- FindStat

Identifier
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Images
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            [1,2]=>1=>1=>[1,1]
[2,1]=>0=>0=>[2]
[1,2,3]=>11=>11=>[1,1,1]
[1,3,2]=>10=>01=>[2,1]
[2,1,3]=>01=>10=>[1,2]
[2,3,1]=>00=>00=>[3]
[3,1,2]=>00=>00=>[3]
[3,2,1]=>00=>00=>[3]
[1,2,3,4]=>111=>111=>[1,1,1,1]
[1,2,4,3]=>110=>011=>[2,1,1]
[1,3,2,4]=>101=>101=>[1,2,1]
[1,3,4,2]=>100=>001=>[3,1]
[1,4,2,3]=>100=>001=>[3,1]
[1,4,3,2]=>100=>001=>[3,1]
[2,1,3,4]=>011=>110=>[1,1,2]
[2,1,4,3]=>010=>010=>[2,2]
[2,3,1,4]=>001=>100=>[1,3]
[2,3,4,1]=>000=>000=>[4]
[2,4,1,3]=>000=>000=>[4]
[2,4,3,1]=>000=>000=>[4]
[3,1,2,4]=>001=>100=>[1,3]
[3,1,4,2]=>000=>000=>[4]
[3,2,1,4]=>001=>100=>[1,3]
[3,2,4,1]=>000=>000=>[4]
[3,4,1,2]=>000=>000=>[4]
[3,4,2,1]=>000=>000=>[4]
[4,1,2,3]=>000=>000=>[4]
[4,1,3,2]=>000=>000=>[4]
[4,2,1,3]=>000=>000=>[4]
[4,2,3,1]=>000=>000=>[4]
[4,3,1,2]=>000=>000=>[4]
[4,3,2,1]=>000=>000=>[4]
[1,2,3,4,5]=>1111=>1111=>[1,1,1,1,1]
[1,2,3,5,4]=>1110=>0111=>[2,1,1,1]
[1,2,4,3,5]=>1101=>1011=>[1,2,1,1]
[1,2,4,5,3]=>1100=>0011=>[3,1,1]
[1,2,5,3,4]=>1100=>0011=>[3,1,1]
[1,2,5,4,3]=>1100=>0011=>[3,1,1]
[1,3,2,4,5]=>1011=>1101=>[1,1,2,1]
[1,3,2,5,4]=>1010=>0101=>[2,2,1]
[1,3,4,2,5]=>1001=>1001=>[1,3,1]
[1,3,4,5,2]=>1000=>0001=>[4,1]
[1,3,5,2,4]=>1000=>0001=>[4,1]
[1,3,5,4,2]=>1000=>0001=>[4,1]
[1,4,2,3,5]=>1001=>1001=>[1,3,1]
[1,4,2,5,3]=>1000=>0001=>[4,1]
[1,4,3,2,5]=>1001=>1001=>[1,3,1]
[1,4,3,5,2]=>1000=>0001=>[4,1]
[1,4,5,2,3]=>1000=>0001=>[4,1]
[1,4,5,3,2]=>1000=>0001=>[4,1]
[1,5,2,3,4]=>1000=>0001=>[4,1]
[1,5,2,4,3]=>1000=>0001=>[4,1]
[1,5,3,2,4]=>1000=>0001=>[4,1]
[1,5,3,4,2]=>1000=>0001=>[4,1]
[1,5,4,2,3]=>1000=>0001=>[4,1]
[1,5,4,3,2]=>1000=>0001=>[4,1]
[2,1,3,4,5]=>0111=>1110=>[1,1,1,2]
[2,1,3,5,4]=>0110=>0110=>[2,1,2]
[2,1,4,3,5]=>0101=>1010=>[1,2,2]
[2,1,4,5,3]=>0100=>0010=>[3,2]
[2,1,5,3,4]=>0100=>0010=>[3,2]
[2,1,5,4,3]=>0100=>0010=>[3,2]
[2,3,1,4,5]=>0011=>1100=>[1,1,3]
[2,3,1,5,4]=>0010=>0100=>[2,3]
[2,3,4,1,5]=>0001=>1000=>[1,4]
[2,3,4,5,1]=>0000=>0000=>[5]
[2,3,5,1,4]=>0000=>0000=>[5]
[2,3,5,4,1]=>0000=>0000=>[5]
[2,4,1,3,5]=>0001=>1000=>[1,4]
[2,4,1,5,3]=>0000=>0000=>[5]
[2,4,3,1,5]=>0001=>1000=>[1,4]
[2,4,3,5,1]=>0000=>0000=>[5]
[2,4,5,1,3]=>0000=>0000=>[5]
[2,4,5,3,1]=>0000=>0000=>[5]
[2,5,1,3,4]=>0000=>0000=>[5]
[2,5,1,4,3]=>0000=>0000=>[5]
[2,5,3,1,4]=>0000=>0000=>[5]
[2,5,3,4,1]=>0000=>0000=>[5]
[2,5,4,1,3]=>0000=>0000=>[5]
[2,5,4,3,1]=>0000=>0000=>[5]
[3,1,2,4,5]=>0011=>1100=>[1,1,3]
[3,1,2,5,4]=>0010=>0100=>[2,3]
[3,1,4,2,5]=>0001=>1000=>[1,4]
[3,1,4,5,2]=>0000=>0000=>[5]
[3,1,5,2,4]=>0000=>0000=>[5]
[3,1,5,4,2]=>0000=>0000=>[5]
[3,2,1,4,5]=>0011=>1100=>[1,1,3]
[3,2,1,5,4]=>0010=>0100=>[2,3]
[3,2,4,1,5]=>0001=>1000=>[1,4]
[3,2,4,5,1]=>0000=>0000=>[5]
[3,2,5,1,4]=>0000=>0000=>[5]
[3,2,5,4,1]=>0000=>0000=>[5]
[3,4,1,2,5]=>0001=>1000=>[1,4]
[3,4,1,5,2]=>0000=>0000=>[5]
[3,4,2,1,5]=>0001=>1000=>[1,4]
[3,4,2,5,1]=>0000=>0000=>[5]
[3,4,5,1,2]=>0000=>0000=>[5]
[3,4,5,2,1]=>0000=>0000=>[5]
[3,5,1,2,4]=>0000=>0000=>[5]
[3,5,1,4,2]=>0000=>0000=>[5]
[3,5,2,1,4]=>0000=>0000=>[5]
[3,5,2,4,1]=>0000=>0000=>[5]
[3,5,4,1,2]=>0000=>0000=>[5]
[3,5,4,2,1]=>0000=>0000=>[5]
[4,1,2,3,5]=>0001=>1000=>[1,4]
[4,1,2,5,3]=>0000=>0000=>[5]
[4,1,3,2,5]=>0001=>1000=>[1,4]
[4,1,3,5,2]=>0000=>0000=>[5]
[4,1,5,2,3]=>0000=>0000=>[5]
[4,1,5,3,2]=>0000=>0000=>[5]
[4,2,1,3,5]=>0001=>1000=>[1,4]
[4,2,1,5,3]=>0000=>0000=>[5]
[4,2,3,1,5]=>0001=>1000=>[1,4]
[4,2,3,5,1]=>0000=>0000=>[5]
[4,2,5,1,3]=>0000=>0000=>[5]
[4,2,5,3,1]=>0000=>0000=>[5]
[4,3,1,2,5]=>0001=>1000=>[1,4]
[4,3,1,5,2]=>0000=>0000=>[5]
[4,3,2,1,5]=>0001=>1000=>[1,4]
[4,3,2,5,1]=>0000=>0000=>[5]
[4,3,5,1,2]=>0000=>0000=>[5]
[4,3,5,2,1]=>0000=>0000=>[5]
[4,5,1,2,3]=>0000=>0000=>[5]
[4,5,1,3,2]=>0000=>0000=>[5]
[4,5,2,1,3]=>0000=>0000=>[5]
[4,5,2,3,1]=>0000=>0000=>[5]
[4,5,3,1,2]=>0000=>0000=>[5]
[4,5,3,2,1]=>0000=>0000=>[5]
[5,1,2,3,4]=>0000=>0000=>[5]
[5,1,2,4,3]=>0000=>0000=>[5]
[5,1,3,2,4]=>0000=>0000=>[5]
[5,1,3,4,2]=>0000=>0000=>[5]
[5,1,4,2,3]=>0000=>0000=>[5]
[5,1,4,3,2]=>0000=>0000=>[5]
[5,2,1,3,4]=>0000=>0000=>[5]
[5,2,1,4,3]=>0000=>0000=>[5]
[5,2,3,1,4]=>0000=>0000=>[5]
[5,2,3,4,1]=>0000=>0000=>[5]
[5,2,4,1,3]=>0000=>0000=>[5]
[5,2,4,3,1]=>0000=>0000=>[5]
[5,3,1,2,4]=>0000=>0000=>[5]
[5,3,1,4,2]=>0000=>0000=>[5]
[5,3,2,1,4]=>0000=>0000=>[5]
[5,3,2,4,1]=>0000=>0000=>[5]
[5,3,4,1,2]=>0000=>0000=>[5]
[5,3,4,2,1]=>0000=>0000=>[5]
[5,4,1,2,3]=>0000=>0000=>[5]
[5,4,1,3,2]=>0000=>0000=>[5]
[5,4,2,1,3]=>0000=>0000=>[5]
[5,4,2,3,1]=>0000=>0000=>[5]
[5,4,3,1,2]=>0000=>0000=>[5]
[5,4,3,2,1]=>0000=>0000=>[5]
[1,2,3,4,5,6]=>11111=>11111=>[1,1,1,1,1,1]
[1,2,3,4,6,5]=>11110=>01111=>[2,1,1,1,1]
[1,2,3,5,4,6]=>11101=>10111=>[1,2,1,1,1]
[1,2,3,5,6,4]=>11100=>00111=>[3,1,1,1]
[1,2,3,6,4,5]=>11100=>00111=>[3,1,1,1]
[1,2,3,6,5,4]=>11100=>00111=>[3,1,1,1]
[1,2,4,3,5,6]=>11011=>11011=>[1,1,2,1,1]
[1,2,4,3,6,5]=>11010=>01011=>[2,2,1,1]
[1,2,4,5,3,6]=>11001=>10011=>[1,3,1,1]
[1,2,4,5,6,3]=>11000=>00011=>[4,1,1]
[1,2,4,6,3,5]=>11000=>00011=>[4,1,1]
[1,2,4,6,5,3]=>11000=>00011=>[4,1,1]
[1,2,5,3,4,6]=>11001=>10011=>[1,3,1,1]
[1,2,5,3,6,4]=>11000=>00011=>[4,1,1]
[1,2,5,4,3,6]=>11001=>10011=>[1,3,1,1]
[1,2,5,4,6,3]=>11000=>00011=>[4,1,1]
[1,2,5,6,3,4]=>11000=>00011=>[4,1,1]
[1,2,5,6,4,3]=>11000=>00011=>[4,1,1]
[1,2,6,3,4,5]=>11000=>00011=>[4,1,1]
[1,2,6,3,5,4]=>11000=>00011=>[4,1,1]
[1,2,6,4,3,5]=>11000=>00011=>[4,1,1]
[1,2,6,4,5,3]=>11000=>00011=>[4,1,1]
[1,2,6,5,3,4]=>11000=>00011=>[4,1,1]
[1,2,6,5,4,3]=>11000=>00011=>[4,1,1]
[1,3,2,4,5,6]=>10111=>11101=>[1,1,1,2,1]
[1,3,2,4,6,5]=>10110=>01101=>[2,1,2,1]
[1,3,2,5,4,6]=>10101=>10101=>[1,2,2,1]
[1,3,2,5,6,4]=>10100=>00101=>[3,2,1]
[1,3,2,6,4,5]=>10100=>00101=>[3,2,1]
[1,3,2,6,5,4]=>10100=>00101=>[3,2,1]
[1,3,4,2,5,6]=>10011=>11001=>[1,1,3,1]
[1,3,4,2,6,5]=>10010=>01001=>[2,3,1]
[1,3,4,5,2,6]=>10001=>10001=>[1,4,1]
[1,3,4,5,6,2]=>10000=>00001=>[5,1]
[1,3,4,6,2,5]=>10000=>00001=>[5,1]
[1,3,4,6,5,2]=>10000=>00001=>[5,1]
[1,3,5,2,4,6]=>10001=>10001=>[1,4,1]
[1,3,5,2,6,4]=>10000=>00001=>[5,1]
[1,3,5,4,2,6]=>10001=>10001=>[1,4,1]
[1,3,5,4,6,2]=>10000=>00001=>[5,1]
[1,3,5,6,2,4]=>10000=>00001=>[5,1]
[1,3,5,6,4,2]=>10000=>00001=>[5,1]
[1,3,6,2,4,5]=>10000=>00001=>[5,1]
[1,3,6,2,5,4]=>10000=>00001=>[5,1]
[1,3,6,4,2,5]=>10000=>00001=>[5,1]
[1,3,6,4,5,2]=>10000=>00001=>[5,1]
[1,3,6,5,2,4]=>10000=>00001=>[5,1]
[1,3,6,5,4,2]=>10000=>00001=>[5,1]
[1,4,2,3,5,6]=>10011=>11001=>[1,1,3,1]
[1,4,2,3,6,5]=>10010=>01001=>[2,3,1]
[1,4,2,5,3,6]=>10001=>10001=>[1,4,1]
[1,4,2,5,6,3]=>10000=>00001=>[5,1]
[1,4,2,6,3,5]=>10000=>00001=>[5,1]
[1,4,2,6,5,3]=>10000=>00001=>[5,1]
[1,4,3,2,5,6]=>10011=>11001=>[1,1,3,1]
[1,4,3,2,6,5]=>10010=>01001=>[2,3,1]
[1,4,3,5,2,6]=>10001=>10001=>[1,4,1]
[1,4,3,5,6,2]=>10000=>00001=>[5,1]
[1,4,3,6,2,5]=>10000=>00001=>[5,1]
[1,4,3,6,5,2]=>10000=>00001=>[5,1]
[1,4,5,2,3,6]=>10001=>10001=>[1,4,1]
[1,4,5,2,6,3]=>10000=>00001=>[5,1]
[1,4,5,3,2,6]=>10001=>10001=>[1,4,1]
[1,4,5,3,6,2]=>10000=>00001=>[5,1]
[1,4,5,6,2,3]=>10000=>00001=>[5,1]
[1,4,5,6,3,2]=>10000=>00001=>[5,1]
[1,4,6,2,3,5]=>10000=>00001=>[5,1]
[1,4,6,2,5,3]=>10000=>00001=>[5,1]
[1,4,6,3,2,5]=>10000=>00001=>[5,1]
[1,4,6,3,5,2]=>10000=>00001=>[5,1]
[1,4,6,5,2,3]=>10000=>00001=>[5,1]
[1,4,6,5,3,2]=>10000=>00001=>[5,1]
[1,5,2,3,4,6]=>10001=>10001=>[1,4,1]
[1,5,2,3,6,4]=>10000=>00001=>[5,1]
[1,5,2,4,3,6]=>10001=>10001=>[1,4,1]
[1,5,2,4,6,3]=>10000=>00001=>[5,1]
[1,5,2,6,3,4]=>10000=>00001=>[5,1]
[1,5,2,6,4,3]=>10000=>00001=>[5,1]
[1,5,3,2,4,6]=>10001=>10001=>[1,4,1]
[1,5,3,2,6,4]=>10000=>00001=>[5,1]
[1,5,3,4,2,6]=>10001=>10001=>[1,4,1]
[1,5,3,4,6,2]=>10000=>00001=>[5,1]
[1,5,3,6,2,4]=>10000=>00001=>[5,1]
[1,5,3,6,4,2]=>10000=>00001=>[5,1]
[1,5,4,2,3,6]=>10001=>10001=>[1,4,1]
[1,5,4,2,6,3]=>10000=>00001=>[5,1]
[1,5,4,3,2,6]=>10001=>10001=>[1,4,1]
[1,5,4,3,6,2]=>10000=>00001=>[5,1]
[1,5,4,6,2,3]=>10000=>00001=>[5,1]
[1,5,4,6,3,2]=>10000=>00001=>[5,1]
[1,5,6,2,3,4]=>10000=>00001=>[5,1]
[1,5,6,2,4,3]=>10000=>00001=>[5,1]
[1,5,6,3,2,4]=>10000=>00001=>[5,1]
[1,5,6,3,4,2]=>10000=>00001=>[5,1]
[1,5,6,4,2,3]=>10000=>00001=>[5,1]
[1,5,6,4,3,2]=>10000=>00001=>[5,1]
[1,6,2,3,4,5]=>10000=>00001=>[5,1]
[1,6,2,3,5,4]=>10000=>00001=>[5,1]
[1,6,2,4,3,5]=>10000=>00001=>[5,1]
[1,6,2,4,5,3]=>10000=>00001=>[5,1]
[1,6,2,5,3,4]=>10000=>00001=>[5,1]
[1,6,2,5,4,3]=>10000=>00001=>[5,1]
[1,6,3,2,4,5]=>10000=>00001=>[5,1]
[1,6,3,2,5,4]=>10000=>00001=>[5,1]
[1,6,3,4,2,5]=>10000=>00001=>[5,1]
[1,6,3,4,5,2]=>10000=>00001=>[5,1]
[1,6,3,5,2,4]=>10000=>00001=>[5,1]
[1,6,3,5,4,2]=>10000=>00001=>[5,1]
[1,6,4,2,3,5]=>10000=>00001=>[5,1]
[1,6,4,2,5,3]=>10000=>00001=>[5,1]
[1,6,4,3,2,5]=>10000=>00001=>[5,1]
[1,6,4,3,5,2]=>10000=>00001=>[5,1]
[1,6,4,5,2,3]=>10000=>00001=>[5,1]
[1,6,4,5,3,2]=>10000=>00001=>[5,1]
[1,6,5,2,3,4]=>10000=>00001=>[5,1]
[1,6,5,2,4,3]=>10000=>00001=>[5,1]
[1,6,5,3,2,4]=>10000=>00001=>[5,1]
[1,6,5,3,4,2]=>10000=>00001=>[5,1]
[1,6,5,4,2,3]=>10000=>00001=>[5,1]
[1,6,5,4,3,2]=>10000=>00001=>[5,1]
[2,1,3,4,5,6]=>01111=>11110=>[1,1,1,1,2]
[2,1,3,4,6,5]=>01110=>01110=>[2,1,1,2]
[2,1,3,5,4,6]=>01101=>10110=>[1,2,1,2]
[2,1,3,5,6,4]=>01100=>00110=>[3,1,2]
[2,1,3,6,4,5]=>01100=>00110=>[3,1,2]
[2,1,3,6,5,4]=>01100=>00110=>[3,1,2]
[2,1,4,3,5,6]=>01011=>11010=>[1,1,2,2]
[2,1,4,3,6,5]=>01010=>01010=>[2,2,2]
[2,1,4,5,3,6]=>01001=>10010=>[1,3,2]
[2,1,4,5,6,3]=>01000=>00010=>[4,2]
[2,1,4,6,3,5]=>01000=>00010=>[4,2]
[2,1,4,6,5,3]=>01000=>00010=>[4,2]
[2,1,5,3,4,6]=>01001=>10010=>[1,3,2]
[2,1,5,3,6,4]=>01000=>00010=>[4,2]
[2,1,5,4,3,6]=>01001=>10010=>[1,3,2]
[2,1,5,4,6,3]=>01000=>00010=>[4,2]
[2,1,5,6,3,4]=>01000=>00010=>[4,2]
[2,1,5,6,4,3]=>01000=>00010=>[4,2]
[2,1,6,3,4,5]=>01000=>00010=>[4,2]
[2,1,6,3,5,4]=>01000=>00010=>[4,2]
[2,1,6,4,3,5]=>01000=>00010=>[4,2]
[2,1,6,4,5,3]=>01000=>00010=>[4,2]
[2,1,6,5,3,4]=>01000=>00010=>[4,2]
[2,1,6,5,4,3]=>01000=>00010=>[4,2]
[2,3,1,4,5,6]=>00111=>11100=>[1,1,1,3]
[2,3,1,4,6,5]=>00110=>01100=>[2,1,3]
[2,3,1,5,4,6]=>00101=>10100=>[1,2,3]
[2,3,1,5,6,4]=>00100=>00100=>[3,3]
[2,3,1,6,4,5]=>00100=>00100=>[3,3]
[2,3,1,6,5,4]=>00100=>00100=>[3,3]
[2,3,4,1,5,6]=>00011=>11000=>[1,1,4]
[2,3,4,1,6,5]=>00010=>01000=>[2,4]
[2,3,4,5,1,6]=>00001=>10000=>[1,5]
[2,3,4,5,6,1]=>00000=>00000=>[6]
[2,3,4,6,1,5]=>00000=>00000=>[6]
[2,3,4,6,5,1]=>00000=>00000=>[6]
[2,3,5,1,4,6]=>00001=>10000=>[1,5]
[2,3,5,1,6,4]=>00000=>00000=>[6]
[2,3,5,4,1,6]=>00001=>10000=>[1,5]
[2,3,5,4,6,1]=>00000=>00000=>[6]
[2,3,5,6,1,4]=>00000=>00000=>[6]
[2,3,5,6,4,1]=>00000=>00000=>[6]
[2,3,6,1,4,5]=>00000=>00000=>[6]
[2,3,6,1,5,4]=>00000=>00000=>[6]
[2,3,6,4,1,5]=>00000=>00000=>[6]
[2,3,6,4,5,1]=>00000=>00000=>[6]
[2,3,6,5,1,4]=>00000=>00000=>[6]
[2,3,6,5,4,1]=>00000=>00000=>[6]
[2,4,1,3,5,6]=>00011=>11000=>[1,1,4]
[2,4,1,3,6,5]=>00010=>01000=>[2,4]
[2,4,1,5,3,6]=>00001=>10000=>[1,5]
[2,4,1,5,6,3]=>00000=>00000=>[6]
[2,4,1,6,3,5]=>00000=>00000=>[6]
[2,4,1,6,5,3]=>00000=>00000=>[6]
[2,4,3,1,5,6]=>00011=>11000=>[1,1,4]
[2,4,3,1,6,5]=>00010=>01000=>[2,4]
[2,4,3,5,1,6]=>00001=>10000=>[1,5]
[2,4,3,5,6,1]=>00000=>00000=>[6]
[2,4,3,6,1,5]=>00000=>00000=>[6]
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[1,2,4,5,3,7,6]=>110010=>010011=>[2,3,1,1]
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[1,2,5,4,3,7,6]=>110010=>010011=>[2,3,1,1]
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[1,2,7,4,6,5,3]=>110000=>000011=>[5,1,1]
[1,2,7,5,3,4,6]=>110000=>000011=>[5,1,1]
[1,2,7,5,3,6,4]=>110000=>000011=>[5,1,1]
[1,2,7,5,4,3,6]=>110000=>000011=>[5,1,1]
[1,2,7,5,4,6,3]=>110000=>000011=>[5,1,1]
[1,2,7,5,6,3,4]=>110000=>000011=>[5,1,1]
[1,2,7,5,6,4,3]=>110000=>000011=>[5,1,1]
[1,2,7,6,3,4,5]=>110000=>000011=>[5,1,1]
[1,2,7,6,3,5,4]=>110000=>000011=>[5,1,1]
[1,2,7,6,4,3,5]=>110000=>000011=>[5,1,1]
[1,2,7,6,4,5,3]=>110000=>000011=>[5,1,1]
[1,2,7,6,5,3,4]=>110000=>000011=>[5,1,1]
[1,2,7,6,5,4,3]=>110000=>000011=>[5,1,1]
[1,3,2,4,5,6,7]=>101111=>111101=>[1,1,1,1,2,1]
[1,3,2,4,5,7,6]=>101110=>011101=>[2,1,1,2,1]
[1,3,2,4,6,5,7]=>101101=>101101=>[1,2,1,2,1]
[1,3,2,4,6,7,5]=>101100=>001101=>[3,1,2,1]
[1,3,2,4,7,5,6]=>101100=>001101=>[3,1,2,1]
[1,3,2,4,7,6,5]=>101100=>001101=>[3,1,2,1]
[1,3,2,5,4,6,7]=>101011=>110101=>[1,1,2,2,1]
[1,3,2,5,4,7,6]=>101010=>010101=>[2,2,2,1]
[1,3,2,5,6,4,7]=>101001=>100101=>[1,3,2,1]
[1,3,2,5,6,7,4]=>101000=>000101=>[4,2,1]
[1,3,2,5,7,4,6]=>101000=>000101=>[4,2,1]
[1,3,2,5,7,6,4]=>101000=>000101=>[4,2,1]
[1,3,2,6,4,5,7]=>101001=>100101=>[1,3,2,1]
[1,3,2,6,4,7,5]=>101000=>000101=>[4,2,1]
[1,3,2,6,5,4,7]=>101001=>100101=>[1,3,2,1]
[1,3,2,6,5,7,4]=>101000=>000101=>[4,2,1]
[1,3,2,6,7,4,5]=>101000=>000101=>[4,2,1]
[1,3,2,6,7,5,4]=>101000=>000101=>[4,2,1]
[1,3,2,7,4,5,6]=>101000=>000101=>[4,2,1]
[1,3,2,7,4,6,5]=>101000=>000101=>[4,2,1]
[1,3,2,7,5,4,6]=>101000=>000101=>[4,2,1]
[1,3,2,7,5,6,4]=>101000=>000101=>[4,2,1]
[1,3,2,7,6,4,5]=>101000=>000101=>[4,2,1]
[1,3,2,7,6,5,4]=>101000=>000101=>[4,2,1]
[1,3,4,2,5,6,7]=>100111=>111001=>[1,1,1,3,1]
[1,3,4,2,5,7,6]=>100110=>011001=>[2,1,3,1]
[1,3,4,2,6,5,7]=>100101=>101001=>[1,2,3,1]
[1,3,4,2,6,7,5]=>100100=>001001=>[3,3,1]
[1,3,4,2,7,5,6]=>100100=>001001=>[3,3,1]
[1,3,4,2,7,6,5]=>100100=>001001=>[3,3,1]
[1,3,4,5,2,6,7]=>100011=>110001=>[1,1,4,1]
[1,3,4,5,2,7,6]=>100010=>010001=>[2,4,1]
[1,3,4,5,6,2,7]=>100001=>100001=>[1,5,1]
[1,3,4,5,6,7,2]=>100000=>000001=>[6,1]
[1,3,4,5,7,2,6]=>100000=>000001=>[6,1]
[1,3,4,5,7,6,2]=>100000=>000001=>[6,1]
[1,3,4,6,2,5,7]=>100001=>100001=>[1,5,1]
[1,3,4,6,2,7,5]=>100000=>000001=>[6,1]
[1,3,4,6,5,2,7]=>100001=>100001=>[1,5,1]
[1,3,4,6,5,7,2]=>100000=>000001=>[6,1]
[1,3,4,6,7,2,5]=>100000=>000001=>[6,1]
[1,3,4,6,7,5,2]=>100000=>000001=>[6,1]
[1,3,4,7,2,5,6]=>100000=>000001=>[6,1]
[1,3,4,7,2,6,5]=>100000=>000001=>[6,1]
[1,3,4,7,5,2,6]=>100000=>000001=>[6,1]
[1,3,4,7,5,6,2]=>100000=>000001=>[6,1]
[1,3,4,7,6,2,5]=>100000=>000001=>[6,1]
[1,3,4,7,6,5,2]=>100000=>000001=>[6,1]
[1,3,5,2,4,6,7]=>100011=>110001=>[1,1,4,1]
[1,3,5,2,4,7,6]=>100010=>010001=>[2,4,1]
[1,3,5,2,6,4,7]=>100001=>100001=>[1,5,1]
[1,3,5,2,6,7,4]=>100000=>000001=>[6,1]
[1,3,5,2,7,4,6]=>100000=>000001=>[6,1]
[1,3,5,2,7,6,4]=>100000=>000001=>[6,1]
[1,3,5,4,2,6,7]=>100011=>110001=>[1,1,4,1]
[1,3,5,4,2,7,6]=>100010=>010001=>[2,4,1]
[1,3,5,4,6,2,7]=>100001=>100001=>[1,5,1]
[1,3,5,4,6,7,2]=>100000=>000001=>[6,1]
[1,3,5,4,7,2,6]=>100000=>000001=>[6,1]
[1,3,5,4,7,6,2]=>100000=>000001=>[6,1]
[1,3,5,6,2,4,7]=>100001=>100001=>[1,5,1]
[1,3,5,6,2,7,4]=>100000=>000001=>[6,1]
[1,3,5,6,4,2,7]=>100001=>100001=>[1,5,1]
[1,3,5,6,4,7,2]=>100000=>000001=>[6,1]
[1,3,5,6,7,2,4]=>100000=>000001=>[6,1]
[1,3,5,6,7,4,2]=>100000=>000001=>[6,1]
[1,3,5,7,2,4,6]=>100000=>000001=>[6,1]
[1,3,5,7,2,6,4]=>100000=>000001=>[6,1]
[1,3,5,7,4,2,6]=>100000=>000001=>[6,1]
[1,3,5,7,4,6,2]=>100000=>000001=>[6,1]
[1,3,5,7,6,2,4]=>100000=>000001=>[6,1]
[1,3,5,7,6,4,2]=>100000=>000001=>[6,1]
[1,3,6,2,4,5,7]=>100001=>100001=>[1,5,1]
[1,3,6,2,4,7,5]=>100000=>000001=>[6,1]
[1,3,6,2,5,4,7]=>100001=>100001=>[1,5,1]
[1,3,6,2,5,7,4]=>100000=>000001=>[6,1]
[1,3,6,2,7,4,5]=>100000=>000001=>[6,1]
[1,3,6,2,7,5,4]=>100000=>000001=>[6,1]
[1,3,6,4,2,5,7]=>100001=>100001=>[1,5,1]
[1,3,6,4,2,7,5]=>100000=>000001=>[6,1]
[1,3,6,4,5,2,7]=>100001=>100001=>[1,5,1]
[1,3,6,4,5,7,2]=>100000=>000001=>[6,1]
[1,3,6,4,7,2,5]=>100000=>000001=>[6,1]
[1,3,6,4,7,5,2]=>100000=>000001=>[6,1]
[1,3,6,5,2,4,7]=>100001=>100001=>[1,5,1]
[1,3,6,5,2,7,4]=>100000=>000001=>[6,1]
[1,3,6,5,4,2,7]=>100001=>100001=>[1,5,1]
[1,3,6,5,4,7,2]=>100000=>000001=>[6,1]
[1,3,6,5,7,2,4]=>100000=>000001=>[6,1]
[1,3,6,5,7,4,2]=>100000=>000001=>[6,1]
[1,3,6,7,2,4,5]=>100000=>000001=>[6,1]
[1,3,6,7,2,5,4]=>100000=>000001=>[6,1]
[1,3,6,7,4,2,5]=>100000=>000001=>[6,1]
[1,3,6,7,4,5,2]=>100000=>000001=>[6,1]
[1,3,6,7,5,2,4]=>100000=>000001=>[6,1]
[1,3,6,7,5,4,2]=>100000=>000001=>[6,1]
[1,3,7,2,4,5,6]=>100000=>000001=>[6,1]
[1,3,7,2,4,6,5]=>100000=>000001=>[6,1]
[1,3,7,2,5,4,6]=>100000=>000001=>[6,1]
[1,3,7,2,5,6,4]=>100000=>000001=>[6,1]
[1,3,7,2,6,4,5]=>100000=>000001=>[6,1]
[1,3,7,2,6,5,4]=>100000=>000001=>[6,1]
[1,3,7,4,2,5,6]=>100000=>000001=>[6,1]
[1,3,7,4,2,6,5]=>100000=>000001=>[6,1]
[1,3,7,4,5,2,6]=>100000=>000001=>[6,1]
[1,3,7,4,5,6,2]=>100000=>000001=>[6,1]
[1,3,7,4,6,2,5]=>100000=>000001=>[6,1]
[1,3,7,4,6,5,2]=>100000=>000001=>[6,1]
[1,3,7,5,2,4,6]=>100000=>000001=>[6,1]
[1,3,7,5,2,6,4]=>100000=>000001=>[6,1]
[1,3,7,5,4,2,6]=>100000=>000001=>[6,1]
[1,3,7,5,4,6,2]=>100000=>000001=>[6,1]
[1,3,7,5,6,2,4]=>100000=>000001=>[6,1]
[1,3,7,5,6,4,2]=>100000=>000001=>[6,1]
[1,3,7,6,2,4,5]=>100000=>000001=>[6,1]
[1,3,7,6,2,5,4]=>100000=>000001=>[6,1]
[1,3,7,6,4,2,5]=>100000=>000001=>[6,1]
[1,3,7,6,4,5,2]=>100000=>000001=>[6,1]
[1,3,7,6,5,2,4]=>100000=>000001=>[6,1]
[1,3,7,6,5,4,2]=>100000=>000001=>[6,1]
[1,4,2,3,5,6,7]=>100111=>111001=>[1,1,1,3,1]
[1,4,2,3,5,7,6]=>100110=>011001=>[2,1,3,1]
[1,4,2,3,6,5,7]=>100101=>101001=>[1,2,3,1]
[1,4,2,3,6,7,5]=>100100=>001001=>[3,3,1]
[1,4,2,3,7,5,6]=>100100=>001001=>[3,3,1]
[1,4,2,3,7,6,5]=>100100=>001001=>[3,3,1]
[1,4,2,5,3,6,7]=>100011=>110001=>[1,1,4,1]
[1,4,2,5,3,7,6]=>100010=>010001=>[2,4,1]
[1,4,2,5,6,3,7]=>100001=>100001=>[1,5,1]
[1,4,2,5,6,7,3]=>100000=>000001=>[6,1]
[1,4,2,5,7,3,6]=>100000=>000001=>[6,1]
[1,4,2,5,7,6,3]=>100000=>000001=>[6,1]
[1,4,2,6,3,5,7]=>100001=>100001=>[1,5,1]
[1,4,2,6,3,7,5]=>100000=>000001=>[6,1]
[1,4,2,6,5,3,7]=>100001=>100001=>[1,5,1]
[1,4,2,6,5,7,3]=>100000=>000001=>[6,1]
[1,4,2,6,7,3,5]=>100000=>000001=>[6,1]
[1,4,2,6,7,5,3]=>100000=>000001=>[6,1]
[1,4,2,7,3,5,6]=>100000=>000001=>[6,1]
[1,4,2,7,3,6,5]=>100000=>000001=>[6,1]
[1,4,2,7,5,3,6]=>100000=>000001=>[6,1]
[1,4,2,7,5,6,3]=>100000=>000001=>[6,1]
[1,4,2,7,6,3,5]=>100000=>000001=>[6,1]
[1,4,2,7,6,5,3]=>100000=>000001=>[6,1]
[1,4,3,2,5,6,7]=>100111=>111001=>[1,1,1,3,1]
[1,4,3,2,5,7,6]=>100110=>011001=>[2,1,3,1]
[1,4,3,2,6,5,7]=>100101=>101001=>[1,2,3,1]
[1,4,3,2,6,7,5]=>100100=>001001=>[3,3,1]
[1,4,3,2,7,5,6]=>100100=>001001=>[3,3,1]
[1,4,3,2,7,6,5]=>100100=>001001=>[3,3,1]
[1,4,3,5,2,6,7]=>100011=>110001=>[1,1,4,1]
[1,4,3,5,2,7,6]=>100010=>010001=>[2,4,1]
[1,4,3,5,6,2,7]=>100001=>100001=>[1,5,1]
[1,4,3,5,6,7,2]=>100000=>000001=>[6,1]
[1,4,3,5,7,2,6]=>100000=>000001=>[6,1]
[1,4,3,5,7,6,2]=>100000=>000001=>[6,1]
[1,4,3,6,2,5,7]=>100001=>100001=>[1,5,1]
[1,4,3,6,2,7,5]=>100000=>000001=>[6,1]
[1,4,3,6,5,2,7]=>100001=>100001=>[1,5,1]
[1,4,3,6,5,7,2]=>100000=>000001=>[6,1]
[1,4,3,6,7,2,5]=>100000=>000001=>[6,1]
[1,4,3,6,7,5,2]=>100000=>000001=>[6,1]
[1,4,3,7,2,5,6]=>100000=>000001=>[6,1]
[1,4,3,7,2,6,5]=>100000=>000001=>[6,1]
[1,4,3,7,5,2,6]=>100000=>000001=>[6,1]
[1,4,3,7,5,6,2]=>100000=>000001=>[6,1]
[1,4,3,7,6,2,5]=>100000=>000001=>[6,1]
[1,4,3,7,6,5,2]=>100000=>000001=>[6,1]
[1,4,5,2,3,6,7]=>100011=>110001=>[1,1,4,1]
[1,4,5,2,3,7,6]=>100010=>010001=>[2,4,1]
[1,4,5,2,6,3,7]=>100001=>100001=>[1,5,1]
[1,4,5,2,6,7,3]=>100000=>000001=>[6,1]
[1,4,5,2,7,3,6]=>100000=>000001=>[6,1]
[1,4,5,2,7,6,3]=>100000=>000001=>[6,1]
[1,4,5,3,2,6,7]=>100011=>110001=>[1,1,4,1]
[1,4,5,3,2,7,6]=>100010=>010001=>[2,4,1]
[1,4,5,3,6,2,7]=>100001=>100001=>[1,5,1]
[1,4,5,3,6,7,2]=>100000=>000001=>[6,1]
[1,4,5,3,7,2,6]=>100000=>000001=>[6,1]
[1,4,5,3,7,6,2]=>100000=>000001=>[6,1]
[1,4,5,6,2,3,7]=>100001=>100001=>[1,5,1]
[1,4,5,6,2,7,3]=>100000=>000001=>[6,1]
[1,4,5,6,3,2,7]=>100001=>100001=>[1,5,1]
[1,4,5,6,3,7,2]=>100000=>000001=>[6,1]
[1,4,5,6,7,2,3]=>100000=>000001=>[6,1]
[1,4,5,6,7,3,2]=>100000=>000001=>[6,1]
[1,4,5,7,2,3,6]=>100000=>000001=>[6,1]
[1,4,5,7,2,6,3]=>100000=>000001=>[6,1]
[1,4,5,7,3,2,6]=>100000=>000001=>[6,1]
[1,4,5,7,3,6,2]=>100000=>000001=>[6,1]
[1,4,5,7,6,2,3]=>100000=>000001=>[6,1]
[1,4,5,7,6,3,2]=>100000=>000001=>[6,1]
[1,4,6,2,3,5,7]=>100001=>100001=>[1,5,1]
[1,4,6,2,3,7,5]=>100000=>000001=>[6,1]
[1,4,6,2,5,3,7]=>100001=>100001=>[1,5,1]
[1,4,6,2,5,7,3]=>100000=>000001=>[6,1]
[1,4,6,2,7,3,5]=>100000=>000001=>[6,1]
[1,4,6,2,7,5,3]=>100000=>000001=>[6,1]
[1,4,6,3,2,5,7]=>100001=>100001=>[1,5,1]
[1,4,6,3,2,7,5]=>100000=>000001=>[6,1]
[1,4,6,3,5,2,7]=>100001=>100001=>[1,5,1]
[1,4,6,3,5,7,2]=>100000=>000001=>[6,1]
[1,4,6,3,7,2,5]=>100000=>000001=>[6,1]
[1,4,6,3,7,5,2]=>100000=>000001=>[6,1]
[1,4,6,5,2,3,7]=>100001=>100001=>[1,5,1]
[1,4,6,5,2,7,3]=>100000=>000001=>[6,1]
[1,4,6,5,3,2,7]=>100001=>100001=>[1,5,1]
[1,4,6,5,3,7,2]=>100000=>000001=>[6,1]
[1,4,6,5,7,2,3]=>100000=>000001=>[6,1]
[1,4,6,5,7,3,2]=>100000=>000001=>[6,1]
[1,4,6,7,2,3,5]=>100000=>000001=>[6,1]
[1,4,6,7,2,5,3]=>100000=>000001=>[6,1]
[1,4,6,7,3,2,5]=>100000=>000001=>[6,1]
[1,4,6,7,3,5,2]=>100000=>000001=>[6,1]
[1,4,6,7,5,2,3]=>100000=>000001=>[6,1]
[1,4,6,7,5,3,2]=>100000=>000001=>[6,1]
[1,4,7,2,3,5,6]=>100000=>000001=>[6,1]
[1,4,7,2,3,6,5]=>100000=>000001=>[6,1]
[1,4,7,2,5,3,6]=>100000=>000001=>[6,1]
[1,4,7,2,5,6,3]=>100000=>000001=>[6,1]
[1,4,7,2,6,3,5]=>100000=>000001=>[6,1]
[1,4,7,2,6,5,3]=>100000=>000001=>[6,1]
[1,4,7,3,2,5,6]=>100000=>000001=>[6,1]
[1,4,7,3,2,6,5]=>100000=>000001=>[6,1]
[1,4,7,3,5,2,6]=>100000=>000001=>[6,1]
[1,4,7,3,5,6,2]=>100000=>000001=>[6,1]
[1,4,7,3,6,2,5]=>100000=>000001=>[6,1]
[1,4,7,3,6,5,2]=>100000=>000001=>[6,1]
[1,4,7,5,2,3,6]=>100000=>000001=>[6,1]
[1,4,7,5,2,6,3]=>100000=>000001=>[6,1]
[1,4,7,5,3,2,6]=>100000=>000001=>[6,1]
[1,4,7,5,3,6,2]=>100000=>000001=>[6,1]
[1,4,7,5,6,2,3]=>100000=>000001=>[6,1]
[1,4,7,5,6,3,2]=>100000=>000001=>[6,1]
[1,4,7,6,2,3,5]=>100000=>000001=>[6,1]
[1,4,7,6,2,5,3]=>100000=>000001=>[6,1]
[1,4,7,6,3,2,5]=>100000=>000001=>[6,1]
[1,4,7,6,3,5,2]=>100000=>000001=>[6,1]
[1,4,7,6,5,2,3]=>100000=>000001=>[6,1]
[1,4,7,6,5,3,2]=>100000=>000001=>[6,1]
[1,5,2,3,4,6,7]=>100011=>110001=>[1,1,4,1]
[1,5,2,3,4,7,6]=>100010=>010001=>[2,4,1]
[1,5,2,3,6,4,7]=>100001=>100001=>[1,5,1]
[1,5,2,3,6,7,4]=>100000=>000001=>[6,1]
[1,5,2,3,7,4,6]=>100000=>000001=>[6,1]
[1,5,2,3,7,6,4]=>100000=>000001=>[6,1]
[1,5,2,4,3,6,7]=>100011=>110001=>[1,1,4,1]
[1,5,2,4,3,7,6]=>100010=>010001=>[2,4,1]
[1,5,2,4,6,3,7]=>100001=>100001=>[1,5,1]
[1,5,2,4,6,7,3]=>100000=>000001=>[6,1]
[1,5,2,4,7,3,6]=>100000=>000001=>[6,1]
[1,5,2,4,7,6,3]=>100000=>000001=>[6,1]
[1,5,2,6,3,4,7]=>100001=>100001=>[1,5,1]
[1,5,2,6,3,7,4]=>100000=>000001=>[6,1]
[1,5,2,6,4,3,7]=>100001=>100001=>[1,5,1]
[1,5,2,6,4,7,3]=>100000=>000001=>[6,1]
[1,5,2,6,7,3,4]=>100000=>000001=>[6,1]
[1,5,2,6,7,4,3]=>100000=>000001=>[6,1]
[1,5,2,7,3,4,6]=>100000=>000001=>[6,1]
[1,5,2,7,3,6,4]=>100000=>000001=>[6,1]
[1,5,2,7,4,3,6]=>100000=>000001=>[6,1]
[1,5,2,7,4,6,3]=>100000=>000001=>[6,1]
[1,5,2,7,6,3,4]=>100000=>000001=>[6,1]
[1,5,2,7,6,4,3]=>100000=>000001=>[6,1]
[1,5,3,2,4,6,7]=>100011=>110001=>[1,1,4,1]
[1,5,3,2,4,7,6]=>100010=>010001=>[2,4,1]
[1,5,3,2,6,4,7]=>100001=>100001=>[1,5,1]
[1,5,3,2,6,7,4]=>100000=>000001=>[6,1]
[1,5,3,2,7,4,6]=>100000=>000001=>[6,1]
[1,5,3,2,7,6,4]=>100000=>000001=>[6,1]
[1,5,3,4,2,6,7]=>100011=>110001=>[1,1,4,1]
[1,5,3,4,2,7,6]=>100010=>010001=>[2,4,1]
[1,5,3,4,6,2,7]=>100001=>100001=>[1,5,1]
[1,5,3,4,6,7,2]=>100000=>000001=>[6,1]
[1,5,3,4,7,2,6]=>100000=>000001=>[6,1]
[1,5,3,4,7,6,2]=>100000=>000001=>[6,1]
[1,5,3,6,2,4,7]=>100001=>100001=>[1,5,1]
[1,5,3,6,2,7,4]=>100000=>000001=>[6,1]
[1,5,3,6,4,2,7]=>100001=>100001=>[1,5,1]
[1,5,3,6,4,7,2]=>100000=>000001=>[6,1]
[1,5,3,6,7,2,4]=>100000=>000001=>[6,1]
[1,5,3,6,7,4,2]=>100000=>000001=>[6,1]
[1,5,3,7,2,4,6]=>100000=>000001=>[6,1]
[1,5,3,7,2,6,4]=>100000=>000001=>[6,1]
[1,5,3,7,4,2,6]=>100000=>000001=>[6,1]
[1,5,3,7,4,6,2]=>100000=>000001=>[6,1]
[1,5,3,7,6,2,4]=>100000=>000001=>[6,1]
[1,5,3,7,6,4,2]=>100000=>000001=>[6,1]
[1,5,4,2,3,6,7]=>100011=>110001=>[1,1,4,1]
[1,5,4,2,3,7,6]=>100010=>010001=>[2,4,1]
[1,5,4,2,6,3,7]=>100001=>100001=>[1,5,1]
[1,5,4,2,6,7,3]=>100000=>000001=>[6,1]
[1,5,4,2,7,3,6]=>100000=>000001=>[6,1]
[1,5,4,2,7,6,3]=>100000=>000001=>[6,1]
[1,5,4,3,2,6,7]=>100011=>110001=>[1,1,4,1]
[1,5,4,3,2,7,6]=>100010=>010001=>[2,4,1]
[1,5,4,3,6,2,7]=>100001=>100001=>[1,5,1]
[1,5,4,3,6,7,2]=>100000=>000001=>[6,1]
[1,5,4,3,7,2,6]=>100000=>000001=>[6,1]
[1,5,4,3,7,6,2]=>100000=>000001=>[6,1]
[1,5,4,6,2,3,7]=>100001=>100001=>[1,5,1]
[1,5,4,6,2,7,3]=>100000=>000001=>[6,1]
[1,5,4,6,3,2,7]=>100001=>100001=>[1,5,1]
[1,5,4,6,3,7,2]=>100000=>000001=>[6,1]
[1,5,4,6,7,2,3]=>100000=>000001=>[6,1]
[1,5,4,6,7,3,2]=>100000=>000001=>[6,1]
[1,5,4,7,2,3,6]=>100000=>000001=>[6,1]
[1,5,4,7,2,6,3]=>100000=>000001=>[6,1]
[1,5,4,7,3,2,6]=>100000=>000001=>[6,1]
[1,5,4,7,3,6,2]=>100000=>000001=>[6,1]
[1,5,4,7,6,2,3]=>100000=>000001=>[6,1]
[1,5,4,7,6,3,2]=>100000=>000001=>[6,1]
[1,5,6,2,3,4,7]=>100001=>100001=>[1,5,1]
[1,5,6,2,3,7,4]=>100000=>000001=>[6,1]
[1,5,6,2,4,3,7]=>100001=>100001=>[1,5,1]
[1,5,6,2,4,7,3]=>100000=>000001=>[6,1]
[1,5,6,2,7,3,4]=>100000=>000001=>[6,1]
[1,5,6,2,7,4,3]=>100000=>000001=>[6,1]
[1,5,6,3,2,4,7]=>100001=>100001=>[1,5,1]
[1,5,6,3,2,7,4]=>100000=>000001=>[6,1]
[1,5,6,3,4,2,7]=>100001=>100001=>[1,5,1]
[1,5,6,3,4,7,2]=>100000=>000001=>[6,1]
[1,5,6,3,7,2,4]=>100000=>000001=>[6,1]
[1,5,6,3,7,4,2]=>100000=>000001=>[6,1]
[1,5,6,4,2,3,7]=>100001=>100001=>[1,5,1]
[1,5,6,4,2,7,3]=>100000=>000001=>[6,1]
[1,5,6,4,3,2,7]=>100001=>100001=>[1,5,1]
[1,5,6,4,3,7,2]=>100000=>000001=>[6,1]
[1,5,6,4,7,2,3]=>100000=>000001=>[6,1]
[1,5,6,4,7,3,2]=>100000=>000001=>[6,1]
[1,5,6,7,2,3,4]=>100000=>000001=>[6,1]
[1,5,6,7,2,4,3]=>100000=>000001=>[6,1]
[1,5,6,7,3,2,4]=>100000=>000001=>[6,1]
[1,5,6,7,3,4,2]=>100000=>000001=>[6,1]
[1,5,6,7,4,2,3]=>100000=>000001=>[6,1]
[1,5,6,7,4,3,2]=>100000=>000001=>[6,1]
[1,5,7,2,3,4,6]=>100000=>000001=>[6,1]
[1,5,7,2,3,6,4]=>100000=>000001=>[6,1]
[1,5,7,2,4,3,6]=>100000=>000001=>[6,1]
[1,5,7,2,4,6,3]=>100000=>000001=>[6,1]
[1,5,7,2,6,3,4]=>100000=>000001=>[6,1]
[1,5,7,2,6,4,3]=>100000=>000001=>[6,1]
[1,5,7,3,2,4,6]=>100000=>000001=>[6,1]
[1,5,7,3,2,6,4]=>100000=>000001=>[6,1]
[1,5,7,3,4,2,6]=>100000=>000001=>[6,1]
[1,5,7,3,4,6,2]=>100000=>000001=>[6,1]
[1,5,7,3,6,2,4]=>100000=>000001=>[6,1]
[1,5,7,3,6,4,2]=>100000=>000001=>[6,1]
[1,5,7,4,2,3,6]=>100000=>000001=>[6,1]
[1,5,7,4,2,6,3]=>100000=>000001=>[6,1]
[1,5,7,4,3,2,6]=>100000=>000001=>[6,1]
[1,5,7,4,3,6,2]=>100000=>000001=>[6,1]
[1,5,7,4,6,2,3]=>100000=>000001=>[6,1]
[1,5,7,4,6,3,2]=>100000=>000001=>[6,1]
[1,5,7,6,2,3,4]=>100000=>000001=>[6,1]
[1,5,7,6,2,4,3]=>100000=>000001=>[6,1]
[1,5,7,6,3,2,4]=>100000=>000001=>[6,1]
[1,5,7,6,3,4,2]=>100000=>000001=>[6,1]
[1,5,7,6,4,2,3]=>100000=>000001=>[6,1]
[1,5,7,6,4,3,2]=>100000=>000001=>[6,1]
[1,6,2,3,4,5,7]=>100001=>100001=>[1,5,1]
[1,6,2,3,4,7,5]=>100000=>000001=>[6,1]
[1,6,2,3,5,4,7]=>100001=>100001=>[1,5,1]
[1,6,2,3,5,7,4]=>100000=>000001=>[6,1]
[1,6,2,3,7,4,5]=>100000=>000001=>[6,1]
[1,6,2,3,7,5,4]=>100000=>000001=>[6,1]
[1,6,2,4,3,5,7]=>100001=>100001=>[1,5,1]
[1,6,2,4,3,7,5]=>100000=>000001=>[6,1]
[1,6,2,4,5,3,7]=>100001=>100001=>[1,5,1]
[1,6,2,4,5,7,3]=>100000=>000001=>[6,1]
[1,6,2,4,7,3,5]=>100000=>000001=>[6,1]
[1,6,2,4,7,5,3]=>100000=>000001=>[6,1]
[1,6,2,5,3,4,7]=>100001=>100001=>[1,5,1]
[1,6,2,5,3,7,4]=>100000=>000001=>[6,1]
[1,6,2,5,4,3,7]=>100001=>100001=>[1,5,1]
[1,6,2,5,4,7,3]=>100000=>000001=>[6,1]
[1,6,2,5,7,3,4]=>100000=>000001=>[6,1]
[1,6,2,5,7,4,3]=>100000=>000001=>[6,1]
[1,6,2,7,3,4,5]=>100000=>000001=>[6,1]
[1,6,2,7,3,5,4]=>100000=>000001=>[6,1]
[1,6,2,7,4,3,5]=>100000=>000001=>[6,1]
[1,6,2,7,4,5,3]=>100000=>000001=>[6,1]
[1,6,2,7,5,3,4]=>100000=>000001=>[6,1]
[1,6,2,7,5,4,3]=>100000=>000001=>[6,1]
[1,6,3,2,4,5,7]=>100001=>100001=>[1,5,1]
[1,6,3,2,4,7,5]=>100000=>000001=>[6,1]
[1,6,3,2,5,4,7]=>100001=>100001=>[1,5,1]
[1,6,3,2,5,7,4]=>100000=>000001=>[6,1]
[1,6,3,2,7,4,5]=>100000=>000001=>[6,1]
[1,6,3,2,7,5,4]=>100000=>000001=>[6,1]
[1,6,3,4,2,5,7]=>100001=>100001=>[1,5,1]
[1,6,3,4,2,7,5]=>100000=>000001=>[6,1]
[1,6,3,4,5,2,7]=>100001=>100001=>[1,5,1]
[1,6,3,4,5,7,2]=>100000=>000001=>[6,1]
[1,6,3,4,7,2,5]=>100000=>000001=>[6,1]
[1,6,3,4,7,5,2]=>100000=>000001=>[6,1]
[1,6,3,5,2,4,7]=>100001=>100001=>[1,5,1]
[1,6,3,5,2,7,4]=>100000=>000001=>[6,1]
[1,6,3,5,4,2,7]=>100001=>100001=>[1,5,1]
[1,6,3,5,4,7,2]=>100000=>000001=>[6,1]
[1,6,3,5,7,2,4]=>100000=>000001=>[6,1]
[1,6,3,5,7,4,2]=>100000=>000001=>[6,1]
[1,6,3,7,2,4,5]=>100000=>000001=>[6,1]
[1,6,3,7,2,5,4]=>100000=>000001=>[6,1]
[1,6,3,7,4,2,5]=>100000=>000001=>[6,1]
[1,6,3,7,4,5,2]=>100000=>000001=>[6,1]
[1,6,3,7,5,2,4]=>100000=>000001=>[6,1]
[1,6,3,7,5,4,2]=>100000=>000001=>[6,1]
[1,6,4,2,3,5,7]=>100001=>100001=>[1,5,1]
[1,6,4,2,3,7,5]=>100000=>000001=>[6,1]
[1,6,4,2,5,3,7]=>100001=>100001=>[1,5,1]
[1,6,4,2,5,7,3]=>100000=>000001=>[6,1]
[1,6,4,2,7,3,5]=>100000=>000001=>[6,1]
[1,6,4,2,7,5,3]=>100000=>000001=>[6,1]
[1,6,4,3,2,5,7]=>100001=>100001=>[1,5,1]
[1,6,4,3,2,7,5]=>100000=>000001=>[6,1]
[1,6,4,3,5,2,7]=>100001=>100001=>[1,5,1]
[1,6,4,3,5,7,2]=>100000=>000001=>[6,1]
[1,6,4,3,7,2,5]=>100000=>000001=>[6,1]
[1,6,4,3,7,5,2]=>100000=>000001=>[6,1]
[1,6,4,5,2,3,7]=>100001=>100001=>[1,5,1]
[1,6,4,5,2,7,3]=>100000=>000001=>[6,1]
[1,6,4,5,3,2,7]=>100001=>100001=>[1,5,1]
[1,6,4,5,3,7,2]=>100000=>000001=>[6,1]
[1,6,4,5,7,2,3]=>100000=>000001=>[6,1]
[1,6,4,5,7,3,2]=>100000=>000001=>[6,1]
[1,6,4,7,2,3,5]=>100000=>000001=>[6,1]
[1,6,4,7,2,5,3]=>100000=>000001=>[6,1]
[1,6,4,7,3,2,5]=>100000=>000001=>[6,1]
[1,6,4,7,3,5,2]=>100000=>000001=>[6,1]
[1,6,4,7,5,2,3]=>100000=>000001=>[6,1]
[1,6,4,7,5,3,2]=>100000=>000001=>[6,1]
[1,6,5,2,3,4,7]=>100001=>100001=>[1,5,1]
[1,6,5,2,3,7,4]=>100000=>000001=>[6,1]
[1,6,5,2,4,3,7]=>100001=>100001=>[1,5,1]
[1,6,5,2,4,7,3]=>100000=>000001=>[6,1]
[1,6,5,2,7,3,4]=>100000=>000001=>[6,1]
[1,6,5,2,7,4,3]=>100000=>000001=>[6,1]
[1,6,5,3,2,4,7]=>100001=>100001=>[1,5,1]
[1,6,5,3,2,7,4]=>100000=>000001=>[6,1]
[1,6,5,3,4,2,7]=>100001=>100001=>[1,5,1]
[1,6,5,3,4,7,2]=>100000=>000001=>[6,1]
[1,6,5,3,7,2,4]=>100000=>000001=>[6,1]
[1,6,5,3,7,4,2]=>100000=>000001=>[6,1]
[1,6,5,4,2,3,7]=>100001=>100001=>[1,5,1]
[1,6,5,4,2,7,3]=>100000=>000001=>[6,1]
[1,6,5,4,3,2,7]=>100001=>100001=>[1,5,1]
[1,6,5,4,3,7,2]=>100000=>000001=>[6,1]
[1,6,5,4,7,2,3]=>100000=>000001=>[6,1]
[1,6,5,4,7,3,2]=>100000=>000001=>[6,1]
[1,6,5,7,2,3,4]=>100000=>000001=>[6,1]
[1,6,5,7,2,4,3]=>100000=>000001=>[6,1]
[1,6,5,7,3,2,4]=>100000=>000001=>[6,1]
[1,6,5,7,3,4,2]=>100000=>000001=>[6,1]
[1,6,5,7,4,2,3]=>100000=>000001=>[6,1]
[1,6,5,7,4,3,2]=>100000=>000001=>[6,1]
[1,6,7,2,3,4,5]=>100000=>000001=>[6,1]
[1,6,7,2,3,5,4]=>100000=>000001=>[6,1]
[1,6,7,2,4,3,5]=>100000=>000001=>[6,1]
[1,6,7,2,4,5,3]=>100000=>000001=>[6,1]
[1,6,7,2,5,3,4]=>100000=>000001=>[6,1]
[1,6,7,2,5,4,3]=>100000=>000001=>[6,1]
[1,6,7,3,2,4,5]=>100000=>000001=>[6,1]
[1,6,7,3,2,5,4]=>100000=>000001=>[6,1]
[1,6,7,3,4,2,5]=>100000=>000001=>[6,1]
[1,6,7,3,4,5,2]=>100000=>000001=>[6,1]
[1,6,7,3,5,2,4]=>100000=>000001=>[6,1]
[1,6,7,3,5,4,2]=>100000=>000001=>[6,1]
[1,6,7,4,2,3,5]=>100000=>000001=>[6,1]
[1,6,7,4,2,5,3]=>100000=>000001=>[6,1]
[1,6,7,4,3,2,5]=>100000=>000001=>[6,1]
[1,6,7,4,3,5,2]=>100000=>000001=>[6,1]
[1,6,7,4,5,2,3]=>100000=>000001=>[6,1]
[1,6,7,4,5,3,2]=>100000=>000001=>[6,1]
[1,6,7,5,2,3,4]=>100000=>000001=>[6,1]
[1,6,7,5,2,4,3]=>100000=>000001=>[6,1]
[1,6,7,5,3,2,4]=>100000=>000001=>[6,1]
[1,6,7,5,3,4,2]=>100000=>000001=>[6,1]
[1,6,7,5,4,2,3]=>100000=>000001=>[6,1]
[1,6,7,5,4,3,2]=>100000=>000001=>[6,1]
[1,7,2,3,4,5,6]=>100000=>000001=>[6,1]
[1,7,2,3,4,6,5]=>100000=>000001=>[6,1]
[1,7,2,3,5,4,6]=>100000=>000001=>[6,1]
[1,7,2,3,5,6,4]=>100000=>000001=>[6,1]
[1,7,2,3,6,4,5]=>100000=>000001=>[6,1]
[1,7,2,3,6,5,4]=>100000=>000001=>[6,1]
[1,7,2,4,3,5,6]=>100000=>000001=>[6,1]
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[1,7,2,4,5,6,3]=>100000=>000001=>[6,1]
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[1,7,2,4,6,5,3]=>100000=>000001=>[6,1]
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[1,7,3,5,2,6,4]=>100000=>000001=>[6,1]
[1,7,3,5,4,2,6]=>100000=>000001=>[6,1]
[1,7,3,5,4,6,2]=>100000=>000001=>[6,1]
[1,7,3,5,6,2,4]=>100000=>000001=>[6,1]
[1,7,3,5,6,4,2]=>100000=>000001=>[6,1]
[1,7,3,6,2,4,5]=>100000=>000001=>[6,1]
[1,7,3,6,2,5,4]=>100000=>000001=>[6,1]
[1,7,3,6,4,2,5]=>100000=>000001=>[6,1]
[1,7,3,6,4,5,2]=>100000=>000001=>[6,1]
[1,7,3,6,5,2,4]=>100000=>000001=>[6,1]
[1,7,3,6,5,4,2]=>100000=>000001=>[6,1]
[1,7,4,2,3,5,6]=>100000=>000001=>[6,1]
[1,7,4,2,3,6,5]=>100000=>000001=>[6,1]
[1,7,4,2,5,3,6]=>100000=>000001=>[6,1]
[1,7,4,2,5,6,3]=>100000=>000001=>[6,1]
[1,7,4,2,6,3,5]=>100000=>000001=>[6,1]
[1,7,4,2,6,5,3]=>100000=>000001=>[6,1]
[1,7,4,3,2,5,6]=>100000=>000001=>[6,1]
[1,7,4,3,2,6,5]=>100000=>000001=>[6,1]
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[1,7,4,3,5,6,2]=>100000=>000001=>[6,1]
[1,7,4,3,6,2,5]=>100000=>000001=>[6,1]
[1,7,4,3,6,5,2]=>100000=>000001=>[6,1]
[1,7,4,5,2,3,6]=>100000=>000001=>[6,1]
[1,7,4,5,2,6,3]=>100000=>000001=>[6,1]
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[1,7,4,5,3,6,2]=>100000=>000001=>[6,1]
[1,7,4,5,6,2,3]=>100000=>000001=>[6,1]
[1,7,4,5,6,3,2]=>100000=>000001=>[6,1]
[1,7,4,6,2,3,5]=>100000=>000001=>[6,1]
[1,7,4,6,2,5,3]=>100000=>000001=>[6,1]
[1,7,4,6,3,2,5]=>100000=>000001=>[6,1]
[1,7,4,6,3,5,2]=>100000=>000001=>[6,1]
[1,7,4,6,5,2,3]=>100000=>000001=>[6,1]
[1,7,4,6,5,3,2]=>100000=>000001=>[6,1]
[1,7,5,2,3,4,6]=>100000=>000001=>[6,1]
[1,7,5,2,3,6,4]=>100000=>000001=>[6,1]
[1,7,5,2,4,3,6]=>100000=>000001=>[6,1]
[1,7,5,2,4,6,3]=>100000=>000001=>[6,1]
[1,7,5,2,6,3,4]=>100000=>000001=>[6,1]
[1,7,5,2,6,4,3]=>100000=>000001=>[6,1]
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[1,7,5,3,2,6,4]=>100000=>000001=>[6,1]
[1,7,5,3,4,2,6]=>100000=>000001=>[6,1]
[1,7,5,3,4,6,2]=>100000=>000001=>[6,1]
[1,7,5,3,6,2,4]=>100000=>000001=>[6,1]
[1,7,5,3,6,4,2]=>100000=>000001=>[6,1]
[1,7,5,4,2,3,6]=>100000=>000001=>[6,1]
[1,7,5,4,2,6,3]=>100000=>000001=>[6,1]
[1,7,5,4,3,2,6]=>100000=>000001=>[6,1]
[1,7,5,4,3,6,2]=>100000=>000001=>[6,1]
[1,7,5,4,6,2,3]=>100000=>000001=>[6,1]
[1,7,5,4,6,3,2]=>100000=>000001=>[6,1]
[1,7,5,6,2,3,4]=>100000=>000001=>[6,1]
[1,7,5,6,2,4,3]=>100000=>000001=>[6,1]
[1,7,5,6,3,2,4]=>100000=>000001=>[6,1]
[1,7,5,6,3,4,2]=>100000=>000001=>[6,1]
[1,7,5,6,4,2,3]=>100000=>000001=>[6,1]
[1,7,5,6,4,3,2]=>100000=>000001=>[6,1]
[1,7,6,2,3,4,5]=>100000=>000001=>[6,1]
[1,7,6,2,3,5,4]=>100000=>000001=>[6,1]
[1,7,6,2,4,3,5]=>100000=>000001=>[6,1]
[1,7,6,2,4,5,3]=>100000=>000001=>[6,1]
[1,7,6,2,5,3,4]=>100000=>000001=>[6,1]
[1,7,6,2,5,4,3]=>100000=>000001=>[6,1]
[1,7,6,3,2,4,5]=>100000=>000001=>[6,1]
[1,7,6,3,2,5,4]=>100000=>000001=>[6,1]
[1,7,6,3,4,2,5]=>100000=>000001=>[6,1]
[1,7,6,3,4,5,2]=>100000=>000001=>[6,1]
[1,7,6,3,5,2,4]=>100000=>000001=>[6,1]
[1,7,6,3,5,4,2]=>100000=>000001=>[6,1]
[1,7,6,4,2,3,5]=>100000=>000001=>[6,1]
[1,7,6,4,2,5,3]=>100000=>000001=>[6,1]
[1,7,6,4,3,2,5]=>100000=>000001=>[6,1]
[1,7,6,4,3,5,2]=>100000=>000001=>[6,1]
[1,7,6,4,5,2,3]=>100000=>000001=>[6,1]
[1,7,6,4,5,3,2]=>100000=>000001=>[6,1]
[1,7,6,5,2,3,4]=>100000=>000001=>[6,1]
[1,7,6,5,2,4,3]=>100000=>000001=>[6,1]
[1,7,6,5,3,2,4]=>100000=>000001=>[6,1]
[1,7,6,5,3,4,2]=>100000=>000001=>[6,1]
[1,7,6,5,4,2,3]=>100000=>000001=>[6,1]
[1,7,6,5,4,3,2]=>100000=>000001=>[6,1]
[2,1,3,4,5,6,7]=>011111=>111110=>[1,1,1,1,1,2]
[2,1,3,4,5,7,6]=>011110=>011110=>[2,1,1,1,2]
[2,1,3,4,6,5,7]=>011101=>101110=>[1,2,1,1,2]
[2,1,3,4,6,7,5]=>011100=>001110=>[3,1,1,2]
[2,1,3,4,7,5,6]=>011100=>001110=>[3,1,1,2]
[2,1,3,4,7,6,5]=>011100=>001110=>[3,1,1,2]
[2,1,3,5,4,6,7]=>011011=>110110=>[1,1,2,1,2]
[2,1,3,5,4,7,6]=>011010=>010110=>[2,2,1,2]
[2,1,3,5,6,4,7]=>011001=>100110=>[1,3,1,2]
[2,1,3,5,6,7,4]=>011000=>000110=>[4,1,2]
[2,1,3,5,7,4,6]=>011000=>000110=>[4,1,2]
[2,1,3,5,7,6,4]=>011000=>000110=>[4,1,2]
[2,1,3,6,4,5,7]=>011001=>100110=>[1,3,1,2]
[2,1,3,6,4,7,5]=>011000=>000110=>[4,1,2]
[2,1,3,6,5,4,7]=>011001=>100110=>[1,3,1,2]
[2,1,3,6,5,7,4]=>011000=>000110=>[4,1,2]
[2,1,3,6,7,4,5]=>011000=>000110=>[4,1,2]
[2,1,3,6,7,5,4]=>011000=>000110=>[4,1,2]
[2,1,3,7,4,5,6]=>011000=>000110=>[4,1,2]
[2,1,3,7,4,6,5]=>011000=>000110=>[4,1,2]
[2,1,3,7,5,4,6]=>011000=>000110=>[4,1,2]
[2,1,3,7,5,6,4]=>011000=>000110=>[4,1,2]
[2,1,3,7,6,4,5]=>011000=>000110=>[4,1,2]
[2,1,3,7,6,5,4]=>011000=>000110=>[4,1,2]
[2,1,4,3,5,6,7]=>010111=>111010=>[1,1,1,2,2]
[2,1,4,3,5,7,6]=>010110=>011010=>[2,1,2,2]
[2,1,4,3,6,5,7]=>010101=>101010=>[1,2,2,2]
[2,1,4,3,6,7,5]=>010100=>001010=>[3,2,2]
[2,1,4,3,7,5,6]=>010100=>001010=>[3,2,2]
[2,1,4,3,7,6,5]=>010100=>001010=>[3,2,2]
[2,1,4,5,3,6,7]=>010011=>110010=>[1,1,3,2]
[2,1,4,5,3,7,6]=>010010=>010010=>[2,3,2]
[2,1,4,5,6,3,7]=>010001=>100010=>[1,4,2]
[2,1,4,5,6,7,3]=>010000=>000010=>[5,2]
[2,1,4,5,7,3,6]=>010000=>000010=>[5,2]
[2,1,4,5,7,6,3]=>010000=>000010=>[5,2]
[2,1,4,6,3,5,7]=>010001=>100010=>[1,4,2]
[2,1,4,6,3,7,5]=>010000=>000010=>[5,2]
[2,1,4,6,5,3,7]=>010001=>100010=>[1,4,2]
[2,1,4,6,5,7,3]=>010000=>000010=>[5,2]
[2,1,4,6,7,3,5]=>010000=>000010=>[5,2]
[2,1,4,6,7,5,3]=>010000=>000010=>[5,2]
[2,1,4,7,3,5,6]=>010000=>000010=>[5,2]
[2,1,4,7,3,6,5]=>010000=>000010=>[5,2]
[2,1,4,7,5,3,6]=>010000=>000010=>[5,2]
[2,1,4,7,5,6,3]=>010000=>000010=>[5,2]
[2,1,4,7,6,3,5]=>010000=>000010=>[5,2]
[2,1,4,7,6,5,3]=>010000=>000010=>[5,2]
[2,1,5,3,4,6,7]=>010011=>110010=>[1,1,3,2]
[2,1,5,3,4,7,6]=>010010=>010010=>[2,3,2]
[2,1,5,3,6,4,7]=>010001=>100010=>[1,4,2]
[2,1,5,3,6,7,4]=>010000=>000010=>[5,2]
[2,1,5,3,7,4,6]=>010000=>000010=>[5,2]
[2,1,5,3,7,6,4]=>010000=>000010=>[5,2]
[2,1,5,4,3,6,7]=>010011=>110010=>[1,1,3,2]
[2,1,5,4,3,7,6]=>010010=>010010=>[2,3,2]
[2,1,5,4,6,3,7]=>010001=>100010=>[1,4,2]
[2,1,5,4,6,7,3]=>010000=>000010=>[5,2]
[2,1,5,4,7,3,6]=>010000=>000010=>[5,2]
[2,1,5,4,7,6,3]=>010000=>000010=>[5,2]
[2,1,5,6,3,4,7]=>010001=>100010=>[1,4,2]
[2,1,5,6,3,7,4]=>010000=>000010=>[5,2]
[2,1,5,6,4,3,7]=>010001=>100010=>[1,4,2]
[2,1,5,6,4,7,3]=>010000=>000010=>[5,2]
[2,1,5,6,7,3,4]=>010000=>000010=>[5,2]
[2,1,5,6,7,4,3]=>010000=>000010=>[5,2]
[2,1,5,7,3,4,6]=>010000=>000010=>[5,2]
[2,1,5,7,3,6,4]=>010000=>000010=>[5,2]
[2,1,5,7,4,3,6]=>010000=>000010=>[5,2]
[2,1,5,7,4,6,3]=>010000=>000010=>[5,2]
[2,1,5,7,6,3,4]=>010000=>000010=>[5,2]
[2,1,5,7,6,4,3]=>010000=>000010=>[5,2]
[2,1,6,3,4,5,7]=>010001=>100010=>[1,4,2]
[2,1,6,3,4,7,5]=>010000=>000010=>[5,2]
[2,1,6,3,5,4,7]=>010001=>100010=>[1,4,2]
[2,1,6,3,5,7,4]=>010000=>000010=>[5,2]
[2,1,6,3,7,4,5]=>010000=>000010=>[5,2]
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[2,1,6,4,3,5,7]=>010001=>100010=>[1,4,2]
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[2,1,6,4,5,3,7]=>010001=>100010=>[1,4,2]
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[2,1,6,5,4,3,7]=>010001=>100010=>[1,4,2]
[2,1,6,5,4,7,3]=>010000=>000010=>[5,2]
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[2,1,6,5,7,4,3]=>010000=>000010=>[5,2]
[2,1,6,7,3,4,5]=>010000=>000010=>[5,2]
[2,1,6,7,3,5,4]=>010000=>000010=>[5,2]
[2,1,6,7,4,3,5]=>010000=>000010=>[5,2]
[2,1,6,7,4,5,3]=>010000=>000010=>[5,2]
[2,1,6,7,5,3,4]=>010000=>000010=>[5,2]
[2,1,6,7,5,4,3]=>010000=>000010=>[5,2]
[2,1,7,3,4,5,6]=>010000=>000010=>[5,2]
[2,1,7,3,4,6,5]=>010000=>000010=>[5,2]
[2,1,7,3,5,4,6]=>010000=>000010=>[5,2]
[2,1,7,3,5,6,4]=>010000=>000010=>[5,2]
[2,1,7,3,6,4,5]=>010000=>000010=>[5,2]
[2,1,7,3,6,5,4]=>010000=>000010=>[5,2]
[2,1,7,4,3,5,6]=>010000=>000010=>[5,2]
[2,1,7,4,3,6,5]=>010000=>000010=>[5,2]
[2,1,7,4,5,3,6]=>010000=>000010=>[5,2]
[2,1,7,4,5,6,3]=>010000=>000010=>[5,2]
[2,1,7,4,6,3,5]=>010000=>000010=>[5,2]
[2,1,7,4,6,5,3]=>010000=>000010=>[5,2]
[2,1,7,5,3,4,6]=>010000=>000010=>[5,2]
[2,1,7,5,3,6,4]=>010000=>000010=>[5,2]
[2,1,7,5,4,3,6]=>010000=>000010=>[5,2]
[2,1,7,5,4,6,3]=>010000=>000010=>[5,2]
[2,1,7,5,6,3,4]=>010000=>000010=>[5,2]
[2,1,7,5,6,4,3]=>010000=>000010=>[5,2]
[2,1,7,6,3,4,5]=>010000=>000010=>[5,2]
[2,1,7,6,3,5,4]=>010000=>000010=>[5,2]
[2,1,7,6,4,3,5]=>010000=>000010=>[5,2]
[2,1,7,6,4,5,3]=>010000=>000010=>[5,2]
[2,1,7,6,5,3,4]=>010000=>000010=>[5,2]
[2,1,7,6,5,4,3]=>010000=>000010=>[5,2]
[2,3,1,4,5,6,7]=>001111=>111100=>[1,1,1,1,3]
[2,3,1,4,5,7,6]=>001110=>011100=>[2,1,1,3]
[2,3,1,4,6,5,7]=>001101=>101100=>[1,2,1,3]
[2,3,1,4,6,7,5]=>001100=>001100=>[3,1,3]
[2,3,1,4,7,5,6]=>001100=>001100=>[3,1,3]
[2,3,1,4,7,6,5]=>001100=>001100=>[3,1,3]
[2,3,1,5,4,6,7]=>001011=>110100=>[1,1,2,3]
[2,3,1,5,4,7,6]=>001010=>010100=>[2,2,3]
[2,3,1,5,6,4,7]=>001001=>100100=>[1,3,3]
[2,3,1,5,6,7,4]=>001000=>000100=>[4,3]
[2,3,1,5,7,4,6]=>001000=>000100=>[4,3]
[2,3,1,5,7,6,4]=>001000=>000100=>[4,3]
[2,3,1,6,4,5,7]=>001001=>100100=>[1,3,3]
[2,3,1,6,4,7,5]=>001000=>000100=>[4,3]
[2,3,1,6,5,4,7]=>001001=>100100=>[1,3,3]
[2,3,1,6,5,7,4]=>001000=>000100=>[4,3]
[2,3,1,6,7,4,5]=>001000=>000100=>[4,3]
[2,3,1,6,7,5,4]=>001000=>000100=>[4,3]
[2,3,1,7,4,5,6]=>001000=>000100=>[4,3]
[2,3,1,7,4,6,5]=>001000=>000100=>[4,3]
[2,3,1,7,5,4,6]=>001000=>000100=>[4,3]
[2,3,1,7,5,6,4]=>001000=>000100=>[4,3]
[2,3,1,7,6,4,5]=>001000=>000100=>[4,3]
[2,3,1,7,6,5,4]=>001000=>000100=>[4,3]
[2,3,4,1,5,6,7]=>000111=>111000=>[1,1,1,4]
[2,3,4,1,5,7,6]=>000110=>011000=>[2,1,4]
[2,3,4,1,6,5,7]=>000101=>101000=>[1,2,4]
[2,3,4,1,6,7,5]=>000100=>001000=>[3,4]
[2,3,4,1,7,5,6]=>000100=>001000=>[3,4]
[2,3,4,1,7,6,5]=>000100=>001000=>[3,4]
[2,3,4,5,1,6,7]=>000011=>110000=>[1,1,5]
[2,3,4,5,1,7,6]=>000010=>010000=>[2,5]
[2,3,4,5,6,1,7]=>000001=>100000=>[1,6]
[2,3,4,5,6,7,1]=>000000=>000000=>[7]
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[2,3,4,5,7,6,1]=>000000=>000000=>[7]
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[2,3,5,1,4,6,7]=>000011=>110000=>[1,1,5]
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[2,3,5,4,1,6,7]=>000011=>110000=>[1,1,5]
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[2,3,7,6,5,4,1]=>000000=>000000=>[7]
[2,4,1,3,5,6,7]=>000111=>111000=>[1,1,1,4]
[2,4,1,3,5,7,6]=>000110=>011000=>[2,1,4]
[2,4,1,3,6,5,7]=>000101=>101000=>[1,2,4]
[2,4,1,3,6,7,5]=>000100=>001000=>[3,4]
[2,4,1,3,7,5,6]=>000100=>001000=>[3,4]
[2,4,1,3,7,6,5]=>000100=>001000=>[3,4]
[2,4,1,5,3,6,7]=>000011=>110000=>[1,1,5]
[2,4,1,5,3,7,6]=>000010=>010000=>[2,5]
[2,4,1,5,6,3,7]=>000001=>100000=>[1,6]
[2,4,1,5,6,7,3]=>000000=>000000=>[7]
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[8,7,6,2,3,4,5,1]=>0000000=>0000000=>[8]
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[8,6,7,2,3,4,5,1]=>0000000=>0000000=>[8]
[7,6,8,2,3,4,5,1]=>0000000=>0000000=>[8]
[6,7,8,2,3,4,5,1]=>0000000=>0000000=>[8]
[7,8,4,3,5,2,6,1]=>0000000=>0000000=>[8]
[7,8,4,3,2,5,6,1]=>0000000=>0000000=>[8]
[8,4,5,3,6,2,7,1]=>0000000=>0000000=>[8]
[8,6,4,2,3,5,7,1]=>0000000=>0000000=>[8]
[4,5,6,7,3,2,8,1]=>0000000=>0000000=>[8]
[6,5,4,3,7,2,8,1]=>0000000=>0000000=>[8]
[6,4,5,3,7,2,8,1]=>0000000=>0000000=>[8]
[5,4,6,3,7,2,8,1]=>0000000=>0000000=>[8]
[6,5,3,4,7,2,8,1]=>0000000=>0000000=>[8]
[5,6,3,4,7,2,8,1]=>0000000=>0000000=>[8]
[5,4,3,6,7,2,8,1]=>0000000=>0000000=>[8]
[6,7,5,4,2,3,8,1]=>0000000=>0000000=>[8]
[6,5,7,4,2,3,8,1]=>0000000=>0000000=>[8]
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[6,5,7,3,2,4,8,1]=>0000000=>0000000=>[8]
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[5,4,6,3,2,7,8,1]=>0000000=>0000000=>[8]
[5,4,3,6,2,7,8,1]=>0000000=>0000000=>[8]
[3,4,5,6,2,7,8,1]=>0000000=>0000000=>[8]
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[5,4,6,2,3,7,8,1]=>0000000=>0000000=>[8]
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[2,3,4,5,6,7,8,1]=>0000000=>0000000=>[8]
[7,8,6,5,4,3,1,2]=>0000000=>0000000=>[8]
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[4,3,5,6,7,8,1,2]=>0000000=>0000000=>[8]
[3,4,5,6,7,8,1,2]=>0000000=>0000000=>[8]
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[7,6,3,2,4,5,1,8]=>0000001=>1000000=>[1,7]
[6,7,3,2,4,5,1,8]=>0000001=>1000000=>[1,7]
[7,6,2,3,4,5,1,8]=>0000001=>1000000=>[1,7]
[7,4,5,3,2,6,1,8]=>0000001=>1000000=>[1,7]
[7,4,3,5,2,6,1,8]=>0000001=>1000000=>[1,7]
[7,5,3,2,4,6,1,8]=>0000001=>1000000=>[1,7]
[5,4,6,3,2,7,1,8]=>0000001=>1000000=>[1,7]
[5,6,3,4,2,7,1,8]=>0000001=>1000000=>[1,7]
[6,3,4,5,2,7,1,8]=>0000001=>1000000=>[1,7]
[5,4,3,6,2,7,1,8]=>0000001=>1000000=>[1,7]
[4,5,3,6,2,7,1,8]=>0000001=>1000000=>[1,7]
[3,4,5,6,2,7,1,8]=>0000001=>1000000=>[1,7]
[6,3,2,4,5,7,1,8]=>0000001=>1000000=>[1,7]
[6,2,3,4,5,7,1,8]=>0000001=>1000000=>[1,7]
[5,4,3,2,6,7,1,8]=>0000001=>1000000=>[1,7]
[6,5,7,3,4,1,2,8]=>0000001=>1000000=>[1,7]
[6,7,3,4,5,1,2,8]=>0000001=>1000000=>[1,7]
[6,4,5,3,7,1,2,8]=>0000001=>1000000=>[1,7]
[3,4,5,6,7,1,2,8]=>0000001=>1000000=>[1,7]
[5,6,7,4,1,2,3,8]=>0000001=>1000000=>[1,7]
[5,6,4,7,1,2,3,8]=>0000001=>1000000=>[1,7]
[5,4,6,7,1,2,3,8]=>0000001=>1000000=>[1,7]
[5,6,7,3,1,2,4,8]=>0000001=>1000000=>[1,7]
[5,6,7,2,1,3,4,8]=>0000001=>1000000=>[1,7]
[7,6,5,1,2,3,4,8]=>0000001=>1000000=>[1,7]
[6,7,5,1,2,3,4,8]=>0000001=>1000000=>[1,7]
[7,5,6,1,2,3,4,8]=>0000001=>1000000=>[1,7]
[6,5,7,1,2,3,4,8]=>0000001=>1000000=>[1,7]
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[7,3,1,2,4,5,6,8]=>0000001=>1000000=>[1,7]
[7,1,2,3,4,5,6,8]=>0000001=>1000000=>[1,7]
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[4,5,6,3,2,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,3,6,2,1,7,8]=>0000011=>1100000=>[1,1,6]
[3,4,5,6,2,1,7,8]=>0000011=>1100000=>[1,1,6]
[6,5,2,3,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,6,2,3,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[6,4,3,2,5,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,3,2,6,1,7,8]=>0000011=>1100000=>[1,1,6]
[4,5,3,2,6,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,3,2,4,6,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,6,4,3,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,6,3,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,6,3,4,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[6,4,3,5,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,3,6,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,6,4,2,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,6,2,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[5,6,3,2,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[6,4,3,2,1,5,7,8]=>0000011=>1100000=>[1,1,6]
[6,3,4,2,1,5,7,8]=>0000011=>1100000=>[1,1,6]
[6,4,3,1,2,5,7,8]=>0000011=>1100000=>[1,1,6]
[6,4,2,1,3,5,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,3,2,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,5,3,2,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,3,4,2,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,3,5,2,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[3,4,5,2,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,4,2,3,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,5,2,3,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,3,2,4,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,2,3,4,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,3,2,5,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[3,4,2,5,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,2,3,5,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[3,2,4,5,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[2,3,4,5,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,4,3,1,2,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,3,4,1,2,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,4,2,1,3,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,4,1,2,3,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,5,1,2,3,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,3,2,1,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,2,3,1,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,3,1,2,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,2,1,3,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,1,2,3,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,3,2,1,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[3,4,2,1,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[4,2,3,1,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[3,2,4,1,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[2,3,4,1,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[4,3,1,2,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[3,4,1,2,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[4,2,1,3,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[4,1,2,3,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[3,2,1,4,5,6,7,8]=>0011111=>1111100=>[1,1,1,1,1,3]
[2,3,1,4,5,6,7,8]=>0011111=>1111100=>[1,1,1,1,1,3]
[3,1,2,4,5,6,7,8]=>0011111=>1111100=>[1,1,1,1,1,3]
[2,1,3,4,5,6,7,8]=>0111111=>1111110=>[1,1,1,1,1,1,2]
[1,2,3,4,5,6,7,8]=>1111111=>1111111=>[1,1,1,1,1,1,1,1]
[5,8,7,6,4,3,2,1]=>0000000=>0000000=>[8]
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[4,6,7,5,8,3,2,1]=>0000000=>0000000=>[8]
[5,4,7,6,8,3,2,1]=>0000000=>0000000=>[8]
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[3,4,8,7,6,5,2,1]=>0000000=>0000000=>[8]
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[4,3,5,7,8,6,2,1]=>0000000=>0000000=>[8]
[4,5,6,3,8,7,2,1]=>0000000=>0000000=>[8]
[4,3,6,5,8,7,2,1]=>0000000=>0000000=>[8]
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[4,3,5,6,8,7,2,1]=>0000000=>0000000=>[8]
[3,4,7,6,5,8,2,1]=>0000000=>0000000=>[8]
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[4,3,5,7,6,8,2,1]=>0000000=>0000000=>[8]
[3,4,6,5,7,8,2,1]=>0000000=>0000000=>[8]
[2,8,7,6,5,4,3,1]=>0000000=>0000000=>[8]
[2,5,6,7,8,4,3,1]=>0000000=>0000000=>[8]
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[2,4,6,8,7,5,3,1]=>0000000=>0000000=>[8]
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[2,3,5,6,7,8,4,1]=>0000000=>0000000=>[8]
[4,3,2,8,7,6,5,1]=>0000000=>0000000=>[8]
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[2,4,3,8,7,6,5,1]=>0000000=>0000000=>[8]
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[5,4,3,2,8,7,6,1]=>0000000=>0000000=>[8]
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[2,4,5,3,8,7,6,1]=>0000000=>0000000=>[8]
[2,3,5,4,8,7,6,1]=>0000000=>0000000=>[8]
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[6,5,4,3,2,8,7,1]=>0000000=>0000000=>[8]
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[2,4,6,5,3,8,7,1]=>0000000=>0000000=>[8]
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[3,4,2,6,5,8,7,1]=>0000000=>0000000=>[8]
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[2,3,4,5,6,8,7,1]=>0000000=>0000000=>[8]
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[2,4,6,5,7,3,8,1]=>0000000=>0000000=>[8]
[3,2,6,7,5,4,8,1]=>0000000=>0000000=>[8]
[2,3,7,6,5,4,8,1]=>0000000=>0000000=>[8]
[4,3,2,7,6,5,8,1]=>0000000=>0000000=>[8]
[3,4,2,7,6,5,8,1]=>0000000=>0000000=>[8]
[2,4,3,7,6,5,8,1]=>0000000=>0000000=>[8]
[3,2,4,7,6,5,8,1]=>0000000=>0000000=>[8]
[2,3,4,7,6,5,8,1]=>0000000=>0000000=>[8]
[5,4,3,2,7,6,8,1]=>0000000=>0000000=>[8]
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[2,6,5,4,3,7,8,1]=>0000000=>0000000=>[8]
[2,3,6,5,4,7,8,1]=>0000000=>0000000=>[8]
[4,3,2,6,5,7,8,1]=>0000000=>0000000=>[8]
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[2,3,4,6,5,7,8,1]=>0000000=>0000000=>[8]
[2,5,4,3,6,7,8,1]=>0000000=>0000000=>[8]
[2,4,3,5,6,7,8,1]=>0000000=>0000000=>[8]
[1,8,7,6,5,4,3,2]=>1000000=>0000001=>[7,1]
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[1,6,8,7,5,4,3,2]=>1000000=>0000001=>[7,1]
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[1,7,6,5,8,4,3,2]=>1000000=>0000001=>[7,1]
[1,6,7,5,8,4,3,2]=>1000000=>0000001=>[7,1]
[1,5,7,6,8,4,3,2]=>1000000=>0000001=>[7,1]
[1,6,5,7,8,4,3,2]=>1000000=>0000001=>[7,1]
[1,5,6,7,8,4,3,2]=>1000000=>0000001=>[7,1]
[1,4,8,7,6,5,3,2]=>1000000=>0000001=>[7,1]
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[1,4,6,8,7,5,3,2]=>1000000=>0000001=>[7,1]
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[1,4,6,5,8,7,3,2]=>1000000=>0000001=>[7,1]
[1,4,7,6,5,8,3,2]=>1000000=>0000001=>[7,1]
[1,6,5,4,7,8,3,2]=>1000000=>0000001=>[7,1]
[1,5,4,6,7,8,3,2]=>1000000=>0000001=>[7,1]
[1,3,8,7,6,5,4,2]=>1000000=>0000001=>[7,1]
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[1,3,6,7,8,5,4,2]=>1000000=>0000001=>[7,1]
[1,3,5,8,7,6,4,2]=>1000000=>0000001=>[7,1]
[1,3,5,7,8,6,4,2]=>1000000=>0000001=>[7,1]
[1,3,6,5,7,8,4,2]=>1000000=>0000001=>[7,1]
[1,3,5,6,7,8,4,2]=>1000000=>0000001=>[7,1]
[1,4,3,8,7,6,5,2]=>1000000=>0000001=>[7,1]
[1,4,3,7,8,6,5,2]=>1000000=>0000001=>[7,1]
[1,4,3,6,8,7,5,2]=>1000000=>0000001=>[7,1]
[1,4,3,7,6,8,5,2]=>1000000=>0000001=>[7,1]
[1,3,4,8,7,6,5,2]=>1000000=>0000001=>[7,1]
[1,3,4,7,6,8,5,2]=>1000000=>0000001=>[7,1]
[1,3,4,6,7,8,5,2]=>1000000=>0000001=>[7,1]
[1,4,3,5,8,7,6,2]=>1000000=>0000001=>[7,1]
[1,4,3,5,7,8,6,2]=>1000000=>0000001=>[7,1]
[1,6,5,4,3,8,7,2]=>1000000=>0000001=>[7,1]
[1,5,6,4,3,8,7,2]=>1000000=>0000001=>[7,1]
[1,4,6,5,3,8,7,2]=>1000000=>0000001=>[7,1]
[1,3,6,5,4,8,7,2]=>1000000=>0000001=>[7,1]
[1,4,3,6,5,8,7,2]=>1000000=>0000001=>[7,1]
[1,5,4,3,6,8,7,2]=>1000000=>0000001=>[7,1]
[1,3,4,7,6,5,8,2]=>1000000=>0000001=>[7,1]
[1,5,4,3,6,7,8,2]=>1000000=>0000001=>[7,1]
[2,1,8,7,6,5,4,3]=>0100000=>0000010=>[6,2]
[2,1,6,7,8,5,4,3]=>0100000=>0000010=>[6,2]
[2,1,5,6,7,8,4,3]=>0100000=>0000010=>[6,2]
[2,1,4,8,7,6,5,3]=>0100000=>0000010=>[6,2]
[2,1,4,7,8,6,5,3]=>0100000=>0000010=>[6,2]
[2,1,4,6,7,8,5,3]=>0100000=>0000010=>[6,2]
[2,1,4,6,5,8,7,3]=>0100000=>0000010=>[6,2]
[2,1,4,5,6,8,7,3]=>0100000=>0000010=>[6,2]
[2,1,5,6,7,4,8,3]=>0100000=>0000010=>[6,2]
[2,1,4,7,6,5,8,3]=>0100000=>0000010=>[6,2]
[2,1,5,4,7,6,8,3]=>0100000=>0000010=>[6,2]
[1,2,8,7,6,5,4,3]=>1100000=>0000011=>[6,1,1]
[1,2,6,7,8,5,4,3]=>1100000=>0000011=>[6,1,1]
[1,2,5,6,7,8,4,3]=>1100000=>0000011=>[6,1,1]
[1,2,4,8,7,6,5,3]=>1100000=>0000011=>[6,1,1]
[1,2,4,7,8,6,5,3]=>1100000=>0000011=>[6,1,1]
[1,2,4,6,8,7,5,3]=>1100000=>0000011=>[6,1,1]
[1,2,5,4,8,7,6,3]=>1100000=>0000011=>[6,1,1]
[1,2,5,4,7,8,6,3]=>1100000=>0000011=>[6,1,1]
[1,2,6,5,4,8,7,3]=>1100000=>0000011=>[6,1,1]
[1,2,4,6,5,8,7,3]=>1100000=>0000011=>[6,1,1]
[1,2,5,4,6,8,7,3]=>1100000=>0000011=>[6,1,1]
[1,2,4,7,6,5,8,3]=>1100000=>0000011=>[6,1,1]
[3,2,1,8,7,6,5,4]=>0010000=>0000100=>[5,3]
[3,2,1,7,8,6,5,4]=>0010000=>0000100=>[5,3]
[3,2,1,6,8,7,5,4]=>0010000=>0000100=>[5,3]
[3,2,1,7,6,8,5,4]=>0010000=>0000100=>[5,3]
[3,2,1,6,7,8,5,4]=>0010000=>0000100=>[5,3]
[3,2,1,5,8,7,6,4]=>0010000=>0000100=>[5,3]
[3,2,1,5,7,8,6,4]=>0010000=>0000100=>[5,3]
[3,2,1,6,5,8,7,4]=>0010000=>0000100=>[5,3]
[3,2,1,5,6,8,7,4]=>0010000=>0000100=>[5,3]
[3,2,1,7,6,5,8,4]=>0010000=>0000100=>[5,3]
[3,2,1,6,7,5,8,4]=>0010000=>0000100=>[5,3]
[3,2,1,5,7,6,8,4]=>0010000=>0000100=>[5,3]
[3,2,1,6,5,7,8,4]=>0010000=>0000100=>[5,3]
[3,2,1,5,6,7,8,4]=>0010000=>0000100=>[5,3]
[2,3,1,8,7,6,5,4]=>0010000=>0000100=>[5,3]
[2,3,1,6,8,7,5,4]=>0010000=>0000100=>[5,3]
[2,3,1,7,6,8,5,4]=>0010000=>0000100=>[5,3]
[2,3,1,6,7,8,5,4]=>0010000=>0000100=>[5,3]
[2,3,1,6,5,8,7,4]=>0010000=>0000100=>[5,3]
[2,3,1,5,6,7,8,4]=>0010000=>0000100=>[5,3]
[1,3,2,8,7,6,5,4]=>1010000=>0000101=>[5,2,1]
[1,3,2,6,8,7,5,4]=>1010000=>0000101=>[5,2,1]
[1,3,2,6,5,8,7,4]=>1010000=>0000101=>[5,2,1]
[2,1,3,8,7,6,5,4]=>0110000=>0000110=>[5,1,2]
[2,1,3,7,8,6,5,4]=>0110000=>0000110=>[5,1,2]
[2,1,3,6,8,7,5,4]=>0110000=>0000110=>[5,1,2]
[1,2,3,8,7,6,5,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,8,6,5,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,6,8,7,5,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,6,8,5,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,6,7,8,5,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,5,8,7,6,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,5,7,8,6,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,6,5,8,7,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,5,6,8,7,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,6,5,8,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,6,7,5,8,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,5,7,6,8,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,6,5,7,8,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,5,6,7,8,4]=>1110000=>0000111=>[5,1,1,1]
[4,3,2,1,8,7,6,5]=>0001000=>0001000=>[4,4]
[4,3,2,1,7,8,6,5]=>0001000=>0001000=>[4,4]
[4,3,2,1,6,8,7,5]=>0001000=>0001000=>[4,4]
[4,3,2,1,7,6,8,5]=>0001000=>0001000=>[4,4]
[4,3,2,1,6,7,8,5]=>0001000=>0001000=>[4,4]
[3,4,2,1,8,7,6,5]=>0001000=>0001000=>[4,4]
[3,4,2,1,7,8,6,5]=>0001000=>0001000=>[4,4]
[3,4,2,1,6,7,8,5]=>0001000=>0001000=>[4,4]
[2,4,3,1,8,7,6,5]=>0001000=>0001000=>[4,4]
[2,4,3,1,7,6,8,5]=>0001000=>0001000=>[4,4]
[3,2,4,1,8,7,6,5]=>0001000=>0001000=>[4,4]
[3,2,4,1,7,8,6,5]=>0001000=>0001000=>[4,4]
[3,2,4,1,6,8,7,5]=>0001000=>0001000=>[4,4]
[2,3,4,1,8,7,6,5]=>0001000=>0001000=>[4,4]
[2,3,4,1,6,7,8,5]=>0001000=>0001000=>[4,4]
[1,4,3,2,8,7,6,5]=>1001000=>0001001=>[4,3,1]
[1,4,3,2,6,7,8,5]=>1001000=>0001001=>[4,3,1]
[1,3,4,2,8,7,6,5]=>1001000=>0001001=>[4,3,1]
[1,3,4,2,7,8,6,5]=>1001000=>0001001=>[4,3,1]
[1,3,4,2,6,8,7,5]=>1001000=>0001001=>[4,3,1]
[2,1,4,3,8,7,6,5]=>0101000=>0001010=>[4,2,2]
[2,1,4,3,7,8,6,5]=>0101000=>0001010=>[4,2,2]
[2,1,4,3,6,8,7,5]=>0101000=>0001010=>[4,2,2]
[1,2,4,3,8,7,6,5]=>1101000=>0001011=>[4,2,1,1]
[1,2,4,3,7,8,6,5]=>1101000=>0001011=>[4,2,1,1]
[1,2,4,3,6,8,7,5]=>1101000=>0001011=>[4,2,1,1]
[1,2,4,3,6,7,8,5]=>1101000=>0001011=>[4,2,1,1]
[3,2,1,4,8,7,6,5]=>0011000=>0001100=>[4,1,3]
[3,2,1,4,7,8,6,5]=>0011000=>0001100=>[4,1,3]
[3,2,1,4,6,8,7,5]=>0011000=>0001100=>[4,1,3]
[2,3,1,4,8,7,6,5]=>0011000=>0001100=>[4,1,3]
[2,3,1,4,7,8,6,5]=>0011000=>0001100=>[4,1,3]
[1,3,2,4,8,7,6,5]=>1011000=>0001101=>[4,1,2,1]
[1,3,2,4,6,8,7,5]=>1011000=>0001101=>[4,1,2,1]
[1,3,2,4,6,7,8,5]=>1011000=>0001101=>[4,1,2,1]
[2,1,3,4,8,7,6,5]=>0111000=>0001110=>[4,1,1,2]
[2,1,3,4,6,7,8,5]=>0111000=>0001110=>[4,1,1,2]
[1,2,3,4,8,7,6,5]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,3,4,7,8,6,5]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,3,4,6,8,7,5]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,3,4,7,6,8,5]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,3,4,6,7,8,5]=>1111000=>0001111=>[4,1,1,1,1]
[5,4,3,2,1,8,7,6]=>0000100=>0010000=>[3,5]
[5,4,3,2,1,7,8,6]=>0000100=>0010000=>[3,5]
[4,5,3,2,1,8,7,6]=>0000100=>0010000=>[3,5]
[3,5,4,2,1,8,7,6]=>0000100=>0010000=>[3,5]
[3,5,4,2,1,7,8,6]=>0000100=>0010000=>[3,5]
[4,3,5,2,1,8,7,6]=>0000100=>0010000=>[3,5]
[3,4,5,2,1,8,7,6]=>0000100=>0010000=>[3,5]
[2,5,4,3,1,8,7,6]=>0000100=>0010000=>[3,5]
[2,4,5,3,1,8,7,6]=>0000100=>0010000=>[3,5]
[3,2,5,4,1,8,7,6]=>0000100=>0010000=>[3,5]
[3,2,5,4,1,7,8,6]=>0000100=>0010000=>[3,5]
[2,3,5,4,1,8,7,6]=>0000100=>0010000=>[3,5]
[4,3,2,5,1,8,7,6]=>0000100=>0010000=>[3,5]
[3,4,2,5,1,8,7,6]=>0000100=>0010000=>[3,5]
[2,4,3,5,1,8,7,6]=>0000100=>0010000=>[3,5]
[3,2,4,5,1,8,7,6]=>0000100=>0010000=>[3,5]
[2,3,4,5,1,8,7,6]=>0000100=>0010000=>[3,5]
[1,2,5,4,3,7,8,6]=>1100100=>0010011=>[3,3,1,1]
[1,2,4,5,3,8,7,6]=>1100100=>0010011=>[3,3,1,1]
[1,3,2,5,4,8,7,6]=>1010100=>0010101=>[3,2,2,1]
[1,3,2,5,4,7,8,6]=>1010100=>0010101=>[3,2,2,1]
[2,1,3,5,4,8,7,6]=>0110100=>0010110=>[3,2,1,2]
[1,2,3,5,4,8,7,6]=>1110100=>0010111=>[3,2,1,1,1]
[1,2,3,5,4,7,8,6]=>1110100=>0010111=>[3,2,1,1,1]
[4,3,2,1,5,8,7,6]=>0001100=>0011000=>[3,1,4]
[4,3,2,1,5,7,8,6]=>0001100=>0011000=>[3,1,4]
[3,2,4,1,5,8,7,6]=>0001100=>0011000=>[3,1,4]
[1,4,3,2,5,8,7,6]=>1001100=>0011001=>[3,1,3,1]
[1,3,4,2,5,7,8,6]=>1001100=>0011001=>[3,1,3,1]
[1,2,4,3,5,7,8,6]=>1101100=>0011011=>[3,1,2,1,1]
[3,2,1,4,5,8,7,6]=>0011100=>0011100=>[3,1,1,3]
[3,2,1,4,5,7,8,6]=>0011100=>0011100=>[3,1,1,3]
[2,3,1,4,5,7,8,6]=>0011100=>0011100=>[3,1,1,3]
[1,2,3,4,5,8,7,6]=>1111100=>0011111=>[3,1,1,1,1,1]
[1,2,3,4,5,7,8,6]=>1111100=>0011111=>[3,1,1,1,1,1]
[6,5,4,3,2,1,8,7]=>0000010=>0100000=>[2,6]
[4,5,6,3,2,1,8,7]=>0000010=>0100000=>[2,6]
[4,3,6,5,2,1,8,7]=>0000010=>0100000=>[2,6]
[3,4,5,6,2,1,8,7]=>0000010=>0100000=>[2,6]
[5,4,3,2,6,1,8,7]=>0000010=>0100000=>[2,6]
[4,5,3,2,6,1,8,7]=>0000010=>0100000=>[2,6]
[3,5,4,2,6,1,8,7]=>0000010=>0100000=>[2,6]
[1,5,4,6,3,2,8,7]=>1000010=>0100001=>[2,5,1]
[1,3,6,5,4,2,8,7]=>1000010=>0100001=>[2,5,1]
[2,1,6,5,4,3,8,7]=>0100010=>0100010=>[2,4,2]
[2,1,5,6,4,3,8,7]=>0100010=>0100010=>[2,4,2]
[2,1,4,5,6,3,8,7]=>0100010=>0100010=>[2,4,2]
[2,3,1,6,5,4,8,7]=>0010010=>0100100=>[2,3,3]
[2,1,3,6,5,4,8,7]=>0110010=>0100110=>[2,3,1,2]
[1,2,3,6,5,4,8,7]=>1110010=>0100111=>[2,3,1,1,1]
[1,2,3,5,6,4,8,7]=>1110010=>0100111=>[2,3,1,1,1]
[4,3,2,1,6,5,8,7]=>0001010=>0101000=>[2,2,4]
[3,4,2,1,6,5,8,7]=>0001010=>0101000=>[2,2,4]
[3,2,4,1,6,5,8,7]=>0001010=>0101000=>[2,2,4]
[2,1,4,3,6,5,8,7]=>0101010=>0101010=>[2,2,2,2]
[1,2,4,3,6,5,8,7]=>1101010=>0101011=>[2,2,2,1,1]
[1,3,2,4,6,5,8,7]=>1011010=>0101101=>[2,2,1,2,1]
[2,1,3,4,6,5,8,7]=>0111010=>0101110=>[2,2,1,1,2]
[1,2,3,4,6,5,8,7]=>1111010=>0101111=>[2,2,1,1,1,1]
[5,4,3,2,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[4,5,3,2,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[3,5,4,2,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[2,5,4,3,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[2,4,5,3,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[3,2,5,4,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[1,3,5,4,2,6,8,7]=>1000110=>0110001=>[2,1,4,1]
[2,1,5,4,3,6,8,7]=>0100110=>0110010=>[2,1,3,2]
[1,2,5,4,3,6,8,7]=>1100110=>0110011=>[2,1,3,1,1]
[2,1,3,5,4,6,8,7]=>0110110=>0110110=>[2,1,2,1,2]
[4,3,2,1,5,6,8,7]=>0001110=>0111000=>[2,1,1,4]
[1,4,3,2,5,6,8,7]=>1001110=>0111001=>[2,1,1,3,1]
[2,1,4,3,5,6,8,7]=>0101110=>0111010=>[2,1,1,2,2]
[1,2,4,3,5,6,8,7]=>1101110=>0111011=>[2,1,1,2,1,1]
[2,1,3,4,5,6,8,7]=>0111110=>0111110=>[2,1,1,1,1,2]
[1,2,3,4,5,6,8,7]=>1111110=>0111111=>[2,1,1,1,1,1,1]
[5,7,6,4,3,2,1,8]=>0000001=>1000000=>[1,7]
[4,7,6,5,3,2,1,8]=>0000001=>1000000=>[1,7]
[4,6,7,5,3,2,1,8]=>0000001=>1000000=>[1,7]
[4,5,7,6,3,2,1,8]=>0000001=>1000000=>[1,7]
[4,6,5,7,3,2,1,8]=>0000001=>1000000=>[1,7]
[3,5,7,6,4,2,1,8]=>0000001=>1000000=>[1,7]
[3,5,6,7,4,2,1,8]=>0000001=>1000000=>[1,7]
[3,4,7,6,5,2,1,8]=>0000001=>1000000=>[1,7]
[4,5,3,7,6,2,1,8]=>0000001=>1000000=>[1,7]
[3,5,4,7,6,2,1,8]=>0000001=>1000000=>[1,7]
[4,3,5,7,6,2,1,8]=>0000001=>1000000=>[1,7]
[2,5,6,7,4,3,1,8]=>0000001=>1000000=>[1,7]
[2,4,6,7,5,3,1,8]=>0000001=>1000000=>[1,7]
[3,2,7,6,5,4,1,8]=>0000001=>1000000=>[1,7]
[3,2,6,7,5,4,1,8]=>0000001=>1000000=>[1,7]
[3,2,5,7,6,4,1,8]=>0000001=>1000000=>[1,7]
[2,3,7,6,5,4,1,8]=>0000001=>1000000=>[1,7]
[2,3,6,7,5,4,1,8]=>0000001=>1000000=>[1,7]
[2,3,5,7,6,4,1,8]=>0000001=>1000000=>[1,7]
[2,3,6,5,7,4,1,8]=>0000001=>1000000=>[1,7]
[2,3,5,6,7,4,1,8]=>0000001=>1000000=>[1,7]
[3,2,4,6,7,5,1,8]=>0000001=>1000000=>[1,7]
[2,3,4,7,6,5,1,8]=>0000001=>1000000=>[1,7]
[5,4,3,2,7,6,1,8]=>0000001=>1000000=>[1,7]
[4,5,3,2,7,6,1,8]=>0000001=>1000000=>[1,7]
[3,5,4,2,7,6,1,8]=>0000001=>1000000=>[1,7]
[3,2,5,4,7,6,1,8]=>0000001=>1000000=>[1,7]
[3,4,6,5,2,7,1,8]=>0000001=>1000000=>[1,7]
[3,5,4,6,2,7,1,8]=>0000001=>1000000=>[1,7]
[2,5,4,6,3,7,1,8]=>0000001=>1000000=>[1,7]
[3,2,6,5,4,7,1,8]=>0000001=>1000000=>[1,7]
[3,4,2,6,5,7,1,8]=>0000001=>1000000=>[1,7]
[2,4,3,6,5,7,1,8]=>0000001=>1000000=>[1,7]
[3,5,4,2,6,7,1,8]=>0000001=>1000000=>[1,7]
[2,5,4,3,6,7,1,8]=>0000001=>1000000=>[1,7]
[1,5,6,7,4,3,2,8]=>1000001=>1000001=>[1,6,1]
[1,4,6,5,7,3,2,8]=>1000001=>1000001=>[1,6,1]
[1,3,5,7,6,4,2,8]=>1000001=>1000001=>[1,6,1]
[1,3,5,6,7,4,2,8]=>1000001=>1000001=>[1,6,1]
[1,3,5,4,7,6,2,8]=>1000001=>1000001=>[1,6,1]
[1,4,3,5,7,6,2,8]=>1000001=>1000001=>[1,6,1]
[1,5,4,6,3,7,2,8]=>1000001=>1000001=>[1,6,1]
[1,3,6,5,4,7,2,8]=>1000001=>1000001=>[1,6,1]
[1,4,3,6,5,7,2,8]=>1000001=>1000001=>[1,6,1]
[1,3,4,5,6,7,2,8]=>1000001=>1000001=>[1,6,1]
[2,1,5,6,7,4,3,8]=>0100001=>1000010=>[1,5,2]
[1,2,5,7,6,4,3,8]=>1100001=>1000011=>[1,5,1,1]
[1,2,5,6,7,4,3,8]=>1100001=>1000011=>[1,5,1,1]
[1,2,5,6,4,7,3,8]=>1100001=>1000011=>[1,5,1,1]
[1,2,5,4,6,7,3,8]=>1100001=>1000011=>[1,5,1,1]
[3,2,1,5,7,6,4,8]=>0010001=>1000100=>[1,4,3]
[3,2,1,6,5,7,4,8]=>0010001=>1000100=>[1,4,3]
[2,3,1,6,5,7,4,8]=>0010001=>1000100=>[1,4,3]
[1,3,2,6,5,7,4,8]=>1010001=>1000101=>[1,4,2,1]
[2,1,3,6,7,5,4,8]=>0110001=>1000110=>[1,4,1,2]
[1,2,3,7,6,5,4,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,2,3,6,7,5,4,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,2,3,5,7,6,4,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,2,3,6,5,7,4,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,2,3,5,6,7,4,8]=>1110001=>1000111=>[1,4,1,1,1]
[4,3,2,1,7,6,5,8]=>0001001=>1001000=>[1,3,4]
[4,3,2,1,6,7,5,8]=>0001001=>1001000=>[1,3,4]
[1,4,3,2,7,6,5,8]=>1001001=>1001001=>[1,3,3,1]
[1,4,3,2,6,7,5,8]=>1001001=>1001001=>[1,3,3,1]
[1,3,4,2,6,7,5,8]=>1001001=>1001001=>[1,3,3,1]
[2,1,4,3,6,7,5,8]=>0101001=>1001010=>[1,3,2,2]
[1,2,4,3,6,7,5,8]=>1101001=>1001011=>[1,3,2,1,1]
[3,2,1,4,7,6,5,8]=>0011001=>1001100=>[1,3,1,3]
[1,3,2,4,7,6,5,8]=>1011001=>1001101=>[1,3,1,2,1]
[1,2,3,4,7,6,5,8]=>1111001=>1001111=>[1,3,1,1,1,1]
[1,2,3,4,6,7,5,8]=>1111001=>1001111=>[1,3,1,1,1,1]
[5,4,3,2,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[3,5,4,2,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[2,4,5,3,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[3,2,5,4,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[3,4,2,5,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[2,4,3,5,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[1,4,3,5,2,7,6,8]=>1000101=>1010001=>[1,2,4,1]
[3,2,1,5,4,7,6,8]=>0010101=>1010100=>[1,2,2,3]
[2,3,1,5,4,7,6,8]=>0010101=>1010100=>[1,2,2,3]
[1,3,2,5,4,7,6,8]=>1010101=>1010101=>[1,2,2,2,1]
[1,2,3,5,4,7,6,8]=>1110101=>1010111=>[1,2,2,1,1,1]
[4,3,2,1,5,7,6,8]=>0001101=>1011000=>[1,2,1,4]
[1,4,3,2,5,7,6,8]=>1001101=>1011001=>[1,2,1,3,1]
[1,3,2,4,5,7,6,8]=>1011101=>1011101=>[1,2,1,1,2,1]
[1,2,3,4,5,7,6,8]=>1111101=>1011111=>[1,2,1,1,1,1,1]
[4,3,6,5,2,1,7,8]=>0000011=>1100000=>[1,1,6]
[2,4,6,5,3,1,7,8]=>0000011=>1100000=>[1,1,6]
[2,4,5,6,3,1,7,8]=>0000011=>1100000=>[1,1,6]
[4,3,2,6,5,1,7,8]=>0000011=>1100000=>[1,1,6]
[3,5,4,2,6,1,7,8]=>0000011=>1100000=>[1,1,6]
[1,5,6,4,3,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,4,6,5,3,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,5,4,6,3,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,4,5,6,3,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,3,5,6,4,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,4,3,6,5,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,5,4,3,6,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[2,1,5,6,4,3,7,8]=>0100011=>1100010=>[1,1,4,2]
[2,1,4,6,5,3,7,8]=>0100011=>1100010=>[1,1,4,2]
[1,2,6,5,4,3,7,8]=>1100011=>1100011=>[1,1,4,1,1]
[1,2,4,5,6,3,7,8]=>1100011=>1100011=>[1,1,4,1,1]
[3,2,1,5,6,4,7,8]=>0010011=>1100100=>[1,1,3,3]
[1,2,3,5,6,4,7,8]=>1110011=>1100111=>[1,1,3,1,1,1]
[4,3,2,1,6,5,7,8]=>0001011=>1101000=>[1,1,2,4]
[3,2,4,1,6,5,7,8]=>0001011=>1101000=>[1,1,2,4]
[2,1,4,3,6,5,7,8]=>0101011=>1101010=>[1,1,2,2,2]
[1,2,4,3,6,5,7,8]=>1101011=>1101011=>[1,1,2,2,1,1]
[1,3,2,4,6,5,7,8]=>1011011=>1101101=>[1,1,2,1,2,1]
[2,1,3,4,6,5,7,8]=>0111011=>1101110=>[1,1,2,1,1,2]
[1,2,3,4,6,5,7,8]=>1111011=>1101111=>[1,1,2,1,1,1,1]
[3,5,4,2,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[2,5,4,3,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[2,4,5,3,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[3,2,5,4,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[2,3,5,4,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[2,4,3,5,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[1,3,2,5,4,6,7,8]=>1010111=>1110101=>[1,1,1,2,2,1]
[1,2,3,5,4,6,7,8]=>1110111=>1110111=>[1,1,1,2,1,1,1]
[2,4,3,1,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[1,4,3,2,5,6,7,8]=>1001111=>1111001=>[1,1,1,1,3,1]
[1,3,4,2,5,6,7,8]=>1001111=>1111001=>[1,1,1,1,3,1]
[2,1,4,3,5,6,7,8]=>0101111=>1111010=>[1,1,1,1,2,2]
[1,2,4,3,5,6,7,8]=>1101111=>1111011=>[1,1,1,1,2,1,1]
[1,3,2,4,5,6,7,8]=>1011111=>1111101=>[1,1,1,1,1,2,1]
[1,2,3,4,8,6,7,5]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,3,5,8,6,7,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,5,6,4,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,2,3,7,5,6,8,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,5,6,7,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,5,7,6,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,6,5,7,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,6,7,5,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,4,5,8,6,7,3]=>1100000=>0000011=>[6,1,1]
[1,2,4,8,6,5,7,3]=>1100000=>0000011=>[6,1,1]
[1,2,5,4,8,6,7,3]=>1100000=>0000011=>[6,1,1]
[1,2,6,4,5,3,7,8]=>1100011=>1100011=>[1,1,4,1,1]
[1,2,8,4,5,6,7,3]=>1100000=>0000011=>[6,1,1]
[1,2,7,5,4,6,8,3]=>1100000=>0000011=>[6,1,1]
[1,2,8,5,4,6,7,3]=>1100000=>0000011=>[6,1,1]
[1,2,8,5,4,7,6,3]=>1100000=>0000011=>[6,1,1]
[1,3,2,7,5,6,8,4]=>1010000=>0000101=>[5,2,1]
[1,3,2,8,5,7,6,4]=>1010000=>0000101=>[5,2,1]
[1,3,6,4,5,2,8,7]=>1000010=>0100001=>[2,5,1]
[1,3,6,4,5,7,2,8]=>1000001=>1000001=>[1,6,1]
[1,3,6,4,5,8,7,2]=>1000000=>0000001=>[7,1]
[1,3,8,4,5,6,7,2]=>1000000=>0000001=>[7,1]
[1,3,8,4,6,7,5,2]=>1000000=>0000001=>[7,1]
[1,3,8,5,4,6,7,2]=>1000000=>0000001=>[7,1]
[1,3,8,5,6,7,4,2]=>1000000=>0000001=>[7,1]
[1,3,8,5,7,6,4,2]=>1000000=>0000001=>[7,1]
[1,3,8,6,5,7,4,2]=>1000000=>0000001=>[7,1]
[1,3,8,7,5,6,4,2]=>1000000=>0000001=>[7,1]
[1,4,3,8,5,6,7,2]=>1000000=>0000001=>[7,1]
[1,4,3,8,5,7,6,2]=>1000000=>0000001=>[7,1]
[1,4,3,8,6,7,5,2]=>1000000=>0000001=>[7,1]
[1,5,3,4,2,7,8,6]=>1000100=>0010001=>[3,4,1]
[1,5,3,4,2,8,7,6]=>1000100=>0010001=>[3,4,1]
[1,5,3,4,8,6,7,2]=>1000000=>0000001=>[7,1]
[1,8,3,4,6,7,5,2]=>1000000=>0000001=>[7,1]
[1,6,3,5,4,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,6,3,5,4,8,7,2]=>1000000=>0000001=>[7,1]
[1,8,3,5,6,4,7,2]=>1000000=>0000001=>[7,1]
[1,8,3,5,7,6,4,2]=>1000000=>0000001=>[7,1]
[1,8,3,6,5,4,7,2]=>1000000=>0000001=>[7,1]
[1,8,3,7,6,5,4,2]=>1000000=>0000001=>[7,1]
[1,6,4,3,5,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,8,4,3,5,6,7,2]=>1000000=>0000001=>[7,1]
[1,8,4,3,5,7,6,2]=>1000000=>0000001=>[7,1]
[1,6,4,5,3,8,7,2]=>1000000=>0000001=>[7,1]
[1,8,4,5,6,7,3,2]=>1000000=>0000001=>[7,1]
[1,8,4,6,5,7,3,2]=>1000000=>0000001=>[7,1]
[1,8,4,7,6,5,3,2]=>1000000=>0000001=>[7,1]
[1,7,5,4,3,6,8,2]=>1000000=>0000001=>[7,1]
[1,8,5,4,3,6,7,2]=>1000000=>0000001=>[7,1]
[1,8,5,4,6,3,7,2]=>1000000=>0000001=>[7,1]
[1,8,5,4,6,7,3,2]=>1000000=>0000001=>[7,1]
[1,8,5,4,7,6,3,2]=>1000000=>0000001=>[7,1]
[1,8,6,4,5,7,3,2]=>1000000=>0000001=>[7,1]
[1,8,6,5,4,7,3,2]=>1000000=>0000001=>[7,1]
[1,8,7,5,6,4,3,2]=>1000000=>0000001=>[7,1]
[2,1,3,4,8,6,7,5]=>0111000=>0001110=>[4,1,1,2]
[2,1,4,8,6,5,7,3]=>0100000=>0000010=>[6,2]
[2,1,6,4,5,8,7,3]=>0100000=>0000010=>[6,2]
[2,1,8,5,4,6,7,3]=>0100000=>0000010=>[6,2]
[2,1,8,5,4,7,6,3]=>0100000=>0000010=>[6,2]
[2,1,7,5,6,4,8,3]=>0100000=>0000010=>[6,2]
[2,1,8,7,5,6,4,3]=>0100000=>0000010=>[6,2]
[2,3,1,8,6,7,5,4]=>0010000=>0000100=>[5,3]
[2,3,6,4,5,7,8,1]=>0000000=>0000000=>[8]
[2,3,7,4,5,6,8,1]=>0000000=>0000000=>[8]
[2,3,8,4,5,6,7,1]=>0000000=>0000000=>[8]
[2,3,7,4,6,5,8,1]=>0000000=>0000000=>[8]
[2,3,7,5,4,6,8,1]=>0000000=>0000000=>[8]
[2,3,7,5,6,4,1,8]=>0000001=>1000000=>[1,7]
[2,3,7,5,6,4,8,1]=>0000000=>0000000=>[8]
[2,4,3,5,8,6,7,1]=>0000000=>0000000=>[8]
[2,5,3,4,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[2,5,3,4,1,8,7,6]=>0000100=>0010000=>[3,5]
[2,5,3,4,6,7,1,8]=>0000001=>1000000=>[1,7]
[2,5,3,4,8,7,6,1]=>0000000=>0000000=>[8]
[2,6,3,4,5,7,8,1]=>0000000=>0000000=>[8]
[2,6,3,5,4,1,8,7]=>0000010=>0100000=>[2,6]
[2,6,3,5,4,7,8,1]=>0000000=>0000000=>[8]
[2,7,3,5,4,6,8,1]=>0000000=>0000000=>[8]
[2,7,3,5,6,4,8,1]=>0000000=>0000000=>[8]
[2,8,3,5,7,6,4,1]=>0000000=>0000000=>[8]
[2,7,3,6,5,4,1,8]=>0000001=>1000000=>[1,7]
[2,5,4,3,8,6,7,1]=>0000000=>0000000=>[8]
[2,6,4,3,5,7,8,1]=>0000000=>0000000=>[8]
[2,8,4,3,5,6,7,1]=>0000000=>0000000=>[8]
[2,8,4,3,7,6,5,1]=>0000000=>0000000=>[8]
[2,6,4,5,3,1,7,8]=>0000011=>1100000=>[1,1,6]
[2,6,4,5,3,7,8,1]=>0000000=>0000000=>[8]
[2,7,5,4,3,6,8,1]=>0000000=>0000000=>[8]
[2,7,5,4,6,3,8,1]=>0000000=>0000000=>[8]
[2,8,5,4,7,6,3,1]=>0000000=>0000000=>[8]
[2,8,7,5,4,6,3,1]=>0000000=>0000000=>[8]
[2,8,7,5,6,4,3,1]=>0000000=>0000000=>[8]
[3,2,1,4,8,6,7,5]=>0011000=>0001100=>[4,1,3]
[3,2,1,5,8,6,7,4]=>0010000=>0000100=>[5,3]
[3,2,1,7,5,6,4,8]=>0010001=>1000100=>[1,4,3]
[3,2,1,7,5,6,8,4]=>0010000=>0000100=>[5,3]
[3,2,1,8,5,6,7,4]=>0010000=>0000100=>[5,3]
[3,2,1,8,5,7,6,4]=>0010000=>0000100=>[5,3]
[3,2,1,8,6,5,7,4]=>0010000=>0000100=>[5,3]
[3,2,1,8,6,7,5,4]=>0010000=>0000100=>[5,3]
[3,2,4,1,8,6,7,5]=>0001000=>0001000=>[4,4]
[3,2,7,4,6,5,1,8]=>0000001=>1000000=>[1,7]
[3,2,7,4,6,5,8,1]=>0000000=>0000000=>[8]
[3,2,8,5,4,6,7,1]=>0000000=>0000000=>[8]
[3,2,7,5,6,4,1,8]=>0000001=>1000000=>[1,7]
[3,2,8,5,7,6,4,1]=>0000000=>0000000=>[8]
[4,2,3,1,8,6,7,5]=>0001000=>0001000=>[4,4]
[4,2,3,1,8,7,6,5]=>0001000=>0001000=>[4,4]
[4,2,3,5,1,7,8,6]=>0000100=>0010000=>[3,5]
[4,2,3,5,1,8,7,6]=>0000100=>0010000=>[3,5]
[4,2,3,5,6,8,7,1]=>0000000=>0000000=>[8]
[4,2,3,7,5,6,1,8]=>0000001=>1000000=>[1,7]
[4,2,3,8,5,6,7,1]=>0000000=>0000000=>[8]
[4,2,3,7,6,5,8,1]=>0000000=>0000000=>[8]
[4,2,3,8,7,6,5,1]=>0000000=>0000000=>[8]
[5,2,3,4,1,8,7,6]=>0000100=>0010000=>[3,5]
[5,2,3,4,8,7,6,1]=>0000000=>0000000=>[8]
[6,2,3,5,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[6,2,3,5,4,1,8,7]=>0000010=>0100000=>[2,6]
[6,2,3,5,4,7,1,8]=>0000001=>1000000=>[1,7]
[7,2,3,5,6,4,1,8]=>0000001=>1000000=>[1,7]
[7,2,3,6,5,4,1,8]=>0000001=>1000000=>[1,7]
[5,2,4,3,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,2,4,3,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[5,2,4,3,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[5,2,4,3,1,8,7,6]=>0000100=>0010000=>[3,5]
[5,2,4,3,6,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,2,4,3,6,1,8,7]=>0000010=>0100000=>[2,6]
[5,2,4,3,7,6,1,8]=>0000001=>1000000=>[1,7]
[5,2,4,3,7,6,8,1]=>0000000=>0000000=>[8]
[7,2,4,3,6,5,1,8]=>0000001=>1000000=>[1,7]
[7,2,4,3,6,5,8,1]=>0000000=>0000000=>[8]
[6,2,4,5,3,1,7,8]=>0000011=>1100000=>[1,1,6]
[7,2,4,5,3,6,1,8]=>0000001=>1000000=>[1,7]
[7,2,4,5,3,6,8,1]=>0000000=>0000000=>[8]
[8,2,4,7,6,5,3,1]=>0000000=>0000000=>[8]
[6,2,5,4,3,1,8,7]=>0000010=>0100000=>[2,6]
[7,2,5,4,3,6,1,8]=>0000001=>1000000=>[1,7]
[8,2,6,4,5,7,3,1]=>0000000=>0000000=>[8]
[8,2,7,5,6,4,3,1]=>0000000=>0000000=>[8]
[8,2,7,6,5,4,3,1]=>0000000=>0000000=>[8]
[4,3,2,1,8,6,7,5]=>0001000=>0001000=>[4,4]
[4,3,2,7,5,6,8,1]=>0000000=>0000000=>[8]
[4,3,2,8,5,6,7,1]=>0000000=>0000000=>[8]
[4,3,2,8,6,7,5,1]=>0000000=>0000000=>[8]
[5,3,2,4,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[5,3,2,4,1,8,7,6]=>0000100=>0010000=>[3,5]
[5,3,2,4,6,1,8,7]=>0000010=>0100000=>[2,6]
[6,3,2,5,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[6,3,2,5,4,1,8,7]=>0000010=>0100000=>[2,6]
[6,3,2,5,4,7,1,8]=>0000001=>1000000=>[1,7]
[8,3,2,5,4,7,6,1]=>0000000=>0000000=>[8]
[8,3,2,5,6,4,7,1]=>0000000=>0000000=>[8]
[8,3,2,7,6,5,4,1]=>0000000=>0000000=>[8]
[5,3,4,2,1,7,8,6]=>0000100=>0010000=>[3,5]
[5,3,4,2,1,8,7,6]=>0000100=>0010000=>[3,5]
[5,3,4,2,7,6,1,8]=>0000001=>1000000=>[1,7]
[7,3,4,2,6,5,1,8]=>0000001=>1000000=>[1,7]
[7,3,4,2,6,5,8,1]=>0000000=>0000000=>[8]
[7,3,4,6,5,2,1,8]=>0000001=>1000000=>[1,7]
[6,3,5,4,2,7,1,8]=>0000001=>1000000=>[1,7]
[7,3,5,4,6,2,1,8]=>0000001=>1000000=>[1,7]
[7,3,6,4,5,2,1,8]=>0000001=>1000000=>[1,7]
[7,3,6,5,4,2,1,8]=>0000001=>1000000=>[1,7]
[5,4,3,2,8,6,7,1]=>0000000=>0000000=>[8]
[6,4,3,5,2,1,8,7]=>0000010=>0100000=>[2,6]
[7,4,3,6,5,2,1,8]=>0000001=>1000000=>[1,7]
[7,4,3,6,5,2,8,1]=>0000000=>0000000=>[8]
[6,5,3,4,2,1,8,7]=>0000010=>0100000=>[2,6]
[8,5,3,4,7,6,2,1]=>0000000=>0000000=>[8]
[8,7,3,6,5,4,2,1]=>0000000=>0000000=>[8]
[8,5,4,3,2,7,6,1]=>0000000=>0000000=>[8]
[8,7,4,3,6,5,2,1]=>0000000=>0000000=>[8]
[2,4,6,1,3,5,8,7]=>0000010=>0100000=>[2,6]
[2,1,4,6,3,8,5,7]=>0100000=>0000010=>[6,2]
[2,4,1,6,3,8,5,7]=>0000000=>0000000=>[8]
[2,4,6,1,3,8,5,7]=>0000000=>0000000=>[8]
[2,4,6,1,8,3,5,7]=>0000000=>0000000=>[8]
[2,4,6,8,1,3,5,7]=>0000000=>0000000=>[8]
[2,4,1,3,6,5,7,8]=>0001011=>1101000=>[1,1,2,4]
[2,4,1,6,3,7,5,8]=>0000001=>1000000=>[1,7]
[2,4,6,1,3,7,5,8]=>0000001=>1000000=>[1,7]
[2,4,1,6,3,7,8,5]=>0000000=>0000000=>[8]
[2,4,1,6,7,3,8,5]=>0000000=>0000000=>[8]
[2,4,6,1,7,3,8,5]=>0000000=>0000000=>[8]
[2,4,6,7,1,3,8,5]=>0000000=>0000000=>[8]
[2,4,1,6,7,8,3,5]=>0000000=>0000000=>[8]
[2,4,6,7,8,1,3,5]=>0000000=>0000000=>[8]
[2,1,4,3,7,5,8,6]=>0101000=>0001010=>[4,2,2]
[2,4,1,3,7,5,8,6]=>0001000=>0001000=>[4,4]
[2,4,1,7,3,5,8,6]=>0000000=>0000000=>[8]
[2,4,7,1,3,5,8,6]=>0000000=>0000000=>[8]
[2,1,4,3,7,8,5,6]=>0101000=>0001010=>[4,2,2]
[2,4,1,3,7,8,5,6]=>0001000=>0001000=>[4,4]
[2,4,1,7,3,8,5,6]=>0000000=>0000000=>[8]
[2,4,1,7,8,3,5,6]=>0000000=>0000000=>[8]
[2,4,1,5,3,7,6,8]=>0000101=>1010000=>[1,2,5]
[2,4,1,3,5,7,8,6]=>0001100=>0011000=>[3,1,4]
[2,4,1,5,3,7,8,6]=>0000100=>0010000=>[3,5]
[2,4,5,1,3,7,8,6]=>0000100=>0010000=>[3,5]
[2,1,4,5,7,3,8,6]=>0100000=>0000010=>[6,2]
[2,4,1,5,7,3,8,6]=>0000000=>0000000=>[8]
[2,4,5,1,7,3,8,6]=>0000000=>0000000=>[8]
[2,4,1,3,8,5,6,7]=>0001000=>0001000=>[4,4]
[2,1,4,8,3,5,6,7]=>0100000=>0000010=>[6,2]
[2,4,1,8,3,5,6,7]=>0000000=>0000000=>[8]
[2,4,1,5,3,8,6,7]=>0000100=>0010000=>[3,5]
[2,1,4,5,8,3,6,7]=>0100000=>0000010=>[6,2]
[2,4,1,5,6,3,8,7]=>0000010=>0100000=>[2,6]
[2,1,4,5,6,8,3,7]=>0100000=>0000010=>[6,2]
[2,4,1,3,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[2,4,1,5,6,3,7,8]=>0000011=>1100000=>[1,1,6]
[2,4,5,6,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[2,4,5,6,7,1,3,8]=>0000001=>1000000=>[1,7]
[2,4,5,6,7,1,8,3]=>0000000=>0000000=>[8]
[2,1,5,3,6,4,8,7]=>0100010=>0100010=>[2,4,2]
[2,1,5,6,3,4,8,7]=>0100010=>0100010=>[2,4,2]
[2,1,5,3,6,8,4,7]=>0100000=>0000010=>[6,2]
[2,5,1,3,6,8,4,7]=>0000000=>0000000=>[8]
[2,1,5,6,3,4,7,8]=>0100011=>1100010=>[1,1,4,2]
[2,5,1,6,3,4,7,8]=>0000011=>1100000=>[1,1,6]
[2,1,5,3,6,7,4,8]=>0100001=>1000010=>[1,5,2]
[2,1,5,6,3,7,4,8]=>0100001=>1000010=>[1,5,2]
[2,5,1,6,3,7,4,8]=>0000001=>1000000=>[1,7]
[2,5,6,1,3,7,4,8]=>0000001=>1000000=>[1,7]
[2,1,5,6,7,3,4,8]=>0100001=>1000010=>[1,5,2]
[2,5,1,3,6,7,8,4]=>0000000=>0000000=>[8]
[2,1,5,6,3,7,8,4]=>0100000=>0000010=>[6,2]
[2,5,6,1,3,7,8,4]=>0000000=>0000000=>[8]
[2,1,5,6,7,8,3,4]=>0100000=>0000010=>[6,2]
[2,1,5,3,7,4,8,6]=>0100000=>0000010=>[6,2]
[2,1,5,7,3,4,8,6]=>0100000=>0000010=>[6,2]
[2,5,1,7,3,4,8,6]=>0000000=>0000000=>[8]
[2,5,7,1,3,4,8,6]=>0000000=>0000000=>[8]
[2,1,5,3,7,8,4,6]=>0100000=>0000010=>[6,2]
[2,5,1,3,7,8,4,6]=>0000000=>0000000=>[8]
[2,1,5,7,3,8,4,6]=>0100000=>0000010=>[6,2]
[2,1,5,7,8,3,4,6]=>0100000=>0000010=>[6,2]
[2,5,1,7,8,3,4,6]=>0000000=>0000000=>[8]
[2,5,1,3,7,4,6,8]=>0000001=>1000000=>[1,7]
[2,1,5,7,3,4,6,8]=>0100001=>1000010=>[1,5,2]
[2,3,5,7,1,4,8,6]=>0000000=>0000000=>[8]
[2,3,5,6,1,8,4,7]=>0000000=>0000000=>[8]
[2,3,5,6,8,1,4,7]=>0000000=>0000000=>[8]
[2,5,1,3,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[2,3,5,6,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[2,3,5,6,1,7,8,4]=>0000000=>0000000=>[8]
[2,3,5,6,7,8,1,4]=>0000000=>0000000=>[8]
[2,1,6,3,7,4,8,5]=>0100000=>0000010=>[6,2]
[2,6,1,3,7,4,8,5]=>0000000=>0000000=>[8]
[2,6,7,1,3,4,8,5]=>0000000=>0000000=>[8]
[2,1,6,3,7,8,4,5]=>0100000=>0000010=>[6,2]
[2,6,1,7,3,8,4,5]=>0000000=>0000000=>[8]
[2,1,6,7,8,3,4,5]=>0100000=>0000010=>[6,2]
[2,6,1,7,8,3,4,5]=>0000000=>0000000=>[8]
[2,6,7,8,1,3,4,5]=>0000000=>0000000=>[8]
[2,6,1,7,3,4,5,8]=>0000001=>1000000=>[1,7]
[2,6,7,1,3,4,5,8]=>0000001=>1000000=>[1,7]
[2,3,1,6,4,7,5,8]=>0010001=>1000100=>[1,4,3]
[2,3,6,1,4,7,5,8]=>0000001=>1000000=>[1,7]
[2,1,6,3,4,7,8,5]=>0100000=>0000010=>[6,2]
[2,3,6,1,4,7,8,5]=>0000000=>0000000=>[8]
[2,1,3,6,7,4,8,5]=>0110000=>0000110=>[5,1,2]
[2,3,1,6,7,8,4,5]=>0010000=>0000100=>[5,3]
[2,3,6,7,8,1,4,5]=>0000000=>0000000=>[8]
[2,6,1,8,3,4,5,7]=>0000000=>0000000=>[8]
[2,1,6,3,4,8,5,7]=>0100000=>0000010=>[6,2]
[2,3,6,1,4,5,8,7]=>0000010=>0100000=>[2,6]
[2,3,4,1,6,8,5,7]=>0001000=>0001000=>[4,4]
[2,3,4,6,7,8,1,5]=>0000000=>0000000=>[8]
[2,1,7,8,3,4,5,6]=>0100000=>0000010=>[6,2]
[2,7,1,8,3,4,5,6]=>0000000=>0000000=>[8]
[2,7,8,1,3,4,5,6]=>0000000=>0000000=>[8]
[2,1,7,3,4,8,5,6]=>0100000=>0000010=>[6,2]
[2,1,3,7,4,8,5,6]=>0110000=>0000110=>[5,1,2]
[2,3,7,1,4,5,8,6]=>0000000=>0000000=>[8]
[2,1,3,4,7,8,5,6]=>0111000=>0001110=>[4,1,1,2]
[2,1,3,8,4,5,6,7]=>0110000=>0000110=>[5,1,2]
[2,3,1,8,4,5,6,7]=>0010000=>0000100=>[5,3]
[2,1,3,4,8,5,6,7]=>0111000=>0001110=>[4,1,1,2]
[2,3,4,8,1,5,6,7]=>0000000=>0000000=>[8]
[3,1,4,2,6,5,8,7]=>0001010=>0101000=>[2,2,4]
[3,4,1,2,6,5,8,7]=>0001010=>0101000=>[2,2,4]
[3,4,6,1,2,5,8,7]=>0000010=>0100000=>[2,6]
[3,1,4,2,6,8,5,7]=>0001000=>0001000=>[4,4]
[3,1,4,6,8,2,5,7]=>0000000=>0000000=>[8]
[3,1,4,2,6,5,7,8]=>0001011=>1101000=>[1,1,2,4]
[3,4,1,2,6,5,7,8]=>0001011=>1101000=>[1,1,2,4]
[3,1,4,2,6,7,5,8]=>0001001=>1001000=>[1,3,4]
[3,4,1,6,2,7,5,8]=>0000001=>1000000=>[1,7]
[3,1,4,2,6,7,8,5]=>0001000=>0001000=>[4,4]
[3,4,1,2,6,7,8,5]=>0001000=>0001000=>[4,4]
[3,4,6,1,7,2,8,5]=>0000000=>0000000=>[8]
[3,1,4,6,7,8,2,5]=>0000000=>0000000=>[8]
[3,4,6,1,7,8,2,5]=>0000000=>0000000=>[8]
[3,4,6,7,1,8,2,5]=>0000000=>0000000=>[8]
[3,4,6,7,8,1,2,5]=>0000000=>0000000=>[8]
[3,1,4,2,7,5,8,6]=>0001000=>0001000=>[4,4]
[3,4,1,2,7,5,8,6]=>0001000=>0001000=>[4,4]
[3,4,7,1,2,5,8,6]=>0000000=>0000000=>[8]
[3,1,4,2,7,8,5,6]=>0001000=>0001000=>[4,4]
[3,4,1,2,7,8,5,6]=>0001000=>0001000=>[4,4]
[3,4,7,1,8,2,5,6]=>0000000=>0000000=>[8]
[3,1,4,2,7,5,6,8]=>0001001=>1001000=>[1,3,4]
[3,4,1,5,2,7,6,8]=>0000101=>1010000=>[1,2,5]
[3,1,4,2,5,7,8,6]=>0001100=>0011000=>[3,1,4]
[3,1,4,5,2,7,8,6]=>0000100=>0010000=>[3,5]
[3,1,4,5,7,8,2,6]=>0000000=>0000000=>[8]
[3,4,1,5,7,8,2,6]=>0000000=>0000000=>[8]
[3,4,5,1,7,8,2,6]=>0000000=>0000000=>[8]
[3,4,1,8,2,5,6,7]=>0000000=>0000000=>[8]
[3,1,4,2,5,8,6,7]=>0001100=>0011000=>[3,1,4]
[3,4,1,5,2,8,6,7]=>0000100=>0010000=>[3,5]
[3,4,1,5,8,2,6,7]=>0000000=>0000000=>[8]
[3,4,1,2,5,6,8,7]=>0001110=>0111000=>[2,1,1,4]
[3,4,5,6,1,2,8,7]=>0000010=>0100000=>[2,6]
[3,4,5,6,1,8,2,7]=>0000000=>0000000=>[8]
[3,4,5,6,8,1,2,7]=>0000000=>0000000=>[8]
[3,1,4,2,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[3,4,1,5,6,7,2,8]=>0000001=>1000000=>[1,7]
[3,4,5,6,1,7,2,8]=>0000001=>1000000=>[1,7]
[3,4,5,1,6,7,8,2]=>0000000=>0000000=>[8]
[3,4,5,6,1,7,8,2]=>0000000=>0000000=>[8]
[3,1,5,2,6,4,8,7]=>0000010=>0100000=>[2,6]
[3,1,5,6,2,4,8,7]=>0000010=>0100000=>[2,6]
[3,5,1,6,2,4,8,7]=>0000010=>0100000=>[2,6]
[3,5,1,2,6,8,4,7]=>0000000=>0000000=>[8]
[3,1,5,6,2,8,4,7]=>0000000=>0000000=>[8]
[3,5,6,1,2,8,4,7]=>0000000=>0000000=>[8]
[3,1,5,6,8,2,4,7]=>0000000=>0000000=>[8]
[3,5,6,1,8,2,4,7]=>0000000=>0000000=>[8]
[3,1,5,6,2,4,7,8]=>0000011=>1100000=>[1,1,6]
[3,5,1,6,2,4,7,8]=>0000011=>1100000=>[1,1,6]
[3,5,1,6,2,7,4,8]=>0000001=>1000000=>[1,7]
[3,5,6,1,2,7,4,8]=>0000001=>1000000=>[1,7]
[3,1,5,2,6,7,8,4]=>0000000=>0000000=>[8]
[3,5,1,2,6,7,8,4]=>0000000=>0000000=>[8]
[3,5,1,6,2,7,8,4]=>0000000=>0000000=>[8]
[3,1,5,6,7,2,8,4]=>0000000=>0000000=>[8]
[3,5,1,6,7,8,2,4]=>0000000=>0000000=>[8]
[3,5,6,1,7,8,2,4]=>0000000=>0000000=>[8]
[3,1,5,2,7,4,8,6]=>0000000=>0000000=>[8]
[3,5,1,2,7,4,8,6]=>0000000=>0000000=>[8]
[3,1,5,7,2,4,8,6]=>0000000=>0000000=>[8]
[3,5,1,7,2,4,8,6]=>0000000=>0000000=>[8]
[3,5,7,1,2,4,8,6]=>0000000=>0000000=>[8]
[3,1,5,2,7,8,4,6]=>0000000=>0000000=>[8]
[3,5,1,2,7,8,4,6]=>0000000=>0000000=>[8]
[3,1,5,7,2,8,4,6]=>0000000=>0000000=>[8]
[3,5,1,7,2,8,4,6]=>0000000=>0000000=>[8]
[3,1,5,7,8,2,4,6]=>0000000=>0000000=>[8]
[3,5,1,7,8,2,4,6]=>0000000=>0000000=>[8]
[3,1,5,2,7,4,6,8]=>0000001=>1000000=>[1,7]
[3,1,5,7,2,4,6,8]=>0000001=>1000000=>[1,7]
[3,5,1,7,2,4,6,8]=>0000001=>1000000=>[1,7]
[3,5,7,1,2,4,6,8]=>0000001=>1000000=>[1,7]
[1,3,5,7,2,4,6,8]=>1000001=>1000001=>[1,6,1]
[3,5,1,2,4,7,8,6]=>0000100=>0010000=>[3,5]
[3,1,2,5,7,4,8,6]=>0010000=>0000100=>[5,3]
[1,3,5,2,7,4,8,6]=>1000000=>0000001=>[7,1]
[1,3,5,7,2,4,8,6]=>1000000=>0000001=>[7,1]
[1,3,5,2,7,8,4,6]=>1000000=>0000001=>[7,1]
[3,1,5,2,8,4,6,7]=>0000000=>0000000=>[8]
[3,5,1,2,8,4,6,7]=>0000000=>0000000=>[8]
[3,1,5,8,2,4,6,7]=>0000000=>0000000=>[8]
[3,5,1,8,2,4,6,7]=>0000000=>0000000=>[8]
[3,1,5,2,4,8,6,7]=>0000100=>0010000=>[3,5]
[3,5,1,2,4,8,6,7]=>0000100=>0010000=>[3,5]
[1,3,2,5,4,8,6,7]=>1010100=>0010101=>[3,2,2,1]
[1,3,5,2,4,8,6,7]=>1000100=>0010001=>[3,4,1]
[3,1,2,5,8,4,6,7]=>0010000=>0000100=>[5,3]
[1,3,2,5,8,4,6,7]=>1010000=>0000101=>[5,2,1]
[1,3,5,2,8,4,6,7]=>1000000=>0000001=>[7,1]
[1,3,5,8,2,4,6,7]=>1000000=>0000001=>[7,1]
[3,5,1,2,4,6,8,7]=>0000110=>0110000=>[2,1,5]
[3,1,2,5,4,6,8,7]=>0010110=>0110100=>[2,1,2,3]
[1,3,5,2,4,6,8,7]=>1000110=>0110001=>[2,1,4,1]
[1,3,5,2,6,4,8,7]=>1000010=>0100001=>[2,5,1]
[1,3,5,6,2,4,8,7]=>1000010=>0100001=>[2,5,1]
[3,1,2,5,6,8,4,7]=>0010000=>0000100=>[5,3]
[1,3,5,2,6,8,4,7]=>1000000=>0000001=>[7,1]
[3,5,1,2,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[1,3,5,6,2,4,7,8]=>1000011=>1100001=>[1,1,5,1]
[3,1,2,5,6,7,4,8]=>0010001=>1000100=>[1,4,3]
[1,3,5,2,6,7,4,8]=>1000001=>1000001=>[1,6,1]
[1,3,5,6,2,7,4,8]=>1000001=>1000001=>[1,6,1]
[1,3,5,6,7,2,4,8]=>1000001=>1000001=>[1,6,1]
[3,1,2,5,6,7,8,4]=>0010000=>0000100=>[5,3]
[1,3,5,6,7,8,2,4]=>1000000=>0000001=>[7,1]
[3,1,6,2,7,4,8,5]=>0000000=>0000000=>[8]
[3,6,1,2,7,4,8,5]=>0000000=>0000000=>[8]
[3,6,1,7,2,4,8,5]=>0000000=>0000000=>[8]
[3,6,7,1,2,4,8,5]=>0000000=>0000000=>[8]
[3,1,6,7,2,8,4,5]=>0000000=>0000000=>[8]
[3,6,1,7,2,8,4,5]=>0000000=>0000000=>[8]
[3,6,7,1,2,8,4,5]=>0000000=>0000000=>[8]
[3,6,1,7,8,2,4,5]=>0000000=>0000000=>[8]
[3,6,7,8,1,2,4,5]=>0000000=>0000000=>[8]
[3,1,6,7,2,4,5,8]=>0000001=>1000000=>[1,7]
[3,6,7,1,2,4,5,8]=>0000001=>1000000=>[1,7]
[3,1,6,2,4,7,5,8]=>0000001=>1000000=>[1,7]
[3,1,2,6,4,7,5,8]=>0010001=>1000100=>[1,4,3]
[1,3,2,6,4,7,5,8]=>1010001=>1000101=>[1,4,2,1]
[1,3,6,2,4,7,5,8]=>1000001=>1000001=>[1,6,1]
[3,1,6,2,4,7,8,5]=>0000000=>0000000=>[8]
[3,6,1,2,4,7,8,5]=>0000000=>0000000=>[8]
[3,1,2,6,4,7,8,5]=>0010000=>0000100=>[5,3]
[1,3,6,2,4,7,8,5]=>1000000=>0000001=>[7,1]
[3,1,2,6,7,4,8,5]=>0010000=>0000100=>[5,3]
[1,3,6,2,7,4,8,5]=>1000000=>0000001=>[7,1]
[1,3,6,7,2,4,8,5]=>1000000=>0000001=>[7,1]
[1,3,6,2,7,8,4,5]=>1000000=>0000001=>[7,1]
[3,1,6,2,8,4,5,7]=>0000000=>0000000=>[8]
[3,1,6,8,2,4,5,7]=>0000000=>0000000=>[8]
[3,6,1,8,2,4,5,7]=>0000000=>0000000=>[8]
[3,1,6,2,4,8,5,7]=>0000000=>0000000=>[8]
[1,3,2,6,4,8,5,7]=>1010000=>0000101=>[5,2,1]
[1,3,6,2,4,8,5,7]=>1000000=>0000001=>[7,1]
[3,1,6,2,4,5,8,7]=>0000010=>0100000=>[2,6]
[3,1,2,6,4,5,8,7]=>0010010=>0100100=>[2,3,3]
[1,3,4,6,2,5,8,7]=>1000010=>0100001=>[2,5,1]
[3,1,2,4,6,8,5,7]=>0011000=>0001100=>[4,1,3]
[1,3,2,4,6,8,5,7]=>1011000=>0001101=>[4,1,2,1]
[1,3,4,6,8,2,5,7]=>1000000=>0000001=>[7,1]
[3,1,6,2,4,5,7,8]=>0000011=>1100000=>[1,1,6]
[1,3,2,6,4,5,7,8]=>1010011=>1100101=>[1,1,3,2,1]
[1,3,6,2,4,5,7,8]=>1000011=>1100001=>[1,1,5,1]
[3,1,2,4,6,7,5,8]=>0011001=>1001100=>[1,3,1,3]
[3,1,2,4,6,7,8,5]=>0011000=>0001100=>[4,1,3]
[3,7,1,2,8,4,5,6]=>0000000=>0000000=>[8]
[3,1,7,8,2,4,5,6]=>0000000=>0000000=>[8]
[3,7,1,2,4,8,5,6]=>0000000=>0000000=>[8]
[3,1,2,7,4,8,5,6]=>0010000=>0000100=>[5,3]
[1,3,2,7,4,8,5,6]=>1010000=>0000101=>[5,2,1]
[1,3,7,2,4,8,5,6]=>1000000=>0000001=>[7,1]
[1,3,7,2,8,4,5,6]=>1000000=>0000001=>[7,1]
[1,3,7,2,4,5,8,6]=>1000000=>0000001=>[7,1]
[3,1,2,4,7,5,8,6]=>0011000=>0001100=>[4,1,3]
[1,3,2,4,7,5,8,6]=>1011000=>0001101=>[4,1,2,1]
[1,3,4,7,2,5,8,6]=>1000000=>0000001=>[7,1]
[3,7,1,2,4,5,6,8]=>0000001=>1000000=>[1,7]
[1,3,2,7,4,5,6,8]=>1010001=>1000101=>[1,4,2,1]
[1,3,4,5,7,8,2,6]=>1000000=>0000001=>[7,1]
[3,1,2,8,4,5,6,7]=>0010000=>0000100=>[5,3]
[1,3,2,8,4,5,6,7]=>1010000=>0000101=>[5,2,1]
[1,3,8,2,4,5,6,7]=>1000000=>0000001=>[7,1]
[3,1,2,4,8,5,6,7]=>0011000=>0001100=>[4,1,3]
[1,3,2,4,8,5,6,7]=>1011000=>0001101=>[4,1,2,1]
[1,3,4,2,8,5,6,7]=>1001000=>0001001=>[4,3,1]
[1,3,4,8,2,5,6,7]=>1000000=>0000001=>[7,1]
[3,1,2,4,5,8,6,7]=>0011100=>0011100=>[3,1,1,3]
[1,3,2,4,5,8,6,7]=>1011100=>0011101=>[3,1,1,2,1]
[1,3,4,2,5,8,6,7]=>1001100=>0011001=>[3,1,3,1]
[1,3,4,5,2,8,6,7]=>1000100=>0010001=>[3,4,1]
[4,1,5,2,6,3,8,7]=>0000010=>0100000=>[2,6]
[4,5,1,2,6,3,8,7]=>0000010=>0100000=>[2,6]
[4,1,5,6,2,3,8,7]=>0000010=>0100000=>[2,6]
[4,5,6,1,2,3,8,7]=>0000010=>0100000=>[2,6]
[4,1,5,2,6,8,3,7]=>0000000=>0000000=>[8]
[4,5,1,2,6,8,3,7]=>0000000=>0000000=>[8]
[4,5,1,6,2,8,3,7]=>0000000=>0000000=>[8]
[4,1,5,6,8,2,3,7]=>0000000=>0000000=>[8]
[4,5,6,8,1,2,3,7]=>0000000=>0000000=>[8]
[4,5,1,6,2,7,3,8]=>0000001=>1000000=>[1,7]
[4,1,5,6,7,2,3,8]=>0000001=>1000000=>[1,7]
[4,5,1,6,7,2,3,8]=>0000001=>1000000=>[1,7]
[4,1,5,2,6,7,8,3]=>0000000=>0000000=>[8]
[4,5,1,2,6,7,8,3]=>0000000=>0000000=>[8]
[4,5,1,6,2,7,8,3]=>0000000=>0000000=>[8]
[4,5,1,6,7,2,8,3]=>0000000=>0000000=>[8]
[4,5,6,1,7,2,8,3]=>0000000=>0000000=>[8]
[4,5,1,6,7,8,2,3]=>0000000=>0000000=>[8]
[4,1,5,2,7,3,8,6]=>0000000=>0000000=>[8]
[4,5,1,2,7,3,8,6]=>0000000=>0000000=>[8]
[4,5,1,7,2,3,8,6]=>0000000=>0000000=>[8]
[4,1,5,2,7,8,3,6]=>0000000=>0000000=>[8]
[4,5,1,2,7,8,3,6]=>0000000=>0000000=>[8]
[4,1,5,7,2,8,3,6]=>0000000=>0000000=>[8]
[4,5,1,7,2,8,3,6]=>0000000=>0000000=>[8]
[4,5,7,1,2,8,3,6]=>0000000=>0000000=>[8]
[4,5,1,7,8,2,3,6]=>0000000=>0000000=>[8]
[4,1,5,2,7,3,6,8]=>0000001=>1000000=>[1,7]
[4,5,1,2,7,3,6,8]=>0000001=>1000000=>[1,7]
[1,4,2,5,3,7,6,8]=>1000101=>1010001=>[1,2,4,1]
[4,1,2,5,7,3,6,8]=>0000001=>1000000=>[1,7]
[1,4,2,5,7,3,6,8]=>1000001=>1000001=>[1,6,1]
[1,4,5,2,7,3,6,8]=>1000001=>1000001=>[1,6,1]
[1,4,5,7,2,3,6,8]=>1000001=>1000001=>[1,6,1]
[4,1,5,2,3,7,8,6]=>0000100=>0010000=>[3,5]
[4,1,2,5,3,7,8,6]=>0000100=>0010000=>[3,5]
[1,4,5,2,3,7,8,6]=>1000100=>0010001=>[3,4,1]
[4,1,2,5,7,3,8,6]=>0000000=>0000000=>[8]
[1,4,2,5,7,3,8,6]=>1000000=>0000001=>[7,1]
[1,4,5,2,7,3,8,6]=>1000000=>0000001=>[7,1]
[1,4,2,5,7,8,3,6]=>1000000=>0000001=>[7,1]
[1,4,5,2,7,8,3,6]=>1000000=>0000001=>[7,1]
[1,4,5,7,8,2,3,6]=>1000000=>0000001=>[7,1]
[4,1,5,2,8,3,6,7]=>0000000=>0000000=>[8]
[4,5,1,2,8,3,6,7]=>0000000=>0000000=>[8]
[4,5,1,8,2,3,6,7]=>0000000=>0000000=>[8]
[4,5,8,1,2,3,6,7]=>0000000=>0000000=>[8]
[4,1,5,2,3,8,6,7]=>0000100=>0010000=>[3,5]
[4,5,1,2,3,8,6,7]=>0000100=>0010000=>[3,5]
[4,1,2,5,3,8,6,7]=>0000100=>0010000=>[3,5]
[1,4,2,5,3,8,6,7]=>1000100=>0010001=>[3,4,1]
[1,4,5,2,3,8,6,7]=>1000100=>0010001=>[3,4,1]
[4,1,2,5,8,3,6,7]=>0000000=>0000000=>[8]
[1,4,2,5,8,3,6,7]=>1000000=>0000001=>[7,1]
[1,4,2,5,3,6,8,7]=>1000110=>0110001=>[2,1,4,1]
[4,1,2,5,6,3,8,7]=>0000010=>0100000=>[2,6]
[1,4,5,2,6,3,8,7]=>1000010=>0100001=>[2,5,1]
[4,1,2,5,6,8,3,7]=>0000000=>0000000=>[8]
[1,4,5,2,6,8,3,7]=>1000000=>0000001=>[7,1]
[1,4,5,6,8,2,3,7]=>1000000=>0000001=>[7,1]
[1,4,2,5,3,6,7,8]=>1000111=>1110001=>[1,1,1,4,1]
[1,4,5,2,3,6,7,8]=>1000111=>1110001=>[1,1,1,4,1]
[4,1,2,5,6,3,7,8]=>0000011=>1100000=>[1,1,6]
[1,4,5,2,6,3,7,8]=>1000011=>1100001=>[1,1,5,1]
[4,1,2,5,6,7,3,8]=>0000001=>1000000=>[1,7]
[1,4,2,5,6,7,3,8]=>1000001=>1000001=>[1,6,1]
[1,4,5,6,7,2,3,8]=>1000001=>1000001=>[1,6,1]
[1,4,5,2,6,7,8,3]=>1000000=>0000001=>[7,1]
[1,4,5,6,7,2,8,3]=>1000000=>0000001=>[7,1]
[4,1,6,2,7,3,8,5]=>0000000=>0000000=>[8]
[4,6,7,1,2,3,8,5]=>0000000=>0000000=>[8]
[4,6,7,1,8,2,3,5]=>0000000=>0000000=>[8]
[4,6,7,8,1,2,3,5]=>0000000=>0000000=>[8]
[4,1,6,2,7,3,5,8]=>0000001=>1000000=>[1,7]
[4,6,1,2,7,3,5,8]=>0000001=>1000000=>[1,7]
[4,1,6,7,2,3,5,8]=>0000001=>1000000=>[1,7]
[4,6,1,7,2,3,5,8]=>0000001=>1000000=>[1,7]
[4,6,1,2,3,7,5,8]=>0000001=>1000000=>[1,7]
[4,1,2,6,3,7,5,8]=>0000001=>1000000=>[1,7]
[1,4,2,6,3,7,5,8]=>1000001=>1000001=>[1,6,1]
[4,1,2,6,7,3,5,8]=>0000001=>1000000=>[1,7]
[1,4,2,6,7,3,5,8]=>1000001=>1000001=>[1,6,1]
[1,4,6,2,7,3,5,8]=>1000001=>1000001=>[1,6,1]
[4,1,6,2,3,7,8,5]=>0000000=>0000000=>[8]
[4,1,2,6,3,7,8,5]=>0000000=>0000000=>[8]
[1,4,6,2,3,7,8,5]=>1000000=>0000001=>[7,1]
[1,4,6,2,7,3,8,5]=>1000000=>0000001=>[7,1]
[1,4,2,6,7,8,3,5]=>1000000=>0000001=>[7,1]
[1,4,6,2,7,8,3,5]=>1000000=>0000001=>[7,1]
[1,4,6,7,2,8,3,5]=>1000000=>0000001=>[7,1]
[4,1,6,2,8,3,5,7]=>0000000=>0000000=>[8]
[4,6,1,2,8,3,5,7]=>0000000=>0000000=>[8]
[4,1,6,8,2,3,5,7]=>0000000=>0000000=>[8]
[4,6,1,8,2,3,5,7]=>0000000=>0000000=>[8]
[4,6,1,2,3,8,5,7]=>0000000=>0000000=>[8]
[4,1,2,6,3,8,5,7]=>0000000=>0000000=>[8]
[1,4,2,6,3,8,5,7]=>1000000=>0000001=>[7,1]
[1,4,6,2,3,8,5,7]=>1000000=>0000001=>[7,1]
[1,4,2,6,8,3,5,7]=>1000000=>0000001=>[7,1]
[1,4,6,8,2,3,5,7]=>1000000=>0000001=>[7,1]
[1,4,2,6,3,5,8,7]=>1000010=>0100001=>[2,5,1]
[1,4,2,3,6,5,8,7]=>1001010=>0101001=>[2,2,3,1]
[1,2,4,3,6,8,5,7]=>1101000=>0001011=>[4,2,1,1]
[1,2,4,6,3,8,5,7]=>1100000=>0000011=>[6,1,1]
[1,2,4,6,8,3,5,7]=>1100000=>0000011=>[6,1,1]
[1,4,2,6,3,5,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,4,2,3,6,5,7,8]=>1001011=>1101001=>[1,1,2,3,1]
[1,2,4,6,3,5,7,8]=>1100011=>1100011=>[1,1,4,1,1]
[4,1,2,3,6,7,8,5]=>0001000=>0001000=>[4,4]
[1,4,2,3,6,7,8,5]=>1001000=>0001001=>[4,3,1]
[4,1,7,2,8,3,5,6]=>0000000=>0000000=>[8]
[4,7,1,8,2,3,5,6]=>0000000=>0000000=>[8]
[4,1,7,2,3,8,5,6]=>0000000=>0000000=>[8]
[1,4,2,7,3,8,5,6]=>1000000=>0000001=>[7,1]
[1,4,7,2,3,8,5,6]=>1000000=>0000001=>[7,1]
[4,1,2,7,8,3,5,6]=>0000000=>0000000=>[8]
[1,4,2,7,8,3,5,6]=>1000000=>0000001=>[7,1]
[4,1,7,2,3,5,8,6]=>0000000=>0000000=>[8]
[4,1,2,7,3,5,8,6]=>0000000=>0000000=>[8]
[1,4,2,7,3,5,8,6]=>1000000=>0000001=>[7,1]
[1,4,7,2,3,5,8,6]=>1000000=>0000001=>[7,1]
[4,1,2,3,7,5,8,6]=>0001000=>0001000=>[4,4]
[1,2,4,3,7,5,8,6]=>1101000=>0001011=>[4,2,1,1]
[1,4,2,3,7,8,5,6]=>1001000=>0001001=>[4,3,1]
[1,2,4,3,7,8,5,6]=>1101000=>0001011=>[4,2,1,1]
[1,2,4,7,3,8,5,6]=>1100000=>0000011=>[6,1,1]
[1,4,2,7,3,5,6,8]=>1000001=>1000001=>[1,6,1]
[1,4,2,3,7,5,6,8]=>1001001=>1001001=>[1,3,3,1]
[1,4,2,3,5,7,6,8]=>1001101=>1011001=>[1,2,1,3,1]
[4,1,2,3,5,7,8,6]=>0001100=>0011000=>[3,1,4]
[1,4,2,3,5,7,8,6]=>1001100=>0011001=>[3,1,3,1]
[1,2,4,5,7,3,8,6]=>1100000=>0000011=>[6,1,1]
[4,8,1,2,3,5,6,7]=>0000000=>0000000=>[8]
[1,4,2,8,3,5,6,7]=>1000000=>0000001=>[7,1]
[1,4,8,2,3,5,6,7]=>1000000=>0000001=>[7,1]
[4,1,2,3,8,5,6,7]=>0001000=>0001000=>[4,4]
[1,4,2,3,8,5,6,7]=>1001000=>0001001=>[4,3,1]
[1,2,4,3,8,5,6,7]=>1101000=>0001011=>[4,2,1,1]
[1,2,4,8,3,5,6,7]=>1100000=>0000011=>[6,1,1]
[1,4,2,3,5,8,6,7]=>1001100=>0011001=>[3,1,3,1]
[1,2,4,3,5,8,6,7]=>1101100=>0011011=>[3,1,2,1,1]
[1,4,2,3,5,6,8,7]=>1001110=>0111001=>[2,1,1,3,1]
[1,4,2,3,5,6,7,8]=>1001111=>1111001=>[1,1,1,1,3,1]
[5,1,6,2,7,3,8,4]=>0000000=>0000000=>[8]
[5,6,7,1,2,3,8,4]=>0000000=>0000000=>[8]
[5,1,6,7,2,8,3,4]=>0000000=>0000000=>[8]
[5,6,7,1,2,8,3,4]=>0000000=>0000000=>[8]
[5,1,6,7,8,2,3,4]=>0000000=>0000000=>[8]
[5,6,1,7,8,2,3,4]=>0000000=>0000000=>[8]
[5,6,7,1,8,2,3,4]=>0000000=>0000000=>[8]
[1,5,2,6,3,7,4,8]=>1000001=>1000001=>[1,6,1]
[5,1,2,6,7,3,4,8]=>0000001=>1000000=>[1,7]
[1,5,2,6,7,3,4,8]=>1000001=>1000001=>[1,6,1]
[1,5,2,6,3,7,8,4]=>1000000=>0000001=>[7,1]
[1,5,6,2,3,7,8,4]=>1000000=>0000001=>[7,1]
[1,5,6,7,2,3,8,4]=>1000000=>0000001=>[7,1]
[1,5,6,7,8,2,3,4]=>1000000=>0000001=>[7,1]
[5,1,6,2,8,3,4,7]=>0000000=>0000000=>[8]
[5,6,8,1,2,3,4,7]=>0000000=>0000000=>[8]
[5,1,6,2,3,8,4,7]=>0000000=>0000000=>[8]
[5,6,1,2,3,8,4,7]=>0000000=>0000000=>[8]
[5,1,2,6,3,8,4,7]=>0000000=>0000000=>[8]
[1,5,2,6,3,8,4,7]=>1000000=>0000001=>[7,1]
[1,5,6,2,3,8,4,7]=>1000000=>0000001=>[7,1]
[5,1,2,6,8,3,4,7]=>0000000=>0000000=>[8]
[1,5,2,6,8,3,4,7]=>1000000=>0000001=>[7,1]
[1,5,6,2,8,3,4,7]=>1000000=>0000001=>[7,1]
[1,5,2,6,3,4,8,7]=>1000010=>0100001=>[2,5,1]
[1,5,6,2,3,4,8,7]=>1000010=>0100001=>[2,5,1]
[1,5,2,3,6,4,8,7]=>1000010=>0100001=>[2,5,1]
[1,2,5,3,6,4,8,7]=>1100010=>0100011=>[2,4,1,1]
[1,2,5,6,3,4,8,7]=>1100010=>0100011=>[2,4,1,1]
[5,1,2,3,6,8,4,7]=>0000000=>0000000=>[8]
[1,5,2,3,6,8,4,7]=>1000000=>0000001=>[7,1]
[1,2,5,6,3,8,4,7]=>1100000=>0000011=>[6,1,1]
[1,2,5,6,8,3,4,7]=>1100000=>0000011=>[6,1,1]
[5,1,2,6,3,4,7,8]=>0000011=>1100000=>[1,1,6]
[1,5,2,6,3,4,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,2,5,6,3,4,7,8]=>1100011=>1100011=>[1,1,4,1,1]
[1,2,5,6,3,7,4,8]=>1100001=>1000011=>[1,5,1,1]
[5,1,2,3,6,7,8,4]=>0000000=>0000000=>[8]
[1,5,2,3,6,7,8,4]=>1000000=>0000001=>[7,1]
[1,2,5,3,6,7,8,4]=>1100000=>0000011=>[6,1,1]
[1,2,5,6,3,7,8,4]=>1100000=>0000011=>[6,1,1]
[5,1,7,2,8,3,4,6]=>0000000=>0000000=>[8]
[5,7,1,2,8,3,4,6]=>0000000=>0000000=>[8]
[5,7,8,1,2,3,4,6]=>0000000=>0000000=>[8]
[5,1,2,7,3,8,4,6]=>0000000=>0000000=>[8]
[1,5,2,7,3,8,4,6]=>1000000=>0000001=>[7,1]
[1,5,7,2,3,8,4,6]=>1000000=>0000001=>[7,1]
[5,1,2,7,8,3,4,6]=>0000000=>0000000=>[8]
[1,5,2,7,8,3,4,6]=>1000000=>0000001=>[7,1]
[1,5,7,2,8,3,4,6]=>1000000=>0000001=>[7,1]
[5,1,2,7,3,4,8,6]=>0000000=>0000000=>[8]
[1,5,2,7,3,4,8,6]=>1000000=>0000001=>[7,1]
[1,5,7,2,3,4,8,6]=>1000000=>0000001=>[7,1]
[5,1,2,3,7,4,8,6]=>0000000=>0000000=>[8]
[1,5,2,3,7,4,8,6]=>1000000=>0000001=>[7,1]
[1,2,5,3,7,4,8,6]=>1100000=>0000011=>[6,1,1]
[1,2,5,7,3,4,8,6]=>1100000=>0000011=>[6,1,1]
[5,1,2,3,7,8,4,6]=>0000000=>0000000=>[8]
[1,5,2,3,7,8,4,6]=>1000000=>0000001=>[7,1]
[1,2,5,3,7,8,4,6]=>1100000=>0000011=>[6,1,1]
[1,2,5,7,3,8,4,6]=>1100000=>0000011=>[6,1,1]
[1,2,5,7,8,3,4,6]=>1100000=>0000011=>[6,1,1]
[5,7,1,2,3,4,6,8]=>0000001=>1000000=>[1,7]
[1,5,2,7,3,4,6,8]=>1000001=>1000001=>[1,6,1]
[1,2,5,7,3,4,6,8]=>1100001=>1000011=>[1,5,1,1]
[1,5,2,3,4,7,6,8]=>1000101=>1010001=>[1,2,4,1]
[1,2,3,5,7,4,6,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,5,2,3,4,7,8,6]=>1000100=>0010001=>[3,4,1]
[1,2,3,5,7,4,8,6]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,5,7,8,4,6]=>1110000=>0000111=>[5,1,1,1]
[5,1,2,8,3,4,6,7]=>0000000=>0000000=>[8]
[1,5,2,8,3,4,6,7]=>1000000=>0000001=>[7,1]
[1,5,2,3,8,4,6,7]=>1000000=>0000001=>[7,1]
[1,2,5,3,8,4,6,7]=>1100000=>0000011=>[6,1,1]
[1,2,5,8,3,4,6,7]=>1100000=>0000011=>[6,1,1]
[1,5,2,3,4,8,6,7]=>1000100=>0010001=>[3,4,1]
[1,2,5,3,4,8,6,7]=>1100100=>0010011=>[3,3,1,1]
[1,2,3,5,4,8,6,7]=>1110100=>0010111=>[3,2,1,1,1]
[1,2,3,5,8,4,6,7]=>1110000=>0000111=>[5,1,1,1]
[1,5,2,3,4,6,8,7]=>1000110=>0110001=>[2,1,4,1]
[1,2,3,5,6,8,4,7]=>1110000=>0000111=>[5,1,1,1]
[1,5,2,3,4,6,7,8]=>1000111=>1110001=>[1,1,1,4,1]
[6,1,7,2,8,3,4,5]=>0000000=>0000000=>[8]
[6,1,7,8,2,3,4,5]=>0000000=>0000000=>[8]
[6,7,1,8,2,3,4,5]=>0000000=>0000000=>[8]
[6,7,1,2,3,8,4,5]=>0000000=>0000000=>[8]
[1,6,2,7,3,8,4,5]=>1000000=>0000001=>[7,1]
[1,6,7,2,3,8,4,5]=>1000000=>0000001=>[7,1]
[1,6,7,2,8,3,4,5]=>1000000=>0000001=>[7,1]
[1,6,7,8,2,3,4,5]=>1000000=>0000001=>[7,1]
[6,1,2,7,3,4,8,5]=>0000000=>0000000=>[8]
[1,6,2,7,3,4,8,5]=>1000000=>0000001=>[7,1]
[1,6,7,2,3,4,8,5]=>1000000=>0000001=>[7,1]
[1,6,2,3,7,4,8,5]=>1000000=>0000001=>[7,1]
[1,2,6,3,7,4,8,5]=>1100000=>0000011=>[6,1,1]
[1,2,6,7,3,4,8,5]=>1100000=>0000011=>[6,1,1]
[1,2,6,7,3,8,4,5]=>1100000=>0000011=>[6,1,1]
[1,2,6,7,8,3,4,5]=>1100000=>0000011=>[6,1,1]
[6,1,7,2,3,4,5,8]=>0000001=>1000000=>[1,7]
[1,6,2,7,3,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,6,7,2,3,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,6,2,3,4,7,5,8]=>1000001=>1000001=>[1,6,1]
[1,2,6,3,4,7,5,8]=>1100001=>1000011=>[1,5,1,1]
[1,2,3,6,4,7,5,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,2,6,3,4,7,8,5]=>1100000=>0000011=>[6,1,1]
[1,2,3,6,4,7,8,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,6,7,4,8,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,6,7,8,4,5]=>1110000=>0000111=>[5,1,1,1]
[6,1,8,2,3,4,5,7]=>0000000=>0000000=>[8]
[6,1,2,8,3,4,5,7]=>0000000=>0000000=>[8]
[1,6,2,8,3,4,5,7]=>1000000=>0000001=>[7,1]
[1,6,8,2,3,4,5,7]=>1000000=>0000001=>[7,1]
[1,6,2,3,8,4,5,7]=>1000000=>0000001=>[7,1]
[1,2,6,3,8,4,5,7]=>1100000=>0000011=>[6,1,1]
[1,6,2,3,4,8,5,7]=>1000000=>0000001=>[7,1]
[1,2,6,3,4,8,5,7]=>1100000=>0000011=>[6,1,1]
[1,2,3,6,4,8,5,7]=>1110000=>0000111=>[5,1,1,1]
[1,6,2,3,4,5,8,7]=>1000010=>0100001=>[2,5,1]
[1,2,6,3,4,5,8,7]=>1100010=>0100011=>[2,4,1,1]
[1,2,3,6,4,5,8,7]=>1110010=>0100111=>[2,3,1,1,1]
[1,2,3,4,6,8,5,7]=>1111000=>0001111=>[4,1,1,1,1]
[1,6,2,3,4,5,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,2,6,3,4,5,7,8]=>1100011=>1100011=>[1,1,4,1,1]
[1,2,3,6,4,5,7,8]=>1110011=>1100111=>[1,1,3,1,1,1]
[7,1,2,8,3,4,5,6]=>0000000=>0000000=>[8]
[1,7,2,8,3,4,5,6]=>1000000=>0000001=>[7,1]
[1,7,8,2,3,4,5,6]=>1000000=>0000001=>[7,1]
[1,2,7,8,3,4,5,6]=>1100000=>0000011=>[6,1,1]
[1,2,7,3,4,8,5,6]=>1100000=>0000011=>[6,1,1]
[1,2,3,7,4,8,5,6]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,8,4,5,6]=>1110000=>0000111=>[5,1,1,1]
[1,2,7,3,4,5,8,6]=>1100000=>0000011=>[6,1,1]
[1,2,3,7,4,5,8,6]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,4,7,5,8,6]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,3,4,7,8,5,6]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,7,3,4,5,6,8]=>1100001=>1000011=>[1,5,1,1]
[1,2,3,7,4,5,6,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,2,3,4,7,5,6,8]=>1111001=>1001111=>[1,3,1,1,1,1]
[1,8,2,3,4,5,6,7]=>1000000=>0000001=>[7,1]
[1,2,8,3,4,5,6,7]=>1100000=>0000011=>[6,1,1]
[1,2,3,8,4,5,6,7]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,4,8,5,6,7]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,3,4,5,8,6,7]=>1111100=>0011111=>[3,1,1,1,1,1]
[5,3,2,6,1,4,8,7]=>0000010=>0100000=>[2,6]
[7,3,2,5,4,8,1,6]=>0000000=>0000000=>[8]
[8,4,5,2,3,7,6,1]=>0000000=>0000000=>[8]
[7,4,5,2,3,8,1,6]=>0000000=>0000000=>[8]
[6,4,5,2,3,1,8,7]=>0000010=>0100000=>[2,6]
[5,4,6,2,1,3,8,7]=>0000010=>0100000=>[2,6]
[3,6,1,5,4,2,8,7]=>0000010=>0100000=>[2,6]
[4,6,5,1,3,2,8,7]=>0000010=>0100000=>[2,6]
[5,6,4,3,1,2,8,7]=>0000010=>0100000=>[2,6]
[7,5,4,3,2,8,1,6]=>0000000=>0000000=>[8]
[8,6,4,3,7,2,5,1]=>0000000=>0000000=>[8]
[7,6,4,3,8,2,1,5]=>0000000=>0000000=>[8]
[6,7,4,3,8,1,2,5]=>0000000=>0000000=>[8]
[5,7,4,3,1,8,2,6]=>0000000=>0000000=>[8]
[4,7,5,1,3,8,2,6]=>0000000=>0000000=>[8]
[3,7,1,5,4,8,2,6]=>0000000=>0000000=>[8]
[2,1,7,5,4,8,3,6]=>0100000=>0000010=>[6,2]
[3,8,1,5,4,7,6,2]=>0000000=>0000000=>[8]
[4,8,5,1,3,7,6,2]=>0000000=>0000000=>[8]
[5,8,4,3,1,7,6,2]=>0000000=>0000000=>[8]
[6,8,4,3,7,1,5,2]=>0000000=>0000000=>[8]
[7,8,4,3,6,5,1,2]=>0000000=>0000000=>[8]
[6,8,5,7,3,1,4,2]=>0000000=>0000000=>[8]
[5,8,6,7,1,3,4,2]=>0000000=>0000000=>[8]
[4,8,6,1,7,3,5,2]=>0000000=>0000000=>[8]
[3,8,1,6,7,4,5,2]=>0000000=>0000000=>[8]
[2,1,8,6,7,4,5,3]=>0100000=>0000010=>[6,2]
[2,1,7,6,8,4,3,5]=>0100000=>0000010=>[6,2]
[3,7,1,6,8,4,2,5]=>0000000=>0000000=>[8]
[4,7,6,1,8,3,2,5]=>0000000=>0000000=>[8]
[5,7,6,8,1,3,2,4]=>0000000=>0000000=>[8]
[5,4,7,2,1,8,3,6]=>0000000=>0000000=>[8]
[6,4,7,2,8,1,3,5]=>0000000=>0000000=>[8]
[7,4,6,2,8,3,1,5]=>0000000=>0000000=>[8]
[8,4,6,2,7,3,5,1]=>0000000=>0000000=>[8]
[8,3,2,6,7,4,5,1]=>0000000=>0000000=>[8]
[7,3,2,6,8,4,1,5]=>0000000=>0000000=>[8]
[6,3,2,7,8,1,4,5]=>0000000=>0000000=>[8]
[5,3,2,7,1,8,4,6]=>0000000=>0000000=>[8]
[4,3,2,1,7,8,5,6]=>0001000=>0001000=>[4,4]
[3,4,1,2,8,7,6,5]=>0001000=>0001000=>[4,4]
[5,3,2,8,1,7,6,4]=>0000000=>0000000=>[8]
[6,3,2,8,7,1,5,4]=>0000000=>0000000=>[8]
[7,3,2,8,6,5,1,4]=>0000000=>0000000=>[8]
[8,4,7,2,6,5,3,1]=>0000000=>0000000=>[8]
[7,4,8,2,6,5,1,3]=>0000000=>0000000=>[8]
[6,4,8,2,7,1,5,3]=>0000000=>0000000=>[8]
[5,4,8,2,1,7,6,3]=>0000000=>0000000=>[8]
[4,5,8,1,2,7,6,3]=>0000000=>0000000=>[8]
[3,5,1,8,2,7,6,4]=>0000000=>0000000=>[8]
[2,1,5,8,3,7,6,4]=>0100000=>0000010=>[6,2]
[2,1,6,8,7,3,5,4]=>0100000=>0000010=>[6,2]
[3,6,1,8,7,2,5,4]=>0000000=>0000000=>[8]
[4,6,8,1,7,2,5,3]=>0000000=>0000000=>[8]
[5,6,8,7,1,2,4,3]=>0000000=>0000000=>[8]
[6,5,8,7,2,1,4,3]=>0000000=>0000000=>[8]
[7,5,8,6,2,4,1,3]=>0000000=>0000000=>[8]
[8,5,7,6,2,4,3,1]=>0000000=>0000000=>[8]
[5,7,8,6,1,4,2,3]=>0000000=>0000000=>[8]
[4,7,8,1,6,5,2,3]=>0000000=>0000000=>[8]
[3,7,1,8,6,5,2,4]=>0000000=>0000000=>[8]
[2,1,7,8,6,5,3,4]=>0100000=>0000010=>[6,2]
[3,8,1,7,6,5,4,2]=>0000000=>0000000=>[8]
[4,8,7,1,6,5,3,2]=>0000000=>0000000=>[8]
[5,8,7,6,1,4,3,2]=>0000000=>0000000=>[8]
[6,8,7,5,4,1,3,2]=>0000000=>0000000=>[8]
[3,2,5,1,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,2,4,1,3,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[3,2,6,1,4,5,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,7,1,2,3,6,8]=>0000001=>1000000=>[1,7]
[6,2,7,1,3,4,5,8]=>0000001=>1000000=>[1,7]
[6,3,7,1,2,4,5,8]=>0000001=>1000000=>[1,7]
[6,4,7,1,2,3,5,8]=>0000001=>1000000=>[1,7]
[7,4,6,1,2,3,5,8]=>0000001=>1000000=>[1,7]
[3,2,8,1,4,5,6,7]=>0000000=>0000000=>[8]
[5,4,8,1,2,3,6,7]=>0000000=>0000000=>[8]
[6,5,8,1,2,3,4,7]=>0000000=>0000000=>[8]
[7,5,8,1,2,3,4,6]=>0000000=>0000000=>[8]
[8,5,7,1,2,3,4,6]=>0000000=>0000000=>[8]
[3,2,5,7,1,4,6,8]=>0000001=>1000000=>[1,7]
[4,2,6,7,1,3,5,8]=>0000001=>1000000=>[1,7]
[5,2,6,7,1,3,4,8]=>0000001=>1000000=>[1,7]
[5,3,6,7,1,2,4,8]=>0000001=>1000000=>[1,7]
[3,2,5,8,1,4,6,7]=>0000000=>0000000=>[8]
[4,2,5,8,1,3,6,7]=>0000000=>0000000=>[8]
[4,3,5,8,1,2,6,7]=>0000000=>0000000=>[8]
[5,2,4,8,1,3,6,7]=>0000000=>0000000=>[8]
[3,2,6,8,1,4,5,7]=>0000000=>0000000=>[8]
[5,2,6,8,1,3,4,7]=>0000000=>0000000=>[8]
[6,2,4,8,1,3,5,7]=>0000000=>0000000=>[8]
[6,2,5,8,1,3,4,7]=>0000000=>0000000=>[8]
[3,2,7,8,1,4,5,6]=>0000000=>0000000=>[8]
[4,3,7,8,1,2,5,6]=>0000000=>0000000=>[8]
[5,4,7,8,1,2,3,6]=>0000000=>0000000=>[8]
[6,2,7,8,1,3,4,5]=>0000000=>0000000=>[8]
[6,3,7,8,1,2,4,5]=>0000000=>0000000=>[8]
[6,4,7,8,1,2,3,5]=>0000000=>0000000=>[8]
[7,2,4,8,1,3,5,6]=>0000000=>0000000=>[8]
[7,4,5,8,1,2,3,6]=>0000000=>0000000=>[8]
[8,2,6,7,1,3,4,5]=>0000000=>0000000=>[8]
[8,4,6,7,1,2,3,5]=>0000000=>0000000=>[8]
[4,6,2,5,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,6,3,5,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,6,2,4,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,7,3,5,1,2,6,8]=>0000001=>1000000=>[1,7]
[5,7,2,4,1,3,6,8]=>0000001=>1000000=>[1,7]
[3,7,2,6,1,4,5,8]=>0000001=>1000000=>[1,7]
[5,7,2,6,1,3,4,8]=>0000001=>1000000=>[1,7]
[6,7,2,5,1,3,4,8]=>0000001=>1000000=>[1,7]
[4,8,2,5,1,3,6,7]=>0000000=>0000000=>[8]
[5,8,3,4,1,2,6,7]=>0000000=>0000000=>[8]
[5,8,3,6,1,2,4,7]=>0000000=>0000000=>[8]
[6,8,3,5,1,2,4,7]=>0000000=>0000000=>[8]
[3,8,2,7,1,4,5,6]=>0000000=>0000000=>[8]
[4,8,2,7,1,3,5,6]=>0000000=>0000000=>[8]
[4,8,3,7,1,2,5,6]=>0000000=>0000000=>[8]
[5,8,2,7,1,3,4,6]=>0000000=>0000000=>[8]
[6,8,2,7,1,3,4,5]=>0000000=>0000000=>[8]
[6,8,3,7,1,2,4,5]=>0000000=>0000000=>[8]
[6,8,5,7,1,2,3,4]=>0000000=>0000000=>[8]
[7,8,2,4,1,3,5,6]=>0000000=>0000000=>[8]
[7,8,2,5,1,3,4,6]=>0000000=>0000000=>[8]
[7,8,4,6,1,2,3,5]=>0000000=>0000000=>[8]
[4,3,2,6,1,5,7,8]=>0000011=>1100000=>[1,1,6]
[5,3,2,6,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,2,6,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,3,2,7,1,5,6,8]=>0000001=>1000000=>[1,7]
[5,3,2,7,1,4,6,8]=>0000001=>1000000=>[1,7]
[5,4,3,7,1,2,6,8]=>0000001=>1000000=>[1,7]
[6,3,2,7,1,4,5,8]=>0000001=>1000000=>[1,7]
[6,4,2,7,1,3,5,8]=>0000001=>1000000=>[1,7]
[6,4,3,7,1,2,5,8]=>0000001=>1000000=>[1,7]
[6,5,3,7,1,2,4,8]=>0000001=>1000000=>[1,7]
[7,4,2,5,1,3,6,8]=>0000001=>1000000=>[1,7]
[7,4,3,6,1,2,5,8]=>0000001=>1000000=>[1,7]
[7,5,2,6,1,3,4,8]=>0000001=>1000000=>[1,7]
[7,5,3,6,1,2,4,8]=>0000001=>1000000=>[1,7]
[7,6,3,5,1,2,4,8]=>0000001=>1000000=>[1,7]
[4,3,2,8,1,5,6,7]=>0000000=>0000000=>[8]
[5,3,2,8,1,4,6,7]=>0000000=>0000000=>[8]
[5,4,3,8,1,2,6,7]=>0000000=>0000000=>[8]
[6,3,2,8,1,4,5,7]=>0000000=>0000000=>[8]
[6,4,3,8,1,2,5,7]=>0000000=>0000000=>[8]
[6,5,2,8,1,3,4,7]=>0000000=>0000000=>[8]
[6,5,3,8,1,2,4,7]=>0000000=>0000000=>[8]
[7,4,2,8,1,3,5,6]=>0000000=>0000000=>[8]
[7,5,3,8,1,2,4,6]=>0000000=>0000000=>[8]
[7,6,2,8,1,3,4,5]=>0000000=>0000000=>[8]
[8,4,2,5,1,3,6,7]=>0000000=>0000000=>[8]
[8,4,2,6,1,3,5,7]=>0000000=>0000000=>[8]
[8,5,3,6,1,2,4,7]=>0000000=>0000000=>[8]
[8,6,2,5,1,3,4,7]=>0000000=>0000000=>[8]
[8,4,2,7,1,3,5,6]=>0000000=>0000000=>[8]
[8,4,3,7,1,2,5,6]=>0000000=>0000000=>[8]
[8,5,2,7,1,3,4,6]=>0000000=>0000000=>[8]
[8,5,3,7,1,2,4,6]=>0000000=>0000000=>[8]
[8,7,2,4,1,3,5,6]=>0000000=>0000000=>[8]
[8,7,2,5,1,3,4,6]=>0000000=>0000000=>[8]
[8,7,3,5,1,2,4,6]=>0000000=>0000000=>[8]
[8,7,2,6,1,3,4,5]=>0000000=>0000000=>[8]
[8,7,3,6,1,2,4,5]=>0000000=>0000000=>[8]
[8,7,4,6,1,2,3,5]=>0000000=>0000000=>[8]
[5,6,2,4,8,1,3,7]=>0000000=>0000000=>[8]
[4,7,3,5,8,1,2,6]=>0000000=>0000000=>[8]
[4,7,3,6,8,1,2,5]=>0000000=>0000000=>[8]
[4,8,3,5,7,1,2,6]=>0000000=>0000000=>[8]
[7,8,2,4,6,1,3,5]=>0000000=>0000000=>[8]
[7,8,3,4,6,1,2,5]=>0000000=>0000000=>[8]
[7,8,2,5,6,1,3,4]=>0000000=>0000000=>[8]
[7,8,3,5,6,1,2,4]=>0000000=>0000000=>[8]
[4,3,2,6,8,1,5,7]=>0000000=>0000000=>[8]
[5,4,2,6,8,1,3,7]=>0000000=>0000000=>[8]
[5,4,3,6,8,1,2,7]=>0000000=>0000000=>[8]
[6,3,2,5,8,1,4,7]=>0000000=>0000000=>[8]
[6,5,2,4,8,1,3,7]=>0000000=>0000000=>[8]
[4,3,2,7,8,1,5,6]=>0000000=>0000000=>[8]
[5,3,2,7,8,1,4,6]=>0000000=>0000000=>[8]
[5,4,2,7,8,1,3,6]=>0000000=>0000000=>[8]
[5,4,3,7,8,1,2,6]=>0000000=>0000000=>[8]
[6,4,2,7,8,1,3,5]=>0000000=>0000000=>[8]
[6,4,3,7,8,1,2,5]=>0000000=>0000000=>[8]
[6,5,2,7,8,1,3,4]=>0000000=>0000000=>[8]
[8,4,2,5,7,1,3,6]=>0000000=>0000000=>[8]
[8,5,2,6,7,1,3,4]=>0000000=>0000000=>[8]
[8,5,3,6,7,1,2,4]=>0000000=>0000000=>[8]
[8,6,2,5,7,1,3,4]=>0000000=>0000000=>[8]
[8,6,3,5,7,1,2,4]=>0000000=>0000000=>[8]
[8,7,2,4,6,1,3,5]=>0000000=>0000000=>[8]
[8,7,3,4,6,1,2,5]=>0000000=>0000000=>[8]
[8,7,2,5,6,1,3,4]=>0000000=>0000000=>[8]
[4,3,7,2,6,1,5,8]=>0000001=>1000000=>[1,7]
[5,3,7,2,6,1,4,8]=>0000001=>1000000=>[1,7]
[5,4,7,2,6,1,3,8]=>0000001=>1000000=>[1,7]
[6,3,7,2,5,1,4,8]=>0000001=>1000000=>[1,7]
[6,4,7,2,5,1,3,8]=>0000001=>1000000=>[1,7]
[7,3,6,2,5,1,4,8]=>0000001=>1000000=>[1,7]
[4,3,8,2,6,1,5,7]=>0000000=>0000000=>[8]
[5,3,8,2,6,1,4,7]=>0000000=>0000000=>[8]
[5,4,8,2,6,1,3,7]=>0000000=>0000000=>[8]
[6,4,8,2,5,1,3,7]=>0000000=>0000000=>[8]
[6,4,8,3,5,1,2,7]=>0000000=>0000000=>[8]
[4,3,8,2,7,1,5,6]=>0000000=>0000000=>[8]
[5,4,8,2,7,1,3,6]=>0000000=>0000000=>[8]
[6,4,8,2,7,1,3,5]=>0000000=>0000000=>[8]
[7,3,8,2,5,1,4,6]=>0000000=>0000000=>[8]
[7,4,8,3,5,1,2,6]=>0000000=>0000000=>[8]
[7,5,8,2,4,1,3,6]=>0000000=>0000000=>[8]
[7,5,8,2,6,1,3,4]=>0000000=>0000000=>[8]
[7,5,8,4,6,1,2,3]=>0000000=>0000000=>[8]
[8,3,6,2,5,1,4,7]=>0000000=>0000000=>[8]
[8,4,6,2,5,1,3,7]=>0000000=>0000000=>[8]
[8,3,7,2,5,1,4,6]=>0000000=>0000000=>[8]
[8,4,7,3,5,1,2,6]=>0000000=>0000000=>[8]
[8,3,7,2,6,1,4,5]=>0000000=>0000000=>[8]
[8,4,7,2,6,1,3,5]=>0000000=>0000000=>[8]
[8,4,7,3,6,1,2,5]=>0000000=>0000000=>[8]
[8,5,7,2,6,1,3,4]=>0000000=>0000000=>[8]
[8,6,7,2,4,1,3,5]=>0000000=>0000000=>[8]
[8,6,7,2,5,1,3,4]=>0000000=>0000000=>[8]
[5,4,3,2,7,1,6,8]=>0000001=>1000000=>[1,7]
[6,5,3,2,7,1,4,8]=>0000001=>1000000=>[1,7]
[7,5,3,2,6,1,4,8]=>0000001=>1000000=>[1,7]
[5,4,3,2,8,1,6,7]=>0000000=>0000000=>[8]
[6,5,3,2,8,1,4,7]=>0000000=>0000000=>[8]
[7,5,3,2,8,1,4,6]=>0000000=>0000000=>[8]
[7,6,4,3,8,1,2,5]=>0000000=>0000000=>[8]
[8,5,3,2,6,1,4,7]=>0000000=>0000000=>[8]
[8,5,4,2,6,1,3,7]=>0000000=>0000000=>[8]
[8,5,3,2,7,1,4,6]=>0000000=>0000000=>[8]
[8,6,3,2,7,1,4,5]=>0000000=>0000000=>[8]
[8,7,5,2,6,1,3,4]=>0000000=>0000000=>[8]
[8,7,6,2,4,1,3,5]=>0000000=>0000000=>[8]
[4,8,3,7,2,6,1,5]=>0000000=>0000000=>[8]
[5,8,3,7,2,6,1,4]=>0000000=>0000000=>[8]
[5,8,4,7,2,6,1,3]=>0000000=>0000000=>[8]
[5,8,4,7,3,6,1,2]=>0000000=>0000000=>[8]
[6,8,3,7,2,5,1,4]=>0000000=>0000000=>[8]
[6,8,4,7,2,5,1,3]=>0000000=>0000000=>[8]
[6,8,4,7,3,5,1,2]=>0000000=>0000000=>[8]
[6,8,5,7,2,4,1,3]=>0000000=>0000000=>[8]
[6,8,5,7,3,4,1,2]=>0000000=>0000000=>[8]
[7,8,3,6,2,5,1,4]=>0000000=>0000000=>[8]
[7,8,4,6,2,5,1,3]=>0000000=>0000000=>[8]
[7,8,4,6,3,5,1,2]=>0000000=>0000000=>[8]
[7,8,5,6,2,4,1,3]=>0000000=>0000000=>[8]
[6,4,3,8,2,7,1,5]=>0000000=>0000000=>[8]
[7,5,3,8,2,6,1,4]=>0000000=>0000000=>[8]
[7,5,4,8,2,6,1,3]=>0000000=>0000000=>[8]
[7,6,3,8,2,5,1,4]=>0000000=>0000000=>[8]
[7,6,4,8,2,5,1,3]=>0000000=>0000000=>[8]
[7,6,5,8,2,4,1,3]=>0000000=>0000000=>[8]
[8,5,3,7,2,6,1,4]=>0000000=>0000000=>[8]
[8,6,4,7,2,5,1,3]=>0000000=>0000000=>[8]
[8,6,4,7,3,5,1,2]=>0000000=>0000000=>[8]
[8,6,5,7,2,4,1,3]=>0000000=>0000000=>[8]
[6,5,4,3,2,8,1,7]=>0000000=>0000000=>[8]
[8,7,6,3,2,5,1,4]=>0000000=>0000000=>[8]
[8,7,6,5,2,4,1,3]=>0000000=>0000000=>[8]
[6,1,2,5,3,8,4,7]=>0000000=>0000000=>[8]
[4,1,2,8,7,3,5,6]=>0000000=>0000000=>[8]
[4,1,2,7,6,3,8,5]=>0000000=>0000000=>[8]
[8,1,2,5,6,3,4,7]=>0000000=>0000000=>[8]
[8,1,2,7,6,3,4,5]=>0000000=>0000000=>[8]
[7,1,2,5,6,3,8,4]=>0000000=>0000000=>[8]
[8,1,2,5,6,7,3,4]=>0000000=>0000000=>[8]
[3,1,7,2,6,4,8,5]=>0000000=>0000000=>[8]
[3,1,8,2,6,7,4,5]=>0000000=>0000000=>[8]
[6,1,4,2,3,8,5,7]=>0000000=>0000000=>[8]
[7,1,5,2,3,4,8,6]=>0000000=>0000000=>[8]
[6,1,5,2,3,8,4,7]=>0000000=>0000000=>[8]
[6,1,5,2,3,7,8,4]=>0000000=>0000000=>[8]
[5,1,4,2,8,3,6,7]=>0000000=>0000000=>[8]
[5,1,4,2,7,3,8,6]=>0000000=>0000000=>[8]
[7,1,4,2,6,3,8,5]=>0000000=>0000000=>[8]
[8,1,5,2,7,3,4,6]=>0000000=>0000000=>[8]
[5,1,4,2,8,7,3,6]=>0000000=>0000000=>[8]
[8,1,4,2,6,7,3,5]=>0000000=>0000000=>[8]
[8,1,5,2,6,7,3,4]=>0000000=>0000000=>[8]
[5,1,4,2,6,7,8,3]=>0000000=>0000000=>[8]
[3,1,8,6,2,4,5,7]=>0000000=>0000000=>[8]
[3,1,8,5,2,7,4,6]=>0000000=>0000000=>[8]
[3,1,8,6,2,7,4,5]=>0000000=>0000000=>[8]
[8,1,4,5,2,3,6,7]=>0000000=>0000000=>[8]
[7,1,8,6,2,3,4,5]=>0000000=>0000000=>[8]
[7,1,6,5,2,3,8,4]=>0000000=>0000000=>[8]
[3,1,4,8,6,2,5,7]=>0000000=>0000000=>[8]
[3,1,7,5,6,2,8,4]=>0000000=>0000000=>[8]
[8,1,4,7,6,2,3,5]=>0000000=>0000000=>[8]
[3,1,8,5,6,7,2,4]=>0000000=>0000000=>[8]
[8,1,4,5,6,7,2,3]=>0000000=>0000000=>[8]
[2,8,1,3,6,7,4,5]=>0000000=>0000000=>[8]
[2,4,1,8,3,7,5,6]=>0000000=>0000000=>[8]
[2,6,1,5,3,8,4,7]=>0000000=>0000000=>[8]
[2,6,1,5,3,7,8,4]=>0000000=>0000000=>[8]
[2,8,1,7,6,3,4,5]=>0000000=>0000000=>[8]
[5,3,1,2,8,4,6,7]=>0000000=>0000000=>[8]
[5,3,1,2,8,7,4,6]=>0000000=>0000000=>[8]
[5,4,1,2,8,3,6,7]=>0000000=>0000000=>[8]
[7,4,1,2,6,3,8,5]=>0000000=>0000000=>[8]
[5,8,1,2,7,3,4,6]=>0000000=>0000000=>[8]
[8,7,1,2,6,3,4,5]=>0000000=>0000000=>[8]
[5,7,1,2,6,3,8,4]=>0000000=>0000000=>[8]
[8,4,1,2,6,7,3,5]=>0000000=>0000000=>[8]
[5,8,1,2,6,7,3,4]=>0000000=>0000000=>[8]
[5,4,1,2,6,7,8,3]=>0000000=>0000000=>[8]
[4,3,1,6,2,8,5,7]=>0000000=>0000000=>[8]
[4,3,1,6,2,7,8,5]=>0000000=>0000000=>[8]
[8,3,1,5,2,4,6,7]=>0000000=>0000000=>[8]
[8,3,1,6,2,4,5,7]=>0000000=>0000000=>[8]
[7,3,1,6,2,4,8,5]=>0000000=>0000000=>[8]
[8,3,1,6,2,7,4,5]=>0000000=>0000000=>[8]
[6,3,1,5,2,7,8,4]=>0000000=>0000000=>[8]
[7,4,1,5,2,3,8,6]=>0000000=>0000000=>[8]
[8,4,1,6,2,3,5,7]=>0000000=>0000000=>[8]
[7,4,1,8,2,3,5,6]=>0000000=>0000000=>[8]
[7,4,1,6,2,3,8,5]=>0000000=>0000000=>[8]
[8,7,1,6,2,3,4,5]=>0000000=>0000000=>[8]
[6,7,1,5,2,3,8,4]=>0000000=>0000000=>[8]
[6,8,1,5,2,7,3,4]=>0000000=>0000000=>[8]
[6,4,1,5,2,7,8,3]=>0000000=>0000000=>[8]
[4,3,1,8,7,2,5,6]=>0000000=>0000000=>[8]
[8,3,1,5,6,2,4,7]=>0000000=>0000000=>[8]
[8,3,1,5,7,2,4,6]=>0000000=>0000000=>[8]
[7,3,1,5,6,2,8,4]=>0000000=>0000000=>[8]
[7,8,1,5,6,2,3,4]=>0000000=>0000000=>[8]
[8,4,1,5,6,7,2,3]=>0000000=>0000000=>[8]
[2,3,7,1,6,4,8,5]=>0000000=>0000000=>[8]
[2,3,5,1,8,7,4,6]=>0000000=>0000000=>[8]
[2,8,4,1,3,5,6,7]=>0000000=>0000000=>[8]
[2,6,4,1,3,7,8,5]=>0000000=>0000000=>[8]
[2,6,5,1,3,7,8,4]=>0000000=>0000000=>[8]
[2,7,4,1,6,3,8,5]=>0000000=>0000000=>[8]
[2,8,5,1,7,3,4,6]=>0000000=>0000000=>[8]
[2,7,5,1,6,3,8,4]=>0000000=>0000000=>[8]
[6,3,4,1,2,7,8,5]=>0000000=>0000000=>[8]
[7,3,5,1,2,4,8,6]=>0000000=>0000000=>[8]
[6,3,7,1,2,4,8,5]=>0000000=>0000000=>[8]
[6,3,8,1,2,7,4,5]=>0000000=>0000000=>[8]
[6,7,4,1,2,3,8,5]=>0000000=>0000000=>[8]
[6,8,5,1,2,3,4,7]=>0000000=>0000000=>[8]
[8,5,4,1,2,7,3,6]=>0000000=>0000000=>[8]
[6,8,4,1,2,7,3,5]=>0000000=>0000000=>[8]
[6,8,5,1,2,7,3,4]=>0000000=>0000000=>[8]
[8,3,4,1,7,2,5,6]=>0000000=>0000000=>[8]
[8,3,5,1,6,2,4,7]=>0000000=>0000000=>[8]
[7,3,8,1,6,2,4,5]=>0000000=>0000000=>[8]
[8,5,4,1,6,2,3,7]=>0000000=>0000000=>[8]
[7,8,4,1,6,2,3,5]=>0000000=>0000000=>[8]
[7,8,5,1,6,2,3,4]=>0000000=>0000000=>[8]
[5,3,4,1,6,7,8,2]=>0000000=>0000000=>[8]
[2,3,7,6,1,4,8,5]=>0000000=>0000000=>[8]
[2,3,6,5,1,8,4,7]=>0000000=>0000000=>[8]
[2,3,6,5,1,7,8,4]=>0000000=>0000000=>[8]
[2,7,4,8,1,3,5,6]=>0000000=>0000000=>[8]
[2,7,4,6,1,3,8,5]=>0000000=>0000000=>[8]
[2,7,6,5,1,3,8,4]=>0000000=>0000000=>[8]
[2,6,4,5,1,8,3,7]=>0000000=>0000000=>[8]
[2,8,4,6,1,7,3,5]=>0000000=>0000000=>[8]
[7,3,8,5,1,2,4,6]=>0000000=>0000000=>[8]
[8,6,4,5,1,7,2,3]=>0000000=>0000000=>[8]
[2,3,8,5,7,1,4,6]=>0000000=>0000000=>[8]
[2,3,7,5,6,1,8,4]=>0000000=>0000000=>[8]
[2,8,4,7,6,1,3,5]=>0000000=>0000000=>[8]
[2,8,7,5,6,1,3,4]=>0000000=>0000000=>[8]
[8,3,7,5,6,1,2,4]=>0000000=>0000000=>[8]
[2,8,4,5,6,7,1,3]=>0000000=>0000000=>[8]
[6,5,8,7,3,4,1,2]=>0000000=>0000000=>[8]
[4,6,7,3,8,5,1,2]=>0000000=>0000000=>[8]
[3,6,7,4,5,8,1,2]=>0000000=>0000000=>[8]
[2,6,7,4,5,1,8,3]=>0000000=>0000000=>[8]
[1,6,7,4,5,2,3,8]=>1000001=>1000001=>[1,6,1]
[1,5,4,7,6,2,3,8]=>1000001=>1000001=>[1,6,1]
[2,5,4,7,6,1,8,3]=>0000000=>0000000=>[8]
[3,5,4,7,6,8,1,2]=>0000000=>0000000=>[8]
[4,5,3,7,8,6,1,2]=>0000000=>0000000=>[8]
[5,4,3,8,7,6,1,2]=>0000000=>0000000=>[8]
[6,4,8,3,7,5,1,2]=>0000000=>0000000=>[8]
[6,3,8,4,5,7,1,2]=>0000000=>0000000=>[8]
[5,3,4,8,6,7,1,2]=>0000000=>0000000=>[8]
[4,3,5,6,8,7,1,2]=>0000000=>0000000=>[8]
[3,2,5,6,1,8,7,4]=>0000000=>0000000=>[8]
[4,2,5,6,8,1,7,3]=>0000000=>0000000=>[8]
[5,2,4,8,6,1,7,3]=>0000000=>0000000=>[8]
[6,2,8,4,5,1,7,3]=>0000000=>0000000=>[8]
[7,8,2,4,5,1,6,3]=>0000000=>0000000=>[8]
[7,8,1,4,5,2,3,6]=>0000000=>0000000=>[8]
[6,1,8,4,5,2,3,7]=>0000000=>0000000=>[8]
[5,1,4,8,6,2,3,7]=>0000000=>0000000=>[8]
[4,1,3,2,8,6,5,7]=>0001000=>0001000=>[4,4]
[5,1,3,8,2,6,4,7]=>0000000=>0000000=>[8]
[6,1,8,3,2,5,4,7]=>0000000=>0000000=>[8]
[7,8,1,3,2,5,4,6]=>0000000=>0000000=>[8]
[7,8,2,3,1,5,6,4]=>0000000=>0000000=>[8]
[6,2,8,3,1,5,7,4]=>0000000=>0000000=>[8]
[5,2,3,8,1,6,7,4]=>0000000=>0000000=>[8]
[6,3,8,2,1,7,5,4]=>0000000=>0000000=>[8]
[7,8,3,2,1,6,5,4]=>0000000=>0000000=>[8]
[7,8,4,2,6,1,5,3]=>0000000=>0000000=>[8]
[5,4,2,8,7,1,6,3]=>0000000=>0000000=>[8]
[4,5,2,7,8,1,6,3]=>0000000=>0000000=>[8]
[3,5,2,7,1,8,6,4]=>0000000=>0000000=>[8]
[2,5,3,7,1,6,8,4]=>0000000=>0000000=>[8]
[1,5,3,7,2,6,4,8]=>1000001=>1000001=>[1,6,1]
[1,6,7,3,2,5,4,8]=>1000001=>1000001=>[1,6,1]
[2,6,7,3,1,5,8,4]=>0000000=>0000000=>[8]
[3,6,7,2,1,8,5,4]=>0000000=>0000000=>[8]
[4,6,7,2,8,1,5,3]=>0000000=>0000000=>[8]
[5,6,7,8,2,1,4,3]=>0000000=>0000000=>[8]
[7,8,5,6,2,1,4,3]=>0000000=>0000000=>[8]
[6,5,8,7,1,2,3,4]=>0000000=>0000000=>[8]
[5,4,1,8,7,2,3,6]=>0000000=>0000000=>[8]
[6,4,8,1,7,2,3,5]=>0000000=>0000000=>[8]
[7,8,3,1,2,6,4,5]=>0000000=>0000000=>[8]
[5,3,1,8,2,7,4,6]=>0000000=>0000000=>[8]
[4,3,1,2,8,7,5,6]=>0001000=>0001000=>[4,4]
[4,2,1,3,8,5,7,6]=>0001000=>0001000=>[4,4]
[5,2,1,8,3,4,7,6]=>0000000=>0000000=>[8]
[6,2,8,1,3,4,7,5]=>0000000=>0000000=>[8]
[7,8,2,1,3,4,6,5]=>0000000=>0000000=>[8]
[4,5,2,3,7,6,1,8]=>0000001=>1000000=>[1,7]
[6,4,3,7,2,5,1,8]=>0000001=>1000000=>[1,7]
[8,4,3,6,5,1,2,7]=>0000000=>0000000=>[8]
[1,5,6,3,4,8,7,2]=>1000000=>0000001=>[7,1]
[4,6,2,7,3,5,1,8]=>0000001=>1000000=>[1,7]
[3,2,6,7,4,5,1,8]=>0000001=>1000000=>[1,7]
[4,1,2,6,5,8,7,3]=>0000000=>0000000=>[8]
[5,1,6,2,4,8,7,3]=>0000000=>0000000=>[8]
[8,1,5,4,7,6,2,3]=>0000000=>0000000=>[8]
[1,8,6,7,4,5,3,2]=>1000000=>0000001=>[7,1]
[8,1,6,7,4,5,2,3]=>0000000=>0000000=>[8]
[6,1,7,8,2,4,5,3]=>0000000=>0000000=>[8]
[5,1,7,2,8,4,6,3]=>0000000=>0000000=>[8]
[4,1,2,7,8,5,6,3]=>0000000=>0000000=>[8]
[3,2,1,7,8,5,6,4]=>0010000=>0000100=>[5,3]
[4,8,2,7,1,5,3,6]=>0000000=>0000000=>[8]
[5,8,7,2,1,4,3,6]=>0000000=>0000000=>[8]
[6,8,7,1,2,4,3,5]=>0000000=>0000000=>[8]
[8,7,6,1,4,3,2,5]=>0000000=>0000000=>[8]
[1,6,7,8,3,4,5,2]=>1000000=>0000001=>[7,1]
[7,6,8,1,3,2,4,5]=>0000000=>0000000=>[8]
[5,7,8,2,1,3,4,6]=>0000000=>0000000=>[8]
[4,7,2,8,1,3,5,6]=>0000000=>0000000=>[8]
[3,2,6,8,4,1,5,7]=>0000000=>0000000=>[8]
[4,6,2,8,3,1,5,7]=>0000000=>0000000=>[8]
[5,6,8,2,3,1,4,7]=>0000000=>0000000=>[8]
[7,5,8,3,1,2,4,6]=>0000000=>0000000=>[8]
[1,5,7,3,8,4,6,2]=>1000000=>0000001=>[7,1]
[1,4,3,7,8,5,6,2]=>1000000=>0000001=>[7,1]
[6,4,3,8,2,1,5,7]=>0000000=>0000000=>[8]
[4,5,2,3,8,1,6,7]=>0000000=>0000000=>[8]
[3,2,5,4,8,1,6,7]=>0000000=>0000000=>[8]
[4,5,2,3,1,8,7,6]=>0000100=>0010000=>[3,5]
[6,4,3,1,2,8,7,5]=>0000000=>0000000=>[8]
[7,4,3,1,8,2,6,5]=>0000000=>0000000=>[8]
[8,4,3,1,7,6,2,5]=>0000000=>0000000=>[8]
[1,5,8,3,7,6,4,2]=>1000000=>0000001=>[7,1]
[7,5,1,3,8,2,6,4]=>0000000=>0000000=>[8]
[5,6,1,2,3,8,7,4]=>0000000=>0000000=>[8]
[4,6,2,1,3,8,7,5]=>0000000=>0000000=>[8]
[3,2,6,1,4,8,7,5]=>0000000=>0000000=>[8]
[3,2,7,1,8,4,6,5]=>0000000=>0000000=>[8]
[5,7,1,2,8,3,6,4]=>0000000=>0000000=>[8]
[6,7,1,8,2,3,5,4]=>0000000=>0000000=>[8]
[7,6,1,8,3,2,5,4]=>0000000=>0000000=>[8]
[8,7,1,6,5,3,2,4]=>0000000=>0000000=>[8]
[7,8,1,6,5,2,3,4]=>0000000=>0000000=>[8]
[6,8,1,7,2,5,3,4]=>0000000=>0000000=>[8]
[5,8,1,2,7,6,3,4]=>0000000=>0000000=>[8]
[3,2,8,1,7,6,4,5]=>0000000=>0000000=>[8]
[4,1,2,8,7,6,5,3]=>0000000=>0000000=>[8]
[5,1,8,2,7,6,4,3]=>0000000=>0000000=>[8]
[6,1,8,7,2,5,4,3]=>0000000=>0000000=>[8]
[8,1,7,6,5,4,2,3]=>0000000=>0000000=>[8]
[3,2,5,4,7,1,8,6]=>0000000=>0000000=>[8]
[4,2,5,3,6,1,8,7]=>0000010=>0100000=>[2,6]
[4,3,5,2,7,1,8,6]=>0000000=>0000000=>[8]
[4,1,5,3,7,2,8,6]=>0000000=>0000000=>[8]
[2,1,5,4,7,3,8,6]=>0100000=>0000010=>[6,2]
[4,3,6,5,7,1,8,2]=>0000000=>0000000=>[8]
[4,1,6,3,7,5,8,2]=>0000000=>0000000=>[8]
[2,1,6,4,7,3,8,5]=>0100000=>0000010=>[6,2]
[3,1,6,4,7,2,8,5]=>0000000=>0000000=>[8]
[4,1,6,3,7,2,8,5]=>0000000=>0000000=>[8]
[5,2,6,3,7,1,8,4]=>0000000=>0000000=>[8]
[4,2,6,1,7,3,8,5]=>0000000=>0000000=>[8]
[4,2,6,3,7,1,8,5]=>0000000=>0000000=>[8]
[3,2,6,4,7,1,8,5]=>0000000=>0000000=>[8]
[3,2,6,1,7,4,8,5]=>0000000=>0000000=>[8]
[3,1,4,2,7,6,8,5]=>0001000=>0001000=>[4,4]
[3,2,6,1,7,5,8,4]=>0000000=>0000000=>[8]
[4,2,6,1,7,5,8,3]=>0000000=>0000000=>[8]
[4,1,6,2,7,5,8,3]=>0000000=>0000000=>[8]
[5,4,6,2,7,1,8,3]=>0000000=>0000000=>[8]
[3,1,6,5,7,2,8,4]=>0000000=>0000000=>[8]
[4,1,6,5,7,3,8,2]=>0000000=>0000000=>[8]
[8,6,1,3,4,2,5,7]=>0000000=>0000000=>[8]
[8,3,5,2,1,6,4,7]=>0000000=>0000000=>[8]
[8,6,3,5,2,4,1,7]=>0000000=>0000000=>[8]
[8,3,7,5,2,4,6,1]=>0000000=>0000000=>[8]
[2,4,5,7,3,1,8,6]=>0000000=>0000000=>[8]
[8,2,4,6,5,3,1,7]=>0000000=>0000000=>[8]
[8,1,2,4,5,6,3,7]=>0000000=>0000000=>[8]
[8,2,5,1,3,6,4,7]=>0000000=>0000000=>[8]
[8,1,5,6,4,3,2,7]=>0000000=>0000000=>[8]
[8,5,7,4,3,2,6,1]=>0000000=>0000000=>[8]
[8,5,7,4,2,1,6,3]=>0000000=>0000000=>[8]
[1,7,4,8,6,3,5,2]=>1000000=>0000001=>[7,1]
[8,4,7,6,3,5,2,1]=>0000000=>0000000=>[8]
[4,8,1,6,7,3,5,2]=>0000000=>0000000=>[8]
[3,6,4,1,8,7,5,2]=>0000000=>0000000=>[8]
[8,2,6,1,4,7,5,3]=>0000000=>0000000=>[8]
[3,7,6,5,8,2,1,4]=>0000000=>0000000=>[8]
[3,6,8,5,7,2,4,1]=>0000000=>0000000=>[8]
[2,1,6,5,7,8,3,4]=>0100000=>0000010=>[6,2]
[5,2,7,1,3,8,4,6]=>0000000=>0000000=>[8]
[5,3,1,7,8,2,4,6]=>0000000=>0000000=>[8]
[3,7,2,6,4,8,1,5]=>0000000=>0000000=>[8]
[3,2,6,1,4,7,8,5]=>0000000=>0000000=>[8]
[5,3,7,2,1,8,4,6]=>0000000=>0000000=>[8]
[4,7,3,2,1,5,8,6]=>0000000=>0000000=>[8]
[1,7,3,4,2,5,8,6]=>1000000=>0000001=>[7,1]
[4,7,2,1,3,5,8,6]=>0000000=>0000000=>[8]
[8,7,6,1,3,4,2,5]=>0000000=>0000000=>[8]
[8,5,7,3,2,1,6,4]=>0000000=>0000000=>[8]
[8,7,6,3,5,2,4,1]=>0000000=>0000000=>[8]
[2,7,4,8,1,6,5,3]=>0000000=>0000000=>[8]
[4,6,8,2,1,7,5,3]=>0000000=>0000000=>[8]
[8,5,3,7,1,6,2,4]=>0000000=>0000000=>[8]
[8,5,7,2,1,3,6,4]=>0000000=>0000000=>[8]
[4,6,1,8,7,2,5,3]=>0000000=>0000000=>[8]
[8,1,2,5,6,7,4,3]=>0000000=>0000000=>[8]
[8,2,6,5,7,4,1,3]=>0000000=>0000000=>[8]
[1,7,2,5,8,6,4,3]=>1000000=>0000001=>[7,1]
[3,7,8,1,6,5,2,4]=>0000000=>0000000=>[8]
[8,7,6,3,5,1,4,2]=>0000000=>0000000=>[8]
[8,4,7,6,5,1,3,2]=>0000000=>0000000=>[8]
[8,7,1,5,6,4,3,2]=>0000000=>0000000=>[8]
[8,1,6,7,5,4,3,2]=>0000000=>0000000=>[8]
[3,2,5,1,6,8,4,7]=>0000000=>0000000=>[8]
[3,6,2,5,4,8,1,7]=>0000000=>0000000=>[8]
[3,5,2,4,7,1,8,6]=>0000000=>0000000=>[8]
[3,5,8,2,4,7,6,1]=>0000000=>0000000=>[8]
[4,2,6,5,3,8,1,7]=>0000000=>0000000=>[8]
[5,3,1,6,8,2,4,7]=>0000000=>0000000=>[8]
[5,6,2,8,1,3,4,7]=>0000000=>0000000=>[8]
[5,4,3,2,7,1,8,6]=>0000000=>0000000=>[8]
[5,4,3,8,2,7,6,1]=>0000000=>0000000=>[8]
[4,3,6,2,8,7,5,1]=>0000000=>0000000=>[8]
[6,4,3,1,7,2,8,5]=>0000000=>0000000=>[8]
[1,4,7,5,8,3,2,6]=>1000000=>0000001=>[7,1]
[2,8,5,7,4,6,1,3]=>0000000=>0000000=>[8]
[3,5,8,7,1,4,6,2]=>0000000=>0000000=>[8]
[4,3,7,1,8,6,5,2]=>0000000=>0000000=>[8]
[4,8,3,7,6,5,2,1]=>0000000=>0000000=>[8]
[7,5,3,1,8,6,4,2]=>0000000=>0000000=>[8]
[1,5,8,6,3,7,4,2]=>1000000=>0000001=>[7,1]
[6,2,8,7,4,5,1,3]=>0000000=>0000000=>[8]
[6,1,7,5,3,2,8,4]=>0000000=>0000000=>[8]
[6,5,2,1,7,3,8,4]=>0000000=>0000000=>[8]
[6,1,7,4,2,8,3,5]=>0000000=>0000000=>[8]
[6,7,2,1,8,3,4,5]=>0000000=>0000000=>[8]
[7,5,8,2,1,3,4,6]=>0000000=>0000000=>[8]
[5,7,3,1,8,2,4,6]=>0000000=>0000000=>[8]
[4,7,1,5,2,8,3,6]=>0000000=>0000000=>[8]
[2,4,8,6,3,7,5,1]=>0000000=>0000000=>[8]
[3,5,2,7,1,8,4,6]=>0000000=>0000000=>[8]
[4,3,7,8,2,1,5,6]=>0000000=>0000000=>[8]
[8,3,7,1,4,6,2,5]=>0000000=>0000000=>[8]
[3,8,2,5,7,1,6,4]=>0000000=>0000000=>[8]
[7,8,3,6,2,1,5,4]=>0000000=>0000000=>[8]
[8,7,3,6,2,5,4,1]=>0000000=>0000000=>[8]
[4,2,6,8,1,7,5,3]=>0000000=>0000000=>[8]
[5,4,8,2,7,1,6,3]=>0000000=>0000000=>[8]
[5,8,3,7,1,6,2,4]=>0000000=>0000000=>[8]
[5,8,7,2,6,1,3,4]=>0000000=>0000000=>[8]
[8,6,2,7,5,1,3,4]=>0000000=>0000000=>[8]
[6,4,8,1,7,2,5,3]=>0000000=>0000000=>[8]
[5,1,6,8,2,7,4,3]=>0000000=>0000000=>[8]
[6,5,2,8,1,7,4,3]=>0000000=>0000000=>[8]
[5,2,7,1,8,6,4,3]=>0000000=>0000000=>[8]
[5,8,2,7,6,4,3,1]=>0000000=>0000000=>[8]
[6,1,7,2,8,5,4,3]=>0000000=>0000000=>[8]
[4,7,1,8,6,2,5,3]=>0000000=>0000000=>[8]
[8,7,4,6,1,5,3,2]=>0000000=>0000000=>[8]
[8,5,7,1,6,4,3,2]=>0000000=>0000000=>[8]
[6,8,1,7,5,4,3,2]=>0000000=>0000000=>[8]
[7,1,8,6,5,4,3,2]=>0000000=>0000000=>[8]
[4,3,5,6,1,2,8,7]=>0000010=>0100000=>[2,6]
[6,5,2,7,1,8,3,4]=>0000000=>0000000=>[8]
[3,5,2,6,4,1,8,7]=>0000010=>0100000=>[2,6]
[2,1,6,3,5,4,8,7]=>0100010=>0100010=>[2,4,2]
[5,3,1,4,6,2,8,7]=>0000010=>0100000=>[2,6]
[3,4,7,8,5,2,1,6]=>0000000=>0000000=>[8]
[2,4,6,3,7,5,8,1]=>0000000=>0000000=>[8]
[4,1,6,3,8,5,7,2]=>0000000=>0000000=>[8]
[3,7,4,2,8,6,5,1]=>0000000=>0000000=>[8]
[2,1,5,7,4,8,6,3]=>0100000=>0000010=>[6,2]
[3,1,8,2,7,6,5,4]=>0000000=>0000000=>[8]
[4,3,7,2,6,8,5,1]=>0000000=>0000000=>[8]
[8,1,2,3,5,6,7,4]=>0000000=>0000000=>[8]
[7,8,2,4,3,6,1,5]=>0000000=>0000000=>[8]
[2,1,7,8,5,4,3,6]=>0100000=>0000010=>[6,2]
[5,7,3,8,1,4,2,6]=>0000000=>0000000=>[8]
[8,3,6,1,4,2,7,5]=>0000000=>0000000=>[8]
[4,1,3,2,8,5,7,6]=>0001000=>0001000=>[4,4]
[2,1,4,3,8,5,7,6]=>0101000=>0001010=>[4,2,2]
[4,1,3,2,6,7,8,5]=>0001000=>0001000=>[4,4]
[5,3,6,1,8,7,2,4]=>0000000=>0000000=>[8]
[5,6,2,8,7,4,1,3]=>0000000=>0000000=>[8]
[7,8,5,6,1,4,2,3]=>0000000=>0000000=>[8]
[8,1,6,4,5,7,2,3]=>0000000=>0000000=>[8]
[2,1,8,6,5,7,3,4]=>0100000=>0000010=>[6,2]
[2,1,7,5,3,6,8,4]=>0100000=>0000010=>[6,2]
[4,1,2,5,8,6,7,3]=>0000000=>0000000=>[8]
[3,1,4,5,6,8,7,2]=>0000000=>0000000=>[8]
[6,3,1,5,2,4,8,7]=>0000010=>0100000=>[2,6]
[3,1,6,5,4,2,8,7]=>0000010=>0100000=>[2,6]
[5,1,7,3,8,4,6,2]=>0000000=>0000000=>[8]
[2,5,7,3,8,6,4,1]=>0000000=>0000000=>[8]
[5,6,3,7,4,8,1,2]=>0000000=>0000000=>[8]
[2,1,6,7,4,8,5,3]=>0100000=>0000010=>[6,2]
[2,8,6,3,1,5,7,4]=>0000000=>0000000=>[8]
[8,1,6,3,2,5,4,7]=>0000000=>0000000=>[8]
[2,8,4,1,6,3,7,5]=>0000000=>0000000=>[8]
[4,8,1,2,7,6,3,5]=>0000000=>0000000=>[8]
[6,5,3,2,8,7,1,4]=>0000000=>0000000=>[8]
[2,4,1,8,7,6,5,3]=>0000000=>0000000=>[8]
[4,1,2,8,7,5,6,3]=>0000000=>0000000=>[8]
[8,4,2,1,7,5,3,6]=>0000000=>0000000=>[8]
[4,3,1,8,6,7,5,2]=>0000000=>0000000=>[8]
[6,4,3,5,8,1,7,2]=>0000000=>0000000=>[8]
[5,7,3,6,1,8,2,4]=>0000000=>0000000=>[8]
[8,6,2,5,1,7,4,3]=>0000000=>0000000=>[8]
[7,5,2,8,3,4,6,1]=>0000000=>0000000=>[8]
[4,7,2,8,1,5,3,6]=>0000000=>0000000=>[8]
[8,7,2,1,4,5,6,3]=>0000000=>0000000=>[8]
[3,6,8,7,1,5,4,2]=>0000000=>0000000=>[8]
[5,7,8,6,3,4,1,2]=>0000000=>0000000=>[8]
[5,7,3,8,1,4,6,2]=>0000000=>0000000=>[8]
[2,1,7,8,5,4,6,3]=>0100000=>0000010=>[6,2]
[8,4,1,3,7,2,6,5]=>0000000=>0000000=>[8]
[4,3,8,2,5,1,7,6]=>0000000=>0000000=>[8]
[2,1,4,8,3,5,7,6]=>0100000=>0000010=>[6,2]
[7,8,5,6,1,4,3,2]=>0000000=>0000000=>[8]
[7,8,4,2,1,5,3,6]=>0000000=>0000000=>[8]
[7,8,2,1,6,5,3,4]=>0000000=>0000000=>[8]
[6,4,1,2,5,7,3,8]=>0000001=>1000000=>[1,7]
[4,3,8,1,7,2,5,6]=>0000000=>0000000=>[8]
[6,3,1,4,7,2,5,8]=>0000001=>1000000=>[1,7]
[7,8,1,4,6,2,5,3]=>0000000=>0000000=>[8]
[7,8,3,5,4,2,1,6]=>0000000=>0000000=>[8]
[7,8,4,1,2,3,6,5]=>0000000=>0000000=>[8]
[7,8,2,6,4,1,3,5]=>0000000=>0000000=>[8]
[7,8,1,6,5,4,3,2]=>0000000=>0000000=>[8]
[1,3,8,2,6,4,7,5]=>1000000=>0000001=>[7,1]
[5,3,7,1,6,4,8,2]=>0000000=>0000000=>[8]
[6,1,2,5,8,7,4,3]=>0000000=>0000000=>[8]
[6,3,1,8,4,2,7,5]=>0000000=>0000000=>[8]
[6,4,2,1,5,3,8,7]=>0000010=>0100000=>[2,6]
[6,4,3,7,5,8,1,2]=>0000000=>0000000=>[8]
[2,4,7,1,5,3,6,8]=>0000001=>1000000=>[1,7]
[3,7,2,8,6,4,1,5]=>0000000=>0000000=>[8]
[3,8,1,7,6,4,5,2]=>0000000=>0000000=>[8]
[2,7,5,8,3,6,1,4]=>0000000=>0000000=>[8]
[1,5,6,8,2,4,7,3]=>1000000=>0000001=>[7,1]
[2,6,1,4,7,3,5,8]=>0000001=>1000000=>[1,7]
[3,6,8,4,7,5,1,2]=>0000000=>0000000=>[8]
[5,6,7,3,8,4,1,2]=>0000000=>0000000=>[8]
[4,5,7,6,1,8,3,2]=>0000000=>0000000=>[8]
[4,7,5,6,3,1,8,2]=>0000000=>0000000=>[8]
[5,1,6,3,4,2,8,7]=>0000010=>0100000=>[2,6]
[5,7,1,4,2,3,8,6]=>0000000=>0000000=>[8]
[5,7,6,4,3,8,1,2]=>0000000=>0000000=>[8]
[6,3,4,5,8,7,1,2]=>0000000=>0000000=>[8]
[6,2,4,1,8,3,7,5]=>0000000=>0000000=>[8]
[6,2,3,5,4,8,1,7]=>0000000=>0000000=>[8]
[5,1,4,2,7,6,8,3]=>0000000=>0000000=>[8]
[1,6,2,4,7,8,3,5]=>1000000=>0000001=>[7,1]
[6,1,4,2,8,5,3,7]=>0000000=>0000000=>[8]
[6,7,5,8,1,4,3,2]=>0000000=>0000000=>[8]
[5,8,7,6,3,4,1,2]=>0000000=>0000000=>[8]
[5,8,7,6,2,3,1,4]=>0000000=>0000000=>[8]
[4,1,7,2,6,5,3,8]=>0000001=>1000000=>[1,7]
[4,2,7,8,1,6,3,5]=>0000000=>0000000=>[8]
[2,1,8,7,6,5,3,4]=>0100000=>0000010=>[6,2]
[4,2,7,1,6,3,8,5]=>0000000=>0000000=>[8]
[4,3,7,5,6,8,1,2]=>0000000=>0000000=>[8]
[3,8,6,5,2,4,1,7]=>0000000=>0000000=>[8]
[3,8,5,6,1,4,7,2]=>0000000=>0000000=>[8]
[5,3,7,8,2,1,6,4]=>0000000=>0000000=>[8]
[5,2,8,7,1,6,4,3]=>0000000=>0000000=>[8]
[3,6,7,8,5,1,4,2]=>0000000=>0000000=>[8]
[3,7,8,5,1,2,4,6]=>0000000=>0000000=>[8]
[4,1,8,6,2,3,5,7]=>0000000=>0000000=>[8]
[3,8,7,6,5,4,1,2]=>0000000=>0000000=>[8]
[2,8,6,7,5,1,3,4]=>0000000=>0000000=>[8]
[5,3,7,8,2,1,4,6]=>0000000=>0000000=>[8]
[7,6,1,2,5,8,3,4]=>0000000=>0000000=>[8]
[2,1,7,8,4,3,5,6]=>0100000=>0000010=>[6,2]
[7,8,1,2,5,4,6,3]=>0000000=>0000000=>[8]
[8,4,1,3,7,6,2,5]=>0000000=>0000000=>[8]
[4,7,2,8,1,3,6,5]=>0000000=>0000000=>[8]
[7,3,8,6,1,2,5,4]=>0000000=>0000000=>[8]
[3,4,7,1,8,2,6,5]=>0000000=>0000000=>[8]
[1,8,2,4,3,5,6,7]=>1000000=>0000001=>[7,1]
[1,7,2,4,3,5,6,8]=>1000001=>1000001=>[1,6,1]
[1,5,2,4,3,6,7,8]=>1000111=>1110001=>[1,1,1,4,1]
[1,7,2,5,3,4,6,8]=>1000001=>1000001=>[1,6,1]
[1,8,2,5,3,4,6,7]=>1000000=>0000001=>[7,1]
[1,8,2,6,3,4,5,7]=>1000000=>0000001=>[7,1]
[1,8,2,7,3,4,5,6]=>1000000=>0000001=>[7,1]
[1,8,2,7,3,5,4,6]=>1000000=>0000001=>[7,1]
[1,7,2,8,3,5,4,6]=>1000000=>0000001=>[7,1]
[1,6,2,8,3,5,4,7]=>1000000=>0000001=>[7,1]
[1,5,2,8,3,6,4,7]=>1000000=>0000001=>[7,1]
[1,4,2,8,3,6,5,7]=>1000000=>0000001=>[7,1]
[1,3,2,8,4,6,5,7]=>1010000=>0000101=>[5,2,1]
[1,2,3,8,4,6,5,7]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,4,6,5,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,3,2,7,4,6,5,8]=>1010001=>1000101=>[1,4,2,1]
[1,4,2,7,3,6,5,8]=>1000001=>1000001=>[1,6,1]
[1,5,2,7,3,6,4,8]=>1000001=>1000001=>[1,6,1]
[1,6,2,7,3,5,4,8]=>1000001=>1000001=>[1,6,1]
[1,7,2,6,3,5,4,8]=>1000001=>1000001=>[1,6,1]
[1,8,2,6,3,5,4,7]=>1000000=>0000001=>[7,1]
[1,8,2,5,3,6,4,7]=>1000000=>0000001=>[7,1]
[1,7,2,5,3,6,4,8]=>1000001=>1000001=>[1,6,1]
[1,6,2,5,3,7,4,8]=>1000001=>1000001=>[1,6,1]
[1,5,2,4,3,7,6,8]=>1000101=>1010001=>[1,2,4,1]
[1,6,2,4,3,7,5,8]=>1000001=>1000001=>[1,6,1]
[1,7,2,4,3,6,5,8]=>1000001=>1000001=>[1,6,1]
[1,8,2,4,3,6,5,7]=>1000000=>0000001=>[7,1]
[1,8,2,4,3,7,5,6]=>1000000=>0000001=>[7,1]
[1,7,2,4,3,8,5,6]=>1000000=>0000001=>[7,1]
[1,6,2,4,3,8,5,7]=>1000000=>0000001=>[7,1]
[1,5,2,4,3,8,6,7]=>1000100=>0010001=>[3,4,1]
[1,6,2,5,3,8,4,7]=>1000000=>0000001=>[7,1]
[1,7,2,5,3,8,4,6]=>1000000=>0000001=>[7,1]
[1,8,2,5,3,7,4,6]=>1000000=>0000001=>[7,1]
[1,8,2,6,3,7,4,5]=>1000000=>0000001=>[7,1]
[1,7,2,6,3,8,4,5]=>1000000=>0000001=>[7,1]
[1,2,3,8,4,7,5,6]=>1110000=>0000111=>[5,1,1,1]
[1,3,2,8,4,7,5,6]=>1010000=>0000101=>[5,2,1]
[1,4,2,8,3,7,5,6]=>1000000=>0000001=>[7,1]
[1,5,2,8,3,7,4,6]=>1000000=>0000001=>[7,1]
[1,6,2,8,3,7,4,5]=>1000000=>0000001=>[7,1]
[1,7,2,8,3,6,4,5]=>1000000=>0000001=>[7,1]
[1,8,2,7,3,6,4,5]=>1000000=>0000001=>[7,1]
[2,8,4,1,6,5,3,7]=>0000000=>0000000=>[8]
[7,2,8,5,1,6,4,3]=>0000000=>0000000=>[8]
[1,3,7,5,2,6,4,8]=>1000001=>1000001=>[1,6,1]
[1,3,7,5,4,2,6,8]=>1000001=>1000001=>[1,6,1]
[2,8,5,3,4,1,6,7]=>0000000=>0000000=>[8]
[6,2,3,8,5,1,7,4]=>0000000=>0000000=>[8]
[6,3,2,8,5,1,4,7]=>0000000=>0000000=>[8]
[7,4,8,5,2,1,3,6]=>0000000=>0000000=>[8]
[4,3,2,1,8,6,5,7]=>0001000=>0001000=>[4,4]
[4,2,1,3,8,7,6,5]=>0001000=>0001000=>[4,4]
[7,1,6,8,4,3,5,2]=>0000000=>0000000=>[8]
[5,6,8,2,3,1,7,4]=>0000000=>0000000=>[8]
[7,5,3,8,2,4,1,6]=>0000000=>0000000=>[8]
[5,2,1,8,7,6,3,4]=>0000000=>0000000=>[8]
[4,1,8,3,6,2,7,5]=>0000000=>0000000=>[8]
[2,3,4,8,6,1,7,5]=>0000000=>0000000=>[8]
[2,3,4,8,6,5,1,7]=>0000000=>0000000=>[8]
[1,5,4,6,2,7,3,8]=>1000001=>1000001=>[1,6,1]
[6,3,5,1,8,2,7,4]=>0000000=>0000000=>[8]
[5,7,1,6,3,8,4,2]=>0000000=>0000000=>[8]
[3,2,4,1,7,8,5,6]=>0001000=>0001000=>[4,4]
[2,5,4,6,1,7,8,3]=>0000000=>0000000=>[8]
[7,3,4,1,2,6,5,8]=>0000001=>1000000=>[1,7]
[7,4,3,2,1,6,5,8]=>0000001=>1000000=>[1,7]
[6,7,3,2,5,4,8,1]=>0000000=>0000000=>[8]
[1,8,5,4,3,2,7,6]=>1000000=>0000001=>[7,1]
[2,6,8,4,3,7,1,5]=>0000000=>0000000=>[8]
[2,7,8,4,3,6,5,1]=>0000000=>0000000=>[8]
[2,7,8,5,6,3,4,1]=>0000000=>0000000=>[8]
[5,3,7,1,6,8,4,2]=>0000000=>0000000=>[8]
[5,4,7,6,1,8,3,2]=>0000000=>0000000=>[8]
[4,5,7,6,8,1,3,2]=>0000000=>0000000=>[8]
[4,6,5,7,8,2,1,3]=>0000000=>0000000=>[8]
[5,2,1,6,7,8,3,4]=>0000000=>0000000=>[8]
[6,2,1,5,7,3,8,4]=>0000000=>0000000=>[8]
[5,6,4,7,2,8,1,3]=>0000000=>0000000=>[8]
[1,8,4,6,2,7,3,5]=>1000000=>0000001=>[7,1]
[1,8,3,2,6,7,4,5]=>1000000=>0000001=>[7,1]
[6,5,3,2,7,1,8,4]=>0000000=>0000000=>[8]
[6,4,3,2,1,7,8,5]=>0000000=>0000000=>[8]
[6,2,1,4,3,7,8,5]=>0000000=>0000000=>[8]
[4,5,3,2,8,1,7,6]=>0000000=>0000000=>[8]
[4,6,3,2,8,7,1,5]=>0000000=>0000000=>[8]
[4,7,3,2,8,6,5,1]=>0000000=>0000000=>[8]
[1,8,3,2,7,6,5,4]=>1000000=>0000001=>[7,1]
[1,8,4,7,2,6,5,3]=>1000000=>0000001=>[7,1]
[3,6,4,8,2,7,1,5]=>0000000=>0000000=>[8]
[3,4,5,8,1,2,7,6]=>0000000=>0000000=>[8]
[4,2,1,5,8,3,7,6]=>0000000=>0000000=>[8]
[3,6,5,8,7,2,1,4]=>0000000=>0000000=>[8]
[3,6,7,8,5,4,1,2]=>0000000=>0000000=>[8]
[3,5,7,8,6,1,4,2]=>0000000=>0000000=>[8]
[4,2,1,7,8,6,5,3]=>0000000=>0000000=>[8]
[2,3,8,1,7,6,5,4]=>0000000=>0000000=>[8]
[2,4,8,7,1,6,5,3]=>0000000=>0000000=>[8]
[8,1,6,7,3,2,5,4]=>0000000=>0000000=>[8]
[8,1,6,7,2,3,4,5]=>0000000=>0000000=>[8]
[8,1,4,3,2,7,6,5]=>0000000=>0000000=>[8]
[8,1,5,3,7,2,6,4]=>0000000=>0000000=>[8]
[8,1,3,5,6,2,7,4]=>0000000=>0000000=>[8]
[4,7,8,5,6,1,2,3]=>0000000=>0000000=>[8]
[3,7,8,5,6,2,1,4]=>0000000=>0000000=>[8]
[3,7,8,4,2,6,1,5]=>0000000=>0000000=>[8]
[3,7,8,2,4,5,1,6]=>0000000=>0000000=>[8]
[3,6,2,8,4,5,1,7]=>0000000=>0000000=>[8]
[2,3,6,7,4,5,8,1]=>0000000=>0000000=>[8]
[3,5,2,4,8,6,1,7]=>0000000=>0000000=>[8]
[3,5,4,2,8,7,1,6]=>0000000=>0000000=>[8]
[6,4,5,1,7,8,2,3]=>0000000=>0000000=>[8]
[5,4,2,3,1,8,6,7]=>0000100=>0010000=>[3,5]
[6,5,3,1,8,2,7,4]=>0000000=>0000000=>[8]
[6,5,4,1,8,7,2,3]=>0000000=>0000000=>[8]
[7,5,1,4,8,6,2,3]=>0000000=>0000000=>[8]
[7,4,1,3,2,8,6,5]=>0000000=>0000000=>[8]
[7,4,1,2,3,8,5,6]=>0000000=>0000000=>[8]
[6,4,2,1,3,8,5,7]=>0000000=>0000000=>[8]
[2,6,4,8,3,7,5,1]=>0000000=>0000000=>[8]
[2,6,5,8,7,3,4,1]=>0000000=>0000000=>[8]
[6,5,2,1,8,3,4,7]=>0000000=>0000000=>[8]
[7,5,1,2,8,3,4,6]=>0000000=>0000000=>[8]
[7,6,1,8,2,3,4,5]=>0000000=>0000000=>[8]
[7,6,1,8,4,5,2,3]=>0000000=>0000000=>[8]
[6,7,8,1,4,5,2,3]=>0000000=>0000000=>[8]
[6,7,8,1,3,2,5,4]=>0000000=>0000000=>[8]
[4,2,6,7,3,1,5,8]=>0000001=>1000000=>[1,7]
[4,7,8,2,3,1,5,6]=>0000000=>0000000=>[8]
[4,7,8,3,2,1,6,5]=>0000000=>0000000=>[8]
[5,7,8,3,1,2,6,4]=>0000000=>0000000=>[8]
[5,7,8,4,1,6,2,3]=>0000000=>0000000=>[8]
[4,6,3,8,2,1,7,5]=>0000000=>0000000=>[8]
[4,2,5,3,7,1,6,8]=>0000001=>1000000=>[1,7]
[3,5,6,7,8,2,1,4]=>0000000=>0000000=>[8]
[7,3,5,1,8,4,6,2]=>0000000=>0000000=>[8]
[4,5,7,3,1,8,6,2]=>0000000=>0000000=>[8]
[4,5,6,2,1,8,7,3]=>0000000=>0000000=>[8]
[1,6,5,2,7,4,3,8]=>1000001=>1000001=>[1,6,1]
[7,4,3,1,8,6,5,2]=>0000000=>0000000=>[8]
[7,5,6,1,8,3,4,2]=>0000000=>0000000=>[8]
[7,6,5,1,8,4,3,2]=>0000000=>0000000=>[8]
[6,4,2,1,8,7,5,3]=>0000000=>0000000=>[8]
[2,6,5,1,7,8,4,3]=>0000000=>0000000=>[8]
[4,5,7,1,3,8,2,6]=>0000000=>0000000=>[8]
[4,3,1,2,8,6,5,7]=>0001000=>0001000=>[4,4]
[6,1,2,5,8,3,4,7]=>0000000=>0000000=>[8]
[7,1,3,4,8,2,5,6]=>0000000=>0000000=>[8]
[2,6,1,5,7,8,3,4]=>0000000=>0000000=>[8]
[6,2,5,1,8,4,7,3]=>0000000=>0000000=>[8]
[6,1,5,2,8,3,7,4]=>0000000=>0000000=>[8]
[7,3,1,4,8,6,2,5]=>0000000=>0000000=>[8]
[5,2,1,3,8,7,4,6]=>0000000=>0000000=>[8]
[6,1,4,2,8,3,7,5]=>0000000=>0000000=>[8]
[7,1,4,3,8,2,6,5]=>0000000=>0000000=>[8]
[5,1,3,2,8,4,7,6]=>0000000=>0000000=>[8]
[2,6,1,4,7,8,3,5]=>0000000=>0000000=>[8]
[7,1,3,5,8,2,4,6]=>0000000=>0000000=>[8]
[7,8,5,6,1,3,4,2]=>0000000=>0000000=>[8]
[7,8,1,3,6,2,5,4]=>0000000=>0000000=>[8]
[4,6,1,2,5,7,3,8]=>0000001=>1000000=>[1,7]
[1,4,8,2,5,7,3,6]=>1000000=>0000001=>[7,1]
[7,8,4,2,5,1,3,6]=>0000000=>0000000=>[8]
[7,8,1,5,4,6,3,2]=>0000000=>0000000=>[8]
[7,8,2,1,6,3,4,5]=>0000000=>0000000=>[8]
[7,8,3,5,6,4,1,2]=>0000000=>0000000=>[8]
[7,8,4,5,3,1,6,2]=>0000000=>0000000=>[8]
[2,6,4,8,3,7,1,5]=>0000000=>0000000=>[8]
[1,4,6,8,3,7,5,2]=>1000000=>0000001=>[7,1]
[2,5,8,1,4,7,6,3]=>0000000=>0000000=>[8]
[1,6,2,4,7,3,8,5]=>1000000=>0000001=>[7,1]
[5,6,2,1,4,7,8,3]=>0000000=>0000000=>[8]
[4,7,5,1,3,6,8,2]=>0000000=>0000000=>[8]
[5,7,3,6,1,4,8,2]=>0000000=>0000000=>[8]
[1,4,7,2,5,3,8,6]=>1000000=>0000001=>[7,1]
[6,4,7,3,5,8,1,2]=>0000000=>0000000=>[8]
[3,5,6,7,8,1,4,2]=>0000000=>0000000=>[8]
[3,6,5,7,8,2,1,4]=>0000000=>0000000=>[8]
[2,7,5,6,8,4,1,3]=>0000000=>0000000=>[8]
[2,1,6,8,4,5,3,7]=>0100000=>0000010=>[6,2]
[2,7,1,8,5,3,4,6]=>0000000=>0000000=>[8]
[3,7,6,8,5,4,1,2]=>0000000=>0000000=>[8]
[4,3,8,5,6,7,1,2]=>0000000=>0000000=>[8]
[4,2,8,1,6,3,7,5]=>0000000=>0000000=>[8]
[3,1,8,5,4,6,7,2]=>0000000=>0000000=>[8]
[3,4,2,8,6,1,7,5]=>0000000=>0000000=>[8]
[1,7,3,8,5,2,6,4]=>1000000=>0000001=>[7,1]
[4,1,8,3,6,2,5,7]=>0000000=>0000000=>[8]
[5,7,8,6,3,2,1,4]=>0000000=>0000000=>[8]
[5,7,8,6,1,3,4,2]=>0000000=>0000000=>[8]
[7,6,5,8,1,3,4,2]=>0000000=>0000000=>[8]
[1,6,4,3,8,2,5,7]=>1000000=>0000001=>[7,1]
[2,6,3,4,5,8,1,7]=>0000000=>0000000=>[8]
[2,6,4,1,8,3,7,5]=>0000000=>0000000=>[8]
[3,6,4,5,8,7,1,2]=>0000000=>0000000=>[8]
[7,2,1,4,8,3,5,6]=>0000000=>0000000=>[8]
[7,1,6,5,3,8,4,2]=>0000000=>0000000=>[8]
[7,2,5,6,3,8,1,4]=>0000000=>0000000=>[8]
[5,6,2,7,3,1,4,8]=>0000001=>1000000=>[1,7]
[6,7,1,5,2,8,3,4]=>0000000=>0000000=>[8]
[6,1,5,2,8,3,4,7]=>0000000=>0000000=>[8]
[7,5,2,4,3,1,6,8]=>0000001=>1000000=>[1,7]
[6,8,1,3,7,5,4,2]=>0000000=>0000000=>[8]
[7,4,2,6,5,1,3,8]=>0000001=>1000000=>[1,7]
[7,4,6,3,1,5,2,8]=>0000001=>1000000=>[1,7]
[7,2,3,5,4,1,6,8]=>0000001=>1000000=>[1,7]
[2,5,1,7,8,3,6,4]=>0000000=>0000000=>[8]
[2,5,3,6,8,4,7,1]=>0000000=>0000000=>[8]
[3,5,7,4,1,6,2,8]=>0000001=>1000000=>[1,7]
[5,2,8,4,6,1,7,3]=>0000000=>0000000=>[8]
[5,2,1,8,6,3,7,4]=>0000000=>0000000=>[8]
[1,4,2,7,5,8,6,3]=>1000000=>0000001=>[7,1]
[5,3,8,7,6,2,4,1]=>0000000=>0000000=>[8]
[5,8,4,7,6,2,1,3]=>0000000=>0000000=>[8]
[5,8,7,4,3,6,1,2]=>0000000=>0000000=>[8]
[6,4,8,3,1,7,2,5]=>0000000=>0000000=>[8]
[6,4,2,8,7,1,3,5]=>0000000=>0000000=>[8]
[6,3,8,7,2,5,1,4]=>0000000=>0000000=>[8]
[5,8,3,7,1,6,4,2]=>0000000=>0000000=>[8]
[6,8,5,2,4,3,7,1]=>0000000=>0000000=>[8]
[6,8,5,3,1,2,7,4]=>0000000=>0000000=>[8]
[4,5,1,2,7,6,3,8]=>0000001=>1000000=>[1,7]
[4,5,1,2,6,8,7,3]=>0000000=>0000000=>[8]
[3,5,6,1,8,4,7,2]=>0000000=>0000000=>[8]
[3,5,7,1,2,8,6,4]=>0000000=>0000000=>[8]
[4,2,6,1,7,3,5,8]=>0000001=>1000000=>[1,7]
[4,6,3,1,2,7,5,8]=>0000001=>1000000=>[1,7]
[3,5,2,7,8,1,6,4]=>0000000=>0000000=>[8]
[3,1,4,7,5,6,2,8]=>0000001=>1000000=>[1,7]
[3,1,4,5,8,6,7,2]=>0000000=>0000000=>[8]
[3,4,6,8,5,2,7,1]=>0000000=>0000000=>[8]
[2,1,7,5,8,6,4,3]=>0100000=>0000010=>[6,2]
[1,2,7,5,3,8,6,4]=>1100000=>0000011=>[6,1,1]
[4,1,2,7,3,8,6,5]=>0000000=>0000000=>[8]
[7,1,4,2,5,3,8,6]=>0000000=>0000000=>[8]
[6,1,3,7,5,2,4,8]=>0000001=>1000000=>[1,7]
[3,1,2,6,8,5,4,7]=>0010000=>0000100=>[5,3]
[3,7,1,2,5,4,8,6]=>0000000=>0000000=>[8]
[1,3,7,2,4,8,6,5]=>1000000=>0000001=>[7,1]
[3,2,7,8,1,6,5,4]=>0000000=>0000000=>[8]
[2,4,1,7,8,6,5,3]=>0000000=>0000000=>[8]
[2,6,8,3,1,5,7,4]=>0000000=>0000000=>[8]
[3,6,4,8,5,1,7,2]=>0000000=>0000000=>[8]
[6,3,7,4,5,1,8,2]=>0000000=>0000000=>[8]
[2,6,3,7,5,8,1,4]=>0000000=>0000000=>[8]
[5,2,1,7,8,3,4,6]=>0000000=>0000000=>[8]
[5,7,4,6,2,8,1,3]=>0000000=>0000000=>[8]
[4,2,8,3,6,7,1,5]=>0000000=>0000000=>[8]
[4,8,3,1,7,2,5,6]=>0000000=>0000000=>[8]
[5,2,8,4,7,1,6,3]=>0000000=>0000000=>[8]
[5,8,4,7,3,1,6,2]=>0000000=>0000000=>[8]
[4,6,8,3,1,7,5,2]=>0000000=>0000000=>[8]
[6,3,8,2,7,1,5,4]=>0000000=>0000000=>[8]
[3,5,1,8,2,7,4,6]=>0000000=>0000000=>[8]
[7,5,1,3,6,2,4,8]=>0000001=>1000000=>[1,7]
[5,1,8,4,2,7,3,6]=>0000000=>0000000=>[8]
[4,1,6,2,8,3,7,5]=>0000000=>0000000=>[8]
[1,6,2,8,5,3,7,4]=>1000000=>0000001=>[7,1]
[6,8,5,3,1,7,4,2]=>0000000=>0000000=>[8]
[5,6,7,3,1,8,4,2]=>0000000=>0000000=>[8]
[5,6,2,1,7,8,4,3]=>0000000=>0000000=>[8]
[8,4,5,1,2,6,3,7]=>0000000=>0000000=>[8]
[5,6,3,7,1,2,4,8]=>0000001=>1000000=>[1,7]
[1,6,3,7,2,8,4,5]=>1000000=>0000001=>[7,1]
[6,4,7,2,8,1,5,3]=>0000000=>0000000=>[8]
[6,7,4,8,3,1,5,2]=>0000000=>0000000=>[8]
[4,5,7,8,3,1,6,2]=>0000000=>0000000=>[8]
[4,7,2,5,8,1,6,3]=>0000000=>0000000=>[8]
[5,7,3,8,2,6,1,4]=>0000000=>0000000=>[8]
[3,4,7,8,2,6,1,5]=>0000000=>0000000=>[8]
[8,1,3,4,6,2,5,7]=>0000000=>0000000=>[8]
[2,4,5,6,8,1,7,3]=>0000000=>0000000=>[8]
[8,4,3,6,5,1,7,2]=>0000000=>0000000=>[8]
[8,6,5,4,3,1,7,2]=>0000000=>0000000=>[8]
[1,8,6,5,2,7,3,4]=>1000000=>0000001=>[7,1]
[8,7,5,4,1,6,3,2]=>0000000=>0000000=>[8]
[7,8,5,4,1,3,6,2]=>0000000=>0000000=>[8]
[3,2,8,6,5,1,7,4]=>0000000=>0000000=>[8]
[8,1,6,5,2,3,7,4]=>0000000=>0000000=>[8]
[8,1,7,2,6,3,5,4]=>0000000=>0000000=>[8]
[7,1,8,2,6,4,3,5]=>0000000=>0000000=>[8]
[5,1,8,3,2,7,4,6]=>0000000=>0000000=>[8]
[3,2,8,7,1,6,5,4]=>0000000=>0000000=>[8]
[4,8,2,7,1,6,5,3]=>0000000=>0000000=>[8]
[5,8,7,2,1,6,4,3]=>0000000=>0000000=>[8]
[8,7,6,1,5,4,3,2]=>0000000=>0000000=>[8]
[8,6,7,1,4,5,3,2]=>0000000=>0000000=>[8]
[7,6,8,1,4,3,5,2]=>0000000=>0000000=>[8]
[6,7,8,1,3,4,5,2]=>0000000=>0000000=>[8]
[5,7,8,2,1,4,6,3]=>0000000=>0000000=>[8]
[4,7,2,8,1,5,6,3]=>0000000=>0000000=>[8]
[3,2,7,8,1,5,6,4]=>0000000=>0000000=>[8]
[3,2,6,8,4,1,7,5]=>0000000=>0000000=>[8]
[4,6,2,8,3,1,7,5]=>0000000=>0000000=>[8]
[6,5,8,3,2,1,7,4]=>0000000=>0000000=>[8]
[7,5,8,3,1,4,6,2]=>0000000=>0000000=>[8]
[8,4,3,7,1,6,5,2]=>0000000=>0000000=>[8]
[6,4,3,8,2,1,7,5]=>0000000=>0000000=>[8]
[5,4,3,2,8,1,7,6]=>0000000=>0000000=>[8]
[4,5,2,3,8,1,7,6]=>0000000=>0000000=>[8]
[3,2,5,4,8,1,7,6]=>0000000=>0000000=>[8]
[6,4,3,1,5,2,7,8]=>0000011=>1100000=>[1,1,6]
[7,4,3,1,2,6,5,8]=>0000001=>1000000=>[1,7]
[1,5,4,2,3,6,7,8]=>1000111=>1110001=>[1,1,1,4,1]
[7,5,1,4,2,6,3,8]=>0000001=>1000000=>[1,7]
[4,6,2,1,5,3,7,8]=>0000011=>1100000=>[1,1,6]
[3,2,6,1,5,4,7,8]=>0000011=>1100000=>[1,1,6]
[5,7,1,3,2,6,4,8]=>0000001=>1000000=>[1,7]
[6,7,1,2,4,5,3,8]=>0000001=>1000000=>[1,7]
[7,6,1,2,5,4,3,8]=>0000001=>1000000=>[1,7]
[8,6,1,2,5,3,7,4]=>0000000=>0000000=>[8]
[7,8,1,2,3,5,6,4]=>0000000=>0000000=>[8]
[3,2,8,1,4,5,7,6]=>0000000=>0000000=>[8]
[4,1,3,2,5,6,7,8]=>0001111=>1111000=>[1,1,1,1,4]
[5,1,2,4,3,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,8,7,3,4,1,2,6]=>0000000=>0000000=>[8]
[6,7,3,8,5,1,2,4]=>0000000=>0000000=>[8]
[6,7,4,5,1,8,3,2]=>0000000=>0000000=>[8]
[5,4,7,6,2,3,8,1]=>0000000=>0000000=>[8]
[4,3,8,7,6,1,2,5]=>0000000=>0000000=>[8]
[4,8,3,7,5,1,2,6]=>0000000=>0000000=>[8]
[4,5,6,7,1,8,3,2]=>0000000=>0000000=>[8]
[2,5,6,8,1,7,3,4]=>0000000=>0000000=>[8]
[8,2,4,5,1,6,3,7]=>0000000=>0000000=>[8]
[1,4,8,6,2,3,7,5]=>1000000=>0000001=>[7,1]
[1,5,6,8,2,3,7,4]=>1000000=>0000001=>[7,1]
[1,5,6,2,8,4,7,3]=>1000000=>0000001=>[7,1]
[1,4,2,6,8,5,7,3]=>1000000=>0000001=>[7,1]
[8,1,3,2,5,4,6,7]=>0000000=>0000000=>[8]
[4,3,1,7,6,8,5,2]=>0000000=>0000000=>[8]
[3,8,2,1,7,5,4,6]=>0000000=>0000000=>[8]
[8,3,2,1,6,5,4,7]=>0000000=>0000000=>[8]
[8,4,2,6,1,5,3,7]=>0000000=>0000000=>[8]
[4,2,8,7,1,6,3,5]=>0000000=>0000000=>[8]
[5,3,7,2,6,4,8,1]=>0000000=>0000000=>[8]
[6,7,3,1,5,8,4,2]=>0000000=>0000000=>[8]
[6,7,2,1,8,5,4,3]=>0000000=>0000000=>[8]
[6,7,2,8,1,5,3,4]=>0000000=>0000000=>[8]
[6,7,8,2,1,4,3,5]=>0000000=>0000000=>[8]
[8,5,6,2,1,4,3,7]=>0000000=>0000000=>[8]
[5,8,7,1,2,3,4,6]=>0000000=>0000000=>[8]
[6,7,1,2,8,4,5,3]=>0000000=>0000000=>[8]
[6,7,1,3,4,8,5,2]=>0000000=>0000000=>[8]
[5,1,7,3,4,8,6,2]=>0000000=>0000000=>[8]
[5,1,7,8,2,3,6,4]=>0000000=>0000000=>[8]
[4,8,1,7,2,3,5,6]=>0000000=>0000000=>[8]
[3,8,1,2,7,4,5,6]=>0000000=>0000000=>[8]
[3,1,8,2,7,4,6,5]=>0000000=>0000000=>[8]
[3,1,2,8,7,5,6,4]=>0010000=>0000100=>[5,3]
[4,1,3,7,5,8,6,2]=>0000000=>0000000=>[8]
[1,8,2,3,4,5,7,6]=>1000000=>0000001=>[7,1]
[1,2,8,3,4,6,7,5]=>1100000=>0000011=>[6,1,1]
[3,6,4,8,5,7,1,2]=>0000000=>0000000=>[8]
[5,1,4,8,6,3,7,2]=>0000000=>0000000=>[8]
[3,4,7,1,8,6,5,2]=>0000000=>0000000=>[8]
[6,3,8,4,2,7,1,5]=>0000000=>0000000=>[8]
[3,6,8,7,1,4,2,5]=>0000000=>0000000=>[8]
[4,6,1,2,7,8,5,3]=>0000000=>0000000=>[8]
[3,6,4,2,8,7,5,1]=>0000000=>0000000=>[8]
[5,8,1,4,6,7,2,3]=>0000000=>0000000=>[8]
[3,6,4,5,7,2,8,1]=>0000000=>0000000=>[8]
[5,4,2,7,3,6,8,1]=>0000000=>0000000=>[8]
[4,2,5,7,3,6,8,1]=>0000000=>0000000=>[8]
[1,6,5,3,4,8,2,7]=>1000000=>0000001=>[7,1]
[1,8,6,3,7,5,2,4]=>1000000=>0000001=>[7,1]
[8,7,5,2,6,4,3,1]=>0000000=>0000000=>[8]
[8,7,1,6,2,5,4,3]=>0000000=>0000000=>[8]
[7,8,1,6,3,2,5,4]=>0000000=>0000000=>[8]
[2,8,1,7,3,5,6,4]=>0000000=>0000000=>[8]
[4,8,1,3,7,2,6,5]=>0000000=>0000000=>[8]
[4,2,8,5,7,3,6,1]=>0000000=>0000000=>[8]
[6,7,3,1,8,4,2,5]=>0000000=>0000000=>[8]
[1,7,3,8,4,5,2,6]=>1000000=>0000001=>[7,1]
[1,7,2,8,5,3,4,6]=>1000000=>0000001=>[7,1]
[7,6,1,8,4,3,2,5]=>0000000=>0000000=>[8]
[7,1,2,8,3,5,4,6]=>0000000=>0000000=>[8]
[6,3,7,2,1,8,4,5]=>0000000=>0000000=>[8]
[8,2,6,1,7,3,5,4]=>0000000=>0000000=>[8]
[5,4,3,1,6,8,2,7]=>0000000=>0000000=>[8]
[1,5,3,4,6,8,2,7]=>1000000=>0000001=>[7,1]
[4,3,5,1,6,8,2,7]=>0000000=>0000000=>[8]
[4,7,5,6,8,3,2,1]=>0000000=>0000000=>[8]
[5,7,3,8,2,6,4,1]=>0000000=>0000000=>[8]
[2,3,8,7,4,5,6,1]=>0000000=>0000000=>[8]
[7,2,8,6,4,3,5,1]=>0000000=>0000000=>[8]
[1,3,8,7,4,6,2,5]=>1000000=>0000001=>[7,1]
[4,7,1,8,6,5,2,3]=>0000000=>0000000=>[8]
[6,7,4,8,3,5,1,2]=>0000000=>0000000=>[8]
[6,7,4,5,2,8,1,3]=>0000000=>0000000=>[8]
[5,7,4,6,2,3,1,8]=>0000001=>1000000=>[1,7]
[5,7,4,6,3,8,1,2]=>0000000=>0000000=>[8]
[5,7,4,8,3,6,1,2]=>0000000=>0000000=>[8]
[6,8,4,5,3,7,1,2]=>0000000=>0000000=>[8]
[5,8,4,6,3,7,1,2]=>0000000=>0000000=>[8]
[5,6,4,8,3,7,1,2]=>0000000=>0000000=>[8]
[5,6,3,7,2,4,1,8]=>0000001=>1000000=>[1,7]
[5,6,3,7,2,8,1,4]=>0000000=>0000000=>[8]
[5,6,3,8,2,7,1,4]=>0000000=>0000000=>[8]
[5,6,4,8,2,7,1,3]=>0000000=>0000000=>[8]
[5,8,4,6,2,7,1,3]=>0000000=>0000000=>[8]
[6,8,4,5,2,7,1,3]=>0000000=>0000000=>[8]
[7,8,4,5,2,6,1,3]=>0000000=>0000000=>[8]
[6,8,4,5,2,3,1,7]=>0000000=>0000000=>[8]
[5,8,4,6,2,3,1,7]=>0000000=>0000000=>[8]
[5,6,4,8,2,3,1,7]=>0000000=>0000000=>[8]
[5,6,3,8,2,4,1,7]=>0000000=>0000000=>[8]
[5,6,3,4,2,8,1,7]=>0000000=>0000000=>[8]
[4,6,3,5,2,7,1,8]=>0000001=>1000000=>[1,7]
[4,6,3,5,2,8,1,7]=>0000000=>0000000=>[8]
[4,6,3,8,2,5,1,7]=>0000000=>0000000=>[8]
[4,8,3,6,2,5,1,7]=>0000000=>0000000=>[8]
[5,8,3,6,2,4,1,7]=>0000000=>0000000=>[8]
[6,8,3,5,2,4,1,7]=>0000000=>0000000=>[8]
[7,8,3,5,2,4,1,6]=>0000000=>0000000=>[8]
[7,8,3,5,2,6,1,4]=>0000000=>0000000=>[8]
[6,8,3,5,2,7,1,4]=>0000000=>0000000=>[8]
[5,8,3,6,2,7,1,4]=>0000000=>0000000=>[8]
[4,8,3,6,2,7,1,5]=>0000000=>0000000=>[8]
[4,6,3,8,2,7,1,5]=>0000000=>0000000=>[8]
[4,6,3,7,2,8,1,5]=>0000000=>0000000=>[8]
[4,6,3,7,2,5,1,8]=>0000001=>1000000=>[1,7]
[4,7,3,6,2,5,1,8]=>0000001=>1000000=>[1,7]
[4,7,3,6,2,8,1,5]=>0000000=>0000000=>[8]
[4,7,3,8,2,6,1,5]=>0000000=>0000000=>[8]
[5,7,4,8,2,6,1,3]=>0000000=>0000000=>[8]
[5,7,3,6,2,8,1,4]=>0000000=>0000000=>[8]
[5,7,3,6,2,4,1,8]=>0000001=>1000000=>[1,7]
[6,7,3,5,2,4,1,8]=>0000001=>1000000=>[1,7]
[6,7,3,5,2,8,1,4]=>0000000=>0000000=>[8]
[6,7,3,8,2,5,1,4]=>0000000=>0000000=>[8]
[6,7,4,8,2,5,1,3]=>0000000=>0000000=>[8]
[6,7,5,8,2,4,1,3]=>0000000=>0000000=>[8]
[6,8,5,7,2,3,1,4]=>0000000=>0000000=>[8]
[6,7,4,8,2,3,1,5]=>0000000=>0000000=>[8]
[6,7,3,8,2,4,1,5]=>0000000=>0000000=>[8]
[6,7,3,4,2,8,1,5]=>0000000=>0000000=>[8]
[5,7,3,4,2,6,1,8]=>0000001=>1000000=>[1,7]
[5,7,3,4,2,8,1,6]=>0000000=>0000000=>[8]
[5,7,3,8,2,4,1,6]=>0000000=>0000000=>[8]
[5,7,4,8,2,3,1,6]=>0000000=>0000000=>[8]
[5,8,4,7,2,3,1,6]=>0000000=>0000000=>[8]
[6,8,4,7,2,3,1,5]=>0000000=>0000000=>[8]
[7,8,4,6,2,3,1,5]=>0000000=>0000000=>[8]
[7,8,3,6,2,4,1,5]=>0000000=>0000000=>[8]
[6,8,3,7,2,4,1,5]=>0000000=>0000000=>[8]
[5,8,3,7,2,4,1,6]=>0000000=>0000000=>[8]
[4,8,3,7,2,5,1,6]=>0000000=>0000000=>[8]
[4,7,3,8,2,5,1,6]=>0000000=>0000000=>[8]
[4,7,3,5,2,8,1,6]=>0000000=>0000000=>[8]
[4,7,3,5,2,6,1,8]=>0000001=>1000000=>[1,7]
[4,5,3,7,2,6,1,8]=>0000001=>1000000=>[1,7]
[4,5,3,7,2,8,1,6]=>0000000=>0000000=>[8]
[4,5,3,8,2,7,1,6]=>0000000=>0000000=>[8]
[4,8,3,5,2,7,1,6]=>0000000=>0000000=>[8]
[5,8,3,4,2,7,1,6]=>0000000=>0000000=>[8]
[6,8,3,4,2,7,1,5]=>0000000=>0000000=>[8]
[7,8,3,4,2,6,1,5]=>0000000=>0000000=>[8]
[6,8,3,4,2,5,1,7]=>0000000=>0000000=>[8]
[5,8,3,4,2,6,1,7]=>0000000=>0000000=>[8]
[4,8,3,5,2,6,1,7]=>0000000=>0000000=>[8]
[4,5,3,8,2,6,1,7]=>0000000=>0000000=>[8]
[4,5,3,6,2,8,1,7]=>0000000=>0000000=>[8]
[4,6,5,2,1,3,8,7]=>0000010=>0100000=>[2,6]
[7,4,8,1,6,5,3,2]=>0000000=>0000000=>[8]
[7,4,5,3,1,8,2,6]=>0000000=>0000000=>[8]
[6,4,8,1,7,5,2,3]=>0000000=>0000000=>[8]
[6,4,7,1,8,2,5,3]=>0000000=>0000000=>[8]
[8,4,7,3,6,2,5,1]=>0000000=>0000000=>[8]
[5,7,8,6,2,3,1,4]=>0000000=>0000000=>[8]
[5,8,7,6,3,2,1,4]=>0000000=>0000000=>[8]
[6,7,4,2,8,1,5,3]=>0000000=>0000000=>[8]
[6,8,4,2,7,5,1,3]=>0000000=>0000000=>[8]
[5,7,4,2,3,8,1,6]=>0000000=>0000000=>[8]
[2,1,8,6,7,5,3,4]=>0100000=>0000010=>[6,2]
[5,8,6,7,3,1,2,4]=>0000000=>0000000=>[8]
[6,7,5,8,1,3,4,2]=>0000000=>0000000=>[8]
[7,6,5,8,1,4,3,2]=>0000000=>0000000=>[8]
[2,1,7,6,8,3,5,4]=>0100000=>0000010=>[6,2]
[7,5,6,8,1,4,2,3]=>0000000=>0000000=>[8]
[8,1,3,7,4,6,5,2]=>0000000=>0000000=>[8]
[6,1,5,4,3,8,7,2]=>0000000=>0000000=>[8]
[6,1,8,3,4,5,7,2]=>0000000=>0000000=>[8]
[5,6,2,1,4,8,3,7]=>0000000=>0000000=>[8]
[8,5,2,7,3,1,6,4]=>0000000=>0000000=>[8]
[8,5,6,4,2,1,7,3]=>0000000=>0000000=>[8]
[2,6,4,1,8,5,7,3]=>0000000=>0000000=>[8]
[1,5,7,3,2,4,6,8]=>1000001=>1000001=>[1,6,1]
[5,8,2,4,1,3,7,6]=>0000000=>0000000=>[8]
[4,8,1,6,3,2,7,5]=>0000000=>0000000=>[8]
[3,1,8,6,4,2,7,5]=>0000000=>0000000=>[8]
[4,2,1,3,7,8,5,6]=>0001000=>0001000=>[4,4]
[8,6,1,3,7,2,4,5]=>0000000=>0000000=>[8]
[5,2,7,8,6,4,1,3]=>0000000=>0000000=>[8]
[1,4,2,7,8,6,3,5]=>1000000=>0000001=>[7,1]
[1,6,2,4,8,5,3,7]=>1000000=>0000001=>[7,1]
[1,6,2,4,7,5,3,8]=>1000001=>1000001=>[1,6,1]
[1,7,3,2,8,6,4,5]=>1000000=>0000001=>[7,1]
[7,8,3,6,5,2,1,4]=>0000000=>0000000=>[8]
[4,7,2,8,6,1,5,3]=>0000000=>0000000=>[8]
[1,3,6,4,8,5,7,2]=>1000000=>0000001=>[7,1]
[1,3,6,4,7,5,8,2]=>1000000=>0000001=>[7,1]
[6,2,1,3,7,8,4,5]=>0000000=>0000000=>[8]
[7,2,5,1,8,3,4,6]=>0000000=>0000000=>[8]
[7,8,2,1,4,3,5,6]=>0000000=>0000000=>[8]
[7,5,4,2,6,8,1,3]=>0000000=>0000000=>[8]
[8,2,5,4,6,7,1,3]=>0000000=>0000000=>[8]
[8,2,6,4,3,1,7,5]=>0000000=>0000000=>[8]
[8,2,7,4,1,3,5,6]=>0000000=>0000000=>[8]
[1,2,8,4,3,5,6,7]=>1100000=>0000011=>[6,1,1]
[1,8,7,4,3,2,5,6]=>1000000=>0000001=>[7,1]
[5,8,4,7,2,1,6,3]=>0000000=>0000000=>[8]
[1,8,7,5,4,3,6,2]=>1000000=>0000001=>[7,1]
[1,6,8,4,3,7,5,2]=>1000000=>0000001=>[7,1]
[6,8,7,3,2,5,1,4]=>0000000=>0000000=>[8]
[5,3,8,1,2,7,4,6]=>0000000=>0000000=>[8]
[5,1,8,3,2,6,4,7]=>0000000=>0000000=>[8]
[5,7,3,1,2,6,4,8]=>0000001=>1000000=>[1,7]
[1,4,6,2,8,3,7,5]=>1000000=>0000001=>[7,1]
[5,2,6,7,8,4,1,3]=>0000000=>0000000=>[8]
[5,3,6,1,2,8,4,7]=>0000000=>0000000=>[8]
[1,6,3,2,7,8,4,5]=>1000000=>0000001=>[7,1]
[6,7,3,8,5,2,1,4]=>0000000=>0000000=>[8]
[4,6,2,7,8,1,5,3]=>0000000=>0000000=>[8]
[1,6,4,7,8,3,5,2]=>1000000=>0000001=>[7,1]
[4,5,7,2,1,8,6,3]=>0000000=>0000000=>[8]
[7,8,3,4,2,1,6,5]=>0000000=>0000000=>[8]
[6,3,4,1,2,5,8,7]=>0000010=>0100000=>[2,6]
[6,3,1,4,2,7,5,8]=>0000001=>1000000=>[1,7]
[1,8,3,2,4,5,6,7]=>1000000=>0000001=>[7,1]
[9,10,7,8,5,6,3,4,1,2]=>000000000=>000000000=>[10]
[7,8,3,5,4,6,1,2]=>0000000=>0000000=>[8]
[6,8,3,7,5,1,4,2]=>0000000=>0000000=>[8]
[5,7,3,8,1,6,2,4]=>0000000=>0000000=>[8]
[7,8,4,6,1,5,2,3]=>0000000=>0000000=>[8]
[7,8,1,6,4,5,2,3]=>0000000=>0000000=>[8]
[6,8,1,7,4,5,2,3]=>0000000=>0000000=>[8]
[1,8,6,7,4,5,2,3]=>1000000=>0000001=>[7,1]
[1,8,6,7,3,5,2,4]=>1000000=>0000001=>[7,1]
[6,8,1,7,3,5,2,4]=>0000000=>0000000=>[8]
[7,8,1,6,3,5,2,4]=>0000000=>0000000=>[8]
[7,8,3,6,1,5,2,4]=>0000000=>0000000=>[8]
[7,8,3,6,4,5,1,2]=>0000000=>0000000=>[8]
[7,8,2,6,4,5,1,3]=>0000000=>0000000=>[8]
[7,8,2,6,3,5,1,4]=>0000000=>0000000=>[8]
[7,8,2,6,1,5,3,4]=>0000000=>0000000=>[8]
[7,8,1,6,2,5,3,4]=>0000000=>0000000=>[8]
[1,8,6,7,2,5,3,4]=>1000000=>0000001=>[7,1]
[1,8,5,7,2,6,3,4]=>1000000=>0000001=>[7,1]
[5,8,1,7,2,6,3,4]=>0000000=>0000000=>[8]
[5,8,2,7,1,6,3,4]=>0000000=>0000000=>[8]
[6,8,2,7,1,5,3,4]=>0000000=>0000000=>[8]
[6,8,2,7,3,5,1,4]=>0000000=>0000000=>[8]
[6,8,2,7,4,5,1,3]=>0000000=>0000000=>[8]
[6,8,3,7,4,5,1,2]=>0000000=>0000000=>[8]
[3,8,6,7,4,5,1,2]=>0000000=>0000000=>[8]
[2,8,6,7,4,5,1,3]=>0000000=>0000000=>[8]
[2,8,6,7,3,5,1,4]=>0000000=>0000000=>[8]
[2,8,6,7,1,5,3,4]=>0000000=>0000000=>[8]
[2,8,5,7,1,6,3,4]=>0000000=>0000000=>[8]
[2,8,1,7,5,6,3,4]=>0000000=>0000000=>[8]
[1,8,2,7,5,6,3,4]=>1000000=>0000001=>[7,1]
[1,8,2,7,4,6,3,5]=>1000000=>0000001=>[7,1]
[2,8,1,7,4,6,3,5]=>0000000=>0000000=>[8]
[2,8,4,7,1,6,3,5]=>0000000=>0000000=>[8]
[2,8,4,7,3,6,1,5]=>0000000=>0000000=>[8]
[2,8,5,7,3,6,1,4]=>0000000=>0000000=>[8]
[3,8,5,7,4,6,1,2]=>0000000=>0000000=>[8]
[5,8,3,7,4,6,1,2]=>0000000=>0000000=>[8]
[5,8,2,7,4,6,1,3]=>0000000=>0000000=>[8]
[5,8,2,7,3,6,1,4]=>0000000=>0000000=>[8]
[4,8,2,7,3,6,1,5]=>0000000=>0000000=>[8]
[4,8,2,7,1,6,3,5]=>0000000=>0000000=>[8]
[4,8,1,7,2,6,3,5]=>0000000=>0000000=>[8]
[1,8,4,7,2,6,3,5]=>1000000=>0000001=>[7,1]
[1,8,4,7,3,6,2,5]=>1000000=>0000001=>[7,1]
[4,8,1,7,3,6,2,5]=>0000000=>0000000=>[8]
[4,8,3,7,1,6,2,5]=>0000000=>0000000=>[8]
[6,8,3,7,1,5,2,4]=>0000000=>0000000=>[8]
[5,8,1,7,3,6,2,4]=>0000000=>0000000=>[8]
[1,8,5,7,3,6,2,4]=>1000000=>0000001=>[7,1]
[1,8,5,7,4,6,2,3]=>1000000=>0000001=>[7,1]
[5,8,1,7,4,6,2,3]=>0000000=>0000000=>[8]
[5,8,4,7,1,6,2,3]=>0000000=>0000000=>[8]
[6,8,4,7,1,5,2,3]=>0000000=>0000000=>[8]
[6,8,5,7,1,4,2,3]=>0000000=>0000000=>[8]
[5,8,6,7,3,4,1,2]=>0000000=>0000000=>[8]
[5,8,6,7,2,4,1,3]=>0000000=>0000000=>[8]
[5,8,6,7,1,4,2,3]=>0000000=>0000000=>[8]
[4,8,6,7,1,5,2,3]=>0000000=>0000000=>[8]
[4,8,5,7,1,6,2,3]=>0000000=>0000000=>[8]
[4,8,1,7,5,6,2,3]=>0000000=>0000000=>[8]
[1,8,4,7,5,6,2,3]=>1000000=>0000001=>[7,1]
[1,8,3,7,5,6,2,4]=>1000000=>0000001=>[7,1]
[3,8,1,7,5,6,2,4]=>0000000=>0000000=>[8]
[3,8,5,7,1,6,2,4]=>0000000=>0000000=>[8]
[3,8,6,7,1,5,2,4]=>0000000=>0000000=>[8]
[3,8,6,7,2,5,1,4]=>0000000=>0000000=>[8]
[4,8,6,7,2,5,1,3]=>0000000=>0000000=>[8]
[4,8,6,7,3,5,1,2]=>0000000=>0000000=>[8]
[4,8,5,7,3,6,1,2]=>0000000=>0000000=>[8]
[4,8,5,7,2,6,1,3]=>0000000=>0000000=>[8]
[3,8,5,7,2,6,1,4]=>0000000=>0000000=>[8]
[3,8,4,7,2,6,1,5]=>0000000=>0000000=>[8]
[3,8,4,7,1,6,2,5]=>0000000=>0000000=>[8]
[3,8,1,7,4,6,2,5]=>0000000=>0000000=>[8]
[1,8,3,7,4,6,2,5]=>1000000=>0000001=>[7,1]
[1,8,3,7,2,6,4,5]=>1000000=>0000001=>[7,1]
[3,8,1,7,2,6,4,5]=>0000000=>0000000=>[8]
[3,8,2,7,1,6,4,5]=>0000000=>0000000=>[8]
[3,8,2,7,4,6,1,5]=>0000000=>0000000=>[8]
[3,8,2,7,5,6,1,4]=>0000000=>0000000=>[8]
[4,8,2,7,5,6,1,3]=>0000000=>0000000=>[8]
[4,8,3,7,5,6,1,2]=>0000000=>0000000=>[8]
[3,8,4,7,5,6,1,2]=>0000000=>0000000=>[8]
[2,8,4,7,5,6,1,3]=>0000000=>0000000=>[8]
[2,8,3,7,5,6,1,4]=>0000000=>0000000=>[8]
[2,8,3,7,4,6,1,5]=>0000000=>0000000=>[8]
[2,8,3,7,1,6,4,5]=>0000000=>0000000=>[8]
[2,8,1,7,3,6,4,5]=>0000000=>0000000=>[8]
[7,5,2,8,6,4,1,3]=>0000000=>0000000=>[8]
[7,4,8,6,1,5,2,3]=>0000000=>0000000=>[8]
[7,1,8,4,5,2,6,3]=>0000000=>0000000=>[8]
[1,6,7,4,2,8,5,3]=>1000000=>0000001=>[7,1]
[1,6,7,3,8,5,2,4]=>1000000=>0000001=>[7,1]
[7,1,8,3,5,6,2,4]=>0000000=>0000000=>[8]
[7,3,8,6,2,5,1,4]=>0000000=>0000000=>[8]
[7,4,2,8,6,1,3,5]=>0000000=>0000000=>[8]
[6,8,1,7,2,3,4,5]=>0000000=>0000000=>[8]
[1,5,7,8,2,6,3,4]=>1000000=>0000001=>[7,1]
[2,5,3,7,8,1,6,4]=>0000000=>0000000=>[8]
[2,5,4,1,3,7,8,6]=>0000100=>0010000=>[3,5]
[3,1,5,4,7,8,2,6]=>0000000=>0000000=>[8]
[5,3,1,4,8,2,6,7]=>0000000=>0000000=>[8]
[5,2,4,8,6,1,3,7]=>0000000=>0000000=>[8]
[4,8,1,3,6,7,2,5]=>0000000=>0000000=>[8]
[5,3,8,2,4,7,1,6]=>0000000=>0000000=>[8]
[5,4,3,8,1,2,7,6]=>0000000=>0000000=>[8]
[6,4,3,1,2,8,5,7]=>0000000=>0000000=>[8]
[6,4,2,8,1,3,7,5]=>0000000=>0000000=>[8]
[6,3,8,2,5,1,7,4]=>0000000=>0000000=>[8]
[6,3,8,1,4,7,2,5]=>0000000=>0000000=>[8]
[1,5,7,3,6,8,4,2]=>1000000=>0000001=>[7,1]
[1,5,7,4,2,6,8,3]=>1000000=>0000001=>[7,1]
[5,8,1,4,2,6,3,7]=>0000000=>0000000=>[8]
[6,5,3,1,4,2,8,7]=>0000010=>0100000=>[2,6]
[5,3,1,6,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,2,6,4,1,7,3,8]=>0000001=>1000000=>[1,7]
[4,6,1,7,5,2,8,3]=>0000000=>0000000=>[8]
[3,5,6,1,2,8,7,4]=>0000000=>0000000=>[8]
[3,5,7,1,8,6,2,4]=>0000000=>0000000=>[8]
[3,6,2,7,5,1,8,4]=>0000000=>0000000=>[8]
[4,3,1,5,7,2,6,8]=>0000001=>1000000=>[1,7]
[3,4,7,2,8,6,1,5]=>0000000=>0000000=>[8]
[3,4,5,8,2,7,1,6]=>0000000=>0000000=>[8]
[5,3,6,8,4,7,2,1]=>0000000=>0000000=>[8]
[5,1,6,8,4,3,2,7]=>0000000=>0000000=>[8]
[6,7,8,1,4,3,2,5]=>0000000=>0000000=>[8]
[4,7,1,5,8,3,2,6]=>0000000=>0000000=>[8]
[8,4,1,5,7,3,2,6]=>0000000=>0000000=>[8]
[8,3,6,1,4,7,2,5]=>0000000=>0000000=>[8]
[3,7,6,1,4,8,2,5]=>0000000=>0000000=>[8]
[6,7,8,2,4,3,5,1]=>0000000=>0000000=>[8]
[5,7,3,8,4,6,2,1]=>0000000=>0000000=>[8]
[4,7,3,5,8,6,2,1]=>0000000=>0000000=>[8]
[8,7,2,1,4,3,6,5]=>0000000=>0000000=>[8]
[8,7,3,1,4,6,2,5]=>0000000=>0000000=>[8]
[8,7,6,3,2,5,4,1]=>0000000=>0000000=>[8]
[8,7,3,5,1,6,2,4]=>0000000=>0000000=>[8]
[8,7,2,5,1,3,6,4]=>0000000=>0000000=>[8]
[8,4,6,5,7,1,2,3]=>0000000=>0000000=>[8]
[8,7,6,5,2,1,4,3]=>0000000=>0000000=>[8]
[3,6,4,8,7,5,1,2]=>0000000=>0000000=>[8]
[5,6,4,3,8,7,1,2]=>0000000=>0000000=>[8]
[1,6,2,4,7,8,5,3]=>1000000=>0000001=>[7,1]
[3,6,2,4,8,1,5,7]=>0000000=>0000000=>[8]
[3,4,7,2,8,1,6,5]=>0000000=>0000000=>[8]
[7,3,8,4,5,6,1,2]=>0000000=>0000000=>[8]
[3,8,7,5,4,6,1,2]=>0000000=>0000000=>[8]
[4,3,6,7,8,5,1,2]=>0000000=>0000000=>[8]
[3,5,6,4,8,7,1,2]=>0000000=>0000000=>[8]
[4,6,8,5,3,7,1,2]=>0000000=>0000000=>[8]
[6,5,2,1,4,7,8,3]=>0000000=>0000000=>[8]
[4,2,7,5,1,8,6,3]=>0000000=>0000000=>[8]
[2,1,6,4,8,7,5,3]=>0100000=>0000010=>[6,2]
[7,8,1,4,2,6,5,3]=>0000000=>0000000=>[8]
[6,5,1,3,4,2,8,7]=>0000010=>0100000=>[2,6]
[4,8,5,3,1,7,2,6]=>0000000=>0000000=>[8]
[7,4,5,3,2,8,1,6]=>0000000=>0000000=>[8]
[5,8,3,6,1,4,2,7]=>0000000=>0000000=>[8]
[1,6,8,7,4,2,3,5]=>1000000=>0000001=>[7,1]
[7,6,1,8,3,2,4,5]=>0000000=>0000000=>[8]
[7,1,8,6,3,4,2,5]=>0000000=>0000000=>[8]
[1,8,7,6,4,3,2,5]=>1000000=>0000001=>[7,1]
[2,1,7,5,6,3,8,4]=>0100000=>0000010=>[6,2]
[3,1,6,7,5,8,2,4]=>0000000=>0000000=>[8]
[7,8,1,6,5,3,2,4]=>0000000=>0000000=>[8]
[7,8,2,1,4,5,6,3]=>0000000=>0000000=>[8]
[4,2,6,1,8,5,7,3]=>0000000=>0000000=>[8]
[2,8,1,5,4,6,7,3]=>0000000=>0000000=>[8]
[1,2,8,3,6,5,7,4]=>1100000=>0000011=>[6,1,1]
[2,6,4,1,7,5,8,3]=>0000000=>0000000=>[8]
[7,6,5,8,1,4,2,3]=>0000000=>0000000=>[8]
[5,8,6,7,3,2,1,4]=>0000000=>0000000=>[8]
[1,6,4,3,7,2,8,5]=>1000000=>0000001=>[7,1]
[4,1,6,3,8,2,7,5]=>0000000=>0000000=>[8]
[7,8,1,3,4,2,6,5]=>0000000=>0000000=>[8]
[2,8,5,7,4,3,1,6]=>0000000=>0000000=>[8]
[7,2,5,8,3,4,1,6]=>0000000=>0000000=>[8]
[3,5,7,8,4,1,2,6]=>0000000=>0000000=>[8]
[5,4,7,3,6,8,1,2]=>0000000=>0000000=>[8]
[1,4,7,2,5,8,3,6]=>1000000=>0000001=>[7,1]
[3,6,2,4,7,1,5,8]=>0000001=>1000000=>[1,7]
[7,6,3,5,4,8,1,2]=>0000000=>0000000=>[8]
[4,5,6,3,8,7,1,2]=>0000000=>0000000=>[8]
[4,8,2,6,1,5,3,7]=>0000000=>0000000=>[8]
[7,1,3,6,8,4,2,5]=>0000000=>0000000=>[8]
[1,8,3,6,7,4,5,2]=>1000000=>0000001=>[7,1]
[7,1,5,8,3,6,2,4]=>0000000=>0000000=>[8]
[3,1,6,4,7,2,5,8]=>0000001=>1000000=>[1,7]
[5,8,7,1,2,4,3,6]=>0000000=>0000000=>[8]
[6,8,5,1,3,4,2,7]=>0000000=>0000000=>[8]
[7,6,5,1,4,3,2,8]=>0000001=>1000000=>[1,7]
[2,6,4,5,1,3,8,7]=>0000010=>0100000=>[2,6]
[3,5,6,4,1,8,2,7]=>0000000=>0000000=>[8]
[7,8,5,4,1,3,2,6]=>0000000=>0000000=>[8]
[7,8,2,3,4,1,6,5]=>0000000=>0000000=>[8]
[4,2,6,3,8,1,7,5]=>0000000=>0000000=>[8]
[7,2,3,5,4,1,8,6]=>0000000=>0000000=>[8]
[6,2,4,3,1,5,7,8]=>0000011=>1100000=>[1,1,6]
[4,2,8,3,1,7,5,6]=>0000000=>0000000=>[8]
[5,3,7,4,1,6,2,8]=>0000001=>1000000=>[1,7]
[2,4,7,3,6,1,8,5]=>0000000=>0000000=>[8]
[5,8,7,6,3,1,2,4]=>0000000=>0000000=>[8]
[7,5,6,8,1,4,3,2]=>0000000=>0000000=>[8]
[2,4,7,1,6,5,3,8]=>0000001=>1000000=>[1,7]
[5,2,7,1,8,4,6,3]=>0000000=>0000000=>[8]
[4,2,1,3,6,5,8,7]=>0001010=>0101000=>[2,2,4]
[4,2,6,1,8,5,3,7]=>0000000=>0000000=>[8]
[7,8,2,1,4,5,3,6]=>0000000=>0000000=>[8]
[7,8,4,1,5,3,6,2]=>0000000=>0000000=>[8]
[7,5,1,6,4,3,8,2]=>0000000=>0000000=>[8]
[5,8,1,6,3,4,7,2]=>0000000=>0000000=>[8]
[6,8,1,7,5,2,3,4]=>0000000=>0000000=>[8]
[5,6,1,7,4,8,2,3]=>0000000=>0000000=>[8]
[7,8,5,1,6,4,2,3]=>0000000=>0000000=>[8]
[2,6,5,7,3,4,8,1]=>0000000=>0000000=>[8]
[1,6,4,7,5,8,2,3]=>1000000=>0000001=>[7,1]
[1,3,7,4,6,8,2,5]=>1000000=>0000001=>[7,1]
[5,2,4,7,3,6,8,1]=>0000000=>0000000=>[8]
[8,1,6,5,7,2,4,3]=>0000000=>0000000=>[8]
[1,2,7,6,8,3,4,5]=>1100000=>0000011=>[6,1,1]
[7,8,1,6,2,4,5,3]=>0000000=>0000000=>[8]
[2,8,1,7,4,3,6,5]=>0000000=>0000000=>[8]
[3,7,4,1,8,5,2,6]=>0000000=>0000000=>[8]
[6,7,1,4,8,3,2,5]=>0000000=>0000000=>[8]
[2,7,1,8,4,5,3,6]=>0000000=>0000000=>[8]
[6,1,2,8,4,3,5,7]=>0000000=>0000000=>[8]
[5,1,2,4,8,3,6,7]=>0000000=>0000000=>[8]
[4,1,3,2,8,5,6,7]=>0001000=>0001000=>[4,4]
[3,2,1,4,8,5,6,7]=>0011000=>0001100=>[4,1,3]
[4,3,6,1,5,8,2,7]=>0000000=>0000000=>[8]
[2,6,1,4,5,8,3,7]=>0000000=>0000000=>[8]
[1,6,2,5,8,3,4,7]=>1000000=>0000001=>[7,1]
[8,4,2,1,7,3,6,5]=>0000000=>0000000=>[8]
[7,4,2,1,8,5,3,6]=>0000000=>0000000=>[8]
[1,5,4,2,8,3,6,7]=>1000000=>0000001=>[7,1]
[6,4,3,1,5,8,2,7]=>0000000=>0000000=>[8]
[5,4,3,2,1,8,6,7]=>0000100=>0010000=>[3,5]
[2,5,3,4,1,8,6,7]=>0000100=>0010000=>[3,5]
[4,3,5,2,1,8,6,7]=>0000100=>0010000=>[3,5]
[3,7,6,8,4,5,2,1]=>0000000=>0000000=>[8]
[1,7,6,8,5,4,2,3]=>1000000=>0000001=>[7,1]
[2,4,8,6,7,3,5,1]=>0000000=>0000000=>[8]
[6,3,5,8,4,7,2,1]=>0000000=>0000000=>[8]
[5,4,3,8,6,7,2,1]=>0000000=>0000000=>[8]
[3,2,8,5,7,4,6,1]=>0000000=>0000000=>[8]
[3,1,8,5,7,6,2,4]=>0000000=>0000000=>[8]
[5,8,6,7,4,3,2,1]=>0000000=>0000000=>[8]
[4,8,7,5,6,3,2,1]=>0000000=>0000000=>[8]
[6,2,1,4,3,8,5,7]=>0000000=>0000000=>[8]
[2,1,6,4,3,5,8,7]=>0100010=>0100010=>[2,4,2]
[8,4,2,1,3,6,5,7]=>0000000=>0000000=>[8]
[6,4,2,1,8,3,5,7]=>0000000=>0000000=>[8]
[4,6,2,1,3,8,5,7]=>0000000=>0000000=>[8]
[2,6,1,4,3,8,5,7]=>0000000=>0000000=>[8]
[4,8,2,1,3,6,5,7]=>0000000=>0000000=>[8]
[2,6,1,4,8,3,5,7]=>0000000=>0000000=>[8]
[2,6,4,1,8,3,5,7]=>0000000=>0000000=>[8]
[2,6,4,8,1,3,5,7]=>0000000=>0000000=>[8]
[4,6,2,8,1,3,5,7]=>0000000=>0000000=>[8]
[6,2,4,1,8,3,5,7]=>0000000=>0000000=>[8]
[4,2,1,6,8,3,5,7]=>0000000=>0000000=>[8]
[4,2,1,3,8,6,5,7]=>0001000=>0001000=>[4,4]
[4,2,1,8,3,6,5,7]=>0000000=>0000000=>[8]
[2,4,8,1,6,3,5,7]=>0000000=>0000000=>[8]
[2,8,6,4,1,3,5,7]=>0000000=>0000000=>[8]
[4,8,6,2,1,3,5,7]=>0000000=>0000000=>[8]
[3,2,6,1,5,4,8,7]=>0000010=>0100000=>[2,6]
[4,3,6,1,5,2,8,7]=>0000010=>0100000=>[2,6]
[4,3,8,2,6,1,7,5]=>0000000=>0000000=>[8]
[4,3,8,1,7,2,6,5]=>0000000=>0000000=>[8]
[4,3,8,1,5,2,7,6]=>0000000=>0000000=>[8]
[2,1,5,4,8,3,7,6]=>0100000=>0000010=>[6,2]
[5,4,7,6,8,1,3,2]=>0000000=>0000000=>[8]
[4,3,7,1,8,5,6,2]=>0000000=>0000000=>[8]
[4,3,6,5,8,1,7,2]=>0000000=>0000000=>[8]
[7,4,6,5,8,1,3,2]=>0000000=>0000000=>[8]
[8,4,6,1,3,2,7,5]=>0000000=>0000000=>[8]
[8,1,6,3,4,2,7,5]=>0000000=>0000000=>[8]
[8,3,5,2,6,1,7,4]=>0000000=>0000000=>[8]
[8,2,7,1,5,3,6,4]=>0000000=>0000000=>[8]
[2,1,8,3,5,4,7,6]=>0100000=>0000010=>[6,2]
[8,1,3,2,5,4,7,6]=>0000000=>0000000=>[8]
[8,1,5,2,4,3,7,6]=>0000000=>0000000=>[8]
[8,2,4,1,5,3,7,6]=>0000000=>0000000=>[8]
[3,2,8,4,6,1,7,5]=>0000000=>0000000=>[8]
[3,2,8,1,7,4,6,5]=>0000000=>0000000=>[8]
[3,2,7,1,8,5,6,4]=>0000000=>0000000=>[8]
[3,2,6,5,8,1,7,4]=>0000000=>0000000=>[8]
[7,6,8,1,5,2,4,3]=>0000000=>0000000=>[8]
[7,6,8,1,3,2,5,4]=>0000000=>0000000=>[8]
[7,1,8,2,6,4,5,3]=>0000000=>0000000=>[8]
[5,4,7,2,6,3,8,1]=>0000000=>0000000=>[8]
[6,1,8,4,7,2,5,3]=>0000000=>0000000=>[8]
[2,1,6,5,8,3,7,4]=>0100000=>0000010=>[6,2]
[3,2,1,5,8,4,6,7]=>0010000=>0000100=>[5,3]
[2,8,3,1,5,4,6,7]=>0000000=>0000000=>[8]
[2,4,8,3,5,7,6,1]=>0000000=>0000000=>[8]
[1,8,4,2,5,3,6,7]=>1000000=>0000001=>[7,1]
[8,1,5,3,2,4,6,7]=>0000000=>0000000=>[8]
[3,8,1,5,2,4,6,7]=>0000000=>0000000=>[8]
[5,4,1,3,8,2,6,7]=>0000000=>0000000=>[8]
[1,5,7,3,8,4,2,6]=>1000000=>0000001=>[7,1]
[5,1,4,7,8,3,2,6]=>0000000=>0000000=>[8]
[1,4,3,8,7,5,6,2]=>1000000=>0000001=>[7,1]
[1,6,8,5,3,7,4,2]=>1000000=>0000001=>[7,1]
[6,4,8,1,7,3,5,2]=>0000000=>0000000=>[8]
[6,4,8,7,1,5,2,3]=>0000000=>0000000=>[8]
[7,1,6,8,4,3,2,5]=>0000000=>0000000=>[8]
[1,6,7,2,8,4,3,5]=>1000000=>0000001=>[7,1]
[6,7,1,4,2,8,3,5]=>0000000=>0000000=>[8]
[6,3,7,1,4,8,2,5]=>0000000=>0000000=>[8]
[3,7,8,1,5,2,4,6]=>0000000=>0000000=>[8]
[7,1,2,8,5,3,4,6]=>0000000=>0000000=>[8]
[1,7,2,8,4,5,3,6]=>1000000=>0000001=>[7,1]
[4,2,1,7,8,5,3,6]=>0000000=>0000000=>[8]
[7,2,6,3,4,1,8,5]=>0000000=>0000000=>[8]
[2,7,1,8,3,5,4,6]=>0000000=>0000000=>[8]
[2,1,7,3,5,8,4,6]=>0100000=>0000010=>[6,2]
[1,2,7,5,8,3,4,6]=>1100000=>0000011=>[6,1,1]
[8,7,1,3,6,2,4,5]=>0000000=>0000000=>[8]
[8,2,1,7,3,5,6,4]=>0000000=>0000000=>[8]
[7,8,2,6,3,1,5,4]=>0000000=>0000000=>[8]
[2,8,4,1,6,7,5,3]=>0000000=>0000000=>[8]
[8,3,7,1,5,6,2,4]=>0000000=>0000000=>[8]
[8,1,6,2,7,4,5,3]=>0000000=>0000000=>[8]
[1,8,5,2,6,7,4,3]=>1000000=>0000001=>[7,1]
[5,2,1,8,6,7,4,3]=>0000000=>0000000=>[8]
[7,8,1,6,4,2,5,3]=>0000000=>0000000=>[8]
[8,7,6,5,1,4,2,3]=>0000000=>0000000=>[8]
[8,7,6,1,5,3,4,2]=>0000000=>0000000=>[8]
[8,1,7,5,6,4,3,2]=>0000000=>0000000=>[8]
[1,8,6,7,5,4,3,2]=>1000000=>0000001=>[7,1]
[6,5,3,1,2,4,8,7]=>0000010=>0100000=>[2,6]
[4,5,3,6,1,2,8,7]=>0000010=>0100000=>[2,6]
[8,1,4,7,3,6,2,5]=>0000000=>0000000=>[8]
[6,3,4,7,5,8,1,2]=>0000000=>0000000=>[8]
[4,7,1,3,5,8,6,2]=>0000000=>0000000=>[8]
[4,8,3,7,1,2,6,5]=>0000000=>0000000=>[8]
[8,1,7,4,5,2,3,6]=>0000000=>0000000=>[8]
[5,3,7,8,2,4,6,1]=>0000000=>0000000=>[8]
[5,3,7,6,2,1,8,4]=>0000000=>0000000=>[8]
[2,1,6,7,5,8,3,4]=>0100000=>0000010=>[6,2]
[2,1,5,7,3,6,8,4]=>0100000=>0000010=>[6,2]
[2,4,7,1,6,5,8,3]=>0000000=>0000000=>[8]
[3,4,6,2,7,8,5,1]=>0000000=>0000000=>[8]
[3,5,6,4,7,1,8,2]=>0000000=>0000000=>[8]
[3,4,1,5,7,6,8,2]=>0000000=>0000000=>[8]
[4,2,1,7,3,5,8,6]=>0000000=>0000000=>[8]
[7,3,1,5,4,2,8,6]=>0000000=>0000000=>[8]
[6,3,1,4,2,8,5,7]=>0000000=>0000000=>[8]
[8,4,1,5,2,7,6,3]=>0000000=>0000000=>[8]
[3,6,2,7,1,4,8,5]=>0000000=>0000000=>[8]
[2,7,5,4,1,3,8,6]=>0000000=>0000000=>[8]
[6,4,3,2,1,8,5,7]=>0000000=>0000000=>[8]
[1,7,6,2,4,8,3,5]=>1000000=>0000001=>[7,1]
[7,1,8,5,3,6,4,2]=>0000000=>0000000=>[8]
[1,8,5,7,2,4,6,3]=>1000000=>0000001=>[7,1]
[7,2,8,5,6,1,4,3]=>0000000=>0000000=>[8]
[3,6,5,8,1,4,2,7]=>0000000=>0000000=>[8]
[4,3,6,7,8,1,2,5]=>0000000=>0000000=>[8]
[5,4,6,7,2,8,1,3]=>0000000=>0000000=>[8]
[3,5,7,1,4,8,2,6]=>0000000=>0000000=>[8]
[8,1,5,2,7,4,6,3]=>0000000=>0000000=>[8]
[5,4,1,6,8,2,3,7]=>0000000=>0000000=>[8]
[5,3,6,4,7,8,1,2]=>0000000=>0000000=>[8]
[6,4,7,8,1,5,3,2]=>0000000=>0000000=>[8]
[6,3,7,8,5,2,4,1]=>0000000=>0000000=>[8]
[4,6,8,2,7,1,5,3]=>0000000=>0000000=>[8]
[2,5,8,7,1,3,6,4]=>0000000=>0000000=>[8]
[8,2,7,6,5,1,4,3]=>0000000=>0000000=>[8]
[4,3,8,7,6,2,1,5]=>0000000=>0000000=>[8]
[4,7,3,8,6,5,1,2]=>0000000=>0000000=>[8]
[5,8,7,3,6,4,2,1]=>0000000=>0000000=>[8]
[2,8,7,6,5,4,1,3]=>0000000=>0000000=>[8]
[5,4,3,2,1,6,7,8,9,10]=>000011111=>111110000=>[1,1,1,1,1,5]
[6,4,3,2,7,1,5,8,9,10]=>000000111=>111000000=>[1,1,1,7]
[7,5,3,8,2,6,1,4,9,10]=>000000011=>110000000=>[1,1,8]
[8,6,9,4,7,2,5,1,3,10]=>000000001=>100000000=>[1,9]
[7,8,5,6,3,1,4,2]=>0000000=>0000000=>[8]
[7,5,8,3,1,4,2,6]=>0000000=>0000000=>[8]
[7,8,5,3,1,6,2,4]=>0000000=>0000000=>[8]
[7,8,5,3,1,6,4,2]=>0000000=>0000000=>[8]
[7,8,5,3,6,4,1,2]=>0000000=>0000000=>[8]
[7,5,8,3,1,2,6,4]=>0000000=>0000000=>[8]
[7,5,6,3,4,1,8,2]=>0000000=>0000000=>[8]
[7,5,3,1,6,4,8,2]=>0000000=>0000000=>[8]
[7,5,3,6,4,1,8,2]=>0000000=>0000000=>[8]
[7,5,3,8,4,6,1,2]=>0000000=>0000000=>[8]
[7,5,3,8,4,1,6,2]=>0000000=>0000000=>[8]
[7,5,3,8,1,4,6,2]=>0000000=>0000000=>[8]
[7,5,3,1,8,4,6,2]=>0000000=>0000000=>[8]
[7,5,3,1,8,2,6,4]=>0000000=>0000000=>[8]
[7,5,3,1,8,6,2,4]=>0000000=>0000000=>[8]
[7,5,3,8,6,1,4,2]=>0000000=>0000000=>[8]
[7,5,3,8,1,4,2,6]=>0000000=>0000000=>[8]
[7,5,3,8,6,1,2,4]=>0000000=>0000000=>[8]
[7,5,8,6,3,1,2,4]=>0000000=>0000000=>[8]
[7,5,8,6,3,1,4,2]=>0000000=>0000000=>[8]
[7,5,8,6,3,4,1,2]=>0000000=>0000000=>[8]
[7,5,6,8,3,1,4,2]=>0000000=>0000000=>[8]
[7,5,6,3,8,1,2,4]=>0000000=>0000000=>[8]
[7,5,6,3,1,8,4,2]=>0000000=>0000000=>[8]
[7,5,3,6,1,8,4,2]=>0000000=>0000000=>[8]
[7,5,3,4,1,6,8,2]=>0000000=>0000000=>[8]
[4,6,8,3,5,7,1,2]=>0000000=>0000000=>[8]
[6,8,1,2,4,5,7,3]=>0000000=>0000000=>[8]
[8,3,5,2,4,1,6,7]=>0000000=>0000000=>[8]
[3,5,7,2,4,6,1,8]=>0000001=>1000000=>[1,7]
[4,2,5,7,3,6,1,8]=>0000001=>1000000=>[1,7]
[4,5,2,8,3,1,6,7]=>0000000=>0000000=>[8]
[2,1,6,8,4,7,3,5]=>0100000=>0000010=>[6,2]
[1,2,5,8,3,6,7,4]=>1100000=>0000011=>[6,1,1]
[5,3,6,8,4,7,1,2]=>0000000=>0000000=>[8]
[4,3,6,2,7,5,1,8]=>0000001=>1000000=>[1,7]
[4,3,1,7,8,2,6,5]=>0000000=>0000000=>[8]
[5,4,7,3,8,6,1,2]=>0000000=>0000000=>[8]
[5,8,4,7,6,3,1,2]=>0000000=>0000000=>[8]
[5,8,7,1,4,2,6,3]=>0000000=>0000000=>[8]
[8,3,5,1,2,7,6,4]=>0000000=>0000000=>[8]
[4,7,3,6,5,2,1,8]=>0000001=>1000000=>[1,7]
[5,3,7,6,4,2,1,8]=>0000001=>1000000=>[1,7]
[5,3,1,6,4,2,8,7]=>0000010=>0100000=>[2,6]
[1,3,8,5,4,2,7,6]=>1000000=>0000001=>[7,1]
[1,8,3,6,2,7,5,4]=>1000000=>0000001=>[7,1]
[1,6,8,7,4,2,5,3]=>1000000=>0000001=>[7,1]
[6,4,8,7,5,3,1,2]=>0000000=>0000000=>[8]
[3,1,2,7,6,4,8,5]=>0010000=>0000100=>[5,3]
[5,2,6,3,7,4,1,8]=>0000001=>1000000=>[1,7]
[2,8,5,3,1,6,4,7]=>0000000=>0000000=>[8]
[2,1,7,3,8,5,4,6]=>0100000=>0000010=>[6,2]
[1,6,2,3,7,8,5,4]=>1000000=>0000001=>[7,1]
[1,6,7,2,8,4,5,3]=>1000000=>0000001=>[7,1]
[6,3,7,4,8,5,1,2]=>0000000=>0000000=>[8]
[5,7,1,8,2,4,6,3]=>0000000=>0000000=>[8]
[5,1,2,7,8,3,6,4]=>0000000=>0000000=>[8]
[4,2,1,7,3,8,5,6]=>0000000=>0000000=>[8]
[6,2,8,4,3,1,5,7]=>0000000=>0000000=>[8]
[6,4,2,7,3,5,1,8]=>0000001=>1000000=>[1,7]
[7,3,2,1,8,4,5,6]=>0000000=>0000000=>[8]
[3,7,2,8,6,1,4,5]=>0000000=>0000000=>[8]
[7,1,8,2,4,5,6,3]=>0000000=>0000000=>[8]
[8,7,6,1,2,4,5,3]=>0000000=>0000000=>[8]
[8,3,6,5,2,1,4,7]=>0000000=>0000000=>[8]
[8,2,4,1,6,5,3,7]=>0000000=>0000000=>[8]
[8,5,1,2,7,3,6,4]=>0000000=>0000000=>[8]
[6,1,8,2,3,7,5,4]=>0000000=>0000000=>[8]
[8,1,2,6,4,3,7,5]=>0000000=>0000000=>[8]
[1,7,2,8,3,6,5,4]=>1000000=>0000001=>[7,1]
[7,3,8,6,5,4,1,2]=>0000000=>0000000=>[8]
[8,1,7,3,2,6,5,4]=>0000000=>0000000=>[8]
[4,3,1,2,8,7,6,5]=>0001000=>0001000=>[4,4]
[8,6,4,3,1,5,7,2]=>0000000=>0000000=>[8]
[8,6,4,1,5,2,7,3]=>0000000=>0000000=>[8]
[8,7,2,4,5,3,1,6]=>0000000=>0000000=>[8]
[8,5,1,2,6,7,3,4]=>0000000=>0000000=>[8]
[8,5,1,6,4,2,7,3]=>0000000=>0000000=>[8]
[8,5,1,3,6,4,7,2]=>0000000=>0000000=>[8]
[7,4,8,3,1,6,2,5]=>0000000=>0000000=>[8]
[7,1,5,8,3,2,6,4]=>0000000=>0000000=>[8]
[5,7,4,1,8,2,6,3]=>0000000=>0000000=>[8]
[5,7,4,3,1,8,6,2]=>0000000=>0000000=>[8]
[8,5,7,4,6,1,3,2]=>0000000=>0000000=>[8]
[1,8,7,2,5,4,6,3]=>1000000=>0000001=>[7,1]
[4,3,1,8,7,5,2,6]=>0000000=>0000000=>[8]
[3,1,4,6,8,7,2,5]=>0000000=>0000000=>[8]
[1,6,2,4,8,7,5,3]=>1000000=>0000001=>[7,1]
[7,1,6,4,8,5,2,3]=>0000000=>0000000=>[8]
[1,3,7,2,6,8,4,5]=>1000000=>0000001=>[7,1]
[6,1,2,7,8,5,3,4]=>0000000=>0000000=>[8]
[6,1,2,7,4,8,5,3]=>0000000=>0000000=>[8]
[3,1,6,4,7,8,5,2]=>0000000=>0000000=>[8]
[5,7,1,3,8,4,6,2]=>0000000=>0000000=>[8]
[5,7,1,8,4,2,6,3]=>0000000=>0000000=>[8]
[5,7,1,2,8,6,3,4]=>0000000=>0000000=>[8]
[4,2,6,3,8,1,5,7]=>0000000=>0000000=>[8]
[4,2,6,7,3,5,1,8]=>0000001=>1000000=>[1,7]
[3,6,2,4,7,5,1,8]=>0000001=>1000000=>[1,7]
[3,6,2,4,1,8,5,7]=>0000000=>0000000=>[8]
[7,1,4,5,2,8,6,3]=>0000000=>0000000=>[8]
[4,7,3,1,5,8,6,2]=>0000000=>0000000=>[8]
[4,2,8,1,5,7,3,6]=>0000000=>0000000=>[8]
[8,5,7,6,1,4,2,3]=>0000000=>0000000=>[8]
[1,8,2,4,6,7,3,5]=>1000000=>0000001=>[7,1]
[1,2,7,4,8,6,3,5]=>1100000=>0000011=>[6,1,1]
[1,2,7,8,3,6,5,4]=>1100000=>0000011=>[6,1,1]
[1,8,5,7,4,3,2,6]=>1000000=>0000001=>[7,1]
[7,1,5,8,3,4,6,2]=>0000000=>0000000=>[8]
[7,1,5,8,4,3,2,6]=>0000000=>0000000=>[8]
[7,1,2,5,8,3,6,4]=>0000000=>0000000=>[8]
[2,7,1,4,8,3,5,6]=>0000000=>0000000=>[8]
[7,1,4,6,5,8,3,2]=>0000000=>0000000=>[8]
[7,1,2,3,8,5,4,6]=>0000000=>0000000=>[8]
[7,1,3,4,2,6,8,5]=>0000000=>0000000=>[8]
[3,6,7,1,4,8,5,2]=>0000000=>0000000=>[8]
[3,5,1,4,8,6,2,7]=>0000000=>0000000=>[8]
[3,6,2,4,7,8,1,5]=>0000000=>0000000=>[8]
[6,5,8,7,2,3,1,4]=>0000000=>0000000=>[8]
[3,4,7,2,5,8,1,6]=>0000000=>0000000=>[8]
[4,3,8,1,2,7,5,6]=>0000000=>0000000=>[8]
[5,6,7,8,1,3,4,2]=>0000000=>0000000=>[8]
[5,7,8,6,1,2,3,4]=>0000000=>0000000=>[8]
[2,8,3,1,5,6,4,7]=>0000000=>0000000=>[8]
[3,8,7,1,5,4,2,6]=>0000000=>0000000=>[8]
[4,3,1,7,6,8,2,5]=>0000000=>0000000=>[8]
[3,4,1,7,5,6,8,2]=>0000000=>0000000=>[8]
[2,4,6,1,7,5,8,3]=>0000000=>0000000=>[8]
[4,2,1,5,6,3,7,8]=>0000011=>1100000=>[1,1,6]
[5,8,1,6,4,3,2,7]=>0000000=>0000000=>[8]
[5,8,1,6,3,7,2,4]=>0000000=>0000000=>[8]
[7,6,5,1,3,8,2,4]=>0000000=>0000000=>[8]
[7,6,5,1,3,4,8,2]=>0000000=>0000000=>[8]
[7,2,6,4,1,3,8,5]=>0000000=>0000000=>[8]
[4,6,3,8,5,1,7,2]=>0000000=>0000000=>[8]
[2,6,4,3,1,5,7,8]=>0000011=>1100000=>[1,1,6]
[3,6,4,8,1,7,2,5]=>0000000=>0000000=>[8]
[7,3,8,4,1,5,2,6]=>0000000=>0000000=>[8]
[4,2,8,3,6,1,5,7]=>0000000=>0000000=>[8]
[6,7,5,8,2,1,4,3]=>0000000=>0000000=>[8]
[6,8,5,7,2,1,3,4]=>0000000=>0000000=>[8]
[6,3,5,2,1,7,4,8]=>0000001=>1000000=>[1,7]
[3,6,5,4,2,8,1,7]=>0000000=>0000000=>[8]
[7,4,5,3,8,2,1,6]=>0000000=>0000000=>[8]
[1,6,4,7,2,5,3,8]=>1000001=>1000001=>[1,6,1]
[1,4,3,7,2,6,5,8]=>1000001=>1000001=>[1,6,1]
[1,5,7,2,4,8,3,6]=>1000000=>0000001=>[7,1]
[1,6,5,7,2,4,3,8]=>1000001=>1000001=>[1,6,1]
[1,7,6,2,8,3,4,5]=>1000000=>0000001=>[7,1]
[1,4,2,3,5,8,7,6]=>1001100=>0011001=>[3,1,3,1]
[1,5,2,3,4,8,7,6]=>1000100=>0010001=>[3,4,1]
[1,6,5,2,3,8,7,4]=>1000000=>0000001=>[7,1]
[1,7,6,5,2,8,4,3]=>1000000=>0000001=>[7,1]
[1,6,5,2,3,8,4,7]=>1000000=>0000001=>[7,1]
[1,6,7,5,2,3,8,4]=>1000000=>0000001=>[7,1]
[1,7,5,2,8,4,3,6]=>1000000=>0000001=>[7,1]
[1,7,5,6,2,8,3,4]=>1000000=>0000001=>[7,1]
[1,5,7,6,2,4,8,3]=>1000000=>0000001=>[7,1]
[1,4,7,6,2,5,8,3]=>1000000=>0000001=>[7,1]
[1,2,6,5,3,7,4,8]=>1100001=>1000011=>[1,5,1,1]
[1,3,7,5,2,6,8,4]=>1000000=>0000001=>[7,1]
[1,7,4,6,2,8,3,5]=>1000000=>0000001=>[7,1]
[1,7,3,5,2,8,4,6]=>1000000=>0000001=>[7,1]
[1,3,7,4,2,6,8,5]=>1000000=>0000001=>[7,1]
[1,4,7,3,2,5,8,6]=>1000000=>0000001=>[7,1]
[1,5,7,3,2,4,8,6]=>1000000=>0000001=>[7,1]
[1,7,3,4,2,8,5,6]=>1000000=>0000001=>[7,1]
[1,7,4,2,8,5,3,6]=>1000000=>0000001=>[7,1]
[1,6,7,4,2,3,8,5]=>1000000=>0000001=>[7,1]
[1,4,3,2,5,8,6,7]=>1001100=>0011001=>[3,1,3,1]
[1,5,3,2,4,8,6,7]=>1000100=>0010001=>[3,4,1]
[1,6,4,2,3,8,5,7]=>1000000=>0000001=>[7,1]
[1,7,6,4,2,8,5,3]=>1000000=>0000001=>[7,1]
[1,6,4,2,3,8,7,5]=>1000000=>0000001=>[7,1]
[1,5,3,2,4,8,7,6]=>1000100=>0010001=>[3,4,1]
[6,8,5,4,3,2,1,7]=>0000000=>0000000=>[8]
[7,6,5,1,3,8,4,2]=>0000000=>0000000=>[8]
[5,6,8,4,3,1,7,2]=>0000000=>0000000=>[8]
[7,5,8,4,3,2,1,6]=>0000000=>0000000=>[8]
[4,8,5,7,3,2,1,6]=>0000000=>0000000=>[8]
[7,8,1,2,4,3,5,6]=>0000000=>0000000=>[8]
[7,8,2,1,4,3,6,5]=>0000000=>0000000=>[8]
[3,4,6,5,7,8,1,2]=>0000000=>0000000=>[8]
[4,3,6,5,8,7,1,2]=>0000000=>0000000=>[8]
[4,2,6,1,8,3,7,5]=>0000000=>0000000=>[8]
[6,7,3,8,4,5,1,2]=>0000000=>0000000=>[8]
[6,7,4,5,1,8,2,3]=>0000000=>0000000=>[8]
[4,7,5,6,1,8,2,3]=>0000000=>0000000=>[8]
[4,5,3,8,6,7,1,2]=>0000000=>0000000=>[8]
[5,6,3,8,4,7,1,2]=>0000000=>0000000=>[8]
[5,6,2,7,3,4,1,8]=>0000001=>1000000=>[1,7]
[4,5,1,8,6,7,2,3]=>0000000=>0000000=>[8]
[7,8,4,5,1,6,2,3]=>0000000=>0000000=>[8]
[4,5,2,3,1,8,6,7]=>0000100=>0010000=>[3,5]
[5,6,2,3,1,8,4,7]=>0000000=>0000000=>[8]
[5,6,3,4,1,8,2,7]=>0000000=>0000000=>[8]
[3,6,4,5,1,8,2,7]=>0000000=>0000000=>[8]
[2,6,4,8,1,5,3,7]=>0000000=>0000000=>[8]
[2,8,3,4,1,6,5,7]=>0000000=>0000000=>[8]
[7,8,1,5,3,6,2,4]=>0000000=>0000000=>[8]
[1,6,4,7,3,8,2,5]=>1000000=>0000001=>[7,1]
[1,7,2,8,4,6,3,5]=>1000000=>0000001=>[7,1]
[1,7,5,8,2,6,3,4]=>1000000=>0000001=>[7,1]
[6,7,1,8,2,5,3,4]=>0000000=>0000000=>[8]
[6,7,1,8,4,5,2,3]=>0000000=>0000000=>[8]
[6,7,5,8,1,4,2,3]=>0000000=>0000000=>[8]
[5,8,6,7,2,3,1,4]=>0000000=>0000000=>[8]
[6,7,2,3,1,8,4,5]=>0000000=>0000000=>[8]
[6,7,2,8,1,4,3,5]=>0000000=>0000000=>[8]
[6,7,3,4,1,8,2,5]=>0000000=>0000000=>[8]
[2,7,5,8,1,4,3,6]=>0000000=>0000000=>[8]
[2,3,1,8,6,7,4,5]=>0010000=>0000100=>[5,3]
[7,8,2,3,1,6,4,5]=>0000000=>0000000=>[8]
[2,8,1,4,3,7,5,6]=>0000000=>0000000=>[8]
[2,8,1,7,3,5,4,6]=>0000000=>0000000=>[8]
[4,5,1,7,3,8,2,6]=>0000000=>0000000=>[8]
[3,8,1,5,2,7,4,6]=>0000000=>0000000=>[8]
[3,4,1,8,6,7,2,5]=>0000000=>0000000=>[8]
[7,8,3,4,1,6,2,5]=>0000000=>0000000=>[8]
[2,5,4,1,6,3,8,7]=>0000010=>0100000=>[2,6]
[3,6,5,1,2,4,8,7]=>0000010=>0100000=>[2,6]
[5,6,7,8,1,4,3,2]=>0000000=>0000000=>[8]
[2,1,4,7,6,3,8,5]=>0100000=>0000010=>[6,2]
[7,4,3,8,2,1,5,6]=>0000000=>0000000=>[8]
[2,4,1,5,8,3,7,6]=>0000000=>0000000=>[8]
[2,1,5,8,7,3,4,6]=>0100000=>0000010=>[6,2]
[8,5,7,3,6,1,4,2]=>0000000=>0000000=>[8]
[4,2,5,1,6,7,8,3]=>0000000=>0000000=>[8]
[6,1,8,5,2,7,4,3]=>0000000=>0000000=>[8]
[6,8,7,2,5,3,1,4]=>0000000=>0000000=>[8]
[7,8,2,5,6,1,4,3]=>0000000=>0000000=>[8]
[7,8,4,2,5,1,6,3]=>0000000=>0000000=>[8]
[6,1,2,3,7,5,8,4]=>0000000=>0000000=>[8]
[4,1,6,3,5,8,7,2]=>0000000=>0000000=>[8]
[8,6,7,1,5,4,3,2]=>0000000=>0000000=>[8]
[2,1,6,5,8,4,7,3]=>0100000=>0000010=>[6,2]
[2,6,4,8,7,3,5,1]=>0000000=>0000000=>[8]
[7,4,8,6,3,2,5,1]=>0000000=>0000000=>[8]
[2,1,8,4,3,7,5,6]=>0100000=>0000010=>[6,2]
[6,3,8,2,4,5,7,1]=>0000000=>0000000=>[8]
[5,8,2,4,3,1,6,7]=>0000000=>0000000=>[8]
[7,3,5,8,1,4,2,6]=>0000000=>0000000=>[8]
[3,8,7,6,1,4,2,5]=>0000000=>0000000=>[8]
[5,1,8,3,6,7,2,4]=>0000000=>0000000=>[8]
[3,6,1,4,7,8,5,2]=>0000000=>0000000=>[8]
[1,6,8,4,7,5,2,3]=>1000000=>0000001=>[7,1]
[6,8,1,3,5,7,2,4]=>0000000=>0000000=>[8]
[7,6,1,4,3,8,2,5]=>0000000=>0000000=>[8]
[8,4,2,6,7,5,3,1]=>0000000=>0000000=>[8]
[7,4,1,6,8,2,5,3]=>0000000=>0000000=>[8]
[1,8,6,2,5,3,4,7]=>1000000=>0000001=>[7,1]
[4,7,1,2,5,3,8,6]=>0000000=>0000000=>[8]
[5,7,8,6,2,1,4,3]=>0000000=>0000000=>[8]
[1,8,6,4,5,2,3,7]=>1000000=>0000001=>[7,1]
[1,4,7,2,6,8,3,5]=>1000000=>0000001=>[7,1]
[2,5,4,3,6,8,1,7]=>0000000=>0000000=>[8]
[3,8,5,4,6,2,1,7]=>0000000=>0000000=>[8]
[4,8,2,1,3,7,5,6]=>0000000=>0000000=>[8]
[1,8,3,2,5,6,7,4]=>1000000=>0000001=>[7,1]
[6,4,1,2,7,5,8,3]=>0000000=>0000000=>[8]
[4,3,7,8,5,1,6,2]=>0000000=>0000000=>[8]
[1,2,7,3,6,5,8,4]=>1100000=>0000011=>[6,1,1]
[2,8,7,6,3,4,1,5]=>0000000=>0000000=>[8]
[5,8,2,6,3,4,1,7]=>0000000=>0000000=>[8]
[1,2,4,5,8,3,7,6]=>1100000=>0000011=>[6,1,1]
[4,8,1,5,2,3,7,6]=>0000000=>0000000=>[8]
[2,4,6,3,7,1,8,5]=>0000000=>0000000=>[8]
[6,5,8,7,1,3,4,2]=>0000000=>0000000=>[8]
[1,5,2,7,4,3,8,6]=>1000000=>0000001=>[7,1]
[7,6,1,2,8,3,5,4]=>0000000=>0000000=>[8]
[6,7,8,1,5,2,4,3]=>0000000=>0000000=>[8]
[5,7,8,4,1,2,6,3]=>0000000=>0000000=>[8]
[4,7,8,5,6,1,3,2]=>0000000=>0000000=>[8]
[6,5,4,1,2,3,8,7]=>0000010=>0100000=>[2,6]
[7,5,1,6,2,3,8,4]=>0000000=>0000000=>[8]
[4,5,6,7,8,1,3,2]=>0000000=>0000000=>[8]
[8,1,3,6,7,4,5,2]=>0000000=>0000000=>[8]
[4,5,3,2,8,1,6,7]=>0000000=>0000000=>[8]
[7,4,1,5,3,2,6,8]=>0000001=>1000000=>[1,7]
[8,1,5,4,3,2,6,7]=>0000000=>0000000=>[8]
[8,1,6,4,2,5,3,7]=>0000000=>0000000=>[8]
[6,5,3,1,2,7,4,8]=>0000001=>1000000=>[1,7]
[5,6,3,8,1,4,2,7]=>0000000=>0000000=>[8]
[4,6,3,8,2,1,5,7]=>0000000=>0000000=>[8]
[4,7,8,3,2,1,5,6]=>0000000=>0000000=>[8]
[5,7,8,3,1,4,2,6]=>0000000=>0000000=>[8]
[8,1,7,2,5,4,3,6]=>0000000=>0000000=>[8]
[8,1,7,2,4,5,6,3]=>0000000=>0000000=>[8]
[7,6,1,2,4,5,8,3]=>0000000=>0000000=>[8]
[7,5,1,3,2,6,8,4]=>0000000=>0000000=>[8]
[8,1,6,3,2,5,7,4]=>0000000=>0000000=>[8]
[5,4,2,3,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[6,3,2,1,5,7,4,8]=>0000001=>1000000=>[1,7]
[3,6,5,8,2,4,1,7]=>0000000=>0000000=>[8]
[6,2,4,5,8,3,1,7]=>0000000=>0000000=>[8]
[4,8,1,2,5,6,3,7]=>0000000=>0000000=>[8]
[8,1,3,5,2,6,4,7]=>0000000=>0000000=>[8]
[5,2,1,6,3,8,4,7]=>0000000=>0000000=>[8]
[6,1,4,5,8,3,2,7]=>0000000=>0000000=>[8]
[6,5,4,3,8,2,1,7]=>0000000=>0000000=>[8]
[4,6,8,3,7,2,5,1]=>0000000=>0000000=>[8]
[4,7,8,5,3,1,2,6]=>0000000=>0000000=>[8]
[8,5,4,7,6,2,1,3]=>0000000=>0000000=>[8]
[5,8,7,3,1,4,6,2]=>0000000=>0000000=>[8]
[8,5,7,4,3,6,1,2]=>0000000=>0000000=>[8]
[1,3,8,6,4,7,5,2]=>1000000=>0000001=>[7,1]
[7,6,8,1,4,3,2,5]=>0000000=>0000000=>[8]
[3,2,6,8,5,7,4,1]=>0000000=>0000000=>[8]
[1,6,4,7,2,3,8,5]=>1000000=>0000001=>[7,1]
[3,1,7,5,2,8,4,6]=>0000000=>0000000=>[8]
[1,7,4,5,2,8,3,6]=>1000000=>0000001=>[7,1]
[6,3,2,1,7,8,4,5]=>0000000=>0000000=>[8]
[5,7,3,8,2,1,4,6]=>0000000=>0000000=>[8]
[3,7,1,8,4,2,5,6]=>0000000=>0000000=>[8]
[4,2,1,3,7,5,8,6]=>0001000=>0001000=>[4,4]
[8,4,2,1,3,7,6,5]=>0000000=>0000000=>[8]
[3,6,2,8,7,1,5,4]=>0000000=>0000000=>[8]
[7,3,2,8,1,6,5,4]=>0000000=>0000000=>[8]
[3,8,7,2,6,5,4,1]=>0000000=>0000000=>[8]
[4,2,7,8,6,1,5,3]=>0000000=>0000000=>[8]
[5,8,4,2,7,1,6,3]=>0000000=>0000000=>[8]
[8,5,3,1,7,2,6,4]=>0000000=>0000000=>[8]
[8,2,1,6,3,7,5,4]=>0000000=>0000000=>[8]
[1,4,6,8,2,7,5,3]=>1000000=>0000001=>[7,1]
[8,2,1,7,6,5,4,3]=>0000000=>0000000=>[8]
[8,6,7,5,1,4,3,2]=>0000000=>0000000=>[8]
[6,4,7,3,2,1,8,5]=>0000000=>0000000=>[8]
[4,8,7,3,2,1,6,5]=>0000000=>0000000=>[8]
[6,4,3,7,2,1,8,5]=>0000000=>0000000=>[8]
[5,3,7,6,2,1,4,8]=>0000001=>1000000=>[1,7]
[3,8,7,6,2,1,4,5]=>0000000=>0000000=>[8]
[5,8,4,2,6,1,3,7]=>0000000=>0000000=>[8]
[4,8,7,2,5,1,3,6]=>0000000=>0000000=>[8]
[4,3,7,2,5,1,8,6]=>0000000=>0000000=>[8]
[5,4,2,6,7,1,3,8]=>0000001=>1000000=>[1,7]
[2,8,7,6,5,1,3,4]=>0000000=>0000000=>[8]
[6,4,7,3,1,5,8,2]=>0000000=>0000000=>[8]
[4,8,7,3,1,5,6,2]=>0000000=>0000000=>[8]
[6,5,3,7,1,4,8,2]=>0000000=>0000000=>[8]
[6,4,3,7,1,5,8,2]=>0000000=>0000000=>[8]
[5,3,7,6,1,4,8,2]=>0000000=>0000000=>[8]
[3,8,7,6,1,4,5,2]=>0000000=>0000000=>[8]
[5,8,4,2,1,7,3,6]=>0000000=>0000000=>[8]
[6,4,7,2,1,5,3,8]=>0000001=>1000000=>[1,7]
[5,8,3,2,1,4,7,6]=>0000000=>0000000=>[8]
[6,3,7,2,1,4,5,8]=>0000001=>1000000=>[1,7]
[6,5,2,7,1,4,3,8]=>0000001=>1000000=>[1,7]
[5,8,2,6,1,4,3,7]=>0000000=>0000000=>[8]
[2,8,7,6,1,4,3,5]=>0000000=>0000000=>[8]
[5,8,4,1,6,7,3,2]=>0000000=>0000000=>[8]
[6,5,3,1,8,4,7,2]=>0000000=>0000000=>[8]
[6,4,3,1,5,8,7,2]=>0000000=>0000000=>[8]
[5,8,2,1,6,4,3,7]=>0000000=>0000000=>[8]
[6,4,2,1,5,8,3,7]=>0000000=>0000000=>[8]
[4,2,7,1,5,6,3,8]=>0000001=>1000000=>[1,7]
[6,5,1,7,8,4,3,2]=>0000000=>0000000=>[8]
[5,4,1,6,7,8,3,2]=>0000000=>0000000=>[8]
[4,3,1,6,5,7,8,2]=>0000000=>0000000=>[8]
[5,2,1,6,7,4,3,8]=>0000001=>1000000=>[1,7]
[4,2,1,6,5,7,3,8]=>0000001=>1000000=>[1,7]
[6,1,7,8,5,4,3,2]=>0000000=>0000000=>[8]
[5,1,7,6,8,4,3,2]=>0000000=>0000000=>[8]
[4,5,8,1,7,2,3,6]=>0000000=>0000000=>[8]
[8,1,3,5,7,2,4,6]=>0000000=>0000000=>[8]
[3,6,8,1,7,2,4,5]=>0000000=>0000000=>[8]
[8,2,3,5,6,7,1,4]=>0000000=>0000000=>[8]
[8,7,2,1,6,3,4,5]=>0000000=>0000000=>[8]
[8,6,4,1,7,5,3,2]=>0000000=>0000000=>[8]
[2,3,6,7,8,1,5,4]=>0000000=>0000000=>[8]
[3,1,7,2,5,4,8,6]=>0000000=>0000000=>[8]
[7,1,8,2,5,3,6,4]=>0000000=>0000000=>[8]
[7,3,8,4,5,1,6,2]=>0000000=>0000000=>[8]
[8,1,2,6,5,4,3,7]=>0000000=>0000000=>[8]
[8,2,7,5,6,1,4,3]=>0000000=>0000000=>[8]
[3,6,8,1,7,5,4,2]=>0000000=>0000000=>[8]
[8,2,6,7,5,4,1,3]=>0000000=>0000000=>[8]
[8,6,7,2,3,1,5,4]=>0000000=>0000000=>[8]
[8,1,7,6,5,4,3,2]=>0000000=>0000000=>[8]
[8,6,1,5,2,7,4,3]=>0000000=>0000000=>[8]
[8,5,1,7,4,2,6,3]=>0000000=>0000000=>[8]
[2,1,7,8,3,6,5,4]=>0100000=>0000010=>[6,2]
[7,8,1,5,2,6,3,4]=>0000000=>0000000=>[8]
[6,4,1,5,2,3,8,7]=>0000010=>0100000=>[2,6]
[5,3,7,4,6,8,1,2]=>0000000=>0000000=>[8]
[4,2,6,3,8,5,1,7]=>0000000=>0000000=>[8]
[5,8,2,1,7,6,4,3]=>0000000=>0000000=>[8]
[8,3,2,4,1,7,5,6]=>0000000=>0000000=>[8]
[7,8,3,1,5,4,6,2]=>0000000=>0000000=>[8]
[7,2,8,1,4,6,5,3]=>0000000=>0000000=>[8]
[5,7,1,8,3,6,2,4]=>0000000=>0000000=>[8]
[4,2,1,3,6,7,8,5]=>0001000=>0001000=>[4,4]
[6,3,5,4,1,2,8,7]=>0000010=>0100000=>[2,6]
[3,4,7,2,8,1,5,6]=>0000000=>0000000=>[8]
[4,2,3,5,8,1,6,7]=>0000000=>0000000=>[8]
[3,2,4,6,1,5,8,7]=>0000010=>0100000=>[2,6]
[6,5,4,3,1,8,7,2]=>0000000=>0000000=>[8]
[8,7,5,4,3,1,6,2]=>0000000=>0000000=>[8]
[3,4,6,2,8,5,1,7]=>0000000=>0000000=>[8]
[3,4,7,2,8,5,6,1]=>0000000=>0000000=>[8]
[3,5,2,6,8,4,1,7]=>0000000=>0000000=>[8]
[3,5,2,7,4,8,6,1]=>0000000=>0000000=>[8]
[3,5,6,2,8,4,1,7]=>0000000=>0000000=>[8]
[3,5,7,2,4,8,6,1]=>0000000=>0000000=>[8]
[3,5,7,8,4,1,6,2]=>0000000=>0000000=>[8]
[3,5,8,2,4,1,6,7]=>0000000=>0000000=>[8]
[3,6,2,7,4,8,5,1]=>0000000=>0000000=>[8]
[3,6,2,7,8,5,4,1]=>0000000=>0000000=>[8]
[3,6,8,2,4,5,1,7]=>0000000=>0000000=>[8]
[3,7,2,1,4,8,6,5]=>0000000=>0000000=>[8]
[3,7,2,8,4,5,6,1]=>0000000=>0000000=>[8]
[4,1,5,7,3,8,6,2]=>0000000=>0000000=>[8]
[4,1,5,7,8,2,6,3]=>0000000=>0000000=>[8]
[4,1,5,8,3,2,6,7]=>0000000=>0000000=>[8]
[4,1,6,3,7,8,5,2]=>0000000=>0000000=>[8]
[4,1,6,3,8,5,2,7]=>0000000=>0000000=>[8]
[4,1,6,8,3,5,2,7]=>0000000=>0000000=>[8]
[4,1,7,3,8,5,6,2]=>0000000=>0000000=>[8]
[4,1,8,3,2,5,6,7]=>0000000=>0000000=>[8]
[4,5,2,7,3,8,6,1]=>0000000=>0000000=>[8]
[4,5,7,3,2,8,6,1]=>0000000=>0000000=>[8]
[4,5,8,3,2,1,6,7]=>0000000=>0000000=>[8]
[4,6,2,8,3,5,1,7]=>0000000=>0000000=>[8]
[5,1,2,6,8,4,3,7]=>0000000=>0000000=>[8]
[5,1,6,3,7,8,2,4]=>0000000=>0000000=>[8]
[5,1,6,3,8,4,2,7]=>0000000=>0000000=>[8]
[5,1,6,7,4,8,2,3]=>0000000=>0000000=>[8]
[5,6,2,7,4,8,1,3]=>0000000=>0000000=>[8]
[5,6,2,7,8,4,1,3]=>0000000=>0000000=>[8]
[5,7,8,3,4,2,6,1]=>0000000=>0000000=>[8]
[6,1,2,3,7,8,5,4]=>0000000=>0000000=>[8]
[6,1,2,7,8,5,4,3]=>0000000=>0000000=>[8]
[6,7,2,8,4,5,3,1]=>0000000=>0000000=>[8]
[7,1,2,3,8,5,6,4]=>0000000=>0000000=>[8]
[7,1,8,3,4,5,6,2]=>0000000=>0000000=>[8]
[2,4,6,1,8,5,7,3]=>0000000=>0000000=>[8]
[3,5,8,6,1,2,4,7]=>0000000=>0000000=>[8]
[3,5,1,8,2,4,7,6]=>0000000=>0000000=>[8]
[3,1,6,8,2,4,7,5]=>0000000=>0000000=>[8]
[5,6,4,8,2,1,7,3]=>0000000=>0000000=>[8]
[2,5,7,8,6,3,1,4]=>0000000=>0000000=>[8]
[2,4,8,1,5,6,7,3]=>0000000=>0000000=>[8]
[8,4,1,2,5,6,3,7]=>0000000=>0000000=>[8]
[8,3,1,6,5,2,4,7]=>0000000=>0000000=>[8]
[2,5,3,8,7,6,1,4]=>0000000=>0000000=>[8]
[5,1,8,4,7,6,3,2]=>0000000=>0000000=>[8]
[8,2,3,6,5,1,7,4]=>0000000=>0000000=>[8]
[4,8,6,5,7,3,2,1]=>0000000=>0000000=>[8]
[4,8,5,6,7,3,2,1]=>0000000=>0000000=>[8]
[7,2,8,6,5,4,1,3]=>0000000=>0000000=>[8]
[6,3,2,8,5,1,7,4]=>0000000=>0000000=>[8]
[6,8,5,4,3,1,7,2]=>0000000=>0000000=>[8]
[7,6,3,8,5,2,1,4]=>0000000=>0000000=>[8]
[5,8,7,4,1,6,3,2]=>0000000=>0000000=>[8]
[6,8,3,4,5,1,7,2]=>0000000=>0000000=>[8]
[5,2,8,4,1,6,7,3]=>0000000=>0000000=>[8]
[4,1,3,6,8,2,5,7]=>0000000=>0000000=>[8]
[8,3,2,1,5,4,7,6]=>0000000=>0000000=>[8]
[2,5,1,8,4,3,7,6]=>0000000=>0000000=>[8]
[5,3,6,2,4,8,1,7]=>0000000=>0000000=>[8]
[1,6,2,4,5,8,3,7]=>1000000=>0000001=>[7,1]
[5,3,2,1,6,8,4,7]=>0000000=>0000000=>[8]
[2,6,5,8,1,3,4,7]=>0000000=>0000000=>[8]
[8,3,4,1,5,2,7,6]=>0000000=>0000000=>[8]
[8,2,6,4,1,7,3,5]=>0000000=>0000000=>[8]
[5,4,6,8,1,2,7,3]=>0000000=>0000000=>[8]
[3,4,7,8,6,2,5,1]=>0000000=>0000000=>[8]
[7,5,8,2,4,6,1,3]=>0000000=>0000000=>[8]
[8,2,7,4,6,1,3,5]=>0000000=>0000000=>[8]
[4,7,3,2,8,1,6,5]=>0000000=>0000000=>[8]
[1,2,8,3,5,6,7,4]=>1100000=>0000011=>[6,1,1]
[4,2,3,7,1,8,6,5]=>0000000=>0000000=>[8]
[3,2,6,4,8,1,7,5]=>0000000=>0000000=>[8]
[8,2,1,6,7,3,4,5]=>0000000=>0000000=>[8]
[2,7,8,5,4,1,3,6]=>0000000=>0000000=>[8]
[1,7,5,3,8,4,2,6]=>1000000=>0000001=>[7,1]
[4,7,5,3,1,2,8,6]=>0000000=>0000000=>[8]
[5,6,7,3,8,4,2,1]=>0000000=>0000000=>[8]
[5,7,3,2,4,1,8,6]=>0000000=>0000000=>[8]
[8,4,1,3,7,2,5,6]=>0000000=>0000000=>[8]
[2,8,4,7,1,3,5,6]=>0000000=>0000000=>[8]
[3,5,2,8,6,1,7,4]=>0000000=>0000000=>[8]
[1,7,6,3,2,5,8,4]=>1000000=>0000001=>[7,1]
[3,8,1,5,6,2,7,4]=>0000000=>0000000=>[8]
[7,1,5,2,8,6,4,3]=>0000000=>0000000=>[8]
[1,8,5,3,6,2,7,4]=>1000000=>0000001=>[7,1]
[6,5,8,7,2,1,3,4]=>0000000=>0000000=>[8]
[3,6,2,1,7,5,8,4]=>0000000=>0000000=>[8]
[4,7,2,6,5,8,1,3]=>0000000=>0000000=>[8]
[6,8,1,4,2,7,3,5]=>0000000=>0000000=>[8]
[6,3,4,7,1,8,2,5]=>0000000=>0000000=>[8]
[3,4,7,8,2,5,6,1]=>0000000=>0000000=>[8]
[1,8,2,4,5,6,7,3]=>1000000=>0000001=>[7,1]
[3,2,5,7,6,1,8,4]=>0000000=>0000000=>[8]
[4,3,5,6,1,8,7,2]=>0000000=>0000000=>[8]
[1,2,3,4,8,6,5,7]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,3,8,5,4,6,7]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,5,6,4,7]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,6,5,4,7]=>1110000=>0000111=>[5,1,1,1]
[1,8,3,4,2,5,6,7]=>1000000=>0000001=>[7,1]
[1,2,8,5,4,3,6,7]=>1100000=>0000011=>[6,1,1]
[1,8,4,3,2,5,6,7]=>1000000=>0000001=>[7,1]
[8,4,7,3,6,5,2,1]=>0000000=>0000000=>[8]
[8,1,7,4,6,5,3,2]=>0000000=>0000000=>[8]
[8,4,7,1,6,5,3,2]=>0000000=>0000000=>[8]
[8,3,7,1,6,5,4,2]=>0000000=>0000000=>[8]
[8,2,7,1,6,5,4,3]=>0000000=>0000000=>[8]
[8,1,7,2,6,5,4,3]=>0000000=>0000000=>[8]
[8,3,7,1,6,4,5,2]=>0000000=>0000000=>[8]
[8,4,7,2,6,3,5,1]=>0000000=>0000000=>[8]
[8,4,7,6,5,2,3,1]=>0000000=>0000000=>[8]
[8,3,7,6,5,1,4,2]=>0000000=>0000000=>[8]
[8,4,7,5,6,1,3,2]=>0000000=>0000000=>[8]
[8,1,7,3,6,2,5,4]=>0000000=>0000000=>[8]
[8,3,7,2,6,1,5,4]=>0000000=>0000000=>[8]
[8,5,7,2,6,1,4,3]=>0000000=>0000000=>[8]
[8,7,6,1,5,2,4,3]=>0000000=>0000000=>[8]
[4,6,7,3,8,5,2,1]=>0000000=>0000000=>[8]
[6,7,8,9,10,5,4,3,2,1]=>000000000=>000000000=>[10]
[1,4,8,2,6,3,5,7]=>1000000=>0000001=>[7,1]
[1,6,2,4,8,3,5,7]=>1000000=>0000001=>[7,1]
[1,5,2,3,8,4,7,6]=>1000000=>0000001=>[7,1]
[1,7,2,3,5,4,8,6]=>1000000=>0000001=>[7,1]
[1,8,2,3,5,4,6,7]=>1000000=>0000001=>[7,1]
[1,7,8,2,4,5,3,6]=>1000000=>0000001=>[7,1]
[1,2,8,3,6,4,5,7]=>1100000=>0000011=>[6,1,1]
[1,5,8,2,3,7,4,6]=>1000000=>0000001=>[7,1]
[1,6,8,2,3,5,4,7]=>1000000=>0000001=>[7,1]
[5,7,2,6,3,8,1,4]=>0000000=>0000000=>[8]
[5,7,1,6,8,4,3,2]=>0000000=>0000000=>[8]
[4,8,1,2,5,7,3,6]=>0000000=>0000000=>[8]
[3,7,5,4,8,2,1,6]=>0000000=>0000000=>[8]
[4,7,1,3,2,8,6,5]=>0000000=>0000000=>[8]
[2,7,3,1,5,8,4,6]=>0000000=>0000000=>[8]
[3,8,7,1,6,4,5,2]=>0000000=>0000000=>[8]
[4,3,2,1,5,8,6,7]=>0001100=>0011000=>[3,1,4]
[4,1,3,7,5,6,8,2]=>0000000=>0000000=>[8]
[3,4,6,1,5,8,2,7]=>0000000=>0000000=>[8]
[6,5,8,7,1,4,2,3]=>0000000=>0000000=>[8]
[4,1,7,3,8,5,2,6]=>0000000=>0000000=>[8]
[5,6,8,7,2,4,1,3]=>0000000=>0000000=>[8]
[7,1,3,4,2,8,5,6]=>0000000=>0000000=>[8]
[7,6,1,4,3,5,8,2]=>0000000=>0000000=>[8]
[3,5,4,1,6,7,8,2]=>0000000=>0000000=>[8]
[2,5,3,4,8,6,1,7]=>0000000=>0000000=>[8]
[2,4,8,3,6,1,7,5]=>0000000=>0000000=>[8]
[6,8,2,1,5,7,3,4]=>0000000=>0000000=>[8]
[1,2,4,8,6,5,3,7]=>1100000=>0000011=>[6,1,1]
[7,1,5,6,8,4,3,2]=>0000000=>0000000=>[8]
[7,3,5,6,1,4,8,2]=>0000000=>0000000=>[8]
[3,7,6,5,1,4,8,2]=>0000000=>0000000=>[8]
[2,7,6,5,3,8,1,4]=>0000000=>0000000=>[8]
[2,7,8,1,4,6,3,5]=>0000000=>0000000=>[8]
[4,1,6,8,5,3,7,2]=>0000000=>0000000=>[8]
[5,2,6,4,8,3,1,7]=>0000000=>0000000=>[8]
[1,2,6,3,4,8,7,5]=>1100000=>0000011=>[6,1,1]
[5,3,6,1,4,7,8,2]=>0000000=>0000000=>[8]
[6,7,1,3,4,5,8,2]=>0000000=>0000000=>[8]
[1,7,3,2,4,8,5,6]=>1000000=>0000001=>[7,1]
[6,1,4,2,8,3,5,7]=>0000000=>0000000=>[8]
[5,8,6,7,2,1,4,3]=>0000000=>0000000=>[8]
[8,6,1,3,5,4,2,7]=>0000000=>0000000=>[8]
[2,7,6,3,4,5,8,1]=>0000000=>0000000=>[8]
[5,3,8,6,1,2,4,7]=>0000000=>0000000=>[8]
[3,8,7,2,6,4,5,1]=>0000000=>0000000=>[8]
[4,5,8,7,2,6,3,1]=>0000000=>0000000=>[8]
[8,5,2,7,1,4,3,6]=>0000000=>0000000=>[8]
[3,7,5,8,2,6,1,4]=>0000000=>0000000=>[8]
[1,6,7,4,8,2,3,5]=>1000000=>0000001=>[7,1]
[8,2,1,3,5,6,7,4]=>0000000=>0000000=>[8]
[4,1,3,8,2,6,7,5]=>0000000=>0000000=>[8]
[3,6,1,4,7,2,8,5]=>0000000=>0000000=>[8]
[6,2,7,4,5,8,1,3]=>0000000=>0000000=>[8]
[1,8,5,7,3,2,4,6]=>1000000=>0000001=>[7,1]
[3,2,1,6,4,8,5,7]=>0010000=>0000100=>[5,3]
[2,7,4,1,5,3,8,6]=>0000000=>0000000=>[8]
[7,4,8,6,2,3,1,5]=>0000000=>0000000=>[8]
[7,3,2,4,8,6,1,5]=>0000000=>0000000=>[8]
[5,1,7,4,2,3,8,6]=>0000000=>0000000=>[8]
[4,8,5,3,6,2,7,1]=>0000000=>0000000=>[8]
[5,7,4,3,6,2,8,1]=>0000000=>0000000=>[8]
[6,7,5,1,2,8,3,4]=>0000000=>0000000=>[8]
[7,5,1,4,2,6,8,3]=>0000000=>0000000=>[8]
[5,2,6,8,3,4,7,1]=>0000000=>0000000=>[8]
[6,2,7,5,8,3,1,4]=>0000000=>0000000=>[8]
[2,1,5,6,8,3,7,4]=>0100000=>0000010=>[6,2]
[1,2,7,4,8,3,6,5]=>1100000=>0000011=>[6,1,1]
[1,6,8,3,2,7,4,5]=>1000000=>0000001=>[7,1]
[5,7,3,8,2,4,6,1]=>0000000=>0000000=>[8]
[5,7,3,6,4,8,2,1]=>0000000=>0000000=>[8]
[3,6,2,4,7,1,8,5]=>0000000=>0000000=>[8]
[4,2,8,5,1,6,7,3]=>0000000=>0000000=>[8]
[1,2,8,3,7,5,4,6]=>1100000=>0000011=>[6,1,1]
[1,6,3,8,7,4,2,5]=>1000000=>0000001=>[7,1]
[3,8,5,7,1,4,2,6]=>0000000=>0000000=>[8]
[4,7,2,5,1,3,8,6]=>0000000=>0000000=>[8]
[5,1,7,4,8,6,3,2]=>0000000=>0000000=>[8]
[3,6,5,2,1,8,7,4]=>0000000=>0000000=>[8]
[5,2,7,4,1,3,6,8]=>0000001=>1000000=>[1,7]
[5,2,6,4,1,8,7,3]=>0000000=>0000000=>[8]
[6,3,2,1,4,8,7,5]=>0000000=>0000000=>[8]
[5,4,7,6,3,8,1,2]=>0000000=>0000000=>[8]
[4,6,3,7,5,8,1,2]=>0000000=>0000000=>[8]
[5,7,4,3,8,1,2,6]=>0000000=>0000000=>[8]
[1,5,7,4,8,6,3,2]=>1000000=>0000001=>[7,1]
[1,8,2,7,6,5,4,3]=>1000000=>0000001=>[7,1]
[3,8,1,6,7,5,4,2]=>0000000=>0000000=>[8]
[3,7,2,6,8,5,1,4]=>0000000=>0000000=>[8]
[8,2,4,3,6,1,5,7]=>0000000=>0000000=>[8]
[1,7,8,5,4,3,6,2]=>1000000=>0000001=>[7,1]
[7,3,8,1,4,2,6,5]=>0000000=>0000000=>[8]
[1,8,4,5,3,2,6,7]=>1000000=>0000001=>[7,1]
[3,7,8,1,2,6,5,4]=>0000000=>0000000=>[8]
[1,6,4,5,7,2,3,8]=>1000001=>1000001=>[1,6,1]
[8,3,6,1,7,2,4,5]=>0000000=>0000000=>[8]
[7,3,5,2,1,8,4,6]=>0000000=>0000000=>[8]
[6,4,2,8,7,5,1,3]=>0000000=>0000000=>[8]
[1,5,3,6,8,7,4,2]=>1000000=>0000001=>[7,1]
[3,5,4,6,1,8,2,7]=>0000000=>0000000=>[8]
[3,1,5,7,6,8,2,4]=>0000000=>0000000=>[8]
[6,4,5,7,2,8,1,3]=>0000000=>0000000=>[8]
[2,6,3,5,4,8,1,7]=>0000000=>0000000=>[8]
[3,7,4,5,6,8,1,2]=>0000000=>0000000=>[8]
[2,5,7,3,6,8,1,4]=>0000000=>0000000=>[8]
[5,4,3,1,8,2,7,6]=>0000000=>0000000=>[8]
[1,2,8,3,5,4,6,7]=>1100000=>0000011=>[6,1,1]
[1,7,8,4,3,5,6,2]=>1000000=>0000001=>[7,1]
[3,1,6,8,4,5,7,2]=>0000000=>0000000=>[8]
[1,4,5,8,3,6,7,2]=>1000000=>0000001=>[7,1]
[2,5,7,1,8,3,6,4]=>0000000=>0000000=>[8]
[6,2,7,1,8,4,5,3]=>0000000=>0000000=>[8]
[4,7,1,3,8,5,6,2]=>0000000=>0000000=>[8]
[3,7,2,1,8,4,5,6]=>0000000=>0000000=>[8]
[4,2,7,1,8,3,6,5]=>0000000=>0000000=>[8]
[4,3,1,6,8,2,7,5]=>0000000=>0000000=>[8]
[5,3,4,6,8,2,7,1]=>0000000=>0000000=>[8]
[3,5,1,6,8,2,7,4]=>0000000=>0000000=>[8]
[5,8,3,2,6,4,1,7]=>0000000=>0000000=>[8]
[7,3,8,2,6,4,1,5]=>0000000=>0000000=>[8]
[3,8,7,4,5,6,1,2]=>0000000=>0000000=>[8]
[2,7,6,3,5,4,1,8]=>0000001=>1000000=>[1,7]
[3,8,7,4,6,2,5,1]=>0000000=>0000000=>[8]
[5,8,3,7,6,2,4,1]=>0000000=>0000000=>[8]
[5,8,7,4,3,6,2,1]=>0000000=>0000000=>[8]
[5,8,6,4,3,7,1,2]=>0000000=>0000000=>[8]
[6,5,8,4,3,1,7,2]=>0000000=>0000000=>[8]
[2,6,4,7,1,5,3,8]=>0000001=>1000000=>[1,7]
[2,5,6,8,4,3,7,1]=>0000000=>0000000=>[8]
[5,3,8,1,7,6,4,2]=>0000000=>0000000=>[8]
[5,4,8,7,1,6,3,2]=>0000000=>0000000=>[8]
[4,8,6,7,5,3,1,2]=>0000000=>0000000=>[8]
[4,8,6,5,7,2,1,3]=>0000000=>0000000=>[8]
[6,2,1,5,8,3,7,4]=>0000000=>0000000=>[8]
[5,8,3,2,7,6,4,1]=>0000000=>0000000=>[8]
[5,8,3,2,6,7,1,4]=>0000000=>0000000=>[8]
[6,5,3,2,8,1,7,4]=>0000000=>0000000=>[8]
[6,4,3,2,1,8,7,5]=>0000000=>0000000=>[8]
[6,3,4,1,2,8,7,5]=>0000000=>0000000=>[8]
[5,2,1,4,3,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,6,3,2,5,1,7,8]=>0000011=>1100000=>[1,1,6]
[3,5,7,4,2,6,1,8]=>0000001=>1000000=>[1,7]
[4,3,6,1,5,2,7,8]=>0000011=>1100000=>[1,1,6]
[4,2,1,5,7,6,3,8]=>0000001=>1000000=>[1,7]
[3,5,4,7,1,6,2,8]=>0000001=>1000000=>[1,7]
[3,4,5,8,6,7,1,2]=>0000000=>0000000=>[8]
[4,3,5,1,6,8,7,2]=>0000000=>0000000=>[8]
[2,1,5,3,8,4,7,6]=>0100000=>0000010=>[6,2]
[3,1,8,2,5,4,7,6]=>0000000=>0000000=>[8]
[8,1,3,2,6,4,7,5]=>0000000=>0000000=>[8]
[3,1,8,2,6,4,7,5]=>0000000=>0000000=>[8]
[2,1,8,3,6,4,7,5]=>0100000=>0000010=>[6,2]
[2,1,7,3,5,4,8,6]=>0100000=>0000010=>[6,2]
[2,1,7,3,6,4,8,5]=>0100000=>0000010=>[6,2]
[2,1,7,3,8,4,6,5]=>0100000=>0000010=>[6,2]
[8,1,4,2,7,3,6,5]=>0000000=>0000000=>[8]
[4,1,7,2,8,3,6,5]=>0000000=>0000000=>[8]
[3,1,7,2,8,4,6,5]=>0000000=>0000000=>[8]
[3,1,6,2,5,4,8,7]=>0000010=>0100000=>[2,6]
[7,1,3,2,6,4,8,5]=>0000000=>0000000=>[8]
[7,1,8,2,4,3,6,5]=>0000000=>0000000=>[8]
[7,1,5,2,8,3,6,4]=>0000000=>0000000=>[8]
[4,1,6,2,5,3,8,7]=>0000010=>0100000=>[2,6]
[4,1,7,2,5,3,8,6]=>0000000=>0000000=>[8]
[4,1,7,2,6,3,8,5]=>0000000=>0000000=>[8]
[5,1,7,2,6,3,8,4]=>0000000=>0000000=>[8]
[5,1,7,2,8,3,6,4]=>0000000=>0000000=>[8]
[8,1,5,2,7,3,6,4]=>0000000=>0000000=>[8]
[8,1,5,2,6,3,7,4]=>0000000=>0000000=>[8]
[5,1,8,2,6,3,7,4]=>0000000=>0000000=>[8]
[5,1,6,2,8,3,7,4]=>0000000=>0000000=>[8]
[3,1,6,2,8,4,7,5]=>0000000=>0000000=>[8]
[4,1,8,2,6,3,7,5]=>0000000=>0000000=>[8]
[8,1,4,2,6,3,7,5]=>0000000=>0000000=>[8]
[8,1,4,2,5,3,7,6]=>0000000=>0000000=>[8]
[4,1,8,2,5,3,7,6]=>0000000=>0000000=>[8]
[4,1,5,2,8,3,7,6]=>0000000=>0000000=>[8]
[3,1,5,2,8,4,7,6]=>0000000=>0000000=>[8]
[5,1,4,2,8,3,7,6]=>0000000=>0000000=>[8]
[6,1,3,2,8,4,7,5]=>0000000=>0000000=>[8]
[6,1,3,2,7,4,8,5]=>0000000=>0000000=>[8]
[6,1,4,2,7,3,8,5]=>0000000=>0000000=>[8]
[6,1,7,2,8,3,5,4]=>0000000=>0000000=>[8]
[7,8,3,1,2,5,6,4]=>0000000=>0000000=>[8]
[7,8,1,3,2,4,6,5]=>0000000=>0000000=>[8]
[6,2,8,1,3,5,4,7]=>0000000=>0000000=>[8]
[6,2,8,3,1,7,4,5]=>0000000=>0000000=>[8]
[3,2,5,7,1,8,4,6]=>0000000=>0000000=>[8]
[3,5,2,8,1,7,4,6]=>0000000=>0000000=>[8]
[5,1,3,7,2,6,8,4]=>0000000=>0000000=>[8]
[2,5,4,6,8,1,7,3]=>0000000=>0000000=>[8]
[4,3,5,7,6,8,1,2]=>0000000=>0000000=>[8]
[7,6,4,3,2,1,8,5]=>0000000=>0000000=>[8]
[7,6,5,8,2,1,4,3]=>0000000=>0000000=>[8]
[7,8,4,3,2,1,6,5]=>0000000=>0000000=>[8]
[7,6,3,8,2,1,5,4]=>0000000=>0000000=>[8]
[7,6,5,8,4,1,3,2]=>0000000=>0000000=>[8]
[7,4,8,3,2,1,6,5]=>0000000=>0000000=>[8]
[7,6,8,5,2,1,4,3]=>0000000=>0000000=>[8]
[4,8,6,1,7,5,2,3]=>0000000=>0000000=>[8]
[4,8,7,2,6,5,1,3]=>0000000=>0000000=>[8]
[8,4,7,3,6,5,1,2]=>0000000=>0000000=>[8]
[6,8,4,3,7,2,1,5]=>0000000=>0000000=>[8]
[6,7,4,2,8,3,1,5]=>0000000=>0000000=>[8]
[2,8,7,6,5,1,4,3]=>0000000=>0000000=>[8]
[7,3,2,5,4,1,6,8]=>0000001=>1000000=>[1,7]
[7,1,4,2,6,3,5,8]=>0000001=>1000000=>[1,7]
[7,3,2,5,1,6,4,8]=>0000001=>1000000=>[1,7]
[7,4,1,3,5,2,6,8]=>0000001=>1000000=>[1,7]
[2,3,6,1,4,8,7,5]=>0000000=>0000000=>[8]
[5,6,8,2,4,1,3,7]=>0000000=>0000000=>[8]
[5,6,8,7,4,3,1,2]=>0000000=>0000000=>[8]
[2,4,8,1,6,3,7,5]=>0000000=>0000000=>[8]
[1,8,4,5,2,6,7,3]=>1000000=>0000001=>[7,1]
[5,6,7,3,2,8,1,4]=>0000000=>0000000=>[8]
[5,3,2,1,4,8,6,7]=>0000100=>0010000=>[3,5]
[3,4,7,8,1,2,6,5]=>0000000=>0000000=>[8]
[3,6,7,8,1,4,5,2]=>0000000=>0000000=>[8]
[2,3,6,8,5,1,4,7]=>0000000=>0000000=>[8]
[3,1,6,4,8,2,5,7]=>0000000=>0000000=>[8]
[7,3,2,6,8,5,1,4]=>0000000=>0000000=>[8]
[5,7,8,3,1,4,6,2]=>0000000=>0000000=>[8]
[7,4,8,3,2,5,1,6]=>0000000=>0000000=>[8]
[7,3,8,2,4,5,6,1]=>0000000=>0000000=>[8]
[4,2,7,1,5,3,8,6]=>0000000=>0000000=>[8]
[1,2,7,3,4,8,6,5]=>1100000=>0000011=>[6,1,1]
[4,7,2,1,5,8,6,3]=>0000000=>0000000=>[8]
[4,8,3,6,5,1,7,2]=>0000000=>0000000=>[8]
[6,4,7,3,5,1,8,2]=>0000000=>0000000=>[8]
[3,1,6,4,7,8,2,5]=>0000000=>0000000=>[8]
[1,2,5,8,3,7,4,6]=>1100000=>0000011=>[6,1,1]
[8,2,4,1,7,5,6,3]=>0000000=>0000000=>[8]
[3,8,4,7,5,1,6,2]=>0000000=>0000000=>[8]
[8,4,3,6,1,7,5,2]=>0000000=>0000000=>[8]
[2,1,8,6,7,3,5,4]=>0100000=>0000010=>[6,2]
[1,2,8,6,3,4,7,5]=>1100000=>0000011=>[6,1,1]
[7,3,2,5,6,1,4,8]=>0000001=>1000000=>[1,7]
[8,4,1,2,7,5,3,6]=>0000000=>0000000=>[8]
[1,5,2,8,6,3,7,4]=>1000000=>0000001=>[7,1]
[5,8,6,3,1,7,4,2]=>0000000=>0000000=>[8]
[7,8,1,4,2,5,3,6]=>0000000=>0000000=>[8]
[5,6,2,7,1,3,4,8]=>0000001=>1000000=>[1,7]
[1,6,2,7,4,8,3,5]=>1000000=>0000001=>[7,1]
[6,2,1,7,8,5,3,4]=>0000000=>0000000=>[8]
[6,7,3,8,4,1,5,2]=>0000000=>0000000=>[8]
[2,7,1,8,5,6,3,4]=>0000000=>0000000=>[8]
[2,1,7,8,6,3,4,5]=>0100000=>0000010=>[6,2]
[7,8,6,2,1,3,5,4]=>0000000=>0000000=>[8]
[6,1,3,4,2,8,7,5]=>0000000=>0000000=>[8]
[7,1,3,8,6,4,5,2]=>0000000=>0000000=>[8]
[7,4,2,1,8,6,5,3]=>0000000=>0000000=>[8]
[2,1,6,3,4,8,7,5]=>0100000=>0000010=>[6,2]
[8,1,4,2,5,6,7,3]=>0000000=>0000000=>[8]
[8,1,3,2,5,6,7,4]=>0000000=>0000000=>[8]
[2,1,4,8,7,5,3,6]=>0100000=>0000010=>[6,2]
[7,1,5,8,2,6,3,4]=>0000000=>0000000=>[8]
[3,6,8,2,4,1,5,7]=>0000000=>0000000=>[8]
[6,2,8,1,7,5,4,3]=>0000000=>0000000=>[8]
[7,8,5,6,4,1,3,2]=>0000000=>0000000=>[8]
[3,8,1,4,5,6,2,7]=>0000000=>0000000=>[8]
[5,8,7,3,6,1,4,2]=>0000000=>0000000=>[8]
[5,8,3,7,6,1,4,2]=>0000000=>0000000=>[8]
[7,5,8,4,6,1,3,2]=>0000000=>0000000=>[8]
[2,4,8,1,3,7,6,5]=>0000000=>0000000=>[8]
[2,5,1,3,8,4,7,6]=>0000000=>0000000=>[8]
[2,8,1,5,4,7,3,6]=>0000000=>0000000=>[8]
[8,3,2,6,1,4,7,5]=>0000000=>0000000=>[8]
[2,5,7,1,3,8,6,4]=>0000000=>0000000=>[8]
[2,7,1,6,5,3,8,4]=>0000000=>0000000=>[8]
[2,8,1,7,6,5,4,3]=>0000000=>0000000=>[8]
[8,3,2,7,1,6,5,4]=>0000000=>0000000=>[8]
[7,4,2,8,1,6,5,3]=>0000000=>0000000=>[8]
[8,7,5,3,2,1,6,4]=>0000000=>0000000=>[8]
[7,4,5,8,6,2,1,3]=>0000000=>0000000=>[8]
[4,6,8,5,1,7,3,2]=>0000000=>0000000=>[8]
[4,7,5,1,3,8,6,2]=>0000000=>0000000=>[8]
[5,1,7,6,4,2,8,3]=>0000000=>0000000=>[8]
[5,1,8,7,6,4,3,2]=>0000000=>0000000=>[8]
[5,1,6,2,8,7,4,3]=>0000000=>0000000=>[8]
[4,5,6,1,8,7,2,3]=>0000000=>0000000=>[8]
[3,5,6,8,7,1,4,2]=>0000000=>0000000=>[8]
[3,6,1,7,4,8,2,5]=>0000000=>0000000=>[8]
[8,4,2,6,3,1,5,7]=>0000000=>0000000=>[8]
[3,4,8,7,1,2,6,5]=>0000000=>0000000=>[8]
[3,4,6,8,5,7,1,2]=>0000000=>0000000=>[8]
[4,6,8,3,5,7,2,1]=>0000000=>0000000=>[8]
[4,7,3,5,8,2,6,1]=>0000000=>0000000=>[8]
[5,6,8,3,7,2,1,4]=>0000000=>0000000=>[8]
[5,6,8,4,2,7,3,1]=>0000000=>0000000=>[8]
[6,5,2,7,1,3,8,4]=>0000000=>0000000=>[8]
[6,5,4,1,7,2,8,3]=>0000000=>0000000=>[8]
[6,4,7,3,1,8,2,5]=>0000000=>0000000=>[8]
[5,6,3,7,4,2,1,8]=>0000001=>1000000=>[1,7]
[6,1,3,8,5,2,4,7]=>0000000=>0000000=>[8]
[7,4,2,6,3,5,1,8]=>0000001=>1000000=>[1,7]
[3,4,7,5,6,2,1,8]=>0000001=>1000000=>[1,7]
[8,1,3,4,5,2,6,7]=>0000000=>0000000=>[8]
[1,6,8,4,2,5,3,7]=>1000000=>0000001=>[7,1]
[8,7,2,3,6,1,4,5]=>0000000=>0000000=>[8]
[1,4,8,5,2,6,7,3]=>1000000=>0000001=>[7,1]
[6,1,8,4,3,7,2,5]=>0000000=>0000000=>[8]
[1,5,2,4,8,7,3,6]=>1000000=>0000001=>[7,1]
[3,2,6,4,1,8,7,5]=>0000000=>0000000=>[8]
[7,6,4,3,1,8,2,5]=>0000000=>0000000=>[8]
[8,4,6,5,1,7,2,3]=>0000000=>0000000=>[8]
[7,5,4,6,1,2,8,3]=>0000000=>0000000=>[8]
[3,2,5,6,1,7,8,4]=>0000000=>0000000=>[8]
[3,2,8,7,6,1,4,5]=>0000000=>0000000=>[8]
[6,8,4,7,2,1,3,5]=>0000000=>0000000=>[8]
[3,8,7,5,6,1,2,4]=>0000000=>0000000=>[8]
[8,2,7,6,5,1,3,4]=>0000000=>0000000=>[8]
[4,8,6,7,1,5,3,2]=>0000000=>0000000=>[8]
[1,8,6,7,2,3,4,5]=>1000000=>0000001=>[7,1]
[3,5,4,2,7,1,8,6]=>0000000=>0000000=>[8]
[3,2,6,1,5,7,4,8]=>0000001=>1000000=>[1,7]
[5,2,1,4,7,6,3,8]=>0000001=>1000000=>[1,7]
[4,2,1,3,5,8,7,6]=>0001100=>0011000=>[3,1,4]
[7,4,1,5,3,6,8,2]=>0000000=>0000000=>[8]
[6,8,3,4,1,5,2,7]=>0000000=>0000000=>[8]
[5,8,4,1,7,2,6,3]=>0000000=>0000000=>[8]
[4,1,8,3,5,7,2,6]=>0000000=>0000000=>[8]
[2,4,6,3,5,8,1,7]=>0000000=>0000000=>[8]
[4,5,7,2,3,6,8,1]=>0000000=>0000000=>[8]
[2,6,3,4,7,5,8,1]=>0000000=>0000000=>[8]
[4,5,2,7,1,6,8,3]=>0000000=>0000000=>[8]
[2,3,1,7,6,4,8,5]=>0010000=>0000100=>[5,3]
[3,4,1,6,5,8,2,7]=>0000000=>0000000=>[8]
[6,4,2,8,7,1,5,3]=>0000000=>0000000=>[8]
[3,1,8,2,7,6,4,5]=>0000000=>0000000=>[8]
[6,2,8,4,1,7,5,3]=>0000000=>0000000=>[8]
[3,6,4,7,2,5,1,8]=>0000001=>1000000=>[1,7]
[7,3,2,8,6,1,4,5]=>0000000=>0000000=>[8]
[4,3,8,7,1,2,5,6]=>0000000=>0000000=>[8]
[1,2,5,8,4,7,3,6]=>1100000=>0000011=>[6,1,1]
[1,3,6,8,5,2,7,4]=>1000000=>0000001=>[7,1]
[2,5,7,4,1,8,6,3]=>0000000=>0000000=>[8]
[1,4,2,5,8,7,3,6]=>1000000=>0000001=>[7,1]
[3,5,1,7,2,8,6,4]=>0000000=>0000000=>[8]
[4,6,3,1,7,8,5,2]=>0000000=>0000000=>[8]
[5,3,1,6,7,8,4,2]=>0000000=>0000000=>[8]
[2,1,3,4,8,7,5,6]=>0111000=>0001110=>[4,1,1,2]
[4,8,7,3,6,5,1,2]=>0000000=>0000000=>[8]
[4,3,8,7,6,5,1,2]=>0000000=>0000000=>[8]
[2,8,7,6,1,5,4,3]=>0000000=>0000000=>[8]
[5,2,8,7,6,1,4,3]=>0000000=>0000000=>[8]
[6,2,8,7,5,1,4,3]=>0000000=>0000000=>[8]
[7,8,2,6,5,1,4,3]=>0000000=>0000000=>[8]
[6,1,8,7,5,4,3,2]=>0000000=>0000000=>[8]
[4,1,8,7,6,5,3,2]=>0000000=>0000000=>[8]
[3,1,8,7,6,5,4,2]=>0000000=>0000000=>[8]
[7,8,2,6,1,5,4,3]=>0000000=>0000000=>[8]
[4,2,8,1,7,6,5,3]=>0000000=>0000000=>[8]
[3,2,8,1,7,6,5,4]=>0000000=>0000000=>[8]
[2,8,7,1,6,5,4,3]=>0000000=>0000000=>[8]
[3,8,2,1,7,6,5,4]=>0000000=>0000000=>[8]
[4,8,2,7,6,1,5,3]=>0000000=>0000000=>[8]
[3,8,2,7,1,6,5,4]=>0000000=>0000000=>[8]
[3,8,7,2,1,6,5,4]=>0000000=>0000000=>[8]
[4,8,7,2,6,1,5,3]=>0000000=>0000000=>[8]
[5,8,7,6,2,1,4,3]=>0000000=>0000000=>[8]
[6,5,8,7,1,4,3,2]=>0000000=>0000000=>[8]
[3,8,7,1,6,5,4,2]=>0000000=>0000000=>[8]
[4,8,1,7,6,5,3,2]=>0000000=>0000000=>[8]
[5,4,1,8,7,6,3,2]=>0000000=>0000000=>[8]
[6,4,8,1,7,5,3,2]=>0000000=>0000000=>[8]
[7,8,4,1,6,5,3,2]=>0000000=>0000000=>[8]
[7,8,3,1,6,5,4,2]=>0000000=>0000000=>[8]
[5,3,1,8,7,6,4,2]=>0000000=>0000000=>[8]
[4,3,1,8,7,6,5,2]=>0000000=>0000000=>[8]
[4,2,1,8,7,6,5,3]=>0000000=>0000000=>[8]
[6,5,3,1,8,7,4,2]=>0000000=>0000000=>[8]
[5,4,2,1,8,7,6,3]=>0000000=>0000000=>[8]
[8,6,1,4,2,3,5,7]=>0000000=>0000000=>[8]
[6,8,1,4,2,3,5,7]=>0000000=>0000000=>[8]
[4,6,2,3,8,1,5,7]=>0000000=>0000000=>[8]
[6,4,2,3,8,1,5,7]=>0000000=>0000000=>[8]
[2,8,4,3,6,1,5,7]=>0000000=>0000000=>[8]
[2,4,8,3,6,1,5,7]=>0000000=>0000000=>[8]
[8,3,6,2,4,1,5,7]=>0000000=>0000000=>[8]
[8,3,6,2,1,4,5,7]=>0000000=>0000000=>[8]
[2,1,8,3,6,4,5,7]=>0100000=>0000010=>[6,2]
[6,3,8,2,1,4,5,7]=>0000000=>0000000=>[8]
[3,6,4,7,8,5,1,2]=>0000000=>0000000=>[8]
[1,6,4,2,7,5,8,3]=>1000000=>0000001=>[7,1]
[3,4,6,8,7,5,1,2]=>0000000=>0000000=>[8]
[5,4,6,3,8,7,1,2]=>0000000=>0000000=>[8]
[6,4,8,5,3,7,1,2]=>0000000=>0000000=>[8]
[1,8,5,2,6,3,7,4]=>1000000=>0000001=>[7,1]
[1,4,6,2,8,5,7,3]=>1000000=>0000001=>[7,1]
[7,8,1,4,2,5,6,3]=>0000000=>0000000=>[8]
[4,8,5,3,1,6,2,7]=>0000000=>0000000=>[8]
[5,2,8,6,4,1,3,7]=>0000000=>0000000=>[8]
[5,1,6,2,8,7,3,4]=>0000000=>0000000=>[8]
[6,1,8,7,4,2,3,5]=>0000000=>0000000=>[8]
[1,2,8,5,7,3,6,4]=>1100000=>0000011=>[6,1,1]
[1,3,6,8,7,5,2,4]=>1000000=>0000001=>[7,1]
[7,8,1,2,4,6,5,3]=>0000000=>0000000=>[8]
[1,2,6,4,8,7,5,3]=>1100000=>0000011=>[6,1,1]
[1,8,2,5,4,7,6,3]=>1000000=>0000001=>[7,1]
[1,2,7,3,5,8,6,4]=>1100000=>0000011=>[6,1,1]
[4,6,2,1,7,5,3,8]=>0000001=>1000000=>[1,7]
[4,6,2,3,7,8,1,5]=>0000000=>0000000=>[8]
[4,2,1,3,5,7,8,6]=>0001100=>0011000=>[3,1,4]
[7,8,3,2,4,1,6,5]=>0000000=>0000000=>[8]
[7,8,4,2,6,3,1,5]=>0000000=>0000000=>[8]
[5,8,2,7,4,3,1,6]=>0000000=>0000000=>[8]
[7,5,2,8,3,4,1,6]=>0000000=>0000000=>[8]
[6,4,3,5,2,8,1,7]=>0000000=>0000000=>[8]
[4,1,3,6,5,8,7,2]=>0000000=>0000000=>[8]
[2,4,1,3,8,5,7,6]=>0001000=>0001000=>[4,4]
[2,4,1,3,5,8,7,6]=>0001100=>0011000=>[3,1,4]
[4,6,1,3,5,8,7,2]=>0000000=>0000000=>[8]
[1,4,6,3,5,8,7,2]=>1000000=>0000001=>[7,1]
[4,2,1,3,6,5,7,8]=>0001011=>1101000=>[1,1,2,4]
[4,2,1,8,3,5,7,6]=>0000000=>0000000=>[8]
[6,2,1,8,3,5,7,4]=>0000000=>0000000=>[8]
[6,4,1,3,8,5,7,2]=>0000000=>0000000=>[8]
[8,2,1,3,6,5,7,4]=>0000000=>0000000=>[8]
[8,2,1,4,3,5,7,6]=>0000000=>0000000=>[8]
[8,1,4,6,3,5,7,2]=>0000000=>0000000=>[8]
[2,4,8,1,3,5,7,6]=>0000000=>0000000=>[8]
[4,6,8,1,3,5,7,2]=>0000000=>0000000=>[8]
[4,6,1,8,3,5,7,2]=>0000000=>0000000=>[8]
[4,1,6,8,3,5,7,2]=>0000000=>0000000=>[8]
[1,4,6,8,3,5,7,2]=>1000000=>0000001=>[7,1]
[1,4,6,3,8,5,7,2]=>1000000=>0000001=>[7,1]
[4,6,1,3,8,5,7,2]=>0000000=>0000000=>[8]
[2,6,1,3,8,5,7,4]=>0000000=>0000000=>[8]
[2,6,1,8,3,5,7,4]=>0000000=>0000000=>[8]
[2,1,3,6,8,5,7,4]=>0110000=>0000110=>[5,1,2]
[4,1,3,6,8,5,7,2]=>0000000=>0000000=>[8]
[1,4,3,6,8,5,7,2]=>1000000=>0000001=>[7,1]
[2,1,8,3,6,5,7,4]=>0100000=>0000010=>[6,2]
[2,1,8,6,3,5,7,4]=>0100000=>0000010=>[6,2]
[2,1,8,4,3,5,7,6]=>0100000=>0000010=>[6,2]
[2,8,4,1,3,5,7,6]=>0000000=>0000000=>[8]
[6,8,1,4,3,5,7,2]=>0000000=>0000000=>[8]
[1,8,6,4,3,5,7,2]=>1000000=>0000001=>[7,1]
[8,6,1,4,3,5,7,2]=>0000000=>0000000=>[8]
[8,6,4,1,3,5,7,2]=>0000000=>0000000=>[8]
[8,4,2,1,3,5,7,6]=>0000000=>0000000=>[8]
[8,5,7,4,3,2,1,6]=>0000000=>0000000=>[8]
[8,7,6,5,1,4,3,2]=>0000000=>0000000=>[8]
[8,7,3,6,5,2,1,4]=>0000000=>0000000=>[8]
[6,5,8,4,3,2,1,7]=>0000000=>0000000=>[8]
[8,4,7,6,3,2,1,5]=>0000000=>0000000=>[8]
[5,8,7,4,3,2,1,6]=>0000000=>0000000=>[8]
[4,5,2,7,3,1,8,6]=>0000000=>0000000=>[8]
[4,8,2,6,3,5,7,1]=>0000000=>0000000=>[8]
[8,6,1,2,7,4,3,5]=>0000000=>0000000=>[8]
[4,6,2,1,7,8,5,3]=>0000000=>0000000=>[8]
[2,3,8,7,4,1,6,5]=>0000000=>0000000=>[8]
[7,8,2,1,5,6,4,3]=>0000000=>0000000=>[8]
[1,6,2,5,8,4,3,7]=>1000000=>0000001=>[7,1]
[5,2,7,1,8,6,3,4]=>0000000=>0000000=>[8]
[1,2,8,3,7,6,5,4]=>1100000=>0000011=>[6,1,1]
[6,5,2,8,1,7,3,4]=>0000000=>0000000=>[8]
[2,8,3,5,1,7,4,6]=>0000000=>0000000=>[8]
[2,8,5,6,1,7,3,4]=>0000000=>0000000=>[8]
[5,4,2,8,6,1,7,3]=>0000000=>0000000=>[8]
[8,3,7,4,2,6,5,1]=>0000000=>0000000=>[8]
[6,3,2,8,4,1,7,5]=>0000000=>0000000=>[8]
[2,8,3,4,1,7,5,6]=>0000000=>0000000=>[8]
[5,4,2,8,3,1,7,6]=>0000000=>0000000=>[8]
[2,8,6,4,1,7,5,3]=>0000000=>0000000=>[8]
[8,4,7,6,2,5,3,1]=>0000000=>0000000=>[8]
[4,8,7,6,1,5,3,2]=>0000000=>0000000=>[8]
[7,3,8,5,2,1,6,4]=>0000000=>0000000=>[8]
[7,3,8,4,2,1,6,5]=>0000000=>0000000=>[8]
[7,5,4,3,8,2,1,6]=>0000000=>0000000=>[8]
[5,4,2,3,8,1,6,7]=>0000000=>0000000=>[8]
[3,7,8,4,1,2,6,5]=>0000000=>0000000=>[8]
[7,3,4,8,2,1,5,6]=>0000000=>0000000=>[8]
[7,5,8,6,2,1,4,3]=>0000000=>0000000=>[8]
[6,5,8,7,3,1,4,2]=>0000000=>0000000=>[8]
[2,4,8,3,1,5,7,6]=>0000000=>0000000=>[8]
[6,3,2,4,8,1,5,7]=>0000000=>0000000=>[8]
[2,4,3,8,1,6,5,7]=>0000000=>0000000=>[8]
[2,3,8,4,1,6,7,5]=>0000000=>0000000=>[8]
[3,4,8,7,1,5,6,2]=>0000000=>0000000=>[8]
[2,5,3,8,1,6,4,7]=>0000000=>0000000=>[8]
[3,7,4,8,1,5,2,6]=>0000000=>0000000=>[8]
[2,6,8,5,1,3,7,4]=>0000000=>0000000=>[8]
[2,6,8,4,1,3,7,5]=>0000000=>0000000=>[8]
[3,7,5,8,1,4,2,6]=>0000000=>0000000=>[8]
[2,6,5,8,1,4,3,7]=>0000000=>0000000=>[8]
[2,5,8,3,1,4,7,6]=>0000000=>0000000=>[8]
[4,7,6,8,1,3,2,5]=>0000000=>0000000=>[8]
[5,6,8,7,1,3,4,2]=>0000000=>0000000=>[8]
[8,7,4,1,6,2,5,3]=>0000000=>0000000=>[8]
[6,4,7,2,8,5,1,3]=>0000000=>0000000=>[8]
[1,7,6,2,4,3,5,8]=>1000001=>1000001=>[1,6,1]
[8,7,3,2,4,6,5,1]=>0000000=>0000000=>[8]
[6,4,7,3,8,5,2,1]=>0000000=>0000000=>[8]
[2,7,1,5,6,3,4,8]=>0000001=>1000000=>[1,7]
[3,6,4,1,2,8,7,5]=>0000000=>0000000=>[8]
[3,6,5,1,8,2,7,4]=>0000000=>0000000=>[8]
[4,6,5,1,8,7,2,3]=>0000000=>0000000=>[8]
[5,7,1,4,8,6,2,3]=>0000000=>0000000=>[8]
[5,7,1,3,8,2,6,4]=>0000000=>0000000=>[8]
[6,3,7,2,8,4,5,1]=>0000000=>0000000=>[8]
[6,7,1,8,3,2,5,4]=>0000000=>0000000=>[8]
[8,7,6,1,4,5,2,3]=>0000000=>0000000=>[8]
[8,7,6,1,3,2,5,4]=>0000000=>0000000=>[8]
[8,7,3,5,1,2,6,4]=>0000000=>0000000=>[8]
[8,7,4,5,1,6,2,3]=>0000000=>0000000=>[8]
[8,5,6,4,1,7,2,3]=>0000000=>0000000=>[8]
[8,4,6,2,3,1,7,5]=>0000000=>0000000=>[8]
[4,7,3,5,2,1,6,8]=>0000001=>1000000=>[1,7]
[6,7,8,4,1,5,3,2]=>0000000=>0000000=>[8]
[7,1,6,8,4,5,3,2]=>0000000=>0000000=>[8]
[7,5,1,6,4,2,3,8]=>0000001=>1000000=>[1,7]
[8,1,5,7,4,6,3,2]=>0000000=>0000000=>[8]
[1,8,4,6,7,5,3,2]=>1000000=>0000001=>[7,1]
[6,1,8,4,7,5,3,2]=>0000000=>0000000=>[8]
[4,8,5,1,6,7,3,2]=>0000000=>0000000=>[8]
[8,4,1,5,6,7,3,2]=>0000000=>0000000=>[8]
[8,1,4,5,6,7,3,2]=>0000000=>0000000=>[8]
[1,8,4,6,2,5,3,7]=>1000000=>0000001=>[7,1]
[8,5,6,1,2,4,3,7]=>0000000=>0000000=>[8]
[2,8,3,1,5,6,7,4]=>0000000=>0000000=>[8]
[8,3,2,7,1,5,6,4]=>0000000=>0000000=>[8]
[3,2,8,5,7,1,6,4]=>0000000=>0000000=>[8]
[3,6,2,8,5,1,7,4]=>0000000=>0000000=>[8]
[6,2,1,8,4,7,5,3]=>0000000=>0000000=>[8]
[2,8,7,1,4,6,5,3]=>0000000=>0000000=>[8]
[8,2,7,1,5,4,6,3]=>0000000=>0000000=>[8]
[7,3,1,5,6,2,4,8]=>0000001=>1000000=>[1,7]
[7,2,8,1,6,4,5,3]=>0000000=>0000000=>[8]
[7,8,2,6,4,1,5,3]=>0000000=>0000000=>[8]
[8,7,2,4,1,6,5,3]=>0000000=>0000000=>[8]
[1,2,8,6,3,7,5,4]=>1100000=>0000011=>[6,1,1]
[1,8,7,2,3,6,5,4]=>1000000=>0000001=>[7,1]
[1,7,8,2,6,4,3,5]=>1000000=>0000001=>[7,1]
[2,1,7,3,6,8,4,5]=>0100000=>0000010=>[6,2]
[7,1,5,8,3,2,4,6]=>0000000=>0000000=>[8]
[7,8,1,5,2,4,3,6]=>0000000=>0000000=>[8]
[8,7,1,2,5,4,3,6]=>0000000=>0000000=>[8]
[1,6,2,8,4,3,7,5]=>1000000=>0000001=>[7,1]
[1,8,3,7,2,5,4,6]=>1000000=>0000001=>[7,1]
[8,1,4,7,3,2,5,6]=>0000000=>0000000=>[8]
[4,7,8,1,3,2,5,6]=>0000000=>0000000=>[8]
[2,1,8,3,5,7,4,6]=>0100000=>0000010=>[6,2]
[1,2,3,4,8,5,7,6]=>1111000=>0001111=>[4,1,1,1,1]
[3,7,2,5,6,4,1,8]=>0000001=>1000000=>[1,7]
[7,6,2,5,4,3,1,8]=>0000001=>1000000=>[1,7]
[4,7,5,2,6,3,1,8]=>0000001=>1000000=>[1,7]
[5,6,7,2,4,3,1,8]=>0000001=>1000000=>[1,7]
[2,8,3,4,1,6,7,5]=>0000000=>0000000=>[8]
[6,1,3,5,7,2,4,8]=>0000001=>1000000=>[1,7]
[8,1,3,6,2,4,7,5]=>0000000=>0000000=>[8]
[2,1,8,3,7,5,4,6]=>0100000=>0000010=>[6,2]
[7,1,8,2,5,6,3,4]=>0000000=>0000000=>[8]
[6,1,5,8,2,7,3,4]=>0000000=>0000000=>[8]
[6,2,5,8,1,4,7,3]=>0000000=>0000000=>[8]
[3,2,8,5,1,6,7,4]=>0000000=>0000000=>[8]
[1,3,8,2,5,7,4,6]=>1000000=>0000001=>[7,1]
[2,8,7,1,6,4,5,3]=>0000000=>0000000=>[8]
[3,8,7,1,5,6,4,2]=>0000000=>0000000=>[8]
[4,8,7,5,1,6,3,2]=>0000000=>0000000=>[8]
[5,8,6,7,1,4,3,2]=>0000000=>0000000=>[8]
[6,7,8,5,1,4,3,2]=>0000000=>0000000=>[8]
[5,6,3,8,4,1,7,2]=>0000000=>0000000=>[8]
[7,3,8,5,4,1,6,2]=>0000000=>0000000=>[8]
[8,3,7,4,1,6,5,2]=>0000000=>0000000=>[8]
[3,5,6,8,4,1,7,2]=>0000000=>0000000=>[8]
[5,6,4,7,8,1,3,2]=>0000000=>0000000=>[8]
[6,2,3,1,5,4,7,8]=>0000011=>1100000=>[1,1,6]
[8,5,1,3,2,4,7,6]=>0000000=>0000000=>[8]
[7,5,1,3,2,6,4,8]=>0000001=>1000000=>[1,7]
[3,6,4,1,5,2,7,8]=>0000011=>1100000=>[1,1,6]
[4,5,6,1,3,2,7,8]=>0000011=>1100000=>[1,1,6]
[6,7,1,4,2,5,3,8]=>0000001=>1000000=>[1,7]
[2,7,1,3,5,6,4,8]=>0000001=>1000000=>[1,7]
[8,6,1,2,4,3,7,5]=>0000000=>0000000=>[8]
[7,8,1,2,5,3,6,4]=>0000000=>0000000=>[8]
[1,8,2,7,5,4,6,3]=>1000000=>0000001=>[7,1]
[1,8,6,3,7,2,4,5]=>1000000=>0000001=>[7,1]
[1,8,2,5,4,6,7,3]=>1000000=>0000001=>[7,1]
[7,2,8,4,3,5,6,1]=>0000000=>0000000=>[8]
[1,4,7,5,2,6,8,3]=>1000000=>0000001=>[7,1]
[4,6,5,3,7,1,8,2]=>0000000=>0000000=>[8]
[5,6,2,7,3,1,8,4]=>0000000=>0000000=>[8]
[1,6,3,7,5,8,2,4]=>1000000=>0000001=>[7,1]
[5,2,4,8,1,3,7,6]=>0000000=>0000000=>[8]
[3,5,2,4,7,1,6,8]=>0000001=>1000000=>[1,7]
[6,4,5,3,8,2,1,7]=>0000000=>0000000=>[8]
[6,5,3,4,8,7,1,2]=>0000000=>0000000=>[8]
[7,6,3,8,5,4,1,2]=>0000000=>0000000=>[8]
[5,4,8,1,2,7,3,6]=>0000000=>0000000=>[8]
[6,3,8,1,7,2,4,5]=>0000000=>0000000=>[8]
[7,2,8,6,1,3,4,5]=>0000000=>0000000=>[8]
[7,2,8,6,1,5,3,4]=>0000000=>0000000=>[8]
[3,2,4,7,8,1,5,6]=>0000000=>0000000=>[8]
[1,5,7,4,2,8,6,3]=>1000000=>0000001=>[7,1]
[1,3,7,2,8,6,4,5]=>1000000=>0000001=>[7,1]
[1,5,3,6,8,2,7,4]=>1000000=>0000001=>[7,1]
[4,3,6,5,7,8,1,2]=>0000000=>0000000=>[8]
[4,2,3,5,6,8,1,7]=>0000000=>0000000=>[8]
[5,2,6,4,7,8,3,1]=>0000000=>0000000=>[8]
[3,2,5,6,8,1,7,4]=>0000000=>0000000=>[8]
[4,2,3,6,8,1,5,7]=>0000000=>0000000=>[8]
[2,6,1,5,4,8,3,7]=>0000000=>0000000=>[8]
[3,2,1,8,7,5,6,4]=>0010000=>0000100=>[5,3]
[3,1,6,2,5,8,4,7]=>0000000=>0000000=>[8]
[6,5,1,3,4,8,2,7]=>0000000=>0000000=>[8]
[6,2,4,5,8,1,3,7]=>0000000=>0000000=>[8]
[2,3,4,8,1,7,6,5]=>0000000=>0000000=>[8]
[6,2,7,8,4,5,1,3]=>0000000=>0000000=>[8]
[3,1,4,8,7,6,2,5]=>0000000=>0000000=>[8]
[2,3,6,5,8,7,1,4]=>0000000=>0000000=>[8]
[8,4,1,2,7,6,3,5]=>0000000=>0000000=>[8]
[6,3,2,8,5,7,4,1]=>0000000=>0000000=>[8]
[3,2,6,8,5,1,7,4]=>0000000=>0000000=>[8]
[5,2,4,1,7,8,6,3]=>0000000=>0000000=>[8]
[1,8,7,2,4,5,6,3]=>1000000=>0000001=>[7,1]
[5,3,4,7,1,8,6,2]=>0000000=>0000000=>[8]
[5,3,7,1,6,2,8,4]=>0000000=>0000000=>[8]
[4,7,6,5,8,2,1,3]=>0000000=>0000000=>[8]
[1,2,5,3,8,7,6,4]=>1100000=>0000011=>[6,1,1]
[4,8,2,3,6,7,1,5]=>0000000=>0000000=>[8]
[8,2,4,6,7,1,3,5]=>0000000=>0000000=>[8]
[3,7,5,1,8,4,6,2]=>0000000=>0000000=>[8]
[6,5,3,1,8,4,2,7]=>0000000=>0000000=>[8]
[4,2,3,8,5,6,1,7]=>0000000=>0000000=>[8]
[2,4,8,7,1,3,5,6]=>0000000=>0000000=>[8]
[8,2,6,3,4,5,1,7]=>0000000=>0000000=>[8]
[8,1,5,4,3,6,2,7]=>0000000=>0000000=>[8]
[8,6,4,2,1,5,3,7]=>0000000=>0000000=>[8]
[8,3,2,4,6,1,5,7]=>0000000=>0000000=>[8]
[8,2,3,4,7,6,1,5]=>0000000=>0000000=>[8]
[8,1,3,7,6,4,2,5]=>0000000=>0000000=>[8]
[4,8,1,2,7,3,6,5]=>0000000=>0000000=>[8]
[2,5,7,8,4,1,3,6]=>0000000=>0000000=>[8]
[6,3,5,8,7,2,4,1]=>0000000=>0000000=>[8]
[5,2,8,7,1,3,4,6]=>0000000=>0000000=>[8]
[5,2,7,4,8,1,6,3]=>0000000=>0000000=>[8]
[8,1,7,4,5,2,6,3]=>0000000=>0000000=>[8]
[1,7,8,3,5,4,6,2]=>1000000=>0000001=>[7,1]
[4,6,3,5,8,1,7,2]=>0000000=>0000000=>[8]
[8,2,4,1,5,6,7,3]=>0000000=>0000000=>[8]
[3,5,1,7,6,8,2,4]=>0000000=>0000000=>[8]
[2,1,7,6,4,5,8,3]=>0100000=>0000010=>[6,2]
[1,7,6,5,2,4,8,3]=>1000000=>0000001=>[7,1]
[4,6,2,5,3,8,7,1]=>0000000=>0000000=>[8]
[8,6,4,2,3,1,7,5]=>0000000=>0000000=>[8]
[8,6,4,2,1,3,7,5]=>0000000=>0000000=>[8]
[2,5,7,3,8,4,6,1]=>0000000=>0000000=>[8]
[4,2,7,1,8,5,3,6]=>0000000=>0000000=>[8]
[1,3,7,5,8,6,4,2]=>1000000=>0000001=>[7,1]
[3,5,7,1,4,8,6,2]=>0000000=>0000000=>[8]
[3,4,1,2,8,5,7,6]=>0001000=>0001000=>[4,4]
[8,7,3,1,2,6,4,5]=>0000000=>0000000=>[8]
[6,2,3,1,4,8,7,5]=>0000000=>0000000=>[8]
[8,4,3,2,5,7,1,6]=>0000000=>0000000=>[8]
[5,3,6,8,2,1,4,7]=>0000000=>0000000=>[8]
[3,2,6,8,5,4,1,7]=>0000000=>0000000=>[8]
[7,3,8,2,5,4,1,6]=>0000000=>0000000=>[8]
[7,4,2,5,8,3,1,6]=>0000000=>0000000=>[8]
[3,1,2,8,5,6,4,7]=>0010000=>0000100=>[5,3]
[5,2,1,6,8,3,4,7]=>0000000=>0000000=>[8]
[3,1,8,6,5,4,2,7]=>0000000=>0000000=>[8]
[5,6,8,1,4,3,2,7]=>0000000=>0000000=>[8]
[7,8,4,1,5,3,2,6]=>0000000=>0000000=>[8]
[7,3,8,5,1,4,2,6]=>0000000=>0000000=>[8]
[1,5,4,8,3,7,6,2]=>1000000=>0000001=>[7,1]
[4,7,8,3,1,6,5,2]=>0000000=>0000000=>[8]
[8,7,5,3,6,4,2,1]=>0000000=>0000000=>[8]
[4,6,1,3,8,7,5,2]=>0000000=>0000000=>[8]
[3,6,1,2,7,5,8,4]=>0000000=>0000000=>[8]
[3,6,2,5,8,7,4,1]=>0000000=>0000000=>[8]
[2,7,3,1,5,6,8,4]=>0000000=>0000000=>[8]
[6,7,1,3,2,8,4,5]=>0000000=>0000000=>[8]
[6,2,7,1,3,4,8,5]=>0000000=>0000000=>[8]
[5,2,1,7,3,8,4,6]=>0000000=>0000000=>[8]
[3,7,2,4,6,1,8,5]=>0000000=>0000000=>[8]
[5,3,7,2,8,1,4,6]=>0000000=>0000000=>[8]
[7,1,8,3,4,2,5,6]=>0000000=>0000000=>[8]
[7,2,4,1,8,3,5,6]=>0000000=>0000000=>[8]
[4,8,7,6,3,2,1,5]=>0000000=>0000000=>[8]
[7,8,2,4,6,1,5,3]=>0000000=>0000000=>[8]
[3,5,1,8,7,2,6,4]=>0000000=>0000000=>[8]
[5,2,8,1,7,6,3,4]=>0000000=>0000000=>[8]
[6,2,1,3,8,7,5,4]=>0000000=>0000000=>[8]
[6,7,8,1,2,5,4,3]=>0000000=>0000000=>[8]
[5,8,7,1,6,4,3,2]=>0000000=>0000000=>[8]
[6,8,7,5,1,4,3,2]=>0000000=>0000000=>[8]
[8,6,4,3,2,1,7,5]=>0000000=>0000000=>[8]
[6,5,4,3,8,2,7,1]=>0000000=>0000000=>[8]
[8,4,3,2,1,7,6,5]=>0000000=>0000000=>[8]
[3,7,5,8,1,4,6,2]=>0000000=>0000000=>[8]
[4,7,5,8,3,2,1,6]=>0000000=>0000000=>[8]
[5,7,2,3,6,1,8,4]=>0000000=>0000000=>[8]
[7,3,1,4,8,2,5,6]=>0000000=>0000000=>[8]
[7,4,1,2,5,8,3,6]=>0000000=>0000000=>[8]
[4,7,1,6,5,8,3,2]=>0000000=>0000000=>[8]
[8,6,4,2,3,7,5,1]=>0000000=>0000000=>[8]
[7,6,4,2,3,8,1,5]=>0000000=>0000000=>[8]
[3,1,2,4,8,7,6,5]=>0011000=>0001100=>[4,1,3]
[6,5,8,7,3,1,2,4]=>0000000=>0000000=>[8]
[5,6,7,8,1,4,2,3]=>0000000=>0000000=>[8]
[2,6,7,4,5,3,1,8]=>0000001=>1000000=>[1,7]
[1,3,7,4,2,8,5,6]=>1000000=>0000001=>[7,1]
[4,6,1,3,7,2,5,8]=>0000001=>1000000=>[1,7]
[6,5,7,8,3,1,4,2]=>0000000=>0000000=>[8]
[7,5,8,6,2,1,3,4]=>0000000=>0000000=>[8]
[2,8,1,3,6,5,4,7]=>0000000=>0000000=>[8]
[2,8,7,3,5,4,1,6]=>0000000=>0000000=>[8]
[3,4,2,6,8,7,1,5]=>0000000=>0000000=>[8]
[6,1,4,2,7,8,5,3]=>0000000=>0000000=>[8]
[7,3,8,4,1,2,6,5]=>0000000=>0000000=>[8]
[6,8,3,2,7,1,5,4]=>0000000=>0000000=>[8]
[5,1,4,3,6,2,7,8]=>0000011=>1100000=>[1,1,6]
[4,8,5,6,3,2,1,7]=>0000000=>0000000=>[8]
[2,8,5,6,3,7,1,4]=>0000000=>0000000=>[8]
[3,2,6,7,4,8,1,5]=>0000000=>0000000=>[8]
[4,1,8,2,6,3,5,7]=>0000000=>0000000=>[8]
[7,5,6,8,2,1,4,3]=>0000000=>0000000=>[8]
[5,8,6,7,1,2,3,4]=>0000000=>0000000=>[8]
[4,8,1,5,7,2,3,6]=>0000000=>0000000=>[8]
[3,5,1,4,7,6,8,2]=>0000000=>0000000=>[8]
[5,3,2,7,1,6,8,4]=>0000000=>0000000=>[8]
[5,4,1,7,3,6,8,2]=>0000000=>0000000=>[8]
[3,4,7,6,2,5,8,1]=>0000000=>0000000=>[8]
[4,8,3,6,5,2,1,7]=>0000000=>0000000=>[8]
[8,1,7,4,2,5,6,3]=>0000000=>0000000=>[8]
[1,8,7,2,5,3,4,6]=>1000000=>0000001=>[7,1]
[4,8,1,5,2,6,3,7]=>0000000=>0000000=>[8]
[3,6,8,5,1,2,4,7]=>0000000=>0000000=>[8]
[1,5,2,7,8,4,6,3]=>1000000=>0000001=>[7,1]
[6,7,2,8,5,3,1,4]=>0000000=>0000000=>[8]
[6,7,2,8,3,1,5,4]=>0000000=>0000000=>[8]
[3,1,4,6,7,8,5,2]=>0000000=>0000000=>[8]
[7,4,6,1,8,2,3,5]=>0000000=>0000000=>[8]
[3,4,5,1,6,8,7,2]=>0000000=>0000000=>[8]
[5,7,8,3,1,6,4,2]=>0000000=>0000000=>[8]
[7,5,8,3,2,4,1,6]=>0000000=>0000000=>[8]
[5,8,2,6,3,1,4,7]=>0000000=>0000000=>[8]
[8,2,7,5,4,1,3,6]=>0000000=>0000000=>[8]
[6,2,7,3,8,4,1,5]=>0000000=>0000000=>[8]
[3,7,2,4,8,5,1,6]=>0000000=>0000000=>[8]
[1,5,2,6,3,8,7,4]=>1000000=>0000001=>[7,1]
[1,3,6,2,4,8,7,5]=>1000000=>0000001=>[7,1]
[8,3,6,2,5,4,1,7]=>0000000=>0000000=>[8]
[3,5,8,2,4,6,1,7]=>0000000=>0000000=>[8]
[6,4,7,8,2,3,1,5]=>0000000=>0000000=>[8]
[1,5,3,2,8,4,7,6]=>1000000=>0000001=>[7,1]
[3,8,4,7,5,1,2,6]=>0000000=>0000000=>[8]
[6,1,2,7,3,8,5,4]=>0000000=>0000000=>[8]
[2,1,7,3,4,8,6,5]=>0100000=>0000010=>[6,2]
[8,3,1,6,7,2,5,4]=>0000000=>0000000=>[8]
[4,8,3,7,1,5,2,6]=>0000000=>0000000=>[8]
[5,7,4,8,2,1,3,6]=>0000000=>0000000=>[8]
[4,6,8,2,5,1,3,7]=>0000000=>0000000=>[8]
[5,3,7,2,1,4,6,8]=>0000001=>1000000=>[1,7]
[6,4,2,8,3,1,5,7]=>0000000=>0000000=>[8]
[5,7,2,3,8,1,4,6]=>0000000=>0000000=>[8]
[6,4,7,5,8,1,2,3]=>0000000=>0000000=>[8]
[8,6,4,2,1,7,5,3]=>0000000=>0000000=>[8]
[7,6,4,1,8,5,2,3]=>0000000=>0000000=>[8]
[1,6,4,8,7,5,3,2]=>1000000=>0000001=>[7,1]
[6,3,1,2,8,4,7,5]=>0000000=>0000000=>[8]
[7,4,8,1,6,3,5,2]=>0000000=>0000000=>[8]
[1,4,8,7,2,6,5,3]=>1000000=>0000001=>[7,1]
[5,4,1,8,7,3,2,6]=>0000000=>0000000=>[8]
[8,6,1,7,5,4,3,2]=>0000000=>0000000=>[8]
[3,1,8,7,6,5,2,4]=>0000000=>0000000=>[8]
[2,6,8,1,3,7,5,4]=>0000000=>0000000=>[8]
[2,4,8,1,5,7,6,3]=>0000000=>0000000=>[8]
[3,2,8,6,1,7,5,4]=>0000000=>0000000=>[8]
[6,2,8,3,1,7,5,4]=>0000000=>0000000=>[8]
[7,4,3,8,5,2,1,6]=>0000000=>0000000=>[8]
[4,3,8,7,5,1,6,2]=>0000000=>0000000=>[8]
[4,2,3,8,5,1,6,7]=>0000000=>0000000=>[8]
[4,2,8,5,1,7,6,3]=>0000000=>0000000=>[8]
[3,4,2,8,5,6,1,7]=>0000000=>0000000=>[8]
[3,2,4,8,6,1,5,7]=>0000000=>0000000=>[8]
[3,2,5,8,6,1,4,7]=>0000000=>0000000=>[8]
[4,3,7,8,5,1,2,6]=>0000000=>0000000=>[8]
[4,2,6,8,5,1,3,7]=>0000000=>0000000=>[8]
[3,5,2,8,4,6,1,7]=>0000000=>0000000=>[8]
[5,2,6,8,4,1,3,7]=>0000000=>0000000=>[8]
[5,3,7,8,4,1,2,6]=>0000000=>0000000=>[8]
[5,6,2,8,3,4,1,7]=>0000000=>0000000=>[8]
[5,3,8,7,4,1,6,2]=>0000000=>0000000=>[8]
[6,4,2,8,5,3,1,7]=>0000000=>0000000=>[8]
[7,6,4,3,8,2,5,1]=>0000000=>0000000=>[8]
[6,4,5,3,8,2,7,1]=>0000000=>0000000=>[8]
[7,4,5,3,8,2,6,1]=>0000000=>0000000=>[8]
[8,4,6,3,7,2,5,1]=>0000000=>0000000=>[8]
[7,6,8,3,5,2,4,1]=>0000000=>0000000=>[8]
[7,5,8,4,6,2,3,1]=>0000000=>0000000=>[8]
[7,5,8,3,6,2,4,1]=>0000000=>0000000=>[8]
[7,4,8,3,6,2,5,1]=>0000000=>0000000=>[8]
[7,4,8,3,5,2,6,1]=>0000000=>0000000=>[8]
[6,4,8,3,5,2,7,1]=>0000000=>0000000=>[8]
[5,4,7,3,6,2,8,1]=>0000000=>0000000=>[8]
[6,5,7,3,8,2,4,1]=>0000000=>0000000=>[8]
[5,4,6,3,8,2,7,1]=>0000000=>0000000=>[8]
[6,5,3,7,8,2,1,4]=>0000000=>0000000=>[8]
[6,5,4,2,8,7,1,3]=>0000000=>0000000=>[8]
[6,4,3,7,5,2,1,8]=>0000001=>1000000=>[1,7]
[6,3,7,8,5,2,1,4]=>0000000=>0000000=>[8]
[6,3,7,2,5,4,1,8]=>0000001=>1000000=>[1,7]
[6,3,2,7,5,4,1,8]=>0000001=>1000000=>[1,7]
[4,8,2,6,3,7,1,5]=>0000000=>0000000=>[8]
[5,4,8,1,2,3,7,6]=>0000000=>0000000=>[8]
[1,4,7,6,3,2,5,8]=>1000001=>1000001=>[1,6,1]
[4,8,3,2,7,6,1,5]=>0000000=>0000000=>[8]
[4,8,6,7,2,3,1,5]=>0000000=>0000000=>[8]
[4,8,7,3,6,2,1,5]=>0000000=>0000000=>[8]
[4,3,8,2,7,1,6,5]=>0000000=>0000000=>[8]
[4,1,8,7,3,2,5,6]=>0000000=>0000000=>[8]
[4,7,8,1,2,5,3,6]=>0000000=>0000000=>[8]
[2,3,6,7,4,1,8,5]=>0000000=>0000000=>[8]
[2,6,3,4,7,8,1,5]=>0000000=>0000000=>[8]
[3,1,7,8,4,2,5,6]=>0000000=>0000000=>[8]
[4,3,1,2,8,5,7,6]=>0001000=>0001000=>[4,4]
[3,7,6,8,4,2,1,5]=>0000000=>0000000=>[8]
[3,7,8,2,6,4,1,5]=>0000000=>0000000=>[8]
[3,7,2,8,4,6,1,5]=>0000000=>0000000=>[8]
[4,2,8,3,6,1,7,5]=>0000000=>0000000=>[8]
[3,7,2,4,8,6,1,5]=>0000000=>0000000=>[8]
[1,3,6,4,7,2,5,8]=>1000001=>1000001=>[1,6,1]
[2,4,3,6,1,8,7,5]=>0000000=>0000000=>[8]
[2,6,7,3,8,4,1,5]=>0000000=>0000000=>[8]
[2,6,3,7,4,8,1,5]=>0000000=>0000000=>[8]
[1,3,5,7,4,6,8,2]=>1000000=>0000001=>[7,1]
[1,3,5,4,7,2,6,8]=>1000001=>1000001=>[1,6,1]
[1,3,5,4,7,2,8,6]=>1000000=>0000001=>[7,1]
[2,3,7,1,4,8,6,5]=>0000000=>0000000=>[8]
[2,5,7,3,4,8,6,1]=>0000000=>0000000=>[8]
[2,5,4,6,7,1,3,8]=>0000001=>1000000=>[1,7]
[2,4,6,3,7,5,1,8]=>0000001=>1000000=>[1,7]
[5,3,2,7,4,6,1,8]=>0000001=>1000000=>[1,7]
[4,1,2,5,8,3,7,6]=>0000000=>0000000=>[8]
[4,6,1,2,5,8,3,7]=>0000000=>0000000=>[8]
[5,7,6,8,1,4,2,3]=>0000000=>0000000=>[8]
[4,1,6,2,8,5,7,3]=>0000000=>0000000=>[8]
[7,1,4,2,3,6,8,5]=>0000000=>0000000=>[8]
[6,4,2,1,3,8,7,5]=>0000000=>0000000=>[8]
[3,8,6,4,2,1,5,7]=>0000000=>0000000=>[8]
[6,1,2,7,5,3,8,4]=>0000000=>0000000=>[8]
[2,6,1,4,7,3,8,5]=>0000000=>0000000=>[8]
[7,3,2,8,6,4,1,5]=>0000000=>0000000=>[8]
[2,7,8,4,6,3,1,5]=>0000000=>0000000=>[8]
[7,8,2,5,3,6,1,4]=>0000000=>0000000=>[8]
[8,1,6,3,5,7,2,4]=>0000000=>0000000=>[8]
[8,3,2,6,4,7,1,5]=>0000000=>0000000=>[8]
[8,4,2,5,6,7,1,3]=>0000000=>0000000=>[8]
[2,3,8,7,6,5,1,4]=>0000000=>0000000=>[8]
[4,1,8,7,2,6,5,3]=>0000000=>0000000=>[8]
[1,2,8,7,3,6,5,4]=>1100000=>0000011=>[6,1,1]
[1,5,8,7,3,2,6,4]=>1000000=>0000001=>[7,1]
[4,5,8,7,3,2,1,6]=>0000000=>0000000=>[8]
[2,6,8,3,7,5,1,4]=>0000000=>0000000=>[8]
[1,6,8,4,7,2,5,3]=>1000000=>0000001=>[7,1]
[1,6,8,3,7,2,5,4]=>1000000=>0000001=>[7,1]
[2,5,8,1,7,6,4,3]=>0000000=>0000000=>[8]
[3,2,8,4,7,6,1,5]=>0000000=>0000000=>[8]
[1,5,8,4,7,2,6,3]=>1000000=>0000001=>[7,1]
[1,5,8,3,7,2,6,4]=>1000000=>0000001=>[7,1]
[3,1,8,4,7,2,6,5]=>0000000=>0000000=>[8]
[5,6,8,1,2,7,4,3]=>0000000=>0000000=>[8]
[1,6,8,2,3,7,5,4]=>1000000=>0000001=>[7,1]
[1,5,8,4,2,7,6,3]=>1000000=>0000001=>[7,1]
[5,6,8,4,3,2,1,7]=>0000000=>0000000=>[8]
[7,1,4,8,6,2,5,3]=>0000000=>0000000=>[8]
[7,3,4,8,6,2,1,5]=>0000000=>0000000=>[8]
[7,1,4,8,2,6,5,3]=>0000000=>0000000=>[8]
[7,4,5,8,1,2,6,3]=>0000000=>0000000=>[8]
[3,6,2,8,7,5,1,4]=>0000000=>0000000=>[8]
[1,6,4,8,7,2,5,3]=>1000000=>0000001=>[7,1]
[3,2,4,8,7,6,1,5]=>0000000=>0000000=>[8]
[1,4,5,8,7,2,6,3]=>1000000=>0000001=>[7,1]
[3,1,4,8,7,2,6,5]=>0000000=>0000000=>[8]
[1,6,5,8,2,7,4,3]=>1000000=>0000001=>[7,1]
[2,6,5,8,3,7,1,4]=>0000000=>0000000=>[8]
[2,4,5,8,3,7,1,6]=>0000000=>0000000=>[8]
[4,6,5,8,3,2,1,7]=>0000000=>0000000=>[8]
[7,6,2,3,8,5,1,4]=>0000000=>0000000=>[8]
[7,6,1,4,8,2,5,3]=>0000000=>0000000=>[8]
[7,2,5,3,8,6,1,4]=>0000000=>0000000=>[8]
[7,2,1,3,8,6,5,4]=>0000000=>0000000=>[8]
[2,6,5,3,8,7,1,4]=>0000000=>0000000=>[8]
[2,6,1,4,8,7,5,3]=>0000000=>0000000=>[8]
[7,6,5,1,2,8,4,3]=>0000000=>0000000=>[8]
[7,1,5,2,3,8,6,4]=>0000000=>0000000=>[8]
[7,1,2,4,3,8,6,5]=>0000000=>0000000=>[8]
[1,6,2,4,3,8,7,5]=>1000000=>0000001=>[7,1]
[2,6,5,4,3,8,1,7]=>0000000=>0000000=>[8]
[7,6,5,1,3,2,8,4]=>0000000=>0000000=>[8]
[8,2,7,6,5,4,1,3]=>0000000=>0000000=>[8]
[7,2,8,6,5,4,3,1]=>0000000=>0000000=>[8]
[3,2,8,7,6,5,1,4]=>0000000=>0000000=>[8]
[7,8,6,1,5,4,3,2]=>0000000=>0000000=>[8]
[4,8,5,7,6,3,2,1]=>0000000=>0000000=>[8]
[3,2,4,6,8,1,5,7]=>0000000=>0000000=>[8]
[3,5,7,2,4,8,1,6]=>0000000=>0000000=>[8]
[4,5,1,3,6,8,2,7]=>0000000=>0000000=>[8]
[4,3,5,7,2,6,8,1]=>0000000=>0000000=>[8]
[4,3,5,1,7,8,2,6]=>0000000=>0000000=>[8]
[4,6,3,5,7,2,8,1]=>0000000=>0000000=>[8]
[5,1,6,7,3,4,8,2]=>0000000=>0000000=>[8]
[1,6,7,3,4,5,8,2]=>1000000=>0000001=>[7,1]
[2,6,7,4,8,1,3,5]=>0000000=>0000000=>[8]
[6,3,1,7,8,2,4,5]=>0000000=>0000000=>[8]
[5,7,2,8,1,3,4,6]=>0000000=>0000000=>[8]
[6,3,7,2,8,1,4,5]=>0000000=>0000000=>[8]
[2,4,6,7,1,5,8,3]=>0000000=>0000000=>[8]
[2,4,7,1,5,6,8,3]=>0000000=>0000000=>[8]
[3,7,1,5,6,8,2,4]=>0000000=>0000000=>[8]
[1,5,6,7,2,4,8,3]=>1000000=>0000001=>[7,1]
[5,6,2,4,1,7,8,3]=>0000000=>0000000=>[8]
[5,6,4,7,1,3,8,2]=>0000000=>0000000=>[8]
[6,4,3,7,2,5,8,1]=>0000000=>0000000=>[8]
[6,4,3,7,2,8,1,5]=>0000000=>0000000=>[8]
[7,4,5,3,1,6,8,2]=>0000000=>0000000=>[8]
[6,4,3,7,5,1,8,2]=>0000000=>0000000=>[8]
[5,6,3,7,4,1,8,2]=>0000000=>0000000=>[8]
[6,7,4,2,1,5,8,3]=>0000000=>0000000=>[8]
[6,7,4,2,1,8,3,5]=>0000000=>0000000=>[8]
[5,6,7,3,1,8,2,4]=>0000000=>0000000=>[8]
[5,6,3,7,8,1,2,4]=>0000000=>0000000=>[8]
[5,6,3,7,2,4,8,1]=>0000000=>0000000=>[8]
[5,6,7,2,3,8,1,4]=>0000000=>0000000=>[8]
[5,6,7,2,8,1,3,4]=>0000000=>0000000=>[8]
[6,7,3,8,1,2,4,5]=>0000000=>0000000=>[8]
[6,7,3,2,8,1,4,5]=>0000000=>0000000=>[8]
[7,6,4,2,1,3,8,5]=>0000000=>0000000=>[8]
[7,5,3,2,6,1,8,4]=>0000000=>0000000=>[8]
[6,5,3,2,7,8,1,4]=>0000000=>0000000=>[8]
[6,4,7,2,5,1,8,3]=>0000000=>0000000=>[8]
[5,4,6,7,3,1,8,2]=>0000000=>0000000=>[8]
[3,7,8,5,6,1,4,2]=>0000000=>0000000=>[8]
[1,7,8,5,6,3,4,2]=>1000000=>0000001=>[7,1]
[1,7,5,8,6,3,4,2]=>1000000=>0000001=>[7,1]
[5,7,3,8,6,4,1,2]=>0000000=>0000000=>[8]
[1,5,7,8,6,3,4,2]=>1000000=>0000001=>[7,1]
[1,5,7,8,3,6,4,2]=>1000000=>0000001=>[7,1]
[5,3,7,8,1,6,4,2]=>0000000=>0000000=>[8]
[5,3,7,8,6,1,4,2]=>0000000=>0000000=>[8]
[7,8,3,5,6,1,4,2]=>0000000=>0000000=>[8]
[7,1,8,5,6,3,4,2]=>0000000=>0000000=>[8]
[7,1,5,8,6,3,4,2]=>0000000=>0000000=>[8]
[5,1,7,8,6,3,4,2]=>0000000=>0000000=>[8]
[5,1,7,8,3,6,4,2]=>0000000=>0000000=>[8]
[3,1,7,8,5,6,4,2]=>0000000=>0000000=>[8]
[1,3,7,8,5,6,4,2]=>1000000=>0000001=>[7,1]
[3,1,7,5,8,6,4,2]=>0000000=>0000000=>[8]
[5,1,7,3,8,6,4,2]=>0000000=>0000000=>[8]
[7,1,5,3,8,6,4,2]=>0000000=>0000000=>[8]
[7,1,5,8,3,6,4,2]=>0000000=>0000000=>[8]
[7,3,8,5,1,6,4,2]=>0000000=>0000000=>[8]
[7,3,5,8,1,6,4,2]=>0000000=>0000000=>[8]
[7,3,5,1,8,6,4,2]=>0000000=>0000000=>[8]
[5,3,7,1,8,6,4,2]=>0000000=>0000000=>[8]
[3,5,7,1,8,6,4,2]=>0000000=>0000000=>[8]
[1,5,7,3,8,6,4,2]=>1000000=>0000001=>[7,1]
[1,7,5,3,8,6,4,2]=>1000000=>0000001=>[7,1]
[3,7,5,1,8,6,4,2]=>0000000=>0000000=>[8]
[5,7,3,1,8,6,4,2]=>0000000=>0000000=>[8]
[5,7,3,8,6,1,4,2]=>0000000=>0000000=>[8]
[3,7,5,8,1,6,4,2]=>0000000=>0000000=>[8]
[1,7,5,8,3,6,4,2]=>1000000=>0000001=>[7,1]
[1,7,8,5,3,6,4,2]=>1000000=>0000001=>[7,1]
[5,7,8,6,3,1,4,2]=>0000000=>0000000=>[8]
[7,5,8,6,1,3,4,2]=>0000000=>0000000=>[8]
[5,7,8,1,6,3,4,2]=>0000000=>0000000=>[8]
[1,7,8,3,5,6,4,2]=>1000000=>0000001=>[7,1]
[1,7,3,8,5,6,4,2]=>1000000=>0000001=>[7,1]
[3,7,1,8,5,6,4,2]=>0000000=>0000000=>[8]
[5,7,1,8,3,6,4,2]=>0000000=>0000000=>[8]
[5,7,1,8,6,3,4,2]=>0000000=>0000000=>[8]
[7,5,1,8,6,3,4,2]=>0000000=>0000000=>[8]
[7,5,8,1,6,3,4,2]=>0000000=>0000000=>[8]
[7,5,1,8,3,6,4,2]=>0000000=>0000000=>[8]
[7,5,1,3,8,6,4,2]=>0000000=>0000000=>[8]
[5,7,1,3,8,6,4,2]=>0000000=>0000000=>[8]
[3,7,1,5,8,6,4,2]=>0000000=>0000000=>[8]
[1,7,3,5,8,6,4,2]=>1000000=>0000001=>[7,1]
[1,5,3,7,8,6,4,2]=>1000000=>0000001=>[7,1]
[3,5,1,7,8,6,4,2]=>0000000=>0000000=>[8]
[5,3,1,7,8,6,4,2]=>0000000=>0000000=>[8]
[7,3,1,5,8,6,4,2]=>0000000=>0000000=>[8]
[7,3,1,8,5,6,4,2]=>0000000=>0000000=>[8]
[7,1,8,3,5,6,4,2]=>0000000=>0000000=>[8]
[7,1,3,8,5,6,4,2]=>0000000=>0000000=>[8]
[7,1,3,5,8,6,4,2]=>0000000=>0000000=>[8]
[5,1,3,7,8,6,4,2]=>0000000=>0000000=>[8]
[3,1,5,7,8,6,4,2]=>0000000=>0000000=>[8]
[2,3,6,1,5,4,8,7]=>0000010=>0100000=>[2,6]
[3,5,6,2,4,1,8,7]=>0000010=>0100000=>[2,6]
[8,7,6,1,3,2,4,5]=>0000000=>0000000=>[8]
[2,5,3,4,8,1,7,6]=>0000000=>0000000=>[8]
[5,1,8,2,3,4,7,6]=>0000000=>0000000=>[8]
[5,4,7,6,2,8,1,3]=>0000000=>0000000=>[8]
[3,1,8,6,2,7,5,4]=>0000000=>0000000=>[8]
[3,8,1,5,6,7,2,4]=>0000000=>0000000=>[8]
[8,2,3,5,7,1,6,4]=>0000000=>0000000=>[8]
[2,8,3,6,7,5,1,4]=>0000000=>0000000=>[8]
[4,3,8,2,7,6,1,5]=>0000000=>0000000=>[8]
[2,1,4,5,8,3,7,6]=>0100000=>0000010=>[6,2]
[6,4,7,5,2,3,8,1]=>0000000=>0000000=>[8]
[4,2,3,1,8,7,5,6]=>0001000=>0001000=>[4,4]
[4,3,1,2,8,6,7,5]=>0001000=>0001000=>[4,4]
[5,1,6,7,8,4,3,2]=>0000000=>0000000=>[8]
[8,7,2,6,4,1,5,3]=>0000000=>0000000=>[8]
[6,1,7,4,3,2,8,5]=>0000000=>0000000=>[8]
[4,2,6,1,5,7,8,3]=>0000000=>0000000=>[8]
[7,1,4,8,3,5,6,2]=>0000000=>0000000=>[8]
[3,4,8,2,5,7,6,1]=>0000000=>0000000=>[8]
[3,7,1,4,5,6,8,2]=>0000000=>0000000=>[8]
[4,7,5,6,8,3,1,2]=>0000000=>0000000=>[8]
[6,5,3,8,4,7,1,2]=>0000000=>0000000=>[8]
[8,6,4,7,5,3,1,2]=>0000000=>0000000=>[8]
[1,6,3,7,5,8,4,2]=>1000000=>0000001=>[7,1]
[1,3,7,4,5,8,6,2]=>1000000=>0000001=>[7,1]
[7,3,8,5,4,6,1,2]=>0000000=>0000000=>[8]
[3,4,8,5,6,7,1,2]=>0000000=>0000000=>[8]
[4,7,3,8,5,6,1,2]=>0000000=>0000000=>[8]
[6,8,4,7,5,3,1,2]=>0000000=>0000000=>[8]
[1,7,6,5,3,8,4,2]=>1000000=>0000001=>[7,1]
[2,7,6,4,5,1,3,8]=>0000001=>1000000=>[1,7]
[1,8,2,7,3,6,5,4]=>1000000=>0000001=>[7,1]
[2,1,3,8,4,7,5,6]=>0110000=>0000110=>[5,1,2]
[3,1,2,8,4,6,7,5]=>0010000=>0000100=>[5,3]
[4,1,7,2,8,5,6,3]=>0000000=>0000000=>[8]
[5,1,2,4,8,3,7,6]=>0000000=>0000000=>[8]
[1,7,2,8,5,3,6,4]=>1000000=>0000001=>[7,1]
[1,2,3,8,4,5,7,6]=>1110000=>0000111=>[5,1,1,1]
[2,4,8,3,1,5,6,7]=>0000000=>0000000=>[8]
[3,4,2,7,1,5,6,8]=>0000001=>1000000=>[1,7]
[3,2,5,6,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[4,7,3,8,2,1,5,6]=>0000000=>0000000=>[8]
[7,4,8,3,2,1,5,6]=>0000000=>0000000=>[8]
[2,6,4,5,7,1,3,8]=>0000001=>1000000=>[1,7]
[5,4,6,2,7,1,3,8]=>0000001=>1000000=>[1,7]
[7,6,8,5,1,4,3,2]=>0000000=>0000000=>[8]
[6,5,1,2,8,3,7,4]=>0000000=>0000000=>[8]
[6,8,4,1,3,7,5,2]=>0000000=>0000000=>[8]
[6,3,7,1,8,4,5,2]=>0000000=>0000000=>[8]
[4,7,1,2,8,3,6,5]=>0000000=>0000000=>[8]
[1,2,8,7,6,3,5,4]=>1100000=>0000011=>[6,1,1]
[2,3,1,8,7,4,5,6]=>0010000=>0000100=>[5,3]
[8,7,1,6,5,4,3,2]=>0000000=>0000000=>[8]
[3,1,8,7,6,4,5,2]=>0000000=>0000000=>[8]
[1,2,3,4,8,7,5,6]=>1111000=>0001111=>[4,1,1,1,1]
[1,2,3,8,6,4,5,7]=>1110000=>0000111=>[5,1,1,1]
[1,2,8,5,3,4,6,7]=>1100000=>0000011=>[6,1,1]
[1,8,4,2,3,5,6,7]=>1000000=>0000001=>[7,1]
[2,4,7,5,6,8,3,1]=>0000000=>0000000=>[8]
[2,5,3,8,7,4,6,1]=>0000000=>0000000=>[8]
[3,1,8,5,7,4,2,6]=>0000000=>0000000=>[8]
[8,3,6,2,4,5,7,1]=>0000000=>0000000=>[8]
[4,8,1,7,6,3,2,5]=>0000000=>0000000=>[8]
[4,7,8,1,3,6,2,5]=>0000000=>0000000=>[8]
[5,8,7,1,4,3,2,6]=>0000000=>0000000=>[8]
[5,6,1,2,4,3,8,7]=>0000010=>0100000=>[2,6]
[3,6,8,1,2,7,5,4]=>0000000=>0000000=>[8]
[8,4,6,2,1,3,7,5]=>0000000=>0000000=>[8]
[4,8,1,5,3,7,2,6]=>0000000=>0000000=>[8]
[5,4,8,7,3,1,2,6]=>0000000=>0000000=>[8]
[6,4,3,8,1,5,2,7]=>0000000=>0000000=>[8]
[6,8,3,7,2,5,4,1]=>0000000=>0000000=>[8]
[5,3,6,8,7,2,4,1]=>0000000=>0000000=>[8]
[5,7,4,2,8,3,6,1]=>0000000=>0000000=>[8]
[6,4,7,2,1,8,3,5]=>0000000=>0000000=>[8]
[6,5,3,1,4,7,2,8]=>0000001=>1000000=>[1,7]
[5,7,8,2,6,4,1,3]=>0000000=>0000000=>[8]
[3,6,8,5,7,1,4,2]=>0000000=>0000000=>[8]
[1,7,4,8,6,2,3,5]=>1000000=>0000001=>[7,1]
[2,7,4,8,5,6,1,3]=>0000000=>0000000=>[8]
[6,3,7,2,8,5,1,4]=>0000000=>0000000=>[8]
[8,1,3,6,7,2,4,5]=>0000000=>0000000=>[8]
[6,1,3,8,2,7,4,5]=>0000000=>0000000=>[8]
[4,1,5,3,2,8,6,7]=>0000100=>0010000=>[3,5]
[2,7,1,4,3,8,5,6]=>0000000=>0000000=>[8]
[1,7,5,2,8,6,3,4]=>1000000=>0000001=>[7,1]
[7,4,2,5,1,8,6,3]=>0000000=>0000000=>[8]
[5,6,3,2,1,8,7,4]=>0000000=>0000000=>[8]
[4,5,3,2,7,1,8,6]=>0000000=>0000000=>[8]
[6,4,2,8,5,1,7,3]=>0000000=>0000000=>[8]
[1,8,4,7,2,5,3,6]=>1000000=>0000001=>[7,1]
[1,5,8,4,2,6,3,7]=>1000000=>0000001=>[7,1]
[3,5,7,4,1,6,8,2]=>0000000=>0000000=>[8]
[4,5,8,3,1,7,6,2]=>0000000=>0000000=>[8]
[3,4,7,8,2,1,6,5]=>0000000=>0000000=>[8]
[3,5,7,1,2,6,4,8]=>0000001=>1000000=>[1,7]
[3,6,2,1,4,7,5,8]=>0000001=>1000000=>[1,7]
[7,4,1,2,8,6,3,5]=>0000000=>0000000=>[8]
[5,2,6,1,3,4,8,7]=>0000010=>0100000=>[2,6]
[7,5,1,6,8,4,3,2]=>0000000=>0000000=>[8]
[6,2,7,8,5,4,1,3]=>0000000=>0000000=>[8]
[3,8,7,6,2,4,1,5]=>0000000=>0000000=>[8]
[3,5,8,7,2,4,6,1]=>0000000=>0000000=>[8]
[2,7,1,3,6,5,4,8]=>0000001=>1000000=>[1,7]
[6,3,7,1,5,4,2,8]=>0000001=>1000000=>[1,7]
[5,7,8,3,2,1,4,6]=>0000000=>0000000=>[8]
[5,4,2,1,7,8,3,6]=>0000000=>0000000=>[8]
[4,7,8,3,5,2,1,6]=>0000000=>0000000=>[8]
[8,3,2,1,4,7,6,5]=>0000000=>0000000=>[8]
[6,4,1,7,3,8,5,2]=>0000000=>0000000=>[8]
[1,7,5,3,8,2,6,4]=>1000000=>0000001=>[7,1]
[5,1,7,4,2,8,6,3]=>0000000=>0000000=>[8]
[5,1,4,3,2,7,8,6]=>0000100=>0010000=>[3,5]
[3,7,6,2,4,1,8,5]=>0000000=>0000000=>[8]
[6,3,1,7,5,2,8,4]=>0000000=>0000000=>[8]
[4,1,6,8,5,7,3,2]=>0000000=>0000000=>[8]
[1,8,6,7,3,4,2,5]=>1000000=>0000001=>[7,1]
[6,7,1,8,3,4,2,5]=>0000000=>0000000=>[8]
[7,8,2,5,1,6,3,4]=>0000000=>0000000=>[8]
[1,8,5,6,2,7,3,4]=>1000000=>0000001=>[7,1]
[5,6,2,7,1,8,3,4]=>0000000=>0000000=>[8]
[6,7,2,5,1,8,3,4]=>0000000=>0000000=>[8]
[2,5,1,8,6,7,3,4]=>0000000=>0000000=>[8]
[2,6,5,8,1,7,3,4]=>0000000=>0000000=>[8]
[2,4,3,8,5,6,1,7]=>0000000=>0000000=>[8]
[2,3,1,8,5,6,4,7]=>0010000=>0000100=>[5,3]
[4,7,1,6,2,5,3,8]=>0000001=>1000000=>[1,7]
[4,6,3,5,1,7,2,8]=>0000001=>1000000=>[1,7]
[5,6,3,7,1,4,2,8]=>0000001=>1000000=>[1,7]
[1,8,5,6,3,4,2,7]=>1000000=>0000001=>[7,1]
[4,7,1,8,5,6,2,3]=>0000000=>0000000=>[8]
[3,4,2,6,5,8,1,7]=>0000000=>0000000=>[8]
[3,5,4,6,2,8,1,7]=>0000000=>0000000=>[8]
[3,7,1,6,2,8,4,5]=>0000000=>0000000=>[8]
[3,5,2,7,4,8,1,6]=>0000000=>0000000=>[8]
[4,7,2,3,1,8,5,6]=>0000000=>0000000=>[8]
[2,5,8,3,4,1,6,7]=>0000000=>0000000=>[8]
[5,1,7,3,4,2,8,6]=>0000000=>0000000=>[8]
[4,6,7,3,2,5,8,1]=>0000000=>0000000=>[8]
[3,7,2,1,4,5,8,6]=>0000000=>0000000=>[8]
[2,7,1,3,4,8,6,5]=>0000000=>0000000=>[8]
[2,6,7,3,8,5,4,1]=>0000000=>0000000=>[8]
[2,6,1,8,4,5,3,7]=>0000000=>0000000=>[8]
[4,2,1,6,5,3,8,7]=>0000010=>0100000=>[2,6]
[6,2,4,3,1,5,8,7]=>0000010=>0100000=>[2,6]
[4,6,2,1,5,3,8,7]=>0000010=>0100000=>[2,6]
[8,4,2,1,6,5,3,7]=>0000000=>0000000=>[8]
[2,6,4,5,1,8,7,3]=>0000000=>0000000=>[8]
[6,8,7,2,1,4,3,5]=>0000000=>0000000=>[8]
[6,8,2,1,7,4,3,5]=>0000000=>0000000=>[8]
[8,6,2,4,3,1,5,7]=>0000000=>0000000=>[8]
[4,6,5,2,8,3,7,1]=>0000000=>0000000=>[8]
[2,6,4,5,8,3,7,1]=>0000000=>0000000=>[8]
[8,2,4,3,6,5,1,7]=>0000000=>0000000=>[8]
[4,2,1,6,8,7,5,3]=>0000000=>0000000=>[8]
[4,2,1,6,5,8,7,3]=>0000000=>0000000=>[8]
[6,2,1,8,4,3,7,5]=>0000000=>0000000=>[8]
[4,6,5,8,7,2,1,3]=>0000000=>0000000=>[8]
[6,4,8,2,1,5,7,3]=>0000000=>0000000=>[8]
[2,6,8,4,7,1,5,3]=>0000000=>0000000=>[8]
[4,8,6,7,2,1,3,5]=>0000000=>0000000=>[8]
[7,4,5,2,3,8,6,1]=>0000000=>0000000=>[8]
[3,5,1,6,4,2,8,7]=>0000010=>0100000=>[2,6]
[7,2,3,4,5,8,6,1]=>0000000=>0000000=>[8]
[8,2,3,4,5,7,1,6]=>0000000=>0000000=>[8]
[5,7,1,3,8,6,2,4]=>0000000=>0000000=>[8]
[4,7,3,2,8,6,1,5]=>0000000=>0000000=>[8]
[4,8,1,5,6,7,3,2]=>0000000=>0000000=>[8]
[6,8,2,5,1,7,3,4]=>0000000=>0000000=>[8]
[7,8,3,4,6,2,1,5]=>0000000=>0000000=>[8]
[3,8,2,5,4,7,6,1]=>0000000=>0000000=>[8]
[3,7,6,1,8,5,2,4]=>0000000=>0000000=>[8]
[4,6,7,1,8,5,3,2]=>0000000=>0000000=>[8]
[3,6,1,7,8,5,4,2]=>0000000=>0000000=>[8]
[2,1,5,7,3,8,6,4]=>0100000=>0000010=>[6,2]
[7,6,1,4,8,5,2,3]=>0000000=>0000000=>[8]
[4,1,2,3,7,8,6,5]=>0001000=>0001000=>[4,4]
[3,4,2,1,8,5,6,7]=>0001000=>0001000=>[4,4]
[5,4,8,3,6,7,1,2]=>0000000=>0000000=>[8]
[4,5,8,3,6,7,2,1]=>0000000=>0000000=>[8]
[2,1,5,8,4,6,7,3]=>0100000=>0000010=>[6,2]
[4,6,8,3,5,2,7,1]=>0000000=>0000000=>[8]
[5,7,8,3,2,4,1,6]=>0000000=>0000000=>[8]
[3,8,2,4,5,6,7,1]=>0000000=>0000000=>[8]
[4,3,1,6,5,8,7,2]=>0000000=>0000000=>[8]
[8,2,7,4,1,3,6,5]=>0000000=>0000000=>[8]
[3,1,5,2,4,8,7,6]=>0000100=>0010000=>[3,5]
[3,6,4,5,1,8,7,2]=>0000000=>0000000=>[8]
[4,3,6,1,2,8,7,5]=>0000000=>0000000=>[8]
[6,1,3,5,4,8,7,2]=>0000000=>0000000=>[8]
[1,7,3,8,4,6,2,5]=>1000000=>0000001=>[7,1]
[1,6,7,4,8,5,3,2]=>1000000=>0000001=>[7,1]
[8,1,2,5,4,6,3,7]=>0000000=>0000000=>[8]
[8,4,2,5,7,1,6,3]=>0000000=>0000000=>[8]
[1,8,5,3,7,4,6,2]=>1000000=>0000001=>[7,1]
[4,2,1,7,5,3,6,8]=>0000001=>1000000=>[1,7]
[1,4,8,6,5,7,2,3]=>1000000=>0000001=>[7,1]
[3,5,4,8,6,1,2,7]=>0000000=>0000000=>[8]
[4,3,5,8,1,7,2,6]=>0000000=>0000000=>[8]
[1,4,5,8,6,7,3,2]=>1000000=>0000001=>[7,1]
[1,7,6,5,8,3,4,2]=>1000000=>0000001=>[7,1]
[7,3,6,1,8,2,4,5]=>0000000=>0000000=>[8]
[7,6,4,5,8,1,3,2]=>0000000=>0000000=>[8]
[4,3,1,6,8,7,5,2]=>0000000=>0000000=>[8]
[4,3,1,8,5,6,7,2]=>0000000=>0000000=>[8]
[6,2,8,4,3,1,7,5]=>0000000=>0000000=>[8]
[7,1,6,2,3,4,5,8]=>0000001=>1000000=>[1,7]
[1,8,5,4,3,6,2,7]=>1000000=>0000001=>[7,1]
[1,8,3,6,5,2,7,4]=>1000000=>0000001=>[7,1]
[4,7,1,8,2,6,5,3]=>0000000=>0000000=>[8]
[1,4,8,3,5,7,6,2]=>1000000=>0000001=>[7,1]
[6,1,5,2,4,7,8,3]=>0000000=>0000000=>[8]
[4,1,8,5,2,7,6,3]=>0000000=>0000000=>[8]
[4,3,8,5,1,2,6,7]=>0000000=>0000000=>[8]
[4,1,8,2,3,7,5,6]=>0000000=>0000000=>[8]
[1,8,7,6,2,5,4,3]=>1000000=>0000001=>[7,1]
[1,2,3,4,5,10,9,8,7,6]=>111110000=>000011111=>[5,1,1,1,1,1]
[4,6,3,1,5,2,7,8]=>0000011=>1100000=>[1,1,6]
[6,2,7,4,5,1,3,8]=>0000001=>1000000=>[1,7]
[5,7,3,4,1,6,2,8]=>0000001=>1000000=>[1,7]
[4,2,8,1,5,6,7,3]=>0000000=>0000000=>[8]
[1,7,8,4,5,6,2,3]=>1000000=>0000001=>[7,1]
[1,6,8,4,5,2,7,3]=>1000000=>0000001=>[7,1]
[1,5,8,4,2,6,7,3]=>1000000=>0000001=>[7,1]
[1,5,3,8,2,6,7,4]=>1000000=>0000001=>[7,1]
[1,6,3,8,5,2,7,4]=>1000000=>0000001=>[7,1]
[1,7,3,8,5,6,2,4]=>1000000=>0000001=>[7,1]
[6,2,3,7,5,1,4,8]=>0000001=>1000000=>[1,7]
[4,2,6,1,5,3,7,8]=>0000011=>1100000=>[1,1,6]
[5,2,6,4,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[1,2,7,8,5,6,3,4]=>1100000=>0000011=>[6,1,1]
[1,2,6,8,5,3,7,4]=>1100000=>0000011=>[6,1,1]
[1,2,6,4,8,3,7,5]=>1100000=>0000011=>[6,1,1]
[8,7,3,2,1,6,5,4]=>0000000=>0000000=>[8]
[8,7,4,1,6,2,3,5]=>0000000=>0000000=>[8]
[1,8,3,2,6,4,5,7]=>1000000=>0000001=>[7,1]
[7,3,8,1,5,2,4,6]=>0000000=>0000000=>[8]
[3,1,7,2,6,4,5,8]=>0000001=>1000000=>[1,7]
[1,8,4,2,3,6,7,5]=>1000000=>0000001=>[7,1]
[4,1,7,2,3,6,8,5]=>0000000=>0000000=>[8]
[3,1,7,5,4,2,8,6]=>0000000=>0000000=>[8]
[3,2,6,7,4,1,8,5]=>0000000=>0000000=>[8]
[5,6,2,7,1,4,8,3]=>0000000=>0000000=>[8]
[6,4,2,8,1,5,7,3]=>0000000=>0000000=>[8]
[7,3,6,8,5,2,4,1]=>0000000=>0000000=>[8]
[2,7,8,3,6,5,1,4]=>0000000=>0000000=>[8]
[2,7,8,5,4,6,3,1]=>0000000=>0000000=>[8]
[2,6,8,3,4,7,1,5]=>0000000=>0000000=>[8]
[2,5,6,8,3,4,1,7]=>0000000=>0000000=>[8]
[2,7,8,3,6,1,4,5]=>0000000=>0000000=>[8]
[2,1,3,7,8,5,6,4]=>0110000=>0000110=>[5,1,2]
[5,1,2,4,8,7,3,6]=>0000000=>0000000=>[8]
[2,3,6,1,8,5,7,4]=>0000000=>0000000=>[8]
[5,2,6,1,7,8,4,3]=>0000000=>0000000=>[8]
[3,6,5,4,1,8,7,2]=>0000000=>0000000=>[8]
[4,1,8,2,5,7,3,6]=>0000000=>0000000=>[8]
[1,5,8,2,4,7,3,6]=>1000000=>0000001=>[7,1]
[6,2,1,4,7,8,3,5]=>0000000=>0000000=>[8]
[3,8,1,4,2,6,5,7]=>0000000=>0000000=>[8]
[8,3,4,2,1,6,5,7]=>0000000=>0000000=>[8]
[5,3,2,8,1,6,4,7]=>0000000=>0000000=>[8]
[2,4,5,8,3,6,1,7]=>0000000=>0000000=>[8]
[2,6,4,3,7,8,5,1]=>0000000=>0000000=>[8]
[7,4,1,8,3,2,5,6]=>0000000=>0000000=>[8]
[5,6,1,7,4,2,8,3]=>0000000=>0000000=>[8]
[1,3,8,6,2,7,4,5]=>1000000=>0000001=>[7,1]
[4,3,7,5,6,1,8,2]=>0000000=>0000000=>[8]
[6,7,3,8,4,1,2,5]=>0000000=>0000000=>[8]
[4,7,5,8,3,1,2,6]=>0000000=>0000000=>[8]
[5,7,3,1,6,8,4,2]=>0000000=>0000000=>[8]
[4,6,7,2,8,3,1,5]=>0000000=>0000000=>[8]
[4,5,6,7,3,1,8,2]=>0000000=>0000000=>[8]
[8,5,3,2,7,6,1,4]=>0000000=>0000000=>[8]
[7,5,4,6,2,8,1,3]=>0000000=>0000000=>[8]
[2,5,1,3,6,8,7,4]=>0000000=>0000000=>[8]
[7,3,8,5,2,1,4,6]=>0000000=>0000000=>[8]
[5,8,3,6,4,7,1,2]=>0000000=>0000000=>[8]
[4,1,6,3,2,5,8,7]=>0000010=>0100000=>[2,6]
[8,6,1,7,2,5,4,3]=>0000000=>0000000=>[8]
[8,7,6,1,2,3,5,4]=>0000000=>0000000=>[8]
[5,4,1,6,2,3,8,7]=>0000010=>0100000=>[2,6]
[5,8,7,6,1,2,3,4]=>0000000=>0000000=>[8]
[8,2,7,1,5,4,3,6]=>0000000=>0000000=>[8]
[2,1,6,3,8,5,4,7]=>0100000=>0000010=>[6,2]
[2,6,3,1,8,5,4,7]=>0000000=>0000000=>[8]
[4,6,2,8,5,1,3,7]=>0000000=>0000000=>[8]
[4,6,5,2,7,3,8,1]=>0000000=>0000000=>[8]
[3,1,6,2,4,8,7,5]=>0000000=>0000000=>[8]
[2,8,5,7,4,1,3,6]=>0000000=>0000000=>[8]
[6,4,8,3,5,7,1,2]=>0000000=>0000000=>[8]
[8,5,7,4,6,2,1,3]=>0000000=>0000000=>[8]
[4,1,8,5,6,3,2,7]=>0000000=>0000000=>[8]
[5,8,3,2,4,6,1,7]=>0000000=>0000000=>[8]
[2,8,4,1,5,3,7,6]=>0000000=>0000000=>[8]
[2,1,8,6,4,3,7,5]=>0100000=>0000010=>[6,2]
[3,6,7,1,8,5,2,4]=>0000000=>0000000=>[8]
[6,5,7,3,1,8,4,2]=>0000000=>0000000=>[8]
[6,1,5,7,2,4,8,3]=>0000000=>0000000=>[8]
[7,4,5,1,2,3,8,6]=>0000000=>0000000=>[8]
[8,4,7,6,2,1,5,3]=>0000000=>0000000=>[8]
[3,5,7,6,4,1,8,2]=>0000000=>0000000=>[8]
[5,4,1,7,6,2,8,3]=>0000000=>0000000=>[8]
[5,7,2,3,6,4,8,1]=>0000000=>0000000=>[8]
[6,1,8,2,7,3,4,5]=>0000000=>0000000=>[8]
[1,8,5,7,2,3,4,6]=>1000000=>0000001=>[7,1]
[8,1,5,7,2,3,6,4]=>0000000=>0000000=>[8]
[2,3,1,7,8,6,4,5]=>0010000=>0000100=>[5,3]
[5,4,1,6,3,8,7,2]=>0000000=>0000000=>[8]
[5,4,1,2,8,7,6,3]=>0000000=>0000000=>[8]
[5,6,3,7,8,4,2,1]=>0000000=>0000000=>[8]
[4,3,2,6,8,1,7,5]=>0000000=>0000000=>[8]
[1,5,4,2,7,8,3,6]=>1000000=>0000001=>[7,1]
[6,1,2,8,7,4,3,5]=>0000000=>0000000=>[8]
[3,6,5,8,4,7,1,2]=>0000000=>0000000=>[8]
[3,2,8,1,4,7,6,5]=>0000000=>0000000=>[8]
[6,4,3,8,2,5,7,1]=>0000000=>0000000=>[8]
[2,1,7,8,3,4,6,5]=>0100000=>0000010=>[6,2]
[5,6,1,8,2,7,4,3]=>0000000=>0000000=>[8]
[3,6,8,5,2,7,4,1]=>0000000=>0000000=>[8]
[2,1,6,5,4,8,3,7]=>0100000=>0000010=>[6,2]
[2,1,7,3,5,8,6,4]=>0100000=>0000010=>[6,2]
[7,8,1,2,4,5,6,3]=>0000000=>0000000=>[8]
[3,8,7,4,1,2,5,6]=>0000000=>0000000=>[8]
[4,3,8,7,1,6,5,2]=>0000000=>0000000=>[8]
[3,7,5,8,1,6,2,4]=>0000000=>0000000=>[8]
[4,2,7,5,8,3,6,1]=>0000000=>0000000=>[8]
[5,8,2,7,3,4,6,1]=>0000000=>0000000=>[8]
[5,7,2,1,8,3,6,4]=>0000000=>0000000=>[8]
[7,8,1,2,3,4,6,5]=>0000000=>0000000=>[8]
[5,6,2,4,3,1,8,7]=>0000010=>0100000=>[2,6]
[6,3,2,1,4,8,5,7]=>0000000=>0000000=>[8]
[8,7,6,2,4,3,1,5]=>0000000=>0000000=>[8]
[7,6,8,1,5,4,3,2]=>0000000=>0000000=>[8]
[7,6,1,8,5,4,3,2]=>0000000=>0000000=>[8]
[6,5,8,1,7,4,3,2]=>0000000=>0000000=>[8]
[4,3,8,7,6,1,5,2]=>0000000=>0000000=>[8]
[6,5,8,7,4,1,3,2]=>0000000=>0000000=>[8]
[5,4,8,7,6,3,1,2]=>0000000=>0000000=>[8]
[1,4,8,6,3,2,5,7]=>1000000=>0000001=>[7,1]
[1,6,3,8,5,2,4,7]=>1000000=>0000001=>[7,1]
[4,6,3,7,5,2,1,8]=>0000001=>1000000=>[1,7]
[3,7,2,6,5,4,1,8]=>0000001=>1000000=>[1,7]
[3,2,1,6,8,4,5,7]=>0010000=>0000100=>[5,3]
[3,5,7,4,8,6,1,2]=>0000000=>0000000=>[8]
[5,2,7,4,1,6,8,3]=>0000000=>0000000=>[8]
[4,5,8,2,1,7,6,3]=>0000000=>0000000=>[8]
[1,6,4,8,5,2,7,3]=>1000000=>0000001=>[7,1]
[7,4,1,5,3,8,2,6]=>0000000=>0000000=>[8]
[3,4,1,2,7,8,6,5]=>0001000=>0001000=>[4,4]
[3,1,2,4,7,6,8,5]=>0011000=>0001100=>[4,1,3]
[8,1,3,5,4,7,2,6]=>0000000=>0000000=>[8]
[7,1,4,3,5,2,8,6]=>0000000=>0000000=>[8]
[3,2,8,1,6,5,4,7]=>0000000=>0000000=>[8]
[6,8,4,1,2,5,3,7]=>0000000=>0000000=>[8]
[8,2,1,5,6,4,3,7]=>0000000=>0000000=>[8]
[4,7,1,8,2,5,3,6]=>0000000=>0000000=>[8]
[6,7,8,1,4,5,3,2]=>0000000=>0000000=>[8]
[3,2,5,4,7,8,1,6]=>0000000=>0000000=>[8]
[8,4,7,6,2,3,1,5]=>0000000=>0000000=>[8]
[6,1,2,8,7,3,5,4]=>0000000=>0000000=>[8]
[5,7,2,3,8,1,6,4]=>0000000=>0000000=>[8]
[3,5,2,6,1,8,7,4]=>0000000=>0000000=>[8]
[3,2,5,6,7,8,1,4]=>0000000=>0000000=>[8]
[6,4,1,2,8,7,3,5]=>0000000=>0000000=>[8]
[4,3,8,5,2,1,6,7]=>0000000=>0000000=>[8]
[7,5,4,2,3,8,1,6]=>0000000=>0000000=>[8]
[5,6,3,1,8,2,7,4]=>0000000=>0000000=>[8]
[4,5,2,1,6,8,3,7]=>0000000=>0000000=>[8]
[5,6,2,8,1,7,4,3]=>0000000=>0000000=>[8]
[1,5,6,3,4,8,2,7]=>1000000=>0000001=>[7,1]
[2,1,4,5,8,6,3,7]=>0100000=>0000010=>[6,2]
[1,8,3,4,7,6,2,5]=>1000000=>0000001=>[7,1]
[3,1,2,8,6,4,5,7]=>0010000=>0000100=>[5,3]
[2,5,6,1,8,4,3,7]=>0000000=>0000000=>[8]
[5,4,7,6,1,8,2,3]=>0000000=>0000000=>[8]
[3,5,6,8,4,7,2,1]=>0000000=>0000000=>[8]
[2,4,8,5,7,3,6,1]=>0000000=>0000000=>[8]
[5,3,7,8,4,6,2,1]=>0000000=>0000000=>[8]
[6,7,3,8,4,5,2,1]=>0000000=>0000000=>[8]
[2,5,3,7,6,8,1,4]=>0000000=>0000000=>[8]
[4,2,1,8,7,3,5,6]=>0000000=>0000000=>[8]
[8,7,4,6,2,3,1,5]=>0000000=>0000000=>[8]
[6,8,3,5,4,7,1,2]=>0000000=>0000000=>[8]
[1,4,6,3,7,2,8,5]=>1000000=>0000001=>[7,1]
[6,2,1,8,4,5,3,7]=>0000000=>0000000=>[8]
[4,7,3,8,5,2,1,6]=>0000000=>0000000=>[8]
[4,7,5,1,8,6,3,2]=>0000000=>0000000=>[8]
[6,2,4,1,7,5,8,3]=>0000000=>0000000=>[8]
[3,6,5,8,4,1,7,2]=>0000000=>0000000=>[8]
[5,7,3,1,6,4,8,2]=>0000000=>0000000=>[8]
[6,1,3,7,4,8,5,2]=>0000000=>0000000=>[8]
[3,1,5,4,2,8,6,7]=>0000100=>0010000=>[3,5]
[4,1,5,2,7,6,3,8]=>0000001=>1000000=>[1,7]
[6,2,7,1,4,8,5,3]=>0000000=>0000000=>[8]
[4,3,2,1,8,5,7,6]=>0001000=>0001000=>[4,4]
[7,4,3,2,8,1,6,5]=>0000000=>0000000=>[8]
[1,8,5,3,6,4,2,7]=>1000000=>0000001=>[7,1]
[8,1,6,2,7,4,3,5]=>0000000=>0000000=>[8]
[7,3,1,6,5,4,2,8]=>0000001=>1000000=>[1,7]
[2,8,5,6,1,4,3,7]=>0000000=>0000000=>[8]
[3,7,5,8,2,1,4,6]=>0000000=>0000000=>[8]
[6,5,8,4,1,3,7,2]=>0000000=>0000000=>[8]
[5,4,8,3,2,1,7,6]=>0000000=>0000000=>[8]
[2,4,7,1,3,6,5,8]=>0000001=>1000000=>[1,7]
[5,7,4,8,1,3,6,2]=>0000000=>0000000=>[8]
[5,1,7,8,2,4,6,3]=>0000000=>0000000=>[8]
[3,6,7,8,1,2,5,4]=>0000000=>0000000=>[8]
[4,6,7,2,8,1,3,5]=>0000000=>0000000=>[8]
[6,3,7,1,8,2,5,4]=>0000000=>0000000=>[8]
[5,7,1,4,8,2,6,3]=>0000000=>0000000=>[8]
[6,1,2,7,8,3,5,4]=>0000000=>0000000=>[8]
[3,6,4,7,8,1,2,5]=>0000000=>0000000=>[8]
[3,7,4,8,5,2,1,6]=>0000000=>0000000=>[8]
[4,8,2,1,7,5,3,6]=>0000000=>0000000=>[8]
[7,3,8,1,6,4,2,5]=>0000000=>0000000=>[8]
[2,8,7,1,6,3,5,4]=>0000000=>0000000=>[8]
[2,7,6,5,1,4,3,8]=>0000001=>1000000=>[1,7]
[3,8,7,6,2,1,5,4]=>0000000=>0000000=>[8]
[5,8,7,2,6,1,4,3]=>0000000=>0000000=>[8]
[7,3,8,6,5,1,2,4]=>0000000=>0000000=>[8]
[5,8,6,4,3,2,1,7]=>0000000=>0000000=>[8]
[8,1,2,3,4,7,6,5]=>0000000=>0000000=>[8]
[3,8,2,7,6,5,4,1]=>0000000=>0000000=>[8]
[4,2,8,7,6,5,3,1]=>0000000=>0000000=>[8]
[8,3,1,7,6,5,4,2]=>0000000=>0000000=>[8]
[5,2,8,7,6,4,3,1]=>0000000=>0000000=>[8]
[8,3,2,1,7,6,5,4]=>0000000=>0000000=>[8]
[8,4,1,7,6,5,3,2]=>0000000=>0000000=>[8]
[4,5,6,2,3,8,1,7]=>0000000=>0000000=>[8]
[3,2,7,4,5,8,1,6]=>0000000=>0000000=>[8]
[5,4,6,1,3,8,2,7]=>0000000=>0000000=>[8]
[2,4,1,7,5,8,3,6]=>0000000=>0000000=>[8]
[8,1,7,4,2,3,6,5]=>0000000=>0000000=>[8]
[3,5,8,1,2,4,7,6]=>0000000=>0000000=>[8]
[3,8,4,1,2,7,6,5]=>0000000=>0000000=>[8]
[6,4,1,3,2,7,8,5]=>0000000=>0000000=>[8]
[2,7,1,6,8,3,5,4]=>0000000=>0000000=>[8]
[8,5,3,2,6,1,7,4]=>0000000=>0000000=>[8]
[7,8,4,1,2,5,3,6]=>0000000=>0000000=>[8]
[6,1,4,2,7,5,3,8]=>0000001=>1000000=>[1,7]
[7,8,2,1,6,3,5,4]=>0000000=>0000000=>[8]
[1,2,8,3,6,4,7,5]=>1100000=>0000011=>[6,1,1]
[6,2,3,7,4,1,5,8]=>0000001=>1000000=>[1,7]
[6,2,4,1,7,3,5,8]=>0000001=>1000000=>[1,7]
[2,7,3,8,6,4,1,5]=>0000000=>0000000=>[8]
[1,8,3,7,6,4,5,2]=>1000000=>0000001=>[7,1]
[2,6,8,5,3,1,7,4]=>0000000=>0000000=>[8]
[5,6,2,1,7,3,8,4]=>0000000=>0000000=>[8]
[5,3,6,2,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,7,4,2,1,3,6,8]=>0000001=>1000000=>[1,7]
[6,4,2,1,5,3,7,8]=>0000011=>1100000=>[1,1,6]
[5,3,1,4,6,2,7,8]=>0000011=>1100000=>[1,1,6]
[1,6,4,2,8,7,3,5]=>1000000=>0000001=>[7,1]
[4,8,1,2,6,7,3,5]=>0000000=>0000000=>[8]
[3,1,2,4,6,8,7,5]=>0011000=>0001100=>[4,1,3]
[4,2,8,1,5,3,7,6]=>0000000=>0000000=>[8]
[4,3,8,5,7,6,1,2]=>0000000=>0000000=>[8]
[4,8,6,3,7,5,1,2]=>0000000=>0000000=>[8]
[3,8,6,5,2,7,1,4]=>0000000=>0000000=>[8]
[3,8,5,6,1,7,4,2]=>0000000=>0000000=>[8]
[4,2,7,8,1,3,6,5]=>0000000=>0000000=>[8]
[6,8,1,5,4,7,3,2]=>0000000=>0000000=>[8]
[2,6,4,3,1,5,8,7]=>0000010=>0100000=>[2,6]
[5,1,7,2,8,6,4,3]=>0000000=>0000000=>[8]
[6,8,2,5,4,7,1,3]=>0000000=>0000000=>[8]
[5,8,3,2,7,6,1,4]=>0000000=>0000000=>[8]
[4,8,3,2,1,7,6,5]=>0000000=>0000000=>[8]
[2,6,8,3,7,1,4,5]=>0000000=>0000000=>[8]
[6,8,3,7,2,1,5,4]=>0000000=>0000000=>[8]
[4,5,8,1,6,3,2,7]=>0000000=>0000000=>[8]
[6,8,4,7,1,5,3,2]=>0000000=>0000000=>[8]
[4,3,2,1,6,8,5,7]=>0001000=>0001000=>[4,4]
[2,4,1,3,8,7,6,5]=>0001000=>0001000=>[4,4]
[4,8,6,5,1,7,3,2]=>0000000=>0000000=>[8]
[6,5,3,1,7,2,8,4]=>0000000=>0000000=>[8]
[2,1,5,4,8,7,3,6]=>0100000=>0000010=>[6,2]
[2,3,8,5,4,1,6,7]=>0000000=>0000000=>[8]
[2,1,4,8,6,5,3,7]=>0100000=>0000010=>[6,2]
[4,3,2,8,7,6,1,5]=>0000000=>0000000=>[8]
[3,2,8,7,5,4,1,6]=>0000000=>0000000=>[8]
[5,4,2,6,3,1,8,7]=>0000010=>0100000=>[2,6]
[5,6,3,1,2,4,8,7]=>0000010=>0100000=>[2,6]
[3,8,4,1,5,7,2,6]=>0000000=>0000000=>[8]
[5,6,3,7,4,8,2,1]=>0000000=>0000000=>[8]
[8,5,2,6,1,7,3,4]=>0000000=>0000000=>[8]
[5,4,2,6,8,3,7,1]=>0000000=>0000000=>[8]
[7,6,8,5,1,4,2,3]=>0000000=>0000000=>[8]
[2,1,7,8,5,3,4,6]=>0100000=>0000010=>[6,2]
[4,1,8,2,6,5,3,7]=>0000000=>0000000=>[8]
[4,7,3,8,1,2,6,5]=>0000000=>0000000=>[8]
[3,8,1,2,4,6,5,7]=>0000000=>0000000=>[8]
[4,8,7,6,3,5,2,1]=>0000000=>0000000=>[8]
[3,8,7,6,5,2,4,1]=>0000000=>0000000=>[8]
[4,8,7,3,6,5,2,1]=>0000000=>0000000=>[8]
[4,8,7,6,3,2,5,1]=>0000000=>0000000=>[8]
[3,8,7,6,5,2,1,4]=>0000000=>0000000=>[8]
[7,5,8,3,6,2,1,4]=>0000000=>0000000=>[8]
[7,5,8,3,2,6,1,4]=>0000000=>0000000=>[8]
[7,5,8,3,2,1,6,4]=>0000000=>0000000=>[8]
[2,3,7,8,4,1,6,5]=>0000000=>0000000=>[8]
[2,1,7,5,8,4,6,3]=>0100000=>0000010=>[6,2]
[2,5,6,8,1,7,4,3]=>0000000=>0000000=>[8]
[4,2,8,6,1,7,3,5]=>0000000=>0000000=>[8]
[8,6,4,1,3,2,5,7]=>0000000=>0000000=>[8]
[8,1,3,2,6,5,4,7]=>0000000=>0000000=>[8]
[8,5,3,6,2,4,1,7]=>0000000=>0000000=>[8]
[8,4,1,2,6,5,3,7]=>0000000=>0000000=>[8]
[8,3,5,6,2,1,4,7]=>0000000=>0000000=>[8]
[4,1,8,2,3,7,6,5]=>0000000=>0000000=>[8]
[3,7,4,5,8,2,1,6]=>0000000=>0000000=>[8]
[5,3,8,7,4,6,1,2]=>0000000=>0000000=>[8]
[7,5,8,2,1,4,6,3]=>0000000=>0000000=>[8]
[7,4,8,3,2,6,1,5]=>0000000=>0000000=>[8]
[6,8,2,3,1,7,5,4]=>0000000=>0000000=>[8]
[7,4,3,2,6,8,5,1]=>0000000=>0000000=>[8]
[5,1,2,3,6,8,7,4]=>0000000=>0000000=>[8]
[2,4,7,3,8,1,6,5]=>0000000=>0000000=>[8]
[6,3,8,2,7,4,1,5]=>0000000=>0000000=>[8]
[8,2,1,3,6,4,7,5]=>0000000=>0000000=>[8]
[5,7,8,2,1,4,3,6]=>0000000=>0000000=>[8]
[3,5,1,7,8,4,2,6]=>0000000=>0000000=>[8]
[1,7,8,4,5,3,2,6]=>1000000=>0000001=>[7,1]
[3,2,4,8,6,7,1,5]=>0000000=>0000000=>[8]
[3,2,5,7,4,8,1,6]=>0000000=>0000000=>[8]
[8,4,7,1,3,2,5,6]=>0000000=>0000000=>[8]
[8,4,7,2,1,3,5,6]=>0000000=>0000000=>[8]
[6,4,2,1,3,7,8,5]=>0000000=>0000000=>[8]
[7,1,6,3,5,8,2,4]=>0000000=>0000000=>[8]
[5,3,6,7,8,4,2,1]=>0000000=>0000000=>[8]
[1,5,2,7,8,6,4,3]=>1000000=>0000001=>[7,1]
[4,1,7,5,2,6,8,3]=>0000000=>0000000=>[8]
[7,6,2,4,5,1,8,3]=>0000000=>0000000=>[8]
[8,1,4,5,2,6,7,3]=>0000000=>0000000=>[8]
[3,5,7,2,1,6,8,4]=>0000000=>0000000=>[8]
[3,5,2,4,7,6,1,8]=>0000001=>1000000=>[1,7]
[3,5,2,7,4,6,1,8]=>0000001=>1000000=>[1,7]
[3,2,5,7,4,6,1,8]=>0000001=>1000000=>[1,7]
[5,7,3,2,4,6,1,8]=>0000001=>1000000=>[1,7]
[3,7,5,2,4,1,6,8]=>0000001=>1000000=>[1,7]
[3,2,7,5,4,1,6,8]=>0000001=>1000000=>[1,7]
[1,7,3,5,2,4,6,8]=>1000001=>1000001=>[1,6,1]
[3,2,1,5,7,4,6,8]=>0010001=>1000100=>[1,4,3]
[3,5,7,2,1,4,6,8]=>0000001=>1000000=>[1,7]
[3,5,2,7,1,4,6,8]=>0000001=>1000000=>[1,7]
[3,2,5,7,4,1,6,8]=>0000001=>1000000=>[1,7]
[3,5,2,7,4,1,6,8]=>0000001=>1000000=>[1,7]
[3,5,7,2,4,1,6,8]=>0000001=>1000000=>[1,7]
[5,3,7,2,4,1,6,8]=>0000001=>1000000=>[1,7]
[5,3,2,4,7,1,6,8]=>0000001=>1000000=>[1,7]
[3,2,5,4,7,1,6,8]=>0000001=>1000000=>[1,7]
[3,5,2,4,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[3,5,2,1,4,7,6,8]=>0000101=>1010000=>[1,2,5]
[3,5,2,1,7,4,6,8]=>0000001=>1000000=>[1,7]
[5,3,1,7,2,4,6,8]=>0000001=>1000000=>[1,7]
[1,3,7,5,2,4,6,8]=>1000001=>1000001=>[1,6,1]
[3,7,2,1,5,4,6,8]=>0000001=>1000000=>[1,7]
[3,1,7,2,5,4,6,8]=>0000001=>1000000=>[1,7]
[1,7,5,3,2,4,6,8]=>1000001=>1000001=>[1,6,1]
[5,8,7,1,2,6,4,3]=>0000000=>0000000=>[8]
[6,8,2,1,7,5,4,3]=>0000000=>0000000=>[8]
[5,8,7,4,1,2,6,3]=>0000000=>0000000=>[8]
[1,8,5,4,2,7,6,3]=>1000000=>0000001=>[7,1]
[7,6,4,2,8,5,3,1]=>0000000=>0000000=>[8]
[7,6,4,8,5,1,2,3]=>0000000=>0000000=>[8]
[7,6,4,5,1,3,8,2]=>0000000=>0000000=>[8]
[1,6,7,5,3,8,4,2]=>1000000=>0000001=>[7,1]
[7,6,3,5,2,4,8,1]=>0000000=>0000000=>[8]
[7,6,4,2,5,1,8,3]=>0000000=>0000000=>[8]
[2,6,5,7,8,3,4,1]=>0000000=>0000000=>[8]
[5,2,3,4,8,6,1,7]=>0000000=>0000000=>[8]
[5,3,4,8,2,7,6,1]=>0000000=>0000000=>[8]
[5,3,8,2,4,1,7,6]=>0000000=>0000000=>[8]
[5,2,8,4,1,7,3,6]=>0000000=>0000000=>[8]
[6,4,2,5,1,8,7,3]=>0000000=>0000000=>[8]
[6,4,3,5,8,2,1,7]=>0000000=>0000000=>[8]
[6,3,5,4,8,2,7,1]=>0000000=>0000000=>[8]
[1,5,7,3,4,8,6,2]=>1000000=>0000001=>[7,1]
[5,8,4,1,3,7,6,2]=>0000000=>0000000=>[8]
[6,4,5,3,8,1,7,2]=>0000000=>0000000=>[8]
[6,4,3,8,5,7,2,1]=>0000000=>0000000=>[8]
[5,4,2,6,3,1,7,8]=>0000011=>1100000=>[1,1,6]
[4,6,5,3,7,1,2,8]=>0000001=>1000000=>[1,7]
[3,5,7,6,1,4,8,2]=>0000000=>0000000=>[8]
[3,6,5,7,4,8,1,2]=>0000000=>0000000=>[8]
[4,2,6,5,1,7,3,8]=>0000001=>1000000=>[1,7]
[4,3,5,7,2,1,6,8]=>0000001=>1000000=>[1,7]
[3,5,4,7,2,6,1,8]=>0000001=>1000000=>[1,7]
[3,4,7,6,8,1,2,5]=>0000000=>0000000=>[8]
[1,8,4,3,7,5,6,2]=>1000000=>0000001=>[7,1]
[5,2,8,6,4,7,3,1]=>0000000=>0000000=>[8]
[1,8,6,3,7,4,2,5]=>1000000=>0000001=>[7,1]
[1,8,6,5,7,2,3,4]=>1000000=>0000001=>[7,1]
[4,2,8,3,5,7,1,6]=>0000000=>0000000=>[8]
[1,3,7,2,6,5,8,4]=>1000000=>0000001=>[7,1]
[1,5,7,2,4,6,8,3]=>1000000=>0000001=>[7,1]
[1,3,6,4,2,5,8,7]=>1000010=>0100001=>[2,5,1]
[5,6,3,4,7,1,8,2]=>0000000=>0000000=>[8]
[3,5,2,7,4,1,8,6]=>0000000=>0000000=>[8]
[5,2,3,8,4,1,7,6]=>0000000=>0000000=>[8]
[7,5,3,4,8,2,1,6]=>0000000=>0000000=>[8]
[7,6,3,8,4,2,1,5]=>0000000=>0000000=>[8]
[7,2,8,5,1,6,3,4]=>0000000=>0000000=>[8]
[7,4,3,8,5,2,6,1]=>0000000=>0000000=>[8]
[7,2,8,5,1,3,4,6]=>0000000=>0000000=>[8]
[7,6,8,1,2,5,3,4]=>0000000=>0000000=>[8]
[1,5,3,7,6,8,4,2]=>1000000=>0000001=>[7,1]
[1,2,6,4,5,8,3,7]=>1100000=>0000011=>[6,1,1]
[1,2,7,4,8,5,3,6]=>1100000=>0000011=>[6,1,1]
[1,6,3,7,8,2,4,5]=>1000000=>0000001=>[7,1]
[3,2,6,7,8,1,4,5]=>0000000=>0000000=>[8]
[1,4,7,3,5,2,6,8]=>1000001=>1000001=>[1,6,1]
[3,8,4,7,6,1,5,2]=>0000000=>0000000=>[8]
[5,7,4,2,6,3,1,8]=>0000001=>1000000=>[1,7]
[6,1,3,7,4,2,5,8]=>0000001=>1000000=>[1,7]
[2,1,8,3,6,7,4,5]=>0100000=>0000010=>[6,2]
[5,7,1,4,2,6,3,8]=>0000001=>1000000=>[1,7]
[3,2,6,8,1,5,7,4]=>0000000=>0000000=>[8]
[7,8,5,4,1,6,3,2]=>0000000=>0000000=>[8]
[3,6,2,7,8,1,5,4]=>0000000=>0000000=>[8]
[5,7,8,4,1,6,3,2]=>0000000=>0000000=>[8]
[3,4,8,1,2,5,7,6]=>0000000=>0000000=>[8]
[6,3,1,8,2,7,4,5]=>0000000=>0000000=>[8]
[5,2,8,1,3,4,7,6]=>0000000=>0000000=>[8]
[3,2,1,6,4,7,8,5]=>0010000=>0000100=>[5,3]
[6,1,3,4,2,8,5,7]=>0000000=>0000000=>[8]
[3,2,6,1,5,7,8,4]=>0000000=>0000000=>[8]
[3,6,4,2,1,7,8,5]=>0000000=>0000000=>[8]
[1,8,3,2,6,7,5,4]=>1000000=>0000001=>[7,1]
[4,7,5,3,8,2,1,6]=>0000000=>0000000=>[8]
[1,4,7,6,8,2,3,5]=>1000000=>0000001=>[7,1]
[1,3,7,5,6,8,2,4]=>1000000=>0000001=>[7,1]
[3,2,7,1,6,8,4,5]=>0000000=>0000000=>[8]
[3,6,4,7,8,5,2,1]=>0000000=>0000000=>[8]
[6,3,5,8,7,4,1,2]=>0000000=>0000000=>[8]
[4,1,8,3,7,5,6,2]=>0000000=>0000000=>[8]
[4,7,2,8,5,6,3,1]=>0000000=>0000000=>[8]
[1,4,8,7,3,5,6,2]=>1000000=>0000001=>[7,1]
[3,2,8,7,1,5,6,4]=>0000000=>0000000=>[8]
[1,5,8,7,4,6,2,3]=>1000000=>0000001=>[7,1]
[4,8,6,7,5,3,2,1]=>0000000=>0000000=>[8]
[3,8,7,5,6,4,2,1]=>0000000=>0000000=>[8]
[8,3,2,1,5,6,4,7]=>0000000=>0000000=>[8]
[1,7,8,5,4,3,2,6]=>1000000=>0000001=>[7,1]
[1,2,6,7,8,4,3,5]=>1100000=>0000011=>[6,1,1]
[8,5,7,1,3,4,6,2]=>0000000=>0000000=>[8]
[4,7,2,1,5,3,8,6]=>0000000=>0000000=>[8]
[4,3,7,2,6,8,1,5]=>0000000=>0000000=>[8]
[1,7,8,2,6,4,5,3]=>1000000=>0000001=>[7,1]
[8,7,2,5,4,6,1,3]=>0000000=>0000000=>[8]
[8,7,1,2,4,5,6,3]=>0000000=>0000000=>[8]
[8,7,6,1,4,5,3,2]=>0000000=>0000000=>[8]
[8,7,5,6,1,4,3,2]=>0000000=>0000000=>[8]
[6,8,7,1,5,4,3,2]=>0000000=>0000000=>[8]
[8,5,7,6,1,4,3,2]=>0000000=>0000000=>[8]
[6,7,8,1,5,4,3,2]=>0000000=>0000000=>[8]
[8,5,6,7,1,4,3,2]=>0000000=>0000000=>[8]
[8,7,6,3,5,4,1,2]=>0000000=>0000000=>[8]
[8,7,4,5,6,1,3,2]=>0000000=>0000000=>[8]
[4,2,8,7,6,5,1,3]=>0000000=>0000000=>[8]
[7,5,8,1,6,4,3,2]=>0000000=>0000000=>[8]
[1,5,8,7,6,2,4,3]=>1000000=>0000001=>[7,1]
[7,5,8,4,1,6,3,2]=>0000000=>0000000=>[8]
[6,8,5,1,7,4,3,2]=>0000000=>0000000=>[8]
[1,6,8,7,2,5,4,3]=>1000000=>0000001=>[7,1]
[4,8,5,7,1,6,3,2]=>0000000=>0000000=>[8]
[5,4,3,6,7,1,8,2]=>0000000=>0000000=>[8]
[5,4,7,3,6,1,8,2]=>0000000=>0000000=>[8]
[4,8,7,6,3,1,5,2]=>0000000=>0000000=>[8]
[6,8,5,7,3,2,1,4]=>0000000=>0000000=>[8]
[6,8,5,3,7,2,1,4]=>0000000=>0000000=>[8]
[6,8,5,7,4,2,1,3]=>0000000=>0000000=>[8]
[2,1,8,7,6,3,4,5]=>0100000=>0000010=>[6,2]
[5,8,7,6,2,4,1,3]=>0000000=>0000000=>[8]
[6,8,2,7,5,1,4,3]=>0000000=>0000000=>[8]
[5,8,7,2,6,4,1,3]=>0000000=>0000000=>[8]
[6,8,7,5,2,4,1,3]=>0000000=>0000000=>[8]
[5,8,7,6,4,2,3,1]=>0000000=>0000000=>[8]
[2,3,6,1,7,5,8,4]=>0000000=>0000000=>[8]
[2,3,6,1,8,5,4,7]=>0000000=>0000000=>[8]
[2,4,1,6,7,5,8,3]=>0000000=>0000000=>[8]
[2,4,1,7,3,8,6,5]=>0000000=>0000000=>[8]
[2,4,5,3,7,1,8,6]=>0000000=>0000000=>[8]
[2,4,5,7,3,8,6,1]=>0000000=>0000000=>[8]
[2,4,6,3,1,8,5,7]=>0000000=>0000000=>[8]
[2,4,6,3,8,5,1,7]=>0000000=>0000000=>[8]
[2,4,7,3,1,5,8,6]=>0000000=>0000000=>[8]
[2,5,1,6,4,8,3,7]=>0000000=>0000000=>[8]
[2,5,1,7,4,3,8,6]=>0000000=>0000000=>[8]
[2,5,6,7,8,4,1,3]=>0000000=>0000000=>[8]
[2,5,6,8,4,3,1,7]=>0000000=>0000000=>[8]
[2,6,1,7,4,8,5,3]=>0000000=>0000000=>[8]
[7,6,4,8,2,1,3,5]=>0000000=>0000000=>[8]
[7,6,5,2,8,4,1,3]=>0000000=>0000000=>[8]
[7,6,3,8,2,4,1,5]=>0000000=>0000000=>[8]
[7,6,5,8,2,4,3,1]=>0000000=>0000000=>[8]
[6,8,4,7,2,5,3,1]=>0000000=>0000000=>[8]
[6,4,8,7,5,2,3,1]=>0000000=>0000000=>[8]
[6,8,4,2,7,5,3,1]=>0000000=>0000000=>[8]
[6,8,4,7,2,1,5,3]=>0000000=>0000000=>[8]
[6,8,4,7,3,5,2,1]=>0000000=>0000000=>[8]
[6,8,4,2,7,1,5,3]=>0000000=>0000000=>[8]
[6,4,2,8,7,5,3,1]=>0000000=>0000000=>[8]
[6,8,4,7,3,2,5,1]=>0000000=>0000000=>[8]
[6,8,4,2,1,7,5,3]=>0000000=>0000000=>[8]
[6,8,4,7,3,2,1,5]=>0000000=>0000000=>[8]
[6,8,5,7,1,4,3,2]=>0000000=>0000000=>[8]
[1,8,7,3,6,2,5,4]=>1000000=>0000001=>[7,1]
[5,8,7,2,3,6,1,4]=>0000000=>0000000=>[8]
[6,8,2,7,5,4,1,3]=>0000000=>0000000=>[8]
[6,8,3,7,5,2,1,4]=>0000000=>0000000=>[8]
[6,8,1,7,3,5,4,2]=>0000000=>0000000=>[8]
[6,8,4,7,3,1,5,2]=>0000000=>0000000=>[8]
[6,8,1,7,3,2,5,4]=>0000000=>0000000=>[8]
[3,8,2,7,6,5,1,4]=>0000000=>0000000=>[8]
[1,8,4,7,6,2,5,3]=>1000000=>0000001=>[7,1]
[3,8,1,7,6,2,5,4]=>0000000=>0000000=>[8]
[1,8,4,7,3,6,5,2]=>1000000=>0000001=>[7,1]
[4,8,5,7,1,2,6,3]=>0000000=>0000000=>[8]
[1,8,4,7,3,2,6,5]=>1000000=>0000001=>[7,1]
[6,8,5,2,7,4,1,3]=>0000000=>0000000=>[8]
[6,8,1,3,7,2,5,4]=>0000000=>0000000=>[8]
[2,8,1,3,7,6,5,4]=>0000000=>0000000=>[8]
[2,8,3,4,7,6,1,5]=>0000000=>0000000=>[8]
[6,8,1,4,2,7,5,3]=>0000000=>0000000=>[8]
[6,5,4,3,8,7,1,2]=>0000000=>0000000=>[8]
[3,1,7,2,8,5,6,4]=>0000000=>0000000=>[8]
[3,1,6,7,4,8,5,2]=>0000000=>0000000=>[8]
[3,1,5,7,8,4,6,2]=>0000000=>0000000=>[8]
[8,6,5,7,1,4,3,2]=>0000000=>0000000=>[8]
[6,4,8,2,7,5,1,3]=>0000000=>0000000=>[8]
[8,4,7,6,2,5,1,3]=>0000000=>0000000=>[8]
[3,4,5,6,8,7,1,2]=>0000000=>0000000=>[8]
[3,4,5,7,8,6,1,2]=>0000000=>0000000=>[8]
[3,4,5,8,7,6,1,2]=>0000000=>0000000=>[8]
[3,4,6,7,8,5,1,2]=>0000000=>0000000=>[8]
[6,4,7,3,5,2,1,8]=>0000001=>1000000=>[1,7]
[5,4,7,3,6,2,1,8]=>0000001=>1000000=>[1,7]
[5,8,3,6,7,2,1,4]=>0000000=>0000000=>[8]
[6,4,7,3,2,5,1,8]=>0000001=>1000000=>[1,7]
[6,3,7,8,2,4,1,5]=>0000000=>0000000=>[8]
[5,3,7,6,2,4,1,8]=>0000001=>1000000=>[1,7]
[7,5,8,2,6,4,1,3]=>0000000=>0000000=>[8]
[5,4,7,2,6,8,1,3]=>0000000=>0000000=>[8]
[5,4,3,2,6,8,1,7]=>0000000=>0000000=>[8]
[4,8,3,2,5,6,1,7]=>0000000=>0000000=>[8]
[5,3,7,2,6,4,1,8]=>0000001=>1000000=>[1,7]
[6,4,2,7,5,8,1,3]=>0000000=>0000000=>[8]
[7,5,8,4,1,2,6,3]=>0000000=>0000000=>[8]
[7,1,8,2,3,6,5,4]=>0000000=>0000000=>[8]
[7,3,8,4,6,2,1,5]=>0000000=>0000000=>[8]
[7,1,8,4,2,6,5,3]=>0000000=>0000000=>[8]
[7,1,8,3,6,2,5,4]=>0000000=>0000000=>[8]
[7,2,3,4,5,1,8,6]=>0000000=>0000000=>[8]
[2,7,3,4,1,5,6,8]=>0000001=>1000000=>[1,7]
[5,3,6,1,2,7,4,8]=>0000001=>1000000=>[1,7]
[10,8,6,4,2,1,3,5,7,9]=>000000000=>000000000=>[10]
[6,5,4,3,7,8,9,10,1,2]=>000000000=>000000000=>[10]
[3,8,1,4,5,6,7,2]=>0000000=>0000000=>[8]
[4,5,3,1,2,8,7,6]=>0000100=>0010000=>[3,5]
[4,5,3,1,2,6,8,7]=>0000110=>0110000=>[2,1,5]
[6,5,3,2,1,8,7,4]=>0000000=>0000000=>[8]
[4,5,2,1,8,7,6,3]=>0000000=>0000000=>[8]
[3,4,1,8,7,6,5,2]=>0000000=>0000000=>[8]
[8,1,2,4,5,6,7,3]=>0000000=>0000000=>[8]
[5,1,2,4,8,6,7,3]=>0000000=>0000000=>[8]
[4,1,3,8,5,6,7,2]=>0000000=>0000000=>[8]
[6,1,2,3,5,7,8,4]=>0000000=>0000000=>[8]
[5,1,3,8,4,6,7,2]=>0000000=>0000000=>[8]
[4,1,3,5,8,6,7,2]=>0000000=>0000000=>[8]
[7,5,2,8,6,3,4,1]=>0000000=>0000000=>[8]
[5,3,8,4,1,2,6,7]=>0000000=>0000000=>[8]
[6,3,5,8,4,1,2,7]=>0000000=>0000000=>[8]
[6,3,8,4,5,1,2,7]=>0000000=>0000000=>[8]
[8,5,1,7,4,6,2,3]=>0000000=>0000000=>[8]
[7,4,5,1,8,6,2,3]=>0000000=>0000000=>[8]
[4,2,7,5,8,6,3,1]=>0000000=>0000000=>[8]
[4,2,8,5,6,3,1,7]=>0000000=>0000000=>[8]
[4,2,8,5,6,7,3,1]=>0000000=>0000000=>[8]
[7,4,8,5,6,1,2,3]=>0000000=>0000000=>[8]
[7,5,8,6,1,2,3,4]=>0000000=>0000000=>[8]
[7,2,8,3,4,5,6,1]=>0000000=>0000000=>[8]
[5,2,4,8,6,7,3,1]=>0000000=>0000000=>[8]
[7,5,8,6,2,3,1,4]=>0000000=>0000000=>[8]
[7,4,8,5,6,2,3,1]=>0000000=>0000000=>[8]
[3,4,5,7,6,8,1,2]=>0000000=>0000000=>[8]
[4,8,2,5,1,3,7,6]=>0000000=>0000000=>[8]
[4,1,2,8,7,5,3,6]=>0000000=>0000000=>[8]
[3,1,7,6,8,2,4,5]=>0000000=>0000000=>[8]
[7,3,5,1,8,2,4,6]=>0000000=>0000000=>[8]
[7,8,3,1,5,2,4,6]=>0000000=>0000000=>[8]
[1,4,6,7,8,3,5,2]=>1000000=>0000001=>[7,1]
[1,5,6,3,7,8,4,2]=>1000000=>0000001=>[7,1]
[5,1,2,3,8,6,7,4]=>0000000=>0000000=>[8]
[2,8,5,3,1,4,6,7]=>0000000=>0000000=>[8]
[2,4,3,5,7,8,1,6]=>0000000=>0000000=>[8]
[2,6,3,7,8,1,4,5]=>0000000=>0000000=>[8]
[3,4,8,1,5,6,7,2]=>0000000=>0000000=>[8]
[3,5,1,7,4,8,6,2]=>0000000=>0000000=>[8]
[3,5,8,4,1,6,7,2]=>0000000=>0000000=>[8]
[3,6,1,8,5,4,7,2]=>0000000=>0000000=>[8]
[3,6,7,4,8,5,1,2]=>0000000=>0000000=>[8]
[3,6,8,4,5,1,7,2]=>0000000=>0000000=>[8]
[4,1,7,3,5,8,6,2]=>0000000=>0000000=>[8]
[4,6,3,1,8,5,7,2]=>0000000=>0000000=>[8]
[4,6,7,3,5,8,1,2]=>0000000=>0000000=>[8]
[4,6,8,3,5,1,7,2]=>0000000=>0000000=>[8]
[4,7,3,1,8,6,5,2]=>0000000=>0000000=>[8]
[5,1,6,7,4,8,3,2]=>0000000=>0000000=>[8]
[5,1,6,7,8,3,4,2]=>0000000=>0000000=>[8]
[5,6,7,8,4,1,3,2]=>0000000=>0000000=>[8]
[5,7,3,8,4,6,1,2]=>0000000=>0000000=>[8]
[5,7,8,4,3,6,1,2]=>0000000=>0000000=>[8]
[6,1,3,7,8,5,4,2]=>0000000=>0000000=>[8]
[6,1,8,4,5,3,7,2]=>0000000=>0000000=>[8]
[6,7,3,8,5,4,1,2]=>0000000=>0000000=>[8]
[7,1,3,4,8,6,5,2]=>0000000=>0000000=>[8]
[8,5,1,2,4,3,6,7]=>0000000=>0000000=>[8]
[8,5,1,4,2,3,6,7]=>0000000=>0000000=>[8]
[8,7,1,2,3,6,4,5]=>0000000=>0000000=>[8]
[5,6,8,7,2,3,1,4]=>0000000=>0000000=>[8]
[5,2,3,6,7,8,1,4]=>0000000=>0000000=>[8]
[4,2,8,7,5,3,1,6]=>0000000=>0000000=>[8]
[1,3,2,4,8,5,7,6]=>1011000=>0001101=>[4,1,2,1]
[1,6,3,2,5,7,8,4]=>1000000=>0000001=>[7,1]
[7,6,2,1,4,8,3,5]=>0000000=>0000000=>[8]
[2,6,5,1,8,7,3,4]=>0000000=>0000000=>[8]
[1,4,2,7,3,8,6,5]=>1000000=>0000001=>[7,1]
[1,2,7,3,8,6,5,4]=>1100000=>0000011=>[6,1,1]
[3,1,8,4,6,2,7,5]=>0000000=>0000000=>[8]
[1,5,2,3,8,7,4,6]=>1000000=>0000001=>[7,1]
[2,8,7,6,3,1,4,5]=>0000000=>0000000=>[8]
[8,7,6,2,1,4,3,5]=>0000000=>0000000=>[8]
[8,2,7,4,1,5,3,6]=>0000000=>0000000=>[8]
[8,7,3,1,4,2,6,5]=>0000000=>0000000=>[8]
[1,2,5,3,4,8,7,6]=>1100100=>0010011=>[3,3,1,1]
[1,2,3,8,4,7,6,5]=>1110000=>0000111=>[5,1,1,1]
[1,6,2,3,7,5,8,4]=>1000000=>0000001=>[7,1]
[1,4,8,2,6,3,7,5]=>1000000=>0000001=>[7,1]
[8,4,1,7,3,2,5,6]=>0000000=>0000000=>[8]
[1,8,7,3,2,4,6,5]=>1000000=>0000001=>[7,1]
[3,4,1,6,5,7,2,8]=>0000001=>1000000=>[1,7]
[3,5,1,6,2,8,7,4]=>0000000=>0000000=>[8]
[5,4,3,6,1,7,2,8]=>0000001=>1000000=>[1,7]
[4,8,7,2,1,6,5,3]=>0000000=>0000000=>[8]
[6,2,1,8,7,5,4,3]=>0000000=>0000000=>[8]
[5,8,7,6,3,2,4,1]=>0000000=>0000000=>[8]
[5,4,7,2,8,1,6,3]=>0000000=>0000000=>[8]
[2,1,5,8,3,7,4,6]=>0100000=>0000010=>[6,2]
[1,2,3,5,8,7,4,6]=>1110000=>0000111=>[5,1,1,1]
[6,1,2,7,8,4,3,5]=>0000000=>0000000=>[8]
[5,1,4,8,2,7,3,6]=>0000000=>0000000=>[8]
[1,2,5,7,8,6,3,4]=>1100000=>0000011=>[6,1,1]
[2,1,3,4,8,5,7,6]=>0111000=>0001110=>[4,1,1,2]
[6,2,5,1,7,3,8,4]=>0000000=>0000000=>[8]
[2,4,8,1,3,7,5,6]=>0000000=>0000000=>[8]
[2,5,1,8,6,3,7,4]=>0000000=>0000000=>[8]
[2,1,3,7,4,8,6,5]=>0110000=>0000110=>[5,1,2]
[2,6,8,5,1,7,3,4]=>0000000=>0000000=>[8]
[1,3,2,7,8,5,4,6]=>1010000=>0000101=>[5,2,1]
[7,1,2,3,6,8,4,5]=>0000000=>0000000=>[8]
[5,1,2,3,8,4,7,6]=>0000000=>0000000=>[8]
[4,1,2,3,8,7,5,6]=>0001000=>0001000=>[4,4]
[2,3,1,8,5,4,7,6]=>0010000=>0000100=>[5,3]
[2,3,8,4,1,5,7,6]=>0000000=>0000000=>[8]
[5,3,1,8,7,2,4,6]=>0000000=>0000000=>[8]
[1,3,8,4,2,7,6,5]=>1000000=>0000001=>[7,1]
[1,2,3,8,5,7,4,6]=>1110000=>0000111=>[5,1,1,1]
[6,1,7,2,5,8,3,4]=>0000000=>0000000=>[8]
[4,5,1,8,7,2,3,6]=>0000000=>0000000=>[8]
[1,4,2,8,5,3,7,6]=>1000000=>0000001=>[7,1]
[7,8,6,5,2,1,4,3]=>0000000=>0000000=>[8]
[8,6,7,5,2,1,4,3]=>0000000=>0000000=>[8]
[6,7,8,2,1,5,4,3]=>0000000=>0000000=>[8]
[8,7,5,6,2,1,4,3]=>0000000=>0000000=>[8]
[4,2,5,1,8,7,3,6]=>0000000=>0000000=>[8]
[7,2,4,5,8,3,6,1]=>0000000=>0000000=>[8]
[2,4,7,8,6,1,5,3]=>0000000=>0000000=>[8]
[4,2,7,1,5,6,8,3]=>0000000=>0000000=>[8]
[3,2,5,8,1,6,7,4]=>0000000=>0000000=>[8]
[8,1,4,3,2,5,6,7]=>0000000=>0000000=>[8]
[1,7,3,2,4,5,6,8]=>1000001=>1000001=>[1,6,1]
[1,6,3,2,4,5,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,3,8,4,2,5,6,7]=>1000000=>0000001=>[7,1]
[5,1,8,2,4,3,6,7]=>0000000=>0000000=>[8]
[1,7,2,4,5,8,6,3]=>1000000=>0000001=>[7,1]
[1,3,8,2,6,4,5,7]=>1000000=>0000001=>[7,1]
[6,1,2,7,4,3,8,5]=>0000000=>0000000=>[8]
[7,6,1,3,8,2,4,5]=>0000000=>0000000=>[8]
[5,4,1,2,3,8,6,7]=>0000100=>0010000=>[3,5]
[6,7,8,5,2,4,1,3]=>0000000=>0000000=>[8]
[3,4,5,8,2,1,7,6]=>0000000=>0000000=>[8]
[3,4,6,2,7,1,5,8]=>0000001=>1000000=>[1,7]
[3,4,6,1,5,2,7,8]=>0000011=>1100000=>[1,1,6]
[3,4,7,2,1,6,5,8]=>0000001=>1000000=>[1,7]
[3,5,2,6,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[3,5,2,7,1,6,4,8]=>0000001=>1000000=>[1,7]
[3,5,2,1,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[3,5,6,4,8,2,1,7]=>0000000=>0000000=>[8]
[3,5,6,4,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[3,5,6,8,4,2,1,7]=>0000000=>0000000=>[8]
[3,5,6,1,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[3,5,7,4,2,8,1,6]=>0000000=>0000000=>[8]
[3,5,7,4,2,1,6,8]=>0000001=>1000000=>[1,7]
[3,5,7,4,8,1,6,2]=>0000000=>0000000=>[8]
[3,5,7,1,4,6,2,8]=>0000001=>1000000=>[1,7]
[3,5,8,1,4,6,7,2]=>0000000=>0000000=>[8]
[3,6,2,4,8,1,7,5]=>0000000=>0000000=>[8]
[3,6,2,7,8,5,1,4]=>0000000=>0000000=>[8]
[3,6,2,7,8,1,4,5]=>0000000=>0000000=>[8]
[3,6,2,1,5,4,7,8]=>0000011=>1100000=>[1,1,6]
[3,6,7,8,5,1,2,4]=>0000000=>0000000=>[8]
[3,6,7,8,1,5,2,4]=>0000000=>0000000=>[8]
[3,7,2,4,5,8,1,6]=>0000000=>0000000=>[8]
[3,7,2,4,8,1,6,5]=>0000000=>0000000=>[8]
[3,7,2,8,5,6,1,4]=>0000000=>0000000=>[8]
[3,7,2,1,5,6,4,8]=>0000001=>1000000=>[1,7]
[3,7,8,4,5,1,6,2]=>0000000=>0000000=>[8]
[3,8,2,4,1,6,7,5]=>0000000=>0000000=>[8]
[8,1,5,4,3,6,7,2]=>0000000=>0000000=>[8]
[4,1,7,3,5,6,8,2]=>0000000=>0000000=>[8]
[6,1,7,3,8,4,5,2]=>0000000=>0000000=>[8]
[4,1,3,6,7,8,5,2]=>0000000=>0000000=>[8]
[3,5,2,4,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[2,3,7,8,1,6,5,4]=>0000000=>0000000=>[8]
[2,6,5,8,1,3,7,4]=>0000000=>0000000=>[8]
[6,4,7,5,8,2,3,1]=>0000000=>0000000=>[8]
[6,7,4,1,8,2,3,5]=>0000000=>0000000=>[8]
[6,7,8,1,4,2,5,3]=>0000000=>0000000=>[8]
[5,2,6,1,4,8,3,7]=>0000000=>0000000=>[8]
[7,2,3,5,8,1,4,6]=>0000000=>0000000=>[8]
[2,4,7,5,8,1,3,6]=>0000000=>0000000=>[8]
[2,3,6,5,1,8,7,4]=>0000000=>0000000=>[8]
[2,3,4,8,1,5,7,6]=>0000000=>0000000=>[8]
[2,7,8,5,1,4,6,3]=>0000000=>0000000=>[8]
[2,3,7,5,8,1,4,6]=>0000000=>0000000=>[8]
[2,3,6,8,5,1,7,4]=>0000000=>0000000=>[8]
[7,6,4,5,1,8,2,3]=>0000000=>0000000=>[8]
[7,4,6,8,1,5,2,3]=>0000000=>0000000=>[8]
[2,6,7,8,5,3,1,4]=>0000000=>0000000=>[8]
[2,5,6,1,4,8,3,7]=>0000000=>0000000=>[8]
[2,6,4,8,5,7,3,1]=>0000000=>0000000=>[8]
[2,5,8,1,4,6,7,3]=>0000000=>0000000=>[8]
[7,2,3,4,8,1,6,5]=>0000000=>0000000=>[8]
[3,2,5,7,8,1,6,4]=>0000000=>0000000=>[8]
[6,4,1,7,8,2,3,5]=>0000000=>0000000=>[8]
[5,7,6,1,2,8,3,4]=>0000000=>0000000=>[8]
[5,6,8,1,2,4,7,3]=>0000000=>0000000=>[8]
[6,2,3,4,5,8,1,7]=>0000000=>0000000=>[8]
[4,7,1,3,8,2,6,5]=>0000000=>0000000=>[8]
[5,4,1,6,7,8,2,3]=>0000000=>0000000=>[8]
[5,7,1,8,6,2,3,4]=>0000000=>0000000=>[8]
[7,3,5,1,8,2,6,4]=>0000000=>0000000=>[8]
[5,6,7,3,8,2,1,4]=>0000000=>0000000=>[8]
[5,7,3,2,8,6,1,4]=>0000000=>0000000=>[8]
[5,7,8,3,1,6,2,4]=>0000000=>0000000=>[8]
[5,8,3,2,1,6,7,4]=>0000000=>0000000=>[8]
[6,2,7,3,8,5,1,4]=>0000000=>0000000=>[8]
[6,2,3,7,8,5,1,4]=>0000000=>0000000=>[8]
[1,5,8,3,2,6,7,4]=>1000000=>0000001=>[7,1]
[1,6,7,8,5,2,3,4]=>1000000=>0000001=>[7,1]
[1,6,7,8,4,2,3,5]=>1000000=>0000001=>[7,1]
[1,2,6,8,4,3,7,5]=>1100000=>0000011=>[6,1,1]
[1,8,3,4,2,6,7,5]=>1000000=>0000001=>[7,1]
[6,2,7,8,4,1,3,5]=>0000000=>0000000=>[8]
[6,2,3,7,8,1,4,5]=>0000000=>0000000=>[8]
[4,5,7,1,8,6,2,3]=>0000000=>0000000=>[8]
[4,5,7,8,2,6,1,3]=>0000000=>0000000=>[8]
[4,6,2,8,5,1,7,3]=>0000000=>0000000=>[8]
[4,6,7,1,8,5,2,3]=>0000000=>0000000=>[8]
[4,7,2,8,5,6,1,3]=>0000000=>0000000=>[8]
[4,8,2,1,5,6,7,3]=>0000000=>0000000=>[8]
[1,2,8,4,5,3,7,6]=>1100000=>0000011=>[6,1,1]
[1,2,3,7,8,5,4,6]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,5,4,7,6]=>1110000=>0000111=>[5,1,1,1]
[1,7,3,8,5,4,2,6]=>1000000=>0000001=>[7,1]
[5,2,7,4,8,6,1,3]=>0000000=>0000000=>[8]
[5,6,2,7,8,1,4,3]=>0000000=>0000000=>[8]
[5,8,2,4,1,6,7,3]=>0000000=>0000000=>[8]
[6,2,1,7,8,5,4,3]=>0000000=>0000000=>[8]
[6,7,2,8,5,4,1,3]=>0000000=>0000000=>[8]
[6,8,2,4,5,1,7,3]=>0000000=>0000000=>[8]
[3,2,5,6,8,1,4,7]=>0000000=>0000000=>[8]
[7,1,3,2,8,4,5,6]=>0000000=>0000000=>[8]
[7,1,6,3,8,2,4,5]=>0000000=>0000000=>[8]
[6,1,5,8,2,3,4,7]=>0000000=>0000000=>[8]
[8,1,6,7,4,2,3,5]=>0000000=>0000000=>[8]
[6,1,5,8,2,3,7,4]=>0000000=>0000000=>[8]
[4,1,7,2,5,8,3,6]=>0000000=>0000000=>[8]
[8,1,6,3,4,7,2,5]=>0000000=>0000000=>[8]
[8,1,7,3,2,5,6,4]=>0000000=>0000000=>[8]
[4,1,8,2,5,6,7,3]=>0000000=>0000000=>[8]
[3,8,1,2,7,5,4,6]=>0000000=>0000000=>[8]
[8,4,7,1,3,2,6,5]=>0000000=>0000000=>[8]
[8,5,7,3,1,2,6,4]=>0000000=>0000000=>[8]
[3,8,1,2,4,5,7,6]=>0000000=>0000000=>[8]
[7,6,2,1,8,4,3,5]=>0000000=>0000000=>[8]
[8,5,2,3,6,1,4,7]=>0000000=>0000000=>[8]
[8,5,7,1,4,3,2,6]=>0000000=>0000000=>[8]
[3,6,1,4,2,8,5,7]=>0000000=>0000000=>[8]
[7,6,8,1,4,5,2,3]=>0000000=>0000000=>[8]
[3,7,1,4,2,8,6,5]=>0000000=>0000000=>[8]
[5,4,3,8,2,1,7,6]=>0000000=>0000000=>[8]
[5,8,7,3,2,1,6,4]=>0000000=>0000000=>[8]
[2,3,7,1,6,8,5,4]=>0000000=>0000000=>[8]
[2,6,1,5,7,4,8,3]=>0000000=>0000000=>[8]
[2,3,6,1,8,4,7,5]=>0000000=>0000000=>[8]
[3,5,1,4,6,7,8,2]=>0000000=>0000000=>[8]
[4,5,6,2,1,7,8,3]=>0000000=>0000000=>[8]
[5,2,4,7,6,3,8,1]=>0000000=>0000000=>[8]
[8,7,6,1,4,3,5,2]=>0000000=>0000000=>[8]
[8,7,6,1,3,4,5,2]=>0000000=>0000000=>[8]
[8,7,1,4,5,6,3,2]=>0000000=>0000000=>[8]
[8,1,5,6,7,4,3,2]=>0000000=>0000000=>[8]
[5,8,3,4,1,6,2,7]=>0000000=>0000000=>[8]
[4,2,6,1,7,8,5,3]=>0000000=>0000000=>[8]
[1,5,2,6,7,8,4,3]=>1000000=>0000001=>[7,1]
[1,5,6,7,4,8,2,3]=>1000000=>0000001=>[7,1]
[4,2,7,8,5,6,1,3]=>0000000=>0000000=>[8]
[5,6,2,7,3,8,4,1]=>0000000=>0000000=>[8]
[3,7,2,8,4,1,5,6]=>0000000=>0000000=>[8]
[3,5,2,4,7,8,6,1]=>0000000=>0000000=>[8]
[5,1,3,8,2,4,6,7]=>0000000=>0000000=>[8]
[1,8,7,6,3,4,5,2]=>1000000=>0000001=>[7,1]
[8,5,7,6,3,2,1,4]=>0000000=>0000000=>[8]
[8,7,5,3,1,6,4,2]=>0000000=>0000000=>[8]
[7,8,1,4,5,6,3,2]=>0000000=>0000000=>[8]
[4,2,8,3,5,1,7,6]=>0000000=>0000000=>[8]
[4,2,7,8,1,6,5,3]=>0000000=>0000000=>[8]
[5,1,3,4,2,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,2,7,3,1,6,5,8]=>0000001=>1000000=>[1,7]
[2,3,4,5,8,1,7,6]=>0000000=>0000000=>[8]
[4,1,5,3,6,7,8,2]=>0000000=>0000000=>[8]
[5,1,6,3,4,7,8,2]=>0000000=>0000000=>[8]
[2,1,7,5,3,8,6,4]=>0100000=>0000010=>[6,2]
[3,2,1,6,4,5,7,8]=>0010011=>1100100=>[1,1,3,3]
[3,8,1,2,5,4,7,6]=>0000000=>0000000=>[8]
[7,5,8,6,3,2,1,4]=>0000000=>0000000=>[8]
[6,4,2,1,8,5,3,7]=>0000000=>0000000=>[8]
[5,3,8,4,2,1,6,7]=>0000000=>0000000=>[8]
[7,4,5,2,1,8,6,3]=>0000000=>0000000=>[8]
[6,3,8,4,5,2,1,7]=>0000000=>0000000=>[8]
[7,4,8,5,6,2,1,3]=>0000000=>0000000=>[8]
[7,3,8,4,5,6,2,1]=>0000000=>0000000=>[8]
[1,8,7,2,6,5,4,3]=>1000000=>0000001=>[7,1]
[1,8,7,6,2,3,4,5]=>1000000=>0000001=>[7,1]
[1,8,2,5,6,7,4,3]=>1000000=>0000001=>[7,1]
[1,2,8,3,4,5,7,6]=>1100000=>0000011=>[6,1,1]
[7,4,1,2,8,3,5,6]=>0000000=>0000000=>[8]
[6,4,1,2,8,3,5,7]=>0000000=>0000000=>[8]
[4,8,1,2,3,7,5,6]=>0000000=>0000000=>[8]
[6,5,1,2,3,8,4,7]=>0000000=>0000000=>[8]
[1,8,5,2,3,7,4,6]=>1000000=>0000001=>[7,1]
[6,5,1,2,7,3,8,4]=>0000000=>0000000=>[8]
[7,6,4,1,8,2,3,5]=>0000000=>0000000=>[8]
[7,6,3,1,8,2,4,5]=>0000000=>0000000=>[8]
[7,5,4,1,8,2,3,6]=>0000000=>0000000=>[8]
[7,6,1,4,8,2,3,5]=>0000000=>0000000=>[8]
[1,2,8,5,3,7,4,6]=>1100000=>0000011=>[6,1,1]
[1,2,7,3,8,6,4,5]=>1100000=>0000011=>[6,1,1]
[7,5,1,6,8,2,3,4]=>0000000=>0000000=>[8]
[4,1,2,8,6,3,7,5]=>0000000=>0000000=>[8]
[5,4,1,6,2,7,8,3]=>0000000=>0000000=>[8]
[6,5,3,1,8,2,4,7]=>0000000=>0000000=>[8]
[3,8,1,6,7,2,4,5]=>0000000=>0000000=>[8]
[6,5,3,7,1,2,8,4]=>0000000=>0000000=>[8]
[7,1,4,2,6,8,3,5]=>0000000=>0000000=>[8]
[1,2,6,8,3,5,4,7]=>1100000=>0000011=>[6,1,1]
[1,2,3,7,8,6,4,5]=>1110000=>0000111=>[5,1,1,1]
[1,6,8,5,2,7,3,4]=>1000000=>0000001=>[7,1]
[1,4,8,2,3,7,6,5]=>1000000=>0000001=>[7,1]
[1,2,8,3,5,7,6,4]=>1100000=>0000011=>[6,1,1]
[4,5,1,7,6,8,2,3]=>0000000=>0000000=>[8]
[1,4,2,5,6,8,7,3]=>1000000=>0000001=>[7,1]
[8,2,7,3,1,5,6,4]=>0000000=>0000000=>[8]
[7,2,1,8,4,5,6,3]=>0000000=>0000000=>[8]
[4,2,7,1,3,8,6,5]=>0000000=>0000000=>[8]
[8,2,6,3,4,7,1,5]=>0000000=>0000000=>[8]
[7,2,3,4,1,8,6,5]=>0000000=>0000000=>[8]
[4,2,8,1,5,6,3,7]=>0000000=>0000000=>[8]
[8,2,7,3,1,4,5,6]=>0000000=>0000000=>[8]
[5,3,1,6,2,7,8,4]=>0000000=>0000000=>[8]
[5,2,1,3,6,7,8,4]=>0000000=>0000000=>[8]
[6,5,3,8,7,2,1,4]=>0000000=>0000000=>[8]
[5,4,8,7,3,2,1,6]=>0000000=>0000000=>[8]
[6,4,3,8,7,2,1,5]=>0000000=>0000000=>[8]
[5,6,3,1,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,2,6,1,4,3,7,8]=>0000011=>1100000=>[1,1,6]
[5,8,3,1,4,6,7,2]=>0000000=>0000000=>[8]
[6,2,7,4,1,5,3,8]=>0000001=>1000000=>[1,7]
[6,7,3,8,1,5,2,4]=>0000000=>0000000=>[8]
[6,7,3,4,1,5,2,8]=>0000001=>1000000=>[1,7]
[6,7,8,1,5,4,2,3]=>0000000=>0000000=>[8]
[4,5,7,8,2,1,6,3]=>0000000=>0000000=>[8]
[7,2,3,8,1,6,5,4]=>0000000=>0000000=>[8]
[7,2,3,8,5,1,6,4]=>0000000=>0000000=>[8]
[7,2,3,1,5,6,4,8]=>0000001=>1000000=>[1,7]
[7,2,8,4,1,6,5,3]=>0000000=>0000000=>[8]
[7,2,8,4,5,1,6,3]=>0000000=>0000000=>[8]
[4,6,3,8,1,5,7,2]=>0000000=>0000000=>[8]
[4,6,7,3,8,1,2,5]=>0000000=>0000000=>[8]
[4,6,7,8,1,5,3,2]=>0000000=>0000000=>[8]
[4,6,7,1,5,2,3,8]=>0000001=>1000000=>[1,7]
[4,6,8,3,1,5,7,2]=>0000000=>0000000=>[8]
[4,7,3,8,5,1,6,2]=>0000000=>0000000=>[8]
[4,7,3,8,1,6,5,2]=>0000000=>0000000=>[8]
[4,1,8,2,7,3,5,6]=>0000000=>0000000=>[8]
[1,8,4,2,7,3,5,6]=>1000000=>0000001=>[7,1]
[7,4,1,2,6,8,3,5]=>0000000=>0000000=>[8]
[8,7,1,2,4,5,3,6]=>0000000=>0000000=>[8]
[5,4,1,2,7,8,3,6]=>0000000=>0000000=>[8]
[1,5,2,8,3,4,7,6]=>1000000=>0000001=>[7,1]
[7,1,2,5,3,6,8,4]=>0000000=>0000000=>[8]
[1,8,2,5,6,3,7,4]=>1000000=>0000001=>[7,1]
[1,5,2,4,6,7,8,3]=>1000000=>0000001=>[7,1]
[3,1,8,2,5,4,6,7]=>0000000=>0000000=>[8]
[3,1,7,5,8,2,4,6]=>0000000=>0000000=>[8]
[1,7,3,2,8,4,5,6]=>1000000=>0000001=>[7,1]
[1,6,4,2,3,5,8,7]=>1000010=>0100001=>[2,5,1]
[1,7,4,2,3,5,8,6]=>1000000=>0000001=>[7,1]
[1,7,4,2,3,6,8,5]=>1000000=>0000001=>[7,1]
[1,2,7,3,8,4,6,5]=>1100000=>0000011=>[6,1,1]
[7,1,3,4,5,8,2,6]=>0000000=>0000000=>[8]
[1,8,7,6,3,2,4,5]=>1000000=>0000001=>[7,1]
[1,7,4,5,2,6,8,3]=>1000000=>0000001=>[7,1]
[1,4,8,5,6,2,7,3]=>1000000=>0000001=>[7,1]
[3,2,1,8,7,4,5,6]=>0010000=>0000100=>[5,3]
[3,2,8,7,6,1,5,4]=>0000000=>0000000=>[8]
[6,5,8,7,3,2,1,4]=>0000000=>0000000=>[8]
[4,6,2,8,5,3,7,1]=>0000000=>0000000=>[8]
[5,3,8,4,6,2,7,1]=>0000000=>0000000=>[8]
[4,6,2,7,1,8,5,3]=>0000000=>0000000=>[8]
[6,2,5,3,8,4,7,1]=>0000000=>0000000=>[8]
[4,6,5,3,8,2,7,1]=>0000000=>0000000=>[8]
[5,7,8,4,3,2,1,6]=>0000000=>0000000=>[8]
[4,6,8,7,3,2,1,5]=>0000000=>0000000=>[8]
[2,4,8,7,6,5,1,3]=>0000000=>0000000=>[8]
[4,7,6,8,3,2,1,5]=>0000000=>0000000=>[8]
[4,6,7,8,3,2,1,5]=>0000000=>0000000=>[8]
[3,5,6,8,7,2,1,4]=>0000000=>0000000=>[8]
[1,4,8,7,6,3,5,2]=>1000000=>0000001=>[7,1]
[2,5,4,7,3,8,1,6]=>0000000=>0000000=>[8]
[2,4,6,1,5,8,3,7]=>0000000=>0000000=>[8]
[2,5,4,8,6,7,3,1]=>0000000=>0000000=>[8]
[3,4,1,7,6,8,5,2]=>0000000=>0000000=>[8]
[3,6,1,7,8,4,2,5]=>0000000=>0000000=>[8]
[4,3,6,2,8,1,7,5]=>0000000=>0000000=>[8]
[5,3,4,7,2,8,1,6]=>0000000=>0000000=>[8]
[4,5,7,2,1,8,3,6]=>0000000=>0000000=>[8]
[4,5,8,2,1,6,7,3]=>0000000=>0000000=>[8]
[3,6,1,7,2,5,8,4]=>0000000=>0000000=>[8]
[6,3,7,8,2,5,1,4]=>0000000=>0000000=>[8]
[6,7,4,8,2,5,3,1]=>0000000=>0000000=>[8]
[3,5,1,4,7,2,8,6]=>0000000=>0000000=>[8]
[4,7,8,5,6,2,1,3]=>0000000=>0000000=>[8]
[3,5,1,4,8,7,2,6]=>0000000=>0000000=>[8]
[4,5,6,3,8,2,1,7]=>0000000=>0000000=>[8]
[4,2,6,3,7,8,1,5]=>0000000=>0000000=>[8]
[4,2,7,3,5,8,1,6]=>0000000=>0000000=>[8]
[5,1,2,7,8,6,4,3]=>0000000=>0000000=>[8]
[4,1,2,7,8,6,3,5]=>0000000=>0000000=>[8]
[4,1,8,7,2,6,3,5]=>0000000=>0000000=>[8]
[5,1,8,2,7,6,3,4]=>0000000=>0000000=>[8]
[7,1,6,2,8,3,4,5]=>0000000=>0000000=>[8]
[4,5,2,8,7,3,1,6]=>0000000=>0000000=>[8]
[8,2,1,7,4,6,3,5]=>0000000=>0000000=>[8]
[4,5,2,8,7,1,6,3]=>0000000=>0000000=>[8]
[4,2,5,7,3,1,8,6]=>0000000=>0000000=>[8]
[4,2,8,7,1,3,6,5]=>0000000=>0000000=>[8]
[8,2,1,7,3,5,4,6]=>0000000=>0000000=>[8]
[5,2,6,3,8,7,1,4]=>0000000=>0000000=>[8]
[5,2,3,8,7,1,4,6]=>0000000=>0000000=>[8]
[6,1,2,8,3,7,4,5]=>0000000=>0000000=>[8]
[5,6,7,3,8,1,2,4]=>0000000=>0000000=>[8]
[8,1,7,3,5,4,2,6]=>0000000=>0000000=>[8]
[7,1,6,8,5,2,3,4]=>0000000=>0000000=>[8]
[8,1,7,3,5,2,6,4]=>0000000=>0000000=>[8]
[6,2,3,8,7,5,1,4]=>0000000=>0000000=>[8]
[3,8,5,7,2,4,1,6]=>0000000=>0000000=>[8]
[3,6,5,8,2,1,7,4]=>0000000=>0000000=>[8]
[7,6,2,3,4,1,8,5]=>0000000=>0000000=>[8]
[4,8,6,7,1,2,3,5]=>0000000=>0000000=>[8]
[8,5,7,3,1,6,2,4]=>0000000=>0000000=>[8]
[3,8,6,1,4,7,2,5]=>0000000=>0000000=>[8]
[3,7,6,8,2,5,1,4]=>0000000=>0000000=>[8]
[8,6,2,3,1,5,7,4]=>0000000=>0000000=>[8]
[3,8,7,1,2,5,6,4]=>0000000=>0000000=>[8]
[3,4,8,2,5,6,7,1]=>0000000=>0000000=>[8]
[6,3,4,8,7,5,1,2]=>0000000=>0000000=>[8]
[2,1,8,5,6,7,3,4]=>0100000=>0000010=>[6,2]
[8,3,2,5,6,7,1,4]=>0000000=>0000000=>[8]
[4,8,6,7,3,5,2,1]=>0000000=>0000000=>[8]
[4,3,1,2,6,7,8,5]=>0001000=>0001000=>[4,4]
[7,4,6,5,8,3,2,1]=>0000000=>0000000=>[8]
[2,5,8,6,7,3,1,4]=>0000000=>0000000=>[8]
[1,4,6,5,2,7,3,8]=>1000001=>1000001=>[1,6,1]
[2,3,4,1,8,7,5,6]=>0001000=>0001000=>[4,4]
[4,2,6,5,1,8,7,3]=>0000000=>0000000=>[8]
[7,8,4,2,1,5,6,3]=>0000000=>0000000=>[8]
[7,8,2,3,6,1,5,4]=>0000000=>0000000=>[8]
[2,1,7,8,4,5,6,3]=>0100000=>0000010=>[6,2]
[8,6,2,7,1,3,5,4]=>0000000=>0000000=>[8]
[5,8,2,3,4,7,6,1]=>0000000=>0000000=>[8]
[2,5,1,4,3,7,6,8]=>0000101=>1010000=>[1,2,5]
[1,4,5,3,7,2,8,6]=>1000000=>0000001=>[7,1]
[5,1,4,3,7,2,8,6]=>0000000=>0000000=>[8]
[1,6,7,4,3,2,8,5]=>1000000=>0000001=>[7,1]
[2,6,7,3,1,4,5,8]=>0000001=>1000000=>[1,7]
[5,1,4,6,7,2,3,8]=>0000001=>1000000=>[1,7]
[2,6,4,3,1,8,5,7]=>0000000=>0000000=>[8]
[1,6,5,2,3,4,8,7]=>1000010=>0100001=>[2,5,1]
[7,8,2,1,5,4,3,6]=>0000000=>0000000=>[8]
[7,8,1,2,3,6,4,5]=>0000000=>0000000=>[8]
[1,4,7,8,5,2,3,6]=>1000000=>0000001=>[7,1]
[1,3,2,6,5,8,4,7]=>1010000=>0000101=>[5,2,1]
[2,1,5,7,8,4,3,6]=>0100000=>0000010=>[6,2]
[3,1,7,2,6,5,8,4]=>0000000=>0000000=>[8]
[1,3,2,7,5,4,8,6]=>1010000=>0000101=>[5,2,1]
[1,4,5,8,6,2,3,7]=>1000000=>0000001=>[7,1]
[1,6,7,2,3,5,8,4]=>1000000=>0000001=>[7,1]
[2,4,1,8,6,5,3,7]=>0000000=>0000000=>[8]
[2,3,4,6,8,5,7,1]=>0000000=>0000000=>[8]
[3,6,2,4,7,5,8,1]=>0000000=>0000000=>[8]
[4,3,5,8,7,2,6,1]=>0000000=>0000000=>[8]
[5,1,6,3,7,8,4,2]=>0000000=>0000000=>[8]
[4,2,6,7,5,1,8,3]=>0000000=>0000000=>[8]
[6,4,7,5,8,3,2,1]=>0000000=>0000000=>[8]
[3,6,7,5,8,1,4,2]=>0000000=>0000000=>[8]
[3,2,7,4,6,1,8,5]=>0000000=>0000000=>[8]
[8,2,4,1,6,7,5,3]=>0000000=>0000000=>[8]
[3,4,8,7,6,1,5,2]=>0000000=>0000000=>[8]
[4,3,8,7,6,2,5,1]=>0000000=>0000000=>[8]
[4,3,7,5,8,6,2,1]=>0000000=>0000000=>[8]
[3,4,7,5,8,6,1,2]=>0000000=>0000000=>[8]
[2,7,5,6,8,3,4,1]=>0000000=>0000000=>[8]
[7,8,3,4,6,5,1,2]=>0000000=>0000000=>[8]
[2,1,7,6,8,4,5,3]=>0100000=>0000010=>[6,2]
[3,5,4,7,6,1,8,2]=>0000000=>0000000=>[8]
[6,5,4,2,7,8,3,1]=>0000000=>0000000=>[8]
[2,6,8,5,7,4,3,1]=>0000000=>0000000=>[8]
[2,1,8,6,7,5,4,3]=>0100000=>0000010=>[6,2]
[2,5,3,1,6,4,7,8]=>0000011=>1100000=>[1,1,6]
[7,5,4,2,3,1,8,6]=>0000000=>0000000=>[8]
[6,3,2,4,5,8,1,7]=>0000000=>0000000=>[8]
[3,5,4,2,8,6,1,7]=>0000000=>0000000=>[8]
[5,6,8,7,3,2,1,4]=>0000000=>0000000=>[8]
[6,4,5,3,2,8,1,7]=>0000000=>0000000=>[8]
[4,2,5,7,3,1,6,8]=>0000001=>1000000=>[1,7]
[7,4,1,3,2,6,8,5]=>0000000=>0000000=>[8]
[1,6,4,2,3,7,8,5]=>1000000=>0000001=>[7,1]
[1,4,5,3,8,2,6,7]=>1000000=>0000001=>[7,1]
[6,2,5,1,3,7,4,8]=>0000001=>1000000=>[1,7]
[7,6,5,8,1,2,4,3]=>0000000=>0000000=>[8]
[5,7,4,1,3,6,2,8]=>0000001=>1000000=>[1,7]
[4,3,8,1,6,5,7,2]=>0000000=>0000000=>[8]
[3,2,8,1,6,7,4,5]=>0000000=>0000000=>[8]
[7,2,6,3,8,1,5,4]=>0000000=>0000000=>[8]
[7,2,8,1,6,3,5,4]=>0000000=>0000000=>[8]
[7,4,8,2,3,5,6,1]=>0000000=>0000000=>[8]
[7,4,8,1,5,6,2,3]=>0000000=>0000000=>[8]
[7,2,8,1,6,5,4,3]=>0000000=>0000000=>[8]
[8,6,5,7,2,1,4,3]=>0000000=>0000000=>[8]
[2,4,7,8,5,6,3,1]=>0000000=>0000000=>[8]
[2,8,1,3,5,6,7,4]=>0000000=>0000000=>[8]
[3,8,7,5,2,6,4,1]=>0000000=>0000000=>[8]
[1,8,7,3,4,6,5,2]=>1000000=>0000001=>[7,1]
[2,8,1,4,5,7,6,3]=>0000000=>0000000=>[8]
[1,2,6,7,8,3,5,4]=>1100000=>0000011=>[6,1,1]
[1,2,6,8,7,3,4,5]=>1100000=>0000011=>[6,1,1]
[3,7,8,1,5,6,2,4]=>0000000=>0000000=>[8]
[4,1,3,7,6,8,5,2]=>0000000=>0000000=>[8]
[6,5,7,8,1,4,3,2]=>0000000=>0000000=>[8]
[3,1,8,6,7,5,4,2]=>0000000=>0000000=>[8]
[2,8,3,1,7,5,4,6]=>0000000=>0000000=>[8]
[4,1,2,6,7,5,3,8]=>0000001=>1000000=>[1,7]
[1,2,5,3,8,6,4,7]=>1100000=>0000011=>[6,1,1]
[5,8,7,6,2,1,3,4]=>0000000=>0000000=>[8]
[3,6,8,2,5,7,4,1]=>0000000=>0000000=>[8]
[3,2,8,5,6,1,7,4]=>0000000=>0000000=>[8]
[3,4,8,1,5,7,6,2]=>0000000=>0000000=>[8]
[4,5,6,2,7,3,8,1]=>0000000=>0000000=>[8]
[3,5,8,7,4,6,2,1]=>0000000=>0000000=>[8]
[3,5,7,6,2,4,8,1]=>0000000=>0000000=>[8]
[1,6,8,7,4,5,3,2]=>1000000=>0000001=>[7,1]
[1,3,5,6,8,7,2,4]=>1000000=>0000001=>[7,1]
[3,5,6,7,8,2,4,1]=>0000000=>0000000=>[8]
[8,5,6,7,2,4,3,1]=>0000000=>0000000=>[8]
[7,8,4,5,1,6,3,2]=>0000000=>0000000=>[8]
[4,5,6,8,3,7,2,1]=>0000000=>0000000=>[8]
[8,1,4,3,6,5,2,7]=>0000000=>0000000=>[8]
[8,1,2,3,6,5,4,7]=>0000000=>0000000=>[8]
[8,1,2,3,7,6,5,4]=>0000000=>0000000=>[8]
[2,8,1,6,7,5,3,4]=>0000000=>0000000=>[8]
[4,8,5,2,7,1,6,3]=>0000000=>0000000=>[8]
[3,7,8,4,6,2,1,5]=>0000000=>0000000=>[8]
[8,3,1,5,7,6,2,4]=>0000000=>0000000=>[8]
[4,5,2,8,6,7,1,3]=>0000000=>0000000=>[8]
[8,4,5,1,3,2,6,7]=>0000000=>0000000=>[8]
[8,1,6,7,2,5,4,3]=>0000000=>0000000=>[8]
[5,4,1,3,2,8,7,6]=>0000100=>0010000=>[3,5]
[3,2,7,4,1,6,5,8]=>0000001=>1000000=>[1,7]
[5,7,3,2,1,6,4,8]=>0000001=>1000000=>[1,7]
[7,6,5,1,3,4,2,8]=>0000001=>1000000=>[1,7]
[7,6,5,1,4,2,3,8]=>0000001=>1000000=>[1,7]
[1,7,6,3,2,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,5,7,2,4,3,6,8]=>1000001=>1000001=>[1,6,1]
[7,1,6,8,2,4,5,3]=>0000000=>0000000=>[8]
[5,8,1,3,4,7,2,6]=>0000000=>0000000=>[8]
[5,8,6,2,3,1,4,7]=>0000000=>0000000=>[8]
[3,8,2,7,6,4,1,5]=>0000000=>0000000=>[8]
[1,6,8,4,7,5,3,2]=>1000000=>0000001=>[7,1]
[6,5,8,3,7,4,2,1]=>0000000=>0000000=>[8]
[2,6,8,5,4,7,3,1]=>0000000=>0000000=>[8]
[2,7,4,6,8,5,3,1]=>0000000=>0000000=>[8]
[6,4,7,8,3,5,2,1]=>0000000=>0000000=>[8]
[7,3,4,2,6,1,8,5]=>0000000=>0000000=>[8]
[2,3,7,4,6,1,8,5]=>0000000=>0000000=>[8]
[7,5,4,2,6,3,8,1]=>0000000=>0000000=>[8]
[5,4,7,2,6,1,8,3]=>0000000=>0000000=>[8]
[5,2,7,4,6,1,8,3]=>0000000=>0000000=>[8]
[5,2,4,1,7,6,8,3]=>0000000=>0000000=>[8]
[4,2,7,5,6,1,8,3]=>0000000=>0000000=>[8]
[4,2,7,5,6,3,8,1]=>0000000=>0000000=>[8]
[2,6,4,3,7,5,8,1]=>0000000=>0000000=>[8]
[4,3,7,5,8,6,1,2]=>0000000=>0000000=>[8]
[6,7,4,8,3,5,2,1]=>0000000=>0000000=>[8]
[3,6,8,5,4,7,1,2]=>0000000=>0000000=>[8]
[6,7,5,8,2,4,3,1]=>0000000=>0000000=>[8]
[2,5,4,1,7,8,6,3]=>0000000=>0000000=>[8]
[1,6,3,2,5,8,7,4]=>1000000=>0000001=>[7,1]
[1,6,8,3,2,4,7,5]=>1000000=>0000001=>[7,1]
[1,8,7,6,4,2,3,5]=>1000000=>0000001=>[7,1]
[8,6,1,2,4,5,7,3]=>0000000=>0000000=>[8]
[1,8,6,7,3,4,5,2]=>1000000=>0000001=>[7,1]
[1,7,3,8,2,4,6,5]=>1000000=>0000001=>[7,1]
[8,4,3,1,5,6,7,2]=>0000000=>0000000=>[8]
[1,8,7,6,3,4,2,5]=>1000000=>0000001=>[7,1]
[7,1,3,8,4,5,2,6]=>0000000=>0000000=>[8]
[1,8,5,3,7,6,2,4]=>1000000=>0000001=>[7,1]
[3,5,2,6,1,4,8,7]=>0000010=>0100000=>[2,6]
[4,5,7,2,3,8,6,1]=>0000000=>0000000=>[8]
[4,5,7,2,3,8,1,6]=>0000000=>0000000=>[8]
[4,5,6,2,3,1,8,7]=>0000010=>0100000=>[2,6]
[4,5,6,2,1,3,8,7]=>0000010=>0100000=>[2,6]
[4,5,6,1,3,2,8,7]=>0000010=>0100000=>[2,6]
[4,5,6,3,1,2,8,7]=>0000010=>0100000=>[2,6]
[4,5,7,3,2,8,1,6]=>0000000=>0000000=>[8]
[4,6,7,3,8,2,5,1]=>0000000=>0000000=>[8]
[4,6,7,3,8,2,1,5]=>0000000=>0000000=>[8]
[4,5,7,3,1,8,2,6]=>0000000=>0000000=>[8]
[3,5,1,7,4,8,2,6]=>0000000=>0000000=>[8]
[2,1,5,7,4,8,3,6]=>0100000=>0000010=>[6,2]
[4,5,7,1,3,8,6,2]=>0000000=>0000000=>[8]
[4,6,7,3,8,1,5,2]=>0000000=>0000000=>[8]
[5,6,7,8,3,1,4,2]=>0000000=>0000000=>[8]
[4,6,7,1,8,3,5,2]=>0000000=>0000000=>[8]
[3,6,1,7,8,4,5,2]=>0000000=>0000000=>[8]
[2,1,6,7,8,4,5,3]=>0100000=>0000010=>[6,2]
[2,1,6,7,8,4,3,5]=>0100000=>0000010=>[6,2]
[4,6,7,1,8,3,2,5]=>0000000=>0000000=>[8]
[5,6,7,8,1,3,2,4]=>0000000=>0000000=>[8]
[4,6,7,2,8,3,5,1]=>0000000=>0000000=>[8]
[3,6,2,7,8,4,5,1]=>0000000=>0000000=>[8]
[3,6,2,7,8,4,1,5]=>0000000=>0000000=>[8]
[3,4,2,1,7,8,5,6]=>0001000=>0001000=>[4,4]
[4,6,7,2,8,5,3,1]=>0000000=>0000000=>[8]
[4,6,7,2,8,5,1,3]=>0000000=>0000000=>[8]
[4,5,7,1,2,8,6,3]=>0000000=>0000000=>[8]
[2,1,6,7,8,3,5,4]=>0100000=>0000010=>[6,2]
[3,6,1,7,8,2,5,4]=>0000000=>0000000=>[8]
[4,6,7,1,8,2,5,3]=>0000000=>0000000=>[8]
[5,6,7,8,1,2,4,3]=>0000000=>0000000=>[8]
[5,6,7,8,2,4,1,3]=>0000000=>0000000=>[8]
[5,6,7,8,2,4,3,1]=>0000000=>0000000=>[8]
[3,6,1,7,8,5,2,4]=>0000000=>0000000=>[8]
[2,1,6,7,8,5,3,4]=>0100000=>0000010=>[6,2]
[7,4,5,1,2,8,3,6]=>0000000=>0000000=>[8]
[6,4,5,1,2,3,8,7]=>0000010=>0100000=>[2,6]
[5,4,6,1,2,3,8,7]=>0000010=>0100000=>[2,6]
[4,6,5,1,2,3,8,7]=>0000010=>0100000=>[2,6]
[5,6,4,1,2,3,8,7]=>0000010=>0100000=>[2,6]
[7,5,4,1,2,8,3,6]=>0000000=>0000000=>[8]
[8,6,4,1,7,2,3,5]=>0000000=>0000000=>[8]
[2,1,7,5,3,8,4,6]=>0100000=>0000010=>[6,2]
[2,1,8,6,7,3,4,5]=>0100000=>0000010=>[6,2]
[5,7,6,8,1,2,3,4]=>0000000=>0000000=>[8]
[6,4,7,1,8,2,3,5]=>0000000=>0000000=>[8]
[8,4,6,1,7,2,3,5]=>0000000=>0000000=>[8]
[8,3,1,6,7,2,4,5]=>0000000=>0000000=>[8]
[4,3,1,2,7,8,5,6]=>0001000=>0001000=>[4,4]
[7,4,8,1,6,2,3,5]=>0000000=>0000000=>[8]
[4,5,8,1,2,7,3,6]=>0000000=>0000000=>[8]
[5,6,8,7,1,2,3,4]=>0000000=>0000000=>[8]
[8,5,7,6,1,2,3,4]=>0000000=>0000000=>[8]
[3,8,1,7,6,2,4,5]=>0000000=>0000000=>[8]
[6,8,7,5,1,2,3,4]=>0000000=>0000000=>[8]
[6,4,7,3,8,5,1,2]=>0000000=>0000000=>[8]
[5,4,2,7,6,1,3,8]=>0000001=>1000000=>[1,7]
[5,4,2,7,6,1,8,3]=>0000000=>0000000=>[8]
[5,4,3,7,6,8,1,2]=>0000000=>0000000=>[8]
[5,4,3,7,8,6,1,2]=>0000000=>0000000=>[8]
[5,4,3,8,6,7,1,2]=>0000000=>0000000=>[8]
[5,4,3,6,8,7,1,2]=>0000000=>0000000=>[8]
[5,4,2,6,7,1,8,3]=>0000000=>0000000=>[8]
[5,3,2,6,1,7,4,8]=>0000001=>1000000=>[1,7]
[5,3,2,6,1,7,8,4]=>0000000=>0000000=>[8]
[5,3,2,6,1,8,7,4]=>0000000=>0000000=>[8]
[5,4,2,6,8,1,7,3]=>0000000=>0000000=>[8]
[6,4,8,2,5,1,7,3]=>0000000=>0000000=>[8]
[5,4,2,8,6,1,3,7]=>0000000=>0000000=>[8]
[5,3,2,6,1,8,4,7]=>0000000=>0000000=>[8]
[6,3,8,2,1,5,4,7]=>0000000=>0000000=>[8]
[7,8,3,2,1,5,4,6]=>0000000=>0000000=>[8]
[7,8,3,2,1,5,6,4]=>0000000=>0000000=>[8]
[6,3,8,2,1,5,7,4]=>0000000=>0000000=>[8]
[5,3,2,8,1,6,7,4]=>0000000=>0000000=>[8]
[5,4,2,7,8,1,6,3]=>0000000=>0000000=>[8]
[5,3,2,7,1,8,6,4]=>0000000=>0000000=>[8]
[5,3,2,7,1,6,4,8]=>0000001=>1000000=>[1,7]
[6,3,7,2,1,5,4,8]=>0000001=>1000000=>[1,7]
[6,3,7,2,1,5,8,4]=>0000000=>0000000=>[8]
[6,3,7,2,1,8,5,4]=>0000000=>0000000=>[8]
[6,5,7,8,2,1,4,3]=>0000000=>0000000=>[8]
[6,3,7,2,1,4,8,5]=>0000000=>0000000=>[8]
[5,3,2,7,1,4,8,6]=>0000000=>0000000=>[8]
[5,4,2,8,7,1,3,6]=>0000000=>0000000=>[8]
[7,8,4,2,6,1,3,5]=>0000000=>0000000=>[8]
[7,8,3,2,1,6,4,5]=>0000000=>0000000=>[8]
[6,3,8,2,1,7,4,5]=>0000000=>0000000=>[8]
[5,3,2,8,1,7,4,6]=>0000000=>0000000=>[8]
[4,3,2,1,8,7,5,6]=>0001000=>0001000=>[4,4]
[4,3,2,1,7,5,8,6]=>0001000=>0001000=>[4,4]
[4,3,2,1,7,5,6,8]=>0001001=>1001000=>[1,3,4]
[5,3,2,8,1,4,7,6]=>0000000=>0000000=>[8]
[6,3,8,2,1,4,7,5]=>0000000=>0000000=>[8]
[7,8,3,2,1,4,6,5]=>0000000=>0000000=>[8]
[4,3,2,1,8,5,6,7]=>0001000=>0001000=>[4,4]
[7,8,5,6,1,2,4,3]=>0000000=>0000000=>[8]
[7,8,4,1,6,2,5,3]=>0000000=>0000000=>[8]
[1,6,8,3,2,7,5,4]=>1000000=>0000001=>[7,1]
[6,1,8,3,2,7,5,4]=>0000000=>0000000=>[8]
[7,8,1,3,2,6,5,4]=>0000000=>0000000=>[8]
[7,8,3,1,2,6,5,4]=>0000000=>0000000=>[8]
[7,8,2,3,1,6,5,4]=>0000000=>0000000=>[8]
[7,8,2,1,3,6,5,4]=>0000000=>0000000=>[8]
[7,8,1,2,3,6,5,4]=>0000000=>0000000=>[8]
[1,5,2,8,3,7,6,4]=>1000000=>0000001=>[7,1]
[5,1,2,8,3,7,6,4]=>0000000=>0000000=>[8]
[5,2,1,8,3,7,6,4]=>0000000=>0000000=>[8]
[6,2,8,1,3,7,5,4]=>0000000=>0000000=>[8]
[6,2,8,4,7,1,5,3]=>0000000=>0000000=>[8]
[6,3,8,4,7,5,1,2]=>0000000=>0000000=>[8]
[2,6,8,3,1,7,5,4]=>0000000=>0000000=>[8]
[2,5,1,8,3,7,6,4]=>0000000=>0000000=>[8]
[1,2,5,8,3,7,6,4]=>1100000=>0000011=>[6,1,1]
[2,5,3,8,1,7,6,4]=>0000000=>0000000=>[8]
[2,5,4,8,7,1,6,3]=>0000000=>0000000=>[8]
[3,5,4,8,7,6,1,2]=>0000000=>0000000=>[8]
[5,3,4,8,7,6,1,2]=>0000000=>0000000=>[8]
[5,2,4,8,7,1,6,3]=>0000000=>0000000=>[8]
[5,2,3,8,1,7,6,4]=>0000000=>0000000=>[8]
[4,1,2,3,8,7,6,5]=>0001000=>0001000=>[4,4]
[1,4,2,3,8,7,6,5]=>1001000=>0001001=>[4,3,1]
[4,1,3,2,8,7,6,5]=>0001000=>0001000=>[4,4]
[6,3,8,1,2,7,5,4]=>0000000=>0000000=>[8]
[5,3,1,8,2,7,6,4]=>0000000=>0000000=>[8]
[5,1,3,8,2,7,6,4]=>0000000=>0000000=>[8]
[1,5,3,8,2,7,6,4]=>1000000=>0000001=>[7,1]
[1,5,4,8,7,2,6,3]=>1000000=>0000001=>[7,1]
[5,1,4,8,7,2,6,3]=>0000000=>0000000=>[8]
[5,4,1,8,7,2,6,3]=>0000000=>0000000=>[8]
[6,5,8,7,1,2,4,3]=>0000000=>0000000=>[8]
[5,6,8,7,3,4,1,2]=>0000000=>0000000=>[8]
[5,6,8,7,2,1,4,3]=>0000000=>0000000=>[8]
[4,5,1,8,7,2,6,3]=>0000000=>0000000=>[8]
[4,1,5,8,7,2,6,3]=>0000000=>0000000=>[8]
[1,3,5,8,2,7,6,4]=>1000000=>0000001=>[7,1]
[3,1,5,8,2,7,6,4]=>0000000=>0000000=>[8]
[3,6,8,2,1,7,5,4]=>0000000=>0000000=>[8]
[4,6,8,3,7,5,1,2]=>0000000=>0000000=>[8]
[4,5,3,8,7,6,1,2]=>0000000=>0000000=>[8]
[3,5,2,8,1,7,6,4]=>0000000=>0000000=>[8]
[3,1,4,2,8,7,6,5]=>0001000=>0001000=>[4,4]
[3,2,5,8,1,7,6,4]=>0000000=>0000000=>[8]
[4,2,5,8,7,1,6,3]=>0000000=>0000000=>[8]
[4,3,5,8,7,6,1,2]=>0000000=>0000000=>[8]
[2,4,5,8,7,1,6,3]=>0000000=>0000000=>[8]
[2,3,5,8,1,7,6,4]=>0000000=>0000000=>[8]
[5,2,7,1,4,3,8,6]=>0000000=>0000000=>[8]
[6,2,8,1,4,3,7,5]=>0000000=>0000000=>[8]
[6,2,7,1,4,3,8,5]=>0000000=>0000000=>[8]
[6,2,7,1,5,3,8,4]=>0000000=>0000000=>[8]
[7,4,8,1,3,2,6,5]=>0000000=>0000000=>[8]
[8,3,7,1,4,2,6,5]=>0000000=>0000000=>[8]
[6,2,7,3,8,1,5,4]=>0000000=>0000000=>[8]
[6,2,8,3,7,1,5,4]=>0000000=>0000000=>[8]
[5,1,8,3,7,2,6,4]=>0000000=>0000000=>[8]
[4,1,8,3,7,2,6,5]=>0000000=>0000000=>[8]
[3,1,7,4,8,2,6,5]=>0000000=>0000000=>[8]
[5,1,7,3,8,2,6,4]=>0000000=>0000000=>[8]
[7,3,8,2,6,1,5,4]=>0000000=>0000000=>[8]
[3,4,2,6,8,1,5,7]=>0000000=>0000000=>[8]
[5,3,6,2,8,1,4,7]=>0000000=>0000000=>[8]
[7,4,2,5,8,3,6,1]=>0000000=>0000000=>[8]
[4,5,2,6,3,8,1,7]=>0000000=>0000000=>[8]
[3,5,6,1,4,8,2,7]=>0000000=>0000000=>[8]
[4,1,5,6,3,8,2,7]=>0000000=>0000000=>[8]
[4,5,1,6,3,8,2,7]=>0000000=>0000000=>[8]
[4,5,6,3,2,8,1,7]=>0000000=>0000000=>[8]
[6,7,4,8,3,2,5,1]=>0000000=>0000000=>[8]
[6,7,4,8,3,2,1,5]=>0000000=>0000000=>[8]
[6,7,4,1,8,3,2,5]=>0000000=>0000000=>[8]
[5,3,7,8,1,4,2,6]=>0000000=>0000000=>[8]
[7,3,5,8,1,4,6,2]=>0000000=>0000000=>[8]
[4,5,1,7,8,3,6,2]=>0000000=>0000000=>[8]
[7,4,1,5,8,3,6,2]=>0000000=>0000000=>[8]
[6,7,4,3,8,1,5,2]=>0000000=>0000000=>[8]
[5,6,1,7,3,8,4,2]=>0000000=>0000000=>[8]
[5,1,6,7,3,8,4,2]=>0000000=>0000000=>[8]
[6,4,7,1,8,3,5,2]=>0000000=>0000000=>[8]
[6,7,8,3,1,4,5,2]=>0000000=>0000000=>[8]
[6,7,2,8,4,5,1,3]=>0000000=>0000000=>[8]
[6,7,2,8,4,1,3,5]=>0000000=>0000000=>[8]
[6,1,7,4,8,3,2,5]=>0000000=>0000000=>[8]
[5,1,6,7,3,2,8,4]=>0000000=>0000000=>[8]
[5,6,1,7,3,2,8,4]=>0000000=>0000000=>[8]
[5,6,7,3,2,1,8,4]=>0000000=>0000000=>[8]
[5,6,7,3,2,8,4,1]=>0000000=>0000000=>[8]
[7,4,2,5,1,8,3,6]=>0000000=>0000000=>[8]
[6,7,4,2,8,3,5,1]=>0000000=>0000000=>[8]
[3,6,7,2,8,4,5,1]=>0000000=>0000000=>[8]
[3,6,7,2,8,4,1,5]=>0000000=>0000000=>[8]
[3,6,7,2,1,8,4,5]=>0000000=>0000000=>[8]
[3,4,7,8,2,1,5,6]=>0000000=>0000000=>[8]
[3,7,8,1,4,6,2,5]=>0000000=>0000000=>[8]
[3,6,7,2,8,5,1,4]=>0000000=>0000000=>[8]
[3,6,7,8,5,2,1,4]=>0000000=>0000000=>[8]
[3,6,7,8,5,2,4,1]=>0000000=>0000000=>[8]
[6,4,7,8,2,5,3,1]=>0000000=>0000000=>[8]
[6,4,7,8,2,1,5,3]=>0000000=>0000000=>[8]
[5,3,7,8,1,6,2,4]=>0000000=>0000000=>[8]
[6,7,2,8,5,1,3,4]=>0000000=>0000000=>[8]
[6,4,1,7,8,2,5,3]=>0000000=>0000000=>[8]
[5,1,6,2,7,8,4,3]=>0000000=>0000000=>[8]
[5,6,2,7,1,8,4,3]=>0000000=>0000000=>[8]
[5,6,2,7,8,4,3,1]=>0000000=>0000000=>[8]
[5,6,7,2,8,4,3,1]=>0000000=>0000000=>[8]
[5,6,7,2,1,8,4,3]=>0000000=>0000000=>[8]
[5,6,1,7,2,8,4,3]=>0000000=>0000000=>[8]
[5,1,6,7,2,8,4,3]=>0000000=>0000000=>[8]
[6,7,8,3,5,1,4,2]=>0000000=>0000000=>[8]
[5,6,1,7,8,4,3,2]=>0000000=>0000000=>[8]
[5,6,7,1,8,4,3,2]=>0000000=>0000000=>[8]
[8,3,2,5,1,6,4,7]=>0000000=>0000000=>[8]
[5,3,2,7,4,1,8,6]=>0000000=>0000000=>[8]
[7,5,3,8,2,4,6,1]=>0000000=>0000000=>[8]
[8,2,4,5,6,3,1,7]=>0000000=>0000000=>[8]
[8,2,4,5,6,1,3,7]=>0000000=>0000000=>[8]
[8,5,3,6,4,1,2,7]=>0000000=>0000000=>[8]
[8,4,1,5,6,3,2,7]=>0000000=>0000000=>[8]
[8,1,4,5,6,3,2,7]=>0000000=>0000000=>[8]
[4,5,3,7,2,1,8,6]=>0000000=>0000000=>[8]
[7,4,5,8,3,2,6,1]=>0000000=>0000000=>[8]
[4,3,6,7,2,8,5,1]=>0000000=>0000000=>[8]
[4,3,6,7,2,8,1,5]=>0000000=>0000000=>[8]
[1,4,3,6,7,2,8,5]=>1000000=>0000001=>[7,1]
[4,5,3,7,1,8,2,6]=>0000000=>0000000=>[8]
[5,3,4,7,1,2,8,6]=>0000000=>0000000=>[8]
[7,4,5,8,3,6,1,2]=>0000000=>0000000=>[8]
[4,3,6,7,8,1,5,2]=>0000000=>0000000=>[8]
[3,5,6,7,8,4,1,2]=>0000000=>0000000=>[8]
[3,1,5,6,7,8,4,2]=>0000000=>0000000=>[8]
[4,6,1,7,8,3,5,2]=>0000000=>0000000=>[8]
[6,2,4,1,7,8,5,3]=>0000000=>0000000=>[8]
[2,6,7,1,4,8,3,5]=>0000000=>0000000=>[8]
[1,5,3,6,7,8,2,4]=>1000000=>0000001=>[7,1]
[4,5,2,7,8,1,3,6]=>0000000=>0000000=>[8]
[4,2,6,7,8,3,1,5]=>0000000=>0000000=>[8]
[4,2,6,7,8,3,5,1]=>0000000=>0000000=>[8]
[3,6,2,7,4,8,1,5]=>0000000=>0000000=>[8]
[3,7,4,2,1,5,8,6]=>0000000=>0000000=>[8]
[7,8,4,2,1,3,6,5]=>0000000=>0000000=>[8]
[6,3,2,7,1,8,5,4]=>0000000=>0000000=>[8]
[3,6,2,7,1,8,5,4]=>0000000=>0000000=>[8]
[6,7,3,8,2,5,4,1]=>0000000=>0000000=>[8]
[6,4,7,8,5,2,3,1]=>0000000=>0000000=>[8]
[2,6,4,7,8,1,5,3]=>0000000=>0000000=>[8]
[7,4,1,5,8,6,2,3]=>0000000=>0000000=>[8]
[7,5,8,2,1,6,3,4]=>0000000=>0000000=>[8]
[6,2,7,1,3,8,5,4]=>0000000=>0000000=>[8]
[6,3,1,7,8,2,5,4]=>0000000=>0000000=>[8]
[4,6,1,7,8,5,2,3]=>0000000=>0000000=>[8]
[5,1,2,6,7,8,4,3]=>0000000=>0000000=>[8]
[5,2,6,7,8,4,3,1]=>0000000=>0000000=>[8]
[1,6,4,7,8,5,2,3]=>1000000=>0000001=>[7,1]
[2,6,7,1,3,8,5,4]=>0000000=>0000000=>[8]
[6,7,3,8,5,1,4,2]=>0000000=>0000000=>[8]
[6,4,7,8,5,3,1,2]=>0000000=>0000000=>[8]
[3,1,2,6,5,8,7,4]=>0010000=>0000100=>[5,3]
[4,5,1,2,3,8,7,6]=>0000100=>0010000=>[3,5]
[4,6,1,2,3,8,7,5]=>0000000=>0000000=>[8]
[1,6,5,3,4,8,7,2]=>1000000=>0000001=>[7,1]
[6,1,5,2,4,8,7,3]=>0000000=>0000000=>[8]
[6,5,1,2,3,8,7,4]=>0000000=>0000000=>[8]
[6,4,1,2,3,8,7,5]=>0000000=>0000000=>[8]
[5,4,1,2,3,8,7,6]=>0000100=>0010000=>[3,5]
[5,4,1,2,7,3,6,8]=>0000001=>1000000=>[1,7]
[6,4,1,7,2,3,5,8]=>0000001=>1000000=>[1,7]
[6,4,1,8,2,3,5,7]=>0000000=>0000000=>[8]
[7,4,1,2,8,3,6,5]=>0000000=>0000000=>[8]
[7,5,1,2,8,3,6,4]=>0000000=>0000000=>[8]
[7,1,5,2,8,4,6,3]=>0000000=>0000000=>[8]
[1,7,5,3,8,4,6,2]=>1000000=>0000001=>[7,1]
[8,4,1,2,7,3,6,5]=>0000000=>0000000=>[8]
[8,4,1,7,2,3,5,6]=>0000000=>0000000=>[8]
[7,4,1,6,2,3,5,8]=>0000001=>1000000=>[1,7]
[8,6,1,7,2,3,5,4]=>0000000=>0000000=>[8]
[8,1,6,7,2,4,5,3]=>0000000=>0000000=>[8]
[1,7,6,8,3,4,5,2]=>1000000=>0000001=>[7,1]
[7,6,1,8,2,3,5,4]=>0000000=>0000000=>[8]
[3,1,2,7,8,5,6,4]=>0010000=>0000100=>[5,3]
[3,1,8,7,2,4,5,6]=>0000000=>0000000=>[8]
[3,1,7,6,2,4,5,8]=>0000001=>1000000=>[1,7]
[4,7,1,6,2,3,5,8]=>0000001=>1000000=>[1,7]
[4,8,1,6,2,3,5,7]=>0000000=>0000000=>[8]
[5,8,1,2,7,3,6,4]=>0000000=>0000000=>[8]
[5,1,8,2,7,4,6,3]=>0000000=>0000000=>[8]
[1,5,8,3,7,4,6,2]=>1000000=>0000001=>[7,1]
[1,6,8,7,3,4,5,2]=>1000000=>0000001=>[7,1]
[6,1,8,7,2,4,5,3]=>0000000=>0000000=>[8]
[6,8,1,7,2,3,5,4]=>0000000=>0000000=>[8]
[6,8,7,1,2,3,4,5]=>0000000=>0000000=>[8]
[5,8,6,1,2,3,4,7]=>0000000=>0000000=>[8]
[5,7,6,1,2,3,4,8]=>0000001=>1000000=>[1,7]
[7,8,1,6,2,3,5,4]=>0000000=>0000000=>[8]
[7,1,8,6,2,4,5,3]=>0000000=>0000000=>[8]
[1,7,8,6,3,4,5,2]=>1000000=>0000001=>[7,1]
[8,1,7,6,2,4,5,3]=>0000000=>0000000=>[8]
[8,7,1,6,2,3,5,4]=>0000000=>0000000=>[8]
[8,5,3,7,2,1,4,6]=>0000000=>0000000=>[8]
[3,1,6,4,5,2,8,7]=>0000010=>0100000=>[2,6]
[5,8,7,4,2,6,3,1]=>0000000=>0000000=>[8]
[3,7,8,4,5,1,2,6]=>0000000=>0000000=>[8]
[5,6,3,8,1,7,2,4]=>0000000=>0000000=>[8]
[7,6,1,4,5,8,3,2]=>0000000=>0000000=>[8]
[3,7,6,4,5,8,2,1]=>0000000=>0000000=>[8]
[8,5,7,4,1,6,3,2]=>0000000=>0000000=>[8]
[2,5,8,4,7,6,1,3]=>0000000=>0000000=>[8]
[3,8,4,2,5,6,7,1]=>0000000=>0000000=>[8]
[7,5,8,4,3,6,1,2]=>0000000=>0000000=>[8]
[7,3,8,4,2,6,1,5]=>0000000=>0000000=>[8]
[5,6,3,8,4,2,7,1]=>0000000=>0000000=>[8]
[8,6,3,5,1,2,7,4]=>0000000=>0000000=>[8]
[7,8,5,4,2,6,1,3]=>0000000=>0000000=>[8]
[4,8,1,2,5,6,7,3]=>0000000=>0000000=>[8]
[3,4,2,8,5,6,7,1]=>0000000=>0000000=>[8]
[8,4,2,1,5,6,7,3]=>0000000=>0000000=>[8]
[3,8,7,4,5,2,1,6]=>0000000=>0000000=>[8]
[4,6,3,5,8,2,7,1]=>0000000=>0000000=>[8]
[5,4,2,3,7,6,1,8]=>0000001=>1000000=>[1,7]
[3,2,7,6,4,5,1,8]=>0000001=>1000000=>[1,7]
[4,7,2,6,3,5,1,8]=>0000001=>1000000=>[1,7]
[5,7,6,2,3,4,1,8]=>0000001=>1000000=>[1,7]
[1,7,5,2,8,3,4,6]=>1000000=>0000001=>[7,1]
[6,8,5,2,3,1,4,7]=>0000000=>0000000=>[8]
[4,8,2,6,3,1,5,7]=>0000000=>0000000=>[8]
[3,2,8,6,4,1,5,7]=>0000000=>0000000=>[8]
[7,1,5,2,8,3,4,6]=>0000000=>0000000=>[8]
[1,8,5,2,7,3,4,6]=>1000000=>0000001=>[7,1]
[7,1,6,8,2,3,4,5]=>0000000=>0000000=>[8]
[3,2,1,7,8,4,5,6]=>0010000=>0000100=>[5,3]
[3,2,8,7,1,4,5,6]=>0000000=>0000000=>[8]
[5,8,7,2,1,3,4,6]=>0000000=>0000000=>[8]
[1,7,6,8,2,3,4,5]=>1000000=>0000001=>[7,1]
[6,5,8,2,3,1,4,7]=>0000000=>0000000=>[8]
[8,5,7,2,1,3,4,6]=>0000000=>0000000=>[8]
[3,2,5,4,1,8,6,7]=>0000100=>0010000=>[3,5]
[7,4,2,1,8,3,5,6]=>0000000=>0000000=>[8]
[8,4,2,1,7,3,5,6]=>0000000=>0000000=>[8]
[1,4,2,8,7,3,5,6]=>1000000=>0000001=>[7,1]
[1,5,8,2,7,3,4,6]=>1000000=>0000001=>[7,1]
[8,5,1,2,7,3,4,6]=>0000000=>0000000=>[8]
[3,2,6,1,4,8,5,7]=>0000000=>0000000=>[8]
[3,2,7,1,8,4,5,6]=>0000000=>0000000=>[8]
[4,7,2,1,8,3,5,6]=>0000000=>0000000=>[8]
[8,6,1,7,2,3,4,5]=>0000000=>0000000=>[8]
[1,6,8,7,2,3,4,5]=>1000000=>0000001=>[7,1]
[1,7,8,6,2,3,4,5]=>1000000=>0000001=>[7,1]
[7,8,1,6,2,3,4,5]=>0000000=>0000000=>[8]
[4,8,2,1,7,3,5,6]=>0000000=>0000000=>[8]
[3,2,8,1,7,4,5,6]=>0000000=>0000000=>[8]
[5,1,8,2,7,3,4,6]=>0000000=>0000000=>[8]
[6,1,8,7,2,3,4,5]=>0000000=>0000000=>[8]
[8,1,7,6,2,3,4,5]=>0000000=>0000000=>[8]
[2,8,4,1,6,5,7,3]=>0000000=>0000000=>[8]
[7,5,8,6,1,4,2,3]=>0000000=>0000000=>[8]
[7,5,8,2,4,6,3,1]=>0000000=>0000000=>[8]
[7,5,8,6,1,4,3,2]=>0000000=>0000000=>[8]
[3,5,7,2,4,1,8,6]=>0000000=>0000000=>[8]
[6,5,2,7,3,4,8,1]=>0000000=>0000000=>[8]
[5,1,6,7,4,3,8,2]=>0000000=>0000000=>[8]
[4,1,2,3,8,6,5,7]=>0001000=>0001000=>[4,4]
[4,1,2,3,8,6,7,5]=>0001000=>0001000=>[4,4]
[4,1,2,3,8,5,7,6]=>0001000=>0001000=>[4,4]
[4,5,2,6,3,7,1,8]=>0000001=>1000000=>[1,7]
[4,1,2,6,8,5,7,3]=>0000000=>0000000=>[8]
[6,4,2,7,1,3,8,5]=>0000000=>0000000=>[8]
[8,5,3,6,1,7,2,4]=>0000000=>0000000=>[8]
[7,3,6,2,4,8,1,5]=>0000000=>0000000=>[8]
[3,7,5,1,2,4,8,6]=>0000000=>0000000=>[8]
[7,4,8,5,2,6,1,3]=>0000000=>0000000=>[8]
[5,8,2,6,3,7,1,4]=>0000000=>0000000=>[8]
[3,8,6,2,4,7,1,5]=>0000000=>0000000=>[8]
[4,8,6,2,7,1,3,5]=>0000000=>0000000=>[8]
[5,4,7,3,8,1,2,6]=>0000000=>0000000=>[8]
[8,4,1,6,7,2,3,5]=>0000000=>0000000=>[8]
[4,7,1,5,8,6,2,3]=>0000000=>0000000=>[8]
[8,6,1,7,5,2,3,4]=>0000000=>0000000=>[8]
[5,7,2,8,1,6,3,4]=>0000000=>0000000=>[8]
[8,3,7,6,1,2,4,5]=>0000000=>0000000=>[8]
[8,4,7,6,1,2,3,5]=>0000000=>0000000=>[8]
[3,5,8,7,1,2,4,6]=>0000000=>0000000=>[8]
[2,5,8,7,1,3,4,6]=>0000000=>0000000=>[8]
[6,8,4,7,5,1,2,3]=>0000000=>0000000=>[8]
[5,8,7,1,6,2,3,4]=>0000000=>0000000=>[8]
[2,8,7,6,1,3,4,5]=>0000000=>0000000=>[8]
[3,8,7,6,1,2,4,5]=>0000000=>0000000=>[8]
[4,8,7,6,1,2,3,5]=>0000000=>0000000=>[8]
[3,8,7,4,5,1,6,2]=>0000000=>0000000=>[8]
[5,7,3,8,1,2,6,4]=>0000000=>0000000=>[8]
[7,5,1,4,8,6,3,2]=>0000000=>0000000=>[8]
[5,3,2,7,4,6,8,1]=>0000000=>0000000=>[8]
[7,5,3,6,2,4,8,1]=>0000000=>0000000=>[8]
[6,3,2,5,1,8,4,7]=>0000000=>0000000=>[8]
[8,5,3,6,2,7,1,4]=>0000000=>0000000=>[8]
[7,2,6,3,4,5,8,1]=>0000000=>0000000=>[8]
[6,2,7,3,4,5,8,1]=>0000000=>0000000=>[8]
[6,7,3,5,2,4,8,1]=>0000000=>0000000=>[8]
[3,7,6,2,4,5,8,1]=>0000000=>0000000=>[8]
[6,5,3,1,2,8,4,7]=>0000000=>0000000=>[8]
[8,6,5,2,3,7,1,4]=>0000000=>0000000=>[8]
[8,5,2,1,7,3,4,6]=>0000000=>0000000=>[8]
[7,5,2,1,8,3,4,6]=>0000000=>0000000=>[8]
[1,6,3,2,8,4,5,7]=>1000000=>0000001=>[7,1]
[5,4,8,6,2,7,1,3]=>0000000=>0000000=>[8]
[7,8,5,2,3,6,1,4]=>0000000=>0000000=>[8]
[2,8,1,7,3,4,5,6]=>0000000=>0000000=>[8]
[3,8,6,1,7,2,4,5]=>0000000=>0000000=>[8]
[4,2,8,3,7,1,5,6]=>0000000=>0000000=>[8]
[8,1,2,7,3,4,5,6]=>0000000=>0000000=>[8]
[7,2,6,1,8,3,4,5]=>0000000=>0000000=>[8]
[7,3,1,5,8,2,4,6]=>0000000=>0000000=>[8]
[5,4,1,3,6,8,2,7]=>0000000=>0000000=>[8]
[8,5,3,7,6,1,2,4]=>0000000=>0000000=>[8]
[6,1,8,3,7,2,4,5]=>0000000=>0000000=>[8]
[7,6,8,2,3,5,1,4]=>0000000=>0000000=>[8]
[3,7,8,2,4,6,1,5]=>0000000=>0000000=>[8]
[5,4,7,8,2,6,1,3]=>0000000=>0000000=>[8]
[4,2,5,8,7,1,3,6]=>0000000=>0000000=>[8]
[2,3,8,7,1,4,5,6]=>0000000=>0000000=>[8]
[2,1,8,7,3,4,5,6]=>0100000=>0000010=>[6,2]
[8,2,7,6,1,3,4,5]=>0000000=>0000000=>[8]
[1,2,8,7,3,4,5,6]=>1100000=>0000011=>[6,1,1]
[1,3,8,7,2,4,5,6]=>1000000=>0000001=>[7,1]
[1,7,8,3,6,2,4,5]=>1000000=>0000001=>[7,1]
[5,4,8,7,6,1,2,3]=>0000000=>0000000=>[8]
[6,8,3,7,5,1,2,4]=>0000000=>0000000=>[8]
[7,8,6,2,5,1,3,4]=>0000000=>0000000=>[8]
[8,1,6,7,3,2,4,5]=>0000000=>0000000=>[8]
[8,1,5,3,7,2,4,6]=>0000000=>0000000=>[8]
[8,1,5,3,6,2,4,7]=>0000000=>0000000=>[8]
[7,4,8,3,2,6,5,1]=>0000000=>0000000=>[8]
[7,4,1,3,2,6,5,8]=>0000001=>1000000=>[1,7]
[8,1,4,3,2,6,5,7]=>0000000=>0000000=>[8]
[8,1,4,3,2,7,5,6]=>0000000=>0000000=>[8]
[8,1,5,4,6,7,2,3]=>0000000=>0000000=>[8]
[8,1,5,3,6,2,7,4]=>0000000=>0000000=>[8]
[8,1,4,3,2,6,7,5]=>0000000=>0000000=>[8]
[8,1,4,3,2,5,7,6]=>0000000=>0000000=>[8]
[7,4,1,3,2,5,6,8]=>0000001=>1000000=>[1,7]
[7,4,8,3,2,5,6,1]=>0000000=>0000000=>[8]
[6,4,3,1,2,5,8,7]=>0000010=>0100000=>[2,6]
[7,4,1,3,2,5,8,6]=>0000000=>0000000=>[8]
[7,5,1,3,6,2,8,4]=>0000000=>0000000=>[8]
[7,5,1,4,6,8,2,3]=>0000000=>0000000=>[8]
[6,4,3,8,2,5,1,7]=>0000000=>0000000=>[8]
[5,4,3,2,8,6,1,7]=>0000000=>0000000=>[8]
[5,4,3,2,8,7,1,6]=>0000000=>0000000=>[8]
[6,5,4,8,7,1,2,3]=>0000000=>0000000=>[8]
[6,5,4,1,7,8,2,3]=>0000000=>0000000=>[8]
[6,4,3,1,2,7,8,5]=>0000000=>0000000=>[8]
[7,4,1,3,2,8,5,6]=>0000000=>0000000=>[8]
[6,4,3,1,2,7,5,8]=>0000001=>1000000=>[1,7]
[6,4,3,8,2,7,5,1]=>0000000=>0000000=>[8]
[6,5,3,8,7,2,4,1]=>0000000=>0000000=>[8]
[6,5,3,1,7,2,4,8]=>0000001=>1000000=>[1,7]
[7,5,1,3,8,2,4,6]=>0000000=>0000000=>[8]
[6,5,3,7,8,2,4,1]=>0000000=>0000000=>[8]
[6,4,3,7,2,8,5,1]=>0000000=>0000000=>[8]
[6,4,3,7,2,1,5,8]=>0000001=>1000000=>[1,7]
[7,5,8,4,1,6,2,3]=>0000000=>0000000=>[8]
[6,5,4,8,1,7,2,3]=>0000000=>0000000=>[8]
[6,5,3,8,1,2,7,4]=>0000000=>0000000=>[8]
[6,5,4,7,1,8,2,3]=>0000000=>0000000=>[8]
[5,4,3,2,7,8,1,6]=>0000000=>0000000=>[8]
[4,6,3,8,5,1,2,7]=>0000000=>0000000=>[8]
[5,6,8,3,4,1,2,7]=>0000000=>0000000=>[8]
[5,6,8,3,4,1,7,2]=>0000000=>0000000=>[8]
[4,6,2,7,5,3,1,8]=>0000001=>1000000=>[1,7]
[5,6,8,4,3,1,2,7]=>0000000=>0000000=>[8]
[5,7,8,4,1,3,6,2]=>0000000=>0000000=>[8]
[5,6,8,4,2,1,7,3]=>0000000=>0000000=>[8]
[5,6,8,2,4,1,7,3]=>0000000=>0000000=>[8]
[3,2,6,8,5,1,4,7]=>0000000=>0000000=>[8]
[5,6,8,4,2,1,3,7]=>0000000=>0000000=>[8]
[5,7,8,4,1,3,2,6]=>0000000=>0000000=>[8]
[5,7,8,4,1,2,3,6]=>0000000=>0000000=>[8]
[6,7,8,1,5,2,3,4]=>0000000=>0000000=>[8]
[6,7,8,1,5,3,2,4]=>0000000=>0000000=>[8]
[6,7,8,1,3,5,2,4]=>0000000=>0000000=>[8]
[5,7,8,2,1,6,3,4]=>0000000=>0000000=>[8]
[4,7,2,8,1,6,3,5]=>0000000=>0000000=>[8]
[3,2,7,8,1,6,4,5]=>0000000=>0000000=>[8]
[4,7,2,8,1,6,5,3]=>0000000=>0000000=>[8]
[5,7,8,2,1,6,4,3]=>0000000=>0000000=>[8]
[6,7,8,1,3,5,4,2]=>0000000=>0000000=>[8]
[6,7,8,1,5,3,4,2]=>0000000=>0000000=>[8]
[6,7,8,1,4,3,5,2]=>0000000=>0000000=>[8]
[5,6,8,3,2,1,7,4]=>0000000=>0000000=>[8]
[4,7,3,8,1,6,2,5]=>0000000=>0000000=>[8]
[4,7,3,8,1,5,6,2]=>0000000=>0000000=>[8]
[4,7,3,8,1,5,2,6]=>0000000=>0000000=>[8]
[4,7,3,8,1,2,5,6]=>0000000=>0000000=>[8]
[5,7,8,3,1,2,4,6]=>0000000=>0000000=>[8]
[5,6,8,3,2,1,4,7]=>0000000=>0000000=>[8]
[3,2,7,8,1,5,4,6]=>0000000=>0000000=>[8]
[6,7,8,1,3,4,2,5]=>0000000=>0000000=>[8]
[6,7,8,1,4,2,3,5]=>0000000=>0000000=>[8]
[6,7,8,1,2,5,3,4]=>0000000=>0000000=>[8]
[6,7,8,1,2,4,5,3]=>0000000=>0000000=>[8]
[5,7,8,2,1,3,6,4]=>0000000=>0000000=>[8]
[3,2,7,8,1,4,6,5]=>0000000=>0000000=>[8]
[6,7,8,1,3,2,4,5]=>0000000=>0000000=>[8]
[6,7,8,1,2,4,3,5]=>0000000=>0000000=>[8]
[6,7,8,1,2,3,5,4]=>0000000=>0000000=>[8]
[4,6,2,1,7,5,8,3]=>0000000=>0000000=>[8]
[6,7,5,1,8,4,3,2]=>0000000=>0000000=>[8]
[6,8,4,1,7,5,3,2]=>0000000=>0000000=>[8]
[4,6,1,2,7,5,8,3]=>0000000=>0000000=>[8]
[6,7,1,5,8,2,3,4]=>0000000=>0000000=>[8]
[8,4,1,6,7,5,2,3]=>0000000=>0000000=>[8]
[7,6,2,1,5,8,3,4]=>0000000=>0000000=>[8]
[6,1,4,2,7,5,8,3]=>0000000=>0000000=>[8]
[2,5,1,3,7,6,8,4]=>0000000=>0000000=>[8]
[4,7,1,2,8,6,5,3]=>0000000=>0000000=>[8]
[4,6,8,1,2,7,5,3]=>0000000=>0000000=>[8]
[6,8,7,1,5,3,2,4]=>0000000=>0000000=>[8]
[6,8,7,3,5,1,2,4]=>0000000=>0000000=>[8]
[7,8,1,3,6,5,2,4]=>0000000=>0000000=>[8]
[1,7,3,4,8,6,5,2]=>1000000=>0000001=>[7,1]
[4,2,7,1,8,6,5,3]=>0000000=>0000000=>[8]
[7,8,2,3,6,5,1,4]=>0000000=>0000000=>[8]
[8,5,7,1,6,2,3,4]=>0000000=>0000000=>[8]
[8,5,7,1,2,6,3,4]=>0000000=>0000000=>[8]
[6,8,2,7,1,3,5,4]=>0000000=>0000000=>[8]
[6,2,4,8,7,1,5,3]=>0000000=>0000000=>[8]
[1,6,8,3,7,4,5,2]=>1000000=>0000001=>[7,1]
[1,6,8,3,4,7,5,2]=>1000000=>0000001=>[7,1]
[6,2,4,8,1,7,5,3]=>0000000=>0000000=>[8]
[6,8,7,2,3,5,1,4]=>0000000=>0000000=>[8]
[6,8,2,1,7,3,5,4]=>0000000=>0000000=>[8]
[8,5,7,2,1,6,3,4]=>0000000=>0000000=>[8]
[8,5,7,1,2,3,6,4]=>0000000=>0000000=>[8]
[8,5,7,2,3,1,6,4]=>0000000=>0000000=>[8]
[1,8,7,5,3,4,6,2]=>1000000=>0000001=>[7,1]
[1,8,7,3,5,4,6,2]=>1000000=>0000001=>[7,1]
[8,2,5,4,7,1,6,3]=>0000000=>0000000=>[8]
[8,7,6,1,2,4,3,5]=>0000000=>0000000=>[8]
[8,7,6,1,4,2,3,5]=>0000000=>0000000=>[8]
[8,7,6,4,1,3,2,5]=>0000000=>0000000=>[8]
[8,5,7,1,3,2,6,4]=>0000000=>0000000=>[8]
[5,8,4,7,1,2,6,3]=>0000000=>0000000=>[8]
[8,1,2,6,5,7,4,3]=>0000000=>0000000=>[8]
[8,2,5,6,7,4,1,3]=>0000000=>0000000=>[8]
[4,8,5,1,7,2,6,3]=>0000000=>0000000=>[8]
[8,5,3,7,1,2,6,4]=>0000000=>0000000=>[8]
[4,6,2,8,1,7,5,3]=>0000000=>0000000=>[8]
[1,6,4,8,3,7,5,2]=>1000000=>0000001=>[7,1]
[1,8,7,4,5,3,6,2]=>1000000=>0000001=>[7,1]
[4,8,5,7,2,1,6,3]=>0000000=>0000000=>[8]
[8,5,3,7,2,1,6,4]=>0000000=>0000000=>[8]
[8,7,6,3,1,4,2,5]=>0000000=>0000000=>[8]
[8,5,3,2,7,1,6,4]=>0000000=>0000000=>[8]
[1,8,7,4,3,5,6,2]=>1000000=>0000001=>[7,1]
[1,8,7,3,4,5,6,2]=>1000000=>0000001=>[7,1]
[8,2,4,5,7,1,6,3]=>0000000=>0000000=>[8]
[8,5,2,3,7,1,6,4]=>0000000=>0000000=>[8]
[8,3,1,5,2,7,6,4]=>0000000=>0000000=>[8]
[8,7,4,1,6,3,2,5]=>0000000=>0000000=>[8]
[8,7,4,1,6,3,5,2]=>0000000=>0000000=>[8]
[8,7,4,1,6,5,3,2]=>0000000=>0000000=>[8]
[8,7,4,1,6,5,2,3]=>0000000=>0000000=>[8]
[8,3,2,7,6,4,5,1]=>0000000=>0000000=>[8]
[8,5,4,2,3,7,6,1]=>0000000=>0000000=>[8]
[8,7,4,2,6,3,5,1]=>0000000=>0000000=>[8]
[8,7,4,2,6,3,1,5]=>0000000=>0000000=>[8]
[8,3,2,5,4,7,1,6]=>0000000=>0000000=>[8]
[8,3,2,7,6,1,5,4]=>0000000=>0000000=>[8]
[7,4,5,2,3,1,8,6]=>0000000=>0000000=>[8]
[5,2,7,3,4,1,8,6]=>0000000=>0000000=>[8]
[6,2,7,3,4,1,8,5]=>0000000=>0000000=>[8]
[3,1,8,6,7,4,5,2]=>0000000=>0000000=>[8]
[8,5,7,3,4,1,6,2]=>0000000=>0000000=>[8]
[8,4,7,3,5,1,6,2]=>0000000=>0000000=>[8]
[2,1,8,5,7,4,6,3]=>0100000=>0000010=>[6,2]
[6,2,4,1,7,3,8,5]=>0000000=>0000000=>[8]
[8,5,6,2,3,1,7,4]=>0000000=>0000000=>[8]
[7,3,8,5,6,2,4,1]=>0000000=>0000000=>[8]
[3,1,6,2,8,5,7,4]=>0000000=>0000000=>[8]
[5,1,6,2,8,4,7,3]=>0000000=>0000000=>[8]
[7,3,8,4,6,2,5,1]=>0000000=>0000000=>[8]
[4,1,8,5,6,2,7,3]=>0000000=>0000000=>[8]
[3,1,8,5,6,2,7,4]=>0000000=>0000000=>[8]
[6,8,7,3,4,1,2,5]=>0000000=>0000000=>[8]
[5,4,8,7,2,6,3,1]=>0000000=>0000000=>[8]
[5,3,8,7,6,1,2,4]=>0000000=>0000000=>[8]
[8,3,4,6,5,1,2,7]=>0000000=>0000000=>[8]
[3,4,8,7,6,1,2,5]=>0000000=>0000000=>[8]
[3,5,8,7,6,1,2,4]=>0000000=>0000000=>[8]
[4,5,8,7,6,1,2,3]=>0000000=>0000000=>[8]
[4,5,8,7,1,6,3,2]=>0000000=>0000000=>[8]
[3,5,8,2,7,6,4,1]=>0000000=>0000000=>[8]
[3,5,8,1,7,6,4,2]=>0000000=>0000000=>[8]
[2,5,8,7,1,6,3,4]=>0000000=>0000000=>[8]
[2,4,8,7,1,6,3,5]=>0000000=>0000000=>[8]
[2,8,4,7,1,5,3,6]=>0000000=>0000000=>[8]
[8,2,4,6,1,5,3,7]=>0000000=>0000000=>[8]
[8,1,4,6,2,5,3,7]=>0000000=>0000000=>[8]
[1,4,8,7,2,6,3,5]=>1000000=>0000001=>[7,1]
[1,5,8,7,2,6,3,4]=>1000000=>0000001=>[7,1]
[1,5,8,2,7,6,4,3]=>1000000=>0000001=>[7,1]
[2,5,8,3,7,6,4,1]=>0000000=>0000000=>[8]
[1,4,2,8,7,6,5,3]=>1000000=>0000001=>[7,1]
[1,3,8,2,7,6,4,5]=>1000000=>0000001=>[7,1]
[1,8,3,2,7,5,4,6]=>1000000=>0000001=>[7,1]
[8,2,3,1,6,5,4,7]=>0000000=>0000000=>[8]
[2,3,8,1,7,6,4,5]=>0000000=>0000000=>[8]
[5,2,8,7,1,6,3,4]=>0000000=>0000000=>[8]
[5,2,8,1,7,6,4,3]=>0000000=>0000000=>[8]
[5,3,8,2,7,6,4,1]=>0000000=>0000000=>[8]
[6,8,3,2,7,5,4,1]=>0000000=>0000000=>[8]
[6,8,3,1,7,5,4,2]=>0000000=>0000000=>[8]
[6,8,1,2,7,5,4,3]=>0000000=>0000000=>[8]
[6,8,2,3,7,5,4,1]=>0000000=>0000000=>[8]
[5,2,8,3,7,6,4,1]=>0000000=>0000000=>[8]
[5,1,8,3,7,6,4,2]=>0000000=>0000000=>[8]
[5,1,8,7,2,6,3,4]=>0000000=>0000000=>[8]
[4,8,1,7,2,5,3,6]=>0000000=>0000000=>[8]
[8,4,1,6,2,5,3,7]=>0000000=>0000000=>[8]
[8,3,1,2,6,5,4,7]=>0000000=>0000000=>[8]
[3,1,2,8,7,6,5,4]=>0010000=>0000100=>[5,3]
[4,1,3,8,7,6,5,2]=>0000000=>0000000=>[8]
[3,1,4,8,7,6,5,2]=>0000000=>0000000=>[8]
[2,1,8,3,7,6,4,5]=>0100000=>0000010=>[6,2]
[2,8,1,3,7,5,4,6]=>0000000=>0000000=>[8]
[8,2,1,3,6,5,4,7]=>0000000=>0000000=>[8]
[1,8,2,3,7,5,4,6]=>1000000=>0000001=>[7,1]
[1,2,8,3,7,6,4,5]=>1100000=>0000011=>[6,1,1]
[1,4,3,6,8,2,5,7]=>1000000=>0000001=>[7,1]
[1,4,5,2,8,3,7,6]=>1000000=>0000001=>[7,1]
[1,4,2,6,5,8,3,7]=>1000000=>0000001=>[7,1]
[1,5,4,2,6,8,3,7]=>1000000=>0000001=>[7,1]
[3,1,6,5,8,2,4,7]=>0000000=>0000000=>[8]
[1,6,4,2,5,8,3,7]=>1000000=>0000001=>[7,1]
[1,5,2,6,4,8,3,7]=>1000000=>0000001=>[7,1]
[1,2,6,5,4,8,3,7]=>1100000=>0000011=>[6,1,1]
[1,2,5,4,7,3,8,6]=>1100000=>0000011=>[6,1,1]
[4,1,2,6,3,8,7,5]=>0000000=>0000000=>[8]
[7,1,5,4,2,8,3,6]=>0000000=>0000000=>[8]
[1,4,7,5,2,8,3,6]=>1000000=>0000001=>[7,1]
[7,1,3,5,2,8,4,6]=>0000000=>0000000=>[8]
[1,4,5,2,8,7,3,6]=>1000000=>0000001=>[7,1]
[1,6,4,2,8,3,7,5]=>1000000=>0000001=>[7,1]
[1,4,2,8,3,7,6,5]=>1000000=>0000001=>[7,1]
[1,2,8,6,5,3,7,4]=>1100000=>0000011=>[6,1,1]
[6,2,1,8,7,3,4,5]=>0000000=>0000000=>[8]
[7,6,2,1,8,3,4,5]=>0000000=>0000000=>[8]
[7,3,1,6,2,8,4,5]=>0000000=>0000000=>[8]
[1,7,6,4,2,8,3,5]=>1000000=>0000001=>[7,1]
[1,7,5,2,6,3,8,4]=>1000000=>0000001=>[7,1]
[1,6,2,7,5,3,8,4]=>1000000=>0000001=>[7,1]
[1,2,7,6,5,3,8,4]=>1100000=>0000011=>[6,1,1]
[1,2,6,5,3,8,7,4]=>1100000=>0000011=>[6,1,1]
[1,5,2,7,6,3,8,4]=>1000000=>0000001=>[7,1]
[1,6,5,2,7,3,8,4]=>1000000=>0000001=>[7,1]
[1,5,7,4,2,8,3,6]=>1000000=>0000001=>[7,1]
[3,1,8,6,2,4,7,5]=>0000000=>0000000=>[8]
[4,3,7,1,8,2,5,6]=>0000000=>0000000=>[8]
[8,3,1,6,2,4,7,5]=>0000000=>0000000=>[8]
[7,1,8,3,2,4,6,5]=>0000000=>0000000=>[8]
[1,4,2,8,7,3,6,5]=>1000000=>0000001=>[7,1]
[1,7,4,2,8,3,6,5]=>1000000=>0000001=>[7,1]
[8,1,5,4,2,7,3,6]=>0000000=>0000000=>[8]
[1,4,8,5,2,7,3,6]=>1000000=>0000001=>[7,1]
[8,5,3,1,7,2,4,6]=>0000000=>0000000=>[8]
[8,6,2,1,7,3,4,5]=>0000000=>0000000=>[8]
[1,8,6,4,2,7,3,5]=>1000000=>0000001=>[7,1]
[1,5,2,7,3,8,6,4]=>1000000=>0000001=>[7,1]
[1,2,8,5,3,7,6,4]=>1100000=>0000011=>[6,1,1]
[1,2,6,3,8,7,5,4]=>1100000=>0000011=>[6,1,1]
[1,2,7,6,3,8,5,4]=>1100000=>0000011=>[6,1,1]
[1,6,2,7,3,8,5,4]=>1000000=>0000001=>[7,1]
[1,7,4,2,8,6,3,5]=>1000000=>0000001=>[7,1]
[7,1,8,3,2,6,4,5]=>0000000=>0000000=>[8]
[7,2,1,8,6,3,4,5]=>0000000=>0000000=>[8]
[1,8,7,3,2,6,4,5]=>1000000=>0000001=>[7,1]
[1,4,2,8,7,6,3,5]=>1000000=>0000001=>[7,1]
[1,2,8,7,5,3,6,4]=>1100000=>0000011=>[6,1,1]
[5,7,1,6,2,4,3,8]=>0000001=>1000000=>[1,7]
[6,1,4,5,3,8,7,2]=>0000000=>0000000=>[8]
[6,3,5,8,2,1,7,4]=>0000000=>0000000=>[8]
[8,4,5,7,3,6,1,2]=>0000000=>0000000=>[8]
[8,4,1,5,2,6,3,7]=>0000000=>0000000=>[8]
[8,7,5,6,1,4,2,3]=>0000000=>0000000=>[8]
[2,3,8,1,6,4,7,5]=>0000000=>0000000=>[8]
[5,2,6,1,4,8,7,3]=>0000000=>0000000=>[8]
[5,7,2,3,8,6,1,4]=>0000000=>0000000=>[8]
[5,6,2,3,1,8,7,4]=>0000000=>0000000=>[8]
[5,6,2,1,3,8,7,4]=>0000000=>0000000=>[8]
[5,1,6,4,2,8,7,3]=>0000000=>0000000=>[8]
[5,6,1,3,2,8,7,4]=>0000000=>0000000=>[8]
[5,6,3,1,2,8,7,4]=>0000000=>0000000=>[8]
[5,7,3,2,8,1,6,4]=>0000000=>0000000=>[8]
[6,7,3,8,2,1,5,4]=>0000000=>0000000=>[8]
[6,7,3,8,1,2,5,4]=>0000000=>0000000=>[8]
[5,7,3,1,8,2,6,4]=>0000000=>0000000=>[8]
[5,1,7,4,8,2,6,3]=>0000000=>0000000=>[8]
[1,5,7,4,8,3,6,2]=>1000000=>0000001=>[7,1]
[5,1,7,4,8,6,2,3]=>0000000=>0000000=>[8]
[5,7,3,1,8,6,2,4]=>0000000=>0000000=>[8]
[6,7,8,3,1,4,2,5]=>0000000=>0000000=>[8]
[6,7,1,8,3,5,2,4]=>0000000=>0000000=>[8]
[6,1,7,8,4,5,2,3]=>0000000=>0000000=>[8]
[1,6,7,8,4,5,3,2]=>1000000=>0000001=>[7,1]
[1,6,7,8,4,3,5,2]=>1000000=>0000001=>[7,1]
[6,1,7,8,4,2,5,3]=>0000000=>0000000=>[8]
[6,7,2,8,1,3,5,4]=>0000000=>0000000=>[8]
[6,7,2,8,3,5,1,4]=>0000000=>0000000=>[8]
[6,2,7,8,4,1,5,3]=>0000000=>0000000=>[8]
[6,2,7,8,1,4,5,3]=>0000000=>0000000=>[8]
[4,2,1,7,8,5,6,3]=>0000000=>0000000=>[8]
[4,1,2,7,8,6,5,3]=>0000000=>0000000=>[8]
[6,2,7,8,1,5,4,3]=>0000000=>0000000=>[8]
[6,2,7,8,5,1,4,3]=>0000000=>0000000=>[8]
[5,7,2,1,8,6,3,4]=>0000000=>0000000=>[8]
[1,6,7,8,3,5,4,2]=>1000000=>0000001=>[7,1]
[6,1,7,8,2,5,4,3]=>0000000=>0000000=>[8]
[6,7,8,2,4,1,3,5]=>0000000=>0000000=>[8]
[6,7,8,2,4,3,1,5]=>0000000=>0000000=>[8]
[6,7,1,8,5,2,3,4]=>0000000=>0000000=>[8]
[6,1,7,8,5,2,4,3]=>0000000=>0000000=>[8]
[1,6,7,8,5,3,4,2]=>1000000=>0000001=>[7,1]
[6,1,7,8,5,4,2,3]=>0000000=>0000000=>[8]
[6,7,1,8,5,3,2,4]=>0000000=>0000000=>[8]
[6,7,8,4,1,3,2,5]=>0000000=>0000000=>[8]
[3,7,4,8,5,6,1,2]=>0000000=>0000000=>[8]
[3,7,1,8,5,6,2,4]=>0000000=>0000000=>[8]
[2,7,3,8,5,6,1,4]=>0000000=>0000000=>[8]
[1,7,4,8,5,6,2,3]=>1000000=>0000001=>[7,1]
[2,7,3,8,4,6,1,5]=>0000000=>0000000=>[8]
[3,7,1,8,4,6,2,5]=>0000000=>0000000=>[8]
[1,5,2,8,6,7,3,4]=>1000000=>0000001=>[7,1]
[2,6,1,8,5,7,3,4]=>0000000=>0000000=>[8]
[1,6,2,8,5,7,3,4]=>1000000=>0000001=>[7,1]
[1,6,2,8,4,7,3,5]=>1000000=>0000001=>[7,1]
[2,6,1,8,4,7,3,5]=>0000000=>0000000=>[8]
[3,7,2,6,1,8,4,5]=>0000000=>0000000=>[8]
[4,8,1,6,2,7,3,5]=>0000000=>0000000=>[8]
[5,8,1,6,2,7,3,4]=>0000000=>0000000=>[8]
[5,8,2,6,1,7,3,4]=>0000000=>0000000=>[8]
[4,8,2,6,1,7,3,5]=>0000000=>0000000=>[8]
[1,7,3,6,2,8,4,5]=>1000000=>0000001=>[7,1]
[2,7,3,6,1,8,4,5]=>0000000=>0000000=>[8]
[8,6,1,4,3,2,5,7]=>0000000=>0000000=>[8]
[3,7,5,1,8,2,4,6]=>0000000=>0000000=>[8]
[4,1,5,2,8,7,3,6]=>0000000=>0000000=>[8]
[8,1,2,4,6,5,3,7]=>0000000=>0000000=>[8]
[8,2,6,5,1,3,4,7]=>0000000=>0000000=>[8]
[8,3,1,6,2,5,4,7]=>0000000=>0000000=>[8]
[8,1,2,6,4,5,3,7]=>0000000=>0000000=>[8]
[8,1,2,5,6,4,3,7]=>0000000=>0000000=>[8]
[1,7,5,4,2,8,3,6]=>1000000=>0000001=>[7,1]
[1,4,6,8,2,7,3,5]=>1000000=>0000001=>[7,1]
[1,4,7,6,2,8,3,5]=>1000000=>0000001=>[7,1]
[5,1,4,7,2,8,3,6]=>0000000=>0000000=>[8]
[3,7,5,1,2,8,4,6]=>0000000=>0000000=>[8]
[4,1,5,8,2,7,3,6]=>0000000=>0000000=>[8]
[1,4,6,2,8,7,3,5]=>1000000=>0000001=>[7,1]
[1,4,2,8,6,7,3,5]=>1000000=>0000001=>[7,1]
[3,1,2,6,4,8,7,5]=>0010000=>0000100=>[5,3]
[2,1,7,6,3,4,8,5]=>0100000=>0000010=>[6,2]
[3,1,2,7,4,6,8,5]=>0010000=>0000100=>[5,3]
[1,2,3,6,8,5,7,4]=>1110000=>0000111=>[5,1,1,1]
[5,1,4,2,7,8,3,6]=>0000000=>0000000=>[8]
[1,4,2,7,6,8,3,5]=>1000000=>0000001=>[7,1]
[1,4,2,6,8,7,3,5]=>1000000=>0000001=>[7,1]
[5,3,7,1,8,2,4,6]=>0000000=>0000000=>[8]
[1,7,4,3,2,5,8,6]=>1000000=>0000001=>[7,1]
[4,8,7,2,1,3,5,6]=>0000000=>0000000=>[8]
[1,8,7,3,4,2,5,6]=>1000000=>0000001=>[7,1]
[3,1,7,8,2,6,4,5]=>0000000=>0000000=>[8]
[1,4,2,7,8,3,6,5]=>1000000=>0000001=>[7,1]
[2,1,8,6,3,4,7,5]=>0100000=>0000010=>[6,2]
[1,4,2,6,8,3,7,5]=>1000000=>0000001=>[7,1]
[1,2,3,7,8,5,6,4]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,5,8,6,4]=>1110000=>0000111=>[5,1,1,1]
[3,1,7,2,8,6,4,5]=>0000000=>0000000=>[8]
[1,2,3,8,7,5,6,4]=>1110000=>0000111=>[5,1,1,1]
[5,7,8,4,2,6,1,3]=>0000000=>0000000=>[8]
[6,7,8,4,2,5,1,3]=>0000000=>0000000=>[8]
[8,6,3,7,2,1,5,4]=>0000000=>0000000=>[8]
[6,7,8,3,2,1,5,4]=>0000000=>0000000=>[8]
[5,7,8,3,2,1,6,4]=>0000000=>0000000=>[8]
[2,7,8,4,3,5,6,1]=>0000000=>0000000=>[8]
[3,7,8,4,2,5,1,6]=>0000000=>0000000=>[8]
[7,6,3,8,2,1,4,5]=>0000000=>0000000=>[8]
[8,6,3,7,2,1,4,5]=>0000000=>0000000=>[8]
[5,6,3,8,2,1,4,7]=>0000000=>0000000=>[8]
[3,6,4,8,2,5,1,7]=>0000000=>0000000=>[8]
[2,6,4,8,3,5,7,1]=>0000000=>0000000=>[8]
[2,6,4,7,3,5,8,1]=>0000000=>0000000=>[8]
[4,6,3,7,2,1,5,8]=>0000001=>1000000=>[1,7]
[5,6,3,7,2,1,4,8]=>0000001=>1000000=>[1,7]
[8,4,3,2,1,6,5,7]=>0000000=>0000000=>[8]
[6,4,3,2,1,7,5,8]=>0000001=>1000000=>[1,7]
[4,5,3,2,7,1,6,8]=>0000001=>1000000=>[1,7]
[7,4,3,2,1,8,5,6]=>0000000=>0000000=>[8]
[8,4,3,2,1,7,5,6]=>0000000=>0000000=>[8]
[7,4,3,2,1,8,6,5]=>0000000=>0000000=>[8]
[5,6,3,8,2,1,7,4]=>0000000=>0000000=>[8]
[7,5,3,2,8,1,6,4]=>0000000=>0000000=>[8]
[8,5,4,2,7,6,1,3]=>0000000=>0000000=>[8]
[7,5,4,2,8,6,1,3]=>0000000=>0000000=>[8]
[6,5,4,2,7,8,1,3]=>0000000=>0000000=>[8]
[8,5,4,2,6,7,1,3]=>0000000=>0000000=>[8]
[5,6,3,7,2,1,8,4]=>0000000=>0000000=>[8]
[4,6,3,7,2,1,8,5]=>0000000=>0000000=>[8]
[3,6,4,7,2,8,1,5]=>0000000=>0000000=>[8]
[2,6,4,7,3,8,5,1]=>0000000=>0000000=>[8]
[3,5,4,2,7,8,1,6]=>0000000=>0000000=>[8]
[7,4,3,2,1,6,8,5]=>0000000=>0000000=>[8]
[8,4,3,2,1,6,7,5]=>0000000=>0000000=>[8]
[8,4,3,2,1,5,7,6]=>0000000=>0000000=>[8]
[7,4,3,2,1,5,8,6]=>0000000=>0000000=>[8]
[6,4,3,2,1,5,8,7]=>0000010=>0100000=>[2,6]
[3,5,4,2,6,8,1,7]=>0000000=>0000000=>[8]
[3,2,6,4,8,5,1,7]=>0000000=>0000000=>[8]
[3,2,5,8,4,6,1,7]=>0000000=>0000000=>[8]
[4,2,1,5,7,3,6,8]=>0000001=>1000000=>[1,7]
[4,5,2,3,7,1,6,8]=>0000001=>1000000=>[1,7]
[4,2,5,3,8,1,6,7]=>0000000=>0000000=>[8]
[4,2,5,8,3,1,6,7]=>0000000=>0000000=>[8]
[4,1,5,3,8,2,6,7]=>0000000=>0000000=>[8]
[4,3,2,7,5,1,6,8]=>0000001=>1000000=>[1,7]
[4,3,6,2,5,1,7,8]=>0000011=>1100000=>[1,1,6]
[4,6,7,1,3,2,5,8]=>0000001=>1000000=>[1,7]
[4,5,1,7,3,2,6,8]=>0000001=>1000000=>[1,7]
[4,5,1,3,7,2,6,8]=>0000001=>1000000=>[1,7]
[3,5,1,4,2,7,6,8]=>0000101=>1010000=>[1,2,5]
[2,5,1,4,3,7,8,6]=>0000100=>0010000=>[3,5]
[5,2,1,4,3,7,8,6]=>0000100=>0010000=>[3,5]
[5,3,1,4,2,7,6,8]=>0000101=>1010000=>[1,2,5]
[4,3,1,7,5,2,6,8]=>0000001=>1000000=>[1,7]
[5,3,6,4,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[4,3,6,1,7,2,5,8]=>0000001=>1000000=>[1,7]
[6,3,4,1,2,7,5,8]=>0000001=>1000000=>[1,7]
[6,2,4,1,3,7,8,5]=>0000000=>0000000=>[8]
[3,6,4,1,2,7,5,8]=>0000001=>1000000=>[1,7]
[4,6,3,1,7,2,5,8]=>0000001=>1000000=>[1,7]
[5,3,6,2,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[4,5,2,7,3,1,6,8]=>0000001=>1000000=>[1,7]
[4,6,7,2,3,1,5,8]=>0000001=>1000000=>[1,7]
[4,6,2,1,7,3,5,8]=>0000001=>1000000=>[1,7]
[3,2,6,1,4,7,5,8]=>0000001=>1000000=>[1,7]
[3,6,7,2,4,5,1,8]=>0000001=>1000000=>[1,7]
[7,2,1,4,6,3,8,5]=>0000000=>0000000=>[8]
[7,3,1,4,6,8,2,5]=>0000000=>0000000=>[8]
[3,6,2,1,5,7,4,8]=>0000001=>1000000=>[1,7]
[7,4,1,5,6,2,3,8]=>0000001=>1000000=>[1,7]
[7,3,1,5,2,6,4,8]=>0000001=>1000000=>[1,7]
[7,2,1,5,3,6,8,4]=>0000000=>0000000=>[8]
[6,2,5,1,3,7,8,4]=>0000000=>0000000=>[8]
[6,3,5,1,2,7,4,8]=>0000001=>1000000=>[1,7]
[6,4,5,1,7,2,3,8]=>0000001=>1000000=>[1,7]
[4,6,5,1,7,2,3,8]=>0000001=>1000000=>[1,7]
[3,6,5,1,2,7,4,8]=>0000001=>1000000=>[1,7]
[2,4,1,5,3,8,7,6]=>0000100=>0010000=>[3,5]
[3,4,5,1,2,8,7,6]=>0000100=>0010000=>[3,5]
[3,4,5,2,8,1,7,6]=>0000000=>0000000=>[8]
[2,4,8,6,3,7,1,5]=>0000000=>0000000=>[8]
[1,8,4,6,3,7,2,5]=>1000000=>0000001=>[7,1]
[3,5,6,2,7,8,4,1]=>0000000=>0000000=>[8]
[4,5,6,7,2,8,3,1]=>0000000=>0000000=>[8]
[2,5,8,6,7,3,4,1]=>0000000=>0000000=>[8]
[4,5,6,7,2,1,8,3]=>0000000=>0000000=>[8]
[2,5,1,6,7,8,4,3]=>0000000=>0000000=>[8]
[3,4,6,8,1,7,5,2]=>0000000=>0000000=>[8]
[2,4,8,6,1,7,5,3]=>0000000=>0000000=>[8]
[8,2,4,3,7,1,6,5]=>0000000=>0000000=>[8]
[6,1,5,7,3,2,4,8]=>0000001=>1000000=>[1,7]
[6,1,5,8,3,2,4,7]=>0000000=>0000000=>[8]
[7,3,2,4,6,1,5,8]=>0000001=>1000000=>[1,7]
[5,7,6,1,8,3,4,2]=>0000000=>0000000=>[8]
[3,2,5,1,6,4,7,8]=>0000011=>1100000=>[1,1,6]
[3,8,6,5,1,7,4,2]=>0000000=>0000000=>[8]
[3,7,6,5,1,8,4,2]=>0000000=>0000000=>[8]
[3,2,5,1,6,7,8,4]=>0000000=>0000000=>[8]
[3,2,4,1,6,8,5,7]=>0001000=>0001000=>[4,4]
[8,3,2,4,7,6,1,5]=>0000000=>0000000=>[8]
[3,2,5,1,8,4,7,6]=>0000000=>0000000=>[8]
[3,2,5,1,6,7,4,8]=>0000001=>1000000=>[1,7]
[8,4,2,3,7,5,1,6]=>0000000=>0000000=>[8]
[5,2,6,1,8,3,7,4]=>0000000=>0000000=>[8]
[5,2,6,1,8,4,7,3]=>0000000=>0000000=>[8]
[7,4,2,3,8,5,1,6]=>0000000=>0000000=>[8]
[8,5,1,6,4,2,3,7]=>0000000=>0000000=>[8]
[8,5,6,1,7,3,4,2]=>0000000=>0000000=>[8]
[3,6,8,5,1,7,4,2]=>0000000=>0000000=>[8]
[3,2,5,1,8,6,7,4]=>0000000=>0000000=>[8]
[3,2,5,1,7,8,6,4]=>0000000=>0000000=>[8]
[4,6,3,7,1,8,5,2]=>0000000=>0000000=>[8]
[4,6,3,7,5,1,8,2]=>0000000=>0000000=>[8]
[4,2,6,1,7,5,3,8]=>0000001=>1000000=>[1,7]
[2,5,7,4,1,6,3,8]=>0000001=>1000000=>[1,7]
[2,5,7,4,1,6,8,3]=>0000000=>0000000=>[8]
[5,4,7,8,3,1,6,2]=>0000000=>0000000=>[8]
[4,3,7,5,1,8,6,2]=>0000000=>0000000=>[8]
[6,4,3,8,5,1,7,2]=>0000000=>0000000=>[8]
[5,8,4,3,6,1,7,2]=>0000000=>0000000=>[8]
[5,4,8,3,6,1,7,2]=>0000000=>0000000=>[8]
[2,5,4,6,1,7,3,8]=>0000001=>1000000=>[1,7]
[4,6,2,1,8,5,7,3]=>0000000=>0000000=>[8]
[2,4,1,7,5,8,6,3]=>0000000=>0000000=>[8]
[2,4,1,7,5,3,8,6]=>0000000=>0000000=>[8]
[2,6,4,1,8,5,3,7]=>0000000=>0000000=>[8]
[5,4,8,2,1,6,3,7]=>0000000=>0000000=>[8]
[2,5,8,4,1,6,3,7]=>0000000=>0000000=>[8]
[3,2,5,6,1,8,4,7]=>0000000=>0000000=>[8]
[4,8,3,2,6,1,5,7]=>0000000=>0000000=>[8]
[3,5,2,8,1,6,4,7]=>0000000=>0000000=>[8]
[3,2,1,6,8,5,4,7]=>0010000=>0000100=>[5,3]
[3,2,7,1,5,4,8,6]=>0000000=>0000000=>[8]
[3,2,7,1,5,8,6,4]=>0000000=>0000000=>[8]
[3,8,2,5,1,6,7,4]=>0000000=>0000000=>[8]
[4,8,3,2,6,7,1,5]=>0000000=>0000000=>[8]
[4,3,8,2,6,7,1,5]=>0000000=>0000000=>[8]
[4,3,2,6,7,8,1,5]=>0000000=>0000000=>[8]
[4,3,2,6,7,1,5,8]=>0000001=>1000000=>[1,7]
[4,3,7,8,2,6,1,5]=>0000000=>0000000=>[8]
[2,5,7,4,8,1,6,3]=>0000000=>0000000=>[8]
[3,2,5,7,1,6,8,4]=>0000000=>0000000=>[8]
[3,2,5,7,1,6,4,8]=>0000001=>1000000=>[1,7]
[6,3,2,7,1,5,4,8]=>0000001=>1000000=>[1,7]
[6,3,2,7,1,5,8,4]=>0000000=>0000000=>[8]
[6,3,2,7,8,1,5,4]=>0000000=>0000000=>[8]
[6,5,2,1,7,8,4,3]=>0000000=>0000000=>[8]
[6,2,1,8,5,3,7,4]=>0000000=>0000000=>[8]
[6,3,2,7,1,4,8,5]=>0000000=>0000000=>[8]
[6,3,2,1,4,7,8,5]=>0000000=>0000000=>[8]
[6,3,2,1,4,7,5,8]=>0000001=>1000000=>[1,7]
[3,5,2,1,7,8,4,6]=>0000000=>0000000=>[8]
[4,6,2,1,8,3,7,5]=>0000000=>0000000=>[8]
[3,2,7,1,4,8,6,5]=>0000000=>0000000=>[8]
[3,5,8,2,1,7,4,6]=>0000000=>0000000=>[8]
[4,8,3,7,2,1,5,6]=>0000000=>0000000=>[8]
[4,3,7,2,8,1,5,6]=>0000000=>0000000=>[8]
[4,3,7,2,1,5,6,8]=>0000001=>1000000=>[1,7]
[4,8,3,2,7,1,5,6]=>0000000=>0000000=>[8]
[6,3,2,8,1,4,7,5]=>0000000=>0000000=>[8]
[3,2,1,4,7,5,8,6]=>0011000=>0001100=>[4,1,3]
[5,3,2,1,8,4,6,7]=>0000000=>0000000=>[8]
[4,8,3,2,1,5,6,7]=>0000000=>0000000=>[8]
[4,3,8,2,1,5,6,7]=>0000000=>0000000=>[8]
[6,2,5,3,4,1,8,7]=>0000010=>0100000=>[2,6]
[8,1,7,3,4,2,6,5]=>0000000=>0000000=>[8]
[8,2,7,1,4,3,6,5]=>0000000=>0000000=>[8]
[8,2,3,1,5,4,7,6]=>0000000=>0000000=>[8]
[2,1,8,5,7,3,6,4]=>0100000=>0000010=>[6,2]
[3,6,7,8,4,2,5,1]=>0000000=>0000000=>[8]
[5,2,7,8,1,4,6,3]=>0000000=>0000000=>[8]
[2,8,4,5,3,1,6,7]=>0000000=>0000000=>[8]
[2,7,6,8,4,3,5,1]=>0000000=>0000000=>[8]
[4,6,8,5,1,3,2,7]=>0000000=>0000000=>[8]
[2,4,8,3,6,5,1,7]=>0000000=>0000000=>[8]
[1,7,3,8,5,4,6,2]=>1000000=>0000001=>[7,1]
[2,8,5,4,3,1,6,7]=>0000000=>0000000=>[8]
[1,4,3,2,8,5,6,7]=>1001000=>0001001=>[4,3,1]
[6,4,8,2,5,3,1,7]=>0000000=>0000000=>[8]
[6,2,8,4,5,3,1,7]=>0000000=>0000000=>[8]
[5,1,3,2,4,8,6,7]=>0000100=>0010000=>[3,5]
[2,8,1,5,3,4,7,6]=>0000000=>0000000=>[8]
[1,4,2,8,5,3,6,7]=>1000000=>0000001=>[7,1]
[3,5,1,4,8,2,6,7]=>0000000=>0000000=>[8]
[1,5,2,8,4,3,6,7]=>1000000=>0000001=>[7,1]
[1,2,5,4,3,8,6,7]=>1100100=>0010011=>[3,3,1,1]
[1,2,4,8,5,3,7,6]=>1100000=>0000011=>[6,1,1]
[1,5,2,7,8,4,3,6]=>1000000=>0000001=>[7,1]
[5,1,2,7,4,8,3,6]=>0000000=>0000000=>[8]
[8,3,5,1,4,7,2,6]=>0000000=>0000000=>[8]
[1,2,8,5,7,4,3,6]=>1100000=>0000011=>[6,1,1]
[1,2,4,8,7,5,3,6]=>1100000=>0000011=>[6,1,1]
[2,8,1,4,3,7,6,5]=>0000000=>0000000=>[8]
[7,6,1,4,2,8,3,5]=>0000000=>0000000=>[8]
[7,1,6,2,8,4,3,5]=>0000000=>0000000=>[8]
[1,4,2,7,8,5,3,6]=>1000000=>0000001=>[7,1]
[6,1,2,8,4,3,7,5]=>0000000=>0000000=>[8]
[6,4,1,2,8,3,7,5]=>0000000=>0000000=>[8]
[7,6,1,3,2,4,8,5]=>0000000=>0000000=>[8]
[6,7,1,3,2,4,8,5]=>0000000=>0000000=>[8]
[1,2,7,3,5,8,4,6]=>1100000=>0000011=>[6,1,1]
[5,8,1,3,7,2,4,6]=>0000000=>0000000=>[8]
[1,2,5,8,7,3,4,6]=>1100000=>0000011=>[6,1,1]
[8,6,1,3,2,4,7,5]=>0000000=>0000000=>[8]
[4,2,8,1,7,3,6,5]=>0000000=>0000000=>[8]
[7,1,2,8,4,3,6,5]=>0000000=>0000000=>[8]
[1,2,8,4,7,5,3,6]=>1100000=>0000011=>[6,1,1]
[1,2,8,7,4,5,3,6]=>1100000=>0000011=>[6,1,1]
[2,8,1,7,5,3,4,6]=>0000000=>0000000=>[8]
[8,3,7,1,5,2,4,6]=>0000000=>0000000=>[8]
[8,6,1,4,2,7,3,5]=>0000000=>0000000=>[8]
[7,1,2,8,6,4,3,5]=>0000000=>0000000=>[8]
[3,7,4,8,1,6,2,5]=>0000000=>0000000=>[8]
[3,4,8,7,1,6,2,5]=>0000000=>0000000=>[8]
[4,2,8,1,7,6,3,5]=>0000000=>0000000=>[8]
[2,8,1,7,6,4,3,5]=>0000000=>0000000=>[8]
[7,8,3,4,1,5,2,6]=>0000000=>0000000=>[8]
[6,8,3,4,1,7,2,5]=>0000000=>0000000=>[8]
[5,7,3,4,1,8,2,6]=>0000000=>0000000=>[8]
[5,8,3,4,1,7,2,6]=>0000000=>0000000=>[8]
[4,7,3,5,1,6,2,8]=>0000001=>1000000=>[1,7]
[4,8,3,5,1,6,2,7]=>0000000=>0000000=>[8]
[4,8,3,5,1,7,2,6]=>0000000=>0000000=>[8]
[4,7,3,5,1,8,2,6]=>0000000=>0000000=>[8]
[5,6,2,3,1,7,4,8]=>0000001=>1000000=>[1,7]
[5,6,2,4,1,8,3,7]=>0000000=>0000000=>[8]
[5,6,2,4,1,7,3,8]=>0000001=>1000000=>[1,7]
[4,6,2,5,1,7,3,8]=>0000001=>1000000=>[1,7]
[4,6,2,5,1,8,3,7]=>0000000=>0000000=>[8]
[4,5,1,8,3,7,2,6]=>0000000=>0000000=>[8]
[4,6,2,7,3,8,1,5]=>0000000=>0000000=>[8]
[5,6,2,7,3,8,1,4]=>0000000=>0000000=>[8]
[5,6,2,8,4,7,1,3]=>0000000=>0000000=>[8]
[5,6,2,8,3,7,1,4]=>0000000=>0000000=>[8]
[4,6,2,8,3,7,1,5]=>0000000=>0000000=>[8]
[4,5,1,7,3,6,2,8]=>0000001=>1000000=>[1,7]
[4,5,1,8,3,6,2,7]=>0000000=>0000000=>[8]
[6,3,8,4,5,7,2,1]=>0000000=>0000000=>[8]
[2,5,8,4,7,6,3,1]=>0000000=>0000000=>[8]
[4,3,8,1,5,6,7,2]=>0000000=>0000000=>[8]
[3,8,7,4,1,6,2,5]=>0000000=>0000000=>[8]
[6,1,8,4,5,7,2,3]=>0000000=>0000000=>[8]
[4,5,7,6,2,3,8,1]=>0000000=>0000000=>[8]
[3,5,7,2,6,4,8,1]=>0000000=>0000000=>[8]
[2,5,7,3,6,4,8,1]=>0000000=>0000000=>[8]
[8,4,3,7,6,1,5,2]=>0000000=>0000000=>[8]
[6,7,2,3,5,4,8,1]=>0000000=>0000000=>[8]
[5,2,7,3,6,4,8,1]=>0000000=>0000000=>[8]
[8,3,4,7,6,1,5,2]=>0000000=>0000000=>[8]
[8,2,4,7,1,6,5,3]=>0000000=>0000000=>[8]
[3,1,4,7,6,8,5,2]=>0000000=>0000000=>[8]
[5,1,7,3,6,8,4,2]=>0000000=>0000000=>[8]
[6,7,1,3,5,8,4,2]=>0000000=>0000000=>[8]
[4,8,3,7,6,1,5,2]=>0000000=>0000000=>[8]
[2,8,4,7,1,6,5,3]=>0000000=>0000000=>[8]
[8,1,4,7,2,6,5,3]=>0000000=>0000000=>[8]
[8,1,3,2,7,6,5,4]=>0000000=>0000000=>[8]
[2,8,3,1,7,6,5,4]=>0000000=>0000000=>[8]
[6,7,1,2,8,5,4,3]=>0000000=>0000000=>[8]
[8,2,3,1,7,6,5,4]=>0000000=>0000000=>[8]
[1,4,2,7,8,6,5,3]=>1000000=>0000001=>[7,1]
[8,4,2,7,1,6,5,3]=>0000000=>0000000=>[8]
[8,5,7,2,1,6,4,3]=>0000000=>0000000=>[8]
[1,5,7,2,8,6,4,3]=>1000000=>0000001=>[7,1]
[2,5,7,1,8,6,4,3]=>0000000=>0000000=>[8]
[3,5,7,1,6,8,4,2]=>0000000=>0000000=>[8]
[6,7,4,5,8,1,3,2]=>0000000=>0000000=>[8]
[2,5,7,8,1,6,4,3]=>0000000=>0000000=>[8]
[1,5,7,8,2,6,4,3]=>1000000=>0000001=>[7,1]
[8,5,7,1,2,6,4,3]=>0000000=>0000000=>[8]
[8,4,1,7,2,6,5,3]=>0000000=>0000000=>[8]
[6,7,2,8,1,5,4,3]=>0000000=>0000000=>[8]
[5,2,7,8,1,6,4,3]=>0000000=>0000000=>[8]
[4,2,8,7,1,6,5,3]=>0000000=>0000000=>[8]
[1,3,8,2,7,6,5,4]=>1000000=>0000001=>[7,1]
[8,3,1,2,7,6,5,4]=>0000000=>0000000=>[8]
[8,2,1,3,7,6,5,4]=>0000000=>0000000=>[8]
[2,1,8,3,7,6,5,4]=>0100000=>0000010=>[6,2]
[5,1,7,8,2,6,4,3]=>0000000=>0000000=>[8]
[6,7,1,8,2,5,4,3]=>0000000=>0000000=>[8]
[4,8,1,7,2,6,5,3]=>0000000=>0000000=>[8]
[3,8,1,2,7,6,5,4]=>0000000=>0000000=>[8]
[1,8,2,3,7,6,5,4]=>1000000=>0000001=>[7,1]
[3,7,1,5,8,2,6,4]=>0000000=>0000000=>[8]
[2,7,1,5,8,3,6,4]=>0000000=>0000000=>[8]
[2,6,5,1,8,3,7,4]=>0000000=>0000000=>[8]
[5,6,4,1,8,7,2,3]=>0000000=>0000000=>[8]
[8,1,4,5,7,6,2,3]=>0000000=>0000000=>[8]
[6,4,5,1,8,7,2,3]=>0000000=>0000000=>[8]
[5,4,6,1,8,7,2,3]=>0000000=>0000000=>[8]
[3,5,6,1,8,2,7,4]=>0000000=>0000000=>[8]
[2,5,6,1,8,3,7,4]=>0000000=>0000000=>[8]
[2,4,6,1,3,8,7,5]=>0000000=>0000000=>[8]
[3,4,6,1,2,8,7,5]=>0000000=>0000000=>[8]
[5,3,6,1,8,2,7,4]=>0000000=>0000000=>[8]
[7,3,1,5,8,2,6,4]=>0000000=>0000000=>[8]
[8,1,3,5,7,2,6,4]=>0000000=>0000000=>[8]
[8,1,2,5,7,3,6,4]=>0000000=>0000000=>[8]
[7,2,1,5,8,3,6,4]=>0000000=>0000000=>[8]
[6,2,5,1,8,3,7,4]=>0000000=>0000000=>[8]
[4,2,6,1,3,8,7,5]=>0000000=>0000000=>[8]
[4,2,5,3,1,8,7,6]=>0000100=>0010000=>[3,5]
[6,2,4,1,3,8,7,5]=>0000000=>0000000=>[8]
[7,2,1,4,3,8,6,5]=>0000000=>0000000=>[8]
[8,1,2,4,3,7,6,5]=>0000000=>0000000=>[8]
[8,1,3,4,2,7,6,5]=>0000000=>0000000=>[8]
[7,3,1,4,2,8,6,5]=>0000000=>0000000=>[8]
[4,6,3,1,2,8,7,5]=>0000000=>0000000=>[8]
[2,6,4,1,3,8,7,5]=>0000000=>0000000=>[8]
[2,7,1,4,3,8,6,5]=>0000000=>0000000=>[8]
[8,1,6,7,2,3,5,4]=>0000000=>0000000=>[8]
[4,7,1,2,3,8,6,5]=>0000000=>0000000=>[8]
[3,7,1,2,4,8,6,5]=>0000000=>0000000=>[8]
[2,6,3,1,4,8,7,5]=>0000000=>0000000=>[8]
[3,6,2,1,4,8,7,5]=>0000000=>0000000=>[8]
[5,6,2,1,8,3,7,4]=>0000000=>0000000=>[8]
[6,5,2,1,8,3,7,4]=>0000000=>0000000=>[8]
[8,1,4,2,3,7,6,5]=>0000000=>0000000=>[8]
[7,4,1,2,3,8,6,5]=>0000000=>0000000=>[8]
[5,4,2,3,1,8,7,6]=>0000100=>0010000=>[3,5]
[3,5,2,4,1,8,7,6]=>0000100=>0010000=>[3,5]
[7,3,1,2,4,8,6,5]=>0000000=>0000000=>[8]
[8,1,3,2,4,7,6,5]=>0000000=>0000000=>[8]
[7,2,1,3,4,8,6,5]=>0000000=>0000000=>[8]
[2,4,6,3,5,8,7,1]=>0000000=>0000000=>[8]
[4,2,6,5,8,1,3,7]=>0000000=>0000000=>[8]
[2,4,1,6,5,8,3,7]=>0000000=>0000000=>[8]
[2,6,4,3,8,7,5,1]=>0000000=>0000000=>[8]
[4,2,6,8,5,3,7,1]=>0000000=>0000000=>[8]
[2,4,6,8,1,5,7,3]=>0000000=>0000000=>[8]
[2,1,4,6,8,5,3,7]=>0100000=>0000010=>[6,2]
[2,4,6,1,8,5,3,7]=>0000000=>0000000=>[8]
[2,4,6,8,1,5,3,7]=>0000000=>0000000=>[8]
[2,4,6,8,3,5,7,1]=>0000000=>0000000=>[8]
[2,4,6,3,8,5,7,1]=>0000000=>0000000=>[8]
[2,4,3,6,8,5,7,1]=>0000000=>0000000=>[8]
[2,4,3,6,8,5,1,7]=>0000000=>0000000=>[8]
[2,4,3,6,8,1,5,7]=>0000000=>0000000=>[8]
[4,6,5,2,8,7,1,3]=>0000000=>0000000=>[8]
[2,6,4,1,8,7,5,3]=>0000000=>0000000=>[8]
[1,3,7,4,5,8,2,6]=>1000000=>0000001=>[7,1]
[1,7,6,3,4,8,2,5]=>1000000=>0000001=>[7,1]
[8,1,6,3,7,2,4,5]=>0000000=>0000000=>[8]
[1,2,7,4,8,3,5,6]=>1100000=>0000011=>[6,1,1]
[6,1,7,3,4,8,2,5]=>0000000=>0000000=>[8]
[2,1,7,4,5,8,3,6]=>0100000=>0000010=>[6,2]
[5,1,4,7,3,8,2,6]=>0000000=>0000000=>[8]
[4,3,1,7,5,8,2,6]=>0000000=>0000000=>[8]
[2,8,6,3,7,1,4,5]=>0000000=>0000000=>[8]
[6,8,1,3,7,2,4,5]=>0000000=>0000000=>[8]
[5,8,2,1,7,3,4,6]=>0000000=>0000000=>[8]
[5,7,2,1,8,3,4,6]=>0000000=>0000000=>[8]
[6,7,1,3,8,2,4,5]=>0000000=>0000000=>[8]
[8,5,1,3,7,2,4,6]=>0000000=>0000000=>[8]
[1,5,3,2,8,4,6,7]=>1000000=>0000001=>[7,1]
[2,6,4,8,7,1,3,5]=>0000000=>0000000=>[8]
[1,6,4,8,7,2,3,5]=>1000000=>0000001=>[7,1]
[4,3,2,8,7,1,5,6]=>0000000=>0000000=>[8]
[5,2,4,8,7,1,3,6]=>0000000=>0000000=>[8]
[6,2,8,3,7,1,4,5]=>0000000=>0000000=>[8]
[5,1,4,8,7,2,3,6]=>0000000=>0000000=>[8]
[3,7,2,1,5,4,8,6]=>0000000=>0000000=>[8]
[3,8,2,1,5,4,7,6]=>0000000=>0000000=>[8]
[8,3,2,1,5,4,6,7]=>0000000=>0000000=>[8]
[8,3,2,1,6,4,5,7]=>0000000=>0000000=>[8]
[8,4,2,5,1,6,3,7]=>0000000=>0000000=>[8]
[8,3,2,1,4,6,5,7]=>0000000=>0000000=>[8]
[3,8,2,1,4,5,7,6]=>0000000=>0000000=>[8]
[3,2,7,1,4,6,8,5]=>0000000=>0000000=>[8]
[3,2,8,1,4,6,7,5]=>0000000=>0000000=>[8]
[3,8,2,1,4,7,5,6]=>0000000=>0000000=>[8]
[3,8,2,1,5,7,4,6]=>0000000=>0000000=>[8]
[4,8,2,5,1,7,3,6]=>0000000=>0000000=>[8]
[4,7,2,5,1,8,3,6]=>0000000=>0000000=>[8]
[3,7,2,1,5,8,4,6]=>0000000=>0000000=>[8]
[3,7,2,1,4,8,5,6]=>0000000=>0000000=>[8]
[3,2,1,7,5,8,6,4]=>0010000=>0000100=>[5,3]
[4,2,7,6,1,8,3,5]=>0000000=>0000000=>[8]
[4,3,7,6,8,1,2,5]=>0000000=>0000000=>[8]
[4,3,8,6,7,1,2,5]=>0000000=>0000000=>[8]
[3,8,2,1,7,4,5,6]=>0000000=>0000000=>[8]
[3,2,8,1,6,4,7,5]=>0000000=>0000000=>[8]
[3,2,7,1,6,4,8,5]=>0000000=>0000000=>[8]
[4,2,7,6,1,3,8,5]=>0000000=>0000000=>[8]
[4,2,8,6,1,3,7,5]=>0000000=>0000000=>[8]
[5,7,8,3,4,1,2,6]=>0000000=>0000000=>[8]
[4,2,6,8,1,3,7,5]=>0000000=>0000000=>[8]
[4,2,6,7,1,3,8,5]=>0000000=>0000000=>[8]
[3,2,6,1,8,4,7,5]=>0000000=>0000000=>[8]
[3,7,2,1,8,5,4,6]=>0000000=>0000000=>[8]
[4,7,3,8,5,1,2,6]=>0000000=>0000000=>[8]
[4,3,7,8,6,1,2,5]=>0000000=>0000000=>[8]
[3,2,7,1,8,6,4,5]=>0000000=>0000000=>[8]
[3,2,1,6,8,5,7,4]=>0010000=>0000100=>[5,3]
[3,2,6,1,8,7,4,5]=>0000000=>0000000=>[8]
[4,2,6,8,1,7,3,5]=>0000000=>0000000=>[8]
[4,3,6,8,7,1,2,5]=>0000000=>0000000=>[8]
[4,2,6,7,1,8,3,5]=>0000000=>0000000=>[8]
[3,2,6,1,7,8,4,5]=>0000000=>0000000=>[8]
[5,3,6,4,8,7,1,2]=>0000000=>0000000=>[8]
[1,4,6,2,7,8,5,3]=>1000000=>0000001=>[7,1]
[3,1,8,5,4,2,6,7]=>0000000=>0000000=>[8]
[1,2,7,5,4,8,6,3]=>1100000=>0000011=>[6,1,1]
[6,3,7,5,4,8,1,2]=>0000000=>0000000=>[8]
[1,6,2,5,4,8,7,3]=>1000000=>0000001=>[7,1]
[1,8,2,5,7,3,6,4]=>1000000=>0000001=>[7,1]
[6,2,1,5,4,8,7,3]=>0000000=>0000000=>[8]
[4,1,6,2,8,7,5,3]=>0000000=>0000000=>[8]
[7,8,3,1,4,2,6,5]=>0000000=>0000000=>[8]
[4,3,6,1,8,2,7,5]=>0000000=>0000000=>[8]
[7,5,1,6,4,3,2,8]=>0000001=>1000000=>[1,7]
[6,1,5,7,4,3,2,8]=>0000001=>1000000=>[1,7]
[1,5,8,6,4,3,2,7]=>1000000=>0000001=>[7,1]
[7,8,5,1,6,3,2,4]=>0000000=>0000000=>[8]
[2,6,1,5,7,3,8,4]=>0000000=>0000000=>[8]
[1,6,8,7,4,3,2,5]=>1000000=>0000001=>[7,1]
[6,8,1,7,4,3,2,5]=>0000000=>0000000=>[8]
[5,6,1,7,4,3,2,8]=>0000001=>1000000=>[1,7]
[5,1,7,6,4,3,2,8]=>0000001=>1000000=>[1,7]
[6,1,7,8,4,3,2,5]=>0000000=>0000000=>[8]
[7,1,8,6,4,3,2,5]=>0000000=>0000000=>[8]
[7,2,1,5,4,6,8,3]=>0000000=>0000000=>[8]
[1,2,8,5,6,3,7,4]=>1100000=>0000011=>[6,1,1]
[6,1,2,5,7,3,8,4]=>0000000=>0000000=>[8]
[4,3,6,1,5,7,2,8]=>0000001=>1000000=>[1,7]
[1,3,6,8,5,7,2,4]=>1000000=>0000001=>[7,1]
[1,3,6,4,8,7,2,5]=>1000000=>0000001=>[7,1]
[4,1,6,7,3,8,2,5]=>0000000=>0000000=>[8]
[5,4,6,1,3,7,2,8]=>0000001=>1000000=>[1,7]
[6,4,1,5,2,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,1,7,5,2,3,8,6]=>0000000=>0000000=>[8]
[2,8,3,5,4,1,7,6]=>0000000=>0000000=>[8]
[7,8,1,4,6,3,2,5]=>0000000=>0000000=>[8]
[5,1,8,7,4,3,2,6]=>0000000=>0000000=>[8]
[6,5,1,8,4,3,2,7]=>0000000=>0000000=>[8]
[6,5,7,1,4,3,2,8]=>0000001=>1000000=>[1,7]
[7,5,8,1,4,3,2,6]=>0000000=>0000000=>[8]
[1,5,7,8,4,3,2,6]=>1000000=>0000001=>[7,1]
[2,4,7,5,1,3,8,6]=>0000000=>0000000=>[8]
[7,8,4,6,1,3,2,5]=>0000000=>0000000=>[8]
[1,6,5,8,4,3,2,7]=>1000000=>0000001=>[7,1]
[6,8,5,1,4,3,2,7]=>0000000=>0000000=>[8]
[3,6,2,5,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[4,3,6,2,8,1,5,7]=>0000000=>0000000=>[8]
[6,1,2,5,4,7,8,3]=>0000000=>0000000=>[8]
[6,2,4,5,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,2,8,5,1,3,7,6]=>0000000=>0000000=>[8]
[4,3,6,8,1,7,2,5]=>0000000=>0000000=>[8]
[5,3,6,4,1,7,2,8]=>0000001=>1000000=>[1,7]
[1,6,7,4,8,3,5,2]=>1000000=>0000001=>[7,1]
[1,4,6,3,7,5,8,2]=>1000000=>0000001=>[7,1]
[4,6,7,2,5,8,1,3]=>0000000=>0000000=>[8]
[2,4,6,1,7,5,3,8]=>0000001=>1000000=>[1,7]
[2,7,5,4,1,6,3,8]=>0000001=>1000000=>[1,7]
[1,7,5,4,3,8,6,2]=>1000000=>0000001=>[7,1]
[1,5,8,4,3,6,7,2]=>1000000=>0000001=>[7,1]
[5,4,6,2,7,8,1,3]=>0000000=>0000000=>[8]
[2,5,4,1,6,7,3,8]=>0000001=>1000000=>[1,7]
[5,6,3,2,7,1,4,8]=>0000001=>1000000=>[1,7]
[5,6,3,2,7,1,8,4]=>0000000=>0000000=>[8]
[8,5,6,3,2,7,1,4]=>0000000=>0000000=>[8]
[5,4,6,2,8,1,7,3]=>0000000=>0000000=>[8]
[2,4,1,7,8,5,3,6]=>0000000=>0000000=>[8]
[5,6,3,2,1,8,4,7]=>0000000=>0000000=>[8]
[3,5,2,1,6,4,7,8]=>0000011=>1100000=>[1,1,6]
[6,8,4,3,2,1,5,7]=>0000000=>0000000=>[8]
[5,3,8,2,1,6,4,7]=>0000000=>0000000=>[8]
[7,3,2,8,5,1,6,4]=>0000000=>0000000=>[8]
[8,4,6,3,2,1,7,5]=>0000000=>0000000=>[8]
[5,4,7,2,1,8,6,3]=>0000000=>0000000=>[8]
[5,7,3,2,1,6,8,4]=>0000000=>0000000=>[8]
[6,3,7,2,5,1,8,4]=>0000000=>0000000=>[8]
[6,7,8,3,5,2,1,4]=>0000000=>0000000=>[8]
[6,2,5,7,8,4,1,3]=>0000000=>0000000=>[8]
[2,1,5,7,8,6,3,4]=>0100000=>0000010=>[6,2]
[3,6,7,2,8,1,4,5]=>0000000=>0000000=>[8]
[3,2,6,1,7,4,5,8]=>0000001=>1000000=>[1,7]
[2,5,8,4,1,3,7,6]=>0000000=>0000000=>[8]
[2,4,1,7,8,3,6,5]=>0000000=>0000000=>[8]
[3,6,8,2,1,7,4,5]=>0000000=>0000000=>[8]
[5,3,8,2,1,4,7,6]=>0000000=>0000000=>[8]
[4,8,7,3,2,1,5,6]=>0000000=>0000000=>[8]
[4,7,3,2,1,5,6,8]=>0000001=>1000000=>[1,7]
[8,4,7,3,2,1,5,6]=>0000000=>0000000=>[8]
[8,3,5,2,1,4,7,6]=>0000000=>0000000=>[8]
[3,5,2,1,4,6,8,7]=>0000110=>0110000=>[2,1,5]
[2,7,6,5,1,8,3,4]=>0000000=>0000000=>[8]
[2,7,6,5,1,8,4,3]=>0000000=>0000000=>[8]
[7,3,5,1,8,4,2,6]=>0000000=>0000000=>[8]
[2,3,4,8,7,6,1,5]=>0000000=>0000000=>[8]
[2,1,4,5,8,7,3,6]=>0100000=>0000010=>[6,2]
[6,4,3,5,8,7,1,2]=>0000000=>0000000=>[8]
[5,7,3,6,1,8,4,2]=>0000000=>0000000=>[8]
[2,3,4,8,7,1,6,5]=>0000000=>0000000=>[8]
[6,1,4,2,8,5,7,3]=>0000000=>0000000=>[8]
[1,3,8,5,7,6,2,4]=>1000000=>0000001=>[7,1]
[8,6,1,5,7,2,3,4]=>0000000=>0000000=>[8]
[3,2,8,5,7,6,1,4]=>0000000=>0000000=>[8]
[7,8,5,4,1,6,2,3]=>0000000=>0000000=>[8]
[7,2,6,4,5,1,8,3]=>0000000=>0000000=>[8]
[3,8,2,7,6,1,5,4]=>0000000=>0000000=>[8]
[4,8,7,2,6,5,3,1]=>0000000=>0000000=>[8]
[4,8,7,3,1,6,5,2]=>0000000=>0000000=>[8]
[4,8,7,3,2,6,1,5]=>0000000=>0000000=>[8]
[4,8,7,3,2,6,5,1]=>0000000=>0000000=>[8]
[4,8,7,3,6,2,5,1]=>0000000=>0000000=>[8]
[4,8,7,3,6,1,5,2]=>0000000=>0000000=>[8]
[5,8,7,6,3,4,2,1]=>0000000=>0000000=>[8]
[5,8,7,6,3,1,4,2]=>0000000=>0000000=>[8]
[5,8,7,6,2,4,3,1]=>0000000=>0000000=>[8]
[5,8,7,6,4,2,1,3]=>0000000=>0000000=>[8]
[5,8,7,6,4,1,3,2]=>0000000=>0000000=>[8]
[5,8,7,6,4,3,1,2]=>0000000=>0000000=>[8]
[7,3,5,2,6,4,1,8]=>0000001=>1000000=>[1,7]
[7,2,1,5,6,4,3,8]=>0000001=>1000000=>[1,7]
[6,2,1,5,7,4,8,3]=>0000000=>0000000=>[8]
[3,2,1,5,7,4,8,6]=>0010000=>0000100=>[5,3]
[2,4,6,7,3,8,1,5]=>0000000=>0000000=>[8]
[1,4,6,7,3,8,5,2]=>1000000=>0000001=>[7,1]
[3,2,1,6,7,8,4,5]=>0010000=>0000100=>[5,3]
[5,2,1,6,7,8,4,3]=>0000000=>0000000=>[8]
[5,3,6,1,7,8,4,2]=>0000000=>0000000=>[8]
[4,3,6,2,7,8,5,1]=>0000000=>0000000=>[8]
[4,2,1,5,7,3,8,6]=>0000000=>0000000=>[8]
[1,5,6,7,8,2,4,3]=>1000000=>0000001=>[7,1]
[1,5,6,7,8,4,2,3]=>1000000=>0000001=>[7,1]
[4,3,6,1,7,8,5,2]=>0000000=>0000000=>[8]
[1,4,3,6,2,5,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,4,3,7,2,5,6,8]=>1000001=>1000001=>[1,6,1]
[1,4,3,7,6,8,2,5]=>1000000=>0000001=>[7,1]
[1,4,3,7,5,8,2,6]=>1000000=>0000001=>[7,1]
[1,5,3,7,4,8,2,6]=>1000000=>0000001=>[7,1]
[1,5,4,8,2,6,3,7]=>1000000=>0000001=>[7,1]
[1,5,4,8,3,7,2,6]=>1000000=>0000001=>[7,1]
[1,2,3,6,5,8,4,7]=>1110000=>0000111=>[5,1,1,1]
[7,8,1,4,5,3,6,2]=>0000000=>0000000=>[8]
[5,8,1,4,7,6,3,2]=>0000000=>0000000=>[8]
[7,5,1,8,6,2,4,3]=>0000000=>0000000=>[8]
[7,4,1,8,2,6,3,5]=>0000000=>0000000=>[8]
[7,1,8,4,2,6,3,5]=>0000000=>0000000=>[8]
[7,3,1,8,4,2,6,5]=>0000000=>0000000=>[8]
[7,2,8,3,6,5,1,4]=>0000000=>0000000=>[8]
[7,2,8,3,6,1,5,4]=>0000000=>0000000=>[8]
[6,1,2,8,3,5,4,7]=>0000000=>0000000=>[8]
[5,2,3,8,1,4,7,6]=>0000000=>0000000=>[8]
[6,2,4,1,8,7,3,5]=>0000000=>0000000=>[8]
[3,1,6,4,2,8,5,7]=>0000000=>0000000=>[8]
[2,6,3,8,7,1,5,4]=>0000000=>0000000=>[8]
[2,6,3,8,5,1,4,7]=>0000000=>0000000=>[8]
[2,5,1,8,3,4,7,6]=>0000000=>0000000=>[8]
[1,2,5,3,8,4,7,6]=>1100000=>0000011=>[6,1,1]
[1,2,4,8,3,7,6,5]=>1100000=>0000011=>[6,1,1]
[2,4,8,3,7,1,6,5]=>0000000=>0000000=>[8]
[2,4,8,3,7,6,1,5]=>0000000=>0000000=>[8]
[2,5,3,8,1,7,4,6]=>0000000=>0000000=>[8]
[2,5,4,1,3,8,7,6]=>0000100=>0010000=>[3,5]
[3,1,5,4,8,2,7,6]=>0000000=>0000000=>[8]
[5,3,1,4,8,2,7,6]=>0000000=>0000000=>[8]
[5,2,3,8,4,7,1,6]=>0000000=>0000000=>[8]
[4,8,2,3,7,6,1,5]=>0000000=>0000000=>[8]
[4,8,2,3,7,1,6,5]=>0000000=>0000000=>[8]
[4,8,1,2,3,7,6,5]=>0000000=>0000000=>[8]
[1,4,8,3,7,2,6,5]=>1000000=>0000001=>[7,1]
[6,3,8,1,5,2,4,7]=>0000000=>0000000=>[8]
[5,3,8,1,2,4,7,6]=>0000000=>0000000=>[8]
[5,1,3,8,2,4,7,6]=>0000000=>0000000=>[8]
[1,5,3,8,2,4,7,6]=>1000000=>0000001=>[7,1]
[1,5,4,8,2,7,6,3]=>1000000=>0000001=>[7,1]
[5,1,4,8,2,7,6,3]=>0000000=>0000000=>[8]
[5,4,8,1,2,7,6,3]=>0000000=>0000000=>[8]
[6,5,1,2,8,7,4,3]=>0000000=>0000000=>[8]
[4,1,5,8,2,7,6,3]=>0000000=>0000000=>[8]
[4,1,2,5,8,7,6,3]=>0000000=>0000000=>[8]
[1,4,2,5,8,7,6,3]=>1000000=>0000001=>[7,1]
[1,3,5,2,8,7,4,6]=>1000000=>0000001=>[7,1]
[3,5,1,2,8,7,4,6]=>0000000=>0000000=>[8]
[4,2,6,1,8,7,3,5]=>0000000=>0000000=>[8]
[4,3,1,5,8,2,7,6]=>0000000=>0000000=>[8]
[3,5,2,8,7,1,4,6]=>0000000=>0000000=>[8]
[3,4,8,7,2,6,1,5]=>0000000=>0000000=>[8]
[3,4,8,1,7,2,6,5]=>0000000=>0000000=>[8]
[1,3,4,8,7,2,6,5]=>1000000=>0000001=>[7,1]
[1,3,4,8,2,7,6,5]=>1000000=>0000001=>[7,1]
[3,4,8,1,2,7,6,5]=>0000000=>0000000=>[8]
[3,4,8,2,7,1,6,5]=>0000000=>0000000=>[8]
[3,4,8,2,7,6,1,5]=>0000000=>0000000=>[8]
[4,2,5,8,1,7,6,3]=>0000000=>0000000=>[8]
[4,3,1,2,5,8,7,6]=>0001100=>0011000=>[3,1,4]
[3,1,4,2,5,8,7,6]=>0001100=>0011000=>[3,1,4]
[2,3,5,1,8,7,6,4]=>0000000=>0000000=>[8]
[7,8,2,1,5,3,6,4]=>0000000=>0000000=>[8]
[6,4,1,2,7,3,5,8]=>0000001=>1000000=>[1,7]
[2,3,7,5,4,1,8,6]=>0000000=>0000000=>[8]
[6,3,1,5,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[7,8,1,5,4,2,6,3]=>0000000=>0000000=>[8]
[7,8,3,5,4,1,6,2]=>0000000=>0000000=>[8]
[7,8,2,5,4,1,3,6]=>0000000=>0000000=>[8]
[7,8,2,5,4,6,1,3]=>0000000=>0000000=>[8]
[6,2,1,5,4,7,3,8]=>0000001=>1000000=>[1,7]
[5,3,6,2,4,7,1,8]=>0000001=>1000000=>[1,7]
[6,4,2,1,7,3,8,5]=>0000000=>0000000=>[8]
[2,7,6,5,3,1,4,8]=>0000001=>1000000=>[1,7]
[3,7,6,4,8,5,1,2]=>0000000=>0000000=>[8]
[5,7,6,3,8,4,1,2]=>0000000=>0000000=>[8]
[5,1,6,2,4,8,3,7]=>0000000=>0000000=>[8]
[4,7,6,5,2,1,3,8]=>0000001=>1000000=>[1,7]
[4,7,6,5,2,8,1,3]=>0000000=>0000000=>[8]
[4,7,6,5,1,8,3,2]=>0000000=>0000000=>[8]
[1,7,6,5,2,8,3,4]=>1000000=>0000001=>[7,1]
[1,7,6,5,3,2,8,4]=>1000000=>0000001=>[7,1]
[4,7,6,5,1,2,8,3]=>0000000=>0000000=>[8]
[4,7,6,5,3,1,8,2]=>0000000=>0000000=>[8]
[5,2,6,3,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,1,6,2,4,7,8,3]=>0000000=>0000000=>[8]
[1,7,2,4,8,3,6,5]=>1000000=>0000001=>[7,1]
[4,7,2,1,5,3,6,8]=>0000001=>1000000=>[1,7]
[4,7,1,6,2,3,8,5]=>0000000=>0000000=>[8]
[1,7,2,6,8,3,5,4]=>1000000=>0000001=>[7,1]
[1,2,6,7,4,8,5,3]=>1100000=>0000011=>[6,1,1]
[3,1,6,7,4,2,8,5]=>0000000=>0000000=>[8]
[3,2,8,5,4,6,1,7]=>0000000=>0000000=>[8]
[4,7,6,3,5,8,1,2]=>0000000=>0000000=>[8]
[3,7,6,5,2,4,1,8]=>0000001=>1000000=>[1,7]
[3,7,6,5,2,1,8,4]=>0000000=>0000000=>[8]
[1,7,6,5,8,2,4,3]=>1000000=>0000001=>[7,1]
[3,7,6,5,8,1,4,2]=>0000000=>0000000=>[8]
[3,7,6,5,1,2,4,8]=>0000001=>1000000=>[1,7]
[3,1,6,8,4,2,5,7]=>0000000=>0000000=>[8]
[4,7,6,8,3,5,1,2]=>0000000=>0000000=>[8]
[2,7,6,5,8,1,3,4]=>0000000=>0000000=>[8]
[2,7,6,5,8,4,1,3]=>0000000=>0000000=>[8]
[3,7,5,8,2,4,1,6]=>0000000=>0000000=>[8]
[5,1,7,8,4,3,2,6]=>0000000=>0000000=>[8]
[4,7,1,8,3,6,2,5]=>0000000=>0000000=>[8]
[7,1,2,3,8,6,5,4]=>0000000=>0000000=>[8]
[6,8,1,4,3,7,2,5]=>0000000=>0000000=>[8]
[8,7,3,2,4,1,6,5]=>0000000=>0000000=>[8]
[7,1,2,3,6,8,5,4]=>0000000=>0000000=>[8]
[3,8,7,1,4,2,6,5]=>0000000=>0000000=>[8]
[5,8,3,7,1,4,2,6]=>0000000=>0000000=>[8]
[7,1,2,3,5,6,8,4]=>0000000=>0000000=>[8]
[5,1,2,3,7,8,6,4]=>0000000=>0000000=>[8]
[8,6,3,2,4,7,1,5]=>0000000=>0000000=>[8]
[7,8,1,2,6,3,5,4]=>0000000=>0000000=>[8]
[1,4,8,2,7,3,5,6]=>1000000=>0000001=>[7,1]
[1,2,8,5,4,7,3,6]=>1100000=>0000011=>[6,1,1]
[2,3,6,8,4,7,1,5]=>0000000=>0000000=>[8]
[1,3,6,8,4,7,5,2]=>1000000=>0000001=>[7,1]
[2,4,8,1,7,3,6,5]=>0000000=>0000000=>[8]
[3,4,8,5,7,6,1,2]=>0000000=>0000000=>[8]
[1,2,6,8,4,5,7,3]=>1100000=>0000011=>[6,1,1]
[7,5,1,2,4,3,6,8]=>0000001=>1000000=>[1,7]
[7,4,6,1,5,2,3,8]=>0000001=>1000000=>[1,7]
[6,8,1,4,7,2,3,5]=>0000000=>0000000=>[8]
[1,6,4,2,8,3,5,7]=>1000000=>0000001=>[7,1]
[1,6,3,8,5,4,2,7]=>1000000=>0000001=>[7,1]
[7,1,3,6,5,4,2,8]=>0000001=>1000000=>[1,7]
[7,2,1,4,6,3,5,8]=>0000001=>1000000=>[1,7]
[7,2,3,6,5,1,4,8]=>0000001=>1000000=>[1,7]
[7,1,2,3,6,5,4,8]=>0000001=>1000000=>[1,7]
[6,8,1,2,7,3,5,4]=>0000000=>0000000=>[8]
[1,6,2,3,8,5,4,7]=>1000000=>0000001=>[7,1]
[1,5,8,2,7,6,3,4]=>1000000=>0000001=>[7,1]
[5,8,2,7,6,3,4,1]=>0000000=>0000000=>[8]
[6,2,8,1,7,3,5,4]=>0000000=>0000000=>[8]
[3,6,4,1,2,8,5,7]=>0000000=>0000000=>[8]
[2,5,1,8,7,6,3,4]=>0000000=>0000000=>[8]
[1,2,5,3,8,7,4,6]=>1100000=>0000011=>[6,1,1]
[2,5,3,8,7,1,6,4]=>0000000=>0000000=>[8]
[2,5,8,4,1,7,6,3]=>0000000=>0000000=>[8]
[3,5,8,7,1,4,2,6]=>0000000=>0000000=>[8]
[5,3,8,4,1,7,6,2]=>0000000=>0000000=>[8]
[4,2,8,7,6,3,5,1]=>0000000=>0000000=>[8]
[6,3,1,8,7,2,5,4]=>0000000=>0000000=>[8]
[5,1,3,8,7,6,2,4]=>0000000=>0000000=>[8]
[1,5,3,8,7,6,2,4]=>1000000=>0000001=>[7,1]
[5,1,8,4,7,2,6,3]=>0000000=>0000000=>[8]
[5,8,7,4,6,1,2,3]=>0000000=>0000000=>[8]
[6,8,5,1,2,4,7,3]=>0000000=>0000000=>[8]
[4,5,8,1,7,2,6,3]=>0000000=>0000000=>[8]
[1,3,2,5,8,7,4,6]=>1010000=>0000101=>[5,2,1]
[3,5,1,8,7,4,6,2]=>0000000=>0000000=>[8]
[4,3,6,1,2,8,5,7]=>0000000=>0000000=>[8]
[4,5,8,3,1,7,2,6]=>0000000=>0000000=>[8]
[4,5,2,8,7,1,3,6]=>0000000=>0000000=>[8]
[3,2,5,8,7,1,6,4]=>0000000=>0000000=>[8]
[3,4,8,7,6,2,1,5]=>0000000=>0000000=>[8]
[3,4,8,7,6,5,1,2]=>0000000=>0000000=>[8]
[1,3,4,8,7,6,2,5]=>1000000=>0000001=>[7,1]
[3,4,8,7,6,2,5,1]=>0000000=>0000000=>[8]
[3,2,5,8,7,4,6,1]=>0000000=>0000000=>[8]
[2,1,3,5,8,7,4,6]=>0110000=>0000110=>[5,1,2]
[1,2,7,5,8,6,4,3]=>1100000=>0000011=>[6,1,1]
[6,8,1,3,7,5,2,4]=>0000000=>0000000=>[8]
[1,3,7,8,2,6,5,4]=>1000000=>0000001=>[7,1]
[2,7,8,1,3,6,5,4]=>0000000=>0000000=>[8]
[8,1,2,6,7,3,5,4]=>0000000=>0000000=>[8]
[8,1,2,6,7,5,3,4]=>0000000=>0000000=>[8]
[8,2,5,7,1,3,6,4]=>0000000=>0000000=>[8]
[2,8,1,6,7,3,5,4]=>0000000=>0000000=>[8]
[2,6,8,3,7,1,5,4]=>0000000=>0000000=>[8]
[2,8,6,4,7,1,5,3]=>0000000=>0000000=>[8]
[6,8,3,4,1,7,5,2]=>0000000=>0000000=>[8]
[6,8,3,7,4,1,5,2]=>0000000=>0000000=>[8]
[8,2,5,7,1,6,3,4]=>0000000=>0000000=>[8]
[8,4,7,2,3,6,1,5]=>0000000=>0000000=>[8]
[8,5,7,4,2,6,1,3]=>0000000=>0000000=>[8]
[8,3,5,7,4,1,6,2]=>0000000=>0000000=>[8]
[8,5,2,4,7,1,6,3]=>0000000=>0000000=>[8]
[8,2,4,7,3,6,1,5]=>0000000=>0000000=>[8]
[8,2,7,1,4,6,3,5]=>0000000=>0000000=>[8]
[8,7,1,2,4,6,3,5]=>0000000=>0000000=>[8]
[8,7,1,4,6,2,3,5]=>0000000=>0000000=>[8]
[8,4,7,1,3,6,2,5]=>0000000=>0000000=>[8]
[8,3,5,7,1,2,6,4]=>0000000=>0000000=>[8]
[5,8,7,1,3,6,2,4]=>0000000=>0000000=>[8]
[8,5,4,7,1,6,2,3]=>0000000=>0000000=>[8]
[8,5,4,7,1,2,6,3]=>0000000=>0000000=>[8]
[8,5,1,4,7,2,6,3]=>0000000=>0000000=>[8]
[8,5,6,3,1,7,4,2]=>0000000=>0000000=>[8]
[1,8,4,5,7,2,6,3]=>1000000=>0000001=>[7,1]
[5,8,7,3,6,1,2,4]=>0000000=>0000000=>[8]
[8,3,5,7,1,6,2,4]=>0000000=>0000000=>[8]
[1,6,8,3,7,5,2,4]=>1000000=>0000001=>[7,1]
[6,3,8,2,7,5,1,4]=>0000000=>0000000=>[8]
[8,6,4,7,3,1,5,2]=>0000000=>0000000=>[8]
[8,4,5,7,3,1,6,2]=>0000000=>0000000=>[8]
[8,3,4,7,2,6,1,5]=>0000000=>0000000=>[8]
[8,7,1,3,4,6,2,5]=>0000000=>0000000=>[8]
[8,3,7,2,4,6,1,5]=>0000000=>0000000=>[8]
[2,8,4,5,7,1,6,3]=>0000000=>0000000=>[8]
[8,7,3,4,5,1,6,2]=>0000000=>0000000=>[8]
[8,7,4,5,2,6,1,3]=>0000000=>0000000=>[8]
[8,7,2,3,4,6,1,5]=>0000000=>0000000=>[8]
[8,6,5,1,3,2,7,4]=>0000000=>0000000=>[8]
[8,6,3,1,7,2,4,5]=>0000000=>0000000=>[8]
[8,7,3,1,5,2,4,6]=>0000000=>0000000=>[8]
[8,6,1,2,4,7,3,5]=>0000000=>0000000=>[8]
[8,6,1,5,3,4,7,2]=>0000000=>0000000=>[8]
[8,6,1,5,2,4,7,3]=>0000000=>0000000=>[8]
[8,6,1,2,5,7,3,4]=>0000000=>0000000=>[8]
[5,1,4,2,3,8,6,7]=>0000100=>0010000=>[3,5]
[5,1,4,2,7,3,6,8]=>0000001=>1000000=>[1,7]
[5,7,8,1,2,4,6,3]=>0000000=>0000000=>[8]
[5,7,8,1,3,4,6,2]=>0000000=>0000000=>[8]
[5,8,1,7,3,4,6,2]=>0000000=>0000000=>[8]
[8,1,5,7,2,4,6,3]=>0000000=>0000000=>[8]
[1,4,2,3,8,7,5,6]=>1001000=>0001001=>[4,3,1]
[1,4,2,7,6,3,5,8]=>1000001=>1000001=>[1,6,1]
[6,1,2,8,7,5,3,4]=>0000000=>0000000=>[8]
[6,1,2,4,8,7,5,3]=>0000000=>0000000=>[8]
[3,1,8,4,6,7,5,2]=>0000000=>0000000=>[8]
[3,1,7,6,4,8,5,2]=>0000000=>0000000=>[8]
[7,1,2,4,6,8,5,3]=>0000000=>0000000=>[8]
[7,1,2,6,8,5,3,4]=>0000000=>0000000=>[8]
[7,1,5,3,2,8,6,4]=>0000000=>0000000=>[8]
[8,1,7,5,3,2,6,4]=>0000000=>0000000=>[8]
[8,3,7,1,2,6,4,5]=>0000000=>0000000=>[8]
[3,1,2,8,4,7,5,6]=>0010000=>0000100=>[5,3]
[1,4,2,3,8,6,5,7]=>1001000=>0001001=>[4,3,1]
[1,4,2,3,8,5,7,6]=>1001000=>0001001=>[4,3,1]
[5,8,1,7,2,4,6,3]=>0000000=>0000000=>[8]
[5,8,1,3,4,7,6,2]=>0000000=>0000000=>[8]
[3,1,8,6,4,7,5,2]=>0000000=>0000000=>[8]
[8,1,2,6,7,4,5,3]=>0000000=>0000000=>[8]
[1,2,3,5,8,4,7,6]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,5,8,6,4,7]=>1110000=>0000111=>[5,1,1,1]
[7,1,2,8,3,6,5,4]=>0000000=>0000000=>[8]
[7,1,2,8,6,4,5,3]=>0000000=>0000000=>[8]
[3,1,7,8,4,6,5,2]=>0000000=>0000000=>[8]
[8,1,2,7,4,6,5,3]=>0000000=>0000000=>[8]
[8,1,2,7,3,6,5,4]=>0000000=>0000000=>[8]
[1,2,3,6,8,5,4,7]=>1110000=>0000111=>[5,1,1,1]
[5,4,8,3,2,7,6,1]=>0000000=>0000000=>[8]
[2,1,5,8,4,7,6,3]=>0100000=>0000010=>[6,2]
[8,3,2,6,7,5,4,1]=>0000000=>0000000=>[8]
[8,4,5,3,2,7,6,1]=>0000000=>0000000=>[8]
[8,4,6,3,7,5,2,1]=>0000000=>0000000=>[8]
[3,6,2,8,7,5,4,1]=>0000000=>0000000=>[8]
[1,6,4,8,2,5,3,7]=>1000000=>0000001=>[7,1]
[1,6,5,8,2,4,3,7]=>1000000=>0000001=>[7,1]
[1,6,8,2,4,3,7,5]=>1000000=>0000001=>[7,1]
[1,6,2,4,3,7,8,5]=>1000000=>0000001=>[7,1]
[1,5,6,2,4,7,3,8]=>1000001=>1000001=>[1,6,1]
[1,5,6,2,4,7,8,3]=>1000000=>0000001=>[7,1]
[1,6,7,2,4,3,8,5]=>1000000=>0000001=>[7,1]
[1,5,8,2,4,6,7,3]=>1000000=>0000001=>[7,1]
[1,5,7,8,3,2,4,6]=>1000000=>0000001=>[7,1]
[1,5,8,3,2,4,6,7]=>1000000=>0000001=>[7,1]
[1,5,6,2,4,8,3,7]=>1000000=>0000001=>[7,1]
[1,7,3,4,2,8,6,5]=>1000000=>0000001=>[7,1]
[1,5,6,2,4,8,7,3]=>1000000=>0000001=>[7,1]
[1,5,8,7,3,2,4,6]=>1000000=>0000001=>[7,1]
[1,7,4,2,8,6,5,3]=>1000000=>0000001=>[7,1]
[1,5,8,3,2,4,7,6]=>1000000=>0000001=>[7,1]
[1,6,5,2,3,7,4,8]=>1000001=>1000001=>[1,6,1]
[1,6,5,2,3,7,8,4]=>1000000=>0000001=>[7,1]
[1,6,8,4,2,3,7,5]=>1000000=>0000001=>[7,1]
[1,6,8,5,2,3,7,4]=>1000000=>0000001=>[7,1]
[1,6,4,2,3,7,5,8]=>1000001=>1000001=>[1,6,1]
[1,5,8,6,2,4,7,3]=>1000000=>0000001=>[7,1]
[1,7,5,2,8,6,4,3]=>1000000=>0000001=>[7,1]
[3,7,5,6,1,4,8,2]=>0000000=>0000000=>[8]
[8,6,1,4,2,7,5,3]=>0000000=>0000000=>[8]
[1,6,7,4,3,5,8,2]=>1000000=>0000001=>[7,1]
[6,7,1,4,3,5,8,2]=>0000000=>0000000=>[8]
[4,7,1,6,3,5,8,2]=>0000000=>0000000=>[8]
[3,1,4,7,6,5,8,2]=>0000000=>0000000=>[8]
[6,1,7,4,3,5,8,2]=>0000000=>0000000=>[8]
[7,1,6,4,3,5,8,2]=>0000000=>0000000=>[8]
[1,7,6,4,3,5,8,2]=>1000000=>0000001=>[7,1]
[8,1,6,4,2,7,5,3]=>0000000=>0000000=>[8]
[4,7,1,3,8,2,5,6]=>0000000=>0000000=>[8]
[7,4,1,3,8,2,5,6]=>0000000=>0000000=>[8]
[1,3,6,4,2,8,5,7]=>1000000=>0000001=>[7,1]
[4,7,3,1,2,8,5,6]=>0000000=>0000000=>[8]
[4,7,8,1,2,6,5,3]=>0000000=>0000000=>[8]
[1,8,6,4,2,7,5,3]=>1000000=>0000001=>[7,1]
[4,8,1,3,7,2,5,6]=>0000000=>0000000=>[8]
[8,7,1,3,6,2,5,4]=>0000000=>0000000=>[8]
[1,8,4,3,7,2,5,6]=>1000000=>0000001=>[7,1]
[3,7,4,6,8,2,1,5]=>0000000=>0000000=>[8]
[2,4,3,7,8,6,1,5]=>0000000=>0000000=>[8]
[1,4,7,3,8,2,5,6]=>1000000=>0000001=>[7,1]
[5,7,6,8,3,2,1,4]=>0000000=>0000000=>[8]
[6,1,4,3,8,2,5,7]=>0000000=>0000000=>[8]
[4,1,7,3,8,2,5,6]=>0000000=>0000000=>[8]
[8,1,4,3,7,2,5,6]=>0000000=>0000000=>[8]
[4,2,3,7,8,6,1,5]=>0000000=>0000000=>[8]
[2,7,5,6,3,8,1,4]=>0000000=>0000000=>[8]
[5,7,2,6,8,4,1,3]=>0000000=>0000000=>[8]
[7,2,5,6,8,4,1,3]=>0000000=>0000000=>[8]
[5,2,3,8,7,6,1,4]=>0000000=>0000000=>[8]
[8,2,3,7,5,6,1,4]=>0000000=>0000000=>[8]
[6,1,8,3,7,2,5,4]=>0000000=>0000000=>[8]
[1,7,8,4,2,6,5,3]=>1000000=>0000001=>[7,1]
[4,7,1,8,2,5,6,3]=>0000000=>0000000=>[8]
[1,4,8,3,6,2,5,7]=>1000000=>0000001=>[7,1]
[3,7,5,8,6,2,1,4]=>0000000=>0000000=>[8]
[3,7,8,6,5,2,1,4]=>0000000=>0000000=>[8]
[6,8,7,5,3,2,1,4]=>0000000=>0000000=>[8]
[5,7,6,8,3,4,1,2]=>0000000=>0000000=>[8]
[3,7,6,8,4,5,1,2]=>0000000=>0000000=>[8]
[1,5,4,7,6,8,2,3]=>1000000=>0000001=>[7,1]
[1,7,4,6,5,8,2,3]=>1000000=>0000001=>[7,1]
[3,7,4,6,5,8,1,2]=>0000000=>0000000=>[8]
[3,5,4,8,6,7,1,2]=>0000000=>0000000=>[8]
[3,8,4,6,5,7,1,2]=>0000000=>0000000=>[8]
[3,6,4,7,5,8,1,2]=>0000000=>0000000=>[8]
[1,6,2,7,5,8,3,4]=>1000000=>0000001=>[7,1]
[1,6,4,8,5,7,2,3]=>1000000=>0000001=>[7,1]
[1,8,4,6,5,7,2,3]=>1000000=>0000001=>[7,1]
[1,5,4,8,6,7,2,3]=>1000000=>0000001=>[7,1]
[7,8,1,5,4,6,2,3]=>0000000=>0000000=>[8]
[1,8,2,6,5,7,3,4]=>1000000=>0000001=>[7,1]
[1,7,2,8,5,6,3,4]=>1000000=>0000001=>[7,1]
[1,7,2,6,5,8,3,4]=>1000000=>0000001=>[7,1]
[1,5,2,7,6,8,3,4]=>1000000=>0000001=>[7,1]
[1,7,6,8,2,5,3,4]=>1000000=>0000001=>[7,1]
[1,7,6,8,4,5,2,3]=>1000000=>0000001=>[7,1]
[7,8,5,6,1,3,2,4]=>0000000=>0000000=>[8]
[5,8,6,7,1,3,2,4]=>0000000=>0000000=>[8]
[1,3,2,7,6,8,4,5]=>1010000=>0000101=>[5,2,1]
[1,7,6,8,2,4,3,5]=>1000000=>0000001=>[7,1]
[1,3,2,8,6,7,4,5]=>1010000=>0000101=>[5,2,1]
[7,8,1,3,2,6,4,5]=>0000000=>0000000=>[8]
[7,8,1,6,2,4,3,5]=>0000000=>0000000=>[8]
[1,8,6,7,2,4,3,5]=>1000000=>0000001=>[7,1]
[7,8,1,4,2,6,3,5]=>0000000=>0000000=>[8]
[8,4,7,5,2,6,1,3]=>0000000=>0000000=>[8]
[5,4,6,8,2,1,7,3]=>0000000=>0000000=>[8]
[4,8,7,5,6,1,3,2]=>0000000=>0000000=>[8]
[3,2,6,8,5,7,1,4]=>0000000=>0000000=>[8]
[7,4,8,6,5,2,1,3]=>0000000=>0000000=>[8]
[2,5,3,7,4,1,8,6]=>0000000=>0000000=>[8]
[4,2,8,7,3,5,6,1]=>0000000=>0000000=>[8]
[2,6,3,5,8,7,1,4]=>0000000=>0000000=>[8]
[8,1,6,4,7,3,2,5]=>0000000=>0000000=>[8]
[4,8,7,5,6,1,2,3]=>0000000=>0000000=>[8]
[6,1,4,8,7,3,5,2]=>0000000=>0000000=>[8]
[2,8,3,7,1,5,6,4]=>0000000=>0000000=>[8]
[4,1,6,5,8,2,3,7]=>0000000=>0000000=>[8]
[8,3,6,1,4,5,2,7]=>0000000=>0000000=>[8]
[2,8,6,1,7,4,5,3]=>0000000=>0000000=>[8]
[1,8,5,2,3,6,7,4]=>1000000=>0000001=>[7,1]
[4,8,3,2,5,6,7,1]=>0000000=>0000000=>[8]
[2,1,8,3,5,6,7,4]=>0100000=>0000010=>[6,2]
[4,2,7,1,8,6,3,5]=>0000000=>0000000=>[8]
[3,8,4,1,2,6,7,5]=>0000000=>0000000=>[8]
[7,6,1,5,8,2,3,4]=>0000000=>0000000=>[8]
[4,2,1,8,5,6,7,3]=>0000000=>0000000=>[8]
[6,5,4,8,7,1,3,2]=>0000000=>0000000=>[8]
[6,5,4,8,1,2,7,3]=>0000000=>0000000=>[8]
[7,5,1,6,8,2,4,3]=>0000000=>0000000=>[8]
[6,5,4,1,8,2,7,3]=>0000000=>0000000=>[8]
[6,5,4,7,1,2,8,3]=>0000000=>0000000=>[8]
[6,5,4,7,8,1,3,2]=>0000000=>0000000=>[8]
[6,5,3,7,1,4,2,8]=>0000001=>1000000=>[1,7]
[7,5,1,4,8,3,2,6]=>0000000=>0000000=>[8]
[8,1,6,4,7,3,5,2]=>0000000=>0000000=>[8]
[7,5,1,4,8,3,6,2]=>0000000=>0000000=>[8]
[7,4,1,5,3,8,6,2]=>0000000=>0000000=>[8]
[8,1,5,4,3,7,6,2]=>0000000=>0000000=>[8]
[8,1,5,4,3,7,2,6]=>0000000=>0000000=>[8]
[6,5,3,8,1,4,2,7]=>0000000=>0000000=>[8]
[8,1,7,2,5,4,6,3]=>0000000=>0000000=>[8]
[7,6,1,2,5,4,8,3]=>0000000=>0000000=>[8]
[6,5,3,8,1,4,7,2]=>0000000=>0000000=>[8]
[6,5,3,1,2,7,8,4]=>0000000=>0000000=>[8]
[8,1,6,4,2,5,7,3]=>0000000=>0000000=>[8]
[8,1,5,4,3,2,7,6]=>0000000=>0000000=>[8]
[7,4,1,5,3,2,8,6]=>0000000=>0000000=>[8]
[6,4,3,1,5,2,8,7]=>0000010=>0100000=>[2,6]
[6,4,3,1,5,7,2,8]=>0000001=>1000000=>[1,7]
[7,4,1,5,3,6,2,8]=>0000001=>1000000=>[1,7]
[6,4,3,1,5,7,8,2]=>0000000=>0000000=>[8]
[7,1,5,8,4,6,2,3]=>0000000=>0000000=>[8]
[8,6,7,1,4,2,5,3]=>0000000=>0000000=>[8]
[8,6,3,7,5,1,2,4]=>0000000=>0000000=>[8]
[8,6,1,7,3,2,5,4]=>0000000=>0000000=>[8]
[7,6,1,8,3,5,2,4]=>0000000=>0000000=>[8]
[7,6,1,3,8,5,2,4]=>0000000=>0000000=>[8]
[7,6,8,2,4,5,1,3]=>0000000=>0000000=>[8]
[7,6,2,8,3,5,1,4]=>0000000=>0000000=>[8]
[8,7,1,5,2,6,3,4]=>0000000=>0000000=>[8]
[8,7,1,5,2,3,6,4]=>0000000=>0000000=>[8]
[8,5,2,3,1,7,6,4]=>0000000=>0000000=>[8]
[8,6,2,3,7,1,5,4]=>0000000=>0000000=>[8]
[8,6,2,7,3,1,5,4]=>0000000=>0000000=>[8]
[8,6,7,2,4,1,5,3]=>0000000=>0000000=>[8]
[6,8,7,3,4,1,5,2]=>0000000=>0000000=>[8]
[8,7,2,5,1,6,3,4]=>0000000=>0000000=>[8]
[8,7,2,1,4,6,3,5]=>0000000=>0000000=>[8]
[8,4,2,1,7,6,3,5]=>0000000=>0000000=>[8]
[8,5,2,7,1,6,3,4]=>0000000=>0000000=>[8]
[8,5,7,2,1,4,3,6]=>0000000=>0000000=>[8]
[5,8,7,3,1,4,2,6]=>0000000=>0000000=>[8]
[8,5,7,2,1,4,6,3]=>0000000=>0000000=>[8]
[8,5,2,7,1,3,6,4]=>0000000=>0000000=>[8]
[8,7,4,1,2,3,6,5]=>0000000=>0000000=>[8]
[8,7,4,1,2,6,3,5]=>0000000=>0000000=>[8]
[8,4,3,1,7,2,6,5]=>0000000=>0000000=>[8]
[8,4,3,1,2,7,6,5]=>0000000=>0000000=>[8]
[8,6,1,3,7,2,5,4]=>0000000=>0000000=>[8]
[8,5,1,3,2,7,6,4]=>0000000=>0000000=>[8]
[8,5,7,4,1,6,2,3]=>0000000=>0000000=>[8]
[8,5,7,4,1,2,6,3]=>0000000=>0000000=>[8]
[8,1,5,4,2,7,6,3]=>0000000=>0000000=>[8]
[8,1,6,4,7,2,5,3]=>0000000=>0000000=>[8]
[6,1,5,8,4,2,7,3]=>0000000=>0000000=>[8]
[5,8,3,6,4,1,2,7]=>0000000=>0000000=>[8]
[8,4,7,5,1,6,2,3]=>0000000=>0000000=>[8]
[8,4,7,5,1,2,6,3]=>0000000=>0000000=>[8]
[8,4,7,5,1,2,3,6]=>0000000=>0000000=>[8]
[8,3,2,6,5,1,4,7]=>0000000=>0000000=>[8]
[4,8,6,3,5,1,2,7]=>0000000=>0000000=>[8]
[4,8,7,3,1,5,2,6]=>0000000=>0000000=>[8]
[8,4,7,2,1,5,3,6]=>0000000=>0000000=>[8]
[8,3,2,7,1,5,4,6]=>0000000=>0000000=>[8]
[8,3,2,1,7,6,4,5]=>0000000=>0000000=>[8]
[8,7,3,1,6,2,4,5]=>0000000=>0000000=>[8]
[8,7,3,1,2,4,6,5]=>0000000=>0000000=>[8]
[8,3,2,1,7,4,6,5]=>0000000=>0000000=>[8]
[8,4,7,2,1,5,6,3]=>0000000=>0000000=>[8]
[8,7,2,1,3,6,4,5]=>0000000=>0000000=>[8]
[8,7,2,1,3,4,6,5]=>0000000=>0000000=>[8]
[1,2,7,3,5,4,8,6]=>1100000=>0000011=>[6,1,1]
[1,5,7,2,3,6,4,8]=>1000001=>1000001=>[1,6,1]
[1,3,8,2,4,5,7,6]=>1000000=>0000001=>[7,1]
[1,2,3,8,4,6,7,5]=>1110000=>0000111=>[5,1,1,1]
[1,7,8,2,3,6,4,5]=>1000000=>0000001=>[7,1]
[1,6,7,8,2,3,5,4]=>1000000=>0000001=>[7,1]
[1,7,8,2,5,3,6,4]=>1000000=>0000001=>[7,1]
[1,8,2,3,6,4,5,7]=>1000000=>0000001=>[7,1]
[1,2,7,8,3,6,4,5]=>1100000=>0000011=>[6,1,1]
[1,5,2,7,8,3,6,4]=>1000000=>0000001=>[7,1]
[1,3,2,8,4,6,7,5]=>1010000=>0000101=>[5,2,1]
[1,8,2,3,4,6,7,5]=>1000000=>0000001=>[7,1]
[1,7,8,2,4,3,6,5]=>1000000=>0000001=>[7,1]
[6,7,3,1,5,2,8,4]=>0000000=>0000000=>[8]
[7,3,6,1,5,2,4,8]=>0000001=>1000000=>[1,7]
[6,2,1,7,5,3,8,4]=>0000000=>0000000=>[8]
[4,6,5,7,8,1,2,3]=>0000000=>0000000=>[8]
[5,7,4,6,1,8,2,3]=>0000000=>0000000=>[8]
[5,7,3,1,6,8,2,4]=>0000000=>0000000=>[8]
[2,5,4,7,3,6,1,8]=>0000001=>1000000=>[1,7]
[4,2,7,3,6,5,1,8]=>0000001=>1000000=>[1,7]
[4,2,6,3,1,5,8,7]=>0000010=>0100000=>[2,6]
[2,5,3,1,6,4,8,7]=>0000010=>0100000=>[2,6]
[2,5,3,7,6,4,1,8]=>0000001=>1000000=>[1,7]
[2,6,5,3,7,4,1,8]=>0000001=>1000000=>[1,7]
[4,2,7,6,3,5,1,8]=>0000001=>1000000=>[1,7]
[2,7,5,3,6,4,1,8]=>0000001=>1000000=>[1,7]
[2,6,3,7,5,4,1,8]=>0000001=>1000000=>[1,7]
[1,7,5,2,3,8,4,6]=>1000000=>0000001=>[7,1]
[2,1,3,7,5,4,8,6]=>0110000=>0000110=>[5,1,2]
[2,3,1,8,6,5,4,7]=>0010000=>0000100=>[5,3]
[2,5,3,1,8,6,4,7]=>0000000=>0000000=>[8]
[4,2,8,3,1,6,5,7]=>0000000=>0000000=>[8]
[8,3,2,6,4,1,5,7]=>0000000=>0000000=>[8]
[3,6,8,2,1,4,5,7]=>0000000=>0000000=>[8]
[1,2,6,3,8,7,4,5]=>1100000=>0000011=>[6,1,1]
[1,2,7,6,3,4,8,5]=>1100000=>0000011=>[6,1,1]
[2,1,3,8,7,5,4,6]=>0110000=>0000110=>[5,1,2]
[1,2,3,8,6,4,7,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,4,8,6,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,7,6,3,8,4,5]=>1100000=>0000011=>[6,1,1]
[1,2,3,6,4,8,7,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,6,4,8,5]=>1110000=>0000111=>[5,1,1,1]
[2,1,3,8,5,4,7,6]=>0110000=>0000110=>[5,1,2]
[7,1,8,4,2,3,5,6]=>0000000=>0000000=>[8]
[4,2,6,3,1,8,5,7]=>0000000=>0000000=>[8]
[5,4,2,8,3,1,6,7]=>0000000=>0000000=>[8]
[2,5,4,8,3,1,6,7]=>0000000=>0000000=>[8]
[1,8,7,4,2,3,5,6]=>1000000=>0000001=>[7,1]
[1,5,2,8,7,3,4,6]=>1000000=>0000001=>[7,1]
[1,2,7,3,6,4,8,5]=>1100000=>0000011=>[6,1,1]
[1,2,8,6,3,7,4,5]=>1100000=>0000011=>[6,1,1]
[1,2,6,3,8,4,7,5]=>1100000=>0000011=>[6,1,1]
[4,2,1,8,3,7,5,6]=>0000000=>0000000=>[8]
[8,3,2,1,7,4,5,6]=>0000000=>0000000=>[8]
[1,2,3,8,7,4,6,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,7,6,4,5]=>1110000=>0000111=>[5,1,1,1]
[2,6,5,7,1,4,3,8]=>0000001=>1000000=>[1,7]
[2,6,5,7,1,3,8,4]=>0000000=>0000000=>[8]
[3,8,5,7,1,2,6,4]=>0000000=>0000000=>[8]
[3,8,5,7,2,6,4,1]=>0000000=>0000000=>[8]
[3,4,8,6,2,5,7,1]=>0000000=>0000000=>[8]
[3,4,8,6,1,2,5,7]=>0000000=>0000000=>[8]
[2,5,7,1,4,8,6,3]=>0000000=>0000000=>[8]
[2,8,1,7,5,6,4,3]=>0000000=>0000000=>[8]
[2,3,8,1,6,5,7,4]=>0000000=>0000000=>[8]
[3,5,7,6,1,2,4,8]=>0000001=>1000000=>[1,7]
[4,8,6,7,2,3,5,1]=>0000000=>0000000=>[8]
[4,8,6,7,1,3,5,2]=>0000000=>0000000=>[8]
[3,4,8,6,1,5,7,2]=>0000000=>0000000=>[8]
[3,8,5,7,1,6,4,2]=>0000000=>0000000=>[8]
[3,8,5,7,2,1,6,4]=>0000000=>0000000=>[8]
[3,4,8,6,2,1,5,7]=>0000000=>0000000=>[8]
[3,5,7,6,2,1,4,8]=>0000001=>1000000=>[1,7]
[5,8,6,7,3,4,2,1]=>0000000=>0000000=>[8]
[5,8,6,7,2,1,3,4]=>0000000=>0000000=>[8]
[4,8,6,7,2,1,5,3]=>0000000=>0000000=>[8]
[4,3,1,7,5,2,8,6]=>0000000=>0000000=>[8]
[4,3,2,8,5,1,7,6]=>0000000=>0000000=>[8]
[4,3,8,5,1,6,7,2]=>0000000=>0000000=>[8]
[5,8,6,7,2,3,4,1]=>0000000=>0000000=>[8]
[5,8,6,7,2,4,3,1]=>0000000=>0000000=>[8]
[5,8,6,7,1,2,4,3]=>0000000=>0000000=>[8]
[3,2,5,7,6,1,4,8]=>0000001=>1000000=>[1,7]
[4,8,6,7,1,3,2,5]=>0000000=>0000000=>[8]
[4,8,6,7,1,2,5,3]=>0000000=>0000000=>[8]
[4,8,6,7,2,5,3,1]=>0000000=>0000000=>[8]
[4,3,8,5,2,6,7,1]=>0000000=>0000000=>[8]
[4,2,6,7,5,1,3,8]=>0000001=>1000000=>[1,7]
[3,8,4,7,1,5,2,6]=>0000000=>0000000=>[8]
[3,5,1,7,4,6,2,8]=>0000001=>1000000=>[1,7]
[3,8,4,7,2,5,1,6]=>0000000=>0000000=>[8]
[4,1,3,8,5,2,6,7]=>0000000=>0000000=>[8]
[4,2,6,7,5,3,8,1]=>0000000=>0000000=>[8]
[4,8,6,7,3,2,5,1]=>0000000=>0000000=>[8]
[4,8,6,7,3,1,2,5]=>0000000=>0000000=>[8]
[3,1,5,7,6,2,4,8]=>0000001=>1000000=>[1,7]
[3,4,1,7,5,6,2,8]=>0000001=>1000000=>[1,7]
[4,1,7,5,2,8,6,3]=>0000000=>0000000=>[8]
[4,1,6,7,5,2,3,8]=>0000001=>1000000=>[1,7]
[5,8,6,7,3,2,4,1]=>0000000=>0000000=>[8]
[5,8,6,7,4,2,3,1]=>0000000=>0000000=>[8]
[5,8,6,7,4,1,2,3]=>0000000=>0000000=>[8]
[5,8,6,7,4,1,3,2]=>0000000=>0000000=>[8]
[5,8,6,7,3,1,4,2]=>0000000=>0000000=>[8]
[4,8,6,7,3,1,5,2]=>0000000=>0000000=>[8]
[4,1,6,7,5,3,8,2]=>0000000=>0000000=>[8]
[4,1,7,5,3,2,8,6]=>0000000=>0000000=>[8]
[4,2,8,5,3,1,7,6]=>0000000=>0000000=>[8]
[4,2,1,6,7,5,3,8]=>0000001=>1000000=>[1,7]
[4,8,6,7,3,2,1,5]=>0000000=>0000000=>[8]
[5,8,6,7,4,2,1,3]=>0000000=>0000000=>[8]
[5,8,6,7,4,3,1,2]=>0000000=>0000000=>[8]
[2,7,1,5,8,6,3,4]=>0000000=>0000000=>[8]
[2,4,7,1,8,5,6,3]=>0000000=>0000000=>[8]
[4,7,5,8,3,1,6,2]=>0000000=>0000000=>[8]
[7,3,5,8,6,2,1,4]=>0000000=>0000000=>[8]
[1,2,7,6,8,3,5,4]=>1100000=>0000011=>[6,1,1]
[6,7,4,1,8,5,3,2]=>0000000=>0000000=>[8]
[7,2,6,8,5,4,1,3]=>0000000=>0000000=>[8]
[6,7,3,1,8,5,4,2]=>0000000=>0000000=>[8]
[6,7,1,8,5,4,3,2]=>0000000=>0000000=>[8]
[7,8,4,2,1,6,5,3]=>0000000=>0000000=>[8]
[6,2,3,4,8,7,1,5]=>0000000=>0000000=>[8]
[6,2,3,4,7,8,1,5]=>0000000=>0000000=>[8]
[7,8,3,6,4,2,1,5]=>0000000=>0000000=>[8]
[7,8,3,5,6,2,1,4]=>0000000=>0000000=>[8]
[5,2,6,3,8,1,7,4]=>0000000=>0000000=>[8]
[6,3,2,5,8,7,1,4]=>0000000=>0000000=>[8]
[6,3,2,8,4,7,1,5]=>0000000=>0000000=>[8]
[6,4,3,8,7,5,1,2]=>0000000=>0000000=>[8]
[6,4,3,7,8,5,1,2]=>0000000=>0000000=>[8]
[6,3,2,7,4,8,1,5]=>0000000=>0000000=>[8]
[6,3,2,5,7,8,1,4]=>0000000=>0000000=>[8]
[5,8,2,3,6,1,7,4]=>0000000=>0000000=>[8]
[4,5,6,8,3,2,1,7]=>0000000=>0000000=>[8]
[4,6,8,5,3,2,1,7]=>0000000=>0000000=>[8]
[5,6,1,4,2,3,7,8]=>0000011=>1100000=>[1,1,6]
[5,6,8,4,3,7,1,2]=>0000000=>0000000=>[8]
[5,6,1,4,2,3,8,7]=>0000010=>0100000=>[2,6]
[5,2,8,3,4,1,7,6]=>0000000=>0000000=>[8]
[4,5,8,6,3,2,1,7]=>0000000=>0000000=>[8]
[4,7,5,6,3,2,1,8]=>0000001=>1000000=>[1,7]
[5,1,4,3,6,2,8,7]=>0000010=>0100000=>[2,6]
[5,1,4,3,8,2,7,6]=>0000000=>0000000=>[8]
[5,6,2,4,1,8,7,3]=>0000000=>0000000=>[8]
[5,7,2,4,1,8,6,3]=>0000000=>0000000=>[8]
[6,1,4,2,8,7,5,3]=>0000000=>0000000=>[8]
[5,8,2,4,1,7,6,3]=>0000000=>0000000=>[8]
[5,4,1,3,7,2,6,8]=>0000001=>1000000=>[1,7]
[5,8,1,4,2,3,7,6]=>0000000=>0000000=>[8]
[5,1,6,3,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[4,8,6,5,3,2,1,7]=>0000000=>0000000=>[8]
[5,4,7,8,3,2,1,6]=>0000000=>0000000=>[8]
[4,7,8,5,3,2,1,6]=>0000000=>0000000=>[8]
[5,7,1,3,4,2,6,8]=>0000001=>1000000=>[1,7]
[5,1,8,4,2,3,6,7]=>0000000=>0000000=>[8]
[5,1,7,4,2,3,6,8]=>0000001=>1000000=>[1,7]
[5,8,1,3,4,2,6,7]=>0000000=>0000000=>[8]
[4,8,7,5,3,2,1,6]=>0000000=>0000000=>[8]
[4,7,8,6,3,2,1,5]=>0000000=>0000000=>[8]
[4,8,7,6,3,1,2,5]=>0000000=>0000000=>[8]
[1,4,3,8,2,6,5,7]=>1000000=>0000001=>[7,1]
[4,1,3,8,2,6,5,7]=>0000000=>0000000=>[8]
[3,6,7,8,4,1,2,5]=>0000000=>0000000=>[8]
[3,7,8,2,6,4,5,1]=>0000000=>0000000=>[8]
[4,2,3,8,1,6,5,7]=>0000000=>0000000=>[8]
[7,3,6,8,4,2,1,5]=>0000000=>0000000=>[8]
[1,3,2,4,8,6,5,7]=>1011000=>0001101=>[4,1,2,1]
[3,1,2,4,8,6,5,7]=>0011000=>0001100=>[4,1,3]
[3,7,4,8,5,1,2,6]=>0000000=>0000000=>[8]
[2,1,3,4,8,6,5,7]=>0111000=>0001110=>[4,1,1,2]
[3,5,7,8,6,1,2,4]=>0000000=>0000000=>[8]
[5,1,6,3,8,4,7,2]=>0000000=>0000000=>[8]
[2,5,1,6,8,3,7,4]=>0000000=>0000000=>[8]
[5,1,2,6,8,3,7,4]=>0000000=>0000000=>[8]
[6,1,7,5,2,8,3,4]=>0000000=>0000000=>[8]
[5,7,2,8,6,1,3,4]=>0000000=>0000000=>[8]
[1,2,6,7,5,8,3,4]=>1100000=>0000011=>[6,1,1]
[1,6,7,4,5,2,8,3]=>1000000=>0000001=>[7,1]
[6,2,7,4,5,1,8,3]=>0000000=>0000000=>[8]
[7,5,1,6,3,8,2,4]=>0000000=>0000000=>[8]
[2,7,6,1,3,8,5,4]=>0000000=>0000000=>[8]
[2,6,7,4,1,8,3,5]=>0000000=>0000000=>[8]
[2,1,6,7,3,8,5,4]=>0100000=>0000010=>[6,2]
[3,7,5,4,8,1,6,2]=>0000000=>0000000=>[8]
[4,6,1,5,8,7,3,2]=>0000000=>0000000=>[8]
[8,3,4,6,2,1,5,7]=>0000000=>0000000=>[8]
[3,5,6,2,1,8,4,7]=>0000000=>0000000=>[8]
[7,5,3,2,8,4,1,6]=>0000000=>0000000=>[8]
[7,5,3,2,8,4,6,1]=>0000000=>0000000=>[8]
[4,2,5,6,8,3,1,7]=>0000000=>0000000=>[8]
[5,3,6,8,1,4,2,7]=>0000000=>0000000=>[8]
[4,5,6,8,1,3,2,7]=>0000000=>0000000=>[8]
[1,4,5,6,8,3,2,7]=>1000000=>0000001=>[7,1]
[4,5,3,7,2,8,6,1]=>0000000=>0000000=>[8]
[6,4,7,3,2,8,5,1]=>0000000=>0000000=>[8]
[6,1,4,7,3,2,8,5]=>0000000=>0000000=>[8]
[5,1,7,3,8,4,2,6]=>0000000=>0000000=>[8]
[5,3,7,1,4,8,6,2]=>0000000=>0000000=>[8]
[6,4,3,1,7,8,5,2]=>0000000=>0000000=>[8]
[5,6,1,3,7,8,4,2]=>0000000=>0000000=>[8]
[5,6,1,7,8,3,4,2]=>0000000=>0000000=>[8]
[1,6,3,7,4,8,5,2]=>1000000=>0000001=>[7,1]
[6,7,2,4,1,8,5,3]=>0000000=>0000000=>[8]
[6,7,2,1,4,3,8,5]=>0000000=>0000000=>[8]
[6,4,7,3,1,2,8,5]=>0000000=>0000000=>[8]
[5,6,3,1,2,7,8,4]=>0000000=>0000000=>[8]
[5,6,1,3,2,7,8,4]=>0000000=>0000000=>[8]
[5,6,3,2,1,7,8,4]=>0000000=>0000000=>[8]
[5,6,3,2,7,8,4,1]=>0000000=>0000000=>[8]
[2,5,6,3,7,8,4,1]=>0000000=>0000000=>[8]
[2,5,6,3,1,7,8,4]=>0000000=>0000000=>[8]
[2,6,4,7,3,1,8,5]=>0000000=>0000000=>[8]
[6,3,7,2,8,4,1,5]=>0000000=>0000000=>[8]
[6,3,2,7,1,8,4,5]=>0000000=>0000000=>[8]
[7,5,3,2,1,8,4,6]=>0000000=>0000000=>[8]
[7,3,8,4,2,1,5,6]=>0000000=>0000000=>[8]
[4,7,2,1,3,8,6,5]=>0000000=>0000000=>[8]
[1,3,7,8,6,4,2,5]=>1000000=>0000001=>[7,1]
[5,7,3,8,2,1,6,4]=>0000000=>0000000=>[8]
[4,6,2,7,8,5,3,1]=>0000000=>0000000=>[8]
[2,5,1,7,3,8,6,4]=>0000000=>0000000=>[8]
[6,7,2,1,3,8,5,4]=>0000000=>0000000=>[8]
[5,1,6,7,8,2,4,3]=>0000000=>0000000=>[8]
[6,3,7,1,8,5,2,4]=>0000000=>0000000=>[8]
[6,2,1,7,3,8,5,4]=>0000000=>0000000=>[8]
[6,2,7,1,8,5,4,3]=>0000000=>0000000=>[8]
[6,3,1,7,8,5,4,2]=>0000000=>0000000=>[8]
[5,3,2,1,8,4,7,6]=>0000000=>0000000=>[8]
[4,5,2,1,3,8,7,6]=>0000100=>0010000=>[3,5]
[3,2,6,4,5,8,1,7]=>0000000=>0000000=>[8]
[2,4,6,5,8,1,3,7]=>0000000=>0000000=>[8]
[1,3,4,6,5,8,2,7]=>1000000=>0000001=>[7,1]
[1,6,3,4,5,8,2,7]=>1000000=>0000001=>[7,1]
[3,4,1,8,5,2,7,6]=>0000000=>0000000=>[8]
[2,8,4,1,7,6,3,5]=>0000000=>0000000=>[8]
[1,5,3,2,8,7,4,6]=>1000000=>0000001=>[7,1]
[8,2,1,7,5,3,4,6]=>0000000=>0000000=>[8]
[1,7,6,4,5,8,3,2]=>1000000=>0000001=>[7,1]
[5,8,7,4,6,2,1,3]=>0000000=>0000000=>[8]
[3,4,2,5,8,6,7,1]=>0000000=>0000000=>[8]
[4,1,3,5,6,8,7,2]=>0000000=>0000000=>[8]
[2,4,8,6,7,1,3,5]=>0000000=>0000000=>[8]
[3,7,4,8,2,1,6,5]=>0000000=>0000000=>[8]
[2,3,5,8,6,7,1,4]=>0000000=>0000000=>[8]
[3,2,5,6,8,7,1,4]=>0000000=>0000000=>[8]
[7,2,4,8,5,3,1,6]=>0000000=>0000000=>[8]
[4,8,3,1,2,7,6,5]=>0000000=>0000000=>[8]
[8,4,2,3,7,1,5,6]=>0000000=>0000000=>[8]
[3,5,2,7,6,1,8,4]=>0000000=>0000000=>[8]
[5,8,7,3,4,6,2,1]=>0000000=>0000000=>[8]
[5,8,2,7,4,1,6,3]=>0000000=>0000000=>[8]
[5,1,4,2,8,7,6,3]=>0000000=>0000000=>[8]
[5,2,6,8,7,1,3,4]=>0000000=>0000000=>[8]
[6,3,2,1,8,5,7,4]=>0000000=>0000000=>[8]
[2,7,5,4,1,8,6,3]=>0000000=>0000000=>[8]
[4,2,5,6,8,7,1,3]=>0000000=>0000000=>[8]
[1,8,4,2,5,6,7,3]=>1000000=>0000001=>[7,1]
[3,8,4,1,5,6,7,2]=>0000000=>0000000=>[8]
[4,2,8,5,6,7,1,3]=>0000000=>0000000=>[8]
[5,2,4,7,1,8,6,3]=>0000000=>0000000=>[8]
[8,1,3,6,5,2,4,7]=>0000000=>0000000=>[8]
[8,3,2,4,6,5,1,7]=>0000000=>0000000=>[8]
[8,3,6,4,1,5,2,7]=>0000000=>0000000=>[8]
[1,3,4,8,5,7,2,6]=>1000000=>0000001=>[7,1]
[5,8,4,7,6,2,3,1]=>0000000=>0000000=>[8]
[1,3,4,7,5,8,2,6]=>1000000=>0000001=>[7,1]
[1,3,5,2,4,8,7,6]=>1000100=>0010001=>[3,4,1]
[2,6,5,1,3,8,7,4]=>0000000=>0000000=>[8]
[2,8,5,1,4,7,6,3]=>0000000=>0000000=>[8]
[4,3,1,5,8,6,7,2]=>0000000=>0000000=>[8]
[5,4,2,1,6,8,7,3]=>0000000=>0000000=>[8]
[6,8,4,3,2,7,1,5]=>0000000=>0000000=>[8]
[5,1,3,2,8,6,7,4]=>0000000=>0000000=>[8]
[5,3,1,2,8,6,7,4]=>0000000=>0000000=>[8]
[5,2,3,1,6,8,7,4]=>0000000=>0000000=>[8]
[5,3,2,1,8,6,7,4]=>0000000=>0000000=>[8]
[5,2,1,3,6,8,7,4]=>0000000=>0000000=>[8]
[2,7,4,5,8,3,1,6]=>0000000=>0000000=>[8]
[1,8,4,3,7,2,6,5]=>1000000=>0000001=>[7,1]
[3,4,8,7,2,1,6,5]=>0000000=>0000000=>[8]
[5,4,7,8,3,6,2,1]=>0000000=>0000000=>[8]
[6,3,8,7,4,1,2,5]=>0000000=>0000000=>[8]
[8,4,7,2,3,1,5,6]=>0000000=>0000000=>[8]
[8,6,4,1,3,2,7,5]=>0000000=>0000000=>[8]
[3,5,7,2,6,1,8,4]=>0000000=>0000000=>[8]
[6,1,3,8,5,7,2,4]=>0000000=>0000000=>[8]
[2,8,1,5,4,7,6,3]=>0000000=>0000000=>[8]
[1,7,2,4,6,5,8,3]=>1000000=>0000001=>[7,1]
[5,8,2,6,1,3,7,4]=>0000000=>0000000=>[8]
[6,3,5,8,7,2,1,4]=>0000000=>0000000=>[8]
[2,5,7,8,4,1,6,3]=>0000000=>0000000=>[8]
[4,1,5,2,6,8,7,3]=>0000000=>0000000=>[8]
[4,1,8,5,2,6,7,3]=>0000000=>0000000=>[8]
[2,7,1,8,5,4,6,3]=>0000000=>0000000=>[8]
[5,8,6,2,1,3,7,4]=>0000000=>0000000=>[8]
[3,4,5,1,8,6,7,2]=>0000000=>0000000=>[8]
[5,1,3,6,4,8,7,2]=>0000000=>0000000=>[8]
[1,3,2,7,5,8,6,4]=>1010000=>0000101=>[5,2,1]
[1,4,2,5,8,3,7,6]=>1000000=>0000001=>[7,1]
[1,4,2,7,8,5,6,3]=>1000000=>0000001=>[7,1]
[5,1,2,6,8,4,7,3]=>0000000=>0000000=>[8]
[3,1,2,6,5,8,4,7]=>0010000=>0000100=>[5,3]
[4,1,2,6,8,5,3,7]=>0000000=>0000000=>[8]
[1,5,2,4,8,7,6,3]=>1000000=>0000001=>[7,1]
[1,2,7,4,8,6,5,3]=>1100000=>0000011=>[6,1,1]
[1,3,2,7,5,8,4,6]=>1010000=>0000101=>[5,2,1]
[2,3,1,7,5,4,8,6]=>0010000=>0000100=>[5,3]
[1,3,2,8,5,7,4,6]=>1010000=>0000101=>[5,2,1]
[1,2,6,4,8,7,3,5]=>1100000=>0000011=>[6,1,1]
[1,2,6,8,5,7,3,4]=>1100000=>0000011=>[6,1,1]
[1,5,6,8,2,7,3,4]=>1000000=>0000001=>[7,1]
[1,3,8,2,6,7,4,5]=>1000000=>0000001=>[7,1]
[1,4,7,2,8,6,3,5]=>1000000=>0000001=>[7,1]
[1,6,7,8,2,5,3,4]=>1000000=>0000001=>[7,1]
[1,2,6,8,3,7,5,4]=>1100000=>0000011=>[6,1,1]
[1,5,7,8,2,3,6,4]=>1000000=>0000001=>[7,1]
[1,4,7,2,8,3,6,5]=>1000000=>0000001=>[7,1]
[1,6,7,3,4,8,5,2]=>1000000=>0000001=>[7,1]
[1,5,3,7,4,8,6,2]=>1000000=>0000001=>[7,1]
[1,3,6,4,2,8,7,5]=>1000000=>0000001=>[7,1]
[1,3,7,4,2,8,6,5]=>1000000=>0000001=>[7,1]
[1,2,8,4,7,3,6,5]=>1100000=>0000011=>[6,1,1]
[1,5,2,4,8,3,7,6]=>1000000=>0000001=>[7,1]
[1,8,4,5,7,2,3,6]=>1000000=>0000001=>[7,1]
[1,8,3,5,2,7,4,6]=>1000000=>0000001=>[7,1]
[2,8,3,5,1,4,7,6]=>0000000=>0000000=>[8]
[2,3,8,6,1,4,7,5]=>0000000=>0000000=>[8]
[1,4,8,6,7,2,3,5]=>1000000=>0000001=>[7,1]
[1,5,6,8,7,2,3,4]=>1000000=>0000001=>[7,1]
[1,2,7,8,5,3,6,4]=>1100000=>0000011=>[6,1,1]
[1,2,5,8,7,3,6,4]=>1100000=>0000011=>[6,1,1]
[1,2,6,8,7,3,5,4]=>1100000=>0000011=>[6,1,1]
[1,2,7,8,6,3,5,4]=>1100000=>0000011=>[6,1,1]
[1,5,7,8,6,2,3,4]=>1000000=>0000001=>[7,1]
[1,3,7,6,2,8,4,5]=>1000000=>0000001=>[7,1]
[1,2,8,4,7,6,3,5]=>1100000=>0000011=>[6,1,1]
[1,2,5,8,7,6,3,4]=>1100000=>0000011=>[6,1,1]
[1,2,6,8,7,5,3,4]=>1100000=>0000011=>[6,1,1]
[1,2,7,8,6,5,3,4]=>1100000=>0000011=>[6,1,1]
[5,2,6,7,3,4,8,1]=>0000000=>0000000=>[8]
[5,6,2,1,7,8,3,4]=>0000000=>0000000=>[8]
[5,6,2,1,4,8,7,3]=>0000000=>0000000=>[8]
[2,6,1,4,5,8,7,3]=>0000000=>0000000=>[8]
[5,4,2,7,6,3,8,1]=>0000000=>0000000=>[8]
[2,3,7,6,4,5,8,1]=>0000000=>0000000=>[8]
[2,6,1,7,5,8,3,4]=>0000000=>0000000=>[8]
[5,1,2,7,8,4,3,6]=>0000000=>0000000=>[8]
[2,6,1,7,4,8,3,5]=>0000000=>0000000=>[8]
[3,6,4,1,7,8,2,5]=>0000000=>0000000=>[8]
[5,4,6,1,7,8,2,3]=>0000000=>0000000=>[8]
[5,4,6,1,3,8,7,2]=>0000000=>0000000=>[8]
[3,6,4,1,5,8,7,2]=>0000000=>0000000=>[8]
[2,6,1,5,4,8,7,3]=>0000000=>0000000=>[8]
[2,6,1,4,7,8,5,3]=>0000000=>0000000=>[8]
[5,1,2,4,8,7,6,3]=>0000000=>0000000=>[8]
[2,1,5,3,8,6,4,7]=>0100000=>0000010=>[6,2]
[5,1,2,4,8,6,3,7]=>0000000=>0000000=>[8]
[5,6,3,1,4,8,2,7]=>0000000=>0000000=>[8]
[2,5,4,3,1,8,6,7]=>0000100=>0010000=>[3,5]
[5,4,6,3,1,8,7,2]=>0000000=>0000000=>[8]
[2,1,3,7,8,6,4,5]=>0110000=>0000110=>[5,1,2]
[5,1,4,2,8,6,7,3]=>0000000=>0000000=>[8]
[1,2,3,8,6,7,4,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,7,5,4,6]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,8,7,4,5,6]=>1110000=>0000111=>[5,1,1,1]
[2,1,3,6,8,7,4,5]=>0110000=>0000110=>[5,1,2]
[3,1,6,2,8,7,5,4]=>0000000=>0000000=>[8]
[6,8,1,3,2,5,4,7]=>0000000=>0000000=>[8]
[6,8,1,4,2,5,3,7]=>0000000=>0000000=>[8]
[7,8,3,6,1,4,2,5]=>0000000=>0000000=>[8]
[7,8,2,5,1,4,3,6]=>0000000=>0000000=>[8]
[7,8,1,4,3,6,2,5]=>0000000=>0000000=>[8]
[5,8,1,4,3,7,2,6]=>0000000=>0000000=>[8]
[6,8,2,5,1,4,3,7]=>0000000=>0000000=>[8]
[6,8,2,5,3,7,1,4]=>0000000=>0000000=>[8]
[2,5,4,7,6,8,1,3]=>0000000=>0000000=>[8]
[2,6,1,4,3,7,5,8]=>0000001=>1000000=>[1,7]
[2,6,1,5,3,7,4,8]=>0000001=>1000000=>[1,7]
[2,6,4,7,5,8,1,3]=>0000000=>0000000=>[8]
[5,8,2,6,4,7,1,3]=>0000000=>0000000=>[8]
[6,8,3,7,1,4,2,5]=>0000000=>0000000=>[8]
[5,8,1,3,2,6,4,7]=>0000000=>0000000=>[8]
[5,8,4,7,1,3,2,6]=>0000000=>0000000=>[8]
[6,8,4,7,1,3,2,5]=>0000000=>0000000=>[8]
[6,8,5,7,1,3,2,4]=>0000000=>0000000=>[8]
[5,7,6,8,2,4,1,3]=>0000000=>0000000=>[8]
[4,7,5,8,1,3,2,6]=>0000000=>0000000=>[8]
[4,7,1,3,2,6,5,8]=>0000001=>1000000=>[1,7]
[3,7,1,4,2,6,5,8]=>0000001=>1000000=>[1,7]
[3,7,6,8,1,4,2,5]=>0000000=>0000000=>[8]
[4,7,6,8,2,5,1,3]=>0000000=>0000000=>[8]
[4,7,5,8,3,6,1,2]=>0000000=>0000000=>[8]
[4,7,5,8,2,6,1,3]=>0000000=>0000000=>[8]
[3,7,4,8,2,6,1,5]=>0000000=>0000000=>[8]
[3,7,1,5,2,6,4,8]=>0000001=>1000000=>[1,7]
[3,7,2,6,1,5,4,8]=>0000001=>1000000=>[1,7]
[3,7,2,6,5,8,1,4]=>0000000=>0000000=>[8]
[4,7,3,6,5,8,1,2]=>0000000=>0000000=>[8]
[2,6,5,8,4,7,1,3]=>0000000=>0000000=>[8]
[2,6,3,7,1,5,4,8]=>0000001=>1000000=>[1,7]
[7,6,4,8,5,2,3,1]=>0000000=>0000000=>[8]
[6,7,4,3,5,1,8,2]=>0000000=>0000000=>[8]
[6,7,3,5,4,8,2,1]=>0000000=>0000000=>[8]
[6,8,3,7,5,2,4,1]=>0000000=>0000000=>[8]
[7,6,3,5,8,2,4,1]=>0000000=>0000000=>[8]
[7,6,2,8,4,1,5,3]=>0000000=>0000000=>[8]
[7,6,3,4,8,2,5,1]=>0000000=>0000000=>[8]
[6,8,3,7,4,5,2,1]=>0000000=>0000000=>[8]
[6,7,3,5,8,4,2,1]=>0000000=>0000000=>[8]
[5,7,8,3,6,2,1,4]=>0000000=>0000000=>[8]
[6,3,4,8,7,2,5,1]=>0000000=>0000000=>[8]
[6,3,8,4,7,2,1,5]=>0000000=>0000000=>[8]
[6,3,4,7,5,8,2,1]=>0000000=>0000000=>[8]
[6,3,5,7,8,4,2,1]=>0000000=>0000000=>[8]
[5,7,3,6,8,2,1,4]=>0000000=>0000000=>[8]
[5,6,7,3,4,1,8,2]=>0000000=>0000000=>[8]
[4,6,7,8,3,5,2,1]=>0000000=>0000000=>[8]
[4,7,3,5,6,8,2,1]=>0000000=>0000000=>[8]
[5,3,4,7,8,2,1,6]=>0000000=>0000000=>[8]
[5,3,8,2,4,1,6,7]=>0000000=>0000000=>[8]
[5,3,4,8,2,6,1,7]=>0000000=>0000000=>[8]
[4,8,3,6,2,5,7,1]=>0000000=>0000000=>[8]
[4,8,3,5,7,2,6,1]=>0000000=>0000000=>[8]
[4,8,3,5,6,7,2,1]=>0000000=>0000000=>[8]
[4,7,8,3,5,6,2,1]=>0000000=>0000000=>[8]
[4,7,8,3,6,2,5,1]=>0000000=>0000000=>[8]
[4,8,3,6,7,2,5,1]=>0000000=>0000000=>[8]
[4,8,3,7,2,5,6,1]=>0000000=>0000000=>[8]
[5,8,3,7,2,6,4,1]=>0000000=>0000000=>[8]
[5,7,3,4,8,2,1,6]=>0000000=>0000000=>[8]
[5,8,4,2,3,1,6,7]=>0000000=>0000000=>[8]
[5,8,4,2,3,1,7,6]=>0000000=>0000000=>[8]
[6,4,8,5,3,7,2,1]=>0000000=>0000000=>[8]
[6,4,2,7,3,1,8,5]=>0000000=>0000000=>[8]
[6,4,3,7,8,5,2,1]=>0000000=>0000000=>[8]
[6,4,5,3,7,1,8,2]=>0000000=>0000000=>[8]
[5,7,4,2,3,1,6,8]=>0000001=>1000000=>[1,7]
[5,6,3,7,1,8,2,4]=>0000000=>0000000=>[8]
[5,6,3,4,8,2,1,7]=>0000000=>0000000=>[8]
[6,3,5,7,4,8,2,1]=>0000000=>0000000=>[8]
[6,3,5,4,7,8,2,1]=>0000000=>0000000=>[8]
[6,4,3,5,7,1,8,2]=>0000000=>0000000=>[8]
[6,4,2,5,1,7,3,8]=>0000001=>1000000=>[1,7]
[5,3,4,7,2,6,1,8]=>0000001=>1000000=>[1,7]
[4,7,3,6,2,5,8,1]=>0000000=>0000000=>[8]
[4,7,3,6,8,2,5,1]=>0000000=>0000000=>[8]
[4,6,7,3,5,8,2,1]=>0000000=>0000000=>[8]
[4,5,7,8,3,6,2,1]=>0000000=>0000000=>[8]
[4,5,8,3,7,2,6,1]=>0000000=>0000000=>[8]
[5,3,4,6,8,2,1,7]=>0000000=>0000000=>[8]
[5,3,6,7,1,8,2,4]=>0000000=>0000000=>[8]
[5,3,4,6,7,1,8,2]=>0000000=>0000000=>[8]
[4,6,3,5,7,8,2,1]=>0000000=>0000000=>[8]
[4,5,7,3,6,8,2,1]=>0000000=>0000000=>[8]
[7,1,4,5,8,2,3,6]=>0000000=>0000000=>[8]
[2,1,7,5,8,3,4,6]=>0100000=>0000010=>[6,2]
[7,1,5,4,8,2,3,6]=>0000000=>0000000=>[8]
[8,3,7,1,2,4,6,5]=>0000000=>0000000=>[8]
[8,3,7,5,1,2,4,6]=>0000000=>0000000=>[8]
[6,7,1,8,4,2,3,5]=>0000000=>0000000=>[8]
[6,8,1,7,4,2,3,5]=>0000000=>0000000=>[8]
[7,1,8,4,5,2,3,6]=>0000000=>0000000=>[8]
[6,1,2,3,8,7,5,4]=>0000000=>0000000=>[8]
[6,8,3,1,2,7,4,5]=>0000000=>0000000=>[8]
[6,7,3,1,2,8,4,5]=>0000000=>0000000=>[8]
[6,7,1,4,2,3,8,5]=>0000000=>0000000=>[8]
[4,3,6,8,5,7,1,2]=>0000000=>0000000=>[8]
[6,1,2,5,4,8,3,7]=>0000000=>0000000=>[8]
[1,3,6,8,7,4,2,5]=>1000000=>0000001=>[7,1]
[1,2,8,5,7,3,4,6]=>1100000=>0000011=>[6,1,1]
[3,6,1,4,2,7,8,5]=>0000000=>0000000=>[8]
[1,2,6,3,5,8,7,4]=>1100000=>0000011=>[6,1,1]
[2,3,5,1,8,4,7,6]=>0000000=>0000000=>[8]
[3,1,7,5,4,8,6,2]=>0000000=>0000000=>[8]
[1,2,7,6,4,8,5,3]=>1100000=>0000011=>[6,1,1]
[1,2,7,3,6,8,5,4]=>1100000=>0000011=>[6,1,1]
[1,2,6,8,5,4,3,7]=>1100000=>0000011=>[6,1,1]
[1,4,6,8,3,2,5,7]=>1000000=>0000001=>[7,1]
[1,2,6,7,3,8,5,4]=>1100000=>0000011=>[6,1,1]
[1,2,5,7,3,8,6,4]=>1100000=>0000011=>[6,1,1]
[4,6,2,7,5,8,3,1]=>0000000=>0000000=>[8]
[3,5,7,4,8,2,6,1]=>0000000=>0000000=>[8]
[1,3,5,8,2,7,4,6]=>1000000=>0000001=>[7,1]
[1,2,5,8,4,7,6,3]=>1100000=>0000011=>[6,1,1]
[1,2,5,8,7,4,3,6]=>1100000=>0000011=>[6,1,1]
[1,3,5,8,7,2,4,6]=>1000000=>0000001=>[7,1]
[3,2,7,4,6,8,1,5]=>0000000=>0000000=>[8]
[5,3,6,2,7,1,4,8]=>0000001=>1000000=>[1,7]
[2,6,3,4,7,1,5,8]=>0000001=>1000000=>[1,7]
[2,7,3,4,5,8,1,6]=>0000000=>0000000=>[8]
[4,7,6,2,3,8,1,5]=>0000000=>0000000=>[8]
[7,3,5,2,4,8,1,6]=>0000000=>0000000=>[8]
[7,6,2,4,5,8,1,3]=>0000000=>0000000=>[8]
[6,5,2,3,4,8,1,7]=>0000000=>0000000=>[8]
[5,3,1,2,8,4,7,6]=>0000000=>0000000=>[8]
[6,5,2,3,7,1,4,8]=>0000001=>1000000=>[1,7]
[5,2,1,7,3,4,6,8]=>0000001=>1000000=>[1,7]
[5,2,1,8,3,4,6,7]=>0000000=>0000000=>[8]
[6,3,2,8,4,5,7,1]=>0000000=>0000000=>[8]
[7,3,1,2,8,4,6,5]=>0000000=>0000000=>[8]
[6,2,3,1,8,4,7,5]=>0000000=>0000000=>[8]
[8,3,5,2,7,1,4,6]=>0000000=>0000000=>[8]
[8,6,2,4,7,1,5,3]=>0000000=>0000000=>[8]
[8,2,1,7,3,4,5,6]=>0000000=>0000000=>[8]
[8,6,3,7,2,4,5,1]=>0000000=>0000000=>[8]
[8,2,7,3,4,5,6,1]=>0000000=>0000000=>[8]
[8,1,6,2,3,4,5,7]=>0000000=>0000000=>[8]
[8,1,7,3,4,5,6,2]=>0000000=>0000000=>[8]
[8,6,1,7,2,4,5,3]=>0000000=>0000000=>[8]
[1,7,5,8,2,3,6,4]=>1000000=>0000001=>[7,1]
[7,2,1,8,3,4,5,6]=>0000000=>0000000=>[8]
[1,7,8,3,4,5,6,2]=>1000000=>0000001=>[7,1]
[1,6,2,8,4,5,7,3]=>1000000=>0000001=>[7,1]
[4,1,3,6,8,2,7,5]=>0000000=>0000000=>[8]
[4,6,3,8,7,1,2,5]=>0000000=>0000000=>[8]
[6,4,5,8,7,1,2,3]=>0000000=>0000000=>[8]
[5,3,4,8,7,1,2,6]=>0000000=>0000000=>[8]
[3,2,8,7,1,4,6,5]=>0000000=>0000000=>[8]
[3,1,8,7,2,4,6,5]=>0000000=>0000000=>[8]
[5,3,7,6,1,2,4,8]=>0000001=>1000000=>[1,7]
[1,8,3,7,2,4,5,6]=>1000000=>0000001=>[7,1]
[3,8,1,7,2,4,5,6]=>0000000=>0000000=>[8]
[6,8,2,3,5,1,4,7]=>0000000=>0000000=>[8]
[4,7,8,2,6,1,3,5]=>0000000=>0000000=>[8]
[6,2,8,7,1,4,5,3]=>0000000=>0000000=>[8]
[3,8,7,1,4,5,6,2]=>0000000=>0000000=>[8]
[2,8,6,1,3,4,5,7]=>0000000=>0000000=>[8]
[2,7,6,1,3,4,5,8]=>0000001=>1000000=>[1,7]
[1,7,6,2,3,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,8,6,2,3,4,5,7]=>1000000=>0000001=>[7,1]
[2,8,7,3,4,5,6,1]=>0000000=>0000000=>[8]
[3,8,7,2,4,5,6,1]=>0000000=>0000000=>[8]
[7,8,3,6,2,4,5,1]=>0000000=>0000000=>[8]
[1,5,8,7,2,3,6,4]=>1000000=>0000001=>[7,1]
[7,8,10,9,5,6,3,4,1,2]=>000000000=>000000000=>[10]
[9,10,5,6,8,7,3,4,1,2]=>000000000=>000000000=>[10]
[5,8,10,6,9,7,3,4,1,2]=>000000000=>000000000=>[10]
[5,6,7,10,9,8,3,4,1,2]=>000000000=>000000000=>[10]
[9,10,7,8,3,4,6,5,1,2]=>000000000=>000000000=>[10]
[7,8,10,9,3,4,6,5,1,2]=>000000000=>000000000=>[10]
[9,10,3,6,8,4,7,5,1,2]=>000000000=>000000000=>[10]
[3,8,10,6,9,4,7,5,1,2]=>000000000=>000000000=>[10]
[3,6,7,10,9,4,8,5,1,2]=>000000000=>000000000=>[10]
[9,10,3,4,5,8,7,6,1,2]=>000000000=>000000000=>[10]
[3,8,10,4,5,9,7,6,1,2]=>000000000=>000000000=>[10]
[3,4,7,10,5,9,8,6,1,2]=>000000000=>000000000=>[10]
[3,4,5,6,10,9,8,7,1,2]=>000000000=>000000000=>[10]
[9,10,7,8,5,6,1,2,4,3]=>000000000=>000000000=>[10]
[7,8,10,9,5,6,1,2,4,3]=>000000000=>000000000=>[10]
[9,10,5,6,8,7,1,2,4,3]=>000000000=>000000000=>[10]
[5,8,10,6,9,7,1,2,4,3]=>000000000=>000000000=>[10]
[5,6,7,10,9,8,1,2,4,3]=>000000000=>000000000=>[10]
[9,10,7,8,1,4,6,2,5,3]=>000000000=>000000000=>[10]
[7,8,10,9,1,4,6,2,5,3]=>000000000=>000000000=>[10]
[9,10,1,6,8,4,7,2,5,3]=>000000000=>000000000=>[10]
[1,8,10,6,9,4,7,2,5,3]=>100000000=>000000001=>[9,1]
[1,6,7,10,9,4,8,2,5,3]=>100000000=>000000001=>[9,1]
[9,10,1,4,5,8,7,2,6,3]=>000000000=>000000000=>[10]
[1,8,10,4,5,9,7,2,6,3]=>100000000=>000000001=>[9,1]
[1,4,7,10,5,9,8,2,6,3]=>100000000=>000000001=>[9,1]
[1,4,5,6,10,9,8,2,7,3]=>100000000=>000000001=>[9,1]
[9,10,7,8,1,2,3,6,5,4]=>000000000=>000000000=>[10]
[7,8,10,9,1,2,3,6,5,4]=>000000000=>000000000=>[10]
[9,10,1,6,8,2,3,7,5,4]=>000000000=>000000000=>[10]
[1,8,10,6,9,2,3,7,5,4]=>100000000=>000000001=>[9,1]
[1,6,7,10,9,2,3,8,5,4]=>100000000=>000000001=>[9,1]
[9,10,1,2,5,8,3,7,6,4]=>000000000=>000000000=>[10]
[1,8,10,2,5,9,3,7,6,4]=>100000000=>000000001=>[9,1]
[1,2,7,10,5,9,3,8,6,4]=>110000000=>000000011=>[8,1,1]
[1,2,5,6,10,9,3,8,7,4]=>110000000=>000000011=>[8,1,1]
[9,10,1,2,3,4,8,7,6,5]=>000000000=>000000000=>[10]
[1,8,10,2,3,4,9,7,6,5]=>100000000=>000000001=>[9,1]
[1,2,7,10,3,4,9,8,6,5]=>110000000=>000000011=>[8,1,1]
[1,2,3,6,10,4,9,8,7,5]=>111000000=>000000111=>[7,1,1,1]
[1,10,12,8,11,6,9,4,7,2,5,3]=>10000000000=>00000000001=>[11,1]
[1,8,9,12,11,6,10,4,7,2,5,3]=>10000000000=>00000000001=>[11,1]
[1,10,12,6,7,11,9,4,8,2,5,3]=>10000000000=>00000000001=>[11,1]
[1,6,9,12,7,11,10,4,8,2,5,3]=>10000000000=>00000000001=>[11,1]
[1,6,7,8,12,11,10,4,9,2,5,3]=>10000000000=>00000000001=>[11,1]
[1,10,12,8,11,4,5,9,7,2,6,3]=>10000000000=>00000000001=>[11,1]
[1,8,9,12,11,4,5,10,7,2,6,3]=>10000000000=>00000000001=>[11,1]
[1,10,12,4,7,11,5,9,8,2,6,3]=>10000000000=>00000000001=>[11,1]
[1,4,9,12,7,11,5,10,8,2,6,3]=>10000000000=>00000000001=>[11,1]
[1,4,7,8,12,11,5,10,9,2,6,3]=>10000000000=>00000000001=>[11,1]
[1,10,12,4,5,6,11,9,8,2,7,3]=>10000000000=>00000000001=>[11,1]
[1,4,9,12,5,6,11,10,8,2,7,3]=>10000000000=>00000000001=>[11,1]
[1,4,5,8,12,6,11,10,9,2,7,3]=>10000000000=>00000000001=>[11,1]
[1,4,5,6,7,12,11,10,9,2,8,3]=>10000000000=>00000000001=>[11,1]
[1,10,12,8,11,6,9,2,3,7,5,4]=>10000000000=>00000000001=>[11,1]
[1,8,9,12,11,6,10,2,3,7,5,4]=>10000000000=>00000000001=>[11,1]
[1,10,12,6,7,11,9,2,3,8,5,4]=>10000000000=>00000000001=>[11,1]
[1,6,9,12,7,11,10,2,3,8,5,4]=>10000000000=>00000000001=>[11,1]
[1,6,7,8,12,11,10,2,3,9,5,4]=>10000000000=>00000000001=>[11,1]
[1,10,12,8,11,2,5,9,3,7,6,4]=>10000000000=>00000000001=>[11,1]
[1,8,9,12,11,2,5,10,3,7,6,4]=>10000000000=>00000000001=>[11,1]
[1,10,12,2,7,11,5,9,3,8,6,4]=>10000000000=>00000000001=>[11,1]
[1,2,9,12,7,11,5,10,3,8,6,4]=>11000000000=>00000000011=>[10,1,1]
[1,2,7,8,12,11,5,10,3,9,6,4]=>11000000000=>00000000011=>[10,1,1]
[1,10,12,2,5,6,11,9,3,8,7,4]=>10000000000=>00000000001=>[11,1]
[1,2,9,12,5,6,11,10,3,8,7,4]=>11000000000=>00000000011=>[10,1,1]
[1,2,5,8,12,6,11,10,3,9,7,4]=>11000000000=>00000000011=>[10,1,1]
[1,2,5,6,7,12,11,10,3,9,8,4]=>11000000000=>00000000011=>[10,1,1]
[1,10,12,8,11,2,3,4,9,7,6,5]=>10000000000=>00000000001=>[11,1]
[1,8,9,12,11,2,3,4,10,7,6,5]=>10000000000=>00000000001=>[11,1]
[1,10,12,2,7,11,3,4,9,8,6,5]=>10000000000=>00000000001=>[11,1]
[1,2,9,12,7,11,3,4,10,8,6,5]=>11000000000=>00000000011=>[10,1,1]
[1,2,7,8,12,11,3,4,10,9,6,5]=>11000000000=>00000000011=>[10,1,1]
[1,10,12,2,3,6,11,4,9,8,7,5]=>10000000000=>00000000001=>[11,1]
[1,2,9,12,3,6,11,4,10,8,7,5]=>11000000000=>00000000011=>[10,1,1]
[1,10,12,2,3,4,5,11,9,8,7,6]=>10000000000=>00000000001=>[11,1]
[1,2,9,12,3,4,5,11,10,8,7,6]=>11000000000=>00000000011=>[10,1,1]
[1,7,3,6,5,2,8,4]=>1000000=>0000001=>[7,1]
[8,6,2,5,4,1,7,3]=>0000000=>0000000=>[8]
[3,2,6,4,7,5,1,8]=>0000001=>1000000=>[1,7]
[6,2,3,7,5,4,1,8]=>0000001=>1000000=>[1,7]
[1,3,4,7,6,2,8,5]=>1000000=>0000001=>[7,1]
[2,8,3,6,1,7,5,4]=>0000000=>0000000=>[8]
[8,7,2,5,1,6,4,3]=>0000000=>0000000=>[8]
[3,8,2,6,5,1,7,4]=>0000000=>0000000=>[8]
[7,8,2,5,4,1,6,3]=>0000000=>0000000=>[8]
[4,8,5,2,6,1,7,3]=>0000000=>0000000=>[8]
[4,5,1,3,7,2,8,6]=>0000000=>0000000=>[8]
[6,1,3,7,5,2,8,4]=>0000000=>0000000=>[8]
[7,1,3,6,2,8,5,4]=>0000000=>0000000=>[8]
[8,1,3,6,2,7,5,4]=>0000000=>0000000=>[8]
[1,2,4,7,3,8,6,5]=>1100000=>0000011=>[6,1,1]
[7,1,8,2,6,5,4,3]=>0000000=>0000000=>[8]
[4,1,7,8,2,6,5,3]=>0000000=>0000000=>[8]
[3,4,8,6,5,1,7,2]=>0000000=>0000000=>[8]
[8,3,7,5,1,6,4,2]=>0000000=>0000000=>[8]
[1,4,8,6,2,7,5,3]=>1000000=>0000001=>[7,1]
[8,4,6,7,1,5,3,2]=>0000000=>0000000=>[8]
[3,4,6,5,1,2,8,7]=>0000010=>0100000=>[2,6]
[7,3,5,1,2,8,6,4]=>0000000=>0000000=>[8]
[1,4,6,2,3,8,7,5]=>1000000=>0000001=>[7,1]
[1,3,2,7,4,8,6,5]=>1010000=>0000101=>[5,2,1]
[7,2,1,6,3,8,5,4]=>0000000=>0000000=>[8]
[4,5,2,1,7,3,8,6]=>0000000=>0000000=>[8]
[5,6,7,1,2,8,4,3]=>0000000=>0000000=>[8]
[4,7,5,1,2,8,6,3]=>0000000=>0000000=>[8]
[3,7,1,6,2,8,5,4]=>0000000=>0000000=>[8]
[7,6,1,2,8,5,4,3]=>0000000=>0000000=>[8]
[2,7,1,3,8,6,5,4]=>0000000=>0000000=>[8]
[8,6,1,2,7,5,4,3]=>0000000=>0000000=>[8]
[1,7,2,3,8,6,5,4]=>1000000=>0000001=>[7,1]
[8,7,1,2,6,5,4,3]=>0000000=>0000000=>[8]
[7,8,1,2,6,5,4,3]=>0000000=>0000000=>[8]
[3,8,1,6,2,7,5,4]=>0000000=>0000000=>[8]
[4,8,5,1,2,7,6,3]=>0000000=>0000000=>[8]
[1,8,2,7,4,3,5,6]=>1000000=>0000001=>[7,1]
[1,8,6,4,7,2,3,5]=>1000000=>0000001=>[7,1]
[1,8,4,2,6,3,5,7]=>1000000=>0000001=>[7,1]
[7,4,8,1,5,2,3,6]=>0000000=>0000000=>[8]
[4,1,7,2,6,3,5,8]=>0000001=>1000000=>[1,7]
[5,1,7,4,3,6,2,8]=>0000001=>1000000=>[1,7]
[1,8,5,4,3,7,2,6]=>1000000=>0000001=>[7,1]
[1,8,4,2,5,3,7,6]=>1000000=>0000001=>[7,1]
[1,8,5,4,2,6,7,3]=>1000000=>0000001=>[7,1]
[7,4,8,2,1,3,5,6]=>0000000=>0000000=>[8]
[4,1,7,3,2,5,6,8]=>0000001=>1000000=>[1,7]
[7,5,4,8,2,3,6,1]=>0000000=>0000000=>[8]
[3,1,7,2,6,8,4,5]=>0000000=>0000000=>[8]
[5,1,7,4,2,6,8,3]=>0000000=>0000000=>[8]
[4,3,1,6,2,5,7,8]=>0000011=>1100000=>[1,1,6]
[6,5,4,3,7,1,8,2]=>0000000=>0000000=>[8]
[6,5,1,7,3,8,2,4]=>0000000=>0000000=>[8]
[6,3,2,8,5,7,1,4]=>0000000=>0000000=>[8]
[5,4,8,2,1,7,3,6]=>0000000=>0000000=>[8]
[7,2,8,6,3,1,4,5]=>0000000=>0000000=>[8]
[2,1,7,8,3,6,4,5]=>0100000=>0000010=>[6,2]
[4,2,1,6,7,3,5,8]=>0000001=>1000000=>[1,7]
[4,3,1,5,2,7,6,8]=>0000101=>1010000=>[1,2,5]
[5,4,2,7,3,8,1,6]=>0000000=>0000000=>[8]
[3,1,6,2,8,7,4,5]=>0000000=>0000000=>[8]
[6,5,4,1,7,8,3,2]=>0000000=>0000000=>[8]
[5,4,3,1,6,7,2,8]=>0000001=>1000000=>[1,7]
[5,4,2,6,3,8,7,1]=>0000000=>0000000=>[8]
[4,3,1,5,2,6,8,7]=>0000110=>0110000=>[2,1,5]
[5,4,2,1,6,7,8,3]=>0000000=>0000000=>[8]
[5,4,3,1,6,7,8,2]=>0000000=>0000000=>[8]
[7,8,2,4,5,1,3,6]=>0000000=>0000000=>[8]
[4,6,7,2,5,1,3,8]=>0000001=>1000000=>[1,7]
[7,8,1,3,2,4,5,6]=>0000000=>0000000=>[8]
[7,8,4,1,5,2,3,6]=>0000000=>0000000=>[8]
[3,6,7,2,1,4,5,8]=>0000001=>1000000=>[1,7]
[5,2,3,6,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[2,5,3,6,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[6,4,7,1,5,2,3,8]=>0000001=>1000000=>[1,7]
[6,2,7,3,1,4,5,8]=>0000001=>1000000=>[1,7]
[3,5,4,6,7,8,1,2]=>0000000=>0000000=>[8]
[1,5,4,6,7,2,3,8]=>1000001=>1000001=>[1,6,1]
[1,6,7,3,2,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,5,3,6,2,4,7,8]=>1000011=>1100001=>[1,1,5,1]
[5,1,3,6,2,4,7,8]=>0000011=>1100000=>[1,1,6]
[5,2,4,6,7,1,3,8]=>0000001=>1000000=>[1,7]
[2,6,7,4,5,1,3,8]=>0000001=>1000000=>[1,7]
[4,2,5,6,7,1,3,8]=>0000001=>1000000=>[1,7]
[4,5,2,6,7,1,3,8]=>0000001=>1000000=>[1,7]
[5,3,1,6,2,4,7,8]=>0000011=>1100000=>[1,1,6]
[6,1,7,3,2,4,5,8]=>0000001=>1000000=>[1,7]
[6,1,7,4,5,2,3,8]=>0000001=>1000000=>[1,7]
[6,3,7,4,5,8,1,2]=>0000000=>0000000=>[8]
[5,4,1,6,7,2,3,8]=>0000001=>1000000=>[1,7]
[5,2,1,6,3,4,7,8]=>0000011=>1100000=>[1,1,6]
[1,3,6,7,5,2,8,4]=>1000000=>0000001=>[7,1]
[1,3,4,5,8,7,2,6]=>1000000=>0000001=>[7,1]
[3,1,2,5,6,8,7,4]=>0010000=>0000100=>[5,3]
[7,1,5,2,6,8,3,4]=>0000000=>0000000=>[8]
[2,3,6,7,5,1,8,4]=>0000000=>0000000=>[8]
[4,3,2,6,7,1,8,5]=>0000000=>0000000=>[8]
[7,1,5,4,6,8,3,2]=>0000000=>0000000=>[8]
[5,7,4,6,1,8,3,2]=>0000000=>0000000=>[8]
[6,3,4,5,8,1,2,7]=>0000000=>0000000=>[8]
[6,2,1,7,3,5,4,8]=>0000001=>1000000=>[1,7]
[2,1,8,6,3,5,4,7]=>0100000=>0000010=>[6,2]
[2,7,3,1,5,4,6,8]=>0000001=>1000000=>[1,7]
[2,6,3,1,4,8,5,7]=>0000000=>0000000=>[8]
[4,2,1,8,3,6,7,5]=>0000000=>0000000=>[8]
[6,2,1,7,3,5,8,4]=>0000000=>0000000=>[8]
[2,7,3,1,4,8,5,6]=>0000000=>0000000=>[8]
[3,2,1,5,7,8,4,6]=>0010000=>0000100=>[5,3]
[2,4,7,5,1,6,8,3]=>0000000=>0000000=>[8]
[4,3,6,8,5,1,7,2]=>0000000=>0000000=>[8]
[2,1,6,8,3,7,4,5]=>0100000=>0000010=>[6,2]
[3,2,1,5,6,8,4,7]=>0010000=>0000100=>[5,3]
[2,1,7,3,6,4,5,8]=>0100001=>1000010=>[1,5,2]
[2,1,6,3,5,8,4,7]=>0100000=>0000010=>[6,2]
[2,6,1,8,3,5,4,7]=>0000000=>0000000=>[8]
[2,7,3,1,5,6,4,8]=>0000001=>1000000=>[1,7]
[2,4,7,5,1,6,3,8]=>0000001=>1000000=>[1,7]
[8,2,4,1,7,5,3,6]=>0000000=>0000000=>[8]
[2,4,7,1,8,5,3,6]=>0000000=>0000000=>[8]
[2,4,8,5,1,6,3,7]=>0000000=>0000000=>[8]
[6,2,1,7,3,4,8,5]=>0000000=>0000000=>[8]
[6,2,1,7,8,3,5,4]=>0000000=>0000000=>[8]
[2,7,1,8,3,5,6,4]=>0000000=>0000000=>[8]
[3,2,1,6,7,4,5,8]=>0010001=>1000100=>[1,4,3]
[3,2,1,7,4,5,6,8]=>0010001=>1000100=>[1,4,3]
[2,1,8,3,7,4,5,6]=>0100000=>0000010=>[6,2]
[2,4,8,5,1,6,7,3]=>0000000=>0000000=>[8]
[4,3,8,5,6,1,7,2]=>0000000=>0000000=>[8]
[3,2,1,8,4,5,6,7]=>0010000=>0000100=>[5,3]
[1,6,8,3,7,2,4,5]=>1000000=>0000001=>[7,1]
[3,8,1,5,7,2,4,6]=>0000000=>0000000=>[8]
[1,2,6,8,4,7,3,5]=>1100000=>0000011=>[6,1,1]
[6,1,5,8,2,4,7,3]=>0000000=>0000000=>[8]
[1,2,4,8,3,6,7,5]=>1100000=>0000011=>[6,1,1]
[4,1,2,7,8,3,6,5]=>0000000=>0000000=>[8]
[5,3,8,4,7,6,1,2]=>0000000=>0000000=>[8]
[8,7,1,2,5,4,6,3]=>0000000=>0000000=>[8]
[5,8,1,2,3,7,6,4]=>0000000=>0000000=>[8]
[1,2,8,4,3,5,7,6]=>1100000=>0000011=>[6,1,1]
[1,2,5,3,7,6,4,8]=>1100001=>1000011=>[1,5,1,1]
[6,1,2,8,7,4,5,3]=>0000000=>0000000=>[8]
[7,1,6,2,8,4,5,3]=>0000000=>0000000=>[8]
[1,2,6,3,8,5,4,7]=>1100000=>0000011=>[6,1,1]
[1,2,8,5,3,6,4,7]=>1100000=>0000011=>[6,1,1]
[1,2,7,3,8,5,4,6]=>1100000=>0000011=>[6,1,1]
[1,6,2,8,4,3,5,7]=>1000000=>0000001=>[7,1]
[1,6,4,2,7,3,5,8]=>1000001=>1000001=>[1,6,1]
[1,8,6,3,2,4,5,7]=>1000000=>0000001=>[7,1]
[3,1,7,8,6,2,4,5]=>0000000=>0000000=>[8]
[1,8,7,3,5,6,2,4]=>1000000=>0000001=>[7,1]
[1,3,2,8,7,4,5,6]=>1010000=>0000101=>[5,2,1]
[1,2,8,4,3,7,5,6]=>1100000=>0000011=>[6,1,1]
[8,5,1,7,2,4,6,3]=>0000000=>0000000=>[8]
[3,8,6,4,7,5,1,2]=>0000000=>0000000=>[8]
[6,1,8,2,7,4,5,3]=>0000000=>0000000=>[8]
[1,2,7,5,3,6,4,8]=>1100001=>1000011=>[1,5,1,1]
[1,2,6,3,7,5,4,8]=>1100001=>1000011=>[1,5,1,1]
[1,2,3,7,5,4,8,6]=>1110000=>0000111=>[5,1,1,1]
[3,7,4,8,6,5,1,2]=>0000000=>0000000=>[8]
[1,8,2,7,6,4,5,3]=>1000000=>0000001=>[7,1]
[7,4,6,3,8,5,1,2]=>0000000=>0000000=>[8]
[8,4,6,2,7,5,3,1]=>0000000=>0000000=>[8]
[6,5,7,8,4,1,3,2]=>0000000=>0000000=>[8]
[7,5,6,8,2,4,1,3]=>0000000=>0000000=>[8]
[7,4,6,2,8,5,1,3]=>0000000=>0000000=>[8]
[4,3,2,6,8,5,1,7]=>0000000=>0000000=>[8]
[3,5,6,8,2,4,1,7]=>0000000=>0000000=>[8]
[2,6,7,8,1,4,5,3]=>0000000=>0000000=>[8]
[3,6,7,8,1,4,2,5]=>0000000=>0000000=>[8]
[3,5,7,8,2,1,4,6]=>0000000=>0000000=>[8]
[2,6,7,8,1,4,3,5]=>0000000=>0000000=>[8]
[2,5,7,8,3,1,4,6]=>0000000=>0000000=>[8]
[2,4,7,3,8,1,5,6]=>0000000=>0000000=>[8]
[6,4,7,3,8,1,5,2]=>0000000=>0000000=>[8]
[6,4,7,3,8,1,2,5]=>0000000=>0000000=>[8]
[7,4,6,3,8,2,1,5]=>0000000=>0000000=>[8]
[6,3,2,5,4,8,1,7]=>0000000=>0000000=>[8]
[6,4,5,2,3,8,1,7]=>0000000=>0000000=>[8]
[5,4,6,3,8,2,1,7]=>0000000=>0000000=>[8]
[5,4,7,3,8,1,6,2]=>0000000=>0000000=>[8]
[2,5,7,8,3,1,6,4]=>0000000=>0000000=>[8]
[4,5,7,8,3,1,2,6]=>0000000=>0000000=>[8]
[4,5,6,8,2,3,1,7]=>0000000=>0000000=>[8]
[5,4,6,2,8,3,1,7]=>0000000=>0000000=>[8]
[5,3,2,6,8,4,1,7]=>0000000=>0000000=>[8]
[5,4,7,2,8,1,3,6]=>0000000=>0000000=>[8]
[4,5,7,8,2,1,3,6]=>0000000=>0000000=>[8]
[4,6,7,8,1,3,2,5]=>0000000=>0000000=>[8]
[4,6,7,8,1,3,5,2]=>0000000=>0000000=>[8]
[2,6,7,8,1,3,5,4]=>0000000=>0000000=>[8]
[2,6,7,8,1,5,3,4]=>0000000=>0000000=>[8]
[4,6,7,8,1,5,2,3]=>0000000=>0000000=>[8]
[4,6,7,8,1,2,5,3]=>0000000=>0000000=>[8]
[5,3,2,7,8,1,6,4]=>0000000=>0000000=>[8]
[4,3,2,7,8,1,6,5]=>0000000=>0000000=>[8]
[3,5,7,8,2,1,6,4]=>0000000=>0000000=>[8]
[3,6,7,8,1,5,4,2]=>0000000=>0000000=>[8]
[2,6,7,8,1,5,4,3]=>0000000=>0000000=>[8]
[4,5,8,3,6,7,1,2]=>0000000=>0000000=>[8]
[4,5,8,3,7,6,1,2]=>0000000=>0000000=>[8]
[4,2,8,3,7,1,6,5]=>0000000=>0000000=>[8]
[7,2,3,4,8,1,5,6]=>0000000=>0000000=>[8]
[7,6,3,4,8,5,1,2]=>0000000=>0000000=>[8]
[7,6,3,5,8,4,1,2]=>0000000=>0000000=>[8]
[7,6,3,8,4,5,1,2]=>0000000=>0000000=>[8]
[7,2,3,8,5,1,4,6]=>0000000=>0000000=>[8]
[2,6,4,8,1,5,7,3]=>0000000=>0000000=>[8]
[7,2,3,8,4,1,5,6]=>0000000=>0000000=>[8]
[7,8,2,3,6,1,4,5]=>0000000=>0000000=>[8]
[4,2,6,3,7,1,5,8]=>0000001=>1000000=>[1,7]
[7,2,3,5,8,1,6,4]=>0000000=>0000000=>[8]
[7,2,3,8,4,1,6,5]=>0000000=>0000000=>[8]
[2,6,4,8,1,3,7,5]=>0000000=>0000000=>[8]
[3,6,4,8,1,7,5,2]=>0000000=>0000000=>[8]
[7,6,5,1,2,3,8,4]=>0000000=>0000000=>[8]
[7,6,5,1,4,2,8,3]=>0000000=>0000000=>[8]
[7,8,5,4,1,2,6,3]=>0000000=>0000000=>[8]
[3,5,6,4,1,2,8,7]=>0000010=>0100000=>[2,6]
[7,6,5,1,2,4,3,8]=>0000001=>1000000=>[1,7]
[7,6,5,1,2,4,8,3]=>0000000=>0000000=>[8]
[7,6,5,1,3,2,4,8]=>0000001=>1000000=>[1,7]
[2,6,4,3,1,8,7,5]=>0000000=>0000000=>[8]
[3,5,8,4,1,2,7,6]=>0000000=>0000000=>[8]
[3,5,8,4,1,2,6,7]=>0000000=>0000000=>[8]
[3,5,8,4,1,6,2,7]=>0000000=>0000000=>[8]
[2,5,8,4,1,7,3,6]=>0000000=>0000000=>[8]
[3,6,4,2,1,7,5,8]=>0000001=>1000000=>[1,7]
[3,5,6,4,1,8,7,2]=>0000000=>0000000=>[8]
[2,6,4,5,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[7,6,5,1,4,3,8,2]=>0000000=>0000000=>[8]
[7,6,5,1,2,8,3,4]=>0000000=>0000000=>[8]
[7,6,5,1,8,2,4,3]=>0000000=>0000000=>[8]
[7,6,5,1,8,2,3,4]=>0000000=>0000000=>[8]
[7,6,5,1,8,3,2,4]=>0000000=>0000000=>[8]
[7,6,5,1,4,8,2,3]=>0000000=>0000000=>[8]
[3,6,4,5,1,7,2,8]=>0000001=>1000000=>[1,7]
[2,5,6,4,1,7,8,3]=>0000000=>0000000=>[8]
[2,5,6,4,1,7,3,8]=>0000001=>1000000=>[1,7]
[3,6,4,5,1,7,8,2]=>0000000=>0000000=>[8]
[7,6,5,1,4,8,3,2]=>0000000=>0000000=>[8]
[7,6,5,1,8,3,4,2]=>0000000=>0000000=>[8]
[7,6,5,1,8,4,2,3]=>0000000=>0000000=>[8]
[6,7,4,2,5,3,1,8]=>0000001=>1000000=>[1,7]
[7,6,4,8,3,1,5,2]=>0000000=>0000000=>[8]
[7,4,8,5,6,1,3,2]=>0000000=>0000000=>[8]
[7,4,2,5,6,3,1,8]=>0000001=>1000000=>[1,7]
[4,2,7,5,6,3,1,8]=>0000001=>1000000=>[1,7]
[4,7,3,5,6,2,1,8]=>0000001=>1000000=>[1,7]
[1,6,8,5,2,7,4,3]=>1000000=>0000001=>[7,1]
[6,2,8,5,1,7,4,3]=>0000000=>0000000=>[8]
[6,7,4,8,2,1,5,3]=>0000000=>0000000=>[8]
[3,2,7,8,6,1,5,4]=>0000000=>0000000=>[8]
[6,8,4,1,2,3,7,5]=>0000000=>0000000=>[8]
[1,8,2,5,6,4,3,7]=>1000000=>0000001=>[7,1]
[6,1,8,5,3,7,4,2]=>0000000=>0000000=>[8]
[3,8,1,5,2,7,6,4]=>0000000=>0000000=>[8]
[8,2,1,5,3,7,6,4]=>0000000=>0000000=>[8]
[8,1,6,5,3,7,2,4]=>0000000=>0000000=>[8]
[7,1,4,6,3,2,8,5]=>0000000=>0000000=>[8]
[3,2,6,4,1,7,8,5]=>0000000=>0000000=>[8]
[7,6,4,3,1,2,8,5]=>0000000=>0000000=>[8]
[8,6,3,5,1,7,2,4]=>0000000=>0000000=>[8]
[4,5,3,1,6,7,8,2]=>0000000=>0000000=>[8]
[3,5,2,1,6,7,8,4]=>0000000=>0000000=>[8]
[5,2,3,1,6,7,8,4]=>0000000=>0000000=>[8]
[1,5,3,2,6,7,8,4]=>1000000=>0000001=>[7,1]
[8,2,7,5,6,1,3,4]=>0000000=>0000000=>[8]
[1,7,4,6,2,3,8,5]=>1000000=>0000001=>[7,1]
[7,6,4,2,1,5,8,3]=>0000000=>0000000=>[8]
[5,7,4,6,1,3,8,2]=>0000000=>0000000=>[8]
[8,6,4,7,3,1,2,5]=>0000000=>0000000=>[8]
[5,2,4,3,7,1,8,6]=>0000000=>0000000=>[8]
[8,6,4,1,3,5,2,7]=>0000000=>0000000=>[8]
[6,7,4,1,5,3,8,2]=>0000000=>0000000=>[8]
[7,5,4,1,2,6,8,3]=>0000000=>0000000=>[8]
[1,8,2,5,3,7,6,4]=>1000000=>0000001=>[7,1]
[3,8,1,5,6,4,2,7]=>0000000=>0000000=>[8]
[7,6,4,1,5,2,8,3]=>0000000=>0000000=>[8]
[8,6,1,5,4,7,2,3]=>0000000=>0000000=>[8]
[5,2,1,4,6,7,8,3]=>0000000=>0000000=>[8]
[5,4,1,3,6,7,8,2]=>0000000=>0000000=>[8]
[8,4,1,5,3,7,2,6]=>0000000=>0000000=>[8]
[7,5,4,1,3,2,8,6]=>0000000=>0000000=>[8]
[3,2,5,1,4,7,8,6]=>0000100=>0010000=>[3,5]
[5,1,3,4,6,7,8,2]=>0000000=>0000000=>[8]
[5,7,4,1,8,6,3,2]=>0000000=>0000000=>[8]
[3,6,7,4,5,8,2,1]=>0000000=>0000000=>[8]
[5,4,6,1,7,8,3,2]=>0000000=>0000000=>[8]
[3,7,1,5,4,6,8,2]=>0000000=>0000000=>[8]
[6,7,1,4,5,3,8,2]=>0000000=>0000000=>[8]
[5,4,7,2,8,3,6,1]=>0000000=>0000000=>[8]
[3,8,1,5,4,6,2,7]=>0000000=>0000000=>[8]
[3,6,1,5,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[3,6,1,5,4,8,2,7]=>0000000=>0000000=>[8]
[3,4,1,2,6,8,7,5]=>0001000=>0001000=>[4,4]
[3,8,1,5,4,7,2,6]=>0000000=>0000000=>[8]
[7,8,3,1,4,6,2,5]=>0000000=>0000000=>[8]
[6,5,8,7,3,4,2,1]=>0000000=>0000000=>[8]
[3,7,1,5,4,2,6,8]=>0000001=>1000000=>[1,7]
[3,8,1,5,4,2,7,6]=>0000000=>0000000=>[8]
[6,7,3,1,4,5,8,2]=>0000000=>0000000=>[8]
[2,5,6,1,4,7,8,3]=>0000000=>0000000=>[8]
[1,8,4,5,2,7,3,6]=>1000000=>0000001=>[7,1]
[1,8,4,5,2,7,6,3]=>1000000=>0000001=>[7,1]
[1,8,4,3,6,2,5,7]=>1000000=>0000001=>[7,1]
[2,7,6,4,8,5,3,1]=>0000000=>0000000=>[8]
[1,8,4,5,2,6,3,7]=>1000000=>0000001=>[7,1]
[7,3,5,8,4,6,2,1]=>0000000=>0000000=>[8]
[8,2,1,3,5,7,4,6]=>0000000=>0000000=>[8]
[7,5,4,1,3,8,2,6]=>0000000=>0000000=>[8]
[7,3,8,5,4,1,2,6]=>0000000=>0000000=>[8]
[1,7,2,3,5,8,4,6]=>1000000=>0000001=>[7,1]
[3,5,2,6,7,1,8,4]=>0000000=>0000000=>[8]
[3,2,8,4,7,5,1,6]=>0000000=>0000000=>[8]
[6,8,3,1,7,2,4,5]=>0000000=>0000000=>[8]
[2,7,5,3,8,4,1,6]=>0000000=>0000000=>[8]
[8,3,2,1,5,7,4,6]=>0000000=>0000000=>[8]
[1,2,8,3,5,7,4,6]=>1100000=>0000011=>[6,1,1]
[6,5,1,7,4,2,8,3]=>0000000=>0000000=>[8]
[7,3,6,4,8,2,1,5]=>0000000=>0000000=>[8]
[4,6,1,7,3,5,2,8]=>0000001=>1000000=>[1,7]
[5,6,1,7,3,4,2,8]=>0000001=>1000000=>[1,7]
[6,1,7,3,4,2,8,5]=>0000000=>0000000=>[8]
[7,3,8,1,6,5,2,4]=>0000000=>0000000=>[8]
[8,3,7,1,6,5,2,4]=>0000000=>0000000=>[8]
[2,8,1,7,6,5,3,4]=>0000000=>0000000=>[8]
[4,2,8,6,5,1,7,3]=>0000000=>0000000=>[8]
[8,6,4,7,1,5,2,3]=>0000000=>0000000=>[8]
[7,6,4,8,1,5,2,3]=>0000000=>0000000=>[8]
[5,1,6,4,2,3,8,7]=>0000010=>0100000=>[2,6]
[4,2,3,8,7,5,1,6]=>0000000=>0000000=>[8]
[3,8,7,1,6,5,2,4]=>0000000=>0000000=>[8]
[2,4,3,8,1,6,7,5]=>0000000=>0000000=>[8]
[2,4,3,7,1,6,8,5]=>0000000=>0000000=>[8]
[4,2,3,7,8,5,1,6]=>0000000=>0000000=>[8]
[5,1,6,4,2,3,7,8]=>0000011=>1100000=>[1,1,6]
[6,4,7,8,1,5,2,3]=>0000000=>0000000=>[8]
[8,7,4,6,1,5,2,3]=>0000000=>0000000=>[8]
[6,5,7,8,1,4,2,3]=>0000000=>0000000=>[8]
[4,7,8,6,1,5,2,3]=>0000000=>0000000=>[8]
[3,2,4,8,7,1,5,6]=>0000000=>0000000=>[8]
[4,8,7,6,1,5,2,3]=>0000000=>0000000=>[8]
[5,8,7,6,1,4,2,3]=>0000000=>0000000=>[8]
[8,6,5,7,1,4,2,3]=>0000000=>0000000=>[8]
[5,1,6,7,4,2,3,8]=>0000001=>1000000=>[1,7]
[6,7,4,8,1,5,2,3]=>0000000=>0000000=>[8]
[8,4,7,6,1,5,2,3]=>0000000=>0000000=>[8]
[8,3,2,4,7,1,5,6]=>0000000=>0000000=>[8]
[7,3,2,4,8,1,5,6]=>0000000=>0000000=>[8]
[2,5,3,7,1,6,4,8]=>0000001=>1000000=>[1,7]
[8,4,6,7,1,5,2,3]=>0000000=>0000000=>[8]
[5,1,6,8,4,2,3,7]=>0000000=>0000000=>[8]
[4,2,3,7,5,1,6,8]=>0000001=>1000000=>[1,7]
[2,4,3,7,1,6,5,8]=>0000001=>1000000=>[1,7]
[2,4,7,1,5,8,6,3]=>0000000=>0000000=>[8]
[3,2,4,7,6,1,5,8]=>0000001=>1000000=>[1,7]
[4,7,6,8,1,5,2,3]=>0000000=>0000000=>[8]
[8,5,6,7,1,4,2,3]=>0000000=>0000000=>[8]
[8,6,7,5,1,4,2,3]=>0000000=>0000000=>[8]
[6,8,7,5,1,4,2,3]=>0000000=>0000000=>[8]
[5,6,8,7,1,4,2,3]=>0000000=>0000000=>[8]
[4,6,8,7,1,5,2,3]=>0000000=>0000000=>[8]
[3,2,4,6,1,5,7,8]=>0000011=>1100000=>[1,1,6]
[6,7,8,5,1,4,2,3]=>0000000=>0000000=>[8]
[7,8,6,5,1,4,2,3]=>0000000=>0000000=>[8]
[2,1,8,5,4,6,3,7]=>0100000=>0000010=>[6,2]
[4,1,8,5,2,3,6,7]=>0000000=>0000000=>[8]
[5,4,1,3,6,7,2,8]=>0000001=>1000000=>[1,7]
[8,4,1,2,6,3,7,5]=>0000000=>0000000=>[8]
[8,2,7,1,5,3,4,6]=>0000000=>0000000=>[8]
[3,2,7,1,5,8,4,6]=>0000000=>0000000=>[8]
[7,3,8,1,5,4,2,6]=>0000000=>0000000=>[8]
[7,1,5,3,8,4,2,6]=>0000000=>0000000=>[8]
[3,6,8,1,5,4,2,7]=>0000000=>0000000=>[8]
[6,8,3,1,5,4,2,7]=>0000000=>0000000=>[8]
[7,6,3,1,5,4,2,8]=>0000001=>1000000=>[1,7]
[3,6,2,1,5,8,4,7]=>0000000=>0000000=>[8]
[8,6,2,1,5,3,4,7]=>0000000=>0000000=>[8]
[2,3,8,1,5,7,4,6]=>0000000=>0000000=>[8]
[7,1,3,2,8,6,4,5]=>0000000=>0000000=>[8]
[4,7,1,2,6,3,8,5]=>0000000=>0000000=>[8]
[2,7,8,1,5,3,4,6]=>0000000=>0000000=>[8]
[6,7,2,1,5,3,4,8]=>0000001=>1000000=>[1,7]
[4,7,2,1,8,5,3,6]=>0000000=>0000000=>[8]
[8,7,2,1,4,5,3,6]=>0000000=>0000000=>[8]
[5,7,8,6,1,4,3,2]=>0000000=>0000000=>[8]
[2,7,4,1,6,5,3,8]=>0000001=>1000000=>[1,7]
[7,1,6,4,5,8,3,2]=>0000000=>0000000=>[8]
[2,6,4,1,7,5,3,8]=>0000001=>1000000=>[1,7]
[5,6,8,7,1,4,3,2]=>0000000=>0000000=>[8]
[4,2,8,1,6,5,3,7]=>0000000=>0000000=>[8]
[6,2,4,1,8,5,3,7]=>0000000=>0000000=>[8]
[8,3,1,4,5,6,7,2]=>0000000=>0000000=>[8]
[5,3,1,4,8,6,7,2]=>0000000=>0000000=>[8]
[7,5,1,6,3,4,8,2]=>0000000=>0000000=>[8]
[7,1,5,8,4,3,6,2]=>0000000=>0000000=>[8]
[5,8,1,6,4,3,7,2]=>0000000=>0000000=>[8]
[5,3,1,8,4,6,7,2]=>0000000=>0000000=>[8]
[8,3,1,5,4,6,7,2]=>0000000=>0000000=>[8]
[8,2,6,1,4,5,3,7]=>0000000=>0000000=>[8]
[6,2,8,1,4,5,3,7]=>0000000=>0000000=>[8]
[7,2,6,1,5,3,4,8]=>0000001=>1000000=>[1,7]
[2,8,6,1,5,3,4,7]=>0000000=>0000000=>[8]
[4,2,1,5,6,3,8,7]=>0000010=>0100000=>[2,6]
[7,1,2,5,8,3,4,6]=>0000000=>0000000=>[8]
[7,1,4,5,6,8,3,2]=>0000000=>0000000=>[8]
[2,6,7,1,4,5,3,8]=>0000001=>1000000=>[1,7]
[3,5,1,7,4,6,8,2]=>0000000=>0000000=>[8]
[7,1,5,6,4,8,3,2]=>0000000=>0000000=>[8]
[7,1,6,5,4,8,3,2]=>0000000=>0000000=>[8]
[2,7,6,1,4,5,3,8]=>0000001=>1000000=>[1,7]
[5,7,6,8,1,4,3,2]=>0000000=>0000000=>[8]
[7,8,6,5,1,4,3,2]=>0000000=>0000000=>[8]
[5,3,1,2,4,8,7,6]=>0000100=>0010000=>[3,5]
[5,3,6,2,1,8,7,4]=>0000000=>0000000=>[8]
[5,3,7,2,8,4,1,6]=>0000000=>0000000=>[8]
[7,2,4,5,8,3,1,6]=>0000000=>0000000=>[8]
[7,2,4,5,1,3,6,8]=>0000001=>1000000=>[1,7]
[6,2,4,5,1,8,7,3]=>0000000=>0000000=>[8]
[3,1,4,5,2,8,7,6]=>0000100=>0010000=>[3,5]
[1,6,4,5,2,8,7,3]=>1000000=>0000001=>[7,1]
[3,7,4,5,1,2,6,8]=>0000001=>1000000=>[1,7]
[1,7,4,2,6,3,5,8]=>1000001=>1000001=>[1,6,1]
[8,7,4,5,2,1,6,3]=>0000000=>0000000=>[8]
[6,3,7,1,8,4,2,5]=>0000000=>0000000=>[8]
[5,7,4,1,6,3,2,8]=>0000001=>1000000=>[1,7]
[1,7,4,8,6,3,2,5]=>1000000=>0000001=>[7,1]
[5,7,4,8,6,3,1,2]=>0000000=>0000000=>[8]
[4,8,3,5,6,7,1,2]=>0000000=>0000000=>[8]
[1,8,3,5,6,7,2,4]=>1000000=>0000001=>[7,1]
[4,8,1,5,6,7,2,3]=>0000000=>0000000=>[8]
[4,1,3,5,6,7,2,8]=>0000001=>1000000=>[1,7]
[5,8,4,3,6,1,2,7]=>0000000=>0000000=>[8]
[5,3,8,4,1,7,2,6]=>0000000=>0000000=>[8]
[1,5,8,4,6,7,3,2]=>1000000=>0000001=>[7,1]
[1,4,8,3,6,7,5,2]=>1000000=>0000001=>[7,1]
[4,3,8,2,1,7,5,6]=>0000000=>0000000=>[8]
[3,8,4,2,6,1,5,7]=>0000000=>0000000=>[8]
[3,8,1,5,6,7,4,2]=>0000000=>0000000=>[8]
[3,8,2,5,6,7,1,4]=>0000000=>0000000=>[8]
[8,2,1,5,6,7,4,3]=>0000000=>0000000=>[8]
[8,1,3,5,6,7,4,2]=>0000000=>0000000=>[8]
[7,1,4,3,6,2,5,8]=>0000001=>1000000=>[1,7]
[7,8,4,3,6,2,1,5]=>0000000=>0000000=>[8]
[4,3,1,8,5,7,6,2]=>0000000=>0000000=>[8]
[6,3,5,8,2,7,1,4]=>0000000=>0000000=>[8]
[7,5,4,8,6,2,1,3]=>0000000=>0000000=>[8]
[7,1,4,8,6,2,3,5]=>0000000=>0000000=>[8]
[7,5,4,1,6,2,3,8]=>0000001=>1000000=>[1,7]
[1,6,4,5,8,2,3,7]=>1000000=>0000001=>[7,1]
[1,8,5,3,6,7,4,2]=>1000000=>0000001=>[7,1]
[8,3,5,2,1,7,4,6]=>0000000=>0000000=>[8]
[4,1,8,5,6,7,3,2]=>0000000=>0000000=>[8]
[1,2,8,5,6,7,3,4]=>1100000=>0000011=>[6,1,1]
[4,2,1,5,6,7,3,8]=>0000001=>1000000=>[1,7]
[1,5,3,8,6,7,4,2]=>1000000=>0000001=>[7,1]
[1,4,8,5,6,7,2,3]=>1000000=>0000001=>[7,1]
[2,6,5,7,3,1,8,4]=>0000000=>0000000=>[8]
[6,3,2,4,7,5,1,8]=>0000001=>1000000=>[1,7]
[4,2,1,6,3,7,5,8]=>0000001=>1000000=>[1,7]
[4,2,1,6,3,7,8,5]=>0000000=>0000000=>[8]
[4,2,1,3,7,8,6,5]=>0001000=>0001000=>[4,4]
[5,8,1,7,4,3,2,6]=>0000000=>0000000=>[8]
[7,3,4,2,6,8,1,5]=>0000000=>0000000=>[8]
[3,6,7,5,2,4,8,1]=>0000000=>0000000=>[8]
[4,8,1,7,3,6,5,2]=>0000000=>0000000=>[8]
[4,2,1,8,3,7,6,5]=>0000000=>0000000=>[8]
[2,6,1,5,4,7,8,3]=>0000000=>0000000=>[8]
[4,6,3,5,8,7,1,2]=>0000000=>0000000=>[8]
[4,7,5,2,1,3,6,8]=>0000001=>1000000=>[1,7]
[3,5,6,2,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[3,1,8,5,2,7,6,4]=>0000000=>0000000=>[8]
[4,8,1,5,2,7,3,6]=>0000000=>0000000=>[8]
[4,1,2,5,3,8,7,6]=>0000100=>0010000=>[3,5]
[4,3,6,8,7,5,1,2]=>0000000=>0000000=>[8]
[6,4,8,1,2,5,3,7]=>0000000=>0000000=>[8]
[6,5,1,2,3,4,8,7]=>0000010=>0100000=>[2,6]
[6,7,4,1,2,5,3,8]=>0000001=>1000000=>[1,7]
[1,2,6,7,5,3,8,4]=>1100000=>0000011=>[6,1,1]
[1,7,5,3,2,8,4,6]=>1000000=>0000001=>[7,1]
[1,6,5,7,2,3,8,4]=>1000000=>0000001=>[7,1]
[1,3,8,2,6,5,7,4]=>1000000=>0000001=>[7,1]
[1,2,5,7,6,3,4,8]=>1100001=>1000011=>[1,5,1,1]
[1,3,4,8,2,5,7,6]=>1000000=>0000001=>[7,1]
[1,5,7,6,2,3,4,8]=>1000001=>1000001=>[1,6,1]
[1,5,3,8,2,6,4,7]=>1000000=>0000001=>[7,1]
[1,4,8,3,2,5,7,6]=>1000000=>0000001=>[7,1]
[1,2,4,8,3,5,7,6]=>1100000=>0000011=>[6,1,1]
[1,3,8,4,2,6,7,5]=>1000000=>0000001=>[7,1]
[1,4,8,2,3,5,7,6]=>1000000=>0000001=>[7,1]
[4,2,6,7,5,8,3,1]=>0000000=>0000000=>[8]
[6,7,5,2,1,8,4,3]=>0000000=>0000000=>[8]
[3,4,8,7,5,2,1,6]=>0000000=>0000000=>[8]
[1,7,5,2,8,4,6,3]=>1000000=>0000001=>[7,1]
[5,6,8,3,1,7,2,4]=>0000000=>0000000=>[8]
[6,1,4,8,3,2,7,5]=>0000000=>0000000=>[8]
[3,4,7,1,8,6,2,5]=>0000000=>0000000=>[8]
[3,4,6,8,2,1,5,7]=>0000000=>0000000=>[8]
[3,8,2,5,6,1,4,7]=>0000000=>0000000=>[8]
[3,5,2,8,6,4,1,7]=>0000000=>0000000=>[8]
[4,2,5,7,3,8,6,1]=>0000000=>0000000=>[8]
[7,4,2,5,3,8,1,6]=>0000000=>0000000=>[8]
[1,5,6,8,3,4,2,7]=>1000000=>0000001=>[7,1]
[4,5,1,6,8,3,2,7]=>0000000=>0000000=>[8]
[4,5,7,3,8,2,6,1]=>0000000=>0000000=>[8]
[6,4,3,7,8,2,5,1]=>0000000=>0000000=>[8]
[6,4,3,1,7,8,2,5]=>0000000=>0000000=>[8]
[4,5,3,1,7,8,2,6]=>0000000=>0000000=>[8]
[7,1,3,5,4,8,2,6]=>0000000=>0000000=>[8]
[7,5,2,8,1,4,3,6]=>0000000=>0000000=>[8]
[1,4,5,7,3,8,6,2]=>1000000=>0000001=>[7,1]
[4,6,3,7,8,5,2,1]=>0000000=>0000000=>[8]
[1,5,3,6,7,8,4,2]=>1000000=>0000001=>[7,1]
[4,6,1,7,3,8,5,2]=>0000000=>0000000=>[8]
[6,7,2,4,8,1,5,3]=>0000000=>0000000=>[8]
[5,2,3,6,7,8,4,1]=>0000000=>0000000=>[8]
[6,4,2,7,1,8,3,5]=>0000000=>0000000=>[8]
[4,2,6,3,7,8,5,1]=>0000000=>0000000=>[8]
[6,7,3,8,2,4,5,1]=>0000000=>0000000=>[8]
[3,6,2,7,4,1,8,5]=>0000000=>0000000=>[8]
[6,7,3,2,1,4,8,5]=>0000000=>0000000=>[8]
[7,2,4,8,6,1,3,5]=>0000000=>0000000=>[8]
[3,5,7,2,1,8,6,4]=>0000000=>0000000=>[8]
[6,7,8,3,2,5,1,4]=>0000000=>0000000=>[8]
[6,3,7,8,2,5,4,1]=>0000000=>0000000=>[8]
[2,6,7,4,8,5,3,1]=>0000000=>0000000=>[8]
[6,2,4,7,1,8,5,3]=>0000000=>0000000=>[8]
[1,7,4,8,5,2,6,3]=>1000000=>0000001=>[7,1]
[1,3,7,8,5,2,6,4]=>1000000=>0000001=>[7,1]
[2,5,7,8,1,6,3,4]=>0000000=>0000000=>[8]
[1,6,4,7,8,2,5,3]=>1000000=>0000001=>[7,1]
[2,5,6,1,7,8,4,3]=>0000000=>0000000=>[8]
[5,6,1,2,7,8,4,3]=>0000000=>0000000=>[8]
[6,7,2,1,8,5,3,4]=>0000000=>0000000=>[8]
[6,4,2,5,3,8,7,1]=>0000000=>0000000=>[8]
[2,6,4,5,8,7,3,1]=>0000000=>0000000=>[8]
[2,6,4,8,7,5,3,1]=>0000000=>0000000=>[8]
[8,2,4,6,7,5,3,1]=>0000000=>0000000=>[8]
[4,2,6,8,7,5,3,1]=>0000000=>0000000=>[8]
[4,2,6,5,8,7,3,1]=>0000000=>0000000=>[8]
[6,4,8,7,2,5,3,1]=>0000000=>0000000=>[8]
[4,6,5,8,7,2,3,1]=>0000000=>0000000=>[8]
[4,7,8,3,1,2,6,5]=>0000000=>0000000=>[8]
[4,7,8,2,1,3,6,5]=>0000000=>0000000=>[8]
[3,6,2,8,4,7,1,5]=>0000000=>0000000=>[8]
[3,2,6,8,4,7,1,5]=>0000000=>0000000=>[8]
[4,2,6,8,3,1,7,5]=>0000000=>0000000=>[8]
[4,2,5,1,8,3,7,6]=>0000000=>0000000=>[8]
[4,2,5,3,8,1,7,6]=>0000000=>0000000=>[8]
[3,2,5,4,8,7,1,6]=>0000000=>0000000=>[8]
[5,4,3,1,2,8,7,6]=>0000100=>0010000=>[3,5]
[5,3,1,4,2,8,7,6]=>0000100=>0010000=>[3,5]
[5,3,2,1,4,8,7,6]=>0000100=>0010000=>[3,5]
[4,3,2,5,8,1,7,6]=>0000000=>0000000=>[8]
[3,2,4,5,8,7,1,6]=>0000000=>0000000=>[8]
[1,7,2,3,5,6,8,4]=>1000000=>0000001=>[7,1]
[3,7,4,2,1,5,6,8]=>0000001=>1000000=>[1,7]
[3,4,6,2,8,5,7,1]=>0000000=>0000000=>[8]
[4,2,1,7,5,8,3,6]=>0000000=>0000000=>[8]
[4,7,2,6,5,1,3,8]=>0000001=>1000000=>[1,7]
[3,7,4,1,2,5,8,6]=>0000000=>0000000=>[8]
[4,7,1,6,5,2,8,3]=>0000000=>0000000=>[8]
[4,7,3,6,5,1,8,2]=>0000000=>0000000=>[8]
[4,3,7,1,6,8,5,2]=>0000000=>0000000=>[8]
[4,2,1,7,5,6,8,3]=>0000000=>0000000=>[8]
[4,2,6,8,7,3,1,5]=>0000000=>0000000=>[8]
[3,4,6,1,8,5,2,7]=>0000000=>0000000=>[8]
[4,1,6,7,5,8,2,3]=>0000000=>0000000=>[8]
[4,3,6,7,5,1,2,8]=>0000001=>1000000=>[1,7]
[4,3,7,1,6,8,2,5]=>0000000=>0000000=>[8]
[4,3,7,5,6,8,2,1]=>0000000=>0000000=>[8]
[4,1,7,3,6,5,2,8]=>0000001=>1000000=>[1,7]
[2,8,7,4,5,3,1,6]=>0000000=>0000000=>[8]
[2,8,7,4,3,5,1,6]=>0000000=>0000000=>[8]
[4,1,7,3,6,2,5,8]=>0000001=>1000000=>[1,7]
[5,8,7,6,1,2,4,3]=>0000000=>0000000=>[8]
[4,1,7,2,6,8,5,3]=>0000000=>0000000=>[8]
[4,2,7,3,6,1,8,5]=>0000000=>0000000=>[8]
[4,2,7,3,6,5,8,1]=>0000000=>0000000=>[8]
[3,8,5,6,2,4,1,7]=>0000000=>0000000=>[8]
[2,8,6,5,3,7,1,4]=>0000000=>0000000=>[8]
[3,8,6,5,1,4,7,2]=>0000000=>0000000=>[8]
[3,8,2,1,4,6,7,5]=>0000000=>0000000=>[8]
[3,8,2,5,4,6,7,1]=>0000000=>0000000=>[8]
[4,2,6,7,5,3,1,8]=>0000001=>1000000=>[1,7]
[3,2,6,1,4,5,8,7]=>0000010=>0100000=>[2,6]
[2,8,7,3,4,5,1,6]=>0000000=>0000000=>[8]
[5,8,7,6,1,3,4,2]=>0000000=>0000000=>[8]
[5,8,7,6,2,3,4,1]=>0000000=>0000000=>[8]
[4,1,7,5,6,2,3,8]=>0000001=>1000000=>[1,7]
[3,8,1,5,2,6,4,7]=>0000000=>0000000=>[8]
[2,8,7,5,3,4,1,6]=>0000000=>0000000=>[8]
[2,8,7,5,4,3,1,6]=>0000000=>0000000=>[8]
[4,1,7,5,6,3,2,8]=>0000001=>1000000=>[1,7]
[5,8,7,6,1,3,2,4]=>0000000=>0000000=>[8]
[5,8,7,6,4,1,2,3]=>0000000=>0000000=>[8]
[8,1,7,2,4,5,3,6]=>0000000=>0000000=>[8]
[8,1,3,6,2,5,4,7]=>0000000=>0000000=>[8]
[7,2,1,6,3,5,4,8]=>0000001=>1000000=>[1,7]
[2,7,1,6,3,5,4,8]=>0000001=>1000000=>[1,7]
[2,7,1,5,4,3,6,8]=>0000001=>1000000=>[1,7]
[7,2,1,5,4,3,6,8]=>0000001=>1000000=>[1,7]
[8,1,3,5,4,2,6,7]=>0000000=>0000000=>[8]
[8,1,5,3,4,2,6,7]=>0000000=>0000000=>[8]
[8,1,5,6,2,3,7,4]=>0000000=>0000000=>[8]
[8,1,4,5,3,2,6,7]=>0000000=>0000000=>[8]
[8,1,4,3,5,2,6,7]=>0000000=>0000000=>[8]
[7,2,1,4,5,3,6,8]=>0000001=>1000000=>[1,7]
[2,7,1,4,5,3,6,8]=>0000001=>1000000=>[1,7]
[2,6,3,1,5,4,7,8]=>0000011=>1100000=>[1,1,6]
[6,3,2,1,5,4,7,8]=>0000011=>1100000=>[1,1,6]
[7,3,1,4,5,2,6,8]=>0000001=>1000000=>[1,7]
[7,3,1,5,4,2,6,8]=>0000001=>1000000=>[1,7]
[7,3,1,6,2,5,4,8]=>0000001=>1000000=>[1,7]
[3,7,1,6,2,5,4,8]=>0000001=>1000000=>[1,7]
[3,7,1,4,5,2,6,8]=>0000001=>1000000=>[1,7]
[2,3,6,1,5,4,7,8]=>0000011=>1100000=>[1,1,6]
[6,3,4,1,5,2,7,8]=>0000011=>1100000=>[1,1,6]
[6,2,4,1,5,3,7,8]=>0000011=>1100000=>[1,1,6]
[2,6,4,1,5,3,7,8]=>0000011=>1100000=>[1,1,6]
[2,6,5,1,3,7,4,8]=>0000001=>1000000=>[1,7]
[6,5,2,1,3,7,4,8]=>0000001=>1000000=>[1,7]
[7,6,1,2,4,5,3,8]=>0000001=>1000000=>[1,7]
[6,7,1,2,8,3,5,4]=>0000000=>0000000=>[8]
[6,7,1,2,5,4,3,8]=>0000001=>1000000=>[1,7]
[5,6,2,1,3,7,4,8]=>0000001=>1000000=>[1,7]
[5,2,6,1,3,7,4,8]=>0000001=>1000000=>[1,7]
[2,4,6,1,5,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,7,1,3,5,2,6,8]=>0000001=>1000000=>[1,7]
[4,7,1,5,3,2,6,8]=>0000001=>1000000=>[1,7]
[5,7,1,6,2,3,8,4]=>0000000=>0000000=>[8]
[5,6,3,1,2,7,4,8]=>0000001=>1000000=>[1,7]
[4,2,5,3,1,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,8,7,3,2,6,4,1]=>0000000=>0000000=>[8]
[8,1,7,2,5,6,3,4]=>0000000=>0000000=>[8]
[4,8,1,5,2,6,7,3]=>0000000=>0000000=>[8]
[7,1,2,8,5,6,3,4]=>0000000=>0000000=>[8]
[8,7,2,1,5,6,3,4]=>0000000=>0000000=>[8]
[8,6,7,1,5,2,3,4]=>0000000=>0000000=>[8]
[6,1,7,8,5,2,3,4]=>0000000=>0000000=>[8]
[8,7,5,2,1,6,4,3]=>0000000=>0000000=>[8]
[4,6,8,1,5,3,7,2]=>0000000=>0000000=>[8]
[6,5,8,1,3,4,7,2]=>0000000=>0000000=>[8]
[5,8,2,4,3,6,7,1]=>0000000=>0000000=>[8]
[8,1,3,7,5,2,6,4]=>0000000=>0000000=>[8]
[3,6,8,2,4,1,7,5]=>0000000=>0000000=>[8]
[2,5,8,4,6,7,3,1]=>0000000=>0000000=>[8]
[5,8,4,1,6,7,2,3]=>0000000=>0000000=>[8]
[1,6,4,5,2,3,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,7,4,5,2,3,6,8]=>1000001=>1000001=>[1,6,1]
[1,6,3,5,2,4,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,6,3,4,2,5,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,7,3,4,2,5,6,8]=>1000001=>1000001=>[1,6,1]
[1,8,5,7,3,4,2,6]=>1000000=>0000001=>[7,1]
[1,7,3,4,2,6,5,8]=>1000001=>1000001=>[1,6,1]
[1,5,2,8,4,7,3,6]=>1000000=>0000001=>[7,1]
[1,4,2,8,5,7,3,6]=>1000000=>0000001=>[7,1]
[1,7,3,5,2,6,4,8]=>1000001=>1000001=>[1,6,1]
[1,8,4,7,3,5,2,6]=>1000000=>0000001=>[7,1]
[1,7,3,6,2,5,4,8]=>1000001=>1000001=>[1,6,1]
[1,7,3,6,2,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,7,4,6,2,3,5,8]=>1000001=>1000001=>[1,6,1]
[1,8,5,6,2,3,4,7]=>1000000=>0000001=>[7,1]
[1,8,5,6,2,4,3,7]=>1000000=>0000001=>[7,1]
[1,3,2,8,5,6,4,7]=>1010000=>0000101=>[5,2,1]
[1,4,2,8,5,6,3,7]=>1000000=>0000001=>[7,1]
[1,5,2,8,4,6,3,7]=>1000000=>0000001=>[7,1]
[1,6,2,8,4,5,3,7]=>1000000=>0000001=>[7,1]
[8,6,4,7,2,1,3,5]=>0000000=>0000000=>[8]
[1,6,4,7,2,8,3,5]=>1000000=>0000001=>[7,1]
[1,4,7,3,5,8,2,6]=>1000000=>0000001=>[7,1]
[8,4,6,2,3,5,1,7]=>0000000=>0000000=>[8]
[5,4,8,2,3,6,1,7]=>0000000=>0000000=>[8]
[7,4,8,5,2,3,1,6]=>0000000=>0000000=>[8]
[3,8,6,2,4,5,1,7]=>0000000=>0000000=>[8]
[4,8,6,2,3,5,1,7]=>0000000=>0000000=>[8]
[1,7,5,3,4,8,2,6]=>1000000=>0000001=>[7,1]
[1,7,6,4,8,2,3,5]=>1000000=>0000001=>[7,1]
[5,8,7,4,1,2,3,6]=>0000000=>0000000=>[8]
[6,8,5,3,4,1,2,7]=>0000000=>0000000=>[8]
[6,8,3,7,2,1,4,5]=>0000000=>0000000=>[8]
[8,5,1,6,3,7,2,4]=>0000000=>0000000=>[8]
[6,1,3,7,4,8,2,5]=>0000000=>0000000=>[8]
[4,1,7,3,5,8,2,6]=>0000000=>0000000=>[8]
[7,1,6,4,8,2,3,5]=>0000000=>0000000=>[8]
[5,1,7,3,8,2,4,6]=>0000000=>0000000=>[8]
[6,1,5,7,8,2,3,4]=>0000000=>0000000=>[8]
[7,4,8,6,1,2,3,5]=>0000000=>0000000=>[8]
[3,8,7,5,1,2,4,6]=>0000000=>0000000=>[8]
[3,7,6,1,2,4,5,8]=>0000001=>1000000=>[1,7]
[4,7,6,1,2,3,5,8]=>0000001=>1000000=>[1,7]
[1,6,5,8,2,3,4,7]=>1000000=>0000001=>[7,1]
[6,5,8,4,1,2,3,7]=>0000000=>0000000=>[8]
[8,5,7,4,1,2,3,6]=>0000000=>0000000=>[8]
[1,5,7,4,8,2,3,6]=>1000000=>0000001=>[7,1]
[7,6,2,3,8,1,4,5]=>0000000=>0000000=>[8]
[7,4,8,5,1,6,2,3]=>0000000=>0000000=>[8]
[8,6,2,3,1,7,4,5]=>0000000=>0000000=>[8]
[8,6,4,1,2,7,3,5]=>0000000=>0000000=>[8]
[1,7,2,8,6,3,4,5]=>1000000=>0000001=>[7,1]
[7,5,8,1,3,6,2,4]=>0000000=>0000000=>[8]
[5,4,1,8,2,3,6,7]=>0000000=>0000000=>[8]
[1,4,8,7,2,3,5,6]=>1000000=>0000001=>[7,1]
[1,5,8,7,2,3,4,6]=>1000000=>0000001=>[7,1]
[6,5,1,8,2,3,4,7]=>0000000=>0000000=>[8]
[5,7,1,3,8,2,4,6]=>0000000=>0000000=>[8]
[7,6,8,1,5,2,3,4]=>0000000=>0000000=>[8]
[7,1,5,8,6,2,3,4]=>0000000=>0000000=>[8]
[4,1,8,7,2,3,5,6]=>0000000=>0000000=>[8]
[5,1,8,7,2,3,4,6]=>0000000=>0000000=>[8]
[7,1,5,8,3,4,2,6]=>0000000=>0000000=>[8]
[7,1,4,3,2,5,6,8]=>0000001=>1000000=>[1,7]
[6,4,2,3,8,5,7,1]=>0000000=>0000000=>[8]
[6,4,2,7,5,8,3,1]=>0000000=>0000000=>[8]
[7,1,4,6,5,2,3,8]=>0000001=>1000000=>[1,7]
[7,1,4,6,5,8,2,3]=>0000000=>0000000=>[8]
[7,1,4,6,3,8,2,5]=>0000000=>0000000=>[8]
[7,1,4,3,2,5,8,6]=>0000000=>0000000=>[8]
[7,1,4,6,5,2,8,3]=>0000000=>0000000=>[8]
[7,1,4,6,5,3,8,2]=>0000000=>0000000=>[8]
[7,1,4,6,5,3,2,8]=>0000001=>1000000=>[1,7]
[6,4,2,7,5,3,8,1]=>0000000=>0000000=>[8]
[3,4,7,2,6,8,5,1]=>0000000=>0000000=>[8]
[3,4,7,1,6,8,2,5]=>0000000=>0000000=>[8]
[3,4,7,1,6,8,5,2]=>0000000=>0000000=>[8]
[2,4,1,7,5,3,6,8]=>0000001=>1000000=>[1,7]
[3,4,1,7,8,6,2,5]=>0000000=>0000000=>[8]
[6,4,2,3,8,5,1,7]=>0000000=>0000000=>[8]
[6,4,2,7,5,3,1,8]=>0000001=>1000000=>[1,7]
[3,4,7,2,6,8,1,5]=>0000000=>0000000=>[8]
[5,4,7,3,6,8,2,1]=>0000000=>0000000=>[8]
[3,4,7,2,6,5,1,8]=>0000001=>1000000=>[1,7]
[4,8,7,3,5,1,2,6]=>0000000=>0000000=>[8]
[4,8,7,1,3,5,2,6]=>0000000=>0000000=>[8]
[4,8,3,1,2,6,5,7]=>0000000=>0000000=>[8]
[3,4,7,1,6,2,5,8]=>0000001=>1000000=>[1,7]
[3,4,7,1,6,2,8,5]=>0000000=>0000000=>[8]
[3,4,7,2,6,5,8,1]=>0000000=>0000000=>[8]
[4,8,3,1,2,6,7,5]=>0000000=>0000000=>[8]
[5,8,1,6,3,4,2,7]=>0000000=>0000000=>[8]
[6,8,5,1,3,7,2,4]=>0000000=>0000000=>[8]
[6,8,5,1,3,4,7,2]=>0000000=>0000000=>[8]
[5,8,3,4,2,6,7,1]=>0000000=>0000000=>[8]
[6,4,3,7,5,1,2,8]=>0000001=>1000000=>[1,7]
[3,8,7,4,1,5,2,6]=>0000000=>0000000=>[8]
[2,4,7,3,6,1,5,8]=>0000001=>1000000=>[1,7]
[5,8,3,2,1,6,4,7]=>0000000=>0000000=>[8]
[5,8,7,4,3,1,2,6]=>0000000=>0000000=>[8]
[5,3,7,2,4,6,8,1]=>0000000=>0000000=>[8]
[4,2,1,5,8,6,3,7]=>0000000=>0000000=>[8]
[3,2,1,8,5,4,6,7]=>0010000=>0000100=>[5,3]
[6,7,2,1,8,4,5,3]=>0000000=>0000000=>[8]
[4,3,1,6,7,8,5,2]=>0000000=>0000000=>[8]
[4,2,1,6,8,5,3,7]=>0000000=>0000000=>[8]
[5,2,6,1,8,3,4,7]=>0000000=>0000000=>[8]
[4,2,1,7,8,6,3,5]=>0000000=>0000000=>[8]
[3,2,1,8,6,4,7,5]=>0010000=>0000100=>[5,3]
[3,2,1,8,6,4,5,7]=>0010000=>0000100=>[5,3]
[3,2,1,8,4,6,5,7]=>0010000=>0000100=>[5,3]
[3,2,1,8,4,6,7,5]=>0010000=>0000100=>[5,3]
[4,2,1,7,8,3,5,6]=>0000000=>0000000=>[8]
[3,2,1,8,4,5,7,6]=>0010000=>0000100=>[5,3]
[7,4,8,6,2,5,3,1]=>0000000=>0000000=>[8]
[7,3,8,6,2,4,5,1]=>0000000=>0000000=>[8]
[7,4,3,1,8,2,5,6]=>0000000=>0000000=>[8]
[7,4,2,8,5,6,1,3]=>0000000=>0000000=>[8]
[7,3,8,5,2,4,6,1]=>0000000=>0000000=>[8]
[6,3,8,2,4,5,1,7]=>0000000=>0000000=>[8]
[6,3,8,2,5,7,4,1]=>0000000=>0000000=>[8]
[5,6,7,3,8,2,4,1]=>0000000=>0000000=>[8]
[5,3,8,2,4,6,7,1]=>0000000=>0000000=>[8]
[6,3,8,2,4,7,5,1]=>0000000=>0000000=>[8]
[5,7,4,2,6,8,1,3]=>0000000=>0000000=>[8]
[6,5,3,1,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,7,4,2,6,1,3,8]=>0000001=>1000000=>[1,7]
[5,6,4,2,3,8,1,7]=>0000000=>0000000=>[8]
[5,6,3,7,8,2,4,1]=>0000000=>0000000=>[8]
[5,6,3,8,2,4,7,1]=>0000000=>0000000=>[8]
[6,3,7,2,4,5,1,8]=>0000001=>1000000=>[1,7]
[6,3,7,2,5,8,4,1]=>0000000=>0000000=>[8]
[5,3,6,8,2,4,7,1]=>0000000=>0000000=>[8]
[5,4,6,2,3,8,1,7]=>0000000=>0000000=>[8]
[5,3,6,7,8,2,4,1]=>0000000=>0000000=>[8]
[5,6,3,4,2,1,8,7]=>0000010=>0100000=>[2,6]
[5,6,4,2,1,3,8,7]=>0000010=>0100000=>[2,6]
[2,8,6,3,5,4,1,7]=>0000000=>0000000=>[8]
[4,3,8,5,7,6,2,1]=>0000000=>0000000=>[8]
[3,8,5,6,4,2,1,7]=>0000000=>0000000=>[8]
[6,3,7,8,4,2,1,5]=>0000000=>0000000=>[8]
[7,8,4,2,1,6,3,5]=>0000000=>0000000=>[8]
[8,5,7,6,2,1,4,3]=>0000000=>0000000=>[8]
[4,8,5,7,6,2,1,3]=>0000000=>0000000=>[8]
[8,4,2,6,3,1,7,5]=>0000000=>0000000=>[8]
[1,5,3,7,4,2,8,6]=>1000000=>0000001=>[7,1]
[1,6,7,3,4,2,8,5]=>1000000=>0000001=>[7,1]
[8,6,5,2,3,1,7,4]=>0000000=>0000000=>[8]
[1,7,6,3,4,2,8,5]=>1000000=>0000001=>[7,1]
[1,8,6,3,2,5,7,4]=>1000000=>0000001=>[7,1]
[8,7,5,2,1,4,6,3]=>0000000=>0000000=>[8]
[7,8,5,2,1,4,6,3]=>0000000=>0000000=>[8]
[6,8,5,2,3,1,7,4]=>0000000=>0000000=>[8]
[5,8,6,2,3,1,7,4]=>0000000=>0000000=>[8]
[4,8,2,6,3,1,7,5]=>0000000=>0000000=>[8]
[3,2,8,6,4,1,7,5]=>0000000=>0000000=>[8]
[3,2,1,7,5,4,8,6]=>0010000=>0000100=>[5,3]
[4,1,3,7,5,2,8,6]=>0000000=>0000000=>[8]
[7,1,6,3,2,5,8,4]=>0000000=>0000000=>[8]
[1,2,7,4,3,6,8,5]=>1100000=>0000011=>[6,1,1]
[6,1,8,2,4,5,7,3]=>0000000=>0000000=>[8]
[5,1,8,3,2,6,7,4]=>0000000=>0000000=>[8]
[4,8,2,7,1,5,6,3]=>0000000=>0000000=>[8]
[5,8,7,2,1,4,6,3]=>0000000=>0000000=>[8]
[6,8,7,1,3,4,5,2]=>0000000=>0000000=>[8]
[7,8,6,1,3,4,5,2]=>0000000=>0000000=>[8]
[1,7,8,2,4,5,6,3]=>1000000=>0000001=>[7,1]
[8,6,7,1,3,4,5,2]=>0000000=>0000000=>[8]
[7,6,8,1,3,4,5,2]=>0000000=>0000000=>[8]
[6,5,8,2,3,1,7,4]=>0000000=>0000000=>[8]
[1,6,8,3,2,5,7,4]=>1000000=>0000001=>[7,1]
[8,4,2,7,1,5,6,3]=>0000000=>0000000=>[8]
[7,4,2,8,1,5,6,3]=>0000000=>0000000=>[8]
[6,4,2,8,3,1,7,5]=>0000000=>0000000=>[8]
[5,4,2,3,8,1,7,6]=>0000000=>0000000=>[8]
[4,5,2,3,1,6,8,7]=>0000110=>0110000=>[2,1,5]
[7,4,2,1,3,6,8,5]=>0000000=>0000000=>[8]
[8,4,2,1,3,6,7,5]=>0000000=>0000000=>[8]
[1,5,3,2,4,7,8,6]=>1000100=>0010001=>[3,4,1]
[8,5,1,3,2,6,7,4]=>0000000=>0000000=>[8]
[5,6,1,3,4,2,8,7]=>0000010=>0100000=>[2,6]
[4,7,2,1,3,6,8,5]=>0000000=>0000000=>[8]
[5,7,1,3,2,6,8,4]=>0000000=>0000000=>[8]
[6,7,1,2,4,5,8,3]=>0000000=>0000000=>[8]
[1,8,2,3,5,6,7,4]=>1000000=>0000001=>[7,1]
[5,8,1,3,2,6,7,4]=>0000000=>0000000=>[8]
[4,8,2,1,3,6,7,5]=>0000000=>0000000=>[8]
[4,1,3,2,5,7,8,6]=>0001100=>0011000=>[3,1,4]
[5,1,2,4,3,7,8,6]=>0000100=>0010000=>[3,5]
[1,2,6,4,7,5,8,3]=>1100000=>0000011=>[6,1,1]
[3,1,7,5,4,2,6,8]=>0000001=>1000000=>[1,7]
[6,3,8,5,4,7,1,2]=>0000000=>0000000=>[8]
[1,6,2,5,4,7,8,3]=>1000000=>0000001=>[7,1]
[1,2,6,4,8,5,7,3]=>1100000=>0000011=>[6,1,1]
[7,8,3,1,4,2,5,6]=>0000000=>0000000=>[8]
[4,8,1,5,2,3,6,7]=>0000000=>0000000=>[8]
[7,4,1,5,2,3,6,8]=>0000001=>1000000=>[1,7]
[5,6,1,8,4,3,2,7]=>0000000=>0000000=>[8]
[5,1,8,6,4,3,2,7]=>0000000=>0000000=>[8]
[5,1,6,3,8,7,2,4]=>0000000=>0000000=>[8]
[6,1,2,5,8,3,7,4]=>0000000=>0000000=>[8]
[6,1,8,7,4,3,2,5]=>0000000=>0000000=>[8]
[7,1,2,5,4,8,6,3]=>0000000=>0000000=>[8]
[1,2,7,5,8,3,6,4]=>1100000=>0000011=>[6,1,1]
[4,1,6,3,7,5,2,8]=>0000001=>1000000=>[1,7]
[1,3,6,7,8,5,2,4]=>1000000=>0000001=>[7,1]
[1,2,6,4,7,8,5,3]=>1100000=>0000011=>[6,1,1]
[4,1,6,3,7,8,2,5]=>0000000=>0000000=>[8]
[3,1,6,4,8,2,7,5]=>0000000=>0000000=>[8]
[7,8,4,1,6,3,2,5]=>0000000=>0000000=>[8]
[4,1,6,3,8,7,2,5]=>0000000=>0000000=>[8]
[7,5,1,8,4,3,2,6]=>0000000=>0000000=>[8]
[6,5,1,7,4,3,2,8]=>0000001=>1000000=>[1,7]
[4,1,8,5,2,3,7,6]=>0000000=>0000000=>[8]
[4,1,6,8,3,7,2,5]=>0000000=>0000000=>[8]
[6,5,8,1,4,3,2,7]=>0000000=>0000000=>[8]
[1,6,3,2,7,4,8,5]=>1000000=>0000001=>[7,1]
[1,3,7,5,2,4,8,6]=>1000000=>0000001=>[7,1]
[2,5,3,7,4,8,1,6]=>0000000=>0000000=>[8]
[3,2,6,7,8,1,5,4]=>0000000=>0000000=>[8]
[3,5,2,7,8,4,1,6]=>0000000=>0000000=>[8]
[3,5,2,6,8,4,7,1]=>0000000=>0000000=>[8]
[2,5,7,4,3,8,6,1]=>0000000=>0000000=>[8]
[1,5,7,2,4,8,6,3]=>1000000=>0000001=>[7,1]
[4,6,3,7,2,8,5,1]=>0000000=>0000000=>[8]
[1,4,7,3,8,6,2,5]=>1000000=>0000001=>[7,1]
[5,1,6,8,2,4,3,7]=>0000000=>0000000=>[8]
[5,3,7,8,2,4,1,6]=>0000000=>0000000=>[8]
[8,5,3,7,2,4,1,6]=>0000000=>0000000=>[8]
[8,2,4,7,3,1,5,6]=>0000000=>0000000=>[8]
[2,4,7,8,3,1,5,6]=>0000000=>0000000=>[8]
[6,3,1,5,8,2,4,7]=>0000000=>0000000=>[8]
[6,5,3,4,2,8,1,7]=>0000000=>0000000=>[8]
[5,2,4,3,8,1,6,7]=>0000000=>0000000=>[8]
[3,2,4,8,1,5,6,7]=>0000000=>0000000=>[8]
[8,1,5,7,3,2,4,6]=>0000000=>0000000=>[8]
[8,4,6,7,2,3,1,5]=>0000000=>0000000=>[8]
[4,6,7,8,2,3,1,5]=>0000000=>0000000=>[8]
[7,4,6,8,2,3,1,5]=>0000000=>0000000=>[8]
[7,2,4,8,3,1,5,6]=>0000000=>0000000=>[8]
[5,3,8,7,2,4,1,6]=>0000000=>0000000=>[8]
[2,4,8,7,3,1,5,6]=>0000000=>0000000=>[8]
[4,6,8,7,2,3,1,5]=>0000000=>0000000=>[8]
[6,4,8,7,2,3,1,5]=>0000000=>0000000=>[8]
[3,1,7,4,2,8,6,5]=>0000000=>0000000=>[8]
[3,2,8,4,1,7,6,5]=>0000000=>0000000=>[8]
[7,6,4,8,2,3,1,5]=>0000000=>0000000=>[8]
[5,7,6,8,2,3,1,4]=>0000000=>0000000=>[8]
[4,7,6,8,2,3,1,5]=>0000000=>0000000=>[8]
[8,6,4,7,2,3,1,5]=>0000000=>0000000=>[8]
[8,2,3,7,4,1,6,5]=>0000000=>0000000=>[8]
[3,7,4,8,2,5,1,6]=>0000000=>0000000=>[8]
[2,3,7,4,1,6,8,5]=>0000000=>0000000=>[8]
[8,1,6,4,2,3,7,5]=>0000000=>0000000=>[8]
[4,7,8,6,2,3,1,5]=>0000000=>0000000=>[8]
[6,3,1,7,4,2,8,5]=>0000000=>0000000=>[8]
[8,5,7,6,2,3,1,4]=>0000000=>0000000=>[8]
[7,1,6,4,2,3,8,5]=>0000000=>0000000=>[8]
[3,1,7,6,4,2,8,5]=>0000000=>0000000=>[8]
[4,8,7,6,2,3,1,5]=>0000000=>0000000=>[8]
[6,8,7,5,2,3,1,4]=>0000000=>0000000=>[8]
[4,3,6,1,5,8,7,2]=>0000000=>0000000=>[8]
[4,3,6,5,1,8,7,2]=>0000000=>0000000=>[8]
[4,6,3,5,1,8,7,2]=>0000000=>0000000=>[8]
[4,6,3,1,5,8,7,2]=>0000000=>0000000=>[8]
[4,1,6,5,3,8,7,2]=>0000000=>0000000=>[8]
[4,6,1,5,3,8,7,2]=>0000000=>0000000=>[8]
[2,6,5,3,1,8,7,4]=>0000000=>0000000=>[8]
[2,6,5,8,3,1,7,4]=>0000000=>0000000=>[8]
[2,6,5,3,8,1,7,4]=>0000000=>0000000=>[8]
[4,6,1,5,8,3,7,2]=>0000000=>0000000=>[8]
[4,1,6,5,8,3,7,2]=>0000000=>0000000=>[8]
[1,4,6,5,8,3,7,2]=>1000000=>0000001=>[7,1]
[4,1,6,5,8,7,3,2]=>0000000=>0000000=>[8]
[6,4,3,8,7,1,5,2]=>0000000=>0000000=>[8]
[6,4,8,3,7,1,5,2]=>0000000=>0000000=>[8]
[2,6,8,5,3,7,1,4]=>0000000=>0000000=>[8]
[4,6,8,1,5,7,3,2]=>0000000=>0000000=>[8]
[4,6,1,8,5,7,3,2]=>0000000=>0000000=>[8]
[1,4,6,8,5,7,3,2]=>1000000=>0000001=>[7,1]
[1,4,6,8,5,3,7,2]=>1000000=>0000001=>[7,1]
[4,6,1,8,5,3,7,2]=>0000000=>0000000=>[8]
[4,6,3,8,5,7,1,2]=>0000000=>0000000=>[8]
[4,3,6,8,1,5,7,2]=>0000000=>0000000=>[8]
[4,3,6,1,8,5,7,2]=>0000000=>0000000=>[8]
[4,3,1,6,8,5,7,2]=>0000000=>0000000=>[8]
[4,1,3,6,8,7,5,2]=>0000000=>0000000=>[8]
[4,3,6,1,8,7,5,2]=>0000000=>0000000=>[8]
[4,3,6,8,1,7,5,2]=>0000000=>0000000=>[8]
[6,5,2,8,7,3,1,4]=>0000000=>0000000=>[8]
[6,5,2,8,7,1,3,4]=>0000000=>0000000=>[8]
[6,2,5,8,7,1,3,4]=>0000000=>0000000=>[8]
[6,2,5,8,7,3,1,4]=>0000000=>0000000=>[8]
[4,6,3,8,1,7,5,2]=>0000000=>0000000=>[8]
[4,6,3,1,8,7,5,2]=>0000000=>0000000=>[8]
[4,1,6,3,8,7,5,2]=>0000000=>0000000=>[8]
[1,4,6,3,8,7,5,2]=>1000000=>0000001=>[7,1]
[4,1,6,8,3,7,5,2]=>0000000=>0000000=>[8]
[4,6,1,8,3,7,5,2]=>0000000=>0000000=>[8]
[4,6,8,1,3,7,5,2]=>0000000=>0000000=>[8]
[6,2,8,5,7,3,1,4]=>0000000=>0000000=>[8]
[6,2,8,5,7,1,3,4]=>0000000=>0000000=>[8]
[2,4,8,7,1,5,3,6]=>0000000=>0000000=>[8]
[6,4,1,8,7,5,3,2]=>0000000=>0000000=>[8]
[6,1,4,8,7,5,3,2]=>0000000=>0000000=>[8]
[1,6,4,8,7,3,5,2]=>1000000=>0000001=>[7,1]
[6,4,1,8,7,3,5,2]=>0000000=>0000000=>[8]
[4,2,8,7,5,1,3,6]=>0000000=>0000000=>[8]
[2,4,8,7,3,5,1,6]=>0000000=>0000000=>[8]
[1,5,3,2,6,4,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,7,3,2,8,5,4,6]=>1000000=>0000001=>[7,1]
[1,6,2,8,5,3,4,7]=>1000000=>0000001=>[7,1]
[1,5,7,2,8,4,3,6]=>1000000=>0000001=>[7,1]
[2,3,1,8,4,5,7,6]=>0010000=>0000100=>[5,3]
[7,8,1,4,3,5,2,6]=>0000000=>0000000=>[8]
[8,4,2,5,3,1,6,7]=>0000000=>0000000=>[8]
[2,4,7,8,1,5,3,6]=>0000000=>0000000=>[8]
[6,1,2,8,5,3,4,7]=>0000000=>0000000=>[8]
[6,8,1,3,4,7,2,5]=>0000000=>0000000=>[8]
[6,7,2,3,4,1,8,5]=>0000000=>0000000=>[8]
[4,8,7,3,5,6,1,2]=>0000000=>0000000=>[8]
[4,8,7,5,3,6,1,2]=>0000000=>0000000=>[8]
[5,8,7,3,4,6,1,2]=>0000000=>0000000=>[8]
[5,8,4,2,1,6,7,3]=>0000000=>0000000=>[8]
[5,8,4,1,2,6,7,3]=>0000000=>0000000=>[8]
[5,3,7,2,6,1,8,4]=>0000000=>0000000=>[8]
[5,2,8,1,6,3,7,4]=>0000000=>0000000=>[8]
[5,8,2,1,4,7,6,3]=>0000000=>0000000=>[8]
[4,8,2,5,1,7,6,3]=>0000000=>0000000=>[8]
[7,8,4,1,2,6,5,3]=>0000000=>0000000=>[8]
[4,8,1,5,2,7,6,3]=>0000000=>0000000=>[8]
[5,8,1,2,4,7,6,3]=>0000000=>0000000=>[8]
[5,2,8,3,6,7,1,4]=>0000000=>0000000=>[8]
[2,8,7,6,4,1,3,5]=>0000000=>0000000=>[8]
[7,8,2,6,5,1,3,4]=>0000000=>0000000=>[8]
[1,8,7,6,2,4,3,5]=>1000000=>0000001=>[7,1]
[2,8,1,4,5,6,7,3]=>0000000=>0000000=>[8]
[2,1,7,3,6,5,8,4]=>0100000=>0000010=>[6,2]
[3,2,7,1,6,5,8,4]=>0000000=>0000000=>[8]
[6,1,2,8,5,7,3,4]=>0000000=>0000000=>[8]
[6,2,1,8,5,7,3,4]=>0000000=>0000000=>[8]
[6,3,1,8,5,7,2,4]=>0000000=>0000000=>[8]
[6,4,2,1,7,5,8,3]=>0000000=>0000000=>[8]
[6,1,3,8,5,2,7,4]=>0000000=>0000000=>[8]
[1,3,7,2,6,8,5,4]=>1000000=>0000001=>[7,1]
[7,8,2,6,5,3,1,4]=>0000000=>0000000=>[8]
[3,2,6,7,5,8,1,4]=>0000000=>0000000=>[8]
[1,2,7,5,6,3,8,4]=>1100000=>0000011=>[6,1,1]
[2,8,7,6,4,3,1,5]=>0000000=>0000000=>[8]
[3,8,7,6,1,2,5,4]=>0000000=>0000000=>[8]
[4,8,7,6,2,1,3,5]=>0000000=>0000000=>[8]
[4,8,7,6,1,3,2,5]=>0000000=>0000000=>[8]
[3,8,7,6,4,1,2,5]=>0000000=>0000000=>[8]
[7,8,3,6,5,1,2,4]=>0000000=>0000000=>[8]
[2,3,7,5,6,8,1,4]=>0000000=>0000000=>[8]
[3,8,7,6,4,2,1,5]=>0000000=>0000000=>[8]
[3,4,2,6,7,8,1,5]=>0000000=>0000000=>[8]
[3,1,4,2,6,8,7,5]=>0001000=>0001000=>[4,4]
[8,3,4,2,6,1,7,5]=>0000000=>0000000=>[8]
[2,6,7,3,5,4,1,8]=>0000001=>1000000=>[1,7]
[2,7,8,3,5,4,1,6]=>0000000=>0000000=>[8]
[2,6,8,3,5,4,1,7]=>0000000=>0000000=>[8]
[4,7,1,2,8,5,3,6]=>0000000=>0000000=>[8]
[4,8,1,2,7,5,3,6]=>0000000=>0000000=>[8]
[2,1,6,3,7,5,4,8]=>0100001=>1000010=>[1,5,2]
[2,7,1,3,6,8,4,5]=>0000000=>0000000=>[8]
[7,4,1,2,8,5,3,6]=>0000000=>0000000=>[8]
[8,7,4,2,1,5,3,6]=>0000000=>0000000=>[8]
[7,4,1,2,6,5,3,8]=>0000001=>1000000=>[1,7]
[7,4,3,1,5,6,8,2]=>0000000=>0000000=>[8]
[6,7,4,1,5,8,3,2]=>0000000=>0000000=>[8]
[4,7,5,1,6,8,3,2]=>0000000=>0000000=>[8]
[4,5,3,1,7,6,8,2]=>0000000=>0000000=>[8]
[4,6,1,2,7,5,3,8]=>0000001=>1000000=>[1,7]
[4,6,1,2,8,5,3,7]=>0000000=>0000000=>[8]
[4,5,3,1,8,6,7,2]=>0000000=>0000000=>[8]
[4,8,5,6,3,1,7,2]=>0000000=>0000000=>[8]
[5,1,3,4,8,6,7,2]=>0000000=>0000000=>[8]
[5,4,3,8,1,6,7,2]=>0000000=>0000000=>[8]
[8,5,3,4,1,6,7,2]=>0000000=>0000000=>[8]
[6,4,8,2,1,5,3,7]=>0000000=>0000000=>[8]
[6,7,3,2,5,1,4,8]=>0000001=>1000000=>[1,7]
[6,8,3,2,5,1,4,7]=>0000000=>0000000=>[8]
[5,7,1,4,6,8,3,2]=>0000000=>0000000=>[8]
[5,1,3,4,7,6,8,2]=>0000000=>0000000=>[8]
[5,4,3,7,1,6,8,2]=>0000000=>0000000=>[8]
[6,7,5,4,1,8,3,2]=>0000000=>0000000=>[8]
[7,6,4,2,1,5,3,8]=>0000001=>1000000=>[1,7]
[8,5,6,1,3,2,4,7]=>0000000=>0000000=>[8]
[8,6,1,5,3,2,4,7]=>0000000=>0000000=>[8]
[7,8,1,5,3,2,4,6]=>0000000=>0000000=>[8]
[8,1,7,5,3,2,4,6]=>0000000=>0000000=>[8]
[8,6,1,4,5,2,3,7]=>0000000=>0000000=>[8]
[8,6,3,1,5,2,4,7]=>0000000=>0000000=>[8]
[8,4,6,1,5,2,3,7]=>0000000=>0000000=>[8]
[8,6,2,1,5,4,3,7]=>0000000=>0000000=>[8]
[8,5,2,6,1,4,3,7]=>0000000=>0000000=>[8]
[8,5,2,1,7,4,3,6]=>0000000=>0000000=>[8]
[8,2,7,5,1,3,4,6]=>0000000=>0000000=>[8]
[8,4,1,7,5,2,3,6]=>0000000=>0000000=>[8]
[8,2,6,1,7,4,3,5]=>0000000=>0000000=>[8]
[8,1,7,4,3,2,6,5]=>0000000=>0000000=>[8]
[8,1,5,7,3,2,6,4]=>0000000=>0000000=>[8]
[5,7,8,1,3,2,6,4]=>0000000=>0000000=>[8]
[8,2,6,1,5,7,3,4]=>0000000=>0000000=>[8]
[5,8,1,6,7,2,3,4]=>0000000=>0000000=>[8]
[5,7,6,1,8,2,3,4]=>0000000=>0000000=>[8]
[8,1,5,6,7,2,3,4]=>0000000=>0000000=>[8]
[6,5,7,1,8,2,3,4]=>0000000=>0000000=>[8]
[8,1,6,4,7,2,3,5]=>0000000=>0000000=>[8]
[7,5,8,1,3,2,4,6]=>0000000=>0000000=>[8]
[7,8,4,1,3,2,5,6]=>0000000=>0000000=>[8]
[8,3,7,4,1,2,5,6]=>0000000=>0000000=>[8]
[8,5,1,7,3,2,4,6]=>0000000=>0000000=>[8]
[6,8,1,7,3,2,4,5]=>0000000=>0000000=>[8]
[7,1,8,4,3,6,2,5]=>0000000=>0000000=>[8]
[7,3,1,8,6,4,2,5]=>0000000=>0000000=>[8]
[8,3,1,7,4,6,2,5]=>0000000=>0000000=>[8]
[8,4,5,1,7,2,3,6]=>0000000=>0000000=>[8]
[5,6,8,1,7,2,3,4]=>0000000=>0000000=>[8]
[6,5,8,1,2,7,3,4]=>0000000=>0000000=>[8]
[7,3,1,8,5,6,2,4]=>0000000=>0000000=>[8]
[6,2,7,8,3,1,5,4]=>0000000=>0000000=>[8]
[5,8,1,7,3,2,6,4]=>0000000=>0000000=>[8]
[8,4,1,7,3,2,6,5]=>0000000=>0000000=>[8]
[8,3,4,7,1,2,6,5]=>0000000=>0000000=>[8]
[7,4,8,2,1,3,6,5]=>0000000=>0000000=>[8]
[7,4,3,8,1,2,6,5]=>0000000=>0000000=>[8]
[8,2,3,6,7,1,5,4]=>0000000=>0000000=>[8]
[6,8,5,2,3,4,7,1]=>0000000=>0000000=>[8]
[5,3,7,1,4,2,8,6]=>0000000=>0000000=>[8]
[3,7,5,1,2,8,6,4]=>0000000=>0000000=>[8]
[7,3,5,8,1,2,6,4]=>0000000=>0000000=>[8]
[2,5,7,4,8,6,1,3]=>0000000=>0000000=>[8]
[3,6,2,5,8,7,1,4]=>0000000=>0000000=>[8]
[5,2,8,4,7,6,1,3]=>0000000=>0000000=>[8]
[2,5,1,4,7,3,8,6]=>0000000=>0000000=>[8]
[3,1,5,6,2,8,7,4]=>0000000=>0000000=>[8]
[1,2,4,6,3,8,7,5]=>1100000=>0000011=>[6,1,1]
[7,2,3,5,1,8,6,4]=>0000000=>0000000=>[8]
[1,6,4,2,8,7,5,3]=>1000000=>0000001=>[7,1]
[4,6,2,7,5,1,8,3]=>0000000=>0000000=>[8]
[1,5,3,6,2,8,7,4]=>1000000=>0000001=>[7,1]
[3,5,2,1,7,4,8,6]=>0000000=>0000000=>[8]
[6,3,1,7,2,8,5,4]=>0000000=>0000000=>[8]
[7,5,1,2,8,6,4,3]=>0000000=>0000000=>[8]
[4,5,1,2,8,7,6,3]=>0000000=>0000000=>[8]
[5,8,2,7,1,6,4,3]=>0000000=>0000000=>[8]
[2,1,6,4,5,8,3,7]=>0100000=>0000010=>[6,2]
[8,6,3,7,5,2,1,4]=>0000000=>0000000=>[8]
[4,6,3,8,5,2,1,7]=>0000000=>0000000=>[8]
[4,6,3,7,5,2,8,1]=>0000000=>0000000=>[8]
[4,8,3,7,5,2,1,6]=>0000000=>0000000=>[8]
[5,2,8,3,7,6,1,4]=>0000000=>0000000=>[8]
[8,2,7,3,1,6,4,5]=>0000000=>0000000=>[8]
[8,6,7,4,1,5,3,2]=>0000000=>0000000=>[8]
[4,8,6,7,5,1,3,2]=>0000000=>0000000=>[8]
[7,1,8,4,6,5,2,3]=>0000000=>0000000=>[8]
[8,7,1,5,4,6,2,3]=>0000000=>0000000=>[8]
[8,5,7,1,4,6,3,2]=>0000000=>0000000=>[8]
[6,4,8,5,1,7,3,2]=>0000000=>0000000=>[8]
[8,4,7,1,5,6,3,2]=>0000000=>0000000=>[8]
[8,7,5,1,4,6,2,3]=>0000000=>0000000=>[8]
[8,7,2,5,1,4,6,3]=>0000000=>0000000=>[8]
[4,8,7,2,5,1,6,3]=>0000000=>0000000=>[8]
[8,7,1,4,2,5,6,3]=>0000000=>0000000=>[8]
[8,7,5,1,2,4,6,3]=>0000000=>0000000=>[8]
[7,1,8,5,6,2,3,4]=>0000000=>0000000=>[8]
[3,5,8,7,1,2,6,4]=>0000000=>0000000=>[8]
[2,3,8,5,7,1,6,4]=>0000000=>0000000=>[8]
[3,8,7,1,5,6,2,4]=>0000000=>0000000=>[8]
[3,5,8,7,1,6,2,4]=>0000000=>0000000=>[8]
[2,3,8,6,7,5,1,4]=>0000000=>0000000=>[8]
[3,2,8,6,7,5,1,4]=>0000000=>0000000=>[8]
[4,1,8,6,2,7,5,3]=>0000000=>0000000=>[8]
[8,7,4,1,2,6,5,3]=>0000000=>0000000=>[8]
[1,3,8,6,7,5,2,4]=>1000000=>0000001=>[7,1]
[5,7,1,8,2,6,3,4]=>0000000=>0000000=>[8]
[2,8,7,1,5,6,3,4]=>0000000=>0000000=>[8]
[8,7,1,5,2,4,6,3]=>0000000=>0000000=>[8]
[7,1,8,2,4,6,5,3]=>0000000=>0000000=>[8]
[1,6,2,8,4,7,5,3]=>1000000=>0000001=>[7,1]
[1,3,8,5,7,2,6,4]=>1000000=>0000001=>[7,1]
[1,8,3,7,2,5,6,4]=>1000000=>0000001=>[7,1]
[2,8,7,1,3,5,6,4]=>0000000=>0000000=>[8]
[5,7,1,8,2,3,6,4]=>0000000=>0000000=>[8]
[7,1,8,2,3,5,6,4]=>0000000=>0000000=>[8]
[8,6,3,7,4,1,5,2]=>0000000=>0000000=>[8]
[4,2,8,6,7,5,1,3]=>0000000=>0000000=>[8]
[8,4,2,7,5,6,1,3]=>0000000=>0000000=>[8]
[4,8,3,6,1,7,5,2]=>0000000=>0000000=>[8]
[8,3,4,7,5,1,6,2]=>0000000=>0000000=>[8]
[8,3,7,4,5,1,6,2]=>0000000=>0000000=>[8]
[8,7,4,2,5,6,1,3]=>0000000=>0000000=>[8]
[8,7,5,1,6,2,3,4]=>0000000=>0000000=>[8]
[8,7,2,4,1,5,6,3]=>0000000=>0000000=>[8]
[4,8,6,1,7,2,5,3]=>0000000=>0000000=>[8]
[4,2,8,6,7,1,5,3]=>0000000=>0000000=>[8]
[8,7,4,1,2,5,6,3]=>0000000=>0000000=>[8]
[8,2,7,1,6,3,4,5]=>0000000=>0000000=>[8]
[8,2,7,1,3,6,4,5]=>0000000=>0000000=>[8]
[2,8,3,6,7,1,5,4]=>0000000=>0000000=>[8]
[8,7,2,1,3,5,6,4]=>0000000=>0000000=>[8]
[1,8,7,2,3,6,4,5]=>1000000=>0000001=>[7,1]
[1,8,7,2,6,3,4,5]=>1000000=>0000001=>[7,1]
[8,2,7,3,6,1,4,5]=>0000000=>0000000=>[8]
[1,8,7,3,6,2,4,5]=>1000000=>0000001=>[7,1]
[1,8,2,7,6,3,4,5]=>1000000=>0000001=>[7,1]
[8,2,7,4,1,5,6,3]=>0000000=>0000000=>[8]
[8,2,1,7,5,6,3,4]=>0000000=>0000000=>[8]
[8,7,3,1,5,6,2,4]=>0000000=>0000000=>[8]
[2,8,7,3,5,6,1,4]=>0000000=>0000000=>[8]
[8,3,1,6,7,5,2,4]=>0000000=>0000000=>[8]
[8,5,2,1,6,7,4,3]=>0000000=>0000000=>[8]
[1,5,2,8,6,7,4,3]=>1000000=>0000001=>[7,1]
[1,2,8,6,7,5,3,4]=>1100000=>0000011=>[6,1,1]
[1,8,3,6,7,5,2,4]=>1000000=>0000001=>[7,1]
[8,2,3,6,7,5,1,4]=>0000000=>0000000=>[8]
[8,3,7,2,5,6,1,4]=>0000000=>0000000=>[8]
[8,1,3,7,5,6,2,4]=>0000000=>0000000=>[8]
[8,4,1,2,7,5,6,3]=>0000000=>0000000=>[8]
[8,1,4,2,6,7,5,3]=>0000000=>0000000=>[8]
[1,2,8,6,7,3,5,4]=>1100000=>0000011=>[6,1,1]
[8,1,2,7,3,6,4,5]=>0000000=>0000000=>[8]
[8,1,7,3,6,2,4,5]=>0000000=>0000000=>[8]
[8,1,7,2,6,3,4,5]=>0000000=>0000000=>[8]
[8,1,7,2,3,6,4,5]=>0000000=>0000000=>[8]
[8,1,3,7,2,5,6,4]=>0000000=>0000000=>[8]
[1,8,3,6,7,2,5,4]=>1000000=>0000001=>[7,1]
[1,7,8,2,3,6,5,4]=>1000000=>0000001=>[7,1]
[8,3,7,1,2,5,6,4]=>0000000=>0000000=>[8]
[7,4,2,6,1,5,3,8]=>0000001=>1000000=>[1,7]
[7,4,2,5,6,1,3,8]=>0000001=>1000000=>[1,7]
[7,3,5,6,4,2,1,8]=>0000001=>1000000=>[1,7]
[7,4,3,1,5,6,2,8]=>0000001=>1000000=>[1,7]
[7,4,5,2,6,1,3,8]=>0000001=>1000000=>[1,7]
[5,3,7,2,8,6,4,1]=>0000000=>0000000=>[8]
[5,3,8,2,6,7,4,1]=>0000000=>0000000=>[8]
[6,3,8,2,5,4,7,1]=>0000000=>0000000=>[8]
[6,4,3,1,8,2,7,5]=>0000000=>0000000=>[8]
[5,3,7,8,2,6,4,1]=>0000000=>0000000=>[8]
[4,7,8,5,6,3,2,1]=>0000000=>0000000=>[8]
[5,3,7,6,8,2,4,1]=>0000000=>0000000=>[8]
[5,7,8,4,6,2,1,3]=>0000000=>0000000=>[8]
[5,8,4,3,6,7,1,2]=>0000000=>0000000=>[8]
[5,8,6,4,7,2,1,3]=>0000000=>0000000=>[8]
[5,3,8,6,2,7,4,1]=>0000000=>0000000=>[8]
[4,7,5,8,6,3,2,1]=>0000000=>0000000=>[8]
[6,3,8,7,2,4,1,5]=>0000000=>0000000=>[8]
[5,3,8,7,2,6,4,1]=>0000000=>0000000=>[8]
[5,3,8,6,7,2,4,1]=>0000000=>0000000=>[8]
[5,3,7,8,6,2,4,1]=>0000000=>0000000=>[8]
[5,7,6,4,8,2,1,3]=>0000000=>0000000=>[8]
[5,8,4,6,7,2,1,3]=>0000000=>0000000=>[8]
[6,4,2,8,1,7,3,5]=>0000000=>0000000=>[8]
[6,5,2,4,3,7,8,1]=>0000000=>0000000=>[8]
[5,4,6,2,8,7,1,3]=>0000000=>0000000=>[8]
[5,6,3,8,7,2,4,1]=>0000000=>0000000=>[8]
[6,7,4,3,1,8,2,5]=>0000000=>0000000=>[8]
[5,7,4,3,6,8,1,2]=>0000000=>0000000=>[8]
[5,7,3,8,6,2,4,1]=>0000000=>0000000=>[8]
[4,5,8,6,7,3,2,1]=>0000000=>0000000=>[8]
[4,6,8,5,7,3,2,1]=>0000000=>0000000=>[8]
[5,6,8,3,7,2,4,1]=>0000000=>0000000=>[8]
[5,4,6,8,2,7,1,3]=>0000000=>0000000=>[8]
[7,8,4,5,1,3,2,6]=>0000000=>0000000=>[8]
[6,7,1,3,2,5,4,8]=>0000001=>1000000=>[1,7]
[6,7,1,4,3,5,2,8]=>0000001=>1000000=>[1,7]
[7,8,2,3,1,5,4,6]=>0000000=>0000000=>[8]
[7,8,2,4,3,5,1,6]=>0000000=>0000000=>[8]
[7,8,2,4,1,5,3,6]=>0000000=>0000000=>[8]
[1,4,2,6,5,7,3,8]=>1000001=>1000001=>[1,6,1]
[5,6,1,4,2,7,3,8]=>0000001=>1000000=>[1,7]
[6,7,2,4,1,5,3,8]=>0000001=>1000000=>[1,7]
[6,7,2,4,3,5,1,8]=>0000001=>1000000=>[1,7]
[6,7,2,3,1,5,4,8]=>0000001=>1000000=>[1,7]
[6,7,3,5,4,8,1,2]=>0000000=>0000000=>[8]
[2,4,1,6,5,7,3,8]=>0000001=>1000000=>[1,7]
[1,5,2,6,4,7,3,8]=>1000001=>1000001=>[1,6,1]
[2,5,1,6,4,7,3,8]=>0000001=>1000000=>[1,7]
[5,6,2,4,3,7,1,8]=>0000001=>1000000=>[1,7]
[4,5,2,6,1,7,3,8]=>0000001=>1000000=>[1,7]
[4,5,1,6,3,7,2,8]=>0000001=>1000000=>[1,7]
[4,5,3,6,1,7,2,8]=>0000001=>1000000=>[1,7]
[5,6,3,4,1,7,2,8]=>0000001=>1000000=>[1,7]
[5,6,1,4,3,7,2,8]=>0000001=>1000000=>[1,7]
[5,6,1,3,2,7,4,8]=>0000001=>1000000=>[1,7]
[5,6,4,7,1,3,2,8]=>0000001=>1000000=>[1,7]
[6,7,4,5,1,3,2,8]=>0000001=>1000000=>[1,7]
[6,7,5,8,1,3,2,4]=>0000000=>0000000=>[8]
[4,5,1,3,2,7,6,8]=>0000101=>1010000=>[1,2,5]
[4,6,5,7,1,3,2,8]=>0000001=>1000000=>[1,7]
[4,6,1,3,2,7,5,8]=>0000001=>1000000=>[1,7]
[1,4,3,6,2,7,5,8]=>1000001=>1000001=>[1,6,1]
[4,5,2,3,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[4,5,3,7,6,8,1,2]=>0000000=>0000000=>[8]
[4,6,5,7,3,8,1,2]=>0000000=>0000000=>[8]
[4,6,5,7,2,3,1,8]=>0000001=>1000000=>[1,7]
[3,5,4,6,1,7,2,8]=>0000001=>1000000=>[1,7]
[3,5,1,6,4,7,2,8]=>0000001=>1000000=>[1,7]
[1,5,3,6,4,7,2,8]=>1000001=>1000001=>[1,6,1]
[1,5,3,6,2,7,4,8]=>1000001=>1000001=>[1,6,1]
[3,5,2,6,1,7,4,8]=>0000001=>1000000=>[1,7]
[3,5,2,6,4,7,1,8]=>0000001=>1000000=>[1,7]
[3,4,2,6,1,7,5,8]=>0000001=>1000000=>[1,7]
[4,6,2,3,1,7,5,8]=>0000001=>1000000=>[1,7]
[2,4,3,6,1,7,5,8]=>0000001=>1000000=>[1,7]
[2,5,3,6,4,7,1,8]=>0000001=>1000000=>[1,7]
[2,5,3,6,1,7,4,8]=>0000001=>1000000=>[1,7]
[3,6,2,7,5,4,8,1]=>0000000=>0000000=>[8]
[5,2,6,7,4,3,8,1]=>0000000=>0000000=>[8]
[3,5,2,7,6,4,8,1]=>0000000=>0000000=>[8]
[2,1,5,6,8,4,3,7]=>0100000=>0000010=>[6,2]
[1,3,7,2,8,5,4,6]=>1000000=>0000001=>[7,1]
[4,6,2,7,1,8,3,5]=>0000000=>0000000=>[8]
[1,5,4,3,6,8,2,7]=>1000000=>0000001=>[7,1]
[1,6,4,5,7,8,3,2]=>1000000=>0000001=>[7,1]
[2,1,5,6,8,4,7,3]=>0100000=>0000010=>[6,2]
[2,1,5,6,8,7,3,4]=>0100000=>0000010=>[6,2]
[3,6,5,2,7,8,4,1]=>0000000=>0000000=>[8]
[6,2,4,7,5,8,3,1]=>0000000=>0000000=>[8]
[1,5,7,8,4,2,6,3]=>1000000=>0000001=>[7,1]
[3,7,4,1,8,6,2,5]=>0000000=>0000000=>[8]
[3,4,6,8,5,7,2,1]=>0000000=>0000000=>[8]
[4,5,6,2,8,7,3,1]=>0000000=>0000000=>[8]
[4,5,6,1,8,7,3,2]=>0000000=>0000000=>[8]
[4,5,6,3,1,8,7,2]=>0000000=>0000000=>[8]
[4,3,6,2,1,7,5,8]=>0000001=>1000000=>[1,7]
[4,6,3,2,1,7,5,8]=>0000001=>1000000=>[1,7]
[4,6,3,1,7,5,2,8]=>0000001=>1000000=>[1,7]
[4,5,3,7,6,1,8,2]=>0000000=>0000000=>[8]
[4,5,1,7,3,8,6,2]=>0000000=>0000000=>[8]
[2,5,7,1,4,3,8,6]=>0000000=>0000000=>[8]
[4,3,5,7,6,1,8,2]=>0000000=>0000000=>[8]
[4,3,6,1,7,5,2,8]=>0000001=>1000000=>[1,7]
[4,3,2,6,1,7,5,8]=>0000001=>1000000=>[1,7]
[5,3,2,1,6,4,7,8]=>0000011=>1100000=>[1,1,6]
[5,3,1,6,2,7,4,8]=>0000001=>1000000=>[1,7]
[5,1,6,3,2,7,4,8]=>0000001=>1000000=>[1,7]
[2,6,1,4,7,5,3,8]=>0000001=>1000000=>[1,7]
[3,6,1,7,4,2,5,8]=>0000001=>1000000=>[1,7]
[4,6,1,7,5,3,2,8]=>0000001=>1000000=>[1,7]
[5,1,6,3,7,4,2,8]=>0000001=>1000000=>[1,7]
[5,3,6,4,2,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,3,2,6,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,2,1,6,3,7,4,8]=>0000001=>1000000=>[1,7]
[5,2,6,3,1,7,4,8]=>0000001=>1000000=>[1,7]
[4,2,6,3,1,7,8,5]=>0000000=>0000000=>[8]
[3,6,2,1,7,4,5,8]=>0000001=>1000000=>[1,7]
[3,6,2,7,4,1,5,8]=>0000001=>1000000=>[1,7]
[3,5,7,2,8,6,4,1]=>0000000=>0000000=>[8]
[2,6,1,3,7,5,4,8]=>0000001=>1000000=>[1,7]
[3,6,1,7,5,2,4,8]=>0000001=>1000000=>[1,7]
[5,1,6,2,7,4,3,8]=>0000001=>1000000=>[1,7]
[5,2,6,4,3,1,7,8]=>0000011=>1100000=>[1,1,6]
[5,2,1,6,4,3,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,2,1,6,3,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,1,6,2,7,3,8]=>0000001=>1000000=>[1,7]
[5,1,6,4,2,7,3,8]=>0000001=>1000000=>[1,7]
[3,6,1,7,5,4,8,2]=>0000000=>0000000=>[8]
[2,6,1,5,4,3,7,8]=>0000011=>1100000=>[1,1,6]
[3,1,6,2,5,4,7,8]=>0000011=>1100000=>[1,1,6]
[4,1,6,3,2,7,8,5]=>0000000=>0000000=>[8]
[5,1,6,4,3,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,1,6,3,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,3,1,6,2,7,8]=>0000011=>1100000=>[1,1,6]
[4,5,1,8,7,6,2,3]=>0000000=>0000000=>[8]
[6,8,3,5,7,1,4,2]=>0000000=>0000000=>[8]
[1,5,8,2,7,3,6,4]=>1000000=>0000001=>[7,1]
[6,7,4,8,1,5,3,2]=>0000000=>0000000=>[8]
[6,8,5,3,7,2,4,1]=>0000000=>0000000=>[8]
[7,5,3,8,2,6,4,1]=>0000000=>0000000=>[8]
[3,6,8,4,5,7,1,2]=>0000000=>0000000=>[8]
[1,6,8,4,7,2,3,5]=>1000000=>0000001=>[7,1]
[1,4,5,7,8,2,6,3]=>1000000=>0000001=>[7,1]
[1,4,5,8,7,2,3,6]=>1000000=>0000001=>[7,1]
[1,2,5,8,3,6,4,7]=>1100000=>0000011=>[6,1,1]
[7,8,1,4,6,2,3,5]=>0000000=>0000000=>[8]
[1,6,7,4,8,2,5,3]=>1000000=>0000001=>[7,1]
[1,4,5,6,8,2,7,3]=>1000000=>0000001=>[7,1]
[1,4,5,8,6,2,7,3]=>1000000=>0000001=>[7,1]
[1,2,5,8,3,4,7,6]=>1100000=>0000011=>[6,1,1]
[7,8,1,2,3,5,4,6]=>0000000=>0000000=>[8]
[1,6,7,2,3,5,4,8]=>1000001=>1000001=>[1,6,1]
[1,4,5,7,6,2,3,8]=>1000001=>1000001=>[1,6,1]
[1,2,5,7,3,6,4,8]=>1100001=>1000011=>[1,5,1,1]
[1,2,5,7,3,6,8,4]=>1100000=>0000011=>[6,1,1]
[1,6,8,2,3,5,7,4]=>1000000=>0000001=>[7,1]
[1,6,8,4,5,2,3,7]=>1000000=>0000001=>[7,1]
[1,6,8,2,3,4,7,5]=>1000000=>0000001=>[7,1]
[1,6,8,2,3,7,4,5]=>1000000=>0000001=>[7,1]
[1,4,5,7,6,2,8,3]=>1000000=>0000001=>[7,1]
[7,8,1,4,5,2,6,3]=>0000000=>0000000=>[8]
[1,6,7,2,3,8,5,4]=>1000000=>0000001=>[7,1]
[1,2,5,6,3,8,7,4]=>1100000=>0000011=>[6,1,1]
[2,7,4,8,3,5,1,6]=>0000000=>0000000=>[8]
[2,7,4,8,3,5,6,1]=>0000000=>0000000=>[8]
[7,2,8,4,3,5,1,6]=>0000000=>0000000=>[8]
[8,4,2,1,5,3,6,7]=>0000000=>0000000=>[8]
[8,4,1,5,3,2,6,7]=>0000000=>0000000=>[8]
[6,7,3,8,4,2,5,1]=>0000000=>0000000=>[8]
[6,7,3,8,4,2,1,5]=>0000000=>0000000=>[8]
[7,1,8,4,3,5,2,6]=>0000000=>0000000=>[8]
[1,7,8,4,3,5,2,6]=>1000000=>0000001=>[7,1]
[7,1,4,8,3,5,2,6]=>0000000=>0000000=>[8]
[7,1,8,4,3,5,6,2]=>0000000=>0000000=>[8]
[6,7,3,1,8,4,5,2]=>0000000=>0000000=>[8]
[6,7,1,4,8,3,5,2]=>0000000=>0000000=>[8]
[6,7,4,1,3,8,2,5]=>0000000=>0000000=>[8]
[1,6,7,8,4,3,2,5]=>1000000=>0000001=>[7,1]
[7,2,1,8,4,5,3,6]=>0000000=>0000000=>[8]
[6,2,7,1,8,4,3,5]=>0000000=>0000000=>[8]
[6,2,7,8,4,3,1,5]=>0000000=>0000000=>[8]
[6,2,7,8,4,3,5,1]=>0000000=>0000000=>[8]
[2,6,7,4,8,3,5,1]=>0000000=>0000000=>[8]
[2,6,7,4,8,3,1,5]=>0000000=>0000000=>[8]
[7,8,1,3,6,2,4,5]=>0000000=>0000000=>[8]
[1,2,7,8,6,3,4,5]=>1100000=>0000011=>[6,1,1]
[2,6,7,1,8,5,3,4]=>0000000=>0000000=>[8]
[2,6,7,8,5,3,4,1]=>0000000=>0000000=>[8]
[6,2,7,8,4,5,3,1]=>0000000=>0000000=>[8]
[1,7,2,8,4,5,6,3]=>1000000=>0000001=>[7,1]
[6,3,7,8,1,5,2,4]=>0000000=>0000000=>[8]
[6,7,1,2,8,5,3,4]=>0000000=>0000000=>[8]
[1,6,7,8,4,2,5,3]=>1000000=>0000001=>[7,1]
[4,1,5,7,3,2,6,8]=>0000001=>1000000=>[1,7]
[4,6,1,7,3,2,5,8]=>0000001=>1000000=>[1,7]
[8,1,7,4,6,3,2,5]=>0000000=>0000000=>[8]
[6,7,3,5,1,4,8,2]=>0000000=>0000000=>[8]
[5,7,8,4,2,6,3,1]=>0000000=>0000000=>[8]
[5,4,7,6,2,8,3,1]=>0000000=>0000000=>[8]
[5,7,4,1,6,8,3,2]=>0000000=>0000000=>[8]
[6,8,4,5,7,1,3,2]=>0000000=>0000000=>[8]
[5,8,4,6,1,7,3,2]=>0000000=>0000000=>[8]
[5,6,1,4,7,8,3,2]=>0000000=>0000000=>[8]
[5,6,7,2,4,8,3,1]=>0000000=>0000000=>[8]
[5,3,6,7,4,8,2,1]=>0000000=>0000000=>[8]
[5,3,2,8,6,7,4,1]=>0000000=>0000000=>[8]
[5,4,8,2,6,7,3,1]=>0000000=>0000000=>[8]
[5,4,8,6,2,7,3,1]=>0000000=>0000000=>[8]
[6,4,8,5,7,2,3,1]=>0000000=>0000000=>[8]
[4,6,8,5,7,2,3,1]=>0000000=>0000000=>[8]
[5,6,8,2,4,7,3,1]=>0000000=>0000000=>[8]
[5,6,3,8,4,7,2,1]=>0000000=>0000000=>[8]
[4,6,3,5,8,7,2,1]=>0000000=>0000000=>[8]
[4,6,3,2,8,7,5,1]=>0000000=>0000000=>[8]
[5,6,3,8,2,7,4,1]=>0000000=>0000000=>[8]
[3,6,5,8,7,2,4,1]=>0000000=>0000000=>[8]
[5,3,6,8,2,7,4,1]=>0000000=>0000000=>[8]
[4,3,7,2,8,6,5,1]=>0000000=>0000000=>[8]
[5,4,7,2,6,8,3,1]=>0000000=>0000000=>[8]
[5,3,2,7,6,8,4,1]=>0000000=>0000000=>[8]
[6,7,3,8,5,2,4,1]=>0000000=>0000000=>[8]
[6,3,2,7,5,4,8,1]=>0000000=>0000000=>[8]
[6,4,7,2,5,3,8,1]=>0000000=>0000000=>[8]
[6,2,7,5,1,4,8,3]=>0000000=>0000000=>[8]
[2,7,8,5,3,6,1,4]=>0000000=>0000000=>[8]
[6,3,7,8,4,2,5,1]=>0000000=>0000000=>[8]
[3,5,7,8,4,6,2,1]=>0000000=>0000000=>[8]
[5,7,8,2,4,6,3,1]=>0000000=>0000000=>[8]
[2,5,8,4,3,7,6,1]=>0000000=>0000000=>[8]
[2,6,8,4,7,3,5,1]=>0000000=>0000000=>[8]
[3,7,4,8,6,2,1,5]=>0000000=>0000000=>[8]
[3,6,4,8,7,2,5,1]=>0000000=>0000000=>[8]
[3,5,4,8,2,7,6,1]=>0000000=>0000000=>[8]
[4,5,7,3,8,6,2,1]=>0000000=>0000000=>[8]
[6,3,1,8,7,5,4,2]=>0000000=>0000000=>[8]
[8,5,4,1,7,6,3,2]=>0000000=>0000000=>[8]
[1,8,2,5,6,3,4,7]=>1000000=>0000001=>[7,1]
[7,2,8,4,5,1,3,6]=>0000000=>0000000=>[8]
[1,3,7,5,6,2,4,8]=>1000001=>1000001=>[1,6,1]
[1,6,7,4,3,5,2,8]=>1000001=>1000001=>[1,6,1]
[1,8,2,5,3,6,7,4]=>1000000=>0000001=>[7,1]
[2,6,8,4,3,5,7,1]=>0000000=>0000000=>[8]
[7,2,8,4,1,5,6,3]=>0000000=>0000000=>[8]
[7,5,8,1,2,6,3,4]=>0000000=>0000000=>[8]
[1,5,2,6,4,7,8,3]=>1000000=>0000001=>[7,1]
[1,5,4,6,2,3,7,8]=>1000011=>1100001=>[1,1,5,1]
[6,2,5,7,1,4,8,3]=>0000000=>0000000=>[8]
[6,5,4,3,8,1,7,2]=>0000000=>0000000=>[8]
[2,6,5,8,3,4,1,7]=>0000000=>0000000=>[8]
[2,6,5,7,3,4,1,8]=>0000001=>1000000=>[1,7]
[6,2,5,7,4,1,3,8]=>0000001=>1000000=>[1,7]
[6,2,5,8,4,1,3,7]=>0000000=>0000000=>[8]
[2,7,8,4,6,1,3,5]=>0000000=>0000000=>[8]
[6,1,2,8,5,4,7,3]=>0000000=>0000000=>[8]
[6,2,5,7,8,1,3,4]=>0000000=>0000000=>[8]
[1,5,4,2,6,7,3,8]=>1000001=>1000001=>[1,6,1]
[2,6,5,7,3,8,1,4]=>0000000=>0000000=>[8]
[1,6,2,7,5,8,4,3]=>1000000=>0000001=>[7,1]
[1,3,2,7,8,5,6,4]=>1010000=>0000101=>[5,2,1]
[1,6,2,4,8,7,3,5]=>1000000=>0000001=>[7,1]
[6,5,2,1,8,7,3,4]=>0000000=>0000000=>[8]
[2,6,5,3,7,8,4,1]=>0000000=>0000000=>[8]
[6,5,2,3,8,7,1,4]=>0000000=>0000000=>[8]
[5,1,4,2,3,7,8,6]=>0000100=>0010000=>[3,5]
[1,5,4,2,6,3,8,7]=>1000010=>0100001=>[2,5,1]
[6,5,8,7,4,3,1,2]=>0000000=>0000000=>[8]
[1,2,7,5,4,8,3,6]=>1100000=>0000011=>[6,1,1]
[3,2,7,5,4,8,1,6]=>0000000=>0000000=>[8]
[6,8,3,2,4,7,1,5]=>0000000=>0000000=>[8]
[3,7,2,5,4,8,1,6]=>0000000=>0000000=>[8]
[1,3,7,5,4,8,2,6]=>1000000=>0000001=>[7,1]
[2,7,3,5,4,8,1,6]=>0000000=>0000000=>[8]
[6,3,5,2,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[2,3,5,8,1,4,7,6]=>0000000=>0000000=>[8]
[6,3,8,5,2,7,1,4]=>0000000=>0000000=>[8]
[2,3,6,8,1,4,7,5]=>0000000=>0000000=>[8]
[2,5,8,1,7,3,6,4]=>0000000=>0000000=>[8]
[2,8,1,5,7,3,6,4]=>0000000=>0000000=>[8]
[2,6,8,1,5,7,3,4]=>0000000=>0000000=>[8]
[2,7,1,5,8,3,4,6]=>0000000=>0000000=>[8]
[3,7,5,8,1,2,6,4]=>0000000=>0000000=>[8]
[7,3,6,1,2,8,4,5]=>0000000=>0000000=>[8]
[6,8,4,5,1,7,2,3]=>0000000=>0000000=>[8]
[5,1,8,7,6,2,3,4]=>0000000=>0000000=>[8]
[4,6,1,8,7,5,2,3]=>0000000=>0000000=>[8]
[3,4,8,7,1,2,5,6]=>0000000=>0000000=>[8]
[5,6,8,3,7,1,4,2]=>0000000=>0000000=>[8]
[6,4,7,1,2,8,5,3]=>0000000=>0000000=>[8]
[6,5,1,8,2,7,3,4]=>0000000=>0000000=>[8]
[6,5,1,8,7,2,3,4]=>0000000=>0000000=>[8]
[6,5,1,7,2,8,3,4]=>0000000=>0000000=>[8]
[6,5,1,7,2,3,8,4]=>0000000=>0000000=>[8]
[5,6,8,7,4,1,2,3]=>0000000=>0000000=>[8]
[6,8,5,7,4,1,2,3]=>0000000=>0000000=>[8]
[6,8,3,1,5,2,4,7]=>0000000=>0000000=>[8]
[6,8,4,3,1,5,7,2]=>0000000=>0000000=>[8]
[6,8,4,2,1,5,7,3]=>0000000=>0000000=>[8]
[6,3,2,1,7,4,5,8]=>0000001=>1000000=>[1,7]
[6,4,2,1,7,5,3,8]=>0000001=>1000000=>[1,7]
[6,3,2,8,7,1,4,5]=>0000000=>0000000=>[8]
[4,2,8,1,7,3,5,6]=>0000000=>0000000=>[8]
[4,3,1,6,2,7,5,8]=>0000001=>1000000=>[1,7]
[5,4,1,7,2,8,6,3]=>0000000=>0000000=>[8]
[5,4,2,1,6,7,3,8]=>0000001=>1000000=>[1,7]
[8,6,1,4,5,7,2,3]=>0000000=>0000000=>[8]
[5,2,8,3,7,4,6,1]=>0000000=>0000000=>[8]
[6,2,8,5,4,7,3,1]=>0000000=>0000000=>[8]
[5,2,8,4,3,6,7,1]=>0000000=>0000000=>[8]
[5,4,2,7,3,6,1,8]=>0000001=>1000000=>[1,7]
[5,4,2,8,3,6,1,7]=>0000000=>0000000=>[8]
[6,5,3,8,4,7,2,1]=>0000000=>0000000=>[8]
[5,2,8,4,3,7,1,6]=>0000000=>0000000=>[8]
[6,2,8,3,7,4,1,5]=>0000000=>0000000=>[8]
[5,4,2,7,3,1,8,6]=>0000000=>0000000=>[8]
[6,4,3,7,1,2,8,5]=>0000000=>0000000=>[8]
[6,4,3,8,1,2,7,5]=>0000000=>0000000=>[8]
[7,2,8,4,3,1,5,6]=>0000000=>0000000=>[8]
[7,5,3,8,4,2,6,1]=>0000000=>0000000=>[8]
[6,4,2,7,3,1,5,8]=>0000001=>1000000=>[1,7]
[7,6,4,8,2,3,5,1]=>0000000=>0000000=>[8]
[5,3,1,7,8,4,6,2]=>0000000=>0000000=>[8]
[5,3,2,7,8,4,6,1]=>0000000=>0000000=>[8]
[6,5,1,7,8,2,3,4]=>0000000=>0000000=>[8]
[6,3,1,7,8,4,2,5]=>0000000=>0000000=>[8]
[5,4,1,7,3,8,2,6]=>0000000=>0000000=>[8]
[6,3,2,7,8,4,1,5]=>0000000=>0000000=>[8]
[8,7,6,1,3,5,2,4]=>0000000=>0000000=>[8]
[5,7,2,1,6,3,8,4]=>0000000=>0000000=>[8]
[6,4,8,1,3,2,7,5]=>0000000=>0000000=>[8]
[3,6,7,8,4,2,1,5]=>0000000=>0000000=>[8]
[2,5,8,3,1,6,7,4]=>0000000=>0000000=>[8]
[4,8,7,2,1,6,3,5]=>0000000=>0000000=>[8]
[3,6,1,2,5,8,4,7]=>0000000=>0000000=>[8]
[1,4,5,8,2,3,7,6]=>1000000=>0000001=>[7,1]
[1,5,2,4,6,8,3,7]=>1000000=>0000001=>[7,1]
[3,6,1,5,8,2,4,7]=>0000000=>0000000=>[8]
[2,6,5,1,4,8,3,7]=>0000000=>0000000=>[8]
[2,5,1,8,4,7,3,6]=>0000000=>0000000=>[8]
[2,7,1,4,3,6,8,5]=>0000000=>0000000=>[8]
[1,3,7,5,8,2,4,6]=>1000000=>0000001=>[7,1]
[8,2,1,5,7,3,4,6]=>0000000=>0000000=>[8]
[2,5,4,8,1,3,7,6]=>0000000=>0000000=>[8]
[2,4,1,3,8,6,7,5]=>0001000=>0001000=>[4,4]
[8,4,3,7,1,2,6,5]=>0000000=>0000000=>[8]
[1,7,3,5,8,2,6,4]=>1000000=>0000001=>[7,1]
[1,8,4,2,6,7,3,5]=>1000000=>0000001=>[7,1]
[3,1,6,8,7,2,4,5]=>0000000=>0000000=>[8]
[7,2,1,6,8,3,4,5]=>0000000=>0000000=>[8]
[4,1,7,2,6,8,3,5]=>0000000=>0000000=>[8]
[5,1,7,2,3,6,8,4]=>0000000=>0000000=>[8]
[7,2,1,6,3,5,8,4]=>0000000=>0000000=>[8]
[2,6,1,7,3,5,8,4]=>0000000=>0000000=>[8]
[8,1,3,2,4,6,7,5]=>0000000=>0000000=>[8]
[7,3,1,2,4,6,8,5]=>0000000=>0000000=>[8]
[1,8,3,4,7,2,5,6]=>1000000=>0000001=>[7,1]
[3,5,8,1,2,7,4,6]=>0000000=>0000000=>[8]
[3,6,8,1,2,4,7,5]=>0000000=>0000000=>[8]
[4,1,3,8,7,2,6,5]=>0000000=>0000000=>[8]
[1,3,7,4,8,2,6,5]=>1000000=>0000001=>[7,1]
[1,4,6,8,2,3,7,5]=>1000000=>0000001=>[7,1]
[3,5,8,1,7,2,4,6]=>0000000=>0000000=>[8]
[2,6,8,1,7,3,4,5]=>0000000=>0000000=>[8]
[1,8,3,2,7,5,6,4]=>1000000=>0000001=>[7,1]
[2,6,7,3,8,1,5,4]=>0000000=>0000000=>[8]
[8,4,1,7,3,6,2,5]=>0000000=>0000000=>[8]
[3,7,2,8,6,1,5,4]=>0000000=>0000000=>[8]
[6,2,3,8,7,1,5,4]=>0000000=>0000000=>[8]
[3,7,8,2,4,1,5,6]=>0000000=>0000000=>[8]
[1,7,2,4,5,8,3,6]=>1000000=>0000001=>[7,1]
[1,7,4,5,8,3,2,6]=>1000000=>0000001=>[7,1]
[2,6,4,7,8,3,5,1]=>0000000=>0000000=>[8]
[1,2,6,4,7,8,3,5]=>1100000=>0000011=>[6,1,1]
[6,1,4,7,8,3,5,2]=>0000000=>0000000=>[8]
[3,6,4,7,2,8,5,1]=>0000000=>0000000=>[8]
[6,1,4,7,8,5,2,3]=>0000000=>0000000=>[8]
[6,8,5,7,4,2,3,1]=>0000000=>0000000=>[8]
[2,3,8,7,1,6,4,5]=>0000000=>0000000=>[8]
[4,8,1,2,7,3,5,6]=>0000000=>0000000=>[8]
[6,4,8,7,5,1,2,3]=>0000000=>0000000=>[8]
[6,3,8,7,2,1,4,5]=>0000000=>0000000=>[8]
[2,6,7,8,5,1,3,4]=>0000000=>0000000=>[8]
[2,8,3,4,1,5,7,6]=>0000000=>0000000=>[8]
[4,5,3,2,8,6,7,1]=>0000000=>0000000=>[8]
[3,5,8,6,1,4,7,2]=>0000000=>0000000=>[8]
[2,6,4,8,5,1,7,3]=>0000000=>0000000=>[8]
[7,5,3,2,8,6,1,4]=>0000000=>0000000=>[8]
[4,5,1,2,8,6,7,3]=>0000000=>0000000=>[8]
[1,6,4,8,3,2,5,7]=>1000000=>0000001=>[7,1]
[1,8,3,5,6,2,4,7]=>1000000=>0000001=>[7,1]
[1,4,8,5,6,2,3,7]=>1000000=>0000001=>[7,1]
[6,1,4,8,2,3,5,7]=>0000000=>0000000=>[8]
[8,7,2,5,6,1,4,3]=>0000000=>0000000=>[8]
[1,8,2,5,4,7,3,6]=>1000000=>0000001=>[7,1]
[5,7,4,1,2,3,8,6]=>0000000=>0000000=>[8]
[1,7,4,2,5,3,8,6]=>1000000=>0000001=>[7,1]
[6,7,4,2,1,3,8,5]=>0000000=>0000000=>[8]
[6,4,3,8,5,7,1,2]=>0000000=>0000000=>[8]
[7,4,3,6,2,1,5,8]=>0000001=>1000000=>[1,7]
[7,2,5,3,4,1,6,8]=>0000001=>1000000=>[1,7]
[8,3,7,4,5,6,1,2]=>0000000=>0000000=>[8]
[2,7,4,3,1,5,6,8]=>0000001=>1000000=>[1,7]
[6,8,4,2,3,1,5,7]=>0000000=>0000000=>[8]
[2,1,7,4,8,3,5,6]=>0100000=>0000010=>[6,2]
[5,2,8,6,1,3,4,7]=>0000000=>0000000=>[8]
[2,8,3,1,4,5,6,7]=>0000000=>0000000=>[8]
[7,4,8,2,3,1,5,6]=>0000000=>0000000=>[8]
[4,2,7,3,1,5,6,8]=>0000001=>1000000=>[1,7]
[8,3,7,2,1,4,5,6]=>0000000=>0000000=>[8]
[6,5,2,4,7,1,3,8]=>0000001=>1000000=>[1,7]
[6,5,7,4,1,8,2,3]=>0000000=>0000000=>[8]
[8,6,4,1,3,7,2,5]=>0000000=>0000000=>[8]
[6,4,3,1,8,2,5,7]=>0000000=>0000000=>[8]
[4,8,1,3,5,7,2,6]=>0000000=>0000000=>[8]
[7,8,4,1,3,6,2,5]=>0000000=>0000000=>[8]
[6,5,8,1,3,7,2,4]=>0000000=>0000000=>[8]
[5,3,6,1,8,2,4,7]=>0000000=>0000000=>[8]
[4,7,3,1,8,2,5,6]=>0000000=>0000000=>[8]
[8,3,1,7,2,4,5,6]=>0000000=>0000000=>[8]
[2,8,1,4,7,3,5,6]=>0000000=>0000000=>[8]
[3,1,8,5,4,7,6,2]=>0000000=>0000000=>[8]
[4,1,5,8,3,7,6,2]=>0000000=>0000000=>[8]
[4,1,5,3,8,7,6,2]=>0000000=>0000000=>[8]
[4,5,1,8,2,7,6,3]=>0000000=>0000000=>[8]
[4,8,5,3,1,7,6,2]=>0000000=>0000000=>[8]
[4,5,2,8,1,7,6,3]=>0000000=>0000000=>[8]
[4,6,2,8,7,1,5,3]=>0000000=>0000000=>[8]
[4,8,6,3,7,1,5,2]=>0000000=>0000000=>[8]
[4,6,8,2,7,5,1,3]=>0000000=>0000000=>[8]
[4,6,2,8,7,5,1,3]=>0000000=>0000000=>[8]
[5,6,2,7,4,1,8,3]=>0000000=>0000000=>[8]
[5,6,7,2,3,1,8,4]=>0000000=>0000000=>[8]
[5,6,7,2,8,3,1,4]=>0000000=>0000000=>[8]
[5,6,7,2,1,8,3,4]=>0000000=>0000000=>[8]
[5,6,7,2,1,3,8,4]=>0000000=>0000000=>[8]
[5,6,1,7,8,2,4,3]=>0000000=>0000000=>[8]
[5,6,1,7,2,4,8,3]=>0000000=>0000000=>[8]
[4,1,6,8,7,3,5,2]=>0000000=>0000000=>[8]
[4,1,6,8,7,5,3,2]=>0000000=>0000000=>[8]
[5,6,1,7,8,4,2,3]=>0000000=>0000000=>[8]
[4,6,8,1,7,5,2,3]=>0000000=>0000000=>[8]
[4,8,6,1,7,5,3,2]=>0000000=>0000000=>[8]
[5,6,7,1,8,3,2,4]=>0000000=>0000000=>[8]
[5,6,7,1,3,8,2,4]=>0000000=>0000000=>[8]
[5,6,7,1,3,2,8,4]=>0000000=>0000000=>[8]
[5,6,7,3,1,2,8,4]=>0000000=>0000000=>[8]
[5,6,8,7,4,2,1,3]=>0000000=>0000000=>[8]
[1,3,7,5,8,2,6,4]=>1000000=>0000001=>[7,1]
[3,1,7,5,8,2,6,4]=>0000000=>0000000=>[8]
[3,5,7,1,8,4,6,2]=>0000000=>0000000=>[8]
[5,2,8,1,7,3,4,6]=>0000000=>0000000=>[8]
[5,8,3,2,7,1,4,6]=>0000000=>0000000=>[8]
[5,1,8,3,7,2,4,6]=>0000000=>0000000=>[8]
[5,1,8,4,6,2,3,7]=>0000000=>0000000=>[8]
[4,8,5,2,6,1,3,7]=>0000000=>0000000=>[8]
[4,1,7,5,6,2,8,3]=>0000000=>0000000=>[8]
[5,7,4,3,8,1,6,2]=>0000000=>0000000=>[8]
[5,7,4,3,8,2,6,1]=>0000000=>0000000=>[8]
[3,8,4,2,6,7,5,1]=>0000000=>0000000=>[8]
[3,8,4,1,6,7,5,2]=>0000000=>0000000=>[8]
[6,1,7,5,2,8,4,3]=>0000000=>0000000=>[8]
[5,6,4,3,2,8,1,7]=>0000000=>0000000=>[8]
[2,6,7,5,3,8,4,1]=>0000000=>0000000=>[8]
[2,1,6,7,5,3,8,4]=>0100000=>0000010=>[6,2]
[3,8,4,2,1,6,7,5]=>0000000=>0000000=>[8]
[5,7,4,3,8,2,1,6]=>0000000=>0000000=>[8]
[6,7,4,8,1,2,5,3]=>0000000=>0000000=>[8]
[6,7,5,8,1,2,4,3]=>0000000=>0000000=>[8]
[6,7,4,8,3,1,2,5]=>0000000=>0000000=>[8]
[6,1,3,4,8,2,5,7]=>0000000=>0000000=>[8]
[6,2,3,4,8,1,5,7]=>0000000=>0000000=>[8]
[3,4,8,2,1,5,7,6]=>0000000=>0000000=>[8]
[6,7,5,8,3,1,4,2]=>0000000=>0000000=>[8]
[2,5,7,6,1,4,8,3]=>0000000=>0000000=>[8]
[6,7,4,8,2,3,5,1]=>0000000=>0000000=>[8]
[6,7,4,8,1,3,5,2]=>0000000=>0000000=>[8]
[2,6,7,5,1,3,8,4]=>0000000=>0000000=>[8]
[6,3,1,4,8,2,5,7]=>0000000=>0000000=>[8]
[6,7,4,8,1,3,2,5]=>0000000=>0000000=>[8]
[6,7,5,8,4,1,3,2]=>0000000=>0000000=>[8]
[6,7,4,8,2,1,3,5]=>0000000=>0000000=>[8]
[6,7,4,8,1,2,3,5]=>0000000=>0000000=>[8]
[7,8,3,2,6,1,4,5]=>0000000=>0000000=>[8]
[3,4,8,2,6,1,7,5]=>0000000=>0000000=>[8]
[7,8,4,1,5,6,3,2]=>0000000=>0000000=>[8]
[7,8,1,2,6,3,4,5]=>0000000=>0000000=>[8]
[7,8,5,1,4,6,3,2]=>0000000=>0000000=>[8]
[5,3,8,4,1,6,7,2]=>0000000=>0000000=>[8]
[6,2,4,8,1,5,3,7]=>0000000=>0000000=>[8]
[3,4,8,5,1,6,7,2]=>0000000=>0000000=>[8]
[5,3,8,1,4,6,7,2]=>0000000=>0000000=>[8]
[4,2,6,8,1,5,3,7]=>0000000=>0000000=>[8]
[7,4,2,8,1,5,3,6]=>0000000=>0000000=>[8]
[6,1,7,5,8,4,3,2]=>0000000=>0000000=>[8]
[1,2,7,8,5,3,4,6]=>1100000=>0000011=>[6,1,1]
[6,3,7,8,5,4,1,2]=>0000000=>0000000=>[8]
[6,1,5,7,8,4,3,2]=>0000000=>0000000=>[8]
[1,7,5,6,8,4,3,2]=>1000000=>0000001=>[7,1]
[3,1,8,4,5,6,7,2]=>0000000=>0000000=>[8]
[4,2,1,8,6,5,3,7]=>0000000=>0000000=>[8]
[3,2,7,8,5,1,4,6]=>0000000=>0000000=>[8]
[2,3,7,8,5,1,4,6]=>0000000=>0000000=>[8]
[2,7,3,8,5,1,4,6]=>0000000=>0000000=>[8]
[3,6,2,8,5,1,4,7]=>0000000=>0000000=>[8]
[1,4,2,8,7,5,3,6]=>1000000=>0000001=>[7,1]
[7,3,6,8,5,4,1,2]=>0000000=>0000000=>[8]
[7,2,1,8,5,3,4,6]=>0000000=>0000000=>[8]
[1,2,6,8,4,5,3,7]=>1100000=>0000011=>[6,1,1]
[7,1,6,5,8,4,3,2]=>0000000=>0000000=>[8]
[6,5,7,1,8,4,3,2]=>0000000=>0000000=>[8]
[5,7,6,1,8,4,3,2]=>0000000=>0000000=>[8]
[6,7,1,5,8,4,3,2]=>0000000=>0000000=>[8]
[7,1,2,8,4,5,3,6]=>0000000=>0000000=>[8]
[7,6,1,5,8,4,3,2]=>0000000=>0000000=>[8]
[7,5,6,1,8,4,3,2]=>0000000=>0000000=>[8]
[9,10,7,8,5,6,2,1,3,4]=>000000000=>000000000=>[10]
[9,10,7,8,4,3,5,6,1,2]=>000000000=>000000000=>[10]
[9,10,7,8,4,2,5,1,3,6]=>000000000=>000000000=>[10]
[9,10,7,8,3,2,1,4,5,6]=>000000000=>000000000=>[10]
[9,10,6,5,7,8,3,4,1,2]=>000000000=>000000000=>[10]
[9,10,6,5,7,8,2,1,3,4]=>000000000=>000000000=>[10]
[9,10,6,4,7,3,5,8,1,2]=>000000000=>000000000=>[10]
[9,10,6,4,7,2,5,1,3,8]=>000000000=>000000000=>[10]
[9,10,6,3,7,2,1,4,5,8]=>000000000=>000000000=>[10]
[9,10,5,4,3,6,7,8,1,2]=>000000000=>000000000=>[10]
[9,10,5,4,2,6,7,1,3,8]=>000000000=>000000000=>[10]
[9,10,5,3,2,6,1,4,7,8]=>000000000=>000000000=>[10]
[9,10,4,3,2,1,5,6,7,8]=>000000000=>000000000=>[10]
[8,7,9,10,5,6,3,4,1,2]=>000000000=>000000000=>[10]
[8,7,9,10,5,6,2,1,3,4]=>000000000=>000000000=>[10]
[8,7,9,10,4,3,5,6,1,2]=>000000000=>000000000=>[10]
[8,7,9,10,4,2,5,1,3,6]=>000000000=>000000000=>[10]
[8,7,9,10,3,2,1,4,5,6]=>000000000=>000000000=>[10]
[8,6,9,5,7,10,3,4,1,2]=>000000000=>000000000=>[10]
[8,6,9,5,7,10,2,1,3,4]=>000000000=>000000000=>[10]
[8,6,9,4,7,3,5,10,1,2]=>000000000=>000000000=>[10]
[8,6,9,3,7,2,1,4,5,10]=>000000001=>100000000=>[1,9]
[8,5,9,4,3,6,7,10,1,2]=>000000000=>000000000=>[10]
[8,5,9,4,2,6,7,1,3,10]=>000000001=>100000000=>[1,9]
[8,5,9,3,2,6,1,4,7,10]=>000000001=>100000000=>[1,9]
[8,4,9,3,2,1,5,6,7,10]=>000000001=>100000000=>[1,9]
[7,6,5,8,9,10,3,4,1,2]=>000000000=>000000000=>[10]
[7,6,5,8,9,10,2,1,3,4]=>000000000=>000000000=>[10]
[7,6,4,8,9,3,5,10,1,2]=>000000000=>000000000=>[10]
[7,6,4,8,9,2,5,1,3,10]=>000000001=>100000000=>[1,9]
[7,6,3,8,9,2,1,4,5,10]=>000000001=>100000000=>[1,9]
[7,5,4,8,3,6,9,10,1,2]=>000000000=>000000000=>[10]
[7,5,4,8,2,6,9,1,3,10]=>000000001=>100000000=>[1,9]
[7,4,3,8,2,1,5,6,9,10]=>000000011=>110000000=>[1,1,8]
[6,5,4,2,7,8,9,1,3,10]=>000000001=>100000000=>[1,9]
[6,5,3,2,7,8,1,4,9,10]=>000000011=>110000000=>[1,1,8]
[10,8,11,6,9,4,7,2,5,1,3,12]=>00000000001=>10000000000=>[1,11]
[10,8,11,6,9,3,7,2,1,4,5,12]=>00000000001=>10000000000=>[1,11]
[10,8,11,5,9,4,2,6,7,1,3,12]=>00000000001=>10000000000=>[1,11]
[10,8,11,5,9,3,2,6,1,4,7,12]=>00000000001=>10000000000=>[1,11]
[10,8,11,4,9,3,2,1,5,6,7,12]=>00000000001=>10000000000=>[1,11]
[10,7,11,6,4,8,9,2,5,1,3,12]=>00000000001=>10000000000=>[1,11]
[10,7,11,6,3,8,9,2,1,4,5,12]=>00000000001=>10000000000=>[1,11]
[10,7,11,5,4,8,2,6,9,1,3,12]=>00000000001=>10000000000=>[1,11]
[10,7,11,5,3,8,2,6,1,4,9,12]=>00000000001=>10000000000=>[1,11]
[10,7,11,4,3,8,2,1,5,6,9,12]=>00000000001=>10000000000=>[1,11]
[10,6,11,5,4,2,7,8,9,1,3,12]=>00000000001=>10000000000=>[1,11]
[10,6,11,5,3,2,7,8,1,4,9,12]=>00000000001=>10000000000=>[1,11]
[10,6,11,4,3,2,7,1,5,8,9,12]=>00000000001=>10000000000=>[1,11]
[10,5,11,4,3,2,1,6,7,8,9,12]=>00000000001=>10000000000=>[1,11]
[9,8,6,10,11,4,7,2,5,1,3,12]=>00000000001=>10000000000=>[1,11]
[9,8,6,10,11,3,7,2,1,4,5,12]=>00000000001=>10000000000=>[1,11]
[9,8,5,10,11,4,2,6,7,1,3,12]=>00000000001=>10000000000=>[1,11]
[9,8,5,10,11,3,2,6,1,4,7,12]=>00000000001=>10000000000=>[1,11]
[9,8,4,10,11,3,2,1,5,6,7,12]=>00000000001=>10000000000=>[1,11]
[9,7,6,10,4,8,11,2,5,1,3,12]=>00000000001=>10000000000=>[1,11]
[9,7,6,10,3,8,11,2,1,4,5,12]=>00000000001=>10000000000=>[1,11]
[9,7,5,10,4,8,2,6,11,1,3,12]=>00000000001=>10000000000=>[1,11]
[9,7,5,10,3,8,2,6,1,4,11,12]=>00000000011=>11000000000=>[1,1,10]
[9,7,4,10,3,8,2,1,5,6,11,12]=>00000000011=>11000000000=>[1,1,10]
[9,6,5,10,4,2,7,8,11,1,3,12]=>00000000001=>10000000000=>[1,11]
[9,6,5,10,3,2,7,8,1,4,11,12]=>00000000011=>11000000000=>[1,1,10]
[9,6,4,10,3,2,7,1,5,8,11,12]=>00000000011=>11000000000=>[1,1,10]
[9,5,4,10,3,2,1,6,7,8,11,12]=>00000000011=>11000000000=>[1,1,10]
[8,7,6,4,9,10,11,2,5,1,3,12]=>00000000001=>10000000000=>[1,11]
[8,7,6,3,9,10,11,2,1,4,5,12]=>00000000001=>10000000000=>[1,11]
[8,7,5,4,9,10,2,6,11,1,3,12]=>00000000001=>10000000000=>[1,11]
[8,7,5,3,9,10,2,6,1,4,11,12]=>00000000011=>11000000000=>[1,1,10]
[8,7,4,3,9,10,2,1,5,6,11,12]=>00000000011=>11000000000=>[1,1,10]
[8,6,5,4,9,2,7,10,11,1,3,12]=>00000000001=>10000000000=>[1,11]
[8,6,5,3,9,2,7,10,1,4,11,12]=>00000000011=>11000000000=>[1,1,10]
[7,6,5,4,2,8,9,10,11,1,3,12]=>00000000001=>10000000000=>[1,11]
[7,6,5,3,2,8,9,10,1,4,11,12]=>00000000011=>11000000000=>[1,1,10]
[1,8,7,5,3,2,4,6]=>1000000=>0000001=>[7,1]
[1,8,7,4,2,5,3,6]=>1000000=>0000001=>[7,1]
[5,3,7,1,6,4,2,8]=>0000001=>1000000=>[1,7]
[1,5,3,8,7,4,2,6]=>1000000=>0000001=>[7,1]
[1,8,6,3,5,7,4,2]=>1000000=>0000001=>[7,1]
[1,8,6,3,2,4,7,5]=>1000000=>0000001=>[7,1]
[1,7,5,8,6,3,2,4]=>1000000=>0000001=>[7,1]
[1,7,4,2,5,8,6,3]=>1000000=>0000001=>[7,1]
[8,7,4,2,5,3,1,6]=>0000000=>0000000=>[8]
[1,8,5,2,7,4,6,3]=>1000000=>0000001=>[7,1]
[1,7,4,6,3,8,5,2]=>1000000=>0000001=>[7,1]
[4,1,8,5,7,3,2,6]=>0000000=>0000000=>[8]
[4,7,2,8,3,6,1,5]=>0000000=>0000000=>[8]
[1,8,5,4,2,3,7,6]=>1000000=>0000001=>[7,1]
[3,5,4,8,1,2,7,6]=>0000000=>0000000=>[8]
[5,6,3,8,7,1,2,4]=>0000000=>0000000=>[8]
[2,6,8,4,1,7,3,5]=>0000000=>0000000=>[8]
[1,8,7,4,2,6,3,5]=>1000000=>0000001=>[7,1]
[5,2,8,6,7,1,3,4]=>0000000=>0000000=>[8]
[6,2,8,7,5,1,3,4]=>0000000=>0000000=>[8]
[1,8,5,7,6,2,3,4]=>1000000=>0000001=>[7,1]
[1,8,6,7,5,2,3,4]=>1000000=>0000001=>[7,1]
[5,2,8,7,1,4,3,6]=>0000000=>0000000=>[8]
[6,1,7,3,2,8,5,4]=>0000000=>0000000=>[8]
[4,7,2,1,6,3,8,5]=>0000000=>0000000=>[8]
[6,1,8,3,7,5,2,4]=>0000000=>0000000=>[8]
[6,1,8,4,5,2,7,3]=>0000000=>0000000=>[8]
[3,5,2,7,1,6,8,4]=>0000000=>0000000=>[8]
[6,1,4,2,5,3,7,8]=>0000011=>1100000=>[1,1,6]
[1,3,7,5,4,2,8,6]=>1000000=>0000001=>[7,1]
[6,1,3,5,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[6,1,2,5,4,7,3,8]=>0000001=>1000000=>[1,7]
[5,2,6,3,4,7,1,8]=>0000001=>1000000=>[1,7]
[2,4,7,1,5,3,8,6]=>0000000=>0000000=>[8]
[2,3,6,7,4,8,1,5]=>0000000=>0000000=>[8]
[1,3,6,7,4,8,5,2]=>1000000=>0000001=>[7,1]
[2,7,6,5,3,1,8,4]=>0000000=>0000000=>[8]
[5,2,6,1,4,7,8,3]=>0000000=>0000000=>[8]
[4,7,6,5,2,1,8,3]=>0000000=>0000000=>[8]
[6,3,1,5,4,7,8,2]=>0000000=>0000000=>[8]
[5,3,6,1,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[1,7,4,2,6,3,8,5]=>1000000=>0000001=>[7,1]
[5,7,4,1,2,3,6,8]=>0000001=>1000000=>[1,7]
[6,4,1,2,5,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,7,6,3,8,5,1,2]=>0000000=>0000000=>[8]
[3,7,6,5,2,8,1,4]=>0000000=>0000000=>[8]
[3,7,6,5,1,2,8,4]=>0000000=>0000000=>[8]
[4,7,2,6,1,3,8,5]=>0000000=>0000000=>[8]
[2,7,6,5,8,1,4,3]=>0000000=>0000000=>[8]
[4,2,6,8,3,1,5,7]=>0000000=>0000000=>[8]
[3,7,6,2,4,5,1,8]=>0000001=>1000000=>[1,7]
[2,3,6,5,8,1,4,7]=>0000000=>0000000=>[8]
[2,3,5,8,6,1,4,7]=>0000000=>0000000=>[8]
[4,2,3,8,6,1,5,7]=>0000000=>0000000=>[8]
[1,2,3,7,4,6,8,5]=>1110000=>0000111=>[5,1,1,1]
[3,2,7,1,4,5,8,6]=>0000000=>0000000=>[8]
[2,1,5,3,8,7,4,6]=>0100000=>0000010=>[6,2]
[5,8,3,2,4,1,6,7]=>0000000=>0000000=>[8]
[4,2,7,1,8,3,5,6]=>0000000=>0000000=>[8]
[1,2,7,5,3,8,4,6]=>1100000=>0000011=>[6,1,1]
[3,2,7,1,4,8,5,6]=>0000000=>0000000=>[8]
[1,2,3,7,6,8,4,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,6,8,7,4,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,7,8,4,6,5]=>1110000=>0000111=>[5,1,1,1]
[1,2,3,6,8,4,7,5]=>1110000=>0000111=>[5,1,1,1]
[6,2,8,3,7,5,1,4]=>0000000=>0000000=>[8]
[4,2,8,3,7,5,6,1]=>0000000=>0000000=>[8]
[7,3,4,8,6,5,1,2]=>0000000=>0000000=>[8]
[5,3,4,8,7,2,6,1]=>0000000=>0000000=>[8]
[4,6,3,8,5,7,2,1]=>0000000=>0000000=>[8]
[7,5,3,8,6,2,4,1]=>0000000=>0000000=>[8]
[2,6,8,3,7,4,5,1]=>0000000=>0000000=>[8]
[2,5,8,3,7,4,6,1]=>0000000=>0000000=>[8]
[7,4,3,8,6,2,5,1]=>0000000=>0000000=>[8]
[3,5,4,8,7,2,6,1]=>0000000=>0000000=>[8]
[4,5,3,8,6,7,2,1]=>0000000=>0000000=>[8]
[3,6,7,8,4,5,2,1]=>0000000=>0000000=>[8]
[1,8,5,6,4,7,3,2]=>1000000=>0000001=>[7,1]
[2,5,8,6,4,7,3,1]=>0000000=>0000000=>[8]
[6,3,7,8,4,5,2,1]=>0000000=>0000000=>[8]
[4,3,7,8,5,6,2,1]=>0000000=>0000000=>[8]
[4,2,8,6,5,7,3,1]=>0000000=>0000000=>[8]
[3,2,8,6,7,4,5,1]=>0000000=>0000000=>[8]
[2,3,8,7,5,4,6,1]=>0000000=>0000000=>[8]
[1,8,2,7,4,5,6,3]=>1000000=>0000001=>[7,1]
[7,2,8,6,3,4,5,1]=>0000000=>0000000=>[8]
[6,2,8,4,5,7,3,1]=>0000000=>0000000=>[8]
[5,2,8,4,6,7,3,1]=>0000000=>0000000=>[8]
[4,3,6,8,5,7,2,1]=>0000000=>0000000=>[8]
[3,4,6,8,7,2,5,1]=>0000000=>0000000=>[8]
[7,3,5,8,6,2,4,1]=>0000000=>0000000=>[8]
[1,8,3,5,7,4,6,2]=>1000000=>0000001=>[7,1]
[2,7,8,4,5,6,3,1]=>0000000=>0000000=>[8]
[3,7,5,8,4,6,2,1]=>0000000=>0000000=>[8]
[5,7,4,6,8,3,2,1]=>0000000=>0000000=>[8]
[3,6,5,8,4,7,2,1]=>0000000=>0000000=>[8]
[2,6,8,4,5,7,3,1]=>0000000=>0000000=>[8]
[4,2,7,1,3,8,5,6]=>0000000=>0000000=>[8]
[4,2,5,1,3,8,6,7]=>0000100=>0010000=>[3,5]
[5,3,6,1,7,2,4,8]=>0000001=>1000000=>[1,7]
[3,7,1,2,5,8,6,4]=>0000000=>0000000=>[8]
[3,7,4,1,2,8,5,6]=>0000000=>0000000=>[8]
[7,5,1,3,4,8,6,2]=>0000000=>0000000=>[8]
[7,5,1,2,4,8,6,3]=>0000000=>0000000=>[8]
[6,4,2,3,7,1,5,8]=>0000001=>1000000=>[1,7]
[7,6,3,8,1,2,5,4]=>0000000=>0000000=>[8]
[7,4,2,3,8,1,6,5]=>0000000=>0000000=>[8]
[4,7,5,2,8,1,3,6]=>0000000=>0000000=>[8]
[8,2,6,3,7,1,4,5]=>0000000=>0000000=>[8]
[8,6,1,2,7,4,5,3]=>0000000=>0000000=>[8]
[8,4,7,1,2,3,6,5]=>0000000=>0000000=>[8]
[8,5,7,1,2,4,6,3]=>0000000=>0000000=>[8]
[3,8,5,6,1,2,4,7]=>0000000=>0000000=>[8]
[3,7,5,8,1,2,4,6]=>0000000=>0000000=>[8]
[7,6,4,8,1,3,5,2]=>0000000=>0000000=>[8]
[6,5,8,1,2,4,7,3]=>0000000=>0000000=>[8]
[3,6,8,1,2,5,7,4]=>0000000=>0000000=>[8]
[4,6,3,8,1,2,5,7]=>0000000=>0000000=>[8]
[4,6,3,7,1,2,5,8]=>0000001=>1000000=>[1,7]
[4,1,7,8,2,3,6,5]=>0000000=>0000000=>[8]
[5,1,2,8,6,3,4,7]=>0000000=>0000000=>[8]
[5,3,8,1,6,2,4,7]=>0000000=>0000000=>[8]
[6,1,8,5,2,3,4,7]=>0000000=>0000000=>[8]
[6,1,7,5,2,3,4,8]=>0000001=>1000000=>[1,7]
[6,8,1,3,7,4,5,2]=>0000000=>0000000=>[8]
[7,2,8,1,6,3,4,5]=>0000000=>0000000=>[8]
[4,7,8,2,5,1,3,6]=>0000000=>0000000=>[8]
[6,8,2,7,1,4,5,3]=>0000000=>0000000=>[8]
[4,8,7,1,3,5,6,2]=>0000000=>0000000=>[8]
[3,8,7,1,2,4,6,5]=>0000000=>0000000=>[8]
[4,8,7,1,2,3,6,5]=>0000000=>0000000=>[8]
[5,8,7,1,2,4,6,3]=>0000000=>0000000=>[8]
[5,8,7,1,3,4,6,2]=>0000000=>0000000=>[8]
[7,1,8,6,2,3,5,4]=>0000000=>0000000=>[8]
[5,8,6,4,1,2,3,7]=>0000000=>0000000=>[8]
[5,1,3,4,6,7,2,8]=>0000001=>1000000=>[1,7]
[1,3,4,8,7,5,2,6]=>1000000=>0000001=>[7,1]
[8,2,4,1,7,3,5,6]=>0000000=>0000000=>[8]
[8,6,1,4,2,3,7,5]=>0000000=>0000000=>[8]
[3,6,1,4,2,8,7,5]=>0000000=>0000000=>[8]
[1,6,8,4,3,7,2,5]=>1000000=>0000001=>[7,1]
[3,1,4,7,8,5,2,6]=>0000000=>0000000=>[8]
[6,1,7,4,3,8,2,5]=>0000000=>0000000=>[8]
[1,8,7,4,3,6,2,5]=>1000000=>0000001=>[7,1]
[7,4,1,3,8,2,6,5]=>0000000=>0000000=>[8]
[4,8,2,3,1,5,7,6]=>0000000=>0000000=>[8]
[4,8,6,2,1,3,7,5]=>0000000=>0000000=>[8]
[2,7,4,1,8,3,5,6]=>0000000=>0000000=>[8]
[1,7,8,4,2,3,6,5]=>1000000=>0000001=>[7,1]
[8,7,1,3,4,2,6,5]=>0000000=>0000000=>[8]
[1,7,4,3,6,2,8,5]=>1000000=>0000001=>[7,1]
[3,8,6,4,5,2,1,7]=>0000000=>0000000=>[8]
[3,8,4,6,5,2,1,7]=>0000000=>0000000=>[8]
[2,4,3,7,5,8,1,6]=>0000000=>0000000=>[8]
[1,4,7,3,6,2,8,5]=>1000000=>0000001=>[7,1]
[6,4,1,3,7,2,8,5]=>0000000=>0000000=>[8]
[8,1,4,3,6,2,7,5]=>0000000=>0000000=>[8]
[4,2,3,8,5,7,1,6]=>0000000=>0000000=>[8]
[2,8,5,7,3,4,1,6]=>0000000=>0000000=>[8]
[5,8,2,6,4,3,1,7]=>0000000=>0000000=>[8]
[7,2,5,8,4,3,1,6]=>0000000=>0000000=>[8]
[4,2,3,5,8,7,1,6]=>0000000=>0000000=>[8]
[8,2,3,5,4,7,1,6]=>0000000=>0000000=>[8]
[6,1,8,3,4,2,7,5]=>0000000=>0000000=>[8]
[1,8,6,4,2,3,7,5]=>1000000=>0000001=>[7,1]
[3,8,4,5,6,2,1,7]=>0000000=>0000000=>[8]
[3,8,6,5,4,2,1,7]=>0000000=>0000000=>[8]
[6,3,1,4,2,8,7,5]=>0000000=>0000000=>[8]
[7,3,8,1,2,6,4,5]=>0000000=>0000000=>[8]
[7,1,4,5,3,2,6,8]=>0000001=>1000000=>[1,7]
[1,8,4,2,6,5,3,7]=>1000000=>0000001=>[7,1]
[5,1,4,8,6,3,2,7]=>0000000=>0000000=>[8]
[5,3,1,8,4,7,2,6]=>0000000=>0000000=>[8]
[4,3,8,1,5,7,2,6]=>0000000=>0000000=>[8]
[6,3,1,2,5,7,4,8]=>0000001=>1000000=>[1,7]
[7,1,4,2,6,5,3,8]=>0000001=>1000000=>[1,7]
[3,8,4,1,6,5,2,7]=>0000000=>0000000=>[8]
[8,7,2,4,5,1,6,3]=>0000000=>0000000=>[8]
[7,1,5,4,8,6,3,2]=>0000000=>0000000=>[8]
[5,7,1,4,8,6,3,2]=>0000000=>0000000=>[8]
[6,5,3,7,4,8,2,1]=>0000000=>0000000=>[8]
[2,7,8,4,5,1,6,3]=>0000000=>0000000=>[8]
[5,6,3,8,1,4,7,2]=>0000000=>0000000=>[8]
[8,7,3,1,5,4,2,6]=>0000000=>0000000=>[8]
[3,5,4,7,6,1,2,8]=>0000001=>1000000=>[1,7]
[3,5,7,4,6,1,8,2]=>0000000=>0000000=>[8]
[3,5,7,4,6,1,2,8]=>0000001=>1000000=>[1,7]
[3,5,7,4,6,2,1,8]=>0000001=>1000000=>[1,7]
[3,5,2,7,6,4,1,8]=>0000001=>1000000=>[1,7]
[3,5,7,2,6,4,1,8]=>0000001=>1000000=>[1,7]
[5,3,7,6,1,2,8,4]=>0000000=>0000000=>[8]
[5,3,7,6,1,4,2,8]=>0000001=>1000000=>[1,7]
[5,3,7,6,4,1,2,8]=>0000001=>1000000=>[1,7]
[3,5,7,2,6,1,4,8]=>0000001=>1000000=>[1,7]
[3,5,2,7,6,1,4,8]=>0000001=>1000000=>[1,7]
[5,3,7,6,4,1,8,2]=>0000000=>0000000=>[8]
[3,7,5,4,1,8,2,6]=>0000000=>0000000=>[8]
[3,7,5,4,1,8,6,2]=>0000000=>0000000=>[8]
[3,7,5,1,4,8,6,2]=>0000000=>0000000=>[8]
[3,7,5,1,4,8,2,6]=>0000000=>0000000=>[8]
[3,5,7,1,2,6,8,4]=>0000000=>0000000=>[8]
[3,5,7,2,1,6,4,8]=>0000001=>1000000=>[1,7]
[5,3,7,1,6,2,4,8]=>0000001=>1000000=>[1,7]
[3,5,7,1,4,6,8,2]=>0000000=>0000000=>[8]
[3,5,7,1,4,2,6,8]=>0000001=>1000000=>[1,7]
[3,5,7,4,1,2,6,8]=>0000001=>1000000=>[1,7]
[3,5,4,7,1,6,8,2]=>0000000=>0000000=>[8]
[3,5,4,7,1,2,6,8]=>0000001=>1000000=>[1,7]
[3,5,4,7,2,1,6,8]=>0000001=>1000000=>[1,7]
[3,5,4,2,7,1,6,8]=>0000001=>1000000=>[1,7]
[3,5,4,7,2,1,8,6]=>0000000=>0000000=>[8]
[3,5,4,7,1,2,8,6]=>0000000=>0000000=>[8]
[5,7,6,3,1,8,4,2]=>0000000=>0000000=>[8]
[5,7,6,3,1,8,2,4]=>0000000=>0000000=>[8]
[3,5,7,4,1,2,8,6]=>0000000=>0000000=>[8]
[3,5,7,4,2,1,8,6]=>0000000=>0000000=>[8]
[3,2,5,7,4,1,8,6]=>0000000=>0000000=>[8]
[3,2,5,7,1,4,8,6]=>0000000=>0000000=>[8]
[3,5,2,7,1,4,8,6]=>0000000=>0000000=>[8]
[3,5,7,2,1,4,8,6]=>0000000=>0000000=>[8]
[3,5,7,1,4,2,8,6]=>0000000=>0000000=>[8]
[3,7,5,2,1,8,6,4]=>0000000=>0000000=>[8]
[3,7,2,5,1,8,6,4]=>0000000=>0000000=>[8]
[3,2,7,5,1,8,6,4]=>0000000=>0000000=>[8]
[3,2,7,5,1,8,4,6]=>0000000=>0000000=>[8]
[3,7,2,5,1,8,4,6]=>0000000=>0000000=>[8]
[3,7,5,2,1,8,4,6]=>0000000=>0000000=>[8]
[3,8,4,1,7,6,5,2]=>0000000=>0000000=>[8]
[5,8,2,4,1,6,3,7]=>0000000=>0000000=>[8]
[3,2,6,8,1,5,4,7]=>0000000=>0000000=>[8]
[3,2,6,8,7,1,5,4]=>0000000=>0000000=>[8]
[8,7,3,2,5,6,1,4]=>0000000=>0000000=>[8]
[7,2,4,1,8,3,6,5]=>0000000=>0000000=>[8]
[1,7,2,3,6,8,5,4]=>1000000=>0000001=>[7,1]
[3,5,6,4,8,2,7,1]=>0000000=>0000000=>[8]
[3,5,1,4,8,2,7,6]=>0000000=>0000000=>[8]
[1,7,5,4,8,2,6,3]=>1000000=>0000001=>[7,1]
[3,7,5,1,6,4,8,2]=>0000000=>0000000=>[8]
[2,7,5,4,8,1,3,6]=>0000000=>0000000=>[8]
[2,7,5,4,8,6,1,3]=>0000000=>0000000=>[8]
[1,7,5,4,8,6,3,2]=>1000000=>0000001=>[7,1]
[2,5,1,4,8,7,3,6]=>0000000=>0000000=>[8]
[3,6,4,2,8,7,1,5]=>0000000=>0000000=>[8]
[3,5,2,4,8,1,6,7]=>0000000=>0000000=>[8]
[4,5,6,1,7,3,8,2]=>0000000=>0000000=>[8]
[3,5,6,4,8,1,2,7]=>0000000=>0000000=>[8]
[1,5,6,4,8,7,2,3]=>1000000=>0000001=>[7,1]
[3,6,4,1,8,7,2,5]=>0000000=>0000000=>[8]
[3,6,4,5,8,7,2,1]=>0000000=>0000000=>[8]
[1,6,4,3,8,5,2,7]=>1000000=>0000001=>[7,1]
[7,6,1,4,5,3,8,2]=>0000000=>0000000=>[8]
[7,6,1,3,5,4,8,2]=>0000000=>0000000=>[8]
[7,1,3,2,5,8,4,6]=>0000000=>0000000=>[8]
[1,6,4,2,8,5,3,7]=>1000000=>0000001=>[7,1]
[7,6,5,8,3,1,4,2]=>0000000=>0000000=>[8]
[2,6,4,3,8,1,7,5]=>0000000=>0000000=>[8]
[2,6,4,3,8,5,7,1]=>0000000=>0000000=>[8]
[7,2,3,1,5,8,6,4]=>0000000=>0000000=>[8]
[7,1,5,6,3,8,4,2]=>0000000=>0000000=>[8]
[7,3,6,5,1,4,8,2]=>0000000=>0000000=>[8]
[7,2,6,5,3,8,1,4]=>0000000=>0000000=>[8]
[7,2,3,1,4,8,6,5]=>0000000=>0000000=>[8]
[7,2,3,5,4,8,6,1]=>0000000=>0000000=>[8]
[2,6,4,5,8,1,7,3]=>0000000=>0000000=>[8]
[1,5,6,4,8,3,7,2]=>1000000=>0000001=>[7,1]
[2,5,6,4,8,3,1,7]=>0000000=>0000000=>[8]
[3,5,6,1,4,7,8,2]=>0000000=>0000000=>[8]
[7,6,1,3,4,5,8,2]=>0000000=>0000000=>[8]
[7,1,3,2,4,8,5,6]=>0000000=>0000000=>[8]
[7,6,1,5,3,4,8,2]=>0000000=>0000000=>[8]
[7,6,1,5,4,3,8,2]=>0000000=>0000000=>[8]
[1,6,4,5,8,3,2,7]=>1000000=>0000001=>[7,1]
[7,6,5,8,1,3,2,4]=>0000000=>0000000=>[8]
[3,4,6,8,7,2,1,5]=>0000000=>0000000=>[8]
[3,5,6,8,2,1,7,4]=>0000000=>0000000=>[8]
[4,2,1,5,3,7,8,6]=>0000100=>0010000=>[3,5]
[4,2,5,6,3,1,8,7]=>0000010=>0100000=>[2,6]
[3,5,6,8,1,7,2,4]=>0000000=>0000000=>[8]
[4,1,5,6,3,2,8,7]=>0000010=>0100000=>[2,6]
[4,5,3,1,7,2,8,6]=>0000000=>0000000=>[8]
[4,1,3,5,2,7,8,6]=>0000100=>0010000=>[3,5]
[2,5,4,7,3,8,6,1]=>0000000=>0000000=>[8]
[3,5,7,1,8,4,2,6]=>0000000=>0000000=>[8]
[4,1,5,3,2,7,8,6]=>0000100=>0010000=>[3,5]
[4,5,3,7,1,2,8,6]=>0000000=>0000000=>[8]
[4,3,6,1,2,7,5,8]=>0000001=>1000000=>[1,7]
[5,1,3,2,4,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[3,6,1,7,4,5,2,8]=>0000001=>1000000=>[1,7]
[5,3,1,4,2,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[4,5,2,3,7,1,8,6]=>0000000=>0000000=>[8]
[4,2,6,1,3,7,5,8]=>0000001=>1000000=>[1,7]
[4,6,2,1,3,7,5,8]=>0000001=>1000000=>[1,7]
[3,6,2,1,7,4,8,5]=>0000000=>0000000=>[8]
[3,1,4,7,6,5,2,8]=>0000001=>1000000=>[1,7]
[3,6,2,7,1,5,8,4]=>0000000=>0000000=>[8]
[4,6,2,7,1,3,5,8]=>0000001=>1000000=>[1,7]
[3,5,7,1,8,2,6,4]=>0000000=>0000000=>[8]
[5,1,4,2,3,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[2,6,5,3,4,7,8,1]=>0000000=>0000000=>[8]
[3,6,1,7,5,4,2,8]=>0000001=>1000000=>[1,7]
[5,1,4,3,2,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,4,1,3,2,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[6,7,4,8,5,1,3,2]=>0000000=>0000000=>[8]
[3,6,5,8,7,1,4,2]=>0000000=>0000000=>[8]
[5,6,8,3,1,7,4,2]=>0000000=>0000000=>[8]
[5,3,8,1,7,2,6,4]=>0000000=>0000000=>[8]
[6,5,3,8,2,7,4,1]=>0000000=>0000000=>[8]
[6,4,8,1,3,7,5,2]=>0000000=>0000000=>[8]
[4,2,8,7,6,3,1,5]=>0000000=>0000000=>[8]
[7,6,3,1,8,4,2,5]=>0000000=>0000000=>[8]
[5,2,7,4,1,8,6,3]=>0000000=>0000000=>[8]
[1,3,7,6,5,8,2,4]=>1000000=>0000001=>[7,1]
[6,3,1,4,7,5,2,8]=>0000001=>1000000=>[1,7]
[4,6,7,2,5,3,1,8]=>0000001=>1000000=>[1,7]
[4,2,6,8,7,1,5,3]=>0000000=>0000000=>[8]
[6,3,7,1,2,8,5,4]=>0000000=>0000000=>[8]
[1,8,2,3,6,5,4,7]=>1000000=>0000001=>[7,1]
[3,5,8,4,7,2,6,1]=>0000000=>0000000=>[8]
[1,8,5,4,6,2,3,7]=>1000000=>0000001=>[7,1]
[3,8,5,4,6,1,2,7]=>0000000=>0000000=>[8]
[3,8,5,1,6,4,2,7]=>0000000=>0000000=>[8]
[2,8,5,4,6,1,3,7]=>0000000=>0000000=>[8]
[2,8,5,4,6,3,1,7]=>0000000=>0000000=>[8]
[1,8,5,4,6,3,2,7]=>1000000=>0000001=>[7,1]
[2,5,8,4,7,3,6,1]=>0000000=>0000000=>[8]
[3,6,4,2,7,8,5,1]=>0000000=>0000000=>[8]
[3,6,4,2,7,8,1,5]=>0000000=>0000000=>[8]
[3,5,4,1,6,2,7,8]=>0000011=>1100000=>[1,1,6]
[4,5,8,1,7,6,2,3]=>0000000=>0000000=>[8]
[3,5,8,4,7,1,6,2]=>0000000=>0000000=>[8]
[1,5,8,4,7,3,6,2]=>1000000=>0000001=>[7,1]
[3,6,4,1,7,8,5,2]=>0000000=>0000000=>[8]
[3,6,4,8,7,5,2,1]=>0000000=>0000000=>[8]
[1,6,4,3,7,8,5,2]=>1000000=>0000001=>[7,1]
[7,6,1,3,8,4,2,5]=>0000000=>0000000=>[8]
[1,6,4,2,7,8,3,5]=>1000000=>0000001=>[7,1]
[2,6,4,3,7,1,8,5]=>0000000=>0000000=>[8]
[2,6,4,1,7,8,3,5]=>0000000=>0000000=>[8]
[7,2,3,4,8,6,5,1]=>0000000=>0000000=>[8]
[7,2,3,1,8,6,4,5]=>0000000=>0000000=>[8]
[7,2,3,4,1,6,8,5]=>0000000=>0000000=>[8]
[1,2,4,3,8,5,7,6]=>1101000=>0001011=>[4,2,1,1]
[7,3,8,6,1,4,2,5]=>0000000=>0000000=>[8]
[7,2,8,6,3,4,1,5]=>0000000=>0000000=>[8]
[7,2,3,1,5,6,8,4]=>0000000=>0000000=>[8]
[7,2,3,8,5,6,4,1]=>0000000=>0000000=>[8]
[2,6,4,8,7,1,5,3]=>0000000=>0000000=>[8]
[1,5,8,4,7,6,2,3]=>1000000=>0000001=>[7,1]
[3,5,8,1,6,7,2,4]=>0000000=>0000000=>[8]
[7,6,1,3,5,8,2,4]=>0000000=>0000000=>[8]
[7,1,3,2,5,6,8,4]=>0000000=>0000000=>[8]
[7,1,3,8,2,6,5,4]=>0000000=>0000000=>[8]
[7,6,1,8,5,4,2,3]=>0000000=>0000000=>[8]
[4,3,7,1,6,5,8,2]=>0000000=>0000000=>[8]
[5,2,6,4,8,1,7,3]=>0000000=>0000000=>[8]
[5,3,7,4,8,1,6,2]=>0000000=>0000000=>[8]
[4,3,7,1,6,2,8,5]=>0000000=>0000000=>[8]
[4,1,7,8,6,3,2,5]=>0000000=>0000000=>[8]
[1,2,6,8,3,7,4,5]=>1100000=>0000011=>[6,1,1]
[6,8,2,4,1,3,7,5]=>0000000=>0000000=>[8]
[6,1,2,7,5,8,4,3]=>0000000=>0000000=>[8]
[4,5,2,6,8,3,7,1]=>0000000=>0000000=>[8]
[6,8,4,1,5,3,7,2]=>0000000=>0000000=>[8]
[8,3,6,1,5,7,4,2]=>0000000=>0000000=>[8]
[2,4,6,7,8,1,5,3]=>0000000=>0000000=>[8]
[7,4,3,8,6,2,1,5]=>0000000=>0000000=>[8]
[4,3,6,2,1,8,5,7]=>0000000=>0000000=>[8]
[4,6,2,3,7,5,8,1]=>0000000=>0000000=>[8]
[8,4,5,3,2,1,7,6]=>0000000=>0000000=>[8]
[6,4,8,3,2,7,1,5]=>0000000=>0000000=>[8]
[5,8,3,7,2,1,6,4]=>0000000=>0000000=>[8]
[1,2,6,5,8,7,3,4]=>1100000=>0000011=>[6,1,1]
[5,6,3,4,8,7,2,1]=>0000000=>0000000=>[8]
[6,5,3,4,8,7,2,1]=>0000000=>0000000=>[8]
[7,5,3,8,4,6,2,1]=>0000000=>0000000=>[8]
[8,5,3,7,4,6,2,1]=>0000000=>0000000=>[8]
[5,8,1,2,3,4,7,6]=>0000000=>0000000=>[8]
[4,3,8,7,5,6,2,1]=>0000000=>0000000=>[8]
[5,8,3,7,4,6,2,1]=>0000000=>0000000=>[8]
[6,8,7,3,4,5,2,1]=>0000000=>0000000=>[8]
[8,6,2,3,5,1,4,7]=>0000000=>0000000=>[8]
[8,2,4,5,7,3,1,6]=>0000000=>0000000=>[8]
[2,6,3,8,7,5,4,1]=>0000000=>0000000=>[8]
[8,2,3,7,5,4,1,6]=>0000000=>0000000=>[8]
[8,2,6,3,5,4,1,7]=>0000000=>0000000=>[8]
[8,6,1,5,2,4,3,7]=>0000000=>0000000=>[8]
[8,6,2,4,1,5,3,7]=>0000000=>0000000=>[8]
[8,4,1,6,5,3,2,7]=>0000000=>0000000=>[8]
[8,3,6,1,5,4,2,7]=>0000000=>0000000=>[8]
[8,3,2,6,5,4,1,7]=>0000000=>0000000=>[8]
[8,3,2,5,7,4,1,6]=>0000000=>0000000=>[8]
[8,3,1,7,5,4,2,6]=>0000000=>0000000=>[8]
[6,1,3,8,7,5,4,2]=>0000000=>0000000=>[8]
[3,6,1,8,7,5,4,2]=>0000000=>0000000=>[8]
[3,8,1,5,7,6,4,2]=>0000000=>0000000=>[8]
[3,5,2,8,7,6,4,1]=>0000000=>0000000=>[8]
[3,4,8,2,7,6,5,1]=>0000000=>0000000=>[8]
[3,4,8,7,1,6,5,2]=>0000000=>0000000=>[8]
[8,1,3,5,7,6,4,2]=>0000000=>0000000=>[8]
[4,1,8,5,7,6,3,2]=>0000000=>0000000=>[8]
[8,2,7,1,4,5,6,3]=>0000000=>0000000=>[8]
[8,1,7,3,4,6,2,5]=>0000000=>0000000=>[8]
[8,3,1,7,2,6,5,4]=>0000000=>0000000=>[8]
[3,8,2,4,7,6,5,1]=>0000000=>0000000=>[8]
[2,8,3,7,4,6,5,1]=>0000000=>0000000=>[8]
[8,2,3,7,1,6,5,4]=>0000000=>0000000=>[8]
[8,2,7,1,3,6,5,4]=>0000000=>0000000=>[8]
[8,1,7,2,6,4,3,5]=>0000000=>0000000=>[8]
[8,1,7,5,2,4,3,6]=>0000000=>0000000=>[8]
[8,2,3,7,4,6,1,5]=>0000000=>0000000=>[8]
[2,4,8,5,7,6,3,1]=>0000000=>0000000=>[8]
[8,2,4,3,7,6,1,5]=>0000000=>0000000=>[8]
[8,2,7,3,5,1,4,6]=>0000000=>0000000=>[8]
[8,2,7,4,3,1,5,6]=>0000000=>0000000=>[8]
[8,2,1,5,7,6,4,3]=>0000000=>0000000=>[8]
[6,1,8,2,7,5,4,3]=>0000000=>0000000=>[8]
[8,1,5,2,7,6,4,3]=>0000000=>0000000=>[8]
[8,1,7,2,4,6,5,3]=>0000000=>0000000=>[8]
[8,2,4,1,7,6,5,3]=>0000000=>0000000=>[8]
[4,2,8,3,7,6,5,1]=>0000000=>0000000=>[8]
[4,8,2,1,7,6,5,3]=>0000000=>0000000=>[8]
[5,1,8,7,2,6,4,3]=>0000000=>0000000=>[8]
[5,8,1,3,7,6,2,4]=>0000000=>0000000=>[8]
[8,2,5,4,1,7,6,3]=>0000000=>0000000=>[8]
[5,1,4,8,7,6,3,2]=>0000000=>0000000=>[8]
[8,1,4,3,7,6,5,2]=>0000000=>0000000=>[8]
[4,8,1,3,7,6,5,2]=>0000000=>0000000=>[8]
[4,3,8,1,7,6,5,2]=>0000000=>0000000=>[8]
[6,2,8,1,5,7,3,4]=>0000000=>0000000=>[8]
[7,3,2,8,5,6,1,4]=>0000000=>0000000=>[8]
[4,7,6,5,1,3,8,2]=>0000000=>0000000=>[8]
[1,7,6,3,2,8,4,5]=>1000000=>0000001=>[7,1]
[5,4,2,1,7,3,6,8]=>0000001=>1000000=>[1,7]
[3,7,6,2,8,4,5,1]=>0000000=>0000000=>[8]
[4,3,6,8,5,1,2,7]=>0000000=>0000000=>[8]
[2,7,1,5,8,4,3,6]=>0000000=>0000000=>[8]
[7,1,2,6,3,5,4,8]=>0000001=>1000000=>[1,7]
[6,7,8,4,2,5,3,1]=>0000000=>0000000=>[8]
[4,7,3,1,2,6,8,5]=>0000000=>0000000=>[8]
[3,8,5,6,4,2,7,1]=>0000000=>0000000=>[8]
[3,2,6,4,7,8,5,1]=>0000000=>0000000=>[8]
[5,2,1,4,7,8,3,6]=>0000000=>0000000=>[8]
[5,6,2,7,3,4,8,1]=>0000000=>0000000=>[8]
[1,5,8,6,4,2,3,7]=>1000000=>0000001=>[7,1]
[1,6,2,3,5,8,7,4]=>1000000=>0000001=>[7,1]
[4,3,8,2,5,7,1,6]=>0000000=>0000000=>[8]
[6,7,2,3,1,5,8,4]=>0000000=>0000000=>[8]
[4,7,5,8,6,3,1,2]=>0000000=>0000000=>[8]
[7,3,2,5,8,1,6,4]=>0000000=>0000000=>[8]
[2,4,8,3,7,1,5,6]=>0000000=>0000000=>[8]
[5,2,8,4,1,6,3,7]=>0000000=>0000000=>[8]
[7,6,5,2,1,8,4,3]=>0000000=>0000000=>[8]
[2,7,5,1,8,3,6,4]=>0000000=>0000000=>[8]
[5,7,1,3,2,4,8,6]=>0000000=>0000000=>[8]
[4,2,7,6,3,5,8,1]=>0000000=>0000000=>[8]
[8,1,7,4,2,3,5,6]=>0000000=>0000000=>[8]
[8,6,5,1,7,4,3,2]=>0000000=>0000000=>[8]
[7,6,4,1,3,5,8,2]=>0000000=>0000000=>[8]
[8,2,3,7,1,4,5,6]=>0000000=>0000000=>[8]
[5,6,2,7,4,3,1,8]=>0000001=>1000000=>[1,7]
[4,8,6,5,1,2,7,3]=>0000000=>0000000=>[8]
[4,8,6,5,1,2,3,7]=>0000000=>0000000=>[8]
[5,8,2,6,1,4,7,3]=>0000000=>0000000=>[8]
[3,8,7,5,6,1,4,2]=>0000000=>0000000=>[8]
[7,4,6,5,1,3,8,2]=>0000000=>0000000=>[8]
[4,6,3,8,7,5,1,2]=>0000000=>0000000=>[8]
[2,8,4,1,5,7,6,3]=>0000000=>0000000=>[8]
[1,8,4,2,5,7,6,3]=>1000000=>0000001=>[7,1]
[2,8,5,4,1,7,6,3]=>0000000=>0000000=>[8]
[2,5,8,3,7,1,6,4]=>0000000=>0000000=>[8]
[1,8,5,2,4,7,6,3]=>1000000=>0000001=>[7,1]
[1,4,6,2,8,7,5,3]=>1000000=>0000001=>[7,1]
[7,8,2,4,1,6,5,3]=>0000000=>0000000=>[8]
[2,4,6,1,8,7,5,3]=>0000000=>0000000=>[8]
[2,8,4,5,1,7,6,3]=>0000000=>0000000=>[8]
[3,5,8,1,7,6,2,4]=>0000000=>0000000=>[8]
[3,5,8,2,7,6,1,4]=>0000000=>0000000=>[8]
[2,1,6,8,7,5,3,4]=>0100000=>0000010=>[6,2]
[1,8,2,4,5,7,6,3]=>1000000=>0000001=>[7,1]
[1,3,8,2,5,7,6,4]=>1000000=>0000001=>[7,1]
[2,3,8,1,5,7,6,4]=>0000000=>0000000=>[8]
[2,6,1,8,7,5,3,4]=>0000000=>0000000=>[8]
[1,6,2,8,7,5,3,4]=>1000000=>0000001=>[7,1]
[1,6,3,8,7,5,2,4]=>1000000=>0000001=>[7,1]
[2,6,3,8,7,5,1,4]=>0000000=>0000000=>[8]
[3,2,8,1,5,7,6,4]=>0000000=>0000000=>[8]
[3,1,8,2,5,7,6,4]=>0000000=>0000000=>[8]
[2,1,8,3,5,7,6,4]=>0100000=>0000010=>[6,2]
[7,8,2,1,4,6,5,3]=>0000000=>0000000=>[8]
[2,3,6,8,7,5,1,4]=>0000000=>0000000=>[8]
[3,1,6,8,7,2,5,4]=>0000000=>0000000=>[8]
[3,8,4,5,1,6,2,7]=>0000000=>0000000=>[8]
[6,1,4,5,7,2,3,8]=>0000001=>1000000=>[1,7]
[8,1,4,7,6,3,2,5]=>0000000=>0000000=>[8]
[8,3,1,6,4,7,2,5]=>0000000=>0000000=>[8]
[5,3,8,6,2,7,1,4]=>0000000=>0000000=>[8]
[8,3,6,1,5,7,2,4]=>0000000=>0000000=>[8]
[6,8,1,4,5,2,3,7]=>0000000=>0000000=>[8]
[1,5,8,4,6,2,3,7]=>1000000=>0000001=>[7,1]
[5,6,8,1,4,2,3,7]=>0000000=>0000000=>[8]
[5,7,4,8,1,2,3,6]=>0000000=>0000000=>[8]
[4,7,8,1,2,6,3,5]=>0000000=>0000000=>[8]
[8,7,1,5,6,2,3,4]=>0000000=>0000000=>[8]
[1,6,5,8,7,2,3,4]=>1000000=>0000001=>[7,1]
[3,7,1,6,2,4,8,5]=>0000000=>0000000=>[8]
[5,1,2,7,6,8,3,4]=>0000000=>0000000=>[8]
[1,7,6,5,8,2,3,4]=>1000000=>0000001=>[7,1]
[1,6,8,5,7,2,3,4]=>1000000=>0000001=>[7,1]
[7,5,1,2,6,8,3,4]=>0000000=>0000000=>[8]
[6,1,5,2,7,8,3,4]=>0000000=>0000000=>[8]
[5,1,2,6,8,7,3,4]=>0000000=>0000000=>[8]
[1,8,6,2,5,7,3,4]=>1000000=>0000001=>[7,1]
[5,7,8,1,2,6,3,4]=>0000000=>0000000=>[8]
[8,1,5,7,6,2,3,4]=>0000000=>0000000=>[8]
[3,7,1,2,8,4,6,5]=>0000000=>0000000=>[8]
[1,5,8,7,6,2,3,4]=>1000000=>0000001=>[7,1]
[7,8,6,1,5,2,3,4]=>0000000=>0000000=>[8]
[2,6,4,7,5,3,8,1]=>0000000=>0000000=>[8]
[2,6,8,7,5,3,1,4]=>0000000=>0000000=>[8]
[6,4,1,7,5,2,8,3]=>0000000=>0000000=>[8]
[1,3,8,5,2,7,4,6]=>1000000=>0000001=>[7,1]
[1,3,8,6,7,2,4,5]=>1000000=>0000001=>[7,1]
[2,8,3,7,6,1,4,5]=>0000000=>0000000=>[8]
[1,3,8,7,6,2,4,5]=>1000000=>0000001=>[7,1]
[1,4,6,8,7,2,3,5]=>1000000=>0000001=>[7,1]
[7,6,4,8,5,1,3,2]=>0000000=>0000000=>[8]
[4,6,5,7,2,8,1,3]=>0000000=>0000000=>[8]
[5,3,6,7,8,1,4,2]=>0000000=>0000000=>[8]
[6,3,2,8,5,4,1,7]=>0000000=>0000000=>[8]
[4,3,5,1,2,7,6,8]=>0000101=>1010000=>[1,2,5]
[7,3,2,1,6,4,5,8]=>0000001=>1000000=>[1,7]
[2,8,6,1,7,4,3,5]=>0000000=>0000000=>[8]
[2,5,4,6,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[2,5,6,4,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[8,5,2,6,1,3,7,4]=>0000000=>0000000=>[8]
[7,1,2,6,5,4,3,8]=>0000001=>1000000=>[1,7]
[8,2,1,5,6,3,7,4]=>0000000=>0000000=>[8]
[2,8,5,1,6,4,7,3]=>0000000=>0000000=>[8]
[5,6,3,8,7,4,1,2]=>0000000=>0000000=>[8]
[5,2,6,8,7,4,1,3]=>0000000=>0000000=>[8]
[5,2,3,1,4,8,6,7]=>0000100=>0010000=>[3,5]
[5,4,1,3,2,8,6,7]=>0000100=>0010000=>[3,5]
[5,1,3,4,2,8,6,7]=>0000100=>0010000=>[3,5]
[4,2,7,3,8,5,1,6]=>0000000=>0000000=>[8]
[1,3,2,6,4,8,7,5]=>1010000=>0000101=>[5,2,1]
[1,6,2,5,3,8,7,4]=>1000000=>0000001=>[7,1]
[1,8,2,6,3,7,5,4]=>1000000=>0000001=>[7,1]
[1,8,3,6,4,7,5,2]=>1000000=>0000001=>[7,1]
[1,7,2,6,3,8,5,4]=>1000000=>0000001=>[7,1]
[1,5,2,7,4,8,6,3]=>1000000=>0000001=>[7,1]
[1,4,2,8,5,7,6,3]=>1000000=>0000001=>[7,1]
[1,5,3,8,4,7,6,2]=>1000000=>0000001=>[7,1]
[6,8,7,3,1,5,4,2]=>0000000=>0000000=>[8]
[2,5,8,7,4,6,3,1]=>0000000=>0000000=>[8]
[6,8,4,1,5,2,7,3]=>0000000=>0000000=>[8]
[4,8,7,5,1,6,2,3]=>0000000=>0000000=>[8]
[4,5,2,1,8,6,7,3]=>0000000=>0000000=>[8]
[2,6,7,4,1,3,8,5]=>0000000=>0000000=>[8]
[2,4,6,3,5,7,8,1]=>0000000=>0000000=>[8]
[2,3,6,1,5,7,8,4]=>0000000=>0000000=>[8]
[1,4,5,8,6,3,2,7]=>1000000=>0000001=>[7,1]
[5,2,6,3,1,7,8,4]=>0000000=>0000000=>[8]
[5,7,6,1,2,3,8,4]=>0000000=>0000000=>[8]
[4,3,6,2,1,8,7,5]=>0000000=>0000000=>[8]
[5,3,6,4,8,2,1,7]=>0000000=>0000000=>[8]
[3,7,4,5,1,6,2,8]=>0000001=>1000000=>[1,7]
[3,6,4,5,8,2,1,7]=>0000000=>0000000=>[8]
[6,1,4,5,2,8,7,3]=>0000000=>0000000=>[8]
[7,2,4,5,1,6,3,8]=>0000001=>1000000=>[1,7]
[7,5,4,1,6,3,2,8]=>0000001=>1000000=>[1,7]
[1,5,4,8,6,3,2,7]=>1000000=>0000001=>[7,1]
[7,5,4,8,6,3,1,2]=>0000000=>0000000=>[8]
[1,8,7,5,3,6,4,2]=>1000000=>0000001=>[7,1]
[8,3,7,4,1,6,2,5]=>0000000=>0000000=>[8]
[8,5,4,1,6,3,2,7]=>0000000=>0000000=>[8]
[1,7,4,2,6,5,3,8]=>1000001=>1000001=>[1,6,1]
[8,2,1,5,6,7,3,4]=>0000000=>0000000=>[8]
[6,3,1,8,4,7,2,5]=>0000000=>0000000=>[8]
[7,1,4,8,6,3,2,5]=>0000000=>0000000=>[8]
[4,1,8,5,6,7,2,3]=>0000000=>0000000=>[8]
[5,7,4,8,6,2,1,3]=>0000000=>0000000=>[8]
[5,3,6,8,2,7,1,4]=>0000000=>0000000=>[8]
[6,3,7,4,8,2,1,5]=>0000000=>0000000=>[8]
[5,3,6,1,4,7,2,8]=>0000001=>1000000=>[1,7]
[4,3,6,8,2,7,1,5]=>0000000=>0000000=>[8]
[5,3,7,4,8,2,1,6]=>0000000=>0000000=>[8]
[5,3,8,4,1,6,2,7]=>0000000=>0000000=>[8]
[5,3,8,1,4,7,2,6]=>0000000=>0000000=>[8]
[5,8,4,1,6,3,2,7]=>0000000=>0000000=>[8]
[7,3,8,4,1,6,2,5]=>0000000=>0000000=>[8]
[1,5,8,3,6,7,4,2]=>1000000=>0000001=>[7,1]
[1,8,2,5,6,7,3,4]=>1000000=>0000001=>[7,1]
[7,8,4,1,6,5,2,3]=>0000000=>0000000=>[8]
[6,3,8,1,5,7,2,4]=>0000000=>0000000=>[8]
[8,3,1,2,5,7,4,6]=>0000000=>0000000=>[8]
[8,1,4,2,6,5,3,7]=>0000000=>0000000=>[8]
[3,8,5,6,2,7,1,4]=>0000000=>0000000=>[8]
[2,4,5,8,7,3,1,6]=>0000000=>0000000=>[8]
[4,5,1,8,6,7,3,2]=>0000000=>0000000=>[8]
[3,4,5,8,7,1,2,6]=>0000000=>0000000=>[8]
[6,5,4,7,1,3,8,2]=>0000000=>0000000=>[8]
[6,1,4,7,2,3,8,5]=>0000000=>0000000=>[8]
[1,6,2,5,4,8,3,7]=>1000000=>0000001=>[7,1]
[4,1,2,7,5,8,3,6]=>0000000=>0000000=>[8]
[6,1,3,5,8,2,4,7]=>0000000=>0000000=>[8]
[5,6,4,3,1,8,2,7]=>0000000=>0000000=>[8]
[6,2,3,5,8,1,4,7]=>0000000=>0000000=>[8]
[6,7,2,3,8,4,5,1]=>0000000=>0000000=>[8]
[6,7,2,1,3,8,4,5]=>0000000=>0000000=>[8]
[5,7,4,1,8,3,2,6]=>0000000=>0000000=>[8]
[4,1,7,5,8,3,6,2]=>0000000=>0000000=>[8]
[6,7,1,3,8,4,5,2]=>0000000=>0000000=>[8]
[1,6,7,4,3,8,5,2]=>1000000=>0000001=>[7,1]
[6,1,7,4,2,8,5,3]=>0000000=>0000000=>[8]
[2,1,6,7,4,3,8,5]=>0100000=>0000010=>[6,2]
[6,7,3,2,1,8,4,5]=>0000000=>0000000=>[8]
[2,5,7,3,1,4,8,6]=>0000000=>0000000=>[8]
[6,7,3,2,8,4,5,1]=>0000000=>0000000=>[8]
[2,6,7,4,3,8,5,1]=>0000000=>0000000=>[8]
[1,2,6,7,4,3,8,5]=>1100000=>0000011=>[6,1,1]
[1,7,5,8,2,4,3,6]=>1000000=>0000001=>[7,1]
[2,7,1,8,4,6,3,5]=>0000000=>0000000=>[8]
[2,7,5,8,1,6,3,4]=>0000000=>0000000=>[8]
[1,6,7,3,8,5,4,2]=>1000000=>0000001=>[7,1]
[6,7,1,8,4,5,3,2]=>0000000=>0000000=>[8]
[8,6,1,5,4,3,2,7]=>0000000=>0000000=>[8]
[1,5,6,7,3,8,2,4]=>1000000=>0000001=>[7,1]
[1,6,5,4,8,3,2,7]=>1000000=>0000001=>[7,1]
[1,3,7,6,4,8,5,2]=>1000000=>0000001=>[7,1]
[3,1,8,7,6,4,2,5]=>0000000=>0000000=>[8]
[3,1,8,7,5,4,2,6]=>0000000=>0000000=>[8]
[3,1,7,6,5,4,2,8]=>0000001=>1000000=>[1,7]
[4,7,1,6,5,3,2,8]=>0000001=>1000000=>[1,7]
[4,8,1,6,5,3,2,7]=>0000000=>0000000=>[8]
[4,8,1,7,5,3,2,6]=>0000000=>0000000=>[8]
[8,4,1,7,6,3,2,5]=>0000000=>0000000=>[8]
[5,4,1,8,6,3,2,7]=>0000000=>0000000=>[8]
[5,4,1,7,6,3,2,8]=>0000001=>1000000=>[1,7]
[6,4,1,7,5,3,2,8]=>0000001=>1000000=>[1,7]
[6,4,1,8,5,3,2,7]=>0000000=>0000000=>[8]
[8,4,1,7,5,3,2,6]=>0000000=>0000000=>[8]
[7,4,1,6,5,3,2,8]=>0000001=>1000000=>[1,7]
[7,5,6,1,4,3,2,8]=>0000001=>1000000=>[1,7]
[8,5,6,1,4,3,2,7]=>0000000=>0000000=>[8]
[5,7,6,1,4,3,2,8]=>0000001=>1000000=>[1,7]
[5,8,6,1,4,3,2,7]=>0000000=>0000000=>[8]
[6,7,5,1,4,3,2,8]=>0000001=>1000000=>[1,7]
[8,7,5,1,4,3,2,6]=>0000000=>0000000=>[8]
[8,6,5,1,4,3,2,7]=>0000000=>0000000=>[8]
[1,8,6,3,4,2,5,7]=>1000000=>0000001=>[7,1]
[3,1,6,4,5,8,7,2]=>0000000=>0000000=>[8]
[8,2,7,6,1,4,3,5]=>0000000=>0000000=>[8]
[5,2,7,8,1,4,3,6]=>0000000=>0000000=>[8]
[5,2,3,7,1,6,8,4]=>0000000=>0000000=>[8]
[1,7,5,2,6,4,8,3]=>1000000=>0000001=>[7,1]
[7,1,3,6,8,2,4,5]=>0000000=>0000000=>[8]
[1,2,5,7,8,4,6,3]=>1100000=>0000011=>[6,1,1]
[3,1,2,7,5,4,8,6]=>0010000=>0000100=>[5,3]
[6,7,4,1,3,2,8,5]=>0000000=>0000000=>[8]
[1,7,2,8,4,3,5,6]=>1000000=>0000001=>[7,1]
[4,1,6,5,7,8,2,3]=>0000000=>0000000=>[8]
[1,6,3,5,7,8,2,4]=>1000000=>0000001=>[7,1]
[8,6,1,7,5,2,4,3]=>0000000=>0000000=>[8]
[7,6,4,1,8,3,2,5]=>0000000=>0000000=>[8]
[8,4,1,6,5,2,7,3]=>0000000=>0000000=>[8]
[1,5,3,4,7,8,2,6]=>1000000=>0000001=>[7,1]
[4,2,1,5,7,8,3,6]=>0000000=>0000000=>[8]
[5,1,4,6,7,8,2,3]=>0000000=>0000000=>[8]
[4,1,5,3,7,8,2,6]=>0000000=>0000000=>[8]
[8,1,4,6,5,2,7,3]=>0000000=>0000000=>[8]
[7,1,5,4,6,3,2,8]=>0000001=>1000000=>[1,7]
[8,2,1,6,7,5,4,3]=>0000000=>0000000=>[8]
[1,2,4,7,6,3,8,5]=>1100000=>0000011=>[6,1,1]
[6,7,4,1,8,5,2,3]=>0000000=>0000000=>[8]
[8,6,4,1,5,7,3,2]=>0000000=>0000000=>[8]
[5,2,4,3,7,1,6,8]=>0000001=>1000000=>[1,7]
[6,1,5,4,8,3,2,7]=>0000000=>0000000=>[8]
[1,2,8,7,4,3,6,5]=>1100000=>0000011=>[6,1,1]
[3,2,1,7,5,8,4,6]=>0010000=>0000100=>[5,3]
[8,1,7,6,4,2,5,3]=>0000000=>0000000=>[8]
[1,3,6,4,7,8,2,5]=>1000000=>0000001=>[7,1]
[5,1,3,4,7,8,2,6]=>0000000=>0000000=>[8]
[4,5,1,3,7,8,2,6]=>0000000=>0000000=>[8]
[5,2,3,1,7,8,4,6]=>0000000=>0000000=>[8]
[1,6,4,3,7,8,2,5]=>1000000=>0000001=>[7,1]
[7,6,4,3,1,5,2,8]=>0000001=>1000000=>[1,7]
[3,2,6,4,1,8,5,7]=>0000000=>0000000=>[8]
[7,5,4,6,1,3,2,8]=>0000001=>1000000=>[1,7]
[8,4,6,5,1,2,7,3]=>0000000=>0000000=>[8]
[1,5,6,3,7,8,2,4]=>1000000=>0000001=>[7,1]
[4,2,5,1,7,8,3,6]=>0000000=>0000000=>[8]
[4,7,8,1,6,5,3,2]=>0000000=>0000000=>[8]
[1,8,4,2,7,6,3,5]=>1000000=>0000001=>[7,1]
[3,7,2,8,1,5,4,6]=>0000000=>0000000=>[8]
[7,3,8,1,6,5,4,2]=>0000000=>0000000=>[8]
[2,4,1,8,7,3,6,5]=>0000000=>0000000=>[8]
[7,3,8,6,1,5,4,2]=>0000000=>0000000=>[8]
[3,5,1,7,8,2,6,4]=>0000000=>0000000=>[8]
[5,4,7,8,2,1,6,3]=>0000000=>0000000=>[8]
[6,4,7,1,5,3,2,8]=>0000001=>1000000=>[1,7]
[3,4,6,2,1,8,5,7]=>0000000=>0000000=>[8]
[5,6,4,8,3,2,1,7]=>0000000=>0000000=>[8]
[5,7,4,8,2,1,6,3]=>0000000=>0000000=>[8]
[4,7,5,8,2,1,6,3]=>0000000=>0000000=>[8]
[4,7,3,2,8,1,5,6]=>0000000=>0000000=>[8]
[7,1,2,6,3,8,5,4]=>0000000=>0000000=>[8]
[8,1,2,6,3,7,5,4]=>0000000=>0000000=>[8]
[8,1,2,7,6,3,5,4]=>0000000=>0000000=>[8]
[4,8,7,3,1,6,2,5]=>0000000=>0000000=>[8]
[4,7,8,3,1,6,2,5]=>0000000=>0000000=>[8]
[7,4,3,1,6,2,8,5]=>0000000=>0000000=>[8]
[3,7,6,2,4,8,1,5]=>0000000=>0000000=>[8]
[5,1,2,7,3,8,6,4]=>0000000=>0000000=>[8]
[6,1,2,7,3,5,8,4]=>0000000=>0000000=>[8]
[6,2,5,4,1,8,7,3]=>0000000=>0000000=>[8]
[4,6,3,2,1,8,7,5]=>0000000=>0000000=>[8]
[8,4,3,2,7,6,1,5]=>0000000=>0000000=>[8]
[1,5,8,4,7,6,3,2]=>1000000=>0000001=>[7,1]
[3,2,7,4,8,6,1,5]=>0000000=>0000000=>[8]
[7,4,3,2,8,6,1,5]=>0000000=>0000000=>[8]
[6,4,3,8,5,2,1,7]=>0000000=>0000000=>[8]
[8,2,5,4,7,6,1,3]=>0000000=>0000000=>[8]
[7,2,5,4,8,6,1,3]=>0000000=>0000000=>[8]
[6,2,8,7,5,4,1,3]=>0000000=>0000000=>[8]
[4,5,3,2,8,6,1,7]=>0000000=>0000000=>[8]
[3,2,5,4,8,6,1,7]=>0000000=>0000000=>[8]
[3,2,8,6,5,4,1,7]=>0000000=>0000000=>[8]
[8,4,3,6,5,2,1,7]=>0000000=>0000000=>[8]
[8,4,3,7,5,2,1,6]=>0000000=>0000000=>[8]
[3,2,7,8,5,4,1,6]=>0000000=>0000000=>[8]
[6,8,7,4,3,2,1,5]=>0000000=>0000000=>[8]
[6,3,2,1,8,7,4,5]=>0000000=>0000000=>[8]
[6,2,3,1,8,7,4,5]=>0000000=>0000000=>[8]
[3,4,8,1,7,5,6,2]=>0000000=>0000000=>[8]
[7,2,1,5,8,4,6,3]=>0000000=>0000000=>[8]
[3,7,4,1,5,8,6,2]=>0000000=>0000000=>[8]
[6,7,1,4,3,8,5,2]=>0000000=>0000000=>[8]
[8,5,3,6,1,7,4,2]=>0000000=>0000000=>[8]
[8,5,6,1,2,7,4,3]=>0000000=>0000000=>[8]
[3,6,1,5,7,8,2,4]=>0000000=>0000000=>[8]
[2,1,5,8,6,3,7,4]=>0100000=>0000010=>[6,2]
[3,7,8,5,4,1,6,2]=>0000000=>0000000=>[8]
[4,6,5,1,7,3,8,2]=>0000000=>0000000=>[8]
[5,7,3,1,2,4,8,6]=>0000000=>0000000=>[8]
[6,3,2,5,1,7,4,8]=>0000001=>1000000=>[1,7]
[6,3,1,7,2,5,8,4]=>0000000=>0000000=>[8]
[6,8,4,3,1,7,2,5]=>0000000=>0000000=>[8]
[4,8,1,3,7,5,6,2]=>0000000=>0000000=>[8]
[2,1,6,8,5,3,4,7]=>0100000=>0000010=>[6,2]
[4,5,1,3,8,6,7,2]=>0000000=>0000000=>[8]
[6,3,2,4,7,1,8,5]=>0000000=>0000000=>[8]
[5,7,6,3,8,1,2,4]=>0000000=>0000000=>[8]
[1,2,5,3,6,8,7,4]=>1100000=>0000011=>[6,1,1]
[7,1,5,6,2,3,8,4]=>0000000=>0000000=>[8]
[8,2,1,4,6,7,3,5]=>0000000=>0000000=>[8]
[7,2,6,1,3,4,8,5]=>0000000=>0000000=>[8]
[4,1,3,7,2,5,8,6]=>0000000=>0000000=>[8]
[6,2,7,5,1,3,8,4]=>0000000=>0000000=>[8]
[1,7,5,6,2,3,8,4]=>1000000=>0000001=>[7,1]
[3,7,6,1,2,4,8,5]=>0000000=>0000000=>[8]
[8,6,1,3,5,7,2,4]=>0000000=>0000000=>[8]
[1,7,4,3,8,2,5,6]=>1000000=>0000001=>[7,1]
[6,1,5,3,4,8,2,7]=>0000000=>0000000=>[8]
[3,6,7,5,2,8,1,4]=>0000000=>0000000=>[8]
[7,8,4,1,5,6,2,3]=>0000000=>0000000=>[8]
[5,8,1,3,6,7,2,4]=>0000000=>0000000=>[8]
[2,8,4,3,7,1,5,6]=>0000000=>0000000=>[8]
[3,8,4,6,7,1,2,5]=>0000000=>0000000=>[8]
[6,3,8,4,7,1,2,5]=>0000000=>0000000=>[8]
[1,2,5,4,8,3,6,7]=>1100000=>0000011=>[6,1,1]
[7,1,3,8,2,4,5,6]=>0000000=>0000000=>[8]
[8,1,3,7,2,4,5,6]=>0000000=>0000000=>[8]
[3,5,4,7,8,1,2,6]=>0000000=>0000000=>[8]
[8,3,1,4,7,2,5,6]=>0000000=>0000000=>[8]
[1,6,4,7,8,2,3,5]=>1000000=>0000001=>[7,1]
[1,3,7,8,5,6,2,4]=>1000000=>0000001=>[7,1]
[7,5,4,8,6,1,2,3]=>0000000=>0000000=>[8]
[8,2,6,7,5,1,3,4]=>0000000=>0000000=>[8]
[8,1,7,4,6,2,3,5]=>0000000=>0000000=>[8]
[2,5,8,4,7,1,3,6]=>0000000=>0000000=>[8]
[4,5,8,7,1,2,3,6]=>0000000=>0000000=>[8]
[4,1,8,5,7,2,3,6]=>0000000=>0000000=>[8]
[1,8,7,4,6,2,3,5]=>1000000=>0000001=>[7,1]
[2,6,5,4,1,8,3,7]=>0000000=>0000000=>[8]
[8,5,4,1,3,6,7,2]=>0000000=>0000000=>[8]
[8,4,7,6,5,3,1,2]=>0000000=>0000000=>[8]
[1,8,4,2,3,7,6,5]=>1000000=>0000001=>[7,1]
[2,3,1,8,7,6,4,5]=>0010000=>0000100=>[5,3]
[8,2,7,5,6,4,1,3]=>0000000=>0000000=>[8]
[1,8,4,7,6,5,2,3]=>1000000=>0000001=>[7,1]
[2,1,7,5,8,3,6,4]=>0100000=>0000010=>[6,2]
[2,6,3,5,8,7,4,1]=>0000000=>0000000=>[8]
[5,1,6,3,8,2,4,7]=>0000000=>0000000=>[8]
[4,3,5,8,2,1,6,7]=>0000000=>0000000=>[8]
[7,8,6,3,1,4,2,5]=>0000000=>0000000=>[8]
[6,5,3,7,2,4,8,1]=>0000000=>0000000=>[8]
[5,6,2,8,4,3,7,1]=>0000000=>0000000=>[8]
[4,6,2,7,8,3,5,1]=>0000000=>0000000=>[8]
[3,1,2,4,8,5,7,6]=>0011000=>0001100=>[4,1,3]
[4,6,3,5,2,8,7,1]=>0000000=>0000000=>[8]
[5,3,2,6,8,4,7,1]=>0000000=>0000000=>[8]
[5,6,3,4,8,2,7,1]=>0000000=>0000000=>[8]
[5,2,6,4,1,7,8,3]=>0000000=>0000000=>[8]
[5,8,4,6,3,2,7,1]=>0000000=>0000000=>[8]
[5,4,3,8,6,2,7,1]=>0000000=>0000000=>[8]
[5,7,8,2,4,3,6,1]=>0000000=>0000000=>[8]
[5,6,2,4,8,3,7,1]=>0000000=>0000000=>[8]
[5,4,2,8,6,3,7,1]=>0000000=>0000000=>[8]
[5,7,4,2,6,3,8,1]=>0000000=>0000000=>[8]
[6,4,7,8,2,3,5,1]=>0000000=>0000000=>[8]
[3,7,5,2,4,8,1,6]=>0000000=>0000000=>[8]
[4,7,5,2,3,8,6,1]=>0000000=>0000000=>[8]
[6,4,7,3,2,5,8,1]=>0000000=>0000000=>[8]
[6,3,7,8,2,4,5,1]=>0000000=>0000000=>[8]
[5,7,3,2,8,4,6,1]=>0000000=>0000000=>[8]
[5,3,7,2,8,4,6,1]=>0000000=>0000000=>[8]
[4,3,7,2,5,8,6,1]=>0000000=>0000000=>[8]
[4,7,3,2,5,8,6,1]=>0000000=>0000000=>[8]
[4,7,3,2,6,8,5,1]=>0000000=>0000000=>[8]
[7,5,3,2,6,4,8,1]=>0000000=>0000000=>[8]
[5,7,3,2,6,4,8,1]=>0000000=>0000000=>[8]
[5,3,2,8,6,4,7,1]=>0000000=>0000000=>[8]
[8,5,2,6,7,3,4,1]=>0000000=>0000000=>[8]
[8,4,2,6,3,7,5,1]=>0000000=>0000000=>[8]
[7,4,6,2,3,8,5,1]=>0000000=>0000000=>[8]
[7,5,6,2,8,3,4,1]=>0000000=>0000000=>[8]
[6,3,7,5,2,4,8,1]=>0000000=>0000000=>[8]
[5,7,6,2,8,3,4,1]=>0000000=>0000000=>[8]
[4,7,6,2,3,8,5,1]=>0000000=>0000000=>[8]
[7,6,3,2,5,8,1,4]=>0000000=>0000000=>[8]
[7,6,4,2,5,8,3,1]=>0000000=>0000000=>[8]
[4,8,3,7,1,6,5,2]=>0000000=>0000000=>[8]
[8,7,2,6,5,1,4,3]=>0000000=>0000000=>[8]
[5,8,3,2,1,7,6,4]=>0000000=>0000000=>[8]
[5,4,3,8,1,7,6,2]=>0000000=>0000000=>[8]
[6,5,3,8,7,1,4,2]=>0000000=>0000000=>[8]
[4,3,8,2,7,6,5,1]=>0000000=>0000000=>[8]
[4,8,2,7,6,5,3,1]=>0000000=>0000000=>[8]
[7,8,2,6,5,4,1,3]=>0000000=>0000000=>[8]
[3,8,7,6,2,5,1,4]=>0000000=>0000000=>[8]
[4,8,3,7,2,1,6,5]=>0000000=>0000000=>[8]
[8,6,3,1,7,5,4,2]=>0000000=>0000000=>[8]
[8,6,3,7,1,5,4,2]=>0000000=>0000000=>[8]
[4,8,3,7,6,2,5,1]=>0000000=>0000000=>[8]
[8,4,2,1,7,6,5,3]=>0000000=>0000000=>[8]
[1,6,4,2,5,3,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,6,7,2,5,3,4,8]=>1000001=>1000001=>[1,6,1]
[1,8,6,2,7,3,4,5]=>1000000=>0000001=>[7,1]
[1,5,2,6,4,3,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,5,2,4,6,3,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,8,6,2,3,7,4,5]=>1000000=>0000001=>[7,1]
[1,5,2,8,6,3,4,7]=>1000000=>0000001=>[7,1]
[1,7,3,2,6,8,4,5]=>1000000=>0000001=>[7,1]
[1,3,6,8,2,7,4,5]=>1000000=>0000001=>[7,1]
[1,4,3,8,2,5,6,7]=>1000000=>0000001=>[7,1]
[1,7,2,3,8,5,4,6]=>1000000=>0000001=>[7,1]
[1,6,2,8,5,4,3,7]=>1000000=>0000001=>[7,1]
[1,7,2,3,8,6,4,5]=>1000000=>0000001=>[7,1]
[1,5,3,8,2,7,4,6]=>1000000=>0000001=>[7,1]
[1,7,2,5,3,4,8,6]=>1000000=>0000001=>[7,1]
[1,4,8,2,5,6,3,7]=>1000000=>0000001=>[7,1]
[1,2,7,3,6,8,4,5]=>1100000=>0000011=>[6,1,1]
[1,7,2,3,6,8,4,5]=>1000000=>0000001=>[7,1]
[1,4,8,3,2,5,6,7]=>1000000=>0000001=>[7,1]
[1,7,2,5,8,3,4,6]=>1000000=>0000001=>[7,1]
[1,5,6,3,4,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,5,3,6,4,2,7,8]=>1000011=>1100001=>[1,1,5,1]
[2,5,7,4,1,3,8,6]=>0000000=>0000000=>[8]
[3,5,6,1,8,7,2,4]=>0000000=>0000000=>[8]
[2,4,6,8,7,3,1,5]=>0000000=>0000000=>[8]
[7,2,4,8,6,3,1,5]=>0000000=>0000000=>[8]
[8,5,3,6,2,1,7,4]=>0000000=>0000000=>[8]
[4,5,7,3,1,2,8,6]=>0000000=>0000000=>[8]
[4,5,1,8,3,2,7,6]=>0000000=>0000000=>[8]
[2,5,3,8,4,1,7,6]=>0000000=>0000000=>[8]
[2,6,4,5,8,1,3,7]=>0000000=>0000000=>[8]
[6,4,1,3,5,8,2,7]=>0000000=>0000000=>[8]
[3,1,6,4,8,7,5,2]=>0000000=>0000000=>[8]
[4,2,6,1,3,7,8,5]=>0000000=>0000000=>[8]
[8,5,4,2,7,6,3,1]=>0000000=>0000000=>[8]
[2,8,4,6,7,1,3,5]=>0000000=>0000000=>[8]
[5,8,2,1,4,6,7,3]=>0000000=>0000000=>[8]
[3,6,7,1,8,2,5,4]=>0000000=>0000000=>[8]
[3,1,5,7,2,8,6,4]=>0000000=>0000000=>[8]
[4,1,8,3,2,7,6,5]=>0000000=>0000000=>[8]
[3,8,2,4,7,1,6,5]=>0000000=>0000000=>[8]
[3,2,4,8,7,1,6,5]=>0000000=>0000000=>[8]
[3,2,5,7,1,8,6,4]=>0000000=>0000000=>[8]
[4,2,8,3,1,7,6,5]=>0000000=>0000000=>[8]
[4,8,2,1,3,7,6,5]=>0000000=>0000000=>[8]
[4,2,8,1,3,7,6,5]=>0000000=>0000000=>[8]
[2,3,4,6,8,7,1,5]=>0000000=>0000000=>[8]
[6,7,2,8,3,1,4,5]=>0000000=>0000000=>[8]
[6,3,7,8,4,1,2,5]=>0000000=>0000000=>[8]
[7,6,2,3,1,8,4,5]=>0000000=>0000000=>[8]
[2,3,7,8,5,4,1,6]=>0000000=>0000000=>[8]
[2,8,7,4,5,1,6,3]=>0000000=>0000000=>[8]
[1,3,8,5,2,6,7,4]=>1000000=>0000001=>[7,1]
[8,6,2,4,1,5,7,3]=>0000000=>0000000=>[8]
[1,6,4,3,2,7,8,5]=>1000000=>0000001=>[7,1]
[8,5,3,2,1,6,7,4]=>0000000=>0000000=>[8]
[8,5,3,2,1,6,4,7]=>0000000=>0000000=>[8]
[8,7,6,1,5,2,3,4]=>0000000=>0000000=>[8]
[8,7,5,1,3,6,2,4]=>0000000=>0000000=>[8]
[8,3,2,7,4,6,5,1]=>0000000=>0000000=>[8]
[7,4,8,2,6,3,1,5]=>0000000=>0000000=>[8]
[8,7,3,1,4,6,5,2]=>0000000=>0000000=>[8]
[8,7,3,1,6,2,5,4]=>0000000=>0000000=>[8]
[8,7,3,2,6,1,5,4]=>0000000=>0000000=>[8]
[1,4,8,6,7,5,3,2]=>1000000=>0000001=>[7,1]
[7,1,3,6,8,5,4,2]=>0000000=>0000000=>[8]
[6,7,2,5,8,1,4,3]=>0000000=>0000000=>[8]
[6,5,7,3,8,1,4,2]=>0000000=>0000000=>[8]
[6,3,7,4,8,1,5,2]=>0000000=>0000000=>[8]
[6,2,7,4,8,1,5,3]=>0000000=>0000000=>[8]
[7,2,1,5,3,8,6,4]=>0000000=>0000000=>[8]
[5,8,2,7,6,1,3,4]=>0000000=>0000000=>[8]
[4,2,3,1,5,8,6,7]=>0001100=>0011000=>[3,1,4]
[1,8,3,6,7,4,2,5]=>1000000=>0000001=>[7,1]
[8,1,7,2,5,6,4,3]=>0000000=>0000000=>[8]
[8,1,3,5,2,7,6,4]=>0000000=>0000000=>[8]
[8,1,7,4,3,6,5,2]=>0000000=>0000000=>[8]
[2,7,1,5,4,8,6,3]=>0000000=>0000000=>[8]
[8,6,2,4,3,7,5,1]=>0000000=>0000000=>[8]
[8,1,4,5,6,3,7,2]=>0000000=>0000000=>[8]
[8,1,4,5,6,2,7,3]=>0000000=>0000000=>[8]
[8,1,4,7,6,2,5,3]=>0000000=>0000000=>[8]
[2,5,1,7,8,6,4,3]=>0000000=>0000000=>[8]
[3,5,6,2,8,7,4,1]=>0000000=>0000000=>[8]
[3,5,6,1,8,7,4,2]=>0000000=>0000000=>[8]
[2,4,5,1,7,6,3,8]=>0000001=>1000000=>[1,7]
[7,3,1,5,6,4,2,8]=>0000001=>1000000=>[1,7]
[8,6,2,4,7,3,1,5]=>0000000=>0000000=>[8]
[8,4,7,3,5,2,1,6]=>0000000=>0000000=>[8]
[8,4,5,3,7,6,2,1]=>0000000=>0000000=>[8]
[3,4,5,6,2,8,1,7]=>0000000=>0000000=>[8]
[3,7,4,2,8,5,1,6]=>0000000=>0000000=>[8]
[7,3,4,1,6,8,2,5]=>0000000=>0000000=>[8]
[2,6,3,1,4,7,5,8]=>0000001=>1000000=>[1,7]
[7,2,1,6,3,4,8,5]=>0000000=>0000000=>[8]
[7,3,4,1,6,5,8,2]=>0000000=>0000000=>[8]
[3,7,4,2,5,8,6,1]=>0000000=>0000000=>[8]
[2,3,5,1,4,8,7,6]=>0000100=>0010000=>[3,5]
[2,7,1,3,6,8,5,4]=>0000000=>0000000=>[8]
[2,7,1,3,8,4,6,5]=>0000000=>0000000=>[8]
[3,8,7,1,6,2,5,4]=>0000000=>0000000=>[8]
[3,8,7,1,4,5,2,6]=>0000000=>0000000=>[8]
[3,7,4,2,1,8,6,5]=>0000000=>0000000=>[8]
[4,8,5,7,2,6,3,1]=>0000000=>0000000=>[8]
[8,4,5,7,3,2,6,1]=>0000000=>0000000=>[8]
[8,3,7,2,4,1,5,6]=>0000000=>0000000=>[8]
[8,6,7,2,1,4,3,5]=>0000000=>0000000=>[8]
[8,3,7,5,1,2,6,4]=>0000000=>0000000=>[8]
[7,3,4,6,2,1,5,8]=>0000001=>1000000=>[1,7]
[3,7,4,6,1,5,2,8]=>0000001=>1000000=>[1,7]
[3,4,7,6,1,2,8,5]=>0000000=>0000000=>[8]
[4,5,8,7,6,1,3,2]=>0000000=>0000000=>[8]
[8,7,3,5,6,1,4,2]=>0000000=>0000000=>[8]
[8,5,2,7,6,1,3,4]=>0000000=>0000000=>[8]
[6,4,7,2,1,5,8,3]=>0000000=>0000000=>[8]
[8,5,3,1,6,4,7,2]=>0000000=>0000000=>[8]
[7,4,8,2,6,1,5,3]=>0000000=>0000000=>[8]
[8,5,3,1,6,4,2,7]=>0000000=>0000000=>[8]
[8,7,3,1,4,2,5,6]=>0000000=>0000000=>[8]
[8,7,4,1,2,5,3,6]=>0000000=>0000000=>[8]
[1,6,7,3,2,8,4,5]=>1000000=>0000001=>[7,1]
[1,4,6,2,8,5,3,7]=>1000000=>0000001=>[7,1]
[1,5,6,2,8,4,3,7]=>1000000=>0000001=>[7,1]
[3,4,8,6,5,7,2,1]=>0000000=>0000000=>[8]
[2,3,8,6,7,1,5,4]=>0000000=>0000000=>[8]
[1,2,5,7,4,6,8,3]=>1100000=>0000011=>[6,1,1]
[1,2,4,7,6,8,3,5]=>1100000=>0000011=>[6,1,1]
[1,8,3,5,6,2,7,4]=>1000000=>0000001=>[7,1]
[4,2,5,1,6,8,7,3]=>0000000=>0000000=>[8]
[5,4,2,7,8,6,1,3]=>0000000=>0000000=>[8]
[6,7,2,8,1,3,4,5]=>0000000=>0000000=>[8]
[1,7,8,5,2,6,3,4]=>1000000=>0000001=>[7,1]
[7,6,2,4,8,1,5,3]=>0000000=>0000000=>[8]
[4,8,3,1,7,6,5,2]=>0000000=>0000000=>[8]
[5,3,8,7,1,6,4,2]=>0000000=>0000000=>[8]
[5,8,7,3,1,6,4,2]=>0000000=>0000000=>[8]
[5,3,8,2,1,7,6,4]=>0000000=>0000000=>[8]
[3,8,7,2,6,5,1,4]=>0000000=>0000000=>[8]
[7,4,1,8,6,5,3,2]=>0000000=>0000000=>[8]
[5,4,2,8,1,7,6,3]=>0000000=>0000000=>[8]
[5,8,4,7,1,6,3,2]=>0000000=>0000000=>[8]
[8,5,6,1,4,7,2,3]=>0000000=>0000000=>[8]
[6,7,4,1,2,5,8,3]=>0000000=>0000000=>[8]
[3,6,7,5,8,1,2,4]=>0000000=>0000000=>[8]
[6,5,8,7,4,2,3,1]=>0000000=>0000000=>[8]
[6,1,7,3,8,5,2,4]=>0000000=>0000000=>[8]
[4,6,5,8,7,3,1,2]=>0000000=>0000000=>[8]
[8,4,5,1,7,6,2,3]=>0000000=>0000000=>[8]
[8,5,6,1,7,2,4,3]=>0000000=>0000000=>[8]
[7,5,6,1,3,8,4,2]=>0000000=>0000000=>[8]
[5,7,6,1,3,8,4,2]=>0000000=>0000000=>[8]
[6,7,1,4,2,8,5,3]=>0000000=>0000000=>[8]
[2,1,6,4,8,3,7,5]=>0100000=>0000010=>[6,2]
[7,4,5,1,3,8,6,2]=>0000000=>0000000=>[8]
[5,8,7,4,6,2,3,1]=>0000000=>0000000=>[8]
[6,4,8,1,5,7,3,2]=>0000000=>0000000=>[8]
[2,4,7,8,5,6,1,3]=>0000000=>0000000=>[8]
[3,4,6,8,2,1,7,5]=>0000000=>0000000=>[8]
[2,8,7,1,4,3,6,5]=>0000000=>0000000=>[8]
[1,2,7,8,4,3,6,5]=>1100000=>0000011=>[6,1,1]
[2,8,5,4,1,3,7,6]=>0000000=>0000000=>[8]
[5,4,6,3,1,7,2,8]=>0000001=>1000000=>[1,7]
[1,4,8,3,6,5,2,7]=>1000000=>0000001=>[7,1]
[1,2,8,6,4,3,7,5]=>1100000=>0000011=>[6,1,1]
[6,5,1,8,7,4,3,2]=>0000000=>0000000=>[8]
[7,5,1,8,6,4,3,2]=>0000000=>0000000=>[8]
[8,5,1,7,6,4,3,2]=>0000000=>0000000=>[8]
[8,5,3,7,6,1,4,2]=>0000000=>0000000=>[8]
[3,8,7,6,1,5,4,2]=>0000000=>0000000=>[8]
[8,5,2,6,1,4,7,3]=>0000000=>0000000=>[8]
[2,7,5,8,1,4,6,3]=>0000000=>0000000=>[8]
[8,5,6,1,7,3,2,4]=>0000000=>0000000=>[8]
[3,2,6,7,1,8,5,4]=>0000000=>0000000=>[8]
[3,4,6,7,8,2,1,5]=>0000000=>0000000=>[8]
[6,7,1,3,8,5,4,2]=>0000000=>0000000=>[8]
[1,6,2,7,8,5,3,4]=>1000000=>0000001=>[7,1]
[1,2,6,7,8,5,3,4]=>1100000=>0000011=>[6,1,1]
[1,6,7,4,8,3,2,5]=>1000000=>0000001=>[7,1]
[3,7,2,1,8,4,6,5]=>0000000=>0000000=>[8]
[3,7,2,4,1,8,6,5]=>0000000=>0000000=>[8]
[3,2,6,4,8,7,5,1]=>0000000=>0000000=>[8]
[4,7,2,8,6,5,1,3]=>0000000=>0000000=>[8]
[4,7,1,8,6,5,3,2]=>0000000=>0000000=>[8]
[2,7,4,8,3,6,1,5]=>0000000=>0000000=>[8]
[4,7,3,8,6,1,5,2]=>0000000=>0000000=>[8]
[4,7,3,8,6,2,1,5]=>0000000=>0000000=>[8]
[4,3,6,8,7,2,5,1]=>0000000=>0000000=>[8]
[4,3,8,2,5,7,6,1]=>0000000=>0000000=>[8]
[4,3,8,1,5,7,6,2]=>0000000=>0000000=>[8]
[4,1,2,6,8,7,5,3]=>0000000=>0000000=>[8]
[2,4,3,6,8,7,1,5]=>0000000=>0000000=>[8]
[3,1,6,4,8,7,2,5]=>0000000=>0000000=>[8]
[4,1,6,8,7,5,2,3]=>0000000=>0000000=>[8]
[3,8,1,4,5,7,2,6]=>0000000=>0000000=>[8]
[3,8,1,4,2,5,7,6]=>0000000=>0000000=>[8]
[4,1,8,3,5,2,7,6]=>0000000=>0000000=>[8]
[4,2,3,6,8,7,1,5]=>0000000=>0000000=>[8]
[4,2,8,3,5,7,6,1]=>0000000=>0000000=>[8]
[3,8,2,4,5,7,6,1]=>0000000=>0000000=>[8]
[3,8,2,4,1,5,7,6]=>0000000=>0000000=>[8]
[3,8,2,5,1,4,7,6]=>0000000=>0000000=>[8]
[4,2,8,5,7,1,3,6]=>0000000=>0000000=>[8]
[3,8,1,5,2,4,7,6]=>0000000=>0000000=>[8]
[7,3,2,1,4,6,5,8]=>0000001=>1000000=>[1,7]
[2,7,1,3,5,6,8,4]=>0000000=>0000000=>[8]
[2,3,6,1,5,8,7,4]=>0000000=>0000000=>[8]
[4,5,2,3,8,6,7,1]=>0000000=>0000000=>[8]
[4,8,5,3,2,6,7,1]=>0000000=>0000000=>[8]
[6,4,1,8,5,2,7,3]=>0000000=>0000000=>[8]
[2,6,1,8,5,4,7,3]=>0000000=>0000000=>[8]
[3,1,6,8,5,4,7,2]=>0000000=>0000000=>[8]
[7,5,6,1,2,3,8,4]=>0000000=>0000000=>[8]
[1,5,7,6,3,2,8,4]=>1000000=>0000001=>[7,1]
[7,5,2,1,4,3,8,6]=>0000000=>0000000=>[8]
[3,1,7,8,5,4,2,6]=>0000000=>0000000=>[8]
[7,6,4,8,3,1,2,5]=>0000000=>0000000=>[8]
[6,2,8,5,1,3,4,7]=>0000000=>0000000=>[8]
[3,2,7,8,6,1,4,5]=>0000000=>0000000=>[8]
[6,8,2,5,1,3,7,4]=>0000000=>0000000=>[8]
[6,7,4,2,1,5,3,8]=>0000001=>1000000=>[1,7]
[5,7,4,1,6,8,2,3]=>0000000=>0000000=>[8]
[5,6,8,1,3,7,2,4]=>0000000=>0000000=>[8]
[3,7,4,8,6,1,2,5]=>0000000=>0000000=>[8]
[1,6,8,5,3,2,4,7]=>1000000=>0000001=>[7,1]
[7,2,8,4,6,1,3,5]=>0000000=>0000000=>[8]
[7,1,3,4,6,2,8,5]=>0000000=>0000000=>[8]
[5,8,7,4,2,1,3,6]=>0000000=>0000000=>[8]
[1,8,7,3,2,5,4,6]=>1000000=>0000001=>[7,1]
[1,2,5,4,8,7,3,6]=>1100000=>0000011=>[6,1,1]
[1,2,4,8,6,3,5,7]=>1100000=>0000011=>[6,1,1]
[1,7,3,4,2,6,8,5]=>1000000=>0000001=>[7,1]
[1,6,3,5,8,4,2,7]=>1000000=>0000001=>[7,1]
[1,8,5,7,6,3,2,4]=>1000000=>0000001=>[7,1]
[1,6,3,5,7,8,4,2]=>1000000=>0000001=>[7,1]
[7,6,2,5,3,4,1,8]=>0000001=>1000000=>[1,7]
[7,6,2,4,5,3,1,8]=>0000001=>1000000=>[1,7]
[7,6,2,4,3,5,1,8]=>0000001=>1000000=>[1,7]
[7,6,2,3,5,4,1,8]=>0000001=>1000000=>[1,7]
[8,4,2,7,1,6,3,5]=>0000000=>0000000=>[8]
[8,7,6,1,5,3,2,4]=>0000000=>0000000=>[8]
[8,7,6,1,3,5,4,2]=>0000000=>0000000=>[8]
[8,7,6,1,5,4,2,3]=>0000000=>0000000=>[8]
[4,5,3,8,2,1,6,7]=>0000000=>0000000=>[8]
[7,5,8,2,1,4,3,6]=>0000000=>0000000=>[8]
[8,7,6,1,2,5,3,4]=>0000000=>0000000=>[8]
[8,7,6,1,2,5,4,3]=>0000000=>0000000=>[8]
[8,7,6,1,4,2,5,3]=>0000000=>0000000=>[8]
[6,1,4,8,5,2,7,3]=>0000000=>0000000=>[8]
[3,1,6,8,5,2,7,4]=>0000000=>0000000=>[8]
[5,8,2,7,3,4,1,6]=>0000000=>0000000=>[8]
[5,3,8,1,6,7,4,2]=>0000000=>0000000=>[8]
[4,8,2,1,3,5,6,7]=>0000000=>0000000=>[8]
[5,1,8,3,6,7,4,2]=>0000000=>0000000=>[8]
[8,4,1,6,5,2,3,7]=>0000000=>0000000=>[8]
[6,8,7,3,2,4,1,5]=>0000000=>0000000=>[8]
[3,2,4,7,5,8,1,6]=>0000000=>0000000=>[8]
[1,2,7,4,6,3,8,5]=>1100000=>0000011=>[6,1,1]
[2,8,7,6,4,5,1,3]=>0000000=>0000000=>[8]
[3,5,7,6,1,8,4,2]=>0000000=>0000000=>[8]
[3,5,7,6,2,8,4,1]=>0000000=>0000000=>[8]
[5,3,6,2,8,7,4,1]=>0000000=>0000000=>[8]
[5,8,3,1,7,6,4,2]=>0000000=>0000000=>[8]
[6,2,3,8,7,5,4,1]=>0000000=>0000000=>[8]
[4,1,3,5,8,7,6,2]=>0000000=>0000000=>[8]
[4,2,5,3,7,6,1,8]=>0000001=>1000000=>[1,7]
[6,2,4,3,7,5,1,8]=>0000001=>1000000=>[1,7]
[1,3,6,4,7,5,2,8]=>1000001=>1000001=>[1,6,1]
[8,2,5,3,6,4,1,7]=>0000000=>0000000=>[8]
[7,2,5,3,6,4,1,8]=>0000001=>1000000=>[1,7]
[6,2,5,3,7,4,1,8]=>0000001=>1000000=>[1,7]
[4,2,6,3,7,5,1,8]=>0000001=>1000000=>[1,7]
[5,2,7,3,6,4,1,8]=>0000001=>1000000=>[1,7]
[7,3,6,2,5,4,1,8]=>0000001=>1000000=>[1,7]
[6,3,8,2,5,4,1,7]=>0000000=>0000000=>[8]
[7,3,1,4,6,5,2,8]=>0000001=>1000000=>[1,7]
[8,3,7,2,5,4,1,6]=>0000000=>0000000=>[8]
[5,2,8,3,6,4,1,7]=>0000000=>0000000=>[8]
[4,2,8,3,6,5,1,7]=>0000000=>0000000=>[8]
[3,2,8,4,6,5,1,7]=>0000000=>0000000=>[8]
[1,4,7,3,6,5,2,8]=>1000001=>1000001=>[1,6,1]
[8,2,5,4,1,6,3,7]=>0000000=>0000000=>[8]
[1,3,6,5,2,7,4,8]=>1000001=>1000001=>[1,6,1]
[8,2,6,4,1,5,3,7]=>0000000=>0000000=>[8]
[1,4,8,3,7,5,2,6]=>1000000=>0000001=>[7,1]
[6,2,1,4,8,5,3,7]=>0000000=>0000000=>[8]
[5,2,1,4,8,6,3,7]=>0000000=>0000000=>[8]
[3,2,1,5,8,6,4,7]=>0010000=>0000100=>[5,3]
[4,2,8,3,7,5,1,6]=>0000000=>0000000=>[8]
[5,2,8,3,7,4,1,6]=>0000000=>0000000=>[8]
[8,3,7,2,6,4,1,5]=>0000000=>0000000=>[8]
[7,3,1,4,8,5,2,6]=>0000000=>0000000=>[8]
[1,3,7,4,8,5,2,6]=>1000000=>0000001=>[7,1]
[8,2,6,3,7,4,1,5]=>0000000=>0000000=>[8]
[7,2,6,3,8,4,1,5]=>0000000=>0000000=>[8]
[5,2,7,3,8,4,1,6]=>0000000=>0000000=>[8]
[3,2,7,4,8,5,1,6]=>0000000=>0000000=>[8]
[5,2,6,3,8,4,1,7]=>0000000=>0000000=>[8]
[6,2,5,3,8,4,1,7]=>0000000=>0000000=>[8]
[7,2,5,3,8,4,1,6]=>0000000=>0000000=>[8]
[8,2,5,3,7,4,1,6]=>0000000=>0000000=>[8]
[1,3,6,4,8,5,2,7]=>1000000=>0000001=>[7,1]
[1,3,5,4,8,6,2,7]=>1000000=>0000001=>[7,1]
[8,2,4,3,7,5,1,6]=>0000000=>0000000=>[8]
[7,2,4,3,8,5,1,6]=>0000000=>0000000=>[8]
[6,2,4,3,8,5,1,7]=>0000000=>0000000=>[8]
[5,2,4,3,8,6,1,7]=>0000000=>0000000=>[8]
[4,2,5,3,8,6,1,7]=>0000000=>0000000=>[8]
[4,2,5,3,1,7,6,8]=>0000101=>1010000=>[1,2,5]
[6,2,4,3,1,7,5,8]=>0000001=>1000000=>[1,7]
[7,2,4,3,1,6,5,8]=>0000001=>1000000=>[1,7]
[8,5,1,3,6,4,2,7]=>0000000=>0000000=>[8]
[8,4,1,3,6,5,2,7]=>0000000=>0000000=>[8]
[1,5,2,4,7,6,3,8]=>1000001=>1000001=>[1,6,1]
[7,2,5,3,1,6,4,8]=>0000001=>1000000=>[1,7]
[6,2,5,3,1,7,4,8]=>0000001=>1000000=>[1,7]
[4,2,6,3,1,7,5,8]=>0000001=>1000000=>[1,7]
[3,2,6,4,1,7,5,8]=>0000001=>1000000=>[1,7]
[5,2,7,3,1,6,4,8]=>0000001=>1000000=>[1,7]
[6,2,7,3,1,5,4,8]=>0000001=>1000000=>[1,7]
[7,2,6,3,1,5,4,8]=>0000001=>1000000=>[1,7]
[1,5,2,4,8,6,3,7]=>1000000=>0000001=>[7,1]
[8,4,1,3,7,5,2,6]=>0000000=>0000000=>[8]
[6,2,1,5,3,7,4,8]=>0000001=>1000000=>[1,7]
[3,2,1,6,4,7,5,8]=>0010001=>1000100=>[1,4,3]
[3,2,8,5,1,6,4,7]=>0000000=>0000000=>[8]
[4,2,8,5,1,6,3,7]=>0000000=>0000000=>[8]
[6,2,8,4,1,5,3,7]=>0000000=>0000000=>[8]
[1,4,8,5,2,6,3,7]=>1000000=>0000001=>[7,1]
[8,3,7,4,1,5,2,6]=>0000000=>0000000=>[8]
[7,1,3,2,5,6,4,8]=>0000001=>1000000=>[1,7]
[1,5,2,8,7,4,3,6]=>1000000=>0000001=>[7,1]
[5,7,2,8,1,4,3,6]=>0000000=>0000000=>[8]
[2,7,1,5,6,4,3,8]=>0000001=>1000000=>[1,7]
[1,7,3,4,5,2,8,6]=>1000000=>0000001=>[7,1]
[3,2,1,7,8,5,4,6]=>0010000=>0000100=>[5,3]
[1,7,6,3,2,4,8,5]=>1000000=>0000001=>[7,1]
[1,8,5,3,2,4,7,6]=>1000000=>0000001=>[7,1]
[2,6,1,5,4,7,3,8]=>0000001=>1000000=>[1,7]
[1,3,8,5,4,2,6,7]=>1000000=>0000001=>[7,1]
[2,3,6,8,4,1,7,5]=>0000000=>0000000=>[8]
[1,7,2,8,6,3,5,4]=>1000000=>0000001=>[7,1]
[4,2,7,6,1,8,5,3]=>0000000=>0000000=>[8]
[7,3,2,1,6,4,8,5]=>0000000=>0000000=>[8]
[6,7,2,4,3,5,8,1]=>0000000=>0000000=>[8]
[4,3,8,2,1,5,7,6]=>0000000=>0000000=>[8]
[4,3,2,8,1,6,7,5]=>0000000=>0000000=>[8]
[4,5,8,3,2,7,1,6]=>0000000=>0000000=>[8]
[4,3,8,2,1,6,7,5]=>0000000=>0000000=>[8]
[4,6,7,2,5,3,8,1]=>0000000=>0000000=>[8]
[6,4,7,8,3,1,5,2]=>0000000=>0000000=>[8]
[5,6,7,1,8,3,4,2]=>0000000=>0000000=>[8]
[7,1,8,6,2,5,4,3]=>0000000=>0000000=>[8]
[1,5,8,2,6,4,7,3]=>1000000=>0000001=>[7,1]
[1,5,7,4,6,8,3,2]=>1000000=>0000001=>[7,1]
[3,1,8,6,5,2,7,4]=>0000000=>0000000=>[8]
[2,3,7,6,5,8,1,4]=>0000000=>0000000=>[8]
[2,3,7,6,5,1,8,4]=>0000000=>0000000=>[8]
[7,3,5,2,1,6,8,4]=>0000000=>0000000=>[8]
[1,5,4,7,8,6,2,3]=>1000000=>0000001=>[7,1]
[3,6,2,1,4,7,8,5]=>0000000=>0000000=>[8]
[6,3,8,7,5,4,2,1]=>0000000=>0000000=>[8]
[6,8,2,7,5,4,3,1]=>0000000=>0000000=>[8]
[5,8,1,7,6,4,3,2]=>0000000=>0000000=>[8]
[4,2,6,3,8,5,7,1]=>0000000=>0000000=>[8]
[8,2,7,4,5,1,6,3]=>0000000=>0000000=>[8]
[1,7,5,2,4,8,6,3]=>1000000=>0000001=>[7,1]
[7,2,8,5,3,1,6,4]=>0000000=>0000000=>[8]
[4,7,6,1,5,8,3,2]=>0000000=>0000000=>[8]
[5,4,7,3,8,2,1,6]=>0000000=>0000000=>[8]
[4,3,5,7,2,6,1,8]=>0000001=>1000000=>[1,7]
[1,7,2,8,5,4,3,6]=>1000000=>0000001=>[7,1]
[5,4,8,3,6,2,1,7]=>0000000=>0000000=>[8]
[4,7,3,2,5,1,6,8]=>0000001=>1000000=>[1,7]
[4,2,5,3,8,7,1,6]=>0000000=>0000000=>[8]
[6,7,3,2,5,4,1,8]=>0000001=>1000000=>[1,7]
[4,5,6,2,7,3,1,8]=>0000001=>1000000=>[1,7]
[7,4,8,6,5,1,2,3]=>0000000=>0000000=>[8]
[4,5,8,2,7,3,1,6]=>0000000=>0000000=>[8]
[6,5,8,2,7,3,1,4]=>0000000=>0000000=>[8]
[6,4,8,2,7,3,1,5]=>0000000=>0000000=>[8]
[7,8,1,3,6,4,2,5]=>0000000=>0000000=>[8]
[4,5,7,8,3,2,1,6]=>0000000=>0000000=>[8]
[5,3,7,2,1,8,6,4]=>0000000=>0000000=>[8]
[5,4,3,7,2,1,6,8]=>0000001=>1000000=>[1,7]
[5,4,3,7,8,2,1,6]=>0000000=>0000000=>[8]
[6,1,3,5,8,7,4,2]=>0000000=>0000000=>[8]
[6,8,5,7,3,4,2,1]=>0000000=>0000000=>[8]
[5,3,6,8,4,2,1,7]=>0000000=>0000000=>[8]
[5,1,6,8,4,7,3,2]=>0000000=>0000000=>[8]
[6,2,8,3,4,1,5,7]=>0000000=>0000000=>[8]
[2,4,1,8,7,6,3,5]=>0000000=>0000000=>[8]
[1,3,5,8,4,7,2,6]=>1000000=>0000001=>[7,1]
[2,3,8,7,5,1,6,4]=>0000000=>0000000=>[8]
[8,5,4,7,6,1,3,2]=>0000000=>0000000=>[8]
[5,8,7,2,4,1,3,6]=>0000000=>0000000=>[8]
[4,1,3,5,6,2,8,7]=>0000010=>0100000=>[2,6]
[6,3,8,5,1,7,4,2]=>0000000=>0000000=>[8]
[5,2,4,6,1,3,8,7]=>0000010=>0100000=>[2,6]
[8,2,4,6,1,3,7,5]=>0000000=>0000000=>[8]
[6,4,8,7,3,5,2,1]=>0000000=>0000000=>[8]
[8,2,3,5,6,1,4,7]=>0000000=>0000000=>[8]
[4,3,5,6,8,2,7,1]=>0000000=>0000000=>[8]
[8,2,3,4,6,1,7,5]=>0000000=>0000000=>[8]
[1,7,4,3,5,2,8,6]=>1000000=>0000001=>[7,1]
[2,7,4,3,8,1,5,6]=>0000000=>0000000=>[8]
[5,3,6,2,1,8,4,7]=>0000000=>0000000=>[8]
[4,3,8,6,2,7,1,5]=>0000000=>0000000=>[8]
[8,2,1,4,6,3,7,5]=>0000000=>0000000=>[8]
[3,1,6,8,2,7,5,4]=>0000000=>0000000=>[8]
[5,3,8,6,7,2,1,4]=>0000000=>0000000=>[8]
[5,8,7,2,4,6,1,3]=>0000000=>0000000=>[8]
[1,5,2,8,7,6,4,3]=>1000000=>0000001=>[7,1]
[2,7,1,4,6,5,3,8]=>0000001=>1000000=>[1,7]
[4,7,1,2,6,5,8,3]=>0000000=>0000000=>[8]
[3,2,4,5,1,8,6,7]=>0000100=>0010000=>[3,5]
[4,2,5,6,8,7,3,1]=>0000000=>0000000=>[8]
[8,2,5,1,6,3,7,4]=>0000000=>0000000=>[8]
[8,3,4,5,1,6,7,2]=>0000000=>0000000=>[8]
[3,5,7,6,4,8,1,2]=>0000000=>0000000=>[8]
[1,3,7,8,5,4,6,2]=>1000000=>0000001=>[7,1]
[7,2,8,6,5,1,4,3]=>0000000=>0000000=>[8]
[4,2,7,5,3,1,8,6]=>0000000=>0000000=>[8]
[7,3,2,5,4,1,8,6]=>0000000=>0000000=>[8]
[3,6,4,1,8,2,7,5]=>0000000=>0000000=>[8]
[4,6,3,8,7,2,1,5]=>0000000=>0000000=>[8]
[4,3,5,1,8,7,2,6]=>0000000=>0000000=>[8]
[7,5,2,8,4,3,1,6]=>0000000=>0000000=>[8]
[1,7,2,4,5,3,6,8]=>1000001=>1000001=>[1,6,1]
[1,7,4,5,3,2,6,8]=>1000001=>1000001=>[1,6,1]
[1,6,4,7,3,5,2,8]=>1000001=>1000001=>[1,6,1]
[8,3,5,6,1,4,7,2]=>0000000=>0000000=>[8]
[1,6,4,7,5,2,3,8]=>1000001=>1000001=>[1,6,1]
[1,5,2,6,7,4,3,8]=>1000001=>1000001=>[1,6,1]
[8,5,6,1,4,3,7,2]=>0000000=>0000000=>[8]
[5,4,7,8,3,1,2,6]=>0000000=>0000000=>[8]
[2,5,4,7,8,3,1,6]=>0000000=>0000000=>[8]
[6,4,5,8,2,3,1,7]=>0000000=>0000000=>[8]
[8,6,1,3,2,5,7,4]=>0000000=>0000000=>[8]
[7,5,8,1,4,6,3,2]=>0000000=>0000000=>[8]
[4,2,6,7,8,1,5,3]=>0000000=>0000000=>[8]
[3,4,6,7,8,1,5,2]=>0000000=>0000000=>[8]
[4,3,2,7,5,8,1,6]=>0000000=>0000000=>[8]
[4,8,5,3,2,6,1,7]=>0000000=>0000000=>[8]
[2,8,4,5,3,6,1,7]=>0000000=>0000000=>[8]
[8,1,5,3,2,4,7,6]=>0000000=>0000000=>[8]
[8,1,2,4,5,3,7,6]=>0000000=>0000000=>[8]
[8,1,4,5,3,2,7,6]=>0000000=>0000000=>[8]
[7,8,4,1,3,6,5,2]=>0000000=>0000000=>[8]
[8,6,1,3,2,7,4,5]=>0000000=>0000000=>[8]
[7,3,8,2,4,1,6,5]=>0000000=>0000000=>[8]
[6,2,3,7,8,1,5,4]=>0000000=>0000000=>[8]
[6,3,7,8,1,5,4,2]=>0000000=>0000000=>[8]
[2,6,3,7,8,1,5,4]=>0000000=>0000000=>[8]
[7,5,8,1,6,4,2,3]=>0000000=>0000000=>[8]
[1,3,6,4,2,5,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,7,6,4,2,3,5,8]=>1000001=>1000001=>[1,6,1]
[1,2,3,7,6,4,5,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,3,2,5,8,6,4,7]=>1010000=>0000101=>[5,2,1]
[4,8,2,7,1,3,6,5]=>0000000=>0000000=>[8]
[7,1,8,4,6,3,5,2]=>0000000=>0000000=>[8]
[4,1,5,2,3,8,7,6]=>0000100=>0010000=>[3,5]
[2,8,7,1,4,6,3,5]=>0000000=>0000000=>[8]
[3,1,2,8,5,7,4,6]=>0010000=>0000100=>[5,3]
[2,1,8,6,3,7,5,4]=>0100000=>0000010=>[6,2]
[1,6,5,3,2,4,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,7,2,4,6,5,3,8]=>1000001=>1000001=>[1,6,1]
[1,4,7,2,6,5,3,8]=>1000001=>1000001=>[1,6,1]
[1,3,7,2,4,6,5,8]=>1000001=>1000001=>[1,6,1]
[1,7,2,6,4,3,5,8]=>1000001=>1000001=>[1,6,1]
[1,2,6,8,7,4,3,5]=>1100000=>0000011=>[6,1,1]
[1,2,7,4,3,5,8,6]=>1100000=>0000011=>[6,1,1]
[1,8,6,3,5,2,7,4]=>1000000=>0000001=>[7,1]
[1,6,2,8,7,4,3,5]=>1000000=>0000001=>[7,1]
[1,3,8,7,5,4,6,2]=>1000000=>0000001=>[7,1]
[1,2,8,6,3,5,7,4]=>1100000=>0000011=>[6,1,1]
[1,8,5,2,3,6,4,7]=>1000000=>0000001=>[7,1]
[1,7,4,8,5,2,3,6]=>1000000=>0000001=>[7,1]
[1,4,7,5,8,6,3,2]=>1000000=>0000001=>[7,1]
[1,4,7,5,2,8,6,3]=>1000000=>0000001=>[7,1]
[1,6,3,7,4,2,8,5]=>1000000=>0000001=>[7,1]
[1,8,5,2,7,4,3,6]=>1000000=>0000001=>[7,1]
[1,4,8,6,3,2,7,5]=>1000000=>0000001=>[7,1]
[1,4,8,7,5,3,2,6]=>1000000=>0000001=>[7,1]
[1,2,5,8,6,3,7,4]=>1100000=>0000011=>[6,1,1]
[1,2,4,7,5,8,6,3]=>1100000=>0000011=>[6,1,1]
[1,3,5,8,7,6,2,4]=>1000000=>0000001=>[7,1]
[1,5,2,4,3,6,8,7]=>1000110=>0110001=>[2,1,4,1]
[1,6,8,7,5,3,2,4]=>1000000=>0000001=>[7,1]
[1,2,5,7,4,3,8,6]=>1100000=>0000011=>[6,1,1]
[1,5,3,2,6,8,7,4]=>1000000=>0000001=>[7,1]
[1,4,2,6,8,7,5,3]=>1000000=>0000001=>[7,1]
[1,5,8,6,3,2,7,4]=>1000000=>0000001=>[7,1]
[1,8,5,2,6,3,4,7]=>1000000=>0000001=>[7,1]
[1,7,4,6,3,2,8,5]=>1000000=>0000001=>[7,1]
[1,6,3,2,8,5,4,7]=>1000000=>0000001=>[7,1]
[1,4,2,8,6,3,5,7]=>1000000=>0000001=>[7,1]
[1,3,8,6,4,2,5,7]=>1000000=>0000001=>[7,1]
[1,5,7,4,2,3,8,6]=>1000000=>0000001=>[7,1]
[8,2,7,3,1,5,4,6]=>0000000=>0000000=>[8]
[8,4,7,2,5,3,1,6]=>0000000=>0000000=>[8]
[8,6,1,4,7,3,5,2]=>0000000=>0000000=>[8]
[5,3,6,7,2,8,4,1]=>0000000=>0000000=>[8]
[1,3,8,2,5,6,7,4]=>1000000=>0000001=>[7,1]
[5,1,7,4,3,6,8,2]=>0000000=>0000000=>[8]
[7,1,3,6,5,2,8,4]=>0000000=>0000000=>[8]
[6,1,8,5,2,7,3,4]=>0000000=>0000000=>[8]
[5,4,1,3,7,2,8,6]=>0000000=>0000000=>[8]
[3,1,8,7,5,2,4,6]=>0000000=>0000000=>[8]
[6,5,8,7,2,4,3,1]=>0000000=>0000000=>[8]
[4,3,6,5,8,2,1,7]=>0000000=>0000000=>[8]
[4,7,3,1,8,5,2,6]=>0000000=>0000000=>[8]
[5,1,7,8,6,2,3,4]=>0000000=>0000000=>[8]
[8,5,1,6,7,2,3,4]=>0000000=>0000000=>[8]
[1,8,3,6,4,5,7,2]=>1000000=>0000001=>[7,1]
[8,1,6,4,2,3,5,7]=>0000000=>0000000=>[8]
[7,1,8,2,5,3,4,6]=>0000000=>0000000=>[8]
[5,1,7,2,6,3,4,8]=>0000001=>1000000=>[1,7]
[1,6,3,8,4,5,7,2]=>1000000=>0000001=>[7,1]
[2,7,4,3,8,5,1,6]=>0000000=>0000000=>[8]
[2,4,7,3,5,1,6,8]=>0000001=>1000000=>[1,7]
[2,4,8,6,3,5,1,7]=>0000000=>0000000=>[8]
[2,3,7,5,4,1,6,8]=>0000001=>1000000=>[1,7]
[3,4,6,2,1,5,8,7]=>0000010=>0100000=>[2,6]
[2,3,6,1,5,8,4,7]=>0000000=>0000000=>[8]
[2,3,7,1,6,5,8,4]=>0000000=>0000000=>[8]
[2,4,7,1,3,6,8,5]=>0000000=>0000000=>[8]
[5,4,7,8,1,3,2,6]=>0000000=>0000000=>[8]
[2,5,7,1,4,6,3,8]=>0000001=>1000000=>[1,7]
[2,4,7,1,6,3,5,8]=>0000001=>1000000=>[1,7]
[2,3,7,1,6,5,4,8]=>0000001=>1000000=>[1,7]
[2,5,7,1,4,3,6,8]=>0000001=>1000000=>[1,7]
[2,5,7,3,1,4,6,8]=>0000001=>1000000=>[1,7]
[3,4,7,2,1,6,8,5]=>0000000=>0000000=>[8]
[5,7,3,2,8,1,4,6]=>0000000=>0000000=>[8]
[5,4,7,8,1,3,6,2]=>0000000=>0000000=>[8]
[2,5,7,1,4,6,8,3]=>0000000=>0000000=>[8]
[2,4,7,1,6,3,8,5]=>0000000=>0000000=>[8]
[2,4,7,1,6,8,3,5]=>0000000=>0000000=>[8]
[8,7,5,1,4,2,3,6]=>0000000=>0000000=>[8]
[6,8,3,2,4,5,1,7]=>0000000=>0000000=>[8]
[3,8,5,2,4,6,1,7]=>0000000=>0000000=>[8]
[8,2,4,5,3,1,6,7]=>0000000=>0000000=>[8]
[4,8,2,5,3,1,6,7]=>0000000=>0000000=>[8]
[4,3,7,5,2,1,6,8]=>0000001=>1000000=>[1,7]
[1,6,7,4,3,2,5,8]=>1000001=>1000001=>[1,6,1]
[1,4,5,7,3,2,6,8]=>1000001=>1000001=>[1,6,1]
[3,5,1,4,7,2,6,8]=>0000001=>1000000=>[1,7]
[2,5,4,7,8,1,3,6]=>0000000=>0000000=>[8]
[2,5,1,4,7,8,3,6]=>0000000=>0000000=>[8]
[4,3,7,1,5,2,6,8]=>0000001=>1000000=>[1,7]
[3,5,1,6,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[6,4,3,1,7,2,5,8]=>0000001=>1000000=>[1,7]
[6,2,7,4,3,1,5,8]=>0000001=>1000000=>[1,7]
[2,6,4,1,7,3,5,8]=>0000001=>1000000=>[1,7]
[6,3,2,7,4,5,1,8]=>0000001=>1000000=>[1,7]
[7,2,4,1,3,6,8,5]=>0000000=>0000000=>[8]
[6,3,2,5,7,1,4,8]=>0000001=>1000000=>[1,7]
[3,2,6,5,7,1,4,8]=>0000001=>1000000=>[1,7]
[1,7,3,2,5,6,4,8]=>1000001=>1000001=>[1,6,1]
[2,1,7,3,5,6,8,4]=>0100000=>0000010=>[6,2]
[2,1,6,3,5,7,8,4]=>0100000=>0000010=>[6,2]
[1,6,3,2,5,7,4,8]=>1000001=>1000001=>[1,6,1]
[5,6,2,1,4,3,7,8]=>0000011=>1100000=>[1,1,6]
[2,5,1,6,4,3,7,8]=>0000011=>1100000=>[1,1,6]
[2,5,4,1,6,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,6,1,5,2,7,3,8]=>0000001=>1000000=>[1,7]
[1,6,5,3,7,2,4,8]=>1000001=>1000001=>[1,6,1]
[2,6,1,8,5,4,3,7]=>0000000=>0000000=>[8]
[4,5,8,6,2,1,3,7]=>0000000=>0000000=>[8]
[4,2,8,5,3,6,1,7]=>0000000=>0000000=>[8]
[5,6,3,2,8,1,7,4]=>0000000=>0000000=>[8]
[8,2,6,3,1,5,7,4]=>0000000=>0000000=>[8]
[8,2,5,3,4,7,6,1]=>0000000=>0000000=>[8]
[7,5,3,2,4,1,8,6]=>0000000=>0000000=>[8]
[6,5,3,2,4,8,1,7]=>0000000=>0000000=>[8]
[3,1,8,4,6,5,7,2]=>0000000=>0000000=>[8]
[3,4,7,5,8,2,6,1]=>0000000=>0000000=>[8]
[8,7,1,4,6,5,2,3]=>0000000=>0000000=>[8]
[8,3,7,6,4,5,1,2]=>0000000=>0000000=>[8]
[5,3,8,6,4,1,7,2]=>0000000=>0000000=>[8]
[6,4,7,1,8,5,2,3]=>0000000=>0000000=>[8]
[3,8,2,5,1,7,4,6]=>0000000=>0000000=>[8]
[8,6,4,1,7,3,2,5]=>0000000=>0000000=>[8]
[3,4,7,8,5,1,2,6]=>0000000=>0000000=>[8]
[5,7,2,4,3,6,8,1]=>0000000=>0000000=>[8]
[4,7,3,2,5,6,8,1]=>0000000=>0000000=>[8]
[3,2,7,6,4,5,8,1]=>0000000=>0000000=>[8]
[1,7,3,6,8,4,2,5]=>1000000=>0000001=>[7,1]
[8,3,1,2,6,4,7,5]=>0000000=>0000000=>[8]
[1,7,8,2,4,3,5,6]=>1000000=>0000001=>[7,1]
[3,6,4,7,1,2,8,5]=>0000000=>0000000=>[8]
[2,4,7,8,5,1,3,6]=>0000000=>0000000=>[8]
[5,7,4,8,1,3,2,6]=>0000000=>0000000=>[8]
[4,3,7,8,1,5,2,6]=>0000000=>0000000=>[8]
[8,5,4,2,6,1,7,3]=>0000000=>0000000=>[8]
[3,2,6,8,7,4,1,5]=>0000000=>0000000=>[8]
[2,3,7,5,1,8,6,4]=>0000000=>0000000=>[8]
[6,3,1,2,8,7,4,5]=>0000000=>0000000=>[8]
[5,2,1,3,8,7,6,4]=>0000000=>0000000=>[8]
[7,2,1,5,3,8,4,6]=>0000000=>0000000=>[8]
[1,5,8,2,4,3,6,7]=>1000000=>0000001=>[7,1]
[4,3,6,8,1,5,2,7]=>0000000=>0000000=>[8]
[2,4,6,8,5,1,3,7]=>0000000=>0000000=>[8]
[1,6,8,2,4,3,5,7]=>1000000=>0000001=>[7,1]
[5,4,6,8,3,1,7,2]=>0000000=>0000000=>[8]
[8,6,1,7,2,4,3,5]=>0000000=>0000000=>[8]
[7,3,1,2,8,6,4,5]=>0000000=>0000000=>[8]
[2,3,7,6,1,8,5,4]=>0000000=>0000000=>[8]
[3,2,7,8,6,4,1,5]=>0000000=>0000000=>[8]
[6,2,8,3,1,4,7,5]=>0000000=>0000000=>[8]
[3,1,2,8,7,4,5,6]=>0010000=>0000100=>[5,3]
[2,1,3,8,7,4,6,5]=>0110000=>0000110=>[5,1,2]
[2,1,3,8,7,4,5,6]=>0110000=>0000110=>[5,1,2]
[8,5,1,7,2,4,3,6]=>0000000=>0000000=>[8]
[8,3,1,6,2,7,5,4]=>0000000=>0000000=>[8]
[1,3,2,8,7,6,4,5]=>1010000=>0000101=>[5,2,1]
[2,1,3,8,7,6,4,5]=>0110000=>0000110=>[5,1,2]
[3,5,8,2,4,1,7,6]=>0000000=>0000000=>[8]
[1,3,6,8,5,4,2,7]=>1000000=>0000001=>[7,1]
[1,4,2,5,7,6,3,8]=>1000001=>1000001=>[1,6,1]
[1,4,2,6,8,5,3,7]=>1000000=>0000001=>[7,1]
[1,5,3,2,6,8,4,7]=>1000000=>0000001=>[7,1]
[1,5,4,2,3,6,8,7]=>1000110=>0110001=>[2,1,4,1]
[1,6,8,3,5,4,2,7]=>1000000=>0000001=>[7,1]
[1,5,3,2,4,6,8,7]=>1000110=>0110001=>[2,1,4,1]
[1,5,8,7,6,3,2,4]=>1000000=>0000001=>[7,1]
[1,5,7,6,3,2,4,8]=>1000001=>1000001=>[1,6,1]
[1,6,3,2,4,7,5,8]=>1000001=>1000001=>[1,6,1]
[1,6,3,2,4,8,7,5]=>1000000=>0000001=>[7,1]
[1,2,7,6,4,3,5,8]=>1100001=>1000011=>[1,5,1,1]
[1,8,7,5,2,4,6,3]=>1000000=>0000001=>[7,1]
[1,7,5,2,4,6,3,8]=>1000001=>1000001=>[1,6,1]
[1,7,4,2,5,3,6,8]=>1000001=>1000001=>[1,6,1]
[1,8,4,7,5,2,6,3]=>1000000=>0000001=>[7,1]
[1,7,5,2,3,6,4,8]=>1000001=>1000001=>[1,6,1]
[1,7,5,2,6,3,4,8]=>1000001=>1000001=>[1,6,1]
[1,6,3,7,4,2,5,8]=>1000001=>1000001=>[1,6,1]
[1,6,3,2,7,5,4,8]=>1000001=>1000001=>[1,6,1]
[1,4,8,7,5,2,6,3]=>1000000=>0000001=>[7,1]
[1,4,7,5,2,6,3,8]=>1000001=>1000001=>[1,6,1]
[1,3,6,4,8,7,5,2]=>1000000=>0000001=>[7,1]
[1,3,7,6,4,2,5,8]=>1000001=>1000001=>[1,6,1]
[1,3,8,7,5,2,4,6]=>1000000=>0000001=>[7,1]
[1,4,6,3,2,7,5,8]=>1000001=>1000001=>[1,6,1]
[1,4,6,3,2,8,7,5]=>1000000=>0000001=>[7,1]
[1,5,7,6,4,2,3,8]=>1000001=>1000001=>[1,6,1]
[1,2,6,4,7,5,3,8]=>1100001=>1000011=>[1,5,1,1]
[1,6,3,2,8,4,7,5]=>1000000=>0000001=>[7,1]
[1,5,2,7,4,3,6,8]=>1000001=>1000001=>[1,6,1]
[1,6,3,5,2,7,4,8]=>1000001=>1000001=>[1,6,1]
[1,6,3,5,2,8,7,4]=>1000000=>0000001=>[7,1]
[1,8,3,7,5,2,4,6]=>1000000=>0000001=>[7,1]
[1,8,4,6,3,2,7,5]=>1000000=>0000001=>[7,1]
[3,2,1,4,8,5,7,6]=>0011000=>0001100=>[4,1,3]
[7,4,1,6,2,5,3,8]=>0000001=>1000000=>[1,7]
[5,4,1,8,2,6,3,7]=>0000000=>0000000=>[8]
[5,4,1,6,2,8,3,7]=>0000000=>0000000=>[8]
[2,8,6,4,5,1,7,3]=>0000000=>0000000=>[8]
[2,8,3,1,4,5,7,6]=>0000000=>0000000=>[8]
[6,1,7,2,8,4,5,3]=>0000000=>0000000=>[8]
[8,3,2,1,5,6,7,4]=>0000000=>0000000=>[8]
[7,2,8,1,4,5,6,3]=>0000000=>0000000=>[8]
[5,1,7,3,8,6,2,4]=>0000000=>0000000=>[8]
[3,2,5,8,7,4,1,6]=>0000000=>0000000=>[8]
[4,2,5,8,7,3,1,6]=>0000000=>0000000=>[8]
[8,3,4,1,6,5,2,7]=>0000000=>0000000=>[8]
[3,4,8,5,7,2,1,6]=>0000000=>0000000=>[8]
[3,6,4,8,5,7,2,1]=>0000000=>0000000=>[8]
[5,8,4,7,3,6,2,1]=>0000000=>0000000=>[8]
[4,2,8,7,3,1,6,5]=>0000000=>0000000=>[8]
[6,5,8,2,1,7,4,3]=>0000000=>0000000=>[8]
[6,1,4,3,8,7,2,5]=>0000000=>0000000=>[8]
[5,1,3,2,6,8,7,4]=>0000000=>0000000=>[8]
[6,1,3,8,7,2,4,5]=>0000000=>0000000=>[8]
[1,2,8,4,5,7,3,6]=>1100000=>0000011=>[6,1,1]
[4,2,1,8,7,6,3,5]=>0000000=>0000000=>[8]
[3,2,5,8,7,1,4,6]=>0000000=>0000000=>[8]
[5,6,3,8,7,2,1,4]=>0000000=>0000000=>[8]
[2,5,8,4,7,1,6,3]=>0000000=>0000000=>[8]
[1,6,2,4,8,5,7,3]=>1000000=>0000001=>[7,1]
[3,1,6,5,8,7,2,4]=>0000000=>0000000=>[8]
[4,8,5,3,6,7,1,2]=>0000000=>0000000=>[8]
[1,8,5,3,4,7,6,2]=>1000000=>0000001=>[7,1]
[1,4,6,2,5,3,7,8]=>1000011=>1100001=>[1,1,5,1]
[4,3,6,5,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[1,3,8,7,6,5,2,4]=>1000000=>0000001=>[7,1]
[1,8,7,2,6,3,5,4]=>1000000=>0000001=>[7,1]
[2,8,7,1,6,3,4,5]=>0000000=>0000000=>[8]
[1,3,7,5,4,8,6,2]=>1000000=>0000001=>[7,1]
[1,5,6,3,8,4,2,7]=>1000000=>0000001=>[7,1]
[2,6,5,3,8,4,1,7]=>0000000=>0000000=>[8]
[2,3,6,5,4,8,1,7]=>0000000=>0000000=>[8]
[2,7,5,1,8,4,6,3]=>0000000=>0000000=>[8]
[1,7,6,4,8,2,5,3]=>1000000=>0000001=>[7,1]
[6,3,8,7,2,4,5,1]=>0000000=>0000000=>[8]
[2,4,3,8,7,1,6,5]=>0000000=>0000000=>[8]
[8,3,7,2,1,6,5,4]=>0000000=>0000000=>[8]
[8,4,7,3,6,2,1,5]=>0000000=>0000000=>[8]
[3,8,7,5,6,4,1,2]=>0000000=>0000000=>[8]
[3,8,7,5,6,2,1,4]=>0000000=>0000000=>[8]
[3,8,7,5,6,2,4,1]=>0000000=>0000000=>[8]
[2,8,7,5,6,4,1,3]=>0000000=>0000000=>[8]
[3,6,2,4,8,7,1,5]=>0000000=>0000000=>[8]
[1,5,6,3,8,2,7,4]=>1000000=>0000001=>[7,1]
[2,6,3,8,4,7,1,5]=>0000000=>0000000=>[8]
[2,6,3,5,7,8,1,4]=>0000000=>0000000=>[8]
[1,5,6,3,7,2,8,4]=>1000000=>0000001=>[7,1]
[1,7,5,3,6,2,8,4]=>1000000=>0000001=>[7,1]
[1,5,7,3,4,2,8,6]=>1000000=>0000001=>[7,1]
[1,5,8,3,4,2,7,6]=>1000000=>0000001=>[7,1]
[1,4,5,3,8,2,7,6]=>1000000=>0000001=>[7,1]
[6,5,1,4,2,7,8,3]=>0000000=>0000000=>[8]
[6,5,1,4,2,8,7,3]=>0000000=>0000000=>[8]
[1,7,5,4,2,8,6,3]=>1000000=>0000001=>[7,1]
[1,4,8,2,6,5,3,7]=>1000000=>0000001=>[7,1]
[7,5,1,8,3,4,2,6]=>0000000=>0000000=>[8]
[1,2,5,6,8,7,3,4]=>1100000=>0000011=>[6,1,1]
[2,6,7,3,4,1,8,5]=>0000000=>0000000=>[8]
[1,3,7,2,6,4,8,5]=>1000000=>0000001=>[7,1]
[7,6,1,2,3,5,4,8]=>0000001=>1000000=>[1,7]
[6,1,3,4,2,5,7,8]=>0000011=>1100000=>[1,1,6]
[5,3,8,2,4,6,1,7]=>0000000=>0000000=>[8]
[4,1,5,6,3,2,7,8]=>0000011=>1100000=>[1,1,6]
[4,5,8,3,2,6,1,7]=>0000000=>0000000=>[8]
[5,8,2,1,4,6,3,7]=>0000000=>0000000=>[8]
[4,1,5,8,3,6,2,7]=>0000000=>0000000=>[8]
[4,5,8,3,6,1,2,7]=>0000000=>0000000=>[8]
[1,6,3,4,7,8,5,2]=>1000000=>0000001=>[7,1]
[8,1,3,4,2,6,5,7]=>0000000=>0000000=>[8]
[4,7,8,5,2,3,1,6]=>0000000=>0000000=>[8]
[4,1,5,8,6,2,3,7]=>0000000=>0000000=>[8]
[5,8,2,1,6,3,4,7]=>0000000=>0000000=>[8]
[2,6,7,8,4,1,3,5]=>0000000=>0000000=>[8]
[2,6,7,8,4,3,1,5]=>0000000=>0000000=>[8]
[1,7,8,5,4,2,3,6]=>1000000=>0000001=>[7,1]
[3,6,4,5,2,8,1,7]=>0000000=>0000000=>[8]
[8,1,5,4,7,6,3,2]=>0000000=>0000000=>[8]
[2,5,1,4,6,7,3,8]=>0000001=>1000000=>[1,7]
[8,6,3,5,4,1,2,7]=>0000000=>0000000=>[8]
[8,2,6,5,4,1,3,7]=>0000000=>0000000=>[8]
[8,2,6,5,4,3,1,7]=>0000000=>0000000=>[8]
[8,3,2,6,1,5,4,7]=>0000000=>0000000=>[8]
[8,1,6,5,4,3,2,7]=>0000000=>0000000=>[8]
[4,8,1,7,6,3,5,2]=>0000000=>0000000=>[8]
[8,5,1,7,4,3,6,2]=>0000000=>0000000=>[8]
[8,5,7,6,2,1,3,4]=>0000000=>0000000=>[8]
[5,4,8,3,1,7,2,6]=>0000000=>0000000=>[8]
[5,1,4,8,3,2,7,6]=>0000000=>0000000=>[8]
[4,8,1,7,6,5,2,3]=>0000000=>0000000=>[8]
[4,3,8,7,2,6,1,5]=>0000000=>0000000=>[8]
[3,8,7,2,6,4,1,5]=>0000000=>0000000=>[8]
[8,2,7,6,4,1,5,3]=>0000000=>0000000=>[8]
[4,3,8,7,2,6,5,1]=>0000000=>0000000=>[8]
[8,2,5,7,4,3,6,1]=>0000000=>0000000=>[8]
[3,8,7,4,6,1,2,5]=>0000000=>0000000=>[8]
[8,3,7,5,4,1,6,2]=>0000000=>0000000=>[8]
[2,8,4,7,6,1,5,3]=>0000000=>0000000=>[8]
[2,5,4,8,3,1,7,6]=>0000000=>0000000=>[8]
[5,4,8,2,1,3,7,6]=>0000000=>0000000=>[8]
[3,8,7,2,6,1,5,4]=>0000000=>0000000=>[8]
[1,8,4,7,6,3,5,2]=>1000000=>0000001=>[7,1]
[1,8,3,7,6,5,2,4]=>1000000=>0000001=>[7,1]
[1,4,3,8,7,2,6,5]=>1000000=>0000001=>[7,1]
[8,1,2,7,6,5,4,3]=>0000000=>0000000=>[8]
[7,8,1,3,6,4,5,2]=>0000000=>0000000=>[8]
[7,2,6,8,4,5,3,1]=>0000000=>0000000=>[8]
[7,3,6,8,5,1,4,2]=>0000000=>0000000=>[8]
[7,5,8,1,6,2,4,3]=>0000000=>0000000=>[8]
[5,7,8,1,6,3,2,4]=>0000000=>0000000=>[8]
[7,2,6,8,5,1,4,3]=>0000000=>0000000=>[8]
[6,7,8,3,5,4,2,1]=>0000000=>0000000=>[8]
[6,7,8,4,2,1,5,3]=>0000000=>0000000=>[8]
[7,2,6,8,4,3,1,5]=>0000000=>0000000=>[8]
[7,5,2,4,8,3,1,6]=>0000000=>0000000=>[8]
[5,6,2,4,3,8,1,7]=>0000000=>0000000=>[8]
[7,8,3,1,6,2,5,4]=>0000000=>0000000=>[8]
[6,7,8,4,3,1,5,2]=>0000000=>0000000=>[8]
[7,8,2,6,3,5,4,1]=>0000000=>0000000=>[8]
[7,8,3,6,4,1,5,2]=>0000000=>0000000=>[8]
[6,1,5,2,4,8,3,7]=>0000000=>0000000=>[8]
[1,5,6,3,8,2,4,7]=>1000000=>0000001=>[7,1]
[7,3,8,1,6,4,5,2]=>0000000=>0000000=>[8]
[7,2,6,8,4,3,5,1]=>0000000=>0000000=>[8]
[7,5,2,4,8,3,6,1]=>0000000=>0000000=>[8]
[1,7,5,8,2,4,6,3]=>1000000=>0000001=>[7,1]
[7,5,2,8,1,4,6,3]=>0000000=>0000000=>[8]
[3,7,8,2,6,5,1,4]=>0000000=>0000000=>[8]
[3,7,8,2,1,6,4,5]=>0000000=>0000000=>[8]
[7,2,8,1,6,4,3,5]=>0000000=>0000000=>[8]
[7,8,1,6,3,5,4,2]=>0000000=>0000000=>[8]
[6,7,8,3,2,5,4,1]=>0000000=>0000000=>[8]
[6,7,8,2,5,4,3,1]=>0000000=>0000000=>[8]
[6,7,8,3,1,5,4,2]=>0000000=>0000000=>[8]
[7,8,1,6,2,5,4,3]=>0000000=>0000000=>[8]
[5,6,1,4,3,8,2,7]=>0000000=>0000000=>[8]
[1,6,4,5,2,7,3,8]=>1000001=>1000001=>[1,6,1]
[6,2,1,5,7,3,4,8]=>0000001=>1000000=>[1,7]
[1,6,7,4,2,8,3,5]=>1000000=>0000001=>[7,1]
[1,4,7,2,3,6,8,5]=>1000000=>0000001=>[7,1]
[3,1,2,6,7,8,5,4]=>0010000=>0000100=>[5,3]
[1,6,3,4,7,8,2,5]=>1000000=>0000001=>[7,1]
[3,1,5,7,6,2,8,4]=>0000000=>0000000=>[8]
[6,3,1,4,2,7,8,5]=>0000000=>0000000=>[8]
[2,4,3,7,6,1,8,5]=>0000000=>0000000=>[8]
[3,1,6,5,2,8,7,4]=>0000000=>0000000=>[8]
[3,1,7,6,5,2,8,4]=>0000000=>0000000=>[8]
[1,4,7,6,8,3,2,5]=>1000000=>0000001=>[7,1]
[7,2,1,5,6,3,8,4]=>0000000=>0000000=>[8]
[4,3,1,8,6,2,7,5]=>0000000=>0000000=>[8]
[3,1,5,2,8,7,6,4]=>0000000=>0000000=>[8]
[1,2,8,4,3,7,6,5]=>1100000=>0000011=>[6,1,1]
[1,8,5,4,2,7,3,6]=>1000000=>0000001=>[7,1]
[3,1,8,5,4,7,2,6]=>0000000=>0000000=>[8]
[2,6,1,8,7,4,3,5]=>0000000=>0000000=>[8]
[7,5,1,8,3,2,6,4]=>0000000=>0000000=>[8]
[4,7,6,3,1,8,2,5]=>0000000=>0000000=>[8]
[5,3,1,8,6,2,4,7]=>0000000=>0000000=>[8]
[5,1,8,6,3,2,4,7]=>0000000=>0000000=>[8]
[1,5,4,2,8,6,3,7]=>1000000=>0000001=>[7,1]
[8,3,1,6,4,2,5,7]=>0000000=>0000000=>[8]
[3,6,7,1,8,4,2,5]=>0000000=>0000000=>[8]
[1,7,4,8,3,5,2,6]=>1000000=>0000001=>[7,1]
[7,3,2,4,8,5,1,6]=>0000000=>0000000=>[8]
[6,3,4,7,1,8,5,2]=>0000000=>0000000=>[8]
[5,7,8,1,4,2,6,3]=>0000000=>0000000=>[8]
[5,7,1,2,3,8,6,4]=>0000000=>0000000=>[8]
[7,2,8,1,4,3,6,5]=>0000000=>0000000=>[8]
[2,6,3,8,1,7,5,4]=>0000000=>0000000=>[8]
[1,8,3,6,4,7,2,5]=>1000000=>0000001=>[7,1]
[2,8,6,4,1,7,3,5]=>0000000=>0000000=>[8]
[1,8,4,2,7,5,3,6]=>1000000=>0000001=>[7,1]
[6,5,1,7,2,8,4,3]=>0000000=>0000000=>[8]
[2,8,1,7,5,3,6,4]=>0000000=>0000000=>[8]
[1,2,8,7,6,4,3,5]=>1100000=>0000011=>[6,1,1]
[1,6,5,8,7,4,2,3]=>1000000=>0000001=>[7,1]
[4,3,5,7,1,6,2,8]=>0000001=>1000000=>[1,7]
[4,2,8,5,3,6,7,1]=>0000000=>0000000=>[8]
[4,1,8,5,3,6,2,7]=>0000000=>0000000=>[8]
[6,4,2,5,3,1,7,8]=>0000011=>1100000=>[1,1,6]
[3,1,5,8,2,7,4,6]=>0000000=>0000000=>[8]
[6,4,1,5,3,2,7,8]=>0000011=>1100000=>[1,1,6]
[6,2,1,5,4,3,7,8]=>0000011=>1100000=>[1,1,6]
[3,1,8,5,4,6,2,7]=>0000000=>0000000=>[8]
[6,2,8,4,5,3,7,1]=>0000000=>0000000=>[8]
[6,1,8,4,5,3,2,7]=>0000000=>0000000=>[8]
[4,5,2,7,1,6,3,8]=>0000001=>1000000=>[1,7]
[4,3,5,7,1,6,8,2]=>0000000=>0000000=>[8]
[4,1,8,5,3,6,7,2]=>0000000=>0000000=>[8]
[6,3,8,4,5,1,7,2]=>0000000=>0000000=>[8]
[3,1,6,8,5,7,4,2]=>0000000=>0000000=>[8]
[2,6,1,8,5,7,4,3]=>0000000=>0000000=>[8]
[6,5,8,7,1,3,2,4]=>0000000=>0000000=>[8]
[6,5,8,7,2,3,4,1]=>0000000=>0000000=>[8]
[6,5,8,7,3,2,4,1]=>0000000=>0000000=>[8]
[6,3,8,4,5,2,7,1]=>0000000=>0000000=>[8]
[3,1,6,8,5,7,2,4]=>0000000=>0000000=>[8]
[2,1,6,8,5,3,7,4]=>0100000=>0000010=>[6,2]
[3,1,6,8,5,4,2,7]=>0000000=>0000000=>[8]
[3,2,6,8,5,4,7,1]=>0000000=>0000000=>[8]
[4,1,8,5,2,6,3,7]=>0000000=>0000000=>[8]
[3,1,6,8,5,2,4,7]=>0000000=>0000000=>[8]
[6,2,8,4,5,1,3,7]=>0000000=>0000000=>[8]
[6,5,8,7,4,1,2,3]=>0000000=>0000000=>[8]
[6,5,8,7,4,2,1,3]=>0000000=>0000000=>[8]
[6,5,8,7,2,4,1,3]=>0000000=>0000000=>[8]
[6,2,8,4,5,7,1,3]=>0000000=>0000000=>[8]
[6,1,8,4,5,7,3,2]=>0000000=>0000000=>[8]
[4,2,7,3,5,8,6,1]=>0000000=>0000000=>[8]
[3,6,2,4,8,5,7,1]=>0000000=>0000000=>[8]
[3,5,1,8,4,7,6,2]=>0000000=>0000000=>[8]
[2,4,8,3,7,6,5,1]=>0000000=>0000000=>[8]
[3,6,8,5,2,4,7,1]=>0000000=>0000000=>[8]
[2,6,8,5,4,3,7,1]=>0000000=>0000000=>[8]
[3,6,8,2,5,4,7,1]=>0000000=>0000000=>[8]
[4,6,8,3,2,5,7,1]=>0000000=>0000000=>[8]
[4,6,2,8,3,5,7,1]=>0000000=>0000000=>[8]
[3,6,1,8,5,7,4,2]=>0000000=>0000000=>[8]
[3,5,8,2,7,4,6,1]=>0000000=>0000000=>[8]
[2,4,8,7,3,6,5,1]=>0000000=>0000000=>[8]
[2,5,8,7,4,3,6,1]=>0000000=>0000000=>[8]
[2,4,8,7,6,3,5,1]=>0000000=>0000000=>[8]
[4,7,2,5,6,3,1,8]=>0000001=>1000000=>[1,7]
[6,1,2,8,7,3,4,5]=>0000000=>0000000=>[8]
[3,2,6,1,5,8,4,7]=>0000000=>0000000=>[8]
[4,5,2,1,7,8,3,6]=>0000000=>0000000=>[8]
[2,3,7,8,5,1,6,4]=>0000000=>0000000=>[8]
[8,1,3,2,5,6,4,7]=>0000000=>0000000=>[8]
[3,2,5,8,4,7,1,6]=>0000000=>0000000=>[8]
[8,6,4,1,5,2,3,7]=>0000000=>0000000=>[8]
[2,5,8,1,3,4,7,6]=>0000000=>0000000=>[8]
[8,1,5,2,3,7,6,4]=>0000000=>0000000=>[8]
[6,4,7,2,8,3,1,5]=>0000000=>0000000=>[8]
[4,8,1,2,7,6,5,3]=>0000000=>0000000=>[8]
[3,7,4,8,5,2,6,1]=>0000000=>0000000=>[8]
[3,4,2,8,6,7,5,1]=>0000000=>0000000=>[8]
[3,6,1,5,2,7,8,4]=>0000000=>0000000=>[8]
[7,1,6,8,3,4,2,5]=>0000000=>0000000=>[8]
[6,2,8,4,7,1,3,5]=>0000000=>0000000=>[8]
[1,8,4,3,7,6,2,5]=>1000000=>0000001=>[7,1]
[4,3,8,7,1,2,6,5]=>0000000=>0000000=>[8]
[1,8,3,6,7,2,4,5]=>1000000=>0000001=>[7,1]
[1,8,4,5,7,6,2,3]=>1000000=>0000001=>[7,1]
[4,3,8,5,7,1,6,2]=>0000000=>0000000=>[8]
[6,3,4,8,7,2,1,5]=>0000000=>0000000=>[8]
[5,3,8,4,7,1,6,2]=>0000000=>0000000=>[8]
[5,2,8,7,1,4,6,3]=>0000000=>0000000=>[8]
[3,2,8,7,1,6,4,5]=>0000000=>0000000=>[8]
[2,7,8,3,1,6,4,5]=>0000000=>0000000=>[8]
[3,5,8,7,4,1,6,2]=>0000000=>0000000=>[8]
[7,4,6,8,3,5,1,2]=>0000000=>0000000=>[8]
[7,2,8,4,1,3,6,5]=>0000000=>0000000=>[8]
[2,7,8,1,3,6,4,5]=>0000000=>0000000=>[8]
[2,7,8,1,5,4,6,3]=>0000000=>0000000=>[8]
[2,7,8,1,4,5,6,3]=>0000000=>0000000=>[8]
[3,6,7,8,2,4,1,5]=>0000000=>0000000=>[8]
[4,5,7,8,6,3,1,2]=>0000000=>0000000=>[8]
[5,4,6,8,7,3,1,2]=>0000000=>0000000=>[8]
[4,5,8,6,7,1,3,2]=>0000000=>0000000=>[8]
[5,7,6,8,2,1,3,4]=>0000000=>0000000=>[8]
[3,7,6,8,2,4,1,5]=>0000000=>0000000=>[8]
[5,4,7,8,6,3,1,2]=>0000000=>0000000=>[8]
[3,6,7,8,2,1,4,5]=>0000000=>0000000=>[8]
[4,5,6,8,7,3,1,2]=>0000000=>0000000=>[8]
[5,3,6,2,4,1,8,7]=>0000010=>0100000=>[2,6]
[4,5,3,7,1,2,6,8]=>0000001=>1000000=>[1,7]
[6,7,2,8,4,3,1,5]=>0000000=>0000000=>[8]
[6,7,3,2,8,4,1,5]=>0000000=>0000000=>[8]
[4,5,8,1,3,2,6,7]=>0000000=>0000000=>[8]
[5,7,2,8,3,4,6,1]=>0000000=>0000000=>[8]
[3,1,5,8,6,4,7,2]=>0000000=>0000000=>[8]
[3,6,2,8,4,7,5,1]=>0000000=>0000000=>[8]
[2,3,8,6,7,5,4,1]=>0000000=>0000000=>[8]
[3,1,5,8,6,2,4,7]=>0000000=>0000000=>[8]
[1,5,8,6,3,4,2,7]=>1000000=>0000001=>[7,1]
[5,3,7,8,4,2,6,1]=>0000000=>0000000=>[8]
[5,1,6,4,3,8,7,2]=>0000000=>0000000=>[8]
[4,7,6,8,3,1,5,2]=>0000000=>0000000=>[8]
[3,5,4,7,1,8,6,2]=>0000000=>0000000=>[8]
[1,8,5,4,2,3,6,7]=>1000000=>0000001=>[7,1]
[6,1,3,8,4,5,2,7]=>0000000=>0000000=>[8]
[4,1,5,7,6,3,2,8]=>0000001=>1000000=>[1,7]
[5,3,8,2,7,1,6,4]=>0000000=>0000000=>[8]
[4,5,1,7,6,3,2,8]=>0000001=>1000000=>[1,7]
[1,5,3,7,4,2,6,8]=>1000001=>1000001=>[1,6,1]
[1,5,4,2,3,8,7,6]=>1000100=>0010001=>[3,4,1]
[1,5,4,2,3,8,6,7]=>1000100=>0010001=>[3,4,1]
[1,5,4,2,3,7,8,6]=>1000100=>0010001=>[3,4,1]
[3,6,5,2,4,1,7,8]=>0000011=>1100000=>[1,1,6]
[4,6,7,2,5,1,8,3]=>0000000=>0000000=>[8]
[3,6,2,5,1,7,8,4]=>0000000=>0000000=>[8]
[8,7,3,6,2,1,5,4]=>0000000=>0000000=>[8]
[7,3,5,4,1,2,6,8]=>0000001=>1000000=>[1,7]
[7,1,3,8,2,5,4,6]=>0000000=>0000000=>[8]
[6,7,1,8,3,4,5,2]=>0000000=>0000000=>[8]
[8,6,7,2,5,3,1,4]=>0000000=>0000000=>[8]
[1,2,8,6,4,5,3,7]=>1100000=>0000011=>[6,1,1]
[1,5,7,8,4,2,3,6]=>1000000=>0000001=>[7,1]
[1,2,3,7,5,4,6,8]=>1110001=>1000111=>[1,4,1,1,1]
[1,3,4,8,5,2,7,6]=>1000000=>0000001=>[7,1]
[4,6,5,2,1,7,8,3]=>0000000=>0000000=>[8]
[3,5,6,2,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[4,3,6,5,1,7,8,2]=>0000000=>0000000=>[8]
[4,6,5,3,1,7,8,2]=>0000000=>0000000=>[8]
[5,1,3,4,8,2,6,7]=>0000000=>0000000=>[8]
[5,8,1,4,2,3,6,7]=>0000000=>0000000=>[8]
[4,3,1,8,5,2,6,7]=>0000000=>0000000=>[8]
[4,5,8,2,3,1,6,7]=>0000000=>0000000=>[8]
[3,5,4,8,1,7,2,6]=>0000000=>0000000=>[8]
[5,3,6,8,1,4,7,2]=>0000000=>0000000=>[8]
[5,1,6,8,3,4,7,2]=>0000000=>0000000=>[8]
[3,5,1,8,6,4,7,2]=>0000000=>0000000=>[8]
[6,4,8,1,5,7,2,3]=>0000000=>0000000=>[8]
[4,7,2,8,3,1,6,5]=>0000000=>0000000=>[8]
[1,2,5,6,8,3,7,4]=>1100000=>0000011=>[6,1,1]
[5,1,6,8,7,2,3,4]=>0000000=>0000000=>[8]
[1,5,6,8,3,7,2,4]=>1000000=>0000001=>[7,1]
[5,6,8,1,2,3,7,4]=>0000000=>0000000=>[8]
[2,8,1,3,5,7,4,6]=>0000000=>0000000=>[8]
[7,4,8,1,5,2,6,3]=>0000000=>0000000=>[8]
[8,3,2,1,6,5,7,4]=>0000000=>0000000=>[8]
[4,1,5,6,8,7,2,3]=>0000000=>0000000=>[8]
[1,2,5,6,8,4,7,3]=>1100000=>0000011=>[6,1,1]
[1,5,6,8,4,7,2,3]=>1000000=>0000001=>[7,1]
[6,8,1,4,5,7,2,3]=>0000000=>0000000=>[8]
[4,3,5,1,8,6,7,2]=>0000000=>0000000=>[8]
[1,3,5,6,8,4,7,2]=>1000000=>0000001=>[7,1]
[5,6,8,1,3,4,7,2]=>0000000=>0000000=>[8]
[5,6,8,2,3,4,7,1]=>0000000=>0000000=>[8]
[2,3,1,7,6,8,4,5]=>0010000=>0000100=>[5,3]
[2,7,4,1,3,6,8,5]=>0000000=>0000000=>[8]
[6,3,2,8,1,7,5,4]=>0000000=>0000000=>[8]
[4,5,3,1,2,8,6,7]=>0000100=>0010000=>[3,5]
[6,2,1,7,5,8,4,3]=>0000000=>0000000=>[8]
[1,5,7,8,6,4,2,3]=>1000000=>0000001=>[7,1]
[1,6,4,8,5,3,7,2]=>1000000=>0000001=>[7,1]
[4,2,6,7,8,1,3,5]=>0000000=>0000000=>[8]
[4,5,1,7,6,3,8,2]=>0000000=>0000000=>[8]
[8,1,5,4,2,3,6,7]=>0000000=>0000000=>[8]
[6,1,4,8,7,2,3,5]=>0000000=>0000000=>[8]
[6,1,7,5,8,2,3,4]=>0000000=>0000000=>[8]
[6,1,7,4,8,2,3,5]=>0000000=>0000000=>[8]
[3,5,8,6,2,1,4,7]=>0000000=>0000000=>[8]
[8,7,3,6,5,2,4,1]=>0000000=>0000000=>[8]
[7,3,8,6,2,1,4,5]=>0000000=>0000000=>[8]
[2,5,1,4,7,3,6,8]=>0000001=>1000000=>[1,7]
[3,1,6,5,7,2,4,8]=>0000001=>1000000=>[1,7]
[2,5,7,1,6,3,4,8]=>0000001=>1000000=>[1,7]
[2,5,7,1,6,3,8,4]=>0000000=>0000000=>[8]
[2,6,1,5,7,4,3,8]=>0000001=>1000000=>[1,7]
[3,1,6,5,2,4,7,8]=>0000011=>1100000=>[1,1,6]
[3,6,5,1,4,2,7,8]=>0000011=>1100000=>[1,1,6]
[3,5,6,2,8,1,7,4]=>0000000=>0000000=>[8]
[3,6,5,1,7,2,4,8]=>0000001=>1000000=>[1,7]
[3,6,5,2,1,4,7,8]=>0000011=>1100000=>[1,1,6]
[4,5,2,7,6,1,3,8]=>0000001=>1000000=>[1,7]
[4,6,5,3,1,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,4,1,6,3,7,2,8]=>0000001=>1000000=>[1,7]
[5,4,2,6,3,7,8,1]=>0000000=>0000000=>[8]
[3,6,5,7,1,4,2,8]=>0000001=>1000000=>[1,7]
[3,6,5,1,4,7,2,8]=>0000001=>1000000=>[1,7]
[4,3,6,5,7,1,2,8]=>0000001=>1000000=>[1,7]
[4,2,6,5,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,1,6,5,3,7,8,2]=>0000000=>0000000=>[8]
[4,1,5,7,6,3,8,2]=>0000000=>0000000=>[8]
[4,2,5,7,6,1,3,8]=>0000001=>1000000=>[1,7]
[3,4,7,6,1,2,5,8]=>0000001=>1000000=>[1,7]
[3,4,7,6,8,2,5,1]=>0000000=>0000000=>[8]
[4,2,5,7,6,3,8,1]=>0000000=>0000000=>[8]
[4,1,6,5,2,7,3,8]=>0000001=>1000000=>[1,7]
[4,2,6,5,7,3,1,8]=>0000001=>1000000=>[1,7]
[3,6,5,7,2,1,4,8]=>0000001=>1000000=>[1,7]
[3,5,7,6,2,4,1,8]=>0000001=>1000000=>[1,7]
[5,4,2,6,3,7,1,8]=>0000001=>1000000=>[1,7]
[4,6,5,2,7,3,1,8]=>0000001=>1000000=>[1,7]
[4,5,2,7,6,3,8,1]=>0000000=>0000000=>[8]
[4,6,5,2,1,7,3,8]=>0000001=>1000000=>[1,7]
[3,5,8,2,1,4,6,7]=>0000000=>0000000=>[8]
[3,5,8,2,4,6,7,1]=>0000000=>0000000=>[8]
[5,3,8,2,1,4,6,7]=>0000000=>0000000=>[8]
[5,3,1,8,2,4,6,7]=>0000000=>0000000=>[8]
[1,5,3,8,2,4,6,7]=>1000000=>0000001=>[7,1]
[1,5,8,4,2,3,6,7]=>1000000=>0000001=>[7,1]
[5,8,2,1,4,3,6,7]=>0000000=>0000000=>[8]
[5,8,2,4,6,3,1,7]=>0000000=>0000000=>[8]
[5,8,2,4,3,6,1,7]=>0000000=>0000000=>[8]
[5,8,1,4,6,2,3,7]=>0000000=>0000000=>[8]
[1,5,8,4,6,7,2,3]=>1000000=>0000001=>[7,1]
[5,1,8,4,6,7,2,3]=>0000000=>0000000=>[8]
[5,8,2,4,6,3,7,1]=>0000000=>0000000=>[8]
[3,8,4,6,7,2,1,5]=>0000000=>0000000=>[8]
[3,8,4,6,7,2,5,1]=>0000000=>0000000=>[8]
[8,4,3,6,7,2,5,1]=>0000000=>0000000=>[8]
[8,4,3,6,7,2,1,5]=>0000000=>0000000=>[8]
[8,6,2,4,5,3,7,1]=>0000000=>0000000=>[8]
[8,6,4,1,5,7,2,3]=>0000000=>0000000=>[8]
[1,8,6,4,5,7,2,3]=>1000000=>0000001=>[7,1]
[8,1,6,4,5,2,3,7]=>0000000=>0000000=>[8]
[8,6,2,4,5,3,1,7]=>0000000=>0000000=>[8]
[1,8,6,4,2,3,5,7]=>1000000=>0000001=>[7,1]
[3,8,1,6,2,4,5,7]=>0000000=>0000000=>[8]
[1,3,8,6,2,4,5,7]=>1000000=>0000001=>[7,1]
[3,8,6,2,1,4,5,7]=>0000000=>0000000=>[8]
[3,8,6,2,4,1,5,7]=>0000000=>0000000=>[8]
[3,8,6,2,4,5,7,1]=>0000000=>0000000=>[8]
[8,3,6,2,4,5,1,7]=>0000000=>0000000=>[8]
[1,8,3,6,2,4,5,7]=>1000000=>0000001=>[7,1]
[8,1,3,6,2,4,5,7]=>0000000=>0000000=>[8]
[8,3,6,7,2,1,4,5]=>0000000=>0000000=>[8]
[2,5,8,4,6,1,7,3]=>0000000=>0000000=>[8]
[3,8,6,7,2,1,4,5]=>0000000=>0000000=>[8]
[3,1,8,6,7,2,4,5]=>0000000=>0000000=>[8]
[8,2,6,4,5,1,7,3]=>0000000=>0000000=>[8]
[8,4,6,1,7,2,5,3]=>0000000=>0000000=>[8]
[1,8,4,6,7,5,2,3]=>1000000=>0000001=>[7,1]
[8,1,4,6,7,5,2,3]=>0000000=>0000000=>[8]
[8,4,6,1,3,7,2,5]=>0000000=>0000000=>[8]
[8,1,4,6,3,7,2,5]=>0000000=>0000000=>[8]
[8,4,1,6,3,7,2,5]=>0000000=>0000000=>[8]
[8,2,4,6,1,7,5,3]=>0000000=>0000000=>[8]
[8,4,6,2,3,7,5,1]=>0000000=>0000000=>[8]
[8,4,7,2,1,3,6,5]=>0000000=>0000000=>[8]
[8,4,2,1,5,3,7,6]=>0000000=>0000000=>[8]
[8,2,1,4,7,3,6,5]=>0000000=>0000000=>[8]
[2,8,4,1,7,5,3,6]=>0000000=>0000000=>[8]
[4,7,3,1,8,6,2,5]=>0000000=>0000000=>[8]
[2,1,5,8,7,3,6,4]=>0100000=>0000010=>[6,2]
[4,3,1,7,8,5,2,6]=>0000000=>0000000=>[8]
[5,8,2,6,4,3,7,1]=>0000000=>0000000=>[8]
[2,8,5,3,6,4,7,1]=>0000000=>0000000=>[8]
[1,2,8,6,4,7,3,5]=>1100000=>0000011=>[6,1,1]
[4,2,7,8,3,5,6,1]=>0000000=>0000000=>[8]
[2,8,3,7,1,4,6,5]=>0000000=>0000000=>[8]
[3,2,4,8,7,5,6,1]=>0000000=>0000000=>[8]
[1,8,6,4,7,5,3,2]=>1000000=>0000001=>[7,1]
[8,6,4,7,5,1,2,3]=>0000000=>0000000=>[8]
[2,7,4,6,3,8,5,1]=>0000000=>0000000=>[8]
[1,2,8,6,4,7,5,3]=>1100000=>0000011=>[6,1,1]
[1,6,5,4,3,8,2,7]=>1000000=>0000001=>[7,1]
[6,4,2,1,5,7,3,8]=>0000001=>1000000=>[1,7]
[3,1,5,8,7,2,4,6]=>0000000=>0000000=>[8]
[3,2,5,7,8,4,1,6]=>0000000=>0000000=>[8]
[3,2,5,7,8,4,6,1]=>0000000=>0000000=>[8]
[5,3,7,4,2,6,8,1]=>0000000=>0000000=>[8]
[5,3,7,4,2,6,1,8]=>0000001=>1000000=>[1,7]
[5,2,8,4,3,1,6,7]=>0000000=>0000000=>[8]
[5,1,8,4,3,2,6,7]=>0000000=>0000000=>[8]
[5,2,7,4,3,6,1,8]=>0000001=>1000000=>[1,7]
[5,2,7,4,3,6,8,1]=>0000000=>0000000=>[8]
[5,3,7,4,1,6,8,2]=>0000000=>0000000=>[8]
[3,1,5,7,8,4,2,6]=>0000000=>0000000=>[8]
[1,2,8,6,4,5,7,3]=>1100000=>0000011=>[6,1,1]
[6,2,3,7,4,1,8,5]=>0000000=>0000000=>[8]
[5,2,7,4,1,3,8,6]=>0000000=>0000000=>[8]
[6,2,3,7,4,8,5,1]=>0000000=>0000000=>[8]
[6,2,3,7,4,8,1,5]=>0000000=>0000000=>[8]
[6,1,3,7,4,2,8,5]=>0000000=>0000000=>[8]
[6,2,3,7,4,5,1,8]=>0000001=>1000000=>[1,7]
[6,2,3,7,4,5,8,1]=>0000000=>0000000=>[8]
[6,1,3,7,4,5,8,2]=>0000000=>0000000=>[8]
[1,2,8,6,4,3,5,7]=>1100000=>0000011=>[6,1,1]
[6,1,3,7,4,5,2,8]=>0000001=>1000000=>[1,7]
[1,8,6,3,5,4,2,7]=>1000000=>0000001=>[7,1]
[2,5,4,1,8,6,7,3]=>0000000=>0000000=>[8]
[1,8,5,3,2,6,7,4]=>1000000=>0000001=>[7,1]
[5,6,8,3,4,2,7,1]=>0000000=>0000000=>[8]
[6,3,8,2,4,1,7,5]=>0000000=>0000000=>[8]
[5,1,7,8,2,4,3,6]=>0000000=>0000000=>[8]
[5,3,2,4,8,1,7,6]=>0000000=>0000000=>[8]
[5,3,2,4,8,1,6,7]=>0000000=>0000000=>[8]
[5,3,2,4,7,1,8,6]=>0000000=>0000000=>[8]
[8,4,5,3,7,1,2,6]=>0000000=>0000000=>[8]
[5,3,2,4,6,8,1,7]=>0000000=>0000000=>[8]
[7,6,4,2,8,3,1,5]=>0000000=>0000000=>[8]
[1,2,6,4,7,3,5,8]=>1100001=>1000011=>[1,5,1,1]
[7,5,4,1,3,6,8,2]=>0000000=>0000000=>[8]
[6,7,2,4,5,1,8,3]=>0000000=>0000000=>[8]
[5,2,7,8,3,6,1,4]=>0000000=>0000000=>[8]
[2,7,8,5,6,1,4,3]=>0000000=>0000000=>[8]
[5,2,8,3,1,4,7,6]=>0000000=>0000000=>[8]
[8,3,5,1,2,4,7,6]=>0000000=>0000000=>[8]
[8,3,6,5,4,1,2,7]=>0000000=>0000000=>[8]
[8,4,1,7,5,2,6,3]=>0000000=>0000000=>[8]
[8,4,2,7,5,3,1,6]=>0000000=>0000000=>[8]
[1,5,2,6,8,3,7,4]=>1000000=>0000001=>[7,1]
[7,2,8,4,1,3,5,6]=>0000000=>0000000=>[8]
[6,7,8,5,2,1,4,3]=>0000000=>0000000=>[8]
[1,6,2,7,8,4,3,5]=>1000000=>0000001=>[7,1]
[4,3,8,6,5,2,7,1]=>0000000=>0000000=>[8]
[2,3,8,6,5,1,7,4]=>0000000=>0000000=>[8]
[7,3,2,6,1,4,8,5]=>0000000=>0000000=>[8]
[8,4,7,1,2,5,3,6]=>0000000=>0000000=>[8]
[8,5,6,7,2,1,4,3]=>0000000=>0000000=>[8]
[8,5,6,7,3,1,4,2]=>0000000=>0000000=>[8]
[5,7,8,1,3,2,4,6]=>0000000=>0000000=>[8]
[7,8,6,1,3,5,4,2]=>0000000=>0000000=>[8]
[1,2,5,7,8,3,6,4]=>1100000=>0000011=>[6,1,1]
[3,4,5,8,1,7,2,6]=>0000000=>0000000=>[8]
[4,3,8,6,7,5,1,2]=>0000000=>0000000=>[8]
[4,5,6,2,7,8,3,1]=>0000000=>0000000=>[8]
[4,5,6,2,7,1,8,3]=>0000000=>0000000=>[8]
[4,5,6,2,1,7,3,8]=>0000001=>1000000=>[1,7]
[4,5,6,1,7,8,3,2]=>0000000=>0000000=>[8]
[4,5,1,6,7,8,3,2]=>0000000=>0000000=>[8]
[4,5,1,6,7,3,8,2]=>0000000=>0000000=>[8]
[4,5,1,6,7,3,2,8]=>0000001=>1000000=>[1,7]
[4,5,6,1,7,3,2,8]=>0000001=>1000000=>[1,7]
[1,6,4,3,8,2,7,5]=>1000000=>0000001=>[7,1]
[7,8,1,4,3,2,5,6]=>0000000=>0000000=>[8]
[1,7,8,4,5,3,6,2]=>1000000=>0000001=>[7,1]
[2,7,6,3,4,1,8,5]=>0000000=>0000000=>[8]
[8,1,7,4,3,5,6,2]=>0000000=>0000000=>[8]
[7,1,8,4,5,3,6,2]=>0000000=>0000000=>[8]
[4,3,1,8,6,5,7,2]=>0000000=>0000000=>[8]
[4,3,2,7,5,1,8,6]=>0000000=>0000000=>[8]
[5,2,3,7,4,1,8,6]=>0000000=>0000000=>[8]
[2,1,7,4,3,6,8,5]=>0100000=>0000010=>[6,2]
[7,1,2,4,5,6,8,3]=>0000000=>0000000=>[8]
[2,8,7,1,4,5,6,3]=>0000000=>0000000=>[8]
[8,7,1,3,4,5,6,2]=>0000000=>0000000=>[8]
[7,8,1,3,4,5,6,2]=>0000000=>0000000=>[8]
[1,7,2,5,4,6,8,3]=>1000000=>0000001=>[7,1]
[2,5,3,8,1,6,7,4]=>0000000=>0000000=>[8]
[1,6,4,2,5,7,8,3]=>1000000=>0000001=>[7,1]
[8,5,3,1,4,6,7,2]=>0000000=>0000000=>[8]
[6,5,3,4,1,7,8,2]=>0000000=>0000000=>[8]
[5,6,3,4,1,7,8,2]=>0000000=>0000000=>[8]
[2,5,3,1,4,7,8,6]=>0000100=>0010000=>[3,5]
[2,6,1,4,3,7,8,5]=>0000000=>0000000=>[8]
[6,8,2,3,1,5,7,4]=>0000000=>0000000=>[8]
[6,1,3,4,2,7,8,5]=>0000000=>0000000=>[8]
[4,3,1,5,2,7,8,6]=>0000100=>0010000=>[3,5]
[5,2,3,1,4,7,8,6]=>0000100=>0010000=>[3,5]
[7,2,1,3,5,6,8,4]=>0000000=>0000000=>[8]
[5,2,4,7,8,6,3,1]=>0000000=>0000000=>[8]
[8,4,2,7,6,1,5,3]=>0000000=>0000000=>[8]
[5,3,7,6,1,8,4,2]=>0000000=>0000000=>[8]
[8,6,4,1,2,5,3,7]=>0000000=>0000000=>[8]
[8,6,1,4,2,5,7,3]=>0000000=>0000000=>[8]
[8,6,4,1,2,5,7,3]=>0000000=>0000000=>[8]
[8,6,1,4,7,2,5,3]=>0000000=>0000000=>[8]
[4,2,6,3,5,1,7,8]=>0000011=>1100000=>[1,1,6]
[3,4,6,8,7,1,2,5]=>0000000=>0000000=>[8]
[2,5,4,8,3,7,6,1]=>0000000=>0000000=>[8]
[1,3,6,2,5,8,7,4]=>1000000=>0000001=>[7,1]
[1,3,5,8,6,4,7,2]=>1000000=>0000001=>[7,1]
[5,8,7,1,4,6,3,2]=>0000000=>0000000=>[8]
[6,2,5,1,3,4,8,7]=>0000010=>0100000=>[2,6]
[2,6,5,1,3,4,8,7]=>0000010=>0100000=>[2,6]
[4,6,5,1,2,7,3,8]=>0000001=>1000000=>[1,7]
[5,6,4,1,2,7,3,8]=>0000001=>1000000=>[1,7]
[8,1,5,6,2,4,3,7]=>0000000=>0000000=>[8]
[6,4,5,1,2,7,3,8]=>0000001=>1000000=>[1,7]
[5,4,6,1,3,2,7,8]=>0000011=>1100000=>[1,1,6]
[5,7,1,4,3,2,6,8]=>0000001=>1000000=>[1,7]
[2,6,4,1,3,7,5,8]=>0000001=>1000000=>[1,7]
[6,3,2,5,7,4,8,1]=>0000000=>0000000=>[8]
[4,5,2,7,6,3,1,8]=>0000001=>1000000=>[1,7]
[4,5,2,1,7,6,3,8]=>0000001=>1000000=>[1,7]
[5,4,1,6,7,2,8,3]=>0000000=>0000000=>[8]
[4,1,6,5,2,7,8,3]=>0000000=>0000000=>[8]
[5,4,6,2,7,8,3,1]=>0000000=>0000000=>[8]
[3,5,2,6,7,8,4,1]=>0000000=>0000000=>[8]
[6,3,2,5,1,7,8,4]=>0000000=>0000000=>[8]
[4,6,3,7,8,2,1,5]=>0000000=>0000000=>[8]
[5,6,7,1,8,4,2,3]=>0000000=>0000000=>[8]
[5,6,7,2,8,4,1,3]=>0000000=>0000000=>[8]
[2,8,4,7,6,3,1,5]=>0000000=>0000000=>[8]
[6,4,8,7,2,1,5,3]=>0000000=>0000000=>[8]
[2,5,1,8,4,7,6,3]=>0000000=>0000000=>[8]
[2,4,5,8,1,7,6,3]=>0000000=>0000000=>[8]
[2,6,8,1,4,3,7,5]=>0000000=>0000000=>[8]
[2,6,1,5,8,7,3,4]=>0000000=>0000000=>[8]
[7,5,8,1,6,2,3,4]=>0000000=>0000000=>[8]
[7,6,1,3,5,2,4,8]=>0000001=>1000000=>[1,7]
[6,2,4,5,3,8,1,7]=>0000000=>0000000=>[8]
[1,2,5,4,7,8,3,6]=>1100000=>0000011=>[6,1,1]
[3,6,2,4,7,8,5,1]=>0000000=>0000000=>[8]
[1,3,5,4,8,7,2,6]=>1000000=>0000001=>[7,1]
[1,6,2,4,8,3,7,5]=>1000000=>0000001=>[7,1]
[7,1,4,2,3,8,6,5]=>0000000=>0000000=>[8]
[1,7,3,2,4,6,5,8]=>1000001=>1000001=>[1,6,1]
[1,5,7,3,2,6,4,8]=>1000001=>1000001=>[1,6,1]
[5,1,3,7,2,6,4,8]=>0000001=>1000000=>[1,7]
[1,7,8,5,4,2,6,3]=>1000000=>0000001=>[7,1]
[8,1,7,5,4,2,6,3]=>0000000=>0000000=>[8]
[1,6,5,2,7,4,8,3]=>1000000=>0000001=>[7,1]
[1,5,4,2,8,6,7,3]=>1000000=>0000001=>[7,1]
[1,6,3,5,2,7,8,4]=>1000000=>0000001=>[7,1]
[3,1,2,6,8,7,5,4]=>0010000=>0000100=>[5,3]
[6,4,8,2,5,7,1,3]=>0000000=>0000000=>[8]
[6,8,4,2,7,1,3,5]=>0000000=>0000000=>[8]
[6,8,2,4,1,7,3,5]=>0000000=>0000000=>[8]
[2,5,4,7,6,1,3,8]=>0000001=>1000000=>[1,7]
[5,2,3,7,6,1,4,8]=>0000001=>1000000=>[1,7]
[4,2,3,7,6,1,5,8]=>0000001=>1000000=>[1,7]
[4,2,7,3,5,1,6,8]=>0000001=>1000000=>[1,7]
[5,6,2,3,8,4,7,1]=>0000000=>0000000=>[8]
[5,6,2,3,1,7,8,4]=>0000000=>0000000=>[8]
[5,7,2,3,4,1,6,8]=>0000001=>1000000=>[1,7]
[6,2,7,3,5,1,4,8]=>0000001=>1000000=>[1,7]
[7,2,6,3,5,1,4,8]=>0000001=>1000000=>[1,7]
[6,5,2,3,1,7,8,4]=>0000000=>0000000=>[8]
[6,5,2,3,8,4,7,1]=>0000000=>0000000=>[8]
[7,5,2,1,4,6,8,3]=>0000000=>0000000=>[8]
[8,5,2,1,4,6,7,3]=>0000000=>0000000=>[8]
[8,5,2,3,1,6,4,7]=>0000000=>0000000=>[8]
[8,6,2,3,1,5,4,7]=>0000000=>0000000=>[8]
[8,2,6,3,1,7,4,5]=>0000000=>0000000=>[8]
[1,6,3,4,2,7,5,8]=>1000001=>1000001=>[1,6,1]
[8,5,2,7,3,4,6,1]=>0000000=>0000000=>[8]
[1,7,2,4,5,6,8,3]=>1000000=>0000001=>[7,1]
[1,8,3,2,5,6,4,7]=>1000000=>0000001=>[7,1]
[8,6,1,3,4,5,7,2]=>0000000=>0000000=>[8]
[6,8,1,3,4,5,7,2]=>0000000=>0000000=>[8]
[7,2,8,1,4,6,3,5]=>0000000=>0000000=>[8]
[2,7,8,1,5,6,3,4]=>0000000=>0000000=>[8]
[6,8,2,3,1,5,4,7]=>0000000=>0000000=>[8]
[5,8,2,3,1,6,4,7]=>0000000=>0000000=>[8]
[5,7,2,1,4,6,8,3]=>0000000=>0000000=>[8]
[4,2,3,8,1,7,5,6]=>0000000=>0000000=>[8]
[5,2,3,8,1,7,4,6]=>0000000=>0000000=>[8]
[2,5,4,8,1,7,3,6]=>0000000=>0000000=>[8]
[2,5,4,1,3,8,6,7]=>0000100=>0010000=>[3,5]
[4,2,1,5,3,7,6,8]=>0000101=>1010000=>[1,2,5]
[5,1,3,2,6,7,8,4]=>0000000=>0000000=>[8]
[5,1,3,4,2,7,6,8]=>0000101=>1010000=>[1,2,5]
[6,1,3,4,2,7,5,8]=>0000001=>1000000=>[1,7]
[7,2,1,3,5,8,4,6]=>0000000=>0000000=>[8]
[6,1,2,4,5,7,8,3]=>0000000=>0000000=>[8]
[6,8,7,2,3,4,5,1]=>0000000=>0000000=>[8]
[2,8,7,5,1,3,4,6]=>0000000=>0000000=>[8]
[8,3,7,5,1,4,2,6]=>0000000=>0000000=>[8]
[8,3,7,1,6,4,2,5]=>0000000=>0000000=>[8]
[4,2,6,5,3,1,7,8]=>0000011=>1100000=>[1,1,6]
[4,3,7,5,1,6,2,8]=>0000001=>1000000=>[1,7]
[3,5,2,8,6,7,4,1]=>0000000=>0000000=>[8]
[5,3,7,4,2,8,6,1]=>0000000=>0000000=>[8]
[5,6,2,8,7,1,4,3]=>0000000=>0000000=>[8]
[4,3,7,5,2,6,1,8]=>0000001=>1000000=>[1,7]
[4,6,3,5,2,7,8,1]=>0000000=>0000000=>[8]
[4,1,6,3,5,7,2,8]=>0000001=>1000000=>[1,7]
[3,1,5,7,4,6,8,2]=>0000000=>0000000=>[8]
[7,2,5,8,6,1,4,3]=>0000000=>0000000=>[8]
[7,8,4,5,1,3,6,2]=>0000000=>0000000=>[8]
[4,3,6,1,5,7,8,2]=>0000000=>0000000=>[8]
[6,4,7,1,3,5,2,8]=>0000001=>1000000=>[1,7]
[3,5,4,1,2,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,3,1,4,6,7,8,2]=>0000000=>0000000=>[8]
[6,2,1,4,7,5,8,3]=>0000000=>0000000=>[8]
[4,6,7,1,3,5,8,2]=>0000000=>0000000=>[8]
[5,6,1,3,4,7,2,8]=>0000001=>1000000=>[1,7]
[2,5,3,7,8,4,6,1]=>0000000=>0000000=>[8]
[4,5,7,2,3,6,1,8]=>0000001=>1000000=>[1,7]
[4,6,2,1,3,7,8,5]=>0000000=>0000000=>[8]
[3,6,2,4,1,7,5,8]=>0000001=>1000000=>[1,7]
[3,2,6,7,4,8,5,1]=>0000000=>0000000=>[8]
[7,3,4,8,5,2,1,6]=>0000000=>0000000=>[8]
[7,1,8,3,4,6,2,5]=>0000000=>0000000=>[8]
[6,3,2,7,5,8,4,1]=>0000000=>0000000=>[8]
[6,2,7,1,4,5,3,8]=>0000001=>1000000=>[1,7]
[4,2,6,1,5,7,3,8]=>0000001=>1000000=>[1,7]
[2,7,5,8,6,3,4,1]=>0000000=>0000000=>[8]
[2,5,4,1,3,6,7,8]=>0000111=>1110000=>[1,1,1,5]
[5,4,1,2,6,7,3,8]=>0000001=>1000000=>[1,7]
[6,5,2,7,4,1,3,8]=>0000001=>1000000=>[1,7]
[6,5,7,3,1,4,2,8]=>0000001=>1000000=>[1,7]
[6,7,4,3,1,5,8,2]=>0000000=>0000000=>[8]
[6,4,1,2,7,8,3,5]=>0000000=>0000000=>[8]
[5,1,4,7,2,6,8,3]=>0000000=>0000000=>[8]
[5,2,6,8,3,7,1,4]=>0000000=>0000000=>[8]
[1,7,2,4,3,5,8,6]=>1000000=>0000001=>[7,1]
[8,4,1,5,2,6,7,3]=>0000000=>0000000=>[8]
[7,4,1,3,6,5,2,8]=>0000001=>1000000=>[1,7]
[5,7,2,8,1,3,6,4]=>0000000=>0000000=>[8]
[5,4,1,2,6,3,8,7]=>0000010=>0100000=>[2,6]
[2,7,8,4,1,3,6,5]=>0000000=>0000000=>[8]
[3,6,5,1,4,8,2,7]=>0000000=>0000000=>[8]
[3,6,4,1,2,7,8,5]=>0000000=>0000000=>[8]
[4,1,7,3,8,6,2,5]=>0000000=>0000000=>[8]
[4,8,2,7,6,5,1,3]=>0000000=>0000000=>[8]
[5,4,2,8,7,6,1,3]=>0000000=>0000000=>[8]
[7,4,2,8,6,5,1,3]=>0000000=>0000000=>[8]
[6,5,8,2,7,4,1,3]=>0000000=>0000000=>[8]
[8,6,5,2,7,1,4,3]=>0000000=>0000000=>[8]
[7,8,5,2,1,6,4,3]=>0000000=>0000000=>[8]
[6,8,5,2,7,1,4,3]=>0000000=>0000000=>[8]
[6,5,8,2,7,1,4,3]=>0000000=>0000000=>[8]
[7,5,8,2,1,6,4,3]=>0000000=>0000000=>[8]
[3,2,1,6,5,8,4,7]=>0010000=>0000100=>[5,3]
[6,3,1,4,5,8,2,7]=>0000000=>0000000=>[8]
[3,4,8,5,2,1,7,6]=>0000000=>0000000=>[8]
[4,8,7,1,3,2,6,5]=>0000000=>0000000=>[8]
[3,5,1,4,2,8,7,6]=>0000100=>0010000=>[3,5]
[5,8,7,4,6,1,3,2]=>0000000=>0000000=>[8]
[5,1,8,7,4,6,3,2]=>0000000=>0000000=>[8]
[3,4,1,8,7,6,2,5]=>0000000=>0000000=>[8]
[3,5,2,8,6,4,7,1]=>0000000=>0000000=>[8]
[2,8,7,5,4,1,6,3]=>0000000=>0000000=>[8]
[4,2,5,8,6,7,1,3]=>0000000=>0000000=>[8]
[8,1,5,7,4,2,6,3]=>0000000=>0000000=>[8]
[8,4,5,3,1,6,7,2]=>0000000=>0000000=>[8]
[5,8,7,3,4,1,6,2]=>0000000=>0000000=>[8]
[2,4,5,8,1,3,7,6]=>0000000=>0000000=>[8]
[7,1,4,3,8,5,6,2]=>0000000=>0000000=>[8]
[6,3,2,5,8,4,1,7]=>0000000=>0000000=>[8]
[8,4,1,3,7,6,5,2]=>0000000=>0000000=>[8]
[5,1,6,4,7,8,2,3]=>0000000=>0000000=>[8]
[2,8,3,5,6,1,4,7]=>0000000=>0000000=>[8]
[1,3,6,4,2,7,5,8]=>1000001=>1000001=>[1,6,1]
[3,2,8,5,6,1,4,7]=>0000000=>0000000=>[8]
[7,2,5,8,1,4,6,3]=>0000000=>0000000=>[8]
[4,7,5,8,1,2,6,3]=>0000000=>0000000=>[8]
[5,4,7,8,2,1,3,6]=>0000000=>0000000=>[8]
[4,7,5,8,1,2,3,6]=>0000000=>0000000=>[8]
[3,4,7,5,2,8,1,6]=>0000000=>0000000=>[8]
[4,3,2,5,7,8,1,6]=>0000000=>0000000=>[8]
[5,4,8,6,2,3,1,7]=>0000000=>0000000=>[8]
[2,4,7,5,8,3,1,6]=>0000000=>0000000=>[8]
[7,2,5,8,1,6,3,4]=>0000000=>0000000=>[8]
[3,7,8,4,2,1,6,5]=>0000000=>0000000=>[8]
[1,5,4,8,7,6,2,3]=>1000000=>0000001=>[7,1]
[1,3,6,8,2,4,7,5]=>1000000=>0000001=>[7,1]
[4,7,2,8,5,1,6,3]=>0000000=>0000000=>[8]
[4,7,5,2,6,3,8,1]=>0000000=>0000000=>[8]
[3,5,6,2,8,1,4,7]=>0000000=>0000000=>[8]
[1,6,8,2,5,3,4,7]=>1000000=>0000001=>[7,1]
[8,6,3,5,2,1,4,7]=>0000000=>0000000=>[8]
[8,7,3,2,6,5,1,4]=>0000000=>0000000=>[8]
[5,2,8,7,6,4,1,3]=>0000000=>0000000=>[8]
[4,1,3,8,5,6,2,7]=>0000000=>0000000=>[8]
[3,2,4,8,5,7,1,6]=>0000000=>0000000=>[8]
[4,5,2,8,3,7,1,6]=>0000000=>0000000=>[8]
[7,8,5,1,6,4,3,2]=>0000000=>0000000=>[8]
[8,7,5,1,6,4,3,2]=>0000000=>0000000=>[8]
[4,5,8,3,1,2,7,6]=>0000000=>0000000=>[8]
[7,1,6,8,5,4,3,2]=>0000000=>0000000=>[8]
[5,8,1,3,4,2,7,6]=>0000000=>0000000=>[8]
[1,4,6,3,7,5,2,8]=>1000001=>1000001=>[1,6,1]
[1,3,2,8,7,4,6,5]=>1010000=>0000101=>[5,2,1]
[7,5,2,8,3,1,6,4]=>0000000=>0000000=>[8]
[6,7,1,3,2,5,8,4]=>0000000=>0000000=>[8]
[6,3,5,4,8,1,2,7]=>0000000=>0000000=>[8]
[6,2,5,4,1,7,8,3]=>0000000=>0000000=>[8]
[4,1,5,6,3,8,7,2]=>0000000=>0000000=>[8]
[8,1,5,4,6,7,3,2]=>0000000=>0000000=>[8]
[2,4,5,8,3,7,6,1]=>0000000=>0000000=>[8]
[6,1,3,5,4,8,2,7]=>0000000=>0000000=>[8]
[1,3,8,7,2,5,6,4]=>1000000=>0000001=>[7,1]
[2,5,4,1,8,3,7,6]=>0000000=>0000000=>[8]
[6,1,5,4,3,8,2,7]=>0000000=>0000000=>[8]
[1,4,8,3,2,7,6,5]=>1000000=>0000001=>[7,1]
[5,1,4,8,3,7,6,2]=>0000000=>0000000=>[8]
[3,5,8,2,1,4,7,6]=>0000000=>0000000=>[8]
[8,4,1,2,7,6,5,3]=>0000000=>0000000=>[8]
[4,8,3,2,7,6,5,1]=>0000000=>0000000=>[8]
[2,4,8,1,7,6,5,3]=>0000000=>0000000=>[8]
[8,7,3,2,1,4,6,5]=>0000000=>0000000=>[8]
[1,4,8,5,2,3,6,7]=>1000000=>0000001=>[7,1]
[6,1,4,2,8,7,3,5]=>0000000=>0000000=>[8]
[1,5,8,7,2,4,3,6]=>1000000=>0000001=>[7,1]
[8,7,1,3,2,5,4,6]=>0000000=>0000000=>[8]
[6,7,4,2,8,1,3,5]=>0000000=>0000000=>[8]
[8,5,1,4,7,6,3,2]=>0000000=>0000000=>[8]
[8,1,3,7,2,4,6,5]=>0000000=>0000000=>[8]
[5,3,1,6,4,8,2,7]=>0000000=>0000000=>[8]
[2,5,6,7,1,4,8,3]=>0000000=>0000000=>[8]
[1,4,2,7,5,8,3,6]=>1000000=>0000001=>[7,1]
[5,8,1,2,7,4,3,6]=>0000000=>0000000=>[8]
[4,6,3,7,8,1,5,2]=>0000000=>0000000=>[8]
[2,4,7,3,6,8,1,5]=>0000000=>0000000=>[8]
[2,7,3,1,8,5,4,6]=>0000000=>0000000=>[8]
[2,3,1,6,8,7,4,5]=>0010000=>0000100=>[5,3]
[6,4,8,2,1,7,3,5]=>0000000=>0000000=>[8]
[8,5,1,2,7,4,3,6]=>0000000=>0000000=>[8]
[1,3,7,6,8,4,2,5]=>1000000=>0000001=>[7,1]
[2,1,5,7,4,6,8,3]=>0100000=>0000010=>[6,2]
[2,3,5,7,8,1,6,4]=>0000000=>0000000=>[8]
[1,6,4,2,3,5,7,8]=>1000011=>1100001=>[1,1,5,1]
[1,5,7,4,2,3,6,8]=>1000001=>1000001=>[1,6,1]
[8,1,7,2,4,6,3,5]=>0000000=>0000000=>[8]
[2,4,7,8,3,5,1,6]=>0000000=>0000000=>[8]
[1,3,6,2,5,8,4,7]=>1000000=>0000001=>[7,1]
[1,5,3,6,8,2,4,7]=>1000000=>0000001=>[7,1]
[2,8,5,1,4,3,7,6]=>0000000=>0000000=>[8]
[1,8,6,2,4,3,7,5]=>1000000=>0000001=>[7,1]
[4,1,6,5,2,3,7,8]=>0000011=>1100000=>[1,1,6]
[4,1,3,6,7,2,5,8]=>0000001=>1000000=>[1,7]
[2,7,5,8,1,3,6,4]=>0000000=>0000000=>[8]
[5,1,6,7,3,2,4,8]=>0000001=>1000000=>[1,7]
[7,4,1,2,3,6,8,5]=>0000000=>0000000=>[8]
[9,10,6,4,2,1,3,5,8,7]=>000000000=>000000000=>[10]
[10,7,8,4,2,1,3,6,5,9]=>000000000=>000000000=>[10]
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[10,5,6,7,8,4,3,2,1,9]=>000000000=>000000000=>[10]
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[2,7,4,1,5,8,3,6]=>0000000=>0000000=>[8]
[6,1,7,3,4,2,5,8]=>0000001=>1000000=>[1,7]
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[6,8,4,3,1,5,2,7]=>0000000=>0000000=>[8]
[3,2,4,8,6,1,7,5]=>0000000=>0000000=>[8]
[2,1,3,8,4,5,7,6]=>0110000=>0000110=>[5,1,2]
[2,1,3,7,8,4,6,5]=>0110000=>0000110=>[5,1,2]
[2,1,3,8,4,7,6,5]=>0110000=>0000110=>[5,1,2]
[3,1,2,8,4,5,7,6]=>0010000=>0000100=>[5,3]
[1,2,8,7,5,4,6,3]=>1100000=>0000011=>[6,1,1]
[1,3,6,8,2,7,5,4]=>1000000=>0000001=>[7,1]
[3,2,6,5,1,8,4,7]=>0000000=>0000000=>[8]
[2,8,3,7,6,1,5,4]=>0000000=>0000000=>[8]
[5,4,2,6,8,7,3,1]=>0000000=>0000000=>[8]
[3,7,2,5,8,6,4,1]=>0000000=>0000000=>[8]
[5,4,3,7,2,8,6,1]=>0000000=>0000000=>[8]
[4,6,5,3,8,1,7,2]=>0000000=>0000000=>[8]
[2,4,8,7,6,1,5,3]=>0000000=>0000000=>[8]
[4,8,5,2,7,6,3,1]=>0000000=>0000000=>[8]
[2,8,6,5,7,1,3,4]=>0000000=>0000000=>[8]
[1,8,7,4,5,2,3,6]=>1000000=>0000001=>[7,1]
[5,8,1,7,6,2,3,4]=>0000000=>0000000=>[8]
[1,7,6,2,4,3,8,5]=>1000000=>0000001=>[7,1]
[5,6,8,7,1,3,2,4]=>0000000=>0000000=>[8]
[7,1,6,8,2,5,4,3]=>0000000=>0000000=>[8]
[6,4,2,7,1,5,8,3]=>0000000=>0000000=>[8]
[5,3,6,7,4,2,8,1]=>0000000=>0000000=>[8]
[2,6,3,7,5,4,8,1]=>0000000=>0000000=>[8]
[1,7,3,2,4,8,6,5]=>1000000=>0000001=>[7,1]
[6,4,1,3,8,7,5,2]=>0000000=>0000000=>[8]
[4,3,1,8,2,6,7,5]=>0000000=>0000000=>[8]
[4,8,1,3,2,5,7,6]=>0000000=>0000000=>[8]
[7,2,6,5,8,3,4,1]=>0000000=>0000000=>[8]
[1,7,5,3,8,6,2,4]=>1000000=>0000001=>[7,1]
[2,5,3,8,1,4,7,6]=>0000000=>0000000=>[8]
[4,2,5,8,1,3,7,6]=>0000000=>0000000=>[8]
[8,1,2,4,3,5,7,6]=>0000000=>0000000=>[8]
[2,4,3,8,1,5,7,6]=>0000000=>0000000=>[8]
[7,5,2,3,8,4,6,1]=>0000000=>0000000=>[8]
[2,7,5,1,4,8,3,6]=>0000000=>0000000=>[8]
[3,1,7,4,8,6,5,2]=>0000000=>0000000=>[8]
[6,4,5,3,2,8,7,1]=>0000000=>0000000=>[8]
[2,7,3,8,5,1,6,4]=>0000000=>0000000=>[8]
[8,7,3,2,5,6,4,1]=>0000000=>0000000=>[8]
[1,5,8,2,6,4,3,7]=>1000000=>0000001=>[7,1]
[3,1,8,2,6,5,4,7]=>0000000=>0000000=>[8]
[7,6,2,8,1,4,5,3]=>0000000=>0000000=>[8]
[8,4,2,3,1,5,7,6]=>0000000=>0000000=>[8]
[8,2,3,4,1,5,7,6]=>0000000=>0000000=>[8]
[2,5,6,3,8,1,4,7]=>0000000=>0000000=>[8]
[7,3,5,6,1,8,4,2]=>0000000=>0000000=>[8]
[7,4,5,6,8,1,3,2]=>0000000=>0000000=>[8]
[7,5,1,8,4,6,3,2]=>0000000=>0000000=>[8]
[2,8,1,7,4,5,3,6]=>0000000=>0000000=>[8]
[6,1,5,3,8,4,7,2]=>0000000=>0000000=>[8]
[1,6,5,3,8,4,7,2]=>1000000=>0000001=>[7,1]
[7,6,2,3,5,4,8,1]=>0000000=>0000000=>[8]
[7,6,2,3,5,1,4,8]=>0000001=>1000000=>[1,7]
[6,1,5,2,3,4,8,7]=>0000010=>0100000=>[2,6]
[6,2,5,3,4,8,1,7]=>0000000=>0000000=>[8]
[6,2,5,3,4,8,7,1]=>0000000=>0000000=>[8]
[2,6,5,3,4,8,7,1]=>0000000=>0000000=>[8]
[2,6,5,3,4,8,1,7]=>0000000=>0000000=>[8]
[2,5,1,4,8,3,7,6]=>0000000=>0000000=>[8]
[1,2,5,4,8,3,7,6]=>1100000=>0000011=>[6,1,1]
[5,3,4,8,1,7,2,6]=>0000000=>0000000=>[8]
[5,1,3,4,8,7,2,6]=>0000000=>0000000=>[8]
[1,5,3,4,8,7,2,6]=>1000000=>0000001=>[7,1]
[5,1,3,8,4,7,6,2]=>0000000=>0000000=>[8]
[5,3,8,1,4,7,6,2]=>0000000=>0000000=>[8]
[4,3,5,8,1,7,6,2]=>0000000=>0000000=>[8]
[3,6,5,4,8,1,2,7]=>0000000=>0000000=>[8]
[3,6,5,4,8,2,7,1]=>0000000=>0000000=>[8]
[4,3,5,8,2,1,7,6]=>0000000=>0000000=>[8]
[3,5,2,4,8,7,6,1]=>0000000=>0000000=>[8]
[2,3,6,5,8,4,1,7]=>0000000=>0000000=>[8]
[5,2,3,8,7,4,1,6]=>0000000=>0000000=>[8]
[2,3,1,7,4,8,6,5]=>0010000=>0000100=>[5,3]
[7,4,1,3,6,2,5,8]=>0000001=>1000000=>[1,7]
[7,2,5,8,1,3,6,4]=>0000000=>0000000=>[8]
[1,2,6,5,3,4,7,8]=>1100011=>1100011=>[1,1,4,1,1]
[1,4,6,5,7,2,3,8]=>1000001=>1000001=>[1,6,1]
[2,4,6,5,7,1,8,3]=>0000000=>0000000=>[8]
[3,5,2,1,7,8,6,4]=>0000000=>0000000=>[8]
[7,1,6,3,2,4,8,5]=>0000000=>0000000=>[8]
[6,4,8,1,2,3,7,5]=>0000000=>0000000=>[8]
[4,3,5,1,7,8,6,2]=>0000000=>0000000=>[8]
[4,6,7,2,3,8,5,1]=>0000000=>0000000=>[8]
[2,3,5,8,7,4,1,6]=>0000000=>0000000=>[8]
[2,3,5,8,7,4,6,1]=>0000000=>0000000=>[8]
[1,7,4,5,8,3,6,2]=>1000000=>0000001=>[7,1]
[7,1,5,2,4,8,3,6]=>0000000=>0000000=>[8]
[8,1,5,2,4,7,3,6]=>0000000=>0000000=>[8]
[7,5,8,1,4,2,3,6]=>0000000=>0000000=>[8]
[1,3,4,8,5,6,2,7]=>1000000=>0000001=>[7,1]
[4,8,3,6,1,7,2,5]=>0000000=>0000000=>[8]
[4,6,3,1,2,5,7,8]=>0000011=>1100000=>[1,1,6]
[7,4,6,8,3,1,2,5]=>0000000=>0000000=>[8]
[8,5,4,7,3,1,2,6]=>0000000=>0000000=>[8]
[2,5,6,4,8,1,3,7]=>0000000=>0000000=>[8]
[5,4,1,6,2,3,7,8]=>0000011=>1100000=>[1,1,6]
[1,5,6,4,2,3,7,8]=>1000011=>1100001=>[1,1,5,1]
[2,5,1,4,6,3,8,7]=>0000010=>0100000=>[2,6]
[8,1,4,3,7,5,6,2]=>0000000=>0000000=>[8]
[8,3,7,6,2,4,5,1]=>0000000=>0000000=>[8]
[8,1,2,7,6,4,5,3]=>0000000=>0000000=>[8]
[1,7,3,8,6,2,5,4]=>1000000=>0000001=>[7,1]
[1,2,4,6,8,3,7,5]=>1100000=>0000011=>[6,1,1]
[1,3,5,6,4,8,2,7]=>1000000=>0000001=>[7,1]
[6,3,5,7,1,4,2,8]=>0000001=>1000000=>[1,7]
[5,4,8,6,3,7,1,2]=>0000000=>0000000=>[8]
[3,4,8,5,6,1,2,7]=>0000000=>0000000=>[8]
[1,7,6,2,5,4,8,3]=>1000000=>0000001=>[7,1]
[3,7,2,1,5,6,8,4]=>0000000=>0000000=>[8]
[8,1,6,4,3,5,2,7]=>0000000=>0000000=>[8]
[4,6,8,5,1,3,7,2]=>0000000=>0000000=>[8]
[4,3,1,8,5,7,2,6]=>0000000=>0000000=>[8]
[4,8,3,6,1,5,2,7]=>0000000=>0000000=>[8]
[8,3,2,4,7,1,6,5]=>0000000=>0000000=>[8]
[7,3,2,4,8,1,6,5]=>0000000=>0000000=>[8]
[8,3,2,4,6,1,7,5]=>0000000=>0000000=>[8]
[8,3,2,4,5,7,1,6]=>0000000=>0000000=>[8]
[8,3,6,2,4,1,7,5]=>0000000=>0000000=>[8]
[7,4,6,2,1,3,8,5]=>0000000=>0000000=>[8]
[3,2,4,5,7,8,1,6]=>0000000=>0000000=>[8]
[3,6,7,2,4,1,8,5]=>0000000=>0000000=>[8]
[7,3,5,2,8,1,4,6]=>0000000=>0000000=>[8]
[2,6,8,4,5,1,7,3]=>0000000=>0000000=>[8]
[1,5,8,7,4,2,3,6]=>1000000=>0000001=>[7,1]
[1,5,2,7,6,4,8,3]=>1000000=>0000001=>[7,1]
[1,4,6,8,7,2,5,3]=>1000000=>0000001=>[7,1]
[1,3,6,8,7,2,5,4]=>1000000=>0000001=>[7,1]
[1,4,3,6,8,7,2,5]=>1000000=>0000001=>[7,1]
[1,6,2,7,5,3,4,8]=>1000001=>1000001=>[1,6,1]
[1,7,2,5,4,3,8,6]=>1000000=>0000001=>[7,1]
[1,6,3,7,2,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,3,2,6,8,5,4,7]=>1010000=>0000101=>[5,2,1]
[1,6,3,2,7,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,5,8,6,2,7,4,3]=>1000000=>0000001=>[7,1]
[1,3,7,2,6,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,3,7,5,8,6,2,4]=>1000000=>0000001=>[7,1]
[1,7,3,2,8,5,6,4]=>1000000=>0000001=>[7,1]
[1,6,5,2,4,8,3,7]=>1000000=>0000001=>[7,1]
[1,4,7,6,2,3,5,8]=>1000001=>1000001=>[1,6,1]
[1,7,3,8,4,2,5,6]=>1000000=>0000001=>[7,1]
[1,6,2,4,7,5,8,3]=>1000000=>0000001=>[7,1]
[1,6,2,7,4,3,8,5]=>1000000=>0000001=>[7,1]
[1,5,8,2,3,6,4,7]=>1000000=>0000001=>[7,1]
[5,4,7,8,1,6,3,2]=>0000000=>0000000=>[8]
[1,7,8,4,3,6,5,2]=>1000000=>0000001=>[7,1]
[1,7,8,3,6,5,4,2]=>1000000=>0000001=>[7,1]
[1,8,4,2,3,7,5,6]=>1000000=>0000001=>[7,1]
[6,5,1,3,8,4,2,7]=>0000000=>0000000=>[8]
[6,1,4,2,7,8,3,5]=>0000000=>0000000=>[8]
[6,5,1,3,7,8,4,2]=>0000000=>0000000=>[8]
[5,6,8,2,4,7,1,3]=>0000000=>0000000=>[8]
[5,1,3,2,6,8,4,7]=>0000000=>0000000=>[8]
[1,5,7,3,6,4,2,8]=>1000001=>1000001=>[1,6,1]
[1,6,3,5,7,4,8,2]=>1000000=>0000001=>[7,1]
[1,7,2,4,8,3,5,6]=>1000000=>0000001=>[7,1]
[1,6,7,2,4,8,3,5]=>1000000=>0000001=>[7,1]
[1,6,7,8,2,4,3,5]=>1000000=>0000001=>[7,1]
[3,1,6,7,8,4,2,5]=>0000000=>0000000=>[8]
[3,1,6,7,8,4,5,2]=>0000000=>0000000=>[8]
[1,6,7,8,2,4,5,3]=>1000000=>0000001=>[7,1]
[4,2,7,6,8,5,1,3]=>0000000=>0000000=>[8]
[5,3,4,1,7,8,6,2]=>0000000=>0000000=>[8]
[3,7,5,6,1,8,4,2]=>0000000=>0000000=>[8]
[2,4,7,5,8,3,6,1]=>0000000=>0000000=>[8]
[6,8,7,4,2,5,1,3]=>0000000=>0000000=>[8]
[7,6,3,1,2,8,5,4]=>0000000=>0000000=>[8]
[3,1,8,6,4,7,2,5]=>0000000=>0000000=>[8]
[6,2,7,8,3,4,5,1]=>0000000=>0000000=>[8]
[8,1,3,5,6,4,7,2]=>0000000=>0000000=>[8]
[2,3,7,5,8,4,6,1]=>0000000=>0000000=>[8]
[8,1,7,4,2,5,3,6]=>0000000=>0000000=>[8]
[5,2,6,4,1,3,8,7]=>0000010=>0100000=>[2,6]
[2,1,8,5,4,3,7,6]=>0100000=>0000010=>[6,2]
[5,2,4,7,8,1,3,6]=>0000000=>0000000=>[8]
[1,7,6,2,8,5,3,4]=>1000000=>0000001=>[7,1]
[5,6,2,8,1,7,3,4]=>0000000=>0000000=>[8]
[3,1,2,4,8,6,7,5]=>0011000=>0001100=>[4,1,3]
[1,8,7,2,3,4,5,6]=>1000000=>0000001=>[7,1]
[3,7,5,2,8,1,4,6]=>0000000=>0000000=>[8]
[1,2,7,4,8,5,6,3]=>1100000=>0000011=>[6,1,1]
[5,6,3,4,2,8,7,1]=>0000000=>0000000=>[8]
[3,2,7,5,8,1,6,4]=>0000000=>0000000=>[8]
[3,6,5,8,2,7,4,1]=>0000000=>0000000=>[8]
[2,7,1,8,5,6,4,3]=>0000000=>0000000=>[8]
[4,3,6,8,5,2,1,7]=>0000000=>0000000=>[8]
[4,3,6,8,5,2,7,1]=>0000000=>0000000=>[8]
[4,5,3,2,1,8,6,7]=>0000100=>0010000=>[3,5]
[3,6,5,8,1,7,4,2]=>0000000=>0000000=>[8]
[3,6,5,8,1,2,7,4]=>0000000=>0000000=>[8]
[4,1,6,8,5,2,3,7]=>0000000=>0000000=>[8]
[4,5,2,8,6,7,3,1]=>0000000=>0000000=>[8]
[3,5,8,6,2,4,7,1]=>0000000=>0000000=>[8]
[3,2,4,5,8,6,1,7]=>0000000=>0000000=>[8]
[3,4,5,8,6,2,1,7]=>0000000=>0000000=>[8]
[3,4,5,8,6,2,7,1]=>0000000=>0000000=>[8]
[4,5,2,1,3,8,6,7]=>0000100=>0010000=>[3,5]
[4,2,3,6,8,5,1,7]=>0000000=>0000000=>[8]
[4,1,3,6,8,5,2,7]=>0000000=>0000000=>[8]
[3,1,4,5,8,6,2,7]=>0000000=>0000000=>[8]
[4,5,1,3,2,8,6,7]=>0000100=>0010000=>[3,5]
[3,4,5,8,6,1,7,2]=>0000000=>0000000=>[8]
[3,4,5,8,6,1,2,7]=>0000000=>0000000=>[8]
[8,2,5,4,1,3,7,6]=>0000000=>0000000=>[8]
[8,2,6,4,1,3,7,5]=>0000000=>0000000=>[8]
[1,5,8,2,4,3,7,6]=>1000000=>0000001=>[7,1]
[2,4,8,3,5,7,1,6]=>0000000=>0000000=>[8]
[1,4,8,5,7,2,3,6]=>1000000=>0000001=>[7,1]
[1,8,7,3,2,4,5,6]=>1000000=>0000001=>[7,1]
[2,8,4,3,5,7,1,6]=>0000000=>0000000=>[8]
[5,6,2,7,8,3,1,4]=>0000000=>0000000=>[8]
[8,6,2,7,3,4,1,5]=>0000000=>0000000=>[8]
[8,6,2,7,3,4,5,1]=>0000000=>0000000=>[8]
[5,6,2,7,8,3,4,1]=>0000000=>0000000=>[8]
[5,6,3,2,8,7,1,4]=>0000000=>0000000=>[8]
[6,8,5,3,1,7,2,4]=>0000000=>0000000=>[8]
[8,6,1,7,3,4,2,5]=>0000000=>0000000=>[8]
[5,1,6,7,8,3,2,4]=>0000000=>0000000=>[8]
[1,5,6,3,7,2,4,8]=>1000001=>1000001=>[1,6,1]
[6,2,4,8,3,7,1,5]=>0000000=>0000000=>[8]
[1,6,8,7,5,2,3,4]=>1000000=>0000001=>[7,1]
[1,5,6,7,4,2,3,8]=>1000001=>1000001=>[1,6,1]
[5,1,6,7,3,4,2,8]=>0000001=>1000000=>[1,7]
[8,6,1,7,3,4,5,2]=>0000000=>0000000=>[8]
[6,1,8,7,4,5,2,3]=>0000000=>0000000=>[8]
[2,6,8,4,7,5,1,3]=>0000000=>0000000=>[8]
[6,8,5,1,7,4,2,3]=>0000000=>0000000=>[8]
[4,6,5,7,2,3,8,1]=>0000000=>0000000=>[8]
[5,3,7,4,6,2,8,1]=>0000000=>0000000=>[8]
[3,6,7,2,5,8,4,1]=>0000000=>0000000=>[8]
[3,5,7,6,8,2,1,4]=>0000000=>0000000=>[8]
[5,3,6,7,4,8,1,2]=>0000000=>0000000=>[8]
[3,5,7,6,8,1,4,2]=>0000000=>0000000=>[8]
[4,2,7,8,3,6,5,1]=>0000000=>0000000=>[8]
[5,4,3,7,8,1,6,2]=>0000000=>0000000=>[8]
[5,3,6,7,8,2,1,4]=>0000000=>0000000=>[8]
[3,5,7,8,4,2,1,6]=>0000000=>0000000=>[8]
[4,6,7,8,2,1,3,5]=>0000000=>0000000=>[8]
[4,6,7,3,2,8,1,5]=>0000000=>0000000=>[8]
[4,6,5,3,7,8,1,2]=>0000000=>0000000=>[8]
[4,6,5,2,7,8,3,1]=>0000000=>0000000=>[8]
[3,7,5,2,8,6,1,4]=>0000000=>0000000=>[8]
[5,6,2,4,7,8,3,1]=>0000000=>0000000=>[8]
[5,4,6,2,8,3,7,1]=>0000000=>0000000=>[8]
[5,6,3,2,8,4,7,1]=>0000000=>0000000=>[8]
[5,6,2,8,3,4,7,1]=>0000000=>0000000=>[8]
[3,7,4,8,1,6,5,2]=>0000000=>0000000=>[8]
[5,2,6,4,8,7,3,1]=>0000000=>0000000=>[8]
[2,4,7,8,6,5,1,3]=>0000000=>0000000=>[8]
[2,5,7,8,6,1,4,3]=>0000000=>0000000=>[8]
[1,3,6,4,8,2,7,5]=>1000000=>0000001=>[7,1]
[2,4,5,3,8,7,1,6]=>0000000=>0000000=>[8]
[8,6,3,7,2,4,1,5]=>0000000=>0000000=>[8]
[1,8,5,6,4,2,3,7]=>1000000=>0000001=>[7,1]
[1,7,6,2,3,5,8,4]=>1000000=>0000001=>[7,1]
[8,1,6,5,2,7,4,3]=>0000000=>0000000=>[8]
[2,7,1,5,3,8,6,4]=>0000000=>0000000=>[8]
[7,3,2,1,4,8,6,5]=>0000000=>0000000=>[8]
[8,3,7,2,6,5,1,4]=>0000000=>0000000=>[8]
[7,5,8,2,6,1,4,3]=>0000000=>0000000=>[8]
[8,5,1,3,2,4,6,7]=>0000000=>0000000=>[8]
[3,8,5,1,2,4,6,7]=>0000000=>0000000=>[8]
[5,1,3,2,4,6,8,7]=>0000110=>0110000=>[2,1,5]
[5,3,8,1,4,2,6,7]=>0000000=>0000000=>[8]
[5,8,4,1,2,3,6,7]=>0000000=>0000000=>[8]
[5,1,7,8,4,2,3,6]=>0000000=>0000000=>[8]
[1,5,7,8,2,4,3,6]=>1000000=>0000001=>[7,1]
[3,5,8,1,4,2,7,6]=>0000000=>0000000=>[8]
[2,8,5,7,1,4,3,6]=>0000000=>0000000=>[8]
[4,8,7,5,1,2,3,6]=>0000000=>0000000=>[8]
[8,6,4,1,2,3,7,5]=>0000000=>0000000=>[8]
[8,1,2,4,6,3,7,5]=>0000000=>0000000=>[8]
[6,3,8,4,1,7,2,5]=>0000000=>0000000=>[8]
[7,6,1,4,2,3,8,5]=>0000000=>0000000=>[8]
[1,7,5,2,3,4,8,6]=>1000000=>0000001=>[7,1]
[7,8,1,2,5,3,4,6]=>0000000=>0000000=>[8]
[1,8,7,5,2,3,4,6]=>1000000=>0000001=>[7,1]
[7,1,4,8,2,3,6,5]=>0000000=>0000000=>[8]
[1,8,4,7,5,2,3,6]=>1000000=>0000001=>[7,1]
[7,3,4,1,8,6,2,5]=>0000000=>0000000=>[8]
[8,4,7,2,1,6,3,5]=>0000000=>0000000=>[8]
[3,4,7,8,6,1,2,5]=>0000000=>0000000=>[8]
[7,6,1,8,2,5,4,3]=>0000000=>0000000=>[8]
[5,8,4,2,1,6,3,7]=>0000000=>0000000=>[8]
[7,6,4,1,2,5,3,8]=>0000001=>1000000=>[1,7]
[4,8,6,5,1,3,7,2]=>0000000=>0000000=>[8]
[1,7,5,4,8,6,2,3]=>1000000=>0000001=>[7,1]
[1,6,3,7,2,4,8,5]=>1000000=>0000001=>[7,1]
[8,7,2,4,1,5,3,6]=>0000000=>0000000=>[8]
[5,2,4,1,8,3,6,7]=>0000000=>0000000=>[8]
[4,3,1,6,7,2,5,8]=>0000001=>1000000=>[1,7]
[6,3,1,5,7,2,4,8]=>0000001=>1000000=>[1,7]
[4,5,2,1,3,7,6,8]=>0000101=>1010000=>[1,2,5]
[2,7,6,4,5,1,8,3]=>0000000=>0000000=>[8]
[2,8,4,6,3,1,5,7]=>0000000=>0000000=>[8]
[2,8,3,1,6,7,4,5]=>0000000=>0000000=>[8]
[4,8,5,7,1,2,3,6]=>0000000=>0000000=>[8]
[7,4,8,3,6,2,1,5]=>0000000=>0000000=>[8]
[1,5,7,4,8,6,2,3]=>1000000=>0000001=>[7,1]
[4,8,7,5,2,3,1,6]=>0000000=>0000000=>[8]
[1,2,7,8,6,4,3,5]=>1100000=>0000011=>[6,1,1]
[3,5,1,7,8,6,2,4]=>0000000=>0000000=>[8]
[1,8,6,7,4,2,3,5]=>1000000=>0000001=>[7,1]
[1,5,4,7,3,8,6,2]=>1000000=>0000001=>[7,1]
[2,5,6,4,1,3,8,7]=>0000010=>0100000=>[2,6]
[7,2,3,1,6,8,4,5]=>0000000=>0000000=>[8]
[5,7,8,1,6,2,3,4]=>0000000=>0000000=>[8]
[1,6,3,8,2,7,4,5]=>1000000=>0000001=>[7,1]
[1,4,2,5,8,6,3,7]=>1000000=>0000001=>[7,1]
[4,8,2,1,5,7,3,6]=>0000000=>0000000=>[8]
[5,2,7,1,6,3,4,8]=>0000001=>1000000=>[1,7]
[4,8,2,5,1,6,3,7]=>0000000=>0000000=>[8]
[5,8,1,2,4,6,3,7]=>0000000=>0000000=>[8]
[5,1,7,3,6,4,2,8]=>0000001=>1000000=>[1,7]
[3,1,7,5,6,2,4,8]=>0000001=>1000000=>[1,7]
[3,2,7,5,6,1,4,8]=>0000001=>1000000=>[1,7]
[3,2,7,1,6,4,5,8]=>0000001=>1000000=>[1,7]
[6,3,1,7,5,4,2,8]=>0000001=>1000000=>[1,7]
[5,8,3,2,4,1,7,6]=>0000000=>0000000=>[8]
[2,7,5,6,8,3,1,4]=>0000000=>0000000=>[8]
[1,7,8,6,3,4,2,5]=>1000000=>0000001=>[7,1]
[7,3,2,1,4,6,8,5]=>0000000=>0000000=>[8]
[7,8,5,3,2,1,6,4]=>0000000=>0000000=>[8]
[1,4,7,2,5,3,6,8]=>1000001=>1000001=>[1,6,1]
[4,5,1,3,8,2,6,7]=>0000000=>0000000=>[8]
[4,1,5,3,2,7,6,8]=>0000101=>1010000=>[1,2,5]
[7,3,5,1,4,2,6,8]=>0000001=>1000000=>[1,7]
[7,5,2,4,1,3,8,6]=>0000000=>0000000=>[8]
[6,2,1,7,4,3,8,5]=>0000000=>0000000=>[8]
[2,4,3,6,7,1,5,8]=>0000001=>1000000=>[1,7]
[3,1,7,4,2,6,8,5]=>0000000=>0000000=>[8]
[7,3,5,2,1,6,4,8]=>0000001=>1000000=>[1,7]
[4,6,5,2,1,3,7,8]=>0000011=>1100000=>[1,1,6]
[1,4,7,2,5,6,3,8]=>1000001=>1000001=>[1,6,1]
[7,2,5,6,1,3,8,4]=>0000000=>0000000=>[8]
[2,5,6,1,4,3,7,8]=>0000011=>1100000=>[1,1,6]
[6,1,5,3,7,2,4,8]=>0000001=>1000000=>[1,7]
[3,6,5,4,1,7,2,8]=>0000001=>1000000=>[1,7]
[6,8,5,7,2,1,4,3]=>0000000=>0000000=>[8]
[1,4,2,6,7,8,5,3]=>1000000=>0000001=>[7,1]
[5,6,4,2,1,8,3,7]=>0000000=>0000000=>[8]
[4,1,2,6,7,8,5,3]=>0000000=>0000000=>[8]
[5,6,2,7,8,1,3,4]=>0000000=>0000000=>[8]
[3,7,8,2,1,4,5,6]=>0000000=>0000000=>[8]
[5,1,4,7,8,3,6,2]=>0000000=>0000000=>[8]
[5,6,4,1,7,3,8,2]=>0000000=>0000000=>[8]
[2,7,1,6,5,8,3,4]=>0000000=>0000000=>[8]
[4,6,1,7,3,2,8,5]=>0000000=>0000000=>[8]
[1,7,3,6,4,2,8,5]=>1000000=>0000001=>[7,1]
[1,3,7,6,2,4,8,5]=>1000000=>0000001=>[7,1]
[4,7,3,5,1,2,8,6]=>0000000=>0000000=>[8]
[2,5,1,8,3,7,4,6]=>0000000=>0000000=>[8]
[5,1,2,4,3,6,8,7]=>0000110=>0110000=>[2,1,5]
[4,8,3,5,2,1,6,7]=>0000000=>0000000=>[8]
[3,8,4,1,7,5,2,6]=>0000000=>0000000=>[8]
[4,7,3,2,6,5,1,8]=>0000001=>1000000=>[1,7]
[4,7,5,2,3,6,1,8]=>0000001=>1000000=>[1,7]
[4,3,7,8,2,1,6,5]=>0000000=>0000000=>[8]
[4,8,7,2,1,5,6,3]=>0000000=>0000000=>[8]
[7,3,8,2,5,1,6,4]=>0000000=>0000000=>[8]
[4,5,3,8,2,1,7,6]=>0000000=>0000000=>[8]
[4,5,3,8,6,1,2,7]=>0000000=>0000000=>[8]
[7,3,8,4,5,1,2,6]=>0000000=>0000000=>[8]
[4,8,7,5,1,3,2,6]=>0000000=>0000000=>[8]
[4,8,7,5,1,2,6,3]=>0000000=>0000000=>[8]
[7,8,4,6,1,3,5,2]=>0000000=>0000000=>[8]
[4,8,7,5,1,3,6,2]=>0000000=>0000000=>[8]
[4,5,3,6,8,1,2,7]=>0000000=>0000000=>[8]
[7,8,6,2,1,4,3,5]=>0000000=>0000000=>[8]
[4,7,5,8,2,1,3,6]=>0000000=>0000000=>[8]
[4,8,5,7,1,3,2,6]=>0000000=>0000000=>[8]
[7,8,6,3,1,2,5,4]=>0000000=>0000000=>[8]
[5,3,1,2,4,6,8,7]=>0000110=>0110000=>[2,1,5]
[6,1,5,2,8,7,4,3]=>0000000=>0000000=>[8]
[3,2,6,1,5,8,7,4]=>0000000=>0000000=>[8]
[4,5,2,1,6,7,8,3]=>0000000=>0000000=>[8]
[1,4,7,2,6,5,8,3]=>1000000=>0000001=>[7,1]
[1,7,6,2,8,5,4,3]=>1000000=>0000001=>[7,1]
[1,2,7,8,3,4,6,5]=>1100000=>0000011=>[6,1,1]
[2,8,4,3,1,6,5,7]=>0000000=>0000000=>[8]
[2,4,3,8,6,5,1,7]=>0000000=>0000000=>[8]
[2,8,6,4,3,1,7,5]=>0000000=>0000000=>[8]
[7,4,5,8,1,3,6,2]=>0000000=>0000000=>[8]
[4,2,5,7,1,6,8,3]=>0000000=>0000000=>[8]
[4,5,3,7,1,6,8,2]=>0000000=>0000000=>[8]
[6,8,4,1,5,7,3,2]=>0000000=>0000000=>[8]
[6,8,4,1,5,7,2,3]=>0000000=>0000000=>[8]
[5,2,6,7,4,1,8,3]=>0000000=>0000000=>[8]
[5,6,7,4,3,1,8,2]=>0000000=>0000000=>[8]
[8,5,6,4,1,7,3,2]=>0000000=>0000000=>[8]
[5,8,2,6,1,7,4,3]=>0000000=>0000000=>[8]
[7,8,3,1,6,4,5,2]=>0000000=>0000000=>[8]
[5,8,2,6,3,1,7,4]=>0000000=>0000000=>[8]
[4,5,8,1,6,3,7,2]=>0000000=>0000000=>[8]
[8,1,4,6,2,5,7,3]=>0000000=>0000000=>[8]
[4,8,1,3,6,2,7,5]=>0000000=>0000000=>[8]
[4,5,8,1,6,2,7,3]=>0000000=>0000000=>[8]
[5,2,6,8,1,4,3,7]=>0000000=>0000000=>[8]
[6,2,7,3,8,1,4,5]=>0000000=>0000000=>[8]
[6,7,3,8,2,1,4,5]=>0000000=>0000000=>[8]
[6,2,7,8,3,1,4,5]=>0000000=>0000000=>[8]
[8,7,3,1,2,5,6,4]=>0000000=>0000000=>[8]
[2,8,3,6,4,1,7,5]=>0000000=>0000000=>[8]
[6,1,3,7,2,8,5,4]=>0000000=>0000000=>[8]
[5,4,3,6,1,7,8,2]=>0000000=>0000000=>[8]
[4,8,3,2,1,7,5,6]=>0000000=>0000000=>[8]
[1,3,7,8,4,6,2,5]=>1000000=>0000001=>[7,1]
[5,8,4,3,7,1,2,6]=>0000000=>0000000=>[8]
[5,6,4,8,7,2,1,3]=>0000000=>0000000=>[8]
[4,1,7,8,6,5,2,3]=>0000000=>0000000=>[8]
[2,1,8,7,3,5,4,6]=>0100000=>0000010=>[6,2]
[1,7,6,2,3,8,5,4]=>1000000=>0000001=>[7,1]
[1,8,5,3,2,7,4,6]=>1000000=>0000001=>[7,1]
[4,5,1,3,7,6,2,8]=>0000001=>1000000=>[1,7]
[7,2,3,8,6,4,5,1]=>0000000=>0000000=>[8]
[3,5,8,1,7,4,2,6]=>0000000=>0000000=>[8]
[5,8,1,2,7,6,4,3]=>0000000=>0000000=>[8]
[8,7,1,3,2,6,4,5]=>0000000=>0000000=>[8]
[8,1,6,3,7,5,4,2]=>0000000=>0000000=>[8]
[8,5,1,3,7,6,4,2]=>0000000=>0000000=>[8]
[1,6,4,7,3,8,5,2]=>1000000=>0000001=>[7,1]
[2,8,1,5,6,4,3,7]=>0000000=>0000000=>[8]
[1,2,6,8,3,4,7,5]=>1100000=>0000011=>[6,1,1]
[1,6,7,5,8,4,2,3]=>1000000=>0000001=>[7,1]
[5,3,8,2,7,6,1,4]=>0000000=>0000000=>[8]
[7,4,2,8,6,5,3,1]=>0000000=>0000000=>[8]
[5,8,2,7,6,1,4,3]=>0000000=>0000000=>[8]
[7,4,8,3,1,6,5,2]=>0000000=>0000000=>[8]
[5,8,7,2,6,4,3,1]=>0000000=>0000000=>[8]
[6,8,7,5,2,1,4,3]=>0000000=>0000000=>[8]
[6,8,7,3,5,1,4,2]=>0000000=>0000000=>[8]
[7,2,5,4,1,3,8,6]=>0000000=>0000000=>[8]
[1,5,7,2,4,3,8,6]=>1000000=>0000001=>[7,1]
[1,2,7,5,8,4,3,6]=>1100000=>0000011=>[6,1,1]
[5,1,3,8,2,7,4,6]=>0000000=>0000000=>[8]
[5,7,1,3,2,8,4,6]=>0000000=>0000000=>[8]
[7,1,6,3,2,8,4,5]=>0000000=>0000000=>[8]
[8,1,7,2,3,6,5,4]=>0000000=>0000000=>[8]
[1,7,2,5,8,4,3,6]=>1000000=>0000001=>[7,1]
[7,1,2,6,4,3,8,5]=>0000000=>0000000=>[8]
[1,4,7,8,3,2,5,6]=>1000000=>0000001=>[7,1]
[8,7,1,3,2,4,6,5]=>0000000=>0000000=>[8]
[8,1,6,3,2,4,7,5]=>0000000=>0000000=>[8]
[1,8,2,7,6,3,5,4]=>1000000=>0000001=>[7,1]
[1,8,6,2,7,4,3,5]=>1000000=>0000001=>[7,1]
[8,1,6,3,2,7,4,5]=>0000000=>0000000=>[8]
[8,2,1,7,6,3,4,5]=>0000000=>0000000=>[8]
[6,4,5,3,1,8,7,2]=>0000000=>0000000=>[8]
[1,8,2,3,5,6,4,7]=>1000000=>0000001=>[7,1]
[2,8,1,3,5,6,4,7]=>0000000=>0000000=>[8]
[2,5,7,4,8,3,6,1]=>0000000=>0000000=>[8]
[2,6,3,4,7,8,5,1]=>0000000=>0000000=>[8]
[2,3,5,4,7,1,8,6]=>0000000=>0000000=>[8]
[7,4,1,3,6,8,5,2]=>0000000=>0000000=>[8]
[7,2,1,3,6,8,4,5]=>0000000=>0000000=>[8]
[7,4,2,3,6,8,5,1]=>0000000=>0000000=>[8]
[7,2,3,6,8,5,4,1]=>0000000=>0000000=>[8]
[7,6,3,1,8,5,2,4]=>0000000=>0000000=>[8]
[7,2,1,3,6,8,5,4]=>0000000=>0000000=>[8]
[7,6,3,8,1,5,2,4]=>0000000=>0000000=>[8]
[1,6,4,7,8,5,3,2]=>1000000=>0000001=>[7,1]
[7,2,5,1,6,4,3,8]=>0000001=>1000000=>[1,7]
[1,2,4,6,8,5,7,3]=>1100000=>0000011=>[6,1,1]
[2,6,3,7,4,1,8,5]=>0000000=>0000000=>[8]
[3,8,5,1,2,4,7,6]=>0000000=>0000000=>[8]
[1,8,3,7,5,2,6,4]=>1000000=>0000001=>[7,1]
[8,1,3,6,5,2,7,4]=>0000000=>0000000=>[8]
[7,1,3,8,5,2,6,4]=>0000000=>0000000=>[8]
[4,7,1,5,2,6,8,3]=>0000000=>0000000=>[8]
[7,4,1,5,2,6,8,3]=>0000000=>0000000=>[8]
[3,1,6,7,5,2,8,4]=>0000000=>0000000=>[8]
[8,6,2,4,5,1,7,3]=>0000000=>0000000=>[8]
[4,6,2,5,3,1,7,8]=>0000011=>1100000=>[1,1,6]
[7,1,4,5,2,6,8,3]=>0000000=>0000000=>[8]
[5,7,6,8,2,1,4,3]=>0000000=>0000000=>[8]
[4,5,1,3,6,7,8,2]=>0000000=>0000000=>[8]
[6,4,7,1,5,2,8,3]=>0000000=>0000000=>[8]
[3,5,6,2,1,7,8,4]=>0000000=>0000000=>[8]
[4,5,1,6,2,8,7,3]=>0000000=>0000000=>[8]
[3,2,5,8,6,1,7,4]=>0000000=>0000000=>[8]
[5,6,3,2,7,4,1,8]=>0000001=>1000000=>[1,7]
[5,2,6,7,4,3,1,8]=>0000001=>1000000=>[1,7]
[8,5,1,6,4,3,2,7]=>0000000=>0000000=>[8]
[8,5,1,6,4,3,7,2]=>0000000=>0000000=>[8]
[8,5,2,1,6,4,3,7]=>0000000=>0000000=>[8]
[8,6,3,5,2,7,1,4]=>0000000=>0000000=>[8]
[8,4,6,2,1,5,7,3]=>0000000=>0000000=>[8]
[5,6,2,1,8,4,7,3]=>0000000=>0000000=>[8]
[8,5,2,1,6,4,7,3]=>0000000=>0000000=>[8]
[1,7,2,8,5,4,6,3]=>1000000=>0000001=>[7,1]
[6,7,1,4,8,5,3,2]=>0000000=>0000000=>[8]
[7,4,8,2,1,5,6,3]=>0000000=>0000000=>[8]
[7,3,2,8,5,1,4,6]=>0000000=>0000000=>[8]
[6,7,1,4,3,2,8,5]=>0000000=>0000000=>[8]
[4,1,7,3,2,8,5,6]=>0000000=>0000000=>[8]
[8,3,5,2,4,7,1,6]=>0000000=>0000000=>[8]
[4,3,7,8,6,1,5,2]=>0000000=>0000000=>[8]
[6,2,8,4,3,7,1,5]=>0000000=>0000000=>[8]
[1,2,6,3,7,8,5,4]=>1100000=>0000011=>[6,1,1]
[6,1,3,2,7,8,5,4]=>0000000=>0000000=>[8]
[6,7,1,3,2,8,5,4]=>0000000=>0000000=>[8]
[2,6,4,7,5,3,1,8]=>0000001=>1000000=>[1,7]
[5,6,1,8,7,2,3,4]=>0000000=>0000000=>[8]
[1,4,7,5,2,3,6,8]=>1000001=>1000001=>[1,6,1]
[1,5,8,6,2,3,4,7]=>1000000=>0000001=>[7,1]
[5,8,4,3,6,2,7,1]=>0000000=>0000000=>[8]
[4,6,5,8,3,2,7,1]=>0000000=>0000000=>[8]
[3,4,7,5,6,8,2,1]=>0000000=>0000000=>[8]
[3,4,7,8,5,2,6,1]=>0000000=>0000000=>[8]
[2,3,8,4,7,1,6,5]=>0000000=>0000000=>[8]
[1,8,7,5,2,6,3,4]=>1000000=>0000001=>[7,1]
[1,8,7,5,4,3,2,6]=>1000000=>0000001=>[7,1]
[1,7,6,3,4,5,8,2]=>1000000=>0000001=>[7,1]
[1,8,7,4,5,6,2,3]=>1000000=>0000001=>[7,1]
[1,8,7,3,6,4,2,5]=>1000000=>0000001=>[7,1]
[1,8,7,2,4,6,3,5]=>1000000=>0000001=>[7,1]
[1,4,7,8,6,2,5,3]=>1000000=>0000001=>[7,1]
[1,7,6,4,2,5,3,8]=>1000001=>1000001=>[1,6,1]
[1,4,7,5,8,2,3,6]=>1000000=>0000001=>[7,1]
[1,4,7,5,8,2,6,3]=>1000000=>0000001=>[7,1]
[1,6,8,3,4,2,5,7]=>1000000=>0000001=>[7,1]
[1,4,7,2,3,6,5,8]=>1000001=>1000001=>[1,6,1]
[1,3,2,6,8,4,7,5]=>1010000=>0000101=>[5,2,1]
[1,7,2,5,6,3,4,8]=>1000001=>1000001=>[1,6,1]
[1,5,8,3,6,4,7,2]=>1000000=>0000001=>[7,1]
[1,2,6,5,8,3,4,7]=>1100000=>0000011=>[6,1,1]
[1,6,8,2,7,3,4,5]=>1000000=>0000001=>[7,1]
[1,4,5,8,2,6,3,7]=>1000000=>0000001=>[7,1]
[3,5,6,7,2,4,1,8]=>0000001=>1000000=>[1,7]
[6,4,7,5,2,3,1,8]=>0000001=>1000000=>[1,7]
[1,5,6,4,8,3,2,7]=>1000000=>0000001=>[7,1]
[5,2,6,4,8,7,1,3]=>0000000=>0000000=>[8]
[2,1,5,6,4,8,3,7]=>0100000=>0000010=>[6,2]
[5,1,4,7,8,6,2,3]=>0000000=>0000000=>[8]
[2,5,7,1,8,6,3,4]=>0000000=>0000000=>[8]
[1,6,7,2,8,5,4,3]=>1000000=>0000001=>[7,1]
[4,6,1,7,8,5,3,2]=>0000000=>0000000=>[8]
[5,3,2,1,7,8,6,4]=>0000000=>0000000=>[8]
[7,4,3,8,6,1,5,2]=>0000000=>0000000=>[8]
[4,3,7,1,5,8,6,2]=>0000000=>0000000=>[8]
[8,2,4,5,3,1,7,6]=>0000000=>0000000=>[8]
[8,5,3,2,4,1,7,6]=>0000000=>0000000=>[8]
[1,4,3,2,7,5,8,6]=>1001000=>0001001=>[4,3,1]
[7,2,5,3,4,6,1,8]=>0000001=>1000000=>[1,7]
[7,1,2,6,4,3,5,8]=>0000001=>1000000=>[1,7]
[7,1,2,6,3,4,5,8]=>0000001=>1000000=>[1,7]
[7,1,2,6,4,5,3,8]=>0000001=>1000000=>[1,7]
[7,1,2,6,5,3,4,8]=>0000001=>1000000=>[1,7]
[5,3,1,4,7,2,8,6]=>0000000=>0000000=>[8]
[7,1,3,8,2,6,4,5]=>0000000=>0000000=>[8]
[1,8,3,7,2,4,6,5]=>1000000=>0000001=>[7,1]
[7,4,3,1,6,5,2,8]=>0000001=>1000000=>[1,7]
[3,5,1,2,6,8,7,4]=>0000000=>0000000=>[8]
[1,5,2,4,3,8,7,6]=>1000100=>0010001=>[3,4,1]
[3,1,2,4,8,7,5,6]=>0011000=>0001100=>[4,1,3]
[5,2,1,6,3,8,7,4]=>0000000=>0000000=>[8]
[3,4,6,7,2,1,5,8]=>0000001=>1000000=>[1,7]
[2,5,7,4,6,8,1,3]=>0000000=>0000000=>[8]
[4,6,2,7,5,8,1,3]=>0000000=>0000000=>[8]
[4,7,2,5,3,8,1,6]=>0000000=>0000000=>[8]
[2,4,7,6,3,8,1,5]=>0000000=>0000000=>[8]
[5,8,3,6,4,1,7,2]=>0000000=>0000000=>[8]
[4,6,8,5,1,2,3,7]=>0000000=>0000000=>[8]
[4,6,5,7,1,2,3,8]=>0000001=>1000000=>[1,7]
[4,6,5,7,1,3,8,2]=>0000000=>0000000=>[8]
[3,4,7,6,1,8,2,5]=>0000000=>0000000=>[8]
[1,6,5,7,3,8,2,4]=>1000000=>0000001=>[7,1]
[8,6,2,7,5,3,1,4]=>0000000=>0000000=>[8]
[4,3,7,1,2,8,5,6]=>0000000=>0000000=>[8]
[2,6,7,1,4,3,8,5]=>0000000=>0000000=>[8]
[4,5,2,1,6,3,8,7]=>0000010=>0100000=>[2,6]
[4,5,2,1,6,7,3,8]=>0000001=>1000000=>[1,7]
[5,3,8,6,2,4,7,1]=>0000000=>0000000=>[8]
[2,5,1,6,4,3,8,7]=>0000010=>0100000=>[2,6]
[3,6,2,8,5,7,1,4]=>0000000=>0000000=>[8]
[4,6,8,1,5,7,2,3]=>0000000=>0000000=>[8]
[4,1,2,5,7,6,3,8]=>0000001=>1000000=>[1,7]
[5,2,3,8,7,1,6,4]=>0000000=>0000000=>[8]
[3,2,8,1,7,5,4,6]=>0000000=>0000000=>[8]
[4,8,5,1,3,7,2,6]=>0000000=>0000000=>[8]
[4,6,5,8,1,7,3,2]=>0000000=>0000000=>[8]
[2,1,3,6,4,8,7,5]=>0110000=>0000110=>[5,1,2]
[4,8,2,1,6,7,5,3]=>0000000=>0000000=>[8]
[4,8,1,2,7,5,6,3]=>0000000=>0000000=>[8]
[5,2,8,1,7,4,6,3]=>0000000=>0000000=>[8]
[5,7,4,8,1,2,6,3]=>0000000=>0000000=>[8]
[8,1,6,7,3,4,2,5]=>0000000=>0000000=>[8]
[4,5,1,6,8,7,2,3]=>0000000=>0000000=>[8]
[3,4,7,2,5,8,6,1]=>0000000=>0000000=>[8]
[3,4,7,1,5,8,2,6]=>0000000=>0000000=>[8]
[6,2,7,4,5,3,1,8]=>0000001=>1000000=>[1,7]
[8,6,4,7,5,1,3,2]=>0000000=>0000000=>[8]
[5,1,4,8,2,3,7,6]=>0000000=>0000000=>[8]
[4,5,2,3,8,6,1,7]=>0000000=>0000000=>[8]
[4,5,1,3,2,6,8,7]=>0000110=>0110000=>[2,1,5]
[4,7,1,8,5,3,6,2]=>0000000=>0000000=>[8]
[6,4,7,5,1,3,2,8]=>0000001=>1000000=>[1,7]
[6,7,2,4,1,8,3,5]=>0000000=>0000000=>[8]
[5,1,6,3,2,7,8,4]=>0000000=>0000000=>[8]
[2,3,7,8,5,4,6,1]=>0000000=>0000000=>[8]
[7,4,5,1,2,6,8,3]=>0000000=>0000000=>[8]
[6,7,8,2,1,5,3,4]=>0000000=>0000000=>[8]
[5,2,1,6,4,7,3,8]=>0000001=>1000000=>[1,7]
[6,7,2,5,4,1,3,8]=>0000001=>1000000=>[1,7]
[7,4,8,6,3,5,1,2]=>0000000=>0000000=>[8]
[4,6,3,5,1,8,2,7]=>0000000=>0000000=>[8]
[8,5,7,6,2,3,4,1]=>0000000=>0000000=>[8]
[2,4,7,5,8,6,3,1]=>0000000=>0000000=>[8]
[1,4,6,5,3,8,2,7]=>1000000=>0000001=>[7,1]
[2,4,5,8,7,1,3,6]=>0000000=>0000000=>[8]
[3,1,6,8,7,5,4,2]=>0000000=>0000000=>[8]
[3,1,8,7,5,6,4,2]=>0000000=>0000000=>[8]
[5,1,8,7,6,3,4,2]=>0000000=>0000000=>[8]
[1,3,8,4,7,2,6,5]=>1000000=>0000001=>[7,1]
[1,8,2,4,7,3,6,5]=>1000000=>0000001=>[7,1]
[8,2,7,5,3,6,4,1]=>0000000=>0000000=>[8]
[8,4,1,3,6,7,2,5]=>0000000=>0000000=>[8]
[8,7,2,3,1,5,6,4]=>0000000=>0000000=>[8]
[1,2,8,6,7,5,4,3]=>1100000=>0000011=>[6,1,1]
[2,8,5,7,6,1,3,4]=>0000000=>0000000=>[8]
[1,8,7,2,6,4,5,3]=>1000000=>0000001=>[7,1]
[8,7,2,1,6,4,5,3]=>0000000=>0000000=>[8]
[8,7,2,4,3,6,5,1]=>0000000=>0000000=>[8]
[4,2,8,7,3,6,5,1]=>0000000=>0000000=>[8]
[8,7,1,6,4,3,5,2]=>0000000=>0000000=>[8]
[8,4,1,7,3,6,5,2]=>0000000=>0000000=>[8]
[4,5,1,8,7,3,6,2]=>0000000=>0000000=>[8]
[4,3,8,5,2,6,1,7]=>0000000=>0000000=>[8]
[5,7,4,1,2,6,8,3]=>0000000=>0000000=>[8]
[2,8,6,7,5,3,1,4]=>0000000=>0000000=>[8]
[5,2,6,3,7,8,4,1]=>0000000=>0000000=>[8]
[3,6,2,5,7,8,4,1]=>0000000=>0000000=>[8]
[2,7,4,6,8,3,5,1]=>0000000=>0000000=>[8]
[2,7,3,6,8,5,4,1]=>0000000=>0000000=>[8]
[3,7,6,8,1,5,4,2]=>0000000=>0000000=>[8]
[4,7,6,8,2,3,5,1]=>0000000=>0000000=>[8]
[3,7,5,6,8,2,4,1]=>0000000=>0000000=>[8]
[3,7,2,6,8,4,5,1]=>0000000=>0000000=>[8]
[1,5,7,6,8,4,2,3]=>1000000=>0000001=>[7,1]
[2,7,5,6,8,4,3,1]=>0000000=>0000000=>[8]
[3,7,6,8,5,1,4,2]=>0000000=>0000000=>[8]
[7,1,3,8,6,2,4,5]=>0000000=>0000000=>[8]
[2,7,1,8,6,5,3,4]=>0000000=>0000000=>[8]
[5,3,4,7,6,2,1,8]=>0000001=>1000000=>[1,7]
[7,1,4,6,8,5,3,2]=>0000000=>0000000=>[8]
[7,2,5,1,6,4,8,3]=>0000000=>0000000=>[8]
[2,7,1,5,6,4,8,3]=>0000000=>0000000=>[8]
[1,5,7,8,4,6,3,2]=>1000000=>0000001=>[7,1]
[1,4,8,5,7,6,3,2]=>1000000=>0000001=>[7,1]
[2,8,1,5,6,4,7,3]=>0000000=>0000000=>[8]
[8,2,1,5,6,4,7,3]=>0000000=>0000000=>[8]
[2,8,5,1,6,4,3,7]=>0000000=>0000000=>[8]
[3,7,2,8,1,5,6,4]=>0000000=>0000000=>[8]
[7,3,2,5,1,6,8,4]=>0000000=>0000000=>[8]
[8,7,2,1,3,6,5,4]=>0000000=>0000000=>[8]
[7,3,2,8,1,4,6,5]=>0000000=>0000000=>[8]
[2,7,8,1,5,4,3,6]=>0000000=>0000000=>[8]
[3,6,2,1,8,4,7,5]=>0000000=>0000000=>[8]
[3,8,6,1,5,7,4,2]=>0000000=>0000000=>[8]
[6,4,2,3,7,8,1,5]=>0000000=>0000000=>[8]
[5,4,3,1,7,2,8,6]=>0000000=>0000000=>[8]
[5,3,1,6,4,7,2,8]=>0000001=>1000000=>[1,7]
[6,5,2,4,1,7,8,3]=>0000000=>0000000=>[8]
[4,3,6,2,5,8,1,7]=>0000000=>0000000=>[8]
[1,6,2,7,8,4,5,3]=>1000000=>0000001=>[7,1]
[8,5,2,4,1,3,7,6]=>0000000=>0000000=>[8]
[6,3,2,8,4,5,1,7]=>0000000=>0000000=>[8]
[5,4,7,2,1,3,8,6]=>0000000=>0000000=>[8]
[4,1,7,6,5,2,8,3]=>0000000=>0000000=>[8]
[6,4,7,1,2,3,8,5]=>0000000=>0000000=>[8]
[8,2,3,1,6,4,7,5]=>0000000=>0000000=>[8]
[3,1,8,5,7,2,6,4]=>0000000=>0000000=>[8]
[5,6,4,2,1,7,3,8]=>0000001=>1000000=>[1,7]
[6,5,7,1,2,8,3,4]=>0000000=>0000000=>[8]
[6,4,7,1,2,5,3,8]=>0000001=>1000000=>[1,7]
[1,2,4,8,5,7,3,6]=>1100000=>0000011=>[6,1,1]
[1,2,7,5,8,6,3,4]=>1100000=>0000011=>[6,1,1]
[7,4,5,1,6,8,2,3]=>0000000=>0000000=>[8]
[1,7,8,4,2,6,3,5]=>1000000=>0000001=>[7,1]
[6,3,2,5,7,4,1,8]=>0000001=>1000000=>[1,7]
[6,4,7,5,3,8,1,2]=>0000000=>0000000=>[8]
[6,2,1,5,3,7,8,4]=>0000000=>0000000=>[8]
[4,1,7,8,3,6,5,2]=>0000000=>0000000=>[8]
[6,3,2,4,8,5,1,7]=>0000000=>0000000=>[8]
[6,4,2,1,7,3,5,8]=>0000001=>1000000=>[1,7]
[5,7,4,2,1,6,3,8]=>0000001=>1000000=>[1,7]
[5,8,4,2,1,3,6,7]=>0000000=>0000000=>[8]
[8,3,2,6,5,1,7,4]=>0000000=>0000000=>[8]
[1,8,5,6,4,3,7,2]=>1000000=>0000001=>[7,1]
[1,7,5,8,4,6,3,2]=>1000000=>0000001=>[7,1]
[8,3,5,6,1,7,2,4]=>0000000=>0000000=>[8]
[1,5,3,7,8,4,6,2]=>1000000=>0000001=>[7,1]
[1,4,7,3,5,8,6,2]=>1000000=>0000001=>[7,1]
[1,6,3,7,8,5,4,2]=>1000000=>0000001=>[7,1]
[8,5,6,1,7,4,2,3]=>0000000=>0000000=>[8]
[8,6,1,4,3,7,2,5]=>0000000=>0000000=>[8]
[3,7,8,2,5,1,6,4]=>0000000=>0000000=>[8]
[8,1,3,5,6,4,2,7]=>0000000=>0000000=>[8]
[8,6,1,4,3,2,7,5]=>0000000=>0000000=>[8]
[7,3,8,2,4,1,5,6]=>0000000=>0000000=>[8]
[6,3,7,8,1,2,5,4]=>0000000=>0000000=>[8]
[7,5,8,1,2,3,6,4]=>0000000=>0000000=>[8]
[8,6,1,5,3,7,2,4]=>0000000=>0000000=>[8]
[8,1,7,5,6,4,2,3]=>0000000=>0000000=>[8]
[8,1,4,7,6,5,2,3]=>0000000=>0000000=>[8]
[6,1,4,8,2,7,5,3]=>0000000=>0000000=>[8]
[8,6,4,2,7,3,5,1]=>0000000=>0000000=>[8]
[6,8,7,5,2,1,3,4]=>0000000=>0000000=>[8]
[7,6,1,5,2,3,8,4]=>0000000=>0000000=>[8]
[5,1,8,6,7,2,3,4]=>0000000=>0000000=>[8]
[5,7,1,6,8,2,3,4]=>0000000=>0000000=>[8]
[5,1,7,6,8,2,3,4]=>0000000=>0000000=>[8]
[6,1,5,7,2,8,3,4]=>0000000=>0000000=>[8]
[6,8,4,2,1,7,3,5]=>0000000=>0000000=>[8]
[5,8,6,1,7,2,3,4]=>0000000=>0000000=>[8]
[6,3,2,8,1,7,4,5]=>0000000=>0000000=>[8]
[1,4,7,8,3,5,2,6]=>1000000=>0000001=>[7,1]
[2,5,6,8,1,4,7,3]=>0000000=>0000000=>[8]
[8,4,5,1,6,7,2,3]=>0000000=>0000000=>[8]
[7,3,6,1,4,2,8,5]=>0000000=>0000000=>[8]
[7,4,1,6,5,2,3,8]=>0000001=>1000000=>[1,7]
[4,1,6,5,2,3,8,7]=>0000010=>0100000=>[2,6]
[4,5,1,7,8,6,2,3]=>0000000=>0000000=>[8]
[8,3,1,4,6,2,7,5]=>0000000=>0000000=>[8]
[2,5,3,4,6,8,1,7]=>0000000=>0000000=>[8]
[8,3,6,1,5,2,4,7]=>0000000=>0000000=>[8]
[4,7,1,2,5,6,3,8]=>0000001=>1000000=>[1,7]
[6,7,3,1,8,2,4,5]=>0000000=>0000000=>[8]
[7,3,1,4,6,2,8,5]=>0000000=>0000000=>[8]
[7,4,1,2,5,6,3,8]=>0000001=>1000000=>[1,7]
[4,5,1,3,6,8,7,2]=>0000000=>0000000=>[8]
[8,4,1,2,5,7,3,6]=>0000000=>0000000=>[8]
[8,4,1,3,6,7,5,2]=>0000000=>0000000=>[8]
[5,4,1,6,3,7,8,2]=>0000000=>0000000=>[8]
[6,7,3,1,5,2,4,8]=>0000001=>1000000=>[1,7]
[5,4,1,3,6,8,7,2]=>0000000=>0000000=>[8]
[6,4,1,2,5,8,3,7]=>0000000=>0000000=>[8]
[5,7,4,8,1,6,3,2]=>0000000=>0000000=>[8]
[7,5,3,6,4,2,1,8]=>0000001=>1000000=>[1,7]
[4,3,1,2,6,5,7,8]=>0001011=>1101000=>[1,1,2,4]
[4,3,1,2,5,7,6,8]=>0001101=>1011000=>[1,2,1,4]
[4,7,3,1,5,2,8,6]=>0000000=>0000000=>[8]
[6,5,1,2,7,4,8,3]=>0000000=>0000000=>[8]
[5,3,8,1,4,2,7,6]=>0000000=>0000000=>[8]
[6,5,3,4,1,8,2,7]=>0000000=>0000000=>[8]
[3,1,8,4,2,7,6,5]=>0000000=>0000000=>[8]
[2,8,7,4,1,3,6,5]=>0000000=>0000000=>[8]
[8,2,3,1,7,6,4,5]=>0000000=>0000000=>[8]
[5,2,4,1,6,8,3,7]=>0000000=>0000000=>[8]
[8,7,2,3,1,6,4,5]=>0000000=>0000000=>[8]
[6,2,3,1,7,8,4,5]=>0000000=>0000000=>[8]
[7,2,5,8,3,1,4,6]=>0000000=>0000000=>[8]
[6,8,2,3,1,7,4,5]=>0000000=>0000000=>[8]
[8,2,5,7,3,1,4,6]=>0000000=>0000000=>[8]
[2,5,8,7,3,1,4,6]=>0000000=>0000000=>[8]
[2,8,7,3,1,4,5,6]=>0000000=>0000000=>[8]
[8,2,3,1,6,7,4,5]=>0000000=>0000000=>[8]
[2,8,4,1,3,6,7,5]=>0000000=>0000000=>[8]
[2,7,3,1,4,5,8,6]=>0000000=>0000000=>[8]
[7,2,8,3,1,4,5,6]=>0000000=>0000000=>[8]
[2,7,8,3,1,4,5,6]=>0000000=>0000000=>[8]
[5,3,2,8,7,1,6,4]=>0000000=>0000000=>[8]
[6,8,7,2,1,5,4,3]=>0000000=>0000000=>[8]
[4,8,5,3,6,1,7,2]=>0000000=>0000000=>[8]
[6,3,1,5,4,8,2,7]=>0000000=>0000000=>[8]
[8,4,2,6,5,7,3,1]=>0000000=>0000000=>[8]
[4,7,6,3,5,2,8,1]=>0000000=>0000000=>[8]
[1,7,5,3,4,8,6,2]=>1000000=>0000001=>[7,1]
[4,8,6,2,5,7,3,1]=>0000000=>0000000=>[8]
[8,7,3,2,6,4,5,1]=>0000000=>0000000=>[8]
[8,3,1,4,7,5,2,6]=>0000000=>0000000=>[8]
[5,3,1,6,4,8,7,2]=>0000000=>0000000=>[8]
[3,4,8,5,7,2,6,1]=>0000000=>0000000=>[8]
[4,1,7,8,3,2,5,6]=>0000000=>0000000=>[8]
[8,5,1,2,7,6,4,3]=>0000000=>0000000=>[8]
[4,6,5,3,1,8,7,2]=>0000000=>0000000=>[8]
[6,4,7,2,5,3,1,8]=>0000001=>1000000=>[1,7]
[4,3,6,1,2,7,8,5]=>0000000=>0000000=>[8]
[2,7,4,6,3,8,1,5]=>0000000=>0000000=>[8]
[7,3,5,6,4,1,8,2]=>0000000=>0000000=>[8]
[5,7,6,3,4,2,1,8]=>0000001=>1000000=>[1,7]
[3,7,5,6,4,2,1,8]=>0000001=>1000000=>[1,7]
[5,7,3,6,4,2,1,8]=>0000001=>1000000=>[1,7]
[5,7,3,6,4,1,8,2]=>0000000=>0000000=>[8]
[3,7,5,6,4,1,8,2]=>0000000=>0000000=>[8]
[5,7,6,3,4,1,8,2]=>0000000=>0000000=>[8]
[3,2,7,5,6,1,8,4]=>0000000=>0000000=>[8]
[5,3,4,7,6,1,8,2]=>0000000=>0000000=>[8]
[5,3,4,2,7,1,8,6]=>0000000=>0000000=>[8]
[3,5,4,1,7,8,6,2]=>0000000=>0000000=>[8]
[3,1,2,7,5,8,4,6]=>0010000=>0000100=>[5,3]
[8,4,1,5,6,2,7,3]=>0000000=>0000000=>[8]
[1,8,5,3,2,4,6,7]=>1000000=>0000001=>[7,1]
[4,8,5,1,2,3,6,7]=>0000000=>0000000=>[8]
[3,5,1,4,2,6,8,7]=>0000110=>0110000=>[2,1,5]
[4,8,7,1,2,5,3,6]=>0000000=>0000000=>[8]
[8,7,2,6,1,4,3,5]=>0000000=>0000000=>[8]
[1,7,6,8,4,2,3,5]=>1000000=>0000001=>[7,1]
[1,7,4,8,2,5,3,6]=>1000000=>0000001=>[7,1]
[6,1,7,3,8,2,4,5]=>0000000=>0000000=>[8]
[1,5,8,2,3,4,7,6]=>1000000=>0000001=>[7,1]
[8,4,2,7,1,3,6,5]=>0000000=>0000000=>[8]
[7,1,8,6,4,2,3,5]=>0000000=>0000000=>[8]
[1,7,8,6,4,2,3,5]=>1000000=>0000001=>[7,1]
[5,1,7,3,2,6,8,4]=>0000000=>0000000=>[8]
[8,7,5,3,2,6,4,1]=>0000000=>0000000=>[8]
[4,5,2,3,8,7,1,6]=>0000000=>0000000=>[8]
[4,6,7,5,2,3,1,8]=>0000001=>1000000=>[1,7]
[6,5,2,3,1,8,7,4]=>0000000=>0000000=>[8]
[6,2,5,3,1,8,7,4]=>0000000=>0000000=>[8]
[6,2,5,3,8,7,1,4]=>0000000=>0000000=>[8]
[6,4,5,3,8,7,1,2]=>0000000=>0000000=>[8]
[1,6,4,5,8,7,3,2]=>1000000=>0000001=>[7,1]
[8,4,7,5,2,3,1,6]=>0000000=>0000000=>[8]
[8,2,7,4,5,3,1,6]=>0000000=>0000000=>[8]
[6,2,4,7,5,3,1,8]=>0000001=>1000000=>[1,7]
[8,2,4,7,5,3,1,6]=>0000000=>0000000=>[8]
[8,2,6,7,5,3,1,4]=>0000000=>0000000=>[8]
[8,4,6,7,5,3,1,2]=>0000000=>0000000=>[8]
[6,4,5,8,7,3,1,2]=>0000000=>0000000=>[8]
[6,2,8,7,5,3,1,4]=>0000000=>0000000=>[8]
[2,4,8,7,5,3,1,6]=>0000000=>0000000=>[8]
[4,6,8,7,5,3,1,2]=>0000000=>0000000=>[8]
[4,6,5,3,8,7,1,2]=>0000000=>0000000=>[8]
[2,6,5,8,7,3,1,4]=>0000000=>0000000=>[8]
[6,7,2,4,5,3,1,8]=>0000001=>1000000=>[1,7]
[4,5,8,7,2,3,1,6]=>0000000=>0000000=>[8]
[4,8,7,2,5,3,1,6]=>0000000=>0000000=>[8]
[6,8,7,4,5,3,1,2]=>0000000=>0000000=>[8]
[2,8,4,7,5,3,1,6]=>0000000=>0000000=>[8]
[4,8,2,7,5,3,1,6]=>0000000=>0000000=>[8]
[6,8,2,7,5,3,1,4]=>0000000=>0000000=>[8]
[7,4,3,8,1,6,5,2]=>0000000=>0000000=>[8]
[3,7,4,6,2,1,8,5]=>0000000=>0000000=>[8]
[2,6,5,7,8,3,1,4]=>0000000=>0000000=>[8]
[3,4,8,6,2,1,7,5]=>0000000=>0000000=>[8]
[1,6,2,3,8,5,7,4]=>1000000=>0000001=>[7,1]
[1,2,7,3,8,5,6,4]=>1100000=>0000011=>[6,1,1]
[2,3,6,5,8,4,7,1]=>0000000=>0000000=>[8]
[3,4,2,6,8,5,7,1]=>0000000=>0000000=>[8]
[2,4,7,3,8,5,1,6]=>0000000=>0000000=>[8]
[1,2,8,3,5,4,7,6]=>1100000=>0000011=>[6,1,1]
[1,3,6,7,4,5,8,2]=>1000000=>0000001=>[7,1]
[7,4,1,3,6,8,2,5]=>0000000=>0000000=>[8]
[5,1,7,3,4,6,8,2]=>0000000=>0000000=>[8]
[6,1,7,3,5,8,2,4]=>0000000=>0000000=>[8]
[6,8,1,2,7,3,4,5]=>0000000=>0000000=>[8]
[5,6,2,1,8,3,4,7]=>0000000=>0000000=>[8]
[6,4,1,3,7,8,2,5]=>0000000=>0000000=>[8]
[1,6,2,8,7,3,4,5]=>1000000=>0000001=>[7,1]
[5,2,8,4,7,1,3,6]=>0000000=>0000000=>[8]
[3,8,7,2,6,1,4,5]=>0000000=>0000000=>[8]
[2,5,1,8,3,6,4,7]=>0000000=>0000000=>[8]
[2,3,8,1,4,6,5,7]=>0000000=>0000000=>[8]
[1,3,8,2,5,4,7,6]=>1000000=>0000001=>[7,1]
[3,1,8,4,6,2,5,7]=>0000000=>0000000=>[8]
[6,3,2,4,8,7,1,5]=>0000000=>0000000=>[8]
[1,4,8,6,2,3,5,7]=>1000000=>0000001=>[7,1]
[3,1,8,4,5,6,2,7]=>0000000=>0000000=>[8]
[4,5,8,3,6,1,7,2]=>0000000=>0000000=>[8]
[3,5,4,8,6,1,7,2]=>0000000=>0000000=>[8]
[4,2,7,8,6,3,1,5]=>0000000=>0000000=>[8]
[7,1,4,2,8,6,3,5]=>0000000=>0000000=>[8]
[2,3,7,4,8,1,6,5]=>0000000=>0000000=>[8]
[8,3,1,2,5,4,7,6]=>0000000=>0000000=>[8]
[6,5,1,2,8,4,7,3]=>0000000=>0000000=>[8]
[8,1,5,3,7,4,2,6]=>0000000=>0000000=>[8]
[1,3,4,8,6,2,7,5]=>1000000=>0000001=>[7,1]
[1,2,4,8,6,7,3,5]=>1100000=>0000011=>[6,1,1]
[8,1,2,6,5,7,3,4]=>0000000=>0000000=>[8]
[7,1,2,6,5,8,3,4]=>0000000=>0000000=>[8]
[7,1,6,8,3,2,4,5]=>0000000=>0000000=>[8]
[2,6,1,4,7,5,8,3]=>0000000=>0000000=>[8]
[5,1,4,3,7,8,6,2]=>0000000=>0000000=>[8]
[6,4,1,3,7,8,5,2]=>0000000=>0000000=>[8]
[3,1,5,7,2,6,8,4]=>0000000=>0000000=>[8]
[7,2,4,8,5,1,6,3]=>0000000=>0000000=>[8]
[3,1,7,5,2,6,8,4]=>0000000=>0000000=>[8]
[3,2,7,5,1,6,8,4]=>0000000=>0000000=>[8]
[5,2,7,3,1,6,8,4]=>0000000=>0000000=>[8]
[6,7,2,1,3,4,8,5]=>0000000=>0000000=>[8]
[4,6,3,1,2,7,8,5]=>0000000=>0000000=>[8]
[6,7,3,1,2,4,8,5]=>0000000=>0000000=>[8]
[3,8,5,2,1,6,7,4]=>0000000=>0000000=>[8]
[6,4,7,8,3,5,1,2]=>0000000=>0000000=>[8]
[6,4,7,8,1,2,5,3]=>0000000=>0000000=>[8]
[3,5,6,7,1,8,4,2]=>0000000=>0000000=>[8]
[1,7,4,5,2,8,6,3]=>1000000=>0000001=>[7,1]
[1,7,3,8,2,5,4,6]=>1000000=>0000001=>[7,1]
[8,6,4,5,1,3,7,2]=>0000000=>0000000=>[8]
[7,5,8,4,1,3,6,2]=>0000000=>0000000=>[8]
[4,7,5,3,6,8,1,2]=>0000000=>0000000=>[8]
[4,8,5,3,7,1,2,6]=>0000000=>0000000=>[8]
[2,8,1,6,5,7,3,4]=>0000000=>0000000=>[8]
[4,7,5,3,8,1,6,2]=>0000000=>0000000=>[8]
[7,4,8,5,3,6,1,2]=>0000000=>0000000=>[8]
[7,4,5,3,8,1,6,2]=>0000000=>0000000=>[8]
[8,4,6,5,1,3,7,2]=>0000000=>0000000=>[8]
[6,3,5,8,1,7,4,2]=>0000000=>0000000=>[8]
[7,3,6,1,5,8,4,2]=>0000000=>0000000=>[8]
[4,5,3,8,7,1,2,6]=>0000000=>0000000=>[8]
[8,5,4,7,6,1,2,3]=>0000000=>0000000=>[8]
[3,7,6,1,5,8,4,2]=>0000000=>0000000=>[8]
[8,2,3,6,4,1,7,5]=>0000000=>0000000=>[8]
[2,7,3,6,4,1,8,5]=>0000000=>0000000=>[8]
[2,3,7,8,1,4,6,5]=>0000000=>0000000=>[8]
[2,7,3,5,4,1,8,6]=>0000000=>0000000=>[8]
[8,2,3,5,4,1,7,6]=>0000000=>0000000=>[8]
[7,1,3,8,2,4,6,5]=>0000000=>0000000=>[8]
[7,2,3,6,4,1,8,5]=>0000000=>0000000=>[8]
[6,5,2,4,1,8,3,7]=>0000000=>0000000=>[8]
[5,7,2,4,1,3,8,6]=>0000000=>0000000=>[8]
[6,2,5,4,1,8,3,7]=>0000000=>0000000=>[8]
[8,1,2,5,3,7,6,4]=>0000000=>0000000=>[8]
[1,8,5,4,2,6,3,7]=>1000000=>0000001=>[7,1]
[8,3,6,5,4,2,1,7]=>0000000=>0000000=>[8]
[5,4,8,7,6,2,3,1]=>0000000=>0000000=>[8]
[6,8,4,7,5,1,3,2]=>0000000=>0000000=>[8]
[1,7,2,5,6,8,3,4]=>1000000=>0000001=>[7,1]
[4,1,7,5,6,8,2,3]=>0000000=>0000000=>[8]
[1,5,8,3,2,7,4,6]=>1000000=>0000001=>[7,1]
[7,6,4,2,5,3,1,8]=>0000001=>1000000=>[1,7]
[1,8,6,5,2,7,4,3]=>1000000=>0000001=>[7,1]
[8,2,6,5,1,7,4,3]=>0000000=>0000000=>[8]
[6,1,4,7,2,5,8,3]=>0000000=>0000000=>[8]
[6,8,2,5,1,7,4,3]=>0000000=>0000000=>[8]
[1,6,4,7,2,5,8,3]=>1000000=>0000001=>[7,1]
[7,6,4,1,2,5,8,3]=>0000000=>0000000=>[8]
[6,8,1,5,2,7,4,3]=>0000000=>0000000=>[8]
[8,6,5,2,1,7,4,3]=>0000000=>0000000=>[8]
[1,6,5,2,8,7,4,3]=>1000000=>0000001=>[7,1]
[1,8,5,2,7,6,4,3]=>1000000=>0000001=>[7,1]
[1,8,6,7,2,5,4,3]=>1000000=>0000001=>[7,1]
[1,7,6,8,2,5,4,3]=>1000000=>0000001=>[7,1]
[1,7,8,6,2,5,4,3]=>1000000=>0000001=>[7,1]
[8,1,7,6,2,5,4,3]=>0000000=>0000000=>[8]
[1,7,8,6,3,5,4,2]=>1000000=>0000001=>[7,1]
[1,4,2,3,7,8,6,5]=>1001000=>0001001=>[4,3,1]
[1,8,4,2,3,6,5,7]=>1000000=>0000001=>[7,1]
[1,3,8,5,6,4,2,7]=>1000000=>0000001=>[7,1]
[1,6,3,7,8,4,2,5]=>1000000=>0000001=>[7,1]
[1,6,3,8,4,2,5,7]=>1000000=>0000001=>[7,1]
[1,7,8,4,2,3,5,6]=>1000000=>0000001=>[7,1]
[1,7,8,5,6,4,2,3]=>1000000=>0000001=>[7,1]
[1,6,3,4,2,5,8,7]=>1000010=>0100001=>[2,5,1]
[1,3,5,8,6,4,2,7]=>1000000=>0000001=>[7,1]
[1,7,6,2,3,8,4,5]=>1000000=>0000001=>[7,1]
[1,5,7,6,2,3,8,4]=>1000000=>0000001=>[7,1]
[1,3,7,6,2,4,5,8]=>1000001=>1000001=>[1,6,1]
[1,4,3,7,6,2,5,8]=>1000001=>1000001=>[1,6,1]
[1,5,8,4,3,7,6,2]=>1000000=>0000001=>[7,1]
[1,7,5,8,4,3,6,2]=>1000000=>0000001=>[7,1]
[4,1,5,7,3,8,2,6]=>0000000=>0000000=>[8]
[1,3,7,4,6,8,5,2]=>1000000=>0000001=>[7,1]
[1,5,2,6,8,7,4,3]=>1000000=>0000001=>[7,1]
[1,3,7,6,4,8,2,5]=>1000000=>0000001=>[7,1]
[6,5,1,4,3,8,7,2]=>0000000=>0000000=>[8]
[5,6,1,4,3,8,7,2]=>0000000=>0000000=>[8]
[5,8,6,4,3,1,7,2]=>0000000=>0000000=>[8]
[4,1,3,7,8,6,5,2]=>0000000=>0000000=>[8]
[8,5,6,4,3,1,7,2]=>0000000=>0000000=>[8]
[8,4,3,1,7,6,5,2]=>0000000=>0000000=>[8]
[3,2,7,1,8,6,5,4]=>0000000=>0000000=>[8]
          
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
Map
reverse
Description
Return the reversal of a binary word.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.