Identifier
Mp00114:
Permutations
—connectivity set⟶
Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Images
=>
Cc0002;cc-rep-3
[1,2]=>1=>[1,1]=>[1,1]
[2,1]=>0=>[2]=>[2]
[1,2,3]=>11=>[1,1,1]=>[1,1,1]
[1,3,2]=>10=>[1,2]=>[2,1]
[2,1,3]=>01=>[2,1]=>[2,1]
[2,3,1]=>00=>[3]=>[3]
[3,1,2]=>00=>[3]=>[3]
[3,2,1]=>00=>[3]=>[3]
[1,2,3,4]=>111=>[1,1,1,1]=>[1,1,1,1]
[1,2,4,3]=>110=>[1,1,2]=>[2,1,1]
[1,3,2,4]=>101=>[1,2,1]=>[2,1,1]
[1,3,4,2]=>100=>[1,3]=>[3,1]
[1,4,2,3]=>100=>[1,3]=>[3,1]
[1,4,3,2]=>100=>[1,3]=>[3,1]
[2,1,3,4]=>011=>[2,1,1]=>[2,1,1]
[2,1,4,3]=>010=>[2,2]=>[2,2]
[2,3,1,4]=>001=>[3,1]=>[3,1]
[2,3,4,1]=>000=>[4]=>[4]
[2,4,1,3]=>000=>[4]=>[4]
[2,4,3,1]=>000=>[4]=>[4]
[3,1,2,4]=>001=>[3,1]=>[3,1]
[3,1,4,2]=>000=>[4]=>[4]
[3,2,1,4]=>001=>[3,1]=>[3,1]
[3,2,4,1]=>000=>[4]=>[4]
[3,4,1,2]=>000=>[4]=>[4]
[3,4,2,1]=>000=>[4]=>[4]
[4,1,2,3]=>000=>[4]=>[4]
[4,1,3,2]=>000=>[4]=>[4]
[4,2,1,3]=>000=>[4]=>[4]
[4,2,3,1]=>000=>[4]=>[4]
[4,3,1,2]=>000=>[4]=>[4]
[4,3,2,1]=>000=>[4]=>[4]
[1,2,3,4,5]=>1111=>[1,1,1,1,1]=>[1,1,1,1,1]
[1,2,3,5,4]=>1110=>[1,1,1,2]=>[2,1,1,1]
[1,2,4,3,5]=>1101=>[1,1,2,1]=>[2,1,1,1]
[1,2,4,5,3]=>1100=>[1,1,3]=>[3,1,1]
[1,2,5,3,4]=>1100=>[1,1,3]=>[3,1,1]
[1,2,5,4,3]=>1100=>[1,1,3]=>[3,1,1]
[1,3,2,4,5]=>1011=>[1,2,1,1]=>[2,1,1,1]
[1,3,2,5,4]=>1010=>[1,2,2]=>[2,2,1]
[1,3,4,2,5]=>1001=>[1,3,1]=>[3,1,1]
[1,3,4,5,2]=>1000=>[1,4]=>[4,1]
[1,3,5,2,4]=>1000=>[1,4]=>[4,1]
[1,3,5,4,2]=>1000=>[1,4]=>[4,1]
[1,4,2,3,5]=>1001=>[1,3,1]=>[3,1,1]
[1,4,2,5,3]=>1000=>[1,4]=>[4,1]
[1,4,3,2,5]=>1001=>[1,3,1]=>[3,1,1]
[1,4,3,5,2]=>1000=>[1,4]=>[4,1]
[1,4,5,2,3]=>1000=>[1,4]=>[4,1]
[1,4,5,3,2]=>1000=>[1,4]=>[4,1]
[1,5,2,3,4]=>1000=>[1,4]=>[4,1]
[1,5,2,4,3]=>1000=>[1,4]=>[4,1]
[1,5,3,2,4]=>1000=>[1,4]=>[4,1]
[1,5,3,4,2]=>1000=>[1,4]=>[4,1]
[1,5,4,2,3]=>1000=>[1,4]=>[4,1]
[1,5,4,3,2]=>1000=>[1,4]=>[4,1]
[2,1,3,4,5]=>0111=>[2,1,1,1]=>[2,1,1,1]
[2,1,3,5,4]=>0110=>[2,1,2]=>[2,2,1]
[2,1,4,3,5]=>0101=>[2,2,1]=>[2,2,1]
[2,1,4,5,3]=>0100=>[2,3]=>[3,2]
[2,1,5,3,4]=>0100=>[2,3]=>[3,2]
[2,1,5,4,3]=>0100=>[2,3]=>[3,2]
[2,3,1,4,5]=>0011=>[3,1,1]=>[3,1,1]
[2,3,1,5,4]=>0010=>[3,2]=>[3,2]
[2,3,4,1,5]=>0001=>[4,1]=>[4,1]
[2,3,4,5,1]=>0000=>[5]=>[5]
[2,3,5,1,4]=>0000=>[5]=>[5]
[2,3,5,4,1]=>0000=>[5]=>[5]
[2,4,1,3,5]=>0001=>[4,1]=>[4,1]
[2,4,1,5,3]=>0000=>[5]=>[5]
[2,4,3,1,5]=>0001=>[4,1]=>[4,1]
[2,4,3,5,1]=>0000=>[5]=>[5]
[2,4,5,1,3]=>0000=>[5]=>[5]
[2,4,5,3,1]=>0000=>[5]=>[5]
[2,5,1,3,4]=>0000=>[5]=>[5]
[2,5,1,4,3]=>0000=>[5]=>[5]
[2,5,3,1,4]=>0000=>[5]=>[5]
[2,5,3,4,1]=>0000=>[5]=>[5]
[2,5,4,1,3]=>0000=>[5]=>[5]
[2,5,4,3,1]=>0000=>[5]=>[5]
[3,1,2,4,5]=>0011=>[3,1,1]=>[3,1,1]
[3,1,2,5,4]=>0010=>[3,2]=>[3,2]
[3,1,4,2,5]=>0001=>[4,1]=>[4,1]
[3,1,4,5,2]=>0000=>[5]=>[5]
[3,1,5,2,4]=>0000=>[5]=>[5]
[3,1,5,4,2]=>0000=>[5]=>[5]
[3,2,1,4,5]=>0011=>[3,1,1]=>[3,1,1]
[3,2,1,5,4]=>0010=>[3,2]=>[3,2]
[3,2,4,1,5]=>0001=>[4,1]=>[4,1]
[3,2,4,5,1]=>0000=>[5]=>[5]
[3,2,5,1,4]=>0000=>[5]=>[5]
[3,2,5,4,1]=>0000=>[5]=>[5]
[3,4,1,2,5]=>0001=>[4,1]=>[4,1]
[3,4,1,5,2]=>0000=>[5]=>[5]
[3,4,2,1,5]=>0001=>[4,1]=>[4,1]
[3,4,2,5,1]=>0000=>[5]=>[5]
[3,4,5,1,2]=>0000=>[5]=>[5]
[3,4,5,2,1]=>0000=>[5]=>[5]
[3,5,1,2,4]=>0000=>[5]=>[5]
[3,5,1,4,2]=>0000=>[5]=>[5]
[3,5,2,1,4]=>0000=>[5]=>[5]
[3,5,2,4,1]=>0000=>[5]=>[5]
[3,5,4,1,2]=>0000=>[5]=>[5]
[3,5,4,2,1]=>0000=>[5]=>[5]
[4,1,2,3,5]=>0001=>[4,1]=>[4,1]
[4,1,2,5,3]=>0000=>[5]=>[5]
[4,1,3,2,5]=>0001=>[4,1]=>[4,1]
[4,1,3,5,2]=>0000=>[5]=>[5]
[4,1,5,2,3]=>0000=>[5]=>[5]
[4,1,5,3,2]=>0000=>[5]=>[5]
[4,2,1,3,5]=>0001=>[4,1]=>[4,1]
[4,2,1,5,3]=>0000=>[5]=>[5]
[4,2,3,1,5]=>0001=>[4,1]=>[4,1]
[4,2,3,5,1]=>0000=>[5]=>[5]
[4,2,5,1,3]=>0000=>[5]=>[5]
[4,2,5,3,1]=>0000=>[5]=>[5]
[4,3,1,2,5]=>0001=>[4,1]=>[4,1]
[4,3,1,5,2]=>0000=>[5]=>[5]
[4,3,2,1,5]=>0001=>[4,1]=>[4,1]
[4,3,2,5,1]=>0000=>[5]=>[5]
[4,3,5,1,2]=>0000=>[5]=>[5]
[4,3,5,2,1]=>0000=>[5]=>[5]
[4,5,1,2,3]=>0000=>[5]=>[5]
[4,5,1,3,2]=>0000=>[5]=>[5]
[4,5,2,1,3]=>0000=>[5]=>[5]
[4,5,2,3,1]=>0000=>[5]=>[5]
[4,5,3,1,2]=>0000=>[5]=>[5]
[4,5,3,2,1]=>0000=>[5]=>[5]
[5,1,2,3,4]=>0000=>[5]=>[5]
[5,1,2,4,3]=>0000=>[5]=>[5]
[5,1,3,2,4]=>0000=>[5]=>[5]
[5,1,3,4,2]=>0000=>[5]=>[5]
[5,1,4,2,3]=>0000=>[5]=>[5]
[5,1,4,3,2]=>0000=>[5]=>[5]
[5,2,1,3,4]=>0000=>[5]=>[5]
[5,2,1,4,3]=>0000=>[5]=>[5]
[5,2,3,1,4]=>0000=>[5]=>[5]
[5,2,3,4,1]=>0000=>[5]=>[5]
[5,2,4,1,3]=>0000=>[5]=>[5]
[5,2,4,3,1]=>0000=>[5]=>[5]
[5,3,1,2,4]=>0000=>[5]=>[5]
[5,3,1,4,2]=>0000=>[5]=>[5]
[5,3,2,1,4]=>0000=>[5]=>[5]
[5,3,2,4,1]=>0000=>[5]=>[5]
[5,3,4,1,2]=>0000=>[5]=>[5]
[5,3,4,2,1]=>0000=>[5]=>[5]
[5,4,1,2,3]=>0000=>[5]=>[5]
[5,4,1,3,2]=>0000=>[5]=>[5]
[5,4,2,1,3]=>0000=>[5]=>[5]
[5,4,2,3,1]=>0000=>[5]=>[5]
[5,4,3,1,2]=>0000=>[5]=>[5]
[5,4,3,2,1]=>0000=>[5]=>[5]
[1,2,3,4,5,6]=>11111=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]
[1,2,3,4,6,5]=>11110=>[1,1,1,1,2]=>[2,1,1,1,1]
[1,2,3,5,4,6]=>11101=>[1,1,1,2,1]=>[2,1,1,1,1]
[1,2,3,5,6,4]=>11100=>[1,1,1,3]=>[3,1,1,1]
[1,2,3,6,4,5]=>11100=>[1,1,1,3]=>[3,1,1,1]
[1,2,3,6,5,4]=>11100=>[1,1,1,3]=>[3,1,1,1]
[1,2,4,3,5,6]=>11011=>[1,1,2,1,1]=>[2,1,1,1,1]
[1,2,4,3,6,5]=>11010=>[1,1,2,2]=>[2,2,1,1]
[1,2,4,5,3,6]=>11001=>[1,1,3,1]=>[3,1,1,1]
[1,2,4,5,6,3]=>11000=>[1,1,4]=>[4,1,1]
[1,2,4,6,3,5]=>11000=>[1,1,4]=>[4,1,1]
[1,2,4,6,5,3]=>11000=>[1,1,4]=>[4,1,1]
[1,2,5,3,4,6]=>11001=>[1,1,3,1]=>[3,1,1,1]
[1,2,5,3,6,4]=>11000=>[1,1,4]=>[4,1,1]
[1,2,5,4,3,6]=>11001=>[1,1,3,1]=>[3,1,1,1]
[1,2,5,4,6,3]=>11000=>[1,1,4]=>[4,1,1]
[1,2,5,6,3,4]=>11000=>[1,1,4]=>[4,1,1]
[1,2,5,6,4,3]=>11000=>[1,1,4]=>[4,1,1]
[1,2,6,3,4,5]=>11000=>[1,1,4]=>[4,1,1]
[1,2,6,3,5,4]=>11000=>[1,1,4]=>[4,1,1]
[1,2,6,4,3,5]=>11000=>[1,1,4]=>[4,1,1]
[1,2,6,4,5,3]=>11000=>[1,1,4]=>[4,1,1]
[1,2,6,5,3,4]=>11000=>[1,1,4]=>[4,1,1]
[1,2,6,5,4,3]=>11000=>[1,1,4]=>[4,1,1]
[1,3,2,4,5,6]=>10111=>[1,2,1,1,1]=>[2,1,1,1,1]
[1,3,2,4,6,5]=>10110=>[1,2,1,2]=>[2,2,1,1]
[1,3,2,5,4,6]=>10101=>[1,2,2,1]=>[2,2,1,1]
[1,3,2,5,6,4]=>10100=>[1,2,3]=>[3,2,1]
[1,3,2,6,4,5]=>10100=>[1,2,3]=>[3,2,1]
[1,3,2,6,5,4]=>10100=>[1,2,3]=>[3,2,1]
[1,3,4,2,5,6]=>10011=>[1,3,1,1]=>[3,1,1,1]
[1,3,4,2,6,5]=>10010=>[1,3,2]=>[3,2,1]
[1,3,4,5,2,6]=>10001=>[1,4,1]=>[4,1,1]
[1,3,4,5,6,2]=>10000=>[1,5]=>[5,1]
[1,3,4,6,2,5]=>10000=>[1,5]=>[5,1]
[1,3,4,6,5,2]=>10000=>[1,5]=>[5,1]
[1,3,5,2,4,6]=>10001=>[1,4,1]=>[4,1,1]
[1,3,5,2,6,4]=>10000=>[1,5]=>[5,1]
[1,3,5,4,2,6]=>10001=>[1,4,1]=>[4,1,1]
[1,3,5,4,6,2]=>10000=>[1,5]=>[5,1]
[1,3,5,6,2,4]=>10000=>[1,5]=>[5,1]
[1,3,5,6,4,2]=>10000=>[1,5]=>[5,1]
[1,3,6,2,4,5]=>10000=>[1,5]=>[5,1]
[1,3,6,2,5,4]=>10000=>[1,5]=>[5,1]
[1,3,6,4,2,5]=>10000=>[1,5]=>[5,1]
[1,3,6,4,5,2]=>10000=>[1,5]=>[5,1]
[1,3,6,5,2,4]=>10000=>[1,5]=>[5,1]
[1,3,6,5,4,2]=>10000=>[1,5]=>[5,1]
[1,4,2,3,5,6]=>10011=>[1,3,1,1]=>[3,1,1,1]
[1,4,2,3,6,5]=>10010=>[1,3,2]=>[3,2,1]
[1,4,2,5,3,6]=>10001=>[1,4,1]=>[4,1,1]
[1,4,2,5,6,3]=>10000=>[1,5]=>[5,1]
[1,4,2,6,3,5]=>10000=>[1,5]=>[5,1]
[1,4,2,6,5,3]=>10000=>[1,5]=>[5,1]
[1,4,3,2,5,6]=>10011=>[1,3,1,1]=>[3,1,1,1]
[1,4,3,2,6,5]=>10010=>[1,3,2]=>[3,2,1]
[1,4,3,5,2,6]=>10001=>[1,4,1]=>[4,1,1]
[1,4,3,5,6,2]=>10000=>[1,5]=>[5,1]
[1,4,3,6,2,5]=>10000=>[1,5]=>[5,1]
[1,4,3,6,5,2]=>10000=>[1,5]=>[5,1]
[1,4,5,2,3,6]=>10001=>[1,4,1]=>[4,1,1]
[1,4,5,2,6,3]=>10000=>[1,5]=>[5,1]
[1,4,5,3,2,6]=>10001=>[1,4,1]=>[4,1,1]
[1,4,5,3,6,2]=>10000=>[1,5]=>[5,1]
[1,4,5,6,2,3]=>10000=>[1,5]=>[5,1]
[1,4,5,6,3,2]=>10000=>[1,5]=>[5,1]
[1,4,6,2,3,5]=>10000=>[1,5]=>[5,1]
[1,4,6,2,5,3]=>10000=>[1,5]=>[5,1]
[1,4,6,3,2,5]=>10000=>[1,5]=>[5,1]
[1,4,6,3,5,2]=>10000=>[1,5]=>[5,1]
[1,4,6,5,2,3]=>10000=>[1,5]=>[5,1]
[1,4,6,5,3,2]=>10000=>[1,5]=>[5,1]
[1,5,2,3,4,6]=>10001=>[1,4,1]=>[4,1,1]
[1,5,2,3,6,4]=>10000=>[1,5]=>[5,1]
[1,5,2,4,3,6]=>10001=>[1,4,1]=>[4,1,1]
[1,5,2,4,6,3]=>10000=>[1,5]=>[5,1]
[1,5,2,6,3,4]=>10000=>[1,5]=>[5,1]
[1,5,2,6,4,3]=>10000=>[1,5]=>[5,1]
[1,5,3,2,4,6]=>10001=>[1,4,1]=>[4,1,1]
[1,5,3,2,6,4]=>10000=>[1,5]=>[5,1]
[1,5,3,4,2,6]=>10001=>[1,4,1]=>[4,1,1]
[1,5,3,4,6,2]=>10000=>[1,5]=>[5,1]
[1,5,3,6,2,4]=>10000=>[1,5]=>[5,1]
[1,5,3,6,4,2]=>10000=>[1,5]=>[5,1]
[1,5,4,2,3,6]=>10001=>[1,4,1]=>[4,1,1]
[1,5,4,2,6,3]=>10000=>[1,5]=>[5,1]
[1,5,4,3,2,6]=>10001=>[1,4,1]=>[4,1,1]
[1,5,4,3,6,2]=>10000=>[1,5]=>[5,1]
[1,5,4,6,2,3]=>10000=>[1,5]=>[5,1]
[1,5,4,6,3,2]=>10000=>[1,5]=>[5,1]
[1,5,6,2,3,4]=>10000=>[1,5]=>[5,1]
[1,5,6,2,4,3]=>10000=>[1,5]=>[5,1]
[1,5,6,3,2,4]=>10000=>[1,5]=>[5,1]
[1,5,6,3,4,2]=>10000=>[1,5]=>[5,1]
[1,5,6,4,2,3]=>10000=>[1,5]=>[5,1]
[1,5,6,4,3,2]=>10000=>[1,5]=>[5,1]
[1,6,2,3,4,5]=>10000=>[1,5]=>[5,1]
[1,6,2,3,5,4]=>10000=>[1,5]=>[5,1]
[1,6,2,4,3,5]=>10000=>[1,5]=>[5,1]
[1,6,2,4,5,3]=>10000=>[1,5]=>[5,1]
[1,6,2,5,3,4]=>10000=>[1,5]=>[5,1]
[1,6,2,5,4,3]=>10000=>[1,5]=>[5,1]
[1,6,3,2,4,5]=>10000=>[1,5]=>[5,1]
[1,6,3,2,5,4]=>10000=>[1,5]=>[5,1]
[1,6,3,4,2,5]=>10000=>[1,5]=>[5,1]
[1,6,3,4,5,2]=>10000=>[1,5]=>[5,1]
[1,6,3,5,2,4]=>10000=>[1,5]=>[5,1]
[1,6,3,5,4,2]=>10000=>[1,5]=>[5,1]
[1,6,4,2,3,5]=>10000=>[1,5]=>[5,1]
[1,6,4,2,5,3]=>10000=>[1,5]=>[5,1]
[1,6,4,3,2,5]=>10000=>[1,5]=>[5,1]
[1,6,4,3,5,2]=>10000=>[1,5]=>[5,1]
[1,6,4,5,2,3]=>10000=>[1,5]=>[5,1]
[1,6,4,5,3,2]=>10000=>[1,5]=>[5,1]
[1,6,5,2,3,4]=>10000=>[1,5]=>[5,1]
[1,6,5,2,4,3]=>10000=>[1,5]=>[5,1]
[1,6,5,3,2,4]=>10000=>[1,5]=>[5,1]
[1,6,5,3,4,2]=>10000=>[1,5]=>[5,1]
[1,6,5,4,2,3]=>10000=>[1,5]=>[5,1]
[1,6,5,4,3,2]=>10000=>[1,5]=>[5,1]
[2,1,3,4,5,6]=>01111=>[2,1,1,1,1]=>[2,1,1,1,1]
[2,1,3,4,6,5]=>01110=>[2,1,1,2]=>[2,2,1,1]
[2,1,3,5,4,6]=>01101=>[2,1,2,1]=>[2,2,1,1]
[2,1,3,5,6,4]=>01100=>[2,1,3]=>[3,2,1]
[2,1,3,6,4,5]=>01100=>[2,1,3]=>[3,2,1]
[2,1,3,6,5,4]=>01100=>[2,1,3]=>[3,2,1]
[2,1,4,3,5,6]=>01011=>[2,2,1,1]=>[2,2,1,1]
[2,1,4,3,6,5]=>01010=>[2,2,2]=>[2,2,2]
[2,1,4,5,3,6]=>01001=>[2,3,1]=>[3,2,1]
[2,1,4,5,6,3]=>01000=>[2,4]=>[4,2]
[2,1,4,6,3,5]=>01000=>[2,4]=>[4,2]
[2,1,4,6,5,3]=>01000=>[2,4]=>[4,2]
[2,1,5,3,4,6]=>01001=>[2,3,1]=>[3,2,1]
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[1,2,3,7,4,6,5]=>111000=>[1,1,1,4]=>[4,1,1,1]
[1,2,3,7,5,4,6]=>111000=>[1,1,1,4]=>[4,1,1,1]
[1,2,3,7,5,6,4]=>111000=>[1,1,1,4]=>[4,1,1,1]
[1,2,3,7,6,4,5]=>111000=>[1,1,1,4]=>[4,1,1,1]
[1,2,3,7,6,5,4]=>111000=>[1,1,1,4]=>[4,1,1,1]
[1,2,4,3,5,6,7]=>110111=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]
[1,2,4,3,5,7,6]=>110110=>[1,1,2,1,2]=>[2,2,1,1,1]
[1,2,4,3,6,5,7]=>110101=>[1,1,2,2,1]=>[2,2,1,1,1]
[1,2,4,3,6,7,5]=>110100=>[1,1,2,3]=>[3,2,1,1]
[1,2,4,3,7,5,6]=>110100=>[1,1,2,3]=>[3,2,1,1]
[1,2,4,3,7,6,5]=>110100=>[1,1,2,3]=>[3,2,1,1]
[1,2,4,5,3,6,7]=>110011=>[1,1,3,1,1]=>[3,1,1,1,1]
[1,2,4,5,3,7,6]=>110010=>[1,1,3,2]=>[3,2,1,1]
[1,2,4,5,6,3,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,4,5,6,7,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,5,7,3,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,5,7,6,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,6,3,5,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,4,6,3,7,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,6,5,3,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,4,6,5,7,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,6,7,3,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,6,7,5,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,7,3,5,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,7,3,6,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,7,5,3,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,7,5,6,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,7,6,3,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,4,7,6,5,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,3,4,6,7]=>110011=>[1,1,3,1,1]=>[3,1,1,1,1]
[1,2,5,3,4,7,6]=>110010=>[1,1,3,2]=>[3,2,1,1]
[1,2,5,3,6,4,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,5,3,6,7,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,3,7,4,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,3,7,6,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,4,3,6,7]=>110011=>[1,1,3,1,1]=>[3,1,1,1,1]
[1,2,5,4,3,7,6]=>110010=>[1,1,3,2]=>[3,2,1,1]
[1,2,5,4,6,3,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,5,4,6,7,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,4,7,3,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,4,7,6,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,6,3,4,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,5,6,3,7,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,6,4,3,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,5,6,4,7,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,6,7,3,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,6,7,4,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,7,3,4,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,7,3,6,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,7,4,3,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,7,4,6,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,7,6,3,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,5,7,6,4,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,3,4,5,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,6,3,4,7,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,3,5,4,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,6,3,5,7,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,3,7,4,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,3,7,5,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,4,3,5,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,6,4,3,7,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,4,5,3,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,6,4,5,7,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,4,7,3,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,4,7,5,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,5,3,4,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,6,5,3,7,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,5,4,3,7]=>110001=>[1,1,4,1]=>[4,1,1,1]
[1,2,6,5,4,7,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,5,7,3,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,5,7,4,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,7,3,4,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,7,3,5,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,7,4,3,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,7,4,5,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,7,5,3,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,6,7,5,4,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,3,4,5,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,3,4,6,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,3,5,4,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,3,5,6,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,3,6,4,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,3,6,5,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,4,3,5,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,4,3,6,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,4,5,3,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,4,5,6,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,4,6,3,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,4,6,5,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,5,3,4,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,5,3,6,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,5,4,3,6]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,5,4,6,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,5,6,3,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,5,6,4,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,6,3,4,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,6,3,5,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,6,4,3,5]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,6,4,5,3]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,6,5,3,4]=>110000=>[1,1,5]=>[5,1,1]
[1,2,7,6,5,4,3]=>110000=>[1,1,5]=>[5,1,1]
[1,3,2,4,5,6,7]=>101111=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]
[1,3,2,4,5,7,6]=>101110=>[1,2,1,1,2]=>[2,2,1,1,1]
[1,3,2,4,6,5,7]=>101101=>[1,2,1,2,1]=>[2,2,1,1,1]
[1,3,2,4,6,7,5]=>101100=>[1,2,1,3]=>[3,2,1,1]
[1,3,2,4,7,5,6]=>101100=>[1,2,1,3]=>[3,2,1,1]
[1,3,2,4,7,6,5]=>101100=>[1,2,1,3]=>[3,2,1,1]
[1,3,2,5,4,6,7]=>101011=>[1,2,2,1,1]=>[2,2,1,1,1]
[1,3,2,5,4,7,6]=>101010=>[1,2,2,2]=>[2,2,2,1]
[1,3,2,5,6,4,7]=>101001=>[1,2,3,1]=>[3,2,1,1]
[1,3,2,5,6,7,4]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,5,7,4,6]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,5,7,6,4]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,6,4,5,7]=>101001=>[1,2,3,1]=>[3,2,1,1]
[1,3,2,6,4,7,5]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,6,5,4,7]=>101001=>[1,2,3,1]=>[3,2,1,1]
[1,3,2,6,5,7,4]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,6,7,4,5]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,6,7,5,4]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,7,4,5,6]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,7,4,6,5]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,7,5,4,6]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,7,5,6,4]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,7,6,4,5]=>101000=>[1,2,4]=>[4,2,1]
[1,3,2,7,6,5,4]=>101000=>[1,2,4]=>[4,2,1]
[1,3,4,2,5,6,7]=>100111=>[1,3,1,1,1]=>[3,1,1,1,1]
[1,3,4,2,5,7,6]=>100110=>[1,3,1,2]=>[3,2,1,1]
[1,3,4,2,6,5,7]=>100101=>[1,3,2,1]=>[3,2,1,1]
[1,3,4,2,6,7,5]=>100100=>[1,3,3]=>[3,3,1]
[1,3,4,2,7,5,6]=>100100=>[1,3,3]=>[3,3,1]
[1,3,4,2,7,6,5]=>100100=>[1,3,3]=>[3,3,1]
[1,3,4,5,2,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,3,4,5,2,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,3,4,5,6,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,4,5,6,7,2]=>100000=>[1,6]=>[6,1]
[1,3,4,5,7,2,6]=>100000=>[1,6]=>[6,1]
[1,3,4,5,7,6,2]=>100000=>[1,6]=>[6,1]
[1,3,4,6,2,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,4,6,2,7,5]=>100000=>[1,6]=>[6,1]
[1,3,4,6,5,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,4,6,5,7,2]=>100000=>[1,6]=>[6,1]
[1,3,4,6,7,2,5]=>100000=>[1,6]=>[6,1]
[1,3,4,6,7,5,2]=>100000=>[1,6]=>[6,1]
[1,3,4,7,2,5,6]=>100000=>[1,6]=>[6,1]
[1,3,4,7,2,6,5]=>100000=>[1,6]=>[6,1]
[1,3,4,7,5,2,6]=>100000=>[1,6]=>[6,1]
[1,3,4,7,5,6,2]=>100000=>[1,6]=>[6,1]
[1,3,4,7,6,2,5]=>100000=>[1,6]=>[6,1]
[1,3,4,7,6,5,2]=>100000=>[1,6]=>[6,1]
[1,3,5,2,4,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,3,5,2,4,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,3,5,2,6,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,5,2,6,7,4]=>100000=>[1,6]=>[6,1]
[1,3,5,2,7,4,6]=>100000=>[1,6]=>[6,1]
[1,3,5,2,7,6,4]=>100000=>[1,6]=>[6,1]
[1,3,5,4,2,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,3,5,4,2,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,3,5,4,6,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,5,4,6,7,2]=>100000=>[1,6]=>[6,1]
[1,3,5,4,7,2,6]=>100000=>[1,6]=>[6,1]
[1,3,5,4,7,6,2]=>100000=>[1,6]=>[6,1]
[1,3,5,6,2,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,5,6,2,7,4]=>100000=>[1,6]=>[6,1]
[1,3,5,6,4,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,5,6,4,7,2]=>100000=>[1,6]=>[6,1]
[1,3,5,6,7,2,4]=>100000=>[1,6]=>[6,1]
[1,3,5,6,7,4,2]=>100000=>[1,6]=>[6,1]
[1,3,5,7,2,4,6]=>100000=>[1,6]=>[6,1]
[1,3,5,7,2,6,4]=>100000=>[1,6]=>[6,1]
[1,3,5,7,4,2,6]=>100000=>[1,6]=>[6,1]
[1,3,5,7,4,6,2]=>100000=>[1,6]=>[6,1]
[1,3,5,7,6,2,4]=>100000=>[1,6]=>[6,1]
[1,3,5,7,6,4,2]=>100000=>[1,6]=>[6,1]
[1,3,6,2,4,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,6,2,4,7,5]=>100000=>[1,6]=>[6,1]
[1,3,6,2,5,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,6,2,5,7,4]=>100000=>[1,6]=>[6,1]
[1,3,6,2,7,4,5]=>100000=>[1,6]=>[6,1]
[1,3,6,2,7,5,4]=>100000=>[1,6]=>[6,1]
[1,3,6,4,2,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,6,4,2,7,5]=>100000=>[1,6]=>[6,1]
[1,3,6,4,5,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,6,4,5,7,2]=>100000=>[1,6]=>[6,1]
[1,3,6,4,7,2,5]=>100000=>[1,6]=>[6,1]
[1,3,6,4,7,5,2]=>100000=>[1,6]=>[6,1]
[1,3,6,5,2,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,6,5,2,7,4]=>100000=>[1,6]=>[6,1]
[1,3,6,5,4,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,3,6,5,4,7,2]=>100000=>[1,6]=>[6,1]
[1,3,6,5,7,2,4]=>100000=>[1,6]=>[6,1]
[1,3,6,5,7,4,2]=>100000=>[1,6]=>[6,1]
[1,3,6,7,2,4,5]=>100000=>[1,6]=>[6,1]
[1,3,6,7,2,5,4]=>100000=>[1,6]=>[6,1]
[1,3,6,7,4,2,5]=>100000=>[1,6]=>[6,1]
[1,3,6,7,4,5,2]=>100000=>[1,6]=>[6,1]
[1,3,6,7,5,2,4]=>100000=>[1,6]=>[6,1]
[1,3,6,7,5,4,2]=>100000=>[1,6]=>[6,1]
[1,3,7,2,4,5,6]=>100000=>[1,6]=>[6,1]
[1,3,7,2,4,6,5]=>100000=>[1,6]=>[6,1]
[1,3,7,2,5,4,6]=>100000=>[1,6]=>[6,1]
[1,3,7,2,5,6,4]=>100000=>[1,6]=>[6,1]
[1,3,7,2,6,4,5]=>100000=>[1,6]=>[6,1]
[1,3,7,2,6,5,4]=>100000=>[1,6]=>[6,1]
[1,3,7,4,2,5,6]=>100000=>[1,6]=>[6,1]
[1,3,7,4,2,6,5]=>100000=>[1,6]=>[6,1]
[1,3,7,4,5,2,6]=>100000=>[1,6]=>[6,1]
[1,3,7,4,5,6,2]=>100000=>[1,6]=>[6,1]
[1,3,7,4,6,2,5]=>100000=>[1,6]=>[6,1]
[1,3,7,4,6,5,2]=>100000=>[1,6]=>[6,1]
[1,3,7,5,2,4,6]=>100000=>[1,6]=>[6,1]
[1,3,7,5,2,6,4]=>100000=>[1,6]=>[6,1]
[1,3,7,5,4,2,6]=>100000=>[1,6]=>[6,1]
[1,3,7,5,4,6,2]=>100000=>[1,6]=>[6,1]
[1,3,7,5,6,2,4]=>100000=>[1,6]=>[6,1]
[1,3,7,5,6,4,2]=>100000=>[1,6]=>[6,1]
[1,3,7,6,2,4,5]=>100000=>[1,6]=>[6,1]
[1,3,7,6,2,5,4]=>100000=>[1,6]=>[6,1]
[1,3,7,6,4,2,5]=>100000=>[1,6]=>[6,1]
[1,3,7,6,4,5,2]=>100000=>[1,6]=>[6,1]
[1,3,7,6,5,2,4]=>100000=>[1,6]=>[6,1]
[1,3,7,6,5,4,2]=>100000=>[1,6]=>[6,1]
[1,4,2,3,5,6,7]=>100111=>[1,3,1,1,1]=>[3,1,1,1,1]
[1,4,2,3,5,7,6]=>100110=>[1,3,1,2]=>[3,2,1,1]
[1,4,2,3,6,5,7]=>100101=>[1,3,2,1]=>[3,2,1,1]
[1,4,2,3,6,7,5]=>100100=>[1,3,3]=>[3,3,1]
[1,4,2,3,7,5,6]=>100100=>[1,3,3]=>[3,3,1]
[1,4,2,3,7,6,5]=>100100=>[1,3,3]=>[3,3,1]
[1,4,2,5,3,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,4,2,5,3,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,4,2,5,6,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,2,5,6,7,3]=>100000=>[1,6]=>[6,1]
[1,4,2,5,7,3,6]=>100000=>[1,6]=>[6,1]
[1,4,2,5,7,6,3]=>100000=>[1,6]=>[6,1]
[1,4,2,6,3,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,2,6,3,7,5]=>100000=>[1,6]=>[6,1]
[1,4,2,6,5,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,2,6,5,7,3]=>100000=>[1,6]=>[6,1]
[1,4,2,6,7,3,5]=>100000=>[1,6]=>[6,1]
[1,4,2,6,7,5,3]=>100000=>[1,6]=>[6,1]
[1,4,2,7,3,5,6]=>100000=>[1,6]=>[6,1]
[1,4,2,7,3,6,5]=>100000=>[1,6]=>[6,1]
[1,4,2,7,5,3,6]=>100000=>[1,6]=>[6,1]
[1,4,2,7,5,6,3]=>100000=>[1,6]=>[6,1]
[1,4,2,7,6,3,5]=>100000=>[1,6]=>[6,1]
[1,4,2,7,6,5,3]=>100000=>[1,6]=>[6,1]
[1,4,3,2,5,6,7]=>100111=>[1,3,1,1,1]=>[3,1,1,1,1]
[1,4,3,2,5,7,6]=>100110=>[1,3,1,2]=>[3,2,1,1]
[1,4,3,2,6,5,7]=>100101=>[1,3,2,1]=>[3,2,1,1]
[1,4,3,2,6,7,5]=>100100=>[1,3,3]=>[3,3,1]
[1,4,3,2,7,5,6]=>100100=>[1,3,3]=>[3,3,1]
[1,4,3,2,7,6,5]=>100100=>[1,3,3]=>[3,3,1]
[1,4,3,5,2,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,4,3,5,2,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,4,3,5,6,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,3,5,6,7,2]=>100000=>[1,6]=>[6,1]
[1,4,3,5,7,2,6]=>100000=>[1,6]=>[6,1]
[1,4,3,5,7,6,2]=>100000=>[1,6]=>[6,1]
[1,4,3,6,2,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,3,6,2,7,5]=>100000=>[1,6]=>[6,1]
[1,4,3,6,5,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,3,6,5,7,2]=>100000=>[1,6]=>[6,1]
[1,4,3,6,7,2,5]=>100000=>[1,6]=>[6,1]
[1,4,3,6,7,5,2]=>100000=>[1,6]=>[6,1]
[1,4,3,7,2,5,6]=>100000=>[1,6]=>[6,1]
[1,4,3,7,2,6,5]=>100000=>[1,6]=>[6,1]
[1,4,3,7,5,2,6]=>100000=>[1,6]=>[6,1]
[1,4,3,7,5,6,2]=>100000=>[1,6]=>[6,1]
[1,4,3,7,6,2,5]=>100000=>[1,6]=>[6,1]
[1,4,3,7,6,5,2]=>100000=>[1,6]=>[6,1]
[1,4,5,2,3,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,4,5,2,3,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,4,5,2,6,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,5,2,6,7,3]=>100000=>[1,6]=>[6,1]
[1,4,5,2,7,3,6]=>100000=>[1,6]=>[6,1]
[1,4,5,2,7,6,3]=>100000=>[1,6]=>[6,1]
[1,4,5,3,2,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,4,5,3,2,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,4,5,3,6,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,5,3,6,7,2]=>100000=>[1,6]=>[6,1]
[1,4,5,3,7,2,6]=>100000=>[1,6]=>[6,1]
[1,4,5,3,7,6,2]=>100000=>[1,6]=>[6,1]
[1,4,5,6,2,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,5,6,2,7,3]=>100000=>[1,6]=>[6,1]
[1,4,5,6,3,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,5,6,3,7,2]=>100000=>[1,6]=>[6,1]
[1,4,5,6,7,2,3]=>100000=>[1,6]=>[6,1]
[1,4,5,6,7,3,2]=>100000=>[1,6]=>[6,1]
[1,4,5,7,2,3,6]=>100000=>[1,6]=>[6,1]
[1,4,5,7,2,6,3]=>100000=>[1,6]=>[6,1]
[1,4,5,7,3,2,6]=>100000=>[1,6]=>[6,1]
[1,4,5,7,3,6,2]=>100000=>[1,6]=>[6,1]
[1,4,5,7,6,2,3]=>100000=>[1,6]=>[6,1]
[1,4,5,7,6,3,2]=>100000=>[1,6]=>[6,1]
[1,4,6,2,3,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,6,2,3,7,5]=>100000=>[1,6]=>[6,1]
[1,4,6,2,5,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,6,2,5,7,3]=>100000=>[1,6]=>[6,1]
[1,4,6,2,7,3,5]=>100000=>[1,6]=>[6,1]
[1,4,6,2,7,5,3]=>100000=>[1,6]=>[6,1]
[1,4,6,3,2,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,6,3,2,7,5]=>100000=>[1,6]=>[6,1]
[1,4,6,3,5,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,6,3,5,7,2]=>100000=>[1,6]=>[6,1]
[1,4,6,3,7,2,5]=>100000=>[1,6]=>[6,1]
[1,4,6,3,7,5,2]=>100000=>[1,6]=>[6,1]
[1,4,6,5,2,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,6,5,2,7,3]=>100000=>[1,6]=>[6,1]
[1,4,6,5,3,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,4,6,5,3,7,2]=>100000=>[1,6]=>[6,1]
[1,4,6,5,7,2,3]=>100000=>[1,6]=>[6,1]
[1,4,6,5,7,3,2]=>100000=>[1,6]=>[6,1]
[1,4,6,7,2,3,5]=>100000=>[1,6]=>[6,1]
[1,4,6,7,2,5,3]=>100000=>[1,6]=>[6,1]
[1,4,6,7,3,2,5]=>100000=>[1,6]=>[6,1]
[1,4,6,7,3,5,2]=>100000=>[1,6]=>[6,1]
[1,4,6,7,5,2,3]=>100000=>[1,6]=>[6,1]
[1,4,6,7,5,3,2]=>100000=>[1,6]=>[6,1]
[1,4,7,2,3,5,6]=>100000=>[1,6]=>[6,1]
[1,4,7,2,3,6,5]=>100000=>[1,6]=>[6,1]
[1,4,7,2,5,3,6]=>100000=>[1,6]=>[6,1]
[1,4,7,2,5,6,3]=>100000=>[1,6]=>[6,1]
[1,4,7,2,6,3,5]=>100000=>[1,6]=>[6,1]
[1,4,7,2,6,5,3]=>100000=>[1,6]=>[6,1]
[1,4,7,3,2,5,6]=>100000=>[1,6]=>[6,1]
[1,4,7,3,2,6,5]=>100000=>[1,6]=>[6,1]
[1,4,7,3,5,2,6]=>100000=>[1,6]=>[6,1]
[1,4,7,3,5,6,2]=>100000=>[1,6]=>[6,1]
[1,4,7,3,6,2,5]=>100000=>[1,6]=>[6,1]
[1,4,7,3,6,5,2]=>100000=>[1,6]=>[6,1]
[1,4,7,5,2,3,6]=>100000=>[1,6]=>[6,1]
[1,4,7,5,2,6,3]=>100000=>[1,6]=>[6,1]
[1,4,7,5,3,2,6]=>100000=>[1,6]=>[6,1]
[1,4,7,5,3,6,2]=>100000=>[1,6]=>[6,1]
[1,4,7,5,6,2,3]=>100000=>[1,6]=>[6,1]
[1,4,7,5,6,3,2]=>100000=>[1,6]=>[6,1]
[1,4,7,6,2,3,5]=>100000=>[1,6]=>[6,1]
[1,4,7,6,2,5,3]=>100000=>[1,6]=>[6,1]
[1,4,7,6,3,2,5]=>100000=>[1,6]=>[6,1]
[1,4,7,6,3,5,2]=>100000=>[1,6]=>[6,1]
[1,4,7,6,5,2,3]=>100000=>[1,6]=>[6,1]
[1,4,7,6,5,3,2]=>100000=>[1,6]=>[6,1]
[1,5,2,3,4,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,5,2,3,4,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,5,2,3,6,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,2,3,6,7,4]=>100000=>[1,6]=>[6,1]
[1,5,2,3,7,4,6]=>100000=>[1,6]=>[6,1]
[1,5,2,3,7,6,4]=>100000=>[1,6]=>[6,1]
[1,5,2,4,3,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,5,2,4,3,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,5,2,4,6,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,2,4,6,7,3]=>100000=>[1,6]=>[6,1]
[1,5,2,4,7,3,6]=>100000=>[1,6]=>[6,1]
[1,5,2,4,7,6,3]=>100000=>[1,6]=>[6,1]
[1,5,2,6,3,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,2,6,3,7,4]=>100000=>[1,6]=>[6,1]
[1,5,2,6,4,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,2,6,4,7,3]=>100000=>[1,6]=>[6,1]
[1,5,2,6,7,3,4]=>100000=>[1,6]=>[6,1]
[1,5,2,6,7,4,3]=>100000=>[1,6]=>[6,1]
[1,5,2,7,3,4,6]=>100000=>[1,6]=>[6,1]
[1,5,2,7,3,6,4]=>100000=>[1,6]=>[6,1]
[1,5,2,7,4,3,6]=>100000=>[1,6]=>[6,1]
[1,5,2,7,4,6,3]=>100000=>[1,6]=>[6,1]
[1,5,2,7,6,3,4]=>100000=>[1,6]=>[6,1]
[1,5,2,7,6,4,3]=>100000=>[1,6]=>[6,1]
[1,5,3,2,4,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,5,3,2,4,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,5,3,2,6,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,3,2,6,7,4]=>100000=>[1,6]=>[6,1]
[1,5,3,2,7,4,6]=>100000=>[1,6]=>[6,1]
[1,5,3,2,7,6,4]=>100000=>[1,6]=>[6,1]
[1,5,3,4,2,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,5,3,4,2,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,5,3,4,6,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,3,4,6,7,2]=>100000=>[1,6]=>[6,1]
[1,5,3,4,7,2,6]=>100000=>[1,6]=>[6,1]
[1,5,3,4,7,6,2]=>100000=>[1,6]=>[6,1]
[1,5,3,6,2,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,3,6,2,7,4]=>100000=>[1,6]=>[6,1]
[1,5,3,6,4,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,3,6,4,7,2]=>100000=>[1,6]=>[6,1]
[1,5,3,6,7,2,4]=>100000=>[1,6]=>[6,1]
[1,5,3,6,7,4,2]=>100000=>[1,6]=>[6,1]
[1,5,3,7,2,4,6]=>100000=>[1,6]=>[6,1]
[1,5,3,7,2,6,4]=>100000=>[1,6]=>[6,1]
[1,5,3,7,4,2,6]=>100000=>[1,6]=>[6,1]
[1,5,3,7,4,6,2]=>100000=>[1,6]=>[6,1]
[1,5,3,7,6,2,4]=>100000=>[1,6]=>[6,1]
[1,5,3,7,6,4,2]=>100000=>[1,6]=>[6,1]
[1,5,4,2,3,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,5,4,2,3,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,5,4,2,6,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,4,2,6,7,3]=>100000=>[1,6]=>[6,1]
[1,5,4,2,7,3,6]=>100000=>[1,6]=>[6,1]
[1,5,4,2,7,6,3]=>100000=>[1,6]=>[6,1]
[1,5,4,3,2,6,7]=>100011=>[1,4,1,1]=>[4,1,1,1]
[1,5,4,3,2,7,6]=>100010=>[1,4,2]=>[4,2,1]
[1,5,4,3,6,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,4,3,6,7,2]=>100000=>[1,6]=>[6,1]
[1,5,4,3,7,2,6]=>100000=>[1,6]=>[6,1]
[1,5,4,3,7,6,2]=>100000=>[1,6]=>[6,1]
[1,5,4,6,2,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,4,6,2,7,3]=>100000=>[1,6]=>[6,1]
[1,5,4,6,3,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,4,6,3,7,2]=>100000=>[1,6]=>[6,1]
[1,5,4,6,7,2,3]=>100000=>[1,6]=>[6,1]
[1,5,4,6,7,3,2]=>100000=>[1,6]=>[6,1]
[1,5,4,7,2,3,6]=>100000=>[1,6]=>[6,1]
[1,5,4,7,2,6,3]=>100000=>[1,6]=>[6,1]
[1,5,4,7,3,2,6]=>100000=>[1,6]=>[6,1]
[1,5,4,7,3,6,2]=>100000=>[1,6]=>[6,1]
[1,5,4,7,6,2,3]=>100000=>[1,6]=>[6,1]
[1,5,4,7,6,3,2]=>100000=>[1,6]=>[6,1]
[1,5,6,2,3,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,6,2,3,7,4]=>100000=>[1,6]=>[6,1]
[1,5,6,2,4,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,6,2,4,7,3]=>100000=>[1,6]=>[6,1]
[1,5,6,2,7,3,4]=>100000=>[1,6]=>[6,1]
[1,5,6,2,7,4,3]=>100000=>[1,6]=>[6,1]
[1,5,6,3,2,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,6,3,2,7,4]=>100000=>[1,6]=>[6,1]
[1,5,6,3,4,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,6,3,4,7,2]=>100000=>[1,6]=>[6,1]
[1,5,6,3,7,2,4]=>100000=>[1,6]=>[6,1]
[1,5,6,3,7,4,2]=>100000=>[1,6]=>[6,1]
[1,5,6,4,2,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,6,4,2,7,3]=>100000=>[1,6]=>[6,1]
[1,5,6,4,3,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,5,6,4,3,7,2]=>100000=>[1,6]=>[6,1]
[1,5,6,4,7,2,3]=>100000=>[1,6]=>[6,1]
[1,5,6,4,7,3,2]=>100000=>[1,6]=>[6,1]
[1,5,6,7,2,3,4]=>100000=>[1,6]=>[6,1]
[1,5,6,7,2,4,3]=>100000=>[1,6]=>[6,1]
[1,5,6,7,3,2,4]=>100000=>[1,6]=>[6,1]
[1,5,6,7,3,4,2]=>100000=>[1,6]=>[6,1]
[1,5,6,7,4,2,3]=>100000=>[1,6]=>[6,1]
[1,5,6,7,4,3,2]=>100000=>[1,6]=>[6,1]
[1,5,7,2,3,4,6]=>100000=>[1,6]=>[6,1]
[1,5,7,2,3,6,4]=>100000=>[1,6]=>[6,1]
[1,5,7,2,4,3,6]=>100000=>[1,6]=>[6,1]
[1,5,7,2,4,6,3]=>100000=>[1,6]=>[6,1]
[1,5,7,2,6,3,4]=>100000=>[1,6]=>[6,1]
[1,5,7,2,6,4,3]=>100000=>[1,6]=>[6,1]
[1,5,7,3,2,4,6]=>100000=>[1,6]=>[6,1]
[1,5,7,3,2,6,4]=>100000=>[1,6]=>[6,1]
[1,5,7,3,4,2,6]=>100000=>[1,6]=>[6,1]
[1,5,7,3,4,6,2]=>100000=>[1,6]=>[6,1]
[1,5,7,3,6,2,4]=>100000=>[1,6]=>[6,1]
[1,5,7,3,6,4,2]=>100000=>[1,6]=>[6,1]
[1,5,7,4,2,3,6]=>100000=>[1,6]=>[6,1]
[1,5,7,4,2,6,3]=>100000=>[1,6]=>[6,1]
[1,5,7,4,3,2,6]=>100000=>[1,6]=>[6,1]
[1,5,7,4,3,6,2]=>100000=>[1,6]=>[6,1]
[1,5,7,4,6,2,3]=>100000=>[1,6]=>[6,1]
[1,5,7,4,6,3,2]=>100000=>[1,6]=>[6,1]
[1,5,7,6,2,3,4]=>100000=>[1,6]=>[6,1]
[1,5,7,6,2,4,3]=>100000=>[1,6]=>[6,1]
[1,5,7,6,3,2,4]=>100000=>[1,6]=>[6,1]
[1,5,7,6,3,4,2]=>100000=>[1,6]=>[6,1]
[1,5,7,6,4,2,3]=>100000=>[1,6]=>[6,1]
[1,5,7,6,4,3,2]=>100000=>[1,6]=>[6,1]
[1,6,2,3,4,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,2,3,4,7,5]=>100000=>[1,6]=>[6,1]
[1,6,2,3,5,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,2,3,5,7,4]=>100000=>[1,6]=>[6,1]
[1,6,2,3,7,4,5]=>100000=>[1,6]=>[6,1]
[1,6,2,3,7,5,4]=>100000=>[1,6]=>[6,1]
[1,6,2,4,3,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,2,4,3,7,5]=>100000=>[1,6]=>[6,1]
[1,6,2,4,5,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,2,4,5,7,3]=>100000=>[1,6]=>[6,1]
[1,6,2,4,7,3,5]=>100000=>[1,6]=>[6,1]
[1,6,2,4,7,5,3]=>100000=>[1,6]=>[6,1]
[1,6,2,5,3,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,2,5,3,7,4]=>100000=>[1,6]=>[6,1]
[1,6,2,5,4,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,2,5,4,7,3]=>100000=>[1,6]=>[6,1]
[1,6,2,5,7,3,4]=>100000=>[1,6]=>[6,1]
[1,6,2,5,7,4,3]=>100000=>[1,6]=>[6,1]
[1,6,2,7,3,4,5]=>100000=>[1,6]=>[6,1]
[1,6,2,7,3,5,4]=>100000=>[1,6]=>[6,1]
[1,6,2,7,4,3,5]=>100000=>[1,6]=>[6,1]
[1,6,2,7,4,5,3]=>100000=>[1,6]=>[6,1]
[1,6,2,7,5,3,4]=>100000=>[1,6]=>[6,1]
[1,6,2,7,5,4,3]=>100000=>[1,6]=>[6,1]
[1,6,3,2,4,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,3,2,4,7,5]=>100000=>[1,6]=>[6,1]
[1,6,3,2,5,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,3,2,5,7,4]=>100000=>[1,6]=>[6,1]
[1,6,3,2,7,4,5]=>100000=>[1,6]=>[6,1]
[1,6,3,2,7,5,4]=>100000=>[1,6]=>[6,1]
[1,6,3,4,2,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,3,4,2,7,5]=>100000=>[1,6]=>[6,1]
[1,6,3,4,5,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,3,4,5,7,2]=>100000=>[1,6]=>[6,1]
[1,6,3,4,7,2,5]=>100000=>[1,6]=>[6,1]
[1,6,3,4,7,5,2]=>100000=>[1,6]=>[6,1]
[1,6,3,5,2,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,3,5,2,7,4]=>100000=>[1,6]=>[6,1]
[1,6,3,5,4,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,3,5,4,7,2]=>100000=>[1,6]=>[6,1]
[1,6,3,5,7,2,4]=>100000=>[1,6]=>[6,1]
[1,6,3,5,7,4,2]=>100000=>[1,6]=>[6,1]
[1,6,3,7,2,4,5]=>100000=>[1,6]=>[6,1]
[1,6,3,7,2,5,4]=>100000=>[1,6]=>[6,1]
[1,6,3,7,4,2,5]=>100000=>[1,6]=>[6,1]
[1,6,3,7,4,5,2]=>100000=>[1,6]=>[6,1]
[1,6,3,7,5,2,4]=>100000=>[1,6]=>[6,1]
[1,6,3,7,5,4,2]=>100000=>[1,6]=>[6,1]
[1,6,4,2,3,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,4,2,3,7,5]=>100000=>[1,6]=>[6,1]
[1,6,4,2,5,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,4,2,5,7,3]=>100000=>[1,6]=>[6,1]
[1,6,4,2,7,3,5]=>100000=>[1,6]=>[6,1]
[1,6,4,2,7,5,3]=>100000=>[1,6]=>[6,1]
[1,6,4,3,2,5,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,4,3,2,7,5]=>100000=>[1,6]=>[6,1]
[1,6,4,3,5,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,4,3,5,7,2]=>100000=>[1,6]=>[6,1]
[1,6,4,3,7,2,5]=>100000=>[1,6]=>[6,1]
[1,6,4,3,7,5,2]=>100000=>[1,6]=>[6,1]
[1,6,4,5,2,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,4,5,2,7,3]=>100000=>[1,6]=>[6,1]
[1,6,4,5,3,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,4,5,3,7,2]=>100000=>[1,6]=>[6,1]
[1,6,4,5,7,2,3]=>100000=>[1,6]=>[6,1]
[1,6,4,5,7,3,2]=>100000=>[1,6]=>[6,1]
[1,6,4,7,2,3,5]=>100000=>[1,6]=>[6,1]
[1,6,4,7,2,5,3]=>100000=>[1,6]=>[6,1]
[1,6,4,7,3,2,5]=>100000=>[1,6]=>[6,1]
[1,6,4,7,3,5,2]=>100000=>[1,6]=>[6,1]
[1,6,4,7,5,2,3]=>100000=>[1,6]=>[6,1]
[1,6,4,7,5,3,2]=>100000=>[1,6]=>[6,1]
[1,6,5,2,3,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,5,2,3,7,4]=>100000=>[1,6]=>[6,1]
[1,6,5,2,4,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,5,2,4,7,3]=>100000=>[1,6]=>[6,1]
[1,6,5,2,7,3,4]=>100000=>[1,6]=>[6,1]
[1,6,5,2,7,4,3]=>100000=>[1,6]=>[6,1]
[1,6,5,3,2,4,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,5,3,2,7,4]=>100000=>[1,6]=>[6,1]
[1,6,5,3,4,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,5,3,4,7,2]=>100000=>[1,6]=>[6,1]
[1,6,5,3,7,2,4]=>100000=>[1,6]=>[6,1]
[1,6,5,3,7,4,2]=>100000=>[1,6]=>[6,1]
[1,6,5,4,2,3,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,5,4,2,7,3]=>100000=>[1,6]=>[6,1]
[1,6,5,4,3,2,7]=>100001=>[1,5,1]=>[5,1,1]
[1,6,5,4,3,7,2]=>100000=>[1,6]=>[6,1]
[1,6,5,4,7,2,3]=>100000=>[1,6]=>[6,1]
[1,6,5,4,7,3,2]=>100000=>[1,6]=>[6,1]
[1,6,5,7,2,3,4]=>100000=>[1,6]=>[6,1]
[1,6,5,7,2,4,3]=>100000=>[1,6]=>[6,1]
[1,6,5,7,3,2,4]=>100000=>[1,6]=>[6,1]
[1,6,5,7,3,4,2]=>100000=>[1,6]=>[6,1]
[1,6,5,7,4,2,3]=>100000=>[1,6]=>[6,1]
[1,6,5,7,4,3,2]=>100000=>[1,6]=>[6,1]
[1,6,7,2,3,4,5]=>100000=>[1,6]=>[6,1]
[1,6,7,2,3,5,4]=>100000=>[1,6]=>[6,1]
[1,6,7,2,4,3,5]=>100000=>[1,6]=>[6,1]
[1,6,7,2,4,5,3]=>100000=>[1,6]=>[6,1]
[1,6,7,2,5,3,4]=>100000=>[1,6]=>[6,1]
[1,6,7,2,5,4,3]=>100000=>[1,6]=>[6,1]
[1,6,7,3,2,4,5]=>100000=>[1,6]=>[6,1]
[1,6,7,3,2,5,4]=>100000=>[1,6]=>[6,1]
[1,6,7,3,4,2,5]=>100000=>[1,6]=>[6,1]
[1,6,7,3,4,5,2]=>100000=>[1,6]=>[6,1]
[1,6,7,3,5,2,4]=>100000=>[1,6]=>[6,1]
[1,6,7,3,5,4,2]=>100000=>[1,6]=>[6,1]
[1,6,7,4,2,3,5]=>100000=>[1,6]=>[6,1]
[1,6,7,4,2,5,3]=>100000=>[1,6]=>[6,1]
[1,6,7,4,3,2,5]=>100000=>[1,6]=>[6,1]
[1,6,7,4,3,5,2]=>100000=>[1,6]=>[6,1]
[1,6,7,4,5,2,3]=>100000=>[1,6]=>[6,1]
[1,6,7,4,5,3,2]=>100000=>[1,6]=>[6,1]
[1,6,7,5,2,3,4]=>100000=>[1,6]=>[6,1]
[1,6,7,5,2,4,3]=>100000=>[1,6]=>[6,1]
[1,6,7,5,3,2,4]=>100000=>[1,6]=>[6,1]
[1,6,7,5,3,4,2]=>100000=>[1,6]=>[6,1]
[1,6,7,5,4,2,3]=>100000=>[1,6]=>[6,1]
[1,6,7,5,4,3,2]=>100000=>[1,6]=>[6,1]
[1,7,2,3,4,5,6]=>100000=>[1,6]=>[6,1]
[1,7,2,3,4,6,5]=>100000=>[1,6]=>[6,1]
[1,7,2,3,5,4,6]=>100000=>[1,6]=>[6,1]
[1,7,2,3,5,6,4]=>100000=>[1,6]=>[6,1]
[1,7,2,3,6,4,5]=>100000=>[1,6]=>[6,1]
[1,7,2,3,6,5,4]=>100000=>[1,6]=>[6,1]
[1,7,2,4,3,5,6]=>100000=>[1,6]=>[6,1]
[1,7,2,4,3,6,5]=>100000=>[1,6]=>[6,1]
[1,7,2,4,5,3,6]=>100000=>[1,6]=>[6,1]
[1,7,2,4,5,6,3]=>100000=>[1,6]=>[6,1]
[1,7,2,4,6,3,5]=>100000=>[1,6]=>[6,1]
[1,7,2,4,6,5,3]=>100000=>[1,6]=>[6,1]
[1,7,2,5,3,4,6]=>100000=>[1,6]=>[6,1]
[1,7,2,5,3,6,4]=>100000=>[1,6]=>[6,1]
[1,7,2,5,4,3,6]=>100000=>[1,6]=>[6,1]
[1,7,2,5,4,6,3]=>100000=>[1,6]=>[6,1]
[1,7,2,5,6,3,4]=>100000=>[1,6]=>[6,1]
[1,7,2,5,6,4,3]=>100000=>[1,6]=>[6,1]
[1,7,2,6,3,4,5]=>100000=>[1,6]=>[6,1]
[1,7,2,6,3,5,4]=>100000=>[1,6]=>[6,1]
[1,7,2,6,4,3,5]=>100000=>[1,6]=>[6,1]
[1,7,2,6,4,5,3]=>100000=>[1,6]=>[6,1]
[1,7,2,6,5,3,4]=>100000=>[1,6]=>[6,1]
[1,7,2,6,5,4,3]=>100000=>[1,6]=>[6,1]
[1,7,3,2,4,5,6]=>100000=>[1,6]=>[6,1]
[1,7,3,2,4,6,5]=>100000=>[1,6]=>[6,1]
[1,7,3,2,5,4,6]=>100000=>[1,6]=>[6,1]
[1,7,3,2,5,6,4]=>100000=>[1,6]=>[6,1]
[1,7,3,2,6,4,5]=>100000=>[1,6]=>[6,1]
[1,7,3,2,6,5,4]=>100000=>[1,6]=>[6,1]
[1,7,3,4,2,5,6]=>100000=>[1,6]=>[6,1]
[1,7,3,4,2,6,5]=>100000=>[1,6]=>[6,1]
[1,7,3,4,5,2,6]=>100000=>[1,6]=>[6,1]
[1,7,3,4,5,6,2]=>100000=>[1,6]=>[6,1]
[1,7,3,4,6,2,5]=>100000=>[1,6]=>[6,1]
[1,7,3,4,6,5,2]=>100000=>[1,6]=>[6,1]
[1,7,3,5,2,4,6]=>100000=>[1,6]=>[6,1]
[1,7,3,5,2,6,4]=>100000=>[1,6]=>[6,1]
[1,7,3,5,4,2,6]=>100000=>[1,6]=>[6,1]
[1,7,3,5,4,6,2]=>100000=>[1,6]=>[6,1]
[1,7,3,5,6,2,4]=>100000=>[1,6]=>[6,1]
[1,7,3,5,6,4,2]=>100000=>[1,6]=>[6,1]
[1,7,3,6,2,4,5]=>100000=>[1,6]=>[6,1]
[1,7,3,6,2,5,4]=>100000=>[1,6]=>[6,1]
[1,7,3,6,4,2,5]=>100000=>[1,6]=>[6,1]
[1,7,3,6,4,5,2]=>100000=>[1,6]=>[6,1]
[1,7,3,6,5,2,4]=>100000=>[1,6]=>[6,1]
[1,7,3,6,5,4,2]=>100000=>[1,6]=>[6,1]
[1,7,4,2,3,5,6]=>100000=>[1,6]=>[6,1]
[1,7,4,2,3,6,5]=>100000=>[1,6]=>[6,1]
[1,7,4,2,5,3,6]=>100000=>[1,6]=>[6,1]
[1,7,4,2,5,6,3]=>100000=>[1,6]=>[6,1]
[1,7,4,2,6,3,5]=>100000=>[1,6]=>[6,1]
[1,7,4,2,6,5,3]=>100000=>[1,6]=>[6,1]
[1,7,4,3,2,5,6]=>100000=>[1,6]=>[6,1]
[1,7,4,3,2,6,5]=>100000=>[1,6]=>[6,1]
[1,7,4,3,5,2,6]=>100000=>[1,6]=>[6,1]
[1,7,4,3,5,6,2]=>100000=>[1,6]=>[6,1]
[1,7,4,3,6,2,5]=>100000=>[1,6]=>[6,1]
[1,7,4,3,6,5,2]=>100000=>[1,6]=>[6,1]
[1,7,4,5,2,3,6]=>100000=>[1,6]=>[6,1]
[1,7,4,5,2,6,3]=>100000=>[1,6]=>[6,1]
[1,7,4,5,3,2,6]=>100000=>[1,6]=>[6,1]
[1,7,4,5,3,6,2]=>100000=>[1,6]=>[6,1]
[1,7,4,5,6,2,3]=>100000=>[1,6]=>[6,1]
[1,7,4,5,6,3,2]=>100000=>[1,6]=>[6,1]
[1,7,4,6,2,3,5]=>100000=>[1,6]=>[6,1]
[1,7,4,6,2,5,3]=>100000=>[1,6]=>[6,1]
[1,7,4,6,3,2,5]=>100000=>[1,6]=>[6,1]
[1,7,4,6,3,5,2]=>100000=>[1,6]=>[6,1]
[1,7,4,6,5,2,3]=>100000=>[1,6]=>[6,1]
[1,7,4,6,5,3,2]=>100000=>[1,6]=>[6,1]
[1,7,5,2,3,4,6]=>100000=>[1,6]=>[6,1]
[1,7,5,2,3,6,4]=>100000=>[1,6]=>[6,1]
[1,7,5,2,4,3,6]=>100000=>[1,6]=>[6,1]
[1,7,5,2,4,6,3]=>100000=>[1,6]=>[6,1]
[1,7,5,2,6,3,4]=>100000=>[1,6]=>[6,1]
[1,7,5,2,6,4,3]=>100000=>[1,6]=>[6,1]
[1,7,5,3,2,4,6]=>100000=>[1,6]=>[6,1]
[1,7,5,3,2,6,4]=>100000=>[1,6]=>[6,1]
[1,7,5,3,4,2,6]=>100000=>[1,6]=>[6,1]
[1,7,5,3,4,6,2]=>100000=>[1,6]=>[6,1]
[1,7,5,3,6,2,4]=>100000=>[1,6]=>[6,1]
[1,7,5,3,6,4,2]=>100000=>[1,6]=>[6,1]
[1,7,5,4,2,3,6]=>100000=>[1,6]=>[6,1]
[1,7,5,4,2,6,3]=>100000=>[1,6]=>[6,1]
[1,7,5,4,3,2,6]=>100000=>[1,6]=>[6,1]
[1,7,5,4,3,6,2]=>100000=>[1,6]=>[6,1]
[1,7,5,4,6,2,3]=>100000=>[1,6]=>[6,1]
[1,7,5,4,6,3,2]=>100000=>[1,6]=>[6,1]
[1,7,5,6,2,3,4]=>100000=>[1,6]=>[6,1]
[1,7,5,6,2,4,3]=>100000=>[1,6]=>[6,1]
[1,7,5,6,3,2,4]=>100000=>[1,6]=>[6,1]
[1,7,5,6,3,4,2]=>100000=>[1,6]=>[6,1]
[1,7,5,6,4,2,3]=>100000=>[1,6]=>[6,1]
[1,7,5,6,4,3,2]=>100000=>[1,6]=>[6,1]
[1,7,6,2,3,4,5]=>100000=>[1,6]=>[6,1]
[1,7,6,2,3,5,4]=>100000=>[1,6]=>[6,1]
[1,7,6,2,4,3,5]=>100000=>[1,6]=>[6,1]
[1,7,6,2,4,5,3]=>100000=>[1,6]=>[6,1]
[1,7,6,2,5,3,4]=>100000=>[1,6]=>[6,1]
[1,7,6,2,5,4,3]=>100000=>[1,6]=>[6,1]
[1,7,6,3,2,4,5]=>100000=>[1,6]=>[6,1]
[1,7,6,3,2,5,4]=>100000=>[1,6]=>[6,1]
[1,7,6,3,4,2,5]=>100000=>[1,6]=>[6,1]
[1,7,6,3,4,5,2]=>100000=>[1,6]=>[6,1]
[1,7,6,3,5,2,4]=>100000=>[1,6]=>[6,1]
[1,7,6,3,5,4,2]=>100000=>[1,6]=>[6,1]
[1,7,6,4,2,3,5]=>100000=>[1,6]=>[6,1]
[1,7,6,4,2,5,3]=>100000=>[1,6]=>[6,1]
[1,7,6,4,3,2,5]=>100000=>[1,6]=>[6,1]
[1,7,6,4,3,5,2]=>100000=>[1,6]=>[6,1]
[1,7,6,4,5,2,3]=>100000=>[1,6]=>[6,1]
[1,7,6,4,5,3,2]=>100000=>[1,6]=>[6,1]
[1,7,6,5,2,3,4]=>100000=>[1,6]=>[6,1]
[1,7,6,5,2,4,3]=>100000=>[1,6]=>[6,1]
[1,7,6,5,3,2,4]=>100000=>[1,6]=>[6,1]
[1,7,6,5,3,4,2]=>100000=>[1,6]=>[6,1]
[1,7,6,5,4,2,3]=>100000=>[1,6]=>[6,1]
[1,7,6,5,4,3,2]=>100000=>[1,6]=>[6,1]
[2,1,3,4,5,6,7]=>011111=>[2,1,1,1,1,1]=>[2,1,1,1,1,1]
[2,1,3,4,5,7,6]=>011110=>[2,1,1,1,2]=>[2,2,1,1,1]
[2,1,3,4,6,5,7]=>011101=>[2,1,1,2,1]=>[2,2,1,1,1]
[2,1,3,4,6,7,5]=>011100=>[2,1,1,3]=>[3,2,1,1]
[2,1,3,4,7,5,6]=>011100=>[2,1,1,3]=>[3,2,1,1]
[2,1,3,4,7,6,5]=>011100=>[2,1,1,3]=>[3,2,1,1]
[2,1,3,5,4,6,7]=>011011=>[2,1,2,1,1]=>[2,2,1,1,1]
[2,1,3,5,4,7,6]=>011010=>[2,1,2,2]=>[2,2,2,1]
[2,1,3,5,6,4,7]=>011001=>[2,1,3,1]=>[3,2,1,1]
[2,1,3,5,6,7,4]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,5,7,4,6]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,5,7,6,4]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,6,4,5,7]=>011001=>[2,1,3,1]=>[3,2,1,1]
[2,1,3,6,4,7,5]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,6,5,4,7]=>011001=>[2,1,3,1]=>[3,2,1,1]
[2,1,3,6,5,7,4]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,6,7,4,5]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,6,7,5,4]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,7,4,5,6]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,7,4,6,5]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,7,5,4,6]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,7,5,6,4]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,7,6,4,5]=>011000=>[2,1,4]=>[4,2,1]
[2,1,3,7,6,5,4]=>011000=>[2,1,4]=>[4,2,1]
[2,1,4,3,5,6,7]=>010111=>[2,2,1,1,1]=>[2,2,1,1,1]
[2,1,4,3,5,7,6]=>010110=>[2,2,1,2]=>[2,2,2,1]
[2,1,4,3,6,5,7]=>010101=>[2,2,2,1]=>[2,2,2,1]
[2,1,4,3,6,7,5]=>010100=>[2,2,3]=>[3,2,2]
[2,1,4,3,7,5,6]=>010100=>[2,2,3]=>[3,2,2]
[2,1,4,3,7,6,5]=>010100=>[2,2,3]=>[3,2,2]
[2,1,4,5,3,6,7]=>010011=>[2,3,1,1]=>[3,2,1,1]
[2,1,4,5,3,7,6]=>010010=>[2,3,2]=>[3,2,2]
[2,1,4,5,6,3,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,4,5,6,7,3]=>010000=>[2,5]=>[5,2]
[2,1,4,5,7,3,6]=>010000=>[2,5]=>[5,2]
[2,1,4,5,7,6,3]=>010000=>[2,5]=>[5,2]
[2,1,4,6,3,5,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,4,6,3,7,5]=>010000=>[2,5]=>[5,2]
[2,1,4,6,5,3,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,4,6,5,7,3]=>010000=>[2,5]=>[5,2]
[2,1,4,6,7,3,5]=>010000=>[2,5]=>[5,2]
[2,1,4,6,7,5,3]=>010000=>[2,5]=>[5,2]
[2,1,4,7,3,5,6]=>010000=>[2,5]=>[5,2]
[2,1,4,7,3,6,5]=>010000=>[2,5]=>[5,2]
[2,1,4,7,5,3,6]=>010000=>[2,5]=>[5,2]
[2,1,4,7,5,6,3]=>010000=>[2,5]=>[5,2]
[2,1,4,7,6,3,5]=>010000=>[2,5]=>[5,2]
[2,1,4,7,6,5,3]=>010000=>[2,5]=>[5,2]
[2,1,5,3,4,6,7]=>010011=>[2,3,1,1]=>[3,2,1,1]
[2,1,5,3,4,7,6]=>010010=>[2,3,2]=>[3,2,2]
[2,1,5,3,6,4,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,5,3,6,7,4]=>010000=>[2,5]=>[5,2]
[2,1,5,3,7,4,6]=>010000=>[2,5]=>[5,2]
[2,1,5,3,7,6,4]=>010000=>[2,5]=>[5,2]
[2,1,5,4,3,6,7]=>010011=>[2,3,1,1]=>[3,2,1,1]
[2,1,5,4,3,7,6]=>010010=>[2,3,2]=>[3,2,2]
[2,1,5,4,6,3,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,5,4,6,7,3]=>010000=>[2,5]=>[5,2]
[2,1,5,4,7,3,6]=>010000=>[2,5]=>[5,2]
[2,1,5,4,7,6,3]=>010000=>[2,5]=>[5,2]
[2,1,5,6,3,4,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,5,6,3,7,4]=>010000=>[2,5]=>[5,2]
[2,1,5,6,4,3,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,5,6,4,7,3]=>010000=>[2,5]=>[5,2]
[2,1,5,6,7,3,4]=>010000=>[2,5]=>[5,2]
[2,1,5,6,7,4,3]=>010000=>[2,5]=>[5,2]
[2,1,5,7,3,4,6]=>010000=>[2,5]=>[5,2]
[2,1,5,7,3,6,4]=>010000=>[2,5]=>[5,2]
[2,1,5,7,4,3,6]=>010000=>[2,5]=>[5,2]
[2,1,5,7,4,6,3]=>010000=>[2,5]=>[5,2]
[2,1,5,7,6,3,4]=>010000=>[2,5]=>[5,2]
[2,1,5,7,6,4,3]=>010000=>[2,5]=>[5,2]
[2,1,6,3,4,5,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,6,3,4,7,5]=>010000=>[2,5]=>[5,2]
[2,1,6,3,5,4,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,6,3,5,7,4]=>010000=>[2,5]=>[5,2]
[2,1,6,3,7,4,5]=>010000=>[2,5]=>[5,2]
[2,1,6,3,7,5,4]=>010000=>[2,5]=>[5,2]
[2,1,6,4,3,5,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,6,4,3,7,5]=>010000=>[2,5]=>[5,2]
[2,1,6,4,5,3,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,6,4,5,7,3]=>010000=>[2,5]=>[5,2]
[2,1,6,4,7,3,5]=>010000=>[2,5]=>[5,2]
[2,1,6,4,7,5,3]=>010000=>[2,5]=>[5,2]
[2,1,6,5,3,4,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,6,5,3,7,4]=>010000=>[2,5]=>[5,2]
[2,1,6,5,4,3,7]=>010001=>[2,4,1]=>[4,2,1]
[2,1,6,5,4,7,3]=>010000=>[2,5]=>[5,2]
[2,1,6,5,7,3,4]=>010000=>[2,5]=>[5,2]
[2,1,6,5,7,4,3]=>010000=>[2,5]=>[5,2]
[2,1,6,7,3,4,5]=>010000=>[2,5]=>[5,2]
[2,1,6,7,3,5,4]=>010000=>[2,5]=>[5,2]
[2,1,6,7,4,3,5]=>010000=>[2,5]=>[5,2]
[2,1,6,7,4,5,3]=>010000=>[2,5]=>[5,2]
[2,1,6,7,5,3,4]=>010000=>[2,5]=>[5,2]
[2,1,6,7,5,4,3]=>010000=>[2,5]=>[5,2]
[2,1,7,3,4,5,6]=>010000=>[2,5]=>[5,2]
[2,1,7,3,4,6,5]=>010000=>[2,5]=>[5,2]
[2,1,7,3,5,4,6]=>010000=>[2,5]=>[5,2]
[2,1,7,3,5,6,4]=>010000=>[2,5]=>[5,2]
[2,1,7,3,6,4,5]=>010000=>[2,5]=>[5,2]
[2,1,7,3,6,5,4]=>010000=>[2,5]=>[5,2]
[2,1,7,4,3,5,6]=>010000=>[2,5]=>[5,2]
[2,1,7,4,3,6,5]=>010000=>[2,5]=>[5,2]
[2,1,7,4,5,3,6]=>010000=>[2,5]=>[5,2]
[2,1,7,4,5,6,3]=>010000=>[2,5]=>[5,2]
[2,1,7,4,6,3,5]=>010000=>[2,5]=>[5,2]
[2,1,7,4,6,5,3]=>010000=>[2,5]=>[5,2]
[2,1,7,5,3,4,6]=>010000=>[2,5]=>[5,2]
[2,1,7,5,3,6,4]=>010000=>[2,5]=>[5,2]
[2,1,7,5,4,3,6]=>010000=>[2,5]=>[5,2]
[2,1,7,5,4,6,3]=>010000=>[2,5]=>[5,2]
[2,1,7,5,6,3,4]=>010000=>[2,5]=>[5,2]
[2,1,7,5,6,4,3]=>010000=>[2,5]=>[5,2]
[2,1,7,6,3,4,5]=>010000=>[2,5]=>[5,2]
[2,1,7,6,3,5,4]=>010000=>[2,5]=>[5,2]
[2,1,7,6,4,3,5]=>010000=>[2,5]=>[5,2]
[2,1,7,6,4,5,3]=>010000=>[2,5]=>[5,2]
[2,1,7,6,5,3,4]=>010000=>[2,5]=>[5,2]
[2,1,7,6,5,4,3]=>010000=>[2,5]=>[5,2]
[2,3,1,4,5,6,7]=>001111=>[3,1,1,1,1]=>[3,1,1,1,1]
[2,3,1,4,5,7,6]=>001110=>[3,1,1,2]=>[3,2,1,1]
[2,3,1,4,6,5,7]=>001101=>[3,1,2,1]=>[3,2,1,1]
[2,3,1,4,6,7,5]=>001100=>[3,1,3]=>[3,3,1]
[2,3,1,4,7,5,6]=>001100=>[3,1,3]=>[3,3,1]
[2,3,1,4,7,6,5]=>001100=>[3,1,3]=>[3,3,1]
[2,3,1,5,4,6,7]=>001011=>[3,2,1,1]=>[3,2,1,1]
[2,3,1,5,4,7,6]=>001010=>[3,2,2]=>[3,2,2]
[2,3,1,5,6,4,7]=>001001=>[3,3,1]=>[3,3,1]
[2,3,1,5,6,7,4]=>001000=>[3,4]=>[4,3]
[2,3,1,5,7,4,6]=>001000=>[3,4]=>[4,3]
[2,3,1,5,7,6,4]=>001000=>[3,4]=>[4,3]
[2,3,1,6,4,5,7]=>001001=>[3,3,1]=>[3,3,1]
[2,3,1,6,4,7,5]=>001000=>[3,4]=>[4,3]
[2,3,1,6,5,4,7]=>001001=>[3,3,1]=>[3,3,1]
[2,3,1,6,5,7,4]=>001000=>[3,4]=>[4,3]
[2,3,1,6,7,4,5]=>001000=>[3,4]=>[4,3]
[2,3,1,6,7,5,4]=>001000=>[3,4]=>[4,3]
[2,3,1,7,4,5,6]=>001000=>[3,4]=>[4,3]
[2,3,1,7,4,6,5]=>001000=>[3,4]=>[4,3]
[2,3,1,7,5,4,6]=>001000=>[3,4]=>[4,3]
[2,3,1,7,5,6,4]=>001000=>[3,4]=>[4,3]
[2,3,1,7,6,4,5]=>001000=>[3,4]=>[4,3]
[2,3,1,7,6,5,4]=>001000=>[3,4]=>[4,3]
[2,3,4,1,5,6,7]=>000111=>[4,1,1,1]=>[4,1,1,1]
[2,3,4,1,5,7,6]=>000110=>[4,1,2]=>[4,2,1]
[2,3,4,1,6,5,7]=>000101=>[4,2,1]=>[4,2,1]
[2,3,4,1,6,7,5]=>000100=>[4,3]=>[4,3]
[2,3,4,1,7,5,6]=>000100=>[4,3]=>[4,3]
[2,3,4,1,7,6,5]=>000100=>[4,3]=>[4,3]
[2,3,4,5,1,6,7]=>000011=>[5,1,1]=>[5,1,1]
[2,3,4,5,1,7,6]=>000010=>[5,2]=>[5,2]
[2,3,4,5,6,1,7]=>000001=>[6,1]=>[6,1]
[2,3,4,5,6,7,1]=>000000=>[7]=>[7]
[2,3,4,5,7,1,6]=>000000=>[7]=>[7]
[2,3,4,5,7,6,1]=>000000=>[7]=>[7]
[2,3,4,6,1,5,7]=>000001=>[6,1]=>[6,1]
[2,3,4,6,1,7,5]=>000000=>[7]=>[7]
[2,3,4,6,5,1,7]=>000001=>[6,1]=>[6,1]
[2,3,4,6,5,7,1]=>000000=>[7]=>[7]
[2,3,4,6,7,1,5]=>000000=>[7]=>[7]
[2,3,4,6,7,5,1]=>000000=>[7]=>[7]
[2,3,4,7,1,5,6]=>000000=>[7]=>[7]
[2,3,4,7,1,6,5]=>000000=>[7]=>[7]
[2,3,4,7,5,1,6]=>000000=>[7]=>[7]
[2,3,4,7,5,6,1]=>000000=>[7]=>[7]
[2,3,4,7,6,1,5]=>000000=>[7]=>[7]
[2,3,4,7,6,5,1]=>000000=>[7]=>[7]
[2,3,5,1,4,6,7]=>000011=>[5,1,1]=>[5,1,1]
[2,3,5,1,4,7,6]=>000010=>[5,2]=>[5,2]
[2,3,5,1,6,4,7]=>000001=>[6,1]=>[6,1]
[2,3,5,1,6,7,4]=>000000=>[7]=>[7]
[2,3,5,1,7,4,6]=>000000=>[7]=>[7]
[2,3,5,1,7,6,4]=>000000=>[7]=>[7]
[2,3,5,4,1,6,7]=>000011=>[5,1,1]=>[5,1,1]
[2,3,5,4,1,7,6]=>000010=>[5,2]=>[5,2]
[2,3,5,4,6,1,7]=>000001=>[6,1]=>[6,1]
[2,3,5,4,6,7,1]=>000000=>[7]=>[7]
[2,3,5,4,7,1,6]=>000000=>[7]=>[7]
[2,3,5,4,7,6,1]=>000000=>[7]=>[7]
[2,3,5,6,1,4,7]=>000001=>[6,1]=>[6,1]
[2,3,5,6,1,7,4]=>000000=>[7]=>[7]
[2,3,5,6,4,1,7]=>000001=>[6,1]=>[6,1]
[2,3,5,6,4,7,1]=>000000=>[7]=>[7]
[2,3,5,6,7,1,4]=>000000=>[7]=>[7]
[2,3,5,6,7,4,1]=>000000=>[7]=>[7]
[2,3,5,7,1,4,6]=>000000=>[7]=>[7]
[2,3,5,7,1,6,4]=>000000=>[7]=>[7]
[2,3,5,7,4,1,6]=>000000=>[7]=>[7]
[2,3,5,7,4,6,1]=>000000=>[7]=>[7]
[2,3,5,7,6,1,4]=>000000=>[7]=>[7]
[2,3,5,7,6,4,1]=>000000=>[7]=>[7]
[2,3,6,1,4,5,7]=>000001=>[6,1]=>[6,1]
[2,3,6,1,4,7,5]=>000000=>[7]=>[7]
[2,3,6,1,5,4,7]=>000001=>[6,1]=>[6,1]
[2,3,6,1,5,7,4]=>000000=>[7]=>[7]
[2,3,6,1,7,4,5]=>000000=>[7]=>[7]
[2,3,6,1,7,5,4]=>000000=>[7]=>[7]
[2,3,6,4,1,5,7]=>000001=>[6,1]=>[6,1]
[2,3,6,4,1,7,5]=>000000=>[7]=>[7]
[2,3,6,4,5,1,7]=>000001=>[6,1]=>[6,1]
[2,3,6,4,5,7,1]=>000000=>[7]=>[7]
[2,3,6,4,7,1,5]=>000000=>[7]=>[7]
[2,3,6,4,7,5,1]=>000000=>[7]=>[7]
[2,3,6,5,1,4,7]=>000001=>[6,1]=>[6,1]
[2,3,6,5,1,7,4]=>000000=>[7]=>[7]
[2,3,6,5,4,1,7]=>000001=>[6,1]=>[6,1]
[2,3,6,5,4,7,1]=>000000=>[7]=>[7]
[2,3,6,5,7,1,4]=>000000=>[7]=>[7]
[2,3,6,5,7,4,1]=>000000=>[7]=>[7]
[2,3,6,7,1,4,5]=>000000=>[7]=>[7]
[2,3,6,7,1,5,4]=>000000=>[7]=>[7]
[2,3,6,7,4,1,5]=>000000=>[7]=>[7]
[2,3,6,7,4,5,1]=>000000=>[7]=>[7]
[2,3,6,7,5,1,4]=>000000=>[7]=>[7]
[2,3,6,7,5,4,1]=>000000=>[7]=>[7]
[2,3,7,1,4,5,6]=>000000=>[7]=>[7]
[2,3,7,1,4,6,5]=>000000=>[7]=>[7]
[2,3,7,1,5,4,6]=>000000=>[7]=>[7]
[2,3,7,1,5,6,4]=>000000=>[7]=>[7]
[2,3,7,1,6,4,5]=>000000=>[7]=>[7]
[2,3,7,1,6,5,4]=>000000=>[7]=>[7]
[2,3,7,4,1,5,6]=>000000=>[7]=>[7]
[2,3,7,4,1,6,5]=>000000=>[7]=>[7]
[2,3,7,4,5,1,6]=>000000=>[7]=>[7]
[2,3,7,4,5,6,1]=>000000=>[7]=>[7]
[2,3,7,4,6,1,5]=>000000=>[7]=>[7]
[2,3,7,4,6,5,1]=>000000=>[7]=>[7]
[2,3,7,5,1,4,6]=>000000=>[7]=>[7]
[2,3,7,5,1,6,4]=>000000=>[7]=>[7]
[2,3,7,5,4,1,6]=>000000=>[7]=>[7]
[2,3,7,5,4,6,1]=>000000=>[7]=>[7]
[2,3,7,5,6,1,4]=>000000=>[7]=>[7]
[2,3,7,5,6,4,1]=>000000=>[7]=>[7]
[2,3,7,6,1,4,5]=>000000=>[7]=>[7]
[2,3,7,6,1,5,4]=>000000=>[7]=>[7]
[2,3,7,6,4,1,5]=>000000=>[7]=>[7]
[2,3,7,6,4,5,1]=>000000=>[7]=>[7]
[2,3,7,6,5,1,4]=>000000=>[7]=>[7]
[2,3,7,6,5,4,1]=>000000=>[7]=>[7]
[2,4,1,3,5,6,7]=>000111=>[4,1,1,1]=>[4,1,1,1]
[2,4,1,3,5,7,6]=>000110=>[4,1,2]=>[4,2,1]
[2,4,1,3,6,5,7]=>000101=>[4,2,1]=>[4,2,1]
[2,4,1,3,6,7,5]=>000100=>[4,3]=>[4,3]
[2,4,1,3,7,5,6]=>000100=>[4,3]=>[4,3]
[2,4,1,3,7,6,5]=>000100=>[4,3]=>[4,3]
[2,4,1,5,3,6,7]=>000011=>[5,1,1]=>[5,1,1]
[2,4,1,5,3,7,6]=>000010=>[5,2]=>[5,2]
[2,4,1,5,6,3,7]=>000001=>[6,1]=>[6,1]
[2,4,1,5,6,7,3]=>000000=>[7]=>[7]
[2,4,1,5,7,3,6]=>000000=>[7]=>[7]
[2,4,1,5,7,6,3]=>000000=>[7]=>[7]
[2,4,1,6,3,5,7]=>000001=>[6,1]=>[6,1]
[2,4,1,6,3,7,5]=>000000=>[7]=>[7]
[2,4,1,6,5,3,7]=>000001=>[6,1]=>[6,1]
[2,4,1,6,5,7,3]=>000000=>[7]=>[7]
[2,4,1,6,7,3,5]=>000000=>[7]=>[7]
[2,4,1,6,7,5,3]=>000000=>[7]=>[7]
[2,4,1,7,3,5,6]=>000000=>[7]=>[7]
[2,4,1,7,3,6,5]=>000000=>[7]=>[7]
[2,4,1,7,5,3,6]=>000000=>[7]=>[7]
[2,4,1,7,5,6,3]=>000000=>[7]=>[7]
[2,4,1,7,6,3,5]=>000000=>[7]=>[7]
[2,4,1,7,6,5,3]=>000000=>[7]=>[7]
[2,4,3,1,5,6,7]=>000111=>[4,1,1,1]=>[4,1,1,1]
[2,4,3,1,5,7,6]=>000110=>[4,1,2]=>[4,2,1]
[2,4,3,1,6,5,7]=>000101=>[4,2,1]=>[4,2,1]
[2,4,3,1,6,7,5]=>000100=>[4,3]=>[4,3]
[2,4,3,1,7,5,6]=>000100=>[4,3]=>[4,3]
[2,4,3,1,7,6,5]=>000100=>[4,3]=>[4,3]
[2,4,3,5,1,6,7]=>000011=>[5,1,1]=>[5,1,1]
[2,4,3,5,1,7,6]=>000010=>[5,2]=>[5,2]
[2,4,3,5,6,1,7]=>000001=>[6,1]=>[6,1]
[2,4,3,5,6,7,1]=>000000=>[7]=>[7]
[2,4,3,5,7,1,6]=>000000=>[7]=>[7]
[2,4,3,5,7,6,1]=>000000=>[7]=>[7]
[2,4,3,6,1,5,7]=>000001=>[6,1]=>[6,1]
[2,4,3,6,1,7,5]=>000000=>[7]=>[7]
[2,4,3,6,5,1,7]=>000001=>[6,1]=>[6,1]
[2,4,3,6,5,7,1]=>000000=>[7]=>[7]
[2,4,3,6,7,1,5]=>000000=>[7]=>[7]
[2,4,3,6,7,5,1]=>000000=>[7]=>[7]
[2,4,3,7,1,5,6]=>000000=>[7]=>[7]
[2,4,3,7,1,6,5]=>000000=>[7]=>[7]
[2,4,3,7,5,1,6]=>000000=>[7]=>[7]
[2,4,3,7,5,6,1]=>000000=>[7]=>[7]
[2,4,3,7,6,1,5]=>000000=>[7]=>[7]
[2,4,3,7,6,5,1]=>000000=>[7]=>[7]
[2,4,5,1,3,6,7]=>000011=>[5,1,1]=>[5,1,1]
[2,4,5,1,3,7,6]=>000010=>[5,2]=>[5,2]
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[8,5,6,7,3,2,4,1]=>0000000=>[8]=>[8]
[7,6,5,8,3,2,4,1]=>0000000=>[8]=>[8]
[6,7,5,8,3,2,4,1]=>0000000=>[8]=>[8]
[5,6,7,8,3,2,4,1]=>0000000=>[8]=>[8]
[8,7,6,5,2,3,4,1]=>0000000=>[8]=>[8]
[8,6,7,5,2,3,4,1]=>0000000=>[8]=>[8]
[6,7,8,5,2,3,4,1]=>0000000=>[8]=>[8]
[8,7,5,6,2,3,4,1]=>0000000=>[8]=>[8]
[8,6,5,7,2,3,4,1]=>0000000=>[8]=>[8]
[8,5,6,7,2,3,4,1]=>0000000=>[8]=>[8]
[7,6,5,8,2,3,4,1]=>0000000=>[8]=>[8]
[6,7,5,8,2,3,4,1]=>0000000=>[8]=>[8]
[6,5,7,8,2,3,4,1]=>0000000=>[8]=>[8]
[5,6,7,8,2,3,4,1]=>0000000=>[8]=>[8]
[6,7,8,4,2,3,5,1]=>0000000=>[8]=>[8]
[8,6,7,3,2,4,5,1]=>0000000=>[8]=>[8]
[6,7,8,3,2,4,5,1]=>0000000=>[8]=>[8]
[8,7,6,2,3,4,5,1]=>0000000=>[8]=>[8]
[7,8,6,2,3,4,5,1]=>0000000=>[8]=>[8]
[8,6,7,2,3,4,5,1]=>0000000=>[8]=>[8]
[7,6,8,2,3,4,5,1]=>0000000=>[8]=>[8]
[6,7,8,2,3,4,5,1]=>0000000=>[8]=>[8]
[7,8,4,3,5,2,6,1]=>0000000=>[8]=>[8]
[7,8,4,3,2,5,6,1]=>0000000=>[8]=>[8]
[8,4,5,3,6,2,7,1]=>0000000=>[8]=>[8]
[8,6,4,2,3,5,7,1]=>0000000=>[8]=>[8]
[4,5,6,7,3,2,8,1]=>0000000=>[8]=>[8]
[6,5,4,3,7,2,8,1]=>0000000=>[8]=>[8]
[6,4,5,3,7,2,8,1]=>0000000=>[8]=>[8]
[5,4,6,3,7,2,8,1]=>0000000=>[8]=>[8]
[6,5,3,4,7,2,8,1]=>0000000=>[8]=>[8]
[5,6,3,4,7,2,8,1]=>0000000=>[8]=>[8]
[5,4,3,6,7,2,8,1]=>0000000=>[8]=>[8]
[6,7,5,4,2,3,8,1]=>0000000=>[8]=>[8]
[6,5,7,4,2,3,8,1]=>0000000=>[8]=>[8]
[6,7,4,5,2,3,8,1]=>0000000=>[8]=>[8]
[6,5,4,7,2,3,8,1]=>0000000=>[8]=>[8]
[5,4,6,7,2,3,8,1]=>0000000=>[8]=>[8]
[6,7,5,3,2,4,8,1]=>0000000=>[8]=>[8]
[6,5,7,3,2,4,8,1]=>0000000=>[8]=>[8]
[7,6,5,2,3,4,8,1]=>0000000=>[8]=>[8]
[5,6,7,2,3,4,8,1]=>0000000=>[8]=>[8]
[6,7,4,3,2,5,8,1]=>0000000=>[8]=>[8]
[7,6,4,2,3,5,8,1]=>0000000=>[8]=>[8]
[6,7,2,3,4,5,8,1]=>0000000=>[8]=>[8]
[6,5,4,3,2,7,8,1]=>0000000=>[8]=>[8]
[5,4,6,3,2,7,8,1]=>0000000=>[8]=>[8]
[5,4,3,6,2,7,8,1]=>0000000=>[8]=>[8]
[3,4,5,6,2,7,8,1]=>0000000=>[8]=>[8]
[5,6,4,2,3,7,8,1]=>0000000=>[8]=>[8]
[5,4,6,2,3,7,8,1]=>0000000=>[8]=>[8]
[6,5,2,3,4,7,8,1]=>0000000=>[8]=>[8]
[5,4,3,2,6,7,8,1]=>0000000=>[8]=>[8]
[2,3,4,5,6,7,8,1]=>0000000=>[8]=>[8]
[7,8,6,5,4,3,1,2]=>0000000=>[8]=>[8]
[7,6,5,8,4,3,1,2]=>0000000=>[8]=>[8]
[6,7,5,8,4,3,1,2]=>0000000=>[8]=>[8]
[7,5,6,8,4,3,1,2]=>0000000=>[8]=>[8]
[5,6,7,8,4,3,1,2]=>0000000=>[8]=>[8]
[8,6,7,4,5,3,1,2]=>0000000=>[8]=>[8]
[7,8,4,5,6,3,1,2]=>0000000=>[8]=>[8]
[6,5,7,4,8,3,1,2]=>0000000=>[8]=>[8]
[7,6,4,5,8,3,1,2]=>0000000=>[8]=>[8]
[6,7,4,5,8,3,1,2]=>0000000=>[8]=>[8]
[4,5,6,7,8,3,1,2]=>0000000=>[8]=>[8]
[7,8,5,6,3,4,1,2]=>0000000=>[8]=>[8]
[7,6,5,8,3,4,1,2]=>0000000=>[8]=>[8]
[6,7,5,8,3,4,1,2]=>0000000=>[8]=>[8]
[7,5,6,8,3,4,1,2]=>0000000=>[8]=>[8]
[6,5,7,8,3,4,1,2]=>0000000=>[8]=>[8]
[5,6,7,8,3,4,1,2]=>0000000=>[8]=>[8]
[8,7,6,3,4,5,1,2]=>0000000=>[8]=>[8]
[7,8,6,3,4,5,1,2]=>0000000=>[8]=>[8]
[8,7,4,5,3,6,1,2]=>0000000=>[8]=>[8]
[7,8,4,5,3,6,1,2]=>0000000=>[8]=>[8]
[7,8,5,3,4,6,1,2]=>0000000=>[8]=>[8]
[8,7,4,3,5,6,1,2]=>0000000=>[8]=>[8]
[7,8,4,3,5,6,1,2]=>0000000=>[8]=>[8]
[7,8,3,4,5,6,1,2]=>0000000=>[8]=>[8]
[8,5,4,6,3,7,1,2]=>0000000=>[8]=>[8]
[5,6,7,4,3,8,1,2]=>0000000=>[8]=>[8]
[6,7,4,5,3,8,1,2]=>0000000=>[8]=>[8]
[7,5,4,6,3,8,1,2]=>0000000=>[8]=>[8]
[6,5,4,7,3,8,1,2]=>0000000=>[8]=>[8]
[5,6,4,7,3,8,1,2]=>0000000=>[8]=>[8]
[4,5,6,7,3,8,1,2]=>0000000=>[8]=>[8]
[7,6,3,4,5,8,1,2]=>0000000=>[8]=>[8]
[7,4,5,3,6,8,1,2]=>0000000=>[8]=>[8]
[6,5,4,3,7,8,1,2]=>0000000=>[8]=>[8]
[5,4,6,3,7,8,1,2]=>0000000=>[8]=>[8]
[4,5,6,3,7,8,1,2]=>0000000=>[8]=>[8]
[5,6,3,4,7,8,1,2]=>0000000=>[8]=>[8]
[6,4,3,5,7,8,1,2]=>0000000=>[8]=>[8]
[6,3,4,5,7,8,1,2]=>0000000=>[8]=>[8]
[5,4,3,6,7,8,1,2]=>0000000=>[8]=>[8]
[4,5,3,6,7,8,1,2]=>0000000=>[8]=>[8]
[5,3,4,6,7,8,1,2]=>0000000=>[8]=>[8]
[4,3,5,6,7,8,1,2]=>0000000=>[8]=>[8]
[3,4,5,6,7,8,1,2]=>0000000=>[8]=>[8]
[8,7,6,5,4,2,1,3]=>0000000=>[8]=>[8]
[7,6,8,5,4,2,1,3]=>0000000=>[8]=>[8]
[7,8,5,6,4,2,1,3]=>0000000=>[8]=>[8]
[7,6,5,8,4,2,1,3]=>0000000=>[8]=>[8]
[6,7,5,8,4,2,1,3]=>0000000=>[8]=>[8]
[7,5,6,8,4,2,1,3]=>0000000=>[8]=>[8]
[5,6,7,8,4,2,1,3]=>0000000=>[8]=>[8]
[7,6,4,5,8,2,1,3]=>0000000=>[8]=>[8]
[4,5,6,7,8,2,1,3]=>0000000=>[8]=>[8]
[6,7,8,5,4,1,2,3]=>0000000=>[8]=>[8]
[8,5,6,7,4,1,2,3]=>0000000=>[8]=>[8]
[7,6,5,8,4,1,2,3]=>0000000=>[8]=>[8]
[6,7,5,8,4,1,2,3]=>0000000=>[8]=>[8]
[6,5,7,8,4,1,2,3]=>0000000=>[8]=>[8]
[5,6,7,8,4,1,2,3]=>0000000=>[8]=>[8]
[8,6,7,4,5,1,2,3]=>0000000=>[8]=>[8]
[8,7,5,4,6,1,2,3]=>0000000=>[8]=>[8]
[8,6,5,4,7,1,2,3]=>0000000=>[8]=>[8]
[8,6,4,5,7,1,2,3]=>0000000=>[8]=>[8]
[7,6,5,4,8,1,2,3]=>0000000=>[8]=>[8]
[6,7,4,5,8,1,2,3]=>0000000=>[8]=>[8]
[6,5,4,7,8,1,2,3]=>0000000=>[8]=>[8]
[5,4,6,7,8,1,2,3]=>0000000=>[8]=>[8]
[8,7,6,5,3,2,1,4]=>0000000=>[8]=>[8]
[7,8,6,5,3,2,1,4]=>0000000=>[8]=>[8]
[8,6,7,5,3,2,1,4]=>0000000=>[8]=>[8]
[7,6,8,5,3,2,1,4]=>0000000=>[8]=>[8]
[6,7,8,5,3,2,1,4]=>0000000=>[8]=>[8]
[8,7,5,6,3,2,1,4]=>0000000=>[8]=>[8]
[7,8,5,6,3,2,1,4]=>0000000=>[8]=>[8]
[8,6,5,7,3,2,1,4]=>0000000=>[8]=>[8]
[8,5,6,7,3,2,1,4]=>0000000=>[8]=>[8]
[7,6,5,8,3,2,1,4]=>0000000=>[8]=>[8]
[6,7,5,8,3,2,1,4]=>0000000=>[8]=>[8]
[7,5,6,8,3,2,1,4]=>0000000=>[8]=>[8]
[6,5,7,8,3,2,1,4]=>0000000=>[8]=>[8]
[5,6,7,8,3,2,1,4]=>0000000=>[8]=>[8]
[8,7,6,5,2,3,1,4]=>0000000=>[8]=>[8]
[7,8,6,5,2,3,1,4]=>0000000=>[8]=>[8]
[8,6,7,5,2,3,1,4]=>0000000=>[8]=>[8]
[7,6,8,5,2,3,1,4]=>0000000=>[8]=>[8]
[6,7,8,5,2,3,1,4]=>0000000=>[8]=>[8]
[8,7,5,6,2,3,1,4]=>0000000=>[8]=>[8]
[7,8,5,6,2,3,1,4]=>0000000=>[8]=>[8]
[8,6,5,7,2,3,1,4]=>0000000=>[8]=>[8]
[8,5,6,7,2,3,1,4]=>0000000=>[8]=>[8]
[7,6,5,8,2,3,1,4]=>0000000=>[8]=>[8]
[6,7,5,8,2,3,1,4]=>0000000=>[8]=>[8]
[7,5,6,8,2,3,1,4]=>0000000=>[8]=>[8]
[6,5,7,8,2,3,1,4]=>0000000=>[8]=>[8]
[5,6,7,8,2,3,1,4]=>0000000=>[8]=>[8]
[7,8,5,6,3,1,2,4]=>0000000=>[8]=>[8]
[7,6,5,8,3,1,2,4]=>0000000=>[8]=>[8]
[6,7,5,8,3,1,2,4]=>0000000=>[8]=>[8]
[7,5,6,8,3,1,2,4]=>0000000=>[8]=>[8]
[6,5,7,8,3,1,2,4]=>0000000=>[8]=>[8]
[5,6,7,8,3,1,2,4]=>0000000=>[8]=>[8]
[8,7,6,5,2,1,3,4]=>0000000=>[8]=>[8]
[6,7,8,5,2,1,3,4]=>0000000=>[8]=>[8]
[7,8,5,6,2,1,3,4]=>0000000=>[8]=>[8]
[8,6,5,7,2,1,3,4]=>0000000=>[8]=>[8]
[7,6,5,8,2,1,3,4]=>0000000=>[8]=>[8]
[6,7,5,8,2,1,3,4]=>0000000=>[8]=>[8]
[7,5,6,8,2,1,3,4]=>0000000=>[8]=>[8]
[6,5,7,8,2,1,3,4]=>0000000=>[8]=>[8]
[5,6,7,8,2,1,3,4]=>0000000=>[8]=>[8]
[8,7,6,5,1,2,3,4]=>0000000=>[8]=>[8]
[7,8,6,5,1,2,3,4]=>0000000=>[8]=>[8]
[8,6,7,5,1,2,3,4]=>0000000=>[8]=>[8]
[7,6,8,5,1,2,3,4]=>0000000=>[8]=>[8]
[6,7,8,5,1,2,3,4]=>0000000=>[8]=>[8]
[8,7,5,6,1,2,3,4]=>0000000=>[8]=>[8]
[7,8,5,6,1,2,3,4]=>0000000=>[8]=>[8]
[8,6,5,7,1,2,3,4]=>0000000=>[8]=>[8]
[8,5,6,7,1,2,3,4]=>0000000=>[8]=>[8]
[7,6,5,8,1,2,3,4]=>0000000=>[8]=>[8]
[6,7,5,8,1,2,3,4]=>0000000=>[8]=>[8]
[7,5,6,8,1,2,3,4]=>0000000=>[8]=>[8]
[6,5,7,8,1,2,3,4]=>0000000=>[8]=>[8]
[5,6,7,8,1,2,3,4]=>0000000=>[8]=>[8]
[8,7,6,4,3,2,1,5]=>0000000=>[8]=>[8]
[7,8,6,4,3,2,1,5]=>0000000=>[8]=>[8]
[8,6,7,4,3,2,1,5]=>0000000=>[8]=>[8]
[7,6,8,4,3,2,1,5]=>0000000=>[8]=>[8]
[6,7,8,4,3,2,1,5]=>0000000=>[8]=>[8]
[8,7,6,3,4,2,1,5]=>0000000=>[8]=>[8]
[6,7,8,3,4,2,1,5]=>0000000=>[8]=>[8]
[8,7,6,4,2,3,1,5]=>0000000=>[8]=>[8]
[7,6,8,4,2,3,1,5]=>0000000=>[8]=>[8]
[6,7,8,4,2,3,1,5]=>0000000=>[8]=>[8]
[8,7,6,3,2,4,1,5]=>0000000=>[8]=>[8]
[8,6,7,3,2,4,1,5]=>0000000=>[8]=>[8]
[6,7,8,3,2,4,1,5]=>0000000=>[8]=>[8]
[8,7,6,2,3,4,1,5]=>0000000=>[8]=>[8]
[6,7,8,2,3,4,1,5]=>0000000=>[8]=>[8]
[8,7,6,4,3,1,2,5]=>0000000=>[8]=>[8]
[6,7,8,4,3,1,2,5]=>0000000=>[8]=>[8]
[8,7,6,3,4,1,2,5]=>0000000=>[8]=>[8]
[6,7,8,3,4,1,2,5]=>0000000=>[8]=>[8]
[8,7,6,4,2,1,3,5]=>0000000=>[8]=>[8]
[6,7,8,4,2,1,3,5]=>0000000=>[8]=>[8]
[8,7,6,4,1,2,3,5]=>0000000=>[8]=>[8]
[6,7,8,4,1,2,3,5]=>0000000=>[8]=>[8]
[8,7,6,3,2,1,4,5]=>0000000=>[8]=>[8]
[7,6,8,3,2,1,4,5]=>0000000=>[8]=>[8]
[6,7,8,3,2,1,4,5]=>0000000=>[8]=>[8]
[8,7,6,2,3,1,4,5]=>0000000=>[8]=>[8]
[7,6,8,2,3,1,4,5]=>0000000=>[8]=>[8]
[6,7,8,2,3,1,4,5]=>0000000=>[8]=>[8]
[8,7,6,3,1,2,4,5]=>0000000=>[8]=>[8]
[7,8,6,3,1,2,4,5]=>0000000=>[8]=>[8]
[6,7,8,3,1,2,4,5]=>0000000=>[8]=>[8]
[8,7,6,2,1,3,4,5]=>0000000=>[8]=>[8]
[7,8,6,2,1,3,4,5]=>0000000=>[8]=>[8]
[6,7,8,2,1,3,4,5]=>0000000=>[8]=>[8]
[8,7,6,1,2,3,4,5]=>0000000=>[8]=>[8]
[7,8,6,1,2,3,4,5]=>0000000=>[8]=>[8]
[8,6,7,1,2,3,4,5]=>0000000=>[8]=>[8]
[7,6,8,1,2,3,4,5]=>0000000=>[8]=>[8]
[6,7,8,1,2,3,4,5]=>0000000=>[8]=>[8]
[8,7,5,4,3,2,1,6]=>0000000=>[8]=>[8]
[7,8,5,4,3,2,1,6]=>0000000=>[8]=>[8]
[7,8,3,4,5,2,1,6]=>0000000=>[8]=>[8]
[8,7,4,5,2,3,1,6]=>0000000=>[8]=>[8]
[7,8,4,5,2,3,1,6]=>0000000=>[8]=>[8]
[7,8,4,3,2,5,1,6]=>0000000=>[8]=>[8]
[7,8,3,4,2,5,1,6]=>0000000=>[8]=>[8]
[8,7,5,3,4,1,2,6]=>0000000=>[8]=>[8]
[7,8,5,4,1,2,3,6]=>0000000=>[8]=>[8]
[8,7,5,2,1,3,4,6]=>0000000=>[8]=>[8]
[7,8,5,2,1,3,4,6]=>0000000=>[8]=>[8]
[8,7,5,1,2,3,4,6]=>0000000=>[8]=>[8]
[7,8,5,1,2,3,4,6]=>0000000=>[8]=>[8]
[8,7,4,3,2,1,5,6]=>0000000=>[8]=>[8]
[7,8,4,3,2,1,5,6]=>0000000=>[8]=>[8]
[8,7,3,4,2,1,5,6]=>0000000=>[8]=>[8]
[7,8,3,4,2,1,5,6]=>0000000=>[8]=>[8]
[7,8,4,2,3,1,5,6]=>0000000=>[8]=>[8]
[8,7,3,2,4,1,5,6]=>0000000=>[8]=>[8]
[7,8,3,2,4,1,5,6]=>0000000=>[8]=>[8]
[7,8,2,3,4,1,5,6]=>0000000=>[8]=>[8]
[7,8,4,3,1,2,5,6]=>0000000=>[8]=>[8]
[7,8,3,4,1,2,5,6]=>0000000=>[8]=>[8]
[7,8,4,2,1,3,5,6]=>0000000=>[8]=>[8]
[7,8,4,1,2,3,5,6]=>0000000=>[8]=>[8]
[8,7,3,2,1,4,5,6]=>0000000=>[8]=>[8]
[7,8,3,2,1,4,5,6]=>0000000=>[8]=>[8]
[7,8,2,3,1,4,5,6]=>0000000=>[8]=>[8]
[7,8,3,1,2,4,5,6]=>0000000=>[8]=>[8]
[8,7,2,1,3,4,5,6]=>0000000=>[8]=>[8]
[7,8,2,1,3,4,5,6]=>0000000=>[8]=>[8]
[7,8,1,2,3,4,5,6]=>0000000=>[8]=>[8]
[8,6,5,4,3,2,1,7]=>0000000=>[8]=>[8]
[8,5,6,4,3,2,1,7]=>0000000=>[8]=>[8]
[8,4,5,6,3,2,1,7]=>0000000=>[8]=>[8]
[8,4,5,3,6,2,1,7]=>0000000=>[8]=>[8]
[8,3,4,5,6,2,1,7]=>0000000=>[8]=>[8]
[8,6,5,2,3,4,1,7]=>0000000=>[8]=>[8]
[8,6,4,2,3,5,1,7]=>0000000=>[8]=>[8]
[8,6,4,5,3,1,2,7]=>0000000=>[8]=>[8]
[8,5,6,3,4,1,2,7]=>0000000=>[8]=>[8]
[8,4,3,5,6,1,2,7]=>0000000=>[8]=>[8]
[8,3,4,5,6,1,2,7]=>0000000=>[8]=>[8]
[8,6,5,4,2,1,3,7]=>0000000=>[8]=>[8]
[8,4,5,6,1,2,3,7]=>0000000=>[8]=>[8]
[8,6,5,2,3,1,4,7]=>0000000=>[8]=>[8]
[8,5,6,2,3,1,4,7]=>0000000=>[8]=>[8]
[8,5,6,2,1,3,4,7]=>0000000=>[8]=>[8]
[8,6,5,1,2,3,4,7]=>0000000=>[8]=>[8]
[8,5,6,1,2,3,4,7]=>0000000=>[8]=>[8]
[8,6,4,3,2,1,5,7]=>0000000=>[8]=>[8]
[8,6,3,4,2,1,5,7]=>0000000=>[8]=>[8]
[8,6,4,2,3,1,5,7]=>0000000=>[8]=>[8]
[8,6,3,2,4,1,5,7]=>0000000=>[8]=>[8]
[8,6,3,4,1,2,5,7]=>0000000=>[8]=>[8]
[8,6,4,2,1,3,5,7]=>0000000=>[8]=>[8]
[8,6,3,2,1,4,5,7]=>0000000=>[8]=>[8]
[8,4,5,3,2,1,6,7]=>0000000=>[8]=>[8]
[8,4,3,5,2,1,6,7]=>0000000=>[8]=>[8]
[8,5,4,2,1,3,6,7]=>0000000=>[8]=>[8]
[8,4,3,2,1,5,6,7]=>0000000=>[8]=>[8]
[8,2,3,4,1,5,6,7]=>0000000=>[8]=>[8]
[8,3,2,1,4,5,6,7]=>0000000=>[8]=>[8]
[8,2,3,1,4,5,6,7]=>0000000=>[8]=>[8]
[7,6,5,4,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[6,7,5,4,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,5,6,4,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[6,5,7,4,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,4,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,4,5,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[6,5,4,7,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,4,7,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,6,7,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,5,6,3,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,3,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,3,4,5,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,3,4,5,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[6,5,4,3,7,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,6,3,7,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,3,6,7,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,4,2,3,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,4,5,2,3,1,8]=>0000001=>[7,1]=>[7,1]
[6,7,4,5,2,3,1,8]=>0000001=>[7,1]=>[7,1]
[6,5,4,7,2,3,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,4,7,2,3,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,3,2,4,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,5,2,3,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,7,5,2,3,4,1,8]=>0000001=>[7,1]=>[7,1]
[7,5,6,2,3,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,5,7,2,3,4,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,2,3,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,7,4,3,2,5,1,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,4,2,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,4,2,3,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,3,2,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,2,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,2,3,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,4,5,3,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[7,4,3,5,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[7,5,3,2,4,6,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,6,3,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,3,4,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[6,3,4,5,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,3,6,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,3,6,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[3,4,5,6,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[6,3,2,4,5,7,1,8]=>0000001=>[7,1]=>[7,1]
[6,2,3,4,5,7,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,3,2,6,7,1,8]=>0000001=>[7,1]=>[7,1]
[6,5,7,3,4,1,2,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,4,5,1,2,8]=>0000001=>[7,1]=>[7,1]
[6,4,5,3,7,1,2,8]=>0000001=>[7,1]=>[7,1]
[3,4,5,6,7,1,2,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,4,1,2,3,8]=>0000001=>[7,1]=>[7,1]
[5,6,4,7,1,2,3,8]=>0000001=>[7,1]=>[7,1]
[5,4,6,7,1,2,3,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,3,1,2,4,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,2,1,3,4,8]=>0000001=>[7,1]=>[7,1]
[7,6,5,1,2,3,4,8]=>0000001=>[7,1]=>[7,1]
[6,7,5,1,2,3,4,8]=>0000001=>[7,1]=>[7,1]
[7,5,6,1,2,3,4,8]=>0000001=>[7,1]=>[7,1]
[6,5,7,1,2,3,4,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,1,2,3,4,8]=>0000001=>[7,1]=>[7,1]
[7,6,4,3,2,1,5,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,4,2,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,6,4,2,3,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,6,3,2,4,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,6,2,3,4,1,5,8]=>0000001=>[7,1]=>[7,1]
[6,7,2,3,4,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,6,3,2,1,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,2,1,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,1,2,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,7,1,2,3,4,5,8]=>0000001=>[7,1]=>[7,1]
[7,5,2,3,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[7,2,3,4,5,1,6,8]=>0000001=>[7,1]=>[7,1]
[7,4,5,1,2,3,6,8]=>0000001=>[7,1]=>[7,1]
[7,5,3,2,1,4,6,8]=>0000001=>[7,1]=>[7,1]
[7,5,3,1,2,4,6,8]=>0000001=>[7,1]=>[7,1]
[7,5,1,2,3,4,6,8]=>0000001=>[7,1]=>[7,1]
[7,4,3,2,1,5,6,8]=>0000001=>[7,1]=>[7,1]
[7,4,3,1,2,5,6,8]=>0000001=>[7,1]=>[7,1]
[7,3,1,2,4,5,6,8]=>0000001=>[7,1]=>[7,1]
[7,1,2,3,4,5,6,8]=>0000001=>[7,1]=>[7,1]
[5,4,6,3,2,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,5,6,3,2,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,3,6,2,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,4,5,6,2,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,5,2,3,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,6,2,3,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,4,3,2,5,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,3,2,6,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,5,3,2,6,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,3,2,4,6,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,6,4,3,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,6,3,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,6,3,4,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,4,3,5,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,3,6,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,6,4,2,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,6,2,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,6,3,2,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,4,3,2,1,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,3,4,2,1,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,4,3,1,2,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,4,2,1,3,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,3,2,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,5,3,2,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,3,4,2,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,3,5,2,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[3,4,5,2,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,4,2,3,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,5,2,3,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,3,2,4,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,2,3,4,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,3,2,5,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[3,4,2,5,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,2,3,5,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[3,2,4,5,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[2,3,4,5,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,4,3,1,2,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,3,4,1,2,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,4,2,1,3,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,4,1,2,3,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,5,1,2,3,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,3,2,1,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,2,3,1,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,3,1,2,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,2,1,3,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,1,2,3,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,3,2,1,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[3,4,2,1,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[4,2,3,1,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[3,2,4,1,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[2,3,4,1,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[4,3,1,2,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[3,4,1,2,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[4,2,1,3,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[4,1,2,3,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[3,2,1,4,5,6,7,8]=>0011111=>[3,1,1,1,1,1]=>[3,1,1,1,1,1]
[2,3,1,4,5,6,7,8]=>0011111=>[3,1,1,1,1,1]=>[3,1,1,1,1,1]
[3,1,2,4,5,6,7,8]=>0011111=>[3,1,1,1,1,1]=>[3,1,1,1,1,1]
[2,1,3,4,5,6,7,8]=>0111111=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8]=>1111111=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]
[5,8,7,6,4,3,2,1]=>0000000=>[8]=>[8]
[6,5,8,7,4,3,2,1]=>0000000=>[8]=>[8]
[4,8,7,6,5,3,2,1]=>0000000=>[8]=>[8]
[4,7,8,6,5,3,2,1]=>0000000=>[8]=>[8]
[4,6,8,7,5,3,2,1]=>0000000=>[8]=>[8]
[4,7,6,8,5,3,2,1]=>0000000=>[8]=>[8]
[4,6,7,8,5,3,2,1]=>0000000=>[8]=>[8]
[4,5,8,7,6,3,2,1]=>0000000=>[8]=>[8]
[4,5,7,8,6,3,2,1]=>0000000=>[8]=>[8]
[4,6,5,8,7,3,2,1]=>0000000=>[8]=>[8]
[4,5,6,8,7,3,2,1]=>0000000=>[8]=>[8]
[5,7,6,4,8,3,2,1]=>0000000=>[8]=>[8]
[4,7,6,5,8,3,2,1]=>0000000=>[8]=>[8]
[4,6,7,5,8,3,2,1]=>0000000=>[8]=>[8]
[5,4,7,6,8,3,2,1]=>0000000=>[8]=>[8]
[4,5,7,6,8,3,2,1]=>0000000=>[8]=>[8]
[4,6,5,7,8,3,2,1]=>0000000=>[8]=>[8]
[3,8,7,6,5,4,2,1]=>0000000=>[8]=>[8]
[3,5,6,7,8,4,2,1]=>0000000=>[8]=>[8]
[4,3,6,7,8,5,2,1]=>0000000=>[8]=>[8]
[3,4,8,7,6,5,2,1]=>0000000=>[8]=>[8]
[4,5,3,7,8,6,2,1]=>0000000=>[8]=>[8]
[4,3,5,7,8,6,2,1]=>0000000=>[8]=>[8]
[4,5,6,3,8,7,2,1]=>0000000=>[8]=>[8]
[4,3,6,5,8,7,2,1]=>0000000=>[8]=>[8]
[5,4,3,6,8,7,2,1]=>0000000=>[8]=>[8]
[4,5,3,6,8,7,2,1]=>0000000=>[8]=>[8]
[4,3,5,6,8,7,2,1]=>0000000=>[8]=>[8]
[3,4,7,6,5,8,2,1]=>0000000=>[8]=>[8]
[4,5,3,7,6,8,2,1]=>0000000=>[8]=>[8]
[4,3,5,7,6,8,2,1]=>0000000=>[8]=>[8]
[3,4,6,5,7,8,2,1]=>0000000=>[8]=>[8]
[2,8,7,6,5,4,3,1]=>0000000=>[8]=>[8]
[2,5,6,7,8,4,3,1]=>0000000=>[8]=>[8]
[2,4,8,7,6,5,3,1]=>0000000=>[8]=>[8]
[2,4,6,8,7,5,3,1]=>0000000=>[8]=>[8]
[2,5,4,8,7,6,3,1]=>0000000=>[8]=>[8]
[2,5,6,4,8,7,3,1]=>0000000=>[8]=>[8]
[2,4,7,6,5,8,3,1]=>0000000=>[8]=>[8]
[2,6,5,4,7,8,3,1]=>0000000=>[8]=>[8]
[3,2,8,7,6,5,4,1]=>0000000=>[8]=>[8]
[3,2,6,8,7,5,4,1]=>0000000=>[8]=>[8]
[3,2,5,6,7,8,4,1]=>0000000=>[8]=>[8]
[2,3,8,7,6,5,4,1]=>0000000=>[8]=>[8]
[2,3,5,8,7,6,4,1]=>0000000=>[8]=>[8]
[2,3,5,6,7,8,4,1]=>0000000=>[8]=>[8]
[4,3,2,8,7,6,5,1]=>0000000=>[8]=>[8]
[4,3,2,7,8,6,5,1]=>0000000=>[8]=>[8]
[4,3,2,6,8,7,5,1]=>0000000=>[8]=>[8]
[3,4,2,8,7,6,5,1]=>0000000=>[8]=>[8]
[3,4,2,7,8,6,5,1]=>0000000=>[8]=>[8]
[2,4,3,8,7,6,5,1]=>0000000=>[8]=>[8]
[3,2,4,8,7,6,5,1]=>0000000=>[8]=>[8]
[2,3,4,8,7,6,5,1]=>0000000=>[8]=>[8]
[5,4,3,2,8,7,6,1]=>0000000=>[8]=>[8]
[5,4,3,2,7,8,6,1]=>0000000=>[8]=>[8]
[4,5,3,2,8,7,6,1]=>0000000=>[8]=>[8]
[4,3,5,2,8,7,6,1]=>0000000=>[8]=>[8]
[2,5,4,3,8,7,6,1]=>0000000=>[8]=>[8]
[2,5,4,3,7,8,6,1]=>0000000=>[8]=>[8]
[2,4,5,3,8,7,6,1]=>0000000=>[8]=>[8]
[2,3,5,4,8,7,6,1]=>0000000=>[8]=>[8]
[4,3,2,5,8,7,6,1]=>0000000=>[8]=>[8]
[6,5,4,3,2,8,7,1]=>0000000=>[8]=>[8]
[4,6,5,3,2,8,7,1]=>0000000=>[8]=>[8]
[5,4,6,3,2,8,7,1]=>0000000=>[8]=>[8]
[4,5,6,3,2,8,7,1]=>0000000=>[8]=>[8]
[4,3,6,5,2,8,7,1]=>0000000=>[8]=>[8]
[2,4,6,5,3,8,7,1]=>0000000=>[8]=>[8]
[4,3,2,6,5,8,7,1]=>0000000=>[8]=>[8]
[3,4,2,6,5,8,7,1]=>0000000=>[8]=>[8]
[2,4,3,6,5,8,7,1]=>0000000=>[8]=>[8]
[2,3,4,6,5,8,7,1]=>0000000=>[8]=>[8]
[5,4,3,2,6,8,7,1]=>0000000=>[8]=>[8]
[2,5,4,3,6,8,7,1]=>0000000=>[8]=>[8]
[4,3,2,5,6,8,7,1]=>0000000=>[8]=>[8]
[3,4,2,5,6,8,7,1]=>0000000=>[8]=>[8]
[2,4,3,5,6,8,7,1]=>0000000=>[8]=>[8]
[2,3,4,5,6,8,7,1]=>0000000=>[8]=>[8]
[4,6,5,7,3,2,8,1]=>0000000=>[8]=>[8]
[3,5,7,6,4,2,8,1]=>0000000=>[8]=>[8]
[4,3,6,7,5,2,8,1]=>0000000=>[8]=>[8]
[5,4,3,7,6,2,8,1]=>0000000=>[8]=>[8]
[4,6,5,3,7,2,8,1]=>0000000=>[8]=>[8]
[3,6,5,4,7,2,8,1]=>0000000=>[8]=>[8]
[2,5,4,7,6,3,8,1]=>0000000=>[8]=>[8]
[2,4,6,5,7,3,8,1]=>0000000=>[8]=>[8]
[3,2,6,7,5,4,8,1]=>0000000=>[8]=>[8]
[2,3,7,6,5,4,8,1]=>0000000=>[8]=>[8]
[4,3,2,7,6,5,8,1]=>0000000=>[8]=>[8]
[3,4,2,7,6,5,8,1]=>0000000=>[8]=>[8]
[2,4,3,7,6,5,8,1]=>0000000=>[8]=>[8]
[3,2,4,7,6,5,8,1]=>0000000=>[8]=>[8]
[2,3,4,7,6,5,8,1]=>0000000=>[8]=>[8]
[5,4,3,2,7,6,8,1]=>0000000=>[8]=>[8]
[2,5,4,3,7,6,8,1]=>0000000=>[8]=>[8]
[2,4,3,5,7,6,8,1]=>0000000=>[8]=>[8]
[2,6,5,4,3,7,8,1]=>0000000=>[8]=>[8]
[2,3,6,5,4,7,8,1]=>0000000=>[8]=>[8]
[4,3,2,6,5,7,8,1]=>0000000=>[8]=>[8]
[2,4,3,6,5,7,8,1]=>0000000=>[8]=>[8]
[2,3,4,6,5,7,8,1]=>0000000=>[8]=>[8]
[2,5,4,3,6,7,8,1]=>0000000=>[8]=>[8]
[2,4,3,5,6,7,8,1]=>0000000=>[8]=>[8]
[1,8,7,6,5,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,7,8,6,5,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,6,8,7,5,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,7,6,8,5,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,6,7,8,5,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,7,6,5,8,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,6,7,5,8,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,5,7,6,8,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,6,5,7,8,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,5,6,7,8,4,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,8,7,6,5,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,7,8,6,5,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,6,8,7,5,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,6,7,8,5,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,6,5,8,7,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,7,6,5,8,3,2]=>1000000=>[1,7]=>[7,1]
[1,6,5,4,7,8,3,2]=>1000000=>[1,7]=>[7,1]
[1,5,4,6,7,8,3,2]=>1000000=>[1,7]=>[7,1]
[1,3,8,7,6,5,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,6,8,7,5,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,6,7,8,5,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,5,8,7,6,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,5,7,8,6,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,6,5,7,8,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,5,6,7,8,4,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,8,7,6,5,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,7,8,6,5,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,6,8,7,5,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,7,6,8,5,2]=>1000000=>[1,7]=>[7,1]
[1,3,4,8,7,6,5,2]=>1000000=>[1,7]=>[7,1]
[1,3,4,7,6,8,5,2]=>1000000=>[1,7]=>[7,1]
[1,3,4,6,7,8,5,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,5,8,7,6,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,5,7,8,6,2]=>1000000=>[1,7]=>[7,1]
[1,6,5,4,3,8,7,2]=>1000000=>[1,7]=>[7,1]
[1,5,6,4,3,8,7,2]=>1000000=>[1,7]=>[7,1]
[1,4,6,5,3,8,7,2]=>1000000=>[1,7]=>[7,1]
[1,3,6,5,4,8,7,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,6,5,8,7,2]=>1000000=>[1,7]=>[7,1]
[1,5,4,3,6,8,7,2]=>1000000=>[1,7]=>[7,1]
[1,3,4,7,6,5,8,2]=>1000000=>[1,7]=>[7,1]
[1,5,4,3,6,7,8,2]=>1000000=>[1,7]=>[7,1]
[2,1,8,7,6,5,4,3]=>0100000=>[2,6]=>[6,2]
[2,1,6,7,8,5,4,3]=>0100000=>[2,6]=>[6,2]
[2,1,5,6,7,8,4,3]=>0100000=>[2,6]=>[6,2]
[2,1,4,8,7,6,5,3]=>0100000=>[2,6]=>[6,2]
[2,1,4,7,8,6,5,3]=>0100000=>[2,6]=>[6,2]
[2,1,4,6,7,8,5,3]=>0100000=>[2,6]=>[6,2]
[2,1,4,6,5,8,7,3]=>0100000=>[2,6]=>[6,2]
[2,1,4,5,6,8,7,3]=>0100000=>[2,6]=>[6,2]
[2,1,5,6,7,4,8,3]=>0100000=>[2,6]=>[6,2]
[2,1,4,7,6,5,8,3]=>0100000=>[2,6]=>[6,2]
[2,1,5,4,7,6,8,3]=>0100000=>[2,6]=>[6,2]
[1,2,8,7,6,5,4,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,7,8,5,4,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,6,7,8,4,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,8,7,6,5,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,7,8,6,5,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,6,8,7,5,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,4,8,7,6,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,4,7,8,6,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,5,4,8,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,6,5,8,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,4,6,8,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,7,6,5,8,3]=>1100000=>[1,1,6]=>[6,1,1]
[3,2,1,8,7,6,5,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,7,8,6,5,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,6,8,7,5,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,7,6,8,5,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,6,7,8,5,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,5,8,7,6,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,5,7,8,6,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,6,5,8,7,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,5,6,8,7,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,7,6,5,8,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,6,7,5,8,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,5,7,6,8,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,6,5,7,8,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,5,6,7,8,4]=>0010000=>[3,5]=>[5,3]
[2,3,1,8,7,6,5,4]=>0010000=>[3,5]=>[5,3]
[2,3,1,6,8,7,5,4]=>0010000=>[3,5]=>[5,3]
[2,3,1,7,6,8,5,4]=>0010000=>[3,5]=>[5,3]
[2,3,1,6,7,8,5,4]=>0010000=>[3,5]=>[5,3]
[2,3,1,6,5,8,7,4]=>0010000=>[3,5]=>[5,3]
[2,3,1,5,6,7,8,4]=>0010000=>[3,5]=>[5,3]
[1,3,2,8,7,6,5,4]=>1010000=>[1,2,5]=>[5,2,1]
[1,3,2,6,8,7,5,4]=>1010000=>[1,2,5]=>[5,2,1]
[1,3,2,6,5,8,7,4]=>1010000=>[1,2,5]=>[5,2,1]
[2,1,3,8,7,6,5,4]=>0110000=>[2,1,5]=>[5,2,1]
[2,1,3,7,8,6,5,4]=>0110000=>[2,1,5]=>[5,2,1]
[2,1,3,6,8,7,5,4]=>0110000=>[2,1,5]=>[5,2,1]
[1,2,3,8,7,6,5,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,8,6,5,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,6,8,7,5,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,6,8,5,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,6,7,8,5,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,5,8,7,6,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,5,7,8,6,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,6,5,8,7,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,5,6,8,7,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,6,5,8,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,6,7,5,8,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,5,7,6,8,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,6,5,7,8,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,5,6,7,8,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[4,3,2,1,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[4,3,2,1,7,8,6,5]=>0001000=>[4,4]=>[4,4]
[4,3,2,1,6,8,7,5]=>0001000=>[4,4]=>[4,4]
[4,3,2,1,7,6,8,5]=>0001000=>[4,4]=>[4,4]
[4,3,2,1,6,7,8,5]=>0001000=>[4,4]=>[4,4]
[3,4,2,1,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[3,4,2,1,7,8,6,5]=>0001000=>[4,4]=>[4,4]
[3,4,2,1,6,7,8,5]=>0001000=>[4,4]=>[4,4]
[2,4,3,1,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[2,4,3,1,7,6,8,5]=>0001000=>[4,4]=>[4,4]
[3,2,4,1,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[3,2,4,1,7,8,6,5]=>0001000=>[4,4]=>[4,4]
[3,2,4,1,6,8,7,5]=>0001000=>[4,4]=>[4,4]
[2,3,4,1,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[2,3,4,1,6,7,8,5]=>0001000=>[4,4]=>[4,4]
[1,4,3,2,8,7,6,5]=>1001000=>[1,3,4]=>[4,3,1]
[1,4,3,2,6,7,8,5]=>1001000=>[1,3,4]=>[4,3,1]
[1,3,4,2,8,7,6,5]=>1001000=>[1,3,4]=>[4,3,1]
[1,3,4,2,7,8,6,5]=>1001000=>[1,3,4]=>[4,3,1]
[1,3,4,2,6,8,7,5]=>1001000=>[1,3,4]=>[4,3,1]
[2,1,4,3,8,7,6,5]=>0101000=>[2,2,4]=>[4,2,2]
[2,1,4,3,7,8,6,5]=>0101000=>[2,2,4]=>[4,2,2]
[2,1,4,3,6,8,7,5]=>0101000=>[2,2,4]=>[4,2,2]
[1,2,4,3,8,7,6,5]=>1101000=>[1,1,2,4]=>[4,2,1,1]
[1,2,4,3,7,8,6,5]=>1101000=>[1,1,2,4]=>[4,2,1,1]
[1,2,4,3,6,8,7,5]=>1101000=>[1,1,2,4]=>[4,2,1,1]
[1,2,4,3,6,7,8,5]=>1101000=>[1,1,2,4]=>[4,2,1,1]
[3,2,1,4,8,7,6,5]=>0011000=>[3,1,4]=>[4,3,1]
[3,2,1,4,7,8,6,5]=>0011000=>[3,1,4]=>[4,3,1]
[3,2,1,4,6,8,7,5]=>0011000=>[3,1,4]=>[4,3,1]
[2,3,1,4,8,7,6,5]=>0011000=>[3,1,4]=>[4,3,1]
[2,3,1,4,7,8,6,5]=>0011000=>[3,1,4]=>[4,3,1]
[1,3,2,4,8,7,6,5]=>1011000=>[1,2,1,4]=>[4,2,1,1]
[1,3,2,4,6,8,7,5]=>1011000=>[1,2,1,4]=>[4,2,1,1]
[1,3,2,4,6,7,8,5]=>1011000=>[1,2,1,4]=>[4,2,1,1]
[2,1,3,4,8,7,6,5]=>0111000=>[2,1,1,4]=>[4,2,1,1]
[2,1,3,4,6,7,8,5]=>0111000=>[2,1,1,4]=>[4,2,1,1]
[1,2,3,4,8,7,6,5]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,3,4,7,8,6,5]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,3,4,6,8,7,5]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,3,4,7,6,8,5]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,3,4,6,7,8,5]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[5,4,3,2,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,4,3,2,1,7,8,6]=>0000100=>[5,3]=>[5,3]
[4,5,3,2,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,5,4,2,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,5,4,2,1,7,8,6]=>0000100=>[5,3]=>[5,3]
[4,3,5,2,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,4,5,2,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[2,5,4,3,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[2,4,5,3,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,2,5,4,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,2,5,4,1,7,8,6]=>0000100=>[5,3]=>[5,3]
[2,3,5,4,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[4,3,2,5,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,4,2,5,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[2,4,3,5,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,2,4,5,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[2,3,4,5,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[1,2,5,4,3,7,8,6]=>1100100=>[1,1,3,3]=>[3,3,1,1]
[1,2,4,5,3,8,7,6]=>1100100=>[1,1,3,3]=>[3,3,1,1]
[1,3,2,5,4,8,7,6]=>1010100=>[1,2,2,3]=>[3,2,2,1]
[1,3,2,5,4,7,8,6]=>1010100=>[1,2,2,3]=>[3,2,2,1]
[2,1,3,5,4,8,7,6]=>0110100=>[2,1,2,3]=>[3,2,2,1]
[1,2,3,5,4,8,7,6]=>1110100=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,2,3,5,4,7,8,6]=>1110100=>[1,1,1,2,3]=>[3,2,1,1,1]
[4,3,2,1,5,8,7,6]=>0001100=>[4,1,3]=>[4,3,1]
[4,3,2,1,5,7,8,6]=>0001100=>[4,1,3]=>[4,3,1]
[3,2,4,1,5,8,7,6]=>0001100=>[4,1,3]=>[4,3,1]
[1,4,3,2,5,8,7,6]=>1001100=>[1,3,1,3]=>[3,3,1,1]
[1,3,4,2,5,7,8,6]=>1001100=>[1,3,1,3]=>[3,3,1,1]
[1,2,4,3,5,7,8,6]=>1101100=>[1,1,2,1,3]=>[3,2,1,1,1]
[3,2,1,4,5,8,7,6]=>0011100=>[3,1,1,3]=>[3,3,1,1]
[3,2,1,4,5,7,8,6]=>0011100=>[3,1,1,3]=>[3,3,1,1]
[2,3,1,4,5,7,8,6]=>0011100=>[3,1,1,3]=>[3,3,1,1]
[1,2,3,4,5,8,7,6]=>1111100=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[1,2,3,4,5,7,8,6]=>1111100=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[6,5,4,3,2,1,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,6,3,2,1,8,7]=>0000010=>[6,2]=>[6,2]
[4,3,6,5,2,1,8,7]=>0000010=>[6,2]=>[6,2]
[3,4,5,6,2,1,8,7]=>0000010=>[6,2]=>[6,2]
[5,4,3,2,6,1,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,3,2,6,1,8,7]=>0000010=>[6,2]=>[6,2]
[3,5,4,2,6,1,8,7]=>0000010=>[6,2]=>[6,2]
[1,5,4,6,3,2,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,3,6,5,4,2,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[2,1,6,5,4,3,8,7]=>0100010=>[2,4,2]=>[4,2,2]
[2,1,5,6,4,3,8,7]=>0100010=>[2,4,2]=>[4,2,2]
[2,1,4,5,6,3,8,7]=>0100010=>[2,4,2]=>[4,2,2]
[2,3,1,6,5,4,8,7]=>0010010=>[3,3,2]=>[3,3,2]
[2,1,3,6,5,4,8,7]=>0110010=>[2,1,3,2]=>[3,2,2,1]
[1,2,3,6,5,4,8,7]=>1110010=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,2,3,5,6,4,8,7]=>1110010=>[1,1,1,3,2]=>[3,2,1,1,1]
[4,3,2,1,6,5,8,7]=>0001010=>[4,2,2]=>[4,2,2]
[3,4,2,1,6,5,8,7]=>0001010=>[4,2,2]=>[4,2,2]
[3,2,4,1,6,5,8,7]=>0001010=>[4,2,2]=>[4,2,2]
[2,1,4,3,6,5,8,7]=>0101010=>[2,2,2,2]=>[2,2,2,2]
[1,2,4,3,6,5,8,7]=>1101010=>[1,1,2,2,2]=>[2,2,2,1,1]
[1,3,2,4,6,5,8,7]=>1011010=>[1,2,1,2,2]=>[2,2,2,1,1]
[2,1,3,4,6,5,8,7]=>0111010=>[2,1,1,2,2]=>[2,2,2,1,1]
[1,2,3,4,6,5,8,7]=>1111010=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]
[5,4,3,2,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[4,5,3,2,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[3,5,4,2,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[2,5,4,3,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[2,4,5,3,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[3,2,5,4,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[1,3,5,4,2,6,8,7]=>1000110=>[1,4,1,2]=>[4,2,1,1]
[2,1,5,4,3,6,8,7]=>0100110=>[2,3,1,2]=>[3,2,2,1]
[1,2,5,4,3,6,8,7]=>1100110=>[1,1,3,1,2]=>[3,2,1,1,1]
[2,1,3,5,4,6,8,7]=>0110110=>[2,1,2,1,2]=>[2,2,2,1,1]
[4,3,2,1,5,6,8,7]=>0001110=>[4,1,1,2]=>[4,2,1,1]
[1,4,3,2,5,6,8,7]=>1001110=>[1,3,1,1,2]=>[3,2,1,1,1]
[2,1,4,3,5,6,8,7]=>0101110=>[2,2,1,1,2]=>[2,2,2,1,1]
[1,2,4,3,5,6,8,7]=>1101110=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]
[2,1,3,4,5,6,8,7]=>0111110=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]
[1,2,3,4,5,6,8,7]=>1111110=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]
[5,7,6,4,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[4,7,6,5,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[4,6,7,5,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,7,6,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[4,6,5,7,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,6,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,6,7,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,6,5,2,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,3,7,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,7,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[4,3,5,7,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[2,5,6,7,4,3,1,8]=>0000001=>[7,1]=>[7,1]
[2,4,6,7,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,7,6,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,7,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,5,7,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,3,7,6,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,3,6,7,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,3,5,7,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,3,6,5,7,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,3,5,6,7,4,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,4,6,7,5,1,8]=>0000001=>[7,1]=>[7,1]
[2,3,4,7,6,5,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,3,2,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,3,2,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,2,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,5,4,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[3,4,6,5,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,6,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[2,5,4,6,3,7,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,5,4,7,1,8]=>0000001=>[7,1]=>[7,1]
[3,4,2,6,5,7,1,8]=>0000001=>[7,1]=>[7,1]
[2,4,3,6,5,7,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,2,6,7,1,8]=>0000001=>[7,1]=>[7,1]
[2,5,4,3,6,7,1,8]=>0000001=>[7,1]=>[7,1]
[1,5,6,7,4,3,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,6,5,7,3,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,5,7,6,4,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,5,6,7,4,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,5,4,7,6,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,3,5,7,6,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,4,6,3,7,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,6,5,4,7,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,3,6,5,7,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,4,5,6,7,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,1,5,6,7,4,3,8]=>0100001=>[2,5,1]=>[5,2,1]
[1,2,5,7,6,4,3,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,2,5,6,7,4,3,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,2,5,6,4,7,3,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,2,5,4,6,7,3,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[3,2,1,5,7,6,4,8]=>0010001=>[3,4,1]=>[4,3,1]
[3,2,1,6,5,7,4,8]=>0010001=>[3,4,1]=>[4,3,1]
[2,3,1,6,5,7,4,8]=>0010001=>[3,4,1]=>[4,3,1]
[1,3,2,6,5,7,4,8]=>1010001=>[1,2,4,1]=>[4,2,1,1]
[2,1,3,6,7,5,4,8]=>0110001=>[2,1,4,1]=>[4,2,1,1]
[1,2,3,7,6,5,4,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,2,3,6,7,5,4,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,2,3,5,7,6,4,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,2,3,6,5,7,4,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,2,3,5,6,7,4,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[4,3,2,1,7,6,5,8]=>0001001=>[4,3,1]=>[4,3,1]
[4,3,2,1,6,7,5,8]=>0001001=>[4,3,1]=>[4,3,1]
[1,4,3,2,7,6,5,8]=>1001001=>[1,3,3,1]=>[3,3,1,1]
[1,4,3,2,6,7,5,8]=>1001001=>[1,3,3,1]=>[3,3,1,1]
[1,3,4,2,6,7,5,8]=>1001001=>[1,3,3,1]=>[3,3,1,1]
[2,1,4,3,6,7,5,8]=>0101001=>[2,2,3,1]=>[3,2,2,1]
[1,2,4,3,6,7,5,8]=>1101001=>[1,1,2,3,1]=>[3,2,1,1,1]
[3,2,1,4,7,6,5,8]=>0011001=>[3,1,3,1]=>[3,3,1,1]
[1,3,2,4,7,6,5,8]=>1011001=>[1,2,1,3,1]=>[3,2,1,1,1]
[1,2,3,4,7,6,5,8]=>1111001=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,2,3,4,6,7,5,8]=>1111001=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[5,4,3,2,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[3,5,4,2,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[2,4,5,3,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[3,2,5,4,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[3,4,2,5,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[2,4,3,5,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[1,4,3,5,2,7,6,8]=>1000101=>[1,4,2,1]=>[4,2,1,1]
[3,2,1,5,4,7,6,8]=>0010101=>[3,2,2,1]=>[3,2,2,1]
[2,3,1,5,4,7,6,8]=>0010101=>[3,2,2,1]=>[3,2,2,1]
[1,3,2,5,4,7,6,8]=>1010101=>[1,2,2,2,1]=>[2,2,2,1,1]
[1,2,3,5,4,7,6,8]=>1110101=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]
[4,3,2,1,5,7,6,8]=>0001101=>[4,1,2,1]=>[4,2,1,1]
[1,4,3,2,5,7,6,8]=>1001101=>[1,3,1,2,1]=>[3,2,1,1,1]
[1,3,2,4,5,7,6,8]=>1011101=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]
[1,2,3,4,5,7,6,8]=>1111101=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]
[4,3,6,5,2,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,4,6,5,3,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,4,5,6,3,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,3,2,6,5,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,5,4,2,6,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,5,6,4,3,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,4,6,5,3,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,5,4,6,3,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,4,5,6,3,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,3,5,6,4,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,4,3,6,5,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,5,4,3,6,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[2,1,5,6,4,3,7,8]=>0100011=>[2,4,1,1]=>[4,2,1,1]
[2,1,4,6,5,3,7,8]=>0100011=>[2,4,1,1]=>[4,2,1,1]
[1,2,6,5,4,3,7,8]=>1100011=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,2,4,5,6,3,7,8]=>1100011=>[1,1,4,1,1]=>[4,1,1,1,1]
[3,2,1,5,6,4,7,8]=>0010011=>[3,3,1,1]=>[3,3,1,1]
[1,2,3,5,6,4,7,8]=>1110011=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[4,3,2,1,6,5,7,8]=>0001011=>[4,2,1,1]=>[4,2,1,1]
[3,2,4,1,6,5,7,8]=>0001011=>[4,2,1,1]=>[4,2,1,1]
[2,1,4,3,6,5,7,8]=>0101011=>[2,2,2,1,1]=>[2,2,2,1,1]
[1,2,4,3,6,5,7,8]=>1101011=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]
[1,3,2,4,6,5,7,8]=>1011011=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]
[2,1,3,4,6,5,7,8]=>0111011=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]
[1,2,3,4,6,5,7,8]=>1111011=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]
[3,5,4,2,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[2,5,4,3,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[2,4,5,3,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[3,2,5,4,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[2,3,5,4,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[2,4,3,5,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[1,3,2,5,4,6,7,8]=>1010111=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]
[1,2,3,5,4,6,7,8]=>1110111=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]
[2,4,3,1,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[1,4,3,2,5,6,7,8]=>1001111=>[1,3,1,1,1,1]=>[3,1,1,1,1,1]
[1,3,4,2,5,6,7,8]=>1001111=>[1,3,1,1,1,1]=>[3,1,1,1,1,1]
[2,1,4,3,5,6,7,8]=>0101111=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]
[1,2,4,3,5,6,7,8]=>1101111=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,3,2,4,5,6,7,8]=>1011111=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]
[1,2,3,4,8,6,7,5]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,3,5,8,6,7,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,5,6,4,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,2,3,7,5,6,8,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,5,6,7,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,5,7,6,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,6,5,7,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,6,7,5,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,4,5,8,6,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,8,6,5,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,4,8,6,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,4,5,3,7,8]=>1100011=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,2,8,4,5,6,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,5,4,6,8,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,8,5,4,6,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,8,5,4,7,6,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,2,7,5,6,8,4]=>1010000=>[1,2,5]=>[5,2,1]
[1,3,2,8,5,7,6,4]=>1010000=>[1,2,5]=>[5,2,1]
[1,3,6,4,5,2,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,3,6,4,5,7,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,6,4,5,8,7,2]=>1000000=>[1,7]=>[7,1]
[1,3,8,4,5,6,7,2]=>1000000=>[1,7]=>[7,1]
[1,3,8,4,6,7,5,2]=>1000000=>[1,7]=>[7,1]
[1,3,8,5,4,6,7,2]=>1000000=>[1,7]=>[7,1]
[1,3,8,5,6,7,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,8,5,7,6,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,8,6,5,7,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,8,7,5,6,4,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,8,5,6,7,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,8,5,7,6,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,8,6,7,5,2]=>1000000=>[1,7]=>[7,1]
[1,5,3,4,2,7,8,6]=>1000100=>[1,4,3]=>[4,3,1]
[1,5,3,4,2,8,7,6]=>1000100=>[1,4,3]=>[4,3,1]
[1,5,3,4,8,6,7,2]=>1000000=>[1,7]=>[7,1]
[1,8,3,4,6,7,5,2]=>1000000=>[1,7]=>[7,1]
[1,6,3,5,4,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,6,3,5,4,8,7,2]=>1000000=>[1,7]=>[7,1]
[1,8,3,5,6,4,7,2]=>1000000=>[1,7]=>[7,1]
[1,8,3,5,7,6,4,2]=>1000000=>[1,7]=>[7,1]
[1,8,3,6,5,4,7,2]=>1000000=>[1,7]=>[7,1]
[1,8,3,7,6,5,4,2]=>1000000=>[1,7]=>[7,1]
[1,6,4,3,5,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,8,4,3,5,6,7,2]=>1000000=>[1,7]=>[7,1]
[1,8,4,3,5,7,6,2]=>1000000=>[1,7]=>[7,1]
[1,6,4,5,3,8,7,2]=>1000000=>[1,7]=>[7,1]
[1,8,4,5,6,7,3,2]=>1000000=>[1,7]=>[7,1]
[1,8,4,6,5,7,3,2]=>1000000=>[1,7]=>[7,1]
[1,8,4,7,6,5,3,2]=>1000000=>[1,7]=>[7,1]
[1,7,5,4,3,6,8,2]=>1000000=>[1,7]=>[7,1]
[1,8,5,4,3,6,7,2]=>1000000=>[1,7]=>[7,1]
[1,8,5,4,6,3,7,2]=>1000000=>[1,7]=>[7,1]
[1,8,5,4,6,7,3,2]=>1000000=>[1,7]=>[7,1]
[1,8,5,4,7,6,3,2]=>1000000=>[1,7]=>[7,1]
[1,8,6,4,5,7,3,2]=>1000000=>[1,7]=>[7,1]
[1,8,6,5,4,7,3,2]=>1000000=>[1,7]=>[7,1]
[1,8,7,5,6,4,3,2]=>1000000=>[1,7]=>[7,1]
[2,1,3,4,8,6,7,5]=>0111000=>[2,1,1,4]=>[4,2,1,1]
[2,1,4,8,6,5,7,3]=>0100000=>[2,6]=>[6,2]
[2,1,6,4,5,8,7,3]=>0100000=>[2,6]=>[6,2]
[2,1,8,5,4,6,7,3]=>0100000=>[2,6]=>[6,2]
[2,1,8,5,4,7,6,3]=>0100000=>[2,6]=>[6,2]
[2,1,7,5,6,4,8,3]=>0100000=>[2,6]=>[6,2]
[2,1,8,7,5,6,4,3]=>0100000=>[2,6]=>[6,2]
[2,3,1,8,6,7,5,4]=>0010000=>[3,5]=>[5,3]
[2,3,6,4,5,7,8,1]=>0000000=>[8]=>[8]
[2,3,7,4,5,6,8,1]=>0000000=>[8]=>[8]
[2,3,8,4,5,6,7,1]=>0000000=>[8]=>[8]
[2,3,7,4,6,5,8,1]=>0000000=>[8]=>[8]
[2,3,7,5,4,6,8,1]=>0000000=>[8]=>[8]
[2,3,7,5,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,3,7,5,6,4,8,1]=>0000000=>[8]=>[8]
[2,4,3,5,8,6,7,1]=>0000000=>[8]=>[8]
[2,5,3,4,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[2,5,3,4,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[2,5,3,4,6,7,1,8]=>0000001=>[7,1]=>[7,1]
[2,5,3,4,8,7,6,1]=>0000000=>[8]=>[8]
[2,6,3,4,5,7,8,1]=>0000000=>[8]=>[8]
[2,6,3,5,4,1,8,7]=>0000010=>[6,2]=>[6,2]
[2,6,3,5,4,7,8,1]=>0000000=>[8]=>[8]
[2,7,3,5,4,6,8,1]=>0000000=>[8]=>[8]
[2,7,3,5,6,4,8,1]=>0000000=>[8]=>[8]
[2,8,3,5,7,6,4,1]=>0000000=>[8]=>[8]
[2,7,3,6,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,5,4,3,8,6,7,1]=>0000000=>[8]=>[8]
[2,6,4,3,5,7,8,1]=>0000000=>[8]=>[8]
[2,8,4,3,5,6,7,1]=>0000000=>[8]=>[8]
[2,8,4,3,7,6,5,1]=>0000000=>[8]=>[8]
[2,6,4,5,3,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,6,4,5,3,7,8,1]=>0000000=>[8]=>[8]
[2,7,5,4,3,6,8,1]=>0000000=>[8]=>[8]
[2,7,5,4,6,3,8,1]=>0000000=>[8]=>[8]
[2,8,5,4,7,6,3,1]=>0000000=>[8]=>[8]
[2,8,7,5,4,6,3,1]=>0000000=>[8]=>[8]
[2,8,7,5,6,4,3,1]=>0000000=>[8]=>[8]
[3,2,1,4,8,6,7,5]=>0011000=>[3,1,4]=>[4,3,1]
[3,2,1,5,8,6,7,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,7,5,6,4,8]=>0010001=>[3,4,1]=>[4,3,1]
[3,2,1,7,5,6,8,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,8,5,6,7,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,8,5,7,6,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,8,6,5,7,4]=>0010000=>[3,5]=>[5,3]
[3,2,1,8,6,7,5,4]=>0010000=>[3,5]=>[5,3]
[3,2,4,1,8,6,7,5]=>0001000=>[4,4]=>[4,4]
[3,2,7,4,6,5,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,7,4,6,5,8,1]=>0000000=>[8]=>[8]
[3,2,8,5,4,6,7,1]=>0000000=>[8]=>[8]
[3,2,7,5,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,8,5,7,6,4,1]=>0000000=>[8]=>[8]
[4,2,3,1,8,6,7,5]=>0001000=>[4,4]=>[4,4]
[4,2,3,1,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[4,2,3,5,1,7,8,6]=>0000100=>[5,3]=>[5,3]
[4,2,3,5,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[4,2,3,5,6,8,7,1]=>0000000=>[8]=>[8]
[4,2,3,7,5,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,2,3,8,5,6,7,1]=>0000000=>[8]=>[8]
[4,2,3,7,6,5,8,1]=>0000000=>[8]=>[8]
[4,2,3,8,7,6,5,1]=>0000000=>[8]=>[8]
[5,2,3,4,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,2,3,4,8,7,6,1]=>0000000=>[8]=>[8]
[6,2,3,5,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,2,3,5,4,1,8,7]=>0000010=>[6,2]=>[6,2]
[6,2,3,5,4,7,1,8]=>0000001=>[7,1]=>[7,1]
[7,2,3,5,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[7,2,3,6,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[5,2,4,3,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,2,4,3,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[5,2,4,3,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[5,2,4,3,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,2,4,3,6,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,2,4,3,6,1,8,7]=>0000010=>[6,2]=>[6,2]
[5,2,4,3,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[5,2,4,3,7,6,8,1]=>0000000=>[8]=>[8]
[7,2,4,3,6,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,2,4,3,6,5,8,1]=>0000000=>[8]=>[8]
[6,2,4,5,3,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[7,2,4,5,3,6,1,8]=>0000001=>[7,1]=>[7,1]
[7,2,4,5,3,6,8,1]=>0000000=>[8]=>[8]
[8,2,4,7,6,5,3,1]=>0000000=>[8]=>[8]
[6,2,5,4,3,1,8,7]=>0000010=>[6,2]=>[6,2]
[7,2,5,4,3,6,1,8]=>0000001=>[7,1]=>[7,1]
[8,2,6,4,5,7,3,1]=>0000000=>[8]=>[8]
[8,2,7,5,6,4,3,1]=>0000000=>[8]=>[8]
[8,2,7,6,5,4,3,1]=>0000000=>[8]=>[8]
[4,3,2,1,8,6,7,5]=>0001000=>[4,4]=>[4,4]
[4,3,2,7,5,6,8,1]=>0000000=>[8]=>[8]
[4,3,2,8,5,6,7,1]=>0000000=>[8]=>[8]
[4,3,2,8,6,7,5,1]=>0000000=>[8]=>[8]
[5,3,2,4,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[5,3,2,4,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,3,2,4,6,1,8,7]=>0000010=>[6,2]=>[6,2]
[6,3,2,5,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,3,2,5,4,1,8,7]=>0000010=>[6,2]=>[6,2]
[6,3,2,5,4,7,1,8]=>0000001=>[7,1]=>[7,1]
[8,3,2,5,4,7,6,1]=>0000000=>[8]=>[8]
[8,3,2,5,6,4,7,1]=>0000000=>[8]=>[8]
[8,3,2,7,6,5,4,1]=>0000000=>[8]=>[8]
[5,3,4,2,1,7,8,6]=>0000100=>[5,3]=>[5,3]
[5,3,4,2,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,3,4,2,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[7,3,4,2,6,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,3,4,2,6,5,8,1]=>0000000=>[8]=>[8]
[7,3,4,6,5,2,1,8]=>0000001=>[7,1]=>[7,1]
[6,3,5,4,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[7,3,5,4,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,3,6,4,5,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,3,6,5,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,3,2,8,6,7,1]=>0000000=>[8]=>[8]
[6,4,3,5,2,1,8,7]=>0000010=>[6,2]=>[6,2]
[7,4,3,6,5,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,4,3,6,5,2,8,1]=>0000000=>[8]=>[8]
[6,5,3,4,2,1,8,7]=>0000010=>[6,2]=>[6,2]
[8,5,3,4,7,6,2,1]=>0000000=>[8]=>[8]
[8,7,3,6,5,4,2,1]=>0000000=>[8]=>[8]
[8,5,4,3,2,7,6,1]=>0000000=>[8]=>[8]
[8,7,4,3,6,5,2,1]=>0000000=>[8]=>[8]
[2,4,6,1,3,5,8,7]=>0000010=>[6,2]=>[6,2]
[2,1,4,6,3,8,5,7]=>0100000=>[2,6]=>[6,2]
[2,4,1,6,3,8,5,7]=>0000000=>[8]=>[8]
[2,4,6,1,3,8,5,7]=>0000000=>[8]=>[8]
[2,4,6,1,8,3,5,7]=>0000000=>[8]=>[8]
[2,4,6,8,1,3,5,7]=>0000000=>[8]=>[8]
[2,4,1,3,6,5,7,8]=>0001011=>[4,2,1,1]=>[4,2,1,1]
[2,4,1,6,3,7,5,8]=>0000001=>[7,1]=>[7,1]
[2,4,6,1,3,7,5,8]=>0000001=>[7,1]=>[7,1]
[2,4,1,6,3,7,8,5]=>0000000=>[8]=>[8]
[2,4,1,6,7,3,8,5]=>0000000=>[8]=>[8]
[2,4,6,1,7,3,8,5]=>0000000=>[8]=>[8]
[2,4,6,7,1,3,8,5]=>0000000=>[8]=>[8]
[2,4,1,6,7,8,3,5]=>0000000=>[8]=>[8]
[2,4,6,7,8,1,3,5]=>0000000=>[8]=>[8]
[2,1,4,3,7,5,8,6]=>0101000=>[2,2,4]=>[4,2,2]
[2,4,1,3,7,5,8,6]=>0001000=>[4,4]=>[4,4]
[2,4,1,7,3,5,8,6]=>0000000=>[8]=>[8]
[2,4,7,1,3,5,8,6]=>0000000=>[8]=>[8]
[2,1,4,3,7,8,5,6]=>0101000=>[2,2,4]=>[4,2,2]
[2,4,1,3,7,8,5,6]=>0001000=>[4,4]=>[4,4]
[2,4,1,7,3,8,5,6]=>0000000=>[8]=>[8]
[2,4,1,7,8,3,5,6]=>0000000=>[8]=>[8]
[2,4,1,5,3,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[2,4,1,3,5,7,8,6]=>0001100=>[4,1,3]=>[4,3,1]
[2,4,1,5,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[2,4,5,1,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[2,1,4,5,7,3,8,6]=>0100000=>[2,6]=>[6,2]
[2,4,1,5,7,3,8,6]=>0000000=>[8]=>[8]
[2,4,5,1,7,3,8,6]=>0000000=>[8]=>[8]
[2,4,1,3,8,5,6,7]=>0001000=>[4,4]=>[4,4]
[2,1,4,8,3,5,6,7]=>0100000=>[2,6]=>[6,2]
[2,4,1,8,3,5,6,7]=>0000000=>[8]=>[8]
[2,4,1,5,3,8,6,7]=>0000100=>[5,3]=>[5,3]
[2,1,4,5,8,3,6,7]=>0100000=>[2,6]=>[6,2]
[2,4,1,5,6,3,8,7]=>0000010=>[6,2]=>[6,2]
[2,1,4,5,6,8,3,7]=>0100000=>[2,6]=>[6,2]
[2,4,1,3,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[2,4,1,5,6,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,4,5,6,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,4,5,6,7,1,3,8]=>0000001=>[7,1]=>[7,1]
[2,4,5,6,7,1,8,3]=>0000000=>[8]=>[8]
[2,1,5,3,6,4,8,7]=>0100010=>[2,4,2]=>[4,2,2]
[2,1,5,6,3,4,8,7]=>0100010=>[2,4,2]=>[4,2,2]
[2,1,5,3,6,8,4,7]=>0100000=>[2,6]=>[6,2]
[2,5,1,3,6,8,4,7]=>0000000=>[8]=>[8]
[2,1,5,6,3,4,7,8]=>0100011=>[2,4,1,1]=>[4,2,1,1]
[2,5,1,6,3,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,1,5,3,6,7,4,8]=>0100001=>[2,5,1]=>[5,2,1]
[2,1,5,6,3,7,4,8]=>0100001=>[2,5,1]=>[5,2,1]
[2,5,1,6,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[2,5,6,1,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[2,1,5,6,7,3,4,8]=>0100001=>[2,5,1]=>[5,2,1]
[2,5,1,3,6,7,8,4]=>0000000=>[8]=>[8]
[2,1,5,6,3,7,8,4]=>0100000=>[2,6]=>[6,2]
[2,5,6,1,3,7,8,4]=>0000000=>[8]=>[8]
[2,1,5,6,7,8,3,4]=>0100000=>[2,6]=>[6,2]
[2,1,5,3,7,4,8,6]=>0100000=>[2,6]=>[6,2]
[2,1,5,7,3,4,8,6]=>0100000=>[2,6]=>[6,2]
[2,5,1,7,3,4,8,6]=>0000000=>[8]=>[8]
[2,5,7,1,3,4,8,6]=>0000000=>[8]=>[8]
[2,1,5,3,7,8,4,6]=>0100000=>[2,6]=>[6,2]
[2,5,1,3,7,8,4,6]=>0000000=>[8]=>[8]
[2,1,5,7,3,8,4,6]=>0100000=>[2,6]=>[6,2]
[2,1,5,7,8,3,4,6]=>0100000=>[2,6]=>[6,2]
[2,5,1,7,8,3,4,6]=>0000000=>[8]=>[8]
[2,5,1,3,7,4,6,8]=>0000001=>[7,1]=>[7,1]
[2,1,5,7,3,4,6,8]=>0100001=>[2,5,1]=>[5,2,1]
[2,3,5,7,1,4,8,6]=>0000000=>[8]=>[8]
[2,3,5,6,1,8,4,7]=>0000000=>[8]=>[8]
[2,3,5,6,8,1,4,7]=>0000000=>[8]=>[8]
[2,5,1,3,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[2,3,5,6,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,3,5,6,1,7,8,4]=>0000000=>[8]=>[8]
[2,3,5,6,7,8,1,4]=>0000000=>[8]=>[8]
[2,1,6,3,7,4,8,5]=>0100000=>[2,6]=>[6,2]
[2,6,1,3,7,4,8,5]=>0000000=>[8]=>[8]
[2,6,7,1,3,4,8,5]=>0000000=>[8]=>[8]
[2,1,6,3,7,8,4,5]=>0100000=>[2,6]=>[6,2]
[2,6,1,7,3,8,4,5]=>0000000=>[8]=>[8]
[2,1,6,7,8,3,4,5]=>0100000=>[2,6]=>[6,2]
[2,6,1,7,8,3,4,5]=>0000000=>[8]=>[8]
[2,6,7,8,1,3,4,5]=>0000000=>[8]=>[8]
[2,6,1,7,3,4,5,8]=>0000001=>[7,1]=>[7,1]
[2,6,7,1,3,4,5,8]=>0000001=>[7,1]=>[7,1]
[2,3,1,6,4,7,5,8]=>0010001=>[3,4,1]=>[4,3,1]
[2,3,6,1,4,7,5,8]=>0000001=>[7,1]=>[7,1]
[2,1,6,3,4,7,8,5]=>0100000=>[2,6]=>[6,2]
[2,3,6,1,4,7,8,5]=>0000000=>[8]=>[8]
[2,1,3,6,7,4,8,5]=>0110000=>[2,1,5]=>[5,2,1]
[2,3,1,6,7,8,4,5]=>0010000=>[3,5]=>[5,3]
[2,3,6,7,8,1,4,5]=>0000000=>[8]=>[8]
[2,6,1,8,3,4,5,7]=>0000000=>[8]=>[8]
[2,1,6,3,4,8,5,7]=>0100000=>[2,6]=>[6,2]
[2,3,6,1,4,5,8,7]=>0000010=>[6,2]=>[6,2]
[2,3,4,1,6,8,5,7]=>0001000=>[4,4]=>[4,4]
[2,3,4,6,7,8,1,5]=>0000000=>[8]=>[8]
[2,1,7,8,3,4,5,6]=>0100000=>[2,6]=>[6,2]
[2,7,1,8,3,4,5,6]=>0000000=>[8]=>[8]
[2,7,8,1,3,4,5,6]=>0000000=>[8]=>[8]
[2,1,7,3,4,8,5,6]=>0100000=>[2,6]=>[6,2]
[2,1,3,7,4,8,5,6]=>0110000=>[2,1,5]=>[5,2,1]
[2,3,7,1,4,5,8,6]=>0000000=>[8]=>[8]
[2,1,3,4,7,8,5,6]=>0111000=>[2,1,1,4]=>[4,2,1,1]
[2,1,3,8,4,5,6,7]=>0110000=>[2,1,5]=>[5,2,1]
[2,3,1,8,4,5,6,7]=>0010000=>[3,5]=>[5,3]
[2,1,3,4,8,5,6,7]=>0111000=>[2,1,1,4]=>[4,2,1,1]
[2,3,4,8,1,5,6,7]=>0000000=>[8]=>[8]
[3,1,4,2,6,5,8,7]=>0001010=>[4,2,2]=>[4,2,2]
[3,4,1,2,6,5,8,7]=>0001010=>[4,2,2]=>[4,2,2]
[3,4,6,1,2,5,8,7]=>0000010=>[6,2]=>[6,2]
[3,1,4,2,6,8,5,7]=>0001000=>[4,4]=>[4,4]
[3,1,4,6,8,2,5,7]=>0000000=>[8]=>[8]
[3,1,4,2,6,5,7,8]=>0001011=>[4,2,1,1]=>[4,2,1,1]
[3,4,1,2,6,5,7,8]=>0001011=>[4,2,1,1]=>[4,2,1,1]
[3,1,4,2,6,7,5,8]=>0001001=>[4,3,1]=>[4,3,1]
[3,4,1,6,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[3,1,4,2,6,7,8,5]=>0001000=>[4,4]=>[4,4]
[3,4,1,2,6,7,8,5]=>0001000=>[4,4]=>[4,4]
[3,4,6,1,7,2,8,5]=>0000000=>[8]=>[8]
[3,1,4,6,7,8,2,5]=>0000000=>[8]=>[8]
[3,4,6,1,7,8,2,5]=>0000000=>[8]=>[8]
[3,4,6,7,1,8,2,5]=>0000000=>[8]=>[8]
[3,4,6,7,8,1,2,5]=>0000000=>[8]=>[8]
[3,1,4,2,7,5,8,6]=>0001000=>[4,4]=>[4,4]
[3,4,1,2,7,5,8,6]=>0001000=>[4,4]=>[4,4]
[3,4,7,1,2,5,8,6]=>0000000=>[8]=>[8]
[3,1,4,2,7,8,5,6]=>0001000=>[4,4]=>[4,4]
[3,4,1,2,7,8,5,6]=>0001000=>[4,4]=>[4,4]
[3,4,7,1,8,2,5,6]=>0000000=>[8]=>[8]
[3,1,4,2,7,5,6,8]=>0001001=>[4,3,1]=>[4,3,1]
[3,4,1,5,2,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[3,1,4,2,5,7,8,6]=>0001100=>[4,1,3]=>[4,3,1]
[3,1,4,5,2,7,8,6]=>0000100=>[5,3]=>[5,3]
[3,1,4,5,7,8,2,6]=>0000000=>[8]=>[8]
[3,4,1,5,7,8,2,6]=>0000000=>[8]=>[8]
[3,4,5,1,7,8,2,6]=>0000000=>[8]=>[8]
[3,4,1,8,2,5,6,7]=>0000000=>[8]=>[8]
[3,1,4,2,5,8,6,7]=>0001100=>[4,1,3]=>[4,3,1]
[3,4,1,5,2,8,6,7]=>0000100=>[5,3]=>[5,3]
[3,4,1,5,8,2,6,7]=>0000000=>[8]=>[8]
[3,4,1,2,5,6,8,7]=>0001110=>[4,1,1,2]=>[4,2,1,1]
[3,4,5,6,1,2,8,7]=>0000010=>[6,2]=>[6,2]
[3,4,5,6,1,8,2,7]=>0000000=>[8]=>[8]
[3,4,5,6,8,1,2,7]=>0000000=>[8]=>[8]
[3,1,4,2,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[3,4,1,5,6,7,2,8]=>0000001=>[7,1]=>[7,1]
[3,4,5,6,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[3,4,5,1,6,7,8,2]=>0000000=>[8]=>[8]
[3,4,5,6,1,7,8,2]=>0000000=>[8]=>[8]
[3,1,5,2,6,4,8,7]=>0000010=>[6,2]=>[6,2]
[3,1,5,6,2,4,8,7]=>0000010=>[6,2]=>[6,2]
[3,5,1,6,2,4,8,7]=>0000010=>[6,2]=>[6,2]
[3,5,1,2,6,8,4,7]=>0000000=>[8]=>[8]
[3,1,5,6,2,8,4,7]=>0000000=>[8]=>[8]
[3,5,6,1,2,8,4,7]=>0000000=>[8]=>[8]
[3,1,5,6,8,2,4,7]=>0000000=>[8]=>[8]
[3,5,6,1,8,2,4,7]=>0000000=>[8]=>[8]
[3,1,5,6,2,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,5,1,6,2,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,5,1,6,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[3,5,6,1,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[3,1,5,2,6,7,8,4]=>0000000=>[8]=>[8]
[3,5,1,2,6,7,8,4]=>0000000=>[8]=>[8]
[3,5,1,6,2,7,8,4]=>0000000=>[8]=>[8]
[3,1,5,6,7,2,8,4]=>0000000=>[8]=>[8]
[3,5,1,6,7,8,2,4]=>0000000=>[8]=>[8]
[3,5,6,1,7,8,2,4]=>0000000=>[8]=>[8]
[3,1,5,2,7,4,8,6]=>0000000=>[8]=>[8]
[3,5,1,2,7,4,8,6]=>0000000=>[8]=>[8]
[3,1,5,7,2,4,8,6]=>0000000=>[8]=>[8]
[3,5,1,7,2,4,8,6]=>0000000=>[8]=>[8]
[3,5,7,1,2,4,8,6]=>0000000=>[8]=>[8]
[3,1,5,2,7,8,4,6]=>0000000=>[8]=>[8]
[3,5,1,2,7,8,4,6]=>0000000=>[8]=>[8]
[3,1,5,7,2,8,4,6]=>0000000=>[8]=>[8]
[3,5,1,7,2,8,4,6]=>0000000=>[8]=>[8]
[3,1,5,7,8,2,4,6]=>0000000=>[8]=>[8]
[3,5,1,7,8,2,4,6]=>0000000=>[8]=>[8]
[3,1,5,2,7,4,6,8]=>0000001=>[7,1]=>[7,1]
[3,1,5,7,2,4,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,1,7,2,4,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,1,2,4,6,8]=>0000001=>[7,1]=>[7,1]
[1,3,5,7,2,4,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[3,5,1,2,4,7,8,6]=>0000100=>[5,3]=>[5,3]
[3,1,2,5,7,4,8,6]=>0010000=>[3,5]=>[5,3]
[1,3,5,2,7,4,8,6]=>1000000=>[1,7]=>[7,1]
[1,3,5,7,2,4,8,6]=>1000000=>[1,7]=>[7,1]
[1,3,5,2,7,8,4,6]=>1000000=>[1,7]=>[7,1]
[3,1,5,2,8,4,6,7]=>0000000=>[8]=>[8]
[3,5,1,2,8,4,6,7]=>0000000=>[8]=>[8]
[3,1,5,8,2,4,6,7]=>0000000=>[8]=>[8]
[3,5,1,8,2,4,6,7]=>0000000=>[8]=>[8]
[3,1,5,2,4,8,6,7]=>0000100=>[5,3]=>[5,3]
[3,5,1,2,4,8,6,7]=>0000100=>[5,3]=>[5,3]
[1,3,2,5,4,8,6,7]=>1010100=>[1,2,2,3]=>[3,2,2,1]
[1,3,5,2,4,8,6,7]=>1000100=>[1,4,3]=>[4,3,1]
[3,1,2,5,8,4,6,7]=>0010000=>[3,5]=>[5,3]
[1,3,2,5,8,4,6,7]=>1010000=>[1,2,5]=>[5,2,1]
[1,3,5,2,8,4,6,7]=>1000000=>[1,7]=>[7,1]
[1,3,5,8,2,4,6,7]=>1000000=>[1,7]=>[7,1]
[3,5,1,2,4,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[3,1,2,5,4,6,8,7]=>0010110=>[3,2,1,2]=>[3,2,2,1]
[1,3,5,2,4,6,8,7]=>1000110=>[1,4,1,2]=>[4,2,1,1]
[1,3,5,2,6,4,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,3,5,6,2,4,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[3,1,2,5,6,8,4,7]=>0010000=>[3,5]=>[5,3]
[1,3,5,2,6,8,4,7]=>1000000=>[1,7]=>[7,1]
[3,5,1,2,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[1,3,5,6,2,4,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[3,1,2,5,6,7,4,8]=>0010001=>[3,4,1]=>[4,3,1]
[1,3,5,2,6,7,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,5,6,2,7,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,5,6,7,2,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[3,1,2,5,6,7,8,4]=>0010000=>[3,5]=>[5,3]
[1,3,5,6,7,8,2,4]=>1000000=>[1,7]=>[7,1]
[3,1,6,2,7,4,8,5]=>0000000=>[8]=>[8]
[3,6,1,2,7,4,8,5]=>0000000=>[8]=>[8]
[3,6,1,7,2,4,8,5]=>0000000=>[8]=>[8]
[3,6,7,1,2,4,8,5]=>0000000=>[8]=>[8]
[3,1,6,7,2,8,4,5]=>0000000=>[8]=>[8]
[3,6,1,7,2,8,4,5]=>0000000=>[8]=>[8]
[3,6,7,1,2,8,4,5]=>0000000=>[8]=>[8]
[3,6,1,7,8,2,4,5]=>0000000=>[8]=>[8]
[3,6,7,8,1,2,4,5]=>0000000=>[8]=>[8]
[3,1,6,7,2,4,5,8]=>0000001=>[7,1]=>[7,1]
[3,6,7,1,2,4,5,8]=>0000001=>[7,1]=>[7,1]
[3,1,6,2,4,7,5,8]=>0000001=>[7,1]=>[7,1]
[3,1,2,6,4,7,5,8]=>0010001=>[3,4,1]=>[4,3,1]
[1,3,2,6,4,7,5,8]=>1010001=>[1,2,4,1]=>[4,2,1,1]
[1,3,6,2,4,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[3,1,6,2,4,7,8,5]=>0000000=>[8]=>[8]
[3,6,1,2,4,7,8,5]=>0000000=>[8]=>[8]
[3,1,2,6,4,7,8,5]=>0010000=>[3,5]=>[5,3]
[1,3,6,2,4,7,8,5]=>1000000=>[1,7]=>[7,1]
[3,1,2,6,7,4,8,5]=>0010000=>[3,5]=>[5,3]
[1,3,6,2,7,4,8,5]=>1000000=>[1,7]=>[7,1]
[1,3,6,7,2,4,8,5]=>1000000=>[1,7]=>[7,1]
[1,3,6,2,7,8,4,5]=>1000000=>[1,7]=>[7,1]
[3,1,6,2,8,4,5,7]=>0000000=>[8]=>[8]
[3,1,6,8,2,4,5,7]=>0000000=>[8]=>[8]
[3,6,1,8,2,4,5,7]=>0000000=>[8]=>[8]
[3,1,6,2,4,8,5,7]=>0000000=>[8]=>[8]
[1,3,2,6,4,8,5,7]=>1010000=>[1,2,5]=>[5,2,1]
[1,3,6,2,4,8,5,7]=>1000000=>[1,7]=>[7,1]
[3,1,6,2,4,5,8,7]=>0000010=>[6,2]=>[6,2]
[3,1,2,6,4,5,8,7]=>0010010=>[3,3,2]=>[3,3,2]
[1,3,4,6,2,5,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[3,1,2,4,6,8,5,7]=>0011000=>[3,1,4]=>[4,3,1]
[1,3,2,4,6,8,5,7]=>1011000=>[1,2,1,4]=>[4,2,1,1]
[1,3,4,6,8,2,5,7]=>1000000=>[1,7]=>[7,1]
[3,1,6,2,4,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,3,2,6,4,5,7,8]=>1010011=>[1,2,3,1,1]=>[3,2,1,1,1]
[1,3,6,2,4,5,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[3,1,2,4,6,7,5,8]=>0011001=>[3,1,3,1]=>[3,3,1,1]
[3,1,2,4,6,7,8,5]=>0011000=>[3,1,4]=>[4,3,1]
[3,7,1,2,8,4,5,6]=>0000000=>[8]=>[8]
[3,1,7,8,2,4,5,6]=>0000000=>[8]=>[8]
[3,7,1,2,4,8,5,6]=>0000000=>[8]=>[8]
[3,1,2,7,4,8,5,6]=>0010000=>[3,5]=>[5,3]
[1,3,2,7,4,8,5,6]=>1010000=>[1,2,5]=>[5,2,1]
[1,3,7,2,4,8,5,6]=>1000000=>[1,7]=>[7,1]
[1,3,7,2,8,4,5,6]=>1000000=>[1,7]=>[7,1]
[1,3,7,2,4,5,8,6]=>1000000=>[1,7]=>[7,1]
[3,1,2,4,7,5,8,6]=>0011000=>[3,1,4]=>[4,3,1]
[1,3,2,4,7,5,8,6]=>1011000=>[1,2,1,4]=>[4,2,1,1]
[1,3,4,7,2,5,8,6]=>1000000=>[1,7]=>[7,1]
[3,7,1,2,4,5,6,8]=>0000001=>[7,1]=>[7,1]
[1,3,2,7,4,5,6,8]=>1010001=>[1,2,4,1]=>[4,2,1,1]
[1,3,4,5,7,8,2,6]=>1000000=>[1,7]=>[7,1]
[3,1,2,8,4,5,6,7]=>0010000=>[3,5]=>[5,3]
[1,3,2,8,4,5,6,7]=>1010000=>[1,2,5]=>[5,2,1]
[1,3,8,2,4,5,6,7]=>1000000=>[1,7]=>[7,1]
[3,1,2,4,8,5,6,7]=>0011000=>[3,1,4]=>[4,3,1]
[1,3,2,4,8,5,6,7]=>1011000=>[1,2,1,4]=>[4,2,1,1]
[1,3,4,2,8,5,6,7]=>1001000=>[1,3,4]=>[4,3,1]
[1,3,4,8,2,5,6,7]=>1000000=>[1,7]=>[7,1]
[3,1,2,4,5,8,6,7]=>0011100=>[3,1,1,3]=>[3,3,1,1]
[1,3,2,4,5,8,6,7]=>1011100=>[1,2,1,1,3]=>[3,2,1,1,1]
[1,3,4,2,5,8,6,7]=>1001100=>[1,3,1,3]=>[3,3,1,1]
[1,3,4,5,2,8,6,7]=>1000100=>[1,4,3]=>[4,3,1]
[4,1,5,2,6,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,1,2,6,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,1,5,6,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,6,1,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,1,5,2,6,8,3,7]=>0000000=>[8]=>[8]
[4,5,1,2,6,8,3,7]=>0000000=>[8]=>[8]
[4,5,1,6,2,8,3,7]=>0000000=>[8]=>[8]
[4,1,5,6,8,2,3,7]=>0000000=>[8]=>[8]
[4,5,6,8,1,2,3,7]=>0000000=>[8]=>[8]
[4,5,1,6,2,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,1,5,6,7,2,3,8]=>0000001=>[7,1]=>[7,1]
[4,5,1,6,7,2,3,8]=>0000001=>[7,1]=>[7,1]
[4,1,5,2,6,7,8,3]=>0000000=>[8]=>[8]
[4,5,1,2,6,7,8,3]=>0000000=>[8]=>[8]
[4,5,1,6,2,7,8,3]=>0000000=>[8]=>[8]
[4,5,1,6,7,2,8,3]=>0000000=>[8]=>[8]
[4,5,6,1,7,2,8,3]=>0000000=>[8]=>[8]
[4,5,1,6,7,8,2,3]=>0000000=>[8]=>[8]
[4,1,5,2,7,3,8,6]=>0000000=>[8]=>[8]
[4,5,1,2,7,3,8,6]=>0000000=>[8]=>[8]
[4,5,1,7,2,3,8,6]=>0000000=>[8]=>[8]
[4,1,5,2,7,8,3,6]=>0000000=>[8]=>[8]
[4,5,1,2,7,8,3,6]=>0000000=>[8]=>[8]
[4,1,5,7,2,8,3,6]=>0000000=>[8]=>[8]
[4,5,1,7,2,8,3,6]=>0000000=>[8]=>[8]
[4,5,7,1,2,8,3,6]=>0000000=>[8]=>[8]
[4,5,1,7,8,2,3,6]=>0000000=>[8]=>[8]
[4,1,5,2,7,3,6,8]=>0000001=>[7,1]=>[7,1]
[4,5,1,2,7,3,6,8]=>0000001=>[7,1]=>[7,1]
[1,4,2,5,3,7,6,8]=>1000101=>[1,4,2,1]=>[4,2,1,1]
[4,1,2,5,7,3,6,8]=>0000001=>[7,1]=>[7,1]
[1,4,2,5,7,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,5,2,7,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,5,7,2,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[4,1,5,2,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[4,1,2,5,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[1,4,5,2,3,7,8,6]=>1000100=>[1,4,3]=>[4,3,1]
[4,1,2,5,7,3,8,6]=>0000000=>[8]=>[8]
[1,4,2,5,7,3,8,6]=>1000000=>[1,7]=>[7,1]
[1,4,5,2,7,3,8,6]=>1000000=>[1,7]=>[7,1]
[1,4,2,5,7,8,3,6]=>1000000=>[1,7]=>[7,1]
[1,4,5,2,7,8,3,6]=>1000000=>[1,7]=>[7,1]
[1,4,5,7,8,2,3,6]=>1000000=>[1,7]=>[7,1]
[4,1,5,2,8,3,6,7]=>0000000=>[8]=>[8]
[4,5,1,2,8,3,6,7]=>0000000=>[8]=>[8]
[4,5,1,8,2,3,6,7]=>0000000=>[8]=>[8]
[4,5,8,1,2,3,6,7]=>0000000=>[8]=>[8]
[4,1,5,2,3,8,6,7]=>0000100=>[5,3]=>[5,3]
[4,5,1,2,3,8,6,7]=>0000100=>[5,3]=>[5,3]
[4,1,2,5,3,8,6,7]=>0000100=>[5,3]=>[5,3]
[1,4,2,5,3,8,6,7]=>1000100=>[1,4,3]=>[4,3,1]
[1,4,5,2,3,8,6,7]=>1000100=>[1,4,3]=>[4,3,1]
[4,1,2,5,8,3,6,7]=>0000000=>[8]=>[8]
[1,4,2,5,8,3,6,7]=>1000000=>[1,7]=>[7,1]
[1,4,2,5,3,6,8,7]=>1000110=>[1,4,1,2]=>[4,2,1,1]
[4,1,2,5,6,3,8,7]=>0000010=>[6,2]=>[6,2]
[1,4,5,2,6,3,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[4,1,2,5,6,8,3,7]=>0000000=>[8]=>[8]
[1,4,5,2,6,8,3,7]=>1000000=>[1,7]=>[7,1]
[1,4,5,6,8,2,3,7]=>1000000=>[1,7]=>[7,1]
[1,4,2,5,3,6,7,8]=>1000111=>[1,4,1,1,1]=>[4,1,1,1,1]
[1,4,5,2,3,6,7,8]=>1000111=>[1,4,1,1,1]=>[4,1,1,1,1]
[4,1,2,5,6,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,4,5,2,6,3,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[4,1,2,5,6,7,3,8]=>0000001=>[7,1]=>[7,1]
[1,4,2,5,6,7,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,5,6,7,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,5,2,6,7,8,3]=>1000000=>[1,7]=>[7,1]
[1,4,5,6,7,2,8,3]=>1000000=>[1,7]=>[7,1]
[4,1,6,2,7,3,8,5]=>0000000=>[8]=>[8]
[4,6,7,1,2,3,8,5]=>0000000=>[8]=>[8]
[4,6,7,1,8,2,3,5]=>0000000=>[8]=>[8]
[4,6,7,8,1,2,3,5]=>0000000=>[8]=>[8]
[4,1,6,2,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,1,2,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[4,1,6,7,2,3,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,1,7,2,3,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,1,2,3,7,5,8]=>0000001=>[7,1]=>[7,1]
[4,1,2,6,3,7,5,8]=>0000001=>[7,1]=>[7,1]
[1,4,2,6,3,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[4,1,2,6,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[1,4,2,6,7,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,6,2,7,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[4,1,6,2,3,7,8,5]=>0000000=>[8]=>[8]
[4,1,2,6,3,7,8,5]=>0000000=>[8]=>[8]
[1,4,6,2,3,7,8,5]=>1000000=>[1,7]=>[7,1]
[1,4,6,2,7,3,8,5]=>1000000=>[1,7]=>[7,1]
[1,4,2,6,7,8,3,5]=>1000000=>[1,7]=>[7,1]
[1,4,6,2,7,8,3,5]=>1000000=>[1,7]=>[7,1]
[1,4,6,7,2,8,3,5]=>1000000=>[1,7]=>[7,1]
[4,1,6,2,8,3,5,7]=>0000000=>[8]=>[8]
[4,6,1,2,8,3,5,7]=>0000000=>[8]=>[8]
[4,1,6,8,2,3,5,7]=>0000000=>[8]=>[8]
[4,6,1,8,2,3,5,7]=>0000000=>[8]=>[8]
[4,6,1,2,3,8,5,7]=>0000000=>[8]=>[8]
[4,1,2,6,3,8,5,7]=>0000000=>[8]=>[8]
[1,4,2,6,3,8,5,7]=>1000000=>[1,7]=>[7,1]
[1,4,6,2,3,8,5,7]=>1000000=>[1,7]=>[7,1]
[1,4,2,6,8,3,5,7]=>1000000=>[1,7]=>[7,1]
[1,4,6,8,2,3,5,7]=>1000000=>[1,7]=>[7,1]
[1,4,2,6,3,5,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,4,2,3,6,5,8,7]=>1001010=>[1,3,2,2]=>[3,2,2,1]
[1,2,4,3,6,8,5,7]=>1101000=>[1,1,2,4]=>[4,2,1,1]
[1,2,4,6,3,8,5,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,6,8,3,5,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,4,2,6,3,5,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,4,2,3,6,5,7,8]=>1001011=>[1,3,2,1,1]=>[3,2,1,1,1]
[1,2,4,6,3,5,7,8]=>1100011=>[1,1,4,1,1]=>[4,1,1,1,1]
[4,1,2,3,6,7,8,5]=>0001000=>[4,4]=>[4,4]
[1,4,2,3,6,7,8,5]=>1001000=>[1,3,4]=>[4,3,1]
[4,1,7,2,8,3,5,6]=>0000000=>[8]=>[8]
[4,7,1,8,2,3,5,6]=>0000000=>[8]=>[8]
[4,1,7,2,3,8,5,6]=>0000000=>[8]=>[8]
[1,4,2,7,3,8,5,6]=>1000000=>[1,7]=>[7,1]
[1,4,7,2,3,8,5,6]=>1000000=>[1,7]=>[7,1]
[4,1,2,7,8,3,5,6]=>0000000=>[8]=>[8]
[1,4,2,7,8,3,5,6]=>1000000=>[1,7]=>[7,1]
[4,1,7,2,3,5,8,6]=>0000000=>[8]=>[8]
[4,1,2,7,3,5,8,6]=>0000000=>[8]=>[8]
[1,4,2,7,3,5,8,6]=>1000000=>[1,7]=>[7,1]
[1,4,7,2,3,5,8,6]=>1000000=>[1,7]=>[7,1]
[4,1,2,3,7,5,8,6]=>0001000=>[4,4]=>[4,4]
[1,2,4,3,7,5,8,6]=>1101000=>[1,1,2,4]=>[4,2,1,1]
[1,4,2,3,7,8,5,6]=>1001000=>[1,3,4]=>[4,3,1]
[1,2,4,3,7,8,5,6]=>1101000=>[1,1,2,4]=>[4,2,1,1]
[1,2,4,7,3,8,5,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,4,2,7,3,5,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,2,3,7,5,6,8]=>1001001=>[1,3,3,1]=>[3,3,1,1]
[1,4,2,3,5,7,6,8]=>1001101=>[1,3,1,2,1]=>[3,2,1,1,1]
[4,1,2,3,5,7,8,6]=>0001100=>[4,1,3]=>[4,3,1]
[1,4,2,3,5,7,8,6]=>1001100=>[1,3,1,3]=>[3,3,1,1]
[1,2,4,5,7,3,8,6]=>1100000=>[1,1,6]=>[6,1,1]
[4,8,1,2,3,5,6,7]=>0000000=>[8]=>[8]
[1,4,2,8,3,5,6,7]=>1000000=>[1,7]=>[7,1]
[1,4,8,2,3,5,6,7]=>1000000=>[1,7]=>[7,1]
[4,1,2,3,8,5,6,7]=>0001000=>[4,4]=>[4,4]
[1,4,2,3,8,5,6,7]=>1001000=>[1,3,4]=>[4,3,1]
[1,2,4,3,8,5,6,7]=>1101000=>[1,1,2,4]=>[4,2,1,1]
[1,2,4,8,3,5,6,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,4,2,3,5,8,6,7]=>1001100=>[1,3,1,3]=>[3,3,1,1]
[1,2,4,3,5,8,6,7]=>1101100=>[1,1,2,1,3]=>[3,2,1,1,1]
[1,4,2,3,5,6,8,7]=>1001110=>[1,3,1,1,2]=>[3,2,1,1,1]
[1,4,2,3,5,6,7,8]=>1001111=>[1,3,1,1,1,1]=>[3,1,1,1,1,1]
[5,1,6,2,7,3,8,4]=>0000000=>[8]=>[8]
[5,6,7,1,2,3,8,4]=>0000000=>[8]=>[8]
[5,1,6,7,2,8,3,4]=>0000000=>[8]=>[8]
[5,6,7,1,2,8,3,4]=>0000000=>[8]=>[8]
[5,1,6,7,8,2,3,4]=>0000000=>[8]=>[8]
[5,6,1,7,8,2,3,4]=>0000000=>[8]=>[8]
[5,6,7,1,8,2,3,4]=>0000000=>[8]=>[8]
[1,5,2,6,3,7,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[5,1,2,6,7,3,4,8]=>0000001=>[7,1]=>[7,1]
[1,5,2,6,7,3,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,2,6,3,7,8,4]=>1000000=>[1,7]=>[7,1]
[1,5,6,2,3,7,8,4]=>1000000=>[1,7]=>[7,1]
[1,5,6,7,2,3,8,4]=>1000000=>[1,7]=>[7,1]
[1,5,6,7,8,2,3,4]=>1000000=>[1,7]=>[7,1]
[5,1,6,2,8,3,4,7]=>0000000=>[8]=>[8]
[5,6,8,1,2,3,4,7]=>0000000=>[8]=>[8]
[5,1,6,2,3,8,4,7]=>0000000=>[8]=>[8]
[5,6,1,2,3,8,4,7]=>0000000=>[8]=>[8]
[5,1,2,6,3,8,4,7]=>0000000=>[8]=>[8]
[1,5,2,6,3,8,4,7]=>1000000=>[1,7]=>[7,1]
[1,5,6,2,3,8,4,7]=>1000000=>[1,7]=>[7,1]
[5,1,2,6,8,3,4,7]=>0000000=>[8]=>[8]
[1,5,2,6,8,3,4,7]=>1000000=>[1,7]=>[7,1]
[1,5,6,2,8,3,4,7]=>1000000=>[1,7]=>[7,1]
[1,5,2,6,3,4,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,5,6,2,3,4,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,5,2,3,6,4,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,2,5,3,6,4,8,7]=>1100010=>[1,1,4,2]=>[4,2,1,1]
[1,2,5,6,3,4,8,7]=>1100010=>[1,1,4,2]=>[4,2,1,1]
[5,1,2,3,6,8,4,7]=>0000000=>[8]=>[8]
[1,5,2,3,6,8,4,7]=>1000000=>[1,7]=>[7,1]
[1,2,5,6,3,8,4,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,6,8,3,4,7]=>1100000=>[1,1,6]=>[6,1,1]
[5,1,2,6,3,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,5,2,6,3,4,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,2,5,6,3,4,7,8]=>1100011=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,2,5,6,3,7,4,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[5,1,2,3,6,7,8,4]=>0000000=>[8]=>[8]
[1,5,2,3,6,7,8,4]=>1000000=>[1,7]=>[7,1]
[1,2,5,3,6,7,8,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,6,3,7,8,4]=>1100000=>[1,1,6]=>[6,1,1]
[5,1,7,2,8,3,4,6]=>0000000=>[8]=>[8]
[5,7,1,2,8,3,4,6]=>0000000=>[8]=>[8]
[5,7,8,1,2,3,4,6]=>0000000=>[8]=>[8]
[5,1,2,7,3,8,4,6]=>0000000=>[8]=>[8]
[1,5,2,7,3,8,4,6]=>1000000=>[1,7]=>[7,1]
[1,5,7,2,3,8,4,6]=>1000000=>[1,7]=>[7,1]
[5,1,2,7,8,3,4,6]=>0000000=>[8]=>[8]
[1,5,2,7,8,3,4,6]=>1000000=>[1,7]=>[7,1]
[1,5,7,2,8,3,4,6]=>1000000=>[1,7]=>[7,1]
[5,1,2,7,3,4,8,6]=>0000000=>[8]=>[8]
[1,5,2,7,3,4,8,6]=>1000000=>[1,7]=>[7,1]
[1,5,7,2,3,4,8,6]=>1000000=>[1,7]=>[7,1]
[5,1,2,3,7,4,8,6]=>0000000=>[8]=>[8]
[1,5,2,3,7,4,8,6]=>1000000=>[1,7]=>[7,1]
[1,2,5,3,7,4,8,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,7,3,4,8,6]=>1100000=>[1,1,6]=>[6,1,1]
[5,1,2,3,7,8,4,6]=>0000000=>[8]=>[8]
[1,5,2,3,7,8,4,6]=>1000000=>[1,7]=>[7,1]
[1,2,5,3,7,8,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,7,3,8,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,7,8,3,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[5,7,1,2,3,4,6,8]=>0000001=>[7,1]=>[7,1]
[1,5,2,7,3,4,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,2,5,7,3,4,6,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,5,2,3,4,7,6,8]=>1000101=>[1,4,2,1]=>[4,2,1,1]
[1,2,3,5,7,4,6,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,5,2,3,4,7,8,6]=>1000100=>[1,4,3]=>[4,3,1]
[1,2,3,5,7,4,8,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,5,7,8,4,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[5,1,2,8,3,4,6,7]=>0000000=>[8]=>[8]
[1,5,2,8,3,4,6,7]=>1000000=>[1,7]=>[7,1]
[1,5,2,3,8,4,6,7]=>1000000=>[1,7]=>[7,1]
[1,2,5,3,8,4,6,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,8,3,4,6,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,2,3,4,8,6,7]=>1000100=>[1,4,3]=>[4,3,1]
[1,2,5,3,4,8,6,7]=>1100100=>[1,1,3,3]=>[3,3,1,1]
[1,2,3,5,4,8,6,7]=>1110100=>[1,1,1,2,3]=>[3,2,1,1,1]
[1,2,3,5,8,4,6,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,5,2,3,4,6,8,7]=>1000110=>[1,4,1,2]=>[4,2,1,1]
[1,2,3,5,6,8,4,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,5,2,3,4,6,7,8]=>1000111=>[1,4,1,1,1]=>[4,1,1,1,1]
[6,1,7,2,8,3,4,5]=>0000000=>[8]=>[8]
[6,1,7,8,2,3,4,5]=>0000000=>[8]=>[8]
[6,7,1,8,2,3,4,5]=>0000000=>[8]=>[8]
[6,7,1,2,3,8,4,5]=>0000000=>[8]=>[8]
[1,6,2,7,3,8,4,5]=>1000000=>[1,7]=>[7,1]
[1,6,7,2,3,8,4,5]=>1000000=>[1,7]=>[7,1]
[1,6,7,2,8,3,4,5]=>1000000=>[1,7]=>[7,1]
[1,6,7,8,2,3,4,5]=>1000000=>[1,7]=>[7,1]
[6,1,2,7,3,4,8,5]=>0000000=>[8]=>[8]
[1,6,2,7,3,4,8,5]=>1000000=>[1,7]=>[7,1]
[1,6,7,2,3,4,8,5]=>1000000=>[1,7]=>[7,1]
[1,6,2,3,7,4,8,5]=>1000000=>[1,7]=>[7,1]
[1,2,6,3,7,4,8,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,7,3,4,8,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,7,3,8,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,7,8,3,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[6,1,7,2,3,4,5,8]=>0000001=>[7,1]=>[7,1]
[1,6,2,7,3,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,7,2,3,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,2,3,4,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,2,6,3,4,7,5,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,2,3,6,4,7,5,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,2,6,3,4,7,8,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,3,6,4,7,8,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,6,7,4,8,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,6,7,8,4,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[6,1,8,2,3,4,5,7]=>0000000=>[8]=>[8]
[6,1,2,8,3,4,5,7]=>0000000=>[8]=>[8]
[1,6,2,8,3,4,5,7]=>1000000=>[1,7]=>[7,1]
[1,6,8,2,3,4,5,7]=>1000000=>[1,7]=>[7,1]
[1,6,2,3,8,4,5,7]=>1000000=>[1,7]=>[7,1]
[1,2,6,3,8,4,5,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,2,3,4,8,5,7]=>1000000=>[1,7]=>[7,1]
[1,2,6,3,4,8,5,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,3,6,4,8,5,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,6,2,3,4,5,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,2,6,3,4,5,8,7]=>1100010=>[1,1,4,2]=>[4,2,1,1]
[1,2,3,6,4,5,8,7]=>1110010=>[1,1,1,3,2]=>[3,2,1,1,1]
[1,2,3,4,6,8,5,7]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,6,2,3,4,5,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,2,6,3,4,5,7,8]=>1100011=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,2,3,6,4,5,7,8]=>1110011=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]
[7,1,2,8,3,4,5,6]=>0000000=>[8]=>[8]
[1,7,2,8,3,4,5,6]=>1000000=>[1,7]=>[7,1]
[1,7,8,2,3,4,5,6]=>1000000=>[1,7]=>[7,1]
[1,2,7,8,3,4,5,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,3,4,8,5,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,3,7,4,8,5,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,8,4,5,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,7,3,4,5,8,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,3,7,4,5,8,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,4,7,5,8,6]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,3,4,7,8,5,6]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,7,3,4,5,6,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,2,3,7,4,5,6,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,2,3,4,7,5,6,8]=>1111001=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]
[1,8,2,3,4,5,6,7]=>1000000=>[1,7]=>[7,1]
[1,2,8,3,4,5,6,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,3,8,4,5,6,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,4,8,5,6,7]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,3,4,5,8,6,7]=>1111100=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]
[5,3,2,6,1,4,8,7]=>0000010=>[6,2]=>[6,2]
[7,3,2,5,4,8,1,6]=>0000000=>[8]=>[8]
[8,4,5,2,3,7,6,1]=>0000000=>[8]=>[8]
[7,4,5,2,3,8,1,6]=>0000000=>[8]=>[8]
[6,4,5,2,3,1,8,7]=>0000010=>[6,2]=>[6,2]
[5,4,6,2,1,3,8,7]=>0000010=>[6,2]=>[6,2]
[3,6,1,5,4,2,8,7]=>0000010=>[6,2]=>[6,2]
[4,6,5,1,3,2,8,7]=>0000010=>[6,2]=>[6,2]
[5,6,4,3,1,2,8,7]=>0000010=>[6,2]=>[6,2]
[7,5,4,3,2,8,1,6]=>0000000=>[8]=>[8]
[8,6,4,3,7,2,5,1]=>0000000=>[8]=>[8]
[7,6,4,3,8,2,1,5]=>0000000=>[8]=>[8]
[6,7,4,3,8,1,2,5]=>0000000=>[8]=>[8]
[5,7,4,3,1,8,2,6]=>0000000=>[8]=>[8]
[4,7,5,1,3,8,2,6]=>0000000=>[8]=>[8]
[3,7,1,5,4,8,2,6]=>0000000=>[8]=>[8]
[2,1,7,5,4,8,3,6]=>0100000=>[2,6]=>[6,2]
[3,8,1,5,4,7,6,2]=>0000000=>[8]=>[8]
[4,8,5,1,3,7,6,2]=>0000000=>[8]=>[8]
[5,8,4,3,1,7,6,2]=>0000000=>[8]=>[8]
[6,8,4,3,7,1,5,2]=>0000000=>[8]=>[8]
[7,8,4,3,6,5,1,2]=>0000000=>[8]=>[8]
[6,8,5,7,3,1,4,2]=>0000000=>[8]=>[8]
[5,8,6,7,1,3,4,2]=>0000000=>[8]=>[8]
[4,8,6,1,7,3,5,2]=>0000000=>[8]=>[8]
[3,8,1,6,7,4,5,2]=>0000000=>[8]=>[8]
[2,1,8,6,7,4,5,3]=>0100000=>[2,6]=>[6,2]
[2,1,7,6,8,4,3,5]=>0100000=>[2,6]=>[6,2]
[3,7,1,6,8,4,2,5]=>0000000=>[8]=>[8]
[4,7,6,1,8,3,2,5]=>0000000=>[8]=>[8]
[5,7,6,8,1,3,2,4]=>0000000=>[8]=>[8]
[5,4,7,2,1,8,3,6]=>0000000=>[8]=>[8]
[6,4,7,2,8,1,3,5]=>0000000=>[8]=>[8]
[7,4,6,2,8,3,1,5]=>0000000=>[8]=>[8]
[8,4,6,2,7,3,5,1]=>0000000=>[8]=>[8]
[8,3,2,6,7,4,5,1]=>0000000=>[8]=>[8]
[7,3,2,6,8,4,1,5]=>0000000=>[8]=>[8]
[6,3,2,7,8,1,4,5]=>0000000=>[8]=>[8]
[5,3,2,7,1,8,4,6]=>0000000=>[8]=>[8]
[4,3,2,1,7,8,5,6]=>0001000=>[4,4]=>[4,4]
[3,4,1,2,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[5,3,2,8,1,7,6,4]=>0000000=>[8]=>[8]
[6,3,2,8,7,1,5,4]=>0000000=>[8]=>[8]
[7,3,2,8,6,5,1,4]=>0000000=>[8]=>[8]
[8,4,7,2,6,5,3,1]=>0000000=>[8]=>[8]
[7,4,8,2,6,5,1,3]=>0000000=>[8]=>[8]
[6,4,8,2,7,1,5,3]=>0000000=>[8]=>[8]
[5,4,8,2,1,7,6,3]=>0000000=>[8]=>[8]
[4,5,8,1,2,7,6,3]=>0000000=>[8]=>[8]
[3,5,1,8,2,7,6,4]=>0000000=>[8]=>[8]
[2,1,5,8,3,7,6,4]=>0100000=>[2,6]=>[6,2]
[2,1,6,8,7,3,5,4]=>0100000=>[2,6]=>[6,2]
[3,6,1,8,7,2,5,4]=>0000000=>[8]=>[8]
[4,6,8,1,7,2,5,3]=>0000000=>[8]=>[8]
[5,6,8,7,1,2,4,3]=>0000000=>[8]=>[8]
[6,5,8,7,2,1,4,3]=>0000000=>[8]=>[8]
[7,5,8,6,2,4,1,3]=>0000000=>[8]=>[8]
[8,5,7,6,2,4,3,1]=>0000000=>[8]=>[8]
[5,7,8,6,1,4,2,3]=>0000000=>[8]=>[8]
[4,7,8,1,6,5,2,3]=>0000000=>[8]=>[8]
[3,7,1,8,6,5,2,4]=>0000000=>[8]=>[8]
[2,1,7,8,6,5,3,4]=>0100000=>[2,6]=>[6,2]
[3,8,1,7,6,5,4,2]=>0000000=>[8]=>[8]
[4,8,7,1,6,5,3,2]=>0000000=>[8]=>[8]
[5,8,7,6,1,4,3,2]=>0000000=>[8]=>[8]
[6,8,7,5,4,1,3,2]=>0000000=>[8]=>[8]
[3,2,5,1,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,2,4,1,3,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[3,2,6,1,4,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,7,1,2,3,6,8]=>0000001=>[7,1]=>[7,1]
[6,2,7,1,3,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,3,7,1,2,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,4,7,1,2,3,5,8]=>0000001=>[7,1]=>[7,1]
[7,4,6,1,2,3,5,8]=>0000001=>[7,1]=>[7,1]
[3,2,8,1,4,5,6,7]=>0000000=>[8]=>[8]
[5,4,8,1,2,3,6,7]=>0000000=>[8]=>[8]
[6,5,8,1,2,3,4,7]=>0000000=>[8]=>[8]
[7,5,8,1,2,3,4,6]=>0000000=>[8]=>[8]
[8,5,7,1,2,3,4,6]=>0000000=>[8]=>[8]
[3,2,5,7,1,4,6,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,7,1,3,5,8]=>0000001=>[7,1]=>[7,1]
[5,2,6,7,1,3,4,8]=>0000001=>[7,1]=>[7,1]
[5,3,6,7,1,2,4,8]=>0000001=>[7,1]=>[7,1]
[3,2,5,8,1,4,6,7]=>0000000=>[8]=>[8]
[4,2,5,8,1,3,6,7]=>0000000=>[8]=>[8]
[4,3,5,8,1,2,6,7]=>0000000=>[8]=>[8]
[5,2,4,8,1,3,6,7]=>0000000=>[8]=>[8]
[3,2,6,8,1,4,5,7]=>0000000=>[8]=>[8]
[5,2,6,8,1,3,4,7]=>0000000=>[8]=>[8]
[6,2,4,8,1,3,5,7]=>0000000=>[8]=>[8]
[6,2,5,8,1,3,4,7]=>0000000=>[8]=>[8]
[3,2,7,8,1,4,5,6]=>0000000=>[8]=>[8]
[4,3,7,8,1,2,5,6]=>0000000=>[8]=>[8]
[5,4,7,8,1,2,3,6]=>0000000=>[8]=>[8]
[6,2,7,8,1,3,4,5]=>0000000=>[8]=>[8]
[6,3,7,8,1,2,4,5]=>0000000=>[8]=>[8]
[6,4,7,8,1,2,3,5]=>0000000=>[8]=>[8]
[7,2,4,8,1,3,5,6]=>0000000=>[8]=>[8]
[7,4,5,8,1,2,3,6]=>0000000=>[8]=>[8]
[8,2,6,7,1,3,4,5]=>0000000=>[8]=>[8]
[8,4,6,7,1,2,3,5]=>0000000=>[8]=>[8]
[4,6,2,5,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,6,3,5,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,6,2,4,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,7,3,5,1,2,6,8]=>0000001=>[7,1]=>[7,1]
[5,7,2,4,1,3,6,8]=>0000001=>[7,1]=>[7,1]
[3,7,2,6,1,4,5,8]=>0000001=>[7,1]=>[7,1]
[5,7,2,6,1,3,4,8]=>0000001=>[7,1]=>[7,1]
[6,7,2,5,1,3,4,8]=>0000001=>[7,1]=>[7,1]
[4,8,2,5,1,3,6,7]=>0000000=>[8]=>[8]
[5,8,3,4,1,2,6,7]=>0000000=>[8]=>[8]
[5,8,3,6,1,2,4,7]=>0000000=>[8]=>[8]
[6,8,3,5,1,2,4,7]=>0000000=>[8]=>[8]
[3,8,2,7,1,4,5,6]=>0000000=>[8]=>[8]
[4,8,2,7,1,3,5,6]=>0000000=>[8]=>[8]
[4,8,3,7,1,2,5,6]=>0000000=>[8]=>[8]
[5,8,2,7,1,3,4,6]=>0000000=>[8]=>[8]
[6,8,2,7,1,3,4,5]=>0000000=>[8]=>[8]
[6,8,3,7,1,2,4,5]=>0000000=>[8]=>[8]
[6,8,5,7,1,2,3,4]=>0000000=>[8]=>[8]
[7,8,2,4,1,3,5,6]=>0000000=>[8]=>[8]
[7,8,2,5,1,3,4,6]=>0000000=>[8]=>[8]
[7,8,4,6,1,2,3,5]=>0000000=>[8]=>[8]
[4,3,2,6,1,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,3,2,6,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,2,6,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,3,2,7,1,5,6,8]=>0000001=>[7,1]=>[7,1]
[5,3,2,7,1,4,6,8]=>0000001=>[7,1]=>[7,1]
[5,4,3,7,1,2,6,8]=>0000001=>[7,1]=>[7,1]
[6,3,2,7,1,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,4,2,7,1,3,5,8]=>0000001=>[7,1]=>[7,1]
[6,4,3,7,1,2,5,8]=>0000001=>[7,1]=>[7,1]
[6,5,3,7,1,2,4,8]=>0000001=>[7,1]=>[7,1]
[7,4,2,5,1,3,6,8]=>0000001=>[7,1]=>[7,1]
[7,4,3,6,1,2,5,8]=>0000001=>[7,1]=>[7,1]
[7,5,2,6,1,3,4,8]=>0000001=>[7,1]=>[7,1]
[7,5,3,6,1,2,4,8]=>0000001=>[7,1]=>[7,1]
[7,6,3,5,1,2,4,8]=>0000001=>[7,1]=>[7,1]
[4,3,2,8,1,5,6,7]=>0000000=>[8]=>[8]
[5,3,2,8,1,4,6,7]=>0000000=>[8]=>[8]
[5,4,3,8,1,2,6,7]=>0000000=>[8]=>[8]
[6,3,2,8,1,4,5,7]=>0000000=>[8]=>[8]
[6,4,3,8,1,2,5,7]=>0000000=>[8]=>[8]
[6,5,2,8,1,3,4,7]=>0000000=>[8]=>[8]
[6,5,3,8,1,2,4,7]=>0000000=>[8]=>[8]
[7,4,2,8,1,3,5,6]=>0000000=>[8]=>[8]
[7,5,3,8,1,2,4,6]=>0000000=>[8]=>[8]
[7,6,2,8,1,3,4,5]=>0000000=>[8]=>[8]
[8,4,2,5,1,3,6,7]=>0000000=>[8]=>[8]
[8,4,2,6,1,3,5,7]=>0000000=>[8]=>[8]
[8,5,3,6,1,2,4,7]=>0000000=>[8]=>[8]
[8,6,2,5,1,3,4,7]=>0000000=>[8]=>[8]
[8,4,2,7,1,3,5,6]=>0000000=>[8]=>[8]
[8,4,3,7,1,2,5,6]=>0000000=>[8]=>[8]
[8,5,2,7,1,3,4,6]=>0000000=>[8]=>[8]
[8,5,3,7,1,2,4,6]=>0000000=>[8]=>[8]
[8,7,2,4,1,3,5,6]=>0000000=>[8]=>[8]
[8,7,2,5,1,3,4,6]=>0000000=>[8]=>[8]
[8,7,3,5,1,2,4,6]=>0000000=>[8]=>[8]
[8,7,2,6,1,3,4,5]=>0000000=>[8]=>[8]
[8,7,3,6,1,2,4,5]=>0000000=>[8]=>[8]
[8,7,4,6,1,2,3,5]=>0000000=>[8]=>[8]
[5,6,2,4,8,1,3,7]=>0000000=>[8]=>[8]
[4,7,3,5,8,1,2,6]=>0000000=>[8]=>[8]
[4,7,3,6,8,1,2,5]=>0000000=>[8]=>[8]
[4,8,3,5,7,1,2,6]=>0000000=>[8]=>[8]
[7,8,2,4,6,1,3,5]=>0000000=>[8]=>[8]
[7,8,3,4,6,1,2,5]=>0000000=>[8]=>[8]
[7,8,2,5,6,1,3,4]=>0000000=>[8]=>[8]
[7,8,3,5,6,1,2,4]=>0000000=>[8]=>[8]
[4,3,2,6,8,1,5,7]=>0000000=>[8]=>[8]
[5,4,2,6,8,1,3,7]=>0000000=>[8]=>[8]
[5,4,3,6,8,1,2,7]=>0000000=>[8]=>[8]
[6,3,2,5,8,1,4,7]=>0000000=>[8]=>[8]
[6,5,2,4,8,1,3,7]=>0000000=>[8]=>[8]
[4,3,2,7,8,1,5,6]=>0000000=>[8]=>[8]
[5,3,2,7,8,1,4,6]=>0000000=>[8]=>[8]
[5,4,2,7,8,1,3,6]=>0000000=>[8]=>[8]
[5,4,3,7,8,1,2,6]=>0000000=>[8]=>[8]
[6,4,2,7,8,1,3,5]=>0000000=>[8]=>[8]
[6,4,3,7,8,1,2,5]=>0000000=>[8]=>[8]
[6,5,2,7,8,1,3,4]=>0000000=>[8]=>[8]
[8,4,2,5,7,1,3,6]=>0000000=>[8]=>[8]
[8,5,2,6,7,1,3,4]=>0000000=>[8]=>[8]
[8,5,3,6,7,1,2,4]=>0000000=>[8]=>[8]
[8,6,2,5,7,1,3,4]=>0000000=>[8]=>[8]
[8,6,3,5,7,1,2,4]=>0000000=>[8]=>[8]
[8,7,2,4,6,1,3,5]=>0000000=>[8]=>[8]
[8,7,3,4,6,1,2,5]=>0000000=>[8]=>[8]
[8,7,2,5,6,1,3,4]=>0000000=>[8]=>[8]
[4,3,7,2,6,1,5,8]=>0000001=>[7,1]=>[7,1]
[5,3,7,2,6,1,4,8]=>0000001=>[7,1]=>[7,1]
[5,4,7,2,6,1,3,8]=>0000001=>[7,1]=>[7,1]
[6,3,7,2,5,1,4,8]=>0000001=>[7,1]=>[7,1]
[6,4,7,2,5,1,3,8]=>0000001=>[7,1]=>[7,1]
[7,3,6,2,5,1,4,8]=>0000001=>[7,1]=>[7,1]
[4,3,8,2,6,1,5,7]=>0000000=>[8]=>[8]
[5,3,8,2,6,1,4,7]=>0000000=>[8]=>[8]
[5,4,8,2,6,1,3,7]=>0000000=>[8]=>[8]
[6,4,8,2,5,1,3,7]=>0000000=>[8]=>[8]
[6,4,8,3,5,1,2,7]=>0000000=>[8]=>[8]
[4,3,8,2,7,1,5,6]=>0000000=>[8]=>[8]
[5,4,8,2,7,1,3,6]=>0000000=>[8]=>[8]
[6,4,8,2,7,1,3,5]=>0000000=>[8]=>[8]
[7,3,8,2,5,1,4,6]=>0000000=>[8]=>[8]
[7,4,8,3,5,1,2,6]=>0000000=>[8]=>[8]
[7,5,8,2,4,1,3,6]=>0000000=>[8]=>[8]
[7,5,8,2,6,1,3,4]=>0000000=>[8]=>[8]
[7,5,8,4,6,1,2,3]=>0000000=>[8]=>[8]
[8,3,6,2,5,1,4,7]=>0000000=>[8]=>[8]
[8,4,6,2,5,1,3,7]=>0000000=>[8]=>[8]
[8,3,7,2,5,1,4,6]=>0000000=>[8]=>[8]
[8,4,7,3,5,1,2,6]=>0000000=>[8]=>[8]
[8,3,7,2,6,1,4,5]=>0000000=>[8]=>[8]
[8,4,7,2,6,1,3,5]=>0000000=>[8]=>[8]
[8,4,7,3,6,1,2,5]=>0000000=>[8]=>[8]
[8,5,7,2,6,1,3,4]=>0000000=>[8]=>[8]
[8,6,7,2,4,1,3,5]=>0000000=>[8]=>[8]
[8,6,7,2,5,1,3,4]=>0000000=>[8]=>[8]
[5,4,3,2,7,1,6,8]=>0000001=>[7,1]=>[7,1]
[6,5,3,2,7,1,4,8]=>0000001=>[7,1]=>[7,1]
[7,5,3,2,6,1,4,8]=>0000001=>[7,1]=>[7,1]
[5,4,3,2,8,1,6,7]=>0000000=>[8]=>[8]
[6,5,3,2,8,1,4,7]=>0000000=>[8]=>[8]
[7,5,3,2,8,1,4,6]=>0000000=>[8]=>[8]
[7,6,4,3,8,1,2,5]=>0000000=>[8]=>[8]
[8,5,3,2,6,1,4,7]=>0000000=>[8]=>[8]
[8,5,4,2,6,1,3,7]=>0000000=>[8]=>[8]
[8,5,3,2,7,1,4,6]=>0000000=>[8]=>[8]
[8,6,3,2,7,1,4,5]=>0000000=>[8]=>[8]
[8,7,5,2,6,1,3,4]=>0000000=>[8]=>[8]
[8,7,6,2,4,1,3,5]=>0000000=>[8]=>[8]
[4,8,3,7,2,6,1,5]=>0000000=>[8]=>[8]
[5,8,3,7,2,6,1,4]=>0000000=>[8]=>[8]
[5,8,4,7,2,6,1,3]=>0000000=>[8]=>[8]
[5,8,4,7,3,6,1,2]=>0000000=>[8]=>[8]
[6,8,3,7,2,5,1,4]=>0000000=>[8]=>[8]
[6,8,4,7,2,5,1,3]=>0000000=>[8]=>[8]
[6,8,4,7,3,5,1,2]=>0000000=>[8]=>[8]
[6,8,5,7,2,4,1,3]=>0000000=>[8]=>[8]
[6,8,5,7,3,4,1,2]=>0000000=>[8]=>[8]
[7,8,3,6,2,5,1,4]=>0000000=>[8]=>[8]
[7,8,4,6,2,5,1,3]=>0000000=>[8]=>[8]
[7,8,4,6,3,5,1,2]=>0000000=>[8]=>[8]
[7,8,5,6,2,4,1,3]=>0000000=>[8]=>[8]
[6,4,3,8,2,7,1,5]=>0000000=>[8]=>[8]
[7,5,3,8,2,6,1,4]=>0000000=>[8]=>[8]
[7,5,4,8,2,6,1,3]=>0000000=>[8]=>[8]
[7,6,3,8,2,5,1,4]=>0000000=>[8]=>[8]
[7,6,4,8,2,5,1,3]=>0000000=>[8]=>[8]
[7,6,5,8,2,4,1,3]=>0000000=>[8]=>[8]
[8,5,3,7,2,6,1,4]=>0000000=>[8]=>[8]
[8,6,4,7,2,5,1,3]=>0000000=>[8]=>[8]
[8,6,4,7,3,5,1,2]=>0000000=>[8]=>[8]
[8,6,5,7,2,4,1,3]=>0000000=>[8]=>[8]
[6,5,4,3,2,8,1,7]=>0000000=>[8]=>[8]
[8,7,6,3,2,5,1,4]=>0000000=>[8]=>[8]
[8,7,6,5,2,4,1,3]=>0000000=>[8]=>[8]
[6,1,2,5,3,8,4,7]=>0000000=>[8]=>[8]
[4,1,2,8,7,3,5,6]=>0000000=>[8]=>[8]
[4,1,2,7,6,3,8,5]=>0000000=>[8]=>[8]
[8,1,2,5,6,3,4,7]=>0000000=>[8]=>[8]
[8,1,2,7,6,3,4,5]=>0000000=>[8]=>[8]
[7,1,2,5,6,3,8,4]=>0000000=>[8]=>[8]
[8,1,2,5,6,7,3,4]=>0000000=>[8]=>[8]
[3,1,7,2,6,4,8,5]=>0000000=>[8]=>[8]
[3,1,8,2,6,7,4,5]=>0000000=>[8]=>[8]
[6,1,4,2,3,8,5,7]=>0000000=>[8]=>[8]
[7,1,5,2,3,4,8,6]=>0000000=>[8]=>[8]
[6,1,5,2,3,8,4,7]=>0000000=>[8]=>[8]
[6,1,5,2,3,7,8,4]=>0000000=>[8]=>[8]
[5,1,4,2,8,3,6,7]=>0000000=>[8]=>[8]
[5,1,4,2,7,3,8,6]=>0000000=>[8]=>[8]
[7,1,4,2,6,3,8,5]=>0000000=>[8]=>[8]
[8,1,5,2,7,3,4,6]=>0000000=>[8]=>[8]
[5,1,4,2,8,7,3,6]=>0000000=>[8]=>[8]
[8,1,4,2,6,7,3,5]=>0000000=>[8]=>[8]
[8,1,5,2,6,7,3,4]=>0000000=>[8]=>[8]
[5,1,4,2,6,7,8,3]=>0000000=>[8]=>[8]
[3,1,8,6,2,4,5,7]=>0000000=>[8]=>[8]
[3,1,8,5,2,7,4,6]=>0000000=>[8]=>[8]
[3,1,8,6,2,7,4,5]=>0000000=>[8]=>[8]
[8,1,4,5,2,3,6,7]=>0000000=>[8]=>[8]
[7,1,8,6,2,3,4,5]=>0000000=>[8]=>[8]
[7,1,6,5,2,3,8,4]=>0000000=>[8]=>[8]
[3,1,4,8,6,2,5,7]=>0000000=>[8]=>[8]
[3,1,7,5,6,2,8,4]=>0000000=>[8]=>[8]
[8,1,4,7,6,2,3,5]=>0000000=>[8]=>[8]
[3,1,8,5,6,7,2,4]=>0000000=>[8]=>[8]
[8,1,4,5,6,7,2,3]=>0000000=>[8]=>[8]
[2,8,1,3,6,7,4,5]=>0000000=>[8]=>[8]
[2,4,1,8,3,7,5,6]=>0000000=>[8]=>[8]
[2,6,1,5,3,8,4,7]=>0000000=>[8]=>[8]
[2,6,1,5,3,7,8,4]=>0000000=>[8]=>[8]
[2,8,1,7,6,3,4,5]=>0000000=>[8]=>[8]
[5,3,1,2,8,4,6,7]=>0000000=>[8]=>[8]
[5,3,1,2,8,7,4,6]=>0000000=>[8]=>[8]
[5,4,1,2,8,3,6,7]=>0000000=>[8]=>[8]
[7,4,1,2,6,3,8,5]=>0000000=>[8]=>[8]
[5,8,1,2,7,3,4,6]=>0000000=>[8]=>[8]
[8,7,1,2,6,3,4,5]=>0000000=>[8]=>[8]
[5,7,1,2,6,3,8,4]=>0000000=>[8]=>[8]
[8,4,1,2,6,7,3,5]=>0000000=>[8]=>[8]
[5,8,1,2,6,7,3,4]=>0000000=>[8]=>[8]
[5,4,1,2,6,7,8,3]=>0000000=>[8]=>[8]
[4,3,1,6,2,8,5,7]=>0000000=>[8]=>[8]
[4,3,1,6,2,7,8,5]=>0000000=>[8]=>[8]
[8,3,1,5,2,4,6,7]=>0000000=>[8]=>[8]
[8,3,1,6,2,4,5,7]=>0000000=>[8]=>[8]
[7,3,1,6,2,4,8,5]=>0000000=>[8]=>[8]
[8,3,1,6,2,7,4,5]=>0000000=>[8]=>[8]
[6,3,1,5,2,7,8,4]=>0000000=>[8]=>[8]
[7,4,1,5,2,3,8,6]=>0000000=>[8]=>[8]
[8,4,1,6,2,3,5,7]=>0000000=>[8]=>[8]
[7,4,1,8,2,3,5,6]=>0000000=>[8]=>[8]
[7,4,1,6,2,3,8,5]=>0000000=>[8]=>[8]
[8,7,1,6,2,3,4,5]=>0000000=>[8]=>[8]
[6,7,1,5,2,3,8,4]=>0000000=>[8]=>[8]
[6,8,1,5,2,7,3,4]=>0000000=>[8]=>[8]
[6,4,1,5,2,7,8,3]=>0000000=>[8]=>[8]
[4,3,1,8,7,2,5,6]=>0000000=>[8]=>[8]
[8,3,1,5,6,2,4,7]=>0000000=>[8]=>[8]
[8,3,1,5,7,2,4,6]=>0000000=>[8]=>[8]
[7,3,1,5,6,2,8,4]=>0000000=>[8]=>[8]
[7,8,1,5,6,2,3,4]=>0000000=>[8]=>[8]
[8,4,1,5,6,7,2,3]=>0000000=>[8]=>[8]
[2,3,7,1,6,4,8,5]=>0000000=>[8]=>[8]
[2,3,5,1,8,7,4,6]=>0000000=>[8]=>[8]
[2,8,4,1,3,5,6,7]=>0000000=>[8]=>[8]
[2,6,4,1,3,7,8,5]=>0000000=>[8]=>[8]
[2,6,5,1,3,7,8,4]=>0000000=>[8]=>[8]
[2,7,4,1,6,3,8,5]=>0000000=>[8]=>[8]
[2,8,5,1,7,3,4,6]=>0000000=>[8]=>[8]
[2,7,5,1,6,3,8,4]=>0000000=>[8]=>[8]
[6,3,4,1,2,7,8,5]=>0000000=>[8]=>[8]
[7,3,5,1,2,4,8,6]=>0000000=>[8]=>[8]
[6,3,7,1,2,4,8,5]=>0000000=>[8]=>[8]
[6,3,8,1,2,7,4,5]=>0000000=>[8]=>[8]
[6,7,4,1,2,3,8,5]=>0000000=>[8]=>[8]
[6,8,5,1,2,3,4,7]=>0000000=>[8]=>[8]
[8,5,4,1,2,7,3,6]=>0000000=>[8]=>[8]
[6,8,4,1,2,7,3,5]=>0000000=>[8]=>[8]
[6,8,5,1,2,7,3,4]=>0000000=>[8]=>[8]
[8,3,4,1,7,2,5,6]=>0000000=>[8]=>[8]
[8,3,5,1,6,2,4,7]=>0000000=>[8]=>[8]
[7,3,8,1,6,2,4,5]=>0000000=>[8]=>[8]
[8,5,4,1,6,2,3,7]=>0000000=>[8]=>[8]
[7,8,4,1,6,2,3,5]=>0000000=>[8]=>[8]
[7,8,5,1,6,2,3,4]=>0000000=>[8]=>[8]
[5,3,4,1,6,7,8,2]=>0000000=>[8]=>[8]
[2,3,7,6,1,4,8,5]=>0000000=>[8]=>[8]
[2,3,6,5,1,8,4,7]=>0000000=>[8]=>[8]
[2,3,6,5,1,7,8,4]=>0000000=>[8]=>[8]
[2,7,4,8,1,3,5,6]=>0000000=>[8]=>[8]
[2,7,4,6,1,3,8,5]=>0000000=>[8]=>[8]
[2,7,6,5,1,3,8,4]=>0000000=>[8]=>[8]
[2,6,4,5,1,8,3,7]=>0000000=>[8]=>[8]
[2,8,4,6,1,7,3,5]=>0000000=>[8]=>[8]
[7,3,8,5,1,2,4,6]=>0000000=>[8]=>[8]
[8,6,4,5,1,7,2,3]=>0000000=>[8]=>[8]
[2,3,8,5,7,1,4,6]=>0000000=>[8]=>[8]
[2,3,7,5,6,1,8,4]=>0000000=>[8]=>[8]
[2,8,4,7,6,1,3,5]=>0000000=>[8]=>[8]
[2,8,7,5,6,1,3,4]=>0000000=>[8]=>[8]
[8,3,7,5,6,1,2,4]=>0000000=>[8]=>[8]
[2,8,4,5,6,7,1,3]=>0000000=>[8]=>[8]
[6,5,8,7,3,4,1,2]=>0000000=>[8]=>[8]
[4,6,7,3,8,5,1,2]=>0000000=>[8]=>[8]
[3,6,7,4,5,8,1,2]=>0000000=>[8]=>[8]
[2,6,7,4,5,1,8,3]=>0000000=>[8]=>[8]
[1,6,7,4,5,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,4,7,6,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,5,4,7,6,1,8,3]=>0000000=>[8]=>[8]
[3,5,4,7,6,8,1,2]=>0000000=>[8]=>[8]
[4,5,3,7,8,6,1,2]=>0000000=>[8]=>[8]
[5,4,3,8,7,6,1,2]=>0000000=>[8]=>[8]
[6,4,8,3,7,5,1,2]=>0000000=>[8]=>[8]
[6,3,8,4,5,7,1,2]=>0000000=>[8]=>[8]
[5,3,4,8,6,7,1,2]=>0000000=>[8]=>[8]
[4,3,5,6,8,7,1,2]=>0000000=>[8]=>[8]
[3,2,5,6,1,8,7,4]=>0000000=>[8]=>[8]
[4,2,5,6,8,1,7,3]=>0000000=>[8]=>[8]
[5,2,4,8,6,1,7,3]=>0000000=>[8]=>[8]
[6,2,8,4,5,1,7,3]=>0000000=>[8]=>[8]
[7,8,2,4,5,1,6,3]=>0000000=>[8]=>[8]
[7,8,1,4,5,2,3,6]=>0000000=>[8]=>[8]
[6,1,8,4,5,2,3,7]=>0000000=>[8]=>[8]
[5,1,4,8,6,2,3,7]=>0000000=>[8]=>[8]
[4,1,3,2,8,6,5,7]=>0001000=>[4,4]=>[4,4]
[5,1,3,8,2,6,4,7]=>0000000=>[8]=>[8]
[6,1,8,3,2,5,4,7]=>0000000=>[8]=>[8]
[7,8,1,3,2,5,4,6]=>0000000=>[8]=>[8]
[7,8,2,3,1,5,6,4]=>0000000=>[8]=>[8]
[6,2,8,3,1,5,7,4]=>0000000=>[8]=>[8]
[5,2,3,8,1,6,7,4]=>0000000=>[8]=>[8]
[6,3,8,2,1,7,5,4]=>0000000=>[8]=>[8]
[7,8,3,2,1,6,5,4]=>0000000=>[8]=>[8]
[7,8,4,2,6,1,5,3]=>0000000=>[8]=>[8]
[5,4,2,8,7,1,6,3]=>0000000=>[8]=>[8]
[4,5,2,7,8,1,6,3]=>0000000=>[8]=>[8]
[3,5,2,7,1,8,6,4]=>0000000=>[8]=>[8]
[2,5,3,7,1,6,8,4]=>0000000=>[8]=>[8]
[1,5,3,7,2,6,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,7,3,2,5,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,6,7,3,1,5,8,4]=>0000000=>[8]=>[8]
[3,6,7,2,1,8,5,4]=>0000000=>[8]=>[8]
[4,6,7,2,8,1,5,3]=>0000000=>[8]=>[8]
[5,6,7,8,2,1,4,3]=>0000000=>[8]=>[8]
[7,8,5,6,2,1,4,3]=>0000000=>[8]=>[8]
[6,5,8,7,1,2,3,4]=>0000000=>[8]=>[8]
[5,4,1,8,7,2,3,6]=>0000000=>[8]=>[8]
[6,4,8,1,7,2,3,5]=>0000000=>[8]=>[8]
[7,8,3,1,2,6,4,5]=>0000000=>[8]=>[8]
[5,3,1,8,2,7,4,6]=>0000000=>[8]=>[8]
[4,3,1,2,8,7,5,6]=>0001000=>[4,4]=>[4,4]
[4,2,1,3,8,5,7,6]=>0001000=>[4,4]=>[4,4]
[5,2,1,8,3,4,7,6]=>0000000=>[8]=>[8]
[6,2,8,1,3,4,7,5]=>0000000=>[8]=>[8]
[7,8,2,1,3,4,6,5]=>0000000=>[8]=>[8]
[4,5,2,3,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[6,4,3,7,2,5,1,8]=>0000001=>[7,1]=>[7,1]
[8,4,3,6,5,1,2,7]=>0000000=>[8]=>[8]
[1,5,6,3,4,8,7,2]=>1000000=>[1,7]=>[7,1]
[4,6,2,7,3,5,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,7,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[4,1,2,6,5,8,7,3]=>0000000=>[8]=>[8]
[5,1,6,2,4,8,7,3]=>0000000=>[8]=>[8]
[8,1,5,4,7,6,2,3]=>0000000=>[8]=>[8]
[1,8,6,7,4,5,3,2]=>1000000=>[1,7]=>[7,1]
[8,1,6,7,4,5,2,3]=>0000000=>[8]=>[8]
[6,1,7,8,2,4,5,3]=>0000000=>[8]=>[8]
[5,1,7,2,8,4,6,3]=>0000000=>[8]=>[8]
[4,1,2,7,8,5,6,3]=>0000000=>[8]=>[8]
[3,2,1,7,8,5,6,4]=>0010000=>[3,5]=>[5,3]
[4,8,2,7,1,5,3,6]=>0000000=>[8]=>[8]
[5,8,7,2,1,4,3,6]=>0000000=>[8]=>[8]
[6,8,7,1,2,4,3,5]=>0000000=>[8]=>[8]
[8,7,6,1,4,3,2,5]=>0000000=>[8]=>[8]
[1,6,7,8,3,4,5,2]=>1000000=>[1,7]=>[7,1]
[7,6,8,1,3,2,4,5]=>0000000=>[8]=>[8]
[5,7,8,2,1,3,4,6]=>0000000=>[8]=>[8]
[4,7,2,8,1,3,5,6]=>0000000=>[8]=>[8]
[3,2,6,8,4,1,5,7]=>0000000=>[8]=>[8]
[4,6,2,8,3,1,5,7]=>0000000=>[8]=>[8]
[5,6,8,2,3,1,4,7]=>0000000=>[8]=>[8]
[7,5,8,3,1,2,4,6]=>0000000=>[8]=>[8]
[1,5,7,3,8,4,6,2]=>1000000=>[1,7]=>[7,1]
[1,4,3,7,8,5,6,2]=>1000000=>[1,7]=>[7,1]
[6,4,3,8,2,1,5,7]=>0000000=>[8]=>[8]
[4,5,2,3,8,1,6,7]=>0000000=>[8]=>[8]
[3,2,5,4,8,1,6,7]=>0000000=>[8]=>[8]
[4,5,2,3,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[6,4,3,1,2,8,7,5]=>0000000=>[8]=>[8]
[7,4,3,1,8,2,6,5]=>0000000=>[8]=>[8]
[8,4,3,1,7,6,2,5]=>0000000=>[8]=>[8]
[1,5,8,3,7,6,4,2]=>1000000=>[1,7]=>[7,1]
[7,5,1,3,8,2,6,4]=>0000000=>[8]=>[8]
[5,6,1,2,3,8,7,4]=>0000000=>[8]=>[8]
[4,6,2,1,3,8,7,5]=>0000000=>[8]=>[8]
[3,2,6,1,4,8,7,5]=>0000000=>[8]=>[8]
[3,2,7,1,8,4,6,5]=>0000000=>[8]=>[8]
[5,7,1,2,8,3,6,4]=>0000000=>[8]=>[8]
[6,7,1,8,2,3,5,4]=>0000000=>[8]=>[8]
[7,6,1,8,3,2,5,4]=>0000000=>[8]=>[8]
[8,7,1,6,5,3,2,4]=>0000000=>[8]=>[8]
[7,8,1,6,5,2,3,4]=>0000000=>[8]=>[8]
[6,8,1,7,2,5,3,4]=>0000000=>[8]=>[8]
[5,8,1,2,7,6,3,4]=>0000000=>[8]=>[8]
[3,2,8,1,7,6,4,5]=>0000000=>[8]=>[8]
[4,1,2,8,7,6,5,3]=>0000000=>[8]=>[8]
[5,1,8,2,7,6,4,3]=>0000000=>[8]=>[8]
[6,1,8,7,2,5,4,3]=>0000000=>[8]=>[8]
[8,1,7,6,5,4,2,3]=>0000000=>[8]=>[8]
[3,2,5,4,7,1,8,6]=>0000000=>[8]=>[8]
[4,2,5,3,6,1,8,7]=>0000010=>[6,2]=>[6,2]
[4,3,5,2,7,1,8,6]=>0000000=>[8]=>[8]
[4,1,5,3,7,2,8,6]=>0000000=>[8]=>[8]
[2,1,5,4,7,3,8,6]=>0100000=>[2,6]=>[6,2]
[4,3,6,5,7,1,8,2]=>0000000=>[8]=>[8]
[4,1,6,3,7,5,8,2]=>0000000=>[8]=>[8]
[2,1,6,4,7,3,8,5]=>0100000=>[2,6]=>[6,2]
[3,1,6,4,7,2,8,5]=>0000000=>[8]=>[8]
[4,1,6,3,7,2,8,5]=>0000000=>[8]=>[8]
[5,2,6,3,7,1,8,4]=>0000000=>[8]=>[8]
[4,2,6,1,7,3,8,5]=>0000000=>[8]=>[8]
[4,2,6,3,7,1,8,5]=>0000000=>[8]=>[8]
[3,2,6,4,7,1,8,5]=>0000000=>[8]=>[8]
[3,2,6,1,7,4,8,5]=>0000000=>[8]=>[8]
[3,1,4,2,7,6,8,5]=>0001000=>[4,4]=>[4,4]
[3,2,6,1,7,5,8,4]=>0000000=>[8]=>[8]
[4,2,6,1,7,5,8,3]=>0000000=>[8]=>[8]
[4,1,6,2,7,5,8,3]=>0000000=>[8]=>[8]
[5,4,6,2,7,1,8,3]=>0000000=>[8]=>[8]
[3,1,6,5,7,2,8,4]=>0000000=>[8]=>[8]
[4,1,6,5,7,3,8,2]=>0000000=>[8]=>[8]
[8,6,1,3,4,2,5,7]=>0000000=>[8]=>[8]
[8,3,5,2,1,6,4,7]=>0000000=>[8]=>[8]
[8,6,3,5,2,4,1,7]=>0000000=>[8]=>[8]
[8,3,7,5,2,4,6,1]=>0000000=>[8]=>[8]
[2,4,5,7,3,1,8,6]=>0000000=>[8]=>[8]
[8,2,4,6,5,3,1,7]=>0000000=>[8]=>[8]
[8,1,2,4,5,6,3,7]=>0000000=>[8]=>[8]
[8,2,5,1,3,6,4,7]=>0000000=>[8]=>[8]
[8,1,5,6,4,3,2,7]=>0000000=>[8]=>[8]
[8,5,7,4,3,2,6,1]=>0000000=>[8]=>[8]
[8,5,7,4,2,1,6,3]=>0000000=>[8]=>[8]
[1,7,4,8,6,3,5,2]=>1000000=>[1,7]=>[7,1]
[8,4,7,6,3,5,2,1]=>0000000=>[8]=>[8]
[4,8,1,6,7,3,5,2]=>0000000=>[8]=>[8]
[3,6,4,1,8,7,5,2]=>0000000=>[8]=>[8]
[8,2,6,1,4,7,5,3]=>0000000=>[8]=>[8]
[3,7,6,5,8,2,1,4]=>0000000=>[8]=>[8]
[3,6,8,5,7,2,4,1]=>0000000=>[8]=>[8]
[2,1,6,5,7,8,3,4]=>0100000=>[2,6]=>[6,2]
[5,2,7,1,3,8,4,6]=>0000000=>[8]=>[8]
[5,3,1,7,8,2,4,6]=>0000000=>[8]=>[8]
[3,7,2,6,4,8,1,5]=>0000000=>[8]=>[8]
[3,2,6,1,4,7,8,5]=>0000000=>[8]=>[8]
[5,3,7,2,1,8,4,6]=>0000000=>[8]=>[8]
[4,7,3,2,1,5,8,6]=>0000000=>[8]=>[8]
[1,7,3,4,2,5,8,6]=>1000000=>[1,7]=>[7,1]
[4,7,2,1,3,5,8,6]=>0000000=>[8]=>[8]
[8,7,6,1,3,4,2,5]=>0000000=>[8]=>[8]
[8,5,7,3,2,1,6,4]=>0000000=>[8]=>[8]
[8,7,6,3,5,2,4,1]=>0000000=>[8]=>[8]
[2,7,4,8,1,6,5,3]=>0000000=>[8]=>[8]
[4,6,8,2,1,7,5,3]=>0000000=>[8]=>[8]
[8,5,3,7,1,6,2,4]=>0000000=>[8]=>[8]
[8,5,7,2,1,3,6,4]=>0000000=>[8]=>[8]
[4,6,1,8,7,2,5,3]=>0000000=>[8]=>[8]
[8,1,2,5,6,7,4,3]=>0000000=>[8]=>[8]
[8,2,6,5,7,4,1,3]=>0000000=>[8]=>[8]
[1,7,2,5,8,6,4,3]=>1000000=>[1,7]=>[7,1]
[3,7,8,1,6,5,2,4]=>0000000=>[8]=>[8]
[8,7,6,3,5,1,4,2]=>0000000=>[8]=>[8]
[8,4,7,6,5,1,3,2]=>0000000=>[8]=>[8]
[8,7,1,5,6,4,3,2]=>0000000=>[8]=>[8]
[8,1,6,7,5,4,3,2]=>0000000=>[8]=>[8]
[3,2,5,1,6,8,4,7]=>0000000=>[8]=>[8]
[3,6,2,5,4,8,1,7]=>0000000=>[8]=>[8]
[3,5,2,4,7,1,8,6]=>0000000=>[8]=>[8]
[3,5,8,2,4,7,6,1]=>0000000=>[8]=>[8]
[4,2,6,5,3,8,1,7]=>0000000=>[8]=>[8]
[5,3,1,6,8,2,4,7]=>0000000=>[8]=>[8]
[5,6,2,8,1,3,4,7]=>0000000=>[8]=>[8]
[5,4,3,2,7,1,8,6]=>0000000=>[8]=>[8]
[5,4,3,8,2,7,6,1]=>0000000=>[8]=>[8]
[4,3,6,2,8,7,5,1]=>0000000=>[8]=>[8]
[6,4,3,1,7,2,8,5]=>0000000=>[8]=>[8]
[1,4,7,5,8,3,2,6]=>1000000=>[1,7]=>[7,1]
[2,8,5,7,4,6,1,3]=>0000000=>[8]=>[8]
[3,5,8,7,1,4,6,2]=>0000000=>[8]=>[8]
[4,3,7,1,8,6,5,2]=>0000000=>[8]=>[8]
[4,8,3,7,6,5,2,1]=>0000000=>[8]=>[8]
[7,5,3,1,8,6,4,2]=>0000000=>[8]=>[8]
[1,5,8,6,3,7,4,2]=>1000000=>[1,7]=>[7,1]
[6,2,8,7,4,5,1,3]=>0000000=>[8]=>[8]
[6,1,7,5,3,2,8,4]=>0000000=>[8]=>[8]
[6,5,2,1,7,3,8,4]=>0000000=>[8]=>[8]
[6,1,7,4,2,8,3,5]=>0000000=>[8]=>[8]
[6,7,2,1,8,3,4,5]=>0000000=>[8]=>[8]
[7,5,8,2,1,3,4,6]=>0000000=>[8]=>[8]
[5,7,3,1,8,2,4,6]=>0000000=>[8]=>[8]
[4,7,1,5,2,8,3,6]=>0000000=>[8]=>[8]
[2,4,8,6,3,7,5,1]=>0000000=>[8]=>[8]
[3,5,2,7,1,8,4,6]=>0000000=>[8]=>[8]
[4,3,7,8,2,1,5,6]=>0000000=>[8]=>[8]
[8,3,7,1,4,6,2,5]=>0000000=>[8]=>[8]
[3,8,2,5,7,1,6,4]=>0000000=>[8]=>[8]
[7,8,3,6,2,1,5,4]=>0000000=>[8]=>[8]
[8,7,3,6,2,5,4,1]=>0000000=>[8]=>[8]
[4,2,6,8,1,7,5,3]=>0000000=>[8]=>[8]
[5,4,8,2,7,1,6,3]=>0000000=>[8]=>[8]
[5,8,3,7,1,6,2,4]=>0000000=>[8]=>[8]
[5,8,7,2,6,1,3,4]=>0000000=>[8]=>[8]
[8,6,2,7,5,1,3,4]=>0000000=>[8]=>[8]
[6,4,8,1,7,2,5,3]=>0000000=>[8]=>[8]
[5,1,6,8,2,7,4,3]=>0000000=>[8]=>[8]
[6,5,2,8,1,7,4,3]=>0000000=>[8]=>[8]
[5,2,7,1,8,6,4,3]=>0000000=>[8]=>[8]
[5,8,2,7,6,4,3,1]=>0000000=>[8]=>[8]
[6,1,7,2,8,5,4,3]=>0000000=>[8]=>[8]
[4,7,1,8,6,2,5,3]=>0000000=>[8]=>[8]
[8,7,4,6,1,5,3,2]=>0000000=>[8]=>[8]
[8,5,7,1,6,4,3,2]=>0000000=>[8]=>[8]
[6,8,1,7,5,4,3,2]=>0000000=>[8]=>[8]
[7,1,8,6,5,4,3,2]=>0000000=>[8]=>[8]
[4,3,5,6,1,2,8,7]=>0000010=>[6,2]=>[6,2]
[6,5,2,7,1,8,3,4]=>0000000=>[8]=>[8]
[3,5,2,6,4,1,8,7]=>0000010=>[6,2]=>[6,2]
[2,1,6,3,5,4,8,7]=>0100010=>[2,4,2]=>[4,2,2]
[5,3,1,4,6,2,8,7]=>0000010=>[6,2]=>[6,2]
[3,4,7,8,5,2,1,6]=>0000000=>[8]=>[8]
[2,4,6,3,7,5,8,1]=>0000000=>[8]=>[8]
[4,1,6,3,8,5,7,2]=>0000000=>[8]=>[8]
[3,7,4,2,8,6,5,1]=>0000000=>[8]=>[8]
[2,1,5,7,4,8,6,3]=>0100000=>[2,6]=>[6,2]
[3,1,8,2,7,6,5,4]=>0000000=>[8]=>[8]
[4,3,7,2,6,8,5,1]=>0000000=>[8]=>[8]
[8,1,2,3,5,6,7,4]=>0000000=>[8]=>[8]
[7,8,2,4,3,6,1,5]=>0000000=>[8]=>[8]
[2,1,7,8,5,4,3,6]=>0100000=>[2,6]=>[6,2]
[5,7,3,8,1,4,2,6]=>0000000=>[8]=>[8]
[8,3,6,1,4,2,7,5]=>0000000=>[8]=>[8]
[4,1,3,2,8,5,7,6]=>0001000=>[4,4]=>[4,4]
[2,1,4,3,8,5,7,6]=>0101000=>[2,2,4]=>[4,2,2]
[4,1,3,2,6,7,8,5]=>0001000=>[4,4]=>[4,4]
[5,3,6,1,8,7,2,4]=>0000000=>[8]=>[8]
[5,6,2,8,7,4,1,3]=>0000000=>[8]=>[8]
[7,8,5,6,1,4,2,3]=>0000000=>[8]=>[8]
[8,1,6,4,5,7,2,3]=>0000000=>[8]=>[8]
[2,1,8,6,5,7,3,4]=>0100000=>[2,6]=>[6,2]
[2,1,7,5,3,6,8,4]=>0100000=>[2,6]=>[6,2]
[4,1,2,5,8,6,7,3]=>0000000=>[8]=>[8]
[3,1,4,5,6,8,7,2]=>0000000=>[8]=>[8]
[6,3,1,5,2,4,8,7]=>0000010=>[6,2]=>[6,2]
[3,1,6,5,4,2,8,7]=>0000010=>[6,2]=>[6,2]
[5,1,7,3,8,4,6,2]=>0000000=>[8]=>[8]
[2,5,7,3,8,6,4,1]=>0000000=>[8]=>[8]
[5,6,3,7,4,8,1,2]=>0000000=>[8]=>[8]
[2,1,6,7,4,8,5,3]=>0100000=>[2,6]=>[6,2]
[2,8,6,3,1,5,7,4]=>0000000=>[8]=>[8]
[8,1,6,3,2,5,4,7]=>0000000=>[8]=>[8]
[2,8,4,1,6,3,7,5]=>0000000=>[8]=>[8]
[4,8,1,2,7,6,3,5]=>0000000=>[8]=>[8]
[6,5,3,2,8,7,1,4]=>0000000=>[8]=>[8]
[2,4,1,8,7,6,5,3]=>0000000=>[8]=>[8]
[4,1,2,8,7,5,6,3]=>0000000=>[8]=>[8]
[8,4,2,1,7,5,3,6]=>0000000=>[8]=>[8]
[4,3,1,8,6,7,5,2]=>0000000=>[8]=>[8]
[6,4,3,5,8,1,7,2]=>0000000=>[8]=>[8]
[5,7,3,6,1,8,2,4]=>0000000=>[8]=>[8]
[8,6,2,5,1,7,4,3]=>0000000=>[8]=>[8]
[7,5,2,8,3,4,6,1]=>0000000=>[8]=>[8]
[4,7,2,8,1,5,3,6]=>0000000=>[8]=>[8]
[8,7,2,1,4,5,6,3]=>0000000=>[8]=>[8]
[3,6,8,7,1,5,4,2]=>0000000=>[8]=>[8]
[5,7,8,6,3,4,1,2]=>0000000=>[8]=>[8]
[5,7,3,8,1,4,6,2]=>0000000=>[8]=>[8]
[2,1,7,8,5,4,6,3]=>0100000=>[2,6]=>[6,2]
[8,4,1,3,7,2,6,5]=>0000000=>[8]=>[8]
[4,3,8,2,5,1,7,6]=>0000000=>[8]=>[8]
[2,1,4,8,3,5,7,6]=>0100000=>[2,6]=>[6,2]
[7,8,5,6,1,4,3,2]=>0000000=>[8]=>[8]
[7,8,4,2,1,5,3,6]=>0000000=>[8]=>[8]
[7,8,2,1,6,5,3,4]=>0000000=>[8]=>[8]
[6,4,1,2,5,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,3,8,1,7,2,5,6]=>0000000=>[8]=>[8]
[6,3,1,4,7,2,5,8]=>0000001=>[7,1]=>[7,1]
[7,8,1,4,6,2,5,3]=>0000000=>[8]=>[8]
[7,8,3,5,4,2,1,6]=>0000000=>[8]=>[8]
[7,8,4,1,2,3,6,5]=>0000000=>[8]=>[8]
[7,8,2,6,4,1,3,5]=>0000000=>[8]=>[8]
[7,8,1,6,5,4,3,2]=>0000000=>[8]=>[8]
[1,3,8,2,6,4,7,5]=>1000000=>[1,7]=>[7,1]
[5,3,7,1,6,4,8,2]=>0000000=>[8]=>[8]
[6,1,2,5,8,7,4,3]=>0000000=>[8]=>[8]
[6,3,1,8,4,2,7,5]=>0000000=>[8]=>[8]
[6,4,2,1,5,3,8,7]=>0000010=>[6,2]=>[6,2]
[6,4,3,7,5,8,1,2]=>0000000=>[8]=>[8]
[2,4,7,1,5,3,6,8]=>0000001=>[7,1]=>[7,1]
[3,7,2,8,6,4,1,5]=>0000000=>[8]=>[8]
[3,8,1,7,6,4,5,2]=>0000000=>[8]=>[8]
[2,7,5,8,3,6,1,4]=>0000000=>[8]=>[8]
[1,5,6,8,2,4,7,3]=>1000000=>[1,7]=>[7,1]
[2,6,1,4,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[3,6,8,4,7,5,1,2]=>0000000=>[8]=>[8]
[5,6,7,3,8,4,1,2]=>0000000=>[8]=>[8]
[4,5,7,6,1,8,3,2]=>0000000=>[8]=>[8]
[4,7,5,6,3,1,8,2]=>0000000=>[8]=>[8]
[5,1,6,3,4,2,8,7]=>0000010=>[6,2]=>[6,2]
[5,7,1,4,2,3,8,6]=>0000000=>[8]=>[8]
[5,7,6,4,3,8,1,2]=>0000000=>[8]=>[8]
[6,3,4,5,8,7,1,2]=>0000000=>[8]=>[8]
[6,2,4,1,8,3,7,5]=>0000000=>[8]=>[8]
[6,2,3,5,4,8,1,7]=>0000000=>[8]=>[8]
[5,1,4,2,7,6,8,3]=>0000000=>[8]=>[8]
[1,6,2,4,7,8,3,5]=>1000000=>[1,7]=>[7,1]
[6,1,4,2,8,5,3,7]=>0000000=>[8]=>[8]
[6,7,5,8,1,4,3,2]=>0000000=>[8]=>[8]
[5,8,7,6,3,4,1,2]=>0000000=>[8]=>[8]
[5,8,7,6,2,3,1,4]=>0000000=>[8]=>[8]
[4,1,7,2,6,5,3,8]=>0000001=>[7,1]=>[7,1]
[4,2,7,8,1,6,3,5]=>0000000=>[8]=>[8]
[2,1,8,7,6,5,3,4]=>0100000=>[2,6]=>[6,2]
[4,2,7,1,6,3,8,5]=>0000000=>[8]=>[8]
[4,3,7,5,6,8,1,2]=>0000000=>[8]=>[8]
[3,8,6,5,2,4,1,7]=>0000000=>[8]=>[8]
[3,8,5,6,1,4,7,2]=>0000000=>[8]=>[8]
[5,3,7,8,2,1,6,4]=>0000000=>[8]=>[8]
[5,2,8,7,1,6,4,3]=>0000000=>[8]=>[8]
[3,6,7,8,5,1,4,2]=>0000000=>[8]=>[8]
[3,7,8,5,1,2,4,6]=>0000000=>[8]=>[8]
[4,1,8,6,2,3,5,7]=>0000000=>[8]=>[8]
[3,8,7,6,5,4,1,2]=>0000000=>[8]=>[8]
[2,8,6,7,5,1,3,4]=>0000000=>[8]=>[8]
[5,3,7,8,2,1,4,6]=>0000000=>[8]=>[8]
[7,6,1,2,5,8,3,4]=>0000000=>[8]=>[8]
[2,1,7,8,4,3,5,6]=>0100000=>[2,6]=>[6,2]
[7,8,1,2,5,4,6,3]=>0000000=>[8]=>[8]
[8,4,1,3,7,6,2,5]=>0000000=>[8]=>[8]
[4,7,2,8,1,3,6,5]=>0000000=>[8]=>[8]
[7,3,8,6,1,2,5,4]=>0000000=>[8]=>[8]
[3,4,7,1,8,2,6,5]=>0000000=>[8]=>[8]
[1,8,2,4,3,5,6,7]=>1000000=>[1,7]=>[7,1]
[1,7,2,4,3,5,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,2,4,3,6,7,8]=>1000111=>[1,4,1,1,1]=>[4,1,1,1,1]
[1,7,2,5,3,4,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,2,5,3,4,6,7]=>1000000=>[1,7]=>[7,1]
[1,8,2,6,3,4,5,7]=>1000000=>[1,7]=>[7,1]
[1,8,2,7,3,4,5,6]=>1000000=>[1,7]=>[7,1]
[1,8,2,7,3,5,4,6]=>1000000=>[1,7]=>[7,1]
[1,7,2,8,3,5,4,6]=>1000000=>[1,7]=>[7,1]
[1,6,2,8,3,5,4,7]=>1000000=>[1,7]=>[7,1]
[1,5,2,8,3,6,4,7]=>1000000=>[1,7]=>[7,1]
[1,4,2,8,3,6,5,7]=>1000000=>[1,7]=>[7,1]
[1,3,2,8,4,6,5,7]=>1010000=>[1,2,5]=>[5,2,1]
[1,2,3,8,4,6,5,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,4,6,5,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,3,2,7,4,6,5,8]=>1010001=>[1,2,4,1]=>[4,2,1,1]
[1,4,2,7,3,6,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,2,7,3,6,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,2,7,3,5,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,2,6,3,5,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,2,6,3,5,4,7]=>1000000=>[1,7]=>[7,1]
[1,8,2,5,3,6,4,7]=>1000000=>[1,7]=>[7,1]
[1,7,2,5,3,6,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,2,5,3,7,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,2,4,3,7,6,8]=>1000101=>[1,4,2,1]=>[4,2,1,1]
[1,6,2,4,3,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,2,4,3,6,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,2,4,3,6,5,7]=>1000000=>[1,7]=>[7,1]
[1,8,2,4,3,7,5,6]=>1000000=>[1,7]=>[7,1]
[1,7,2,4,3,8,5,6]=>1000000=>[1,7]=>[7,1]
[1,6,2,4,3,8,5,7]=>1000000=>[1,7]=>[7,1]
[1,5,2,4,3,8,6,7]=>1000100=>[1,4,3]=>[4,3,1]
[1,6,2,5,3,8,4,7]=>1000000=>[1,7]=>[7,1]
[1,7,2,5,3,8,4,6]=>1000000=>[1,7]=>[7,1]
[1,8,2,5,3,7,4,6]=>1000000=>[1,7]=>[7,1]
[1,8,2,6,3,7,4,5]=>1000000=>[1,7]=>[7,1]
[1,7,2,6,3,8,4,5]=>1000000=>[1,7]=>[7,1]
[1,2,3,8,4,7,5,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,3,2,8,4,7,5,6]=>1010000=>[1,2,5]=>[5,2,1]
[1,4,2,8,3,7,5,6]=>1000000=>[1,7]=>[7,1]
[1,5,2,8,3,7,4,6]=>1000000=>[1,7]=>[7,1]
[1,6,2,8,3,7,4,5]=>1000000=>[1,7]=>[7,1]
[1,7,2,8,3,6,4,5]=>1000000=>[1,7]=>[7,1]
[1,8,2,7,3,6,4,5]=>1000000=>[1,7]=>[7,1]
[2,8,4,1,6,5,3,7]=>0000000=>[8]=>[8]
[7,2,8,5,1,6,4,3]=>0000000=>[8]=>[8]
[1,3,7,5,2,6,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,7,5,4,2,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,8,5,3,4,1,6,7]=>0000000=>[8]=>[8]
[6,2,3,8,5,1,7,4]=>0000000=>[8]=>[8]
[6,3,2,8,5,1,4,7]=>0000000=>[8]=>[8]
[7,4,8,5,2,1,3,6]=>0000000=>[8]=>[8]
[4,3,2,1,8,6,5,7]=>0001000=>[4,4]=>[4,4]
[4,2,1,3,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[7,1,6,8,4,3,5,2]=>0000000=>[8]=>[8]
[5,6,8,2,3,1,7,4]=>0000000=>[8]=>[8]
[7,5,3,8,2,4,1,6]=>0000000=>[8]=>[8]
[5,2,1,8,7,6,3,4]=>0000000=>[8]=>[8]
[4,1,8,3,6,2,7,5]=>0000000=>[8]=>[8]
[2,3,4,8,6,1,7,5]=>0000000=>[8]=>[8]
[2,3,4,8,6,5,1,7]=>0000000=>[8]=>[8]
[1,5,4,6,2,7,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[6,3,5,1,8,2,7,4]=>0000000=>[8]=>[8]
[5,7,1,6,3,8,4,2]=>0000000=>[8]=>[8]
[3,2,4,1,7,8,5,6]=>0001000=>[4,4]=>[4,4]
[2,5,4,6,1,7,8,3]=>0000000=>[8]=>[8]
[7,3,4,1,2,6,5,8]=>0000001=>[7,1]=>[7,1]
[7,4,3,2,1,6,5,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,2,5,4,8,1]=>0000000=>[8]=>[8]
[1,8,5,4,3,2,7,6]=>1000000=>[1,7]=>[7,1]
[2,6,8,4,3,7,1,5]=>0000000=>[8]=>[8]
[2,7,8,4,3,6,5,1]=>0000000=>[8]=>[8]
[2,7,8,5,6,3,4,1]=>0000000=>[8]=>[8]
[5,3,7,1,6,8,4,2]=>0000000=>[8]=>[8]
[5,4,7,6,1,8,3,2]=>0000000=>[8]=>[8]
[4,5,7,6,8,1,3,2]=>0000000=>[8]=>[8]
[4,6,5,7,8,2,1,3]=>0000000=>[8]=>[8]
[5,2,1,6,7,8,3,4]=>0000000=>[8]=>[8]
[6,2,1,5,7,3,8,4]=>0000000=>[8]=>[8]
[5,6,4,7,2,8,1,3]=>0000000=>[8]=>[8]
[1,8,4,6,2,7,3,5]=>1000000=>[1,7]=>[7,1]
[1,8,3,2,6,7,4,5]=>1000000=>[1,7]=>[7,1]
[6,5,3,2,7,1,8,4]=>0000000=>[8]=>[8]
[6,4,3,2,1,7,8,5]=>0000000=>[8]=>[8]
[6,2,1,4,3,7,8,5]=>0000000=>[8]=>[8]
[4,5,3,2,8,1,7,6]=>0000000=>[8]=>[8]
[4,6,3,2,8,7,1,5]=>0000000=>[8]=>[8]
[4,7,3,2,8,6,5,1]=>0000000=>[8]=>[8]
[1,8,3,2,7,6,5,4]=>1000000=>[1,7]=>[7,1]
[1,8,4,7,2,6,5,3]=>1000000=>[1,7]=>[7,1]
[3,6,4,8,2,7,1,5]=>0000000=>[8]=>[8]
[3,4,5,8,1,2,7,6]=>0000000=>[8]=>[8]
[4,2,1,5,8,3,7,6]=>0000000=>[8]=>[8]
[3,6,5,8,7,2,1,4]=>0000000=>[8]=>[8]
[3,6,7,8,5,4,1,2]=>0000000=>[8]=>[8]
[3,5,7,8,6,1,4,2]=>0000000=>[8]=>[8]
[4,2,1,7,8,6,5,3]=>0000000=>[8]=>[8]
[2,3,8,1,7,6,5,4]=>0000000=>[8]=>[8]
[2,4,8,7,1,6,5,3]=>0000000=>[8]=>[8]
[8,1,6,7,3,2,5,4]=>0000000=>[8]=>[8]
[8,1,6,7,2,3,4,5]=>0000000=>[8]=>[8]
[8,1,4,3,2,7,6,5]=>0000000=>[8]=>[8]
[8,1,5,3,7,2,6,4]=>0000000=>[8]=>[8]
[8,1,3,5,6,2,7,4]=>0000000=>[8]=>[8]
[4,7,8,5,6,1,2,3]=>0000000=>[8]=>[8]
[3,7,8,5,6,2,1,4]=>0000000=>[8]=>[8]
[3,7,8,4,2,6,1,5]=>0000000=>[8]=>[8]
[3,7,8,2,4,5,1,6]=>0000000=>[8]=>[8]
[3,6,2,8,4,5,1,7]=>0000000=>[8]=>[8]
[2,3,6,7,4,5,8,1]=>0000000=>[8]=>[8]
[3,5,2,4,8,6,1,7]=>0000000=>[8]=>[8]
[3,5,4,2,8,7,1,6]=>0000000=>[8]=>[8]
[6,4,5,1,7,8,2,3]=>0000000=>[8]=>[8]
[5,4,2,3,1,8,6,7]=>0000100=>[5,3]=>[5,3]
[6,5,3,1,8,2,7,4]=>0000000=>[8]=>[8]
[6,5,4,1,8,7,2,3]=>0000000=>[8]=>[8]
[7,5,1,4,8,6,2,3]=>0000000=>[8]=>[8]
[7,4,1,3,2,8,6,5]=>0000000=>[8]=>[8]
[7,4,1,2,3,8,5,6]=>0000000=>[8]=>[8]
[6,4,2,1,3,8,5,7]=>0000000=>[8]=>[8]
[2,6,4,8,3,7,5,1]=>0000000=>[8]=>[8]
[2,6,5,8,7,3,4,1]=>0000000=>[8]=>[8]
[6,5,2,1,8,3,4,7]=>0000000=>[8]=>[8]
[7,5,1,2,8,3,4,6]=>0000000=>[8]=>[8]
[7,6,1,8,2,3,4,5]=>0000000=>[8]=>[8]
[7,6,1,8,4,5,2,3]=>0000000=>[8]=>[8]
[6,7,8,1,4,5,2,3]=>0000000=>[8]=>[8]
[6,7,8,1,3,2,5,4]=>0000000=>[8]=>[8]
[4,2,6,7,3,1,5,8]=>0000001=>[7,1]=>[7,1]
[4,7,8,2,3,1,5,6]=>0000000=>[8]=>[8]
[4,7,8,3,2,1,6,5]=>0000000=>[8]=>[8]
[5,7,8,3,1,2,6,4]=>0000000=>[8]=>[8]
[5,7,8,4,1,6,2,3]=>0000000=>[8]=>[8]
[4,6,3,8,2,1,7,5]=>0000000=>[8]=>[8]
[4,2,5,3,7,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,6,7,8,2,1,4]=>0000000=>[8]=>[8]
[7,3,5,1,8,4,6,2]=>0000000=>[8]=>[8]
[4,5,7,3,1,8,6,2]=>0000000=>[8]=>[8]
[4,5,6,2,1,8,7,3]=>0000000=>[8]=>[8]
[1,6,5,2,7,4,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[7,4,3,1,8,6,5,2]=>0000000=>[8]=>[8]
[7,5,6,1,8,3,4,2]=>0000000=>[8]=>[8]
[7,6,5,1,8,4,3,2]=>0000000=>[8]=>[8]
[6,4,2,1,8,7,5,3]=>0000000=>[8]=>[8]
[2,6,5,1,7,8,4,3]=>0000000=>[8]=>[8]
[4,5,7,1,3,8,2,6]=>0000000=>[8]=>[8]
[4,3,1,2,8,6,5,7]=>0001000=>[4,4]=>[4,4]
[6,1,2,5,8,3,4,7]=>0000000=>[8]=>[8]
[7,1,3,4,8,2,5,6]=>0000000=>[8]=>[8]
[2,6,1,5,7,8,3,4]=>0000000=>[8]=>[8]
[6,2,5,1,8,4,7,3]=>0000000=>[8]=>[8]
[6,1,5,2,8,3,7,4]=>0000000=>[8]=>[8]
[7,3,1,4,8,6,2,5]=>0000000=>[8]=>[8]
[5,2,1,3,8,7,4,6]=>0000000=>[8]=>[8]
[6,1,4,2,8,3,7,5]=>0000000=>[8]=>[8]
[7,1,4,3,8,2,6,5]=>0000000=>[8]=>[8]
[5,1,3,2,8,4,7,6]=>0000000=>[8]=>[8]
[2,6,1,4,7,8,3,5]=>0000000=>[8]=>[8]
[7,1,3,5,8,2,4,6]=>0000000=>[8]=>[8]
[7,8,5,6,1,3,4,2]=>0000000=>[8]=>[8]
[7,8,1,3,6,2,5,4]=>0000000=>[8]=>[8]
[4,6,1,2,5,7,3,8]=>0000001=>[7,1]=>[7,1]
[1,4,8,2,5,7,3,6]=>1000000=>[1,7]=>[7,1]
[7,8,4,2,5,1,3,6]=>0000000=>[8]=>[8]
[7,8,1,5,4,6,3,2]=>0000000=>[8]=>[8]
[7,8,2,1,6,3,4,5]=>0000000=>[8]=>[8]
[7,8,3,5,6,4,1,2]=>0000000=>[8]=>[8]
[7,8,4,5,3,1,6,2]=>0000000=>[8]=>[8]
[2,6,4,8,3,7,1,5]=>0000000=>[8]=>[8]
[1,4,6,8,3,7,5,2]=>1000000=>[1,7]=>[7,1]
[2,5,8,1,4,7,6,3]=>0000000=>[8]=>[8]
[1,6,2,4,7,3,8,5]=>1000000=>[1,7]=>[7,1]
[5,6,2,1,4,7,8,3]=>0000000=>[8]=>[8]
[4,7,5,1,3,6,8,2]=>0000000=>[8]=>[8]
[5,7,3,6,1,4,8,2]=>0000000=>[8]=>[8]
[1,4,7,2,5,3,8,6]=>1000000=>[1,7]=>[7,1]
[6,4,7,3,5,8,1,2]=>0000000=>[8]=>[8]
[3,5,6,7,8,1,4,2]=>0000000=>[8]=>[8]
[3,6,5,7,8,2,1,4]=>0000000=>[8]=>[8]
[2,7,5,6,8,4,1,3]=>0000000=>[8]=>[8]
[2,1,6,8,4,5,3,7]=>0100000=>[2,6]=>[6,2]
[2,7,1,8,5,3,4,6]=>0000000=>[8]=>[8]
[3,7,6,8,5,4,1,2]=>0000000=>[8]=>[8]
[4,3,8,5,6,7,1,2]=>0000000=>[8]=>[8]
[4,2,8,1,6,3,7,5]=>0000000=>[8]=>[8]
[3,1,8,5,4,6,7,2]=>0000000=>[8]=>[8]
[3,4,2,8,6,1,7,5]=>0000000=>[8]=>[8]
[1,7,3,8,5,2,6,4]=>1000000=>[1,7]=>[7,1]
[4,1,8,3,6,2,5,7]=>0000000=>[8]=>[8]
[5,7,8,6,3,2,1,4]=>0000000=>[8]=>[8]
[5,7,8,6,1,3,4,2]=>0000000=>[8]=>[8]
[7,6,5,8,1,3,4,2]=>0000000=>[8]=>[8]
[1,6,4,3,8,2,5,7]=>1000000=>[1,7]=>[7,1]
[2,6,3,4,5,8,1,7]=>0000000=>[8]=>[8]
[2,6,4,1,8,3,7,5]=>0000000=>[8]=>[8]
[3,6,4,5,8,7,1,2]=>0000000=>[8]=>[8]
[7,2,1,4,8,3,5,6]=>0000000=>[8]=>[8]
[7,1,6,5,3,8,4,2]=>0000000=>[8]=>[8]
[7,2,5,6,3,8,1,4]=>0000000=>[8]=>[8]
[5,6,2,7,3,1,4,8]=>0000001=>[7,1]=>[7,1]
[6,7,1,5,2,8,3,4]=>0000000=>[8]=>[8]
[6,1,5,2,8,3,4,7]=>0000000=>[8]=>[8]
[7,5,2,4,3,1,6,8]=>0000001=>[7,1]=>[7,1]
[6,8,1,3,7,5,4,2]=>0000000=>[8]=>[8]
[7,4,2,6,5,1,3,8]=>0000001=>[7,1]=>[7,1]
[7,4,6,3,1,5,2,8]=>0000001=>[7,1]=>[7,1]
[7,2,3,5,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[2,5,1,7,8,3,6,4]=>0000000=>[8]=>[8]
[2,5,3,6,8,4,7,1]=>0000000=>[8]=>[8]
[3,5,7,4,1,6,2,8]=>0000001=>[7,1]=>[7,1]
[5,2,8,4,6,1,7,3]=>0000000=>[8]=>[8]
[5,2,1,8,6,3,7,4]=>0000000=>[8]=>[8]
[1,4,2,7,5,8,6,3]=>1000000=>[1,7]=>[7,1]
[5,3,8,7,6,2,4,1]=>0000000=>[8]=>[8]
[5,8,4,7,6,2,1,3]=>0000000=>[8]=>[8]
[5,8,7,4,3,6,1,2]=>0000000=>[8]=>[8]
[6,4,8,3,1,7,2,5]=>0000000=>[8]=>[8]
[6,4,2,8,7,1,3,5]=>0000000=>[8]=>[8]
[6,3,8,7,2,5,1,4]=>0000000=>[8]=>[8]
[5,8,3,7,1,6,4,2]=>0000000=>[8]=>[8]
[6,8,5,2,4,3,7,1]=>0000000=>[8]=>[8]
[6,8,5,3,1,2,7,4]=>0000000=>[8]=>[8]
[4,5,1,2,7,6,3,8]=>0000001=>[7,1]=>[7,1]
[4,5,1,2,6,8,7,3]=>0000000=>[8]=>[8]
[3,5,6,1,8,4,7,2]=>0000000=>[8]=>[8]
[3,5,7,1,2,8,6,4]=>0000000=>[8]=>[8]
[4,2,6,1,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,3,1,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,7,8,1,6,4]=>0000000=>[8]=>[8]
[3,1,4,7,5,6,2,8]=>0000001=>[7,1]=>[7,1]
[3,1,4,5,8,6,7,2]=>0000000=>[8]=>[8]
[3,4,6,8,5,2,7,1]=>0000000=>[8]=>[8]
[2,1,7,5,8,6,4,3]=>0100000=>[2,6]=>[6,2]
[1,2,7,5,3,8,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[4,1,2,7,3,8,6,5]=>0000000=>[8]=>[8]
[7,1,4,2,5,3,8,6]=>0000000=>[8]=>[8]
[6,1,3,7,5,2,4,8]=>0000001=>[7,1]=>[7,1]
[3,1,2,6,8,5,4,7]=>0010000=>[3,5]=>[5,3]
[3,7,1,2,5,4,8,6]=>0000000=>[8]=>[8]
[1,3,7,2,4,8,6,5]=>1000000=>[1,7]=>[7,1]
[3,2,7,8,1,6,5,4]=>0000000=>[8]=>[8]
[2,4,1,7,8,6,5,3]=>0000000=>[8]=>[8]
[2,6,8,3,1,5,7,4]=>0000000=>[8]=>[8]
[3,6,4,8,5,1,7,2]=>0000000=>[8]=>[8]
[6,3,7,4,5,1,8,2]=>0000000=>[8]=>[8]
[2,6,3,7,5,8,1,4]=>0000000=>[8]=>[8]
[5,2,1,7,8,3,4,6]=>0000000=>[8]=>[8]
[5,7,4,6,2,8,1,3]=>0000000=>[8]=>[8]
[4,2,8,3,6,7,1,5]=>0000000=>[8]=>[8]
[4,8,3,1,7,2,5,6]=>0000000=>[8]=>[8]
[5,2,8,4,7,1,6,3]=>0000000=>[8]=>[8]
[5,8,4,7,3,1,6,2]=>0000000=>[8]=>[8]
[4,6,8,3,1,7,5,2]=>0000000=>[8]=>[8]
[6,3,8,2,7,1,5,4]=>0000000=>[8]=>[8]
[3,5,1,8,2,7,4,6]=>0000000=>[8]=>[8]
[7,5,1,3,6,2,4,8]=>0000001=>[7,1]=>[7,1]
[5,1,8,4,2,7,3,6]=>0000000=>[8]=>[8]
[4,1,6,2,8,3,7,5]=>0000000=>[8]=>[8]
[1,6,2,8,5,3,7,4]=>1000000=>[1,7]=>[7,1]
[6,8,5,3,1,7,4,2]=>0000000=>[8]=>[8]
[5,6,7,3,1,8,4,2]=>0000000=>[8]=>[8]
[5,6,2,1,7,8,4,3]=>0000000=>[8]=>[8]
[8,4,5,1,2,6,3,7]=>0000000=>[8]=>[8]
[5,6,3,7,1,2,4,8]=>0000001=>[7,1]=>[7,1]
[1,6,3,7,2,8,4,5]=>1000000=>[1,7]=>[7,1]
[6,4,7,2,8,1,5,3]=>0000000=>[8]=>[8]
[6,7,4,8,3,1,5,2]=>0000000=>[8]=>[8]
[4,5,7,8,3,1,6,2]=>0000000=>[8]=>[8]
[4,7,2,5,8,1,6,3]=>0000000=>[8]=>[8]
[5,7,3,8,2,6,1,4]=>0000000=>[8]=>[8]
[3,4,7,8,2,6,1,5]=>0000000=>[8]=>[8]
[8,1,3,4,6,2,5,7]=>0000000=>[8]=>[8]
[2,4,5,6,8,1,7,3]=>0000000=>[8]=>[8]
[8,4,3,6,5,1,7,2]=>0000000=>[8]=>[8]
[8,6,5,4,3,1,7,2]=>0000000=>[8]=>[8]
[1,8,6,5,2,7,3,4]=>1000000=>[1,7]=>[7,1]
[8,7,5,4,1,6,3,2]=>0000000=>[8]=>[8]
[7,8,5,4,1,3,6,2]=>0000000=>[8]=>[8]
[3,2,8,6,5,1,7,4]=>0000000=>[8]=>[8]
[8,1,6,5,2,3,7,4]=>0000000=>[8]=>[8]
[8,1,7,2,6,3,5,4]=>0000000=>[8]=>[8]
[7,1,8,2,6,4,3,5]=>0000000=>[8]=>[8]
[5,1,8,3,2,7,4,6]=>0000000=>[8]=>[8]
[3,2,8,7,1,6,5,4]=>0000000=>[8]=>[8]
[4,8,2,7,1,6,5,3]=>0000000=>[8]=>[8]
[5,8,7,2,1,6,4,3]=>0000000=>[8]=>[8]
[8,7,6,1,5,4,3,2]=>0000000=>[8]=>[8]
[8,6,7,1,4,5,3,2]=>0000000=>[8]=>[8]
[7,6,8,1,4,3,5,2]=>0000000=>[8]=>[8]
[6,7,8,1,3,4,5,2]=>0000000=>[8]=>[8]
[5,7,8,2,1,4,6,3]=>0000000=>[8]=>[8]
[4,7,2,8,1,5,6,3]=>0000000=>[8]=>[8]
[3,2,7,8,1,5,6,4]=>0000000=>[8]=>[8]
[3,2,6,8,4,1,7,5]=>0000000=>[8]=>[8]
[4,6,2,8,3,1,7,5]=>0000000=>[8]=>[8]
[6,5,8,3,2,1,7,4]=>0000000=>[8]=>[8]
[7,5,8,3,1,4,6,2]=>0000000=>[8]=>[8]
[8,4,3,7,1,6,5,2]=>0000000=>[8]=>[8]
[6,4,3,8,2,1,7,5]=>0000000=>[8]=>[8]
[5,4,3,2,8,1,7,6]=>0000000=>[8]=>[8]
[4,5,2,3,8,1,7,6]=>0000000=>[8]=>[8]
[3,2,5,4,8,1,7,6]=>0000000=>[8]=>[8]
[6,4,3,1,5,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[7,4,3,1,2,6,5,8]=>0000001=>[7,1]=>[7,1]
[1,5,4,2,3,6,7,8]=>1000111=>[1,4,1,1,1]=>[4,1,1,1,1]
[7,5,1,4,2,6,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,2,1,5,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,2,6,1,5,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,7,1,3,2,6,4,8]=>0000001=>[7,1]=>[7,1]
[6,7,1,2,4,5,3,8]=>0000001=>[7,1]=>[7,1]
[7,6,1,2,5,4,3,8]=>0000001=>[7,1]=>[7,1]
[8,6,1,2,5,3,7,4]=>0000000=>[8]=>[8]
[7,8,1,2,3,5,6,4]=>0000000=>[8]=>[8]
[3,2,8,1,4,5,7,6]=>0000000=>[8]=>[8]
[4,1,3,2,5,6,7,8]=>0001111=>[4,1,1,1,1]=>[4,1,1,1,1]
[5,1,2,4,3,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,8,7,3,4,1,2,6]=>0000000=>[8]=>[8]
[6,7,3,8,5,1,2,4]=>0000000=>[8]=>[8]
[6,7,4,5,1,8,3,2]=>0000000=>[8]=>[8]
[5,4,7,6,2,3,8,1]=>0000000=>[8]=>[8]
[4,3,8,7,6,1,2,5]=>0000000=>[8]=>[8]
[4,8,3,7,5,1,2,6]=>0000000=>[8]=>[8]
[4,5,6,7,1,8,3,2]=>0000000=>[8]=>[8]
[2,5,6,8,1,7,3,4]=>0000000=>[8]=>[8]
[8,2,4,5,1,6,3,7]=>0000000=>[8]=>[8]
[1,4,8,6,2,3,7,5]=>1000000=>[1,7]=>[7,1]
[1,5,6,8,2,3,7,4]=>1000000=>[1,7]=>[7,1]
[1,5,6,2,8,4,7,3]=>1000000=>[1,7]=>[7,1]
[1,4,2,6,8,5,7,3]=>1000000=>[1,7]=>[7,1]
[8,1,3,2,5,4,6,7]=>0000000=>[8]=>[8]
[4,3,1,7,6,8,5,2]=>0000000=>[8]=>[8]
[3,8,2,1,7,5,4,6]=>0000000=>[8]=>[8]
[8,3,2,1,6,5,4,7]=>0000000=>[8]=>[8]
[8,4,2,6,1,5,3,7]=>0000000=>[8]=>[8]
[4,2,8,7,1,6,3,5]=>0000000=>[8]=>[8]
[5,3,7,2,6,4,8,1]=>0000000=>[8]=>[8]
[6,7,3,1,5,8,4,2]=>0000000=>[8]=>[8]
[6,7,2,1,8,5,4,3]=>0000000=>[8]=>[8]
[6,7,2,8,1,5,3,4]=>0000000=>[8]=>[8]
[6,7,8,2,1,4,3,5]=>0000000=>[8]=>[8]
[8,5,6,2,1,4,3,7]=>0000000=>[8]=>[8]
[5,8,7,1,2,3,4,6]=>0000000=>[8]=>[8]
[6,7,1,2,8,4,5,3]=>0000000=>[8]=>[8]
[6,7,1,3,4,8,5,2]=>0000000=>[8]=>[8]
[5,1,7,3,4,8,6,2]=>0000000=>[8]=>[8]
[5,1,7,8,2,3,6,4]=>0000000=>[8]=>[8]
[4,8,1,7,2,3,5,6]=>0000000=>[8]=>[8]
[3,8,1,2,7,4,5,6]=>0000000=>[8]=>[8]
[3,1,8,2,7,4,6,5]=>0000000=>[8]=>[8]
[3,1,2,8,7,5,6,4]=>0010000=>[3,5]=>[5,3]
[4,1,3,7,5,8,6,2]=>0000000=>[8]=>[8]
[1,8,2,3,4,5,7,6]=>1000000=>[1,7]=>[7,1]
[1,2,8,3,4,6,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[3,6,4,8,5,7,1,2]=>0000000=>[8]=>[8]
[5,1,4,8,6,3,7,2]=>0000000=>[8]=>[8]
[3,4,7,1,8,6,5,2]=>0000000=>[8]=>[8]
[6,3,8,4,2,7,1,5]=>0000000=>[8]=>[8]
[3,6,8,7,1,4,2,5]=>0000000=>[8]=>[8]
[4,6,1,2,7,8,5,3]=>0000000=>[8]=>[8]
[3,6,4,2,8,7,5,1]=>0000000=>[8]=>[8]
[5,8,1,4,6,7,2,3]=>0000000=>[8]=>[8]
[3,6,4,5,7,2,8,1]=>0000000=>[8]=>[8]
[5,4,2,7,3,6,8,1]=>0000000=>[8]=>[8]
[4,2,5,7,3,6,8,1]=>0000000=>[8]=>[8]
[1,6,5,3,4,8,2,7]=>1000000=>[1,7]=>[7,1]
[1,8,6,3,7,5,2,4]=>1000000=>[1,7]=>[7,1]
[8,7,5,2,6,4,3,1]=>0000000=>[8]=>[8]
[8,7,1,6,2,5,4,3]=>0000000=>[8]=>[8]
[7,8,1,6,3,2,5,4]=>0000000=>[8]=>[8]
[2,8,1,7,3,5,6,4]=>0000000=>[8]=>[8]
[4,8,1,3,7,2,6,5]=>0000000=>[8]=>[8]
[4,2,8,5,7,3,6,1]=>0000000=>[8]=>[8]
[6,7,3,1,8,4,2,5]=>0000000=>[8]=>[8]
[1,7,3,8,4,5,2,6]=>1000000=>[1,7]=>[7,1]
[1,7,2,8,5,3,4,6]=>1000000=>[1,7]=>[7,1]
[7,6,1,8,4,3,2,5]=>0000000=>[8]=>[8]
[7,1,2,8,3,5,4,6]=>0000000=>[8]=>[8]
[6,3,7,2,1,8,4,5]=>0000000=>[8]=>[8]
[8,2,6,1,7,3,5,4]=>0000000=>[8]=>[8]
[5,4,3,1,6,8,2,7]=>0000000=>[8]=>[8]
[1,5,3,4,6,8,2,7]=>1000000=>[1,7]=>[7,1]
[4,3,5,1,6,8,2,7]=>0000000=>[8]=>[8]
[4,7,5,6,8,3,2,1]=>0000000=>[8]=>[8]
[5,7,3,8,2,6,4,1]=>0000000=>[8]=>[8]
[2,3,8,7,4,5,6,1]=>0000000=>[8]=>[8]
[7,2,8,6,4,3,5,1]=>0000000=>[8]=>[8]
[1,3,8,7,4,6,2,5]=>1000000=>[1,7]=>[7,1]
[4,7,1,8,6,5,2,3]=>0000000=>[8]=>[8]
[6,7,4,8,3,5,1,2]=>0000000=>[8]=>[8]
[6,7,4,5,2,8,1,3]=>0000000=>[8]=>[8]
[5,7,4,6,2,3,1,8]=>0000001=>[7,1]=>[7,1]
[5,7,4,6,3,8,1,2]=>0000000=>[8]=>[8]
[5,7,4,8,3,6,1,2]=>0000000=>[8]=>[8]
[6,8,4,5,3,7,1,2]=>0000000=>[8]=>[8]
[5,8,4,6,3,7,1,2]=>0000000=>[8]=>[8]
[5,6,4,8,3,7,1,2]=>0000000=>[8]=>[8]
[5,6,3,7,2,4,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,3,7,2,8,1,4]=>0000000=>[8]=>[8]
[5,6,3,8,2,7,1,4]=>0000000=>[8]=>[8]
[5,6,4,8,2,7,1,3]=>0000000=>[8]=>[8]
[5,8,4,6,2,7,1,3]=>0000000=>[8]=>[8]
[6,8,4,5,2,7,1,3]=>0000000=>[8]=>[8]
[7,8,4,5,2,6,1,3]=>0000000=>[8]=>[8]
[6,8,4,5,2,3,1,7]=>0000000=>[8]=>[8]
[5,8,4,6,2,3,1,7]=>0000000=>[8]=>[8]
[5,6,4,8,2,3,1,7]=>0000000=>[8]=>[8]
[5,6,3,8,2,4,1,7]=>0000000=>[8]=>[8]
[5,6,3,4,2,8,1,7]=>0000000=>[8]=>[8]
[4,6,3,5,2,7,1,8]=>0000001=>[7,1]=>[7,1]
[4,6,3,5,2,8,1,7]=>0000000=>[8]=>[8]
[4,6,3,8,2,5,1,7]=>0000000=>[8]=>[8]
[4,8,3,6,2,5,1,7]=>0000000=>[8]=>[8]
[5,8,3,6,2,4,1,7]=>0000000=>[8]=>[8]
[6,8,3,5,2,4,1,7]=>0000000=>[8]=>[8]
[7,8,3,5,2,4,1,6]=>0000000=>[8]=>[8]
[7,8,3,5,2,6,1,4]=>0000000=>[8]=>[8]
[6,8,3,5,2,7,1,4]=>0000000=>[8]=>[8]
[5,8,3,6,2,7,1,4]=>0000000=>[8]=>[8]
[4,8,3,6,2,7,1,5]=>0000000=>[8]=>[8]
[4,6,3,8,2,7,1,5]=>0000000=>[8]=>[8]
[4,6,3,7,2,8,1,5]=>0000000=>[8]=>[8]
[4,6,3,7,2,5,1,8]=>0000001=>[7,1]=>[7,1]
[4,7,3,6,2,5,1,8]=>0000001=>[7,1]=>[7,1]
[4,7,3,6,2,8,1,5]=>0000000=>[8]=>[8]
[4,7,3,8,2,6,1,5]=>0000000=>[8]=>[8]
[5,7,4,8,2,6,1,3]=>0000000=>[8]=>[8]
[5,7,3,6,2,8,1,4]=>0000000=>[8]=>[8]
[5,7,3,6,2,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,5,2,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,5,2,8,1,4]=>0000000=>[8]=>[8]
[6,7,3,8,2,5,1,4]=>0000000=>[8]=>[8]
[6,7,4,8,2,5,1,3]=>0000000=>[8]=>[8]
[6,7,5,8,2,4,1,3]=>0000000=>[8]=>[8]
[6,8,5,7,2,3,1,4]=>0000000=>[8]=>[8]
[6,7,4,8,2,3,1,5]=>0000000=>[8]=>[8]
[6,7,3,8,2,4,1,5]=>0000000=>[8]=>[8]
[6,7,3,4,2,8,1,5]=>0000000=>[8]=>[8]
[5,7,3,4,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[5,7,3,4,2,8,1,6]=>0000000=>[8]=>[8]
[5,7,3,8,2,4,1,6]=>0000000=>[8]=>[8]
[5,7,4,8,2,3,1,6]=>0000000=>[8]=>[8]
[5,8,4,7,2,3,1,6]=>0000000=>[8]=>[8]
[6,8,4,7,2,3,1,5]=>0000000=>[8]=>[8]
[7,8,4,6,2,3,1,5]=>0000000=>[8]=>[8]
[7,8,3,6,2,4,1,5]=>0000000=>[8]=>[8]
[6,8,3,7,2,4,1,5]=>0000000=>[8]=>[8]
[5,8,3,7,2,4,1,6]=>0000000=>[8]=>[8]
[4,8,3,7,2,5,1,6]=>0000000=>[8]=>[8]
[4,7,3,8,2,5,1,6]=>0000000=>[8]=>[8]
[4,7,3,5,2,8,1,6]=>0000000=>[8]=>[8]
[4,7,3,5,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,3,7,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,3,7,2,8,1,6]=>0000000=>[8]=>[8]
[4,5,3,8,2,7,1,6]=>0000000=>[8]=>[8]
[4,8,3,5,2,7,1,6]=>0000000=>[8]=>[8]
[5,8,3,4,2,7,1,6]=>0000000=>[8]=>[8]
[6,8,3,4,2,7,1,5]=>0000000=>[8]=>[8]
[7,8,3,4,2,6,1,5]=>0000000=>[8]=>[8]
[6,8,3,4,2,5,1,7]=>0000000=>[8]=>[8]
[5,8,3,4,2,6,1,7]=>0000000=>[8]=>[8]
[4,8,3,5,2,6,1,7]=>0000000=>[8]=>[8]
[4,5,3,8,2,6,1,7]=>0000000=>[8]=>[8]
[4,5,3,6,2,8,1,7]=>0000000=>[8]=>[8]
[4,6,5,2,1,3,8,7]=>0000010=>[6,2]=>[6,2]
[7,4,8,1,6,5,3,2]=>0000000=>[8]=>[8]
[7,4,5,3,1,8,2,6]=>0000000=>[8]=>[8]
[6,4,8,1,7,5,2,3]=>0000000=>[8]=>[8]
[6,4,7,1,8,2,5,3]=>0000000=>[8]=>[8]
[8,4,7,3,6,2,5,1]=>0000000=>[8]=>[8]
[5,7,8,6,2,3,1,4]=>0000000=>[8]=>[8]
[5,8,7,6,3,2,1,4]=>0000000=>[8]=>[8]
[6,7,4,2,8,1,5,3]=>0000000=>[8]=>[8]
[6,8,4,2,7,5,1,3]=>0000000=>[8]=>[8]
[5,7,4,2,3,8,1,6]=>0000000=>[8]=>[8]
[2,1,8,6,7,5,3,4]=>0100000=>[2,6]=>[6,2]
[5,8,6,7,3,1,2,4]=>0000000=>[8]=>[8]
[6,7,5,8,1,3,4,2]=>0000000=>[8]=>[8]
[7,6,5,8,1,4,3,2]=>0000000=>[8]=>[8]
[2,1,7,6,8,3,5,4]=>0100000=>[2,6]=>[6,2]
[7,5,6,8,1,4,2,3]=>0000000=>[8]=>[8]
[8,1,3,7,4,6,5,2]=>0000000=>[8]=>[8]
[6,1,5,4,3,8,7,2]=>0000000=>[8]=>[8]
[6,1,8,3,4,5,7,2]=>0000000=>[8]=>[8]
[5,6,2,1,4,8,3,7]=>0000000=>[8]=>[8]
[8,5,2,7,3,1,6,4]=>0000000=>[8]=>[8]
[8,5,6,4,2,1,7,3]=>0000000=>[8]=>[8]
[2,6,4,1,8,5,7,3]=>0000000=>[8]=>[8]
[1,5,7,3,2,4,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[5,8,2,4,1,3,7,6]=>0000000=>[8]=>[8]
[4,8,1,6,3,2,7,5]=>0000000=>[8]=>[8]
[3,1,8,6,4,2,7,5]=>0000000=>[8]=>[8]
[4,2,1,3,7,8,5,6]=>0001000=>[4,4]=>[4,4]
[8,6,1,3,7,2,4,5]=>0000000=>[8]=>[8]
[5,2,7,8,6,4,1,3]=>0000000=>[8]=>[8]
[1,4,2,7,8,6,3,5]=>1000000=>[1,7]=>[7,1]
[1,6,2,4,8,5,3,7]=>1000000=>[1,7]=>[7,1]
[1,6,2,4,7,5,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,3,2,8,6,4,5]=>1000000=>[1,7]=>[7,1]
[7,8,3,6,5,2,1,4]=>0000000=>[8]=>[8]
[4,7,2,8,6,1,5,3]=>0000000=>[8]=>[8]
[1,3,6,4,8,5,7,2]=>1000000=>[1,7]=>[7,1]
[1,3,6,4,7,5,8,2]=>1000000=>[1,7]=>[7,1]
[6,2,1,3,7,8,4,5]=>0000000=>[8]=>[8]
[7,2,5,1,8,3,4,6]=>0000000=>[8]=>[8]
[7,8,2,1,4,3,5,6]=>0000000=>[8]=>[8]
[7,5,4,2,6,8,1,3]=>0000000=>[8]=>[8]
[8,2,5,4,6,7,1,3]=>0000000=>[8]=>[8]
[8,2,6,4,3,1,7,5]=>0000000=>[8]=>[8]
[8,2,7,4,1,3,5,6]=>0000000=>[8]=>[8]
[1,2,8,4,3,5,6,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,7,4,3,2,5,6]=>1000000=>[1,7]=>[7,1]
[5,8,4,7,2,1,6,3]=>0000000=>[8]=>[8]
[1,8,7,5,4,3,6,2]=>1000000=>[1,7]=>[7,1]
[1,6,8,4,3,7,5,2]=>1000000=>[1,7]=>[7,1]
[6,8,7,3,2,5,1,4]=>0000000=>[8]=>[8]
[5,3,8,1,2,7,4,6]=>0000000=>[8]=>[8]
[5,1,8,3,2,6,4,7]=>0000000=>[8]=>[8]
[5,7,3,1,2,6,4,8]=>0000001=>[7,1]=>[7,1]
[1,4,6,2,8,3,7,5]=>1000000=>[1,7]=>[7,1]
[5,2,6,7,8,4,1,3]=>0000000=>[8]=>[8]
[5,3,6,1,2,8,4,7]=>0000000=>[8]=>[8]
[1,6,3,2,7,8,4,5]=>1000000=>[1,7]=>[7,1]
[6,7,3,8,5,2,1,4]=>0000000=>[8]=>[8]
[4,6,2,7,8,1,5,3]=>0000000=>[8]=>[8]
[1,6,4,7,8,3,5,2]=>1000000=>[1,7]=>[7,1]
[4,5,7,2,1,8,6,3]=>0000000=>[8]=>[8]
[7,8,3,4,2,1,6,5]=>0000000=>[8]=>[8]
[6,3,4,1,2,5,8,7]=>0000010=>[6,2]=>[6,2]
[6,3,1,4,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[1,8,3,2,4,5,6,7]=>1000000=>[1,7]=>[7,1]
[9,10,7,8,5,6,3,4,1,2]=>000000000=>[10]=>[10]
[7,8,3,5,4,6,1,2]=>0000000=>[8]=>[8]
[6,8,3,7,5,1,4,2]=>0000000=>[8]=>[8]
[5,7,3,8,1,6,2,4]=>0000000=>[8]=>[8]
[7,8,4,6,1,5,2,3]=>0000000=>[8]=>[8]
[7,8,1,6,4,5,2,3]=>0000000=>[8]=>[8]
[6,8,1,7,4,5,2,3]=>0000000=>[8]=>[8]
[1,8,6,7,4,5,2,3]=>1000000=>[1,7]=>[7,1]
[1,8,6,7,3,5,2,4]=>1000000=>[1,7]=>[7,1]
[6,8,1,7,3,5,2,4]=>0000000=>[8]=>[8]
[7,8,1,6,3,5,2,4]=>0000000=>[8]=>[8]
[7,8,3,6,1,5,2,4]=>0000000=>[8]=>[8]
[7,8,3,6,4,5,1,2]=>0000000=>[8]=>[8]
[7,8,2,6,4,5,1,3]=>0000000=>[8]=>[8]
[7,8,2,6,3,5,1,4]=>0000000=>[8]=>[8]
[7,8,2,6,1,5,3,4]=>0000000=>[8]=>[8]
[7,8,1,6,2,5,3,4]=>0000000=>[8]=>[8]
[1,8,6,7,2,5,3,4]=>1000000=>[1,7]=>[7,1]
[1,8,5,7,2,6,3,4]=>1000000=>[1,7]=>[7,1]
[5,8,1,7,2,6,3,4]=>0000000=>[8]=>[8]
[5,8,2,7,1,6,3,4]=>0000000=>[8]=>[8]
[6,8,2,7,1,5,3,4]=>0000000=>[8]=>[8]
[6,8,2,7,3,5,1,4]=>0000000=>[8]=>[8]
[6,8,2,7,4,5,1,3]=>0000000=>[8]=>[8]
[6,8,3,7,4,5,1,2]=>0000000=>[8]=>[8]
[3,8,6,7,4,5,1,2]=>0000000=>[8]=>[8]
[2,8,6,7,4,5,1,3]=>0000000=>[8]=>[8]
[2,8,6,7,3,5,1,4]=>0000000=>[8]=>[8]
[2,8,6,7,1,5,3,4]=>0000000=>[8]=>[8]
[2,8,5,7,1,6,3,4]=>0000000=>[8]=>[8]
[2,8,1,7,5,6,3,4]=>0000000=>[8]=>[8]
[1,8,2,7,5,6,3,4]=>1000000=>[1,7]=>[7,1]
[1,8,2,7,4,6,3,5]=>1000000=>[1,7]=>[7,1]
[2,8,1,7,4,6,3,5]=>0000000=>[8]=>[8]
[2,8,4,7,1,6,3,5]=>0000000=>[8]=>[8]
[2,8,4,7,3,6,1,5]=>0000000=>[8]=>[8]
[2,8,5,7,3,6,1,4]=>0000000=>[8]=>[8]
[3,8,5,7,4,6,1,2]=>0000000=>[8]=>[8]
[5,8,3,7,4,6,1,2]=>0000000=>[8]=>[8]
[5,8,2,7,4,6,1,3]=>0000000=>[8]=>[8]
[5,8,2,7,3,6,1,4]=>0000000=>[8]=>[8]
[4,8,2,7,3,6,1,5]=>0000000=>[8]=>[8]
[4,8,2,7,1,6,3,5]=>0000000=>[8]=>[8]
[4,8,1,7,2,6,3,5]=>0000000=>[8]=>[8]
[1,8,4,7,2,6,3,5]=>1000000=>[1,7]=>[7,1]
[1,8,4,7,3,6,2,5]=>1000000=>[1,7]=>[7,1]
[4,8,1,7,3,6,2,5]=>0000000=>[8]=>[8]
[4,8,3,7,1,6,2,5]=>0000000=>[8]=>[8]
[6,8,3,7,1,5,2,4]=>0000000=>[8]=>[8]
[5,8,1,7,3,6,2,4]=>0000000=>[8]=>[8]
[1,8,5,7,3,6,2,4]=>1000000=>[1,7]=>[7,1]
[1,8,5,7,4,6,2,3]=>1000000=>[1,7]=>[7,1]
[5,8,1,7,4,6,2,3]=>0000000=>[8]=>[8]
[5,8,4,7,1,6,2,3]=>0000000=>[8]=>[8]
[6,8,4,7,1,5,2,3]=>0000000=>[8]=>[8]
[6,8,5,7,1,4,2,3]=>0000000=>[8]=>[8]
[5,8,6,7,3,4,1,2]=>0000000=>[8]=>[8]
[5,8,6,7,2,4,1,3]=>0000000=>[8]=>[8]
[5,8,6,7,1,4,2,3]=>0000000=>[8]=>[8]
[4,8,6,7,1,5,2,3]=>0000000=>[8]=>[8]
[4,8,5,7,1,6,2,3]=>0000000=>[8]=>[8]
[4,8,1,7,5,6,2,3]=>0000000=>[8]=>[8]
[1,8,4,7,5,6,2,3]=>1000000=>[1,7]=>[7,1]
[1,8,3,7,5,6,2,4]=>1000000=>[1,7]=>[7,1]
[3,8,1,7,5,6,2,4]=>0000000=>[8]=>[8]
[3,8,5,7,1,6,2,4]=>0000000=>[8]=>[8]
[3,8,6,7,1,5,2,4]=>0000000=>[8]=>[8]
[3,8,6,7,2,5,1,4]=>0000000=>[8]=>[8]
[4,8,6,7,2,5,1,3]=>0000000=>[8]=>[8]
[4,8,6,7,3,5,1,2]=>0000000=>[8]=>[8]
[4,8,5,7,3,6,1,2]=>0000000=>[8]=>[8]
[4,8,5,7,2,6,1,3]=>0000000=>[8]=>[8]
[3,8,5,7,2,6,1,4]=>0000000=>[8]=>[8]
[3,8,4,7,2,6,1,5]=>0000000=>[8]=>[8]
[3,8,4,7,1,6,2,5]=>0000000=>[8]=>[8]
[3,8,1,7,4,6,2,5]=>0000000=>[8]=>[8]
[1,8,3,7,4,6,2,5]=>1000000=>[1,7]=>[7,1]
[1,8,3,7,2,6,4,5]=>1000000=>[1,7]=>[7,1]
[3,8,1,7,2,6,4,5]=>0000000=>[8]=>[8]
[3,8,2,7,1,6,4,5]=>0000000=>[8]=>[8]
[3,8,2,7,4,6,1,5]=>0000000=>[8]=>[8]
[3,8,2,7,5,6,1,4]=>0000000=>[8]=>[8]
[4,8,2,7,5,6,1,3]=>0000000=>[8]=>[8]
[4,8,3,7,5,6,1,2]=>0000000=>[8]=>[8]
[3,8,4,7,5,6,1,2]=>0000000=>[8]=>[8]
[2,8,4,7,5,6,1,3]=>0000000=>[8]=>[8]
[2,8,3,7,5,6,1,4]=>0000000=>[8]=>[8]
[2,8,3,7,4,6,1,5]=>0000000=>[8]=>[8]
[2,8,3,7,1,6,4,5]=>0000000=>[8]=>[8]
[2,8,1,7,3,6,4,5]=>0000000=>[8]=>[8]
[7,5,2,8,6,4,1,3]=>0000000=>[8]=>[8]
[7,4,8,6,1,5,2,3]=>0000000=>[8]=>[8]
[7,1,8,4,5,2,6,3]=>0000000=>[8]=>[8]
[1,6,7,4,2,8,5,3]=>1000000=>[1,7]=>[7,1]
[1,6,7,3,8,5,2,4]=>1000000=>[1,7]=>[7,1]
[7,1,8,3,5,6,2,4]=>0000000=>[8]=>[8]
[7,3,8,6,2,5,1,4]=>0000000=>[8]=>[8]
[7,4,2,8,6,1,3,5]=>0000000=>[8]=>[8]
[6,8,1,7,2,3,4,5]=>0000000=>[8]=>[8]
[1,5,7,8,2,6,3,4]=>1000000=>[1,7]=>[7,1]
[2,5,3,7,8,1,6,4]=>0000000=>[8]=>[8]
[2,5,4,1,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[3,1,5,4,7,8,2,6]=>0000000=>[8]=>[8]
[5,3,1,4,8,2,6,7]=>0000000=>[8]=>[8]
[5,2,4,8,6,1,3,7]=>0000000=>[8]=>[8]
[4,8,1,3,6,7,2,5]=>0000000=>[8]=>[8]
[5,3,8,2,4,7,1,6]=>0000000=>[8]=>[8]
[5,4,3,8,1,2,7,6]=>0000000=>[8]=>[8]
[6,4,3,1,2,8,5,7]=>0000000=>[8]=>[8]
[6,4,2,8,1,3,7,5]=>0000000=>[8]=>[8]
[6,3,8,2,5,1,7,4]=>0000000=>[8]=>[8]
[6,3,8,1,4,7,2,5]=>0000000=>[8]=>[8]
[1,5,7,3,6,8,4,2]=>1000000=>[1,7]=>[7,1]
[1,5,7,4,2,6,8,3]=>1000000=>[1,7]=>[7,1]
[5,8,1,4,2,6,3,7]=>0000000=>[8]=>[8]
[6,5,3,1,4,2,8,7]=>0000010=>[6,2]=>[6,2]
[5,3,1,6,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,2,6,4,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,1,7,5,2,8,3]=>0000000=>[8]=>[8]
[3,5,6,1,2,8,7,4]=>0000000=>[8]=>[8]
[3,5,7,1,8,6,2,4]=>0000000=>[8]=>[8]
[3,6,2,7,5,1,8,4]=>0000000=>[8]=>[8]
[4,3,1,5,7,2,6,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,2,8,6,1,5]=>0000000=>[8]=>[8]
[3,4,5,8,2,7,1,6]=>0000000=>[8]=>[8]
[5,3,6,8,4,7,2,1]=>0000000=>[8]=>[8]
[5,1,6,8,4,3,2,7]=>0000000=>[8]=>[8]
[6,7,8,1,4,3,2,5]=>0000000=>[8]=>[8]
[4,7,1,5,8,3,2,6]=>0000000=>[8]=>[8]
[8,4,1,5,7,3,2,6]=>0000000=>[8]=>[8]
[8,3,6,1,4,7,2,5]=>0000000=>[8]=>[8]
[3,7,6,1,4,8,2,5]=>0000000=>[8]=>[8]
[6,7,8,2,4,3,5,1]=>0000000=>[8]=>[8]
[5,7,3,8,4,6,2,1]=>0000000=>[8]=>[8]
[4,7,3,5,8,6,2,1]=>0000000=>[8]=>[8]
[8,7,2,1,4,3,6,5]=>0000000=>[8]=>[8]
[8,7,3,1,4,6,2,5]=>0000000=>[8]=>[8]
[8,7,6,3,2,5,4,1]=>0000000=>[8]=>[8]
[8,7,3,5,1,6,2,4]=>0000000=>[8]=>[8]
[8,7,2,5,1,3,6,4]=>0000000=>[8]=>[8]
[8,4,6,5,7,1,2,3]=>0000000=>[8]=>[8]
[8,7,6,5,2,1,4,3]=>0000000=>[8]=>[8]
[3,6,4,8,7,5,1,2]=>0000000=>[8]=>[8]
[5,6,4,3,8,7,1,2]=>0000000=>[8]=>[8]
[1,6,2,4,7,8,5,3]=>1000000=>[1,7]=>[7,1]
[3,6,2,4,8,1,5,7]=>0000000=>[8]=>[8]
[3,4,7,2,8,1,6,5]=>0000000=>[8]=>[8]
[7,3,8,4,5,6,1,2]=>0000000=>[8]=>[8]
[3,8,7,5,4,6,1,2]=>0000000=>[8]=>[8]
[4,3,6,7,8,5,1,2]=>0000000=>[8]=>[8]
[3,5,6,4,8,7,1,2]=>0000000=>[8]=>[8]
[4,6,8,5,3,7,1,2]=>0000000=>[8]=>[8]
[6,5,2,1,4,7,8,3]=>0000000=>[8]=>[8]
[4,2,7,5,1,8,6,3]=>0000000=>[8]=>[8]
[2,1,6,4,8,7,5,3]=>0100000=>[2,6]=>[6,2]
[7,8,1,4,2,6,5,3]=>0000000=>[8]=>[8]
[6,5,1,3,4,2,8,7]=>0000010=>[6,2]=>[6,2]
[4,8,5,3,1,7,2,6]=>0000000=>[8]=>[8]
[7,4,5,3,2,8,1,6]=>0000000=>[8]=>[8]
[5,8,3,6,1,4,2,7]=>0000000=>[8]=>[8]
[1,6,8,7,4,2,3,5]=>1000000=>[1,7]=>[7,1]
[7,6,1,8,3,2,4,5]=>0000000=>[8]=>[8]
[7,1,8,6,3,4,2,5]=>0000000=>[8]=>[8]
[1,8,7,6,4,3,2,5]=>1000000=>[1,7]=>[7,1]
[2,1,7,5,6,3,8,4]=>0100000=>[2,6]=>[6,2]
[3,1,6,7,5,8,2,4]=>0000000=>[8]=>[8]
[7,8,1,6,5,3,2,4]=>0000000=>[8]=>[8]
[7,8,2,1,4,5,6,3]=>0000000=>[8]=>[8]
[4,2,6,1,8,5,7,3]=>0000000=>[8]=>[8]
[2,8,1,5,4,6,7,3]=>0000000=>[8]=>[8]
[1,2,8,3,6,5,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,6,4,1,7,5,8,3]=>0000000=>[8]=>[8]
[7,6,5,8,1,4,2,3]=>0000000=>[8]=>[8]
[5,8,6,7,3,2,1,4]=>0000000=>[8]=>[8]
[1,6,4,3,7,2,8,5]=>1000000=>[1,7]=>[7,1]
[4,1,6,3,8,2,7,5]=>0000000=>[8]=>[8]
[7,8,1,3,4,2,6,5]=>0000000=>[8]=>[8]
[2,8,5,7,4,3,1,6]=>0000000=>[8]=>[8]
[7,2,5,8,3,4,1,6]=>0000000=>[8]=>[8]
[3,5,7,8,4,1,2,6]=>0000000=>[8]=>[8]
[5,4,7,3,6,8,1,2]=>0000000=>[8]=>[8]
[1,4,7,2,5,8,3,6]=>1000000=>[1,7]=>[7,1]
[3,6,2,4,7,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,6,3,5,4,8,1,2]=>0000000=>[8]=>[8]
[4,5,6,3,8,7,1,2]=>0000000=>[8]=>[8]
[4,8,2,6,1,5,3,7]=>0000000=>[8]=>[8]
[7,1,3,6,8,4,2,5]=>0000000=>[8]=>[8]
[1,8,3,6,7,4,5,2]=>1000000=>[1,7]=>[7,1]
[7,1,5,8,3,6,2,4]=>0000000=>[8]=>[8]
[3,1,6,4,7,2,5,8]=>0000001=>[7,1]=>[7,1]
[5,8,7,1,2,4,3,6]=>0000000=>[8]=>[8]
[6,8,5,1,3,4,2,7]=>0000000=>[8]=>[8]
[7,6,5,1,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[2,6,4,5,1,3,8,7]=>0000010=>[6,2]=>[6,2]
[3,5,6,4,1,8,2,7]=>0000000=>[8]=>[8]
[7,8,5,4,1,3,2,6]=>0000000=>[8]=>[8]
[7,8,2,3,4,1,6,5]=>0000000=>[8]=>[8]
[4,2,6,3,8,1,7,5]=>0000000=>[8]=>[8]
[7,2,3,5,4,1,8,6]=>0000000=>[8]=>[8]
[6,2,4,3,1,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,2,8,3,1,7,5,6]=>0000000=>[8]=>[8]
[5,3,7,4,1,6,2,8]=>0000001=>[7,1]=>[7,1]
[2,4,7,3,6,1,8,5]=>0000000=>[8]=>[8]
[5,8,7,6,3,1,2,4]=>0000000=>[8]=>[8]
[7,5,6,8,1,4,3,2]=>0000000=>[8]=>[8]
[2,4,7,1,6,5,3,8]=>0000001=>[7,1]=>[7,1]
[5,2,7,1,8,4,6,3]=>0000000=>[8]=>[8]
[4,2,1,3,6,5,8,7]=>0001010=>[4,2,2]=>[4,2,2]
[4,2,6,1,8,5,3,7]=>0000000=>[8]=>[8]
[7,8,2,1,4,5,3,6]=>0000000=>[8]=>[8]
[7,8,4,1,5,3,6,2]=>0000000=>[8]=>[8]
[7,5,1,6,4,3,8,2]=>0000000=>[8]=>[8]
[5,8,1,6,3,4,7,2]=>0000000=>[8]=>[8]
[6,8,1,7,5,2,3,4]=>0000000=>[8]=>[8]
[5,6,1,7,4,8,2,3]=>0000000=>[8]=>[8]
[7,8,5,1,6,4,2,3]=>0000000=>[8]=>[8]
[2,6,5,7,3,4,8,1]=>0000000=>[8]=>[8]
[1,6,4,7,5,8,2,3]=>1000000=>[1,7]=>[7,1]
[1,3,7,4,6,8,2,5]=>1000000=>[1,7]=>[7,1]
[5,2,4,7,3,6,8,1]=>0000000=>[8]=>[8]
[8,1,6,5,7,2,4,3]=>0000000=>[8]=>[8]
[1,2,7,6,8,3,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[7,8,1,6,2,4,5,3]=>0000000=>[8]=>[8]
[2,8,1,7,4,3,6,5]=>0000000=>[8]=>[8]
[3,7,4,1,8,5,2,6]=>0000000=>[8]=>[8]
[6,7,1,4,8,3,2,5]=>0000000=>[8]=>[8]
[2,7,1,8,4,5,3,6]=>0000000=>[8]=>[8]
[6,1,2,8,4,3,5,7]=>0000000=>[8]=>[8]
[5,1,2,4,8,3,6,7]=>0000000=>[8]=>[8]
[4,1,3,2,8,5,6,7]=>0001000=>[4,4]=>[4,4]
[3,2,1,4,8,5,6,7]=>0011000=>[3,1,4]=>[4,3,1]
[4,3,6,1,5,8,2,7]=>0000000=>[8]=>[8]
[2,6,1,4,5,8,3,7]=>0000000=>[8]=>[8]
[1,6,2,5,8,3,4,7]=>1000000=>[1,7]=>[7,1]
[8,4,2,1,7,3,6,5]=>0000000=>[8]=>[8]
[7,4,2,1,8,5,3,6]=>0000000=>[8]=>[8]
[1,5,4,2,8,3,6,7]=>1000000=>[1,7]=>[7,1]
[6,4,3,1,5,8,2,7]=>0000000=>[8]=>[8]
[5,4,3,2,1,8,6,7]=>0000100=>[5,3]=>[5,3]
[2,5,3,4,1,8,6,7]=>0000100=>[5,3]=>[5,3]
[4,3,5,2,1,8,6,7]=>0000100=>[5,3]=>[5,3]
[3,7,6,8,4,5,2,1]=>0000000=>[8]=>[8]
[1,7,6,8,5,4,2,3]=>1000000=>[1,7]=>[7,1]
[2,4,8,6,7,3,5,1]=>0000000=>[8]=>[8]
[6,3,5,8,4,7,2,1]=>0000000=>[8]=>[8]
[5,4,3,8,6,7,2,1]=>0000000=>[8]=>[8]
[3,2,8,5,7,4,6,1]=>0000000=>[8]=>[8]
[3,1,8,5,7,6,2,4]=>0000000=>[8]=>[8]
[5,8,6,7,4,3,2,1]=>0000000=>[8]=>[8]
[4,8,7,5,6,3,2,1]=>0000000=>[8]=>[8]
[6,2,1,4,3,8,5,7]=>0000000=>[8]=>[8]
[2,1,6,4,3,5,8,7]=>0100010=>[2,4,2]=>[4,2,2]
[8,4,2,1,3,6,5,7]=>0000000=>[8]=>[8]
[6,4,2,1,8,3,5,7]=>0000000=>[8]=>[8]
[4,6,2,1,3,8,5,7]=>0000000=>[8]=>[8]
[2,6,1,4,3,8,5,7]=>0000000=>[8]=>[8]
[4,8,2,1,3,6,5,7]=>0000000=>[8]=>[8]
[2,6,1,4,8,3,5,7]=>0000000=>[8]=>[8]
[2,6,4,1,8,3,5,7]=>0000000=>[8]=>[8]
[2,6,4,8,1,3,5,7]=>0000000=>[8]=>[8]
[4,6,2,8,1,3,5,7]=>0000000=>[8]=>[8]
[6,2,4,1,8,3,5,7]=>0000000=>[8]=>[8]
[4,2,1,6,8,3,5,7]=>0000000=>[8]=>[8]
[4,2,1,3,8,6,5,7]=>0001000=>[4,4]=>[4,4]
[4,2,1,8,3,6,5,7]=>0000000=>[8]=>[8]
[2,4,8,1,6,3,5,7]=>0000000=>[8]=>[8]
[2,8,6,4,1,3,5,7]=>0000000=>[8]=>[8]
[4,8,6,2,1,3,5,7]=>0000000=>[8]=>[8]
[3,2,6,1,5,4,8,7]=>0000010=>[6,2]=>[6,2]
[4,3,6,1,5,2,8,7]=>0000010=>[6,2]=>[6,2]
[4,3,8,2,6,1,7,5]=>0000000=>[8]=>[8]
[4,3,8,1,7,2,6,5]=>0000000=>[8]=>[8]
[4,3,8,1,5,2,7,6]=>0000000=>[8]=>[8]
[2,1,5,4,8,3,7,6]=>0100000=>[2,6]=>[6,2]
[5,4,7,6,8,1,3,2]=>0000000=>[8]=>[8]
[4,3,7,1,8,5,6,2]=>0000000=>[8]=>[8]
[4,3,6,5,8,1,7,2]=>0000000=>[8]=>[8]
[7,4,6,5,8,1,3,2]=>0000000=>[8]=>[8]
[8,4,6,1,3,2,7,5]=>0000000=>[8]=>[8]
[8,1,6,3,4,2,7,5]=>0000000=>[8]=>[8]
[8,3,5,2,6,1,7,4]=>0000000=>[8]=>[8]
[8,2,7,1,5,3,6,4]=>0000000=>[8]=>[8]
[2,1,8,3,5,4,7,6]=>0100000=>[2,6]=>[6,2]
[8,1,3,2,5,4,7,6]=>0000000=>[8]=>[8]
[8,1,5,2,4,3,7,6]=>0000000=>[8]=>[8]
[8,2,4,1,5,3,7,6]=>0000000=>[8]=>[8]
[3,2,8,4,6,1,7,5]=>0000000=>[8]=>[8]
[3,2,8,1,7,4,6,5]=>0000000=>[8]=>[8]
[3,2,7,1,8,5,6,4]=>0000000=>[8]=>[8]
[3,2,6,5,8,1,7,4]=>0000000=>[8]=>[8]
[7,6,8,1,5,2,4,3]=>0000000=>[8]=>[8]
[7,6,8,1,3,2,5,4]=>0000000=>[8]=>[8]
[7,1,8,2,6,4,5,3]=>0000000=>[8]=>[8]
[5,4,7,2,6,3,8,1]=>0000000=>[8]=>[8]
[6,1,8,4,7,2,5,3]=>0000000=>[8]=>[8]
[2,1,6,5,8,3,7,4]=>0100000=>[2,6]=>[6,2]
[3,2,1,5,8,4,6,7]=>0010000=>[3,5]=>[5,3]
[2,8,3,1,5,4,6,7]=>0000000=>[8]=>[8]
[2,4,8,3,5,7,6,1]=>0000000=>[8]=>[8]
[1,8,4,2,5,3,6,7]=>1000000=>[1,7]=>[7,1]
[8,1,5,3,2,4,6,7]=>0000000=>[8]=>[8]
[3,8,1,5,2,4,6,7]=>0000000=>[8]=>[8]
[5,4,1,3,8,2,6,7]=>0000000=>[8]=>[8]
[1,5,7,3,8,4,2,6]=>1000000=>[1,7]=>[7,1]
[5,1,4,7,8,3,2,6]=>0000000=>[8]=>[8]
[1,4,3,8,7,5,6,2]=>1000000=>[1,7]=>[7,1]
[1,6,8,5,3,7,4,2]=>1000000=>[1,7]=>[7,1]
[6,4,8,1,7,3,5,2]=>0000000=>[8]=>[8]
[6,4,8,7,1,5,2,3]=>0000000=>[8]=>[8]
[7,1,6,8,4,3,2,5]=>0000000=>[8]=>[8]
[1,6,7,2,8,4,3,5]=>1000000=>[1,7]=>[7,1]
[6,7,1,4,2,8,3,5]=>0000000=>[8]=>[8]
[6,3,7,1,4,8,2,5]=>0000000=>[8]=>[8]
[3,7,8,1,5,2,4,6]=>0000000=>[8]=>[8]
[7,1,2,8,5,3,4,6]=>0000000=>[8]=>[8]
[1,7,2,8,4,5,3,6]=>1000000=>[1,7]=>[7,1]
[4,2,1,7,8,5,3,6]=>0000000=>[8]=>[8]
[7,2,6,3,4,1,8,5]=>0000000=>[8]=>[8]
[2,7,1,8,3,5,4,6]=>0000000=>[8]=>[8]
[2,1,7,3,5,8,4,6]=>0100000=>[2,6]=>[6,2]
[1,2,7,5,8,3,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[8,7,1,3,6,2,4,5]=>0000000=>[8]=>[8]
[8,2,1,7,3,5,6,4]=>0000000=>[8]=>[8]
[7,8,2,6,3,1,5,4]=>0000000=>[8]=>[8]
[2,8,4,1,6,7,5,3]=>0000000=>[8]=>[8]
[8,3,7,1,5,6,2,4]=>0000000=>[8]=>[8]
[8,1,6,2,7,4,5,3]=>0000000=>[8]=>[8]
[1,8,5,2,6,7,4,3]=>1000000=>[1,7]=>[7,1]
[5,2,1,8,6,7,4,3]=>0000000=>[8]=>[8]
[7,8,1,6,4,2,5,3]=>0000000=>[8]=>[8]
[8,7,6,5,1,4,2,3]=>0000000=>[8]=>[8]
[8,7,6,1,5,3,4,2]=>0000000=>[8]=>[8]
[8,1,7,5,6,4,3,2]=>0000000=>[8]=>[8]
[1,8,6,7,5,4,3,2]=>1000000=>[1,7]=>[7,1]
[6,5,3,1,2,4,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,3,6,1,2,8,7]=>0000010=>[6,2]=>[6,2]
[8,1,4,7,3,6,2,5]=>0000000=>[8]=>[8]
[6,3,4,7,5,8,1,2]=>0000000=>[8]=>[8]
[4,7,1,3,5,8,6,2]=>0000000=>[8]=>[8]
[4,8,3,7,1,2,6,5]=>0000000=>[8]=>[8]
[8,1,7,4,5,2,3,6]=>0000000=>[8]=>[8]
[5,3,7,8,2,4,6,1]=>0000000=>[8]=>[8]
[5,3,7,6,2,1,8,4]=>0000000=>[8]=>[8]
[2,1,6,7,5,8,3,4]=>0100000=>[2,6]=>[6,2]
[2,1,5,7,3,6,8,4]=>0100000=>[2,6]=>[6,2]
[2,4,7,1,6,5,8,3]=>0000000=>[8]=>[8]
[3,4,6,2,7,8,5,1]=>0000000=>[8]=>[8]
[3,5,6,4,7,1,8,2]=>0000000=>[8]=>[8]
[3,4,1,5,7,6,8,2]=>0000000=>[8]=>[8]
[4,2,1,7,3,5,8,6]=>0000000=>[8]=>[8]
[7,3,1,5,4,2,8,6]=>0000000=>[8]=>[8]
[6,3,1,4,2,8,5,7]=>0000000=>[8]=>[8]
[8,4,1,5,2,7,6,3]=>0000000=>[8]=>[8]
[3,6,2,7,1,4,8,5]=>0000000=>[8]=>[8]
[2,7,5,4,1,3,8,6]=>0000000=>[8]=>[8]
[6,4,3,2,1,8,5,7]=>0000000=>[8]=>[8]
[1,7,6,2,4,8,3,5]=>1000000=>[1,7]=>[7,1]
[7,1,8,5,3,6,4,2]=>0000000=>[8]=>[8]
[1,8,5,7,2,4,6,3]=>1000000=>[1,7]=>[7,1]
[7,2,8,5,6,1,4,3]=>0000000=>[8]=>[8]
[3,6,5,8,1,4,2,7]=>0000000=>[8]=>[8]
[4,3,6,7,8,1,2,5]=>0000000=>[8]=>[8]
[5,4,6,7,2,8,1,3]=>0000000=>[8]=>[8]
[3,5,7,1,4,8,2,6]=>0000000=>[8]=>[8]
[8,1,5,2,7,4,6,3]=>0000000=>[8]=>[8]
[5,4,1,6,8,2,3,7]=>0000000=>[8]=>[8]
[5,3,6,4,7,8,1,2]=>0000000=>[8]=>[8]
[6,4,7,8,1,5,3,2]=>0000000=>[8]=>[8]
[6,3,7,8,5,2,4,1]=>0000000=>[8]=>[8]
[4,6,8,2,7,1,5,3]=>0000000=>[8]=>[8]
[2,5,8,7,1,3,6,4]=>0000000=>[8]=>[8]
[8,2,7,6,5,1,4,3]=>0000000=>[8]=>[8]
[4,3,8,7,6,2,1,5]=>0000000=>[8]=>[8]
[4,7,3,8,6,5,1,2]=>0000000=>[8]=>[8]
[5,8,7,3,6,4,2,1]=>0000000=>[8]=>[8]
[2,8,7,6,5,4,1,3]=>0000000=>[8]=>[8]
[5,4,3,2,1,6,7,8,9,10]=>000011111=>[5,1,1,1,1,1]=>[5,1,1,1,1,1]
[6,4,3,2,7,1,5,8,9,10]=>000000111=>[7,1,1,1]=>[7,1,1,1]
[7,5,3,8,2,6,1,4,9,10]=>000000011=>[8,1,1]=>[8,1,1]
[8,6,9,4,7,2,5,1,3,10]=>000000001=>[9,1]=>[9,1]
[7,8,5,6,3,1,4,2]=>0000000=>[8]=>[8]
[7,5,8,3,1,4,2,6]=>0000000=>[8]=>[8]
[7,8,5,3,1,6,2,4]=>0000000=>[8]=>[8]
[7,8,5,3,1,6,4,2]=>0000000=>[8]=>[8]
[7,8,5,3,6,4,1,2]=>0000000=>[8]=>[8]
[7,5,8,3,1,2,6,4]=>0000000=>[8]=>[8]
[7,5,6,3,4,1,8,2]=>0000000=>[8]=>[8]
[7,5,3,1,6,4,8,2]=>0000000=>[8]=>[8]
[7,5,3,6,4,1,8,2]=>0000000=>[8]=>[8]
[7,5,3,8,4,6,1,2]=>0000000=>[8]=>[8]
[7,5,3,8,4,1,6,2]=>0000000=>[8]=>[8]
[7,5,3,8,1,4,6,2]=>0000000=>[8]=>[8]
[7,5,3,1,8,4,6,2]=>0000000=>[8]=>[8]
[7,5,3,1,8,2,6,4]=>0000000=>[8]=>[8]
[7,5,3,1,8,6,2,4]=>0000000=>[8]=>[8]
[7,5,3,8,6,1,4,2]=>0000000=>[8]=>[8]
[7,5,3,8,1,4,2,6]=>0000000=>[8]=>[8]
[7,5,3,8,6,1,2,4]=>0000000=>[8]=>[8]
[7,5,8,6,3,1,2,4]=>0000000=>[8]=>[8]
[7,5,8,6,3,1,4,2]=>0000000=>[8]=>[8]
[7,5,8,6,3,4,1,2]=>0000000=>[8]=>[8]
[7,5,6,8,3,1,4,2]=>0000000=>[8]=>[8]
[7,5,6,3,8,1,2,4]=>0000000=>[8]=>[8]
[7,5,6,3,1,8,4,2]=>0000000=>[8]=>[8]
[7,5,3,6,1,8,4,2]=>0000000=>[8]=>[8]
[7,5,3,4,1,6,8,2]=>0000000=>[8]=>[8]
[4,6,8,3,5,7,1,2]=>0000000=>[8]=>[8]
[6,8,1,2,4,5,7,3]=>0000000=>[8]=>[8]
[8,3,5,2,4,1,6,7]=>0000000=>[8]=>[8]
[3,5,7,2,4,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,2,5,7,3,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,2,8,3,1,6,7]=>0000000=>[8]=>[8]
[2,1,6,8,4,7,3,5]=>0100000=>[2,6]=>[6,2]
[1,2,5,8,3,6,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[5,3,6,8,4,7,1,2]=>0000000=>[8]=>[8]
[4,3,6,2,7,5,1,8]=>0000001=>[7,1]=>[7,1]
[4,3,1,7,8,2,6,5]=>0000000=>[8]=>[8]
[5,4,7,3,8,6,1,2]=>0000000=>[8]=>[8]
[5,8,4,7,6,3,1,2]=>0000000=>[8]=>[8]
[5,8,7,1,4,2,6,3]=>0000000=>[8]=>[8]
[8,3,5,1,2,7,6,4]=>0000000=>[8]=>[8]
[4,7,3,6,5,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,3,7,6,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,3,1,6,4,2,8,7]=>0000010=>[6,2]=>[6,2]
[1,3,8,5,4,2,7,6]=>1000000=>[1,7]=>[7,1]
[1,8,3,6,2,7,5,4]=>1000000=>[1,7]=>[7,1]
[1,6,8,7,4,2,5,3]=>1000000=>[1,7]=>[7,1]
[6,4,8,7,5,3,1,2]=>0000000=>[8]=>[8]
[3,1,2,7,6,4,8,5]=>0010000=>[3,5]=>[5,3]
[5,2,6,3,7,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,8,5,3,1,6,4,7]=>0000000=>[8]=>[8]
[2,1,7,3,8,5,4,6]=>0100000=>[2,6]=>[6,2]
[1,6,2,3,7,8,5,4]=>1000000=>[1,7]=>[7,1]
[1,6,7,2,8,4,5,3]=>1000000=>[1,7]=>[7,1]
[6,3,7,4,8,5,1,2]=>0000000=>[8]=>[8]
[5,7,1,8,2,4,6,3]=>0000000=>[8]=>[8]
[5,1,2,7,8,3,6,4]=>0000000=>[8]=>[8]
[4,2,1,7,3,8,5,6]=>0000000=>[8]=>[8]
[6,2,8,4,3,1,5,7]=>0000000=>[8]=>[8]
[6,4,2,7,3,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,3,2,1,8,4,5,6]=>0000000=>[8]=>[8]
[3,7,2,8,6,1,4,5]=>0000000=>[8]=>[8]
[7,1,8,2,4,5,6,3]=>0000000=>[8]=>[8]
[8,7,6,1,2,4,5,3]=>0000000=>[8]=>[8]
[8,3,6,5,2,1,4,7]=>0000000=>[8]=>[8]
[8,2,4,1,6,5,3,7]=>0000000=>[8]=>[8]
[8,5,1,2,7,3,6,4]=>0000000=>[8]=>[8]
[6,1,8,2,3,7,5,4]=>0000000=>[8]=>[8]
[8,1,2,6,4,3,7,5]=>0000000=>[8]=>[8]
[1,7,2,8,3,6,5,4]=>1000000=>[1,7]=>[7,1]
[7,3,8,6,5,4,1,2]=>0000000=>[8]=>[8]
[8,1,7,3,2,6,5,4]=>0000000=>[8]=>[8]
[4,3,1,2,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[8,6,4,3,1,5,7,2]=>0000000=>[8]=>[8]
[8,6,4,1,5,2,7,3]=>0000000=>[8]=>[8]
[8,7,2,4,5,3,1,6]=>0000000=>[8]=>[8]
[8,5,1,2,6,7,3,4]=>0000000=>[8]=>[8]
[8,5,1,6,4,2,7,3]=>0000000=>[8]=>[8]
[8,5,1,3,6,4,7,2]=>0000000=>[8]=>[8]
[7,4,8,3,1,6,2,5]=>0000000=>[8]=>[8]
[7,1,5,8,3,2,6,4]=>0000000=>[8]=>[8]
[5,7,4,1,8,2,6,3]=>0000000=>[8]=>[8]
[5,7,4,3,1,8,6,2]=>0000000=>[8]=>[8]
[8,5,7,4,6,1,3,2]=>0000000=>[8]=>[8]
[1,8,7,2,5,4,6,3]=>1000000=>[1,7]=>[7,1]
[4,3,1,8,7,5,2,6]=>0000000=>[8]=>[8]
[3,1,4,6,8,7,2,5]=>0000000=>[8]=>[8]
[1,6,2,4,8,7,5,3]=>1000000=>[1,7]=>[7,1]
[7,1,6,4,8,5,2,3]=>0000000=>[8]=>[8]
[1,3,7,2,6,8,4,5]=>1000000=>[1,7]=>[7,1]
[6,1,2,7,8,5,3,4]=>0000000=>[8]=>[8]
[6,1,2,7,4,8,5,3]=>0000000=>[8]=>[8]
[3,1,6,4,7,8,5,2]=>0000000=>[8]=>[8]
[5,7,1,3,8,4,6,2]=>0000000=>[8]=>[8]
[5,7,1,8,4,2,6,3]=>0000000=>[8]=>[8]
[5,7,1,2,8,6,3,4]=>0000000=>[8]=>[8]
[4,2,6,3,8,1,5,7]=>0000000=>[8]=>[8]
[4,2,6,7,3,5,1,8]=>0000001=>[7,1]=>[7,1]
[3,6,2,4,7,5,1,8]=>0000001=>[7,1]=>[7,1]
[3,6,2,4,1,8,5,7]=>0000000=>[8]=>[8]
[7,1,4,5,2,8,6,3]=>0000000=>[8]=>[8]
[4,7,3,1,5,8,6,2]=>0000000=>[8]=>[8]
[4,2,8,1,5,7,3,6]=>0000000=>[8]=>[8]
[8,5,7,6,1,4,2,3]=>0000000=>[8]=>[8]
[1,8,2,4,6,7,3,5]=>1000000=>[1,7]=>[7,1]
[1,2,7,4,8,6,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,8,3,6,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,5,7,4,3,2,6]=>1000000=>[1,7]=>[7,1]
[7,1,5,8,3,4,6,2]=>0000000=>[8]=>[8]
[7,1,5,8,4,3,2,6]=>0000000=>[8]=>[8]
[7,1,2,5,8,3,6,4]=>0000000=>[8]=>[8]
[2,7,1,4,8,3,5,6]=>0000000=>[8]=>[8]
[7,1,4,6,5,8,3,2]=>0000000=>[8]=>[8]
[7,1,2,3,8,5,4,6]=>0000000=>[8]=>[8]
[7,1,3,4,2,6,8,5]=>0000000=>[8]=>[8]
[3,6,7,1,4,8,5,2]=>0000000=>[8]=>[8]
[3,5,1,4,8,6,2,7]=>0000000=>[8]=>[8]
[3,6,2,4,7,8,1,5]=>0000000=>[8]=>[8]
[6,5,8,7,2,3,1,4]=>0000000=>[8]=>[8]
[3,4,7,2,5,8,1,6]=>0000000=>[8]=>[8]
[4,3,8,1,2,7,5,6]=>0000000=>[8]=>[8]
[5,6,7,8,1,3,4,2]=>0000000=>[8]=>[8]
[5,7,8,6,1,2,3,4]=>0000000=>[8]=>[8]
[2,8,3,1,5,6,4,7]=>0000000=>[8]=>[8]
[3,8,7,1,5,4,2,6]=>0000000=>[8]=>[8]
[4,3,1,7,6,8,2,5]=>0000000=>[8]=>[8]
[3,4,1,7,5,6,8,2]=>0000000=>[8]=>[8]
[2,4,6,1,7,5,8,3]=>0000000=>[8]=>[8]
[4,2,1,5,6,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,8,1,6,4,3,2,7]=>0000000=>[8]=>[8]
[5,8,1,6,3,7,2,4]=>0000000=>[8]=>[8]
[7,6,5,1,3,8,2,4]=>0000000=>[8]=>[8]
[7,6,5,1,3,4,8,2]=>0000000=>[8]=>[8]
[7,2,6,4,1,3,8,5]=>0000000=>[8]=>[8]
[4,6,3,8,5,1,7,2]=>0000000=>[8]=>[8]
[2,6,4,3,1,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,6,4,8,1,7,2,5]=>0000000=>[8]=>[8]
[7,3,8,4,1,5,2,6]=>0000000=>[8]=>[8]
[4,2,8,3,6,1,5,7]=>0000000=>[8]=>[8]
[6,7,5,8,2,1,4,3]=>0000000=>[8]=>[8]
[6,8,5,7,2,1,3,4]=>0000000=>[8]=>[8]
[6,3,5,2,1,7,4,8]=>0000001=>[7,1]=>[7,1]
[3,6,5,4,2,8,1,7]=>0000000=>[8]=>[8]
[7,4,5,3,8,2,1,6]=>0000000=>[8]=>[8]
[1,6,4,7,2,5,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,3,7,2,6,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,7,2,4,8,3,6]=>1000000=>[1,7]=>[7,1]
[1,6,5,7,2,4,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,6,2,8,3,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,2,3,5,8,7,6]=>1001100=>[1,3,1,3]=>[3,3,1,1]
[1,5,2,3,4,8,7,6]=>1000100=>[1,4,3]=>[4,3,1]
[1,6,5,2,3,8,7,4]=>1000000=>[1,7]=>[7,1]
[1,7,6,5,2,8,4,3]=>1000000=>[1,7]=>[7,1]
[1,6,5,2,3,8,4,7]=>1000000=>[1,7]=>[7,1]
[1,6,7,5,2,3,8,4]=>1000000=>[1,7]=>[7,1]
[1,7,5,2,8,4,3,6]=>1000000=>[1,7]=>[7,1]
[1,7,5,6,2,8,3,4]=>1000000=>[1,7]=>[7,1]
[1,5,7,6,2,4,8,3]=>1000000=>[1,7]=>[7,1]
[1,4,7,6,2,5,8,3]=>1000000=>[1,7]=>[7,1]
[1,2,6,5,3,7,4,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,3,7,5,2,6,8,4]=>1000000=>[1,7]=>[7,1]
[1,7,4,6,2,8,3,5]=>1000000=>[1,7]=>[7,1]
[1,7,3,5,2,8,4,6]=>1000000=>[1,7]=>[7,1]
[1,3,7,4,2,6,8,5]=>1000000=>[1,7]=>[7,1]
[1,4,7,3,2,5,8,6]=>1000000=>[1,7]=>[7,1]
[1,5,7,3,2,4,8,6]=>1000000=>[1,7]=>[7,1]
[1,7,3,4,2,8,5,6]=>1000000=>[1,7]=>[7,1]
[1,7,4,2,8,5,3,6]=>1000000=>[1,7]=>[7,1]
[1,6,7,4,2,3,8,5]=>1000000=>[1,7]=>[7,1]
[1,4,3,2,5,8,6,7]=>1001100=>[1,3,1,3]=>[3,3,1,1]
[1,5,3,2,4,8,6,7]=>1000100=>[1,4,3]=>[4,3,1]
[1,6,4,2,3,8,5,7]=>1000000=>[1,7]=>[7,1]
[1,7,6,4,2,8,5,3]=>1000000=>[1,7]=>[7,1]
[1,6,4,2,3,8,7,5]=>1000000=>[1,7]=>[7,1]
[1,5,3,2,4,8,7,6]=>1000100=>[1,4,3]=>[4,3,1]
[6,8,5,4,3,2,1,7]=>0000000=>[8]=>[8]
[7,6,5,1,3,8,4,2]=>0000000=>[8]=>[8]
[5,6,8,4,3,1,7,2]=>0000000=>[8]=>[8]
[7,5,8,4,3,2,1,6]=>0000000=>[8]=>[8]
[4,8,5,7,3,2,1,6]=>0000000=>[8]=>[8]
[7,8,1,2,4,3,5,6]=>0000000=>[8]=>[8]
[7,8,2,1,4,3,6,5]=>0000000=>[8]=>[8]
[3,4,6,5,7,8,1,2]=>0000000=>[8]=>[8]
[4,3,6,5,8,7,1,2]=>0000000=>[8]=>[8]
[4,2,6,1,8,3,7,5]=>0000000=>[8]=>[8]
[6,7,3,8,4,5,1,2]=>0000000=>[8]=>[8]
[6,7,4,5,1,8,2,3]=>0000000=>[8]=>[8]
[4,7,5,6,1,8,2,3]=>0000000=>[8]=>[8]
[4,5,3,8,6,7,1,2]=>0000000=>[8]=>[8]
[5,6,3,8,4,7,1,2]=>0000000=>[8]=>[8]
[5,6,2,7,3,4,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,1,8,6,7,2,3]=>0000000=>[8]=>[8]
[7,8,4,5,1,6,2,3]=>0000000=>[8]=>[8]
[4,5,2,3,1,8,6,7]=>0000100=>[5,3]=>[5,3]
[5,6,2,3,1,8,4,7]=>0000000=>[8]=>[8]
[5,6,3,4,1,8,2,7]=>0000000=>[8]=>[8]
[3,6,4,5,1,8,2,7]=>0000000=>[8]=>[8]
[2,6,4,8,1,5,3,7]=>0000000=>[8]=>[8]
[2,8,3,4,1,6,5,7]=>0000000=>[8]=>[8]
[7,8,1,5,3,6,2,4]=>0000000=>[8]=>[8]
[1,6,4,7,3,8,2,5]=>1000000=>[1,7]=>[7,1]
[1,7,2,8,4,6,3,5]=>1000000=>[1,7]=>[7,1]
[1,7,5,8,2,6,3,4]=>1000000=>[1,7]=>[7,1]
[6,7,1,8,2,5,3,4]=>0000000=>[8]=>[8]
[6,7,1,8,4,5,2,3]=>0000000=>[8]=>[8]
[6,7,5,8,1,4,2,3]=>0000000=>[8]=>[8]
[5,8,6,7,2,3,1,4]=>0000000=>[8]=>[8]
[6,7,2,3,1,8,4,5]=>0000000=>[8]=>[8]
[6,7,2,8,1,4,3,5]=>0000000=>[8]=>[8]
[6,7,3,4,1,8,2,5]=>0000000=>[8]=>[8]
[2,7,5,8,1,4,3,6]=>0000000=>[8]=>[8]
[2,3,1,8,6,7,4,5]=>0010000=>[3,5]=>[5,3]
[7,8,2,3,1,6,4,5]=>0000000=>[8]=>[8]
[2,8,1,4,3,7,5,6]=>0000000=>[8]=>[8]
[2,8,1,7,3,5,4,6]=>0000000=>[8]=>[8]
[4,5,1,7,3,8,2,6]=>0000000=>[8]=>[8]
[3,8,1,5,2,7,4,6]=>0000000=>[8]=>[8]
[3,4,1,8,6,7,2,5]=>0000000=>[8]=>[8]
[7,8,3,4,1,6,2,5]=>0000000=>[8]=>[8]
[2,5,4,1,6,3,8,7]=>0000010=>[6,2]=>[6,2]
[3,6,5,1,2,4,8,7]=>0000010=>[6,2]=>[6,2]
[5,6,7,8,1,4,3,2]=>0000000=>[8]=>[8]
[2,1,4,7,6,3,8,5]=>0100000=>[2,6]=>[6,2]
[7,4,3,8,2,1,5,6]=>0000000=>[8]=>[8]
[2,4,1,5,8,3,7,6]=>0000000=>[8]=>[8]
[2,1,5,8,7,3,4,6]=>0100000=>[2,6]=>[6,2]
[8,5,7,3,6,1,4,2]=>0000000=>[8]=>[8]
[4,2,5,1,6,7,8,3]=>0000000=>[8]=>[8]
[6,1,8,5,2,7,4,3]=>0000000=>[8]=>[8]
[6,8,7,2,5,3,1,4]=>0000000=>[8]=>[8]
[7,8,2,5,6,1,4,3]=>0000000=>[8]=>[8]
[7,8,4,2,5,1,6,3]=>0000000=>[8]=>[8]
[6,1,2,3,7,5,8,4]=>0000000=>[8]=>[8]
[4,1,6,3,5,8,7,2]=>0000000=>[8]=>[8]
[8,6,7,1,5,4,3,2]=>0000000=>[8]=>[8]
[2,1,6,5,8,4,7,3]=>0100000=>[2,6]=>[6,2]
[2,6,4,8,7,3,5,1]=>0000000=>[8]=>[8]
[7,4,8,6,3,2,5,1]=>0000000=>[8]=>[8]
[2,1,8,4,3,7,5,6]=>0100000=>[2,6]=>[6,2]
[6,3,8,2,4,5,7,1]=>0000000=>[8]=>[8]
[5,8,2,4,3,1,6,7]=>0000000=>[8]=>[8]
[7,3,5,8,1,4,2,6]=>0000000=>[8]=>[8]
[3,8,7,6,1,4,2,5]=>0000000=>[8]=>[8]
[5,1,8,3,6,7,2,4]=>0000000=>[8]=>[8]
[3,6,1,4,7,8,5,2]=>0000000=>[8]=>[8]
[1,6,8,4,7,5,2,3]=>1000000=>[1,7]=>[7,1]
[6,8,1,3,5,7,2,4]=>0000000=>[8]=>[8]
[7,6,1,4,3,8,2,5]=>0000000=>[8]=>[8]
[8,4,2,6,7,5,3,1]=>0000000=>[8]=>[8]
[7,4,1,6,8,2,5,3]=>0000000=>[8]=>[8]
[1,8,6,2,5,3,4,7]=>1000000=>[1,7]=>[7,1]
[4,7,1,2,5,3,8,6]=>0000000=>[8]=>[8]
[5,7,8,6,2,1,4,3]=>0000000=>[8]=>[8]
[1,8,6,4,5,2,3,7]=>1000000=>[1,7]=>[7,1]
[1,4,7,2,6,8,3,5]=>1000000=>[1,7]=>[7,1]
[2,5,4,3,6,8,1,7]=>0000000=>[8]=>[8]
[3,8,5,4,6,2,1,7]=>0000000=>[8]=>[8]
[4,8,2,1,3,7,5,6]=>0000000=>[8]=>[8]
[1,8,3,2,5,6,7,4]=>1000000=>[1,7]=>[7,1]
[6,4,1,2,7,5,8,3]=>0000000=>[8]=>[8]
[4,3,7,8,5,1,6,2]=>0000000=>[8]=>[8]
[1,2,7,3,6,5,8,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,8,7,6,3,4,1,5]=>0000000=>[8]=>[8]
[5,8,2,6,3,4,1,7]=>0000000=>[8]=>[8]
[1,2,4,5,8,3,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[4,8,1,5,2,3,7,6]=>0000000=>[8]=>[8]
[2,4,6,3,7,1,8,5]=>0000000=>[8]=>[8]
[6,5,8,7,1,3,4,2]=>0000000=>[8]=>[8]
[1,5,2,7,4,3,8,6]=>1000000=>[1,7]=>[7,1]
[7,6,1,2,8,3,5,4]=>0000000=>[8]=>[8]
[6,7,8,1,5,2,4,3]=>0000000=>[8]=>[8]
[5,7,8,4,1,2,6,3]=>0000000=>[8]=>[8]
[4,7,8,5,6,1,3,2]=>0000000=>[8]=>[8]
[6,5,4,1,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[7,5,1,6,2,3,8,4]=>0000000=>[8]=>[8]
[4,5,6,7,8,1,3,2]=>0000000=>[8]=>[8]
[8,1,3,6,7,4,5,2]=>0000000=>[8]=>[8]
[4,5,3,2,8,1,6,7]=>0000000=>[8]=>[8]
[7,4,1,5,3,2,6,8]=>0000001=>[7,1]=>[7,1]
[8,1,5,4,3,2,6,7]=>0000000=>[8]=>[8]
[8,1,6,4,2,5,3,7]=>0000000=>[8]=>[8]
[6,5,3,1,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[5,6,3,8,1,4,2,7]=>0000000=>[8]=>[8]
[4,6,3,8,2,1,5,7]=>0000000=>[8]=>[8]
[4,7,8,3,2,1,5,6]=>0000000=>[8]=>[8]
[5,7,8,3,1,4,2,6]=>0000000=>[8]=>[8]
[8,1,7,2,5,4,3,6]=>0000000=>[8]=>[8]
[8,1,7,2,4,5,6,3]=>0000000=>[8]=>[8]
[7,6,1,2,4,5,8,3]=>0000000=>[8]=>[8]
[7,5,1,3,2,6,8,4]=>0000000=>[8]=>[8]
[8,1,6,3,2,5,7,4]=>0000000=>[8]=>[8]
[5,4,2,3,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[6,3,2,1,5,7,4,8]=>0000001=>[7,1]=>[7,1]
[3,6,5,8,2,4,1,7]=>0000000=>[8]=>[8]
[6,2,4,5,8,3,1,7]=>0000000=>[8]=>[8]
[4,8,1,2,5,6,3,7]=>0000000=>[8]=>[8]
[8,1,3,5,2,6,4,7]=>0000000=>[8]=>[8]
[5,2,1,6,3,8,4,7]=>0000000=>[8]=>[8]
[6,1,4,5,8,3,2,7]=>0000000=>[8]=>[8]
[6,5,4,3,8,2,1,7]=>0000000=>[8]=>[8]
[4,6,8,3,7,2,5,1]=>0000000=>[8]=>[8]
[4,7,8,5,3,1,2,6]=>0000000=>[8]=>[8]
[8,5,4,7,6,2,1,3]=>0000000=>[8]=>[8]
[5,8,7,3,1,4,6,2]=>0000000=>[8]=>[8]
[8,5,7,4,3,6,1,2]=>0000000=>[8]=>[8]
[1,3,8,6,4,7,5,2]=>1000000=>[1,7]=>[7,1]
[7,6,8,1,4,3,2,5]=>0000000=>[8]=>[8]
[3,2,6,8,5,7,4,1]=>0000000=>[8]=>[8]
[1,6,4,7,2,3,8,5]=>1000000=>[1,7]=>[7,1]
[3,1,7,5,2,8,4,6]=>0000000=>[8]=>[8]
[1,7,4,5,2,8,3,6]=>1000000=>[1,7]=>[7,1]
[6,3,2,1,7,8,4,5]=>0000000=>[8]=>[8]
[5,7,3,8,2,1,4,6]=>0000000=>[8]=>[8]
[3,7,1,8,4,2,5,6]=>0000000=>[8]=>[8]
[4,2,1,3,7,5,8,6]=>0001000=>[4,4]=>[4,4]
[8,4,2,1,3,7,6,5]=>0000000=>[8]=>[8]
[3,6,2,8,7,1,5,4]=>0000000=>[8]=>[8]
[7,3,2,8,1,6,5,4]=>0000000=>[8]=>[8]
[3,8,7,2,6,5,4,1]=>0000000=>[8]=>[8]
[4,2,7,8,6,1,5,3]=>0000000=>[8]=>[8]
[5,8,4,2,7,1,6,3]=>0000000=>[8]=>[8]
[8,5,3,1,7,2,6,4]=>0000000=>[8]=>[8]
[8,2,1,6,3,7,5,4]=>0000000=>[8]=>[8]
[1,4,6,8,2,7,5,3]=>1000000=>[1,7]=>[7,1]
[8,2,1,7,6,5,4,3]=>0000000=>[8]=>[8]
[8,6,7,5,1,4,3,2]=>0000000=>[8]=>[8]
[6,4,7,3,2,1,8,5]=>0000000=>[8]=>[8]
[4,8,7,3,2,1,6,5]=>0000000=>[8]=>[8]
[6,4,3,7,2,1,8,5]=>0000000=>[8]=>[8]
[5,3,7,6,2,1,4,8]=>0000001=>[7,1]=>[7,1]
[3,8,7,6,2,1,4,5]=>0000000=>[8]=>[8]
[5,8,4,2,6,1,3,7]=>0000000=>[8]=>[8]
[4,8,7,2,5,1,3,6]=>0000000=>[8]=>[8]
[4,3,7,2,5,1,8,6]=>0000000=>[8]=>[8]
[5,4,2,6,7,1,3,8]=>0000001=>[7,1]=>[7,1]
[2,8,7,6,5,1,3,4]=>0000000=>[8]=>[8]
[6,4,7,3,1,5,8,2]=>0000000=>[8]=>[8]
[4,8,7,3,1,5,6,2]=>0000000=>[8]=>[8]
[6,5,3,7,1,4,8,2]=>0000000=>[8]=>[8]
[6,4,3,7,1,5,8,2]=>0000000=>[8]=>[8]
[5,3,7,6,1,4,8,2]=>0000000=>[8]=>[8]
[3,8,7,6,1,4,5,2]=>0000000=>[8]=>[8]
[5,8,4,2,1,7,3,6]=>0000000=>[8]=>[8]
[6,4,7,2,1,5,3,8]=>0000001=>[7,1]=>[7,1]
[5,8,3,2,1,4,7,6]=>0000000=>[8]=>[8]
[6,3,7,2,1,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,5,2,7,1,4,3,8]=>0000001=>[7,1]=>[7,1]
[5,8,2,6,1,4,3,7]=>0000000=>[8]=>[8]
[2,8,7,6,1,4,3,5]=>0000000=>[8]=>[8]
[5,8,4,1,6,7,3,2]=>0000000=>[8]=>[8]
[6,5,3,1,8,4,7,2]=>0000000=>[8]=>[8]
[6,4,3,1,5,8,7,2]=>0000000=>[8]=>[8]
[5,8,2,1,6,4,3,7]=>0000000=>[8]=>[8]
[6,4,2,1,5,8,3,7]=>0000000=>[8]=>[8]
[4,2,7,1,5,6,3,8]=>0000001=>[7,1]=>[7,1]
[6,5,1,7,8,4,3,2]=>0000000=>[8]=>[8]
[5,4,1,6,7,8,3,2]=>0000000=>[8]=>[8]
[4,3,1,6,5,7,8,2]=>0000000=>[8]=>[8]
[5,2,1,6,7,4,3,8]=>0000001=>[7,1]=>[7,1]
[4,2,1,6,5,7,3,8]=>0000001=>[7,1]=>[7,1]
[6,1,7,8,5,4,3,2]=>0000000=>[8]=>[8]
[5,1,7,6,8,4,3,2]=>0000000=>[8]=>[8]
[4,5,8,1,7,2,3,6]=>0000000=>[8]=>[8]
[8,1,3,5,7,2,4,6]=>0000000=>[8]=>[8]
[3,6,8,1,7,2,4,5]=>0000000=>[8]=>[8]
[8,2,3,5,6,7,1,4]=>0000000=>[8]=>[8]
[8,7,2,1,6,3,4,5]=>0000000=>[8]=>[8]
[8,6,4,1,7,5,3,2]=>0000000=>[8]=>[8]
[2,3,6,7,8,1,5,4]=>0000000=>[8]=>[8]
[3,1,7,2,5,4,8,6]=>0000000=>[8]=>[8]
[7,1,8,2,5,3,6,4]=>0000000=>[8]=>[8]
[7,3,8,4,5,1,6,2]=>0000000=>[8]=>[8]
[8,1,2,6,5,4,3,7]=>0000000=>[8]=>[8]
[8,2,7,5,6,1,4,3]=>0000000=>[8]=>[8]
[3,6,8,1,7,5,4,2]=>0000000=>[8]=>[8]
[8,2,6,7,5,4,1,3]=>0000000=>[8]=>[8]
[8,6,7,2,3,1,5,4]=>0000000=>[8]=>[8]
[8,1,7,6,5,4,3,2]=>0000000=>[8]=>[8]
[8,6,1,5,2,7,4,3]=>0000000=>[8]=>[8]
[8,5,1,7,4,2,6,3]=>0000000=>[8]=>[8]
[2,1,7,8,3,6,5,4]=>0100000=>[2,6]=>[6,2]
[7,8,1,5,2,6,3,4]=>0000000=>[8]=>[8]
[6,4,1,5,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[5,3,7,4,6,8,1,2]=>0000000=>[8]=>[8]
[4,2,6,3,8,5,1,7]=>0000000=>[8]=>[8]
[5,8,2,1,7,6,4,3]=>0000000=>[8]=>[8]
[8,3,2,4,1,7,5,6]=>0000000=>[8]=>[8]
[7,8,3,1,5,4,6,2]=>0000000=>[8]=>[8]
[7,2,8,1,4,6,5,3]=>0000000=>[8]=>[8]
[5,7,1,8,3,6,2,4]=>0000000=>[8]=>[8]
[4,2,1,3,6,7,8,5]=>0001000=>[4,4]=>[4,4]
[6,3,5,4,1,2,8,7]=>0000010=>[6,2]=>[6,2]
[3,4,7,2,8,1,5,6]=>0000000=>[8]=>[8]
[4,2,3,5,8,1,6,7]=>0000000=>[8]=>[8]
[3,2,4,6,1,5,8,7]=>0000010=>[6,2]=>[6,2]
[6,5,4,3,1,8,7,2]=>0000000=>[8]=>[8]
[8,7,5,4,3,1,6,2]=>0000000=>[8]=>[8]
[3,4,6,2,8,5,1,7]=>0000000=>[8]=>[8]
[3,4,7,2,8,5,6,1]=>0000000=>[8]=>[8]
[3,5,2,6,8,4,1,7]=>0000000=>[8]=>[8]
[3,5,2,7,4,8,6,1]=>0000000=>[8]=>[8]
[3,5,6,2,8,4,1,7]=>0000000=>[8]=>[8]
[3,5,7,2,4,8,6,1]=>0000000=>[8]=>[8]
[3,5,7,8,4,1,6,2]=>0000000=>[8]=>[8]
[3,5,8,2,4,1,6,7]=>0000000=>[8]=>[8]
[3,6,2,7,4,8,5,1]=>0000000=>[8]=>[8]
[3,6,2,7,8,5,4,1]=>0000000=>[8]=>[8]
[3,6,8,2,4,5,1,7]=>0000000=>[8]=>[8]
[3,7,2,1,4,8,6,5]=>0000000=>[8]=>[8]
[3,7,2,8,4,5,6,1]=>0000000=>[8]=>[8]
[4,1,5,7,3,8,6,2]=>0000000=>[8]=>[8]
[4,1,5,7,8,2,6,3]=>0000000=>[8]=>[8]
[4,1,5,8,3,2,6,7]=>0000000=>[8]=>[8]
[4,1,6,3,7,8,5,2]=>0000000=>[8]=>[8]
[4,1,6,3,8,5,2,7]=>0000000=>[8]=>[8]
[4,1,6,8,3,5,2,7]=>0000000=>[8]=>[8]
[4,1,7,3,8,5,6,2]=>0000000=>[8]=>[8]
[4,1,8,3,2,5,6,7]=>0000000=>[8]=>[8]
[4,5,2,7,3,8,6,1]=>0000000=>[8]=>[8]
[4,5,7,3,2,8,6,1]=>0000000=>[8]=>[8]
[4,5,8,3,2,1,6,7]=>0000000=>[8]=>[8]
[4,6,2,8,3,5,1,7]=>0000000=>[8]=>[8]
[5,1,2,6,8,4,3,7]=>0000000=>[8]=>[8]
[5,1,6,3,7,8,2,4]=>0000000=>[8]=>[8]
[5,1,6,3,8,4,2,7]=>0000000=>[8]=>[8]
[5,1,6,7,4,8,2,3]=>0000000=>[8]=>[8]
[5,6,2,7,4,8,1,3]=>0000000=>[8]=>[8]
[5,6,2,7,8,4,1,3]=>0000000=>[8]=>[8]
[5,7,8,3,4,2,6,1]=>0000000=>[8]=>[8]
[6,1,2,3,7,8,5,4]=>0000000=>[8]=>[8]
[6,1,2,7,8,5,4,3]=>0000000=>[8]=>[8]
[6,7,2,8,4,5,3,1]=>0000000=>[8]=>[8]
[7,1,2,3,8,5,6,4]=>0000000=>[8]=>[8]
[7,1,8,3,4,5,6,2]=>0000000=>[8]=>[8]
[2,4,6,1,8,5,7,3]=>0000000=>[8]=>[8]
[3,5,8,6,1,2,4,7]=>0000000=>[8]=>[8]
[3,5,1,8,2,4,7,6]=>0000000=>[8]=>[8]
[3,1,6,8,2,4,7,5]=>0000000=>[8]=>[8]
[5,6,4,8,2,1,7,3]=>0000000=>[8]=>[8]
[2,5,7,8,6,3,1,4]=>0000000=>[8]=>[8]
[2,4,8,1,5,6,7,3]=>0000000=>[8]=>[8]
[8,4,1,2,5,6,3,7]=>0000000=>[8]=>[8]
[8,3,1,6,5,2,4,7]=>0000000=>[8]=>[8]
[2,5,3,8,7,6,1,4]=>0000000=>[8]=>[8]
[5,1,8,4,7,6,3,2]=>0000000=>[8]=>[8]
[8,2,3,6,5,1,7,4]=>0000000=>[8]=>[8]
[4,8,6,5,7,3,2,1]=>0000000=>[8]=>[8]
[4,8,5,6,7,3,2,1]=>0000000=>[8]=>[8]
[7,2,8,6,5,4,1,3]=>0000000=>[8]=>[8]
[6,3,2,8,5,1,7,4]=>0000000=>[8]=>[8]
[6,8,5,4,3,1,7,2]=>0000000=>[8]=>[8]
[7,6,3,8,5,2,1,4]=>0000000=>[8]=>[8]
[5,8,7,4,1,6,3,2]=>0000000=>[8]=>[8]
[6,8,3,4,5,1,7,2]=>0000000=>[8]=>[8]
[5,2,8,4,1,6,7,3]=>0000000=>[8]=>[8]
[4,1,3,6,8,2,5,7]=>0000000=>[8]=>[8]
[8,3,2,1,5,4,7,6]=>0000000=>[8]=>[8]
[2,5,1,8,4,3,7,6]=>0000000=>[8]=>[8]
[5,3,6,2,4,8,1,7]=>0000000=>[8]=>[8]
[1,6,2,4,5,8,3,7]=>1000000=>[1,7]=>[7,1]
[5,3,2,1,6,8,4,7]=>0000000=>[8]=>[8]
[2,6,5,8,1,3,4,7]=>0000000=>[8]=>[8]
[8,3,4,1,5,2,7,6]=>0000000=>[8]=>[8]
[8,2,6,4,1,7,3,5]=>0000000=>[8]=>[8]
[5,4,6,8,1,2,7,3]=>0000000=>[8]=>[8]
[3,4,7,8,6,2,5,1]=>0000000=>[8]=>[8]
[7,5,8,2,4,6,1,3]=>0000000=>[8]=>[8]
[8,2,7,4,6,1,3,5]=>0000000=>[8]=>[8]
[4,7,3,2,8,1,6,5]=>0000000=>[8]=>[8]
[1,2,8,3,5,6,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[4,2,3,7,1,8,6,5]=>0000000=>[8]=>[8]
[3,2,6,4,8,1,7,5]=>0000000=>[8]=>[8]
[8,2,1,6,7,3,4,5]=>0000000=>[8]=>[8]
[2,7,8,5,4,1,3,6]=>0000000=>[8]=>[8]
[1,7,5,3,8,4,2,6]=>1000000=>[1,7]=>[7,1]
[4,7,5,3,1,2,8,6]=>0000000=>[8]=>[8]
[5,6,7,3,8,4,2,1]=>0000000=>[8]=>[8]
[5,7,3,2,4,1,8,6]=>0000000=>[8]=>[8]
[8,4,1,3,7,2,5,6]=>0000000=>[8]=>[8]
[2,8,4,7,1,3,5,6]=>0000000=>[8]=>[8]
[3,5,2,8,6,1,7,4]=>0000000=>[8]=>[8]
[1,7,6,3,2,5,8,4]=>1000000=>[1,7]=>[7,1]
[3,8,1,5,6,2,7,4]=>0000000=>[8]=>[8]
[7,1,5,2,8,6,4,3]=>0000000=>[8]=>[8]
[1,8,5,3,6,2,7,4]=>1000000=>[1,7]=>[7,1]
[6,5,8,7,2,1,3,4]=>0000000=>[8]=>[8]
[3,6,2,1,7,5,8,4]=>0000000=>[8]=>[8]
[4,7,2,6,5,8,1,3]=>0000000=>[8]=>[8]
[6,8,1,4,2,7,3,5]=>0000000=>[8]=>[8]
[6,3,4,7,1,8,2,5]=>0000000=>[8]=>[8]
[3,4,7,8,2,5,6,1]=>0000000=>[8]=>[8]
[1,8,2,4,5,6,7,3]=>1000000=>[1,7]=>[7,1]
[3,2,5,7,6,1,8,4]=>0000000=>[8]=>[8]
[4,3,5,6,1,8,7,2]=>0000000=>[8]=>[8]
[1,2,3,4,8,6,5,7]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,3,8,5,4,6,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,5,6,4,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,6,5,4,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,8,3,4,2,5,6,7]=>1000000=>[1,7]=>[7,1]
[1,2,8,5,4,3,6,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,4,3,2,5,6,7]=>1000000=>[1,7]=>[7,1]
[8,4,7,3,6,5,2,1]=>0000000=>[8]=>[8]
[8,1,7,4,6,5,3,2]=>0000000=>[8]=>[8]
[8,4,7,1,6,5,3,2]=>0000000=>[8]=>[8]
[8,3,7,1,6,5,4,2]=>0000000=>[8]=>[8]
[8,2,7,1,6,5,4,3]=>0000000=>[8]=>[8]
[8,1,7,2,6,5,4,3]=>0000000=>[8]=>[8]
[8,3,7,1,6,4,5,2]=>0000000=>[8]=>[8]
[8,4,7,2,6,3,5,1]=>0000000=>[8]=>[8]
[8,4,7,6,5,2,3,1]=>0000000=>[8]=>[8]
[8,3,7,6,5,1,4,2]=>0000000=>[8]=>[8]
[8,4,7,5,6,1,3,2]=>0000000=>[8]=>[8]
[8,1,7,3,6,2,5,4]=>0000000=>[8]=>[8]
[8,3,7,2,6,1,5,4]=>0000000=>[8]=>[8]
[8,5,7,2,6,1,4,3]=>0000000=>[8]=>[8]
[8,7,6,1,5,2,4,3]=>0000000=>[8]=>[8]
[4,6,7,3,8,5,2,1]=>0000000=>[8]=>[8]
[6,7,8,9,10,5,4,3,2,1]=>000000000=>[10]=>[10]
[1,4,8,2,6,3,5,7]=>1000000=>[1,7]=>[7,1]
[1,6,2,4,8,3,5,7]=>1000000=>[1,7]=>[7,1]
[1,5,2,3,8,4,7,6]=>1000000=>[1,7]=>[7,1]
[1,7,2,3,5,4,8,6]=>1000000=>[1,7]=>[7,1]
[1,8,2,3,5,4,6,7]=>1000000=>[1,7]=>[7,1]
[1,7,8,2,4,5,3,6]=>1000000=>[1,7]=>[7,1]
[1,2,8,3,6,4,5,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,8,2,3,7,4,6]=>1000000=>[1,7]=>[7,1]
[1,6,8,2,3,5,4,7]=>1000000=>[1,7]=>[7,1]
[5,7,2,6,3,8,1,4]=>0000000=>[8]=>[8]
[5,7,1,6,8,4,3,2]=>0000000=>[8]=>[8]
[4,8,1,2,5,7,3,6]=>0000000=>[8]=>[8]
[3,7,5,4,8,2,1,6]=>0000000=>[8]=>[8]
[4,7,1,3,2,8,6,5]=>0000000=>[8]=>[8]
[2,7,3,1,5,8,4,6]=>0000000=>[8]=>[8]
[3,8,7,1,6,4,5,2]=>0000000=>[8]=>[8]
[4,3,2,1,5,8,6,7]=>0001100=>[4,1,3]=>[4,3,1]
[4,1,3,7,5,6,8,2]=>0000000=>[8]=>[8]
[3,4,6,1,5,8,2,7]=>0000000=>[8]=>[8]
[6,5,8,7,1,4,2,3]=>0000000=>[8]=>[8]
[4,1,7,3,8,5,2,6]=>0000000=>[8]=>[8]
[5,6,8,7,2,4,1,3]=>0000000=>[8]=>[8]
[7,1,3,4,2,8,5,6]=>0000000=>[8]=>[8]
[7,6,1,4,3,5,8,2]=>0000000=>[8]=>[8]
[3,5,4,1,6,7,8,2]=>0000000=>[8]=>[8]
[2,5,3,4,8,6,1,7]=>0000000=>[8]=>[8]
[2,4,8,3,6,1,7,5]=>0000000=>[8]=>[8]
[6,8,2,1,5,7,3,4]=>0000000=>[8]=>[8]
[1,2,4,8,6,5,3,7]=>1100000=>[1,1,6]=>[6,1,1]
[7,1,5,6,8,4,3,2]=>0000000=>[8]=>[8]
[7,3,5,6,1,4,8,2]=>0000000=>[8]=>[8]
[3,7,6,5,1,4,8,2]=>0000000=>[8]=>[8]
[2,7,6,5,3,8,1,4]=>0000000=>[8]=>[8]
[2,7,8,1,4,6,3,5]=>0000000=>[8]=>[8]
[4,1,6,8,5,3,7,2]=>0000000=>[8]=>[8]
[5,2,6,4,8,3,1,7]=>0000000=>[8]=>[8]
[1,2,6,3,4,8,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[5,3,6,1,4,7,8,2]=>0000000=>[8]=>[8]
[6,7,1,3,4,5,8,2]=>0000000=>[8]=>[8]
[1,7,3,2,4,8,5,6]=>1000000=>[1,7]=>[7,1]
[6,1,4,2,8,3,5,7]=>0000000=>[8]=>[8]
[5,8,6,7,2,1,4,3]=>0000000=>[8]=>[8]
[8,6,1,3,5,4,2,7]=>0000000=>[8]=>[8]
[2,7,6,3,4,5,8,1]=>0000000=>[8]=>[8]
[5,3,8,6,1,2,4,7]=>0000000=>[8]=>[8]
[3,8,7,2,6,4,5,1]=>0000000=>[8]=>[8]
[4,5,8,7,2,6,3,1]=>0000000=>[8]=>[8]
[8,5,2,7,1,4,3,6]=>0000000=>[8]=>[8]
[3,7,5,8,2,6,1,4]=>0000000=>[8]=>[8]
[1,6,7,4,8,2,3,5]=>1000000=>[1,7]=>[7,1]
[8,2,1,3,5,6,7,4]=>0000000=>[8]=>[8]
[4,1,3,8,2,6,7,5]=>0000000=>[8]=>[8]
[3,6,1,4,7,2,8,5]=>0000000=>[8]=>[8]
[6,2,7,4,5,8,1,3]=>0000000=>[8]=>[8]
[1,8,5,7,3,2,4,6]=>1000000=>[1,7]=>[7,1]
[3,2,1,6,4,8,5,7]=>0010000=>[3,5]=>[5,3]
[2,7,4,1,5,3,8,6]=>0000000=>[8]=>[8]
[7,4,8,6,2,3,1,5]=>0000000=>[8]=>[8]
[7,3,2,4,8,6,1,5]=>0000000=>[8]=>[8]
[5,1,7,4,2,3,8,6]=>0000000=>[8]=>[8]
[4,8,5,3,6,2,7,1]=>0000000=>[8]=>[8]
[5,7,4,3,6,2,8,1]=>0000000=>[8]=>[8]
[6,7,5,1,2,8,3,4]=>0000000=>[8]=>[8]
[7,5,1,4,2,6,8,3]=>0000000=>[8]=>[8]
[5,2,6,8,3,4,7,1]=>0000000=>[8]=>[8]
[6,2,7,5,8,3,1,4]=>0000000=>[8]=>[8]
[2,1,5,6,8,3,7,4]=>0100000=>[2,6]=>[6,2]
[1,2,7,4,8,3,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,8,3,2,7,4,5]=>1000000=>[1,7]=>[7,1]
[5,7,3,8,2,4,6,1]=>0000000=>[8]=>[8]
[5,7,3,6,4,8,2,1]=>0000000=>[8]=>[8]
[3,6,2,4,7,1,8,5]=>0000000=>[8]=>[8]
[4,2,8,5,1,6,7,3]=>0000000=>[8]=>[8]
[1,2,8,3,7,5,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,3,8,7,4,2,5]=>1000000=>[1,7]=>[7,1]
[3,8,5,7,1,4,2,6]=>0000000=>[8]=>[8]
[4,7,2,5,1,3,8,6]=>0000000=>[8]=>[8]
[5,1,7,4,8,6,3,2]=>0000000=>[8]=>[8]
[3,6,5,2,1,8,7,4]=>0000000=>[8]=>[8]
[5,2,7,4,1,3,6,8]=>0000001=>[7,1]=>[7,1]
[5,2,6,4,1,8,7,3]=>0000000=>[8]=>[8]
[6,3,2,1,4,8,7,5]=>0000000=>[8]=>[8]
[5,4,7,6,3,8,1,2]=>0000000=>[8]=>[8]
[4,6,3,7,5,8,1,2]=>0000000=>[8]=>[8]
[5,7,4,3,8,1,2,6]=>0000000=>[8]=>[8]
[1,5,7,4,8,6,3,2]=>1000000=>[1,7]=>[7,1]
[1,8,2,7,6,5,4,3]=>1000000=>[1,7]=>[7,1]
[3,8,1,6,7,5,4,2]=>0000000=>[8]=>[8]
[3,7,2,6,8,5,1,4]=>0000000=>[8]=>[8]
[8,2,4,3,6,1,5,7]=>0000000=>[8]=>[8]
[1,7,8,5,4,3,6,2]=>1000000=>[1,7]=>[7,1]
[7,3,8,1,4,2,6,5]=>0000000=>[8]=>[8]
[1,8,4,5,3,2,6,7]=>1000000=>[1,7]=>[7,1]
[3,7,8,1,2,6,5,4]=>0000000=>[8]=>[8]
[1,6,4,5,7,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,3,6,1,7,2,4,5]=>0000000=>[8]=>[8]
[7,3,5,2,1,8,4,6]=>0000000=>[8]=>[8]
[6,4,2,8,7,5,1,3]=>0000000=>[8]=>[8]
[1,5,3,6,8,7,4,2]=>1000000=>[1,7]=>[7,1]
[3,5,4,6,1,8,2,7]=>0000000=>[8]=>[8]
[3,1,5,7,6,8,2,4]=>0000000=>[8]=>[8]
[6,4,5,7,2,8,1,3]=>0000000=>[8]=>[8]
[2,6,3,5,4,8,1,7]=>0000000=>[8]=>[8]
[3,7,4,5,6,8,1,2]=>0000000=>[8]=>[8]
[2,5,7,3,6,8,1,4]=>0000000=>[8]=>[8]
[5,4,3,1,8,2,7,6]=>0000000=>[8]=>[8]
[1,2,8,3,5,4,6,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,7,8,4,3,5,6,2]=>1000000=>[1,7]=>[7,1]
[3,1,6,8,4,5,7,2]=>0000000=>[8]=>[8]
[1,4,5,8,3,6,7,2]=>1000000=>[1,7]=>[7,1]
[2,5,7,1,8,3,6,4]=>0000000=>[8]=>[8]
[6,2,7,1,8,4,5,3]=>0000000=>[8]=>[8]
[4,7,1,3,8,5,6,2]=>0000000=>[8]=>[8]
[3,7,2,1,8,4,5,6]=>0000000=>[8]=>[8]
[4,2,7,1,8,3,6,5]=>0000000=>[8]=>[8]
[4,3,1,6,8,2,7,5]=>0000000=>[8]=>[8]
[5,3,4,6,8,2,7,1]=>0000000=>[8]=>[8]
[3,5,1,6,8,2,7,4]=>0000000=>[8]=>[8]
[5,8,3,2,6,4,1,7]=>0000000=>[8]=>[8]
[7,3,8,2,6,4,1,5]=>0000000=>[8]=>[8]
[3,8,7,4,5,6,1,2]=>0000000=>[8]=>[8]
[2,7,6,3,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[3,8,7,4,6,2,5,1]=>0000000=>[8]=>[8]
[5,8,3,7,6,2,4,1]=>0000000=>[8]=>[8]
[5,8,7,4,3,6,2,1]=>0000000=>[8]=>[8]
[5,8,6,4,3,7,1,2]=>0000000=>[8]=>[8]
[6,5,8,4,3,1,7,2]=>0000000=>[8]=>[8]
[2,6,4,7,1,5,3,8]=>0000001=>[7,1]=>[7,1]
[2,5,6,8,4,3,7,1]=>0000000=>[8]=>[8]
[5,3,8,1,7,6,4,2]=>0000000=>[8]=>[8]
[5,4,8,7,1,6,3,2]=>0000000=>[8]=>[8]
[4,8,6,7,5,3,1,2]=>0000000=>[8]=>[8]
[4,8,6,5,7,2,1,3]=>0000000=>[8]=>[8]
[6,2,1,5,8,3,7,4]=>0000000=>[8]=>[8]
[5,8,3,2,7,6,4,1]=>0000000=>[8]=>[8]
[5,8,3,2,6,7,1,4]=>0000000=>[8]=>[8]
[6,5,3,2,8,1,7,4]=>0000000=>[8]=>[8]
[6,4,3,2,1,8,7,5]=>0000000=>[8]=>[8]
[6,3,4,1,2,8,7,5]=>0000000=>[8]=>[8]
[5,2,1,4,3,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,6,3,2,5,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,5,7,4,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,3,6,1,5,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,2,1,5,7,6,3,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,7,1,6,2,8]=>0000001=>[7,1]=>[7,1]
[3,4,5,8,6,7,1,2]=>0000000=>[8]=>[8]
[4,3,5,1,6,8,7,2]=>0000000=>[8]=>[8]
[2,1,5,3,8,4,7,6]=>0100000=>[2,6]=>[6,2]
[3,1,8,2,5,4,7,6]=>0000000=>[8]=>[8]
[8,1,3,2,6,4,7,5]=>0000000=>[8]=>[8]
[3,1,8,2,6,4,7,5]=>0000000=>[8]=>[8]
[2,1,8,3,6,4,7,5]=>0100000=>[2,6]=>[6,2]
[2,1,7,3,5,4,8,6]=>0100000=>[2,6]=>[6,2]
[2,1,7,3,6,4,8,5]=>0100000=>[2,6]=>[6,2]
[2,1,7,3,8,4,6,5]=>0100000=>[2,6]=>[6,2]
[8,1,4,2,7,3,6,5]=>0000000=>[8]=>[8]
[4,1,7,2,8,3,6,5]=>0000000=>[8]=>[8]
[3,1,7,2,8,4,6,5]=>0000000=>[8]=>[8]
[3,1,6,2,5,4,8,7]=>0000010=>[6,2]=>[6,2]
[7,1,3,2,6,4,8,5]=>0000000=>[8]=>[8]
[7,1,8,2,4,3,6,5]=>0000000=>[8]=>[8]
[7,1,5,2,8,3,6,4]=>0000000=>[8]=>[8]
[4,1,6,2,5,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,1,7,2,5,3,8,6]=>0000000=>[8]=>[8]
[4,1,7,2,6,3,8,5]=>0000000=>[8]=>[8]
[5,1,7,2,6,3,8,4]=>0000000=>[8]=>[8]
[5,1,7,2,8,3,6,4]=>0000000=>[8]=>[8]
[8,1,5,2,7,3,6,4]=>0000000=>[8]=>[8]
[8,1,5,2,6,3,7,4]=>0000000=>[8]=>[8]
[5,1,8,2,6,3,7,4]=>0000000=>[8]=>[8]
[5,1,6,2,8,3,7,4]=>0000000=>[8]=>[8]
[3,1,6,2,8,4,7,5]=>0000000=>[8]=>[8]
[4,1,8,2,6,3,7,5]=>0000000=>[8]=>[8]
[8,1,4,2,6,3,7,5]=>0000000=>[8]=>[8]
[8,1,4,2,5,3,7,6]=>0000000=>[8]=>[8]
[4,1,8,2,5,3,7,6]=>0000000=>[8]=>[8]
[4,1,5,2,8,3,7,6]=>0000000=>[8]=>[8]
[3,1,5,2,8,4,7,6]=>0000000=>[8]=>[8]
[5,1,4,2,8,3,7,6]=>0000000=>[8]=>[8]
[6,1,3,2,8,4,7,5]=>0000000=>[8]=>[8]
[6,1,3,2,7,4,8,5]=>0000000=>[8]=>[8]
[6,1,4,2,7,3,8,5]=>0000000=>[8]=>[8]
[6,1,7,2,8,3,5,4]=>0000000=>[8]=>[8]
[7,8,3,1,2,5,6,4]=>0000000=>[8]=>[8]
[7,8,1,3,2,4,6,5]=>0000000=>[8]=>[8]
[6,2,8,1,3,5,4,7]=>0000000=>[8]=>[8]
[6,2,8,3,1,7,4,5]=>0000000=>[8]=>[8]
[3,2,5,7,1,8,4,6]=>0000000=>[8]=>[8]
[3,5,2,8,1,7,4,6]=>0000000=>[8]=>[8]
[5,1,3,7,2,6,8,4]=>0000000=>[8]=>[8]
[2,5,4,6,8,1,7,3]=>0000000=>[8]=>[8]
[4,3,5,7,6,8,1,2]=>0000000=>[8]=>[8]
[7,6,4,3,2,1,8,5]=>0000000=>[8]=>[8]
[7,6,5,8,2,1,4,3]=>0000000=>[8]=>[8]
[7,8,4,3,2,1,6,5]=>0000000=>[8]=>[8]
[7,6,3,8,2,1,5,4]=>0000000=>[8]=>[8]
[7,6,5,8,4,1,3,2]=>0000000=>[8]=>[8]
[7,4,8,3,2,1,6,5]=>0000000=>[8]=>[8]
[7,6,8,5,2,1,4,3]=>0000000=>[8]=>[8]
[4,8,6,1,7,5,2,3]=>0000000=>[8]=>[8]
[4,8,7,2,6,5,1,3]=>0000000=>[8]=>[8]
[8,4,7,3,6,5,1,2]=>0000000=>[8]=>[8]
[6,8,4,3,7,2,1,5]=>0000000=>[8]=>[8]
[6,7,4,2,8,3,1,5]=>0000000=>[8]=>[8]
[2,8,7,6,5,1,4,3]=>0000000=>[8]=>[8]
[7,3,2,5,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[7,1,4,2,6,3,5,8]=>0000001=>[7,1]=>[7,1]
[7,3,2,5,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[7,4,1,3,5,2,6,8]=>0000001=>[7,1]=>[7,1]
[2,3,6,1,4,8,7,5]=>0000000=>[8]=>[8]
[5,6,8,2,4,1,3,7]=>0000000=>[8]=>[8]
[5,6,8,7,4,3,1,2]=>0000000=>[8]=>[8]
[2,4,8,1,6,3,7,5]=>0000000=>[8]=>[8]
[1,8,4,5,2,6,7,3]=>1000000=>[1,7]=>[7,1]
[5,6,7,3,2,8,1,4]=>0000000=>[8]=>[8]
[5,3,2,1,4,8,6,7]=>0000100=>[5,3]=>[5,3]
[3,4,7,8,1,2,6,5]=>0000000=>[8]=>[8]
[3,6,7,8,1,4,5,2]=>0000000=>[8]=>[8]
[2,3,6,8,5,1,4,7]=>0000000=>[8]=>[8]
[3,1,6,4,8,2,5,7]=>0000000=>[8]=>[8]
[7,3,2,6,8,5,1,4]=>0000000=>[8]=>[8]
[5,7,8,3,1,4,6,2]=>0000000=>[8]=>[8]
[7,4,8,3,2,5,1,6]=>0000000=>[8]=>[8]
[7,3,8,2,4,5,6,1]=>0000000=>[8]=>[8]
[4,2,7,1,5,3,8,6]=>0000000=>[8]=>[8]
[1,2,7,3,4,8,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[4,7,2,1,5,8,6,3]=>0000000=>[8]=>[8]
[4,8,3,6,5,1,7,2]=>0000000=>[8]=>[8]
[6,4,7,3,5,1,8,2]=>0000000=>[8]=>[8]
[3,1,6,4,7,8,2,5]=>0000000=>[8]=>[8]
[1,2,5,8,3,7,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[8,2,4,1,7,5,6,3]=>0000000=>[8]=>[8]
[3,8,4,7,5,1,6,2]=>0000000=>[8]=>[8]
[8,4,3,6,1,7,5,2]=>0000000=>[8]=>[8]
[2,1,8,6,7,3,5,4]=>0100000=>[2,6]=>[6,2]
[1,2,8,6,3,4,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[7,3,2,5,6,1,4,8]=>0000001=>[7,1]=>[7,1]
[8,4,1,2,7,5,3,6]=>0000000=>[8]=>[8]
[1,5,2,8,6,3,7,4]=>1000000=>[1,7]=>[7,1]
[5,8,6,3,1,7,4,2]=>0000000=>[8]=>[8]
[7,8,1,4,2,5,3,6]=>0000000=>[8]=>[8]
[5,6,2,7,1,3,4,8]=>0000001=>[7,1]=>[7,1]
[1,6,2,7,4,8,3,5]=>1000000=>[1,7]=>[7,1]
[6,2,1,7,8,5,3,4]=>0000000=>[8]=>[8]
[6,7,3,8,4,1,5,2]=>0000000=>[8]=>[8]
[2,7,1,8,5,6,3,4]=>0000000=>[8]=>[8]
[2,1,7,8,6,3,4,5]=>0100000=>[2,6]=>[6,2]
[7,8,6,2,1,3,5,4]=>0000000=>[8]=>[8]
[6,1,3,4,2,8,7,5]=>0000000=>[8]=>[8]
[7,1,3,8,6,4,5,2]=>0000000=>[8]=>[8]
[7,4,2,1,8,6,5,3]=>0000000=>[8]=>[8]
[2,1,6,3,4,8,7,5]=>0100000=>[2,6]=>[6,2]
[8,1,4,2,5,6,7,3]=>0000000=>[8]=>[8]
[8,1,3,2,5,6,7,4]=>0000000=>[8]=>[8]
[2,1,4,8,7,5,3,6]=>0100000=>[2,6]=>[6,2]
[7,1,5,8,2,6,3,4]=>0000000=>[8]=>[8]
[3,6,8,2,4,1,5,7]=>0000000=>[8]=>[8]
[6,2,8,1,7,5,4,3]=>0000000=>[8]=>[8]
[7,8,5,6,4,1,3,2]=>0000000=>[8]=>[8]
[3,8,1,4,5,6,2,7]=>0000000=>[8]=>[8]
[5,8,7,3,6,1,4,2]=>0000000=>[8]=>[8]
[5,8,3,7,6,1,4,2]=>0000000=>[8]=>[8]
[7,5,8,4,6,1,3,2]=>0000000=>[8]=>[8]
[2,4,8,1,3,7,6,5]=>0000000=>[8]=>[8]
[2,5,1,3,8,4,7,6]=>0000000=>[8]=>[8]
[2,8,1,5,4,7,3,6]=>0000000=>[8]=>[8]
[8,3,2,6,1,4,7,5]=>0000000=>[8]=>[8]
[2,5,7,1,3,8,6,4]=>0000000=>[8]=>[8]
[2,7,1,6,5,3,8,4]=>0000000=>[8]=>[8]
[2,8,1,7,6,5,4,3]=>0000000=>[8]=>[8]
[8,3,2,7,1,6,5,4]=>0000000=>[8]=>[8]
[7,4,2,8,1,6,5,3]=>0000000=>[8]=>[8]
[8,7,5,3,2,1,6,4]=>0000000=>[8]=>[8]
[7,4,5,8,6,2,1,3]=>0000000=>[8]=>[8]
[4,6,8,5,1,7,3,2]=>0000000=>[8]=>[8]
[4,7,5,1,3,8,6,2]=>0000000=>[8]=>[8]
[5,1,7,6,4,2,8,3]=>0000000=>[8]=>[8]
[5,1,8,7,6,4,3,2]=>0000000=>[8]=>[8]
[5,1,6,2,8,7,4,3]=>0000000=>[8]=>[8]
[4,5,6,1,8,7,2,3]=>0000000=>[8]=>[8]
[3,5,6,8,7,1,4,2]=>0000000=>[8]=>[8]
[3,6,1,7,4,8,2,5]=>0000000=>[8]=>[8]
[8,4,2,6,3,1,5,7]=>0000000=>[8]=>[8]
[3,4,8,7,1,2,6,5]=>0000000=>[8]=>[8]
[3,4,6,8,5,7,1,2]=>0000000=>[8]=>[8]
[4,6,8,3,5,7,2,1]=>0000000=>[8]=>[8]
[4,7,3,5,8,2,6,1]=>0000000=>[8]=>[8]
[5,6,8,3,7,2,1,4]=>0000000=>[8]=>[8]
[5,6,8,4,2,7,3,1]=>0000000=>[8]=>[8]
[6,5,2,7,1,3,8,4]=>0000000=>[8]=>[8]
[6,5,4,1,7,2,8,3]=>0000000=>[8]=>[8]
[6,4,7,3,1,8,2,5]=>0000000=>[8]=>[8]
[5,6,3,7,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[6,1,3,8,5,2,4,7]=>0000000=>[8]=>[8]
[7,4,2,6,3,5,1,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,5,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[8,1,3,4,5,2,6,7]=>0000000=>[8]=>[8]
[1,6,8,4,2,5,3,7]=>1000000=>[1,7]=>[7,1]
[8,7,2,3,6,1,4,5]=>0000000=>[8]=>[8]
[1,4,8,5,2,6,7,3]=>1000000=>[1,7]=>[7,1]
[6,1,8,4,3,7,2,5]=>0000000=>[8]=>[8]
[1,5,2,4,8,7,3,6]=>1000000=>[1,7]=>[7,1]
[3,2,6,4,1,8,7,5]=>0000000=>[8]=>[8]
[7,6,4,3,1,8,2,5]=>0000000=>[8]=>[8]
[8,4,6,5,1,7,2,3]=>0000000=>[8]=>[8]
[7,5,4,6,1,2,8,3]=>0000000=>[8]=>[8]
[3,2,5,6,1,7,8,4]=>0000000=>[8]=>[8]
[3,2,8,7,6,1,4,5]=>0000000=>[8]=>[8]
[6,8,4,7,2,1,3,5]=>0000000=>[8]=>[8]
[3,8,7,5,6,1,2,4]=>0000000=>[8]=>[8]
[8,2,7,6,5,1,3,4]=>0000000=>[8]=>[8]
[4,8,6,7,1,5,3,2]=>0000000=>[8]=>[8]
[1,8,6,7,2,3,4,5]=>1000000=>[1,7]=>[7,1]
[3,5,4,2,7,1,8,6]=>0000000=>[8]=>[8]
[3,2,6,1,5,7,4,8]=>0000001=>[7,1]=>[7,1]
[5,2,1,4,7,6,3,8]=>0000001=>[7,1]=>[7,1]
[4,2,1,3,5,8,7,6]=>0001100=>[4,1,3]=>[4,3,1]
[7,4,1,5,3,6,8,2]=>0000000=>[8]=>[8]
[6,8,3,4,1,5,2,7]=>0000000=>[8]=>[8]
[5,8,4,1,7,2,6,3]=>0000000=>[8]=>[8]
[4,1,8,3,5,7,2,6]=>0000000=>[8]=>[8]
[2,4,6,3,5,8,1,7]=>0000000=>[8]=>[8]
[4,5,7,2,3,6,8,1]=>0000000=>[8]=>[8]
[2,6,3,4,7,5,8,1]=>0000000=>[8]=>[8]
[4,5,2,7,1,6,8,3]=>0000000=>[8]=>[8]
[2,3,1,7,6,4,8,5]=>0010000=>[3,5]=>[5,3]
[3,4,1,6,5,8,2,7]=>0000000=>[8]=>[8]
[6,4,2,8,7,1,5,3]=>0000000=>[8]=>[8]
[3,1,8,2,7,6,4,5]=>0000000=>[8]=>[8]
[6,2,8,4,1,7,5,3]=>0000000=>[8]=>[8]
[3,6,4,7,2,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,3,2,8,6,1,4,5]=>0000000=>[8]=>[8]
[4,3,8,7,1,2,5,6]=>0000000=>[8]=>[8]
[1,2,5,8,4,7,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,6,8,5,2,7,4]=>1000000=>[1,7]=>[7,1]
[2,5,7,4,1,8,6,3]=>0000000=>[8]=>[8]
[1,4,2,5,8,7,3,6]=>1000000=>[1,7]=>[7,1]
[3,5,1,7,2,8,6,4]=>0000000=>[8]=>[8]
[4,6,3,1,7,8,5,2]=>0000000=>[8]=>[8]
[5,3,1,6,7,8,4,2]=>0000000=>[8]=>[8]
[2,1,3,4,8,7,5,6]=>0111000=>[2,1,1,4]=>[4,2,1,1]
[4,8,7,3,6,5,1,2]=>0000000=>[8]=>[8]
[4,3,8,7,6,5,1,2]=>0000000=>[8]=>[8]
[2,8,7,6,1,5,4,3]=>0000000=>[8]=>[8]
[5,2,8,7,6,1,4,3]=>0000000=>[8]=>[8]
[6,2,8,7,5,1,4,3]=>0000000=>[8]=>[8]
[7,8,2,6,5,1,4,3]=>0000000=>[8]=>[8]
[6,1,8,7,5,4,3,2]=>0000000=>[8]=>[8]
[4,1,8,7,6,5,3,2]=>0000000=>[8]=>[8]
[3,1,8,7,6,5,4,2]=>0000000=>[8]=>[8]
[7,8,2,6,1,5,4,3]=>0000000=>[8]=>[8]
[4,2,8,1,7,6,5,3]=>0000000=>[8]=>[8]
[3,2,8,1,7,6,5,4]=>0000000=>[8]=>[8]
[2,8,7,1,6,5,4,3]=>0000000=>[8]=>[8]
[3,8,2,1,7,6,5,4]=>0000000=>[8]=>[8]
[4,8,2,7,6,1,5,3]=>0000000=>[8]=>[8]
[3,8,2,7,1,6,5,4]=>0000000=>[8]=>[8]
[3,8,7,2,1,6,5,4]=>0000000=>[8]=>[8]
[4,8,7,2,6,1,5,3]=>0000000=>[8]=>[8]
[5,8,7,6,2,1,4,3]=>0000000=>[8]=>[8]
[6,5,8,7,1,4,3,2]=>0000000=>[8]=>[8]
[3,8,7,1,6,5,4,2]=>0000000=>[8]=>[8]
[4,8,1,7,6,5,3,2]=>0000000=>[8]=>[8]
[5,4,1,8,7,6,3,2]=>0000000=>[8]=>[8]
[6,4,8,1,7,5,3,2]=>0000000=>[8]=>[8]
[7,8,4,1,6,5,3,2]=>0000000=>[8]=>[8]
[7,8,3,1,6,5,4,2]=>0000000=>[8]=>[8]
[5,3,1,8,7,6,4,2]=>0000000=>[8]=>[8]
[4,3,1,8,7,6,5,2]=>0000000=>[8]=>[8]
[4,2,1,8,7,6,5,3]=>0000000=>[8]=>[8]
[6,5,3,1,8,7,4,2]=>0000000=>[8]=>[8]
[5,4,2,1,8,7,6,3]=>0000000=>[8]=>[8]
[8,6,1,4,2,3,5,7]=>0000000=>[8]=>[8]
[6,8,1,4,2,3,5,7]=>0000000=>[8]=>[8]
[4,6,2,3,8,1,5,7]=>0000000=>[8]=>[8]
[6,4,2,3,8,1,5,7]=>0000000=>[8]=>[8]
[2,8,4,3,6,1,5,7]=>0000000=>[8]=>[8]
[2,4,8,3,6,1,5,7]=>0000000=>[8]=>[8]
[8,3,6,2,4,1,5,7]=>0000000=>[8]=>[8]
[8,3,6,2,1,4,5,7]=>0000000=>[8]=>[8]
[2,1,8,3,6,4,5,7]=>0100000=>[2,6]=>[6,2]
[6,3,8,2,1,4,5,7]=>0000000=>[8]=>[8]
[3,6,4,7,8,5,1,2]=>0000000=>[8]=>[8]
[1,6,4,2,7,5,8,3]=>1000000=>[1,7]=>[7,1]
[3,4,6,8,7,5,1,2]=>0000000=>[8]=>[8]
[5,4,6,3,8,7,1,2]=>0000000=>[8]=>[8]
[6,4,8,5,3,7,1,2]=>0000000=>[8]=>[8]
[1,8,5,2,6,3,7,4]=>1000000=>[1,7]=>[7,1]
[1,4,6,2,8,5,7,3]=>1000000=>[1,7]=>[7,1]
[7,8,1,4,2,5,6,3]=>0000000=>[8]=>[8]
[4,8,5,3,1,6,2,7]=>0000000=>[8]=>[8]
[5,2,8,6,4,1,3,7]=>0000000=>[8]=>[8]
[5,1,6,2,8,7,3,4]=>0000000=>[8]=>[8]
[6,1,8,7,4,2,3,5]=>0000000=>[8]=>[8]
[1,2,8,5,7,3,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,6,8,7,5,2,4]=>1000000=>[1,7]=>[7,1]
[7,8,1,2,4,6,5,3]=>0000000=>[8]=>[8]
[1,2,6,4,8,7,5,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,2,5,4,7,6,3]=>1000000=>[1,7]=>[7,1]
[1,2,7,3,5,8,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[4,6,2,1,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,2,3,7,8,1,5]=>0000000=>[8]=>[8]
[4,2,1,3,5,7,8,6]=>0001100=>[4,1,3]=>[4,3,1]
[7,8,3,2,4,1,6,5]=>0000000=>[8]=>[8]
[7,8,4,2,6,3,1,5]=>0000000=>[8]=>[8]
[5,8,2,7,4,3,1,6]=>0000000=>[8]=>[8]
[7,5,2,8,3,4,1,6]=>0000000=>[8]=>[8]
[6,4,3,5,2,8,1,7]=>0000000=>[8]=>[8]
[4,1,3,6,5,8,7,2]=>0000000=>[8]=>[8]
[2,4,1,3,8,5,7,6]=>0001000=>[4,4]=>[4,4]
[2,4,1,3,5,8,7,6]=>0001100=>[4,1,3]=>[4,3,1]
[4,6,1,3,5,8,7,2]=>0000000=>[8]=>[8]
[1,4,6,3,5,8,7,2]=>1000000=>[1,7]=>[7,1]
[4,2,1,3,6,5,7,8]=>0001011=>[4,2,1,1]=>[4,2,1,1]
[4,2,1,8,3,5,7,6]=>0000000=>[8]=>[8]
[6,2,1,8,3,5,7,4]=>0000000=>[8]=>[8]
[6,4,1,3,8,5,7,2]=>0000000=>[8]=>[8]
[8,2,1,3,6,5,7,4]=>0000000=>[8]=>[8]
[8,2,1,4,3,5,7,6]=>0000000=>[8]=>[8]
[8,1,4,6,3,5,7,2]=>0000000=>[8]=>[8]
[2,4,8,1,3,5,7,6]=>0000000=>[8]=>[8]
[4,6,8,1,3,5,7,2]=>0000000=>[8]=>[8]
[4,6,1,8,3,5,7,2]=>0000000=>[8]=>[8]
[4,1,6,8,3,5,7,2]=>0000000=>[8]=>[8]
[1,4,6,8,3,5,7,2]=>1000000=>[1,7]=>[7,1]
[1,4,6,3,8,5,7,2]=>1000000=>[1,7]=>[7,1]
[4,6,1,3,8,5,7,2]=>0000000=>[8]=>[8]
[2,6,1,3,8,5,7,4]=>0000000=>[8]=>[8]
[2,6,1,8,3,5,7,4]=>0000000=>[8]=>[8]
[2,1,3,6,8,5,7,4]=>0110000=>[2,1,5]=>[5,2,1]
[4,1,3,6,8,5,7,2]=>0000000=>[8]=>[8]
[1,4,3,6,8,5,7,2]=>1000000=>[1,7]=>[7,1]
[2,1,8,3,6,5,7,4]=>0100000=>[2,6]=>[6,2]
[2,1,8,6,3,5,7,4]=>0100000=>[2,6]=>[6,2]
[2,1,8,4,3,5,7,6]=>0100000=>[2,6]=>[6,2]
[2,8,4,1,3,5,7,6]=>0000000=>[8]=>[8]
[6,8,1,4,3,5,7,2]=>0000000=>[8]=>[8]
[1,8,6,4,3,5,7,2]=>1000000=>[1,7]=>[7,1]
[8,6,1,4,3,5,7,2]=>0000000=>[8]=>[8]
[8,6,4,1,3,5,7,2]=>0000000=>[8]=>[8]
[8,4,2,1,3,5,7,6]=>0000000=>[8]=>[8]
[8,5,7,4,3,2,1,6]=>0000000=>[8]=>[8]
[8,7,6,5,1,4,3,2]=>0000000=>[8]=>[8]
[8,7,3,6,5,2,1,4]=>0000000=>[8]=>[8]
[6,5,8,4,3,2,1,7]=>0000000=>[8]=>[8]
[8,4,7,6,3,2,1,5]=>0000000=>[8]=>[8]
[5,8,7,4,3,2,1,6]=>0000000=>[8]=>[8]
[4,5,2,7,3,1,8,6]=>0000000=>[8]=>[8]
[4,8,2,6,3,5,7,1]=>0000000=>[8]=>[8]
[8,6,1,2,7,4,3,5]=>0000000=>[8]=>[8]
[4,6,2,1,7,8,5,3]=>0000000=>[8]=>[8]
[2,3,8,7,4,1,6,5]=>0000000=>[8]=>[8]
[7,8,2,1,5,6,4,3]=>0000000=>[8]=>[8]
[1,6,2,5,8,4,3,7]=>1000000=>[1,7]=>[7,1]
[5,2,7,1,8,6,3,4]=>0000000=>[8]=>[8]
[1,2,8,3,7,6,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[6,5,2,8,1,7,3,4]=>0000000=>[8]=>[8]
[2,8,3,5,1,7,4,6]=>0000000=>[8]=>[8]
[2,8,5,6,1,7,3,4]=>0000000=>[8]=>[8]
[5,4,2,8,6,1,7,3]=>0000000=>[8]=>[8]
[8,3,7,4,2,6,5,1]=>0000000=>[8]=>[8]
[6,3,2,8,4,1,7,5]=>0000000=>[8]=>[8]
[2,8,3,4,1,7,5,6]=>0000000=>[8]=>[8]
[5,4,2,8,3,1,7,6]=>0000000=>[8]=>[8]
[2,8,6,4,1,7,5,3]=>0000000=>[8]=>[8]
[8,4,7,6,2,5,3,1]=>0000000=>[8]=>[8]
[4,8,7,6,1,5,3,2]=>0000000=>[8]=>[8]
[7,3,8,5,2,1,6,4]=>0000000=>[8]=>[8]
[7,3,8,4,2,1,6,5]=>0000000=>[8]=>[8]
[7,5,4,3,8,2,1,6]=>0000000=>[8]=>[8]
[5,4,2,3,8,1,6,7]=>0000000=>[8]=>[8]
[3,7,8,4,1,2,6,5]=>0000000=>[8]=>[8]
[7,3,4,8,2,1,5,6]=>0000000=>[8]=>[8]
[7,5,8,6,2,1,4,3]=>0000000=>[8]=>[8]
[6,5,8,7,3,1,4,2]=>0000000=>[8]=>[8]
[2,4,8,3,1,5,7,6]=>0000000=>[8]=>[8]
[6,3,2,4,8,1,5,7]=>0000000=>[8]=>[8]
[2,4,3,8,1,6,5,7]=>0000000=>[8]=>[8]
[2,3,8,4,1,6,7,5]=>0000000=>[8]=>[8]
[3,4,8,7,1,5,6,2]=>0000000=>[8]=>[8]
[2,5,3,8,1,6,4,7]=>0000000=>[8]=>[8]
[3,7,4,8,1,5,2,6]=>0000000=>[8]=>[8]
[2,6,8,5,1,3,7,4]=>0000000=>[8]=>[8]
[2,6,8,4,1,3,7,5]=>0000000=>[8]=>[8]
[3,7,5,8,1,4,2,6]=>0000000=>[8]=>[8]
[2,6,5,8,1,4,3,7]=>0000000=>[8]=>[8]
[2,5,8,3,1,4,7,6]=>0000000=>[8]=>[8]
[4,7,6,8,1,3,2,5]=>0000000=>[8]=>[8]
[5,6,8,7,1,3,4,2]=>0000000=>[8]=>[8]
[8,7,4,1,6,2,5,3]=>0000000=>[8]=>[8]
[6,4,7,2,8,5,1,3]=>0000000=>[8]=>[8]
[1,7,6,2,4,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,7,3,2,4,6,5,1]=>0000000=>[8]=>[8]
[6,4,7,3,8,5,2,1]=>0000000=>[8]=>[8]
[2,7,1,5,6,3,4,8]=>0000001=>[7,1]=>[7,1]
[3,6,4,1,2,8,7,5]=>0000000=>[8]=>[8]
[3,6,5,1,8,2,7,4]=>0000000=>[8]=>[8]
[4,6,5,1,8,7,2,3]=>0000000=>[8]=>[8]
[5,7,1,4,8,6,2,3]=>0000000=>[8]=>[8]
[5,7,1,3,8,2,6,4]=>0000000=>[8]=>[8]
[6,3,7,2,8,4,5,1]=>0000000=>[8]=>[8]
[6,7,1,8,3,2,5,4]=>0000000=>[8]=>[8]
[8,7,6,1,4,5,2,3]=>0000000=>[8]=>[8]
[8,7,6,1,3,2,5,4]=>0000000=>[8]=>[8]
[8,7,3,5,1,2,6,4]=>0000000=>[8]=>[8]
[8,7,4,5,1,6,2,3]=>0000000=>[8]=>[8]
[8,5,6,4,1,7,2,3]=>0000000=>[8]=>[8]
[8,4,6,2,3,1,7,5]=>0000000=>[8]=>[8]
[4,7,3,5,2,1,6,8]=>0000001=>[7,1]=>[7,1]
[6,7,8,4,1,5,3,2]=>0000000=>[8]=>[8]
[7,1,6,8,4,5,3,2]=>0000000=>[8]=>[8]
[7,5,1,6,4,2,3,8]=>0000001=>[7,1]=>[7,1]
[8,1,5,7,4,6,3,2]=>0000000=>[8]=>[8]
[1,8,4,6,7,5,3,2]=>1000000=>[1,7]=>[7,1]
[6,1,8,4,7,5,3,2]=>0000000=>[8]=>[8]
[4,8,5,1,6,7,3,2]=>0000000=>[8]=>[8]
[8,4,1,5,6,7,3,2]=>0000000=>[8]=>[8]
[8,1,4,5,6,7,3,2]=>0000000=>[8]=>[8]
[1,8,4,6,2,5,3,7]=>1000000=>[1,7]=>[7,1]
[8,5,6,1,2,4,3,7]=>0000000=>[8]=>[8]
[2,8,3,1,5,6,7,4]=>0000000=>[8]=>[8]
[8,3,2,7,1,5,6,4]=>0000000=>[8]=>[8]
[3,2,8,5,7,1,6,4]=>0000000=>[8]=>[8]
[3,6,2,8,5,1,7,4]=>0000000=>[8]=>[8]
[6,2,1,8,4,7,5,3]=>0000000=>[8]=>[8]
[2,8,7,1,4,6,5,3]=>0000000=>[8]=>[8]
[8,2,7,1,5,4,6,3]=>0000000=>[8]=>[8]
[7,3,1,5,6,2,4,8]=>0000001=>[7,1]=>[7,1]
[7,2,8,1,6,4,5,3]=>0000000=>[8]=>[8]
[7,8,2,6,4,1,5,3]=>0000000=>[8]=>[8]
[8,7,2,4,1,6,5,3]=>0000000=>[8]=>[8]
[1,2,8,6,3,7,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,7,2,3,6,5,4]=>1000000=>[1,7]=>[7,1]
[1,7,8,2,6,4,3,5]=>1000000=>[1,7]=>[7,1]
[2,1,7,3,6,8,4,5]=>0100000=>[2,6]=>[6,2]
[7,1,5,8,3,2,4,6]=>0000000=>[8]=>[8]
[7,8,1,5,2,4,3,6]=>0000000=>[8]=>[8]
[8,7,1,2,5,4,3,6]=>0000000=>[8]=>[8]
[1,6,2,8,4,3,7,5]=>1000000=>[1,7]=>[7,1]
[1,8,3,7,2,5,4,6]=>1000000=>[1,7]=>[7,1]
[8,1,4,7,3,2,5,6]=>0000000=>[8]=>[8]
[4,7,8,1,3,2,5,6]=>0000000=>[8]=>[8]
[2,1,8,3,5,7,4,6]=>0100000=>[2,6]=>[6,2]
[1,2,3,4,8,5,7,6]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[3,7,2,5,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,2,5,4,3,1,8]=>0000001=>[7,1]=>[7,1]
[4,7,5,2,6,3,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,7,2,4,3,1,8]=>0000001=>[7,1]=>[7,1]
[2,8,3,4,1,6,7,5]=>0000000=>[8]=>[8]
[6,1,3,5,7,2,4,8]=>0000001=>[7,1]=>[7,1]
[8,1,3,6,2,4,7,5]=>0000000=>[8]=>[8]
[2,1,8,3,7,5,4,6]=>0100000=>[2,6]=>[6,2]
[7,1,8,2,5,6,3,4]=>0000000=>[8]=>[8]
[6,1,5,8,2,7,3,4]=>0000000=>[8]=>[8]
[6,2,5,8,1,4,7,3]=>0000000=>[8]=>[8]
[3,2,8,5,1,6,7,4]=>0000000=>[8]=>[8]
[1,3,8,2,5,7,4,6]=>1000000=>[1,7]=>[7,1]
[2,8,7,1,6,4,5,3]=>0000000=>[8]=>[8]
[3,8,7,1,5,6,4,2]=>0000000=>[8]=>[8]
[4,8,7,5,1,6,3,2]=>0000000=>[8]=>[8]
[5,8,6,7,1,4,3,2]=>0000000=>[8]=>[8]
[6,7,8,5,1,4,3,2]=>0000000=>[8]=>[8]
[5,6,3,8,4,1,7,2]=>0000000=>[8]=>[8]
[7,3,8,5,4,1,6,2]=>0000000=>[8]=>[8]
[8,3,7,4,1,6,5,2]=>0000000=>[8]=>[8]
[3,5,6,8,4,1,7,2]=>0000000=>[8]=>[8]
[5,6,4,7,8,1,3,2]=>0000000=>[8]=>[8]
[6,2,3,1,5,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[8,5,1,3,2,4,7,6]=>0000000=>[8]=>[8]
[7,5,1,3,2,6,4,8]=>0000001=>[7,1]=>[7,1]
[3,6,4,1,5,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,5,6,1,3,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,7,1,4,2,5,3,8]=>0000001=>[7,1]=>[7,1]
[2,7,1,3,5,6,4,8]=>0000001=>[7,1]=>[7,1]
[8,6,1,2,4,3,7,5]=>0000000=>[8]=>[8]
[7,8,1,2,5,3,6,4]=>0000000=>[8]=>[8]
[1,8,2,7,5,4,6,3]=>1000000=>[1,7]=>[7,1]
[1,8,6,3,7,2,4,5]=>1000000=>[1,7]=>[7,1]
[1,8,2,5,4,6,7,3]=>1000000=>[1,7]=>[7,1]
[7,2,8,4,3,5,6,1]=>0000000=>[8]=>[8]
[1,4,7,5,2,6,8,3]=>1000000=>[1,7]=>[7,1]
[4,6,5,3,7,1,8,2]=>0000000=>[8]=>[8]
[5,6,2,7,3,1,8,4]=>0000000=>[8]=>[8]
[1,6,3,7,5,8,2,4]=>1000000=>[1,7]=>[7,1]
[5,2,4,8,1,3,7,6]=>0000000=>[8]=>[8]
[3,5,2,4,7,1,6,8]=>0000001=>[7,1]=>[7,1]
[6,4,5,3,8,2,1,7]=>0000000=>[8]=>[8]
[6,5,3,4,8,7,1,2]=>0000000=>[8]=>[8]
[7,6,3,8,5,4,1,2]=>0000000=>[8]=>[8]
[5,4,8,1,2,7,3,6]=>0000000=>[8]=>[8]
[6,3,8,1,7,2,4,5]=>0000000=>[8]=>[8]
[7,2,8,6,1,3,4,5]=>0000000=>[8]=>[8]
[7,2,8,6,1,5,3,4]=>0000000=>[8]=>[8]
[3,2,4,7,8,1,5,6]=>0000000=>[8]=>[8]
[1,5,7,4,2,8,6,3]=>1000000=>[1,7]=>[7,1]
[1,3,7,2,8,6,4,5]=>1000000=>[1,7]=>[7,1]
[1,5,3,6,8,2,7,4]=>1000000=>[1,7]=>[7,1]
[4,3,6,5,7,8,1,2]=>0000000=>[8]=>[8]
[4,2,3,5,6,8,1,7]=>0000000=>[8]=>[8]
[5,2,6,4,7,8,3,1]=>0000000=>[8]=>[8]
[3,2,5,6,8,1,7,4]=>0000000=>[8]=>[8]
[4,2,3,6,8,1,5,7]=>0000000=>[8]=>[8]
[2,6,1,5,4,8,3,7]=>0000000=>[8]=>[8]
[3,2,1,8,7,5,6,4]=>0010000=>[3,5]=>[5,3]
[3,1,6,2,5,8,4,7]=>0000000=>[8]=>[8]
[6,5,1,3,4,8,2,7]=>0000000=>[8]=>[8]
[6,2,4,5,8,1,3,7]=>0000000=>[8]=>[8]
[2,3,4,8,1,7,6,5]=>0000000=>[8]=>[8]
[6,2,7,8,4,5,1,3]=>0000000=>[8]=>[8]
[3,1,4,8,7,6,2,5]=>0000000=>[8]=>[8]
[2,3,6,5,8,7,1,4]=>0000000=>[8]=>[8]
[8,4,1,2,7,6,3,5]=>0000000=>[8]=>[8]
[6,3,2,8,5,7,4,1]=>0000000=>[8]=>[8]
[3,2,6,8,5,1,7,4]=>0000000=>[8]=>[8]
[5,2,4,1,7,8,6,3]=>0000000=>[8]=>[8]
[1,8,7,2,4,5,6,3]=>1000000=>[1,7]=>[7,1]
[5,3,4,7,1,8,6,2]=>0000000=>[8]=>[8]
[5,3,7,1,6,2,8,4]=>0000000=>[8]=>[8]
[4,7,6,5,8,2,1,3]=>0000000=>[8]=>[8]
[1,2,5,3,8,7,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[4,8,2,3,6,7,1,5]=>0000000=>[8]=>[8]
[8,2,4,6,7,1,3,5]=>0000000=>[8]=>[8]
[3,7,5,1,8,4,6,2]=>0000000=>[8]=>[8]
[6,5,3,1,8,4,2,7]=>0000000=>[8]=>[8]
[4,2,3,8,5,6,1,7]=>0000000=>[8]=>[8]
[2,4,8,7,1,3,5,6]=>0000000=>[8]=>[8]
[8,2,6,3,4,5,1,7]=>0000000=>[8]=>[8]
[8,1,5,4,3,6,2,7]=>0000000=>[8]=>[8]
[8,6,4,2,1,5,3,7]=>0000000=>[8]=>[8]
[8,3,2,4,6,1,5,7]=>0000000=>[8]=>[8]
[8,2,3,4,7,6,1,5]=>0000000=>[8]=>[8]
[8,1,3,7,6,4,2,5]=>0000000=>[8]=>[8]
[4,8,1,2,7,3,6,5]=>0000000=>[8]=>[8]
[2,5,7,8,4,1,3,6]=>0000000=>[8]=>[8]
[6,3,5,8,7,2,4,1]=>0000000=>[8]=>[8]
[5,2,8,7,1,3,4,6]=>0000000=>[8]=>[8]
[5,2,7,4,8,1,6,3]=>0000000=>[8]=>[8]
[8,1,7,4,5,2,6,3]=>0000000=>[8]=>[8]
[1,7,8,3,5,4,6,2]=>1000000=>[1,7]=>[7,1]
[4,6,3,5,8,1,7,2]=>0000000=>[8]=>[8]
[8,2,4,1,5,6,7,3]=>0000000=>[8]=>[8]
[3,5,1,7,6,8,2,4]=>0000000=>[8]=>[8]
[2,1,7,6,4,5,8,3]=>0100000=>[2,6]=>[6,2]
[1,7,6,5,2,4,8,3]=>1000000=>[1,7]=>[7,1]
[4,6,2,5,3,8,7,1]=>0000000=>[8]=>[8]
[8,6,4,2,3,1,7,5]=>0000000=>[8]=>[8]
[8,6,4,2,1,3,7,5]=>0000000=>[8]=>[8]
[2,5,7,3,8,4,6,1]=>0000000=>[8]=>[8]
[4,2,7,1,8,5,3,6]=>0000000=>[8]=>[8]
[1,3,7,5,8,6,4,2]=>1000000=>[1,7]=>[7,1]
[3,5,7,1,4,8,6,2]=>0000000=>[8]=>[8]
[3,4,1,2,8,5,7,6]=>0001000=>[4,4]=>[4,4]
[8,7,3,1,2,6,4,5]=>0000000=>[8]=>[8]
[6,2,3,1,4,8,7,5]=>0000000=>[8]=>[8]
[8,4,3,2,5,7,1,6]=>0000000=>[8]=>[8]
[5,3,6,8,2,1,4,7]=>0000000=>[8]=>[8]
[3,2,6,8,5,4,1,7]=>0000000=>[8]=>[8]
[7,3,8,2,5,4,1,6]=>0000000=>[8]=>[8]
[7,4,2,5,8,3,1,6]=>0000000=>[8]=>[8]
[3,1,2,8,5,6,4,7]=>0010000=>[3,5]=>[5,3]
[5,2,1,6,8,3,4,7]=>0000000=>[8]=>[8]
[3,1,8,6,5,4,2,7]=>0000000=>[8]=>[8]
[5,6,8,1,4,3,2,7]=>0000000=>[8]=>[8]
[7,8,4,1,5,3,2,6]=>0000000=>[8]=>[8]
[7,3,8,5,1,4,2,6]=>0000000=>[8]=>[8]
[1,5,4,8,3,7,6,2]=>1000000=>[1,7]=>[7,1]
[4,7,8,3,1,6,5,2]=>0000000=>[8]=>[8]
[8,7,5,3,6,4,2,1]=>0000000=>[8]=>[8]
[4,6,1,3,8,7,5,2]=>0000000=>[8]=>[8]
[3,6,1,2,7,5,8,4]=>0000000=>[8]=>[8]
[3,6,2,5,8,7,4,1]=>0000000=>[8]=>[8]
[2,7,3,1,5,6,8,4]=>0000000=>[8]=>[8]
[6,7,1,3,2,8,4,5]=>0000000=>[8]=>[8]
[6,2,7,1,3,4,8,5]=>0000000=>[8]=>[8]
[5,2,1,7,3,8,4,6]=>0000000=>[8]=>[8]
[3,7,2,4,6,1,8,5]=>0000000=>[8]=>[8]
[5,3,7,2,8,1,4,6]=>0000000=>[8]=>[8]
[7,1,8,3,4,2,5,6]=>0000000=>[8]=>[8]
[7,2,4,1,8,3,5,6]=>0000000=>[8]=>[8]
[4,8,7,6,3,2,1,5]=>0000000=>[8]=>[8]
[7,8,2,4,6,1,5,3]=>0000000=>[8]=>[8]
[3,5,1,8,7,2,6,4]=>0000000=>[8]=>[8]
[5,2,8,1,7,6,3,4]=>0000000=>[8]=>[8]
[6,2,1,3,8,7,5,4]=>0000000=>[8]=>[8]
[6,7,8,1,2,5,4,3]=>0000000=>[8]=>[8]
[5,8,7,1,6,4,3,2]=>0000000=>[8]=>[8]
[6,8,7,5,1,4,3,2]=>0000000=>[8]=>[8]
[8,6,4,3,2,1,7,5]=>0000000=>[8]=>[8]
[6,5,4,3,8,2,7,1]=>0000000=>[8]=>[8]
[8,4,3,2,1,7,6,5]=>0000000=>[8]=>[8]
[3,7,5,8,1,4,6,2]=>0000000=>[8]=>[8]
[4,7,5,8,3,2,1,6]=>0000000=>[8]=>[8]
[5,7,2,3,6,1,8,4]=>0000000=>[8]=>[8]
[7,3,1,4,8,2,5,6]=>0000000=>[8]=>[8]
[7,4,1,2,5,8,3,6]=>0000000=>[8]=>[8]
[4,7,1,6,5,8,3,2]=>0000000=>[8]=>[8]
[8,6,4,2,3,7,5,1]=>0000000=>[8]=>[8]
[7,6,4,2,3,8,1,5]=>0000000=>[8]=>[8]
[3,1,2,4,8,7,6,5]=>0011000=>[3,1,4]=>[4,3,1]
[6,5,8,7,3,1,2,4]=>0000000=>[8]=>[8]
[5,6,7,8,1,4,2,3]=>0000000=>[8]=>[8]
[2,6,7,4,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[1,3,7,4,2,8,5,6]=>1000000=>[1,7]=>[7,1]
[4,6,1,3,7,2,5,8]=>0000001=>[7,1]=>[7,1]
[6,5,7,8,3,1,4,2]=>0000000=>[8]=>[8]
[7,5,8,6,2,1,3,4]=>0000000=>[8]=>[8]
[2,8,1,3,6,5,4,7]=>0000000=>[8]=>[8]
[2,8,7,3,5,4,1,6]=>0000000=>[8]=>[8]
[3,4,2,6,8,7,1,5]=>0000000=>[8]=>[8]
[6,1,4,2,7,8,5,3]=>0000000=>[8]=>[8]
[7,3,8,4,1,2,6,5]=>0000000=>[8]=>[8]
[6,8,3,2,7,1,5,4]=>0000000=>[8]=>[8]
[5,1,4,3,6,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,8,5,6,3,2,1,7]=>0000000=>[8]=>[8]
[2,8,5,6,3,7,1,4]=>0000000=>[8]=>[8]
[3,2,6,7,4,8,1,5]=>0000000=>[8]=>[8]
[4,1,8,2,6,3,5,7]=>0000000=>[8]=>[8]
[7,5,6,8,2,1,4,3]=>0000000=>[8]=>[8]
[5,8,6,7,1,2,3,4]=>0000000=>[8]=>[8]
[4,8,1,5,7,2,3,6]=>0000000=>[8]=>[8]
[3,5,1,4,7,6,8,2]=>0000000=>[8]=>[8]
[5,3,2,7,1,6,8,4]=>0000000=>[8]=>[8]
[5,4,1,7,3,6,8,2]=>0000000=>[8]=>[8]
[3,4,7,6,2,5,8,1]=>0000000=>[8]=>[8]
[4,8,3,6,5,2,1,7]=>0000000=>[8]=>[8]
[8,1,7,4,2,5,6,3]=>0000000=>[8]=>[8]
[1,8,7,2,5,3,4,6]=>1000000=>[1,7]=>[7,1]
[4,8,1,5,2,6,3,7]=>0000000=>[8]=>[8]
[3,6,8,5,1,2,4,7]=>0000000=>[8]=>[8]
[1,5,2,7,8,4,6,3]=>1000000=>[1,7]=>[7,1]
[6,7,2,8,5,3,1,4]=>0000000=>[8]=>[8]
[6,7,2,8,3,1,5,4]=>0000000=>[8]=>[8]
[3,1,4,6,7,8,5,2]=>0000000=>[8]=>[8]
[7,4,6,1,8,2,3,5]=>0000000=>[8]=>[8]
[3,4,5,1,6,8,7,2]=>0000000=>[8]=>[8]
[5,7,8,3,1,6,4,2]=>0000000=>[8]=>[8]
[7,5,8,3,2,4,1,6]=>0000000=>[8]=>[8]
[5,8,2,6,3,1,4,7]=>0000000=>[8]=>[8]
[8,2,7,5,4,1,3,6]=>0000000=>[8]=>[8]
[6,2,7,3,8,4,1,5]=>0000000=>[8]=>[8]
[3,7,2,4,8,5,1,6]=>0000000=>[8]=>[8]
[1,5,2,6,3,8,7,4]=>1000000=>[1,7]=>[7,1]
[1,3,6,2,4,8,7,5]=>1000000=>[1,7]=>[7,1]
[8,3,6,2,5,4,1,7]=>0000000=>[8]=>[8]
[3,5,8,2,4,6,1,7]=>0000000=>[8]=>[8]
[6,4,7,8,2,3,1,5]=>0000000=>[8]=>[8]
[1,5,3,2,8,4,7,6]=>1000000=>[1,7]=>[7,1]
[3,8,4,7,5,1,2,6]=>0000000=>[8]=>[8]
[6,1,2,7,3,8,5,4]=>0000000=>[8]=>[8]
[2,1,7,3,4,8,6,5]=>0100000=>[2,6]=>[6,2]
[8,3,1,6,7,2,5,4]=>0000000=>[8]=>[8]
[4,8,3,7,1,5,2,6]=>0000000=>[8]=>[8]
[5,7,4,8,2,1,3,6]=>0000000=>[8]=>[8]
[4,6,8,2,5,1,3,7]=>0000000=>[8]=>[8]
[5,3,7,2,1,4,6,8]=>0000001=>[7,1]=>[7,1]
[6,4,2,8,3,1,5,7]=>0000000=>[8]=>[8]
[5,7,2,3,8,1,4,6]=>0000000=>[8]=>[8]
[6,4,7,5,8,1,2,3]=>0000000=>[8]=>[8]
[8,6,4,2,1,7,5,3]=>0000000=>[8]=>[8]
[7,6,4,1,8,5,2,3]=>0000000=>[8]=>[8]
[1,6,4,8,7,5,3,2]=>1000000=>[1,7]=>[7,1]
[6,3,1,2,8,4,7,5]=>0000000=>[8]=>[8]
[7,4,8,1,6,3,5,2]=>0000000=>[8]=>[8]
[1,4,8,7,2,6,5,3]=>1000000=>[1,7]=>[7,1]
[5,4,1,8,7,3,2,6]=>0000000=>[8]=>[8]
[8,6,1,7,5,4,3,2]=>0000000=>[8]=>[8]
[3,1,8,7,6,5,2,4]=>0000000=>[8]=>[8]
[2,6,8,1,3,7,5,4]=>0000000=>[8]=>[8]
[2,4,8,1,5,7,6,3]=>0000000=>[8]=>[8]
[3,2,8,6,1,7,5,4]=>0000000=>[8]=>[8]
[6,2,8,3,1,7,5,4]=>0000000=>[8]=>[8]
[7,4,3,8,5,2,1,6]=>0000000=>[8]=>[8]
[4,3,8,7,5,1,6,2]=>0000000=>[8]=>[8]
[4,2,3,8,5,1,6,7]=>0000000=>[8]=>[8]
[4,2,8,5,1,7,6,3]=>0000000=>[8]=>[8]
[3,4,2,8,5,6,1,7]=>0000000=>[8]=>[8]
[3,2,4,8,6,1,5,7]=>0000000=>[8]=>[8]
[3,2,5,8,6,1,4,7]=>0000000=>[8]=>[8]
[4,3,7,8,5,1,2,6]=>0000000=>[8]=>[8]
[4,2,6,8,5,1,3,7]=>0000000=>[8]=>[8]
[3,5,2,8,4,6,1,7]=>0000000=>[8]=>[8]
[5,2,6,8,4,1,3,7]=>0000000=>[8]=>[8]
[5,3,7,8,4,1,2,6]=>0000000=>[8]=>[8]
[5,6,2,8,3,4,1,7]=>0000000=>[8]=>[8]
[5,3,8,7,4,1,6,2]=>0000000=>[8]=>[8]
[6,4,2,8,5,3,1,7]=>0000000=>[8]=>[8]
[7,6,4,3,8,2,5,1]=>0000000=>[8]=>[8]
[6,4,5,3,8,2,7,1]=>0000000=>[8]=>[8]
[7,4,5,3,8,2,6,1]=>0000000=>[8]=>[8]
[8,4,6,3,7,2,5,1]=>0000000=>[8]=>[8]
[7,6,8,3,5,2,4,1]=>0000000=>[8]=>[8]
[7,5,8,4,6,2,3,1]=>0000000=>[8]=>[8]
[7,5,8,3,6,2,4,1]=>0000000=>[8]=>[8]
[7,4,8,3,6,2,5,1]=>0000000=>[8]=>[8]
[7,4,8,3,5,2,6,1]=>0000000=>[8]=>[8]
[6,4,8,3,5,2,7,1]=>0000000=>[8]=>[8]
[5,4,7,3,6,2,8,1]=>0000000=>[8]=>[8]
[6,5,7,3,8,2,4,1]=>0000000=>[8]=>[8]
[5,4,6,3,8,2,7,1]=>0000000=>[8]=>[8]
[6,5,3,7,8,2,1,4]=>0000000=>[8]=>[8]
[6,5,4,2,8,7,1,3]=>0000000=>[8]=>[8]
[6,4,3,7,5,2,1,8]=>0000001=>[7,1]=>[7,1]
[6,3,7,8,5,2,1,4]=>0000000=>[8]=>[8]
[6,3,7,2,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,3,2,7,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[4,8,2,6,3,7,1,5]=>0000000=>[8]=>[8]
[5,4,8,1,2,3,7,6]=>0000000=>[8]=>[8]
[1,4,7,6,3,2,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[4,8,3,2,7,6,1,5]=>0000000=>[8]=>[8]
[4,8,6,7,2,3,1,5]=>0000000=>[8]=>[8]
[4,8,7,3,6,2,1,5]=>0000000=>[8]=>[8]
[4,3,8,2,7,1,6,5]=>0000000=>[8]=>[8]
[4,1,8,7,3,2,5,6]=>0000000=>[8]=>[8]
[4,7,8,1,2,5,3,6]=>0000000=>[8]=>[8]
[2,3,6,7,4,1,8,5]=>0000000=>[8]=>[8]
[2,6,3,4,7,8,1,5]=>0000000=>[8]=>[8]
[3,1,7,8,4,2,5,6]=>0000000=>[8]=>[8]
[4,3,1,2,8,5,7,6]=>0001000=>[4,4]=>[4,4]
[3,7,6,8,4,2,1,5]=>0000000=>[8]=>[8]
[3,7,8,2,6,4,1,5]=>0000000=>[8]=>[8]
[3,7,2,8,4,6,1,5]=>0000000=>[8]=>[8]
[4,2,8,3,6,1,7,5]=>0000000=>[8]=>[8]
[3,7,2,4,8,6,1,5]=>0000000=>[8]=>[8]
[1,3,6,4,7,2,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,4,3,6,1,8,7,5]=>0000000=>[8]=>[8]
[2,6,7,3,8,4,1,5]=>0000000=>[8]=>[8]
[2,6,3,7,4,8,1,5]=>0000000=>[8]=>[8]
[1,3,5,7,4,6,8,2]=>1000000=>[1,7]=>[7,1]
[1,3,5,4,7,2,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,5,4,7,2,8,6]=>1000000=>[1,7]=>[7,1]
[2,3,7,1,4,8,6,5]=>0000000=>[8]=>[8]
[2,5,7,3,4,8,6,1]=>0000000=>[8]=>[8]
[2,5,4,6,7,1,3,8]=>0000001=>[7,1]=>[7,1]
[2,4,6,3,7,5,1,8]=>0000001=>[7,1]=>[7,1]
[5,3,2,7,4,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,1,2,5,8,3,7,6]=>0000000=>[8]=>[8]
[4,6,1,2,5,8,3,7]=>0000000=>[8]=>[8]
[5,7,6,8,1,4,2,3]=>0000000=>[8]=>[8]
[4,1,6,2,8,5,7,3]=>0000000=>[8]=>[8]
[7,1,4,2,3,6,8,5]=>0000000=>[8]=>[8]
[6,4,2,1,3,8,7,5]=>0000000=>[8]=>[8]
[3,8,6,4,2,1,5,7]=>0000000=>[8]=>[8]
[6,1,2,7,5,3,8,4]=>0000000=>[8]=>[8]
[2,6,1,4,7,3,8,5]=>0000000=>[8]=>[8]
[7,3,2,8,6,4,1,5]=>0000000=>[8]=>[8]
[2,7,8,4,6,3,1,5]=>0000000=>[8]=>[8]
[7,8,2,5,3,6,1,4]=>0000000=>[8]=>[8]
[8,1,6,3,5,7,2,4]=>0000000=>[8]=>[8]
[8,3,2,6,4,7,1,5]=>0000000=>[8]=>[8]
[8,4,2,5,6,7,1,3]=>0000000=>[8]=>[8]
[2,3,8,7,6,5,1,4]=>0000000=>[8]=>[8]
[4,1,8,7,2,6,5,3]=>0000000=>[8]=>[8]
[1,2,8,7,3,6,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,8,7,3,2,6,4]=>1000000=>[1,7]=>[7,1]
[4,5,8,7,3,2,1,6]=>0000000=>[8]=>[8]
[2,6,8,3,7,5,1,4]=>0000000=>[8]=>[8]
[1,6,8,4,7,2,5,3]=>1000000=>[1,7]=>[7,1]
[1,6,8,3,7,2,5,4]=>1000000=>[1,7]=>[7,1]
[2,5,8,1,7,6,4,3]=>0000000=>[8]=>[8]
[3,2,8,4,7,6,1,5]=>0000000=>[8]=>[8]
[1,5,8,4,7,2,6,3]=>1000000=>[1,7]=>[7,1]
[1,5,8,3,7,2,6,4]=>1000000=>[1,7]=>[7,1]
[3,1,8,4,7,2,6,5]=>0000000=>[8]=>[8]
[5,6,8,1,2,7,4,3]=>0000000=>[8]=>[8]
[1,6,8,2,3,7,5,4]=>1000000=>[1,7]=>[7,1]
[1,5,8,4,2,7,6,3]=>1000000=>[1,7]=>[7,1]
[5,6,8,4,3,2,1,7]=>0000000=>[8]=>[8]
[7,1,4,8,6,2,5,3]=>0000000=>[8]=>[8]
[7,3,4,8,6,2,1,5]=>0000000=>[8]=>[8]
[7,1,4,8,2,6,5,3]=>0000000=>[8]=>[8]
[7,4,5,8,1,2,6,3]=>0000000=>[8]=>[8]
[3,6,2,8,7,5,1,4]=>0000000=>[8]=>[8]
[1,6,4,8,7,2,5,3]=>1000000=>[1,7]=>[7,1]
[3,2,4,8,7,6,1,5]=>0000000=>[8]=>[8]
[1,4,5,8,7,2,6,3]=>1000000=>[1,7]=>[7,1]
[3,1,4,8,7,2,6,5]=>0000000=>[8]=>[8]
[1,6,5,8,2,7,4,3]=>1000000=>[1,7]=>[7,1]
[2,6,5,8,3,7,1,4]=>0000000=>[8]=>[8]
[2,4,5,8,3,7,1,6]=>0000000=>[8]=>[8]
[4,6,5,8,3,2,1,7]=>0000000=>[8]=>[8]
[7,6,2,3,8,5,1,4]=>0000000=>[8]=>[8]
[7,6,1,4,8,2,5,3]=>0000000=>[8]=>[8]
[7,2,5,3,8,6,1,4]=>0000000=>[8]=>[8]
[7,2,1,3,8,6,5,4]=>0000000=>[8]=>[8]
[2,6,5,3,8,7,1,4]=>0000000=>[8]=>[8]
[2,6,1,4,8,7,5,3]=>0000000=>[8]=>[8]
[7,6,5,1,2,8,4,3]=>0000000=>[8]=>[8]
[7,1,5,2,3,8,6,4]=>0000000=>[8]=>[8]
[7,1,2,4,3,8,6,5]=>0000000=>[8]=>[8]
[1,6,2,4,3,8,7,5]=>1000000=>[1,7]=>[7,1]
[2,6,5,4,3,8,1,7]=>0000000=>[8]=>[8]
[7,6,5,1,3,2,8,4]=>0000000=>[8]=>[8]
[8,2,7,6,5,4,1,3]=>0000000=>[8]=>[8]
[7,2,8,6,5,4,3,1]=>0000000=>[8]=>[8]
[3,2,8,7,6,5,1,4]=>0000000=>[8]=>[8]
[7,8,6,1,5,4,3,2]=>0000000=>[8]=>[8]
[4,8,5,7,6,3,2,1]=>0000000=>[8]=>[8]
[3,2,4,6,8,1,5,7]=>0000000=>[8]=>[8]
[3,5,7,2,4,8,1,6]=>0000000=>[8]=>[8]
[4,5,1,3,6,8,2,7]=>0000000=>[8]=>[8]
[4,3,5,7,2,6,8,1]=>0000000=>[8]=>[8]
[4,3,5,1,7,8,2,6]=>0000000=>[8]=>[8]
[4,6,3,5,7,2,8,1]=>0000000=>[8]=>[8]
[5,1,6,7,3,4,8,2]=>0000000=>[8]=>[8]
[1,6,7,3,4,5,8,2]=>1000000=>[1,7]=>[7,1]
[2,6,7,4,8,1,3,5]=>0000000=>[8]=>[8]
[6,3,1,7,8,2,4,5]=>0000000=>[8]=>[8]
[5,7,2,8,1,3,4,6]=>0000000=>[8]=>[8]
[6,3,7,2,8,1,4,5]=>0000000=>[8]=>[8]
[2,4,6,7,1,5,8,3]=>0000000=>[8]=>[8]
[2,4,7,1,5,6,8,3]=>0000000=>[8]=>[8]
[3,7,1,5,6,8,2,4]=>0000000=>[8]=>[8]
[1,5,6,7,2,4,8,3]=>1000000=>[1,7]=>[7,1]
[5,6,2,4,1,7,8,3]=>0000000=>[8]=>[8]
[5,6,4,7,1,3,8,2]=>0000000=>[8]=>[8]
[6,4,3,7,2,5,8,1]=>0000000=>[8]=>[8]
[6,4,3,7,2,8,1,5]=>0000000=>[8]=>[8]
[7,4,5,3,1,6,8,2]=>0000000=>[8]=>[8]
[6,4,3,7,5,1,8,2]=>0000000=>[8]=>[8]
[5,6,3,7,4,1,8,2]=>0000000=>[8]=>[8]
[6,7,4,2,1,5,8,3]=>0000000=>[8]=>[8]
[6,7,4,2,1,8,3,5]=>0000000=>[8]=>[8]
[5,6,7,3,1,8,2,4]=>0000000=>[8]=>[8]
[5,6,3,7,8,1,2,4]=>0000000=>[8]=>[8]
[5,6,3,7,2,4,8,1]=>0000000=>[8]=>[8]
[5,6,7,2,3,8,1,4]=>0000000=>[8]=>[8]
[5,6,7,2,8,1,3,4]=>0000000=>[8]=>[8]
[6,7,3,8,1,2,4,5]=>0000000=>[8]=>[8]
[6,7,3,2,8,1,4,5]=>0000000=>[8]=>[8]
[7,6,4,2,1,3,8,5]=>0000000=>[8]=>[8]
[7,5,3,2,6,1,8,4]=>0000000=>[8]=>[8]
[6,5,3,2,7,8,1,4]=>0000000=>[8]=>[8]
[6,4,7,2,5,1,8,3]=>0000000=>[8]=>[8]
[5,4,6,7,3,1,8,2]=>0000000=>[8]=>[8]
[3,7,8,5,6,1,4,2]=>0000000=>[8]=>[8]
[1,7,8,5,6,3,4,2]=>1000000=>[1,7]=>[7,1]
[1,7,5,8,6,3,4,2]=>1000000=>[1,7]=>[7,1]
[5,7,3,8,6,4,1,2]=>0000000=>[8]=>[8]
[1,5,7,8,6,3,4,2]=>1000000=>[1,7]=>[7,1]
[1,5,7,8,3,6,4,2]=>1000000=>[1,7]=>[7,1]
[5,3,7,8,1,6,4,2]=>0000000=>[8]=>[8]
[5,3,7,8,6,1,4,2]=>0000000=>[8]=>[8]
[7,8,3,5,6,1,4,2]=>0000000=>[8]=>[8]
[7,1,8,5,6,3,4,2]=>0000000=>[8]=>[8]
[7,1,5,8,6,3,4,2]=>0000000=>[8]=>[8]
[5,1,7,8,6,3,4,2]=>0000000=>[8]=>[8]
[5,1,7,8,3,6,4,2]=>0000000=>[8]=>[8]
[3,1,7,8,5,6,4,2]=>0000000=>[8]=>[8]
[1,3,7,8,5,6,4,2]=>1000000=>[1,7]=>[7,1]
[3,1,7,5,8,6,4,2]=>0000000=>[8]=>[8]
[5,1,7,3,8,6,4,2]=>0000000=>[8]=>[8]
[7,1,5,3,8,6,4,2]=>0000000=>[8]=>[8]
[7,1,5,8,3,6,4,2]=>0000000=>[8]=>[8]
[7,3,8,5,1,6,4,2]=>0000000=>[8]=>[8]
[7,3,5,8,1,6,4,2]=>0000000=>[8]=>[8]
[7,3,5,1,8,6,4,2]=>0000000=>[8]=>[8]
[5,3,7,1,8,6,4,2]=>0000000=>[8]=>[8]
[3,5,7,1,8,6,4,2]=>0000000=>[8]=>[8]
[1,5,7,3,8,6,4,2]=>1000000=>[1,7]=>[7,1]
[1,7,5,3,8,6,4,2]=>1000000=>[1,7]=>[7,1]
[3,7,5,1,8,6,4,2]=>0000000=>[8]=>[8]
[5,7,3,1,8,6,4,2]=>0000000=>[8]=>[8]
[5,7,3,8,6,1,4,2]=>0000000=>[8]=>[8]
[3,7,5,8,1,6,4,2]=>0000000=>[8]=>[8]
[1,7,5,8,3,6,4,2]=>1000000=>[1,7]=>[7,1]
[1,7,8,5,3,6,4,2]=>1000000=>[1,7]=>[7,1]
[5,7,8,6,3,1,4,2]=>0000000=>[8]=>[8]
[7,5,8,6,1,3,4,2]=>0000000=>[8]=>[8]
[5,7,8,1,6,3,4,2]=>0000000=>[8]=>[8]
[1,7,8,3,5,6,4,2]=>1000000=>[1,7]=>[7,1]
[1,7,3,8,5,6,4,2]=>1000000=>[1,7]=>[7,1]
[3,7,1,8,5,6,4,2]=>0000000=>[8]=>[8]
[5,7,1,8,3,6,4,2]=>0000000=>[8]=>[8]
[5,7,1,8,6,3,4,2]=>0000000=>[8]=>[8]
[7,5,1,8,6,3,4,2]=>0000000=>[8]=>[8]
[7,5,8,1,6,3,4,2]=>0000000=>[8]=>[8]
[7,5,1,8,3,6,4,2]=>0000000=>[8]=>[8]
[7,5,1,3,8,6,4,2]=>0000000=>[8]=>[8]
[5,7,1,3,8,6,4,2]=>0000000=>[8]=>[8]
[3,7,1,5,8,6,4,2]=>0000000=>[8]=>[8]
[1,7,3,5,8,6,4,2]=>1000000=>[1,7]=>[7,1]
[1,5,3,7,8,6,4,2]=>1000000=>[1,7]=>[7,1]
[3,5,1,7,8,6,4,2]=>0000000=>[8]=>[8]
[5,3,1,7,8,6,4,2]=>0000000=>[8]=>[8]
[7,3,1,5,8,6,4,2]=>0000000=>[8]=>[8]
[7,3,1,8,5,6,4,2]=>0000000=>[8]=>[8]
[7,1,8,3,5,6,4,2]=>0000000=>[8]=>[8]
[7,1,3,8,5,6,4,2]=>0000000=>[8]=>[8]
[7,1,3,5,8,6,4,2]=>0000000=>[8]=>[8]
[5,1,3,7,8,6,4,2]=>0000000=>[8]=>[8]
[3,1,5,7,8,6,4,2]=>0000000=>[8]=>[8]
[2,3,6,1,5,4,8,7]=>0000010=>[6,2]=>[6,2]
[3,5,6,2,4,1,8,7]=>0000010=>[6,2]=>[6,2]
[8,7,6,1,3,2,4,5]=>0000000=>[8]=>[8]
[2,5,3,4,8,1,7,6]=>0000000=>[8]=>[8]
[5,1,8,2,3,4,7,6]=>0000000=>[8]=>[8]
[5,4,7,6,2,8,1,3]=>0000000=>[8]=>[8]
[3,1,8,6,2,7,5,4]=>0000000=>[8]=>[8]
[3,8,1,5,6,7,2,4]=>0000000=>[8]=>[8]
[8,2,3,5,7,1,6,4]=>0000000=>[8]=>[8]
[2,8,3,6,7,5,1,4]=>0000000=>[8]=>[8]
[4,3,8,2,7,6,1,5]=>0000000=>[8]=>[8]
[2,1,4,5,8,3,7,6]=>0100000=>[2,6]=>[6,2]
[6,4,7,5,2,3,8,1]=>0000000=>[8]=>[8]
[4,2,3,1,8,7,5,6]=>0001000=>[4,4]=>[4,4]
[4,3,1,2,8,6,7,5]=>0001000=>[4,4]=>[4,4]
[5,1,6,7,8,4,3,2]=>0000000=>[8]=>[8]
[8,7,2,6,4,1,5,3]=>0000000=>[8]=>[8]
[6,1,7,4,3,2,8,5]=>0000000=>[8]=>[8]
[4,2,6,1,5,7,8,3]=>0000000=>[8]=>[8]
[7,1,4,8,3,5,6,2]=>0000000=>[8]=>[8]
[3,4,8,2,5,7,6,1]=>0000000=>[8]=>[8]
[3,7,1,4,5,6,8,2]=>0000000=>[8]=>[8]
[4,7,5,6,8,3,1,2]=>0000000=>[8]=>[8]
[6,5,3,8,4,7,1,2]=>0000000=>[8]=>[8]
[8,6,4,7,5,3,1,2]=>0000000=>[8]=>[8]
[1,6,3,7,5,8,4,2]=>1000000=>[1,7]=>[7,1]
[1,3,7,4,5,8,6,2]=>1000000=>[1,7]=>[7,1]
[7,3,8,5,4,6,1,2]=>0000000=>[8]=>[8]
[3,4,8,5,6,7,1,2]=>0000000=>[8]=>[8]
[4,7,3,8,5,6,1,2]=>0000000=>[8]=>[8]
[6,8,4,7,5,3,1,2]=>0000000=>[8]=>[8]
[1,7,6,5,3,8,4,2]=>1000000=>[1,7]=>[7,1]
[2,7,6,4,5,1,3,8]=>0000001=>[7,1]=>[7,1]
[1,8,2,7,3,6,5,4]=>1000000=>[1,7]=>[7,1]
[2,1,3,8,4,7,5,6]=>0110000=>[2,1,5]=>[5,2,1]
[3,1,2,8,4,6,7,5]=>0010000=>[3,5]=>[5,3]
[4,1,7,2,8,5,6,3]=>0000000=>[8]=>[8]
[5,1,2,4,8,3,7,6]=>0000000=>[8]=>[8]
[1,7,2,8,5,3,6,4]=>1000000=>[1,7]=>[7,1]
[1,2,3,8,4,5,7,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[2,4,8,3,1,5,6,7]=>0000000=>[8]=>[8]
[3,4,2,7,1,5,6,8]=>0000001=>[7,1]=>[7,1]
[3,2,5,6,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,7,3,8,2,1,5,6]=>0000000=>[8]=>[8]
[7,4,8,3,2,1,5,6]=>0000000=>[8]=>[8]
[2,6,4,5,7,1,3,8]=>0000001=>[7,1]=>[7,1]
[5,4,6,2,7,1,3,8]=>0000001=>[7,1]=>[7,1]
[7,6,8,5,1,4,3,2]=>0000000=>[8]=>[8]
[6,5,1,2,8,3,7,4]=>0000000=>[8]=>[8]
[6,8,4,1,3,7,5,2]=>0000000=>[8]=>[8]
[6,3,7,1,8,4,5,2]=>0000000=>[8]=>[8]
[4,7,1,2,8,3,6,5]=>0000000=>[8]=>[8]
[1,2,8,7,6,3,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,3,1,8,7,4,5,6]=>0010000=>[3,5]=>[5,3]
[8,7,1,6,5,4,3,2]=>0000000=>[8]=>[8]
[3,1,8,7,6,4,5,2]=>0000000=>[8]=>[8]
[1,2,3,4,8,7,5,6]=>1111000=>[1,1,1,1,4]=>[4,1,1,1,1]
[1,2,3,8,6,4,5,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,8,5,3,4,6,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,4,2,3,5,6,7]=>1000000=>[1,7]=>[7,1]
[2,4,7,5,6,8,3,1]=>0000000=>[8]=>[8]
[2,5,3,8,7,4,6,1]=>0000000=>[8]=>[8]
[3,1,8,5,7,4,2,6]=>0000000=>[8]=>[8]
[8,3,6,2,4,5,7,1]=>0000000=>[8]=>[8]
[4,8,1,7,6,3,2,5]=>0000000=>[8]=>[8]
[4,7,8,1,3,6,2,5]=>0000000=>[8]=>[8]
[5,8,7,1,4,3,2,6]=>0000000=>[8]=>[8]
[5,6,1,2,4,3,8,7]=>0000010=>[6,2]=>[6,2]
[3,6,8,1,2,7,5,4]=>0000000=>[8]=>[8]
[8,4,6,2,1,3,7,5]=>0000000=>[8]=>[8]
[4,8,1,5,3,7,2,6]=>0000000=>[8]=>[8]
[5,4,8,7,3,1,2,6]=>0000000=>[8]=>[8]
[6,4,3,8,1,5,2,7]=>0000000=>[8]=>[8]
[6,8,3,7,2,5,4,1]=>0000000=>[8]=>[8]
[5,3,6,8,7,2,4,1]=>0000000=>[8]=>[8]
[5,7,4,2,8,3,6,1]=>0000000=>[8]=>[8]
[6,4,7,2,1,8,3,5]=>0000000=>[8]=>[8]
[6,5,3,1,4,7,2,8]=>0000001=>[7,1]=>[7,1]
[5,7,8,2,6,4,1,3]=>0000000=>[8]=>[8]
[3,6,8,5,7,1,4,2]=>0000000=>[8]=>[8]
[1,7,4,8,6,2,3,5]=>1000000=>[1,7]=>[7,1]
[2,7,4,8,5,6,1,3]=>0000000=>[8]=>[8]
[6,3,7,2,8,5,1,4]=>0000000=>[8]=>[8]
[8,1,3,6,7,2,4,5]=>0000000=>[8]=>[8]
[6,1,3,8,2,7,4,5]=>0000000=>[8]=>[8]
[4,1,5,3,2,8,6,7]=>0000100=>[5,3]=>[5,3]
[2,7,1,4,3,8,5,6]=>0000000=>[8]=>[8]
[1,7,5,2,8,6,3,4]=>1000000=>[1,7]=>[7,1]
[7,4,2,5,1,8,6,3]=>0000000=>[8]=>[8]
[5,6,3,2,1,8,7,4]=>0000000=>[8]=>[8]
[4,5,3,2,7,1,8,6]=>0000000=>[8]=>[8]
[6,4,2,8,5,1,7,3]=>0000000=>[8]=>[8]
[1,8,4,7,2,5,3,6]=>1000000=>[1,7]=>[7,1]
[1,5,8,4,2,6,3,7]=>1000000=>[1,7]=>[7,1]
[3,5,7,4,1,6,8,2]=>0000000=>[8]=>[8]
[4,5,8,3,1,7,6,2]=>0000000=>[8]=>[8]
[3,4,7,8,2,1,6,5]=>0000000=>[8]=>[8]
[3,5,7,1,2,6,4,8]=>0000001=>[7,1]=>[7,1]
[3,6,2,1,4,7,5,8]=>0000001=>[7,1]=>[7,1]
[7,4,1,2,8,6,3,5]=>0000000=>[8]=>[8]
[5,2,6,1,3,4,8,7]=>0000010=>[6,2]=>[6,2]
[7,5,1,6,8,4,3,2]=>0000000=>[8]=>[8]
[6,2,7,8,5,4,1,3]=>0000000=>[8]=>[8]
[3,8,7,6,2,4,1,5]=>0000000=>[8]=>[8]
[3,5,8,7,2,4,6,1]=>0000000=>[8]=>[8]
[2,7,1,3,6,5,4,8]=>0000001=>[7,1]=>[7,1]
[6,3,7,1,5,4,2,8]=>0000001=>[7,1]=>[7,1]
[5,7,8,3,2,1,4,6]=>0000000=>[8]=>[8]
[5,4,2,1,7,8,3,6]=>0000000=>[8]=>[8]
[4,7,8,3,5,2,1,6]=>0000000=>[8]=>[8]
[8,3,2,1,4,7,6,5]=>0000000=>[8]=>[8]
[6,4,1,7,3,8,5,2]=>0000000=>[8]=>[8]
[1,7,5,3,8,2,6,4]=>1000000=>[1,7]=>[7,1]
[5,1,7,4,2,8,6,3]=>0000000=>[8]=>[8]
[5,1,4,3,2,7,8,6]=>0000100=>[5,3]=>[5,3]
[3,7,6,2,4,1,8,5]=>0000000=>[8]=>[8]
[6,3,1,7,5,2,8,4]=>0000000=>[8]=>[8]
[4,1,6,8,5,7,3,2]=>0000000=>[8]=>[8]
[1,8,6,7,3,4,2,5]=>1000000=>[1,7]=>[7,1]
[6,7,1,8,3,4,2,5]=>0000000=>[8]=>[8]
[7,8,2,5,1,6,3,4]=>0000000=>[8]=>[8]
[1,8,5,6,2,7,3,4]=>1000000=>[1,7]=>[7,1]
[5,6,2,7,1,8,3,4]=>0000000=>[8]=>[8]
[6,7,2,5,1,8,3,4]=>0000000=>[8]=>[8]
[2,5,1,8,6,7,3,4]=>0000000=>[8]=>[8]
[2,6,5,8,1,7,3,4]=>0000000=>[8]=>[8]
[2,4,3,8,5,6,1,7]=>0000000=>[8]=>[8]
[2,3,1,8,5,6,4,7]=>0010000=>[3,5]=>[5,3]
[4,7,1,6,2,5,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,3,5,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[5,6,3,7,1,4,2,8]=>0000001=>[7,1]=>[7,1]
[1,8,5,6,3,4,2,7]=>1000000=>[1,7]=>[7,1]
[4,7,1,8,5,6,2,3]=>0000000=>[8]=>[8]
[3,4,2,6,5,8,1,7]=>0000000=>[8]=>[8]
[3,5,4,6,2,8,1,7]=>0000000=>[8]=>[8]
[3,7,1,6,2,8,4,5]=>0000000=>[8]=>[8]
[3,5,2,7,4,8,1,6]=>0000000=>[8]=>[8]
[4,7,2,3,1,8,5,6]=>0000000=>[8]=>[8]
[2,5,8,3,4,1,6,7]=>0000000=>[8]=>[8]
[5,1,7,3,4,2,8,6]=>0000000=>[8]=>[8]
[4,6,7,3,2,5,8,1]=>0000000=>[8]=>[8]
[3,7,2,1,4,5,8,6]=>0000000=>[8]=>[8]
[2,7,1,3,4,8,6,5]=>0000000=>[8]=>[8]
[2,6,7,3,8,5,4,1]=>0000000=>[8]=>[8]
[2,6,1,8,4,5,3,7]=>0000000=>[8]=>[8]
[4,2,1,6,5,3,8,7]=>0000010=>[6,2]=>[6,2]
[6,2,4,3,1,5,8,7]=>0000010=>[6,2]=>[6,2]
[4,6,2,1,5,3,8,7]=>0000010=>[6,2]=>[6,2]
[8,4,2,1,6,5,3,7]=>0000000=>[8]=>[8]
[2,6,4,5,1,8,7,3]=>0000000=>[8]=>[8]
[6,8,7,2,1,4,3,5]=>0000000=>[8]=>[8]
[6,8,2,1,7,4,3,5]=>0000000=>[8]=>[8]
[8,6,2,4,3,1,5,7]=>0000000=>[8]=>[8]
[4,6,5,2,8,3,7,1]=>0000000=>[8]=>[8]
[2,6,4,5,8,3,7,1]=>0000000=>[8]=>[8]
[8,2,4,3,6,5,1,7]=>0000000=>[8]=>[8]
[4,2,1,6,8,7,5,3]=>0000000=>[8]=>[8]
[4,2,1,6,5,8,7,3]=>0000000=>[8]=>[8]
[6,2,1,8,4,3,7,5]=>0000000=>[8]=>[8]
[4,6,5,8,7,2,1,3]=>0000000=>[8]=>[8]
[6,4,8,2,1,5,7,3]=>0000000=>[8]=>[8]
[2,6,8,4,7,1,5,3]=>0000000=>[8]=>[8]
[4,8,6,7,2,1,3,5]=>0000000=>[8]=>[8]
[7,4,5,2,3,8,6,1]=>0000000=>[8]=>[8]
[3,5,1,6,4,2,8,7]=>0000010=>[6,2]=>[6,2]
[7,2,3,4,5,8,6,1]=>0000000=>[8]=>[8]
[8,2,3,4,5,7,1,6]=>0000000=>[8]=>[8]
[5,7,1,3,8,6,2,4]=>0000000=>[8]=>[8]
[4,7,3,2,8,6,1,5]=>0000000=>[8]=>[8]
[4,8,1,5,6,7,3,2]=>0000000=>[8]=>[8]
[6,8,2,5,1,7,3,4]=>0000000=>[8]=>[8]
[7,8,3,4,6,2,1,5]=>0000000=>[8]=>[8]
[3,8,2,5,4,7,6,1]=>0000000=>[8]=>[8]
[3,7,6,1,8,5,2,4]=>0000000=>[8]=>[8]
[4,6,7,1,8,5,3,2]=>0000000=>[8]=>[8]
[3,6,1,7,8,5,4,2]=>0000000=>[8]=>[8]
[2,1,5,7,3,8,6,4]=>0100000=>[2,6]=>[6,2]
[7,6,1,4,8,5,2,3]=>0000000=>[8]=>[8]
[4,1,2,3,7,8,6,5]=>0001000=>[4,4]=>[4,4]
[3,4,2,1,8,5,6,7]=>0001000=>[4,4]=>[4,4]
[5,4,8,3,6,7,1,2]=>0000000=>[8]=>[8]
[4,5,8,3,6,7,2,1]=>0000000=>[8]=>[8]
[2,1,5,8,4,6,7,3]=>0100000=>[2,6]=>[6,2]
[4,6,8,3,5,2,7,1]=>0000000=>[8]=>[8]
[5,7,8,3,2,4,1,6]=>0000000=>[8]=>[8]
[3,8,2,4,5,6,7,1]=>0000000=>[8]=>[8]
[4,3,1,6,5,8,7,2]=>0000000=>[8]=>[8]
[8,2,7,4,1,3,6,5]=>0000000=>[8]=>[8]
[3,1,5,2,4,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,6,4,5,1,8,7,2]=>0000000=>[8]=>[8]
[4,3,6,1,2,8,7,5]=>0000000=>[8]=>[8]
[6,1,3,5,4,8,7,2]=>0000000=>[8]=>[8]
[1,7,3,8,4,6,2,5]=>1000000=>[1,7]=>[7,1]
[1,6,7,4,8,5,3,2]=>1000000=>[1,7]=>[7,1]
[8,1,2,5,4,6,3,7]=>0000000=>[8]=>[8]
[8,4,2,5,7,1,6,3]=>0000000=>[8]=>[8]
[1,8,5,3,7,4,6,2]=>1000000=>[1,7]=>[7,1]
[4,2,1,7,5,3,6,8]=>0000001=>[7,1]=>[7,1]
[1,4,8,6,5,7,2,3]=>1000000=>[1,7]=>[7,1]
[3,5,4,8,6,1,2,7]=>0000000=>[8]=>[8]
[4,3,5,8,1,7,2,6]=>0000000=>[8]=>[8]
[1,4,5,8,6,7,3,2]=>1000000=>[1,7]=>[7,1]
[1,7,6,5,8,3,4,2]=>1000000=>[1,7]=>[7,1]
[7,3,6,1,8,2,4,5]=>0000000=>[8]=>[8]
[7,6,4,5,8,1,3,2]=>0000000=>[8]=>[8]
[4,3,1,6,8,7,5,2]=>0000000=>[8]=>[8]
[4,3,1,8,5,6,7,2]=>0000000=>[8]=>[8]
[6,2,8,4,3,1,7,5]=>0000000=>[8]=>[8]
[7,1,6,2,3,4,5,8]=>0000001=>[7,1]=>[7,1]
[1,8,5,4,3,6,2,7]=>1000000=>[1,7]=>[7,1]
[1,8,3,6,5,2,7,4]=>1000000=>[1,7]=>[7,1]
[4,7,1,8,2,6,5,3]=>0000000=>[8]=>[8]
[1,4,8,3,5,7,6,2]=>1000000=>[1,7]=>[7,1]
[6,1,5,2,4,7,8,3]=>0000000=>[8]=>[8]
[4,1,8,5,2,7,6,3]=>0000000=>[8]=>[8]
[4,3,8,5,1,2,6,7]=>0000000=>[8]=>[8]
[4,1,8,2,3,7,5,6]=>0000000=>[8]=>[8]
[1,8,7,6,2,5,4,3]=>1000000=>[1,7]=>[7,1]
[1,2,3,4,5,10,9,8,7,6]=>111110000=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]
[4,6,3,1,5,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,2,7,4,5,1,3,8]=>0000001=>[7,1]=>[7,1]
[5,7,3,4,1,6,2,8]=>0000001=>[7,1]=>[7,1]
[4,2,8,1,5,6,7,3]=>0000000=>[8]=>[8]
[1,7,8,4,5,6,2,3]=>1000000=>[1,7]=>[7,1]
[1,6,8,4,5,2,7,3]=>1000000=>[1,7]=>[7,1]
[1,5,8,4,2,6,7,3]=>1000000=>[1,7]=>[7,1]
[1,5,3,8,2,6,7,4]=>1000000=>[1,7]=>[7,1]
[1,6,3,8,5,2,7,4]=>1000000=>[1,7]=>[7,1]
[1,7,3,8,5,6,2,4]=>1000000=>[1,7]=>[7,1]
[6,2,3,7,5,1,4,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,1,5,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,2,6,4,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,2,7,8,5,6,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,8,5,3,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,4,8,3,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[8,7,3,2,1,6,5,4]=>0000000=>[8]=>[8]
[8,7,4,1,6,2,3,5]=>0000000=>[8]=>[8]
[1,8,3,2,6,4,5,7]=>1000000=>[1,7]=>[7,1]
[7,3,8,1,5,2,4,6]=>0000000=>[8]=>[8]
[3,1,7,2,6,4,5,8]=>0000001=>[7,1]=>[7,1]
[1,8,4,2,3,6,7,5]=>1000000=>[1,7]=>[7,1]
[4,1,7,2,3,6,8,5]=>0000000=>[8]=>[8]
[3,1,7,5,4,2,8,6]=>0000000=>[8]=>[8]
[3,2,6,7,4,1,8,5]=>0000000=>[8]=>[8]
[5,6,2,7,1,4,8,3]=>0000000=>[8]=>[8]
[6,4,2,8,1,5,7,3]=>0000000=>[8]=>[8]
[7,3,6,8,5,2,4,1]=>0000000=>[8]=>[8]
[2,7,8,3,6,5,1,4]=>0000000=>[8]=>[8]
[2,7,8,5,4,6,3,1]=>0000000=>[8]=>[8]
[2,6,8,3,4,7,1,5]=>0000000=>[8]=>[8]
[2,5,6,8,3,4,1,7]=>0000000=>[8]=>[8]
[2,7,8,3,6,1,4,5]=>0000000=>[8]=>[8]
[2,1,3,7,8,5,6,4]=>0110000=>[2,1,5]=>[5,2,1]
[5,1,2,4,8,7,3,6]=>0000000=>[8]=>[8]
[2,3,6,1,8,5,7,4]=>0000000=>[8]=>[8]
[5,2,6,1,7,8,4,3]=>0000000=>[8]=>[8]
[3,6,5,4,1,8,7,2]=>0000000=>[8]=>[8]
[4,1,8,2,5,7,3,6]=>0000000=>[8]=>[8]
[1,5,8,2,4,7,3,6]=>1000000=>[1,7]=>[7,1]
[6,2,1,4,7,8,3,5]=>0000000=>[8]=>[8]
[3,8,1,4,2,6,5,7]=>0000000=>[8]=>[8]
[8,3,4,2,1,6,5,7]=>0000000=>[8]=>[8]
[5,3,2,8,1,6,4,7]=>0000000=>[8]=>[8]
[2,4,5,8,3,6,1,7]=>0000000=>[8]=>[8]
[2,6,4,3,7,8,5,1]=>0000000=>[8]=>[8]
[7,4,1,8,3,2,5,6]=>0000000=>[8]=>[8]
[5,6,1,7,4,2,8,3]=>0000000=>[8]=>[8]
[1,3,8,6,2,7,4,5]=>1000000=>[1,7]=>[7,1]
[4,3,7,5,6,1,8,2]=>0000000=>[8]=>[8]
[6,7,3,8,4,1,2,5]=>0000000=>[8]=>[8]
[4,7,5,8,3,1,2,6]=>0000000=>[8]=>[8]
[5,7,3,1,6,8,4,2]=>0000000=>[8]=>[8]
[4,6,7,2,8,3,1,5]=>0000000=>[8]=>[8]
[4,5,6,7,3,1,8,2]=>0000000=>[8]=>[8]
[8,5,3,2,7,6,1,4]=>0000000=>[8]=>[8]
[7,5,4,6,2,8,1,3]=>0000000=>[8]=>[8]
[2,5,1,3,6,8,7,4]=>0000000=>[8]=>[8]
[7,3,8,5,2,1,4,6]=>0000000=>[8]=>[8]
[5,8,3,6,4,7,1,2]=>0000000=>[8]=>[8]
[4,1,6,3,2,5,8,7]=>0000010=>[6,2]=>[6,2]
[8,6,1,7,2,5,4,3]=>0000000=>[8]=>[8]
[8,7,6,1,2,3,5,4]=>0000000=>[8]=>[8]
[5,4,1,6,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[5,8,7,6,1,2,3,4]=>0000000=>[8]=>[8]
[8,2,7,1,5,4,3,6]=>0000000=>[8]=>[8]
[2,1,6,3,8,5,4,7]=>0100000=>[2,6]=>[6,2]
[2,6,3,1,8,5,4,7]=>0000000=>[8]=>[8]
[4,6,2,8,5,1,3,7]=>0000000=>[8]=>[8]
[4,6,5,2,7,3,8,1]=>0000000=>[8]=>[8]
[3,1,6,2,4,8,7,5]=>0000000=>[8]=>[8]
[2,8,5,7,4,1,3,6]=>0000000=>[8]=>[8]
[6,4,8,3,5,7,1,2]=>0000000=>[8]=>[8]
[8,5,7,4,6,2,1,3]=>0000000=>[8]=>[8]
[4,1,8,5,6,3,2,7]=>0000000=>[8]=>[8]
[5,8,3,2,4,6,1,7]=>0000000=>[8]=>[8]
[2,8,4,1,5,3,7,6]=>0000000=>[8]=>[8]
[2,1,8,6,4,3,7,5]=>0100000=>[2,6]=>[6,2]
[3,6,7,1,8,5,2,4]=>0000000=>[8]=>[8]
[6,5,7,3,1,8,4,2]=>0000000=>[8]=>[8]
[6,1,5,7,2,4,8,3]=>0000000=>[8]=>[8]
[7,4,5,1,2,3,8,6]=>0000000=>[8]=>[8]
[8,4,7,6,2,1,5,3]=>0000000=>[8]=>[8]
[3,5,7,6,4,1,8,2]=>0000000=>[8]=>[8]
[5,4,1,7,6,2,8,3]=>0000000=>[8]=>[8]
[5,7,2,3,6,4,8,1]=>0000000=>[8]=>[8]
[6,1,8,2,7,3,4,5]=>0000000=>[8]=>[8]
[1,8,5,7,2,3,4,6]=>1000000=>[1,7]=>[7,1]
[8,1,5,7,2,3,6,4]=>0000000=>[8]=>[8]
[2,3,1,7,8,6,4,5]=>0010000=>[3,5]=>[5,3]
[5,4,1,6,3,8,7,2]=>0000000=>[8]=>[8]
[5,4,1,2,8,7,6,3]=>0000000=>[8]=>[8]
[5,6,3,7,8,4,2,1]=>0000000=>[8]=>[8]
[4,3,2,6,8,1,7,5]=>0000000=>[8]=>[8]
[1,5,4,2,7,8,3,6]=>1000000=>[1,7]=>[7,1]
[6,1,2,8,7,4,3,5]=>0000000=>[8]=>[8]
[3,6,5,8,4,7,1,2]=>0000000=>[8]=>[8]
[3,2,8,1,4,7,6,5]=>0000000=>[8]=>[8]
[6,4,3,8,2,5,7,1]=>0000000=>[8]=>[8]
[2,1,7,8,3,4,6,5]=>0100000=>[2,6]=>[6,2]
[5,6,1,8,2,7,4,3]=>0000000=>[8]=>[8]
[3,6,8,5,2,7,4,1]=>0000000=>[8]=>[8]
[2,1,6,5,4,8,3,7]=>0100000=>[2,6]=>[6,2]
[2,1,7,3,5,8,6,4]=>0100000=>[2,6]=>[6,2]
[7,8,1,2,4,5,6,3]=>0000000=>[8]=>[8]
[3,8,7,4,1,2,5,6]=>0000000=>[8]=>[8]
[4,3,8,7,1,6,5,2]=>0000000=>[8]=>[8]
[3,7,5,8,1,6,2,4]=>0000000=>[8]=>[8]
[4,2,7,5,8,3,6,1]=>0000000=>[8]=>[8]
[5,8,2,7,3,4,6,1]=>0000000=>[8]=>[8]
[5,7,2,1,8,3,6,4]=>0000000=>[8]=>[8]
[7,8,1,2,3,4,6,5]=>0000000=>[8]=>[8]
[5,6,2,4,3,1,8,7]=>0000010=>[6,2]=>[6,2]
[6,3,2,1,4,8,5,7]=>0000000=>[8]=>[8]
[8,7,6,2,4,3,1,5]=>0000000=>[8]=>[8]
[7,6,8,1,5,4,3,2]=>0000000=>[8]=>[8]
[7,6,1,8,5,4,3,2]=>0000000=>[8]=>[8]
[6,5,8,1,7,4,3,2]=>0000000=>[8]=>[8]
[4,3,8,7,6,1,5,2]=>0000000=>[8]=>[8]
[6,5,8,7,4,1,3,2]=>0000000=>[8]=>[8]
[5,4,8,7,6,3,1,2]=>0000000=>[8]=>[8]
[1,4,8,6,3,2,5,7]=>1000000=>[1,7]=>[7,1]
[1,6,3,8,5,2,4,7]=>1000000=>[1,7]=>[7,1]
[4,6,3,7,5,2,1,8]=>0000001=>[7,1]=>[7,1]
[3,7,2,6,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,1,6,8,4,5,7]=>0010000=>[3,5]=>[5,3]
[3,5,7,4,8,6,1,2]=>0000000=>[8]=>[8]
[5,2,7,4,1,6,8,3]=>0000000=>[8]=>[8]
[4,5,8,2,1,7,6,3]=>0000000=>[8]=>[8]
[1,6,4,8,5,2,7,3]=>1000000=>[1,7]=>[7,1]
[7,4,1,5,3,8,2,6]=>0000000=>[8]=>[8]
[3,4,1,2,7,8,6,5]=>0001000=>[4,4]=>[4,4]
[3,1,2,4,7,6,8,5]=>0011000=>[3,1,4]=>[4,3,1]
[8,1,3,5,4,7,2,6]=>0000000=>[8]=>[8]
[7,1,4,3,5,2,8,6]=>0000000=>[8]=>[8]
[3,2,8,1,6,5,4,7]=>0000000=>[8]=>[8]
[6,8,4,1,2,5,3,7]=>0000000=>[8]=>[8]
[8,2,1,5,6,4,3,7]=>0000000=>[8]=>[8]
[4,7,1,8,2,5,3,6]=>0000000=>[8]=>[8]
[6,7,8,1,4,5,3,2]=>0000000=>[8]=>[8]
[3,2,5,4,7,8,1,6]=>0000000=>[8]=>[8]
[8,4,7,6,2,3,1,5]=>0000000=>[8]=>[8]
[6,1,2,8,7,3,5,4]=>0000000=>[8]=>[8]
[5,7,2,3,8,1,6,4]=>0000000=>[8]=>[8]
[3,5,2,6,1,8,7,4]=>0000000=>[8]=>[8]
[3,2,5,6,7,8,1,4]=>0000000=>[8]=>[8]
[6,4,1,2,8,7,3,5]=>0000000=>[8]=>[8]
[4,3,8,5,2,1,6,7]=>0000000=>[8]=>[8]
[7,5,4,2,3,8,1,6]=>0000000=>[8]=>[8]
[5,6,3,1,8,2,7,4]=>0000000=>[8]=>[8]
[4,5,2,1,6,8,3,7]=>0000000=>[8]=>[8]
[5,6,2,8,1,7,4,3]=>0000000=>[8]=>[8]
[1,5,6,3,4,8,2,7]=>1000000=>[1,7]=>[7,1]
[2,1,4,5,8,6,3,7]=>0100000=>[2,6]=>[6,2]
[1,8,3,4,7,6,2,5]=>1000000=>[1,7]=>[7,1]
[3,1,2,8,6,4,5,7]=>0010000=>[3,5]=>[5,3]
[2,5,6,1,8,4,3,7]=>0000000=>[8]=>[8]
[5,4,7,6,1,8,2,3]=>0000000=>[8]=>[8]
[3,5,6,8,4,7,2,1]=>0000000=>[8]=>[8]
[2,4,8,5,7,3,6,1]=>0000000=>[8]=>[8]
[5,3,7,8,4,6,2,1]=>0000000=>[8]=>[8]
[6,7,3,8,4,5,2,1]=>0000000=>[8]=>[8]
[2,5,3,7,6,8,1,4]=>0000000=>[8]=>[8]
[4,2,1,8,7,3,5,6]=>0000000=>[8]=>[8]
[8,7,4,6,2,3,1,5]=>0000000=>[8]=>[8]
[6,8,3,5,4,7,1,2]=>0000000=>[8]=>[8]
[1,4,6,3,7,2,8,5]=>1000000=>[1,7]=>[7,1]
[6,2,1,8,4,5,3,7]=>0000000=>[8]=>[8]
[4,7,3,8,5,2,1,6]=>0000000=>[8]=>[8]
[4,7,5,1,8,6,3,2]=>0000000=>[8]=>[8]
[6,2,4,1,7,5,8,3]=>0000000=>[8]=>[8]
[3,6,5,8,4,1,7,2]=>0000000=>[8]=>[8]
[5,7,3,1,6,4,8,2]=>0000000=>[8]=>[8]
[6,1,3,7,4,8,5,2]=>0000000=>[8]=>[8]
[3,1,5,4,2,8,6,7]=>0000100=>[5,3]=>[5,3]
[4,1,5,2,7,6,3,8]=>0000001=>[7,1]=>[7,1]
[6,2,7,1,4,8,5,3]=>0000000=>[8]=>[8]
[4,3,2,1,8,5,7,6]=>0001000=>[4,4]=>[4,4]
[7,4,3,2,8,1,6,5]=>0000000=>[8]=>[8]
[1,8,5,3,6,4,2,7]=>1000000=>[1,7]=>[7,1]
[8,1,6,2,7,4,3,5]=>0000000=>[8]=>[8]
[7,3,1,6,5,4,2,8]=>0000001=>[7,1]=>[7,1]
[2,8,5,6,1,4,3,7]=>0000000=>[8]=>[8]
[3,7,5,8,2,1,4,6]=>0000000=>[8]=>[8]
[6,5,8,4,1,3,7,2]=>0000000=>[8]=>[8]
[5,4,8,3,2,1,7,6]=>0000000=>[8]=>[8]
[2,4,7,1,3,6,5,8]=>0000001=>[7,1]=>[7,1]
[5,7,4,8,1,3,6,2]=>0000000=>[8]=>[8]
[5,1,7,8,2,4,6,3]=>0000000=>[8]=>[8]
[3,6,7,8,1,2,5,4]=>0000000=>[8]=>[8]
[4,6,7,2,8,1,3,5]=>0000000=>[8]=>[8]
[6,3,7,1,8,2,5,4]=>0000000=>[8]=>[8]
[5,7,1,4,8,2,6,3]=>0000000=>[8]=>[8]
[6,1,2,7,8,3,5,4]=>0000000=>[8]=>[8]
[3,6,4,7,8,1,2,5]=>0000000=>[8]=>[8]
[3,7,4,8,5,2,1,6]=>0000000=>[8]=>[8]
[4,8,2,1,7,5,3,6]=>0000000=>[8]=>[8]
[7,3,8,1,6,4,2,5]=>0000000=>[8]=>[8]
[2,8,7,1,6,3,5,4]=>0000000=>[8]=>[8]
[2,7,6,5,1,4,3,8]=>0000001=>[7,1]=>[7,1]
[3,8,7,6,2,1,5,4]=>0000000=>[8]=>[8]
[5,8,7,2,6,1,4,3]=>0000000=>[8]=>[8]
[7,3,8,6,5,1,2,4]=>0000000=>[8]=>[8]
[5,8,6,4,3,2,1,7]=>0000000=>[8]=>[8]
[8,1,2,3,4,7,6,5]=>0000000=>[8]=>[8]
[3,8,2,7,6,5,4,1]=>0000000=>[8]=>[8]
[4,2,8,7,6,5,3,1]=>0000000=>[8]=>[8]
[8,3,1,7,6,5,4,2]=>0000000=>[8]=>[8]
[5,2,8,7,6,4,3,1]=>0000000=>[8]=>[8]
[8,3,2,1,7,6,5,4]=>0000000=>[8]=>[8]
[8,4,1,7,6,5,3,2]=>0000000=>[8]=>[8]
[4,5,6,2,3,8,1,7]=>0000000=>[8]=>[8]
[3,2,7,4,5,8,1,6]=>0000000=>[8]=>[8]
[5,4,6,1,3,8,2,7]=>0000000=>[8]=>[8]
[2,4,1,7,5,8,3,6]=>0000000=>[8]=>[8]
[8,1,7,4,2,3,6,5]=>0000000=>[8]=>[8]
[3,5,8,1,2,4,7,6]=>0000000=>[8]=>[8]
[3,8,4,1,2,7,6,5]=>0000000=>[8]=>[8]
[6,4,1,3,2,7,8,5]=>0000000=>[8]=>[8]
[2,7,1,6,8,3,5,4]=>0000000=>[8]=>[8]
[8,5,3,2,6,1,7,4]=>0000000=>[8]=>[8]
[7,8,4,1,2,5,3,6]=>0000000=>[8]=>[8]
[6,1,4,2,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[7,8,2,1,6,3,5,4]=>0000000=>[8]=>[8]
[1,2,8,3,6,4,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[6,2,3,7,4,1,5,8]=>0000001=>[7,1]=>[7,1]
[6,2,4,1,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[2,7,3,8,6,4,1,5]=>0000000=>[8]=>[8]
[1,8,3,7,6,4,5,2]=>1000000=>[1,7]=>[7,1]
[2,6,8,5,3,1,7,4]=>0000000=>[8]=>[8]
[5,6,2,1,7,3,8,4]=>0000000=>[8]=>[8]
[5,3,6,2,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,7,4,2,1,3,6,8]=>0000001=>[7,1]=>[7,1]
[6,4,2,1,5,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,3,1,4,6,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,6,4,2,8,7,3,5]=>1000000=>[1,7]=>[7,1]
[4,8,1,2,6,7,3,5]=>0000000=>[8]=>[8]
[3,1,2,4,6,8,7,5]=>0011000=>[3,1,4]=>[4,3,1]
[4,2,8,1,5,3,7,6]=>0000000=>[8]=>[8]
[4,3,8,5,7,6,1,2]=>0000000=>[8]=>[8]
[4,8,6,3,7,5,1,2]=>0000000=>[8]=>[8]
[3,8,6,5,2,7,1,4]=>0000000=>[8]=>[8]
[3,8,5,6,1,7,4,2]=>0000000=>[8]=>[8]
[4,2,7,8,1,3,6,5]=>0000000=>[8]=>[8]
[6,8,1,5,4,7,3,2]=>0000000=>[8]=>[8]
[2,6,4,3,1,5,8,7]=>0000010=>[6,2]=>[6,2]
[5,1,7,2,8,6,4,3]=>0000000=>[8]=>[8]
[6,8,2,5,4,7,1,3]=>0000000=>[8]=>[8]
[5,8,3,2,7,6,1,4]=>0000000=>[8]=>[8]
[4,8,3,2,1,7,6,5]=>0000000=>[8]=>[8]
[2,6,8,3,7,1,4,5]=>0000000=>[8]=>[8]
[6,8,3,7,2,1,5,4]=>0000000=>[8]=>[8]
[4,5,8,1,6,3,2,7]=>0000000=>[8]=>[8]
[6,8,4,7,1,5,3,2]=>0000000=>[8]=>[8]
[4,3,2,1,6,8,5,7]=>0001000=>[4,4]=>[4,4]
[2,4,1,3,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[4,8,6,5,1,7,3,2]=>0000000=>[8]=>[8]
[6,5,3,1,7,2,8,4]=>0000000=>[8]=>[8]
[2,1,5,4,8,7,3,6]=>0100000=>[2,6]=>[6,2]
[2,3,8,5,4,1,6,7]=>0000000=>[8]=>[8]
[2,1,4,8,6,5,3,7]=>0100000=>[2,6]=>[6,2]
[4,3,2,8,7,6,1,5]=>0000000=>[8]=>[8]
[3,2,8,7,5,4,1,6]=>0000000=>[8]=>[8]
[5,4,2,6,3,1,8,7]=>0000010=>[6,2]=>[6,2]
[5,6,3,1,2,4,8,7]=>0000010=>[6,2]=>[6,2]
[3,8,4,1,5,7,2,6]=>0000000=>[8]=>[8]
[5,6,3,7,4,8,2,1]=>0000000=>[8]=>[8]
[8,5,2,6,1,7,3,4]=>0000000=>[8]=>[8]
[5,4,2,6,8,3,7,1]=>0000000=>[8]=>[8]
[7,6,8,5,1,4,2,3]=>0000000=>[8]=>[8]
[2,1,7,8,5,3,4,6]=>0100000=>[2,6]=>[6,2]
[4,1,8,2,6,5,3,7]=>0000000=>[8]=>[8]
[4,7,3,8,1,2,6,5]=>0000000=>[8]=>[8]
[3,8,1,2,4,6,5,7]=>0000000=>[8]=>[8]
[4,8,7,6,3,5,2,1]=>0000000=>[8]=>[8]
[3,8,7,6,5,2,4,1]=>0000000=>[8]=>[8]
[4,8,7,3,6,5,2,1]=>0000000=>[8]=>[8]
[4,8,7,6,3,2,5,1]=>0000000=>[8]=>[8]
[3,8,7,6,5,2,1,4]=>0000000=>[8]=>[8]
[7,5,8,3,6,2,1,4]=>0000000=>[8]=>[8]
[7,5,8,3,2,6,1,4]=>0000000=>[8]=>[8]
[7,5,8,3,2,1,6,4]=>0000000=>[8]=>[8]
[2,3,7,8,4,1,6,5]=>0000000=>[8]=>[8]
[2,1,7,5,8,4,6,3]=>0100000=>[2,6]=>[6,2]
[2,5,6,8,1,7,4,3]=>0000000=>[8]=>[8]
[4,2,8,6,1,7,3,5]=>0000000=>[8]=>[8]
[8,6,4,1,3,2,5,7]=>0000000=>[8]=>[8]
[8,1,3,2,6,5,4,7]=>0000000=>[8]=>[8]
[8,5,3,6,2,4,1,7]=>0000000=>[8]=>[8]
[8,4,1,2,6,5,3,7]=>0000000=>[8]=>[8]
[8,3,5,6,2,1,4,7]=>0000000=>[8]=>[8]
[4,1,8,2,3,7,6,5]=>0000000=>[8]=>[8]
[3,7,4,5,8,2,1,6]=>0000000=>[8]=>[8]
[5,3,8,7,4,6,1,2]=>0000000=>[8]=>[8]
[7,5,8,2,1,4,6,3]=>0000000=>[8]=>[8]
[7,4,8,3,2,6,1,5]=>0000000=>[8]=>[8]
[6,8,2,3,1,7,5,4]=>0000000=>[8]=>[8]
[7,4,3,2,6,8,5,1]=>0000000=>[8]=>[8]
[5,1,2,3,6,8,7,4]=>0000000=>[8]=>[8]
[2,4,7,3,8,1,6,5]=>0000000=>[8]=>[8]
[6,3,8,2,7,4,1,5]=>0000000=>[8]=>[8]
[8,2,1,3,6,4,7,5]=>0000000=>[8]=>[8]
[5,7,8,2,1,4,3,6]=>0000000=>[8]=>[8]
[3,5,1,7,8,4,2,6]=>0000000=>[8]=>[8]
[1,7,8,4,5,3,2,6]=>1000000=>[1,7]=>[7,1]
[3,2,4,8,6,7,1,5]=>0000000=>[8]=>[8]
[3,2,5,7,4,8,1,6]=>0000000=>[8]=>[8]
[8,4,7,1,3,2,5,6]=>0000000=>[8]=>[8]
[8,4,7,2,1,3,5,6]=>0000000=>[8]=>[8]
[6,4,2,1,3,7,8,5]=>0000000=>[8]=>[8]
[7,1,6,3,5,8,2,4]=>0000000=>[8]=>[8]
[5,3,6,7,8,4,2,1]=>0000000=>[8]=>[8]
[1,5,2,7,8,6,4,3]=>1000000=>[1,7]=>[7,1]
[4,1,7,5,2,6,8,3]=>0000000=>[8]=>[8]
[7,6,2,4,5,1,8,3]=>0000000=>[8]=>[8]
[8,1,4,5,2,6,7,3]=>0000000=>[8]=>[8]
[3,5,7,2,1,6,8,4]=>0000000=>[8]=>[8]
[3,5,2,4,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,7,4,6,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,5,7,4,6,1,8]=>0000001=>[7,1]=>[7,1]
[5,7,3,2,4,6,1,8]=>0000001=>[7,1]=>[7,1]
[3,7,5,2,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,2,7,5,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[1,7,3,5,2,4,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[3,2,1,5,7,4,6,8]=>0010001=>[3,4,1]=>[4,3,1]
[3,5,7,2,1,4,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,7,1,4,6,8]=>0000001=>[7,1]=>[7,1]
[3,2,5,7,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,7,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,2,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[5,3,7,2,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[5,3,2,4,7,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,2,5,4,7,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,4,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[3,5,2,1,4,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[3,5,2,1,7,4,6,8]=>0000001=>[7,1]=>[7,1]
[5,3,1,7,2,4,6,8]=>0000001=>[7,1]=>[7,1]
[1,3,7,5,2,4,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[3,7,2,1,5,4,6,8]=>0000001=>[7,1]=>[7,1]
[3,1,7,2,5,4,6,8]=>0000001=>[7,1]=>[7,1]
[1,7,5,3,2,4,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[5,8,7,1,2,6,4,3]=>0000000=>[8]=>[8]
[6,8,2,1,7,5,4,3]=>0000000=>[8]=>[8]
[5,8,7,4,1,2,6,3]=>0000000=>[8]=>[8]
[1,8,5,4,2,7,6,3]=>1000000=>[1,7]=>[7,1]
[7,6,4,2,8,5,3,1]=>0000000=>[8]=>[8]
[7,6,4,8,5,1,2,3]=>0000000=>[8]=>[8]
[7,6,4,5,1,3,8,2]=>0000000=>[8]=>[8]
[1,6,7,5,3,8,4,2]=>1000000=>[1,7]=>[7,1]
[7,6,3,5,2,4,8,1]=>0000000=>[8]=>[8]
[7,6,4,2,5,1,8,3]=>0000000=>[8]=>[8]
[2,6,5,7,8,3,4,1]=>0000000=>[8]=>[8]
[5,2,3,4,8,6,1,7]=>0000000=>[8]=>[8]
[5,3,4,8,2,7,6,1]=>0000000=>[8]=>[8]
[5,3,8,2,4,1,7,6]=>0000000=>[8]=>[8]
[5,2,8,4,1,7,3,6]=>0000000=>[8]=>[8]
[6,4,2,5,1,8,7,3]=>0000000=>[8]=>[8]
[6,4,3,5,8,2,1,7]=>0000000=>[8]=>[8]
[6,3,5,4,8,2,7,1]=>0000000=>[8]=>[8]
[1,5,7,3,4,8,6,2]=>1000000=>[1,7]=>[7,1]
[5,8,4,1,3,7,6,2]=>0000000=>[8]=>[8]
[6,4,5,3,8,1,7,2]=>0000000=>[8]=>[8]
[6,4,3,8,5,7,2,1]=>0000000=>[8]=>[8]
[5,4,2,6,3,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,6,5,3,7,1,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,6,1,4,8,2]=>0000000=>[8]=>[8]
[3,6,5,7,4,8,1,2]=>0000000=>[8]=>[8]
[4,2,6,5,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,3,5,7,2,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,7,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,6,8,1,2,5]=>0000000=>[8]=>[8]
[1,8,4,3,7,5,6,2]=>1000000=>[1,7]=>[7,1]
[5,2,8,6,4,7,3,1]=>0000000=>[8]=>[8]
[1,8,6,3,7,4,2,5]=>1000000=>[1,7]=>[7,1]
[1,8,6,5,7,2,3,4]=>1000000=>[1,7]=>[7,1]
[4,2,8,3,5,7,1,6]=>0000000=>[8]=>[8]
[1,3,7,2,6,5,8,4]=>1000000=>[1,7]=>[7,1]
[1,5,7,2,4,6,8,3]=>1000000=>[1,7]=>[7,1]
[1,3,6,4,2,5,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[5,6,3,4,7,1,8,2]=>0000000=>[8]=>[8]
[3,5,2,7,4,1,8,6]=>0000000=>[8]=>[8]
[5,2,3,8,4,1,7,6]=>0000000=>[8]=>[8]
[7,5,3,4,8,2,1,6]=>0000000=>[8]=>[8]
[7,6,3,8,4,2,1,5]=>0000000=>[8]=>[8]
[7,2,8,5,1,6,3,4]=>0000000=>[8]=>[8]
[7,4,3,8,5,2,6,1]=>0000000=>[8]=>[8]
[7,2,8,5,1,3,4,6]=>0000000=>[8]=>[8]
[7,6,8,1,2,5,3,4]=>0000000=>[8]=>[8]
[1,5,3,7,6,8,4,2]=>1000000=>[1,7]=>[7,1]
[1,2,6,4,5,8,3,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,4,8,5,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,3,7,8,2,4,5]=>1000000=>[1,7]=>[7,1]
[3,2,6,7,8,1,4,5]=>0000000=>[8]=>[8]
[1,4,7,3,5,2,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[3,8,4,7,6,1,5,2]=>0000000=>[8]=>[8]
[5,7,4,2,6,3,1,8]=>0000001=>[7,1]=>[7,1]
[6,1,3,7,4,2,5,8]=>0000001=>[7,1]=>[7,1]
[2,1,8,3,6,7,4,5]=>0100000=>[2,6]=>[6,2]
[5,7,1,4,2,6,3,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,8,1,5,7,4]=>0000000=>[8]=>[8]
[7,8,5,4,1,6,3,2]=>0000000=>[8]=>[8]
[3,6,2,7,8,1,5,4]=>0000000=>[8]=>[8]
[5,7,8,4,1,6,3,2]=>0000000=>[8]=>[8]
[3,4,8,1,2,5,7,6]=>0000000=>[8]=>[8]
[6,3,1,8,2,7,4,5]=>0000000=>[8]=>[8]
[5,2,8,1,3,4,7,6]=>0000000=>[8]=>[8]
[3,2,1,6,4,7,8,5]=>0010000=>[3,5]=>[5,3]
[6,1,3,4,2,8,5,7]=>0000000=>[8]=>[8]
[3,2,6,1,5,7,8,4]=>0000000=>[8]=>[8]
[3,6,4,2,1,7,8,5]=>0000000=>[8]=>[8]
[1,8,3,2,6,7,5,4]=>1000000=>[1,7]=>[7,1]
[4,7,5,3,8,2,1,6]=>0000000=>[8]=>[8]
[1,4,7,6,8,2,3,5]=>1000000=>[1,7]=>[7,1]
[1,3,7,5,6,8,2,4]=>1000000=>[1,7]=>[7,1]
[3,2,7,1,6,8,4,5]=>0000000=>[8]=>[8]
[3,6,4,7,8,5,2,1]=>0000000=>[8]=>[8]
[6,3,5,8,7,4,1,2]=>0000000=>[8]=>[8]
[4,1,8,3,7,5,6,2]=>0000000=>[8]=>[8]
[4,7,2,8,5,6,3,1]=>0000000=>[8]=>[8]
[1,4,8,7,3,5,6,2]=>1000000=>[1,7]=>[7,1]
[3,2,8,7,1,5,6,4]=>0000000=>[8]=>[8]
[1,5,8,7,4,6,2,3]=>1000000=>[1,7]=>[7,1]
[4,8,6,7,5,3,2,1]=>0000000=>[8]=>[8]
[3,8,7,5,6,4,2,1]=>0000000=>[8]=>[8]
[8,3,2,1,5,6,4,7]=>0000000=>[8]=>[8]
[1,7,8,5,4,3,2,6]=>1000000=>[1,7]=>[7,1]
[1,2,6,7,8,4,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[8,5,7,1,3,4,6,2]=>0000000=>[8]=>[8]
[4,7,2,1,5,3,8,6]=>0000000=>[8]=>[8]
[4,3,7,2,6,8,1,5]=>0000000=>[8]=>[8]
[1,7,8,2,6,4,5,3]=>1000000=>[1,7]=>[7,1]
[8,7,2,5,4,6,1,3]=>0000000=>[8]=>[8]
[8,7,1,2,4,5,6,3]=>0000000=>[8]=>[8]
[8,7,6,1,4,5,3,2]=>0000000=>[8]=>[8]
[8,7,5,6,1,4,3,2]=>0000000=>[8]=>[8]
[6,8,7,1,5,4,3,2]=>0000000=>[8]=>[8]
[8,5,7,6,1,4,3,2]=>0000000=>[8]=>[8]
[6,7,8,1,5,4,3,2]=>0000000=>[8]=>[8]
[8,5,6,7,1,4,3,2]=>0000000=>[8]=>[8]
[8,7,6,3,5,4,1,2]=>0000000=>[8]=>[8]
[8,7,4,5,6,1,3,2]=>0000000=>[8]=>[8]
[4,2,8,7,6,5,1,3]=>0000000=>[8]=>[8]
[7,5,8,1,6,4,3,2]=>0000000=>[8]=>[8]
[1,5,8,7,6,2,4,3]=>1000000=>[1,7]=>[7,1]
[7,5,8,4,1,6,3,2]=>0000000=>[8]=>[8]
[6,8,5,1,7,4,3,2]=>0000000=>[8]=>[8]
[1,6,8,7,2,5,4,3]=>1000000=>[1,7]=>[7,1]
[4,8,5,7,1,6,3,2]=>0000000=>[8]=>[8]
[5,4,3,6,7,1,8,2]=>0000000=>[8]=>[8]
[5,4,7,3,6,1,8,2]=>0000000=>[8]=>[8]
[4,8,7,6,3,1,5,2]=>0000000=>[8]=>[8]
[6,8,5,7,3,2,1,4]=>0000000=>[8]=>[8]
[6,8,5,3,7,2,1,4]=>0000000=>[8]=>[8]
[6,8,5,7,4,2,1,3]=>0000000=>[8]=>[8]
[2,1,8,7,6,3,4,5]=>0100000=>[2,6]=>[6,2]
[5,8,7,6,2,4,1,3]=>0000000=>[8]=>[8]
[6,8,2,7,5,1,4,3]=>0000000=>[8]=>[8]
[5,8,7,2,6,4,1,3]=>0000000=>[8]=>[8]
[6,8,7,5,2,4,1,3]=>0000000=>[8]=>[8]
[5,8,7,6,4,2,3,1]=>0000000=>[8]=>[8]
[2,3,6,1,7,5,8,4]=>0000000=>[8]=>[8]
[2,3,6,1,8,5,4,7]=>0000000=>[8]=>[8]
[2,4,1,6,7,5,8,3]=>0000000=>[8]=>[8]
[2,4,1,7,3,8,6,5]=>0000000=>[8]=>[8]
[2,4,5,3,7,1,8,6]=>0000000=>[8]=>[8]
[2,4,5,7,3,8,6,1]=>0000000=>[8]=>[8]
[2,4,6,3,1,8,5,7]=>0000000=>[8]=>[8]
[2,4,6,3,8,5,1,7]=>0000000=>[8]=>[8]
[2,4,7,3,1,5,8,6]=>0000000=>[8]=>[8]
[2,5,1,6,4,8,3,7]=>0000000=>[8]=>[8]
[2,5,1,7,4,3,8,6]=>0000000=>[8]=>[8]
[2,5,6,7,8,4,1,3]=>0000000=>[8]=>[8]
[2,5,6,8,4,3,1,7]=>0000000=>[8]=>[8]
[2,6,1,7,4,8,5,3]=>0000000=>[8]=>[8]
[7,6,4,8,2,1,3,5]=>0000000=>[8]=>[8]
[7,6,5,2,8,4,1,3]=>0000000=>[8]=>[8]
[7,6,3,8,2,4,1,5]=>0000000=>[8]=>[8]
[7,6,5,8,2,4,3,1]=>0000000=>[8]=>[8]
[6,8,4,7,2,5,3,1]=>0000000=>[8]=>[8]
[6,4,8,7,5,2,3,1]=>0000000=>[8]=>[8]
[6,8,4,2,7,5,3,1]=>0000000=>[8]=>[8]
[6,8,4,7,2,1,5,3]=>0000000=>[8]=>[8]
[6,8,4,7,3,5,2,1]=>0000000=>[8]=>[8]
[6,8,4,2,7,1,5,3]=>0000000=>[8]=>[8]
[6,4,2,8,7,5,3,1]=>0000000=>[8]=>[8]
[6,8,4,7,3,2,5,1]=>0000000=>[8]=>[8]
[6,8,4,2,1,7,5,3]=>0000000=>[8]=>[8]
[6,8,4,7,3,2,1,5]=>0000000=>[8]=>[8]
[6,8,5,7,1,4,3,2]=>0000000=>[8]=>[8]
[1,8,7,3,6,2,5,4]=>1000000=>[1,7]=>[7,1]
[5,8,7,2,3,6,1,4]=>0000000=>[8]=>[8]
[6,8,2,7,5,4,1,3]=>0000000=>[8]=>[8]
[6,8,3,7,5,2,1,4]=>0000000=>[8]=>[8]
[6,8,1,7,3,5,4,2]=>0000000=>[8]=>[8]
[6,8,4,7,3,1,5,2]=>0000000=>[8]=>[8]
[6,8,1,7,3,2,5,4]=>0000000=>[8]=>[8]
[3,8,2,7,6,5,1,4]=>0000000=>[8]=>[8]
[1,8,4,7,6,2,5,3]=>1000000=>[1,7]=>[7,1]
[3,8,1,7,6,2,5,4]=>0000000=>[8]=>[8]
[1,8,4,7,3,6,5,2]=>1000000=>[1,7]=>[7,1]
[4,8,5,7,1,2,6,3]=>0000000=>[8]=>[8]
[1,8,4,7,3,2,6,5]=>1000000=>[1,7]=>[7,1]
[6,8,5,2,7,4,1,3]=>0000000=>[8]=>[8]
[6,8,1,3,7,2,5,4]=>0000000=>[8]=>[8]
[2,8,1,3,7,6,5,4]=>0000000=>[8]=>[8]
[2,8,3,4,7,6,1,5]=>0000000=>[8]=>[8]
[6,8,1,4,2,7,5,3]=>0000000=>[8]=>[8]
[6,5,4,3,8,7,1,2]=>0000000=>[8]=>[8]
[3,1,7,2,8,5,6,4]=>0000000=>[8]=>[8]
[3,1,6,7,4,8,5,2]=>0000000=>[8]=>[8]
[3,1,5,7,8,4,6,2]=>0000000=>[8]=>[8]
[8,6,5,7,1,4,3,2]=>0000000=>[8]=>[8]
[6,4,8,2,7,5,1,3]=>0000000=>[8]=>[8]
[8,4,7,6,2,5,1,3]=>0000000=>[8]=>[8]
[3,4,5,6,8,7,1,2]=>0000000=>[8]=>[8]
[3,4,5,7,8,6,1,2]=>0000000=>[8]=>[8]
[3,4,5,8,7,6,1,2]=>0000000=>[8]=>[8]
[3,4,6,7,8,5,1,2]=>0000000=>[8]=>[8]
[6,4,7,3,5,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,7,3,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,8,3,6,7,2,1,4]=>0000000=>[8]=>[8]
[6,4,7,3,2,5,1,8]=>0000001=>[7,1]=>[7,1]
[6,3,7,8,2,4,1,5]=>0000000=>[8]=>[8]
[5,3,7,6,2,4,1,8]=>0000001=>[7,1]=>[7,1]
[7,5,8,2,6,4,1,3]=>0000000=>[8]=>[8]
[5,4,7,2,6,8,1,3]=>0000000=>[8]=>[8]
[5,4,3,2,6,8,1,7]=>0000000=>[8]=>[8]
[4,8,3,2,5,6,1,7]=>0000000=>[8]=>[8]
[5,3,7,2,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,4,2,7,5,8,1,3]=>0000000=>[8]=>[8]
[7,5,8,4,1,2,6,3]=>0000000=>[8]=>[8]
[7,1,8,2,3,6,5,4]=>0000000=>[8]=>[8]
[7,3,8,4,6,2,1,5]=>0000000=>[8]=>[8]
[7,1,8,4,2,6,5,3]=>0000000=>[8]=>[8]
[7,1,8,3,6,2,5,4]=>0000000=>[8]=>[8]
[7,2,3,4,5,1,8,6]=>0000000=>[8]=>[8]
[2,7,3,4,1,5,6,8]=>0000001=>[7,1]=>[7,1]
[5,3,6,1,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[10,8,6,4,2,1,3,5,7,9]=>000000000=>[10]=>[10]
[6,5,4,3,7,8,9,10,1,2]=>000000000=>[10]=>[10]
[3,8,1,4,5,6,7,2]=>0000000=>[8]=>[8]
[4,5,3,1,2,8,7,6]=>0000100=>[5,3]=>[5,3]
[4,5,3,1,2,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[6,5,3,2,1,8,7,4]=>0000000=>[8]=>[8]
[4,5,2,1,8,7,6,3]=>0000000=>[8]=>[8]
[3,4,1,8,7,6,5,2]=>0000000=>[8]=>[8]
[8,1,2,4,5,6,7,3]=>0000000=>[8]=>[8]
[5,1,2,4,8,6,7,3]=>0000000=>[8]=>[8]
[4,1,3,8,5,6,7,2]=>0000000=>[8]=>[8]
[6,1,2,3,5,7,8,4]=>0000000=>[8]=>[8]
[5,1,3,8,4,6,7,2]=>0000000=>[8]=>[8]
[4,1,3,5,8,6,7,2]=>0000000=>[8]=>[8]
[7,5,2,8,6,3,4,1]=>0000000=>[8]=>[8]
[5,3,8,4,1,2,6,7]=>0000000=>[8]=>[8]
[6,3,5,8,4,1,2,7]=>0000000=>[8]=>[8]
[6,3,8,4,5,1,2,7]=>0000000=>[8]=>[8]
[8,5,1,7,4,6,2,3]=>0000000=>[8]=>[8]
[7,4,5,1,8,6,2,3]=>0000000=>[8]=>[8]
[4,2,7,5,8,6,3,1]=>0000000=>[8]=>[8]
[4,2,8,5,6,3,1,7]=>0000000=>[8]=>[8]
[4,2,8,5,6,7,3,1]=>0000000=>[8]=>[8]
[7,4,8,5,6,1,2,3]=>0000000=>[8]=>[8]
[7,5,8,6,1,2,3,4]=>0000000=>[8]=>[8]
[7,2,8,3,4,5,6,1]=>0000000=>[8]=>[8]
[5,2,4,8,6,7,3,1]=>0000000=>[8]=>[8]
[7,5,8,6,2,3,1,4]=>0000000=>[8]=>[8]
[7,4,8,5,6,2,3,1]=>0000000=>[8]=>[8]
[3,4,5,7,6,8,1,2]=>0000000=>[8]=>[8]
[4,8,2,5,1,3,7,6]=>0000000=>[8]=>[8]
[4,1,2,8,7,5,3,6]=>0000000=>[8]=>[8]
[3,1,7,6,8,2,4,5]=>0000000=>[8]=>[8]
[7,3,5,1,8,2,4,6]=>0000000=>[8]=>[8]
[7,8,3,1,5,2,4,6]=>0000000=>[8]=>[8]
[1,4,6,7,8,3,5,2]=>1000000=>[1,7]=>[7,1]
[1,5,6,3,7,8,4,2]=>1000000=>[1,7]=>[7,1]
[5,1,2,3,8,6,7,4]=>0000000=>[8]=>[8]
[2,8,5,3,1,4,6,7]=>0000000=>[8]=>[8]
[2,4,3,5,7,8,1,6]=>0000000=>[8]=>[8]
[2,6,3,7,8,1,4,5]=>0000000=>[8]=>[8]
[3,4,8,1,5,6,7,2]=>0000000=>[8]=>[8]
[3,5,1,7,4,8,6,2]=>0000000=>[8]=>[8]
[3,5,8,4,1,6,7,2]=>0000000=>[8]=>[8]
[3,6,1,8,5,4,7,2]=>0000000=>[8]=>[8]
[3,6,7,4,8,5,1,2]=>0000000=>[8]=>[8]
[3,6,8,4,5,1,7,2]=>0000000=>[8]=>[8]
[4,1,7,3,5,8,6,2]=>0000000=>[8]=>[8]
[4,6,3,1,8,5,7,2]=>0000000=>[8]=>[8]
[4,6,7,3,5,8,1,2]=>0000000=>[8]=>[8]
[4,6,8,3,5,1,7,2]=>0000000=>[8]=>[8]
[4,7,3,1,8,6,5,2]=>0000000=>[8]=>[8]
[5,1,6,7,4,8,3,2]=>0000000=>[8]=>[8]
[5,1,6,7,8,3,4,2]=>0000000=>[8]=>[8]
[5,6,7,8,4,1,3,2]=>0000000=>[8]=>[8]
[5,7,3,8,4,6,1,2]=>0000000=>[8]=>[8]
[5,7,8,4,3,6,1,2]=>0000000=>[8]=>[8]
[6,1,3,7,8,5,4,2]=>0000000=>[8]=>[8]
[6,1,8,4,5,3,7,2]=>0000000=>[8]=>[8]
[6,7,3,8,5,4,1,2]=>0000000=>[8]=>[8]
[7,1,3,4,8,6,5,2]=>0000000=>[8]=>[8]
[8,5,1,2,4,3,6,7]=>0000000=>[8]=>[8]
[8,5,1,4,2,3,6,7]=>0000000=>[8]=>[8]
[8,7,1,2,3,6,4,5]=>0000000=>[8]=>[8]
[5,6,8,7,2,3,1,4]=>0000000=>[8]=>[8]
[5,2,3,6,7,8,1,4]=>0000000=>[8]=>[8]
[4,2,8,7,5,3,1,6]=>0000000=>[8]=>[8]
[1,3,2,4,8,5,7,6]=>1011000=>[1,2,1,4]=>[4,2,1,1]
[1,6,3,2,5,7,8,4]=>1000000=>[1,7]=>[7,1]
[7,6,2,1,4,8,3,5]=>0000000=>[8]=>[8]
[2,6,5,1,8,7,3,4]=>0000000=>[8]=>[8]
[1,4,2,7,3,8,6,5]=>1000000=>[1,7]=>[7,1]
[1,2,7,3,8,6,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[3,1,8,4,6,2,7,5]=>0000000=>[8]=>[8]
[1,5,2,3,8,7,4,6]=>1000000=>[1,7]=>[7,1]
[2,8,7,6,3,1,4,5]=>0000000=>[8]=>[8]
[8,7,6,2,1,4,3,5]=>0000000=>[8]=>[8]
[8,2,7,4,1,5,3,6]=>0000000=>[8]=>[8]
[8,7,3,1,4,2,6,5]=>0000000=>[8]=>[8]
[1,2,5,3,4,8,7,6]=>1100100=>[1,1,3,3]=>[3,3,1,1]
[1,2,3,8,4,7,6,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,6,2,3,7,5,8,4]=>1000000=>[1,7]=>[7,1]
[1,4,8,2,6,3,7,5]=>1000000=>[1,7]=>[7,1]
[8,4,1,7,3,2,5,6]=>0000000=>[8]=>[8]
[1,8,7,3,2,4,6,5]=>1000000=>[1,7]=>[7,1]
[3,4,1,6,5,7,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,1,6,2,8,7,4]=>0000000=>[8]=>[8]
[5,4,3,6,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[4,8,7,2,1,6,5,3]=>0000000=>[8]=>[8]
[6,2,1,8,7,5,4,3]=>0000000=>[8]=>[8]
[5,8,7,6,3,2,4,1]=>0000000=>[8]=>[8]
[5,4,7,2,8,1,6,3]=>0000000=>[8]=>[8]
[2,1,5,8,3,7,4,6]=>0100000=>[2,6]=>[6,2]
[1,2,3,5,8,7,4,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[6,1,2,7,8,4,3,5]=>0000000=>[8]=>[8]
[5,1,4,8,2,7,3,6]=>0000000=>[8]=>[8]
[1,2,5,7,8,6,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,1,3,4,8,5,7,6]=>0111000=>[2,1,1,4]=>[4,2,1,1]
[6,2,5,1,7,3,8,4]=>0000000=>[8]=>[8]
[2,4,8,1,3,7,5,6]=>0000000=>[8]=>[8]
[2,5,1,8,6,3,7,4]=>0000000=>[8]=>[8]
[2,1,3,7,4,8,6,5]=>0110000=>[2,1,5]=>[5,2,1]
[2,6,8,5,1,7,3,4]=>0000000=>[8]=>[8]
[1,3,2,7,8,5,4,6]=>1010000=>[1,2,5]=>[5,2,1]
[7,1,2,3,6,8,4,5]=>0000000=>[8]=>[8]
[5,1,2,3,8,4,7,6]=>0000000=>[8]=>[8]
[4,1,2,3,8,7,5,6]=>0001000=>[4,4]=>[4,4]
[2,3,1,8,5,4,7,6]=>0010000=>[3,5]=>[5,3]
[2,3,8,4,1,5,7,6]=>0000000=>[8]=>[8]
[5,3,1,8,7,2,4,6]=>0000000=>[8]=>[8]
[1,3,8,4,2,7,6,5]=>1000000=>[1,7]=>[7,1]
[1,2,3,8,5,7,4,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[6,1,7,2,5,8,3,4]=>0000000=>[8]=>[8]
[4,5,1,8,7,2,3,6]=>0000000=>[8]=>[8]
[1,4,2,8,5,3,7,6]=>1000000=>[1,7]=>[7,1]
[7,8,6,5,2,1,4,3]=>0000000=>[8]=>[8]
[8,6,7,5,2,1,4,3]=>0000000=>[8]=>[8]
[6,7,8,2,1,5,4,3]=>0000000=>[8]=>[8]
[8,7,5,6,2,1,4,3]=>0000000=>[8]=>[8]
[4,2,5,1,8,7,3,6]=>0000000=>[8]=>[8]
[7,2,4,5,8,3,6,1]=>0000000=>[8]=>[8]
[2,4,7,8,6,1,5,3]=>0000000=>[8]=>[8]
[4,2,7,1,5,6,8,3]=>0000000=>[8]=>[8]
[3,2,5,8,1,6,7,4]=>0000000=>[8]=>[8]
[8,1,4,3,2,5,6,7]=>0000000=>[8]=>[8]
[1,7,3,2,4,5,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,3,2,4,5,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,3,8,4,2,5,6,7]=>1000000=>[1,7]=>[7,1]
[5,1,8,2,4,3,6,7]=>0000000=>[8]=>[8]
[1,7,2,4,5,8,6,3]=>1000000=>[1,7]=>[7,1]
[1,3,8,2,6,4,5,7]=>1000000=>[1,7]=>[7,1]
[6,1,2,7,4,3,8,5]=>0000000=>[8]=>[8]
[7,6,1,3,8,2,4,5]=>0000000=>[8]=>[8]
[5,4,1,2,3,8,6,7]=>0000100=>[5,3]=>[5,3]
[6,7,8,5,2,4,1,3]=>0000000=>[8]=>[8]
[3,4,5,8,2,1,7,6]=>0000000=>[8]=>[8]
[3,4,6,2,7,1,5,8]=>0000001=>[7,1]=>[7,1]
[3,4,6,1,5,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,4,7,2,1,6,5,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,6,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,5,2,7,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,1,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[3,5,6,4,8,2,1,7]=>0000000=>[8]=>[8]
[3,5,6,4,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,5,6,8,4,2,1,7]=>0000000=>[8]=>[8]
[3,5,6,1,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,5,7,4,2,8,1,6]=>0000000=>[8]=>[8]
[3,5,7,4,2,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,4,8,1,6,2]=>0000000=>[8]=>[8]
[3,5,7,1,4,6,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,8,1,4,6,7,2]=>0000000=>[8]=>[8]
[3,6,2,4,8,1,7,5]=>0000000=>[8]=>[8]
[3,6,2,7,8,5,1,4]=>0000000=>[8]=>[8]
[3,6,2,7,8,1,4,5]=>0000000=>[8]=>[8]
[3,6,2,1,5,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,6,7,8,5,1,2,4]=>0000000=>[8]=>[8]
[3,6,7,8,1,5,2,4]=>0000000=>[8]=>[8]
[3,7,2,4,5,8,1,6]=>0000000=>[8]=>[8]
[3,7,2,4,8,1,6,5]=>0000000=>[8]=>[8]
[3,7,2,8,5,6,1,4]=>0000000=>[8]=>[8]
[3,7,2,1,5,6,4,8]=>0000001=>[7,1]=>[7,1]
[3,7,8,4,5,1,6,2]=>0000000=>[8]=>[8]
[3,8,2,4,1,6,7,5]=>0000000=>[8]=>[8]
[8,1,5,4,3,6,7,2]=>0000000=>[8]=>[8]
[4,1,7,3,5,6,8,2]=>0000000=>[8]=>[8]
[6,1,7,3,8,4,5,2]=>0000000=>[8]=>[8]
[4,1,3,6,7,8,5,2]=>0000000=>[8]=>[8]
[3,5,2,4,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[2,3,7,8,1,6,5,4]=>0000000=>[8]=>[8]
[2,6,5,8,1,3,7,4]=>0000000=>[8]=>[8]
[6,4,7,5,8,2,3,1]=>0000000=>[8]=>[8]
[6,7,4,1,8,2,3,5]=>0000000=>[8]=>[8]
[6,7,8,1,4,2,5,3]=>0000000=>[8]=>[8]
[5,2,6,1,4,8,3,7]=>0000000=>[8]=>[8]
[7,2,3,5,8,1,4,6]=>0000000=>[8]=>[8]
[2,4,7,5,8,1,3,6]=>0000000=>[8]=>[8]
[2,3,6,5,1,8,7,4]=>0000000=>[8]=>[8]
[2,3,4,8,1,5,7,6]=>0000000=>[8]=>[8]
[2,7,8,5,1,4,6,3]=>0000000=>[8]=>[8]
[2,3,7,5,8,1,4,6]=>0000000=>[8]=>[8]
[2,3,6,8,5,1,7,4]=>0000000=>[8]=>[8]
[7,6,4,5,1,8,2,3]=>0000000=>[8]=>[8]
[7,4,6,8,1,5,2,3]=>0000000=>[8]=>[8]
[2,6,7,8,5,3,1,4]=>0000000=>[8]=>[8]
[2,5,6,1,4,8,3,7]=>0000000=>[8]=>[8]
[2,6,4,8,5,7,3,1]=>0000000=>[8]=>[8]
[2,5,8,1,4,6,7,3]=>0000000=>[8]=>[8]
[7,2,3,4,8,1,6,5]=>0000000=>[8]=>[8]
[3,2,5,7,8,1,6,4]=>0000000=>[8]=>[8]
[6,4,1,7,8,2,3,5]=>0000000=>[8]=>[8]
[5,7,6,1,2,8,3,4]=>0000000=>[8]=>[8]
[5,6,8,1,2,4,7,3]=>0000000=>[8]=>[8]
[6,2,3,4,5,8,1,7]=>0000000=>[8]=>[8]
[4,7,1,3,8,2,6,5]=>0000000=>[8]=>[8]
[5,4,1,6,7,8,2,3]=>0000000=>[8]=>[8]
[5,7,1,8,6,2,3,4]=>0000000=>[8]=>[8]
[7,3,5,1,8,2,6,4]=>0000000=>[8]=>[8]
[5,6,7,3,8,2,1,4]=>0000000=>[8]=>[8]
[5,7,3,2,8,6,1,4]=>0000000=>[8]=>[8]
[5,7,8,3,1,6,2,4]=>0000000=>[8]=>[8]
[5,8,3,2,1,6,7,4]=>0000000=>[8]=>[8]
[6,2,7,3,8,5,1,4]=>0000000=>[8]=>[8]
[6,2,3,7,8,5,1,4]=>0000000=>[8]=>[8]
[1,5,8,3,2,6,7,4]=>1000000=>[1,7]=>[7,1]
[1,6,7,8,5,2,3,4]=>1000000=>[1,7]=>[7,1]
[1,6,7,8,4,2,3,5]=>1000000=>[1,7]=>[7,1]
[1,2,6,8,4,3,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,3,4,2,6,7,5]=>1000000=>[1,7]=>[7,1]
[6,2,7,8,4,1,3,5]=>0000000=>[8]=>[8]
[6,2,3,7,8,1,4,5]=>0000000=>[8]=>[8]
[4,5,7,1,8,6,2,3]=>0000000=>[8]=>[8]
[4,5,7,8,2,6,1,3]=>0000000=>[8]=>[8]
[4,6,2,8,5,1,7,3]=>0000000=>[8]=>[8]
[4,6,7,1,8,5,2,3]=>0000000=>[8]=>[8]
[4,7,2,8,5,6,1,3]=>0000000=>[8]=>[8]
[4,8,2,1,5,6,7,3]=>0000000=>[8]=>[8]
[1,2,8,4,5,3,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,3,7,8,5,4,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,5,4,7,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,7,3,8,5,4,2,6]=>1000000=>[1,7]=>[7,1]
[5,2,7,4,8,6,1,3]=>0000000=>[8]=>[8]
[5,6,2,7,8,1,4,3]=>0000000=>[8]=>[8]
[5,8,2,4,1,6,7,3]=>0000000=>[8]=>[8]
[6,2,1,7,8,5,4,3]=>0000000=>[8]=>[8]
[6,7,2,8,5,4,1,3]=>0000000=>[8]=>[8]
[6,8,2,4,5,1,7,3]=>0000000=>[8]=>[8]
[3,2,5,6,8,1,4,7]=>0000000=>[8]=>[8]
[7,1,3,2,8,4,5,6]=>0000000=>[8]=>[8]
[7,1,6,3,8,2,4,5]=>0000000=>[8]=>[8]
[6,1,5,8,2,3,4,7]=>0000000=>[8]=>[8]
[8,1,6,7,4,2,3,5]=>0000000=>[8]=>[8]
[6,1,5,8,2,3,7,4]=>0000000=>[8]=>[8]
[4,1,7,2,5,8,3,6]=>0000000=>[8]=>[8]
[8,1,6,3,4,7,2,5]=>0000000=>[8]=>[8]
[8,1,7,3,2,5,6,4]=>0000000=>[8]=>[8]
[4,1,8,2,5,6,7,3]=>0000000=>[8]=>[8]
[3,8,1,2,7,5,4,6]=>0000000=>[8]=>[8]
[8,4,7,1,3,2,6,5]=>0000000=>[8]=>[8]
[8,5,7,3,1,2,6,4]=>0000000=>[8]=>[8]
[3,8,1,2,4,5,7,6]=>0000000=>[8]=>[8]
[7,6,2,1,8,4,3,5]=>0000000=>[8]=>[8]
[8,5,2,3,6,1,4,7]=>0000000=>[8]=>[8]
[8,5,7,1,4,3,2,6]=>0000000=>[8]=>[8]
[3,6,1,4,2,8,5,7]=>0000000=>[8]=>[8]
[7,6,8,1,4,5,2,3]=>0000000=>[8]=>[8]
[3,7,1,4,2,8,6,5]=>0000000=>[8]=>[8]
[5,4,3,8,2,1,7,6]=>0000000=>[8]=>[8]
[5,8,7,3,2,1,6,4]=>0000000=>[8]=>[8]
[2,3,7,1,6,8,5,4]=>0000000=>[8]=>[8]
[2,6,1,5,7,4,8,3]=>0000000=>[8]=>[8]
[2,3,6,1,8,4,7,5]=>0000000=>[8]=>[8]
[3,5,1,4,6,7,8,2]=>0000000=>[8]=>[8]
[4,5,6,2,1,7,8,3]=>0000000=>[8]=>[8]
[5,2,4,7,6,3,8,1]=>0000000=>[8]=>[8]
[8,7,6,1,4,3,5,2]=>0000000=>[8]=>[8]
[8,7,6,1,3,4,5,2]=>0000000=>[8]=>[8]
[8,7,1,4,5,6,3,2]=>0000000=>[8]=>[8]
[8,1,5,6,7,4,3,2]=>0000000=>[8]=>[8]
[5,8,3,4,1,6,2,7]=>0000000=>[8]=>[8]
[4,2,6,1,7,8,5,3]=>0000000=>[8]=>[8]
[1,5,2,6,7,8,4,3]=>1000000=>[1,7]=>[7,1]
[1,5,6,7,4,8,2,3]=>1000000=>[1,7]=>[7,1]
[4,2,7,8,5,6,1,3]=>0000000=>[8]=>[8]
[5,6,2,7,3,8,4,1]=>0000000=>[8]=>[8]
[3,7,2,8,4,1,5,6]=>0000000=>[8]=>[8]
[3,5,2,4,7,8,6,1]=>0000000=>[8]=>[8]
[5,1,3,8,2,4,6,7]=>0000000=>[8]=>[8]
[1,8,7,6,3,4,5,2]=>1000000=>[1,7]=>[7,1]
[8,5,7,6,3,2,1,4]=>0000000=>[8]=>[8]
[8,7,5,3,1,6,4,2]=>0000000=>[8]=>[8]
[7,8,1,4,5,6,3,2]=>0000000=>[8]=>[8]
[4,2,8,3,5,1,7,6]=>0000000=>[8]=>[8]
[4,2,7,8,1,6,5,3]=>0000000=>[8]=>[8]
[5,1,3,4,2,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,2,7,3,1,6,5,8]=>0000001=>[7,1]=>[7,1]
[2,3,4,5,8,1,7,6]=>0000000=>[8]=>[8]
[4,1,5,3,6,7,8,2]=>0000000=>[8]=>[8]
[5,1,6,3,4,7,8,2]=>0000000=>[8]=>[8]
[2,1,7,5,3,8,6,4]=>0100000=>[2,6]=>[6,2]
[3,2,1,6,4,5,7,8]=>0010011=>[3,3,1,1]=>[3,3,1,1]
[3,8,1,2,5,4,7,6]=>0000000=>[8]=>[8]
[7,5,8,6,3,2,1,4]=>0000000=>[8]=>[8]
[6,4,2,1,8,5,3,7]=>0000000=>[8]=>[8]
[5,3,8,4,2,1,6,7]=>0000000=>[8]=>[8]
[7,4,5,2,1,8,6,3]=>0000000=>[8]=>[8]
[6,3,8,4,5,2,1,7]=>0000000=>[8]=>[8]
[7,4,8,5,6,2,1,3]=>0000000=>[8]=>[8]
[7,3,8,4,5,6,2,1]=>0000000=>[8]=>[8]
[1,8,7,2,6,5,4,3]=>1000000=>[1,7]=>[7,1]
[1,8,7,6,2,3,4,5]=>1000000=>[1,7]=>[7,1]
[1,8,2,5,6,7,4,3]=>1000000=>[1,7]=>[7,1]
[1,2,8,3,4,5,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[7,4,1,2,8,3,5,6]=>0000000=>[8]=>[8]
[6,4,1,2,8,3,5,7]=>0000000=>[8]=>[8]
[4,8,1,2,3,7,5,6]=>0000000=>[8]=>[8]
[6,5,1,2,3,8,4,7]=>0000000=>[8]=>[8]
[1,8,5,2,3,7,4,6]=>1000000=>[1,7]=>[7,1]
[6,5,1,2,7,3,8,4]=>0000000=>[8]=>[8]
[7,6,4,1,8,2,3,5]=>0000000=>[8]=>[8]
[7,6,3,1,8,2,4,5]=>0000000=>[8]=>[8]
[7,5,4,1,8,2,3,6]=>0000000=>[8]=>[8]
[7,6,1,4,8,2,3,5]=>0000000=>[8]=>[8]
[1,2,8,5,3,7,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,3,8,6,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[7,5,1,6,8,2,3,4]=>0000000=>[8]=>[8]
[4,1,2,8,6,3,7,5]=>0000000=>[8]=>[8]
[5,4,1,6,2,7,8,3]=>0000000=>[8]=>[8]
[6,5,3,1,8,2,4,7]=>0000000=>[8]=>[8]
[3,8,1,6,7,2,4,5]=>0000000=>[8]=>[8]
[6,5,3,7,1,2,8,4]=>0000000=>[8]=>[8]
[7,1,4,2,6,8,3,5]=>0000000=>[8]=>[8]
[1,2,6,8,3,5,4,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,3,7,8,6,4,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,6,8,5,2,7,3,4]=>1000000=>[1,7]=>[7,1]
[1,4,8,2,3,7,6,5]=>1000000=>[1,7]=>[7,1]
[1,2,8,3,5,7,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[4,5,1,7,6,8,2,3]=>0000000=>[8]=>[8]
[1,4,2,5,6,8,7,3]=>1000000=>[1,7]=>[7,1]
[8,2,7,3,1,5,6,4]=>0000000=>[8]=>[8]
[7,2,1,8,4,5,6,3]=>0000000=>[8]=>[8]
[4,2,7,1,3,8,6,5]=>0000000=>[8]=>[8]
[8,2,6,3,4,7,1,5]=>0000000=>[8]=>[8]
[7,2,3,4,1,8,6,5]=>0000000=>[8]=>[8]
[4,2,8,1,5,6,3,7]=>0000000=>[8]=>[8]
[8,2,7,3,1,4,5,6]=>0000000=>[8]=>[8]
[5,3,1,6,2,7,8,4]=>0000000=>[8]=>[8]
[5,2,1,3,6,7,8,4]=>0000000=>[8]=>[8]
[6,5,3,8,7,2,1,4]=>0000000=>[8]=>[8]
[5,4,8,7,3,2,1,6]=>0000000=>[8]=>[8]
[6,4,3,8,7,2,1,5]=>0000000=>[8]=>[8]
[5,6,3,1,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,2,6,1,4,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,8,3,1,4,6,7,2]=>0000000=>[8]=>[8]
[6,2,7,4,1,5,3,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,8,1,5,2,4]=>0000000=>[8]=>[8]
[6,7,3,4,1,5,2,8]=>0000001=>[7,1]=>[7,1]
[6,7,8,1,5,4,2,3]=>0000000=>[8]=>[8]
[4,5,7,8,2,1,6,3]=>0000000=>[8]=>[8]
[7,2,3,8,1,6,5,4]=>0000000=>[8]=>[8]
[7,2,3,8,5,1,6,4]=>0000000=>[8]=>[8]
[7,2,3,1,5,6,4,8]=>0000001=>[7,1]=>[7,1]
[7,2,8,4,1,6,5,3]=>0000000=>[8]=>[8]
[7,2,8,4,5,1,6,3]=>0000000=>[8]=>[8]
[4,6,3,8,1,5,7,2]=>0000000=>[8]=>[8]
[4,6,7,3,8,1,2,5]=>0000000=>[8]=>[8]
[4,6,7,8,1,5,3,2]=>0000000=>[8]=>[8]
[4,6,7,1,5,2,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,8,3,1,5,7,2]=>0000000=>[8]=>[8]
[4,7,3,8,5,1,6,2]=>0000000=>[8]=>[8]
[4,7,3,8,1,6,5,2]=>0000000=>[8]=>[8]
[4,1,8,2,7,3,5,6]=>0000000=>[8]=>[8]
[1,8,4,2,7,3,5,6]=>1000000=>[1,7]=>[7,1]
[7,4,1,2,6,8,3,5]=>0000000=>[8]=>[8]
[8,7,1,2,4,5,3,6]=>0000000=>[8]=>[8]
[5,4,1,2,7,8,3,6]=>0000000=>[8]=>[8]
[1,5,2,8,3,4,7,6]=>1000000=>[1,7]=>[7,1]
[7,1,2,5,3,6,8,4]=>0000000=>[8]=>[8]
[1,8,2,5,6,3,7,4]=>1000000=>[1,7]=>[7,1]
[1,5,2,4,6,7,8,3]=>1000000=>[1,7]=>[7,1]
[3,1,8,2,5,4,6,7]=>0000000=>[8]=>[8]
[3,1,7,5,8,2,4,6]=>0000000=>[8]=>[8]
[1,7,3,2,8,4,5,6]=>1000000=>[1,7]=>[7,1]
[1,6,4,2,3,5,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,7,4,2,3,5,8,6]=>1000000=>[1,7]=>[7,1]
[1,7,4,2,3,6,8,5]=>1000000=>[1,7]=>[7,1]
[1,2,7,3,8,4,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[7,1,3,4,5,8,2,6]=>0000000=>[8]=>[8]
[1,8,7,6,3,2,4,5]=>1000000=>[1,7]=>[7,1]
[1,7,4,5,2,6,8,3]=>1000000=>[1,7]=>[7,1]
[1,4,8,5,6,2,7,3]=>1000000=>[1,7]=>[7,1]
[3,2,1,8,7,4,5,6]=>0010000=>[3,5]=>[5,3]
[3,2,8,7,6,1,5,4]=>0000000=>[8]=>[8]
[6,5,8,7,3,2,1,4]=>0000000=>[8]=>[8]
[4,6,2,8,5,3,7,1]=>0000000=>[8]=>[8]
[5,3,8,4,6,2,7,1]=>0000000=>[8]=>[8]
[4,6,2,7,1,8,5,3]=>0000000=>[8]=>[8]
[6,2,5,3,8,4,7,1]=>0000000=>[8]=>[8]
[4,6,5,3,8,2,7,1]=>0000000=>[8]=>[8]
[5,7,8,4,3,2,1,6]=>0000000=>[8]=>[8]
[4,6,8,7,3,2,1,5]=>0000000=>[8]=>[8]
[2,4,8,7,6,5,1,3]=>0000000=>[8]=>[8]
[4,7,6,8,3,2,1,5]=>0000000=>[8]=>[8]
[4,6,7,8,3,2,1,5]=>0000000=>[8]=>[8]
[3,5,6,8,7,2,1,4]=>0000000=>[8]=>[8]
[1,4,8,7,6,3,5,2]=>1000000=>[1,7]=>[7,1]
[2,5,4,7,3,8,1,6]=>0000000=>[8]=>[8]
[2,4,6,1,5,8,3,7]=>0000000=>[8]=>[8]
[2,5,4,8,6,7,3,1]=>0000000=>[8]=>[8]
[3,4,1,7,6,8,5,2]=>0000000=>[8]=>[8]
[3,6,1,7,8,4,2,5]=>0000000=>[8]=>[8]
[4,3,6,2,8,1,7,5]=>0000000=>[8]=>[8]
[5,3,4,7,2,8,1,6]=>0000000=>[8]=>[8]
[4,5,7,2,1,8,3,6]=>0000000=>[8]=>[8]
[4,5,8,2,1,6,7,3]=>0000000=>[8]=>[8]
[3,6,1,7,2,5,8,4]=>0000000=>[8]=>[8]
[6,3,7,8,2,5,1,4]=>0000000=>[8]=>[8]
[6,7,4,8,2,5,3,1]=>0000000=>[8]=>[8]
[3,5,1,4,7,2,8,6]=>0000000=>[8]=>[8]
[4,7,8,5,6,2,1,3]=>0000000=>[8]=>[8]
[3,5,1,4,8,7,2,6]=>0000000=>[8]=>[8]
[4,5,6,3,8,2,1,7]=>0000000=>[8]=>[8]
[4,2,6,3,7,8,1,5]=>0000000=>[8]=>[8]
[4,2,7,3,5,8,1,6]=>0000000=>[8]=>[8]
[5,1,2,7,8,6,4,3]=>0000000=>[8]=>[8]
[4,1,2,7,8,6,3,5]=>0000000=>[8]=>[8]
[4,1,8,7,2,6,3,5]=>0000000=>[8]=>[8]
[5,1,8,2,7,6,3,4]=>0000000=>[8]=>[8]
[7,1,6,2,8,3,4,5]=>0000000=>[8]=>[8]
[4,5,2,8,7,3,1,6]=>0000000=>[8]=>[8]
[8,2,1,7,4,6,3,5]=>0000000=>[8]=>[8]
[4,5,2,8,7,1,6,3]=>0000000=>[8]=>[8]
[4,2,5,7,3,1,8,6]=>0000000=>[8]=>[8]
[4,2,8,7,1,3,6,5]=>0000000=>[8]=>[8]
[8,2,1,7,3,5,4,6]=>0000000=>[8]=>[8]
[5,2,6,3,8,7,1,4]=>0000000=>[8]=>[8]
[5,2,3,8,7,1,4,6]=>0000000=>[8]=>[8]
[6,1,2,8,3,7,4,5]=>0000000=>[8]=>[8]
[5,6,7,3,8,1,2,4]=>0000000=>[8]=>[8]
[8,1,7,3,5,4,2,6]=>0000000=>[8]=>[8]
[7,1,6,8,5,2,3,4]=>0000000=>[8]=>[8]
[8,1,7,3,5,2,6,4]=>0000000=>[8]=>[8]
[6,2,3,8,7,5,1,4]=>0000000=>[8]=>[8]
[3,8,5,7,2,4,1,6]=>0000000=>[8]=>[8]
[3,6,5,8,2,1,7,4]=>0000000=>[8]=>[8]
[7,6,2,3,4,1,8,5]=>0000000=>[8]=>[8]
[4,8,6,7,1,2,3,5]=>0000000=>[8]=>[8]
[8,5,7,3,1,6,2,4]=>0000000=>[8]=>[8]
[3,8,6,1,4,7,2,5]=>0000000=>[8]=>[8]
[3,7,6,8,2,5,1,4]=>0000000=>[8]=>[8]
[8,6,2,3,1,5,7,4]=>0000000=>[8]=>[8]
[3,8,7,1,2,5,6,4]=>0000000=>[8]=>[8]
[3,4,8,2,5,6,7,1]=>0000000=>[8]=>[8]
[6,3,4,8,7,5,1,2]=>0000000=>[8]=>[8]
[2,1,8,5,6,7,3,4]=>0100000=>[2,6]=>[6,2]
[8,3,2,5,6,7,1,4]=>0000000=>[8]=>[8]
[4,8,6,7,3,5,2,1]=>0000000=>[8]=>[8]
[4,3,1,2,6,7,8,5]=>0001000=>[4,4]=>[4,4]
[7,4,6,5,8,3,2,1]=>0000000=>[8]=>[8]
[2,5,8,6,7,3,1,4]=>0000000=>[8]=>[8]
[1,4,6,5,2,7,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,3,4,1,8,7,5,6]=>0001000=>[4,4]=>[4,4]
[4,2,6,5,1,8,7,3]=>0000000=>[8]=>[8]
[7,8,4,2,1,5,6,3]=>0000000=>[8]=>[8]
[7,8,2,3,6,1,5,4]=>0000000=>[8]=>[8]
[2,1,7,8,4,5,6,3]=>0100000=>[2,6]=>[6,2]
[8,6,2,7,1,3,5,4]=>0000000=>[8]=>[8]
[5,8,2,3,4,7,6,1]=>0000000=>[8]=>[8]
[2,5,1,4,3,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[1,4,5,3,7,2,8,6]=>1000000=>[1,7]=>[7,1]
[5,1,4,3,7,2,8,6]=>0000000=>[8]=>[8]
[1,6,7,4,3,2,8,5]=>1000000=>[1,7]=>[7,1]
[2,6,7,3,1,4,5,8]=>0000001=>[7,1]=>[7,1]
[5,1,4,6,7,2,3,8]=>0000001=>[7,1]=>[7,1]
[2,6,4,3,1,8,5,7]=>0000000=>[8]=>[8]
[1,6,5,2,3,4,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[7,8,2,1,5,4,3,6]=>0000000=>[8]=>[8]
[7,8,1,2,3,6,4,5]=>0000000=>[8]=>[8]
[1,4,7,8,5,2,3,6]=>1000000=>[1,7]=>[7,1]
[1,3,2,6,5,8,4,7]=>1010000=>[1,2,5]=>[5,2,1]
[2,1,5,7,8,4,3,6]=>0100000=>[2,6]=>[6,2]
[3,1,7,2,6,5,8,4]=>0000000=>[8]=>[8]
[1,3,2,7,5,4,8,6]=>1010000=>[1,2,5]=>[5,2,1]
[1,4,5,8,6,2,3,7]=>1000000=>[1,7]=>[7,1]
[1,6,7,2,3,5,8,4]=>1000000=>[1,7]=>[7,1]
[2,4,1,8,6,5,3,7]=>0000000=>[8]=>[8]
[2,3,4,6,8,5,7,1]=>0000000=>[8]=>[8]
[3,6,2,4,7,5,8,1]=>0000000=>[8]=>[8]
[4,3,5,8,7,2,6,1]=>0000000=>[8]=>[8]
[5,1,6,3,7,8,4,2]=>0000000=>[8]=>[8]
[4,2,6,7,5,1,8,3]=>0000000=>[8]=>[8]
[6,4,7,5,8,3,2,1]=>0000000=>[8]=>[8]
[3,6,7,5,8,1,4,2]=>0000000=>[8]=>[8]
[3,2,7,4,6,1,8,5]=>0000000=>[8]=>[8]
[8,2,4,1,6,7,5,3]=>0000000=>[8]=>[8]
[3,4,8,7,6,1,5,2]=>0000000=>[8]=>[8]
[4,3,8,7,6,2,5,1]=>0000000=>[8]=>[8]
[4,3,7,5,8,6,2,1]=>0000000=>[8]=>[8]
[3,4,7,5,8,6,1,2]=>0000000=>[8]=>[8]
[2,7,5,6,8,3,4,1]=>0000000=>[8]=>[8]
[7,8,3,4,6,5,1,2]=>0000000=>[8]=>[8]
[2,1,7,6,8,4,5,3]=>0100000=>[2,6]=>[6,2]
[3,5,4,7,6,1,8,2]=>0000000=>[8]=>[8]
[6,5,4,2,7,8,3,1]=>0000000=>[8]=>[8]
[2,6,8,5,7,4,3,1]=>0000000=>[8]=>[8]
[2,1,8,6,7,5,4,3]=>0100000=>[2,6]=>[6,2]
[2,5,3,1,6,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[7,5,4,2,3,1,8,6]=>0000000=>[8]=>[8]
[6,3,2,4,5,8,1,7]=>0000000=>[8]=>[8]
[3,5,4,2,8,6,1,7]=>0000000=>[8]=>[8]
[5,6,8,7,3,2,1,4]=>0000000=>[8]=>[8]
[6,4,5,3,2,8,1,7]=>0000000=>[8]=>[8]
[4,2,5,7,3,1,6,8]=>0000001=>[7,1]=>[7,1]
[7,4,1,3,2,6,8,5]=>0000000=>[8]=>[8]
[1,6,4,2,3,7,8,5]=>1000000=>[1,7]=>[7,1]
[1,4,5,3,8,2,6,7]=>1000000=>[1,7]=>[7,1]
[6,2,5,1,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[7,6,5,8,1,2,4,3]=>0000000=>[8]=>[8]
[5,7,4,1,3,6,2,8]=>0000001=>[7,1]=>[7,1]
[4,3,8,1,6,5,7,2]=>0000000=>[8]=>[8]
[3,2,8,1,6,7,4,5]=>0000000=>[8]=>[8]
[7,2,6,3,8,1,5,4]=>0000000=>[8]=>[8]
[7,2,8,1,6,3,5,4]=>0000000=>[8]=>[8]
[7,4,8,2,3,5,6,1]=>0000000=>[8]=>[8]
[7,4,8,1,5,6,2,3]=>0000000=>[8]=>[8]
[7,2,8,1,6,5,4,3]=>0000000=>[8]=>[8]
[8,6,5,7,2,1,4,3]=>0000000=>[8]=>[8]
[2,4,7,8,5,6,3,1]=>0000000=>[8]=>[8]
[2,8,1,3,5,6,7,4]=>0000000=>[8]=>[8]
[3,8,7,5,2,6,4,1]=>0000000=>[8]=>[8]
[1,8,7,3,4,6,5,2]=>1000000=>[1,7]=>[7,1]
[2,8,1,4,5,7,6,3]=>0000000=>[8]=>[8]
[1,2,6,7,8,3,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,8,7,3,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[3,7,8,1,5,6,2,4]=>0000000=>[8]=>[8]
[4,1,3,7,6,8,5,2]=>0000000=>[8]=>[8]
[6,5,7,8,1,4,3,2]=>0000000=>[8]=>[8]
[3,1,8,6,7,5,4,2]=>0000000=>[8]=>[8]
[2,8,3,1,7,5,4,6]=>0000000=>[8]=>[8]
[4,1,2,6,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[1,2,5,3,8,6,4,7]=>1100000=>[1,1,6]=>[6,1,1]
[5,8,7,6,2,1,3,4]=>0000000=>[8]=>[8]
[3,6,8,2,5,7,4,1]=>0000000=>[8]=>[8]
[3,2,8,5,6,1,7,4]=>0000000=>[8]=>[8]
[3,4,8,1,5,7,6,2]=>0000000=>[8]=>[8]
[4,5,6,2,7,3,8,1]=>0000000=>[8]=>[8]
[3,5,8,7,4,6,2,1]=>0000000=>[8]=>[8]
[3,5,7,6,2,4,8,1]=>0000000=>[8]=>[8]
[1,6,8,7,4,5,3,2]=>1000000=>[1,7]=>[7,1]
[1,3,5,6,8,7,2,4]=>1000000=>[1,7]=>[7,1]
[3,5,6,7,8,2,4,1]=>0000000=>[8]=>[8]
[8,5,6,7,2,4,3,1]=>0000000=>[8]=>[8]
[7,8,4,5,1,6,3,2]=>0000000=>[8]=>[8]
[4,5,6,8,3,7,2,1]=>0000000=>[8]=>[8]
[8,1,4,3,6,5,2,7]=>0000000=>[8]=>[8]
[8,1,2,3,6,5,4,7]=>0000000=>[8]=>[8]
[8,1,2,3,7,6,5,4]=>0000000=>[8]=>[8]
[2,8,1,6,7,5,3,4]=>0000000=>[8]=>[8]
[4,8,5,2,7,1,6,3]=>0000000=>[8]=>[8]
[3,7,8,4,6,2,1,5]=>0000000=>[8]=>[8]
[8,3,1,5,7,6,2,4]=>0000000=>[8]=>[8]
[4,5,2,8,6,7,1,3]=>0000000=>[8]=>[8]
[8,4,5,1,3,2,6,7]=>0000000=>[8]=>[8]
[8,1,6,7,2,5,4,3]=>0000000=>[8]=>[8]
[5,4,1,3,2,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,2,7,4,1,6,5,8]=>0000001=>[7,1]=>[7,1]
[5,7,3,2,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[7,6,5,1,3,4,2,8]=>0000001=>[7,1]=>[7,1]
[7,6,5,1,4,2,3,8]=>0000001=>[7,1]=>[7,1]
[1,7,6,3,2,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,7,2,4,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[7,1,6,8,2,4,5,3]=>0000000=>[8]=>[8]
[5,8,1,3,4,7,2,6]=>0000000=>[8]=>[8]
[5,8,6,2,3,1,4,7]=>0000000=>[8]=>[8]
[3,8,2,7,6,4,1,5]=>0000000=>[8]=>[8]
[1,6,8,4,7,5,3,2]=>1000000=>[1,7]=>[7,1]
[6,5,8,3,7,4,2,1]=>0000000=>[8]=>[8]
[2,6,8,5,4,7,3,1]=>0000000=>[8]=>[8]
[2,7,4,6,8,5,3,1]=>0000000=>[8]=>[8]
[6,4,7,8,3,5,2,1]=>0000000=>[8]=>[8]
[7,3,4,2,6,1,8,5]=>0000000=>[8]=>[8]
[2,3,7,4,6,1,8,5]=>0000000=>[8]=>[8]
[7,5,4,2,6,3,8,1]=>0000000=>[8]=>[8]
[5,4,7,2,6,1,8,3]=>0000000=>[8]=>[8]
[5,2,7,4,6,1,8,3]=>0000000=>[8]=>[8]
[5,2,4,1,7,6,8,3]=>0000000=>[8]=>[8]
[4,2,7,5,6,1,8,3]=>0000000=>[8]=>[8]
[4,2,7,5,6,3,8,1]=>0000000=>[8]=>[8]
[2,6,4,3,7,5,8,1]=>0000000=>[8]=>[8]
[4,3,7,5,8,6,1,2]=>0000000=>[8]=>[8]
[6,7,4,8,3,5,2,1]=>0000000=>[8]=>[8]
[3,6,8,5,4,7,1,2]=>0000000=>[8]=>[8]
[6,7,5,8,2,4,3,1]=>0000000=>[8]=>[8]
[2,5,4,1,7,8,6,3]=>0000000=>[8]=>[8]
[1,6,3,2,5,8,7,4]=>1000000=>[1,7]=>[7,1]
[1,6,8,3,2,4,7,5]=>1000000=>[1,7]=>[7,1]
[1,8,7,6,4,2,3,5]=>1000000=>[1,7]=>[7,1]
[8,6,1,2,4,5,7,3]=>0000000=>[8]=>[8]
[1,8,6,7,3,4,5,2]=>1000000=>[1,7]=>[7,1]
[1,7,3,8,2,4,6,5]=>1000000=>[1,7]=>[7,1]
[8,4,3,1,5,6,7,2]=>0000000=>[8]=>[8]
[1,8,7,6,3,4,2,5]=>1000000=>[1,7]=>[7,1]
[7,1,3,8,4,5,2,6]=>0000000=>[8]=>[8]
[1,8,5,3,7,6,2,4]=>1000000=>[1,7]=>[7,1]
[3,5,2,6,1,4,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,7,2,3,8,6,1]=>0000000=>[8]=>[8]
[4,5,7,2,3,8,1,6]=>0000000=>[8]=>[8]
[4,5,6,2,3,1,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,6,2,1,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,6,1,3,2,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,6,3,1,2,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,7,3,2,8,1,6]=>0000000=>[8]=>[8]
[4,6,7,3,8,2,5,1]=>0000000=>[8]=>[8]
[4,6,7,3,8,2,1,5]=>0000000=>[8]=>[8]
[4,5,7,3,1,8,2,6]=>0000000=>[8]=>[8]
[3,5,1,7,4,8,2,6]=>0000000=>[8]=>[8]
[2,1,5,7,4,8,3,6]=>0100000=>[2,6]=>[6,2]
[4,5,7,1,3,8,6,2]=>0000000=>[8]=>[8]
[4,6,7,3,8,1,5,2]=>0000000=>[8]=>[8]
[5,6,7,8,3,1,4,2]=>0000000=>[8]=>[8]
[4,6,7,1,8,3,5,2]=>0000000=>[8]=>[8]
[3,6,1,7,8,4,5,2]=>0000000=>[8]=>[8]
[2,1,6,7,8,4,5,3]=>0100000=>[2,6]=>[6,2]
[2,1,6,7,8,4,3,5]=>0100000=>[2,6]=>[6,2]
[4,6,7,1,8,3,2,5]=>0000000=>[8]=>[8]
[5,6,7,8,1,3,2,4]=>0000000=>[8]=>[8]
[4,6,7,2,8,3,5,1]=>0000000=>[8]=>[8]
[3,6,2,7,8,4,5,1]=>0000000=>[8]=>[8]
[3,6,2,7,8,4,1,5]=>0000000=>[8]=>[8]
[3,4,2,1,7,8,5,6]=>0001000=>[4,4]=>[4,4]
[4,6,7,2,8,5,3,1]=>0000000=>[8]=>[8]
[4,6,7,2,8,5,1,3]=>0000000=>[8]=>[8]
[4,5,7,1,2,8,6,3]=>0000000=>[8]=>[8]
[2,1,6,7,8,3,5,4]=>0100000=>[2,6]=>[6,2]
[3,6,1,7,8,2,5,4]=>0000000=>[8]=>[8]
[4,6,7,1,8,2,5,3]=>0000000=>[8]=>[8]
[5,6,7,8,1,2,4,3]=>0000000=>[8]=>[8]
[5,6,7,8,2,4,1,3]=>0000000=>[8]=>[8]
[5,6,7,8,2,4,3,1]=>0000000=>[8]=>[8]
[3,6,1,7,8,5,2,4]=>0000000=>[8]=>[8]
[2,1,6,7,8,5,3,4]=>0100000=>[2,6]=>[6,2]
[7,4,5,1,2,8,3,6]=>0000000=>[8]=>[8]
[6,4,5,1,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[5,4,6,1,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,6,5,1,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[5,6,4,1,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[7,5,4,1,2,8,3,6]=>0000000=>[8]=>[8]
[8,6,4,1,7,2,3,5]=>0000000=>[8]=>[8]
[2,1,7,5,3,8,4,6]=>0100000=>[2,6]=>[6,2]
[2,1,8,6,7,3,4,5]=>0100000=>[2,6]=>[6,2]
[5,7,6,8,1,2,3,4]=>0000000=>[8]=>[8]
[6,4,7,1,8,2,3,5]=>0000000=>[8]=>[8]
[8,4,6,1,7,2,3,5]=>0000000=>[8]=>[8]
[8,3,1,6,7,2,4,5]=>0000000=>[8]=>[8]
[4,3,1,2,7,8,5,6]=>0001000=>[4,4]=>[4,4]
[7,4,8,1,6,2,3,5]=>0000000=>[8]=>[8]
[4,5,8,1,2,7,3,6]=>0000000=>[8]=>[8]
[5,6,8,7,1,2,3,4]=>0000000=>[8]=>[8]
[8,5,7,6,1,2,3,4]=>0000000=>[8]=>[8]
[3,8,1,7,6,2,4,5]=>0000000=>[8]=>[8]
[6,8,7,5,1,2,3,4]=>0000000=>[8]=>[8]
[6,4,7,3,8,5,1,2]=>0000000=>[8]=>[8]
[5,4,2,7,6,1,3,8]=>0000001=>[7,1]=>[7,1]
[5,4,2,7,6,1,8,3]=>0000000=>[8]=>[8]
[5,4,3,7,6,8,1,2]=>0000000=>[8]=>[8]
[5,4,3,7,8,6,1,2]=>0000000=>[8]=>[8]
[5,4,3,8,6,7,1,2]=>0000000=>[8]=>[8]
[5,4,3,6,8,7,1,2]=>0000000=>[8]=>[8]
[5,4,2,6,7,1,8,3]=>0000000=>[8]=>[8]
[5,3,2,6,1,7,4,8]=>0000001=>[7,1]=>[7,1]
[5,3,2,6,1,7,8,4]=>0000000=>[8]=>[8]
[5,3,2,6,1,8,7,4]=>0000000=>[8]=>[8]
[5,4,2,6,8,1,7,3]=>0000000=>[8]=>[8]
[6,4,8,2,5,1,7,3]=>0000000=>[8]=>[8]
[5,4,2,8,6,1,3,7]=>0000000=>[8]=>[8]
[5,3,2,6,1,8,4,7]=>0000000=>[8]=>[8]
[6,3,8,2,1,5,4,7]=>0000000=>[8]=>[8]
[7,8,3,2,1,5,4,6]=>0000000=>[8]=>[8]
[7,8,3,2,1,5,6,4]=>0000000=>[8]=>[8]
[6,3,8,2,1,5,7,4]=>0000000=>[8]=>[8]
[5,3,2,8,1,6,7,4]=>0000000=>[8]=>[8]
[5,4,2,7,8,1,6,3]=>0000000=>[8]=>[8]
[5,3,2,7,1,8,6,4]=>0000000=>[8]=>[8]
[5,3,2,7,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[6,3,7,2,1,5,4,8]=>0000001=>[7,1]=>[7,1]
[6,3,7,2,1,5,8,4]=>0000000=>[8]=>[8]
[6,3,7,2,1,8,5,4]=>0000000=>[8]=>[8]
[6,5,7,8,2,1,4,3]=>0000000=>[8]=>[8]
[6,3,7,2,1,4,8,5]=>0000000=>[8]=>[8]
[5,3,2,7,1,4,8,6]=>0000000=>[8]=>[8]
[5,4,2,8,7,1,3,6]=>0000000=>[8]=>[8]
[7,8,4,2,6,1,3,5]=>0000000=>[8]=>[8]
[7,8,3,2,1,6,4,5]=>0000000=>[8]=>[8]
[6,3,8,2,1,7,4,5]=>0000000=>[8]=>[8]
[5,3,2,8,1,7,4,6]=>0000000=>[8]=>[8]
[4,3,2,1,8,7,5,6]=>0001000=>[4,4]=>[4,4]
[4,3,2,1,7,5,8,6]=>0001000=>[4,4]=>[4,4]
[4,3,2,1,7,5,6,8]=>0001001=>[4,3,1]=>[4,3,1]
[5,3,2,8,1,4,7,6]=>0000000=>[8]=>[8]
[6,3,8,2,1,4,7,5]=>0000000=>[8]=>[8]
[7,8,3,2,1,4,6,5]=>0000000=>[8]=>[8]
[4,3,2,1,8,5,6,7]=>0001000=>[4,4]=>[4,4]
[7,8,5,6,1,2,4,3]=>0000000=>[8]=>[8]
[7,8,4,1,6,2,5,3]=>0000000=>[8]=>[8]
[1,6,8,3,2,7,5,4]=>1000000=>[1,7]=>[7,1]
[6,1,8,3,2,7,5,4]=>0000000=>[8]=>[8]
[7,8,1,3,2,6,5,4]=>0000000=>[8]=>[8]
[7,8,3,1,2,6,5,4]=>0000000=>[8]=>[8]
[7,8,2,3,1,6,5,4]=>0000000=>[8]=>[8]
[7,8,2,1,3,6,5,4]=>0000000=>[8]=>[8]
[7,8,1,2,3,6,5,4]=>0000000=>[8]=>[8]
[1,5,2,8,3,7,6,4]=>1000000=>[1,7]=>[7,1]
[5,1,2,8,3,7,6,4]=>0000000=>[8]=>[8]
[5,2,1,8,3,7,6,4]=>0000000=>[8]=>[8]
[6,2,8,1,3,7,5,4]=>0000000=>[8]=>[8]
[6,2,8,4,7,1,5,3]=>0000000=>[8]=>[8]
[6,3,8,4,7,5,1,2]=>0000000=>[8]=>[8]
[2,6,8,3,1,7,5,4]=>0000000=>[8]=>[8]
[2,5,1,8,3,7,6,4]=>0000000=>[8]=>[8]
[1,2,5,8,3,7,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,5,3,8,1,7,6,4]=>0000000=>[8]=>[8]
[2,5,4,8,7,1,6,3]=>0000000=>[8]=>[8]
[3,5,4,8,7,6,1,2]=>0000000=>[8]=>[8]
[5,3,4,8,7,6,1,2]=>0000000=>[8]=>[8]
[5,2,4,8,7,1,6,3]=>0000000=>[8]=>[8]
[5,2,3,8,1,7,6,4]=>0000000=>[8]=>[8]
[4,1,2,3,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[1,4,2,3,8,7,6,5]=>1001000=>[1,3,4]=>[4,3,1]
[4,1,3,2,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[6,3,8,1,2,7,5,4]=>0000000=>[8]=>[8]
[5,3,1,8,2,7,6,4]=>0000000=>[8]=>[8]
[5,1,3,8,2,7,6,4]=>0000000=>[8]=>[8]
[1,5,3,8,2,7,6,4]=>1000000=>[1,7]=>[7,1]
[1,5,4,8,7,2,6,3]=>1000000=>[1,7]=>[7,1]
[5,1,4,8,7,2,6,3]=>0000000=>[8]=>[8]
[5,4,1,8,7,2,6,3]=>0000000=>[8]=>[8]
[6,5,8,7,1,2,4,3]=>0000000=>[8]=>[8]
[5,6,8,7,3,4,1,2]=>0000000=>[8]=>[8]
[5,6,8,7,2,1,4,3]=>0000000=>[8]=>[8]
[4,5,1,8,7,2,6,3]=>0000000=>[8]=>[8]
[4,1,5,8,7,2,6,3]=>0000000=>[8]=>[8]
[1,3,5,8,2,7,6,4]=>1000000=>[1,7]=>[7,1]
[3,1,5,8,2,7,6,4]=>0000000=>[8]=>[8]
[3,6,8,2,1,7,5,4]=>0000000=>[8]=>[8]
[4,6,8,3,7,5,1,2]=>0000000=>[8]=>[8]
[4,5,3,8,7,6,1,2]=>0000000=>[8]=>[8]
[3,5,2,8,1,7,6,4]=>0000000=>[8]=>[8]
[3,1,4,2,8,7,6,5]=>0001000=>[4,4]=>[4,4]
[3,2,5,8,1,7,6,4]=>0000000=>[8]=>[8]
[4,2,5,8,7,1,6,3]=>0000000=>[8]=>[8]
[4,3,5,8,7,6,1,2]=>0000000=>[8]=>[8]
[2,4,5,8,7,1,6,3]=>0000000=>[8]=>[8]
[2,3,5,8,1,7,6,4]=>0000000=>[8]=>[8]
[5,2,7,1,4,3,8,6]=>0000000=>[8]=>[8]
[6,2,8,1,4,3,7,5]=>0000000=>[8]=>[8]
[6,2,7,1,4,3,8,5]=>0000000=>[8]=>[8]
[6,2,7,1,5,3,8,4]=>0000000=>[8]=>[8]
[7,4,8,1,3,2,6,5]=>0000000=>[8]=>[8]
[8,3,7,1,4,2,6,5]=>0000000=>[8]=>[8]
[6,2,7,3,8,1,5,4]=>0000000=>[8]=>[8]
[6,2,8,3,7,1,5,4]=>0000000=>[8]=>[8]
[5,1,8,3,7,2,6,4]=>0000000=>[8]=>[8]
[4,1,8,3,7,2,6,5]=>0000000=>[8]=>[8]
[3,1,7,4,8,2,6,5]=>0000000=>[8]=>[8]
[5,1,7,3,8,2,6,4]=>0000000=>[8]=>[8]
[7,3,8,2,6,1,5,4]=>0000000=>[8]=>[8]
[3,4,2,6,8,1,5,7]=>0000000=>[8]=>[8]
[5,3,6,2,8,1,4,7]=>0000000=>[8]=>[8]
[7,4,2,5,8,3,6,1]=>0000000=>[8]=>[8]
[4,5,2,6,3,8,1,7]=>0000000=>[8]=>[8]
[3,5,6,1,4,8,2,7]=>0000000=>[8]=>[8]
[4,1,5,6,3,8,2,7]=>0000000=>[8]=>[8]
[4,5,1,6,3,8,2,7]=>0000000=>[8]=>[8]
[4,5,6,3,2,8,1,7]=>0000000=>[8]=>[8]
[6,7,4,8,3,2,5,1]=>0000000=>[8]=>[8]
[6,7,4,8,3,2,1,5]=>0000000=>[8]=>[8]
[6,7,4,1,8,3,2,5]=>0000000=>[8]=>[8]
[5,3,7,8,1,4,2,6]=>0000000=>[8]=>[8]
[7,3,5,8,1,4,6,2]=>0000000=>[8]=>[8]
[4,5,1,7,8,3,6,2]=>0000000=>[8]=>[8]
[7,4,1,5,8,3,6,2]=>0000000=>[8]=>[8]
[6,7,4,3,8,1,5,2]=>0000000=>[8]=>[8]
[5,6,1,7,3,8,4,2]=>0000000=>[8]=>[8]
[5,1,6,7,3,8,4,2]=>0000000=>[8]=>[8]
[6,4,7,1,8,3,5,2]=>0000000=>[8]=>[8]
[6,7,8,3,1,4,5,2]=>0000000=>[8]=>[8]
[6,7,2,8,4,5,1,3]=>0000000=>[8]=>[8]
[6,7,2,8,4,1,3,5]=>0000000=>[8]=>[8]
[6,1,7,4,8,3,2,5]=>0000000=>[8]=>[8]
[5,1,6,7,3,2,8,4]=>0000000=>[8]=>[8]
[5,6,1,7,3,2,8,4]=>0000000=>[8]=>[8]
[5,6,7,3,2,1,8,4]=>0000000=>[8]=>[8]
[5,6,7,3,2,8,4,1]=>0000000=>[8]=>[8]
[7,4,2,5,1,8,3,6]=>0000000=>[8]=>[8]
[6,7,4,2,8,3,5,1]=>0000000=>[8]=>[8]
[3,6,7,2,8,4,5,1]=>0000000=>[8]=>[8]
[3,6,7,2,8,4,1,5]=>0000000=>[8]=>[8]
[3,6,7,2,1,8,4,5]=>0000000=>[8]=>[8]
[3,4,7,8,2,1,5,6]=>0000000=>[8]=>[8]
[3,7,8,1,4,6,2,5]=>0000000=>[8]=>[8]
[3,6,7,2,8,5,1,4]=>0000000=>[8]=>[8]
[3,6,7,8,5,2,1,4]=>0000000=>[8]=>[8]
[3,6,7,8,5,2,4,1]=>0000000=>[8]=>[8]
[6,4,7,8,2,5,3,1]=>0000000=>[8]=>[8]
[6,4,7,8,2,1,5,3]=>0000000=>[8]=>[8]
[5,3,7,8,1,6,2,4]=>0000000=>[8]=>[8]
[6,7,2,8,5,1,3,4]=>0000000=>[8]=>[8]
[6,4,1,7,8,2,5,3]=>0000000=>[8]=>[8]
[5,1,6,2,7,8,4,3]=>0000000=>[8]=>[8]
[5,6,2,7,1,8,4,3]=>0000000=>[8]=>[8]
[5,6,2,7,8,4,3,1]=>0000000=>[8]=>[8]
[5,6,7,2,8,4,3,1]=>0000000=>[8]=>[8]
[5,6,7,2,1,8,4,3]=>0000000=>[8]=>[8]
[5,6,1,7,2,8,4,3]=>0000000=>[8]=>[8]
[5,1,6,7,2,8,4,3]=>0000000=>[8]=>[8]
[6,7,8,3,5,1,4,2]=>0000000=>[8]=>[8]
[5,6,1,7,8,4,3,2]=>0000000=>[8]=>[8]
[5,6,7,1,8,4,3,2]=>0000000=>[8]=>[8]
[8,3,2,5,1,6,4,7]=>0000000=>[8]=>[8]
[5,3,2,7,4,1,8,6]=>0000000=>[8]=>[8]
[7,5,3,8,2,4,6,1]=>0000000=>[8]=>[8]
[8,2,4,5,6,3,1,7]=>0000000=>[8]=>[8]
[8,2,4,5,6,1,3,7]=>0000000=>[8]=>[8]
[8,5,3,6,4,1,2,7]=>0000000=>[8]=>[8]
[8,4,1,5,6,3,2,7]=>0000000=>[8]=>[8]
[8,1,4,5,6,3,2,7]=>0000000=>[8]=>[8]
[4,5,3,7,2,1,8,6]=>0000000=>[8]=>[8]
[7,4,5,8,3,2,6,1]=>0000000=>[8]=>[8]
[4,3,6,7,2,8,5,1]=>0000000=>[8]=>[8]
[4,3,6,7,2,8,1,5]=>0000000=>[8]=>[8]
[1,4,3,6,7,2,8,5]=>1000000=>[1,7]=>[7,1]
[4,5,3,7,1,8,2,6]=>0000000=>[8]=>[8]
[5,3,4,7,1,2,8,6]=>0000000=>[8]=>[8]
[7,4,5,8,3,6,1,2]=>0000000=>[8]=>[8]
[4,3,6,7,8,1,5,2]=>0000000=>[8]=>[8]
[3,5,6,7,8,4,1,2]=>0000000=>[8]=>[8]
[3,1,5,6,7,8,4,2]=>0000000=>[8]=>[8]
[4,6,1,7,8,3,5,2]=>0000000=>[8]=>[8]
[6,2,4,1,7,8,5,3]=>0000000=>[8]=>[8]
[2,6,7,1,4,8,3,5]=>0000000=>[8]=>[8]
[1,5,3,6,7,8,2,4]=>1000000=>[1,7]=>[7,1]
[4,5,2,7,8,1,3,6]=>0000000=>[8]=>[8]
[4,2,6,7,8,3,1,5]=>0000000=>[8]=>[8]
[4,2,6,7,8,3,5,1]=>0000000=>[8]=>[8]
[3,6,2,7,4,8,1,5]=>0000000=>[8]=>[8]
[3,7,4,2,1,5,8,6]=>0000000=>[8]=>[8]
[7,8,4,2,1,3,6,5]=>0000000=>[8]=>[8]
[6,3,2,7,1,8,5,4]=>0000000=>[8]=>[8]
[3,6,2,7,1,8,5,4]=>0000000=>[8]=>[8]
[6,7,3,8,2,5,4,1]=>0000000=>[8]=>[8]
[6,4,7,8,5,2,3,1]=>0000000=>[8]=>[8]
[2,6,4,7,8,1,5,3]=>0000000=>[8]=>[8]
[7,4,1,5,8,6,2,3]=>0000000=>[8]=>[8]
[7,5,8,2,1,6,3,4]=>0000000=>[8]=>[8]
[6,2,7,1,3,8,5,4]=>0000000=>[8]=>[8]
[6,3,1,7,8,2,5,4]=>0000000=>[8]=>[8]
[4,6,1,7,8,5,2,3]=>0000000=>[8]=>[8]
[5,1,2,6,7,8,4,3]=>0000000=>[8]=>[8]
[5,2,6,7,8,4,3,1]=>0000000=>[8]=>[8]
[1,6,4,7,8,5,2,3]=>1000000=>[1,7]=>[7,1]
[2,6,7,1,3,8,5,4]=>0000000=>[8]=>[8]
[6,7,3,8,5,1,4,2]=>0000000=>[8]=>[8]
[6,4,7,8,5,3,1,2]=>0000000=>[8]=>[8]
[3,1,2,6,5,8,7,4]=>0010000=>[3,5]=>[5,3]
[4,5,1,2,3,8,7,6]=>0000100=>[5,3]=>[5,3]
[4,6,1,2,3,8,7,5]=>0000000=>[8]=>[8]
[1,6,5,3,4,8,7,2]=>1000000=>[1,7]=>[7,1]
[6,1,5,2,4,8,7,3]=>0000000=>[8]=>[8]
[6,5,1,2,3,8,7,4]=>0000000=>[8]=>[8]
[6,4,1,2,3,8,7,5]=>0000000=>[8]=>[8]
[5,4,1,2,3,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,4,1,2,7,3,6,8]=>0000001=>[7,1]=>[7,1]
[6,4,1,7,2,3,5,8]=>0000001=>[7,1]=>[7,1]
[6,4,1,8,2,3,5,7]=>0000000=>[8]=>[8]
[7,4,1,2,8,3,6,5]=>0000000=>[8]=>[8]
[7,5,1,2,8,3,6,4]=>0000000=>[8]=>[8]
[7,1,5,2,8,4,6,3]=>0000000=>[8]=>[8]
[1,7,5,3,8,4,6,2]=>1000000=>[1,7]=>[7,1]
[8,4,1,2,7,3,6,5]=>0000000=>[8]=>[8]
[8,4,1,7,2,3,5,6]=>0000000=>[8]=>[8]
[7,4,1,6,2,3,5,8]=>0000001=>[7,1]=>[7,1]
[8,6,1,7,2,3,5,4]=>0000000=>[8]=>[8]
[8,1,6,7,2,4,5,3]=>0000000=>[8]=>[8]
[1,7,6,8,3,4,5,2]=>1000000=>[1,7]=>[7,1]
[7,6,1,8,2,3,5,4]=>0000000=>[8]=>[8]
[3,1,2,7,8,5,6,4]=>0010000=>[3,5]=>[5,3]
[3,1,8,7,2,4,5,6]=>0000000=>[8]=>[8]
[3,1,7,6,2,4,5,8]=>0000001=>[7,1]=>[7,1]
[4,7,1,6,2,3,5,8]=>0000001=>[7,1]=>[7,1]
[4,8,1,6,2,3,5,7]=>0000000=>[8]=>[8]
[5,8,1,2,7,3,6,4]=>0000000=>[8]=>[8]
[5,1,8,2,7,4,6,3]=>0000000=>[8]=>[8]
[1,5,8,3,7,4,6,2]=>1000000=>[1,7]=>[7,1]
[1,6,8,7,3,4,5,2]=>1000000=>[1,7]=>[7,1]
[6,1,8,7,2,4,5,3]=>0000000=>[8]=>[8]
[6,8,1,7,2,3,5,4]=>0000000=>[8]=>[8]
[6,8,7,1,2,3,4,5]=>0000000=>[8]=>[8]
[5,8,6,1,2,3,4,7]=>0000000=>[8]=>[8]
[5,7,6,1,2,3,4,8]=>0000001=>[7,1]=>[7,1]
[7,8,1,6,2,3,5,4]=>0000000=>[8]=>[8]
[7,1,8,6,2,4,5,3]=>0000000=>[8]=>[8]
[1,7,8,6,3,4,5,2]=>1000000=>[1,7]=>[7,1]
[8,1,7,6,2,4,5,3]=>0000000=>[8]=>[8]
[8,7,1,6,2,3,5,4]=>0000000=>[8]=>[8]
[8,5,3,7,2,1,4,6]=>0000000=>[8]=>[8]
[3,1,6,4,5,2,8,7]=>0000010=>[6,2]=>[6,2]
[5,8,7,4,2,6,3,1]=>0000000=>[8]=>[8]
[3,7,8,4,5,1,2,6]=>0000000=>[8]=>[8]
[5,6,3,8,1,7,2,4]=>0000000=>[8]=>[8]
[7,6,1,4,5,8,3,2]=>0000000=>[8]=>[8]
[3,7,6,4,5,8,2,1]=>0000000=>[8]=>[8]
[8,5,7,4,1,6,3,2]=>0000000=>[8]=>[8]
[2,5,8,4,7,6,1,3]=>0000000=>[8]=>[8]
[3,8,4,2,5,6,7,1]=>0000000=>[8]=>[8]
[7,5,8,4,3,6,1,2]=>0000000=>[8]=>[8]
[7,3,8,4,2,6,1,5]=>0000000=>[8]=>[8]
[5,6,3,8,4,2,7,1]=>0000000=>[8]=>[8]
[8,6,3,5,1,2,7,4]=>0000000=>[8]=>[8]
[7,8,5,4,2,6,1,3]=>0000000=>[8]=>[8]
[4,8,1,2,5,6,7,3]=>0000000=>[8]=>[8]
[3,4,2,8,5,6,7,1]=>0000000=>[8]=>[8]
[8,4,2,1,5,6,7,3]=>0000000=>[8]=>[8]
[3,8,7,4,5,2,1,6]=>0000000=>[8]=>[8]
[4,6,3,5,8,2,7,1]=>0000000=>[8]=>[8]
[5,4,2,3,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,7,6,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[4,7,2,6,3,5,1,8]=>0000001=>[7,1]=>[7,1]
[5,7,6,2,3,4,1,8]=>0000001=>[7,1]=>[7,1]
[1,7,5,2,8,3,4,6]=>1000000=>[1,7]=>[7,1]
[6,8,5,2,3,1,4,7]=>0000000=>[8]=>[8]
[4,8,2,6,3,1,5,7]=>0000000=>[8]=>[8]
[3,2,8,6,4,1,5,7]=>0000000=>[8]=>[8]
[7,1,5,2,8,3,4,6]=>0000000=>[8]=>[8]
[1,8,5,2,7,3,4,6]=>1000000=>[1,7]=>[7,1]
[7,1,6,8,2,3,4,5]=>0000000=>[8]=>[8]
[3,2,1,7,8,4,5,6]=>0010000=>[3,5]=>[5,3]
[3,2,8,7,1,4,5,6]=>0000000=>[8]=>[8]
[5,8,7,2,1,3,4,6]=>0000000=>[8]=>[8]
[1,7,6,8,2,3,4,5]=>1000000=>[1,7]=>[7,1]
[6,5,8,2,3,1,4,7]=>0000000=>[8]=>[8]
[8,5,7,2,1,3,4,6]=>0000000=>[8]=>[8]
[3,2,5,4,1,8,6,7]=>0000100=>[5,3]=>[5,3]
[7,4,2,1,8,3,5,6]=>0000000=>[8]=>[8]
[8,4,2,1,7,3,5,6]=>0000000=>[8]=>[8]
[1,4,2,8,7,3,5,6]=>1000000=>[1,7]=>[7,1]
[1,5,8,2,7,3,4,6]=>1000000=>[1,7]=>[7,1]
[8,5,1,2,7,3,4,6]=>0000000=>[8]=>[8]
[3,2,6,1,4,8,5,7]=>0000000=>[8]=>[8]
[3,2,7,1,8,4,5,6]=>0000000=>[8]=>[8]
[4,7,2,1,8,3,5,6]=>0000000=>[8]=>[8]
[8,6,1,7,2,3,4,5]=>0000000=>[8]=>[8]
[1,6,8,7,2,3,4,5]=>1000000=>[1,7]=>[7,1]
[1,7,8,6,2,3,4,5]=>1000000=>[1,7]=>[7,1]
[7,8,1,6,2,3,4,5]=>0000000=>[8]=>[8]
[4,8,2,1,7,3,5,6]=>0000000=>[8]=>[8]
[3,2,8,1,7,4,5,6]=>0000000=>[8]=>[8]
[5,1,8,2,7,3,4,6]=>0000000=>[8]=>[8]
[6,1,8,7,2,3,4,5]=>0000000=>[8]=>[8]
[8,1,7,6,2,3,4,5]=>0000000=>[8]=>[8]
[2,8,4,1,6,5,7,3]=>0000000=>[8]=>[8]
[7,5,8,6,1,4,2,3]=>0000000=>[8]=>[8]
[7,5,8,2,4,6,3,1]=>0000000=>[8]=>[8]
[7,5,8,6,1,4,3,2]=>0000000=>[8]=>[8]
[3,5,7,2,4,1,8,6]=>0000000=>[8]=>[8]
[6,5,2,7,3,4,8,1]=>0000000=>[8]=>[8]
[5,1,6,7,4,3,8,2]=>0000000=>[8]=>[8]
[4,1,2,3,8,6,5,7]=>0001000=>[4,4]=>[4,4]
[4,1,2,3,8,6,7,5]=>0001000=>[4,4]=>[4,4]
[4,1,2,3,8,5,7,6]=>0001000=>[4,4]=>[4,4]
[4,5,2,6,3,7,1,8]=>0000001=>[7,1]=>[7,1]
[4,1,2,6,8,5,7,3]=>0000000=>[8]=>[8]
[6,4,2,7,1,3,8,5]=>0000000=>[8]=>[8]
[8,5,3,6,1,7,2,4]=>0000000=>[8]=>[8]
[7,3,6,2,4,8,1,5]=>0000000=>[8]=>[8]
[3,7,5,1,2,4,8,6]=>0000000=>[8]=>[8]
[7,4,8,5,2,6,1,3]=>0000000=>[8]=>[8]
[5,8,2,6,3,7,1,4]=>0000000=>[8]=>[8]
[3,8,6,2,4,7,1,5]=>0000000=>[8]=>[8]
[4,8,6,2,7,1,3,5]=>0000000=>[8]=>[8]
[5,4,7,3,8,1,2,6]=>0000000=>[8]=>[8]
[8,4,1,6,7,2,3,5]=>0000000=>[8]=>[8]
[4,7,1,5,8,6,2,3]=>0000000=>[8]=>[8]
[8,6,1,7,5,2,3,4]=>0000000=>[8]=>[8]
[5,7,2,8,1,6,3,4]=>0000000=>[8]=>[8]
[8,3,7,6,1,2,4,5]=>0000000=>[8]=>[8]
[8,4,7,6,1,2,3,5]=>0000000=>[8]=>[8]
[3,5,8,7,1,2,4,6]=>0000000=>[8]=>[8]
[2,5,8,7,1,3,4,6]=>0000000=>[8]=>[8]
[6,8,4,7,5,1,2,3]=>0000000=>[8]=>[8]
[5,8,7,1,6,2,3,4]=>0000000=>[8]=>[8]
[2,8,7,6,1,3,4,5]=>0000000=>[8]=>[8]
[3,8,7,6,1,2,4,5]=>0000000=>[8]=>[8]
[4,8,7,6,1,2,3,5]=>0000000=>[8]=>[8]
[3,8,7,4,5,1,6,2]=>0000000=>[8]=>[8]
[5,7,3,8,1,2,6,4]=>0000000=>[8]=>[8]
[7,5,1,4,8,6,3,2]=>0000000=>[8]=>[8]
[5,3,2,7,4,6,8,1]=>0000000=>[8]=>[8]
[7,5,3,6,2,4,8,1]=>0000000=>[8]=>[8]
[6,3,2,5,1,8,4,7]=>0000000=>[8]=>[8]
[8,5,3,6,2,7,1,4]=>0000000=>[8]=>[8]
[7,2,6,3,4,5,8,1]=>0000000=>[8]=>[8]
[6,2,7,3,4,5,8,1]=>0000000=>[8]=>[8]
[6,7,3,5,2,4,8,1]=>0000000=>[8]=>[8]
[3,7,6,2,4,5,8,1]=>0000000=>[8]=>[8]
[6,5,3,1,2,8,4,7]=>0000000=>[8]=>[8]
[8,6,5,2,3,7,1,4]=>0000000=>[8]=>[8]
[8,5,2,1,7,3,4,6]=>0000000=>[8]=>[8]
[7,5,2,1,8,3,4,6]=>0000000=>[8]=>[8]
[1,6,3,2,8,4,5,7]=>1000000=>[1,7]=>[7,1]
[5,4,8,6,2,7,1,3]=>0000000=>[8]=>[8]
[7,8,5,2,3,6,1,4]=>0000000=>[8]=>[8]
[2,8,1,7,3,4,5,6]=>0000000=>[8]=>[8]
[3,8,6,1,7,2,4,5]=>0000000=>[8]=>[8]
[4,2,8,3,7,1,5,6]=>0000000=>[8]=>[8]
[8,1,2,7,3,4,5,6]=>0000000=>[8]=>[8]
[7,2,6,1,8,3,4,5]=>0000000=>[8]=>[8]
[7,3,1,5,8,2,4,6]=>0000000=>[8]=>[8]
[5,4,1,3,6,8,2,7]=>0000000=>[8]=>[8]
[8,5,3,7,6,1,2,4]=>0000000=>[8]=>[8]
[6,1,8,3,7,2,4,5]=>0000000=>[8]=>[8]
[7,6,8,2,3,5,1,4]=>0000000=>[8]=>[8]
[3,7,8,2,4,6,1,5]=>0000000=>[8]=>[8]
[5,4,7,8,2,6,1,3]=>0000000=>[8]=>[8]
[4,2,5,8,7,1,3,6]=>0000000=>[8]=>[8]
[2,3,8,7,1,4,5,6]=>0000000=>[8]=>[8]
[2,1,8,7,3,4,5,6]=>0100000=>[2,6]=>[6,2]
[8,2,7,6,1,3,4,5]=>0000000=>[8]=>[8]
[1,2,8,7,3,4,5,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,8,7,2,4,5,6]=>1000000=>[1,7]=>[7,1]
[1,7,8,3,6,2,4,5]=>1000000=>[1,7]=>[7,1]
[5,4,8,7,6,1,2,3]=>0000000=>[8]=>[8]
[6,8,3,7,5,1,2,4]=>0000000=>[8]=>[8]
[7,8,6,2,5,1,3,4]=>0000000=>[8]=>[8]
[8,1,6,7,3,2,4,5]=>0000000=>[8]=>[8]
[8,1,5,3,7,2,4,6]=>0000000=>[8]=>[8]
[8,1,5,3,6,2,4,7]=>0000000=>[8]=>[8]
[7,4,8,3,2,6,5,1]=>0000000=>[8]=>[8]
[7,4,1,3,2,6,5,8]=>0000001=>[7,1]=>[7,1]
[8,1,4,3,2,6,5,7]=>0000000=>[8]=>[8]
[8,1,4,3,2,7,5,6]=>0000000=>[8]=>[8]
[8,1,5,4,6,7,2,3]=>0000000=>[8]=>[8]
[8,1,5,3,6,2,7,4]=>0000000=>[8]=>[8]
[8,1,4,3,2,6,7,5]=>0000000=>[8]=>[8]
[8,1,4,3,2,5,7,6]=>0000000=>[8]=>[8]
[7,4,1,3,2,5,6,8]=>0000001=>[7,1]=>[7,1]
[7,4,8,3,2,5,6,1]=>0000000=>[8]=>[8]
[6,4,3,1,2,5,8,7]=>0000010=>[6,2]=>[6,2]
[7,4,1,3,2,5,8,6]=>0000000=>[8]=>[8]
[7,5,1,3,6,2,8,4]=>0000000=>[8]=>[8]
[7,5,1,4,6,8,2,3]=>0000000=>[8]=>[8]
[6,4,3,8,2,5,1,7]=>0000000=>[8]=>[8]
[5,4,3,2,8,6,1,7]=>0000000=>[8]=>[8]
[5,4,3,2,8,7,1,6]=>0000000=>[8]=>[8]
[6,5,4,8,7,1,2,3]=>0000000=>[8]=>[8]
[6,5,4,1,7,8,2,3]=>0000000=>[8]=>[8]
[6,4,3,1,2,7,8,5]=>0000000=>[8]=>[8]
[7,4,1,3,2,8,5,6]=>0000000=>[8]=>[8]
[6,4,3,1,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[6,4,3,8,2,7,5,1]=>0000000=>[8]=>[8]
[6,5,3,8,7,2,4,1]=>0000000=>[8]=>[8]
[6,5,3,1,7,2,4,8]=>0000001=>[7,1]=>[7,1]
[7,5,1,3,8,2,4,6]=>0000000=>[8]=>[8]
[6,5,3,7,8,2,4,1]=>0000000=>[8]=>[8]
[6,4,3,7,2,8,5,1]=>0000000=>[8]=>[8]
[6,4,3,7,2,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,5,8,4,1,6,2,3]=>0000000=>[8]=>[8]
[6,5,4,8,1,7,2,3]=>0000000=>[8]=>[8]
[6,5,3,8,1,2,7,4]=>0000000=>[8]=>[8]
[6,5,4,7,1,8,2,3]=>0000000=>[8]=>[8]
[5,4,3,2,7,8,1,6]=>0000000=>[8]=>[8]
[4,6,3,8,5,1,2,7]=>0000000=>[8]=>[8]
[5,6,8,3,4,1,2,7]=>0000000=>[8]=>[8]
[5,6,8,3,4,1,7,2]=>0000000=>[8]=>[8]
[4,6,2,7,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,8,4,3,1,2,7]=>0000000=>[8]=>[8]
[5,7,8,4,1,3,6,2]=>0000000=>[8]=>[8]
[5,6,8,4,2,1,7,3]=>0000000=>[8]=>[8]
[5,6,8,2,4,1,7,3]=>0000000=>[8]=>[8]
[3,2,6,8,5,1,4,7]=>0000000=>[8]=>[8]
[5,6,8,4,2,1,3,7]=>0000000=>[8]=>[8]
[5,7,8,4,1,3,2,6]=>0000000=>[8]=>[8]
[5,7,8,4,1,2,3,6]=>0000000=>[8]=>[8]
[6,7,8,1,5,2,3,4]=>0000000=>[8]=>[8]
[6,7,8,1,5,3,2,4]=>0000000=>[8]=>[8]
[6,7,8,1,3,5,2,4]=>0000000=>[8]=>[8]
[5,7,8,2,1,6,3,4]=>0000000=>[8]=>[8]
[4,7,2,8,1,6,3,5]=>0000000=>[8]=>[8]
[3,2,7,8,1,6,4,5]=>0000000=>[8]=>[8]
[4,7,2,8,1,6,5,3]=>0000000=>[8]=>[8]
[5,7,8,2,1,6,4,3]=>0000000=>[8]=>[8]
[6,7,8,1,3,5,4,2]=>0000000=>[8]=>[8]
[6,7,8,1,5,3,4,2]=>0000000=>[8]=>[8]
[6,7,8,1,4,3,5,2]=>0000000=>[8]=>[8]
[5,6,8,3,2,1,7,4]=>0000000=>[8]=>[8]
[4,7,3,8,1,6,2,5]=>0000000=>[8]=>[8]
[4,7,3,8,1,5,6,2]=>0000000=>[8]=>[8]
[4,7,3,8,1,5,2,6]=>0000000=>[8]=>[8]
[4,7,3,8,1,2,5,6]=>0000000=>[8]=>[8]
[5,7,8,3,1,2,4,6]=>0000000=>[8]=>[8]
[5,6,8,3,2,1,4,7]=>0000000=>[8]=>[8]
[3,2,7,8,1,5,4,6]=>0000000=>[8]=>[8]
[6,7,8,1,3,4,2,5]=>0000000=>[8]=>[8]
[6,7,8,1,4,2,3,5]=>0000000=>[8]=>[8]
[6,7,8,1,2,5,3,4]=>0000000=>[8]=>[8]
[6,7,8,1,2,4,5,3]=>0000000=>[8]=>[8]
[5,7,8,2,1,3,6,4]=>0000000=>[8]=>[8]
[3,2,7,8,1,4,6,5]=>0000000=>[8]=>[8]
[6,7,8,1,3,2,4,5]=>0000000=>[8]=>[8]
[6,7,8,1,2,4,3,5]=>0000000=>[8]=>[8]
[6,7,8,1,2,3,5,4]=>0000000=>[8]=>[8]
[4,6,2,1,7,5,8,3]=>0000000=>[8]=>[8]
[6,7,5,1,8,4,3,2]=>0000000=>[8]=>[8]
[6,8,4,1,7,5,3,2]=>0000000=>[8]=>[8]
[4,6,1,2,7,5,8,3]=>0000000=>[8]=>[8]
[6,7,1,5,8,2,3,4]=>0000000=>[8]=>[8]
[8,4,1,6,7,5,2,3]=>0000000=>[8]=>[8]
[7,6,2,1,5,8,3,4]=>0000000=>[8]=>[8]
[6,1,4,2,7,5,8,3]=>0000000=>[8]=>[8]
[2,5,1,3,7,6,8,4]=>0000000=>[8]=>[8]
[4,7,1,2,8,6,5,3]=>0000000=>[8]=>[8]
[4,6,8,1,2,7,5,3]=>0000000=>[8]=>[8]
[6,8,7,1,5,3,2,4]=>0000000=>[8]=>[8]
[6,8,7,3,5,1,2,4]=>0000000=>[8]=>[8]
[7,8,1,3,6,5,2,4]=>0000000=>[8]=>[8]
[1,7,3,4,8,6,5,2]=>1000000=>[1,7]=>[7,1]
[4,2,7,1,8,6,5,3]=>0000000=>[8]=>[8]
[7,8,2,3,6,5,1,4]=>0000000=>[8]=>[8]
[8,5,7,1,6,2,3,4]=>0000000=>[8]=>[8]
[8,5,7,1,2,6,3,4]=>0000000=>[8]=>[8]
[6,8,2,7,1,3,5,4]=>0000000=>[8]=>[8]
[6,2,4,8,7,1,5,3]=>0000000=>[8]=>[8]
[1,6,8,3,7,4,5,2]=>1000000=>[1,7]=>[7,1]
[1,6,8,3,4,7,5,2]=>1000000=>[1,7]=>[7,1]
[6,2,4,8,1,7,5,3]=>0000000=>[8]=>[8]
[6,8,7,2,3,5,1,4]=>0000000=>[8]=>[8]
[6,8,2,1,7,3,5,4]=>0000000=>[8]=>[8]
[8,5,7,2,1,6,3,4]=>0000000=>[8]=>[8]
[8,5,7,1,2,3,6,4]=>0000000=>[8]=>[8]
[8,5,7,2,3,1,6,4]=>0000000=>[8]=>[8]
[1,8,7,5,3,4,6,2]=>1000000=>[1,7]=>[7,1]
[1,8,7,3,5,4,6,2]=>1000000=>[1,7]=>[7,1]
[8,2,5,4,7,1,6,3]=>0000000=>[8]=>[8]
[8,7,6,1,2,4,3,5]=>0000000=>[8]=>[8]
[8,7,6,1,4,2,3,5]=>0000000=>[8]=>[8]
[8,7,6,4,1,3,2,5]=>0000000=>[8]=>[8]
[8,5,7,1,3,2,6,4]=>0000000=>[8]=>[8]
[5,8,4,7,1,2,6,3]=>0000000=>[8]=>[8]
[8,1,2,6,5,7,4,3]=>0000000=>[8]=>[8]
[8,2,5,6,7,4,1,3]=>0000000=>[8]=>[8]
[4,8,5,1,7,2,6,3]=>0000000=>[8]=>[8]
[8,5,3,7,1,2,6,4]=>0000000=>[8]=>[8]
[4,6,2,8,1,7,5,3]=>0000000=>[8]=>[8]
[1,6,4,8,3,7,5,2]=>1000000=>[1,7]=>[7,1]
[1,8,7,4,5,3,6,2]=>1000000=>[1,7]=>[7,1]
[4,8,5,7,2,1,6,3]=>0000000=>[8]=>[8]
[8,5,3,7,2,1,6,4]=>0000000=>[8]=>[8]
[8,7,6,3,1,4,2,5]=>0000000=>[8]=>[8]
[8,5,3,2,7,1,6,4]=>0000000=>[8]=>[8]
[1,8,7,4,3,5,6,2]=>1000000=>[1,7]=>[7,1]
[1,8,7,3,4,5,6,2]=>1000000=>[1,7]=>[7,1]
[8,2,4,5,7,1,6,3]=>0000000=>[8]=>[8]
[8,5,2,3,7,1,6,4]=>0000000=>[8]=>[8]
[8,3,1,5,2,7,6,4]=>0000000=>[8]=>[8]
[8,7,4,1,6,3,2,5]=>0000000=>[8]=>[8]
[8,7,4,1,6,3,5,2]=>0000000=>[8]=>[8]
[8,7,4,1,6,5,3,2]=>0000000=>[8]=>[8]
[8,7,4,1,6,5,2,3]=>0000000=>[8]=>[8]
[8,3,2,7,6,4,5,1]=>0000000=>[8]=>[8]
[8,5,4,2,3,7,6,1]=>0000000=>[8]=>[8]
[8,7,4,2,6,3,5,1]=>0000000=>[8]=>[8]
[8,7,4,2,6,3,1,5]=>0000000=>[8]=>[8]
[8,3,2,5,4,7,1,6]=>0000000=>[8]=>[8]
[8,3,2,7,6,1,5,4]=>0000000=>[8]=>[8]
[7,4,5,2,3,1,8,6]=>0000000=>[8]=>[8]
[5,2,7,3,4,1,8,6]=>0000000=>[8]=>[8]
[6,2,7,3,4,1,8,5]=>0000000=>[8]=>[8]
[3,1,8,6,7,4,5,2]=>0000000=>[8]=>[8]
[8,5,7,3,4,1,6,2]=>0000000=>[8]=>[8]
[8,4,7,3,5,1,6,2]=>0000000=>[8]=>[8]
[2,1,8,5,7,4,6,3]=>0100000=>[2,6]=>[6,2]
[6,2,4,1,7,3,8,5]=>0000000=>[8]=>[8]
[8,5,6,2,3,1,7,4]=>0000000=>[8]=>[8]
[7,3,8,5,6,2,4,1]=>0000000=>[8]=>[8]
[3,1,6,2,8,5,7,4]=>0000000=>[8]=>[8]
[5,1,6,2,8,4,7,3]=>0000000=>[8]=>[8]
[7,3,8,4,6,2,5,1]=>0000000=>[8]=>[8]
[4,1,8,5,6,2,7,3]=>0000000=>[8]=>[8]
[3,1,8,5,6,2,7,4]=>0000000=>[8]=>[8]
[6,8,7,3,4,1,2,5]=>0000000=>[8]=>[8]
[5,4,8,7,2,6,3,1]=>0000000=>[8]=>[8]
[5,3,8,7,6,1,2,4]=>0000000=>[8]=>[8]
[8,3,4,6,5,1,2,7]=>0000000=>[8]=>[8]
[3,4,8,7,6,1,2,5]=>0000000=>[8]=>[8]
[3,5,8,7,6,1,2,4]=>0000000=>[8]=>[8]
[4,5,8,7,6,1,2,3]=>0000000=>[8]=>[8]
[4,5,8,7,1,6,3,2]=>0000000=>[8]=>[8]
[3,5,8,2,7,6,4,1]=>0000000=>[8]=>[8]
[3,5,8,1,7,6,4,2]=>0000000=>[8]=>[8]
[2,5,8,7,1,6,3,4]=>0000000=>[8]=>[8]
[2,4,8,7,1,6,3,5]=>0000000=>[8]=>[8]
[2,8,4,7,1,5,3,6]=>0000000=>[8]=>[8]
[8,2,4,6,1,5,3,7]=>0000000=>[8]=>[8]
[8,1,4,6,2,5,3,7]=>0000000=>[8]=>[8]
[1,4,8,7,2,6,3,5]=>1000000=>[1,7]=>[7,1]
[1,5,8,7,2,6,3,4]=>1000000=>[1,7]=>[7,1]
[1,5,8,2,7,6,4,3]=>1000000=>[1,7]=>[7,1]
[2,5,8,3,7,6,4,1]=>0000000=>[8]=>[8]
[1,4,2,8,7,6,5,3]=>1000000=>[1,7]=>[7,1]
[1,3,8,2,7,6,4,5]=>1000000=>[1,7]=>[7,1]
[1,8,3,2,7,5,4,6]=>1000000=>[1,7]=>[7,1]
[8,2,3,1,6,5,4,7]=>0000000=>[8]=>[8]
[2,3,8,1,7,6,4,5]=>0000000=>[8]=>[8]
[5,2,8,7,1,6,3,4]=>0000000=>[8]=>[8]
[5,2,8,1,7,6,4,3]=>0000000=>[8]=>[8]
[5,3,8,2,7,6,4,1]=>0000000=>[8]=>[8]
[6,8,3,2,7,5,4,1]=>0000000=>[8]=>[8]
[6,8,3,1,7,5,4,2]=>0000000=>[8]=>[8]
[6,8,1,2,7,5,4,3]=>0000000=>[8]=>[8]
[6,8,2,3,7,5,4,1]=>0000000=>[8]=>[8]
[5,2,8,3,7,6,4,1]=>0000000=>[8]=>[8]
[5,1,8,3,7,6,4,2]=>0000000=>[8]=>[8]
[5,1,8,7,2,6,3,4]=>0000000=>[8]=>[8]
[4,8,1,7,2,5,3,6]=>0000000=>[8]=>[8]
[8,4,1,6,2,5,3,7]=>0000000=>[8]=>[8]
[8,3,1,2,6,5,4,7]=>0000000=>[8]=>[8]
[3,1,2,8,7,6,5,4]=>0010000=>[3,5]=>[5,3]
[4,1,3,8,7,6,5,2]=>0000000=>[8]=>[8]
[3,1,4,8,7,6,5,2]=>0000000=>[8]=>[8]
[2,1,8,3,7,6,4,5]=>0100000=>[2,6]=>[6,2]
[2,8,1,3,7,5,4,6]=>0000000=>[8]=>[8]
[8,2,1,3,6,5,4,7]=>0000000=>[8]=>[8]
[1,8,2,3,7,5,4,6]=>1000000=>[1,7]=>[7,1]
[1,2,8,3,7,6,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,4,3,6,8,2,5,7]=>1000000=>[1,7]=>[7,1]
[1,4,5,2,8,3,7,6]=>1000000=>[1,7]=>[7,1]
[1,4,2,6,5,8,3,7]=>1000000=>[1,7]=>[7,1]
[1,5,4,2,6,8,3,7]=>1000000=>[1,7]=>[7,1]
[3,1,6,5,8,2,4,7]=>0000000=>[8]=>[8]
[1,6,4,2,5,8,3,7]=>1000000=>[1,7]=>[7,1]
[1,5,2,6,4,8,3,7]=>1000000=>[1,7]=>[7,1]
[1,2,6,5,4,8,3,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,4,7,3,8,6]=>1100000=>[1,1,6]=>[6,1,1]
[4,1,2,6,3,8,7,5]=>0000000=>[8]=>[8]
[7,1,5,4,2,8,3,6]=>0000000=>[8]=>[8]
[1,4,7,5,2,8,3,6]=>1000000=>[1,7]=>[7,1]
[7,1,3,5,2,8,4,6]=>0000000=>[8]=>[8]
[1,4,5,2,8,7,3,6]=>1000000=>[1,7]=>[7,1]
[1,6,4,2,8,3,7,5]=>1000000=>[1,7]=>[7,1]
[1,4,2,8,3,7,6,5]=>1000000=>[1,7]=>[7,1]
[1,2,8,6,5,3,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[6,2,1,8,7,3,4,5]=>0000000=>[8]=>[8]
[7,6,2,1,8,3,4,5]=>0000000=>[8]=>[8]
[7,3,1,6,2,8,4,5]=>0000000=>[8]=>[8]
[1,7,6,4,2,8,3,5]=>1000000=>[1,7]=>[7,1]
[1,7,5,2,6,3,8,4]=>1000000=>[1,7]=>[7,1]
[1,6,2,7,5,3,8,4]=>1000000=>[1,7]=>[7,1]
[1,2,7,6,5,3,8,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,5,3,8,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,2,7,6,3,8,4]=>1000000=>[1,7]=>[7,1]
[1,6,5,2,7,3,8,4]=>1000000=>[1,7]=>[7,1]
[1,5,7,4,2,8,3,6]=>1000000=>[1,7]=>[7,1]
[3,1,8,6,2,4,7,5]=>0000000=>[8]=>[8]
[4,3,7,1,8,2,5,6]=>0000000=>[8]=>[8]
[8,3,1,6,2,4,7,5]=>0000000=>[8]=>[8]
[7,1,8,3,2,4,6,5]=>0000000=>[8]=>[8]
[1,4,2,8,7,3,6,5]=>1000000=>[1,7]=>[7,1]
[1,7,4,2,8,3,6,5]=>1000000=>[1,7]=>[7,1]
[8,1,5,4,2,7,3,6]=>0000000=>[8]=>[8]
[1,4,8,5,2,7,3,6]=>1000000=>[1,7]=>[7,1]
[8,5,3,1,7,2,4,6]=>0000000=>[8]=>[8]
[8,6,2,1,7,3,4,5]=>0000000=>[8]=>[8]
[1,8,6,4,2,7,3,5]=>1000000=>[1,7]=>[7,1]
[1,5,2,7,3,8,6,4]=>1000000=>[1,7]=>[7,1]
[1,2,8,5,3,7,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,3,8,7,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,6,3,8,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,2,7,3,8,5,4]=>1000000=>[1,7]=>[7,1]
[1,7,4,2,8,6,3,5]=>1000000=>[1,7]=>[7,1]
[7,1,8,3,2,6,4,5]=>0000000=>[8]=>[8]
[7,2,1,8,6,3,4,5]=>0000000=>[8]=>[8]
[1,8,7,3,2,6,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,2,8,7,6,3,5]=>1000000=>[1,7]=>[7,1]
[1,2,8,7,5,3,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[5,7,1,6,2,4,3,8]=>0000001=>[7,1]=>[7,1]
[6,1,4,5,3,8,7,2]=>0000000=>[8]=>[8]
[6,3,5,8,2,1,7,4]=>0000000=>[8]=>[8]
[8,4,5,7,3,6,1,2]=>0000000=>[8]=>[8]
[8,4,1,5,2,6,3,7]=>0000000=>[8]=>[8]
[8,7,5,6,1,4,2,3]=>0000000=>[8]=>[8]
[2,3,8,1,6,4,7,5]=>0000000=>[8]=>[8]
[5,2,6,1,4,8,7,3]=>0000000=>[8]=>[8]
[5,7,2,3,8,6,1,4]=>0000000=>[8]=>[8]
[5,6,2,3,1,8,7,4]=>0000000=>[8]=>[8]
[5,6,2,1,3,8,7,4]=>0000000=>[8]=>[8]
[5,1,6,4,2,8,7,3]=>0000000=>[8]=>[8]
[5,6,1,3,2,8,7,4]=>0000000=>[8]=>[8]
[5,6,3,1,2,8,7,4]=>0000000=>[8]=>[8]
[5,7,3,2,8,1,6,4]=>0000000=>[8]=>[8]
[6,7,3,8,2,1,5,4]=>0000000=>[8]=>[8]
[6,7,3,8,1,2,5,4]=>0000000=>[8]=>[8]
[5,7,3,1,8,2,6,4]=>0000000=>[8]=>[8]
[5,1,7,4,8,2,6,3]=>0000000=>[8]=>[8]
[1,5,7,4,8,3,6,2]=>1000000=>[1,7]=>[7,1]
[5,1,7,4,8,6,2,3]=>0000000=>[8]=>[8]
[5,7,3,1,8,6,2,4]=>0000000=>[8]=>[8]
[6,7,8,3,1,4,2,5]=>0000000=>[8]=>[8]
[6,7,1,8,3,5,2,4]=>0000000=>[8]=>[8]
[6,1,7,8,4,5,2,3]=>0000000=>[8]=>[8]
[1,6,7,8,4,5,3,2]=>1000000=>[1,7]=>[7,1]
[1,6,7,8,4,3,5,2]=>1000000=>[1,7]=>[7,1]
[6,1,7,8,4,2,5,3]=>0000000=>[8]=>[8]
[6,7,2,8,1,3,5,4]=>0000000=>[8]=>[8]
[6,7,2,8,3,5,1,4]=>0000000=>[8]=>[8]
[6,2,7,8,4,1,5,3]=>0000000=>[8]=>[8]
[6,2,7,8,1,4,5,3]=>0000000=>[8]=>[8]
[4,2,1,7,8,5,6,3]=>0000000=>[8]=>[8]
[4,1,2,7,8,6,5,3]=>0000000=>[8]=>[8]
[6,2,7,8,1,5,4,3]=>0000000=>[8]=>[8]
[6,2,7,8,5,1,4,3]=>0000000=>[8]=>[8]
[5,7,2,1,8,6,3,4]=>0000000=>[8]=>[8]
[1,6,7,8,3,5,4,2]=>1000000=>[1,7]=>[7,1]
[6,1,7,8,2,5,4,3]=>0000000=>[8]=>[8]
[6,7,8,2,4,1,3,5]=>0000000=>[8]=>[8]
[6,7,8,2,4,3,1,5]=>0000000=>[8]=>[8]
[6,7,1,8,5,2,3,4]=>0000000=>[8]=>[8]
[6,1,7,8,5,2,4,3]=>0000000=>[8]=>[8]
[1,6,7,8,5,3,4,2]=>1000000=>[1,7]=>[7,1]
[6,1,7,8,5,4,2,3]=>0000000=>[8]=>[8]
[6,7,1,8,5,3,2,4]=>0000000=>[8]=>[8]
[6,7,8,4,1,3,2,5]=>0000000=>[8]=>[8]
[3,7,4,8,5,6,1,2]=>0000000=>[8]=>[8]
[3,7,1,8,5,6,2,4]=>0000000=>[8]=>[8]
[2,7,3,8,5,6,1,4]=>0000000=>[8]=>[8]
[1,7,4,8,5,6,2,3]=>1000000=>[1,7]=>[7,1]
[2,7,3,8,4,6,1,5]=>0000000=>[8]=>[8]
[3,7,1,8,4,6,2,5]=>0000000=>[8]=>[8]
[1,5,2,8,6,7,3,4]=>1000000=>[1,7]=>[7,1]
[2,6,1,8,5,7,3,4]=>0000000=>[8]=>[8]
[1,6,2,8,5,7,3,4]=>1000000=>[1,7]=>[7,1]
[1,6,2,8,4,7,3,5]=>1000000=>[1,7]=>[7,1]
[2,6,1,8,4,7,3,5]=>0000000=>[8]=>[8]
[3,7,2,6,1,8,4,5]=>0000000=>[8]=>[8]
[4,8,1,6,2,7,3,5]=>0000000=>[8]=>[8]
[5,8,1,6,2,7,3,4]=>0000000=>[8]=>[8]
[5,8,2,6,1,7,3,4]=>0000000=>[8]=>[8]
[4,8,2,6,1,7,3,5]=>0000000=>[8]=>[8]
[1,7,3,6,2,8,4,5]=>1000000=>[1,7]=>[7,1]
[2,7,3,6,1,8,4,5]=>0000000=>[8]=>[8]
[8,6,1,4,3,2,5,7]=>0000000=>[8]=>[8]
[3,7,5,1,8,2,4,6]=>0000000=>[8]=>[8]
[4,1,5,2,8,7,3,6]=>0000000=>[8]=>[8]
[8,1,2,4,6,5,3,7]=>0000000=>[8]=>[8]
[8,2,6,5,1,3,4,7]=>0000000=>[8]=>[8]
[8,3,1,6,2,5,4,7]=>0000000=>[8]=>[8]
[8,1,2,6,4,5,3,7]=>0000000=>[8]=>[8]
[8,1,2,5,6,4,3,7]=>0000000=>[8]=>[8]
[1,7,5,4,2,8,3,6]=>1000000=>[1,7]=>[7,1]
[1,4,6,8,2,7,3,5]=>1000000=>[1,7]=>[7,1]
[1,4,7,6,2,8,3,5]=>1000000=>[1,7]=>[7,1]
[5,1,4,7,2,8,3,6]=>0000000=>[8]=>[8]
[3,7,5,1,2,8,4,6]=>0000000=>[8]=>[8]
[4,1,5,8,2,7,3,6]=>0000000=>[8]=>[8]
[1,4,6,2,8,7,3,5]=>1000000=>[1,7]=>[7,1]
[1,4,2,8,6,7,3,5]=>1000000=>[1,7]=>[7,1]
[3,1,2,6,4,8,7,5]=>0010000=>[3,5]=>[5,3]
[2,1,7,6,3,4,8,5]=>0100000=>[2,6]=>[6,2]
[3,1,2,7,4,6,8,5]=>0010000=>[3,5]=>[5,3]
[1,2,3,6,8,5,7,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[5,1,4,2,7,8,3,6]=>0000000=>[8]=>[8]
[1,4,2,7,6,8,3,5]=>1000000=>[1,7]=>[7,1]
[1,4,2,6,8,7,3,5]=>1000000=>[1,7]=>[7,1]
[5,3,7,1,8,2,4,6]=>0000000=>[8]=>[8]
[1,7,4,3,2,5,8,6]=>1000000=>[1,7]=>[7,1]
[4,8,7,2,1,3,5,6]=>0000000=>[8]=>[8]
[1,8,7,3,4,2,5,6]=>1000000=>[1,7]=>[7,1]
[3,1,7,8,2,6,4,5]=>0000000=>[8]=>[8]
[1,4,2,7,8,3,6,5]=>1000000=>[1,7]=>[7,1]
[2,1,8,6,3,4,7,5]=>0100000=>[2,6]=>[6,2]
[1,4,2,6,8,3,7,5]=>1000000=>[1,7]=>[7,1]
[1,2,3,7,8,5,6,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,5,8,6,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[3,1,7,2,8,6,4,5]=>0000000=>[8]=>[8]
[1,2,3,8,7,5,6,4]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[5,7,8,4,2,6,1,3]=>0000000=>[8]=>[8]
[6,7,8,4,2,5,1,3]=>0000000=>[8]=>[8]
[8,6,3,7,2,1,5,4]=>0000000=>[8]=>[8]
[6,7,8,3,2,1,5,4]=>0000000=>[8]=>[8]
[5,7,8,3,2,1,6,4]=>0000000=>[8]=>[8]
[2,7,8,4,3,5,6,1]=>0000000=>[8]=>[8]
[3,7,8,4,2,5,1,6]=>0000000=>[8]=>[8]
[7,6,3,8,2,1,4,5]=>0000000=>[8]=>[8]
[8,6,3,7,2,1,4,5]=>0000000=>[8]=>[8]
[5,6,3,8,2,1,4,7]=>0000000=>[8]=>[8]
[3,6,4,8,2,5,1,7]=>0000000=>[8]=>[8]
[2,6,4,8,3,5,7,1]=>0000000=>[8]=>[8]
[2,6,4,7,3,5,8,1]=>0000000=>[8]=>[8]
[4,6,3,7,2,1,5,8]=>0000001=>[7,1]=>[7,1]
[5,6,3,7,2,1,4,8]=>0000001=>[7,1]=>[7,1]
[8,4,3,2,1,6,5,7]=>0000000=>[8]=>[8]
[6,4,3,2,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[4,5,3,2,7,1,6,8]=>0000001=>[7,1]=>[7,1]
[7,4,3,2,1,8,5,6]=>0000000=>[8]=>[8]
[8,4,3,2,1,7,5,6]=>0000000=>[8]=>[8]
[7,4,3,2,1,8,6,5]=>0000000=>[8]=>[8]
[5,6,3,8,2,1,7,4]=>0000000=>[8]=>[8]
[7,5,3,2,8,1,6,4]=>0000000=>[8]=>[8]
[8,5,4,2,7,6,1,3]=>0000000=>[8]=>[8]
[7,5,4,2,8,6,1,3]=>0000000=>[8]=>[8]
[6,5,4,2,7,8,1,3]=>0000000=>[8]=>[8]
[8,5,4,2,6,7,1,3]=>0000000=>[8]=>[8]
[5,6,3,7,2,1,8,4]=>0000000=>[8]=>[8]
[4,6,3,7,2,1,8,5]=>0000000=>[8]=>[8]
[3,6,4,7,2,8,1,5]=>0000000=>[8]=>[8]
[2,6,4,7,3,8,5,1]=>0000000=>[8]=>[8]
[3,5,4,2,7,8,1,6]=>0000000=>[8]=>[8]
[7,4,3,2,1,6,8,5]=>0000000=>[8]=>[8]
[8,4,3,2,1,6,7,5]=>0000000=>[8]=>[8]
[8,4,3,2,1,5,7,6]=>0000000=>[8]=>[8]
[7,4,3,2,1,5,8,6]=>0000000=>[8]=>[8]
[6,4,3,2,1,5,8,7]=>0000010=>[6,2]=>[6,2]
[3,5,4,2,6,8,1,7]=>0000000=>[8]=>[8]
[3,2,6,4,8,5,1,7]=>0000000=>[8]=>[8]
[3,2,5,8,4,6,1,7]=>0000000=>[8]=>[8]
[4,2,1,5,7,3,6,8]=>0000001=>[7,1]=>[7,1]
[4,5,2,3,7,1,6,8]=>0000001=>[7,1]=>[7,1]
[4,2,5,3,8,1,6,7]=>0000000=>[8]=>[8]
[4,2,5,8,3,1,6,7]=>0000000=>[8]=>[8]
[4,1,5,3,8,2,6,7]=>0000000=>[8]=>[8]
[4,3,2,7,5,1,6,8]=>0000001=>[7,1]=>[7,1]
[4,3,6,2,5,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,6,7,1,3,2,5,8]=>0000001=>[7,1]=>[7,1]
[4,5,1,7,3,2,6,8]=>0000001=>[7,1]=>[7,1]
[4,5,1,3,7,2,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,1,4,2,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[2,5,1,4,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[5,2,1,4,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[5,3,1,4,2,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[4,3,1,7,5,2,6,8]=>0000001=>[7,1]=>[7,1]
[5,3,6,4,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,3,6,1,7,2,5,8]=>0000001=>[7,1]=>[7,1]
[6,3,4,1,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[6,2,4,1,3,7,8,5]=>0000000=>[8]=>[8]
[3,6,4,1,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,3,1,7,2,5,8]=>0000001=>[7,1]=>[7,1]
[5,3,6,2,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,5,2,7,3,1,6,8]=>0000001=>[7,1]=>[7,1]
[4,6,7,2,3,1,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,2,1,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,1,4,7,5,8]=>0000001=>[7,1]=>[7,1]
[3,6,7,2,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,2,1,4,6,3,8,5]=>0000000=>[8]=>[8]
[7,3,1,4,6,8,2,5]=>0000000=>[8]=>[8]
[3,6,2,1,5,7,4,8]=>0000001=>[7,1]=>[7,1]
[7,4,1,5,6,2,3,8]=>0000001=>[7,1]=>[7,1]
[7,3,1,5,2,6,4,8]=>0000001=>[7,1]=>[7,1]
[7,2,1,5,3,6,8,4]=>0000000=>[8]=>[8]
[6,2,5,1,3,7,8,4]=>0000000=>[8]=>[8]
[6,3,5,1,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[6,4,5,1,7,2,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,5,1,7,2,3,8]=>0000001=>[7,1]=>[7,1]
[3,6,5,1,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[2,4,1,5,3,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,4,5,1,2,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,4,5,2,8,1,7,6]=>0000000=>[8]=>[8]
[2,4,8,6,3,7,1,5]=>0000000=>[8]=>[8]
[1,8,4,6,3,7,2,5]=>1000000=>[1,7]=>[7,1]
[3,5,6,2,7,8,4,1]=>0000000=>[8]=>[8]
[4,5,6,7,2,8,3,1]=>0000000=>[8]=>[8]
[2,5,8,6,7,3,4,1]=>0000000=>[8]=>[8]
[4,5,6,7,2,1,8,3]=>0000000=>[8]=>[8]
[2,5,1,6,7,8,4,3]=>0000000=>[8]=>[8]
[3,4,6,8,1,7,5,2]=>0000000=>[8]=>[8]
[2,4,8,6,1,7,5,3]=>0000000=>[8]=>[8]
[8,2,4,3,7,1,6,5]=>0000000=>[8]=>[8]
[6,1,5,7,3,2,4,8]=>0000001=>[7,1]=>[7,1]
[6,1,5,8,3,2,4,7]=>0000000=>[8]=>[8]
[7,3,2,4,6,1,5,8]=>0000001=>[7,1]=>[7,1]
[5,7,6,1,8,3,4,2]=>0000000=>[8]=>[8]
[3,2,5,1,6,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,8,6,5,1,7,4,2]=>0000000=>[8]=>[8]
[3,7,6,5,1,8,4,2]=>0000000=>[8]=>[8]
[3,2,5,1,6,7,8,4]=>0000000=>[8]=>[8]
[3,2,4,1,6,8,5,7]=>0001000=>[4,4]=>[4,4]
[8,3,2,4,7,6,1,5]=>0000000=>[8]=>[8]
[3,2,5,1,8,4,7,6]=>0000000=>[8]=>[8]
[3,2,5,1,6,7,4,8]=>0000001=>[7,1]=>[7,1]
[8,4,2,3,7,5,1,6]=>0000000=>[8]=>[8]
[5,2,6,1,8,3,7,4]=>0000000=>[8]=>[8]
[5,2,6,1,8,4,7,3]=>0000000=>[8]=>[8]
[7,4,2,3,8,5,1,6]=>0000000=>[8]=>[8]
[8,5,1,6,4,2,3,7]=>0000000=>[8]=>[8]
[8,5,6,1,7,3,4,2]=>0000000=>[8]=>[8]
[3,6,8,5,1,7,4,2]=>0000000=>[8]=>[8]
[3,2,5,1,8,6,7,4]=>0000000=>[8]=>[8]
[3,2,5,1,7,8,6,4]=>0000000=>[8]=>[8]
[4,6,3,7,1,8,5,2]=>0000000=>[8]=>[8]
[4,6,3,7,5,1,8,2]=>0000000=>[8]=>[8]
[4,2,6,1,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[2,5,7,4,1,6,3,8]=>0000001=>[7,1]=>[7,1]
[2,5,7,4,1,6,8,3]=>0000000=>[8]=>[8]
[5,4,7,8,3,1,6,2]=>0000000=>[8]=>[8]
[4,3,7,5,1,8,6,2]=>0000000=>[8]=>[8]
[6,4,3,8,5,1,7,2]=>0000000=>[8]=>[8]
[5,8,4,3,6,1,7,2]=>0000000=>[8]=>[8]
[5,4,8,3,6,1,7,2]=>0000000=>[8]=>[8]
[2,5,4,6,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,2,1,8,5,7,3]=>0000000=>[8]=>[8]
[2,4,1,7,5,8,6,3]=>0000000=>[8]=>[8]
[2,4,1,7,5,3,8,6]=>0000000=>[8]=>[8]
[2,6,4,1,8,5,3,7]=>0000000=>[8]=>[8]
[5,4,8,2,1,6,3,7]=>0000000=>[8]=>[8]
[2,5,8,4,1,6,3,7]=>0000000=>[8]=>[8]
[3,2,5,6,1,8,4,7]=>0000000=>[8]=>[8]
[4,8,3,2,6,1,5,7]=>0000000=>[8]=>[8]
[3,5,2,8,1,6,4,7]=>0000000=>[8]=>[8]
[3,2,1,6,8,5,4,7]=>0010000=>[3,5]=>[5,3]
[3,2,7,1,5,4,8,6]=>0000000=>[8]=>[8]
[3,2,7,1,5,8,6,4]=>0000000=>[8]=>[8]
[3,8,2,5,1,6,7,4]=>0000000=>[8]=>[8]
[4,8,3,2,6,7,1,5]=>0000000=>[8]=>[8]
[4,3,8,2,6,7,1,5]=>0000000=>[8]=>[8]
[4,3,2,6,7,8,1,5]=>0000000=>[8]=>[8]
[4,3,2,6,7,1,5,8]=>0000001=>[7,1]=>[7,1]
[4,3,7,8,2,6,1,5]=>0000000=>[8]=>[8]
[2,5,7,4,8,1,6,3]=>0000000=>[8]=>[8]
[3,2,5,7,1,6,8,4]=>0000000=>[8]=>[8]
[3,2,5,7,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[6,3,2,7,1,5,4,8]=>0000001=>[7,1]=>[7,1]
[6,3,2,7,1,5,8,4]=>0000000=>[8]=>[8]
[6,3,2,7,8,1,5,4]=>0000000=>[8]=>[8]
[6,5,2,1,7,8,4,3]=>0000000=>[8]=>[8]
[6,2,1,8,5,3,7,4]=>0000000=>[8]=>[8]
[6,3,2,7,1,4,8,5]=>0000000=>[8]=>[8]
[6,3,2,1,4,7,8,5]=>0000000=>[8]=>[8]
[6,3,2,1,4,7,5,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,1,7,8,4,6]=>0000000=>[8]=>[8]
[4,6,2,1,8,3,7,5]=>0000000=>[8]=>[8]
[3,2,7,1,4,8,6,5]=>0000000=>[8]=>[8]
[3,5,8,2,1,7,4,6]=>0000000=>[8]=>[8]
[4,8,3,7,2,1,5,6]=>0000000=>[8]=>[8]
[4,3,7,2,8,1,5,6]=>0000000=>[8]=>[8]
[4,3,7,2,1,5,6,8]=>0000001=>[7,1]=>[7,1]
[4,8,3,2,7,1,5,6]=>0000000=>[8]=>[8]
[6,3,2,8,1,4,7,5]=>0000000=>[8]=>[8]
[3,2,1,4,7,5,8,6]=>0011000=>[3,1,4]=>[4,3,1]
[5,3,2,1,8,4,6,7]=>0000000=>[8]=>[8]
[4,8,3,2,1,5,6,7]=>0000000=>[8]=>[8]
[4,3,8,2,1,5,6,7]=>0000000=>[8]=>[8]
[6,2,5,3,4,1,8,7]=>0000010=>[6,2]=>[6,2]
[8,1,7,3,4,2,6,5]=>0000000=>[8]=>[8]
[8,2,7,1,4,3,6,5]=>0000000=>[8]=>[8]
[8,2,3,1,5,4,7,6]=>0000000=>[8]=>[8]
[2,1,8,5,7,3,6,4]=>0100000=>[2,6]=>[6,2]
[3,6,7,8,4,2,5,1]=>0000000=>[8]=>[8]
[5,2,7,8,1,4,6,3]=>0000000=>[8]=>[8]
[2,8,4,5,3,1,6,7]=>0000000=>[8]=>[8]
[2,7,6,8,4,3,5,1]=>0000000=>[8]=>[8]
[4,6,8,5,1,3,2,7]=>0000000=>[8]=>[8]
[2,4,8,3,6,5,1,7]=>0000000=>[8]=>[8]
[1,7,3,8,5,4,6,2]=>1000000=>[1,7]=>[7,1]
[2,8,5,4,3,1,6,7]=>0000000=>[8]=>[8]
[1,4,3,2,8,5,6,7]=>1001000=>[1,3,4]=>[4,3,1]
[6,4,8,2,5,3,1,7]=>0000000=>[8]=>[8]
[6,2,8,4,5,3,1,7]=>0000000=>[8]=>[8]
[5,1,3,2,4,8,6,7]=>0000100=>[5,3]=>[5,3]
[2,8,1,5,3,4,7,6]=>0000000=>[8]=>[8]
[1,4,2,8,5,3,6,7]=>1000000=>[1,7]=>[7,1]
[3,5,1,4,8,2,6,7]=>0000000=>[8]=>[8]
[1,5,2,8,4,3,6,7]=>1000000=>[1,7]=>[7,1]
[1,2,5,4,3,8,6,7]=>1100100=>[1,1,3,3]=>[3,3,1,1]
[1,2,4,8,5,3,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,2,7,8,4,3,6]=>1000000=>[1,7]=>[7,1]
[5,1,2,7,4,8,3,6]=>0000000=>[8]=>[8]
[8,3,5,1,4,7,2,6]=>0000000=>[8]=>[8]
[1,2,8,5,7,4,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,8,7,5,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[2,8,1,4,3,7,6,5]=>0000000=>[8]=>[8]
[7,6,1,4,2,8,3,5]=>0000000=>[8]=>[8]
[7,1,6,2,8,4,3,5]=>0000000=>[8]=>[8]
[1,4,2,7,8,5,3,6]=>1000000=>[1,7]=>[7,1]
[6,1,2,8,4,3,7,5]=>0000000=>[8]=>[8]
[6,4,1,2,8,3,7,5]=>0000000=>[8]=>[8]
[7,6,1,3,2,4,8,5]=>0000000=>[8]=>[8]
[6,7,1,3,2,4,8,5]=>0000000=>[8]=>[8]
[1,2,7,3,5,8,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[5,8,1,3,7,2,4,6]=>0000000=>[8]=>[8]
[1,2,5,8,7,3,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[8,6,1,3,2,4,7,5]=>0000000=>[8]=>[8]
[4,2,8,1,7,3,6,5]=>0000000=>[8]=>[8]
[7,1,2,8,4,3,6,5]=>0000000=>[8]=>[8]
[1,2,8,4,7,5,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,8,7,4,5,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[2,8,1,7,5,3,4,6]=>0000000=>[8]=>[8]
[8,3,7,1,5,2,4,6]=>0000000=>[8]=>[8]
[8,6,1,4,2,7,3,5]=>0000000=>[8]=>[8]
[7,1,2,8,6,4,3,5]=>0000000=>[8]=>[8]
[3,7,4,8,1,6,2,5]=>0000000=>[8]=>[8]
[3,4,8,7,1,6,2,5]=>0000000=>[8]=>[8]
[4,2,8,1,7,6,3,5]=>0000000=>[8]=>[8]
[2,8,1,7,6,4,3,5]=>0000000=>[8]=>[8]
[7,8,3,4,1,5,2,6]=>0000000=>[8]=>[8]
[6,8,3,4,1,7,2,5]=>0000000=>[8]=>[8]
[5,7,3,4,1,8,2,6]=>0000000=>[8]=>[8]
[5,8,3,4,1,7,2,6]=>0000000=>[8]=>[8]
[4,7,3,5,1,6,2,8]=>0000001=>[7,1]=>[7,1]
[4,8,3,5,1,6,2,7]=>0000000=>[8]=>[8]
[4,8,3,5,1,7,2,6]=>0000000=>[8]=>[8]
[4,7,3,5,1,8,2,6]=>0000000=>[8]=>[8]
[5,6,2,3,1,7,4,8]=>0000001=>[7,1]=>[7,1]
[5,6,2,4,1,8,3,7]=>0000000=>[8]=>[8]
[5,6,2,4,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,2,5,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,2,5,1,8,3,7]=>0000000=>[8]=>[8]
[4,5,1,8,3,7,2,6]=>0000000=>[8]=>[8]
[4,6,2,7,3,8,1,5]=>0000000=>[8]=>[8]
[5,6,2,7,3,8,1,4]=>0000000=>[8]=>[8]
[5,6,2,8,4,7,1,3]=>0000000=>[8]=>[8]
[5,6,2,8,3,7,1,4]=>0000000=>[8]=>[8]
[4,6,2,8,3,7,1,5]=>0000000=>[8]=>[8]
[4,5,1,7,3,6,2,8]=>0000001=>[7,1]=>[7,1]
[4,5,1,8,3,6,2,7]=>0000000=>[8]=>[8]
[6,3,8,4,5,7,2,1]=>0000000=>[8]=>[8]
[2,5,8,4,7,6,3,1]=>0000000=>[8]=>[8]
[4,3,8,1,5,6,7,2]=>0000000=>[8]=>[8]
[3,8,7,4,1,6,2,5]=>0000000=>[8]=>[8]
[6,1,8,4,5,7,2,3]=>0000000=>[8]=>[8]
[4,5,7,6,2,3,8,1]=>0000000=>[8]=>[8]
[3,5,7,2,6,4,8,1]=>0000000=>[8]=>[8]
[2,5,7,3,6,4,8,1]=>0000000=>[8]=>[8]
[8,4,3,7,6,1,5,2]=>0000000=>[8]=>[8]
[6,7,2,3,5,4,8,1]=>0000000=>[8]=>[8]
[5,2,7,3,6,4,8,1]=>0000000=>[8]=>[8]
[8,3,4,7,6,1,5,2]=>0000000=>[8]=>[8]
[8,2,4,7,1,6,5,3]=>0000000=>[8]=>[8]
[3,1,4,7,6,8,5,2]=>0000000=>[8]=>[8]
[5,1,7,3,6,8,4,2]=>0000000=>[8]=>[8]
[6,7,1,3,5,8,4,2]=>0000000=>[8]=>[8]
[4,8,3,7,6,1,5,2]=>0000000=>[8]=>[8]
[2,8,4,7,1,6,5,3]=>0000000=>[8]=>[8]
[8,1,4,7,2,6,5,3]=>0000000=>[8]=>[8]
[8,1,3,2,7,6,5,4]=>0000000=>[8]=>[8]
[2,8,3,1,7,6,5,4]=>0000000=>[8]=>[8]
[6,7,1,2,8,5,4,3]=>0000000=>[8]=>[8]
[8,2,3,1,7,6,5,4]=>0000000=>[8]=>[8]
[1,4,2,7,8,6,5,3]=>1000000=>[1,7]=>[7,1]
[8,4,2,7,1,6,5,3]=>0000000=>[8]=>[8]
[8,5,7,2,1,6,4,3]=>0000000=>[8]=>[8]
[1,5,7,2,8,6,4,3]=>1000000=>[1,7]=>[7,1]
[2,5,7,1,8,6,4,3]=>0000000=>[8]=>[8]
[3,5,7,1,6,8,4,2]=>0000000=>[8]=>[8]
[6,7,4,5,8,1,3,2]=>0000000=>[8]=>[8]
[2,5,7,8,1,6,4,3]=>0000000=>[8]=>[8]
[1,5,7,8,2,6,4,3]=>1000000=>[1,7]=>[7,1]
[8,5,7,1,2,6,4,3]=>0000000=>[8]=>[8]
[8,4,1,7,2,6,5,3]=>0000000=>[8]=>[8]
[6,7,2,8,1,5,4,3]=>0000000=>[8]=>[8]
[5,2,7,8,1,6,4,3]=>0000000=>[8]=>[8]
[4,2,8,7,1,6,5,3]=>0000000=>[8]=>[8]
[1,3,8,2,7,6,5,4]=>1000000=>[1,7]=>[7,1]
[8,3,1,2,7,6,5,4]=>0000000=>[8]=>[8]
[8,2,1,3,7,6,5,4]=>0000000=>[8]=>[8]
[2,1,8,3,7,6,5,4]=>0100000=>[2,6]=>[6,2]
[5,1,7,8,2,6,4,3]=>0000000=>[8]=>[8]
[6,7,1,8,2,5,4,3]=>0000000=>[8]=>[8]
[4,8,1,7,2,6,5,3]=>0000000=>[8]=>[8]
[3,8,1,2,7,6,5,4]=>0000000=>[8]=>[8]
[1,8,2,3,7,6,5,4]=>1000000=>[1,7]=>[7,1]
[3,7,1,5,8,2,6,4]=>0000000=>[8]=>[8]
[2,7,1,5,8,3,6,4]=>0000000=>[8]=>[8]
[2,6,5,1,8,3,7,4]=>0000000=>[8]=>[8]
[5,6,4,1,8,7,2,3]=>0000000=>[8]=>[8]
[8,1,4,5,7,6,2,3]=>0000000=>[8]=>[8]
[6,4,5,1,8,7,2,3]=>0000000=>[8]=>[8]
[5,4,6,1,8,7,2,3]=>0000000=>[8]=>[8]
[3,5,6,1,8,2,7,4]=>0000000=>[8]=>[8]
[2,5,6,1,8,3,7,4]=>0000000=>[8]=>[8]
[2,4,6,1,3,8,7,5]=>0000000=>[8]=>[8]
[3,4,6,1,2,8,7,5]=>0000000=>[8]=>[8]
[5,3,6,1,8,2,7,4]=>0000000=>[8]=>[8]
[7,3,1,5,8,2,6,4]=>0000000=>[8]=>[8]
[8,1,3,5,7,2,6,4]=>0000000=>[8]=>[8]
[8,1,2,5,7,3,6,4]=>0000000=>[8]=>[8]
[7,2,1,5,8,3,6,4]=>0000000=>[8]=>[8]
[6,2,5,1,8,3,7,4]=>0000000=>[8]=>[8]
[4,2,6,1,3,8,7,5]=>0000000=>[8]=>[8]
[4,2,5,3,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[6,2,4,1,3,8,7,5]=>0000000=>[8]=>[8]
[7,2,1,4,3,8,6,5]=>0000000=>[8]=>[8]
[8,1,2,4,3,7,6,5]=>0000000=>[8]=>[8]
[8,1,3,4,2,7,6,5]=>0000000=>[8]=>[8]
[7,3,1,4,2,8,6,5]=>0000000=>[8]=>[8]
[4,6,3,1,2,8,7,5]=>0000000=>[8]=>[8]
[2,6,4,1,3,8,7,5]=>0000000=>[8]=>[8]
[2,7,1,4,3,8,6,5]=>0000000=>[8]=>[8]
[8,1,6,7,2,3,5,4]=>0000000=>[8]=>[8]
[4,7,1,2,3,8,6,5]=>0000000=>[8]=>[8]
[3,7,1,2,4,8,6,5]=>0000000=>[8]=>[8]
[2,6,3,1,4,8,7,5]=>0000000=>[8]=>[8]
[3,6,2,1,4,8,7,5]=>0000000=>[8]=>[8]
[5,6,2,1,8,3,7,4]=>0000000=>[8]=>[8]
[6,5,2,1,8,3,7,4]=>0000000=>[8]=>[8]
[8,1,4,2,3,7,6,5]=>0000000=>[8]=>[8]
[7,4,1,2,3,8,6,5]=>0000000=>[8]=>[8]
[5,4,2,3,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,5,2,4,1,8,7,6]=>0000100=>[5,3]=>[5,3]
[7,3,1,2,4,8,6,5]=>0000000=>[8]=>[8]
[8,1,3,2,4,7,6,5]=>0000000=>[8]=>[8]
[7,2,1,3,4,8,6,5]=>0000000=>[8]=>[8]
[2,4,6,3,5,8,7,1]=>0000000=>[8]=>[8]
[4,2,6,5,8,1,3,7]=>0000000=>[8]=>[8]
[2,4,1,6,5,8,3,7]=>0000000=>[8]=>[8]
[2,6,4,3,8,7,5,1]=>0000000=>[8]=>[8]
[4,2,6,8,5,3,7,1]=>0000000=>[8]=>[8]
[2,4,6,8,1,5,7,3]=>0000000=>[8]=>[8]
[2,1,4,6,8,5,3,7]=>0100000=>[2,6]=>[6,2]
[2,4,6,1,8,5,3,7]=>0000000=>[8]=>[8]
[2,4,6,8,1,5,3,7]=>0000000=>[8]=>[8]
[2,4,6,8,3,5,7,1]=>0000000=>[8]=>[8]
[2,4,6,3,8,5,7,1]=>0000000=>[8]=>[8]
[2,4,3,6,8,5,7,1]=>0000000=>[8]=>[8]
[2,4,3,6,8,5,1,7]=>0000000=>[8]=>[8]
[2,4,3,6,8,1,5,7]=>0000000=>[8]=>[8]
[4,6,5,2,8,7,1,3]=>0000000=>[8]=>[8]
[2,6,4,1,8,7,5,3]=>0000000=>[8]=>[8]
[1,3,7,4,5,8,2,6]=>1000000=>[1,7]=>[7,1]
[1,7,6,3,4,8,2,5]=>1000000=>[1,7]=>[7,1]
[8,1,6,3,7,2,4,5]=>0000000=>[8]=>[8]
[1,2,7,4,8,3,5,6]=>1100000=>[1,1,6]=>[6,1,1]
[6,1,7,3,4,8,2,5]=>0000000=>[8]=>[8]
[2,1,7,4,5,8,3,6]=>0100000=>[2,6]=>[6,2]
[5,1,4,7,3,8,2,6]=>0000000=>[8]=>[8]
[4,3,1,7,5,8,2,6]=>0000000=>[8]=>[8]
[2,8,6,3,7,1,4,5]=>0000000=>[8]=>[8]
[6,8,1,3,7,2,4,5]=>0000000=>[8]=>[8]
[5,8,2,1,7,3,4,6]=>0000000=>[8]=>[8]
[5,7,2,1,8,3,4,6]=>0000000=>[8]=>[8]
[6,7,1,3,8,2,4,5]=>0000000=>[8]=>[8]
[8,5,1,3,7,2,4,6]=>0000000=>[8]=>[8]
[1,5,3,2,8,4,6,7]=>1000000=>[1,7]=>[7,1]
[2,6,4,8,7,1,3,5]=>0000000=>[8]=>[8]
[1,6,4,8,7,2,3,5]=>1000000=>[1,7]=>[7,1]
[4,3,2,8,7,1,5,6]=>0000000=>[8]=>[8]
[5,2,4,8,7,1,3,6]=>0000000=>[8]=>[8]
[6,2,8,3,7,1,4,5]=>0000000=>[8]=>[8]
[5,1,4,8,7,2,3,6]=>0000000=>[8]=>[8]
[3,7,2,1,5,4,8,6]=>0000000=>[8]=>[8]
[3,8,2,1,5,4,7,6]=>0000000=>[8]=>[8]
[8,3,2,1,5,4,6,7]=>0000000=>[8]=>[8]
[8,3,2,1,6,4,5,7]=>0000000=>[8]=>[8]
[8,4,2,5,1,6,3,7]=>0000000=>[8]=>[8]
[8,3,2,1,4,6,5,7]=>0000000=>[8]=>[8]
[3,8,2,1,4,5,7,6]=>0000000=>[8]=>[8]
[3,2,7,1,4,6,8,5]=>0000000=>[8]=>[8]
[3,2,8,1,4,6,7,5]=>0000000=>[8]=>[8]
[3,8,2,1,4,7,5,6]=>0000000=>[8]=>[8]
[3,8,2,1,5,7,4,6]=>0000000=>[8]=>[8]
[4,8,2,5,1,7,3,6]=>0000000=>[8]=>[8]
[4,7,2,5,1,8,3,6]=>0000000=>[8]=>[8]
[3,7,2,1,5,8,4,6]=>0000000=>[8]=>[8]
[3,7,2,1,4,8,5,6]=>0000000=>[8]=>[8]
[3,2,1,7,5,8,6,4]=>0010000=>[3,5]=>[5,3]
[4,2,7,6,1,8,3,5]=>0000000=>[8]=>[8]
[4,3,7,6,8,1,2,5]=>0000000=>[8]=>[8]
[4,3,8,6,7,1,2,5]=>0000000=>[8]=>[8]
[3,8,2,1,7,4,5,6]=>0000000=>[8]=>[8]
[3,2,8,1,6,4,7,5]=>0000000=>[8]=>[8]
[3,2,7,1,6,4,8,5]=>0000000=>[8]=>[8]
[4,2,7,6,1,3,8,5]=>0000000=>[8]=>[8]
[4,2,8,6,1,3,7,5]=>0000000=>[8]=>[8]
[5,7,8,3,4,1,2,6]=>0000000=>[8]=>[8]
[4,2,6,8,1,3,7,5]=>0000000=>[8]=>[8]
[4,2,6,7,1,3,8,5]=>0000000=>[8]=>[8]
[3,2,6,1,8,4,7,5]=>0000000=>[8]=>[8]
[3,7,2,1,8,5,4,6]=>0000000=>[8]=>[8]
[4,7,3,8,5,1,2,6]=>0000000=>[8]=>[8]
[4,3,7,8,6,1,2,5]=>0000000=>[8]=>[8]
[3,2,7,1,8,6,4,5]=>0000000=>[8]=>[8]
[3,2,1,6,8,5,7,4]=>0010000=>[3,5]=>[5,3]
[3,2,6,1,8,7,4,5]=>0000000=>[8]=>[8]
[4,2,6,8,1,7,3,5]=>0000000=>[8]=>[8]
[4,3,6,8,7,1,2,5]=>0000000=>[8]=>[8]
[4,2,6,7,1,8,3,5]=>0000000=>[8]=>[8]
[3,2,6,1,7,8,4,5]=>0000000=>[8]=>[8]
[5,3,6,4,8,7,1,2]=>0000000=>[8]=>[8]
[1,4,6,2,7,8,5,3]=>1000000=>[1,7]=>[7,1]
[3,1,8,5,4,2,6,7]=>0000000=>[8]=>[8]
[1,2,7,5,4,8,6,3]=>1100000=>[1,1,6]=>[6,1,1]
[6,3,7,5,4,8,1,2]=>0000000=>[8]=>[8]
[1,6,2,5,4,8,7,3]=>1000000=>[1,7]=>[7,1]
[1,8,2,5,7,3,6,4]=>1000000=>[1,7]=>[7,1]
[6,2,1,5,4,8,7,3]=>0000000=>[8]=>[8]
[4,1,6,2,8,7,5,3]=>0000000=>[8]=>[8]
[7,8,3,1,4,2,6,5]=>0000000=>[8]=>[8]
[4,3,6,1,8,2,7,5]=>0000000=>[8]=>[8]
[7,5,1,6,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[6,1,5,7,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[1,5,8,6,4,3,2,7]=>1000000=>[1,7]=>[7,1]
[7,8,5,1,6,3,2,4]=>0000000=>[8]=>[8]
[2,6,1,5,7,3,8,4]=>0000000=>[8]=>[8]
[1,6,8,7,4,3,2,5]=>1000000=>[1,7]=>[7,1]
[6,8,1,7,4,3,2,5]=>0000000=>[8]=>[8]
[5,6,1,7,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[5,1,7,6,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[6,1,7,8,4,3,2,5]=>0000000=>[8]=>[8]
[7,1,8,6,4,3,2,5]=>0000000=>[8]=>[8]
[7,2,1,5,4,6,8,3]=>0000000=>[8]=>[8]
[1,2,8,5,6,3,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[6,1,2,5,7,3,8,4]=>0000000=>[8]=>[8]
[4,3,6,1,5,7,2,8]=>0000001=>[7,1]=>[7,1]
[1,3,6,8,5,7,2,4]=>1000000=>[1,7]=>[7,1]
[1,3,6,4,8,7,2,5]=>1000000=>[1,7]=>[7,1]
[4,1,6,7,3,8,2,5]=>0000000=>[8]=>[8]
[5,4,6,1,3,7,2,8]=>0000001=>[7,1]=>[7,1]
[6,4,1,5,2,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,1,7,5,2,3,8,6]=>0000000=>[8]=>[8]
[2,8,3,5,4,1,7,6]=>0000000=>[8]=>[8]
[7,8,1,4,6,3,2,5]=>0000000=>[8]=>[8]
[5,1,8,7,4,3,2,6]=>0000000=>[8]=>[8]
[6,5,1,8,4,3,2,7]=>0000000=>[8]=>[8]
[6,5,7,1,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[7,5,8,1,4,3,2,6]=>0000000=>[8]=>[8]
[1,5,7,8,4,3,2,6]=>1000000=>[1,7]=>[7,1]
[2,4,7,5,1,3,8,6]=>0000000=>[8]=>[8]
[7,8,4,6,1,3,2,5]=>0000000=>[8]=>[8]
[1,6,5,8,4,3,2,7]=>1000000=>[1,7]=>[7,1]
[6,8,5,1,4,3,2,7]=>0000000=>[8]=>[8]
[3,6,2,5,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,3,6,2,8,1,5,7]=>0000000=>[8]=>[8]
[6,1,2,5,4,7,8,3]=>0000000=>[8]=>[8]
[6,2,4,5,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,2,8,5,1,3,7,6]=>0000000=>[8]=>[8]
[4,3,6,8,1,7,2,5]=>0000000=>[8]=>[8]
[5,3,6,4,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[1,6,7,4,8,3,5,2]=>1000000=>[1,7]=>[7,1]
[1,4,6,3,7,5,8,2]=>1000000=>[1,7]=>[7,1]
[4,6,7,2,5,8,1,3]=>0000000=>[8]=>[8]
[2,4,6,1,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[2,7,5,4,1,6,3,8]=>0000001=>[7,1]=>[7,1]
[1,7,5,4,3,8,6,2]=>1000000=>[1,7]=>[7,1]
[1,5,8,4,3,6,7,2]=>1000000=>[1,7]=>[7,1]
[5,4,6,2,7,8,1,3]=>0000000=>[8]=>[8]
[2,5,4,1,6,7,3,8]=>0000001=>[7,1]=>[7,1]
[5,6,3,2,7,1,4,8]=>0000001=>[7,1]=>[7,1]
[5,6,3,2,7,1,8,4]=>0000000=>[8]=>[8]
[8,5,6,3,2,7,1,4]=>0000000=>[8]=>[8]
[5,4,6,2,8,1,7,3]=>0000000=>[8]=>[8]
[2,4,1,7,8,5,3,6]=>0000000=>[8]=>[8]
[5,6,3,2,1,8,4,7]=>0000000=>[8]=>[8]
[3,5,2,1,6,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,8,4,3,2,1,5,7]=>0000000=>[8]=>[8]
[5,3,8,2,1,6,4,7]=>0000000=>[8]=>[8]
[7,3,2,8,5,1,6,4]=>0000000=>[8]=>[8]
[8,4,6,3,2,1,7,5]=>0000000=>[8]=>[8]
[5,4,7,2,1,8,6,3]=>0000000=>[8]=>[8]
[5,7,3,2,1,6,8,4]=>0000000=>[8]=>[8]
[6,3,7,2,5,1,8,4]=>0000000=>[8]=>[8]
[6,7,8,3,5,2,1,4]=>0000000=>[8]=>[8]
[6,2,5,7,8,4,1,3]=>0000000=>[8]=>[8]
[2,1,5,7,8,6,3,4]=>0100000=>[2,6]=>[6,2]
[3,6,7,2,8,1,4,5]=>0000000=>[8]=>[8]
[3,2,6,1,7,4,5,8]=>0000001=>[7,1]=>[7,1]
[2,5,8,4,1,3,7,6]=>0000000=>[8]=>[8]
[2,4,1,7,8,3,6,5]=>0000000=>[8]=>[8]
[3,6,8,2,1,7,4,5]=>0000000=>[8]=>[8]
[5,3,8,2,1,4,7,6]=>0000000=>[8]=>[8]
[4,8,7,3,2,1,5,6]=>0000000=>[8]=>[8]
[4,7,3,2,1,5,6,8]=>0000001=>[7,1]=>[7,1]
[8,4,7,3,2,1,5,6]=>0000000=>[8]=>[8]
[8,3,5,2,1,4,7,6]=>0000000=>[8]=>[8]
[3,5,2,1,4,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[2,7,6,5,1,8,3,4]=>0000000=>[8]=>[8]
[2,7,6,5,1,8,4,3]=>0000000=>[8]=>[8]
[7,3,5,1,8,4,2,6]=>0000000=>[8]=>[8]
[2,3,4,8,7,6,1,5]=>0000000=>[8]=>[8]
[2,1,4,5,8,7,3,6]=>0100000=>[2,6]=>[6,2]
[6,4,3,5,8,7,1,2]=>0000000=>[8]=>[8]
[5,7,3,6,1,8,4,2]=>0000000=>[8]=>[8]
[2,3,4,8,7,1,6,5]=>0000000=>[8]=>[8]
[6,1,4,2,8,5,7,3]=>0000000=>[8]=>[8]
[1,3,8,5,7,6,2,4]=>1000000=>[1,7]=>[7,1]
[8,6,1,5,7,2,3,4]=>0000000=>[8]=>[8]
[3,2,8,5,7,6,1,4]=>0000000=>[8]=>[8]
[7,8,5,4,1,6,2,3]=>0000000=>[8]=>[8]
[7,2,6,4,5,1,8,3]=>0000000=>[8]=>[8]
[3,8,2,7,6,1,5,4]=>0000000=>[8]=>[8]
[4,8,7,2,6,5,3,1]=>0000000=>[8]=>[8]
[4,8,7,3,1,6,5,2]=>0000000=>[8]=>[8]
[4,8,7,3,2,6,1,5]=>0000000=>[8]=>[8]
[4,8,7,3,2,6,5,1]=>0000000=>[8]=>[8]
[4,8,7,3,6,2,5,1]=>0000000=>[8]=>[8]
[4,8,7,3,6,1,5,2]=>0000000=>[8]=>[8]
[5,8,7,6,3,4,2,1]=>0000000=>[8]=>[8]
[5,8,7,6,3,1,4,2]=>0000000=>[8]=>[8]
[5,8,7,6,2,4,3,1]=>0000000=>[8]=>[8]
[5,8,7,6,4,2,1,3]=>0000000=>[8]=>[8]
[5,8,7,6,4,1,3,2]=>0000000=>[8]=>[8]
[5,8,7,6,4,3,1,2]=>0000000=>[8]=>[8]
[7,3,5,2,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[7,2,1,5,6,4,3,8]=>0000001=>[7,1]=>[7,1]
[6,2,1,5,7,4,8,3]=>0000000=>[8]=>[8]
[3,2,1,5,7,4,8,6]=>0010000=>[3,5]=>[5,3]
[2,4,6,7,3,8,1,5]=>0000000=>[8]=>[8]
[1,4,6,7,3,8,5,2]=>1000000=>[1,7]=>[7,1]
[3,2,1,6,7,8,4,5]=>0010000=>[3,5]=>[5,3]
[5,2,1,6,7,8,4,3]=>0000000=>[8]=>[8]
[5,3,6,1,7,8,4,2]=>0000000=>[8]=>[8]
[4,3,6,2,7,8,5,1]=>0000000=>[8]=>[8]
[4,2,1,5,7,3,8,6]=>0000000=>[8]=>[8]
[1,5,6,7,8,2,4,3]=>1000000=>[1,7]=>[7,1]
[1,5,6,7,8,4,2,3]=>1000000=>[1,7]=>[7,1]
[4,3,6,1,7,8,5,2]=>0000000=>[8]=>[8]
[1,4,3,6,2,5,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,4,3,7,2,5,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,3,7,6,8,2,5]=>1000000=>[1,7]=>[7,1]
[1,4,3,7,5,8,2,6]=>1000000=>[1,7]=>[7,1]
[1,5,3,7,4,8,2,6]=>1000000=>[1,7]=>[7,1]
[1,5,4,8,2,6,3,7]=>1000000=>[1,7]=>[7,1]
[1,5,4,8,3,7,2,6]=>1000000=>[1,7]=>[7,1]
[1,2,3,6,5,8,4,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[7,8,1,4,5,3,6,2]=>0000000=>[8]=>[8]
[5,8,1,4,7,6,3,2]=>0000000=>[8]=>[8]
[7,5,1,8,6,2,4,3]=>0000000=>[8]=>[8]
[7,4,1,8,2,6,3,5]=>0000000=>[8]=>[8]
[7,1,8,4,2,6,3,5]=>0000000=>[8]=>[8]
[7,3,1,8,4,2,6,5]=>0000000=>[8]=>[8]
[7,2,8,3,6,5,1,4]=>0000000=>[8]=>[8]
[7,2,8,3,6,1,5,4]=>0000000=>[8]=>[8]
[6,1,2,8,3,5,4,7]=>0000000=>[8]=>[8]
[5,2,3,8,1,4,7,6]=>0000000=>[8]=>[8]
[6,2,4,1,8,7,3,5]=>0000000=>[8]=>[8]
[3,1,6,4,2,8,5,7]=>0000000=>[8]=>[8]
[2,6,3,8,7,1,5,4]=>0000000=>[8]=>[8]
[2,6,3,8,5,1,4,7]=>0000000=>[8]=>[8]
[2,5,1,8,3,4,7,6]=>0000000=>[8]=>[8]
[1,2,5,3,8,4,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,8,3,7,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[2,4,8,3,7,1,6,5]=>0000000=>[8]=>[8]
[2,4,8,3,7,6,1,5]=>0000000=>[8]=>[8]
[2,5,3,8,1,7,4,6]=>0000000=>[8]=>[8]
[2,5,4,1,3,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,1,5,4,8,2,7,6]=>0000000=>[8]=>[8]
[5,3,1,4,8,2,7,6]=>0000000=>[8]=>[8]
[5,2,3,8,4,7,1,6]=>0000000=>[8]=>[8]
[4,8,2,3,7,6,1,5]=>0000000=>[8]=>[8]
[4,8,2,3,7,1,6,5]=>0000000=>[8]=>[8]
[4,8,1,2,3,7,6,5]=>0000000=>[8]=>[8]
[1,4,8,3,7,2,6,5]=>1000000=>[1,7]=>[7,1]
[6,3,8,1,5,2,4,7]=>0000000=>[8]=>[8]
[5,3,8,1,2,4,7,6]=>0000000=>[8]=>[8]
[5,1,3,8,2,4,7,6]=>0000000=>[8]=>[8]
[1,5,3,8,2,4,7,6]=>1000000=>[1,7]=>[7,1]
[1,5,4,8,2,7,6,3]=>1000000=>[1,7]=>[7,1]
[5,1,4,8,2,7,6,3]=>0000000=>[8]=>[8]
[5,4,8,1,2,7,6,3]=>0000000=>[8]=>[8]
[6,5,1,2,8,7,4,3]=>0000000=>[8]=>[8]
[4,1,5,8,2,7,6,3]=>0000000=>[8]=>[8]
[4,1,2,5,8,7,6,3]=>0000000=>[8]=>[8]
[1,4,2,5,8,7,6,3]=>1000000=>[1,7]=>[7,1]
[1,3,5,2,8,7,4,6]=>1000000=>[1,7]=>[7,1]
[3,5,1,2,8,7,4,6]=>0000000=>[8]=>[8]
[4,2,6,1,8,7,3,5]=>0000000=>[8]=>[8]
[4,3,1,5,8,2,7,6]=>0000000=>[8]=>[8]
[3,5,2,8,7,1,4,6]=>0000000=>[8]=>[8]
[3,4,8,7,2,6,1,5]=>0000000=>[8]=>[8]
[3,4,8,1,7,2,6,5]=>0000000=>[8]=>[8]
[1,3,4,8,7,2,6,5]=>1000000=>[1,7]=>[7,1]
[1,3,4,8,2,7,6,5]=>1000000=>[1,7]=>[7,1]
[3,4,8,1,2,7,6,5]=>0000000=>[8]=>[8]
[3,4,8,2,7,1,6,5]=>0000000=>[8]=>[8]
[3,4,8,2,7,6,1,5]=>0000000=>[8]=>[8]
[4,2,5,8,1,7,6,3]=>0000000=>[8]=>[8]
[4,3,1,2,5,8,7,6]=>0001100=>[4,1,3]=>[4,3,1]
[3,1,4,2,5,8,7,6]=>0001100=>[4,1,3]=>[4,3,1]
[2,3,5,1,8,7,6,4]=>0000000=>[8]=>[8]
[7,8,2,1,5,3,6,4]=>0000000=>[8]=>[8]
[6,4,1,2,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[2,3,7,5,4,1,8,6]=>0000000=>[8]=>[8]
[6,3,1,5,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[7,8,1,5,4,2,6,3]=>0000000=>[8]=>[8]
[7,8,3,5,4,1,6,2]=>0000000=>[8]=>[8]
[7,8,2,5,4,1,3,6]=>0000000=>[8]=>[8]
[7,8,2,5,4,6,1,3]=>0000000=>[8]=>[8]
[6,2,1,5,4,7,3,8]=>0000001=>[7,1]=>[7,1]
[5,3,6,2,4,7,1,8]=>0000001=>[7,1]=>[7,1]
[6,4,2,1,7,3,8,5]=>0000000=>[8]=>[8]
[2,7,6,5,3,1,4,8]=>0000001=>[7,1]=>[7,1]
[3,7,6,4,8,5,1,2]=>0000000=>[8]=>[8]
[5,7,6,3,8,4,1,2]=>0000000=>[8]=>[8]
[5,1,6,2,4,8,3,7]=>0000000=>[8]=>[8]
[4,7,6,5,2,1,3,8]=>0000001=>[7,1]=>[7,1]
[4,7,6,5,2,8,1,3]=>0000000=>[8]=>[8]
[4,7,6,5,1,8,3,2]=>0000000=>[8]=>[8]
[1,7,6,5,2,8,3,4]=>1000000=>[1,7]=>[7,1]
[1,7,6,5,3,2,8,4]=>1000000=>[1,7]=>[7,1]
[4,7,6,5,1,2,8,3]=>0000000=>[8]=>[8]
[4,7,6,5,3,1,8,2]=>0000000=>[8]=>[8]
[5,2,6,3,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,1,6,2,4,7,8,3]=>0000000=>[8]=>[8]
[1,7,2,4,8,3,6,5]=>1000000=>[1,7]=>[7,1]
[4,7,2,1,5,3,6,8]=>0000001=>[7,1]=>[7,1]
[4,7,1,6,2,3,8,5]=>0000000=>[8]=>[8]
[1,7,2,6,8,3,5,4]=>1000000=>[1,7]=>[7,1]
[1,2,6,7,4,8,5,3]=>1100000=>[1,1,6]=>[6,1,1]
[3,1,6,7,4,2,8,5]=>0000000=>[8]=>[8]
[3,2,8,5,4,6,1,7]=>0000000=>[8]=>[8]
[4,7,6,3,5,8,1,2]=>0000000=>[8]=>[8]
[3,7,6,5,2,4,1,8]=>0000001=>[7,1]=>[7,1]
[3,7,6,5,2,1,8,4]=>0000000=>[8]=>[8]
[1,7,6,5,8,2,4,3]=>1000000=>[1,7]=>[7,1]
[3,7,6,5,8,1,4,2]=>0000000=>[8]=>[8]
[3,7,6,5,1,2,4,8]=>0000001=>[7,1]=>[7,1]
[3,1,6,8,4,2,5,7]=>0000000=>[8]=>[8]
[4,7,6,8,3,5,1,2]=>0000000=>[8]=>[8]
[2,7,6,5,8,1,3,4]=>0000000=>[8]=>[8]
[2,7,6,5,8,4,1,3]=>0000000=>[8]=>[8]
[3,7,5,8,2,4,1,6]=>0000000=>[8]=>[8]
[5,1,7,8,4,3,2,6]=>0000000=>[8]=>[8]
[4,7,1,8,3,6,2,5]=>0000000=>[8]=>[8]
[7,1,2,3,8,6,5,4]=>0000000=>[8]=>[8]
[6,8,1,4,3,7,2,5]=>0000000=>[8]=>[8]
[8,7,3,2,4,1,6,5]=>0000000=>[8]=>[8]
[7,1,2,3,6,8,5,4]=>0000000=>[8]=>[8]
[3,8,7,1,4,2,6,5]=>0000000=>[8]=>[8]
[5,8,3,7,1,4,2,6]=>0000000=>[8]=>[8]
[7,1,2,3,5,6,8,4]=>0000000=>[8]=>[8]
[5,1,2,3,7,8,6,4]=>0000000=>[8]=>[8]
[8,6,3,2,4,7,1,5]=>0000000=>[8]=>[8]
[7,8,1,2,6,3,5,4]=>0000000=>[8]=>[8]
[1,4,8,2,7,3,5,6]=>1000000=>[1,7]=>[7,1]
[1,2,8,5,4,7,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[2,3,6,8,4,7,1,5]=>0000000=>[8]=>[8]
[1,3,6,8,4,7,5,2]=>1000000=>[1,7]=>[7,1]
[2,4,8,1,7,3,6,5]=>0000000=>[8]=>[8]
[3,4,8,5,7,6,1,2]=>0000000=>[8]=>[8]
[1,2,6,8,4,5,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[7,5,1,2,4,3,6,8]=>0000001=>[7,1]=>[7,1]
[7,4,6,1,5,2,3,8]=>0000001=>[7,1]=>[7,1]
[6,8,1,4,7,2,3,5]=>0000000=>[8]=>[8]
[1,6,4,2,8,3,5,7]=>1000000=>[1,7]=>[7,1]
[1,6,3,8,5,4,2,7]=>1000000=>[1,7]=>[7,1]
[7,1,3,6,5,4,2,8]=>0000001=>[7,1]=>[7,1]
[7,2,1,4,6,3,5,8]=>0000001=>[7,1]=>[7,1]
[7,2,3,6,5,1,4,8]=>0000001=>[7,1]=>[7,1]
[7,1,2,3,6,5,4,8]=>0000001=>[7,1]=>[7,1]
[6,8,1,2,7,3,5,4]=>0000000=>[8]=>[8]
[1,6,2,3,8,5,4,7]=>1000000=>[1,7]=>[7,1]
[1,5,8,2,7,6,3,4]=>1000000=>[1,7]=>[7,1]
[5,8,2,7,6,3,4,1]=>0000000=>[8]=>[8]
[6,2,8,1,7,3,5,4]=>0000000=>[8]=>[8]
[3,6,4,1,2,8,5,7]=>0000000=>[8]=>[8]
[2,5,1,8,7,6,3,4]=>0000000=>[8]=>[8]
[1,2,5,3,8,7,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[2,5,3,8,7,1,6,4]=>0000000=>[8]=>[8]
[2,5,8,4,1,7,6,3]=>0000000=>[8]=>[8]
[3,5,8,7,1,4,2,6]=>0000000=>[8]=>[8]
[5,3,8,4,1,7,6,2]=>0000000=>[8]=>[8]
[4,2,8,7,6,3,5,1]=>0000000=>[8]=>[8]
[6,3,1,8,7,2,5,4]=>0000000=>[8]=>[8]
[5,1,3,8,7,6,2,4]=>0000000=>[8]=>[8]
[1,5,3,8,7,6,2,4]=>1000000=>[1,7]=>[7,1]
[5,1,8,4,7,2,6,3]=>0000000=>[8]=>[8]
[5,8,7,4,6,1,2,3]=>0000000=>[8]=>[8]
[6,8,5,1,2,4,7,3]=>0000000=>[8]=>[8]
[4,5,8,1,7,2,6,3]=>0000000=>[8]=>[8]
[1,3,2,5,8,7,4,6]=>1010000=>[1,2,5]=>[5,2,1]
[3,5,1,8,7,4,6,2]=>0000000=>[8]=>[8]
[4,3,6,1,2,8,5,7]=>0000000=>[8]=>[8]
[4,5,8,3,1,7,2,6]=>0000000=>[8]=>[8]
[4,5,2,8,7,1,3,6]=>0000000=>[8]=>[8]
[3,2,5,8,7,1,6,4]=>0000000=>[8]=>[8]
[3,4,8,7,6,2,1,5]=>0000000=>[8]=>[8]
[3,4,8,7,6,5,1,2]=>0000000=>[8]=>[8]
[1,3,4,8,7,6,2,5]=>1000000=>[1,7]=>[7,1]
[3,4,8,7,6,2,5,1]=>0000000=>[8]=>[8]
[3,2,5,8,7,4,6,1]=>0000000=>[8]=>[8]
[2,1,3,5,8,7,4,6]=>0110000=>[2,1,5]=>[5,2,1]
[1,2,7,5,8,6,4,3]=>1100000=>[1,1,6]=>[6,1,1]
[6,8,1,3,7,5,2,4]=>0000000=>[8]=>[8]
[1,3,7,8,2,6,5,4]=>1000000=>[1,7]=>[7,1]
[2,7,8,1,3,6,5,4]=>0000000=>[8]=>[8]
[8,1,2,6,7,3,5,4]=>0000000=>[8]=>[8]
[8,1,2,6,7,5,3,4]=>0000000=>[8]=>[8]
[8,2,5,7,1,3,6,4]=>0000000=>[8]=>[8]
[2,8,1,6,7,3,5,4]=>0000000=>[8]=>[8]
[2,6,8,3,7,1,5,4]=>0000000=>[8]=>[8]
[2,8,6,4,7,1,5,3]=>0000000=>[8]=>[8]
[6,8,3,4,1,7,5,2]=>0000000=>[8]=>[8]
[6,8,3,7,4,1,5,2]=>0000000=>[8]=>[8]
[8,2,5,7,1,6,3,4]=>0000000=>[8]=>[8]
[8,4,7,2,3,6,1,5]=>0000000=>[8]=>[8]
[8,5,7,4,2,6,1,3]=>0000000=>[8]=>[8]
[8,3,5,7,4,1,6,2]=>0000000=>[8]=>[8]
[8,5,2,4,7,1,6,3]=>0000000=>[8]=>[8]
[8,2,4,7,3,6,1,5]=>0000000=>[8]=>[8]
[8,2,7,1,4,6,3,5]=>0000000=>[8]=>[8]
[8,7,1,2,4,6,3,5]=>0000000=>[8]=>[8]
[8,7,1,4,6,2,3,5]=>0000000=>[8]=>[8]
[8,4,7,1,3,6,2,5]=>0000000=>[8]=>[8]
[8,3,5,7,1,2,6,4]=>0000000=>[8]=>[8]
[5,8,7,1,3,6,2,4]=>0000000=>[8]=>[8]
[8,5,4,7,1,6,2,3]=>0000000=>[8]=>[8]
[8,5,4,7,1,2,6,3]=>0000000=>[8]=>[8]
[8,5,1,4,7,2,6,3]=>0000000=>[8]=>[8]
[8,5,6,3,1,7,4,2]=>0000000=>[8]=>[8]
[1,8,4,5,7,2,6,3]=>1000000=>[1,7]=>[7,1]
[5,8,7,3,6,1,2,4]=>0000000=>[8]=>[8]
[8,3,5,7,1,6,2,4]=>0000000=>[8]=>[8]
[1,6,8,3,7,5,2,4]=>1000000=>[1,7]=>[7,1]
[6,3,8,2,7,5,1,4]=>0000000=>[8]=>[8]
[8,6,4,7,3,1,5,2]=>0000000=>[8]=>[8]
[8,4,5,7,3,1,6,2]=>0000000=>[8]=>[8]
[8,3,4,7,2,6,1,5]=>0000000=>[8]=>[8]
[8,7,1,3,4,6,2,5]=>0000000=>[8]=>[8]
[8,3,7,2,4,6,1,5]=>0000000=>[8]=>[8]
[2,8,4,5,7,1,6,3]=>0000000=>[8]=>[8]
[8,7,3,4,5,1,6,2]=>0000000=>[8]=>[8]
[8,7,4,5,2,6,1,3]=>0000000=>[8]=>[8]
[8,7,2,3,4,6,1,5]=>0000000=>[8]=>[8]
[8,6,5,1,3,2,7,4]=>0000000=>[8]=>[8]
[8,6,3,1,7,2,4,5]=>0000000=>[8]=>[8]
[8,7,3,1,5,2,4,6]=>0000000=>[8]=>[8]
[8,6,1,2,4,7,3,5]=>0000000=>[8]=>[8]
[8,6,1,5,3,4,7,2]=>0000000=>[8]=>[8]
[8,6,1,5,2,4,7,3]=>0000000=>[8]=>[8]
[8,6,1,2,5,7,3,4]=>0000000=>[8]=>[8]
[5,1,4,2,3,8,6,7]=>0000100=>[5,3]=>[5,3]
[5,1,4,2,7,3,6,8]=>0000001=>[7,1]=>[7,1]
[5,7,8,1,2,4,6,3]=>0000000=>[8]=>[8]
[5,7,8,1,3,4,6,2]=>0000000=>[8]=>[8]
[5,8,1,7,3,4,6,2]=>0000000=>[8]=>[8]
[8,1,5,7,2,4,6,3]=>0000000=>[8]=>[8]
[1,4,2,3,8,7,5,6]=>1001000=>[1,3,4]=>[4,3,1]
[1,4,2,7,6,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[6,1,2,8,7,5,3,4]=>0000000=>[8]=>[8]
[6,1,2,4,8,7,5,3]=>0000000=>[8]=>[8]
[3,1,8,4,6,7,5,2]=>0000000=>[8]=>[8]
[3,1,7,6,4,8,5,2]=>0000000=>[8]=>[8]
[7,1,2,4,6,8,5,3]=>0000000=>[8]=>[8]
[7,1,2,6,8,5,3,4]=>0000000=>[8]=>[8]
[7,1,5,3,2,8,6,4]=>0000000=>[8]=>[8]
[8,1,7,5,3,2,6,4]=>0000000=>[8]=>[8]
[8,3,7,1,2,6,4,5]=>0000000=>[8]=>[8]
[3,1,2,8,4,7,5,6]=>0010000=>[3,5]=>[5,3]
[1,4,2,3,8,6,5,7]=>1001000=>[1,3,4]=>[4,3,1]
[1,4,2,3,8,5,7,6]=>1001000=>[1,3,4]=>[4,3,1]
[5,8,1,7,2,4,6,3]=>0000000=>[8]=>[8]
[5,8,1,3,4,7,6,2]=>0000000=>[8]=>[8]
[3,1,8,6,4,7,5,2]=>0000000=>[8]=>[8]
[8,1,2,6,7,4,5,3]=>0000000=>[8]=>[8]
[1,2,3,5,8,4,7,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,5,8,6,4,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[7,1,2,8,3,6,5,4]=>0000000=>[8]=>[8]
[7,1,2,8,6,4,5,3]=>0000000=>[8]=>[8]
[3,1,7,8,4,6,5,2]=>0000000=>[8]=>[8]
[8,1,2,7,4,6,5,3]=>0000000=>[8]=>[8]
[8,1,2,7,3,6,5,4]=>0000000=>[8]=>[8]
[1,2,3,6,8,5,4,7]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[5,4,8,3,2,7,6,1]=>0000000=>[8]=>[8]
[2,1,5,8,4,7,6,3]=>0100000=>[2,6]=>[6,2]
[8,3,2,6,7,5,4,1]=>0000000=>[8]=>[8]
[8,4,5,3,2,7,6,1]=>0000000=>[8]=>[8]
[8,4,6,3,7,5,2,1]=>0000000=>[8]=>[8]
[3,6,2,8,7,5,4,1]=>0000000=>[8]=>[8]
[1,6,4,8,2,5,3,7]=>1000000=>[1,7]=>[7,1]
[1,6,5,8,2,4,3,7]=>1000000=>[1,7]=>[7,1]
[1,6,8,2,4,3,7,5]=>1000000=>[1,7]=>[7,1]
[1,6,2,4,3,7,8,5]=>1000000=>[1,7]=>[7,1]
[1,5,6,2,4,7,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,6,2,4,7,8,3]=>1000000=>[1,7]=>[7,1]
[1,6,7,2,4,3,8,5]=>1000000=>[1,7]=>[7,1]
[1,5,8,2,4,6,7,3]=>1000000=>[1,7]=>[7,1]
[1,5,7,8,3,2,4,6]=>1000000=>[1,7]=>[7,1]
[1,5,8,3,2,4,6,7]=>1000000=>[1,7]=>[7,1]
[1,5,6,2,4,8,3,7]=>1000000=>[1,7]=>[7,1]
[1,7,3,4,2,8,6,5]=>1000000=>[1,7]=>[7,1]
[1,5,6,2,4,8,7,3]=>1000000=>[1,7]=>[7,1]
[1,5,8,7,3,2,4,6]=>1000000=>[1,7]=>[7,1]
[1,7,4,2,8,6,5,3]=>1000000=>[1,7]=>[7,1]
[1,5,8,3,2,4,7,6]=>1000000=>[1,7]=>[7,1]
[1,6,5,2,3,7,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,5,2,3,7,8,4]=>1000000=>[1,7]=>[7,1]
[1,6,8,4,2,3,7,5]=>1000000=>[1,7]=>[7,1]
[1,6,8,5,2,3,7,4]=>1000000=>[1,7]=>[7,1]
[1,6,4,2,3,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,8,6,2,4,7,3]=>1000000=>[1,7]=>[7,1]
[1,7,5,2,8,6,4,3]=>1000000=>[1,7]=>[7,1]
[3,7,5,6,1,4,8,2]=>0000000=>[8]=>[8]
[8,6,1,4,2,7,5,3]=>0000000=>[8]=>[8]
[1,6,7,4,3,5,8,2]=>1000000=>[1,7]=>[7,1]
[6,7,1,4,3,5,8,2]=>0000000=>[8]=>[8]
[4,7,1,6,3,5,8,2]=>0000000=>[8]=>[8]
[3,1,4,7,6,5,8,2]=>0000000=>[8]=>[8]
[6,1,7,4,3,5,8,2]=>0000000=>[8]=>[8]
[7,1,6,4,3,5,8,2]=>0000000=>[8]=>[8]
[1,7,6,4,3,5,8,2]=>1000000=>[1,7]=>[7,1]
[8,1,6,4,2,7,5,3]=>0000000=>[8]=>[8]
[4,7,1,3,8,2,5,6]=>0000000=>[8]=>[8]
[7,4,1,3,8,2,5,6]=>0000000=>[8]=>[8]
[1,3,6,4,2,8,5,7]=>1000000=>[1,7]=>[7,1]
[4,7,3,1,2,8,5,6]=>0000000=>[8]=>[8]
[4,7,8,1,2,6,5,3]=>0000000=>[8]=>[8]
[1,8,6,4,2,7,5,3]=>1000000=>[1,7]=>[7,1]
[4,8,1,3,7,2,5,6]=>0000000=>[8]=>[8]
[8,7,1,3,6,2,5,4]=>0000000=>[8]=>[8]
[1,8,4,3,7,2,5,6]=>1000000=>[1,7]=>[7,1]
[3,7,4,6,8,2,1,5]=>0000000=>[8]=>[8]
[2,4,3,7,8,6,1,5]=>0000000=>[8]=>[8]
[1,4,7,3,8,2,5,6]=>1000000=>[1,7]=>[7,1]
[5,7,6,8,3,2,1,4]=>0000000=>[8]=>[8]
[6,1,4,3,8,2,5,7]=>0000000=>[8]=>[8]
[4,1,7,3,8,2,5,6]=>0000000=>[8]=>[8]
[8,1,4,3,7,2,5,6]=>0000000=>[8]=>[8]
[4,2,3,7,8,6,1,5]=>0000000=>[8]=>[8]
[2,7,5,6,3,8,1,4]=>0000000=>[8]=>[8]
[5,7,2,6,8,4,1,3]=>0000000=>[8]=>[8]
[7,2,5,6,8,4,1,3]=>0000000=>[8]=>[8]
[5,2,3,8,7,6,1,4]=>0000000=>[8]=>[8]
[8,2,3,7,5,6,1,4]=>0000000=>[8]=>[8]
[6,1,8,3,7,2,5,4]=>0000000=>[8]=>[8]
[1,7,8,4,2,6,5,3]=>1000000=>[1,7]=>[7,1]
[4,7,1,8,2,5,6,3]=>0000000=>[8]=>[8]
[1,4,8,3,6,2,5,7]=>1000000=>[1,7]=>[7,1]
[3,7,5,8,6,2,1,4]=>0000000=>[8]=>[8]
[3,7,8,6,5,2,1,4]=>0000000=>[8]=>[8]
[6,8,7,5,3,2,1,4]=>0000000=>[8]=>[8]
[5,7,6,8,3,4,1,2]=>0000000=>[8]=>[8]
[3,7,6,8,4,5,1,2]=>0000000=>[8]=>[8]
[1,5,4,7,6,8,2,3]=>1000000=>[1,7]=>[7,1]
[1,7,4,6,5,8,2,3]=>1000000=>[1,7]=>[7,1]
[3,7,4,6,5,8,1,2]=>0000000=>[8]=>[8]
[3,5,4,8,6,7,1,2]=>0000000=>[8]=>[8]
[3,8,4,6,5,7,1,2]=>0000000=>[8]=>[8]
[3,6,4,7,5,8,1,2]=>0000000=>[8]=>[8]
[1,6,2,7,5,8,3,4]=>1000000=>[1,7]=>[7,1]
[1,6,4,8,5,7,2,3]=>1000000=>[1,7]=>[7,1]
[1,8,4,6,5,7,2,3]=>1000000=>[1,7]=>[7,1]
[1,5,4,8,6,7,2,3]=>1000000=>[1,7]=>[7,1]
[7,8,1,5,4,6,2,3]=>0000000=>[8]=>[8]
[1,8,2,6,5,7,3,4]=>1000000=>[1,7]=>[7,1]
[1,7,2,8,5,6,3,4]=>1000000=>[1,7]=>[7,1]
[1,7,2,6,5,8,3,4]=>1000000=>[1,7]=>[7,1]
[1,5,2,7,6,8,3,4]=>1000000=>[1,7]=>[7,1]
[1,7,6,8,2,5,3,4]=>1000000=>[1,7]=>[7,1]
[1,7,6,8,4,5,2,3]=>1000000=>[1,7]=>[7,1]
[7,8,5,6,1,3,2,4]=>0000000=>[8]=>[8]
[5,8,6,7,1,3,2,4]=>0000000=>[8]=>[8]
[1,3,2,7,6,8,4,5]=>1010000=>[1,2,5]=>[5,2,1]
[1,7,6,8,2,4,3,5]=>1000000=>[1,7]=>[7,1]
[1,3,2,8,6,7,4,5]=>1010000=>[1,2,5]=>[5,2,1]
[7,8,1,3,2,6,4,5]=>0000000=>[8]=>[8]
[7,8,1,6,2,4,3,5]=>0000000=>[8]=>[8]
[1,8,6,7,2,4,3,5]=>1000000=>[1,7]=>[7,1]
[7,8,1,4,2,6,3,5]=>0000000=>[8]=>[8]
[8,4,7,5,2,6,1,3]=>0000000=>[8]=>[8]
[5,4,6,8,2,1,7,3]=>0000000=>[8]=>[8]
[4,8,7,5,6,1,3,2]=>0000000=>[8]=>[8]
[3,2,6,8,5,7,1,4]=>0000000=>[8]=>[8]
[7,4,8,6,5,2,1,3]=>0000000=>[8]=>[8]
[2,5,3,7,4,1,8,6]=>0000000=>[8]=>[8]
[4,2,8,7,3,5,6,1]=>0000000=>[8]=>[8]
[2,6,3,5,8,7,1,4]=>0000000=>[8]=>[8]
[8,1,6,4,7,3,2,5]=>0000000=>[8]=>[8]
[4,8,7,5,6,1,2,3]=>0000000=>[8]=>[8]
[6,1,4,8,7,3,5,2]=>0000000=>[8]=>[8]
[2,8,3,7,1,5,6,4]=>0000000=>[8]=>[8]
[4,1,6,5,8,2,3,7]=>0000000=>[8]=>[8]
[8,3,6,1,4,5,2,7]=>0000000=>[8]=>[8]
[2,8,6,1,7,4,5,3]=>0000000=>[8]=>[8]
[1,8,5,2,3,6,7,4]=>1000000=>[1,7]=>[7,1]
[4,8,3,2,5,6,7,1]=>0000000=>[8]=>[8]
[2,1,8,3,5,6,7,4]=>0100000=>[2,6]=>[6,2]
[4,2,7,1,8,6,3,5]=>0000000=>[8]=>[8]
[3,8,4,1,2,6,7,5]=>0000000=>[8]=>[8]
[7,6,1,5,8,2,3,4]=>0000000=>[8]=>[8]
[4,2,1,8,5,6,7,3]=>0000000=>[8]=>[8]
[6,5,4,8,7,1,3,2]=>0000000=>[8]=>[8]
[6,5,4,8,1,2,7,3]=>0000000=>[8]=>[8]
[7,5,1,6,8,2,4,3]=>0000000=>[8]=>[8]
[6,5,4,1,8,2,7,3]=>0000000=>[8]=>[8]
[6,5,4,7,1,2,8,3]=>0000000=>[8]=>[8]
[6,5,4,7,8,1,3,2]=>0000000=>[8]=>[8]
[6,5,3,7,1,4,2,8]=>0000001=>[7,1]=>[7,1]
[7,5,1,4,8,3,2,6]=>0000000=>[8]=>[8]
[8,1,6,4,7,3,5,2]=>0000000=>[8]=>[8]
[7,5,1,4,8,3,6,2]=>0000000=>[8]=>[8]
[7,4,1,5,3,8,6,2]=>0000000=>[8]=>[8]
[8,1,5,4,3,7,6,2]=>0000000=>[8]=>[8]
[8,1,5,4,3,7,2,6]=>0000000=>[8]=>[8]
[6,5,3,8,1,4,2,7]=>0000000=>[8]=>[8]
[8,1,7,2,5,4,6,3]=>0000000=>[8]=>[8]
[7,6,1,2,5,4,8,3]=>0000000=>[8]=>[8]
[6,5,3,8,1,4,7,2]=>0000000=>[8]=>[8]
[6,5,3,1,2,7,8,4]=>0000000=>[8]=>[8]
[8,1,6,4,2,5,7,3]=>0000000=>[8]=>[8]
[8,1,5,4,3,2,7,6]=>0000000=>[8]=>[8]
[7,4,1,5,3,2,8,6]=>0000000=>[8]=>[8]
[6,4,3,1,5,2,8,7]=>0000010=>[6,2]=>[6,2]
[6,4,3,1,5,7,2,8]=>0000001=>[7,1]=>[7,1]
[7,4,1,5,3,6,2,8]=>0000001=>[7,1]=>[7,1]
[6,4,3,1,5,7,8,2]=>0000000=>[8]=>[8]
[7,1,5,8,4,6,2,3]=>0000000=>[8]=>[8]
[8,6,7,1,4,2,5,3]=>0000000=>[8]=>[8]
[8,6,3,7,5,1,2,4]=>0000000=>[8]=>[8]
[8,6,1,7,3,2,5,4]=>0000000=>[8]=>[8]
[7,6,1,8,3,5,2,4]=>0000000=>[8]=>[8]
[7,6,1,3,8,5,2,4]=>0000000=>[8]=>[8]
[7,6,8,2,4,5,1,3]=>0000000=>[8]=>[8]
[7,6,2,8,3,5,1,4]=>0000000=>[8]=>[8]
[8,7,1,5,2,6,3,4]=>0000000=>[8]=>[8]
[8,7,1,5,2,3,6,4]=>0000000=>[8]=>[8]
[8,5,2,3,1,7,6,4]=>0000000=>[8]=>[8]
[8,6,2,3,7,1,5,4]=>0000000=>[8]=>[8]
[8,6,2,7,3,1,5,4]=>0000000=>[8]=>[8]
[8,6,7,2,4,1,5,3]=>0000000=>[8]=>[8]
[6,8,7,3,4,1,5,2]=>0000000=>[8]=>[8]
[8,7,2,5,1,6,3,4]=>0000000=>[8]=>[8]
[8,7,2,1,4,6,3,5]=>0000000=>[8]=>[8]
[8,4,2,1,7,6,3,5]=>0000000=>[8]=>[8]
[8,5,2,7,1,6,3,4]=>0000000=>[8]=>[8]
[8,5,7,2,1,4,3,6]=>0000000=>[8]=>[8]
[5,8,7,3,1,4,2,6]=>0000000=>[8]=>[8]
[8,5,7,2,1,4,6,3]=>0000000=>[8]=>[8]
[8,5,2,7,1,3,6,4]=>0000000=>[8]=>[8]
[8,7,4,1,2,3,6,5]=>0000000=>[8]=>[8]
[8,7,4,1,2,6,3,5]=>0000000=>[8]=>[8]
[8,4,3,1,7,2,6,5]=>0000000=>[8]=>[8]
[8,4,3,1,2,7,6,5]=>0000000=>[8]=>[8]
[8,6,1,3,7,2,5,4]=>0000000=>[8]=>[8]
[8,5,1,3,2,7,6,4]=>0000000=>[8]=>[8]
[8,5,7,4,1,6,2,3]=>0000000=>[8]=>[8]
[8,5,7,4,1,2,6,3]=>0000000=>[8]=>[8]
[8,1,5,4,2,7,6,3]=>0000000=>[8]=>[8]
[8,1,6,4,7,2,5,3]=>0000000=>[8]=>[8]
[6,1,5,8,4,2,7,3]=>0000000=>[8]=>[8]
[5,8,3,6,4,1,2,7]=>0000000=>[8]=>[8]
[8,4,7,5,1,6,2,3]=>0000000=>[8]=>[8]
[8,4,7,5,1,2,6,3]=>0000000=>[8]=>[8]
[8,4,7,5,1,2,3,6]=>0000000=>[8]=>[8]
[8,3,2,6,5,1,4,7]=>0000000=>[8]=>[8]
[4,8,6,3,5,1,2,7]=>0000000=>[8]=>[8]
[4,8,7,3,1,5,2,6]=>0000000=>[8]=>[8]
[8,4,7,2,1,5,3,6]=>0000000=>[8]=>[8]
[8,3,2,7,1,5,4,6]=>0000000=>[8]=>[8]
[8,3,2,1,7,6,4,5]=>0000000=>[8]=>[8]
[8,7,3,1,6,2,4,5]=>0000000=>[8]=>[8]
[8,7,3,1,2,4,6,5]=>0000000=>[8]=>[8]
[8,3,2,1,7,4,6,5]=>0000000=>[8]=>[8]
[8,4,7,2,1,5,6,3]=>0000000=>[8]=>[8]
[8,7,2,1,3,6,4,5]=>0000000=>[8]=>[8]
[8,7,2,1,3,4,6,5]=>0000000=>[8]=>[8]
[1,2,7,3,5,4,8,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,7,2,3,6,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,8,2,4,5,7,6]=>1000000=>[1,7]=>[7,1]
[1,2,3,8,4,6,7,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,7,8,2,3,6,4,5]=>1000000=>[1,7]=>[7,1]
[1,6,7,8,2,3,5,4]=>1000000=>[1,7]=>[7,1]
[1,7,8,2,5,3,6,4]=>1000000=>[1,7]=>[7,1]
[1,8,2,3,6,4,5,7]=>1000000=>[1,7]=>[7,1]
[1,2,7,8,3,6,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,2,7,8,3,6,4]=>1000000=>[1,7]=>[7,1]
[1,3,2,8,4,6,7,5]=>1010000=>[1,2,5]=>[5,2,1]
[1,8,2,3,4,6,7,5]=>1000000=>[1,7]=>[7,1]
[1,7,8,2,4,3,6,5]=>1000000=>[1,7]=>[7,1]
[6,7,3,1,5,2,8,4]=>0000000=>[8]=>[8]
[7,3,6,1,5,2,4,8]=>0000001=>[7,1]=>[7,1]
[6,2,1,7,5,3,8,4]=>0000000=>[8]=>[8]
[4,6,5,7,8,1,2,3]=>0000000=>[8]=>[8]
[5,7,4,6,1,8,2,3]=>0000000=>[8]=>[8]
[5,7,3,1,6,8,2,4]=>0000000=>[8]=>[8]
[2,5,4,7,3,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,2,7,3,6,5,1,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,3,1,5,8,7]=>0000010=>[6,2]=>[6,2]
[2,5,3,1,6,4,8,7]=>0000010=>[6,2]=>[6,2]
[2,5,3,7,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,6,5,3,7,4,1,8]=>0000001=>[7,1]=>[7,1]
[4,2,7,6,3,5,1,8]=>0000001=>[7,1]=>[7,1]
[2,7,5,3,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,6,3,7,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[1,7,5,2,3,8,4,6]=>1000000=>[1,7]=>[7,1]
[2,1,3,7,5,4,8,6]=>0110000=>[2,1,5]=>[5,2,1]
[2,3,1,8,6,5,4,7]=>0010000=>[3,5]=>[5,3]
[2,5,3,1,8,6,4,7]=>0000000=>[8]=>[8]
[4,2,8,3,1,6,5,7]=>0000000=>[8]=>[8]
[8,3,2,6,4,1,5,7]=>0000000=>[8]=>[8]
[3,6,8,2,1,4,5,7]=>0000000=>[8]=>[8]
[1,2,6,3,8,7,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,6,3,4,8,5]=>1100000=>[1,1,6]=>[6,1,1]
[2,1,3,8,7,5,4,6]=>0110000=>[2,1,5]=>[5,2,1]
[1,2,3,8,6,4,7,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,4,8,6,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,7,6,3,8,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,3,6,4,8,7,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,6,4,8,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[2,1,3,8,5,4,7,6]=>0110000=>[2,1,5]=>[5,2,1]
[7,1,8,4,2,3,5,6]=>0000000=>[8]=>[8]
[4,2,6,3,1,8,5,7]=>0000000=>[8]=>[8]
[5,4,2,8,3,1,6,7]=>0000000=>[8]=>[8]
[2,5,4,8,3,1,6,7]=>0000000=>[8]=>[8]
[1,8,7,4,2,3,5,6]=>1000000=>[1,7]=>[7,1]
[1,5,2,8,7,3,4,6]=>1000000=>[1,7]=>[7,1]
[1,2,7,3,6,4,8,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,8,6,3,7,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,3,8,4,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[4,2,1,8,3,7,5,6]=>0000000=>[8]=>[8]
[8,3,2,1,7,4,5,6]=>0000000=>[8]=>[8]
[1,2,3,8,7,4,6,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,7,6,4,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[2,6,5,7,1,4,3,8]=>0000001=>[7,1]=>[7,1]
[2,6,5,7,1,3,8,4]=>0000000=>[8]=>[8]
[3,8,5,7,1,2,6,4]=>0000000=>[8]=>[8]
[3,8,5,7,2,6,4,1]=>0000000=>[8]=>[8]
[3,4,8,6,2,5,7,1]=>0000000=>[8]=>[8]
[3,4,8,6,1,2,5,7]=>0000000=>[8]=>[8]
[2,5,7,1,4,8,6,3]=>0000000=>[8]=>[8]
[2,8,1,7,5,6,4,3]=>0000000=>[8]=>[8]
[2,3,8,1,6,5,7,4]=>0000000=>[8]=>[8]
[3,5,7,6,1,2,4,8]=>0000001=>[7,1]=>[7,1]
[4,8,6,7,2,3,5,1]=>0000000=>[8]=>[8]
[4,8,6,7,1,3,5,2]=>0000000=>[8]=>[8]
[3,4,8,6,1,5,7,2]=>0000000=>[8]=>[8]
[3,8,5,7,1,6,4,2]=>0000000=>[8]=>[8]
[3,8,5,7,2,1,6,4]=>0000000=>[8]=>[8]
[3,4,8,6,2,1,5,7]=>0000000=>[8]=>[8]
[3,5,7,6,2,1,4,8]=>0000001=>[7,1]=>[7,1]
[5,8,6,7,3,4,2,1]=>0000000=>[8]=>[8]
[5,8,6,7,2,1,3,4]=>0000000=>[8]=>[8]
[4,8,6,7,2,1,5,3]=>0000000=>[8]=>[8]
[4,3,1,7,5,2,8,6]=>0000000=>[8]=>[8]
[4,3,2,8,5,1,7,6]=>0000000=>[8]=>[8]
[4,3,8,5,1,6,7,2]=>0000000=>[8]=>[8]
[5,8,6,7,2,3,4,1]=>0000000=>[8]=>[8]
[5,8,6,7,2,4,3,1]=>0000000=>[8]=>[8]
[5,8,6,7,1,2,4,3]=>0000000=>[8]=>[8]
[3,2,5,7,6,1,4,8]=>0000001=>[7,1]=>[7,1]
[4,8,6,7,1,3,2,5]=>0000000=>[8]=>[8]
[4,8,6,7,1,2,5,3]=>0000000=>[8]=>[8]
[4,8,6,7,2,5,3,1]=>0000000=>[8]=>[8]
[4,3,8,5,2,6,7,1]=>0000000=>[8]=>[8]
[4,2,6,7,5,1,3,8]=>0000001=>[7,1]=>[7,1]
[3,8,4,7,1,5,2,6]=>0000000=>[8]=>[8]
[3,5,1,7,4,6,2,8]=>0000001=>[7,1]=>[7,1]
[3,8,4,7,2,5,1,6]=>0000000=>[8]=>[8]
[4,1,3,8,5,2,6,7]=>0000000=>[8]=>[8]
[4,2,6,7,5,3,8,1]=>0000000=>[8]=>[8]
[4,8,6,7,3,2,5,1]=>0000000=>[8]=>[8]
[4,8,6,7,3,1,2,5]=>0000000=>[8]=>[8]
[3,1,5,7,6,2,4,8]=>0000001=>[7,1]=>[7,1]
[3,4,1,7,5,6,2,8]=>0000001=>[7,1]=>[7,1]
[4,1,7,5,2,8,6,3]=>0000000=>[8]=>[8]
[4,1,6,7,5,2,3,8]=>0000001=>[7,1]=>[7,1]
[5,8,6,7,3,2,4,1]=>0000000=>[8]=>[8]
[5,8,6,7,4,2,3,1]=>0000000=>[8]=>[8]
[5,8,6,7,4,1,2,3]=>0000000=>[8]=>[8]
[5,8,6,7,4,1,3,2]=>0000000=>[8]=>[8]
[5,8,6,7,3,1,4,2]=>0000000=>[8]=>[8]
[4,8,6,7,3,1,5,2]=>0000000=>[8]=>[8]
[4,1,6,7,5,3,8,2]=>0000000=>[8]=>[8]
[4,1,7,5,3,2,8,6]=>0000000=>[8]=>[8]
[4,2,8,5,3,1,7,6]=>0000000=>[8]=>[8]
[4,2,1,6,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[4,8,6,7,3,2,1,5]=>0000000=>[8]=>[8]
[5,8,6,7,4,2,1,3]=>0000000=>[8]=>[8]
[5,8,6,7,4,3,1,2]=>0000000=>[8]=>[8]
[2,7,1,5,8,6,3,4]=>0000000=>[8]=>[8]
[2,4,7,1,8,5,6,3]=>0000000=>[8]=>[8]
[4,7,5,8,3,1,6,2]=>0000000=>[8]=>[8]
[7,3,5,8,6,2,1,4]=>0000000=>[8]=>[8]
[1,2,7,6,8,3,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[6,7,4,1,8,5,3,2]=>0000000=>[8]=>[8]
[7,2,6,8,5,4,1,3]=>0000000=>[8]=>[8]
[6,7,3,1,8,5,4,2]=>0000000=>[8]=>[8]
[6,7,1,8,5,4,3,2]=>0000000=>[8]=>[8]
[7,8,4,2,1,6,5,3]=>0000000=>[8]=>[8]
[6,2,3,4,8,7,1,5]=>0000000=>[8]=>[8]
[6,2,3,4,7,8,1,5]=>0000000=>[8]=>[8]
[7,8,3,6,4,2,1,5]=>0000000=>[8]=>[8]
[7,8,3,5,6,2,1,4]=>0000000=>[8]=>[8]
[5,2,6,3,8,1,7,4]=>0000000=>[8]=>[8]
[6,3,2,5,8,7,1,4]=>0000000=>[8]=>[8]
[6,3,2,8,4,7,1,5]=>0000000=>[8]=>[8]
[6,4,3,8,7,5,1,2]=>0000000=>[8]=>[8]
[6,4,3,7,8,5,1,2]=>0000000=>[8]=>[8]
[6,3,2,7,4,8,1,5]=>0000000=>[8]=>[8]
[6,3,2,5,7,8,1,4]=>0000000=>[8]=>[8]
[5,8,2,3,6,1,7,4]=>0000000=>[8]=>[8]
[4,5,6,8,3,2,1,7]=>0000000=>[8]=>[8]
[4,6,8,5,3,2,1,7]=>0000000=>[8]=>[8]
[5,6,1,4,2,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,6,8,4,3,7,1,2]=>0000000=>[8]=>[8]
[5,6,1,4,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[5,2,8,3,4,1,7,6]=>0000000=>[8]=>[8]
[4,5,8,6,3,2,1,7]=>0000000=>[8]=>[8]
[4,7,5,6,3,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,1,4,3,6,2,8,7]=>0000010=>[6,2]=>[6,2]
[5,1,4,3,8,2,7,6]=>0000000=>[8]=>[8]
[5,6,2,4,1,8,7,3]=>0000000=>[8]=>[8]
[5,7,2,4,1,8,6,3]=>0000000=>[8]=>[8]
[6,1,4,2,8,7,5,3]=>0000000=>[8]=>[8]
[5,8,2,4,1,7,6,3]=>0000000=>[8]=>[8]
[5,4,1,3,7,2,6,8]=>0000001=>[7,1]=>[7,1]
[5,8,1,4,2,3,7,6]=>0000000=>[8]=>[8]
[5,1,6,3,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,8,6,5,3,2,1,7]=>0000000=>[8]=>[8]
[5,4,7,8,3,2,1,6]=>0000000=>[8]=>[8]
[4,7,8,5,3,2,1,6]=>0000000=>[8]=>[8]
[5,7,1,3,4,2,6,8]=>0000001=>[7,1]=>[7,1]
[5,1,8,4,2,3,6,7]=>0000000=>[8]=>[8]
[5,1,7,4,2,3,6,8]=>0000001=>[7,1]=>[7,1]
[5,8,1,3,4,2,6,7]=>0000000=>[8]=>[8]
[4,8,7,5,3,2,1,6]=>0000000=>[8]=>[8]
[4,7,8,6,3,2,1,5]=>0000000=>[8]=>[8]
[4,8,7,6,3,1,2,5]=>0000000=>[8]=>[8]
[1,4,3,8,2,6,5,7]=>1000000=>[1,7]=>[7,1]
[4,1,3,8,2,6,5,7]=>0000000=>[8]=>[8]
[3,6,7,8,4,1,2,5]=>0000000=>[8]=>[8]
[3,7,8,2,6,4,5,1]=>0000000=>[8]=>[8]
[4,2,3,8,1,6,5,7]=>0000000=>[8]=>[8]
[7,3,6,8,4,2,1,5]=>0000000=>[8]=>[8]
[1,3,2,4,8,6,5,7]=>1011000=>[1,2,1,4]=>[4,2,1,1]
[3,1,2,4,8,6,5,7]=>0011000=>[3,1,4]=>[4,3,1]
[3,7,4,8,5,1,2,6]=>0000000=>[8]=>[8]
[2,1,3,4,8,6,5,7]=>0111000=>[2,1,1,4]=>[4,2,1,1]
[3,5,7,8,6,1,2,4]=>0000000=>[8]=>[8]
[5,1,6,3,8,4,7,2]=>0000000=>[8]=>[8]
[2,5,1,6,8,3,7,4]=>0000000=>[8]=>[8]
[5,1,2,6,8,3,7,4]=>0000000=>[8]=>[8]
[6,1,7,5,2,8,3,4]=>0000000=>[8]=>[8]
[5,7,2,8,6,1,3,4]=>0000000=>[8]=>[8]
[1,2,6,7,5,8,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,7,4,5,2,8,3]=>1000000=>[1,7]=>[7,1]
[6,2,7,4,5,1,8,3]=>0000000=>[8]=>[8]
[7,5,1,6,3,8,2,4]=>0000000=>[8]=>[8]
[2,7,6,1,3,8,5,4]=>0000000=>[8]=>[8]
[2,6,7,4,1,8,3,5]=>0000000=>[8]=>[8]
[2,1,6,7,3,8,5,4]=>0100000=>[2,6]=>[6,2]
[3,7,5,4,8,1,6,2]=>0000000=>[8]=>[8]
[4,6,1,5,8,7,3,2]=>0000000=>[8]=>[8]
[8,3,4,6,2,1,5,7]=>0000000=>[8]=>[8]
[3,5,6,2,1,8,4,7]=>0000000=>[8]=>[8]
[7,5,3,2,8,4,1,6]=>0000000=>[8]=>[8]
[7,5,3,2,8,4,6,1]=>0000000=>[8]=>[8]
[4,2,5,6,8,3,1,7]=>0000000=>[8]=>[8]
[5,3,6,8,1,4,2,7]=>0000000=>[8]=>[8]
[4,5,6,8,1,3,2,7]=>0000000=>[8]=>[8]
[1,4,5,6,8,3,2,7]=>1000000=>[1,7]=>[7,1]
[4,5,3,7,2,8,6,1]=>0000000=>[8]=>[8]
[6,4,7,3,2,8,5,1]=>0000000=>[8]=>[8]
[6,1,4,7,3,2,8,5]=>0000000=>[8]=>[8]
[5,1,7,3,8,4,2,6]=>0000000=>[8]=>[8]
[5,3,7,1,4,8,6,2]=>0000000=>[8]=>[8]
[6,4,3,1,7,8,5,2]=>0000000=>[8]=>[8]
[5,6,1,3,7,8,4,2]=>0000000=>[8]=>[8]
[5,6,1,7,8,3,4,2]=>0000000=>[8]=>[8]
[1,6,3,7,4,8,5,2]=>1000000=>[1,7]=>[7,1]
[6,7,2,4,1,8,5,3]=>0000000=>[8]=>[8]
[6,7,2,1,4,3,8,5]=>0000000=>[8]=>[8]
[6,4,7,3,1,2,8,5]=>0000000=>[8]=>[8]
[5,6,3,1,2,7,8,4]=>0000000=>[8]=>[8]
[5,6,1,3,2,7,8,4]=>0000000=>[8]=>[8]
[5,6,3,2,1,7,8,4]=>0000000=>[8]=>[8]
[5,6,3,2,7,8,4,1]=>0000000=>[8]=>[8]
[2,5,6,3,7,8,4,1]=>0000000=>[8]=>[8]
[2,5,6,3,1,7,8,4]=>0000000=>[8]=>[8]
[2,6,4,7,3,1,8,5]=>0000000=>[8]=>[8]
[6,3,7,2,8,4,1,5]=>0000000=>[8]=>[8]
[6,3,2,7,1,8,4,5]=>0000000=>[8]=>[8]
[7,5,3,2,1,8,4,6]=>0000000=>[8]=>[8]
[7,3,8,4,2,1,5,6]=>0000000=>[8]=>[8]
[4,7,2,1,3,8,6,5]=>0000000=>[8]=>[8]
[1,3,7,8,6,4,2,5]=>1000000=>[1,7]=>[7,1]
[5,7,3,8,2,1,6,4]=>0000000=>[8]=>[8]
[4,6,2,7,8,5,3,1]=>0000000=>[8]=>[8]
[2,5,1,7,3,8,6,4]=>0000000=>[8]=>[8]
[6,7,2,1,3,8,5,4]=>0000000=>[8]=>[8]
[5,1,6,7,8,2,4,3]=>0000000=>[8]=>[8]
[6,3,7,1,8,5,2,4]=>0000000=>[8]=>[8]
[6,2,1,7,3,8,5,4]=>0000000=>[8]=>[8]
[6,2,7,1,8,5,4,3]=>0000000=>[8]=>[8]
[6,3,1,7,8,5,4,2]=>0000000=>[8]=>[8]
[5,3,2,1,8,4,7,6]=>0000000=>[8]=>[8]
[4,5,2,1,3,8,7,6]=>0000100=>[5,3]=>[5,3]
[3,2,6,4,5,8,1,7]=>0000000=>[8]=>[8]
[2,4,6,5,8,1,3,7]=>0000000=>[8]=>[8]
[1,3,4,6,5,8,2,7]=>1000000=>[1,7]=>[7,1]
[1,6,3,4,5,8,2,7]=>1000000=>[1,7]=>[7,1]
[3,4,1,8,5,2,7,6]=>0000000=>[8]=>[8]
[2,8,4,1,7,6,3,5]=>0000000=>[8]=>[8]
[1,5,3,2,8,7,4,6]=>1000000=>[1,7]=>[7,1]
[8,2,1,7,5,3,4,6]=>0000000=>[8]=>[8]
[1,7,6,4,5,8,3,2]=>1000000=>[1,7]=>[7,1]
[5,8,7,4,6,2,1,3]=>0000000=>[8]=>[8]
[3,4,2,5,8,6,7,1]=>0000000=>[8]=>[8]
[4,1,3,5,6,8,7,2]=>0000000=>[8]=>[8]
[2,4,8,6,7,1,3,5]=>0000000=>[8]=>[8]
[3,7,4,8,2,1,6,5]=>0000000=>[8]=>[8]
[2,3,5,8,6,7,1,4]=>0000000=>[8]=>[8]
[3,2,5,6,8,7,1,4]=>0000000=>[8]=>[8]
[7,2,4,8,5,3,1,6]=>0000000=>[8]=>[8]
[4,8,3,1,2,7,6,5]=>0000000=>[8]=>[8]
[8,4,2,3,7,1,5,6]=>0000000=>[8]=>[8]
[3,5,2,7,6,1,8,4]=>0000000=>[8]=>[8]
[5,8,7,3,4,6,2,1]=>0000000=>[8]=>[8]
[5,8,2,7,4,1,6,3]=>0000000=>[8]=>[8]
[5,1,4,2,8,7,6,3]=>0000000=>[8]=>[8]
[5,2,6,8,7,1,3,4]=>0000000=>[8]=>[8]
[6,3,2,1,8,5,7,4]=>0000000=>[8]=>[8]
[2,7,5,4,1,8,6,3]=>0000000=>[8]=>[8]
[4,2,5,6,8,7,1,3]=>0000000=>[8]=>[8]
[1,8,4,2,5,6,7,3]=>1000000=>[1,7]=>[7,1]
[3,8,4,1,5,6,7,2]=>0000000=>[8]=>[8]
[4,2,8,5,6,7,1,3]=>0000000=>[8]=>[8]
[5,2,4,7,1,8,6,3]=>0000000=>[8]=>[8]
[8,1,3,6,5,2,4,7]=>0000000=>[8]=>[8]
[8,3,2,4,6,5,1,7]=>0000000=>[8]=>[8]
[8,3,6,4,1,5,2,7]=>0000000=>[8]=>[8]
[1,3,4,8,5,7,2,6]=>1000000=>[1,7]=>[7,1]
[5,8,4,7,6,2,3,1]=>0000000=>[8]=>[8]
[1,3,4,7,5,8,2,6]=>1000000=>[1,7]=>[7,1]
[1,3,5,2,4,8,7,6]=>1000100=>[1,4,3]=>[4,3,1]
[2,6,5,1,3,8,7,4]=>0000000=>[8]=>[8]
[2,8,5,1,4,7,6,3]=>0000000=>[8]=>[8]
[4,3,1,5,8,6,7,2]=>0000000=>[8]=>[8]
[5,4,2,1,6,8,7,3]=>0000000=>[8]=>[8]
[6,8,4,3,2,7,1,5]=>0000000=>[8]=>[8]
[5,1,3,2,8,6,7,4]=>0000000=>[8]=>[8]
[5,3,1,2,8,6,7,4]=>0000000=>[8]=>[8]
[5,2,3,1,6,8,7,4]=>0000000=>[8]=>[8]
[5,3,2,1,8,6,7,4]=>0000000=>[8]=>[8]
[5,2,1,3,6,8,7,4]=>0000000=>[8]=>[8]
[2,7,4,5,8,3,1,6]=>0000000=>[8]=>[8]
[1,8,4,3,7,2,6,5]=>1000000=>[1,7]=>[7,1]
[3,4,8,7,2,1,6,5]=>0000000=>[8]=>[8]
[5,4,7,8,3,6,2,1]=>0000000=>[8]=>[8]
[6,3,8,7,4,1,2,5]=>0000000=>[8]=>[8]
[8,4,7,2,3,1,5,6]=>0000000=>[8]=>[8]
[8,6,4,1,3,2,7,5]=>0000000=>[8]=>[8]
[3,5,7,2,6,1,8,4]=>0000000=>[8]=>[8]
[6,1,3,8,5,7,2,4]=>0000000=>[8]=>[8]
[2,8,1,5,4,7,6,3]=>0000000=>[8]=>[8]
[1,7,2,4,6,5,8,3]=>1000000=>[1,7]=>[7,1]
[5,8,2,6,1,3,7,4]=>0000000=>[8]=>[8]
[6,3,5,8,7,2,1,4]=>0000000=>[8]=>[8]
[2,5,7,8,4,1,6,3]=>0000000=>[8]=>[8]
[4,1,5,2,6,8,7,3]=>0000000=>[8]=>[8]
[4,1,8,5,2,6,7,3]=>0000000=>[8]=>[8]
[2,7,1,8,5,4,6,3]=>0000000=>[8]=>[8]
[5,8,6,2,1,3,7,4]=>0000000=>[8]=>[8]
[3,4,5,1,8,6,7,2]=>0000000=>[8]=>[8]
[5,1,3,6,4,8,7,2]=>0000000=>[8]=>[8]
[1,3,2,7,5,8,6,4]=>1010000=>[1,2,5]=>[5,2,1]
[1,4,2,5,8,3,7,6]=>1000000=>[1,7]=>[7,1]
[1,4,2,7,8,5,6,3]=>1000000=>[1,7]=>[7,1]
[5,1,2,6,8,4,7,3]=>0000000=>[8]=>[8]
[3,1,2,6,5,8,4,7]=>0010000=>[3,5]=>[5,3]
[4,1,2,6,8,5,3,7]=>0000000=>[8]=>[8]
[1,5,2,4,8,7,6,3]=>1000000=>[1,7]=>[7,1]
[1,2,7,4,8,6,5,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,2,7,5,8,4,6]=>1010000=>[1,2,5]=>[5,2,1]
[2,3,1,7,5,4,8,6]=>0010000=>[3,5]=>[5,3]
[1,3,2,8,5,7,4,6]=>1010000=>[1,2,5]=>[5,2,1]
[1,2,6,4,8,7,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,8,5,7,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,6,8,2,7,3,4]=>1000000=>[1,7]=>[7,1]
[1,3,8,2,6,7,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,7,2,8,6,3,5]=>1000000=>[1,7]=>[7,1]
[1,6,7,8,2,5,3,4]=>1000000=>[1,7]=>[7,1]
[1,2,6,8,3,7,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,7,8,2,3,6,4]=>1000000=>[1,7]=>[7,1]
[1,4,7,2,8,3,6,5]=>1000000=>[1,7]=>[7,1]
[1,6,7,3,4,8,5,2]=>1000000=>[1,7]=>[7,1]
[1,5,3,7,4,8,6,2]=>1000000=>[1,7]=>[7,1]
[1,3,6,4,2,8,7,5]=>1000000=>[1,7]=>[7,1]
[1,3,7,4,2,8,6,5]=>1000000=>[1,7]=>[7,1]
[1,2,8,4,7,3,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,2,4,8,3,7,6]=>1000000=>[1,7]=>[7,1]
[1,8,4,5,7,2,3,6]=>1000000=>[1,7]=>[7,1]
[1,8,3,5,2,7,4,6]=>1000000=>[1,7]=>[7,1]
[2,8,3,5,1,4,7,6]=>0000000=>[8]=>[8]
[2,3,8,6,1,4,7,5]=>0000000=>[8]=>[8]
[1,4,8,6,7,2,3,5]=>1000000=>[1,7]=>[7,1]
[1,5,6,8,7,2,3,4]=>1000000=>[1,7]=>[7,1]
[1,2,7,8,5,3,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,8,7,3,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,8,7,3,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,8,6,3,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,7,8,6,2,3,4]=>1000000=>[1,7]=>[7,1]
[1,3,7,6,2,8,4,5]=>1000000=>[1,7]=>[7,1]
[1,2,8,4,7,6,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,8,7,6,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,8,7,5,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,8,6,5,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[5,2,6,7,3,4,8,1]=>0000000=>[8]=>[8]
[5,6,2,1,7,8,3,4]=>0000000=>[8]=>[8]
[5,6,2,1,4,8,7,3]=>0000000=>[8]=>[8]
[2,6,1,4,5,8,7,3]=>0000000=>[8]=>[8]
[5,4,2,7,6,3,8,1]=>0000000=>[8]=>[8]
[2,3,7,6,4,5,8,1]=>0000000=>[8]=>[8]
[2,6,1,7,5,8,3,4]=>0000000=>[8]=>[8]
[5,1,2,7,8,4,3,6]=>0000000=>[8]=>[8]
[2,6,1,7,4,8,3,5]=>0000000=>[8]=>[8]
[3,6,4,1,7,8,2,5]=>0000000=>[8]=>[8]
[5,4,6,1,7,8,2,3]=>0000000=>[8]=>[8]
[5,4,6,1,3,8,7,2]=>0000000=>[8]=>[8]
[3,6,4,1,5,8,7,2]=>0000000=>[8]=>[8]
[2,6,1,5,4,8,7,3]=>0000000=>[8]=>[8]
[2,6,1,4,7,8,5,3]=>0000000=>[8]=>[8]
[5,1,2,4,8,7,6,3]=>0000000=>[8]=>[8]
[2,1,5,3,8,6,4,7]=>0100000=>[2,6]=>[6,2]
[5,1,2,4,8,6,3,7]=>0000000=>[8]=>[8]
[5,6,3,1,4,8,2,7]=>0000000=>[8]=>[8]
[2,5,4,3,1,8,6,7]=>0000100=>[5,3]=>[5,3]
[5,4,6,3,1,8,7,2]=>0000000=>[8]=>[8]
[2,1,3,7,8,6,4,5]=>0110000=>[2,1,5]=>[5,2,1]
[5,1,4,2,8,6,7,3]=>0000000=>[8]=>[8]
[1,2,3,8,6,7,4,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,7,5,4,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,8,7,4,5,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[2,1,3,6,8,7,4,5]=>0110000=>[2,1,5]=>[5,2,1]
[3,1,6,2,8,7,5,4]=>0000000=>[8]=>[8]
[6,8,1,3,2,5,4,7]=>0000000=>[8]=>[8]
[6,8,1,4,2,5,3,7]=>0000000=>[8]=>[8]
[7,8,3,6,1,4,2,5]=>0000000=>[8]=>[8]
[7,8,2,5,1,4,3,6]=>0000000=>[8]=>[8]
[7,8,1,4,3,6,2,5]=>0000000=>[8]=>[8]
[5,8,1,4,3,7,2,6]=>0000000=>[8]=>[8]
[6,8,2,5,1,4,3,7]=>0000000=>[8]=>[8]
[6,8,2,5,3,7,1,4]=>0000000=>[8]=>[8]
[2,5,4,7,6,8,1,3]=>0000000=>[8]=>[8]
[2,6,1,4,3,7,5,8]=>0000001=>[7,1]=>[7,1]
[2,6,1,5,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[2,6,4,7,5,8,1,3]=>0000000=>[8]=>[8]
[5,8,2,6,4,7,1,3]=>0000000=>[8]=>[8]
[6,8,3,7,1,4,2,5]=>0000000=>[8]=>[8]
[5,8,1,3,2,6,4,7]=>0000000=>[8]=>[8]
[5,8,4,7,1,3,2,6]=>0000000=>[8]=>[8]
[6,8,4,7,1,3,2,5]=>0000000=>[8]=>[8]
[6,8,5,7,1,3,2,4]=>0000000=>[8]=>[8]
[5,7,6,8,2,4,1,3]=>0000000=>[8]=>[8]
[4,7,5,8,1,3,2,6]=>0000000=>[8]=>[8]
[4,7,1,3,2,6,5,8]=>0000001=>[7,1]=>[7,1]
[3,7,1,4,2,6,5,8]=>0000001=>[7,1]=>[7,1]
[3,7,6,8,1,4,2,5]=>0000000=>[8]=>[8]
[4,7,6,8,2,5,1,3]=>0000000=>[8]=>[8]
[4,7,5,8,3,6,1,2]=>0000000=>[8]=>[8]
[4,7,5,8,2,6,1,3]=>0000000=>[8]=>[8]
[3,7,4,8,2,6,1,5]=>0000000=>[8]=>[8]
[3,7,1,5,2,6,4,8]=>0000001=>[7,1]=>[7,1]
[3,7,2,6,1,5,4,8]=>0000001=>[7,1]=>[7,1]
[3,7,2,6,5,8,1,4]=>0000000=>[8]=>[8]
[4,7,3,6,5,8,1,2]=>0000000=>[8]=>[8]
[2,6,5,8,4,7,1,3]=>0000000=>[8]=>[8]
[2,6,3,7,1,5,4,8]=>0000001=>[7,1]=>[7,1]
[7,6,4,8,5,2,3,1]=>0000000=>[8]=>[8]
[6,7,4,3,5,1,8,2]=>0000000=>[8]=>[8]
[6,7,3,5,4,8,2,1]=>0000000=>[8]=>[8]
[6,8,3,7,5,2,4,1]=>0000000=>[8]=>[8]
[7,6,3,5,8,2,4,1]=>0000000=>[8]=>[8]
[7,6,2,8,4,1,5,3]=>0000000=>[8]=>[8]
[7,6,3,4,8,2,5,1]=>0000000=>[8]=>[8]
[6,8,3,7,4,5,2,1]=>0000000=>[8]=>[8]
[6,7,3,5,8,4,2,1]=>0000000=>[8]=>[8]
[5,7,8,3,6,2,1,4]=>0000000=>[8]=>[8]
[6,3,4,8,7,2,5,1]=>0000000=>[8]=>[8]
[6,3,8,4,7,2,1,5]=>0000000=>[8]=>[8]
[6,3,4,7,5,8,2,1]=>0000000=>[8]=>[8]
[6,3,5,7,8,4,2,1]=>0000000=>[8]=>[8]
[5,7,3,6,8,2,1,4]=>0000000=>[8]=>[8]
[5,6,7,3,4,1,8,2]=>0000000=>[8]=>[8]
[4,6,7,8,3,5,2,1]=>0000000=>[8]=>[8]
[4,7,3,5,6,8,2,1]=>0000000=>[8]=>[8]
[5,3,4,7,8,2,1,6]=>0000000=>[8]=>[8]
[5,3,8,2,4,1,6,7]=>0000000=>[8]=>[8]
[5,3,4,8,2,6,1,7]=>0000000=>[8]=>[8]
[4,8,3,6,2,5,7,1]=>0000000=>[8]=>[8]
[4,8,3,5,7,2,6,1]=>0000000=>[8]=>[8]
[4,8,3,5,6,7,2,1]=>0000000=>[8]=>[8]
[4,7,8,3,5,6,2,1]=>0000000=>[8]=>[8]
[4,7,8,3,6,2,5,1]=>0000000=>[8]=>[8]
[4,8,3,6,7,2,5,1]=>0000000=>[8]=>[8]
[4,8,3,7,2,5,6,1]=>0000000=>[8]=>[8]
[5,8,3,7,2,6,4,1]=>0000000=>[8]=>[8]
[5,7,3,4,8,2,1,6]=>0000000=>[8]=>[8]
[5,8,4,2,3,1,6,7]=>0000000=>[8]=>[8]
[5,8,4,2,3,1,7,6]=>0000000=>[8]=>[8]
[6,4,8,5,3,7,2,1]=>0000000=>[8]=>[8]
[6,4,2,7,3,1,8,5]=>0000000=>[8]=>[8]
[6,4,3,7,8,5,2,1]=>0000000=>[8]=>[8]
[6,4,5,3,7,1,8,2]=>0000000=>[8]=>[8]
[5,7,4,2,3,1,6,8]=>0000001=>[7,1]=>[7,1]
[5,6,3,7,1,8,2,4]=>0000000=>[8]=>[8]
[5,6,3,4,8,2,1,7]=>0000000=>[8]=>[8]
[6,3,5,7,4,8,2,1]=>0000000=>[8]=>[8]
[6,3,5,4,7,8,2,1]=>0000000=>[8]=>[8]
[6,4,3,5,7,1,8,2]=>0000000=>[8]=>[8]
[6,4,2,5,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[5,3,4,7,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,7,3,6,2,5,8,1]=>0000000=>[8]=>[8]
[4,7,3,6,8,2,5,1]=>0000000=>[8]=>[8]
[4,6,7,3,5,8,2,1]=>0000000=>[8]=>[8]
[4,5,7,8,3,6,2,1]=>0000000=>[8]=>[8]
[4,5,8,3,7,2,6,1]=>0000000=>[8]=>[8]
[5,3,4,6,8,2,1,7]=>0000000=>[8]=>[8]
[5,3,6,7,1,8,2,4]=>0000000=>[8]=>[8]
[5,3,4,6,7,1,8,2]=>0000000=>[8]=>[8]
[4,6,3,5,7,8,2,1]=>0000000=>[8]=>[8]
[4,5,7,3,6,8,2,1]=>0000000=>[8]=>[8]
[7,1,4,5,8,2,3,6]=>0000000=>[8]=>[8]
[2,1,7,5,8,3,4,6]=>0100000=>[2,6]=>[6,2]
[7,1,5,4,8,2,3,6]=>0000000=>[8]=>[8]
[8,3,7,1,2,4,6,5]=>0000000=>[8]=>[8]
[8,3,7,5,1,2,4,6]=>0000000=>[8]=>[8]
[6,7,1,8,4,2,3,5]=>0000000=>[8]=>[8]
[6,8,1,7,4,2,3,5]=>0000000=>[8]=>[8]
[7,1,8,4,5,2,3,6]=>0000000=>[8]=>[8]
[6,1,2,3,8,7,5,4]=>0000000=>[8]=>[8]
[6,8,3,1,2,7,4,5]=>0000000=>[8]=>[8]
[6,7,3,1,2,8,4,5]=>0000000=>[8]=>[8]
[6,7,1,4,2,3,8,5]=>0000000=>[8]=>[8]
[4,3,6,8,5,7,1,2]=>0000000=>[8]=>[8]
[6,1,2,5,4,8,3,7]=>0000000=>[8]=>[8]
[1,3,6,8,7,4,2,5]=>1000000=>[1,7]=>[7,1]
[1,2,8,5,7,3,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[3,6,1,4,2,7,8,5]=>0000000=>[8]=>[8]
[1,2,6,3,5,8,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,3,5,1,8,4,7,6]=>0000000=>[8]=>[8]
[3,1,7,5,4,8,6,2]=>0000000=>[8]=>[8]
[1,2,7,6,4,8,5,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,3,6,8,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,6,8,5,4,3,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,4,6,8,3,2,5,7]=>1000000=>[1,7]=>[7,1]
[1,2,6,7,3,8,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,7,3,8,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[4,6,2,7,5,8,3,1]=>0000000=>[8]=>[8]
[3,5,7,4,8,2,6,1]=>0000000=>[8]=>[8]
[1,3,5,8,2,7,4,6]=>1000000=>[1,7]=>[7,1]
[1,2,5,8,4,7,6,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,8,7,4,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,5,8,7,2,4,6]=>1000000=>[1,7]=>[7,1]
[3,2,7,4,6,8,1,5]=>0000000=>[8]=>[8]
[5,3,6,2,7,1,4,8]=>0000001=>[7,1]=>[7,1]
[2,6,3,4,7,1,5,8]=>0000001=>[7,1]=>[7,1]
[2,7,3,4,5,8,1,6]=>0000000=>[8]=>[8]
[4,7,6,2,3,8,1,5]=>0000000=>[8]=>[8]
[7,3,5,2,4,8,1,6]=>0000000=>[8]=>[8]
[7,6,2,4,5,8,1,3]=>0000000=>[8]=>[8]
[6,5,2,3,4,8,1,7]=>0000000=>[8]=>[8]
[5,3,1,2,8,4,7,6]=>0000000=>[8]=>[8]
[6,5,2,3,7,1,4,8]=>0000001=>[7,1]=>[7,1]
[5,2,1,7,3,4,6,8]=>0000001=>[7,1]=>[7,1]
[5,2,1,8,3,4,6,7]=>0000000=>[8]=>[8]
[6,3,2,8,4,5,7,1]=>0000000=>[8]=>[8]
[7,3,1,2,8,4,6,5]=>0000000=>[8]=>[8]
[6,2,3,1,8,4,7,5]=>0000000=>[8]=>[8]
[8,3,5,2,7,1,4,6]=>0000000=>[8]=>[8]
[8,6,2,4,7,1,5,3]=>0000000=>[8]=>[8]
[8,2,1,7,3,4,5,6]=>0000000=>[8]=>[8]
[8,6,3,7,2,4,5,1]=>0000000=>[8]=>[8]
[8,2,7,3,4,5,6,1]=>0000000=>[8]=>[8]
[8,1,6,2,3,4,5,7]=>0000000=>[8]=>[8]
[8,1,7,3,4,5,6,2]=>0000000=>[8]=>[8]
[8,6,1,7,2,4,5,3]=>0000000=>[8]=>[8]
[1,7,5,8,2,3,6,4]=>1000000=>[1,7]=>[7,1]
[7,2,1,8,3,4,5,6]=>0000000=>[8]=>[8]
[1,7,8,3,4,5,6,2]=>1000000=>[1,7]=>[7,1]
[1,6,2,8,4,5,7,3]=>1000000=>[1,7]=>[7,1]
[4,1,3,6,8,2,7,5]=>0000000=>[8]=>[8]
[4,6,3,8,7,1,2,5]=>0000000=>[8]=>[8]
[6,4,5,8,7,1,2,3]=>0000000=>[8]=>[8]
[5,3,4,8,7,1,2,6]=>0000000=>[8]=>[8]
[3,2,8,7,1,4,6,5]=>0000000=>[8]=>[8]
[3,1,8,7,2,4,6,5]=>0000000=>[8]=>[8]
[5,3,7,6,1,2,4,8]=>0000001=>[7,1]=>[7,1]
[1,8,3,7,2,4,5,6]=>1000000=>[1,7]=>[7,1]
[3,8,1,7,2,4,5,6]=>0000000=>[8]=>[8]
[6,8,2,3,5,1,4,7]=>0000000=>[8]=>[8]
[4,7,8,2,6,1,3,5]=>0000000=>[8]=>[8]
[6,2,8,7,1,4,5,3]=>0000000=>[8]=>[8]
[3,8,7,1,4,5,6,2]=>0000000=>[8]=>[8]
[2,8,6,1,3,4,5,7]=>0000000=>[8]=>[8]
[2,7,6,1,3,4,5,8]=>0000001=>[7,1]=>[7,1]
[1,7,6,2,3,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,6,2,3,4,5,7]=>1000000=>[1,7]=>[7,1]
[2,8,7,3,4,5,6,1]=>0000000=>[8]=>[8]
[3,8,7,2,4,5,6,1]=>0000000=>[8]=>[8]
[7,8,3,6,2,4,5,1]=>0000000=>[8]=>[8]
[1,5,8,7,2,3,6,4]=>1000000=>[1,7]=>[7,1]
[7,8,10,9,5,6,3,4,1,2]=>000000000=>[10]=>[10]
[9,10,5,6,8,7,3,4,1,2]=>000000000=>[10]=>[10]
[5,8,10,6,9,7,3,4,1,2]=>000000000=>[10]=>[10]
[5,6,7,10,9,8,3,4,1,2]=>000000000=>[10]=>[10]
[9,10,7,8,3,4,6,5,1,2]=>000000000=>[10]=>[10]
[7,8,10,9,3,4,6,5,1,2]=>000000000=>[10]=>[10]
[9,10,3,6,8,4,7,5,1,2]=>000000000=>[10]=>[10]
[3,8,10,6,9,4,7,5,1,2]=>000000000=>[10]=>[10]
[3,6,7,10,9,4,8,5,1,2]=>000000000=>[10]=>[10]
[9,10,3,4,5,8,7,6,1,2]=>000000000=>[10]=>[10]
[3,8,10,4,5,9,7,6,1,2]=>000000000=>[10]=>[10]
[3,4,7,10,5,9,8,6,1,2]=>000000000=>[10]=>[10]
[3,4,5,6,10,9,8,7,1,2]=>000000000=>[10]=>[10]
[9,10,7,8,5,6,1,2,4,3]=>000000000=>[10]=>[10]
[7,8,10,9,5,6,1,2,4,3]=>000000000=>[10]=>[10]
[9,10,5,6,8,7,1,2,4,3]=>000000000=>[10]=>[10]
[5,8,10,6,9,7,1,2,4,3]=>000000000=>[10]=>[10]
[5,6,7,10,9,8,1,2,4,3]=>000000000=>[10]=>[10]
[9,10,7,8,1,4,6,2,5,3]=>000000000=>[10]=>[10]
[7,8,10,9,1,4,6,2,5,3]=>000000000=>[10]=>[10]
[9,10,1,6,8,4,7,2,5,3]=>000000000=>[10]=>[10]
[1,8,10,6,9,4,7,2,5,3]=>100000000=>[1,9]=>[9,1]
[1,6,7,10,9,4,8,2,5,3]=>100000000=>[1,9]=>[9,1]
[9,10,1,4,5,8,7,2,6,3]=>000000000=>[10]=>[10]
[1,8,10,4,5,9,7,2,6,3]=>100000000=>[1,9]=>[9,1]
[1,4,7,10,5,9,8,2,6,3]=>100000000=>[1,9]=>[9,1]
[1,4,5,6,10,9,8,2,7,3]=>100000000=>[1,9]=>[9,1]
[9,10,7,8,1,2,3,6,5,4]=>000000000=>[10]=>[10]
[7,8,10,9,1,2,3,6,5,4]=>000000000=>[10]=>[10]
[9,10,1,6,8,2,3,7,5,4]=>000000000=>[10]=>[10]
[1,8,10,6,9,2,3,7,5,4]=>100000000=>[1,9]=>[9,1]
[1,6,7,10,9,2,3,8,5,4]=>100000000=>[1,9]=>[9,1]
[9,10,1,2,5,8,3,7,6,4]=>000000000=>[10]=>[10]
[1,8,10,2,5,9,3,7,6,4]=>100000000=>[1,9]=>[9,1]
[1,2,7,10,5,9,3,8,6,4]=>110000000=>[1,1,8]=>[8,1,1]
[1,2,5,6,10,9,3,8,7,4]=>110000000=>[1,1,8]=>[8,1,1]
[9,10,1,2,3,4,8,7,6,5]=>000000000=>[10]=>[10]
[1,8,10,2,3,4,9,7,6,5]=>100000000=>[1,9]=>[9,1]
[1,2,7,10,3,4,9,8,6,5]=>110000000=>[1,1,8]=>[8,1,1]
[1,2,3,6,10,4,9,8,7,5]=>111000000=>[1,1,1,7]=>[7,1,1,1]
[1,7,3,6,5,2,8,4]=>1000000=>[1,7]=>[7,1]
[8,6,2,5,4,1,7,3]=>0000000=>[8]=>[8]
[3,2,6,4,7,5,1,8]=>0000001=>[7,1]=>[7,1]
[6,2,3,7,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[1,3,4,7,6,2,8,5]=>1000000=>[1,7]=>[7,1]
[2,8,3,6,1,7,5,4]=>0000000=>[8]=>[8]
[8,7,2,5,1,6,4,3]=>0000000=>[8]=>[8]
[3,8,2,6,5,1,7,4]=>0000000=>[8]=>[8]
[7,8,2,5,4,1,6,3]=>0000000=>[8]=>[8]
[4,8,5,2,6,1,7,3]=>0000000=>[8]=>[8]
[4,5,1,3,7,2,8,6]=>0000000=>[8]=>[8]
[6,1,3,7,5,2,8,4]=>0000000=>[8]=>[8]
[7,1,3,6,2,8,5,4]=>0000000=>[8]=>[8]
[8,1,3,6,2,7,5,4]=>0000000=>[8]=>[8]
[1,2,4,7,3,8,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[7,1,8,2,6,5,4,3]=>0000000=>[8]=>[8]
[4,1,7,8,2,6,5,3]=>0000000=>[8]=>[8]
[3,4,8,6,5,1,7,2]=>0000000=>[8]=>[8]
[8,3,7,5,1,6,4,2]=>0000000=>[8]=>[8]
[1,4,8,6,2,7,5,3]=>1000000=>[1,7]=>[7,1]
[8,4,6,7,1,5,3,2]=>0000000=>[8]=>[8]
[3,4,6,5,1,2,8,7]=>0000010=>[6,2]=>[6,2]
[7,3,5,1,2,8,6,4]=>0000000=>[8]=>[8]
[1,4,6,2,3,8,7,5]=>1000000=>[1,7]=>[7,1]
[1,3,2,7,4,8,6,5]=>1010000=>[1,2,5]=>[5,2,1]
[7,2,1,6,3,8,5,4]=>0000000=>[8]=>[8]
[4,5,2,1,7,3,8,6]=>0000000=>[8]=>[8]
[5,6,7,1,2,8,4,3]=>0000000=>[8]=>[8]
[4,7,5,1,2,8,6,3]=>0000000=>[8]=>[8]
[3,7,1,6,2,8,5,4]=>0000000=>[8]=>[8]
[7,6,1,2,8,5,4,3]=>0000000=>[8]=>[8]
[2,7,1,3,8,6,5,4]=>0000000=>[8]=>[8]
[8,6,1,2,7,5,4,3]=>0000000=>[8]=>[8]
[1,7,2,3,8,6,5,4]=>1000000=>[1,7]=>[7,1]
[8,7,1,2,6,5,4,3]=>0000000=>[8]=>[8]
[7,8,1,2,6,5,4,3]=>0000000=>[8]=>[8]
[3,8,1,6,2,7,5,4]=>0000000=>[8]=>[8]
[4,8,5,1,2,7,6,3]=>0000000=>[8]=>[8]
[1,8,2,7,4,3,5,6]=>1000000=>[1,7]=>[7,1]
[1,8,6,4,7,2,3,5]=>1000000=>[1,7]=>[7,1]
[1,8,4,2,6,3,5,7]=>1000000=>[1,7]=>[7,1]
[7,4,8,1,5,2,3,6]=>0000000=>[8]=>[8]
[4,1,7,2,6,3,5,8]=>0000001=>[7,1]=>[7,1]
[5,1,7,4,3,6,2,8]=>0000001=>[7,1]=>[7,1]
[1,8,5,4,3,7,2,6]=>1000000=>[1,7]=>[7,1]
[1,8,4,2,5,3,7,6]=>1000000=>[1,7]=>[7,1]
[1,8,5,4,2,6,7,3]=>1000000=>[1,7]=>[7,1]
[7,4,8,2,1,3,5,6]=>0000000=>[8]=>[8]
[4,1,7,3,2,5,6,8]=>0000001=>[7,1]=>[7,1]
[7,5,4,8,2,3,6,1]=>0000000=>[8]=>[8]
[3,1,7,2,6,8,4,5]=>0000000=>[8]=>[8]
[5,1,7,4,2,6,8,3]=>0000000=>[8]=>[8]
[4,3,1,6,2,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,5,4,3,7,1,8,2]=>0000000=>[8]=>[8]
[6,5,1,7,3,8,2,4]=>0000000=>[8]=>[8]
[6,3,2,8,5,7,1,4]=>0000000=>[8]=>[8]
[5,4,8,2,1,7,3,6]=>0000000=>[8]=>[8]
[7,2,8,6,3,1,4,5]=>0000000=>[8]=>[8]
[2,1,7,8,3,6,4,5]=>0100000=>[2,6]=>[6,2]
[4,2,1,6,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[4,3,1,5,2,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[5,4,2,7,3,8,1,6]=>0000000=>[8]=>[8]
[3,1,6,2,8,7,4,5]=>0000000=>[8]=>[8]
[6,5,4,1,7,8,3,2]=>0000000=>[8]=>[8]
[5,4,3,1,6,7,2,8]=>0000001=>[7,1]=>[7,1]
[5,4,2,6,3,8,7,1]=>0000000=>[8]=>[8]
[4,3,1,5,2,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[5,4,2,1,6,7,8,3]=>0000000=>[8]=>[8]
[5,4,3,1,6,7,8,2]=>0000000=>[8]=>[8]
[7,8,2,4,5,1,3,6]=>0000000=>[8]=>[8]
[4,6,7,2,5,1,3,8]=>0000001=>[7,1]=>[7,1]
[7,8,1,3,2,4,5,6]=>0000000=>[8]=>[8]
[7,8,4,1,5,2,3,6]=>0000000=>[8]=>[8]
[3,6,7,2,1,4,5,8]=>0000001=>[7,1]=>[7,1]
[5,2,3,6,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,5,3,6,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,4,7,1,5,2,3,8]=>0000001=>[7,1]=>[7,1]
[6,2,7,3,1,4,5,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,6,7,8,1,2]=>0000000=>[8]=>[8]
[1,5,4,6,7,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,7,3,2,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,3,6,2,4,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[5,1,3,6,2,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,2,4,6,7,1,3,8]=>0000001=>[7,1]=>[7,1]
[2,6,7,4,5,1,3,8]=>0000001=>[7,1]=>[7,1]
[4,2,5,6,7,1,3,8]=>0000001=>[7,1]=>[7,1]
[4,5,2,6,7,1,3,8]=>0000001=>[7,1]=>[7,1]
[5,3,1,6,2,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,1,7,3,2,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,1,7,4,5,2,3,8]=>0000001=>[7,1]=>[7,1]
[6,3,7,4,5,8,1,2]=>0000000=>[8]=>[8]
[5,4,1,6,7,2,3,8]=>0000001=>[7,1]=>[7,1]
[5,2,1,6,3,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,3,6,7,5,2,8,4]=>1000000=>[1,7]=>[7,1]
[1,3,4,5,8,7,2,6]=>1000000=>[1,7]=>[7,1]
[3,1,2,5,6,8,7,4]=>0010000=>[3,5]=>[5,3]
[7,1,5,2,6,8,3,4]=>0000000=>[8]=>[8]
[2,3,6,7,5,1,8,4]=>0000000=>[8]=>[8]
[4,3,2,6,7,1,8,5]=>0000000=>[8]=>[8]
[7,1,5,4,6,8,3,2]=>0000000=>[8]=>[8]
[5,7,4,6,1,8,3,2]=>0000000=>[8]=>[8]
[6,3,4,5,8,1,2,7]=>0000000=>[8]=>[8]
[6,2,1,7,3,5,4,8]=>0000001=>[7,1]=>[7,1]
[2,1,8,6,3,5,4,7]=>0100000=>[2,6]=>[6,2]
[2,7,3,1,5,4,6,8]=>0000001=>[7,1]=>[7,1]
[2,6,3,1,4,8,5,7]=>0000000=>[8]=>[8]
[4,2,1,8,3,6,7,5]=>0000000=>[8]=>[8]
[6,2,1,7,3,5,8,4]=>0000000=>[8]=>[8]
[2,7,3,1,4,8,5,6]=>0000000=>[8]=>[8]
[3,2,1,5,7,8,4,6]=>0010000=>[3,5]=>[5,3]
[2,4,7,5,1,6,8,3]=>0000000=>[8]=>[8]
[4,3,6,8,5,1,7,2]=>0000000=>[8]=>[8]
[2,1,6,8,3,7,4,5]=>0100000=>[2,6]=>[6,2]
[3,2,1,5,6,8,4,7]=>0010000=>[3,5]=>[5,3]
[2,1,7,3,6,4,5,8]=>0100001=>[2,5,1]=>[5,2,1]
[2,1,6,3,5,8,4,7]=>0100000=>[2,6]=>[6,2]
[2,6,1,8,3,5,4,7]=>0000000=>[8]=>[8]
[2,7,3,1,5,6,4,8]=>0000001=>[7,1]=>[7,1]
[2,4,7,5,1,6,3,8]=>0000001=>[7,1]=>[7,1]
[8,2,4,1,7,5,3,6]=>0000000=>[8]=>[8]
[2,4,7,1,8,5,3,6]=>0000000=>[8]=>[8]
[2,4,8,5,1,6,3,7]=>0000000=>[8]=>[8]
[6,2,1,7,3,4,8,5]=>0000000=>[8]=>[8]
[6,2,1,7,8,3,5,4]=>0000000=>[8]=>[8]
[2,7,1,8,3,5,6,4]=>0000000=>[8]=>[8]
[3,2,1,6,7,4,5,8]=>0010001=>[3,4,1]=>[4,3,1]
[3,2,1,7,4,5,6,8]=>0010001=>[3,4,1]=>[4,3,1]
[2,1,8,3,7,4,5,6]=>0100000=>[2,6]=>[6,2]
[2,4,8,5,1,6,7,3]=>0000000=>[8]=>[8]
[4,3,8,5,6,1,7,2]=>0000000=>[8]=>[8]
[3,2,1,8,4,5,6,7]=>0010000=>[3,5]=>[5,3]
[1,6,8,3,7,2,4,5]=>1000000=>[1,7]=>[7,1]
[3,8,1,5,7,2,4,6]=>0000000=>[8]=>[8]
[1,2,6,8,4,7,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[6,1,5,8,2,4,7,3]=>0000000=>[8]=>[8]
[1,2,4,8,3,6,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[4,1,2,7,8,3,6,5]=>0000000=>[8]=>[8]
[5,3,8,4,7,6,1,2]=>0000000=>[8]=>[8]
[8,7,1,2,5,4,6,3]=>0000000=>[8]=>[8]
[5,8,1,2,3,7,6,4]=>0000000=>[8]=>[8]
[1,2,8,4,3,5,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,5,3,7,6,4,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[6,1,2,8,7,4,5,3]=>0000000=>[8]=>[8]
[7,1,6,2,8,4,5,3]=>0000000=>[8]=>[8]
[1,2,6,3,8,5,4,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,8,5,3,6,4,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,3,8,5,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,2,8,4,3,5,7]=>1000000=>[1,7]=>[7,1]
[1,6,4,2,7,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,6,3,2,4,5,7]=>1000000=>[1,7]=>[7,1]
[3,1,7,8,6,2,4,5]=>0000000=>[8]=>[8]
[1,8,7,3,5,6,2,4]=>1000000=>[1,7]=>[7,1]
[1,3,2,8,7,4,5,6]=>1010000=>[1,2,5]=>[5,2,1]
[1,2,8,4,3,7,5,6]=>1100000=>[1,1,6]=>[6,1,1]
[8,5,1,7,2,4,6,3]=>0000000=>[8]=>[8]
[3,8,6,4,7,5,1,2]=>0000000=>[8]=>[8]
[6,1,8,2,7,4,5,3]=>0000000=>[8]=>[8]
[1,2,7,5,3,6,4,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,2,6,3,7,5,4,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,2,3,7,5,4,8,6]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[3,7,4,8,6,5,1,2]=>0000000=>[8]=>[8]
[1,8,2,7,6,4,5,3]=>1000000=>[1,7]=>[7,1]
[7,4,6,3,8,5,1,2]=>0000000=>[8]=>[8]
[8,4,6,2,7,5,3,1]=>0000000=>[8]=>[8]
[6,5,7,8,4,1,3,2]=>0000000=>[8]=>[8]
[7,5,6,8,2,4,1,3]=>0000000=>[8]=>[8]
[7,4,6,2,8,5,1,3]=>0000000=>[8]=>[8]
[4,3,2,6,8,5,1,7]=>0000000=>[8]=>[8]
[3,5,6,8,2,4,1,7]=>0000000=>[8]=>[8]
[2,6,7,8,1,4,5,3]=>0000000=>[8]=>[8]
[3,6,7,8,1,4,2,5]=>0000000=>[8]=>[8]
[3,5,7,8,2,1,4,6]=>0000000=>[8]=>[8]
[2,6,7,8,1,4,3,5]=>0000000=>[8]=>[8]
[2,5,7,8,3,1,4,6]=>0000000=>[8]=>[8]
[2,4,7,3,8,1,5,6]=>0000000=>[8]=>[8]
[6,4,7,3,8,1,5,2]=>0000000=>[8]=>[8]
[6,4,7,3,8,1,2,5]=>0000000=>[8]=>[8]
[7,4,6,3,8,2,1,5]=>0000000=>[8]=>[8]
[6,3,2,5,4,8,1,7]=>0000000=>[8]=>[8]
[6,4,5,2,3,8,1,7]=>0000000=>[8]=>[8]
[5,4,6,3,8,2,1,7]=>0000000=>[8]=>[8]
[5,4,7,3,8,1,6,2]=>0000000=>[8]=>[8]
[2,5,7,8,3,1,6,4]=>0000000=>[8]=>[8]
[4,5,7,8,3,1,2,6]=>0000000=>[8]=>[8]
[4,5,6,8,2,3,1,7]=>0000000=>[8]=>[8]
[5,4,6,2,8,3,1,7]=>0000000=>[8]=>[8]
[5,3,2,6,8,4,1,7]=>0000000=>[8]=>[8]
[5,4,7,2,8,1,3,6]=>0000000=>[8]=>[8]
[4,5,7,8,2,1,3,6]=>0000000=>[8]=>[8]
[4,6,7,8,1,3,2,5]=>0000000=>[8]=>[8]
[4,6,7,8,1,3,5,2]=>0000000=>[8]=>[8]
[2,6,7,8,1,3,5,4]=>0000000=>[8]=>[8]
[2,6,7,8,1,5,3,4]=>0000000=>[8]=>[8]
[4,6,7,8,1,5,2,3]=>0000000=>[8]=>[8]
[4,6,7,8,1,2,5,3]=>0000000=>[8]=>[8]
[5,3,2,7,8,1,6,4]=>0000000=>[8]=>[8]
[4,3,2,7,8,1,6,5]=>0000000=>[8]=>[8]
[3,5,7,8,2,1,6,4]=>0000000=>[8]=>[8]
[3,6,7,8,1,5,4,2]=>0000000=>[8]=>[8]
[2,6,7,8,1,5,4,3]=>0000000=>[8]=>[8]
[4,5,8,3,6,7,1,2]=>0000000=>[8]=>[8]
[4,5,8,3,7,6,1,2]=>0000000=>[8]=>[8]
[4,2,8,3,7,1,6,5]=>0000000=>[8]=>[8]
[7,2,3,4,8,1,5,6]=>0000000=>[8]=>[8]
[7,6,3,4,8,5,1,2]=>0000000=>[8]=>[8]
[7,6,3,5,8,4,1,2]=>0000000=>[8]=>[8]
[7,6,3,8,4,5,1,2]=>0000000=>[8]=>[8]
[7,2,3,8,5,1,4,6]=>0000000=>[8]=>[8]
[2,6,4,8,1,5,7,3]=>0000000=>[8]=>[8]
[7,2,3,8,4,1,5,6]=>0000000=>[8]=>[8]
[7,8,2,3,6,1,4,5]=>0000000=>[8]=>[8]
[4,2,6,3,7,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,2,3,5,8,1,6,4]=>0000000=>[8]=>[8]
[7,2,3,8,4,1,6,5]=>0000000=>[8]=>[8]
[2,6,4,8,1,3,7,5]=>0000000=>[8]=>[8]
[3,6,4,8,1,7,5,2]=>0000000=>[8]=>[8]
[7,6,5,1,2,3,8,4]=>0000000=>[8]=>[8]
[7,6,5,1,4,2,8,3]=>0000000=>[8]=>[8]
[7,8,5,4,1,2,6,3]=>0000000=>[8]=>[8]
[3,5,6,4,1,2,8,7]=>0000010=>[6,2]=>[6,2]
[7,6,5,1,2,4,3,8]=>0000001=>[7,1]=>[7,1]
[7,6,5,1,2,4,8,3]=>0000000=>[8]=>[8]
[7,6,5,1,3,2,4,8]=>0000001=>[7,1]=>[7,1]
[2,6,4,3,1,8,7,5]=>0000000=>[8]=>[8]
[3,5,8,4,1,2,7,6]=>0000000=>[8]=>[8]
[3,5,8,4,1,2,6,7]=>0000000=>[8]=>[8]
[3,5,8,4,1,6,2,7]=>0000000=>[8]=>[8]
[2,5,8,4,1,7,3,6]=>0000000=>[8]=>[8]
[3,6,4,2,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[3,5,6,4,1,8,7,2]=>0000000=>[8]=>[8]
[2,6,4,5,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[7,6,5,1,4,3,8,2]=>0000000=>[8]=>[8]
[7,6,5,1,2,8,3,4]=>0000000=>[8]=>[8]
[7,6,5,1,8,2,4,3]=>0000000=>[8]=>[8]
[7,6,5,1,8,2,3,4]=>0000000=>[8]=>[8]
[7,6,5,1,8,3,2,4]=>0000000=>[8]=>[8]
[7,6,5,1,4,8,2,3]=>0000000=>[8]=>[8]
[3,6,4,5,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[2,5,6,4,1,7,8,3]=>0000000=>[8]=>[8]
[2,5,6,4,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[3,6,4,5,1,7,8,2]=>0000000=>[8]=>[8]
[7,6,5,1,4,8,3,2]=>0000000=>[8]=>[8]
[7,6,5,1,8,3,4,2]=>0000000=>[8]=>[8]
[7,6,5,1,8,4,2,3]=>0000000=>[8]=>[8]
[6,7,4,2,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,4,8,3,1,5,2]=>0000000=>[8]=>[8]
[7,4,8,5,6,1,3,2]=>0000000=>[8]=>[8]
[7,4,2,5,6,3,1,8]=>0000001=>[7,1]=>[7,1]
[4,2,7,5,6,3,1,8]=>0000001=>[7,1]=>[7,1]
[4,7,3,5,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[1,6,8,5,2,7,4,3]=>1000000=>[1,7]=>[7,1]
[6,2,8,5,1,7,4,3]=>0000000=>[8]=>[8]
[6,7,4,8,2,1,5,3]=>0000000=>[8]=>[8]
[3,2,7,8,6,1,5,4]=>0000000=>[8]=>[8]
[6,8,4,1,2,3,7,5]=>0000000=>[8]=>[8]
[1,8,2,5,6,4,3,7]=>1000000=>[1,7]=>[7,1]
[6,1,8,5,3,7,4,2]=>0000000=>[8]=>[8]
[3,8,1,5,2,7,6,4]=>0000000=>[8]=>[8]
[8,2,1,5,3,7,6,4]=>0000000=>[8]=>[8]
[8,1,6,5,3,7,2,4]=>0000000=>[8]=>[8]
[7,1,4,6,3,2,8,5]=>0000000=>[8]=>[8]
[3,2,6,4,1,7,8,5]=>0000000=>[8]=>[8]
[7,6,4,3,1,2,8,5]=>0000000=>[8]=>[8]
[8,6,3,5,1,7,2,4]=>0000000=>[8]=>[8]
[4,5,3,1,6,7,8,2]=>0000000=>[8]=>[8]
[3,5,2,1,6,7,8,4]=>0000000=>[8]=>[8]
[5,2,3,1,6,7,8,4]=>0000000=>[8]=>[8]
[1,5,3,2,6,7,8,4]=>1000000=>[1,7]=>[7,1]
[8,2,7,5,6,1,3,4]=>0000000=>[8]=>[8]
[1,7,4,6,2,3,8,5]=>1000000=>[1,7]=>[7,1]
[7,6,4,2,1,5,8,3]=>0000000=>[8]=>[8]
[5,7,4,6,1,3,8,2]=>0000000=>[8]=>[8]
[8,6,4,7,3,1,2,5]=>0000000=>[8]=>[8]
[5,2,4,3,7,1,8,6]=>0000000=>[8]=>[8]
[8,6,4,1,3,5,2,7]=>0000000=>[8]=>[8]
[6,7,4,1,5,3,8,2]=>0000000=>[8]=>[8]
[7,5,4,1,2,6,8,3]=>0000000=>[8]=>[8]
[1,8,2,5,3,7,6,4]=>1000000=>[1,7]=>[7,1]
[3,8,1,5,6,4,2,7]=>0000000=>[8]=>[8]
[7,6,4,1,5,2,8,3]=>0000000=>[8]=>[8]
[8,6,1,5,4,7,2,3]=>0000000=>[8]=>[8]
[5,2,1,4,6,7,8,3]=>0000000=>[8]=>[8]
[5,4,1,3,6,7,8,2]=>0000000=>[8]=>[8]
[8,4,1,5,3,7,2,6]=>0000000=>[8]=>[8]
[7,5,4,1,3,2,8,6]=>0000000=>[8]=>[8]
[3,2,5,1,4,7,8,6]=>0000100=>[5,3]=>[5,3]
[5,1,3,4,6,7,8,2]=>0000000=>[8]=>[8]
[5,7,4,1,8,6,3,2]=>0000000=>[8]=>[8]
[3,6,7,4,5,8,2,1]=>0000000=>[8]=>[8]
[5,4,6,1,7,8,3,2]=>0000000=>[8]=>[8]
[3,7,1,5,4,6,8,2]=>0000000=>[8]=>[8]
[6,7,1,4,5,3,8,2]=>0000000=>[8]=>[8]
[5,4,7,2,8,3,6,1]=>0000000=>[8]=>[8]
[3,8,1,5,4,6,2,7]=>0000000=>[8]=>[8]
[3,6,1,5,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,6,1,5,4,8,2,7]=>0000000=>[8]=>[8]
[3,4,1,2,6,8,7,5]=>0001000=>[4,4]=>[4,4]
[3,8,1,5,4,7,2,6]=>0000000=>[8]=>[8]
[7,8,3,1,4,6,2,5]=>0000000=>[8]=>[8]
[6,5,8,7,3,4,2,1]=>0000000=>[8]=>[8]
[3,7,1,5,4,2,6,8]=>0000001=>[7,1]=>[7,1]
[3,8,1,5,4,2,7,6]=>0000000=>[8]=>[8]
[6,7,3,1,4,5,8,2]=>0000000=>[8]=>[8]
[2,5,6,1,4,7,8,3]=>0000000=>[8]=>[8]
[1,8,4,5,2,7,3,6]=>1000000=>[1,7]=>[7,1]
[1,8,4,5,2,7,6,3]=>1000000=>[1,7]=>[7,1]
[1,8,4,3,6,2,5,7]=>1000000=>[1,7]=>[7,1]
[2,7,6,4,8,5,3,1]=>0000000=>[8]=>[8]
[1,8,4,5,2,6,3,7]=>1000000=>[1,7]=>[7,1]
[7,3,5,8,4,6,2,1]=>0000000=>[8]=>[8]
[8,2,1,3,5,7,4,6]=>0000000=>[8]=>[8]
[7,5,4,1,3,8,2,6]=>0000000=>[8]=>[8]
[7,3,8,5,4,1,2,6]=>0000000=>[8]=>[8]
[1,7,2,3,5,8,4,6]=>1000000=>[1,7]=>[7,1]
[3,5,2,6,7,1,8,4]=>0000000=>[8]=>[8]
[3,2,8,4,7,5,1,6]=>0000000=>[8]=>[8]
[6,8,3,1,7,2,4,5]=>0000000=>[8]=>[8]
[2,7,5,3,8,4,1,6]=>0000000=>[8]=>[8]
[8,3,2,1,5,7,4,6]=>0000000=>[8]=>[8]
[1,2,8,3,5,7,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[6,5,1,7,4,2,8,3]=>0000000=>[8]=>[8]
[7,3,6,4,8,2,1,5]=>0000000=>[8]=>[8]
[4,6,1,7,3,5,2,8]=>0000001=>[7,1]=>[7,1]
[5,6,1,7,3,4,2,8]=>0000001=>[7,1]=>[7,1]
[6,1,7,3,4,2,8,5]=>0000000=>[8]=>[8]
[7,3,8,1,6,5,2,4]=>0000000=>[8]=>[8]
[8,3,7,1,6,5,2,4]=>0000000=>[8]=>[8]
[2,8,1,7,6,5,3,4]=>0000000=>[8]=>[8]
[4,2,8,6,5,1,7,3]=>0000000=>[8]=>[8]
[8,6,4,7,1,5,2,3]=>0000000=>[8]=>[8]
[7,6,4,8,1,5,2,3]=>0000000=>[8]=>[8]
[5,1,6,4,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,2,3,8,7,5,1,6]=>0000000=>[8]=>[8]
[3,8,7,1,6,5,2,4]=>0000000=>[8]=>[8]
[2,4,3,8,1,6,7,5]=>0000000=>[8]=>[8]
[2,4,3,7,1,6,8,5]=>0000000=>[8]=>[8]
[4,2,3,7,8,5,1,6]=>0000000=>[8]=>[8]
[5,1,6,4,2,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,4,7,8,1,5,2,3]=>0000000=>[8]=>[8]
[8,7,4,6,1,5,2,3]=>0000000=>[8]=>[8]
[6,5,7,8,1,4,2,3]=>0000000=>[8]=>[8]
[4,7,8,6,1,5,2,3]=>0000000=>[8]=>[8]
[3,2,4,8,7,1,5,6]=>0000000=>[8]=>[8]
[4,8,7,6,1,5,2,3]=>0000000=>[8]=>[8]
[5,8,7,6,1,4,2,3]=>0000000=>[8]=>[8]
[8,6,5,7,1,4,2,3]=>0000000=>[8]=>[8]
[5,1,6,7,4,2,3,8]=>0000001=>[7,1]=>[7,1]
[6,7,4,8,1,5,2,3]=>0000000=>[8]=>[8]
[8,4,7,6,1,5,2,3]=>0000000=>[8]=>[8]
[8,3,2,4,7,1,5,6]=>0000000=>[8]=>[8]
[7,3,2,4,8,1,5,6]=>0000000=>[8]=>[8]
[2,5,3,7,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[8,4,6,7,1,5,2,3]=>0000000=>[8]=>[8]
[5,1,6,8,4,2,3,7]=>0000000=>[8]=>[8]
[4,2,3,7,5,1,6,8]=>0000001=>[7,1]=>[7,1]
[2,4,3,7,1,6,5,8]=>0000001=>[7,1]=>[7,1]
[2,4,7,1,5,8,6,3]=>0000000=>[8]=>[8]
[3,2,4,7,6,1,5,8]=>0000001=>[7,1]=>[7,1]
[4,7,6,8,1,5,2,3]=>0000000=>[8]=>[8]
[8,5,6,7,1,4,2,3]=>0000000=>[8]=>[8]
[8,6,7,5,1,4,2,3]=>0000000=>[8]=>[8]
[6,8,7,5,1,4,2,3]=>0000000=>[8]=>[8]
[5,6,8,7,1,4,2,3]=>0000000=>[8]=>[8]
[4,6,8,7,1,5,2,3]=>0000000=>[8]=>[8]
[3,2,4,6,1,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,7,8,5,1,4,2,3]=>0000000=>[8]=>[8]
[7,8,6,5,1,4,2,3]=>0000000=>[8]=>[8]
[2,1,8,5,4,6,3,7]=>0100000=>[2,6]=>[6,2]
[4,1,8,5,2,3,6,7]=>0000000=>[8]=>[8]
[5,4,1,3,6,7,2,8]=>0000001=>[7,1]=>[7,1]
[8,4,1,2,6,3,7,5]=>0000000=>[8]=>[8]
[8,2,7,1,5,3,4,6]=>0000000=>[8]=>[8]
[3,2,7,1,5,8,4,6]=>0000000=>[8]=>[8]
[7,3,8,1,5,4,2,6]=>0000000=>[8]=>[8]
[7,1,5,3,8,4,2,6]=>0000000=>[8]=>[8]
[3,6,8,1,5,4,2,7]=>0000000=>[8]=>[8]
[6,8,3,1,5,4,2,7]=>0000000=>[8]=>[8]
[7,6,3,1,5,4,2,8]=>0000001=>[7,1]=>[7,1]
[3,6,2,1,5,8,4,7]=>0000000=>[8]=>[8]
[8,6,2,1,5,3,4,7]=>0000000=>[8]=>[8]
[2,3,8,1,5,7,4,6]=>0000000=>[8]=>[8]
[7,1,3,2,8,6,4,5]=>0000000=>[8]=>[8]
[4,7,1,2,6,3,8,5]=>0000000=>[8]=>[8]
[2,7,8,1,5,3,4,6]=>0000000=>[8]=>[8]
[6,7,2,1,5,3,4,8]=>0000001=>[7,1]=>[7,1]
[4,7,2,1,8,5,3,6]=>0000000=>[8]=>[8]
[8,7,2,1,4,5,3,6]=>0000000=>[8]=>[8]
[5,7,8,6,1,4,3,2]=>0000000=>[8]=>[8]
[2,7,4,1,6,5,3,8]=>0000001=>[7,1]=>[7,1]
[7,1,6,4,5,8,3,2]=>0000000=>[8]=>[8]
[2,6,4,1,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[5,6,8,7,1,4,3,2]=>0000000=>[8]=>[8]
[4,2,8,1,6,5,3,7]=>0000000=>[8]=>[8]
[6,2,4,1,8,5,3,7]=>0000000=>[8]=>[8]
[8,3,1,4,5,6,7,2]=>0000000=>[8]=>[8]
[5,3,1,4,8,6,7,2]=>0000000=>[8]=>[8]
[7,5,1,6,3,4,8,2]=>0000000=>[8]=>[8]
[7,1,5,8,4,3,6,2]=>0000000=>[8]=>[8]
[5,8,1,6,4,3,7,2]=>0000000=>[8]=>[8]
[5,3,1,8,4,6,7,2]=>0000000=>[8]=>[8]
[8,3,1,5,4,6,7,2]=>0000000=>[8]=>[8]
[8,2,6,1,4,5,3,7]=>0000000=>[8]=>[8]
[6,2,8,1,4,5,3,7]=>0000000=>[8]=>[8]
[7,2,6,1,5,3,4,8]=>0000001=>[7,1]=>[7,1]
[2,8,6,1,5,3,4,7]=>0000000=>[8]=>[8]
[4,2,1,5,6,3,8,7]=>0000010=>[6,2]=>[6,2]
[7,1,2,5,8,3,4,6]=>0000000=>[8]=>[8]
[7,1,4,5,6,8,3,2]=>0000000=>[8]=>[8]
[2,6,7,1,4,5,3,8]=>0000001=>[7,1]=>[7,1]
[3,5,1,7,4,6,8,2]=>0000000=>[8]=>[8]
[7,1,5,6,4,8,3,2]=>0000000=>[8]=>[8]
[7,1,6,5,4,8,3,2]=>0000000=>[8]=>[8]
[2,7,6,1,4,5,3,8]=>0000001=>[7,1]=>[7,1]
[5,7,6,8,1,4,3,2]=>0000000=>[8]=>[8]
[7,8,6,5,1,4,3,2]=>0000000=>[8]=>[8]
[5,3,1,2,4,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,3,6,2,1,8,7,4]=>0000000=>[8]=>[8]
[5,3,7,2,8,4,1,6]=>0000000=>[8]=>[8]
[7,2,4,5,8,3,1,6]=>0000000=>[8]=>[8]
[7,2,4,5,1,3,6,8]=>0000001=>[7,1]=>[7,1]
[6,2,4,5,1,8,7,3]=>0000000=>[8]=>[8]
[3,1,4,5,2,8,7,6]=>0000100=>[5,3]=>[5,3]
[1,6,4,5,2,8,7,3]=>1000000=>[1,7]=>[7,1]
[3,7,4,5,1,2,6,8]=>0000001=>[7,1]=>[7,1]
[1,7,4,2,6,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,7,4,5,2,1,6,3]=>0000000=>[8]=>[8]
[6,3,7,1,8,4,2,5]=>0000000=>[8]=>[8]
[5,7,4,1,6,3,2,8]=>0000001=>[7,1]=>[7,1]
[1,7,4,8,6,3,2,5]=>1000000=>[1,7]=>[7,1]
[5,7,4,8,6,3,1,2]=>0000000=>[8]=>[8]
[4,8,3,5,6,7,1,2]=>0000000=>[8]=>[8]
[1,8,3,5,6,7,2,4]=>1000000=>[1,7]=>[7,1]
[4,8,1,5,6,7,2,3]=>0000000=>[8]=>[8]
[4,1,3,5,6,7,2,8]=>0000001=>[7,1]=>[7,1]
[5,8,4,3,6,1,2,7]=>0000000=>[8]=>[8]
[5,3,8,4,1,7,2,6]=>0000000=>[8]=>[8]
[1,5,8,4,6,7,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,8,3,6,7,5,2]=>1000000=>[1,7]=>[7,1]
[4,3,8,2,1,7,5,6]=>0000000=>[8]=>[8]
[3,8,4,2,6,1,5,7]=>0000000=>[8]=>[8]
[3,8,1,5,6,7,4,2]=>0000000=>[8]=>[8]
[3,8,2,5,6,7,1,4]=>0000000=>[8]=>[8]
[8,2,1,5,6,7,4,3]=>0000000=>[8]=>[8]
[8,1,3,5,6,7,4,2]=>0000000=>[8]=>[8]
[7,1,4,3,6,2,5,8]=>0000001=>[7,1]=>[7,1]
[7,8,4,3,6,2,1,5]=>0000000=>[8]=>[8]
[4,3,1,8,5,7,6,2]=>0000000=>[8]=>[8]
[6,3,5,8,2,7,1,4]=>0000000=>[8]=>[8]
[7,5,4,8,6,2,1,3]=>0000000=>[8]=>[8]
[7,1,4,8,6,2,3,5]=>0000000=>[8]=>[8]
[7,5,4,1,6,2,3,8]=>0000001=>[7,1]=>[7,1]
[1,6,4,5,8,2,3,7]=>1000000=>[1,7]=>[7,1]
[1,8,5,3,6,7,4,2]=>1000000=>[1,7]=>[7,1]
[8,3,5,2,1,7,4,6]=>0000000=>[8]=>[8]
[4,1,8,5,6,7,3,2]=>0000000=>[8]=>[8]
[1,2,8,5,6,7,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[4,2,1,5,6,7,3,8]=>0000001=>[7,1]=>[7,1]
[1,5,3,8,6,7,4,2]=>1000000=>[1,7]=>[7,1]
[1,4,8,5,6,7,2,3]=>1000000=>[1,7]=>[7,1]
[2,6,5,7,3,1,8,4]=>0000000=>[8]=>[8]
[6,3,2,4,7,5,1,8]=>0000001=>[7,1]=>[7,1]
[4,2,1,6,3,7,5,8]=>0000001=>[7,1]=>[7,1]
[4,2,1,6,3,7,8,5]=>0000000=>[8]=>[8]
[4,2,1,3,7,8,6,5]=>0001000=>[4,4]=>[4,4]
[5,8,1,7,4,3,2,6]=>0000000=>[8]=>[8]
[7,3,4,2,6,8,1,5]=>0000000=>[8]=>[8]
[3,6,7,5,2,4,8,1]=>0000000=>[8]=>[8]
[4,8,1,7,3,6,5,2]=>0000000=>[8]=>[8]
[4,2,1,8,3,7,6,5]=>0000000=>[8]=>[8]
[2,6,1,5,4,7,8,3]=>0000000=>[8]=>[8]
[4,6,3,5,8,7,1,2]=>0000000=>[8]=>[8]
[4,7,5,2,1,3,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,6,2,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,1,8,5,2,7,6,4]=>0000000=>[8]=>[8]
[4,8,1,5,2,7,3,6]=>0000000=>[8]=>[8]
[4,1,2,5,3,8,7,6]=>0000100=>[5,3]=>[5,3]
[4,3,6,8,7,5,1,2]=>0000000=>[8]=>[8]
[6,4,8,1,2,5,3,7]=>0000000=>[8]=>[8]
[6,5,1,2,3,4,8,7]=>0000010=>[6,2]=>[6,2]
[6,7,4,1,2,5,3,8]=>0000001=>[7,1]=>[7,1]
[1,2,6,7,5,3,8,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,7,5,3,2,8,4,6]=>1000000=>[1,7]=>[7,1]
[1,6,5,7,2,3,8,4]=>1000000=>[1,7]=>[7,1]
[1,3,8,2,6,5,7,4]=>1000000=>[1,7]=>[7,1]
[1,2,5,7,6,3,4,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,3,4,8,2,5,7,6]=>1000000=>[1,7]=>[7,1]
[1,5,7,6,2,3,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,3,8,2,6,4,7]=>1000000=>[1,7]=>[7,1]
[1,4,8,3,2,5,7,6]=>1000000=>[1,7]=>[7,1]
[1,2,4,8,3,5,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,8,4,2,6,7,5]=>1000000=>[1,7]=>[7,1]
[1,4,8,2,3,5,7,6]=>1000000=>[1,7]=>[7,1]
[4,2,6,7,5,8,3,1]=>0000000=>[8]=>[8]
[6,7,5,2,1,8,4,3]=>0000000=>[8]=>[8]
[3,4,8,7,5,2,1,6]=>0000000=>[8]=>[8]
[1,7,5,2,8,4,6,3]=>1000000=>[1,7]=>[7,1]
[5,6,8,3,1,7,2,4]=>0000000=>[8]=>[8]
[6,1,4,8,3,2,7,5]=>0000000=>[8]=>[8]
[3,4,7,1,8,6,2,5]=>0000000=>[8]=>[8]
[3,4,6,8,2,1,5,7]=>0000000=>[8]=>[8]
[3,8,2,5,6,1,4,7]=>0000000=>[8]=>[8]
[3,5,2,8,6,4,1,7]=>0000000=>[8]=>[8]
[4,2,5,7,3,8,6,1]=>0000000=>[8]=>[8]
[7,4,2,5,3,8,1,6]=>0000000=>[8]=>[8]
[1,5,6,8,3,4,2,7]=>1000000=>[1,7]=>[7,1]
[4,5,1,6,8,3,2,7]=>0000000=>[8]=>[8]
[4,5,7,3,8,2,6,1]=>0000000=>[8]=>[8]
[6,4,3,7,8,2,5,1]=>0000000=>[8]=>[8]
[6,4,3,1,7,8,2,5]=>0000000=>[8]=>[8]
[4,5,3,1,7,8,2,6]=>0000000=>[8]=>[8]
[7,1,3,5,4,8,2,6]=>0000000=>[8]=>[8]
[7,5,2,8,1,4,3,6]=>0000000=>[8]=>[8]
[1,4,5,7,3,8,6,2]=>1000000=>[1,7]=>[7,1]
[4,6,3,7,8,5,2,1]=>0000000=>[8]=>[8]
[1,5,3,6,7,8,4,2]=>1000000=>[1,7]=>[7,1]
[4,6,1,7,3,8,5,2]=>0000000=>[8]=>[8]
[6,7,2,4,8,1,5,3]=>0000000=>[8]=>[8]
[5,2,3,6,7,8,4,1]=>0000000=>[8]=>[8]
[6,4,2,7,1,8,3,5]=>0000000=>[8]=>[8]
[4,2,6,3,7,8,5,1]=>0000000=>[8]=>[8]
[6,7,3,8,2,4,5,1]=>0000000=>[8]=>[8]
[3,6,2,7,4,1,8,5]=>0000000=>[8]=>[8]
[6,7,3,2,1,4,8,5]=>0000000=>[8]=>[8]
[7,2,4,8,6,1,3,5]=>0000000=>[8]=>[8]
[3,5,7,2,1,8,6,4]=>0000000=>[8]=>[8]
[6,7,8,3,2,5,1,4]=>0000000=>[8]=>[8]
[6,3,7,8,2,5,4,1]=>0000000=>[8]=>[8]
[2,6,7,4,8,5,3,1]=>0000000=>[8]=>[8]
[6,2,4,7,1,8,5,3]=>0000000=>[8]=>[8]
[1,7,4,8,5,2,6,3]=>1000000=>[1,7]=>[7,1]
[1,3,7,8,5,2,6,4]=>1000000=>[1,7]=>[7,1]
[2,5,7,8,1,6,3,4]=>0000000=>[8]=>[8]
[1,6,4,7,8,2,5,3]=>1000000=>[1,7]=>[7,1]
[2,5,6,1,7,8,4,3]=>0000000=>[8]=>[8]
[5,6,1,2,7,8,4,3]=>0000000=>[8]=>[8]
[6,7,2,1,8,5,3,4]=>0000000=>[8]=>[8]
[6,4,2,5,3,8,7,1]=>0000000=>[8]=>[8]
[2,6,4,5,8,7,3,1]=>0000000=>[8]=>[8]
[2,6,4,8,7,5,3,1]=>0000000=>[8]=>[8]
[8,2,4,6,7,5,3,1]=>0000000=>[8]=>[8]
[4,2,6,8,7,5,3,1]=>0000000=>[8]=>[8]
[4,2,6,5,8,7,3,1]=>0000000=>[8]=>[8]
[6,4,8,7,2,5,3,1]=>0000000=>[8]=>[8]
[4,6,5,8,7,2,3,1]=>0000000=>[8]=>[8]
[4,7,8,3,1,2,6,5]=>0000000=>[8]=>[8]
[4,7,8,2,1,3,6,5]=>0000000=>[8]=>[8]
[3,6,2,8,4,7,1,5]=>0000000=>[8]=>[8]
[3,2,6,8,4,7,1,5]=>0000000=>[8]=>[8]
[4,2,6,8,3,1,7,5]=>0000000=>[8]=>[8]
[4,2,5,1,8,3,7,6]=>0000000=>[8]=>[8]
[4,2,5,3,8,1,7,6]=>0000000=>[8]=>[8]
[3,2,5,4,8,7,1,6]=>0000000=>[8]=>[8]
[5,4,3,1,2,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,3,1,4,2,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,3,2,1,4,8,7,6]=>0000100=>[5,3]=>[5,3]
[4,3,2,5,8,1,7,6]=>0000000=>[8]=>[8]
[3,2,4,5,8,7,1,6]=>0000000=>[8]=>[8]
[1,7,2,3,5,6,8,4]=>1000000=>[1,7]=>[7,1]
[3,7,4,2,1,5,6,8]=>0000001=>[7,1]=>[7,1]
[3,4,6,2,8,5,7,1]=>0000000=>[8]=>[8]
[4,2,1,7,5,8,3,6]=>0000000=>[8]=>[8]
[4,7,2,6,5,1,3,8]=>0000001=>[7,1]=>[7,1]
[3,7,4,1,2,5,8,6]=>0000000=>[8]=>[8]
[4,7,1,6,5,2,8,3]=>0000000=>[8]=>[8]
[4,7,3,6,5,1,8,2]=>0000000=>[8]=>[8]
[4,3,7,1,6,8,5,2]=>0000000=>[8]=>[8]
[4,2,1,7,5,6,8,3]=>0000000=>[8]=>[8]
[4,2,6,8,7,3,1,5]=>0000000=>[8]=>[8]
[3,4,6,1,8,5,2,7]=>0000000=>[8]=>[8]
[4,1,6,7,5,8,2,3]=>0000000=>[8]=>[8]
[4,3,6,7,5,1,2,8]=>0000001=>[7,1]=>[7,1]
[4,3,7,1,6,8,2,5]=>0000000=>[8]=>[8]
[4,3,7,5,6,8,2,1]=>0000000=>[8]=>[8]
[4,1,7,3,6,5,2,8]=>0000001=>[7,1]=>[7,1]
[2,8,7,4,5,3,1,6]=>0000000=>[8]=>[8]
[2,8,7,4,3,5,1,6]=>0000000=>[8]=>[8]
[4,1,7,3,6,2,5,8]=>0000001=>[7,1]=>[7,1]
[5,8,7,6,1,2,4,3]=>0000000=>[8]=>[8]
[4,1,7,2,6,8,5,3]=>0000000=>[8]=>[8]
[4,2,7,3,6,1,8,5]=>0000000=>[8]=>[8]
[4,2,7,3,6,5,8,1]=>0000000=>[8]=>[8]
[3,8,5,6,2,4,1,7]=>0000000=>[8]=>[8]
[2,8,6,5,3,7,1,4]=>0000000=>[8]=>[8]
[3,8,6,5,1,4,7,2]=>0000000=>[8]=>[8]
[3,8,2,1,4,6,7,5]=>0000000=>[8]=>[8]
[3,8,2,5,4,6,7,1]=>0000000=>[8]=>[8]
[4,2,6,7,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,1,4,5,8,7]=>0000010=>[6,2]=>[6,2]
[2,8,7,3,4,5,1,6]=>0000000=>[8]=>[8]
[5,8,7,6,1,3,4,2]=>0000000=>[8]=>[8]
[5,8,7,6,2,3,4,1]=>0000000=>[8]=>[8]
[4,1,7,5,6,2,3,8]=>0000001=>[7,1]=>[7,1]
[3,8,1,5,2,6,4,7]=>0000000=>[8]=>[8]
[2,8,7,5,3,4,1,6]=>0000000=>[8]=>[8]
[2,8,7,5,4,3,1,6]=>0000000=>[8]=>[8]
[4,1,7,5,6,3,2,8]=>0000001=>[7,1]=>[7,1]
[5,8,7,6,1,3,2,4]=>0000000=>[8]=>[8]
[5,8,7,6,4,1,2,3]=>0000000=>[8]=>[8]
[8,1,7,2,4,5,3,6]=>0000000=>[8]=>[8]
[8,1,3,6,2,5,4,7]=>0000000=>[8]=>[8]
[7,2,1,6,3,5,4,8]=>0000001=>[7,1]=>[7,1]
[2,7,1,6,3,5,4,8]=>0000001=>[7,1]=>[7,1]
[2,7,1,5,4,3,6,8]=>0000001=>[7,1]=>[7,1]
[7,2,1,5,4,3,6,8]=>0000001=>[7,1]=>[7,1]
[8,1,3,5,4,2,6,7]=>0000000=>[8]=>[8]
[8,1,5,3,4,2,6,7]=>0000000=>[8]=>[8]
[8,1,5,6,2,3,7,4]=>0000000=>[8]=>[8]
[8,1,4,5,3,2,6,7]=>0000000=>[8]=>[8]
[8,1,4,3,5,2,6,7]=>0000000=>[8]=>[8]
[7,2,1,4,5,3,6,8]=>0000001=>[7,1]=>[7,1]
[2,7,1,4,5,3,6,8]=>0000001=>[7,1]=>[7,1]
[2,6,3,1,5,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,3,2,1,5,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[7,3,1,4,5,2,6,8]=>0000001=>[7,1]=>[7,1]
[7,3,1,5,4,2,6,8]=>0000001=>[7,1]=>[7,1]
[7,3,1,6,2,5,4,8]=>0000001=>[7,1]=>[7,1]
[3,7,1,6,2,5,4,8]=>0000001=>[7,1]=>[7,1]
[3,7,1,4,5,2,6,8]=>0000001=>[7,1]=>[7,1]
[2,3,6,1,5,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,3,4,1,5,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,2,4,1,5,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,6,4,1,5,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,6,5,1,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[6,5,2,1,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[7,6,1,2,4,5,3,8]=>0000001=>[7,1]=>[7,1]
[6,7,1,2,8,3,5,4]=>0000000=>[8]=>[8]
[6,7,1,2,5,4,3,8]=>0000001=>[7,1]=>[7,1]
[5,6,2,1,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[5,2,6,1,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[2,4,6,1,5,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,7,1,3,5,2,6,8]=>0000001=>[7,1]=>[7,1]
[4,7,1,5,3,2,6,8]=>0000001=>[7,1]=>[7,1]
[5,7,1,6,2,3,8,4]=>0000000=>[8]=>[8]
[5,6,3,1,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[4,2,5,3,1,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,8,7,3,2,6,4,1]=>0000000=>[8]=>[8]
[8,1,7,2,5,6,3,4]=>0000000=>[8]=>[8]
[4,8,1,5,2,6,7,3]=>0000000=>[8]=>[8]
[7,1,2,8,5,6,3,4]=>0000000=>[8]=>[8]
[8,7,2,1,5,6,3,4]=>0000000=>[8]=>[8]
[8,6,7,1,5,2,3,4]=>0000000=>[8]=>[8]
[6,1,7,8,5,2,3,4]=>0000000=>[8]=>[8]
[8,7,5,2,1,6,4,3]=>0000000=>[8]=>[8]
[4,6,8,1,5,3,7,2]=>0000000=>[8]=>[8]
[6,5,8,1,3,4,7,2]=>0000000=>[8]=>[8]
[5,8,2,4,3,6,7,1]=>0000000=>[8]=>[8]
[8,1,3,7,5,2,6,4]=>0000000=>[8]=>[8]
[3,6,8,2,4,1,7,5]=>0000000=>[8]=>[8]
[2,5,8,4,6,7,3,1]=>0000000=>[8]=>[8]
[5,8,4,1,6,7,2,3]=>0000000=>[8]=>[8]
[1,6,4,5,2,3,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,7,4,5,2,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,3,5,2,4,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,6,3,4,2,5,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,7,3,4,2,5,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,5,7,3,4,2,6]=>1000000=>[1,7]=>[7,1]
[1,7,3,4,2,6,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,2,8,4,7,3,6]=>1000000=>[1,7]=>[7,1]
[1,4,2,8,5,7,3,6]=>1000000=>[1,7]=>[7,1]
[1,7,3,5,2,6,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,4,7,3,5,2,6]=>1000000=>[1,7]=>[7,1]
[1,7,3,6,2,5,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,3,6,2,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,4,6,2,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,5,6,2,3,4,7]=>1000000=>[1,7]=>[7,1]
[1,8,5,6,2,4,3,7]=>1000000=>[1,7]=>[7,1]
[1,3,2,8,5,6,4,7]=>1010000=>[1,2,5]=>[5,2,1]
[1,4,2,8,5,6,3,7]=>1000000=>[1,7]=>[7,1]
[1,5,2,8,4,6,3,7]=>1000000=>[1,7]=>[7,1]
[1,6,2,8,4,5,3,7]=>1000000=>[1,7]=>[7,1]
[8,6,4,7,2,1,3,5]=>0000000=>[8]=>[8]
[1,6,4,7,2,8,3,5]=>1000000=>[1,7]=>[7,1]
[1,4,7,3,5,8,2,6]=>1000000=>[1,7]=>[7,1]
[8,4,6,2,3,5,1,7]=>0000000=>[8]=>[8]
[5,4,8,2,3,6,1,7]=>0000000=>[8]=>[8]
[7,4,8,5,2,3,1,6]=>0000000=>[8]=>[8]
[3,8,6,2,4,5,1,7]=>0000000=>[8]=>[8]
[4,8,6,2,3,5,1,7]=>0000000=>[8]=>[8]
[1,7,5,3,4,8,2,6]=>1000000=>[1,7]=>[7,1]
[1,7,6,4,8,2,3,5]=>1000000=>[1,7]=>[7,1]
[5,8,7,4,1,2,3,6]=>0000000=>[8]=>[8]
[6,8,5,3,4,1,2,7]=>0000000=>[8]=>[8]
[6,8,3,7,2,1,4,5]=>0000000=>[8]=>[8]
[8,5,1,6,3,7,2,4]=>0000000=>[8]=>[8]
[6,1,3,7,4,8,2,5]=>0000000=>[8]=>[8]
[4,1,7,3,5,8,2,6]=>0000000=>[8]=>[8]
[7,1,6,4,8,2,3,5]=>0000000=>[8]=>[8]
[5,1,7,3,8,2,4,6]=>0000000=>[8]=>[8]
[6,1,5,7,8,2,3,4]=>0000000=>[8]=>[8]
[7,4,8,6,1,2,3,5]=>0000000=>[8]=>[8]
[3,8,7,5,1,2,4,6]=>0000000=>[8]=>[8]
[3,7,6,1,2,4,5,8]=>0000001=>[7,1]=>[7,1]
[4,7,6,1,2,3,5,8]=>0000001=>[7,1]=>[7,1]
[1,6,5,8,2,3,4,7]=>1000000=>[1,7]=>[7,1]
[6,5,8,4,1,2,3,7]=>0000000=>[8]=>[8]
[8,5,7,4,1,2,3,6]=>0000000=>[8]=>[8]
[1,5,7,4,8,2,3,6]=>1000000=>[1,7]=>[7,1]
[7,6,2,3,8,1,4,5]=>0000000=>[8]=>[8]
[7,4,8,5,1,6,2,3]=>0000000=>[8]=>[8]
[8,6,2,3,1,7,4,5]=>0000000=>[8]=>[8]
[8,6,4,1,2,7,3,5]=>0000000=>[8]=>[8]
[1,7,2,8,6,3,4,5]=>1000000=>[1,7]=>[7,1]
[7,5,8,1,3,6,2,4]=>0000000=>[8]=>[8]
[5,4,1,8,2,3,6,7]=>0000000=>[8]=>[8]
[1,4,8,7,2,3,5,6]=>1000000=>[1,7]=>[7,1]
[1,5,8,7,2,3,4,6]=>1000000=>[1,7]=>[7,1]
[6,5,1,8,2,3,4,7]=>0000000=>[8]=>[8]
[5,7,1,3,8,2,4,6]=>0000000=>[8]=>[8]
[7,6,8,1,5,2,3,4]=>0000000=>[8]=>[8]
[7,1,5,8,6,2,3,4]=>0000000=>[8]=>[8]
[4,1,8,7,2,3,5,6]=>0000000=>[8]=>[8]
[5,1,8,7,2,3,4,6]=>0000000=>[8]=>[8]
[7,1,5,8,3,4,2,6]=>0000000=>[8]=>[8]
[7,1,4,3,2,5,6,8]=>0000001=>[7,1]=>[7,1]
[6,4,2,3,8,5,7,1]=>0000000=>[8]=>[8]
[6,4,2,7,5,8,3,1]=>0000000=>[8]=>[8]
[7,1,4,6,5,2,3,8]=>0000001=>[7,1]=>[7,1]
[7,1,4,6,5,8,2,3]=>0000000=>[8]=>[8]
[7,1,4,6,3,8,2,5]=>0000000=>[8]=>[8]
[7,1,4,3,2,5,8,6]=>0000000=>[8]=>[8]
[7,1,4,6,5,2,8,3]=>0000000=>[8]=>[8]
[7,1,4,6,5,3,8,2]=>0000000=>[8]=>[8]
[7,1,4,6,5,3,2,8]=>0000001=>[7,1]=>[7,1]
[6,4,2,7,5,3,8,1]=>0000000=>[8]=>[8]
[3,4,7,2,6,8,5,1]=>0000000=>[8]=>[8]
[3,4,7,1,6,8,2,5]=>0000000=>[8]=>[8]
[3,4,7,1,6,8,5,2]=>0000000=>[8]=>[8]
[2,4,1,7,5,3,6,8]=>0000001=>[7,1]=>[7,1]
[3,4,1,7,8,6,2,5]=>0000000=>[8]=>[8]
[6,4,2,3,8,5,1,7]=>0000000=>[8]=>[8]
[6,4,2,7,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,2,6,8,1,5]=>0000000=>[8]=>[8]
[5,4,7,3,6,8,2,1]=>0000000=>[8]=>[8]
[3,4,7,2,6,5,1,8]=>0000001=>[7,1]=>[7,1]
[4,8,7,3,5,1,2,6]=>0000000=>[8]=>[8]
[4,8,7,1,3,5,2,6]=>0000000=>[8]=>[8]
[4,8,3,1,2,6,5,7]=>0000000=>[8]=>[8]
[3,4,7,1,6,2,5,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,1,6,2,8,5]=>0000000=>[8]=>[8]
[3,4,7,2,6,5,8,1]=>0000000=>[8]=>[8]
[4,8,3,1,2,6,7,5]=>0000000=>[8]=>[8]
[5,8,1,6,3,4,2,7]=>0000000=>[8]=>[8]
[6,8,5,1,3,7,2,4]=>0000000=>[8]=>[8]
[6,8,5,1,3,4,7,2]=>0000000=>[8]=>[8]
[5,8,3,4,2,6,7,1]=>0000000=>[8]=>[8]
[6,4,3,7,5,1,2,8]=>0000001=>[7,1]=>[7,1]
[3,8,7,4,1,5,2,6]=>0000000=>[8]=>[8]
[2,4,7,3,6,1,5,8]=>0000001=>[7,1]=>[7,1]
[5,8,3,2,1,6,4,7]=>0000000=>[8]=>[8]
[5,8,7,4,3,1,2,6]=>0000000=>[8]=>[8]
[5,3,7,2,4,6,8,1]=>0000000=>[8]=>[8]
[4,2,1,5,8,6,3,7]=>0000000=>[8]=>[8]
[3,2,1,8,5,4,6,7]=>0010000=>[3,5]=>[5,3]
[6,7,2,1,8,4,5,3]=>0000000=>[8]=>[8]
[4,3,1,6,7,8,5,2]=>0000000=>[8]=>[8]
[4,2,1,6,8,5,3,7]=>0000000=>[8]=>[8]
[5,2,6,1,8,3,4,7]=>0000000=>[8]=>[8]
[4,2,1,7,8,6,3,5]=>0000000=>[8]=>[8]
[3,2,1,8,6,4,7,5]=>0010000=>[3,5]=>[5,3]
[3,2,1,8,6,4,5,7]=>0010000=>[3,5]=>[5,3]
[3,2,1,8,4,6,5,7]=>0010000=>[3,5]=>[5,3]
[3,2,1,8,4,6,7,5]=>0010000=>[3,5]=>[5,3]
[4,2,1,7,8,3,5,6]=>0000000=>[8]=>[8]
[3,2,1,8,4,5,7,6]=>0010000=>[3,5]=>[5,3]
[7,4,8,6,2,5,3,1]=>0000000=>[8]=>[8]
[7,3,8,6,2,4,5,1]=>0000000=>[8]=>[8]
[7,4,3,1,8,2,5,6]=>0000000=>[8]=>[8]
[7,4,2,8,5,6,1,3]=>0000000=>[8]=>[8]
[7,3,8,5,2,4,6,1]=>0000000=>[8]=>[8]
[6,3,8,2,4,5,1,7]=>0000000=>[8]=>[8]
[6,3,8,2,5,7,4,1]=>0000000=>[8]=>[8]
[5,6,7,3,8,2,4,1]=>0000000=>[8]=>[8]
[5,3,8,2,4,6,7,1]=>0000000=>[8]=>[8]
[6,3,8,2,4,7,5,1]=>0000000=>[8]=>[8]
[5,7,4,2,6,8,1,3]=>0000000=>[8]=>[8]
[6,5,3,1,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,7,4,2,6,1,3,8]=>0000001=>[7,1]=>[7,1]
[5,6,4,2,3,8,1,7]=>0000000=>[8]=>[8]
[5,6,3,7,8,2,4,1]=>0000000=>[8]=>[8]
[5,6,3,8,2,4,7,1]=>0000000=>[8]=>[8]
[6,3,7,2,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[6,3,7,2,5,8,4,1]=>0000000=>[8]=>[8]
[5,3,6,8,2,4,7,1]=>0000000=>[8]=>[8]
[5,4,6,2,3,8,1,7]=>0000000=>[8]=>[8]
[5,3,6,7,8,2,4,1]=>0000000=>[8]=>[8]
[5,6,3,4,2,1,8,7]=>0000010=>[6,2]=>[6,2]
[5,6,4,2,1,3,8,7]=>0000010=>[6,2]=>[6,2]
[2,8,6,3,5,4,1,7]=>0000000=>[8]=>[8]
[4,3,8,5,7,6,2,1]=>0000000=>[8]=>[8]
[3,8,5,6,4,2,1,7]=>0000000=>[8]=>[8]
[6,3,7,8,4,2,1,5]=>0000000=>[8]=>[8]
[7,8,4,2,1,6,3,5]=>0000000=>[8]=>[8]
[8,5,7,6,2,1,4,3]=>0000000=>[8]=>[8]
[4,8,5,7,6,2,1,3]=>0000000=>[8]=>[8]
[8,4,2,6,3,1,7,5]=>0000000=>[8]=>[8]
[1,5,3,7,4,2,8,6]=>1000000=>[1,7]=>[7,1]
[1,6,7,3,4,2,8,5]=>1000000=>[1,7]=>[7,1]
[8,6,5,2,3,1,7,4]=>0000000=>[8]=>[8]
[1,7,6,3,4,2,8,5]=>1000000=>[1,7]=>[7,1]
[1,8,6,3,2,5,7,4]=>1000000=>[1,7]=>[7,1]
[8,7,5,2,1,4,6,3]=>0000000=>[8]=>[8]
[7,8,5,2,1,4,6,3]=>0000000=>[8]=>[8]
[6,8,5,2,3,1,7,4]=>0000000=>[8]=>[8]
[5,8,6,2,3,1,7,4]=>0000000=>[8]=>[8]
[4,8,2,6,3,1,7,5]=>0000000=>[8]=>[8]
[3,2,8,6,4,1,7,5]=>0000000=>[8]=>[8]
[3,2,1,7,5,4,8,6]=>0010000=>[3,5]=>[5,3]
[4,1,3,7,5,2,8,6]=>0000000=>[8]=>[8]
[7,1,6,3,2,5,8,4]=>0000000=>[8]=>[8]
[1,2,7,4,3,6,8,5]=>1100000=>[1,1,6]=>[6,1,1]
[6,1,8,2,4,5,7,3]=>0000000=>[8]=>[8]
[5,1,8,3,2,6,7,4]=>0000000=>[8]=>[8]
[4,8,2,7,1,5,6,3]=>0000000=>[8]=>[8]
[5,8,7,2,1,4,6,3]=>0000000=>[8]=>[8]
[6,8,7,1,3,4,5,2]=>0000000=>[8]=>[8]
[7,8,6,1,3,4,5,2]=>0000000=>[8]=>[8]
[1,7,8,2,4,5,6,3]=>1000000=>[1,7]=>[7,1]
[8,6,7,1,3,4,5,2]=>0000000=>[8]=>[8]
[7,6,8,1,3,4,5,2]=>0000000=>[8]=>[8]
[6,5,8,2,3,1,7,4]=>0000000=>[8]=>[8]
[1,6,8,3,2,5,7,4]=>1000000=>[1,7]=>[7,1]
[8,4,2,7,1,5,6,3]=>0000000=>[8]=>[8]
[7,4,2,8,1,5,6,3]=>0000000=>[8]=>[8]
[6,4,2,8,3,1,7,5]=>0000000=>[8]=>[8]
[5,4,2,3,8,1,7,6]=>0000000=>[8]=>[8]
[4,5,2,3,1,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[7,4,2,1,3,6,8,5]=>0000000=>[8]=>[8]
[8,4,2,1,3,6,7,5]=>0000000=>[8]=>[8]
[1,5,3,2,4,7,8,6]=>1000100=>[1,4,3]=>[4,3,1]
[8,5,1,3,2,6,7,4]=>0000000=>[8]=>[8]
[5,6,1,3,4,2,8,7]=>0000010=>[6,2]=>[6,2]
[4,7,2,1,3,6,8,5]=>0000000=>[8]=>[8]
[5,7,1,3,2,6,8,4]=>0000000=>[8]=>[8]
[6,7,1,2,4,5,8,3]=>0000000=>[8]=>[8]
[1,8,2,3,5,6,7,4]=>1000000=>[1,7]=>[7,1]
[5,8,1,3,2,6,7,4]=>0000000=>[8]=>[8]
[4,8,2,1,3,6,7,5]=>0000000=>[8]=>[8]
[4,1,3,2,5,7,8,6]=>0001100=>[4,1,3]=>[4,3,1]
[5,1,2,4,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[1,2,6,4,7,5,8,3]=>1100000=>[1,1,6]=>[6,1,1]
[3,1,7,5,4,2,6,8]=>0000001=>[7,1]=>[7,1]
[6,3,8,5,4,7,1,2]=>0000000=>[8]=>[8]
[1,6,2,5,4,7,8,3]=>1000000=>[1,7]=>[7,1]
[1,2,6,4,8,5,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[7,8,3,1,4,2,5,6]=>0000000=>[8]=>[8]
[4,8,1,5,2,3,6,7]=>0000000=>[8]=>[8]
[7,4,1,5,2,3,6,8]=>0000001=>[7,1]=>[7,1]
[5,6,1,8,4,3,2,7]=>0000000=>[8]=>[8]
[5,1,8,6,4,3,2,7]=>0000000=>[8]=>[8]
[5,1,6,3,8,7,2,4]=>0000000=>[8]=>[8]
[6,1,2,5,8,3,7,4]=>0000000=>[8]=>[8]
[6,1,8,7,4,3,2,5]=>0000000=>[8]=>[8]
[7,1,2,5,4,8,6,3]=>0000000=>[8]=>[8]
[1,2,7,5,8,3,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[4,1,6,3,7,5,2,8]=>0000001=>[7,1]=>[7,1]
[1,3,6,7,8,5,2,4]=>1000000=>[1,7]=>[7,1]
[1,2,6,4,7,8,5,3]=>1100000=>[1,1,6]=>[6,1,1]
[4,1,6,3,7,8,2,5]=>0000000=>[8]=>[8]
[3,1,6,4,8,2,7,5]=>0000000=>[8]=>[8]
[7,8,4,1,6,3,2,5]=>0000000=>[8]=>[8]
[4,1,6,3,8,7,2,5]=>0000000=>[8]=>[8]
[7,5,1,8,4,3,2,6]=>0000000=>[8]=>[8]
[6,5,1,7,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[4,1,8,5,2,3,7,6]=>0000000=>[8]=>[8]
[4,1,6,8,3,7,2,5]=>0000000=>[8]=>[8]
[6,5,8,1,4,3,2,7]=>0000000=>[8]=>[8]
[1,6,3,2,7,4,8,5]=>1000000=>[1,7]=>[7,1]
[1,3,7,5,2,4,8,6]=>1000000=>[1,7]=>[7,1]
[2,5,3,7,4,8,1,6]=>0000000=>[8]=>[8]
[3,2,6,7,8,1,5,4]=>0000000=>[8]=>[8]
[3,5,2,7,8,4,1,6]=>0000000=>[8]=>[8]
[3,5,2,6,8,4,7,1]=>0000000=>[8]=>[8]
[2,5,7,4,3,8,6,1]=>0000000=>[8]=>[8]
[1,5,7,2,4,8,6,3]=>1000000=>[1,7]=>[7,1]
[4,6,3,7,2,8,5,1]=>0000000=>[8]=>[8]
[1,4,7,3,8,6,2,5]=>1000000=>[1,7]=>[7,1]
[5,1,6,8,2,4,3,7]=>0000000=>[8]=>[8]
[5,3,7,8,2,4,1,6]=>0000000=>[8]=>[8]
[8,5,3,7,2,4,1,6]=>0000000=>[8]=>[8]
[8,2,4,7,3,1,5,6]=>0000000=>[8]=>[8]
[2,4,7,8,3,1,5,6]=>0000000=>[8]=>[8]
[6,3,1,5,8,2,4,7]=>0000000=>[8]=>[8]
[6,5,3,4,2,8,1,7]=>0000000=>[8]=>[8]
[5,2,4,3,8,1,6,7]=>0000000=>[8]=>[8]
[3,2,4,8,1,5,6,7]=>0000000=>[8]=>[8]
[8,1,5,7,3,2,4,6]=>0000000=>[8]=>[8]
[8,4,6,7,2,3,1,5]=>0000000=>[8]=>[8]
[4,6,7,8,2,3,1,5]=>0000000=>[8]=>[8]
[7,4,6,8,2,3,1,5]=>0000000=>[8]=>[8]
[7,2,4,8,3,1,5,6]=>0000000=>[8]=>[8]
[5,3,8,7,2,4,1,6]=>0000000=>[8]=>[8]
[2,4,8,7,3,1,5,6]=>0000000=>[8]=>[8]
[4,6,8,7,2,3,1,5]=>0000000=>[8]=>[8]
[6,4,8,7,2,3,1,5]=>0000000=>[8]=>[8]
[3,1,7,4,2,8,6,5]=>0000000=>[8]=>[8]
[3,2,8,4,1,7,6,5]=>0000000=>[8]=>[8]
[7,6,4,8,2,3,1,5]=>0000000=>[8]=>[8]
[5,7,6,8,2,3,1,4]=>0000000=>[8]=>[8]
[4,7,6,8,2,3,1,5]=>0000000=>[8]=>[8]
[8,6,4,7,2,3,1,5]=>0000000=>[8]=>[8]
[8,2,3,7,4,1,6,5]=>0000000=>[8]=>[8]
[3,7,4,8,2,5,1,6]=>0000000=>[8]=>[8]
[2,3,7,4,1,6,8,5]=>0000000=>[8]=>[8]
[8,1,6,4,2,3,7,5]=>0000000=>[8]=>[8]
[4,7,8,6,2,3,1,5]=>0000000=>[8]=>[8]
[6,3,1,7,4,2,8,5]=>0000000=>[8]=>[8]
[8,5,7,6,2,3,1,4]=>0000000=>[8]=>[8]
[7,1,6,4,2,3,8,5]=>0000000=>[8]=>[8]
[3,1,7,6,4,2,8,5]=>0000000=>[8]=>[8]
[4,8,7,6,2,3,1,5]=>0000000=>[8]=>[8]
[6,8,7,5,2,3,1,4]=>0000000=>[8]=>[8]
[4,3,6,1,5,8,7,2]=>0000000=>[8]=>[8]
[4,3,6,5,1,8,7,2]=>0000000=>[8]=>[8]
[4,6,3,5,1,8,7,2]=>0000000=>[8]=>[8]
[4,6,3,1,5,8,7,2]=>0000000=>[8]=>[8]
[4,1,6,5,3,8,7,2]=>0000000=>[8]=>[8]
[4,6,1,5,3,8,7,2]=>0000000=>[8]=>[8]
[2,6,5,3,1,8,7,4]=>0000000=>[8]=>[8]
[2,6,5,8,3,1,7,4]=>0000000=>[8]=>[8]
[2,6,5,3,8,1,7,4]=>0000000=>[8]=>[8]
[4,6,1,5,8,3,7,2]=>0000000=>[8]=>[8]
[4,1,6,5,8,3,7,2]=>0000000=>[8]=>[8]
[1,4,6,5,8,3,7,2]=>1000000=>[1,7]=>[7,1]
[4,1,6,5,8,7,3,2]=>0000000=>[8]=>[8]
[6,4,3,8,7,1,5,2]=>0000000=>[8]=>[8]
[6,4,8,3,7,1,5,2]=>0000000=>[8]=>[8]
[2,6,8,5,3,7,1,4]=>0000000=>[8]=>[8]
[4,6,8,1,5,7,3,2]=>0000000=>[8]=>[8]
[4,6,1,8,5,7,3,2]=>0000000=>[8]=>[8]
[1,4,6,8,5,7,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,6,8,5,3,7,2]=>1000000=>[1,7]=>[7,1]
[4,6,1,8,5,3,7,2]=>0000000=>[8]=>[8]
[4,6,3,8,5,7,1,2]=>0000000=>[8]=>[8]
[4,3,6,8,1,5,7,2]=>0000000=>[8]=>[8]
[4,3,6,1,8,5,7,2]=>0000000=>[8]=>[8]
[4,3,1,6,8,5,7,2]=>0000000=>[8]=>[8]
[4,1,3,6,8,7,5,2]=>0000000=>[8]=>[8]
[4,3,6,1,8,7,5,2]=>0000000=>[8]=>[8]
[4,3,6,8,1,7,5,2]=>0000000=>[8]=>[8]
[6,5,2,8,7,3,1,4]=>0000000=>[8]=>[8]
[6,5,2,8,7,1,3,4]=>0000000=>[8]=>[8]
[6,2,5,8,7,1,3,4]=>0000000=>[8]=>[8]
[6,2,5,8,7,3,1,4]=>0000000=>[8]=>[8]
[4,6,3,8,1,7,5,2]=>0000000=>[8]=>[8]
[4,6,3,1,8,7,5,2]=>0000000=>[8]=>[8]
[4,1,6,3,8,7,5,2]=>0000000=>[8]=>[8]
[1,4,6,3,8,7,5,2]=>1000000=>[1,7]=>[7,1]
[4,1,6,8,3,7,5,2]=>0000000=>[8]=>[8]
[4,6,1,8,3,7,5,2]=>0000000=>[8]=>[8]
[4,6,8,1,3,7,5,2]=>0000000=>[8]=>[8]
[6,2,8,5,7,3,1,4]=>0000000=>[8]=>[8]
[6,2,8,5,7,1,3,4]=>0000000=>[8]=>[8]
[2,4,8,7,1,5,3,6]=>0000000=>[8]=>[8]
[6,4,1,8,7,5,3,2]=>0000000=>[8]=>[8]
[6,1,4,8,7,5,3,2]=>0000000=>[8]=>[8]
[1,6,4,8,7,3,5,2]=>1000000=>[1,7]=>[7,1]
[6,4,1,8,7,3,5,2]=>0000000=>[8]=>[8]
[4,2,8,7,5,1,3,6]=>0000000=>[8]=>[8]
[2,4,8,7,3,5,1,6]=>0000000=>[8]=>[8]
[1,5,3,2,6,4,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,7,3,2,8,5,4,6]=>1000000=>[1,7]=>[7,1]
[1,6,2,8,5,3,4,7]=>1000000=>[1,7]=>[7,1]
[1,5,7,2,8,4,3,6]=>1000000=>[1,7]=>[7,1]
[2,3,1,8,4,5,7,6]=>0010000=>[3,5]=>[5,3]
[7,8,1,4,3,5,2,6]=>0000000=>[8]=>[8]
[8,4,2,5,3,1,6,7]=>0000000=>[8]=>[8]
[2,4,7,8,1,5,3,6]=>0000000=>[8]=>[8]
[6,1,2,8,5,3,4,7]=>0000000=>[8]=>[8]
[6,8,1,3,4,7,2,5]=>0000000=>[8]=>[8]
[6,7,2,3,4,1,8,5]=>0000000=>[8]=>[8]
[4,8,7,3,5,6,1,2]=>0000000=>[8]=>[8]
[4,8,7,5,3,6,1,2]=>0000000=>[8]=>[8]
[5,8,7,3,4,6,1,2]=>0000000=>[8]=>[8]
[5,8,4,2,1,6,7,3]=>0000000=>[8]=>[8]
[5,8,4,1,2,6,7,3]=>0000000=>[8]=>[8]
[5,3,7,2,6,1,8,4]=>0000000=>[8]=>[8]
[5,2,8,1,6,3,7,4]=>0000000=>[8]=>[8]
[5,8,2,1,4,7,6,3]=>0000000=>[8]=>[8]
[4,8,2,5,1,7,6,3]=>0000000=>[8]=>[8]
[7,8,4,1,2,6,5,3]=>0000000=>[8]=>[8]
[4,8,1,5,2,7,6,3]=>0000000=>[8]=>[8]
[5,8,1,2,4,7,6,3]=>0000000=>[8]=>[8]
[5,2,8,3,6,7,1,4]=>0000000=>[8]=>[8]
[2,8,7,6,4,1,3,5]=>0000000=>[8]=>[8]
[7,8,2,6,5,1,3,4]=>0000000=>[8]=>[8]
[1,8,7,6,2,4,3,5]=>1000000=>[1,7]=>[7,1]
[2,8,1,4,5,6,7,3]=>0000000=>[8]=>[8]
[2,1,7,3,6,5,8,4]=>0100000=>[2,6]=>[6,2]
[3,2,7,1,6,5,8,4]=>0000000=>[8]=>[8]
[6,1,2,8,5,7,3,4]=>0000000=>[8]=>[8]
[6,2,1,8,5,7,3,4]=>0000000=>[8]=>[8]
[6,3,1,8,5,7,2,4]=>0000000=>[8]=>[8]
[6,4,2,1,7,5,8,3]=>0000000=>[8]=>[8]
[6,1,3,8,5,2,7,4]=>0000000=>[8]=>[8]
[1,3,7,2,6,8,5,4]=>1000000=>[1,7]=>[7,1]
[7,8,2,6,5,3,1,4]=>0000000=>[8]=>[8]
[3,2,6,7,5,8,1,4]=>0000000=>[8]=>[8]
[1,2,7,5,6,3,8,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,8,7,6,4,3,1,5]=>0000000=>[8]=>[8]
[3,8,7,6,1,2,5,4]=>0000000=>[8]=>[8]
[4,8,7,6,2,1,3,5]=>0000000=>[8]=>[8]
[4,8,7,6,1,3,2,5]=>0000000=>[8]=>[8]
[3,8,7,6,4,1,2,5]=>0000000=>[8]=>[8]
[7,8,3,6,5,1,2,4]=>0000000=>[8]=>[8]
[2,3,7,5,6,8,1,4]=>0000000=>[8]=>[8]
[3,8,7,6,4,2,1,5]=>0000000=>[8]=>[8]
[3,4,2,6,7,8,1,5]=>0000000=>[8]=>[8]
[3,1,4,2,6,8,7,5]=>0001000=>[4,4]=>[4,4]
[8,3,4,2,6,1,7,5]=>0000000=>[8]=>[8]
[2,6,7,3,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[2,7,8,3,5,4,1,6]=>0000000=>[8]=>[8]
[2,6,8,3,5,4,1,7]=>0000000=>[8]=>[8]
[4,7,1,2,8,5,3,6]=>0000000=>[8]=>[8]
[4,8,1,2,7,5,3,6]=>0000000=>[8]=>[8]
[2,1,6,3,7,5,4,8]=>0100001=>[2,5,1]=>[5,2,1]
[2,7,1,3,6,8,4,5]=>0000000=>[8]=>[8]
[7,4,1,2,8,5,3,6]=>0000000=>[8]=>[8]
[8,7,4,2,1,5,3,6]=>0000000=>[8]=>[8]
[7,4,1,2,6,5,3,8]=>0000001=>[7,1]=>[7,1]
[7,4,3,1,5,6,8,2]=>0000000=>[8]=>[8]
[6,7,4,1,5,8,3,2]=>0000000=>[8]=>[8]
[4,7,5,1,6,8,3,2]=>0000000=>[8]=>[8]
[4,5,3,1,7,6,8,2]=>0000000=>[8]=>[8]
[4,6,1,2,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,1,2,8,5,3,7]=>0000000=>[8]=>[8]
[4,5,3,1,8,6,7,2]=>0000000=>[8]=>[8]
[4,8,5,6,3,1,7,2]=>0000000=>[8]=>[8]
[5,1,3,4,8,6,7,2]=>0000000=>[8]=>[8]
[5,4,3,8,1,6,7,2]=>0000000=>[8]=>[8]
[8,5,3,4,1,6,7,2]=>0000000=>[8]=>[8]
[6,4,8,2,1,5,3,7]=>0000000=>[8]=>[8]
[6,7,3,2,5,1,4,8]=>0000001=>[7,1]=>[7,1]
[6,8,3,2,5,1,4,7]=>0000000=>[8]=>[8]
[5,7,1,4,6,8,3,2]=>0000000=>[8]=>[8]
[5,1,3,4,7,6,8,2]=>0000000=>[8]=>[8]
[5,4,3,7,1,6,8,2]=>0000000=>[8]=>[8]
[6,7,5,4,1,8,3,2]=>0000000=>[8]=>[8]
[7,6,4,2,1,5,3,8]=>0000001=>[7,1]=>[7,1]
[8,5,6,1,3,2,4,7]=>0000000=>[8]=>[8]
[8,6,1,5,3,2,4,7]=>0000000=>[8]=>[8]
[7,8,1,5,3,2,4,6]=>0000000=>[8]=>[8]
[8,1,7,5,3,2,4,6]=>0000000=>[8]=>[8]
[8,6,1,4,5,2,3,7]=>0000000=>[8]=>[8]
[8,6,3,1,5,2,4,7]=>0000000=>[8]=>[8]
[8,4,6,1,5,2,3,7]=>0000000=>[8]=>[8]
[8,6,2,1,5,4,3,7]=>0000000=>[8]=>[8]
[8,5,2,6,1,4,3,7]=>0000000=>[8]=>[8]
[8,5,2,1,7,4,3,6]=>0000000=>[8]=>[8]
[8,2,7,5,1,3,4,6]=>0000000=>[8]=>[8]
[8,4,1,7,5,2,3,6]=>0000000=>[8]=>[8]
[8,2,6,1,7,4,3,5]=>0000000=>[8]=>[8]
[8,1,7,4,3,2,6,5]=>0000000=>[8]=>[8]
[8,1,5,7,3,2,6,4]=>0000000=>[8]=>[8]
[5,7,8,1,3,2,6,4]=>0000000=>[8]=>[8]
[8,2,6,1,5,7,3,4]=>0000000=>[8]=>[8]
[5,8,1,6,7,2,3,4]=>0000000=>[8]=>[8]
[5,7,6,1,8,2,3,4]=>0000000=>[8]=>[8]
[8,1,5,6,7,2,3,4]=>0000000=>[8]=>[8]
[6,5,7,1,8,2,3,4]=>0000000=>[8]=>[8]
[8,1,6,4,7,2,3,5]=>0000000=>[8]=>[8]
[7,5,8,1,3,2,4,6]=>0000000=>[8]=>[8]
[7,8,4,1,3,2,5,6]=>0000000=>[8]=>[8]
[8,3,7,4,1,2,5,6]=>0000000=>[8]=>[8]
[8,5,1,7,3,2,4,6]=>0000000=>[8]=>[8]
[6,8,1,7,3,2,4,5]=>0000000=>[8]=>[8]
[7,1,8,4,3,6,2,5]=>0000000=>[8]=>[8]
[7,3,1,8,6,4,2,5]=>0000000=>[8]=>[8]
[8,3,1,7,4,6,2,5]=>0000000=>[8]=>[8]
[8,4,5,1,7,2,3,6]=>0000000=>[8]=>[8]
[5,6,8,1,7,2,3,4]=>0000000=>[8]=>[8]
[6,5,8,1,2,7,3,4]=>0000000=>[8]=>[8]
[7,3,1,8,5,6,2,4]=>0000000=>[8]=>[8]
[6,2,7,8,3,1,5,4]=>0000000=>[8]=>[8]
[5,8,1,7,3,2,6,4]=>0000000=>[8]=>[8]
[8,4,1,7,3,2,6,5]=>0000000=>[8]=>[8]
[8,3,4,7,1,2,6,5]=>0000000=>[8]=>[8]
[7,4,8,2,1,3,6,5]=>0000000=>[8]=>[8]
[7,4,3,8,1,2,6,5]=>0000000=>[8]=>[8]
[8,2,3,6,7,1,5,4]=>0000000=>[8]=>[8]
[6,8,5,2,3,4,7,1]=>0000000=>[8]=>[8]
[5,3,7,1,4,2,8,6]=>0000000=>[8]=>[8]
[3,7,5,1,2,8,6,4]=>0000000=>[8]=>[8]
[7,3,5,8,1,2,6,4]=>0000000=>[8]=>[8]
[2,5,7,4,8,6,1,3]=>0000000=>[8]=>[8]
[3,6,2,5,8,7,1,4]=>0000000=>[8]=>[8]
[5,2,8,4,7,6,1,3]=>0000000=>[8]=>[8]
[2,5,1,4,7,3,8,6]=>0000000=>[8]=>[8]
[3,1,5,6,2,8,7,4]=>0000000=>[8]=>[8]
[1,2,4,6,3,8,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[7,2,3,5,1,8,6,4]=>0000000=>[8]=>[8]
[1,6,4,2,8,7,5,3]=>1000000=>[1,7]=>[7,1]
[4,6,2,7,5,1,8,3]=>0000000=>[8]=>[8]
[1,5,3,6,2,8,7,4]=>1000000=>[1,7]=>[7,1]
[3,5,2,1,7,4,8,6]=>0000000=>[8]=>[8]
[6,3,1,7,2,8,5,4]=>0000000=>[8]=>[8]
[7,5,1,2,8,6,4,3]=>0000000=>[8]=>[8]
[4,5,1,2,8,7,6,3]=>0000000=>[8]=>[8]
[5,8,2,7,1,6,4,3]=>0000000=>[8]=>[8]
[2,1,6,4,5,8,3,7]=>0100000=>[2,6]=>[6,2]
[8,6,3,7,5,2,1,4]=>0000000=>[8]=>[8]
[4,6,3,8,5,2,1,7]=>0000000=>[8]=>[8]
[4,6,3,7,5,2,8,1]=>0000000=>[8]=>[8]
[4,8,3,7,5,2,1,6]=>0000000=>[8]=>[8]
[5,2,8,3,7,6,1,4]=>0000000=>[8]=>[8]
[8,2,7,3,1,6,4,5]=>0000000=>[8]=>[8]
[8,6,7,4,1,5,3,2]=>0000000=>[8]=>[8]
[4,8,6,7,5,1,3,2]=>0000000=>[8]=>[8]
[7,1,8,4,6,5,2,3]=>0000000=>[8]=>[8]
[8,7,1,5,4,6,2,3]=>0000000=>[8]=>[8]
[8,5,7,1,4,6,3,2]=>0000000=>[8]=>[8]
[6,4,8,5,1,7,3,2]=>0000000=>[8]=>[8]
[8,4,7,1,5,6,3,2]=>0000000=>[8]=>[8]
[8,7,5,1,4,6,2,3]=>0000000=>[8]=>[8]
[8,7,2,5,1,4,6,3]=>0000000=>[8]=>[8]
[4,8,7,2,5,1,6,3]=>0000000=>[8]=>[8]
[8,7,1,4,2,5,6,3]=>0000000=>[8]=>[8]
[8,7,5,1,2,4,6,3]=>0000000=>[8]=>[8]
[7,1,8,5,6,2,3,4]=>0000000=>[8]=>[8]
[3,5,8,7,1,2,6,4]=>0000000=>[8]=>[8]
[2,3,8,5,7,1,6,4]=>0000000=>[8]=>[8]
[3,8,7,1,5,6,2,4]=>0000000=>[8]=>[8]
[3,5,8,7,1,6,2,4]=>0000000=>[8]=>[8]
[2,3,8,6,7,5,1,4]=>0000000=>[8]=>[8]
[3,2,8,6,7,5,1,4]=>0000000=>[8]=>[8]
[4,1,8,6,2,7,5,3]=>0000000=>[8]=>[8]
[8,7,4,1,2,6,5,3]=>0000000=>[8]=>[8]
[1,3,8,6,7,5,2,4]=>1000000=>[1,7]=>[7,1]
[5,7,1,8,2,6,3,4]=>0000000=>[8]=>[8]
[2,8,7,1,5,6,3,4]=>0000000=>[8]=>[8]
[8,7,1,5,2,4,6,3]=>0000000=>[8]=>[8]
[7,1,8,2,4,6,5,3]=>0000000=>[8]=>[8]
[1,6,2,8,4,7,5,3]=>1000000=>[1,7]=>[7,1]
[1,3,8,5,7,2,6,4]=>1000000=>[1,7]=>[7,1]
[1,8,3,7,2,5,6,4]=>1000000=>[1,7]=>[7,1]
[2,8,7,1,3,5,6,4]=>0000000=>[8]=>[8]
[5,7,1,8,2,3,6,4]=>0000000=>[8]=>[8]
[7,1,8,2,3,5,6,4]=>0000000=>[8]=>[8]
[8,6,3,7,4,1,5,2]=>0000000=>[8]=>[8]
[4,2,8,6,7,5,1,3]=>0000000=>[8]=>[8]
[8,4,2,7,5,6,1,3]=>0000000=>[8]=>[8]
[4,8,3,6,1,7,5,2]=>0000000=>[8]=>[8]
[8,3,4,7,5,1,6,2]=>0000000=>[8]=>[8]
[8,3,7,4,5,1,6,2]=>0000000=>[8]=>[8]
[8,7,4,2,5,6,1,3]=>0000000=>[8]=>[8]
[8,7,5,1,6,2,3,4]=>0000000=>[8]=>[8]
[8,7,2,4,1,5,6,3]=>0000000=>[8]=>[8]
[4,8,6,1,7,2,5,3]=>0000000=>[8]=>[8]
[4,2,8,6,7,1,5,3]=>0000000=>[8]=>[8]
[8,7,4,1,2,5,6,3]=>0000000=>[8]=>[8]
[8,2,7,1,6,3,4,5]=>0000000=>[8]=>[8]
[8,2,7,1,3,6,4,5]=>0000000=>[8]=>[8]
[2,8,3,6,7,1,5,4]=>0000000=>[8]=>[8]
[8,7,2,1,3,5,6,4]=>0000000=>[8]=>[8]
[1,8,7,2,3,6,4,5]=>1000000=>[1,7]=>[7,1]
[1,8,7,2,6,3,4,5]=>1000000=>[1,7]=>[7,1]
[8,2,7,3,6,1,4,5]=>0000000=>[8]=>[8]
[1,8,7,3,6,2,4,5]=>1000000=>[1,7]=>[7,1]
[1,8,2,7,6,3,4,5]=>1000000=>[1,7]=>[7,1]
[8,2,7,4,1,5,6,3]=>0000000=>[8]=>[8]
[8,2,1,7,5,6,3,4]=>0000000=>[8]=>[8]
[8,7,3,1,5,6,2,4]=>0000000=>[8]=>[8]
[2,8,7,3,5,6,1,4]=>0000000=>[8]=>[8]
[8,3,1,6,7,5,2,4]=>0000000=>[8]=>[8]
[8,5,2,1,6,7,4,3]=>0000000=>[8]=>[8]
[1,5,2,8,6,7,4,3]=>1000000=>[1,7]=>[7,1]
[1,2,8,6,7,5,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,3,6,7,5,2,4]=>1000000=>[1,7]=>[7,1]
[8,2,3,6,7,5,1,4]=>0000000=>[8]=>[8]
[8,3,7,2,5,6,1,4]=>0000000=>[8]=>[8]
[8,1,3,7,5,6,2,4]=>0000000=>[8]=>[8]
[8,4,1,2,7,5,6,3]=>0000000=>[8]=>[8]
[8,1,4,2,6,7,5,3]=>0000000=>[8]=>[8]
[1,2,8,6,7,3,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[8,1,2,7,3,6,4,5]=>0000000=>[8]=>[8]
[8,1,7,3,6,2,4,5]=>0000000=>[8]=>[8]
[8,1,7,2,6,3,4,5]=>0000000=>[8]=>[8]
[8,1,7,2,3,6,4,5]=>0000000=>[8]=>[8]
[8,1,3,7,2,5,6,4]=>0000000=>[8]=>[8]
[1,8,3,6,7,2,5,4]=>1000000=>[1,7]=>[7,1]
[1,7,8,2,3,6,5,4]=>1000000=>[1,7]=>[7,1]
[8,3,7,1,2,5,6,4]=>0000000=>[8]=>[8]
[7,4,2,6,1,5,3,8]=>0000001=>[7,1]=>[7,1]
[7,4,2,5,6,1,3,8]=>0000001=>[7,1]=>[7,1]
[7,3,5,6,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,4,3,1,5,6,2,8]=>0000001=>[7,1]=>[7,1]
[7,4,5,2,6,1,3,8]=>0000001=>[7,1]=>[7,1]
[5,3,7,2,8,6,4,1]=>0000000=>[8]=>[8]
[5,3,8,2,6,7,4,1]=>0000000=>[8]=>[8]
[6,3,8,2,5,4,7,1]=>0000000=>[8]=>[8]
[6,4,3,1,8,2,7,5]=>0000000=>[8]=>[8]
[5,3,7,8,2,6,4,1]=>0000000=>[8]=>[8]
[4,7,8,5,6,3,2,1]=>0000000=>[8]=>[8]
[5,3,7,6,8,2,4,1]=>0000000=>[8]=>[8]
[5,7,8,4,6,2,1,3]=>0000000=>[8]=>[8]
[5,8,4,3,6,7,1,2]=>0000000=>[8]=>[8]
[5,8,6,4,7,2,1,3]=>0000000=>[8]=>[8]
[5,3,8,6,2,7,4,1]=>0000000=>[8]=>[8]
[4,7,5,8,6,3,2,1]=>0000000=>[8]=>[8]
[6,3,8,7,2,4,1,5]=>0000000=>[8]=>[8]
[5,3,8,7,2,6,4,1]=>0000000=>[8]=>[8]
[5,3,8,6,7,2,4,1]=>0000000=>[8]=>[8]
[5,3,7,8,6,2,4,1]=>0000000=>[8]=>[8]
[5,7,6,4,8,2,1,3]=>0000000=>[8]=>[8]
[5,8,4,6,7,2,1,3]=>0000000=>[8]=>[8]
[6,4,2,8,1,7,3,5]=>0000000=>[8]=>[8]
[6,5,2,4,3,7,8,1]=>0000000=>[8]=>[8]
[5,4,6,2,8,7,1,3]=>0000000=>[8]=>[8]
[5,6,3,8,7,2,4,1]=>0000000=>[8]=>[8]
[6,7,4,3,1,8,2,5]=>0000000=>[8]=>[8]
[5,7,4,3,6,8,1,2]=>0000000=>[8]=>[8]
[5,7,3,8,6,2,4,1]=>0000000=>[8]=>[8]
[4,5,8,6,7,3,2,1]=>0000000=>[8]=>[8]
[4,6,8,5,7,3,2,1]=>0000000=>[8]=>[8]
[5,6,8,3,7,2,4,1]=>0000000=>[8]=>[8]
[5,4,6,8,2,7,1,3]=>0000000=>[8]=>[8]
[7,8,4,5,1,3,2,6]=>0000000=>[8]=>[8]
[6,7,1,3,2,5,4,8]=>0000001=>[7,1]=>[7,1]
[6,7,1,4,3,5,2,8]=>0000001=>[7,1]=>[7,1]
[7,8,2,3,1,5,4,6]=>0000000=>[8]=>[8]
[7,8,2,4,3,5,1,6]=>0000000=>[8]=>[8]
[7,8,2,4,1,5,3,6]=>0000000=>[8]=>[8]
[1,4,2,6,5,7,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[5,6,1,4,2,7,3,8]=>0000001=>[7,1]=>[7,1]
[6,7,2,4,1,5,3,8]=>0000001=>[7,1]=>[7,1]
[6,7,2,4,3,5,1,8]=>0000001=>[7,1]=>[7,1]
[6,7,2,3,1,5,4,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,5,4,8,1,2]=>0000000=>[8]=>[8]
[2,4,1,6,5,7,3,8]=>0000001=>[7,1]=>[7,1]
[1,5,2,6,4,7,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,5,1,6,4,7,3,8]=>0000001=>[7,1]=>[7,1]
[5,6,2,4,3,7,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,2,6,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,5,1,6,3,7,2,8]=>0000001=>[7,1]=>[7,1]
[4,5,3,6,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[5,6,3,4,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[5,6,1,4,3,7,2,8]=>0000001=>[7,1]=>[7,1]
[5,6,1,3,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[5,6,4,7,1,3,2,8]=>0000001=>[7,1]=>[7,1]
[6,7,4,5,1,3,2,8]=>0000001=>[7,1]=>[7,1]
[6,7,5,8,1,3,2,4]=>0000000=>[8]=>[8]
[4,5,1,3,2,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[4,6,5,7,1,3,2,8]=>0000001=>[7,1]=>[7,1]
[4,6,1,3,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[1,4,3,6,2,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[4,5,2,3,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[4,5,3,7,6,8,1,2]=>0000000=>[8]=>[8]
[4,6,5,7,3,8,1,2]=>0000000=>[8]=>[8]
[4,6,5,7,2,3,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,6,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,1,6,4,7,2,8]=>0000001=>[7,1]=>[7,1]
[1,5,3,6,4,7,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,3,6,2,7,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[3,5,2,6,1,7,4,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,6,4,7,1,8]=>0000001=>[7,1]=>[7,1]
[3,4,2,6,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,2,3,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[2,4,3,6,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[2,5,3,6,4,7,1,8]=>0000001=>[7,1]=>[7,1]
[2,5,3,6,1,7,4,8]=>0000001=>[7,1]=>[7,1]
[3,6,2,7,5,4,8,1]=>0000000=>[8]=>[8]
[5,2,6,7,4,3,8,1]=>0000000=>[8]=>[8]
[3,5,2,7,6,4,8,1]=>0000000=>[8]=>[8]
[2,1,5,6,8,4,3,7]=>0100000=>[2,6]=>[6,2]
[1,3,7,2,8,5,4,6]=>1000000=>[1,7]=>[7,1]
[4,6,2,7,1,8,3,5]=>0000000=>[8]=>[8]
[1,5,4,3,6,8,2,7]=>1000000=>[1,7]=>[7,1]
[1,6,4,5,7,8,3,2]=>1000000=>[1,7]=>[7,1]
[2,1,5,6,8,4,7,3]=>0100000=>[2,6]=>[6,2]
[2,1,5,6,8,7,3,4]=>0100000=>[2,6]=>[6,2]
[3,6,5,2,7,8,4,1]=>0000000=>[8]=>[8]
[6,2,4,7,5,8,3,1]=>0000000=>[8]=>[8]
[1,5,7,8,4,2,6,3]=>1000000=>[1,7]=>[7,1]
[3,7,4,1,8,6,2,5]=>0000000=>[8]=>[8]
[3,4,6,8,5,7,2,1]=>0000000=>[8]=>[8]
[4,5,6,2,8,7,3,1]=>0000000=>[8]=>[8]
[4,5,6,1,8,7,3,2]=>0000000=>[8]=>[8]
[4,5,6,3,1,8,7,2]=>0000000=>[8]=>[8]
[4,3,6,2,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,3,2,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,3,1,7,5,2,8]=>0000001=>[7,1]=>[7,1]
[4,5,3,7,6,1,8,2]=>0000000=>[8]=>[8]
[4,5,1,7,3,8,6,2]=>0000000=>[8]=>[8]
[2,5,7,1,4,3,8,6]=>0000000=>[8]=>[8]
[4,3,5,7,6,1,8,2]=>0000000=>[8]=>[8]
[4,3,6,1,7,5,2,8]=>0000001=>[7,1]=>[7,1]
[4,3,2,6,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[5,3,2,1,6,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,3,1,6,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[5,1,6,3,2,7,4,8]=>0000001=>[7,1]=>[7,1]
[2,6,1,4,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[3,6,1,7,4,2,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,1,7,5,3,2,8]=>0000001=>[7,1]=>[7,1]
[5,1,6,3,7,4,2,8]=>0000001=>[7,1]=>[7,1]
[5,3,6,4,2,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,3,2,6,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,2,1,6,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[5,2,6,3,1,7,4,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,3,1,7,8,5]=>0000000=>[8]=>[8]
[3,6,2,1,7,4,5,8]=>0000001=>[7,1]=>[7,1]
[3,6,2,7,4,1,5,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,2,8,6,4,1]=>0000000=>[8]=>[8]
[2,6,1,3,7,5,4,8]=>0000001=>[7,1]=>[7,1]
[3,6,1,7,5,2,4,8]=>0000001=>[7,1]=>[7,1]
[5,1,6,2,7,4,3,8]=>0000001=>[7,1]=>[7,1]
[5,2,6,4,3,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,2,1,6,4,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,2,1,6,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,1,6,2,7,3,8]=>0000001=>[7,1]=>[7,1]
[5,1,6,4,2,7,3,8]=>0000001=>[7,1]=>[7,1]
[3,6,1,7,5,4,8,2]=>0000000=>[8]=>[8]
[2,6,1,5,4,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,1,6,2,5,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,1,6,3,2,7,8,5]=>0000000=>[8]=>[8]
[5,1,6,4,3,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,1,6,3,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,3,1,6,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,5,1,8,7,6,2,3]=>0000000=>[8]=>[8]
[6,8,3,5,7,1,4,2]=>0000000=>[8]=>[8]
[1,5,8,2,7,3,6,4]=>1000000=>[1,7]=>[7,1]
[6,7,4,8,1,5,3,2]=>0000000=>[8]=>[8]
[6,8,5,3,7,2,4,1]=>0000000=>[8]=>[8]
[7,5,3,8,2,6,4,1]=>0000000=>[8]=>[8]
[3,6,8,4,5,7,1,2]=>0000000=>[8]=>[8]
[1,6,8,4,7,2,3,5]=>1000000=>[1,7]=>[7,1]
[1,4,5,7,8,2,6,3]=>1000000=>[1,7]=>[7,1]
[1,4,5,8,7,2,3,6]=>1000000=>[1,7]=>[7,1]
[1,2,5,8,3,6,4,7]=>1100000=>[1,1,6]=>[6,1,1]
[7,8,1,4,6,2,3,5]=>0000000=>[8]=>[8]
[1,6,7,4,8,2,5,3]=>1000000=>[1,7]=>[7,1]
[1,4,5,6,8,2,7,3]=>1000000=>[1,7]=>[7,1]
[1,4,5,8,6,2,7,3]=>1000000=>[1,7]=>[7,1]
[1,2,5,8,3,4,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[7,8,1,2,3,5,4,6]=>0000000=>[8]=>[8]
[1,6,7,2,3,5,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,5,7,6,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,2,5,7,3,6,4,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,2,5,7,3,6,8,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,8,2,3,5,7,4]=>1000000=>[1,7]=>[7,1]
[1,6,8,4,5,2,3,7]=>1000000=>[1,7]=>[7,1]
[1,6,8,2,3,4,7,5]=>1000000=>[1,7]=>[7,1]
[1,6,8,2,3,7,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,5,7,6,2,8,3]=>1000000=>[1,7]=>[7,1]
[7,8,1,4,5,2,6,3]=>0000000=>[8]=>[8]
[1,6,7,2,3,8,5,4]=>1000000=>[1,7]=>[7,1]
[1,2,5,6,3,8,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,7,4,8,3,5,1,6]=>0000000=>[8]=>[8]
[2,7,4,8,3,5,6,1]=>0000000=>[8]=>[8]
[7,2,8,4,3,5,1,6]=>0000000=>[8]=>[8]
[8,4,2,1,5,3,6,7]=>0000000=>[8]=>[8]
[8,4,1,5,3,2,6,7]=>0000000=>[8]=>[8]
[6,7,3,8,4,2,5,1]=>0000000=>[8]=>[8]
[6,7,3,8,4,2,1,5]=>0000000=>[8]=>[8]
[7,1,8,4,3,5,2,6]=>0000000=>[8]=>[8]
[1,7,8,4,3,5,2,6]=>1000000=>[1,7]=>[7,1]
[7,1,4,8,3,5,2,6]=>0000000=>[8]=>[8]
[7,1,8,4,3,5,6,2]=>0000000=>[8]=>[8]
[6,7,3,1,8,4,5,2]=>0000000=>[8]=>[8]
[6,7,1,4,8,3,5,2]=>0000000=>[8]=>[8]
[6,7,4,1,3,8,2,5]=>0000000=>[8]=>[8]
[1,6,7,8,4,3,2,5]=>1000000=>[1,7]=>[7,1]
[7,2,1,8,4,5,3,6]=>0000000=>[8]=>[8]
[6,2,7,1,8,4,3,5]=>0000000=>[8]=>[8]
[6,2,7,8,4,3,1,5]=>0000000=>[8]=>[8]
[6,2,7,8,4,3,5,1]=>0000000=>[8]=>[8]
[2,6,7,4,8,3,5,1]=>0000000=>[8]=>[8]
[2,6,7,4,8,3,1,5]=>0000000=>[8]=>[8]
[7,8,1,3,6,2,4,5]=>0000000=>[8]=>[8]
[1,2,7,8,6,3,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[2,6,7,1,8,5,3,4]=>0000000=>[8]=>[8]
[2,6,7,8,5,3,4,1]=>0000000=>[8]=>[8]
[6,2,7,8,4,5,3,1]=>0000000=>[8]=>[8]
[1,7,2,8,4,5,6,3]=>1000000=>[1,7]=>[7,1]
[6,3,7,8,1,5,2,4]=>0000000=>[8]=>[8]
[6,7,1,2,8,5,3,4]=>0000000=>[8]=>[8]
[1,6,7,8,4,2,5,3]=>1000000=>[1,7]=>[7,1]
[4,1,5,7,3,2,6,8]=>0000001=>[7,1]=>[7,1]
[4,6,1,7,3,2,5,8]=>0000001=>[7,1]=>[7,1]
[8,1,7,4,6,3,2,5]=>0000000=>[8]=>[8]
[6,7,3,5,1,4,8,2]=>0000000=>[8]=>[8]
[5,7,8,4,2,6,3,1]=>0000000=>[8]=>[8]
[5,4,7,6,2,8,3,1]=>0000000=>[8]=>[8]
[5,7,4,1,6,8,3,2]=>0000000=>[8]=>[8]
[6,8,4,5,7,1,3,2]=>0000000=>[8]=>[8]
[5,8,4,6,1,7,3,2]=>0000000=>[8]=>[8]
[5,6,1,4,7,8,3,2]=>0000000=>[8]=>[8]
[5,6,7,2,4,8,3,1]=>0000000=>[8]=>[8]
[5,3,6,7,4,8,2,1]=>0000000=>[8]=>[8]
[5,3,2,8,6,7,4,1]=>0000000=>[8]=>[8]
[5,4,8,2,6,7,3,1]=>0000000=>[8]=>[8]
[5,4,8,6,2,7,3,1]=>0000000=>[8]=>[8]
[6,4,8,5,7,2,3,1]=>0000000=>[8]=>[8]
[4,6,8,5,7,2,3,1]=>0000000=>[8]=>[8]
[5,6,8,2,4,7,3,1]=>0000000=>[8]=>[8]
[5,6,3,8,4,7,2,1]=>0000000=>[8]=>[8]
[4,6,3,5,8,7,2,1]=>0000000=>[8]=>[8]
[4,6,3,2,8,7,5,1]=>0000000=>[8]=>[8]
[5,6,3,8,2,7,4,1]=>0000000=>[8]=>[8]
[3,6,5,8,7,2,4,1]=>0000000=>[8]=>[8]
[5,3,6,8,2,7,4,1]=>0000000=>[8]=>[8]
[4,3,7,2,8,6,5,1]=>0000000=>[8]=>[8]
[5,4,7,2,6,8,3,1]=>0000000=>[8]=>[8]
[5,3,2,7,6,8,4,1]=>0000000=>[8]=>[8]
[6,7,3,8,5,2,4,1]=>0000000=>[8]=>[8]
[6,3,2,7,5,4,8,1]=>0000000=>[8]=>[8]
[6,4,7,2,5,3,8,1]=>0000000=>[8]=>[8]
[6,2,7,5,1,4,8,3]=>0000000=>[8]=>[8]
[2,7,8,5,3,6,1,4]=>0000000=>[8]=>[8]
[6,3,7,8,4,2,5,1]=>0000000=>[8]=>[8]
[3,5,7,8,4,6,2,1]=>0000000=>[8]=>[8]
[5,7,8,2,4,6,3,1]=>0000000=>[8]=>[8]
[2,5,8,4,3,7,6,1]=>0000000=>[8]=>[8]
[2,6,8,4,7,3,5,1]=>0000000=>[8]=>[8]
[3,7,4,8,6,2,1,5]=>0000000=>[8]=>[8]
[3,6,4,8,7,2,5,1]=>0000000=>[8]=>[8]
[3,5,4,8,2,7,6,1]=>0000000=>[8]=>[8]
[4,5,7,3,8,6,2,1]=>0000000=>[8]=>[8]
[6,3,1,8,7,5,4,2]=>0000000=>[8]=>[8]
[8,5,4,1,7,6,3,2]=>0000000=>[8]=>[8]
[1,8,2,5,6,3,4,7]=>1000000=>[1,7]=>[7,1]
[7,2,8,4,5,1,3,6]=>0000000=>[8]=>[8]
[1,3,7,5,6,2,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,7,4,3,5,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,2,5,3,6,7,4]=>1000000=>[1,7]=>[7,1]
[2,6,8,4,3,5,7,1]=>0000000=>[8]=>[8]
[7,2,8,4,1,5,6,3]=>0000000=>[8]=>[8]
[7,5,8,1,2,6,3,4]=>0000000=>[8]=>[8]
[1,5,2,6,4,7,8,3]=>1000000=>[1,7]=>[7,1]
[1,5,4,6,2,3,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[6,2,5,7,1,4,8,3]=>0000000=>[8]=>[8]
[6,5,4,3,8,1,7,2]=>0000000=>[8]=>[8]
[2,6,5,8,3,4,1,7]=>0000000=>[8]=>[8]
[2,6,5,7,3,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,2,5,7,4,1,3,8]=>0000001=>[7,1]=>[7,1]
[6,2,5,8,4,1,3,7]=>0000000=>[8]=>[8]
[2,7,8,4,6,1,3,5]=>0000000=>[8]=>[8]
[6,1,2,8,5,4,7,3]=>0000000=>[8]=>[8]
[6,2,5,7,8,1,3,4]=>0000000=>[8]=>[8]
[1,5,4,2,6,7,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,6,5,7,3,8,1,4]=>0000000=>[8]=>[8]
[1,6,2,7,5,8,4,3]=>1000000=>[1,7]=>[7,1]
[1,3,2,7,8,5,6,4]=>1010000=>[1,2,5]=>[5,2,1]
[1,6,2,4,8,7,3,5]=>1000000=>[1,7]=>[7,1]
[6,5,2,1,8,7,3,4]=>0000000=>[8]=>[8]
[2,6,5,3,7,8,4,1]=>0000000=>[8]=>[8]
[6,5,2,3,8,7,1,4]=>0000000=>[8]=>[8]
[5,1,4,2,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[1,5,4,2,6,3,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[6,5,8,7,4,3,1,2]=>0000000=>[8]=>[8]
[1,2,7,5,4,8,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[3,2,7,5,4,8,1,6]=>0000000=>[8]=>[8]
[6,8,3,2,4,7,1,5]=>0000000=>[8]=>[8]
[3,7,2,5,4,8,1,6]=>0000000=>[8]=>[8]
[1,3,7,5,4,8,2,6]=>1000000=>[1,7]=>[7,1]
[2,7,3,5,4,8,1,6]=>0000000=>[8]=>[8]
[6,3,5,2,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,3,5,8,1,4,7,6]=>0000000=>[8]=>[8]
[6,3,8,5,2,7,1,4]=>0000000=>[8]=>[8]
[2,3,6,8,1,4,7,5]=>0000000=>[8]=>[8]
[2,5,8,1,7,3,6,4]=>0000000=>[8]=>[8]
[2,8,1,5,7,3,6,4]=>0000000=>[8]=>[8]
[2,6,8,1,5,7,3,4]=>0000000=>[8]=>[8]
[2,7,1,5,8,3,4,6]=>0000000=>[8]=>[8]
[3,7,5,8,1,2,6,4]=>0000000=>[8]=>[8]
[7,3,6,1,2,8,4,5]=>0000000=>[8]=>[8]
[6,8,4,5,1,7,2,3]=>0000000=>[8]=>[8]
[5,1,8,7,6,2,3,4]=>0000000=>[8]=>[8]
[4,6,1,8,7,5,2,3]=>0000000=>[8]=>[8]
[3,4,8,7,1,2,5,6]=>0000000=>[8]=>[8]
[5,6,8,3,7,1,4,2]=>0000000=>[8]=>[8]
[6,4,7,1,2,8,5,3]=>0000000=>[8]=>[8]
[6,5,1,8,2,7,3,4]=>0000000=>[8]=>[8]
[6,5,1,8,7,2,3,4]=>0000000=>[8]=>[8]
[6,5,1,7,2,8,3,4]=>0000000=>[8]=>[8]
[6,5,1,7,2,3,8,4]=>0000000=>[8]=>[8]
[5,6,8,7,4,1,2,3]=>0000000=>[8]=>[8]
[6,8,5,7,4,1,2,3]=>0000000=>[8]=>[8]
[6,8,3,1,5,2,4,7]=>0000000=>[8]=>[8]
[6,8,4,3,1,5,7,2]=>0000000=>[8]=>[8]
[6,8,4,2,1,5,7,3]=>0000000=>[8]=>[8]
[6,3,2,1,7,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,4,2,1,7,5,3,8]=>0000001=>[7,1]=>[7,1]
[6,3,2,8,7,1,4,5]=>0000000=>[8]=>[8]
[4,2,8,1,7,3,5,6]=>0000000=>[8]=>[8]
[4,3,1,6,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[5,4,1,7,2,8,6,3]=>0000000=>[8]=>[8]
[5,4,2,1,6,7,3,8]=>0000001=>[7,1]=>[7,1]
[8,6,1,4,5,7,2,3]=>0000000=>[8]=>[8]
[5,2,8,3,7,4,6,1]=>0000000=>[8]=>[8]
[6,2,8,5,4,7,3,1]=>0000000=>[8]=>[8]
[5,2,8,4,3,6,7,1]=>0000000=>[8]=>[8]
[5,4,2,7,3,6,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,2,8,3,6,1,7]=>0000000=>[8]=>[8]
[6,5,3,8,4,7,2,1]=>0000000=>[8]=>[8]
[5,2,8,4,3,7,1,6]=>0000000=>[8]=>[8]
[6,2,8,3,7,4,1,5]=>0000000=>[8]=>[8]
[5,4,2,7,3,1,8,6]=>0000000=>[8]=>[8]
[6,4,3,7,1,2,8,5]=>0000000=>[8]=>[8]
[6,4,3,8,1,2,7,5]=>0000000=>[8]=>[8]
[7,2,8,4,3,1,5,6]=>0000000=>[8]=>[8]
[7,5,3,8,4,2,6,1]=>0000000=>[8]=>[8]
[6,4,2,7,3,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,6,4,8,2,3,5,1]=>0000000=>[8]=>[8]
[5,3,1,7,8,4,6,2]=>0000000=>[8]=>[8]
[5,3,2,7,8,4,6,1]=>0000000=>[8]=>[8]
[6,5,1,7,8,2,3,4]=>0000000=>[8]=>[8]
[6,3,1,7,8,4,2,5]=>0000000=>[8]=>[8]
[5,4,1,7,3,8,2,6]=>0000000=>[8]=>[8]
[6,3,2,7,8,4,1,5]=>0000000=>[8]=>[8]
[8,7,6,1,3,5,2,4]=>0000000=>[8]=>[8]
[5,7,2,1,6,3,8,4]=>0000000=>[8]=>[8]
[6,4,8,1,3,2,7,5]=>0000000=>[8]=>[8]
[3,6,7,8,4,2,1,5]=>0000000=>[8]=>[8]
[2,5,8,3,1,6,7,4]=>0000000=>[8]=>[8]
[4,8,7,2,1,6,3,5]=>0000000=>[8]=>[8]
[3,6,1,2,5,8,4,7]=>0000000=>[8]=>[8]
[1,4,5,8,2,3,7,6]=>1000000=>[1,7]=>[7,1]
[1,5,2,4,6,8,3,7]=>1000000=>[1,7]=>[7,1]
[3,6,1,5,8,2,4,7]=>0000000=>[8]=>[8]
[2,6,5,1,4,8,3,7]=>0000000=>[8]=>[8]
[2,5,1,8,4,7,3,6]=>0000000=>[8]=>[8]
[2,7,1,4,3,6,8,5]=>0000000=>[8]=>[8]
[1,3,7,5,8,2,4,6]=>1000000=>[1,7]=>[7,1]
[8,2,1,5,7,3,4,6]=>0000000=>[8]=>[8]
[2,5,4,8,1,3,7,6]=>0000000=>[8]=>[8]
[2,4,1,3,8,6,7,5]=>0001000=>[4,4]=>[4,4]
[8,4,3,7,1,2,6,5]=>0000000=>[8]=>[8]
[1,7,3,5,8,2,6,4]=>1000000=>[1,7]=>[7,1]
[1,8,4,2,6,7,3,5]=>1000000=>[1,7]=>[7,1]
[3,1,6,8,7,2,4,5]=>0000000=>[8]=>[8]
[7,2,1,6,8,3,4,5]=>0000000=>[8]=>[8]
[4,1,7,2,6,8,3,5]=>0000000=>[8]=>[8]
[5,1,7,2,3,6,8,4]=>0000000=>[8]=>[8]
[7,2,1,6,3,5,8,4]=>0000000=>[8]=>[8]
[2,6,1,7,3,5,8,4]=>0000000=>[8]=>[8]
[8,1,3,2,4,6,7,5]=>0000000=>[8]=>[8]
[7,3,1,2,4,6,8,5]=>0000000=>[8]=>[8]
[1,8,3,4,7,2,5,6]=>1000000=>[1,7]=>[7,1]
[3,5,8,1,2,7,4,6]=>0000000=>[8]=>[8]
[3,6,8,1,2,4,7,5]=>0000000=>[8]=>[8]
[4,1,3,8,7,2,6,5]=>0000000=>[8]=>[8]
[1,3,7,4,8,2,6,5]=>1000000=>[1,7]=>[7,1]
[1,4,6,8,2,3,7,5]=>1000000=>[1,7]=>[7,1]
[3,5,8,1,7,2,4,6]=>0000000=>[8]=>[8]
[2,6,8,1,7,3,4,5]=>0000000=>[8]=>[8]
[1,8,3,2,7,5,6,4]=>1000000=>[1,7]=>[7,1]
[2,6,7,3,8,1,5,4]=>0000000=>[8]=>[8]
[8,4,1,7,3,6,2,5]=>0000000=>[8]=>[8]
[3,7,2,8,6,1,5,4]=>0000000=>[8]=>[8]
[6,2,3,8,7,1,5,4]=>0000000=>[8]=>[8]
[3,7,8,2,4,1,5,6]=>0000000=>[8]=>[8]
[1,7,2,4,5,8,3,6]=>1000000=>[1,7]=>[7,1]
[1,7,4,5,8,3,2,6]=>1000000=>[1,7]=>[7,1]
[2,6,4,7,8,3,5,1]=>0000000=>[8]=>[8]
[1,2,6,4,7,8,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[6,1,4,7,8,3,5,2]=>0000000=>[8]=>[8]
[3,6,4,7,2,8,5,1]=>0000000=>[8]=>[8]
[6,1,4,7,8,5,2,3]=>0000000=>[8]=>[8]
[6,8,5,7,4,2,3,1]=>0000000=>[8]=>[8]
[2,3,8,7,1,6,4,5]=>0000000=>[8]=>[8]
[4,8,1,2,7,3,5,6]=>0000000=>[8]=>[8]
[6,4,8,7,5,1,2,3]=>0000000=>[8]=>[8]
[6,3,8,7,2,1,4,5]=>0000000=>[8]=>[8]
[2,6,7,8,5,1,3,4]=>0000000=>[8]=>[8]
[2,8,3,4,1,5,7,6]=>0000000=>[8]=>[8]
[4,5,3,2,8,6,7,1]=>0000000=>[8]=>[8]
[3,5,8,6,1,4,7,2]=>0000000=>[8]=>[8]
[2,6,4,8,5,1,7,3]=>0000000=>[8]=>[8]
[7,5,3,2,8,6,1,4]=>0000000=>[8]=>[8]
[4,5,1,2,8,6,7,3]=>0000000=>[8]=>[8]
[1,6,4,8,3,2,5,7]=>1000000=>[1,7]=>[7,1]
[1,8,3,5,6,2,4,7]=>1000000=>[1,7]=>[7,1]
[1,4,8,5,6,2,3,7]=>1000000=>[1,7]=>[7,1]
[6,1,4,8,2,3,5,7]=>0000000=>[8]=>[8]
[8,7,2,5,6,1,4,3]=>0000000=>[8]=>[8]
[1,8,2,5,4,7,3,6]=>1000000=>[1,7]=>[7,1]
[5,7,4,1,2,3,8,6]=>0000000=>[8]=>[8]
[1,7,4,2,5,3,8,6]=>1000000=>[1,7]=>[7,1]
[6,7,4,2,1,3,8,5]=>0000000=>[8]=>[8]
[6,4,3,8,5,7,1,2]=>0000000=>[8]=>[8]
[7,4,3,6,2,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,2,5,3,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[8,3,7,4,5,6,1,2]=>0000000=>[8]=>[8]
[2,7,4,3,1,5,6,8]=>0000001=>[7,1]=>[7,1]
[6,8,4,2,3,1,5,7]=>0000000=>[8]=>[8]
[2,1,7,4,8,3,5,6]=>0100000=>[2,6]=>[6,2]
[5,2,8,6,1,3,4,7]=>0000000=>[8]=>[8]
[2,8,3,1,4,5,6,7]=>0000000=>[8]=>[8]
[7,4,8,2,3,1,5,6]=>0000000=>[8]=>[8]
[4,2,7,3,1,5,6,8]=>0000001=>[7,1]=>[7,1]
[8,3,7,2,1,4,5,6]=>0000000=>[8]=>[8]
[6,5,2,4,7,1,3,8]=>0000001=>[7,1]=>[7,1]
[6,5,7,4,1,8,2,3]=>0000000=>[8]=>[8]
[8,6,4,1,3,7,2,5]=>0000000=>[8]=>[8]
[6,4,3,1,8,2,5,7]=>0000000=>[8]=>[8]
[4,8,1,3,5,7,2,6]=>0000000=>[8]=>[8]
[7,8,4,1,3,6,2,5]=>0000000=>[8]=>[8]
[6,5,8,1,3,7,2,4]=>0000000=>[8]=>[8]
[5,3,6,1,8,2,4,7]=>0000000=>[8]=>[8]
[4,7,3,1,8,2,5,6]=>0000000=>[8]=>[8]
[8,3,1,7,2,4,5,6]=>0000000=>[8]=>[8]
[2,8,1,4,7,3,5,6]=>0000000=>[8]=>[8]
[3,1,8,5,4,7,6,2]=>0000000=>[8]=>[8]
[4,1,5,8,3,7,6,2]=>0000000=>[8]=>[8]
[4,1,5,3,8,7,6,2]=>0000000=>[8]=>[8]
[4,5,1,8,2,7,6,3]=>0000000=>[8]=>[8]
[4,8,5,3,1,7,6,2]=>0000000=>[8]=>[8]
[4,5,2,8,1,7,6,3]=>0000000=>[8]=>[8]
[4,6,2,8,7,1,5,3]=>0000000=>[8]=>[8]
[4,8,6,3,7,1,5,2]=>0000000=>[8]=>[8]
[4,6,8,2,7,5,1,3]=>0000000=>[8]=>[8]
[4,6,2,8,7,5,1,3]=>0000000=>[8]=>[8]
[5,6,2,7,4,1,8,3]=>0000000=>[8]=>[8]
[5,6,7,2,3,1,8,4]=>0000000=>[8]=>[8]
[5,6,7,2,8,3,1,4]=>0000000=>[8]=>[8]
[5,6,7,2,1,8,3,4]=>0000000=>[8]=>[8]
[5,6,7,2,1,3,8,4]=>0000000=>[8]=>[8]
[5,6,1,7,8,2,4,3]=>0000000=>[8]=>[8]
[5,6,1,7,2,4,8,3]=>0000000=>[8]=>[8]
[4,1,6,8,7,3,5,2]=>0000000=>[8]=>[8]
[4,1,6,8,7,5,3,2]=>0000000=>[8]=>[8]
[5,6,1,7,8,4,2,3]=>0000000=>[8]=>[8]
[4,6,8,1,7,5,2,3]=>0000000=>[8]=>[8]
[4,8,6,1,7,5,3,2]=>0000000=>[8]=>[8]
[5,6,7,1,8,3,2,4]=>0000000=>[8]=>[8]
[5,6,7,1,3,8,2,4]=>0000000=>[8]=>[8]
[5,6,7,1,3,2,8,4]=>0000000=>[8]=>[8]
[5,6,7,3,1,2,8,4]=>0000000=>[8]=>[8]
[5,6,8,7,4,2,1,3]=>0000000=>[8]=>[8]
[1,3,7,5,8,2,6,4]=>1000000=>[1,7]=>[7,1]
[3,1,7,5,8,2,6,4]=>0000000=>[8]=>[8]
[3,5,7,1,8,4,6,2]=>0000000=>[8]=>[8]
[5,2,8,1,7,3,4,6]=>0000000=>[8]=>[8]
[5,8,3,2,7,1,4,6]=>0000000=>[8]=>[8]
[5,1,8,3,7,2,4,6]=>0000000=>[8]=>[8]
[5,1,8,4,6,2,3,7]=>0000000=>[8]=>[8]
[4,8,5,2,6,1,3,7]=>0000000=>[8]=>[8]
[4,1,7,5,6,2,8,3]=>0000000=>[8]=>[8]
[5,7,4,3,8,1,6,2]=>0000000=>[8]=>[8]
[5,7,4,3,8,2,6,1]=>0000000=>[8]=>[8]
[3,8,4,2,6,7,5,1]=>0000000=>[8]=>[8]
[3,8,4,1,6,7,5,2]=>0000000=>[8]=>[8]
[6,1,7,5,2,8,4,3]=>0000000=>[8]=>[8]
[5,6,4,3,2,8,1,7]=>0000000=>[8]=>[8]
[2,6,7,5,3,8,4,1]=>0000000=>[8]=>[8]
[2,1,6,7,5,3,8,4]=>0100000=>[2,6]=>[6,2]
[3,8,4,2,1,6,7,5]=>0000000=>[8]=>[8]
[5,7,4,3,8,2,1,6]=>0000000=>[8]=>[8]
[6,7,4,8,1,2,5,3]=>0000000=>[8]=>[8]
[6,7,5,8,1,2,4,3]=>0000000=>[8]=>[8]
[6,7,4,8,3,1,2,5]=>0000000=>[8]=>[8]
[6,1,3,4,8,2,5,7]=>0000000=>[8]=>[8]
[6,2,3,4,8,1,5,7]=>0000000=>[8]=>[8]
[3,4,8,2,1,5,7,6]=>0000000=>[8]=>[8]
[6,7,5,8,3,1,4,2]=>0000000=>[8]=>[8]
[2,5,7,6,1,4,8,3]=>0000000=>[8]=>[8]
[6,7,4,8,2,3,5,1]=>0000000=>[8]=>[8]
[6,7,4,8,1,3,5,2]=>0000000=>[8]=>[8]
[2,6,7,5,1,3,8,4]=>0000000=>[8]=>[8]
[6,3,1,4,8,2,5,7]=>0000000=>[8]=>[8]
[6,7,4,8,1,3,2,5]=>0000000=>[8]=>[8]
[6,7,5,8,4,1,3,2]=>0000000=>[8]=>[8]
[6,7,4,8,2,1,3,5]=>0000000=>[8]=>[8]
[6,7,4,8,1,2,3,5]=>0000000=>[8]=>[8]
[7,8,3,2,6,1,4,5]=>0000000=>[8]=>[8]
[3,4,8,2,6,1,7,5]=>0000000=>[8]=>[8]
[7,8,4,1,5,6,3,2]=>0000000=>[8]=>[8]
[7,8,1,2,6,3,4,5]=>0000000=>[8]=>[8]
[7,8,5,1,4,6,3,2]=>0000000=>[8]=>[8]
[5,3,8,4,1,6,7,2]=>0000000=>[8]=>[8]
[6,2,4,8,1,5,3,7]=>0000000=>[8]=>[8]
[3,4,8,5,1,6,7,2]=>0000000=>[8]=>[8]
[5,3,8,1,4,6,7,2]=>0000000=>[8]=>[8]
[4,2,6,8,1,5,3,7]=>0000000=>[8]=>[8]
[7,4,2,8,1,5,3,6]=>0000000=>[8]=>[8]
[6,1,7,5,8,4,3,2]=>0000000=>[8]=>[8]
[1,2,7,8,5,3,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[6,3,7,8,5,4,1,2]=>0000000=>[8]=>[8]
[6,1,5,7,8,4,3,2]=>0000000=>[8]=>[8]
[1,7,5,6,8,4,3,2]=>1000000=>[1,7]=>[7,1]
[3,1,8,4,5,6,7,2]=>0000000=>[8]=>[8]
[4,2,1,8,6,5,3,7]=>0000000=>[8]=>[8]
[3,2,7,8,5,1,4,6]=>0000000=>[8]=>[8]
[2,3,7,8,5,1,4,6]=>0000000=>[8]=>[8]
[2,7,3,8,5,1,4,6]=>0000000=>[8]=>[8]
[3,6,2,8,5,1,4,7]=>0000000=>[8]=>[8]
[1,4,2,8,7,5,3,6]=>1000000=>[1,7]=>[7,1]
[7,3,6,8,5,4,1,2]=>0000000=>[8]=>[8]
[7,2,1,8,5,3,4,6]=>0000000=>[8]=>[8]
[1,2,6,8,4,5,3,7]=>1100000=>[1,1,6]=>[6,1,1]
[7,1,6,5,8,4,3,2]=>0000000=>[8]=>[8]
[6,5,7,1,8,4,3,2]=>0000000=>[8]=>[8]
[5,7,6,1,8,4,3,2]=>0000000=>[8]=>[8]
[6,7,1,5,8,4,3,2]=>0000000=>[8]=>[8]
[7,1,2,8,4,5,3,6]=>0000000=>[8]=>[8]
[7,6,1,5,8,4,3,2]=>0000000=>[8]=>[8]
[7,5,6,1,8,4,3,2]=>0000000=>[8]=>[8]
[9,10,7,8,5,6,2,1,3,4]=>000000000=>[10]=>[10]
[9,10,7,8,4,3,5,6,1,2]=>000000000=>[10]=>[10]
[9,10,7,8,4,2,5,1,3,6]=>000000000=>[10]=>[10]
[9,10,7,8,3,2,1,4,5,6]=>000000000=>[10]=>[10]
[9,10,6,5,7,8,3,4,1,2]=>000000000=>[10]=>[10]
[9,10,6,5,7,8,2,1,3,4]=>000000000=>[10]=>[10]
[9,10,6,4,7,3,5,8,1,2]=>000000000=>[10]=>[10]
[9,10,6,4,7,2,5,1,3,8]=>000000000=>[10]=>[10]
[9,10,6,3,7,2,1,4,5,8]=>000000000=>[10]=>[10]
[9,10,5,4,3,6,7,8,1,2]=>000000000=>[10]=>[10]
[9,10,5,4,2,6,7,1,3,8]=>000000000=>[10]=>[10]
[9,10,5,3,2,6,1,4,7,8]=>000000000=>[10]=>[10]
[9,10,4,3,2,1,5,6,7,8]=>000000000=>[10]=>[10]
[8,7,9,10,5,6,3,4,1,2]=>000000000=>[10]=>[10]
[8,7,9,10,5,6,2,1,3,4]=>000000000=>[10]=>[10]
[8,7,9,10,4,3,5,6,1,2]=>000000000=>[10]=>[10]
[8,7,9,10,4,2,5,1,3,6]=>000000000=>[10]=>[10]
[8,7,9,10,3,2,1,4,5,6]=>000000000=>[10]=>[10]
[8,6,9,5,7,10,3,4,1,2]=>000000000=>[10]=>[10]
[8,6,9,5,7,10,2,1,3,4]=>000000000=>[10]=>[10]
[8,6,9,4,7,3,5,10,1,2]=>000000000=>[10]=>[10]
[8,6,9,3,7,2,1,4,5,10]=>000000001=>[9,1]=>[9,1]
[8,5,9,4,3,6,7,10,1,2]=>000000000=>[10]=>[10]
[8,5,9,4,2,6,7,1,3,10]=>000000001=>[9,1]=>[9,1]
[8,5,9,3,2,6,1,4,7,10]=>000000001=>[9,1]=>[9,1]
[8,4,9,3,2,1,5,6,7,10]=>000000001=>[9,1]=>[9,1]
[7,6,5,8,9,10,3,4,1,2]=>000000000=>[10]=>[10]
[7,6,5,8,9,10,2,1,3,4]=>000000000=>[10]=>[10]
[7,6,4,8,9,3,5,10,1,2]=>000000000=>[10]=>[10]
[7,6,4,8,9,2,5,1,3,10]=>000000001=>[9,1]=>[9,1]
[7,6,3,8,9,2,1,4,5,10]=>000000001=>[9,1]=>[9,1]
[7,5,4,8,3,6,9,10,1,2]=>000000000=>[10]=>[10]
[7,5,4,8,2,6,9,1,3,10]=>000000001=>[9,1]=>[9,1]
[7,4,3,8,2,1,5,6,9,10]=>000000011=>[8,1,1]=>[8,1,1]
[6,5,4,2,7,8,9,1,3,10]=>000000001=>[9,1]=>[9,1]
[6,5,3,2,7,8,1,4,9,10]=>000000011=>[8,1,1]=>[8,1,1]
[1,8,7,5,3,2,4,6]=>1000000=>[1,7]=>[7,1]
[1,8,7,4,2,5,3,6]=>1000000=>[1,7]=>[7,1]
[5,3,7,1,6,4,2,8]=>0000001=>[7,1]=>[7,1]
[1,5,3,8,7,4,2,6]=>1000000=>[1,7]=>[7,1]
[1,8,6,3,5,7,4,2]=>1000000=>[1,7]=>[7,1]
[1,8,6,3,2,4,7,5]=>1000000=>[1,7]=>[7,1]
[1,7,5,8,6,3,2,4]=>1000000=>[1,7]=>[7,1]
[1,7,4,2,5,8,6,3]=>1000000=>[1,7]=>[7,1]
[8,7,4,2,5,3,1,6]=>0000000=>[8]=>[8]
[1,8,5,2,7,4,6,3]=>1000000=>[1,7]=>[7,1]
[1,7,4,6,3,8,5,2]=>1000000=>[1,7]=>[7,1]
[4,1,8,5,7,3,2,6]=>0000000=>[8]=>[8]
[4,7,2,8,3,6,1,5]=>0000000=>[8]=>[8]
[1,8,5,4,2,3,7,6]=>1000000=>[1,7]=>[7,1]
[3,5,4,8,1,2,7,6]=>0000000=>[8]=>[8]
[5,6,3,8,7,1,2,4]=>0000000=>[8]=>[8]
[2,6,8,4,1,7,3,5]=>0000000=>[8]=>[8]
[1,8,7,4,2,6,3,5]=>1000000=>[1,7]=>[7,1]
[5,2,8,6,7,1,3,4]=>0000000=>[8]=>[8]
[6,2,8,7,5,1,3,4]=>0000000=>[8]=>[8]
[1,8,5,7,6,2,3,4]=>1000000=>[1,7]=>[7,1]
[1,8,6,7,5,2,3,4]=>1000000=>[1,7]=>[7,1]
[5,2,8,7,1,4,3,6]=>0000000=>[8]=>[8]
[6,1,7,3,2,8,5,4]=>0000000=>[8]=>[8]
[4,7,2,1,6,3,8,5]=>0000000=>[8]=>[8]
[6,1,8,3,7,5,2,4]=>0000000=>[8]=>[8]
[6,1,8,4,5,2,7,3]=>0000000=>[8]=>[8]
[3,5,2,7,1,6,8,4]=>0000000=>[8]=>[8]
[6,1,4,2,5,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,3,7,5,4,2,8,6]=>1000000=>[1,7]=>[7,1]
[6,1,3,5,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,1,2,5,4,7,3,8]=>0000001=>[7,1]=>[7,1]
[5,2,6,3,4,7,1,8]=>0000001=>[7,1]=>[7,1]
[2,4,7,1,5,3,8,6]=>0000000=>[8]=>[8]
[2,3,6,7,4,8,1,5]=>0000000=>[8]=>[8]
[1,3,6,7,4,8,5,2]=>1000000=>[1,7]=>[7,1]
[2,7,6,5,3,1,8,4]=>0000000=>[8]=>[8]
[5,2,6,1,4,7,8,3]=>0000000=>[8]=>[8]
[4,7,6,5,2,1,8,3]=>0000000=>[8]=>[8]
[6,3,1,5,4,7,8,2]=>0000000=>[8]=>[8]
[5,3,6,1,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,7,4,2,6,3,8,5]=>1000000=>[1,7]=>[7,1]
[5,7,4,1,2,3,6,8]=>0000001=>[7,1]=>[7,1]
[6,4,1,2,5,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,7,6,3,8,5,1,2]=>0000000=>[8]=>[8]
[3,7,6,5,2,8,1,4]=>0000000=>[8]=>[8]
[3,7,6,5,1,2,8,4]=>0000000=>[8]=>[8]
[4,7,2,6,1,3,8,5]=>0000000=>[8]=>[8]
[2,7,6,5,8,1,4,3]=>0000000=>[8]=>[8]
[4,2,6,8,3,1,5,7]=>0000000=>[8]=>[8]
[3,7,6,2,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[2,3,6,5,8,1,4,7]=>0000000=>[8]=>[8]
[2,3,5,8,6,1,4,7]=>0000000=>[8]=>[8]
[4,2,3,8,6,1,5,7]=>0000000=>[8]=>[8]
[1,2,3,7,4,6,8,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[3,2,7,1,4,5,8,6]=>0000000=>[8]=>[8]
[2,1,5,3,8,7,4,6]=>0100000=>[2,6]=>[6,2]
[5,8,3,2,4,1,6,7]=>0000000=>[8]=>[8]
[4,2,7,1,8,3,5,6]=>0000000=>[8]=>[8]
[1,2,7,5,3,8,4,6]=>1100000=>[1,1,6]=>[6,1,1]
[3,2,7,1,4,8,5,6]=>0000000=>[8]=>[8]
[1,2,3,7,6,8,4,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,6,8,7,4,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,7,8,4,6,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[1,2,3,6,8,4,7,5]=>1110000=>[1,1,1,5]=>[5,1,1,1]
[6,2,8,3,7,5,1,4]=>0000000=>[8]=>[8]
[4,2,8,3,7,5,6,1]=>0000000=>[8]=>[8]
[7,3,4,8,6,5,1,2]=>0000000=>[8]=>[8]
[5,3,4,8,7,2,6,1]=>0000000=>[8]=>[8]
[4,6,3,8,5,7,2,1]=>0000000=>[8]=>[8]
[7,5,3,8,6,2,4,1]=>0000000=>[8]=>[8]
[2,6,8,3,7,4,5,1]=>0000000=>[8]=>[8]
[2,5,8,3,7,4,6,1]=>0000000=>[8]=>[8]
[7,4,3,8,6,2,5,1]=>0000000=>[8]=>[8]
[3,5,4,8,7,2,6,1]=>0000000=>[8]=>[8]
[4,5,3,8,6,7,2,1]=>0000000=>[8]=>[8]
[3,6,7,8,4,5,2,1]=>0000000=>[8]=>[8]
[1,8,5,6,4,7,3,2]=>1000000=>[1,7]=>[7,1]
[2,5,8,6,4,7,3,1]=>0000000=>[8]=>[8]
[6,3,7,8,4,5,2,1]=>0000000=>[8]=>[8]
[4,3,7,8,5,6,2,1]=>0000000=>[8]=>[8]
[4,2,8,6,5,7,3,1]=>0000000=>[8]=>[8]
[3,2,8,6,7,4,5,1]=>0000000=>[8]=>[8]
[2,3,8,7,5,4,6,1]=>0000000=>[8]=>[8]
[1,8,2,7,4,5,6,3]=>1000000=>[1,7]=>[7,1]
[7,2,8,6,3,4,5,1]=>0000000=>[8]=>[8]
[6,2,8,4,5,7,3,1]=>0000000=>[8]=>[8]
[5,2,8,4,6,7,3,1]=>0000000=>[8]=>[8]
[4,3,6,8,5,7,2,1]=>0000000=>[8]=>[8]
[3,4,6,8,7,2,5,1]=>0000000=>[8]=>[8]
[7,3,5,8,6,2,4,1]=>0000000=>[8]=>[8]
[1,8,3,5,7,4,6,2]=>1000000=>[1,7]=>[7,1]
[2,7,8,4,5,6,3,1]=>0000000=>[8]=>[8]
[3,7,5,8,4,6,2,1]=>0000000=>[8]=>[8]
[5,7,4,6,8,3,2,1]=>0000000=>[8]=>[8]
[3,6,5,8,4,7,2,1]=>0000000=>[8]=>[8]
[2,6,8,4,5,7,3,1]=>0000000=>[8]=>[8]
[4,2,7,1,3,8,5,6]=>0000000=>[8]=>[8]
[4,2,5,1,3,8,6,7]=>0000100=>[5,3]=>[5,3]
[5,3,6,1,7,2,4,8]=>0000001=>[7,1]=>[7,1]
[3,7,1,2,5,8,6,4]=>0000000=>[8]=>[8]
[3,7,4,1,2,8,5,6]=>0000000=>[8]=>[8]
[7,5,1,3,4,8,6,2]=>0000000=>[8]=>[8]
[7,5,1,2,4,8,6,3]=>0000000=>[8]=>[8]
[6,4,2,3,7,1,5,8]=>0000001=>[7,1]=>[7,1]
[7,6,3,8,1,2,5,4]=>0000000=>[8]=>[8]
[7,4,2,3,8,1,6,5]=>0000000=>[8]=>[8]
[4,7,5,2,8,1,3,6]=>0000000=>[8]=>[8]
[8,2,6,3,7,1,4,5]=>0000000=>[8]=>[8]
[8,6,1,2,7,4,5,3]=>0000000=>[8]=>[8]
[8,4,7,1,2,3,6,5]=>0000000=>[8]=>[8]
[8,5,7,1,2,4,6,3]=>0000000=>[8]=>[8]
[3,8,5,6,1,2,4,7]=>0000000=>[8]=>[8]
[3,7,5,8,1,2,4,6]=>0000000=>[8]=>[8]
[7,6,4,8,1,3,5,2]=>0000000=>[8]=>[8]
[6,5,8,1,2,4,7,3]=>0000000=>[8]=>[8]
[3,6,8,1,2,5,7,4]=>0000000=>[8]=>[8]
[4,6,3,8,1,2,5,7]=>0000000=>[8]=>[8]
[4,6,3,7,1,2,5,8]=>0000001=>[7,1]=>[7,1]
[4,1,7,8,2,3,6,5]=>0000000=>[8]=>[8]
[5,1,2,8,6,3,4,7]=>0000000=>[8]=>[8]
[5,3,8,1,6,2,4,7]=>0000000=>[8]=>[8]
[6,1,8,5,2,3,4,7]=>0000000=>[8]=>[8]
[6,1,7,5,2,3,4,8]=>0000001=>[7,1]=>[7,1]
[6,8,1,3,7,4,5,2]=>0000000=>[8]=>[8]
[7,2,8,1,6,3,4,5]=>0000000=>[8]=>[8]
[4,7,8,2,5,1,3,6]=>0000000=>[8]=>[8]
[6,8,2,7,1,4,5,3]=>0000000=>[8]=>[8]
[4,8,7,1,3,5,6,2]=>0000000=>[8]=>[8]
[3,8,7,1,2,4,6,5]=>0000000=>[8]=>[8]
[4,8,7,1,2,3,6,5]=>0000000=>[8]=>[8]
[5,8,7,1,2,4,6,3]=>0000000=>[8]=>[8]
[5,8,7,1,3,4,6,2]=>0000000=>[8]=>[8]
[7,1,8,6,2,3,5,4]=>0000000=>[8]=>[8]
[5,8,6,4,1,2,3,7]=>0000000=>[8]=>[8]
[5,1,3,4,6,7,2,8]=>0000001=>[7,1]=>[7,1]
[1,3,4,8,7,5,2,6]=>1000000=>[1,7]=>[7,1]
[8,2,4,1,7,3,5,6]=>0000000=>[8]=>[8]
[8,6,1,4,2,3,7,5]=>0000000=>[8]=>[8]
[3,6,1,4,2,8,7,5]=>0000000=>[8]=>[8]
[1,6,8,4,3,7,2,5]=>1000000=>[1,7]=>[7,1]
[3,1,4,7,8,5,2,6]=>0000000=>[8]=>[8]
[6,1,7,4,3,8,2,5]=>0000000=>[8]=>[8]
[1,8,7,4,3,6,2,5]=>1000000=>[1,7]=>[7,1]
[7,4,1,3,8,2,6,5]=>0000000=>[8]=>[8]
[4,8,2,3,1,5,7,6]=>0000000=>[8]=>[8]
[4,8,6,2,1,3,7,5]=>0000000=>[8]=>[8]
[2,7,4,1,8,3,5,6]=>0000000=>[8]=>[8]
[1,7,8,4,2,3,6,5]=>1000000=>[1,7]=>[7,1]
[8,7,1,3,4,2,6,5]=>0000000=>[8]=>[8]
[1,7,4,3,6,2,8,5]=>1000000=>[1,7]=>[7,1]
[3,8,6,4,5,2,1,7]=>0000000=>[8]=>[8]
[3,8,4,6,5,2,1,7]=>0000000=>[8]=>[8]
[2,4,3,7,5,8,1,6]=>0000000=>[8]=>[8]
[1,4,7,3,6,2,8,5]=>1000000=>[1,7]=>[7,1]
[6,4,1,3,7,2,8,5]=>0000000=>[8]=>[8]
[8,1,4,3,6,2,7,5]=>0000000=>[8]=>[8]
[4,2,3,8,5,7,1,6]=>0000000=>[8]=>[8]
[2,8,5,7,3,4,1,6]=>0000000=>[8]=>[8]
[5,8,2,6,4,3,1,7]=>0000000=>[8]=>[8]
[7,2,5,8,4,3,1,6]=>0000000=>[8]=>[8]
[4,2,3,5,8,7,1,6]=>0000000=>[8]=>[8]
[8,2,3,5,4,7,1,6]=>0000000=>[8]=>[8]
[6,1,8,3,4,2,7,5]=>0000000=>[8]=>[8]
[1,8,6,4,2,3,7,5]=>1000000=>[1,7]=>[7,1]
[3,8,4,5,6,2,1,7]=>0000000=>[8]=>[8]
[3,8,6,5,4,2,1,7]=>0000000=>[8]=>[8]
[6,3,1,4,2,8,7,5]=>0000000=>[8]=>[8]
[7,3,8,1,2,6,4,5]=>0000000=>[8]=>[8]
[7,1,4,5,3,2,6,8]=>0000001=>[7,1]=>[7,1]
[1,8,4,2,6,5,3,7]=>1000000=>[1,7]=>[7,1]
[5,1,4,8,6,3,2,7]=>0000000=>[8]=>[8]
[5,3,1,8,4,7,2,6]=>0000000=>[8]=>[8]
[4,3,8,1,5,7,2,6]=>0000000=>[8]=>[8]
[6,3,1,2,5,7,4,8]=>0000001=>[7,1]=>[7,1]
[7,1,4,2,6,5,3,8]=>0000001=>[7,1]=>[7,1]
[3,8,4,1,6,5,2,7]=>0000000=>[8]=>[8]
[8,7,2,4,5,1,6,3]=>0000000=>[8]=>[8]
[7,1,5,4,8,6,3,2]=>0000000=>[8]=>[8]
[5,7,1,4,8,6,3,2]=>0000000=>[8]=>[8]
[6,5,3,7,4,8,2,1]=>0000000=>[8]=>[8]
[2,7,8,4,5,1,6,3]=>0000000=>[8]=>[8]
[5,6,3,8,1,4,7,2]=>0000000=>[8]=>[8]
[8,7,3,1,5,4,2,6]=>0000000=>[8]=>[8]
[3,5,4,7,6,1,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,4,6,1,8,2]=>0000000=>[8]=>[8]
[3,5,7,4,6,1,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,4,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,7,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,2,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[5,3,7,6,1,2,8,4]=>0000000=>[8]=>[8]
[5,3,7,6,1,4,2,8]=>0000001=>[7,1]=>[7,1]
[5,3,7,6,4,1,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,2,6,1,4,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,7,6,1,4,8]=>0000001=>[7,1]=>[7,1]
[5,3,7,6,4,1,8,2]=>0000000=>[8]=>[8]
[3,7,5,4,1,8,2,6]=>0000000=>[8]=>[8]
[3,7,5,4,1,8,6,2]=>0000000=>[8]=>[8]
[3,7,5,1,4,8,6,2]=>0000000=>[8]=>[8]
[3,7,5,1,4,8,2,6]=>0000000=>[8]=>[8]
[3,5,7,1,2,6,8,4]=>0000000=>[8]=>[8]
[3,5,7,2,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[5,3,7,1,6,2,4,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,1,4,6,8,2]=>0000000=>[8]=>[8]
[3,5,7,1,4,2,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,4,1,2,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,7,1,6,8,2]=>0000000=>[8]=>[8]
[3,5,4,7,1,2,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,7,2,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,2,7,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,7,2,1,8,6]=>0000000=>[8]=>[8]
[3,5,4,7,1,2,8,6]=>0000000=>[8]=>[8]
[5,7,6,3,1,8,4,2]=>0000000=>[8]=>[8]
[5,7,6,3,1,8,2,4]=>0000000=>[8]=>[8]
[3,5,7,4,1,2,8,6]=>0000000=>[8]=>[8]
[3,5,7,4,2,1,8,6]=>0000000=>[8]=>[8]
[3,2,5,7,4,1,8,6]=>0000000=>[8]=>[8]
[3,2,5,7,1,4,8,6]=>0000000=>[8]=>[8]
[3,5,2,7,1,4,8,6]=>0000000=>[8]=>[8]
[3,5,7,2,1,4,8,6]=>0000000=>[8]=>[8]
[3,5,7,1,4,2,8,6]=>0000000=>[8]=>[8]
[3,7,5,2,1,8,6,4]=>0000000=>[8]=>[8]
[3,7,2,5,1,8,6,4]=>0000000=>[8]=>[8]
[3,2,7,5,1,8,6,4]=>0000000=>[8]=>[8]
[3,2,7,5,1,8,4,6]=>0000000=>[8]=>[8]
[3,7,2,5,1,8,4,6]=>0000000=>[8]=>[8]
[3,7,5,2,1,8,4,6]=>0000000=>[8]=>[8]
[3,8,4,1,7,6,5,2]=>0000000=>[8]=>[8]
[5,8,2,4,1,6,3,7]=>0000000=>[8]=>[8]
[3,2,6,8,1,5,4,7]=>0000000=>[8]=>[8]
[3,2,6,8,7,1,5,4]=>0000000=>[8]=>[8]
[8,7,3,2,5,6,1,4]=>0000000=>[8]=>[8]
[7,2,4,1,8,3,6,5]=>0000000=>[8]=>[8]
[1,7,2,3,6,8,5,4]=>1000000=>[1,7]=>[7,1]
[3,5,6,4,8,2,7,1]=>0000000=>[8]=>[8]
[3,5,1,4,8,2,7,6]=>0000000=>[8]=>[8]
[1,7,5,4,8,2,6,3]=>1000000=>[1,7]=>[7,1]
[3,7,5,1,6,4,8,2]=>0000000=>[8]=>[8]
[2,7,5,4,8,1,3,6]=>0000000=>[8]=>[8]
[2,7,5,4,8,6,1,3]=>0000000=>[8]=>[8]
[1,7,5,4,8,6,3,2]=>1000000=>[1,7]=>[7,1]
[2,5,1,4,8,7,3,6]=>0000000=>[8]=>[8]
[3,6,4,2,8,7,1,5]=>0000000=>[8]=>[8]
[3,5,2,4,8,1,6,7]=>0000000=>[8]=>[8]
[4,5,6,1,7,3,8,2]=>0000000=>[8]=>[8]
[3,5,6,4,8,1,2,7]=>0000000=>[8]=>[8]
[1,5,6,4,8,7,2,3]=>1000000=>[1,7]=>[7,1]
[3,6,4,1,8,7,2,5]=>0000000=>[8]=>[8]
[3,6,4,5,8,7,2,1]=>0000000=>[8]=>[8]
[1,6,4,3,8,5,2,7]=>1000000=>[1,7]=>[7,1]
[7,6,1,4,5,3,8,2]=>0000000=>[8]=>[8]
[7,6,1,3,5,4,8,2]=>0000000=>[8]=>[8]
[7,1,3,2,5,8,4,6]=>0000000=>[8]=>[8]
[1,6,4,2,8,5,3,7]=>1000000=>[1,7]=>[7,1]
[7,6,5,8,3,1,4,2]=>0000000=>[8]=>[8]
[2,6,4,3,8,1,7,5]=>0000000=>[8]=>[8]
[2,6,4,3,8,5,7,1]=>0000000=>[8]=>[8]
[7,2,3,1,5,8,6,4]=>0000000=>[8]=>[8]
[7,1,5,6,3,8,4,2]=>0000000=>[8]=>[8]
[7,3,6,5,1,4,8,2]=>0000000=>[8]=>[8]
[7,2,6,5,3,8,1,4]=>0000000=>[8]=>[8]
[7,2,3,1,4,8,6,5]=>0000000=>[8]=>[8]
[7,2,3,5,4,8,6,1]=>0000000=>[8]=>[8]
[2,6,4,5,8,1,7,3]=>0000000=>[8]=>[8]
[1,5,6,4,8,3,7,2]=>1000000=>[1,7]=>[7,1]
[2,5,6,4,8,3,1,7]=>0000000=>[8]=>[8]
[3,5,6,1,4,7,8,2]=>0000000=>[8]=>[8]
[7,6,1,3,4,5,8,2]=>0000000=>[8]=>[8]
[7,1,3,2,4,8,5,6]=>0000000=>[8]=>[8]
[7,6,1,5,3,4,8,2]=>0000000=>[8]=>[8]
[7,6,1,5,4,3,8,2]=>0000000=>[8]=>[8]
[1,6,4,5,8,3,2,7]=>1000000=>[1,7]=>[7,1]
[7,6,5,8,1,3,2,4]=>0000000=>[8]=>[8]
[3,4,6,8,7,2,1,5]=>0000000=>[8]=>[8]
[3,5,6,8,2,1,7,4]=>0000000=>[8]=>[8]
[4,2,1,5,3,7,8,6]=>0000100=>[5,3]=>[5,3]
[4,2,5,6,3,1,8,7]=>0000010=>[6,2]=>[6,2]
[3,5,6,8,1,7,2,4]=>0000000=>[8]=>[8]
[4,1,5,6,3,2,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,3,1,7,2,8,6]=>0000000=>[8]=>[8]
[4,1,3,5,2,7,8,6]=>0000100=>[5,3]=>[5,3]
[2,5,4,7,3,8,6,1]=>0000000=>[8]=>[8]
[3,5,7,1,8,4,2,6]=>0000000=>[8]=>[8]
[4,1,5,3,2,7,8,6]=>0000100=>[5,3]=>[5,3]
[4,5,3,7,1,2,8,6]=>0000000=>[8]=>[8]
[4,3,6,1,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[5,1,3,2,4,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[3,6,1,7,4,5,2,8]=>0000001=>[7,1]=>[7,1]
[5,3,1,4,2,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[4,5,2,3,7,1,8,6]=>0000000=>[8]=>[8]
[4,2,6,1,3,7,5,8]=>0000001=>[7,1]=>[7,1]
[4,6,2,1,3,7,5,8]=>0000001=>[7,1]=>[7,1]
[3,6,2,1,7,4,8,5]=>0000000=>[8]=>[8]
[3,1,4,7,6,5,2,8]=>0000001=>[7,1]=>[7,1]
[3,6,2,7,1,5,8,4]=>0000000=>[8]=>[8]
[4,6,2,7,1,3,5,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,1,8,2,6,4]=>0000000=>[8]=>[8]
[5,1,4,2,3,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[2,6,5,3,4,7,8,1]=>0000000=>[8]=>[8]
[3,6,1,7,5,4,2,8]=>0000001=>[7,1]=>[7,1]
[5,1,4,3,2,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,4,1,3,2,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[6,7,4,8,5,1,3,2]=>0000000=>[8]=>[8]
[3,6,5,8,7,1,4,2]=>0000000=>[8]=>[8]
[5,6,8,3,1,7,4,2]=>0000000=>[8]=>[8]
[5,3,8,1,7,2,6,4]=>0000000=>[8]=>[8]
[6,5,3,8,2,7,4,1]=>0000000=>[8]=>[8]
[6,4,8,1,3,7,5,2]=>0000000=>[8]=>[8]
[4,2,8,7,6,3,1,5]=>0000000=>[8]=>[8]
[7,6,3,1,8,4,2,5]=>0000000=>[8]=>[8]
[5,2,7,4,1,8,6,3]=>0000000=>[8]=>[8]
[1,3,7,6,5,8,2,4]=>1000000=>[1,7]=>[7,1]
[6,3,1,4,7,5,2,8]=>0000001=>[7,1]=>[7,1]
[4,6,7,2,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,8,7,1,5,3]=>0000000=>[8]=>[8]
[6,3,7,1,2,8,5,4]=>0000000=>[8]=>[8]
[1,8,2,3,6,5,4,7]=>1000000=>[1,7]=>[7,1]
[3,5,8,4,7,2,6,1]=>0000000=>[8]=>[8]
[1,8,5,4,6,2,3,7]=>1000000=>[1,7]=>[7,1]
[3,8,5,4,6,1,2,7]=>0000000=>[8]=>[8]
[3,8,5,1,6,4,2,7]=>0000000=>[8]=>[8]
[2,8,5,4,6,1,3,7]=>0000000=>[8]=>[8]
[2,8,5,4,6,3,1,7]=>0000000=>[8]=>[8]
[1,8,5,4,6,3,2,7]=>1000000=>[1,7]=>[7,1]
[2,5,8,4,7,3,6,1]=>0000000=>[8]=>[8]
[3,6,4,2,7,8,5,1]=>0000000=>[8]=>[8]
[3,6,4,2,7,8,1,5]=>0000000=>[8]=>[8]
[3,5,4,1,6,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,5,8,1,7,6,2,3]=>0000000=>[8]=>[8]
[3,5,8,4,7,1,6,2]=>0000000=>[8]=>[8]
[1,5,8,4,7,3,6,2]=>1000000=>[1,7]=>[7,1]
[3,6,4,1,7,8,5,2]=>0000000=>[8]=>[8]
[3,6,4,8,7,5,2,1]=>0000000=>[8]=>[8]
[1,6,4,3,7,8,5,2]=>1000000=>[1,7]=>[7,1]
[7,6,1,3,8,4,2,5]=>0000000=>[8]=>[8]
[1,6,4,2,7,8,3,5]=>1000000=>[1,7]=>[7,1]
[2,6,4,3,7,1,8,5]=>0000000=>[8]=>[8]
[2,6,4,1,7,8,3,5]=>0000000=>[8]=>[8]
[7,2,3,4,8,6,5,1]=>0000000=>[8]=>[8]
[7,2,3,1,8,6,4,5]=>0000000=>[8]=>[8]
[7,2,3,4,1,6,8,5]=>0000000=>[8]=>[8]
[1,2,4,3,8,5,7,6]=>1101000=>[1,1,2,4]=>[4,2,1,1]
[7,3,8,6,1,4,2,5]=>0000000=>[8]=>[8]
[7,2,8,6,3,4,1,5]=>0000000=>[8]=>[8]
[7,2,3,1,5,6,8,4]=>0000000=>[8]=>[8]
[7,2,3,8,5,6,4,1]=>0000000=>[8]=>[8]
[2,6,4,8,7,1,5,3]=>0000000=>[8]=>[8]
[1,5,8,4,7,6,2,3]=>1000000=>[1,7]=>[7,1]
[3,5,8,1,6,7,2,4]=>0000000=>[8]=>[8]
[7,6,1,3,5,8,2,4]=>0000000=>[8]=>[8]
[7,1,3,2,5,6,8,4]=>0000000=>[8]=>[8]
[7,1,3,8,2,6,5,4]=>0000000=>[8]=>[8]
[7,6,1,8,5,4,2,3]=>0000000=>[8]=>[8]
[4,3,7,1,6,5,8,2]=>0000000=>[8]=>[8]
[5,2,6,4,8,1,7,3]=>0000000=>[8]=>[8]
[5,3,7,4,8,1,6,2]=>0000000=>[8]=>[8]
[4,3,7,1,6,2,8,5]=>0000000=>[8]=>[8]
[4,1,7,8,6,3,2,5]=>0000000=>[8]=>[8]
[1,2,6,8,3,7,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[6,8,2,4,1,3,7,5]=>0000000=>[8]=>[8]
[6,1,2,7,5,8,4,3]=>0000000=>[8]=>[8]
[4,5,2,6,8,3,7,1]=>0000000=>[8]=>[8]
[6,8,4,1,5,3,7,2]=>0000000=>[8]=>[8]
[8,3,6,1,5,7,4,2]=>0000000=>[8]=>[8]
[2,4,6,7,8,1,5,3]=>0000000=>[8]=>[8]
[7,4,3,8,6,2,1,5]=>0000000=>[8]=>[8]
[4,3,6,2,1,8,5,7]=>0000000=>[8]=>[8]
[4,6,2,3,7,5,8,1]=>0000000=>[8]=>[8]
[8,4,5,3,2,1,7,6]=>0000000=>[8]=>[8]
[6,4,8,3,2,7,1,5]=>0000000=>[8]=>[8]
[5,8,3,7,2,1,6,4]=>0000000=>[8]=>[8]
[1,2,6,5,8,7,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[5,6,3,4,8,7,2,1]=>0000000=>[8]=>[8]
[6,5,3,4,8,7,2,1]=>0000000=>[8]=>[8]
[7,5,3,8,4,6,2,1]=>0000000=>[8]=>[8]
[8,5,3,7,4,6,2,1]=>0000000=>[8]=>[8]
[5,8,1,2,3,4,7,6]=>0000000=>[8]=>[8]
[4,3,8,7,5,6,2,1]=>0000000=>[8]=>[8]
[5,8,3,7,4,6,2,1]=>0000000=>[8]=>[8]
[6,8,7,3,4,5,2,1]=>0000000=>[8]=>[8]
[8,6,2,3,5,1,4,7]=>0000000=>[8]=>[8]
[8,2,4,5,7,3,1,6]=>0000000=>[8]=>[8]
[2,6,3,8,7,5,4,1]=>0000000=>[8]=>[8]
[8,2,3,7,5,4,1,6]=>0000000=>[8]=>[8]
[8,2,6,3,5,4,1,7]=>0000000=>[8]=>[8]
[8,6,1,5,2,4,3,7]=>0000000=>[8]=>[8]
[8,6,2,4,1,5,3,7]=>0000000=>[8]=>[8]
[8,4,1,6,5,3,2,7]=>0000000=>[8]=>[8]
[8,3,6,1,5,4,2,7]=>0000000=>[8]=>[8]
[8,3,2,6,5,4,1,7]=>0000000=>[8]=>[8]
[8,3,2,5,7,4,1,6]=>0000000=>[8]=>[8]
[8,3,1,7,5,4,2,6]=>0000000=>[8]=>[8]
[6,1,3,8,7,5,4,2]=>0000000=>[8]=>[8]
[3,6,1,8,7,5,4,2]=>0000000=>[8]=>[8]
[3,8,1,5,7,6,4,2]=>0000000=>[8]=>[8]
[3,5,2,8,7,6,4,1]=>0000000=>[8]=>[8]
[3,4,8,2,7,6,5,1]=>0000000=>[8]=>[8]
[3,4,8,7,1,6,5,2]=>0000000=>[8]=>[8]
[8,1,3,5,7,6,4,2]=>0000000=>[8]=>[8]
[4,1,8,5,7,6,3,2]=>0000000=>[8]=>[8]
[8,2,7,1,4,5,6,3]=>0000000=>[8]=>[8]
[8,1,7,3,4,6,2,5]=>0000000=>[8]=>[8]
[8,3,1,7,2,6,5,4]=>0000000=>[8]=>[8]
[3,8,2,4,7,6,5,1]=>0000000=>[8]=>[8]
[2,8,3,7,4,6,5,1]=>0000000=>[8]=>[8]
[8,2,3,7,1,6,5,4]=>0000000=>[8]=>[8]
[8,2,7,1,3,6,5,4]=>0000000=>[8]=>[8]
[8,1,7,2,6,4,3,5]=>0000000=>[8]=>[8]
[8,1,7,5,2,4,3,6]=>0000000=>[8]=>[8]
[8,2,3,7,4,6,1,5]=>0000000=>[8]=>[8]
[2,4,8,5,7,6,3,1]=>0000000=>[8]=>[8]
[8,2,4,3,7,6,1,5]=>0000000=>[8]=>[8]
[8,2,7,3,5,1,4,6]=>0000000=>[8]=>[8]
[8,2,7,4,3,1,5,6]=>0000000=>[8]=>[8]
[8,2,1,5,7,6,4,3]=>0000000=>[8]=>[8]
[6,1,8,2,7,5,4,3]=>0000000=>[8]=>[8]
[8,1,5,2,7,6,4,3]=>0000000=>[8]=>[8]
[8,1,7,2,4,6,5,3]=>0000000=>[8]=>[8]
[8,2,4,1,7,6,5,3]=>0000000=>[8]=>[8]
[4,2,8,3,7,6,5,1]=>0000000=>[8]=>[8]
[4,8,2,1,7,6,5,3]=>0000000=>[8]=>[8]
[5,1,8,7,2,6,4,3]=>0000000=>[8]=>[8]
[5,8,1,3,7,6,2,4]=>0000000=>[8]=>[8]
[8,2,5,4,1,7,6,3]=>0000000=>[8]=>[8]
[5,1,4,8,7,6,3,2]=>0000000=>[8]=>[8]
[8,1,4,3,7,6,5,2]=>0000000=>[8]=>[8]
[4,8,1,3,7,6,5,2]=>0000000=>[8]=>[8]
[4,3,8,1,7,6,5,2]=>0000000=>[8]=>[8]
[6,2,8,1,5,7,3,4]=>0000000=>[8]=>[8]
[7,3,2,8,5,6,1,4]=>0000000=>[8]=>[8]
[4,7,6,5,1,3,8,2]=>0000000=>[8]=>[8]
[1,7,6,3,2,8,4,5]=>1000000=>[1,7]=>[7,1]
[5,4,2,1,7,3,6,8]=>0000001=>[7,1]=>[7,1]
[3,7,6,2,8,4,5,1]=>0000000=>[8]=>[8]
[4,3,6,8,5,1,2,7]=>0000000=>[8]=>[8]
[2,7,1,5,8,4,3,6]=>0000000=>[8]=>[8]
[7,1,2,6,3,5,4,8]=>0000001=>[7,1]=>[7,1]
[6,7,8,4,2,5,3,1]=>0000000=>[8]=>[8]
[4,7,3,1,2,6,8,5]=>0000000=>[8]=>[8]
[3,8,5,6,4,2,7,1]=>0000000=>[8]=>[8]
[3,2,6,4,7,8,5,1]=>0000000=>[8]=>[8]
[5,2,1,4,7,8,3,6]=>0000000=>[8]=>[8]
[5,6,2,7,3,4,8,1]=>0000000=>[8]=>[8]
[1,5,8,6,4,2,3,7]=>1000000=>[1,7]=>[7,1]
[1,6,2,3,5,8,7,4]=>1000000=>[1,7]=>[7,1]
[4,3,8,2,5,7,1,6]=>0000000=>[8]=>[8]
[6,7,2,3,1,5,8,4]=>0000000=>[8]=>[8]
[4,7,5,8,6,3,1,2]=>0000000=>[8]=>[8]
[7,3,2,5,8,1,6,4]=>0000000=>[8]=>[8]
[2,4,8,3,7,1,5,6]=>0000000=>[8]=>[8]
[5,2,8,4,1,6,3,7]=>0000000=>[8]=>[8]
[7,6,5,2,1,8,4,3]=>0000000=>[8]=>[8]
[2,7,5,1,8,3,6,4]=>0000000=>[8]=>[8]
[5,7,1,3,2,4,8,6]=>0000000=>[8]=>[8]
[4,2,7,6,3,5,8,1]=>0000000=>[8]=>[8]
[8,1,7,4,2,3,5,6]=>0000000=>[8]=>[8]
[8,6,5,1,7,4,3,2]=>0000000=>[8]=>[8]
[7,6,4,1,3,5,8,2]=>0000000=>[8]=>[8]
[8,2,3,7,1,4,5,6]=>0000000=>[8]=>[8]
[5,6,2,7,4,3,1,8]=>0000001=>[7,1]=>[7,1]
[4,8,6,5,1,2,7,3]=>0000000=>[8]=>[8]
[4,8,6,5,1,2,3,7]=>0000000=>[8]=>[8]
[5,8,2,6,1,4,7,3]=>0000000=>[8]=>[8]
[3,8,7,5,6,1,4,2]=>0000000=>[8]=>[8]
[7,4,6,5,1,3,8,2]=>0000000=>[8]=>[8]
[4,6,3,8,7,5,1,2]=>0000000=>[8]=>[8]
[2,8,4,1,5,7,6,3]=>0000000=>[8]=>[8]
[1,8,4,2,5,7,6,3]=>1000000=>[1,7]=>[7,1]
[2,8,5,4,1,7,6,3]=>0000000=>[8]=>[8]
[2,5,8,3,7,1,6,4]=>0000000=>[8]=>[8]
[1,8,5,2,4,7,6,3]=>1000000=>[1,7]=>[7,1]
[1,4,6,2,8,7,5,3]=>1000000=>[1,7]=>[7,1]
[7,8,2,4,1,6,5,3]=>0000000=>[8]=>[8]
[2,4,6,1,8,7,5,3]=>0000000=>[8]=>[8]
[2,8,4,5,1,7,6,3]=>0000000=>[8]=>[8]
[3,5,8,1,7,6,2,4]=>0000000=>[8]=>[8]
[3,5,8,2,7,6,1,4]=>0000000=>[8]=>[8]
[2,1,6,8,7,5,3,4]=>0100000=>[2,6]=>[6,2]
[1,8,2,4,5,7,6,3]=>1000000=>[1,7]=>[7,1]
[1,3,8,2,5,7,6,4]=>1000000=>[1,7]=>[7,1]
[2,3,8,1,5,7,6,4]=>0000000=>[8]=>[8]
[2,6,1,8,7,5,3,4]=>0000000=>[8]=>[8]
[1,6,2,8,7,5,3,4]=>1000000=>[1,7]=>[7,1]
[1,6,3,8,7,5,2,4]=>1000000=>[1,7]=>[7,1]
[2,6,3,8,7,5,1,4]=>0000000=>[8]=>[8]
[3,2,8,1,5,7,6,4]=>0000000=>[8]=>[8]
[3,1,8,2,5,7,6,4]=>0000000=>[8]=>[8]
[2,1,8,3,5,7,6,4]=>0100000=>[2,6]=>[6,2]
[7,8,2,1,4,6,5,3]=>0000000=>[8]=>[8]
[2,3,6,8,7,5,1,4]=>0000000=>[8]=>[8]
[3,1,6,8,7,2,5,4]=>0000000=>[8]=>[8]
[3,8,4,5,1,6,2,7]=>0000000=>[8]=>[8]
[6,1,4,5,7,2,3,8]=>0000001=>[7,1]=>[7,1]
[8,1,4,7,6,3,2,5]=>0000000=>[8]=>[8]
[8,3,1,6,4,7,2,5]=>0000000=>[8]=>[8]
[5,3,8,6,2,7,1,4]=>0000000=>[8]=>[8]
[8,3,6,1,5,7,2,4]=>0000000=>[8]=>[8]
[6,8,1,4,5,2,3,7]=>0000000=>[8]=>[8]
[1,5,8,4,6,2,3,7]=>1000000=>[1,7]=>[7,1]
[5,6,8,1,4,2,3,7]=>0000000=>[8]=>[8]
[5,7,4,8,1,2,3,6]=>0000000=>[8]=>[8]
[4,7,8,1,2,6,3,5]=>0000000=>[8]=>[8]
[8,7,1,5,6,2,3,4]=>0000000=>[8]=>[8]
[1,6,5,8,7,2,3,4]=>1000000=>[1,7]=>[7,1]
[3,7,1,6,2,4,8,5]=>0000000=>[8]=>[8]
[5,1,2,7,6,8,3,4]=>0000000=>[8]=>[8]
[1,7,6,5,8,2,3,4]=>1000000=>[1,7]=>[7,1]
[1,6,8,5,7,2,3,4]=>1000000=>[1,7]=>[7,1]
[7,5,1,2,6,8,3,4]=>0000000=>[8]=>[8]
[6,1,5,2,7,8,3,4]=>0000000=>[8]=>[8]
[5,1,2,6,8,7,3,4]=>0000000=>[8]=>[8]
[1,8,6,2,5,7,3,4]=>1000000=>[1,7]=>[7,1]
[5,7,8,1,2,6,3,4]=>0000000=>[8]=>[8]
[8,1,5,7,6,2,3,4]=>0000000=>[8]=>[8]
[3,7,1,2,8,4,6,5]=>0000000=>[8]=>[8]
[1,5,8,7,6,2,3,4]=>1000000=>[1,7]=>[7,1]
[7,8,6,1,5,2,3,4]=>0000000=>[8]=>[8]
[2,6,4,7,5,3,8,1]=>0000000=>[8]=>[8]
[2,6,8,7,5,3,1,4]=>0000000=>[8]=>[8]
[6,4,1,7,5,2,8,3]=>0000000=>[8]=>[8]
[1,3,8,5,2,7,4,6]=>1000000=>[1,7]=>[7,1]
[1,3,8,6,7,2,4,5]=>1000000=>[1,7]=>[7,1]
[2,8,3,7,6,1,4,5]=>0000000=>[8]=>[8]
[1,3,8,7,6,2,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,6,8,7,2,3,5]=>1000000=>[1,7]=>[7,1]
[7,6,4,8,5,1,3,2]=>0000000=>[8]=>[8]
[4,6,5,7,2,8,1,3]=>0000000=>[8]=>[8]
[5,3,6,7,8,1,4,2]=>0000000=>[8]=>[8]
[6,3,2,8,5,4,1,7]=>0000000=>[8]=>[8]
[4,3,5,1,2,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[7,3,2,1,6,4,5,8]=>0000001=>[7,1]=>[7,1]
[2,8,6,1,7,4,3,5]=>0000000=>[8]=>[8]
[2,5,4,6,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,5,6,4,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[8,5,2,6,1,3,7,4]=>0000000=>[8]=>[8]
[7,1,2,6,5,4,3,8]=>0000001=>[7,1]=>[7,1]
[8,2,1,5,6,3,7,4]=>0000000=>[8]=>[8]
[2,8,5,1,6,4,7,3]=>0000000=>[8]=>[8]
[5,6,3,8,7,4,1,2]=>0000000=>[8]=>[8]
[5,2,6,8,7,4,1,3]=>0000000=>[8]=>[8]
[5,2,3,1,4,8,6,7]=>0000100=>[5,3]=>[5,3]
[5,4,1,3,2,8,6,7]=>0000100=>[5,3]=>[5,3]
[5,1,3,4,2,8,6,7]=>0000100=>[5,3]=>[5,3]
[4,2,7,3,8,5,1,6]=>0000000=>[8]=>[8]
[1,3,2,6,4,8,7,5]=>1010000=>[1,2,5]=>[5,2,1]
[1,6,2,5,3,8,7,4]=>1000000=>[1,7]=>[7,1]
[1,8,2,6,3,7,5,4]=>1000000=>[1,7]=>[7,1]
[1,8,3,6,4,7,5,2]=>1000000=>[1,7]=>[7,1]
[1,7,2,6,3,8,5,4]=>1000000=>[1,7]=>[7,1]
[1,5,2,7,4,8,6,3]=>1000000=>[1,7]=>[7,1]
[1,4,2,8,5,7,6,3]=>1000000=>[1,7]=>[7,1]
[1,5,3,8,4,7,6,2]=>1000000=>[1,7]=>[7,1]
[6,8,7,3,1,5,4,2]=>0000000=>[8]=>[8]
[2,5,8,7,4,6,3,1]=>0000000=>[8]=>[8]
[6,8,4,1,5,2,7,3]=>0000000=>[8]=>[8]
[4,8,7,5,1,6,2,3]=>0000000=>[8]=>[8]
[4,5,2,1,8,6,7,3]=>0000000=>[8]=>[8]
[2,6,7,4,1,3,8,5]=>0000000=>[8]=>[8]
[2,4,6,3,5,7,8,1]=>0000000=>[8]=>[8]
[2,3,6,1,5,7,8,4]=>0000000=>[8]=>[8]
[1,4,5,8,6,3,2,7]=>1000000=>[1,7]=>[7,1]
[5,2,6,3,1,7,8,4]=>0000000=>[8]=>[8]
[5,7,6,1,2,3,8,4]=>0000000=>[8]=>[8]
[4,3,6,2,1,8,7,5]=>0000000=>[8]=>[8]
[5,3,6,4,8,2,1,7]=>0000000=>[8]=>[8]
[3,7,4,5,1,6,2,8]=>0000001=>[7,1]=>[7,1]
[3,6,4,5,8,2,1,7]=>0000000=>[8]=>[8]
[6,1,4,5,2,8,7,3]=>0000000=>[8]=>[8]
[7,2,4,5,1,6,3,8]=>0000001=>[7,1]=>[7,1]
[7,5,4,1,6,3,2,8]=>0000001=>[7,1]=>[7,1]
[1,5,4,8,6,3,2,7]=>1000000=>[1,7]=>[7,1]
[7,5,4,8,6,3,1,2]=>0000000=>[8]=>[8]
[1,8,7,5,3,6,4,2]=>1000000=>[1,7]=>[7,1]
[8,3,7,4,1,6,2,5]=>0000000=>[8]=>[8]
[8,5,4,1,6,3,2,7]=>0000000=>[8]=>[8]
[1,7,4,2,6,5,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,2,1,5,6,7,3,4]=>0000000=>[8]=>[8]
[6,3,1,8,4,7,2,5]=>0000000=>[8]=>[8]
[7,1,4,8,6,3,2,5]=>0000000=>[8]=>[8]
[4,1,8,5,6,7,2,3]=>0000000=>[8]=>[8]
[5,7,4,8,6,2,1,3]=>0000000=>[8]=>[8]
[5,3,6,8,2,7,1,4]=>0000000=>[8]=>[8]
[6,3,7,4,8,2,1,5]=>0000000=>[8]=>[8]
[5,3,6,1,4,7,2,8]=>0000001=>[7,1]=>[7,1]
[4,3,6,8,2,7,1,5]=>0000000=>[8]=>[8]
[5,3,7,4,8,2,1,6]=>0000000=>[8]=>[8]
[5,3,8,4,1,6,2,7]=>0000000=>[8]=>[8]
[5,3,8,1,4,7,2,6]=>0000000=>[8]=>[8]
[5,8,4,1,6,3,2,7]=>0000000=>[8]=>[8]
[7,3,8,4,1,6,2,5]=>0000000=>[8]=>[8]
[1,5,8,3,6,7,4,2]=>1000000=>[1,7]=>[7,1]
[1,8,2,5,6,7,3,4]=>1000000=>[1,7]=>[7,1]
[7,8,4,1,6,5,2,3]=>0000000=>[8]=>[8]
[6,3,8,1,5,7,2,4]=>0000000=>[8]=>[8]
[8,3,1,2,5,7,4,6]=>0000000=>[8]=>[8]
[8,1,4,2,6,5,3,7]=>0000000=>[8]=>[8]
[3,8,5,6,2,7,1,4]=>0000000=>[8]=>[8]
[2,4,5,8,7,3,1,6]=>0000000=>[8]=>[8]
[4,5,1,8,6,7,3,2]=>0000000=>[8]=>[8]
[3,4,5,8,7,1,2,6]=>0000000=>[8]=>[8]
[6,5,4,7,1,3,8,2]=>0000000=>[8]=>[8]
[6,1,4,7,2,3,8,5]=>0000000=>[8]=>[8]
[1,6,2,5,4,8,3,7]=>1000000=>[1,7]=>[7,1]
[4,1,2,7,5,8,3,6]=>0000000=>[8]=>[8]
[6,1,3,5,8,2,4,7]=>0000000=>[8]=>[8]
[5,6,4,3,1,8,2,7]=>0000000=>[8]=>[8]
[6,2,3,5,8,1,4,7]=>0000000=>[8]=>[8]
[6,7,2,3,8,4,5,1]=>0000000=>[8]=>[8]
[6,7,2,1,3,8,4,5]=>0000000=>[8]=>[8]
[5,7,4,1,8,3,2,6]=>0000000=>[8]=>[8]
[4,1,7,5,8,3,6,2]=>0000000=>[8]=>[8]
[6,7,1,3,8,4,5,2]=>0000000=>[8]=>[8]
[1,6,7,4,3,8,5,2]=>1000000=>[1,7]=>[7,1]
[6,1,7,4,2,8,5,3]=>0000000=>[8]=>[8]
[2,1,6,7,4,3,8,5]=>0100000=>[2,6]=>[6,2]
[6,7,3,2,1,8,4,5]=>0000000=>[8]=>[8]
[2,5,7,3,1,4,8,6]=>0000000=>[8]=>[8]
[6,7,3,2,8,4,5,1]=>0000000=>[8]=>[8]
[2,6,7,4,3,8,5,1]=>0000000=>[8]=>[8]
[1,2,6,7,4,3,8,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,7,5,8,2,4,3,6]=>1000000=>[1,7]=>[7,1]
[2,7,1,8,4,6,3,5]=>0000000=>[8]=>[8]
[2,7,5,8,1,6,3,4]=>0000000=>[8]=>[8]
[1,6,7,3,8,5,4,2]=>1000000=>[1,7]=>[7,1]
[6,7,1,8,4,5,3,2]=>0000000=>[8]=>[8]
[8,6,1,5,4,3,2,7]=>0000000=>[8]=>[8]
[1,5,6,7,3,8,2,4]=>1000000=>[1,7]=>[7,1]
[1,6,5,4,8,3,2,7]=>1000000=>[1,7]=>[7,1]
[1,3,7,6,4,8,5,2]=>1000000=>[1,7]=>[7,1]
[3,1,8,7,6,4,2,5]=>0000000=>[8]=>[8]
[3,1,8,7,5,4,2,6]=>0000000=>[8]=>[8]
[3,1,7,6,5,4,2,8]=>0000001=>[7,1]=>[7,1]
[4,7,1,6,5,3,2,8]=>0000001=>[7,1]=>[7,1]
[4,8,1,6,5,3,2,7]=>0000000=>[8]=>[8]
[4,8,1,7,5,3,2,6]=>0000000=>[8]=>[8]
[8,4,1,7,6,3,2,5]=>0000000=>[8]=>[8]
[5,4,1,8,6,3,2,7]=>0000000=>[8]=>[8]
[5,4,1,7,6,3,2,8]=>0000001=>[7,1]=>[7,1]
[6,4,1,7,5,3,2,8]=>0000001=>[7,1]=>[7,1]
[6,4,1,8,5,3,2,7]=>0000000=>[8]=>[8]
[8,4,1,7,5,3,2,6]=>0000000=>[8]=>[8]
[7,4,1,6,5,3,2,8]=>0000001=>[7,1]=>[7,1]
[7,5,6,1,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[8,5,6,1,4,3,2,7]=>0000000=>[8]=>[8]
[5,7,6,1,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[5,8,6,1,4,3,2,7]=>0000000=>[8]=>[8]
[6,7,5,1,4,3,2,8]=>0000001=>[7,1]=>[7,1]
[8,7,5,1,4,3,2,6]=>0000000=>[8]=>[8]
[8,6,5,1,4,3,2,7]=>0000000=>[8]=>[8]
[1,8,6,3,4,2,5,7]=>1000000=>[1,7]=>[7,1]
[3,1,6,4,5,8,7,2]=>0000000=>[8]=>[8]
[8,2,7,6,1,4,3,5]=>0000000=>[8]=>[8]
[5,2,7,8,1,4,3,6]=>0000000=>[8]=>[8]
[5,2,3,7,1,6,8,4]=>0000000=>[8]=>[8]
[1,7,5,2,6,4,8,3]=>1000000=>[1,7]=>[7,1]
[7,1,3,6,8,2,4,5]=>0000000=>[8]=>[8]
[1,2,5,7,8,4,6,3]=>1100000=>[1,1,6]=>[6,1,1]
[3,1,2,7,5,4,8,6]=>0010000=>[3,5]=>[5,3]
[6,7,4,1,3,2,8,5]=>0000000=>[8]=>[8]
[1,7,2,8,4,3,5,6]=>1000000=>[1,7]=>[7,1]
[4,1,6,5,7,8,2,3]=>0000000=>[8]=>[8]
[1,6,3,5,7,8,2,4]=>1000000=>[1,7]=>[7,1]
[8,6,1,7,5,2,4,3]=>0000000=>[8]=>[8]
[7,6,4,1,8,3,2,5]=>0000000=>[8]=>[8]
[8,4,1,6,5,2,7,3]=>0000000=>[8]=>[8]
[1,5,3,4,7,8,2,6]=>1000000=>[1,7]=>[7,1]
[4,2,1,5,7,8,3,6]=>0000000=>[8]=>[8]
[5,1,4,6,7,8,2,3]=>0000000=>[8]=>[8]
[4,1,5,3,7,8,2,6]=>0000000=>[8]=>[8]
[8,1,4,6,5,2,7,3]=>0000000=>[8]=>[8]
[7,1,5,4,6,3,2,8]=>0000001=>[7,1]=>[7,1]
[8,2,1,6,7,5,4,3]=>0000000=>[8]=>[8]
[1,2,4,7,6,3,8,5]=>1100000=>[1,1,6]=>[6,1,1]
[6,7,4,1,8,5,2,3]=>0000000=>[8]=>[8]
[8,6,4,1,5,7,3,2]=>0000000=>[8]=>[8]
[5,2,4,3,7,1,6,8]=>0000001=>[7,1]=>[7,1]
[6,1,5,4,8,3,2,7]=>0000000=>[8]=>[8]
[1,2,8,7,4,3,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[3,2,1,7,5,8,4,6]=>0010000=>[3,5]=>[5,3]
[8,1,7,6,4,2,5,3]=>0000000=>[8]=>[8]
[1,3,6,4,7,8,2,5]=>1000000=>[1,7]=>[7,1]
[5,1,3,4,7,8,2,6]=>0000000=>[8]=>[8]
[4,5,1,3,7,8,2,6]=>0000000=>[8]=>[8]
[5,2,3,1,7,8,4,6]=>0000000=>[8]=>[8]
[1,6,4,3,7,8,2,5]=>1000000=>[1,7]=>[7,1]
[7,6,4,3,1,5,2,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,4,1,8,5,7]=>0000000=>[8]=>[8]
[7,5,4,6,1,3,2,8]=>0000001=>[7,1]=>[7,1]
[8,4,6,5,1,2,7,3]=>0000000=>[8]=>[8]
[1,5,6,3,7,8,2,4]=>1000000=>[1,7]=>[7,1]
[4,2,5,1,7,8,3,6]=>0000000=>[8]=>[8]
[4,7,8,1,6,5,3,2]=>0000000=>[8]=>[8]
[1,8,4,2,7,6,3,5]=>1000000=>[1,7]=>[7,1]
[3,7,2,8,1,5,4,6]=>0000000=>[8]=>[8]
[7,3,8,1,6,5,4,2]=>0000000=>[8]=>[8]
[2,4,1,8,7,3,6,5]=>0000000=>[8]=>[8]
[7,3,8,6,1,5,4,2]=>0000000=>[8]=>[8]
[3,5,1,7,8,2,6,4]=>0000000=>[8]=>[8]
[5,4,7,8,2,1,6,3]=>0000000=>[8]=>[8]
[6,4,7,1,5,3,2,8]=>0000001=>[7,1]=>[7,1]
[3,4,6,2,1,8,5,7]=>0000000=>[8]=>[8]
[5,6,4,8,3,2,1,7]=>0000000=>[8]=>[8]
[5,7,4,8,2,1,6,3]=>0000000=>[8]=>[8]
[4,7,5,8,2,1,6,3]=>0000000=>[8]=>[8]
[4,7,3,2,8,1,5,6]=>0000000=>[8]=>[8]
[7,1,2,6,3,8,5,4]=>0000000=>[8]=>[8]
[8,1,2,6,3,7,5,4]=>0000000=>[8]=>[8]
[8,1,2,7,6,3,5,4]=>0000000=>[8]=>[8]
[4,8,7,3,1,6,2,5]=>0000000=>[8]=>[8]
[4,7,8,3,1,6,2,5]=>0000000=>[8]=>[8]
[7,4,3,1,6,2,8,5]=>0000000=>[8]=>[8]
[3,7,6,2,4,8,1,5]=>0000000=>[8]=>[8]
[5,1,2,7,3,8,6,4]=>0000000=>[8]=>[8]
[6,1,2,7,3,5,8,4]=>0000000=>[8]=>[8]
[6,2,5,4,1,8,7,3]=>0000000=>[8]=>[8]
[4,6,3,2,1,8,7,5]=>0000000=>[8]=>[8]
[8,4,3,2,7,6,1,5]=>0000000=>[8]=>[8]
[1,5,8,4,7,6,3,2]=>1000000=>[1,7]=>[7,1]
[3,2,7,4,8,6,1,5]=>0000000=>[8]=>[8]
[7,4,3,2,8,6,1,5]=>0000000=>[8]=>[8]
[6,4,3,8,5,2,1,7]=>0000000=>[8]=>[8]
[8,2,5,4,7,6,1,3]=>0000000=>[8]=>[8]
[7,2,5,4,8,6,1,3]=>0000000=>[8]=>[8]
[6,2,8,7,5,4,1,3]=>0000000=>[8]=>[8]
[4,5,3,2,8,6,1,7]=>0000000=>[8]=>[8]
[3,2,5,4,8,6,1,7]=>0000000=>[8]=>[8]
[3,2,8,6,5,4,1,7]=>0000000=>[8]=>[8]
[8,4,3,6,5,2,1,7]=>0000000=>[8]=>[8]
[8,4,3,7,5,2,1,6]=>0000000=>[8]=>[8]
[3,2,7,8,5,4,1,6]=>0000000=>[8]=>[8]
[6,8,7,4,3,2,1,5]=>0000000=>[8]=>[8]
[6,3,2,1,8,7,4,5]=>0000000=>[8]=>[8]
[6,2,3,1,8,7,4,5]=>0000000=>[8]=>[8]
[3,4,8,1,7,5,6,2]=>0000000=>[8]=>[8]
[7,2,1,5,8,4,6,3]=>0000000=>[8]=>[8]
[3,7,4,1,5,8,6,2]=>0000000=>[8]=>[8]
[6,7,1,4,3,8,5,2]=>0000000=>[8]=>[8]
[8,5,3,6,1,7,4,2]=>0000000=>[8]=>[8]
[8,5,6,1,2,7,4,3]=>0000000=>[8]=>[8]
[3,6,1,5,7,8,2,4]=>0000000=>[8]=>[8]
[2,1,5,8,6,3,7,4]=>0100000=>[2,6]=>[6,2]
[3,7,8,5,4,1,6,2]=>0000000=>[8]=>[8]
[4,6,5,1,7,3,8,2]=>0000000=>[8]=>[8]
[5,7,3,1,2,4,8,6]=>0000000=>[8]=>[8]
[6,3,2,5,1,7,4,8]=>0000001=>[7,1]=>[7,1]
[6,3,1,7,2,5,8,4]=>0000000=>[8]=>[8]
[6,8,4,3,1,7,2,5]=>0000000=>[8]=>[8]
[4,8,1,3,7,5,6,2]=>0000000=>[8]=>[8]
[2,1,6,8,5,3,4,7]=>0100000=>[2,6]=>[6,2]
[4,5,1,3,8,6,7,2]=>0000000=>[8]=>[8]
[6,3,2,4,7,1,8,5]=>0000000=>[8]=>[8]
[5,7,6,3,8,1,2,4]=>0000000=>[8]=>[8]
[1,2,5,3,6,8,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[7,1,5,6,2,3,8,4]=>0000000=>[8]=>[8]
[8,2,1,4,6,7,3,5]=>0000000=>[8]=>[8]
[7,2,6,1,3,4,8,5]=>0000000=>[8]=>[8]
[4,1,3,7,2,5,8,6]=>0000000=>[8]=>[8]
[6,2,7,5,1,3,8,4]=>0000000=>[8]=>[8]
[1,7,5,6,2,3,8,4]=>1000000=>[1,7]=>[7,1]
[3,7,6,1,2,4,8,5]=>0000000=>[8]=>[8]
[8,6,1,3,5,7,2,4]=>0000000=>[8]=>[8]
[1,7,4,3,8,2,5,6]=>1000000=>[1,7]=>[7,1]
[6,1,5,3,4,8,2,7]=>0000000=>[8]=>[8]
[3,6,7,5,2,8,1,4]=>0000000=>[8]=>[8]
[7,8,4,1,5,6,2,3]=>0000000=>[8]=>[8]
[5,8,1,3,6,7,2,4]=>0000000=>[8]=>[8]
[2,8,4,3,7,1,5,6]=>0000000=>[8]=>[8]
[3,8,4,6,7,1,2,5]=>0000000=>[8]=>[8]
[6,3,8,4,7,1,2,5]=>0000000=>[8]=>[8]
[1,2,5,4,8,3,6,7]=>1100000=>[1,1,6]=>[6,1,1]
[7,1,3,8,2,4,5,6]=>0000000=>[8]=>[8]
[8,1,3,7,2,4,5,6]=>0000000=>[8]=>[8]
[3,5,4,7,8,1,2,6]=>0000000=>[8]=>[8]
[8,3,1,4,7,2,5,6]=>0000000=>[8]=>[8]
[1,6,4,7,8,2,3,5]=>1000000=>[1,7]=>[7,1]
[1,3,7,8,5,6,2,4]=>1000000=>[1,7]=>[7,1]
[7,5,4,8,6,1,2,3]=>0000000=>[8]=>[8]
[8,2,6,7,5,1,3,4]=>0000000=>[8]=>[8]
[8,1,7,4,6,2,3,5]=>0000000=>[8]=>[8]
[2,5,8,4,7,1,3,6]=>0000000=>[8]=>[8]
[4,5,8,7,1,2,3,6]=>0000000=>[8]=>[8]
[4,1,8,5,7,2,3,6]=>0000000=>[8]=>[8]
[1,8,7,4,6,2,3,5]=>1000000=>[1,7]=>[7,1]
[2,6,5,4,1,8,3,7]=>0000000=>[8]=>[8]
[8,5,4,1,3,6,7,2]=>0000000=>[8]=>[8]
[8,4,7,6,5,3,1,2]=>0000000=>[8]=>[8]
[1,8,4,2,3,7,6,5]=>1000000=>[1,7]=>[7,1]
[2,3,1,8,7,6,4,5]=>0010000=>[3,5]=>[5,3]
[8,2,7,5,6,4,1,3]=>0000000=>[8]=>[8]
[1,8,4,7,6,5,2,3]=>1000000=>[1,7]=>[7,1]
[2,1,7,5,8,3,6,4]=>0100000=>[2,6]=>[6,2]
[2,6,3,5,8,7,4,1]=>0000000=>[8]=>[8]
[5,1,6,3,8,2,4,7]=>0000000=>[8]=>[8]
[4,3,5,8,2,1,6,7]=>0000000=>[8]=>[8]
[7,8,6,3,1,4,2,5]=>0000000=>[8]=>[8]
[6,5,3,7,2,4,8,1]=>0000000=>[8]=>[8]
[5,6,2,8,4,3,7,1]=>0000000=>[8]=>[8]
[4,6,2,7,8,3,5,1]=>0000000=>[8]=>[8]
[3,1,2,4,8,5,7,6]=>0011000=>[3,1,4]=>[4,3,1]
[4,6,3,5,2,8,7,1]=>0000000=>[8]=>[8]
[5,3,2,6,8,4,7,1]=>0000000=>[8]=>[8]
[5,6,3,4,8,2,7,1]=>0000000=>[8]=>[8]
[5,2,6,4,1,7,8,3]=>0000000=>[8]=>[8]
[5,8,4,6,3,2,7,1]=>0000000=>[8]=>[8]
[5,4,3,8,6,2,7,1]=>0000000=>[8]=>[8]
[5,7,8,2,4,3,6,1]=>0000000=>[8]=>[8]
[5,6,2,4,8,3,7,1]=>0000000=>[8]=>[8]
[5,4,2,8,6,3,7,1]=>0000000=>[8]=>[8]
[5,7,4,2,6,3,8,1]=>0000000=>[8]=>[8]
[6,4,7,8,2,3,5,1]=>0000000=>[8]=>[8]
[3,7,5,2,4,8,1,6]=>0000000=>[8]=>[8]
[4,7,5,2,3,8,6,1]=>0000000=>[8]=>[8]
[6,4,7,3,2,5,8,1]=>0000000=>[8]=>[8]
[6,3,7,8,2,4,5,1]=>0000000=>[8]=>[8]
[5,7,3,2,8,4,6,1]=>0000000=>[8]=>[8]
[5,3,7,2,8,4,6,1]=>0000000=>[8]=>[8]
[4,3,7,2,5,8,6,1]=>0000000=>[8]=>[8]
[4,7,3,2,5,8,6,1]=>0000000=>[8]=>[8]
[4,7,3,2,6,8,5,1]=>0000000=>[8]=>[8]
[7,5,3,2,6,4,8,1]=>0000000=>[8]=>[8]
[5,7,3,2,6,4,8,1]=>0000000=>[8]=>[8]
[5,3,2,8,6,4,7,1]=>0000000=>[8]=>[8]
[8,5,2,6,7,3,4,1]=>0000000=>[8]=>[8]
[8,4,2,6,3,7,5,1]=>0000000=>[8]=>[8]
[7,4,6,2,3,8,5,1]=>0000000=>[8]=>[8]
[7,5,6,2,8,3,4,1]=>0000000=>[8]=>[8]
[6,3,7,5,2,4,8,1]=>0000000=>[8]=>[8]
[5,7,6,2,8,3,4,1]=>0000000=>[8]=>[8]
[4,7,6,2,3,8,5,1]=>0000000=>[8]=>[8]
[7,6,3,2,5,8,1,4]=>0000000=>[8]=>[8]
[7,6,4,2,5,8,3,1]=>0000000=>[8]=>[8]
[4,8,3,7,1,6,5,2]=>0000000=>[8]=>[8]
[8,7,2,6,5,1,4,3]=>0000000=>[8]=>[8]
[5,8,3,2,1,7,6,4]=>0000000=>[8]=>[8]
[5,4,3,8,1,7,6,2]=>0000000=>[8]=>[8]
[6,5,3,8,7,1,4,2]=>0000000=>[8]=>[8]
[4,3,8,2,7,6,5,1]=>0000000=>[8]=>[8]
[4,8,2,7,6,5,3,1]=>0000000=>[8]=>[8]
[7,8,2,6,5,4,1,3]=>0000000=>[8]=>[8]
[3,8,7,6,2,5,1,4]=>0000000=>[8]=>[8]
[4,8,3,7,2,1,6,5]=>0000000=>[8]=>[8]
[8,6,3,1,7,5,4,2]=>0000000=>[8]=>[8]
[8,6,3,7,1,5,4,2]=>0000000=>[8]=>[8]
[4,8,3,7,6,2,5,1]=>0000000=>[8]=>[8]
[8,4,2,1,7,6,5,3]=>0000000=>[8]=>[8]
[1,6,4,2,5,3,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,6,7,2,5,3,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,6,2,7,3,4,5]=>1000000=>[1,7]=>[7,1]
[1,5,2,6,4,3,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,5,2,4,6,3,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,8,6,2,3,7,4,5]=>1000000=>[1,7]=>[7,1]
[1,5,2,8,6,3,4,7]=>1000000=>[1,7]=>[7,1]
[1,7,3,2,6,8,4,5]=>1000000=>[1,7]=>[7,1]
[1,3,6,8,2,7,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,3,8,2,5,6,7]=>1000000=>[1,7]=>[7,1]
[1,7,2,3,8,5,4,6]=>1000000=>[1,7]=>[7,1]
[1,6,2,8,5,4,3,7]=>1000000=>[1,7]=>[7,1]
[1,7,2,3,8,6,4,5]=>1000000=>[1,7]=>[7,1]
[1,5,3,8,2,7,4,6]=>1000000=>[1,7]=>[7,1]
[1,7,2,5,3,4,8,6]=>1000000=>[1,7]=>[7,1]
[1,4,8,2,5,6,3,7]=>1000000=>[1,7]=>[7,1]
[1,2,7,3,6,8,4,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,7,2,3,6,8,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,8,3,2,5,6,7]=>1000000=>[1,7]=>[7,1]
[1,7,2,5,8,3,4,6]=>1000000=>[1,7]=>[7,1]
[1,5,6,3,4,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,5,3,6,4,2,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[2,5,7,4,1,3,8,6]=>0000000=>[8]=>[8]
[3,5,6,1,8,7,2,4]=>0000000=>[8]=>[8]
[2,4,6,8,7,3,1,5]=>0000000=>[8]=>[8]
[7,2,4,8,6,3,1,5]=>0000000=>[8]=>[8]
[8,5,3,6,2,1,7,4]=>0000000=>[8]=>[8]
[4,5,7,3,1,2,8,6]=>0000000=>[8]=>[8]
[4,5,1,8,3,2,7,6]=>0000000=>[8]=>[8]
[2,5,3,8,4,1,7,6]=>0000000=>[8]=>[8]
[2,6,4,5,8,1,3,7]=>0000000=>[8]=>[8]
[6,4,1,3,5,8,2,7]=>0000000=>[8]=>[8]
[3,1,6,4,8,7,5,2]=>0000000=>[8]=>[8]
[4,2,6,1,3,7,8,5]=>0000000=>[8]=>[8]
[8,5,4,2,7,6,3,1]=>0000000=>[8]=>[8]
[2,8,4,6,7,1,3,5]=>0000000=>[8]=>[8]
[5,8,2,1,4,6,7,3]=>0000000=>[8]=>[8]
[3,6,7,1,8,2,5,4]=>0000000=>[8]=>[8]
[3,1,5,7,2,8,6,4]=>0000000=>[8]=>[8]
[4,1,8,3,2,7,6,5]=>0000000=>[8]=>[8]
[3,8,2,4,7,1,6,5]=>0000000=>[8]=>[8]
[3,2,4,8,7,1,6,5]=>0000000=>[8]=>[8]
[3,2,5,7,1,8,6,4]=>0000000=>[8]=>[8]
[4,2,8,3,1,7,6,5]=>0000000=>[8]=>[8]
[4,8,2,1,3,7,6,5]=>0000000=>[8]=>[8]
[4,2,8,1,3,7,6,5]=>0000000=>[8]=>[8]
[2,3,4,6,8,7,1,5]=>0000000=>[8]=>[8]
[6,7,2,8,3,1,4,5]=>0000000=>[8]=>[8]
[6,3,7,8,4,1,2,5]=>0000000=>[8]=>[8]
[7,6,2,3,1,8,4,5]=>0000000=>[8]=>[8]
[2,3,7,8,5,4,1,6]=>0000000=>[8]=>[8]
[2,8,7,4,5,1,6,3]=>0000000=>[8]=>[8]
[1,3,8,5,2,6,7,4]=>1000000=>[1,7]=>[7,1]
[8,6,2,4,1,5,7,3]=>0000000=>[8]=>[8]
[1,6,4,3,2,7,8,5]=>1000000=>[1,7]=>[7,1]
[8,5,3,2,1,6,7,4]=>0000000=>[8]=>[8]
[8,5,3,2,1,6,4,7]=>0000000=>[8]=>[8]
[8,7,6,1,5,2,3,4]=>0000000=>[8]=>[8]
[8,7,5,1,3,6,2,4]=>0000000=>[8]=>[8]
[8,3,2,7,4,6,5,1]=>0000000=>[8]=>[8]
[7,4,8,2,6,3,1,5]=>0000000=>[8]=>[8]
[8,7,3,1,4,6,5,2]=>0000000=>[8]=>[8]
[8,7,3,1,6,2,5,4]=>0000000=>[8]=>[8]
[8,7,3,2,6,1,5,4]=>0000000=>[8]=>[8]
[1,4,8,6,7,5,3,2]=>1000000=>[1,7]=>[7,1]
[7,1,3,6,8,5,4,2]=>0000000=>[8]=>[8]
[6,7,2,5,8,1,4,3]=>0000000=>[8]=>[8]
[6,5,7,3,8,1,4,2]=>0000000=>[8]=>[8]
[6,3,7,4,8,1,5,2]=>0000000=>[8]=>[8]
[6,2,7,4,8,1,5,3]=>0000000=>[8]=>[8]
[7,2,1,5,3,8,6,4]=>0000000=>[8]=>[8]
[5,8,2,7,6,1,3,4]=>0000000=>[8]=>[8]
[4,2,3,1,5,8,6,7]=>0001100=>[4,1,3]=>[4,3,1]
[1,8,3,6,7,4,2,5]=>1000000=>[1,7]=>[7,1]
[8,1,7,2,5,6,4,3]=>0000000=>[8]=>[8]
[8,1,3,5,2,7,6,4]=>0000000=>[8]=>[8]
[8,1,7,4,3,6,5,2]=>0000000=>[8]=>[8]
[2,7,1,5,4,8,6,3]=>0000000=>[8]=>[8]
[8,6,2,4,3,7,5,1]=>0000000=>[8]=>[8]
[8,1,4,5,6,3,7,2]=>0000000=>[8]=>[8]
[8,1,4,5,6,2,7,3]=>0000000=>[8]=>[8]
[8,1,4,7,6,2,5,3]=>0000000=>[8]=>[8]
[2,5,1,7,8,6,4,3]=>0000000=>[8]=>[8]
[3,5,6,2,8,7,4,1]=>0000000=>[8]=>[8]
[3,5,6,1,8,7,4,2]=>0000000=>[8]=>[8]
[2,4,5,1,7,6,3,8]=>0000001=>[7,1]=>[7,1]
[7,3,1,5,6,4,2,8]=>0000001=>[7,1]=>[7,1]
[8,6,2,4,7,3,1,5]=>0000000=>[8]=>[8]
[8,4,7,3,5,2,1,6]=>0000000=>[8]=>[8]
[8,4,5,3,7,6,2,1]=>0000000=>[8]=>[8]
[3,4,5,6,2,8,1,7]=>0000000=>[8]=>[8]
[3,7,4,2,8,5,1,6]=>0000000=>[8]=>[8]
[7,3,4,1,6,8,2,5]=>0000000=>[8]=>[8]
[2,6,3,1,4,7,5,8]=>0000001=>[7,1]=>[7,1]
[7,2,1,6,3,4,8,5]=>0000000=>[8]=>[8]
[7,3,4,1,6,5,8,2]=>0000000=>[8]=>[8]
[3,7,4,2,5,8,6,1]=>0000000=>[8]=>[8]
[2,3,5,1,4,8,7,6]=>0000100=>[5,3]=>[5,3]
[2,7,1,3,6,8,5,4]=>0000000=>[8]=>[8]
[2,7,1,3,8,4,6,5]=>0000000=>[8]=>[8]
[3,8,7,1,6,2,5,4]=>0000000=>[8]=>[8]
[3,8,7,1,4,5,2,6]=>0000000=>[8]=>[8]
[3,7,4,2,1,8,6,5]=>0000000=>[8]=>[8]
[4,8,5,7,2,6,3,1]=>0000000=>[8]=>[8]
[8,4,5,7,3,2,6,1]=>0000000=>[8]=>[8]
[8,3,7,2,4,1,5,6]=>0000000=>[8]=>[8]
[8,6,7,2,1,4,3,5]=>0000000=>[8]=>[8]
[8,3,7,5,1,2,6,4]=>0000000=>[8]=>[8]
[7,3,4,6,2,1,5,8]=>0000001=>[7,1]=>[7,1]
[3,7,4,6,1,5,2,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,6,1,2,8,5]=>0000000=>[8]=>[8]
[4,5,8,7,6,1,3,2]=>0000000=>[8]=>[8]
[8,7,3,5,6,1,4,2]=>0000000=>[8]=>[8]
[8,5,2,7,6,1,3,4]=>0000000=>[8]=>[8]
[6,4,7,2,1,5,8,3]=>0000000=>[8]=>[8]
[8,5,3,1,6,4,7,2]=>0000000=>[8]=>[8]
[7,4,8,2,6,1,5,3]=>0000000=>[8]=>[8]
[8,5,3,1,6,4,2,7]=>0000000=>[8]=>[8]
[8,7,3,1,4,2,5,6]=>0000000=>[8]=>[8]
[8,7,4,1,2,5,3,6]=>0000000=>[8]=>[8]
[1,6,7,3,2,8,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,6,2,8,5,3,7]=>1000000=>[1,7]=>[7,1]
[1,5,6,2,8,4,3,7]=>1000000=>[1,7]=>[7,1]
[3,4,8,6,5,7,2,1]=>0000000=>[8]=>[8]
[2,3,8,6,7,1,5,4]=>0000000=>[8]=>[8]
[1,2,5,7,4,6,8,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,7,6,8,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,3,5,6,2,7,4]=>1000000=>[1,7]=>[7,1]
[4,2,5,1,6,8,7,3]=>0000000=>[8]=>[8]
[5,4,2,7,8,6,1,3]=>0000000=>[8]=>[8]
[6,7,2,8,1,3,4,5]=>0000000=>[8]=>[8]
[1,7,8,5,2,6,3,4]=>1000000=>[1,7]=>[7,1]
[7,6,2,4,8,1,5,3]=>0000000=>[8]=>[8]
[4,8,3,1,7,6,5,2]=>0000000=>[8]=>[8]
[5,3,8,7,1,6,4,2]=>0000000=>[8]=>[8]
[5,8,7,3,1,6,4,2]=>0000000=>[8]=>[8]
[5,3,8,2,1,7,6,4]=>0000000=>[8]=>[8]
[3,8,7,2,6,5,1,4]=>0000000=>[8]=>[8]
[7,4,1,8,6,5,3,2]=>0000000=>[8]=>[8]
[5,4,2,8,1,7,6,3]=>0000000=>[8]=>[8]
[5,8,4,7,1,6,3,2]=>0000000=>[8]=>[8]
[8,5,6,1,4,7,2,3]=>0000000=>[8]=>[8]
[6,7,4,1,2,5,8,3]=>0000000=>[8]=>[8]
[3,6,7,5,8,1,2,4]=>0000000=>[8]=>[8]
[6,5,8,7,4,2,3,1]=>0000000=>[8]=>[8]
[6,1,7,3,8,5,2,4]=>0000000=>[8]=>[8]
[4,6,5,8,7,3,1,2]=>0000000=>[8]=>[8]
[8,4,5,1,7,6,2,3]=>0000000=>[8]=>[8]
[8,5,6,1,7,2,4,3]=>0000000=>[8]=>[8]
[7,5,6,1,3,8,4,2]=>0000000=>[8]=>[8]
[5,7,6,1,3,8,4,2]=>0000000=>[8]=>[8]
[6,7,1,4,2,8,5,3]=>0000000=>[8]=>[8]
[2,1,6,4,8,3,7,5]=>0100000=>[2,6]=>[6,2]
[7,4,5,1,3,8,6,2]=>0000000=>[8]=>[8]
[5,8,7,4,6,2,3,1]=>0000000=>[8]=>[8]
[6,4,8,1,5,7,3,2]=>0000000=>[8]=>[8]
[2,4,7,8,5,6,1,3]=>0000000=>[8]=>[8]
[3,4,6,8,2,1,7,5]=>0000000=>[8]=>[8]
[2,8,7,1,4,3,6,5]=>0000000=>[8]=>[8]
[1,2,7,8,4,3,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[2,8,5,4,1,3,7,6]=>0000000=>[8]=>[8]
[5,4,6,3,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[1,4,8,3,6,5,2,7]=>1000000=>[1,7]=>[7,1]
[1,2,8,6,4,3,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[6,5,1,8,7,4,3,2]=>0000000=>[8]=>[8]
[7,5,1,8,6,4,3,2]=>0000000=>[8]=>[8]
[8,5,1,7,6,4,3,2]=>0000000=>[8]=>[8]
[8,5,3,7,6,1,4,2]=>0000000=>[8]=>[8]
[3,8,7,6,1,5,4,2]=>0000000=>[8]=>[8]
[8,5,2,6,1,4,7,3]=>0000000=>[8]=>[8]
[2,7,5,8,1,4,6,3]=>0000000=>[8]=>[8]
[8,5,6,1,7,3,2,4]=>0000000=>[8]=>[8]
[3,2,6,7,1,8,5,4]=>0000000=>[8]=>[8]
[3,4,6,7,8,2,1,5]=>0000000=>[8]=>[8]
[6,7,1,3,8,5,4,2]=>0000000=>[8]=>[8]
[1,6,2,7,8,5,3,4]=>1000000=>[1,7]=>[7,1]
[1,2,6,7,8,5,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,7,4,8,3,2,5]=>1000000=>[1,7]=>[7,1]
[3,7,2,1,8,4,6,5]=>0000000=>[8]=>[8]
[3,7,2,4,1,8,6,5]=>0000000=>[8]=>[8]
[3,2,6,4,8,7,5,1]=>0000000=>[8]=>[8]
[4,7,2,8,6,5,1,3]=>0000000=>[8]=>[8]
[4,7,1,8,6,5,3,2]=>0000000=>[8]=>[8]
[2,7,4,8,3,6,1,5]=>0000000=>[8]=>[8]
[4,7,3,8,6,1,5,2]=>0000000=>[8]=>[8]
[4,7,3,8,6,2,1,5]=>0000000=>[8]=>[8]
[4,3,6,8,7,2,5,1]=>0000000=>[8]=>[8]
[4,3,8,2,5,7,6,1]=>0000000=>[8]=>[8]
[4,3,8,1,5,7,6,2]=>0000000=>[8]=>[8]
[4,1,2,6,8,7,5,3]=>0000000=>[8]=>[8]
[2,4,3,6,8,7,1,5]=>0000000=>[8]=>[8]
[3,1,6,4,8,7,2,5]=>0000000=>[8]=>[8]
[4,1,6,8,7,5,2,3]=>0000000=>[8]=>[8]
[3,8,1,4,5,7,2,6]=>0000000=>[8]=>[8]
[3,8,1,4,2,5,7,6]=>0000000=>[8]=>[8]
[4,1,8,3,5,2,7,6]=>0000000=>[8]=>[8]
[4,2,3,6,8,7,1,5]=>0000000=>[8]=>[8]
[4,2,8,3,5,7,6,1]=>0000000=>[8]=>[8]
[3,8,2,4,5,7,6,1]=>0000000=>[8]=>[8]
[3,8,2,4,1,5,7,6]=>0000000=>[8]=>[8]
[3,8,2,5,1,4,7,6]=>0000000=>[8]=>[8]
[4,2,8,5,7,1,3,6]=>0000000=>[8]=>[8]
[3,8,1,5,2,4,7,6]=>0000000=>[8]=>[8]
[7,3,2,1,4,6,5,8]=>0000001=>[7,1]=>[7,1]
[2,7,1,3,5,6,8,4]=>0000000=>[8]=>[8]
[2,3,6,1,5,8,7,4]=>0000000=>[8]=>[8]
[4,5,2,3,8,6,7,1]=>0000000=>[8]=>[8]
[4,8,5,3,2,6,7,1]=>0000000=>[8]=>[8]
[6,4,1,8,5,2,7,3]=>0000000=>[8]=>[8]
[2,6,1,8,5,4,7,3]=>0000000=>[8]=>[8]
[3,1,6,8,5,4,7,2]=>0000000=>[8]=>[8]
[7,5,6,1,2,3,8,4]=>0000000=>[8]=>[8]
[1,5,7,6,3,2,8,4]=>1000000=>[1,7]=>[7,1]
[7,5,2,1,4,3,8,6]=>0000000=>[8]=>[8]
[3,1,7,8,5,4,2,6]=>0000000=>[8]=>[8]
[7,6,4,8,3,1,2,5]=>0000000=>[8]=>[8]
[6,2,8,5,1,3,4,7]=>0000000=>[8]=>[8]
[3,2,7,8,6,1,4,5]=>0000000=>[8]=>[8]
[6,8,2,5,1,3,7,4]=>0000000=>[8]=>[8]
[6,7,4,2,1,5,3,8]=>0000001=>[7,1]=>[7,1]
[5,7,4,1,6,8,2,3]=>0000000=>[8]=>[8]
[5,6,8,1,3,7,2,4]=>0000000=>[8]=>[8]
[3,7,4,8,6,1,2,5]=>0000000=>[8]=>[8]
[1,6,8,5,3,2,4,7]=>1000000=>[1,7]=>[7,1]
[7,2,8,4,6,1,3,5]=>0000000=>[8]=>[8]
[7,1,3,4,6,2,8,5]=>0000000=>[8]=>[8]
[5,8,7,4,2,1,3,6]=>0000000=>[8]=>[8]
[1,8,7,3,2,5,4,6]=>1000000=>[1,7]=>[7,1]
[1,2,5,4,8,7,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,8,6,3,5,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,7,3,4,2,6,8,5]=>1000000=>[1,7]=>[7,1]
[1,6,3,5,8,4,2,7]=>1000000=>[1,7]=>[7,1]
[1,8,5,7,6,3,2,4]=>1000000=>[1,7]=>[7,1]
[1,6,3,5,7,8,4,2]=>1000000=>[1,7]=>[7,1]
[7,6,2,5,3,4,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,2,4,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,2,4,3,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,6,2,3,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[8,4,2,7,1,6,3,5]=>0000000=>[8]=>[8]
[8,7,6,1,5,3,2,4]=>0000000=>[8]=>[8]
[8,7,6,1,3,5,4,2]=>0000000=>[8]=>[8]
[8,7,6,1,5,4,2,3]=>0000000=>[8]=>[8]
[4,5,3,8,2,1,6,7]=>0000000=>[8]=>[8]
[7,5,8,2,1,4,3,6]=>0000000=>[8]=>[8]
[8,7,6,1,2,5,3,4]=>0000000=>[8]=>[8]
[8,7,6,1,2,5,4,3]=>0000000=>[8]=>[8]
[8,7,6,1,4,2,5,3]=>0000000=>[8]=>[8]
[6,1,4,8,5,2,7,3]=>0000000=>[8]=>[8]
[3,1,6,8,5,2,7,4]=>0000000=>[8]=>[8]
[5,8,2,7,3,4,1,6]=>0000000=>[8]=>[8]
[5,3,8,1,6,7,4,2]=>0000000=>[8]=>[8]
[4,8,2,1,3,5,6,7]=>0000000=>[8]=>[8]
[5,1,8,3,6,7,4,2]=>0000000=>[8]=>[8]
[8,4,1,6,5,2,3,7]=>0000000=>[8]=>[8]
[6,8,7,3,2,4,1,5]=>0000000=>[8]=>[8]
[3,2,4,7,5,8,1,6]=>0000000=>[8]=>[8]
[1,2,7,4,6,3,8,5]=>1100000=>[1,1,6]=>[6,1,1]
[2,8,7,6,4,5,1,3]=>0000000=>[8]=>[8]
[3,5,7,6,1,8,4,2]=>0000000=>[8]=>[8]
[3,5,7,6,2,8,4,1]=>0000000=>[8]=>[8]
[5,3,6,2,8,7,4,1]=>0000000=>[8]=>[8]
[5,8,3,1,7,6,4,2]=>0000000=>[8]=>[8]
[6,2,3,8,7,5,4,1]=>0000000=>[8]=>[8]
[4,1,3,5,8,7,6,2]=>0000000=>[8]=>[8]
[4,2,5,3,7,6,1,8]=>0000001=>[7,1]=>[7,1]
[6,2,4,3,7,5,1,8]=>0000001=>[7,1]=>[7,1]
[1,3,6,4,7,5,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,2,5,3,6,4,1,7]=>0000000=>[8]=>[8]
[7,2,5,3,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,2,5,3,7,4,1,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,3,7,5,1,8]=>0000001=>[7,1]=>[7,1]
[5,2,7,3,6,4,1,8]=>0000001=>[7,1]=>[7,1]
[7,3,6,2,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,3,8,2,5,4,1,7]=>0000000=>[8]=>[8]
[7,3,1,4,6,5,2,8]=>0000001=>[7,1]=>[7,1]
[8,3,7,2,5,4,1,6]=>0000000=>[8]=>[8]
[5,2,8,3,6,4,1,7]=>0000000=>[8]=>[8]
[4,2,8,3,6,5,1,7]=>0000000=>[8]=>[8]
[3,2,8,4,6,5,1,7]=>0000000=>[8]=>[8]
[1,4,7,3,6,5,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,2,5,4,1,6,3,7]=>0000000=>[8]=>[8]
[1,3,6,5,2,7,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,2,6,4,1,5,3,7]=>0000000=>[8]=>[8]
[1,4,8,3,7,5,2,6]=>1000000=>[1,7]=>[7,1]
[6,2,1,4,8,5,3,7]=>0000000=>[8]=>[8]
[5,2,1,4,8,6,3,7]=>0000000=>[8]=>[8]
[3,2,1,5,8,6,4,7]=>0010000=>[3,5]=>[5,3]
[4,2,8,3,7,5,1,6]=>0000000=>[8]=>[8]
[5,2,8,3,7,4,1,6]=>0000000=>[8]=>[8]
[8,3,7,2,6,4,1,5]=>0000000=>[8]=>[8]
[7,3,1,4,8,5,2,6]=>0000000=>[8]=>[8]
[1,3,7,4,8,5,2,6]=>1000000=>[1,7]=>[7,1]
[8,2,6,3,7,4,1,5]=>0000000=>[8]=>[8]
[7,2,6,3,8,4,1,5]=>0000000=>[8]=>[8]
[5,2,7,3,8,4,1,6]=>0000000=>[8]=>[8]
[3,2,7,4,8,5,1,6]=>0000000=>[8]=>[8]
[5,2,6,3,8,4,1,7]=>0000000=>[8]=>[8]
[6,2,5,3,8,4,1,7]=>0000000=>[8]=>[8]
[7,2,5,3,8,4,1,6]=>0000000=>[8]=>[8]
[8,2,5,3,7,4,1,6]=>0000000=>[8]=>[8]
[1,3,6,4,8,5,2,7]=>1000000=>[1,7]=>[7,1]
[1,3,5,4,8,6,2,7]=>1000000=>[1,7]=>[7,1]
[8,2,4,3,7,5,1,6]=>0000000=>[8]=>[8]
[7,2,4,3,8,5,1,6]=>0000000=>[8]=>[8]
[6,2,4,3,8,5,1,7]=>0000000=>[8]=>[8]
[5,2,4,3,8,6,1,7]=>0000000=>[8]=>[8]
[4,2,5,3,8,6,1,7]=>0000000=>[8]=>[8]
[4,2,5,3,1,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[6,2,4,3,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[7,2,4,3,1,6,5,8]=>0000001=>[7,1]=>[7,1]
[8,5,1,3,6,4,2,7]=>0000000=>[8]=>[8]
[8,4,1,3,6,5,2,7]=>0000000=>[8]=>[8]
[1,5,2,4,7,6,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[7,2,5,3,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[6,2,5,3,1,7,4,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,3,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,4,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[5,2,7,3,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[6,2,7,3,1,5,4,8]=>0000001=>[7,1]=>[7,1]
[7,2,6,3,1,5,4,8]=>0000001=>[7,1]=>[7,1]
[1,5,2,4,8,6,3,7]=>1000000=>[1,7]=>[7,1]
[8,4,1,3,7,5,2,6]=>0000000=>[8]=>[8]
[6,2,1,5,3,7,4,8]=>0000001=>[7,1]=>[7,1]
[3,2,1,6,4,7,5,8]=>0010001=>[3,4,1]=>[4,3,1]
[3,2,8,5,1,6,4,7]=>0000000=>[8]=>[8]
[4,2,8,5,1,6,3,7]=>0000000=>[8]=>[8]
[6,2,8,4,1,5,3,7]=>0000000=>[8]=>[8]
[1,4,8,5,2,6,3,7]=>1000000=>[1,7]=>[7,1]
[8,3,7,4,1,5,2,6]=>0000000=>[8]=>[8]
[7,1,3,2,5,6,4,8]=>0000001=>[7,1]=>[7,1]
[1,5,2,8,7,4,3,6]=>1000000=>[1,7]=>[7,1]
[5,7,2,8,1,4,3,6]=>0000000=>[8]=>[8]
[2,7,1,5,6,4,3,8]=>0000001=>[7,1]=>[7,1]
[1,7,3,4,5,2,8,6]=>1000000=>[1,7]=>[7,1]
[3,2,1,7,8,5,4,6]=>0010000=>[3,5]=>[5,3]
[1,7,6,3,2,4,8,5]=>1000000=>[1,7]=>[7,1]
[1,8,5,3,2,4,7,6]=>1000000=>[1,7]=>[7,1]
[2,6,1,5,4,7,3,8]=>0000001=>[7,1]=>[7,1]
[1,3,8,5,4,2,6,7]=>1000000=>[1,7]=>[7,1]
[2,3,6,8,4,1,7,5]=>0000000=>[8]=>[8]
[1,7,2,8,6,3,5,4]=>1000000=>[1,7]=>[7,1]
[4,2,7,6,1,8,5,3]=>0000000=>[8]=>[8]
[7,3,2,1,6,4,8,5]=>0000000=>[8]=>[8]
[6,7,2,4,3,5,8,1]=>0000000=>[8]=>[8]
[4,3,8,2,1,5,7,6]=>0000000=>[8]=>[8]
[4,3,2,8,1,6,7,5]=>0000000=>[8]=>[8]
[4,5,8,3,2,7,1,6]=>0000000=>[8]=>[8]
[4,3,8,2,1,6,7,5]=>0000000=>[8]=>[8]
[4,6,7,2,5,3,8,1]=>0000000=>[8]=>[8]
[6,4,7,8,3,1,5,2]=>0000000=>[8]=>[8]
[5,6,7,1,8,3,4,2]=>0000000=>[8]=>[8]
[7,1,8,6,2,5,4,3]=>0000000=>[8]=>[8]
[1,5,8,2,6,4,7,3]=>1000000=>[1,7]=>[7,1]
[1,5,7,4,6,8,3,2]=>1000000=>[1,7]=>[7,1]
[3,1,8,6,5,2,7,4]=>0000000=>[8]=>[8]
[2,3,7,6,5,8,1,4]=>0000000=>[8]=>[8]
[2,3,7,6,5,1,8,4]=>0000000=>[8]=>[8]
[7,3,5,2,1,6,8,4]=>0000000=>[8]=>[8]
[1,5,4,7,8,6,2,3]=>1000000=>[1,7]=>[7,1]
[3,6,2,1,4,7,8,5]=>0000000=>[8]=>[8]
[6,3,8,7,5,4,2,1]=>0000000=>[8]=>[8]
[6,8,2,7,5,4,3,1]=>0000000=>[8]=>[8]
[5,8,1,7,6,4,3,2]=>0000000=>[8]=>[8]
[4,2,6,3,8,5,7,1]=>0000000=>[8]=>[8]
[8,2,7,4,5,1,6,3]=>0000000=>[8]=>[8]
[1,7,5,2,4,8,6,3]=>1000000=>[1,7]=>[7,1]
[7,2,8,5,3,1,6,4]=>0000000=>[8]=>[8]
[4,7,6,1,5,8,3,2]=>0000000=>[8]=>[8]
[5,4,7,3,8,2,1,6]=>0000000=>[8]=>[8]
[4,3,5,7,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[1,7,2,8,5,4,3,6]=>1000000=>[1,7]=>[7,1]
[5,4,8,3,6,2,1,7]=>0000000=>[8]=>[8]
[4,7,3,2,5,1,6,8]=>0000001=>[7,1]=>[7,1]
[4,2,5,3,8,7,1,6]=>0000000=>[8]=>[8]
[6,7,3,2,5,4,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,6,2,7,3,1,8]=>0000001=>[7,1]=>[7,1]
[7,4,8,6,5,1,2,3]=>0000000=>[8]=>[8]
[4,5,8,2,7,3,1,6]=>0000000=>[8]=>[8]
[6,5,8,2,7,3,1,4]=>0000000=>[8]=>[8]
[6,4,8,2,7,3,1,5]=>0000000=>[8]=>[8]
[7,8,1,3,6,4,2,5]=>0000000=>[8]=>[8]
[4,5,7,8,3,2,1,6]=>0000000=>[8]=>[8]
[5,3,7,2,1,8,6,4]=>0000000=>[8]=>[8]
[5,4,3,7,2,1,6,8]=>0000001=>[7,1]=>[7,1]
[5,4,3,7,8,2,1,6]=>0000000=>[8]=>[8]
[6,1,3,5,8,7,4,2]=>0000000=>[8]=>[8]
[6,8,5,7,3,4,2,1]=>0000000=>[8]=>[8]
[5,3,6,8,4,2,1,7]=>0000000=>[8]=>[8]
[5,1,6,8,4,7,3,2]=>0000000=>[8]=>[8]
[6,2,8,3,4,1,5,7]=>0000000=>[8]=>[8]
[2,4,1,8,7,6,3,5]=>0000000=>[8]=>[8]
[1,3,5,8,4,7,2,6]=>1000000=>[1,7]=>[7,1]
[2,3,8,7,5,1,6,4]=>0000000=>[8]=>[8]
[8,5,4,7,6,1,3,2]=>0000000=>[8]=>[8]
[5,8,7,2,4,1,3,6]=>0000000=>[8]=>[8]
[4,1,3,5,6,2,8,7]=>0000010=>[6,2]=>[6,2]
[6,3,8,5,1,7,4,2]=>0000000=>[8]=>[8]
[5,2,4,6,1,3,8,7]=>0000010=>[6,2]=>[6,2]
[8,2,4,6,1,3,7,5]=>0000000=>[8]=>[8]
[6,4,8,7,3,5,2,1]=>0000000=>[8]=>[8]
[8,2,3,5,6,1,4,7]=>0000000=>[8]=>[8]
[4,3,5,6,8,2,7,1]=>0000000=>[8]=>[8]
[8,2,3,4,6,1,7,5]=>0000000=>[8]=>[8]
[1,7,4,3,5,2,8,6]=>1000000=>[1,7]=>[7,1]
[2,7,4,3,8,1,5,6]=>0000000=>[8]=>[8]
[5,3,6,2,1,8,4,7]=>0000000=>[8]=>[8]
[4,3,8,6,2,7,1,5]=>0000000=>[8]=>[8]
[8,2,1,4,6,3,7,5]=>0000000=>[8]=>[8]
[3,1,6,8,2,7,5,4]=>0000000=>[8]=>[8]
[5,3,8,6,7,2,1,4]=>0000000=>[8]=>[8]
[5,8,7,2,4,6,1,3]=>0000000=>[8]=>[8]
[1,5,2,8,7,6,4,3]=>1000000=>[1,7]=>[7,1]
[2,7,1,4,6,5,3,8]=>0000001=>[7,1]=>[7,1]
[4,7,1,2,6,5,8,3]=>0000000=>[8]=>[8]
[3,2,4,5,1,8,6,7]=>0000100=>[5,3]=>[5,3]
[4,2,5,6,8,7,3,1]=>0000000=>[8]=>[8]
[8,2,5,1,6,3,7,4]=>0000000=>[8]=>[8]
[8,3,4,5,1,6,7,2]=>0000000=>[8]=>[8]
[3,5,7,6,4,8,1,2]=>0000000=>[8]=>[8]
[1,3,7,8,5,4,6,2]=>1000000=>[1,7]=>[7,1]
[7,2,8,6,5,1,4,3]=>0000000=>[8]=>[8]
[4,2,7,5,3,1,8,6]=>0000000=>[8]=>[8]
[7,3,2,5,4,1,8,6]=>0000000=>[8]=>[8]
[3,6,4,1,8,2,7,5]=>0000000=>[8]=>[8]
[4,6,3,8,7,2,1,5]=>0000000=>[8]=>[8]
[4,3,5,1,8,7,2,6]=>0000000=>[8]=>[8]
[7,5,2,8,4,3,1,6]=>0000000=>[8]=>[8]
[1,7,2,4,5,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,4,5,3,2,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,4,7,3,5,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,3,5,6,1,4,7,2]=>0000000=>[8]=>[8]
[1,6,4,7,5,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,2,6,7,4,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,5,6,1,4,3,7,2]=>0000000=>[8]=>[8]
[5,4,7,8,3,1,2,6]=>0000000=>[8]=>[8]
[2,5,4,7,8,3,1,6]=>0000000=>[8]=>[8]
[6,4,5,8,2,3,1,7]=>0000000=>[8]=>[8]
[8,6,1,3,2,5,7,4]=>0000000=>[8]=>[8]
[7,5,8,1,4,6,3,2]=>0000000=>[8]=>[8]
[4,2,6,7,8,1,5,3]=>0000000=>[8]=>[8]
[3,4,6,7,8,1,5,2]=>0000000=>[8]=>[8]
[4,3,2,7,5,8,1,6]=>0000000=>[8]=>[8]
[4,8,5,3,2,6,1,7]=>0000000=>[8]=>[8]
[2,8,4,5,3,6,1,7]=>0000000=>[8]=>[8]
[8,1,5,3,2,4,7,6]=>0000000=>[8]=>[8]
[8,1,2,4,5,3,7,6]=>0000000=>[8]=>[8]
[8,1,4,5,3,2,7,6]=>0000000=>[8]=>[8]
[7,8,4,1,3,6,5,2]=>0000000=>[8]=>[8]
[8,6,1,3,2,7,4,5]=>0000000=>[8]=>[8]
[7,3,8,2,4,1,6,5]=>0000000=>[8]=>[8]
[6,2,3,7,8,1,5,4]=>0000000=>[8]=>[8]
[6,3,7,8,1,5,4,2]=>0000000=>[8]=>[8]
[2,6,3,7,8,1,5,4]=>0000000=>[8]=>[8]
[7,5,8,1,6,4,2,3]=>0000000=>[8]=>[8]
[1,3,6,4,2,5,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,7,6,4,2,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,2,3,7,6,4,5,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,3,2,5,8,6,4,7]=>1010000=>[1,2,5]=>[5,2,1]
[4,8,2,7,1,3,6,5]=>0000000=>[8]=>[8]
[7,1,8,4,6,3,5,2]=>0000000=>[8]=>[8]
[4,1,5,2,3,8,7,6]=>0000100=>[5,3]=>[5,3]
[2,8,7,1,4,6,3,5]=>0000000=>[8]=>[8]
[3,1,2,8,5,7,4,6]=>0010000=>[3,5]=>[5,3]
[2,1,8,6,3,7,5,4]=>0100000=>[2,6]=>[6,2]
[1,6,5,3,2,4,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,7,2,4,6,5,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,7,2,6,5,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,7,2,4,6,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,2,6,4,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,2,6,8,7,4,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,4,3,5,8,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,6,3,5,2,7,4]=>1000000=>[1,7]=>[7,1]
[1,6,2,8,7,4,3,5]=>1000000=>[1,7]=>[7,1]
[1,3,8,7,5,4,6,2]=>1000000=>[1,7]=>[7,1]
[1,2,8,6,3,5,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,5,2,3,6,4,7]=>1000000=>[1,7]=>[7,1]
[1,7,4,8,5,2,3,6]=>1000000=>[1,7]=>[7,1]
[1,4,7,5,8,6,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,7,5,2,8,6,3]=>1000000=>[1,7]=>[7,1]
[1,6,3,7,4,2,8,5]=>1000000=>[1,7]=>[7,1]
[1,8,5,2,7,4,3,6]=>1000000=>[1,7]=>[7,1]
[1,4,8,6,3,2,7,5]=>1000000=>[1,7]=>[7,1]
[1,4,8,7,5,3,2,6]=>1000000=>[1,7]=>[7,1]
[1,2,5,8,6,3,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,4,7,5,8,6,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,5,8,7,6,2,4]=>1000000=>[1,7]=>[7,1]
[1,5,2,4,3,6,8,7]=>1000110=>[1,4,1,2]=>[4,2,1,1]
[1,6,8,7,5,3,2,4]=>1000000=>[1,7]=>[7,1]
[1,2,5,7,4,3,8,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,3,2,6,8,7,4]=>1000000=>[1,7]=>[7,1]
[1,4,2,6,8,7,5,3]=>1000000=>[1,7]=>[7,1]
[1,5,8,6,3,2,7,4]=>1000000=>[1,7]=>[7,1]
[1,8,5,2,6,3,4,7]=>1000000=>[1,7]=>[7,1]
[1,7,4,6,3,2,8,5]=>1000000=>[1,7]=>[7,1]
[1,6,3,2,8,5,4,7]=>1000000=>[1,7]=>[7,1]
[1,4,2,8,6,3,5,7]=>1000000=>[1,7]=>[7,1]
[1,3,8,6,4,2,5,7]=>1000000=>[1,7]=>[7,1]
[1,5,7,4,2,3,8,6]=>1000000=>[1,7]=>[7,1]
[8,2,7,3,1,5,4,6]=>0000000=>[8]=>[8]
[8,4,7,2,5,3,1,6]=>0000000=>[8]=>[8]
[8,6,1,4,7,3,5,2]=>0000000=>[8]=>[8]
[5,3,6,7,2,8,4,1]=>0000000=>[8]=>[8]
[1,3,8,2,5,6,7,4]=>1000000=>[1,7]=>[7,1]
[5,1,7,4,3,6,8,2]=>0000000=>[8]=>[8]
[7,1,3,6,5,2,8,4]=>0000000=>[8]=>[8]
[6,1,8,5,2,7,3,4]=>0000000=>[8]=>[8]
[5,4,1,3,7,2,8,6]=>0000000=>[8]=>[8]
[3,1,8,7,5,2,4,6]=>0000000=>[8]=>[8]
[6,5,8,7,2,4,3,1]=>0000000=>[8]=>[8]
[4,3,6,5,8,2,1,7]=>0000000=>[8]=>[8]
[4,7,3,1,8,5,2,6]=>0000000=>[8]=>[8]
[5,1,7,8,6,2,3,4]=>0000000=>[8]=>[8]
[8,5,1,6,7,2,3,4]=>0000000=>[8]=>[8]
[1,8,3,6,4,5,7,2]=>1000000=>[1,7]=>[7,1]
[8,1,6,4,2,3,5,7]=>0000000=>[8]=>[8]
[7,1,8,2,5,3,4,6]=>0000000=>[8]=>[8]
[5,1,7,2,6,3,4,8]=>0000001=>[7,1]=>[7,1]
[1,6,3,8,4,5,7,2]=>1000000=>[1,7]=>[7,1]
[2,7,4,3,8,5,1,6]=>0000000=>[8]=>[8]
[2,4,7,3,5,1,6,8]=>0000001=>[7,1]=>[7,1]
[2,4,8,6,3,5,1,7]=>0000000=>[8]=>[8]
[2,3,7,5,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[3,4,6,2,1,5,8,7]=>0000010=>[6,2]=>[6,2]
[2,3,6,1,5,8,4,7]=>0000000=>[8]=>[8]
[2,3,7,1,6,5,8,4]=>0000000=>[8]=>[8]
[2,4,7,1,3,6,8,5]=>0000000=>[8]=>[8]
[5,4,7,8,1,3,2,6]=>0000000=>[8]=>[8]
[2,5,7,1,4,6,3,8]=>0000001=>[7,1]=>[7,1]
[2,4,7,1,6,3,5,8]=>0000001=>[7,1]=>[7,1]
[2,3,7,1,6,5,4,8]=>0000001=>[7,1]=>[7,1]
[2,5,7,1,4,3,6,8]=>0000001=>[7,1]=>[7,1]
[2,5,7,3,1,4,6,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,2,1,6,8,5]=>0000000=>[8]=>[8]
[5,7,3,2,8,1,4,6]=>0000000=>[8]=>[8]
[5,4,7,8,1,3,6,2]=>0000000=>[8]=>[8]
[2,5,7,1,4,6,8,3]=>0000000=>[8]=>[8]
[2,4,7,1,6,3,8,5]=>0000000=>[8]=>[8]
[2,4,7,1,6,8,3,5]=>0000000=>[8]=>[8]
[8,7,5,1,4,2,3,6]=>0000000=>[8]=>[8]
[6,8,3,2,4,5,1,7]=>0000000=>[8]=>[8]
[3,8,5,2,4,6,1,7]=>0000000=>[8]=>[8]
[8,2,4,5,3,1,6,7]=>0000000=>[8]=>[8]
[4,8,2,5,3,1,6,7]=>0000000=>[8]=>[8]
[4,3,7,5,2,1,6,8]=>0000001=>[7,1]=>[7,1]
[1,6,7,4,3,2,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,5,7,3,2,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[3,5,1,4,7,2,6,8]=>0000001=>[7,1]=>[7,1]
[2,5,4,7,8,1,3,6]=>0000000=>[8]=>[8]
[2,5,1,4,7,8,3,6]=>0000000=>[8]=>[8]
[4,3,7,1,5,2,6,8]=>0000001=>[7,1]=>[7,1]
[3,5,1,6,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,4,3,1,7,2,5,8]=>0000001=>[7,1]=>[7,1]
[6,2,7,4,3,1,5,8]=>0000001=>[7,1]=>[7,1]
[2,6,4,1,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[6,3,2,7,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[7,2,4,1,3,6,8,5]=>0000000=>[8]=>[8]
[6,3,2,5,7,1,4,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,5,7,1,4,8]=>0000001=>[7,1]=>[7,1]
[1,7,3,2,5,6,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,1,7,3,5,6,8,4]=>0100000=>[2,6]=>[6,2]
[2,1,6,3,5,7,8,4]=>0100000=>[2,6]=>[6,2]
[1,6,3,2,5,7,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[5,6,2,1,4,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,5,1,6,4,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[2,5,4,1,6,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,6,1,5,2,7,3,8]=>0000001=>[7,1]=>[7,1]
[1,6,5,3,7,2,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,6,1,8,5,4,3,7]=>0000000=>[8]=>[8]
[4,5,8,6,2,1,3,7]=>0000000=>[8]=>[8]
[4,2,8,5,3,6,1,7]=>0000000=>[8]=>[8]
[5,6,3,2,8,1,7,4]=>0000000=>[8]=>[8]
[8,2,6,3,1,5,7,4]=>0000000=>[8]=>[8]
[8,2,5,3,4,7,6,1]=>0000000=>[8]=>[8]
[7,5,3,2,4,1,8,6]=>0000000=>[8]=>[8]
[6,5,3,2,4,8,1,7]=>0000000=>[8]=>[8]
[3,1,8,4,6,5,7,2]=>0000000=>[8]=>[8]
[3,4,7,5,8,2,6,1]=>0000000=>[8]=>[8]
[8,7,1,4,6,5,2,3]=>0000000=>[8]=>[8]
[8,3,7,6,4,5,1,2]=>0000000=>[8]=>[8]
[5,3,8,6,4,1,7,2]=>0000000=>[8]=>[8]
[6,4,7,1,8,5,2,3]=>0000000=>[8]=>[8]
[3,8,2,5,1,7,4,6]=>0000000=>[8]=>[8]
[8,6,4,1,7,3,2,5]=>0000000=>[8]=>[8]
[3,4,7,8,5,1,2,6]=>0000000=>[8]=>[8]
[5,7,2,4,3,6,8,1]=>0000000=>[8]=>[8]
[4,7,3,2,5,6,8,1]=>0000000=>[8]=>[8]
[3,2,7,6,4,5,8,1]=>0000000=>[8]=>[8]
[1,7,3,6,8,4,2,5]=>1000000=>[1,7]=>[7,1]
[8,3,1,2,6,4,7,5]=>0000000=>[8]=>[8]
[1,7,8,2,4,3,5,6]=>1000000=>[1,7]=>[7,1]
[3,6,4,7,1,2,8,5]=>0000000=>[8]=>[8]
[2,4,7,8,5,1,3,6]=>0000000=>[8]=>[8]
[5,7,4,8,1,3,2,6]=>0000000=>[8]=>[8]
[4,3,7,8,1,5,2,6]=>0000000=>[8]=>[8]
[8,5,4,2,6,1,7,3]=>0000000=>[8]=>[8]
[3,2,6,8,7,4,1,5]=>0000000=>[8]=>[8]
[2,3,7,5,1,8,6,4]=>0000000=>[8]=>[8]
[6,3,1,2,8,7,4,5]=>0000000=>[8]=>[8]
[5,2,1,3,8,7,6,4]=>0000000=>[8]=>[8]
[7,2,1,5,3,8,4,6]=>0000000=>[8]=>[8]
[1,5,8,2,4,3,6,7]=>1000000=>[1,7]=>[7,1]
[4,3,6,8,1,5,2,7]=>0000000=>[8]=>[8]
[2,4,6,8,5,1,3,7]=>0000000=>[8]=>[8]
[1,6,8,2,4,3,5,7]=>1000000=>[1,7]=>[7,1]
[5,4,6,8,3,1,7,2]=>0000000=>[8]=>[8]
[8,6,1,7,2,4,3,5]=>0000000=>[8]=>[8]
[7,3,1,2,8,6,4,5]=>0000000=>[8]=>[8]
[2,3,7,6,1,8,5,4]=>0000000=>[8]=>[8]
[3,2,7,8,6,4,1,5]=>0000000=>[8]=>[8]
[6,2,8,3,1,4,7,5]=>0000000=>[8]=>[8]
[3,1,2,8,7,4,5,6]=>0010000=>[3,5]=>[5,3]
[2,1,3,8,7,4,6,5]=>0110000=>[2,1,5]=>[5,2,1]
[2,1,3,8,7,4,5,6]=>0110000=>[2,1,5]=>[5,2,1]
[8,5,1,7,2,4,3,6]=>0000000=>[8]=>[8]
[8,3,1,6,2,7,5,4]=>0000000=>[8]=>[8]
[1,3,2,8,7,6,4,5]=>1010000=>[1,2,5]=>[5,2,1]
[2,1,3,8,7,6,4,5]=>0110000=>[2,1,5]=>[5,2,1]
[3,5,8,2,4,1,7,6]=>0000000=>[8]=>[8]
[1,3,6,8,5,4,2,7]=>1000000=>[1,7]=>[7,1]
[1,4,2,5,7,6,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,2,6,8,5,3,7]=>1000000=>[1,7]=>[7,1]
[1,5,3,2,6,8,4,7]=>1000000=>[1,7]=>[7,1]
[1,5,4,2,3,6,8,7]=>1000110=>[1,4,1,2]=>[4,2,1,1]
[1,6,8,3,5,4,2,7]=>1000000=>[1,7]=>[7,1]
[1,5,3,2,4,6,8,7]=>1000110=>[1,4,1,2]=>[4,2,1,1]
[1,5,8,7,6,3,2,4]=>1000000=>[1,7]=>[7,1]
[1,5,7,6,3,2,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,3,2,4,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,3,2,4,8,7,5]=>1000000=>[1,7]=>[7,1]
[1,2,7,6,4,3,5,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,8,7,5,2,4,6,3]=>1000000=>[1,7]=>[7,1]
[1,7,5,2,4,6,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,4,2,5,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,8,4,7,5,2,6,3]=>1000000=>[1,7]=>[7,1]
[1,7,5,2,3,6,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,5,2,6,3,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,3,7,4,2,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,3,2,7,5,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,8,7,5,2,6,3]=>1000000=>[1,7]=>[7,1]
[1,4,7,5,2,6,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,6,4,8,7,5,2]=>1000000=>[1,7]=>[7,1]
[1,3,7,6,4,2,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,8,7,5,2,4,6]=>1000000=>[1,7]=>[7,1]
[1,4,6,3,2,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,6,3,2,8,7,5]=>1000000=>[1,7]=>[7,1]
[1,5,7,6,4,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,2,6,4,7,5,3,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[1,6,3,2,8,4,7,5]=>1000000=>[1,7]=>[7,1]
[1,5,2,7,4,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,3,5,2,7,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,3,5,2,8,7,4]=>1000000=>[1,7]=>[7,1]
[1,8,3,7,5,2,4,6]=>1000000=>[1,7]=>[7,1]
[1,8,4,6,3,2,7,5]=>1000000=>[1,7]=>[7,1]
[3,2,1,4,8,5,7,6]=>0011000=>[3,1,4]=>[4,3,1]
[7,4,1,6,2,5,3,8]=>0000001=>[7,1]=>[7,1]
[5,4,1,8,2,6,3,7]=>0000000=>[8]=>[8]
[5,4,1,6,2,8,3,7]=>0000000=>[8]=>[8]
[2,8,6,4,5,1,7,3]=>0000000=>[8]=>[8]
[2,8,3,1,4,5,7,6]=>0000000=>[8]=>[8]
[6,1,7,2,8,4,5,3]=>0000000=>[8]=>[8]
[8,3,2,1,5,6,7,4]=>0000000=>[8]=>[8]
[7,2,8,1,4,5,6,3]=>0000000=>[8]=>[8]
[5,1,7,3,8,6,2,4]=>0000000=>[8]=>[8]
[3,2,5,8,7,4,1,6]=>0000000=>[8]=>[8]
[4,2,5,8,7,3,1,6]=>0000000=>[8]=>[8]
[8,3,4,1,6,5,2,7]=>0000000=>[8]=>[8]
[3,4,8,5,7,2,1,6]=>0000000=>[8]=>[8]
[3,6,4,8,5,7,2,1]=>0000000=>[8]=>[8]
[5,8,4,7,3,6,2,1]=>0000000=>[8]=>[8]
[4,2,8,7,3,1,6,5]=>0000000=>[8]=>[8]
[6,5,8,2,1,7,4,3]=>0000000=>[8]=>[8]
[6,1,4,3,8,7,2,5]=>0000000=>[8]=>[8]
[5,1,3,2,6,8,7,4]=>0000000=>[8]=>[8]
[6,1,3,8,7,2,4,5]=>0000000=>[8]=>[8]
[1,2,8,4,5,7,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[4,2,1,8,7,6,3,5]=>0000000=>[8]=>[8]
[3,2,5,8,7,1,4,6]=>0000000=>[8]=>[8]
[5,6,3,8,7,2,1,4]=>0000000=>[8]=>[8]
[2,5,8,4,7,1,6,3]=>0000000=>[8]=>[8]
[1,6,2,4,8,5,7,3]=>1000000=>[1,7]=>[7,1]
[3,1,6,5,8,7,2,4]=>0000000=>[8]=>[8]
[4,8,5,3,6,7,1,2]=>0000000=>[8]=>[8]
[1,8,5,3,4,7,6,2]=>1000000=>[1,7]=>[7,1]
[1,4,6,2,5,3,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[4,3,6,5,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,3,8,7,6,5,2,4]=>1000000=>[1,7]=>[7,1]
[1,8,7,2,6,3,5,4]=>1000000=>[1,7]=>[7,1]
[2,8,7,1,6,3,4,5]=>0000000=>[8]=>[8]
[1,3,7,5,4,8,6,2]=>1000000=>[1,7]=>[7,1]
[1,5,6,3,8,4,2,7]=>1000000=>[1,7]=>[7,1]
[2,6,5,3,8,4,1,7]=>0000000=>[8]=>[8]
[2,3,6,5,4,8,1,7]=>0000000=>[8]=>[8]
[2,7,5,1,8,4,6,3]=>0000000=>[8]=>[8]
[1,7,6,4,8,2,5,3]=>1000000=>[1,7]=>[7,1]
[6,3,8,7,2,4,5,1]=>0000000=>[8]=>[8]
[2,4,3,8,7,1,6,5]=>0000000=>[8]=>[8]
[8,3,7,2,1,6,5,4]=>0000000=>[8]=>[8]
[8,4,7,3,6,2,1,5]=>0000000=>[8]=>[8]
[3,8,7,5,6,4,1,2]=>0000000=>[8]=>[8]
[3,8,7,5,6,2,1,4]=>0000000=>[8]=>[8]
[3,8,7,5,6,2,4,1]=>0000000=>[8]=>[8]
[2,8,7,5,6,4,1,3]=>0000000=>[8]=>[8]
[3,6,2,4,8,7,1,5]=>0000000=>[8]=>[8]
[1,5,6,3,8,2,7,4]=>1000000=>[1,7]=>[7,1]
[2,6,3,8,4,7,1,5]=>0000000=>[8]=>[8]
[2,6,3,5,7,8,1,4]=>0000000=>[8]=>[8]
[1,5,6,3,7,2,8,4]=>1000000=>[1,7]=>[7,1]
[1,7,5,3,6,2,8,4]=>1000000=>[1,7]=>[7,1]
[1,5,7,3,4,2,8,6]=>1000000=>[1,7]=>[7,1]
[1,5,8,3,4,2,7,6]=>1000000=>[1,7]=>[7,1]
[1,4,5,3,8,2,7,6]=>1000000=>[1,7]=>[7,1]
[6,5,1,4,2,7,8,3]=>0000000=>[8]=>[8]
[6,5,1,4,2,8,7,3]=>0000000=>[8]=>[8]
[1,7,5,4,2,8,6,3]=>1000000=>[1,7]=>[7,1]
[1,4,8,2,6,5,3,7]=>1000000=>[1,7]=>[7,1]
[7,5,1,8,3,4,2,6]=>0000000=>[8]=>[8]
[1,2,5,6,8,7,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,6,7,3,4,1,8,5]=>0000000=>[8]=>[8]
[1,3,7,2,6,4,8,5]=>1000000=>[1,7]=>[7,1]
[7,6,1,2,3,5,4,8]=>0000001=>[7,1]=>[7,1]
[6,1,3,4,2,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,3,8,2,4,6,1,7]=>0000000=>[8]=>[8]
[4,1,5,6,3,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,5,8,3,2,6,1,7]=>0000000=>[8]=>[8]
[5,8,2,1,4,6,3,7]=>0000000=>[8]=>[8]
[4,1,5,8,3,6,2,7]=>0000000=>[8]=>[8]
[4,5,8,3,6,1,2,7]=>0000000=>[8]=>[8]
[1,6,3,4,7,8,5,2]=>1000000=>[1,7]=>[7,1]
[8,1,3,4,2,6,5,7]=>0000000=>[8]=>[8]
[4,7,8,5,2,3,1,6]=>0000000=>[8]=>[8]
[4,1,5,8,6,2,3,7]=>0000000=>[8]=>[8]
[5,8,2,1,6,3,4,7]=>0000000=>[8]=>[8]
[2,6,7,8,4,1,3,5]=>0000000=>[8]=>[8]
[2,6,7,8,4,3,1,5]=>0000000=>[8]=>[8]
[1,7,8,5,4,2,3,6]=>1000000=>[1,7]=>[7,1]
[3,6,4,5,2,8,1,7]=>0000000=>[8]=>[8]
[8,1,5,4,7,6,3,2]=>0000000=>[8]=>[8]
[2,5,1,4,6,7,3,8]=>0000001=>[7,1]=>[7,1]
[8,6,3,5,4,1,2,7]=>0000000=>[8]=>[8]
[8,2,6,5,4,1,3,7]=>0000000=>[8]=>[8]
[8,2,6,5,4,3,1,7]=>0000000=>[8]=>[8]
[8,3,2,6,1,5,4,7]=>0000000=>[8]=>[8]
[8,1,6,5,4,3,2,7]=>0000000=>[8]=>[8]
[4,8,1,7,6,3,5,2]=>0000000=>[8]=>[8]
[8,5,1,7,4,3,6,2]=>0000000=>[8]=>[8]
[8,5,7,6,2,1,3,4]=>0000000=>[8]=>[8]
[5,4,8,3,1,7,2,6]=>0000000=>[8]=>[8]
[5,1,4,8,3,2,7,6]=>0000000=>[8]=>[8]
[4,8,1,7,6,5,2,3]=>0000000=>[8]=>[8]
[4,3,8,7,2,6,1,5]=>0000000=>[8]=>[8]
[3,8,7,2,6,4,1,5]=>0000000=>[8]=>[8]
[8,2,7,6,4,1,5,3]=>0000000=>[8]=>[8]
[4,3,8,7,2,6,5,1]=>0000000=>[8]=>[8]
[8,2,5,7,4,3,6,1]=>0000000=>[8]=>[8]
[3,8,7,4,6,1,2,5]=>0000000=>[8]=>[8]
[8,3,7,5,4,1,6,2]=>0000000=>[8]=>[8]
[2,8,4,7,6,1,5,3]=>0000000=>[8]=>[8]
[2,5,4,8,3,1,7,6]=>0000000=>[8]=>[8]
[5,4,8,2,1,3,7,6]=>0000000=>[8]=>[8]
[3,8,7,2,6,1,5,4]=>0000000=>[8]=>[8]
[1,8,4,7,6,3,5,2]=>1000000=>[1,7]=>[7,1]
[1,8,3,7,6,5,2,4]=>1000000=>[1,7]=>[7,1]
[1,4,3,8,7,2,6,5]=>1000000=>[1,7]=>[7,1]
[8,1,2,7,6,5,4,3]=>0000000=>[8]=>[8]
[7,8,1,3,6,4,5,2]=>0000000=>[8]=>[8]
[7,2,6,8,4,5,3,1]=>0000000=>[8]=>[8]
[7,3,6,8,5,1,4,2]=>0000000=>[8]=>[8]
[7,5,8,1,6,2,4,3]=>0000000=>[8]=>[8]
[5,7,8,1,6,3,2,4]=>0000000=>[8]=>[8]
[7,2,6,8,5,1,4,3]=>0000000=>[8]=>[8]
[6,7,8,3,5,4,2,1]=>0000000=>[8]=>[8]
[6,7,8,4,2,1,5,3]=>0000000=>[8]=>[8]
[7,2,6,8,4,3,1,5]=>0000000=>[8]=>[8]
[7,5,2,4,8,3,1,6]=>0000000=>[8]=>[8]
[5,6,2,4,3,8,1,7]=>0000000=>[8]=>[8]
[7,8,3,1,6,2,5,4]=>0000000=>[8]=>[8]
[6,7,8,4,3,1,5,2]=>0000000=>[8]=>[8]
[7,8,2,6,3,5,4,1]=>0000000=>[8]=>[8]
[7,8,3,6,4,1,5,2]=>0000000=>[8]=>[8]
[6,1,5,2,4,8,3,7]=>0000000=>[8]=>[8]
[1,5,6,3,8,2,4,7]=>1000000=>[1,7]=>[7,1]
[7,3,8,1,6,4,5,2]=>0000000=>[8]=>[8]
[7,2,6,8,4,3,5,1]=>0000000=>[8]=>[8]
[7,5,2,4,8,3,6,1]=>0000000=>[8]=>[8]
[1,7,5,8,2,4,6,3]=>1000000=>[1,7]=>[7,1]
[7,5,2,8,1,4,6,3]=>0000000=>[8]=>[8]
[3,7,8,2,6,5,1,4]=>0000000=>[8]=>[8]
[3,7,8,2,1,6,4,5]=>0000000=>[8]=>[8]
[7,2,8,1,6,4,3,5]=>0000000=>[8]=>[8]
[7,8,1,6,3,5,4,2]=>0000000=>[8]=>[8]
[6,7,8,3,2,5,4,1]=>0000000=>[8]=>[8]
[6,7,8,2,5,4,3,1]=>0000000=>[8]=>[8]
[6,7,8,3,1,5,4,2]=>0000000=>[8]=>[8]
[7,8,1,6,2,5,4,3]=>0000000=>[8]=>[8]
[5,6,1,4,3,8,2,7]=>0000000=>[8]=>[8]
[1,6,4,5,2,7,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[6,2,1,5,7,3,4,8]=>0000001=>[7,1]=>[7,1]
[1,6,7,4,2,8,3,5]=>1000000=>[1,7]=>[7,1]
[1,4,7,2,3,6,8,5]=>1000000=>[1,7]=>[7,1]
[3,1,2,6,7,8,5,4]=>0010000=>[3,5]=>[5,3]
[1,6,3,4,7,8,2,5]=>1000000=>[1,7]=>[7,1]
[3,1,5,7,6,2,8,4]=>0000000=>[8]=>[8]
[6,3,1,4,2,7,8,5]=>0000000=>[8]=>[8]
[2,4,3,7,6,1,8,5]=>0000000=>[8]=>[8]
[3,1,6,5,2,8,7,4]=>0000000=>[8]=>[8]
[3,1,7,6,5,2,8,4]=>0000000=>[8]=>[8]
[1,4,7,6,8,3,2,5]=>1000000=>[1,7]=>[7,1]
[7,2,1,5,6,3,8,4]=>0000000=>[8]=>[8]
[4,3,1,8,6,2,7,5]=>0000000=>[8]=>[8]
[3,1,5,2,8,7,6,4]=>0000000=>[8]=>[8]
[1,2,8,4,3,7,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,8,5,4,2,7,3,6]=>1000000=>[1,7]=>[7,1]
[3,1,8,5,4,7,2,6]=>0000000=>[8]=>[8]
[2,6,1,8,7,4,3,5]=>0000000=>[8]=>[8]
[7,5,1,8,3,2,6,4]=>0000000=>[8]=>[8]
[4,7,6,3,1,8,2,5]=>0000000=>[8]=>[8]
[5,3,1,8,6,2,4,7]=>0000000=>[8]=>[8]
[5,1,8,6,3,2,4,7]=>0000000=>[8]=>[8]
[1,5,4,2,8,6,3,7]=>1000000=>[1,7]=>[7,1]
[8,3,1,6,4,2,5,7]=>0000000=>[8]=>[8]
[3,6,7,1,8,4,2,5]=>0000000=>[8]=>[8]
[1,7,4,8,3,5,2,6]=>1000000=>[1,7]=>[7,1]
[7,3,2,4,8,5,1,6]=>0000000=>[8]=>[8]
[6,3,4,7,1,8,5,2]=>0000000=>[8]=>[8]
[5,7,8,1,4,2,6,3]=>0000000=>[8]=>[8]
[5,7,1,2,3,8,6,4]=>0000000=>[8]=>[8]
[7,2,8,1,4,3,6,5]=>0000000=>[8]=>[8]
[2,6,3,8,1,7,5,4]=>0000000=>[8]=>[8]
[1,8,3,6,4,7,2,5]=>1000000=>[1,7]=>[7,1]
[2,8,6,4,1,7,3,5]=>0000000=>[8]=>[8]
[1,8,4,2,7,5,3,6]=>1000000=>[1,7]=>[7,1]
[6,5,1,7,2,8,4,3]=>0000000=>[8]=>[8]
[2,8,1,7,5,3,6,4]=>0000000=>[8]=>[8]
[1,2,8,7,6,4,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,5,8,7,4,2,3]=>1000000=>[1,7]=>[7,1]
[4,3,5,7,1,6,2,8]=>0000001=>[7,1]=>[7,1]
[4,2,8,5,3,6,7,1]=>0000000=>[8]=>[8]
[4,1,8,5,3,6,2,7]=>0000000=>[8]=>[8]
[6,4,2,5,3,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,1,5,8,2,7,4,6]=>0000000=>[8]=>[8]
[6,4,1,5,3,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,2,1,5,4,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,1,8,5,4,6,2,7]=>0000000=>[8]=>[8]
[6,2,8,4,5,3,7,1]=>0000000=>[8]=>[8]
[6,1,8,4,5,3,2,7]=>0000000=>[8]=>[8]
[4,5,2,7,1,6,3,8]=>0000001=>[7,1]=>[7,1]
[4,3,5,7,1,6,8,2]=>0000000=>[8]=>[8]
[4,1,8,5,3,6,7,2]=>0000000=>[8]=>[8]
[6,3,8,4,5,1,7,2]=>0000000=>[8]=>[8]
[3,1,6,8,5,7,4,2]=>0000000=>[8]=>[8]
[2,6,1,8,5,7,4,3]=>0000000=>[8]=>[8]
[6,5,8,7,1,3,2,4]=>0000000=>[8]=>[8]
[6,5,8,7,2,3,4,1]=>0000000=>[8]=>[8]
[6,5,8,7,3,2,4,1]=>0000000=>[8]=>[8]
[6,3,8,4,5,2,7,1]=>0000000=>[8]=>[8]
[3,1,6,8,5,7,2,4]=>0000000=>[8]=>[8]
[2,1,6,8,5,3,7,4]=>0100000=>[2,6]=>[6,2]
[3,1,6,8,5,4,2,7]=>0000000=>[8]=>[8]
[3,2,6,8,5,4,7,1]=>0000000=>[8]=>[8]
[4,1,8,5,2,6,3,7]=>0000000=>[8]=>[8]
[3,1,6,8,5,2,4,7]=>0000000=>[8]=>[8]
[6,2,8,4,5,1,3,7]=>0000000=>[8]=>[8]
[6,5,8,7,4,1,2,3]=>0000000=>[8]=>[8]
[6,5,8,7,4,2,1,3]=>0000000=>[8]=>[8]
[6,5,8,7,2,4,1,3]=>0000000=>[8]=>[8]
[6,2,8,4,5,7,1,3]=>0000000=>[8]=>[8]
[6,1,8,4,5,7,3,2]=>0000000=>[8]=>[8]
[4,2,7,3,5,8,6,1]=>0000000=>[8]=>[8]
[3,6,2,4,8,5,7,1]=>0000000=>[8]=>[8]
[3,5,1,8,4,7,6,2]=>0000000=>[8]=>[8]
[2,4,8,3,7,6,5,1]=>0000000=>[8]=>[8]
[3,6,8,5,2,4,7,1]=>0000000=>[8]=>[8]
[2,6,8,5,4,3,7,1]=>0000000=>[8]=>[8]
[3,6,8,2,5,4,7,1]=>0000000=>[8]=>[8]
[4,6,8,3,2,5,7,1]=>0000000=>[8]=>[8]
[4,6,2,8,3,5,7,1]=>0000000=>[8]=>[8]
[3,6,1,8,5,7,4,2]=>0000000=>[8]=>[8]
[3,5,8,2,7,4,6,1]=>0000000=>[8]=>[8]
[2,4,8,7,3,6,5,1]=>0000000=>[8]=>[8]
[2,5,8,7,4,3,6,1]=>0000000=>[8]=>[8]
[2,4,8,7,6,3,5,1]=>0000000=>[8]=>[8]
[4,7,2,5,6,3,1,8]=>0000001=>[7,1]=>[7,1]
[6,1,2,8,7,3,4,5]=>0000000=>[8]=>[8]
[3,2,6,1,5,8,4,7]=>0000000=>[8]=>[8]
[4,5,2,1,7,8,3,6]=>0000000=>[8]=>[8]
[2,3,7,8,5,1,6,4]=>0000000=>[8]=>[8]
[8,1,3,2,5,6,4,7]=>0000000=>[8]=>[8]
[3,2,5,8,4,7,1,6]=>0000000=>[8]=>[8]
[8,6,4,1,5,2,3,7]=>0000000=>[8]=>[8]
[2,5,8,1,3,4,7,6]=>0000000=>[8]=>[8]
[8,1,5,2,3,7,6,4]=>0000000=>[8]=>[8]
[6,4,7,2,8,3,1,5]=>0000000=>[8]=>[8]
[4,8,1,2,7,6,5,3]=>0000000=>[8]=>[8]
[3,7,4,8,5,2,6,1]=>0000000=>[8]=>[8]
[3,4,2,8,6,7,5,1]=>0000000=>[8]=>[8]
[3,6,1,5,2,7,8,4]=>0000000=>[8]=>[8]
[7,1,6,8,3,4,2,5]=>0000000=>[8]=>[8]
[6,2,8,4,7,1,3,5]=>0000000=>[8]=>[8]
[1,8,4,3,7,6,2,5]=>1000000=>[1,7]=>[7,1]
[4,3,8,7,1,2,6,5]=>0000000=>[8]=>[8]
[1,8,3,6,7,2,4,5]=>1000000=>[1,7]=>[7,1]
[1,8,4,5,7,6,2,3]=>1000000=>[1,7]=>[7,1]
[4,3,8,5,7,1,6,2]=>0000000=>[8]=>[8]
[6,3,4,8,7,2,1,5]=>0000000=>[8]=>[8]
[5,3,8,4,7,1,6,2]=>0000000=>[8]=>[8]
[5,2,8,7,1,4,6,3]=>0000000=>[8]=>[8]
[3,2,8,7,1,6,4,5]=>0000000=>[8]=>[8]
[2,7,8,3,1,6,4,5]=>0000000=>[8]=>[8]
[3,5,8,7,4,1,6,2]=>0000000=>[8]=>[8]
[7,4,6,8,3,5,1,2]=>0000000=>[8]=>[8]
[7,2,8,4,1,3,6,5]=>0000000=>[8]=>[8]
[2,7,8,1,3,6,4,5]=>0000000=>[8]=>[8]
[2,7,8,1,5,4,6,3]=>0000000=>[8]=>[8]
[2,7,8,1,4,5,6,3]=>0000000=>[8]=>[8]
[3,6,7,8,2,4,1,5]=>0000000=>[8]=>[8]
[4,5,7,8,6,3,1,2]=>0000000=>[8]=>[8]
[5,4,6,8,7,3,1,2]=>0000000=>[8]=>[8]
[4,5,8,6,7,1,3,2]=>0000000=>[8]=>[8]
[5,7,6,8,2,1,3,4]=>0000000=>[8]=>[8]
[3,7,6,8,2,4,1,5]=>0000000=>[8]=>[8]
[5,4,7,8,6,3,1,2]=>0000000=>[8]=>[8]
[3,6,7,8,2,1,4,5]=>0000000=>[8]=>[8]
[4,5,6,8,7,3,1,2]=>0000000=>[8]=>[8]
[5,3,6,2,4,1,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,3,7,1,2,6,8]=>0000001=>[7,1]=>[7,1]
[6,7,2,8,4,3,1,5]=>0000000=>[8]=>[8]
[6,7,3,2,8,4,1,5]=>0000000=>[8]=>[8]
[4,5,8,1,3,2,6,7]=>0000000=>[8]=>[8]
[5,7,2,8,3,4,6,1]=>0000000=>[8]=>[8]
[3,1,5,8,6,4,7,2]=>0000000=>[8]=>[8]
[3,6,2,8,4,7,5,1]=>0000000=>[8]=>[8]
[2,3,8,6,7,5,4,1]=>0000000=>[8]=>[8]
[3,1,5,8,6,2,4,7]=>0000000=>[8]=>[8]
[1,5,8,6,3,4,2,7]=>1000000=>[1,7]=>[7,1]
[5,3,7,8,4,2,6,1]=>0000000=>[8]=>[8]
[5,1,6,4,3,8,7,2]=>0000000=>[8]=>[8]
[4,7,6,8,3,1,5,2]=>0000000=>[8]=>[8]
[3,5,4,7,1,8,6,2]=>0000000=>[8]=>[8]
[1,8,5,4,2,3,6,7]=>1000000=>[1,7]=>[7,1]
[6,1,3,8,4,5,2,7]=>0000000=>[8]=>[8]
[4,1,5,7,6,3,2,8]=>0000001=>[7,1]=>[7,1]
[5,3,8,2,7,1,6,4]=>0000000=>[8]=>[8]
[4,5,1,7,6,3,2,8]=>0000001=>[7,1]=>[7,1]
[1,5,3,7,4,2,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,4,2,3,8,7,6]=>1000100=>[1,4,3]=>[4,3,1]
[1,5,4,2,3,8,6,7]=>1000100=>[1,4,3]=>[4,3,1]
[1,5,4,2,3,7,8,6]=>1000100=>[1,4,3]=>[4,3,1]
[3,6,5,2,4,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,6,7,2,5,1,8,3]=>0000000=>[8]=>[8]
[3,6,2,5,1,7,8,4]=>0000000=>[8]=>[8]
[8,7,3,6,2,1,5,4]=>0000000=>[8]=>[8]
[7,3,5,4,1,2,6,8]=>0000001=>[7,1]=>[7,1]
[7,1,3,8,2,5,4,6]=>0000000=>[8]=>[8]
[6,7,1,8,3,4,5,2]=>0000000=>[8]=>[8]
[8,6,7,2,5,3,1,4]=>0000000=>[8]=>[8]
[1,2,8,6,4,5,3,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,7,8,4,2,3,6]=>1000000=>[1,7]=>[7,1]
[1,2,3,7,5,4,6,8]=>1110001=>[1,1,1,4,1]=>[4,1,1,1,1]
[1,3,4,8,5,2,7,6]=>1000000=>[1,7]=>[7,1]
[4,6,5,2,1,7,8,3]=>0000000=>[8]=>[8]
[3,5,6,2,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,3,6,5,1,7,8,2]=>0000000=>[8]=>[8]
[4,6,5,3,1,7,8,2]=>0000000=>[8]=>[8]
[5,1,3,4,8,2,6,7]=>0000000=>[8]=>[8]
[5,8,1,4,2,3,6,7]=>0000000=>[8]=>[8]
[4,3,1,8,5,2,6,7]=>0000000=>[8]=>[8]
[4,5,8,2,3,1,6,7]=>0000000=>[8]=>[8]
[3,5,4,8,1,7,2,6]=>0000000=>[8]=>[8]
[5,3,6,8,1,4,7,2]=>0000000=>[8]=>[8]
[5,1,6,8,3,4,7,2]=>0000000=>[8]=>[8]
[3,5,1,8,6,4,7,2]=>0000000=>[8]=>[8]
[6,4,8,1,5,7,2,3]=>0000000=>[8]=>[8]
[4,7,2,8,3,1,6,5]=>0000000=>[8]=>[8]
[1,2,5,6,8,3,7,4]=>1100000=>[1,1,6]=>[6,1,1]
[5,1,6,8,7,2,3,4]=>0000000=>[8]=>[8]
[1,5,6,8,3,7,2,4]=>1000000=>[1,7]=>[7,1]
[5,6,8,1,2,3,7,4]=>0000000=>[8]=>[8]
[2,8,1,3,5,7,4,6]=>0000000=>[8]=>[8]
[7,4,8,1,5,2,6,3]=>0000000=>[8]=>[8]
[8,3,2,1,6,5,7,4]=>0000000=>[8]=>[8]
[4,1,5,6,8,7,2,3]=>0000000=>[8]=>[8]
[1,2,5,6,8,4,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,5,6,8,4,7,2,3]=>1000000=>[1,7]=>[7,1]
[6,8,1,4,5,7,2,3]=>0000000=>[8]=>[8]
[4,3,5,1,8,6,7,2]=>0000000=>[8]=>[8]
[1,3,5,6,8,4,7,2]=>1000000=>[1,7]=>[7,1]
[5,6,8,1,3,4,7,2]=>0000000=>[8]=>[8]
[5,6,8,2,3,4,7,1]=>0000000=>[8]=>[8]
[2,3,1,7,6,8,4,5]=>0010000=>[3,5]=>[5,3]
[2,7,4,1,3,6,8,5]=>0000000=>[8]=>[8]
[6,3,2,8,1,7,5,4]=>0000000=>[8]=>[8]
[4,5,3,1,2,8,6,7]=>0000100=>[5,3]=>[5,3]
[6,2,1,7,5,8,4,3]=>0000000=>[8]=>[8]
[1,5,7,8,6,4,2,3]=>1000000=>[1,7]=>[7,1]
[1,6,4,8,5,3,7,2]=>1000000=>[1,7]=>[7,1]
[4,2,6,7,8,1,3,5]=>0000000=>[8]=>[8]
[4,5,1,7,6,3,8,2]=>0000000=>[8]=>[8]
[8,1,5,4,2,3,6,7]=>0000000=>[8]=>[8]
[6,1,4,8,7,2,3,5]=>0000000=>[8]=>[8]
[6,1,7,5,8,2,3,4]=>0000000=>[8]=>[8]
[6,1,7,4,8,2,3,5]=>0000000=>[8]=>[8]
[3,5,8,6,2,1,4,7]=>0000000=>[8]=>[8]
[8,7,3,6,5,2,4,1]=>0000000=>[8]=>[8]
[7,3,8,6,2,1,4,5]=>0000000=>[8]=>[8]
[2,5,1,4,7,3,6,8]=>0000001=>[7,1]=>[7,1]
[3,1,6,5,7,2,4,8]=>0000001=>[7,1]=>[7,1]
[2,5,7,1,6,3,4,8]=>0000001=>[7,1]=>[7,1]
[2,5,7,1,6,3,8,4]=>0000000=>[8]=>[8]
[2,6,1,5,7,4,3,8]=>0000001=>[7,1]=>[7,1]
[3,1,6,5,2,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,6,5,1,4,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,5,6,2,8,1,7,4]=>0000000=>[8]=>[8]
[3,6,5,1,7,2,4,8]=>0000001=>[7,1]=>[7,1]
[3,6,5,2,1,4,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,5,2,7,6,1,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,5,3,1,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,4,1,6,3,7,2,8]=>0000001=>[7,1]=>[7,1]
[5,4,2,6,3,7,8,1]=>0000000=>[8]=>[8]
[3,6,5,7,1,4,2,8]=>0000001=>[7,1]=>[7,1]
[3,6,5,1,4,7,2,8]=>0000001=>[7,1]=>[7,1]
[4,3,6,5,7,1,2,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,5,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,1,6,5,3,7,8,2]=>0000000=>[8]=>[8]
[4,1,5,7,6,3,8,2]=>0000000=>[8]=>[8]
[4,2,5,7,6,1,3,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,6,1,2,5,8]=>0000001=>[7,1]=>[7,1]
[3,4,7,6,8,2,5,1]=>0000000=>[8]=>[8]
[4,2,5,7,6,3,8,1]=>0000000=>[8]=>[8]
[4,1,6,5,2,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,5,7,3,1,8]=>0000001=>[7,1]=>[7,1]
[3,6,5,7,2,1,4,8]=>0000001=>[7,1]=>[7,1]
[3,5,7,6,2,4,1,8]=>0000001=>[7,1]=>[7,1]
[5,4,2,6,3,7,1,8]=>0000001=>[7,1]=>[7,1]
[4,6,5,2,7,3,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,2,7,6,3,8,1]=>0000000=>[8]=>[8]
[4,6,5,2,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[3,5,8,2,1,4,6,7]=>0000000=>[8]=>[8]
[3,5,8,2,4,6,7,1]=>0000000=>[8]=>[8]
[5,3,8,2,1,4,6,7]=>0000000=>[8]=>[8]
[5,3,1,8,2,4,6,7]=>0000000=>[8]=>[8]
[1,5,3,8,2,4,6,7]=>1000000=>[1,7]=>[7,1]
[1,5,8,4,2,3,6,7]=>1000000=>[1,7]=>[7,1]
[5,8,2,1,4,3,6,7]=>0000000=>[8]=>[8]
[5,8,2,4,6,3,1,7]=>0000000=>[8]=>[8]
[5,8,2,4,3,6,1,7]=>0000000=>[8]=>[8]
[5,8,1,4,6,2,3,7]=>0000000=>[8]=>[8]
[1,5,8,4,6,7,2,3]=>1000000=>[1,7]=>[7,1]
[5,1,8,4,6,7,2,3]=>0000000=>[8]=>[8]
[5,8,2,4,6,3,7,1]=>0000000=>[8]=>[8]
[3,8,4,6,7,2,1,5]=>0000000=>[8]=>[8]
[3,8,4,6,7,2,5,1]=>0000000=>[8]=>[8]
[8,4,3,6,7,2,5,1]=>0000000=>[8]=>[8]
[8,4,3,6,7,2,1,5]=>0000000=>[8]=>[8]
[8,6,2,4,5,3,7,1]=>0000000=>[8]=>[8]
[8,6,4,1,5,7,2,3]=>0000000=>[8]=>[8]
[1,8,6,4,5,7,2,3]=>1000000=>[1,7]=>[7,1]
[8,1,6,4,5,2,3,7]=>0000000=>[8]=>[8]
[8,6,2,4,5,3,1,7]=>0000000=>[8]=>[8]
[1,8,6,4,2,3,5,7]=>1000000=>[1,7]=>[7,1]
[3,8,1,6,2,4,5,7]=>0000000=>[8]=>[8]
[1,3,8,6,2,4,5,7]=>1000000=>[1,7]=>[7,1]
[3,8,6,2,1,4,5,7]=>0000000=>[8]=>[8]
[3,8,6,2,4,1,5,7]=>0000000=>[8]=>[8]
[3,8,6,2,4,5,7,1]=>0000000=>[8]=>[8]
[8,3,6,2,4,5,1,7]=>0000000=>[8]=>[8]
[1,8,3,6,2,4,5,7]=>1000000=>[1,7]=>[7,1]
[8,1,3,6,2,4,5,7]=>0000000=>[8]=>[8]
[8,3,6,7,2,1,4,5]=>0000000=>[8]=>[8]
[2,5,8,4,6,1,7,3]=>0000000=>[8]=>[8]
[3,8,6,7,2,1,4,5]=>0000000=>[8]=>[8]
[3,1,8,6,7,2,4,5]=>0000000=>[8]=>[8]
[8,2,6,4,5,1,7,3]=>0000000=>[8]=>[8]
[8,4,6,1,7,2,5,3]=>0000000=>[8]=>[8]
[1,8,4,6,7,5,2,3]=>1000000=>[1,7]=>[7,1]
[8,1,4,6,7,5,2,3]=>0000000=>[8]=>[8]
[8,4,6,1,3,7,2,5]=>0000000=>[8]=>[8]
[8,1,4,6,3,7,2,5]=>0000000=>[8]=>[8]
[8,4,1,6,3,7,2,5]=>0000000=>[8]=>[8]
[8,2,4,6,1,7,5,3]=>0000000=>[8]=>[8]
[8,4,6,2,3,7,5,1]=>0000000=>[8]=>[8]
[8,4,7,2,1,3,6,5]=>0000000=>[8]=>[8]
[8,4,2,1,5,3,7,6]=>0000000=>[8]=>[8]
[8,2,1,4,7,3,6,5]=>0000000=>[8]=>[8]
[2,8,4,1,7,5,3,6]=>0000000=>[8]=>[8]
[4,7,3,1,8,6,2,5]=>0000000=>[8]=>[8]
[2,1,5,8,7,3,6,4]=>0100000=>[2,6]=>[6,2]
[4,3,1,7,8,5,2,6]=>0000000=>[8]=>[8]
[5,8,2,6,4,3,7,1]=>0000000=>[8]=>[8]
[2,8,5,3,6,4,7,1]=>0000000=>[8]=>[8]
[1,2,8,6,4,7,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[4,2,7,8,3,5,6,1]=>0000000=>[8]=>[8]
[2,8,3,7,1,4,6,5]=>0000000=>[8]=>[8]
[3,2,4,8,7,5,6,1]=>0000000=>[8]=>[8]
[1,8,6,4,7,5,3,2]=>1000000=>[1,7]=>[7,1]
[8,6,4,7,5,1,2,3]=>0000000=>[8]=>[8]
[2,7,4,6,3,8,5,1]=>0000000=>[8]=>[8]
[1,2,8,6,4,7,5,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,5,4,3,8,2,7]=>1000000=>[1,7]=>[7,1]
[6,4,2,1,5,7,3,8]=>0000001=>[7,1]=>[7,1]
[3,1,5,8,7,2,4,6]=>0000000=>[8]=>[8]
[3,2,5,7,8,4,1,6]=>0000000=>[8]=>[8]
[3,2,5,7,8,4,6,1]=>0000000=>[8]=>[8]
[5,3,7,4,2,6,8,1]=>0000000=>[8]=>[8]
[5,3,7,4,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[5,2,8,4,3,1,6,7]=>0000000=>[8]=>[8]
[5,1,8,4,3,2,6,7]=>0000000=>[8]=>[8]
[5,2,7,4,3,6,1,8]=>0000001=>[7,1]=>[7,1]
[5,2,7,4,3,6,8,1]=>0000000=>[8]=>[8]
[5,3,7,4,1,6,8,2]=>0000000=>[8]=>[8]
[3,1,5,7,8,4,2,6]=>0000000=>[8]=>[8]
[1,2,8,6,4,5,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[6,2,3,7,4,1,8,5]=>0000000=>[8]=>[8]
[5,2,7,4,1,3,8,6]=>0000000=>[8]=>[8]
[6,2,3,7,4,8,5,1]=>0000000=>[8]=>[8]
[6,2,3,7,4,8,1,5]=>0000000=>[8]=>[8]
[6,1,3,7,4,2,8,5]=>0000000=>[8]=>[8]
[6,2,3,7,4,5,1,8]=>0000001=>[7,1]=>[7,1]
[6,2,3,7,4,5,8,1]=>0000000=>[8]=>[8]
[6,1,3,7,4,5,8,2]=>0000000=>[8]=>[8]
[1,2,8,6,4,3,5,7]=>1100000=>[1,1,6]=>[6,1,1]
[6,1,3,7,4,5,2,8]=>0000001=>[7,1]=>[7,1]
[1,8,6,3,5,4,2,7]=>1000000=>[1,7]=>[7,1]
[2,5,4,1,8,6,7,3]=>0000000=>[8]=>[8]
[1,8,5,3,2,6,7,4]=>1000000=>[1,7]=>[7,1]
[5,6,8,3,4,2,7,1]=>0000000=>[8]=>[8]
[6,3,8,2,4,1,7,5]=>0000000=>[8]=>[8]
[5,1,7,8,2,4,3,6]=>0000000=>[8]=>[8]
[5,3,2,4,8,1,7,6]=>0000000=>[8]=>[8]
[5,3,2,4,8,1,6,7]=>0000000=>[8]=>[8]
[5,3,2,4,7,1,8,6]=>0000000=>[8]=>[8]
[8,4,5,3,7,1,2,6]=>0000000=>[8]=>[8]
[5,3,2,4,6,8,1,7]=>0000000=>[8]=>[8]
[7,6,4,2,8,3,1,5]=>0000000=>[8]=>[8]
[1,2,6,4,7,3,5,8]=>1100001=>[1,1,5,1]=>[5,1,1,1]
[7,5,4,1,3,6,8,2]=>0000000=>[8]=>[8]
[6,7,2,4,5,1,8,3]=>0000000=>[8]=>[8]
[5,2,7,8,3,6,1,4]=>0000000=>[8]=>[8]
[2,7,8,5,6,1,4,3]=>0000000=>[8]=>[8]
[5,2,8,3,1,4,7,6]=>0000000=>[8]=>[8]
[8,3,5,1,2,4,7,6]=>0000000=>[8]=>[8]
[8,3,6,5,4,1,2,7]=>0000000=>[8]=>[8]
[8,4,1,7,5,2,6,3]=>0000000=>[8]=>[8]
[8,4,2,7,5,3,1,6]=>0000000=>[8]=>[8]
[1,5,2,6,8,3,7,4]=>1000000=>[1,7]=>[7,1]
[7,2,8,4,1,3,5,6]=>0000000=>[8]=>[8]
[6,7,8,5,2,1,4,3]=>0000000=>[8]=>[8]
[1,6,2,7,8,4,3,5]=>1000000=>[1,7]=>[7,1]
[4,3,8,6,5,2,7,1]=>0000000=>[8]=>[8]
[2,3,8,6,5,1,7,4]=>0000000=>[8]=>[8]
[7,3,2,6,1,4,8,5]=>0000000=>[8]=>[8]
[8,4,7,1,2,5,3,6]=>0000000=>[8]=>[8]
[8,5,6,7,2,1,4,3]=>0000000=>[8]=>[8]
[8,5,6,7,3,1,4,2]=>0000000=>[8]=>[8]
[5,7,8,1,3,2,4,6]=>0000000=>[8]=>[8]
[7,8,6,1,3,5,4,2]=>0000000=>[8]=>[8]
[1,2,5,7,8,3,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[3,4,5,8,1,7,2,6]=>0000000=>[8]=>[8]
[4,3,8,6,7,5,1,2]=>0000000=>[8]=>[8]
[4,5,6,2,7,8,3,1]=>0000000=>[8]=>[8]
[4,5,6,2,7,1,8,3]=>0000000=>[8]=>[8]
[4,5,6,2,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[4,5,6,1,7,8,3,2]=>0000000=>[8]=>[8]
[4,5,1,6,7,8,3,2]=>0000000=>[8]=>[8]
[4,5,1,6,7,3,8,2]=>0000000=>[8]=>[8]
[4,5,1,6,7,3,2,8]=>0000001=>[7,1]=>[7,1]
[4,5,6,1,7,3,2,8]=>0000001=>[7,1]=>[7,1]
[1,6,4,3,8,2,7,5]=>1000000=>[1,7]=>[7,1]
[7,8,1,4,3,2,5,6]=>0000000=>[8]=>[8]
[1,7,8,4,5,3,6,2]=>1000000=>[1,7]=>[7,1]
[2,7,6,3,4,1,8,5]=>0000000=>[8]=>[8]
[8,1,7,4,3,5,6,2]=>0000000=>[8]=>[8]
[7,1,8,4,5,3,6,2]=>0000000=>[8]=>[8]
[4,3,1,8,6,5,7,2]=>0000000=>[8]=>[8]
[4,3,2,7,5,1,8,6]=>0000000=>[8]=>[8]
[5,2,3,7,4,1,8,6]=>0000000=>[8]=>[8]
[2,1,7,4,3,6,8,5]=>0100000=>[2,6]=>[6,2]
[7,1,2,4,5,6,8,3]=>0000000=>[8]=>[8]
[2,8,7,1,4,5,6,3]=>0000000=>[8]=>[8]
[8,7,1,3,4,5,6,2]=>0000000=>[8]=>[8]
[7,8,1,3,4,5,6,2]=>0000000=>[8]=>[8]
[1,7,2,5,4,6,8,3]=>1000000=>[1,7]=>[7,1]
[2,5,3,8,1,6,7,4]=>0000000=>[8]=>[8]
[1,6,4,2,5,7,8,3]=>1000000=>[1,7]=>[7,1]
[8,5,3,1,4,6,7,2]=>0000000=>[8]=>[8]
[6,5,3,4,1,7,8,2]=>0000000=>[8]=>[8]
[5,6,3,4,1,7,8,2]=>0000000=>[8]=>[8]
[2,5,3,1,4,7,8,6]=>0000100=>[5,3]=>[5,3]
[2,6,1,4,3,7,8,5]=>0000000=>[8]=>[8]
[6,8,2,3,1,5,7,4]=>0000000=>[8]=>[8]
[6,1,3,4,2,7,8,5]=>0000000=>[8]=>[8]
[4,3,1,5,2,7,8,6]=>0000100=>[5,3]=>[5,3]
[5,2,3,1,4,7,8,6]=>0000100=>[5,3]=>[5,3]
[7,2,1,3,5,6,8,4]=>0000000=>[8]=>[8]
[5,2,4,7,8,6,3,1]=>0000000=>[8]=>[8]
[8,4,2,7,6,1,5,3]=>0000000=>[8]=>[8]
[5,3,7,6,1,8,4,2]=>0000000=>[8]=>[8]
[8,6,4,1,2,5,3,7]=>0000000=>[8]=>[8]
[8,6,1,4,2,5,7,3]=>0000000=>[8]=>[8]
[8,6,4,1,2,5,7,3]=>0000000=>[8]=>[8]
[8,6,1,4,7,2,5,3]=>0000000=>[8]=>[8]
[4,2,6,3,5,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[3,4,6,8,7,1,2,5]=>0000000=>[8]=>[8]
[2,5,4,8,3,7,6,1]=>0000000=>[8]=>[8]
[1,3,6,2,5,8,7,4]=>1000000=>[1,7]=>[7,1]
[1,3,5,8,6,4,7,2]=>1000000=>[1,7]=>[7,1]
[5,8,7,1,4,6,3,2]=>0000000=>[8]=>[8]
[6,2,5,1,3,4,8,7]=>0000010=>[6,2]=>[6,2]
[2,6,5,1,3,4,8,7]=>0000010=>[6,2]=>[6,2]
[4,6,5,1,2,7,3,8]=>0000001=>[7,1]=>[7,1]
[5,6,4,1,2,7,3,8]=>0000001=>[7,1]=>[7,1]
[8,1,5,6,2,4,3,7]=>0000000=>[8]=>[8]
[6,4,5,1,2,7,3,8]=>0000001=>[7,1]=>[7,1]
[5,4,6,1,3,2,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[5,7,1,4,3,2,6,8]=>0000001=>[7,1]=>[7,1]
[2,6,4,1,3,7,5,8]=>0000001=>[7,1]=>[7,1]
[6,3,2,5,7,4,8,1]=>0000000=>[8]=>[8]
[4,5,2,7,6,3,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,2,1,7,6,3,8]=>0000001=>[7,1]=>[7,1]
[5,4,1,6,7,2,8,3]=>0000000=>[8]=>[8]
[4,1,6,5,2,7,8,3]=>0000000=>[8]=>[8]
[5,4,6,2,7,8,3,1]=>0000000=>[8]=>[8]
[3,5,2,6,7,8,4,1]=>0000000=>[8]=>[8]
[6,3,2,5,1,7,8,4]=>0000000=>[8]=>[8]
[4,6,3,7,8,2,1,5]=>0000000=>[8]=>[8]
[5,6,7,1,8,4,2,3]=>0000000=>[8]=>[8]
[5,6,7,2,8,4,1,3]=>0000000=>[8]=>[8]
[2,8,4,7,6,3,1,5]=>0000000=>[8]=>[8]
[6,4,8,7,2,1,5,3]=>0000000=>[8]=>[8]
[2,5,1,8,4,7,6,3]=>0000000=>[8]=>[8]
[2,4,5,8,1,7,6,3]=>0000000=>[8]=>[8]
[2,6,8,1,4,3,7,5]=>0000000=>[8]=>[8]
[2,6,1,5,8,7,3,4]=>0000000=>[8]=>[8]
[7,5,8,1,6,2,3,4]=>0000000=>[8]=>[8]
[7,6,1,3,5,2,4,8]=>0000001=>[7,1]=>[7,1]
[6,2,4,5,3,8,1,7]=>0000000=>[8]=>[8]
[1,2,5,4,7,8,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[3,6,2,4,7,8,5,1]=>0000000=>[8]=>[8]
[1,3,5,4,8,7,2,6]=>1000000=>[1,7]=>[7,1]
[1,6,2,4,8,3,7,5]=>1000000=>[1,7]=>[7,1]
[7,1,4,2,3,8,6,5]=>0000000=>[8]=>[8]
[1,7,3,2,4,6,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,7,3,2,6,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[5,1,3,7,2,6,4,8]=>0000001=>[7,1]=>[7,1]
[1,7,8,5,4,2,6,3]=>1000000=>[1,7]=>[7,1]
[8,1,7,5,4,2,6,3]=>0000000=>[8]=>[8]
[1,6,5,2,7,4,8,3]=>1000000=>[1,7]=>[7,1]
[1,5,4,2,8,6,7,3]=>1000000=>[1,7]=>[7,1]
[1,6,3,5,2,7,8,4]=>1000000=>[1,7]=>[7,1]
[3,1,2,6,8,7,5,4]=>0010000=>[3,5]=>[5,3]
[6,4,8,2,5,7,1,3]=>0000000=>[8]=>[8]
[6,8,4,2,7,1,3,5]=>0000000=>[8]=>[8]
[6,8,2,4,1,7,3,5]=>0000000=>[8]=>[8]
[2,5,4,7,6,1,3,8]=>0000001=>[7,1]=>[7,1]
[5,2,3,7,6,1,4,8]=>0000001=>[7,1]=>[7,1]
[4,2,3,7,6,1,5,8]=>0000001=>[7,1]=>[7,1]
[4,2,7,3,5,1,6,8]=>0000001=>[7,1]=>[7,1]
[5,6,2,3,8,4,7,1]=>0000000=>[8]=>[8]
[5,6,2,3,1,7,8,4]=>0000000=>[8]=>[8]
[5,7,2,3,4,1,6,8]=>0000001=>[7,1]=>[7,1]
[6,2,7,3,5,1,4,8]=>0000001=>[7,1]=>[7,1]
[7,2,6,3,5,1,4,8]=>0000001=>[7,1]=>[7,1]
[6,5,2,3,1,7,8,4]=>0000000=>[8]=>[8]
[6,5,2,3,8,4,7,1]=>0000000=>[8]=>[8]
[7,5,2,1,4,6,8,3]=>0000000=>[8]=>[8]
[8,5,2,1,4,6,7,3]=>0000000=>[8]=>[8]
[8,5,2,3,1,6,4,7]=>0000000=>[8]=>[8]
[8,6,2,3,1,5,4,7]=>0000000=>[8]=>[8]
[8,2,6,3,1,7,4,5]=>0000000=>[8]=>[8]
[1,6,3,4,2,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,5,2,7,3,4,6,1]=>0000000=>[8]=>[8]
[1,7,2,4,5,6,8,3]=>1000000=>[1,7]=>[7,1]
[1,8,3,2,5,6,4,7]=>1000000=>[1,7]=>[7,1]
[8,6,1,3,4,5,7,2]=>0000000=>[8]=>[8]
[6,8,1,3,4,5,7,2]=>0000000=>[8]=>[8]
[7,2,8,1,4,6,3,5]=>0000000=>[8]=>[8]
[2,7,8,1,5,6,3,4]=>0000000=>[8]=>[8]
[6,8,2,3,1,5,4,7]=>0000000=>[8]=>[8]
[5,8,2,3,1,6,4,7]=>0000000=>[8]=>[8]
[5,7,2,1,4,6,8,3]=>0000000=>[8]=>[8]
[4,2,3,8,1,7,5,6]=>0000000=>[8]=>[8]
[5,2,3,8,1,7,4,6]=>0000000=>[8]=>[8]
[2,5,4,8,1,7,3,6]=>0000000=>[8]=>[8]
[2,5,4,1,3,8,6,7]=>0000100=>[5,3]=>[5,3]
[4,2,1,5,3,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[5,1,3,2,6,7,8,4]=>0000000=>[8]=>[8]
[5,1,3,4,2,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[6,1,3,4,2,7,5,8]=>0000001=>[7,1]=>[7,1]
[7,2,1,3,5,8,4,6]=>0000000=>[8]=>[8]
[6,1,2,4,5,7,8,3]=>0000000=>[8]=>[8]
[6,8,7,2,3,4,5,1]=>0000000=>[8]=>[8]
[2,8,7,5,1,3,4,6]=>0000000=>[8]=>[8]
[8,3,7,5,1,4,2,6]=>0000000=>[8]=>[8]
[8,3,7,1,6,4,2,5]=>0000000=>[8]=>[8]
[4,2,6,5,3,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,3,7,5,1,6,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,2,8,6,7,4,1]=>0000000=>[8]=>[8]
[5,3,7,4,2,8,6,1]=>0000000=>[8]=>[8]
[5,6,2,8,7,1,4,3]=>0000000=>[8]=>[8]
[4,3,7,5,2,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,6,3,5,2,7,8,1]=>0000000=>[8]=>[8]
[4,1,6,3,5,7,2,8]=>0000001=>[7,1]=>[7,1]
[3,1,5,7,4,6,8,2]=>0000000=>[8]=>[8]
[7,2,5,8,6,1,4,3]=>0000000=>[8]=>[8]
[7,8,4,5,1,3,6,2]=>0000000=>[8]=>[8]
[4,3,6,1,5,7,8,2]=>0000000=>[8]=>[8]
[6,4,7,1,3,5,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,4,1,2,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,3,1,4,6,7,8,2]=>0000000=>[8]=>[8]
[6,2,1,4,7,5,8,3]=>0000000=>[8]=>[8]
[4,6,7,1,3,5,8,2]=>0000000=>[8]=>[8]
[5,6,1,3,4,7,2,8]=>0000001=>[7,1]=>[7,1]
[2,5,3,7,8,4,6,1]=>0000000=>[8]=>[8]
[4,5,7,2,3,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,6,2,1,3,7,8,5]=>0000000=>[8]=>[8]
[3,6,2,4,1,7,5,8]=>0000001=>[7,1]=>[7,1]
[3,2,6,7,4,8,5,1]=>0000000=>[8]=>[8]
[7,3,4,8,5,2,1,6]=>0000000=>[8]=>[8]
[7,1,8,3,4,6,2,5]=>0000000=>[8]=>[8]
[6,3,2,7,5,8,4,1]=>0000000=>[8]=>[8]
[6,2,7,1,4,5,3,8]=>0000001=>[7,1]=>[7,1]
[4,2,6,1,5,7,3,8]=>0000001=>[7,1]=>[7,1]
[2,7,5,8,6,3,4,1]=>0000000=>[8]=>[8]
[2,5,4,1,3,6,7,8]=>0000111=>[5,1,1,1]=>[5,1,1,1]
[5,4,1,2,6,7,3,8]=>0000001=>[7,1]=>[7,1]
[6,5,2,7,4,1,3,8]=>0000001=>[7,1]=>[7,1]
[6,5,7,3,1,4,2,8]=>0000001=>[7,1]=>[7,1]
[6,7,4,3,1,5,8,2]=>0000000=>[8]=>[8]
[6,4,1,2,7,8,3,5]=>0000000=>[8]=>[8]
[5,1,4,7,2,6,8,3]=>0000000=>[8]=>[8]
[5,2,6,8,3,7,1,4]=>0000000=>[8]=>[8]
[1,7,2,4,3,5,8,6]=>1000000=>[1,7]=>[7,1]
[8,4,1,5,2,6,7,3]=>0000000=>[8]=>[8]
[7,4,1,3,6,5,2,8]=>0000001=>[7,1]=>[7,1]
[5,7,2,8,1,3,6,4]=>0000000=>[8]=>[8]
[5,4,1,2,6,3,8,7]=>0000010=>[6,2]=>[6,2]
[2,7,8,4,1,3,6,5]=>0000000=>[8]=>[8]
[3,6,5,1,4,8,2,7]=>0000000=>[8]=>[8]
[3,6,4,1,2,7,8,5]=>0000000=>[8]=>[8]
[4,1,7,3,8,6,2,5]=>0000000=>[8]=>[8]
[4,8,2,7,6,5,1,3]=>0000000=>[8]=>[8]
[5,4,2,8,7,6,1,3]=>0000000=>[8]=>[8]
[7,4,2,8,6,5,1,3]=>0000000=>[8]=>[8]
[6,5,8,2,7,4,1,3]=>0000000=>[8]=>[8]
[8,6,5,2,7,1,4,3]=>0000000=>[8]=>[8]
[7,8,5,2,1,6,4,3]=>0000000=>[8]=>[8]
[6,8,5,2,7,1,4,3]=>0000000=>[8]=>[8]
[6,5,8,2,7,1,4,3]=>0000000=>[8]=>[8]
[7,5,8,2,1,6,4,3]=>0000000=>[8]=>[8]
[3,2,1,6,5,8,4,7]=>0010000=>[3,5]=>[5,3]
[6,3,1,4,5,8,2,7]=>0000000=>[8]=>[8]
[3,4,8,5,2,1,7,6]=>0000000=>[8]=>[8]
[4,8,7,1,3,2,6,5]=>0000000=>[8]=>[8]
[3,5,1,4,2,8,7,6]=>0000100=>[5,3]=>[5,3]
[5,8,7,4,6,1,3,2]=>0000000=>[8]=>[8]
[5,1,8,7,4,6,3,2]=>0000000=>[8]=>[8]
[3,4,1,8,7,6,2,5]=>0000000=>[8]=>[8]
[3,5,2,8,6,4,7,1]=>0000000=>[8]=>[8]
[2,8,7,5,4,1,6,3]=>0000000=>[8]=>[8]
[4,2,5,8,6,7,1,3]=>0000000=>[8]=>[8]
[8,1,5,7,4,2,6,3]=>0000000=>[8]=>[8]
[8,4,5,3,1,6,7,2]=>0000000=>[8]=>[8]
[5,8,7,3,4,1,6,2]=>0000000=>[8]=>[8]
[2,4,5,8,1,3,7,6]=>0000000=>[8]=>[8]
[7,1,4,3,8,5,6,2]=>0000000=>[8]=>[8]
[6,3,2,5,8,4,1,7]=>0000000=>[8]=>[8]
[8,4,1,3,7,6,5,2]=>0000000=>[8]=>[8]
[5,1,6,4,7,8,2,3]=>0000000=>[8]=>[8]
[2,8,3,5,6,1,4,7]=>0000000=>[8]=>[8]
[1,3,6,4,2,7,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[3,2,8,5,6,1,4,7]=>0000000=>[8]=>[8]
[7,2,5,8,1,4,6,3]=>0000000=>[8]=>[8]
[4,7,5,8,1,2,6,3]=>0000000=>[8]=>[8]
[5,4,7,8,2,1,3,6]=>0000000=>[8]=>[8]
[4,7,5,8,1,2,3,6]=>0000000=>[8]=>[8]
[3,4,7,5,2,8,1,6]=>0000000=>[8]=>[8]
[4,3,2,5,7,8,1,6]=>0000000=>[8]=>[8]
[5,4,8,6,2,3,1,7]=>0000000=>[8]=>[8]
[2,4,7,5,8,3,1,6]=>0000000=>[8]=>[8]
[7,2,5,8,1,6,3,4]=>0000000=>[8]=>[8]
[3,7,8,4,2,1,6,5]=>0000000=>[8]=>[8]
[1,5,4,8,7,6,2,3]=>1000000=>[1,7]=>[7,1]
[1,3,6,8,2,4,7,5]=>1000000=>[1,7]=>[7,1]
[4,7,2,8,5,1,6,3]=>0000000=>[8]=>[8]
[4,7,5,2,6,3,8,1]=>0000000=>[8]=>[8]
[3,5,6,2,8,1,4,7]=>0000000=>[8]=>[8]
[1,6,8,2,5,3,4,7]=>1000000=>[1,7]=>[7,1]
[8,6,3,5,2,1,4,7]=>0000000=>[8]=>[8]
[8,7,3,2,6,5,1,4]=>0000000=>[8]=>[8]
[5,2,8,7,6,4,1,3]=>0000000=>[8]=>[8]
[4,1,3,8,5,6,2,7]=>0000000=>[8]=>[8]
[3,2,4,8,5,7,1,6]=>0000000=>[8]=>[8]
[4,5,2,8,3,7,1,6]=>0000000=>[8]=>[8]
[7,8,5,1,6,4,3,2]=>0000000=>[8]=>[8]
[8,7,5,1,6,4,3,2]=>0000000=>[8]=>[8]
[4,5,8,3,1,2,7,6]=>0000000=>[8]=>[8]
[7,1,6,8,5,4,3,2]=>0000000=>[8]=>[8]
[5,8,1,3,4,2,7,6]=>0000000=>[8]=>[8]
[1,4,6,3,7,5,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,2,8,7,4,6,5]=>1010000=>[1,2,5]=>[5,2,1]
[7,5,2,8,3,1,6,4]=>0000000=>[8]=>[8]
[6,7,1,3,2,5,8,4]=>0000000=>[8]=>[8]
[6,3,5,4,8,1,2,7]=>0000000=>[8]=>[8]
[6,2,5,4,1,7,8,3]=>0000000=>[8]=>[8]
[4,1,5,6,3,8,7,2]=>0000000=>[8]=>[8]
[8,1,5,4,6,7,3,2]=>0000000=>[8]=>[8]
[2,4,5,8,3,7,6,1]=>0000000=>[8]=>[8]
[6,1,3,5,4,8,2,7]=>0000000=>[8]=>[8]
[1,3,8,7,2,5,6,4]=>1000000=>[1,7]=>[7,1]
[2,5,4,1,8,3,7,6]=>0000000=>[8]=>[8]
[6,1,5,4,3,8,2,7]=>0000000=>[8]=>[8]
[1,4,8,3,2,7,6,5]=>1000000=>[1,7]=>[7,1]
[5,1,4,8,3,7,6,2]=>0000000=>[8]=>[8]
[3,5,8,2,1,4,7,6]=>0000000=>[8]=>[8]
[8,4,1,2,7,6,5,3]=>0000000=>[8]=>[8]
[4,8,3,2,7,6,5,1]=>0000000=>[8]=>[8]
[2,4,8,1,7,6,5,3]=>0000000=>[8]=>[8]
[8,7,3,2,1,4,6,5]=>0000000=>[8]=>[8]
[1,4,8,5,2,3,6,7]=>1000000=>[1,7]=>[7,1]
[6,1,4,2,8,7,3,5]=>0000000=>[8]=>[8]
[1,5,8,7,2,4,3,6]=>1000000=>[1,7]=>[7,1]
[8,7,1,3,2,5,4,6]=>0000000=>[8]=>[8]
[6,7,4,2,8,1,3,5]=>0000000=>[8]=>[8]
[8,5,1,4,7,6,3,2]=>0000000=>[8]=>[8]
[8,1,3,7,2,4,6,5]=>0000000=>[8]=>[8]
[5,3,1,6,4,8,2,7]=>0000000=>[8]=>[8]
[2,5,6,7,1,4,8,3]=>0000000=>[8]=>[8]
[1,4,2,7,5,8,3,6]=>1000000=>[1,7]=>[7,1]
[5,8,1,2,7,4,3,6]=>0000000=>[8]=>[8]
[4,6,3,7,8,1,5,2]=>0000000=>[8]=>[8]
[2,4,7,3,6,8,1,5]=>0000000=>[8]=>[8]
[2,7,3,1,8,5,4,6]=>0000000=>[8]=>[8]
[2,3,1,6,8,7,4,5]=>0010000=>[3,5]=>[5,3]
[6,4,8,2,1,7,3,5]=>0000000=>[8]=>[8]
[8,5,1,2,7,4,3,6]=>0000000=>[8]=>[8]
[1,3,7,6,8,4,2,5]=>1000000=>[1,7]=>[7,1]
[2,1,5,7,4,6,8,3]=>0100000=>[2,6]=>[6,2]
[2,3,5,7,8,1,6,4]=>0000000=>[8]=>[8]
[1,6,4,2,3,5,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[1,5,7,4,2,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[8,1,7,2,4,6,3,5]=>0000000=>[8]=>[8]
[2,4,7,8,3,5,1,6]=>0000000=>[8]=>[8]
[1,3,6,2,5,8,4,7]=>1000000=>[1,7]=>[7,1]
[1,5,3,6,8,2,4,7]=>1000000=>[1,7]=>[7,1]
[2,8,5,1,4,3,7,6]=>0000000=>[8]=>[8]
[1,8,6,2,4,3,7,5]=>1000000=>[1,7]=>[7,1]
[4,1,6,5,2,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[4,1,3,6,7,2,5,8]=>0000001=>[7,1]=>[7,1]
[2,7,5,8,1,3,6,4]=>0000000=>[8]=>[8]
[5,1,6,7,3,2,4,8]=>0000001=>[7,1]=>[7,1]
[7,4,1,2,3,6,8,5]=>0000000=>[8]=>[8]
[9,10,6,4,2,1,3,5,8,7]=>000000000=>[10]=>[10]
[10,7,8,4,2,1,3,6,5,9]=>000000000=>[10]=>[10]
[9,7,10,4,2,1,3,6,8,5]=>000000000=>[10]=>[10]
[8,9,10,4,2,1,3,7,6,5]=>000000000=>[10]=>[10]
[10,8,5,6,2,1,4,3,7,9]=>000000000=>[10]=>[10]
[9,10,5,6,2,1,4,3,8,7]=>000000000=>[10]=>[10]
[10,7,5,8,2,1,4,6,3,9]=>000000000=>[10]=>[10]
[9,7,5,10,2,1,4,6,8,3]=>000000000=>[10]=>[10]
[8,9,5,10,2,1,4,7,6,3]=>000000000=>[10]=>[10]
[10,6,7,8,2,1,5,4,3,9]=>000000000=>[10]=>[10]
[9,6,7,10,2,1,5,4,8,3]=>000000000=>[10]=>[10]
[8,6,9,10,2,1,5,7,4,3]=>000000000=>[10]=>[10]
[7,8,9,10,2,1,6,5,4,3]=>000000000=>[10]=>[10]
[10,8,6,3,4,2,1,5,7,9]=>000000000=>[10]=>[10]
[9,10,6,3,4,2,1,5,8,7]=>000000000=>[10]=>[10]
[10,7,8,3,4,2,1,6,5,9]=>000000000=>[10]=>[10]
[9,7,10,3,4,2,1,6,8,5]=>000000000=>[10]=>[10]
[8,9,10,3,4,2,1,7,6,5]=>000000000=>[10]=>[10]
[10,8,5,3,6,2,4,1,7,9]=>000000000=>[10]=>[10]
[9,10,5,3,6,2,4,1,8,7]=>000000000=>[10]=>[10]
[10,7,5,3,8,2,4,6,1,9]=>000000000=>[10]=>[10]
[9,7,5,3,10,2,4,6,8,1]=>000000000=>[10]=>[10]
[8,9,5,3,10,2,4,7,6,1]=>000000000=>[10]=>[10]
[10,6,7,3,8,2,5,4,1,9]=>000000000=>[10]=>[10]
[9,6,7,3,10,2,5,4,8,1]=>000000000=>[10]=>[10]
[8,6,9,3,10,2,5,7,4,1]=>000000000=>[10]=>[10]
[7,8,9,3,10,2,6,5,4,1]=>000000000=>[10]=>[10]
[10,8,4,5,6,3,2,1,7,9]=>000000000=>[10]=>[10]
[9,10,4,5,6,3,2,1,8,7]=>000000000=>[10]=>[10]
[10,7,4,5,8,3,2,6,1,9]=>000000000=>[10]=>[10]
[9,7,4,5,10,3,2,6,8,1]=>000000000=>[10]=>[10]
[8,9,4,5,10,3,2,7,6,1]=>000000000=>[10]=>[10]
[10,6,4,7,8,3,5,2,1,9]=>000000000=>[10]=>[10]
[9,6,4,7,10,3,5,2,8,1]=>000000000=>[10]=>[10]
[8,6,4,9,10,3,5,7,2,1]=>000000000=>[10]=>[10]
[7,8,4,9,10,3,6,5,2,1]=>000000000=>[10]=>[10]
[10,5,6,7,8,4,3,2,1,9]=>000000000=>[10]=>[10]
[9,5,6,7,10,4,3,2,8,1]=>000000000=>[10]=>[10]
[8,5,6,9,10,4,3,7,2,1]=>000000000=>[10]=>[10]
[7,5,8,9,10,4,6,3,2,1]=>000000000=>[10]=>[10]
[2,7,4,1,5,8,3,6]=>0000000=>[8]=>[8]
[6,1,7,3,4,2,5,8]=>0000001=>[7,1]=>[7,1]
[2,6,4,7,8,5,3,1]=>0000000=>[8]=>[8]
[6,8,4,3,1,5,2,7]=>0000000=>[8]=>[8]
[3,2,4,8,6,1,7,5]=>0000000=>[8]=>[8]
[2,1,3,8,4,5,7,6]=>0110000=>[2,1,5]=>[5,2,1]
[2,1,3,7,8,4,6,5]=>0110000=>[2,1,5]=>[5,2,1]
[2,1,3,8,4,7,6,5]=>0110000=>[2,1,5]=>[5,2,1]
[3,1,2,8,4,5,7,6]=>0010000=>[3,5]=>[5,3]
[1,2,8,7,5,4,6,3]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,6,8,2,7,5,4]=>1000000=>[1,7]=>[7,1]
[3,2,6,5,1,8,4,7]=>0000000=>[8]=>[8]
[2,8,3,7,6,1,5,4]=>0000000=>[8]=>[8]
[5,4,2,6,8,7,3,1]=>0000000=>[8]=>[8]
[3,7,2,5,8,6,4,1]=>0000000=>[8]=>[8]
[5,4,3,7,2,8,6,1]=>0000000=>[8]=>[8]
[4,6,5,3,8,1,7,2]=>0000000=>[8]=>[8]
[2,4,8,7,6,1,5,3]=>0000000=>[8]=>[8]
[4,8,5,2,7,6,3,1]=>0000000=>[8]=>[8]
[2,8,6,5,7,1,3,4]=>0000000=>[8]=>[8]
[1,8,7,4,5,2,3,6]=>1000000=>[1,7]=>[7,1]
[5,8,1,7,6,2,3,4]=>0000000=>[8]=>[8]
[1,7,6,2,4,3,8,5]=>1000000=>[1,7]=>[7,1]
[5,6,8,7,1,3,2,4]=>0000000=>[8]=>[8]
[7,1,6,8,2,5,4,3]=>0000000=>[8]=>[8]
[6,4,2,7,1,5,8,3]=>0000000=>[8]=>[8]
[5,3,6,7,4,2,8,1]=>0000000=>[8]=>[8]
[2,6,3,7,5,4,8,1]=>0000000=>[8]=>[8]
[1,7,3,2,4,8,6,5]=>1000000=>[1,7]=>[7,1]
[6,4,1,3,8,7,5,2]=>0000000=>[8]=>[8]
[4,3,1,8,2,6,7,5]=>0000000=>[8]=>[8]
[4,8,1,3,2,5,7,6]=>0000000=>[8]=>[8]
[7,2,6,5,8,3,4,1]=>0000000=>[8]=>[8]
[1,7,5,3,8,6,2,4]=>1000000=>[1,7]=>[7,1]
[2,5,3,8,1,4,7,6]=>0000000=>[8]=>[8]
[4,2,5,8,1,3,7,6]=>0000000=>[8]=>[8]
[8,1,2,4,3,5,7,6]=>0000000=>[8]=>[8]
[2,4,3,8,1,5,7,6]=>0000000=>[8]=>[8]
[7,5,2,3,8,4,6,1]=>0000000=>[8]=>[8]
[2,7,5,1,4,8,3,6]=>0000000=>[8]=>[8]
[3,1,7,4,8,6,5,2]=>0000000=>[8]=>[8]
[6,4,5,3,2,8,7,1]=>0000000=>[8]=>[8]
[2,7,3,8,5,1,6,4]=>0000000=>[8]=>[8]
[8,7,3,2,5,6,4,1]=>0000000=>[8]=>[8]
[1,5,8,2,6,4,3,7]=>1000000=>[1,7]=>[7,1]
[3,1,8,2,6,5,4,7]=>0000000=>[8]=>[8]
[7,6,2,8,1,4,5,3]=>0000000=>[8]=>[8]
[8,4,2,3,1,5,7,6]=>0000000=>[8]=>[8]
[8,2,3,4,1,5,7,6]=>0000000=>[8]=>[8]
[2,5,6,3,8,1,4,7]=>0000000=>[8]=>[8]
[7,3,5,6,1,8,4,2]=>0000000=>[8]=>[8]
[7,4,5,6,8,1,3,2]=>0000000=>[8]=>[8]
[7,5,1,8,4,6,3,2]=>0000000=>[8]=>[8]
[2,8,1,7,4,5,3,6]=>0000000=>[8]=>[8]
[6,1,5,3,8,4,7,2]=>0000000=>[8]=>[8]
[1,6,5,3,8,4,7,2]=>1000000=>[1,7]=>[7,1]
[7,6,2,3,5,4,8,1]=>0000000=>[8]=>[8]
[7,6,2,3,5,1,4,8]=>0000001=>[7,1]=>[7,1]
[6,1,5,2,3,4,8,7]=>0000010=>[6,2]=>[6,2]
[6,2,5,3,4,8,1,7]=>0000000=>[8]=>[8]
[6,2,5,3,4,8,7,1]=>0000000=>[8]=>[8]
[2,6,5,3,4,8,7,1]=>0000000=>[8]=>[8]
[2,6,5,3,4,8,1,7]=>0000000=>[8]=>[8]
[2,5,1,4,8,3,7,6]=>0000000=>[8]=>[8]
[1,2,5,4,8,3,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[5,3,4,8,1,7,2,6]=>0000000=>[8]=>[8]
[5,1,3,4,8,7,2,6]=>0000000=>[8]=>[8]
[1,5,3,4,8,7,2,6]=>1000000=>[1,7]=>[7,1]
[5,1,3,8,4,7,6,2]=>0000000=>[8]=>[8]
[5,3,8,1,4,7,6,2]=>0000000=>[8]=>[8]
[4,3,5,8,1,7,6,2]=>0000000=>[8]=>[8]
[3,6,5,4,8,1,2,7]=>0000000=>[8]=>[8]
[3,6,5,4,8,2,7,1]=>0000000=>[8]=>[8]
[4,3,5,8,2,1,7,6]=>0000000=>[8]=>[8]
[3,5,2,4,8,7,6,1]=>0000000=>[8]=>[8]
[2,3,6,5,8,4,1,7]=>0000000=>[8]=>[8]
[5,2,3,8,7,4,1,6]=>0000000=>[8]=>[8]
[2,3,1,7,4,8,6,5]=>0010000=>[3,5]=>[5,3]
[7,4,1,3,6,2,5,8]=>0000001=>[7,1]=>[7,1]
[7,2,5,8,1,3,6,4]=>0000000=>[8]=>[8]
[1,2,6,5,3,4,7,8]=>1100011=>[1,1,4,1,1]=>[4,1,1,1,1]
[1,4,6,5,7,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[2,4,6,5,7,1,8,3]=>0000000=>[8]=>[8]
[3,5,2,1,7,8,6,4]=>0000000=>[8]=>[8]
[7,1,6,3,2,4,8,5]=>0000000=>[8]=>[8]
[6,4,8,1,2,3,7,5]=>0000000=>[8]=>[8]
[4,3,5,1,7,8,6,2]=>0000000=>[8]=>[8]
[4,6,7,2,3,8,5,1]=>0000000=>[8]=>[8]
[2,3,5,8,7,4,1,6]=>0000000=>[8]=>[8]
[2,3,5,8,7,4,6,1]=>0000000=>[8]=>[8]
[1,7,4,5,8,3,6,2]=>1000000=>[1,7]=>[7,1]
[7,1,5,2,4,8,3,6]=>0000000=>[8]=>[8]
[8,1,5,2,4,7,3,6]=>0000000=>[8]=>[8]
[7,5,8,1,4,2,3,6]=>0000000=>[8]=>[8]
[1,3,4,8,5,6,2,7]=>1000000=>[1,7]=>[7,1]
[4,8,3,6,1,7,2,5]=>0000000=>[8]=>[8]
[4,6,3,1,2,5,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[7,4,6,8,3,1,2,5]=>0000000=>[8]=>[8]
[8,5,4,7,3,1,2,6]=>0000000=>[8]=>[8]
[2,5,6,4,8,1,3,7]=>0000000=>[8]=>[8]
[5,4,1,6,2,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,5,6,4,2,3,7,8]=>1000011=>[1,5,1,1]=>[5,1,1,1]
[2,5,1,4,6,3,8,7]=>0000010=>[6,2]=>[6,2]
[8,1,4,3,7,5,6,2]=>0000000=>[8]=>[8]
[8,3,7,6,2,4,5,1]=>0000000=>[8]=>[8]
[8,1,2,7,6,4,5,3]=>0000000=>[8]=>[8]
[1,7,3,8,6,2,5,4]=>1000000=>[1,7]=>[7,1]
[1,2,4,6,8,3,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,5,6,4,8,2,7]=>1000000=>[1,7]=>[7,1]
[6,3,5,7,1,4,2,8]=>0000001=>[7,1]=>[7,1]
[5,4,8,6,3,7,1,2]=>0000000=>[8]=>[8]
[3,4,8,5,6,1,2,7]=>0000000=>[8]=>[8]
[1,7,6,2,5,4,8,3]=>1000000=>[1,7]=>[7,1]
[3,7,2,1,5,6,8,4]=>0000000=>[8]=>[8]
[8,1,6,4,3,5,2,7]=>0000000=>[8]=>[8]
[4,6,8,5,1,3,7,2]=>0000000=>[8]=>[8]
[4,3,1,8,5,7,2,6]=>0000000=>[8]=>[8]
[4,8,3,6,1,5,2,7]=>0000000=>[8]=>[8]
[8,3,2,4,7,1,6,5]=>0000000=>[8]=>[8]
[7,3,2,4,8,1,6,5]=>0000000=>[8]=>[8]
[8,3,2,4,6,1,7,5]=>0000000=>[8]=>[8]
[8,3,2,4,5,7,1,6]=>0000000=>[8]=>[8]
[8,3,6,2,4,1,7,5]=>0000000=>[8]=>[8]
[7,4,6,2,1,3,8,5]=>0000000=>[8]=>[8]
[3,2,4,5,7,8,1,6]=>0000000=>[8]=>[8]
[3,6,7,2,4,1,8,5]=>0000000=>[8]=>[8]
[7,3,5,2,8,1,4,6]=>0000000=>[8]=>[8]
[2,6,8,4,5,1,7,3]=>0000000=>[8]=>[8]
[1,5,8,7,4,2,3,6]=>1000000=>[1,7]=>[7,1]
[1,5,2,7,6,4,8,3]=>1000000=>[1,7]=>[7,1]
[1,4,6,8,7,2,5,3]=>1000000=>[1,7]=>[7,1]
[1,3,6,8,7,2,5,4]=>1000000=>[1,7]=>[7,1]
[1,4,3,6,8,7,2,5]=>1000000=>[1,7]=>[7,1]
[1,6,2,7,5,3,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,2,5,4,3,8,6]=>1000000=>[1,7]=>[7,1]
[1,6,3,7,2,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,2,6,8,5,4,7]=>1010000=>[1,2,5]=>[5,2,1]
[1,6,3,2,7,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,8,6,2,7,4,3]=>1000000=>[1,7]=>[7,1]
[1,3,7,2,6,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,7,5,8,6,2,4]=>1000000=>[1,7]=>[7,1]
[1,7,3,2,8,5,6,4]=>1000000=>[1,7]=>[7,1]
[1,6,5,2,4,8,3,7]=>1000000=>[1,7]=>[7,1]
[1,4,7,6,2,3,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,7,3,8,4,2,5,6]=>1000000=>[1,7]=>[7,1]
[1,6,2,4,7,5,8,3]=>1000000=>[1,7]=>[7,1]
[1,6,2,7,4,3,8,5]=>1000000=>[1,7]=>[7,1]
[1,5,8,2,3,6,4,7]=>1000000=>[1,7]=>[7,1]
[5,4,7,8,1,6,3,2]=>0000000=>[8]=>[8]
[1,7,8,4,3,6,5,2]=>1000000=>[1,7]=>[7,1]
[1,7,8,3,6,5,4,2]=>1000000=>[1,7]=>[7,1]
[1,8,4,2,3,7,5,6]=>1000000=>[1,7]=>[7,1]
[6,5,1,3,8,4,2,7]=>0000000=>[8]=>[8]
[6,1,4,2,7,8,3,5]=>0000000=>[8]=>[8]
[6,5,1,3,7,8,4,2]=>0000000=>[8]=>[8]
[5,6,8,2,4,7,1,3]=>0000000=>[8]=>[8]
[5,1,3,2,6,8,4,7]=>0000000=>[8]=>[8]
[1,5,7,3,6,4,2,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,6,3,5,7,4,8,2]=>1000000=>[1,7]=>[7,1]
[1,7,2,4,8,3,5,6]=>1000000=>[1,7]=>[7,1]
[1,6,7,2,4,8,3,5]=>1000000=>[1,7]=>[7,1]
[1,6,7,8,2,4,3,5]=>1000000=>[1,7]=>[7,1]
[3,1,6,7,8,4,2,5]=>0000000=>[8]=>[8]
[3,1,6,7,8,4,5,2]=>0000000=>[8]=>[8]
[1,6,7,8,2,4,5,3]=>1000000=>[1,7]=>[7,1]
[4,2,7,6,8,5,1,3]=>0000000=>[8]=>[8]
[5,3,4,1,7,8,6,2]=>0000000=>[8]=>[8]
[3,7,5,6,1,8,4,2]=>0000000=>[8]=>[8]
[2,4,7,5,8,3,6,1]=>0000000=>[8]=>[8]
[6,8,7,4,2,5,1,3]=>0000000=>[8]=>[8]
[7,6,3,1,2,8,5,4]=>0000000=>[8]=>[8]
[3,1,8,6,4,7,2,5]=>0000000=>[8]=>[8]
[6,2,7,8,3,4,5,1]=>0000000=>[8]=>[8]
[8,1,3,5,6,4,7,2]=>0000000=>[8]=>[8]
[2,3,7,5,8,4,6,1]=>0000000=>[8]=>[8]
[8,1,7,4,2,5,3,6]=>0000000=>[8]=>[8]
[5,2,6,4,1,3,8,7]=>0000010=>[6,2]=>[6,2]
[2,1,8,5,4,3,7,6]=>0100000=>[2,6]=>[6,2]
[5,2,4,7,8,1,3,6]=>0000000=>[8]=>[8]
[1,7,6,2,8,5,3,4]=>1000000=>[1,7]=>[7,1]
[5,6,2,8,1,7,3,4]=>0000000=>[8]=>[8]
[3,1,2,4,8,6,7,5]=>0011000=>[3,1,4]=>[4,3,1]
[1,8,7,2,3,4,5,6]=>1000000=>[1,7]=>[7,1]
[3,7,5,2,8,1,4,6]=>0000000=>[8]=>[8]
[1,2,7,4,8,5,6,3]=>1100000=>[1,1,6]=>[6,1,1]
[5,6,3,4,2,8,7,1]=>0000000=>[8]=>[8]
[3,2,7,5,8,1,6,4]=>0000000=>[8]=>[8]
[3,6,5,8,2,7,4,1]=>0000000=>[8]=>[8]
[2,7,1,8,5,6,4,3]=>0000000=>[8]=>[8]
[4,3,6,8,5,2,1,7]=>0000000=>[8]=>[8]
[4,3,6,8,5,2,7,1]=>0000000=>[8]=>[8]
[4,5,3,2,1,8,6,7]=>0000100=>[5,3]=>[5,3]
[3,6,5,8,1,7,4,2]=>0000000=>[8]=>[8]
[3,6,5,8,1,2,7,4]=>0000000=>[8]=>[8]
[4,1,6,8,5,2,3,7]=>0000000=>[8]=>[8]
[4,5,2,8,6,7,3,1]=>0000000=>[8]=>[8]
[3,5,8,6,2,4,7,1]=>0000000=>[8]=>[8]
[3,2,4,5,8,6,1,7]=>0000000=>[8]=>[8]
[3,4,5,8,6,2,1,7]=>0000000=>[8]=>[8]
[3,4,5,8,6,2,7,1]=>0000000=>[8]=>[8]
[4,5,2,1,3,8,6,7]=>0000100=>[5,3]=>[5,3]
[4,2,3,6,8,5,1,7]=>0000000=>[8]=>[8]
[4,1,3,6,8,5,2,7]=>0000000=>[8]=>[8]
[3,1,4,5,8,6,2,7]=>0000000=>[8]=>[8]
[4,5,1,3,2,8,6,7]=>0000100=>[5,3]=>[5,3]
[3,4,5,8,6,1,7,2]=>0000000=>[8]=>[8]
[3,4,5,8,6,1,2,7]=>0000000=>[8]=>[8]
[8,2,5,4,1,3,7,6]=>0000000=>[8]=>[8]
[8,2,6,4,1,3,7,5]=>0000000=>[8]=>[8]
[1,5,8,2,4,3,7,6]=>1000000=>[1,7]=>[7,1]
[2,4,8,3,5,7,1,6]=>0000000=>[8]=>[8]
[1,4,8,5,7,2,3,6]=>1000000=>[1,7]=>[7,1]
[1,8,7,3,2,4,5,6]=>1000000=>[1,7]=>[7,1]
[2,8,4,3,5,7,1,6]=>0000000=>[8]=>[8]
[5,6,2,7,8,3,1,4]=>0000000=>[8]=>[8]
[8,6,2,7,3,4,1,5]=>0000000=>[8]=>[8]
[8,6,2,7,3,4,5,1]=>0000000=>[8]=>[8]
[5,6,2,7,8,3,4,1]=>0000000=>[8]=>[8]
[5,6,3,2,8,7,1,4]=>0000000=>[8]=>[8]
[6,8,5,3,1,7,2,4]=>0000000=>[8]=>[8]
[8,6,1,7,3,4,2,5]=>0000000=>[8]=>[8]
[5,1,6,7,8,3,2,4]=>0000000=>[8]=>[8]
[1,5,6,3,7,2,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[6,2,4,8,3,7,1,5]=>0000000=>[8]=>[8]
[1,6,8,7,5,2,3,4]=>1000000=>[1,7]=>[7,1]
[1,5,6,7,4,2,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[5,1,6,7,3,4,2,8]=>0000001=>[7,1]=>[7,1]
[8,6,1,7,3,4,5,2]=>0000000=>[8]=>[8]
[6,1,8,7,4,5,2,3]=>0000000=>[8]=>[8]
[2,6,8,4,7,5,1,3]=>0000000=>[8]=>[8]
[6,8,5,1,7,4,2,3]=>0000000=>[8]=>[8]
[4,6,5,7,2,3,8,1]=>0000000=>[8]=>[8]
[5,3,7,4,6,2,8,1]=>0000000=>[8]=>[8]
[3,6,7,2,5,8,4,1]=>0000000=>[8]=>[8]
[3,5,7,6,8,2,1,4]=>0000000=>[8]=>[8]
[5,3,6,7,4,8,1,2]=>0000000=>[8]=>[8]
[3,5,7,6,8,1,4,2]=>0000000=>[8]=>[8]
[4,2,7,8,3,6,5,1]=>0000000=>[8]=>[8]
[5,4,3,7,8,1,6,2]=>0000000=>[8]=>[8]
[5,3,6,7,8,2,1,4]=>0000000=>[8]=>[8]
[3,5,7,8,4,2,1,6]=>0000000=>[8]=>[8]
[4,6,7,8,2,1,3,5]=>0000000=>[8]=>[8]
[4,6,7,3,2,8,1,5]=>0000000=>[8]=>[8]
[4,6,5,3,7,8,1,2]=>0000000=>[8]=>[8]
[4,6,5,2,7,8,3,1]=>0000000=>[8]=>[8]
[3,7,5,2,8,6,1,4]=>0000000=>[8]=>[8]
[5,6,2,4,7,8,3,1]=>0000000=>[8]=>[8]
[5,4,6,2,8,3,7,1]=>0000000=>[8]=>[8]
[5,6,3,2,8,4,7,1]=>0000000=>[8]=>[8]
[5,6,2,8,3,4,7,1]=>0000000=>[8]=>[8]
[3,7,4,8,1,6,5,2]=>0000000=>[8]=>[8]
[5,2,6,4,8,7,3,1]=>0000000=>[8]=>[8]
[2,4,7,8,6,5,1,3]=>0000000=>[8]=>[8]
[2,5,7,8,6,1,4,3]=>0000000=>[8]=>[8]
[1,3,6,4,8,2,7,5]=>1000000=>[1,7]=>[7,1]
[2,4,5,3,8,7,1,6]=>0000000=>[8]=>[8]
[8,6,3,7,2,4,1,5]=>0000000=>[8]=>[8]
[1,8,5,6,4,2,3,7]=>1000000=>[1,7]=>[7,1]
[1,7,6,2,3,5,8,4]=>1000000=>[1,7]=>[7,1]
[8,1,6,5,2,7,4,3]=>0000000=>[8]=>[8]
[2,7,1,5,3,8,6,4]=>0000000=>[8]=>[8]
[7,3,2,1,4,8,6,5]=>0000000=>[8]=>[8]
[8,3,7,2,6,5,1,4]=>0000000=>[8]=>[8]
[7,5,8,2,6,1,4,3]=>0000000=>[8]=>[8]
[8,5,1,3,2,4,6,7]=>0000000=>[8]=>[8]
[3,8,5,1,2,4,6,7]=>0000000=>[8]=>[8]
[5,1,3,2,4,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[5,3,8,1,4,2,6,7]=>0000000=>[8]=>[8]
[5,8,4,1,2,3,6,7]=>0000000=>[8]=>[8]
[5,1,7,8,4,2,3,6]=>0000000=>[8]=>[8]
[1,5,7,8,2,4,3,6]=>1000000=>[1,7]=>[7,1]
[3,5,8,1,4,2,7,6]=>0000000=>[8]=>[8]
[2,8,5,7,1,4,3,6]=>0000000=>[8]=>[8]
[4,8,7,5,1,2,3,6]=>0000000=>[8]=>[8]
[8,6,4,1,2,3,7,5]=>0000000=>[8]=>[8]
[8,1,2,4,6,3,7,5]=>0000000=>[8]=>[8]
[6,3,8,4,1,7,2,5]=>0000000=>[8]=>[8]
[7,6,1,4,2,3,8,5]=>0000000=>[8]=>[8]
[1,7,5,2,3,4,8,6]=>1000000=>[1,7]=>[7,1]
[7,8,1,2,5,3,4,6]=>0000000=>[8]=>[8]
[1,8,7,5,2,3,4,6]=>1000000=>[1,7]=>[7,1]
[7,1,4,8,2,3,6,5]=>0000000=>[8]=>[8]
[1,8,4,7,5,2,3,6]=>1000000=>[1,7]=>[7,1]
[7,3,4,1,8,6,2,5]=>0000000=>[8]=>[8]
[8,4,7,2,1,6,3,5]=>0000000=>[8]=>[8]
[3,4,7,8,6,1,2,5]=>0000000=>[8]=>[8]
[7,6,1,8,2,5,4,3]=>0000000=>[8]=>[8]
[5,8,4,2,1,6,3,7]=>0000000=>[8]=>[8]
[7,6,4,1,2,5,3,8]=>0000001=>[7,1]=>[7,1]
[4,8,6,5,1,3,7,2]=>0000000=>[8]=>[8]
[1,7,5,4,8,6,2,3]=>1000000=>[1,7]=>[7,1]
[1,6,3,7,2,4,8,5]=>1000000=>[1,7]=>[7,1]
[8,7,2,4,1,5,3,6]=>0000000=>[8]=>[8]
[5,2,4,1,8,3,6,7]=>0000000=>[8]=>[8]
[4,3,1,6,7,2,5,8]=>0000001=>[7,1]=>[7,1]
[6,3,1,5,7,2,4,8]=>0000001=>[7,1]=>[7,1]
[4,5,2,1,3,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[2,7,6,4,5,1,8,3]=>0000000=>[8]=>[8]
[2,8,4,6,3,1,5,7]=>0000000=>[8]=>[8]
[2,8,3,1,6,7,4,5]=>0000000=>[8]=>[8]
[4,8,5,7,1,2,3,6]=>0000000=>[8]=>[8]
[7,4,8,3,6,2,1,5]=>0000000=>[8]=>[8]
[1,5,7,4,8,6,2,3]=>1000000=>[1,7]=>[7,1]
[4,8,7,5,2,3,1,6]=>0000000=>[8]=>[8]
[1,2,7,8,6,4,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[3,5,1,7,8,6,2,4]=>0000000=>[8]=>[8]
[1,8,6,7,4,2,3,5]=>1000000=>[1,7]=>[7,1]
[1,5,4,7,3,8,6,2]=>1000000=>[1,7]=>[7,1]
[2,5,6,4,1,3,8,7]=>0000010=>[6,2]=>[6,2]
[7,2,3,1,6,8,4,5]=>0000000=>[8]=>[8]
[5,7,8,1,6,2,3,4]=>0000000=>[8]=>[8]
[1,6,3,8,2,7,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,2,5,8,6,3,7]=>1000000=>[1,7]=>[7,1]
[4,8,2,1,5,7,3,6]=>0000000=>[8]=>[8]
[5,2,7,1,6,3,4,8]=>0000001=>[7,1]=>[7,1]
[4,8,2,5,1,6,3,7]=>0000000=>[8]=>[8]
[5,8,1,2,4,6,3,7]=>0000000=>[8]=>[8]
[5,1,7,3,6,4,2,8]=>0000001=>[7,1]=>[7,1]
[3,1,7,5,6,2,4,8]=>0000001=>[7,1]=>[7,1]
[3,2,7,5,6,1,4,8]=>0000001=>[7,1]=>[7,1]
[3,2,7,1,6,4,5,8]=>0000001=>[7,1]=>[7,1]
[6,3,1,7,5,4,2,8]=>0000001=>[7,1]=>[7,1]
[5,8,3,2,4,1,7,6]=>0000000=>[8]=>[8]
[2,7,5,6,8,3,1,4]=>0000000=>[8]=>[8]
[1,7,8,6,3,4,2,5]=>1000000=>[1,7]=>[7,1]
[7,3,2,1,4,6,8,5]=>0000000=>[8]=>[8]
[7,8,5,3,2,1,6,4]=>0000000=>[8]=>[8]
[1,4,7,2,5,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[4,5,1,3,8,2,6,7]=>0000000=>[8]=>[8]
[4,1,5,3,2,7,6,8]=>0000101=>[5,2,1]=>[5,2,1]
[7,3,5,1,4,2,6,8]=>0000001=>[7,1]=>[7,1]
[7,5,2,4,1,3,8,6]=>0000000=>[8]=>[8]
[6,2,1,7,4,3,8,5]=>0000000=>[8]=>[8]
[2,4,3,6,7,1,5,8]=>0000001=>[7,1]=>[7,1]
[3,1,7,4,2,6,8,5]=>0000000=>[8]=>[8]
[7,3,5,2,1,6,4,8]=>0000001=>[7,1]=>[7,1]
[4,6,5,2,1,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[1,4,7,2,5,6,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[7,2,5,6,1,3,8,4]=>0000000=>[8]=>[8]
[2,5,6,1,4,3,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[6,1,5,3,7,2,4,8]=>0000001=>[7,1]=>[7,1]
[3,6,5,4,1,7,2,8]=>0000001=>[7,1]=>[7,1]
[6,8,5,7,2,1,4,3]=>0000000=>[8]=>[8]
[1,4,2,6,7,8,5,3]=>1000000=>[1,7]=>[7,1]
[5,6,4,2,1,8,3,7]=>0000000=>[8]=>[8]
[4,1,2,6,7,8,5,3]=>0000000=>[8]=>[8]
[5,6,2,7,8,1,3,4]=>0000000=>[8]=>[8]
[3,7,8,2,1,4,5,6]=>0000000=>[8]=>[8]
[5,1,4,7,8,3,6,2]=>0000000=>[8]=>[8]
[5,6,4,1,7,3,8,2]=>0000000=>[8]=>[8]
[2,7,1,6,5,8,3,4]=>0000000=>[8]=>[8]
[4,6,1,7,3,2,8,5]=>0000000=>[8]=>[8]
[1,7,3,6,4,2,8,5]=>1000000=>[1,7]=>[7,1]
[1,3,7,6,2,4,8,5]=>1000000=>[1,7]=>[7,1]
[4,7,3,5,1,2,8,6]=>0000000=>[8]=>[8]
[2,5,1,8,3,7,4,6]=>0000000=>[8]=>[8]
[5,1,2,4,3,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[4,8,3,5,2,1,6,7]=>0000000=>[8]=>[8]
[3,8,4,1,7,5,2,6]=>0000000=>[8]=>[8]
[4,7,3,2,6,5,1,8]=>0000001=>[7,1]=>[7,1]
[4,7,5,2,3,6,1,8]=>0000001=>[7,1]=>[7,1]
[4,3,7,8,2,1,6,5]=>0000000=>[8]=>[8]
[4,8,7,2,1,5,6,3]=>0000000=>[8]=>[8]
[7,3,8,2,5,1,6,4]=>0000000=>[8]=>[8]
[4,5,3,8,2,1,7,6]=>0000000=>[8]=>[8]
[4,5,3,8,6,1,2,7]=>0000000=>[8]=>[8]
[7,3,8,4,5,1,2,6]=>0000000=>[8]=>[8]
[4,8,7,5,1,3,2,6]=>0000000=>[8]=>[8]
[4,8,7,5,1,2,6,3]=>0000000=>[8]=>[8]
[7,8,4,6,1,3,5,2]=>0000000=>[8]=>[8]
[4,8,7,5,1,3,6,2]=>0000000=>[8]=>[8]
[4,5,3,6,8,1,2,7]=>0000000=>[8]=>[8]
[7,8,6,2,1,4,3,5]=>0000000=>[8]=>[8]
[4,7,5,8,2,1,3,6]=>0000000=>[8]=>[8]
[4,8,5,7,1,3,2,6]=>0000000=>[8]=>[8]
[7,8,6,3,1,2,5,4]=>0000000=>[8]=>[8]
[5,3,1,2,4,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[6,1,5,2,8,7,4,3]=>0000000=>[8]=>[8]
[3,2,6,1,5,8,7,4]=>0000000=>[8]=>[8]
[4,5,2,1,6,7,8,3]=>0000000=>[8]=>[8]
[1,4,7,2,6,5,8,3]=>1000000=>[1,7]=>[7,1]
[1,7,6,2,8,5,4,3]=>1000000=>[1,7]=>[7,1]
[1,2,7,8,3,4,6,5]=>1100000=>[1,1,6]=>[6,1,1]
[2,8,4,3,1,6,5,7]=>0000000=>[8]=>[8]
[2,4,3,8,6,5,1,7]=>0000000=>[8]=>[8]
[2,8,6,4,3,1,7,5]=>0000000=>[8]=>[8]
[7,4,5,8,1,3,6,2]=>0000000=>[8]=>[8]
[4,2,5,7,1,6,8,3]=>0000000=>[8]=>[8]
[4,5,3,7,1,6,8,2]=>0000000=>[8]=>[8]
[6,8,4,1,5,7,3,2]=>0000000=>[8]=>[8]
[6,8,4,1,5,7,2,3]=>0000000=>[8]=>[8]
[5,2,6,7,4,1,8,3]=>0000000=>[8]=>[8]
[5,6,7,4,3,1,8,2]=>0000000=>[8]=>[8]
[8,5,6,4,1,7,3,2]=>0000000=>[8]=>[8]
[5,8,2,6,1,7,4,3]=>0000000=>[8]=>[8]
[7,8,3,1,6,4,5,2]=>0000000=>[8]=>[8]
[5,8,2,6,3,1,7,4]=>0000000=>[8]=>[8]
[4,5,8,1,6,3,7,2]=>0000000=>[8]=>[8]
[8,1,4,6,2,5,7,3]=>0000000=>[8]=>[8]
[4,8,1,3,6,2,7,5]=>0000000=>[8]=>[8]
[4,5,8,1,6,2,7,3]=>0000000=>[8]=>[8]
[5,2,6,8,1,4,3,7]=>0000000=>[8]=>[8]
[6,2,7,3,8,1,4,5]=>0000000=>[8]=>[8]
[6,7,3,8,2,1,4,5]=>0000000=>[8]=>[8]
[6,2,7,8,3,1,4,5]=>0000000=>[8]=>[8]
[8,7,3,1,2,5,6,4]=>0000000=>[8]=>[8]
[2,8,3,6,4,1,7,5]=>0000000=>[8]=>[8]
[6,1,3,7,2,8,5,4]=>0000000=>[8]=>[8]
[5,4,3,6,1,7,8,2]=>0000000=>[8]=>[8]
[4,8,3,2,1,7,5,6]=>0000000=>[8]=>[8]
[1,3,7,8,4,6,2,5]=>1000000=>[1,7]=>[7,1]
[5,8,4,3,7,1,2,6]=>0000000=>[8]=>[8]
[5,6,4,8,7,2,1,3]=>0000000=>[8]=>[8]
[4,1,7,8,6,5,2,3]=>0000000=>[8]=>[8]
[2,1,8,7,3,5,4,6]=>0100000=>[2,6]=>[6,2]
[1,7,6,2,3,8,5,4]=>1000000=>[1,7]=>[7,1]
[1,8,5,3,2,7,4,6]=>1000000=>[1,7]=>[7,1]
[4,5,1,3,7,6,2,8]=>0000001=>[7,1]=>[7,1]
[7,2,3,8,6,4,5,1]=>0000000=>[8]=>[8]
[3,5,8,1,7,4,2,6]=>0000000=>[8]=>[8]
[5,8,1,2,7,6,4,3]=>0000000=>[8]=>[8]
[8,7,1,3,2,6,4,5]=>0000000=>[8]=>[8]
[8,1,6,3,7,5,4,2]=>0000000=>[8]=>[8]
[8,5,1,3,7,6,4,2]=>0000000=>[8]=>[8]
[1,6,4,7,3,8,5,2]=>1000000=>[1,7]=>[7,1]
[2,8,1,5,6,4,3,7]=>0000000=>[8]=>[8]
[1,2,6,8,3,4,7,5]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,7,5,8,4,2,3]=>1000000=>[1,7]=>[7,1]
[5,3,8,2,7,6,1,4]=>0000000=>[8]=>[8]
[7,4,2,8,6,5,3,1]=>0000000=>[8]=>[8]
[5,8,2,7,6,1,4,3]=>0000000=>[8]=>[8]
[7,4,8,3,1,6,5,2]=>0000000=>[8]=>[8]
[5,8,7,2,6,4,3,1]=>0000000=>[8]=>[8]
[6,8,7,5,2,1,4,3]=>0000000=>[8]=>[8]
[6,8,7,3,5,1,4,2]=>0000000=>[8]=>[8]
[7,2,5,4,1,3,8,6]=>0000000=>[8]=>[8]
[1,5,7,2,4,3,8,6]=>1000000=>[1,7]=>[7,1]
[1,2,7,5,8,4,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[5,1,3,8,2,7,4,6]=>0000000=>[8]=>[8]
[5,7,1,3,2,8,4,6]=>0000000=>[8]=>[8]
[7,1,6,3,2,8,4,5]=>0000000=>[8]=>[8]
[8,1,7,2,3,6,5,4]=>0000000=>[8]=>[8]
[1,7,2,5,8,4,3,6]=>1000000=>[1,7]=>[7,1]
[7,1,2,6,4,3,8,5]=>0000000=>[8]=>[8]
[1,4,7,8,3,2,5,6]=>1000000=>[1,7]=>[7,1]
[8,7,1,3,2,4,6,5]=>0000000=>[8]=>[8]
[8,1,6,3,2,4,7,5]=>0000000=>[8]=>[8]
[1,8,2,7,6,3,5,4]=>1000000=>[1,7]=>[7,1]
[1,8,6,2,7,4,3,5]=>1000000=>[1,7]=>[7,1]
[8,1,6,3,2,7,4,5]=>0000000=>[8]=>[8]
[8,2,1,7,6,3,4,5]=>0000000=>[8]=>[8]
[6,4,5,3,1,8,7,2]=>0000000=>[8]=>[8]
[1,8,2,3,5,6,4,7]=>1000000=>[1,7]=>[7,1]
[2,8,1,3,5,6,4,7]=>0000000=>[8]=>[8]
[2,5,7,4,8,3,6,1]=>0000000=>[8]=>[8]
[2,6,3,4,7,8,5,1]=>0000000=>[8]=>[8]
[2,3,5,4,7,1,8,6]=>0000000=>[8]=>[8]
[7,4,1,3,6,8,5,2]=>0000000=>[8]=>[8]
[7,2,1,3,6,8,4,5]=>0000000=>[8]=>[8]
[7,4,2,3,6,8,5,1]=>0000000=>[8]=>[8]
[7,2,3,6,8,5,4,1]=>0000000=>[8]=>[8]
[7,6,3,1,8,5,2,4]=>0000000=>[8]=>[8]
[7,2,1,3,6,8,5,4]=>0000000=>[8]=>[8]
[7,6,3,8,1,5,2,4]=>0000000=>[8]=>[8]
[1,6,4,7,8,5,3,2]=>1000000=>[1,7]=>[7,1]
[7,2,5,1,6,4,3,8]=>0000001=>[7,1]=>[7,1]
[1,2,4,6,8,5,7,3]=>1100000=>[1,1,6]=>[6,1,1]
[2,6,3,7,4,1,8,5]=>0000000=>[8]=>[8]
[3,8,5,1,2,4,7,6]=>0000000=>[8]=>[8]
[1,8,3,7,5,2,6,4]=>1000000=>[1,7]=>[7,1]
[8,1,3,6,5,2,7,4]=>0000000=>[8]=>[8]
[7,1,3,8,5,2,6,4]=>0000000=>[8]=>[8]
[4,7,1,5,2,6,8,3]=>0000000=>[8]=>[8]
[7,4,1,5,2,6,8,3]=>0000000=>[8]=>[8]
[3,1,6,7,5,2,8,4]=>0000000=>[8]=>[8]
[8,6,2,4,5,1,7,3]=>0000000=>[8]=>[8]
[4,6,2,5,3,1,7,8]=>0000011=>[6,1,1]=>[6,1,1]
[7,1,4,5,2,6,8,3]=>0000000=>[8]=>[8]
[5,7,6,8,2,1,4,3]=>0000000=>[8]=>[8]
[4,5,1,3,6,7,8,2]=>0000000=>[8]=>[8]
[6,4,7,1,5,2,8,3]=>0000000=>[8]=>[8]
[3,5,6,2,1,7,8,4]=>0000000=>[8]=>[8]
[4,5,1,6,2,8,7,3]=>0000000=>[8]=>[8]
[3,2,5,8,6,1,7,4]=>0000000=>[8]=>[8]
[5,6,3,2,7,4,1,8]=>0000001=>[7,1]=>[7,1]
[5,2,6,7,4,3,1,8]=>0000001=>[7,1]=>[7,1]
[8,5,1,6,4,3,2,7]=>0000000=>[8]=>[8]
[8,5,1,6,4,3,7,2]=>0000000=>[8]=>[8]
[8,5,2,1,6,4,3,7]=>0000000=>[8]=>[8]
[8,6,3,5,2,7,1,4]=>0000000=>[8]=>[8]
[8,4,6,2,1,5,7,3]=>0000000=>[8]=>[8]
[5,6,2,1,8,4,7,3]=>0000000=>[8]=>[8]
[8,5,2,1,6,4,7,3]=>0000000=>[8]=>[8]
[1,7,2,8,5,4,6,3]=>1000000=>[1,7]=>[7,1]
[6,7,1,4,8,5,3,2]=>0000000=>[8]=>[8]
[7,4,8,2,1,5,6,3]=>0000000=>[8]=>[8]
[7,3,2,8,5,1,4,6]=>0000000=>[8]=>[8]
[6,7,1,4,3,2,8,5]=>0000000=>[8]=>[8]
[4,1,7,3,2,8,5,6]=>0000000=>[8]=>[8]
[8,3,5,2,4,7,1,6]=>0000000=>[8]=>[8]
[4,3,7,8,6,1,5,2]=>0000000=>[8]=>[8]
[6,2,8,4,3,7,1,5]=>0000000=>[8]=>[8]
[1,2,6,3,7,8,5,4]=>1100000=>[1,1,6]=>[6,1,1]
[6,1,3,2,7,8,5,4]=>0000000=>[8]=>[8]
[6,7,1,3,2,8,5,4]=>0000000=>[8]=>[8]
[2,6,4,7,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[5,6,1,8,7,2,3,4]=>0000000=>[8]=>[8]
[1,4,7,5,2,3,6,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,8,6,2,3,4,7]=>1000000=>[1,7]=>[7,1]
[5,8,4,3,6,2,7,1]=>0000000=>[8]=>[8]
[4,6,5,8,3,2,7,1]=>0000000=>[8]=>[8]
[3,4,7,5,6,8,2,1]=>0000000=>[8]=>[8]
[3,4,7,8,5,2,6,1]=>0000000=>[8]=>[8]
[2,3,8,4,7,1,6,5]=>0000000=>[8]=>[8]
[1,8,7,5,2,6,3,4]=>1000000=>[1,7]=>[7,1]
[1,8,7,5,4,3,2,6]=>1000000=>[1,7]=>[7,1]
[1,7,6,3,4,5,8,2]=>1000000=>[1,7]=>[7,1]
[1,8,7,4,5,6,2,3]=>1000000=>[1,7]=>[7,1]
[1,8,7,3,6,4,2,5]=>1000000=>[1,7]=>[7,1]
[1,8,7,2,4,6,3,5]=>1000000=>[1,7]=>[7,1]
[1,4,7,8,6,2,5,3]=>1000000=>[1,7]=>[7,1]
[1,7,6,4,2,5,3,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,7,5,8,2,3,6]=>1000000=>[1,7]=>[7,1]
[1,4,7,5,8,2,6,3]=>1000000=>[1,7]=>[7,1]
[1,6,8,3,4,2,5,7]=>1000000=>[1,7]=>[7,1]
[1,4,7,2,3,6,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,3,2,6,8,4,7,5]=>1010000=>[1,2,5]=>[5,2,1]
[1,7,2,5,6,3,4,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,8,3,6,4,7,2]=>1000000=>[1,7]=>[7,1]
[1,2,6,5,8,3,4,7]=>1100000=>[1,1,6]=>[6,1,1]
[1,6,8,2,7,3,4,5]=>1000000=>[1,7]=>[7,1]
[1,4,5,8,2,6,3,7]=>1000000=>[1,7]=>[7,1]
[3,5,6,7,2,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,4,7,5,2,3,1,8]=>0000001=>[7,1]=>[7,1]
[1,5,6,4,8,3,2,7]=>1000000=>[1,7]=>[7,1]
[5,2,6,4,8,7,1,3]=>0000000=>[8]=>[8]
[2,1,5,6,4,8,3,7]=>0100000=>[2,6]=>[6,2]
[5,1,4,7,8,6,2,3]=>0000000=>[8]=>[8]
[2,5,7,1,8,6,3,4]=>0000000=>[8]=>[8]
[1,6,7,2,8,5,4,3]=>1000000=>[1,7]=>[7,1]
[4,6,1,7,8,5,3,2]=>0000000=>[8]=>[8]
[5,3,2,1,7,8,6,4]=>0000000=>[8]=>[8]
[7,4,3,8,6,1,5,2]=>0000000=>[8]=>[8]
[4,3,7,1,5,8,6,2]=>0000000=>[8]=>[8]
[8,2,4,5,3,1,7,6]=>0000000=>[8]=>[8]
[8,5,3,2,4,1,7,6]=>0000000=>[8]=>[8]
[1,4,3,2,7,5,8,6]=>1001000=>[1,3,4]=>[4,3,1]
[7,2,5,3,4,6,1,8]=>0000001=>[7,1]=>[7,1]
[7,1,2,6,4,3,5,8]=>0000001=>[7,1]=>[7,1]
[7,1,2,6,3,4,5,8]=>0000001=>[7,1]=>[7,1]
[7,1,2,6,4,5,3,8]=>0000001=>[7,1]=>[7,1]
[7,1,2,6,5,3,4,8]=>0000001=>[7,1]=>[7,1]
[5,3,1,4,7,2,8,6]=>0000000=>[8]=>[8]
[7,1,3,8,2,6,4,5]=>0000000=>[8]=>[8]
[1,8,3,7,2,4,6,5]=>1000000=>[1,7]=>[7,1]
[7,4,3,1,6,5,2,8]=>0000001=>[7,1]=>[7,1]
[3,5,1,2,6,8,7,4]=>0000000=>[8]=>[8]
[1,5,2,4,3,8,7,6]=>1000100=>[1,4,3]=>[4,3,1]
[3,1,2,4,8,7,5,6]=>0011000=>[3,1,4]=>[4,3,1]
[5,2,1,6,3,8,7,4]=>0000000=>[8]=>[8]
[3,4,6,7,2,1,5,8]=>0000001=>[7,1]=>[7,1]
[2,5,7,4,6,8,1,3]=>0000000=>[8]=>[8]
[4,6,2,7,5,8,1,3]=>0000000=>[8]=>[8]
[4,7,2,5,3,8,1,6]=>0000000=>[8]=>[8]
[2,4,7,6,3,8,1,5]=>0000000=>[8]=>[8]
[5,8,3,6,4,1,7,2]=>0000000=>[8]=>[8]
[4,6,8,5,1,2,3,7]=>0000000=>[8]=>[8]
[4,6,5,7,1,2,3,8]=>0000001=>[7,1]=>[7,1]
[4,6,5,7,1,3,8,2]=>0000000=>[8]=>[8]
[3,4,7,6,1,8,2,5]=>0000000=>[8]=>[8]
[1,6,5,7,3,8,2,4]=>1000000=>[1,7]=>[7,1]
[8,6,2,7,5,3,1,4]=>0000000=>[8]=>[8]
[4,3,7,1,2,8,5,6]=>0000000=>[8]=>[8]
[2,6,7,1,4,3,8,5]=>0000000=>[8]=>[8]
[4,5,2,1,6,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,2,1,6,7,3,8]=>0000001=>[7,1]=>[7,1]
[5,3,8,6,2,4,7,1]=>0000000=>[8]=>[8]
[2,5,1,6,4,3,8,7]=>0000010=>[6,2]=>[6,2]
[3,6,2,8,5,7,1,4]=>0000000=>[8]=>[8]
[4,6,8,1,5,7,2,3]=>0000000=>[8]=>[8]
[4,1,2,5,7,6,3,8]=>0000001=>[7,1]=>[7,1]
[5,2,3,8,7,1,6,4]=>0000000=>[8]=>[8]
[3,2,8,1,7,5,4,6]=>0000000=>[8]=>[8]
[4,8,5,1,3,7,2,6]=>0000000=>[8]=>[8]
[4,6,5,8,1,7,3,2]=>0000000=>[8]=>[8]
[2,1,3,6,4,8,7,5]=>0110000=>[2,1,5]=>[5,2,1]
[4,8,2,1,6,7,5,3]=>0000000=>[8]=>[8]
[4,8,1,2,7,5,6,3]=>0000000=>[8]=>[8]
[5,2,8,1,7,4,6,3]=>0000000=>[8]=>[8]
[5,7,4,8,1,2,6,3]=>0000000=>[8]=>[8]
[8,1,6,7,3,4,2,5]=>0000000=>[8]=>[8]
[4,5,1,6,8,7,2,3]=>0000000=>[8]=>[8]
[3,4,7,2,5,8,6,1]=>0000000=>[8]=>[8]
[3,4,7,1,5,8,2,6]=>0000000=>[8]=>[8]
[6,2,7,4,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[8,6,4,7,5,1,3,2]=>0000000=>[8]=>[8]
[5,1,4,8,2,3,7,6]=>0000000=>[8]=>[8]
[4,5,2,3,8,6,1,7]=>0000000=>[8]=>[8]
[4,5,1,3,2,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[4,7,1,8,5,3,6,2]=>0000000=>[8]=>[8]
[6,4,7,5,1,3,2,8]=>0000001=>[7,1]=>[7,1]
[6,7,2,4,1,8,3,5]=>0000000=>[8]=>[8]
[5,1,6,3,2,7,8,4]=>0000000=>[8]=>[8]
[2,3,7,8,5,4,6,1]=>0000000=>[8]=>[8]
[7,4,5,1,2,6,8,3]=>0000000=>[8]=>[8]
[6,7,8,2,1,5,3,4]=>0000000=>[8]=>[8]
[5,2,1,6,4,7,3,8]=>0000001=>[7,1]=>[7,1]
[6,7,2,5,4,1,3,8]=>0000001=>[7,1]=>[7,1]
[7,4,8,6,3,5,1,2]=>0000000=>[8]=>[8]
[4,6,3,5,1,8,2,7]=>0000000=>[8]=>[8]
[8,5,7,6,2,3,4,1]=>0000000=>[8]=>[8]
[2,4,7,5,8,6,3,1]=>0000000=>[8]=>[8]
[1,4,6,5,3,8,2,7]=>1000000=>[1,7]=>[7,1]
[2,4,5,8,7,1,3,6]=>0000000=>[8]=>[8]
[3,1,6,8,7,5,4,2]=>0000000=>[8]=>[8]
[3,1,8,7,5,6,4,2]=>0000000=>[8]=>[8]
[5,1,8,7,6,3,4,2]=>0000000=>[8]=>[8]
[1,3,8,4,7,2,6,5]=>1000000=>[1,7]=>[7,1]
[1,8,2,4,7,3,6,5]=>1000000=>[1,7]=>[7,1]
[8,2,7,5,3,6,4,1]=>0000000=>[8]=>[8]
[8,4,1,3,6,7,2,5]=>0000000=>[8]=>[8]
[8,7,2,3,1,5,6,4]=>0000000=>[8]=>[8]
[1,2,8,6,7,5,4,3]=>1100000=>[1,1,6]=>[6,1,1]
[2,8,5,7,6,1,3,4]=>0000000=>[8]=>[8]
[1,8,7,2,6,4,5,3]=>1000000=>[1,7]=>[7,1]
[8,7,2,1,6,4,5,3]=>0000000=>[8]=>[8]
[8,7,2,4,3,6,5,1]=>0000000=>[8]=>[8]
[4,2,8,7,3,6,5,1]=>0000000=>[8]=>[8]
[8,7,1,6,4,3,5,2]=>0000000=>[8]=>[8]
[8,4,1,7,3,6,5,2]=>0000000=>[8]=>[8]
[4,5,1,8,7,3,6,2]=>0000000=>[8]=>[8]
[4,3,8,5,2,6,1,7]=>0000000=>[8]=>[8]
[5,7,4,1,2,6,8,3]=>0000000=>[8]=>[8]
[2,8,6,7,5,3,1,4]=>0000000=>[8]=>[8]
[5,2,6,3,7,8,4,1]=>0000000=>[8]=>[8]
[3,6,2,5,7,8,4,1]=>0000000=>[8]=>[8]
[2,7,4,6,8,3,5,1]=>0000000=>[8]=>[8]
[2,7,3,6,8,5,4,1]=>0000000=>[8]=>[8]
[3,7,6,8,1,5,4,2]=>0000000=>[8]=>[8]
[4,7,6,8,2,3,5,1]=>0000000=>[8]=>[8]
[3,7,5,6,8,2,4,1]=>0000000=>[8]=>[8]
[3,7,2,6,8,4,5,1]=>0000000=>[8]=>[8]
[1,5,7,6,8,4,2,3]=>1000000=>[1,7]=>[7,1]
[2,7,5,6,8,4,3,1]=>0000000=>[8]=>[8]
[3,7,6,8,5,1,4,2]=>0000000=>[8]=>[8]
[7,1,3,8,6,2,4,5]=>0000000=>[8]=>[8]
[2,7,1,8,6,5,3,4]=>0000000=>[8]=>[8]
[5,3,4,7,6,2,1,8]=>0000001=>[7,1]=>[7,1]
[7,1,4,6,8,5,3,2]=>0000000=>[8]=>[8]
[7,2,5,1,6,4,8,3]=>0000000=>[8]=>[8]
[2,7,1,5,6,4,8,3]=>0000000=>[8]=>[8]
[1,5,7,8,4,6,3,2]=>1000000=>[1,7]=>[7,1]
[1,4,8,5,7,6,3,2]=>1000000=>[1,7]=>[7,1]
[2,8,1,5,6,4,7,3]=>0000000=>[8]=>[8]
[8,2,1,5,6,4,7,3]=>0000000=>[8]=>[8]
[2,8,5,1,6,4,3,7]=>0000000=>[8]=>[8]
[3,7,2,8,1,5,6,4]=>0000000=>[8]=>[8]
[7,3,2,5,1,6,8,4]=>0000000=>[8]=>[8]
[8,7,2,1,3,6,5,4]=>0000000=>[8]=>[8]
[7,3,2,8,1,4,6,5]=>0000000=>[8]=>[8]
[2,7,8,1,5,4,3,6]=>0000000=>[8]=>[8]
[3,6,2,1,8,4,7,5]=>0000000=>[8]=>[8]
[3,8,6,1,5,7,4,2]=>0000000=>[8]=>[8]
[6,4,2,3,7,8,1,5]=>0000000=>[8]=>[8]
[5,4,3,1,7,2,8,6]=>0000000=>[8]=>[8]
[5,3,1,6,4,7,2,8]=>0000001=>[7,1]=>[7,1]
[6,5,2,4,1,7,8,3]=>0000000=>[8]=>[8]
[4,3,6,2,5,8,1,7]=>0000000=>[8]=>[8]
[1,6,2,7,8,4,5,3]=>1000000=>[1,7]=>[7,1]
[8,5,2,4,1,3,7,6]=>0000000=>[8]=>[8]
[6,3,2,8,4,5,1,7]=>0000000=>[8]=>[8]
[5,4,7,2,1,3,8,6]=>0000000=>[8]=>[8]
[4,1,7,6,5,2,8,3]=>0000000=>[8]=>[8]
[6,4,7,1,2,3,8,5]=>0000000=>[8]=>[8]
[8,2,3,1,6,4,7,5]=>0000000=>[8]=>[8]
[3,1,8,5,7,2,6,4]=>0000000=>[8]=>[8]
[5,6,4,2,1,7,3,8]=>0000001=>[7,1]=>[7,1]
[6,5,7,1,2,8,3,4]=>0000000=>[8]=>[8]
[6,4,7,1,2,5,3,8]=>0000001=>[7,1]=>[7,1]
[1,2,4,8,5,7,3,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,2,7,5,8,6,3,4]=>1100000=>[1,1,6]=>[6,1,1]
[7,4,5,1,6,8,2,3]=>0000000=>[8]=>[8]
[1,7,8,4,2,6,3,5]=>1000000=>[1,7]=>[7,1]
[6,3,2,5,7,4,1,8]=>0000001=>[7,1]=>[7,1]
[6,4,7,5,3,8,1,2]=>0000000=>[8]=>[8]
[6,2,1,5,3,7,8,4]=>0000000=>[8]=>[8]
[4,1,7,8,3,6,5,2]=>0000000=>[8]=>[8]
[6,3,2,4,8,5,1,7]=>0000000=>[8]=>[8]
[6,4,2,1,7,3,5,8]=>0000001=>[7,1]=>[7,1]
[5,7,4,2,1,6,3,8]=>0000001=>[7,1]=>[7,1]
[5,8,4,2,1,3,6,7]=>0000000=>[8]=>[8]
[8,3,2,6,5,1,7,4]=>0000000=>[8]=>[8]
[1,8,5,6,4,3,7,2]=>1000000=>[1,7]=>[7,1]
[1,7,5,8,4,6,3,2]=>1000000=>[1,7]=>[7,1]
[8,3,5,6,1,7,2,4]=>0000000=>[8]=>[8]
[1,5,3,7,8,4,6,2]=>1000000=>[1,7]=>[7,1]
[1,4,7,3,5,8,6,2]=>1000000=>[1,7]=>[7,1]
[1,6,3,7,8,5,4,2]=>1000000=>[1,7]=>[7,1]
[8,5,6,1,7,4,2,3]=>0000000=>[8]=>[8]
[8,6,1,4,3,7,2,5]=>0000000=>[8]=>[8]
[3,7,8,2,5,1,6,4]=>0000000=>[8]=>[8]
[8,1,3,5,6,4,2,7]=>0000000=>[8]=>[8]
[8,6,1,4,3,2,7,5]=>0000000=>[8]=>[8]
[7,3,8,2,4,1,5,6]=>0000000=>[8]=>[8]
[6,3,7,8,1,2,5,4]=>0000000=>[8]=>[8]
[7,5,8,1,2,3,6,4]=>0000000=>[8]=>[8]
[8,6,1,5,3,7,2,4]=>0000000=>[8]=>[8]
[8,1,7,5,6,4,2,3]=>0000000=>[8]=>[8]
[8,1,4,7,6,5,2,3]=>0000000=>[8]=>[8]
[6,1,4,8,2,7,5,3]=>0000000=>[8]=>[8]
[8,6,4,2,7,3,5,1]=>0000000=>[8]=>[8]
[6,8,7,5,2,1,3,4]=>0000000=>[8]=>[8]
[7,6,1,5,2,3,8,4]=>0000000=>[8]=>[8]
[5,1,8,6,7,2,3,4]=>0000000=>[8]=>[8]
[5,7,1,6,8,2,3,4]=>0000000=>[8]=>[8]
[5,1,7,6,8,2,3,4]=>0000000=>[8]=>[8]
[6,1,5,7,2,8,3,4]=>0000000=>[8]=>[8]
[6,8,4,2,1,7,3,5]=>0000000=>[8]=>[8]
[5,8,6,1,7,2,3,4]=>0000000=>[8]=>[8]
[6,3,2,8,1,7,4,5]=>0000000=>[8]=>[8]
[1,4,7,8,3,5,2,6]=>1000000=>[1,7]=>[7,1]
[2,5,6,8,1,4,7,3]=>0000000=>[8]=>[8]
[8,4,5,1,6,7,2,3]=>0000000=>[8]=>[8]
[7,3,6,1,4,2,8,5]=>0000000=>[8]=>[8]
[7,4,1,6,5,2,3,8]=>0000001=>[7,1]=>[7,1]
[4,1,6,5,2,3,8,7]=>0000010=>[6,2]=>[6,2]
[4,5,1,7,8,6,2,3]=>0000000=>[8]=>[8]
[8,3,1,4,6,2,7,5]=>0000000=>[8]=>[8]
[2,5,3,4,6,8,1,7]=>0000000=>[8]=>[8]
[8,3,6,1,5,2,4,7]=>0000000=>[8]=>[8]
[4,7,1,2,5,6,3,8]=>0000001=>[7,1]=>[7,1]
[6,7,3,1,8,2,4,5]=>0000000=>[8]=>[8]
[7,3,1,4,6,2,8,5]=>0000000=>[8]=>[8]
[7,4,1,2,5,6,3,8]=>0000001=>[7,1]=>[7,1]
[4,5,1,3,6,8,7,2]=>0000000=>[8]=>[8]
[8,4,1,2,5,7,3,6]=>0000000=>[8]=>[8]
[8,4,1,3,6,7,5,2]=>0000000=>[8]=>[8]
[5,4,1,6,3,7,8,2]=>0000000=>[8]=>[8]
[6,7,3,1,5,2,4,8]=>0000001=>[7,1]=>[7,1]
[5,4,1,3,6,8,7,2]=>0000000=>[8]=>[8]
[6,4,1,2,5,8,3,7]=>0000000=>[8]=>[8]
[5,7,4,8,1,6,3,2]=>0000000=>[8]=>[8]
[7,5,3,6,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[4,3,1,2,6,5,7,8]=>0001011=>[4,2,1,1]=>[4,2,1,1]
[4,3,1,2,5,7,6,8]=>0001101=>[4,1,2,1]=>[4,2,1,1]
[4,7,3,1,5,2,8,6]=>0000000=>[8]=>[8]
[6,5,1,2,7,4,8,3]=>0000000=>[8]=>[8]
[5,3,8,1,4,2,7,6]=>0000000=>[8]=>[8]
[6,5,3,4,1,8,2,7]=>0000000=>[8]=>[8]
[3,1,8,4,2,7,6,5]=>0000000=>[8]=>[8]
[2,8,7,4,1,3,6,5]=>0000000=>[8]=>[8]
[8,2,3,1,7,6,4,5]=>0000000=>[8]=>[8]
[5,2,4,1,6,8,3,7]=>0000000=>[8]=>[8]
[8,7,2,3,1,6,4,5]=>0000000=>[8]=>[8]
[6,2,3,1,7,8,4,5]=>0000000=>[8]=>[8]
[7,2,5,8,3,1,4,6]=>0000000=>[8]=>[8]
[6,8,2,3,1,7,4,5]=>0000000=>[8]=>[8]
[8,2,5,7,3,1,4,6]=>0000000=>[8]=>[8]
[2,5,8,7,3,1,4,6]=>0000000=>[8]=>[8]
[2,8,7,3,1,4,5,6]=>0000000=>[8]=>[8]
[8,2,3,1,6,7,4,5]=>0000000=>[8]=>[8]
[2,8,4,1,3,6,7,5]=>0000000=>[8]=>[8]
[2,7,3,1,4,5,8,6]=>0000000=>[8]=>[8]
[7,2,8,3,1,4,5,6]=>0000000=>[8]=>[8]
[2,7,8,3,1,4,5,6]=>0000000=>[8]=>[8]
[5,3,2,8,7,1,6,4]=>0000000=>[8]=>[8]
[6,8,7,2,1,5,4,3]=>0000000=>[8]=>[8]
[4,8,5,3,6,1,7,2]=>0000000=>[8]=>[8]
[6,3,1,5,4,8,2,7]=>0000000=>[8]=>[8]
[8,4,2,6,5,7,3,1]=>0000000=>[8]=>[8]
[4,7,6,3,5,2,8,1]=>0000000=>[8]=>[8]
[1,7,5,3,4,8,6,2]=>1000000=>[1,7]=>[7,1]
[4,8,6,2,5,7,3,1]=>0000000=>[8]=>[8]
[8,7,3,2,6,4,5,1]=>0000000=>[8]=>[8]
[8,3,1,4,7,5,2,6]=>0000000=>[8]=>[8]
[5,3,1,6,4,8,7,2]=>0000000=>[8]=>[8]
[3,4,8,5,7,2,6,1]=>0000000=>[8]=>[8]
[4,1,7,8,3,2,5,6]=>0000000=>[8]=>[8]
[8,5,1,2,7,6,4,3]=>0000000=>[8]=>[8]
[4,6,5,3,1,8,7,2]=>0000000=>[8]=>[8]
[6,4,7,2,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[4,3,6,1,2,7,8,5]=>0000000=>[8]=>[8]
[2,7,4,6,3,8,1,5]=>0000000=>[8]=>[8]
[7,3,5,6,4,1,8,2]=>0000000=>[8]=>[8]
[5,7,6,3,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[3,7,5,6,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,7,3,6,4,2,1,8]=>0000001=>[7,1]=>[7,1]
[5,7,3,6,4,1,8,2]=>0000000=>[8]=>[8]
[3,7,5,6,4,1,8,2]=>0000000=>[8]=>[8]
[5,7,6,3,4,1,8,2]=>0000000=>[8]=>[8]
[3,2,7,5,6,1,8,4]=>0000000=>[8]=>[8]
[5,3,4,7,6,1,8,2]=>0000000=>[8]=>[8]
[5,3,4,2,7,1,8,6]=>0000000=>[8]=>[8]
[3,5,4,1,7,8,6,2]=>0000000=>[8]=>[8]
[3,1,2,7,5,8,4,6]=>0010000=>[3,5]=>[5,3]
[8,4,1,5,6,2,7,3]=>0000000=>[8]=>[8]
[1,8,5,3,2,4,6,7]=>1000000=>[1,7]=>[7,1]
[4,8,5,1,2,3,6,7]=>0000000=>[8]=>[8]
[3,5,1,4,2,6,8,7]=>0000110=>[5,1,2]=>[5,2,1]
[4,8,7,1,2,5,3,6]=>0000000=>[8]=>[8]
[8,7,2,6,1,4,3,5]=>0000000=>[8]=>[8]
[1,7,6,8,4,2,3,5]=>1000000=>[1,7]=>[7,1]
[1,7,4,8,2,5,3,6]=>1000000=>[1,7]=>[7,1]
[6,1,7,3,8,2,4,5]=>0000000=>[8]=>[8]
[1,5,8,2,3,4,7,6]=>1000000=>[1,7]=>[7,1]
[8,4,2,7,1,3,6,5]=>0000000=>[8]=>[8]
[7,1,8,6,4,2,3,5]=>0000000=>[8]=>[8]
[1,7,8,6,4,2,3,5]=>1000000=>[1,7]=>[7,1]
[5,1,7,3,2,6,8,4]=>0000000=>[8]=>[8]
[8,7,5,3,2,6,4,1]=>0000000=>[8]=>[8]
[4,5,2,3,8,7,1,6]=>0000000=>[8]=>[8]
[4,6,7,5,2,3,1,8]=>0000001=>[7,1]=>[7,1]
[6,5,2,3,1,8,7,4]=>0000000=>[8]=>[8]
[6,2,5,3,1,8,7,4]=>0000000=>[8]=>[8]
[6,2,5,3,8,7,1,4]=>0000000=>[8]=>[8]
[6,4,5,3,8,7,1,2]=>0000000=>[8]=>[8]
[1,6,4,5,8,7,3,2]=>1000000=>[1,7]=>[7,1]
[8,4,7,5,2,3,1,6]=>0000000=>[8]=>[8]
[8,2,7,4,5,3,1,6]=>0000000=>[8]=>[8]
[6,2,4,7,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[8,2,4,7,5,3,1,6]=>0000000=>[8]=>[8]
[8,2,6,7,5,3,1,4]=>0000000=>[8]=>[8]
[8,4,6,7,5,3,1,2]=>0000000=>[8]=>[8]
[6,4,5,8,7,3,1,2]=>0000000=>[8]=>[8]
[6,2,8,7,5,3,1,4]=>0000000=>[8]=>[8]
[2,4,8,7,5,3,1,6]=>0000000=>[8]=>[8]
[4,6,8,7,5,3,1,2]=>0000000=>[8]=>[8]
[4,6,5,3,8,7,1,2]=>0000000=>[8]=>[8]
[2,6,5,8,7,3,1,4]=>0000000=>[8]=>[8]
[6,7,2,4,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[4,5,8,7,2,3,1,6]=>0000000=>[8]=>[8]
[4,8,7,2,5,3,1,6]=>0000000=>[8]=>[8]
[6,8,7,4,5,3,1,2]=>0000000=>[8]=>[8]
[2,8,4,7,5,3,1,6]=>0000000=>[8]=>[8]
[4,8,2,7,5,3,1,6]=>0000000=>[8]=>[8]
[6,8,2,7,5,3,1,4]=>0000000=>[8]=>[8]
[7,4,3,8,1,6,5,2]=>0000000=>[8]=>[8]
[3,7,4,6,2,1,8,5]=>0000000=>[8]=>[8]
[2,6,5,7,8,3,1,4]=>0000000=>[8]=>[8]
[3,4,8,6,2,1,7,5]=>0000000=>[8]=>[8]
[1,6,2,3,8,5,7,4]=>1000000=>[1,7]=>[7,1]
[1,2,7,3,8,5,6,4]=>1100000=>[1,1,6]=>[6,1,1]
[2,3,6,5,8,4,7,1]=>0000000=>[8]=>[8]
[3,4,2,6,8,5,7,1]=>0000000=>[8]=>[8]
[2,4,7,3,8,5,1,6]=>0000000=>[8]=>[8]
[1,2,8,3,5,4,7,6]=>1100000=>[1,1,6]=>[6,1,1]
[1,3,6,7,4,5,8,2]=>1000000=>[1,7]=>[7,1]
[7,4,1,3,6,8,2,5]=>0000000=>[8]=>[8]
[5,1,7,3,4,6,8,2]=>0000000=>[8]=>[8]
[6,1,7,3,5,8,2,4]=>0000000=>[8]=>[8]
[6,8,1,2,7,3,4,5]=>0000000=>[8]=>[8]
[5,6,2,1,8,3,4,7]=>0000000=>[8]=>[8]
[6,4,1,3,7,8,2,5]=>0000000=>[8]=>[8]
[1,6,2,8,7,3,4,5]=>1000000=>[1,7]=>[7,1]
[5,2,8,4,7,1,3,6]=>0000000=>[8]=>[8]
[3,8,7,2,6,1,4,5]=>0000000=>[8]=>[8]
[2,5,1,8,3,6,4,7]=>0000000=>[8]=>[8]
[2,3,8,1,4,6,5,7]=>0000000=>[8]=>[8]
[1,3,8,2,5,4,7,6]=>1000000=>[1,7]=>[7,1]
[3,1,8,4,6,2,5,7]=>0000000=>[8]=>[8]
[6,3,2,4,8,7,1,5]=>0000000=>[8]=>[8]
[1,4,8,6,2,3,5,7]=>1000000=>[1,7]=>[7,1]
[3,1,8,4,5,6,2,7]=>0000000=>[8]=>[8]
[4,5,8,3,6,1,7,2]=>0000000=>[8]=>[8]
[3,5,4,8,6,1,7,2]=>0000000=>[8]=>[8]
[4,2,7,8,6,3,1,5]=>0000000=>[8]=>[8]
[7,1,4,2,8,6,3,5]=>0000000=>[8]=>[8]
[2,3,7,4,8,1,6,5]=>0000000=>[8]=>[8]
[8,3,1,2,5,4,7,6]=>0000000=>[8]=>[8]
[6,5,1,2,8,4,7,3]=>0000000=>[8]=>[8]
[8,1,5,3,7,4,2,6]=>0000000=>[8]=>[8]
[1,3,4,8,6,2,7,5]=>1000000=>[1,7]=>[7,1]
[1,2,4,8,6,7,3,5]=>1100000=>[1,1,6]=>[6,1,1]
[8,1,2,6,5,7,3,4]=>0000000=>[8]=>[8]
[7,1,2,6,5,8,3,4]=>0000000=>[8]=>[8]
[7,1,6,8,3,2,4,5]=>0000000=>[8]=>[8]
[2,6,1,4,7,5,8,3]=>0000000=>[8]=>[8]
[5,1,4,3,7,8,6,2]=>0000000=>[8]=>[8]
[6,4,1,3,7,8,5,2]=>0000000=>[8]=>[8]
[3,1,5,7,2,6,8,4]=>0000000=>[8]=>[8]
[7,2,4,8,5,1,6,3]=>0000000=>[8]=>[8]
[3,1,7,5,2,6,8,4]=>0000000=>[8]=>[8]
[3,2,7,5,1,6,8,4]=>0000000=>[8]=>[8]
[5,2,7,3,1,6,8,4]=>0000000=>[8]=>[8]
[6,7,2,1,3,4,8,5]=>0000000=>[8]=>[8]
[4,6,3,1,2,7,8,5]=>0000000=>[8]=>[8]
[6,7,3,1,2,4,8,5]=>0000000=>[8]=>[8]
[3,8,5,2,1,6,7,4]=>0000000=>[8]=>[8]
[6,4,7,8,3,5,1,2]=>0000000=>[8]=>[8]
[6,4,7,8,1,2,5,3]=>0000000=>[8]=>[8]
[3,5,6,7,1,8,4,2]=>0000000=>[8]=>[8]
[1,7,4,5,2,8,6,3]=>1000000=>[1,7]=>[7,1]
[1,7,3,8,2,5,4,6]=>1000000=>[1,7]=>[7,1]
[8,6,4,5,1,3,7,2]=>0000000=>[8]=>[8]
[7,5,8,4,1,3,6,2]=>0000000=>[8]=>[8]
[4,7,5,3,6,8,1,2]=>0000000=>[8]=>[8]
[4,8,5,3,7,1,2,6]=>0000000=>[8]=>[8]
[2,8,1,6,5,7,3,4]=>0000000=>[8]=>[8]
[4,7,5,3,8,1,6,2]=>0000000=>[8]=>[8]
[7,4,8,5,3,6,1,2]=>0000000=>[8]=>[8]
[7,4,5,3,8,1,6,2]=>0000000=>[8]=>[8]
[8,4,6,5,1,3,7,2]=>0000000=>[8]=>[8]
[6,3,5,8,1,7,4,2]=>0000000=>[8]=>[8]
[7,3,6,1,5,8,4,2]=>0000000=>[8]=>[8]
[4,5,3,8,7,1,2,6]=>0000000=>[8]=>[8]
[8,5,4,7,6,1,2,3]=>0000000=>[8]=>[8]
[3,7,6,1,5,8,4,2]=>0000000=>[8]=>[8]
[8,2,3,6,4,1,7,5]=>0000000=>[8]=>[8]
[2,7,3,6,4,1,8,5]=>0000000=>[8]=>[8]
[2,3,7,8,1,4,6,5]=>0000000=>[8]=>[8]
[2,7,3,5,4,1,8,6]=>0000000=>[8]=>[8]
[8,2,3,5,4,1,7,6]=>0000000=>[8]=>[8]
[7,1,3,8,2,4,6,5]=>0000000=>[8]=>[8]
[7,2,3,6,4,1,8,5]=>0000000=>[8]=>[8]
[6,5,2,4,1,8,3,7]=>0000000=>[8]=>[8]
[5,7,2,4,1,3,8,6]=>0000000=>[8]=>[8]
[6,2,5,4,1,8,3,7]=>0000000=>[8]=>[8]
[8,1,2,5,3,7,6,4]=>0000000=>[8]=>[8]
[1,8,5,4,2,6,3,7]=>1000000=>[1,7]=>[7,1]
[8,3,6,5,4,2,1,7]=>0000000=>[8]=>[8]
[5,4,8,7,6,2,3,1]=>0000000=>[8]=>[8]
[6,8,4,7,5,1,3,2]=>0000000=>[8]=>[8]
[1,7,2,5,6,8,3,4]=>1000000=>[1,7]=>[7,1]
[4,1,7,5,6,8,2,3]=>0000000=>[8]=>[8]
[1,5,8,3,2,7,4,6]=>1000000=>[1,7]=>[7,1]
[7,6,4,2,5,3,1,8]=>0000001=>[7,1]=>[7,1]
[1,8,6,5,2,7,4,3]=>1000000=>[1,7]=>[7,1]
[8,2,6,5,1,7,4,3]=>0000000=>[8]=>[8]
[6,1,4,7,2,5,8,3]=>0000000=>[8]=>[8]
[6,8,2,5,1,7,4,3]=>0000000=>[8]=>[8]
[1,6,4,7,2,5,8,3]=>1000000=>[1,7]=>[7,1]
[7,6,4,1,2,5,8,3]=>0000000=>[8]=>[8]
[6,8,1,5,2,7,4,3]=>0000000=>[8]=>[8]
[8,6,5,2,1,7,4,3]=>0000000=>[8]=>[8]
[1,6,5,2,8,7,4,3]=>1000000=>[1,7]=>[7,1]
[1,8,5,2,7,6,4,3]=>1000000=>[1,7]=>[7,1]
[1,8,6,7,2,5,4,3]=>1000000=>[1,7]=>[7,1]
[1,7,6,8,2,5,4,3]=>1000000=>[1,7]=>[7,1]
[1,7,8,6,2,5,4,3]=>1000000=>[1,7]=>[7,1]
[8,1,7,6,2,5,4,3]=>0000000=>[8]=>[8]
[1,7,8,6,3,5,4,2]=>1000000=>[1,7]=>[7,1]
[1,4,2,3,7,8,6,5]=>1001000=>[1,3,4]=>[4,3,1]
[1,8,4,2,3,6,5,7]=>1000000=>[1,7]=>[7,1]
[1,3,8,5,6,4,2,7]=>1000000=>[1,7]=>[7,1]
[1,6,3,7,8,4,2,5]=>1000000=>[1,7]=>[7,1]
[1,6,3,8,4,2,5,7]=>1000000=>[1,7]=>[7,1]
[1,7,8,4,2,3,5,6]=>1000000=>[1,7]=>[7,1]
[1,7,8,5,6,4,2,3]=>1000000=>[1,7]=>[7,1]
[1,6,3,4,2,5,8,7]=>1000010=>[1,5,2]=>[5,2,1]
[1,3,5,8,6,4,2,7]=>1000000=>[1,7]=>[7,1]
[1,7,6,2,3,8,4,5]=>1000000=>[1,7]=>[7,1]
[1,5,7,6,2,3,8,4]=>1000000=>[1,7]=>[7,1]
[1,3,7,6,2,4,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,4,3,7,6,2,5,8]=>1000001=>[1,6,1]=>[6,1,1]
[1,5,8,4,3,7,6,2]=>1000000=>[1,7]=>[7,1]
[1,7,5,8,4,3,6,2]=>1000000=>[1,7]=>[7,1]
[4,1,5,7,3,8,2,6]=>0000000=>[8]=>[8]
[1,3,7,4,6,8,5,2]=>1000000=>[1,7]=>[7,1]
[1,5,2,6,8,7,4,3]=>1000000=>[1,7]=>[7,1]
[1,3,7,6,4,8,2,5]=>1000000=>[1,7]=>[7,1]
[6,5,1,4,3,8,7,2]=>0000000=>[8]=>[8]
[5,6,1,4,3,8,7,2]=>0000000=>[8]=>[8]
[5,8,6,4,3,1,7,2]=>0000000=>[8]=>[8]
[4,1,3,7,8,6,5,2]=>0000000=>[8]=>[8]
[8,5,6,4,3,1,7,2]=>0000000=>[8]=>[8]
[8,4,3,1,7,6,5,2]=>0000000=>[8]=>[8]
[3,2,7,1,8,6,5,4]=>0000000=>[8]=>[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.
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
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
searching the database
Sorry, this map was not found in the database.