4,1]=>0110011=>1100110=>[1,1,3,1,2]
[8,7,5,2,3,1,6,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,8,5,2,3,4,7,1]=>0110001=>1000110=>[1,4,1,2]
[5,7,3,4,6,8,1,2]=>0100010=>0100010=>[2,4,2]
[5,7,3,4,6,1,2,8]=>0100100=>0010010=>[3,3,2]
[7,3,5,6,1,2,8,4]=>1001001=>1001001=>[1,3,3,1]
[5,7,3,1,4,6,8,2]=>0110001=>1000110=>[1,4,1,2]
[5,7,3,1,4,8,6,2]=>0110011=>1100110=>[1,1,3,1,2]
[5,7,3,1,4,8,2,6]=>0110010=>0100110=>[2,3,1,2]
[5,3,7,4,1,2,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[5,3,7,4,1,2,6,8]=>1011000=>0001101=>[4,1,2,1]
[5,3,7,1,4,2,6,8]=>1010100=>0010101=>[3,2,2,1]
[5,3,7,1,4,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[3,7,5,1,2,8,6,4]=>0110011=>1100110=>[1,1,3,1,2]
[7,8,3,5,1,2,6,4]=>0101001=>1001010=>[1,3,2,2]
[7,3,8,5,1,2,6,4]=>1011001=>1001101=>[1,3,1,2,1]
[7,3,5,8,1,2,6,4]=>1001001=>1001001=>[1,3,3,1]
[3,7,5,1,2,6,4,8]=>0110010=>0100110=>[2,3,1,2]
[3,7,5,1,2,6,8,4]=>0110001=>1000110=>[1,4,1,2]
[3,5,7,2,8,6,1,4]=>0010110=>0110100=>[2,1,2,3]
[2,5,7,4,8,6,1,3]=>0010110=>0110100=>[2,1,2,3]
[2,6,4,8,7,5,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[3,6,2,5,8,7,1,4]=>0100110=>0110010=>[2,1,3,2]
[5,2,8,4,7,6,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,4,8,7,5,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[2,5,1,4,7,3,8,6]=>0100101=>1010010=>[1,2,3,2]
[3,1,5,6,2,8,7,4]=>1001011=>1101001=>[1,1,2,3,1]
[7,1,4,2,8,6,5,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,1,5,3,2,8,7,6]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,2,3,5,1,8,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[1,6,4,2,8,7,5,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,6,2,7,5,1,8,3]=>0101101=>1011010=>[1,2,1,2,2]
[1,5,3,6,2,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[3,6,2,5,1,4,8,7]=>0101001=>1001010=>[1,3,2,2]
[5,2,8,4,1,3,7,6]=>1011001=>1001101=>[1,3,1,2,1]
[2,4,8,7,1,3,6,5]=>0011001=>1001100=>[1,3,1,3]
[6,3,1,7,2,8,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,5,1,2,8,6,4,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[1,5,2,3,8,7,6,4]=>0100111=>1110010=>[1,1,1,3,2]
[4,5,1,2,8,7,6,3]=>0100111=>1110010=>[1,1,1,3,2]
[3,5,8,7,2,6,4,1]=>0011011=>1101100=>[1,1,2,1,3]
[5,8,2,7,1,6,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,6,4,5,8,3,7]=>1010010=>0100101=>[2,3,2,1]
[8,6,3,7,5,2,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,6,3,8,5,2,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[4,6,3,7,5,2,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,7,8,2,6,1,4]=>0001010=>0101000=>[2,2,4]
[4,2,3,6,1,5,8,7]=>1001001=>1001001=>[1,3,3,1]
[3,8,6,4,5,1,2,7]=>0110100=>0010110=>[3,2,1,2]
[4,8,3,7,5,2,1,6]=>0101110=>0111010=>[2,1,1,2,2]
[8,7,3,6,5,1,2,4]=>1101100=>0011011=>[3,1,2,1,1]
[5,2,8,3,7,6,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[8,2,7,3,1,6,4,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,6,7,4,1,5,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,8,6,7,5,1,3,2]=>0101101=>1011010=>[1,2,1,2,2]
[7,1,8,4,6,5,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[8,7,1,5,4,6,2,3]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,7,1,4,6,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[6,4,8,5,1,7,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,4,7,1,5,6,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[8,7,5,1,4,6,2,3]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,2,5,1,4,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[4,8,7,2,5,1,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[8,7,1,4,2,5,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[8,7,5,1,2,4,6,3]=>1110001=>1000111=>[1,4,1,1,1]
[7,1,8,5,6,2,3,4]=>1010100=>0010101=>[3,2,2,1]
[3,5,8,7,1,2,6,4]=>0011001=>1001100=>[1,3,1,3]
[2,3,8,5,7,1,6,4]=>0010101=>1010100=>[1,2,2,3]
[3,8,7,1,5,6,2,4]=>0110010=>0100110=>[2,3,1,2]
[3,5,8,7,1,6,2,4]=>0011010=>0101100=>[2,2,1,3]
[2,3,8,6,7,5,1,4]=>0010110=>0110100=>[2,1,2,3]
[3,2,8,6,7,5,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[4,1,8,6,2,7,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,7,4,1,2,6,5,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[1,3,8,6,7,5,2,4]=>0010110=>0110100=>[2,1,2,3]
[5,7,1,8,2,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[2,8,7,1,5,6,3,4]=>0110010=>0100110=>[2,3,1,2]
[8,7,1,5,2,4,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[7,1,8,2,4,6,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[1,6,2,8,4,7,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,8,5,7,2,6,4]=>0010101=>1010100=>[1,2,2,3]
[1,8,3,7,2,5,6,4]=>0101001=>1001010=>[1,3,2,2]
[2,8,7,1,3,5,6,4]=>0110001=>1000110=>[1,4,1,2]
[5,7,1,8,2,3,6,4]=>0101001=>1001010=>[1,3,2,2]
[7,1,8,2,3,5,6,4]=>1010001=>1000101=>[1,4,2,1]
[8,6,3,7,4,1,5,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,2,8,6,7,5,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,2,7,5,6,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[4,8,3,6,1,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[8,3,4,7,5,1,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[8,3,7,4,5,1,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,7,4,2,5,6,1,3]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,5,1,6,2,3,4]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,2,4,1,5,6,3]=>1101001=>1001011=>[1,3,2,1,1]
[4,8,6,1,7,2,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[4,2,8,6,7,1,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,7,4,1,2,5,6,3]=>1110001=>1000111=>[1,4,1,1,1]
[8,2,7,1,6,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[8,2,7,1,3,6,4,5]=>1010010=>0100101=>[2,3,2,1]
[2,8,3,6,7,1,5,4]=>0100101=>1010010=>[1,2,3,2]
[8,7,2,1,3,5,6,4]=>1110001=>1000111=>[1,4,1,1,1]
[1,8,7,2,3,6,4,5]=>0110010=>0100110=>[2,3,1,2]
[1,8,7,2,6,3,4,5]=>0110100=>0010110=>[3,2,1,2]
[8,2,7,3,6,1,4,5]=>1010100=>0010101=>[3,2,2,1]
[1,8,7,3,6,2,4,5]=>0110100=>0010110=>[3,2,1,2]
[1,8,2,7,6,3,4,5]=>0101100=>0011010=>[3,1,2,2]
[8,2,7,4,1,5,6,3]=>1011001=>1001101=>[1,3,1,2,1]
[8,2,1,7,5,6,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,3,1,5,6,2,4]=>1110010=>0100111=>[2,3,1,1,1]
[2,8,7,3,5,6,1,4]=>0110010=>0100110=>[2,3,1,2]
[8,3,1,6,7,5,2,4]=>1100110=>0110011=>[2,1,3,1,1]
[8,5,2,1,6,7,4,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[1,5,2,8,6,7,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,2,8,6,7,5,3,4]=>0010110=>0110100=>[2,1,2,3]
[1,8,3,6,7,5,2,4]=>0100110=>0110010=>[2,1,3,2]
[8,2,3,6,7,5,1,4]=>1000110=>0110001=>[2,1,4,1]
[8,3,7,2,5,6,1,4]=>1010010=>0100101=>[2,3,2,1]
[8,1,3,7,5,6,2,4]=>1001010=>0101001=>[2,2,3,1]
[8,4,1,2,7,5,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[8,1,4,2,6,7,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[1,2,8,6,7,3,5,4]=>0010101=>1010100=>[1,2,2,3]
[8,1,2,7,3,6,4,5]=>1001010=>0101001=>[2,2,3,1]
[8,1,7,3,6,2,4,5]=>1010100=>0010101=>[3,2,2,1]
[8,1,7,2,6,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[8,1,7,2,3,6,4,5]=>1010010=>0100101=>[2,3,2,1]
[8,1,3,7,2,5,6,4]=>1001001=>1001001=>[1,3,3,1]
[1,8,3,6,7,2,5,4]=>0100101=>1010010=>[1,2,3,2]
[1,7,8,2,3,6,5,4]=>0010011=>1100100=>[1,1,3,3]
[8,3,7,1,2,5,6,4]=>1010001=>1000101=>[1,4,2,1]
[7,4,2,6,1,5,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,2,5,6,1,3,8]=>1100100=>0010011=>[3,3,1,1]
[7,3,5,6,4,2,1,8]=>1001110=>0111001=>[2,1,1,3,1]
[7,4,3,1,5,6,2,8]=>1110010=>0100111=>[2,3,1,1,1]
[7,4,5,2,6,1,3,8]=>1010100=>0010101=>[3,2,2,1]
[5,3,7,2,8,6,4,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,3,8,2,6,7,4,1]=>1010011=>1100101=>[1,1,3,2,1]
[6,3,8,2,5,4,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,4,3,1,8,2,7,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,3,7,8,2,6,4,1]=>1001011=>1101001=>[1,1,2,3,1]
[4,7,8,5,6,3,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[5,3,7,6,8,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,8,4,6,2,1,3]=>0010110=>0110100=>[2,1,2,3]
[5,8,4,3,6,7,1,2]=>0110010=>0100110=>[2,3,1,2]
[5,8,6,4,7,2,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[5,3,8,6,2,7,4,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,7,5,8,6,3,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[6,3,8,7,2,4,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[5,3,8,7,2,6,4,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,3,8,6,7,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,7,8,6,2,4,1]=>1001101=>1011001=>[1,2,1,3,1]
[5,7,6,4,8,2,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[5,8,4,6,7,2,1,3]=>0100110=>0110010=>[2,1,3,2]
[6,4,2,8,1,7,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,2,4,3,7,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[5,4,6,2,8,7,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[5,6,3,8,7,2,4,1]=>0101101=>1011010=>[1,2,1,2,2]
[6,7,4,3,1,8,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[5,7,4,3,6,8,1,2]=>0110010=>0100110=>[2,3,1,2]
[5,7,3,8,6,2,4,1]=>0101101=>1011010=>[1,2,1,2,2]
[4,5,8,6,7,3,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,6,8,5,7,3,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[5,6,8,3,7,2,4,1]=>0010101=>1010100=>[1,2,2,3]
[5,4,6,8,2,7,1,3]=>1001010=>0101001=>[2,2,3,1]
[7,8,4,5,1,3,2,6]=>0101010=>0101010=>[2,2,2,2]
[6,7,1,3,2,5,4,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,1,4,3,5,2,8]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,3,1,5,4,6]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,4,3,5,1,6]=>0101010=>0101010=>[2,2,2,2]
[7,8,2,4,1,5,3,6]=>0101010=>0101010=>[2,2,2,2]
[1,4,2,6,5,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,1,4,2,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,2,4,1,5,3,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,2,4,3,5,1,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,2,3,1,5,4,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,3,5,4,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[2,4,1,6,5,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[1,5,2,6,4,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[2,5,1,6,4,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,2,4,3,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,2,6,1,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,1,6,3,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,3,6,1,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,3,4,1,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,1,4,3,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,1,3,2,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[5,6,4,7,1,3,2,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,4,5,1,3,2,8]=>0101010=>0101010=>[2,2,2,2]
[6,7,5,8,1,3,2,4]=>0101010=>0101010=>[2,2,2,2]
[4,5,1,3,2,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[4,6,5,7,1,3,2,8]=>0101010=>0101010=>[2,2,2,2]
[4,6,1,3,2,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[1,4,3,6,2,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,2,3,1,7,6,8]=>0101010=>0101010=>[2,2,2,2]
[4,5,3,7,6,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[4,6,5,7,3,8,1,2]=>0101010=>0101010=>[2,2,2,2]
[4,6,5,7,2,3,1,8]=>0101010=>0101010=>[2,2,2,2]
[3,5,4,6,1,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[3,5,1,6,4,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[1,5,3,6,4,7,2,8]=>0101010=>0101010=>[2,2,2,2]
[1,5,3,6,2,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[3,5,2,6,1,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[3,5,2,6,4,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[3,4,2,6,1,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[4,6,2,3,1,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[2,4,3,6,1,7,5,8]=>0101010=>0101010=>[2,2,2,2]
[2,5,3,6,4,7,1,8]=>0101010=>0101010=>[2,2,2,2]
[2,5,3,6,1,7,4,8]=>0101010=>0101010=>[2,2,2,2]
[3,6,2,7,5,4,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,2,6,7,4,3,8,1]=>1001101=>1011001=>[1,2,1,3,1]
[3,5,2,7,6,4,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[1,3,7,2,8,5,6,4]=>0010101=>1010100=>[1,2,2,3]
[2,1,5,6,8,4,3,7]=>1000110=>0110001=>[2,1,4,1]
[1,3,7,2,8,5,4,6]=>0010110=>0110100=>[2,1,2,3]
[1,5,4,3,6,8,2,7]=>0110010=>0100110=>[2,3,1,2]
[1,6,4,5,7,8,3,2]=>0100011=>1100010=>[1,1,4,2]
[2,1,5,6,8,4,7,3]=>1000101=>1010001=>[1,2,4,1]
[2,1,5,6,8,7,3,4]=>1000110=>0110001=>[2,1,4,1]
[3,6,5,2,7,8,4,1]=>0110011=>1100110=>[1,1,3,1,2]
[6,2,4,7,5,8,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[1,5,7,8,4,2,6,3]=>0001101=>1011000=>[1,2,1,4]
[3,7,4,1,8,6,2,5]=>0110110=>0110110=>[2,1,2,1,2]
[3,4,6,8,5,7,2,1]=>0001011=>1101000=>[1,1,2,4]
[4,5,6,2,8,7,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[4,5,6,1,8,7,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[4,5,6,3,1,8,7,2]=>0011011=>1101100=>[1,1,2,1,3]
[4,3,6,2,1,7,5,8]=>1011010=>0101101=>[2,2,1,2,1]
[4,6,3,2,1,7,5,8]=>0111010=>0101110=>[2,2,1,1,2]
[4,6,3,1,7,5,2,8]=>0110110=>0110110=>[2,1,2,1,2]
[4,5,3,7,6,1,8,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,5,1,7,3,8,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,7,1,4,3,8,6]=>0010101=>1010100=>[1,2,2,3]
[4,3,5,7,6,1,8,2]=>1001101=>1011001=>[1,2,1,3,1]
[4,3,6,1,7,5,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,3,2,6,1,7,5,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,3,2,1,6,4,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[5,3,1,6,2,7,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,1,6,3,2,7,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[2,6,1,4,7,5,3,8]=>0100110=>0110010=>[2,1,3,2]
[3,6,1,7,4,2,5,8]=>0101100=>0011010=>[3,1,2,2]
[4,6,1,7,5,3,2,8]=>0101110=>0111010=>[2,1,1,2,2]
[5,1,6,3,7,4,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,3,6,4,2,1,7,8]=>1011100=>0011101=>[3,1,1,2,1]
[5,3,2,6,4,1,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[5,2,1,6,3,7,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,2,6,3,1,7,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[4,2,6,3,1,7,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[3,6,2,1,7,4,5,8]=>0110100=>0010110=>[3,2,1,2]
[3,6,2,7,4,1,5,8]=>0101100=>0011010=>[3,1,2,2]
[3,5,7,2,8,6,4,1]=>0010111=>1110100=>[1,1,1,2,3]
[2,6,1,3,7,5,4,8]=>0100110=>0110010=>[2,1,3,2]
[3,6,1,7,5,2,4,8]=>0101100=>0011010=>[3,1,2,2]
[5,1,6,2,7,4,3,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,6,4,3,1,7,8]=>1011100=>0011101=>[3,1,1,2,1]
[5,2,1,6,4,3,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[5,4,2,1,6,3,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[5,4,1,6,2,7,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,1,6,4,2,7,3,8]=>1011010=>0101101=>[2,2,1,2,1]
[3,6,1,7,5,4,8,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,6,1,5,4,3,7,8]=>0101100=>0011010=>[3,1,2,2]
[3,1,6,2,5,4,7,8]=>1010100=>0010101=>[3,2,2,1]
[4,1,6,3,2,7,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[5,1,6,4,3,2,7,8]=>1011100=>0011101=>[3,1,1,2,1]
[5,4,1,6,3,2,7,8]=>1101100=>0011011=>[3,1,2,1,1]
[5,4,3,1,6,2,7,8]=>1110100=>0010111=>[3,2,1,1,1]
[1,2,8,7,4,6,3,5]=>0011010=>0101100=>[2,2,1,3]
[4,5,1,8,7,6,2,3]=>0101110=>0111010=>[2,1,1,2,2]
[4,1,5,8,7,6,2,3]=>1001110=>0111001=>[2,1,1,3,1]
[7,5,8,4,2,6,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,8,4,5,2,7,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,8,2,5,3,7,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,3,8,4,2,7,5,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,2,5,3,8,6,4,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,4,7,5,8,6,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[3,6,7,4,8,5,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[6,7,4,2,8,5,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[4,7,5,2,8,6,3,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,6,2,8,3,7,4,1]=>0101011=>1101010=>[1,1,2,2,2]
[1,5,8,2,7,3,6,4]=>0010101=>1010100=>[1,2,2,3]
[5,8,4,7,2,3,6,1]=>0101001=>1001010=>[1,3,2,2]
[6,7,4,8,1,5,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,8,5,3,7,2,4,1]=>0110101=>1010110=>[1,2,2,1,2]
[7,5,3,8,2,6,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,7,4,5,8,6,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[7,4,2,5,8,6,3,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,8,4,2,5,7,3,1]=>0110011=>1100110=>[1,1,3,1,2]
[7,5,8,3,4,6,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[7,4,5,8,1,6,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[6,3,4,7,8,5,2,1]=>1000111=>1110001=>[1,1,1,4,1]
[3,6,8,4,5,7,1,2]=>0010010=>0100100=>[2,3,3]
[1,6,8,4,7,2,3,5]=>0010100=>0010100=>[3,2,3]
[1,4,5,7,8,2,6,3]=>0000101=>1010000=>[1,2,5]
[1,4,5,8,7,2,3,6]=>0001100=>0011000=>[3,1,4]
[1,2,5,8,3,6,4,7]=>0001010=>0101000=>[2,2,4]
[7,8,1,4,6,2,3,5]=>0100100=>0010010=>[3,3,2]
[1,6,7,4,8,2,5,3]=>0010101=>1010100=>[1,2,2,3]
[1,4,5,6,8,2,7,3]=>0000101=>1010000=>[1,2,5]
[1,4,5,8,6,2,7,3]=>0001101=>1011000=>[1,2,1,4]
[1,2,5,8,3,4,7,6]=>0001001=>1001000=>[1,3,4]
[7,8,1,2,3,5,4,6]=>0100010=>0100010=>[2,4,2]
[1,6,7,2,3,5,4,8]=>0010010=>0100100=>[2,3,3]
[1,4,5,7,6,2,3,8]=>0001100=>0011000=>[3,1,4]
[1,2,5,7,3,6,4,8]=>0001010=>0101000=>[2,2,4]
[1,2,5,7,3,6,8,4]=>0001001=>1001000=>[1,3,4]
[1,6,8,2,3,5,7,4]=>0010001=>1000100=>[1,4,3]
[1,6,8,4,5,2,3,7]=>0010100=>0010100=>[3,2,3]
[1,6,8,2,3,4,7,5]=>0010001=>1000100=>[1,4,3]
[1,6,8,2,3,7,4,5]=>0010010=>0100100=>[2,3,3]
[1,4,5,7,6,2,8,3]=>0001101=>1011000=>[1,2,1,4]
[7,8,1,4,5,2,6,3]=>0100101=>1010010=>[1,2,3,2]
[1,6,7,2,3,8,5,4]=>0010011=>1100100=>[1,1,3,3]
[1,2,5,6,3,8,7,4]=>0001011=>1101000=>[1,1,2,4]
[2,7,4,8,3,5,1,6]=>0101010=>0101010=>[2,2,2,2]
[2,7,4,8,3,5,6,1]=>0101001=>1001010=>[1,3,2,2]
[7,2,8,4,3,5,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[8,4,2,1,5,3,6,7]=>1110100=>0010111=>[3,2,1,1,1]
[8,4,1,5,3,2,6,7]=>1101100=>0011011=>[3,1,2,1,1]
[6,7,3,8,4,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[6,7,3,8,4,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[7,1,8,4,3,5,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,7,8,4,3,5,2,6]=>0011010=>0101100=>[2,2,1,3]
[7,1,4,8,3,5,2,6]=>1001010=>0101001=>[2,2,3,1]
[7,1,8,4,3,5,6,2]=>1011001=>1001101=>[1,3,1,2,1]
[6,7,3,1,8,4,5,2]=>0110101=>1010110=>[1,2,2,1,2]
[6,7,1,4,8,3,5,2]=>0100101=>1010010=>[1,2,3,2]
[6,7,4,1,3,8,2,5]=>0110010=>0100110=>[2,3,1,2]
[1,6,7,8,4,3,2,5]=>0001110=>0111000=>[2,1,1,4]
[7,2,1,8,4,5,3,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,2,7,1,8,4,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,7,8,4,3,1,5]=>1001110=>0111001=>[2,1,1,3,1]
[6,2,7,8,4,3,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[2,6,7,4,8,3,5,1]=>0010101=>1010100=>[1,2,2,3]
[2,6,7,4,8,3,1,5]=>0010110=>0110100=>[2,1,2,3]
[7,8,1,3,6,2,4,5]=>0100100=>0010010=>[3,3,2]
[1,2,7,8,6,3,4,5]=>0001100=>0011000=>[3,1,4]
[2,6,7,1,8,5,3,4]=>0010110=>0110100=>[2,1,2,3]
[2,6,7,8,5,3,4,1]=>0001101=>1011000=>[1,2,1,4]
[6,2,7,8,4,5,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[1,7,2,8,4,5,6,3]=>0101001=>1001010=>[1,3,2,2]
[6,3,7,8,1,5,2,4]=>1001010=>0101001=>[2,2,3,1]
[6,7,1,2,8,5,3,4]=>0100110=>0110010=>[2,1,3,2]
[1,6,7,8,4,2,5,3]=>0001101=>1011000=>[1,2,1,4]
[3,1,2,7,6,5,8,4]=>1001101=>1011001=>[1,2,1,3,1]
[6,1,2,4,7,3,8,5]=>1000101=>1010001=>[1,2,4,1]
[1,7,5,3,6,4,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,1,2,6,7,4,8,3]=>1000101=>1010001=>[1,2,4,1]
[4,1,5,7,3,2,6,8]=>1001100=>0011001=>[3,1,3,1]
[4,6,1,7,3,2,5,8]=>0101100=>0011010=>[3,1,2,2]
[4,6,1,8,3,2,5,7]=>0101100=>0011010=>[3,1,2,2]
[4,1,7,8,6,2,3,5]=>1001100=>0011001=>[3,1,3,1]
[1,6,5,7,8,3,4,2]=>0100101=>1010010=>[1,2,3,2]
[1,6,5,8,7,3,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,1,8,7,6,2,3,5]=>1011100=>0011101=>[3,1,1,2,1]
[4,8,1,7,3,5,2,6]=>0101010=>0101010=>[2,2,2,2]
[4,8,1,6,3,2,5,7]=>0101100=>0011010=>[3,1,2,2]
[4,7,1,6,3,2,5,8]=>0101100=>0011010=>[3,1,2,2]
[6,1,2,3,7,5,4,8]=>1000110=>0110001=>[2,1,4,1]
[6,8,1,5,3,7,2,4]=>0101010=>0101010=>[2,2,2,2]
[8,7,5,2,4,1,6,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[1,5,8,3,4,7,6,2]=>0010011=>1100100=>[1,1,3,3]
[7,8,5,2,4,1,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[7,1,2,3,5,6,4,8]=>1000010=>0100001=>[2,5,1]
[7,1,8,4,6,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[6,8,2,4,3,1,5,7]=>0101100=>0011010=>[3,1,2,2]
[6,7,2,4,3,1,5,8]=>0101100=>0011010=>[3,1,2,2]
[3,7,1,8,6,4,2,5]=>0101110=>0111010=>[2,1,1,2,2]
[1,6,4,3,7,5,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[3,1,2,6,7,5,8,4]=>1000101=>1010001=>[1,2,4,1]
[3,8,1,7,6,4,2,5]=>0101110=>0111010=>[2,1,1,2,2]
[7,6,2,4,3,1,5,8]=>1101100=>0011011=>[3,1,2,1,1]
[8,7,2,4,3,5,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,1,7,4,6,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,1,7,6,5,3,2,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[1,5,7,3,4,6,8,2]=>0010001=>1000100=>[1,4,3]
[8,7,2,5,3,6,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[7,1,2,3,5,4,8,6]=>1000101=>1010001=>[1,2,4,1]
[6,1,2,3,5,8,4,7]=>1000010=>0100001=>[2,5,1]
[6,1,2,3,5,7,4,8]=>1000010=>0100001=>[2,5,1]
[5,1,2,3,7,6,4,8]=>1000110=>0110001=>[2,1,4,1]
[5,1,2,3,8,6,4,7]=>1000110=>0110001=>[2,1,4,1]
[1,5,6,3,4,7,8,2]=>0010001=>1000100=>[1,4,3]
[8,6,5,2,4,7,1,3]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,2,5,3,1,8,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,7,3,5,1,4,8,2]=>0101001=>1001010=>[1,3,2,2]
[5,3,6,7,4,8,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[5,3,2,8,6,7,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,4,8,2,6,7,3,1]=>1010011=>1100101=>[1,1,3,2,1]
[5,4,8,6,2,7,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,6,3,8,4,7,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,3,8,5,2,4,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,7,8,4,6,2,1]=>0001011=>1101000=>[1,1,2,4]
[5,7,8,2,4,6,3,1]=>0010011=>1100100=>[1,1,3,3]
[2,5,8,4,3,7,6,1]=>0011011=>1101100=>[1,1,2,1,3]
[3,7,4,8,6,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[3,6,4,8,7,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,4,8,2,7,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,5,7,3,8,6,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[6,3,1,8,7,5,4,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[5,4,8,1,7,6,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,8,4,1,7,6,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[7,5,4,1,8,6,3,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,5,4,1,7,6,3,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[1,8,2,5,6,3,4,7]=>0100100=>0010010=>[3,3,2]
[7,2,8,4,5,1,3,6]=>1010100=>0010101=>[3,2,2,1]
[1,3,7,5,6,2,4,8]=>0010100=>0010100=>[3,2,3]
[1,6,7,4,3,5,2,8]=>0011010=>0101100=>[2,2,1,3]
[1,8,2,5,3,6,7,4]=>0101001=>1001010=>[1,3,2,2]
[2,6,8,4,3,5,7,1]=>0011001=>1001100=>[1,3,1,3]
[7,2,8,4,1,5,6,3]=>1011001=>1001101=>[1,3,1,2,1]
[7,5,8,1,2,6,3,4]=>1010010=>0100101=>[2,3,2,1]
[1,5,2,6,4,7,8,3]=>0101001=>1001010=>[1,3,2,2]
[1,5,4,6,2,3,7,8]=>0101000=>0001010=>[4,2,2]
[6,2,5,7,1,4,8,3]=>1001001=>1001001=>[1,3,3,1]
[6,5,4,3,8,1,7,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,6,5,8,3,4,1,7]=>0101010=>0101010=>[2,2,2,2]
[2,6,5,7,3,4,1,8]=>0101010=>0101010=>[2,2,2,2]
[6,2,5,7,4,1,3,8]=>1001100=>0011001=>[3,1,3,1]
[6,2,5,8,4,1,3,7]=>1001100=>0011001=>[3,1,3,1]
[2,7,8,4,6,1,3,5]=>0010100=>0010100=>[3,2,3]
[6,1,2,8,5,4,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[6,2,5,7,8,1,3,4]=>1000100=>0010001=>[3,4,1]
[1,5,4,2,6,7,3,8]=>0110010=>0100110=>[2,3,1,2]
[2,6,5,7,3,8,1,4]=>0101010=>0101010=>[2,2,2,2]
[1,6,2,7,5,8,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,2,7,8,5,6,4]=>0100101=>1010010=>[1,2,3,2]
[1,6,2,4,8,7,3,5]=>0100110=>0110010=>[2,1,3,2]
[6,5,2,1,8,7,3,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[2,6,5,3,7,8,4,1]=>0110011=>1100110=>[1,1,3,1,2]
[6,5,2,3,8,7,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[5,1,4,2,3,7,8,6]=>1010001=>1000101=>[1,4,2,1]
[1,5,4,2,6,3,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[5,1,6,3,8,2,7,4]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,8,7,4,3,1,2]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,4,2,7,8,5,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[6,1,4,8,7,5,2,3]=>1001110=>0111001=>[2,1,1,3,1]
[1,6,4,8,7,5,2,3]=>0101110=>0111010=>[2,1,1,2,2]
[1,8,6,2,4,7,3,5]=>0110010=>0100110=>[2,3,1,2]
[8,1,6,2,4,7,3,5]=>1010010=>0100101=>[2,3,2,1]
[6,4,1,7,8,5,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[7,6,1,2,4,8,3,5]=>1100010=>0100011=>[2,4,1,1]
[1,8,6,3,4,7,2,5]=>0110010=>0100110=>[2,3,1,2]
[1,7,2,5,4,8,3,6]=>0101010=>0101010=>[2,2,2,2]
[7,1,2,5,4,8,3,6]=>1001010=>0101001=>[2,2,3,1]
[2,7,1,5,4,8,3,6]=>0101010=>0101010=>[2,2,2,2]
[2,8,6,1,4,7,3,5]=>0110010=>0100110=>[2,3,1,2]
[7,2,1,5,4,8,3,6]=>1101010=>0101011=>[2,2,2,1,1]
[1,2,7,5,4,8,3,6]=>0011010=>0101100=>[2,2,1,3]
[3,2,7,5,4,8,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[2,5,8,4,7,3,1,6]=>0010110=>0110100=>[2,1,2,3]
[2,3,7,5,4,8,1,6]=>0011010=>0101100=>[2,2,1,3]
[6,8,3,2,4,7,1,5]=>0110010=>0100110=>[2,3,1,2]
[3,7,2,5,4,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[3,1,7,5,4,8,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[1,3,7,5,4,8,2,6]=>0011010=>0101100=>[2,2,1,3]
[1,5,8,4,7,3,2,6]=>0010110=>0110100=>[2,1,2,3]
[5,1,8,4,7,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,8,2,4,7,3,1,6]=>0100110=>0110010=>[2,1,3,2]
[6,8,4,3,7,5,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[8,5,2,4,7,3,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[8,1,5,4,7,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[1,8,5,4,7,3,2,6]=>0110110=>0110110=>[2,1,2,1,2]
[1,7,3,5,4,8,2,6]=>0101010=>0101010=>[2,2,2,2]
[8,6,3,1,4,7,2,5]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,4,1,7,2,5,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,3,7,4,6,8,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[4,1,3,2,7,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[1,4,3,2,7,8,5,6]=>0110010=>0100110=>[2,3,1,2]
[2,4,3,1,7,8,5,6]=>0110010=>0100110=>[2,3,1,2]
[2,7,3,5,4,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[2,8,5,4,7,3,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[5,7,3,4,6,8,2,1]=>0100011=>1100010=>[1,1,4,2]
[8,2,5,4,7,3,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,3,5,4,8,1,6]=>1001010=>0101001=>[2,2,3,1]
[3,2,1,4,7,8,5,6]=>1100010=>0100011=>[2,4,1,1]
[8,1,7,6,4,3,5,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,6,4,5,2,7,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[7,1,8,6,4,3,5,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,4,2,5,1,6,3,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,3,6,5,2,1,4,8]=>1011100=>0011101=>[3,1,1,2,1]
[8,3,6,5,2,1,7,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,3,6,5,2,1,8,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,4,2,8,1,3,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[5,8,2,6,4,1,3,7]=>0101100=>0011010=>[3,1,2,2]
[6,4,2,5,1,8,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,5,2,1,4,7,8]=>1011000=>0001101=>[4,1,2,1]
[2,3,5,8,1,4,7,6]=>0001001=>1001000=>[1,3,4]
[2,3,6,8,1,5,7,4]=>0001001=>1001000=>[1,3,4]
[6,3,8,5,2,7,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[6,3,7,5,2,1,4,8]=>1011100=>0011101=>[3,1,1,2,1]
[2,5,7,6,3,1,4,8]=>0011100=>0011100=>[3,1,1,3]
[2,8,7,6,3,1,5,4]=>0111101=>1011110=>[1,2,1,1,1,2]
[2,5,8,7,6,3,1,4]=>0011110=>0111100=>[2,1,1,1,3]
[2,4,8,1,6,5,7,3]=>0010101=>1010100=>[1,2,2,3]
[2,8,7,3,6,1,4,5]=>0110100=>0010110=>[3,2,1,2]
[8,4,2,5,1,3,7,6]=>1101001=>1001011=>[1,3,2,1,1]
[2,3,6,8,1,4,7,5]=>0001001=>1001000=>[1,3,4]
[2,7,8,6,3,1,4,5]=>0011100=>0011100=>[3,1,1,3]
[2,8,6,3,1,4,5,7]=>0111000=>0001110=>[4,1,1,2]
[8,3,5,2,1,4,6,7]=>1011000=>0001101=>[4,1,2,1]
[2,5,8,1,7,3,6,4]=>0010101=>1010100=>[1,2,2,3]
[2,7,1,5,8,3,4,6]=>0100100=>0010010=>[3,3,2]
[3,7,5,8,1,2,6,4]=>0101001=>1001010=>[1,3,2,2]
[7,3,6,1,2,8,4,5]=>1010010=>0100101=>[2,3,2,1]
[7,4,8,1,6,5,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[6,8,4,5,1,7,2,3]=>0101010=>0101010=>[2,2,2,2]
[5,1,8,7,6,2,3,4]=>1011100=>0011101=>[3,1,1,2,1]
[4,6,1,8,7,5,2,3]=>0101110=>0111010=>[2,1,1,2,2]
[3,4,8,7,1,2,5,6]=>0011000=>0001100=>[4,1,3]
[6,4,8,7,1,2,5,3]=>1011001=>1001101=>[1,3,1,2,1]
[6,5,1,8,2,7,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,1,7,2,8,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,1,7,2,3,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[5,6,8,7,4,1,2,3]=>0011100=>0011100=>[3,1,1,3]
[6,8,3,1,5,2,4,7]=>0110100=>0010110=>[3,2,1,2]
[4,2,7,1,6,3,5,8]=>1010100=>0010101=>[3,2,2,1]
[5,1,7,4,2,6,3,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,8,2,1,4,7,3,6]=>0110010=>0100110=>[2,3,1,2]
[6,8,4,3,1,5,7,2]=>0111001=>1001110=>[1,3,1,1,2]
[6,8,4,2,1,5,7,3]=>0111001=>1001110=>[1,3,1,1,2]
[6,8,3,2,1,4,5,7]=>0111000=>0001110=>[4,1,1,2]
[4,2,1,6,5,8,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,2,1,7,4,5,8]=>1110100=>0010111=>[3,2,1,1,1]
[6,4,2,1,7,5,3,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[5,3,2,7,6,1,4,8]=>1101100=>0011011=>[3,1,2,1,1]
[5,3,2,8,6,1,4,7]=>1101100=>0011011=>[3,1,2,1,1]
[6,3,2,8,7,1,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[4,2,8,1,7,3,5,6]=>1010100=>0010101=>[3,2,2,1]
[4,3,8,7,2,1,5,6]=>1011100=>0011101=>[3,1,1,2,1]
[2,1,5,8,4,7,3,6]=>1001010=>0101001=>[2,2,3,1]
[4,3,2,5,8,1,6,7]=>1100100=>0010011=>[3,3,1,1]
[4,3,2,5,7,1,6,8]=>1100100=>0010011=>[3,3,1,1]
[4,3,1,6,2,7,5,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,1,7,2,8,6,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,2,1,4,8,7,5,6]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,1,4,6,8,5,7]=>1100010=>0100011=>[2,4,1,1]
[8,6,1,4,5,7,2,3]=>1100010=>0100011=>[2,4,1,1]
[3,8,6,4,5,7,1,2]=>0110010=>0100110=>[2,3,1,2]
[5,2,8,3,7,4,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,2,8,5,4,7,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,2,8,4,3,6,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[5,4,2,7,3,6,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,2,8,3,6,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,3,8,4,7,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,2,8,4,3,7,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[6,2,8,3,7,4,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[5,4,2,7,3,1,8,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,4,3,7,1,2,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[6,4,3,8,1,2,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[7,2,8,4,3,1,5,6]=>1011100=>0011101=>[3,1,1,2,1]
[7,5,3,8,4,2,6,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,4,2,7,3,1,5,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,6,4,8,2,3,5,1]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,1,7,8,4,6,2]=>1100101=>1010011=>[1,2,3,1,1]
[5,3,2,7,8,4,6,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,5,1,7,8,2,3,4]=>1100100=>0010011=>[3,3,1,1]
[6,3,1,7,8,4,2,5]=>1100110=>0110011=>[2,1,3,1,1]
[5,4,1,7,3,8,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,3,2,7,8,4,1,5]=>1100110=>0110011=>[2,1,3,1,1]
[6,1,5,4,3,2,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,7,6,1,3,5,2,4]=>1110010=>0100111=>[2,3,1,1,1]
[8,1,6,5,7,3,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,1,5,7,6,2,3]=>1100110=>0110011=>[2,1,3,1,1]
[7,8,6,2,5,3,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,1,3,5,2,8,4,7]=>1001010=>0101001=>[2,2,3,1]
[8,1,3,7,4,2,5,6]=>1001100=>0011001=>[3,1,3,1]
[4,3,8,7,5,2,1,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[6,7,1,8,5,3,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,7,6,4,8,3,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,5,2,7,1,4,8,3]=>1101001=>1001011=>[1,3,2,1,1]
[7,4,6,1,3,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,2,1,3,8,4,6]=>1110010=>0100111=>[2,3,1,1,1]
[8,4,7,6,3,1,5,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,4,1,5,6,3,8,2]=>1100101=>1010011=>[1,2,3,1,1]
[3,4,7,5,6,1,8,2]=>0010101=>1010100=>[1,2,2,3]
[2,7,6,1,3,4,8,5]=>0110001=>1000110=>[1,4,1,2]
[5,7,2,1,6,3,8,4]=>0110101=>1010110=>[1,2,2,1,2]
[4,7,2,5,6,3,8,1]=>0100101=>1010010=>[1,2,3,2]
[8,6,2,5,7,1,4,3]=>1100101=>1010011=>[1,2,3,1,1]
[2,7,4,5,3,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[6,8,7,1,3,2,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,6,5,7,1,4,3]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,4,3,2,6,7,1]=>0111001=>1001110=>[1,3,1,1,2]
[1,8,5,6,2,4,7,3]=>0101001=>1001010=>[1,3,2,2]
[8,1,5,6,2,4,7,3]=>1001001=>1001001=>[1,3,3,1]
[6,4,8,1,3,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,1,2,8,6,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[8,4,5,2,1,6,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[3,1,2,6,8,4,7,5]=>1000101=>1010001=>[1,2,4,1]
[5,1,3,2,7,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[4,6,7,8,3,1,5,2]=>0001101=>1011000=>[1,2,1,4]
[5,2,8,6,3,4,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[5,6,8,4,3,2,7,1]=>0011101=>1011100=>[1,2,1,1,3]
[5,3,8,1,7,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[3,6,7,8,4,2,1,5]=>0001110=>0111000=>[2,1,1,4]
[6,5,1,8,4,3,7,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[6,3,8,4,2,1,7,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,5,8,3,1,6,7,4]=>0011001=>1001100=>[1,3,1,3]
[3,5,8,1,2,6,7,4]=>0010001=>1000100=>[1,4,3]
[3,2,7,8,4,6,1,5]=>1001010=>0101001=>[2,2,3,1]
[5,1,8,3,4,6,7,2]=>1010001=>1000101=>[1,4,2,1]
[4,8,7,2,1,6,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[2,8,1,6,3,4,7,5]=>0101001=>1001010=>[1,3,2,2]
[3,6,1,2,5,8,4,7]=>0100010=>0100010=>[2,4,2]
[1,4,5,8,2,3,7,6]=>0001001=>1001000=>[1,3,4]
[1,5,2,4,6,8,3,7]=>0100010=>0100010=>[2,4,2]
[3,6,1,5,8,2,4,7]=>0100100=>0010010=>[3,3,2]
[2,6,5,1,4,8,3,7]=>0110010=>0100110=>[2,3,1,2]
[2,5,1,8,4,7,3,6]=>0101010=>0101010=>[2,2,2,2]
[2,7,1,4,3,6,8,5]=>0101001=>1001010=>[1,3,2,2]
[1,3,7,5,8,2,4,6]=>0010100=>0010100=>[3,2,3]
[8,2,1,5,7,3,4,6]=>1100100=>0010011=>[3,3,1,1]
[2,5,4,8,1,3,7,6]=>0101001=>1001010=>[1,3,2,2]
[2,4,1,3,8,6,7,5]=>0100101=>1010010=>[1,2,3,2]
[8,4,3,7,1,2,6,5]=>1101001=>1001011=>[1,3,2,1,1]
[1,7,3,5,8,2,6,4]=>0100101=>1010010=>[1,2,3,2]
[1,8,4,2,6,7,3,5]=>0110010=>0100110=>[2,3,1,2]
[3,1,6,8,7,2,4,5]=>1001100=>0011001=>[3,1,3,1]
[7,2,1,6,8,3,4,5]=>1100100=>0010011=>[3,3,1,1]
[4,1,7,2,6,8,3,5]=>1010010=>0100101=>[2,3,2,1]
[5,1,7,2,3,6,8,4]=>1010001=>1000101=>[1,4,2,1]
[7,2,1,6,3,5,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[2,6,1,7,3,5,8,4]=>0101001=>1001010=>[1,3,2,2]
[8,1,3,2,4,6,7,5]=>1010001=>1000101=>[1,4,2,1]
[7,3,1,2,4,6,8,5]=>1100001=>1000011=>[1,5,1,1]
[1,8,3,4,7,2,5,6]=>0100100=>0010010=>[3,3,2]
[3,5,8,1,2,7,4,6]=>0010010=>0100100=>[2,3,3]
[3,6,8,1,2,4,7,5]=>0010001=>1000100=>[1,4,3]
[4,1,3,8,7,2,6,5]=>1001101=>1011001=>[1,2,1,3,1]
[1,3,7,4,8,2,6,5]=>0010101=>1010100=>[1,2,2,3]
[1,4,6,8,2,3,7,5]=>0001001=>1001000=>[1,3,4]
[3,5,8,1,7,2,4,6]=>0010100=>0010100=>[3,2,3]
[2,6,8,1,7,3,4,5]=>0010100=>0010100=>[3,2,3]
[1,8,3,2,7,5,6,4]=>0110101=>1010110=>[1,2,2,1,2]
[2,6,7,3,8,1,5,4]=>0010101=>1010100=>[1,2,2,3]
[8,4,1,7,3,6,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[3,7,2,8,6,1,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[6,2,3,8,7,1,5,4]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,7,8,4,2,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,8,7,4,2,6,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,7,2,8,3,6,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,1,7,8,5,3,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,7,4,8,3,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,8,7,5,3,6,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[4,8,2,7,3,6,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[4,7,2,6,3,5,8,1]=>0101001=>1001010=>[1,3,2,2]
[6,8,2,4,3,7,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,2,4,3,8,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,8,7,2,4,1,5,6]=>0110100=>0010110=>[3,2,1,2]
[3,7,8,2,4,1,5,6]=>0010100=>0010100=>[3,2,3]
[3,6,8,2,4,5,7,1]=>0010001=>1000100=>[1,4,3]
[3,6,7,2,4,5,8,1]=>0010001=>1000100=>[1,4,3]
[1,7,5,3,8,2,4,6]=>0110100=>0010110=>[3,2,1,2]
[1,7,2,4,5,8,3,6]=>0100010=>0100010=>[2,4,2]
[1,7,4,5,8,3,2,6]=>0100110=>0110010=>[2,1,3,2]
[2,6,4,7,8,3,5,1]=>0100101=>1010010=>[1,2,3,2]
[1,2,6,4,7,8,3,5]=>0010010=>0100100=>[2,3,3]
[2,7,4,5,8,1,3,6]=>0100100=>0010010=>[3,3,2]
[2,7,5,3,1,8,4,6]=>0111010=>0101110=>[2,2,1,1,2]
[6,1,4,7,8,3,5,2]=>1000101=>1010001=>[1,2,4,1]
[3,6,4,7,8,1,5,2]=>0100101=>1010010=>[1,2,3,2]
[4,3,6,7,1,8,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[4,3,6,7,1,8,2,5]=>1001010=>0101001=>[2,2,3,1]
[3,7,4,5,2,1,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[1,3,6,4,7,2,8,5]=>0010101=>1010100=>[1,2,2,3]
[3,6,4,7,2,8,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,1,7,3,8,2,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[1,6,7,3,8,2,5,4]=>0010101=>1010100=>[1,2,2,3]
[6,1,4,7,8,5,2,3]=>1000110=>0110001=>[2,1,4,1]
[6,3,2,1,7,8,5,4]=>1110011=>1100111=>[1,1,3,1,1,1]
[6,2,7,3,1,8,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,2,4,7,8,1,5,3]=>1000101=>1010001=>[1,2,4,1]
[2,6,7,3,1,8,5,4]=>0011011=>1101100=>[1,1,2,1,3]
[8,6,5,1,3,2,4,7]=>1110100=>0010111=>[3,2,1,1,1]
[6,4,7,8,3,2,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[3,8,4,7,1,2,5,6]=>0101000=>0001010=>[4,2,2]
[4,8,6,1,5,3,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[5,8,6,4,1,3,2,7]=>0111010=>0101110=>[2,2,1,1,2]
[8,3,6,4,5,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,8,5,7,4,2,3,1]=>0101101=>1011010=>[1,2,1,2,2]
[2,3,8,7,1,6,4,5]=>0011010=>0101100=>[2,2,1,3]
[4,3,7,8,1,6,2,5]=>1001010=>0101001=>[2,2,3,1]
[3,5,8,7,4,1,2,6]=>0011100=>0011100=>[3,1,1,3]
[7,3,8,4,1,2,5,6]=>1011000=>0001101=>[4,1,2,1]
[4,8,1,2,7,3,5,6]=>0100100=>0010010=>[3,3,2]
[6,8,1,2,7,4,5,3]=>0100101=>1010010=>[1,2,3,2]
[5,6,8,4,1,3,7,2]=>0011001=>1001100=>[1,3,1,3]
[8,5,4,7,1,6,3,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,5,8,7,3,6,4,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,4,8,7,5,6,1,3]=>0011010=>0101100=>[2,2,1,3]
[3,7,4,8,5,6,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,4,8,7,5,1,2,3]=>1011100=>0011101=>[3,1,1,2,1]
[3,8,5,2,4,6,7,1]=>0110001=>1000110=>[1,4,1,2]
[5,7,1,8,4,6,2,3]=>0101010=>0101010=>[2,2,2,2]
[6,3,8,7,2,1,4,5]=>1011100=>0011101=>[3,1,1,2,1]
[2,3,7,8,5,6,1,4]=>0001010=>0101000=>[2,2,4]
[3,7,6,8,5,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[2,6,7,8,5,1,3,4]=>0001100=>0011000=>[3,1,4]
[2,4,7,8,1,6,3,5]=>0001010=>0101000=>[2,2,4]
[5,4,7,8,2,6,3,1]=>1001011=>1101001=>[1,1,2,3,1]
[2,8,3,4,1,5,7,6]=>0101001=>1001010=>[1,3,2,2]
[6,8,3,4,1,2,7,5]=>0101001=>1001010=>[1,3,2,2]
[6,8,7,1,5,2,3,4]=>0110100=>0010110=>[3,2,1,2]
[2,5,3,1,8,6,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[4,5,3,2,8,6,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[3,5,8,6,1,4,7,2]=>0011001=>1001100=>[1,3,1,3]
[2,8,5,6,1,4,7,3]=>0101001=>1001010=>[1,3,2,2]
[4,8,6,1,5,2,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[5,8,2,3,7,6,1,4]=>0100110=>0110010=>[2,1,3,2]
[4,6,8,5,3,2,7,1]=>0011101=>1011100=>[1,2,1,1,3]
[2,6,4,8,5,1,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,6,4,8,5,2,1,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,4,8,6,5,2,7,1]=>0011101=>1011100=>[1,2,1,1,3]
[3,4,8,7,5,6,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[7,5,3,2,8,6,1,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[2,5,1,3,8,6,7,4]=>0100101=>1010010=>[1,2,3,2]
[4,5,1,2,8,6,7,3]=>0100101=>1010010=>[1,2,3,2]
[5,4,8,1,3,6,7,2]=>1010001=>1000101=>[1,4,2,1]
[8,3,5,4,1,6,7,2]=>1011001=>1001101=>[1,3,1,2,1]
[5,1,6,4,3,2,8,7]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,3,7,1,4,6,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[2,8,3,6,4,7,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,2,1,7,5,8,3,4]=>1101010=>0101011=>[2,2,2,1,1]
[6,7,2,1,5,8,4,3]=>0110011=>1100110=>[1,1,3,1,2]
[1,6,4,8,3,2,5,7]=>0101100=>0011010=>[3,1,2,2]
[1,8,3,5,6,2,4,7]=>0100100=>0010010=>[3,3,2]
[1,4,8,5,6,2,3,7]=>0010100=>0010100=>[3,2,3]
[6,1,4,8,2,3,5,7]=>1001000=>0001001=>[4,3,1]
[8,7,2,5,6,1,4,3]=>1100101=>1010011=>[1,2,3,1,1]
[1,8,2,5,4,7,3,6]=>0101010=>0101010=>[2,2,2,2]
[5,7,4,1,2,3,8,6]=>0110001=>1000110=>[1,4,1,2]
[1,7,4,2,5,3,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[6,7,4,2,1,3,8,5]=>0111001=>1001110=>[1,3,1,1,2]
[6,4,3,8,5,7,1,2]=>1101010=>0101011=>[2,2,2,1,1]
[6,8,4,2,3,1,5,7]=>0110100=>0010110=>[3,2,1,2]
[8,6,4,1,3,7,2,5]=>1110010=>0100111=>[2,3,1,1,1]
[5,3,6,1,8,2,4,7]=>1010100=>0010101=>[3,2,2,1]
[3,1,8,5,4,7,6,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,1,5,8,3,7,6,2]=>1001011=>1101001=>[1,1,2,3,1]
[4,1,5,3,8,7,6,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,5,1,8,2,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[4,8,5,3,1,7,6,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,5,2,8,1,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[4,6,2,8,7,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,8,6,3,7,1,5,2]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,8,2,7,5,1,3]=>0010110=>0110100=>[2,1,2,3]
[4,6,2,8,7,5,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[5,6,2,7,4,1,8,3]=>0101101=>1011010=>[1,2,1,2,2]
[5,6,7,2,3,1,8,4]=>0010101=>1010100=>[1,2,2,3]
[5,6,7,2,8,3,1,4]=>0010110=>0110100=>[2,1,2,3]
[5,6,7,2,1,8,3,4]=>0011010=>0101100=>[2,2,1,3]
[5,6,7,2,1,3,8,4]=>0011001=>1001100=>[1,3,1,3]
[5,6,1,7,8,2,4,3]=>0100101=>1010010=>[1,2,3,2]
[5,6,1,7,2,4,8,3]=>0101001=>1001010=>[1,3,2,2]
[4,1,6,8,7,3,5,2]=>1001101=>1011001=>[1,2,1,3,1]
[4,1,6,8,7,5,3,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[5,6,1,7,8,4,2,3]=>0100110=>0110010=>[2,1,3,2]
[4,6,8,1,7,5,2,3]=>0010110=>0110100=>[2,1,2,3]
[4,8,6,1,7,5,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,6,7,1,8,3,2,4]=>0010110=>0110100=>[2,1,2,3]
[5,6,7,1,3,8,2,4]=>0010010=>0100100=>[2,3,3]
[5,6,7,1,3,2,8,4]=>0010101=>1010100=>[1,2,2,3]
[5,6,7,3,1,2,8,4]=>0011001=>1001100=>[1,3,1,3]
[5,6,8,7,4,2,1,3]=>0011110=>0111100=>[2,1,1,1,3]
[7,8,1,3,5,6,2,4]=>0100010=>0100010=>[2,4,2]
[7,8,3,1,5,6,2,4]=>0110010=>0100110=>[2,3,1,2]
[7,1,3,8,5,6,2,4]=>1001010=>0101001=>[2,2,3,1]
[5,1,7,8,3,4,6,2]=>1001001=>1001001=>[1,3,3,1]
[1,5,7,8,3,4,6,2]=>0001001=>1001000=>[1,3,4]
[3,7,1,5,8,6,2,4]=>0100110=>0110010=>[2,1,3,2]
[1,3,7,8,2,5,6,4]=>0001001=>1001000=>[1,3,4]
[3,1,7,8,5,2,6,4]=>1001101=>1011001=>[1,2,1,3,1]
[1,3,7,5,8,2,6,4]=>0010101=>1010100=>[1,2,2,3]
[3,1,7,5,8,2,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,5,7,1,8,4,6,2]=>0010101=>1010100=>[1,2,2,3]
[3,5,7,8,1,4,6,2]=>0001001=>1001000=>[1,3,4]
[5,3,7,8,4,6,1,2]=>1001010=>0101001=>[2,2,3,1]
[5,3,7,8,4,1,6,2]=>1001101=>1011001=>[1,2,1,3,1]
[5,3,7,8,1,4,6,2]=>1001001=>1001001=>[1,3,3,1]
[5,3,7,1,8,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[1,5,3,7,8,4,2,6]=>0100110=>0110010=>[2,1,3,2]
[5,1,3,7,8,4,2,6]=>1000110=>0110001=>[2,1,4,1]
[3,6,2,1,4,5,8,7]=>0110001=>1000110=>[1,4,1,2]
[6,4,2,5,1,3,8,7]=>1101001=>1001011=>[1,3,2,1,1]
[8,6,1,7,3,2,4,5]=>1101100=>0011011=>[3,1,2,1,1]
[2,5,8,1,7,3,4,6]=>0010100=>0010100=>[3,2,3]
[6,8,2,7,3,1,4,5]=>0101100=>0011010=>[3,1,2,2]
[6,8,2,3,7,1,4,5]=>0100100=>0010010=>[3,3,2]
[8,6,2,7,4,5,1,3]=>1101010=>0101011=>[2,2,2,1,1]
[5,2,8,1,7,3,4,6]=>1010100=>0010101=>[3,2,2,1]
[4,2,3,8,1,5,6,7]=>1001000=>0001001=>[4,3,1]
[5,2,8,3,7,1,4,6]=>1010100=>0010101=>[3,2,2,1]
[5,2,8,4,6,1,3,7]=>1010100=>0010101=>[3,2,2,1]
[2,1,5,8,4,3,6,7]=>1001100=>0011001=>[3,1,3,1]
[5,8,3,2,7,1,4,6]=>0110100=>0010110=>[3,2,1,2]
[4,1,3,8,2,5,6,7]=>1001000=>0001001=>[4,3,1]
[5,1,8,3,7,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[5,1,8,4,6,2,3,7]=>1010100=>0010101=>[3,2,2,1]
[5,8,4,1,6,2,3,7]=>0110100=>0010110=>[3,2,1,2]
[4,5,8,1,6,2,3,7]=>0010100=>0010100=>[3,2,3]
[5,4,8,1,6,2,3,7]=>1010100=>0010101=>[3,2,2,1]
[4,8,5,1,6,2,3,7]=>0110100=>0010110=>[3,2,1,2]
[2,1,5,4,8,3,6,7]=>1010100=>0010101=>[3,2,2,1]
[2,4,3,8,1,5,6,7]=>0101000=>0001010=>[4,2,2]
[3,1,8,4,2,5,6,7]=>1011000=>0001101=>[4,1,2,1]
[3,8,4,2,1,5,6,7]=>0111000=>0001110=>[4,1,1,2]
[2,3,8,4,1,5,6,7]=>0011000=>0001100=>[4,1,3]
[3,4,2,8,1,5,6,7]=>0101000=>0001010=>[4,2,2]
[3,8,5,2,7,1,4,6]=>0110100=>0010110=>[3,2,1,2]
[4,8,5,2,6,1,3,7]=>0110100=>0010110=>[3,2,1,2]
[2,1,4,8,5,3,6,7]=>1001100=>0011001=>[3,1,3,1]
[3,2,8,4,1,5,6,7]=>1011000=>0001101=>[4,1,2,1]
[2,8,4,3,1,5,6,7]=>0111000=>0001110=>[4,1,1,2]
[4,1,7,5,6,2,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,4,3,8,1,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,7,4,3,8,2,6,1]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,4,2,6,7,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[3,8,4,1,6,7,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,1,7,5,2,8,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,6,4,3,2,8,1,7]=>0111010=>0101110=>[2,2,1,1,2]
[2,6,7,5,3,8,4,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,1,6,7,5,3,8,4]=>1001101=>1011001=>[1,2,1,3,1]
[3,8,4,2,1,6,7,5]=>0111001=>1001110=>[1,3,1,1,2]
[5,7,4,3,8,2,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[6,7,4,8,1,2,5,3]=>0101001=>1001010=>[1,3,2,2]
[6,7,5,8,1,2,4,3]=>0101001=>1001010=>[1,3,2,2]
[6,7,4,8,3,1,2,5]=>0101100=>0011010=>[3,1,2,2]
[6,1,3,4,8,2,5,7]=>1000100=>0010001=>[3,4,1]
[6,2,3,4,8,1,5,7]=>1000100=>0010001=>[3,4,1]
[3,4,8,2,1,5,7,6]=>0011001=>1001100=>[1,3,1,3]
[6,7,5,8,3,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[2,5,7,6,1,4,8,3]=>0011001=>1001100=>[1,3,1,3]
[6,7,4,8,2,3,5,1]=>0101001=>1001010=>[1,3,2,2]
[6,7,4,8,1,3,5,2]=>0101001=>1001010=>[1,3,2,2]
[2,6,7,5,1,3,8,4]=>0011001=>1001100=>[1,3,1,3]
[6,3,1,4,8,2,5,7]=>1100100=>0010011=>[3,3,1,1]
[6,7,4,8,1,3,2,5]=>0101010=>0101010=>[2,2,2,2]
[6,7,5,8,4,1,3,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,7,4,8,2,1,3,5]=>0101100=>0011010=>[3,1,2,2]
[6,7,4,8,1,2,3,5]=>0101000=>0001010=>[4,2,2]
[7,8,3,2,6,1,4,5]=>0110100=>0010110=>[3,2,1,2]
[3,4,8,2,6,1,7,5]=>0010101=>1010100=>[1,2,2,3]
[7,8,4,1,5,6,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[7,8,1,2,6,3,4,5]=>0100100=>0010010=>[3,3,2]
[7,8,5,1,4,6,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[5,3,8,4,1,6,7,2]=>1011001=>1001101=>[1,3,1,2,1]
[6,2,4,8,1,5,3,7]=>1001010=>0101001=>[2,2,3,1]
[3,4,8,5,1,6,7,2]=>0011001=>1001100=>[1,3,1,3]
[5,3,8,1,4,6,7,2]=>1010001=>1000101=>[1,4,2,1]
[4,2,6,8,1,5,3,7]=>1001010=>0101001=>[2,2,3,1]
[7,4,2,8,1,5,3,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,1,7,5,8,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,2,7,8,5,3,4,6]=>0001100=>0011000=>[3,1,4]
[6,3,7,8,5,4,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[6,1,5,7,8,4,3,2]=>1000111=>1110001=>[1,1,1,4,1]
[1,7,5,6,8,4,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[3,1,8,4,5,6,7,2]=>1010001=>1000101=>[1,4,2,1]
[4,2,1,8,6,5,3,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,2,7,8,5,1,4,6]=>1001100=>0011001=>[3,1,3,1]
[2,3,7,8,5,1,4,6]=>0001100=>0011000=>[3,1,4]
[2,7,3,8,5,1,4,6]=>0101100=>0011010=>[3,1,2,2]
[3,6,2,8,5,1,4,7]=>0101100=>0011010=>[3,1,2,2]
[1,4,2,8,7,5,3,6]=>0101110=>0111010=>[2,1,1,2,2]
[7,3,6,8,5,4,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[7,2,1,8,5,3,4,6]=>1101100=>0011011=>[3,1,2,1,1]
[1,2,6,8,4,5,3,7]=>0001010=>0101000=>[2,2,4]
[7,1,6,5,8,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,5,7,1,8,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,7,6,1,8,4,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,7,1,5,8,4,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[7,1,2,8,4,5,3,6]=>1001010=>0101001=>[2,2,3,1]
[7,6,1,5,8,4,3,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,5,6,1,8,4,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[9,10,7,8,5,6,2,1,3,4]=>010101100=>001101010=>[3,1,2,2,2]
[9,10,7,8,4,3,5,6,1,2]=>010110010=>010011010=>[2,3,1,2,2]
[9,10,7,8,4,2,5,1,3,6]=>010110100=>001011010=>[3,2,1,2,2]
[9,10,7,8,3,2,1,4,5,6]=>010111000=>000111010=>[4,1,1,2,2]
[9,10,6,5,7,8,3,4,1,2]=>011001010=>010100110=>[2,2,3,1,2]
[9,10,6,5,7,8,2,1,3,4]=>011001100=>001100110=>[3,1,3,1,2]
[9,10,6,4,7,3,5,8,1,2]=>011010010=>010010110=>[2,3,2,1,2]
[9,10,6,4,7,2,5,1,3,8]=>011010100=>001010110=>[3,2,2,1,2]
[9,10,6,3,7,2,1,4,5,8]=>011011000=>000110110=>[4,1,2,1,2]
[9,10,5,4,3,6,7,8,1,2]=>011100010=>010001110=>[2,4,1,1,2]
[9,10,5,4,2,6,7,1,3,8]=>011100100=>001001110=>[3,3,1,1,2]
[9,10,5,3,2,6,1,4,7,8]=>011101000=>000101110=>[4,2,1,1,2]
[9,10,4,3,2,1,5,6,7,8]=>011110000=>000011110=>[5,1,1,1,2]
[8,7,9,10,5,6,3,4,1,2]=>100101010=>010101001=>[2,2,2,3,1]
[8,7,9,10,5,6,2,1,3,4]=>100101100=>001101001=>[3,1,2,3,1]
[8,7,9,10,4,3,5,6,1,2]=>100110010=>010011001=>[2,3,1,3,1]
[8,7,9,10,4,2,5,1,3,6]=>100110100=>001011001=>[3,2,1,3,1]
[8,7,9,10,3,2,1,4,5,6]=>100111000=>000111001=>[4,1,1,3,1]
[8,6,9,5,7,10,3,4,1,2]=>101001010=>010100101=>[2,2,3,2,1]
[8,6,9,5,7,10,2,1,3,4]=>101001100=>001100101=>[3,1,3,2,1]
[8,6,9,4,7,3,5,10,1,2]=>101010010=>010010101=>[2,3,2,2,1]
[8,6,9,3,7,2,1,4,5,10]=>101011000=>000110101=>[4,1,2,2,1]
[8,5,9,4,3,6,7,10,1,2]=>101100010=>010001101=>[2,4,1,2,1]
[8,5,9,4,2,6,7,1,3,10]=>101100100=>001001101=>[3,3,1,2,1]
[8,5,9,3,2,6,1,4,7,10]=>101101000=>000101101=>[4,2,1,2,1]
[8,4,9,3,2,1,5,6,7,10]=>101110000=>000011101=>[5,1,1,2,1]
[7,6,5,8,9,10,3,4,1,2]=>110001010=>010100011=>[2,2,4,1,1]
[7,6,5,8,9,10,2,1,3,4]=>110001100=>001100011=>[3,1,4,1,1]
[7,6,4,8,9,3,5,10,1,2]=>110010010=>010010011=>[2,3,3,1,1]
[7,6,4,8,9,2,5,1,3,10]=>110010100=>001010011=>[3,2,3,1,1]
[7,6,3,8,9,2,1,4,5,10]=>110011000=>000110011=>[4,1,3,1,1]
[7,5,4,8,3,6,9,10,1,2]=>110100010=>010001011=>[2,4,2,1,1]
[7,5,4,8,2,6,9,1,3,10]=>110100100=>001001011=>[3,3,2,1,1]
[7,4,3,8,2,1,5,6,9,10]=>110110000=>000011011=>[5,1,2,1,1]
[6,5,4,2,7,8,9,1,3,10]=>111000100=>001000111=>[3,4,1,1,1]
[6,5,3,2,7,8,1,4,9,10]=>111001000=>000100111=>[4,3,1,1,1]
[7,1,6,5,3,2,4,8]=>1011100=>0011101=>[3,1,1,2,1]
[1,8,7,5,3,2,4,6]=>0111100=>0011110=>[3,1,1,1,2]
[1,8,7,4,2,5,3,6]=>0111010=>0101110=>[2,2,1,1,2]
[8,7,4,2,5,3,6,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,1,6,4,2,5,3,8]=>1011010=>0101101=>[2,2,1,2,1]
[2,6,5,4,7,1,3,8]=>0110100=>0010110=>[3,2,1,2]
[7,1,5,3,6,4,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,3,7,1,6,4,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,3,6,4,2,7,1,8]=>1011010=>0101101=>[2,2,1,2,1]
[1,5,3,8,7,4,2,6]=>0101110=>0111010=>[2,1,1,2,2]
[7,4,2,8,6,3,5,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,3,6,1,8,7,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,1,5,3,8,7,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,8,7,5,4,6,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[2,3,1,8,7,5,4,6]=>0101110=>0111010=>[2,1,1,2,2]
[7,4,2,1,8,6,3,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[1,8,6,3,5,7,4,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,3,8,5,2,1,7,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,6,3,7,4,2,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[2,8,6,4,7,5,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[5,1,8,6,3,7,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,3,7,4,1,8,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,5,2,6,3,7,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,1,8,7,4,2,5,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,6,3,7,4,2,5,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,8,6,3,2,4,7,5]=>0111001=>1001110=>[1,3,1,1,2]
[8,6,3,2,4,7,5,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,5,1,8,6,3,2,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,1,8,7,5,3,2,4]=>1011110=>0111101=>[2,1,1,1,2,1]
[2,4,5,1,3,8,7,6]=>0010011=>1100100=>[1,1,3,3]
[1,7,5,8,6,3,2,4]=>0101110=>0111010=>[2,1,1,2,2]
[1,7,4,2,5,8,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[8,6,3,1,7,4,2,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,7,4,2,5,3,1,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[5,3,1,8,7,4,2,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,1,8,7,5,3,2,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[2,8,6,4,1,3,7,5]=>0111001=>1001110=>[1,3,1,1,2]
[4,1,8,6,3,2,7,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,4,2,8,6,3,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,3,1,8,5,2,7,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,2,6,3,1,7,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,4,8,5,2,6,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,8,5,2,7,4,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[7,4,6,3,1,8,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,3,1,7,4,8,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,1,7,5,8,6,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,3,1,7,5,8,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[7,4,8,5,2,1,6,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[1,7,4,6,3,8,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,6,5,2,1,4,8,7]=>0111001=>1001110=>[1,3,1,1,2]
[3,5,6,2,1,4,8,7]=>0011001=>1001100=>[1,3,1,3]
[3,5,7,8,1,4,2,6]=>0001010=>0101000=>[2,2,4]
[4,1,8,5,7,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[4,1,7,5,8,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[2,1,5,8,7,4,3,6]=>1001110=>0111001=>[2,1,1,3,1]
[5,1,7,4,8,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[4,7,2,8,3,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,6,2,7,3,1,8,5]=>0101101=>1011010=>[1,2,1,2,2]
[3,7,8,2,4,1,6,5]=>0010101=>1010100=>[1,2,2,3]
[3,8,7,2,4,1,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,6,2,4,1,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[6,2,8,4,1,7,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,3,4,8,1,6,2,5]=>1001010=>0101001=>[2,2,3,1]
[6,3,4,8,1,7,2,5]=>1001010=>0101001=>[2,2,3,1]
[5,3,4,8,1,2,7,6]=>1001001=>1001001=>[1,3,3,1]
[4,3,5,8,1,2,7,6]=>1001001=>1001001=>[1,3,3,1]
[1,8,5,4,2,3,7,6]=>0111001=>1001110=>[1,3,1,1,2]
[3,5,4,8,1,2,7,6]=>0101001=>1001010=>[1,3,2,2]
[4,5,3,8,1,2,7,6]=>0101001=>1001010=>[1,3,2,2]
[6,4,3,8,1,7,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,3,8,1,6,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,3,8,7,1,2,4]=>1101100=>0011011=>[3,1,2,1,1]
[5,6,3,8,7,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[4,6,3,8,1,7,2,5]=>0101010=>0101010=>[2,2,2,2]
[2,6,8,4,1,7,3,5]=>0011010=>0101100=>[2,2,1,3]
[1,8,7,4,2,6,3,5]=>0111010=>0101110=>[2,2,1,1,2]
[5,7,3,8,6,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[3,7,5,8,6,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[2,7,8,5,6,1,3,4]=>0010100=>0010100=>[3,2,3]
[1,8,7,5,6,2,3,4]=>0110100=>0010110=>[3,2,1,2]
[2,6,8,5,7,1,3,4]=>0010100=>0010100=>[3,2,3]
[5,3,6,8,7,1,2,4]=>1001100=>0011001=>[3,1,3,1]
[7,2,8,5,6,1,3,4]=>1010100=>0010101=>[3,2,2,1]
[5,2,8,6,7,1,3,4]=>1010100=>0010101=>[3,2,2,1]
[1,8,3,2,7,6,4,5]=>0110110=>0110110=>[2,1,2,1,2]
[5,2,8,7,6,1,3,4]=>1011100=>0011101=>[3,1,1,2,1]
[6,2,8,7,5,1,3,4]=>1011100=>0011101=>[3,1,1,2,1]
[3,4,7,8,1,6,2,5]=>0001010=>0101000=>[2,2,4]
[1,8,5,7,6,2,3,4]=>0101100=>0011010=>[3,1,2,2]
[2,5,8,7,6,1,3,4]=>0011100=>0011100=>[3,1,1,3]
[7,4,6,5,8,1,2,3]=>1010100=>0010101=>[3,2,2,1]
[2,6,8,7,5,1,3,4]=>0011100=>0011100=>[3,1,1,3]
[1,8,6,7,5,2,3,4]=>0101100=>0011010=>[3,1,2,2]
[2,7,8,6,5,1,3,4]=>0011100=>0011100=>[3,1,1,3]
[5,7,6,4,8,1,2,3]=>0110100=>0010110=>[3,2,1,2]
[6,1,3,2,4,8,7,5]=>1010011=>1100101=>[1,1,3,2,1]
[8,7,4,2,3,6,1,5]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,1,5,4,2,3,6]=>1101100=>0011011=>[3,1,2,1,1]
[3,7,1,5,2,8,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[8,7,2,5,4,1,3,6]=>1101100=>0011011=>[3,1,2,1,1]
[5,2,8,7,1,4,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,8,6,2,4,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,1,6,2,7,5,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,1,6,2,8,5,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,4,3,5,1,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,7,2,3,8,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[8,2,3,5,1,7,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[7,6,3,1,4,8,2,5]=>1110010=>0100111=>[2,3,1,1,1]
[7,2,8,1,6,5,3,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,6,4,3,8,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[5,1,7,4,3,8,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[5,3,1,7,4,8,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,8,2,1,5,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[8,2,4,1,6,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,5,1,6,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,1,7,3,2,8,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,7,2,1,6,3,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[6,2,1,5,3,8,4,7]=>1101010=>0101011=>[2,2,2,1,1]
[5,3,1,6,2,8,4,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,1,5,2,8,4,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,3,8,1,5,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,8,1,5,3,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[6,1,5,3,2,8,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[6,3,2,8,4,1,5,7]=>1101100=>0011011=>[3,1,2,1,1]
[7,3,4,2,8,5,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,5,1,3,7,4,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[3,8,6,1,5,2,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,5,6,1,7,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[6,7,1,3,8,5,2,4]=>0100110=>0110010=>[2,1,3,2]
[3,6,7,1,5,2,8,4]=>0010101=>1010100=>[1,2,2,3]
[7,1,3,8,4,2,6,5]=>1001101=>1011001=>[1,2,1,3,1]
[5,6,2,7,1,3,8,4]=>0101001=>1001010=>[1,3,2,2]
[5,6,2,8,1,3,7,4]=>0101001=>1001010=>[1,3,2,2]
[6,1,8,3,7,5,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,2,1,5,8,3,6]=>1110010=>0100111=>[2,3,1,1,1]
[7,4,1,5,8,3,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[7,3,2,6,4,8,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[6,4,2,7,3,8,1,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,8,3,1,5,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[5,2,1,7,4,8,3,6]=>1101010=>0101011=>[2,2,2,1,1]
[6,1,8,4,5,2,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,6,4,5,2,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[3,5,2,7,1,6,8,4]=>0101001=>1001010=>[1,3,2,2]
[4,5,7,3,1,6,8,2]=>0011001=>1001100=>[1,3,1,3]
[4,5,7,2,8,6,1,3]=>0010110=>0110100=>[2,1,2,3]
[4,5,7,2,8,1,3,6]=>0010100=>0010100=>[3,2,3]
[4,6,7,2,1,5,8,3]=>0011001=>1001100=>[1,3,1,3]
[4,6,7,1,3,8,5,2]=>0010011=>1100100=>[1,1,3,3]
[3,6,1,5,7,8,4,2]=>0100011=>1100010=>[1,1,4,2]
[4,6,7,1,5,8,3,2]=>0010011=>1100100=>[1,1,3,3]
[6,1,4,2,5,3,7,8]=>1010100=>0010101=>[3,2,2,1]
[1,3,7,5,4,2,8,6]=>0011101=>1011100=>[1,2,1,1,3]
[6,1,3,5,4,2,7,8]=>1001100=>0011001=>[3,1,3,1]
[6,1,2,5,4,7,3,8]=>1001010=>0101001=>[2,2,3,1]
[5,2,6,3,4,7,1,8]=>1010010=>0100101=>[2,3,2,1]
[2,4,7,1,5,3,8,6]=>0010101=>1010100=>[1,2,2,3]
[2,3,6,7,4,8,1,5]=>0001010=>0101000=>[2,2,4]
[1,3,6,7,4,8,5,2]=>0001011=>1101000=>[1,1,2,4]
[2,7,6,5,3,1,8,4]=>0111101=>1011110=>[1,2,1,1,1,2]
[5,2,6,1,4,7,8,3]=>1010001=>1000101=>[1,4,2,1]
[4,7,6,5,2,1,8,3]=>0111101=>1011110=>[1,2,1,1,1,2]
[6,3,1,5,4,7,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,6,1,4,2,7,8]=>1010100=>0010101=>[3,2,2,1]
[1,7,4,2,6,3,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[5,7,4,1,2,3,6,8]=>0110000=>0000110=>[5,1,2]
[6,4,1,2,5,3,7,8]=>1100100=>0010011=>[3,3,1,1]
[4,7,6,3,8,5,1,2]=>0110110=>0110110=>[2,1,2,1,2]
[3,7,6,5,2,8,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[3,7,6,5,1,2,8,4]=>0111001=>1001110=>[1,3,1,1,2]
[4,7,2,6,1,3,8,5]=>0101001=>1001010=>[1,3,2,2]
[2,7,6,5,8,1,4,3]=>0110101=>1010110=>[1,2,2,1,2]
[4,2,6,8,3,1,5,7]=>1001100=>0011001=>[3,1,3,1]
[3,7,6,2,4,5,1,8]=>0110010=>0100110=>[2,3,1,2]
[2,3,6,5,8,1,4,7]=>0010100=>0010100=>[3,2,3]
[2,3,5,8,6,1,4,7]=>0001100=>0011000=>[3,1,4]
[4,2,3,8,6,1,5,7]=>1001100=>0011001=>[3,1,3,1]
[1,2,3,7,4,6,8,5]=>0001001=>1001000=>[1,3,4]
[3,2,7,1,4,5,8,6]=>1010001=>1000101=>[1,4,2,1]
[2,1,5,3,8,7,4,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,8,3,2,4,1,6,7]=>0110100=>0010110=>[3,2,1,2]
[4,2,7,1,8,3,5,6]=>1010100=>0010101=>[3,2,2,1]
[1,2,7,5,3,8,4,6]=>0011010=>0101100=>[2,2,1,3]
[3,2,7,1,4,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[1,2,3,7,6,8,4,5]=>0001010=>0101000=>[2,2,4]
[1,2,3,6,8,7,4,5]=>0000110=>0110000=>[2,1,5]
[1,2,3,7,8,4,6,5]=>0000101=>1010000=>[1,2,5]
[1,2,3,6,8,4,7,5]=>0000101=>1010000=>[1,2,5]
[6,2,8,3,7,5,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,8,3,7,5,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,4,8,6,5,1,2]=>1001110=>0111001=>[2,1,1,3,1]
[5,3,4,8,7,2,6,1]=>1001101=>1011001=>[1,2,1,3,1]
[4,6,3,8,5,7,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[7,5,3,8,6,2,4,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,6,8,3,7,4,5,1]=>0010101=>1010100=>[1,2,2,3]
[2,5,8,3,7,4,6,1]=>0010101=>1010100=>[1,2,2,3]
[7,4,3,8,6,2,5,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,5,4,8,7,2,6,1]=>0101101=>1011010=>[1,2,1,2,2]
[4,5,3,8,6,7,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,6,7,8,4,5,2,1]=>0001011=>1101000=>[1,1,2,4]
[1,8,5,6,4,7,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[2,5,8,6,4,7,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[6,3,7,8,4,5,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[4,3,7,8,5,6,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,8,6,5,7,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,2,8,6,7,4,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[2,3,8,7,5,4,6,1]=>0011101=>1011100=>[1,2,1,1,3]
[1,8,2,7,4,5,6,3]=>0101001=>1001010=>[1,3,2,2]
[7,2,8,6,3,4,5,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,2,8,4,5,7,3,1]=>1010011=>1100101=>[1,1,3,2,1]
[5,2,8,4,6,7,3,1]=>1010011=>1100101=>[1,1,3,2,1]
[4,3,6,8,5,7,2,1]=>1001011=>1101001=>[1,1,2,3,1]
[3,4,6,8,7,2,5,1]=>0001101=>1011000=>[1,2,1,4]
[7,3,5,8,6,2,4,1]=>1001101=>1011001=>[1,2,1,3,1]
[1,8,3,5,7,4,6,2]=>0100101=>1010010=>[1,2,3,2]
[2,7,8,4,5,6,3,1]=>0010011=>1100100=>[1,1,3,3]
[3,7,5,8,4,6,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[5,7,4,6,8,3,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[3,6,5,8,4,7,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,8,4,5,7,3,1]=>0010011=>1100100=>[1,1,3,3]
[4,2,7,1,3,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[4,2,5,1,3,8,6,7]=>1010010=>0100101=>[2,3,2,1]
[5,3,6,1,7,2,4,8]=>1010100=>0010101=>[3,2,2,1]
[3,7,1,2,5,8,6,4]=>0100011=>1100010=>[1,1,4,2]
[3,7,4,1,2,8,5,6]=>0110010=>0100110=>[2,3,1,2]
[7,5,1,3,4,8,6,2]=>1100011=>1100011=>[1,1,4,1,1]
[7,5,1,2,4,8,6,3]=>1100011=>1100011=>[1,1,4,1,1]
[6,4,2,3,7,1,5,8]=>1100100=>0010011=>[3,3,1,1]
[7,6,3,8,1,2,5,4]=>1101001=>1001011=>[1,3,2,1,1]
[7,4,2,3,8,1,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[4,7,5,2,8,1,3,6]=>0110100=>0010110=>[3,2,1,2]
[8,2,6,3,7,1,4,5]=>1010100=>0010101=>[3,2,2,1]
[8,6,1,2,7,4,5,3]=>1100101=>1010011=>[1,2,3,1,1]
[8,4,7,1,2,3,6,5]=>1010001=>1000101=>[1,4,2,1]
[8,5,7,1,2,4,6,3]=>1010001=>1000101=>[1,4,2,1]
[3,8,5,6,1,2,4,7]=>0101000=>0001010=>[4,2,2]
[3,7,5,8,1,2,4,6]=>0101000=>0001010=>[4,2,2]
[7,6,4,8,1,3,5,2]=>1101001=>1001011=>[1,3,2,1,1]
[6,5,8,1,2,4,7,3]=>1010001=>1000101=>[1,4,2,1]
[3,6,8,1,2,5,7,4]=>0010001=>1000100=>[1,4,3]
[4,6,3,8,1,2,5,7]=>0101000=>0001010=>[4,2,2]
[4,6,3,7,1,2,5,8]=>0101000=>0001010=>[4,2,2]
[4,1,7,8,2,3,6,5]=>1001001=>1001001=>[1,3,3,1]
[5,1,2,8,6,3,4,7]=>1001100=>0011001=>[3,1,3,1]
[5,3,8,1,6,2,4,7]=>1010100=>0010101=>[3,2,2,1]
[6,1,8,5,2,3,4,7]=>1011000=>0001101=>[4,1,2,1]
[6,1,7,5,2,3,4,8]=>1011000=>0001101=>[4,1,2,1]
[6,8,1,3,7,4,5,2]=>0100101=>1010010=>[1,2,3,2]
[7,2,8,1,6,3,4,5]=>1010100=>0010101=>[3,2,2,1]
[4,7,8,2,5,1,3,6]=>0010100=>0010100=>[3,2,3]
[6,8,2,7,1,4,5,3]=>0101001=>1001010=>[1,3,2,2]
[4,8,7,1,3,5,6,2]=>0110001=>1000110=>[1,4,1,2]
[3,8,7,1,2,4,6,5]=>0110001=>1000110=>[1,4,1,2]
[4,8,7,1,2,3,6,5]=>0110001=>1000110=>[1,4,1,2]
[5,8,7,1,2,4,6,3]=>0110001=>1000110=>[1,4,1,2]
[5,8,7,1,3,4,6,2]=>0110001=>1000110=>[1,4,1,2]
[7,1,8,6,2,3,5,4]=>1011001=>1001101=>[1,3,1,2,1]
[5,8,6,4,1,2,3,7]=>0111000=>0001110=>[4,1,1,2]
[5,1,3,4,6,7,2,8]=>1000010=>0100001=>[2,5,1]
[1,3,4,8,7,5,2,6]=>0001110=>0111000=>[2,1,1,4]
[8,2,4,1,7,3,5,6]=>1010100=>0010101=>[3,2,2,1]
[8,6,1,4,2,3,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[3,6,1,4,2,8,7,5]=>0101011=>1101010=>[1,1,2,2,2]
[1,6,8,4,3,7,2,5]=>0011010=>0101100=>[2,2,1,3]
[3,1,4,7,8,5,2,6]=>1000110=>0110001=>[2,1,4,1]
[6,1,7,4,3,8,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[1,8,7,4,3,6,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[7,4,1,3,8,2,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[4,8,2,3,1,5,7,6]=>0101001=>1001010=>[1,3,2,2]
[4,8,6,2,1,3,7,5]=>0111001=>1001110=>[1,3,1,1,2]
[2,7,4,1,8,3,5,6]=>0110100=>0010110=>[3,2,1,2]
[1,7,8,4,2,3,6,5]=>0011001=>1001100=>[1,3,1,3]
[8,7,1,3,4,2,6,5]=>1100101=>1010011=>[1,2,3,1,1]
[1,7,4,3,6,2,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,6,4,5,2,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[3,8,4,6,5,2,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[2,4,3,7,5,8,1,6]=>0101010=>0101010=>[2,2,2,2]
[1,4,7,3,6,2,8,5]=>0010101=>1010100=>[1,2,2,3]
[6,4,1,3,7,2,8,5]=>1100101=>1010011=>[1,2,3,1,1]
[8,1,4,3,6,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,3,8,5,7,1,6]=>1001010=>0101001=>[2,2,3,1]
[2,8,5,7,3,4,1,6]=>0101010=>0101010=>[2,2,2,2]
[5,8,2,6,4,3,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[7,2,5,8,4,3,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[4,2,3,5,8,7,1,6]=>1000110=>0110001=>[2,1,4,1]
[8,2,3,5,4,7,1,6]=>1001010=>0101001=>[2,2,3,1]
[6,1,8,3,4,2,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[1,8,6,4,2,3,7,5]=>0111001=>1001110=>[1,3,1,1,2]
[3,8,4,5,6,2,1,7]=>0100110=>0110010=>[2,1,3,2]
[3,8,6,5,4,2,1,7]=>0111110=>0111110=>[2,1,1,1,1,2]
[6,3,1,4,2,8,7,5]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,3,8,1,2,6,4,5]=>1010010=>0100101=>[2,3,2,1]
[7,1,4,5,3,2,6,8]=>1001100=>0011001=>[3,1,3,1]
[1,8,4,2,6,5,3,7]=>0110110=>0110110=>[2,1,2,1,2]
[5,1,4,8,6,3,2,7]=>1001110=>0111001=>[2,1,1,3,1]
[5,3,1,8,4,7,2,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,3,8,1,5,7,2,6]=>1010010=>0100101=>[2,3,2,1]
[6,3,1,2,5,7,4,8]=>1100010=>0100011=>[2,4,1,1]
[7,1,4,2,6,5,3,8]=>1010110=>0110101=>[2,1,2,2,1]
[3,8,4,1,6,5,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[7,5,3,6,4,8,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,3,6,4,5,8,2,1]=>1010011=>1100101=>[1,1,3,2,1]
[8,7,2,4,5,1,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[7,1,5,4,8,6,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,8,3,7,4,1,6,2]=>0101101=>1011010=>[1,2,1,2,2]
[8,1,7,4,2,6,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,6,3,1,8,4,7,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,7,1,4,8,6,3,2]=>0100111=>1110010=>[1,1,1,3,2]
[5,3,7,4,8,6,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,5,3,6,1,4,7,2]=>1101001=>1001011=>[1,3,2,1,1]
[5,4,3,6,8,2,7,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,5,3,7,4,8,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,7,8,4,5,1,6,3]=>0010101=>1010100=>[1,2,2,3]
[5,6,3,8,1,4,7,2]=>0101001=>1001010=>[1,3,2,2]
[8,4,1,2,5,6,7,3]=>1100001=>1000011=>[1,5,1,1]
[6,8,3,1,2,5,7,4]=>0110001=>1000110=>[1,4,1,2]
[8,7,1,4,5,2,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[8,7,3,1,5,4,2,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[3,5,4,7,6,1,2,8]=>0101100=>0011010=>[3,1,2,2]
[3,5,7,4,6,1,8,2]=>0010101=>1010100=>[1,2,2,3]
[3,5,7,4,6,1,2,8]=>0010100=>0010100=>[3,2,3]
[3,5,7,4,6,2,1,8]=>0010110=>0110100=>[2,1,2,3]
[3,5,2,7,6,4,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[3,5,7,2,6,4,1,8]=>0010110=>0110100=>[2,1,2,3]
[5,3,7,6,1,2,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[5,3,7,6,1,4,2,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,3,7,6,4,1,2,8]=>1011100=>0011101=>[3,1,1,2,1]
[3,5,7,2,6,1,4,8]=>0010100=>0010100=>[3,2,3]
[3,5,2,7,6,1,4,8]=>0101100=>0011010=>[3,1,2,2]
[5,3,7,6,4,1,8,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,7,5,4,1,8,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[3,7,5,4,1,8,6,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,7,5,1,4,8,6,2]=>0110011=>1100110=>[1,1,3,1,2]
[3,7,5,1,4,8,2,6]=>0110010=>0100110=>[2,3,1,2]
[3,5,7,1,2,6,8,4]=>0010001=>1000100=>[1,4,3]
[3,5,7,2,1,6,4,8]=>0011010=>0101100=>[2,2,1,3]
[5,3,7,1,6,2,4,8]=>1010100=>0010101=>[3,2,2,1]
[3,5,7,1,4,6,8,2]=>0010001=>1000100=>[1,4,3]
[3,5,7,1,4,2,6,8]=>0010100=>0010100=>[3,2,3]
[3,5,7,4,1,2,6,8]=>0011000=>0001100=>[4,1,3]
[3,5,4,7,1,6,8,2]=>0101001=>1001010=>[1,3,2,2]
[3,5,4,7,1,2,6,8]=>0101000=>0001010=>[4,2,2]
[3,5,4,7,2,1,6,8]=>0101100=>0011010=>[3,1,2,2]
[3,5,4,2,7,1,6,8]=>0110100=>0010110=>[3,2,1,2]
[3,5,4,7,2,1,8,6]=>0101101=>1011010=>[1,2,1,2,2]
[3,5,4,7,1,2,8,6]=>0101001=>1001010=>[1,3,2,2]
[5,7,6,3,1,8,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,7,6,3,1,8,2,4]=>0111010=>0101110=>[2,2,1,1,2]
[3,5,7,4,1,2,8,6]=>0011001=>1001100=>[1,3,1,3]
[3,5,7,4,2,1,8,6]=>0011101=>1011100=>[1,2,1,1,3]
[3,2,5,7,4,1,8,6]=>1001101=>1011001=>[1,2,1,3,1]
[3,2,5,7,1,4,8,6]=>1001001=>1001001=>[1,3,3,1]
[3,5,2,7,1,4,8,6]=>0101001=>1001010=>[1,3,2,2]
[3,5,7,2,1,4,8,6]=>0011001=>1001100=>[1,3,1,3]
[3,5,7,1,4,2,8,6]=>0010101=>1010100=>[1,2,2,3]
[3,7,5,2,1,8,6,4]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,7,2,5,1,8,6,4]=>0101011=>1101010=>[1,1,2,2,2]
[3,2,7,5,1,8,6,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,2,7,5,1,8,4,6]=>1011010=>0101101=>[2,2,1,2,1]
[3,7,2,5,1,8,4,6]=>0101010=>0101010=>[2,2,2,2]
[3,7,5,2,1,8,4,6]=>0111010=>0101110=>[2,2,1,1,2]
[5,8,3,4,1,7,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[5,8,7,2,4,1,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,6,4,1,7,5,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,3,5,6,8,1,7,2]=>1000101=>1010001=>[1,2,4,1]
[3,7,6,4,1,8,5,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,7,4,1,8,6,5,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,8,4,1,7,6,5,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,2,7,6,1,5,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,7,8,2,4,1,6,3]=>0010101=>1010100=>[1,2,2,3]
[4,2,5,8,1,6,7,3]=>1001001=>1001001=>[1,3,3,1]
[5,8,2,4,1,6,3,7]=>0101010=>0101010=>[2,2,2,2]
[8,4,2,6,5,1,3,7]=>1101100=>0011011=>[3,1,2,1,1]
[3,2,6,8,1,5,4,7]=>1001010=>0101001=>[2,2,3,1]
[8,3,2,5,6,1,4,7]=>1100100=>0010011=>[3,3,1,1]
[3,2,8,6,7,1,5,4]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,6,8,7,1,5,4]=>1001101=>1011001=>[1,2,1,3,1]
[3,2,6,7,1,5,4,8]=>1001010=>0101001=>[2,2,3,1]
[8,7,3,2,5,6,1,4]=>1110010=>0100111=>[2,3,1,1,1]
[7,2,8,1,5,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,2,7,5,1,3,6]=>1101100=>0011011=>[3,1,2,1,1]
[7,4,2,8,5,1,3,6]=>1101100=>0011011=>[3,1,2,1,1]
[7,2,4,1,8,3,6,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,3,4,2,8,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,5,3,6,2,4,7,1]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,6,3,7,4,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,5,6,2,7,4,3,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,7,6,3,4,1,5,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[1,7,2,3,6,8,5,4]=>0100011=>1100010=>[1,1,4,2]
[3,5,6,4,8,2,7,1]=>0010101=>1010100=>[1,2,2,3]
[3,5,1,4,8,2,7,6]=>0100101=>1010010=>[1,2,3,2]
[1,7,5,4,8,2,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,7,5,1,6,4,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,5,4,8,1,3,6]=>0110100=>0010110=>[3,2,1,2]
[2,7,5,4,8,6,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[1,7,5,4,8,6,3,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[2,5,1,4,8,7,3,6]=>0100110=>0110010=>[2,1,3,2]
[3,6,4,2,8,7,1,5]=>0110110=>0110110=>[2,1,2,1,2]
[3,5,2,4,8,1,6,7]=>0100100=>0010010=>[3,3,2]
[4,5,6,1,7,3,8,2]=>0010101=>1010100=>[1,2,2,3]
[3,5,6,4,8,1,2,7]=>0010100=>0010100=>[3,2,3]
[1,5,6,4,8,7,2,3]=>0010110=>0110100=>[2,1,2,3]
[3,6,4,1,8,7,2,5]=>0110110=>0110110=>[2,1,2,1,2]
[3,6,4,5,8,7,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[1,6,4,3,8,5,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[7,6,1,4,5,3,8,2]=>1100101=>1010011=>[1,2,3,1,1]
[7,6,1,3,5,4,8,2]=>1100101=>1010011=>[1,2,3,1,1]
[7,1,3,2,5,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[1,6,4,2,8,5,3,7]=>0110110=>0110110=>[2,1,2,1,2]
[7,6,5,8,3,1,4,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,6,4,3,8,1,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[2,6,4,3,8,5,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[7,2,3,1,5,8,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[7,1,5,6,3,8,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[7,3,6,5,1,4,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[7,2,6,5,3,8,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[7,2,3,1,4,8,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[7,2,3,5,4,8,6,1]=>1001011=>1101001=>[1,1,2,3,1]
[2,6,4,5,8,1,7,3]=>0100101=>1010010=>[1,2,3,2]
[1,5,6,4,8,3,7,2]=>0010101=>1010100=>[1,2,2,3]
[2,5,6,4,8,3,1,7]=>0010110=>0110100=>[2,1,2,3]
[3,5,6,1,4,7,8,2]=>0010001=>1000100=>[1,4,3]
[7,6,1,3,4,5,8,2]=>1100001=>1000011=>[1,5,1,1]
[7,1,3,2,4,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[7,6,1,5,3,4,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[7,6,1,5,4,3,8,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,6,4,5,8,3,2,7]=>0100110=>0110010=>[2,1,3,2]
[7,6,5,8,1,3,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[3,4,6,8,7,2,1,5]=>0001110=>0111000=>[2,1,1,4]
[3,5,6,8,2,1,7,4]=>0001101=>1011000=>[1,2,1,4]
[4,2,1,5,3,7,8,6]=>1101001=>1001011=>[1,3,2,1,1]
[4,2,5,6,3,1,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[3,5,6,8,1,7,2,4]=>0001010=>0101000=>[2,2,4]
[4,1,5,6,3,2,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[4,5,3,1,7,2,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[4,1,3,5,2,7,8,6]=>1001001=>1001001=>[1,3,3,1]
[2,5,4,7,3,8,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,7,1,8,4,2,6]=>0010110=>0110100=>[2,1,2,3]
[4,1,5,3,2,7,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[4,5,3,7,1,2,8,6]=>0101001=>1001010=>[1,3,2,2]
[4,3,6,1,2,7,5,8]=>1010010=>0100101=>[2,3,2,1]
[5,1,3,2,4,6,7,8]=>1010000=>0000101=>[5,2,1]
[3,6,1,7,4,5,2,8]=>0101010=>0101010=>[2,2,2,2]
[5,3,1,4,2,6,7,8]=>1101000=>0001011=>[4,2,1,1]
[4,5,2,3,7,1,8,6]=>0100101=>1010010=>[1,2,3,2]
[4,2,6,1,3,7,5,8]=>1010010=>0100101=>[2,3,2,1]
[4,6,2,1,3,7,5,8]=>0110010=>0100110=>[2,3,1,2]
[3,6,2,1,7,4,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,1,4,7,6,5,2,8]=>1001110=>0111001=>[2,1,1,3,1]
[3,6,2,7,1,5,8,4]=>0101001=>1001010=>[1,3,2,2]
[4,6,2,7,1,3,5,8]=>0101000=>0001010=>[4,2,2]
[3,5,7,1,8,2,6,4]=>0010101=>1010100=>[1,2,2,3]
[5,1,4,2,3,6,7,8]=>1010000=>0000101=>[5,2,1]
[2,6,5,3,4,7,8,1]=>0110001=>1000110=>[1,4,1,2]
[3,6,1,7,5,4,2,8]=>0101110=>0111010=>[2,1,1,2,2]
[5,1,4,3,2,6,7,8]=>1011000=>0001101=>[4,1,2,1]
[5,4,1,3,2,6,7,8]=>1101000=>0001011=>[4,2,1,1]
[6,4,2,5,3,8,1,7]=>1101010=>0101011=>[2,2,2,1,1]
[4,6,2,3,5,1,8,7]=>0100101=>1010010=>[1,2,3,2]
[6,2,4,5,1,8,3,7]=>1001010=>0101001=>[2,2,3,1]
[8,2,6,7,1,4,5,3]=>1001001=>1001001=>[1,3,3,1]
[8,2,6,7,4,1,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[4,6,2,3,5,8,1,7]=>0100010=>0100010=>[2,4,2]
[2,6,4,1,5,8,3,7]=>0110010=>0100110=>[2,3,1,2]
[2,8,1,6,7,4,5,3]=>0100101=>1010010=>[1,2,3,2]
[2,8,6,1,4,7,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,8,1,6,4,7,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,1,4,8,5,3,7]=>0100110=>0110010=>[2,1,3,2]
[6,4,5,2,8,3,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,3,6,1,8,5,7]=>1001010=>0101001=>[2,2,3,1]
[4,2,3,1,6,8,5,7]=>1010010=>0100101=>[2,3,2,1]
[4,2,3,8,6,1,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[6,4,5,8,2,3,7,1]=>1001001=>1001001=>[1,3,3,1]
[6,4,8,5,2,3,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[2,4,8,1,3,6,7,5]=>0010001=>1000100=>[1,4,3]
[2,4,1,8,3,6,7,5]=>0101001=>1001010=>[1,3,2,2]
[2,1,4,8,6,3,7,5]=>1001101=>1011001=>[1,2,1,3,1]
[6,4,8,2,5,3,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,6,2,4,7,5,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[4,6,8,2,3,5,7,1]=>0010001=>1000100=>[1,4,3]
[2,1,6,8,4,5,7,3]=>1001001=>1001001=>[1,3,3,1]
[2,8,1,4,6,7,3,5]=>0100010=>0100010=>[2,4,2]
[4,8,6,2,3,7,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[8,4,2,6,7,3,1,5]=>1100110=>0110011=>[2,1,3,1,1]
[5,1,8,3,6,4,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,3,8,7,6,4,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[3,8,5,6,1,7,2,4]=>0101010=>0101010=>[2,2,2,2]
[6,7,4,8,5,1,3,2]=>0101101=>1011010=>[1,2,1,2,2]
[3,6,5,8,7,1,4,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,5,3,8,2,7,4,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,4,8,1,3,7,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[7,6,3,1,4,2,5,8]=>1110100=>0010111=>[3,2,1,1,1]
[1,5,4,3,7,8,2,6]=>0110010=>0100110=>[2,3,1,2]
[7,8,4,2,5,3,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[4,2,7,8,5,3,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[4,2,5,3,1,7,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[4,2,8,7,6,3,1,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,2,7,6,3,1,5,8]=>1011100=>0011101=>[3,1,1,2,1]
[6,3,1,8,7,5,2,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,2,7,6,3,1,8,5]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,6,3,1,8,4,2,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,6,4,2,1,8,3,5]=>1111010=>0101111=>[2,2,1,1,1,1]
[1,8,2,7,6,4,3,5]=>0101110=>0111010=>[2,1,1,2,2]
[8,4,2,5,7,6,3,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,5,2,4,8,6,3,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,7,5,2,4,6,3,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,5,2,4,6,3,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[5,2,8,6,3,7,4,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,4,7,5,2,6,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,3,6,4,7,5,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[7,5,2,1,8,3,6,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,5,2,6,3,1,8,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,2,7,4,1,8,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,2,8,7,4,1,6,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[8,7,4,1,5,2,6,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,4,1,5,2,8,6,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,6,3,1,4,2,8,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,5,2,8,6,3,1,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,5,2,1,3,6,4,8]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,5,2,1,3,6,4]=>1111001=>1001111=>[1,3,1,1,1,1]
[1,3,7,6,5,8,2,4]=>0011010=>0101100=>[2,2,1,3]
[8,6,4,7,5,2,1,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,4,7,5,2,1,3,8]=>1011100=>0011101=>[3,1,1,2,1]
[6,3,1,4,7,5,2,8]=>1100110=>0110011=>[2,1,3,1,1]
[6,3,1,4,8,7,5,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[8,6,3,1,4,7,5,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[1,8,2,6,4,7,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[7,5,2,1,6,4,8,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,3,8,7,4,1,5,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,3,7,4,1,5,2,8]=>1011010=>0101101=>[2,2,1,2,1]
[7,4,1,6,3,5,2,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,1,8,6,3,5,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,4,6,3,1,7,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,4,7,5,2,1,8,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[1,6,4,7,5,3,8,2]=>0101101=>1011010=>[1,2,1,2,2]
[6,3,5,2,7,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,6,7,2,5,3,1,8]=>0010110=>0110100=>[2,1,2,3]
[2,4,7,8,1,6,5,3]=>0001011=>1101000=>[1,1,2,4]
[4,2,6,8,7,1,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,1,8,4,2,7,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,6,7,1,2,8,5,3]=>0010011=>1100100=>[1,1,3,3]
[5,7,4,1,2,8,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[6,3,7,1,2,8,5,4]=>1010011=>1100101=>[1,1,3,2,1]
[1,8,2,3,6,5,4,7]=>0100110=>0110010=>[2,1,3,2]
[3,5,8,4,7,2,6,1]=>0010101=>1010100=>[1,2,2,3]
[1,8,5,4,6,2,3,7]=>0110100=>0010110=>[3,2,1,2]
[3,8,5,4,6,1,2,7]=>0110100=>0010110=>[3,2,1,2]
[3,8,5,1,6,4,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[2,8,5,4,6,1,3,7]=>0110100=>0010110=>[3,2,1,2]
[2,8,5,4,6,3,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[1,8,5,4,6,3,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[2,5,8,4,7,3,6,1]=>0010101=>1010100=>[1,2,2,3]
[3,6,4,2,7,8,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[3,6,4,2,7,8,1,5]=>0110010=>0100110=>[2,3,1,2]
[3,5,4,1,6,2,7,8]=>0110100=>0010110=>[3,2,1,2]
[4,5,8,1,7,6,2,3]=>0010110=>0110100=>[2,1,2,3]
[3,5,8,4,7,1,6,2]=>0010101=>1010100=>[1,2,2,3]
[1,5,8,4,7,3,6,2]=>0010101=>1010100=>[1,2,2,3]
[3,6,4,1,7,8,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[3,6,4,8,7,5,2,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[1,6,4,3,7,8,5,2]=>0110011=>1100110=>[1,1,3,1,2]
[7,6,1,3,8,4,2,5]=>1100110=>0110011=>[2,1,3,1,1]
[1,6,4,2,7,8,3,5]=>0110010=>0100110=>[2,3,1,2]
[2,6,4,3,7,1,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[2,6,4,1,7,8,3,5]=>0110010=>0100110=>[2,3,1,2]
[7,2,3,4,8,6,5,1]=>1000111=>1110001=>[1,1,1,4,1]
[7,2,3,1,8,6,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,3,4,1,6,8,5]=>1001001=>1001001=>[1,3,3,1]
[1,2,4,3,8,5,7,6]=>0010101=>1010100=>[1,2,2,3]
[7,3,8,6,1,4,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,2,8,6,3,4,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,2,3,1,5,6,8,4]=>1010001=>1000101=>[1,4,2,1]
[7,2,3,8,5,6,4,1]=>1001011=>1101001=>[1,1,2,3,1]
[2,6,4,8,7,1,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[1,5,8,4,7,6,2,3]=>0010110=>0110100=>[2,1,2,3]
[3,5,8,1,6,7,2,4]=>0010010=>0100100=>[2,3,3]
[7,6,1,3,5,8,2,4]=>1100010=>0100011=>[2,4,1,1]
[7,1,3,2,5,6,8,4]=>1010001=>1000101=>[1,4,2,1]
[7,1,3,8,2,6,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[7,6,1,8,5,4,2,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,2,6,5,8,4,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,7,1,6,5,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,2,6,4,8,3,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,7,5,8,2,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,7,4,8,2,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,7,4,8,1,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,8,2,6,3,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,7,5,2,3,6,8]=>1011000=>0001101=>[4,1,2,1]
[4,1,7,8,6,3,2,5]=>1001110=>0111001=>[2,1,1,3,1]
[6,8,3,2,1,4,7,5]=>0111001=>1001110=>[1,3,1,1,2]
[6,8,2,4,1,3,7,5]=>0101001=>1001010=>[1,3,2,2]
[6,1,2,7,5,8,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,7,3,8,5,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,2,6,8,3,7,1]=>0100101=>1010010=>[1,2,3,2]
[4,8,3,2,5,7,6,1]=>0110011=>1100110=>[1,1,3,1,2]
[8,4,7,6,2,3,5,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,8,4,1,5,3,7,2]=>0110101=>1010110=>[1,2,2,1,2]
[8,3,4,7,6,2,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[1,8,3,5,2,6,7,4]=>0101001=>1001010=>[1,3,2,2]
[5,8,2,4,3,7,6,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,5,3,8,4,2,7,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,4,5,1,6,2,8,3]=>1010101=>1010101=>[1,2,2,2,1]
[4,7,3,5,6,2,8,1]=>0100101=>1010010=>[1,2,3,2]
[6,7,8,4,1,3,5,2]=>0011001=>1001100=>[1,3,1,3]
[3,1,6,8,4,7,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[8,3,6,1,5,7,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[3,2,7,5,8,6,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[2,4,6,7,8,1,5,3]=>0000101=>1010000=>[1,2,5]
[2,4,6,8,1,7,5,3]=>0001011=>1101000=>[1,1,2,4]
[7,4,3,8,6,2,1,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[4,3,6,2,1,8,5,7]=>1011010=>0101101=>[2,2,1,2,1]
[4,6,2,3,7,5,8,1]=>0100101=>1010010=>[1,2,3,2]
[5,8,4,2,3,6,7,1]=>0110001=>1000110=>[1,4,1,2]
[8,4,5,3,2,1,7,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,8,4,2,3,7,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[6,4,8,3,2,7,1,5]=>1011010=>0101101=>[2,2,1,2,1]
[5,8,3,7,2,1,6,4]=>0101101=>1011010=>[1,2,1,2,2]
[2,5,6,4,7,1,8,3]=>0010101=>1010100=>[1,2,2,3]
[2,5,4,8,1,6,7,3]=>0101001=>1001010=>[1,3,2,2]
[1,2,6,5,8,7,3,4]=>0010110=>0110100=>[2,1,2,3]
[5,6,3,4,8,7,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[6,5,3,4,8,7,2,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,5,3,8,4,6,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,3,7,4,6,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,8,1,2,3,4,7,6]=>0100001=>1000010=>[1,5,2]
[7,1,2,8,3,6,4,5]=>1001010=>0101001=>[2,2,3,1]
[6,1,8,2,3,5,7,4]=>1010001=>1000101=>[1,4,2,1]
[6,1,7,2,3,5,8,4]=>1010001=>1000101=>[1,4,2,1]
[4,3,8,7,5,6,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,1,6,2,3,5,8,4]=>1010001=>1000101=>[1,4,2,1]
[8,1,6,2,3,5,7,4]=>1010001=>1000101=>[1,4,2,1]
[8,1,7,2,3,5,6,4]=>1010001=>1000101=>[1,4,2,1]
[5,8,3,7,4,6,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[6,8,7,3,4,5,2,1]=>0110011=>1100110=>[1,1,3,1,2]
[8,6,1,2,3,4,7,5]=>1100001=>1000011=>[1,5,1,1]
[8,6,2,3,5,1,4,7]=>1100100=>0010011=>[3,3,1,1]
[8,2,4,5,7,3,1,6]=>1000110=>0110001=>[2,1,4,1]
[2,6,3,8,7,5,4,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[8,2,3,7,5,4,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[8,2,6,3,5,4,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,6,1,5,2,4,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,6,2,4,1,5,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,1,6,5,3,2,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,3,6,1,5,4,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[8,3,2,6,5,4,1,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,3,2,5,7,4,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[8,3,1,7,5,4,2,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,1,3,8,7,5,4,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[3,6,1,8,7,5,4,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[3,8,1,5,7,6,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[3,5,2,8,7,6,4,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[3,4,8,2,7,6,5,1]=>0010111=>1110100=>[1,1,1,2,3]
[3,4,8,7,1,6,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[8,1,3,5,7,6,4,2]=>1000111=>1110001=>[1,1,1,4,1]
[4,1,8,5,7,6,3,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,2,7,1,4,5,6,3]=>1010001=>1000101=>[1,4,2,1]
[8,1,7,3,4,6,2,5]=>1010010=>0100101=>[2,3,2,1]
[8,3,1,7,2,6,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[3,8,2,4,7,6,5,1]=>0100111=>1110010=>[1,1,1,3,2]
[2,8,3,7,4,6,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[8,2,3,7,1,6,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[8,2,7,1,3,6,5,4]=>1010011=>1100101=>[1,1,3,2,1]
[8,1,7,2,6,4,3,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,1,7,5,2,4,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[8,2,3,7,4,6,1,5]=>1001010=>0101001=>[2,2,3,1]
[2,4,8,5,7,6,3,1]=>0010111=>1110100=>[1,1,1,2,3]
[8,2,4,3,7,6,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,2,7,3,5,1,4,6]=>1010100=>0010101=>[3,2,2,1]
[8,2,7,4,3,1,5,6]=>1011100=>0011101=>[3,1,1,2,1]
[8,2,1,5,7,6,4,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,1,8,2,7,5,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,1,5,2,7,6,4,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[8,1,7,2,4,6,5,3]=>1010011=>1100101=>[1,1,3,2,1]
[8,2,4,1,7,6,5,3]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,2,8,3,7,6,5,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,8,2,1,7,6,5,3]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,1,8,7,2,6,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,8,1,3,7,6,2,4]=>0100110=>0110010=>[2,1,3,2]
[8,2,5,4,1,7,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,1,4,8,7,6,3,2]=>1001111=>1111001=>[1,1,1,1,3,1]
[8,1,4,3,7,6,5,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,8,1,3,7,6,5,2]=>0100111=>1110010=>[1,1,1,3,2]
[4,3,8,1,7,6,5,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[6,2,8,1,5,7,3,4]=>1010010=>0100101=>[2,3,2,1]
[7,2,5,4,1,8,6,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,3,2,8,5,6,1,4]=>1101010=>0101011=>[2,2,2,1,1]
[5,4,6,8,7,2,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[1,7,6,3,2,8,4,5]=>0111010=>0101110=>[2,2,1,1,2]
[6,5,8,3,4,1,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[4,1,2,8,5,3,6,7]=>1001100=>0011001=>[3,1,3,1]
[3,5,8,2,6,1,7,4]=>0010101=>1010100=>[1,2,2,3]
[3,7,6,2,8,4,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[4,3,6,8,5,1,2,7]=>1001100=>0011001=>[3,1,3,1]
[2,7,1,5,8,4,3,6]=>0100110=>0110010=>[2,1,3,2]
[2,7,6,1,8,4,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[7,1,2,6,3,5,4,8]=>1001010=>0101001=>[2,2,3,1]
[7,2,6,3,4,5,1,8]=>1010010=>0100101=>[2,3,2,1]
[4,1,2,7,8,5,3,6]=>1000110=>0110001=>[2,1,4,1]
[4,7,3,1,2,6,8,5]=>0110001=>1000110=>[1,4,1,2]
[3,8,5,6,4,2,7,1]=>0101101=>1011010=>[1,2,1,2,2]
[3,2,6,4,7,8,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,7,5,8,3,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,1,4,7,8,3,6]=>1100010=>0100011=>[2,4,1,1]
[5,6,2,7,3,4,8,1]=>0101001=>1001010=>[1,3,2,2]
[1,5,8,6,4,2,3,7]=>0011100=>0011100=>[3,1,1,3]
[2,5,8,6,4,1,7,3]=>0011101=>1011100=>[1,2,1,1,3]
[4,7,2,3,1,6,8,5]=>0101001=>1001010=>[1,3,2,2]
[7,4,6,2,8,3,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,4,6,5,1,2,7,8]=>0011000=>0001100=>[4,1,3]
[4,3,8,2,5,7,1,6]=>1010010=>0100101=>[2,3,2,1]
[4,1,6,2,5,3,7,8]=>1010100=>0010101=>[3,2,2,1]
[4,2,6,1,5,3,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,2,3,1,5,8,4]=>0101001=>1001010=>[1,3,2,2]
[2,1,5,7,8,3,6,4]=>1000101=>1010001=>[1,2,4,1]
[4,7,5,8,6,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[2,4,8,3,7,1,5,6]=>0010100=>0010100=>[3,2,3]
[5,2,8,4,1,6,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[7,6,5,2,1,8,4,3]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[2,7,5,1,8,3,6,4]=>0110101=>1010110=>[1,2,2,1,2]
[5,1,8,7,4,3,6,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,8,7,2,4,6,1,5]=>0110010=>0100110=>[2,3,1,2]
[5,7,1,3,2,4,8,6]=>0101001=>1001010=>[1,3,2,2]
[4,2,7,6,3,5,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[8,4,7,6,3,5,1,2]=>1011010=>0101101=>[2,2,1,2,1]
[8,1,7,4,2,3,5,6]=>1011000=>0001101=>[4,1,2,1]
[6,5,1,3,8,7,4,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[6,1,8,5,3,7,2,4]=>1011010=>0101101=>[2,2,1,2,1]
[5,1,6,8,3,7,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[8,6,5,1,7,4,3,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[7,6,4,1,3,5,8,2]=>1110001=>1000111=>[1,4,1,1,1]
[8,2,3,7,1,4,5,6]=>1001000=>0001001=>[4,3,1]
[5,6,2,7,4,3,1,8]=>0101110=>0111010=>[2,1,1,2,2]
[3,7,8,2,6,1,4,5]=>0010100=>0010100=>[3,2,3]
[3,7,8,5,2,1,4,6]=>0011100=>0011100=>[3,1,1,3]
[4,8,6,5,1,2,7,3]=>0111001=>1001110=>[1,3,1,1,2]
[4,8,6,5,1,2,3,7]=>0111000=>0001110=>[4,1,1,2]
[3,8,7,6,5,1,2,4]=>0111100=>0011110=>[3,1,1,1,2]
[5,8,2,6,1,4,7,3]=>0101001=>1001010=>[1,3,2,2]
[3,8,7,5,6,1,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,3,8,7,5,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[2,8,4,1,5,7,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[1,8,4,2,5,7,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,8,5,4,1,7,6,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[2,5,8,3,7,1,6,4]=>0010101=>1010100=>[1,2,2,3]
[1,8,5,2,4,7,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[1,4,6,2,8,7,5,3]=>0010111=>1110100=>[1,1,1,2,3]
[7,8,2,4,1,6,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,4,6,1,8,7,5,3]=>0010111=>1110100=>[1,1,1,2,3]
[2,8,4,5,1,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[3,5,8,1,7,6,2,4]=>0010110=>0110100=>[2,1,2,3]
[3,5,8,2,7,6,1,4]=>0010110=>0110100=>[2,1,2,3]
[2,1,6,8,7,5,3,4]=>1001110=>0111001=>[2,1,1,3,1]
[1,8,2,4,5,7,6,3]=>0100011=>1100010=>[1,1,4,2]
[1,3,8,2,5,7,6,4]=>0010011=>1100100=>[1,1,3,3]
[2,3,8,1,5,7,6,4]=>0010011=>1100100=>[1,1,3,3]
[2,6,1,8,7,5,3,4]=>0101110=>0111010=>[2,1,1,2,2]
[1,6,2,8,7,5,3,4]=>0101110=>0111010=>[2,1,1,2,2]
[1,6,3,8,7,5,2,4]=>0101110=>0111010=>[2,1,1,2,2]
[2,6,3,8,7,5,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[3,2,8,1,5,7,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[3,1,8,2,5,7,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[2,1,8,3,5,7,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[7,8,2,1,4,6,5,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,3,6,8,7,5,1,4]=>0001110=>0111000=>[2,1,1,4]
[3,1,6,8,7,2,5,4]=>1001101=>1011001=>[1,2,1,3,1]
[3,8,4,5,1,6,2,7]=>0101010=>0101010=>[2,2,2,2]
[6,1,4,5,7,2,3,8]=>1000100=>0010001=>[3,4,1]
[8,1,4,7,6,3,2,5]=>1001110=>0111001=>[2,1,1,3,1]
[8,3,1,6,4,7,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[5,3,8,6,2,7,1,4]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,6,1,5,7,2,4]=>1010010=>0100101=>[2,3,2,1]
[8,4,6,3,1,2,5,7]=>1011000=>0001101=>[4,1,2,1]
[6,8,1,4,5,2,3,7]=>0100100=>0010010=>[3,3,2]
[1,5,8,4,6,2,3,7]=>0010100=>0010100=>[3,2,3]
[5,6,8,1,4,2,3,7]=>0010100=>0010100=>[3,2,3]
[5,7,4,8,1,2,3,6]=>0101000=>0001010=>[4,2,2]
[4,7,8,1,2,6,3,5]=>0010010=>0100100=>[2,3,3]
[8,7,1,5,6,2,3,4]=>1100100=>0010011=>[3,3,1,1]
[1,6,5,8,7,2,3,4]=>0101100=>0011010=>[3,1,2,2]
[3,7,1,6,2,4,8,5]=>0101001=>1001010=>[1,3,2,2]
[5,1,2,7,6,8,3,4]=>1001010=>0101001=>[2,2,3,1]
[1,7,6,5,8,2,3,4]=>0110100=>0010110=>[3,2,1,2]
[1,6,8,5,7,2,3,4]=>0010100=>0010100=>[3,2,3]
[7,5,1,2,6,8,3,4]=>1100010=>0100011=>[2,4,1,1]
[6,1,5,2,7,8,3,4]=>1010010=>0100101=>[2,3,2,1]
[5,1,2,6,8,7,3,4]=>1000110=>0110001=>[2,1,4,1]
[1,8,6,2,5,7,3,4]=>0110010=>0100110=>[2,3,1,2]
[5,7,8,1,2,6,3,4]=>0010010=>0100100=>[2,3,3]
[8,1,5,7,6,2,3,4]=>1001100=>0011001=>[3,1,3,1]
[3,7,1,2,8,4,6,5]=>0100101=>1010010=>[1,2,3,2]
[1,5,8,7,6,2,3,4]=>0011100=>0011100=>[3,1,1,3]
[7,8,6,1,5,2,3,4]=>0110100=>0010110=>[3,2,1,2]
[4,5,7,2,3,1,8,6]=>0010101=>1010100=>[1,2,2,3]
[3,7,8,1,4,6,5,2]=>0010011=>1100100=>[1,1,3,3]
[2,5,8,7,4,1,3,6]=>0011100=>0011100=>[3,1,1,3]
[2,6,4,7,5,3,8,1]=>0101101=>1011010=>[1,2,1,2,2]
[6,2,4,7,1,3,8,5]=>1001001=>1001001=>[1,3,3,1]
[7,3,5,1,4,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,7,1,3,2,8,6]=>1010101=>1010101=>[1,2,2,2,1]
[6,1,4,7,5,3,8,2]=>1001101=>1011001=>[1,2,1,3,1]
[8,7,4,3,1,5,6,2]=>1111001=>1001111=>[1,3,1,1,1,1]
[8,7,1,4,3,5,6,2]=>1101001=>1001011=>[1,3,2,1,1]
[6,1,8,4,7,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[4,7,3,6,1,2,8,5]=>0101001=>1001010=>[1,3,2,2]
[5,2,1,7,4,3,8,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,7,6,2,3,1,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[7,6,8,2,5,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[2,3,6,1,8,7,5,4]=>0010111=>1110100=>[1,1,1,2,3]
[2,6,8,7,5,3,1,4]=>0011110=>0111100=>[2,1,1,1,3]
[6,4,1,7,5,2,8,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,7,8,2,3,6,1,4]=>0010010=>0100100=>[2,3,3]
[4,8,7,1,2,5,6,3]=>0110001=>1000110=>[1,4,1,2]
[2,8,7,4,1,5,6,3]=>0111001=>1001110=>[1,3,1,1,2]
[8,6,2,1,5,7,4,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[3,8,6,7,5,2,1,4]=>0101110=>0111010=>[2,1,1,2,2]
[6,1,3,7,5,8,2,4]=>1001010=>0101001=>[2,2,3,1]
[4,7,3,1,8,5,6,2]=>0110101=>1010110=>[1,2,2,1,2]
[1,3,8,5,2,7,4,6]=>0011010=>0101100=>[2,2,1,3]
[1,3,8,6,7,2,4,5]=>0010100=>0010100=>[3,2,3]
[2,8,3,7,6,1,4,5]=>0101100=>0011010=>[3,1,2,2]
[1,3,8,7,6,2,4,5]=>0011100=>0011100=>[3,1,1,3]
[1,4,6,8,7,2,3,5]=>0001100=>0011000=>[3,1,4]
[7,6,4,8,5,1,3,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,2,6,5,8,1,3,4]=>1010100=>0010101=>[3,2,2,1]
[3,6,7,5,2,8,4,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,6,5,7,2,8,1,3]=>0101010=>0101010=>[2,2,2,2]
[5,3,6,7,8,1,4,2]=>1000101=>1010001=>[1,2,4,1]
[6,3,2,8,5,4,1,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,8,4,1,5,2,6,7]=>0110100=>0010110=>[3,2,1,2]
[2,5,7,4,3,1,6,8]=>0011100=>0011100=>[3,1,1,3]
[5,3,4,2,7,1,6,8]=>1010100=>0010101=>[3,2,2,1]
[3,7,5,4,1,2,6,8]=>0111000=>0001110=>[4,1,1,2]
[4,2,5,1,3,8,7,6]=>1010011=>1100101=>[1,1,3,2,1]
[4,3,5,1,2,7,6,8]=>1010010=>0100101=>[2,3,2,1]
[5,3,4,1,7,2,6,8]=>1010100=>0010101=>[3,2,2,1]
[4,1,6,3,5,2,7,8]=>1010100=>0010101=>[3,2,2,1]
[3,1,7,2,5,6,4,8]=>1010010=>0100101=>[2,3,2,1]
[3,7,5,4,2,1,6,8]=>0111100=>0011110=>[3,1,1,1,2]
[7,3,2,1,6,4,5,8]=>1110100=>0010111=>[3,2,1,1,1]
[2,8,6,1,7,4,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[2,5,4,6,1,3,7,8]=>0101000=>0001010=>[4,2,2]
[2,5,6,4,1,3,7,8]=>0011000=>0001100=>[4,1,3]
[8,5,2,6,1,3,7,4]=>1101001=>1001011=>[1,3,2,1,1]
[7,1,5,6,3,2,4,8]=>1001100=>0011001=>[3,1,3,1]
[7,1,2,5,4,6,3,8]=>1001010=>0101001=>[2,2,3,1]
[2,4,1,6,5,3,7,8]=>0101100=>0011010=>[3,1,2,2]
[4,1,2,7,5,6,3,8]=>1001010=>0101001=>[2,2,3,1]
[7,1,2,6,5,4,3,8]=>1001110=>0111001=>[2,1,1,3,1]
[8,2,1,5,6,3,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[6,1,4,5,3,2,7,8]=>1001100=>0011001=>[3,1,3,1]
[3,1,6,5,4,2,7,8]=>1011100=>0011101=>[3,1,1,2,1]
[3,1,4,6,5,2,7,8]=>1001100=>0011001=>[3,1,3,1]
[5,6,3,8,7,4,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[5,2,6,8,7,4,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[5,2,3,1,4,8,6,7]=>1010010=>0100101=>[2,3,2,1]
[5,4,1,3,2,8,6,7]=>1101010=>0101011=>[2,2,2,1,1]
[5,1,3,4,2,8,6,7]=>1001010=>0101001=>[2,2,3,1]
[4,2,7,3,8,5,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[4,3,7,2,8,5,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,1,2,4,8,6,7]=>1100010=>0100011=>[2,4,1,1]
[1,3,2,6,4,8,7,5]=>0101011=>1101010=>[1,1,2,2,2]
[1,6,2,5,3,8,7,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,2,6,3,7,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,8,3,6,4,7,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,7,2,6,3,8,5,4]=>0101011=>1101010=>[1,1,2,2,2]
[1,5,2,7,4,8,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[1,4,2,8,5,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[4,8,1,3,2,6,5,7]=>0101010=>0101010=>[2,2,2,2]
[1,5,3,8,4,7,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[2,6,3,8,1,5,4,7]=>0101010=>0101010=>[2,2,2,2]
[8,3,1,4,2,6,5,7]=>1101010=>0101011=>[2,2,2,1,1]
[6,8,7,3,5,2,4,1]=>0110101=>1010110=>[1,2,2,1,2]
[8,3,5,1,2,6,4,7]=>1010010=>0100101=>[2,3,2,1]
[8,6,3,1,5,4,2,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,6,4,1,5,3,2,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,6,5,4,1,3,2,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[5,3,8,7,4,6,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,3,8,7,4,6,1,5]=>0011010=>0101100=>[2,2,1,3]
[8,3,5,7,4,1,2,6]=>1001100=>0011001=>[3,1,3,1]
[4,8,5,3,1,2,7,6]=>0111001=>1001110=>[1,3,1,1,2]
[6,8,7,3,1,5,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[6,8,5,4,1,3,7,2]=>0111001=>1001110=>[1,3,1,1,2]
[2,5,8,7,4,6,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,8,7,6,5,1,3,2]=>0111101=>1011110=>[1,2,1,1,1,2]
[3,8,7,5,1,6,2,4]=>0111010=>0101110=>[2,2,1,1,2]
[2,3,8,7,5,6,1,4]=>0011010=>0101100=>[2,2,1,3]
[2,8,7,1,3,6,4,5]=>0110010=>0100110=>[2,3,1,2]
[8,5,4,7,2,1,3,6]=>1101100=>0011011=>[3,1,2,1,1]
[6,8,7,3,5,2,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[3,5,8,6,4,2,7,1]=>0011101=>1011100=>[1,2,1,1,3]
[6,8,4,1,5,2,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,2,1,7,5,3,4]=>0110110=>0110110=>[2,1,2,1,2]
[5,8,4,6,1,2,7,3]=>0101001=>1001010=>[1,3,2,2]
[2,4,8,6,5,1,7,3]=>0011101=>1011100=>[1,2,1,1,3]
[4,8,7,6,5,2,1,3]=>0111110=>0111110=>[2,1,1,1,1,2]
[4,8,7,5,1,6,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[4,5,2,1,8,6,7,3]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,3,5,6,7,1,4]=>0100010=>0100010=>[2,4,2]
[5,6,2,4,7,1,8,3]=>0100101=>1010010=>[1,2,3,2]
[2,7,5,4,6,1,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,7,5,4,6,2,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[2,6,7,4,1,3,8,5]=>0011001=>1001100=>[1,3,1,3]
[6,5,7,4,1,3,8,2]=>1011001=>1001101=>[1,3,1,2,1]
[2,4,6,3,5,7,8,1]=>0010001=>1000100=>[1,4,3]
[3,6,4,2,5,7,8,1]=>0110001=>1000110=>[1,4,1,2]
[2,3,6,1,5,7,8,4]=>0010001=>1000100=>[1,4,3]
[4,3,6,2,5,7,8,1]=>1010001=>1000101=>[1,4,2,1]
[4,6,1,2,5,7,8,3]=>0100001=>1000010=>[1,5,2]
[2,6,4,1,5,7,8,3]=>0110001=>1000110=>[1,4,1,2]
[2,4,1,6,5,7,8,3]=>0101001=>1001010=>[1,3,2,2]
[7,8,4,1,6,3,5,2]=>0110101=>1010110=>[1,2,2,1,2]
[8,7,5,6,1,3,4,2]=>1101001=>1001011=>[1,3,2,1,1]
[1,4,5,8,6,3,2,7]=>0001110=>0111000=>[2,1,1,4]
[8,4,5,7,2,6,1,3]=>1001010=>0101001=>[2,2,3,1]
[8,1,7,5,3,6,2,4]=>1011010=>0101101=>[2,2,1,2,1]
[5,2,8,3,6,1,4,7]=>1010100=>0010101=>[3,2,2,1]
[5,2,6,3,1,7,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[5,7,6,1,2,3,8,4]=>0110001=>1000110=>[1,4,1,2]
[5,3,2,1,8,6,4,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[4,3,6,2,1,8,7,5]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,3,6,4,8,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[3,7,4,5,1,6,2,8]=>0101010=>0101010=>[2,2,2,2]
[3,6,4,5,8,2,1,7]=>0100110=>0110010=>[2,1,3,2]
[6,1,4,5,2,8,7,3]=>1001011=>1101001=>[1,1,2,3,1]
[7,2,4,5,1,6,3,8]=>1001010=>0101001=>[2,2,3,1]
[7,5,4,1,6,3,2,8]=>1110110=>0110111=>[2,1,2,1,1,1]
[1,5,4,8,6,3,2,7]=>0101110=>0111010=>[2,1,1,2,2]
[7,5,4,8,6,3,1,2]=>1101110=>0111011=>[2,1,1,2,1,1]
[1,8,7,5,3,6,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,3,7,4,1,6,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,5,4,1,6,3,2,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[1,7,4,2,6,5,3,8]=>0110110=>0110110=>[2,1,2,1,2]
[8,2,1,5,6,7,3,4]=>1100010=>0100011=>[2,4,1,1]
[6,3,1,8,4,7,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,1,4,8,6,3,2,5]=>1001110=>0111001=>[2,1,1,3,1]
[4,1,8,5,6,7,2,3]=>1010010=>0100101=>[2,3,2,1]
[5,7,4,8,6,2,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[5,3,6,8,2,7,1,4]=>1001010=>0101001=>[2,2,3,1]
[6,3,7,4,8,2,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[5,3,6,1,4,7,2,8]=>1010010=>0100101=>[2,3,2,1]
[4,3,6,8,2,7,1,5]=>1001010=>0101001=>[2,2,3,1]
[5,3,7,4,8,2,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,3,8,4,1,6,2,7]=>1011010=>0101101=>[2,2,1,2,1]
[5,3,8,1,4,7,2,6]=>1010010=>0100101=>[2,3,2,1]
[5,8,4,1,6,3,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[7,3,8,4,1,6,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[1,5,8,3,6,7,4,2]=>0010011=>1100100=>[1,1,3,3]
[1,8,2,5,6,7,3,4]=>0100010=>0100010=>[2,4,2]
[7,8,4,1,6,5,2,3]=>0110110=>0110110=>[2,1,2,1,2]
[6,3,8,1,5,7,2,4]=>1010010=>0100101=>[2,3,2,1]
[8,3,1,2,5,7,4,6]=>1100010=>0100011=>[2,4,1,1]
[8,1,4,2,6,5,3,7]=>1010110=>0110101=>[2,1,2,2,1]
[3,8,5,6,2,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[2,4,5,8,7,3,1,6]=>0001110=>0111000=>[2,1,1,4]
[4,3,1,5,6,2,8,7]=>1100101=>1010011=>[1,2,3,1,1]
[4,1,5,8,6,7,2,3]=>1001010=>0101001=>[2,2,3,1]
[4,3,7,6,1,2,8,5]=>1011001=>1001101=>[1,3,1,2,1]
[4,7,5,6,1,2,8,3]=>0101001=>1001010=>[1,3,2,2]
[4,5,1,8,6,7,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[3,4,5,8,6,7,2,1]=>0001011=>1101000=>[1,1,2,4]
[2,1,5,8,6,7,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[3,4,5,8,7,1,2,6]=>0001100=>0011000=>[3,1,4]
[4,7,1,5,6,2,8,3]=>0100101=>1010010=>[1,2,3,2]
[2,6,4,7,1,3,8,5]=>0101001=>1001010=>[1,3,2,2]
[5,3,8,6,4,7,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,4,1,5,7,8,3,2]=>1100011=>1100011=>[1,1,4,1,1]
[3,6,4,7,2,1,8,5]=>0101101=>1011010=>[1,2,1,2,2]
[3,8,4,6,1,7,2,5]=>0101010=>0101010=>[2,2,2,2]
[3,8,5,6,4,7,2,1]=>0101011=>1101010=>[1,1,2,2,2]
[3,8,6,5,2,7,4,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[3,8,7,5,2,1,4,6]=>0111100=>0011110=>[3,1,1,1,2]
[6,4,1,7,3,2,8,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,1,4,6,7,2,8,3]=>1000101=>1010001=>[1,2,4,1]
[6,5,4,7,1,3,8,2]=>1101001=>1001011=>[1,3,2,1,1]
[2,1,6,5,3,7,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[6,1,4,7,2,3,8,5]=>1001001=>1001001=>[1,3,3,1]
[1,6,2,5,4,8,3,7]=>0101010=>0101010=>[2,2,2,2]
[4,1,2,7,5,8,3,6]=>1001010=>0101001=>[2,2,3,1]
[6,1,3,5,8,2,4,7]=>1000100=>0010001=>[3,4,1]
[5,6,4,3,1,8,2,7]=>0111010=>0101110=>[2,2,1,1,2]
[6,2,3,5,8,1,4,7]=>1000100=>0010001=>[3,4,1]
[6,7,2,3,8,4,5,1]=>0100101=>1010010=>[1,2,3,2]
[6,7,2,1,3,8,4,5]=>0110010=>0100110=>[2,3,1,2]
[5,7,4,1,8,3,2,6]=>0110110=>0110110=>[2,1,2,1,2]
[4,1,7,5,8,3,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,1,3,8,4,5,2]=>0100101=>1010010=>[1,2,3,2]
[1,6,7,4,3,8,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[6,1,7,4,2,8,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,1,6,7,4,3,8,5]=>1001101=>1011001=>[1,2,1,3,1]
[6,7,3,2,1,8,4,5]=>0111010=>0101110=>[2,2,1,1,2]
[2,5,7,3,1,4,8,6]=>0011001=>1001100=>[1,3,1,3]
[6,7,3,2,8,4,5,1]=>0110101=>1010110=>[1,2,2,1,2]
[2,6,7,4,3,8,5,1]=>0011011=>1101100=>[1,1,2,1,3]
[1,2,6,7,4,3,8,5]=>0001101=>1011000=>[1,2,1,4]
[1,7,5,8,2,4,3,6]=>0101010=>0101010=>[2,2,2,2]
[2,7,1,8,4,6,3,5]=>0101010=>0101010=>[2,2,2,2]
[2,7,5,8,1,6,3,4]=>0101010=>0101010=>[2,2,2,2]
[1,6,7,3,8,5,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[6,7,1,8,4,5,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[8,6,1,5,4,3,2,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[2,4,3,8,5,1,6,7]=>0101100=>0011010=>[3,1,2,2]
[1,5,6,7,3,8,2,4]=>0001010=>0101000=>[2,2,4]
[1,6,5,4,8,3,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[3,8,7,2,4,6,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[1,3,7,6,4,8,5,2]=>0011011=>1101100=>[1,1,2,1,3]
[3,1,8,7,6,4,2,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[3,1,8,7,5,4,2,6]=>1011110=>0111101=>[2,1,1,1,2,1]
[3,1,7,6,5,4,2,8]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,7,1,6,5,3,2,8]=>0101110=>0111010=>[2,1,1,2,2]
[4,8,1,6,5,3,2,7]=>0101110=>0111010=>[2,1,1,2,2]
[4,8,1,7,5,3,2,6]=>0101110=>0111010=>[2,1,1,2,2]
[8,4,1,7,6,3,2,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[5,4,1,8,6,3,2,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[5,4,1,7,6,3,2,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,4,1,7,5,3,2,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[6,4,1,8,5,3,2,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,4,1,7,5,3,2,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,4,1,6,5,3,2,8]=>1101110=>0111011=>[2,1,1,2,1,1]
[7,5,6,1,4,3,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[8,5,6,1,4,3,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,7,6,1,4,3,2,8]=>0110110=>0110110=>[2,1,2,1,2]
[5,8,6,1,4,3,2,7]=>0110110=>0110110=>[2,1,2,1,2]
[6,7,5,1,4,3,2,8]=>0110110=>0110110=>[2,1,2,1,2]
[8,7,5,1,4,3,2,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,6,5,1,4,3,2,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[1,8,6,3,4,2,5,7]=>0110100=>0010110=>[3,2,1,2]
[3,1,6,4,5,7,2,8]=>1010010=>0100101=>[2,3,2,1]
[7,6,3,8,4,5,2,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,2,7,6,1,4,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[5,2,7,8,1,4,3,6]=>1001010=>0101001=>[2,2,3,1]
[8,2,7,6,1,4,5,3]=>1011001=>1001101=>[1,3,1,2,1]
[5,2,3,7,1,6,8,4]=>1001001=>1001001=>[1,3,3,1]
[1,7,5,2,6,4,8,3]=>0110101=>1010110=>[1,2,2,1,2]
[7,1,3,6,8,2,4,5]=>1000100=>0010001=>[3,4,1]
[1,2,5,7,8,4,6,3]=>0000101=>1010000=>[1,2,5]
[3,1,2,7,5,4,8,6]=>1001101=>1011001=>[1,2,1,3,1]
[6,7,4,1,3,2,8,5]=>0110101=>1010110=>[1,2,2,1,2]
[1,7,2,8,4,3,5,6]=>0101100=>0011010=>[3,1,2,2]
[4,1,6,5,7,8,2,3]=>1010010=>0100101=>[2,3,2,1]
[1,6,3,5,7,8,2,4]=>0100010=>0100010=>[2,4,2]
[8,6,1,7,5,2,4,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,6,4,1,8,3,2,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,4,1,6,5,2,7,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[1,5,3,4,7,8,2,6]=>0100010=>0100010=>[2,4,2]
[4,2,1,5,7,8,3,6]=>1100010=>0100011=>[2,4,1,1]
[5,1,4,6,7,8,2,3]=>1000010=>0100001=>[2,5,1]
[4,1,5,3,7,8,2,6]=>1010010=>0100101=>[2,3,2,1]
[8,1,4,6,5,2,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[7,1,5,4,6,3,2,8]=>1010110=>0110101=>[2,1,2,2,1]
[8,2,1,6,7,5,4,3]=>1100111=>1110011=>[1,1,1,3,1,1]
[1,2,4,7,6,3,8,5]=>0001101=>1011000=>[1,2,1,4]
[6,7,4,1,8,5,2,3]=>0110110=>0110110=>[2,1,2,1,2]
[8,6,4,1,5,7,3,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[5,2,4,3,7,1,6,8]=>1010100=>0010101=>[3,2,2,1]
[6,1,5,4,8,3,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[1,2,8,7,4,3,6,5]=>0011101=>1011100=>[1,2,1,1,3]
[3,2,1,7,5,8,4,6]=>1101010=>0101011=>[2,2,2,1,1]
[8,1,7,6,4,2,5,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[1,3,6,4,7,8,2,5]=>0010010=>0100100=>[2,3,3]
[5,1,3,4,7,8,2,6]=>1000010=>0100001=>[2,5,1]
[4,5,1,3,7,8,2,6]=>0100010=>0100010=>[2,4,2]
[5,2,3,1,7,8,4,6]=>1010010=>0100101=>[2,3,2,1]
[1,6,4,3,7,8,2,5]=>0110010=>0100110=>[2,3,1,2]
[7,6,4,3,1,5,2,8]=>1111010=>0101111=>[2,2,1,1,1,1]
[3,2,6,4,1,8,5,7]=>1011010=>0101101=>[2,2,1,2,1]
[7,5,4,6,1,3,2,8]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,6,5,1,2,7,3]=>1011001=>1001101=>[1,3,1,2,1]
[1,5,6,3,7,8,2,4]=>0010010=>0100100=>[2,3,3]
[4,2,5,1,7,8,3,6]=>1010010=>0100101=>[2,3,2,1]
[3,5,8,6,1,4,2,7]=>0011010=>0101100=>[2,2,1,3]
[1,8,4,2,7,6,3,5]=>0110110=>0110110=>[2,1,2,1,2]
[7,3,8,1,6,5,4,2]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,4,1,8,7,3,6,5]=>0101101=>1011010=>[1,2,1,2,2]
[7,3,8,6,1,5,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,5,1,7,8,2,6,4]=>0100101=>1010010=>[1,2,3,2]
[5,4,7,8,2,1,6,3]=>1001101=>1011001=>[1,2,1,3,1]
[5,3,6,1,8,4,2,7]=>1010110=>0110101=>[2,1,2,2,1]
[3,4,6,2,1,8,5,7]=>0011010=>0101100=>[2,2,1,3]
[5,6,4,8,3,2,1,7]=>0101110=>0111010=>[2,1,1,2,2]
[5,7,4,8,2,1,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,5,8,2,1,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,3,2,8,1,5,6]=>0110100=>0010110=>[3,2,1,2]
[7,1,2,6,3,8,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,2,6,3,7,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,2,7,6,3,5,4]=>1001101=>1011001=>[1,2,1,3,1]
[4,8,7,3,1,6,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[4,7,8,3,1,6,2,5]=>0011010=>0101100=>[2,2,1,3]
[7,4,3,1,6,2,8,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,4,3,1,8,6,2,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,8,3,2,1,7,4,5]=>0111010=>0101110=>[2,2,1,1,2]
[3,7,6,2,4,8,1,5]=>0110010=>0100110=>[2,3,1,2]
[4,3,7,2,8,6,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[5,1,2,6,3,8,7,4]=>1001011=>1101001=>[1,1,2,3,1]
[5,1,2,7,3,8,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[6,1,2,7,3,5,8,4]=>1001001=>1001001=>[1,3,3,1]
[6,2,5,4,1,8,7,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,6,3,2,1,8,7,5]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,4,3,2,7,6,1,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[1,5,8,4,7,6,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[3,2,7,4,8,6,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,4,3,2,8,6,1,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,4,3,8,5,2,1,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,2,5,4,7,6,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,5,4,8,6,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,8,7,5,4,1,3]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,5,3,2,8,6,1,7]=>0110110=>0110110=>[2,1,2,1,2]
[3,2,5,4,8,6,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,8,6,5,4,1,7]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,4,3,6,5,2,1,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,4,3,7,5,2,1,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[3,2,7,8,5,4,1,6]=>1001110=>0111001=>[2,1,1,3,1]
[6,8,7,4,3,2,1,5]=>0111110=>0111110=>[2,1,1,1,1,2]
[6,3,2,1,8,7,4,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[6,2,3,1,8,7,4,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,1,5,8,4,6,3]=>1100101=>1010011=>[1,2,3,1,1]
[7,3,1,5,2,8,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,1,6,4,2,8,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,7,4,1,5,8,6,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,7,1,4,3,8,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[7,1,6,4,8,3,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,3,6,1,7,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,5,6,1,2,7,4,3]=>1010011=>1100101=>[1,1,3,2,1]
[3,6,4,1,5,2,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,7,2,1,8,3,5]=>0011010=>0101100=>[2,2,1,3]
[3,7,1,8,2,5,4,6]=>0101010=>0101010=>[2,2,2,2]
[4,5,8,6,1,3,7,2]=>0011001=>1001100=>[1,3,1,3]
[4,5,8,6,2,7,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[4,6,7,1,5,3,8,2]=>0010101=>1010100=>[1,2,2,3]
[4,6,7,2,1,8,5,3]=>0011011=>1101100=>[1,1,2,1,3]
[4,1,3,5,6,7,8,2]=>1000001=>1000001=>[1,6,1]
[4,6,8,3,2,7,1,5]=>0011010=>0101100=>[2,2,1,3]
[4,6,8,2,3,7,1,5]=>0010010=>0100100=>[2,3,3]
[4,5,8,3,7,1,2,6]=>0010100=>0010100=>[3,2,3]
[4,5,8,3,7,2,1,6]=>0010110=>0110100=>[2,1,2,3]
[3,7,8,4,6,2,5,1]=>0010101=>1010100=>[1,2,2,3]
[3,6,1,5,7,8,2,4]=>0100010=>0100010=>[2,4,2]
[3,8,2,5,4,7,1,6]=>0101010=>0101010=>[2,2,2,2]
[3,8,6,2,5,1,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[4,5,8,6,2,1,7,3]=>0011101=>1011100=>[1,2,1,1,3]
[4,5,8,6,1,2,7,3]=>0011001=>1001100=>[1,3,1,3]
[2,1,5,8,6,3,7,4]=>1001101=>1011001=>[1,2,1,3,1]
[4,6,8,5,2,7,1,3]=>0011010=>0101100=>[2,2,1,3]
[3,7,8,5,2,6,1,4]=>0011010=>0101100=>[2,2,1,3]
[3,7,8,5,4,1,6,2]=>0011101=>1011100=>[1,2,1,1,3]
[4,6,8,5,3,1,7,2]=>0011101=>1011100=>[1,2,1,1,3]
[7,8,2,3,5,4,1,6]=>0100110=>0110010=>[2,1,3,2]
[4,6,5,1,7,3,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[5,7,3,1,2,4,8,6]=>0110001=>1000110=>[1,4,1,2]
[6,3,2,5,1,7,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[6,1,2,4,8,5,3,7]=>1000110=>0110001=>[2,1,4,1]
[6,3,1,7,2,5,8,4]=>1101001=>1001011=>[1,3,2,1,1]
[3,7,2,8,5,1,4,6]=>0101100=>0011010=>[3,1,2,2]
[3,6,5,2,4,7,1,8]=>0110010=>0100110=>[2,3,1,2]
[1,5,7,8,3,4,2,6]=>0001010=>0101000=>[2,2,4]
[6,8,4,3,1,7,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[8,4,1,3,7,5,6,2]=>1100101=>1010011=>[1,2,3,1,1]
[4,8,1,3,7,5,6,2]=>0100101=>1010010=>[1,2,3,2]
[1,8,5,7,4,2,3,6]=>0101100=>0011010=>[3,1,2,2]
[2,1,6,8,5,3,4,7]=>1001100=>0011001=>[3,1,3,1]
[4,5,1,3,8,6,7,2]=>0100101=>1010010=>[1,2,3,2]
[1,2,6,8,5,3,4,7]=>0001100=>0011000=>[3,1,4]
[5,6,8,7,3,1,2,4]=>0011100=>0011100=>[3,1,1,3]
[1,5,6,8,4,2,3,7]=>0001100=>0011000=>[3,1,4]
[5,7,8,3,6,1,2,4]=>0010100=>0010100=>[3,2,3]
[1,5,8,6,2,4,3,7]=>0011010=>0101100=>[2,2,1,3]
[1,5,3,7,2,6,8,4]=>0101001=>1001010=>[1,3,2,2]
[1,5,2,4,8,6,7,3]=>0100101=>1010010=>[1,2,3,2]
[1,5,4,2,6,8,7,3]=>0110011=>1100110=>[1,1,3,1,2]
[5,7,6,8,3,1,2,4]=>0101100=>0011010=>[3,1,2,2]
[1,2,5,3,6,8,7,4]=>0010011=>1100100=>[1,1,3,3]
[7,1,5,6,2,3,8,4]=>1001001=>1001001=>[1,3,3,1]
[8,2,1,4,6,7,3,5]=>1100010=>0100011=>[2,4,1,1]
[7,2,6,1,3,4,8,5]=>1010001=>1000101=>[1,4,2,1]
[4,1,3,7,2,5,8,6]=>1001001=>1001001=>[1,3,3,1]
[6,2,7,5,1,3,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[1,7,5,6,2,3,8,4]=>0101001=>1001010=>[1,3,2,2]
[3,7,6,1,2,4,8,5]=>0110001=>1000110=>[1,4,1,2]
[8,6,1,3,5,7,2,4]=>1100010=>0100011=>[2,4,1,1]
[1,7,4,3,8,2,5,6]=>0110100=>0010110=>[3,2,1,2]
[6,1,5,3,4,8,2,7]=>1010010=>0100101=>[2,3,2,1]
[3,6,7,5,2,8,1,4]=>0011010=>0101100=>[2,2,1,3]
[7,8,4,1,5,6,2,3]=>0110010=>0100110=>[2,3,1,2]
[5,8,1,3,6,7,2,4]=>0100010=>0100010=>[2,4,2]
[2,8,4,3,7,1,5,6]=>0110100=>0010110=>[3,2,1,2]
[3,8,4,6,7,1,2,5]=>0100100=>0010010=>[3,3,2]
[6,3,8,4,7,1,2,5]=>1010100=>0010101=>[3,2,2,1]
[1,2,5,4,8,3,6,7]=>0010100=>0010100=>[3,2,3]
[7,1,3,8,2,4,5,6]=>1001000=>0001001=>[4,3,1]
[8,1,3,7,2,4,5,6]=>1001000=>0001001=>[4,3,1]
[3,5,4,7,8,1,2,6]=>0100100=>0010010=>[3,3,2]
[8,3,1,4,7,2,5,6]=>1100100=>0010011=>[3,3,1,1]
[1,6,4,7,8,2,3,5]=>0100100=>0010010=>[3,3,2]
[1,3,7,8,5,6,2,4]=>0001010=>0101000=>[2,2,4]
[7,5,4,8,6,1,2,3]=>1101100=>0011011=>[3,1,2,1,1]
[8,2,6,7,5,1,3,4]=>1001100=>0011001=>[3,1,3,1]
[8,1,7,4,6,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[2,5,8,4,7,1,3,6]=>0010100=>0010100=>[3,2,3]
[4,5,8,7,1,2,3,6]=>0011000=>0001100=>[4,1,3]
[4,1,8,5,7,2,3,6]=>1010100=>0010101=>[3,2,2,1]
[1,8,7,4,6,2,3,5]=>0110100=>0010110=>[3,2,1,2]
[2,6,5,4,1,8,3,7]=>0111010=>0101110=>[2,2,1,1,2]
[6,2,5,1,4,8,3,7]=>1010010=>0100101=>[2,3,2,1]
[6,5,4,1,3,8,2,7]=>1110010=>0100111=>[2,3,1,1,1]
[6,3,5,4,2,8,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[1,3,8,7,4,2,6,5]=>0011101=>1011100=>[1,2,1,1,3]
[8,7,4,3,1,5,2,6]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,2,5,1,4,6,7,3]=>1010001=>1000101=>[1,4,2,1]
[3,8,4,5,1,6,7,2]=>0101001=>1001010=>[1,3,2,2]
[8,5,4,1,3,6,7,2]=>1110001=>1000111=>[1,4,1,1,1]
[8,3,1,7,5,6,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,4,7,6,5,3,1,2]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,1,3,7,5,6,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,4,5,7,6,3,2]=>1000111=>1110001=>[1,1,1,4,1]
[2,4,1,8,5,7,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[8,2,1,4,7,6,3,5]=>1100110=>0110011=>[2,1,3,1,1]
[8,3,1,7,4,2,6,5]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,2,7,3,1,6,5,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,8,4,2,3,7,6,5]=>0110011=>1100110=>[1,1,3,1,2]
[3,1,2,8,7,4,6,5]=>1001101=>1011001=>[1,2,1,3,1]
[8,5,1,2,4,3,7,6]=>1100101=>1010011=>[1,2,3,1,1]
[2,8,3,7,4,1,6,5]=>0101101=>1011010=>[1,2,1,2,2]
[2,3,1,8,7,6,4,5]=>0101110=>0111010=>[2,1,1,2,2]
[4,2,8,7,3,1,5,6]=>1011100=>0011101=>[3,1,1,2,1]
[1,3,4,8,7,2,5,6]=>0001100=>0011000=>[3,1,4]
[8,1,3,4,6,7,2,5]=>1000010=>0100001=>[2,5,1]
[3,4,8,2,6,7,1,5]=>0010010=>0100100=>[2,3,3]
[3,6,8,2,5,1,7,4]=>0010101=>1010100=>[1,2,2,3]
[3,8,2,5,7,4,6,1]=>0100101=>1010010=>[1,2,3,2]
[8,4,2,1,7,5,6,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,2,7,5,6,4,1,3]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,8,5,4,1,7,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[6,8,5,4,1,7,2,3]=>0111010=>0101110=>[2,2,1,1,2]
[2,8,1,5,7,6,3,4]=>0100110=>0110010=>[2,1,3,2]
[3,1,8,2,7,5,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,7,1,6,4,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,7,6,5,1,2,3]=>1011100=>0011101=>[3,1,1,2,1]
[2,8,4,7,3,6,5,1]=>0101011=>1101010=>[1,1,2,2,2]
[8,4,7,2,1,6,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[1,8,4,7,6,5,2,3]=>0101110=>0111010=>[2,1,1,2,2]
[8,2,5,7,1,4,6,3]=>1001001=>1001001=>[1,3,3,1]
[3,5,8,1,7,4,6,2]=>0010101=>1010100=>[1,2,2,3]
[8,4,7,1,3,6,5,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,1,7,8,3,4,2,6]=>1001010=>0101001=>[2,2,3,1]
[5,3,6,1,4,2,8,7]=>1010101=>1010101=>[1,2,2,2,1]
[5,7,2,1,4,3,8,6]=>0110101=>1010110=>[1,2,2,1,2]
[7,1,8,3,5,2,4,6]=>1010100=>0010101=>[3,2,2,1]
[7,2,4,8,1,5,6,3]=>1001001=>1001001=>[1,3,3,1]
[7,1,8,4,2,5,6,3]=>1011001=>1001101=>[1,3,1,2,1]
[6,4,2,5,8,1,7,3]=>1100101=>1010011=>[1,2,3,1,1]
[2,1,7,5,8,3,6,4]=>1010101=>1010101=>[1,2,2,2,1]
[7,3,8,5,6,2,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[2,7,4,8,1,5,6,3]=>0101001=>1001010=>[1,3,2,2]
[7,4,8,3,1,5,6,2]=>1011001=>1001101=>[1,3,1,2,1]
[6,1,5,8,3,7,4,2]=>1001011=>1101001=>[1,1,2,3,1]
[2,6,3,5,8,7,4,1]=>0100111=>1110010=>[1,1,1,3,2]
[6,8,1,2,5,7,4,3]=>0100011=>1100010=>[1,1,4,2]
[8,6,5,3,7,2,1,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[4,8,5,3,7,2,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[7,4,8,6,5,3,2,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[6,4,7,1,3,2,8,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,8,4,1,3,5,6,2]=>0110001=>1000110=>[1,4,1,2]
[7,8,3,4,1,5,6,2]=>0101001=>1001010=>[1,3,2,2]
[7,3,1,8,2,5,6,4]=>1101001=>1001011=>[1,3,2,1,1]
[7,2,3,8,1,5,6,4]=>1001001=>1001001=>[1,3,3,1]
[2,7,4,8,6,3,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[6,4,8,2,3,1,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[7,2,1,8,3,5,6,4]=>1101001=>1001011=>[1,3,2,1,1]
[5,1,6,3,8,2,4,7]=>1010100=>0010101=>[3,2,2,1]
[3,5,6,8,1,4,2,7]=>0001010=>0101000=>[2,2,4]
[4,3,5,8,2,1,6,7]=>1001100=>0011001=>[3,1,3,1]
[6,4,7,2,3,1,5,8]=>1010100=>0010101=>[3,2,2,1]
[6,8,1,5,4,2,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,8,6,3,1,4,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[7,8,6,3,5,1,2,4]=>0110100=>0010110=>[3,2,1,2]
[7,2,8,5,4,6,3,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,1,8,4,7,2,3,5]=>1010100=>0010101=>[3,2,2,1]
[6,5,3,7,2,4,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[5,6,2,8,4,3,7,1]=>0101101=>1011010=>[1,2,1,2,2]
[4,6,2,7,8,3,5,1]=>0100101=>1010010=>[1,2,3,2]
[3,1,2,4,8,5,7,6]=>1000101=>1010001=>[1,2,4,1]
[5,1,2,4,6,7,8,3]=>1000001=>1000001=>[1,6,1]
[4,6,3,5,2,8,7,1]=>0101011=>1101010=>[1,1,2,2,2]
[5,3,2,6,8,4,7,1]=>1100101=>1010011=>[1,2,3,1,1]
[5,6,3,4,8,2,7,1]=>0100101=>1010010=>[1,2,3,2]
[5,2,6,4,1,7,8,3]=>1011001=>1001101=>[1,3,1,2,1]
[5,8,4,6,3,2,7,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,4,3,8,6,2,7,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,7,8,2,4,3,6,1]=>0010101=>1010100=>[1,2,2,3]
[5,6,2,4,8,3,7,1]=>0100101=>1010010=>[1,2,3,2]
[5,4,2,8,6,3,7,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,7,4,2,6,3,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,4,7,8,2,3,5,1]=>1001001=>1001001=>[1,3,3,1]
[3,7,5,2,4,8,1,6]=>0110010=>0100110=>[2,3,1,2]
[4,7,5,2,3,8,6,1]=>0110011=>1100110=>[1,1,3,1,2]
[6,4,7,3,2,5,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[6,3,7,8,2,4,5,1]=>1001001=>1001001=>[1,3,3,1]
[5,7,3,2,8,4,6,1]=>0110101=>1010110=>[1,2,2,1,2]
[5,3,7,2,8,4,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,3,7,2,5,8,6,1]=>1010011=>1100101=>[1,1,3,2,1]
[4,7,3,2,5,8,6,1]=>0110011=>1100110=>[1,1,3,1,2]
[4,7,3,2,6,8,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[7,5,3,2,6,4,8,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[5,7,3,2,6,4,8,1]=>0110101=>1010110=>[1,2,2,1,2]
[5,3,2,8,6,4,7,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,5,2,6,7,3,4,1]=>1100101=>1010011=>[1,2,3,1,1]
[8,4,2,6,3,7,5,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,4,6,2,3,8,5,1]=>1010011=>1100101=>[1,1,3,2,1]
[7,5,6,2,8,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,7,5,2,4,8,1]=>1011001=>1001101=>[1,3,1,2,1]
[5,7,6,2,8,3,4,1]=>0110101=>1010110=>[1,2,2,1,2]
[4,7,6,2,3,8,5,1]=>0110011=>1100110=>[1,1,3,1,2]
[7,6,3,2,5,8,1,4]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,4,2,5,8,3,1]=>1110011=>1100111=>[1,1,3,1,1,1]
[6,3,8,5,4,7,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,8,3,7,1,6,5,2]=>0101011=>1101010=>[1,1,2,2,2]
[8,7,2,6,5,1,4,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,8,3,2,1,7,6,4]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,4,3,8,1,7,6,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,5,3,8,7,1,4,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,3,8,2,7,6,5,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,8,2,7,6,5,3,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[7,8,2,6,5,4,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[3,8,7,6,2,5,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[4,8,3,7,2,1,6,5]=>0101101=>1011010=>[1,2,1,2,2]
[8,6,3,1,7,5,4,2]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[8,6,3,7,1,5,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,8,3,7,6,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,8,2,7,6,4,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[8,4,2,1,7,6,5,3]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[1,6,4,2,5,3,7,8]=>0110100=>0010110=>[3,2,1,2]
[1,6,7,2,5,3,4,8]=>0010100=>0010100=>[3,2,3]
[1,8,6,2,7,3,4,5]=>0110100=>0010110=>[3,2,1,2]
[1,5,2,6,4,3,7,8]=>0101100=>0011010=>[3,1,2,2]
[1,5,2,4,6,3,7,8]=>0100100=>0010010=>[3,3,2]
[1,8,6,2,3,7,4,5]=>0110010=>0100110=>[2,3,1,2]
[1,5,2,8,6,3,4,7]=>0101100=>0011010=>[3,1,2,2]
[1,7,3,2,6,8,4,5]=>0110010=>0100110=>[2,3,1,2]
[1,3,6,8,2,7,4,5]=>0001010=>0101000=>[2,2,4]
[1,4,3,8,2,5,6,7]=>0101000=>0001010=>[4,2,2]
[1,7,2,3,8,5,4,6]=>0100110=>0110010=>[2,1,3,2]
[1,6,2,8,5,4,3,7]=>0101110=>0111010=>[2,1,1,2,2]
[1,7,2,3,8,6,4,5]=>0100110=>0110010=>[2,1,3,2]
[1,5,3,8,2,7,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,7,2,5,3,4,8,6]=>0101001=>1001010=>[1,3,2,2]
[1,4,8,2,5,6,3,7]=>0010010=>0100100=>[2,3,3]
[1,2,7,3,6,8,4,5]=>0010010=>0100100=>[2,3,3]
[1,7,2,3,6,8,4,5]=>0100010=>0100010=>[2,4,2]
[1,4,8,3,2,5,6,7]=>0011000=>0001100=>[4,1,3]
[1,7,2,5,8,3,4,6]=>0100100=>0010010=>[3,3,2]
[1,5,6,3,4,2,7,8]=>0010100=>0010100=>[3,2,3]
[1,5,6,3,4,7,2,8]=>0010010=>0100100=>[2,3,3]
[1,5,3,6,4,2,7,8]=>0101100=>0011010=>[3,1,2,2]
[1,7,5,6,8,3,4,2]=>0100101=>1010010=>[1,2,3,2]
[1,7,5,6,3,8,4,2]=>0101011=>1101010=>[1,1,2,2,2]
[1,3,7,5,2,8,6,4]=>0011011=>1101100=>[1,1,2,1,3]
[1,3,7,2,5,8,6,4]=>0010011=>1100100=>[1,1,3,3]
[1,5,3,7,4,6,2,8]=>0101010=>0101010=>[2,2,2,2]
[1,5,3,7,6,4,2,8]=>0101110=>0111010=>[2,1,1,2,2]
[1,5,3,6,7,4,2,8]=>0100110=>0110010=>[2,1,3,2]
[1,5,6,3,7,4,2,8]=>0010110=>0110100=>[2,1,2,3]
[1,5,7,6,3,4,8,2]=>0011001=>1001100=>[1,3,1,3]
[1,5,7,3,6,4,8,2]=>0010101=>1010100=>[1,2,2,3]
[1,3,7,2,5,6,8,4]=>0010001=>1000100=>[1,4,3]
[1,3,7,5,6,2,8,4]=>0010101=>1010100=>[1,2,2,3]
[2,5,7,4,1,3,8,6]=>0011001=>1001100=>[1,3,1,3]
[6,7,3,1,8,5,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[8,3,5,1,7,6,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[3,5,6,1,8,7,2,4]=>0010110=>0110100=>[2,1,2,3]
[2,4,6,8,7,3,1,5]=>0001110=>0111000=>[2,1,1,4]
[2,3,6,4,1,8,7,5]=>0011011=>1101100=>[1,1,2,1,3]
[4,7,5,2,1,8,6,3]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,5,3,6,2,1,7,4]=>1101101=>1011011=>[1,2,1,2,1,1]
[4,5,7,3,1,2,8,6]=>0011001=>1001100=>[1,3,1,3]
[4,5,1,8,3,2,7,6]=>0101101=>1011010=>[1,2,1,2,2]
[3,6,1,2,4,8,7,5]=>0100011=>1100010=>[1,1,4,2]
[2,5,3,8,4,1,7,6]=>0101101=>1011010=>[1,2,1,2,2]
[8,6,2,3,1,7,5,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,3,1,2,4,8,7,5]=>1100011=>1100011=>[1,1,4,1,1]
[2,6,4,5,8,1,3,7]=>0100100=>0010010=>[3,3,2]
[4,2,6,1,3,7,8,5]=>1010001=>1000101=>[1,4,2,1]
[8,5,4,2,7,6,3,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[2,8,4,6,7,1,3,5]=>0100100=>0010010=>[3,3,2]
[5,8,2,1,4,6,7,3]=>0110001=>1000110=>[1,4,1,2]
[3,7,8,4,2,6,5,1]=>0011011=>1101100=>[1,1,2,1,3]
[7,1,3,8,4,5,6,2]=>1001001=>1001001=>[1,3,3,1]
[7,8,1,4,3,5,6,2]=>0101001=>1001010=>[1,3,2,2]
[3,6,7,1,8,2,5,4]=>0010101=>1010100=>[1,2,2,3]
[3,1,5,7,2,8,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[4,1,8,3,2,7,6,5]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,8,2,4,7,1,6,5]=>0100101=>1010010=>[1,2,3,2]
[3,2,4,8,7,1,6,5]=>1001101=>1011001=>[1,2,1,3,1]
[3,2,5,7,1,8,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[4,2,8,3,1,7,6,5]=>1011011=>1101101=>[1,1,2,1,2,1]
[4,8,2,1,3,7,6,5]=>0110011=>1100110=>[1,1,3,1,2]
[4,2,8,1,3,7,6,5]=>1010011=>1100101=>[1,1,3,2,1]
[2,4,6,5,1,3,8,7]=>0011001=>1001100=>[1,3,1,3]
[2,3,4,6,8,7,1,5]=>0000110=>0110000=>[2,1,5]
[2,1,4,6,8,7,3,5]=>1000110=>0110001=>[2,1,4,1]
[4,5,7,1,6,8,3,2]=>0010011=>1100100=>[1,1,3,3]
[6,7,2,8,3,1,4,5]=>0101100=>0011010=>[3,1,2,2]
[7,8,5,2,4,1,3,6]=>0110100=>0010110=>[3,2,1,2]
[7,6,2,3,1,8,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[4,1,3,7,8,5,2,6]=>1000110=>0110001=>[2,1,4,1]
[4,3,1,8,5,2,7,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,1,8,5,4,2,7,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,1,3,2,4,7,8,6]=>1010001=>1000101=>[1,4,2,1]
[2,4,8,5,6,1,7,3]=>0010101=>1010100=>[1,2,2,3]
[2,8,7,4,5,1,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[1,3,8,5,2,6,7,4]=>0011001=>1001100=>[1,3,1,3]
[8,6,2,4,1,5,7,3]=>1101001=>1001011=>[1,3,2,1,1]
[1,6,4,3,2,7,8,5]=>0111001=>1001110=>[1,3,1,1,2]
[8,5,3,2,1,6,7,4]=>1111001=>1001111=>[1,3,1,1,1,1]
[1,7,5,2,3,6,8,4]=>0110001=>1000110=>[1,4,1,2]
[8,1,2,5,3,6,7,4]=>1001001=>1001001=>[1,3,3,1]
[8,2,6,4,3,5,1,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,1,4,6,5,2,7]=>1100110=>0110011=>[2,1,3,1,1]
[5,8,3,1,2,6,4,7]=>0110010=>0100110=>[2,3,1,2]
[4,8,1,7,5,2,3,6]=>0101100=>0011010=>[3,1,2,2]
[4,8,1,7,5,2,6,3]=>0101101=>1011010=>[1,2,1,2,2]
[8,5,1,4,2,6,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,1,3,5,6,2,7]=>1100010=>0100011=>[2,4,1,1]
[8,5,3,2,1,6,4,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[8,1,5,4,2,6,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[8,5,2,4,1,6,3,7]=>1101010=>0101011=>[2,2,2,1,1]
[4,8,7,1,5,2,6,3]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,7,1,5,2,3,6]=>0110100=>0010110=>[3,2,1,2]
[7,6,8,4,1,3,2,5]=>1011010=>0101101=>[2,2,1,2,1]
[7,6,8,4,1,3,5,2]=>1011001=>1001101=>[1,3,1,2,1]
[8,4,2,7,5,1,6,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,8,7,5,4,1,2,6]=>0111100=>0011110=>[3,1,1,1,2]
[7,6,8,4,1,5,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[8,7,6,1,5,2,3,4]=>1110100=>0010111=>[3,2,1,1,1]
[7,1,4,8,6,3,5,2]=>1001101=>1011001=>[1,2,1,3,1]
[8,1,6,5,3,4,7,2]=>1011001=>1001101=>[1,3,1,2,1]
[8,6,2,5,3,4,7,1]=>1101001=>1001011=>[1,3,2,1,1]
[8,6,5,1,3,4,7,2]=>1110001=>1000111=>[1,4,1,1,1]
[8,7,5,1,3,6,2,4]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,1,5,3,6,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,6,1,3,5,4,7,2]=>1100101=>1010011=>[1,2,3,1,1]
[8,1,6,3,5,4,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[7,1,4,8,3,6,5,2]=>1001011=>1101001=>[1,1,2,3,1]
[8,3,2,7,4,6,5,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,8,5,2,4,3,6,1]=>0110101=>1010110=>[1,2,2,1,2]
[7,3,8,2,5,4,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,2,5,3,7,6,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[4,8,1,5,3,7,6,2]=>0101011=>1101010=>[1,1,2,2,2]
[7,4,8,2,6,3,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[7,4,8,2,6,3,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[8,7,3,1,6,4,2,5]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,7,3,1,6,4,5,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,7,3,1,4,6,5,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,4,3,2,7,5,6,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,4,1,7,8,5,3,2]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,6,3,4,1,8,5,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,7,3,1,6,2,5,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[7,8,6,4,2,5,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[7,8,2,4,6,5,1,3]=>0100110=>0110010=>[2,1,3,2]
[8,1,7,3,5,6,2,4]=>1010010=>0100101=>[2,3,2,1]
[8,7,1,6,5,2,3,4]=>1101100=>0011011=>[3,1,2,1,1]
[8,7,5,2,4,6,1,3]=>1110010=>0100111=>[2,3,1,1,1]
[8,1,7,5,4,6,2,3]=>1011010=>0101101=>[2,2,1,2,1]
[8,7,3,2,6,1,5,4]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,1,7,6,5,2,3,4]=>1011100=>0011101=>[3,1,1,2,1]
[8,7,2,6,5,1,3,4]=>1101100=>0011011=>[3,1,2,1,1]
[1,4,8,6,7,5,3,2]=>0010111=>1110100=>[1,1,1,2,3]
[8,6,2,5,7,4,3,1]=>1100111=>1110011=>[1,1,1,3,1,1]
[7,1,3,6,8,5,4,2]=>1000111=>1110001=>[1,1,1,4,1]
[8,1,7,6,4,5,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,1,8,6,4,5,3,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[6,5,7,2,8,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,2,5,8,1,4,3]=>0100101=>1010010=>[1,2,3,2]
[6,3,7,5,8,2,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,5,7,3,8,1,4,2]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,7,4,8,2,5,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,3,7,4,8,1,5,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,7,6,4,2,5,3,1]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[8,7,4,6,2,3,5,1]=>1101001=>1001011=>[1,3,2,1,1]
[6,8,4,5,7,3,2,1]=>0100111=>1110010=>[1,1,1,3,2]
[6,7,5,1,4,3,8,2]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,6,8,3,5,1,4]=>0101010=>0101010=>[2,2,2,2]
[7,2,1,5,3,8,6,4]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,8,2,7,6,1,3,4]=>0101100=>0011010=>[3,1,2,2]
[4,2,3,1,5,8,6,7]=>1010010=>0100101=>[2,3,2,1]
[1,5,7,3,6,8,2,4]=>0010010=>0100100=>[2,3,3]
[8,4,6,2,5,7,1,3]=>1010010=>0100101=>[2,3,2,1]
[1,3,4,7,6,8,2,5]=>0001010=>0101000=>[2,2,4]
[8,1,3,6,7,4,2,5]=>1000110=>0110001=>[2,1,4,1]
[1,2,4,7,8,5,3,6]=>0000110=>0110000=>[2,1,5]
[2,1,4,7,8,5,3,6]=>1000110=>0110001=>[2,1,4,1]
[3,1,4,7,6,8,2,5]=>1001010=>0101001=>[2,2,3,1]
[4,1,3,7,6,8,2,5]=>1001010=>0101001=>[2,2,3,1]
[5,1,7,3,6,8,2,4]=>1010010=>0100101=>[2,3,2,1]
[6,7,8,2,4,5,1,3]=>0010010=>0100100=>[2,3,3]
[5,8,6,2,4,7,1,3]=>0110010=>0100110=>[2,3,1,2]
[3,8,2,6,5,7,1,4]=>0101010=>0101010=>[2,2,2,2]
[2,8,3,6,7,4,1,5]=>0100110=>0110010=>[2,1,3,2]
[1,8,3,6,7,4,2,5]=>0100110=>0110010=>[2,1,3,2]
[8,7,2,5,6,3,1,4]=>1100110=>0110011=>[2,1,3,1,1]
[8,7,1,6,4,3,2,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[1,8,2,7,5,4,3,6]=>0101110=>0111010=>[2,1,1,2,2]
[3,8,1,7,5,4,2,6]=>0101110=>0111010=>[2,1,1,2,2]
[4,8,1,6,7,3,2,5]=>0100110=>0110010=>[2,1,3,2]
[5,8,6,1,7,3,2,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,7,1,2,8,4,3,5]=>0100110=>0110010=>[2,1,3,2]
[2,1,3,8,6,5,4,7]=>1001110=>0111001=>[2,1,1,3,1]
[8,2,1,7,5,4,3,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[1,3,2,8,6,5,4,7]=>0101110=>0111010=>[2,1,1,2,2]
[3,4,1,7,6,8,2,5]=>0101010=>0101010=>[2,2,2,2]
[2,5,7,1,8,4,3,6]=>0010110=>0110100=>[2,1,2,3]
[3,5,7,1,6,8,2,4]=>0010010=>0100100=>[2,3,3]
[4,5,7,6,1,8,2,3]=>0011010=>0101100=>[2,2,1,3]
[5,4,7,6,8,3,1,2]=>1010110=>0110101=>[2,1,2,2,1]
[1,5,7,8,6,3,2,4]=>0001110=>0111000=>[2,1,1,4]
[8,4,6,7,5,2,1,3]=>1001110=>0111001=>[2,1,1,3,1]
[8,3,7,5,6,2,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[1,4,8,6,7,3,2,5]=>0010110=>0110100=>[2,1,2,3]
[2,4,8,6,7,3,1,5]=>0010110=>0110100=>[2,1,2,3]
[2,3,8,7,5,4,1,6]=>0011110=>0111100=>[2,1,1,1,3]
[1,3,8,7,5,4,2,6]=>0011110=>0111100=>[2,1,1,1,3]
[8,2,7,6,4,3,1,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[8,1,7,6,4,3,2,5]=>1011110=>0111101=>[2,1,1,1,2,1]
[4,1,8,6,7,3,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[4,8,7,5,6,2,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[8,1,7,2,5,6,4,3]=>1010011=>1100101=>[1,1,3,2,1]
[8,1,3,5,2,7,6,4]=>1001011=>1101001=>[1,1,2,3,1]
[8,1,7,4,3,6,5,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,7,1,5,4,8,6,3]=>0101011=>1101010=>[1,1,2,2,2]
[8,6,2,4,3,7,5,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[8,1,4,5,6,3,7,2]=>1000101=>1010001=>[1,2,4,1]
[8,1,4,5,6,2,7,3]=>1000101=>1010001=>[1,2,4,1]
[8,1,4,7,6,2,5,3]=>1001101=>1011001=>[1,2,1,3,1]
[2,5,1,7,8,6,4,3]=>0100111=>1110010=>[1,1,1,3,2]
[3,5,6,2,8,7,4,1]=>0010111=>1110100=>[1,1,1,2,3]
[3,5,6,1,8,7,4,2]=>0010111=>1110100=>[1,1,1,2,3]
[2,4,5,1,7,6,3,8]=>0010110=>0110100=>[2,1,2,3]
[7,3,1,5,6,4,2,8]=>1100110=>0110011=>[2,1,3,1,1]
[8,6,2,4,7,3,1,5]=>1100110=>0110011=>[2,1,3,1,1]
[8,4,7,3,5,2,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,5,3,7,6,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[3,4,5,6,2,8,1,7]=>0001010=>0101000=>[2,2,4]
[3,7,4,2,8,5,1,6]=>0110110=>0110110=>[2,1,2,1,2]
[7,3,4,1,6,8,2,5]=>1010010=>0100101=>[2,3,2,1]
[2,6,3,1,4,7,5,8]=>0110010=>0100110=>[2,3,1,2]
[7,2,1,6,3,4,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[7,3,4,1,6,5,8,2]=>1010101=>1010101=>[1,2,2,2,1]
[3,7,4,2,5,8,6,1]=>0110011=>1100110=>[1,1,3,1,2]
[2,3,5,1,4,8,7,6]=>0010011=>1100100=>[1,1,3,3]
[2,7,1,3,6,8,5,4]=>0100011=>1100010=>[1,1,4,2]
[2,7,1,3,8,4,6,5]=>0100101=>1010010=>[1,2,3,2]
[3,8,7,1,6,2,5,4]=>0110101=>1010110=>[1,2,2,1,2]
[3,8,7,1,4,5,2,6]=>0110010=>0100110=>[2,3,1,2]
[3,7,4,2,1,8,6,5]=>0111011=>1101110=>[1,1,2,1,1,2]
[4,8,5,7,2,6,3,1]=>0101011=>1101010=>[1,1,2,2,2]
[8,4,5,7,3,2,6,1]=>1001101=>1011001=>[1,2,1,3,1]
[8,3,7,2,4,1,5,6]=>1010100=>0010101=>[3,2,2,1]
[8,6,7,2,1,4,3,5]=>1011010=>0101101=>[2,2,1,2,1]
[8,3,7,5,1,2,6,4]=>1011001=>1001101=>[1,3,1,2,1]
[7,3,4,6,2,1,5,8]=>1001100=>0011001=>[3,1,3,1]
[3,7,4,6,1,5,2,8]=>0101010=>0101010=>[2,2,2,2]
[3,4,7,6,1,2,8,5]=>0011001=>1001100=>[1,3,1,3]
[4,5,8,7,6,1,3,2]=>0011101=>1011100=>[1,2,1,1,3]
[8,6,3,7,5,1,4,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[8,7,3,5,6,1,4,2]=>1100101=>1010011=>[1,2,3,1,1]
[7,6,3,8,1,4,5,2]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,2,7,6,1,3,4]=>1101100=>0011011=>[3,1,2,1,1]
[7,6,4,8,1,2,5,3]=>1101001=>1001011=>[1,3,2,1,1]
[8,7,3,1,4,5,2,6]=>1110010=>0100111=>[2,3,1,1,1]
[8,4,2,5,1,6,7,3]=>1101001=>1001011=>[1,3,2,1,1]
[8,5,3,1,6,4,7,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,7,3,1,4,5,6,2]=>1110001=>1000111=>[1,4,1,1,1]
[8,7,4,1,5,6,2,3]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,4,1,7,5,2,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,6,3,1,7,4,5,2]=>1110101=>1010111=>[1,2,2,1,1,1]
[8,5,3,1,6,7,4,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,5,3,7,1,6,4,2]=>1101011=>1101011=>[1,1,2,2,1,1]
[7,6,3,8,1,4,2,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,8,2,6,1,5,3]=>1010101=>1010101=>[1,2,2,2,1]
[8,5,3,1,6,4,2,7]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,7,4,1,5,2,3,6]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,5,1,2,6,3,4]=>1110010=>0100111=>[2,3,1,1,1]
[8,6,4,1,2,7,5,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,7,3,1,4,2,5,6]=>1110100=>0010111=>[3,2,1,1,1]
[8,7,4,1,2,5,3,6]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,5,1,2,3,6,4]=>1110001=>1000111=>[1,4,1,1,1]
[1,6,7,3,2,8,4,5]=>0011010=>0101100=>[2,2,1,3]
[1,8,6,3,2,7,4,5]=>0111010=>0101110=>[2,2,1,1,2]
[1,5,3,7,2,8,4,6]=>0101010=>0101010=>[2,2,2,2]
[1,4,6,2,8,5,3,7]=>0010110=>0110100=>[2,1,2,3]
[1,5,6,2,8,4,3,7]=>0010110=>0110100=>[2,1,2,3]
[3,5,2,6,4,7,8,1]=>0101001=>1001010=>[1,3,2,2]
[1,2,5,3,8,6,7,4]=>0010101=>1010100=>[1,2,2,3]
[2,4,6,3,1,7,5,8]=>0011010=>0101100=>[2,2,1,3]
[3,4,8,6,5,7,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,3,8,6,7,1,5,4]=>0010101=>1010100=>[1,2,2,3]
[1,2,5,7,4,6,8,3]=>0001001=>1001000=>[1,3,4]
[2,3,6,8,1,7,4,5]=>0001010=>0101000=>[2,2,4]
[2,4,8,5,6,7,1,3]=>0010010=>0100100=>[2,3,3]
[1,4,8,5,6,7,3,2]=>0010011=>1100100=>[1,1,3,3]
[6,1,3,5,4,2,8,7]=>1001101=>1011001=>[1,2,1,3,1]
[3,6,4,2,5,1,8,7]=>0110101=>1010110=>[1,2,2,1,2]
[2,1,5,8,6,4,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[1,8,3,5,6,2,7,4]=>0100101=>1010010=>[1,2,3,2]
[8,3,2,5,6,1,7,4]=>1100101=>1010011=>[1,2,3,1,1]
[4,2,5,1,6,8,7,3]=>1010011=>1100101=>[1,1,3,2,1]
[5,4,2,7,8,6,1,3]=>1100110=>0110011=>[2,1,3,1,1]
[6,7,1,8,3,2,4,5]=>0101100=>0011010=>[3,1,2,2]
[6,7,2,8,1,3,4,5]=>0101000=>0001010=>[4,2,2]
[1,7,8,5,2,6,3,4]=>0011010=>0101100=>[2,2,1,3]
[5,8,7,2,6,3,4,1]=>0110101=>1010110=>[1,2,2,1,2]
[7,6,2,4,8,1,5,3]=>1100101=>1010011=>[1,2,3,1,1]
[4,8,3,1,7,6,5,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[5,3,8,7,1,6,4,2]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,8,7,3,1,6,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[5,3,8,2,1,7,6,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,8,7,2,6,5,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[7,4,1,8,6,5,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[5,4,2,8,1,7,6,3]=>1101011=>1101011=>[1,1,2,2,1,1]
[5,8,4,7,1,6,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[8,5,6,1,4,7,2,3]=>1010010=>0100101=>[2,3,2,1]
[6,7,4,1,2,5,8,3]=>0110001=>1000110=>[1,4,1,2]
[3,6,7,5,8,1,2,4]=>0010100=>0010100=>[3,2,3]
[6,5,8,7,4,2,3,1]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,7,6,2,8,3,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[2,5,6,3,1,4,8,7]=>0011001=>1001100=>[1,3,1,3]
[3,8,7,2,1,5,4,6]=>0111010=>0101110=>[2,2,1,1,2]
[4,8,5,6,7,3,1,2]=>0100110=>0110010=>[2,1,3,2]
[3,7,6,2,8,5,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[6,1,7,3,8,5,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[4,8,5,6,7,2,1,3]=>0100110=>0110010=>[2,1,3,2]
[5,8,6,2,7,4,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[4,6,5,8,7,3,1,2]=>0101110=>0111010=>[2,1,1,2,2]
[8,3,1,7,2,6,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[8,4,5,1,7,6,2,3]=>1010110=>0110101=>[2,1,2,2,1]
[8,5,6,1,7,2,4,3]=>1010101=>1010101=>[1,2,2,2,1]
[7,5,6,1,3,8,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,7,6,1,3,8,4,2]=>0110011=>1100110=>[1,1,3,1,2]
[6,7,1,4,2,8,5,3]=>0101011=>1101010=>[1,1,2,2,2]
[2,1,6,4,8,3,7,5]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,7,4,6,2,3,1]=>0110101=>1010110=>[1,2,2,1,2]
[6,8,7,1,5,3,4,2]=>0110101=>1010110=>[1,2,2,1,2]
[2,7,8,4,6,5,1,3]=>0010110=>0110100=>[2,1,2,3]
[3,7,8,5,4,6,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,8,7,5,3,6,4,1]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,8,7,3,6,4,5,2]=>0110101=>1010110=>[1,2,2,1,2]
[2,8,7,4,6,1,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,7,2,5,6,3,1]=>0110011=>1100110=>[1,1,3,1,2]
[4,7,8,5,3,6,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[6,4,8,1,5,7,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,5,8,6,3,7,2,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,6,7,8,4,5,1,3]=>0001010=>0101000=>[2,2,4]
[6,1,2,8,4,7,5,3]=>1001011=>1101001=>[1,1,2,3,1]
[4,7,1,8,5,6,3,2]=>0101011=>1101010=>[1,1,2,2,2]
[5,7,1,8,2,6,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[7,2,1,8,6,4,5,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[5,3,8,4,7,6,2,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[2,5,8,1,7,4,6,3]=>0010101=>1010100=>[1,2,2,3]
[4,5,8,3,7,6,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[1,7,2,8,6,4,5,3]=>0101101=>1011010=>[1,2,1,2,2]
[2,4,7,8,5,6,1,3]=>0001010=>0101000=>[2,2,4]
[2,4,8,5,7,6,1,3]=>0010110=>0110100=>[2,1,2,3]
[2,6,3,8,5,1,7,4]=>0101101=>1011010=>[1,2,1,2,2]
[4,1,5,8,6,7,3,2]=>1001011=>1101001=>[1,1,2,3,1]
[3,4,6,8,2,1,7,5]=>0001101=>1011000=>[1,2,1,4]
[5,3,4,7,6,1,2,8]=>1001100=>0011001=>[3,1,3,1]
[1,2,7,8,4,3,6,5]=>0001101=>1011000=>[1,2,1,4]
[2,8,5,4,1,3,7,6]=>0111001=>1001110=>[1,3,1,1,2]
[4,2,8,7,1,3,5,6]=>1011000=>0001101=>[4,1,2,1]
[5,4,6,3,1,7,2,8]=>1011010=>0101101=>[2,2,1,2,1]
[4,3,6,5,1,8,2,7]=>1011010=>0101101=>[2,2,1,2,1]
[1,5,6,8,7,3,2,4]=>0001110=>0111000=>[2,1,1,4]
[1,4,8,3,6,5,2,7]=>0010110=>0110100=>[2,1,2,3]
[1,2,8,6,4,3,7,5]=>0011101=>1011100=>[1,2,1,1,3]
[6,5,1,8,7,3,2,4]=>1101110=>0111011=>[2,1,1,2,1,1]
[8,3,2,6,1,7,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[6,5,1,8,7,4,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[7,5,1,8,6,4,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[8,5,1,7,6,4,3,2]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[8,5,3,7,6,1,4,2]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,8,7,6,1,5,4,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[8,5,2,6,1,4,7,3]=>1101001=>1001011=>[1,3,2,1,1]
[2,7,5,8,1,4,6,3]=>0101001=>1001010=>[1,3,2,2]
[8,5,6,1,7,3,2,4]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,6,7,1,8,5,4]=>1001011=>1101001=>[1,1,2,3,1]
[3,4,6,7,8,2,1,5]=>0000110=>0110000=>[2,1,5]
[6,7,1,3,8,5,4,2]=>0100111=>1110010=>[1,1,1,3,2]
[6,7,1,8,5,2,4,3]=>0101101=>1011010=>[1,2,1,2,2]
[1,6,2,7,8,5,3,4]=>0100110=>0110010=>[2,1,3,2]
[1,2,6,7,8,5,3,4]=>0000110=>0110000=>[2,1,5]
[1,6,7,4,8,3,2,5]=>0010110=>0110100=>[2,1,2,3]
[1,4,6,7,8,3,2,5]=>0000110=>0110000=>[2,1,5]
[8,6,1,2,7,3,4,5]=>1100100=>0010011=>[3,3,1,1]
[3,6,8,2,7,1,5,4]=>0010101=>1010100=>[1,2,2,3]
[2,8,6,1,4,5,7,3]=>0110001=>1000110=>[1,4,1,2]
[6,8,7,2,5,4,1,3]=>0110110=>0110110=>[2,1,2,1,2]
[3,7,2,1,8,4,6,5]=>0110101=>1010110=>[1,2,2,1,2]
[3,7,2,4,1,8,6,5]=>0101011=>1101010=>[1,1,2,2,2]
[3,2,6,4,8,7,5,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[4,7,2,8,6,5,1,3]=>0101110=>0111010=>[2,1,1,2,2]
[4,7,1,8,6,5,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[2,7,4,8,3,6,1,5]=>0101010=>0101010=>[2,2,2,2]
[4,7,3,8,6,1,5,2]=>0101101=>1011010=>[1,2,1,2,2]
[4,7,3,8,6,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[4,3,6,8,7,2,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[4,3,8,2,5,7,6,1]=>1010011=>1100101=>[1,1,3,2,1]
[4,3,8,1,5,7,6,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,1,2,6,8,7,5,3]=>1000111=>1110001=>[1,1,1,4,1]
[2,4,3,6,8,7,1,5]=>0100110=>0110010=>[2,1,3,2]
[3,1,6,4,8,7,2,5]=>1010110=>0110101=>[2,1,2,2,1]
[4,1,6,8,7,5,2,3]=>1001110=>0111001=>[2,1,1,3,1]
[3,8,1,4,5,7,2,6]=>0100010=>0100010=>[2,4,2]
[3,8,1,4,2,5,7,6]=>0101001=>1001010=>[1,3,2,2]
[4,1,8,3,5,2,7,6]=>1010101=>1010101=>[1,2,2,2,1]
[4,2,3,6,8,7,1,5]=>1000110=>0110001=>[2,1,4,1]
[4,2,8,3,5,7,6,1]=>1010011=>1100101=>[1,1,3,2,1]
[3,8,2,4,5,7,6,1]=>0100011=>1100010=>[1,1,4,2]
[3,8,2,4,1,5,7,6]=>0101001=>1001010=>[1,3,2,2]
[3,8,2,5,1,4,7,6]=>0101001=>1001010=>[1,3,2,2]
[4,2,8,5,7,1,3,6]=>1010100=>0010101=>[3,2,2,1]
[3,8,1,5,2,4,7,6]=>0101001=>1001010=>[1,3,2,2]
[7,5,6,4,1,3,2,8]=>1011010=>0101101=>[2,2,1,2,1]
[7,8,6,4,1,3,2,5]=>0111010=>0101110=>[2,2,1,1,2]
[7,1,4,2,5,6,3,8]=>1010010=>0100101=>[2,3,2,1]
[7,3,2,1,4,6,5,8]=>1110010=>0100111=>[2,3,1,1,1]
[7,6,1,4,3,2,5,8]=>1101100=>0011011=>[3,1,2,1,1]
[7,4,1,3,5,6,2,8]=>1100010=>0100011=>[2,4,1,1]
[7,3,1,2,5,6,4,8]=>1100010=>0100011=>[2,4,1,1]
[2,7,1,3,5,6,8,4]=>0100001=>1000010=>[1,5,2]
[3,6,2,1,5,8,7,4]=>0110011=>1100110=>[1,1,3,1,2]
[2,3,6,1,5,8,7,4]=>0010011=>1100100=>[1,1,3,3]
[3,1,7,2,5,6,8,4]=>1010001=>1000101=>[1,4,2,1]
[3,4,7,1,5,6,8,2]=>0010001=>1000100=>[1,4,3]
[3,6,7,4,1,2,8,5]=>0011001=>1001100=>[1,3,1,3]
[4,3,2,7,1,6,8,5]=>1101001=>1001011=>[1,3,2,1,1]
[7,3,2,8,1,6,4,5]=>1101010=>0101011=>[2,2,2,1,1]
[7,4,8,1,5,6,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[2,6,8,1,5,3,7,4]=>0010101=>1010100=>[1,2,2,3]
[6,8,2,1,5,3,7,4]=>0110101=>1010110=>[1,2,2,1,2]
[4,8,2,5,3,6,7,1]=>0101001=>1001010=>[1,3,2,2]
[4,5,8,2,3,6,7,1]=>0010001=>1000100=>[1,4,3]
[2,4,8,5,3,6,7,1]=>0011001=>1001100=>[1,3,1,3]
[4,1,8,6,5,3,7,2]=>1011101=>1011101=>[1,2,1,1,2,1]
[5,7,8,4,6,3,2,1]=>0010111=>1110100=>[1,1,1,2,3]
[5,3,2,6,4,8,7,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[2,4,5,3,8,6,7,1]=>0010101=>1010100=>[1,2,2,3]
[4,3,5,2,8,6,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[4,5,2,3,8,6,7,1]=>0100101=>1010010=>[1,2,3,2]
[4,8,5,3,2,6,7,1]=>0111001=>1001110=>[1,3,1,1,2]
[3,8,4,5,2,6,7,1]=>0101001=>1001010=>[1,3,2,2]
[3,5,4,2,8,6,7,1]=>0110101=>1010110=>[1,2,2,1,2]
[4,1,2,7,5,6,8,3]=>1001001=>1001001=>[1,3,3,1]
[4,8,1,6,5,2,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[5,6,7,4,2,8,3,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,5,7,4,6,8,3,1]=>0010011=>1100100=>[1,1,3,3]
[7,3,5,4,2,8,6,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,5,2,4,3,8,6,1]=>1101011=>1101011=>[1,1,2,2,1,1]
[6,8,1,2,5,4,7,3]=>0100101=>1010010=>[1,2,3,2]
[6,4,1,8,5,2,7,3]=>1101101=>1011011=>[1,2,1,2,1,1]
[2,6,1,8,5,4,7,3]=>0101101=>1011010=>[1,2,1,2,2]
[7,1,2,8,5,6,4,3]=>1001011=>1101001=>[1,1,2,3,1]
[4,3,2,6,8,5,7,1]=>1100101=>1010011=>[1,2,3,1,1]
[3,7,6,4,8,5,2,1]=>0110111=>1110110=>[1,1,1,2,1,2]
[3,1,6,8,5,4,7,2]=>1001101=>1011001=>[1,2,1,3,1]
[2,3,5,8,4,6,7,1]=>0001001=>1001000=>[1,3,4]
[3,4,5,8,2,6,7,1]=>0001001=>1001000=>[1,3,4]
[5,4,2,8,3,6,7,1]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,4,8,2,6,7,1]=>1001001=>1001001=>[1,3,3,1]
[2,5,4,8,3,6,7,1]=>0101001=>1001010=>[1,3,2,2]
[6,3,2,5,8,4,7,1]=>1100101=>1010011=>[1,2,3,1,1]
[6,1,8,3,5,4,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,8,3,2,6,7,1]=>1011001=>1001101=>[1,3,1,2,1]
[5,8,2,3,4,6,7,1]=>0100001=>1000010=>[1,5,2]
[3,4,5,2,7,1,6,8]=>0010100=>0010100=>[3,2,3]
[7,5,6,1,2,3,8,4]=>1010001=>1000101=>[1,4,2,1]
[1,5,7,6,3,2,8,4]=>0011101=>1011100=>[1,2,1,1,3]
[8,4,6,7,3,2,5,1]=>1001101=>1011001=>[1,2,1,3,1]
[8,4,6,2,3,1,5,7]=>1010100=>0010101=>[3,2,2,1]
[7,5,2,1,4,3,8,6]=>1110101=>1010111=>[1,2,2,1,1,1]
[3,1,7,8,5,4,2,6]=>1001110=>0111001=>[2,1,1,3,1]
[3,4,5,2,1,8,6,7]=>0011010=>0101100=>[2,2,1,3]
[7,6,4,8,3,1,2,5]=>1101100=>0011011=>[3,1,2,1,1]
[6,2,8,5,1,3,4,7]=>1011000=>0001101=>[4,1,2,1]
[3,2,7,8,6,1,4,5]=>1001100=>0011001=>[3,1,3,1]
[6,8,2,5,1,3,7,4]=>0101001=>1001010=>[1,3,2,2]
[6,7,4,2,1,5,3,8]=>0111010=>0101110=>[2,2,1,1,2]
[5,6,8,1,3,7,2,4]=>0010010=>0100100=>[2,3,3]
[1,6,8,5,3,2,4,7]=>0011100=>0011100=>[3,1,1,3]
[7,2,8,4,6,1,3,5]=>1010100=>0010101=>[3,2,2,1]
[4,1,6,8,7,3,2,5]=>1001110=>0111001=>[2,1,1,3,1]
[5,1,4,6,7,3,8,2]=>1000101=>1010001=>[1,2,4,1]
[7,1,3,4,6,2,8,5]=>1000101=>1010001=>[1,2,4,1]
[5,8,7,4,2,1,3,6]=>0111100=>0011110=>[3,1,1,1,2]
[3,1,5,2,7,8,6,4]=>1010011=>1100101=>[1,1,3,2,1]
[1,8,7,3,2,5,4,6]=>0111010=>0101110=>[2,2,1,1,2]
[1,2,5,4,8,7,3,6]=>0010110=>0110100=>[2,1,2,3]
[1,2,4,8,6,3,5,7]=>0001100=>0011000=>[3,1,4]
[8,5,3,2,1,4,7,6]=>1111001=>1001111=>[1,3,1,1,1,1]
[1,2,7,6,8,4,3,5]=>0010110=>0110100=>[2,1,2,3]
[1,7,3,4,2,6,8,5]=>0101001=>1001010=>[1,3,2,2]
[1,6,3,5,8,4,2,7]=>0100110=>0110010=>[2,1,3,2]
[1,5,6,3,2,8,4,7]=>0011010=>0101100=>[2,2,1,3]
[1,2,5,8,4,6,3,7]=>0001010=>0101000=>[2,2,4]
[1,2,7,8,4,5,3,6]=>0001010=>0101000=>[2,2,4]
[1,5,3,2,7,8,4,6]=>0110010=>0100110=>[2,3,1,2]
[4,1,8,6,2,3,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[1,7,6,4,3,8,5,2]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,8,5,7,6,3,2,4]=>0101110=>0111010=>[2,1,1,2,2]
[1,6,3,5,7,8,4,2]=>0100011=>1100010=>[1,1,4,2]
[1,5,6,3,2,7,8,4]=>0011001=>1001100=>[1,3,1,3]
[1,8,4,7,5,3,2,6]=>0101110=>0111010=>[2,1,1,2,2]
[7,6,2,5,3,4,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,6,2,4,5,3,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[7,6,2,4,3,5,1,8]=>1101010=>0101011=>[2,2,2,1,1]
[7,6,2,3,5,4,1,8]=>1100110=>0110011=>[2,1,3,1,1]
[8,4,2,7,1,6,3,5]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,6,1,5,3,2,4]=>1110110=>0110111=>[2,1,2,1,1,1]
[8,7,6,1,3,5,4,2]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,7,6,1,5,4,2,3]=>1110110=>0110111=>[2,1,2,1,1,1]
[4,5,3,8,2,1,6,7]=>0101100=>0011010=>[3,1,2,2]
[8,3,5,4,2,1,6,7]=>1011100=>0011101=>[3,1,1,2,1]
[7,8,4,3,1,5,2,6]=>0111010=>0101110=>[2,2,1,1,2]
[7,5,8,2,1,4,3,6]=>1011010=>0101101=>[2,2,1,2,1]
[8,6,3,7,1,5,2,4]=>1101010=>0101011=>[2,2,2,1,1]
[8,7,6,1,2,5,3,4]=>1110010=>0100111=>[2,3,1,1,1]
[8,7,6,1,2,5,4,3]=>1110011=>1100111=>[1,1,3,1,1,1]
[8,7,6,1,4,2,5,3]=>1110101=>1010111=>[1,2,2,1,1,1]
[2,4,7,3,5,6,1,8]=>0010010=>0100100=>[2,3,3]
[5,7,6,4,2,3,1,8]=>0111010=>0101110=>[2,2,1,1,2]
[3,1,4,8,5,6,2,7]=>1001010=>0101001=>[2,2,3,1]
[5,8,2,4,6,1,3,7]=>0100100=>0010010=>[3,3,2]
[2,4,1,8,5,6,3,7]=>0101010=>0101010=>[2,2,2,2]
[6,1,4,8,5,2,7,3]=>1001101=>1011001=>[1,2,1,3,1]
[4,1,2,8,5,3,7,6]=>1001101=>1011001=>[1,2,1,3,1]
[2,4,6,8,5,1,7,3]=>0001101=>1011000=>[1,2,1,4]
[3,1,6,8,5,2,7,4]=>1001101=>1011001=>[1,2,1,3,1]
[2,3,8,1,5,6,4,7]=>0010010=>0100100=>[2,3,3]
[5,1,8,2,4,6,7,3]=>1010001=>1000101=>[1,4,2,1]
[4,1,8,2,3,6,7,5]=>1010001=>1000101=>[1,4,2,1]
[5,8,2,7,3,4,1,6]=>0101010=>0101010=>[2,2,2,2]
[3,8,7,5,2,6,1,4]=>0111010=>0101110=>[2,2,1,1,2]
[5,3,8,1,6,7,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[5,8,2,1,3,7,6,4]=>0110011=>1100110=>[1,1,3,1,2]
[4,8,2,1,3,5,6,7]=>0110000=>0000110=>[5,1,2]
[5,1,8,3,6,7,4,2]=>1010011=>1100101=>[1,1,3,2,1]
[8,4,1,6,5,2,3,7]=>1101100=>0011011=>[3,1,2,1,1]
[6,8,7,3,2,4,1,5]=>0111010=>0101110=>[2,2,1,1,2]
[1,3,7,5,6,8,4,2]=>0010011=>1100100=>[1,1,3,3]
[3,2,4,7,5,8,1,6]=>1001010=>0101001=>[2,2,3,1]
[1,2,7,4,6,3,8,5]=>0010101=>1010100=>[1,2,2,3]
[2,8,7,6,4,5,1,3]=>0111010=>0101110=>[2,2,1,1,2]
[3,5,2,4,7,6,8,1]=>0100101=>1010010=>[1,2,3,2]
[3,5,2,4,6,7,8,1]=>0100001=>1000010=>[1,5,2]
[5,3,2,6,4,7,8,1]=>1101001=>1001011=>[1,3,2,1,1]
[5,3,2,6,7,4,8,1]=>1100101=>1010011=>[1,2,3,1,1]
[5,3,2,7,6,4,8,1]=>1101101=>1011011=>[1,2,1,2,1,1]
[7,3,5,2,8,4,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[3,2,5,7,4,6,8,1]=>1001001=>1001001=>[1,3,3,1]
[2,3,5,7,4,6,8,1]=>0001001=>1001000=>[1,3,4]
[3,2,7,5,4,8,6,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,7,5,2,4,8,6,1]=>0110011=>1100110=>[1,1,3,1,2]
[7,5,3,2,8,6,4,1]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[2,3,7,5,4,8,6,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,4,8,7,5,1,3,6]=>0011100=>0011100=>[3,1,1,3]
[3,5,7,6,1,8,4,2]=>0011011=>1101100=>[1,1,2,1,3]
[3,5,7,6,2,8,4,1]=>0011011=>1101100=>[1,1,2,1,3]
[2,4,6,3,8,7,5,1]=>0010111=>1110100=>[1,1,1,2,3]
[1,5,3,2,8,7,6,4]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,3,1,8,7,4,2,5]=>1101110=>0111011=>[2,1,1,2,1,1]
[5,3,6,2,8,7,4,1]=>1010111=>1110101=>[1,1,1,2,2,1]
[5,8,3,1,7,6,4,2]=>0110111=>1110110=>[1,1,1,2,1,2]
[6,3,5,2,1,8,7,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[3,8,1,4,7,6,5,2]=>0100111=>1110010=>[1,1,1,3,2]
[6,2,3,8,7,5,4,1]=>1001111=>1111001=>[1,1,1,1,3,1]
[4,1,3,5,8,7,6,2]=>1000111=>1110001=>[1,1,1,4,1]
[4,2,5,3,7,6,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,4,3,7,5,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[1,3,6,4,7,5,2,8]=>0010110=>0110100=>[2,1,2,3]
[8,2,5,3,6,4,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,5,3,6,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,5,3,7,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,6,3,7,5,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,7,3,6,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,6,2,5,4,1,8]=>1010110=>0110101=>[2,1,2,2,1]
[6,3,8,2,5,4,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,1,4,6,5,2,8]=>1100110=>0110011=>[2,1,3,1,1]
[8,3,7,2,5,4,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,8,3,6,4,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,8,3,6,5,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,8,4,6,5,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[1,4,7,3,6,5,2,8]=>0010110=>0110100=>[2,1,2,3]
[8,2,5,4,1,6,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[1,3,6,5,2,7,4,8]=>0011010=>0101100=>[2,2,1,3]
[8,2,6,4,1,5,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[1,4,8,3,7,5,2,6]=>0010110=>0110100=>[2,1,2,3]
[6,2,1,4,8,5,3,7]=>1100110=>0110011=>[2,1,3,1,1]
[5,2,1,4,8,6,3,7]=>1100110=>0110011=>[2,1,3,1,1]
[3,2,1,5,8,6,4,7]=>1100110=>0110011=>[2,1,3,1,1]
[4,2,8,3,7,5,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,8,3,7,4,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,3,7,2,6,4,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,3,1,4,8,5,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[1,3,7,4,8,5,2,6]=>0010110=>0110100=>[2,1,2,3]
[8,2,6,3,7,4,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,6,3,8,4,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,7,3,8,4,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,7,4,8,5,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,6,3,8,4,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,5,3,8,4,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,5,3,8,4,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,2,5,3,7,4,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[1,3,6,4,8,5,2,7]=>0010110=>0110100=>[2,1,2,3]
[1,3,5,4,8,6,2,7]=>0010110=>0110100=>[2,1,2,3]
[8,2,4,3,7,5,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,4,3,8,5,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[6,2,4,3,8,5,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[5,2,4,3,8,6,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,5,3,8,6,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[4,2,5,3,1,7,6,8]=>1011010=>0101101=>[2,2,1,2,1]
[6,2,4,3,1,7,5,8]=>1011010=>0101101=>[2,2,1,2,1]
[7,2,4,3,1,6,5,8]=>1011010=>0101101=>[2,2,1,2,1]
[8,5,1,3,6,4,2,7]=>1100110=>0110011=>[2,1,3,1,1]
[8,4,1,3,6,5,2,7]=>1100110=>0110011=>[2,1,3,1,1]
[1,5,2,4,7,6,3,8]=>0100110=>0110010=>[2,1,3,2]
[7,2,5,3,1,6,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[6,2,5,3,1,7,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[4,2,6,3,1,7,5,8]=>1011010=>0101101=>[2,2,1,2,1]
[3,2,6,4,1,7,5,8]=>1011010=>0101101=>[2,2,1,2,1]
[5,2,7,3,1,6,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[6,2,7,3,1,5,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[7,2,6,3,1,5,4,8]=>1011010=>0101101=>[2,2,1,2,1]
[1,5,2,4,8,6,3,7]=>0100110=>0110010=>[2,1,3,2]
[8,4,1,3,7,5,2,6]=>1100110=>0110011=>[2,1,3,1,1]
[6,2,1,5,3,7,4,8]=>1101010=>0101011=>[2,2,2,1,1]
[3,2,1,6,4,7,5,8]=>1101010=>0101011=>[2,2,2,1,1]
[3,2,8,5,1,6,4,7]=>1011010=>0101101=>[2,2,1,2,1]
[4,2,8,5,1,6,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[6,2,8,4,1,5,3,7]=>1011010=>0101101=>[2,2,1,2,1]
[1,4,8,5,2,6,3,7]=>0011010=>0101100=>[2,2,1,3]
[8,3,7,4,1,5,2,6]=>1011010=>0101101=>[2,2,1,2,1]
[7,1,3,2,5,6,4,8]=>1010010=>0100101=>[2,3,2,1]
[1,5,2,8,7,4,3,6]=>0101110=>0111010=>[2,1,1,2,2]
[5,7,2,8,1,4,3,6]=>0101010=>0101010=>[2,2,2,2]
[7,1,5,3,2,6,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[1,7,3,4,5,2,8,6]=>0100101=>1010010=>[1,2,3,2]
[8,6,7,3,5,2,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[3,2,1,7,8,5,4,6]=>1100110=>0110011=>[2,1,3,1,1]
[7,3,4,2,1,5,8,6]=>1011001=>1001101=>[1,3,1,2,1]
[1,7,6,3,2,4,8,5]=>0111001=>1001110=>[1,3,1,1,2]
[1,8,5,3,2,4,7,6]=>0111001=>1001110=>[1,3,1,1,2]
[1,2,8,4,6,3,5,7]=>0010100=>0010100=>[3,2,3]
[2,6,1,5,4,7,3,8]=>0101010=>0101010=>[2,2,2,2]
[1,2,8,5,4,6,3,7]=>0011010=>0101100=>[2,2,1,3]
[1,3,8,5,4,2,6,7]=>0011100=>0011100=>[3,1,1,3]
[1,3,6,8,4,5,7,2]=>0001001=>1001000=>[1,3,4]
[1,2,8,4,6,3,7,5]=>0010101=>1010100=>[1,2,2,3]
[4,6,3,5,7,8,1,2]=>0100010=>0100010=>[2,4,2]
[2,7,6,5,1,4,8,3]=>0111001=>1001110=>[1,3,1,1,2]
[2,7,4,8,1,3,6,5]=>0101001=>1001010=>[1,3,2,2]
[2,3,6,8,4,1,7,5]=>0001101=>1011000=>[1,2,1,4]
[1,2,6,8,4,7,5,3]=>0001011=>1101000=>[1,1,2,4]
[1,7,2,8,6,3,5,4]=>0101101=>1011010=>[1,2,1,2,2]
[2,3,8,5,4,7,1,6]=>0011010=>0101100=>[2,2,1,3]
[2,7,4,1,6,3,5,8]=>0110100=>0010110=>[3,2,1,2]
[1,2,8,4,7,3,5,6]=>0010100=>0010100=>[3,2,3]
[2,6,1,4,8,3,7,5]=>0100101=>1010010=>[1,2,3,2]
[3,7,6,5,2,1,4,8]=>0111100=>0011110=>[3,1,1,1,2]
[2,5,6,1,4,8,7,3]=>0010011=>1100100=>[1,1,3,3]
[7,1,5,2,6,4,3,8]=>1010110=>0110101=>[2,1,2,2,1]
[1,8,5,6,2,7,4,3]=>0101011=>1101010=>[1,1,2,2,2]
[4,2,7,6,1,8,5,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[7,3,2,1,6,4,8,5]=>1110101=>1010111=>[1,2,2,1,1,1]
[6,7,2,4,3,5,8,1]=>0101001=>1001010=>[1,3,2,2]
[4,5,3,7,2,1,6,8]=>0101100=>0011010=>[3,1,2,2]
[4,3,8,2,1,5,7,6]=>1011001=>1001101=>[1,3,1,2,1]
[4,3,2,8,1,6,7,5]=>1101001=>1001011=>[1,3,2,1,1]
[4,5,8,3,2,7,1,6]=>0011010=>0101100=>[2,2,1,3]
[5,4,7,8,2,3,6,1]=>1001001=>1001001=>[1,3,3,1]
[4,3,8,2,1,6,7,5]=>1011001=>1001101=>[1,3,1,2,1]
[4,6,7,2,5,3,8,1]=>0010101=>1010100=>[1,2,2,3]
[6,4,7,8,3,1,5,2]=>1001101=>1011001=>[1,2,1,3,1]
[8,4,7,3,1,5,6,2]=>1011001=>1001101=>[1,3,1,2,1]
[5,6,7,1,8,3,4,2]=>0010101=>1010100=>[1,2,2,3]
[7,1,8,6,2,5,4,3]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,5,1,7,6,4,2,3]=>1101110=>0111011=>[2,1,1,2,1,1]
[1,5,8,2,6,4,7,3]=>0010101=>1010100=>[1,2,2,3]
[1,5,7,4,6,8,3,2]=>0010011=>1100100=>[1,1,3,3]
[8,1,2,6,4,5,7,3]=>1001001=>1001001=>[1,3,3,1]
[3,1,8,6,5,2,7,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[2,3,7,6,5,8,1,4]=>0011010=>0101100=>[2,2,1,3]
[2,3,7,6,5,1,8,4]=>0011101=>1011100=>[1,2,1,1,3]
[7,3,5,2,1,6,8,4]=>1011001=>1001101=>[1,3,1,2,1]
[3,7,2,6,8,1,5,4]=>0100101=>1010010=>[1,2,3,2]
[2,7,6,8,5,1,4,3]=>0101101=>1011010=>[1,2,1,2,2]
[1,5,4,7,8,6,2,3]=>0100110=>0110010=>[2,1,3,2]
[7,3,1,6,8,2,5,4]=>1100101=>1010011=>[1,2,3,1,1]
[7,1,6,8,5,2,4,3]=>1001101=>1011001=>[1,2,1,3,1]
[2,7,6,4,8,1,5,3]=>0110101=>1010110=>[1,2,2,1,2]
[3,6,2,1,4,7,8,5]=>0110001=>1000110=>[1,4,1,2]
[6,3,8,7,5,4,2,1]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[6,8,2,7,5,4,3,1]=>0101111=>1111010=>[1,1,1,1,2,2]
[5,8,1,7,6,4,3,2]=>0101111=>1111010=>[1,1,1,1,2,2]
[4,2,6,3,8,5,7,1]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,6,5,7,3,4,1]=>1010101=>1010101=>[1,2,2,2,1]
[5,1,8,3,7,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,3,7,1,5,4,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,4,7,1,5,3,6,2]=>1010101=>1010101=>[1,2,2,2,1]
[8,2,7,4,5,1,6,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,8,7,1,4,2,3,6]=>0110100=>0010110=>[3,2,1,2]
[1,7,5,2,4,8,6,3]=>0110011=>1100110=>[1,1,3,1,2]
[2,6,3,7,1,4,5,8]=>0101000=>0001010=>[4,2,2]
[7,2,8,5,3,1,6,4]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,2,4,1,3,8,5,6]=>1010010=>0100101=>[2,3,2,1]
[4,7,6,1,5,8,3,2]=>0110011=>1100110=>[1,1,3,1,2]
[4,7,3,8,6,2,5,1]=>0101101=>1011010=>[1,2,1,2,2]
[5,4,7,3,8,2,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[4,3,5,7,2,6,1,8]=>1001010=>0101001=>[2,2,3,1]
[1,7,2,8,5,4,3,6]=>0101110=>0111010=>[2,1,1,2,2]
[5,4,8,3,6,2,1,7]=>1010110=>0110101=>[2,1,2,2,1]
[6,8,3,5,7,2,4,1]=>0100101=>1010010=>[1,2,3,2]
[3,8,6,2,7,5,1,4]=>0110110=>0110110=>[2,1,2,1,2]
[4,7,3,2,5,1,6,8]=>0110100=>0010110=>[3,2,1,2]
[4,2,5,3,8,7,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[7,2,5,3,8,4,6,1]=>1010101=>1010101=>[1,2,2,2,1]
[6,7,3,2,5,4,1,8]=>0110110=>0110110=>[2,1,2,1,2]
[8,7,3,2,5,4,6,1]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,5,6,2,7,3,1,8]=>0010110=>0110100=>[2,1,2,3]
[7,3,4,8,2,1,6,5]=>1001101=>1011001=>[1,2,1,3,1]
[3,8,1,7,5,2,4,6]=>0101100=>0011010=>[3,1,2,2]
[4,5,8,2,7,3,1,6]=>0010110=>0110100=>[2,1,2,3]
[6,5,8,2,7,3,1,4]=>1010110=>0110101=>[2,1,2,2,1]
[6,4,8,2,7,3,1,5]=>1010110=>0110101=>[2,1,2,2,1]
[4,3,8,2,7,5,1,6]=>1010110=>0110101=>[2,1,2,2,1]
[4,5,7,8,3,2,1,6]=>0001110=>0111000=>[2,1,1,4]
[8,1,5,4,6,2,7,3]=>1010101=>1010101=>[1,2,2,2,1]
[5,3,7,2,1,8,6,4]=>1011011=>1101101=>[1,1,2,1,2,1]
[5,4,8,3,2,7,1,6]=>1011010=>0101101=>[2,2,1,2,1]
[5,4,3,7,8,2,6,1]=>1100101=>1010011=>[1,2,3,1,1]
[5,4,3,8,2,6,7,1]=>1101001=>1001011=>[1,3,2,1,1]
[5,4,3,7,8,2,1,6]=>1100110=>0110011=>[2,1,3,1,1]
[2,3,8,7,5,1,6,4]=>0011101=>1011100=>[1,2,1,1,3]
[4,1,3,5,6,2,8,7]=>1000101=>1010001=>[1,2,4,1]
[6,4,8,7,3,5,2,1]=>1011011=>1101101=>[1,1,2,1,2,1]
[8,3,4,5,1,6,7,2]=>1001001=>1001001=>[1,3,3,1]
[7,8,1,5,6,3,2,4]=>0100110=>0110010=>[2,1,3,2]
[1,7,8,3,2,5,4,6]=>0011010=>0101100=>[2,2,1,3]
[7,8,1,3,5,4,2,6]=>0100110=>0110010=>[2,1,3,2]
[7,8,1,3,2,5,6,4]=>0101001=>1001010=>[1,3,2,2]
[7,8,1,3,5,4,6,2]=>0100101=>1010010=>[1,2,3,2]
[7,8,1,3,5,2,4,6]=>0100100=>0010010=>[3,3,2]
[1,3,7,8,5,2,4,6]=>0001100=>0011000=>[3,1,4]
[1,7,8,3,5,2,6,4]=>0010101=>1010100=>[1,2,2,3]
[1,7,8,3,2,5,6,4]=>0011001=>1001100=>[1,3,1,3]
[3,5,7,6,4,8,1,2]=>0011010=>0101100=>[2,2,1,3]
[1,3,7,8,5,4,6,2]=>0001101=>1011000=>[1,2,1,4]
[1,3,7,8,5,4,2,6]=>0001110=>0111000=>[2,1,1,4]
[1,3,7,8,2,5,4,6]=>0001010=>0101000=>[2,2,4]
[1,7,8,5,6,3,2,4]=>0010110=>0110100=>[2,1,2,3]
[5,7,6,8,1,3,4,2]=>0101001=>1001010=>[1,3,2,2]
[1,5,7,6,8,3,2,4]=>0010110=>0110100=>[2,1,2,3]
[3,5,4,7,8,6,1,2]=>0100110=>0110010=>[2,1,3,2]
[3,5,7,6,8,4,1,2]=>0010110=>0110100=>[2,1,2,3]
[1,5,7,6,8,3,4,2]=>0010101=>1010100=>[1,2,2,3]
[3,5,7,4,6,8,1,2]=>0010010=>0100100=>[2,3,3]
[7,2,8,6,5,1,4,3]=>1011101=>1011101=>[1,2,1,1,2,1]
[3,2,5,4,7,6,1,10,8,9]=>101011010=>010110101=>[2,2,1,2,2,1]
[3,2,5,4,9,8,6,7,1,10]=>101011010=>010110101=>[2,2,1,2,2,1]
[3,2,5,4,1,8,6,10,7,9]=>101101010=>010101101=>[2,2,2,1,2,1]
[3,2,5,4,1,10,9,6,7,8]=>101101100=>001101101=>[3,1,2,1,2,1]
[3,2,7,6,4,5,9,8,1,10]=>101100110=>011001101=>[2,1,3,1,2,1]
[3,2,7,6,4,5,1,10,8,9]=>101101010=>010101101=>[2,2,2,1,2,1]
[3,2,9,6,4,8,5,7,1,10]=>101101010=>010101101=>[2,2,2,1,2,1]
[3,2,1,6,4,8,5,10,7,9]=>110101010=>010101011=>[2,2,2,2,1,1]
[3,2,1,6,4,10,9,5,7,8]=>110101100=>001101011=>[3,1,2,2,1,1]
[3,2,9,8,7,4,5,6,1,10]=>101110010=>010011101=>[2,3,1,1,2,1]
[3,2,1,8,7,4,5,10,6,9]=>110110010=>010011011=>[2,3,1,2,1,1]
[3,2,1,10,7,4,9,5,6,8]=>110110100=>001011011=>[3,2,1,2,1,1]
[3,2,1,10,9,8,4,5,6,7]=>110111000=>000111011=>[4,1,1,2,1,1]
[5,4,2,3,7,6,9,8,1,10]=>110010110=>011010011=>[2,1,2,3,1,1]
[5,4,2,3,7,6,1,10,8,9]=>110011010=>010110011=>[2,2,1,3,1,1]
[5,4,2,3,9,8,6,7,1,10]=>110011010=>010110011=>[2,2,1,3,1,1]
[5,4,2,3,1,8,6,10,7,9]=>110101010=>010101011=>[2,2,2,2,1,1]
[5,4,2,3,1,10,9,6,7,8]=>110101100=>001101011=>[3,1,2,2,1,1]
[7,4,2,6,3,5,9,8,1,10]=>110100110=>011001011=>[2,1,3,2,1,1]
[7,4,2,6,3,5,1,10,8,9]=>110101010=>010101011=>[2,2,2,2,1,1]
[9,4,2,6,3,8,5,7,1,10]=>110101010=>010101011=>[2,2,2,2,1,1]
[1,4,2,6,3,10,9,5,7,8]=>010101100=>001101010=>[3,1,2,2,2]
[9,4,2,8,7,3,5,6,1,10]=>110110010=>010011011=>[2,3,1,2,1,1]
[1,4,2,8,7,3,5,10,6,9]=>010110010=>010011010=>[2,3,1,2,2]
[1,4,2,10,7,3,9,5,6,8]=>010110100=>001011010=>[3,2,1,2,2]
[1,4,2,10,9,8,3,5,6,7]=>010111000=>000111010=>[4,1,1,2,2]
[7,6,5,2,3,4,9,8,1,10]=>111000110=>011000111=>[2,1,4,1,1,1]
[7,6,5,2,3,4,1,10,8,9]=>111001010=>010100111=>[2,2,3,1,1,1]
[9,6,5,2,3,8,4,7,1,10]=>111001010=>010100111=>[2,2,3,1,1,1]
[1,6,5,2,3,8,4,10,7,9]=>011001010=>010100110=>[2,2,3,1,2]
[1,6,5,2,3,10,9,4,7,8]=>011001100=>001100110=>[3,1,3,1,2]
[9,8,5,2,7,3,4,6,1,10]=>111010010=>010010111=>[2,3,2,1,1,1]
[1,8,5,2,7,3,4,10,6,9]=>011010010=>010010110=>[2,3,2,1,2]
[1,10,5,2,7,3,9,4,6,8]=>011010100=>001010110=>[3,2,2,1,2]
[1,10,5,2,9,8,3,4,6,7]=>011011000=>000110110=>[4,1,2,1,2]
[9,8,7,6,2,3,4,5,1,10]=>111100010=>010001111=>[2,4,1,1,1,1]
[1,8,7,6,2,3,4,10,5,9]=>011100010=>010001110=>[2,4,1,1,2]
[1,10,7,6,2,3,9,4,5,8]=>011100100=>001001110=>[3,3,1,1,2]
[1,10,9,6,2,8,3,4,5,7]=>011101000=>000101110=>[4,2,1,1,2]
[1,10,9,8,7,2,3,4,5,6]=>011110000=>000011110=>[5,1,1,1,2]
[4,2,7,5,3,1,8,6]=>1011101=>1011101=>[1,2,1,1,2,1]
[7,3,2,5,4,1,8,6]=>1101101=>1011011=>[1,2,1,2,1,1]
[3,6,4,1,8,2,7,5]=>0110101=>1010110=>[1,2,2,1,2]
[4,6,3,8,7,2,1,5]=>0101110=>0111010=>[2,1,1,2,2]
[4,3,5,1,8,7,2,6]=>1010110=>0110101=>[2,1,2,2,1]
[8,4,3,2,7,5,1,6]=>1110110=>0110111=>[2,1,2,1,1,1]
[7,5,2,8,4,3,1,6]=>1101110=>0111011=>[2,1,1,2,1,1]
[1,7,2,4,5,3,6,8]=>0100100=>0010010=>[3,3,2]
[1,7,4,5,3,2,6,8]=>0101100=>0011010=>[3,1,2,2]
[1,6,4,7,3,5,2,8]=>0101010=>0101010=>[2,2,2,2]
[8,3,5,6,1,4,7,2]=>1001001=>1001001=>[1,3,3,1]
[1,6,4,7,5,2,3,8]=>0101100=>0011010=>[3,1,2,2]
[1,5,2,6,7,4,3,8]=>0100110=>0110010=>[2,1,3,2]
[8,5,6,1,4,3,7,2]=>1010101=>1010101=>[1,2,2,2,1]
[5,4,7,8,3,1,2,6]=>1001100=>0011001=>[3,1,3,1]
[2,5,4,7,8,3,1,6]=>0100110=>0110010=>[2,1,3,2]
[6,4,5,8,2,3,1,7]=>1001010=>0101001=>[2,2,3,1]
[8,6,1,3,2,5,7,4]=>1101001=>1001011=>[1,3,2,1,1]
[7,5,8,1,4,6,3,2]=>1010011=>1100101=>[1,1,3,2,1]
[4,2,6,7,8,1,5,3]=>1000101=>1010001=>[1,2,4,1]
[3,4,6,7,8,1,5,2]=>0000101=>1010000=>[1,2,5]
[4,3,2,7,5,8,1,6]=>1101010=>0101011=>[2,2,2,1,1]
[4,8,5,3,2,6,1,7]=>0111010=>0101110=>[2,2,1,1,2]
[2,8,4,5,3,6,1,7]=>0101010=>0101010=>[2,2,2,2]
[8,1,5,3,2,4,7,6]