Identifier
Mp00064:
Permutations
—reverse⟶
Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
[1]=>[1]=>=>
[1,2]=>[2,1]=>0=>0
[2,1]=>[1,2]=>1=>1
[1,2,3]=>[3,2,1]=>00=>00
[1,3,2]=>[2,3,1]=>00=>00
[2,1,3]=>[3,1,2]=>00=>00
[2,3,1]=>[1,3,2]=>10=>01
[3,1,2]=>[2,1,3]=>01=>10
[3,2,1]=>[1,2,3]=>11=>11
[1,2,3,4]=>[4,3,2,1]=>000=>000
[1,2,4,3]=>[3,4,2,1]=>000=>000
[1,3,2,4]=>[4,2,3,1]=>000=>000
[1,3,4,2]=>[2,4,3,1]=>000=>000
[1,4,2,3]=>[3,2,4,1]=>000=>000
[1,4,3,2]=>[2,3,4,1]=>000=>000
[2,1,3,4]=>[4,3,1,2]=>000=>000
[2,1,4,3]=>[3,4,1,2]=>000=>000
[2,3,1,4]=>[4,1,3,2]=>000=>000
[2,3,4,1]=>[1,4,3,2]=>100=>001
[2,4,1,3]=>[3,1,4,2]=>000=>000
[2,4,3,1]=>[1,3,4,2]=>100=>001
[3,1,2,4]=>[4,2,1,3]=>000=>000
[3,1,4,2]=>[2,4,1,3]=>000=>000
[3,2,1,4]=>[4,1,2,3]=>000=>000
[3,2,4,1]=>[1,4,2,3]=>100=>001
[3,4,1,2]=>[2,1,4,3]=>010=>010
[3,4,2,1]=>[1,2,4,3]=>110=>011
[4,1,2,3]=>[3,2,1,4]=>001=>100
[4,1,3,2]=>[2,3,1,4]=>001=>100
[4,2,1,3]=>[3,1,2,4]=>001=>100
[4,2,3,1]=>[1,3,2,4]=>101=>101
[4,3,1,2]=>[2,1,3,4]=>011=>110
[4,3,2,1]=>[1,2,3,4]=>111=>111
[1,2,3,4,5]=>[5,4,3,2,1]=>0000=>0000
[1,2,3,5,4]=>[4,5,3,2,1]=>0000=>0000
[1,2,4,3,5]=>[5,3,4,2,1]=>0000=>0000
[1,2,4,5,3]=>[3,5,4,2,1]=>0000=>0000
[1,2,5,3,4]=>[4,3,5,2,1]=>0000=>0000
[1,2,5,4,3]=>[3,4,5,2,1]=>0000=>0000
[1,3,2,4,5]=>[5,4,2,3,1]=>0000=>0000
[1,3,2,5,4]=>[4,5,2,3,1]=>0000=>0000
[1,3,4,2,5]=>[5,2,4,3,1]=>0000=>0000
[1,3,4,5,2]=>[2,5,4,3,1]=>0000=>0000
[1,3,5,2,4]=>[4,2,5,3,1]=>0000=>0000
[1,3,5,4,2]=>[2,4,5,3,1]=>0000=>0000
[1,4,2,3,5]=>[5,3,2,4,1]=>0000=>0000
[1,4,2,5,3]=>[3,5,2,4,1]=>0000=>0000
[1,4,3,2,5]=>[5,2,3,4,1]=>0000=>0000
[1,4,3,5,2]=>[2,5,3,4,1]=>0000=>0000
[1,4,5,2,3]=>[3,2,5,4,1]=>0000=>0000
[1,4,5,3,2]=>[2,3,5,4,1]=>0000=>0000
[1,5,2,3,4]=>[4,3,2,5,1]=>0000=>0000
[1,5,2,4,3]=>[3,4,2,5,1]=>0000=>0000
[1,5,3,2,4]=>[4,2,3,5,1]=>0000=>0000
[1,5,3,4,2]=>[2,4,3,5,1]=>0000=>0000
[1,5,4,2,3]=>[3,2,4,5,1]=>0000=>0000
[1,5,4,3,2]=>[2,3,4,5,1]=>0000=>0000
[2,1,3,4,5]=>[5,4,3,1,2]=>0000=>0000
[2,1,3,5,4]=>[4,5,3,1,2]=>0000=>0000
[2,1,4,3,5]=>[5,3,4,1,2]=>0000=>0000
[2,1,4,5,3]=>[3,5,4,1,2]=>0000=>0000
[2,1,5,3,4]=>[4,3,5,1,2]=>0000=>0000
[2,1,5,4,3]=>[3,4,5,1,2]=>0000=>0000
[2,3,1,4,5]=>[5,4,1,3,2]=>0000=>0000
[2,3,1,5,4]=>[4,5,1,3,2]=>0000=>0000
[2,3,4,1,5]=>[5,1,4,3,2]=>0000=>0000
[2,3,4,5,1]=>[1,5,4,3,2]=>1000=>0001
[2,3,5,1,4]=>[4,1,5,3,2]=>0000=>0000
[2,3,5,4,1]=>[1,4,5,3,2]=>1000=>0001
[2,4,1,3,5]=>[5,3,1,4,2]=>0000=>0000
[2,4,1,5,3]=>[3,5,1,4,2]=>0000=>0000
[2,4,3,1,5]=>[5,1,3,4,2]=>0000=>0000
[2,4,3,5,1]=>[1,5,3,4,2]=>1000=>0001
[2,4,5,1,3]=>[3,1,5,4,2]=>0000=>0000
[2,4,5,3,1]=>[1,3,5,4,2]=>1000=>0001
[2,5,1,3,4]=>[4,3,1,5,2]=>0000=>0000
[2,5,1,4,3]=>[3,4,1,5,2]=>0000=>0000
[2,5,3,1,4]=>[4,1,3,5,2]=>0000=>0000
[2,5,3,4,1]=>[1,4,3,5,2]=>1000=>0001
[2,5,4,1,3]=>[3,1,4,5,2]=>0000=>0000
[2,5,4,3,1]=>[1,3,4,5,2]=>1000=>0001
[3,1,2,4,5]=>[5,4,2,1,3]=>0000=>0000
[3,1,2,5,4]=>[4,5,2,1,3]=>0000=>0000
[3,1,4,2,5]=>[5,2,4,1,3]=>0000=>0000
[3,1,4,5,2]=>[2,5,4,1,3]=>0000=>0000
[3,1,5,2,4]=>[4,2,5,1,3]=>0000=>0000
[3,1,5,4,2]=>[2,4,5,1,3]=>0000=>0000
[3,2,1,4,5]=>[5,4,1,2,3]=>0000=>0000
[3,2,1,5,4]=>[4,5,1,2,3]=>0000=>0000
[3,2,4,1,5]=>[5,1,4,2,3]=>0000=>0000
[3,2,4,5,1]=>[1,5,4,2,3]=>1000=>0001
[3,2,5,1,4]=>[4,1,5,2,3]=>0000=>0000
[3,2,5,4,1]=>[1,4,5,2,3]=>1000=>0001
[3,4,1,2,5]=>[5,2,1,4,3]=>0000=>0000
[3,4,1,5,2]=>[2,5,1,4,3]=>0000=>0000
[3,4,2,1,5]=>[5,1,2,4,3]=>0000=>0000
[3,4,2,5,1]=>[1,5,2,4,3]=>1000=>0001
[3,4,5,1,2]=>[2,1,5,4,3]=>0100=>0010
[3,4,5,2,1]=>[1,2,5,4,3]=>1100=>0011
[3,5,1,2,4]=>[4,2,1,5,3]=>0000=>0000
[3,5,1,4,2]=>[2,4,1,5,3]=>0000=>0000
[3,5,2,1,4]=>[4,1,2,5,3]=>0000=>0000
[3,5,2,4,1]=>[1,4,2,5,3]=>1000=>0001
[3,5,4,1,2]=>[2,1,4,5,3]=>0100=>0010
[3,5,4,2,1]=>[1,2,4,5,3]=>1100=>0011
[4,1,2,3,5]=>[5,3,2,1,4]=>0000=>0000
[4,1,2,5,3]=>[3,5,2,1,4]=>0000=>0000
[4,1,3,2,5]=>[5,2,3,1,4]=>0000=>0000
[4,1,3,5,2]=>[2,5,3,1,4]=>0000=>0000
[4,1,5,2,3]=>[3,2,5,1,4]=>0000=>0000
[4,1,5,3,2]=>[2,3,5,1,4]=>0000=>0000
[4,2,1,3,5]=>[5,3,1,2,4]=>0000=>0000
[4,2,1,5,3]=>[3,5,1,2,4]=>0000=>0000
[4,2,3,1,5]=>[5,1,3,2,4]=>0000=>0000
[4,2,3,5,1]=>[1,5,3,2,4]=>1000=>0001
[4,2,5,1,3]=>[3,1,5,2,4]=>0000=>0000
[4,2,5,3,1]=>[1,3,5,2,4]=>1000=>0001
[4,3,1,2,5]=>[5,2,1,3,4]=>0000=>0000
[4,3,1,5,2]=>[2,5,1,3,4]=>0000=>0000
[4,3,2,1,5]=>[5,1,2,3,4]=>0000=>0000
[4,3,2,5,1]=>[1,5,2,3,4]=>1000=>0001
[4,3,5,1,2]=>[2,1,5,3,4]=>0100=>0010
[4,3,5,2,1]=>[1,2,5,3,4]=>1100=>0011
[4,5,1,2,3]=>[3,2,1,5,4]=>0010=>0100
[4,5,1,3,2]=>[2,3,1,5,4]=>0010=>0100
[4,5,2,1,3]=>[3,1,2,5,4]=>0010=>0100
[4,5,2,3,1]=>[1,3,2,5,4]=>1010=>0101
[4,5,3,1,2]=>[2,1,3,5,4]=>0110=>0110
[4,5,3,2,1]=>[1,2,3,5,4]=>1110=>0111
[5,1,2,3,4]=>[4,3,2,1,5]=>0001=>1000
[5,1,2,4,3]=>[3,4,2,1,5]=>0001=>1000
[5,1,3,2,4]=>[4,2,3,1,5]=>0001=>1000
[5,1,3,4,2]=>[2,4,3,1,5]=>0001=>1000
[5,1,4,2,3]=>[3,2,4,1,5]=>0001=>1000
[5,1,4,3,2]=>[2,3,4,1,5]=>0001=>1000
[5,2,1,3,4]=>[4,3,1,2,5]=>0001=>1000
[5,2,1,4,3]=>[3,4,1,2,5]=>0001=>1000
[5,2,3,1,4]=>[4,1,3,2,5]=>0001=>1000
[5,2,3,4,1]=>[1,4,3,2,5]=>1001=>1001
[5,2,4,1,3]=>[3,1,4,2,5]=>0001=>1000
[5,2,4,3,1]=>[1,3,4,2,5]=>1001=>1001
[5,3,1,2,4]=>[4,2,1,3,5]=>0001=>1000
[5,3,1,4,2]=>[2,4,1,3,5]=>0001=>1000
[5,3,2,1,4]=>[4,1,2,3,5]=>0001=>1000
[5,3,2,4,1]=>[1,4,2,3,5]=>1001=>1001
[5,3,4,1,2]=>[2,1,4,3,5]=>0101=>1010
[5,3,4,2,1]=>[1,2,4,3,5]=>1101=>1011
[5,4,1,2,3]=>[3,2,1,4,5]=>0011=>1100
[5,4,1,3,2]=>[2,3,1,4,5]=>0011=>1100
[5,4,2,1,3]=>[3,1,2,4,5]=>0011=>1100
[5,4,2,3,1]=>[1,3,2,4,5]=>1011=>1101
[5,4,3,1,2]=>[2,1,3,4,5]=>0111=>1110
[5,4,3,2,1]=>[1,2,3,4,5]=>1111=>1111
[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>00000=>00000
[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>00000=>00000
[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>00000=>00000
[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>00000=>00000
[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>00000=>00000
[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>00000=>00000
[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>00000=>00000
[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>00000=>00000
[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>00000=>00000
[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>00000=>00000
[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>00000=>00000
[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>00000=>00000
[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>00000=>00000
[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>00000=>00000
[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>00000=>00000
[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>00000=>00000
[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>00000=>00000
[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>00000=>00000
[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>00000=>00000
[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>00000=>00000
[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>00000=>00000
[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>00000=>00000
[1,2,6,5,3,4]=>[4,3,5,6,2,1]=>00000=>00000
[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>00000=>00000
[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>00000=>00000
[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>00000=>00000
[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>00000=>00000
[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>00000=>00000
[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>00000=>00000
[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>00000=>00000
[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>00000=>00000
[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>00000=>00000
[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>00000=>00000
[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>00000=>00000
[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>00000=>00000
[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>00000=>00000
[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>00000=>00000
[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>00000=>00000
[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>00000=>00000
[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>00000=>00000
[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>00000=>00000
[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>00000=>00000
[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>00000=>00000
[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>00000=>00000
[1,3,6,4,2,5]=>[5,2,4,6,3,1]=>00000=>00000
[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>00000=>00000
[1,3,6,5,2,4]=>[4,2,5,6,3,1]=>00000=>00000
[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>00000=>00000
[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>00000=>00000
[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>00000=>00000
[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>00000=>00000
[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>00000=>00000
[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>00000=>00000
[1,4,2,6,5,3]=>[3,5,6,2,4,1]=>00000=>00000
[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>00000=>00000
[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>00000=>00000
[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>00000=>00000
[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>00000=>00000
[1,4,3,6,2,5]=>[5,2,6,3,4,1]=>00000=>00000
[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>00000=>00000
[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>00000=>00000
[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>00000=>00000
[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>00000=>00000
[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>00000=>00000
[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>00000=>00000
[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>00000=>00000
[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>00000=>00000
[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>00000=>00000
[1,4,6,3,2,5]=>[5,2,3,6,4,1]=>00000=>00000
[1,4,6,3,5,2]=>[2,5,3,6,4,1]=>00000=>00000
[1,4,6,5,2,3]=>[3,2,5,6,4,1]=>00000=>00000
[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>00000=>00000
[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>00000=>00000
[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>00000=>00000
[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>00000=>00000
[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>00000=>00000
[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>00000=>00000
[1,5,2,6,4,3]=>[3,4,6,2,5,1]=>00000=>00000
[1,5,3,2,4,6]=>[6,4,2,3,5,1]=>00000=>00000
[1,5,3,2,6,4]=>[4,6,2,3,5,1]=>00000=>00000
[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>00000=>00000
[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>00000=>00000
[1,5,3,6,2,4]=>[4,2,6,3,5,1]=>00000=>00000
[1,5,3,6,4,2]=>[2,4,6,3,5,1]=>00000=>00000
[1,5,4,2,3,6]=>[6,3,2,4,5,1]=>00000=>00000
[1,5,4,2,6,3]=>[3,6,2,4,5,1]=>00000=>00000
[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>00000=>00000
[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>00000=>00000
[1,5,4,6,2,3]=>[3,2,6,4,5,1]=>00000=>00000
[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>00000=>00000
[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>00000=>00000
[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>00000=>00000
[1,5,6,3,2,4]=>[4,2,3,6,5,1]=>00000=>00000
[1,5,6,3,4,2]=>[2,4,3,6,5,1]=>00000=>00000
[1,5,6,4,2,3]=>[3,2,4,6,5,1]=>00000=>00000
[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>00000=>00000
[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>00000=>00000
[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>00000=>00000
[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>00000=>00000
[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>00000=>00000
[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>00000=>00000
[1,6,2,5,4,3]=>[3,4,5,2,6,1]=>00000=>00000
[1,6,3,2,4,5]=>[5,4,2,3,6,1]=>00000=>00000
[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>00000=>00000
[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>00000=>00000
[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>00000=>00000
[1,6,3,5,2,4]=>[4,2,5,3,6,1]=>00000=>00000
[1,6,3,5,4,2]=>[2,4,5,3,6,1]=>00000=>00000
[1,6,4,2,3,5]=>[5,3,2,4,6,1]=>00000=>00000
[1,6,4,2,5,3]=>[3,5,2,4,6,1]=>00000=>00000
[1,6,4,3,2,5]=>[5,2,3,4,6,1]=>00000=>00000
[1,6,4,3,5,2]=>[2,5,3,4,6,1]=>00000=>00000
[1,6,4,5,2,3]=>[3,2,5,4,6,1]=>00000=>00000
[1,6,4,5,3,2]=>[2,3,5,4,6,1]=>00000=>00000
[1,6,5,2,3,4]=>[4,3,2,5,6,1]=>00000=>00000
[1,6,5,2,4,3]=>[3,4,2,5,6,1]=>00000=>00000
[1,6,5,3,2,4]=>[4,2,3,5,6,1]=>00000=>00000
[1,6,5,3,4,2]=>[2,4,3,5,6,1]=>00000=>00000
[1,6,5,4,2,3]=>[3,2,4,5,6,1]=>00000=>00000
[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>00000=>00000
[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>00000=>00000
[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>00000=>00000
[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>00000=>00000
[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>00000=>00000
[2,1,3,6,4,5]=>[5,4,6,3,1,2]=>00000=>00000
[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>00000=>00000
[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>00000=>00000
[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>00000=>00000
[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>00000=>00000
[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>00000=>00000
[2,1,4,6,3,5]=>[5,3,6,4,1,2]=>00000=>00000
[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>00000=>00000
[2,1,5,3,4,6]=>[6,4,3,5,1,2]=>00000=>00000
[2,1,5,3,6,4]=>[4,6,3,5,1,2]=>00000=>00000
[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>00000=>00000
[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>00000=>00000
[2,1,5,6,3,4]=>[4,3,6,5,1,2]=>00000=>00000
[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>00000=>00000
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[2,1,6,4,5,3]=>[3,5,4,6,1,2]=>00000=>00000
[2,1,6,5,3,4]=>[4,3,5,6,1,2]=>00000=>00000
[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>00000=>00000
[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>00000=>00000
[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>00000=>00000
[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>00000=>00000
[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>00000=>00000
[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>00000=>00000
[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>00000=>00000
[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>00000=>00000
[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>00000=>00000
[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>00000=>00000
[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>10000=>00001
[2,3,4,6,1,5]=>[5,1,6,4,3,2]=>00000=>00000
[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>10000=>00001
[2,3,5,1,4,6]=>[6,4,1,5,3,2]=>00000=>00000
[2,3,5,1,6,4]=>[4,6,1,5,3,2]=>00000=>00000
[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>00000=>00000
[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>10000=>00001
[2,3,5,6,1,4]=>[4,1,6,5,3,2]=>00000=>00000
[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>10000=>00001
[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>00000=>00000
[2,3,6,1,5,4]=>[4,5,1,6,3,2]=>00000=>00000
[2,3,6,4,1,5]=>[5,1,4,6,3,2]=>00000=>00000
[2,3,6,4,5,1]=>[1,5,4,6,3,2]=>10000=>00001
[2,3,6,5,1,4]=>[4,1,5,6,3,2]=>00000=>00000
[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>10000=>00001
[2,4,1,3,5,6]=>[6,5,3,1,4,2]=>00000=>00000
[2,4,1,3,6,5]=>[5,6,3,1,4,2]=>00000=>00000
[2,4,1,5,3,6]=>[6,3,5,1,4,2]=>00000=>00000
[2,4,1,5,6,3]=>[3,6,5,1,4,2]=>00000=>00000
[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>00000=>00000
[2,4,1,6,5,3]=>[3,5,6,1,4,2]=>00000=>00000
[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>00000=>00000
[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>00000=>00000
[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>00000=>00000
[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>10000=>00001
[2,4,3,6,1,5]=>[5,1,6,3,4,2]=>00000=>00000
[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>10000=>00001
[2,4,5,1,3,6]=>[6,3,1,5,4,2]=>00000=>00000
[2,4,5,1,6,3]=>[3,6,1,5,4,2]=>00000=>00000
[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>00000=>00000
[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>10000=>00001
[2,4,5,6,1,3]=>[3,1,6,5,4,2]=>00000=>00000
[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>10000=>00001
[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>00000=>00000
[2,4,6,1,5,3]=>[3,5,1,6,4,2]=>00000=>00000
[2,4,6,3,1,5]=>[5,1,3,6,4,2]=>00000=>00000
[2,4,6,3,5,1]=>[1,5,3,6,4,2]=>10000=>00001
[2,4,6,5,1,3]=>[3,1,5,6,4,2]=>00000=>00000
[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>10000=>00001
[2,5,1,3,4,6]=>[6,4,3,1,5,2]=>00000=>00000
[2,5,1,3,6,4]=>[4,6,3,1,5,2]=>00000=>00000
[2,5,1,4,3,6]=>[6,3,4,1,5,2]=>00000=>00000
[2,5,1,4,6,3]=>[3,6,4,1,5,2]=>00000=>00000
[2,5,1,6,3,4]=>[4,3,6,1,5,2]=>00000=>00000
[2,5,1,6,4,3]=>[3,4,6,1,5,2]=>00000=>00000
[2,5,3,1,4,6]=>[6,4,1,3,5,2]=>00000=>00000
[2,5,3,1,6,4]=>[4,6,1,3,5,2]=>00000=>00000
[2,5,3,4,1,6]=>[6,1,4,3,5,2]=>00000=>00000
[2,5,3,4,6,1]=>[1,6,4,3,5,2]=>10000=>00001
[2,5,3,6,1,4]=>[4,1,6,3,5,2]=>00000=>00000
[2,5,3,6,4,1]=>[1,4,6,3,5,2]=>10000=>00001
[2,5,4,1,3,6]=>[6,3,1,4,5,2]=>00000=>00000
[2,5,4,1,6,3]=>[3,6,1,4,5,2]=>00000=>00000
[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>00000=>00000
[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>10000=>00001
[2,5,4,6,1,3]=>[3,1,6,4,5,2]=>00000=>00000
[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>10000=>00001
[2,5,6,1,3,4]=>[4,3,1,6,5,2]=>00000=>00000
[2,5,6,1,4,3]=>[3,4,1,6,5,2]=>00000=>00000
[2,5,6,3,1,4]=>[4,1,3,6,5,2]=>00000=>00000
[2,5,6,3,4,1]=>[1,4,3,6,5,2]=>10000=>00001
[2,5,6,4,1,3]=>[3,1,4,6,5,2]=>00000=>00000
[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>10000=>00001
[2,6,1,3,4,5]=>[5,4,3,1,6,2]=>00000=>00000
[2,6,1,3,5,4]=>[4,5,3,1,6,2]=>00000=>00000
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[2,6,1,4,5,3]=>[3,5,4,1,6,2]=>00000=>00000
[2,6,1,5,3,4]=>[4,3,5,1,6,2]=>00000=>00000
[2,6,1,5,4,3]=>[3,4,5,1,6,2]=>00000=>00000
[2,6,3,1,4,5]=>[5,4,1,3,6,2]=>00000=>00000
[2,6,3,1,5,4]=>[4,5,1,3,6,2]=>00000=>00000
[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>00000=>00000
[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>10000=>00001
[2,6,3,5,1,4]=>[4,1,5,3,6,2]=>00000=>00000
[2,6,3,5,4,1]=>[1,4,5,3,6,2]=>10000=>00001
[2,6,4,1,3,5]=>[5,3,1,4,6,2]=>00000=>00000
[2,6,4,1,5,3]=>[3,5,1,4,6,2]=>00000=>00000
[2,6,4,3,1,5]=>[5,1,3,4,6,2]=>00000=>00000
[2,6,4,3,5,1]=>[1,5,3,4,6,2]=>10000=>00001
[2,6,4,5,1,3]=>[3,1,5,4,6,2]=>00000=>00000
[2,6,4,5,3,1]=>[1,3,5,4,6,2]=>10000=>00001
[2,6,5,1,3,4]=>[4,3,1,5,6,2]=>00000=>00000
[2,6,5,1,4,3]=>[3,4,1,5,6,2]=>00000=>00000
[2,6,5,3,1,4]=>[4,1,3,5,6,2]=>00000=>00000
[2,6,5,3,4,1]=>[1,4,3,5,6,2]=>10000=>00001
[2,6,5,4,1,3]=>[3,1,4,5,6,2]=>00000=>00000
[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>10000=>00001
[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>00000=>00000
[3,1,2,4,6,5]=>[5,6,4,2,1,3]=>00000=>00000
[3,1,2,5,4,6]=>[6,4,5,2,1,3]=>00000=>00000
[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>00000=>00000
[3,1,2,6,4,5]=>[5,4,6,2,1,3]=>00000=>00000
[3,1,2,6,5,4]=>[4,5,6,2,1,3]=>00000=>00000
[3,1,4,2,5,6]=>[6,5,2,4,1,3]=>00000=>00000
[3,1,4,2,6,5]=>[5,6,2,4,1,3]=>00000=>00000
[3,1,4,5,2,6]=>[6,2,5,4,1,3]=>00000=>00000
[3,1,4,5,6,2]=>[2,6,5,4,1,3]=>00000=>00000
[3,1,4,6,2,5]=>[5,2,6,4,1,3]=>00000=>00000
[3,1,4,6,5,2]=>[2,5,6,4,1,3]=>00000=>00000
[3,1,5,2,4,6]=>[6,4,2,5,1,3]=>00000=>00000
[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>00000=>00000
[3,1,5,4,2,6]=>[6,2,4,5,1,3]=>00000=>00000
[3,1,5,4,6,2]=>[2,6,4,5,1,3]=>00000=>00000
[3,1,5,6,2,4]=>[4,2,6,5,1,3]=>00000=>00000
[3,1,5,6,4,2]=>[2,4,6,5,1,3]=>00000=>00000
[3,1,6,2,4,5]=>[5,4,2,6,1,3]=>00000=>00000
[3,1,6,2,5,4]=>[4,5,2,6,1,3]=>00000=>00000
[3,1,6,4,2,5]=>[5,2,4,6,1,3]=>00000=>00000
[3,1,6,4,5,2]=>[2,5,4,6,1,3]=>00000=>00000
[3,1,6,5,2,4]=>[4,2,5,6,1,3]=>00000=>00000
[3,1,6,5,4,2]=>[2,4,5,6,1,3]=>00000=>00000
[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>00000=>00000
[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>00000=>00000
[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>00000=>00000
[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>00000=>00000
[3,2,1,6,4,5]=>[5,4,6,1,2,3]=>00000=>00000
[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>00000=>00000
[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>00000=>00000
[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>00000=>00000
[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>00000=>00000
[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>10000=>00001
[3,2,4,6,1,5]=>[5,1,6,4,2,3]=>00000=>00000
[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>10000=>00001
[3,2,5,1,4,6]=>[6,4,1,5,2,3]=>00000=>00000
[3,2,5,1,6,4]=>[4,6,1,5,2,3]=>00000=>00000
[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>00000=>00000
[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>10000=>00001
[3,2,5,6,1,4]=>[4,1,6,5,2,3]=>00000=>00000
[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>10000=>00001
[3,2,6,1,4,5]=>[5,4,1,6,2,3]=>00000=>00000
[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>00000=>00000
[3,2,6,4,1,5]=>[5,1,4,6,2,3]=>00000=>00000
[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>10000=>00001
[3,2,6,5,1,4]=>[4,1,5,6,2,3]=>00000=>00000
[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>10000=>00001
[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>00000=>00000
[3,4,1,2,6,5]=>[5,6,2,1,4,3]=>00000=>00000
[3,4,1,5,2,6]=>[6,2,5,1,4,3]=>00000=>00000
[3,4,1,5,6,2]=>[2,6,5,1,4,3]=>00000=>00000
[3,4,1,6,2,5]=>[5,2,6,1,4,3]=>00000=>00000
[3,4,1,6,5,2]=>[2,5,6,1,4,3]=>00000=>00000
[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>00000=>00000
[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>00000=>00000
[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>00000=>00000
[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>10000=>00001
[3,4,2,6,1,5]=>[5,1,6,2,4,3]=>00000=>00000
[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>10000=>00001
[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>00000=>00000
[3,4,5,1,6,2]=>[2,6,1,5,4,3]=>00000=>00000
[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>00000=>00000
[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>10000=>00001
[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>01000=>00010
[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>11000=>00011
[3,4,6,1,2,5]=>[5,2,1,6,4,3]=>00000=>00000
[3,4,6,1,5,2]=>[2,5,1,6,4,3]=>00000=>00000
[3,4,6,2,1,5]=>[5,1,2,6,4,3]=>00000=>00000
[3,4,6,2,5,1]=>[1,5,2,6,4,3]=>10000=>00001
[3,4,6,5,1,2]=>[2,1,5,6,4,3]=>01000=>00010
[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>11000=>00011
[3,5,1,2,4,6]=>[6,4,2,1,5,3]=>00000=>00000
[3,5,1,2,6,4]=>[4,6,2,1,5,3]=>00000=>00000
[3,5,1,4,2,6]=>[6,2,4,1,5,3]=>00000=>00000
[3,5,1,4,6,2]=>[2,6,4,1,5,3]=>00000=>00000
[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>00000=>00000
[3,5,1,6,4,2]=>[2,4,6,1,5,3]=>00000=>00000
[3,5,2,1,4,6]=>[6,4,1,2,5,3]=>00000=>00000
[3,5,2,1,6,4]=>[4,6,1,2,5,3]=>00000=>00000
[3,5,2,4,1,6]=>[6,1,4,2,5,3]=>00000=>00000
[3,5,2,4,6,1]=>[1,6,4,2,5,3]=>10000=>00001
[3,5,2,6,1,4]=>[4,1,6,2,5,3]=>00000=>00000
[3,5,2,6,4,1]=>[1,4,6,2,5,3]=>10000=>00001
[3,5,4,1,2,6]=>[6,2,1,4,5,3]=>00000=>00000
[3,5,4,1,6,2]=>[2,6,1,4,5,3]=>00000=>00000
[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>00000=>00000
[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>10000=>00001
[3,5,4,6,1,2]=>[2,1,6,4,5,3]=>01000=>00010
[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>11000=>00011
[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>00000=>00000
[3,5,6,1,4,2]=>[2,4,1,6,5,3]=>00000=>00000
[3,5,6,2,1,4]=>[4,1,2,6,5,3]=>00000=>00000
[3,5,6,2,4,1]=>[1,4,2,6,5,3]=>10000=>00001
[3,5,6,4,1,2]=>[2,1,4,6,5,3]=>01000=>00010
[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>11000=>00011
[3,6,1,2,4,5]=>[5,4,2,1,6,3]=>00000=>00000
[3,6,1,2,5,4]=>[4,5,2,1,6,3]=>00000=>00000
[3,6,1,4,2,5]=>[5,2,4,1,6,3]=>00000=>00000
[3,6,1,4,5,2]=>[2,5,4,1,6,3]=>00000=>00000
[3,6,1,5,2,4]=>[4,2,5,1,6,3]=>00000=>00000
[3,6,1,5,4,2]=>[2,4,5,1,6,3]=>00000=>00000
[3,6,2,1,4,5]=>[5,4,1,2,6,3]=>00000=>00000
[3,6,2,1,5,4]=>[4,5,1,2,6,3]=>00000=>00000
[3,6,2,4,1,5]=>[5,1,4,2,6,3]=>00000=>00000
[3,6,2,4,5,1]=>[1,5,4,2,6,3]=>10000=>00001
[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>00000=>00000
[3,6,2,5,4,1]=>[1,4,5,2,6,3]=>10000=>00001
[3,6,4,1,2,5]=>[5,2,1,4,6,3]=>00000=>00000
[3,6,4,1,5,2]=>[2,5,1,4,6,3]=>00000=>00000
[3,6,4,2,1,5]=>[5,1,2,4,6,3]=>00000=>00000
[3,6,4,2,5,1]=>[1,5,2,4,6,3]=>10000=>00001
[3,6,4,5,1,2]=>[2,1,5,4,6,3]=>01000=>00010
[3,6,4,5,2,1]=>[1,2,5,4,6,3]=>11000=>00011
[3,6,5,1,2,4]=>[4,2,1,5,6,3]=>00000=>00000
[3,6,5,1,4,2]=>[2,4,1,5,6,3]=>00000=>00000
[3,6,5,2,1,4]=>[4,1,2,5,6,3]=>00000=>00000
[3,6,5,2,4,1]=>[1,4,2,5,6,3]=>10000=>00001
[3,6,5,4,1,2]=>[2,1,4,5,6,3]=>01000=>00010
[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>11000=>00011
[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>00000=>00000
[4,1,2,3,6,5]=>[5,6,3,2,1,4]=>00000=>00000
[4,1,2,5,3,6]=>[6,3,5,2,1,4]=>00000=>00000
[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>00000=>00000
[4,1,2,6,3,5]=>[5,3,6,2,1,4]=>00000=>00000
[4,1,2,6,5,3]=>[3,5,6,2,1,4]=>00000=>00000
[4,1,3,2,5,6]=>[6,5,2,3,1,4]=>00000=>00000
[4,1,3,2,6,5]=>[5,6,2,3,1,4]=>00000=>00000
[4,1,3,5,2,6]=>[6,2,5,3,1,4]=>00000=>00000
[4,1,3,5,6,2]=>[2,6,5,3,1,4]=>00000=>00000
[4,1,3,6,2,5]=>[5,2,6,3,1,4]=>00000=>00000
[4,1,3,6,5,2]=>[2,5,6,3,1,4]=>00000=>00000
[4,1,5,2,3,6]=>[6,3,2,5,1,4]=>00000=>00000
[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>00000=>00000
[4,1,5,3,2,6]=>[6,2,3,5,1,4]=>00000=>00000
[4,1,5,3,6,2]=>[2,6,3,5,1,4]=>00000=>00000
[4,1,5,6,2,3]=>[3,2,6,5,1,4]=>00000=>00000
[4,1,5,6,3,2]=>[2,3,6,5,1,4]=>00000=>00000
[4,1,6,2,3,5]=>[5,3,2,6,1,4]=>00000=>00000
[4,1,6,2,5,3]=>[3,5,2,6,1,4]=>00000=>00000
[4,1,6,3,2,5]=>[5,2,3,6,1,4]=>00000=>00000
[4,1,6,3,5,2]=>[2,5,3,6,1,4]=>00000=>00000
[4,1,6,5,2,3]=>[3,2,5,6,1,4]=>00000=>00000
[4,1,6,5,3,2]=>[2,3,5,6,1,4]=>00000=>00000
[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>00000=>00000
[4,2,1,3,6,5]=>[5,6,3,1,2,4]=>00000=>00000
[4,2,1,5,3,6]=>[6,3,5,1,2,4]=>00000=>00000
[4,2,1,5,6,3]=>[3,6,5,1,2,4]=>00000=>00000
[4,2,1,6,3,5]=>[5,3,6,1,2,4]=>00000=>00000
[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>00000=>00000
[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>00000=>00000
[4,2,3,1,6,5]=>[5,6,1,3,2,4]=>00000=>00000
[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>00000=>00000
[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>10000=>00001
[4,2,3,6,1,5]=>[5,1,6,3,2,4]=>00000=>00000
[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>10000=>00001
[4,2,5,1,3,6]=>[6,3,1,5,2,4]=>00000=>00000
[4,2,5,1,6,3]=>[3,6,1,5,2,4]=>00000=>00000
[4,2,5,3,1,6]=>[6,1,3,5,2,4]=>00000=>00000
[4,2,5,3,6,1]=>[1,6,3,5,2,4]=>10000=>00001
[4,2,5,6,1,3]=>[3,1,6,5,2,4]=>00000=>00000
[4,2,5,6,3,1]=>[1,3,6,5,2,4]=>10000=>00001
[4,2,6,1,3,5]=>[5,3,1,6,2,4]=>00000=>00000
[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>00000=>00000
[4,2,6,3,1,5]=>[5,1,3,6,2,4]=>00000=>00000
[4,2,6,3,5,1]=>[1,5,3,6,2,4]=>10000=>00001
[4,2,6,5,1,3]=>[3,1,5,6,2,4]=>00000=>00000
[4,2,6,5,3,1]=>[1,3,5,6,2,4]=>10000=>00001
[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>00000=>00000
[4,3,1,2,6,5]=>[5,6,2,1,3,4]=>00000=>00000
[4,3,1,5,2,6]=>[6,2,5,1,3,4]=>00000=>00000
[4,3,1,5,6,2]=>[2,6,5,1,3,4]=>00000=>00000
[4,3,1,6,2,5]=>[5,2,6,1,3,4]=>00000=>00000
[4,3,1,6,5,2]=>[2,5,6,1,3,4]=>00000=>00000
[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>00000=>00000
[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>00000=>00000
[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>00000=>00000
[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>10000=>00001
[4,3,2,6,1,5]=>[5,1,6,2,3,4]=>00000=>00000
[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>10000=>00001
[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>00000=>00000
[4,3,5,1,6,2]=>[2,6,1,5,3,4]=>00000=>00000
[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>00000=>00000
[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>10000=>00001
[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>01000=>00010
[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>11000=>00011
[4,3,6,1,2,5]=>[5,2,1,6,3,4]=>00000=>00000
[4,3,6,1,5,2]=>[2,5,1,6,3,4]=>00000=>00000
[4,3,6,2,1,5]=>[5,1,2,6,3,4]=>00000=>00000
[4,3,6,2,5,1]=>[1,5,2,6,3,4]=>10000=>00001
[4,3,6,5,1,2]=>[2,1,5,6,3,4]=>01000=>00010
[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>11000=>00011
[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>00000=>00000
[4,5,1,2,6,3]=>[3,6,2,1,5,4]=>00000=>00000
[4,5,1,3,2,6]=>[6,2,3,1,5,4]=>00000=>00000
[4,5,1,3,6,2]=>[2,6,3,1,5,4]=>00000=>00000
[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>00000=>00000
[4,5,1,6,3,2]=>[2,3,6,1,5,4]=>00000=>00000
[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>00000=>00000
[4,5,2,1,6,3]=>[3,6,1,2,5,4]=>00000=>00000
[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>00000=>00000
[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>10000=>00001
[4,5,2,6,1,3]=>[3,1,6,2,5,4]=>00000=>00000
[4,5,2,6,3,1]=>[1,3,6,2,5,4]=>10000=>00001
[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>00000=>00000
[4,5,3,1,6,2]=>[2,6,1,3,5,4]=>00000=>00000
[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>00000=>00000
[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>10000=>00001
[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>01000=>00010
[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>11000=>00011
[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>00100=>00100
[4,5,6,1,3,2]=>[2,3,1,6,5,4]=>00100=>00100
[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>00100=>00100
[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>10100=>00101
[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>01100=>00110
[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>11100=>00111
[4,6,1,2,3,5]=>[5,3,2,1,6,4]=>00000=>00000
[4,6,1,2,5,3]=>[3,5,2,1,6,4]=>00000=>00000
[4,6,1,3,2,5]=>[5,2,3,1,6,4]=>00000=>00000
[4,6,1,3,5,2]=>[2,5,3,1,6,4]=>00000=>00000
[4,6,1,5,2,3]=>[3,2,5,1,6,4]=>00000=>00000
[4,6,1,5,3,2]=>[2,3,5,1,6,4]=>00000=>00000
[4,6,2,1,3,5]=>[5,3,1,2,6,4]=>00000=>00000
[4,6,2,1,5,3]=>[3,5,1,2,6,4]=>00000=>00000
[4,6,2,3,1,5]=>[5,1,3,2,6,4]=>00000=>00000
[4,6,2,3,5,1]=>[1,5,3,2,6,4]=>10000=>00001
[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>00000=>00000
[4,6,2,5,3,1]=>[1,3,5,2,6,4]=>10000=>00001
[4,6,3,1,2,5]=>[5,2,1,3,6,4]=>00000=>00000
[4,6,3,1,5,2]=>[2,5,1,3,6,4]=>00000=>00000
[4,6,3,2,1,5]=>[5,1,2,3,6,4]=>00000=>00000
[4,6,3,2,5,1]=>[1,5,2,3,6,4]=>10000=>00001
[4,6,3,5,1,2]=>[2,1,5,3,6,4]=>01000=>00010
[4,6,3,5,2,1]=>[1,2,5,3,6,4]=>11000=>00011
[4,6,5,1,2,3]=>[3,2,1,5,6,4]=>00100=>00100
[4,6,5,1,3,2]=>[2,3,1,5,6,4]=>00100=>00100
[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>00100=>00100
[4,6,5,2,3,1]=>[1,3,2,5,6,4]=>10100=>00101
[4,6,5,3,1,2]=>[2,1,3,5,6,4]=>01100=>00110
[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>11100=>00111
[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>00000=>00000
[5,1,2,3,6,4]=>[4,6,3,2,1,5]=>00000=>00000
[5,1,2,4,3,6]=>[6,3,4,2,1,5]=>00000=>00000
[5,1,2,4,6,3]=>[3,6,4,2,1,5]=>00000=>00000
[5,1,2,6,3,4]=>[4,3,6,2,1,5]=>00000=>00000
[5,1,2,6,4,3]=>[3,4,6,2,1,5]=>00000=>00000
[5,1,3,2,4,6]=>[6,4,2,3,1,5]=>00000=>00000
[5,1,3,2,6,4]=>[4,6,2,3,1,5]=>00000=>00000
[5,1,3,4,2,6]=>[6,2,4,3,1,5]=>00000=>00000
[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>00000=>00000
[5,1,3,6,2,4]=>[4,2,6,3,1,5]=>00000=>00000
[5,1,3,6,4,2]=>[2,4,6,3,1,5]=>00000=>00000
[5,1,4,2,3,6]=>[6,3,2,4,1,5]=>00000=>00000
[5,1,4,2,6,3]=>[3,6,2,4,1,5]=>00000=>00000
[5,1,4,3,2,6]=>[6,2,3,4,1,5]=>00000=>00000
[5,1,4,3,6,2]=>[2,6,3,4,1,5]=>00000=>00000
[5,1,4,6,2,3]=>[3,2,6,4,1,5]=>00000=>00000
[5,1,4,6,3,2]=>[2,3,6,4,1,5]=>00000=>00000
[5,1,6,2,3,4]=>[4,3,2,6,1,5]=>00000=>00000
[5,1,6,2,4,3]=>[3,4,2,6,1,5]=>00000=>00000
[5,1,6,3,2,4]=>[4,2,3,6,1,5]=>00000=>00000
[5,1,6,3,4,2]=>[2,4,3,6,1,5]=>00000=>00000
[5,1,6,4,2,3]=>[3,2,4,6,1,5]=>00000=>00000
[5,1,6,4,3,2]=>[2,3,4,6,1,5]=>00000=>00000
[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>00000=>00000
[5,2,1,3,6,4]=>[4,6,3,1,2,5]=>00000=>00000
[5,2,1,4,3,6]=>[6,3,4,1,2,5]=>00000=>00000
[5,2,1,4,6,3]=>[3,6,4,1,2,5]=>00000=>00000
[5,2,1,6,3,4]=>[4,3,6,1,2,5]=>00000=>00000
[5,2,1,6,4,3]=>[3,4,6,1,2,5]=>00000=>00000
[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>00000=>00000
[5,2,3,1,6,4]=>[4,6,1,3,2,5]=>00000=>00000
[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>00000=>00000
[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>10000=>00001
[5,2,3,6,1,4]=>[4,1,6,3,2,5]=>00000=>00000
[5,2,3,6,4,1]=>[1,4,6,3,2,5]=>10000=>00001
[5,2,4,1,3,6]=>[6,3,1,4,2,5]=>00000=>00000
[5,2,4,1,6,3]=>[3,6,1,4,2,5]=>00000=>00000
[5,2,4,3,1,6]=>[6,1,3,4,2,5]=>00000=>00000
[5,2,4,3,6,1]=>[1,6,3,4,2,5]=>10000=>00001
[5,2,4,6,1,3]=>[3,1,6,4,2,5]=>00000=>00000
[5,2,4,6,3,1]=>[1,3,6,4,2,5]=>10000=>00001
[5,2,6,1,3,4]=>[4,3,1,6,2,5]=>00000=>00000
[5,2,6,1,4,3]=>[3,4,1,6,2,5]=>00000=>00000
[5,2,6,3,1,4]=>[4,1,3,6,2,5]=>00000=>00000
[5,2,6,3,4,1]=>[1,4,3,6,2,5]=>10000=>00001
[5,2,6,4,1,3]=>[3,1,4,6,2,5]=>00000=>00000
[5,2,6,4,3,1]=>[1,3,4,6,2,5]=>10000=>00001
[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>00000=>00000
[5,3,1,2,6,4]=>[4,6,2,1,3,5]=>00000=>00000
[5,3,1,4,2,6]=>[6,2,4,1,3,5]=>00000=>00000
[5,3,1,4,6,2]=>[2,6,4,1,3,5]=>00000=>00000
[5,3,1,6,2,4]=>[4,2,6,1,3,5]=>00000=>00000
[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>00000=>00000
[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>00000=>00000
[5,3,2,1,6,4]=>[4,6,1,2,3,5]=>00000=>00000
[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>00000=>00000
[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>10000=>00001
[5,3,2,6,1,4]=>[4,1,6,2,3,5]=>00000=>00000
[5,3,2,6,4,1]=>[1,4,6,2,3,5]=>10000=>00001
[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>00000=>00000
[5,3,4,1,6,2]=>[2,6,1,4,3,5]=>00000=>00000
[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>00000=>00000
[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>10000=>00001
[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>01000=>00010
[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>11000=>00011
[5,3,6,1,2,4]=>[4,2,1,6,3,5]=>00000=>00000
[5,3,6,1,4,2]=>[2,4,1,6,3,5]=>00000=>00000
[5,3,6,2,1,4]=>[4,1,2,6,3,5]=>00000=>00000
[5,3,6,2,4,1]=>[1,4,2,6,3,5]=>10000=>00001
[5,3,6,4,1,2]=>[2,1,4,6,3,5]=>01000=>00010
[5,3,6,4,2,1]=>[1,2,4,6,3,5]=>11000=>00011
[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>00000=>00000
[5,4,1,2,6,3]=>[3,6,2,1,4,5]=>00000=>00000
[5,4,1,3,2,6]=>[6,2,3,1,4,5]=>00000=>00000
[5,4,1,3,6,2]=>[2,6,3,1,4,5]=>00000=>00000
[5,4,1,6,2,3]=>[3,2,6,1,4,5]=>00000=>00000
[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>00000=>00000
[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>00000=>00000
[5,4,2,1,6,3]=>[3,6,1,2,4,5]=>00000=>00000
[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>00000=>00000
[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>10000=>00001
[5,4,2,6,1,3]=>[3,1,6,2,4,5]=>00000=>00000
[5,4,2,6,3,1]=>[1,3,6,2,4,5]=>10000=>00001
[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>00000=>00000
[5,4,3,1,6,2]=>[2,6,1,3,4,5]=>00000=>00000
[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>00000=>00000
[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>10000=>00001
[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>01000=>00010
[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>11000=>00011
[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>00100=>00100
[5,4,6,1,3,2]=>[2,3,1,6,4,5]=>00100=>00100
[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>00100=>00100
[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>10100=>00101
[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>01100=>00110
[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>11100=>00111
[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>00010=>01000
[5,6,1,2,4,3]=>[3,4,2,1,6,5]=>00010=>01000
[5,6,1,3,2,4]=>[4,2,3,1,6,5]=>00010=>01000
[5,6,1,3,4,2]=>[2,4,3,1,6,5]=>00010=>01000
[5,6,1,4,2,3]=>[3,2,4,1,6,5]=>00010=>01000
[5,6,1,4,3,2]=>[2,3,4,1,6,5]=>00010=>01000
[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>00010=>01000
[5,6,2,1,4,3]=>[3,4,1,2,6,5]=>00010=>01000
[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>00010=>01000
[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>10010=>01001
[5,6,2,4,1,3]=>[3,1,4,2,6,5]=>00010=>01000
[5,6,2,4,3,1]=>[1,3,4,2,6,5]=>10010=>01001
[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>00010=>01000
[5,6,3,1,4,2]=>[2,4,1,3,6,5]=>00010=>01000
[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00010=>01000
[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>10010=>01001
[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>01010=>01010
[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>11010=>01011
[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>00110=>01100
[5,6,4,1,3,2]=>[2,3,1,4,6,5]=>00110=>01100
[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>00110=>01100
[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>10110=>01101
[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>01110=>01110
[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>11110=>01111
[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>00001=>10000
[6,1,2,3,5,4]=>[4,5,3,2,1,6]=>00001=>10000
[6,1,2,4,3,5]=>[5,3,4,2,1,6]=>00001=>10000
[6,1,2,4,5,3]=>[3,5,4,2,1,6]=>00001=>10000
[6,1,2,5,3,4]=>[4,3,5,2,1,6]=>00001=>10000
[6,1,2,5,4,3]=>[3,4,5,2,1,6]=>00001=>10000
[6,1,3,2,4,5]=>[5,4,2,3,1,6]=>00001=>10000
[6,1,3,2,5,4]=>[4,5,2,3,1,6]=>00001=>10000
[6,1,3,4,2,5]=>[5,2,4,3,1,6]=>00001=>10000
[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>00001=>10000
[6,1,3,5,2,4]=>[4,2,5,3,1,6]=>00001=>10000
[6,1,3,5,4,2]=>[2,4,5,3,1,6]=>00001=>10000
[6,1,4,2,3,5]=>[5,3,2,4,1,6]=>00001=>10000
[6,1,4,2,5,3]=>[3,5,2,4,1,6]=>00001=>10000
[6,1,4,3,2,5]=>[5,2,3,4,1,6]=>00001=>10000
[6,1,4,3,5,2]=>[2,5,3,4,1,6]=>00001=>10000
[6,1,4,5,2,3]=>[3,2,5,4,1,6]=>00001=>10000
[6,1,4,5,3,2]=>[2,3,5,4,1,6]=>00001=>10000
[6,1,5,2,3,4]=>[4,3,2,5,1,6]=>00001=>10000
[6,1,5,2,4,3]=>[3,4,2,5,1,6]=>00001=>10000
[6,1,5,3,2,4]=>[4,2,3,5,1,6]=>00001=>10000
[6,1,5,3,4,2]=>[2,4,3,5,1,6]=>00001=>10000
[6,1,5,4,2,3]=>[3,2,4,5,1,6]=>00001=>10000
[6,1,5,4,3,2]=>[2,3,4,5,1,6]=>00001=>10000
[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>00001=>10000
[6,2,1,3,5,4]=>[4,5,3,1,2,6]=>00001=>10000
[6,2,1,4,3,5]=>[5,3,4,1,2,6]=>00001=>10000
[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>00001=>10000
[6,2,1,5,3,4]=>[4,3,5,1,2,6]=>00001=>10000
[6,2,1,5,4,3]=>[3,4,5,1,2,6]=>00001=>10000
[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>00001=>10000
[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>00001=>10000
[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>00001=>10000
[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>10001=>10001
[6,2,3,5,1,4]=>[4,1,5,3,2,6]=>00001=>10000
[6,2,3,5,4,1]=>[1,4,5,3,2,6]=>10001=>10001
[6,2,4,1,3,5]=>[5,3,1,4,2,6]=>00001=>10000
[6,2,4,1,5,3]=>[3,5,1,4,2,6]=>00001=>10000
[6,2,4,3,1,5]=>[5,1,3,4,2,6]=>00001=>10000
[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>10001=>10001
[6,2,4,5,1,3]=>[3,1,5,4,2,6]=>00001=>10000
[6,2,4,5,3,1]=>[1,3,5,4,2,6]=>10001=>10001
[6,2,5,1,3,4]=>[4,3,1,5,2,6]=>00001=>10000
[6,2,5,1,4,3]=>[3,4,1,5,2,6]=>00001=>10000
[6,2,5,3,1,4]=>[4,1,3,5,2,6]=>00001=>10000
[6,2,5,3,4,1]=>[1,4,3,5,2,6]=>10001=>10001
[6,2,5,4,1,3]=>[3,1,4,5,2,6]=>00001=>10000
[6,2,5,4,3,1]=>[1,3,4,5,2,6]=>10001=>10001
[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>00001=>10000
[6,3,1,2,5,4]=>[4,5,2,1,3,6]=>00001=>10000
[6,3,1,4,2,5]=>[5,2,4,1,3,6]=>00001=>10000
[6,3,1,4,5,2]=>[2,5,4,1,3,6]=>00001=>10000
[6,3,1,5,2,4]=>[4,2,5,1,3,6]=>00001=>10000
[6,3,1,5,4,2]=>[2,4,5,1,3,6]=>00001=>10000
[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>00001=>10000
[6,3,2,1,5,4]=>[4,5,1,2,3,6]=>00001=>10000
[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>00001=>10000
[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>10001=>10001
[6,3,2,5,1,4]=>[4,1,5,2,3,6]=>00001=>10000
[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>10001=>10001
[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>00001=>10000
[6,3,4,1,5,2]=>[2,5,1,4,3,6]=>00001=>10000
[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>00001=>10000
[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>10001=>10001
[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>01001=>10010
[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>11001=>10011
[6,3,5,1,2,4]=>[4,2,1,5,3,6]=>00001=>10000
[6,3,5,1,4,2]=>[2,4,1,5,3,6]=>00001=>10000
[6,3,5,2,1,4]=>[4,1,2,5,3,6]=>00001=>10000
[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>10001=>10001
[6,3,5,4,1,2]=>[2,1,4,5,3,6]=>01001=>10010
[6,3,5,4,2,1]=>[1,2,4,5,3,6]=>11001=>10011
[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>00001=>10000
[6,4,1,2,5,3]=>[3,5,2,1,4,6]=>00001=>10000
[6,4,1,3,2,5]=>[5,2,3,1,4,6]=>00001=>10000
[6,4,1,3,5,2]=>[2,5,3,1,4,6]=>00001=>10000
[6,4,1,5,2,3]=>[3,2,5,1,4,6]=>00001=>10000
[6,4,1,5,3,2]=>[2,3,5,1,4,6]=>00001=>10000
[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>00001=>10000
[6,4,2,1,5,3]=>[3,5,1,2,4,6]=>00001=>10000
[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>00001=>10000
[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>10001=>10001
[6,4,2,5,1,3]=>[3,1,5,2,4,6]=>00001=>10000
[6,4,2,5,3,1]=>[1,3,5,2,4,6]=>10001=>10001
[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>00001=>10000
[6,4,3,1,5,2]=>[2,5,1,3,4,6]=>00001=>10000
[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>00001=>10000
[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>10001=>10001
[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>01001=>10010
[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>11001=>10011
[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>00101=>10100
[6,4,5,1,3,2]=>[2,3,1,5,4,6]=>00101=>10100
[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>00101=>10100
[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>10101=>10101
[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>01101=>10110
[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>11101=>10111
[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>00011=>11000
[6,5,1,2,4,3]=>[3,4,2,1,5,6]=>00011=>11000
[6,5,1,3,2,4]=>[4,2,3,1,5,6]=>00011=>11000
[6,5,1,3,4,2]=>[2,4,3,1,5,6]=>00011=>11000
[6,5,1,4,2,3]=>[3,2,4,1,5,6]=>00011=>11000
[6,5,1,4,3,2]=>[2,3,4,1,5,6]=>00011=>11000
[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>00011=>11000
[6,5,2,1,4,3]=>[3,4,1,2,5,6]=>00011=>11000
[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>00011=>11000
[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>10011=>11001
[6,5,2,4,1,3]=>[3,1,4,2,5,6]=>00011=>11000
[6,5,2,4,3,1]=>[1,3,4,2,5,6]=>10011=>11001
[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>00011=>11000
[6,5,3,1,4,2]=>[2,4,1,3,5,6]=>00011=>11000
[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00011=>11000
[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>10011=>11001
[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>01011=>11010
[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>11011=>11011
[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>00111=>11100
[6,5,4,1,3,2]=>[2,3,1,4,5,6]=>00111=>11100
[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>00111=>11100
[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>10111=>11101
[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>01111=>11110
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>11111=>11111
[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>000000=>000000
[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>000000=>000000
[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>000000=>000000
[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>000000=>000000
[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>000000=>000000
[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>000000=>000000
[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>000000=>000000
[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>000000=>000000
[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>000000=>000000
[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>000000=>000000
[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>000000=>000000
[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>000000=>000000
[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>000000=>000000
[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>000000=>000000
[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>000000=>000000
[1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1]=>000000=>000000
[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>000000=>000000
[1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1]=>000000=>000000
[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>000000=>000000
[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>000000=>000000
[1,2,3,7,5,4,6]=>[6,4,5,7,3,2,1]=>000000=>000000
[1,2,3,7,5,6,4]=>[4,6,5,7,3,2,1]=>000000=>000000
[1,2,3,7,6,4,5]=>[5,4,6,7,3,2,1]=>000000=>000000
[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>000000=>000000
[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>000000=>000000
[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>000000=>000000
[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>000000=>000000
[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>000000=>000000
[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>000000=>000000
[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>000000=>000000
[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>000000=>000000
[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>000000=>000000
[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>000000=>000000
[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>000000=>000000
[1,2,4,5,7,3,6]=>[6,3,7,5,4,2,1]=>000000=>000000
[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>000000=>000000
[1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1]=>000000=>000000
[1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1]=>000000=>000000
[1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1]=>000000=>000000
[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>000000=>000000
[1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1]=>000000=>000000
[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>000000=>000000
[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>000000=>000000
[1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1]=>000000=>000000
[1,2,4,7,5,3,6]=>[6,3,5,7,4,2,1]=>000000=>000000
[1,2,4,7,5,6,3]=>[3,6,5,7,4,2,1]=>000000=>000000
[1,2,4,7,6,3,5]=>[5,3,6,7,4,2,1]=>000000=>000000
[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>000000=>000000
[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>000000=>000000
[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>000000=>000000
[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>000000=>000000
[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>000000=>000000
[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>000000=>000000
[1,2,5,3,7,6,4]=>[4,6,7,3,5,2,1]=>000000=>000000
[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>000000=>000000
[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>000000=>000000
[1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1]=>000000=>000000
[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>000000=>000000
[1,2,5,4,7,3,6]=>[6,3,7,4,5,2,1]=>000000=>000000
[1,2,5,4,7,6,3]=>[3,6,7,4,5,2,1]=>000000=>000000
[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>000000=>000000
[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>000000=>000000
[1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1]=>000000=>000000
[1,2,5,6,4,7,3]=>[3,7,4,6,5,2,1]=>000000=>000000
[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>000000=>000000
[1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1]=>000000=>000000
[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>000000=>000000
[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>000000=>000000
[1,2,5,7,4,3,6]=>[6,3,4,7,5,2,1]=>000000=>000000
[1,2,5,7,4,6,3]=>[3,6,4,7,5,2,1]=>000000=>000000
[1,2,5,7,6,3,4]=>[4,3,6,7,5,2,1]=>000000=>000000
[1,2,5,7,6,4,3]=>[3,4,6,7,5,2,1]=>000000=>000000
[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>000000=>000000
[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>000000=>000000
[1,2,6,3,5,4,7]=>[7,4,5,3,6,2,1]=>000000=>000000
[1,2,6,3,5,7,4]=>[4,7,5,3,6,2,1]=>000000=>000000
[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>000000=>000000
[1,2,6,3,7,5,4]=>[4,5,7,3,6,2,1]=>000000=>000000
[1,2,6,4,3,5,7]=>[7,5,3,4,6,2,1]=>000000=>000000
[1,2,6,4,3,7,5]=>[5,7,3,4,6,2,1]=>000000=>000000
[1,2,6,4,5,3,7]=>[7,3,5,4,6,2,1]=>000000=>000000
[1,2,6,4,5,7,3]=>[3,7,5,4,6,2,1]=>000000=>000000
[1,2,6,4,7,3,5]=>[5,3,7,4,6,2,1]=>000000=>000000
[1,2,6,4,7,5,3]=>[3,5,7,4,6,2,1]=>000000=>000000
[1,2,6,5,3,4,7]=>[7,4,3,5,6,2,1]=>000000=>000000
[1,2,6,5,3,7,4]=>[4,7,3,5,6,2,1]=>000000=>000000
[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>000000=>000000
[1,2,6,5,4,7,3]=>[3,7,4,5,6,2,1]=>000000=>000000
[1,2,6,5,7,3,4]=>[4,3,7,5,6,2,1]=>000000=>000000
[1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1]=>000000=>000000
[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>000000=>000000
[1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1]=>000000=>000000
[1,2,6,7,4,3,5]=>[5,3,4,7,6,2,1]=>000000=>000000
[1,2,6,7,4,5,3]=>[3,5,4,7,6,2,1]=>000000=>000000
[1,2,6,7,5,3,4]=>[4,3,5,7,6,2,1]=>000000=>000000
[1,2,6,7,5,4,3]=>[3,4,5,7,6,2,1]=>000000=>000000
[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>000000=>000000
[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>000000=>000000
[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>000000=>000000
[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>000000=>000000
[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>000000=>000000
[1,2,7,3,6,5,4]=>[4,5,6,3,7,2,1]=>000000=>000000
[1,2,7,4,3,5,6]=>[6,5,3,4,7,2,1]=>000000=>000000
[1,2,7,4,3,6,5]=>[5,6,3,4,7,2,1]=>000000=>000000
[1,2,7,4,5,3,6]=>[6,3,5,4,7,2,1]=>000000=>000000
[1,2,7,4,5,6,3]=>[3,6,5,4,7,2,1]=>000000=>000000
[1,2,7,4,6,3,5]=>[5,3,6,4,7,2,1]=>000000=>000000
[1,2,7,4,6,5,3]=>[3,5,6,4,7,2,1]=>000000=>000000
[1,2,7,5,3,4,6]=>[6,4,3,5,7,2,1]=>000000=>000000
[1,2,7,5,3,6,4]=>[4,6,3,5,7,2,1]=>000000=>000000
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[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>110000=>000011
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[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>110000=>000011
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[3,4,6,2,5,7,1]=>[1,7,5,2,6,4,3]=>100000=>000001
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[3,4,6,2,7,5,1]=>[1,5,7,2,6,4,3]=>100000=>000001
[3,4,6,5,1,2,7]=>[7,2,1,5,6,4,3]=>000000=>000000
[3,4,6,5,1,7,2]=>[2,7,1,5,6,4,3]=>000000=>000000
[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>000000=>000000
[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>100000=>000001
[3,4,6,5,7,1,2]=>[2,1,7,5,6,4,3]=>010000=>000010
[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>110000=>000011
[3,4,6,7,1,2,5]=>[5,2,1,7,6,4,3]=>000000=>000000
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[3,4,6,7,5,1,2]=>[2,1,5,7,6,4,3]=>010000=>000010
[3,4,6,7,5,2,1]=>[1,2,5,7,6,4,3]=>110000=>000011
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[3,5,7,4,2,6,1]=>[1,6,2,4,7,5,3]=>100000=>000001
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[3,5,7,4,6,2,1]=>[1,2,6,4,7,5,3]=>110000=>000011
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[3,5,7,6,4,1,2]=>[2,1,4,6,7,5,3]=>010000=>000010
[3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3]=>110000=>000011
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[3,6,4,5,2,7,1]=>[1,7,2,5,4,6,3]=>100000=>000001
[3,6,4,5,7,1,2]=>[2,1,7,5,4,6,3]=>010000=>000010
[3,6,4,5,7,2,1]=>[1,2,7,5,4,6,3]=>110000=>000011
[3,6,4,7,1,2,5]=>[5,2,1,7,4,6,3]=>000000=>000000
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[3,6,4,7,5,1,2]=>[2,1,5,7,4,6,3]=>010000=>000010
[3,6,4,7,5,2,1]=>[1,2,5,7,4,6,3]=>110000=>000011
[3,6,5,1,2,4,7]=>[7,4,2,1,5,6,3]=>000000=>000000
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[4,3,7,6,2,1,5]=>[5,1,2,6,7,3,4]=>000000=>000000
[4,3,7,6,2,5,1]=>[1,5,2,6,7,3,4]=>100000=>000001
[4,3,7,6,5,1,2]=>[2,1,5,6,7,3,4]=>010000=>000010
[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>110000=>000011
[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>000000=>000000
[4,5,1,2,3,7,6]=>[6,7,3,2,1,5,4]=>000000=>000000
[4,5,1,2,6,3,7]=>[7,3,6,2,1,5,4]=>000000=>000000
[4,5,1,2,6,7,3]=>[3,7,6,2,1,5,4]=>000000=>000000
[4,5,1,2,7,3,6]=>[6,3,7,2,1,5,4]=>000000=>000000
[4,5,1,2,7,6,3]=>[3,6,7,2,1,5,4]=>000000=>000000
[4,5,1,3,2,6,7]=>[7,6,2,3,1,5,4]=>000000=>000000
[4,5,1,3,2,7,6]=>[6,7,2,3,1,5,4]=>000000=>000000
[4,5,1,3,6,2,7]=>[7,2,6,3,1,5,4]=>000000=>000000
[4,5,1,3,6,7,2]=>[2,7,6,3,1,5,4]=>000000=>000000
[4,5,1,3,7,2,6]=>[6,2,7,3,1,5,4]=>000000=>000000
[4,5,1,3,7,6,2]=>[2,6,7,3,1,5,4]=>000000=>000000
[4,5,1,6,2,3,7]=>[7,3,2,6,1,5,4]=>000000=>000000
[4,5,1,6,2,7,3]=>[3,7,2,6,1,5,4]=>000000=>000000
[4,5,1,6,3,2,7]=>[7,2,3,6,1,5,4]=>000000=>000000
[4,5,1,6,3,7,2]=>[2,7,3,6,1,5,4]=>000000=>000000
[4,5,1,6,7,2,3]=>[3,2,7,6,1,5,4]=>000000=>000000
[4,5,1,6,7,3,2]=>[2,3,7,6,1,5,4]=>000000=>000000
[4,5,1,7,2,3,6]=>[6,3,2,7,1,5,4]=>000000=>000000
[4,5,1,7,2,6,3]=>[3,6,2,7,1,5,4]=>000000=>000000
[4,5,1,7,3,2,6]=>[6,2,3,7,1,5,4]=>000000=>000000
[4,5,1,7,3,6,2]=>[2,6,3,7,1,5,4]=>000000=>000000
[4,5,1,7,6,2,3]=>[3,2,6,7,1,5,4]=>000000=>000000
[4,5,1,7,6,3,2]=>[2,3,6,7,1,5,4]=>000000=>000000
[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>000000=>000000
[4,5,2,1,3,7,6]=>[6,7,3,1,2,5,4]=>000000=>000000
[4,5,2,1,6,3,7]=>[7,3,6,1,2,5,4]=>000000=>000000
[4,5,2,1,6,7,3]=>[3,7,6,1,2,5,4]=>000000=>000000
[4,5,2,1,7,3,6]=>[6,3,7,1,2,5,4]=>000000=>000000
[4,5,2,1,7,6,3]=>[3,6,7,1,2,5,4]=>000000=>000000
[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>000000=>000000
[4,5,2,3,1,7,6]=>[6,7,1,3,2,5,4]=>000000=>000000
[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>000000=>000000
[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>100000=>000001
[4,5,2,3,7,1,6]=>[6,1,7,3,2,5,4]=>000000=>000000
[4,5,2,3,7,6,1]=>[1,6,7,3,2,5,4]=>100000=>000001
[4,5,2,6,1,3,7]=>[7,3,1,6,2,5,4]=>000000=>000000
[4,5,2,6,1,7,3]=>[3,7,1,6,2,5,4]=>000000=>000000
[4,5,2,6,3,1,7]=>[7,1,3,6,2,5,4]=>000000=>000000
[4,5,2,6,3,7,1]=>[1,7,3,6,2,5,4]=>100000=>000001
[4,5,2,6,7,1,3]=>[3,1,7,6,2,5,4]=>000000=>000000
[4,5,2,6,7,3,1]=>[1,3,7,6,2,5,4]=>100000=>000001
[4,5,2,7,1,3,6]=>[6,3,1,7,2,5,4]=>000000=>000000
[4,5,2,7,1,6,3]=>[3,6,1,7,2,5,4]=>000000=>000000
[4,5,2,7,3,1,6]=>[6,1,3,7,2,5,4]=>000000=>000000
[4,5,2,7,3,6,1]=>[1,6,3,7,2,5,4]=>100000=>000001
[4,5,2,7,6,1,3]=>[3,1,6,7,2,5,4]=>000000=>000000
[4,5,2,7,6,3,1]=>[1,3,6,7,2,5,4]=>100000=>000001
[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>000000=>000000
[4,5,3,1,2,7,6]=>[6,7,2,1,3,5,4]=>000000=>000000
[4,5,3,1,6,2,7]=>[7,2,6,1,3,5,4]=>000000=>000000
[4,5,3,1,6,7,2]=>[2,7,6,1,3,5,4]=>000000=>000000
[4,5,3,1,7,2,6]=>[6,2,7,1,3,5,4]=>000000=>000000
[4,5,3,1,7,6,2]=>[2,6,7,1,3,5,4]=>000000=>000000
[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>000000=>000000
[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>000000=>000000
[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>000000=>000000
[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>100000=>000001
[4,5,3,2,7,1,6]=>[6,1,7,2,3,5,4]=>000000=>000000
[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>100000=>000001
[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>000000=>000000
[4,5,3,6,1,7,2]=>[2,7,1,6,3,5,4]=>000000=>000000
[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>000000=>000000
[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>100000=>000001
[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>010000=>000010
[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>110000=>000011
[4,5,3,7,1,2,6]=>[6,2,1,7,3,5,4]=>000000=>000000
[4,5,3,7,1,6,2]=>[2,6,1,7,3,5,4]=>000000=>000000
[4,5,3,7,2,1,6]=>[6,1,2,7,3,5,4]=>000000=>000000
[4,5,3,7,2,6,1]=>[1,6,2,7,3,5,4]=>100000=>000001
[4,5,3,7,6,1,2]=>[2,1,6,7,3,5,4]=>010000=>000010
[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>110000=>000011
[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>000000=>000000
[4,5,6,1,2,7,3]=>[3,7,2,1,6,5,4]=>000000=>000000
[4,5,6,1,3,2,7]=>[7,2,3,1,6,5,4]=>000000=>000000
[4,5,6,1,3,7,2]=>[2,7,3,1,6,5,4]=>000000=>000000
[4,5,6,1,7,2,3]=>[3,2,7,1,6,5,4]=>000000=>000000
[4,5,6,1,7,3,2]=>[2,3,7,1,6,5,4]=>000000=>000000
[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>000000=>000000
[4,5,6,2,1,7,3]=>[3,7,1,2,6,5,4]=>000000=>000000
[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>000000=>000000
[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>100000=>000001
[4,5,6,2,7,1,3]=>[3,1,7,2,6,5,4]=>000000=>000000
[4,5,6,2,7,3,1]=>[1,3,7,2,6,5,4]=>100000=>000001
[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>000000=>000000
[4,5,6,3,1,7,2]=>[2,7,1,3,6,5,4]=>000000=>000000
[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>000000=>000000
[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>100000=>000001
[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>010000=>000010
[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>110000=>000011
[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>001000=>000100
[4,5,6,7,1,3,2]=>[2,3,1,7,6,5,4]=>001000=>000100
[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>001000=>000100
[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>101000=>000101
[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>011000=>000110
[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>111000=>000111
[4,5,7,1,2,3,6]=>[6,3,2,1,7,5,4]=>000000=>000000
[4,5,7,1,2,6,3]=>[3,6,2,1,7,5,4]=>000000=>000000
[4,5,7,1,3,2,6]=>[6,2,3,1,7,5,4]=>000000=>000000
[4,5,7,1,3,6,2]=>[2,6,3,1,7,5,4]=>000000=>000000
[4,5,7,1,6,2,3]=>[3,2,6,1,7,5,4]=>000000=>000000
[4,5,7,1,6,3,2]=>[2,3,6,1,7,5,4]=>000000=>000000
[4,5,7,2,1,3,6]=>[6,3,1,2,7,5,4]=>000000=>000000
[4,5,7,2,1,6,3]=>[3,6,1,2,7,5,4]=>000000=>000000
[4,5,7,2,3,1,6]=>[6,1,3,2,7,5,4]=>000000=>000000
[4,5,7,2,3,6,1]=>[1,6,3,2,7,5,4]=>100000=>000001
[4,5,7,2,6,1,3]=>[3,1,6,2,7,5,4]=>000000=>000000
[4,5,7,2,6,3,1]=>[1,3,6,2,7,5,4]=>100000=>000001
[4,5,7,3,1,2,6]=>[6,2,1,3,7,5,4]=>000000=>000000
[4,5,7,3,1,6,2]=>[2,6,1,3,7,5,4]=>000000=>000000
[4,5,7,3,2,1,6]=>[6,1,2,3,7,5,4]=>000000=>000000
[4,5,7,3,2,6,1]=>[1,6,2,3,7,5,4]=>100000=>000001
[4,5,7,3,6,1,2]=>[2,1,6,3,7,5,4]=>010000=>000010
[4,5,7,3,6,2,1]=>[1,2,6,3,7,5,4]=>110000=>000011
[4,5,7,6,1,2,3]=>[3,2,1,6,7,5,4]=>001000=>000100
[4,5,7,6,1,3,2]=>[2,3,1,6,7,5,4]=>001000=>000100
[4,5,7,6,2,1,3]=>[3,1,2,6,7,5,4]=>001000=>000100
[4,5,7,6,2,3,1]=>[1,3,2,6,7,5,4]=>101000=>000101
[4,5,7,6,3,1,2]=>[2,1,3,6,7,5,4]=>011000=>000110
[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>111000=>000111
[4,6,1,2,3,5,7]=>[7,5,3,2,1,6,4]=>000000=>000000
[4,6,1,2,3,7,5]=>[5,7,3,2,1,6,4]=>000000=>000000
[4,6,1,2,5,3,7]=>[7,3,5,2,1,6,4]=>000000=>000000
[4,6,1,2,5,7,3]=>[3,7,5,2,1,6,4]=>000000=>000000
[4,6,1,2,7,3,5]=>[5,3,7,2,1,6,4]=>000000=>000000
[4,6,1,2,7,5,3]=>[3,5,7,2,1,6,4]=>000000=>000000
[4,6,1,3,2,5,7]=>[7,5,2,3,1,6,4]=>000000=>000000
[4,6,1,3,2,7,5]=>[5,7,2,3,1,6,4]=>000000=>000000
[4,6,1,3,5,2,7]=>[7,2,5,3,1,6,4]=>000000=>000000
[4,6,1,3,5,7,2]=>[2,7,5,3,1,6,4]=>000000=>000000
[4,6,1,3,7,2,5]=>[5,2,7,3,1,6,4]=>000000=>000000
[4,6,1,3,7,5,2]=>[2,5,7,3,1,6,4]=>000000=>000000
[4,6,1,5,2,3,7]=>[7,3,2,5,1,6,4]=>000000=>000000
[4,6,1,5,2,7,3]=>[3,7,2,5,1,6,4]=>000000=>000000
[4,6,1,5,3,2,7]=>[7,2,3,5,1,6,4]=>000000=>000000
[4,6,1,5,3,7,2]=>[2,7,3,5,1,6,4]=>000000=>000000
[4,6,1,5,7,2,3]=>[3,2,7,5,1,6,4]=>000000=>000000
[4,6,1,5,7,3,2]=>[2,3,7,5,1,6,4]=>000000=>000000
[4,6,1,7,2,3,5]=>[5,3,2,7,1,6,4]=>000000=>000000
[4,6,1,7,2,5,3]=>[3,5,2,7,1,6,4]=>000000=>000000
[4,6,1,7,3,2,5]=>[5,2,3,7,1,6,4]=>000000=>000000
[4,6,1,7,3,5,2]=>[2,5,3,7,1,6,4]=>000000=>000000
[4,6,1,7,5,2,3]=>[3,2,5,7,1,6,4]=>000000=>000000
[4,6,1,7,5,3,2]=>[2,3,5,7,1,6,4]=>000000=>000000
[4,6,2,1,3,5,7]=>[7,5,3,1,2,6,4]=>000000=>000000
[4,6,2,1,3,7,5]=>[5,7,3,1,2,6,4]=>000000=>000000
[4,6,2,1,5,3,7]=>[7,3,5,1,2,6,4]=>000000=>000000
[4,6,2,1,5,7,3]=>[3,7,5,1,2,6,4]=>000000=>000000
[4,6,2,1,7,3,5]=>[5,3,7,1,2,6,4]=>000000=>000000
[4,6,2,1,7,5,3]=>[3,5,7,1,2,6,4]=>000000=>000000
[4,6,2,3,1,5,7]=>[7,5,1,3,2,6,4]=>000000=>000000
[4,6,2,3,1,7,5]=>[5,7,1,3,2,6,4]=>000000=>000000
[4,6,2,3,5,1,7]=>[7,1,5,3,2,6,4]=>000000=>000000
[4,6,2,3,5,7,1]=>[1,7,5,3,2,6,4]=>100000=>000001
[4,6,2,3,7,1,5]=>[5,1,7,3,2,6,4]=>000000=>000000
[4,6,2,3,7,5,1]=>[1,5,7,3,2,6,4]=>100000=>000001
[4,6,2,5,1,3,7]=>[7,3,1,5,2,6,4]=>000000=>000000
[4,6,2,5,1,7,3]=>[3,7,1,5,2,6,4]=>000000=>000000
[4,6,2,5,3,1,7]=>[7,1,3,5,2,6,4]=>000000=>000000
[4,6,2,5,3,7,1]=>[1,7,3,5,2,6,4]=>100000=>000001
[4,6,2,5,7,1,3]=>[3,1,7,5,2,6,4]=>000000=>000000
[4,6,2,5,7,3,1]=>[1,3,7,5,2,6,4]=>100000=>000001
[4,6,2,7,1,3,5]=>[5,3,1,7,2,6,4]=>000000=>000000
[4,6,2,7,1,5,3]=>[3,5,1,7,2,6,4]=>000000=>000000
[4,6,2,7,3,1,5]=>[5,1,3,7,2,6,4]=>000000=>000000
[4,6,2,7,3,5,1]=>[1,5,3,7,2,6,4]=>100000=>000001
[4,6,2,7,5,1,3]=>[3,1,5,7,2,6,4]=>000000=>000000
[4,6,2,7,5,3,1]=>[1,3,5,7,2,6,4]=>100000=>000001
[4,6,3,1,2,5,7]=>[7,5,2,1,3,6,4]=>000000=>000000
[4,6,3,1,2,7,5]=>[5,7,2,1,3,6,4]=>000000=>000000
[4,6,3,1,5,2,7]=>[7,2,5,1,3,6,4]=>000000=>000000
[4,6,3,1,5,7,2]=>[2,7,5,1,3,6,4]=>000000=>000000
[4,6,3,1,7,2,5]=>[5,2,7,1,3,6,4]=>000000=>000000
[4,6,3,1,7,5,2]=>[2,5,7,1,3,6,4]=>000000=>000000
[4,6,3,2,1,5,7]=>[7,5,1,2,3,6,4]=>000000=>000000
[4,6,3,2,1,7,5]=>[5,7,1,2,3,6,4]=>000000=>000000
[4,6,3,2,5,1,7]=>[7,1,5,2,3,6,4]=>000000=>000000
[4,6,3,2,5,7,1]=>[1,7,5,2,3,6,4]=>100000=>000001
[4,6,3,2,7,1,5]=>[5,1,7,2,3,6,4]=>000000=>000000
[4,6,3,2,7,5,1]=>[1,5,7,2,3,6,4]=>100000=>000001
[4,6,3,5,1,2,7]=>[7,2,1,5,3,6,4]=>000000=>000000
[4,6,3,5,1,7,2]=>[2,7,1,5,3,6,4]=>000000=>000000
[4,6,3,5,2,1,7]=>[7,1,2,5,3,6,4]=>000000=>000000
[4,6,3,5,2,7,1]=>[1,7,2,5,3,6,4]=>100000=>000001
[4,6,3,5,7,1,2]=>[2,1,7,5,3,6,4]=>010000=>000010
[4,6,3,5,7,2,1]=>[1,2,7,5,3,6,4]=>110000=>000011
[4,6,3,7,1,2,5]=>[5,2,1,7,3,6,4]=>000000=>000000
[4,6,3,7,1,5,2]=>[2,5,1,7,3,6,4]=>000000=>000000
[4,6,3,7,2,1,5]=>[5,1,2,7,3,6,4]=>000000=>000000
[4,6,3,7,2,5,1]=>[1,5,2,7,3,6,4]=>100000=>000001
[4,6,3,7,5,1,2]=>[2,1,5,7,3,6,4]=>010000=>000010
[4,6,3,7,5,2,1]=>[1,2,5,7,3,6,4]=>110000=>000011
[4,6,5,1,2,3,7]=>[7,3,2,1,5,6,4]=>000000=>000000
[4,6,5,1,2,7,3]=>[3,7,2,1,5,6,4]=>000000=>000000
[4,6,5,1,3,2,7]=>[7,2,3,1,5,6,4]=>000000=>000000
[4,6,5,1,3,7,2]=>[2,7,3,1,5,6,4]=>000000=>000000
[4,6,5,1,7,2,3]=>[3,2,7,1,5,6,4]=>000000=>000000
[4,6,5,1,7,3,2]=>[2,3,7,1,5,6,4]=>000000=>000000
[4,6,5,2,1,3,7]=>[7,3,1,2,5,6,4]=>000000=>000000
[4,6,5,2,1,7,3]=>[3,7,1,2,5,6,4]=>000000=>000000
[4,6,5,2,3,1,7]=>[7,1,3,2,5,6,4]=>000000=>000000
[4,6,5,2,3,7,1]=>[1,7,3,2,5,6,4]=>100000=>000001
[4,6,5,2,7,1,3]=>[3,1,7,2,5,6,4]=>000000=>000000
[4,6,5,2,7,3,1]=>[1,3,7,2,5,6,4]=>100000=>000001
[4,6,5,3,1,2,7]=>[7,2,1,3,5,6,4]=>000000=>000000
[4,6,5,3,1,7,2]=>[2,7,1,3,5,6,4]=>000000=>000000
[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>000000=>000000
[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>100000=>000001
[4,6,5,3,7,1,2]=>[2,1,7,3,5,6,4]=>010000=>000010
[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>110000=>000011
[4,6,5,7,1,2,3]=>[3,2,1,7,5,6,4]=>001000=>000100
[4,6,5,7,1,3,2]=>[2,3,1,7,5,6,4]=>001000=>000100
[4,6,5,7,2,1,3]=>[3,1,2,7,5,6,4]=>001000=>000100
[4,6,5,7,2,3,1]=>[1,3,2,7,5,6,4]=>101000=>000101
[4,6,5,7,3,1,2]=>[2,1,3,7,5,6,4]=>011000=>000110
[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>111000=>000111
[4,6,7,1,2,3,5]=>[5,3,2,1,7,6,4]=>000000=>000000
[4,6,7,1,2,5,3]=>[3,5,2,1,7,6,4]=>000000=>000000
[4,6,7,1,3,2,5]=>[5,2,3,1,7,6,4]=>000000=>000000
[4,6,7,1,3,5,2]=>[2,5,3,1,7,6,4]=>000000=>000000
[4,6,7,1,5,2,3]=>[3,2,5,1,7,6,4]=>000000=>000000
[4,6,7,1,5,3,2]=>[2,3,5,1,7,6,4]=>000000=>000000
[4,6,7,2,1,3,5]=>[5,3,1,2,7,6,4]=>000000=>000000
[4,6,7,2,1,5,3]=>[3,5,1,2,7,6,4]=>000000=>000000
[4,6,7,2,3,1,5]=>[5,1,3,2,7,6,4]=>000000=>000000
[4,6,7,2,3,5,1]=>[1,5,3,2,7,6,4]=>100000=>000001
[4,6,7,2,5,1,3]=>[3,1,5,2,7,6,4]=>000000=>000000
[4,6,7,2,5,3,1]=>[1,3,5,2,7,6,4]=>100000=>000001
[4,6,7,3,1,2,5]=>[5,2,1,3,7,6,4]=>000000=>000000
[4,6,7,3,1,5,2]=>[2,5,1,3,7,6,4]=>000000=>000000
[4,6,7,3,2,1,5]=>[5,1,2,3,7,6,4]=>000000=>000000
[4,6,7,3,2,5,1]=>[1,5,2,3,7,6,4]=>100000=>000001
[4,6,7,3,5,1,2]=>[2,1,5,3,7,6,4]=>010000=>000010
[4,6,7,3,5,2,1]=>[1,2,5,3,7,6,4]=>110000=>000011
[4,6,7,5,1,2,3]=>[3,2,1,5,7,6,4]=>001000=>000100
[4,6,7,5,1,3,2]=>[2,3,1,5,7,6,4]=>001000=>000100
[4,6,7,5,2,1,3]=>[3,1,2,5,7,6,4]=>001000=>000100
[4,6,7,5,2,3,1]=>[1,3,2,5,7,6,4]=>101000=>000101
[4,6,7,5,3,1,2]=>[2,1,3,5,7,6,4]=>011000=>000110
[4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4]=>111000=>000111
[4,7,1,2,3,5,6]=>[6,5,3,2,1,7,4]=>000000=>000000
[4,7,1,2,3,6,5]=>[5,6,3,2,1,7,4]=>000000=>000000
[4,7,1,2,5,3,6]=>[6,3,5,2,1,7,4]=>000000=>000000
[4,7,1,2,5,6,3]=>[3,6,5,2,1,7,4]=>000000=>000000
[4,7,1,2,6,3,5]=>[5,3,6,2,1,7,4]=>000000=>000000
[4,7,1,2,6,5,3]=>[3,5,6,2,1,7,4]=>000000=>000000
[4,7,1,3,2,5,6]=>[6,5,2,3,1,7,4]=>000000=>000000
[4,7,1,3,2,6,5]=>[5,6,2,3,1,7,4]=>000000=>000000
[4,7,1,3,5,2,6]=>[6,2,5,3,1,7,4]=>000000=>000000
[4,7,1,3,5,6,2]=>[2,6,5,3,1,7,4]=>000000=>000000
[4,7,1,3,6,2,5]=>[5,2,6,3,1,7,4]=>000000=>000000
[4,7,1,3,6,5,2]=>[2,5,6,3,1,7,4]=>000000=>000000
[4,7,1,5,2,3,6]=>[6,3,2,5,1,7,4]=>000000=>000000
[4,7,1,5,2,6,3]=>[3,6,2,5,1,7,4]=>000000=>000000
[4,7,1,5,3,2,6]=>[6,2,3,5,1,7,4]=>000000=>000000
[4,7,1,5,3,6,2]=>[2,6,3,5,1,7,4]=>000000=>000000
[4,7,1,5,6,2,3]=>[3,2,6,5,1,7,4]=>000000=>000000
[4,7,1,5,6,3,2]=>[2,3,6,5,1,7,4]=>000000=>000000
[4,7,1,6,2,3,5]=>[5,3,2,6,1,7,4]=>000000=>000000
[4,7,1,6,2,5,3]=>[3,5,2,6,1,7,4]=>000000=>000000
[4,7,1,6,3,2,5]=>[5,2,3,6,1,7,4]=>000000=>000000
[4,7,1,6,3,5,2]=>[2,5,3,6,1,7,4]=>000000=>000000
[4,7,1,6,5,2,3]=>[3,2,5,6,1,7,4]=>000000=>000000
[4,7,1,6,5,3,2]=>[2,3,5,6,1,7,4]=>000000=>000000
[4,7,2,1,3,5,6]=>[6,5,3,1,2,7,4]=>000000=>000000
[4,7,2,1,3,6,5]=>[5,6,3,1,2,7,4]=>000000=>000000
[4,7,2,1,5,3,6]=>[6,3,5,1,2,7,4]=>000000=>000000
[4,7,2,1,5,6,3]=>[3,6,5,1,2,7,4]=>000000=>000000
[4,7,2,1,6,3,5]=>[5,3,6,1,2,7,4]=>000000=>000000
[4,7,2,1,6,5,3]=>[3,5,6,1,2,7,4]=>000000=>000000
[4,7,2,3,1,5,6]=>[6,5,1,3,2,7,4]=>000000=>000000
[4,7,2,3,1,6,5]=>[5,6,1,3,2,7,4]=>000000=>000000
[4,7,2,3,5,1,6]=>[6,1,5,3,2,7,4]=>000000=>000000
[4,7,2,3,5,6,1]=>[1,6,5,3,2,7,4]=>100000=>000001
[4,7,2,3,6,1,5]=>[5,1,6,3,2,7,4]=>000000=>000000
[4,7,2,3,6,5,1]=>[1,5,6,3,2,7,4]=>100000=>000001
[4,7,2,5,1,3,6]=>[6,3,1,5,2,7,4]=>000000=>000000
[4,7,2,5,1,6,3]=>[3,6,1,5,2,7,4]=>000000=>000000
[4,7,2,5,3,1,6]=>[6,1,3,5,2,7,4]=>000000=>000000
[4,7,2,5,3,6,1]=>[1,6,3,5,2,7,4]=>100000=>000001
[4,7,2,5,6,1,3]=>[3,1,6,5,2,7,4]=>000000=>000000
[4,7,2,5,6,3,1]=>[1,3,6,5,2,7,4]=>100000=>000001
[4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4]=>000000=>000000
[4,7,2,6,1,5,3]=>[3,5,1,6,2,7,4]=>000000=>000000
[4,7,2,6,3,1,5]=>[5,1,3,6,2,7,4]=>000000=>000000
[4,7,2,6,3,5,1]=>[1,5,3,6,2,7,4]=>100000=>000001
[4,7,2,6,5,1,3]=>[3,1,5,6,2,7,4]=>000000=>000000
[4,7,2,6,5,3,1]=>[1,3,5,6,2,7,4]=>100000=>000001
[4,7,3,1,2,5,6]=>[6,5,2,1,3,7,4]=>000000=>000000
[4,7,3,1,2,6,5]=>[5,6,2,1,3,7,4]=>000000=>000000
[4,7,3,1,5,2,6]=>[6,2,5,1,3,7,4]=>000000=>000000
[4,7,3,1,5,6,2]=>[2,6,5,1,3,7,4]=>000000=>000000
[4,7,3,1,6,2,5]=>[5,2,6,1,3,7,4]=>000000=>000000
[4,7,3,1,6,5,2]=>[2,5,6,1,3,7,4]=>000000=>000000
[4,7,3,2,1,5,6]=>[6,5,1,2,3,7,4]=>000000=>000000
[4,7,3,2,1,6,5]=>[5,6,1,2,3,7,4]=>000000=>000000
[4,7,3,2,5,1,6]=>[6,1,5,2,3,7,4]=>000000=>000000
[4,7,3,2,5,6,1]=>[1,6,5,2,3,7,4]=>100000=>000001
[4,7,3,2,6,1,5]=>[5,1,6,2,3,7,4]=>000000=>000000
[4,7,3,2,6,5,1]=>[1,5,6,2,3,7,4]=>100000=>000001
[4,7,3,5,1,2,6]=>[6,2,1,5,3,7,4]=>000000=>000000
[4,7,3,5,1,6,2]=>[2,6,1,5,3,7,4]=>000000=>000000
[4,7,3,5,2,1,6]=>[6,1,2,5,3,7,4]=>000000=>000000
[4,7,3,5,2,6,1]=>[1,6,2,5,3,7,4]=>100000=>000001
[4,7,3,5,6,1,2]=>[2,1,6,5,3,7,4]=>010000=>000010
[4,7,3,5,6,2,1]=>[1,2,6,5,3,7,4]=>110000=>000011
[4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4]=>000000=>000000
[4,7,3,6,1,5,2]=>[2,5,1,6,3,7,4]=>000000=>000000
[4,7,3,6,2,1,5]=>[5,1,2,6,3,7,4]=>000000=>000000
[4,7,3,6,2,5,1]=>[1,5,2,6,3,7,4]=>100000=>000001
[4,7,3,6,5,1,2]=>[2,1,5,6,3,7,4]=>010000=>000010
[4,7,3,6,5,2,1]=>[1,2,5,6,3,7,4]=>110000=>000011
[4,7,5,1,2,3,6]=>[6,3,2,1,5,7,4]=>000000=>000000
[4,7,5,1,2,6,3]=>[3,6,2,1,5,7,4]=>000000=>000000
[4,7,5,1,3,2,6]=>[6,2,3,1,5,7,4]=>000000=>000000
[4,7,5,1,3,6,2]=>[2,6,3,1,5,7,4]=>000000=>000000
[4,7,5,1,6,2,3]=>[3,2,6,1,5,7,4]=>000000=>000000
[4,7,5,1,6,3,2]=>[2,3,6,1,5,7,4]=>000000=>000000
[4,7,5,2,1,3,6]=>[6,3,1,2,5,7,4]=>000000=>000000
[4,7,5,2,1,6,3]=>[3,6,1,2,5,7,4]=>000000=>000000
[4,7,5,2,3,1,6]=>[6,1,3,2,5,7,4]=>000000=>000000
[4,7,5,2,3,6,1]=>[1,6,3,2,5,7,4]=>100000=>000001
[4,7,5,2,6,1,3]=>[3,1,6,2,5,7,4]=>000000=>000000
[4,7,5,2,6,3,1]=>[1,3,6,2,5,7,4]=>100000=>000001
[4,7,5,3,1,2,6]=>[6,2,1,3,5,7,4]=>000000=>000000
[4,7,5,3,1,6,2]=>[2,6,1,3,5,7,4]=>000000=>000000
[4,7,5,3,2,1,6]=>[6,1,2,3,5,7,4]=>000000=>000000
[4,7,5,3,2,6,1]=>[1,6,2,3,5,7,4]=>100000=>000001
[4,7,5,3,6,1,2]=>[2,1,6,3,5,7,4]=>010000=>000010
[4,7,5,3,6,2,1]=>[1,2,6,3,5,7,4]=>110000=>000011
[4,7,5,6,1,2,3]=>[3,2,1,6,5,7,4]=>001000=>000100
[4,7,5,6,1,3,2]=>[2,3,1,6,5,7,4]=>001000=>000100
[4,7,5,6,2,1,3]=>[3,1,2,6,5,7,4]=>001000=>000100
[4,7,5,6,2,3,1]=>[1,3,2,6,5,7,4]=>101000=>000101
[4,7,5,6,3,1,2]=>[2,1,3,6,5,7,4]=>011000=>000110
[4,7,5,6,3,2,1]=>[1,2,3,6,5,7,4]=>111000=>000111
[4,7,6,1,2,3,5]=>[5,3,2,1,6,7,4]=>000000=>000000
[4,7,6,1,2,5,3]=>[3,5,2,1,6,7,4]=>000000=>000000
[4,7,6,1,3,2,5]=>[5,2,3,1,6,7,4]=>000000=>000000
[4,7,6,1,3,5,2]=>[2,5,3,1,6,7,4]=>000000=>000000
[4,7,6,1,5,2,3]=>[3,2,5,1,6,7,4]=>000000=>000000
[4,7,6,1,5,3,2]=>[2,3,5,1,6,7,4]=>000000=>000000
[4,7,6,2,1,3,5]=>[5,3,1,2,6,7,4]=>000000=>000000
[4,7,6,2,1,5,3]=>[3,5,1,2,6,7,4]=>000000=>000000
[4,7,6,2,3,1,5]=>[5,1,3,2,6,7,4]=>000000=>000000
[4,7,6,2,3,5,1]=>[1,5,3,2,6,7,4]=>100000=>000001
[4,7,6,2,5,1,3]=>[3,1,5,2,6,7,4]=>000000=>000000
[4,7,6,2,5,3,1]=>[1,3,5,2,6,7,4]=>100000=>000001
[4,7,6,3,1,2,5]=>[5,2,1,3,6,7,4]=>000000=>000000
[4,7,6,3,1,5,2]=>[2,5,1,3,6,7,4]=>000000=>000000
[4,7,6,3,2,1,5]=>[5,1,2,3,6,7,4]=>000000=>000000
[4,7,6,3,2,5,1]=>[1,5,2,3,6,7,4]=>100000=>000001
[4,7,6,3,5,1,2]=>[2,1,5,3,6,7,4]=>010000=>000010
[4,7,6,3,5,2,1]=>[1,2,5,3,6,7,4]=>110000=>000011
[4,7,6,5,1,2,3]=>[3,2,1,5,6,7,4]=>001000=>000100
[4,7,6,5,1,3,2]=>[2,3,1,5,6,7,4]=>001000=>000100
[4,7,6,5,2,1,3]=>[3,1,2,5,6,7,4]=>001000=>000100
[4,7,6,5,2,3,1]=>[1,3,2,5,6,7,4]=>101000=>000101
[4,7,6,5,3,1,2]=>[2,1,3,5,6,7,4]=>011000=>000110
[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>111000=>000111
[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>000000=>000000
[5,1,2,3,4,7,6]=>[6,7,4,3,2,1,5]=>000000=>000000
[5,1,2,3,6,4,7]=>[7,4,6,3,2,1,5]=>000000=>000000
[5,1,2,3,6,7,4]=>[4,7,6,3,2,1,5]=>000000=>000000
[5,1,2,3,7,4,6]=>[6,4,7,3,2,1,5]=>000000=>000000
[5,1,2,3,7,6,4]=>[4,6,7,3,2,1,5]=>000000=>000000
[5,1,2,4,3,6,7]=>[7,6,3,4,2,1,5]=>000000=>000000
[5,1,2,4,3,7,6]=>[6,7,3,4,2,1,5]=>000000=>000000
[5,1,2,4,6,3,7]=>[7,3,6,4,2,1,5]=>000000=>000000
[5,1,2,4,6,7,3]=>[3,7,6,4,2,1,5]=>000000=>000000
[5,1,2,4,7,3,6]=>[6,3,7,4,2,1,5]=>000000=>000000
[5,1,2,4,7,6,3]=>[3,6,7,4,2,1,5]=>000000=>000000
[5,1,2,6,3,4,7]=>[7,4,3,6,2,1,5]=>000000=>000000
[5,1,2,6,3,7,4]=>[4,7,3,6,2,1,5]=>000000=>000000
[5,1,2,6,4,3,7]=>[7,3,4,6,2,1,5]=>000000=>000000
[5,1,2,6,4,7,3]=>[3,7,4,6,2,1,5]=>000000=>000000
[5,1,2,6,7,3,4]=>[4,3,7,6,2,1,5]=>000000=>000000
[5,1,2,6,7,4,3]=>[3,4,7,6,2,1,5]=>000000=>000000
[5,1,2,7,3,4,6]=>[6,4,3,7,2,1,5]=>000000=>000000
[5,1,2,7,3,6,4]=>[4,6,3,7,2,1,5]=>000000=>000000
[5,1,2,7,4,3,6]=>[6,3,4,7,2,1,5]=>000000=>000000
[5,1,2,7,4,6,3]=>[3,6,4,7,2,1,5]=>000000=>000000
[5,1,2,7,6,3,4]=>[4,3,6,7,2,1,5]=>000000=>000000
[5,1,2,7,6,4,3]=>[3,4,6,7,2,1,5]=>000000=>000000
[5,1,3,2,4,6,7]=>[7,6,4,2,3,1,5]=>000000=>000000
[5,1,3,2,4,7,6]=>[6,7,4,2,3,1,5]=>000000=>000000
[5,1,3,2,6,4,7]=>[7,4,6,2,3,1,5]=>000000=>000000
[5,1,3,2,6,7,4]=>[4,7,6,2,3,1,5]=>000000=>000000
[5,1,3,2,7,4,6]=>[6,4,7,2,3,1,5]=>000000=>000000
[5,1,3,2,7,6,4]=>[4,6,7,2,3,1,5]=>000000=>000000
[5,1,3,4,2,6,7]=>[7,6,2,4,3,1,5]=>000000=>000000
[5,1,3,4,2,7,6]=>[6,7,2,4,3,1,5]=>000000=>000000
[5,1,3,4,6,2,7]=>[7,2,6,4,3,1,5]=>000000=>000000
[5,1,3,4,6,7,2]=>[2,7,6,4,3,1,5]=>000000=>000000
[5,1,3,4,7,2,6]=>[6,2,7,4,3,1,5]=>000000=>000000
[5,1,3,4,7,6,2]=>[2,6,7,4,3,1,5]=>000000=>000000
[5,1,3,6,2,4,7]=>[7,4,2,6,3,1,5]=>000000=>000000
[5,1,3,6,2,7,4]=>[4,7,2,6,3,1,5]=>000000=>000000
[5,1,3,6,4,2,7]=>[7,2,4,6,3,1,5]=>000000=>000000
[5,1,3,6,4,7,2]=>[2,7,4,6,3,1,5]=>000000=>000000
[5,1,3,6,7,2,4]=>[4,2,7,6,3,1,5]=>000000=>000000
[5,1,3,6,7,4,2]=>[2,4,7,6,3,1,5]=>000000=>000000
[5,1,3,7,2,4,6]=>[6,4,2,7,3,1,5]=>000000=>000000
[5,1,3,7,2,6,4]=>[4,6,2,7,3,1,5]=>000000=>000000
[5,1,3,7,4,2,6]=>[6,2,4,7,3,1,5]=>000000=>000000
[5,1,3,7,4,6,2]=>[2,6,4,7,3,1,5]=>000000=>000000
[5,1,3,7,6,2,4]=>[4,2,6,7,3,1,5]=>000000=>000000
[5,1,3,7,6,4,2]=>[2,4,6,7,3,1,5]=>000000=>000000
[5,1,4,2,3,6,7]=>[7,6,3,2,4,1,5]=>000000=>000000
[5,1,4,2,3,7,6]=>[6,7,3,2,4,1,5]=>000000=>000000
[5,1,4,2,6,3,7]=>[7,3,6,2,4,1,5]=>000000=>000000
[5,1,4,2,6,7,3]=>[3,7,6,2,4,1,5]=>000000=>000000
[5,1,4,2,7,3,6]=>[6,3,7,2,4,1,5]=>000000=>000000
[5,1,4,2,7,6,3]=>[3,6,7,2,4,1,5]=>000000=>000000
[5,1,4,3,2,6,7]=>[7,6,2,3,4,1,5]=>000000=>000000
[5,1,4,3,2,7,6]=>[6,7,2,3,4,1,5]=>000000=>000000
[5,1,4,3,6,2,7]=>[7,2,6,3,4,1,5]=>000000=>000000
[5,1,4,3,6,7,2]=>[2,7,6,3,4,1,5]=>000000=>000000
[5,1,4,3,7,2,6]=>[6,2,7,3,4,1,5]=>000000=>000000
[5,1,4,3,7,6,2]=>[2,6,7,3,4,1,5]=>000000=>000000
[5,1,4,6,2,3,7]=>[7,3,2,6,4,1,5]=>000000=>000000
[5,1,4,6,2,7,3]=>[3,7,2,6,4,1,5]=>000000=>000000
[5,1,4,6,3,2,7]=>[7,2,3,6,4,1,5]=>000000=>000000
[5,1,4,6,3,7,2]=>[2,7,3,6,4,1,5]=>000000=>000000
[5,1,4,6,7,2,3]=>[3,2,7,6,4,1,5]=>000000=>000000
[5,1,4,6,7,3,2]=>[2,3,7,6,4,1,5]=>000000=>000000
[5,1,4,7,2,3,6]=>[6,3,2,7,4,1,5]=>000000=>000000
[5,1,4,7,2,6,3]=>[3,6,2,7,4,1,5]=>000000=>000000
[5,1,4,7,3,2,6]=>[6,2,3,7,4,1,5]=>000000=>000000
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[5,3,4,1,7,6,2]=>[2,6,7,1,4,3,5]=>000000=>000000
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[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>010000=>000010
[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>110000=>000011
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[5,3,4,7,6,1,2]=>[2,1,6,7,4,3,5]=>010000=>000010
[5,3,4,7,6,2,1]=>[1,2,6,7,4,3,5]=>110000=>000011
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[5,3,6,1,7,4,2]=>[2,4,7,1,6,3,5]=>000000=>000000
[5,3,6,2,1,4,7]=>[7,4,1,2,6,3,5]=>000000=>000000
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[5,3,6,2,4,7,1]=>[1,7,4,2,6,3,5]=>100000=>000001
[5,3,6,2,7,1,4]=>[4,1,7,2,6,3,5]=>000000=>000000
[5,3,6,2,7,4,1]=>[1,4,7,2,6,3,5]=>100000=>000001
[5,3,6,4,1,2,7]=>[7,2,1,4,6,3,5]=>000000=>000000
[5,3,6,4,1,7,2]=>[2,7,1,4,6,3,5]=>000000=>000000
[5,3,6,4,2,1,7]=>[7,1,2,4,6,3,5]=>000000=>000000
[5,3,6,4,2,7,1]=>[1,7,2,4,6,3,5]=>100000=>000001
[5,3,6,4,7,1,2]=>[2,1,7,4,6,3,5]=>010000=>000010
[5,3,6,4,7,2,1]=>[1,2,7,4,6,3,5]=>110000=>000011
[5,3,6,7,1,2,4]=>[4,2,1,7,6,3,5]=>000000=>000000
[5,3,6,7,1,4,2]=>[2,4,1,7,6,3,5]=>000000=>000000
[5,3,6,7,2,1,4]=>[4,1,2,7,6,3,5]=>000000=>000000
[5,3,6,7,2,4,1]=>[1,4,2,7,6,3,5]=>100000=>000001
[5,3,6,7,4,1,2]=>[2,1,4,7,6,3,5]=>010000=>000010
[5,3,6,7,4,2,1]=>[1,2,4,7,6,3,5]=>110000=>000011
[5,3,7,1,2,4,6]=>[6,4,2,1,7,3,5]=>000000=>000000
[5,3,7,1,2,6,4]=>[4,6,2,1,7,3,5]=>000000=>000000
[5,3,7,1,4,2,6]=>[6,2,4,1,7,3,5]=>000000=>000000
[5,3,7,1,4,6,2]=>[2,6,4,1,7,3,5]=>000000=>000000
[5,3,7,1,6,2,4]=>[4,2,6,1,7,3,5]=>000000=>000000
[5,3,7,1,6,4,2]=>[2,4,6,1,7,3,5]=>000000=>000000
[5,3,7,2,1,4,6]=>[6,4,1,2,7,3,5]=>000000=>000000
[5,3,7,2,1,6,4]=>[4,6,1,2,7,3,5]=>000000=>000000
[5,3,7,2,4,1,6]=>[6,1,4,2,7,3,5]=>000000=>000000
[5,3,7,2,4,6,1]=>[1,6,4,2,7,3,5]=>100000=>000001
[5,3,7,2,6,1,4]=>[4,1,6,2,7,3,5]=>000000=>000000
[5,3,7,2,6,4,1]=>[1,4,6,2,7,3,5]=>100000=>000001
[5,3,7,4,1,2,6]=>[6,2,1,4,7,3,5]=>000000=>000000
[5,3,7,4,1,6,2]=>[2,6,1,4,7,3,5]=>000000=>000000
[5,3,7,4,2,1,6]=>[6,1,2,4,7,3,5]=>000000=>000000
[5,3,7,4,2,6,1]=>[1,6,2,4,7,3,5]=>100000=>000001
[5,3,7,4,6,1,2]=>[2,1,6,4,7,3,5]=>010000=>000010
[5,3,7,4,6,2,1]=>[1,2,6,4,7,3,5]=>110000=>000011
[5,3,7,6,1,2,4]=>[4,2,1,6,7,3,5]=>000000=>000000
[5,3,7,6,1,4,2]=>[2,4,1,6,7,3,5]=>000000=>000000
[5,3,7,6,2,1,4]=>[4,1,2,6,7,3,5]=>000000=>000000
[5,3,7,6,2,4,1]=>[1,4,2,6,7,3,5]=>100000=>000001
[5,3,7,6,4,1,2]=>[2,1,4,6,7,3,5]=>010000=>000010
[5,3,7,6,4,2,1]=>[1,2,4,6,7,3,5]=>110000=>000011
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[5,4,1,2,3,7,6]=>[6,7,3,2,1,4,5]=>000000=>000000
[5,4,1,2,6,3,7]=>[7,3,6,2,1,4,5]=>000000=>000000
[5,4,1,2,6,7,3]=>[3,7,6,2,1,4,5]=>000000=>000000
[5,4,1,2,7,3,6]=>[6,3,7,2,1,4,5]=>000000=>000000
[5,4,1,2,7,6,3]=>[3,6,7,2,1,4,5]=>000000=>000000
[5,4,1,3,2,6,7]=>[7,6,2,3,1,4,5]=>000000=>000000
[5,4,1,3,2,7,6]=>[6,7,2,3,1,4,5]=>000000=>000000
[5,4,1,3,6,2,7]=>[7,2,6,3,1,4,5]=>000000=>000000
[5,4,1,3,6,7,2]=>[2,7,6,3,1,4,5]=>000000=>000000
[5,4,1,3,7,2,6]=>[6,2,7,3,1,4,5]=>000000=>000000
[5,4,1,3,7,6,2]=>[2,6,7,3,1,4,5]=>000000=>000000
[5,4,1,6,2,3,7]=>[7,3,2,6,1,4,5]=>000000=>000000
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[5,4,1,6,3,2,7]=>[7,2,3,6,1,4,5]=>000000=>000000
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[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>000000=>000000
[5,4,2,3,1,7,6]=>[6,7,1,3,2,4,5]=>000000=>000000
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[5,4,2,3,7,1,6]=>[6,1,7,3,2,4,5]=>000000=>000000
[5,4,2,3,7,6,1]=>[1,6,7,3,2,4,5]=>100000=>000001
[5,4,2,6,1,3,7]=>[7,3,1,6,2,4,5]=>000000=>000000
[5,4,2,6,1,7,3]=>[3,7,1,6,2,4,5]=>000000=>000000
[5,4,2,6,3,1,7]=>[7,1,3,6,2,4,5]=>000000=>000000
[5,4,2,6,3,7,1]=>[1,7,3,6,2,4,5]=>100000=>000001
[5,4,2,6,7,1,3]=>[3,1,7,6,2,4,5]=>000000=>000000
[5,4,2,6,7,3,1]=>[1,3,7,6,2,4,5]=>100000=>000001
[5,4,2,7,1,3,6]=>[6,3,1,7,2,4,5]=>000000=>000000
[5,4,2,7,1,6,3]=>[3,6,1,7,2,4,5]=>000000=>000000
[5,4,2,7,3,1,6]=>[6,1,3,7,2,4,5]=>000000=>000000
[5,4,2,7,3,6,1]=>[1,6,3,7,2,4,5]=>100000=>000001
[5,4,2,7,6,1,3]=>[3,1,6,7,2,4,5]=>000000=>000000
[5,4,2,7,6,3,1]=>[1,3,6,7,2,4,5]=>100000=>000001
[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>000000=>000000
[5,4,3,1,2,7,6]=>[6,7,2,1,3,4,5]=>000000=>000000
[5,4,3,1,6,2,7]=>[7,2,6,1,3,4,5]=>000000=>000000
[5,4,3,1,6,7,2]=>[2,7,6,1,3,4,5]=>000000=>000000
[5,4,3,1,7,2,6]=>[6,2,7,1,3,4,5]=>000000=>000000
[5,4,3,1,7,6,2]=>[2,6,7,1,3,4,5]=>000000=>000000
[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>000000=>000000
[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>000000=>000000
[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>000000=>000000
[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>100000=>000001
[5,4,3,2,7,1,6]=>[6,1,7,2,3,4,5]=>000000=>000000
[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>100000=>000001
[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>000000=>000000
[5,4,3,6,1,7,2]=>[2,7,1,6,3,4,5]=>000000=>000000
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[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>100000=>000001
[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>010000=>000010
[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>110000=>000011
[5,4,3,7,1,2,6]=>[6,2,1,7,3,4,5]=>000000=>000000
[5,4,3,7,1,6,2]=>[2,6,1,7,3,4,5]=>000000=>000000
[5,4,3,7,2,1,6]=>[6,1,2,7,3,4,5]=>000000=>000000
[5,4,3,7,2,6,1]=>[1,6,2,7,3,4,5]=>100000=>000001
[5,4,3,7,6,1,2]=>[2,1,6,7,3,4,5]=>010000=>000010
[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>110000=>000011
[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>000000=>000000
[5,4,6,1,2,7,3]=>[3,7,2,1,6,4,5]=>000000=>000000
[5,4,6,1,3,2,7]=>[7,2,3,1,6,4,5]=>000000=>000000
[5,4,6,1,3,7,2]=>[2,7,3,1,6,4,5]=>000000=>000000
[5,4,6,1,7,2,3]=>[3,2,7,1,6,4,5]=>000000=>000000
[5,4,6,1,7,3,2]=>[2,3,7,1,6,4,5]=>000000=>000000
[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>000000=>000000
[5,4,6,2,1,7,3]=>[3,7,1,2,6,4,5]=>000000=>000000
[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>000000=>000000
[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>100000=>000001
[5,4,6,2,7,1,3]=>[3,1,7,2,6,4,5]=>000000=>000000
[5,4,6,2,7,3,1]=>[1,3,7,2,6,4,5]=>100000=>000001
[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>000000=>000000
[5,4,6,3,1,7,2]=>[2,7,1,3,6,4,5]=>000000=>000000
[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>000000=>000000
[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>100000=>000001
[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>010000=>000010
[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>110000=>000011
[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>001000=>000100
[5,4,6,7,1,3,2]=>[2,3,1,7,6,4,5]=>001000=>000100
[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>001000=>000100
[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>101000=>000101
[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>011000=>000110
[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>111000=>000111
[5,4,7,1,2,3,6]=>[6,3,2,1,7,4,5]=>000000=>000000
[5,4,7,1,2,6,3]=>[3,6,2,1,7,4,5]=>000000=>000000
[5,4,7,1,3,2,6]=>[6,2,3,1,7,4,5]=>000000=>000000
[5,4,7,1,3,6,2]=>[2,6,3,1,7,4,5]=>000000=>000000
[5,4,7,1,6,2,3]=>[3,2,6,1,7,4,5]=>000000=>000000
[5,4,7,1,6,3,2]=>[2,3,6,1,7,4,5]=>000000=>000000
[5,4,7,2,1,3,6]=>[6,3,1,2,7,4,5]=>000000=>000000
[5,4,7,2,1,6,3]=>[3,6,1,2,7,4,5]=>000000=>000000
[5,4,7,2,3,1,6]=>[6,1,3,2,7,4,5]=>000000=>000000
[5,4,7,2,3,6,1]=>[1,6,3,2,7,4,5]=>100000=>000001
[5,4,7,2,6,1,3]=>[3,1,6,2,7,4,5]=>000000=>000000
[5,4,7,2,6,3,1]=>[1,3,6,2,7,4,5]=>100000=>000001
[5,4,7,3,1,2,6]=>[6,2,1,3,7,4,5]=>000000=>000000
[5,4,7,3,1,6,2]=>[2,6,1,3,7,4,5]=>000000=>000000
[5,4,7,3,2,1,6]=>[6,1,2,3,7,4,5]=>000000=>000000
[5,4,7,3,2,6,1]=>[1,6,2,3,7,4,5]=>100000=>000001
[5,4,7,3,6,1,2]=>[2,1,6,3,7,4,5]=>010000=>000010
[5,4,7,3,6,2,1]=>[1,2,6,3,7,4,5]=>110000=>000011
[5,4,7,6,1,2,3]=>[3,2,1,6,7,4,5]=>001000=>000100
[5,4,7,6,1,3,2]=>[2,3,1,6,7,4,5]=>001000=>000100
[5,4,7,6,2,1,3]=>[3,1,2,6,7,4,5]=>001000=>000100
[5,4,7,6,2,3,1]=>[1,3,2,6,7,4,5]=>101000=>000101
[5,4,7,6,3,1,2]=>[2,1,3,6,7,4,5]=>011000=>000110
[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>111000=>000111
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[5,6,1,2,3,7,4]=>[4,7,3,2,1,6,5]=>000000=>000000
[5,6,1,2,4,3,7]=>[7,3,4,2,1,6,5]=>000000=>000000
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[5,6,2,1,3,7,4]=>[4,7,3,1,2,6,5]=>000000=>000000
[5,6,2,1,4,3,7]=>[7,3,4,1,2,6,5]=>000000=>000000
[5,6,2,1,4,7,3]=>[3,7,4,1,2,6,5]=>000000=>000000
[5,6,2,1,7,3,4]=>[4,3,7,1,2,6,5]=>000000=>000000
[5,6,2,1,7,4,3]=>[3,4,7,1,2,6,5]=>000000=>000000
[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>000000=>000000
[5,6,2,3,1,7,4]=>[4,7,1,3,2,6,5]=>000000=>000000
[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>000000=>000000
[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>100000=>000001
[5,6,2,3,7,1,4]=>[4,1,7,3,2,6,5]=>000000=>000000
[5,6,2,3,7,4,1]=>[1,4,7,3,2,6,5]=>100000=>000001
[5,6,2,4,1,3,7]=>[7,3,1,4,2,6,5]=>000000=>000000
[5,6,2,4,1,7,3]=>[3,7,1,4,2,6,5]=>000000=>000000
[5,6,2,4,3,1,7]=>[7,1,3,4,2,6,5]=>000000=>000000
[5,6,2,4,3,7,1]=>[1,7,3,4,2,6,5]=>100000=>000001
[5,6,2,4,7,1,3]=>[3,1,7,4,2,6,5]=>000000=>000000
[5,6,2,4,7,3,1]=>[1,3,7,4,2,6,5]=>100000=>000001
[5,6,2,7,1,3,4]=>[4,3,1,7,2,6,5]=>000000=>000000
[5,6,2,7,1,4,3]=>[3,4,1,7,2,6,5]=>000000=>000000
[5,6,2,7,3,1,4]=>[4,1,3,7,2,6,5]=>000000=>000000
[5,6,2,7,3,4,1]=>[1,4,3,7,2,6,5]=>100000=>000001
[5,6,2,7,4,1,3]=>[3,1,4,7,2,6,5]=>000000=>000000
[5,6,2,7,4,3,1]=>[1,3,4,7,2,6,5]=>100000=>000001
[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>000000=>000000
[5,6,3,1,2,7,4]=>[4,7,2,1,3,6,5]=>000000=>000000
[5,6,3,1,4,2,7]=>[7,2,4,1,3,6,5]=>000000=>000000
[5,6,3,1,4,7,2]=>[2,7,4,1,3,6,5]=>000000=>000000
[5,6,3,1,7,2,4]=>[4,2,7,1,3,6,5]=>000000=>000000
[5,6,3,1,7,4,2]=>[2,4,7,1,3,6,5]=>000000=>000000
[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>000000=>000000
[5,6,3,2,1,7,4]=>[4,7,1,2,3,6,5]=>000000=>000000
[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>000000=>000000
[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>100000=>000001
[5,6,3,2,7,1,4]=>[4,1,7,2,3,6,5]=>000000=>000000
[5,6,3,2,7,4,1]=>[1,4,7,2,3,6,5]=>100000=>000001
[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>000000=>000000
[5,6,3,4,1,7,2]=>[2,7,1,4,3,6,5]=>000000=>000000
[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>000000=>000000
[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>100000=>000001
[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>010000=>000010
[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>110000=>000011
[5,6,3,7,1,2,4]=>[4,2,1,7,3,6,5]=>000000=>000000
[5,6,3,7,1,4,2]=>[2,4,1,7,3,6,5]=>000000=>000000
[5,6,3,7,2,1,4]=>[4,1,2,7,3,6,5]=>000000=>000000
[5,6,3,7,2,4,1]=>[1,4,2,7,3,6,5]=>100000=>000001
[5,6,3,7,4,1,2]=>[2,1,4,7,3,6,5]=>010000=>000010
[5,6,3,7,4,2,1]=>[1,2,4,7,3,6,5]=>110000=>000011
[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>000000=>000000
[5,6,4,1,2,7,3]=>[3,7,2,1,4,6,5]=>000000=>000000
[5,6,4,1,3,2,7]=>[7,2,3,1,4,6,5]=>000000=>000000
[5,6,4,1,3,7,2]=>[2,7,3,1,4,6,5]=>000000=>000000
[5,6,4,1,7,2,3]=>[3,2,7,1,4,6,5]=>000000=>000000
[5,6,4,1,7,3,2]=>[2,3,7,1,4,6,5]=>000000=>000000
[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>000000=>000000
[5,6,4,2,1,7,3]=>[3,7,1,2,4,6,5]=>000000=>000000
[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>000000=>000000
[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>100000=>000001
[5,6,4,2,7,1,3]=>[3,1,7,2,4,6,5]=>000000=>000000
[5,6,4,2,7,3,1]=>[1,3,7,2,4,6,5]=>100000=>000001
[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>000000=>000000
[5,6,4,3,1,7,2]=>[2,7,1,3,4,6,5]=>000000=>000000
[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>000000=>000000
[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>100000=>000001
[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>010000=>000010
[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>110000=>000011
[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>001000=>000100
[5,6,4,7,1,3,2]=>[2,3,1,7,4,6,5]=>001000=>000100
[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>001000=>000100
[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>101000=>000101
[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>011000=>000110
[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>111000=>000111
[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>000100=>001000
[5,6,7,1,2,4,3]=>[3,4,2,1,7,6,5]=>000100=>001000
[5,6,7,1,3,2,4]=>[4,2,3,1,7,6,5]=>000100=>001000
[5,6,7,1,3,4,2]=>[2,4,3,1,7,6,5]=>000100=>001000
[5,6,7,1,4,2,3]=>[3,2,4,1,7,6,5]=>000100=>001000
[5,6,7,1,4,3,2]=>[2,3,4,1,7,6,5]=>000100=>001000
[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>000100=>001000
[5,6,7,2,1,4,3]=>[3,4,1,2,7,6,5]=>000100=>001000
[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>000100=>001000
[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>100100=>001001
[5,6,7,2,4,1,3]=>[3,1,4,2,7,6,5]=>000100=>001000
[5,6,7,2,4,3,1]=>[1,3,4,2,7,6,5]=>100100=>001001
[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>000100=>001000
[5,6,7,3,1,4,2]=>[2,4,1,3,7,6,5]=>000100=>001000
[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>000100=>001000
[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>100100=>001001
[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>010100=>001010
[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>110100=>001011
[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>001100=>001100
[5,6,7,4,1,3,2]=>[2,3,1,4,7,6,5]=>001100=>001100
[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>001100=>001100
[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>101100=>001101
[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>011100=>001110
[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>111100=>001111
[5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5]=>000000=>000000
[5,7,1,2,3,6,4]=>[4,6,3,2,1,7,5]=>000000=>000000
[5,7,1,2,4,3,6]=>[6,3,4,2,1,7,5]=>000000=>000000
[5,7,1,2,4,6,3]=>[3,6,4,2,1,7,5]=>000000=>000000
[5,7,1,2,6,3,4]=>[4,3,6,2,1,7,5]=>000000=>000000
[5,7,1,2,6,4,3]=>[3,4,6,2,1,7,5]=>000000=>000000
[5,7,1,3,2,4,6]=>[6,4,2,3,1,7,5]=>000000=>000000
[5,7,1,3,2,6,4]=>[4,6,2,3,1,7,5]=>000000=>000000
[5,7,1,3,4,2,6]=>[6,2,4,3,1,7,5]=>000000=>000000
[5,7,1,3,4,6,2]=>[2,6,4,3,1,7,5]=>000000=>000000
[5,7,1,3,6,2,4]=>[4,2,6,3,1,7,5]=>000000=>000000
[5,7,1,3,6,4,2]=>[2,4,6,3,1,7,5]=>000000=>000000
[5,7,1,4,2,3,6]=>[6,3,2,4,1,7,5]=>000000=>000000
[5,7,1,4,2,6,3]=>[3,6,2,4,1,7,5]=>000000=>000000
[5,7,1,4,3,2,6]=>[6,2,3,4,1,7,5]=>000000=>000000
[5,7,1,4,3,6,2]=>[2,6,3,4,1,7,5]=>000000=>000000
[5,7,1,4,6,2,3]=>[3,2,6,4,1,7,5]=>000000=>000000
[5,7,1,4,6,3,2]=>[2,3,6,4,1,7,5]=>000000=>000000
[5,7,1,6,2,3,4]=>[4,3,2,6,1,7,5]=>000000=>000000
[5,7,1,6,2,4,3]=>[3,4,2,6,1,7,5]=>000000=>000000
[5,7,1,6,3,2,4]=>[4,2,3,6,1,7,5]=>000000=>000000
[5,7,1,6,3,4,2]=>[2,4,3,6,1,7,5]=>000000=>000000
[5,7,1,6,4,2,3]=>[3,2,4,6,1,7,5]=>000000=>000000
[5,7,1,6,4,3,2]=>[2,3,4,6,1,7,5]=>000000=>000000
[5,7,2,1,3,4,6]=>[6,4,3,1,2,7,5]=>000000=>000000
[5,7,2,1,3,6,4]=>[4,6,3,1,2,7,5]=>000000=>000000
[5,7,2,1,4,3,6]=>[6,3,4,1,2,7,5]=>000000=>000000
[5,7,2,1,4,6,3]=>[3,6,4,1,2,7,5]=>000000=>000000
[5,7,2,1,6,3,4]=>[4,3,6,1,2,7,5]=>000000=>000000
[5,7,2,1,6,4,3]=>[3,4,6,1,2,7,5]=>000000=>000000
[5,7,2,3,1,4,6]=>[6,4,1,3,2,7,5]=>000000=>000000
[5,7,2,3,1,6,4]=>[4,6,1,3,2,7,5]=>000000=>000000
[5,7,2,3,4,1,6]=>[6,1,4,3,2,7,5]=>000000=>000000
[5,7,2,3,4,6,1]=>[1,6,4,3,2,7,5]=>100000=>000001
[5,7,2,3,6,1,4]=>[4,1,6,3,2,7,5]=>000000=>000000
[5,7,2,3,6,4,1]=>[1,4,6,3,2,7,5]=>100000=>000001
[5,7,2,4,1,3,6]=>[6,3,1,4,2,7,5]=>000000=>000000
[5,7,2,4,1,6,3]=>[3,6,1,4,2,7,5]=>000000=>000000
[5,7,2,4,3,1,6]=>[6,1,3,4,2,7,5]=>000000=>000000
[5,7,2,4,3,6,1]=>[1,6,3,4,2,7,5]=>100000=>000001
[5,7,2,4,6,1,3]=>[3,1,6,4,2,7,5]=>000000=>000000
[5,7,2,4,6,3,1]=>[1,3,6,4,2,7,5]=>100000=>000001
[5,7,2,6,1,3,4]=>[4,3,1,6,2,7,5]=>000000=>000000
[5,7,2,6,1,4,3]=>[3,4,1,6,2,7,5]=>000000=>000000
[5,7,2,6,3,1,4]=>[4,1,3,6,2,7,5]=>000000=>000000
[5,7,2,6,3,4,1]=>[1,4,3,6,2,7,5]=>100000=>000001
[5,7,2,6,4,1,3]=>[3,1,4,6,2,7,5]=>000000=>000000
[5,7,2,6,4,3,1]=>[1,3,4,6,2,7,5]=>100000=>000001
[5,7,3,1,2,4,6]=>[6,4,2,1,3,7,5]=>000000=>000000
[5,7,3,1,2,6,4]=>[4,6,2,1,3,7,5]=>000000=>000000
[5,7,3,1,4,2,6]=>[6,2,4,1,3,7,5]=>000000=>000000
[5,7,3,1,4,6,2]=>[2,6,4,1,3,7,5]=>000000=>000000
[5,7,3,1,6,2,4]=>[4,2,6,1,3,7,5]=>000000=>000000
[5,7,3,1,6,4,2]=>[2,4,6,1,3,7,5]=>000000=>000000
[5,7,3,2,1,4,6]=>[6,4,1,2,3,7,5]=>000000=>000000
[5,7,3,2,1,6,4]=>[4,6,1,2,3,7,5]=>000000=>000000
[5,7,3,2,4,1,6]=>[6,1,4,2,3,7,5]=>000000=>000000
[5,7,3,2,4,6,1]=>[1,6,4,2,3,7,5]=>100000=>000001
[5,7,3,2,6,1,4]=>[4,1,6,2,3,7,5]=>000000=>000000
[5,7,3,2,6,4,1]=>[1,4,6,2,3,7,5]=>100000=>000001
[5,7,3,4,1,2,6]=>[6,2,1,4,3,7,5]=>000000=>000000
[5,7,3,4,1,6,2]=>[2,6,1,4,3,7,5]=>000000=>000000
[5,7,3,4,2,1,6]=>[6,1,2,4,3,7,5]=>000000=>000000
[5,7,3,4,2,6,1]=>[1,6,2,4,3,7,5]=>100000=>000001
[5,7,3,4,6,1,2]=>[2,1,6,4,3,7,5]=>010000=>000010
[5,7,3,4,6,2,1]=>[1,2,6,4,3,7,5]=>110000=>000011
[5,7,3,6,1,2,4]=>[4,2,1,6,3,7,5]=>000000=>000000
[5,7,3,6,1,4,2]=>[2,4,1,6,3,7,5]=>000000=>000000
[5,7,3,6,2,1,4]=>[4,1,2,6,3,7,5]=>000000=>000000
[5,7,3,6,2,4,1]=>[1,4,2,6,3,7,5]=>100000=>000001
[5,7,3,6,4,1,2]=>[2,1,4,6,3,7,5]=>010000=>000010
[5,7,3,6,4,2,1]=>[1,2,4,6,3,7,5]=>110000=>000011
[5,7,4,1,2,3,6]=>[6,3,2,1,4,7,5]=>000000=>000000
[5,7,4,1,2,6,3]=>[3,6,2,1,4,7,5]=>000000=>000000
[5,7,4,1,3,2,6]=>[6,2,3,1,4,7,5]=>000000=>000000
[5,7,4,1,3,6,2]=>[2,6,3,1,4,7,5]=>000000=>000000
[5,7,4,1,6,2,3]=>[3,2,6,1,4,7,5]=>000000=>000000
[5,7,4,1,6,3,2]=>[2,3,6,1,4,7,5]=>000000=>000000
[5,7,4,2,1,3,6]=>[6,3,1,2,4,7,5]=>000000=>000000
[5,7,4,2,1,6,3]=>[3,6,1,2,4,7,5]=>000000=>000000
[5,7,4,2,3,1,6]=>[6,1,3,2,4,7,5]=>000000=>000000
[5,7,4,2,3,6,1]=>[1,6,3,2,4,7,5]=>100000=>000001
[5,7,4,2,6,1,3]=>[3,1,6,2,4,7,5]=>000000=>000000
[5,7,4,2,6,3,1]=>[1,3,6,2,4,7,5]=>100000=>000001
[5,7,4,3,1,2,6]=>[6,2,1,3,4,7,5]=>000000=>000000
[5,7,4,3,1,6,2]=>[2,6,1,3,4,7,5]=>000000=>000000
[5,7,4,3,2,1,6]=>[6,1,2,3,4,7,5]=>000000=>000000
[5,7,4,3,2,6,1]=>[1,6,2,3,4,7,5]=>100000=>000001
[5,7,4,3,6,1,2]=>[2,1,6,3,4,7,5]=>010000=>000010
[5,7,4,3,6,2,1]=>[1,2,6,3,4,7,5]=>110000=>000011
[5,7,4,6,1,2,3]=>[3,2,1,6,4,7,5]=>001000=>000100
[5,7,4,6,1,3,2]=>[2,3,1,6,4,7,5]=>001000=>000100
[5,7,4,6,2,1,3]=>[3,1,2,6,4,7,5]=>001000=>000100
[5,7,4,6,2,3,1]=>[1,3,2,6,4,7,5]=>101000=>000101
[5,7,4,6,3,1,2]=>[2,1,3,6,4,7,5]=>011000=>000110
[5,7,4,6,3,2,1]=>[1,2,3,6,4,7,5]=>111000=>000111
[5,7,6,1,2,3,4]=>[4,3,2,1,6,7,5]=>000100=>001000
[5,7,6,1,2,4,3]=>[3,4,2,1,6,7,5]=>000100=>001000
[5,7,6,1,3,2,4]=>[4,2,3,1,6,7,5]=>000100=>001000
[5,7,6,1,3,4,2]=>[2,4,3,1,6,7,5]=>000100=>001000
[5,7,6,1,4,2,3]=>[3,2,4,1,6,7,5]=>000100=>001000
[5,7,6,1,4,3,2]=>[2,3,4,1,6,7,5]=>000100=>001000
[5,7,6,2,1,3,4]=>[4,3,1,2,6,7,5]=>000100=>001000
[5,7,6,2,1,4,3]=>[3,4,1,2,6,7,5]=>000100=>001000
[5,7,6,2,3,1,4]=>[4,1,3,2,6,7,5]=>000100=>001000
[5,7,6,2,3,4,1]=>[1,4,3,2,6,7,5]=>100100=>001001
[5,7,6,2,4,1,3]=>[3,1,4,2,6,7,5]=>000100=>001000
[5,7,6,2,4,3,1]=>[1,3,4,2,6,7,5]=>100100=>001001
[5,7,6,3,1,2,4]=>[4,2,1,3,6,7,5]=>000100=>001000
[5,7,6,3,1,4,2]=>[2,4,1,3,6,7,5]=>000100=>001000
[5,7,6,3,2,1,4]=>[4,1,2,3,6,7,5]=>000100=>001000
[5,7,6,3,2,4,1]=>[1,4,2,3,6,7,5]=>100100=>001001
[5,7,6,3,4,1,2]=>[2,1,4,3,6,7,5]=>010100=>001010
[5,7,6,3,4,2,1]=>[1,2,4,3,6,7,5]=>110100=>001011
[5,7,6,4,1,2,3]=>[3,2,1,4,6,7,5]=>001100=>001100
[5,7,6,4,1,3,2]=>[2,3,1,4,6,7,5]=>001100=>001100
[5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5]=>001100=>001100
[5,7,6,4,2,3,1]=>[1,3,2,4,6,7,5]=>101100=>001101
[5,7,6,4,3,1,2]=>[2,1,3,4,6,7,5]=>011100=>001110
[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>111100=>001111
[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>000000=>000000
[6,1,2,3,4,7,5]=>[5,7,4,3,2,1,6]=>000000=>000000
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[6,4,5,1,7,3,2]=>[2,3,7,1,5,4,6]=>000000=>000000
[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>000000=>000000
[6,4,5,2,1,7,3]=>[3,7,1,2,5,4,6]=>000000=>000000
[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>000000=>000000
[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>100000=>000001
[6,4,5,2,7,1,3]=>[3,1,7,2,5,4,6]=>000000=>000000
[6,4,5,2,7,3,1]=>[1,3,7,2,5,4,6]=>100000=>000001
[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>000000=>000000
[6,4,5,3,1,7,2]=>[2,7,1,3,5,4,6]=>000000=>000000
[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>000000=>000000
[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>100000=>000001
[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>010000=>000010
[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>110000=>000011
[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>001000=>000100
[6,4,5,7,1,3,2]=>[2,3,1,7,5,4,6]=>001000=>000100
[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>001000=>000100
[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>101000=>000101
[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>011000=>000110
[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>111000=>000111
[6,4,7,1,2,3,5]=>[5,3,2,1,7,4,6]=>000000=>000000
[6,4,7,1,2,5,3]=>[3,5,2,1,7,4,6]=>000000=>000000
[6,4,7,1,3,2,5]=>[5,2,3,1,7,4,6]=>000000=>000000
[6,4,7,1,3,5,2]=>[2,5,3,1,7,4,6]=>000000=>000000
[6,4,7,1,5,2,3]=>[3,2,5,1,7,4,6]=>000000=>000000
[6,4,7,1,5,3,2]=>[2,3,5,1,7,4,6]=>000000=>000000
[6,4,7,2,1,3,5]=>[5,3,1,2,7,4,6]=>000000=>000000
[6,4,7,2,1,5,3]=>[3,5,1,2,7,4,6]=>000000=>000000
[6,4,7,2,3,1,5]=>[5,1,3,2,7,4,6]=>000000=>000000
[6,4,7,2,3,5,1]=>[1,5,3,2,7,4,6]=>100000=>000001
[6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6]=>000000=>000000
[6,4,7,2,5,3,1]=>[1,3,5,2,7,4,6]=>100000=>000001
[6,4,7,3,1,2,5]=>[5,2,1,3,7,4,6]=>000000=>000000
[6,4,7,3,1,5,2]=>[2,5,1,3,7,4,6]=>000000=>000000
[6,4,7,3,2,1,5]=>[5,1,2,3,7,4,6]=>000000=>000000
[6,4,7,3,2,5,1]=>[1,5,2,3,7,4,6]=>100000=>000001
[6,4,7,3,5,1,2]=>[2,1,5,3,7,4,6]=>010000=>000010
[6,4,7,3,5,2,1]=>[1,2,5,3,7,4,6]=>110000=>000011
[6,4,7,5,1,2,3]=>[3,2,1,5,7,4,6]=>001000=>000100
[6,4,7,5,1,3,2]=>[2,3,1,5,7,4,6]=>001000=>000100
[6,4,7,5,2,1,3]=>[3,1,2,5,7,4,6]=>001000=>000100
[6,4,7,5,2,3,1]=>[1,3,2,5,7,4,6]=>101000=>000101
[6,4,7,5,3,1,2]=>[2,1,3,5,7,4,6]=>011000=>000110
[6,4,7,5,3,2,1]=>[1,2,3,5,7,4,6]=>111000=>000111
[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>000000=>000000
[6,5,1,2,3,7,4]=>[4,7,3,2,1,5,6]=>000000=>000000
[6,5,1,2,4,3,7]=>[7,3,4,2,1,5,6]=>000000=>000000
[6,5,1,2,4,7,3]=>[3,7,4,2,1,5,6]=>000000=>000000
[6,5,1,2,7,3,4]=>[4,3,7,2,1,5,6]=>000000=>000000
[6,5,1,2,7,4,3]=>[3,4,7,2,1,5,6]=>000000=>000000
[6,5,1,3,2,4,7]=>[7,4,2,3,1,5,6]=>000000=>000000
[6,5,1,3,2,7,4]=>[4,7,2,3,1,5,6]=>000000=>000000
[6,5,1,3,4,2,7]=>[7,2,4,3,1,5,6]=>000000=>000000
[6,5,1,3,4,7,2]=>[2,7,4,3,1,5,6]=>000000=>000000
[6,5,1,3,7,2,4]=>[4,2,7,3,1,5,6]=>000000=>000000
[6,5,1,3,7,4,2]=>[2,4,7,3,1,5,6]=>000000=>000000
[6,5,1,4,2,3,7]=>[7,3,2,4,1,5,6]=>000000=>000000
[6,5,1,4,2,7,3]=>[3,7,2,4,1,5,6]=>000000=>000000
[6,5,1,4,3,2,7]=>[7,2,3,4,1,5,6]=>000000=>000000
[6,5,1,4,3,7,2]=>[2,7,3,4,1,5,6]=>000000=>000000
[6,5,1,4,7,2,3]=>[3,2,7,4,1,5,6]=>000000=>000000
[6,5,1,4,7,3,2]=>[2,3,7,4,1,5,6]=>000000=>000000
[6,5,1,7,2,3,4]=>[4,3,2,7,1,5,6]=>000000=>000000
[6,5,1,7,2,4,3]=>[3,4,2,7,1,5,6]=>000000=>000000
[6,5,1,7,3,2,4]=>[4,2,3,7,1,5,6]=>000000=>000000
[6,5,1,7,3,4,2]=>[2,4,3,7,1,5,6]=>000000=>000000
[6,5,1,7,4,2,3]=>[3,2,4,7,1,5,6]=>000000=>000000
[6,5,1,7,4,3,2]=>[2,3,4,7,1,5,6]=>000000=>000000
[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>000000=>000000
[6,5,2,1,3,7,4]=>[4,7,3,1,2,5,6]=>000000=>000000
[6,5,2,1,4,3,7]=>[7,3,4,1,2,5,6]=>000000=>000000
[6,5,2,1,4,7,3]=>[3,7,4,1,2,5,6]=>000000=>000000
[6,5,2,1,7,3,4]=>[4,3,7,1,2,5,6]=>000000=>000000
[6,5,2,1,7,4,3]=>[3,4,7,1,2,5,6]=>000000=>000000
[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>000000=>000000
[6,5,2,3,1,7,4]=>[4,7,1,3,2,5,6]=>000000=>000000
[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>000000=>000000
[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>100000=>000001
[6,5,2,3,7,1,4]=>[4,1,7,3,2,5,6]=>000000=>000000
[6,5,2,3,7,4,1]=>[1,4,7,3,2,5,6]=>100000=>000001
[6,5,2,4,1,3,7]=>[7,3,1,4,2,5,6]=>000000=>000000
[6,5,2,4,1,7,3]=>[3,7,1,4,2,5,6]=>000000=>000000
[6,5,2,4,3,1,7]=>[7,1,3,4,2,5,6]=>000000=>000000
[6,5,2,4,3,7,1]=>[1,7,3,4,2,5,6]=>100000=>000001
[6,5,2,4,7,1,3]=>[3,1,7,4,2,5,6]=>000000=>000000
[6,5,2,4,7,3,1]=>[1,3,7,4,2,5,6]=>100000=>000001
[6,5,2,7,1,3,4]=>[4,3,1,7,2,5,6]=>000000=>000000
[6,5,2,7,1,4,3]=>[3,4,1,7,2,5,6]=>000000=>000000
[6,5,2,7,3,1,4]=>[4,1,3,7,2,5,6]=>000000=>000000
[6,5,2,7,3,4,1]=>[1,4,3,7,2,5,6]=>100000=>000001
[6,5,2,7,4,1,3]=>[3,1,4,7,2,5,6]=>000000=>000000
[6,5,2,7,4,3,1]=>[1,3,4,7,2,5,6]=>100000=>000001
[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>000000=>000000
[6,5,3,1,2,7,4]=>[4,7,2,1,3,5,6]=>000000=>000000
[6,5,3,1,4,2,7]=>[7,2,4,1,3,5,6]=>000000=>000000
[6,5,3,1,4,7,2]=>[2,7,4,1,3,5,6]=>000000=>000000
[6,5,3,1,7,2,4]=>[4,2,7,1,3,5,6]=>000000=>000000
[6,5,3,1,7,4,2]=>[2,4,7,1,3,5,6]=>000000=>000000
[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>000000=>000000
[6,5,3,2,1,7,4]=>[4,7,1,2,3,5,6]=>000000=>000000
[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>000000=>000000
[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>100000=>000001
[6,5,3,2,7,1,4]=>[4,1,7,2,3,5,6]=>000000=>000000
[6,5,3,2,7,4,1]=>[1,4,7,2,3,5,6]=>100000=>000001
[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>000000=>000000
[6,5,3,4,1,7,2]=>[2,7,1,4,3,5,6]=>000000=>000000
[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>000000=>000000
[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>100000=>000001
[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>010000=>000010
[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>110000=>000011
[6,5,3,7,1,2,4]=>[4,2,1,7,3,5,6]=>000000=>000000
[6,5,3,7,1,4,2]=>[2,4,1,7,3,5,6]=>000000=>000000
[6,5,3,7,2,1,4]=>[4,1,2,7,3,5,6]=>000000=>000000
[6,5,3,7,2,4,1]=>[1,4,2,7,3,5,6]=>100000=>000001
[6,5,3,7,4,1,2]=>[2,1,4,7,3,5,6]=>010000=>000010
[6,5,3,7,4,2,1]=>[1,2,4,7,3,5,6]=>110000=>000011
[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>000000=>000000
[6,5,4,1,2,7,3]=>[3,7,2,1,4,5,6]=>000000=>000000
[6,5,4,1,3,2,7]=>[7,2,3,1,4,5,6]=>000000=>000000
[6,5,4,1,3,7,2]=>[2,7,3,1,4,5,6]=>000000=>000000
[6,5,4,1,7,2,3]=>[3,2,7,1,4,5,6]=>000000=>000000
[6,5,4,1,7,3,2]=>[2,3,7,1,4,5,6]=>000000=>000000
[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>000000=>000000
[6,5,4,2,1,7,3]=>[3,7,1,2,4,5,6]=>000000=>000000
[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>000000=>000000
[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>100000=>000001
[6,5,4,2,7,1,3]=>[3,1,7,2,4,5,6]=>000000=>000000
[6,5,4,2,7,3,1]=>[1,3,7,2,4,5,6]=>100000=>000001
[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>000000=>000000
[6,5,4,3,1,7,2]=>[2,7,1,3,4,5,6]=>000000=>000000
[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>000000=>000000
[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>100000=>000001
[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>010000=>000010
[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>110000=>000011
[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>001000=>000100
[6,5,4,7,1,3,2]=>[2,3,1,7,4,5,6]=>001000=>000100
[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>001000=>000100
[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>101000=>000101
[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>011000=>000110
[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>111000=>000111
[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>000100=>001000
[6,5,7,1,2,4,3]=>[3,4,2,1,7,5,6]=>000100=>001000
[6,5,7,1,3,2,4]=>[4,2,3,1,7,5,6]=>000100=>001000
[6,5,7,1,3,4,2]=>[2,4,3,1,7,5,6]=>000100=>001000
[6,5,7,1,4,2,3]=>[3,2,4,1,7,5,6]=>000100=>001000
[6,5,7,1,4,3,2]=>[2,3,4,1,7,5,6]=>000100=>001000
[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>000100=>001000
[6,5,7,2,1,4,3]=>[3,4,1,2,7,5,6]=>000100=>001000
[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>000100=>001000
[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>100100=>001001
[6,5,7,2,4,1,3]=>[3,1,4,2,7,5,6]=>000100=>001000
[6,5,7,2,4,3,1]=>[1,3,4,2,7,5,6]=>100100=>001001
[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>000100=>001000
[6,5,7,3,1,4,2]=>[2,4,1,3,7,5,6]=>000100=>001000
[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>000100=>001000
[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>100100=>001001
[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>010100=>001010
[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>110100=>001011
[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>001100=>001100
[6,5,7,4,1,3,2]=>[2,3,1,4,7,5,6]=>001100=>001100
[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>001100=>001100
[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>101100=>001101
[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>011100=>001110
[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>111100=>001111
[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>000010=>010000
[6,7,1,2,3,5,4]=>[4,5,3,2,1,7,6]=>000010=>010000
[6,7,1,2,4,3,5]=>[5,3,4,2,1,7,6]=>000010=>010000
[6,7,1,2,4,5,3]=>[3,5,4,2,1,7,6]=>000010=>010000
[6,7,1,2,5,3,4]=>[4,3,5,2,1,7,6]=>000010=>010000
[6,7,1,2,5,4,3]=>[3,4,5,2,1,7,6]=>000010=>010000
[6,7,1,3,2,4,5]=>[5,4,2,3,1,7,6]=>000010=>010000
[6,7,1,3,2,5,4]=>[4,5,2,3,1,7,6]=>000010=>010000
[6,7,1,3,4,2,5]=>[5,2,4,3,1,7,6]=>000010=>010000
[6,7,1,3,4,5,2]=>[2,5,4,3,1,7,6]=>000010=>010000
[6,7,1,3,5,2,4]=>[4,2,5,3,1,7,6]=>000010=>010000
[6,7,1,3,5,4,2]=>[2,4,5,3,1,7,6]=>000010=>010000
[6,7,1,4,2,3,5]=>[5,3,2,4,1,7,6]=>000010=>010000
[6,7,1,4,2,5,3]=>[3,5,2,4,1,7,6]=>000010=>010000
[6,7,1,4,3,2,5]=>[5,2,3,4,1,7,6]=>000010=>010000
[6,7,1,4,3,5,2]=>[2,5,3,4,1,7,6]=>000010=>010000
[6,7,1,4,5,2,3]=>[3,2,5,4,1,7,6]=>000010=>010000
[6,7,1,4,5,3,2]=>[2,3,5,4,1,7,6]=>000010=>010000
[6,7,1,5,2,3,4]=>[4,3,2,5,1,7,6]=>000010=>010000
[6,7,1,5,2,4,3]=>[3,4,2,5,1,7,6]=>000010=>010000
[6,7,1,5,3,2,4]=>[4,2,3,5,1,7,6]=>000010=>010000
[6,7,1,5,3,4,2]=>[2,4,3,5,1,7,6]=>000010=>010000
[6,7,1,5,4,2,3]=>[3,2,4,5,1,7,6]=>000010=>010000
[6,7,1,5,4,3,2]=>[2,3,4,5,1,7,6]=>000010=>010000
[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>000010=>010000
[6,7,2,1,3,5,4]=>[4,5,3,1,2,7,6]=>000010=>010000
[6,7,2,1,4,3,5]=>[5,3,4,1,2,7,6]=>000010=>010000
[6,7,2,1,4,5,3]=>[3,5,4,1,2,7,6]=>000010=>010000
[6,7,2,1,5,3,4]=>[4,3,5,1,2,7,6]=>000010=>010000
[6,7,2,1,5,4,3]=>[3,4,5,1,2,7,6]=>000010=>010000
[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>000010=>010000
[6,7,2,3,1,5,4]=>[4,5,1,3,2,7,6]=>000010=>010000
[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>000010=>010000
[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>100010=>010001
[6,7,2,3,5,1,4]=>[4,1,5,3,2,7,6]=>000010=>010000
[6,7,2,3,5,4,1]=>[1,4,5,3,2,7,6]=>100010=>010001
[6,7,2,4,1,3,5]=>[5,3,1,4,2,7,6]=>000010=>010000
[6,7,2,4,1,5,3]=>[3,5,1,4,2,7,6]=>000010=>010000
[6,7,2,4,3,1,5]=>[5,1,3,4,2,7,6]=>000010=>010000
[6,7,2,4,3,5,1]=>[1,5,3,4,2,7,6]=>100010=>010001
[6,7,2,4,5,1,3]=>[3,1,5,4,2,7,6]=>000010=>010000
[6,7,2,4,5,3,1]=>[1,3,5,4,2,7,6]=>100010=>010001
[6,7,2,5,1,3,4]=>[4,3,1,5,2,7,6]=>000010=>010000
[6,7,2,5,1,4,3]=>[3,4,1,5,2,7,6]=>000010=>010000
[6,7,2,5,3,1,4]=>[4,1,3,5,2,7,6]=>000010=>010000
[6,7,2,5,3,4,1]=>[1,4,3,5,2,7,6]=>100010=>010001
[6,7,2,5,4,1,3]=>[3,1,4,5,2,7,6]=>000010=>010000
[6,7,2,5,4,3,1]=>[1,3,4,5,2,7,6]=>100010=>010001
[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>000010=>010000
[6,7,3,1,2,5,4]=>[4,5,2,1,3,7,6]=>000010=>010000
[6,7,3,1,4,2,5]=>[5,2,4,1,3,7,6]=>000010=>010000
[6,7,3,1,4,5,2]=>[2,5,4,1,3,7,6]=>000010=>010000
[6,7,3,1,5,2,4]=>[4,2,5,1,3,7,6]=>000010=>010000
[6,7,3,1,5,4,2]=>[2,4,5,1,3,7,6]=>000010=>010000
[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>000010=>010000
[6,7,3,2,1,5,4]=>[4,5,1,2,3,7,6]=>000010=>010000
[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>000010=>010000
[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>100010=>010001
[6,7,3,2,5,1,4]=>[4,1,5,2,3,7,6]=>000010=>010000
[6,7,3,2,5,4,1]=>[1,4,5,2,3,7,6]=>100010=>010001
[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>000010=>010000
[6,7,3,4,1,5,2]=>[2,5,1,4,3,7,6]=>000010=>010000
[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>000010=>010000
[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>100010=>010001
[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>010010=>010010
[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>110010=>010011
[6,7,3,5,1,2,4]=>[4,2,1,5,3,7,6]=>000010=>010000
[6,7,3,5,1,4,2]=>[2,4,1,5,3,7,6]=>000010=>010000
[6,7,3,5,2,1,4]=>[4,1,2,5,3,7,6]=>000010=>010000
[6,7,3,5,2,4,1]=>[1,4,2,5,3,7,6]=>100010=>010001
[6,7,3,5,4,1,2]=>[2,1,4,5,3,7,6]=>010010=>010010
[6,7,3,5,4,2,1]=>[1,2,4,5,3,7,6]=>110010=>010011
[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>000010=>010000
[6,7,4,1,2,5,3]=>[3,5,2,1,4,7,6]=>000010=>010000
[6,7,4,1,3,2,5]=>[5,2,3,1,4,7,6]=>000010=>010000
[6,7,4,1,3,5,2]=>[2,5,3,1,4,7,6]=>000010=>010000
[6,7,4,1,5,2,3]=>[3,2,5,1,4,7,6]=>000010=>010000
[6,7,4,1,5,3,2]=>[2,3,5,1,4,7,6]=>000010=>010000
[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>000010=>010000
[6,7,4,2,1,5,3]=>[3,5,1,2,4,7,6]=>000010=>010000
[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>000010=>010000
[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>100010=>010001
[6,7,4,2,5,1,3]=>[3,1,5,2,4,7,6]=>000010=>010000
[6,7,4,2,5,3,1]=>[1,3,5,2,4,7,6]=>100010=>010001
[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>000010=>010000
[6,7,4,3,1,5,2]=>[2,5,1,3,4,7,6]=>000010=>010000
[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000010=>010000
[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>100010=>010001
[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>010010=>010010
[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>110010=>010011
[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>001010=>010100
[6,7,4,5,1,3,2]=>[2,3,1,5,4,7,6]=>001010=>010100
[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>001010=>010100
[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>101010=>010101
[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>011010=>010110
[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>111010=>010111
[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>000110=>011000
[6,7,5,1,2,4,3]=>[3,4,2,1,5,7,6]=>000110=>011000
[6,7,5,1,3,2,4]=>[4,2,3,1,5,7,6]=>000110=>011000
[6,7,5,1,3,4,2]=>[2,4,3,1,5,7,6]=>000110=>011000
[6,7,5,1,4,2,3]=>[3,2,4,1,5,7,6]=>000110=>011000
[6,7,5,1,4,3,2]=>[2,3,4,1,5,7,6]=>000110=>011000
[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>000110=>011000
[6,7,5,2,1,4,3]=>[3,4,1,2,5,7,6]=>000110=>011000
[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>000110=>011000
[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>100110=>011001
[6,7,5,2,4,1,3]=>[3,1,4,2,5,7,6]=>000110=>011000
[6,7,5,2,4,3,1]=>[1,3,4,2,5,7,6]=>100110=>011001
[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>000110=>011000
[6,7,5,3,1,4,2]=>[2,4,1,3,5,7,6]=>000110=>011000
[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>000110=>011000
[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>100110=>011001
[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>010110=>011010
[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>110110=>011011
[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>001110=>011100
[6,7,5,4,1,3,2]=>[2,3,1,4,5,7,6]=>001110=>011100
[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>001110=>011100
[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>101110=>011101
[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>011110=>011110
[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>111110=>011111
[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>000001=>100000
[7,1,2,3,4,6,5]=>[5,6,4,3,2,1,7]=>000001=>100000
[7,1,2,3,5,4,6]=>[6,4,5,3,2,1,7]=>000001=>100000
[7,1,2,3,5,6,4]=>[4,6,5,3,2,1,7]=>000001=>100000
[7,1,2,3,6,4,5]=>[5,4,6,3,2,1,7]=>000001=>100000
[7,1,2,3,6,5,4]=>[4,5,6,3,2,1,7]=>000001=>100000
[7,1,2,4,3,5,6]=>[6,5,3,4,2,1,7]=>000001=>100000
[7,1,2,4,3,6,5]=>[5,6,3,4,2,1,7]=>000001=>100000
[7,1,2,4,5,3,6]=>[6,3,5,4,2,1,7]=>000001=>100000
[7,1,2,4,5,6,3]=>[3,6,5,4,2,1,7]=>000001=>100000
[7,1,2,4,6,3,5]=>[5,3,6,4,2,1,7]=>000001=>100000
[7,1,2,4,6,5,3]=>[3,5,6,4,2,1,7]=>000001=>100000
[7,1,2,5,3,4,6]=>[6,4,3,5,2,1,7]=>000001=>100000
[7,1,2,5,3,6,4]=>[4,6,3,5,2,1,7]=>000001=>100000
[7,1,2,5,4,3,6]=>[6,3,4,5,2,1,7]=>000001=>100000
[7,1,2,5,4,6,3]=>[3,6,4,5,2,1,7]=>000001=>100000
[7,1,2,5,6,3,4]=>[4,3,6,5,2,1,7]=>000001=>100000
[7,1,2,5,6,4,3]=>[3,4,6,5,2,1,7]=>000001=>100000
[7,1,2,6,3,4,5]=>[5,4,3,6,2,1,7]=>000001=>100000
[7,1,2,6,3,5,4]=>[4,5,3,6,2,1,7]=>000001=>100000
[7,1,2,6,4,3,5]=>[5,3,4,6,2,1,7]=>000001=>100000
[7,1,2,6,4,5,3]=>[3,5,4,6,2,1,7]=>000001=>100000
[7,1,2,6,5,3,4]=>[4,3,5,6,2,1,7]=>000001=>100000
[7,1,2,6,5,4,3]=>[3,4,5,6,2,1,7]=>000001=>100000
[7,1,3,2,4,5,6]=>[6,5,4,2,3,1,7]=>000001=>100000
[7,1,3,2,4,6,5]=>[5,6,4,2,3,1,7]=>000001=>100000
[7,1,3,2,5,4,6]=>[6,4,5,2,3,1,7]=>000001=>100000
[7,1,3,2,5,6,4]=>[4,6,5,2,3,1,7]=>000001=>100000
[7,1,3,2,6,4,5]=>[5,4,6,2,3,1,7]=>000001=>100000
[7,1,3,2,6,5,4]=>[4,5,6,2,3,1,7]=>000001=>100000
[7,1,3,4,2,5,6]=>[6,5,2,4,3,1,7]=>000001=>100000
[7,1,3,4,2,6,5]=>[5,6,2,4,3,1,7]=>000001=>100000
[7,1,3,4,5,2,6]=>[6,2,5,4,3,1,7]=>000001=>100000
[7,1,3,4,5,6,2]=>[2,6,5,4,3,1,7]=>000001=>100000
[7,1,3,4,6,2,5]=>[5,2,6,4,3,1,7]=>000001=>100000
[7,1,3,4,6,5,2]=>[2,5,6,4,3,1,7]=>000001=>100000
[7,1,3,5,2,4,6]=>[6,4,2,5,3,1,7]=>000001=>100000
[7,1,3,5,2,6,4]=>[4,6,2,5,3,1,7]=>000001=>100000
[7,1,3,5,4,2,6]=>[6,2,4,5,3,1,7]=>000001=>100000
[7,1,3,5,4,6,2]=>[2,6,4,5,3,1,7]=>000001=>100000
[7,1,3,5,6,2,4]=>[4,2,6,5,3,1,7]=>000001=>100000
[7,1,3,5,6,4,2]=>[2,4,6,5,3,1,7]=>000001=>100000
[7,1,3,6,2,4,5]=>[5,4,2,6,3,1,7]=>000001=>100000
[7,1,3,6,2,5,4]=>[4,5,2,6,3,1,7]=>000001=>100000
[7,1,3,6,4,2,5]=>[5,2,4,6,3,1,7]=>000001=>100000
[7,1,3,6,4,5,2]=>[2,5,4,6,3,1,7]=>000001=>100000
[7,1,3,6,5,2,4]=>[4,2,5,6,3,1,7]=>000001=>100000
[7,1,3,6,5,4,2]=>[2,4,5,6,3,1,7]=>000001=>100000
[7,1,4,2,3,5,6]=>[6,5,3,2,4,1,7]=>000001=>100000
[7,1,4,2,3,6,5]=>[5,6,3,2,4,1,7]=>000001=>100000
[7,1,4,2,5,3,6]=>[6,3,5,2,4,1,7]=>000001=>100000
[7,1,4,2,5,6,3]=>[3,6,5,2,4,1,7]=>000001=>100000
[7,1,4,2,6,3,5]=>[5,3,6,2,4,1,7]=>000001=>100000
[7,1,4,2,6,5,3]=>[3,5,6,2,4,1,7]=>000001=>100000
[7,1,4,3,2,5,6]=>[6,5,2,3,4,1,7]=>000001=>100000
[7,1,4,3,2,6,5]=>[5,6,2,3,4,1,7]=>000001=>100000
[7,1,4,3,5,2,6]=>[6,2,5,3,4,1,7]=>000001=>100000
[7,1,4,3,5,6,2]=>[2,6,5,3,4,1,7]=>000001=>100000
[7,1,4,3,6,2,5]=>[5,2,6,3,4,1,7]=>000001=>100000
[7,1,4,3,6,5,2]=>[2,5,6,3,4,1,7]=>000001=>100000
[7,1,4,5,2,3,6]=>[6,3,2,5,4,1,7]=>000001=>100000
[7,1,4,5,2,6,3]=>[3,6,2,5,4,1,7]=>000001=>100000
[7,1,4,5,3,2,6]=>[6,2,3,5,4,1,7]=>000001=>100000
[7,1,4,5,3,6,2]=>[2,6,3,5,4,1,7]=>000001=>100000
[7,1,4,5,6,2,3]=>[3,2,6,5,4,1,7]=>000001=>100000
[7,1,4,5,6,3,2]=>[2,3,6,5,4,1,7]=>000001=>100000
[7,1,4,6,2,3,5]=>[5,3,2,6,4,1,7]=>000001=>100000
[7,1,4,6,2,5,3]=>[3,5,2,6,4,1,7]=>000001=>100000
[7,1,4,6,3,2,5]=>[5,2,3,6,4,1,7]=>000001=>100000
[7,1,4,6,3,5,2]=>[2,5,3,6,4,1,7]=>000001=>100000
[7,1,4,6,5,2,3]=>[3,2,5,6,4,1,7]=>000001=>100000
[7,1,4,6,5,3,2]=>[2,3,5,6,4,1,7]=>000001=>100000
[7,1,5,2,3,4,6]=>[6,4,3,2,5,1,7]=>000001=>100000
[7,1,5,2,3,6,4]=>[4,6,3,2,5,1,7]=>000001=>100000
[7,1,5,2,4,3,6]=>[6,3,4,2,5,1,7]=>000001=>100000
[7,1,5,2,4,6,3]=>[3,6,4,2,5,1,7]=>000001=>100000
[7,1,5,2,6,3,4]=>[4,3,6,2,5,1,7]=>000001=>100000
[7,1,5,2,6,4,3]=>[3,4,6,2,5,1,7]=>000001=>100000
[7,1,5,3,2,4,6]=>[6,4,2,3,5,1,7]=>000001=>100000
[7,1,5,3,2,6,4]=>[4,6,2,3,5,1,7]=>000001=>100000
[7,1,5,3,4,2,6]=>[6,2,4,3,5,1,7]=>000001=>100000
[7,1,5,3,4,6,2]=>[2,6,4,3,5,1,7]=>000001=>100000
[7,1,5,3,6,2,4]=>[4,2,6,3,5,1,7]=>000001=>100000
[7,1,5,3,6,4,2]=>[2,4,6,3,5,1,7]=>000001=>100000
[7,1,5,4,2,3,6]=>[6,3,2,4,5,1,7]=>000001=>100000
[7,1,5,4,2,6,3]=>[3,6,2,4,5,1,7]=>000001=>100000
[7,1,5,4,3,2,6]=>[6,2,3,4,5,1,7]=>000001=>100000
[7,1,5,4,3,6,2]=>[2,6,3,4,5,1,7]=>000001=>100000
[7,1,5,4,6,2,3]=>[3,2,6,4,5,1,7]=>000001=>100000
[7,1,5,4,6,3,2]=>[2,3,6,4,5,1,7]=>000001=>100000
[7,1,5,6,2,3,4]=>[4,3,2,6,5,1,7]=>000001=>100000
[7,1,5,6,2,4,3]=>[3,4,2,6,5,1,7]=>000001=>100000
[7,1,5,6,3,2,4]=>[4,2,3,6,5,1,7]=>000001=>100000
[7,1,5,6,3,4,2]=>[2,4,3,6,5,1,7]=>000001=>100000
[7,1,5,6,4,2,3]=>[3,2,4,6,5,1,7]=>000001=>100000
[7,1,5,6,4,3,2]=>[2,3,4,6,5,1,7]=>000001=>100000
[7,1,6,2,3,4,5]=>[5,4,3,2,6,1,7]=>000001=>100000
[7,1,6,2,3,5,4]=>[4,5,3,2,6,1,7]=>000001=>100000
[7,1,6,2,4,3,5]=>[5,3,4,2,6,1,7]=>000001=>100000
[7,1,6,2,4,5,3]=>[3,5,4,2,6,1,7]=>000001=>100000
[7,1,6,2,5,3,4]=>[4,3,5,2,6,1,7]=>000001=>100000
[7,1,6,2,5,4,3]=>[3,4,5,2,6,1,7]=>000001=>100000
[7,1,6,3,2,4,5]=>[5,4,2,3,6,1,7]=>000001=>100000
[7,1,6,3,2,5,4]=>[4,5,2,3,6,1,7]=>000001=>100000
[7,1,6,3,4,2,5]=>[5,2,4,3,6,1,7]=>000001=>100000
[7,1,6,3,4,5,2]=>[2,5,4,3,6,1,7]=>000001=>100000
[7,1,6,3,5,2,4]=>[4,2,5,3,6,1,7]=>000001=>100000
[7,1,6,3,5,4,2]=>[2,4,5,3,6,1,7]=>000001=>100000
[7,1,6,4,2,3,5]=>[5,3,2,4,6,1,7]=>000001=>100000
[7,1,6,4,2,5,3]=>[3,5,2,4,6,1,7]=>000001=>100000
[7,1,6,4,3,2,5]=>[5,2,3,4,6,1,7]=>000001=>100000
[7,1,6,4,3,5,2]=>[2,5,3,4,6,1,7]=>000001=>100000
[7,1,6,4,5,2,3]=>[3,2,5,4,6,1,7]=>000001=>100000
[7,1,6,4,5,3,2]=>[2,3,5,4,6,1,7]=>000001=>100000
[7,1,6,5,2,3,4]=>[4,3,2,5,6,1,7]=>000001=>100000
[7,1,6,5,2,4,3]=>[3,4,2,5,6,1,7]=>000001=>100000
[7,1,6,5,3,2,4]=>[4,2,3,5,6,1,7]=>000001=>100000
[7,1,6,5,3,4,2]=>[2,4,3,5,6,1,7]=>000001=>100000
[7,1,6,5,4,2,3]=>[3,2,4,5,6,1,7]=>000001=>100000
[7,1,6,5,4,3,2]=>[2,3,4,5,6,1,7]=>000001=>100000
[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>000001=>100000
[7,2,1,3,4,6,5]=>[5,6,4,3,1,2,7]=>000001=>100000
[7,2,1,3,5,4,6]=>[6,4,5,3,1,2,7]=>000001=>100000
[7,2,1,3,5,6,4]=>[4,6,5,3,1,2,7]=>000001=>100000
[7,2,1,3,6,4,5]=>[5,4,6,3,1,2,7]=>000001=>100000
[7,2,1,3,6,5,4]=>[4,5,6,3,1,2,7]=>000001=>100000
[7,2,1,4,3,5,6]=>[6,5,3,4,1,2,7]=>000001=>100000
[7,2,1,4,3,6,5]=>[5,6,3,4,1,2,7]=>000001=>100000
[7,2,1,4,5,3,6]=>[6,3,5,4,1,2,7]=>000001=>100000
[7,2,1,4,5,6,3]=>[3,6,5,4,1,2,7]=>000001=>100000
[7,2,1,4,6,3,5]=>[5,3,6,4,1,2,7]=>000001=>100000
[7,2,1,4,6,5,3]=>[3,5,6,4,1,2,7]=>000001=>100000
[7,2,1,5,3,4,6]=>[6,4,3,5,1,2,7]=>000001=>100000
[7,2,1,5,3,6,4]=>[4,6,3,5,1,2,7]=>000001=>100000
[7,2,1,5,4,3,6]=>[6,3,4,5,1,2,7]=>000001=>100000
[7,2,1,5,4,6,3]=>[3,6,4,5,1,2,7]=>000001=>100000
[7,2,1,5,6,3,4]=>[4,3,6,5,1,2,7]=>000001=>100000
[7,2,1,5,6,4,3]=>[3,4,6,5,1,2,7]=>000001=>100000
[7,2,1,6,3,4,5]=>[5,4,3,6,1,2,7]=>000001=>100000
[7,2,1,6,3,5,4]=>[4,5,3,6,1,2,7]=>000001=>100000
[7,2,1,6,4,3,5]=>[5,3,4,6,1,2,7]=>000001=>100000
[7,2,1,6,4,5,3]=>[3,5,4,6,1,2,7]=>000001=>100000
[7,2,1,6,5,3,4]=>[4,3,5,6,1,2,7]=>000001=>100000
[7,2,1,6,5,4,3]=>[3,4,5,6,1,2,7]=>000001=>100000
[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>000001=>100000
[7,2,3,1,4,6,5]=>[5,6,4,1,3,2,7]=>000001=>100000
[7,2,3,1,5,4,6]=>[6,4,5,1,3,2,7]=>000001=>100000
[7,2,3,1,5,6,4]=>[4,6,5,1,3,2,7]=>000001=>100000
[7,2,3,1,6,4,5]=>[5,4,6,1,3,2,7]=>000001=>100000
[7,2,3,1,6,5,4]=>[4,5,6,1,3,2,7]=>000001=>100000
[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>000001=>100000
[7,2,3,4,1,6,5]=>[5,6,1,4,3,2,7]=>000001=>100000
[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>000001=>100000
[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>100001=>100001
[7,2,3,4,6,1,5]=>[5,1,6,4,3,2,7]=>000001=>100000
[7,2,3,4,6,5,1]=>[1,5,6,4,3,2,7]=>100001=>100001
[7,2,3,5,1,4,6]=>[6,4,1,5,3,2,7]=>000001=>100000
[7,2,3,5,1,6,4]=>[4,6,1,5,3,2,7]=>000001=>100000
[7,2,3,5,4,1,6]=>[6,1,4,5,3,2,7]=>000001=>100000
[7,2,3,5,4,6,1]=>[1,6,4,5,3,2,7]=>100001=>100001
[7,2,3,5,6,1,4]=>[4,1,6,5,3,2,7]=>000001=>100000
[7,2,3,5,6,4,1]=>[1,4,6,5,3,2,7]=>100001=>100001
[7,2,3,6,1,4,5]=>[5,4,1,6,3,2,7]=>000001=>100000
[7,2,3,6,1,5,4]=>[4,5,1,6,3,2,7]=>000001=>100000
[7,2,3,6,4,1,5]=>[5,1,4,6,3,2,7]=>000001=>100000
[7,2,3,6,4,5,1]=>[1,5,4,6,3,2,7]=>100001=>100001
[7,2,3,6,5,1,4]=>[4,1,5,6,3,2,7]=>000001=>100000
[7,2,3,6,5,4,1]=>[1,4,5,6,3,2,7]=>100001=>100001
[7,2,4,1,3,5,6]=>[6,5,3,1,4,2,7]=>000001=>100000
[7,2,4,1,3,6,5]=>[5,6,3,1,4,2,7]=>000001=>100000
[7,2,4,1,5,3,6]=>[6,3,5,1,4,2,7]=>000001=>100000
[7,2,4,1,5,6,3]=>[3,6,5,1,4,2,7]=>000001=>100000
[7,2,4,1,6,3,5]=>[5,3,6,1,4,2,7]=>000001=>100000
[7,2,4,1,6,5,3]=>[3,5,6,1,4,2,7]=>000001=>100000
[7,2,4,3,1,5,6]=>[6,5,1,3,4,2,7]=>000001=>100000
[7,2,4,3,1,6,5]=>[5,6,1,3,4,2,7]=>000001=>100000
[7,2,4,3,5,1,6]=>[6,1,5,3,4,2,7]=>000001=>100000
[7,2,4,3,5,6,1]=>[1,6,5,3,4,2,7]=>100001=>100001
[7,2,4,3,6,1,5]=>[5,1,6,3,4,2,7]=>000001=>100000
[7,2,4,3,6,5,1]=>[1,5,6,3,4,2,7]=>100001=>100001
[7,2,4,5,1,3,6]=>[6,3,1,5,4,2,7]=>000001=>100000
[7,2,4,5,1,6,3]=>[3,6,1,5,4,2,7]=>000001=>100000
[7,2,4,5,3,1,6]=>[6,1,3,5,4,2,7]=>000001=>100000
[7,2,4,5,3,6,1]=>[1,6,3,5,4,2,7]=>100001=>100001
[7,2,4,5,6,1,3]=>[3,1,6,5,4,2,7]=>000001=>100000
[7,2,4,5,6,3,1]=>[1,3,6,5,4,2,7]=>100001=>100001
[7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7]=>000001=>100000
[7,2,4,6,1,5,3]=>[3,5,1,6,4,2,7]=>000001=>100000
[7,2,4,6,3,1,5]=>[5,1,3,6,4,2,7]=>000001=>100000
[7,2,4,6,3,5,1]=>[1,5,3,6,4,2,7]=>100001=>100001
[7,2,4,6,5,1,3]=>[3,1,5,6,4,2,7]=>000001=>100000
[7,2,4,6,5,3,1]=>[1,3,5,6,4,2,7]=>100001=>100001
[7,2,5,1,3,4,6]=>[6,4,3,1,5,2,7]=>000001=>100000
[7,2,5,1,3,6,4]=>[4,6,3,1,5,2,7]=>000001=>100000
[7,2,5,1,4,3,6]=>[6,3,4,1,5,2,7]=>000001=>100000
[7,2,5,1,4,6,3]=>[3,6,4,1,5,2,7]=>000001=>100000
[7,2,5,1,6,3,4]=>[4,3,6,1,5,2,7]=>000001=>100000
[7,2,5,1,6,4,3]=>[3,4,6,1,5,2,7]=>000001=>100000
[7,2,5,3,1,4,6]=>[6,4,1,3,5,2,7]=>000001=>100000
[7,2,5,3,1,6,4]=>[4,6,1,3,5,2,7]=>000001=>100000
[7,2,5,3,4,1,6]=>[6,1,4,3,5,2,7]=>000001=>100000
[7,2,5,3,4,6,1]=>[1,6,4,3,5,2,7]=>100001=>100001
[7,2,5,3,6,1,4]=>[4,1,6,3,5,2,7]=>000001=>100000
[7,2,5,3,6,4,1]=>[1,4,6,3,5,2,7]=>100001=>100001
[7,2,5,4,1,3,6]=>[6,3,1,4,5,2,7]=>000001=>100000
[7,2,5,4,1,6,3]=>[3,6,1,4,5,2,7]=>000001=>100000
[7,2,5,4,3,1,6]=>[6,1,3,4,5,2,7]=>000001=>100000
[7,2,5,4,3,6,1]=>[1,6,3,4,5,2,7]=>100001=>100001
[7,2,5,4,6,1,3]=>[3,1,6,4,5,2,7]=>000001=>100000
[7,2,5,4,6,3,1]=>[1,3,6,4,5,2,7]=>100001=>100001
[7,2,5,6,1,3,4]=>[4,3,1,6,5,2,7]=>000001=>100000
[7,2,5,6,1,4,3]=>[3,4,1,6,5,2,7]=>000001=>100000
[7,2,5,6,3,1,4]=>[4,1,3,6,5,2,7]=>000001=>100000
[7,2,5,6,3,4,1]=>[1,4,3,6,5,2,7]=>100001=>100001
[7,2,5,6,4,1,3]=>[3,1,4,6,5,2,7]=>000001=>100000
[7,2,5,6,4,3,1]=>[1,3,4,6,5,2,7]=>100001=>100001
[7,2,6,1,3,4,5]=>[5,4,3,1,6,2,7]=>000001=>100000
[7,2,6,1,3,5,4]=>[4,5,3,1,6,2,7]=>000001=>100000
[7,2,6,1,4,3,5]=>[5,3,4,1,6,2,7]=>000001=>100000
[7,2,6,1,4,5,3]=>[3,5,4,1,6,2,7]=>000001=>100000
[7,2,6,1,5,3,4]=>[4,3,5,1,6,2,7]=>000001=>100000
[7,2,6,1,5,4,3]=>[3,4,5,1,6,2,7]=>000001=>100000
[7,2,6,3,1,4,5]=>[5,4,1,3,6,2,7]=>000001=>100000
[7,2,6,3,1,5,4]=>[4,5,1,3,6,2,7]=>000001=>100000
[7,2,6,3,4,1,5]=>[5,1,4,3,6,2,7]=>000001=>100000
[7,2,6,3,4,5,1]=>[1,5,4,3,6,2,7]=>100001=>100001
[7,2,6,3,5,1,4]=>[4,1,5,3,6,2,7]=>000001=>100000
[7,2,6,3,5,4,1]=>[1,4,5,3,6,2,7]=>100001=>100001
[7,2,6,4,1,3,5]=>[5,3,1,4,6,2,7]=>000001=>100000
[7,2,6,4,1,5,3]=>[3,5,1,4,6,2,7]=>000001=>100000
[7,2,6,4,3,1,5]=>[5,1,3,4,6,2,7]=>000001=>100000
[7,2,6,4,3,5,1]=>[1,5,3,4,6,2,7]=>100001=>100001
[7,2,6,4,5,1,3]=>[3,1,5,4,6,2,7]=>000001=>100000
[7,2,6,4,5,3,1]=>[1,3,5,4,6,2,7]=>100001=>100001
[7,2,6,5,1,3,4]=>[4,3,1,5,6,2,7]=>000001=>100000
[7,2,6,5,1,4,3]=>[3,4,1,5,6,2,7]=>000001=>100000
[7,2,6,5,3,1,4]=>[4,1,3,5,6,2,7]=>000001=>100000
[7,2,6,5,3,4,1]=>[1,4,3,5,6,2,7]=>100001=>100001
[7,2,6,5,4,1,3]=>[3,1,4,5,6,2,7]=>000001=>100000
[7,2,6,5,4,3,1]=>[1,3,4,5,6,2,7]=>100001=>100001
[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>000001=>100000
[7,3,1,2,4,6,5]=>[5,6,4,2,1,3,7]=>000001=>100000
[7,3,1,2,5,4,6]=>[6,4,5,2,1,3,7]=>000001=>100000
[7,3,1,2,5,6,4]=>[4,6,5,2,1,3,7]=>000001=>100000
[7,3,1,2,6,4,5]=>[5,4,6,2,1,3,7]=>000001=>100000
[7,3,1,2,6,5,4]=>[4,5,6,2,1,3,7]=>000001=>100000
[7,3,1,4,2,5,6]=>[6,5,2,4,1,3,7]=>000001=>100000
[7,3,1,4,2,6,5]=>[5,6,2,4,1,3,7]=>000001=>100000
[7,3,1,4,5,2,6]=>[6,2,5,4,1,3,7]=>000001=>100000
[7,3,1,4,5,6,2]=>[2,6,5,4,1,3,7]=>000001=>100000
[7,3,1,4,6,2,5]=>[5,2,6,4,1,3,7]=>000001=>100000
[7,3,1,4,6,5,2]=>[2,5,6,4,1,3,7]=>000001=>100000
[7,3,1,5,2,4,6]=>[6,4,2,5,1,3,7]=>000001=>100000
[7,3,1,5,2,6,4]=>[4,6,2,5,1,3,7]=>000001=>100000
[7,3,1,5,4,2,6]=>[6,2,4,5,1,3,7]=>000001=>100000
[7,3,1,5,4,6,2]=>[2,6,4,5,1,3,7]=>000001=>100000
[7,3,1,5,6,2,4]=>[4,2,6,5,1,3,7]=>000001=>100000
[7,3,1,5,6,4,2]=>[2,4,6,5,1,3,7]=>000001=>100000
[7,3,1,6,2,4,5]=>[5,4,2,6,1,3,7]=>000001=>100000
[7,3,1,6,2,5,4]=>[4,5,2,6,1,3,7]=>000001=>100000
[7,3,1,6,4,2,5]=>[5,2,4,6,1,3,7]=>000001=>100000
[7,3,1,6,4,5,2]=>[2,5,4,6,1,3,7]=>000001=>100000
[7,3,1,6,5,2,4]=>[4,2,5,6,1,3,7]=>000001=>100000
[7,3,1,6,5,4,2]=>[2,4,5,6,1,3,7]=>000001=>100000
[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>000001=>100000
[7,3,2,1,4,6,5]=>[5,6,4,1,2,3,7]=>000001=>100000
[7,3,2,1,5,4,6]=>[6,4,5,1,2,3,7]=>000001=>100000
[7,3,2,1,5,6,4]=>[4,6,5,1,2,3,7]=>000001=>100000
[7,3,2,1,6,4,5]=>[5,4,6,1,2,3,7]=>000001=>100000
[7,3,2,1,6,5,4]=>[4,5,6,1,2,3,7]=>000001=>100000
[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>000001=>100000
[7,3,2,4,1,6,5]=>[5,6,1,4,2,3,7]=>000001=>100000
[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>000001=>100000
[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>100001=>100001
[7,3,2,4,6,1,5]=>[5,1,6,4,2,3,7]=>000001=>100000
[7,3,2,4,6,5,1]=>[1,5,6,4,2,3,7]=>100001=>100001
[7,3,2,5,1,4,6]=>[6,4,1,5,2,3,7]=>000001=>100000
[7,3,2,5,1,6,4]=>[4,6,1,5,2,3,7]=>000001=>100000
[7,3,2,5,4,1,6]=>[6,1,4,5,2,3,7]=>000001=>100000
[7,3,2,5,4,6,1]=>[1,6,4,5,2,3,7]=>100001=>100001
[7,3,2,5,6,1,4]=>[4,1,6,5,2,3,7]=>000001=>100000
[7,3,2,5,6,4,1]=>[1,4,6,5,2,3,7]=>100001=>100001
[7,3,2,6,1,4,5]=>[5,4,1,6,2,3,7]=>000001=>100000
[7,3,2,6,1,5,4]=>[4,5,1,6,2,3,7]=>000001=>100000
[7,3,2,6,4,1,5]=>[5,1,4,6,2,3,7]=>000001=>100000
[7,3,2,6,4,5,1]=>[1,5,4,6,2,3,7]=>100001=>100001
[7,3,2,6,5,1,4]=>[4,1,5,6,2,3,7]=>000001=>100000
[7,3,2,6,5,4,1]=>[1,4,5,6,2,3,7]=>100001=>100001
[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>000001=>100000
[7,3,4,1,2,6,5]=>[5,6,2,1,4,3,7]=>000001=>100000
[7,3,4,1,5,2,6]=>[6,2,5,1,4,3,7]=>000001=>100000
[7,3,4,1,5,6,2]=>[2,6,5,1,4,3,7]=>000001=>100000
[7,3,4,1,6,2,5]=>[5,2,6,1,4,3,7]=>000001=>100000
[7,3,4,1,6,5,2]=>[2,5,6,1,4,3,7]=>000001=>100000
[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>000001=>100000
[7,3,4,2,1,6,5]=>[5,6,1,2,4,3,7]=>000001=>100000
[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>000001=>100000
[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>100001=>100001
[7,3,4,2,6,1,5]=>[5,1,6,2,4,3,7]=>000001=>100000
[7,3,4,2,6,5,1]=>[1,5,6,2,4,3,7]=>100001=>100001
[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>000001=>100000
[7,3,4,5,1,6,2]=>[2,6,1,5,4,3,7]=>000001=>100000
[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>000001=>100000
[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>100001=>100001
[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>010001=>100010
[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>110001=>100011
[7,3,4,6,1,2,5]=>[5,2,1,6,4,3,7]=>000001=>100000
[7,3,4,6,1,5,2]=>[2,5,1,6,4,3,7]=>000001=>100000
[7,3,4,6,2,1,5]=>[5,1,2,6,4,3,7]=>000001=>100000
[7,3,4,6,2,5,1]=>[1,5,2,6,4,3,7]=>100001=>100001
[7,3,4,6,5,1,2]=>[2,1,5,6,4,3,7]=>010001=>100010
[7,3,4,6,5,2,1]=>[1,2,5,6,4,3,7]=>110001=>100011
[7,3,5,1,2,4,6]=>[6,4,2,1,5,3,7]=>000001=>100000
[7,3,5,1,2,6,4]=>[4,6,2,1,5,3,7]=>000001=>100000
[7,3,5,1,4,2,6]=>[6,2,4,1,5,3,7]=>000001=>100000
[7,3,5,1,4,6,2]=>[2,6,4,1,5,3,7]=>000001=>100000
[7,3,5,1,6,2,4]=>[4,2,6,1,5,3,7]=>000001=>100000
[7,3,5,1,6,4,2]=>[2,4,6,1,5,3,7]=>000001=>100000
[7,3,5,2,1,4,6]=>[6,4,1,2,5,3,7]=>000001=>100000
[7,3,5,2,1,6,4]=>[4,6,1,2,5,3,7]=>000001=>100000
[7,3,5,2,4,1,6]=>[6,1,4,2,5,3,7]=>000001=>100000
[7,3,5,2,4,6,1]=>[1,6,4,2,5,3,7]=>100001=>100001
[7,3,5,2,6,1,4]=>[4,1,6,2,5,3,7]=>000001=>100000
[7,3,5,2,6,4,1]=>[1,4,6,2,5,3,7]=>100001=>100001
[7,3,5,4,1,2,6]=>[6,2,1,4,5,3,7]=>000001=>100000
[7,3,5,4,1,6,2]=>[2,6,1,4,5,3,7]=>000001=>100000
[7,3,5,4,2,1,6]=>[6,1,2,4,5,3,7]=>000001=>100000
[7,3,5,4,2,6,1]=>[1,6,2,4,5,3,7]=>100001=>100001
[7,3,5,4,6,1,2]=>[2,1,6,4,5,3,7]=>010001=>100010
[7,3,5,4,6,2,1]=>[1,2,6,4,5,3,7]=>110001=>100011
[7,3,5,6,1,2,4]=>[4,2,1,6,5,3,7]=>000001=>100000
[7,3,5,6,1,4,2]=>[2,4,1,6,5,3,7]=>000001=>100000
[7,3,5,6,2,1,4]=>[4,1,2,6,5,3,7]=>000001=>100000
[7,3,5,6,2,4,1]=>[1,4,2,6,5,3,7]=>100001=>100001
[7,3,5,6,4,1,2]=>[2,1,4,6,5,3,7]=>010001=>100010
[7,3,5,6,4,2,1]=>[1,2,4,6,5,3,7]=>110001=>100011
[7,3,6,1,2,4,5]=>[5,4,2,1,6,3,7]=>000001=>100000
[7,3,6,1,2,5,4]=>[4,5,2,1,6,3,7]=>000001=>100000
[7,3,6,1,4,2,5]=>[5,2,4,1,6,3,7]=>000001=>100000
[7,3,6,1,4,5,2]=>[2,5,4,1,6,3,7]=>000001=>100000
[7,3,6,1,5,2,4]=>[4,2,5,1,6,3,7]=>000001=>100000
[7,3,6,1,5,4,2]=>[2,4,5,1,6,3,7]=>000001=>100000
[7,3,6,2,1,4,5]=>[5,4,1,2,6,3,7]=>000001=>100000
[7,3,6,2,1,5,4]=>[4,5,1,2,6,3,7]=>000001=>100000
[7,3,6,2,4,1,5]=>[5,1,4,2,6,3,7]=>000001=>100000
[7,3,6,2,4,5,1]=>[1,5,4,2,6,3,7]=>100001=>100001
[7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7]=>000001=>100000
[7,3,6,2,5,4,1]=>[1,4,5,2,6,3,7]=>100001=>100001
[7,3,6,4,1,2,5]=>[5,2,1,4,6,3,7]=>000001=>100000
[7,3,6,4,1,5,2]=>[2,5,1,4,6,3,7]=>000001=>100000
[7,3,6,4,2,1,5]=>[5,1,2,4,6,3,7]=>000001=>100000
[7,3,6,4,2,5,1]=>[1,5,2,4,6,3,7]=>100001=>100001
[7,3,6,4,5,1,2]=>[2,1,5,4,6,3,7]=>010001=>100010
[7,3,6,4,5,2,1]=>[1,2,5,4,6,3,7]=>110001=>100011
[7,3,6,5,1,2,4]=>[4,2,1,5,6,3,7]=>000001=>100000
[7,3,6,5,1,4,2]=>[2,4,1,5,6,3,7]=>000001=>100000
[7,3,6,5,2,1,4]=>[4,1,2,5,6,3,7]=>000001=>100000
[7,3,6,5,2,4,1]=>[1,4,2,5,6,3,7]=>100001=>100001
[7,3,6,5,4,1,2]=>[2,1,4,5,6,3,7]=>010001=>100010
[7,3,6,5,4,2,1]=>[1,2,4,5,6,3,7]=>110001=>100011
[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>000001=>100000
[7,4,1,2,3,6,5]=>[5,6,3,2,1,4,7]=>000001=>100000
[7,4,1,2,5,3,6]=>[6,3,5,2,1,4,7]=>000001=>100000
[7,4,1,2,5,6,3]=>[3,6,5,2,1,4,7]=>000001=>100000
[7,4,1,2,6,3,5]=>[5,3,6,2,1,4,7]=>000001=>100000
[7,4,1,2,6,5,3]=>[3,5,6,2,1,4,7]=>000001=>100000
[7,4,1,3,2,5,6]=>[6,5,2,3,1,4,7]=>000001=>100000
[7,4,1,3,2,6,5]=>[5,6,2,3,1,4,7]=>000001=>100000
[7,4,1,3,5,2,6]=>[6,2,5,3,1,4,7]=>000001=>100000
[7,4,1,3,5,6,2]=>[2,6,5,3,1,4,7]=>000001=>100000
[7,4,1,3,6,2,5]=>[5,2,6,3,1,4,7]=>000001=>100000
[7,4,1,3,6,5,2]=>[2,5,6,3,1,4,7]=>000001=>100000
[7,4,1,5,2,3,6]=>[6,3,2,5,1,4,7]=>000001=>100000
[7,4,1,5,2,6,3]=>[3,6,2,5,1,4,7]=>000001=>100000
[7,4,1,5,3,2,6]=>[6,2,3,5,1,4,7]=>000001=>100000
[7,4,1,5,3,6,2]=>[2,6,3,5,1,4,7]=>000001=>100000
[7,4,1,5,6,2,3]=>[3,2,6,5,1,4,7]=>000001=>100000
[7,4,1,5,6,3,2]=>[2,3,6,5,1,4,7]=>000001=>100000
[7,4,1,6,2,3,5]=>[5,3,2,6,1,4,7]=>000001=>100000
[7,4,1,6,2,5,3]=>[3,5,2,6,1,4,7]=>000001=>100000
[7,4,1,6,3,2,5]=>[5,2,3,6,1,4,7]=>000001=>100000
[7,4,1,6,3,5,2]=>[2,5,3,6,1,4,7]=>000001=>100000
[7,4,1,6,5,2,3]=>[3,2,5,6,1,4,7]=>000001=>100000
[7,4,1,6,5,3,2]=>[2,3,5,6,1,4,7]=>000001=>100000
[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>000001=>100000
[7,4,2,1,3,6,5]=>[5,6,3,1,2,4,7]=>000001=>100000
[7,4,2,1,5,3,6]=>[6,3,5,1,2,4,7]=>000001=>100000
[7,4,2,1,5,6,3]=>[3,6,5,1,2,4,7]=>000001=>100000
[7,4,2,1,6,3,5]=>[5,3,6,1,2,4,7]=>000001=>100000
[7,4,2,1,6,5,3]=>[3,5,6,1,2,4,7]=>000001=>100000
[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>000001=>100000
[7,4,2,3,1,6,5]=>[5,6,1,3,2,4,7]=>000001=>100000
[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>000001=>100000
[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>100001=>100001
[7,4,2,3,6,1,5]=>[5,1,6,3,2,4,7]=>000001=>100000
[7,4,2,3,6,5,1]=>[1,5,6,3,2,4,7]=>100001=>100001
[7,4,2,5,1,3,6]=>[6,3,1,5,2,4,7]=>000001=>100000
[7,4,2,5,1,6,3]=>[3,6,1,5,2,4,7]=>000001=>100000
[7,4,2,5,3,1,6]=>[6,1,3,5,2,4,7]=>000001=>100000
[7,4,2,5,3,6,1]=>[1,6,3,5,2,4,7]=>100001=>100001
[7,4,2,5,6,1,3]=>[3,1,6,5,2,4,7]=>000001=>100000
[7,4,2,5,6,3,1]=>[1,3,6,5,2,4,7]=>100001=>100001
[7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7]=>000001=>100000
[7,4,2,6,1,5,3]=>[3,5,1,6,2,4,7]=>000001=>100000
[7,4,2,6,3,1,5]=>[5,1,3,6,2,4,7]=>000001=>100000
[7,4,2,6,3,5,1]=>[1,5,3,6,2,4,7]=>100001=>100001
[7,4,2,6,5,1,3]=>[3,1,5,6,2,4,7]=>000001=>100000
[7,4,2,6,5,3,1]=>[1,3,5,6,2,4,7]=>100001=>100001
[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>000001=>100000
[7,4,3,1,2,6,5]=>[5,6,2,1,3,4,7]=>000001=>100000
[7,4,3,1,5,2,6]=>[6,2,5,1,3,4,7]=>000001=>100000
[7,4,3,1,5,6,2]=>[2,6,5,1,3,4,7]=>000001=>100000
[7,4,3,1,6,2,5]=>[5,2,6,1,3,4,7]=>000001=>100000
[7,4,3,1,6,5,2]=>[2,5,6,1,3,4,7]=>000001=>100000
[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>000001=>100000
[7,4,3,2,1,6,5]=>[5,6,1,2,3,4,7]=>000001=>100000
[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>000001=>100000
[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>100001=>100001
[7,4,3,2,6,1,5]=>[5,1,6,2,3,4,7]=>000001=>100000
[7,4,3,2,6,5,1]=>[1,5,6,2,3,4,7]=>100001=>100001
[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>000001=>100000
[7,4,3,5,1,6,2]=>[2,6,1,5,3,4,7]=>000001=>100000
[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>000001=>100000
[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>100001=>100001
[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>010001=>100010
[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>110001=>100011
[7,4,3,6,1,2,5]=>[5,2,1,6,3,4,7]=>000001=>100000
[7,4,3,6,1,5,2]=>[2,5,1,6,3,4,7]=>000001=>100000
[7,4,3,6,2,1,5]=>[5,1,2,6,3,4,7]=>000001=>100000
[7,4,3,6,2,5,1]=>[1,5,2,6,3,4,7]=>100001=>100001
[7,4,3,6,5,1,2]=>[2,1,5,6,3,4,7]=>010001=>100010
[7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7]=>110001=>100011
[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>000001=>100000
[7,4,5,1,2,6,3]=>[3,6,2,1,5,4,7]=>000001=>100000
[7,4,5,1,3,2,6]=>[6,2,3,1,5,4,7]=>000001=>100000
[7,4,5,1,3,6,2]=>[2,6,3,1,5,4,7]=>000001=>100000
[7,4,5,1,6,2,3]=>[3,2,6,1,5,4,7]=>000001=>100000
[7,4,5,1,6,3,2]=>[2,3,6,1,5,4,7]=>000001=>100000
[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>000001=>100000
[7,4,5,2,1,6,3]=>[3,6,1,2,5,4,7]=>000001=>100000
[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>000001=>100000
[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>100001=>100001
[7,4,5,2,6,1,3]=>[3,1,6,2,5,4,7]=>000001=>100000
[7,4,5,2,6,3,1]=>[1,3,6,2,5,4,7]=>100001=>100001
[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>000001=>100000
[7,4,5,3,1,6,2]=>[2,6,1,3,5,4,7]=>000001=>100000
[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>000001=>100000
[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>100001=>100001
[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>010001=>100010
[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>110001=>100011
[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>001001=>100100
[7,4,5,6,1,3,2]=>[2,3,1,6,5,4,7]=>001001=>100100
[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>001001=>100100
[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>101001=>100101
[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>011001=>100110
[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>111001=>100111
[7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7]=>000001=>100000
[7,4,6,1,2,5,3]=>[3,5,2,1,6,4,7]=>000001=>100000
[7,4,6,1,3,2,5]=>[5,2,3,1,6,4,7]=>000001=>100000
[7,4,6,1,3,5,2]=>[2,5,3,1,6,4,7]=>000001=>100000
[7,4,6,1,5,2,3]=>[3,2,5,1,6,4,7]=>000001=>100000
[7,4,6,1,5,3,2]=>[2,3,5,1,6,4,7]=>000001=>100000
[7,4,6,2,1,3,5]=>[5,3,1,2,6,4,7]=>000001=>100000
[7,4,6,2,1,5,3]=>[3,5,1,2,6,4,7]=>000001=>100000
[7,4,6,2,3,1,5]=>[5,1,3,2,6,4,7]=>000001=>100000
[7,4,6,2,3,5,1]=>[1,5,3,2,6,4,7]=>100001=>100001
[7,4,6,2,5,1,3]=>[3,1,5,2,6,4,7]=>000001=>100000
[7,4,6,2,5,3,1]=>[1,3,5,2,6,4,7]=>100001=>100001
[7,4,6,3,1,2,5]=>[5,2,1,3,6,4,7]=>000001=>100000
[7,4,6,3,1,5,2]=>[2,5,1,3,6,4,7]=>000001=>100000
[7,4,6,3,2,1,5]=>[5,1,2,3,6,4,7]=>000001=>100000
[7,4,6,3,2,5,1]=>[1,5,2,3,6,4,7]=>100001=>100001
[7,4,6,3,5,1,2]=>[2,1,5,3,6,4,7]=>010001=>100010
[7,4,6,3,5,2,1]=>[1,2,5,3,6,4,7]=>110001=>100011
[7,4,6,5,1,2,3]=>[3,2,1,5,6,4,7]=>001001=>100100
[7,4,6,5,1,3,2]=>[2,3,1,5,6,4,7]=>001001=>100100
[7,4,6,5,2,1,3]=>[3,1,2,5,6,4,7]=>001001=>100100
[7,4,6,5,2,3,1]=>[1,3,2,5,6,4,7]=>101001=>100101
[7,4,6,5,3,1,2]=>[2,1,3,5,6,4,7]=>011001=>100110
[7,4,6,5,3,2,1]=>[1,2,3,5,6,4,7]=>111001=>100111
[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>000001=>100000
[7,5,1,2,3,6,4]=>[4,6,3,2,1,5,7]=>000001=>100000
[7,5,1,2,4,3,6]=>[6,3,4,2,1,5,7]=>000001=>100000
[7,5,1,2,4,6,3]=>[3,6,4,2,1,5,7]=>000001=>100000
[7,5,1,2,6,3,4]=>[4,3,6,2,1,5,7]=>000001=>100000
[7,5,1,2,6,4,3]=>[3,4,6,2,1,5,7]=>000001=>100000
[7,5,1,3,2,4,6]=>[6,4,2,3,1,5,7]=>000001=>100000
[7,5,1,3,2,6,4]=>[4,6,2,3,1,5,7]=>000001=>100000
[7,5,1,3,4,2,6]=>[6,2,4,3,1,5,7]=>000001=>100000
[7,5,1,3,4,6,2]=>[2,6,4,3,1,5,7]=>000001=>100000
[7,5,1,3,6,2,4]=>[4,2,6,3,1,5,7]=>000001=>100000
[7,5,1,3,6,4,2]=>[2,4,6,3,1,5,7]=>000001=>100000
[7,5,1,4,2,3,6]=>[6,3,2,4,1,5,7]=>000001=>100000
[7,5,1,4,2,6,3]=>[3,6,2,4,1,5,7]=>000001=>100000
[7,5,1,4,3,2,6]=>[6,2,3,4,1,5,7]=>000001=>100000
[7,5,1,4,3,6,2]=>[2,6,3,4,1,5,7]=>000001=>100000
[7,5,1,4,6,2,3]=>[3,2,6,4,1,5,7]=>000001=>100000
[7,5,1,4,6,3,2]=>[2,3,6,4,1,5,7]=>000001=>100000
[7,5,1,6,2,3,4]=>[4,3,2,6,1,5,7]=>000001=>100000
[7,5,1,6,2,4,3]=>[3,4,2,6,1,5,7]=>000001=>100000
[7,5,1,6,3,2,4]=>[4,2,3,6,1,5,7]=>000001=>100000
[7,5,1,6,3,4,2]=>[2,4,3,6,1,5,7]=>000001=>100000
[7,5,1,6,4,2,3]=>[3,2,4,6,1,5,7]=>000001=>100000
[7,5,1,6,4,3,2]=>[2,3,4,6,1,5,7]=>000001=>100000
[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>000001=>100000
[7,5,2,1,3,6,4]=>[4,6,3,1,2,5,7]=>000001=>100000
[7,5,2,1,4,3,6]=>[6,3,4,1,2,5,7]=>000001=>100000
[7,5,2,1,4,6,3]=>[3,6,4,1,2,5,7]=>000001=>100000
[7,5,2,1,6,3,4]=>[4,3,6,1,2,5,7]=>000001=>100000
[7,5,2,1,6,4,3]=>[3,4,6,1,2,5,7]=>000001=>100000
[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>000001=>100000
[7,5,2,3,1,6,4]=>[4,6,1,3,2,5,7]=>000001=>100000
[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>000001=>100000
[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>100001=>100001
[7,5,2,3,6,1,4]=>[4,1,6,3,2,5,7]=>000001=>100000
[7,5,2,3,6,4,1]=>[1,4,6,3,2,5,7]=>100001=>100001
[7,5,2,4,1,3,6]=>[6,3,1,4,2,5,7]=>000001=>100000
[7,5,2,4,1,6,3]=>[3,6,1,4,2,5,7]=>000001=>100000
[7,5,2,4,3,1,6]=>[6,1,3,4,2,5,7]=>000001=>100000
[7,5,2,4,3,6,1]=>[1,6,3,4,2,5,7]=>100001=>100001
[7,5,2,4,6,1,3]=>[3,1,6,4,2,5,7]=>000001=>100000
[7,5,2,4,6,3,1]=>[1,3,6,4,2,5,7]=>100001=>100001
[7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7]=>000001=>100000
[7,5,2,6,1,4,3]=>[3,4,1,6,2,5,7]=>000001=>100000
[7,5,2,6,3,1,4]=>[4,1,3,6,2,5,7]=>000001=>100000
[7,5,2,6,3,4,1]=>[1,4,3,6,2,5,7]=>100001=>100001
[7,5,2,6,4,1,3]=>[3,1,4,6,2,5,7]=>000001=>100000
[7,5,2,6,4,3,1]=>[1,3,4,6,2,5,7]=>100001=>100001
[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>000001=>100000
[7,5,3,1,2,6,4]=>[4,6,2,1,3,5,7]=>000001=>100000
[7,5,3,1,4,2,6]=>[6,2,4,1,3,5,7]=>000001=>100000
[7,5,3,1,4,6,2]=>[2,6,4,1,3,5,7]=>000001=>100000
[7,5,3,1,6,2,4]=>[4,2,6,1,3,5,7]=>000001=>100000
[7,5,3,1,6,4,2]=>[2,4,6,1,3,5,7]=>000001=>100000
[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>000001=>100000
[7,5,3,2,1,6,4]=>[4,6,1,2,3,5,7]=>000001=>100000
[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>000001=>100000
[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>100001=>100001
[7,5,3,2,6,1,4]=>[4,1,6,2,3,5,7]=>000001=>100000
[7,5,3,2,6,4,1]=>[1,4,6,2,3,5,7]=>100001=>100001
[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>000001=>100000
[7,5,3,4,1,6,2]=>[2,6,1,4,3,5,7]=>000001=>100000
[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>000001=>100000
[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>100001=>100001
[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>010001=>100010
[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>110001=>100011
[7,5,3,6,1,2,4]=>[4,2,1,6,3,5,7]=>000001=>100000
[7,5,3,6,1,4,2]=>[2,4,1,6,3,5,7]=>000001=>100000
[7,5,3,6,2,1,4]=>[4,1,2,6,3,5,7]=>000001=>100000
[7,5,3,6,2,4,1]=>[1,4,2,6,3,5,7]=>100001=>100001
[7,5,3,6,4,1,2]=>[2,1,4,6,3,5,7]=>010001=>100010
[7,5,3,6,4,2,1]=>[1,2,4,6,3,5,7]=>110001=>100011
[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>000001=>100000
[7,5,4,1,2,6,3]=>[3,6,2,1,4,5,7]=>000001=>100000
[7,5,4,1,3,2,6]=>[6,2,3,1,4,5,7]=>000001=>100000
[7,5,4,1,3,6,2]=>[2,6,3,1,4,5,7]=>000001=>100000
[7,5,4,1,6,2,3]=>[3,2,6,1,4,5,7]=>000001=>100000
[7,5,4,1,6,3,2]=>[2,3,6,1,4,5,7]=>000001=>100000
[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>000001=>100000
[7,5,4,2,1,6,3]=>[3,6,1,2,4,5,7]=>000001=>100000
[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>000001=>100000
[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>100001=>100001
[7,5,4,2,6,1,3]=>[3,1,6,2,4,5,7]=>000001=>100000
[7,5,4,2,6,3,1]=>[1,3,6,2,4,5,7]=>100001=>100001
[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>000001=>100000
[7,5,4,3,1,6,2]=>[2,6,1,3,4,5,7]=>000001=>100000
[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>000001=>100000
[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>100001=>100001
[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>010001=>100010
[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>110001=>100011
[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>001001=>100100
[7,5,4,6,1,3,2]=>[2,3,1,6,4,5,7]=>001001=>100100
[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>001001=>100100
[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>101001=>100101
[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>011001=>100110
[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>111001=>100111
[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>000101=>101000
[7,5,6,1,2,4,3]=>[3,4,2,1,6,5,7]=>000101=>101000
[7,5,6,1,3,2,4]=>[4,2,3,1,6,5,7]=>000101=>101000
[7,5,6,1,3,4,2]=>[2,4,3,1,6,5,7]=>000101=>101000
[7,5,6,1,4,2,3]=>[3,2,4,1,6,5,7]=>000101=>101000
[7,5,6,1,4,3,2]=>[2,3,4,1,6,5,7]=>000101=>101000
[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>000101=>101000
[7,5,6,2,1,4,3]=>[3,4,1,2,6,5,7]=>000101=>101000
[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>000101=>101000
[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>100101=>101001
[7,5,6,2,4,1,3]=>[3,1,4,2,6,5,7]=>000101=>101000
[7,5,6,2,4,3,1]=>[1,3,4,2,6,5,7]=>100101=>101001
[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>000101=>101000
[7,5,6,3,1,4,2]=>[2,4,1,3,6,5,7]=>000101=>101000
[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>000101=>101000
[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>100101=>101001
[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>010101=>101010
[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>110101=>101011
[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>001101=>101100
[7,5,6,4,1,3,2]=>[2,3,1,4,6,5,7]=>001101=>101100
[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>001101=>101100
[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>101101=>101101
[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>011101=>101110
[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>111101=>101111
[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>000011=>110000
[7,6,1,2,3,5,4]=>[4,5,3,2,1,6,7]=>000011=>110000
[7,6,1,2,4,3,5]=>[5,3,4,2,1,6,7]=>000011=>110000
[7,6,1,2,4,5,3]=>[3,5,4,2,1,6,7]=>000011=>110000
[7,6,1,2,5,3,4]=>[4,3,5,2,1,6,7]=>000011=>110000
[7,6,1,2,5,4,3]=>[3,4,5,2,1,6,7]=>000011=>110000
[7,6,1,3,2,4,5]=>[5,4,2,3,1,6,7]=>000011=>110000
[7,6,1,3,2,5,4]=>[4,5,2,3,1,6,7]=>000011=>110000
[7,6,1,3,4,2,5]=>[5,2,4,3,1,6,7]=>000011=>110000
[7,6,1,3,4,5,2]=>[2,5,4,3,1,6,7]=>000011=>110000
[7,6,1,3,5,2,4]=>[4,2,5,3,1,6,7]=>000011=>110000
[7,6,1,3,5,4,2]=>[2,4,5,3,1,6,7]=>000011=>110000
[7,6,1,4,2,3,5]=>[5,3,2,4,1,6,7]=>000011=>110000
[7,6,1,4,2,5,3]=>[3,5,2,4,1,6,7]=>000011=>110000
[7,6,1,4,3,2,5]=>[5,2,3,4,1,6,7]=>000011=>110000
[7,6,1,4,3,5,2]=>[2,5,3,4,1,6,7]=>000011=>110000
[7,6,1,4,5,2,3]=>[3,2,5,4,1,6,7]=>000011=>110000
[7,6,1,4,5,3,2]=>[2,3,5,4,1,6,7]=>000011=>110000
[7,6,1,5,2,3,4]=>[4,3,2,5,1,6,7]=>000011=>110000
[7,6,1,5,2,4,3]=>[3,4,2,5,1,6,7]=>000011=>110000
[7,6,1,5,3,2,4]=>[4,2,3,5,1,6,7]=>000011=>110000
[7,6,1,5,3,4,2]=>[2,4,3,5,1,6,7]=>000011=>110000
[7,6,1,5,4,2,3]=>[3,2,4,5,1,6,7]=>000011=>110000
[7,6,1,5,4,3,2]=>[2,3,4,5,1,6,7]=>000011=>110000
[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>000011=>110000
[7,6,2,1,3,5,4]=>[4,5,3,1,2,6,7]=>000011=>110000
[7,6,2,1,4,3,5]=>[5,3,4,1,2,6,7]=>000011=>110000
[7,6,2,1,4,5,3]=>[3,5,4,1,2,6,7]=>000011=>110000
[7,6,2,1,5,3,4]=>[4,3,5,1,2,6,7]=>000011=>110000
[7,6,2,1,5,4,3]=>[3,4,5,1,2,6,7]=>000011=>110000
[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>000011=>110000
[7,6,2,3,1,5,4]=>[4,5,1,3,2,6,7]=>000011=>110000
[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>000011=>110000
[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>100011=>110001
[7,6,2,3,5,1,4]=>[4,1,5,3,2,6,7]=>000011=>110000
[7,6,2,3,5,4,1]=>[1,4,5,3,2,6,7]=>100011=>110001
[7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7]=>000011=>110000
[7,6,2,4,1,5,3]=>[3,5,1,4,2,6,7]=>000011=>110000
[7,6,2,4,3,1,5]=>[5,1,3,4,2,6,7]=>000011=>110000
[7,6,2,4,3,5,1]=>[1,5,3,4,2,6,7]=>100011=>110001
[7,6,2,4,5,1,3]=>[3,1,5,4,2,6,7]=>000011=>110000
[7,6,2,4,5,3,1]=>[1,3,5,4,2,6,7]=>100011=>110001
[7,6,2,5,1,3,4]=>[4,3,1,5,2,6,7]=>000011=>110000
[7,6,2,5,1,4,3]=>[3,4,1,5,2,6,7]=>000011=>110000
[7,6,2,5,3,1,4]=>[4,1,3,5,2,6,7]=>000011=>110000
[7,6,2,5,3,4,1]=>[1,4,3,5,2,6,7]=>100011=>110001
[7,6,2,5,4,1,3]=>[3,1,4,5,2,6,7]=>000011=>110000
[7,6,2,5,4,3,1]=>[1,3,4,5,2,6,7]=>100011=>110001
[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>000011=>110000
[7,6,3,1,2,5,4]=>[4,5,2,1,3,6,7]=>000011=>110000
[7,6,3,1,4,2,5]=>[5,2,4,1,3,6,7]=>000011=>110000
[7,6,3,1,4,5,2]=>[2,5,4,1,3,6,7]=>000011=>110000
[7,6,3,1,5,2,4]=>[4,2,5,1,3,6,7]=>000011=>110000
[7,6,3,1,5,4,2]=>[2,4,5,1,3,6,7]=>000011=>110000
[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>000011=>110000
[7,6,3,2,1,5,4]=>[4,5,1,2,3,6,7]=>000011=>110000
[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>000011=>110000
[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>100011=>110001
[7,6,3,2,5,1,4]=>[4,1,5,2,3,6,7]=>000011=>110000
[7,6,3,2,5,4,1]=>[1,4,5,2,3,6,7]=>100011=>110001
[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>000011=>110000
[7,6,3,4,1,5,2]=>[2,5,1,4,3,6,7]=>000011=>110000
[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>000011=>110000
[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>100011=>110001
[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>010011=>110010
[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>110011=>110011
[7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7]=>000011=>110000
[7,6,3,5,1,4,2]=>[2,4,1,5,3,6,7]=>000011=>110000
[7,6,3,5,2,1,4]=>[4,1,2,5,3,6,7]=>000011=>110000
[7,6,3,5,2,4,1]=>[1,4,2,5,3,6,7]=>100011=>110001
[7,6,3,5,4,1,2]=>[2,1,4,5,3,6,7]=>010011=>110010
[7,6,3,5,4,2,1]=>[1,2,4,5,3,6,7]=>110011=>110011
[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>000011=>110000
[7,6,4,1,2,5,3]=>[3,5,2,1,4,6,7]=>000011=>110000
[7,6,4,1,3,2,5]=>[5,2,3,1,4,6,7]=>000011=>110000
[7,6,4,1,3,5,2]=>[2,5,3,1,4,6,7]=>000011=>110000
[7,6,4,1,5,2,3]=>[3,2,5,1,4,6,7]=>000011=>110000
[7,6,4,1,5,3,2]=>[2,3,5,1,4,6,7]=>000011=>110000
[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>000011=>110000
[7,6,4,2,1,5,3]=>[3,5,1,2,4,6,7]=>000011=>110000
[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>000011=>110000
[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>100011=>110001
[7,6,4,2,5,1,3]=>[3,1,5,2,4,6,7]=>000011=>110000
[7,6,4,2,5,3,1]=>[1,3,5,2,4,6,7]=>100011=>110001
[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>000011=>110000
[7,6,4,3,1,5,2]=>[2,5,1,3,4,6,7]=>000011=>110000
[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000011=>110000
[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>100011=>110001
[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>010011=>110010
[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>110011=>110011
[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>001011=>110100
[7,6,4,5,1,3,2]=>[2,3,1,5,4,6,7]=>001011=>110100
[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>001011=>110100
[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>101011=>110101
[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>011011=>110110
[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>111011=>110111
[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>000111=>111000
[7,6,5,1,2,4,3]=>[3,4,2,1,5,6,7]=>000111=>111000
[7,6,5,1,3,2,4]=>[4,2,3,1,5,6,7]=>000111=>111000
[7,6,5,1,3,4,2]=>[2,4,3,1,5,6,7]=>000111=>111000
[7,6,5,1,4,2,3]=>[3,2,4,1,5,6,7]=>000111=>111000
[7,6,5,1,4,3,2]=>[2,3,4,1,5,6,7]=>000111=>111000
[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>000111=>111000
[7,6,5,2,1,4,3]=>[3,4,1,2,5,6,7]=>000111=>111000
[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>000111=>111000
[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>100111=>111001
[7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7]=>000111=>111000
[7,6,5,2,4,3,1]=>[1,3,4,2,5,6,7]=>100111=>111001
[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>000111=>111000
[7,6,5,3,1,4,2]=>[2,4,1,3,5,6,7]=>000111=>111000
[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>000111=>111000
[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>100111=>111001
[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>010111=>111010
[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>110111=>111011
[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>001111=>111100
[7,6,5,4,1,3,2]=>[2,3,1,4,5,6,7]=>001111=>111100
[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>001111=>111100
[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>101111=>111101
[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>011111=>111110
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>111111=>111111
[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111
[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>1111110=>0111111
[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>1111101=>1011111
[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>1111100=>0011111
[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>1111100=>0011111
[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>1111011=>1101111
[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>1111010=>0101111
[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>1111001=>1001111
[8,5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5,8]=>1111001=>1001111
[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>1111000=>0001111
[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>1111000=>0001111
[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>1111000=>0001111
[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>1111000=>0001111
[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>1111000=>0001111
[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>1110111=>1110111
[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>1110101=>1010111
[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>1110100=>0010111
[6,7,8,4,5,3,2,1]=>[1,2,3,5,4,8,7,6]=>1110100=>0010111
[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>1110011=>1100111
[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>1110010=>0100111
[7,8,4,5,6,3,2,1]=>[1,2,3,6,5,4,8,7]=>1110010=>0100111
[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>1110001=>1000111
[8,5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5,8]=>1110001=>1000111
[8,6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6,8]=>1110001=>1000111
[8,5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5,8]=>1110001=>1000111
[8,4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4,8]=>1110001=>1000111
[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>1110000=>0000111
[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>1110000=>0000111
[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>1110000=>0000111
[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>1110000=>0000111
[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>1110000=>0000111
[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>1110000=>0000111
[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>1110000=>0000111
[7,5,4,6,8,3,2,1]=>[1,2,3,8,6,4,5,7]=>1110000=>0000111
[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>1110000=>0000111
[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>1110000=>0000111
[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>1110000=>0000111
[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>1110000=>0000111
[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>1110000=>0000111
[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>1110000=>0000111
[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>1101111=>1111011
[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>1101110=>0111011
[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>1101100=>0011011
[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>1101011=>1101011
[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>1101010=>0101011
[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>1101000=>0001011
[6,7,5,8,3,4,2,1]=>[1,2,4,3,8,5,7,6]=>1101000=>0001011
[5,6,7,8,3,4,2,1]=>[1,2,4,3,8,7,6,5]=>1101000=>0001011
[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>1100100=>0010011
[6,7,8,4,3,5,2,1]=>[1,2,5,3,4,8,7,6]=>1100100=>0010011
[7,8,6,3,4,5,2,1]=>[1,2,5,4,3,6,8,7]=>1100110=>0110011
[7,6,8,3,4,5,2,1]=>[1,2,5,4,3,8,6,7]=>1100100=>0010011
[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>1100011=>1100011
[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>1100010=>0100011
[8,7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7,8]=>1100011=>1100011
[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>1100011=>1100011
[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>1100001=>1000011
[8,5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5,8]=>1100001=>1000011
[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>1100000=>0000011
[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>1100000=>0000011
[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>1100000=>0000011
[6,7,4,5,3,8,2,1]=>[1,2,8,3,5,4,7,6]=>1100000=>0000011
[7,5,4,6,3,8,2,1]=>[1,2,8,3,6,4,5,7]=>1100000=>0000011
[6,4,5,7,3,8,2,1]=>[1,2,8,3,7,5,4,6]=>1100000=>0000011
[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>1100000=>0000011
[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>1100000=>0000011
[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>1100000=>0000011
[6,7,5,3,4,8,2,1]=>[1,2,8,4,3,5,7,6]=>1100000=>0000011
[6,5,7,3,4,8,2,1]=>[1,2,8,4,3,7,5,6]=>1100000=>0000011
[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>1100000=>0000011
[7,6,4,3,5,8,2,1]=>[1,2,8,5,3,4,6,7]=>1100000=>0000011
[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>1100000=>0000011
[7,5,3,4,6,8,2,1]=>[1,2,8,6,4,3,5,7]=>1100000=>0000011
[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>1100000=>0000011
[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>1100000=>0000011
[5,6,3,4,7,8,2,1]=>[1,2,8,7,4,3,6,5]=>1100000=>0000011
[4,5,3,6,7,8,2,1]=>[1,2,8,7,6,3,5,4]=>1100000=>0000011
[5,3,4,6,7,8,2,1]=>[1,2,8,7,6,4,3,5]=>1100000=>0000011
[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>1100000=>0000011
[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>1011111=>1111101
[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>1011101=>1011101
[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>1011100=>0011101
[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>1011010=>0101101
[8,5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5,8]=>1011001=>1001101
[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>1011000=>0001101
[6,7,5,8,4,2,3,1]=>[1,3,2,4,8,5,7,6]=>1011000=>0001101
[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>1011000=>0001101
[5,6,7,8,4,2,3,1]=>[1,3,2,4,8,7,6,5]=>1011000=>0001101
[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>1010111=>1110101
[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>1010101=>1010101
[7,6,8,4,5,2,3,1]=>[1,3,2,5,4,8,6,7]=>1010100=>0010101
[6,7,8,4,5,2,3,1]=>[1,3,2,5,4,8,7,6]=>1010100=>0010101
[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>1010001=>1000101
[8,5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5,8]=>1010001=>1000101
[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>1010000=>0000101
[7,5,6,4,8,2,3,1]=>[1,3,2,8,4,6,5,7]=>1010000=>0000101
[6,5,7,4,8,2,3,1]=>[1,3,2,8,4,7,5,6]=>1010000=>0000101
[6,5,4,7,8,2,3,1]=>[1,3,2,8,7,4,5,6]=>1010000=>0000101
[5,4,6,7,8,2,3,1]=>[1,3,2,8,7,6,4,5]=>1010000=>0000101
[4,5,6,7,8,2,3,1]=>[1,3,2,8,7,6,5,4]=>1010000=>0000101
[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>1001111=>1111001
[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>1001110=>0111001
[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>1001101=>1011001
[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>1001100=>0011001
[6,7,8,5,3,2,4,1]=>[1,4,2,3,5,8,7,6]=>1001100=>0011001
[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>1001011=>1101001
[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>1001010=>0101001
[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>1001001=>1001001
[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>1001000=>0001001
[6,7,5,8,3,2,4,1]=>[1,4,2,3,8,5,7,6]=>1001000=>0001001
[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>1001000=>0001001
[6,5,7,8,3,2,4,1]=>[1,4,2,3,8,7,5,6]=>1001000=>0001001
[5,6,7,8,3,2,4,1]=>[1,4,2,3,8,7,6,5]=>1001000=>0001001
[8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8]=>1001111=>1111001
[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>1001101=>1011001
[7,6,8,5,2,3,4,1]=>[1,4,3,2,5,8,6,7]=>1001100=>0011001
[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>1001100=>0011001
[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>1001001=>1001001
[7,6,5,8,2,3,4,1]=>[1,4,3,2,8,5,6,7]=>1001000=>0001001
[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>1001000=>0001001
[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>1000111=>1110001
[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>1000110=>0110001
[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>1000101=>1010001
[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>1000100=>0010001
[6,7,8,4,3,2,5,1]=>[1,5,2,3,4,8,7,6]=>1000100=>0010001
[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>1000111=>1110001
[7,8,6,3,4,2,5,1]=>[1,5,2,4,3,6,8,7]=>1000110=>0110001
[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>1000101=>1010001
[7,6,8,3,4,2,5,1]=>[1,5,2,4,3,8,6,7]=>1000100=>0010001
[6,7,8,3,4,2,5,1]=>[1,5,2,4,3,8,7,6]=>1000100=>0010001
[7,8,6,4,2,3,5,1]=>[1,5,3,2,4,6,8,7]=>1000110=>0110001
[7,6,8,4,2,3,5,1]=>[1,5,3,2,4,8,6,7]=>1000100=>0010001
[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>1000100=>0010001
[8,7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7,8]=>1000111=>1110001
[7,8,6,3,2,4,5,1]=>[1,5,4,2,3,6,8,7]=>1000110=>0110001
[7,6,8,3,2,4,5,1]=>[1,5,4,2,3,8,6,7]=>1000100=>0010001
[6,7,8,3,2,4,5,1]=>[1,5,4,2,3,8,7,6]=>1000100=>0010001
[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>1000011=>1100001
[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>1000010=>0100001
[8,7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7,8]=>1000011=>1100001
[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>1000011=>1100001
[7,8,5,3,2,4,6,1]=>[1,6,4,2,3,5,8,7]=>1000010=>0100001
[7,8,4,3,2,5,6,1]=>[1,6,5,2,3,4,8,7]=>1000010=>0100001
[8,7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7,8]=>1000011=>1100001
[8,5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5,8]=>1000001=>1000001
[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>1000001=>1000001
[8,4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4,8]=>1000001=>1000001
[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>1000001=>1000001
[8,5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5,8]=>1000001=>1000001
[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>1000001=>1000001
[8,5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5,8]=>1000001=>1000001
[8,5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5,8]=>1000001=>1000001
[8,5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5,8]=>1000001=>1000001
[8,5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5,8]=>1000001=>1000001
[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>1000000=>0000001
[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>1000000=>0000001
[7,5,4,6,3,2,8,1]=>[1,8,2,3,6,4,5,7]=>1000000=>0000001
[7,4,5,6,3,2,8,1]=>[1,8,2,3,6,5,4,7]=>1000000=>0000001
[6,4,5,7,3,2,8,1]=>[1,8,2,3,7,5,4,6]=>1000000=>0000001
[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>1000000=>0000001
[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>1000000=>0000001
[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>1000000=>0000001
[6,5,7,3,4,2,8,1]=>[1,8,2,4,3,7,5,6]=>1000000=>0000001
[7,6,4,3,5,2,8,1]=>[1,8,2,5,3,4,6,7]=>1000000=>0000001
[7,5,4,3,6,2,8,1]=>[1,8,2,6,3,4,5,7]=>1000000=>0000001
[7,4,5,3,6,2,8,1]=>[1,8,2,6,3,5,4,7]=>1000000=>0000001
[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>1000000=>0000001
[6,4,5,3,7,2,8,1]=>[1,8,2,7,3,5,4,6]=>1000000=>0000001
[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>1000000=>0000001
[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>1000000=>0000001
[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>1000000=>0000001
[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>1000000=>0000001
[4,5,3,6,7,2,8,1]=>[1,8,2,7,6,3,5,4]=>1000000=>0000001
[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>1000000=>0000001
[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>1000000=>0000001
[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>1000000=>0000001
[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>1000000=>0000001
[7,6,5,3,2,4,8,1]=>[1,8,4,2,3,5,6,7]=>1000000=>0000001
[6,5,7,3,2,4,8,1]=>[1,8,4,2,3,7,5,6]=>1000000=>0000001
[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>1000000=>0000001
[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>1000000=>0000001
[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>1000000=>0000001
[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>1000000=>0000001
[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>1000000=>0000001
[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>1000000=>0000001
[7,5,4,3,2,6,8,1]=>[1,8,6,2,3,4,5,7]=>1000000=>0000001
[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>1000000=>0000001
[7,5,3,2,4,6,8,1]=>[1,8,6,4,2,3,5,7]=>1000000=>0000001
[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>1000000=>0000001
[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>1000000=>0000001
[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>1000000=>0000001
[6,4,3,5,2,7,8,1]=>[1,8,7,2,5,3,4,6]=>1000000=>0000001
[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>1000000=>0000001
[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>1000000=>0000001
[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>1000000=>0000001
[6,5,4,2,3,7,8,1]=>[1,8,7,3,2,4,5,6]=>1000000=>0000001
[5,6,4,2,3,7,8,1]=>[1,8,7,3,2,4,6,5]=>1000000=>0000001
[6,4,5,2,3,7,8,1]=>[1,8,7,3,2,5,4,6]=>1000000=>0000001
[5,4,6,2,3,7,8,1]=>[1,8,7,3,2,6,4,5]=>1000000=>0000001
[6,5,3,2,4,7,8,1]=>[1,8,7,4,2,3,5,6]=>1000000=>0000001
[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>1000000=>0000001
[6,4,3,2,5,7,8,1]=>[1,8,7,5,2,3,4,6]=>1000000=>0000001
[6,4,2,3,5,7,8,1]=>[1,8,7,5,3,2,4,6]=>1000000=>0000001
[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>1000000=>0000001
[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>1000000=>0000001
[5,3,4,2,6,7,8,1]=>[1,8,7,6,2,4,3,5]=>1000000=>0000001
[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>1000000=>0000001
[5,4,2,3,6,7,8,1]=>[1,8,7,6,3,2,4,5]=>1000000=>0000001
[5,3,2,4,6,7,8,1]=>[1,8,7,6,4,2,3,5]=>1000000=>0000001
[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>1000000=>0000001
[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>1000000=>0000001
[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>0111111=>1111110
[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>0111110=>0111110
[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>0111011=>1101110
[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>0111010=>0101110
[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>0111000=>0001110
[6,7,5,8,4,3,1,2]=>[2,1,3,4,8,5,7,6]=>0111000=>0001110
[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>0111000=>0001110
[6,5,7,8,4,3,1,2]=>[2,1,3,4,8,7,5,6]=>0111000=>0001110
[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>0111000=>0001110
[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>0110110=>0110110
[6,7,8,4,5,3,1,2]=>[2,1,3,5,4,8,7,6]=>0110100=>0010110
[7,8,4,5,6,3,1,2]=>[2,1,3,6,5,4,8,7]=>0110010=>0100110
[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>0110000=>0000110
[6,7,5,4,8,3,1,2]=>[2,1,3,8,4,5,7,6]=>0110000=>0000110
[6,5,7,4,8,3,1,2]=>[2,1,3,8,4,7,5,6]=>0110000=>0000110
[5,6,7,4,8,3,1,2]=>[2,1,3,8,4,7,6,5]=>0110000=>0000110
[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>0110000=>0000110
[6,5,4,7,8,3,1,2]=>[2,1,3,8,7,4,5,6]=>0110000=>0000110
[5,6,4,7,8,3,1,2]=>[2,1,3,8,7,4,6,5]=>0110000=>0000110
[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>0110000=>0000110
[5,4,6,7,8,3,1,2]=>[2,1,3,8,7,6,4,5]=>0110000=>0000110
[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>0110000=>0000110
[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>0101111=>1111010
[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>0101110=>0111010
[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>0101011=>1101010
[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>0101010=>0101010
[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>0101000=>0001010
[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>0101000=>0001010
[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>0100110=>0110010
[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>0100010=>0100010
[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>0100010=>0100010
[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>0100010=>0100010
[8,5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5,8]=>0100001=>1000010
[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>0100000=>0000010
[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>0100000=>0000010
[6,5,4,7,3,8,1,2]=>[2,1,8,3,7,4,5,6]=>0100000=>0000010
[6,4,5,7,3,8,1,2]=>[2,1,8,3,7,5,4,6]=>0100000=>0000010
[5,4,6,7,3,8,1,2]=>[2,1,8,3,7,6,4,5]=>0100000=>0000010
[4,5,6,7,3,8,1,2]=>[2,1,8,3,7,6,5,4]=>0100000=>0000010
[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>0100000=>0000010
[6,5,7,3,4,8,1,2]=>[2,1,8,4,3,7,5,6]=>0100000=>0000010
[6,7,3,4,5,8,1,2]=>[2,1,8,5,4,3,7,6]=>0100000=>0000010
[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>0100000=>0000010
[6,4,5,3,7,8,1,2]=>[2,1,8,7,3,5,4,6]=>0100000=>0000010
[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>0100000=>0000010
[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>0100000=>0000010
[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>0100000=>0000010
[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0011111=>1111100
[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>0011100=>0011100
[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0011000=>0001100
[6,7,5,8,4,2,1,3]=>[3,1,2,4,8,5,7,6]=>0011000=>0001100
[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0011000=>0001100
[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>0011000=>0001100
[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>0011000=>0001100
[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0010110=>0110100
[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0010010=>0100100
[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>0010000=>0000100
[6,7,5,4,8,2,1,3]=>[3,1,2,8,4,5,7,6]=>0010000=>0000100
[6,5,7,4,8,2,1,3]=>[3,1,2,8,4,7,5,6]=>0010000=>0000100
[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>0010000=>0000100
[6,5,4,7,8,2,1,3]=>[3,1,2,8,7,4,5,6]=>0010000=>0000100
[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>0010000=>0000100
[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>0011111=>1111100
[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>0011100=>0011100
[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>0011001=>1001100
[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>0011000=>0001100
[6,7,5,8,4,1,2,3]=>[3,2,1,4,8,5,7,6]=>0011000=>0001100
[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>0011000=>0001100
[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>0010101=>1010100
[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>0010011=>1100100
[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>0010001=>1000100
[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>0010000=>0000100
[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>0010000=>0000100
[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>0010000=>0000100
[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>0010000=>0000100
[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>0010000=>0000100
[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>0010000=>0000100
[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0001111=>1111000
[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>0001000=>0001000
[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>0001000=>0001000
[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>0001000=>0001000
[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>0001000=>0001000
[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>0001000=>0001000
[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0001111=>1111000
[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>0001000=>0001000
[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>0001000=>0001000
[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>0001000=>0001000
[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>0001000=>0001000
[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>0001111=>1111000
[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>0001100=>0011000
[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>0001011=>1101000
[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>0001010=>0101000
[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>0001000=>0001000
[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>0001000=>0001000
[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>0001000=>0001000
[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0001111=>1111000
[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>0001101=>1011000
[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>0001100=>0011000
[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0001011=>1101000
[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>0001000=>0001000
[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>0001000=>0001000
[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>0001000=>0001000
[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>0001000=>0001000
[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>0001111=>1111000
[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>0001110=>0111000
[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>0001101=>1011000
[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>0001100=>0011000
[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>0001100=>0011000
[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>0001011=>1101000
[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>0001010=>0101000
[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>0001001=>1001000
[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>0001001=>1001000
[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>0001000=>0001000
[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>0001000=>0001000
[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>0001000=>0001000
[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>0001000=>0001000
[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>0001000=>0001000
[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0000111=>1110000
[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0000111=>1110000
[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>0000110=>0110000
[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0000111=>1110000
[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>0000110=>0110000
[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>0000100=>0010000
[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>0000111=>1110000
[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>0000100=>0010000
[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>0000111=>1110000
[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>0000111=>1110000
[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>0000111=>1110000
[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0000111=>1110000
[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0000110=>0110000
[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0000100=>0010000
[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>0000111=>1110000
[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>0000100=>0010000
[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>0000100=>0010000
[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0000111=>1110000
[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>0000100=>0010000
[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0000100=>0010000
[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>0000111=>1110000
[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>0000100=>0010000
[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>0000111=>1110000
[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0000111=>1110000
[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>0000100=>0010000
[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>0000111=>1110000
[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>0000110=>0110000
[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>0000101=>1010000
[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>0000100=>0010000
[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>0000100=>0010000
[7,8,4,3,2,5,1,6]=>[6,1,5,2,3,4,8,7]=>0000010=>0100000
[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>0000011=>1100000
[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>0000011=>1100000
[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>0000011=>1100000
[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0000011=>1100000
[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0000010=>0100000
[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>0000011=>1100000
[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>0000010=>0100000
[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>0000010=>0100000
[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0000010=>0100000
[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>0000010=>0100000
[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>0000010=>0100000
[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000001=>1000000
[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>0000001=>1000000
[8,5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5,8]=>0000001=>1000000
[8,4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4,8]=>0000001=>1000000
[8,5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5,8]=>0000001=>1000000
[8,4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4,8]=>0000001=>1000000
[8,3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3,8]=>0000001=>1000000
[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>0000001=>1000000
[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>0000001=>1000000
[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>0000001=>1000000
[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>0000001=>1000000
[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0000001=>1000000
[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>0000001=>1000000
[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>0000001=>1000000
[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>0000001=>1000000
[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>0000001=>1000000
[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0000001=>1000000
[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>0000001=>1000000
[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>0000001=>1000000
[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>0000001=>1000000
[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0000001=>1000000
[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>0000001=>1000000
[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0000001=>1000000
[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>0000001=>1000000
[8,4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4,8]=>0000001=>1000000
[8,3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3,8]=>0000001=>1000000
[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>0000001=>1000000
[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>0000001=>1000000
[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>0000001=>1000000
[8,3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3,8]=>0000001=>1000000
[8,4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4,8]=>0000001=>1000000
[8,3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3,8]=>0000001=>1000000
[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>0000001=>1000000
[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>0000001=>1000000
[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>0000000=>0000000
[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>0000000=>0000000
[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>0000000=>0000000
[6,7,5,3,4,2,1,8]=>[8,1,2,4,3,5,7,6]=>0000000=>0000000
[5,6,7,3,4,2,1,8]=>[8,1,2,4,3,7,6,5]=>0000000=>0000000
[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>0000000=>0000000
[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>0000000=>0000000
[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>0000000=>0000000
[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>0000000=>0000000
[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>0000000=>0000000
[4,5,3,6,7,2,1,8]=>[8,1,2,7,6,3,5,4]=>0000000=>0000000
[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>0000000=>0000000
[5,6,7,4,2,3,1,8]=>[8,1,3,2,4,7,6,5]=>0000000=>0000000
[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>0000000=>0000000
[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>0000000=>0000000
[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>0000000=>0000000
[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>0000000=>0000000
[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>0000000=>0000000
[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>0000000=>0000000
[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>0000000=>0000000
[6,5,7,2,3,4,1,8]=>[8,1,4,3,2,7,5,6]=>0000000=>0000000
[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>0000000=>0000000
[7,6,4,2,3,5,1,8]=>[8,1,5,3,2,4,6,7]=>0000000=>0000000
[6,7,4,2,3,5,1,8]=>[8,1,5,3,2,4,7,6]=>0000000=>0000000
[7,6,3,2,4,5,1,8]=>[8,1,5,4,2,3,6,7]=>0000000=>0000000
[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>0000000=>0000000
[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>0000000=>0000000
[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>0000000=>0000000
[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>0000000=>0000000
[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>0000000=>0000000
[4,5,6,3,2,7,1,8]=>[8,1,7,2,3,6,5,4]=>0000000=>0000000
[6,3,4,5,2,7,1,8]=>[8,1,7,2,5,4,3,6]=>0000000=>0000000
[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>0000000=>0000000
[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>0000000=>0000000
[5,3,4,6,2,7,1,8]=>[8,1,7,2,6,4,3,5]=>0000000=>0000000
[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>0000000=>0000000
[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>0000000=>0000000
[6,5,3,2,4,7,1,8]=>[8,1,7,4,2,3,5,6]=>0000000=>0000000
[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>0000000=>0000000
[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>0000000=>0000000
[6,3,4,2,5,7,1,8]=>[8,1,7,5,2,4,3,6]=>0000000=>0000000
[6,4,2,3,5,7,1,8]=>[8,1,7,5,3,2,4,6]=>0000000=>0000000
[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>0000000=>0000000
[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>0000000=>0000000
[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>0000000=>0000000
[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>0000000=>0000000
[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>0000000=>0000000
[6,4,3,5,7,1,2,8]=>[8,2,1,7,5,3,4,6]=>0000000=>0000000
[5,4,3,6,7,1,2,8]=>[8,2,1,7,6,3,4,5]=>0000000=>0000000
[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>0000000=>0000000
[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>0000000=>0000000
[7,4,5,6,2,1,3,8]=>[8,3,1,2,6,5,4,7]=>0000000=>0000000
[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>0000000=>0000000
[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>0000000=>0000000
[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>0000000=>0000000
[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>0000000=>0000000
[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>0000000=>0000000
[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>0000000=>0000000
[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>0000000=>0000000
[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>0000000=>0000000
[6,5,4,7,1,2,3,8]=>[8,3,2,1,7,4,5,6]=>0000000=>0000000
[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>0000000=>0000000
[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>0000000=>0000000
[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>0000000=>0000000
[6,7,5,3,1,2,4,8]=>[8,4,2,1,3,5,7,6]=>0000000=>0000000
[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>0000000=>0000000
[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>0000000=>0000000
[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>0000000=>0000000
[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>0000000=>0000000
[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>0000000=>0000000
[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>0000000=>0000000
[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>0000000=>0000000
[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>0000000=>0000000
[7,6,3,4,2,1,5,8]=>[8,5,1,2,4,3,6,7]=>0000000=>0000000
[7,6,4,2,3,1,5,8]=>[8,5,1,3,2,4,6,7]=>0000000=>0000000
[6,7,4,2,3,1,5,8]=>[8,5,1,3,2,4,7,6]=>0000000=>0000000
[7,6,3,2,4,1,5,8]=>[8,5,1,4,2,3,6,7]=>0000000=>0000000
[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>0000000=>0000000
[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>0000000=>0000000
[7,5,2,3,4,1,6,8]=>[8,6,1,4,3,2,5,7]=>0000000=>0000000
[7,3,4,2,5,1,6,8]=>[8,6,1,5,2,4,3,7]=>0000000=>0000000
[7,4,2,3,5,1,6,8]=>[8,6,1,5,3,2,4,7]=>0000000=>0000000
[7,2,3,4,5,1,6,8]=>[8,6,1,5,4,3,2,7]=>0000000=>0000000
[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>0000000=>0000000
[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>0000000=>0000000
[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>0000000=>0000000
[7,5,2,3,1,4,6,8]=>[8,6,4,1,3,2,5,7]=>0000000=>0000000
[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>0000000=>0000000
[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>0000000=>0000000
[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>0000000=>0000000
[7,2,3,4,1,5,6,8]=>[8,6,5,1,4,3,2,7]=>0000000=>0000000
[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>0000000=>0000000
[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>0000000=>0000000
[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>0000000=>0000000
[6,3,4,5,2,1,7,8]=>[8,7,1,2,5,4,3,6]=>0000000=>0000000
[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>0000000=>0000000
[3,4,5,6,2,1,7,8]=>[8,7,1,2,6,5,4,3]=>0000000=>0000000
[5,6,4,2,3,1,7,8]=>[8,7,1,3,2,4,6,5]=>0000000=>0000000
[6,4,5,2,3,1,7,8]=>[8,7,1,3,2,5,4,6]=>0000000=>0000000
[5,4,6,2,3,1,7,8]=>[8,7,1,3,2,6,4,5]=>0000000=>0000000
[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>0000000=>0000000
[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>0000000=>0000000
[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>0000000=>0000000
[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>0000000=>0000000
[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>0000000=>0000000
[5,6,4,3,1,2,7,8]=>[8,7,2,1,3,4,6,5]=>0000000=>0000000
[5,4,6,3,1,2,7,8]=>[8,7,2,1,3,6,4,5]=>0000000=>0000000
[4,5,6,3,1,2,7,8]=>[8,7,2,1,3,6,5,4]=>0000000=>0000000
[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>0000000=>0000000
[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>0000000=>0000000
[5,6,4,2,1,3,7,8]=>[8,7,3,1,2,4,6,5]=>0000000=>0000000
[5,4,6,2,1,3,7,8]=>[8,7,3,1,2,6,4,5]=>0000000=>0000000
[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>0000000=>0000000
[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>0000000=>0000000
[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>0000000=>0000000
[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>0000000=>0000000
[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>0000000=>0000000
[6,3,2,4,1,5,7,8]=>[8,7,5,1,4,2,3,6]=>0000000=>0000000
[6,2,3,4,1,5,7,8]=>[8,7,5,1,4,3,2,6]=>0000000=>0000000
[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>0000000=>0000000
[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>0000000=>0000000
[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>0000000=>0000000
[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>0000000=>0000000
[5,3,4,2,1,6,7,8]=>[8,7,6,1,2,4,3,5]=>0000000=>0000000
[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>0000000=>0000000
[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>0000000=>0000000
[5,4,2,3,1,6,7,8]=>[8,7,6,1,3,2,4,5]=>0000000=>0000000
[4,5,2,3,1,6,7,8]=>[8,7,6,1,3,2,5,4]=>0000000=>0000000
[5,3,2,4,1,6,7,8]=>[8,7,6,1,4,2,3,5]=>0000000=>0000000
[5,2,3,4,1,6,7,8]=>[8,7,6,1,4,3,2,5]=>0000000=>0000000
[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>0000000=>0000000
[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>0000000=>0000000
[4,2,3,5,1,6,7,8]=>[8,7,6,1,5,3,2,4]=>0000000=>0000000
[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>0000000=>0000000
[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>0000000=>0000000
[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>0000000=>0000000
[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>0000000=>0000000
[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>0000000=>0000000
[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>0000000=>0000000
[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>0000000=>0000000
[5,2,3,1,4,6,7,8]=>[8,7,6,4,1,3,2,5]=>0000000=>0000000
[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>0000000=>0000000
[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>0000000=>0000000
[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>0000000=>0000000
[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>0000000=>0000000
[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>0000000=>0000000
[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>0000000=>0000000
[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>0000000=>0000000
[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>0000000=>0000000
[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>0000000=>0000000
[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>0000000=>0000000
[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>0000000=>0000000
[6,8,7,5,4,3,2,1]=>[1,2,3,4,5,7,8,6]=>1111100=>0011111
[5,8,7,6,4,3,2,1]=>[1,2,3,4,6,7,8,5]=>1111000=>0001111
[5,7,8,6,4,3,2,1]=>[1,2,3,4,6,8,7,5]=>1111000=>0001111
[6,5,8,7,4,3,2,1]=>[1,2,3,4,7,8,5,6]=>1111000=>0001111
[5,6,8,7,4,3,2,1]=>[1,2,3,4,7,8,6,5]=>1111000=>0001111
[5,7,6,8,4,3,2,1]=>[1,2,3,4,8,6,7,5]=>1111000=>0001111
[4,8,7,6,5,3,2,1]=>[1,2,3,5,6,7,8,4]=>1110000=>0000111
[4,7,8,6,5,3,2,1]=>[1,2,3,5,6,8,7,4]=>1110000=>0000111
[4,6,8,7,5,3,2,1]=>[1,2,3,5,7,8,6,4]=>1110000=>0000111
[4,7,6,8,5,3,2,1]=>[1,2,3,5,8,6,7,4]=>1110000=>0000111
[4,6,7,8,5,3,2,1]=>[1,2,3,5,8,7,6,4]=>1110000=>0000111
[5,4,8,7,6,3,2,1]=>[1,2,3,6,7,8,4,5]=>1110000=>0000111
[5,4,7,8,6,3,2,1]=>[1,2,3,6,8,7,4,5]=>1110000=>0000111
[4,5,8,7,6,3,2,1]=>[1,2,3,6,7,8,5,4]=>1110000=>0000111
[4,5,7,8,6,3,2,1]=>[1,2,3,6,8,7,5,4]=>1110000=>0000111
[6,5,4,8,7,3,2,1]=>[1,2,3,7,8,4,5,6]=>1110000=>0000111
[5,6,4,8,7,3,2,1]=>[1,2,3,7,8,4,6,5]=>1110000=>0000111
[4,6,5,8,7,3,2,1]=>[1,2,3,7,8,5,6,4]=>1110000=>0000111
[5,4,6,8,7,3,2,1]=>[1,2,3,7,8,6,4,5]=>1110000=>0000111
[4,5,6,8,7,3,2,1]=>[1,2,3,7,8,6,5,4]=>1110000=>0000111
[5,7,6,4,8,3,2,1]=>[1,2,3,8,4,6,7,5]=>1110000=>0000111
[4,7,6,5,8,3,2,1]=>[1,2,3,8,5,6,7,4]=>1110000=>0000111
[4,6,7,5,8,3,2,1]=>[1,2,3,8,5,7,6,4]=>1110000=>0000111
[5,4,7,6,8,3,2,1]=>[1,2,3,8,6,7,4,5]=>1110000=>0000111
[4,5,7,6,8,3,2,1]=>[1,2,3,8,6,7,5,4]=>1110000=>0000111
[4,6,5,7,8,3,2,1]=>[1,2,3,8,7,5,6,4]=>1110000=>0000111
[3,7,6,8,5,4,2,1]=>[1,2,4,5,8,6,7,3]=>1100000=>0000011
[3,5,7,8,6,4,2,1]=>[1,2,4,6,8,7,5,3]=>1100000=>0000011
[3,5,6,8,7,4,2,1]=>[1,2,4,7,8,6,5,3]=>1100000=>0000011
[3,5,6,7,8,4,2,1]=>[1,2,4,8,7,6,5,3]=>1100000=>0000011
[4,3,7,8,6,5,2,1]=>[1,2,5,6,8,7,3,4]=>1100000=>0000011
[4,3,6,8,7,5,2,1]=>[1,2,5,7,8,6,3,4]=>1100000=>0000011
[4,3,6,7,8,5,2,1]=>[1,2,5,8,7,6,3,4]=>1100000=>0000011
[5,4,3,8,7,6,2,1]=>[1,2,6,7,8,3,4,5]=>1100000=>0000011
[5,4,3,7,8,6,2,1]=>[1,2,6,8,7,3,4,5]=>1100000=>0000011
[4,5,3,8,7,6,2,1]=>[1,2,6,7,8,3,5,4]=>1100000=>0000011
[4,5,3,7,8,6,2,1]=>[1,2,6,8,7,3,5,4]=>1100000=>0000011
[4,3,5,8,7,6,2,1]=>[1,2,6,7,8,5,3,4]=>1100000=>0000011
[4,3,5,7,8,6,2,1]=>[1,2,6,8,7,5,3,4]=>1100000=>0000011
[3,4,5,8,7,6,2,1]=>[1,2,6,7,8,5,4,3]=>1100000=>0000011
[6,5,4,3,8,7,2,1]=>[1,2,7,8,3,4,5,6]=>1100000=>0000011
[5,6,4,3,8,7,2,1]=>[1,2,7,8,3,4,6,5]=>1100000=>0000011
[5,4,6,3,8,7,2,1]=>[1,2,7,8,3,6,4,5]=>1100000=>0000011
[4,5,6,3,8,7,2,1]=>[1,2,7,8,3,6,5,4]=>1100000=>0000011
[4,3,6,5,8,7,2,1]=>[1,2,7,8,5,6,3,4]=>1100000=>0000011
[5,4,3,6,8,7,2,1]=>[1,2,7,8,6,3,4,5]=>1100000=>0000011
[4,5,3,6,8,7,2,1]=>[1,2,7,8,6,3,5,4]=>1100000=>0000011
[4,3,5,6,8,7,2,1]=>[1,2,7,8,6,5,3,4]=>1100000=>0000011
[5,7,6,4,3,8,2,1]=>[1,2,8,3,4,6,7,5]=>1100000=>0000011
[4,7,6,5,3,8,2,1]=>[1,2,8,3,5,6,7,4]=>1100000=>0000011
[4,6,7,5,3,8,2,1]=>[1,2,8,3,5,7,6,4]=>1100000=>0000011
[3,7,6,5,4,8,2,1]=>[1,2,8,4,5,6,7,3]=>1100000=>0000011
[4,3,7,6,5,8,2,1]=>[1,2,8,5,6,7,3,4]=>1100000=>0000011
[4,5,3,7,6,8,2,1]=>[1,2,8,6,7,3,5,4]=>1100000=>0000011
[4,3,5,7,6,8,2,1]=>[1,2,8,6,7,5,3,4]=>1100000=>0000011
[3,4,5,7,6,8,2,1]=>[1,2,8,6,7,5,4,3]=>1100000=>0000011
[2,5,8,7,6,4,3,1]=>[1,3,4,6,7,8,5,2]=>1000000=>0000001
[2,5,6,7,8,4,3,1]=>[1,3,4,8,7,6,5,2]=>1000000=>0000001
[2,4,8,7,6,5,3,1]=>[1,3,5,6,7,8,4,2]=>1000000=>0000001
[2,4,6,8,7,5,3,1]=>[1,3,5,7,8,6,4,2]=>1000000=>0000001
[2,4,6,7,8,5,3,1]=>[1,3,5,8,7,6,4,2]=>1000000=>0000001
[2,4,5,8,7,6,3,1]=>[1,3,6,7,8,5,4,2]=>1000000=>0000001
[2,4,5,7,8,6,3,1]=>[1,3,6,8,7,5,4,2]=>1000000=>0000001
[2,4,6,5,8,7,3,1]=>[1,3,7,8,5,6,4,2]=>1000000=>0000001
[2,7,6,5,4,8,3,1]=>[1,3,8,4,5,6,7,2]=>1000000=>0000001
[2,5,7,6,4,8,3,1]=>[1,3,8,4,6,7,5,2]=>1000000=>0000001
[2,4,7,6,5,8,3,1]=>[1,3,8,5,6,7,4,2]=>1000000=>0000001
[2,4,6,7,5,8,3,1]=>[1,3,8,5,7,6,4,2]=>1000000=>0000001
[2,4,6,5,7,8,3,1]=>[1,3,8,7,5,6,4,2]=>1000000=>0000001
[2,4,5,6,7,8,3,1]=>[1,3,8,7,6,5,4,2]=>1000000=>0000001
[3,2,7,6,5,8,4,1]=>[1,4,8,5,6,7,2,3]=>1000000=>0000001
[2,3,7,6,8,5,4,1]=>[1,4,5,8,6,7,3,2]=>1000000=>0000001
[2,3,5,8,7,6,4,1]=>[1,4,6,7,8,5,3,2]=>1000000=>0000001
[2,3,5,7,8,6,4,1]=>[1,4,6,8,7,5,3,2]=>1000000=>0000001
[2,3,5,6,8,7,4,1]=>[1,4,7,8,6,5,3,2]=>1000000=>0000001
[2,3,6,7,5,8,4,1]=>[1,4,8,5,7,6,3,2]=>1000000=>0000001
[2,3,5,7,6,8,4,1]=>[1,4,8,6,7,5,3,2]=>1000000=>0000001
[2,3,5,6,7,8,4,1]=>[1,4,8,7,6,5,3,2]=>1000000=>0000001
[4,3,2,8,7,6,5,1]=>[1,5,6,7,8,2,3,4]=>1000000=>0000001
[4,3,2,7,8,6,5,1]=>[1,5,6,8,7,2,3,4]=>1000000=>0000001
[4,3,2,6,8,7,5,1]=>[1,5,7,8,6,2,3,4]=>1000000=>0000001
[4,3,2,6,7,8,5,1]=>[1,5,8,7,6,2,3,4]=>1000000=>0000001
[3,4,2,8,7,6,5,1]=>[1,5,6,7,8,2,4,3]=>1000000=>0000001
[3,4,2,6,7,8,5,1]=>[1,5,8,7,6,2,4,3]=>1000000=>0000001
[2,4,3,6,8,7,5,1]=>[1,5,7,8,6,3,4,2]=>1000000=>0000001
[3,2,4,8,7,6,5,1]=>[1,5,6,7,8,4,2,3]=>1000000=>0000001
[3,2,4,6,8,7,5,1]=>[1,5,7,8,6,4,2,3]=>1000000=>0000001
[2,3,4,8,7,6,5,1]=>[1,5,6,7,8,4,3,2]=>1000000=>0000001
[5,4,3,2,8,7,6,1]=>[1,6,7,8,2,3,4,5]=>1000000=>0000001
[5,4,3,2,7,8,6,1]=>[1,6,8,7,2,3,4,5]=>1000000=>0000001
[4,5,3,2,8,7,6,1]=>[1,6,7,8,2,3,5,4]=>1000000=>0000001
[4,3,5,2,8,7,6,1]=>[1,6,7,8,2,5,3,4]=>1000000=>0000001
[3,4,5,2,7,8,6,1]=>[1,6,8,7,2,5,4,3]=>1000000=>0000001
[2,5,4,3,8,7,6,1]=>[1,6,7,8,3,4,5,2]=>1000000=>0000001
[2,5,4,3,7,8,6,1]=>[1,6,8,7,3,4,5,2]=>1000000=>0000001
[2,4,5,3,8,7,6,1]=>[1,6,7,8,3,5,4,2]=>1000000=>0000001
[2,3,5,4,8,7,6,1]=>[1,6,7,8,4,5,3,2]=>1000000=>0000001
[2,3,5,4,7,8,6,1]=>[1,6,8,7,4,5,3,2]=>1000000=>0000001
[4,3,2,5,8,7,6,1]=>[1,6,7,8,5,2,3,4]=>1000000=>0000001
[4,3,2,5,7,8,6,1]=>[1,6,8,7,5,2,3,4]=>1000000=>0000001
[2,4,3,5,8,7,6,1]=>[1,6,7,8,5,3,4,2]=>1000000=>0000001
[2,3,4,5,8,7,6,1]=>[1,6,7,8,5,4,3,2]=>1000000=>0000001
[2,3,4,5,7,8,6,1]=>[1,6,8,7,5,4,3,2]=>1000000=>0000001
[6,5,4,3,2,8,7,1]=>[1,7,8,2,3,4,5,6]=>1000000=>0000001
[5,4,6,3,2,8,7,1]=>[1,7,8,2,3,6,4,5]=>1000000=>0000001
[4,5,6,3,2,8,7,1]=>[1,7,8,2,3,6,5,4]=>1000000=>0000001
[3,6,5,4,2,8,7,1]=>[1,7,8,2,4,5,6,3]=>1000000=>0000001
[3,5,4,6,2,8,7,1]=>[1,7,8,2,6,4,5,3]=>1000000=>0000001
[2,6,5,4,3,8,7,1]=>[1,7,8,3,4,5,6,2]=>1000000=>0000001
[2,4,6,5,3,8,7,1]=>[1,7,8,3,5,6,4,2]=>1000000=>0000001
[2,4,5,6,3,8,7,1]=>[1,7,8,3,6,5,4,2]=>1000000=>0000001
[3,2,6,5,4,8,7,1]=>[1,7,8,4,5,6,2,3]=>1000000=>0000001
[2,4,3,6,5,8,7,1]=>[1,7,8,5,6,3,4,2]=>1000000=>0000001
[3,2,4,6,5,8,7,1]=>[1,7,8,5,6,4,2,3]=>1000000=>0000001
[5,4,3,2,6,8,7,1]=>[1,7,8,6,2,3,4,5]=>1000000=>0000001
[3,4,5,2,6,8,7,1]=>[1,7,8,6,2,5,4,3]=>1000000=>0000001
[2,5,4,3,6,8,7,1]=>[1,7,8,6,3,4,5,2]=>1000000=>0000001
[2,4,5,3,6,8,7,1]=>[1,7,8,6,3,5,4,2]=>1000000=>0000001
[2,3,4,5,6,8,7,1]=>[1,7,8,6,5,4,3,2]=>1000000=>0000001
[5,7,6,4,3,2,8,1]=>[1,8,2,3,4,6,7,5]=>1000000=>0000001
[4,7,6,5,3,2,8,1]=>[1,8,2,3,5,6,7,4]=>1000000=>0000001
[3,7,6,5,4,2,8,1]=>[1,8,2,4,5,6,7,3]=>1000000=>0000001
[3,6,7,5,4,2,8,1]=>[1,8,2,4,5,7,6,3]=>1000000=>0000001
[4,3,7,6,5,2,8,1]=>[1,8,2,5,6,7,3,4]=>1000000=>0000001
[3,4,7,6,5,2,8,1]=>[1,8,2,5,6,7,4,3]=>1000000=>0000001
[3,6,5,4,7,2,8,1]=>[1,8,2,7,4,5,6,3]=>1000000=>0000001
[4,3,6,5,7,2,8,1]=>[1,8,2,7,5,6,3,4]=>1000000=>0000001
[3,5,4,6,7,2,8,1]=>[1,8,2,7,6,4,5,3]=>1000000=>0000001
[2,5,7,6,4,3,8,1]=>[1,8,3,4,6,7,5,2]=>1000000=>0000001
[2,4,6,7,5,3,8,1]=>[1,8,3,5,7,6,4,2]=>1000000=>0000001
[2,5,4,7,6,3,8,1]=>[1,8,3,6,7,4,5,2]=>1000000=>0000001
[2,5,4,6,7,3,8,1]=>[1,8,3,7,6,4,5,2]=>1000000=>0000001
[2,4,5,6,7,3,8,1]=>[1,8,3,7,6,5,4,2]=>1000000=>0000001
[3,2,6,7,5,4,8,1]=>[1,8,4,5,7,6,2,3]=>1000000=>0000001
[3,2,5,7,6,4,8,1]=>[1,8,4,6,7,5,2,3]=>1000000=>0000001
[3,2,6,5,7,4,8,1]=>[1,8,4,7,5,6,2,3]=>1000000=>0000001
[3,2,5,6,7,4,8,1]=>[1,8,4,7,6,5,2,3]=>1000000=>0000001
[2,3,7,6,5,4,8,1]=>[1,8,4,5,6,7,3,2]=>1000000=>0000001
[2,3,5,7,6,4,8,1]=>[1,8,4,6,7,5,3,2]=>1000000=>0000001
[2,3,5,6,7,4,8,1]=>[1,8,4,7,6,5,3,2]=>1000000=>0000001
[4,3,2,6,7,5,8,1]=>[1,8,5,7,6,2,3,4]=>1000000=>0000001
[5,4,3,2,7,6,8,1]=>[1,8,6,7,2,3,4,5]=>1000000=>0000001
[4,3,5,2,7,6,8,1]=>[1,8,6,7,2,5,3,4]=>1000000=>0000001
[3,4,5,2,7,6,8,1]=>[1,8,6,7,2,5,4,3]=>1000000=>0000001
[2,5,4,3,7,6,8,1]=>[1,8,6,7,3,4,5,2]=>1000000=>0000001
[3,2,5,4,7,6,8,1]=>[1,8,6,7,4,5,2,3]=>1000000=>0000001
[2,3,5,4,7,6,8,1]=>[1,8,6,7,4,5,3,2]=>1000000=>0000001
[4,3,2,5,7,6,8,1]=>[1,8,6,7,5,2,3,4]=>1000000=>0000001
[2,3,4,5,7,6,8,1]=>[1,8,6,7,5,4,3,2]=>1000000=>0000001
[3,6,5,4,2,7,8,1]=>[1,8,7,2,4,5,6,3]=>1000000=>0000001
[3,5,4,6,2,7,8,1]=>[1,8,7,2,6,4,5,3]=>1000000=>0000001
[2,6,5,4,3,7,8,1]=>[1,8,7,3,4,5,6,2]=>1000000=>0000001
[2,5,6,4,3,7,8,1]=>[1,8,7,3,4,6,5,2]=>1000000=>0000001
[3,2,6,5,4,7,8,1]=>[1,8,7,4,5,6,2,3]=>1000000=>0000001
[2,3,4,6,5,7,8,1]=>[1,8,7,5,6,4,3,2]=>1000000=>0000001
[2,5,4,3,6,7,8,1]=>[1,8,7,6,3,4,5,2]=>1000000=>0000001
[1,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,1]=>0000000=>0000000
[1,7,8,6,5,4,3,2]=>[2,3,4,5,6,8,7,1]=>0000000=>0000000
[1,5,6,7,8,4,3,2]=>[2,3,4,8,7,6,5,1]=>0000000=>0000000
[1,4,8,7,6,5,3,2]=>[2,3,5,6,7,8,4,1]=>0000000=>0000000
[1,4,6,7,8,5,3,2]=>[2,3,5,8,7,6,4,1]=>0000000=>0000000
[1,7,6,5,4,8,3,2]=>[2,3,8,4,5,6,7,1]=>0000000=>0000000
[1,6,5,4,7,8,3,2]=>[2,3,8,7,4,5,6,1]=>0000000=>0000000
[1,4,5,6,7,8,3,2]=>[2,3,8,7,6,5,4,1]=>0000000=>0000000
[1,3,5,7,8,6,4,2]=>[2,4,6,8,7,5,3,1]=>0000000=>0000000
[1,3,6,5,8,7,4,2]=>[2,4,7,8,5,6,3,1]=>0000000=>0000000
[1,3,6,7,5,8,4,2]=>[2,4,8,5,7,6,3,1]=>0000000=>0000000
[1,3,5,6,7,8,4,2]=>[2,4,8,7,6,5,3,1]=>0000000=>0000000
[1,4,3,7,6,8,5,2]=>[2,5,8,6,7,3,4,1]=>0000000=>0000000
[1,3,4,8,7,6,5,2]=>[2,5,6,7,8,4,3,1]=>0000000=>0000000
[1,4,3,5,8,7,6,2]=>[2,6,7,8,5,3,4,1]=>0000000=>0000000
[1,3,6,5,4,8,7,2]=>[2,7,8,4,5,6,3,1]=>0000000=>0000000
[1,4,3,6,5,8,7,2]=>[2,7,8,5,6,3,4,1]=>0000000=>0000000
[1,4,6,7,5,3,8,2]=>[2,8,3,5,7,6,4,1]=>0000000=>0000000
[1,5,6,4,7,3,8,2]=>[2,8,3,7,4,6,5,1]=>0000000=>0000000
[1,6,5,4,3,7,8,2]=>[2,8,7,3,4,5,6,1]=>0000000=>0000000
[1,3,4,6,5,7,8,2]=>[2,8,7,5,6,4,3,1]=>0000000=>0000000
[1,3,4,5,6,7,8,2]=>[2,8,7,6,5,4,3,1]=>0000000=>0000000
[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>0000000=>0000000
[2,1,7,8,6,5,4,3]=>[3,4,5,6,8,7,1,2]=>0000000=>0000000
[2,1,6,8,7,5,4,3]=>[3,4,5,7,8,6,1,2]=>0000000=>0000000
[2,1,7,6,8,5,4,3]=>[3,4,5,8,6,7,1,2]=>0000000=>0000000
[2,1,6,7,8,5,4,3]=>[3,4,5,8,7,6,1,2]=>0000000=>0000000
[2,1,5,8,7,6,4,3]=>[3,4,6,7,8,5,1,2]=>0000000=>0000000
[2,1,5,7,8,6,4,3]=>[3,4,6,8,7,5,1,2]=>0000000=>0000000
[2,1,7,6,5,8,4,3]=>[3,4,8,5,6,7,1,2]=>0000000=>0000000
[2,1,6,7,5,8,4,3]=>[3,4,8,5,7,6,1,2]=>0000000=>0000000
[2,1,5,6,7,8,4,3]=>[3,4,8,7,6,5,1,2]=>0000000=>0000000
[2,1,4,8,7,6,5,3]=>[3,5,6,7,8,4,1,2]=>0000000=>0000000
[2,1,4,5,8,7,6,3]=>[3,6,7,8,5,4,1,2]=>0000000=>0000000
[2,1,6,5,7,4,8,3]=>[3,8,4,7,5,6,1,2]=>0000000=>0000000
[2,1,5,4,7,6,8,3]=>[3,8,6,7,4,5,1,2]=>0000000=>0000000
[2,1,6,5,4,7,8,3]=>[3,8,7,4,5,6,1,2]=>0000000=>0000000
[2,1,4,5,6,7,8,3]=>[3,8,7,6,5,4,1,2]=>0000000=>0000000
[1,2,5,6,7,8,4,3]=>[3,4,8,7,6,5,2,1]=>0000000=>0000000
[1,2,4,8,7,6,5,3]=>[3,5,6,7,8,4,2,1]=>0000000=>0000000
[1,2,5,4,8,7,6,3]=>[3,6,7,8,4,5,2,1]=>0000000=>0000000
[1,2,4,6,5,7,8,3]=>[3,8,7,5,6,4,2,1]=>0000000=>0000000
[1,2,4,5,6,7,8,3]=>[3,8,7,6,5,4,2,1]=>0000000=>0000000
[3,2,1,6,7,8,5,4]=>[4,5,8,7,6,1,2,3]=>0000000=>0000000
[3,2,1,6,5,8,7,4]=>[4,7,8,5,6,1,2,3]=>0000000=>0000000
[3,2,1,6,5,7,8,4]=>[4,8,7,5,6,1,2,3]=>0000000=>0000000
[2,3,1,8,7,6,5,4]=>[4,5,6,7,8,1,3,2]=>0000000=>0000000
[2,3,1,7,6,8,5,4]=>[4,5,8,6,7,1,3,2]=>0000000=>0000000
[2,3,1,6,7,8,5,4]=>[4,5,8,7,6,1,3,2]=>0000000=>0000000
[2,3,1,6,5,8,7,4]=>[4,7,8,5,6,1,3,2]=>0000000=>0000000
[2,3,1,5,7,6,8,4]=>[4,8,6,7,5,1,3,2]=>0000000=>0000000
[2,3,1,6,5,7,8,4]=>[4,8,7,5,6,1,3,2]=>0000000=>0000000
[1,3,2,8,7,6,5,4]=>[4,5,6,7,8,2,3,1]=>0000000=>0000000
[2,1,3,8,7,6,5,4]=>[4,5,6,7,8,3,1,2]=>0000000=>0000000
[2,1,3,7,8,6,5,4]=>[4,5,6,8,7,3,1,2]=>0000000=>0000000
[2,1,3,6,8,7,5,4]=>[4,5,7,8,6,3,1,2]=>0000000=>0000000
[2,1,3,5,7,8,6,4]=>[4,6,8,7,5,3,1,2]=>0000000=>0000000
[2,1,3,5,7,6,8,4]=>[4,8,6,7,5,3,1,2]=>0000000=>0000000
[1,2,3,8,7,6,5,4]=>[4,5,6,7,8,3,2,1]=>0000000=>0000000
[1,2,3,7,8,6,5,4]=>[4,5,6,8,7,3,2,1]=>0000000=>0000000
[1,2,3,6,8,7,5,4]=>[4,5,7,8,6,3,2,1]=>0000000=>0000000
[1,2,3,7,6,8,5,4]=>[4,5,8,6,7,3,2,1]=>0000000=>0000000
[1,2,3,6,7,8,5,4]=>[4,5,8,7,6,3,2,1]=>0000000=>0000000
[1,2,3,5,8,7,6,4]=>[4,6,7,8,5,3,2,1]=>0000000=>0000000
[1,2,3,5,7,8,6,4]=>[4,6,8,7,5,3,2,1]=>0000000=>0000000
[1,2,3,6,5,8,7,4]=>[4,7,8,5,6,3,2,1]=>0000000=>0000000
[1,2,3,5,6,8,7,4]=>[4,7,8,6,5,3,2,1]=>0000000=>0000000
[1,2,3,7,6,5,8,4]=>[4,8,5,6,7,3,2,1]=>0000000=>0000000
[1,2,3,6,7,5,8,4]=>[4,8,5,7,6,3,2,1]=>0000000=>0000000
[1,2,3,5,7,6,8,4]=>[4,8,6,7,5,3,2,1]=>0000000=>0000000
[1,2,3,6,5,7,8,4]=>[4,8,7,5,6,3,2,1]=>0000000=>0000000
[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>0000000=>0000000
[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>0000000=>0000000
[4,3,2,1,7,8,6,5]=>[5,6,8,7,1,2,3,4]=>0000000=>0000000
[4,3,2,1,6,8,7,5]=>[5,7,8,6,1,2,3,4]=>0000000=>0000000
[4,3,2,1,7,6,8,5]=>[5,8,6,7,1,2,3,4]=>0000000=>0000000
[4,3,2,1,6,7,8,5]=>[5,8,7,6,1,2,3,4]=>0000000=>0000000
[3,4,2,1,8,7,6,5]=>[5,6,7,8,1,2,4,3]=>0000000=>0000000
[3,4,2,1,7,8,6,5]=>[5,6,8,7,1,2,4,3]=>0000000=>0000000
[3,4,2,1,7,6,8,5]=>[5,8,6,7,1,2,4,3]=>0000000=>0000000
[3,4,2,1,6,7,8,5]=>[5,8,7,6,1,2,4,3]=>0000000=>0000000
[2,4,3,1,8,7,6,5]=>[5,6,7,8,1,3,4,2]=>0000000=>0000000
[2,4,3,1,7,8,6,5]=>[5,6,8,7,1,3,4,2]=>0000000=>0000000
[2,4,3,1,6,8,7,5]=>[5,7,8,6,1,3,4,2]=>0000000=>0000000
[2,4,3,1,7,6,8,5]=>[5,8,6,7,1,3,4,2]=>0000000=>0000000
[2,4,3,1,6,7,8,5]=>[5,8,7,6,1,3,4,2]=>0000000=>0000000
[3,2,4,1,8,7,6,5]=>[5,6,7,8,1,4,2,3]=>0000000=>0000000
[3,2,4,1,7,8,6,5]=>[5,6,8,7,1,4,2,3]=>0000000=>0000000
[3,2,4,1,6,8,7,5]=>[5,7,8,6,1,4,2,3]=>0000000=>0000000
[3,2,4,1,7,6,8,5]=>[5,8,6,7,1,4,2,3]=>0000000=>0000000
[3,2,4,1,6,7,8,5]=>[5,8,7,6,1,4,2,3]=>0000000=>0000000
[2,3,4,1,8,7,6,5]=>[5,6,7,8,1,4,3,2]=>0000000=>0000000
[2,3,4,1,7,8,6,5]=>[5,6,8,7,1,4,3,2]=>0000000=>0000000
[2,3,4,1,6,8,7,5]=>[5,7,8,6,1,4,3,2]=>0000000=>0000000
[2,3,4,1,7,6,8,5]=>[5,8,6,7,1,4,3,2]=>0000000=>0000000
[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>0000000=>0000000
[1,4,3,2,8,7,6,5]=>[5,6,7,8,2,3,4,1]=>0000000=>0000000
[1,4,3,2,7,6,8,5]=>[5,8,6,7,2,3,4,1]=>0000000=>0000000
[1,4,3,2,6,7,8,5]=>[5,8,7,6,2,3,4,1]=>0000000=>0000000
[1,3,4,2,8,7,6,5]=>[5,6,7,8,2,4,3,1]=>0000000=>0000000
[1,3,4,2,7,6,8,5]=>[5,8,6,7,2,4,3,1]=>0000000=>0000000
[1,3,4,2,6,7,8,5]=>[5,8,7,6,2,4,3,1]=>0000000=>0000000
[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>0000000=>0000000
[2,1,4,3,7,8,6,5]=>[5,6,8,7,3,4,1,2]=>0000000=>0000000
[2,1,4,3,6,8,7,5]=>[5,7,8,6,3,4,1,2]=>0000000=>0000000
[2,1,4,3,7,6,8,5]=>[5,8,6,7,3,4,1,2]=>0000000=>0000000
[2,1,4,3,6,7,8,5]=>[5,8,7,6,3,4,1,2]=>0000000=>0000000
[1,2,4,3,8,7,6,5]=>[5,6,7,8,3,4,2,1]=>0000000=>0000000
[1,2,4,3,7,6,8,5]=>[5,8,6,7,3,4,2,1]=>0000000=>0000000
[1,2,4,3,6,7,8,5]=>[5,8,7,6,3,4,2,1]=>0000000=>0000000
[3,2,1,4,8,7,6,5]=>[5,6,7,8,4,1,2,3]=>0000000=>0000000
[3,2,1,4,7,8,6,5]=>[5,6,8,7,4,1,2,3]=>0000000=>0000000
[3,2,1,4,7,6,8,5]=>[5,8,6,7,4,1,2,3]=>0000000=>0000000
[3,2,1,4,6,7,8,5]=>[5,8,7,6,4,1,2,3]=>0000000=>0000000
[2,3,1,4,8,7,6,5]=>[5,6,7,8,4,1,3,2]=>0000000=>0000000
[2,3,1,4,7,6,8,5]=>[5,8,6,7,4,1,3,2]=>0000000=>0000000
[2,3,1,4,6,7,8,5]=>[5,8,7,6,4,1,3,2]=>0000000=>0000000
[1,3,2,4,8,7,6,5]=>[5,6,7,8,4,2,3,1]=>0000000=>0000000
[1,3,2,4,7,6,8,5]=>[5,8,6,7,4,2,3,1]=>0000000=>0000000
[1,3,2,4,6,7,8,5]=>[5,8,7,6,4,2,3,1]=>0000000=>0000000
[2,1,3,4,8,7,6,5]=>[5,6,7,8,4,3,1,2]=>0000000=>0000000
[2,1,3,4,7,8,6,5]=>[5,6,8,7,4,3,1,2]=>0000000=>0000000
[2,1,3,4,7,6,8,5]=>[5,8,6,7,4,3,1,2]=>0000000=>0000000
[2,1,3,4,6,7,8,5]=>[5,8,7,6,4,3,1,2]=>0000000=>0000000
[1,2,3,4,8,7,6,5]=>[5,6,7,8,4,3,2,1]=>0000000=>0000000
[1,2,3,4,7,6,8,5]=>[5,8,6,7,4,3,2,1]=>0000000=>0000000
[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>0000000=>0000000
[5,4,3,2,1,8,7,6]=>[6,7,8,1,2,3,4,5]=>0000000=>0000000
[5,4,3,2,1,7,8,6]=>[6,8,7,1,2,3,4,5]=>0000000=>0000000
[4,5,3,2,1,8,7,6]=>[6,7,8,1,2,3,5,4]=>0000000=>0000000
[3,5,4,2,1,8,7,6]=>[6,7,8,1,2,4,5,3]=>0000000=>0000000
[4,3,5,2,1,8,7,6]=>[6,7,8,1,2,5,3,4]=>0000000=>0000000
[3,4,5,2,1,8,7,6]=>[6,7,8,1,2,5,4,3]=>0000000=>0000000
[2,5,4,3,1,8,7,6]=>[6,7,8,1,3,4,5,2]=>0000000=>0000000
[2,5,4,3,1,7,8,6]=>[6,8,7,1,3,4,5,2]=>0000000=>0000000
[2,4,5,3,1,8,7,6]=>[6,7,8,1,3,5,4,2]=>0000000=>0000000
[3,2,5,4,1,8,7,6]=>[6,7,8,1,4,5,2,3]=>0000000=>0000000
[2,3,5,4,1,8,7,6]=>[6,7,8,1,4,5,3,2]=>0000000=>0000000
[4,3,2,5,1,8,7,6]=>[6,7,8,1,5,2,3,4]=>0000000=>0000000
[3,4,2,5,1,8,7,6]=>[6,7,8,1,5,2,4,3]=>0000000=>0000000
[2,4,3,5,1,8,7,6]=>[6,7,8,1,5,3,4,2]=>0000000=>0000000
[2,3,4,5,1,8,7,6]=>[6,7,8,1,5,4,3,2]=>0000000=>0000000
[2,3,4,5,1,7,8,6]=>[6,8,7,1,5,4,3,2]=>0000000=>0000000
[1,5,4,3,2,8,7,6]=>[6,7,8,2,3,4,5,1]=>0000000=>0000000
[1,5,4,3,2,7,8,6]=>[6,8,7,2,3,4,5,1]=>0000000=>0000000
[1,3,4,5,2,8,7,6]=>[6,7,8,2,5,4,3,1]=>0000000=>0000000
[1,2,5,4,3,8,7,6]=>[6,7,8,3,4,5,2,1]=>0000000=>0000000
[1,2,5,4,3,7,8,6]=>[6,8,7,3,4,5,2,1]=>0000000=>0000000
[1,2,4,5,3,8,7,6]=>[6,7,8,3,5,4,2,1]=>0000000=>0000000
[1,3,2,5,4,8,7,6]=>[6,7,8,4,5,2,3,1]=>0000000=>0000000
[2,1,3,5,4,7,8,6]=>[6,8,7,4,5,3,1,2]=>0000000=>0000000
[4,3,2,1,5,8,7,6]=>[6,7,8,5,1,2,3,4]=>0000000=>0000000
[4,3,2,1,5,7,8,6]=>[6,8,7,5,1,2,3,4]=>0000000=>0000000
[3,2,4,1,5,8,7,6]=>[6,7,8,5,1,4,2,3]=>0000000=>0000000
[3,2,4,1,5,7,8,6]=>[6,8,7,5,1,4,2,3]=>0000000=>0000000
[2,3,4,1,5,8,7,6]=>[6,7,8,5,1,4,3,2]=>0000000=>0000000
[2,3,4,1,5,7,8,6]=>[6,8,7,5,1,4,3,2]=>0000000=>0000000
[1,4,3,2,5,8,7,6]=>[6,7,8,5,2,3,4,1]=>0000000=>0000000
[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>0000000=>0000000
[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>0000000=>0000000
[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>0000000=>0000000
[5,6,4,3,2,1,8,7]=>[7,8,1,2,3,4,6,5]=>0000000=>0000000
[4,6,5,3,2,1,8,7]=>[7,8,1,2,3,5,6,4]=>0000000=>0000000
[5,4,6,3,2,1,8,7]=>[7,8,1,2,3,6,4,5]=>0000000=>0000000
[4,5,6,3,2,1,8,7]=>[7,8,1,2,3,6,5,4]=>0000000=>0000000
[3,6,5,4,2,1,8,7]=>[7,8,1,2,4,5,6,3]=>0000000=>0000000
[3,5,6,4,2,1,8,7]=>[7,8,1,2,4,6,5,3]=>0000000=>0000000
[5,4,3,6,2,1,8,7]=>[7,8,1,2,6,3,4,5]=>0000000=>0000000
[4,5,3,6,2,1,8,7]=>[7,8,1,2,6,3,5,4]=>0000000=>0000000
[3,4,5,6,2,1,8,7]=>[7,8,1,2,6,5,4,3]=>0000000=>0000000
[2,6,5,4,3,1,8,7]=>[7,8,1,3,4,5,6,2]=>0000000=>0000000
[2,3,6,5,4,1,8,7]=>[7,8,1,4,5,6,3,2]=>0000000=>0000000
[5,4,3,2,6,1,8,7]=>[7,8,1,6,2,3,4,5]=>0000000=>0000000
[4,5,3,2,6,1,8,7]=>[7,8,1,6,2,3,5,4]=>0000000=>0000000
[3,5,4,2,6,1,8,7]=>[7,8,1,6,2,4,5,3]=>0000000=>0000000
[4,3,5,2,6,1,8,7]=>[7,8,1,6,2,5,3,4]=>0000000=>0000000
[3,4,5,2,6,1,8,7]=>[7,8,1,6,2,5,4,3]=>0000000=>0000000
[2,4,5,3,6,1,8,7]=>[7,8,1,6,3,5,4,2]=>0000000=>0000000
[3,2,5,4,6,1,8,7]=>[7,8,1,6,4,5,2,3]=>0000000=>0000000
[4,3,2,5,6,1,8,7]=>[7,8,1,6,5,2,3,4]=>0000000=>0000000
[2,3,4,5,6,1,8,7]=>[7,8,1,6,5,4,3,2]=>0000000=>0000000
[1,4,5,3,6,2,8,7]=>[7,8,2,6,3,5,4,1]=>0000000=>0000000
[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>0000000=>0000000
[2,1,5,6,4,3,8,7]=>[7,8,3,4,6,5,1,2]=>0000000=>0000000
[2,1,4,6,5,3,8,7]=>[7,8,3,5,6,4,1,2]=>0000000=>0000000
[2,1,5,4,6,3,8,7]=>[7,8,3,6,4,5,1,2]=>0000000=>0000000
[2,1,3,6,5,4,8,7]=>[7,8,4,5,6,3,1,2]=>0000000=>0000000
[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>0000000=>0000000
[3,4,2,1,6,5,8,7]=>[7,8,5,6,1,2,4,3]=>0000000=>0000000
[2,4,3,1,6,5,8,7]=>[7,8,5,6,1,3,4,2]=>0000000=>0000000
[3,2,4,1,6,5,8,7]=>[7,8,5,6,1,4,2,3]=>0000000=>0000000
[2,3,4,1,6,5,8,7]=>[7,8,5,6,1,4,3,2]=>0000000=>0000000
[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>0000000=>0000000
[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1]=>0000000=>0000000
[2,3,1,4,6,5,8,7]=>[7,8,5,6,4,1,3,2]=>0000000=>0000000
[5,4,3,2,1,6,8,7]=>[7,8,6,1,2,3,4,5]=>0000000=>0000000
[2,5,4,3,1,6,8,7]=>[7,8,6,1,3,4,5,2]=>0000000=>0000000
[2,4,5,3,1,6,8,7]=>[7,8,6,1,3,5,4,2]=>0000000=>0000000
[4,3,2,5,1,6,8,7]=>[7,8,6,1,5,2,3,4]=>0000000=>0000000
[2,3,4,5,1,6,8,7]=>[7,8,6,1,5,4,3,2]=>0000000=>0000000
[1,5,4,3,2,6,8,7]=>[7,8,6,2,3,4,5,1]=>0000000=>0000000
[2,1,5,4,3,6,8,7]=>[7,8,6,3,4,5,1,2]=>0000000=>0000000
[1,2,5,4,3,6,8,7]=>[7,8,6,3,4,5,2,1]=>0000000=>0000000
[4,3,2,1,5,6,8,7]=>[7,8,6,5,1,2,3,4]=>0000000=>0000000
[3,2,4,1,5,6,8,7]=>[7,8,6,5,1,4,2,3]=>0000000=>0000000
[2,3,4,1,5,6,8,7]=>[7,8,6,5,1,4,3,2]=>0000000=>0000000
[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>0000000=>0000000
[4,7,6,5,3,2,1,8]=>[8,1,2,3,5,6,7,4]=>0000000=>0000000
[3,7,6,5,4,2,1,8]=>[8,1,2,4,5,6,7,3]=>0000000=>0000000
[4,3,7,6,5,2,1,8]=>[8,1,2,5,6,7,3,4]=>0000000=>0000000
[3,4,7,6,5,2,1,8]=>[8,1,2,5,6,7,4,3]=>0000000=>0000000
[4,5,3,7,6,2,1,8]=>[8,1,2,6,7,3,5,4]=>0000000=>0000000
[3,5,4,7,6,2,1,8]=>[8,1,2,6,7,4,5,3]=>0000000=>0000000
[4,3,5,7,6,2,1,8]=>[8,1,2,6,7,5,3,4]=>0000000=>0000000
[3,5,6,4,7,2,1,8]=>[8,1,2,7,4,6,5,3]=>0000000=>0000000
[2,4,7,6,5,3,1,8]=>[8,1,3,5,6,7,4,2]=>0000000=>0000000
[2,4,6,7,5,3,1,8]=>[8,1,3,5,7,6,4,2]=>0000000=>0000000
[2,5,4,7,6,3,1,8]=>[8,1,3,6,7,4,5,2]=>0000000=>0000000
[2,5,6,4,7,3,1,8]=>[8,1,3,7,4,6,5,2]=>0000000=>0000000
[3,2,7,6,5,4,1,8]=>[8,1,4,5,6,7,2,3]=>0000000=>0000000
[3,2,6,7,5,4,1,8]=>[8,1,4,5,7,6,2,3]=>0000000=>0000000
[3,2,5,7,6,4,1,8]=>[8,1,4,6,7,5,2,3]=>0000000=>0000000
[3,2,5,6,7,4,1,8]=>[8,1,4,7,6,5,2,3]=>0000000=>0000000
[2,3,7,6,5,4,1,8]=>[8,1,4,5,6,7,3,2]=>0000000=>0000000
[4,3,2,7,6,5,1,8]=>[8,1,5,6,7,2,3,4]=>0000000=>0000000
[4,3,2,6,7,5,1,8]=>[8,1,5,7,6,2,3,4]=>0000000=>0000000
[2,3,4,7,6,5,1,8]=>[8,1,5,6,7,4,3,2]=>0000000=>0000000
[5,4,3,2,7,6,1,8]=>[8,1,6,7,2,3,4,5]=>0000000=>0000000
[4,5,3,2,7,6,1,8]=>[8,1,6,7,2,3,5,4]=>0000000=>0000000
[3,5,4,2,7,6,1,8]=>[8,1,6,7,2,4,5,3]=>0000000=>0000000
[3,4,5,2,7,6,1,8]=>[8,1,6,7,2,5,4,3]=>0000000=>0000000
[3,2,5,4,7,6,1,8]=>[8,1,6,7,4,5,2,3]=>0000000=>0000000
[2,3,4,5,7,6,1,8]=>[8,1,6,7,5,4,3,2]=>0000000=>0000000
[3,6,5,4,2,7,1,8]=>[8,1,7,2,4,5,6,3]=>0000000=>0000000
[3,5,6,4,2,7,1,8]=>[8,1,7,2,4,6,5,3]=>0000000=>0000000
[4,3,6,5,2,7,1,8]=>[8,1,7,2,5,6,3,4]=>0000000=>0000000
[3,4,6,5,2,7,1,8]=>[8,1,7,2,5,6,4,3]=>0000000=>0000000
[2,3,5,6,4,7,1,8]=>[8,1,7,4,6,5,3,2]=>0000000=>0000000
[3,2,4,6,5,7,1,8]=>[8,1,7,5,6,4,2,3]=>0000000=>0000000
[2,3,4,6,5,7,1,8]=>[8,1,7,5,6,4,3,2]=>0000000=>0000000
[3,5,4,2,6,7,1,8]=>[8,1,7,6,2,4,5,3]=>0000000=>0000000
[1,3,5,7,6,4,2,8]=>[8,2,4,6,7,5,3,1]=>0000000=>0000000
[1,3,5,6,7,4,2,8]=>[8,2,4,7,6,5,3,1]=>0000000=>0000000
[1,6,5,4,3,7,2,8]=>[8,2,7,3,4,5,6,1]=>0000000=>0000000
[1,3,4,6,5,7,2,8]=>[8,2,7,5,6,4,3,1]=>0000000=>0000000
[1,3,4,5,6,7,2,8]=>[8,2,7,6,5,4,3,1]=>0000000=>0000000
[2,1,6,5,4,7,3,8]=>[8,3,7,4,5,6,1,2]=>0000000=>0000000
[2,1,5,4,6,7,3,8]=>[8,3,7,6,4,5,1,2]=>0000000=>0000000
[2,3,1,5,6,7,4,8]=>[8,4,7,6,5,1,3,2]=>0000000=>0000000
[1,3,2,5,6,7,4,8]=>[8,4,7,6,5,2,3,1]=>0000000=>0000000
[2,1,3,5,7,6,4,8]=>[8,4,6,7,5,3,1,2]=>0000000=>0000000
[2,1,3,5,6,7,4,8]=>[8,4,7,6,5,3,1,2]=>0000000=>0000000
[4,3,2,1,7,6,5,8]=>[8,5,6,7,1,2,3,4]=>0000000=>0000000
[4,3,2,1,6,7,5,8]=>[8,5,7,6,1,2,3,4]=>0000000=>0000000
[3,2,4,1,7,6,5,8]=>[8,5,6,7,1,4,2,3]=>0000000=>0000000
[3,2,4,1,6,7,5,8]=>[8,5,7,6,1,4,2,3]=>0000000=>0000000
[2,3,4,1,7,6,5,8]=>[8,5,6,7,1,4,3,2]=>0000000=>0000000
[2,3,4,1,6,7,5,8]=>[8,5,7,6,1,4,3,2]=>0000000=>0000000
[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>0000000=>0000000
[1,4,3,2,6,7,5,8]=>[8,5,7,6,2,3,4,1]=>0000000=>0000000
[1,3,4,2,7,6,5,8]=>[8,5,6,7,2,4,3,1]=>0000000=>0000000
[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>0000000=>0000000
[1,2,4,3,7,6,5,8]=>[8,5,6,7,3,4,2,1]=>0000000=>0000000
[3,2,1,4,7,6,5,8]=>[8,5,6,7,4,1,2,3]=>0000000=>0000000
[1,3,2,4,7,6,5,8]=>[8,5,6,7,4,2,3,1]=>0000000=>0000000
[1,2,3,4,7,6,5,8]=>[8,5,6,7,4,3,2,1]=>0000000=>0000000
[5,4,3,2,1,7,6,8]=>[8,6,7,1,2,3,4,5]=>0000000=>0000000
[2,3,5,4,1,7,6,8]=>[8,6,7,1,4,5,3,2]=>0000000=>0000000
[4,3,2,5,1,7,6,8]=>[8,6,7,1,5,2,3,4]=>0000000=>0000000
[2,3,4,5,1,7,6,8]=>[8,6,7,1,5,4,3,2]=>0000000=>0000000
[1,5,4,3,2,7,6,8]=>[8,6,7,2,3,4,5,1]=>0000000=>0000000
[1,2,5,4,3,7,6,8]=>[8,6,7,3,4,5,2,1]=>0000000=>0000000
[3,2,1,5,4,7,6,8]=>[8,6,7,4,5,1,2,3]=>0000000=>0000000
[4,3,2,1,5,7,6,8]=>[8,6,7,5,1,2,3,4]=>0000000=>0000000
[3,2,4,1,5,7,6,8]=>[8,6,7,5,1,4,2,3]=>0000000=>0000000
[2,3,4,1,5,7,6,8]=>[8,6,7,5,1,4,3,2]=>0000000=>0000000
[1,4,3,2,5,7,6,8]=>[8,6,7,5,2,3,4,1]=>0000000=>0000000
[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>0000000=>0000000
[3,6,5,4,2,1,7,8]=>[8,7,1,2,4,5,6,3]=>0000000=>0000000
[3,2,5,6,4,1,7,8]=>[8,7,1,4,6,5,2,3]=>0000000=>0000000
[2,3,6,5,4,1,7,8]=>[8,7,1,4,5,6,3,2]=>0000000=>0000000
[4,3,2,6,5,1,7,8]=>[8,7,1,5,6,2,3,4]=>0000000=>0000000
[2,3,4,6,5,1,7,8]=>[8,7,1,5,6,4,3,2]=>0000000=>0000000
[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>0000000=>0000000
[2,3,1,6,5,4,7,8]=>[8,7,4,5,6,1,3,2]=>0000000=>0000000
[4,3,2,1,6,5,7,8]=>[8,7,5,6,1,2,3,4]=>0000000=>0000000
[3,2,4,1,6,5,7,8]=>[8,7,5,6,1,4,2,3]=>0000000=>0000000
[2,3,4,1,6,5,7,8]=>[8,7,5,6,1,4,3,2]=>0000000=>0000000
[1,4,3,2,6,5,7,8]=>[8,7,5,6,2,3,4,1]=>0000000=>0000000
[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>0000000=>0000000
[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>0000000=>0000000
[3,5,4,2,1,6,7,8]=>[8,7,6,1,2,4,5,3]=>0000000=>0000000
[2,5,4,3,1,6,7,8]=>[8,7,6,1,3,4,5,2]=>0000000=>0000000
[2,4,5,3,1,6,7,8]=>[8,7,6,1,3,5,4,2]=>0000000=>0000000
[3,2,5,4,1,6,7,8]=>[8,7,6,1,4,5,2,3]=>0000000=>0000000
[2,3,5,4,1,6,7,8]=>[8,7,6,1,4,5,3,2]=>0000000=>0000000
[2,4,3,5,1,6,7,8]=>[8,7,6,1,5,3,4,2]=>0000000=>0000000
[1,5,4,3,2,6,7,8]=>[8,7,6,2,3,4,5,1]=>0000000=>0000000
[2,1,5,4,3,6,7,8]=>[8,7,6,3,4,5,1,2]=>0000000=>0000000
[2,1,4,5,3,6,7,8]=>[8,7,6,3,5,4,1,2]=>0000000=>0000000
[1,2,5,4,3,6,7,8]=>[8,7,6,3,4,5,2,1]=>0000000=>0000000
[1,4,3,2,5,6,7,8]=>[8,7,6,5,2,3,4,1]=>0000000=>0000000
[1,2,3,5,8,6,7,4]=>[4,7,6,8,5,3,2,1]=>0000000=>0000000
[1,2,3,7,5,6,8,4]=>[4,8,6,5,7,3,2,1]=>0000000=>0000000
[1,2,3,8,5,6,7,4]=>[4,7,6,5,8,3,2,1]=>0000000=>0000000
[1,2,3,8,5,7,6,4]=>[4,6,7,5,8,3,2,1]=>0000000=>0000000
[1,2,3,8,6,5,7,4]=>[4,7,5,6,8,3,2,1]=>0000000=>0000000
[1,2,3,8,6,7,5,4]=>[4,5,7,6,8,3,2,1]=>0000000=>0000000
[1,2,5,4,8,6,7,3]=>[3,7,6,8,4,5,2,1]=>0000000=>0000000
[1,2,8,5,4,6,7,3]=>[3,7,6,4,5,8,2,1]=>0000000=>0000000
[1,2,8,5,4,7,6,3]=>[3,6,7,4,5,8,2,1]=>0000000=>0000000
[1,2,8,5,6,7,4,3]=>[3,4,7,6,5,8,2,1]=>0000000=>0000000
[1,2,8,6,5,7,4,3]=>[3,4,7,5,6,8,2,1]=>0000000=>0000000
[1,2,8,7,5,6,4,3]=>[3,4,6,5,7,8,2,1]=>0000000=>0000000
[1,3,4,8,6,5,7,2]=>[2,7,5,6,8,4,3,1]=>0000000=>0000000
[1,3,6,4,5,7,8,2]=>[2,8,7,5,4,6,3,1]=>0000000=>0000000
[1,3,6,4,5,8,7,2]=>[2,7,8,5,4,6,3,1]=>0000000=>0000000
[1,3,7,5,4,6,2,8]=>[8,2,6,4,5,7,3,1]=>0000000=>0000000
[1,3,8,5,6,7,4,2]=>[2,4,7,6,5,8,3,1]=>0000000=>0000000
[1,3,8,6,5,7,4,2]=>[2,4,7,5,6,8,3,1]=>0000000=>0000000
[1,4,3,8,6,5,7,2]=>[2,7,5,6,8,3,4,1]=>0000000=>0000000
[1,5,3,4,2,8,7,6]=>[6,7,8,2,4,3,5,1]=>0000000=>0000000
[1,8,3,7,5,6,4,2]=>[2,4,6,5,7,3,8,1]=>0000000=>0000000
[1,8,4,5,6,7,3,2]=>[2,3,7,6,5,4,8,1]=>0000000=>0000000
[1,8,4,6,5,3,7,2]=>[2,7,3,5,6,4,8,1]=>0000000=>0000000
[1,8,4,6,5,7,3,2]=>[2,3,7,5,6,4,8,1]=>0000000=>0000000
[1,8,5,4,3,6,7,2]=>[2,7,6,3,4,5,8,1]=>0000000=>0000000
[1,8,5,4,6,7,3,2]=>[2,3,7,6,4,5,8,1]=>0000000=>0000000
[1,8,5,4,7,6,3,2]=>[2,3,6,7,4,5,8,1]=>0000000=>0000000
[1,8,6,4,5,3,7,2]=>[2,7,3,5,4,6,8,1]=>0000000=>0000000
[1,8,6,4,5,7,3,2]=>[2,3,7,5,4,6,8,1]=>0000000=>0000000
[1,8,7,4,5,6,3,2]=>[2,3,6,5,4,7,8,1]=>0000000=>0000000
[1,8,6,5,4,7,3,2]=>[2,3,7,4,5,6,8,1]=>0000000=>0000000
[1,8,7,5,4,6,3,2]=>[2,3,6,4,5,7,8,1]=>0000000=>0000000
[1,8,7,5,6,4,3,2]=>[2,3,4,6,5,7,8,1]=>0000000=>0000000
[2,1,3,8,6,5,7,4]=>[4,7,5,6,8,3,1,2]=>0000000=>0000000
[2,1,4,3,8,6,7,5]=>[5,7,6,8,3,4,1,2]=>0000000=>0000000
[2,1,4,5,8,6,7,3]=>[3,7,6,8,5,4,1,2]=>0000000=>0000000
[2,1,5,4,8,6,7,3]=>[3,7,6,8,4,5,1,2]=>0000000=>0000000
[2,1,6,4,5,3,8,7]=>[7,8,3,5,4,6,1,2]=>0000000=>0000000
[2,1,6,4,5,7,8,3]=>[3,8,7,5,4,6,1,2]=>0000000=>0000000
[2,1,8,4,6,7,5,3]=>[3,5,7,6,4,8,1,2]=>0000000=>0000000
[2,1,8,5,4,7,6,3]=>[3,6,7,4,5,8,1,2]=>0000000=>0000000
[2,1,7,5,6,4,8,3]=>[3,8,4,6,5,7,1,2]=>0000000=>0000000
[2,1,8,5,6,4,7,3]=>[3,7,4,6,5,8,1,2]=>0000000=>0000000
[2,1,8,6,5,4,7,3]=>[3,7,4,5,6,8,1,2]=>0000000=>0000000
[2,1,8,7,5,6,4,3]=>[3,4,6,5,7,8,1,2]=>0000000=>0000000
[2,3,1,8,6,7,5,4]=>[4,5,7,6,8,1,3,2]=>0000000=>0000000
[2,3,4,1,8,6,7,5]=>[5,7,6,8,1,4,3,2]=>0000000=>0000000
[2,3,4,5,8,6,7,1]=>[1,7,6,8,5,4,3,2]=>1000000=>0000001
[2,3,4,8,5,6,7,1]=>[1,7,6,5,8,4,3,2]=>1000000=>0000001
[2,3,4,8,5,7,6,1]=>[1,6,7,5,8,4,3,2]=>1000000=>0000001
[2,3,4,8,6,5,7,1]=>[1,7,5,6,8,4,3,2]=>1000000=>0000001
[2,3,4,8,6,7,5,1]=>[1,5,7,6,8,4,3,2]=>1000000=>0000001
[2,3,6,4,5,1,8,7]=>[7,8,1,5,4,6,3,2]=>0000000=>0000000
[2,3,7,4,5,6,8,1]=>[1,8,6,5,4,7,3,2]=>1000000=>0000001
[2,3,7,4,6,5,8,1]=>[1,8,5,6,4,7,3,2]=>1000000=>0000001
[2,3,7,5,4,6,8,1]=>[1,8,6,4,5,7,3,2]=>1000000=>0000001
[2,3,8,5,4,6,7,1]=>[1,7,6,4,5,8,3,2]=>1000000=>0000001
[2,3,7,5,6,4,8,1]=>[1,8,4,6,5,7,3,2]=>1000000=>0000001
[2,3,8,5,6,7,4,1]=>[1,4,7,6,5,8,3,2]=>1000000=>0000001
[2,4,3,8,5,6,7,1]=>[1,7,6,5,8,3,4,2]=>1000000=>0000001
[2,5,3,4,1,6,7,8]=>[8,7,6,1,4,3,5,2]=>0000000=>0000000
[2,5,3,4,6,1,7,8]=>[8,7,1,6,4,3,5,2]=>0000000=>0000000
[2,5,3,4,8,7,6,1]=>[1,6,7,8,4,3,5,2]=>1000000=>0000001
[2,6,3,4,5,7,8,1]=>[1,8,7,5,4,3,6,2]=>1000000=>0000001
[2,6,3,4,5,8,7,1]=>[1,7,8,5,4,3,6,2]=>1000000=>0000001
[2,7,3,4,6,5,8,1]=>[1,8,5,6,4,3,7,2]=>1000000=>0000001
[2,6,3,5,4,1,8,7]=>[7,8,1,4,5,3,6,2]=>0000000=>0000000
[2,6,3,5,4,7,8,1]=>[1,8,7,4,5,3,6,2]=>1000000=>0000001
[2,6,3,5,4,8,7,1]=>[1,7,8,4,5,3,6,2]=>1000000=>0000001
[2,7,3,6,5,4,1,8]=>[8,1,4,5,6,3,7,2]=>0000000=>0000000
[2,5,4,3,8,6,7,1]=>[1,7,6,8,3,4,5,2]=>1000000=>0000001
[2,6,4,3,5,7,8,1]=>[1,8,7,5,3,4,6,2]=>1000000=>0000001
[2,6,4,5,3,7,8,1]=>[1,8,7,3,5,4,6,2]=>1000000=>0000001
[2,6,4,5,3,8,7,1]=>[1,7,8,3,5,4,6,2]=>1000000=>0000001
[2,7,4,5,6,3,8,1]=>[1,8,3,6,5,4,7,2]=>1000000=>0000001
[2,7,4,6,5,3,1,8]=>[8,1,3,5,6,4,7,2]=>0000000=>0000000
[2,7,4,6,5,3,8,1]=>[1,8,3,5,6,4,7,2]=>1000000=>0000001
[2,8,5,4,3,6,7,1]=>[1,7,6,3,4,5,8,2]=>1000000=>0000001
[2,8,5,4,3,7,6,1]=>[1,6,7,3,4,5,8,2]=>1000000=>0000001
[2,7,5,4,6,3,8,1]=>[1,8,3,6,4,5,7,2]=>1000000=>0000001
[2,8,5,4,7,6,3,1]=>[1,3,6,7,4,5,8,2]=>1000000=>0000001
[3,2,1,7,5,6,4,8]=>[8,4,6,5,7,1,2,3]=>0000000=>0000000
[3,2,4,1,8,6,7,5]=>[5,7,6,8,1,4,2,3]=>0000000=>0000000
[3,2,4,5,8,6,7,1]=>[1,7,6,8,5,4,2,3]=>1000000=>0000001
[3,2,4,8,5,7,6,1]=>[1,6,7,5,8,4,2,3]=>1000000=>0000001
[3,2,4,8,6,7,5,1]=>[1,5,7,6,8,4,2,3]=>1000000=>0000001
[3,2,5,4,8,6,7,1]=>[1,7,6,8,4,5,2,3]=>1000000=>0000001
[3,2,6,4,5,1,7,8]=>[8,7,1,5,4,6,2,3]=>0000000=>0000000
[3,2,6,4,5,1,8,7]=>[7,8,1,5,4,6,2,3]=>0000000=>0000000
[3,2,8,4,7,6,5,1]=>[1,5,6,7,4,8,2,3]=>1000000=>0000001
[3,2,7,5,4,6,1,8]=>[8,1,6,4,5,7,2,3]=>0000000=>0000000
[3,2,7,5,4,6,8,1]=>[1,8,6,4,5,7,2,3]=>1000000=>0000001
[3,2,7,5,6,4,8,1]=>[1,8,4,6,5,7,2,3]=>1000000=>0000001
[3,2,8,5,6,4,7,1]=>[1,7,4,6,5,8,2,3]=>1000000=>0000001
[4,2,3,1,6,5,8,7]=>[7,8,5,6,1,3,2,4]=>0000000=>0000000
[4,2,3,1,6,7,8,5]=>[5,8,7,6,1,3,2,4]=>0000000=>0000000
[4,2,3,1,7,6,8,5]=>[5,8,6,7,1,3,2,4]=>0000000=>0000000
[4,2,3,1,8,6,7,5]=>[5,7,6,8,1,3,2,4]=>0000000=>0000000
[4,2,3,1,8,7,6,5]=>[5,6,7,8,1,3,2,4]=>0000000=>0000000
[4,2,3,5,1,7,8,6]=>[6,8,7,1,5,3,2,4]=>0000000=>0000000
[4,2,3,5,1,8,7,6]=>[6,7,8,1,5,3,2,4]=>0000000=>0000000
[4,2,3,5,6,1,8,7]=>[7,8,1,6,5,3,2,4]=>0000000=>0000000
[5,2,3,4,1,8,7,6]=>[6,7,8,1,4,3,2,5]=>0000000=>0000000
[5,2,3,4,8,7,6,1]=>[1,6,7,8,4,3,2,5]=>1000000=>0000001
[7,2,3,4,6,5,1,8]=>[8,1,5,6,4,3,2,7]=>0000000=>0000000
[8,2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2,8]=>1000001=>1000001
[6,2,3,5,4,8,7,1]=>[1,7,8,4,5,3,2,6]=>1000000=>0000001
[7,2,3,6,5,4,1,8]=>[8,1,4,5,6,3,2,7]=>0000000=>0000000
[8,2,3,7,5,6,4,1]=>[1,4,6,5,7,3,2,8]=>1000001=>1000001
[5,2,4,3,1,6,7,8]=>[8,7,6,1,3,4,2,5]=>0000000=>0000000
[5,2,4,3,1,8,7,6]=>[6,7,8,1,3,4,2,5]=>0000000=>0000000
[5,2,4,3,6,7,8,1]=>[1,8,7,6,3,4,2,5]=>1000000=>0000001
[5,2,4,3,6,8,7,1]=>[1,7,8,6,3,4,2,5]=>1000000=>0000001
[5,2,4,3,7,6,1,8]=>[8,1,6,7,3,4,2,5]=>0000000=>0000000
[5,2,4,3,7,6,8,1]=>[1,8,6,7,3,4,2,5]=>1000000=>0000001
[7,2,4,3,6,5,8,1]=>[1,8,5,6,3,4,2,7]=>1000000=>0000001
[6,2,4,5,3,7,1,8]=>[8,1,7,3,5,4,2,6]=>0000000=>0000000
[7,2,4,5,3,6,8,1]=>[1,8,6,3,5,4,2,7]=>1000000=>0000001
[7,2,4,6,5,3,1,8]=>[8,1,3,5,6,4,2,7]=>0000000=>0000000
[8,2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2,8]=>1000001=>1000001
[8,2,7,4,5,6,3,1]=>[1,3,6,5,4,7,2,8]=>1000001=>1000001
[8,2,7,5,4,6,3,1]=>[1,3,6,4,5,7,2,8]=>1000001=>1000001
[8,2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2,8]=>1000001=>1000001
[4,3,2,1,8,6,7,5]=>[5,7,6,8,1,2,3,4]=>0000000=>0000000
[4,3,2,7,5,6,8,1]=>[1,8,6,5,7,2,3,4]=>1000000=>0000001
[4,3,2,8,5,6,7,1]=>[1,7,6,5,8,2,3,4]=>1000000=>0000001
[5,3,2,4,1,8,7,6]=>[6,7,8,1,4,2,3,5]=>0000000=>0000000
[5,3,2,4,7,6,1,8]=>[8,1,6,7,4,2,3,5]=>0000000=>0000000
[5,3,2,4,7,6,8,1]=>[1,8,6,7,4,2,3,5]=>1000000=>0000001
[5,3,2,4,8,6,7,1]=>[1,7,6,8,4,2,3,5]=>1000000=>0000001
[5,3,2,4,8,7,6,1]=>[1,6,7,8,4,2,3,5]=>1000000=>0000001
[7,3,2,4,6,5,8,1]=>[1,8,5,6,4,2,3,7]=>1000000=>0000001
[8,3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3,8]=>1000001=>1000001
[8,3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3,8]=>1000001=>1000001
[6,3,2,5,4,1,8,7]=>[7,8,1,4,5,2,3,6]=>0000000=>0000000
[6,3,2,5,4,7,1,8]=>[8,1,7,4,5,2,3,6]=>0000000=>0000000
[6,3,2,5,4,7,8,1]=>[1,8,7,4,5,2,3,6]=>1000000=>0000001
[7,3,2,5,4,6,1,8]=>[8,1,6,4,5,2,3,7]=>0000000=>0000000
[7,3,2,5,4,6,8,1]=>[1,8,6,4,5,2,3,7]=>1000000=>0000001
[8,3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3,8]=>1000001=>1000001
[8,3,2,7,5,6,4,1]=>[1,4,6,5,7,2,3,8]=>1000001=>1000001
[8,3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3,8]=>1000001=>1000001
[5,3,4,2,1,7,8,6]=>[6,8,7,1,2,4,3,5]=>0000000=>0000000
[5,3,4,2,1,8,7,6]=>[6,7,8,1,2,4,3,5]=>0000000=>0000000
[5,3,4,2,6,1,8,7]=>[7,8,1,6,2,4,3,5]=>0000000=>0000000
[5,3,4,2,7,6,8,1]=>[1,8,6,7,2,4,3,5]=>1000000=>0000001
[5,3,4,2,8,6,7,1]=>[1,7,6,8,2,4,3,5]=>1000000=>0000001
[5,3,4,2,8,7,6,1]=>[1,6,7,8,2,4,3,5]=>1000000=>0000001
[6,3,4,2,5,1,8,7]=>[7,8,1,5,2,4,3,6]=>0000000=>0000000
[7,3,4,2,6,5,1,8]=>[8,1,5,6,2,4,3,7]=>0000000=>0000000
[7,3,4,2,6,5,8,1]=>[1,8,5,6,2,4,3,7]=>1000000=>0000001
[7,3,4,6,5,2,1,8]=>[8,1,2,5,6,4,3,7]=>0000000=>0000000
[7,3,4,6,5,2,8,1]=>[1,8,2,5,6,4,3,7]=>1000000=>0000001
[8,3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3,8]=>1100001=>1000011
[6,3,5,4,2,1,7,8]=>[8,7,1,2,4,5,3,6]=>0000000=>0000000
[6,3,5,4,2,7,1,8]=>[8,1,7,2,4,5,3,6]=>0000000=>0000000
[6,3,5,4,2,8,7,1]=>[1,7,8,2,4,5,3,6]=>1000000=>0000001
[7,3,5,4,6,2,1,8]=>[8,1,2,6,4,5,3,7]=>0000000=>0000000
[7,3,6,4,5,2,1,8]=>[8,1,2,5,4,6,3,7]=>0000000=>0000000
[8,3,7,4,6,5,2,1]=>[1,2,5,6,4,7,3,8]=>1100001=>1000011
[7,3,6,5,4,2,1,8]=>[8,1,2,4,5,6,3,7]=>0000000=>0000000
[5,4,3,2,8,6,7,1]=>[1,7,6,8,2,3,4,5]=>1000000=>0000001
[7,4,3,2,6,5,8,1]=>[1,8,5,6,2,3,4,7]=>1000000=>0000001
[8,4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4,8]=>1000001=>1000001
[6,4,3,5,2,1,8,7]=>[7,8,1,2,5,3,4,6]=>0000000=>0000000
[7,4,3,6,5,2,1,8]=>[8,1,2,5,6,3,4,7]=>0000000=>0000000
[7,4,3,6,5,2,8,1]=>[1,8,2,5,6,3,4,7]=>1000000=>0000001
[8,4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4,8]=>1000001=>1000001
[6,5,3,4,2,1,8,7]=>[7,8,1,2,4,3,5,6]=>0000000=>0000000
[8,6,3,5,4,2,7,1]=>[1,7,2,4,5,3,6,8]=>1000001=>1000001
[8,7,3,5,4,6,2,1]=>[1,2,6,4,5,3,7,8]=>1100011=>1100011
[8,7,3,6,5,4,2,1]=>[1,2,4,5,6,3,7,8]=>1100011=>1100011
[8,5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5,8]=>1000001=>1000001
[8,7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7,8]=>1100011=>1100011
[8,7,4,6,5,3,2,1]=>[1,2,3,5,6,4,7,8]=>1110011=>1100111
[2,4,1,3,6,5,8,7]=>[7,8,5,6,3,1,4,2]=>0000000=>0000000
[2,1,4,6,3,5,8,7]=>[7,8,5,3,6,4,1,2]=>0000000=>0000000
[2,4,6,1,3,5,8,7]=>[7,8,5,3,1,6,4,2]=>0000000=>0000000
[2,1,4,3,6,8,5,7]=>[7,5,8,6,3,4,1,2]=>0000000=>0000000
[2,4,1,3,6,8,5,7]=>[7,5,8,6,3,1,4,2]=>0000000=>0000000
[2,4,1,6,8,3,5,7]=>[7,5,3,8,6,1,4,2]=>0000000=>0000000
[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>0000000=>0000000
[2,4,6,1,3,5,7,8]=>[8,7,5,3,1,6,4,2]=>0000000=>0000000
[2,4,1,6,3,7,5,8]=>[8,5,7,3,6,1,4,2]=>0000000=>0000000
[2,4,1,6,7,3,5,8]=>[8,5,3,7,6,1,4,2]=>0000000=>0000000
[2,4,1,3,6,7,8,5]=>[5,8,7,6,3,1,4,2]=>0000000=>0000000
[2,4,1,6,3,7,8,5]=>[5,8,7,3,6,1,4,2]=>0000000=>0000000
[2,4,6,1,3,7,8,5]=>[5,8,7,3,1,6,4,2]=>0000000=>0000000
[2,4,1,6,7,3,8,5]=>[5,8,3,7,6,1,4,2]=>0000000=>0000000
[2,4,6,1,7,3,8,5]=>[5,8,3,7,1,6,4,2]=>0000000=>0000000
[2,4,6,7,1,3,8,5]=>[5,8,3,1,7,6,4,2]=>0000000=>0000000
[2,4,6,1,7,8,3,5]=>[5,3,8,7,1,6,4,2]=>0000000=>0000000
[2,4,6,7,1,8,3,5]=>[5,3,8,1,7,6,4,2]=>0000000=>0000000
[2,4,6,7,8,1,3,5]=>[5,3,1,8,7,6,4,2]=>0000000=>0000000
[2,1,4,3,7,5,8,6]=>[6,8,5,7,3,4,1,2]=>0000000=>0000000
[2,4,1,3,7,5,8,6]=>[6,8,5,7,3,1,4,2]=>0000000=>0000000
[2,4,7,1,3,5,8,6]=>[6,8,5,3,1,7,4,2]=>0000000=>0000000
[2,1,4,3,7,8,5,6]=>[6,5,8,7,3,4,1,2]=>0000000=>0000000
[2,4,1,3,7,8,5,6]=>[6,5,8,7,3,1,4,2]=>0000000=>0000000
[2,4,1,7,8,3,5,6]=>[6,5,3,8,7,1,4,2]=>0000000=>0000000
[2,4,7,8,1,3,5,6]=>[6,5,3,1,8,7,4,2]=>0000000=>0000000
[2,4,5,1,7,3,6,8]=>[8,6,3,7,1,5,4,2]=>0000000=>0000000
[2,4,5,7,1,3,6,8]=>[8,6,3,1,7,5,4,2]=>0000000=>0000000
[2,4,1,5,3,7,8,6]=>[6,8,7,3,5,1,4,2]=>0000000=>0000000
[2,4,5,1,3,7,8,6]=>[6,8,7,3,1,5,4,2]=>0000000=>0000000
[2,4,1,5,7,3,8,6]=>[6,8,3,7,5,1,4,2]=>0000000=>0000000
[2,4,5,7,1,3,8,6]=>[6,8,3,1,7,5,4,2]=>0000000=>0000000
[2,4,5,7,8,1,3,6]=>[6,3,1,8,7,5,4,2]=>0000000=>0000000
[2,1,4,3,8,5,6,7]=>[7,6,5,8,3,4,1,2]=>0000000=>0000000
[2,4,1,3,8,5,6,7]=>[7,6,5,8,3,1,4,2]=>0000000=>0000000
[2,1,4,5,8,3,6,7]=>[7,6,3,8,5,4,1,2]=>0000000=>0000000
[2,4,5,6,1,3,8,7]=>[7,8,3,1,6,5,4,2]=>0000000=>0000000
[2,1,4,5,6,8,3,7]=>[7,3,8,6,5,4,1,2]=>0000000=>0000000
[2,4,5,1,6,8,3,7]=>[7,3,8,6,1,5,4,2]=>0000000=>0000000
[2,4,5,6,1,8,3,7]=>[7,3,8,1,6,5,4,2]=>0000000=>0000000
[2,4,1,5,3,6,7,8]=>[8,7,6,3,5,1,4,2]=>0000000=>0000000
[2,4,1,5,6,7,3,8]=>[8,3,7,6,5,1,4,2]=>0000000=>0000000
[2,4,5,6,1,7,3,8]=>[8,3,7,1,6,5,4,2]=>0000000=>0000000
[2,4,5,6,7,1,3,8]=>[8,3,1,7,6,5,4,2]=>0000000=>0000000
[2,4,5,1,6,7,8,3]=>[3,8,7,6,1,5,4,2]=>0000000=>0000000
[2,4,5,6,1,7,8,3]=>[3,8,7,1,6,5,4,2]=>0000000=>0000000
[2,4,5,6,7,1,8,3]=>[3,8,1,7,6,5,4,2]=>0000000=>0000000
[2,4,5,6,7,8,1,3]=>[3,1,8,7,6,5,4,2]=>0000000=>0000000
[2,1,5,3,6,4,8,7]=>[7,8,4,6,3,5,1,2]=>0000000=>0000000
[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]=>0000000=>0000000
[2,1,5,3,6,8,4,7]=>[7,4,8,6,3,5,1,2]=>0000000=>0000000
[2,5,6,1,3,8,4,7]=>[7,4,8,3,1,6,5,2]=>0000000=>0000000
[2,5,1,6,8,3,4,7]=>[7,4,3,8,6,1,5,2]=>0000000=>0000000
[2,5,6,1,8,3,4,7]=>[7,4,3,8,1,6,5,2]=>0000000=>0000000
[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]=>0000000=>0000000
[2,1,5,6,3,7,4,8]=>[8,4,7,3,6,5,1,2]=>0000000=>0000000
[2,5,1,6,7,3,4,8]=>[8,4,3,7,6,1,5,2]=>0000000=>0000000
[2,5,6,1,7,3,4,8]=>[8,4,3,7,1,6,5,2]=>0000000=>0000000
[2,5,6,7,1,3,4,8]=>[8,4,3,1,7,6,5,2]=>0000000=>0000000
[2,5,1,3,6,7,8,4]=>[4,8,7,6,3,1,5,2]=>0000000=>0000000
[2,1,5,6,3,7,8,4]=>[4,8,7,3,6,5,1,2]=>0000000=>0000000
[2,5,1,6,3,7,8,4]=>[4,8,7,3,6,1,5,2]=>0000000=>0000000
[2,5,6,1,3,7,8,4]=>[4,8,7,3,1,6,5,2]=>0000000=>0000000
[2,5,1,6,7,3,8,4]=>[4,8,3,7,6,1,5,2]=>0000000=>0000000
[2,5,6,1,7,3,8,4]=>[4,8,3,7,1,6,5,2]=>0000000=>0000000
[2,5,6,7,1,3,8,4]=>[4,8,3,1,7,6,5,2]=>0000000=>0000000
[2,1,5,6,7,8,3,4]=>[4,3,8,7,6,5,1,2]=>0000000=>0000000
[2,5,1,6,7,8,3,4]=>[4,3,8,7,6,1,5,2]=>0000000=>0000000
[2,5,6,1,7,8,3,4]=>[4,3,8,7,1,6,5,2]=>0000000=>0000000
[2,5,6,7,1,8,3,4]=>[4,3,8,1,7,6,5,2]=>0000000=>0000000
[2,5,6,7,8,1,3,4]=>[4,3,1,8,7,6,5,2]=>0000000=>0000000
[2,1,5,3,7,4,8,6]=>[6,8,4,7,3,5,1,2]=>0000000=>0000000
[2,5,1,3,7,4,8,6]=>[6,8,4,7,3,1,5,2]=>0000000=>0000000
[2,5,1,7,3,4,8,6]=>[6,8,4,3,7,1,5,2]=>0000000=>0000000
[2,1,5,7,3,8,4,6]=>[6,4,8,3,7,5,1,2]=>0000000=>0000000
[2,5,1,7,3,8,4,6]=>[6,4,8,3,7,1,5,2]=>0000000=>0000000
[2,1,5,7,8,3,4,6]=>[6,4,3,8,7,5,1,2]=>0000000=>0000000
[2,5,1,7,8,3,4,6]=>[6,4,3,8,7,1,5,2]=>0000000=>0000000
[2,5,1,3,7,4,6,8]=>[8,6,4,7,3,1,5,2]=>0000000=>0000000
[2,3,5,1,4,7,6,8]=>[8,6,7,4,1,5,3,2]=>0000000=>0000000
[2,1,3,5,7,4,6,8]=>[8,6,4,7,5,3,1,2]=>0000000=>0000000
[2,3,5,7,1,4,6,8]=>[8,6,4,1,7,5,3,2]=>0000000=>0000000
[2,1,3,5,7,4,8,6]=>[6,8,4,7,5,3,1,2]=>0000000=>0000000
[2,3,1,5,7,4,8,6]=>[6,8,4,7,5,1,3,2]=>0000000=>0000000
[2,3,5,1,7,4,8,6]=>[6,8,4,7,1,5,3,2]=>0000000=>0000000
[2,3,5,7,1,4,8,6]=>[6,8,4,1,7,5,3,2]=>0000000=>0000000
[2,1,3,5,7,8,4,6]=>[6,4,8,7,5,3,1,2]=>0000000=>0000000
[2,3,5,7,1,8,4,6]=>[6,4,8,1,7,5,3,2]=>0000000=>0000000
[2,3,5,7,8,1,4,6]=>[6,4,1,8,7,5,3,2]=>0000000=>0000000
[2,5,1,3,8,4,6,7]=>[7,6,4,8,3,1,5,2]=>0000000=>0000000
[2,3,1,5,8,4,6,7]=>[7,6,4,8,5,1,3,2]=>0000000=>0000000
[2,3,5,6,1,4,8,7]=>[7,8,4,1,6,5,3,2]=>0000000=>0000000
[2,3,5,6,1,8,4,7]=>[7,4,8,1,6,5,3,2]=>0000000=>0000000
[2,3,5,6,8,1,4,7]=>[7,4,1,8,6,5,3,2]=>0000000=>0000000
[2,3,5,1,6,4,7,8]=>[8,7,4,6,1,5,3,2]=>0000000=>0000000
[2,3,5,6,1,4,7,8]=>[8,7,4,1,6,5,3,2]=>0000000=>0000000
[2,3,5,6,1,7,4,8]=>[8,4,7,1,6,5,3,2]=>0000000=>0000000
[2,3,5,6,7,1,4,8]=>[8,4,1,7,6,5,3,2]=>0000000=>0000000
[2,3,5,1,6,7,8,4]=>[4,8,7,6,1,5,3,2]=>0000000=>0000000
[2,3,5,6,1,7,8,4]=>[4,8,7,1,6,5,3,2]=>0000000=>0000000
[2,3,5,6,7,1,8,4]=>[4,8,1,7,6,5,3,2]=>0000000=>0000000
[2,3,5,6,7,8,1,4]=>[4,1,8,7,6,5,3,2]=>0000000=>0000000
[2,1,6,3,7,4,8,5]=>[5,8,4,7,3,6,1,2]=>0000000=>0000000
[2,6,1,3,7,4,8,5]=>[5,8,4,7,3,1,6,2]=>0000000=>0000000
[2,6,7,1,3,4,8,5]=>[5,8,4,3,1,7,6,2]=>0000000=>0000000
[2,1,6,7,8,3,4,5]=>[5,4,3,8,7,6,1,2]=>0000000=>0000000
[2,6,7,1,8,3,4,5]=>[5,4,3,8,1,7,6,2]=>0000000=>0000000
[2,1,6,3,4,7,5,8]=>[8,5,7,4,3,6,1,2]=>0000000=>0000000
[2,3,1,6,4,7,5,8]=>[8,5,7,4,6,1,3,2]=>0000000=>0000000
[2,3,6,1,4,7,5,8]=>[8,5,7,4,1,6,3,2]=>0000000=>0000000
[2,3,1,6,7,4,5,8]=>[8,5,4,7,6,1,3,2]=>0000000=>0000000
[2,3,6,7,1,4,5,8]=>[8,5,4,1,7,6,3,2]=>0000000=>0000000
[2,1,6,3,4,7,8,5]=>[5,8,7,4,3,6,1,2]=>0000000=>0000000
[2,3,1,6,4,7,8,5]=>[5,8,7,4,6,1,3,2]=>0000000=>0000000
[2,3,6,1,4,7,8,5]=>[5,8,7,4,1,6,3,2]=>0000000=>0000000
[2,1,3,6,7,4,8,5]=>[5,8,4,7,6,3,1,2]=>0000000=>0000000
[2,3,6,1,7,4,8,5]=>[5,8,4,7,1,6,3,2]=>0000000=>0000000
[2,1,3,6,7,8,4,5]=>[5,4,8,7,6,3,1,2]=>0000000=>0000000
[2,3,6,1,7,8,4,5]=>[5,4,8,7,1,6,3,2]=>0000000=>0000000
[2,3,6,7,8,1,4,5]=>[5,4,1,8,7,6,3,2]=>0000000=>0000000
[2,1,6,3,4,8,5,7]=>[7,5,8,4,3,6,1,2]=>0000000=>0000000
[2,3,1,6,4,8,5,7]=>[7,5,8,4,6,1,3,2]=>0000000=>0000000
[2,3,6,1,4,8,5,7]=>[7,5,8,4,1,6,3,2]=>0000000=>0000000
[2,1,3,6,8,4,5,7]=>[7,5,4,8,6,3,1,2]=>0000000=>0000000
[2,3,6,1,4,5,8,7]=>[7,8,5,4,1,6,3,2]=>0000000=>0000000
[2,3,4,6,1,5,8,7]=>[7,8,5,1,6,4,3,2]=>0000000=>0000000
[2,3,4,1,6,8,5,7]=>[7,5,8,6,1,4,3,2]=>0000000=>0000000
[2,3,4,6,1,8,5,7]=>[7,5,8,1,6,4,3,2]=>0000000=>0000000
[2,3,4,6,8,1,5,7]=>[7,5,1,8,6,4,3,2]=>0000000=>0000000
[2,6,1,3,4,5,7,8]=>[8,7,5,4,3,1,6,2]=>0000000=>0000000
[2,3,6,1,4,5,7,8]=>[8,7,5,4,1,6,3,2]=>0000000=>0000000
[2,3,4,6,1,5,7,8]=>[8,7,5,1,6,4,3,2]=>0000000=>0000000
[2,3,4,6,1,7,5,8]=>[8,5,7,1,6,4,3,2]=>0000000=>0000000
[2,3,4,6,7,1,5,8]=>[8,5,1,7,6,4,3,2]=>0000000=>0000000
[2,3,4,6,1,7,8,5]=>[5,8,7,1,6,4,3,2]=>0000000=>0000000
[2,3,4,6,7,1,8,5]=>[5,8,1,7,6,4,3,2]=>0000000=>0000000
[2,3,4,6,7,8,1,5]=>[5,1,8,7,6,4,3,2]=>0000000=>0000000
[2,1,7,8,3,4,5,6]=>[6,5,4,3,8,7,1,2]=>0000000=>0000000
[2,7,1,8,3,4,5,6]=>[6,5,4,3,8,1,7,2]=>0000000=>0000000
[2,7,8,1,3,4,5,6]=>[6,5,4,3,1,8,7,2]=>0000000=>0000000
[2,7,1,3,4,8,5,6]=>[6,5,8,4,3,1,7,2]=>0000000=>0000000
[2,3,1,7,8,4,5,6]=>[6,5,4,8,7,1,3,2]=>0000000=>0000000
[2,7,1,3,4,5,8,6]=>[6,8,5,4,3,1,7,2]=>0000000=>0000000
[2,3,4,1,7,5,8,6]=>[6,8,5,7,1,4,3,2]=>0000000=>0000000
[2,3,4,7,1,5,8,6]=>[6,8,5,1,7,4,3,2]=>0000000=>0000000
[2,1,3,4,7,8,5,6]=>[6,5,8,7,4,3,1,2]=>0000000=>0000000
[2,3,1,4,7,8,5,6]=>[6,5,8,7,4,1,3,2]=>0000000=>0000000
[2,3,4,1,7,8,5,6]=>[6,5,8,7,1,4,3,2]=>0000000=>0000000
[2,3,4,7,1,8,5,6]=>[6,5,8,1,7,4,3,2]=>0000000=>0000000
[2,3,4,7,8,1,5,6]=>[6,5,1,8,7,4,3,2]=>0000000=>0000000
[2,7,1,3,4,5,6,8]=>[8,6,5,4,3,1,7,2]=>0000000=>0000000
[2,3,4,1,7,5,6,8]=>[8,6,5,7,1,4,3,2]=>0000000=>0000000
[2,3,4,7,1,5,6,8]=>[8,6,5,1,7,4,3,2]=>0000000=>0000000
[2,3,4,5,7,1,6,8]=>[8,6,1,7,5,4,3,2]=>0000000=>0000000
[2,3,4,5,7,1,8,6]=>[6,8,1,7,5,4,3,2]=>0000000=>0000000
[2,3,4,5,7,8,1,6]=>[6,1,8,7,5,4,3,2]=>0000000=>0000000
[2,1,3,4,8,5,6,7]=>[7,6,5,8,4,3,1,2]=>0000000=>0000000
[2,3,1,4,8,5,6,7]=>[7,6,5,8,4,1,3,2]=>0000000=>0000000
[2,3,4,1,8,5,6,7]=>[7,6,5,8,1,4,3,2]=>0000000=>0000000
[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]=>0000000=>0000000
[2,3,4,1,5,8,6,7]=>[7,6,8,5,1,4,3,2]=>0000000=>0000000
[2,3,4,5,1,8,6,7]=>[7,6,8,1,5,4,3,2]=>0000000=>0000000
[2,3,4,5,8,1,6,7]=>[7,6,1,8,5,4,3,2]=>0000000=>0000000
[2,3,4,5,6,8,1,7]=>[7,1,8,6,5,4,3,2]=>0000000=>0000000
[3,1,4,2,6,5,8,7]=>[7,8,5,6,2,4,1,3]=>0000000=>0000000
[3,4,1,2,6,5,8,7]=>[7,8,5,6,2,1,4,3]=>0000000=>0000000
[3,4,6,1,2,5,8,7]=>[7,8,5,2,1,6,4,3]=>0000000=>0000000
[3,1,4,2,6,8,5,7]=>[7,5,8,6,2,4,1,3]=>0000000=>0000000
[3,4,1,2,6,8,5,7]=>[7,5,8,6,2,1,4,3]=>0000000=>0000000
[3,1,4,6,2,8,5,7]=>[7,5,8,2,6,4,1,3]=>0000000=>0000000
[3,4,1,6,2,8,5,7]=>[7,5,8,2,6,1,4,3]=>0000000=>0000000
[3,4,6,1,2,8,5,7]=>[7,5,8,2,1,6,4,3]=>0000000=>0000000
[3,1,4,6,8,2,5,7]=>[7,5,2,8,6,4,1,3]=>0000000=>0000000
[3,4,1,2,6,5,7,8]=>[8,7,5,6,2,1,4,3]=>0000000=>0000000
[3,4,6,1,2,5,7,8]=>[8,7,5,2,1,6,4,3]=>0000000=>0000000
[3,4,1,2,6,7,5,8]=>[8,5,7,6,2,1,4,3]=>0000000=>0000000
[3,4,1,6,2,7,5,8]=>[8,5,7,2,6,1,4,3]=>0000000=>0000000
[3,4,6,1,2,7,5,8]=>[8,5,7,2,1,6,4,3]=>0000000=>0000000
[3,1,4,2,6,7,8,5]=>[5,8,7,6,2,4,1,3]=>0000000=>0000000
[3,4,1,2,6,7,8,5]=>[5,8,7,6,2,1,4,3]=>0000000=>0000000
[3,1,4,6,2,7,8,5]=>[5,8,7,2,6,4,1,3]=>0000000=>0000000
[3,4,1,6,2,7,8,5]=>[5,8,7,2,6,1,4,3]=>0000000=>0000000
[3,4,6,1,2,7,8,5]=>[5,8,7,2,1,6,4,3]=>0000000=>0000000
[3,4,1,6,7,2,8,5]=>[5,8,2,7,6,1,4,3]=>0000000=>0000000
[3,4,6,1,7,2,8,5]=>[5,8,2,7,1,6,4,3]=>0000000=>0000000
[3,4,6,7,1,2,8,5]=>[5,8,2,1,7,6,4,3]=>0000000=>0000000
[3,1,4,6,7,8,2,5]=>[5,2,8,7,6,4,1,3]=>0000000=>0000000
[3,4,1,6,7,8,2,5]=>[5,2,8,7,6,1,4,3]=>0000000=>0000000
[3,4,6,1,7,8,2,5]=>[5,2,8,7,1,6,4,3]=>0000000=>0000000
[3,4,6,7,1,8,2,5]=>[5,2,8,1,7,6,4,3]=>0000000=>0000000
[3,1,4,2,7,5,8,6]=>[6,8,5,7,2,4,1,3]=>0000000=>0000000
[3,4,1,2,7,5,8,6]=>[6,8,5,7,2,1,4,3]=>0000000=>0000000
[3,1,4,7,2,5,8,6]=>[6,8,5,2,7,4,1,3]=>0000000=>0000000
[3,4,1,7,2,5,8,6]=>[6,8,5,2,7,1,4,3]=>0000000=>0000000
[3,1,4,2,7,8,5,6]=>[6,5,8,7,2,4,1,3]=>0000000=>0000000
[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]=>0000000=>0000000
[3,1,4,7,2,8,5,6]=>[6,5,8,2,7,4,1,3]=>0000000=>0000000
[3,4,1,7,2,8,5,6]=>[6,5,8,2,7,1,4,3]=>0000000=>0000000
[3,4,7,1,2,8,5,6]=>[6,5,8,2,1,7,4,3]=>0000000=>0000000
[3,4,7,1,8,2,5,6]=>[6,5,2,8,1,7,4,3]=>0000000=>0000000
[3,1,4,2,7,5,6,8]=>[8,6,5,7,2,4,1,3]=>0000000=>0000000
[3,4,1,2,7,5,6,8]=>[8,6,5,7,2,1,4,3]=>0000000=>0000000
[3,4,1,7,2,5,6,8]=>[8,6,5,2,7,1,4,3]=>0000000=>0000000
[3,4,7,1,2,5,6,8]=>[8,6,5,2,1,7,4,3]=>0000000=>0000000
[3,4,1,2,5,7,6,8]=>[8,6,7,5,2,1,4,3]=>0000000=>0000000
[3,1,4,2,5,7,8,6]=>[6,8,7,5,2,4,1,3]=>0000000=>0000000
[3,4,1,2,5,7,8,6]=>[6,8,7,5,2,1,4,3]=>0000000=>0000000
[3,4,5,1,2,7,8,6]=>[6,8,7,2,1,5,4,3]=>0000000=>0000000
[3,1,4,5,7,2,8,6]=>[6,8,2,7,5,4,1,3]=>0000000=>0000000
[3,4,1,5,7,2,8,6]=>[6,8,2,7,5,1,4,3]=>0000000=>0000000
[3,4,5,7,1,2,8,6]=>[6,8,2,1,7,5,4,3]=>0000000=>0000000
[3,1,4,5,7,8,2,6]=>[6,2,8,7,5,4,1,3]=>0000000=>0000000
[3,4,1,5,7,8,2,6]=>[6,2,8,7,5,1,4,3]=>0000000=>0000000
[3,4,5,7,1,8,2,6]=>[6,2,8,1,7,5,4,3]=>0000000=>0000000
[3,4,5,7,8,1,2,6]=>[6,2,1,8,7,5,4,3]=>0000000=>0000000
[3,1,4,2,8,5,6,7]=>[7,6,5,8,2,4,1,3]=>0000000=>0000000
[3,4,1,2,8,5,6,7]=>[7,6,5,8,2,1,4,3]=>0000000=>0000000
[3,1,4,8,2,5,6,7]=>[7,6,5,2,8,4,1,3]=>0000000=>0000000
[3,4,8,1,2,5,6,7]=>[7,6,5,2,1,8,4,3]=>0000000=>0000000
[3,4,1,2,5,8,6,7]=>[7,6,8,5,2,1,4,3]=>0000000=>0000000
[3,4,1,2,5,6,8,7]=>[7,8,6,5,2,1,4,3]=>0000000=>0000000
[3,1,4,5,6,2,8,7]=>[7,8,2,6,5,4,1,3]=>0000000=>0000000
[3,4,1,5,6,2,8,7]=>[7,8,2,6,5,1,4,3]=>0000000=>0000000
[3,4,5,1,6,2,8,7]=>[7,8,2,6,1,5,4,3]=>0000000=>0000000
[3,1,4,5,6,8,2,7]=>[7,2,8,6,5,4,1,3]=>0000000=>0000000
[3,4,1,5,6,8,2,7]=>[7,2,8,6,5,1,4,3]=>0000000=>0000000
[3,4,5,6,1,8,2,7]=>[7,2,8,1,6,5,4,3]=>0000000=>0000000
[3,1,4,2,5,6,7,8]=>[8,7,6,5,2,4,1,3]=>0000000=>0000000
[3,4,1,5,6,2,7,8]=>[8,7,2,6,5,1,4,3]=>0000000=>0000000
[3,1,4,5,6,7,2,8]=>[8,2,7,6,5,4,1,3]=>0000000=>0000000
[3,4,1,5,6,7,2,8]=>[8,2,7,6,5,1,4,3]=>0000000=>0000000
[3,4,5,6,1,7,2,8]=>[8,2,7,1,6,5,4,3]=>0000000=>0000000
[3,1,4,5,6,7,8,2]=>[2,8,7,6,5,4,1,3]=>0000000=>0000000
[3,4,1,5,6,7,8,2]=>[2,8,7,6,5,1,4,3]=>0000000=>0000000
[3,4,5,1,6,7,8,2]=>[2,8,7,6,1,5,4,3]=>0000000=>0000000
[3,4,5,6,1,7,8,2]=>[2,8,7,1,6,5,4,3]=>0000000=>0000000
[3,4,5,6,7,1,8,2]=>[2,8,1,7,6,5,4,3]=>0000000=>0000000
[3,1,5,2,6,4,8,7]=>[7,8,4,6,2,5,1,3]=>0000000=>0000000
[3,5,1,6,2,4,8,7]=>[7,8,4,2,6,1,5,3]=>0000000=>0000000
[3,5,6,1,2,4,8,7]=>[7,8,4,2,1,6,5,3]=>0000000=>0000000
[3,1,5,6,2,8,4,7]=>[7,4,8,2,6,5,1,3]=>0000000=>0000000
[3,5,1,6,2,8,4,7]=>[7,4,8,2,6,1,5,3]=>0000000=>0000000
[3,1,5,6,8,2,4,7]=>[7,4,2,8,6,5,1,3]=>0000000=>0000000
[3,5,6,1,8,2,4,7]=>[7,4,2,8,1,6,5,3]=>0000000=>0000000
[3,5,6,8,1,2,4,7]=>[7,4,2,1,8,6,5,3]=>0000000=>0000000
[3,1,5,2,6,7,4,8]=>[8,4,7,6,2,5,1,3]=>0000000=>0000000
[3,5,1,2,6,7,4,8]=>[8,4,7,6,2,1,5,3]=>0000000=>0000000
[3,5,1,6,7,2,4,8]=>[8,4,2,7,6,1,5,3]=>0000000=>0000000
[3,5,6,1,7,2,4,8]=>[8,4,2,7,1,6,5,3]=>0000000=>0000000
[3,5,6,7,1,2,4,8]=>[8,4,2,1,7,6,5,3]=>0000000=>0000000
[3,5,1,6,2,7,8,4]=>[4,8,7,2,6,1,5,3]=>0000000=>0000000
[3,5,6,1,2,7,8,4]=>[4,8,7,2,1,6,5,3]=>0000000=>0000000
[3,1,5,6,7,2,8,4]=>[4,8,2,7,6,5,1,3]=>0000000=>0000000
[3,5,1,6,7,2,8,4]=>[4,8,2,7,6,1,5,3]=>0000000=>0000000
[3,5,6,1,7,2,8,4]=>[4,8,2,7,1,6,5,3]=>0000000=>0000000
[3,5,6,7,1,2,8,4]=>[4,8,2,1,7,6,5,3]=>0000000=>0000000
[3,1,5,6,7,8,2,4]=>[4,2,8,7,6,5,1,3]=>0000000=>0000000
[3,5,6,1,7,8,2,4]=>[4,2,8,7,1,6,5,3]=>0000000=>0000000
[3,5,6,7,1,8,2,4]=>[4,2,8,1,7,6,5,3]=>0000000=>0000000
[3,5,6,7,8,1,2,4]=>[4,2,1,8,7,6,5,3]=>0000000=>0000000
[3,1,5,2,7,4,8,6]=>[6,8,4,7,2,5,1,3]=>0000000=>0000000
[3,5,1,2,7,4,8,6]=>[6,8,4,7,2,1,5,3]=>0000000=>0000000
[3,1,5,7,2,4,8,6]=>[6,8,4,2,7,5,1,3]=>0000000=>0000000
[3,5,1,7,2,4,8,6]=>[6,8,4,2,7,1,5,3]=>0000000=>0000000
[3,5,7,1,2,4,8,6]=>[6,8,4,2,1,7,5,3]=>0000000=>0000000
[3,5,1,2,7,8,4,6]=>[6,4,8,7,2,1,5,3]=>0000000=>0000000
[3,1,5,7,2,8,4,6]=>[6,4,8,2,7,5,1,3]=>0000000=>0000000
[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]=>0000000=>0000000
[3,1,5,7,8,2,4,6]=>[6,4,2,8,7,5,1,3]=>0000000=>0000000
[3,5,1,7,8,2,4,6]=>[6,4,2,8,7,1,5,3]=>0000000=>0000000
[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]=>0000000=>0000000
[3,1,5,2,7,4,6,8]=>[8,6,4,7,2,5,1,3]=>0000000=>0000000
[3,5,7,1,2,4,6,8]=>[8,6,4,2,1,7,5,3]=>0000000=>0000000
[3,1,5,2,4,7,8,6]=>[6,8,7,4,2,5,1,3]=>0000000=>0000000
[1,3,5,2,7,4,8,6]=>[6,8,4,7,2,5,3,1]=>0000000=>0000000
[1,3,5,7,2,4,8,6]=>[6,8,4,2,7,5,3,1]=>0000000=>0000000
[1,3,2,5,7,8,4,6]=>[6,4,8,7,5,2,3,1]=>0000000=>0000000
[1,3,5,2,7,8,4,6]=>[6,4,8,7,2,5,3,1]=>0000000=>0000000
[1,3,5,7,8,2,4,6]=>[6,4,2,8,7,5,3,1]=>0000000=>0000000
[3,1,5,2,8,4,6,7]=>[7,6,4,8,2,5,1,3]=>0000000=>0000000
[1,3,2,5,8,4,6,7]=>[7,6,4,8,5,2,3,1]=>0000000=>0000000
[1,3,5,8,2,4,6,7]=>[7,6,4,2,8,5,3,1]=>0000000=>0000000
[3,1,2,5,6,8,4,7]=>[7,4,8,6,5,2,1,3]=>0000000=>0000000
[1,3,5,2,6,8,4,7]=>[7,4,8,6,2,5,3,1]=>0000000=>0000000
[1,3,5,6,8,2,4,7]=>[7,4,2,8,6,5,3,1]=>0000000=>0000000
[1,3,5,2,6,7,4,8]=>[8,4,7,6,2,5,3,1]=>0000000=>0000000
[1,3,5,6,2,7,4,8]=>[8,4,7,2,6,5,3,1]=>0000000=>0000000
[1,3,5,6,2,7,8,4]=>[4,8,7,2,6,5,3,1]=>0000000=>0000000
[1,3,5,6,7,2,8,4]=>[4,8,2,7,6,5,3,1]=>0000000=>0000000
[1,3,5,6,7,8,2,4]=>[4,2,8,7,6,5,3,1]=>0000000=>0000000
[3,1,6,2,7,4,8,5]=>[5,8,4,7,2,6,1,3]=>0000000=>0000000
[3,6,1,2,7,4,8,5]=>[5,8,4,7,2,1,6,3]=>0000000=>0000000
[3,6,1,7,2,4,8,5]=>[5,8,4,2,7,1,6,3]=>0000000=>0000000
[3,6,1,7,2,8,4,5]=>[5,4,8,2,7,1,6,3]=>0000000=>0000000
[3,6,7,1,2,8,4,5]=>[5,4,8,2,1,7,6,3]=>0000000=>0000000
[3,1,6,7,8,2,4,5]=>[5,4,2,8,7,6,1,3]=>0000000=>0000000
[3,6,1,7,8,2,4,5]=>[5,4,2,8,7,1,6,3]=>0000000=>0000000
[3,6,7,1,8,2,4,5]=>[5,4,2,8,1,7,6,3]=>0000000=>0000000
[3,6,7,8,1,2,4,5]=>[5,4,2,1,8,7,6,3]=>0000000=>0000000
[3,1,6,7,2,4,5,8]=>[8,5,4,2,7,6,1,3]=>0000000=>0000000
[3,1,6,2,4,7,5,8]=>[8,5,7,4,2,6,1,3]=>0000000=>0000000
[3,6,1,2,4,7,5,8]=>[8,5,7,4,2,1,6,3]=>0000000=>0000000
[3,1,2,6,4,7,5,8]=>[8,5,7,4,6,2,1,3]=>0000000=>0000000
[3,1,2,6,7,4,5,8]=>[8,5,4,7,6,2,1,3]=>0000000=>0000000
[1,3,6,7,2,4,5,8]=>[8,5,4,2,7,6,3,1]=>0000000=>0000000
[3,1,2,6,4,7,8,5]=>[5,8,7,4,6,2,1,3]=>0000000=>0000000
[1,3,2,6,4,7,8,5]=>[5,8,7,4,6,2,3,1]=>0000000=>0000000
[1,3,6,2,4,7,8,5]=>[5,8,7,4,2,6,3,1]=>0000000=>0000000
[3,1,2,6,7,4,8,5]=>[5,8,4,7,6,2,1,3]=>0000000=>0000000
[1,3,2,6,7,4,8,5]=>[5,8,4,7,6,2,3,1]=>0000000=>0000000
[1,3,2,6,7,8,4,5]=>[5,4,8,7,6,2,3,1]=>0000000=>0000000
[1,3,6,2,7,8,4,5]=>[5,4,8,7,2,6,3,1]=>0000000=>0000000
[3,1,6,2,8,4,5,7]=>[7,5,4,8,2,6,1,3]=>0000000=>0000000
[3,1,6,8,2,4,5,7]=>[7,5,4,2,8,6,1,3]=>0000000=>0000000
[1,3,2,6,4,8,5,7]=>[7,5,8,4,6,2,3,1]=>0000000=>0000000
[3,1,6,2,4,5,8,7]=>[7,8,5,4,2,6,1,3]=>0000000=>0000000
[1,3,4,6,2,5,7,8]=>[8,7,5,2,6,4,3,1]=>0000000=>0000000
[3,1,2,4,6,7,8,5]=>[5,8,7,6,4,2,1,3]=>0000000=>0000000
[1,3,4,6,2,7,8,5]=>[5,8,7,2,6,4,3,1]=>0000000=>0000000
[1,3,4,6,7,2,8,5]=>[5,8,2,7,6,4,3,1]=>0000000=>0000000
[1,3,4,6,7,8,2,5]=>[5,2,8,7,6,4,3,1]=>0000000=>0000000
[3,1,7,8,2,4,5,6]=>[6,5,4,2,8,7,1,3]=>0000000=>0000000
[3,1,2,4,7,5,8,6]=>[6,8,5,7,4,2,1,3]=>0000000=>0000000
[1,3,2,4,7,5,8,6]=>[6,8,5,7,4,2,3,1]=>0000000=>0000000
[3,1,2,4,7,8,5,6]=>[6,5,8,7,4,2,1,3]=>0000000=>0000000
[1,3,2,4,7,8,5,6]=>[6,5,8,7,4,2,3,1]=>0000000=>0000000
[1,3,4,2,7,8,5,6]=>[6,5,8,7,2,4,3,1]=>0000000=>0000000
[1,3,4,5,7,2,8,6]=>[6,8,2,7,5,4,3,1]=>0000000=>0000000
[3,1,2,4,8,5,6,7]=>[7,6,5,8,4,2,1,3]=>0000000=>0000000
[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>0000000=>0000000
[1,3,4,2,8,5,6,7]=>[7,6,5,8,2,4,3,1]=>0000000=>0000000
[3,1,2,4,5,8,6,7]=>[7,6,8,5,4,2,1,3]=>0000000=>0000000
[1,3,4,5,6,8,2,7]=>[7,2,8,6,5,4,3,1]=>0000000=>0000000
[4,1,5,2,6,3,8,7]=>[7,8,3,6,2,5,1,4]=>0000000=>0000000
[4,5,1,2,6,3,8,7]=>[7,8,3,6,2,1,5,4]=>0000000=>0000000
[4,5,6,1,2,3,8,7]=>[7,8,3,2,1,6,5,4]=>0000000=>0000000
[4,1,5,2,6,8,3,7]=>[7,3,8,6,2,5,1,4]=>0000000=>0000000
[4,1,5,6,8,2,3,7]=>[7,3,2,8,6,5,1,4]=>0000000=>0000000
[4,5,6,1,8,2,3,7]=>[7,3,2,8,1,6,5,4]=>0000000=>0000000
[4,1,5,6,2,3,7,8]=>[8,7,3,2,6,5,1,4]=>0000000=>0000000
[4,5,1,6,2,3,7,8]=>[8,7,3,2,6,1,5,4]=>0000000=>0000000
[4,1,5,6,2,7,3,8]=>[8,3,7,2,6,5,1,4]=>0000000=>0000000
[4,5,1,6,2,7,3,8]=>[8,3,7,2,6,1,5,4]=>0000000=>0000000
[4,5,6,1,2,7,3,8]=>[8,3,7,2,1,6,5,4]=>0000000=>0000000
[4,5,1,6,7,2,3,8]=>[8,3,2,7,6,1,5,4]=>0000000=>0000000
[4,5,6,1,7,2,3,8]=>[8,3,2,7,1,6,5,4]=>0000000=>0000000
[4,1,5,2,6,7,8,3]=>[3,8,7,6,2,5,1,4]=>0000000=>0000000
[4,5,1,2,6,7,8,3]=>[3,8,7,6,2,1,5,4]=>0000000=>0000000
[4,1,5,6,2,7,8,3]=>[3,8,7,2,6,5,1,4]=>0000000=>0000000
[4,5,1,6,2,7,8,3]=>[3,8,7,2,6,1,5,4]=>0000000=>0000000
[4,5,6,1,2,7,8,3]=>[3,8,7,2,1,6,5,4]=>0000000=>0000000
[4,1,5,6,7,2,8,3]=>[3,8,2,7,6,5,1,4]=>0000000=>0000000
[4,5,1,6,7,2,8,3]=>[3,8,2,7,6,1,5,4]=>0000000=>0000000
[4,5,6,1,7,2,8,3]=>[3,8,2,7,1,6,5,4]=>0000000=>0000000
[4,5,6,7,1,2,8,3]=>[3,8,2,1,7,6,5,4]=>0000000=>0000000
[4,1,5,6,7,8,2,3]=>[3,2,8,7,6,5,1,4]=>0000000=>0000000
[4,5,1,6,7,8,2,3]=>[3,2,8,7,6,1,5,4]=>0000000=>0000000
[4,5,6,1,7,8,2,3]=>[3,2,8,7,1,6,5,4]=>0000000=>0000000
[4,5,6,7,1,8,2,3]=>[3,2,8,1,7,6,5,4]=>0000000=>0000000
[4,1,5,2,7,3,8,6]=>[6,8,3,7,2,5,1,4]=>0000000=>0000000
[4,5,1,2,7,3,8,6]=>[6,8,3,7,2,1,5,4]=>0000000=>0000000
[4,5,1,7,2,3,8,6]=>[6,8,3,2,7,1,5,4]=>0000000=>0000000
[4,1,5,2,7,8,3,6]=>[6,3,8,7,2,5,1,4]=>0000000=>0000000
[4,1,5,7,2,8,3,6]=>[6,3,8,2,7,5,1,4]=>0000000=>0000000
[4,5,1,7,2,8,3,6]=>[6,3,8,2,7,1,5,4]=>0000000=>0000000
[4,5,7,1,2,8,3,6]=>[6,3,8,2,1,7,5,4]=>0000000=>0000000
[4,5,1,7,8,2,3,6]=>[6,3,2,8,7,1,5,4]=>0000000=>0000000
[4,5,7,1,8,2,3,6]=>[6,3,2,8,1,7,5,4]=>0000000=>0000000
[4,5,1,2,7,3,6,8]=>[8,6,3,7,2,1,5,4]=>0000000=>0000000
[4,1,2,5,7,3,6,8]=>[8,6,3,7,5,2,1,4]=>0000000=>0000000
[4,1,5,2,3,7,8,6]=>[6,8,7,3,2,5,1,4]=>0000000=>0000000
[4,1,2,5,7,3,8,6]=>[6,8,3,7,5,2,1,4]=>0000000=>0000000
[1,4,2,5,7,3,8,6]=>[6,8,3,7,5,2,4,1]=>0000000=>0000000
[1,4,5,2,7,3,8,6]=>[6,8,3,7,2,5,4,1]=>0000000=>0000000
[1,4,5,7,2,3,8,6]=>[6,8,3,2,7,5,4,1]=>0000000=>0000000
[4,1,5,2,8,3,6,7]=>[7,6,3,8,2,5,1,4]=>0000000=>0000000
[4,5,1,2,8,3,6,7]=>[7,6,3,8,2,1,5,4]=>0000000=>0000000
[1,4,2,5,3,8,6,7]=>[7,6,8,3,5,2,4,1]=>0000000=>0000000
[4,1,2,5,8,3,6,7]=>[7,6,3,8,5,2,1,4]=>0000000=>0000000
[4,1,2,5,6,3,8,7]=>[7,8,3,6,5,2,1,4]=>0000000=>0000000
[4,1,5,2,3,6,7,8]=>[8,7,6,3,2,5,1,4]=>0000000=>0000000
[1,4,2,5,3,6,7,8]=>[8,7,6,3,5,2,4,1]=>0000000=>0000000
[1,4,5,2,3,6,7,8]=>[8,7,6,3,2,5,4,1]=>0000000=>0000000
[4,1,2,5,6,3,7,8]=>[8,7,3,6,5,2,1,4]=>0000000=>0000000
[1,4,2,5,6,3,7,8]=>[8,7,3,6,5,2,4,1]=>0000000=>0000000
[1,4,5,2,6,3,7,8]=>[8,7,3,6,2,5,4,1]=>0000000=>0000000
[1,4,5,6,7,2,3,8]=>[8,3,2,7,6,5,4,1]=>0000000=>0000000
[4,1,2,5,6,7,8,3]=>[3,8,7,6,5,2,1,4]=>0000000=>0000000
[1,4,2,5,6,7,8,3]=>[3,8,7,6,5,2,4,1]=>0000000=>0000000
[1,4,5,6,2,7,8,3]=>[3,8,7,2,6,5,4,1]=>0000000=>0000000
[1,4,5,6,7,2,8,3]=>[3,8,2,7,6,5,4,1]=>0000000=>0000000
[1,4,5,6,7,8,2,3]=>[3,2,8,7,6,5,4,1]=>0000000=>0000000
[4,1,6,2,7,3,8,5]=>[5,8,3,7,2,6,1,4]=>0000000=>0000000
[4,6,1,2,7,3,8,5]=>[5,8,3,7,2,1,6,4]=>0000000=>0000000
[4,1,6,7,2,3,8,5]=>[5,8,3,2,7,6,1,4]=>0000000=>0000000
[4,6,7,1,2,3,8,5]=>[5,8,3,2,1,7,6,4]=>0000000=>0000000
[4,1,6,7,2,8,3,5]=>[5,3,8,2,7,6,1,4]=>0000000=>0000000
[4,6,1,7,2,8,3,5]=>[5,3,8,2,7,1,6,4]=>0000000=>0000000
[4,6,7,1,2,8,3,5]=>[5,3,8,2,1,7,6,4]=>0000000=>0000000
[4,6,1,7,8,2,3,5]=>[5,3,2,8,7,1,6,4]=>0000000=>0000000
[4,6,7,1,8,2,3,5]=>[5,3,2,8,1,7,6,4]=>0000000=>0000000
[4,1,6,2,7,3,5,8]=>[8,5,3,7,2,6,1,4]=>0000000=>0000000
[4,6,1,2,7,3,5,8]=>[8,5,3,7,2,1,6,4]=>0000000=>0000000
[4,1,6,7,2,3,5,8]=>[8,5,3,2,7,6,1,4]=>0000000=>0000000
[4,6,1,7,2,3,5,8]=>[8,5,3,2,7,1,6,4]=>0000000=>0000000
[4,6,1,2,3,7,5,8]=>[8,5,7,3,2,1,6,4]=>0000000=>0000000
[4,6,1,2,3,7,8,5]=>[5,8,7,3,2,1,6,4]=>0000000=>0000000
[1,4,6,2,3,7,8,5]=>[5,8,7,3,2,6,4,1]=>0000000=>0000000
[1,4,2,6,7,3,8,5]=>[5,8,3,7,6,2,4,1]=>0000000=>0000000
[1,4,6,2,7,3,8,5]=>[5,8,3,7,2,6,4,1]=>0000000=>0000000
[1,4,6,7,2,3,8,5]=>[5,8,3,2,7,6,4,1]=>0000000=>0000000
[1,4,2,6,7,8,3,5]=>[5,3,8,7,6,2,4,1]=>0000000=>0000000
[1,4,6,2,7,8,3,5]=>[5,3,8,7,2,6,4,1]=>0000000=>0000000
[1,4,6,7,2,8,3,5]=>[5,3,8,2,7,6,4,1]=>0000000=>0000000
[4,1,6,2,8,3,5,7]=>[7,5,3,8,2,6,1,4]=>0000000=>0000000
[4,1,6,8,2,3,5,7]=>[7,5,3,2,8,6,1,4]=>0000000=>0000000
[4,6,1,8,2,3,5,7]=>[7,5,3,2,8,1,6,4]=>0000000=>0000000
[4,1,6,2,3,8,5,7]=>[7,5,8,3,2,6,1,4]=>0000000=>0000000
[4,6,1,2,3,8,5,7]=>[7,5,8,3,2,1,6,4]=>0000000=>0000000
[4,1,2,6,3,8,5,7]=>[7,5,8,3,6,2,1,4]=>0000000=>0000000
[1,4,2,6,3,8,5,7]=>[7,5,8,3,6,2,4,1]=>0000000=>0000000
[1,4,2,6,8,3,5,7]=>[7,5,3,8,6,2,4,1]=>0000000=>0000000
[1,4,6,2,8,3,5,7]=>[7,5,3,8,2,6,4,1]=>0000000=>0000000
[4,6,1,2,3,5,8,7]=>[7,8,5,3,2,1,6,4]=>0000000=>0000000
[4,1,2,3,6,5,8,7]=>[7,8,5,6,3,2,1,4]=>0000000=>0000000
[4,1,2,3,6,8,5,7]=>[7,5,8,6,3,2,1,4]=>0000000=>0000000
[4,6,1,2,3,5,7,8]=>[8,7,5,3,2,1,6,4]=>0000000=>0000000
[1,4,6,2,3,5,7,8]=>[8,7,5,3,2,6,4,1]=>0000000=>0000000
[4,1,2,3,6,5,7,8]=>[8,7,5,6,3,2,1,4]=>0000000=>0000000
[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>0000000=>0000000
[4,1,2,3,6,7,5,8]=>[8,5,7,6,3,2,1,4]=>0000000=>0000000
[4,1,2,3,6,7,8,5]=>[5,8,7,6,3,2,1,4]=>0000000=>0000000
[1,4,2,3,6,7,8,5]=>[5,8,7,6,3,2,4,1]=>0000000=>0000000
[1,2,4,6,3,7,8,5]=>[5,8,7,3,6,4,2,1]=>0000000=>0000000
[4,1,7,8,2,3,5,6]=>[6,5,3,2,8,7,1,4]=>0000000=>0000000
[4,7,1,8,2,3,5,6]=>[6,5,3,2,8,1,7,4]=>0000000=>0000000
[4,7,8,1,2,3,5,6]=>[6,5,3,2,1,8,7,4]=>0000000=>0000000
[4,7,1,2,3,8,5,6]=>[6,5,8,3,2,1,7,4]=>0000000=>0000000
[4,1,2,7,8,3,5,6]=>[6,5,3,8,7,2,1,4]=>0000000=>0000000
[1,4,2,7,8,3,5,6]=>[6,5,3,8,7,2,4,1]=>0000000=>0000000
[1,4,7,2,8,3,5,6]=>[6,5,3,8,2,7,4,1]=>0000000=>0000000
[4,1,2,7,3,5,8,6]=>[6,8,5,3,7,2,1,4]=>0000000=>0000000
[1,4,2,7,3,5,8,6]=>[6,8,5,3,7,2,4,1]=>0000000=>0000000
[4,1,2,3,7,5,8,6]=>[6,8,5,7,3,2,1,4]=>0000000=>0000000
[1,2,4,3,7,5,8,6]=>[6,8,5,7,3,4,2,1]=>0000000=>0000000
[4,1,2,3,7,8,5,6]=>[6,5,8,7,3,2,1,4]=>0000000=>0000000
[1,4,2,3,7,8,5,6]=>[6,5,8,7,3,2,4,1]=>0000000=>0000000
[1,2,4,3,7,8,5,6]=>[6,5,8,7,3,4,2,1]=>0000000=>0000000
[1,2,4,7,3,8,5,6]=>[6,5,8,3,7,4,2,1]=>0000000=>0000000
[4,1,2,3,7,5,6,8]=>[8,6,5,7,3,2,1,4]=>0000000=>0000000
[1,4,2,3,7,5,6,8]=>[8,6,5,7,3,2,4,1]=>0000000=>0000000
[4,1,2,3,5,7,6,8]=>[8,6,7,5,3,2,1,4]=>0000000=>0000000
[4,1,2,3,5,7,8,6]=>[6,8,7,5,3,2,1,4]=>0000000=>0000000
[1,2,4,5,7,8,3,6]=>[6,3,8,7,5,4,2,1]=>0000000=>0000000
[4,1,2,3,8,5,6,7]=>[7,6,5,8,3,2,1,4]=>0000000=>0000000
[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>0000000=>0000000
[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>0000000=>0000000
[4,1,2,3,5,8,6,7]=>[7,6,8,5,3,2,1,4]=>0000000=>0000000
[4,1,2,3,5,6,8,7]=>[7,8,6,5,3,2,1,4]=>0000000=>0000000
[5,1,6,2,7,3,8,4]=>[4,8,3,7,2,6,1,5]=>0000000=>0000000
[5,6,1,2,7,3,8,4]=>[4,8,3,7,2,1,6,5]=>0000000=>0000000
[5,1,6,7,2,3,8,4]=>[4,8,3,2,7,6,1,5]=>0000000=>0000000
[5,6,7,1,2,3,8,4]=>[4,8,3,2,1,7,6,5]=>0000000=>0000000
[5,1,6,2,7,8,3,4]=>[4,3,8,7,2,6,1,5]=>0000000=>0000000
[5,1,6,7,2,8,3,4]=>[4,3,8,2,7,6,1,5]=>0000000=>0000000
[5,6,1,7,2,8,3,4]=>[4,3,8,2,7,1,6,5]=>0000000=>0000000
[5,1,6,7,8,2,3,4]=>[4,3,2,8,7,6,1,5]=>0000000=>0000000
[5,1,6,7,2,3,4,8]=>[8,4,3,2,7,6,1,5]=>0000000=>0000000
[5,1,2,6,3,7,4,8]=>[8,4,7,3,6,2,1,5]=>0000000=>0000000
[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>0000000=>0000000
[5,1,6,2,3,7,8,4]=>[4,8,7,3,2,6,1,5]=>0000000=>0000000
[5,6,1,2,3,7,8,4]=>[4,8,7,3,2,1,6,5]=>0000000=>0000000
[5,1,2,6,3,7,8,4]=>[4,8,7,3,6,2,1,5]=>0000000=>0000000
[1,5,2,6,3,7,8,4]=>[4,8,7,3,6,2,5,1]=>0000000=>0000000
[1,5,6,2,3,7,8,4]=>[4,8,7,3,2,6,5,1]=>0000000=>0000000
[1,5,2,6,7,3,8,4]=>[4,8,3,7,6,2,5,1]=>0000000=>0000000
[1,5,6,7,2,3,8,4]=>[4,8,3,2,7,6,5,1]=>0000000=>0000000
[5,1,2,6,7,8,3,4]=>[4,3,8,7,6,2,1,5]=>0000000=>0000000
[1,5,2,6,7,8,3,4]=>[4,3,8,7,6,2,5,1]=>0000000=>0000000
[1,5,6,2,7,8,3,4]=>[4,3,8,7,2,6,5,1]=>0000000=>0000000
[1,5,6,7,2,8,3,4]=>[4,3,8,2,7,6,5,1]=>0000000=>0000000
[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>0000000=>0000000
[5,1,6,8,2,3,4,7]=>[7,4,3,2,8,6,1,5]=>0000000=>0000000
[5,6,1,8,2,3,4,7]=>[7,4,3,2,8,1,6,5]=>0000000=>0000000
[5,6,8,1,2,3,4,7]=>[7,4,3,2,1,8,6,5]=>0000000=>0000000
[5,1,6,2,3,8,4,7]=>[7,4,8,3,2,6,1,5]=>0000000=>0000000
[5,6,1,2,3,8,4,7]=>[7,4,8,3,2,1,6,5]=>0000000=>0000000
[5,1,2,6,3,8,4,7]=>[7,4,8,3,6,2,1,5]=>0000000=>0000000
[1,5,2,6,3,8,4,7]=>[7,4,8,3,6,2,5,1]=>0000000=>0000000
[1,5,6,2,3,8,4,7]=>[7,4,8,3,2,6,5,1]=>0000000=>0000000
[5,1,2,6,8,3,4,7]=>[7,4,3,8,6,2,1,5]=>0000000=>0000000
[1,5,2,6,8,3,4,7]=>[7,4,3,8,6,2,5,1]=>0000000=>0000000
[5,6,1,2,3,4,8,7]=>[7,8,4,3,2,1,6,5]=>0000000=>0000000
[5,1,2,6,3,4,8,7]=>[7,8,4,3,6,2,1,5]=>0000000=>0000000
[1,5,2,3,6,8,4,7]=>[7,4,8,6,3,2,5,1]=>0000000=>0000000
[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>0000000=>0000000
[5,1,2,3,6,7,4,8]=>[8,4,7,6,3,2,1,5]=>0000000=>0000000
[1,2,5,3,6,7,4,8]=>[8,4,7,6,3,5,2,1]=>0000000=>0000000
[1,2,5,6,3,7,4,8]=>[8,4,7,3,6,5,2,1]=>0000000=>0000000
[5,1,2,3,6,7,8,4]=>[4,8,7,6,3,2,1,5]=>0000000=>0000000
[1,5,2,3,6,7,8,4]=>[4,8,7,6,3,2,5,1]=>0000000=>0000000
[1,2,5,3,6,7,8,4]=>[4,8,7,6,3,5,2,1]=>0000000=>0000000
[1,2,5,6,3,7,8,4]=>[4,8,7,3,6,5,2,1]=>0000000=>0000000
[1,2,5,6,7,3,8,4]=>[4,8,3,7,6,5,2,1]=>0000000=>0000000
[5,1,7,2,8,3,4,6]=>[6,4,3,8,2,7,1,5]=>0000000=>0000000
[5,7,8,1,2,3,4,6]=>[6,4,3,2,1,8,7,5]=>0000000=>0000000
[5,1,7,2,3,8,4,6]=>[6,4,8,3,2,7,1,5]=>0000000=>0000000
[5,1,2,7,8,3,4,6]=>[6,4,3,8,7,2,1,5]=>0000000=>0000000
[1,5,7,2,8,3,4,6]=>[6,4,3,8,2,7,5,1]=>0000000=>0000000
[5,1,7,2,3,4,8,6]=>[6,8,4,3,2,7,1,5]=>0000000=>0000000
[5,1,2,7,3,4,8,6]=>[6,8,4,3,7,2,1,5]=>0000000=>0000000
[5,1,2,3,7,4,8,6]=>[6,8,4,7,3,2,1,5]=>0000000=>0000000
[1,5,2,3,7,4,8,6]=>[6,8,4,7,3,2,5,1]=>0000000=>0000000
[1,2,5,3,7,4,8,6]=>[6,8,4,7,3,5,2,1]=>0000000=>0000000
[1,2,5,3,7,8,4,6]=>[6,4,8,7,3,5,2,1]=>0000000=>0000000
[5,7,1,2,3,4,6,8]=>[8,6,4,3,2,1,7,5]=>0000000=>0000000
[1,5,2,7,3,4,6,8]=>[8,6,4,3,7,2,5,1]=>0000000=>0000000
[5,1,2,3,4,7,6,8]=>[8,6,7,4,3,2,1,5]=>0000000=>0000000
[5,1,2,3,4,7,8,6]=>[6,8,7,4,3,2,1,5]=>0000000=>0000000
[5,8,1,2,3,4,6,7]=>[7,6,4,3,2,1,8,5]=>0000000=>0000000
[5,1,2,8,3,4,6,7]=>[7,6,4,3,8,2,1,5]=>0000000=>0000000
[1,5,2,8,3,4,6,7]=>[7,6,4,3,8,2,5,1]=>0000000=>0000000
[5,1,2,3,4,8,6,7]=>[7,6,8,4,3,2,1,5]=>0000000=>0000000
[5,1,2,3,4,6,8,7]=>[7,8,6,4,3,2,1,5]=>0000000=>0000000
[6,7,1,2,8,3,4,5]=>[5,4,3,8,2,1,7,6]=>0000000=>0000000
[6,1,7,8,2,3,4,5]=>[5,4,3,2,8,7,1,6]=>0000000=>0000000
[6,7,1,8,2,3,4,5]=>[5,4,3,2,8,1,7,6]=>0000000=>0000000
[6,7,1,2,3,8,4,5]=>[5,4,8,3,2,1,7,6]=>0000000=>0000000
[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>0000000=>0000000
[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>0000000=>0000000
[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>0000000=>0000000
[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>0000000=>0000000
[6,1,2,3,7,8,4,5]=>[5,4,8,7,3,2,1,6]=>0000000=>0000000
[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>0000000=>0000000
[6,1,2,3,4,7,5,8]=>[8,5,7,4,3,2,1,6]=>0000000=>0000000
[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>0000000=>0000000
[6,1,2,3,4,7,8,5]=>[5,8,7,4,3,2,1,6]=>0000000=>0000000
[1,2,6,3,4,7,8,5]=>[5,8,7,4,3,6,2,1]=>0000000=>0000000
[6,1,8,2,3,4,5,7]=>[7,5,4,3,2,8,1,6]=>0000000=>0000000
[6,1,2,8,3,4,5,7]=>[7,5,4,3,8,2,1,6]=>0000000=>0000000
[6,1,2,3,4,8,5,7]=>[7,5,8,4,3,2,1,6]=>0000000=>0000000
[6,1,2,3,4,5,8,7]=>[7,8,5,4,3,2,1,6]=>0000000=>0000000
[1,2,6,3,4,5,8,7]=>[7,8,5,4,3,6,2,1]=>0000000=>0000000
[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>0000000=>0000000
[7,1,8,2,3,4,5,6]=>[6,5,4,3,2,8,1,7]=>0000000=>0000000
[7,1,2,8,3,4,5,6]=>[6,5,4,3,8,2,1,7]=>0000000=>0000000
[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>0000000=>0000000
[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>0000000=>0000000
[7,1,2,3,4,8,5,6]=>[6,5,8,4,3,2,1,7]=>0000000=>0000000
[7,1,2,3,4,5,8,6]=>[6,8,5,4,3,2,1,7]=>0000000=>0000000
[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>0000000=>0000000
[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>0000000=>0000000
[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>0000000=>0000000
[5,3,2,6,1,4,8,7]=>[7,8,4,1,6,2,3,5]=>0000000=>0000000
[7,3,2,5,4,8,1,6]=>[6,1,8,4,5,2,3,7]=>0000000=>0000000
[8,4,5,2,3,7,6,1]=>[1,6,7,3,2,5,4,8]=>1000001=>1000001
[7,4,5,2,3,8,1,6]=>[6,1,8,3,2,5,4,7]=>0000000=>0000000
[6,4,5,2,3,1,8,7]=>[7,8,1,3,2,5,4,6]=>0000000=>0000000
[5,4,6,2,1,3,8,7]=>[7,8,3,1,2,6,4,5]=>0000000=>0000000
[3,6,1,5,4,2,8,7]=>[7,8,2,4,5,1,6,3]=>0000000=>0000000
[4,6,5,1,3,2,8,7]=>[7,8,2,3,1,5,6,4]=>0000000=>0000000
[5,6,4,3,1,2,8,7]=>[7,8,2,1,3,4,6,5]=>0000000=>0000000
[7,5,4,3,2,8,1,6]=>[6,1,8,2,3,4,5,7]=>0000000=>0000000
[8,6,4,3,7,2,5,1]=>[1,5,2,7,3,4,6,8]=>1000001=>1000001
[7,6,4,3,8,2,1,5]=>[5,1,2,8,3,4,6,7]=>0000000=>0000000
[6,7,4,3,8,1,2,5]=>[5,2,1,8,3,4,7,6]=>0000000=>0000000
[5,7,4,3,1,8,2,6]=>[6,2,8,1,3,4,7,5]=>0000000=>0000000
[4,7,5,1,3,8,2,6]=>[6,2,8,3,1,5,7,4]=>0000000=>0000000
[3,7,1,5,4,8,2,6]=>[6,2,8,4,5,1,7,3]=>0000000=>0000000
[2,1,7,5,4,8,3,6]=>[6,3,8,4,5,7,1,2]=>0000000=>0000000
[3,8,1,5,4,7,6,2]=>[2,6,7,4,5,1,8,3]=>0000000=>0000000
[4,8,5,1,3,7,6,2]=>[2,6,7,3,1,5,8,4]=>0000000=>0000000
[5,8,4,3,1,7,6,2]=>[2,6,7,1,3,4,8,5]=>0000000=>0000000
[6,8,4,3,7,1,5,2]=>[2,5,1,7,3,4,8,6]=>0000000=>0000000
[7,8,4,3,6,5,1,2]=>[2,1,5,6,3,4,8,7]=>0100010=>0100010
[6,8,5,7,3,1,4,2]=>[2,4,1,3,7,5,8,6]=>0001000=>0001000
[5,8,6,7,1,3,4,2]=>[2,4,3,1,7,6,8,5]=>0001000=>0001000
[4,8,6,1,7,3,5,2]=>[2,5,3,7,1,6,8,4]=>0000000=>0000000
[3,8,1,6,7,4,5,2]=>[2,5,4,7,6,1,8,3]=>0000000=>0000000
[2,1,8,6,7,4,5,3]=>[3,5,4,7,6,8,1,2]=>0000000=>0000000
[2,1,7,6,8,4,3,5]=>[5,3,4,8,6,7,1,2]=>0000000=>0000000
[3,7,1,6,8,4,2,5]=>[5,2,4,8,6,1,7,3]=>0000000=>0000000
[4,7,6,1,8,3,2,5]=>[5,2,3,8,1,6,7,4]=>0000000=>0000000
[5,7,6,8,1,3,2,4]=>[4,2,3,1,8,6,7,5]=>0001000=>0001000
[5,4,7,2,1,8,3,6]=>[6,3,8,1,2,7,4,5]=>0000000=>0000000
[6,4,7,2,8,1,3,5]=>[5,3,1,8,2,7,4,6]=>0000000=>0000000
[7,4,6,2,8,3,1,5]=>[5,1,3,8,2,6,4,7]=>0000000=>0000000
[8,4,6,2,7,3,5,1]=>[1,5,3,7,2,6,4,8]=>1000001=>1000001
[8,3,2,6,7,4,5,1]=>[1,5,4,7,6,2,3,8]=>1000001=>1000001
[7,3,2,6,8,4,1,5]=>[5,1,4,8,6,2,3,7]=>0000000=>0000000
[6,3,2,7,8,1,4,5]=>[5,4,1,8,7,2,3,6]=>0000000=>0000000
[5,3,2,7,1,8,4,6]=>[6,4,8,1,7,2,3,5]=>0000000=>0000000
[4,3,2,1,7,8,5,6]=>[6,5,8,7,1,2,3,4]=>0000000=>0000000
[3,4,1,2,8,7,6,5]=>[5,6,7,8,2,1,4,3]=>0000000=>0000000
[5,3,2,8,1,7,6,4]=>[4,6,7,1,8,2,3,5]=>0000000=>0000000
[6,3,2,8,7,1,5,4]=>[4,5,1,7,8,2,3,6]=>0000000=>0000000
[7,3,2,8,6,5,1,4]=>[4,1,5,6,8,2,3,7]=>0000000=>0000000
[8,4,7,2,6,5,3,1]=>[1,3,5,6,2,7,4,8]=>1000001=>1000001
[7,4,8,2,6,5,1,3]=>[3,1,5,6,2,8,4,7]=>0000000=>0000000
[6,4,8,2,7,1,5,3]=>[3,5,1,7,2,8,4,6]=>0000000=>0000000
[5,4,8,2,1,7,6,3]=>[3,6,7,1,2,8,4,5]=>0000000=>0000000
[4,5,8,1,2,7,6,3]=>[3,6,7,2,1,8,5,4]=>0000000=>0000000
[3,5,1,8,2,7,6,4]=>[4,6,7,2,8,1,5,3]=>0000000=>0000000
[2,1,5,8,3,7,6,4]=>[4,6,7,3,8,5,1,2]=>0000000=>0000000
[2,1,6,8,7,3,5,4]=>[4,5,3,7,8,6,1,2]=>0000000=>0000000
[3,6,1,8,7,2,5,4]=>[4,5,2,7,8,1,6,3]=>0000000=>0000000
[4,6,8,1,7,2,5,3]=>[3,5,2,7,1,8,6,4]=>0000000=>0000000
[5,6,8,7,1,2,4,3]=>[3,4,2,1,7,8,6,5]=>0001000=>0001000
[6,5,8,7,2,1,4,3]=>[3,4,1,2,7,8,5,6]=>0001000=>0001000
[7,5,8,6,2,4,1,3]=>[3,1,4,2,6,8,5,7]=>0001000=>0001000
[8,5,7,6,2,4,3,1]=>[1,3,4,2,6,7,5,8]=>1001001=>1001001
[5,7,8,6,1,4,2,3]=>[3,2,4,1,6,8,7,5]=>0001000=>0001000
[4,7,8,1,6,5,2,3]=>[3,2,5,6,1,8,7,4]=>0000000=>0000000
[3,7,1,8,6,5,2,4]=>[4,2,5,6,8,1,7,3]=>0000000=>0000000
[2,1,7,8,6,5,3,4]=>[4,3,5,6,8,7,1,2]=>0000000=>0000000
[3,8,1,7,6,5,4,2]=>[2,4,5,6,7,1,8,3]=>0000000=>0000000
[4,8,7,1,6,5,3,2]=>[2,3,5,6,1,7,8,4]=>0000000=>0000000
[5,8,7,6,1,4,3,2]=>[2,3,4,1,6,7,8,5]=>0001000=>0001000
[6,8,7,5,4,1,3,2]=>[2,3,1,4,5,7,8,6]=>0011100=>0011100
[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>000000000=>000000000
[5,2,4,1,3,6,7,8]=>[8,7,6,3,1,4,2,5]=>0000000=>0000000
[6,3,5,1,2,4,7,8]=>[8,7,4,2,1,5,3,6]=>0000000=>0000000
[7,3,5,1,2,4,6,8]=>[8,6,4,2,1,5,3,7]=>0000000=>0000000
[7,4,6,1,2,3,5,8]=>[8,5,3,2,1,6,4,7]=>0000000=>0000000
[5,2,8,1,3,4,6,7]=>[7,6,4,3,1,8,2,5]=>0000000=>0000000
[6,4,8,1,2,3,5,7]=>[7,5,3,2,1,8,4,6]=>0000000=>0000000
[6,5,8,1,2,3,4,7]=>[7,4,3,2,1,8,5,6]=>0000000=>0000000
[7,5,8,1,2,3,4,6]=>[6,4,3,2,1,8,5,7]=>0000000=>0000000
[8,3,5,1,2,4,6,7]=>[7,6,4,2,1,5,3,8]=>0000001=>1000000
[8,5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5,8]=>0000001=>1000000
[5,2,6,7,1,3,4,8]=>[8,4,3,1,7,6,2,5]=>0000000=>0000000
[5,3,6,7,1,2,4,8]=>[8,4,2,1,7,6,3,5]=>0000000=>0000000
[6,3,4,7,1,2,5,8]=>[8,5,2,1,7,4,3,6]=>0000000=>0000000
[6,3,5,7,1,2,4,8]=>[8,4,2,1,7,5,3,6]=>0000000=>0000000
[7,2,4,6,1,3,5,8]=>[8,5,3,1,6,4,2,7]=>0000000=>0000000
[7,3,4,6,1,2,5,8]=>[8,5,2,1,6,4,3,7]=>0000000=>0000000
[7,3,5,6,1,2,4,8]=>[8,4,2,1,6,5,3,7]=>0000000=>0000000
[3,2,5,8,1,4,6,7]=>[7,6,4,1,8,5,2,3]=>0000000=>0000000
[4,2,5,8,1,3,6,7]=>[7,6,3,1,8,5,2,4]=>0000000=>0000000
[5,2,4,8,1,3,6,7]=>[7,6,3,1,8,4,2,5]=>0000000=>0000000
[5,3,4,8,1,2,6,7]=>[7,6,2,1,8,4,3,5]=>0000000=>0000000
[4,2,6,8,1,3,5,7]=>[7,5,3,1,8,6,2,4]=>0000000=>0000000
[6,3,5,8,1,2,4,7]=>[7,4,2,1,8,5,3,6]=>0000000=>0000000
[3,2,7,8,1,4,5,6]=>[6,5,4,1,8,7,2,3]=>0000000=>0000000
[4,3,7,8,1,2,5,6]=>[6,5,2,1,8,7,3,4]=>0000000=>0000000
[5,4,7,8,1,2,3,6]=>[6,3,2,1,8,7,4,5]=>0000000=>0000000
[7,2,4,8,1,3,5,6]=>[6,5,3,1,8,4,2,7]=>0000000=>0000000
[7,3,5,8,1,2,4,6]=>[6,4,2,1,8,5,3,7]=>0000000=>0000000
[8,2,5,6,1,3,4,7]=>[7,4,3,1,6,5,2,8]=>0000001=>1000000
[8,3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3,8]=>0000001=>1000000
[5,6,2,4,1,3,7,8]=>[8,7,3,1,4,2,6,5]=>0000000=>0000000
[3,7,2,5,1,4,6,8]=>[8,6,4,1,5,2,7,3]=>0000000=>0000000
[5,8,2,6,1,3,4,7]=>[7,4,3,1,6,2,8,5]=>0000000=>0000000
[5,8,4,6,1,2,3,7]=>[7,3,2,1,6,4,8,5]=>0000000=>0000000
[6,8,3,4,1,2,5,7]=>[7,5,2,1,4,3,8,6]=>0000000=>0000000
[3,8,2,7,1,4,5,6]=>[6,5,4,1,7,2,8,3]=>0000000=>0000000
[4,8,2,7,1,3,5,6]=>[6,5,3,1,7,2,8,4]=>0000000=>0000000
[4,8,3,7,1,2,5,6]=>[6,5,2,1,7,3,8,4]=>0000000=>0000000
[5,8,2,7,1,3,4,6]=>[6,4,3,1,7,2,8,5]=>0000000=>0000000
[5,8,3,7,1,2,4,6]=>[6,4,2,1,7,3,8,5]=>0000000=>0000000
[6,8,2,7,1,3,4,5]=>[5,4,3,1,7,2,8,6]=>0000000=>0000000
[6,8,5,7,1,2,3,4]=>[4,3,2,1,7,5,8,6]=>0001000=>0001000
[7,8,2,4,1,3,5,6]=>[6,5,3,1,4,2,8,7]=>0000010=>0100000
[7,8,2,5,1,3,4,6]=>[6,4,3,1,5,2,8,7]=>0000010=>0100000
[7,8,3,5,1,2,4,6]=>[6,4,2,1,5,3,8,7]=>0000010=>0100000
[4,3,2,6,1,5,7,8]=>[8,7,5,1,6,2,3,4]=>0000000=>0000000
[5,3,2,6,1,4,7,8]=>[8,7,4,1,6,2,3,5]=>0000000=>0000000
[5,4,2,6,1,3,7,8]=>[8,7,3,1,6,2,4,5]=>0000000=>0000000
[6,4,2,5,1,3,7,8]=>[8,7,3,1,5,2,4,6]=>0000000=>0000000
[6,5,2,4,1,3,7,8]=>[8,7,3,1,4,2,5,6]=>0000000=>0000000
[5,3,2,7,1,4,6,8]=>[8,6,4,1,7,2,3,5]=>0000000=>0000000
[5,4,2,7,1,3,6,8]=>[8,6,3,1,7,2,4,5]=>0000000=>0000000
[5,4,3,7,1,2,6,8]=>[8,6,2,1,7,3,4,5]=>0000000=>0000000
[6,4,2,7,1,3,5,8]=>[8,5,3,1,7,2,4,6]=>0000000=>0000000
[6,4,3,7,1,2,5,8]=>[8,5,2,1,7,3,4,6]=>0000000=>0000000
[6,5,3,7,1,2,4,8]=>[8,4,2,1,7,3,5,6]=>0000000=>0000000
[7,3,2,5,1,4,6,8]=>[8,6,4,1,5,2,3,7]=>0000000=>0000000
[7,4,2,5,1,3,6,8]=>[8,6,3,1,5,2,4,7]=>0000000=>0000000
[7,3,2,6,1,4,5,8]=>[8,5,4,1,6,2,3,7]=>0000000=>0000000
[7,6,3,5,1,2,4,8]=>[8,4,2,1,5,3,6,7]=>0000000=>0000000
[4,3,2,8,1,5,6,7]=>[7,6,5,1,8,2,3,4]=>0000000=>0000000
[5,3,2,8,1,4,6,7]=>[7,6,4,1,8,2,3,5]=>0000000=>0000000
[5,4,2,8,1,3,6,7]=>[7,6,3,1,8,2,4,5]=>0000000=>0000000
[5,4,3,8,1,2,6,7]=>[7,6,2,1,8,3,4,5]=>0000000=>0000000
[6,3,2,8,1,4,5,7]=>[7,5,4,1,8,2,3,6]=>0000000=>0000000
[6,4,3,8,1,2,5,7]=>[7,5,2,1,8,3,4,6]=>0000000=>0000000
[6,5,2,8,1,3,4,7]=>[7,4,3,1,8,2,5,6]=>0000000=>0000000
[6,5,3,8,1,2,4,7]=>[7,4,2,1,8,3,5,6]=>0000000=>0000000
[6,5,4,8,1,2,3,7]=>[7,3,2,1,8,4,5,6]=>0000000=>0000000
[7,4,2,8,1,3,5,6]=>[6,5,3,1,8,2,4,7]=>0000000=>0000000
[7,4,3,8,1,2,5,6]=>[6,5,2,1,8,3,4,7]=>0000000=>0000000
[7,5,2,8,1,3,4,6]=>[6,4,3,1,8,2,5,7]=>0000000=>0000000
[7,5,3,8,1,2,4,6]=>[6,4,2,1,8,3,5,7]=>0000000=>0000000
[7,6,4,8,1,2,3,5]=>[5,3,2,1,8,4,6,7]=>0000000=>0000000
[8,3,2,6,1,4,5,7]=>[7,5,4,1,6,2,3,8]=>0000001=>1000000
[8,4,2,7,1,3,5,6]=>[6,5,3,1,7,2,4,8]=>0000001=>1000000
[8,5,2,7,1,3,4,6]=>[6,4,3,1,7,2,5,8]=>0000001=>1000000
[8,5,3,7,1,2,4,6]=>[6,4,2,1,7,3,5,8]=>0000001=>1000000
[8,5,4,7,1,2,3,6]=>[6,3,2,1,7,4,5,8]=>0000001=>1000000
[8,6,3,7,1,2,4,5]=>[5,4,2,1,7,3,6,8]=>0000001=>1000000
[8,7,2,4,1,3,5,6]=>[6,5,3,1,4,2,7,8]=>0000011=>1100000
[8,7,2,5,1,3,4,6]=>[6,4,3,1,5,2,7,8]=>0000011=>1100000
[8,7,3,5,1,2,4,6]=>[6,4,2,1,5,3,7,8]=>0000011=>1100000
[8,7,2,6,1,3,4,5]=>[5,4,3,1,6,2,7,8]=>0000011=>1100000
[8,7,3,6,1,2,4,5]=>[5,4,2,1,6,3,7,8]=>0000011=>1100000
[8,7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7,8]=>0000011=>1100000
[5,6,2,4,8,1,3,7]=>[7,3,1,8,4,2,6,5]=>0000000=>0000000
[3,7,2,5,8,1,4,6]=>[6,4,1,8,5,2,7,3]=>0000000=>0000000
[4,7,3,5,8,1,2,6]=>[6,2,1,8,5,3,7,4]=>0000000=>0000000
[5,7,2,4,8,1,3,6]=>[6,3,1,8,4,2,7,5]=>0000000=>0000000
[5,7,3,4,8,1,2,6]=>[6,2,1,8,4,3,7,5]=>0000000=>0000000
[4,7,3,6,8,1,2,5]=>[5,2,1,8,6,3,7,4]=>0000000=>0000000
[5,7,2,6,8,1,3,4]=>[4,3,1,8,6,2,7,5]=>0000000=>0000000
[5,7,4,6,8,1,2,3]=>[3,2,1,8,6,4,7,5]=>0010000=>0000100
[3,8,2,5,7,1,4,6]=>[6,4,1,7,5,2,8,3]=>0000000=>0000000
[4,8,2,5,7,1,3,6]=>[6,3,1,7,5,2,8,4]=>0000000=>0000000
[4,8,3,5,7,1,2,6]=>[6,2,1,7,5,3,8,4]=>0000000=>0000000
[5,8,2,4,7,1,3,6]=>[6,3,1,7,4,2,8,5]=>0000000=>0000000
[5,8,3,4,7,1,2,6]=>[6,2,1,7,4,3,8,5]=>0000000=>0000000
[3,8,2,6,7,1,4,5]=>[5,4,1,7,6,2,8,3]=>0000000=>0000000
[6,8,2,5,7,1,3,4]=>[4,3,1,7,5,2,8,6]=>0000000=>0000000
[6,8,4,5,7,1,2,3]=>[3,2,1,7,5,4,8,6]=>0010000=>0000100
[7,8,2,4,6,1,3,5]=>[5,3,1,6,4,2,8,7]=>0000010=>0100000
[7,8,3,5,6,1,2,4]=>[4,2,1,6,5,3,8,7]=>0000010=>0100000
[5,4,3,6,8,1,2,7]=>[7,2,1,8,6,3,4,5]=>0000000=>0000000
[6,4,3,5,8,1,2,7]=>[7,2,1,8,5,3,4,6]=>0000000=>0000000
[4,3,2,7,8,1,5,6]=>[6,5,1,8,7,2,3,4]=>0000000=>0000000
[5,4,3,7,8,1,2,6]=>[6,2,1,8,7,3,4,5]=>0000000=>0000000
[6,4,2,7,8,1,3,5]=>[5,3,1,8,7,2,4,6]=>0000000=>0000000
[6,5,2,7,8,1,3,4]=>[4,3,1,8,7,2,5,6]=>0000000=>0000000
[6,5,3,7,8,1,2,4]=>[4,2,1,8,7,3,5,6]=>0000000=>0000000
[7,4,2,6,8,1,3,5]=>[5,3,1,8,6,2,4,7]=>0000000=>0000000
[7,6,2,5,8,1,3,4]=>[4,3,1,8,5,2,6,7]=>0000000=>0000000
[8,6,2,5,7,1,3,4]=>[4,3,1,7,5,2,6,8]=>0000001=>1000000
[8,6,3,5,7,1,2,4]=>[4,2,1,7,5,3,6,8]=>0000001=>1000000
[8,7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7,8]=>0000011=>1100000
[8,7,3,4,6,1,2,5]=>[5,2,1,6,4,3,7,8]=>0000011=>1100000
[5,4,7,2,6,1,3,8]=>[8,3,1,6,2,7,4,5]=>0000000=>0000000
[7,3,6,2,5,1,4,8]=>[8,4,1,5,2,6,3,7]=>0000000=>0000000
[5,4,8,2,6,1,3,7]=>[7,3,1,6,2,8,4,5]=>0000000=>0000000
[6,4,8,3,5,1,2,7]=>[7,2,1,5,3,8,4,6]=>0000000=>0000000
[4,3,8,2,7,1,5,6]=>[6,5,1,7,2,8,3,4]=>0000000=>0000000
[6,4,8,3,7,1,2,5]=>[5,2,1,7,3,8,4,6]=>0000000=>0000000
[6,5,8,3,7,1,2,4]=>[4,2,1,7,3,8,5,6]=>0000000=>0000000
[7,5,8,2,4,1,3,6]=>[6,3,1,4,2,8,5,7]=>0000000=>0000000
[7,5,8,3,4,1,2,6]=>[6,2,1,4,3,8,5,7]=>0000000=>0000000
[7,3,8,2,6,1,4,5]=>[5,4,1,6,2,8,3,7]=>0000000=>0000000
[7,4,8,3,6,1,2,5]=>[5,2,1,6,3,8,4,7]=>0000000=>0000000
[7,5,8,2,6,1,3,4]=>[4,3,1,6,2,8,5,7]=>0000000=>0000000
[7,5,8,4,6,1,2,3]=>[3,2,1,6,4,8,5,7]=>0010000=>0000100
[8,4,6,2,5,1,3,7]=>[7,3,1,5,2,6,4,8]=>0000001=>1000000
[8,4,7,3,5,1,2,6]=>[6,2,1,5,3,7,4,8]=>0000001=>1000000
[8,5,7,2,4,1,3,6]=>[6,3,1,4,2,7,5,8]=>0000001=>1000000
[8,3,7,2,6,1,4,5]=>[5,4,1,6,2,7,3,8]=>0000001=>1000000
[8,4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4,8]=>0000001=>1000000
[8,4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4,8]=>0000001=>1000000
[8,5,7,2,6,1,3,4]=>[4,3,1,6,2,7,5,8]=>0000001=>1000000
[8,5,7,3,6,1,2,4]=>[4,2,1,6,3,7,5,8]=>0000001=>1000000
[8,5,7,4,6,1,2,3]=>[3,2,1,6,4,7,5,8]=>0010001=>1000100
[8,6,7,2,4,1,3,5]=>[5,3,1,4,2,7,6,8]=>0000101=>1010000
[8,6,7,2,5,1,3,4]=>[4,3,1,5,2,7,6,8]=>0000101=>1010000
[8,6,7,3,5,1,2,4]=>[4,2,1,5,3,7,6,8]=>0000101=>1010000
[5,4,3,2,7,1,6,8]=>[8,6,1,7,2,3,4,5]=>0000000=>0000000
[6,5,3,2,7,1,4,8]=>[8,4,1,7,2,3,5,6]=>0000000=>0000000
[6,5,4,2,7,1,3,8]=>[8,3,1,7,2,4,5,6]=>0000000=>0000000
[7,5,3,2,6,1,4,8]=>[8,4,1,6,2,3,5,7]=>0000000=>0000000
[7,5,4,2,6,1,3,8]=>[8,3,1,6,2,4,5,7]=>0000000=>0000000
[7,6,4,2,5,1,3,8]=>[8,3,1,5,2,4,6,7]=>0000000=>0000000
[5,4,3,2,8,1,6,7]=>[7,6,1,8,2,3,4,5]=>0000000=>0000000
[6,5,3,2,8,1,4,7]=>[7,4,1,8,2,3,5,6]=>0000000=>0000000
[6,5,4,3,8,1,2,7]=>[7,2,1,8,3,4,5,6]=>0000000=>0000000
[7,4,3,2,8,1,5,6]=>[6,5,1,8,2,3,4,7]=>0000000=>0000000
[7,5,3,2,8,1,4,6]=>[6,4,1,8,2,3,5,7]=>0000000=>0000000
[7,6,3,2,8,1,4,5]=>[5,4,1,8,2,3,6,7]=>0000000=>0000000
[7,6,4,2,8,1,3,5]=>[5,3,1,8,2,4,6,7]=>0000000=>0000000
[7,6,4,3,8,1,2,5]=>[5,2,1,8,3,4,6,7]=>0000000=>0000000
[8,5,3,2,6,1,4,7]=>[7,4,1,6,2,3,5,8]=>0000001=>1000000
[8,6,3,2,5,1,4,7]=>[7,4,1,5,2,3,6,8]=>0000001=>1000000
[8,5,3,2,7,1,4,6]=>[6,4,1,7,2,3,5,8]=>0000001=>1000000
[8,6,4,2,7,1,3,5]=>[5,3,1,7,2,4,6,8]=>0000001=>1000000
[8,6,4,3,7,1,2,5]=>[5,2,1,7,3,4,6,8]=>0000001=>1000000
[8,7,3,2,5,1,4,6]=>[6,4,1,5,2,3,7,8]=>0000011=>1100000
[8,7,3,2,6,1,4,5]=>[5,4,1,6,2,3,7,8]=>0000011=>1100000
[8,7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7,8]=>0000011=>1100000
[8,7,4,3,6,1,2,5]=>[5,2,1,6,3,4,7,8]=>0000011=>1100000
[8,7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7,8]=>0000011=>1100000
[8,7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7,8]=>0000111=>1110000
[4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4]=>0000000=>0000000
[5,8,3,7,2,6,1,4]=>[4,1,6,2,7,3,8,5]=>0000000=>0000000
[5,8,4,7,2,6,1,3]=>[3,1,6,2,7,4,8,5]=>0000000=>0000000
[5,8,4,7,3,6,1,2]=>[2,1,6,3,7,4,8,5]=>0100000=>0000010
[6,8,3,7,2,5,1,4]=>[4,1,5,2,7,3,8,6]=>0000000=>0000000
[6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6]=>0000000=>0000000
[6,8,4,7,3,5,1,2]=>[2,1,5,3,7,4,8,6]=>0100000=>0000010
[6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6]=>0001000=>0001000
[6,8,5,7,3,4,1,2]=>[2,1,4,3,7,5,8,6]=>0101000=>0001010
[7,8,3,6,2,5,1,4]=>[4,1,5,2,6,3,8,7]=>0000010=>0100000
[7,8,4,6,2,5,1,3]=>[3,1,5,2,6,4,8,7]=>0000010=>0100000
[7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7]=>0100010=>0100010
[7,8,5,6,2,4,1,3]=>[3,1,4,2,6,5,8,7]=>0001010=>0101000
[5,4,3,8,2,7,1,6]=>[6,1,7,2,8,3,4,5]=>0000000=>0000000
[6,4,3,8,2,7,1,5]=>[5,1,7,2,8,3,4,6]=>0000000=>0000000
[6,5,3,8,2,7,1,4]=>[4,1,7,2,8,3,5,6]=>0000000=>0000000
[7,4,3,8,2,6,1,5]=>[5,1,6,2,8,3,4,7]=>0000000=>0000000
[7,5,3,8,2,6,1,4]=>[4,1,6,2,8,3,5,7]=>0000000=>0000000
[7,5,4,8,2,6,1,3]=>[3,1,6,2,8,4,5,7]=>0000000=>0000000
[7,6,3,8,2,5,1,4]=>[4,1,5,2,8,3,6,7]=>0000000=>0000000
[7,6,4,8,2,5,1,3]=>[3,1,5,2,8,4,6,7]=>0000000=>0000000
[8,5,3,7,2,6,1,4]=>[4,1,6,2,7,3,5,8]=>0000001=>1000000
[8,6,3,7,2,5,1,4]=>[4,1,5,2,7,3,6,8]=>0000001=>1000000
[8,6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6,8]=>0000001=>1000000
[8,6,5,7,2,4,1,3]=>[3,1,4,2,7,5,6,8]=>0001001=>1001000
[8,7,5,6,2,4,1,3]=>[3,1,4,2,6,5,7,8]=>0001011=>1101000
[8,5,4,3,2,7,1,6]=>[6,1,7,2,3,4,5,8]=>0000001=>1000000
[8,7,5,4,2,6,1,3]=>[3,1,6,2,4,5,7,8]=>0000011=>1100000
[8,7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7,8]=>0001111=>1111000
[8,1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1,8]=>0000001=>1000000
[8,1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1,8]=>0000001=>1000000
[8,1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1,8]=>0000001=>1000000
[8,1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1,8]=>0000001=>1000000
[4,1,2,8,7,3,5,6]=>[6,5,3,7,8,2,1,4]=>0000000=>0000000
[4,1,2,7,6,3,8,5]=>[5,8,3,6,7,2,1,4]=>0000000=>0000000
[8,1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1,8]=>0000001=>1000000
[8,1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1,8]=>0000001=>1000000
[8,1,2,7,6,3,4,5]=>[5,4,3,6,7,2,1,8]=>0000001=>1000000
[7,1,2,5,6,3,8,4]=>[4,8,3,6,5,2,1,7]=>0000000=>0000000
[4,1,2,5,8,7,3,6]=>[6,3,7,8,5,2,1,4]=>0000000=>0000000
[3,1,8,2,6,4,5,7]=>[7,5,4,6,2,8,1,3]=>0000000=>0000000
[3,1,7,2,6,4,8,5]=>[5,8,4,6,2,7,1,3]=>0000000=>0000000
[3,1,8,2,6,7,4,5]=>[5,4,7,6,2,8,1,3]=>0000000=>0000000
[6,1,4,2,3,8,5,7]=>[7,5,8,3,2,4,1,6]=>0000000=>0000000
[6,1,5,2,3,8,4,7]=>[7,4,8,3,2,5,1,6]=>0000000=>0000000
[8,1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1,8]=>0000001=>1000000
[5,1,4,2,8,3,6,7]=>[7,6,3,8,2,4,1,5]=>0000000=>0000000
[5,1,4,2,7,3,8,6]=>[6,8,3,7,2,4,1,5]=>0000000=>0000000
[7,1,4,2,6,3,8,5]=>[5,8,3,6,2,4,1,7]=>0000000=>0000000
[8,1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1,8]=>0000001=>1000000
[7,1,5,2,6,3,8,4]=>[4,8,3,6,2,5,1,7]=>0000000=>0000000
[5,1,4,2,8,7,3,6]=>[6,3,7,8,2,4,1,5]=>0000000=>0000000
[8,1,4,2,6,7,3,5]=>[5,3,7,6,2,4,1,8]=>0000001=>1000000
[5,1,4,2,6,7,8,3]=>[3,8,7,6,2,4,1,5]=>0000000=>0000000
[3,1,8,6,2,4,5,7]=>[7,5,4,2,6,8,1,3]=>0000000=>0000000
[3,1,8,6,2,7,4,5]=>[5,4,7,2,6,8,1,3]=>0000000=>0000000
[7,1,4,6,2,3,8,5]=>[5,8,3,2,6,4,1,7]=>0000000=>0000000
[7,1,8,6,2,3,4,5]=>[5,4,3,2,6,8,1,7]=>0000000=>0000000
[7,1,6,5,2,3,8,4]=>[4,8,3,2,5,6,1,7]=>0000000=>0000000
[6,1,4,5,2,8,3,7]=>[7,3,8,2,5,4,1,6]=>0000000=>0000000
[8,1,4,5,2,7,3,6]=>[6,3,7,2,5,4,1,8]=>0000001=>1000000
[8,1,4,6,2,7,3,5]=>[5,3,7,2,6,4,1,8]=>0000001=>1000000
[3,1,8,5,7,2,4,6]=>[6,4,2,7,5,8,1,3]=>0000000=>0000000
[8,1,4,5,7,2,3,6]=>[6,3,2,7,5,4,1,8]=>0000001=>1000000
[3,1,4,5,8,7,2,6]=>[6,2,7,8,5,4,1,3]=>0000000=>0000000
[8,1,4,5,6,7,2,3]=>[3,2,7,6,5,4,1,8]=>0000001=>1000000
[2,5,1,3,8,7,4,6]=>[6,4,7,8,3,1,5,2]=>0000000=>0000000
[2,4,1,8,3,7,5,6]=>[6,5,7,3,8,1,4,2]=>0000000=>0000000
[2,7,1,6,3,4,8,5]=>[5,8,4,3,6,1,7,2]=>0000000=>0000000
[2,8,1,6,3,7,4,5]=>[5,4,7,3,6,1,8,2]=>0000000=>0000000
[2,8,1,5,7,3,4,6]=>[6,4,3,7,5,1,8,2]=>0000000=>0000000
[2,8,1,7,6,3,4,5]=>[5,4,3,6,7,1,8,2]=>0000000=>0000000
[2,7,1,5,6,3,8,4]=>[4,8,3,6,5,1,7,2]=>0000000=>0000000
[6,3,1,2,4,7,8,5]=>[5,8,7,4,2,1,3,6]=>0000000=>0000000
[5,3,1,2,8,4,6,7]=>[7,6,4,8,2,1,3,5]=>0000000=>0000000
[5,3,1,2,7,4,8,6]=>[6,8,4,7,2,1,3,5]=>0000000=>0000000
[5,3,1,2,6,7,8,4]=>[4,8,7,6,2,1,3,5]=>0000000=>0000000
[5,8,1,2,3,7,4,6]=>[6,4,7,3,2,1,8,5]=>0000000=>0000000
[5,4,1,2,8,3,6,7]=>[7,6,3,8,2,1,4,5]=>0000000=>0000000
[5,4,1,2,7,3,8,6]=>[6,8,3,7,2,1,4,5]=>0000000=>0000000
[5,8,1,2,7,3,4,6]=>[6,4,3,7,2,1,8,5]=>0000000=>0000000
[8,7,1,2,6,3,4,5]=>[5,4,3,6,2,1,7,8]=>0000011=>1100000
[5,4,1,2,6,8,3,7]=>[7,3,8,6,2,1,4,5]=>0000000=>0000000
[8,4,1,2,6,7,3,5]=>[5,3,7,6,2,1,4,8]=>0000001=>1000000
[5,4,1,2,6,7,8,3]=>[3,8,7,6,2,1,4,5]=>0000000=>0000000
[4,3,1,6,2,8,5,7]=>[7,5,8,2,6,1,3,4]=>0000000=>0000000
[4,3,1,6,2,7,8,5]=>[5,8,7,2,6,1,3,4]=>0000000=>0000000
[7,3,1,6,2,4,8,5]=>[5,8,4,2,6,1,3,7]=>0000000=>0000000
[8,3,1,5,2,7,4,6]=>[6,4,7,2,5,1,3,8]=>0000001=>1000000
[8,3,1,6,2,7,4,5]=>[5,4,7,2,6,1,3,8]=>0000001=>1000000
[6,3,1,5,2,7,8,4]=>[4,8,7,2,5,1,3,6]=>0000000=>0000000
[7,4,1,5,2,3,8,6]=>[6,8,3,2,5,1,4,7]=>0000000=>0000000
[8,4,1,6,2,3,5,7]=>[7,5,3,2,6,1,4,8]=>0000001=>1000000
[7,4,1,8,2,3,5,6]=>[6,5,3,2,8,1,4,7]=>0000000=>0000000
[8,7,1,5,2,3,4,6]=>[6,4,3,2,5,1,7,8]=>0000011=>1100000
[8,7,1,6,2,3,4,5]=>[5,4,3,2,6,1,7,8]=>0000011=>1100000
[6,4,1,5,2,8,3,7]=>[7,3,8,2,5,1,4,6]=>0000000=>0000000
[8,4,1,5,2,7,3,6]=>[6,3,7,2,5,1,4,8]=>0000001=>1000000
[8,4,1,6,2,7,3,5]=>[5,3,7,2,6,1,4,8]=>0000001=>1000000
[6,8,1,5,2,7,3,4]=>[4,3,7,2,5,1,8,6]=>0000000=>0000000
[4,3,1,8,7,2,5,6]=>[6,5,2,7,8,1,3,4]=>0000000=>0000000
[8,3,1,5,6,2,4,7]=>[7,4,2,6,5,1,3,8]=>0000001=>1000000
[8,3,1,7,6,2,4,5]=>[5,4,2,6,7,1,3,8]=>0000001=>1000000
[4,3,1,5,6,7,8,2]=>[2,8,7,6,5,1,3,4]=>0000000=>0000000
[2,3,7,1,6,4,8,5]=>[5,8,4,6,1,7,3,2]=>0000000=>0000000
[2,3,5,1,8,7,4,6]=>[6,4,7,8,1,5,3,2]=>0000000=>0000000
[2,3,8,1,6,7,4,5]=>[5,4,7,6,1,8,3,2]=>0000000=>0000000
[2,6,4,1,3,8,5,7]=>[7,5,8,3,1,4,6,2]=>0000000=>0000000
[2,6,4,1,3,7,8,5]=>[5,8,7,3,1,4,6,2]=>0000000=>0000000
[2,7,5,1,3,4,8,6]=>[6,8,4,3,1,5,7,2]=>0000000=>0000000
[2,8,5,1,3,7,4,6]=>[6,4,7,3,1,5,8,2]=>0000000=>0000000
[2,6,5,1,3,7,8,4]=>[4,8,7,3,1,5,6,2]=>0000000=>0000000
[2,8,4,1,7,3,5,6]=>[6,5,3,7,1,4,8,2]=>0000000=>0000000
[2,8,5,1,7,3,4,6]=>[6,4,3,7,1,5,8,2]=>0000000=>0000000
[2,8,4,1,6,7,3,5]=>[5,3,7,6,1,4,8,2]=>0000000=>0000000
[2,5,4,1,6,7,8,3]=>[3,8,7,6,1,4,5,2]=>0000000=>0000000
[6,3,4,1,2,8,5,7]=>[7,5,8,2,1,4,3,6]=>0000000=>0000000
[6,3,4,1,2,7,8,5]=>[5,8,7,2,1,4,3,6]=>0000000=>0000000
[6,3,7,1,2,4,8,5]=>[5,8,4,2,1,7,3,6]=>0000000=>0000000
[8,3,5,1,2,7,4,6]=>[6,4,7,2,1,5,3,8]=>0000001=>1000000
[6,3,8,1,2,7,4,5]=>[5,4,7,2,1,8,3,6]=>0000000=>0000000
[6,7,4,1,2,3,8,5]=>[5,8,3,2,1,4,7,6]=>0000000=>0000000
[6,8,5,1,2,3,4,7]=>[7,4,3,2,1,5,8,6]=>0000000=>0000000
[8,5,4,1,2,7,3,6]=>[6,3,7,2,1,4,5,8]=>0000001=>1000000
[8,3,4,1,7,2,5,6]=>[6,5,2,7,1,4,3,8]=>0000001=>1000000
[7,3,4,1,6,2,8,5]=>[5,8,2,6,1,4,3,7]=>0000000=>0000000
[8,3,5,1,6,2,4,7]=>[7,4,2,6,1,5,3,8]=>0000001=>1000000
[7,3,5,1,6,2,8,4]=>[4,8,2,6,1,5,3,7]=>0000000=>0000000
[8,5,4,1,7,2,3,6]=>[6,3,2,7,1,4,5,8]=>0000001=>1000000
[7,8,4,1,6,2,3,5]=>[5,3,2,6,1,4,8,7]=>0000010=>0100000
[5,3,4,1,6,7,8,2]=>[2,8,7,6,1,4,3,5]=>0000000=>0000000
[2,3,4,8,1,7,5,6]=>[6,5,7,1,8,4,3,2]=>0000000=>0000000
[2,3,7,5,1,4,8,6]=>[6,8,4,1,5,7,3,2]=>0000000=>0000000
[2,3,7,6,1,4,8,5]=>[5,8,4,1,6,7,3,2]=>0000000=>0000000
[2,8,4,6,1,3,5,7]=>[7,5,3,1,6,4,8,2]=>0000000=>0000000
[2,7,4,8,1,3,5,6]=>[6,5,3,1,8,4,7,2]=>0000000=>0000000
[2,8,6,5,1,3,4,7]=>[7,4,3,1,5,6,8,2]=>0000000=>0000000
[2,7,8,5,1,3,4,6]=>[6,4,3,1,5,8,7,2]=>0000000=>0000000
[2,8,4,6,1,7,3,5]=>[5,3,7,1,6,4,8,2]=>0000000=>0000000
[7,3,4,6,1,2,8,5]=>[5,8,2,1,6,4,3,7]=>0000000=>0000000
[7,3,8,5,1,2,4,6]=>[6,4,2,1,5,8,3,7]=>0000000=>0000000
[8,3,6,5,1,7,2,4]=>[4,2,7,1,5,6,3,8]=>0000001=>1000000
[2,3,4,8,6,1,5,7]=>[7,5,1,6,8,4,3,2]=>0000000=>0000000
[2,3,4,8,7,1,5,6]=>[6,5,1,7,8,4,3,2]=>0000000=>0000000
[2,3,8,7,6,1,4,5]=>[5,4,1,6,7,8,3,2]=>0000000=>0000000
[2,8,7,5,6,1,3,4]=>[4,3,1,6,5,7,8,2]=>0000000=>0000000
[8,3,4,7,6,1,2,5]=>[5,2,1,6,7,4,3,8]=>0000001=>1000000
[8,3,7,5,6,1,2,4]=>[4,2,1,6,5,7,3,8]=>0000001=>1000000
[2,3,4,5,8,7,1,6]=>[6,1,7,8,5,4,3,2]=>0000000=>0000000
[2,3,4,8,6,7,1,5]=>[5,1,7,6,8,4,3,2]=>0000000=>0000000
[6,5,8,7,3,4,1,2]=>[2,1,4,3,7,8,5,6]=>0101000=>0001010
[4,6,7,3,8,5,1,2]=>[2,1,5,8,3,7,6,4]=>0100000=>0000010
[3,6,7,4,5,8,1,2]=>[2,1,8,5,4,7,6,3]=>0100000=>0000010
[2,6,7,4,5,1,8,3]=>[3,8,1,5,4,7,6,2]=>0000000=>0000000
[1,6,7,4,5,2,3,8]=>[8,3,2,5,4,7,6,1]=>0000000=>0000000
[1,5,4,7,6,2,3,8]=>[8,3,2,6,7,4,5,1]=>0000000=>0000000
[2,5,4,7,6,1,8,3]=>[3,8,1,6,7,4,5,2]=>0000000=>0000000
[3,5,4,7,6,8,1,2]=>[2,1,8,6,7,4,5,3]=>0100000=>0000010
[4,5,3,7,8,6,1,2]=>[2,1,6,8,7,3,5,4]=>0100000=>0000010
[5,4,3,8,7,6,1,2]=>[2,1,6,7,8,3,4,5]=>0100000=>0000010
[6,4,8,3,7,5,1,2]=>[2,1,5,7,3,8,4,6]=>0100000=>0000010
[6,3,8,4,5,7,1,2]=>[2,1,7,5,4,8,3,6]=>0100000=>0000010
[5,3,4,8,6,7,1,2]=>[2,1,7,6,8,4,3,5]=>0100000=>0000010
[4,3,5,6,8,7,1,2]=>[2,1,7,8,6,5,3,4]=>0100000=>0000010
[3,2,5,6,1,8,7,4]=>[4,7,8,1,6,5,2,3]=>0000000=>0000000
[4,2,5,6,8,1,7,3]=>[3,7,1,8,6,5,2,4]=>0000000=>0000000
[5,2,4,8,6,1,7,3]=>[3,7,1,6,8,4,2,5]=>0000000=>0000000
[6,2,8,4,5,1,7,3]=>[3,7,1,5,4,8,2,6]=>0000000=>0000000
[7,8,2,4,5,1,6,3]=>[3,6,1,5,4,2,8,7]=>0000010=>0100000
[7,8,1,4,5,2,3,6]=>[6,3,2,5,4,1,8,7]=>0000010=>0100000
[6,1,8,4,5,2,3,7]=>[7,3,2,5,4,8,1,6]=>0000000=>0000000
[5,1,4,8,6,2,3,7]=>[7,3,2,6,8,4,1,5]=>0000000=>0000000
[4,1,3,2,8,6,5,7]=>[7,5,6,8,2,3,1,4]=>0000000=>0000000
[5,1,3,8,2,6,4,7]=>[7,4,6,2,8,3,1,5]=>0000000=>0000000
[6,1,8,3,2,5,4,7]=>[7,4,5,2,3,8,1,6]=>0000000=>0000000
[7,8,1,3,2,5,4,6]=>[6,4,5,2,3,1,8,7]=>0000010=>0100000
[6,2,8,3,1,5,7,4]=>[4,7,5,1,3,8,2,6]=>0000000=>0000000
[5,2,3,8,1,6,7,4]=>[4,7,6,1,8,3,2,5]=>0000000=>0000000
[6,3,8,2,1,7,5,4]=>[4,5,7,1,2,8,3,6]=>0000000=>0000000
[7,8,3,2,1,6,5,4]=>[4,5,6,1,2,3,8,7]=>0000010=>0100000
[7,8,4,2,6,1,5,3]=>[3,5,1,6,2,4,8,7]=>0000010=>0100000
[5,4,2,8,7,1,6,3]=>[3,6,1,7,8,2,4,5]=>0000000=>0000000
[4,5,2,7,8,1,6,3]=>[3,6,1,8,7,2,5,4]=>0000000=>0000000
[3,5,2,7,1,8,6,4]=>[4,6,8,1,7,2,5,3]=>0000000=>0000000
[2,5,3,7,1,6,8,4]=>[4,8,6,1,7,3,5,2]=>0000000=>0000000
[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>0000000=>0000000
[1,6,7,3,2,5,4,8]=>[8,4,5,2,3,7,6,1]=>0000000=>0000000
[2,6,7,3,1,5,8,4]=>[4,8,5,1,3,7,6,2]=>0000000=>0000000
[3,6,7,2,1,8,5,4]=>[4,5,8,1,2,7,6,3]=>0000000=>0000000
[4,6,7,2,8,1,5,3]=>[3,5,1,8,2,7,6,4]=>0000000=>0000000
[5,6,7,8,2,1,4,3]=>[3,4,1,2,8,7,6,5]=>0001000=>0001000
[7,8,5,6,2,1,4,3]=>[3,4,1,2,6,5,8,7]=>0001010=>0101000
[6,5,8,7,1,2,3,4]=>[4,3,2,1,7,8,5,6]=>0001000=>0001000
[5,4,1,8,7,2,3,6]=>[6,3,2,7,8,1,4,5]=>0000000=>0000000
[6,4,8,1,7,2,3,5]=>[5,3,2,7,1,8,4,6]=>0000000=>0000000
[7,8,3,1,2,6,4,5]=>[5,4,6,2,1,3,8,7]=>0000010=>0100000
[5,3,1,8,2,7,4,6]=>[6,4,7,2,8,1,3,5]=>0000000=>0000000
[4,3,1,2,8,7,5,6]=>[6,5,7,8,2,1,3,4]=>0000000=>0000000
[4,2,1,3,8,5,7,6]=>[6,7,5,8,3,1,2,4]=>0000000=>0000000
[6,2,8,1,3,4,7,5]=>[5,7,4,3,1,8,2,6]=>0000000=>0000000
[7,8,2,1,3,4,6,5]=>[5,6,4,3,1,2,8,7]=>0000010=>0100000
[4,5,2,3,7,6,1,8]=>[8,1,6,7,3,2,5,4]=>0000000=>0000000
[6,4,3,7,2,5,1,8]=>[8,1,5,2,7,3,4,6]=>0000000=>0000000
[1,5,6,3,4,8,7,2]=>[2,7,8,4,3,6,5,1]=>0000000=>0000000
[4,6,2,7,3,5,1,8]=>[8,1,5,3,7,2,6,4]=>0000000=>0000000
[3,2,6,7,4,5,1,8]=>[8,1,5,4,7,6,2,3]=>0000000=>0000000
[4,7,2,6,5,3,1,8]=>[8,1,3,5,6,2,7,4]=>0000000=>0000000
[4,8,2,6,5,1,3,7]=>[7,3,1,5,6,2,8,4]=>0000000=>0000000
[4,1,2,6,5,8,7,3]=>[3,7,8,5,6,2,1,4]=>0000000=>0000000
[5,1,6,2,4,8,7,3]=>[3,7,8,4,2,6,1,5]=>0000000=>0000000
[6,1,5,4,2,8,7,3]=>[3,7,8,2,4,5,1,6]=>0000000=>0000000
[7,1,5,4,8,2,6,3]=>[3,6,2,8,4,5,1,7]=>0000000=>0000000
[8,1,5,4,7,6,2,3]=>[3,2,6,7,4,5,1,8]=>0000001=>1000000
[8,1,6,7,4,5,2,3]=>[3,2,5,4,7,6,1,8]=>0000001=>1000000
[7,1,6,8,4,2,5,3]=>[3,5,2,4,8,6,1,7]=>0000000=>0000000
[6,1,7,8,2,4,5,3]=>[3,5,4,2,8,7,1,6]=>0000000=>0000000
[5,1,7,2,8,4,6,3]=>[3,6,4,8,2,7,1,5]=>0000000=>0000000
[4,1,2,7,8,5,6,3]=>[3,6,5,8,7,2,1,4]=>0000000=>0000000
[3,2,8,7,1,5,4,6]=>[6,4,5,1,7,8,2,3]=>0000000=>0000000
[5,8,7,2,1,4,3,6]=>[6,3,4,1,2,7,8,5]=>0000000=>0000000
[6,8,7,1,2,4,3,5]=>[5,3,4,2,1,7,8,6]=>0000100=>0010000
[7,8,6,1,4,2,3,5]=>[5,3,2,4,1,6,8,7]=>0000110=>0110000
[8,7,6,1,4,3,2,5]=>[5,2,3,4,1,6,7,8]=>0000111=>1110000
[1,6,7,8,3,4,5,2]=>[2,5,4,3,8,7,6,1]=>0000000=>0000000
[8,6,7,1,3,4,2,5]=>[5,2,4,3,1,7,6,8]=>0000101=>1010000
[7,6,8,1,3,2,4,5]=>[5,4,2,3,1,8,6,7]=>0000100=>0010000
[5,7,8,2,1,3,4,6]=>[6,4,3,1,2,8,7,5]=>0000000=>0000000
[4,7,2,8,1,3,5,6]=>[6,5,3,1,8,2,7,4]=>0000000=>0000000
[3,2,6,8,4,1,5,7]=>[7,5,1,4,8,6,2,3]=>0000000=>0000000
[4,6,2,8,3,1,5,7]=>[7,5,1,3,8,2,6,4]=>0000000=>0000000
[5,6,8,2,3,1,4,7]=>[7,4,1,3,2,8,6,5]=>0000000=>0000000
[6,5,8,3,2,1,4,7]=>[7,4,1,2,3,8,5,6]=>0000000=>0000000
[7,5,8,3,1,2,4,6]=>[6,4,2,1,3,8,5,7]=>0000000=>0000000
[1,5,7,3,8,4,6,2]=>[2,6,4,8,3,7,5,1]=>0000000=>0000000
[1,4,3,7,8,5,6,2]=>[2,6,5,8,7,3,4,1]=>0000000=>0000000
[6,4,3,8,2,1,5,7]=>[7,5,1,2,8,3,4,6]=>0000000=>0000000
[4,5,2,3,8,1,6,7]=>[7,6,1,8,3,2,5,4]=>0000000=>0000000
[3,2,5,4,8,1,6,7]=>[7,6,1,8,4,5,2,3]=>0000000=>0000000
[4,5,2,3,1,8,7,6]=>[6,7,8,1,3,2,5,4]=>0000000=>0000000
[6,4,3,1,2,8,7,5]=>[5,7,8,2,1,3,4,6]=>0000000=>0000000
[7,4,3,1,8,2,6,5]=>[5,6,2,8,1,3,4,7]=>0000000=>0000000
[8,4,3,1,7,6,2,5]=>[5,2,6,7,1,3,4,8]=>0000001=>1000000
[8,5,1,3,7,6,2,4]=>[4,2,6,7,3,1,5,8]=>0000001=>1000000
[7,5,1,3,8,2,6,4]=>[4,6,2,8,3,1,5,7]=>0000000=>0000000
[6,5,1,3,2,8,7,4]=>[4,7,8,2,3,1,5,6]=>0000000=>0000000
[5,6,1,2,3,8,7,4]=>[4,7,8,3,2,1,6,5]=>0000000=>0000000
[4,6,2,1,3,8,7,5]=>[5,7,8,3,1,2,6,4]=>0000000=>0000000
[3,2,6,1,4,8,7,5]=>[5,7,8,4,1,6,2,3]=>0000000=>0000000
[5,7,1,2,8,3,6,4]=>[4,6,3,8,2,1,7,5]=>0000000=>0000000
[6,7,1,8,2,3,5,4]=>[4,5,3,2,8,1,7,6]=>0000000=>0000000
[7,6,1,8,3,2,5,4]=>[4,5,2,3,8,1,6,7]=>0000000=>0000000
[8,6,1,7,3,5,2,4]=>[4,2,5,3,7,1,6,8]=>0000001=>1000000
[1,7,8,6,5,3,4,2]=>[2,4,3,5,6,8,7,1]=>0000000=>0000000
[6,8,1,7,2,5,3,4]=>[4,3,5,2,7,1,8,6]=>0000000=>0000000
[4,1,2,8,7,6,5,3]=>[3,5,6,7,8,2,1,4]=>0000000=>0000000
[3,2,5,1,6,4,8,7]=>[7,8,4,6,1,5,2,3]=>0000000=>0000000
[3,2,5,4,7,1,8,6]=>[6,8,1,7,4,5,2,3]=>0000000=>0000000
[4,2,5,3,7,6,8,1]=>[1,8,6,7,3,5,2,4]=>1000000=>0000001
[4,2,5,3,7,1,8,6]=>[6,8,1,7,3,5,2,4]=>0000000=>0000000
[4,2,5,3,6,1,8,7]=>[7,8,1,6,3,5,2,4]=>0000000=>0000000
[4,2,5,1,6,3,8,7]=>[7,8,3,6,1,5,2,4]=>0000000=>0000000
[3,1,5,4,6,2,8,7]=>[7,8,2,6,4,5,1,3]=>0000000=>0000000
[4,1,5,3,6,2,8,7]=>[7,8,2,6,3,5,1,4]=>0000000=>0000000
[4,3,5,1,6,2,8,7]=>[7,8,2,6,1,5,3,4]=>0000000=>0000000
[4,3,5,2,7,1,8,6]=>[6,8,1,7,2,5,3,4]=>0000000=>0000000
[4,3,6,2,7,5,8,1]=>[1,8,5,7,2,6,3,4]=>1000000=>0000001
[4,3,6,2,7,1,8,5]=>[5,8,1,7,2,6,3,4]=>0000000=>0000000
[4,3,6,1,7,2,8,5]=>[5,8,2,7,1,6,3,4]=>0000000=>0000000
[4,3,5,1,7,2,8,6]=>[6,8,2,7,1,5,3,4]=>0000000=>0000000
[4,1,5,3,7,2,8,6]=>[6,8,2,7,3,5,1,4]=>0000000=>0000000
[3,1,5,4,7,2,8,6]=>[6,8,2,7,4,5,1,3]=>0000000=>0000000
[2,1,5,4,7,3,8,6]=>[6,8,3,7,4,5,1,2]=>0000000=>0000000
[3,1,5,4,7,6,8,2]=>[2,8,6,7,4,5,1,3]=>0000000=>0000000
[4,1,5,3,7,6,8,2]=>[2,8,6,7,3,5,1,4]=>0000000=>0000000
[4,3,5,1,7,6,8,2]=>[2,8,6,7,1,5,3,4]=>0000000=>0000000
[4,3,6,1,7,5,8,2]=>[2,8,5,7,1,6,3,4]=>0000000=>0000000
[4,3,6,5,7,1,8,2]=>[2,8,1,7,5,6,3,4]=>0000000=>0000000
[5,3,6,4,7,2,8,1]=>[1,8,2,7,4,6,3,5]=>1000000=>0000001
[5,3,6,4,7,1,8,2]=>[2,8,1,7,4,6,3,5]=>0000000=>0000000
[5,3,6,1,7,4,8,2]=>[2,8,4,7,1,6,3,5]=>0000000=>0000000
[5,1,6,3,7,4,8,2]=>[2,8,4,7,3,6,1,5]=>0000000=>0000000
[4,1,6,3,7,5,8,2]=>[2,8,5,7,3,6,1,4]=>0000000=>0000000
[3,1,6,4,7,5,8,2]=>[2,8,5,7,4,6,1,3]=>0000000=>0000000
[2,1,6,4,7,5,8,3]=>[3,8,5,7,4,6,1,2]=>0000000=>0000000
[2,1,6,4,7,3,8,5]=>[5,8,3,7,4,6,1,2]=>0000000=>0000000
[3,1,6,4,7,2,8,5]=>[5,8,2,7,4,6,1,3]=>0000000=>0000000
[4,1,6,3,7,2,8,5]=>[5,8,2,7,3,6,1,4]=>0000000=>0000000
[5,1,6,3,7,2,8,4]=>[4,8,2,7,3,6,1,5]=>0000000=>0000000
[5,3,6,1,7,2,8,4]=>[4,8,2,7,1,6,3,5]=>0000000=>0000000
[5,3,6,2,7,1,8,4]=>[4,8,1,7,2,6,3,5]=>0000000=>0000000
[5,3,6,2,7,4,8,1]=>[1,8,4,7,2,6,3,5]=>1000000=>0000001
[5,2,6,3,7,4,8,1]=>[1,8,4,7,3,6,2,5]=>1000000=>0000001
[5,2,6,3,7,1,8,4]=>[4,8,1,7,3,6,2,5]=>0000000=>0000000
[5,2,6,1,7,3,8,4]=>[4,8,3,7,1,6,2,5]=>0000000=>0000000
[4,2,5,1,7,3,8,6]=>[6,8,3,7,1,5,2,4]=>0000000=>0000000
[4,2,6,1,7,3,8,5]=>[5,8,3,7,1,6,2,4]=>0000000=>0000000
[4,2,6,3,7,1,8,5]=>[5,8,1,7,3,6,2,4]=>0000000=>0000000
[4,2,6,3,7,5,8,1]=>[1,8,5,7,3,6,2,4]=>1000000=>0000001
[3,2,6,4,7,5,8,1]=>[1,8,5,7,4,6,2,3]=>1000000=>0000001
[3,2,6,4,7,1,8,5]=>[5,8,1,7,4,6,2,3]=>0000000=>0000000
[3,2,6,1,7,4,8,5]=>[5,8,4,7,1,6,2,3]=>0000000=>0000000
[3,2,5,1,7,4,8,6]=>[6,8,4,7,1,5,2,3]=>0000000=>0000000
[3,2,4,1,7,5,8,6]=>[6,8,5,7,1,4,2,3]=>0000000=>0000000
[3,1,4,2,7,6,8,5]=>[5,8,6,7,2,4,1,3]=>0000000=>0000000
[3,2,5,1,7,6,8,4]=>[4,8,6,7,1,5,2,3]=>0000000=>0000000
[3,2,6,1,7,5,8,4]=>[4,8,5,7,1,6,2,3]=>0000000=>0000000
[3,2,6,5,7,1,8,4]=>[4,8,1,7,5,6,2,3]=>0000000=>0000000
[4,2,6,5,7,3,8,1]=>[1,8,3,7,5,6,2,4]=>1000000=>0000001
[4,2,6,5,7,1,8,3]=>[3,8,1,7,5,6,2,4]=>0000000=>0000000
[4,2,6,1,7,5,8,3]=>[3,8,5,7,1,6,2,4]=>0000000=>0000000
[4,2,5,1,7,6,8,3]=>[3,8,6,7,1,5,2,4]=>0000000=>0000000
[4,1,5,2,7,6,8,3]=>[3,8,6,7,2,5,1,4]=>0000000=>0000000
[3,1,5,2,7,6,8,4]=>[4,8,6,7,2,5,1,3]=>0000000=>0000000
[2,1,5,3,7,6,8,4]=>[4,8,6,7,3,5,1,2]=>0000000=>0000000
[2,1,6,3,7,5,8,4]=>[4,8,5,7,3,6,1,2]=>0000000=>0000000
[3,1,6,2,7,5,8,4]=>[4,8,5,7,2,6,1,3]=>0000000=>0000000
[4,1,6,2,7,5,8,3]=>[3,8,5,7,2,6,1,4]=>0000000=>0000000
[5,1,6,2,7,4,8,3]=>[3,8,4,7,2,6,1,5]=>0000000=>0000000
[5,2,6,1,7,4,8,3]=>[3,8,4,7,1,6,2,5]=>0000000=>0000000
[5,2,6,4,7,1,8,3]=>[3,8,1,7,4,6,2,5]=>0000000=>0000000
[5,2,6,4,7,3,8,1]=>[1,8,3,7,4,6,2,5]=>1000000=>0000001
[5,4,6,2,7,3,8,1]=>[1,8,3,7,2,6,4,5]=>1000000=>0000001
[5,4,6,2,7,1,8,3]=>[3,8,1,7,2,6,4,5]=>0000000=>0000000
[5,4,6,1,7,2,8,3]=>[3,8,2,7,1,6,4,5]=>0000000=>0000000
[5,1,6,4,7,2,8,3]=>[3,8,2,7,4,6,1,5]=>0000000=>0000000
[4,1,6,5,7,2,8,3]=>[3,8,2,7,5,6,1,4]=>0000000=>0000000
[3,1,6,5,7,2,8,4]=>[4,8,2,7,5,6,1,3]=>0000000=>0000000
[2,1,6,5,7,3,8,4]=>[4,8,3,7,5,6,1,2]=>0000000=>0000000
[3,1,6,5,7,4,8,2]=>[2,8,4,7,5,6,1,3]=>0000000=>0000000
[4,1,6,5,7,3,8,2]=>[2,8,3,7,5,6,1,4]=>0000000=>0000000
[5,1,6,4,7,3,8,2]=>[2,8,3,7,4,6,1,5]=>0000000=>0000000
[5,4,6,1,7,3,8,2]=>[2,8,3,7,1,6,4,5]=>0000000=>0000000
[5,4,6,3,7,1,8,2]=>[2,8,1,7,3,6,4,5]=>0000000=>0000000
[8,6,1,3,4,2,5,7]=>[7,5,2,4,3,1,6,8]=>0000001=>1000000
[2,4,5,7,3,1,8,6]=>[6,8,1,3,7,5,4,2]=>0000000=>0000000
[8,1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1,8]=>0000001=>1000000
[8,2,5,1,3,6,4,7]=>[7,4,6,3,1,5,2,8]=>0000001=>1000000
[8,6,1,4,5,3,2,7]=>[7,2,3,5,4,1,6,8]=>0000001=>1000000
[8,5,7,4,3,2,6,1]=>[1,6,2,3,4,7,5,8]=>1000001=>1000001
[4,6,3,8,7,1,5,2]=>[2,5,1,7,8,3,6,4]=>0000000=>0000000
[1,7,4,8,6,3,5,2]=>[2,5,3,6,8,4,7,1]=>0000000=>0000000
[8,2,6,1,4,7,5,3]=>[3,5,7,4,1,6,2,8]=>0000001=>1000000
[3,7,1,6,4,8,2,5]=>[5,2,8,4,6,1,7,3]=>0000000=>0000000
[3,6,8,5,7,2,4,1]=>[1,4,2,7,5,8,6,3]=>1000000=>0000001
[5,2,7,1,3,8,4,6]=>[6,4,8,3,1,7,2,5]=>0000000=>0000000
[5,3,1,7,8,2,4,6]=>[6,4,2,8,7,1,3,5]=>0000000=>0000000
[1,7,3,4,2,5,8,6]=>[6,8,5,2,4,3,7,1]=>0000000=>0000000
[4,7,2,1,3,5,8,6]=>[6,8,5,3,1,2,7,4]=>0000000=>0000000
[8,7,6,1,3,4,2,5]=>[5,2,4,3,1,6,7,8]=>0000111=>1110000
[8,5,7,3,2,1,6,4]=>[4,6,1,2,3,7,5,8]=>0000001=>1000000
[8,3,6,7,2,1,5,4]=>[4,5,1,2,7,6,3,8]=>0000001=>1000000
[3,7,8,6,2,1,5,4]=>[4,5,1,2,6,8,7,3]=>0000000=>0000000
[8,7,6,3,5,2,4,1]=>[1,4,2,5,3,6,7,8]=>1000111=>1110001
[2,7,4,8,1,6,5,3]=>[3,5,6,1,8,4,7,2]=>0000000=>0000000
[4,6,8,2,1,7,5,3]=>[3,5,7,1,2,8,6,4]=>0000000=>0000000
[8,5,3,7,1,6,2,4]=>[4,2,6,1,7,3,5,8]=>0000001=>1000000
[8,5,7,2,1,3,6,4]=>[4,6,3,1,2,7,5,8]=>0000001=>1000000
[4,6,1,8,7,2,5,3]=>[3,5,2,7,8,1,6,4]=>0000000=>0000000
[8,1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1,8]=>0000001=>1000000
[8,2,6,5,7,4,1,3]=>[3,1,4,7,5,6,2,8]=>0000001=>1000000
[2,7,6,8,5,4,1,3]=>[3,1,4,5,8,6,7,2]=>0000000=>0000000
[1,7,2,5,8,6,4,3]=>[3,4,6,8,5,2,7,1]=>0000000=>0000000
[3,2,5,1,6,8,4,7]=>[7,4,8,6,1,5,2,3]=>0000000=>0000000
[3,6,2,5,4,8,1,7]=>[7,1,8,4,5,2,6,3]=>0000000=>0000000
[3,5,8,2,4,7,6,1]=>[1,6,7,4,2,8,5,3]=>1000000=>0000001
[4,2,5,8,3,7,6,1]=>[1,6,7,3,8,5,2,4]=>1000000=>0000001
[4,2,6,5,3,8,1,7]=>[7,1,8,3,5,6,2,4]=>0000000=>0000000
[5,3,1,6,8,2,4,7]=>[7,4,2,8,6,1,3,5]=>0000000=>0000000
[5,6,2,8,1,3,4,7]=>[7,4,3,1,8,2,6,5]=>0000000=>0000000
[5,4,3,2,7,1,8,6]=>[6,8,1,7,2,3,4,5]=>0000000=>0000000
[5,4,3,8,2,7,6,1]=>[1,6,7,2,8,3,4,5]=>1000000=>0000001
[4,3,6,2,8,7,5,1]=>[1,5,7,8,2,6,3,4]=>1000000=>0000001
[4,3,7,6,2,1,8,5]=>[5,8,1,2,6,7,3,4]=>0000000=>0000000
[6,4,3,1,7,2,8,5]=>[5,8,2,7,1,3,4,6]=>0000000=>0000000
[4,3,7,1,8,6,5,2]=>[2,5,6,8,1,7,3,4]=>0000000=>0000000
[7,5,3,1,8,6,4,2]=>[2,4,6,8,1,3,5,7]=>0000000=>0000000
[4,6,1,8,7,3,5,2]=>[2,5,3,7,8,1,6,4]=>0000000=>0000000
[6,8,7,3,1,4,5,2]=>[2,5,4,1,3,7,8,6]=>0000100=>0010000
[6,2,8,7,4,5,1,3]=>[3,1,5,4,7,8,2,6]=>0000000=>0000000
[7,6,2,8,4,1,3,5]=>[5,3,1,4,8,2,6,7]=>0000000=>0000000
[7,3,1,6,8,4,2,5]=>[5,2,4,8,6,1,3,7]=>0000000=>0000000
[7,6,5,3,2,1,8,4]=>[4,8,1,2,3,5,6,7]=>0000000=>0000000
[5,2,7,6,3,1,8,4]=>[4,8,1,3,6,7,2,5]=>0000000=>0000000
[6,5,2,1,7,3,8,4]=>[4,8,3,7,1,2,5,6]=>0000000=>0000000
[6,1,7,4,2,8,3,5]=>[5,3,8,2,4,7,1,6]=>0000000=>0000000
[6,7,2,1,8,3,4,5]=>[5,4,3,8,1,2,7,6]=>0000000=>0000000
[7,5,8,2,1,3,4,6]=>[6,4,3,1,2,8,5,7]=>0000000=>0000000
[5,7,3,1,8,2,4,6]=>[6,4,2,8,1,3,7,5]=>0000000=>0000000
[4,7,1,5,2,8,3,6]=>[6,3,8,2,5,1,7,4]=>0000000=>0000000
[5,2,7,4,1,8,3,6]=>[6,3,8,1,4,7,2,5]=>0000000=>0000000
[2,4,8,6,3,7,5,1]=>[1,5,7,3,6,8,4,2]=>1000000=>0000001
[3,8,6,2,4,7,5,1]=>[1,5,7,4,2,6,8,3]=>1000000=>0000001
[7,3,6,2,4,1,8,5]=>[5,8,1,4,2,6,3,7]=>0000000=>0000000
[3,5,2,7,1,8,4,6]=>[6,4,8,1,7,2,5,3]=>0000000=>0000000
[8,3,7,1,4,6,2,5]=>[5,2,6,4,1,7,3,8]=>0000001=>1000000
[3,8,2,5,7,1,6,4]=>[4,6,1,7,5,2,8,3]=>0000000=>0000000
[7,8,3,6,2,1,5,4]=>[4,5,1,2,6,3,8,7]=>0000010=>0100000
[8,7,3,6,2,5,4,1]=>[1,4,5,2,6,3,7,8]=>1000011=>1100001
[4,7,8,2,1,6,5,3]=>[3,5,6,1,2,8,7,4]=>0000000=>0000000
[4,2,6,8,1,7,5,3]=>[3,5,7,1,8,6,2,4]=>0000000=>0000000
[5,4,8,2,7,1,6,3]=>[3,6,1,7,2,8,4,5]=>0000000=>0000000
[4,8,1,5,7,2,6,3]=>[3,6,2,7,5,1,8,4]=>0000000=>0000000
[5,8,3,7,1,6,2,4]=>[4,2,6,1,7,3,8,5]=>0000000=>0000000
[5,8,7,2,6,1,3,4]=>[4,3,1,6,2,7,8,5]=>0000000=>0000000
[8,6,2,7,5,1,3,4]=>[4,3,1,5,7,2,6,8]=>0000001=>1000000
[6,4,8,1,7,2,5,3]=>[3,5,2,7,1,8,4,6]=>0000000=>0000000
[5,1,6,8,2,7,4,3]=>[3,4,7,2,8,6,1,5]=>0000000=>0000000
[6,5,2,8,1,7,4,3]=>[3,4,7,1,8,2,5,6]=>0000000=>0000000
[6,2,8,7,5,4,3,1]=>[1,3,4,5,7,8,2,6]=>1000000=>0000001
[6,1,7,2,8,5,4,3]=>[3,4,5,8,2,7,1,6]=>0000000=>0000000
[4,1,3,2,6,5,8,7]=>[7,8,5,6,2,3,1,4]=>0000000=>0000000
[6,3,5,1,2,4,8,7]=>[7,8,4,2,1,5,3,6]=>0000000=>0000000
[4,3,5,6,1,2,8,7]=>[7,8,2,1,6,5,3,4]=>0000000=>0000000
[8,3,7,5,2,1,4,6]=>[6,4,1,2,5,7,3,8]=>0000001=>1000000
[6,5,2,7,1,8,3,4]=>[4,3,8,1,7,2,5,6]=>0000000=>0000000
[8,5,2,7,4,1,3,6]=>[6,3,1,4,7,2,5,8]=>0000001=>1000000
[3,5,2,6,4,1,8,7]=>[7,8,1,4,6,2,5,3]=>0000000=>0000000
[6,1,2,4,5,3,8,7]=>[7,8,3,5,4,2,1,6]=>0000000=>0000000
[5,6,3,2,1,4,8,7]=>[7,8,4,1,2,3,6,5]=>0000000=>0000000
[2,1,6,3,5,4,8,7]=>[7,8,4,5,3,6,1,2]=>0000000=>0000000
[5,3,1,4,6,2,8,7]=>[7,8,2,6,4,1,3,5]=>0000000=>0000000
[5,7,4,6,2,8,3,1]=>[1,3,8,2,6,4,7,5]=>1000000=>0000001
[3,4,7,8,5,2,1,6]=>[6,1,2,5,8,7,4,3]=>0000000=>0000000
[2,1,8,5,7,3,4,6]=>[6,4,3,7,5,8,1,2]=>0000000=>0000000
[8,6,3,5,1,7,4,2]=>[2,4,7,1,5,3,6,8]=>0000001=>1000000
[5,1,4,6,8,2,7,3]=>[3,7,2,8,6,4,1,5]=>0000000=>0000000
[2,5,4,6,7,1,8,3]=>[3,8,1,7,6,4,5,2]=>0000000=>0000000
[4,1,6,3,8,5,7,2]=>[2,7,5,8,3,6,1,4]=>0000000=>0000000
[3,7,4,2,8,6,5,1]=>[1,5,6,8,2,4,7,3]=>1000000=>0000001
[8,5,3,7,4,1,6,2]=>[2,6,1,4,7,3,5,8]=>0000001=>1000000
[2,1,5,7,4,8,6,3]=>[3,6,8,4,7,5,1,2]=>0000000=>0000000
[2,1,4,8,3,7,6,5]=>[5,6,7,3,8,4,1,2]=>0000000=>0000000
[2,3,8,1,6,7,5,4]=>[4,5,7,6,1,8,3,2]=>0000000=>0000000
[2,8,1,3,6,5,7,4]=>[4,7,5,6,3,1,8,2]=>0000000=>0000000
[8,1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1,8]=>0000001=>1000000
[7,8,2,4,3,6,1,5]=>[5,1,6,3,4,2,8,7]=>0000010=>0100000
[6,8,3,2,4,1,7,5]=>[5,7,1,4,2,3,8,6]=>0000000=>0000000
[2,1,8,3,4,6,7,5]=>[5,7,6,4,3,8,1,2]=>0000000=>0000000
[2,1,7,8,5,4,3,6]=>[6,3,4,5,8,7,1,2]=>0000000=>0000000
[5,7,3,8,1,4,2,6]=>[6,2,4,1,8,3,7,5]=>0000000=>0000000
[7,1,8,4,5,3,2,6]=>[6,2,3,5,4,8,1,7]=>0000000=>0000000
[8,7,1,6,3,4,2,5]=>[5,2,4,3,6,1,7,8]=>0000011=>1100000
[3,8,6,7,2,4,1,5]=>[5,1,4,2,7,6,8,3]=>0000000=>0000000
[5,3,8,7,4,2,6,1]=>[1,6,2,4,7,8,3,5]=>1000000=>0000001
[7,3,5,8,2,4,1,6]=>[6,1,4,2,8,5,3,7]=>0000000=>0000000
[2,3,4,1,8,5,7,6]=>[6,7,5,8,1,4,3,2]=>0000000=>0000000
[4,1,3,2,8,5,7,6]=>[6,7,5,8,2,3,1,4]=>0000000=>0000000
[2,1,4,3,8,5,7,6]=>[6,7,5,8,3,4,1,2]=>0000000=>0000000
[4,1,3,2,6,7,8,5]=>[5,8,7,6,2,3,1,4]=>0000000=>0000000
[8,3,5,6,2,7,1,4]=>[4,1,7,2,6,5,3,8]=>0000001=>1000000
[5,3,6,1,8,7,2,4]=>[4,2,7,8,1,6,3,5]=>0000000=>0000000
[7,8,5,6,1,4,2,3]=>[3,2,4,1,6,5,8,7]=>0001010=>0101000
[5,8,3,6,1,7,2,4]=>[4,2,7,1,6,3,8,5]=>0000000=>0000000
[2,1,8,6,5,7,3,4]=>[4,3,7,5,6,8,1,2]=>0000000=>0000000
[7,1,4,2,5,6,8,3]=>[3,8,6,5,2,4,1,7]=>0000000=>0000000
[2,7,4,1,6,5,8,3]=>[3,8,5,6,1,4,7,2]=>0000000=>0000000
[4,6,1,2,8,7,3,5]=>[5,3,7,8,2,1,6,4]=>0000000=>0000000
[2,4,1,5,8,7,6,3]=>[3,6,7,8,5,1,4,2]=>0000000=>0000000
[6,4,2,1,5,8,7,3]=>[3,7,8,5,1,2,4,6]=>0000000=>0000000
[7,5,3,2,6,8,1,4]=>[4,1,8,6,2,3,5,7]=>0000000=>0000000
[4,3,1,5,7,6,8,2]=>[2,8,6,7,5,1,3,4]=>0000000=>0000000
[4,5,2,6,3,1,8,7]=>[7,8,1,3,6,2,5,4]=>0000000=>0000000
[6,5,2,1,4,3,8,7]=>[7,8,3,4,1,2,5,6]=>0000000=>0000000
[8,3,7,5,2,1,6,4]=>[4,6,1,2,5,7,3,8]=>0000001=>1000000
[6,3,7,5,2,8,4,1]=>[1,4,8,2,5,7,3,6]=>1000000=>0000001
[6,3,1,5,2,4,8,7]=>[7,8,4,2,5,1,3,6]=>0000000=>0000000
[5,4,3,6,1,2,8,7]=>[7,8,2,1,6,3,4,5]=>0000000=>0000000
[2,6,1,3,5,4,8,7]=>[7,8,4,5,3,1,6,2]=>0000000=>0000000
[5,1,7,3,8,4,6,2]=>[2,6,4,8,3,7,1,5]=>0000000=>0000000
[2,5,7,3,8,6,4,1]=>[1,4,6,8,3,7,5,2]=>1000000=>0000001
[3,6,7,4,1,8,5,2]=>[2,5,8,1,4,7,6,3]=>0000000=>0000000
[2,1,8,7,4,3,6,5]=>[5,6,3,4,7,8,1,2]=>0000000=>0000000
[5,8,3,7,4,2,6,1]=>[1,6,2,4,7,3,8,5]=>1000000=>0000001
[3,8,7,4,1,2,6,5]=>[5,6,2,1,4,7,8,3]=>0000000=>0000000
[5,8,7,3,2,6,1,4]=>[4,1,6,2,3,7,8,5]=>0000000=>0000000
[2,8,6,3,1,5,7,4]=>[4,7,5,1,3,6,8,2]=>0000000=>0000000
[2,8,4,1,6,3,7,5]=>[5,7,3,6,1,4,8,2]=>0000000=>0000000
[6,8,3,5,2,7,4,1]=>[1,4,7,2,5,3,8,6]=>1000000=>0000001
[2,1,8,5,3,7,4,6]=>[6,4,7,3,5,8,1,2]=>0000000=>0000000
[2,4,1,8,7,6,5,3]=>[3,5,6,7,8,1,4,2]=>0000000=>0000000
[4,1,2,8,7,5,6,3]=>[3,6,5,7,8,2,1,4]=>0000000=>0000000
[3,1,4,8,6,5,7,2]=>[2,7,5,6,8,4,1,3]=>0000000=>0000000
[7,3,5,4,8,6,1,2]=>[2,1,6,8,4,5,3,7]=>0100000=>0000010
[6,4,3,5,8,1,7,2]=>[2,7,1,8,5,3,4,6]=>0000000=>0000000
[2,1,7,6,5,8,3,4]=>[4,3,8,5,6,7,1,2]=>0000000=>0000000
[5,7,3,6,1,8,2,4]=>[4,2,8,1,6,3,7,5]=>0000000=>0000000
[2,7,6,4,5,8,1,3]=>[3,1,8,5,4,6,7,2]=>0000000=>0000000
[3,7,5,6,8,4,2,1]=>[1,2,4,8,6,5,7,3]=>1100000=>0000011
[5,7,1,6,8,2,4,3]=>[3,4,2,8,6,1,7,5]=>0000000=>0000000
[4,6,2,5,8,3,7,1]=>[1,7,3,8,5,2,6,4]=>1000000=>0000001
[7,5,2,6,3,8,1,4]=>[4,1,8,3,6,2,5,7]=>0000000=>0000000
[4,1,2,3,6,8,7,5]=>[5,7,8,6,3,2,1,4]=>0000000=>0000000
[2,4,3,1,8,5,6,7]=>[7,6,5,8,1,3,4,2]=>0000000=>0000000
[7,5,2,8,3,4,6,1]=>[1,6,4,3,8,2,5,7]=>1000000=>0000001
[4,7,2,8,1,5,3,6]=>[6,3,5,1,8,2,7,4]=>0000000=>0000000
[5,7,8,6,3,4,1,2]=>[2,1,4,3,6,8,7,5]=>0101000=>0001010
[7,1,8,5,4,3,6,2]=>[2,6,3,4,5,8,1,7]=>0000000=>0000000
[2,7,8,4,5,3,6,1]=>[1,6,3,5,4,8,7,2]=>1000000=>0000001
[5,7,3,8,1,4,6,2]=>[2,6,4,1,8,3,7,5]=>0000000=>0000000
[2,1,7,8,5,4,6,3]=>[3,6,4,5,8,7,1,2]=>0000000=>0000000
[6,5,3,8,4,1,2,7]=>[7,2,1,4,8,3,5,6]=>0000000=>0000000
[7,5,8,4,3,6,2,1]=>[1,2,6,3,4,8,5,7]=>1100000=>0000011
[2,4,8,3,5,6,1,7]=>[7,1,6,5,3,8,4,2]=>0000000=>0000000
[4,1,8,3,6,5,2,7]=>[7,2,5,6,3,8,1,4]=>0000000=>0000000
[8,4,1,3,7,2,6,5]=>[5,6,2,7,3,1,4,8]=>0000001=>1000000
[4,3,8,2,5,1,7,6]=>[6,7,1,5,2,8,3,4]=>0000000=>0000000
[7,4,3,8,2,5,1,6]=>[6,1,5,2,8,3,4,7]=>0000000=>0000000
[7,8,2,1,6,5,3,4]=>[4,3,5,6,1,2,8,7]=>0000010=>0100000
[4,3,8,1,7,2,5,6]=>[6,5,2,7,1,8,3,4]=>0000000=>0000000
[7,8,1,4,6,2,5,3]=>[3,5,2,6,4,1,8,7]=>0000010=>0100000
[7,8,3,6,5,4,1,2]=>[2,1,4,5,6,3,8,7]=>0100010=>0100010
[7,8,2,6,4,1,3,5]=>[5,3,1,4,6,2,8,7]=>0000010=>0100000
[2,1,8,7,5,4,3,6]=>[6,3,4,5,7,8,1,2]=>0000000=>0000000
[5,3,7,1,6,4,8,2]=>[2,8,4,6,1,7,3,5]=>0000000=>0000000
[6,1,2,5,8,7,4,3]=>[3,4,7,8,5,2,1,6]=>0000000=>0000000
[4,3,8,7,5,6,1,2]=>[2,1,6,5,7,8,3,4]=>0100000=>0000010
[1,8,5,7,3,6,4,2]=>[2,4,6,3,7,5,8,1]=>0000000=>0000000
[2,7,5,8,3,6,1,4]=>[4,1,6,3,8,5,7,2]=>0000000=>0000000
[1,5,6,8,2,4,7,3]=>[3,7,4,2,8,6,5,1]=>0000000=>0000000
[3,6,8,4,7,5,1,2]=>[2,1,5,7,4,8,6,3]=>0100000=>0000010
[4,5,6,7,2,8,1,3]=>[3,1,8,2,7,6,5,4]=>0000000=>0000000
[1,5,8,6,2,7,3,4]=>[4,3,7,2,6,8,5,1]=>0000000=>0000000
[5,1,6,3,4,2,8,7]=>[7,8,2,4,3,6,1,5]=>0000000=>0000000
[6,3,4,5,8,7,1,2]=>[2,1,7,8,5,4,3,6]=>0100000=>0000010
[6,2,4,1,8,3,7,5]=>[5,7,3,8,1,4,2,6]=>0000000=>0000000
[5,7,2,4,1,6,3,8]=>[8,3,6,1,4,2,7,5]=>0000000=>0000000
[5,8,7,6,2,3,1,4]=>[4,1,3,2,6,7,8,5]=>0001000=>0001000
[4,2,7,8,1,6,3,5]=>[5,3,6,1,8,7,2,4]=>0000000=>0000000
[2,1,8,7,6,5,3,4]=>[4,3,5,6,7,8,1,2]=>0000000=>0000000
[3,1,4,7,8,2,6,5]=>[5,6,2,8,7,4,1,3]=>0000000=>0000000
[4,3,7,5,6,8,1,2]=>[2,1,8,6,5,7,3,4]=>0100000=>0000010
[4,8,6,3,5,7,1,2]=>[2,1,7,5,3,6,8,4]=>0100000=>0000010
[5,2,8,7,1,6,4,3]=>[3,4,6,1,7,8,2,5]=>0000000=>0000000
[3,7,6,8,5,2,1,4]=>[4,1,2,5,8,6,7,3]=>0000000=>0000000
[2,7,8,6,5,4,1,3]=>[3,1,4,5,6,8,7,2]=>0000000=>0000000
[5,3,7,8,2,1,4,6]=>[6,4,1,2,8,7,3,5]=>0000000=>0000000
[7,6,1,2,5,8,3,4]=>[4,3,8,5,2,1,6,7]=>0000000=>0000000
[2,1,7,8,4,3,5,6]=>[6,5,3,4,8,7,1,2]=>0000000=>0000000
[6,1,8,3,2,4,5,7]=>[7,5,4,2,3,8,1,6]=>0000000=>0000000
[5,8,7,4,2,1,6,3]=>[3,6,1,2,4,7,8,5]=>0000000=>0000000
[4,7,2,8,1,3,6,5]=>[5,6,3,1,8,2,7,4]=>0000000=>0000000
[7,3,8,6,1,2,5,4]=>[4,5,2,1,6,8,3,7]=>0000000=>0000000
[3,4,7,1,8,2,6,5]=>[5,6,2,8,1,7,4,3]=>0000000=>0000000
[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>0000000=>0000000
[1,8,2,7,3,5,4,6]=>[6,4,5,3,7,2,8,1]=>0000000=>0000000
[1,7,2,8,3,5,4,6]=>[6,4,5,3,8,2,7,1]=>0000000=>0000000
[1,6,2,8,3,5,4,7]=>[7,4,5,3,8,2,6,1]=>0000000=>0000000
[1,2,3,8,4,6,5,7]=>[7,5,6,4,8,3,2,1]=>0000000=>0000000
[1,5,2,7,3,6,4,8]=>[8,4,6,3,7,2,5,1]=>0000000=>0000000
[1,7,2,6,3,5,4,8]=>[8,4,5,3,6,2,7,1]=>0000000=>0000000
[1,6,2,5,3,8,4,7]=>[7,4,8,3,5,2,6,1]=>0000000=>0000000
[1,7,2,5,3,8,4,6]=>[6,4,8,3,5,2,7,1]=>0000000=>0000000
[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>0000000=>0000000
[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>0000000=>0000000
[1,4,2,8,3,7,5,6]=>[6,5,7,3,8,2,4,1]=>0000000=>0000000
[1,7,2,8,3,6,4,5]=>[5,4,6,3,8,2,7,1]=>0000000=>0000000
[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>0000000=>0000000
[2,8,4,1,6,5,3,7]=>[7,3,5,6,1,4,8,2]=>0000000=>0000000
[2,8,4,1,5,6,7,3]=>[3,7,6,5,1,4,8,2]=>0000000=>0000000
[2,8,7,4,1,6,3,5]=>[5,3,6,1,4,7,8,2]=>0000000=>0000000
[7,2,8,5,1,6,4,3]=>[3,4,6,1,5,8,2,7]=>0000000=>0000000
[2,8,5,4,3,1,7,6]=>[6,7,1,3,4,5,8,2]=>0000000=>0000000
[2,8,5,3,4,1,6,7]=>[7,6,1,4,3,5,8,2]=>0000000=>0000000
[2,8,7,6,1,4,5,3]=>[3,5,4,1,6,7,8,2]=>0000000=>0000000
[2,8,6,5,7,3,1,4]=>[4,1,3,7,5,6,8,2]=>0000000=>0000000
[6,2,3,8,5,1,7,4]=>[4,7,1,5,8,3,2,6]=>0000000=>0000000
[6,4,8,5,1,3,7,2]=>[2,7,3,1,5,8,4,6]=>0000000=>0000000
[6,3,7,5,2,1,8,4]=>[4,8,1,2,5,7,3,6]=>0000000=>0000000
[4,3,7,5,1,2,8,6]=>[6,8,2,1,5,7,3,4]=>0000000=>0000000
[3,4,1,2,7,6,8,5]=>[5,8,6,7,2,1,4,3]=>0000000=>0000000
[4,3,2,1,8,6,5,7]=>[7,5,6,8,1,2,3,4]=>0000000=>0000000
[4,2,1,3,8,7,6,5]=>[5,6,7,8,3,1,2,4]=>0000000=>0000000
[7,1,6,8,4,3,5,2]=>[2,5,3,4,8,6,1,7]=>0000000=>0000000
[6,1,2,8,4,5,7,3]=>[3,7,5,4,8,2,1,6]=>0000000=>0000000
[5,6,8,2,3,1,7,4]=>[4,7,1,3,2,8,6,5]=>0000000=>0000000
[6,5,8,2,4,3,1,7]=>[7,1,3,4,2,8,5,6]=>0000000=>0000000
[6,5,8,4,2,3,7,1]=>[1,7,3,2,4,8,5,6]=>1000000=>0000001
[7,5,3,8,2,4,1,6]=>[6,1,4,2,8,3,5,7]=>0000000=>0000000
[6,2,5,8,3,7,1,4]=>[4,1,7,3,8,5,2,6]=>0000000=>0000000
[5,2,1,8,7,6,3,4]=>[4,3,6,7,8,1,2,5]=>0000000=>0000000
[7,1,3,8,4,6,2,5]=>[5,2,6,4,8,3,1,7]=>0000000=>0000000
[5,7,8,4,3,6,2,1]=>[1,2,6,3,4,8,7,5]=>1100000=>0000011
[4,1,8,3,5,6,7,2]=>[2,7,6,5,3,8,1,4]=>0000000=>0000000
[4,1,8,3,6,2,7,5]=>[5,7,2,6,3,8,1,4]=>0000000=>0000000
[2,3,4,8,6,1,7,5]=>[5,7,1,6,8,4,3,2]=>0000000=>0000000
[2,3,4,8,6,5,1,7]=>[7,1,5,6,8,4,3,2]=>0000000=>0000000
[2,7,3,5,8,6,1,4]=>[4,1,6,8,5,3,7,2]=>0000000=>0000000
[5,3,6,4,1,8,7,2]=>[2,7,8,1,4,6,3,5]=>0000000=>0000000
[7,3,5,6,8,4,2,1]=>[1,2,4,8,6,5,3,7]=>1100000=>0000011
[6,3,5,1,8,2,7,4]=>[4,7,2,8,1,5,3,6]=>0000000=>0000000
[2,7,6,5,8,3,4,1]=>[1,4,3,8,5,6,7,2]=>1000000=>0000001
[5,7,1,6,3,8,4,2]=>[2,4,8,3,6,1,7,5]=>0000000=>0000000
[3,2,4,1,7,8,5,6]=>[6,5,8,7,1,4,2,3]=>0000000=>0000000
[3,1,4,2,7,8,6,5]=>[5,6,8,7,2,4,1,3]=>0000000=>0000000
[2,5,4,6,1,7,8,3]=>[3,8,7,1,6,4,5,2]=>0000000=>0000000
[7,2,1,4,3,6,5,8]=>[8,5,6,3,4,1,2,7]=>0000000=>0000000
[7,3,4,1,2,6,5,8]=>[8,5,6,2,1,4,3,7]=>0000000=>0000000
[7,4,3,2,1,6,5,8]=>[8,5,6,1,2,3,4,7]=>0000000=>0000000
[7,6,3,2,5,4,1,8]=>[8,1,4,5,2,3,6,7]=>0000000=>0000000
[1,8,3,2,5,4,7,6]=>[6,7,4,5,2,3,8,1]=>0000000=>0000000
[1,8,4,5,2,3,7,6]=>[6,7,3,2,5,4,8,1]=>0000000=>0000000
[7,3,5,1,6,2,4,8]=>[8,4,2,6,1,5,3,7]=>0000000=>0000000
[7,2,1,5,6,3,4,8]=>[8,4,3,6,5,1,2,7]=>0000000=>0000000
[7,2,1,6,5,4,3,8]=>[8,3,4,5,6,1,2,7]=>0000000=>0000000
[7,3,6,1,5,4,2,8]=>[8,2,4,5,1,6,3,7]=>0000000=>0000000
[1,8,5,4,3,2,7,6]=>[6,7,2,3,4,5,8,1]=>0000000=>0000000
[3,2,1,8,5,4,7,6]=>[6,7,4,5,8,1,2,3]=>0000000=>0000000
[2,3,8,1,5,4,7,6]=>[6,7,4,5,1,8,3,2]=>0000000=>0000000
[2,4,8,5,1,3,7,6]=>[6,7,3,1,5,8,4,2]=>0000000=>0000000
[2,5,8,4,3,1,7,6]=>[6,7,1,3,4,8,5,2]=>0000000=>0000000
[2,6,8,4,3,7,1,5]=>[5,1,7,3,4,8,6,2]=>0000000=>0000000
[2,7,8,4,3,6,5,1]=>[1,5,6,3,4,8,7,2]=>1000000=>0000001
[1,8,7,5,6,3,4,2]=>[2,4,3,6,5,7,8,1]=>0000000=>0000000
[2,7,8,5,6,3,4,1]=>[1,4,3,6,5,8,7,2]=>1000000=>0000001
[2,6,8,5,7,3,1,4]=>[4,1,3,7,5,8,6,2]=>0000000=>0000000
[2,5,8,6,7,1,3,4]=>[4,3,1,7,6,8,5,2]=>0000000=>0000000
[2,4,8,6,1,7,3,5]=>[5,3,7,1,6,8,4,2]=>0000000=>0000000
[4,5,7,6,8,1,3,2]=>[2,3,1,8,6,7,5,4]=>0010000=>0000100
[1,8,5,6,7,2,3,4]=>[4,3,2,7,6,5,8,1]=>0000000=>0000000
[4,6,5,7,8,2,1,3]=>[3,1,2,8,7,5,6,4]=>0010000=>0000100
[5,4,6,7,1,8,2,3]=>[3,2,8,1,7,6,4,5]=>0000000=>0000000
[5,3,6,1,7,8,2,4]=>[4,2,8,7,1,6,3,5]=>0000000=>0000000
[5,2,1,6,7,8,3,4]=>[4,3,8,7,6,1,2,5]=>0000000=>0000000
[6,2,1,5,7,3,8,4]=>[4,8,3,7,5,1,2,6]=>0000000=>0000000
[6,3,5,1,7,2,8,4]=>[4,8,2,7,1,5,3,6]=>0000000=>0000000
[6,4,5,7,1,2,8,3]=>[3,8,2,1,7,5,4,6]=>0000000=>0000000
[6,5,4,7,2,1,8,3]=>[3,8,1,2,7,4,5,6]=>0000000=>0000000
[1,8,4,6,2,7,3,5]=>[5,3,7,2,6,4,8,1]=>0000000=>0000000
[1,8,3,2,6,7,4,5]=>[5,4,7,6,2,3,8,1]=>0000000=>0000000
[5,7,3,2,6,8,4,1]=>[1,4,8,6,2,3,7,5]=>1000000=>0000001
[6,5,3,2,7,1,8,4]=>[4,8,1,7,2,3,5,6]=>0000000=>0000000
[6,4,3,2,1,7,8,5]=>[5,8,7,1,2,3,4,6]=>0000000=>0000000
[6,2,1,4,3,7,8,5]=>[5,8,7,3,4,1,2,6]=>0000000=>0000000
[5,2,1,4,3,8,7,6]=>[6,7,8,3,4,1,2,5]=>0000000=>0000000
[5,3,4,1,2,8,7,6]=>[6,7,8,2,1,4,3,5]=>0000000=>0000000
[4,5,3,2,8,1,7,6]=>[6,7,1,8,2,3,5,4]=>0000000=>0000000
[4,6,3,2,8,7,1,5]=>[5,1,7,8,2,3,6,4]=>0000000=>0000000
[4,7,3,2,8,6,5,1]=>[1,5,6,8,2,3,7,4]=>1000000=>0000001
[3,7,4,8,2,6,5,1]=>[1,5,6,2,8,4,7,3]=>1000000=>0000001
[3,6,4,8,2,7,1,5]=>[5,1,7,2,8,4,6,3]=>0000000=>0000000
[3,5,4,8,2,1,7,6]=>[6,7,1,2,8,4,5,3]=>0000000=>0000000
[3,4,5,8,1,2,7,6]=>[6,7,2,1,8,5,4,3]=>0000000=>0000000
[4,3,5,1,8,2,7,6]=>[6,7,2,8,1,5,3,4]=>0000000=>0000000
[4,2,1,5,8,3,7,6]=>[6,7,3,8,5,1,2,4]=>0000000=>0000000
[3,4,6,8,1,7,2,5]=>[5,2,7,1,8,6,4,3]=>0000000=>0000000
[3,5,6,8,7,1,2,4]=>[4,2,1,7,8,6,5,3]=>0000000=>0000000
[3,6,5,8,7,2,1,4]=>[4,1,2,7,8,5,6,3]=>0000000=>0000000
[3,7,5,8,6,2,4,1]=>[1,4,2,6,8,5,7,3]=>1000000=>0000001
[2,3,8,1,7,6,5,4]=>[4,5,6,7,1,8,3,2]=>0000000=>0000000
[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>00000000000=>00000000000
[8,1,6,7,3,2,5,4]=>[4,5,2,3,7,6,1,8]=>0000001=>1000000
[8,1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1,8]=>0000001=>1000000
[8,1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1,8]=>0000001=>1000000
[8,1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1,8]=>0000001=>1000000
[8,1,5,3,7,2,6,4]=>[4,6,2,7,3,5,1,8]=>0000001=>1000000
[2,7,8,3,4,5,6,1]=>[1,6,5,4,3,8,7,2]=>1000000=>0000001
[6,3,2,1,4,5,8,7]=>[7,8,5,4,1,2,3,6]=>0000000=>0000000
[4,7,8,5,6,1,2,3]=>[3,2,1,6,5,8,7,4]=>0010000=>0000100
[3,7,8,5,6,2,1,4]=>[4,1,2,6,5,8,7,3]=>0000000=>0000000
[3,7,8,4,2,6,1,5]=>[5,1,6,2,4,8,7,3]=>0000000=>0000000
[2,3,6,7,4,5,8,1]=>[1,8,5,4,7,6,3,2]=>1000000=>0000001
[3,5,4,2,8,7,1,6]=>[6,1,7,8,2,4,5,3]=>0000000=>0000000
[4,6,5,8,7,1,2,3]=>[3,2,1,7,8,5,6,4]=>0010000=>0000100
[5,4,2,3,1,8,6,7]=>[7,6,8,1,3,2,4,5]=>0000000=>0000000
[6,5,3,1,8,2,7,4]=>[4,7,2,8,1,3,5,6]=>0000000=>0000000
[6,5,4,1,8,7,2,3]=>[3,2,7,8,1,4,5,6]=>0000000=>0000000
[7,5,1,4,8,6,2,3]=>[3,2,6,8,4,1,5,7]=>0000000=>0000000
[7,4,1,3,2,8,6,5]=>[5,6,8,2,3,1,4,7]=>0000000=>0000000
[6,4,2,1,3,8,5,7]=>[7,5,8,3,1,2,4,6]=>0000000=>0000000
[2,6,4,8,3,7,5,1]=>[1,5,7,3,8,4,6,2]=>1000000=>0000001
[2,6,5,8,7,3,4,1]=>[1,4,3,7,8,5,6,2]=>1000000=>0000001
[7,5,1,2,8,3,4,6]=>[6,4,3,8,2,1,5,7]=>0000000=>0000000
[7,6,1,8,2,3,4,5]=>[5,4,3,2,8,1,6,7]=>0000000=>0000000
[7,6,1,8,4,5,2,3]=>[3,2,5,4,8,1,6,7]=>0000000=>0000000
[6,7,8,1,4,5,2,3]=>[3,2,5,4,1,8,7,6]=>0000100=>0010000
[6,7,8,1,3,2,5,4]=>[4,5,2,3,1,8,7,6]=>0000100=>0010000
[2,5,6,7,8,3,4,1]=>[1,4,3,8,7,6,5,2]=>1000000=>0000001
[2,4,6,7,3,8,5,1]=>[1,5,8,3,7,6,4,2]=>1000000=>0000001
[4,7,8,3,2,1,6,5]=>[5,6,1,2,3,8,7,4]=>0000000=>0000000
[5,7,8,3,1,2,6,4]=>[4,6,2,1,3,8,7,5]=>0000000=>0000000
[5,7,8,4,1,6,2,3]=>[3,2,6,1,4,8,7,5]=>0000000=>0000000
[5,6,4,8,1,7,2,3]=>[3,2,7,1,8,4,6,5]=>0000000=>0000000
[4,6,3,8,2,1,7,5]=>[5,7,1,2,8,3,6,4]=>0000000=>0000000
[4,3,6,7,2,1,8,5]=>[5,8,1,2,7,6,3,4]=>0000000=>0000000
[3,5,6,7,8,2,1,4]=>[4,1,2,8,7,6,5,3]=>0000000=>0000000
[3,4,6,7,2,8,1,5]=>[5,1,8,2,7,6,4,3]=>0000000=>0000000
[3,4,5,2,7,8,1,6]=>[6,1,8,7,2,5,4,3]=>0000000=>0000000
[7,4,6,1,8,3,5,2]=>[2,5,3,8,1,6,4,7]=>0000000=>0000000
[7,3,5,1,8,4,6,2]=>[2,6,4,8,1,5,3,7]=>0000000=>0000000
[7,3,4,1,8,5,6,2]=>[2,6,5,8,1,4,3,7]=>0000000=>0000000
[4,5,7,3,1,8,6,2]=>[2,6,8,1,3,7,5,4]=>0000000=>0000000
[4,5,6,2,1,8,7,3]=>[3,7,8,1,2,6,5,4]=>0000000=>0000000
[3,6,7,5,1,8,4,2]=>[2,4,8,1,5,7,6,3]=>0000000=>0000000
[7,5,6,1,8,3,4,2]=>[2,4,3,8,1,6,5,7]=>0000000=>0000000
[7,6,5,1,8,4,3,2]=>[2,3,4,8,1,5,6,7]=>0000000=>0000000
[5,3,2,1,8,7,6,4]=>[4,6,7,8,1,2,3,5]=>0000000=>0000000
[2,6,4,1,7,8,5,3]=>[3,5,8,7,1,4,6,2]=>0000000=>0000000
[2,6,5,1,7,8,4,3]=>[3,4,8,7,1,5,6,2]=>0000000=>0000000
[4,5,7,1,6,8,2,3]=>[3,2,8,6,1,7,5,4]=>0000000=>0000000
[4,5,7,1,3,8,2,6]=>[6,2,8,3,1,7,5,4]=>0000000=>0000000
[6,5,1,2,8,4,3,7]=>[7,3,4,8,2,1,5,6]=>0000000=>0000000
[4,3,1,2,8,6,5,7]=>[7,5,6,8,2,1,3,4]=>0000000=>0000000
[6,1,2,5,8,3,4,7]=>[7,4,3,8,5,2,1,6]=>0000000=>0000000
[2,6,1,5,7,8,3,4]=>[4,3,8,7,5,1,6,2]=>0000000=>0000000
[7,6,1,5,8,3,2,4]=>[4,2,3,8,5,1,6,7]=>0000000=>0000000
[3,6,7,1,5,8,2,4]=>[4,2,8,5,1,7,6,3]=>0000000=>0000000
[7,1,6,5,8,2,4,3]=>[3,4,2,8,5,6,1,7]=>0000000=>0000000
[7,5,1,6,8,4,2,3]=>[3,2,4,8,6,1,5,7]=>0000000=>0000000
[7,4,1,6,8,5,2,3]=>[3,2,5,8,6,1,4,7]=>0000000=>0000000
[5,2,3,1,8,6,7,4]=>[4,7,6,8,1,3,2,5]=>0000000=>0000000
[6,2,1,5,8,7,3,4]=>[4,3,7,8,5,1,2,6]=>0000000=>0000000
[7,3,1,5,8,6,2,4]=>[4,2,6,8,5,1,3,7]=>0000000=>0000000
[6,2,4,1,8,5,7,3]=>[3,7,5,8,1,4,2,6]=>0000000=>0000000
[6,2,5,1,8,4,7,3]=>[3,7,4,8,1,5,2,6]=>0000000=>0000000
[7,1,6,4,8,2,5,3]=>[3,5,2,8,4,6,1,7]=>0000000=>0000000
[7,1,5,3,8,2,6,4]=>[4,6,2,8,3,5,1,7]=>0000000=>0000000
[6,1,5,2,8,3,7,4]=>[4,7,3,8,2,5,1,6]=>0000000=>0000000
[7,3,1,4,8,6,2,5]=>[5,2,6,8,4,1,3,7]=>0000000=>0000000
[6,2,1,4,8,7,3,5]=>[5,3,7,8,4,1,2,6]=>0000000=>0000000
[6,1,4,2,8,3,7,5]=>[5,7,3,8,2,4,1,6]=>0000000=>0000000
[7,1,4,3,8,2,6,5]=>[5,6,2,8,3,4,1,7]=>0000000=>0000000
[5,1,3,2,8,4,7,6]=>[6,7,4,8,2,3,1,5]=>0000000=>0000000
[4,2,1,3,8,7,5,6]=>[6,5,7,8,3,1,2,4]=>0000000=>0000000
[2,6,1,4,7,8,3,5]=>[5,3,8,7,4,1,6,2]=>0000000=>0000000
[7,1,3,5,8,2,4,6]=>[6,4,2,8,5,3,1,7]=>0000000=>0000000
[7,8,4,2,5,1,3,6]=>[6,3,1,5,2,4,8,7]=>0000010=>0100000
[7,8,2,4,5,6,1,3]=>[3,1,6,5,4,2,8,7]=>0000010=>0100000
[2,6,4,8,3,7,1,5]=>[5,1,7,3,8,4,6,2]=>0000000=>0000000
[1,4,6,8,3,7,5,2]=>[2,5,7,3,8,6,4,1]=>0000000=>0000000
[2,1,8,4,7,3,6,5]=>[5,6,3,7,4,8,1,2]=>0000000=>0000000
[3,5,8,4,7,6,1,2]=>[2,1,6,7,4,8,5,3]=>0100000=>0000010
[4,7,5,1,3,6,8,2]=>[2,8,6,3,1,5,7,4]=>0000000=>0000000
[5,7,3,6,1,4,8,2]=>[2,8,4,1,6,3,7,5]=>0000000=>0000000
[5,3,6,7,2,1,8,4]=>[4,8,1,2,7,6,3,5]=>0000000=>0000000
[3,5,6,7,8,1,4,2]=>[2,4,1,8,7,6,5,3]=>0000000=>0000000
[3,6,5,7,8,2,1,4]=>[4,1,2,8,7,5,6,3]=>0000000=>0000000
[2,5,7,6,8,1,3,4]=>[4,3,1,8,6,7,5,2]=>0000000=>0000000
[2,7,1,8,5,3,4,6]=>[6,4,3,5,8,1,7,2]=>0000000=>0000000
[4,2,8,1,6,3,7,5]=>[5,7,3,6,1,8,2,4]=>0000000=>0000000
[3,4,7,1,5,2,6,8]=>[8,6,2,5,1,7,4,3]=>0000000=>0000000
[1,6,4,3,8,2,5,7]=>[7,5,2,8,3,4,6,1]=>0000000=>0000000
[3,6,5,4,1,2,7,8]=>[8,7,2,1,4,5,6,3]=>0000000=>0000000
[2,4,5,1,7,8,6,3]=>[3,6,8,7,1,5,4,2]=>0000000=>0000000
[2,6,4,1,8,3,7,5]=>[5,7,3,8,1,4,6,2]=>0000000=>0000000
[3,6,4,5,8,7,1,2]=>[2,1,7,8,5,4,6,3]=>0100000=>0000010
[5,6,2,7,3,1,4,8]=>[8,4,1,3,7,2,6,5]=>0000000=>0000000
[6,7,1,5,2,8,3,4]=>[4,3,8,2,5,1,7,6]=>0000000=>0000000
[6,7,5,3,8,4,1,2]=>[2,1,4,8,3,5,7,6]=>0100000=>0000010
[7,5,2,4,3,1,6,8]=>[8,6,1,3,4,2,5,7]=>0000000=>0000000
[7,4,6,1,2,5,3,8]=>[8,3,5,2,1,6,4,7]=>0000000=>0000000
[7,1,4,2,5,3,6,8]=>[8,6,3,5,2,4,1,7]=>0000000=>0000000
[6,8,1,3,7,5,4,2]=>[2,4,5,7,3,1,8,6]=>0000000=>0000000
[7,1,3,5,6,4,2,8]=>[8,2,4,6,5,3,1,7]=>0000000=>0000000
[7,4,2,6,5,1,3,8]=>[8,3,1,5,6,2,4,7]=>0000000=>0000000
[2,5,3,6,8,4,7,1]=>[1,7,4,8,6,3,5,2]=>1000000=>0000001
[2,5,3,7,6,1,8,4]=>[4,8,1,6,7,3,5,2]=>0000000=>0000000
[2,5,7,8,1,4,6,3]=>[3,6,4,1,8,7,5,2]=>0000000=>0000000
[3,5,7,4,1,6,2,8]=>[8,2,6,1,4,7,5,3]=>0000000=>0000000
[5,2,1,8,6,3,7,4]=>[4,7,3,6,8,1,2,5]=>0000000=>0000000
[4,1,2,8,5,6,7,3]=>[3,7,6,5,8,2,1,4]=>0000000=>0000000
[1,4,2,7,5,8,6,3]=>[3,6,8,5,7,2,4,1]=>0000000=>0000000
[5,3,8,7,6,2,4,1]=>[1,4,2,6,7,8,3,5]=>1000000=>0000001
[5,8,4,7,6,2,1,3]=>[3,1,2,6,7,4,8,5]=>0010000=>0000100
[5,8,7,4,3,6,1,2]=>[2,1,6,3,4,7,8,5]=>0100000=>0000010
[6,4,8,3,1,7,2,5]=>[5,2,7,1,3,8,4,6]=>0000000=>0000000
[6,4,2,8,7,1,3,5]=>[5,3,1,7,8,2,4,6]=>0000000=>0000000
[6,3,8,7,2,5,1,4]=>[4,1,5,2,7,8,3,6]=>0000000=>0000000
[6,3,1,8,7,2,4,5]=>[5,4,2,7,8,1,3,6]=>0000000=>0000000
[5,8,3,7,1,6,4,2]=>[2,4,6,1,7,3,8,5]=>0000000=>0000000
[5,1,8,4,6,2,7,3]=>[3,7,2,6,4,8,1,5]=>0000000=>0000000
[5,8,7,4,1,6,2,3]=>[3,2,6,1,4,7,8,5]=>0000000=>0000000
[6,4,8,1,2,7,3,5]=>[5,3,7,2,1,8,4,6]=>0000000=>0000000
[6,8,5,1,2,3,7,4]=>[4,7,3,2,1,5,8,6]=>0000000=>0000000
[6,8,5,3,1,2,7,4]=>[4,7,2,1,3,5,8,6]=>0000000=>0000000
[3,5,6,1,8,4,7,2]=>[2,7,4,8,1,6,5,3]=>0000000=>0000000
[4,2,6,1,7,3,5,8]=>[8,5,3,7,1,6,2,4]=>0000000=>0000000
[4,6,3,1,2,7,5,8]=>[8,5,7,2,1,3,6,4]=>0000000=>0000000
[3,5,2,7,8,1,6,4]=>[4,6,1,8,7,2,5,3]=>0000000=>0000000
[3,1,4,7,5,6,2,8]=>[8,2,6,5,7,4,1,3]=>0000000=>0000000
[3,4,6,8,5,2,7,1]=>[1,7,2,5,8,6,4,3]=>1000000=>0000001
[4,2,5,6,1,8,7,3]=>[3,7,8,1,6,5,2,4]=>0000000=>0000000
[2,1,7,5,8,6,4,3]=>[3,4,6,8,5,7,1,2]=>0000000=>0000000
[1,2,7,5,3,8,6,4]=>[4,6,8,3,5,7,2,1]=>0000000=>0000000
[4,1,2,7,3,8,6,5]=>[5,6,8,3,7,2,1,4]=>0000000=>0000000
[7,1,4,2,5,3,8,6]=>[6,8,3,5,2,4,1,7]=>0000000=>0000000
[3,1,2,6,8,5,4,7]=>[7,4,5,8,6,2,1,3]=>0000000=>0000000
[1,3,7,2,4,8,6,5]=>[5,6,8,4,2,7,3,1]=>0000000=>0000000
[3,2,7,8,1,6,5,4]=>[4,5,6,1,8,7,2,3]=>0000000=>0000000
[2,4,1,7,8,6,5,3]=>[3,5,6,8,7,1,4,2]=>0000000=>0000000
[2,3,7,1,5,8,6,4]=>[4,6,8,5,1,7,3,2]=>0000000=>0000000
[5,2,8,1,3,7,4,6]=>[6,4,7,3,1,8,2,5]=>0000000=>0000000
[2,6,8,3,1,5,7,4]=>[4,7,5,1,3,8,6,2]=>0000000=>0000000
[6,3,7,4,5,1,8,2]=>[2,8,1,5,4,7,3,6]=>0000000=>0000000
[5,7,4,6,2,8,1,3]=>[3,1,8,2,6,4,7,5]=>0000000=>0000000
[4,8,3,1,7,2,5,6]=>[6,5,2,7,1,3,8,4]=>0000000=>0000000
[5,2,8,4,7,1,6,3]=>[3,6,1,7,4,8,2,5]=>0000000=>0000000
[5,8,4,7,3,1,6,2]=>[2,6,1,3,7,4,8,5]=>0000000=>0000000
[4,6,8,3,1,7,5,2]=>[2,5,7,1,3,8,6,4]=>0000000=>0000000
[6,3,8,2,7,1,5,4]=>[4,5,1,7,2,8,3,6]=>0000000=>0000000
[3,5,1,8,2,7,4,6]=>[6,4,7,2,8,1,5,3]=>0000000=>0000000
[7,5,1,3,6,2,4,8]=>[8,4,2,6,3,1,5,7]=>0000000=>0000000
[5,7,4,1,6,2,3,8]=>[8,3,2,6,1,4,7,5]=>0000000=>0000000
[4,1,6,2,8,3,7,5]=>[5,7,3,8,2,6,1,4]=>0000000=>0000000
[1,6,2,8,5,3,7,4]=>[4,7,3,5,8,2,6,1]=>0000000=>0000000
[6,8,5,3,1,7,4,2]=>[2,4,7,1,3,5,8,6]=>0000000=>0000000
[5,6,7,3,1,8,4,2]=>[2,4,8,1,3,7,6,5]=>0000000=>0000000
[5,6,2,1,7,8,4,3]=>[3,4,8,7,1,2,6,5]=>0000000=>0000000
[5,6,3,7,1,2,4,8]=>[8,4,2,1,7,3,6,5]=>0000000=>0000000
[6,4,7,2,8,1,5,3]=>[3,5,1,8,2,7,4,6]=>0000000=>0000000
[6,7,4,8,3,1,5,2]=>[2,5,1,3,8,4,7,6]=>0000000=>0000000
[5,7,3,8,2,6,1,4]=>[4,1,6,2,8,3,7,5]=>0000000=>0000000
[3,4,7,8,2,6,1,5]=>[5,1,6,2,8,7,4,3]=>0000000=>0000000
[3,8,2,4,6,7,1,5]=>[5,1,7,6,4,2,8,3]=>0000000=>0000000
[4,8,3,5,6,1,7,2]=>[2,7,1,6,5,3,8,4]=>0000000=>0000000
[8,4,3,6,5,1,7,2]=>[2,7,1,5,6,3,4,8]=>0000001=>1000000
[8,1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1,8]=>0000001=>1000000
[8,7,6,1,5,4,3,2]=>[2,3,4,5,1,6,7,8]=>0000111=>1110000
[1,7,8,2,5,6,3,4]=>[4,3,6,5,2,8,7,1]=>0000000=>0000000
[7,6,8,1,4,3,5,2]=>[2,5,3,4,1,8,6,7]=>0000100=>0010000
[6,7,8,1,3,4,5,2]=>[2,5,4,3,1,8,7,6]=>0000100=>0010000
[5,7,8,2,1,4,6,3]=>[3,6,4,1,2,8,7,5]=>0000000=>0000000
[4,7,2,8,1,5,6,3]=>[3,6,5,1,8,2,7,4]=>0000000=>0000000
[3,2,7,8,1,5,6,4]=>[4,6,5,1,8,7,2,3]=>0000000=>0000000
[3,2,6,8,4,1,7,5]=>[5,7,1,4,8,6,2,3]=>0000000=>0000000
[4,6,2,8,3,1,7,5]=>[5,7,1,3,8,2,6,4]=>0000000=>0000000
[8,5,7,3,1,6,4,2]=>[2,4,6,1,3,7,5,8]=>0000001=>1000000
[1,5,4,8,2,7,3,6]=>[6,3,7,2,8,4,5,1]=>0000000=>0000000
[6,4,3,8,2,1,7,5]=>[5,7,1,2,8,3,4,6]=>0000000=>0000000
[5,4,3,2,8,1,7,6]=>[6,7,1,8,2,3,4,5]=>0000000=>0000000
[4,5,2,3,8,1,7,6]=>[6,7,1,8,3,2,5,4]=>0000000=>0000000
[3,2,5,4,8,1,7,6]=>[6,7,1,8,4,5,2,3]=>0000000=>0000000
[6,4,3,1,5,2,7,8]=>[8,7,2,5,1,3,4,6]=>0000000=>0000000
[7,4,3,1,2,6,5,8]=>[8,5,6,2,1,3,4,7]=>0000000=>0000000
[7,5,1,4,2,6,3,8]=>[8,3,6,2,4,1,5,7]=>0000000=>0000000
[4,6,2,1,5,3,7,8]=>[8,7,3,5,1,2,6,4]=>0000000=>0000000
[3,2,6,1,5,4,7,8]=>[8,7,4,5,1,6,2,3]=>0000000=>0000000
[3,2,7,1,4,6,5,8]=>[8,5,6,4,1,7,2,3]=>0000000=>0000000
[5,7,1,3,2,6,4,8]=>[8,4,6,2,3,1,7,5]=>0000000=>0000000
[8,6,1,2,5,3,7,4]=>[4,7,3,5,2,1,6,8]=>0000001=>1000000
[8,7,1,2,3,6,5,4]=>[4,5,6,3,2,1,7,8]=>0000011=>1100000
[4,1,3,2,5,6,7,8]=>[8,7,6,5,2,3,1,4]=>0000000=>0000000
[5,1,2,4,3,6,7,8]=>[8,7,6,3,4,2,1,5]=>0000000=>0000000
[7,1,2,3,4,6,5,8]=>[8,5,6,4,3,2,1,7]=>0000000=>0000000
[8,1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1,8]=>0000001=>1000000
[5,8,7,3,4,1,2,6]=>[6,2,1,4,3,7,8,5]=>0000000=>0000000
[6,7,3,8,5,1,2,4]=>[4,2,1,5,8,3,7,6]=>0000000=>0000000
[5,4,7,6,2,3,8,1]=>[1,8,3,2,6,7,4,5]=>1000000=>0000001
[4,3,8,7,6,1,2,5]=>[5,2,1,6,7,8,3,4]=>0000000=>0000000
[4,8,3,7,5,1,2,6]=>[6,2,1,5,7,3,8,4]=>0000000=>0000000
[4,5,6,7,1,8,3,2]=>[2,3,8,1,7,6,5,4]=>0000000=>0000000
[3,5,6,2,7,4,8,1]=>[1,8,4,7,2,6,5,3]=>1000000=>0000001
[3,5,6,1,7,8,4,2]=>[2,4,8,7,1,6,5,3]=>0000000=>0000000
[2,5,6,8,1,7,3,4]=>[4,3,7,1,8,6,5,2]=>0000000=>0000000
[1,5,6,8,2,3,7,4]=>[4,7,3,2,8,6,5,1]=>0000000=>0000000
[8,1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1,8]=>0000001=>1000000
[2,4,1,6,8,7,5,3]=>[3,5,7,8,6,1,4,2]=>0000000=>0000000
[5,3,7,2,6,4,8,1]=>[1,8,4,6,2,7,3,5]=>1000000=>0000001
[6,7,2,1,8,5,4,3]=>[3,4,5,8,1,2,7,6]=>0000000=>0000000
[8,5,6,2,1,4,3,7]=>[7,3,4,1,2,6,5,8]=>0000001=>1000000
[5,8,7,1,2,3,4,6]=>[6,4,3,2,1,7,8,5]=>0000000=>0000000
[5,1,7,3,4,8,6,2]=>[2,6,8,4,3,7,1,5]=>0000000=>0000000
[5,1,7,8,2,3,6,4]=>[4,6,3,2,8,7,1,5]=>0000000=>0000000
[4,8,1,7,2,3,5,6]=>[6,5,3,2,7,1,8,4]=>0000000=>0000000
[3,1,8,2,7,4,6,5]=>[5,6,4,7,2,8,1,3]=>0000000=>0000000
[3,1,2,8,7,5,6,4]=>[4,6,5,7,8,2,1,3]=>0000000=>0000000
[2,1,8,3,4,7,6,5]=>[5,6,7,4,3,8,1,2]=>0000000=>0000000
[6,3,8,5,2,7,4,1]=>[1,4,7,2,5,8,3,6]=>1000000=>0000001
[5,6,1,4,8,7,3,2]=>[2,3,7,8,4,1,6,5]=>0000000=>0000000
[3,6,4,8,5,7,1,2]=>[2,1,7,5,8,4,6,3]=>0100000=>0000010
[3,4,7,1,8,6,5,2]=>[2,5,6,8,1,7,4,3]=>0000000=>0000000
[3,6,8,7,1,4,2,5]=>[5,2,4,1,7,8,6,3]=>0000000=>0000000
[5,3,7,1,6,8,2,4]=>[4,2,8,6,1,7,3,5]=>0000000=>0000000
[6,3,7,5,2,8,1,4]=>[4,1,8,2,5,7,3,6]=>0000000=>0000000
[6,5,8,4,3,7,2,1]=>[1,2,7,3,4,8,5,6]=>1100000=>0000011
[6,3,7,4,2,8,5,1]=>[1,5,8,2,4,7,3,6]=>1000000=>0000001
[8,7,1,6,2,4,5,3]=>[3,5,4,2,6,1,7,8]=>0000011=>1100000
[5,3,8,7,4,1,2,6]=>[6,2,1,4,7,8,3,5]=>0000000=>0000000
[3,6,4,5,7,2,8,1]=>[1,8,2,7,5,4,6,3]=>1000000=>0000001
[5,4,2,7,3,6,8,1]=>[1,8,6,3,7,2,4,5]=>1000000=>0000001
[4,2,5,7,3,6,8,1]=>[1,8,6,3,7,5,2,4]=>1000000=>0000001
[3,7,6,4,5,2,8,1]=>[1,8,2,5,4,6,7,3]=>1000000=>0000001
[2,7,6,5,3,4,8,1]=>[1,8,4,3,5,6,7,2]=>1000000=>0000001
[1,6,5,3,4,8,2,7]=>[7,2,8,4,3,5,6,1]=>0000000=>0000000
[6,5,8,4,2,7,3,1]=>[1,3,7,2,4,8,5,6]=>1000000=>0000001
[3,8,6,2,5,7,4,1]=>[1,4,7,5,2,6,8,3]=>1000000=>0000001
[1,8,6,3,7,5,2,4]=>[4,2,5,7,3,6,8,1]=>0000000=>0000000
[2,8,1,7,3,5,6,4]=>[4,6,5,3,7,1,8,2]=>0000000=>0000000
[4,8,1,3,7,2,6,5]=>[5,6,2,7,3,1,8,4]=>0000000=>0000000
[4,2,8,5,7,3,6,1]=>[1,6,3,7,5,8,2,4]=>1000000=>0000001
[6,7,3,1,8,4,2,5]=>[5,2,4,8,1,3,7,6]=>0000000=>0000000
[8,6,1,7,4,2,5,3]=>[3,5,2,4,7,1,6,8]=>0000001=>1000000
[7,1,2,8,3,5,4,6]=>[6,4,5,3,8,2,1,7]=>0000000=>0000000
[6,3,7,2,1,8,4,5]=>[5,4,8,1,2,7,3,6]=>0000000=>0000000
[5,4,2,7,1,8,3,6]=>[6,3,8,1,7,2,4,5]=>0000000=>0000000
[5,4,3,1,6,8,2,7]=>[7,2,8,6,1,3,4,5]=>0000000=>0000000
[1,5,3,4,6,8,2,7]=>[7,2,8,6,4,3,5,1]=>0000000=>0000000
[4,3,5,1,6,8,2,7]=>[7,2,8,6,1,5,3,4]=>0000000=>0000000
[4,7,5,6,8,3,2,1]=>[1,2,3,8,6,5,7,4]=>1110000=>0000111
[6,5,4,8,2,7,3,1]=>[1,3,7,2,8,4,5,6]=>1000000=>0000001
[6,5,1,8,7,4,2,3]=>[3,2,4,7,8,1,5,6]=>0000000=>0000000
[8,6,4,7,5,3,2,1]=>[1,2,3,5,7,4,6,8]=>1110001=>1000111
[7,5,8,3,2,6,4,1]=>[1,4,6,2,3,8,5,7]=>1000000=>0000001
[3,6,8,2,4,7,5,1]=>[1,5,7,4,2,8,6,3]=>1000000=>0000001
[5,7,3,8,2,6,4,1]=>[1,4,6,2,8,3,7,5]=>1000000=>0000001
[5,4,6,8,2,7,3,1]=>[1,3,7,2,8,6,4,5]=>1000000=>0000001
[4,7,2,8,6,3,5,1]=>[1,5,3,6,8,2,7,4]=>1000000=>0000001
[2,3,8,7,4,5,6,1]=>[1,6,5,4,7,8,3,2]=>1000000=>0000001
[7,2,8,6,4,3,5,1]=>[1,5,3,4,6,8,2,7]=>1000000=>0000001
[2,1,8,7,5,6,3,4]=>[4,3,6,5,7,8,1,2]=>0000000=>0000000
[7,1,8,6,5,3,2,4]=>[4,2,3,5,6,8,1,7]=>0000000=>0000000
[1,3,8,7,4,6,2,5]=>[5,2,6,4,7,8,3,1]=>0000000=>0000000
[4,7,1,8,6,5,2,3]=>[3,2,5,6,8,1,7,4]=>0000000=>0000000
[6,8,4,7,5,3,2,1]=>[1,2,3,5,7,4,8,6]=>1110000=>0000111
[6,7,4,8,3,5,1,2]=>[2,1,5,3,8,4,7,6]=>0100000=>0000010
[6,7,4,5,2,8,1,3]=>[3,1,8,2,5,4,7,6]=>0000000=>0000000
[5,7,4,6,2,3,1,8]=>[8,1,3,2,6,4,7,5]=>0000000=>0000000
[5,7,4,6,3,8,1,2]=>[2,1,8,3,6,4,7,5]=>0100000=>0000010
[6,8,4,5,3,7,1,2]=>[2,1,7,3,5,4,8,6]=>0100000=>0000010
[5,8,4,6,3,7,1,2]=>[2,1,7,3,6,4,8,5]=>0100000=>0000010
[5,6,4,8,3,7,1,2]=>[2,1,7,3,8,4,6,5]=>0100000=>0000010
[5,6,3,7,2,4,1,8]=>[8,1,4,2,7,3,6,5]=>0000000=>0000000
[5,6,3,8,2,7,1,4]=>[4,1,7,2,8,3,6,5]=>0000000=>0000000
[5,6,4,8,2,7,1,3]=>[3,1,7,2,8,4,6,5]=>0000000=>0000000
[5,8,4,6,2,7,1,3]=>[3,1,7,2,6,4,8,5]=>0000000=>0000000
[6,8,4,5,2,7,1,3]=>[3,1,7,2,5,4,8,6]=>0000000=>0000000
[7,8,4,5,2,6,1,3]=>[3,1,6,2,5,4,8,7]=>0000010=>0100000
[5,8,4,6,2,3,1,7]=>[7,1,3,2,6,4,8,5]=>0000000=>0000000
[5,6,3,4,2,8,1,7]=>[7,1,8,2,4,3,6,5]=>0000000=>0000000
[4,6,3,5,2,8,1,7]=>[7,1,8,2,5,3,6,4]=>0000000=>0000000
[4,6,3,8,2,5,1,7]=>[7,1,5,2,8,3,6,4]=>0000000=>0000000
[5,8,3,6,2,4,1,7]=>[7,1,4,2,6,3,8,5]=>0000000=>0000000
[6,8,3,5,2,4,1,7]=>[7,1,4,2,5,3,8,6]=>0000000=>0000000
[7,8,3,5,2,6,1,4]=>[4,1,6,2,5,3,8,7]=>0000010=>0100000
[6,8,3,5,2,7,1,4]=>[4,1,7,2,5,3,8,6]=>0000000=>0000000
[5,8,3,6,2,7,1,4]=>[4,1,7,2,6,3,8,5]=>0000000=>0000000
[4,6,3,8,2,7,1,5]=>[5,1,7,2,8,3,6,4]=>0000000=>0000000
[4,6,3,7,2,5,1,8]=>[8,1,5,2,7,3,6,4]=>0000000=>0000000
[4,7,3,6,2,5,1,8]=>[8,1,5,2,6,3,7,4]=>0000000=>0000000
[4,7,3,6,2,8,1,5]=>[5,1,8,2,6,3,7,4]=>0000000=>0000000
[5,7,4,8,2,6,1,3]=>[3,1,6,2,8,4,7,5]=>0000000=>0000000
[5,7,3,6,2,8,1,4]=>[4,1,8,2,6,3,7,5]=>0000000=>0000000
[5,7,3,6,2,4,1,8]=>[8,1,4,2,6,3,7,5]=>0000000=>0000000
[6,7,3,5,2,4,1,8]=>[8,1,4,2,5,3,7,6]=>0000000=>0000000
[6,7,3,5,2,8,1,4]=>[4,1,8,2,5,3,7,6]=>0000000=>0000000
[6,7,3,8,2,5,1,4]=>[4,1,5,2,8,3,7,6]=>0000000=>0000000
[6,7,4,8,2,5,1,3]=>[3,1,5,2,8,4,7,6]=>0000000=>0000000
[6,7,4,8,2,3,1,5]=>[5,1,3,2,8,4,7,6]=>0000000=>0000000
[6,7,3,8,2,4,1,5]=>[5,1,4,2,8,3,7,6]=>0000000=>0000000
[5,7,3,8,2,4,1,6]=>[6,1,4,2,8,3,7,5]=>0000000=>0000000
[5,8,4,7,2,3,1,6]=>[6,1,3,2,7,4,8,5]=>0000000=>0000000
[6,8,3,7,2,4,1,5]=>[5,1,4,2,7,3,8,6]=>0000000=>0000000
[5,8,3,7,2,4,1,6]=>[6,1,4,2,7,3,8,5]=>0000000=>0000000
[4,7,3,8,2,5,1,6]=>[6,1,5,2,8,3,7,4]=>0000000=>0000000
[4,5,3,8,2,7,1,6]=>[6,1,7,2,8,3,5,4]=>0000000=>0000000
[4,6,5,2,1,3,8,7]=>[7,8,3,1,2,5,6,4]=>0000000=>0000000
[5,6,4,2,3,1,8,7]=>[7,8,1,3,2,4,6,5]=>0000000=>0000000
[5,4,6,1,3,2,8,7]=>[7,8,2,3,1,6,4,5]=>0000000=>0000000
[7,4,8,1,6,5,3,2]=>[2,3,5,6,1,8,4,7]=>0000000=>0000000
[7,4,5,3,1,8,2,6]=>[6,2,8,1,3,5,4,7]=>0000000=>0000000
[5,4,7,1,3,8,2,6]=>[6,2,8,3,1,7,4,5]=>0000000=>0000000
[6,4,8,1,7,5,2,3]=>[3,2,5,7,1,8,4,6]=>0000000=>0000000
[6,4,7,1,8,2,5,3]=>[3,5,2,8,1,7,4,6]=>0000000=>0000000
[8,5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5,8]=>0011001=>1001100
[8,4,7,3,6,2,5,1]=>[1,5,2,6,3,7,4,8]=>1000001=>1000001
[7,6,8,5,2,4,3,1]=>[1,3,4,2,5,8,6,7]=>1001100=>0011001
[5,8,7,6,3,2,1,4]=>[4,1,2,3,6,7,8,5]=>0001000=>0001000
[6,8,7,5,3,2,4,1]=>[1,4,2,3,5,7,8,6]=>1001100=>0011001
[7,8,4,2,6,5,3,1]=>[1,3,5,6,2,4,8,7]=>1000010=>0100001
[4,8,6,2,7,3,1,5]=>[5,1,3,7,2,6,8,4]=>0000000=>0000000
[3,7,1,8,6,4,5,2]=>[2,5,4,6,8,1,7,3]=>0000000=>0000000
[6,7,4,2,8,1,5,3]=>[3,5,1,8,2,4,7,6]=>0000000=>0000000
[6,8,4,2,7,5,1,3]=>[3,1,5,7,2,4,8,6]=>0000000=>0000000
[2,1,8,6,7,5,3,4]=>[4,3,5,7,6,8,1,2]=>0000000=>0000000
[8,6,4,3,7,5,1,2]=>[2,1,5,7,3,4,6,8]=>0100001=>1000010
[2,1,7,6,8,3,5,4]=>[4,5,3,8,6,7,1,2]=>0000000=>0000000
[4,1,7,3,6,5,8,2]=>[2,8,5,6,3,7,1,4]=>0000000=>0000000
[5,1,8,4,7,6,2,3]=>[3,2,6,7,4,8,1,5]=>0000000=>0000000
[5,2,8,7,4,6,1,3]=>[3,1,6,4,7,8,2,5]=>0000000=>0000000
[8,1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1,8]=>0000001=>1000000
[6,1,4,5,3,7,8,2]=>[2,8,7,3,5,4,1,6]=>0000000=>0000000
[5,1,7,8,6,2,4,3]=>[3,4,2,6,8,7,1,5]=>0000000=>0000000
[6,3,2,7,5,1,8,4]=>[4,8,1,5,7,2,3,6]=>0000000=>0000000
[6,5,8,2,4,7,3,1]=>[1,3,7,4,2,8,5,6]=>1000000=>0000001
[6,5,2,8,4,1,3,7]=>[7,3,1,4,8,2,5,6]=>0000000=>0000000
[5,6,2,1,4,8,3,7]=>[7,3,8,4,1,2,6,5]=>0000000=>0000000
[3,4,1,2,8,6,5,7]=>[7,5,6,8,2,1,4,3]=>0000000=>0000000
[4,3,1,2,6,8,5,7]=>[7,5,8,6,2,1,3,4]=>0000000=>0000000
[6,3,8,5,2,1,4,7]=>[7,4,1,2,5,8,3,6]=>0000000=>0000000
[8,5,2,7,3,1,6,4]=>[4,6,1,3,7,2,5,8]=>0000001=>1000000
[2,3,8,5,6,1,7,4]=>[4,7,1,6,5,8,3,2]=>0000000=>0000000
[7,4,5,6,3,1,8,2]=>[2,8,1,3,6,5,4,7]=>0000000=>0000000
[7,5,3,6,2,8,1,4]=>[4,1,8,2,6,3,5,7]=>0000000=>0000000
[8,7,5,4,1,6,2,3]=>[3,2,6,1,4,5,7,8]=>0000011=>1100000
[2,6,4,1,8,5,7,3]=>[3,7,5,8,1,4,6,2]=>0000000=>0000000
[6,1,2,3,8,5,7,4]=>[4,7,5,8,3,2,1,6]=>0000000=>0000000
[7,1,2,3,6,5,8,4]=>[4,8,5,6,3,2,1,7]=>0000000=>0000000
[1,5,7,3,2,4,6,8]=>[8,6,4,2,3,7,5,1]=>0000000=>0000000
[8,7,2,6,3,4,1,5]=>[5,1,4,3,6,2,7,8]=>0000011=>1100000
[4,8,1,6,3,2,7,5]=>[5,7,2,3,6,1,8,4]=>0000000=>0000000
[3,5,8,7,2,4,1,6]=>[6,1,4,2,7,8,5,3]=>0000000=>0000000
[4,2,1,3,7,8,5,6]=>[6,5,8,7,3,1,2,4]=>0000000=>0000000
[2,4,1,3,8,7,5,6]=>[6,5,7,8,3,1,4,2]=>0000000=>0000000
[5,1,8,3,2,4,6,7]=>[7,6,4,2,3,8,1,5]=>0000000=>0000000
[5,2,7,8,6,4,1,3]=>[3,1,4,6,8,7,2,5]=>0000000=>0000000
[1,4,2,7,8,6,3,5]=>[5,3,6,8,7,2,4,1]=>0000000=>0000000
[7,8,3,6,5,2,1,4]=>[4,1,2,5,6,3,8,7]=>0000010=>0100000
[4,7,2,8,6,1,5,3]=>[3,5,1,6,8,2,7,4]=>0000000=>0000000
[6,2,1,8,3,4,7,5]=>[5,7,4,3,8,1,2,6]=>0000000=>0000000
[6,2,4,7,5,8,1,3]=>[3,1,8,5,7,4,2,6]=>0000000=>0000000
[6,2,7,3,5,1,8,4]=>[4,8,1,5,3,7,2,6]=>0000000=>0000000
[6,2,1,3,7,8,4,5]=>[5,4,8,7,3,1,2,6]=>0000000=>0000000
[7,2,5,1,8,3,4,6]=>[6,4,3,8,1,5,2,7]=>0000000=>0000000
[7,5,4,2,6,8,1,3]=>[3,1,8,6,2,4,5,7]=>0000000=>0000000
[5,2,6,3,1,8,7,4]=>[4,7,8,1,3,6,2,5]=>0000000=>0000000
[8,2,7,4,1,3,5,6]=>[6,5,3,1,4,7,2,8]=>0000001=>1000000
[1,8,7,4,3,2,5,6]=>[6,5,2,3,4,7,8,1]=>0000000=>0000000
[5,8,4,7,2,1,6,3]=>[3,6,1,2,7,4,8,5]=>0000000=>0000000
[1,8,7,5,4,3,6,2]=>[2,6,3,4,5,7,8,1]=>0000000=>0000000
[1,6,8,4,3,7,5,2]=>[2,5,7,3,4,8,6,1]=>0000000=>0000000
[6,8,7,3,2,5,1,4]=>[4,1,5,2,3,7,8,6]=>0000100=>0010000
[1,6,3,8,2,4,7,5]=>[5,7,4,2,8,3,6,1]=>0000000=>0000000
[5,3,8,1,2,7,4,6]=>[6,4,7,2,1,8,3,5]=>0000000=>0000000
[5,7,3,1,2,6,4,8]=>[8,4,6,2,1,3,7,5]=>0000000=>0000000
[1,7,5,4,2,6,3,8]=>[8,3,6,2,4,5,7,1]=>0000000=>0000000
[1,4,6,2,8,3,7,5]=>[5,7,3,8,2,6,4,1]=>0000000=>0000000
[5,2,6,7,8,4,1,3]=>[3,1,4,8,7,6,2,5]=>0000000=>0000000
[6,7,3,8,5,2,1,4]=>[4,1,2,5,8,3,7,6]=>0000000=>0000000
[4,6,2,7,8,1,5,3]=>[3,5,1,8,7,2,6,4]=>0000000=>0000000
[1,6,4,7,8,3,5,2]=>[2,5,3,8,7,4,6,1]=>0000000=>0000000
[4,5,7,2,1,8,6,3]=>[3,6,8,1,2,7,5,4]=>0000000=>0000000
[7,8,3,4,2,1,6,5]=>[5,6,1,2,4,3,8,7]=>0000010=>0100000
[4,2,5,6,7,8,1,3]=>[3,1,8,7,6,5,2,4]=>0000000=>0000000
[5,2,3,6,7,1,8,4]=>[4,8,1,7,6,3,2,5]=>0000000=>0000000
[6,2,3,4,1,7,8,5]=>[5,8,7,1,4,3,2,6]=>0000000=>0000000
[10,9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9,10]=>000011111=>111110000
[5,6,3,4,1,2,8,7]=>[7,8,2,1,4,3,6,5]=>0000000=>0000000
[6,8,3,7,5,1,4,2]=>[2,4,1,5,7,3,8,6]=>0000000=>0000000
[2,1,7,8,5,6,3,4]=>[4,3,6,5,8,7,1,2]=>0000000=>0000000
[5,7,3,8,1,6,2,4]=>[4,2,6,1,8,3,7,5]=>0000000=>0000000
[7,5,8,4,2,6,1,3]=>[3,1,6,2,4,8,5,7]=>0000000=>0000000
[8,6,3,7,5,2,4,1]=>[1,4,2,5,7,3,6,8]=>1000001=>1000001
[8,5,3,7,2,6,4,1]=>[1,4,6,2,7,3,5,8]=>1000001=>1000001
[8,5,7,4,2,6,3,1]=>[1,3,6,2,4,7,5,8]=>1000001=>1000001
[6,8,1,7,4,5,2,3]=>[3,2,5,4,7,1,8,6]=>0000000=>0000000
[7,8,1,6,3,5,2,4]=>[4,2,5,3,6,1,8,7]=>0000010=>0100000
[6,8,2,7,3,5,1,4]=>[4,1,5,3,7,2,8,6]=>0000000=>0000000
[6,8,3,7,4,5,1,2]=>[2,1,5,4,7,3,8,6]=>0100000=>0000010
[3,8,6,7,4,5,1,2]=>[2,1,5,4,7,6,8,3]=>0100000=>0000010
[2,8,1,7,5,6,3,4]=>[4,3,6,5,7,1,8,2]=>0000000=>0000000
[2,8,5,7,3,6,1,4]=>[4,1,6,3,7,5,8,2]=>0000000=>0000000
[5,8,3,7,4,6,1,2]=>[2,1,6,4,7,3,8,5]=>0100000=>0000010
[5,8,2,7,4,6,1,3]=>[3,1,6,4,7,2,8,5]=>0000000=>0000000
[5,8,2,7,3,6,1,4]=>[4,1,6,3,7,2,8,5]=>0000000=>0000000
[4,8,1,7,3,6,2,5]=>[5,2,6,3,7,1,8,4]=>0000000=>0000000
[5,8,1,7,3,6,2,4]=>[4,2,6,3,7,1,8,5]=>0000000=>0000000
[5,8,1,7,4,6,2,3]=>[3,2,6,4,7,1,8,5]=>0000000=>0000000
[5,8,4,7,1,6,2,3]=>[3,2,6,1,7,4,8,5]=>0000000=>0000000
[5,8,6,7,2,4,1,3]=>[3,1,4,2,7,6,8,5]=>0001000=>0001000
[4,8,5,7,1,6,2,3]=>[3,2,6,1,7,5,8,4]=>0000000=>0000000
[3,8,5,7,1,6,2,4]=>[4,2,6,1,7,5,8,3]=>0000000=>0000000
[3,8,5,7,2,6,1,4]=>[4,1,6,2,7,5,8,3]=>0000000=>0000000
[3,8,1,7,2,6,4,5]=>[5,4,6,2,7,1,8,3]=>0000000=>0000000
[4,8,2,7,5,6,1,3]=>[3,1,6,5,7,2,8,4]=>0000000=>0000000
[2,8,3,7,5,6,1,4]=>[4,1,6,5,7,3,8,2]=>0000000=>0000000
[7,5,2,8,6,4,1,3]=>[3,1,4,6,8,2,5,7]=>0000000=>0000000
[7,5,1,8,6,2,3,4]=>[4,3,2,6,8,1,5,7]=>0000000=>0000000
[7,4,8,6,1,5,2,3]=>[3,2,5,1,6,8,4,7]=>0000000=>0000000
[7,1,8,4,5,2,6,3]=>[3,6,2,5,4,8,1,7]=>0000000=>0000000
[6,8,1,7,4,2,5,3]=>[3,5,2,4,7,1,8,6]=>0000000=>0000000
[1,6,7,4,2,8,5,3]=>[3,5,8,2,4,7,6,1]=>0000000=>0000000
[7,1,8,3,5,6,2,4]=>[4,2,6,5,3,8,1,7]=>0000000=>0000000
[7,3,8,6,2,5,1,4]=>[4,1,5,2,6,8,3,7]=>0000000=>0000000
[7,4,2,8,6,1,3,5]=>[5,3,1,6,8,2,4,7]=>0000000=>0000000
[7,3,1,8,4,2,5,6]=>[6,5,2,4,8,1,3,7]=>0000000=>0000000
[6,8,1,7,2,3,4,5]=>[5,4,3,2,7,1,8,6]=>0000000=>0000000
[1,5,7,8,2,6,3,4]=>[4,3,6,2,8,7,5,1]=>0000000=>0000000
[6,2,3,8,5,7,4,1]=>[1,4,7,5,8,3,2,6]=>1000000=>0000001
[2,4,7,3,6,8,5,1]=>[1,5,8,6,3,7,4,2]=>1000000=>0000001
[3,1,5,4,7,8,2,6]=>[6,2,8,7,4,5,1,3]=>0000000=>0000000
[4,8,2,3,5,7,1,6]=>[6,1,7,5,3,2,8,4]=>0000000=>0000000
[5,3,8,2,4,7,1,6]=>[6,1,7,4,2,8,3,5]=>0000000=>0000000
[5,4,3,8,1,2,7,6]=>[6,7,2,1,8,3,4,5]=>0000000=>0000000
[6,4,3,1,2,8,5,7]=>[7,5,8,2,1,3,4,6]=>0000000=>0000000
[6,4,2,8,1,3,7,5]=>[5,7,3,1,8,2,4,6]=>0000000=>0000000
[6,3,8,2,5,1,7,4]=>[4,7,1,5,2,8,3,6]=>0000000=>0000000
[1,5,7,3,6,8,4,2]=>[2,4,8,6,3,7,5,1]=>0000000=>0000000
[6,5,1,2,8,7,3,4]=>[4,3,7,8,2,1,5,6]=>0000000=>0000000
[6,5,3,1,4,2,8,7]=>[7,8,2,4,1,3,5,6]=>0000000=>0000000
[5,3,1,6,4,2,7,8]=>[8,7,2,4,6,1,3,5]=>0000000=>0000000
[5,2,6,4,1,7,3,8]=>[8,3,7,1,4,6,2,5]=>0000000=>0000000
[4,6,1,7,5,2,8,3]=>[3,8,2,5,7,1,6,4]=>0000000=>0000000
[4,3,1,5,7,2,6,8]=>[8,6,2,7,5,1,3,4]=>0000000=>0000000
[3,4,7,2,8,6,1,5]=>[5,1,6,8,2,7,4,3]=>0000000=>0000000
[3,4,5,8,2,7,1,6]=>[6,1,7,2,8,5,4,3]=>0000000=>0000000
[3,5,2,6,8,1,7,4]=>[4,7,1,8,6,2,5,3]=>0000000=>0000000
[5,3,6,8,4,7,2,1]=>[1,2,7,4,8,6,3,5]=>1100000=>0000011
[3,7,2,5,4,8,6,1]=>[1,6,8,4,5,2,7,3]=>1000000=>0000001
[4,7,2,5,8,3,6,1]=>[1,6,3,8,5,2,7,4]=>1000000=>0000001
[4,2,6,5,8,3,7,1]=>[1,7,3,8,5,6,2,4]=>1000000=>0000001
[6,7,8,1,4,3,2,5]=>[5,2,3,4,1,8,7,6]=>0000100=>0010000
[4,7,1,5,8,3,2,6]=>[6,2,3,8,5,1,7,4]=>0000000=>0000000
[2,7,1,5,4,3,8,6]=>[6,8,3,4,5,1,7,2]=>0000000=>0000000
[8,2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2,8]=>0000001=>1000000
[8,3,1,5,4,7,2,6]=>[6,2,7,4,5,1,3,8]=>0000001=>1000000
[8,4,1,5,7,3,2,6]=>[6,2,3,7,5,1,4,8]=>0000001=>1000000
[8,2,6,1,4,3,7,5]=>[5,7,3,4,1,6,2,8]=>0000001=>1000000
[3,7,6,1,4,8,2,5]=>[5,2,8,4,1,6,7,3]=>0000000=>0000000
[6,7,8,2,4,3,5,1]=>[1,5,3,4,2,8,7,6]=>1000100=>0010001
[4,7,6,2,8,3,5,1]=>[1,5,3,8,2,6,7,4]=>1000000=>0000001
[3,7,6,2,4,8,5,1]=>[1,5,8,4,2,6,7,3]=>1000000=>0000001
[5,7,3,8,4,6,2,1]=>[1,2,6,4,8,3,7,5]=>1100000=>0000011
[4,7,3,5,8,6,2,1]=>[1,2,6,8,5,3,7,4]=>1100000=>0000011
[8,7,2,1,4,3,6,5]=>[5,6,3,4,1,2,7,8]=>0000011=>1100000
[8,7,3,1,4,6,2,5]=>[5,2,6,4,1,3,7,8]=>0000011=>1100000
[8,7,6,3,2,5,4,1]=>[1,4,5,2,3,6,7,8]=>1000111=>1110001
[8,7,3,5,1,6,2,4]=>[4,2,6,1,5,3,7,8]=>0000011=>1100000
[8,7,2,5,1,3,6,4]=>[4,6,3,1,5,2,7,8]=>0000011=>1100000
[8,4,6,5,7,1,2,3]=>[3,2,1,7,5,6,4,8]=>0010001=>1000100
[5,7,6,8,4,1,2,3]=>[3,2,1,4,8,6,7,5]=>0011000=>0001100
[4,7,6,5,8,1,2,3]=>[3,2,1,8,5,6,7,4]=>0010000=>0000100
[3,7,6,5,1,8,2,4]=>[4,2,8,1,5,6,7,3]=>0000000=>0000000
[8,7,6,5,2,1,4,3]=>[3,4,1,2,5,6,7,8]=>0001111=>1111000
[5,6,4,3,8,7,1,2]=>[2,1,7,8,3,4,6,5]=>0100000=>0000010
[3,4,7,2,8,1,6,5]=>[5,6,1,8,2,7,4,3]=>0000000=>0000000
[1,4,7,2,5,8,6,3]=>[3,6,8,5,2,7,4,1]=>0000000=>0000000
[7,3,8,4,5,6,1,2]=>[2,1,6,5,4,8,3,7]=>0100000=>0000010
[4,6,8,5,3,7,1,2]=>[2,1,7,3,5,8,6,4]=>0100000=>0000010
[6,5,2,1,4,7,8,3]=>[3,8,7,4,1,2,5,6]=>0000000=>0000000
[7,8,1,4,2,6,5,3]=>[3,5,6,2,4,1,8,7]=>0000010=>0100000
[7,6,1,8,3,2,4,5]=>[5,4,2,3,8,1,6,7]=>0000000=>0000000
[4,2,6,1,8,5,7,3]=>[3,7,5,8,1,6,2,4]=>0000000=>0000000
[1,6,3,8,5,7,2,4]=>[4,2,7,5,8,3,6,1]=>0000000=>0000000
[1,6,4,3,7,2,8,5]=>[5,8,2,7,3,4,6,1]=>0000000=>0000000
[4,6,3,8,1,2,7,5]=>[5,7,2,1,8,3,6,4]=>0000000=>0000000
[7,8,1,3,4,2,6,5]=>[5,6,2,4,3,1,8,7]=>0000010=>0100000
[7,5,8,4,1,2,3,6]=>[6,3,2,1,4,8,5,7]=>0000000=>0000000
[3,4,7,2,5,1,6,8]=>[8,6,1,5,2,7,4,3]=>0000000=>0000000
[3,6,2,4,7,1,5,8]=>[8,5,1,7,4,2,6,3]=>0000000=>0000000
[4,5,6,3,8,7,1,2]=>[2,1,7,8,3,6,5,4]=>0100000=>0000010
[3,2,7,6,5,1,4,8]=>[8,4,1,5,6,7,2,3]=>0000000=>0000000
[4,3,6,2,5,1,8,7]=>[7,8,1,5,2,6,3,4]=>0000000=>0000000
[7,8,3,2,5,1,4,6]=>[6,4,1,5,2,3,8,7]=>0000010=>0100000
[7,8,1,2,5,6,3,4]=>[4,3,6,5,2,1,8,7]=>0000010=>0100000
[2,1,8,6,4,7,3,5]=>[5,3,7,4,6,8,1,2]=>0000000=>0000000
[1,8,3,6,7,4,5,2]=>[2,5,4,7,6,3,8,1]=>0000000=>0000000
[7,1,5,8,3,6,2,4]=>[4,2,6,3,8,5,1,7]=>0000000=>0000000
[1,5,7,8,2,4,6,3]=>[3,6,4,2,8,7,5,1]=>0000000=>0000000
[7,6,5,1,4,3,2,8]=>[8,2,3,4,1,5,6,7]=>0000000=>0000000
[2,6,4,5,1,3,8,7]=>[7,8,3,1,5,4,6,2]=>0000000=>0000000
[3,5,6,4,1,8,2,7]=>[7,2,8,1,4,6,5,3]=>0000000=>0000000
[4,2,6,3,8,1,7,5]=>[5,7,1,8,3,6,2,4]=>0000000=>0000000
[5,8,7,6,3,1,2,4]=>[4,2,1,3,6,7,8,5]=>0001000=>0001000
[5,2,7,1,8,4,6,3]=>[3,6,4,8,1,7,2,5]=>0000000=>0000000
[4,2,1,3,6,5,8,7]=>[7,8,5,6,3,1,2,4]=>0000000=>0000000
[7,8,2,1,4,5,3,6]=>[6,3,5,4,1,2,8,7]=>0000010=>0100000
[6,5,1,8,2,7,4,3]=>[3,4,7,2,8,1,5,6]=>0000000=>0000000
[7,6,1,8,5,3,2,4]=>[4,2,3,5,8,1,6,7]=>0000000=>0000000
[7,8,5,1,6,4,2,3]=>[3,2,4,6,1,5,8,7]=>0000010=>0100000
[2,6,5,7,3,4,8,1]=>[1,8,4,3,7,5,6,2]=>1000000=>0000001
[1,6,4,7,5,8,2,3]=>[3,2,8,5,7,4,6,1]=>0000000=>0000000
[1,3,7,4,6,8,2,5]=>[5,2,8,6,4,7,3,1]=>0000000=>0000000
[5,2,4,7,3,6,8,1]=>[1,8,6,3,7,4,2,5]=>1000000=>0000001
[7,1,6,5,8,3,2,4]=>[4,2,3,8,5,6,1,7]=>0000000=>0000000
[1,2,7,6,8,3,4,5]=>[5,4,3,8,6,7,2,1]=>0000000=>0000000
[6,1,7,5,3,8,2,4]=>[4,2,8,3,5,7,1,6]=>0000000=>0000000
[4,8,5,6,2,7,3,1]=>[1,3,7,2,6,5,8,4]=>1000000=>0000001
[3,8,6,4,2,7,5,1]=>[1,5,7,2,4,6,8,3]=>1000000=>0000001
[7,8,5,2,4,6,3,1]=>[1,3,6,4,2,5,8,7]=>1000010=>0100001
[7,8,1,6,2,4,5,3]=>[3,5,4,2,6,1,8,7]=>0000010=>0100000
[2,8,1,7,4,3,6,5]=>[5,6,3,4,7,1,8,2]=>0000000=>0000000
[6,8,1,4,7,2,5,3]=>[3,5,2,7,4,1,8,6]=>0000000=>0000000
[3,8,4,1,7,2,6,5]=>[5,6,2,7,1,4,8,3]=>0000000=>0000000
[3,7,4,1,8,5,2,6]=>[6,2,5,8,1,4,7,3]=>0000000=>0000000
[6,7,1,4,8,3,2,5]=>[5,2,3,8,4,1,7,6]=>0000000=>0000000
[6,1,2,8,4,3,5,7]=>[7,5,3,4,8,2,1,6]=>0000000=>0000000
[5,1,2,4,8,3,6,7]=>[7,6,3,8,4,2,1,5]=>0000000=>0000000
[4,1,3,2,8,5,6,7]=>[7,6,5,8,2,3,1,4]=>0000000=>0000000
[3,2,1,4,8,5,6,7]=>[7,6,5,8,4,1,2,3]=>0000000=>0000000
[4,3,6,1,5,8,2,7]=>[7,2,8,5,1,6,3,4]=>0000000=>0000000
[2,6,1,4,5,8,3,7]=>[7,3,8,5,4,1,6,2]=>0000000=>0000000
[1,6,2,5,8,3,4,7]=>[7,4,3,8,5,2,6,1]=>0000000=>0000000
[8,4,2,1,7,3,6,5]=>[5,6,3,7,1,2,4,8]=>0000001=>1000000
[6,4,3,1,5,8,2,7]=>[7,2,8,5,1,3,4,6]=>0000000=>0000000
[5,4,3,2,1,8,6,7]=>[7,6,8,1,2,3,4,5]=>0000000=>0000000
[2,5,3,4,1,8,6,7]=>[7,6,8,1,4,3,5,2]=>0000000=>0000000
[4,3,5,2,1,8,6,7]=>[7,6,8,1,2,5,3,4]=>0000000=>0000000
[3,7,6,8,4,5,2,1]=>[1,2,5,4,8,6,7,3]=>1100000=>0000011
[2,4,8,6,7,3,5,1]=>[1,5,3,7,6,8,4,2]=>1000000=>0000001
[7,3,8,5,4,6,2,1]=>[1,2,6,4,5,8,3,7]=>1100000=>0000011
[6,3,5,8,4,7,2,1]=>[1,2,7,4,8,5,3,6]=>1100000=>0000011
[5,4,3,8,6,7,2,1]=>[1,2,7,6,8,3,4,5]=>1100000=>0000011
[5,4,2,8,7,3,6,1]=>[1,6,3,7,8,2,4,5]=>1000000=>0000001
[3,2,8,5,7,4,6,1]=>[1,6,4,7,5,8,2,3]=>1000000=>0000001
[2,1,8,7,4,6,3,5]=>[5,3,6,4,7,8,1,2]=>0000000=>0000000
[5,4,1,8,7,6,2,3]=>[3,2,6,7,8,1,4,5]=>0000000=>0000000
[5,8,6,7,4,3,2,1]=>[1,2,3,4,7,6,8,5]=>1111000=>0001111
[4,8,7,5,6,3,2,1]=>[1,2,3,6,5,7,8,4]=>1110000=>0000111
[6,2,4,1,3,8,5,7]=>[7,5,8,3,1,4,2,6]=>0000000=>0000000
[4,2,6,1,3,5,8,7]=>[7,8,5,3,1,6,2,4]=>0000000=>0000000
[2,1,6,4,3,5,8,7]=>[7,8,5,3,4,6,1,2]=>0000000=>0000000
[8,4,2,1,6,3,5,7]=>[7,5,3,6,1,2,4,8]=>0000001=>1000000
[6,4,2,1,8,3,5,7]=>[7,5,3,8,1,2,4,6]=>0000000=>0000000
[4,6,2,1,3,8,5,7]=>[7,5,8,3,1,2,6,4]=>0000000=>0000000
[2,8,1,4,3,6,5,7]=>[7,5,6,3,4,1,8,2]=>0000000=>0000000
[2,8,1,4,6,3,5,7]=>[7,5,3,6,4,1,8,2]=>0000000=>0000000
[2,1,6,4,8,3,5,7]=>[7,5,3,8,4,6,1,2]=>0000000=>0000000
[2,6,1,4,8,3,5,7]=>[7,5,3,8,4,1,6,2]=>0000000=>0000000
[2,6,4,1,8,3,5,7]=>[7,5,3,8,1,4,6,2]=>0000000=>0000000
[2,6,4,8,1,3,5,7]=>[7,5,3,1,8,4,6,2]=>0000000=>0000000
[4,6,2,8,1,3,5,7]=>[7,5,3,1,8,2,6,4]=>0000000=>0000000
[6,2,4,1,8,3,5,7]=>[7,5,3,8,1,4,2,6]=>0000000=>0000000
[4,2,1,6,8,3,5,7]=>[7,5,3,8,6,1,2,4]=>0000000=>0000000
[4,2,1,3,6,8,5,7]=>[7,5,8,6,3,1,2,4]=>0000000=>0000000
[2,1,4,3,8,6,5,7]=>[7,5,6,8,3,4,1,2]=>0000000=>0000000
[2,4,1,3,8,6,5,7]=>[7,5,6,8,3,1,4,2]=>0000000=>0000000
[4,2,1,3,8,6,5,7]=>[7,5,6,8,3,1,2,4]=>0000000=>0000000
[4,2,1,8,3,6,5,7]=>[7,5,6,3,8,1,2,4]=>0000000=>0000000
[2,4,8,1,3,6,5,7]=>[7,5,6,3,1,8,4,2]=>0000000=>0000000
[2,4,8,1,6,3,5,7]=>[7,5,3,6,1,8,4,2]=>0000000=>0000000
[2,8,6,1,4,3,5,7]=>[7,5,3,4,1,6,8,2]=>0000000=>0000000
[3,2,6,1,5,4,8,7]=>[7,8,4,5,1,6,2,3]=>0000000=>0000000
[5,2,4,3,8,1,7,6]=>[6,7,1,8,3,4,2,5]=>0000000=>0000000
[6,1,5,2,4,3,8,7]=>[7,8,3,4,2,5,1,6]=>0000000=>0000000
[6,1,3,2,5,4,8,7]=>[7,8,4,5,2,3,1,6]=>0000000=>0000000
[4,3,6,1,5,2,8,7]=>[7,8,2,5,1,6,3,4]=>0000000=>0000000
[4,3,5,2,8,1,7,6]=>[6,7,1,8,2,5,3,4]=>0000000=>0000000
[4,3,7,2,6,5,8,1]=>[1,8,5,6,2,7,3,4]=>1000000=>0000001
[4,3,8,1,7,2,6,5]=>[5,6,2,7,1,8,3,4]=>0000000=>0000000
[4,3,8,1,5,2,7,6]=>[6,7,2,5,1,8,3,4]=>0000000=>0000000
[5,4,8,1,3,2,7,6]=>[6,7,2,3,1,8,4,5]=>0000000=>0000000
[2,1,5,4,8,3,7,6]=>[6,7,3,8,4,5,1,2]=>0000000=>0000000
[5,4,7,6,8,1,3,2]=>[2,3,1,8,6,7,4,5]=>0010000=>0000100
[4,3,7,6,8,1,5,2]=>[2,5,1,8,6,7,3,4]=>0000000=>0000000
[4,3,7,1,8,5,6,2]=>[2,6,5,8,1,7,3,4]=>0000000=>0000000
[4,3,6,5,8,1,7,2]=>[2,7,1,8,5,6,3,4]=>0000000=>0000000
[6,3,5,4,8,1,7,2]=>[2,7,1,8,4,5,3,6]=>0000000=>0000000
[7,1,6,5,8,3,4,2]=>[2,4,3,8,5,6,1,7]=>0000000=>0000000
[7,4,6,5,8,1,3,2]=>[2,3,1,8,5,6,4,7]=>0010000=>0000100
[8,3,5,2,6,1,7,4]=>[4,7,1,6,2,5,3,8]=>0000001=>1000000
[7,3,5,2,6,4,8,1]=>[1,8,4,6,2,5,3,7]=>1000000=>0000001
[8,2,7,1,5,3,6,4]=>[4,6,3,5,1,7,2,8]=>0000001=>1000000
[8,1,7,2,4,3,6,5]=>[5,6,3,4,2,7,1,8]=>0000001=>1000000
[8,1,3,2,7,4,6,5]=>[5,6,4,7,2,3,1,8]=>0000001=>1000000
[2,1,8,3,7,4,6,5]=>[5,6,4,7,3,8,1,2]=>0000000=>0000000
[2,1,8,3,5,4,7,6]=>[6,7,4,5,3,8,1,2]=>0000000=>0000000
[8,1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1,8]=>0000001=>1000000
[8,1,5,2,4,3,7,6]=>[6,7,3,4,2,5,1,8]=>0000001=>1000000
[8,2,4,1,7,3,6,5]=>[5,6,3,7,1,4,2,8]=>0000001=>1000000
[3,2,8,1,5,4,7,6]=>[6,7,4,5,1,8,2,3]=>0000000=>0000000
[3,2,4,1,8,5,7,6]=>[6,7,5,8,1,4,2,3]=>0000000=>0000000
[4,1,3,2,7,6,8,5]=>[5,8,6,7,2,3,1,4]=>0000000=>0000000
[3,2,7,6,8,1,5,4]=>[4,5,1,8,6,7,2,3]=>0000000=>0000000
[3,2,6,5,8,1,7,4]=>[4,7,1,8,5,6,2,3]=>0000000=>0000000
[7,2,4,1,8,5,6,3]=>[3,6,5,8,1,4,2,7]=>0000000=>0000000
[7,6,8,1,3,2,5,4]=>[4,5,2,3,1,8,6,7]=>0000100=>0010000
[7,1,8,5,6,2,4,3]=>[3,4,2,6,5,8,1,7]=>0000000=>0000000
[7,1,8,2,6,4,5,3]=>[3,5,4,6,2,8,1,7]=>0000000=>0000000
[7,2,8,1,5,4,6,3]=>[3,6,4,5,1,8,2,7]=>0000000=>0000000
[5,4,8,2,6,1,7,3]=>[3,7,1,6,2,8,4,5]=>0000000=>0000000
[6,1,8,4,7,2,5,3]=>[3,5,2,7,4,8,1,6]=>0000000=>0000000
[6,5,8,1,3,2,7,4]=>[4,7,2,3,1,8,5,6]=>0000000=>0000000
[2,1,6,5,8,3,7,4]=>[4,7,3,8,5,6,1,2]=>0000000=>0000000
[3,2,1,5,8,4,6,7]=>[7,6,4,8,5,1,2,3]=>0000000=>0000000
[2,8,3,1,5,4,6,7]=>[7,6,4,5,1,3,8,2]=>0000000=>0000000
[2,4,8,3,5,7,6,1]=>[1,6,7,5,3,8,4,2]=>1000000=>0000001
[1,8,4,2,5,3,6,7]=>[7,6,3,5,2,4,8,1]=>0000000=>0000000
[8,1,5,3,2,4,6,7]=>[7,6,4,2,3,5,1,8]=>0000001=>1000000
[3,8,1,5,2,4,6,7]=>[7,6,4,2,5,1,8,3]=>0000000=>0000000
[1,4,3,8,7,5,6,2]=>[2,6,5,7,8,3,4,1]=>0000000=>0000000
[7,1,6,8,4,3,2,5]=>[5,2,3,4,8,6,1,7]=>0000000=>0000000
[1,6,7,2,8,4,3,5]=>[5,3,4,8,2,7,6,1]=>0000000=>0000000
[6,7,1,4,2,8,3,5]=>[5,3,8,2,4,1,7,6]=>0000000=>0000000
[6,3,7,1,4,8,2,5]=>[5,2,8,4,1,7,3,6]=>0000000=>0000000
[3,7,8,1,5,2,4,6]=>[6,4,2,5,1,8,7,3]=>0000000=>0000000
[7,1,2,8,5,3,4,6]=>[6,4,3,5,8,2,1,7]=>0000000=>0000000
[1,7,2,8,4,5,3,6]=>[6,3,5,4,8,2,7,1]=>0000000=>0000000
[2,6,8,4,3,7,5,1]=>[1,5,7,3,4,8,6,2]=>1000000=>0000001
[6,2,4,8,3,7,5,1]=>[1,5,7,3,8,4,2,6]=>1000000=>0000001
[2,6,7,3,1,4,8,5]=>[5,8,4,1,3,7,6,2]=>0000000=>0000000
[2,7,1,8,3,5,4,6]=>[6,4,5,3,8,1,7,2]=>0000000=>0000000
[2,1,7,3,5,8,4,6]=>[6,4,8,5,3,7,1,2]=>0000000=>0000000
[1,2,7,5,8,3,4,6]=>[6,4,3,8,5,7,2,1]=>0000000=>0000000
[8,7,1,3,6,2,4,5]=>[5,4,2,6,3,1,7,8]=>0000011=>1100000
[8,2,1,7,3,5,6,4]=>[4,6,5,3,7,1,2,8]=>0000001=>1000000
[2,8,4,1,6,7,5,3]=>[3,5,7,6,1,4,8,2]=>0000000=>0000000
[2,1,8,4,7,5,6,3]=>[3,6,5,7,4,8,1,2]=>0000000=>0000000
[8,3,7,1,5,6,2,4]=>[4,2,6,5,1,7,3,8]=>0000001=>1000000
[8,6,1,2,7,5,3,4]=>[4,3,5,7,2,1,6,8]=>0000001=>1000000
[8,1,6,2,7,4,5,3]=>[3,5,4,7,2,6,1,8]=>0000001=>1000000
[1,8,5,2,6,7,4,3]=>[3,4,7,6,2,5,8,1]=>0000000=>0000000
[5,2,1,8,6,7,4,3]=>[3,4,7,6,8,1,2,5]=>0000000=>0000000
[8,7,6,5,1,4,2,3]=>[3,2,4,1,5,6,7,8]=>0001111=>1111000
[8,7,6,1,5,3,4,2]=>[2,4,3,5,1,6,7,8]=>0000111=>1110000
[6,3,5,2,1,4,8,7]=>[7,8,4,1,2,5,3,6]=>0000000=>0000000
[8,3,5,7,2,4,1,6]=>[6,1,4,2,7,5,3,8]=>0000001=>1000000
[6,5,3,1,2,4,8,7]=>[7,8,4,2,1,3,5,6]=>0000000=>0000000
[4,5,3,6,1,2,8,7]=>[7,8,2,1,6,3,5,4]=>0000000=>0000000
[3,5,1,4,6,2,8,7]=>[7,8,2,6,4,1,5,3]=>0000000=>0000000
[5,7,4,6,3,8,2,1]=>[1,2,8,3,6,4,7,5]=>1100000=>0000011
[8,1,4,7,3,6,2,5]=>[5,2,6,3,7,4,1,8]=>0000001=>1000000
[8,5,1,4,7,3,2,6]=>[6,2,3,7,4,1,5,8]=>0000001=>1000000
[8,5,3,7,1,4,2,6]=>[6,2,4,1,7,3,5,8]=>0000001=>1000000
[2,1,8,5,7,4,3,6]=>[6,3,4,7,5,8,1,2]=>0000000=>0000000
[5,1,4,6,8,3,7,2]=>[2,7,3,8,6,4,1,5]=>0000000=>0000000
[4,7,1,3,5,8,6,2]=>[2,6,8,5,3,1,7,4]=>0000000=>0000000
[4,8,3,7,1,2,6,5]=>[5,6,2,1,7,3,8,4]=>0000000=>0000000
[8,7,1,4,2,6,3,5]=>[5,3,6,2,4,1,7,8]=>0000011=>1100000
[8,6,3,1,2,4,7,5]=>[5,7,4,2,1,3,6,8]=>0000001=>1000000
[2,1,8,7,5,3,4,6]=>[6,4,3,5,7,8,1,2]=>0000000=>0000000
[8,1,7,4,5,2,3,6]=>[6,3,2,5,4,7,1,8]=>0000001=>1000000
[8,7,2,6,4,1,3,5]=>[5,3,1,4,6,2,7,8]=>0000011=>1100000
[5,3,7,8,2,4,6,1]=>[1,6,4,2,8,7,3,5]=>1000000=>0000001
[5,3,7,6,2,1,8,4]=>[4,8,1,2,6,7,3,5]=>0000000=>0000000
[5,7,8,6,4,2,1,3]=>[3,1,2,4,6,8,7,5]=>0011000=>0001100
[6,7,3,5,1,8,2,4]=>[4,2,8,1,5,3,7,6]=>0000000=>0000000
[2,1,6,7,5,8,3,4]=>[4,3,8,5,7,6,1,2]=>0000000=>0000000
[2,1,5,7,3,6,8,4]=>[4,8,6,3,7,5,1,2]=>0000000=>0000000
[4,1,7,2,5,6,8,3]=>[3,8,6,5,2,7,1,4]=>0000000=>0000000
[2,4,7,1,6,5,8,3]=>[3,8,5,6,1,7,4,2]=>0000000=>0000000
[5,6,3,1,8,7,2,4]=>[4,2,7,8,1,3,6,5]=>0000000=>0000000
[7,2,5,1,4,3,8,6]=>[6,8,3,4,1,5,2,7]=>0000000=>0000000
[4,3,7,2,1,5,8,6]=>[6,8,5,1,2,7,3,4]=>0000000=>0000000
[3,6,2,7,1,4,8,5]=>[5,8,4,1,7,2,6,3]=>0000000=>0000000
[6,4,3,2,1,8,5,7]=>[7,5,8,1,2,3,4,6]=>0000000=>0000000
[6,2,7,5,3,8,1,4]=>[4,1,8,3,5,7,2,6]=>0000000=>0000000
[7,1,8,5,3,6,4,2]=>[2,4,6,3,5,8,1,7]=>0000000=>0000000
[1,8,6,3,2,7,5,4]=>[4,5,7,2,3,6,8,1]=>0000000=>0000000
[8,7,3,1,6,5,4,2]=>[2,4,5,6,1,3,7,8]=>0000011=>1100000
[1,8,5,7,4,3,6,2]=>[2,6,3,4,7,5,8,1]=>0000000=>0000000
[3,8,6,1,7,2,5,4]=>[4,5,2,7,1,6,8,3]=>0000000=>0000000
[5,8,4,6,7,1,3,2]=>[2,3,1,7,6,4,8,5]=>0010000=>0000100
[7,2,8,5,6,1,4,3]=>[3,4,1,6,5,8,2,7]=>0000000=>0000000
[4,3,6,7,8,1,2,5]=>[5,2,1,8,7,6,3,4]=>0000000=>0000000
[5,4,6,7,2,8,1,3]=>[3,1,8,2,7,6,4,5]=>0000000=>0000000
[3,5,7,1,4,8,2,6]=>[6,2,8,4,1,7,5,3]=>0000000=>0000000
[8,1,5,2,7,4,6,3]=>[3,6,4,7,2,5,1,8]=>0000001=>1000000
[5,4,1,6,8,2,3,7]=>[7,3,2,8,6,1,4,5]=>0000000=>0000000
[5,3,1,7,2,8,4,6]=>[6,4,8,2,7,1,3,5]=>0000000=>0000000
[6,5,2,1,7,8,3,4]=>[4,3,8,7,1,2,5,6]=>0000000=>0000000
[6,3,7,4,8,5,2,1]=>[1,2,5,8,4,7,3,6]=>1100000=>0000011
[4,7,2,5,8,6,3,1]=>[1,3,6,8,5,2,7,4]=>1000000=>0000001
[3,6,8,1,4,7,5,2]=>[2,5,7,4,1,8,6,3]=>0000000=>0000000
[6,4,7,8,1,5,3,2]=>[2,3,5,1,8,7,4,6]=>0000000=>0000000
[4,6,8,2,7,1,5,3]=>[3,5,1,7,2,8,6,4]=>0000000=>0000000
[2,5,8,7,1,3,6,4]=>[4,6,3,1,7,8,5,2]=>0000000=>0000000
[8,2,7,6,5,1,4,3]=>[3,4,1,5,6,7,2,8]=>0000001=>1000000
[2,4,8,7,6,1,3,5]=>[5,3,1,6,7,8,4,2]=>0000000=>0000000
[4,7,3,8,6,5,1,2]=>[2,1,5,6,8,3,7,4]=>0100000=>0000010
[7,5,8,6,4,3,2,1]=>[1,2,3,4,6,8,5,7]=>1111000=>0001111
[7,8,5,3,1,6,4,2]=>[2,4,6,1,3,5,8,7]=>0000010=>0100000
[7,5,8,3,1,2,6,4]=>[4,6,2,1,3,8,5,7]=>0000000=>0000000
[7,5,8,3,4,1,6,2]=>[2,6,1,4,3,8,5,7]=>0000000=>0000000
[7,5,6,3,1,2,8,4]=>[4,8,2,1,3,6,5,7]=>0000000=>0000000
[7,5,3,8,4,1,6,2]=>[2,6,1,4,8,3,5,7]=>0000000=>0000000
[7,5,3,8,1,4,6,2]=>[2,6,4,1,8,3,5,7]=>0000000=>0000000
[7,5,3,1,8,4,6,2]=>[2,6,4,8,1,3,5,7]=>0000000=>0000000
[7,5,3,1,8,2,6,4]=>[4,6,2,8,1,3,5,7]=>0000000=>0000000
[7,5,3,1,6,2,4,8]=>[8,4,2,6,1,3,5,7]=>0000000=>0000000
[7,5,3,1,8,4,2,6]=>[6,2,4,8,1,3,5,7]=>0000000=>0000000
[7,5,3,8,1,6,4,2]=>[2,4,6,1,8,3,5,7]=>0000000=>0000000
[7,5,8,3,6,4,1,2]=>[2,1,4,6,3,8,5,7]=>0100000=>0000010
[7,5,8,3,6,1,4,2]=>[2,4,1,6,3,8,5,7]=>0000000=>0000000
[7,5,8,3,1,6,4,2]=>[2,4,6,1,3,8,5,7]=>0000000=>0000000
[7,5,3,8,1,4,2,6]=>[6,2,4,1,8,3,5,7]=>0000000=>0000000
[7,5,3,8,6,1,2,4]=>[4,2,1,6,8,3,5,7]=>0000000=>0000000
[7,5,6,3,8,1,2,4]=>[4,2,1,8,3,6,5,7]=>0000000=>0000000
[7,5,3,6,1,8,4,2]=>[2,4,8,1,6,3,5,7]=>0000000=>0000000
[7,5,3,1,4,6,8,2]=>[2,8,6,4,1,3,5,7]=>0000000=>0000000
[7,5,3,1,2,6,8,4]=>[4,8,6,2,1,3,5,7]=>0000000=>0000000
[4,6,8,3,5,7,1,2]=>[2,1,7,5,3,8,6,4]=>0100000=>0000010
[3,6,8,2,5,7,1,4]=>[4,1,7,5,2,8,6,3]=>0000000=>0000000
[3,5,8,2,4,7,1,6]=>[6,1,7,4,2,8,5,3]=>0000000=>0000000
[3,5,7,2,4,6,1,8]=>[8,1,6,4,2,7,5,3]=>0000000=>0000000
[4,2,5,8,3,7,1,6]=>[6,1,7,3,8,5,2,4]=>0000000=>0000000
[1,4,3,8,2,6,7,5]=>[5,7,6,2,8,3,4,1]=>0000000=>0000000
[4,6,3,2,1,8,5,7]=>[7,5,8,1,2,3,6,4]=>0000000=>0000000
[5,4,7,3,8,6,1,2]=>[2,1,6,8,3,7,4,5]=>0100000=>0000010
[5,8,4,7,6,3,1,2]=>[2,1,3,6,7,4,8,5]=>0110000=>0000110
[5,3,1,6,4,2,8,7]=>[7,8,2,4,6,1,3,5]=>0000000=>0000000
[1,6,3,4,2,8,7,5]=>[5,7,8,2,4,3,6,1]=>0000000=>0000000
[1,6,8,7,4,2,5,3]=>[3,5,2,4,7,8,6,1]=>0000000=>0000000
[3,1,2,7,6,4,8,5]=>[5,8,4,6,7,2,1,3]=>0000000=>0000000
[6,3,2,1,8,5,4,7]=>[7,4,5,8,1,2,3,6]=>0000000=>0000000
[5,2,6,3,7,4,1,8]=>[8,1,4,7,3,6,2,5]=>0000000=>0000000
[1,6,7,2,8,4,5,3]=>[3,5,4,8,2,7,6,1]=>0000000=>0000000
[5,1,2,7,8,3,6,4]=>[4,6,3,8,7,2,1,5]=>0000000=>0000000
[6,4,2,7,3,5,1,8]=>[8,1,5,3,7,2,4,6]=>0000000=>0000000
[7,8,3,2,5,6,1,4]=>[4,1,6,5,2,3,8,7]=>0000010=>0100000
[7,1,8,2,4,5,6,3]=>[3,6,5,4,2,8,1,7]=>0000000=>0000000
[8,7,6,1,2,4,5,3]=>[3,5,4,2,1,6,7,8]=>0000111=>1110000
[8,3,7,6,2,1,4,5]=>[5,4,1,2,6,7,3,8]=>0000001=>1000000
[8,3,6,5,2,1,4,7]=>[7,4,1,2,5,6,3,8]=>0000001=>1000000
[7,4,6,2,5,3,1,8]=>[8,1,3,5,2,6,4,7]=>0000000=>0000000
[8,5,1,2,7,3,6,4]=>[4,6,3,7,2,1,5,8]=>0000001=>1000000
[6,8,3,7,5,4,1,2]=>[2,1,4,5,7,3,8,6]=>0100000=>0000010
[6,1,8,2,3,7,5,4]=>[4,5,7,3,2,8,1,6]=>0000000=>0000000
[1,7,2,4,3,8,6,5]=>[5,6,8,3,4,2,7,1]=>0000000=>0000000
[1,7,8,6,5,2,4,3]=>[3,4,2,5,6,8,7,1]=>0000000=>0000000
[7,3,8,6,5,4,1,2]=>[2,1,4,5,6,8,3,7]=>0100000=>0000010
[4,3,1,2,8,7,6,5]=>[5,6,7,8,2,1,3,4]=>0000000=>0000000
[5,1,4,3,2,8,7,6]=>[6,7,8,2,3,4,1,5]=>0000000=>0000000
[8,6,3,2,1,7,4,5]=>[5,4,7,1,2,3,6,8]=>0000001=>1000000
[8,7,2,4,5,3,1,6]=>[6,1,3,5,4,2,7,8]=>0000011=>1100000
[4,6,3,2,7,5,1,8]=>[8,1,5,7,2,3,6,4]=>0000000=>0000000
[8,5,7,4,6,1,3,2]=>[2,3,1,6,4,7,5,8]=>0010001=>1000100
[4,3,1,8,7,5,2,6]=>[6,2,5,7,8,1,3,4]=>0000000=>0000000
[3,1,4,6,8,7,2,5]=>[5,2,7,8,6,4,1,3]=>0000000=>0000000
[7,1,6,4,8,5,2,3]=>[3,2,5,8,4,6,1,7]=>0000000=>0000000
[7,3,6,8,5,1,2,4]=>[4,2,1,5,8,6,3,7]=>0000000=>0000000
[1,3,7,2,6,8,4,5]=>[5,4,8,6,2,7,3,1]=>0000000=>0000000
[5,7,1,8,4,2,6,3]=>[3,6,2,4,8,1,7,5]=>0000000=>0000000
[3,6,2,4,7,5,1,8]=>[8,1,5,7,4,2,6,3]=>0000000=>0000000
[4,7,3,1,5,8,6,2]=>[2,6,8,5,1,3,7,4]=>0000000=>0000000
[8,7,6,4,3,1,5,2]=>[2,5,1,3,4,6,7,8]=>0000111=>1110000
[8,7,6,4,1,5,2,3]=>[3,2,5,1,4,6,7,8]=>0000111=>1110000
[2,4,8,1,6,5,3,7]=>[7,3,5,6,1,8,4,2]=>0000000=>0000000
[1,2,7,4,8,6,3,5]=>[5,3,6,8,4,7,2,1]=>0000000=>0000000
[1,2,7,8,3,6,5,4]=>[4,5,6,3,8,7,2,1]=>0000000=>0000000
[1,6,8,5,4,3,2,7]=>[7,2,3,4,5,8,6,1]=>0000000=>0000000
[7,1,2,5,8,3,6,4]=>[4,6,3,8,5,2,1,7]=>0000000=>0000000
[8,6,2,4,7,3,5,1]=>[1,5,3,7,4,2,6,8]=>1000001=>1000001
[8,6,2,4,5,7,3,1]=>[1,3,7,5,4,2,6,8]=>1000001=>1000001
[7,1,4,5,6,8,2,3]=>[3,2,8,6,5,4,1,7]=>0000000=>0000000
[3,6,7,1,4,8,5,2]=>[2,5,8,4,1,7,6,3]=>0000000=>0000000
[3,4,7,2,5,8,1,6]=>[6,1,8,5,2,7,4,3]=>0000000=>0000000
[5,6,7,8,1,3,4,2]=>[2,4,3,1,8,7,6,5]=>0001000=>0001000
[5,7,8,6,1,2,3,4]=>[4,3,2,1,6,8,7,5]=>0001000=>0001000
[2,8,3,1,5,6,4,7]=>[7,4,6,5,1,3,8,2]=>0000000=>0000000
[4,3,1,7,6,8,2,5]=>[5,2,8,6,7,1,3,4]=>0000000=>0000000
[2,4,6,1,7,5,8,3]=>[3,8,5,7,1,6,4,2]=>0000000=>0000000
[3,7,4,1,6,2,8,5]=>[5,8,2,6,1,4,7,3]=>0000000=>0000000
[8,4,7,2,5,3,6,1]=>[1,6,3,5,2,7,4,8]=>1000001=>1000001
[4,7,8,1,2,3,6,5]=>[5,6,3,2,1,8,7,4]=>0000000=>0000000
[5,8,1,6,3,7,2,4]=>[4,2,7,3,6,1,8,5]=>0000000=>0000000
[8,4,5,3,7,2,6,1]=>[1,6,2,7,3,5,4,8]=>1000001=>1000001
[4,6,3,8,5,1,7,2]=>[2,7,1,5,8,3,6,4]=>0000000=>0000000
[3,6,4,8,1,7,2,5]=>[5,2,7,1,8,4,6,3]=>0000000=>0000000
[7,2,3,4,1,6,5,8]=>[8,5,6,1,4,3,2,7]=>0000000=>0000000
[4,2,8,3,6,1,5,7]=>[7,5,1,6,3,8,2,4]=>0000000=>0000000
[6,7,5,8,2,1,4,3]=>[3,4,1,2,8,5,7,6]=>0001000=>0001000
[4,8,5,2,7,1,3,6]=>[6,3,1,7,2,5,8,4]=>0000000=>0000000
[6,3,5,2,1,7,4,8]=>[8,4,7,1,2,5,3,6]=>0000000=>0000000
[3,6,5,4,2,8,1,7]=>[7,1,8,2,4,5,6,3]=>0000000=>0000000
[7,4,5,3,8,2,1,6]=>[6,1,2,8,3,5,4,7]=>0000000=>0000000
[1,4,2,3,5,8,7,6]=>[6,7,8,5,3,2,4,1]=>0000000=>0000000
[1,7,4,3,2,8,6,5]=>[5,6,8,2,3,4,7,1]=>0000000=>0000000
[1,7,6,5,2,8,4,3]=>[3,4,8,2,5,6,7,1]=>0000000=>0000000
[1,6,5,2,3,8,4,7]=>[7,4,8,3,2,5,6,1]=>0000000=>0000000
[1,5,7,6,2,4,8,3]=>[3,8,4,2,6,7,5,1]=>0000000=>0000000
[1,3,7,5,2,6,8,4]=>[4,8,6,2,5,7,3,1]=>0000000=>0000000
[1,2,6,4,3,7,8,5]=>[5,8,7,3,4,6,2,1]=>0000000=>0000000
[1,7,6,4,2,8,5,3]=>[3,5,8,2,4,6,7,1]=>0000000=>0000000
[1,5,3,2,4,8,7,6]=>[6,7,8,4,2,3,5,1]=>0000000=>0000000
[7,6,1,4,3,8,5,2]=>[2,5,8,3,4,1,6,7]=>0000000=>0000000
[7,6,5,1,3,8,4,2]=>[2,4,8,3,1,5,6,7]=>0000000=>0000000
[7,3,5,4,8,1,6,2]=>[2,6,1,8,4,5,3,7]=>0000000=>0000000
[1,4,5,8,3,7,6,2]=>[2,6,7,3,8,5,4,1]=>0000000=>0000000
[5,6,8,4,3,1,7,2]=>[2,7,1,3,4,8,6,5]=>0000000=>0000000
[6,8,5,4,1,2,7,3]=>[3,7,2,1,4,5,8,6]=>0000000=>0000000
[1,8,5,2,3,7,6,4]=>[4,6,7,3,2,5,8,1]=>0000000=>0000000
[6,8,2,4,3,7,1,5]=>[5,1,7,3,4,2,8,6]=>0000000=>0000000
[4,8,5,7,3,2,1,6]=>[6,1,2,3,7,5,8,4]=>0000000=>0000000
[7,8,1,2,4,3,5,6]=>[6,5,3,4,2,1,8,7]=>0000010=>0100000
[3,4,6,5,7,8,1,2]=>[2,1,8,7,5,6,4,3]=>0100000=>0000010
[4,2,6,1,8,3,7,5]=>[5,7,3,8,1,6,2,4]=>0000000=>0000000
[6,7,3,8,4,5,1,2]=>[2,1,5,4,8,3,7,6]=>0100000=>0000010
[4,7,5,6,3,8,1,2]=>[2,1,8,3,6,5,7,4]=>0100000=>0000010
[4,5,3,8,6,7,1,2]=>[2,1,7,6,8,3,5,4]=>0100000=>0000010
[4,8,3,6,5,7,1,2]=>[2,1,7,5,6,3,8,4]=>0100000=>0000010
[5,6,4,7,1,8,2,3]=>[3,2,8,1,7,4,6,5]=>0000000=>0000000
[5,6,1,7,3,8,2,4]=>[4,2,8,3,7,1,6,5]=>0000000=>0000000
[4,8,1,6,5,7,2,3]=>[3,2,7,5,6,1,8,4]=>0000000=>0000000
[7,8,4,5,1,6,2,3]=>[3,2,6,1,5,4,8,7]=>0000010=>0100000
[4,5,2,3,1,8,6,7]=>[7,6,8,1,3,2,5,4]=>0000000=>0000000
[5,6,2,3,1,8,4,7]=>[7,4,8,1,3,2,6,5]=>0000000=>0000000
[5,6,3,4,1,8,2,7]=>[7,2,8,1,4,3,6,5]=>0000000=>0000000
[3,6,4,5,2,7,1,8]=>[8,1,7,2,5,4,6,3]=>0000000=>0000000
[2,6,4,8,1,5,3,7]=>[7,3,5,1,8,4,6,2]=>0000000=>0000000
[1,8,3,6,5,7,2,4]=>[4,2,7,5,6,3,8,1]=>0000000=>0000000
[1,8,3,6,2,7,4,5]=>[5,4,7,2,6,3,8,1]=>0000000=>0000000
[1,6,4,8,2,7,3,5]=>[5,3,7,2,8,4,6,1]=>0000000=>0000000
[1,6,4,7,3,8,2,5]=>[5,2,8,3,7,4,6,1]=>0000000=>0000000
[6,7,1,5,3,8,2,4]=>[4,2,8,3,5,1,7,6]=>0000000=>0000000
[6,7,1,8,4,5,2,3]=>[3,2,5,4,8,1,7,6]=>0000000=>0000000
[3,4,2,7,5,6,1,8]=>[8,1,6,5,7,2,4,3]=>0000000=>0000000
[2,3,1,8,6,7,4,5]=>[5,4,7,6,8,1,3,2]=>0000000=>0000000
[2,8,1,7,3,5,4,6]=>[6,4,5,3,7,1,8,2]=>0000000=>0000000
[4,5,1,7,3,8,2,6]=>[6,2,8,3,7,1,5,4]=>0000000=>0000000
[3,8,1,5,2,7,4,6]=>[6,4,7,2,5,1,8,3]=>0000000=>0000000
[3,4,2,5,1,8,6,7]=>[7,6,8,1,5,2,4,3]=>0000000=>0000000
[4,5,3,6,1,8,2,7]=>[7,2,8,1,6,3,5,4]=>0000000=>0000000
[3,6,5,4,1,2,8,7]=>[7,8,2,1,4,5,6,3]=>0000000=>0000000
[3,8,5,6,7,4,1,2]=>[2,1,4,7,6,5,8,3]=>0100000=>0000010
[2,5,7,8,6,3,4,1]=>[1,4,3,6,8,7,5,2]=>1000000=>0000001
[3,6,5,1,2,4,8,7]=>[7,8,4,2,1,5,6,3]=>0000000=>0000000
[5,2,3,6,4,1,8,7]=>[7,8,1,4,6,3,2,5]=>0000000=>0000000
[5,6,7,8,1,4,3,2]=>[2,3,4,1,8,7,6,5]=>0001000=>0001000
[4,2,6,8,5,7,3,1]=>[1,3,7,5,8,6,2,4]=>1000000=>0000001
[2,1,5,8,7,6,3,4]=>[4,3,6,7,8,5,1,2]=>0000000=>0000000
[6,4,7,8,5,3,2,1]=>[1,2,3,5,8,7,4,6]=>1110000=>0000111
[6,3,7,1,5,2,8,4]=>[4,8,2,5,1,7,3,6]=>0000000=>0000000
[3,2,6,8,4,7,5,1]=>[1,5,7,4,8,6,2,3]=>1000000=>0000001
[2,4,1,5,8,3,7,6]=>[6,7,3,8,5,1,4,2]=>0000000=>0000000
[4,7,5,8,1,6,3,2]=>[2,3,6,1,8,5,7,4]=>0000000=>0000000
[2,1,5,8,7,3,4,6]=>[6,4,3,7,8,5,1,2]=>0000000=>0000000
[8,5,7,3,6,1,4,2]=>[2,4,1,6,3,7,5,8]=>0000001=>1000000
[6,4,3,2,7,8,1,5]=>[5,1,8,7,2,3,4,6]=>0000000=>0000000
[7,2,3,4,8,5,6,1]=>[1,6,5,8,4,3,2,7]=>1000000=>0000001
[6,1,8,5,2,7,4,3]=>[3,4,7,2,5,8,1,6]=>0000000=>0000000
[2,1,7,4,5,8,6,3]=>[3,6,8,5,4,7,1,2]=>0000000=>0000000
[6,8,7,2,5,3,1,4]=>[4,1,3,5,2,7,8,6]=>0000100=>0010000
[8,2,1,6,4,7,5,3]=>[3,5,7,4,6,1,2,8]=>0000001=>1000000
[6,1,2,3,7,5,8,4]=>[4,8,5,7,3,2,1,6]=>0000000=>0000000
[7,6,8,4,2,5,3,1]=>[1,3,5,2,4,8,6,7]=>1000100=>0010001
[4,1,2,3,7,6,8,5]=>[5,8,6,7,3,2,1,4]=>0000000=>0000000
[3,2,4,1,8,5,6,7]=>[7,6,5,8,1,4,2,3]=>0000000=>0000000
[6,5,8,2,1,7,3,4]=>[4,3,7,1,2,8,5,6]=>0000000=>0000000
[7,4,3,5,1,6,8,2]=>[2,8,6,1,5,3,4,7]=>0000000=>0000000
[4,1,6,3,5,8,7,2]=>[2,7,8,5,3,6,1,4]=>0000000=>0000000
[2,1,6,5,8,4,7,3]=>[3,7,4,8,5,6,1,2]=>0000000=>0000000
[2,6,4,8,7,3,5,1]=>[1,5,3,7,8,4,6,2]=>1000000=>0000001
[3,1,8,2,7,5,4,6]=>[6,4,5,7,2,8,1,3]=>0000000=>0000000
[8,2,3,1,7,4,6,5]=>[5,6,4,7,1,3,2,8]=>0000001=>1000000
[7,4,8,6,3,2,5,1]=>[1,5,2,3,6,8,4,7]=>1000000=>0000001
[6,3,8,2,4,5,7,1]=>[1,7,5,4,2,8,3,6]=>1000000=>0000001
[5,8,4,2,3,6,1,7]=>[7,1,6,3,2,4,8,5]=>0000000=>0000000
[7,3,5,8,1,4,2,6]=>[6,2,4,1,8,5,3,7]=>0000000=>0000000
[6,8,1,3,5,7,2,4]=>[4,2,7,5,3,1,8,6]=>0000000=>0000000
[4,1,3,7,5,8,2,6]=>[6,2,8,5,7,3,1,4]=>0000000=>0000000
[5,7,8,6,2,1,4,3]=>[3,4,1,2,6,8,7,5]=>0001000=>0001000
[1,4,7,2,6,8,3,5]=>[5,3,8,6,2,7,4,1]=>0000000=>0000000
[4,3,7,8,5,1,6,2]=>[2,6,1,5,8,7,3,4]=>0000000=>0000000
[5,4,8,2,7,6,1,3]=>[3,1,6,7,2,8,4,5]=>0000000=>0000000
[4,1,7,5,8,6,2,3]=>[3,2,6,8,5,7,1,4]=>0000000=>0000000
[7,6,1,2,8,3,5,4]=>[4,5,3,8,2,1,6,7]=>0000000=>0000000
[6,7,8,1,5,2,4,3]=>[3,4,2,5,1,8,7,6]=>0000100=>0010000
[5,7,8,4,1,2,6,3]=>[3,6,2,1,4,8,7,5]=>0000000=>0000000
[4,7,8,5,6,1,3,2]=>[2,3,1,6,5,8,7,4]=>0010000=>0000100
[5,6,4,8,1,2,7,3]=>[3,7,2,1,8,4,6,5]=>0000000=>0000000
[6,5,4,1,2,3,8,7]=>[7,8,3,2,1,4,5,6]=>0000000=>0000000
[7,5,1,6,2,3,8,4]=>[4,8,3,2,6,1,5,7]=>0000000=>0000000
[6,4,5,1,8,2,7,3]=>[3,7,2,8,1,5,4,6]=>0000000=>0000000
[4,5,6,7,8,1,3,2]=>[2,3,1,8,7,6,5,4]=>0010000=>0000100
[4,2,6,7,3,1,8,5]=>[5,8,1,3,7,6,2,4]=>0000000=>0000000
[7,3,1,5,4,8,2,6]=>[6,2,8,4,5,1,3,7]=>0000000=>0000000
[4,5,3,2,8,1,6,7]=>[7,6,1,8,2,3,5,4]=>0000000=>0000000
[7,4,1,5,3,2,6,8]=>[8,6,2,3,5,1,4,7]=>0000000=>0000000
[8,1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1,8]=>0000001=>1000000
[6,5,3,1,2,7,4,8]=>[8,4,7,2,1,3,5,6]=>0000000=>0000000
[5,6,3,8,1,4,2,7]=>[7,2,4,1,8,3,6,5]=>0000000=>0000000
[4,6,3,8,2,1,5,7]=>[7,5,1,2,8,3,6,4]=>0000000=>0000000
[4,7,8,3,2,1,5,6]=>[6,5,1,2,3,8,7,4]=>0000000=>0000000
[5,7,8,3,1,4,2,6]=>[6,2,4,1,3,8,7,5]=>0000000=>0000000
[8,1,7,2,5,4,3,6]=>[6,3,4,5,2,7,1,8]=>0000001=>1000000
[4,7,8,2,3,1,6,5]=>[5,6,1,3,2,8,7,4]=>0000000=>0000000
[8,1,6,3,2,5,7,4]=>[4,7,5,2,3,6,1,8]=>0000001=>1000000
[8,1,5,3,4,2,7,6]=>[6,7,2,4,3,5,1,8]=>0000001=>1000000
[6,3,2,1,5,7,4,8]=>[8,4,7,5,1,2,3,6]=>0000000=>0000000
[7,3,1,4,5,6,2,8]=>[8,2,6,5,4,1,3,7]=>0000000=>0000000
[6,2,3,1,5,7,8,4]=>[4,8,7,5,1,3,2,6]=>0000000=>0000000
[5,3,8,7,2,4,6,1]=>[1,6,4,2,7,8,3,5]=>1000000=>0000001
[3,6,1,5,8,4,2,7]=>[7,2,4,8,5,1,6,3]=>0000000=>0000000
[6,5,4,3,8,2,1,7]=>[7,1,2,8,3,4,5,6]=>0000000=>0000000
[5,4,3,7,2,8,1,6]=>[6,1,8,2,7,3,4,5]=>0000000=>0000000
[5,8,4,3,7,2,6,1]=>[1,6,2,7,3,4,8,5]=>1000000=>0000001
[4,6,8,3,7,2,5,1]=>[1,5,2,7,3,8,6,4]=>1000000=>0000001
[8,4,6,1,7,3,5,2]=>[2,5,3,7,1,6,4,8]=>0000001=>1000000
[8,6,2,7,4,1,5,3]=>[3,5,1,4,7,2,6,8]=>0000001=>1000000
[7,6,2,1,4,3,8,5]=>[5,8,3,4,1,2,6,7]=>0000000=>0000000
[7,6,1,3,4,2,8,5]=>[5,8,2,4,3,1,6,7]=>0000000=>0000000
[3,1,7,5,2,8,4,6]=>[6,4,8,2,5,7,1,3]=>0000000=>0000000
[1,7,4,5,2,8,3,6]=>[6,3,8,2,5,4,7,1]=>0000000=>0000000
[4,2,7,6,3,8,1,5]=>[5,1,8,3,6,7,2,4]=>0000000=>0000000
[3,2,6,8,7,4,5,1]=>[1,5,4,7,8,6,2,3]=>1000000=>0000001
[5,7,3,8,2,1,4,6]=>[6,4,1,2,8,3,7,5]=>0000000=>0000000
[8,4,2,1,3,7,6,5]=>[5,6,7,3,1,2,4,8]=>0000001=>1000000
[8,4,3,7,6,2,1,5]=>[5,1,2,6,7,3,4,8]=>0000001=>1000000
[5,8,4,2,7,1,6,3]=>[3,6,1,7,2,4,8,5]=>0000000=>0000000
[8,5,3,1,7,2,6,4]=>[4,6,2,7,1,3,5,8]=>0000001=>1000000
[1,4,6,8,2,7,5,3]=>[3,5,7,2,8,6,4,1]=>0000000=>0000000
[8,2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2,8]=>0000001=>1000000
[8,1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1,8]=>0000001=>1000000
[5,8,3,6,2,1,4,7]=>[7,4,1,2,6,3,8,5]=>0000000=>0000000
[6,4,3,7,2,1,8,5]=>[5,8,1,2,7,3,4,6]=>0000000=>0000000
[4,8,3,6,2,1,7,5]=>[5,7,1,2,6,3,8,4]=>0000000=>0000000
[5,3,7,6,2,1,4,8]=>[8,4,1,2,6,7,3,5]=>0000000=>0000000
[3,8,7,6,2,1,4,5]=>[5,4,1,2,6,7,8,3]=>0000000=>0000000
[5,8,4,2,6,1,3,7]=>[7,3,1,6,2,4,8,5]=>0000000=>0000000
[4,8,7,2,5,1,3,6]=>[6,3,1,5,2,7,8,4]=>0000000=>0000000
[5,8,3,2,6,1,4,7]=>[7,4,1,6,2,3,8,5]=>0000000=>0000000
[4,8,3,2,5,1,7,6]=>[6,7,1,5,2,3,8,4]=>0000000=>0000000
[4,3,7,2,5,1,8,6]=>[6,8,1,5,2,7,3,4]=>0000000=>0000000
[3,8,7,2,5,1,4,6]=>[6,4,1,5,2,7,8,3]=>0000000=>0000000
[6,4,2,7,5,1,3,8]=>[8,3,1,5,7,2,4,6]=>0000000=>0000000
[4,8,7,3,1,5,6,2]=>[2,6,5,1,3,7,8,4]=>0000000=>0000000
[5,8,3,6,1,4,7,2]=>[2,7,4,1,6,3,8,5]=>0000000=>0000000
[6,4,3,7,1,5,8,2]=>[2,8,5,1,7,3,4,6]=>0000000=>0000000
[4,8,3,6,1,5,7,2]=>[2,7,5,1,6,3,8,4]=>0000000=>0000000
[5,8,4,2,1,7,3,6]=>[6,3,7,1,2,4,8,5]=>0000000=>0000000
[5,8,3,2,1,4,7,6]=>[6,7,4,1,2,3,8,5]=>0000000=>0000000
[6,3,7,2,1,4,5,8]=>[8,5,4,1,2,7,3,6]=>0000000=>0000000
[5,3,7,2,1,4,8,6]=>[6,8,4,1,2,7,3,5]=>0000000=>0000000
[6,5,2,7,1,4,3,8]=>[8,3,4,1,7,2,5,6]=>0000000=>0000000
[4,3,2,6,1,5,8,7]=>[7,8,5,1,6,2,3,4]=>0000000=>0000000
[2,8,7,6,1,4,3,5]=>[5,3,4,1,6,7,8,2]=>0000000=>0000000
[5,8,4,1,6,7,3,2]=>[2,3,7,6,1,4,8,5]=>0000000=>0000000
[4,8,7,1,5,6,3,2]=>[2,3,6,5,1,7,8,4]=>0000000=>0000000
[6,5,3,1,8,4,7,2]=>[2,7,4,8,1,3,5,6]=>0000000=>0000000
[5,8,3,1,6,4,7,2]=>[2,7,4,6,1,3,8,5]=>0000000=>0000000
[4,8,3,1,5,6,7,2]=>[2,7,6,5,1,3,8,4]=>0000000=>0000000
[6,4,2,1,5,8,3,7]=>[7,3,8,5,1,2,4,6]=>0000000=>0000000
[5,3,2,1,6,4,8,7]=>[7,8,4,6,1,2,3,5]=>0000000=>0000000
[3,2,7,1,5,4,6,8]=>[8,6,4,5,1,7,2,3]=>0000000=>0000000
[6,4,1,7,5,8,3,2]=>[2,3,8,5,7,1,4,6]=>0000000=>0000000
[4,8,1,6,5,7,3,2]=>[2,3,7,5,6,1,8,4]=>0000000=>0000000
[5,3,1,6,7,4,8,2]=>[2,8,4,7,6,1,3,5]=>0000000=>0000000
[4,3,1,6,5,7,8,2]=>[2,8,7,5,6,1,3,4]=>0000000=>0000000
[4,2,1,6,5,7,3,8]=>[8,3,7,5,6,1,2,4]=>0000000=>0000000
[3,1,7,6,5,4,8,2]=>[2,8,4,5,6,7,1,3]=>0000000=>0000000
[4,5,8,1,7,2,3,6]=>[6,3,2,7,1,8,5,4]=>0000000=>0000000
[8,1,3,5,7,2,4,6]=>[6,4,2,7,5,3,1,8]=>0000001=>1000000
[8,1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1,8]=>0000001=>1000000
[2,7,8,1,3,5,4,6]=>[6,4,5,3,1,8,7,2]=>0000000=>0000000
[2,7,8,3,5,6,1,4]=>[4,1,6,5,3,8,7,2]=>0000000=>0000000
[2,4,5,7,8,1,6,3]=>[3,6,1,8,7,5,4,2]=>0000000=>0000000
[8,7,2,1,6,3,4,5]=>[5,4,3,6,1,2,7,8]=>0000011=>1100000
[7,4,2,6,8,5,1,3]=>[3,1,5,8,6,2,4,7]=>0000000=>0000000
[7,3,2,5,8,6,1,4]=>[4,1,6,8,5,2,3,7]=>0000000=>0000000
[7,3,1,8,6,2,4,5]=>[5,4,2,6,8,1,3,7]=>0000000=>0000000
[3,1,7,2,5,4,8,6]=>[6,8,4,5,2,7,1,3]=>0000000=>0000000
[3,6,8,1,2,5,4,7]=>[7,4,5,2,1,8,6,3]=>0000000=>0000000
[7,4,1,8,5,2,3,6]=>[6,3,2,5,8,1,4,7]=>0000000=>0000000
[7,1,4,2,8,3,6,5]=>[5,6,3,8,2,4,1,7]=>0000000=>0000000
[7,1,8,2,5,3,6,4]=>[4,6,3,5,2,8,1,7]=>0000000=>0000000
[7,3,8,4,5,1,6,2]=>[2,6,1,5,4,8,3,7]=>0000000=>0000000
[8,3,7,4,6,1,5,2]=>[2,5,1,6,4,7,3,8]=>0000001=>1000000
[8,2,7,1,6,4,5,3]=>[3,5,4,6,1,7,2,8]=>0000001=>1000000
[8,1,7,5,4,2,3,6]=>[6,3,2,4,5,7,1,8]=>0000001=>1000000
[8,1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1,8]=>0000001=>1000000
[8,2,7,5,6,1,4,3]=>[3,4,1,6,5,7,2,8]=>0000001=>1000000
[8,6,7,2,3,1,5,4]=>[4,5,1,3,2,7,6,8]=>0000101=>1010000
[2,7,8,6,3,1,5,4]=>[4,5,1,3,6,8,7,2]=>0000000=>0000000
[8,7,6,3,2,1,5,4]=>[4,5,1,2,3,6,7,8]=>0000111=>1110000
[2,1,8,6,3,7,4,5]=>[5,4,7,3,6,8,1,2]=>0000000=>0000000
[8,5,1,7,4,2,6,3]=>[3,6,2,4,7,1,5,8]=>0000001=>1000000
[2,1,8,4,5,3,6,7]=>[7,6,3,5,4,8,1,2]=>0000000=>0000000
[2,1,7,8,3,6,5,4]=>[4,5,6,3,8,7,1,2]=>0000000=>0000000
[5,2,4,8,6,3,1,7]=>[7,1,3,6,8,4,2,5]=>0000000=>0000000
[4,2,6,3,8,5,1,7]=>[7,1,5,8,3,6,2,4]=>0000000=>0000000
[8,5,2,7,4,6,1,3]=>[3,1,6,4,7,2,5,8]=>0000001=>1000000
[6,3,4,2,1,7,8,5]=>[5,8,7,1,2,4,3,6]=>0000000=>0000000
[7,2,4,3,1,5,8,6]=>[6,8,5,1,3,4,2,7]=>0000000=>0000000
[7,8,3,1,5,4,6,2]=>[2,6,4,5,1,3,8,7]=>0000010=>0100000
[7,2,8,1,4,6,5,3]=>[3,5,6,4,1,8,2,7]=>0000000=>0000000
[6,2,3,1,4,5,8,7]=>[7,8,5,4,1,3,2,6]=>0000000=>0000000
[5,7,1,8,3,6,2,4]=>[4,2,6,3,8,1,7,5]=>0000000=>0000000
[6,8,1,4,5,3,2,7]=>[7,2,3,5,4,1,8,6]=>0000000=>0000000
[8,7,5,1,3,4,2,6]=>[6,2,4,3,1,5,7,8]=>0000011=>1100000
[6,5,7,1,3,8,2,4]=>[4,2,8,3,1,7,5,6]=>0000000=>0000000
[8,2,6,1,4,7,3,5]=>[5,3,7,4,1,6,2,8]=>0000001=>1000000
[5,8,1,6,3,7,4,2]=>[2,4,7,3,6,1,8,5]=>0000000=>0000000
[4,2,1,3,6,7,8,5]=>[5,8,7,6,3,1,2,4]=>0000000=>0000000
[2,3,4,1,8,6,5,7]=>[7,5,6,8,1,4,3,2]=>0000000=>0000000
[8,3,5,6,1,7,4,2]=>[2,4,7,1,6,5,3,8]=>0000001=>1000000
[7,3,5,8,1,6,2,4]=>[4,2,6,1,8,5,3,7]=>0000000=>0000000
[6,3,5,4,1,2,8,7]=>[7,8,2,1,4,5,3,6]=>0000000=>0000000
[2,6,3,5,1,4,8,7]=>[7,8,4,1,5,3,6,2]=>0000000=>0000000
[8,7,3,6,5,1,4,2]=>[2,4,1,5,6,3,7,8]=>0000011=>1100000
[2,8,3,4,6,1,5,7]=>[7,5,1,6,4,3,8,2]=>0000000=>0000000
[2,7,4,3,6,1,8,5]=>[5,8,1,6,3,4,7,2]=>0000000=>0000000
[4,3,2,5,7,1,8,6]=>[6,8,1,7,5,2,3,4]=>0000000=>0000000
[3,2,8,4,7,1,6,5]=>[5,6,1,7,4,8,2,3]=>0000000=>0000000
[3,2,4,6,1,5,8,7]=>[7,8,5,1,6,4,2,3]=>0000000=>0000000
[6,8,5,4,3,7,2,1]=>[1,2,7,3,4,5,8,6]=>1100000=>0000011
[6,5,4,3,1,8,7,2]=>[2,7,8,1,3,4,5,6]=>0000000=>0000000
[3,4,6,7,1,8,5,2]=>[2,5,8,1,7,6,4,3]=>0000000=>0000000
[3,4,7,2,1,8,6,5]=>[5,6,8,1,2,7,4,3]=>0000000=>0000000
[3,4,7,2,8,5,6,1]=>[1,6,5,8,2,7,4,3]=>1000000=>0000001
[3,4,8,2,1,5,6,7]=>[7,6,5,1,2,8,4,3]=>0000000=>0000000
[3,5,2,6,8,4,1,7]=>[7,1,4,8,6,2,5,3]=>0000000=>0000000
[3,5,2,7,4,8,6,1]=>[1,6,8,4,7,2,5,3]=>1000000=>0000001
[3,5,2,7,8,4,6,1]=>[1,6,4,8,7,2,5,3]=>1000000=>0000001
[3,5,2,8,4,1,6,7]=>[7,6,1,4,8,2,5,3]=>0000000=>0000000
[3,5,6,2,7,8,1,4]=>[4,1,8,7,2,6,5,3]=>0000000=>0000000
[3,5,6,2,8,4,1,7]=>[7,1,4,8,2,6,5,3]=>0000000=>0000000
[3,5,7,8,4,1,6,2]=>[2,6,1,4,8,7,5,3]=>0000000=>0000000
[3,6,2,1,8,5,4,7]=>[7,4,5,8,1,2,6,3]=>0000000=>0000000
[3,6,2,7,4,8,5,1]=>[1,5,8,4,7,2,6,3]=>1000000=>0000001
[3,6,2,7,8,5,4,1]=>[1,4,5,8,7,2,6,3]=>1000000=>0000001
[3,6,7,2,4,8,5,1]=>[1,5,8,4,2,7,6,3]=>1000000=>0000001
[4,1,5,6,7,8,3,2]=>[2,3,8,7,6,5,1,4]=>0000000=>0000000
[4,1,5,7,3,8,6,2]=>[2,6,8,3,7,5,1,4]=>0000000=>0000000
[4,1,5,7,8,2,6,3]=>[3,6,2,8,7,5,1,4]=>0000000=>0000000
[4,1,5,8,3,2,6,7]=>[7,6,2,3,8,5,1,4]=>0000000=>0000000
[4,1,6,8,3,5,2,7]=>[7,2,5,3,8,6,1,4]=>0000000=>0000000
[4,1,7,3,8,5,6,2]=>[2,6,5,8,3,7,1,4]=>0000000=>0000000
[4,1,7,8,3,5,6,2]=>[2,6,5,3,8,7,1,4]=>0000000=>0000000
[4,5,2,7,3,8,6,1]=>[1,6,8,3,7,2,5,4]=>1000000=>0000001
[4,5,6,8,3,1,2,7]=>[7,2,1,3,8,6,5,4]=>0000000=>0000000
[4,5,7,3,2,8,6,1]=>[1,6,8,2,3,7,5,4]=>1000000=>0000001
[4,6,2,3,7,8,5,1]=>[1,5,8,7,3,2,6,4]=>1000000=>0000001
[4,6,2,3,8,5,1,7]=>[7,1,5,8,3,2,6,4]=>0000000=>0000000
[4,6,2,7,3,8,5,1]=>[1,5,8,3,7,2,6,4]=>1000000=>0000001
[4,6,8,3,2,5,1,7]=>[7,1,5,2,3,8,6,4]=>0000000=>0000000
[4,7,8,3,2,5,6,1]=>[1,6,5,2,3,8,7,4]=>1000000=>0000001
[4,8,2,3,1,5,6,7]=>[7,6,5,1,3,2,8,4]=>0000000=>0000000
[5,1,2,6,8,4,3,7]=>[7,3,4,8,6,2,1,5]=>0000000=>0000000
[5,1,6,7,4,8,2,3]=>[3,2,8,4,7,6,1,5]=>0000000=>0000000
[5,1,6,7,8,4,2,3]=>[3,2,4,8,7,6,1,5]=>0000000=>0000000
[5,6,2,7,4,8,1,3]=>[3,1,8,4,7,2,6,5]=>0000000=>0000000
[5,6,2,7,8,4,1,3]=>[3,1,4,8,7,2,6,5]=>0000000=>0000000
[5,6,8,3,4,2,1,7]=>[7,1,2,4,3,8,6,5]=>0000000=>0000000
[5,7,8,3,4,2,6,1]=>[1,6,2,4,3,8,7,5]=>1000000=>0000001
[6,1,2,3,7,8,5,4]=>[4,5,8,7,3,2,1,6]=>0000000=>0000000
[6,1,7,3,8,5,4,2]=>[2,4,5,8,3,7,1,6]=>0000000=>0000000
[7,1,2,3,4,8,6,5]=>[5,6,8,4,3,2,1,7]=>0000000=>0000000
[7,1,2,3,8,5,6,4]=>[4,6,5,8,3,2,1,7]=>0000000=>0000000
[7,1,8,3,4,5,6,2]=>[2,6,5,4,3,8,1,7]=>0000000=>0000000
[2,4,6,1,8,5,7,3]=>[3,7,5,8,1,6,4,2]=>0000000=>0000000
[6,4,1,8,2,3,7,5]=>[5,7,3,2,8,1,4,6]=>0000000=>0000000
[5,8,1,6,2,4,3,7]=>[7,3,4,2,6,1,8,5]=>0000000=>0000000
[1,3,5,7,2,6,4,8]=>[8,4,6,2,7,5,3,1]=>0000000=>0000000
[3,5,1,8,2,4,7,6]=>[6,7,4,2,8,1,5,3]=>0000000=>0000000
[2,3,5,6,8,1,7,4]=>[4,7,1,8,6,5,3,2]=>0000000=>0000000
[5,6,4,8,2,1,7,3]=>[3,7,1,2,8,4,6,5]=>0000000=>0000000
[7,1,8,6,3,4,5,2]=>[2,5,4,3,6,8,1,7]=>0000000=>0000000
[6,7,4,5,2,1,8,3]=>[3,8,1,2,5,4,7,6]=>0000000=>0000000
[5,1,7,8,6,4,3,2]=>[2,3,4,6,8,7,1,5]=>0000000=>0000000
[2,5,7,8,6,3,1,4]=>[4,1,3,6,8,7,5,2]=>0000000=>0000000
[6,5,1,2,4,8,3,7]=>[7,3,8,4,2,1,5,6]=>0000000=>0000000
[7,8,1,6,4,2,3,5]=>[5,3,2,4,6,1,8,7]=>0000010=>0100000
[2,4,8,1,5,6,7,3]=>[3,7,6,5,1,8,4,2]=>0000000=>0000000
[8,3,1,6,5,2,4,7]=>[7,4,2,5,6,1,3,8]=>0000001=>1000000
[5,8,7,4,2,6,1,3]=>[3,1,6,2,4,7,8,5]=>0000000=>0000000
[5,1,8,4,7,6,3,2]=>[2,3,6,7,4,8,1,5]=>0000000=>0000000
[4,8,6,5,7,3,2,1]=>[1,2,3,7,5,6,8,4]=>1110000=>0000111
[4,8,5,6,7,3,2,1]=>[1,2,3,7,6,5,8,4]=>1110000=>0000111
[2,8,7,6,3,4,5,1]=>[1,5,4,3,6,7,8,2]=>1000000=>0000001
[8,4,7,2,5,6,3,1]=>[1,3,6,5,2,7,4,8]=>1000001=>1000001
[3,6,1,8,5,2,7,4]=>[4,7,2,5,8,1,6,3]=>0000000=>0000000
[3,4,1,2,8,6,7,5]=>[5,7,6,8,2,1,4,3]=>0000000=>0000000
[7,2,5,8,3,6,1,4]=>[4,1,6,3,8,5,2,7]=>0000000=>0000000
[7,6,3,8,5,2,1,4]=>[4,1,2,5,8,3,6,7]=>0000000=>0000000
[5,8,7,4,1,6,3,2]=>[2,3,6,1,4,7,8,5]=>0000000=>0000000
[4,2,3,1,7,8,5,6]=>[6,5,8,7,1,3,2,4]=>0000000=>0000000
[8,6,3,4,7,2,5,1]=>[1,5,2,7,4,3,6,8]=>1000001=>1000001
[5,2,8,4,1,6,7,3]=>[3,7,6,1,4,8,2,5]=>0000000=>0000000
[5,3,6,2,4,8,1,7]=>[7,1,8,4,2,6,3,5]=>0000000=>0000000
[5,3,2,1,6,8,4,7]=>[7,4,8,6,1,2,3,5]=>0000000=>0000000
[3,4,6,5,7,1,8,2]=>[2,8,1,7,5,6,4,3]=>0000000=>0000000
[7,5,4,2,6,8,3,1]=>[1,3,8,6,2,4,5,7]=>1000000=>0000001
[7,3,8,4,5,2,1,6]=>[6,1,2,5,4,8,3,7]=>0000000=>0000000
[8,7,2,1,5,3,4,6]=>[6,4,3,5,1,2,7,8]=>0000011=>1100000
[6,4,7,2,3,5,8,1]=>[1,8,5,3,2,7,4,6]=>1000000=>0000001
[3,4,7,8,6,2,5,1]=>[1,5,2,6,8,7,4,3]=>1000000=>0000001
[4,1,3,5,7,8,6,2]=>[2,6,8,7,5,3,1,4]=>0000000=>0000000
[5,3,1,8,4,7,6,2]=>[2,6,7,4,8,1,3,5]=>0000000=>0000000
[7,5,8,2,4,6,1,3]=>[3,1,6,4,2,8,5,7]=>0000000=>0000000
[8,2,7,4,6,1,3,5]=>[5,3,1,6,4,7,2,8]=>0000001=>1000000
[7,4,3,6,8,2,5,1]=>[1,5,2,8,6,3,4,7]=>1000000=>0000001
[8,3,2,5,7,6,1,4]=>[4,1,6,7,5,2,3,8]=>0000001=>1000000
[5,6,7,3,8,4,2,1]=>[1,2,4,8,3,7,6,5]=>1100000=>0000011
[4,3,5,6,7,1,8,2]=>[2,8,1,7,6,5,3,4]=>0000000=>0000000
[6,5,8,7,2,1,3,4]=>[4,3,1,2,7,8,5,6]=>0001000=>0001000
[2,5,4,1,8,7,6,3]=>[3,6,7,8,1,4,5,2]=>0000000=>0000000
[4,7,2,6,5,8,1,3]=>[3,1,8,5,6,2,7,4]=>0000000=>0000000
[3,4,7,8,2,5,6,1]=>[1,6,5,2,8,7,4,3]=>1000000=>0000001
[3,1,4,6,5,7,8,2]=>[2,8,7,5,6,4,1,3]=>0000000=>0000000
[1,2,3,8,5,4,6,7]=>[7,6,4,5,8,3,2,1]=>0000000=>0000000
[1,2,3,8,5,6,4,7]=>[7,4,6,5,8,3,2,1]=>0000000=>0000000
[1,2,3,8,6,5,4,7]=>[7,4,5,6,8,3,2,1]=>0000000=>0000000
[1,2,8,5,4,3,6,7]=>[7,6,3,4,5,8,2,1]=>0000000=>0000000
[1,8,4,3,2,5,6,7]=>[7,6,5,2,3,4,8,1]=>0000000=>0000000
[8,5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5,8]=>1111001=>1001111
[8,4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4,8]=>1110001=>1000111
[8,4,7,5,6,3,2,1]=>[1,2,3,6,5,7,4,8]=>1110001=>1000111
[8,5,7,4,6,3,2,1]=>[1,2,3,6,4,7,5,8]=>1110001=>1000111
[8,4,7,3,6,5,2,1]=>[1,2,5,6,3,7,4,8]=>1100001=>1000011
[8,2,7,1,6,5,4,3]=>[3,4,5,6,1,7,2,8]=>0000001=>1000000
[8,1,7,2,6,5,4,3]=>[3,4,5,6,2,7,1,8]=>0000001=>1000000
[8,1,7,2,6,4,5,3]=>[3,5,4,6,2,7,1,8]=>0000001=>1000000
[8,3,7,1,6,4,5,2]=>[2,5,4,6,1,7,3,8]=>0000001=>1000000
[8,4,7,1,6,3,5,2]=>[2,5,3,6,1,7,4,8]=>0000001=>1000000
[8,5,7,1,6,3,4,2]=>[2,4,3,6,1,7,5,8]=>0000001=>1000000
[8,6,7,1,5,3,4,2]=>[2,4,3,5,1,7,6,8]=>0000101=>1010000
[8,6,7,2,5,3,4,1]=>[1,4,3,5,2,7,6,8]=>1000101=>1010001
[8,5,7,2,6,3,4,1]=>[1,4,3,6,2,7,5,8]=>1000001=>1000001
[8,4,7,2,6,3,5,1]=>[1,5,3,6,2,7,4,8]=>1000001=>1000001
[8,3,7,2,6,4,5,1]=>[1,5,4,6,2,7,3,8]=>1000001=>1000001
[8,2,7,3,6,4,5,1]=>[1,5,4,6,3,7,2,8]=>1000001=>1000001
[8,1,7,3,6,4,5,2]=>[2,5,4,6,3,7,1,8]=>0000001=>1000000
[8,1,7,4,6,3,5,2]=>[2,5,3,6,4,7,1,8]=>0000001=>1000000
[8,2,7,4,6,3,5,1]=>[1,5,3,6,4,7,2,8]=>1000001=>1000001
[8,3,7,4,6,2,5,1]=>[1,5,2,6,4,7,3,8]=>1000001=>1000001
[8,5,7,3,6,2,4,1]=>[1,4,2,6,3,7,5,8]=>1000001=>1000001
[8,6,7,3,5,2,4,1]=>[1,4,2,5,3,7,6,8]=>1000101=>1010001
[8,5,7,4,6,2,3,1]=>[1,3,2,6,4,7,5,8]=>1010001=>1000101
[8,4,7,5,6,2,3,1]=>[1,3,2,6,5,7,4,8]=>1010001=>1000101
[8,3,7,5,6,2,4,1]=>[1,4,2,6,5,7,3,8]=>1000001=>1000001
[8,2,7,5,6,3,4,1]=>[1,4,3,6,5,7,2,8]=>1000001=>1000001
[8,1,7,5,6,3,4,2]=>[2,4,3,6,5,7,1,8]=>0000001=>1000000
[8,3,7,6,5,2,4,1]=>[1,4,2,5,6,7,3,8]=>1000001=>1000001
[8,7,6,5,4,1,3,2]=>[2,3,1,4,5,6,7,8]=>0011111=>1111100
[8,1,7,5,6,2,4,3]=>[3,4,2,6,5,7,1,8]=>0000001=>1000000
[8,3,7,5,6,1,4,2]=>[2,4,1,6,5,7,3,8]=>0000001=>1000000
[8,4,7,5,6,1,3,2]=>[2,3,1,6,5,7,4,8]=>0010001=>1000100
[8,6,7,4,5,1,3,2]=>[2,3,1,5,4,7,6,8]=>0010101=>1010100
[8,6,7,3,5,1,4,2]=>[2,4,1,5,3,7,6,8]=>0000101=>1010000
[8,4,7,3,6,1,5,2]=>[2,5,1,6,3,7,4,8]=>0000001=>1000000
[8,2,7,4,6,1,5,3]=>[3,5,1,6,4,7,2,8]=>0000001=>1000000
[8,1,7,4,6,2,5,3]=>[3,5,2,6,4,7,1,8]=>0000001=>1000000
[8,1,7,3,6,2,5,4]=>[4,5,2,6,3,7,1,8]=>0000001=>1000000
[8,2,7,3,6,1,5,4]=>[4,5,1,6,3,7,2,8]=>0000001=>1000000
[8,3,7,2,6,1,5,4]=>[4,5,1,6,2,7,3,8]=>0000001=>1000000
[8,4,7,2,6,1,5,3]=>[3,5,1,6,2,7,4,8]=>0000001=>1000000
[8,5,7,2,6,1,4,3]=>[3,4,1,6,2,7,5,8]=>0000001=>1000000
[8,6,7,2,5,1,4,3]=>[3,4,1,5,2,7,6,8]=>0000101=>1010000
[8,7,6,1,5,2,4,3]=>[3,4,2,5,1,6,7,8]=>0000111=>1110000
[8,6,7,1,5,2,4,3]=>[3,4,2,5,1,7,6,8]=>0000101=>1010000
[8,5,7,1,6,2,4,3]=>[3,4,2,6,1,7,5,8]=>0000001=>1000000
[8,4,7,1,6,2,5,3]=>[3,5,2,6,1,7,4,8]=>0000001=>1000000
[8,3,7,1,6,2,5,4]=>[4,5,2,6,1,7,3,8]=>0000001=>1000000
[8,2,7,1,6,3,5,4]=>[4,5,3,6,1,7,2,8]=>0000001=>1000000
[5,7,4,8,6,3,2,1]=>[1,2,3,6,8,4,7,5]=>1110000=>0000111
[4,6,7,3,8,5,2,1]=>[1,2,5,8,3,7,6,4]=>1100000=>0000011
[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,5,10,9,8,7,6]=>111110000=>000011111
[5,7,8,9,4,10,6,3,2,1]=>[1,2,3,6,10,4,9,8,7,5]=>111000000=>000000111
[4,6,8,3,9,5,10,7,2,1]=>[1,2,7,10,5,9,3,8,6,4]=>110000000=>000000011
[3,5,2,7,4,9,6,10,8,1]=>[1,8,10,6,9,4,7,2,5,3]=>100000000=>000000001
[1,6,2,5,3,4,8,7]=>[7,8,4,3,5,2,6,1]=>0000000=>0000000
[1,6,2,4,8,3,5,7]=>[7,5,3,8,4,2,6,1]=>0000000=>0000000
[1,7,2,3,6,4,8,5]=>[5,8,4,6,3,2,7,1]=>0000000=>0000000
[1,5,2,3,8,4,7,6]=>[6,7,4,8,3,2,5,1]=>0000000=>0000000
[1,3,5,2,8,4,7,6]=>[6,7,4,8,2,5,3,1]=>0000000=>0000000
[1,5,8,2,3,7,4,6]=>[6,4,7,3,2,8,5,1]=>0000000=>0000000
[5,7,2,6,3,8,1,4]=>[4,1,8,3,6,2,7,5]=>0000000=>0000000
[5,7,1,6,8,4,3,2]=>[2,3,4,8,6,1,7,5]=>0000000=>0000000
[8,4,6,2,5,7,3,1]=>[1,3,7,5,2,6,4,8]=>1000001=>1000001
[4,7,1,3,2,8,6,5]=>[5,6,8,2,3,1,7,4]=>0000000=>0000000
[3,8,7,1,6,4,5,2]=>[2,5,4,6,1,7,8,3]=>0000000=>0000000
[4,3,2,1,5,8,6,7]=>[7,6,8,5,1,2,3,4]=>0000000=>0000000
[3,4,6,1,5,8,2,7]=>[7,2,8,5,1,6,4,3]=>0000000=>0000000
[6,5,8,7,1,4,2,3]=>[3,2,4,1,7,8,5,6]=>0001000=>0001000
[6,3,1,2,5,8,4,7]=>[7,4,8,5,2,1,3,6]=>0000000=>0000000
[7,6,1,4,3,5,8,2]=>[2,8,5,3,4,1,6,7]=>0000000=>0000000
[2,5,3,4,8,6,1,7]=>[7,1,6,8,4,3,5,2]=>0000000=>0000000
[2,4,8,3,6,1,7,5]=>[5,7,1,6,3,8,4,2]=>0000000=>0000000
[7,1,5,6,8,4,3,2]=>[2,3,4,8,6,5,1,7]=>0000000=>0000000
[6,1,4,2,8,3,5,7]=>[7,5,3,8,2,4,1,6]=>0000000=>0000000
[7,4,1,5,8,2,3,6]=>[6,3,2,8,5,1,4,7]=>0000000=>0000000
[6,3,4,2,8,7,5,1]=>[1,5,7,8,2,4,3,6]=>1000000=>0000001
[6,8,7,4,2,3,5,1]=>[1,5,3,2,4,7,8,6]=>1000100=>0010001
[2,7,6,3,4,5,8,1]=>[1,8,5,4,3,6,7,2]=>1000000=>0000001
[5,1,7,2,4,3,8,6]=>[6,8,3,4,2,7,1,5]=>0000000=>0000000
[1,5,3,4,8,6,2,7]=>[7,2,6,8,4,3,5,1]=>0000000=>0000000
[3,7,5,8,2,6,1,4]=>[4,1,6,2,8,5,7,3]=>0000000=>0000000
[6,3,1,4,7,5,8,2]=>[2,8,5,7,4,1,3,6]=>0000000=>0000000
[3,6,1,4,7,2,8,5]=>[5,8,2,7,4,1,6,3]=>0000000=>0000000
[6,2,7,4,5,8,1,3]=>[3,1,8,5,4,7,2,6]=>0000000=>0000000
[2,1,8,4,5,7,3,6]=>[6,3,7,5,4,8,1,2]=>0000000=>0000000
[3,2,1,6,4,8,5,7]=>[7,5,8,4,6,1,2,3]=>0000000=>0000000
[2,1,8,5,4,3,6,7]=>[7,6,3,4,5,8,1,2]=>0000000=>0000000
[7,4,8,6,2,3,1,5]=>[5,1,3,2,6,8,4,7]=>0000000=>0000000
[7,3,2,4,8,6,1,5]=>[5,1,6,8,4,2,3,7]=>0000000=>0000000
[2,7,1,4,6,3,8,5]=>[5,8,3,6,4,1,7,2]=>0000000=>0000000
[7,1,3,2,8,5,4,6]=>[6,4,5,8,2,3,1,7]=>0000000=>0000000
[5,1,7,4,2,3,8,6]=>[6,8,3,2,4,7,1,5]=>0000000=>0000000
[8,4,7,5,2,3,6,1]=>[1,6,3,2,5,7,4,8]=>1000001=>1000001
[7,5,2,8,4,6,1,3]=>[3,1,6,4,8,2,5,7]=>0000000=>0000000
[6,7,5,1,2,8,3,4]=>[4,3,8,2,1,5,7,6]=>0000000=>0000000
[7,5,1,4,2,6,8,3]=>[3,8,6,2,4,1,5,7]=>0000000=>0000000
[7,6,2,4,5,8,3,1]=>[1,3,8,5,4,2,6,7]=>1000000=>0000001
[3,6,8,4,7,2,5,1]=>[1,5,2,7,4,8,6,3]=>1000000=>0000001
[2,6,3,8,4,7,5,1]=>[1,5,7,4,8,3,6,2]=>1000000=>0000001
[2,1,5,6,8,3,7,4]=>[4,7,3,8,6,5,1,2]=>0000000=>0000000
[5,8,1,2,6,4,7,3]=>[3,7,4,6,2,1,8,5]=>0000000=>0000000
[1,2,7,4,8,3,6,5]=>[5,6,3,8,4,7,2,1]=>0000000=>0000000
[1,6,7,5,2,8,3,4]=>[4,3,8,2,5,7,6,1]=>0000000=>0000000
[5,4,8,3,6,2,7,1]=>[1,7,2,6,3,8,4,5]=>1000000=>0000001
[5,7,3,8,2,4,6,1]=>[1,6,4,2,8,3,7,5]=>1000000=>0000001
[6,4,5,8,2,7,3,1]=>[1,3,7,2,8,5,4,6]=>1000000=>0000001
[3,4,7,2,5,1,8,6]=>[6,8,1,5,2,7,4,3]=>0000000=>0000000
[6,4,5,8,1,2,7,3]=>[3,7,2,1,8,5,4,6]=>0000000=>0000000
[3,8,5,7,1,4,2,6]=>[6,2,4,1,7,5,8,3]=>0000000=>0000000
[5,1,7,4,8,6,3,2]=>[2,3,6,8,4,7,1,5]=>0000000=>0000000
[3,4,1,6,5,8,7,2]=>[2,7,8,5,6,1,4,3]=>0000000=>0000000
[3,5,1,2,4,8,7,6]=>[6,7,8,4,2,1,5,3]=>0000000=>0000000
[3,7,5,2,1,4,6,8]=>[8,6,4,1,2,5,7,3]=>0000000=>0000000
[3,8,5,2,7,4,1,6]=>[6,1,4,7,2,5,8,3]=>0000000=>0000000
[5,2,8,4,7,3,1,6]=>[6,1,3,7,4,8,2,5]=>0000000=>0000000
[5,2,6,4,1,8,7,3]=>[3,7,8,1,4,6,2,5]=>0000000=>0000000
[6,3,2,1,4,8,7,5]=>[5,7,8,4,1,2,3,6]=>0000000=>0000000
[4,3,5,1,2,8,7,6]=>[6,7,8,2,1,5,3,4]=>0000000=>0000000
[3,1,4,6,2,8,7,5]=>[5,7,8,2,6,4,1,3]=>0000000=>0000000
[3,4,5,8,7,2,1,6]=>[6,1,2,7,8,5,4,3]=>0000000=>0000000
[8,1,4,7,2,3,6,5]=>[5,6,3,2,7,4,1,8]=>0000001=>1000000
[1,8,5,7,3,4,6,2]=>[2,6,4,3,7,5,8,1]=>0000000=>0000000
[6,4,8,5,7,1,2,3]=>[3,2,1,7,5,8,4,6]=>0010000=>0000100
[5,4,7,6,3,8,1,2]=>[2,1,8,3,6,7,4,5]=>0100000=>0000010
[4,6,3,7,5,8,1,2]=>[2,1,8,5,7,3,6,4]=>0100000=>0000010
[7,3,8,1,4,2,6,5]=>[5,6,2,4,1,8,3,7]=>0000000=>0000000
[1,8,4,5,3,2,6,7]=>[7,6,2,3,5,4,8,1]=>0000000=>0000000
[3,8,7,4,2,6,1,5]=>[5,1,6,2,4,7,8,3]=>0000000=>0000000
[3,7,8,1,2,6,5,4]=>[4,5,6,2,1,8,7,3]=>0000000=>0000000
[3,5,6,2,7,1,4,8]=>[8,4,1,7,2,6,5,3]=>0000000=>0000000
[3,6,5,1,2,8,4,7]=>[7,4,8,2,1,5,6,3]=>0000000=>0000000
[3,7,1,6,8,2,4,5]=>[5,4,2,8,6,1,7,3]=>0000000=>0000000
[7,3,5,2,1,8,4,6]=>[6,4,8,1,2,5,3,7]=>0000000=>0000000
[6,4,2,8,7,5,1,3]=>[3,1,5,7,8,2,4,6]=>0000000=>0000000
[5,2,4,6,1,7,3,8]=>[8,3,7,1,6,4,2,5]=>0000000=>0000000
[3,5,4,6,1,8,2,7]=>[7,2,8,1,6,4,5,3]=>0000000=>0000000
[3,1,5,7,6,8,2,4]=>[4,2,8,6,7,5,1,3]=>0000000=>0000000
[4,1,5,3,8,2,7,6]=>[6,7,2,8,3,5,1,4]=>0000000=>0000000
[2,6,3,5,4,8,1,7]=>[7,1,8,4,5,3,6,2]=>0000000=>0000000
[7,6,4,5,2,8,1,3]=>[3,1,8,2,5,4,6,7]=>0000000=>0000000
[5,4,3,1,8,2,7,6]=>[6,7,2,8,1,3,4,5]=>0000000=>0000000
[6,5,4,2,7,3,1,8]=>[8,1,3,7,2,4,5,6]=>0000000=>0000000
[6,5,2,8,3,4,7,1]=>[1,7,4,3,8,2,5,6]=>1000000=>0000001
[6,5,3,4,8,2,7,1]=>[1,7,2,8,4,3,5,6]=>1000000=>0000001
[4,6,3,1,8,2,7,5]=>[5,7,2,8,1,3,6,4]=>0000000=>0000000
[7,5,2,6,4,3,1,8]=>[8,1,3,4,6,2,5,7]=>0000000=>0000000
[8,6,1,7,4,5,2,3]=>[3,2,5,4,7,1,6,8]=>0000001=>1000000
[8,1,3,7,2,6,5,4]=>[4,5,6,2,7,3,1,8]=>0000001=>1000000
[7,3,8,4,5,2,6,1]=>[1,6,2,5,4,8,3,7]=>1000000=>0000001
[6,1,7,4,2,5,3,8]=>[8,3,5,2,4,7,1,6]=>0000000=>0000000
[1,7,8,4,3,5,6,2]=>[2,6,5,3,4,8,7,1]=>0000000=>0000000
[3,1,6,8,4,5,7,2]=>[2,7,5,4,8,6,1,3]=>0000000=>0000000
[2,5,7,1,8,3,6,4]=>[4,6,3,8,1,7,5,2]=>0000000=>0000000
[6,2,7,1,8,4,5,3]=>[3,5,4,8,1,7,2,6]=>0000000=>0000000
[4,7,1,3,8,5,6,2]=>[2,6,5,8,3,1,7,4]=>0000000=>0000000
[3,7,2,1,8,4,5,6]=>[6,5,4,8,1,2,7,3]=>0000000=>0000000
[2,1,5,8,3,6,7,4]=>[4,7,6,3,8,5,1,2]=>0000000=>0000000
[4,2,7,1,8,3,6,5]=>[5,6,3,8,1,7,2,4]=>0000000=>0000000
[4,3,1,6,8,2,7,5]=>[5,7,2,8,6,1,3,4]=>0000000=>0000000
[3,5,1,6,8,2,7,4]=>[4,7,2,8,6,1,5,3]=>0000000=>0000000
[3,8,7,4,6,2,5,1]=>[1,5,2,6,4,7,8,3]=>1000000=>0000001
[5,8,7,4,3,6,2,1]=>[1,2,6,3,4,7,8,5]=>1100000=>0000011
[2,5,6,8,4,3,7,1]=>[1,7,3,4,8,6,5,2]=>1000000=>0000001
[2,4,7,5,8,1,6,3]=>[3,6,1,8,5,7,4,2]=>0000000=>0000000
[5,2,1,8,7,6,4,3]=>[3,4,6,7,8,1,2,5]=>0000000=>0000000
[4,8,5,6,7,1,2,3]=>[3,2,1,7,6,5,8,4]=>0010000=>0000100
[5,4,8,6,1,7,2,3]=>[3,2,7,1,6,8,4,5]=>0000000=>0000000
[5,3,8,1,6,7,2,4]=>[4,2,7,6,1,8,3,5]=>0000000=>0000000
[5,2,1,8,6,7,3,4]=>[4,3,7,6,8,1,2,5]=>0000000=>0000000
[6,2,1,5,8,3,7,4]=>[4,7,3,8,5,1,2,6]=>0000000=>0000000
[6,5,4,8,2,1,7,3]=>[3,7,1,2,8,4,5,6]=>0000000=>0000000
[5,8,4,7,2,6,3,1]=>[1,3,6,2,7,4,8,5]=>1000000=>0000001
[1,5,7,4,8,2,6,3]=>[3,6,2,8,4,7,5,1]=>0000000=>0000000
[6,5,3,2,8,1,7,4]=>[4,7,1,8,2,3,5,6]=>0000000=>0000000
[6,4,3,2,1,8,7,5]=>[5,7,8,1,2,3,4,6]=>0000000=>0000000
[6,3,4,1,2,8,7,5]=>[5,7,8,2,1,4,3,6]=>0000000=>0000000
[6,2,1,4,3,8,7,5]=>[5,7,8,3,4,1,2,6]=>0000000=>0000000
[5,2,1,4,3,6,7,8]=>[8,7,6,3,4,1,2,5]=>0000000=>0000000
[4,6,3,2,5,1,7,8]=>[8,7,1,5,2,3,6,4]=>0000000=>0000000
[4,3,6,1,5,2,7,8]=>[8,7,2,5,1,6,3,4]=>0000000=>0000000
[3,4,6,5,8,1,7,2]=>[2,7,1,8,5,6,4,3]=>0000000=>0000000
[2,1,5,3,8,4,7,6]=>[6,7,4,8,3,5,1,2]=>0000000=>0000000
[3,1,8,2,5,4,7,6]=>[6,7,4,5,2,8,1,3]=>0000000=>0000000
[8,1,3,2,6,4,7,5]=>[5,7,4,6,2,3,1,8]=>0000001=>1000000
[3,1,8,2,6,4,7,5]=>[5,7,4,6,2,8,1,3]=>0000000=>0000000
[2,1,8,3,6,4,7,5]=>[5,7,4,6,3,8,1,2]=>0000000=>0000000
[2,1,6,3,8,4,7,5]=>[5,7,4,8,3,6,1,2]=>0000000=>0000000
[2,1,7,3,5,4,8,6]=>[6,8,4,5,3,7,1,2]=>0000000=>0000000
[2,1,7,3,6,4,8,5]=>[5,8,4,6,3,7,1,2]=>0000000=>0000000
[2,1,7,3,8,4,6,5]=>[5,6,4,8,3,7,1,2]=>0000000=>0000000
[8,1,4,2,7,3,6,5]=>[5,6,3,7,2,4,1,8]=>0000001=>1000000
[4,1,8,2,7,3,6,5]=>[5,6,3,7,2,8,1,4]=>0000000=>0000000
[4,1,7,2,8,3,6,5]=>[5,6,3,8,2,7,1,4]=>0000000=>0000000
[3,1,7,2,8,4,6,5]=>[5,6,4,8,2,7,1,3]=>0000000=>0000000
[3,1,6,2,5,4,8,7]=>[7,8,4,5,2,6,1,3]=>0000000=>0000000
[7,1,3,2,5,4,8,6]=>[6,8,4,5,2,3,1,7]=>0000000=>0000000
[7,1,3,2,6,4,8,5]=>[5,8,4,6,2,3,1,7]=>0000000=>0000000
[7,1,3,2,8,4,6,5]=>[5,6,4,8,2,3,1,7]=>0000000=>0000000
[7,1,8,2,4,3,6,5]=>[5,6,3,4,2,8,1,7]=>0000000=>0000000
[8,1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1,8]=>0000001=>1000000
[7,1,5,2,8,3,6,4]=>[4,6,3,8,2,5,1,7]=>0000000=>0000000
[6,1,4,2,5,3,8,7]=>[7,8,3,5,2,4,1,6]=>0000000=>0000000
[4,1,6,2,5,3,8,7]=>[7,8,3,5,2,6,1,4]=>0000000=>0000000
[4,1,7,2,5,3,8,6]=>[6,8,3,5,2,7,1,4]=>0000000=>0000000
[4,1,7,2,6,3,8,5]=>[5,8,3,6,2,7,1,4]=>0000000=>0000000
[5,1,7,2,6,3,8,4]=>[4,8,3,6,2,7,1,5]=>0000000=>0000000
[5,1,7,2,8,3,6,4]=>[4,6,3,8,2,7,1,5]=>0000000=>0000000
[5,1,8,2,7,3,6,4]=>[4,6,3,7,2,8,1,5]=>0000000=>0000000
[8,1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1,8]=>0000001=>1000000
[8,1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1,8]=>0000001=>1000000
[5,1,8,2,6,3,7,4]=>[4,7,3,6,2,8,1,5]=>0000000=>0000000
[5,1,6,2,8,3,7,4]=>[4,7,3,8,2,6,1,5]=>0000000=>0000000
[3,1,6,2,8,4,7,5]=>[5,7,4,8,2,6,1,3]=>0000000=>0000000
[4,1,8,2,6,3,7,5]=>[5,7,3,6,2,8,1,4]=>0000000=>0000000
[8,1,4,2,6,3,7,5]=>[5,7,3,6,2,4,1,8]=>0000001=>1000000
[8,1,4,2,5,3,7,6]=>[6,7,3,5,2,4,1,8]=>0000001=>1000000
[4,1,8,2,5,3,7,6]=>[6,7,3,5,2,8,1,4]=>0000000=>0000000
[4,1,5,2,8,3,7,6]=>[6,7,3,8,2,5,1,4]=>0000000=>0000000
[3,1,5,2,8,4,7,6]=>[6,7,4,8,2,5,1,3]=>0000000=>0000000
[3,1,4,2,8,5,7,6]=>[6,7,5,8,2,4,1,3]=>0000000=>0000000
[4,1,3,2,7,5,8,6]=>[6,8,5,7,2,3,1,4]=>0000000=>0000000
[5,1,4,2,8,3,7,6]=>[6,7,3,8,2,4,1,5]=>0000000=>0000000
[5,1,8,2,4,3,7,6]=>[6,7,3,4,2,8,1,5]=>0000000=>0000000
[8,1,6,2,4,3,7,5]=>[5,7,3,4,2,6,1,8]=>0000001=>1000000
[6,1,8,2,4,3,7,5]=>[5,7,3,4,2,8,1,6]=>0000000=>0000000
[6,1,3,2,8,4,7,5]=>[5,7,4,8,2,3,1,6]=>0000000=>0000000
[6,1,3,2,7,4,8,5]=>[5,8,4,7,2,3,1,6]=>0000000=>0000000
[5,1,3,2,7,4,8,6]=>[6,8,4,7,2,3,1,5]=>0000000=>0000000
[5,1,3,2,6,4,8,7]=>[7,8,4,6,2,3,1,5]=>0000000=>0000000
[5,1,4,2,6,3,8,7]=>[7,8,3,6,2,4,1,5]=>0000000=>0000000
[6,1,4,2,7,3,8,5]=>[5,8,3,7,2,4,1,6]=>0000000=>0000000
[6,1,5,2,7,3,8,4]=>[4,8,3,7,2,5,1,6]=>0000000=>0000000
[6,1,8,2,5,3,7,4]=>[4,7,3,5,2,8,1,6]=>0000000=>0000000
[8,1,6,2,5,3,7,4]=>[4,7,3,5,2,6,1,8]=>0000001=>1000000
[8,1,6,2,7,3,5,4]=>[4,5,3,7,2,6,1,8]=>0000001=>1000000
[6,1,8,2,7,3,5,4]=>[4,5,3,7,2,8,1,6]=>0000000=>0000000
[6,1,7,2,8,3,5,4]=>[4,5,3,8,2,7,1,6]=>0000000=>0000000
[6,1,7,2,5,3,8,4]=>[4,8,3,5,2,7,1,6]=>0000000=>0000000
[6,1,7,2,4,3,8,5]=>[5,8,3,4,2,7,1,6]=>0000000=>0000000
[5,1,6,2,4,3,8,7]=>[7,8,3,4,2,6,1,5]=>0000000=>0000000
[7,1,5,2,4,3,8,6]=>[6,8,3,4,2,5,1,7]=>0000000=>0000000
[7,1,6,2,4,3,8,5]=>[5,8,3,4,2,6,1,7]=>0000000=>0000000
[7,1,6,2,5,3,8,4]=>[4,8,3,5,2,6,1,7]=>0000000=>0000000
[7,1,6,2,8,3,5,4]=>[4,5,3,8,2,6,1,7]=>0000000=>0000000
[7,1,8,2,6,3,5,4]=>[4,5,3,6,2,8,1,7]=>0000000=>0000000
[7,8,3,1,2,5,6,4]=>[4,6,5,2,1,3,8,7]=>0000010=>0100000
[6,2,8,1,3,5,4,7]=>[7,4,5,3,1,8,2,6]=>0000000=>0000000
[3,2,5,7,1,8,4,6]=>[6,4,8,1,7,5,2,3]=>0000000=>0000000
[3,5,2,8,1,7,4,6]=>[6,4,7,1,8,2,5,3]=>0000000=>0000000
[4,1,3,2,6,8,7,5]=>[5,7,8,6,2,3,1,4]=>0000000=>0000000
[6,1,8,3,2,4,7,5]=>[5,7,4,2,3,8,1,6]=>0000000=>0000000
[4,3,5,7,6,8,1,2]=>[2,1,8,6,7,5,3,4]=>0100000=>0000010
[4,2,1,3,7,6,8,5]=>[5,8,6,7,3,1,2,4]=>0000000=>0000000
[2,4,3,1,8,5,7,6]=>[6,7,5,8,1,3,4,2]=>0000000=>0000000
[3,2,4,1,8,6,5,7]=>[7,5,6,8,1,4,2,3]=>0000000=>0000000
[7,6,5,4,8,1,3,2]=>[2,3,1,8,4,5,6,7]=>0010000=>0000100
[7,6,8,3,2,1,5,4]=>[4,5,1,2,3,8,6,7]=>0000100=>0010000
[8,5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5,8]=>0000001=>1000000
[7,6,5,2,8,1,4,3]=>[3,4,1,8,2,5,6,7]=>0000000=>0000000
[7,6,3,8,2,1,5,4]=>[4,5,1,2,8,3,6,7]=>0000000=>0000000
[7,4,8,3,2,1,6,5]=>[5,6,1,2,3,8,4,7]=>0000000=>0000000
[4,8,6,1,7,5,2,3]=>[3,2,5,7,1,6,8,4]=>0000000=>0000000
[4,7,8,2,6,1,5,3]=>[3,5,1,6,2,8,7,4]=>0000000=>0000000
[7,6,4,2,8,3,5,1]=>[1,5,3,8,2,4,6,7]=>1000000=>0000001
[8,6,4,2,7,5,3,1]=>[1,3,5,7,2,4,6,8]=>1000001=>1000001
[8,4,7,3,6,5,1,2]=>[2,1,5,6,3,7,4,8]=>0100001=>1000010
[6,4,7,1,8,3,2,5]=>[5,2,3,8,1,7,4,6]=>0000000=>0000000
[7,8,4,3,6,2,5,1]=>[1,5,2,6,3,4,8,7]=>1000010=>0100001
[6,8,4,3,7,2,1,5]=>[5,1,2,7,3,4,8,6]=>0000000=>0000000
[6,7,4,2,8,3,1,5]=>[5,1,3,8,2,4,7,6]=>0000000=>0000000
[7,3,2,5,4,1,6,8]=>[8,6,1,4,5,2,3,7]=>0000000=>0000000
[7,1,4,2,6,3,5,8]=>[8,5,3,6,2,4,1,7]=>0000000=>0000000
[7,3,2,5,1,6,4,8]=>[8,4,6,1,5,2,3,7]=>0000000=>0000000
[3,6,2,1,4,8,5,7]=>[7,5,8,4,1,2,6,3]=>0000000=>0000000
[2,3,6,1,4,8,7,5]=>[5,7,8,4,1,6,3,2]=>0000000=>0000000
[3,4,7,1,5,2,8,6]=>[6,8,2,5,1,7,4,3]=>0000000=>0000000
[3,6,7,4,1,5,8,2]=>[2,8,5,1,4,7,6,3]=>0000000=>0000000
[5,6,8,2,4,1,3,7]=>[7,3,1,4,2,8,6,5]=>0000000=>0000000
[1,8,2,7,4,3,6,5]=>[5,6,3,4,7,2,8,1]=>0000000=>0000000
[6,5,8,2,3,7,1,4]=>[4,1,7,3,2,8,5,6]=>0000000=>0000000
[2,4,8,1,6,3,7,5]=>[5,7,3,6,1,8,4,2]=>0000000=>0000000
[3,7,5,4,6,8,2,1]=>[1,2,8,6,4,5,7,3]=>1100000=>0000011
[5,3,2,1,7,6,8,4]=>[4,8,6,7,1,2,3,5]=>0000000=>0000000
[4,3,1,7,5,6,8,2]=>[2,8,6,5,7,1,3,4]=>0000000=>0000000
[5,6,7,3,2,8,1,4]=>[4,1,8,2,3,7,6,5]=>0000000=>0000000
[7,3,2,6,8,5,1,4]=>[4,1,5,8,6,2,3,7]=>0000000=>0000000
[1,8,4,2,3,5,7,6]=>[6,7,5,3,2,4,8,1]=>0000000=>0000000
[6,3,4,8,2,5,7,1]=>[1,7,5,2,8,4,3,6]=>1000000=>0000001
[7,5,4,8,3,6,2,1]=>[1,2,6,3,8,4,5,7]=>1100000=>0000011
[5,7,8,3,1,4,6,2]=>[2,6,4,1,3,8,7,5]=>0000000=>0000000
[7,4,8,3,2,5,1,6]=>[6,1,5,2,3,8,4,7]=>0000000=>0000000
[2,3,4,8,1,6,5,7]=>[7,5,6,1,8,4,3,2]=>0000000=>0000000
[7,3,1,6,8,2,4,5]=>[5,4,2,8,6,1,3,7]=>0000000=>0000000
[4,6,8,2,1,5,7,3]=>[3,7,5,1,2,8,6,4]=>0000000=>0000000
[6,8,2,1,3,5,7,4]=>[4,7,5,3,1,2,8,6]=>0000000=>0000000
[1,2,5,8,3,7,4,6]=>[6,4,7,3,8,5,2,1]=>0000000=>0000000
[8,2,4,1,7,5,6,3]=>[3,6,5,7,1,4,2,8]=>0000001=>1000000
[3,8,4,7,5,1,6,2]=>[2,6,1,5,7,4,8,3]=>0000000=>0000000
[8,4,3,6,1,7,5,2]=>[2,5,7,1,6,3,4,8]=>0000001=>1000000
[2,1,8,6,7,3,5,4]=>[4,5,3,7,6,8,1,2]=>0000000=>0000000
[7,3,2,5,6,1,4,8]=>[8,4,1,6,5,2,3,7]=>0000000=>0000000
[4,6,2,8,1,5,3,7]=>[7,3,5,1,8,2,6,4]=>0000000=>0000000
[1,5,2,8,6,3,7,4]=>[4,7,3,6,8,2,5,1]=>0000000=>0000000
[5,8,6,3,1,7,4,2]=>[2,4,7,1,3,6,8,5]=>0000000=>0000000
[4,5,6,2,7,1,3,8]=>[8,3,1,7,2,6,5,4]=>0000000=>0000000
[5,6,2,7,1,3,4,8]=>[8,4,3,1,7,2,6,5]=>0000000=>0000000
[8,5,1,2,6,3,4,7]=>[7,4,3,6,2,1,5,8]=>0000001=>1000000
[6,7,3,8,4,1,5,2]=>[2,5,1,4,8,3,7,6]=>0000000=>0000000
[2,7,1,8,5,6,3,4]=>[4,3,6,5,8,1,7,2]=>0000000=>0000000
[2,1,7,8,6,3,4,5]=>[5,4,3,6,8,7,1,2]=>0000000=>0000000
[7,8,6,2,1,3,5,4]=>[4,5,3,1,2,6,8,7]=>0000110=>0110000
[5,2,6,3,4,1,8,7]=>[7,8,1,4,3,6,2,5]=>0000000=>0000000
[4,1,2,6,5,3,8,7]=>[7,8,3,5,6,2,1,4]=>0000000=>0000000
[4,7,8,5,1,6,3,2]=>[2,3,6,1,5,8,7,4]=>0000000=>0000000
[4,8,6,1,7,3,2,5]=>[5,2,3,7,1,6,8,4]=>0000000=>0000000
[3,8,5,1,7,2,4,6]=>[6,4,2,7,1,5,8,3]=>0000000=>0000000
[2,1,7,4,8,5,6,3]=>[3,6,5,8,4,7,1,2]=>0000000=>0000000
[8,3,7,4,6,1,2,5]=>[5,2,1,6,4,7,3,8]=>0000001=>1000000
[2,1,6,3,4,8,7,5]=>[5,7,8,4,3,6,1,2]=>0000000=>0000000
[6,5,4,2,8,3,1,7]=>[7,1,3,8,2,4,5,6]=>0000000=>0000000
[8,1,4,2,5,6,7,3]=>[3,7,6,5,2,4,1,8]=>0000001=>1000000
[6,1,4,3,8,5,2,7]=>[7,2,5,8,3,4,1,6]=>0000000=>0000000
[4,2,3,1,7,8,6,5]=>[5,6,8,7,1,3,2,4]=>0000000=>0000000
[2,7,6,8,1,5,3,4]=>[4,3,5,1,8,6,7,2]=>0000000=>0000000
[3,6,8,1,5,2,4,7]=>[7,4,2,5,1,8,6,3]=>0000000=>0000000
[7,4,6,8,5,1,2,3]=>[3,2,1,5,8,6,4,7]=>0010000=>0000100
[2,1,5,8,3,6,4,7]=>[7,4,6,3,8,5,1,2]=>0000000=>0000000
[5,8,7,3,6,1,4,2]=>[2,4,1,6,3,7,8,5]=>0000000=>0000000
[7,6,8,3,5,1,4,2]=>[2,4,1,5,3,8,6,7]=>0000100=>0010000
[5,8,3,7,6,1,4,2]=>[2,4,1,6,7,3,8,5]=>0000000=>0000000
[5,3,8,7,6,1,4,2]=>[2,4,1,6,7,8,3,5]=>0000000=>0000000
[2,4,8,1,3,7,6,5]=>[5,6,7,3,1,8,4,2]=>0000000=>0000000
[2,5,1,3,8,4,7,6]=>[6,7,4,8,3,1,5,2]=>0000000=>0000000
[2,8,1,5,4,7,3,6]=>[6,3,7,4,5,1,8,2]=>0000000=>0000000
[2,6,1,3,8,7,5,4]=>[4,5,7,8,3,1,6,2]=>0000000=>0000000
[2,7,1,5,8,4,6,3]=>[3,6,4,8,5,1,7,2]=>0000000=>0000000
[7,3,6,2,1,5,4,8]=>[8,4,5,1,2,6,3,7]=>0000000=>0000000
[7,4,2,8,1,6,5,3]=>[3,5,6,1,8,2,4,7]=>0000000=>0000000
[7,4,5,8,6,2,1,3]=>[3,1,2,6,8,5,4,7]=>0010000=>0000100
[6,8,4,5,2,1,7,3]=>[3,7,1,2,5,4,8,6]=>0000000=>0000000
[4,7,5,1,3,8,6,2]=>[2,6,8,3,1,5,7,4]=>0000000=>0000000
[5,1,7,6,3,8,2,4]=>[4,2,8,3,6,7,1,5]=>0000000=>0000000
[5,1,8,7,6,4,3,2]=>[2,3,4,6,7,8,1,5]=>0000000=>0000000
[5,1,6,2,8,7,4,3]=>[3,4,7,8,2,6,1,5]=>0000000=>0000000
[3,5,6,8,7,1,4,2]=>[2,4,1,7,8,6,5,3]=>0000000=>0000000
[3,6,1,7,4,8,2,5]=>[5,2,8,4,7,1,6,3]=>0000000=>0000000
[8,4,2,5,7,3,1,6]=>[6,1,3,7,5,2,4,8]=>0000001=>1000000
[4,1,8,5,7,3,6,2]=>[2,6,3,7,5,8,1,4]=>0000000=>0000000
[3,4,8,7,1,2,6,5]=>[5,6,2,1,7,8,4,3]=>0000000=>0000000
[3,4,6,8,5,7,1,2]=>[2,1,7,5,8,6,4,3]=>0100000=>0000010
[4,6,8,3,5,7,2,1]=>[1,2,7,5,3,8,6,4]=>1100000=>0000011
[4,7,3,5,8,2,6,1]=>[1,6,2,8,5,3,7,4]=>1000000=>0000001
[5,4,8,2,7,3,6,1]=>[1,6,3,7,2,8,4,5]=>1000000=>0000001
[5,4,8,7,3,6,1,2]=>[2,1,6,3,7,8,4,5]=>0100000=>0000010
[6,4,3,8,7,1,2,5]=>[5,2,1,7,8,3,4,6]=>0000000=>0000000
[6,3,7,2,4,8,1,5]=>[5,1,8,4,2,7,3,6]=>0000000=>0000000
[5,6,8,3,7,2,1,4]=>[4,1,2,7,3,8,6,5]=>0000000=>0000000
[5,6,8,4,2,7,3,1]=>[1,3,7,2,4,8,6,5]=>1000000=>0000001
[6,5,2,7,1,3,8,4]=>[4,8,3,1,7,2,5,6]=>0000000=>0000000
[8,6,5,4,2,1,7,3]=>[3,7,1,2,4,5,6,8]=>0000001=>1000000
[6,5,4,1,7,2,8,3]=>[3,8,2,7,1,4,5,6]=>0000000=>0000000
[6,8,5,7,4,3,2,1]=>[1,2,3,4,7,5,8,6]=>1111000=>0001111
[7,5,8,4,6,3,2,1]=>[1,2,3,6,4,8,5,7]=>1110000=>0000111
[7,6,4,8,3,5,2,1]=>[1,2,5,3,8,4,6,7]=>1100000=>0000011
[7,6,5,3,8,2,4,1]=>[1,4,2,8,3,5,6,7]=>1000000=>0000001
[6,1,3,8,5,2,4,7]=>[7,4,2,5,8,3,1,6]=>0000000=>0000000
[7,4,8,6,3,1,5,2]=>[2,5,1,3,6,8,4,7]=>0000000=>0000000
[7,4,2,6,3,5,1,8]=>[8,1,5,3,6,2,4,7]=>0000000=>0000000
[3,4,7,5,6,2,1,8]=>[8,1,2,6,5,7,4,3]=>0000000=>0000000
[8,1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1,8]=>0000001=>1000000
[6,2,8,4,1,5,7,3]=>[3,7,5,1,4,8,2,6]=>0000000=>0000000
[3,6,8,4,1,7,5,2]=>[2,5,7,1,4,8,6,3]=>0000000=>0000000
[8,7,2,3,6,1,4,5]=>[5,4,1,6,3,2,7,8]=>0000011=>1100000
[3,2,8,1,5,4,6,7]=>[7,6,4,5,1,8,2,3]=>0000000=>0000000
[8,1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1,8]=>0000001=>1000000
[1,5,2,4,8,7,3,6]=>[6,3,7,8,4,2,5,1]=>0000000=>0000000
[3,5,2,1,8,7,6,4]=>[4,6,7,8,1,2,5,3]=>0000000=>0000000
[3,2,8,7,6,1,4,5]=>[5,4,1,6,7,8,2,3]=>0000000=>0000000
[1,8,6,7,2,3,4,5]=>[5,4,3,2,7,6,8,1]=>0000000=>0000000
[7,6,3,2,1,8,5,4]=>[4,5,8,1,2,3,6,7]=>0000000=>0000000
[5,2,3,4,7,1,8,6]=>[6,8,1,7,4,3,2,5]=>0000000=>0000000
[5,8,3,1,2,4,7,6]=>[6,7,4,2,1,3,8,5]=>0000000=>0000000
[8,4,1,7,2,3,6,5]=>[5,6,3,2,7,1,4,8]=>0000001=>1000000
[3,2,8,1,6,5,7,4]=>[4,7,5,6,1,8,2,3]=>0000000=>0000000
[3,2,6,1,5,7,4,8]=>[8,4,7,5,1,6,2,3]=>0000000=>0000000
[3,5,1,4,6,7,2,8]=>[8,2,7,6,4,1,5,3]=>0000000=>0000000
[4,1,3,2,5,7,6,8]=>[8,6,7,5,2,3,1,4]=>0000000=>0000000
[6,8,5,3,7,1,2,4]=>[4,2,1,7,3,5,8,6]=>0000000=>0000000
[6,8,2,4,5,1,3,7]=>[7,3,1,5,4,2,8,6]=>0000000=>0000000
[3,6,7,2,5,1,4,8]=>[8,4,1,5,2,7,6,3]=>0000000=>0000000
[5,8,4,1,7,2,6,3]=>[3,6,2,7,1,4,8,5]=>0000000=>0000000
[6,8,3,1,4,5,7,2]=>[2,7,5,4,1,3,8,6]=>0000000=>0000000
[5,3,8,4,2,6,7,1]=>[1,7,6,2,4,8,3,5]=>1000000=>0000001
[2,4,6,3,5,8,1,7]=>[7,1,8,5,3,6,4,2]=>0000000=>0000000
[3,4,1,6,5,8,2,7]=>[7,2,8,5,6,1,4,3]=>0000000=>0000000
[6,4,2,8,7,1,5,3]=>[3,5,1,7,8,2,4,6]=>0000000=>0000000
[3,1,8,2,7,6,4,5]=>[5,4,6,7,2,8,1,3]=>0000000=>0000000
[6,2,8,4,1,7,5,3]=>[3,5,7,1,4,8,2,6]=>0000000=>0000000
[7,3,2,8,6,1,4,5]=>[5,4,1,6,8,2,3,7]=>0000000=>0000000
[1,4,2,5,8,7,3,6]=>[6,3,7,8,5,2,4,1]=>0000000=>0000000
[3,5,1,7,2,8,6,4]=>[4,6,8,2,7,1,5,3]=>0000000=>0000000
[4,6,3,1,7,8,5,2]=>[2,5,8,7,1,3,6,4]=>0000000=>0000000
[4,8,7,3,6,5,1,2]=>[2,1,5,6,3,7,8,4]=>0100000=>0000010
[4,3,8,7,6,5,1,2]=>[2,1,5,6,7,8,3,4]=>0100000=>0000010
[2,8,7,6,1,5,4,3]=>[3,4,5,1,6,7,8,2]=>0000000=>0000000
[4,2,8,7,6,1,5,3]=>[3,5,1,6,7,8,2,4]=>0000000=>0000000
[6,2,8,7,5,1,4,3]=>[3,4,1,5,7,8,2,6]=>0000000=>0000000
[4,1,8,7,6,5,3,2]=>[2,3,5,6,7,8,1,4]=>0000000=>0000000
[6,2,8,7,1,5,4,3]=>[3,4,5,1,7,8,2,6]=>0000000=>0000000
[2,8,7,1,6,5,4,3]=>[3,4,5,6,1,7,8,2]=>0000000=>0000000
[3,8,2,7,1,6,5,4]=>[4,5,6,1,7,2,8,3]=>0000000=>0000000
[4,8,7,2,6,1,5,3]=>[3,5,1,6,2,7,8,4]=>0000000=>0000000
[5,8,7,6,2,1,4,3]=>[3,4,1,2,6,7,8,5]=>0001000=>0001000
[5,4,1,8,7,6,3,2]=>[2,3,6,7,8,1,4,5]=>0000000=>0000000
[5,3,1,8,7,6,4,2]=>[2,4,6,7,8,1,3,5]=>0000000=>0000000
[7,8,2,1,6,5,4,3]=>[3,4,5,6,1,2,8,7]=>0000010=>0100000
[5,4,3,1,8,7,6,2]=>[2,6,7,8,1,3,4,5]=>0000000=>0000000
[5,4,2,1,8,7,6,3]=>[3,6,7,8,1,2,4,5]=>0000000=>0000000
[7,3,2,1,8,6,5,4]=>[4,5,6,8,1,2,3,7]=>0000000=>0000000
[6,8,1,4,2,3,5,7]=>[7,5,3,2,4,1,8,6]=>0000000=>0000000
[8,2,3,6,1,4,5,7]=>[7,5,4,1,6,3,2,8]=>0000001=>1000000
[4,6,2,3,8,1,5,7]=>[7,5,1,8,3,2,6,4]=>0000000=>0000000
[6,2,3,8,4,1,5,7]=>[7,5,1,4,8,3,2,6]=>0000000=>0000000
[2,8,4,3,6,1,5,7]=>[7,5,1,6,3,4,8,2]=>0000000=>0000000
[2,6,3,8,4,1,5,7]=>[7,5,1,4,8,3,6,2]=>0000000=>0000000
[2,4,6,3,8,1,5,7]=>[7,5,1,8,3,6,4,2]=>0000000=>0000000
[8,3,6,2,4,1,5,7]=>[7,5,1,4,2,6,3,8]=>0000001=>1000000
[2,1,8,3,6,4,5,7]=>[7,5,4,6,3,8,1,2]=>0000000=>0000000
[6,3,8,2,1,4,5,7]=>[7,5,4,1,2,8,3,6]=>0000000=>0000000
[6,2,4,3,8,1,5,7]=>[7,5,1,8,3,4,2,6]=>0000000=>0000000
[3,6,4,2,7,1,5,8]=>[8,5,1,7,2,4,6,3]=>0000000=>0000000
[5,4,6,3,8,7,1,2]=>[2,1,7,8,3,6,4,5]=>0100000=>0000010
[6,4,8,5,3,7,1,2]=>[2,1,7,3,5,8,4,6]=>0100000=>0000010
[1,6,5,4,2,7,8,3]=>[3,8,7,2,4,5,6,1]=>0000000=>0000000
[1,8,5,2,6,3,7,4]=>[4,7,3,6,2,5,8,1]=>0000000=>0000000
[3,6,5,2,4,1,8,7]=>[7,8,1,4,2,5,6,3]=>0000000=>0000000
[5,2,8,6,4,1,3,7]=>[7,3,1,4,6,8,2,5]=>0000000=>0000000
[5,1,6,2,8,7,3,4]=>[4,3,7,8,2,6,1,5]=>0000000=>0000000
[1,2,6,4,8,7,5,3]=>[3,5,7,8,4,6,2,1]=>0000000=>0000000
[6,1,3,2,5,7,8,4]=>[4,8,7,5,2,3,1,6]=>0000000=>0000000
[4,6,2,1,7,5,3,8]=>[8,3,5,7,1,2,6,4]=>0000000=>0000000
[7,8,3,2,4,1,6,5]=>[5,6,1,4,2,3,8,7]=>0000010=>0100000
[7,5,2,8,3,4,1,6]=>[6,1,4,3,8,2,5,7]=>0000000=>0000000
[4,3,6,8,1,2,7,5]=>[5,7,2,1,8,6,3,4]=>0000000=>0000000
[6,4,3,5,2,8,1,7]=>[7,1,8,2,5,3,4,6]=>0000000=>0000000
[6,5,8,4,2,3,1,7]=>[7,1,3,2,4,8,5,6]=>0000000=>0000000
[2,4,1,3,8,5,7,6]=>[6,7,5,8,3,1,4,2]=>0000000=>0000000
[6,2,1,3,5,8,7,4]=>[4,7,8,5,3,1,2,6]=>0000000=>0000000
[6,2,1,3,8,5,7,4]=>[4,7,5,8,3,1,2,6]=>0000000=>0000000
[6,2,1,4,3,5,7,8]=>[8,7,5,3,4,1,2,6]=>0000000=>0000000
[8,1,4,6,3,5,7,2]=>[2,7,5,3,6,4,1,8]=>0000001=>1000000
[6,1,4,8,3,5,7,2]=>[2,7,5,3,8,4,1,6]=>0000000=>0000000
[2,6,1,3,8,5,7,4]=>[4,7,5,8,3,1,6,2]=>0000000=>0000000
[2,6,1,8,3,5,7,4]=>[4,7,5,3,8,1,6,2]=>0000000=>0000000
[2,1,6,3,8,5,7,4]=>[4,7,5,8,3,6,1,2]=>0000000=>0000000
[2,1,3,6,8,5,7,4]=>[4,7,5,8,6,3,1,2]=>0000000=>0000000
[1,4,3,6,8,5,7,2]=>[2,7,5,8,6,3,4,1]=>0000000=>0000000
[4,1,3,8,6,5,7,2]=>[2,7,5,6,8,3,1,4]=>0000000=>0000000
[2,1,8,6,3,5,7,4]=>[4,7,5,3,6,8,1,2]=>0000000=>0000000
[4,1,8,3,6,5,7,2]=>[2,7,5,6,3,8,1,4]=>0000000=>0000000
[8,7,6,5,1,4,3,2]=>[2,3,4,1,5,6,7,8]=>0001111=>1111000
[8,7,4,3,6,2,1,5]=>[5,1,2,6,3,4,7,8]=>0000011=>1100000
[8,7,3,6,5,2,1,4]=>[4,1,2,5,6,3,7,8]=>0000011=>1100000
[4,5,2,7,3,1,8,6]=>[6,8,1,3,7,2,5,4]=>0000000=>0000000
[4,8,2,6,3,5,7,1]=>[1,7,5,3,6,2,8,4]=>1000000=>0000001
[4,3,7,8,6,5,1,2]=>[2,1,5,6,8,7,3,4]=>0100000=>0000010
[4,6,2,1,7,8,5,3]=>[3,5,8,7,1,2,6,4]=>0000000=>0000000
[7,8,2,1,5,6,4,3]=>[3,4,6,5,1,2,8,7]=>0000010=>0100000
[1,5,8,6,2,3,7,4]=>[4,7,3,2,6,8,5,1]=>0000000=>0000000
[2,4,8,3,1,6,5,7]=>[7,5,6,1,3,8,4,2]=>0000000=>0000000
[5,2,7,1,8,6,3,4]=>[4,3,6,8,1,7,2,5]=>0000000=>0000000
[1,2,8,3,7,6,5,4]=>[4,5,6,7,3,8,2,1]=>0000000=>0000000
[2,6,1,3,8,7,4,5]=>[5,4,7,8,3,1,6,2]=>0000000=>0000000
[6,5,2,8,1,7,3,4]=>[4,3,7,1,8,2,5,6]=>0000000=>0000000
[2,8,5,6,1,7,3,4]=>[4,3,7,1,6,5,8,2]=>0000000=>0000000
[5,4,3,8,7,1,6,2]=>[2,6,1,7,8,3,4,5]=>0000000=>0000000
[8,5,4,3,7,2,6,1]=>[1,6,2,7,3,4,5,8]=>1000001=>1000001
[8,3,7,4,2,6,5,1]=>[1,5,6,2,4,7,3,8]=>1000001=>1000001
[3,8,7,4,1,6,5,2]=>[2,5,6,1,4,7,8,3]=>0000000=>0000000
[5,4,2,8,3,1,7,6]=>[6,7,1,3,8,2,4,5]=>0000000=>0000000
[2,8,5,3,1,7,6,4]=>[4,6,7,1,3,5,8,2]=>0000000=>0000000
[2,8,6,4,1,7,5,3]=>[3,5,7,1,4,6,8,2]=>0000000=>0000000
[8,4,7,6,2,5,3,1]=>[1,3,5,2,6,7,4,8]=>1000001=>1000001
[7,4,8,6,2,1,5,3]=>[3,5,1,2,6,8,4,7]=>0000000=>0000000
[7,3,8,5,2,1,6,4]=>[4,6,1,2,5,8,3,7]=>0000000=>0000000
[7,5,4,3,8,2,1,6]=>[6,1,2,8,3,4,5,7]=>0000000=>0000000
[5,4,2,3,8,1,6,7]=>[7,6,1,8,3,2,4,5]=>0000000=>0000000
[3,7,8,4,1,2,6,5]=>[5,6,2,1,4,8,7,3]=>0000000=>0000000
[6,5,8,7,3,1,4,2]=>[2,4,1,3,7,8,5,6]=>0001000=>0001000
[2,4,3,8,1,6,5,7]=>[7,5,6,1,8,3,4,2]=>0000000=>0000000
[2,3,8,5,1,6,7,4]=>[4,7,6,1,5,8,3,2]=>0000000=>0000000
[6,4,8,7,3,1,5,2]=>[2,5,1,3,7,8,4,6]=>0000000=>0000000
[8,3,4,7,2,5,6,1]=>[1,6,5,2,7,4,3,8]=>1000001=>1000001
[3,4,8,7,1,5,6,2]=>[2,6,5,1,7,8,4,3]=>0000000=>0000000
[2,6,8,5,1,3,7,4]=>[4,7,3,1,5,8,6,2]=>0000000=>0000000
[8,7,4,1,6,2,5,3]=>[3,5,2,6,1,4,7,8]=>0000011=>1100000
[6,3,7,4,5,8,2,1]=>[1,2,8,5,4,7,3,6]=>1100000=>0000011
[3,5,7,4,6,8,2,1]=>[1,2,8,6,4,7,5,3]=>1100000=>0000011
[6,8,4,1,7,2,5,3]=>[3,5,2,7,1,4,8,6]=>0000000=>0000000
[2,5,7,4,6,3,8,1]=>[1,8,3,6,4,7,5,2]=>1000000=>0000001
[6,8,3,1,4,7,2,5]=>[5,2,7,4,1,3,8,6]=>0000000=>0000000
[6,4,7,2,8,5,1,3]=>[3,1,5,8,2,7,4,6]=>0000000=>0000000
[5,8,1,4,7,3,2,6]=>[6,2,3,7,4,1,8,5]=>0000000=>0000000
[8,7,1,4,5,3,2,6]=>[6,2,3,5,4,1,7,8]=>0000011=>1100000
[8,7,4,2,6,5,1,3]=>[3,1,5,6,2,4,7,8]=>0000011=>1100000
[8,7,3,2,4,6,5,1]=>[1,5,6,4,2,3,7,8]=>1000011=>1100001
[8,7,2,4,5,3,6,1]=>[1,6,3,5,4,2,7,8]=>1000011=>1100001
[6,8,4,3,7,5,2,1]=>[1,2,5,7,3,4,8,6]=>1100000=>0000011
[6,4,7,3,8,5,2,1]=>[1,2,5,8,3,7,4,6]=>1100000=>0000011
[6,8,3,2,4,7,5,1]=>[1,5,7,4,2,3,8,6]=>1000000=>0000001
[8,1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1,8]=>0000001=>1000000
[8,1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1,8]=>0000001=>1000000
[2,7,1,5,6,3,4,8]=>[8,4,3,6,5,1,7,2]=>0000000=>0000000
[4,3,7,2,5,6,8,1]=>[1,8,6,5,2,7,3,4]=>1000000=>0000001
[2,6,3,1,4,5,8,7]=>[7,8,5,4,1,3,6,2]=>0000000=>0000000
[4,7,1,5,6,8,2,3]=>[3,2,8,6,5,1,7,4]=>0000000=>0000000
[4,7,3,2,5,6,1,8]=>[8,1,6,5,2,3,7,4]=>0000000=>0000000
[5,3,4,6,2,8,1,7]=>[7,1,8,2,6,4,3,5]=>0000000=>0000000
[6,4,7,2,3,8,1,5]=>[5,1,8,3,2,7,4,6]=>0000000=>0000000
[3,6,5,1,8,2,7,4]=>[4,7,2,8,1,5,6,3]=>0000000=>0000000
[4,6,5,1,8,7,2,3]=>[3,2,7,8,1,5,6,4]=>0000000=>0000000
[5,7,1,4,8,6,2,3]=>[3,2,6,8,4,1,7,5]=>0000000=>0000000
[5,7,1,3,8,2,6,4]=>[4,6,2,8,3,1,7,5]=>0000000=>0000000
[6,7,1,8,3,2,5,4]=>[4,5,2,3,8,1,7,6]=>0000000=>0000000
[8,7,6,1,4,5,2,3]=>[3,2,5,4,1,6,7,8]=>0000111=>1110000
[8,7,6,1,3,2,5,4]=>[4,5,2,3,1,6,7,8]=>0000111=>1110000
[8,7,3,5,1,2,6,4]=>[4,6,2,1,5,3,7,8]=>0000011=>1100000
[8,7,4,5,1,6,2,3]=>[3,2,6,1,5,4,7,8]=>0000011=>1100000
[8,4,6,2,3,1,7,5]=>[5,7,1,3,2,6,4,8]=>0000001=>1000000
[6,7,5,4,1,8,2,3]=>[3,2,8,1,4,5,7,6]=>0000000=>0000000
[6,7,8,4,1,5,3,2]=>[2,3,5,1,4,8,7,6]=>0000100=>0010000
[7,5,1,6,4,2,3,8]=>[8,3,2,4,6,1,5,7]=>0000000=>0000000
[4,5,8,6,1,7,3,2]=>[2,3,7,1,6,8,5,4]=>0000000=>0000000
[8,1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1,8]=>0000001=>1000000
[5,1,8,4,2,6,3,7]=>[7,3,6,2,4,8,1,5]=>0000000=>0000000
[3,5,1,2,8,4,7,6]=>[6,7,4,8,2,1,5,3]=>0000000=>0000000
[2,8,3,1,5,6,7,4]=>[4,7,6,5,1,3,8,2]=>0000000=>0000000
[8,3,2,7,1,5,6,4]=>[4,6,5,1,7,2,3,8]=>0000001=>1000000
[8,2,7,1,5,4,6,3]=>[3,6,4,5,1,7,2,8]=>0000001=>1000000
[7,2,8,1,6,4,5,3]=>[3,5,4,6,1,8,2,7]=>0000000=>0000000
[8,7,2,4,1,6,5,3]=>[3,5,6,1,4,2,7,8]=>0000011=>1100000
[1,2,8,6,3,7,5,4]=>[4,5,7,3,6,8,2,1]=>0000000=>0000000
[1,7,3,8,2,6,4,5]=>[5,4,6,2,8,3,7,1]=>0000000=>0000000
[2,1,7,3,6,8,4,5]=>[5,4,8,6,3,7,1,2]=>0000000=>0000000
[7,1,5,8,3,2,4,6]=>[6,4,2,3,8,5,1,7]=>0000000=>0000000
[4,7,8,1,3,2,5,6]=>[6,5,2,3,1,8,7,4]=>0000000=>0000000
[2,1,8,3,5,7,4,6]=>[6,4,7,5,3,8,1,2]=>0000000=>0000000
[1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1]=>0000000=>0000000
[8,3,5,2,4,1,7,6]=>[6,7,1,4,2,5,3,8]=>0000001=>1000000
[8,6,2,5,3,1,7,4]=>[4,7,1,3,5,2,6,8]=>0000001=>1000000
[3,7,2,5,6,4,1,8]=>[8,1,4,6,5,2,7,3]=>0000000=>0000000
[7,6,2,5,4,3,1,8]=>[8,1,3,4,5,2,6,7]=>0000000=>0000000
[5,6,7,2,4,3,1,8]=>[8,1,3,4,2,7,6,5]=>0000000=>0000000
[8,7,2,3,1,6,5,4]=>[4,5,6,1,3,2,7,8]=>0000011=>1100000
[7,8,2,4,3,1,6,5]=>[5,6,1,3,4,2,8,7]=>0000010=>0100000
[4,5,8,2,3,1,7,6]=>[6,7,1,3,2,8,5,4]=>0000000=>0000000
[5,1,4,3,7,2,6,8]=>[8,6,2,7,3,4,1,5]=>0000000=>0000000
[6,1,3,5,7,2,4,8]=>[8,4,2,7,5,3,1,6]=>0000000=>0000000
[8,1,3,6,2,4,7,5]=>[5,7,4,2,6,3,1,8]=>0000001=>1000000
[6,2,5,8,1,4,7,3]=>[3,7,4,1,8,5,2,6]=>0000000=>0000000
[2,3,8,1,5,6,7,4]=>[4,7,6,5,1,8,3,2]=>0000000=>0000000
[4,8,7,5,1,6,3,2]=>[2,3,6,1,5,7,8,4]=>0000000=>0000000
[7,3,8,5,4,1,6,2]=>[2,6,1,4,5,8,3,7]=>0000000=>0000000
[3,6,4,1,5,2,7,8]=>[8,7,2,5,1,4,6,3]=>0000000=>0000000
[6,8,1,4,2,3,7,5]=>[5,7,3,2,4,1,8,6]=>0000000=>0000000
[1,8,2,7,5,4,6,3]=>[3,6,4,5,7,2,8,1]=>0000000=>0000000
[1,8,6,3,7,2,4,5]=>[5,4,2,7,3,6,8,1]=>0000000=>0000000
[7,2,8,4,3,5,6,1]=>[1,6,5,3,4,8,2,7]=>1000000=>0000001
[4,5,2,3,6,1,8,7]=>[7,8,1,6,3,2,5,4]=>0000000=>0000000
[4,6,5,3,7,1,8,2]=>[2,8,1,7,3,5,6,4]=>0000000=>0000000
[5,6,2,7,3,1,8,4]=>[4,8,1,3,7,2,6,5]=>0000000=>0000000
[1,6,3,7,5,8,2,4]=>[4,2,8,5,7,3,6,1]=>0000000=>0000000
[5,2,4,8,1,3,7,6]=>[6,7,3,1,8,4,2,5]=>0000000=>0000000
[6,2,5,4,8,3,7,1]=>[1,7,3,8,4,5,2,6]=>1000000=>0000001
[6,4,3,5,8,2,7,1]=>[1,7,2,8,5,3,4,6]=>1000000=>0000001
[5,2,3,4,8,1,6,7]=>[7,6,1,8,4,3,2,5]=>0000000=>0000000
[6,4,5,3,8,2,1,7]=>[7,1,2,8,3,5,4,6]=>0000000=>0000000
[6,5,3,4,8,7,1,2]=>[2,1,7,8,4,3,5,6]=>0100000=>0000010
[7,6,3,8,5,4,1,2]=>[2,1,4,5,8,3,6,7]=>0100000=>0000010
[5,4,8,1,2,7,3,6]=>[6,3,7,2,1,8,4,5]=>0000000=>0000000
[4,5,3,7,1,6,2,8]=>[8,2,6,1,7,3,5,4]=>0000000=>0000000
[7,2,8,6,1,3,4,5]=>[5,4,3,1,6,8,2,7]=>0000000=>0000000
[7,2,8,6,1,5,3,4]=>[4,3,5,1,6,8,2,7]=>0000000=>0000000
[5,2,6,4,7,8,3,1]=>[1,3,8,7,4,6,2,5]=>1000000=>0000001
[3,2,5,6,8,1,7,4]=>[4,7,1,8,6,5,2,3]=>0000000=>0000000
[2,6,1,5,4,8,3,7]=>[7,3,8,4,5,1,6,2]=>0000000=>0000000
[3,2,1,8,7,5,6,4]=>[4,6,5,7,8,1,2,3]=>0000000=>0000000
[3,1,6,2,5,8,4,7]=>[7,4,8,5,2,6,1,3]=>0000000=>0000000
[6,5,1,3,4,8,2,7]=>[7,2,8,4,3,1,5,6]=>0000000=>0000000
[2,3,4,8,1,7,6,5]=>[5,6,7,1,8,4,3,2]=>0000000=>0000000
[3,1,4,8,7,6,2,5]=>[5,2,6,7,8,4,1,3]=>0000000=>0000000
[6,3,2,8,5,7,4,1]=>[1,4,7,5,8,2,3,6]=>1000000=>0000001
[3,2,6,8,5,1,7,4]=>[4,7,1,5,8,6,2,3]=>0000000=>0000000
[5,2,4,1,7,8,6,3]=>[3,6,8,7,1,4,2,5]=>0000000=>0000000
[3,8,4,7,2,5,6,1]=>[1,6,5,2,7,4,8,3]=>1000000=>0000001
[5,3,7,1,6,2,8,4]=>[4,8,2,6,1,7,3,5]=>0000000=>0000000
[7,5,1,2,6,8,4,3]=>[3,4,8,6,2,1,5,7]=>0000000=>0000000
[1,2,5,3,8,7,6,4]=>[4,6,7,8,3,5,2,1]=>0000000=>0000000
[2,8,1,5,6,3,7,4]=>[4,7,3,6,5,1,8,2]=>0000000=>0000000
[8,1,2,4,6,7,3,5]=>[5,3,7,6,4,2,1,8]=>0000001=>1000000
[7,2,4,8,5,3,6,1]=>[1,6,3,5,8,4,2,7]=>1000000=>0000001
[3,7,5,1,8,4,6,2]=>[2,6,4,8,1,5,7,3]=>0000000=>0000000
[2,7,8,5,4,6,1,3]=>[3,1,6,4,5,8,7,2]=>0000000=>0000000
[6,5,3,1,8,4,2,7]=>[7,2,4,8,1,3,5,6]=>0000000=>0000000
[5,7,4,3,8,6,2,1]=>[1,2,6,8,3,4,7,5]=>1100000=>0000011
[8,3,1,7,4,2,5,6]=>[6,5,2,4,7,1,3,8]=>0000001=>1000000
[4,3,2,8,5,7,1,6]=>[6,1,7,5,8,2,3,4]=>0000000=>0000000
[3,6,4,2,8,5,7,1]=>[1,7,5,8,2,4,6,3]=>1000000=>0000001
[8,6,2,5,4,1,3,7]=>[7,3,1,4,5,2,6,8]=>0000001=>1000000
[8,3,5,7,6,2,1,4]=>[4,1,2,6,7,5,3,8]=>0000001=>1000000
[8,3,5,6,2,4,1,7]=>[7,1,4,2,6,5,3,8]=>0000001=>1000000
[8,3,2,4,6,1,5,7]=>[7,5,1,6,4,2,3,8]=>0000001=>1000000
[8,1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1,8]=>0000001=>1000000
[5,7,1,8,3,4,6,2]=>[2,6,4,3,8,1,7,5]=>0000000=>0000000
[1,5,6,7,3,4,8,2]=>[2,8,4,3,7,6,5,1]=>0000000=>0000000
[5,3,8,4,7,2,6,1]=>[1,6,2,7,4,8,3,5]=>1000000=>0000001
[4,8,1,2,7,3,6,5]=>[5,6,3,7,2,1,8,4]=>0000000=>0000000
[6,3,5,8,7,2,4,1]=>[1,4,2,7,8,5,3,6]=>1000000=>0000001
[5,2,8,7,1,3,4,6]=>[6,4,3,1,7,8,2,5]=>0000000=>0000000
[3,5,1,7,6,8,2,4]=>[4,2,8,6,7,1,5,3]=>0000000=>0000000
[1,7,6,5,2,4,8,3]=>[3,8,4,2,5,6,7,1]=>0000000=>0000000
[4,2,8,3,1,5,6,7]=>[7,6,5,1,3,8,2,4]=>0000000=>0000000
[2,5,7,3,8,4,6,1]=>[1,6,4,8,3,7,5,2]=>1000000=>0000001
[8,3,6,7,1,5,4,2]=>[2,4,5,1,7,6,3,8]=>0000001=>1000000
[5,7,4,8,3,6,2,1]=>[1,2,6,3,8,4,7,5]=>1100000=>0000011
[3,4,1,2,8,5,7,6]=>[6,7,5,8,2,1,4,3]=>0000000=>0000000
[1,8,3,2,4,7,5,6]=>[6,5,7,4,2,3,8,1]=>0000000=>0000000
[6,2,3,1,4,8,7,5]=>[5,7,8,4,1,3,2,6]=>0000000=>0000000
[8,4,3,2,5,7,1,6]=>[6,1,7,5,2,3,4,8]=>0000001=>1000000
[3,6,4,8,2,5,7,1]=>[1,7,5,2,8,4,6,3]=>1000000=>0000001
[4,3,7,2,5,8,1,6]=>[6,1,8,5,2,7,3,4]=>0000000=>0000000
[3,2,4,7,8,5,6,1]=>[1,6,5,8,7,4,2,3]=>1000000=>0000001
[2,6,4,3,8,5,1,7]=>[7,1,5,8,3,4,6,2]=>0000000=>0000000
[3,8,2,1,6,4,5,7]=>[7,5,4,6,1,2,8,3]=>0000000=>0000000
[5,3,6,8,2,1,4,7]=>[7,4,1,2,8,6,3,5]=>0000000=>0000000
[7,4,2,5,8,3,1,6]=>[6,1,3,8,5,2,4,7]=>0000000=>0000000
[5,6,8,1,4,3,2,7]=>[7,2,3,4,1,8,6,5]=>0000000=>0000000
[6,4,8,3,7,2,5,1]=>[1,5,2,7,3,8,4,6]=>1000000=>0000001
[8,7,5,3,6,4,2,1]=>[1,2,4,6,3,5,7,8]=>1100011=>1100011
[4,6,1,3,8,7,5,2]=>[2,5,7,8,3,1,6,4]=>0000000=>0000000
[6,8,2,1,7,4,5,3]=>[3,5,4,7,1,2,8,6]=>0000000=>0000000
[3,1,2,7,5,6,8,4]=>[4,8,6,5,7,2,1,3]=>0000000=>0000000
[3,6,1,2,7,5,8,4]=>[4,8,5,7,2,1,6,3]=>0000000=>0000000
[3,7,6,2,5,8,1,4]=>[4,1,8,5,2,6,7,3]=>0000000=>0000000
[8,5,2,3,6,7,4,1]=>[1,4,7,6,3,2,5,8]=>1000001=>1000001
[2,7,3,1,5,6,8,4]=>[4,8,6,5,1,3,7,2]=>0000000=>0000000
[6,3,2,4,8,7,5,1]=>[1,5,7,8,4,2,3,6]=>1000000=>0000001
[7,2,4,1,8,3,5,6]=>[6,5,3,8,1,4,2,7]=>0000000=>0000000
[4,8,7,6,3,2,1,5]=>[5,1,2,3,6,7,8,4]=>0000000=>0000000
[7,8,2,4,6,1,5,3]=>[3,5,1,6,4,2,8,7]=>0000010=>0100000
[6,4,8,7,2,5,1,3]=>[3,1,5,2,7,8,4,6]=>0000000=>0000000
[3,5,1,8,7,2,6,4]=>[4,6,2,7,8,1,5,3]=>0000000=>0000000
[6,2,1,3,8,7,5,4]=>[4,5,7,8,3,1,2,6]=>0000000=>0000000
[5,6,1,2,8,7,4,3]=>[3,4,7,8,2,1,6,5]=>0000000=>0000000
[2,7,6,8,1,5,4,3]=>[3,4,5,1,8,6,7,2]=>0000000=>0000000
[6,7,8,1,2,5,4,3]=>[3,4,5,2,1,8,7,6]=>0000100=>0010000
[8,6,4,3,2,1,7,5]=>[5,7,1,2,3,4,6,8]=>0000001=>1000000
[6,5,4,3,8,2,7,1]=>[1,7,2,8,3,4,5,6]=>1000000=>0000001
[7,5,4,3,2,8,6,1]=>[1,6,8,2,3,4,5,7]=>1000000=>0000001
[8,4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4,8]=>0000001=>1000000
[3,7,5,8,1,4,6,2]=>[2,6,4,1,8,5,7,3]=>0000000=>0000000
[5,7,2,4,6,8,1,3]=>[3,1,8,6,4,2,7,5]=>0000000=>0000000
[2,7,5,4,3,8,1,6]=>[6,1,8,3,4,5,7,2]=>0000000=>0000000
[8,6,4,2,3,7,5,1]=>[1,5,7,3,2,4,6,8]=>1000001=>1000001
[5,4,2,7,3,1,6,8]=>[8,6,1,3,7,2,4,5]=>0000000=>0000000
[3,1,2,4,8,7,6,5]=>[5,6,7,8,4,2,1,3]=>0000000=>0000000
[6,5,8,7,3,1,2,4]=>[4,2,1,3,7,8,5,6]=>0001000=>0001000
[5,6,7,8,1,4,2,3]=>[3,2,4,1,8,7,6,5]=>0001000=>0001000
[7,3,8,4,1,2,6,5]=>[5,6,2,1,4,8,3,7]=>0000000=>0000000
[6,8,3,2,7,1,5,4]=>[4,5,1,7,2,3,8,6]=>0000000=>0000000
[6,7,3,1,4,2,8,5]=>[5,8,2,4,1,3,7,6]=>0000000=>0000000
[2,7,8,3,4,5,1,6]=>[6,1,5,4,3,8,7,2]=>0000000=>0000000
[3,7,1,2,4,6,5,8]=>[8,5,6,4,2,1,7,3]=>0000000=>0000000
[5,8,6,7,1,2,3,4]=>[4,3,2,1,7,6,8,5]=>0001000=>0001000
[5,4,1,7,3,6,8,2]=>[2,8,6,3,7,1,4,5]=>0000000=>0000000
[3,4,7,6,2,5,8,1]=>[1,8,5,2,6,7,4,3]=>1000000=>0000001
[5,7,6,3,1,4,8,2]=>[2,8,4,1,3,6,7,5]=>0000000=>0000000
[4,8,3,6,5,2,1,7]=>[7,1,2,5,6,3,8,4]=>0000000=>0000000
[1,5,2,7,8,4,6,3]=>[3,6,4,8,7,2,5,1]=>0000000=>0000000
[7,1,4,5,8,6,2,3]=>[3,2,6,8,5,4,1,7]=>0000000=>0000000
[7,4,6,1,8,2,3,5]=>[5,3,2,8,1,6,4,7]=>0000000=>0000000
[5,7,6,8,4,2,1,3]=>[3,1,2,4,8,6,7,5]=>0011000=>0001100
[5,1,6,8,4,2,7,3]=>[3,7,2,4,8,6,1,5]=>0000000=>0000000
[5,6,8,4,7,3,2,1]=>[1,2,3,7,4,8,6,5]=>1110000=>0000111
[3,6,4,8,5,1,2,7]=>[7,2,1,5,8,4,6,3]=>0000000=>0000000
[7,4,3,8,2,6,5,1]=>[1,5,6,2,8,3,4,7]=>1000000=>0000001
[7,5,8,6,3,4,2,1]=>[1,2,4,3,6,8,5,7]=>1101000=>0001011
[5,7,8,3,1,6,4,2]=>[2,4,6,1,3,8,7,5]=>0000000=>0000000
[7,6,8,3,2,5,4,1]=>[1,4,5,2,3,8,6,7]=>1000100=>0010001
[7,5,8,3,2,4,1,6]=>[6,1,4,2,3,8,5,7]=>0000000=>0000000
[8,7,1,3,5,4,6,2]=>[2,6,4,5,3,1,7,8]=>0000011=>1100000
[7,1,8,3,4,2,6,5]=>[5,6,2,4,3,8,1,7]=>0000000=>0000000
[7,6,8,3,1,4,5,2]=>[2,5,4,1,3,8,6,7]=>0000100=>0010000
[6,4,1,8,2,5,7,3]=>[3,7,5,2,8,1,4,6]=>0000000=>0000000
[6,8,5,2,3,4,1,7]=>[7,1,4,3,2,5,8,6]=>0000000=>0000000
[2,6,8,7,1,5,3,4]=>[4,3,5,1,7,8,6,2]=>0000000=>0000000
[3,7,2,4,8,5,1,6]=>[6,1,5,8,4,2,7,3]=>0000000=>0000000
[7,4,3,2,8,5,1,6]=>[6,1,5,8,2,3,4,7]=>0000000=>0000000
[5,3,2,8,4,6,1,7]=>[7,1,6,4,8,2,3,5]=>0000000=>0000000
[1,5,2,6,3,8,7,4]=>[4,7,8,3,6,2,5,1]=>0000000=>0000000
[1,3,6,2,4,8,7,5]=>[5,7,8,4,2,6,3,1]=>0000000=>0000000
[1,5,3,2,8,4,7,6]=>[6,7,4,8,2,3,5,1]=>0000000=>0000000
[3,8,4,7,5,1,2,6]=>[6,2,1,5,7,4,8,3]=>0000000=>0000000
[2,1,7,3,4,8,6,5]=>[5,6,8,4,3,7,1,2]=>0000000=>0000000
[5,1,3,2,8,7,4,6]=>[6,4,7,8,2,3,1,5]=>0000000=>0000000
[1,8,3,7,2,6,5,4]=>[4,5,6,2,7,3,8,1]=>0000000=>0000000
[5,1,4,8,3,7,2,6]=>[6,2,7,3,8,4,1,5]=>0000000=>0000000
[8,3,1,6,7,2,5,4]=>[4,5,2,7,6,1,3,8]=>0000001=>1000000
[4,8,3,7,1,5,2,6]=>[6,2,5,1,7,3,8,4]=>0000000=>0000000
[1,5,4,8,3,2,7,6]=>[6,7,2,3,8,4,5,1]=>0000000=>0000000
[5,4,7,1,3,2,6,8]=>[8,6,2,3,1,7,4,5]=>0000000=>0000000
[5,7,4,8,2,1,3,6]=>[6,3,1,2,8,4,7,5]=>0000000=>0000000
[5,3,7,2,1,4,6,8]=>[8,6,4,1,2,7,3,5]=>0000000=>0000000
[7,4,8,5,1,6,3,2]=>[2,3,6,1,5,8,4,7]=>0000000=>0000000
[5,8,3,6,1,7,4,2]=>[2,4,7,1,6,3,8,5]=>0000000=>0000000
[8,6,4,2,1,7,5,3]=>[3,5,7,1,2,4,6,8]=>0000001=>1000000
[7,4,2,1,5,8,6,3]=>[3,6,8,5,1,2,4,7]=>0000000=>0000000
[7,6,4,1,8,5,2,3]=>[3,2,5,8,1,4,6,7]=>0000000=>0000000
[6,3,1,2,8,4,7,5]=>[5,7,4,8,2,1,3,6]=>0000000=>0000000
[6,8,4,1,2,7,5,3]=>[3,5,7,2,1,4,8,6]=>0000000=>0000000
[7,5,8,1,2,6,4,3]=>[3,4,6,2,1,8,5,7]=>0000000=>0000000
[6,4,1,8,3,2,7,5]=>[5,7,2,3,8,1,4,6]=>0000000=>0000000
[1,4,8,7,2,6,5,3]=>[3,5,6,2,7,8,4,1]=>0000000=>0000000
[5,4,1,8,7,3,2,6]=>[6,2,3,7,8,1,4,5]=>0000000=>0000000
[2,6,8,1,3,7,5,4]=>[4,5,7,3,1,8,6,2]=>0000000=>0000000
[6,2,8,3,1,7,5,4]=>[4,5,7,1,3,8,2,6]=>0000000=>0000000
[7,4,3,8,5,2,1,6]=>[6,1,2,5,8,3,4,7]=>0000000=>0000000
[6,5,2,8,4,3,1,7]=>[7,1,3,4,8,2,5,6]=>0000000=>0000000
[4,3,8,7,5,1,6,2]=>[2,6,1,5,7,8,3,4]=>0000000=>0000000
[5,2,6,8,4,1,3,7]=>[7,3,1,4,8,6,2,5]=>0000000=>0000000
[5,6,2,8,3,4,1,7]=>[7,1,4,3,8,2,6,5]=>0000000=>0000000
[5,3,8,7,4,1,6,2]=>[2,6,1,4,7,8,3,5]=>0000000=>0000000
[6,4,2,8,5,3,1,7]=>[7,1,3,5,8,2,4,6]=>0000000=>0000000
[8,7,4,3,6,2,5,1]=>[1,5,2,6,3,4,7,8]=>1000011=>1100001
[8,6,5,3,7,2,4,1]=>[1,4,2,7,3,5,6,8]=>1000001=>1000001
[7,6,4,3,8,2,5,1]=>[1,5,2,8,3,4,6,7]=>1000000=>0000001
[7,5,4,3,8,2,6,1]=>[1,6,2,8,3,4,5,7]=>1000000=>0000001
[6,4,5,3,8,2,7,1]=>[1,7,2,8,3,5,4,6]=>1000000=>0000001
[7,4,5,3,8,2,6,1]=>[1,6,2,8,3,5,4,7]=>1000000=>0000001
[7,4,6,3,8,2,5,1]=>[1,5,2,8,3,6,4,7]=>1000000=>0000001
[7,5,6,3,8,2,4,1]=>[1,4,2,8,3,6,5,7]=>1000000=>0000001
[8,5,6,3,7,2,4,1]=>[1,4,2,7,3,6,5,8]=>1000001=>1000001
[8,4,6,3,7,2,5,1]=>[1,5,2,7,3,6,4,8]=>1000001=>1000001
[7,4,6,3,5,2,8,1]=>[1,8,2,5,3,6,4,7]=>1000000=>0000001
[8,4,6,3,5,2,7,1]=>[1,7,2,5,3,6,4,8]=>1000001=>1000001
[8,4,7,3,5,2,6,1]=>[1,6,2,5,3,7,4,8]=>1000001=>1000001
[8,5,7,3,4,2,6,1]=>[1,6,2,4,3,7,5,8]=>1000001=>1000001
[7,5,8,4,3,2,6,1]=>[1,6,2,3,4,8,5,7]=>1000000=>0000001
[6,5,8,3,4,2,7,1]=>[1,7,2,4,3,8,5,6]=>1000000=>0000001
[7,5,8,3,4,2,6,1]=>[1,6,2,4,3,8,5,7]=>1000000=>0000001
[7,6,8,3,5,2,4,1]=>[1,4,2,5,3,8,6,7]=>1000100=>0010001
[7,5,8,4,6,2,3,1]=>[1,3,2,6,4,8,5,7]=>1010000=>0000101
[7,5,8,3,6,2,4,1]=>[1,4,2,6,3,8,5,7]=>1000000=>0000001
[7,4,8,3,6,2,5,1]=>[1,5,2,6,3,8,4,7]=>1000000=>0000001
[7,4,8,3,5,2,6,1]=>[1,6,2,5,3,8,4,7]=>1000000=>0000001
[6,4,8,3,5,2,7,1]=>[1,7,2,5,3,8,4,6]=>1000000=>0000001
[6,4,7,3,5,2,8,1]=>[1,8,2,5,3,7,4,6]=>1000000=>0000001
[5,4,7,3,6,2,8,1]=>[1,8,2,6,3,7,4,5]=>1000000=>0000001
[5,4,8,3,7,2,6,1]=>[1,6,2,7,3,8,4,5]=>1000000=>0000001
[6,5,8,3,7,2,4,1]=>[1,4,2,7,3,8,5,6]=>1000000=>0000001
[6,5,8,4,7,2,3,1]=>[1,3,2,7,4,8,5,6]=>1010000=>0000101
[6,5,8,4,7,3,2,1]=>[1,2,3,7,4,8,5,6]=>1110000=>0000111
[6,5,7,3,8,2,4,1]=>[1,4,2,8,3,7,5,6]=>1000000=>0000001
[6,4,7,3,8,2,5,1]=>[1,5,2,8,3,7,4,6]=>1000000=>0000001
[5,4,7,3,8,2,6,1]=>[1,6,2,8,3,7,4,5]=>1000000=>0000001
[5,4,6,3,8,2,7,1]=>[1,7,2,8,3,6,4,5]=>1000000=>0000001
[6,5,3,7,8,2,1,4]=>[4,1,2,8,7,3,5,6]=>0000000=>0000000
[6,5,4,2,8,7,1,3]=>[3,1,7,8,2,4,5,6]=>0000000=>0000000
[5,8,4,1,2,7,3,6]=>[6,3,7,2,1,4,8,5]=>0000000=>0000000
[5,4,8,1,2,3,7,6]=>[6,7,3,2,1,8,4,5]=>0000000=>0000000
[5,8,1,7,4,2,3,6]=>[6,3,2,4,7,1,8,5]=>0000000=>0000000
[4,3,2,8,1,7,6,5]=>[5,6,7,1,8,2,3,4]=>0000000=>0000000
[4,7,5,1,2,8,3,6]=>[6,3,8,2,1,5,7,4]=>0000000=>0000000
[2,3,6,7,4,1,8,5]=>[5,8,1,4,7,6,3,2]=>0000000=>0000000
[4,1,3,2,8,7,5,6]=>[6,5,7,8,2,3,1,4]=>0000000=>0000000
[4,3,1,2,8,5,7,6]=>[6,7,5,8,2,1,3,4]=>0000000=>0000000
[3,7,6,8,4,2,1,5]=>[5,1,2,4,8,6,7,3]=>0000000=>0000000
[2,4,6,8,3,1,7,5]=>[5,7,1,3,8,6,4,2]=>0000000=>0000000
[2,4,6,3,8,1,7,5]=>[5,7,1,8,3,6,4,2]=>0000000=>0000000
[4,7,1,5,8,2,3,6]=>[6,3,2,8,5,1,7,4]=>0000000=>0000000
[2,4,3,6,1,8,7,5]=>[5,7,8,1,6,3,4,2]=>0000000=>0000000
[2,6,7,3,8,4,1,5]=>[5,1,4,8,3,7,6,2]=>0000000=>0000000
[1,3,5,2,7,6,8,4]=>[4,8,6,7,2,5,3,1]=>0000000=>0000000
[1,3,5,7,6,2,4,8]=>[8,4,2,6,7,5,3,1]=>0000000=>0000000
[1,3,5,7,8,4,6,2]=>[2,6,4,8,7,5,3,1]=>0000000=>0000000
[1,3,5,7,8,6,2,4]=>[4,2,6,8,7,5,3,1]=>0000000=>0000000
[2,3,6,1,7,8,5,4]=>[4,5,8,7,1,6,3,2]=>0000000=>0000000
[2,3,6,7,4,8,5,1]=>[1,5,8,4,7,6,3,2]=>1000000=>0000001
[2,3,6,8,4,5,1,7]=>[7,1,5,4,8,6,3,2]=>0000000=>0000000
[2,5,7,3,4,8,6,1]=>[1,6,8,4,3,7,5,2]=>1000000=>0000001
[2,6,7,3,4,8,5,1]=>[1,5,8,4,3,7,6,2]=>1000000=>0000001
[5,1,4,6,8,2,3,7]=>[7,3,2,8,6,4,1,5]=>0000000=>0000000
[5,3,2,7,4,6,1,8]=>[8,1,6,4,7,2,3,5]=>0000000=>0000000
[4,1,2,5,8,3,7,6]=>[6,7,3,8,5,2,1,4]=>0000000=>0000000
[2,4,1,5,8,6,3,7]=>[7,3,6,8,5,1,4,2]=>0000000=>0000000
[4,6,1,2,5,8,3,7]=>[7,3,8,5,2,1,6,4]=>0000000=>0000000
[4,1,7,2,6,5,8,3]=>[3,8,5,6,2,7,1,4]=>0000000=>0000000
[5,6,7,2,1,4,8,3]=>[3,8,4,1,2,7,6,5]=>0000000=>0000000
[6,4,5,7,1,3,8,2]=>[2,8,3,1,7,5,4,6]=>0000000=>0000000
[5,7,6,8,1,4,2,3]=>[3,2,4,1,8,6,7,5]=>0001000=>0001000
[4,1,6,2,8,5,7,3]=>[3,7,5,8,2,6,1,4]=>0000000=>0000000
[6,4,2,1,3,8,7,5]=>[5,7,8,3,1,2,4,6]=>0000000=>0000000
[8,1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1,8]=>0000001=>1000000
[2,7,8,4,6,3,1,5]=>[5,1,3,6,4,8,7,2]=>0000000=>0000000
[6,3,7,5,1,8,2,4]=>[4,2,8,1,5,7,3,6]=>0000000=>0000000
[2,8,6,4,3,7,1,5]=>[5,1,7,3,4,6,8,2]=>0000000=>0000000
[5,8,4,6,1,7,2,3]=>[3,2,7,1,6,4,8,5]=>0000000=>0000000
[1,5,8,7,2,6,4,3]=>[3,4,6,2,7,8,5,1]=>0000000=>0000000
[2,5,8,7,3,6,1,4]=>[4,1,6,3,7,8,5,2]=>0000000=>0000000
[4,5,8,7,3,2,1,6]=>[6,1,2,3,7,8,5,4]=>0000000=>0000000
[2,6,8,3,7,5,1,4]=>[4,1,5,7,3,8,6,2]=>0000000=>0000000
[1,6,8,4,7,2,5,3]=>[3,5,2,7,4,8,6,1]=>0000000=>0000000
[1,6,8,3,7,2,5,4]=>[4,5,2,7,3,8,6,1]=>0000000=>0000000
[3,2,8,4,7,6,1,5]=>[5,1,6,7,4,8,2,3]=>0000000=>0000000
[1,5,8,4,7,2,6,3]=>[3,6,2,7,4,8,5,1]=>0000000=>0000000
[3,1,8,4,7,2,6,5]=>[5,6,2,7,4,8,1,3]=>0000000=>0000000
[1,6,8,4,2,7,5,3]=>[3,5,7,2,4,8,6,1]=>0000000=>0000000
[1,6,8,2,3,7,5,4]=>[4,5,7,3,2,8,6,1]=>0000000=>0000000
[5,6,8,4,1,2,7,3]=>[3,7,2,1,4,8,6,5]=>0000000=>0000000
[7,1,4,8,6,2,5,3]=>[3,5,2,6,8,4,1,7]=>0000000=>0000000
[7,3,4,8,6,2,1,5]=>[5,1,2,6,8,4,3,7]=>0000000=>0000000
[7,1,5,8,2,6,4,3]=>[3,4,6,2,8,5,1,7]=>0000000=>0000000
[7,1,4,8,2,6,5,3]=>[3,5,6,2,8,4,1,7]=>0000000=>0000000
[7,2,4,8,3,6,1,5]=>[5,1,6,3,8,4,2,7]=>0000000=>0000000
[3,6,2,8,7,5,1,4]=>[4,1,5,7,8,2,6,3]=>0000000=>0000000
[1,4,5,8,7,2,6,3]=>[3,6,2,7,8,5,4,1]=>0000000=>0000000
[3,1,4,8,7,2,6,5]=>[5,6,2,7,8,4,1,3]=>0000000=>0000000
[1,6,5,8,2,7,4,3]=>[3,4,7,2,8,5,6,1]=>0000000=>0000000
[2,6,5,8,3,7,1,4]=>[4,1,7,3,8,5,6,2]=>0000000=>0000000
[4,6,5,8,3,2,1,7]=>[7,1,2,3,8,5,6,4]=>0000000=>0000000
[7,6,2,3,8,5,1,4]=>[4,1,5,8,3,2,6,7]=>0000000=>0000000
[7,6,1,3,8,2,5,4]=>[4,5,2,8,3,1,6,7]=>0000000=>0000000
[7,2,5,3,8,6,1,4]=>[4,1,6,8,3,5,2,7]=>0000000=>0000000
[7,2,3,4,8,6,1,5]=>[5,1,6,8,4,3,2,7]=>0000000=>0000000
[2,6,1,4,8,7,5,3]=>[3,5,7,8,4,1,6,2]=>0000000=>0000000
[1,6,5,4,8,2,7,3]=>[3,7,2,8,4,5,6,1]=>0000000=>0000000
[1,3,5,4,8,2,7,6]=>[6,7,2,8,4,5,3,1]=>0000000=>0000000
[7,6,5,2,3,8,1,4]=>[4,1,8,3,2,5,6,7]=>0000000=>0000000
[7,6,1,4,2,8,5,3]=>[3,5,8,2,4,1,6,7]=>0000000=>0000000
[7,6,1,2,3,8,5,4]=>[4,5,8,3,2,1,6,7]=>0000000=>0000000
[7,1,5,4,2,8,6,3]=>[3,6,8,2,4,5,1,7]=>0000000=>0000000
[1,6,2,4,3,8,7,5]=>[5,7,8,3,4,2,6,1]=>0000000=>0000000
[2,6,5,4,3,8,1,7]=>[7,1,8,3,4,5,6,2]=>0000000=>0000000
[7,2,1,8,6,5,4,3]=>[3,4,5,6,8,1,2,7]=>0000000=>0000000
[4,8,5,7,6,3,2,1]=>[1,2,3,6,7,5,8,4]=>1110000=>0000111
[3,5,7,2,4,6,8,1]=>[1,8,6,4,2,7,5,3]=>1000000=>0000001
[5,2,4,6,8,1,3,7]=>[7,3,1,8,6,4,2,5]=>0000000=>0000000
[5,7,1,3,4,8,2,6]=>[6,2,8,4,3,1,7,5]=>0000000=>0000000
[5,7,1,3,4,6,8,2]=>[2,8,6,4,3,1,7,5]=>0000000=>0000000
[3,5,6,4,1,7,8,2]=>[2,8,7,1,4,6,5,3]=>0000000=>0000000
[2,6,7,4,5,8,1,3]=>[3,1,8,5,4,7,6,2]=>0000000=>0000000
[1,4,6,7,3,8,2,5]=>[5,2,8,3,7,6,4,1]=>0000000=>0000000
[5,3,6,1,2,7,8,4]=>[4,8,7,2,1,6,3,5]=>0000000=>0000000
[3,5,2,6,7,4,8,1]=>[1,8,4,7,6,2,5,3]=>1000000=>0000001
[5,2,6,1,3,7,8,4]=>[4,8,7,3,1,6,2,5]=>0000000=>0000000
[6,3,1,7,8,2,4,5]=>[5,4,2,8,7,1,3,6]=>0000000=>0000000
[5,7,2,8,1,3,4,6]=>[6,4,3,1,8,2,7,5]=>0000000=>0000000
[4,2,6,7,3,5,8,1]=>[1,8,5,3,7,6,2,4]=>1000000=>0000001
[3,5,7,2,6,8,1,4]=>[4,1,8,6,2,7,5,3]=>0000000=>0000000
[6,3,5,7,2,4,8,1]=>[1,8,4,2,7,5,3,6]=>1000000=>0000001
[6,2,4,5,1,7,8,3]=>[3,8,7,1,5,4,2,6]=>0000000=>0000000
[2,4,7,1,5,6,8,3]=>[3,8,6,5,1,7,4,2]=>0000000=>0000000
[3,7,1,5,6,8,2,4]=>[4,2,8,6,5,1,7,3]=>0000000=>0000000
[2,6,7,5,8,1,3,4]=>[4,3,1,8,5,7,6,2]=>0000000=>0000000
[5,6,2,4,1,7,8,3]=>[3,8,7,1,4,2,6,5]=>0000000=>0000000
[1,5,4,6,2,7,8,3]=>[3,8,7,2,6,4,5,1]=>0000000=>0000000
[8,4,5,2,6,1,3,7]=>[7,3,1,6,2,5,4,8]=>0000001=>1000000
[6,4,3,7,2,5,8,1]=>[1,8,5,2,7,3,4,6]=>1000000=>0000001
[6,4,3,7,2,8,1,5]=>[5,1,8,2,7,3,4,6]=>0000000=>0000000
[6,7,3,4,1,5,8,2]=>[2,8,5,1,4,3,7,6]=>0000000=>0000000
[6,7,4,2,1,5,8,3]=>[3,8,5,1,2,4,7,6]=>0000000=>0000000
[6,7,4,2,1,8,3,5]=>[5,3,8,1,2,4,7,6]=>0000000=>0000000
[5,6,7,3,1,8,2,4]=>[4,2,8,1,3,7,6,5]=>0000000=>0000000
[5,6,7,2,3,8,1,4]=>[4,1,8,3,2,7,6,5]=>0000000=>0000000
[7,6,3,4,1,2,8,5]=>[5,8,2,1,4,3,6,7]=>0000000=>0000000
[7,6,3,2,4,1,8,5]=>[5,8,1,4,2,3,6,7]=>0000000=>0000000
[7,5,3,2,6,1,8,4]=>[4,8,1,6,2,3,5,7]=>0000000=>0000000
[6,7,3,2,5,1,8,4]=>[4,8,1,5,2,3,7,6]=>0000000=>0000000
[6,5,3,2,7,8,1,4]=>[4,1,8,7,2,3,5,6]=>0000000=>0000000
[6,4,5,2,7,3,8,1]=>[1,8,3,7,2,5,4,6]=>1000000=>0000001
[6,4,7,2,5,1,8,3]=>[3,8,1,5,2,7,4,6]=>0000000=>0000000
[7,5,6,2,1,3,8,4]=>[4,8,3,1,2,6,5,7]=>0000000=>0000000
[6,4,7,5,1,2,8,3]=>[3,8,2,1,5,7,4,6]=>0000000=>0000000
[5,6,4,2,7,8,1,3]=>[3,1,8,7,2,4,6,5]=>0000000=>0000000
[5,6,4,2,7,3,8,1]=>[1,8,3,7,2,4,6,5]=>1000000=>0000001
[6,4,5,7,1,8,2,3]=>[3,2,8,1,7,5,4,6]=>0000000=>0000000
[6,5,3,7,1,8,2,4]=>[4,2,8,1,7,3,5,6]=>0000000=>0000000
[6,5,7,2,1,8,3,4]=>[4,3,8,1,2,7,5,6]=>0000000=>0000000
[1,7,8,5,6,3,4,2]=>[2,4,3,6,5,8,7,1]=>0000000=>0000000
[1,7,5,8,6,3,4,2]=>[2,4,3,6,8,5,7,1]=>0000000=>0000000
[7,3,5,8,6,4,1,2]=>[2,1,4,6,8,5,3,7]=>0100000=>0000010
[3,5,7,8,1,6,4,2]=>[2,4,6,1,8,7,5,3]=>0000000=>0000000
[7,3,8,5,6,1,4,2]=>[2,4,1,6,5,8,3,7]=>0000000=>0000000
[7,1,5,8,6,3,4,2]=>[2,4,3,6,8,5,1,7]=>0000000=>0000000
[5,1,7,8,6,3,4,2]=>[2,4,3,6,8,7,1,5]=>0000000=>0000000
[7,1,5,8,3,6,4,2]=>[2,4,6,3,8,5,1,7]=>0000000=>0000000
[7,3,8,5,1,6,4,2]=>[2,4,6,1,5,8,3,7]=>0000000=>0000000
[7,3,5,8,1,6,4,2]=>[2,4,6,1,8,5,3,7]=>0000000=>0000000
[7,3,5,1,8,6,4,2]=>[2,4,6,8,1,5,3,7]=>0000000=>0000000
[1,7,5,3,8,6,4,2]=>[2,4,6,8,3,5,7,1]=>0000000=>0000000
[3,7,5,1,8,6,4,2]=>[2,4,6,8,1,5,7,3]=>0000000=>0000000
[3,7,5,8,1,6,4,2]=>[2,4,6,1,8,5,7,3]=>0000000=>0000000
[1,7,5,8,3,6,4,2]=>[2,4,6,3,8,5,7,1]=>0000000=>0000000
[1,7,8,5,3,6,4,2]=>[2,4,6,3,5,8,7,1]=>0000000=>0000000
[5,7,8,1,6,3,4,2]=>[2,4,3,6,1,8,7,5]=>0000000=>0000000
[1,7,8,3,5,6,4,2]=>[2,4,6,5,3,8,7,1]=>0000000=>0000000
[7,5,1,8,6,3,4,2]=>[2,4,3,6,8,1,5,7]=>0000000=>0000000
[7,5,8,1,3,6,4,2]=>[2,4,6,3,1,8,5,7]=>0000000=>0000000
[7,3,1,5,8,6,4,2]=>[2,4,6,8,5,1,3,7]=>0000000=>0000000
[7,3,1,8,5,6,4,2]=>[2,4,6,5,8,1,3,7]=>0000000=>0000000
[5,1,3,7,8,6,4,2]=>[2,4,6,8,7,3,1,5]=>0000000=>0000000
[4,3,1,2,6,5,8,7]=>[7,8,5,6,2,1,3,4]=>0000000=>0000000
[5,4,7,8,6,1,3,2]=>[2,3,1,6,8,7,4,5]=>0010000=>0000100
[7,5,6,2,8,3,1,4]=>[4,1,3,8,2,6,5,7]=>0000000=>0000000
[4,6,3,5,1,2,8,7]=>[7,8,2,1,5,3,6,4]=>0000000=>0000000
[2,3,6,1,5,4,8,7]=>[7,8,4,5,1,6,3,2]=>0000000=>0000000
[2,1,6,5,3,4,8,7]=>[7,8,4,3,5,6,1,2]=>0000000=>0000000
[3,5,6,2,4,1,8,7]=>[7,8,1,4,2,6,5,3]=>0000000=>0000000
[8,7,6,1,3,2,4,5]=>[5,4,2,3,1,6,7,8]=>0000111=>1110000
[5,4,7,6,2,8,1,3]=>[3,1,8,2,6,7,4,5]=>0000000=>0000000
[3,7,8,1,5,4,6,2]=>[2,6,4,5,1,8,7,3]=>0000000=>0000000
[5,8,7,1,4,6,2,3]=>[3,2,6,4,1,7,8,5]=>0000000=>0000000
[4,7,6,1,8,3,5,2]=>[2,5,3,8,1,6,7,4]=>0000000=>0000000
[2,1,6,8,5,7,3,4]=>[4,3,7,5,8,6,1,2]=>0000000=>0000000
[4,7,8,6,3,1,2,5]=>[5,2,1,3,6,8,7,4]=>0000000=>0000000
[8,2,3,5,7,1,6,4]=>[4,6,1,7,5,3,2,8]=>0000001=>1000000
[2,8,3,6,7,5,1,4]=>[4,1,5,7,6,3,8,2]=>0000000=>0000000
[6,8,4,2,1,3,7,5]=>[5,7,3,1,2,4,8,6]=>0000000=>0000000
[4,3,8,2,7,6,1,5]=>[5,1,6,7,2,8,3,4]=>0000000=>0000000
[2,1,4,5,8,3,7,6]=>[6,7,3,8,5,4,1,2]=>0000000=>0000000
[8,4,7,1,5,2,3,6]=>[6,3,2,5,1,7,4,8]=>0000001=>1000000
[2,4,8,3,5,6,7,1]=>[1,7,6,5,3,8,4,2]=>1000000=>0000001
[2,1,4,3,8,7,5,6]=>[6,5,7,8,3,4,1,2]=>0000000=>0000000
[4,3,1,2,8,6,7,5]=>[5,7,6,8,2,1,3,4]=>0000000=>0000000
[5,1,6,7,8,4,3,2]=>[2,3,4,8,7,6,1,5]=>0000000=>0000000
[6,7,5,2,3,1,8,4]=>[4,8,1,3,2,5,7,6]=>0000000=>0000000
[4,7,2,6,5,1,8,3]=>[3,8,1,5,6,2,7,4]=>0000000=>0000000
[6,4,2,1,8,5,7,3]=>[3,7,5,8,1,2,4,6]=>0000000=>0000000
[2,1,5,7,8,4,6,3]=>[3,6,4,8,7,5,1,2]=>0000000=>0000000
[2,5,7,8,3,6,1,4]=>[4,1,6,3,8,7,5,2]=>0000000=>0000000
[7,1,4,8,3,5,6,2]=>[2,6,5,3,8,4,1,7]=>0000000=>0000000
[6,5,3,8,4,7,1,2]=>[2,1,7,4,8,3,5,6]=>0100000=>0000010
[1,6,3,7,5,8,4,2]=>[2,4,8,5,7,3,6,1]=>0000000=>0000000
[1,3,7,4,5,8,6,2]=>[2,6,8,5,4,7,3,1]=>0000000=>0000000
[7,3,8,5,4,6,1,2]=>[2,1,6,4,5,8,3,7]=>0100000=>0000010
[4,7,3,8,5,6,1,2]=>[2,1,6,5,8,3,7,4]=>0100000=>0000010
[2,7,6,3,1,4,5,8]=>[8,5,4,1,3,6,7,2]=>0000000=>0000000
[2,7,6,4,5,1,3,8]=>[8,3,1,5,4,6,7,2]=>0000000=>0000000
[5,7,2,6,4,1,3,8]=>[8,3,1,4,6,2,7,5]=>0000000=>0000000
[2,1,7,4,8,6,3,5]=>[5,3,6,8,4,7,1,2]=>0000000=>0000000
[2,1,3,8,4,7,5,6]=>[6,5,7,4,8,3,1,2]=>0000000=>0000000
[3,1,2,8,4,6,7,5]=>[5,7,6,4,8,2,1,3]=>0000000=>0000000
[5,1,2,4,8,3,7,6]=>[6,7,3,8,4,2,1,5]=>0000000=>0000000
[2,8,4,1,5,6,3,7]=>[7,3,6,5,1,4,8,2]=>0000000=>0000000
[1,7,2,8,5,3,6,4]=>[4,6,3,5,8,2,7,1]=>0000000=>0000000
[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>0000000=>0000000
[2,4,8,3,1,5,6,7]=>[7,6,5,1,3,8,4,2]=>0000000=>0000000
[3,2,5,6,1,4,7,8]=>[8,7,4,1,6,5,2,3]=>0000000=>0000000
[4,7,3,8,2,1,5,6]=>[6,5,1,2,8,3,7,4]=>0000000=>0000000
[7,4,8,3,2,1,5,6]=>[6,5,1,2,3,8,4,7]=>0000000=>0000000
[5,2,7,3,1,4,6,8]=>[8,6,4,1,3,7,2,5]=>0000000=>0000000
[8,3,7,2,1,5,4,6]=>[6,4,5,1,2,7,3,8]=>0000001=>1000000
[6,5,3,8,2,1,4,7]=>[7,4,1,2,8,3,5,6]=>0000000=>0000000
[7,6,2,1,8,5,3,4]=>[4,3,5,8,1,2,6,7]=>0000000=>0000000
[1,7,5,8,6,4,3,2]=>[2,3,4,6,8,5,7,1]=>0000000=>0000000
[6,5,1,2,8,3,7,4]=>[4,7,3,8,2,1,5,6]=>0000000=>0000000
[6,8,4,1,3,7,5,2]=>[2,5,7,3,1,4,8,6]=>0000000=>0000000
[6,3,7,1,8,4,5,2]=>[2,5,4,8,1,7,3,6]=>0000000=>0000000
[4,7,1,2,8,3,6,5]=>[5,6,3,8,2,1,7,4]=>0000000=>0000000
[3,4,1,8,5,6,7,2]=>[2,7,6,5,8,1,4,3]=>0000000=>0000000
[8,3,1,7,5,4,6,2]=>[2,6,4,5,7,1,3,8]=>0000001=>1000000
[2,3,1,8,7,4,5,6]=>[6,5,4,7,8,1,3,2]=>0000000=>0000000
[6,2,7,1,8,5,3,4]=>[4,3,5,8,1,7,2,6]=>0000000=>0000000
[1,2,3,8,6,4,5,7]=>[7,5,4,6,8,3,2,1]=>0000000=>0000000
[2,4,7,5,6,8,3,1]=>[1,3,8,6,5,7,4,2]=>1000000=>0000001
[2,8,5,7,4,6,3,1]=>[1,3,6,4,7,5,8,2]=>1000000=>0000001
[8,3,5,7,4,2,6,1]=>[1,6,2,4,7,5,3,8]=>1000001=>1000001
[2,7,5,8,4,6,3,1]=>[1,3,6,4,8,5,7,2]=>1000000=>0000001
[2,7,6,4,5,8,3,1]=>[1,3,8,5,4,6,7,2]=>1000000=>0000001
[3,1,7,6,4,5,2,8]=>[8,2,5,4,6,7,1,3]=>0000000=>0000000
[6,3,8,7,5,2,4,1]=>[1,4,2,5,7,8,3,6]=>1000000=>0000001
[7,3,5,8,4,2,6,1]=>[1,6,2,4,8,5,3,7]=>1000000=>0000001
[7,8,3,6,2,5,4,1]=>[1,4,5,2,6,3,8,7]=>1000010=>0100001
[7,4,8,2,1,6,3,5]=>[5,3,6,1,2,8,4,7]=>0000000=>0000000
[7,8,5,2,1,4,3,6]=>[6,3,4,1,2,5,8,7]=>0000010=>0100000
[7,4,6,2,3,8,1,5]=>[5,1,8,3,2,6,4,7]=>0000000=>0000000
[5,7,1,3,4,6,2,8]=>[8,2,6,4,3,1,7,5]=>0000000=>0000000
[5,6,1,2,4,3,8,7]=>[7,8,3,4,2,1,6,5]=>0000000=>0000000
[3,6,8,1,2,7,5,4]=>[4,5,7,2,1,8,6,3]=>0000000=>0000000
[8,4,6,2,1,3,7,5]=>[5,7,3,1,2,6,4,8]=>0000001=>1000000
[5,4,8,7,2,3,6,1]=>[1,6,3,2,7,8,4,5]=>1000000=>0000001
[5,4,8,7,3,1,2,6]=>[6,2,1,3,7,8,4,5]=>0000000=>0000000
[6,4,3,8,1,5,2,7]=>[7,2,5,1,8,3,4,6]=>0000000=>0000000
[6,8,3,7,2,5,4,1]=>[1,4,5,2,7,3,8,6]=>1000000=>0000001
[5,3,6,8,7,2,4,1]=>[1,4,2,7,8,6,3,5]=>1000000=>0000001
[5,4,6,8,2,3,7,1]=>[1,7,3,2,8,6,4,5]=>1000000=>0000001
[6,4,7,2,1,8,3,5]=>[5,3,8,1,2,7,4,6]=>0000000=>0000000
[6,5,3,4,1,2,8,7]=>[7,8,2,1,4,3,5,6]=>0000000=>0000000
[6,5,3,1,4,7,2,8]=>[8,2,7,4,1,3,5,6]=>0000000=>0000000
[2,6,8,4,5,7,1,3]=>[3,1,7,5,4,8,6,2]=>0000000=>0000000
[1,7,4,8,6,2,3,5]=>[5,3,2,6,8,4,7,1]=>0000000=>0000000
[6,3,7,2,8,5,1,4]=>[4,1,5,8,2,7,3,6]=>0000000=>0000000
[5,2,7,4,6,8,1,3]=>[3,1,8,6,4,7,2,5]=>0000000=>0000000
[6,2,7,3,1,5,8,4]=>[4,8,5,1,3,7,2,6]=>0000000=>0000000
[6,3,4,1,8,5,7,2]=>[2,7,5,8,1,4,3,6]=>0000000=>0000000
[4,5,3,2,7,1,8,6]=>[6,8,1,7,2,3,5,4]=>0000000=>0000000
[3,6,4,8,1,5,7,2]=>[2,7,5,1,8,4,6,3]=>0000000=>0000000
[4,5,8,3,1,7,6,2]=>[2,6,7,1,3,8,5,4]=>0000000=>0000000
[4,6,3,5,2,1,8,7]=>[7,8,1,2,5,3,6,4]=>0000000=>0000000
[3,6,2,1,4,7,5,8]=>[8,5,7,4,1,2,6,3]=>0000000=>0000000
[7,4,1,2,8,6,3,5]=>[5,3,6,8,2,1,4,7]=>0000000=>0000000
[4,2,7,6,5,8,1,3]=>[3,1,8,5,6,7,2,4]=>0000000=>0000000
[7,3,8,1,5,4,6,2]=>[2,6,4,5,1,8,3,7]=>0000000=>0000000
[5,3,2,6,7,4,1,8]=>[8,1,4,7,6,2,3,5]=>0000000=>0000000
[4,8,2,6,5,7,1,3]=>[3,1,7,5,6,2,8,4]=>0000000=>0000000
[3,8,7,6,2,4,1,5]=>[5,1,4,2,6,7,8,3]=>0000000=>0000000
[5,7,1,4,6,3,2,8]=>[8,2,3,6,4,1,7,5]=>0000000=>0000000
[1,4,8,2,7,6,3,5]=>[5,3,6,7,2,8,4,1]=>0000000=>0000000
[2,5,8,7,4,6,1,3]=>[3,1,6,4,7,8,5,2]=>0000000=>0000000
[5,7,8,3,2,1,4,6]=>[6,4,1,2,3,8,7,5]=>0000000=>0000000
[8,3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3,8]=>0000001=>1000000
[1,7,5,3,8,2,6,4]=>[4,6,2,8,3,5,7,1]=>0000000=>0000000
[2,7,5,1,3,8,6,4]=>[4,6,8,3,1,5,7,2]=>0000000=>0000000
[8,7,4,2,6,1,5,3]=>[3,5,1,6,2,4,7,8]=>0000011=>1100000
[3,4,2,8,7,6,1,5]=>[5,1,6,7,8,2,4,3]=>0000000=>0000000
[6,7,2,5,8,4,3,1]=>[1,3,4,8,5,2,7,6]=>1000000=>0000001
[2,7,6,4,1,3,8,5]=>[5,8,3,1,4,6,7,2]=>0000000=>0000000
[6,2,7,5,3,1,8,4]=>[4,8,1,3,5,7,2,6]=>0000000=>0000000
[1,5,8,2,7,4,6,3]=>[3,6,4,7,2,8,5,1]=>0000000=>0000000
[5,7,3,1,8,4,6,2]=>[2,6,4,8,1,3,7,5]=>0000000=>0000000
[8,4,7,3,1,6,5,2]=>[2,5,6,1,3,7,4,8]=>0000001=>1000000
[5,6,4,8,3,7,2,1]=>[1,2,7,3,8,4,6,5]=>1100000=>0000011
[1,8,6,7,3,4,2,5]=>[5,2,4,3,7,6,8,1]=>0000000=>0000000
[7,8,1,6,3,4,2,5]=>[5,2,4,3,6,1,8,7]=>0000010=>0100000
[7,8,2,5,1,6,3,4]=>[4,3,6,1,5,2,8,7]=>0000010=>0100000
[5,7,1,6,2,8,3,4]=>[4,3,8,2,6,1,7,5]=>0000000=>0000000
[5,6,2,7,1,8,3,4]=>[4,3,8,1,7,2,6,5]=>0000000=>0000000
[6,7,2,5,1,8,3,4]=>[4,3,8,1,5,2,7,6]=>0000000=>0000000
[2,6,5,8,1,7,3,4]=>[4,3,7,1,8,5,6,2]=>0000000=>0000000
[2,3,1,8,5,6,4,7]=>[7,4,6,5,8,1,3,2]=>0000000=>0000000
[5,7,2,3,1,6,4,8]=>[8,4,6,1,3,2,7,5]=>0000000=>0000000
[5,7,2,4,3,6,1,8]=>[8,1,6,3,4,2,7,5]=>0000000=>0000000
[4,7,1,6,2,5,3,8]=>[8,3,5,2,6,1,7,4]=>0000000=>0000000
[4,6,3,5,1,7,2,8]=>[8,2,7,1,5,3,6,4]=>0000000=>0000000
[6,7,3,5,1,4,2,8]=>[8,2,4,1,5,3,7,6]=>0000000=>0000000
[1,8,5,6,3,4,2,7]=>[7,2,4,3,6,5,8,1]=>0000000=>0000000
[1,8,5,6,4,7,2,3]=>[3,2,7,4,6,5,8,1]=>0000000=>0000000
[5,7,1,6,4,8,2,3]=>[3,2,8,4,6,1,7,5]=>0000000=>0000000
[4,6,5,8,1,7,2,3]=>[3,2,7,1,8,5,6,4]=>0000000=>0000000
[4,7,1,8,5,6,2,3]=>[3,2,6,5,8,1,7,4]=>0000000=>0000000
[3,5,4,6,2,8,1,7]=>[7,1,8,2,6,4,5,3]=>0000000=>0000000
[3,5,2,7,4,8,1,6]=>[6,1,8,4,7,2,5,3]=>0000000=>0000000
[2,7,1,3,4,8,6,5]=>[5,6,8,4,3,1,7,2]=>0000000=>0000000
[4,2,1,6,5,3,8,7]=>[7,8,3,5,6,1,2,4]=>0000000=>0000000
[4,2,6,3,5,1,8,7]=>[7,8,1,5,3,6,2,4]=>0000000=>0000000
[6,8,2,1,7,4,3,5]=>[5,3,4,7,1,2,8,6]=>0000000=>0000000
[4,8,2,1,6,7,3,5]=>[5,3,7,6,1,2,8,4]=>0000000=>0000000
[2,8,6,7,4,3,1,5]=>[5,1,3,4,7,6,8,2]=>0000000=>0000000
[2,6,4,5,8,3,7,1]=>[1,7,3,8,5,4,6,2]=>1000000=>0000001
[4,2,1,6,8,7,5,3]=>[3,5,7,8,6,1,2,4]=>0000000=>0000000
[6,4,8,5,7,2,1,3]=>[3,1,2,7,5,8,4,6]=>0010000=>0000100
[4,6,5,8,7,2,1,3]=>[3,1,2,7,8,5,6,4]=>0010000=>0000100
[6,4,8,2,1,5,7,3]=>[3,7,5,1,2,8,4,6]=>0000000=>0000000
[2,6,8,4,7,1,5,3]=>[3,5,1,7,4,8,6,2]=>0000000=>0000000
[6,2,3,5,1,4,8,7]=>[7,8,4,1,5,3,2,6]=>0000000=>0000000
[7,3,2,5,4,8,6,1]=>[1,6,8,4,5,2,3,7]=>1000000=>0000001
[3,5,1,6,4,2,8,7]=>[7,8,2,4,6,1,5,3]=>0000000=>0000000
[3,6,2,4,5,1,8,7]=>[7,8,1,5,4,2,6,3]=>0000000=>0000000
[5,7,1,3,8,6,2,4]=>[4,2,6,8,3,1,7,5]=>0000000=>0000000
[4,8,1,5,6,7,3,2]=>[2,3,7,6,5,1,8,4]=>0000000=>0000000
[5,8,2,4,6,7,1,3]=>[3,1,7,6,4,2,8,5]=>0000000=>0000000
[3,8,2,5,4,7,6,1]=>[1,6,7,4,5,2,8,3]=>1000000=>0000001
[4,6,7,1,8,5,3,2]=>[2,3,5,8,1,7,6,4]=>0000000=>0000000
[3,6,1,7,8,5,4,2]=>[2,4,5,8,7,1,6,3]=>0000000=>0000000
[2,1,5,7,3,8,6,4]=>[4,6,8,3,7,5,1,2]=>0000000=>0000000
[5,4,7,1,2,8,6,3]=>[3,6,8,2,1,7,4,5]=>0000000=>0000000
[6,4,7,2,8,5,3,1]=>[1,3,5,8,2,7,4,6]=>1000000=>0000001
[4,1,2,3,7,8,6,5]=>[5,6,8,7,3,2,1,4]=>0000000=>0000000
[3,4,2,1,8,5,6,7]=>[7,6,5,8,1,2,4,3]=>0000000=>0000000
[7,2,3,6,8,4,1,5]=>[5,1,4,8,6,3,2,7]=>0000000=>0000000
[8,2,3,5,7,1,4,6]=>[6,4,1,7,5,3,2,8]=>0000001=>1000000
[4,5,8,3,6,7,2,1]=>[1,2,7,6,3,8,5,4]=>1100000=>0000011
[2,1,5,8,4,6,7,3]=>[3,7,6,4,8,5,1,2]=>0000000=>0000000
[6,8,2,3,1,4,5,7]=>[7,5,4,1,3,2,8,6]=>0000000=>0000000
[3,1,5,2,4,8,7,6]=>[6,7,8,4,2,5,1,3]=>0000000=>0000000
[3,6,4,5,1,8,7,2]=>[2,7,8,1,5,4,6,3]=>0000000=>0000000
[4,3,6,1,2,8,7,5]=>[5,7,8,2,1,6,3,4]=>0000000=>0000000
[8,1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1,8]=>0000001=>1000000
[6,8,3,1,4,7,5,2]=>[2,5,7,4,1,3,8,6]=>0000000=>0000000
[1,8,3,2,4,5,7,6]=>[6,7,5,4,2,3,8,1]=>0000000=>0000000
[8,4,2,5,7,1,6,3]=>[3,6,1,7,5,2,4,8]=>0000001=>1000000
[1,8,5,3,7,4,6,2]=>[2,6,4,7,3,5,8,1]=>0000000=>0000000
[5,3,2,8,7,1,4,6]=>[6,4,1,7,8,2,3,5]=>0000000=>0000000
[4,2,8,5,7,6,1,3]=>[3,1,6,7,5,8,2,4]=>0000000=>0000000
[4,2,1,7,5,3,6,8]=>[8,6,3,5,7,1,2,4]=>0000000=>0000000
[4,3,1,8,5,6,7,2]=>[2,7,6,5,8,1,3,4]=>0000000=>0000000
[1,8,5,4,3,6,2,7]=>[7,2,6,3,4,5,8,1]=>0000000=>0000000
[4,7,1,8,2,6,5,3]=>[3,5,6,2,8,1,7,4]=>0000000=>0000000
[1,4,8,3,5,7,6,2]=>[2,6,7,5,3,8,4,1]=>0000000=>0000000
[6,3,5,1,4,2,8,7]=>[7,8,2,4,1,5,3,6]=>0000000=>0000000
[6,3,1,2,8,5,7,4]=>[4,7,5,8,2,1,3,6]=>0000000=>0000000
[5,3,8,7,2,1,4,6]=>[6,4,1,2,7,8,3,5]=>0000000=>0000000
[7,6,5,4,1,3,2,8]=>[8,2,3,1,4,5,6,7]=>0000000=>0000000
[1,2,3,4,5,10,9,8,7,6]=>[6,7,8,9,10,5,4,3,2,1]=>000000000=>000000000
[4,6,3,1,5,2,7,8]=>[8,7,2,5,1,3,6,4]=>0000000=>0000000
[5,2,7,4,1,6,3,8]=>[8,3,6,1,4,7,2,5]=>0000000=>0000000
[6,2,3,7,5,1,4,8]=>[8,4,1,5,7,3,2,6]=>0000000=>0000000
[4,2,6,1,5,3,7,8]=>[8,7,3,5,1,6,2,4]=>0000000=>0000000
[5,2,6,4,1,3,7,8]=>[8,7,3,1,4,6,2,5]=>0000000=>0000000
[1,2,7,8,5,6,3,4]=>[4,3,6,5,8,7,2,1]=>0000000=>0000000
[1,2,6,8,5,3,7,4]=>[4,7,3,5,8,6,2,1]=>0000000=>0000000
[1,2,6,4,8,3,7,5]=>[5,7,3,8,4,6,2,1]=>0000000=>0000000
[8,7,4,1,6,2,3,5]=>[5,3,2,6,1,4,7,8]=>0000011=>1100000
[6,4,2,8,1,5,7,3]=>[3,7,5,1,8,2,4,6]=>0000000=>0000000
[7,3,6,8,5,2,4,1]=>[1,4,2,5,8,6,3,7]=>1000000=>0000001
[2,7,8,3,6,5,1,4]=>[4,1,5,6,3,8,7,2]=>0000000=>0000000
[2,7,8,5,4,6,3,1]=>[1,3,6,4,5,8,7,2]=>1000000=>0000001
[2,7,8,3,6,1,4,5]=>[5,4,1,6,3,8,7,2]=>0000000=>0000000
[2,1,3,7,8,5,6,4]=>[4,6,5,8,7,3,1,2]=>0000000=>0000000
[5,1,2,4,8,7,3,6]=>[6,3,7,8,4,2,1,5]=>0000000=>0000000
[2,6,3,1,8,7,4,5]=>[5,4,7,8,1,3,6,2]=>0000000=>0000000
[5,2,6,1,7,8,4,3]=>[3,4,8,7,1,6,2,5]=>0000000=>0000000
[3,6,5,4,1,8,7,2]=>[2,7,8,1,4,5,6,3]=>0000000=>0000000
[5,2,3,4,8,7,1,6]=>[6,1,7,8,4,3,2,5]=>0000000=>0000000
[3,2,7,6,4,1,8,5]=>[5,8,1,4,6,7,2,3]=>0000000=>0000000
[5,3,2,8,1,6,4,7]=>[7,4,6,1,8,2,3,5]=>0000000=>0000000
[6,4,7,2,5,8,1,3]=>[3,1,8,5,2,7,4,6]=>0000000=>0000000
[8,5,1,2,6,4,3,7]=>[7,3,4,6,2,1,5,8]=>0000001=>1000000
[2,4,6,5,1,7,8,3]=>[3,8,7,1,5,6,4,2]=>0000000=>0000000
[5,6,1,7,4,2,8,3]=>[3,8,2,4,7,1,6,5]=>0000000=>0000000
[3,7,4,8,1,2,6,5]=>[5,6,2,1,8,4,7,3]=>0000000=>0000000
[1,3,8,6,2,7,4,5]=>[5,4,7,2,6,8,3,1]=>0000000=>0000000
[4,3,7,5,6,1,8,2]=>[2,8,1,6,5,7,3,4]=>0000000=>0000000
[6,4,7,8,2,1,3,5]=>[5,3,1,2,8,7,4,6]=>0000000=>0000000
[2,7,8,3,4,6,1,5]=>[5,1,6,4,3,8,7,2]=>0000000=>0000000
[3,7,8,1,5,4,2,6]=>[6,2,4,5,1,8,7,3]=>0000000=>0000000
[4,6,7,2,8,3,1,5]=>[5,1,3,8,2,7,6,4]=>0000000=>0000000
[7,6,8,5,1,3,2,4]=>[4,2,3,1,5,8,6,7]=>0001100=>0011000
[4,5,6,7,3,1,8,2]=>[2,8,1,3,7,6,5,4]=>0000000=>0000000
[8,7,6,4,1,2,5,3]=>[3,5,2,1,4,6,7,8]=>0000111=>1110000
[8,5,3,2,7,6,1,4]=>[4,1,6,7,2,3,5,8]=>0000001=>1000000
[2,6,4,5,7,8,3,1]=>[1,3,8,7,5,4,6,2]=>1000000=>0000001
[7,5,2,8,4,1,3,6]=>[6,3,1,4,8,2,5,7]=>0000000=>0000000
[7,3,8,5,2,1,4,6]=>[6,4,1,2,5,8,3,7]=>0000000=>0000000
[5,8,2,1,6,7,4,3]=>[3,4,7,6,1,2,8,5]=>0000000=>0000000
[3,7,6,8,1,2,5,4]=>[4,5,2,1,8,6,7,3]=>0000000=>0000000
[6,5,1,4,2,3,8,7]=>[7,8,3,2,4,1,5,6]=>0000000=>0000000
[4,1,6,3,2,5,8,7]=>[7,8,5,2,3,6,1,4]=>0000000=>0000000
[8,7,6,1,2,3,5,4]=>[4,5,3,2,1,6,7,8]=>0000111=>1110000
[5,4,1,6,2,3,8,7]=>[7,8,3,2,6,1,4,5]=>0000000=>0000000
[5,8,7,6,1,2,3,4]=>[4,3,2,1,6,7,8,5]=>0001000=>0001000
[2,1,8,7,3,6,4,5]=>[5,4,6,3,7,8,1,2]=>0000000=>0000000
[2,1,6,3,8,5,4,7]=>[7,4,5,8,3,6,1,2]=>0000000=>0000000
[2,6,3,1,8,5,4,7]=>[7,4,5,8,1,3,6,2]=>0000000=>0000000
[4,6,2,8,5,1,3,7]=>[7,3,1,5,8,2,6,4]=>0000000=>0000000
[5,2,1,8,7,3,4,6]=>[6,4,3,7,8,1,2,5]=>0000000=>0000000
[6,5,2,7,4,3,8,1]=>[1,8,3,4,7,2,5,6]=>1000000=>0000001
[4,6,5,2,7,3,8,1]=>[1,8,3,7,2,5,6,4]=>1000000=>0000001
[2,7,5,4,8,3,6,1]=>[1,6,3,8,4,5,7,2]=>1000000=>0000001
[3,1,6,2,4,8,7,5]=>[5,7,8,4,2,6,1,3]=>0000000=>0000000
[2,1,7,6,3,8,4,5]=>[5,4,8,3,6,7,1,2]=>0000000=>0000000
[7,1,6,2,3,8,5,4]=>[4,5,8,3,2,6,1,7]=>0000000=>0000000
[8,2,3,4,6,7,1,5]=>[5,1,7,6,4,3,2,8]=>0000001=>1000000
[6,4,8,3,5,7,1,2]=>[2,1,7,5,3,8,4,6]=>0100000=>0000010
[8,5,7,4,6,2,1,3]=>[3,1,2,6,4,7,5,8]=>0010001=>1000100
[5,8,3,2,4,6,1,7]=>[7,1,6,4,2,3,8,5]=>0000000=>0000000
[2,8,4,1,5,3,7,6]=>[6,7,3,5,1,4,8,2]=>0000000=>0000000
[2,1,7,6,5,3,8,4]=>[4,8,3,5,6,7,1,2]=>0000000=>0000000
[4,7,6,1,2,5,8,3]=>[3,8,5,2,1,6,7,4]=>0000000=>0000000
[3,6,7,1,8,5,2,4]=>[4,2,5,8,1,7,6,3]=>0000000=>0000000
[6,5,7,3,1,8,4,2]=>[2,4,8,1,3,7,5,6]=>0000000=>0000000
[5,7,2,3,6,4,8,1]=>[1,8,4,6,3,2,7,5]=>1000000=>0000001
[7,8,6,1,3,2,5,4]=>[4,5,2,3,1,6,8,7]=>0000110=>0110000
[6,8,5,4,2,7,3,1]=>[1,3,7,2,4,5,8,6]=>1000000=>0000001
[4,1,3,8,7,5,6,2]=>[2,6,5,7,8,3,1,4]=>0000000=>0000000
[2,1,4,6,8,3,7,5]=>[5,7,3,8,6,4,1,2]=>0000000=>0000000
[5,4,1,6,3,8,7,2]=>[2,7,8,3,6,1,4,5]=>0000000=>0000000
[3,5,6,2,4,8,7,1]=>[1,7,8,4,2,6,5,3]=>1000000=>0000001
[6,2,7,4,8,1,3,5]=>[5,3,1,8,4,7,2,6]=>0000000=>0000000
[5,4,1,2,8,7,6,3]=>[3,6,7,8,2,1,4,5]=>0000000=>0000000
[4,3,2,6,8,1,7,5]=>[5,7,1,8,6,2,3,4]=>0000000=>0000000
[7,1,5,6,3,8,2,4]=>[4,2,8,3,6,5,1,7]=>0000000=>0000000
[1,5,4,2,7,8,3,6]=>[6,3,8,7,2,4,5,1]=>0000000=>0000000
[6,1,2,8,7,4,3,5]=>[5,3,4,7,8,2,1,6]=>0000000=>0000000
[5,1,6,8,4,7,2,3]=>[3,2,7,4,8,6,1,5]=>0000000=>0000000
[5,6,8,1,7,3,2,4]=>[4,2,3,7,1,8,6,5]=>0000000=>0000000
[6,4,3,8,2,5,7,1]=>[1,7,5,2,8,3,4,6]=>1000000=>0000001
[5,8,2,3,6,4,1,7]=>[7,1,4,6,3,2,8,5]=>0000000=>0000000
[2,1,7,8,3,4,6,5]=>[5,6,4,3,8,7,1,2]=>0000000=>0000000
[3,5,8,7,4,2,6,1]=>[1,6,2,4,7,8,5,3]=>1000000=>0000001
[7,5,1,8,4,2,6,3]=>[3,6,2,4,8,1,5,7]=>0000000=>0000000
[5,6,1,8,2,7,4,3]=>[3,4,7,2,8,1,6,5]=>0000000=>0000000
[2,1,6,5,4,8,3,7]=>[7,3,8,4,5,6,1,2]=>0000000=>0000000
[2,1,7,8,4,6,5,3]=>[3,5,6,4,8,7,1,2]=>0000000=>0000000
[2,1,7,3,5,8,6,4]=>[4,6,8,5,3,7,1,2]=>0000000=>0000000
[3,8,7,4,1,2,5,6]=>[6,5,2,1,4,7,8,3]=>0000000=>0000000
[3,6,8,1,5,7,2,4]=>[4,2,7,5,1,8,6,3]=>0000000=>0000000
[3,5,7,8,4,6,1,2]=>[2,1,6,4,8,7,5,3]=>0100000=>0000010
[7,8,2,4,3,1,5,6]=>[6,5,1,3,4,2,8,7]=>0000010=>0100000
[6,2,7,1,3,5,8,4]=>[4,8,5,3,1,7,2,6]=>0000000=>0000000
[6,1,8,2,3,5,4,7]=>[7,4,5,3,2,8,1,6]=>0000000=>0000000
[7,2,4,1,6,3,8,5]=>[5,8,3,6,1,4,2,7]=>0000000=>0000000
[7,6,2,8,5,1,4,3]=>[3,4,1,5,8,2,6,7]=>0000000=>0000000
[5,3,2,4,7,8,6,1]=>[1,6,8,7,4,2,3,5]=>1000000=>0000001
[5,2,4,3,6,8,1,7]=>[7,1,8,6,3,4,2,5]=>0000000=>0000000
[3,7,5,8,1,6,2,4]=>[4,2,6,1,8,5,7,3]=>0000000=>0000000
[3,7,6,4,5,1,8,2]=>[2,8,1,5,4,6,7,3]=>0000000=>0000000
[4,7,5,6,3,8,2,1]=>[1,2,8,3,6,5,7,4]=>1100000=>0000011
[3,8,5,7,1,4,6,2]=>[2,6,4,1,7,5,8,3]=>0000000=>0000000
[5,8,2,7,3,4,6,1]=>[1,6,4,3,7,2,8,5]=>1000000=>0000001
[5,7,2,8,3,6,1,4]=>[4,1,6,3,8,2,7,5]=>0000000=>0000000
[5,6,2,4,3,1,8,7]=>[7,8,1,3,4,2,6,5]=>0000000=>0000000
[6,8,3,7,5,4,2,1]=>[1,2,4,5,7,3,8,6]=>1100000=>0000011
[6,1,3,4,7,5,8,2]=>[2,8,5,7,4,3,1,6]=>0000000=>0000000
[6,2,1,4,8,7,5,3]=>[3,5,7,8,4,1,2,6]=>0000000=>0000000
[8,7,6,5,1,3,2,4]=>[4,2,3,1,5,6,7,8]=>0001111=>1111000
[8,7,6,2,4,3,1,5]=>[5,1,3,4,2,6,7,8]=>0000111=>1110000
[5,4,8,7,6,1,3,2]=>[2,3,1,6,7,8,4,5]=>0010000=>0000100
[1,6,3,8,5,2,4,7]=>[7,4,2,5,8,3,6,1]=>0000000=>0000000
[4,6,3,7,5,2,1,8]=>[8,1,2,5,7,3,6,4]=>0000000=>0000000
[3,7,2,6,5,4,1,8]=>[8,1,4,5,6,2,7,3]=>0000000=>0000000
[3,2,1,6,8,4,5,7]=>[7,5,4,8,6,1,2,3]=>0000000=>0000000
[6,2,5,1,7,4,8,3]=>[3,8,4,7,1,5,2,6]=>0000000=>0000000
[5,2,7,4,1,6,8,3]=>[3,8,6,1,4,7,2,5]=>0000000=>0000000
[3,4,1,2,7,8,6,5]=>[5,6,8,7,2,1,4,3]=>0000000=>0000000
[5,4,8,3,7,1,6,2]=>[2,6,1,7,3,8,4,5]=>0000000=>0000000
[4,1,3,2,8,6,7,5]=>[5,7,6,8,2,3,1,4]=>0000000=>0000000
[3,1,2,4,7,6,8,5]=>[5,8,6,7,4,2,1,3]=>0000000=>0000000
[6,7,8,1,4,5,3,2]=>[2,3,5,4,1,8,7,6]=>0000100=>0010000
[8,4,6,1,3,5,2,7]=>[7,2,5,3,1,6,4,8]=>0000001=>1000000
[3,2,5,4,7,8,1,6]=>[6,1,8,7,4,5,2,3]=>0000000=>0000000
[3,1,7,6,5,8,2,4]=>[4,2,8,5,6,7,1,3]=>0000000=>0000000
[5,4,2,6,8,7,1,3]=>[3,1,7,8,6,2,4,5]=>0000000=>0000000
[6,4,1,2,8,7,3,5]=>[5,3,7,8,2,1,4,6]=>0000000=>0000000
[6,5,1,4,3,2,8,7]=>[7,8,2,3,4,1,5,6]=>0000000=>0000000
[4,3,8,5,2,1,6,7]=>[7,6,1,2,5,8,3,4]=>0000000=>0000000
[3,6,4,5,2,1,8,7]=>[7,8,1,2,5,4,6,3]=>0000000=>0000000
[5,2,6,7,3,1,4,8]=>[8,4,1,3,7,6,2,5]=>0000000=>0000000
[5,6,3,1,8,2,7,4]=>[4,7,2,8,1,3,6,5]=>0000000=>0000000
[6,5,4,3,1,2,8,7]=>[7,8,2,1,3,4,5,6]=>0000000=>0000000
[4,5,2,1,6,8,3,7]=>[7,3,8,6,1,2,5,4]=>0000000=>0000000
[5,6,2,8,1,7,4,3]=>[3,4,7,1,8,2,6,5]=>0000000=>0000000
[8,1,3,4,7,2,6,5]=>[5,6,2,7,4,3,1,8]=>0000001=>1000000
[2,1,4,5,8,6,3,7]=>[7,3,6,8,5,4,1,2]=>0000000=>0000000
[5,1,7,3,4,8,2,6]=>[6,2,8,4,3,7,1,5]=>0000000=>0000000
[1,8,3,4,7,6,2,5]=>[5,2,6,7,4,3,8,1]=>0000000=>0000000
[8,7,2,3,6,5,4,1]=>[1,4,5,6,3,2,7,8]=>1000011=>1100001
[4,8,1,6,7,2,5,3]=>[3,5,2,7,6,1,8,4]=>0000000=>0000000
[6,7,3,1,5,8,2,4]=>[4,2,8,5,1,3,7,6]=>0000000=>0000000
[5,4,7,6,1,8,2,3]=>[3,2,8,1,6,7,4,5]=>0000000=>0000000
[3,5,6,8,4,7,2,1]=>[1,2,7,4,8,6,5,3]=>1100000=>0000011
[2,5,6,8,7,3,4,1]=>[1,4,3,7,8,6,5,2]=>1000000=>0000001
[8,4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4,8]=>1110001=>1000111
[2,4,8,5,7,3,6,1]=>[1,6,3,7,5,8,4,2]=>1000000=>0000001
[5,3,7,8,4,6,2,1]=>[1,2,6,4,8,7,3,5]=>1100000=>0000011
[6,7,3,8,4,5,2,1]=>[1,2,5,4,8,3,7,6]=>1100000=>0000011
[5,2,7,8,6,3,4,1]=>[1,4,3,6,8,7,2,5]=>1000000=>0000001
[2,1,8,7,6,4,3,5]=>[5,3,4,6,7,8,1,2]=>0000000=>0000000
[6,3,8,7,5,1,2,4]=>[4,2,1,5,7,8,3,6]=>0000000=>0000000
[5,4,8,7,1,3,2,6]=>[6,2,3,1,7,8,4,5]=>0000000=>0000000
[5,4,2,7,6,8,1,3]=>[3,1,8,6,7,2,4,5]=>0000000=>0000000
[5,3,1,4,8,7,2,6]=>[6,2,7,8,4,1,3,5]=>0000000=>0000000
[3,4,2,8,6,1,5,7]=>[7,5,1,6,8,2,4,3]=>0000000=>0000000
[2,8,6,1,7,3,5,4]=>[4,5,3,7,1,6,8,2]=>0000000=>0000000
[1,7,6,3,5,8,2,4]=>[4,2,8,5,3,6,7,1]=>0000000=>0000000
[1,8,2,5,7,6,3,4]=>[4,3,6,7,5,2,8,1]=>0000000=>0000000
[4,1,6,8,2,3,7,5]=>[5,7,3,2,8,6,1,4]=>0000000=>0000000
[8,1,5,6,4,7,2,3]=>[3,2,7,4,6,5,1,8]=>0000001=>1000000
[1,7,4,6,8,2,5,3]=>[3,5,2,8,6,4,7,1]=>0000000=>0000000
[4,7,3,8,5,2,1,6]=>[6,1,2,5,8,3,7,4]=>0000000=>0000000
[3,8,6,2,7,4,1,5]=>[5,1,4,7,2,6,8,3]=>0000000=>0000000
[8,1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1,8]=>0000001=>1000000
[6,4,2,8,5,1,3,7]=>[7,3,1,5,8,2,4,6]=>0000000=>0000000
[6,7,5,1,4,2,8,3]=>[3,8,2,4,1,5,7,6]=>0000000=>0000000
[5,8,4,7,3,2,6,1]=>[1,6,2,3,7,4,8,5]=>1000000=>0000001
[6,2,4,1,7,5,8,3]=>[3,8,5,7,1,4,2,6]=>0000000=>0000000
[3,1,5,4,2,8,6,7]=>[7,6,8,2,4,5,1,3]=>0000000=>0000000
[3,7,4,2,1,8,5,6]=>[6,5,8,1,2,4,7,3]=>0000000=>0000000
[7,5,1,4,2,8,6,3]=>[3,6,8,2,4,1,5,7]=>0000000=>0000000
[4,3,2,1,8,5,7,6]=>[6,7,5,8,1,2,3,4]=>0000000=>0000000
[5,3,2,1,7,6,4,8]=>[8,4,6,7,1,2,3,5]=>0000000=>0000000
[8,1,6,2,7,4,3,5]=>[5,3,4,7,2,6,1,8]=>0000001=>1000000
[8,6,3,2,7,5,4,1]=>[1,4,5,7,2,3,6,8]=>1000001=>1000001
[7,3,1,6,5,4,2,8]=>[8,2,4,5,6,1,3,7]=>0000000=>0000000
[8,5,7,4,3,6,2,1]=>[1,2,6,3,4,7,5,8]=>1100001=>1000011
[8,5,7,2,4,6,3,1]=>[1,3,6,4,2,7,5,8]=>1000001=>1000001
[2,8,5,6,1,4,3,7]=>[7,3,4,1,6,5,8,2]=>0000000=>0000000
[7,2,6,8,4,1,5,3]=>[3,5,1,4,8,6,2,7]=>0000000=>0000000
[7,6,4,8,3,2,5,1]=>[1,5,2,3,8,4,6,7]=>1000000=>0000001
[6,5,8,4,1,3,7,2]=>[2,7,3,1,4,8,5,6]=>0000000=>0000000
[5,4,8,3,2,1,7,6]=>[6,7,1,2,3,8,4,5]=>0000000=>0000000
[2,4,7,1,3,6,5,8]=>[8,5,6,3,1,7,4,2]=>0000000=>0000000
[3,6,8,2,1,5,7,4]=>[4,7,5,1,2,8,6,3]=>0000000=>0000000
[5,1,7,8,2,4,6,3]=>[3,6,4,2,8,7,1,5]=>0000000=>0000000
[3,6,7,8,1,2,5,4]=>[4,5,2,1,8,7,6,3]=>0000000=>0000000
[4,6,7,2,8,1,3,5]=>[5,3,1,8,2,7,6,4]=>0000000=>0000000
[2,7,4,1,8,3,6,5]=>[5,6,3,8,1,4,7,2]=>0000000=>0000000
[3,5,1,8,4,2,7,6]=>[6,7,2,4,8,1,5,3]=>0000000=>0000000
[7,2,5,8,6,3,1,4]=>[4,1,3,6,8,5,2,7]=>0000000=>0000000
[6,8,1,4,7,5,2,3]=>[3,2,5,7,4,1,8,6]=>0000000=>0000000
[3,8,7,6,2,1,5,4]=>[4,5,1,2,6,7,8,3]=>0000000=>0000000
[8,1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1,8]=>0000001=>1000000
[3,8,2,7,6,5,4,1]=>[1,4,5,6,7,2,8,3]=>1000000=>0000001
[4,2,8,7,6,5,3,1]=>[1,3,5,6,7,8,2,4]=>1000000=>0000001
[8,3,1,7,6,5,4,2]=>[2,4,5,6,7,1,3,8]=>0000001=>1000000
[2,5,8,6,3,1,4,7]=>[7,4,1,3,6,8,5,2]=>0000000=>0000000
[6,8,7,2,4,3,5,1]=>[1,5,3,4,2,7,8,6]=>1000100=>0010001
[8,3,4,6,1,5,2,7]=>[7,2,5,1,6,4,3,8]=>0000001=>1000000
[6,3,4,7,8,2,5,1]=>[1,5,2,8,7,4,3,6]=>1000000=>0000001
[5,3,7,4,8,6,1,2]=>[2,1,6,8,4,7,3,5]=>0100000=>0000010
[2,4,7,6,8,3,5,1]=>[1,5,3,8,6,7,4,2]=>1000000=>0000001
[4,8,6,5,7,1,2,3]=>[3,2,1,7,5,6,8,4]=>0010000=>0000100
[8,4,1,5,2,3,7,6]=>[6,7,3,2,5,1,4,8]=>0000001=>1000000
[6,3,2,1,8,4,7,5]=>[5,7,4,8,1,2,3,6]=>0000000=>0000000
[2,3,7,6,8,1,5,4]=>[4,5,1,8,6,7,3,2]=>0000000=>0000000
[2,7,8,5,1,3,6,4]=>[4,6,3,1,5,8,7,2]=>0000000=>0000000
[4,8,7,6,2,3,5,1]=>[1,5,3,2,6,7,8,4]=>1000000=>0000001
[6,7,5,4,2,1,8,3]=>[3,8,1,2,4,5,7,6]=>0000000=>0000000
[4,2,1,5,8,7,6,3]=>[3,6,7,8,5,1,2,4]=>0000000=>0000000
[8,5,3,2,6,1,7,4]=>[4,7,1,6,2,3,5,8]=>0000001=>1000000
[7,3,4,6,1,5,8,2]=>[2,8,5,1,6,4,3,7]=>0000000=>0000000
[7,8,2,1,6,3,5,4]=>[4,5,3,6,1,2,8,7]=>0000010=>0100000
[2,6,8,5,3,1,7,4]=>[4,7,1,3,5,8,6,2]=>0000000=>0000000
[5,6,2,1,7,3,8,4]=>[4,8,3,7,1,2,6,5]=>0000000=>0000000
[6,4,2,1,5,3,7,8]=>[8,7,3,5,1,2,4,6]=>0000000=>0000000
[1,6,4,2,8,7,3,5]=>[5,3,7,8,2,4,6,1]=>0000000=>0000000
[4,8,1,2,6,7,3,5]=>[5,3,7,6,2,1,8,4]=>0000000=>0000000
[4,3,8,5,7,6,1,2]=>[2,1,6,7,5,8,3,4]=>0100000=>0000010
[4,8,6,3,7,5,1,2]=>[2,1,5,7,3,6,8,4]=>0100000=>0000010
[3,8,5,6,1,7,4,2]=>[2,4,7,1,6,5,8,3]=>0000000=>0000000
[2,1,8,7,6,3,5,4]=>[4,5,3,6,7,8,1,2]=>0000000=>0000000
[2,8,1,7,4,6,5,3]=>[3,5,6,4,7,1,8,2]=>0000000=>0000000
[2,8,6,7,5,1,4,3]=>[3,4,1,5,7,6,8,2]=>0000000=>0000000
[5,4,1,6,3,2,8,7]=>[7,8,2,3,6,1,4,5]=>0000000=>0000000
[3,2,6,5,1,4,8,7]=>[7,8,4,1,5,6,2,3]=>0000000=>0000000
[2,5,8,1,7,4,3,6]=>[6,3,4,7,1,8,5,2]=>0000000=>0000000
[2,1,7,6,3,8,5,4]=>[4,5,8,3,6,7,1,2]=>0000000=>0000000
[7,6,2,8,4,3,1,5]=>[5,1,3,4,8,2,6,7]=>0000000=>0000000
[4,2,7,3,1,8,5,6]=>[6,5,8,1,3,7,2,4]=>0000000=>0000000
[5,2,7,3,8,6,1,4]=>[4,1,6,8,3,7,2,5]=>0000000=>0000000
[4,8,3,2,1,7,6,5]=>[5,6,7,1,2,3,8,4]=>0000000=>0000000
[6,8,3,7,2,1,5,4]=>[4,5,1,2,7,3,8,6]=>0000000=>0000000
[3,5,8,1,7,2,6,4]=>[4,6,2,7,1,8,5,3]=>0000000=>0000000
[5,8,3,1,6,2,7,4]=>[4,7,2,6,1,3,8,5]=>0000000=>0000000
[5,1,7,3,6,2,8,4]=>[4,8,2,6,3,7,1,5]=>0000000=>0000000
[4,3,2,1,6,8,5,7]=>[7,5,8,6,1,2,3,4]=>0000000=>0000000
[2,4,1,3,8,7,6,5]=>[5,6,7,8,3,1,4,2]=>0000000=>0000000
[6,5,3,1,7,2,8,4]=>[4,8,2,7,1,3,5,6]=>0000000=>0000000
[3,8,5,4,2,1,7,6]=>[6,7,1,2,4,5,8,3]=>0000000=>0000000
[2,3,8,5,4,1,6,7]=>[7,6,1,4,5,8,3,2]=>0000000=>0000000
[4,3,2,8,7,6,1,5]=>[5,1,6,7,8,2,3,4]=>0000000=>0000000
[5,4,2,6,3,1,8,7]=>[7,8,1,3,6,2,4,5]=>0000000=>0000000
[6,5,2,1,3,4,8,7]=>[7,8,4,3,1,2,5,6]=>0000000=>0000000
[7,5,2,6,3,8,4,1]=>[1,4,8,3,6,2,5,7]=>1000000=>0000001
[7,3,6,5,2,8,4,1]=>[1,4,8,2,5,6,3,7]=>1000000=>0000001
[5,6,3,1,2,4,8,7]=>[7,8,4,2,1,3,6,5]=>0000000=>0000000
[2,7,5,3,8,6,4,1]=>[1,4,6,8,3,5,7,2]=>1000000=>0000001
[3,7,6,4,2,8,5,1]=>[1,5,8,2,4,6,7,3]=>1000000=>0000001
[5,7,3,6,2,8,4,1]=>[1,4,8,2,6,3,7,5]=>1000000=>0000001
[3,8,4,1,5,7,2,6]=>[6,2,7,5,1,4,8,3]=>0000000=>0000000
[4,5,3,6,8,2,7,1]=>[1,7,2,8,6,3,5,4]=>1000000=>0000001
[5,6,3,7,4,8,2,1]=>[1,2,8,4,7,3,6,5]=>1100000=>0000011
[6,3,7,5,8,4,2,1]=>[1,2,4,8,5,7,3,6]=>1100000=>0000011
[7,1,8,5,4,2,3,6]=>[6,3,2,4,5,8,1,7]=>0000000=>0000000
[2,1,7,8,5,3,4,6]=>[6,4,3,5,8,7,1,2]=>0000000=>0000000
[4,7,3,8,1,2,6,5]=>[5,6,2,1,8,3,7,4]=>0000000=>0000000
[5,8,7,4,6,3,2,1]=>[1,2,3,6,4,7,8,5]=>1110000=>0000111
[4,8,7,6,3,5,2,1]=>[1,2,5,3,6,7,8,4]=>1100000=>0000011
[5,8,4,7,6,3,2,1]=>[1,2,3,6,7,4,8,5]=>1110000=>0000111
[4,8,7,3,6,5,2,1]=>[1,2,5,6,3,7,8,4]=>1100000=>0000011
[6,8,5,4,7,3,2,1]=>[1,2,3,7,4,5,8,6]=>1110000=>0000111
[3,8,7,6,2,5,4,1]=>[1,4,5,2,6,7,8,3]=>1000000=>0000001
[4,8,7,6,3,2,5,1]=>[1,5,2,3,6,7,8,4]=>1000000=>0000001
[7,5,8,3,6,2,1,4]=>[4,1,2,6,3,8,5,7]=>0000000=>0000000
[7,5,8,3,2,1,6,4]=>[4,6,1,2,3,8,5,7]=>0000000=>0000000
[7,6,8,2,5,1,4,3]=>[3,4,1,5,2,8,6,7]=>0000100=>0010000
[2,1,7,5,8,4,6,3]=>[3,6,4,8,5,7,1,2]=>0000000=>0000000
[2,7,3,6,8,4,1,5]=>[5,1,4,8,6,3,7,2]=>0000000=>0000000
[2,5,6,8,1,7,4,3]=>[3,4,7,1,8,6,5,2]=>0000000=>0000000
[5,1,7,2,4,8,3,6]=>[6,3,8,4,2,7,1,5]=>0000000=>0000000
[3,5,8,7,2,1,6,4]=>[4,6,1,2,7,8,5,3]=>0000000=>0000000
[8,5,3,6,2,4,1,7]=>[7,1,4,2,6,3,5,8]=>0000001=>1000000
[8,3,5,6,2,1,4,7]=>[7,4,1,2,6,5,3,8]=>0000001=>1000000
[8,1,4,6,3,5,2,7]=>[7,2,5,3,6,4,1,8]=>0000001=>1000000
[5,4,7,6,8,2,3,1]=>[1,3,2,8,6,7,4,5]=>1010000=>0000101
[4,1,8,2,3,7,6,5]=>[5,6,7,3,2,8,1,4]=>0000000=>0000000
[3,7,4,5,8,2,1,6]=>[6,1,2,8,5,4,7,3]=>0000000=>0000000
[5,2,4,6,8,7,3,1]=>[1,3,7,8,6,4,2,5]=>1000000=>0000001
[5,4,1,6,8,2,7,3]=>[3,7,2,8,6,1,4,5]=>0000000=>0000000
[7,5,8,2,1,4,6,3]=>[3,6,4,1,2,8,5,7]=>0000000=>0000000
[7,4,8,3,2,6,1,5]=>[5,1,6,2,3,8,4,7]=>0000000=>0000000
[7,4,3,2,6,8,5,1]=>[1,5,8,6,2,3,4,7]=>1000000=>0000001
[8,3,7,2,1,5,6,4]=>[4,6,5,1,2,7,3,8]=>0000001=>1000000
[5,1,2,3,6,8,7,4]=>[4,7,8,6,3,2,1,5]=>0000000=>0000000
[6,3,8,2,7,4,1,5]=>[5,1,4,7,2,8,3,6]=>0000000=>0000000
[5,7,8,2,1,4,3,6]=>[6,3,4,1,2,8,7,5]=>0000000=>0000000
[3,5,1,7,8,4,2,6]=>[6,2,4,8,7,1,5,3]=>0000000=>0000000
[8,4,7,2,1,3,5,6]=>[6,5,3,1,2,7,4,8]=>0000001=>1000000
[7,1,6,3,5,8,2,4]=>[4,2,8,5,3,6,1,7]=>0000000=>0000000
[1,5,2,7,8,6,4,3]=>[3,4,6,8,7,2,5,1]=>0000000=>0000000
[2,6,8,5,1,4,7,3]=>[3,7,4,1,5,8,6,2]=>0000000=>0000000
[1,4,2,8,6,5,7,3]=>[3,7,5,6,8,2,4,1]=>0000000=>0000000
[3,5,1,6,8,7,2,4]=>[4,2,7,8,6,1,5,3]=>0000000=>0000000
[5,7,6,2,1,3,8,4]=>[4,8,3,1,2,6,7,5]=>0000000=>0000000
[2,5,8,7,4,1,6,3]=>[3,6,1,4,7,8,5,2]=>0000000=>0000000
[8,3,4,1,5,6,7,2]=>[2,7,6,5,1,4,3,8]=>0000001=>1000000
[7,3,5,2,4,6,1,8]=>[8,1,6,4,2,5,3,7]=>0000000=>0000000
[3,5,2,7,4,6,1,8]=>[8,1,6,4,7,2,5,3]=>0000000=>0000000
[3,7,5,2,4,6,1,8]=>[8,1,6,4,2,5,7,3]=>0000000=>0000000
[5,7,3,2,4,6,1,8]=>[8,1,6,4,2,3,7,5]=>0000000=>0000000
[5,7,3,2,1,4,6,8]=>[8,6,4,1,2,3,7,5]=>0000000=>0000000
[5,7,3,2,4,1,6,8]=>[8,6,1,4,2,3,7,5]=>0000000=>0000000
[3,7,5,2,4,1,6,8]=>[8,6,1,4,2,5,7,3]=>0000000=>0000000
[3,2,7,5,4,1,6,8]=>[8,6,1,4,5,7,2,3]=>0000000=>0000000
[5,1,3,2,7,4,6,8]=>[8,6,4,7,2,3,1,5]=>0000000=>0000000
[3,2,1,5,7,4,6,8]=>[8,6,4,7,5,1,2,3]=>0000000=>0000000
[3,2,7,5,1,4,6,8]=>[8,6,4,1,5,7,2,3]=>0000000=>0000000
[5,7,3,1,2,4,6,8]=>[8,6,4,2,1,3,7,5]=>0000000=>0000000
[1,5,3,7,2,4,6,8]=>[8,6,4,2,7,3,5,1]=>0000000=>0000000
[3,5,2,7,4,1,6,8]=>[8,6,1,4,7,2,5,3]=>0000000=>0000000
[3,5,7,2,4,1,6,8]=>[8,6,1,4,2,7,5,3]=>0000000=>0000000
[5,3,7,2,4,1,6,8]=>[8,6,1,4,2,7,3,5]=>0000000=>0000000
[7,3,5,2,1,4,6,8]=>[8,6,4,1,2,5,3,7]=>0000000=>0000000
[3,5,2,4,1,7,6,8]=>[8,6,7,1,4,2,5,3]=>0000000=>0000000
[5,3,1,2,7,4,6,8]=>[8,6,4,7,2,1,3,5]=>0000000=>0000000
[3,2,5,1,7,4,6,8]=>[8,6,4,7,1,5,2,3]=>0000000=>0000000
[7,5,1,3,2,4,6,8]=>[8,6,4,2,3,1,5,7]=>0000000=>0000000
[5,7,1,3,2,4,6,8]=>[8,6,4,2,3,1,7,5]=>0000000=>0000000
[3,2,1,7,5,4,6,8]=>[8,6,4,5,7,1,2,3]=>0000000=>0000000
[7,1,5,3,2,4,6,8]=>[8,6,4,2,3,5,1,7]=>0000000=>0000000
[1,7,5,3,2,4,6,8]=>[8,6,4,2,3,5,7,1]=>0000000=>0000000
[5,8,7,4,1,2,6,3]=>[3,6,2,1,4,7,8,5]=>0000000=>0000000
[2,8,7,4,3,6,1,5]=>[5,1,6,3,4,7,8,2]=>0000000=>0000000
[7,6,4,2,8,5,3,1]=>[1,3,5,8,2,4,6,7]=>1000000=>0000001
[7,6,4,8,5,1,2,3]=>[3,2,1,5,8,4,6,7]=>0010000=>0000100
[7,6,4,5,1,3,8,2]=>[2,8,3,1,5,4,6,7]=>0000000=>0000000
[1,6,7,5,3,8,4,2]=>[2,4,8,3,5,7,6,1]=>0000000=>0000000
[7,6,4,2,5,1,8,3]=>[3,8,1,5,2,4,6,7]=>0000000=>0000000
[7,6,2,8,3,1,4,5]=>[5,4,1,3,8,2,6,7]=>0000000=>0000000
[6,2,3,8,7,4,1,5]=>[5,1,4,7,8,3,2,6]=>0000000=>0000000
[2,6,5,7,8,3,4,1]=>[1,4,3,8,7,5,6,2]=>1000000=>0000001
[2,4,7,3,5,8,6,1]=>[1,6,8,5,3,7,4,2]=>1000000=>0000001
[2,5,3,7,1,8,4,6]=>[6,4,8,1,7,3,5,2]=>0000000=>0000000
[3,2,5,1,7,8,4,6]=>[6,4,8,7,1,5,2,3]=>0000000=>0000000
[5,2,3,4,8,6,1,7]=>[7,1,6,8,4,3,2,5]=>0000000=>0000000
[5,3,4,8,2,7,6,1]=>[1,6,7,2,8,4,3,5]=>1000000=>0000001
[5,3,8,2,4,1,7,6]=>[6,7,1,4,2,8,3,5]=>0000000=>0000000
[5,2,8,4,1,7,3,6]=>[6,3,7,1,4,8,2,5]=>0000000=>0000000
[6,4,2,5,1,8,7,3]=>[3,7,8,1,5,2,4,6]=>0000000=>0000000
[6,4,3,5,8,2,1,7]=>[7,1,2,8,5,3,4,6]=>0000000=>0000000
[6,3,5,4,8,2,7,1]=>[1,7,2,8,4,5,3,6]=>1000000=>0000001
[6,3,5,8,7,1,2,4]=>[4,2,1,7,8,5,3,6]=>0000000=>0000000
[5,8,1,4,3,6,2,7]=>[7,2,6,3,4,1,8,5]=>0000000=>0000000
[6,4,5,3,8,1,7,2]=>[2,7,1,8,3,5,4,6]=>0000000=>0000000
[6,4,3,8,5,7,2,1]=>[1,2,7,5,8,3,4,6]=>1100000=>0000011
[5,4,2,6,3,1,7,8]=>[8,7,1,3,6,2,4,5]=>0000000=>0000000
[4,5,1,3,6,2,8,7]=>[7,8,2,6,3,1,5,4]=>0000000=>0000000
[3,5,7,6,1,4,8,2]=>[2,8,4,1,6,7,5,3]=>0000000=>0000000
[4,2,6,5,1,7,3,8]=>[8,3,7,1,5,6,2,4]=>0000000=>0000000
[3,5,4,7,2,6,1,8]=>[8,1,6,2,7,4,5,3]=>0000000=>0000000
[3,4,7,6,8,1,2,5]=>[5,2,1,8,6,7,4,3]=>0000000=>0000000
[3,5,2,4,6,1,8,7]=>[7,8,1,6,4,2,5,3]=>0000000=>0000000
[1,8,4,3,7,5,6,2]=>[2,6,5,7,3,4,8,1]=>0000000=>0000000
[5,2,8,6,4,7,3,1]=>[1,3,7,4,6,8,2,5]=>1000000=>0000001
[1,8,6,3,7,4,2,5]=>[5,2,4,7,3,6,8,1]=>0000000=>0000000
[1,8,6,5,7,2,3,4]=>[4,3,2,7,5,6,8,1]=>0000000=>0000000
[5,2,3,8,4,1,7,6]=>[6,7,1,4,8,3,2,5]=>0000000=>0000000
[7,5,3,4,8,2,1,6]=>[6,1,2,8,4,3,5,7]=>0000000=>0000000
[7,6,3,8,4,2,1,5]=>[5,1,2,4,8,3,6,7]=>0000000=>0000000
[7,2,8,5,1,6,3,4]=>[4,3,6,1,5,8,2,7]=>0000000=>0000000
[7,4,3,8,5,2,6,1]=>[1,6,2,5,8,3,4,7]=>1000000=>0000001
[7,6,3,8,2,4,5,1]=>[1,5,4,2,8,3,6,7]=>1000000=>0000001
[7,2,8,5,1,3,4,6]=>[6,4,3,1,5,8,2,7]=>0000000=>0000000
[7,6,8,1,2,5,3,4]=>[4,3,5,2,1,8,6,7]=>0000100=>0010000
[1,5,3,7,6,8,4,2]=>[2,4,8,6,7,3,5,1]=>0000000=>0000000
[1,2,7,4,8,5,3,6]=>[6,3,5,8,4,7,2,1]=>0000000=>0000000
[4,2,6,7,5,8,1,3]=>[3,1,8,5,7,6,2,4]=>0000000=>0000000
[5,7,4,2,6,3,1,8]=>[8,1,3,6,2,4,7,5]=>0000000=>0000000
[8,3,4,6,5,1,7,2]=>[2,7,1,5,6,4,3,8]=>0000001=>1000000
[2,1,8,3,6,7,4,5]=>[5,4,7,6,3,8,1,2]=>0000000=>0000000
[5,1,8,6,2,7,3,4]=>[4,3,7,2,6,8,1,5]=>0000000=>0000000
[5,7,1,4,2,6,3,8]=>[8,3,6,2,4,1,7,5]=>0000000=>0000000
[8,2,6,1,5,4,7,3]=>[3,7,4,5,1,6,2,8]=>0000001=>1000000
[7,8,5,4,1,6,3,2]=>[2,3,6,1,4,5,8,7]=>0000010=>0100000
[3,6,2,7,8,1,5,4]=>[4,5,1,8,7,2,6,3]=>0000000=>0000000
[2,6,8,4,1,5,7,3]=>[3,7,5,1,4,8,6,2]=>0000000=>0000000
[5,7,8,4,1,6,3,2]=>[2,3,6,1,4,8,7,5]=>0000000=>0000000
[4,5,6,8,3,1,7,2]=>[2,7,1,3,8,6,5,4]=>0000000=>0000000
[8,4,6,5,3,1,7,2]=>[2,7,1,3,5,6,4,8]=>0000001=>1000000
[5,6,4,8,3,1,7,2]=>[2,7,1,3,8,4,6,5]=>0000000=>0000000
[3,4,8,1,2,5,7,6]=>[6,7,5,2,1,8,4,3]=>0000000=>0000000
[6,3,1,7,5,2,4,8]=>[8,4,2,5,7,1,3,6]=>0000000=>0000000
[4,5,3,1,7,2,6,8]=>[8,6,2,7,1,3,5,4]=>0000000=>0000000
[6,3,1,8,2,7,4,5]=>[5,4,7,2,8,1,3,6]=>0000000=>0000000
[7,8,1,2,4,3,6,5]=>[5,6,3,4,2,1,8,7]=>0000010=>0100000
[5,2,8,1,3,4,7,6]=>[6,7,4,3,1,8,2,5]=>0000000=>0000000
[3,2,1,6,4,7,8,5]=>[5,8,7,4,6,1,2,3]=>0000000=>0000000
[3,2,6,1,5,7,8,4]=>[4,8,7,5,1,6,2,3]=>0000000=>0000000
[3,6,4,2,1,7,8,5]=>[5,8,7,1,2,4,6,3]=>0000000=>0000000
[2,6,5,3,1,7,8,4]=>[4,8,7,1,3,5,6,2]=>0000000=>0000000
[3,8,6,1,4,7,5,2]=>[2,5,7,4,1,6,8,3]=>0000000=>0000000
[1,8,3,2,6,7,5,4]=>[4,5,7,6,2,3,8,1]=>0000000=>0000000
[8,7,1,3,6,5,4,2]=>[2,4,5,6,3,1,7,8]=>0000011=>1100000
[1,8,5,7,4,2,6,3]=>[3,6,2,4,7,5,8,1]=>0000000=>0000000
[2,7,6,5,8,3,1,4]=>[4,1,3,8,5,6,7,2]=>0000000=>0000000
[1,4,7,6,8,2,3,5]=>[5,3,2,8,6,7,4,1]=>0000000=>0000000
[3,5,7,4,8,1,2,6]=>[6,2,1,8,4,7,5,3]=>0000000=>0000000
[4,6,1,7,5,8,2,3]=>[3,2,8,5,7,1,6,4]=>0000000=>0000000
[2,3,6,7,5,8,1,4]=>[4,1,8,5,7,6,3,2]=>0000000=>0000000
[1,3,7,5,6,8,2,4]=>[4,2,8,6,5,7,3,1]=>0000000=>0000000
[8,2,5,3,7,1,6,4]=>[4,6,1,7,3,5,2,8]=>0000001=>1000000
[4,1,8,3,7,5,6,2]=>[2,6,5,7,3,8,1,4]=>0000000=>0000000
[1,4,8,7,3,5,6,2]=>[2,6,5,3,7,8,4,1]=>0000000=>0000000
[1,5,8,7,4,6,2,3]=>[3,2,6,4,7,8,5,1]=>0000000=>0000000
[4,8,6,7,5,3,2,1]=>[1,2,3,5,7,6,8,4]=>1110000=>0000111
[1,8,7,6,5,3,4,2]=>[2,4,3,5,6,7,8,1]=>0000000=>0000000
[1,7,8,3,5,2,4,6]=>[6,4,2,5,3,8,7,1]=>0000000=>0000000
[8,5,3,7,2,4,6,1]=>[1,6,4,2,7,3,5,8]=>1000001=>1000001
[2,7,6,8,4,3,1,5]=>[5,1,3,4,8,6,7,2]=>0000000=>0000000
[8,1,4,6,7,3,5,2]=>[2,5,3,7,6,4,1,8]=>0000001=>1000000
[3,1,6,5,8,7,4,2]=>[2,4,7,8,5,6,1,3]=>0000000=>0000000
[2,3,6,4,1,7,8,5]=>[5,8,7,1,4,6,3,2]=>0000000=>0000000
[3,1,7,4,5,2,8,6]=>[6,8,2,5,4,7,1,3]=>0000000=>0000000
[3,7,5,4,2,1,8,6]=>[6,8,1,2,4,5,7,3]=>0000000=>0000000
[8,7,2,4,6,5,3,1]=>[1,3,5,6,4,2,7,8]=>1000011=>1100001
[8,2,6,7,3,1,5,4]=>[4,5,1,3,7,6,2,8]=>0000001=>1000000
[8,7,6,5,1,3,4,2]=>[2,4,3,1,5,6,7,8]=>0001111=>1111000
[8,7,6,1,4,5,3,2]=>[2,3,5,4,1,6,7,8]=>0000111=>1110000
[6,7,8,1,5,4,3,2]=>[2,3,4,5,1,8,7,6]=>0000100=>0010000
[8,7,6,5,2,4,3,1]=>[1,3,4,2,5,6,7,8]=>1001111=>1111001
[7,6,5,4,2,8,3,1]=>[1,3,8,2,4,5,6,7]=>1000000=>0000001
[8,7,5,4,2,6,3,1]=>[1,3,6,2,4,5,7,8]=>1000011=>1100001
[3,5,8,7,6,2,1,4]=>[4,1,2,6,7,8,5,3]=>0000000=>0000000
[7,3,8,4,6,1,5,2]=>[2,5,1,6,4,8,3,7]=>0000000=>0000000
[4,8,5,7,1,6,3,2]=>[2,3,6,1,7,5,8,4]=>0000000=>0000000
[5,4,3,6,7,1,8,2]=>[2,8,1,7,6,3,4,5]=>0000000=>0000000
[4,8,7,3,5,1,6,2]=>[2,6,1,5,3,7,8,4]=>0000000=>0000000
[4,8,7,6,3,1,5,2]=>[2,5,1,3,6,7,8,4]=>0000000=>0000000
[3,4,5,2,8,1,6,7]=>[7,6,1,8,2,5,4,3]=>0000000=>0000000
[6,5,8,4,7,2,1,3]=>[3,1,2,7,4,8,5,6]=>0010000=>0000100
[6,8,5,7,3,2,1,4]=>[4,1,2,3,7,5,8,6]=>0001000=>0001000
[6,8,5,3,7,2,1,4]=>[4,1,2,7,3,5,8,6]=>0000000=>0000000
[6,5,8,4,7,3,1,2]=>[2,1,3,7,4,8,5,6]=>0110000=>0000110
[6,8,5,7,4,2,1,3]=>[3,1,2,4,7,5,8,6]=>0011000=>0001100
[2,1,8,7,6,3,4,5]=>[5,4,3,6,7,8,1,2]=>0000000=>0000000
[2,1,8,7,3,6,5,4]=>[4,5,6,3,7,8,1,2]=>0000000=>0000000
[5,8,7,6,2,4,1,3]=>[3,1,4,2,6,7,8,5]=>0001000=>0001000
[6,8,7,5,2,4,1,3]=>[3,1,4,2,5,7,8,6]=>0001100=>0011000
[5,8,7,6,4,2,3,1]=>[1,3,2,4,6,7,8,5]=>1011000=>0001101
[2,3,5,7,4,8,6,1]=>[1,6,8,4,7,5,3,2]=>1000000=>0000001
[2,3,5,7,8,4,6,1]=>[1,6,4,8,7,5,3,2]=>1000000=>0000001
[2,3,6,1,7,5,8,4]=>[4,8,5,7,1,6,3,2]=>0000000=>0000000
[2,3,7,1,8,5,6,4]=>[4,6,5,8,1,7,3,2]=>0000000=>0000000
[2,4,1,7,3,8,6,5]=>[5,6,8,3,7,1,4,2]=>0000000=>0000000
[2,4,1,7,8,5,6,3]=>[3,6,5,8,7,1,4,2]=>0000000=>0000000
[2,4,5,3,7,1,8,6]=>[6,8,1,7,3,5,4,2]=>0000000=>0000000
[2,4,6,3,8,5,1,7]=>[7,1,5,8,3,6,4,2]=>0000000=>0000000
[2,4,6,8,3,5,1,7]=>[7,1,5,3,8,6,4,2]=>0000000=>0000000
[2,5,1,6,7,4,8,3]=>[3,8,4,7,6,1,5,2]=>0000000=>0000000
[2,5,6,3,7,4,8,1]=>[1,8,4,7,3,6,5,2]=>1000000=>0000001
[2,5,6,7,8,4,1,3]=>[3,1,4,8,7,6,5,2]=>0000000=>0000000
[2,5,6,8,4,3,1,7]=>[7,1,3,4,8,6,5,2]=>0000000=>0000000
[2,6,1,7,4,8,5,3]=>[3,5,8,4,7,1,6,2]=>0000000=>0000000
[7,6,5,3,8,1,4,2]=>[2,4,1,8,3,5,6,7]=>0000000=>0000000
[7,4,8,3,5,1,6,2]=>[2,6,1,5,3,8,4,7]=>0000000=>0000000
[7,6,3,8,2,4,1,5]=>[5,1,4,2,8,3,6,7]=>0000000=>0000000
[5,1,2,3,4,8,7,6]=>[6,7,8,4,3,2,1,5]=>0000000=>0000000
[4,1,2,3,7,6,5,8]=>[8,5,6,7,3,2,1,4]=>0000000=>0000000
[7,6,5,8,2,4,3,1]=>[1,3,4,2,8,5,6,7]=>1001000=>0001001
[7,8,4,6,5,3,2,1]=>[1,2,3,5,6,4,8,7]=>1110010=>0100111
[6,8,7,4,5,2,3,1]=>[1,3,2,5,4,7,8,6]=>1010100=>0010101
[6,8,4,7,2,5,3,1]=>[1,3,5,2,7,4,8,6]=>1000000=>0000001
[6,8,4,2,7,5,3,1]=>[1,3,5,7,2,4,8,6]=>1000000=>0000001
[6,8,4,7,2,1,5,3]=>[3,5,1,2,7,4,8,6]=>0000000=>0000000
[6,8,4,7,3,5,2,1]=>[1,2,5,3,7,4,8,6]=>1100000=>0000011
[6,8,4,2,7,1,5,3]=>[3,5,1,7,2,4,8,6]=>0000000=>0000000
[6,8,4,7,3,2,5,1]=>[1,5,2,3,7,4,8,6]=>1000000=>0000001
[6,8,4,2,1,7,5,3]=>[3,5,7,1,2,4,8,6]=>0000000=>0000000
[6,8,4,7,3,2,1,5]=>[5,1,2,3,7,4,8,6]=>0000000=>0000000
[4,8,7,6,2,5,1,3]=>[3,1,5,2,6,7,8,4]=>0000000=>0000000
[2,8,7,6,3,5,1,4]=>[4,1,5,3,6,7,8,2]=>0000000=>0000000
[5,8,7,3,6,2,1,4]=>[4,1,2,6,3,7,8,5]=>0000000=>0000000
[5,8,7,2,3,6,1,4]=>[4,1,6,3,2,7,8,5]=>0000000=>0000000
[6,8,3,7,5,2,1,4]=>[4,1,2,5,7,3,8,6]=>0000000=>0000000
[6,8,1,7,3,5,4,2]=>[2,4,5,3,7,1,8,6]=>0000000=>0000000
[6,8,4,7,1,2,5,3]=>[3,5,2,1,7,4,8,6]=>0000000=>0000000
[6,8,1,7,3,2,5,4]=>[4,5,2,3,7,1,8,6]=>0000000=>0000000
[3,8,5,7,6,1,4,2]=>[2,4,1,6,7,5,8,3]=>0000000=>0000000
[4,8,5,7,1,2,6,3]=>[3,6,2,1,7,5,8,4]=>0000000=>0000000
[1,8,5,7,3,2,6,4]=>[4,6,2,3,7,5,8,1]=>0000000=>0000000
[6,8,5,3,7,1,4,2]=>[2,4,1,7,3,5,8,6]=>0000000=>0000000
[6,8,3,4,7,1,5,2]=>[2,5,1,7,4,3,8,6]=>0000000=>0000000
[6,8,1,3,7,2,5,4]=>[4,5,2,7,3,1,8,6]=>0000000=>0000000
[2,8,1,3,7,6,5,4]=>[4,5,6,7,3,1,8,2]=>0000000=>0000000
[6,8,5,4,1,7,3,2]=>[2,3,7,1,4,5,8,6]=>0000000=>0000000
[6,8,1,4,2,7,5,3]=>[3,5,7,2,4,1,8,6]=>0000000=>0000000
[6,5,4,3,8,7,1,2]=>[2,1,7,8,3,4,5,6]=>0100000=>0000010
[6,5,8,4,3,7,1,2]=>[2,1,7,3,4,8,5,6]=>0100000=>0000010
[3,1,6,8,4,5,2,7]=>[7,2,5,4,8,6,1,3]=>0000000=>0000000
[3,1,6,7,4,8,5,2]=>[2,5,8,4,7,6,1,3]=>0000000=>0000000
[8,6,4,2,7,5,1,3]=>[3,1,5,7,2,4,6,8]=>0000001=>1000000
[8,6,4,2,7,1,5,3]=>[3,5,1,7,2,4,6,8]=>0000001=>1000000
[6,4,8,2,7,5,1,3]=>[3,1,5,7,2,8,4,6]=>0000000=>0000000
[3,4,5,8,7,6,1,2]=>[2,1,6,7,8,5,4,3]=>0100000=>0000010
[7,4,8,6,3,2,1,5]=>[5,1,2,3,6,8,4,7]=>0000000=>0000000
[7,4,8,3,5,2,1,6]=>[6,1,2,5,3,8,4,7]=>0000000=>0000000
[5,8,3,6,7,2,1,4]=>[4,1,2,7,6,3,8,5]=>0000000=>0000000
[7,3,8,6,5,2,1,4]=>[4,1,2,5,6,8,3,7]=>0000000=>0000000
[6,8,4,3,2,5,1,7]=>[7,1,5,2,3,4,8,6]=>0000000=>0000000
[4,8,7,3,2,5,1,6]=>[6,1,5,2,3,7,8,4]=>0000000=>0000000
[6,3,7,8,2,4,1,5]=>[5,1,4,2,8,7,3,6]=>0000000=>0000000
[5,3,7,6,2,4,1,8]=>[8,1,4,2,6,7,3,5]=>0000000=>0000000
[5,4,7,2,6,8,1,3]=>[3,1,8,6,2,7,4,5]=>0000000=>0000000
[5,4,3,2,6,8,1,7]=>[7,1,8,6,2,3,4,5]=>0000000=>0000000
[4,8,3,2,5,6,1,7]=>[7,1,6,5,2,3,8,4]=>0000000=>0000000
[7,5,2,6,8,4,1,3]=>[3,1,4,8,6,2,5,7]=>0000000=>0000000
[7,1,8,2,3,6,5,4]=>[4,5,6,3,2,8,1,7]=>0000000=>0000000
[7,1,8,3,6,2,5,4]=>[4,5,2,6,3,8,1,7]=>0000000=>0000000
[6,2,3,4,1,7,5,8]=>[8,5,7,1,4,3,2,6]=>0000000=>0000000
[2,8,3,4,5,1,6,7]=>[7,6,1,5,4,3,8,2]=>0000000=>0000000
[5,3,1,7,2,4,8,6]=>[6,8,4,2,7,1,3,5]=>0000000=>0000000
[5,3,6,1,2,7,4,8]=>[8,4,7,2,1,6,3,5]=>0000000=>0000000
[2,8,5,3,4,6,7,1]=>[1,7,6,4,3,5,8,2]=>1000000=>0000001
[4,5,3,1,2,6,8,7]=>[7,8,6,2,1,3,5,4]=>0000000=>0000000
[3,4,1,2,5,8,7,6]=>[6,7,8,5,2,1,4,3]=>0000000=>0000000
[6,7,4,3,2,1,8,5]=>[5,8,1,2,3,4,7,6]=>0000000=>0000000
[4,5,2,1,8,7,6,3]=>[3,6,7,8,1,2,5,4]=>0000000=>0000000
[7,1,2,3,4,6,8,5]=>[5,8,6,4,3,2,1,7]=>0000000=>0000000
[6,1,2,3,5,8,7,4]=>[4,7,8,5,3,2,1,6]=>0000000=>0000000
[5,1,2,4,8,6,7,3]=>[3,7,6,8,4,2,1,5]=>0000000=>0000000
[7,1,2,3,5,8,6,4]=>[4,6,8,5,3,2,1,7]=>0000000=>0000000
[6,1,2,3,5,7,8,4]=>[4,8,7,5,3,2,1,6]=>0000000=>0000000
[8,6,3,5,2,7,4,1]=>[1,4,7,2,5,3,6,8]=>1000001=>1000001
[7,5,2,8,6,3,4,1]=>[1,4,3,6,8,2,5,7]=>1000000=>0000001
[5,2,8,6,7,3,4,1]=>[1,4,3,7,6,8,2,5]=>1000000=>0000001
[7,5,2,3,8,6,4,1]=>[1,4,6,8,3,2,5,7]=>1000000=>0000001
[5,2,8,3,4,1,6,7]=>[7,6,1,4,3,8,2,5]=>0000000=>0000000
[5,2,3,8,6,7,4,1]=>[1,4,7,6,8,3,2,5]=>1000000=>0000001
[7,4,1,2,6,8,5,3]=>[3,5,8,6,2,1,4,7]=>0000000=>0000000
[5,3,8,4,1,2,6,7]=>[7,6,2,1,4,8,3,5]=>0000000=>0000000
[7,3,5,6,8,4,1,2]=>[2,1,4,8,6,5,3,7]=>0100000=>0000010
[7,4,5,1,8,6,2,3]=>[3,2,6,8,1,5,4,7]=>0000000=>0000000
[6,2,3,4,8,5,1,7]=>[7,1,5,8,4,3,2,6]=>0000000=>0000000
[8,4,5,1,7,3,6,2]=>[2,6,3,7,1,5,4,8]=>0000001=>1000000
[7,2,3,4,6,8,5,1]=>[1,5,8,6,4,3,2,7]=>1000000=>0000001
[4,2,7,5,8,6,3,1]=>[1,3,6,8,5,7,2,4]=>1000000=>0000001
[4,2,8,5,6,7,3,1]=>[1,3,7,6,5,8,2,4]=>1000000=>0000001
[7,4,8,5,6,1,2,3]=>[3,2,1,6,5,8,4,7]=>0010000=>0000100
[7,4,5,8,6,1,2,3]=>[3,2,1,6,8,5,4,7]=>0010000=>0000100
[7,5,8,6,1,2,3,4]=>[4,3,2,1,6,8,5,7]=>0001000=>0001000
[6,4,8,5,2,3,1,7]=>[7,1,3,2,5,8,4,6]=>0000000=>0000000
[7,4,6,8,5,2,3,1]=>[1,3,2,5,8,6,4,7]=>1010000=>0000101
[7,2,3,8,4,5,6,1]=>[1,6,5,4,8,3,2,7]=>1000000=>0000001
[7,2,8,3,4,5,6,1]=>[1,6,5,4,3,8,2,7]=>1000000=>0000001
[8,5,2,7,4,6,3,1]=>[1,3,6,4,7,2,5,8]=>1000001=>1000001
[5,2,4,8,6,7,3,1]=>[1,3,7,6,8,4,2,5]=>1000000=>0000001
[8,5,2,4,6,7,3,1]=>[1,3,7,6,4,2,5,8]=>1000001=>1000001
[5,2,4,8,3,1,6,7]=>[7,6,1,3,8,4,2,5]=>0000000=>0000000
[7,4,5,8,6,2,3,1]=>[1,3,2,6,8,5,4,7]=>1010000=>0000101
[7,4,8,5,6,2,3,1]=>[1,3,2,6,5,8,4,7]=>1010000=>0000101
[4,8,2,5,1,3,7,6]=>[6,7,3,1,5,2,8,4]=>0000000=>0000000
[3,5,4,6,1,7,8,2]=>[2,8,7,1,6,4,5,3]=>0000000=>0000000
[3,1,5,8,2,6,4,7]=>[7,4,6,2,8,5,1,3]=>0000000=>0000000
[2,1,7,8,9,10,6,5,4,3]=>[3,4,5,6,10,9,8,7,1,2]=>000000000=>000000000
[1,5,6,7,8,3,4,2]=>[2,4,3,8,7,6,5,1]=>0000000=>0000000
[1,4,5,7,8,3,6,2]=>[2,6,3,8,7,5,4,1]=>0000000=>0000000
[1,5,6,3,7,8,4,2]=>[2,4,8,7,3,6,5,1]=>0000000=>0000000
[6,1,2,3,4,8,7,5]=>[5,7,8,4,3,2,1,6]=>0000000=>0000000
[5,1,2,3,8,7,6,4]=>[4,6,7,8,3,2,1,5]=>0000000=>0000000
[5,1,2,3,8,6,7,4]=>[4,7,6,8,3,2,1,5]=>0000000=>0000000
[2,8,5,3,1,4,6,7]=>[7,6,4,1,3,5,8,2]=>0000000=>0000000
[2,4,3,6,7,8,1,5]=>[5,1,8,7,6,3,4,2]=>0000000=>0000000
[2,5,3,6,7,8,4,1]=>[1,4,8,7,6,3,5,2]=>1000000=>0000001
[2,5,3,6,7,4,8,1]=>[1,8,4,7,6,3,5,2]=>1000000=>0000001
[3,4,8,1,5,6,7,2]=>[2,7,6,5,1,8,4,3]=>0000000=>0000000
[3,5,1,6,7,8,4,2]=>[2,4,8,7,6,1,5,3]=>0000000=>0000000
[3,5,1,7,4,8,6,2]=>[2,6,8,4,7,1,5,3]=>0000000=>0000000
[3,6,7,4,8,5,1,2]=>[2,1,5,8,4,7,6,3]=>0100000=>0000010
[3,6,8,4,5,1,7,2]=>[2,7,1,5,4,8,6,3]=>0000000=>0000000
[4,1,5,7,8,6,3,2]=>[2,3,6,8,7,5,1,4]=>0000000=>0000000
[4,1,7,3,5,8,6,2]=>[2,6,8,5,3,7,1,4]=>0000000=>0000000
[4,1,7,8,5,6,3,2]=>[2,3,6,5,8,7,1,4]=>0000000=>0000000
[4,5,8,3,1,6,7,2]=>[2,7,6,1,3,8,5,4]=>0000000=>0000000
[4,6,3,1,8,5,7,2]=>[2,7,5,8,1,3,6,4]=>0000000=>0000000
[4,6,3,7,8,5,1,2]=>[2,1,5,8,7,3,6,4]=>0100000=>0000010
[4,6,8,3,5,1,7,2]=>[2,7,1,5,3,8,6,4]=>0000000=>0000000
[5,1,6,4,8,3,7,2]=>[2,7,3,8,4,6,1,5]=>0000000=>0000000
[5,1,7,4,3,8,6,2]=>[2,6,8,3,4,7,1,5]=>0000000=>0000000
[5,6,3,7,8,1,4,2]=>[2,4,1,8,7,3,6,5]=>0000000=>0000000
[5,6,7,8,4,1,3,2]=>[2,3,1,4,8,7,6,5]=>0011000=>0001100
[5,7,3,4,1,8,6,2]=>[2,6,8,1,4,3,7,5]=>0000000=>0000000
[5,7,3,8,4,6,1,2]=>[2,1,6,4,8,3,7,5]=>0100000=>0000010
[5,7,8,4,3,6,1,2]=>[2,1,6,3,4,8,7,5]=>0100000=>0000010
[6,1,3,7,8,5,4,2]=>[2,4,5,8,7,3,1,6]=>0000000=>0000000
[6,1,3,8,5,4,7,2]=>[2,7,4,5,8,3,1,6]=>0000000=>0000000
[6,1,8,4,5,3,7,2]=>[2,7,3,5,4,8,1,6]=>0000000=>0000000
[6,7,3,8,5,4,1,2]=>[2,1,4,5,8,3,7,6]=>0100000=>0000010
[7,1,3,4,8,6,5,2]=>[2,5,6,8,4,3,1,7]=>0000000=>0000000
[7,1,8,4,5,6,3,2]=>[2,3,6,5,4,8,1,7]=>0000000=>0000000
[8,5,1,4,2,3,6,7]=>[7,6,3,2,4,1,5,8]=>0000001=>1000000
[8,5,1,4,3,2,6,7]=>[7,6,2,3,4,1,5,8]=>0000001=>1000000
[8,7,1,2,3,6,4,5]=>[5,4,6,3,2,1,7,8]=>0000011=>1100000
[2,5,8,6,1,7,3,4]=>[4,3,7,1,6,8,5,2]=>0000000=>0000000
[6,8,7,2,3,4,1,5]=>[5,1,4,3,2,7,8,6]=>0000100=>0010000
[3,1,5,4,6,7,8,2]=>[2,8,7,6,4,5,1,3]=>0000000=>0000000
[4,2,8,5,3,1,6,7]=>[7,6,1,3,5,8,2,4]=>0000000=>0000000
[8,1,2,6,5,3,7,4]=>[4,7,3,5,6,2,1,8]=>0000001=>1000000
[1,3,2,4,8,5,7,6]=>[6,7,5,8,4,2,3,1]=>0000000=>0000000
[5,3,1,8,2,4,7,6]=>[6,7,4,2,8,1,3,5]=>0000000=>0000000
[1,5,4,2,8,3,7,6]=>[6,7,3,8,2,4,5,1]=>0000000=>0000000
[1,7,2,5,3,8,6,4]=>[4,6,8,3,5,2,7,1]=>0000000=>0000000
[2,6,1,8,3,7,4,5]=>[5,4,7,3,8,1,6,2]=>0000000=>0000000
[3,5,8,4,1,7,2,6]=>[6,2,7,1,4,8,5,3]=>0000000=>0000000
[5,1,4,6,2,8,7,3]=>[3,7,8,2,6,4,1,5]=>0000000=>0000000
[7,6,2,1,4,8,3,5]=>[5,3,8,4,1,2,6,7]=>0000000=>0000000
[1,4,2,7,3,8,6,5]=>[5,6,8,3,7,2,4,1]=>0000000=>0000000
[1,2,7,3,8,6,5,4]=>[4,5,6,8,3,7,2,1]=>0000000=>0000000
[3,4,5,1,8,2,7,6]=>[6,7,2,8,1,5,4,3]=>0000000=>0000000
[2,8,7,6,3,1,4,5]=>[5,4,1,3,6,7,8,2]=>0000000=>0000000
[7,6,2,3,4,8,1,5]=>[5,1,8,4,3,2,6,7]=>0000000=>0000000
[8,7,6,2,1,4,3,5]=>[5,3,4,1,2,6,7,8]=>0000111=>1110000
[8,7,3,1,4,2,6,5]=>[5,6,2,4,1,3,7,8]=>0000011=>1100000
[1,2,3,8,4,7,6,5]=>[5,6,7,4,8,3,2,1]=>0000000=>0000000
[4,5,1,2,8,3,7,6]=>[6,7,3,8,2,1,5,4]=>0000000=>0000000
[4,1,2,6,5,7,8,3]=>[3,8,7,5,6,2,1,4]=>0000000=>0000000
[8,4,1,7,3,2,5,6]=>[6,5,2,3,7,1,4,8]=>0000001=>1000000
[1,8,7,3,2,4,6,5]=>[5,6,4,2,3,7,8,1]=>0000000=>0000000
[1,8,4,2,7,3,6,5]=>[5,6,3,7,2,4,8,1]=>0000000=>0000000
[1,7,5,2,3,8,6,4]=>[4,6,8,3,2,5,7,1]=>0000000=>0000000
[8,1,4,7,3,5,2,6]=>[6,2,5,3,7,4,1,8]=>0000001=>1000000
[8,4,3,6,1,7,2,5]=>[5,2,7,1,6,3,4,8]=>0000001=>1000000
[8,3,1,5,6,2,7,4]=>[4,7,2,6,5,1,3,8]=>0000001=>1000000
[3,4,1,6,5,7,2,8]=>[8,2,7,5,6,1,4,3]=>0000000=>0000000
[5,4,3,6,1,7,2,8]=>[8,2,7,1,6,3,4,5]=>0000000=>0000000
[4,8,7,6,2,1,5,3]=>[3,5,1,2,6,7,8,4]=>0000000=>0000000
[6,8,5,2,1,7,4,3]=>[3,4,7,1,2,5,8,6]=>0000000=>0000000
[7,8,5,3,6,2,4,1]=>[1,4,2,6,3,5,8,7]=>1000010=>0100001
[7,5,8,3,6,4,2,1]=>[1,2,4,6,3,8,5,7]=>1100000=>0000011
[5,8,7,6,3,2,4,1]=>[1,4,2,3,6,7,8,5]=>1001000=>0001001
[7,5,3,8,6,4,2,1]=>[1,2,4,6,8,3,5,7]=>1100000=>0000011
[5,4,8,1,6,3,7,2]=>[2,7,3,6,1,8,4,5]=>0000000=>0000000
[2,1,5,8,3,7,4,6]=>[6,4,7,3,8,5,1,2]=>0000000=>0000000
[2,1,7,4,8,3,6,5]=>[5,6,3,8,4,7,1,2]=>0000000=>0000000
[5,1,4,8,2,7,3,6]=>[6,3,7,2,8,4,1,5]=>0000000=>0000000
[6,1,3,5,7,2,8,4]=>[4,8,2,7,5,3,1,6]=>0000000=>0000000
[3,1,2,7,8,4,6,5]=>[5,6,4,8,7,2,1,3]=>0000000=>0000000
[3,4,1,2,8,7,5,6]=>[6,5,7,8,2,1,4,3]=>0000000=>0000000
[2,1,3,4,8,5,7,6]=>[6,7,5,8,4,3,1,2]=>0000000=>0000000
[6,2,5,1,7,3,8,4]=>[4,8,3,7,1,5,2,6]=>0000000=>0000000
[2,4,8,1,3,7,5,6]=>[6,5,7,3,1,8,4,2]=>0000000=>0000000
[1,5,4,8,6,2,7,3]=>[3,7,2,6,8,4,5,1]=>0000000=>0000000
[4,2,5,8,1,7,3,6]=>[6,3,7,1,8,5,2,4]=>0000000=>0000000
[2,6,8,5,1,7,3,4]=>[4,3,7,1,5,8,6,2]=>0000000=>0000000
[5,1,2,3,8,4,7,6]=>[6,7,4,8,3,2,1,5]=>0000000=>0000000
[3,4,5,1,8,7,2,6]=>[6,2,7,8,1,5,4,3]=>0000000=>0000000
[4,1,2,3,8,7,5,6]=>[6,5,7,8,3,2,1,4]=>0000000=>0000000
[5,1,4,6,2,7,8,3]=>[3,8,7,2,6,4,1,5]=>0000000=>0000000
[2,3,1,8,5,4,7,6]=>[6,7,4,5,8,1,3,2]=>0000000=>0000000
[5,3,1,8,7,2,4,6]=>[6,4,2,7,8,1,3,5]=>0000000=>0000000
[3,6,1,8,7,2,4,5]=>[5,4,2,7,8,1,6,3]=>0000000=>0000000
[6,3,5,7,1,2,8,4]=>[4,8,2,1,7,5,3,6]=>0000000=>0000000
[1,3,8,4,2,7,6,5]=>[5,6,7,2,4,8,3,1]=>0000000=>0000000
[1,2,3,8,5,7,4,6]=>[6,4,7,5,8,3,2,1]=>0000000=>0000000
[4,5,1,8,7,2,3,6]=>[6,3,2,7,8,1,5,4]=>0000000=>0000000
[3,1,5,2,8,6,7,4]=>[4,7,6,8,2,5,1,3]=>0000000=>0000000
[7,8,6,5,2,1,4,3]=>[3,4,1,2,5,6,8,7]=>0001110=>0111000
[6,7,8,2,1,5,4,3]=>[3,4,5,1,2,8,7,6]=>0000100=>0010000
[8,7,5,6,2,1,4,3]=>[3,4,1,2,6,5,7,8]=>0001011=>1101000
[7,8,4,5,6,1,3,2]=>[2,3,1,6,5,4,8,7]=>0010010=>0100100
[4,2,5,1,8,7,3,6]=>[6,3,7,8,1,5,2,4]=>0000000=>0000000
[7,2,4,5,8,3,6,1]=>[1,6,3,8,5,4,2,7]=>1000000=>0000001
[8,1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1,8]=>0000001=>1000000
[8,2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2,8]=>0000001=>1000000
[7,2,8,4,5,3,1,6]=>[6,1,3,5,4,8,2,7]=>0000000=>0000000
[1,5,7,8,4,6,2,3]=>[3,2,6,4,8,7,5,1]=>0000000=>0000000
[6,5,4,8,2,3,1,7]=>[7,1,3,2,8,4,5,6]=>0000000=>0000000
[5,1,3,2,8,4,6,7]=>[7,6,4,8,2,3,1,5]=>0000000=>0000000
[7,6,1,3,8,2,4,5]=>[5,4,2,8,3,1,6,7]=>0000000=>0000000
[5,4,1,2,3,8,6,7]=>[7,6,8,3,2,1,4,5]=>0000000=>0000000
[7,6,8,5,2,4,1,3]=>[3,1,4,2,5,8,6,7]=>0001100=>0011000
[6,7,8,5,2,4,1,3]=>[3,1,4,2,5,8,7,6]=>0001100=>0011000
[3,4,5,7,2,8,1,6]=>[6,1,8,2,7,5,4,3]=>0000000=>0000000
[3,4,5,8,2,1,7,6]=>[6,7,1,2,8,5,4,3]=>0000000=>0000000
[3,4,6,2,7,8,1,5]=>[5,1,8,7,2,6,4,3]=>0000000=>0000000
[3,4,6,7,5,1,2,8]=>[8,2,1,5,7,6,4,3]=>0000000=>0000000
[3,4,6,1,5,2,7,8]=>[8,7,2,5,1,6,4,3]=>0000000=>0000000
[3,4,7,2,1,6,5,8]=>[8,5,6,1,2,7,4,3]=>0000000=>0000000
[3,4,7,1,5,6,2,8]=>[8,2,6,5,1,7,4,3]=>0000000=>0000000
[3,5,2,6,1,4,7,8]=>[8,7,4,1,6,2,5,3]=>0000000=>0000000
[3,5,2,7,1,6,4,8]=>[8,4,6,1,7,2,5,3]=>0000000=>0000000
[3,5,6,1,4,2,7,8]=>[8,7,2,4,1,6,5,3]=>0000000=>0000000
[3,6,2,4,8,1,7,5]=>[5,7,1,8,4,2,6,3]=>0000000=>0000000
[3,6,2,7,8,5,1,4]=>[4,1,5,8,7,2,6,3]=>0000000=>0000000
[3,6,2,7,8,1,4,5]=>[5,4,1,8,7,2,6,3]=>0000000=>0000000
[3,7,2,1,5,6,4,8]=>[8,4,6,5,1,2,7,3]=>0000000=>0000000
[3,7,8,4,5,1,6,2]=>[2,6,1,5,4,8,7,3]=>0000000=>0000000
[3,8,2,1,5,6,7,4]=>[4,7,6,5,1,2,8,3]=>0000000=>0000000
[8,1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1,8]=>0000001=>1000000
[4,1,7,3,5,6,8,2]=>[2,8,6,5,3,7,1,4]=>0000000=>0000000
[3,5,2,4,1,6,7,8]=>[8,7,6,1,4,2,5,3]=>0000000=>0000000
[4,6,2,3,5,7,1,8]=>[8,1,7,5,3,2,6,4]=>0000000=>0000000
[2,3,7,8,1,6,5,4]=>[4,5,6,1,8,7,3,2]=>0000000=>0000000
[2,7,5,1,8,6,3,4]=>[4,3,6,8,1,5,7,2]=>0000000=>0000000
[2,7,6,1,4,8,3,5]=>[5,3,8,4,1,6,7,2]=>0000000=>0000000
[2,6,8,1,4,5,7,3]=>[3,7,5,4,1,8,6,2]=>0000000=>0000000
[6,4,7,5,8,2,3,1]=>[1,3,2,8,5,7,4,6]=>1010000=>0000101
[6,7,4,1,8,2,3,5]=>[5,3,2,8,1,4,7,6]=>0000000=>0000000
[7,3,6,1,4,8,2,5]=>[5,2,8,4,1,6,3,7]=>0000000=>0000000
[6,7,8,1,4,2,5,3]=>[3,5,2,4,1,8,7,6]=>0000100=>0010000
[6,2,4,5,8,3,7,1]=>[1,7,3,8,5,4,2,6]=>1000000=>0000001
[5,2,6,1,4,8,3,7]=>[7,3,8,4,1,6,2,5]=>0000000=>0000000
[6,2,5,1,8,7,3,4]=>[4,3,7,8,1,5,2,6]=>0000000=>0000000
[7,2,3,5,8,1,4,6]=>[6,4,1,8,5,3,2,7]=>0000000=>0000000
[2,4,7,6,1,8,3,5]=>[5,3,8,1,6,7,4,2]=>0000000=>0000000
[2,3,4,8,1,5,7,6]=>[6,7,5,1,8,4,3,2]=>0000000=>0000000
[2,7,8,5,1,4,6,3]=>[3,6,4,1,5,8,7,2]=>0000000=>0000000
[2,6,7,8,5,3,1,4]=>[4,1,3,5,8,7,6,2]=>0000000=>0000000
[7,2,3,8,6,1,5,4]=>[4,5,1,6,8,3,2,7]=>0000000=>0000000
[5,2,3,4,6,8,1,7]=>[7,1,8,6,4,3,2,5]=>0000000=>0000000
[7,2,3,4,8,1,6,5]=>[5,6,1,8,4,3,2,7]=>0000000=>0000000
[3,2,5,7,8,1,6,4]=>[4,6,1,8,7,5,2,3]=>0000000=>0000000
[5,7,1,6,2,8,4,3]=>[3,4,8,2,6,1,7,5]=>0000000=>0000000
[5,6,1,8,2,3,7,4]=>[4,7,3,2,8,1,6,5]=>0000000=>0000000
[5,7,6,1,2,8,3,4]=>[4,3,8,2,1,6,7,5]=>0000000=>0000000
[5,6,8,1,2,4,7,3]=>[3,7,4,2,1,8,6,5]=>0000000=>0000000
[5,4,1,6,7,8,2,3]=>[3,2,8,7,6,1,4,5]=>0000000=>0000000
[7,4,1,5,8,2,6,3]=>[3,6,2,8,5,1,4,7]=>0000000=>0000000
[5,7,1,8,6,2,3,4]=>[4,3,2,6,8,1,7,5]=>0000000=>0000000
[4,6,1,3,5,8,2,7]=>[7,2,8,5,3,1,6,4]=>0000000=>0000000
[4,8,1,3,5,6,7,2]=>[2,7,6,5,3,1,8,4]=>0000000=>0000000
[8,1,2,3,7,5,6,4]=>[4,6,5,7,3,2,1,8]=>0000001=>1000000
[2,1,8,3,7,5,6,4]=>[4,6,5,7,3,8,1,2]=>0000000=>0000000
[5,6,8,3,1,2,7,4]=>[4,7,2,1,3,8,6,5]=>0000000=>0000000
[5,7,8,3,1,6,2,4]=>[4,2,6,1,3,8,7,5]=>0000000=>0000000
[5,2,6,8,1,3,7,4]=>[4,7,3,1,8,6,2,5]=>0000000=>0000000
[1,5,6,7,8,3,2,4]=>[4,2,3,8,7,6,5,1]=>0000000=>0000000
[1,5,8,3,2,6,7,4]=>[4,7,6,2,3,8,5,1]=>0000000=>0000000
[7,2,3,1,8,6,5,4]=>[4,5,6,8,1,3,2,7]=>0000000=>0000000
[1,6,7,8,5,2,3,4]=>[4,3,2,5,8,7,6,1]=>0000000=>0000000
[6,2,3,7,8,1,4,5]=>[5,4,1,8,7,3,2,6]=>0000000=>0000000
[4,5,7,8,2,6,1,3]=>[3,1,6,2,8,7,5,4]=>0000000=>0000000
[4,6,2,8,5,1,7,3]=>[3,7,1,5,8,2,6,4]=>0000000=>0000000
[4,6,7,1,8,5,2,3]=>[3,2,5,8,1,7,6,4]=>0000000=>0000000
[4,6,8,1,5,2,7,3]=>[3,7,2,5,1,8,6,4]=>0000000=>0000000
[4,8,2,1,5,6,7,3]=>[3,7,6,5,1,2,8,4]=>0000000=>0000000
[1,2,8,4,5,3,7,6]=>[6,7,3,5,4,8,2,1]=>0000000=>0000000
[1,2,3,8,5,4,7,6]=>[6,7,4,5,8,3,2,1]=>0000000=>0000000
[5,2,6,7,8,1,4,3]=>[3,4,1,8,7,6,2,5]=>0000000=>0000000
[5,2,7,8,4,6,1,3]=>[3,1,6,4,8,7,2,5]=>0000000=>0000000
[7,2,3,8,5,4,1,6]=>[6,1,4,5,8,3,2,7]=>0000000=>0000000
[5,7,2,8,4,6,1,3]=>[3,1,6,4,8,2,7,5]=>0000000=>0000000
[6,2,1,7,8,5,4,3]=>[3,4,5,8,7,1,2,6]=>0000000=>0000000
[5,1,2,8,3,6,4,7]=>[7,4,6,3,8,2,1,5]=>0000000=>0000000
[7,1,6,3,8,2,4,5]=>[5,4,2,8,3,6,1,7]=>0000000=>0000000
[4,1,7,2,5,8,3,6]=>[6,3,8,5,2,7,1,4]=>0000000=>0000000
[8,1,6,3,4,7,2,5]=>[5,2,7,4,3,6,1,8]=>0000001=>1000000
[4,1,8,2,5,6,7,3]=>[3,7,6,5,2,8,1,4]=>0000000=>0000000
[3,6,1,2,8,4,7,5]=>[5,7,4,8,2,1,6,3]=>0000000=>0000000
[6,8,2,7,4,1,3,5]=>[5,3,1,4,7,2,8,6]=>0000000=>0000000
[6,5,2,8,1,3,7,4]=>[4,7,3,1,8,2,5,6]=>0000000=>0000000
[5,4,7,1,2,8,3,6]=>[6,3,8,2,1,7,4,5]=>0000000=>0000000
[8,4,7,1,3,5,2,6]=>[6,2,5,3,1,7,4,8]=>0000001=>1000000
[8,4,7,1,3,2,6,5]=>[5,6,2,3,1,7,4,8]=>0000001=>1000000
[8,5,7,3,1,2,6,4]=>[4,6,2,1,3,7,5,8]=>0000001=>1000000
[3,6,1,8,2,7,4,5]=>[5,4,7,2,8,1,6,3]=>0000000=>0000000
[8,6,2,1,4,5,3,7]=>[7,3,5,4,1,2,6,8]=>0000001=>1000000
[8,6,2,3,7,5,1,4]=>[4,1,5,7,3,2,6,8]=>0000001=>1000000
[7,6,8,1,4,5,2,3]=>[3,2,5,4,1,8,6,7]=>0000100=>0010000
[3,7,1,4,2,8,6,5]=>[5,6,8,2,4,1,7,3]=>0000000=>0000000
[2,6,1,5,7,4,8,3]=>[3,8,4,7,5,1,6,2]=>0000000=>0000000
[2,3,6,1,8,4,7,5]=>[5,7,4,8,1,6,3,2]=>0000000=>0000000
[5,2,4,6,3,7,8,1]=>[1,8,7,3,6,4,2,5]=>1000000=>0000001
[2,5,1,7,3,6,8,4]=>[4,8,6,3,7,1,5,2]=>0000000=>0000000
[2,7,1,5,6,8,4,3]=>[3,4,8,6,5,1,7,2]=>0000000=>0000000
[5,2,4,7,6,3,8,1]=>[1,8,3,6,7,4,2,5]=>1000000=>0000001
[8,7,6,1,4,3,5,2]=>[2,5,3,4,1,6,7,8]=>0000111=>1110000
[8,7,6,1,3,4,5,2]=>[2,5,4,3,1,6,7,8]=>0000111=>1110000
[8,1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1,8]=>0000001=>1000000
[4,2,6,1,7,8,5,3]=>[3,5,8,7,1,6,2,4]=>0000000=>0000000
[1,5,2,6,7,8,4,3]=>[3,4,8,7,6,2,5,1]=>0000000=>0000000
[4,5,2,7,8,6,1,3]=>[3,1,6,8,7,2,5,4]=>0000000=>0000000
[4,2,7,8,5,6,1,3]=>[3,1,6,5,8,7,2,4]=>0000000=>0000000
[5,2,3,4,7,8,6,1]=>[1,6,8,7,4,3,2,5]=>1000000=>0000001
[5,6,2,7,3,8,4,1]=>[1,4,8,3,7,2,6,5]=>1000000=>0000001
[3,5,2,8,4,6,7,1]=>[1,7,6,4,8,2,5,3]=>1000000=>0000001
[3,5,2,4,7,8,6,1]=>[1,6,8,7,4,2,5,3]=>1000000=>0000001
[7,2,3,4,6,1,5,8]=>[8,5,1,6,4,3,2,7]=>0000000=>0000000
[3,7,1,5,8,2,4,6]=>[6,4,2,8,5,1,7,3]=>0000000=>0000000
[5,1,3,8,2,4,6,7]=>[7,6,4,2,8,3,1,5]=>0000000=>0000000
[4,2,1,3,8,5,6,7]=>[7,6,5,8,3,1,2,4]=>0000000=>0000000
[1,8,7,6,3,4,5,2]=>[2,5,4,3,6,7,8,1]=>0000000=>0000000
[8,5,7,6,3,4,1,2]=>[2,1,4,3,6,7,5,8]=>0101001=>1001010
[4,2,7,8,1,6,5,3]=>[3,5,6,1,8,7,2,4]=>0000000=>0000000
[7,2,1,4,5,6,3,8]=>[8,3,6,5,4,1,2,7]=>0000000=>0000000
[6,8,1,4,5,3,7,2]=>[2,7,3,5,4,1,8,6]=>0000000=>0000000
[5,1,3,4,2,6,7,8]=>[8,7,6,2,4,3,1,5]=>0000000=>0000000
[2,3,4,5,8,1,7,6]=>[6,7,1,8,5,4,3,2]=>0000000=>0000000
[2,3,4,8,1,6,7,5]=>[5,7,6,1,8,4,3,2]=>0000000=>0000000
[2,1,7,5,3,8,6,4]=>[4,6,8,3,5,7,1,2]=>0000000=>0000000
[5,2,3,4,1,8,6,7]=>[7,6,8,1,4,3,2,5]=>0000000=>0000000
[3,2,1,6,4,5,7,8]=>[8,7,5,4,6,1,2,3]=>0000000=>0000000
[6,4,8,7,5,3,2,1]=>[1,2,3,5,7,8,4,6]=>1110000=>0000111
[7,4,6,8,5,3,2,1]=>[1,2,3,5,8,6,4,7]=>1110000=>0000111
[7,4,5,8,6,3,2,1]=>[1,2,3,6,8,5,4,7]=>1110000=>0000111
[7,4,8,5,6,3,2,1]=>[1,2,3,6,5,8,4,7]=>1110000=>0000111
[7,5,8,6,4,2,1,3]=>[3,1,2,4,6,8,5,7]=>0011000=>0001100
[5,3,8,6,7,4,2,1]=>[1,2,4,7,6,8,3,5]=>1100000=>0000011
[7,4,2,1,6,8,5,3]=>[3,5,8,6,1,2,4,7]=>0000000=>0000000
[6,3,8,7,4,5,2,1]=>[1,2,5,4,7,8,3,6]=>1100000=>0000011
[7,4,8,5,6,2,1,3]=>[3,1,2,6,5,8,4,7]=>0010000=>0000100
[7,3,4,5,8,6,2,1]=>[1,2,6,8,5,4,3,7]=>1100000=>0000011
[7,3,8,4,5,6,2,1]=>[1,2,6,5,4,8,3,7]=>1100000=>0000011
[1,8,7,2,6,5,4,3]=>[3,4,5,6,2,7,8,1]=>0000000=>0000000
[1,8,7,6,2,3,4,5]=>[5,4,3,2,6,7,8,1]=>0000000=>0000000
[6,4,1,7,2,3,8,5]=>[5,8,3,2,7,1,4,6]=>0000000=>0000000
[7,1,8,2,3,5,4,6]=>[6,4,5,3,2,8,1,7]=>0000000=>0000000
[6,5,1,2,3,8,4,7]=>[7,4,8,3,2,1,5,6]=>0000000=>0000000
[1,8,5,2,3,7,4,6]=>[6,4,7,3,2,5,8,1]=>0000000=>0000000
[6,5,1,2,7,3,8,4]=>[4,8,3,7,2,1,5,6]=>0000000=>0000000
[7,6,4,1,8,2,3,5]=>[5,3,2,8,1,4,6,7]=>0000000=>0000000
[5,3,6,1,2,4,8,7]=>[7,8,4,2,1,6,3,5]=>0000000=>0000000
[5,8,3,1,7,2,4,6]=>[6,4,2,7,1,3,8,5]=>0000000=>0000000
[7,5,4,1,8,2,3,6]=>[6,3,2,8,1,4,5,7]=>0000000=>0000000
[4,1,2,8,6,3,7,5]=>[5,7,3,6,8,2,1,4]=>0000000=>0000000
[5,4,1,6,2,7,8,3]=>[3,8,7,2,6,1,4,5]=>0000000=>0000000
[6,5,3,1,8,2,4,7]=>[7,4,2,8,1,3,5,6]=>0000000=>0000000
[3,8,1,6,7,2,4,5]=>[5,4,2,7,6,1,8,3]=>0000000=>0000000
[6,5,3,7,1,2,8,4]=>[4,8,2,1,7,3,5,6]=>0000000=>0000000
[4,6,1,5,2,8,3,7]=>[7,3,8,2,5,1,6,4]=>0000000=>0000000
[1,6,8,5,2,7,3,4]=>[4,3,7,2,5,8,6,1]=>0000000=>0000000
[3,1,8,7,2,6,4,5]=>[5,4,6,2,7,8,1,3]=>0000000=>0000000
[7,3,5,6,1,8,2,4]=>[4,2,8,1,6,5,3,7]=>0000000=>0000000
[1,4,8,2,3,7,6,5]=>[5,6,7,3,2,8,4,1]=>0000000=>0000000
[3,1,8,2,5,6,7,4]=>[4,7,6,5,2,8,1,3]=>0000000=>0000000
[5,3,6,7,8,1,2,4]=>[4,2,1,8,7,6,3,5]=>0000000=>0000000
[4,2,5,6,7,8,3,1]=>[1,3,8,7,6,5,2,4]=>1000000=>0000001
[4,2,5,6,7,3,8,1]=>[1,8,3,7,6,5,2,4]=>1000000=>0000001
[7,2,1,8,4,5,6,3]=>[3,6,5,4,8,1,2,7]=>0000000=>0000000
[4,2,7,1,3,8,6,5]=>[5,6,8,3,1,7,2,4]=>0000000=>0000000
[5,8,6,3,4,1,7,2]=>[2,7,1,4,3,6,8,5]=>0000000=>0000000
[8,2,6,3,4,7,1,5]=>[5,1,7,4,3,6,2,8]=>0000001=>1000000
[6,2,5,8,1,3,7,4]=>[4,7,3,1,8,5,2,6]=>0000000=>0000000
[7,2,3,4,1,8,6,5]=>[5,6,8,1,4,3,2,7]=>0000000=>0000000
[5,7,2,6,4,8,1,3]=>[3,1,8,4,6,2,7,5]=>0000000=>0000000
[5,2,1,3,6,7,8,4]=>[4,8,7,6,3,1,2,5]=>0000000=>0000000
[6,4,8,7,3,2,1,5]=>[5,1,2,3,7,8,4,6]=>0000000=>0000000
[6,5,3,8,7,2,1,4]=>[4,1,2,7,8,3,5,6]=>0000000=>0000000
[6,4,3,8,7,2,1,5]=>[5,1,2,7,8,3,4,6]=>0000000=>0000000
[5,6,8,1,4,2,7,3]=>[3,7,2,4,1,8,6,5]=>0000000=>0000000
[5,7,3,1,4,6,2,8]=>[8,2,6,4,1,3,7,5]=>0000000=>0000000
[5,7,8,1,4,6,2,3]=>[3,2,6,4,1,8,7,5]=>0000000=>0000000
[5,8,1,4,3,6,7,2]=>[2,7,6,3,4,1,8,5]=>0000000=>0000000
[6,2,7,8,1,5,3,4]=>[4,3,5,1,8,7,2,6]=>0000000=>0000000
[6,2,7,4,1,5,3,8]=>[8,3,5,1,4,7,2,6]=>0000000=>0000000
[6,7,3,8,1,5,2,4]=>[4,2,5,1,8,3,7,6]=>0000000=>0000000
[6,7,8,1,5,4,2,3]=>[3,2,4,5,1,8,7,6]=>0000100=>0010000
[4,5,6,7,1,3,2,8]=>[8,2,3,1,7,6,5,4]=>0000000=>0000000
[6,7,1,4,5,3,2,8]=>[8,2,3,5,4,1,7,6]=>0000000=>0000000
[7,2,8,4,1,6,5,3]=>[3,5,6,1,4,8,2,7]=>0000000=>0000000
[7,2,8,4,5,1,6,3]=>[3,6,1,5,4,8,2,7]=>0000000=>0000000
[4,6,3,8,1,5,7,2]=>[2,7,5,1,8,3,6,4]=>0000000=>0000000
[4,6,7,3,8,1,2,5]=>[5,2,1,8,3,7,6,4]=>0000000=>0000000
[4,6,7,8,1,5,3,2]=>[2,3,5,1,8,7,6,4]=>0000000=>0000000
[4,7,3,8,1,6,5,2]=>[2,5,6,1,8,3,7,4]=>0000000=>0000000
[4,8,3,2,1,6,7,5]=>[5,7,6,1,2,3,8,4]=>0000000=>0000000
[1,8,4,2,7,3,5,6]=>[6,5,3,7,2,4,8,1]=>0000000=>0000000
[1,8,5,2,3,4,7,6]=>[6,7,4,3,2,5,8,1]=>0000000=>0000000
[1,8,3,2,7,4,5,6]=>[6,5,4,7,2,3,8,1]=>0000000=>0000000
[6,1,2,8,3,4,7,5]=>[5,7,4,3,8,2,1,6]=>0000000=>0000000
[5,4,1,2,7,8,3,6]=>[6,3,8,7,2,1,4,5]=>0000000=>0000000
[6,3,5,1,8,2,4,7]=>[7,4,2,8,1,5,3,6]=>0000000=>0000000
[6,3,1,5,7,8,2,4]=>[4,2,8,7,5,1,3,6]=>0000000=>0000000
[3,8,7,1,4,2,5,6]=>[6,5,2,4,1,7,8,3]=>0000000=>0000000
[7,6,1,3,4,8,2,5]=>[5,2,8,4,3,1,6,7]=>0000000=>0000000
[1,8,2,7,5,3,6,4]=>[4,6,3,5,7,2,8,1]=>0000000=>0000000
[3,2,1,8,7,6,4,5]=>[5,4,6,7,8,1,2,3]=>0000000=>0000000
[3,2,1,8,7,4,5,6]=>[6,5,4,7,8,1,2,3]=>0000000=>0000000
[3,2,8,7,6,1,5,4]=>[4,5,1,6,7,8,2,3]=>0000000=>0000000
[6,3,8,7,2,1,5,4]=>[4,5,1,2,7,8,3,6]=>0000000=>0000000
[4,5,3,8,6,2,7,1]=>[1,7,2,6,8,3,5,4]=>1000000=>0000001
[4,6,2,8,5,3,7,1]=>[1,7,3,5,8,2,6,4]=>1000000=>0000001
[4,5,8,3,6,2,7,1]=>[1,7,2,6,3,8,5,4]=>1000000=>0000001
[6,2,5,3,8,4,7,1]=>[1,7,4,8,3,5,2,6]=>1000000=>0000001
[6,3,7,4,5,2,8,1]=>[1,8,2,5,4,7,3,6]=>1000000=>0000001
[4,6,8,7,3,2,1,5]=>[5,1,2,3,7,8,6,4]=>0000000=>0000000
[2,4,8,7,6,5,1,3]=>[3,1,5,6,7,8,4,2]=>0000000=>0000000
[4,7,6,8,3,2,1,5]=>[5,1,2,3,8,6,7,4]=>0000000=>0000000
[3,5,6,8,7,2,1,4]=>[4,1,2,7,8,6,5,3]=>0000000=>0000000
[2,3,6,7,8,4,1,5]=>[5,1,4,8,7,6,3,2]=>0000000=>0000000
[2,3,5,7,1,6,8,4]=>[4,8,6,1,7,5,3,2]=>0000000=>0000000
[2,5,6,7,3,1,8,4]=>[4,8,1,3,7,6,5,2]=>0000000=>0000000
[2,5,7,6,3,8,4,1]=>[1,4,8,3,6,7,5,2]=>1000000=>0000001
[2,6,7,5,8,3,4,1]=>[1,4,3,8,5,7,6,2]=>1000000=>0000001
[2,4,7,1,5,8,3,6]=>[6,3,8,5,1,7,4,2]=>0000000=>0000000
[2,4,6,1,5,8,3,7]=>[7,3,8,5,1,6,4,2]=>0000000=>0000000
[2,4,5,1,8,7,3,6]=>[6,3,7,8,1,5,4,2]=>0000000=>0000000
[3,6,1,7,8,4,2,5]=>[5,2,4,8,7,1,6,3]=>0000000=>0000000
[4,3,6,2,8,1,7,5]=>[5,7,1,8,2,6,3,4]=>0000000=>0000000
[4,5,7,2,1,8,3,6]=>[6,3,8,1,2,7,5,4]=>0000000=>0000000
[3,4,1,7,8,2,6,5]=>[5,6,2,8,7,1,4,3]=>0000000=>0000000
[3,6,1,7,2,5,8,4]=>[4,8,5,2,7,1,6,3]=>0000000=>0000000
[6,3,4,7,2,5,8,1]=>[1,8,5,2,7,4,3,6]=>1000000=>0000001
[6,3,7,8,2,5,1,4]=>[4,1,5,2,8,7,3,6]=>0000000=>0000000
[4,7,6,5,2,8,3,1]=>[1,3,8,2,5,6,7,4]=>1000000=>0000001
[4,6,8,5,2,1,7,3]=>[3,7,1,2,5,8,6,4]=>0000000=>0000000
[3,6,1,4,5,7,8,2]=>[2,8,7,5,4,1,6,3]=>0000000=>0000000
[4,3,7,5,6,2,8,1]=>[1,8,2,6,5,7,3,4]=>1000000=>0000001
[4,3,5,7,8,2,6,1]=>[1,6,2,8,7,5,3,4]=>1000000=>0000001
[4,7,8,5,6,2,1,3]=>[3,1,2,6,5,8,7,4]=>0010000=>0000100
[3,5,1,4,8,7,2,6]=>[6,2,7,8,4,1,5,3]=>0000000=>0000000
[4,5,6,3,8,2,1,7]=>[7,1,2,8,3,6,5,4]=>0000000=>0000000
[5,1,2,7,8,6,4,3]=>[3,4,6,8,7,2,1,5]=>0000000=>0000000
[4,1,5,8,7,3,2,6]=>[6,2,3,7,8,5,1,4]=>0000000=>0000000
[5,1,8,2,7,6,3,4]=>[4,3,6,7,2,8,1,5]=>0000000=>0000000
[5,2,1,6,8,4,7,3]=>[3,7,4,8,6,1,2,5]=>0000000=>0000000
[4,5,2,8,7,1,6,3]=>[3,6,1,7,8,2,5,4]=>0000000=>0000000
[5,2,8,1,7,4,3,6]=>[6,3,4,7,1,8,2,5]=>0000000=>0000000
[5,2,1,3,8,4,7,6]=>[6,7,4,8,3,1,2,5]=>0000000=>0000000
[8,2,1,7,3,5,4,6]=>[6,4,5,3,7,1,2,8]=>0000001=>1000000
[6,2,1,7,8,4,3,5]=>[5,3,4,8,7,1,2,6]=>0000000=>0000000
[5,2,3,6,8,4,7,1]=>[1,7,4,8,6,3,2,5]=>1000000=>0000001
[5,1,8,6,4,7,2,3]=>[3,2,7,4,6,8,1,5]=>0000000=>0000000
[6,1,2,8,3,7,4,5]=>[5,4,7,3,8,2,1,6]=>0000000=>0000000
[5,6,7,3,8,1,2,4]=>[4,2,1,8,3,7,6,5]=>0000000=>0000000
[7,1,6,3,4,2,8,5]=>[5,8,2,4,3,6,1,7]=>0000000=>0000000
[7,2,3,4,1,5,8,6]=>[6,8,5,1,4,3,2,7]=>0000000=>0000000
[3,7,8,1,4,5,2,6]=>[6,2,5,4,1,8,7,3]=>0000000=>0000000
[3,8,5,7,2,4,1,6]=>[6,1,4,2,7,5,8,3]=>0000000=>0000000
[8,5,7,3,1,6,2,4]=>[4,2,6,1,3,7,5,8]=>0000001=>1000000
[4,6,5,8,2,3,7,1]=>[1,7,3,2,8,5,6,4]=>1000000=>0000001
[3,8,6,1,4,7,2,5]=>[5,2,7,4,1,6,8,3]=>0000000=>0000000
[3,8,7,1,2,5,6,4]=>[4,6,5,2,1,7,8,3]=>0000000=>0000000
[3,4,8,2,5,6,7,1]=>[1,7,6,5,2,8,4,3]=>1000000=>0000001
[6,3,4,5,1,2,8,7]=>[7,8,2,1,5,4,3,6]=>0000000=>0000000
[6,3,2,5,8,7,4,1]=>[1,4,7,8,5,2,3,6]=>1000000=>0000001
[6,3,4,8,7,5,1,2]=>[2,1,5,7,8,4,3,6]=>0100000=>0000010
[8,5,4,6,2,7,1,3]=>[3,1,7,2,6,4,5,8]=>0000001=>1000000
[4,8,5,6,2,7,1,3]=>[3,1,7,2,6,5,8,4]=>0000000=>0000000
[6,8,4,5,7,2,3,1]=>[1,3,2,7,5,4,8,6]=>1010000=>0000101
[7,3,2,6,8,5,4,1]=>[1,4,5,8,6,2,3,7]=>1000000=>0000001
[4,8,5,3,2,7,6,1]=>[1,6,7,2,3,5,8,4]=>1000000=>0000001
[7,3,5,6,8,1,4,2]=>[2,4,1,8,6,5,3,7]=>0000000=>0000000
[8,3,4,7,6,5,1,2]=>[2,1,5,6,7,4,3,8]=>0100001=>1000010
[7,4,8,3,6,5,2,1]=>[1,2,5,6,3,8,4,7]=>1100000=>0000011
[7,4,6,8,3,5,2,1]=>[1,2,5,3,8,6,4,7]=>1100000=>0000011
[2,4,5,7,6,8,1,3]=>[3,1,8,6,7,5,4,2]=>0000000=>0000000
[2,5,4,6,7,8,1,3]=>[3,1,8,7,6,4,5,2]=>0000000=>0000000
[3,6,7,5,4,1,8,2]=>[2,8,1,4,5,7,6,3]=>0000000=>0000000
[4,3,1,2,6,7,8,5]=>[5,8,7,6,2,1,3,4]=>0000000=>0000000
[7,4,6,5,8,3,2,1]=>[1,2,3,8,5,6,4,7]=>1110000=>0000111
[2,5,8,6,7,3,1,4]=>[4,1,3,7,6,8,5,2]=>0000000=>0000000
[2,3,4,1,8,7,5,6]=>[6,5,7,8,1,4,3,2]=>0000000=>0000000
[4,2,6,5,1,8,7,3]=>[3,7,8,1,5,6,2,4]=>0000000=>0000000
[6,5,4,1,3,2,8,7]=>[7,8,2,3,1,4,5,6]=>0000000=>0000000
[6,5,4,2,1,3,8,7]=>[7,8,3,1,2,4,5,6]=>0000000=>0000000
[8,7,4,3,6,1,5,2]=>[2,5,1,6,3,4,7,8]=>0000011=>1100000
[7,8,4,2,1,5,6,3]=>[3,6,5,1,2,4,8,7]=>0000010=>0100000
[6,8,2,7,3,5,4,1]=>[1,4,5,3,7,2,8,6]=>1000000=>0000001
[7,5,8,3,2,4,6,1]=>[1,6,4,2,3,8,5,7]=>1000000=>0000001
[7,5,8,1,3,4,6,2]=>[2,6,4,3,1,8,5,7]=>0000000=>0000000
[8,6,7,3,4,1,5,2]=>[2,5,1,4,3,7,6,8]=>0000101=>1010000
[8,3,2,7,6,4,1,5]=>[5,1,4,6,7,2,3,8]=>0000001=>1000000
[8,5,4,1,3,7,6,2]=>[2,6,7,3,1,4,5,8]=>0000001=>1000000
[5,8,2,3,4,7,6,1]=>[1,6,7,4,3,2,8,5]=>1000000=>0000001
[6,8,2,7,3,4,1,5]=>[5,1,4,3,7,2,8,6]=>0000000=>0000000
[3,6,5,4,8,7,1,2]=>[2,1,7,8,4,5,6,3]=>0100000=>0000010
[4,5,1,6,3,2,8,7]=>[7,8,2,3,6,1,5,4]=>0000000=>0000000
[1,6,7,4,3,2,8,5]=>[5,8,2,3,4,7,6,1]=>0000000=>0000000
[1,6,5,2,3,4,8,7]=>[7,8,4,3,2,5,6,1]=>0000000=>0000000
[1,3,2,6,5,8,4,7]=>[7,4,8,5,6,2,3,1]=>0000000=>0000000
[2,1,5,7,8,4,3,6]=>[6,3,4,8,7,5,1,2]=>0000000=>0000000
[4,3,7,6,5,8,1,2]=>[2,1,8,5,6,7,3,4]=>0100000=>0000010
[3,7,8,5,4,6,1,2]=>[2,1,6,4,5,8,7,3]=>0100000=>0000010
[4,7,5,2,3,6,8,1]=>[1,8,6,3,2,5,7,4]=>1000000=>0000001
[4,3,5,8,7,2,6,1]=>[1,6,2,7,8,5,3,4]=>1000000=>0000001
[2,3,4,8,7,5,6,1]=>[1,6,5,7,8,4,3,2]=>1000000=>0000001
[5,6,7,2,4,8,1,3]=>[3,1,8,4,2,7,6,5]=>0000000=>0000000
[6,4,7,5,8,3,2,1]=>[1,2,3,8,5,7,4,6]=>1110000=>0000111
[1,8,5,6,7,3,4,2]=>[2,4,3,7,6,5,8,1]=>0000000=>0000000
[4,8,3,2,6,7,5,1]=>[1,5,7,6,2,3,8,4]=>1000000=>0000001
[3,4,8,7,6,1,5,2]=>[2,5,1,6,7,8,4,3]=>0000000=>0000000
[3,7,8,5,6,4,2,1]=>[1,2,4,6,5,8,7,3]=>1100000=>0000011
[4,3,7,5,8,6,2,1]=>[1,2,6,8,5,7,3,4]=>1100000=>0000011
[5,4,6,2,3,1,8,7]=>[7,8,1,3,2,6,4,5]=>0000000=>0000000
[6,3,1,5,4,2,8,7]=>[7,8,2,4,5,1,3,6]=>0000000=>0000000
[6,4,5,3,2,1,8,7]=>[7,8,1,2,3,5,4,6]=>0000000=>0000000
[7,8,3,4,6,5,1,2]=>[2,1,5,6,4,3,8,7]=>0100010=>0100010
[2,1,7,6,8,4,5,3]=>[3,5,4,8,6,7,1,2]=>0000000=>0000000
[2,1,8,5,3,7,6,4]=>[4,6,7,3,5,8,1,2]=>0000000=>0000000
[6,4,7,5,2,8,3,1]=>[1,3,8,2,5,7,4,6]=>1000000=>0000001
[6,5,4,2,7,8,3,1]=>[1,3,8,7,2,4,5,6]=>1000000=>0000001
[2,1,8,6,7,5,4,3]=>[3,4,5,7,6,8,1,2]=>0000000=>0000000
[4,3,1,5,8,7,6,2]=>[2,6,7,8,5,1,3,4]=>0000000=>0000000
[8,6,3,4,2,7,5,1]=>[1,5,7,2,4,3,6,8]=>1000001=>1000001
[7,6,3,4,2,8,1,5]=>[5,1,8,2,4,3,6,7]=>0000000=>0000000
[5,1,3,2,6,4,7,8]=>[8,7,4,6,2,3,1,5]=>0000000=>0000000
[3,5,4,2,8,6,1,7]=>[7,1,6,8,2,4,5,3]=>0000000=>0000000
[5,6,8,7,3,2,1,4]=>[4,1,2,3,7,8,6,5]=>0001000=>0001000
[6,2,7,4,3,1,8,5]=>[5,8,1,3,4,7,2,6]=>0000000=>0000000
[7,4,1,3,2,6,8,5]=>[5,8,6,2,3,1,4,7]=>0000000=>0000000
[7,6,5,8,1,2,4,3]=>[3,4,2,1,8,5,6,7]=>0001000=>0001000
[7,2,3,6,8,1,4,5]=>[5,4,1,8,6,3,2,7]=>0000000=>0000000
[4,3,8,2,5,6,7,1]=>[1,7,6,5,2,8,3,4]=>1000000=>0000001
[5,4,8,2,3,6,7,1]=>[1,7,6,3,2,8,4,5]=>1000000=>0000001
[3,2,8,1,6,7,4,5]=>[5,4,7,6,1,8,2,3]=>0000000=>0000000
[7,2,6,3,8,1,5,4]=>[4,5,1,8,3,6,2,7]=>0000000=>0000000
[6,3,4,5,8,2,7,1]=>[1,7,2,8,5,4,3,6]=>1000000=>0000001
[7,3,8,1,4,5,6,2]=>[2,6,5,4,1,8,3,7]=>0000000=>0000000
[7,3,4,5,8,1,6,2]=>[2,6,1,8,5,4,3,7]=>0000000=>0000000
[7,4,8,1,5,6,2,3]=>[3,2,6,5,1,8,4,7]=>0000000=>0000000
[7,2,8,1,6,5,4,3]=>[3,4,5,6,1,8,2,7]=>0000000=>0000000
[3,8,5,1,7,6,4,2]=>[2,4,6,7,1,5,8,3]=>0000000=>0000000
[2,8,1,3,5,6,7,4]=>[4,7,6,5,3,1,8,2]=>0000000=>0000000
[2,4,8,7,5,6,3,1]=>[1,3,6,5,7,8,4,2]=>1000000=>0000001
[3,8,5,2,6,7,4,1]=>[1,4,7,6,2,5,8,3]=>1000000=>0000001
[1,2,5,3,7,6,8,4]=>[4,8,6,7,3,5,2,1]=>0000000=>0000000
[8,3,7,2,5,6,4,1]=>[1,4,6,5,2,7,3,8]=>1000001=>1000001
[3,7,8,1,5,6,2,4]=>[4,2,6,5,1,8,7,3]=>0000000=>0000000
[4,1,3,7,6,8,5,2]=>[2,5,8,6,7,3,1,4]=>0000000=>0000000
[6,5,7,8,1,4,3,2]=>[2,3,4,1,8,7,5,6]=>0001000=>0001000
[5,8,7,6,2,1,3,4]=>[4,3,1,2,6,7,8,5]=>0001000=>0001000
[4,3,8,5,7,2,6,1]=>[1,6,2,7,5,8,3,4]=>1000000=>0000001
[6,4,8,3,7,5,2,1]=>[1,2,5,7,3,8,4,6]=>1100000=>0000011
[3,6,8,2,5,7,4,1]=>[1,4,7,5,2,8,6,3]=>1000000=>0000001
[8,3,5,6,2,7,4,1]=>[1,4,7,2,6,5,3,8]=>1000001=>1000001
[8,7,3,5,2,6,4,1]=>[1,4,6,2,5,3,7,8]=>1000011=>1100001
[8,7,3,4,1,6,5,2]=>[2,5,6,1,4,3,7,8]=>0000011=>1100000
[3,5,8,7,4,6,2,1]=>[1,2,6,4,7,8,5,3]=>1100000=>0000011
[4,8,5,6,3,7,1,2]=>[2,1,7,3,6,5,8,4]=>0100000=>0000010
[6,4,2,7,8,5,3,1]=>[1,3,5,8,7,2,4,6]=>1000000=>0000001
[4,7,8,5,6,2,3,1]=>[1,3,2,6,5,8,7,4]=>1010000=>0000101
[3,5,6,7,8,2,4,1]=>[1,4,2,8,7,6,5,3]=>1000000=>0000001
[5,2,4,1,6,7,8,3]=>[3,8,7,6,1,4,2,5]=>0000000=>0000000
[4,5,3,6,1,7,8,2]=>[2,8,7,1,6,3,5,4]=>0000000=>0000000
[7,8,4,5,1,6,3,2]=>[2,3,6,1,5,4,8,7]=>0000010=>0100000
[7,6,5,3,8,4,2,1]=>[1,2,4,8,3,5,6,7]=>1100000=>0000011
[4,5,6,8,3,7,2,1]=>[1,2,7,3,8,6,5,4]=>1100000=>0000011
[8,7,4,3,6,5,1,2]=>[2,1,5,6,3,4,7,8]=>0100011=>1100010
[6,1,2,5,4,3,8,7]=>[7,8,3,4,5,2,1,6]=>0000000=>0000000
[2,8,6,3,4,7,1,5]=>[5,1,7,4,3,6,8,2]=>0000000=>0000000
[8,5,2,1,6,3,4,7]=>[7,4,3,6,1,2,5,8]=>0000001=>1000000
[8,1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1,8]=>0000001=>1000000
[2,8,1,6,7,5,3,4]=>[4,3,5,7,6,1,8,2]=>0000000=>0000000
[4,8,5,2,7,1,6,3]=>[3,6,1,7,2,5,8,4]=>0000000=>0000000
[8,3,1,5,7,6,2,4]=>[4,2,6,7,5,1,3,8]=>0000001=>1000000
[8,4,5,1,3,6,2,7]=>[7,2,6,3,1,5,4,8]=>0000001=>1000000
[8,1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1,8]=>0000001=>1000000
[5,4,1,3,2,8,7,6]=>[6,7,8,2,3,1,4,5]=>0000000=>0000000
[5,4,2,1,3,8,7,6]=>[6,7,8,3,1,2,4,5]=>0000000=>0000000
[3,2,7,4,1,6,5,8]=>[8,5,6,1,4,7,2,3]=>0000000=>0000000
[8,7,4,6,1,3,5,2]=>[2,5,3,1,6,4,7,8]=>0000011=>1100000
[6,8,1,3,2,4,5,7]=>[7,5,4,2,3,1,8,6]=>0000000=>0000000
[5,2,8,1,4,3,7,6]=>[6,7,3,4,1,8,2,5]=>0000000=>0000000
[7,1,6,8,2,4,5,3]=>[3,5,4,2,8,6,1,7]=>0000000=>0000000
[8,6,1,3,7,5,2,4]=>[4,2,5,7,3,1,6,8]=>0000001=>1000000
[5,8,3,1,4,6,2,7]=>[7,2,6,4,1,3,8,5]=>0000000=>0000000
[5,8,6,2,3,1,4,7]=>[7,4,1,3,2,6,8,5]=>0000000=>0000000
[5,8,7,3,2,4,6,1]=>[1,6,4,2,3,7,8,5]=>1000000=>0000001
[7,6,2,8,3,5,4,1]=>[1,4,5,3,8,2,6,7]=>1000000=>0000001
[8,2,6,3,1,4,7,5]=>[5,7,4,1,3,6,2,8]=>0000001=>1000000
[8,3,2,7,6,1,4,5]=>[5,4,1,6,7,2,3,8]=>0000001=>1000000
[5,8,4,3,2,7,6,1]=>[1,6,7,2,3,4,8,5]=>1000000=>0000001
[2,4,6,8,7,3,5,1]=>[1,5,3,7,8,6,4,2]=>1000000=>0000001
[6,8,5,7,2,3,4,1]=>[1,4,3,2,7,5,8,6]=>1001000=>0001001
[6,3,5,7,8,2,4,1]=>[1,4,2,8,7,5,3,6]=>1000000=>0000001
[3,5,6,8,7,2,4,1]=>[1,4,2,7,8,6,5,3]=>1000000=>0000001
[3,8,6,5,1,7,2,4]=>[4,2,7,1,5,6,8,3]=>0000000=>0000000
[6,5,8,3,7,4,2,1]=>[1,2,4,7,3,8,5,6]=>1100000=>0000011
[6,7,4,3,8,5,2,1]=>[1,2,5,8,3,4,7,6]=>1100000=>0000011
[2,6,8,5,4,7,3,1]=>[1,3,7,4,5,8,6,2]=>1000000=>0000001
[7,2,4,5,8,6,3,1]=>[1,3,6,8,5,4,2,7]=>1000000=>0000001
[2,7,4,6,8,5,3,1]=>[1,3,5,8,6,4,7,2]=>1000000=>0000001
[6,4,7,8,3,5,2,1]=>[1,2,5,3,8,7,4,6]=>1100000=>0000011
[8,4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4,8]=>1110001=>1000111
[5,2,4,1,6,3,8,7]=>[7,8,3,6,1,4,2,5]=>0000000=>0000000
[4,3,7,2,6,1,8,5]=>[5,8,1,6,2,7,3,4]=>0000000=>0000000
[6,3,5,2,7,4,8,1]=>[1,8,4,7,2,5,3,6]=>1000000=>0000001
[4,5,7,2,6,1,8,3]=>[3,8,1,6,2,7,5,4]=>0000000=>0000000
[7,5,4,2,6,1,8,3]=>[3,8,1,6,2,4,5,7]=>0000000=>0000000
[2,1,7,4,6,3,8,5]=>[5,8,3,6,4,7,1,2]=>0000000=>0000000
[4,5,7,3,6,2,8,1]=>[1,8,2,6,3,7,5,4]=>1000000=>0000001
[7,5,4,2,6,3,8,1]=>[1,8,3,6,2,4,5,7]=>1000000=>0000001
[4,5,7,2,6,3,8,1]=>[1,8,3,6,2,7,5,4]=>1000000=>0000001
[7,2,4,3,6,1,8,5]=>[5,8,1,6,3,4,2,7]=>0000000=>0000000
[6,2,4,3,7,5,8,1]=>[1,8,5,7,3,4,2,6]=>1000000=>0000001
[2,4,7,6,3,5,8,1]=>[1,8,5,3,6,7,4,2]=>1000000=>0000001
[6,7,4,8,3,5,2,1]=>[1,2,5,3,8,4,7,6]=>1100000=>0000011
[2,1,5,8,7,4,6,3]=>[3,6,4,7,8,5,1,2]=>0000000=>0000000
[5,8,3,6,4,7,2,1]=>[1,2,7,4,6,3,8,5]=>1100000=>0000011
[7,5,3,6,8,4,2,1]=>[1,2,4,8,6,3,5,7]=>1100000=>0000011
[8,4,3,5,7,2,6,1]=>[1,6,2,7,5,3,4,8]=>1000001=>1000001
[4,7,8,6,3,5,2,1]=>[1,2,5,3,6,8,7,4]=>1100000=>0000011
[6,8,7,4,5,3,2,1]=>[1,2,3,5,4,7,8,6]=>1110100=>0010111
[7,1,3,8,4,6,5,2]=>[2,5,6,4,8,3,1,7]=>0000000=>0000000
[1,8,6,7,3,4,5,2]=>[2,5,4,3,7,6,8,1]=>0000000=>0000000
[3,5,2,6,1,4,8,7]=>[7,8,4,1,6,2,5,3]=>0000000=>0000000
[4,5,7,2,3,8,6,1]=>[1,6,8,3,2,7,5,4]=>1000000=>0000001
[4,5,7,2,3,8,1,6]=>[6,1,8,3,2,7,5,4]=>0000000=>0000000
[4,5,6,2,3,1,8,7]=>[7,8,1,3,2,6,5,4]=>0000000=>0000000
[4,5,6,2,1,3,8,7]=>[7,8,3,1,2,6,5,4]=>0000000=>0000000
[4,5,6,1,3,2,8,7]=>[7,8,2,3,1,6,5,4]=>0000000=>0000000
[4,5,6,3,1,2,8,7]=>[7,8,2,1,3,6,5,4]=>0000000=>0000000
[4,5,7,3,2,8,1,6]=>[6,1,8,2,3,7,5,4]=>0000000=>0000000
[4,6,7,3,8,2,5,1]=>[1,5,2,8,3,7,6,4]=>1000000=>0000001
[4,6,7,3,8,2,1,5]=>[5,1,2,8,3,7,6,4]=>0000000=>0000000
[4,5,7,3,1,8,2,6]=>[6,2,8,1,3,7,5,4]=>0000000=>0000000
[3,5,1,7,4,8,2,6]=>[6,2,8,4,7,1,5,3]=>0000000=>0000000
[2,1,5,7,4,8,3,6]=>[6,3,8,4,7,5,1,2]=>0000000=>0000000
[4,5,7,1,3,8,6,2]=>[2,6,8,3,1,7,5,4]=>0000000=>0000000
[4,6,7,3,8,1,5,2]=>[2,5,1,8,3,7,6,4]=>0000000=>0000000
[5,6,7,8,3,1,4,2]=>[2,4,1,3,8,7,6,5]=>0001000=>0001000
[4,6,7,1,8,3,5,2]=>[2,5,3,8,1,7,6,4]=>0000000=>0000000
[3,6,1,7,8,4,5,2]=>[2,5,4,8,7,1,6,3]=>0000000=>0000000
[2,1,6,7,8,4,5,3]=>[3,5,4,8,7,6,1,2]=>0000000=>0000000
[2,1,6,7,8,4,3,5]=>[5,3,4,8,7,6,1,2]=>0000000=>0000000
[4,6,7,1,8,3,2,5]=>[5,2,3,8,1,7,6,4]=>0000000=>0000000
[5,6,7,8,1,3,2,4]=>[4,2,3,1,8,7,6,5]=>0001000=>0001000
[4,6,7,2,8,3,5,1]=>[1,5,3,8,2,7,6,4]=>1000000=>0000001
[3,6,2,7,8,4,5,1]=>[1,5,4,8,7,2,6,3]=>1000000=>0000001
[3,6,2,7,8,4,1,5]=>[5,1,4,8,7,2,6,3]=>0000000=>0000000
[3,4,2,1,7,8,5,6]=>[6,5,8,7,1,2,4,3]=>0000000=>0000000
[4,6,7,2,8,5,3,1]=>[1,3,5,8,2,7,6,4]=>1000000=>0000001
[4,6,7,2,8,5,1,3]=>[3,1,5,8,2,7,6,4]=>0000000=>0000000
[4,5,7,1,2,8,6,3]=>[3,6,8,2,1,7,5,4]=>0000000=>0000000
[2,1,6,7,8,3,5,4]=>[4,5,3,8,7,6,1,2]=>0000000=>0000000
[3,6,1,7,8,2,5,4]=>[4,5,2,8,7,1,6,3]=>0000000=>0000000
[4,6,7,1,8,2,5,3]=>[3,5,2,8,1,7,6,4]=>0000000=>0000000
[5,6,7,8,1,2,4,3]=>[3,4,2,1,8,7,6,5]=>0001000=>0001000
[5,6,7,8,2,4,1,3]=>[3,1,4,2,8,7,6,5]=>0001000=>0001000
[5,6,7,8,2,4,3,1]=>[1,3,4,2,8,7,6,5]=>1001000=>0001001
[3,6,1,7,8,5,2,4]=>[4,2,5,8,7,1,6,3]=>0000000=>0000000
[2,1,6,7,8,5,3,4]=>[4,3,5,8,7,6,1,2]=>0000000=>0000000
[3,4,2,1,6,5,8,7,10,9]=>[9,10,7,8,5,6,1,2,4,3]=>000000000=>000000000
[3,5,2,6,4,1,8,7,10,9]=>[9,10,7,8,1,4,6,2,5,3]=>000000000=>000000000
[3,5,2,7,4,8,6,1,10,9]=>[9,10,1,6,8,4,7,2,5,3]=>000000000=>000000000
[2,1,5,6,4,3,8,7,10,9]=>[9,10,7,8,3,4,6,5,1,2]=>000000000=>000000000
[4,5,6,3,2,1,8,7,10,9]=>[9,10,7,8,1,2,3,6,5,4]=>000000000=>000000000
[4,5,7,3,2,8,6,1,10,9]=>[9,10,1,6,8,2,3,7,5,4]=>000000000=>000000000
[4,5,7,3,2,9,6,10,8,1]=>[1,8,10,6,9,2,3,7,5,4]=>100000000=>000000001
[2,1,5,7,4,8,6,3,10,9]=>[9,10,3,6,8,4,7,5,1,2]=>000000000=>000000000
[4,6,7,3,8,5,2,1,10,9]=>[9,10,1,2,5,8,3,7,6,4]=>000000000=>000000000
[4,6,7,3,9,5,2,10,8,1]=>[1,8,10,2,5,9,3,7,6,4]=>100000000=>000000001
[2,1,5,7,4,9,6,10,8,3]=>[3,8,10,6,9,4,7,5,1,2]=>000000000=>000000000
[2,1,4,3,7,8,6,5,10,9]=>[9,10,5,6,8,7,3,4,1,2]=>000000000=>000000000
[3,4,2,1,7,8,6,5,10,9]=>[9,10,5,6,8,7,1,2,4,3]=>000000000=>000000000
[3,6,2,7,8,5,4,1,10,9]=>[9,10,1,4,5,8,7,2,6,3]=>000000000=>000000000
[3,6,2,7,9,5,4,10,8,1]=>[1,8,10,4,5,9,7,2,6,3]=>100000000=>000000001
[2,1,6,7,8,5,4,3,10,9]=>[9,10,3,4,5,8,7,6,1,2]=>000000000=>000000000
[5,6,7,8,4,3,2,1,10,9]=>[9,10,1,2,3,4,8,7,6,5]=>000000000=>000000000
[5,6,7,9,4,3,2,10,8,1]=>[1,8,10,2,3,4,9,7,6,5]=>100000000=>000000001
[2,1,6,7,9,5,4,10,8,3]=>[3,8,10,4,5,9,7,6,1,2]=>000000000=>000000000
[5,6,8,9,4,3,10,7,2,1]=>[1,2,7,10,3,4,9,8,6,5]=>110000000=>000000011
[2,1,4,3,7,9,6,10,8,5]=>[5,8,10,6,9,7,3,4,1,2]=>000000000=>000000000
[3,4,2,1,7,9,6,10,8,5]=>[5,8,10,6,9,7,1,2,4,3]=>000000000=>000000000
[3,6,2,8,9,5,10,7,4,1]=>[1,4,7,10,5,9,8,2,6,3]=>100000000=>000000001
[2,1,6,8,9,5,10,7,4,3]=>[3,4,7,10,5,9,8,6,1,2]=>000000000=>000000000
[2,1,4,3,6,5,9,10,8,7]=>[7,8,10,9,5,6,3,4,1,2]=>000000000=>000000000
[3,4,2,1,6,5,9,10,8,7]=>[7,8,10,9,5,6,1,2,4,3]=>000000000=>000000000
[3,5,2,6,4,1,9,10,8,7]=>[7,8,10,9,1,4,6,2,5,3]=>000000000=>000000000
[3,5,2,8,4,9,10,7,6,1]=>[1,6,7,10,9,4,8,2,5,3]=>100000000=>000000001
[2,1,5,6,4,3,9,10,8,7]=>[7,8,10,9,3,4,6,5,1,2]=>000000000=>000000000
[4,5,6,3,2,1,9,10,8,7]=>[7,8,10,9,1,2,3,6,5,4]=>000000000=>000000000
[4,5,8,3,2,9,10,7,6,1]=>[1,6,7,10,9,2,3,8,5,4]=>100000000=>000000001
[2,1,5,8,4,9,10,7,6,3]=>[3,6,7,10,9,4,8,5,1,2]=>000000000=>000000000
[4,7,8,3,9,10,6,5,2,1]=>[1,2,5,6,10,9,3,8,7,4]=>110000000=>000000011
[2,1,4,3,8,9,10,7,6,5]=>[5,6,7,10,9,8,3,4,1,2]=>000000000=>000000000
[3,4,2,1,8,9,10,7,6,5]=>[5,6,7,10,9,8,1,2,4,3]=>000000000=>000000000
[3,7,2,8,9,10,6,5,4,1]=>[1,4,5,6,10,9,8,2,7,3]=>100000000=>000000001
[5,3,1,6,2,4,8,7]=>[7,8,4,2,6,1,3,5]=>0000000=>0000000
[7,3,1,5,2,8,4,6]=>[6,4,8,2,5,1,3,7]=>0000000=>0000000
[8,4,5,1,2,7,3,6]=>[6,3,7,2,1,5,4,8]=>0000001=>1000000
[7,4,5,1,2,8,3,6]=>[6,3,8,2,1,5,4,7]=>0000000=>0000000
[6,4,5,1,2,3,8,7]=>[7,8,3,2,1,5,4,6]=>0000000=>0000000
[5,4,6,1,2,3,8,7]=>[7,8,3,2,1,6,4,5]=>0000000=>0000000
[3,6,1,5,2,4,8,7]=>[7,8,4,2,5,1,6,3]=>0000000=>0000000
[4,6,5,1,2,3,8,7]=>[7,8,3,2,1,5,6,4]=>0000000=>0000000
[5,6,4,1,2,3,8,7]=>[7,8,3,2,1,4,6,5]=>0000000=>0000000
[7,5,4,1,2,8,3,6]=>[6,3,8,2,1,4,5,7]=>0000000=>0000000
[8,6,4,1,7,2,3,5]=>[5,3,2,7,1,4,6,8]=>0000001=>1000000
[5,7,4,1,2,8,3,6]=>[6,3,8,2,1,4,7,5]=>0000000=>0000000
[3,7,1,5,2,8,4,6]=>[6,4,8,2,5,1,7,3]=>0000000=>0000000
[2,1,7,5,3,8,4,6]=>[6,4,8,3,5,7,1,2]=>0000000=>0000000
[4,8,5,1,2,7,3,6]=>[6,3,7,2,1,5,8,4]=>0000000=>0000000
[6,8,4,1,7,2,3,5]=>[5,3,2,7,1,4,8,6]=>0000000=>0000000
[4,8,6,1,7,2,3,5]=>[5,3,2,7,1,6,8,4]=>0000000=>0000000
[2,1,8,6,7,3,4,5]=>[5,4,3,7,6,8,1,2]=>0000000=>0000000
[2,1,7,6,8,3,4,5]=>[5,4,3,8,6,7,1,2]=>0000000=>0000000
[4,7,6,1,8,2,3,5]=>[5,3,2,8,1,6,7,4]=>0000000=>0000000
[5,7,6,8,1,2,3,4]=>[4,3,2,1,8,6,7,5]=>0001000=>0001000
[6,4,7,1,8,2,3,5]=>[5,3,2,8,1,7,4,6]=>0000000=>0000000
[8,4,6,1,7,2,3,5]=>[5,3,2,7,1,6,4,8]=>0000001=>1000000
[8,3,1,6,7,2,4,5]=>[5,4,2,7,6,1,3,8]=>0000001=>1000000
[4,3,1,2,7,8,5,6]=>[6,5,8,7,2,1,3,4]=>0000000=>0000000
[8,4,7,1,6,2,3,5]=>[5,3,2,6,1,7,4,8]=>0000001=>1000000
[7,4,8,1,6,2,3,5]=>[5,3,2,6,1,8,4,7]=>0000000=>0000000
[4,5,8,1,2,7,3,6]=>[6,3,7,2,1,8,5,4]=>0000000=>0000000
[2,1,6,8,7,3,4,5]=>[5,4,3,7,8,6,1,2]=>0000000=>0000000
[4,6,8,1,7,2,3,5]=>[5,3,2,7,1,8,6,4]=>0000000=>0000000
[5,6,8,7,1,2,3,4]=>[4,3,2,1,7,8,6,5]=>0001000=>0001000
[8,5,7,6,1,2,3,4]=>[4,3,2,1,6,7,5,8]=>0001001=>1001000
[4,7,8,1,6,2,3,5]=>[5,3,2,6,1,8,7,4]=>0000000=>0000000
[3,7,1,8,6,2,4,5]=>[5,4,2,6,8,1,7,3]=>0000000=>0000000
[3,8,1,7,6,2,4,5]=>[5,4,2,6,7,1,8,3]=>0000000=>0000000
[4,8,7,1,6,2,3,5]=>[5,3,2,6,1,7,8,4]=>0000000=>0000000
[6,8,7,5,1,2,3,4]=>[4,3,2,1,5,7,8,6]=>0001100=>0011000
[6,4,7,3,8,5,1,2]=>[2,1,5,8,3,7,4,6]=>0100000=>0000010
[5,4,2,7,6,1,3,8]=>[8,3,1,6,7,2,4,5]=>0000000=>0000000
[5,4,2,7,6,1,8,3]=>[3,8,1,6,7,2,4,5]=>0000000=>0000000
[5,4,3,7,6,8,1,2]=>[2,1,8,6,7,3,4,5]=>0100000=>0000010
[5,4,3,6,8,7,1,2]=>[2,1,7,8,6,3,4,5]=>0100000=>0000010
[5,4,2,6,7,1,8,3]=>[3,8,1,7,6,2,4,5]=>0000000=>0000000
[5,3,2,6,1,8,4,7]=>[7,4,8,1,6,2,3,5]=>0000000=>0000000
[6,3,8,2,1,5,4,7]=>[7,4,5,1,2,8,3,6]=>0000000=>0000000
[7,8,3,2,1,5,4,6]=>[6,4,5,1,2,3,8,7]=>0000010=>0100000
[7,8,3,2,1,5,6,4]=>[4,6,5,1,2,3,8,7]=>0000010=>0100000
[5,3,2,7,1,6,4,8]=>[8,4,6,1,7,2,3,5]=>0000000=>0000000
[6,3,7,2,1,8,5,4]=>[4,5,8,1,2,7,3,6]=>0000000=>0000000
[5,4,2,8,7,1,3,6]=>[6,3,1,7,8,2,4,5]=>0000000=>0000000
[7,8,3,2,1,6,4,5]=>[5,4,6,1,2,3,8,7]=>0000010=>0100000
[5,3,2,8,1,7,4,6]=>[6,4,7,1,8,2,3,5]=>0000000=>0000000
[4,3,2,1,8,7,5,6]=>[6,5,7,8,1,2,3,4]=>0000000=>0000000
[4,3,2,1,7,5,8,6]=>[6,8,5,7,1,2,3,4]=>0000000=>0000000
[4,3,2,1,7,5,6,8]=>[8,6,5,7,1,2,3,4]=>0000000=>0000000
[5,3,2,8,1,4,7,6]=>[6,7,4,1,8,2,3,5]=>0000000=>0000000
[7,8,3,2,1,4,6,5]=>[5,6,4,1,2,3,8,7]=>0000010=>0100000
[4,3,2,1,8,5,6,7]=>[7,6,5,8,1,2,3,4]=>0000000=>0000000
[7,8,5,6,1,2,4,3]=>[3,4,2,1,6,5,8,7]=>0001010=>0101000
[7,8,4,1,6,2,5,3]=>[3,5,2,6,1,4,8,7]=>0000010=>0100000
[1,6,8,3,2,7,5,4]=>[4,5,7,2,3,8,6,1]=>0000000=>0000000
[6,1,8,3,2,7,5,4]=>[4,5,7,2,3,8,1,6]=>0000000=>0000000
[7,8,1,3,2,6,5,4]=>[4,5,6,2,3,1,8,7]=>0000010=>0100000
[7,8,3,1,2,6,5,4]=>[4,5,6,2,1,3,8,7]=>0000010=>0100000
[7,8,2,3,1,6,5,4]=>[4,5,6,1,3,2,8,7]=>0000010=>0100000
[7,8,2,1,3,6,5,4]=>[4,5,6,3,1,2,8,7]=>0000010=>0100000
[7,8,1,2,3,6,5,4]=>[4,5,6,3,2,1,8,7]=>0000010=>0100000
[1,5,2,8,3,7,6,4]=>[4,6,7,3,8,2,5,1]=>0000000=>0000000
[5,1,2,8,3,7,6,4]=>[4,6,7,3,8,2,1,5]=>0000000=>0000000
[5,2,1,8,3,7,6,4]=>[4,6,7,3,8,1,2,5]=>0000000=>0000000
[6,2,8,1,3,7,5,4]=>[4,5,7,3,1,8,2,6]=>0000000=>0000000
[6,2,8,4,7,1,5,3]=>[3,5,1,7,4,8,2,6]=>0000000=>0000000
[6,3,8,4,7,5,1,2]=>[2,1,5,7,4,8,3,6]=>0100000=>0000010
[2,6,8,3,1,7,5,4]=>[4,5,7,1,3,8,6,2]=>0000000=>0000000
[2,5,1,8,3,7,6,4]=>[4,6,7,3,8,1,5,2]=>0000000=>0000000
[1,2,5,8,3,7,6,4]=>[4,6,7,3,8,5,2,1]=>0000000=>0000000
[2,5,3,8,1,7,6,4]=>[4,6,7,1,8,3,5,2]=>0000000=>0000000
[2,5,4,8,7,1,6,3]=>[3,6,1,7,8,4,5,2]=>0000000=>0000000
[3,5,4,8,7,6,1,2]=>[2,1,6,7,8,4,5,3]=>0100000=>0000010
[5,3,4,8,7,6,1,2]=>[2,1,6,7,8,4,3,5]=>0100000=>0000010
[5,2,4,8,7,1,6,3]=>[3,6,1,7,8,4,2,5]=>0000000=>0000000
[5,2,3,8,1,7,6,4]=>[4,6,7,1,8,3,2,5]=>0000000=>0000000
[4,1,2,3,8,7,6,5]=>[5,6,7,8,3,2,1,4]=>0000000=>0000000
[1,4,2,3,8,7,6,5]=>[5,6,7,8,3,2,4,1]=>0000000=>0000000
[4,1,3,2,8,7,6,5]=>[5,6,7,8,2,3,1,4]=>0000000=>0000000
[6,3,8,1,2,7,5,4]=>[4,5,7,2,1,8,3,6]=>0000000=>0000000
[5,3,1,8,2,7,6,4]=>[4,6,7,2,8,1,3,5]=>0000000=>0000000
[5,1,3,8,2,7,6,4]=>[4,6,7,2,8,3,1,5]=>0000000=>0000000
[1,5,3,8,2,7,6,4]=>[4,6,7,2,8,3,5,1]=>0000000=>0000000
[1,5,4,8,7,2,6,3]=>[3,6,2,7,8,4,5,1]=>0000000=>0000000
[5,1,4,8,7,2,6,3]=>[3,6,2,7,8,4,1,5]=>0000000=>0000000
[5,4,1,8,7,2,6,3]=>[3,6,2,7,8,1,4,5]=>0000000=>0000000
[6,5,8,7,1,2,4,3]=>[3,4,2,1,7,8,5,6]=>0001000=>0001000
[5,6,8,7,3,4,1,2]=>[2,1,4,3,7,8,6,5]=>0101000=>0001010
[5,6,8,7,2,1,4,3]=>[3,4,1,2,7,8,6,5]=>0001000=>0001000
[4,5,1,8,7,2,6,3]=>[3,6,2,7,8,1,5,4]=>0000000=>0000000
[4,1,5,8,7,2,6,3]=>[3,6,2,7,8,5,1,4]=>0000000=>0000000
[1,3,5,8,2,7,6,4]=>[4,6,7,2,8,5,3,1]=>0000000=>0000000
[3,1,5,8,2,7,6,4]=>[4,6,7,2,8,5,1,3]=>0000000=>0000000
[3,6,8,2,1,7,5,4]=>[4,5,7,1,2,8,6,3]=>0000000=>0000000
[4,6,8,3,7,5,1,2]=>[2,1,5,7,3,8,6,4]=>0100000=>0000010
[4,5,3,8,7,6,1,2]=>[2,1,6,7,8,3,5,4]=>0100000=>0000010
[3,5,2,8,1,7,6,4]=>[4,6,7,1,8,2,5,3]=>0000000=>0000000
[3,1,4,2,8,7,6,5]=>[5,6,7,8,2,4,1,3]=>0000000=>0000000
[3,2,5,8,1,7,6,4]=>[4,6,7,1,8,5,2,3]=>0000000=>0000000
[4,2,5,8,7,1,6,3]=>[3,6,1,7,8,5,2,4]=>0000000=>0000000
[4,3,5,8,7,6,1,2]=>[2,1,6,7,8,5,3,4]=>0100000=>0000010
[2,4,5,8,7,1,6,3]=>[3,6,1,7,8,5,4,2]=>0000000=>0000000
[2,3,5,8,1,7,6,4]=>[4,6,7,1,8,5,3,2]=>0000000=>0000000
[6,2,5,1,4,3,8,7]=>[7,8,3,4,1,5,2,6]=>0000000=>0000000
[5,2,6,1,4,3,8,7]=>[7,8,3,4,1,6,2,5]=>0000000=>0000000
[5,2,7,1,4,3,8,6]=>[6,8,3,4,1,7,2,5]=>0000000=>0000000
[6,2,8,1,4,3,7,5]=>[5,7,3,4,1,8,2,6]=>0000000=>0000000
[6,2,7,1,4,3,8,5]=>[5,8,3,4,1,7,2,6]=>0000000=>0000000
[7,2,6,1,4,3,8,5]=>[5,8,3,4,1,6,2,7]=>0000000=>0000000
[8,2,5,1,4,3,7,6]=>[6,7,3,4,1,5,2,8]=>0000001=>1000000
[8,1,4,3,7,2,6,5]=>[5,6,2,7,3,4,1,8]=>0000001=>1000000
[8,2,6,1,5,3,7,4]=>[4,7,3,5,1,6,2,8]=>0000001=>1000000
[7,2,6,1,5,3,8,4]=>[4,8,3,5,1,6,2,7]=>0000000=>0000000
[6,2,7,1,5,3,8,4]=>[4,8,3,5,1,7,2,6]=>0000000=>0000000
[6,2,8,1,5,3,7,4]=>[4,7,3,5,1,8,2,6]=>0000000=>0000000
[7,4,8,1,3,2,6,5]=>[5,6,2,3,1,8,4,7]=>0000000=>0000000
[8,3,7,1,4,2,6,5]=>[5,6,2,4,1,7,3,8]=>0000001=>1000000
[8,3,7,1,5,2,6,4]=>[4,6,2,5,1,7,3,8]=>0000001=>1000000
[7,3,8,1,5,2,6,4]=>[4,6,2,5,1,8,3,7]=>0000000=>0000000
[6,2,7,3,8,1,5,4]=>[4,5,1,8,3,7,2,6]=>0000000=>0000000
[6,2,8,3,7,1,5,4]=>[4,5,1,7,3,8,2,6]=>0000000=>0000000
[5,1,8,3,7,2,6,4]=>[4,6,2,7,3,8,1,5]=>0000000=>0000000
[4,1,8,3,7,2,6,5]=>[5,6,2,7,3,8,1,4]=>0000000=>0000000
[3,1,7,4,8,2,6,5]=>[5,6,2,8,4,7,1,3]=>0000000=>0000000
[4,1,7,3,8,2,6,5]=>[5,6,2,8,3,7,1,4]=>0000000=>0000000
[5,1,7,3,8,2,6,4]=>[4,6,2,8,3,7,1,5]=>0000000=>0000000
[7,3,8,2,6,1,5,4]=>[4,5,1,6,2,8,3,7]=>0000000=>0000000
[8,2,6,3,7,1,5,4]=>[4,5,1,7,3,6,2,8]=>0000001=>1000000
[3,4,2,6,8,1,5,7]=>[7,5,1,8,6,2,4,3]=>0000000=>0000000
[5,3,6,2,8,1,4,7]=>[7,4,1,8,2,6,3,5]=>0000000=>0000000
[7,4,2,5,8,3,6,1]=>[1,6,3,8,5,2,4,7]=>1000000=>0000001
[4,5,2,6,3,8,1,7]=>[7,1,8,3,6,2,5,4]=>0000000=>0000000
[3,5,6,1,4,8,2,7]=>[7,2,8,4,1,6,5,3]=>0000000=>0000000
[4,1,5,6,3,8,2,7]=>[7,2,8,3,6,5,1,4]=>0000000=>0000000
[4,5,1,6,3,8,2,7]=>[7,2,8,3,6,1,5,4]=>0000000=>0000000
[4,5,6,3,2,8,1,7]=>[7,1,8,2,3,6,5,4]=>0000000=>0000000
[6,7,4,8,3,2,5,1]=>[1,5,2,3,8,4,7,6]=>1000000=>0000001
[6,7,4,8,3,2,1,5]=>[5,1,2,3,8,4,7,6]=>0000000=>0000000
[6,7,4,1,8,3,2,5]=>[5,2,3,8,1,4,7,6]=>0000000=>0000000
[5,3,7,8,1,4,2,6]=>[6,2,4,1,8,7,3,5]=>0000000=>0000000
[7,3,5,8,1,4,6,2]=>[2,6,4,1,8,5,3,7]=>0000000=>0000000
[4,5,1,7,8,3,6,2]=>[2,6,3,8,7,1,5,4]=>0000000=>0000000
[7,4,1,5,8,3,6,2]=>[2,6,3,8,5,1,4,7]=>0000000=>0000000
[6,7,4,3,8,1,5,2]=>[2,5,1,8,3,4,7,6]=>0000000=>0000000
[5,6,1,7,3,8,4,2]=>[2,4,8,3,7,1,6,5]=>0000000=>0000000
[5,1,6,7,3,8,4,2]=>[2,4,8,3,7,6,1,5]=>0000000=>0000000
[6,4,7,1,8,3,5,2]=>[2,5,3,8,1,7,4,6]=>0000000=>0000000
[6,7,8,3,1,4,5,2]=>[2,5,4,1,3,8,7,6]=>0000100=>0010000
[6,7,2,8,4,5,1,3]=>[3,1,5,4,8,2,7,6]=>0000000=>0000000
[6,7,2,8,4,1,3,5]=>[5,3,1,4,8,2,7,6]=>0000000=>0000000
[6,1,7,4,8,3,2,5]=>[5,2,3,8,4,7,1,6]=>0000000=>0000000
[5,1,6,7,3,2,8,4]=>[4,8,2,3,7,6,1,5]=>0000000=>0000000
[5,6,1,7,3,2,8,4]=>[4,8,2,3,7,1,6,5]=>0000000=>0000000
[5,6,7,3,2,1,8,4]=>[4,8,1,2,3,7,6,5]=>0000000=>0000000
[5,6,7,3,2,8,4,1]=>[1,4,8,2,3,7,6,5]=>1000000=>0000001
[7,4,2,5,1,8,3,6]=>[6,3,8,1,5,2,4,7]=>0000000=>0000000
[6,7,4,2,8,3,5,1]=>[1,5,3,8,2,4,7,6]=>1000000=>0000001
[3,6,7,2,8,4,5,1]=>[1,5,4,8,2,7,6,3]=>1000000=>0000001
[3,6,7,2,8,4,1,5]=>[5,1,4,8,2,7,6,3]=>0000000=>0000000
[3,6,7,2,1,8,4,5]=>[5,4,8,1,2,7,6,3]=>0000000=>0000000
[3,4,7,8,2,1,5,6]=>[6,5,1,2,8,7,4,3]=>0000000=>0000000
[3,7,8,1,4,6,2,5]=>[5,2,6,4,1,8,7,3]=>0000000=>0000000
[3,6,7,2,8,5,1,4]=>[4,1,5,8,2,7,6,3]=>0000000=>0000000
[3,6,7,8,5,2,1,4]=>[4,1,2,5,8,7,6,3]=>0000000=>0000000
[3,6,7,8,5,2,4,1]=>[1,4,2,5,8,7,6,3]=>1000000=>0000001
[6,4,7,8,2,5,3,1]=>[1,3,5,2,8,7,4,6]=>1000000=>0000001
[6,4,7,8,2,1,5,3]=>[3,5,1,2,8,7,4,6]=>0000000=>0000000
[5,3,7,8,1,6,2,4]=>[4,2,6,1,8,7,3,5]=>0000000=>0000000
[6,7,2,8,5,1,3,4]=>[4,3,1,5,8,2,7,6]=>0000000=>0000000
[6,4,1,7,8,2,5,3]=>[3,5,2,8,7,1,4,6]=>0000000=>0000000
[5,1,6,2,7,8,4,3]=>[3,4,8,7,2,6,1,5]=>0000000=>0000000
[5,6,2,7,1,8,4,3]=>[3,4,8,1,7,2,6,5]=>0000000=>0000000
[5,6,2,7,8,4,3,1]=>[1,3,4,8,7,2,6,5]=>1000000=>0000001
[5,6,7,2,8,4,3,1]=>[1,3,4,8,2,7,6,5]=>1000000=>0000001
[5,6,7,2,1,8,4,3]=>[3,4,8,1,2,7,6,5]=>0000000=>0000000
[5,6,1,7,2,8,4,3]=>[3,4,8,2,7,1,6,5]=>0000000=>0000000
[5,1,6,7,2,8,4,3]=>[3,4,8,2,7,6,1,5]=>0000000=>0000000
[6,7,8,3,5,1,4,2]=>[2,4,1,5,3,8,7,6]=>0000100=>0010000
[5,6,1,7,8,4,3,2]=>[2,3,4,8,7,1,6,5]=>0000000=>0000000
[5,6,7,1,8,4,3,2]=>[2,3,4,8,1,7,6,5]=>0000000=>0000000
[8,3,2,5,1,6,4,7]=>[7,4,6,1,5,2,3,8]=>0000001=>1000000
[5,3,2,7,4,1,8,6]=>[6,8,1,4,7,2,3,5]=>0000000=>0000000
[7,5,3,8,2,4,6,1]=>[1,6,4,2,8,3,5,7]=>1000000=>0000001
[8,2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2,8]=>0000001=>1000000
[8,2,4,5,6,1,3,7]=>[7,3,1,6,5,4,2,8]=>0000001=>1000000
[8,5,3,6,4,1,2,7]=>[7,2,1,4,6,3,5,8]=>0000001=>1000000
[8,4,1,5,6,3,2,7]=>[7,2,3,6,5,1,4,8]=>0000001=>1000000
[8,1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1,8]=>0000001=>1000000
[4,5,3,7,2,1,8,6]=>[6,8,1,2,7,3,5,4]=>0000000=>0000000
[7,4,5,8,3,2,6,1]=>[1,6,2,3,8,5,4,7]=>1000000=>0000001
[4,3,6,7,2,8,5,1]=>[1,5,8,2,7,6,3,4]=>1000000=>0000001
[4,3,6,7,2,8,1,5]=>[5,1,8,2,7,6,3,4]=>0000000=>0000000
[1,4,3,6,7,2,8,5]=>[5,8,2,7,6,3,4,1]=>0000000=>0000000
[4,5,3,7,1,8,2,6]=>[6,2,8,1,7,3,5,4]=>0000000=>0000000
[5,3,4,7,1,2,8,6]=>[6,8,2,1,7,4,3,5]=>0000000=>0000000
[7,4,5,8,3,6,1,2]=>[2,1,6,3,8,5,4,7]=>0100000=>0000010
[4,3,6,7,8,1,5,2]=>[2,5,1,8,7,6,3,4]=>0000000=>0000000
[3,5,6,7,8,4,1,2]=>[2,1,4,8,7,6,5,3]=>0100000=>0000010
[3,1,5,6,7,8,4,2]=>[2,4,8,7,6,5,1,3]=>0000000=>0000000
[4,6,1,7,8,3,5,2]=>[2,5,3,8,7,1,6,4]=>0000000=>0000000
[6,2,4,1,7,8,5,3]=>[3,5,8,7,1,4,2,6]=>0000000=>0000000
[2,6,7,1,4,8,3,5]=>[5,3,8,4,1,7,6,2]=>0000000=>0000000
[1,5,3,6,7,8,2,4]=>[4,2,8,7,6,3,5,1]=>0000000=>0000000
[4,5,2,7,8,1,3,6]=>[6,3,1,8,7,2,5,4]=>0000000=>0000000
[4,2,6,7,8,3,1,5]=>[5,1,3,8,7,6,2,4]=>0000000=>0000000
[4,2,6,7,8,3,5,1]=>[1,5,3,8,7,6,2,4]=>1000000=>0000001
[3,6,2,7,4,8,1,5]=>[5,1,8,4,7,2,6,3]=>0000000=>0000000
[3,7,4,2,1,5,8,6]=>[6,8,5,1,2,4,7,3]=>0000000=>0000000
[7,8,4,2,1,3,6,5]=>[5,6,3,1,2,4,8,7]=>0000010=>0100000
[6,3,2,7,1,8,5,4]=>[4,5,8,1,7,2,3,6]=>0000000=>0000000
[3,6,2,7,1,8,5,4]=>[4,5,8,1,7,2,6,3]=>0000000=>0000000
[6,7,3,8,2,5,4,1]=>[1,4,5,2,8,3,7,6]=>1000000=>0000001
[6,4,7,8,5,2,3,1]=>[1,3,2,5,8,7,4,6]=>1010000=>0000101
[2,6,4,7,8,1,5,3]=>[3,5,1,8,7,4,6,2]=>0000000=>0000000
[7,4,1,5,8,6,2,3]=>[3,2,6,8,5,1,4,7]=>0000000=>0000000
[7,5,8,2,1,6,3,4]=>[4,3,6,1,2,8,5,7]=>0000000=>0000000
[6,2,7,1,3,8,5,4]=>[4,5,8,3,1,7,2,6]=>0000000=>0000000
[6,3,1,7,8,2,5,4]=>[4,5,2,8,7,1,3,6]=>0000000=>0000000
[4,6,1,7,8,5,2,3]=>[3,2,5,8,7,1,6,4]=>0000000=>0000000
[5,1,2,6,7,8,4,3]=>[3,4,8,7,6,2,1,5]=>0000000=>0000000
[5,2,6,7,8,4,3,1]=>[1,3,4,8,7,6,2,5]=>1000000=>0000001
[1,6,4,7,8,5,2,3]=>[3,2,5,8,7,4,6,1]=>0000000=>0000000
[2,6,7,1,3,8,5,4]=>[4,5,8,3,1,7,6,2]=>0000000=>0000000
[6,7,3,8,5,1,4,2]=>[2,4,1,5,8,3,7,6]=>0000000=>0000000
[6,4,7,8,5,3,1,2]=>[2,1,3,5,8,7,4,6]=>0110000=>0000110
[3,1,2,6,5,8,7,4]=>[4,7,8,5,6,2,1,3]=>0000000=>0000000
[4,5,1,2,3,8,7,6]=>[6,7,8,3,2,1,5,4]=>0000000=>0000000
[4,6,1,2,3,8,7,5]=>[5,7,8,3,2,1,6,4]=>0000000=>0000000
[1,6,5,3,4,8,7,2]=>[2,7,8,4,3,5,6,1]=>0000000=>0000000
[6,1,5,2,4,8,7,3]=>[3,7,8,4,2,5,1,6]=>0000000=>0000000
[6,5,1,2,3,8,7,4]=>[4,7,8,3,2,1,5,6]=>0000000=>0000000
[6,4,1,2,3,8,7,5]=>[5,7,8,3,2,1,4,6]=>0000000=>0000000
[5,4,1,2,3,8,7,6]=>[6,7,8,3,2,1,4,5]=>0000000=>0000000
[5,4,1,2,7,3,6,8]=>[8,6,3,7,2,1,4,5]=>0000000=>0000000
[6,4,1,7,2,3,5,8]=>[8,5,3,2,7,1,4,6]=>0000000=>0000000
[6,4,1,8,2,3,5,7]=>[7,5,3,2,8,1,4,6]=>0000000=>0000000
[7,4,1,2,8,3,6,5]=>[5,6,3,8,2,1,4,7]=>0000000=>0000000
[7,5,1,2,8,3,6,4]=>[4,6,3,8,2,1,5,7]=>0000000=>0000000
[7,1,5,2,8,4,6,3]=>[3,6,4,8,2,5,1,7]=>0000000=>0000000
[1,7,5,3,8,4,6,2]=>[2,6,4,8,3,5,7,1]=>0000000=>0000000
[8,4,1,2,7,3,6,5]=>[5,6,3,7,2,1,4,8]=>0000001=>1000000
[8,4,1,7,2,3,5,6]=>[6,5,3,2,7,1,4,8]=>0000001=>1000000
[7,4,1,6,2,3,5,8]=>[8,5,3,2,6,1,4,7]=>0000000=>0000000
[8,6,1,7,2,3,5,4]=>[4,5,3,2,7,1,6,8]=>0000001=>1000000
[8,1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1,8]=>0000001=>1000000
[1,7,6,8,3,4,5,2]=>[2,5,4,3,8,6,7,1]=>0000000=>0000000
[7,6,1,8,2,3,5,4]=>[4,5,3,2,8,1,6,7]=>0000000=>0000000
[3,1,2,7,8,5,6,4]=>[4,6,5,8,7,2,1,3]=>0000000=>0000000
[3,1,8,7,2,4,5,6]=>[6,5,4,2,7,8,1,3]=>0000000=>0000000
[3,1,7,6,2,4,5,8]=>[8,5,4,2,6,7,1,3]=>0000000=>0000000
[4,7,1,6,2,3,5,8]=>[8,5,3,2,6,1,7,4]=>0000000=>0000000
[4,8,1,6,2,3,5,7]=>[7,5,3,2,6,1,8,4]=>0000000=>0000000
[5,8,1,2,7,3,6,4]=>[4,6,3,7,2,1,8,5]=>0000000=>0000000
[5,1,8,2,7,4,6,3]=>[3,6,4,7,2,8,1,5]=>0000000=>0000000
[1,5,8,3,7,4,6,2]=>[2,6,4,7,3,8,5,1]=>0000000=>0000000
[1,6,8,7,3,4,5,2]=>[2,5,4,3,7,8,6,1]=>0000000=>0000000
[6,1,8,7,2,4,5,3]=>[3,5,4,2,7,8,1,6]=>0000000=>0000000
[6,8,1,7,2,3,5,4]=>[4,5,3,2,7,1,8,6]=>0000000=>0000000
[6,8,7,1,2,3,4,5]=>[5,4,3,2,1,7,8,6]=>0000100=>0010000
[5,8,6,1,2,3,4,7]=>[7,4,3,2,1,6,8,5]=>0000000=>0000000
[5,7,6,1,2,3,4,8]=>[8,4,3,2,1,6,7,5]=>0000000=>0000000
[7,8,1,6,2,3,5,4]=>[4,5,3,2,6,1,8,7]=>0000010=>0100000
[7,1,8,6,2,4,5,3]=>[3,5,4,2,6,8,1,7]=>0000000=>0000000
[1,7,8,6,3,4,5,2]=>[2,5,4,3,6,8,7,1]=>0000000=>0000000
[8,1,7,6,2,4,5,3]=>[3,5,4,2,6,7,1,8]=>0000001=>1000000
[8,7,1,6,2,3,5,4]=>[4,5,3,2,6,1,7,8]=>0000011=>1100000
[8,5,3,7,2,1,4,6]=>[6,4,1,2,7,3,5,8]=>0000001=>1000000
[6,8,1,4,5,7,3,2]=>[2,3,7,5,4,1,8,6]=>0000000=>0000000
[8,7,2,4,5,1,3,6]=>[6,3,1,5,4,2,7,8]=>0000011=>1100000
[2,6,1,4,5,3,8,7]=>[7,8,3,5,4,1,6,2]=>0000000=>0000000
[6,3,1,4,5,2,8,7]=>[7,8,2,5,4,1,3,6]=>0000000=>0000000
[3,1,6,4,5,2,8,7]=>[7,8,2,5,4,6,1,3]=>0000000=>0000000
[8,3,7,4,5,1,2,6]=>[6,2,1,5,4,7,3,8]=>0000001=>1000000
[5,8,7,4,2,6,3,1]=>[1,3,6,2,4,7,8,5]=>1000000=>0000001
[8,1,7,4,2,6,3,5]=>[5,3,6,2,4,7,1,8]=>0000001=>1000000
[3,7,8,4,5,1,2,6]=>[6,2,1,5,4,8,7,3]=>0000000=>0000000
[5,6,3,8,1,7,2,4]=>[4,2,7,1,8,3,6,5]=>0000000=>0000000
[7,6,1,4,5,8,3,2]=>[2,3,8,5,4,1,6,7]=>0000000=>0000000
[3,7,6,4,5,8,2,1]=>[1,2,8,5,4,6,7,3]=>1100000=>0000011
[8,5,7,4,1,6,3,2]=>[2,3,6,1,4,7,5,8]=>0000001=>1000000
[2,5,8,4,7,6,1,3]=>[3,1,6,7,4,8,5,2]=>0000000=>0000000
[3,8,4,2,5,6,7,1]=>[1,7,6,5,2,4,8,3]=>1000000=>0000001
[8,4,1,3,5,6,7,2]=>[2,7,6,5,3,1,4,8]=>0000001=>1000000
[7,5,8,4,3,6,1,2]=>[2,1,6,3,4,8,5,7]=>0100000=>0000010
[6,5,3,8,4,1,7,2]=>[2,7,1,4,8,3,5,6]=>0000000=>0000000
[2,1,4,8,3,6,7,5]=>[5,7,6,3,8,4,1,2]=>0000000=>0000000
[7,3,8,4,2,6,1,5]=>[5,1,6,2,4,8,3,7]=>0000000=>0000000
[8,3,1,2,5,6,7,4]=>[4,7,6,5,2,1,3,8]=>0000001=>1000000
[4,8,2,3,5,6,7,1]=>[1,7,6,5,3,2,8,4]=>1000000=>0000001
[2,7,8,4,5,3,1,6]=>[6,1,3,5,4,8,7,2]=>0000000=>0000000
[8,7,1,4,3,6,2,5]=>[5,2,6,3,4,1,7,8]=>0000011=>1100000
[5,6,3,8,4,2,7,1]=>[1,7,2,4,8,3,6,5]=>1000000=>0000001
[8,6,3,1,4,2,7,5]=>[5,7,2,4,1,3,6,8]=>0000001=>1000000
[8,6,3,5,1,2,7,4]=>[4,7,2,1,5,3,6,8]=>0000001=>1000000
[5,8,3,2,6,1,7,4]=>[4,7,1,6,2,3,8,5]=>0000000=>0000000
[3,5,8,4,7,6,2,1]=>[1,2,6,7,4,8,5,3]=>1100000=>0000011
[5,8,2,4,7,6,1,3]=>[3,1,6,7,4,2,8,5]=>0000000=>0000000
[7,1,6,4,5,8,2,3]=>[3,2,8,5,4,6,1,7]=>0000000=>0000000
[2,1,8,5,3,6,7,4]=>[4,7,6,3,5,8,1,2]=>0000000=>0000000
[6,8,3,5,2,1,7,4]=>[4,7,1,2,5,3,8,6]=>0000000=>0000000
[7,8,5,4,2,6,1,3]=>[3,1,6,2,4,5,8,7]=>0000010=>0100000
[4,8,1,2,5,6,7,3]=>[3,7,6,5,2,1,8,4]=>0000000=>0000000
[3,4,2,8,5,6,7,1]=>[1,7,6,5,8,2,4,3]=>1000000=>0000001
[2,4,1,8,5,6,7,3]=>[3,7,6,5,8,1,4,2]=>0000000=>0000000
[8,4,2,1,5,6,7,3]=>[3,7,6,5,1,2,4,8]=>0000001=>1000000
[7,5,2,4,8,6,1,3]=>[3,1,6,8,4,2,5,7]=>0000000=>0000000
[2,1,5,3,8,6,7,4]=>[4,7,6,8,3,5,1,2]=>0000000=>0000000
[3,1,4,8,5,6,7,2]=>[2,7,6,5,8,4,1,3]=>0000000=>0000000
[6,5,3,7,2,8,4,1]=>[1,4,8,2,7,3,5,6]=>1000000=>0000001
[6,7,2,4,5,8,3,1]=>[1,3,8,5,4,2,7,6]=>1000000=>0000001
[2,5,7,4,8,6,3,1]=>[1,3,6,8,4,7,5,2]=>1000000=>0000001
[5,6,3,7,1,8,4,2]=>[2,4,8,1,7,3,6,5]=>0000000=>0000000
[3,8,7,4,5,2,1,6]=>[6,1,2,5,4,7,8,3]=>0000000=>0000000
[3,7,5,4,8,6,2,1]=>[1,2,6,8,4,5,7,3]=>1100000=>0000011
[4,6,3,5,8,2,7,1]=>[1,7,2,8,5,3,6,4]=>1000000=>0000001
[3,7,8,4,1,6,2,5]=>[5,2,6,1,4,8,7,3]=>0000000=>0000000
[5,4,2,3,7,6,1,8]=>[8,1,6,7,3,2,4,5]=>0000000=>0000000
[3,2,7,6,4,5,1,8]=>[8,1,5,4,6,7,2,3]=>0000000=>0000000
[4,7,2,6,3,5,1,8]=>[8,1,5,3,6,2,7,4]=>0000000=>0000000
[5,7,6,2,3,4,1,8]=>[8,1,4,3,2,6,7,5]=>0000000=>0000000
[1,7,5,2,8,3,4,6]=>[6,4,3,8,2,5,7,1]=>0000000=>0000000
[6,8,5,2,3,1,4,7]=>[7,4,1,3,2,5,8,6]=>0000000=>0000000
[4,8,2,6,3,1,5,7]=>[7,5,1,3,6,2,8,4]=>0000000=>0000000
[3,2,8,6,4,1,5,7]=>[7,5,1,4,6,8,2,3]=>0000000=>0000000
[7,1,5,2,8,3,4,6]=>[6,4,3,8,2,5,1,7]=>0000000=>0000000
[1,8,5,2,7,3,4,6]=>[6,4,3,7,2,5,8,1]=>0000000=>0000000
[7,1,6,8,2,3,4,5]=>[5,4,3,2,8,6,1,7]=>0000000=>0000000
[3,2,1,7,8,4,5,6]=>[6,5,4,8,7,1,2,3]=>0000000=>0000000
[3,2,8,7,1,4,5,6]=>[6,5,4,1,7,8,2,3]=>0000000=>0000000
[5,8,7,2,1,3,4,6]=>[6,4,3,1,2,7,8,5]=>0000000=>0000000
[1,7,6,8,2,3,4,5]=>[5,4,3,2,8,6,7,1]=>0000000=>0000000
[6,5,8,2,3,1,4,7]=>[7,4,1,3,2,8,5,6]=>0000000=>0000000
[8,5,7,2,1,3,4,6]=>[6,4,3,1,2,7,5,8]=>0000001=>1000000
[3,2,5,4,1,8,6,7]=>[7,6,8,1,4,5,2,3]=>0000000=>0000000
[7,4,2,1,8,3,5,6]=>[6,5,3,8,1,2,4,7]=>0000000=>0000000
[8,4,2,1,7,3,5,6]=>[6,5,3,7,1,2,4,8]=>0000001=>1000000
[1,4,2,8,7,3,5,6]=>[6,5,3,7,8,2,4,1]=>0000000=>0000000
[1,5,8,2,7,3,4,6]=>[6,4,3,7,2,8,5,1]=>0000000=>0000000
[8,5,1,2,7,3,4,6]=>[6,4,3,7,2,1,5,8]=>0000001=>1000000
[3,2,6,1,4,8,5,7]=>[7,5,8,4,1,6,2,3]=>0000000=>0000000
[3,2,7,1,8,4,5,6]=>[6,5,4,8,1,7,2,3]=>0000000=>0000000
[4,7,2,1,8,3,5,6]=>[6,5,3,8,1,2,7,4]=>0000000=>0000000
[8,6,1,7,2,3,4,5]=>[5,4,3,2,7,1,6,8]=>0000001=>1000000
[1,6,8,7,2,3,4,5]=>[5,4,3,2,7,8,6,1]=>0000000=>0000000
[1,7,8,6,2,3,4,5]=>[5,4,3,2,6,8,7,1]=>0000000=>0000000
[7,8,1,6,2,3,4,5]=>[5,4,3,2,6,1,8,7]=>0000010=>0100000
[4,8,2,1,7,3,5,6]=>[6,5,3,7,1,2,8,4]=>0000000=>0000000
[3,2,8,1,7,4,5,6]=>[6,5,4,7,1,8,2,3]=>0000000=>0000000
[5,1,8,2,7,3,4,6]=>[6,4,3,7,2,8,1,5]=>0000000=>0000000
[6,1,8,7,2,3,4,5]=>[5,4,3,2,7,8,1,6]=>0000000=>0000000
[8,1,7,6,2,3,4,5]=>[5,4,3,2,6,7,1,8]=>0000001=>1000000
[2,8,4,1,6,5,7,3]=>[3,7,5,6,1,4,8,2]=>0000000=>0000000
[2,8,5,6,7,4,3,1]=>[1,3,4,7,6,5,8,2]=>1000000=>0000001
[7,5,8,6,1,4,2,3]=>[3,2,4,1,6,8,5,7]=>0001000=>0001000
[3,5,7,6,1,4,2,8]=>[8,2,4,1,6,7,5,3]=>0000000=>0000000
[7,5,8,2,4,1,6,3]=>[3,6,1,4,2,8,5,7]=>0000000=>0000000
[2,8,5,3,4,7,6,1]=>[1,6,7,4,3,5,8,2]=>1000000=>0000001
[2,8,5,3,4,1,7,6]=>[6,7,1,4,3,5,8,2]=>0000000=>0000000
[2,8,5,3,6,1,7,4]=>[4,7,1,6,3,5,8,2]=>0000000=>0000000
[2,8,5,6,7,4,1,3]=>[3,1,4,7,6,5,8,2]=>0000000=>0000000
[2,8,5,3,4,7,1,6]=>[6,1,7,4,3,5,8,2]=>0000000=>0000000
[2,8,5,3,4,6,1,7]=>[7,1,6,4,3,5,8,2]=>0000000=>0000000
[6,5,2,7,3,1,4,8]=>[8,4,1,3,7,2,5,6]=>0000000=>0000000
[6,5,2,8,3,1,7,4]=>[4,7,1,3,8,2,5,6]=>0000000=>0000000
[6,5,2,8,3,1,4,7]=>[7,4,1,3,8,2,5,6]=>0000000=>0000000
[7,5,8,2,4,6,3,1]=>[1,3,6,4,2,8,5,7]=>1000000=>0000001
[7,5,8,6,1,4,3,2]=>[2,3,4,1,6,8,5,7]=>0001000=>0001000
[6,5,8,2,1,3,7,4]=>[4,7,3,1,2,8,5,6]=>0000000=>0000000
[3,5,6,2,1,8,7,4]=>[4,7,8,1,2,6,5,3]=>0000000=>0000000
[3,5,7,2,4,1,8,6]=>[6,8,1,4,2,7,5,3]=>0000000=>0000000
[6,5,2,7,3,1,8,4]=>[4,8,1,3,7,2,5,6]=>0000000=>0000000
[4,5,2,6,3,1,7,8]=>[8,7,1,3,6,2,5,4]=>0000000=>0000000
[6,5,2,7,3,4,8,1]=>[1,8,4,3,7,2,5,6]=>1000000=>0000001
[5,1,6,7,4,3,8,2]=>[2,8,3,4,7,6,1,5]=>0000000=>0000000
[5,1,2,6,4,8,7,3]=>[3,7,8,4,6,2,1,5]=>0000000=>0000000
[5,1,2,8,6,4,7,3]=>[3,7,4,6,8,2,1,5]=>0000000=>0000000
[5,1,6,8,7,3,4,2]=>[2,4,3,7,8,6,1,5]=>0000000=>0000000
[6,5,2,8,3,7,4,1]=>[1,4,7,3,8,2,5,6]=>1000000=>0000001
[4,1,2,3,8,6,5,7]=>[7,5,6,8,3,2,1,4]=>0000000=>0000000
[4,1,2,3,8,6,7,5]=>[5,7,6,8,3,2,1,4]=>0000000=>0000000
[4,1,2,3,8,5,7,6]=>[6,7,5,8,3,2,1,4]=>0000000=>0000000
[6,5,8,2,4,3,7,1]=>[1,7,3,4,2,8,5,6]=>1000000=>0000001
[6,5,2,8,3,7,1,4]=>[4,1,7,3,8,2,5,6]=>0000000=>0000000
[6,5,2,7,3,4,1,8]=>[8,1,4,3,7,2,5,6]=>0000000=>0000000
[5,1,6,7,4,3,2,8]=>[8,2,3,4,7,6,1,5]=>0000000=>0000000
[5,1,6,8,7,3,2,4]=>[4,2,3,7,8,6,1,5]=>0000000=>0000000
[5,7,8,6,3,4,2,1]=>[1,2,4,3,6,8,7,5]=>1101000=>0001011
[3,1,4,8,6,2,7,5]=>[5,7,2,6,8,4,1,3]=>0000000=>0000000
[3,1,4,8,6,5,2,7]=>[7,2,5,6,8,4,1,3]=>0000000=>0000000
[4,1,6,7,8,3,2,5]=>[5,2,3,8,7,6,1,4]=>0000000=>0000000
[4,1,6,5,7,3,2,8]=>[8,2,3,7,5,6,1,4]=>0000000=>0000000
[4,5,2,6,3,7,1,8]=>[8,1,7,3,6,2,5,4]=>0000000=>0000000
[4,5,2,7,3,8,1,6]=>[6,1,8,3,7,2,5,4]=>0000000=>0000000
[3,5,6,2,4,8,1,7]=>[7,1,8,4,2,6,5,3]=>0000000=>0000000
[3,7,5,6,8,4,1,2]=>[2,1,4,8,6,5,7,3]=>0100000=>0000010
[3,6,5,2,8,1,7,4]=>[4,7,1,8,2,5,6,3]=>0000000=>0000000
[6,1,2,5,8,4,7,3]=>[3,7,4,8,5,2,1,6]=>0000000=>0000000
[4,1,2,3,5,8,7,6]=>[6,7,8,5,3,2,1,4]=>0000000=>0000000
[4,1,6,7,8,3,5,2]=>[2,5,3,8,7,6,1,4]=>0000000=>0000000
[4,1,2,6,8,5,7,3]=>[3,7,5,8,6,2,1,4]=>0000000=>0000000
[4,1,2,5,6,8,7,3]=>[3,7,8,6,5,2,1,4]=>0000000=>0000000
[4,5,2,6,3,7,8,1]=>[1,8,7,3,6,2,5,4]=>1000000=>0000001
[7,4,2,5,1,3,8,6]=>[6,8,3,1,5,2,4,7]=>0000000=>0000000
[3,7,5,1,2,4,8,6]=>[6,8,4,2,1,5,7,3]=>0000000=>0000000
[7,4,8,5,2,6,1,3]=>[3,1,6,2,5,8,4,7]=>0000000=>0000000
[3,8,6,2,4,7,1,5]=>[5,1,7,4,2,6,8,3]=>0000000=>0000000
[3,8,5,7,1,2,4,6]=>[6,4,2,1,7,5,8,3]=>0000000=>0000000
[2,7,6,4,8,1,3,5]=>[5,3,1,8,4,6,7,2]=>0000000=>0000000
[5,4,1,7,8,2,3,6]=>[6,3,2,8,7,1,4,5]=>0000000=>0000000
[5,7,2,8,1,6,3,4]=>[4,3,6,1,8,2,7,5]=>0000000=>0000000
[3,6,8,2,7,1,4,5]=>[5,4,1,7,2,8,6,3]=>0000000=>0000000
[8,3,7,6,1,2,4,5]=>[5,4,2,1,6,7,3,8]=>0000001=>1000000
[5,4,8,7,1,2,3,6]=>[6,3,2,1,7,8,4,5]=>0000000=>0000000
[2,5,8,7,1,3,4,6]=>[6,4,3,1,7,8,5,2]=>0000000=>0000000
[6,8,4,7,5,1,2,3]=>[3,2,1,5,7,4,8,6]=>0010000=>0000100
[2,8,7,6,1,3,4,5]=>[5,4,3,1,6,7,8,2]=>0000000=>0000000
[3,8,7,6,1,2,4,5]=>[5,4,2,1,6,7,8,3]=>0000000=>0000000
[7,5,3,8,2,1,6,4]=>[4,6,1,2,8,3,5,7]=>0000000=>0000000
[3,8,7,4,5,1,6,2]=>[2,6,1,5,4,7,8,3]=>0000000=>0000000
[2,1,7,8,5,3,6,4]=>[4,6,3,5,8,7,1,2]=>0000000=>0000000
[5,7,3,8,1,2,6,4]=>[4,6,2,1,8,3,7,5]=>0000000=>0000000
[8,6,3,1,2,5,7,4]=>[4,7,5,2,1,3,6,8]=>0000001=>1000000
[8,7,1,4,2,6,5,3]=>[3,5,6,2,4,1,7,8]=>0000011=>1100000
[7,3,8,4,1,6,5,2]=>[2,5,6,1,4,8,3,7]=>0000000=>0000000
[5,3,2,7,4,6,8,1]=>[1,8,6,4,7,2,3,5]=>1000000=>0000001
[7,5,3,6,2,4,8,1]=>[1,8,4,2,6,3,5,7]=>1000000=>0000001
[6,3,2,5,1,8,4,7]=>[7,4,8,1,5,2,3,6]=>0000000=>0000000
[8,5,3,6,2,7,1,4]=>[4,1,7,2,6,3,5,8]=>0000001=>1000000
[7,2,6,3,4,5,8,1]=>[1,8,5,4,3,6,2,7]=>1000000=>0000001
[6,2,7,3,4,5,8,1]=>[1,8,5,4,3,7,2,6]=>1000000=>0000001
[6,7,3,5,2,4,8,1]=>[1,8,4,2,5,3,7,6]=>1000000=>0000001
[3,7,6,2,4,5,8,1]=>[1,8,5,4,2,6,7,3]=>1000000=>0000001
[6,5,3,1,2,8,4,7]=>[7,4,8,2,1,3,5,6]=>0000000=>0000000
[8,6,5,2,3,7,1,4]=>[4,1,7,3,2,5,6,8]=>0000001=>1000000
[8,5,2,1,7,3,4,6]=>[6,4,3,7,1,2,5,8]=>0000001=>1000000
[7,5,2,1,8,3,4,6]=>[6,4,3,8,1,2,5,7]=>0000000=>0000000
[1,6,3,2,8,4,5,7]=>[7,5,4,8,2,3,6,1]=>0000000=>0000000
[5,4,8,6,2,7,1,3]=>[3,1,7,2,6,8,4,5]=>0000000=>0000000
[7,8,5,2,3,6,1,4]=>[4,1,6,3,2,5,8,7]=>0000010=>0100000
[2,8,1,7,3,4,5,6]=>[6,5,4,3,7,1,8,2]=>0000000=>0000000
[4,2,8,3,7,1,5,6]=>[6,5,1,7,3,8,2,4]=>0000000=>0000000
[4,1,7,5,8,2,3,6]=>[6,3,2,8,5,7,1,4]=>0000000=>0000000
[8,1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1,8]=>0000001=>1000000
[6,3,7,1,2,8,4,5]=>[5,4,8,2,1,7,3,6]=>0000000=>0000000
[5,4,1,3,6,8,2,7]=>[7,2,8,6,3,1,4,5]=>0000000=>0000000
[8,5,3,7,6,1,2,4]=>[4,2,1,6,7,3,5,8]=>0000001=>1000000
[6,1,8,3,7,2,4,5]=>[5,4,2,7,3,8,1,6]=>0000000=>0000000
[7,6,8,2,3,5,1,4]=>[4,1,5,3,2,8,6,7]=>0000100=>0010000
[3,7,8,2,4,6,1,5]=>[5,1,6,4,2,8,7,3]=>0000000=>0000000
[5,4,7,8,2,6,1,3]=>[3,1,6,2,8,7,4,5]=>0000000=>0000000
[2,3,8,7,1,4,5,6]=>[6,5,4,1,7,8,3,2]=>0000000=>0000000
[2,1,8,7,3,4,5,6]=>[6,5,4,3,7,8,1,2]=>0000000=>0000000
[8,2,7,6,1,3,4,5]=>[5,4,3,1,6,7,2,8]=>0000001=>1000000
[1,2,8,7,3,4,5,6]=>[6,5,4,3,7,8,2,1]=>0000000=>0000000
[1,3,8,7,2,4,5,6]=>[6,5,4,2,7,8,3,1]=>0000000=>0000000
[1,7,8,3,6,2,4,5]=>[5,4,2,6,3,8,7,1]=>0000000=>0000000
[5,4,8,7,6,1,2,3]=>[3,2,1,6,7,8,4,5]=>0010000=>0000100
[6,8,3,7,5,1,2,4]=>[4,2,1,5,7,3,8,6]=>0000000=>0000000
[7,8,6,2,5,1,3,4]=>[4,3,1,5,2,6,8,7]=>0000110=>0110000
[8,1,6,7,3,2,4,5]=>[5,4,2,3,7,6,1,8]=>0000001=>1000000
[8,1,5,3,7,2,4,6]=>[6,4,2,7,3,5,1,8]=>0000001=>1000000
[8,1,5,3,6,2,4,7]=>[7,4,2,6,3,5,1,8]=>0000001=>1000000
[7,4,8,3,2,6,5,1]=>[1,5,6,2,3,8,4,7]=>1000000=>0000001
[7,4,1,3,2,6,5,8]=>[8,5,6,2,3,1,4,7]=>0000000=>0000000
[8,1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1,8]=>0000001=>1000000
[8,1,4,3,2,7,5,6]=>[6,5,7,2,3,4,1,8]=>0000001=>1000000
[8,1,5,4,6,7,2,3]=>[3,2,7,6,4,5,1,8]=>0000001=>1000000
[8,1,5,3,6,2,7,4]=>[4,7,2,6,3,5,1,8]=>0000001=>1000000
[8,1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1,8]=>0000001=>1000000
[8,1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1,8]=>0000001=>1000000
[7,4,8,3,2,5,6,1]=>[1,6,5,2,3,8,4,7]=>1000000=>0000001
[6,4,3,1,2,5,8,7]=>[7,8,5,2,1,3,4,6]=>0000000=>0000000
[7,4,1,3,2,5,8,6]=>[6,8,5,2,3,1,4,7]=>0000000=>0000000
[7,5,1,3,6,2,8,4]=>[4,8,2,6,3,1,5,7]=>0000000=>0000000
[7,5,1,4,6,8,2,3]=>[3,2,8,6,4,1,5,7]=>0000000=>0000000
[6,4,3,8,2,5,1,7]=>[7,1,5,2,8,3,4,6]=>0000000=>0000000
[5,4,3,2,8,6,1,7]=>[7,1,6,8,2,3,4,5]=>0000000=>0000000
[5,4,3,2,8,7,1,6]=>[6,1,7,8,2,3,4,5]=>0000000=>0000000
[6,5,4,8,7,1,2,3]=>[3,2,1,7,8,4,5,6]=>0010000=>0000100
[6,5,4,1,7,8,2,3]=>[3,2,8,7,1,4,5,6]=>0000000=>0000000
[6,4,3,1,2,7,8,5]=>[5,8,7,2,1,3,4,6]=>0000000=>0000000
[6,4,3,1,2,7,5,8]=>[8,5,7,2,1,3,4,6]=>0000000=>0000000
[6,4,3,8,2,7,5,1]=>[1,5,7,2,8,3,4,6]=>1000000=>0000001
[6,5,3,8,7,2,4,1]=>[1,4,2,7,8,3,5,6]=>1000000=>0000001
[6,5,3,1,7,2,4,8]=>[8,4,2,7,1,3,5,6]=>0000000=>0000000
[7,5,1,3,8,2,4,6]=>[6,4,2,8,3,1,5,7]=>0000000=>0000000
[6,5,3,7,8,2,4,1]=>[1,4,2,8,7,3,5,6]=>1000000=>0000001
[6,4,3,7,2,8,5,1]=>[1,5,8,2,7,3,4,6]=>1000000=>0000001
[6,4,3,7,2,1,5,8]=>[8,5,1,2,7,3,4,6]=>0000000=>0000000
[7,5,8,4,1,6,2,3]=>[3,2,6,1,4,8,5,7]=>0000000=>0000000
[6,5,4,8,1,7,2,3]=>[3,2,7,1,8,4,5,6]=>0000000=>0000000
[6,5,4,7,1,8,2,3]=>[3,2,8,1,7,4,5,6]=>0000000=>0000000
[5,4,3,2,7,8,1,6]=>[6,1,8,7,2,3,4,5]=>0000000=>0000000
[4,6,3,8,5,1,2,7]=>[7,2,1,5,8,3,6,4]=>0000000=>0000000
[5,6,8,3,4,1,2,7]=>[7,2,1,4,3,8,6,5]=>0000000=>0000000
[5,6,8,3,4,1,7,2]=>[2,7,1,4,3,8,6,5]=>0000000=>0000000
[4,6,2,7,5,3,1,8]=>[8,1,3,5,7,2,6,4]=>0000000=>0000000
[5,6,8,4,3,1,2,7]=>[7,2,1,3,4,8,6,5]=>0000000=>0000000
[5,7,8,4,1,3,6,2]=>[2,6,3,1,4,8,7,5]=>0000000=>0000000
[5,6,8,4,2,1,7,3]=>[3,7,1,2,4,8,6,5]=>0000000=>0000000
[5,6,8,2,4,1,7,3]=>[3,7,1,4,2,8,6,5]=>0000000=>0000000
[3,2,6,8,5,1,4,7]=>[7,4,1,5,8,6,2,3]=>0000000=>0000000
[5,6,8,4,2,1,3,7]=>[7,3,1,2,4,8,6,5]=>0000000=>0000000
[5,7,8,4,1,3,2,6]=>[6,2,3,1,4,8,7,5]=>0000000=>0000000
[5,7,8,4,1,2,3,6]=>[6,3,2,1,4,8,7,5]=>0000000=>0000000
[6,7,8,1,5,2,3,4]=>[4,3,2,5,1,8,7,6]=>0000100=>0010000
[6,7,8,1,5,3,2,4]=>[4,2,3,5,1,8,7,6]=>0000100=>0010000
[6,7,8,1,3,5,2,4]=>[4,2,5,3,1,8,7,6]=>0000100=>0010000
[5,7,8,2,1,6,3,4]=>[4,3,6,1,2,8,7,5]=>0000000=>0000000
[4,7,2,8,1,6,3,5]=>[5,3,6,1,8,2,7,4]=>0000000=>0000000
[3,2,7,8,1,6,4,5]=>[5,4,6,1,8,7,2,3]=>0000000=>0000000
[4,7,2,8,1,6,5,3]=>[3,5,6,1,8,2,7,4]=>0000000=>0000000
[5,7,8,2,1,6,4,3]=>[3,4,6,1,2,8,7,5]=>0000000=>0000000
[6,7,8,1,3,5,4,2]=>[2,4,5,3,1,8,7,6]=>0000100=>0010000
[6,7,8,1,5,3,4,2]=>[2,4,3,5,1,8,7,6]=>0000100=>0010000
[6,7,8,1,4,3,5,2]=>[2,5,3,4,1,8,7,6]=>0000100=>0010000
[5,6,8,3,2,1,7,4]=>[4,7,1,2,3,8,6,5]=>0000000=>0000000
[4,7,3,8,1,6,2,5]=>[5,2,6,1,8,3,7,4]=>0000000=>0000000
[4,7,3,8,1,5,6,2]=>[2,6,5,1,8,3,7,4]=>0000000=>0000000
[4,7,3,8,1,5,2,6]=>[6,2,5,1,8,3,7,4]=>0000000=>0000000
[4,7,3,8,1,2,5,6]=>[6,5,2,1,8,3,7,4]=>0000000=>0000000
[5,7,8,3,1,2,4,6]=>[6,4,2,1,3,8,7,5]=>0000000=>0000000
[5,6,8,3,2,1,4,7]=>[7,4,1,2,3,8,6,5]=>0000000=>0000000
[3,2,7,8,1,5,4,6]=>[6,4,5,1,8,7,2,3]=>0000000=>0000000
[6,7,8,1,3,4,2,5]=>[5,2,4,3,1,8,7,6]=>0000100=>0010000
[6,7,8,1,4,2,3,5]=>[5,3,2,4,1,8,7,6]=>0000100=>0010000
[6,7,8,1,2,5,3,4]=>[4,3,5,2,1,8,7,6]=>0000100=>0010000
[6,7,8,1,2,4,5,3]=>[3,5,4,2,1,8,7,6]=>0000100=>0010000
[5,7,8,2,1,3,6,4]=>[4,6,3,1,2,8,7,5]=>0000000=>0000000
[3,2,7,8,1,4,6,5]=>[5,6,4,1,8,7,2,3]=>0000000=>0000000
[6,7,8,1,3,2,4,5]=>[5,4,2,3,1,8,7,6]=>0000100=>0010000
[6,7,8,1,2,4,3,5]=>[5,3,4,2,1,8,7,6]=>0000100=>0010000
[6,7,8,1,2,3,5,4]=>[4,5,3,2,1,8,7,6]=>0000100=>0010000
[8,3,5,1,7,4,6,2]=>[2,6,4,7,1,5,3,8]=>0000001=>1000000
[8,3,4,1,7,5,6,2]=>[2,6,5,7,1,4,3,8]=>0000001=>1000000
[4,8,3,1,7,5,6,2]=>[2,6,5,7,1,3,8,4]=>0000000=>0000000
[4,6,2,1,7,5,8,3]=>[3,8,5,7,1,2,6,4]=>0000000=>0000000
[1,4,6,2,7,5,8,3]=>[3,8,5,7,2,6,4,1]=>0000000=>0000000
[1,7,5,2,6,8,4,3]=>[3,4,8,6,2,5,7,1]=>0000000=>0000000
[7,5,2,1,6,8,4,3]=>[3,4,8,6,1,2,5,7]=>0000000=>0000000
[6,8,4,3,1,7,5,2]=>[2,5,7,1,3,4,8,6]=>0000000=>0000000
[4,7,5,6,1,8,3,2]=>[2,3,8,1,6,5,7,4]=>0000000=>0000000
[6,7,5,1,8,4,3,2]=>[2,3,4,8,1,5,7,6]=>0000000=>0000000
[6,8,4,1,7,5,3,2]=>[2,3,5,7,1,4,8,6]=>0000000=>0000000
[6,7,5,3,1,8,4,2]=>[2,4,8,1,3,5,7,6]=>0000000=>0000000
[8,4,2,1,6,7,5,3]=>[3,5,7,6,1,2,4,8]=>0000001=>1000000
[1,8,4,2,6,7,5,3]=>[3,5,7,6,2,4,8,1]=>0000000=>0000000
[1,5,3,2,7,6,8,4]=>[4,8,6,7,2,3,5,1]=>0000000=>0000000
[2,5,3,1,7,6,8,4]=>[4,8,6,7,1,3,5,2]=>0000000=>0000000
[2,7,5,1,6,8,4,3]=>[3,4,8,6,1,5,7,2]=>0000000=>0000000
[4,7,1,6,5,8,2,3]=>[3,2,8,5,6,1,7,4]=>0000000=>0000000
[4,6,1,2,7,5,8,3]=>[3,8,5,7,2,1,6,4]=>0000000=>0000000
[8,4,1,2,6,7,5,3]=>[3,5,7,6,2,1,4,8]=>0000001=>1000000
[5,3,1,2,7,6,8,4]=>[4,8,6,7,2,1,3,5]=>0000000=>0000000
[4,3,1,2,7,6,8,5]=>[5,8,6,7,2,1,3,4]=>0000000=>0000000
[3,5,1,2,7,6,8,4]=>[4,8,6,7,2,1,5,3]=>0000000=>0000000
[6,7,1,5,8,2,3,4]=>[4,3,2,8,5,1,7,6]=>0000000=>0000000
[2,7,6,1,5,8,3,4]=>[4,3,8,5,1,6,7,2]=>0000000=>0000000
[2,3,5,1,7,6,8,4]=>[4,8,6,7,1,5,3,2]=>0000000=>0000000
[8,4,1,6,7,5,2,3]=>[3,2,5,7,6,1,4,8]=>0000001=>1000000
[5,2,3,1,7,6,8,4]=>[4,8,6,7,1,3,2,5]=>0000000=>0000000
[3,5,2,1,7,6,8,4]=>[4,8,6,7,1,2,5,3]=>0000000=>0000000
[1,7,6,2,5,8,3,4]=>[4,3,8,5,2,6,7,1]=>0000000=>0000000
[7,6,2,1,5,8,3,4]=>[4,3,8,5,1,2,6,7]=>0000000=>0000000
[8,2,6,4,7,1,5,3]=>[3,5,1,7,4,6,2,8]=>0000001=>1000000
[6,1,5,2,7,4,8,3]=>[3,8,4,7,2,5,1,6]=>0000000=>0000000
[7,6,2,5,8,3,1,4]=>[4,1,3,8,5,2,6,7]=>0000000=>0000000
[1,8,3,5,7,6,2,4]=>[4,2,6,7,5,3,8,1]=>0000000=>0000000
[1,5,2,3,7,6,8,4]=>[4,8,6,7,3,2,5,1]=>0000000=>0000000
[5,2,1,3,7,6,8,4]=>[4,8,6,7,3,1,2,5]=>0000000=>0000000
[8,4,2,6,7,5,1,3]=>[3,1,5,7,6,2,4,8]=>0000001=>1000000
[6,1,4,2,7,5,8,3]=>[3,8,5,7,2,4,1,6]=>0000000=>0000000
[8,2,6,5,7,1,4,3]=>[3,4,1,7,5,6,2,8]=>0000001=>1000000
[5,1,3,2,7,6,8,4]=>[4,8,6,7,2,3,1,5]=>0000000=>0000000
[1,4,2,3,7,6,8,5]=>[5,8,6,7,3,2,4,1]=>0000000=>0000000
[2,4,1,3,7,6,8,5]=>[5,8,6,7,3,1,4,2]=>0000000=>0000000
[2,5,1,3,7,6,8,4]=>[4,8,6,7,3,1,5,2]=>0000000=>0000000
[2,8,3,5,7,6,1,4]=>[4,1,6,7,5,3,8,2]=>0000000=>0000000
[6,8,2,3,5,7,1,4]=>[4,1,7,5,3,2,8,6]=>0000000=>0000000
[6,7,1,3,5,8,2,4]=>[4,2,8,5,3,1,7,6]=>0000000=>0000000
[8,3,5,7,6,1,2,4]=>[4,2,1,6,7,5,3,8]=>0000001=>1000000
[5,1,2,3,7,6,8,4]=>[4,8,6,7,3,2,1,5]=>0000000=>0000000
[4,7,1,2,8,6,5,3]=>[3,5,6,8,2,1,7,4]=>0000000=>0000000
[4,6,8,1,2,7,5,3]=>[3,5,7,2,1,8,6,4]=>0000000=>0000000
[6,8,7,1,5,3,2,4]=>[4,2,3,5,1,7,8,6]=>0000100=>0010000
[6,8,7,3,5,1,2,4]=>[4,2,1,5,3,7,8,6]=>0000100=>0010000
[7,8,1,3,6,5,2,4]=>[4,2,5,6,3,1,8,7]=>0000010=>0100000
[1,7,3,4,8,6,5,2]=>[2,5,6,8,4,3,7,1]=>0000000=>0000000
[4,2,7,1,8,6,5,3]=>[3,5,6,8,1,7,2,4]=>0000000=>0000000
[7,8,2,3,6,5,1,4]=>[4,1,5,6,3,2,8,7]=>0000010=>0100000
[8,5,7,1,6,2,3,4]=>[4,3,2,6,1,7,5,8]=>0000001=>1000000
[8,5,7,1,2,6,3,4]=>[4,3,6,2,1,7,5,8]=>0000001=>1000000
[6,8,2,7,1,3,5,4]=>[4,5,3,1,7,2,8,6]=>0000000=>0000000
[6,2,4,8,7,1,5,3]=>[3,5,1,7,8,4,2,6]=>0000000=>0000000
[1,6,8,3,7,4,5,2]=>[2,5,4,7,3,8,6,1]=>0000000=>0000000
[1,6,8,3,4,7,5,2]=>[2,5,7,4,3,8,6,1]=>0000000=>0000000
[6,2,4,8,1,7,5,3]=>[3,5,7,1,8,4,2,6]=>0000000=>0000000
[6,8,7,2,3,5,1,4]=>[4,1,5,3,2,7,8,6]=>0000100=>0010000
[6,8,2,1,7,3,5,4]=>[4,5,3,7,1,2,8,6]=>0000000=>0000000
[8,5,7,2,1,6,3,4]=>[4,3,6,1,2,7,5,8]=>0000001=>1000000
[8,5,7,1,2,3,6,4]=>[4,6,3,2,1,7,5,8]=>0000001=>1000000
[8,5,7,2,3,1,6,4]=>[4,6,1,3,2,7,5,8]=>0000001=>1000000
[1,8,7,5,3,4,6,2]=>[2,6,4,3,5,7,8,1]=>0000000=>0000000
[1,8,7,3,5,4,6,2]=>[2,6,4,5,3,7,8,1]=>0000000=>0000000
[8,2,5,4,7,1,6,3]=>[3,6,1,7,4,5,2,8]=>0000001=>1000000
[8,7,6,1,2,4,3,5]=>[5,3,4,2,1,6,7,8]=>0000111=>1110000
[8,7,6,1,4,2,3,5]=>[5,3,2,4,1,6,7,8]=>0000111=>1110000
[8,7,6,4,1,3,2,5]=>[5,2,3,1,4,6,7,8]=>0000111=>1110000
[8,5,7,1,3,2,6,4]=>[4,6,2,3,1,7,5,8]=>0000001=>1000000
[5,8,4,7,1,2,6,3]=>[3,6,2,1,7,4,8,5]=>0000000=>0000000
[8,1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1,8]=>0000001=>1000000
[8,2,5,6,7,4,1,3]=>[3,1,4,7,6,5,2,8]=>0000001=>1000000
[4,8,5,1,7,2,6,3]=>[3,6,2,7,1,5,8,4]=>0000000=>0000000
[8,5,3,7,1,2,6,4]=>[4,6,2,1,7,3,5,8]=>0000001=>1000000
[4,6,2,8,1,7,5,3]=>[3,5,7,1,8,2,6,4]=>0000000=>0000000
[1,6,4,8,3,7,5,2]=>[2,5,7,3,8,4,6,1]=>0000000=>0000000
[1,8,7,4,5,3,6,2]=>[2,6,3,5,4,7,8,1]=>0000000=>0000000
[4,8,5,7,2,1,6,3]=>[3,6,1,2,7,5,8,4]=>0000000=>0000000
[8,5,3,7,2,1,6,4]=>[4,6,1,2,7,3,5,8]=>0000001=>1000000
[8,7,6,3,1,4,2,5]=>[5,2,4,1,3,6,7,8]=>0000111=>1110000
[8,5,3,2,7,1,6,4]=>[4,6,1,7,2,3,5,8]=>0000001=>1000000
[1,8,7,4,3,5,6,2]=>[2,6,5,3,4,7,8,1]=>0000000=>0000000
[1,8,7,3,4,5,6,2]=>[2,6,5,4,3,7,8,1]=>0000000=>0000000
[8,2,4,5,7,1,6,3]=>[3,6,1,7,5,4,2,8]=>0000001=>1000000
[8,5,2,3,7,1,6,4]=>[4,6,1,7,3,2,5,8]=>0000001=>1000000
[8,3,1,5,2,7,6,4]=>[4,6,7,2,5,1,3,8]=>0000001=>1000000
[8,5,4,2,1,7,3,6]=>[6,3,7,1,2,4,5,8]=>0000001=>1000000
[8,5,4,2,1,7,6,3]=>[3,6,7,1,2,4,5,8]=>0000001=>1000000
[6,5,4,2,3,1,8,7]=>[7,8,1,3,2,4,5,6]=>0000000=>0000000
[6,3,2,5,1,4,8,7]=>[7,8,4,1,5,2,3,6]=>0000000=>0000000
[8,5,4,1,2,7,6,3]=>[3,6,7,2,1,4,5,8]=>0000001=>1000000
[8,7,4,1,6,3,2,5]=>[5,2,3,6,1,4,7,8]=>0000011=>1100000
[8,7,4,1,6,3,5,2]=>[2,5,3,6,1,4,7,8]=>0000011=>1100000
[8,7,4,1,6,5,3,2]=>[2,3,5,6,1,4,7,8]=>0000011=>1100000
[8,5,4,3,1,7,6,2]=>[2,6,7,1,3,4,5,8]=>0000001=>1000000
[8,3,2,5,1,7,6,4]=>[4,6,7,1,5,2,3,8]=>0000001=>1000000
[8,3,2,5,1,7,4,6]=>[6,4,7,1,5,2,3,8]=>0000001=>1000000
[8,5,4,3,1,7,2,6]=>[6,2,7,1,3,4,5,8]=>0000001=>1000000
[8,5,4,1,3,7,2,6]=>[6,2,7,3,1,4,5,8]=>0000001=>1000000
[8,7,4,1,6,5,2,3]=>[3,2,5,6,1,4,7,8]=>0000011=>1100000
[2,1,8,7,6,4,5,3]=>[3,5,4,6,7,8,1,2]=>0000000=>0000000
[8,3,2,7,6,4,5,1]=>[1,5,4,6,7,2,3,8]=>1000001=>1000001
[8,5,4,2,3,7,6,1]=>[1,6,7,3,2,4,5,8]=>1000001=>1000001
[8,7,4,2,6,5,3,1]=>[1,3,5,6,2,4,7,8]=>1000011=>1100001
[8,7,4,2,6,3,5,1]=>[1,5,3,6,2,4,7,8]=>1000011=>1100001
[8,7,4,2,6,3,1,5]=>[5,1,3,6,2,4,7,8]=>0000011=>1100000
[8,3,1,7,6,4,2,5]=>[5,2,4,6,7,1,3,8]=>0000001=>1000000
[8,3,1,7,6,4,5,2]=>[2,5,4,6,7,1,3,8]=>0000001=>1000000
[8,3,1,5,4,7,6,2]=>[2,6,7,4,5,1,3,8]=>0000001=>1000000
[8,3,1,7,6,5,2,4]=>[4,2,5,6,7,1,3,8]=>0000001=>1000000
[8,3,1,7,6,2,5,4]=>[4,5,2,6,7,1,3,8]=>0000001=>1000000
[8,5,4,2,3,7,1,6]=>[6,1,7,3,2,4,5,8]=>0000001=>1000000
[8,3,2,5,4,7,1,6]=>[6,1,7,4,5,2,3,8]=>0000001=>1000000
[2,1,8,5,4,7,3,6]=>[6,3,7,4,5,8,1,2]=>0000000=>0000000
[8,3,2,7,6,5,1,4]=>[4,1,5,6,7,2,3,8]=>0000001=>1000000
[8,7,6,5,3,1,4,2]=>[2,4,1,3,5,6,7,8]=>0001111=>1111000
[8,3,2,7,6,1,5,4]=>[4,5,1,6,7,2,3,8]=>0000001=>1000000
[8,7,6,5,1,2,4,3]=>[3,4,2,1,5,6,7,8]=>0001111=>1111000
[5,2,3,1,6,4,8,7]=>[7,8,4,6,1,3,2,5]=>0000000=>0000000
[7,4,5,2,3,1,8,6]=>[6,8,1,3,2,5,4,7]=>0000000=>0000000
[7,3,5,2,4,1,8,6]=>[6,8,1,4,2,5,3,7]=>0000000=>0000000
[6,3,5,2,4,1,8,7]=>[7,8,1,4,2,5,3,6]=>0000000=>0000000
[4,1,6,3,5,2,8,7]=>[7,8,2,5,3,6,1,4]=>0000000=>0000000
[6,3,4,1,5,2,8,7]=>[7,8,2,5,1,4,3,6]=>0000000=>0000000
[5,2,7,3,4,1,8,6]=>[6,8,1,4,3,7,2,5]=>0000000=>0000000
[6,2,8,5,7,3,4,1]=>[1,4,3,7,5,8,2,6]=>1000000=>0000001
[6,2,7,3,4,1,8,5]=>[5,8,1,4,3,7,2,6]=>0000000=>0000000
[7,3,4,1,5,2,8,6]=>[6,8,2,5,1,4,3,7]=>0000000=>0000000
[4,1,7,3,5,2,8,6]=>[6,8,2,5,3,7,1,4]=>0000000=>0000000
[2,1,7,4,5,3,8,6]=>[6,8,3,5,4,7,1,2]=>0000000=>0000000
[3,1,8,6,7,4,5,2]=>[2,5,4,7,6,8,1,3]=>0000000=>0000000
[4,1,8,6,7,3,5,2]=>[2,5,3,7,6,8,1,4]=>0000000=>0000000
[8,5,7,3,4,1,6,2]=>[2,6,1,4,3,7,5,8]=>0000001=>1000000
[8,5,6,2,7,3,4,1]=>[1,4,3,7,2,6,5,8]=>1000001=>1000001
[8,4,7,3,5,1,6,2]=>[2,6,1,5,3,7,4,8]=>0000001=>1000000
[5,1,8,4,7,3,6,2]=>[2,6,3,7,4,8,1,5]=>0000000=>0000000
[3,1,8,5,7,4,6,2]=>[2,6,4,7,5,8,1,3]=>0000000=>0000000
[2,1,8,5,7,4,6,3]=>[3,6,4,7,5,8,1,2]=>0000000=>0000000
[3,1,7,4,6,2,8,5]=>[5,8,2,6,4,7,1,3]=>0000000=>0000000
[4,1,7,3,6,2,8,5]=>[5,8,2,6,3,7,1,4]=>0000000=>0000000
[6,2,8,4,7,3,5,1]=>[1,5,3,7,4,8,2,6]=>1000000=>0000001
[7,3,6,2,5,1,8,4]=>[4,8,1,5,2,6,3,7]=>0000000=>0000000
[5,2,4,1,7,3,8,6]=>[6,8,3,7,1,4,2,5]=>0000000=>0000000
[6,2,4,1,7,3,8,5]=>[5,8,3,7,1,4,2,6]=>0000000=>0000000
[7,4,6,2,3,1,8,5]=>[5,8,1,3,2,6,4,7]=>0000000=>0000000
[6,2,3,1,7,4,8,5]=>[5,8,4,7,1,3,2,6]=>0000000=>0000000
[5,2,3,1,7,4,8,6]=>[6,8,4,7,1,3,2,5]=>0000000=>0000000
[4,2,3,1,7,5,8,6]=>[6,8,5,7,1,3,2,4]=>0000000=>0000000
[3,1,4,2,8,6,7,5]=>[5,7,6,8,2,4,1,3]=>0000000=>0000000
[6,2,3,1,8,5,7,4]=>[4,7,5,8,1,3,2,6]=>0000000=>0000000
[8,5,6,2,3,1,7,4]=>[4,7,1,3,2,6,5,8]=>0000001=>1000000
[7,3,8,5,6,2,4,1]=>[1,4,2,6,5,8,3,7]=>1000000=>0000001
[8,5,6,2,4,1,7,3]=>[3,7,1,4,2,6,5,8]=>0000001=>1000000
[5,2,4,1,8,6,7,3]=>[3,7,6,8,1,4,2,5]=>0000000=>0000000
[4,1,5,2,8,6,7,3]=>[3,7,6,8,2,5,1,4]=>0000000=>0000000
[3,1,6,2,8,5,7,4]=>[4,7,5,8,2,6,1,3]=>0000000=>0000000
[5,1,6,2,8,4,7,3]=>[3,7,4,8,2,6,1,5]=>0000000=>0000000
[8,4,6,2,5,1,7,3]=>[3,7,1,5,2,6,4,8]=>0000001=>1000000
[7,3,8,4,6,2,5,1]=>[1,5,2,6,4,8,3,7]=>1000000=>0000001
[6,2,7,3,8,4,5,1]=>[1,5,4,8,3,7,2,6]=>1000000=>0000001
[8,4,5,1,6,2,7,3]=>[3,7,2,6,1,5,4,8]=>0000001=>1000000
[4,1,8,5,6,2,7,3]=>[3,7,2,6,5,8,1,4]=>0000000=>0000000
[3,1,8,5,6,2,7,4]=>[4,7,2,6,5,8,1,3]=>0000000=>0000000
[2,1,8,5,6,3,7,4]=>[4,7,3,6,5,8,1,2]=>0000000=>0000000
[3,1,7,4,8,5,6,2]=>[2,6,5,8,4,7,1,3]=>0000000=>0000000
[7,3,6,2,8,4,5,1]=>[1,5,4,8,2,6,3,7]=>1000000=>0000001
[6,8,7,3,4,1,2,5]=>[5,2,1,4,3,7,8,6]=>0000100=>0010000
[5,4,8,7,2,6,3,1]=>[1,3,6,2,7,8,4,5]=>1000000=>0000001
[8,3,4,6,5,1,2,7]=>[7,2,1,5,6,4,3,8]=>0000001=>1000000
[3,4,8,7,6,1,2,5]=>[5,2,1,6,7,8,4,3]=>0000000=>0000000
[4,5,8,7,6,1,2,3]=>[3,2,1,6,7,8,5,4]=>0010000=>0000100
[2,5,8,7,1,6,3,4]=>[4,3,6,1,7,8,5,2]=>0000000=>0000000
[2,4,8,7,1,6,3,5]=>[5,3,6,1,7,8,4,2]=>0000000=>0000000
[8,1,4,6,2,5,3,7]=>[7,3,5,2,6,4,1,8]=>0000001=>1000000
[1,5,8,7,2,6,3,4]=>[4,3,6,2,7,8,5,1]=>0000000=>0000000
[2,5,8,3,7,6,4,1]=>[1,4,6,7,3,8,5,2]=>1000000=>0000001
[1,4,2,8,7,6,5,3]=>[3,5,6,7,8,2,4,1]=>0000000=>0000000
[5,2,8,1,7,6,4,3]=>[3,4,6,7,1,8,2,5]=>0000000=>0000000
[5,3,8,2,7,6,4,1]=>[1,4,6,7,2,8,3,5]=>1000000=>0000001
[5,1,8,3,7,6,4,2]=>[2,4,6,7,3,8,1,5]=>0000000=>0000000
[3,1,2,8,7,6,5,4]=>[4,5,6,7,8,2,1,3]=>0000000=>0000000
[3,1,4,8,7,6,5,2]=>[2,5,6,7,8,4,1,3]=>0000000=>0000000
[1,2,8,3,7,6,4,5]=>[5,4,6,7,3,8,2,1]=>0000000=>0000000
[1,4,3,6,8,2,5,7]=>[7,5,2,8,6,3,4,1]=>0000000=>0000000
[1,4,5,2,8,3,7,6]=>[6,7,3,8,2,5,4,1]=>0000000=>0000000
[1,4,2,6,5,8,3,7]=>[7,3,8,5,6,2,4,1]=>0000000=>0000000
[1,5,4,2,6,8,3,7]=>[7,3,8,6,2,4,5,1]=>0000000=>0000000
[3,1,6,5,8,2,4,7]=>[7,4,2,8,5,6,1,3]=>0000000=>0000000
[1,6,4,2,5,8,3,7]=>[7,3,8,5,2,4,6,1]=>0000000=>0000000
[1,5,2,6,4,8,3,7]=>[7,3,8,4,6,2,5,1]=>0000000=>0000000
[1,2,6,5,4,8,3,7]=>[7,3,8,4,5,6,2,1]=>0000000=>0000000
[1,2,5,4,7,3,8,6]=>[6,8,3,7,4,5,2,1]=>0000000=>0000000
[4,1,2,6,3,8,7,5]=>[5,7,8,3,6,2,1,4]=>0000000=>0000000
[7,1,5,4,2,8,3,6]=>[6,3,8,2,4,5,1,7]=>0000000=>0000000
[1,4,7,5,2,8,3,6]=>[6,3,8,2,5,7,4,1]=>0000000=>0000000
[7,1,3,5,2,8,4,6]=>[6,4,8,2,5,3,1,7]=>0000000=>0000000
[1,4,5,2,8,7,3,6]=>[6,3,7,8,2,5,4,1]=>0000000=>0000000
[1,6,4,2,8,3,7,5]=>[5,7,3,8,2,4,6,1]=>0000000=>0000000
[1,4,2,8,3,7,6,5]=>[5,6,7,3,8,2,4,1]=>0000000=>0000000
[1,2,8,6,5,3,7,4]=>[4,7,3,5,6,8,2,1]=>0000000=>0000000
[6,2,1,8,7,3,4,5]=>[5,4,3,7,8,1,2,6]=>0000000=>0000000
[7,6,2,1,8,3,4,5]=>[5,4,3,8,1,2,6,7]=>0000000=>0000000
[7,3,1,6,2,8,4,5]=>[5,4,8,2,6,1,3,7]=>0000000=>0000000
[1,7,6,4,2,8,3,5]=>[5,3,8,2,4,6,7,1]=>0000000=>0000000
[1,7,5,2,6,3,8,4]=>[4,8,3,6,2,5,7,1]=>0000000=>0000000
[1,6,2,7,5,3,8,4]=>[4,8,3,5,7,2,6,1]=>0000000=>0000000
[1,2,7,6,5,3,8,4]=>[4,8,3,5,6,7,2,1]=>0000000=>0000000
[1,2,6,5,3,8,7,4]=>[4,7,8,3,5,6,2,1]=>0000000=>0000000
[1,5,2,7,6,3,8,4]=>[4,8,3,6,7,2,5,1]=>0000000=>0000000
[1,6,5,2,7,3,8,4]=>[4,8,3,7,2,5,6,1]=>0000000=>0000000
[1,5,7,4,2,8,3,6]=>[6,3,8,2,4,7,5,1]=>0000000=>0000000
[3,1,8,6,2,4,7,5]=>[5,7,4,2,6,8,1,3]=>0000000=>0000000
[4,3,7,1,8,2,5,6]=>[6,5,2,8,1,7,3,4]=>0000000=>0000000
[8,3,1,6,2,4,7,5]=>[5,7,4,2,6,1,3,8]=>0000001=>1000000
[7,1,8,3,2,4,6,5]=>[5,6,4,2,3,8,1,7]=>0000000=>0000000
[1,4,2,8,7,3,6,5]=>[5,6,3,7,8,2,4,1]=>0000000=>0000000
[1,7,4,2,8,3,6,5]=>[5,6,3,8,2,4,7,1]=>0000000=>0000000
[8,1,5,4,2,7,3,6]=>[6,3,7,2,4,5,1,8]=>0000001=>1000000
[1,4,8,5,2,7,3,6]=>[6,3,7,2,5,8,4,1]=>0000000=>0000000
[8,5,3,1,7,2,4,6]=>[6,4,2,7,1,3,5,8]=>0000001=>1000000
[8,6,2,1,7,3,4,5]=>[5,4,3,7,1,2,6,8]=>0000001=>1000000
[1,8,6,4,2,7,3,5]=>[5,3,7,2,4,6,8,1]=>0000000=>0000000
[1,5,2,7,3,8,6,4]=>[4,6,8,3,7,2,5,1]=>0000000=>0000000
[1,2,8,5,3,7,6,4]=>[4,6,7,3,5,8,2,1]=>0000000=>0000000
[1,2,6,3,8,7,5,4]=>[4,5,7,8,3,6,2,1]=>0000000=>0000000
[1,2,7,6,3,8,5,4]=>[4,5,8,3,6,7,2,1]=>0000000=>0000000
[1,6,2,7,3,8,5,4]=>[4,5,8,3,7,2,6,1]=>0000000=>0000000
[1,7,4,2,8,6,3,5]=>[5,3,6,8,2,4,7,1]=>0000000=>0000000
[7,1,8,3,2,6,4,5]=>[5,4,6,2,3,8,1,7]=>0000000=>0000000
[7,2,1,8,6,3,4,5]=>[5,4,3,6,8,1,2,7]=>0000000=>0000000
[1,8,7,3,2,6,4,5]=>[5,4,6,2,3,7,8,1]=>0000000=>0000000
[1,4,2,8,7,6,3,5]=>[5,3,6,7,8,2,4,1]=>0000000=>0000000
[1,2,8,7,5,3,6,4]=>[4,6,3,5,7,8,2,1]=>0000000=>0000000
[5,1,8,7,6,2,4,3]=>[3,4,2,6,7,8,1,5]=>0000000=>0000000
[8,1,7,6,3,4,5,2]=>[2,5,4,3,6,7,1,8]=>0000001=>1000000
[5,7,8,6,2,4,1,3]=>[3,1,4,2,6,8,7,5]=>0001000=>0001000
[5,7,1,6,2,4,3,8]=>[8,3,4,2,6,1,7,5]=>0000000=>0000000
[6,4,1,5,2,7,3,8]=>[8,3,7,2,5,1,4,6]=>0000000=>0000000
[8,1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1,8]=>0000001=>1000000
[6,1,4,5,3,8,7,2]=>[2,7,8,3,5,4,1,6]=>0000000=>0000000
[7,1,4,5,3,8,6,2]=>[2,6,8,3,5,4,1,7]=>0000000=>0000000
[7,1,4,5,3,6,8,2]=>[2,8,6,3,5,4,1,7]=>0000000=>0000000
[7,4,1,5,2,6,3,8]=>[8,3,6,2,5,1,4,7]=>0000000=>0000000
[6,3,5,7,2,1,4,8]=>[8,4,1,2,7,5,3,6]=>0000000=>0000000
[6,3,5,8,2,1,7,4]=>[4,7,1,2,8,5,3,6]=>0000000=>0000000
[6,3,5,7,2,1,8,4]=>[4,8,1,2,7,5,3,6]=>0000000=>0000000
[8,4,5,7,3,6,1,2]=>[2,1,6,3,7,5,4,8]=>0100001=>1000010
[6,4,5,8,3,7,2,1]=>[1,2,7,3,8,5,4,6]=>1100000=>0000011
[5,4,8,6,3,1,7,2]=>[2,7,1,3,6,8,4,5]=>0000000=>0000000
[5,4,1,8,2,3,7,6]=>[6,7,3,2,8,1,4,5]=>0000000=>0000000
[8,4,1,5,2,6,3,7]=>[7,3,6,2,5,1,4,8]=>0000001=>1000000
[6,3,5,8,2,1,4,7]=>[7,4,1,2,8,5,3,6]=>0000000=>0000000
[2,3,8,5,1,4,7,6]=>[6,7,4,1,5,8,3,2]=>0000000=>0000000
[2,3,8,6,1,5,7,4]=>[4,7,5,1,6,8,3,2]=>0000000=>0000000
[2,8,6,7,1,3,5,4]=>[4,5,3,1,7,6,8,2]=>0000000=>0000000
[8,3,5,7,2,1,6,4]=>[4,6,1,2,7,5,3,8]=>0000001=>1000000
[8,4,5,6,3,1,7,2]=>[2,7,1,3,6,5,4,8]=>0000001=>1000000
[7,3,5,6,2,8,1,4]=>[4,1,8,2,6,5,3,7]=>0000000=>0000000
[7,3,5,8,2,1,6,4]=>[4,6,1,2,8,5,3,7]=>0000000=>0000000
[7,3,5,6,2,1,4,8]=>[8,4,1,2,6,5,3,7]=>0000000=>0000000
[2,7,6,5,1,3,4,8]=>[8,4,3,1,5,6,7,2]=>0000000=>0000000
[2,7,6,8,1,3,5,4]=>[4,5,3,1,8,6,7,2]=>0000000=>0000000
[8,7,5,6,1,4,2,3]=>[3,2,4,1,6,5,7,8]=>0001011=>1101000
[2,7,1,3,6,5,8,4]=>[4,8,5,6,3,1,7,2]=>0000000=>0000000
[2,7,6,1,8,3,4,5]=>[5,4,3,8,1,6,7,2]=>0000000=>0000000
[2,7,6,1,4,3,5,8]=>[8,5,3,4,1,6,7,2]=>0000000=>0000000
[7,3,5,1,2,8,4,6]=>[6,4,8,2,1,5,3,7]=>0000000=>0000000
[2,3,8,6,4,1,7,5]=>[5,7,1,4,6,8,3,2]=>0000000=>0000000
[2,8,6,1,7,3,4,5]=>[5,4,3,7,1,6,8,2]=>0000000=>0000000
[2,3,8,1,6,4,7,5]=>[5,7,4,6,1,8,3,2]=>0000000=>0000000
[2,3,8,1,4,5,7,6]=>[6,7,5,4,1,8,3,2]=>0000000=>0000000
[5,6,2,1,3,8,7,4]=>[4,7,8,3,1,2,6,5]=>0000000=>0000000
[5,1,6,4,2,8,7,3]=>[3,7,8,2,4,6,1,5]=>0000000=>0000000
[5,6,3,1,2,8,7,4]=>[4,7,8,2,1,3,6,5]=>0000000=>0000000
[5,1,7,4,8,2,6,3]=>[3,6,2,8,4,7,1,5]=>0000000=>0000000
[5,1,7,4,8,6,2,3]=>[3,2,6,8,4,7,1,5]=>0000000=>0000000
[5,7,3,1,8,6,2,4]=>[4,2,6,8,1,3,7,5]=>0000000=>0000000
[6,7,1,8,3,5,2,4]=>[4,2,5,3,8,1,7,6]=>0000000=>0000000
[6,1,7,8,4,5,2,3]=>[3,2,5,4,8,7,1,6]=>0000000=>0000000
[1,6,7,8,4,5,3,2]=>[2,3,5,4,8,7,6,1]=>0000000=>0000000
[1,6,7,8,4,3,5,2]=>[2,5,3,4,8,7,6,1]=>0000000=>0000000
[6,2,7,8,4,1,5,3]=>[3,5,1,4,8,7,2,6]=>0000000=>0000000
[4,1,2,7,8,6,5,3]=>[3,5,6,8,7,2,1,4]=>0000000=>0000000
[1,6,7,8,3,5,4,2]=>[2,4,5,3,8,7,6,1]=>0000000=>0000000
[6,7,8,2,4,1,3,5]=>[5,3,1,4,2,8,7,6]=>0000100=>0010000
[6,7,1,8,5,2,3,4]=>[4,3,2,5,8,1,7,6]=>0000000=>0000000
[6,1,7,8,5,4,2,3]=>[3,2,4,5,8,7,1,6]=>0000000=>0000000
[3,7,4,8,5,6,1,2]=>[2,1,6,5,8,4,7,3]=>0100000=>0000010
[2,7,3,8,5,6,1,4]=>[4,1,6,5,8,3,7,2]=>0000000=>0000000
[3,7,1,8,4,6,2,5]=>[5,2,6,4,8,1,7,3]=>0000000=>0000000
[2,6,1,8,4,7,3,5]=>[5,3,7,4,8,1,6,2]=>0000000=>0000000
[4,8,1,6,2,7,3,5]=>[5,3,7,2,6,1,8,4]=>0000000=>0000000
[5,8,2,6,1,7,3,4]=>[4,3,7,1,6,2,8,5]=>0000000=>0000000
[4,8,2,6,1,7,3,5]=>[5,3,7,1,6,2,8,4]=>0000000=>0000000
[8,6,1,4,3,2,5,7]=>[7,5,2,3,4,1,6,8]=>0000001=>1000000
[3,7,5,1,8,2,4,6]=>[6,4,2,8,1,5,7,3]=>0000000=>0000000
[4,1,5,2,8,7,3,6]=>[6,3,7,8,2,5,1,4]=>0000000=>0000000
[8,1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1,8]=>0000001=>1000000
[8,2,6,5,1,3,4,7]=>[7,4,3,1,5,6,2,8]=>0000001=>1000000
[8,3,1,6,2,5,4,7]=>[7,4,5,2,6,1,3,8]=>0000001=>1000000
[8,1,2,6,4,5,3,7]=>[7,3,5,4,6,2,1,8]=>0000001=>1000000
[8,1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1,8]=>0000001=>1000000
[1,7,5,4,2,8,3,6]=>[6,3,8,2,4,5,7,1]=>0000000=>0000000
[1,4,6,8,2,7,3,5]=>[5,3,7,2,8,6,4,1]=>0000000=>0000000
[1,4,7,6,2,8,3,5]=>[5,3,8,2,6,7,4,1]=>0000000=>0000000
[5,1,4,7,2,8,3,6]=>[6,3,8,2,7,4,1,5]=>0000000=>0000000
[3,7,5,1,2,8,4,6]=>[6,4,8,2,1,5,7,3]=>0000000=>0000000
[4,1,5,8,2,7,3,6]=>[6,3,7,2,8,5,1,4]=>0000000=>0000000
[1,4,6,2,8,7,3,5]=>[5,3,7,8,2,6,4,1]=>0000000=>0000000
[1,4,2,8,6,7,3,5]=>[5,3,7,6,8,2,4,1]=>0000000=>0000000
[3,1,2,6,4,8,7,5]=>[5,7,8,4,6,2,1,3]=>0000000=>0000000
[2,1,7,6,3,4,8,5]=>[5,8,4,3,6,7,1,2]=>0000000=>0000000
[3,1,2,7,4,6,8,5]=>[5,8,6,4,7,2,1,3]=>0000000=>0000000
[1,2,3,6,8,5,7,4]=>[4,7,5,8,6,3,2,1]=>0000000=>0000000
[5,1,4,2,7,8,3,6]=>[6,3,8,7,2,4,1,5]=>0000000=>0000000
[1,4,2,7,6,8,3,5]=>[5,3,8,6,7,2,4,1]=>0000000=>0000000
[1,4,2,6,8,7,3,5]=>[5,3,7,8,6,2,4,1]=>0000000=>0000000
[5,3,7,1,8,2,4,6]=>[6,4,2,8,1,7,3,5]=>0000000=>0000000
[1,7,4,3,2,5,8,6]=>[6,8,5,2,3,4,7,1]=>0000000=>0000000
[4,8,7,2,1,3,5,6]=>[6,5,3,1,2,7,8,4]=>0000000=>0000000
[1,8,7,3,4,2,5,6]=>[6,5,2,4,3,7,8,1]=>0000000=>0000000
[3,1,7,8,2,6,4,5]=>[5,4,6,2,8,7,1,3]=>0000000=>0000000
[1,4,2,7,8,3,6,5]=>[5,6,3,8,7,2,4,1]=>0000000=>0000000
[2,1,8,6,3,4,7,5]=>[5,7,4,3,6,8,1,2]=>0000000=>0000000
[1,4,2,6,8,3,7,5]=>[5,7,3,8,6,2,4,1]=>0000000=>0000000
[1,2,3,7,8,5,6,4]=>[4,6,5,8,7,3,2,1]=>0000000=>0000000
[1,2,3,7,5,8,6,4]=>[4,6,8,5,7,3,2,1]=>0000000=>0000000
[3,1,7,2,8,6,4,5]=>[5,4,6,8,2,7,1,3]=>0000000=>0000000
[1,2,3,8,7,5,6,4]=>[4,6,5,7,8,3,2,1]=>0000000=>0000000
[5,7,8,4,2,6,1,3]=>[3,1,6,2,4,8,7,5]=>0000000=>0000000
[6,7,8,4,2,5,1,3]=>[3,1,5,2,4,8,7,6]=>0000100=>0010000
[8,6,3,7,2,1,5,4]=>[4,5,1,2,7,3,6,8]=>0000001=>1000000
[6,7,8,3,2,1,5,4]=>[4,5,1,2,3,8,7,6]=>0000100=>0010000
[5,7,8,3,2,1,6,4]=>[4,6,1,2,3,8,7,5]=>0000000=>0000000
[2,7,8,4,3,5,6,1]=>[1,6,5,3,4,8,7,2]=>1000000=>0000001
[3,7,8,4,2,5,1,6]=>[6,1,5,2,4,8,7,3]=>0000000=>0000000
[7,6,3,8,2,1,4,5]=>[5,4,1,2,8,3,6,7]=>0000000=>0000000
[8,6,3,7,2,1,4,5]=>[5,4,1,2,7,3,6,8]=>0000001=>1000000
[5,6,3,8,2,1,4,7]=>[7,4,1,2,8,3,6,5]=>0000000=>0000000
[3,6,4,8,2,5,1,7]=>[7,1,5,2,8,4,6,3]=>0000000=>0000000
[2,6,4,8,3,5,7,1]=>[1,7,5,3,8,4,6,2]=>1000000=>0000001
[2,6,4,7,3,5,8,1]=>[1,8,5,3,7,4,6,2]=>1000000=>0000001
[5,6,3,7,2,1,4,8]=>[8,4,1,2,7,3,6,5]=>0000000=>0000000
[8,4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4,8]=>0000001=>1000000
[6,4,3,2,1,7,5,8]=>[8,5,7,1,2,3,4,6]=>0000000=>0000000
[4,5,3,2,7,1,6,8]=>[8,6,1,7,2,3,5,4]=>0000000=>0000000
[7,4,3,2,1,8,5,6]=>[6,5,8,1,2,3,4,7]=>0000000=>0000000
[8,4,3,2,1,7,5,6]=>[6,5,7,1,2,3,4,8]=>0000001=>1000000
[7,4,3,2,1,8,6,5]=>[5,6,8,1,2,3,4,7]=>0000000=>0000000
[5,6,3,8,2,1,7,4]=>[4,7,1,2,8,3,6,5]=>0000000=>0000000
[7,5,3,2,8,1,6,4]=>[4,6,1,8,2,3,5,7]=>0000000=>0000000
[8,5,4,2,7,6,1,3]=>[3,1,6,7,2,4,5,8]=>0000001=>1000000
[7,5,4,2,8,6,1,3]=>[3,1,6,8,2,4,5,7]=>0000000=>0000000
[6,5,4,2,7,8,1,3]=>[3,1,8,7,2,4,5,6]=>0000000=>0000000
[8,5,4,2,6,7,1,3]=>[3,1,7,6,2,4,5,8]=>0000001=>1000000
[5,6,3,7,2,1,8,4]=>[4,8,1,2,7,3,6,5]=>0000000=>0000000
[4,6,3,7,2,1,8,5]=>[5,8,1,2,7,3,6,4]=>0000000=>0000000
[3,6,4,7,2,8,1,5]=>[5,1,8,2,7,4,6,3]=>0000000=>0000000
[2,6,4,7,3,8,5,1]=>[1,5,8,3,7,4,6,2]=>1000000=>0000001
[3,5,4,2,7,8,1,6]=>[6,1,8,7,2,4,5,3]=>0000000=>0000000
[7,4,3,2,1,6,8,5]=>[5,8,6,1,2,3,4,7]=>0000000=>0000000
[8,4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4,8]=>0000001=>1000000
[8,4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4,8]=>0000001=>1000000
[7,4,3,2,1,5,8,6]=>[6,8,5,1,2,3,4,7]=>0000000=>0000000
[6,4,3,2,1,5,8,7]=>[7,8,5,1,2,3,4,6]=>0000000=>0000000
[3,5,4,2,6,8,1,7]=>[7,1,8,6,2,4,5,3]=>0000000=>0000000
[3,2,6,4,8,5,1,7]=>[7,1,5,8,4,6,2,3]=>0000000=>0000000
[3,2,5,8,4,6,1,7]=>[7,1,6,4,8,5,2,3]=>0000000=>0000000
[4,2,1,5,7,3,6,8]=>[8,6,3,7,5,1,2,4]=>0000000=>0000000
[4,5,2,3,7,1,6,8]=>[8,6,1,7,3,2,5,4]=>0000000=>0000000
[4,2,5,3,8,1,6,7]=>[7,6,1,8,3,5,2,4]=>0000000=>0000000
[4,2,5,8,3,1,6,7]=>[7,6,1,3,8,5,2,4]=>0000000=>0000000
[4,1,5,3,8,2,6,7]=>[7,6,2,8,3,5,1,4]=>0000000=>0000000
[4,3,2,7,5,1,6,8]=>[8,6,1,5,7,2,3,4]=>0000000=>0000000
[4,3,6,2,5,1,7,8]=>[8,7,1,5,2,6,3,4]=>0000000=>0000000
[4,6,7,1,3,2,5,8]=>[8,5,2,3,1,7,6,4]=>0000000=>0000000
[4,5,1,7,3,2,6,8]=>[8,6,2,3,7,1,5,4]=>0000000=>0000000
[4,5,1,3,7,2,6,8]=>[8,6,2,7,3,1,5,4]=>0000000=>0000000
[3,5,1,4,2,7,6,8]=>[8,6,7,2,4,1,5,3]=>0000000=>0000000
[2,5,1,4,3,7,8,6]=>[6,8,7,3,4,1,5,2]=>0000000=>0000000
[5,2,1,4,3,7,8,6]=>[6,8,7,3,4,1,2,5]=>0000000=>0000000
[5,3,1,4,2,7,6,8]=>[8,6,7,2,4,1,3,5]=>0000000=>0000000
[4,3,1,7,5,2,6,8]=>[8,6,2,5,7,1,3,4]=>0000000=>0000000
[5,3,6,4,1,2,7,8]=>[8,7,2,1,4,6,3,5]=>0000000=>0000000
[4,3,6,1,7,2,5,8]=>[8,5,2,7,1,6,3,4]=>0000000=>0000000
[6,2,4,1,3,7,8,5]=>[5,8,7,3,1,4,2,6]=>0000000=>0000000
[3,6,4,1,2,7,5,8]=>[8,5,7,2,1,4,6,3]=>0000000=>0000000
[4,6,3,1,7,2,5,8]=>[8,5,2,7,1,3,6,4]=>0000000=>0000000
[5,3,6,2,1,4,7,8]=>[8,7,4,1,2,6,3,5]=>0000000=>0000000
[4,5,2,7,3,1,6,8]=>[8,6,1,3,7,2,5,4]=>0000000=>0000000
[4,6,2,1,7,3,5,8]=>[8,5,3,7,1,2,6,4]=>0000000=>0000000
[3,2,6,1,4,7,5,8]=>[8,5,7,4,1,6,2,3]=>0000000=>0000000
[3,6,7,2,4,5,1,8]=>[8,1,5,4,2,7,6,3]=>0000000=>0000000
[7,2,1,4,6,3,8,5]=>[5,8,3,6,4,1,2,7]=>0000000=>0000000
[7,3,1,4,6,8,2,5]=>[5,2,8,6,4,1,3,7]=>0000000=>0000000
[3,6,2,1,5,7,4,8]=>[8,4,7,5,1,2,6,3]=>0000000=>0000000
[7,4,1,5,6,2,3,8]=>[8,3,2,6,5,1,4,7]=>0000000=>0000000
[7,3,1,5,2,6,4,8]=>[8,4,6,2,5,1,3,7]=>0000000=>0000000
[7,2,1,5,3,6,8,4]=>[4,8,6,3,5,1,2,7]=>0000000=>0000000
[6,2,5,1,3,7,8,4]=>[4,8,7,3,1,5,2,6]=>0000000=>0000000
[6,3,5,1,2,7,4,8]=>[8,4,7,2,1,5,3,6]=>0000000=>0000000
[6,4,5,1,7,2,3,8]=>[8,3,2,7,1,5,4,6]=>0000000=>0000000
[4,6,5,1,7,2,3,8]=>[8,3,2,7,1,5,6,4]=>0000000=>0000000
[3,6,5,1,2,7,4,8]=>[8,4,7,2,1,5,6,3]=>0000000=>0000000
[2,4,1,5,3,8,7,6]=>[6,7,8,3,5,1,4,2]=>0000000=>0000000
[3,4,5,1,2,8,7,6]=>[6,7,8,2,1,5,4,3]=>0000000=>0000000
[1,8,4,5,3,2,7,6]=>[6,7,2,3,5,4,8,1]=>0000000=>0000000
[2,4,8,5,3,1,7,6]=>[6,7,1,3,5,8,4,2]=>0000000=>0000000
[3,4,5,2,8,1,7,6]=>[6,7,1,8,2,5,4,3]=>0000000=>0000000
[3,4,6,2,1,7,8,5]=>[5,8,7,1,2,6,4,3]=>0000000=>0000000
[3,4,6,2,1,7,5,8]=>[8,5,7,1,2,6,4,3]=>0000000=>0000000
[3,5,6,2,7,1,8,4]=>[4,8,1,7,2,6,5,3]=>0000000=>0000000
[3,4,6,2,8,7,1,5]=>[5,1,7,8,2,6,4,3]=>0000000=>0000000
[3,4,6,8,2,7,1,5]=>[5,1,7,2,8,6,4,3]=>0000000=>0000000
[2,4,8,6,3,7,1,5]=>[5,1,7,3,6,8,4,2]=>0000000=>0000000
[1,8,4,6,3,7,2,5]=>[5,2,7,3,6,4,8,1]=>0000000=>0000000
[1,8,4,6,3,7,5,2]=>[2,5,7,3,6,4,8,1]=>0000000=>0000000
[3,4,6,8,2,7,5,1]=>[1,5,7,2,8,6,4,3]=>1000000=>0000001
[3,4,6,2,8,7,5,1]=>[1,5,7,8,2,6,4,3]=>1000000=>0000001
[3,5,6,2,7,8,4,1]=>[1,4,8,7,2,6,5,3]=>1000000=>0000001
[3,5,6,2,7,4,1,8]=>[8,1,4,7,2,6,5,3]=>0000000=>0000000
[4,5,6,7,2,8,3,1]=>[1,3,8,2,7,6,5,4]=>1000000=>0000001
[2,5,8,6,7,3,4,1]=>[1,4,3,7,6,8,5,2]=>1000000=>0000001
[1,8,5,6,7,3,2,4]=>[4,2,3,7,6,5,8,1]=>0000000=>0000000
[4,5,6,7,2,1,8,3]=>[3,8,1,2,7,6,5,4]=>0000000=>0000000
[3,4,6,1,8,7,2,5]=>[5,2,7,8,1,6,4,3]=>0000000=>0000000
[2,4,1,6,8,7,3,5]=>[5,3,7,8,6,1,4,2]=>0000000=>0000000
[2,5,1,6,7,8,4,3]=>[3,4,8,7,6,1,5,2]=>0000000=>0000000
[2,5,1,6,7,4,3,8]=>[8,3,4,7,6,1,5,2]=>0000000=>0000000
[3,5,6,1,7,4,2,8]=>[8,2,4,7,1,6,5,3]=>0000000=>0000000
[3,5,6,1,7,4,8,2]=>[2,8,4,7,1,6,5,3]=>0000000=>0000000
[3,4,6,1,8,7,5,2]=>[2,5,7,8,1,6,4,3]=>0000000=>0000000
[2,4,8,6,1,7,5,3]=>[3,5,7,1,6,8,4,2]=>0000000=>0000000
[1,8,4,6,2,7,5,3]=>[3,5,7,2,6,4,8,1]=>0000000=>0000000
[1,8,5,6,7,2,4,3]=>[3,4,2,7,6,5,8,1]=>0000000=>0000000
[2,5,8,6,7,1,4,3]=>[3,4,1,7,6,8,5,2]=>0000000=>0000000
[4,5,6,7,1,3,8,2]=>[2,8,3,1,7,6,5,4]=>0000000=>0000000
[3,5,6,8,7,4,1,2]=>[2,1,4,7,8,6,5,3]=>0100000=>0000010
[2,5,8,6,7,4,1,3]=>[3,1,4,7,6,8,5,2]=>0000000=>0000000
[1,8,5,6,7,4,2,3]=>[3,2,4,7,6,5,8,1]=>0000000=>0000000
[1,8,5,6,7,4,3,2]=>[2,3,4,7,6,5,8,1]=>0000000=>0000000
[2,5,8,6,7,4,3,1]=>[1,3,4,7,6,8,5,2]=>1000000=>0000001
[8,2,4,3,7,1,6,5]=>[5,6,1,7,3,4,2,8]=>0000001=>1000000
[5,8,2,4,3,7,1,6]=>[6,1,7,3,4,2,8,5]=>0000000=>0000000
[4,2,5,6,1,8,3,7]=>[7,3,8,1,6,5,2,4]=>0000000=>0000000
[4,2,5,6,1,7,3,8]=>[8,3,7,1,6,5,2,4]=>0000000=>0000000
[6,1,5,7,3,2,4,8]=>[8,4,2,3,7,5,1,6]=>0000000=>0000000
[6,1,5,8,3,2,4,7]=>[7,4,2,3,8,5,1,6]=>0000000=>0000000
[3,8,2,4,7,1,5,6]=>[6,5,1,7,4,2,8,3]=>0000000=>0000000
[3,6,8,2,4,7,1,5]=>[5,1,7,4,2,8,6,3]=>0000000=>0000000
[7,3,2,4,6,1,5,8]=>[8,5,1,6,4,2,3,7]=>0000000=>0000000
[3,2,5,1,8,4,6,7]=>[7,6,4,8,1,5,2,3]=>0000000=>0000000
[7,8,3,2,4,6,1,5]=>[5,1,6,4,2,3,8,7]=>0000010=>0100000
[6,1,5,7,8,3,2,4]=>[4,2,3,8,7,5,1,6]=>0000000=>0000000
[4,2,5,6,1,7,8,3]=>[3,8,7,1,6,5,2,4]=>0000000=>0000000
[5,7,6,1,8,3,4,2]=>[2,4,3,8,1,6,7,5]=>0000000=>0000000
[5,8,6,1,7,3,4,2]=>[2,4,3,7,1,6,8,5]=>0000000=>0000000
[6,1,5,8,7,3,2,4]=>[4,2,3,7,8,5,1,6]=>0000000=>0000000
[8,7,3,2,4,6,1,5]=>[5,1,6,4,2,3,7,8]=>0000011=>1100000
[3,2,5,1,8,7,4,6]=>[6,4,7,8,1,5,2,3]=>0000000=>0000000
[3,2,5,1,6,4,7,8]=>[8,7,4,6,1,5,2,3]=>0000000=>0000000
[3,2,4,1,8,7,5,6]=>[6,5,7,8,1,4,2,3]=>0000000=>0000000
[3,2,5,1,6,8,7,4]=>[4,7,8,6,1,5,2,3]=>0000000=>0000000
[3,8,6,5,1,7,4,2]=>[2,4,7,1,5,6,8,3]=>0000000=>0000000
[3,7,6,5,1,8,4,2]=>[2,4,8,1,5,6,7,3]=>0000000=>0000000
[6,5,1,7,8,4,2,3]=>[3,2,4,8,7,1,5,6]=>0000000=>0000000
[3,2,5,1,6,7,8,4]=>[4,8,7,6,1,5,2,3]=>0000000=>0000000
[3,2,4,1,7,5,6,8]=>[8,6,5,7,1,4,2,3]=>0000000=>0000000
[3,2,4,1,6,8,5,7]=>[7,5,8,6,1,4,2,3]=>0000000=>0000000
[8,3,2,4,7,6,1,5]=>[5,1,6,7,4,2,3,8]=>0000001=>1000000
[3,2,5,1,8,4,7,6]=>[6,7,4,8,1,5,2,3]=>0000000=>0000000
[3,2,5,1,6,7,4,8]=>[8,4,7,6,1,5,2,3]=>0000000=>0000000
[6,5,1,7,4,2,3,8]=>[8,3,2,4,7,1,5,6]=>0000000=>0000000
[6,5,1,8,4,2,3,7]=>[7,3,2,4,8,1,5,6]=>0000000=>0000000
[8,4,2,3,7,5,1,6]=>[6,1,5,7,3,2,4,8]=>0000001=>1000000
[5,2,6,1,8,3,7,4]=>[4,7,3,8,1,6,2,5]=>0000000=>0000000
[5,2,6,1,8,4,7,3]=>[3,7,4,8,1,6,2,5]=>0000000=>0000000
[7,4,2,3,8,5,1,6]=>[6,1,5,8,3,2,4,7]=>0000000=>0000000
[8,5,1,6,4,2,3,7]=>[7,3,2,4,6,1,5,8]=>0000001=>1000000
[3,2,5,1,7,6,4,8]=>[8,4,6,7,1,5,2,3]=>0000000=>0000000
[3,2,5,1,8,6,4,7]=>[7,4,6,8,1,5,2,3]=>0000000=>0000000
[8,6,1,5,7,3,2,4]=>[4,2,3,7,5,1,6,8]=>0000001=>1000000
[8,5,6,1,7,3,4,2]=>[2,4,3,7,1,6,5,8]=>0000001=>1000000
[3,6,8,5,1,7,4,2]=>[2,4,7,1,5,8,6,3]=>0000000=>0000000
[8,5,1,6,7,4,2,3]=>[3,2,4,7,6,1,5,8]=>0000001=>1000000
[3,2,5,1,8,6,7,4]=>[4,7,6,8,1,5,2,3]=>0000000=>0000000
[3,2,4,1,5,8,6,7]=>[7,6,8,5,1,4,2,3]=>0000000=>0000000
[3,2,5,1,7,8,6,4]=>[4,6,8,7,1,5,2,3]=>0000000=>0000000
[8,7,5,1,6,4,2,3]=>[3,2,4,6,1,5,7,8]=>0000011=>1100000
[3,2,5,1,8,7,6,4]=>[4,6,7,8,1,5,2,3]=>0000000=>0000000
[4,6,3,7,1,8,5,2]=>[2,5,8,1,7,3,6,4]=>0000000=>0000000
[4,6,3,7,5,1,8,2]=>[2,8,1,5,7,3,6,4]=>0000000=>0000000
[4,2,6,1,7,5,3,8]=>[8,3,5,7,1,6,2,4]=>0000000=>0000000
[4,3,7,5,1,8,6,2]=>[2,6,8,1,5,7,3,4]=>0000000=>0000000
[6,4,3,8,5,1,7,2]=>[2,7,1,5,8,3,4,6]=>0000000=>0000000
[2,5,4,6,1,7,3,8]=>[8,3,7,1,6,4,5,2]=>0000000=>0000000
[4,6,2,1,8,5,7,3]=>[3,7,5,8,1,2,6,4]=>0000000=>0000000
[2,4,1,7,5,8,6,3]=>[3,6,8,5,7,1,4,2]=>0000000=>0000000
[2,4,1,7,5,3,8,6]=>[6,8,3,5,7,1,4,2]=>0000000=>0000000
[2,6,4,1,8,5,3,7]=>[7,3,5,8,1,4,6,2]=>0000000=>0000000
[5,4,8,2,1,6,3,7]=>[7,3,6,1,2,8,4,5]=>0000000=>0000000
[4,8,3,2,6,1,5,7]=>[7,5,1,6,2,3,8,4]=>0000000=>0000000
[3,2,7,1,5,4,8,6]=>[6,8,4,5,1,7,2,3]=>0000000=>0000000
[4,3,2,6,7,8,1,5]=>[5,1,8,7,6,2,3,4]=>0000000=>0000000
[4,3,7,8,2,6,1,5]=>[5,1,6,2,8,7,3,4]=>0000000=>0000000
[3,2,5,7,1,6,8,4]=>[4,8,6,1,7,5,2,3]=>0000000=>0000000
[6,3,2,7,1,5,4,8]=>[8,4,5,1,7,2,3,6]=>0000000=>0000000
[6,3,2,7,8,1,5,4]=>[4,5,1,8,7,2,3,6]=>0000000=>0000000
[6,5,2,1,7,8,4,3]=>[3,4,8,7,1,2,5,6]=>0000000=>0000000
[6,2,1,8,5,3,7,4]=>[4,7,3,5,8,1,2,6]=>0000000=>0000000
[6,3,2,1,4,7,8,5]=>[5,8,7,4,1,2,3,6]=>0000000=>0000000
[6,3,2,1,4,7,5,8]=>[8,5,7,4,1,2,3,6]=>0000000=>0000000
[4,6,2,1,8,3,7,5]=>[5,7,3,8,1,2,6,4]=>0000000=>0000000
[3,5,8,2,1,7,4,6]=>[6,4,7,1,2,8,5,3]=>0000000=>0000000
[4,8,3,7,2,1,5,6]=>[6,5,1,2,7,3,8,4]=>0000000=>0000000
[4,3,7,2,8,1,5,6]=>[6,5,1,8,2,7,3,4]=>0000000=>0000000
[4,8,3,2,7,1,5,6]=>[6,5,1,7,2,3,8,4]=>0000000=>0000000
[3,2,1,4,7,5,8,6]=>[6,8,5,7,4,1,2,3]=>0000000=>0000000
[4,8,3,2,1,5,6,7]=>[7,6,5,1,2,3,8,4]=>0000000=>0000000
[4,3,8,2,1,5,6,7]=>[7,6,5,1,2,8,3,4]=>0000000=>0000000
[6,2,3,1,5,4,8,7]=>[7,8,4,5,1,3,2,6]=>0000000=>0000000
[8,4,5,2,3,1,7,6]=>[6,7,1,3,2,5,4,8]=>0000001=>1000000
[8,2,5,3,4,1,7,6]=>[6,7,1,4,3,5,2,8]=>0000001=>1000000
[6,2,5,3,4,1,8,7]=>[7,8,1,4,3,5,2,6]=>0000000=>0000000
[6,4,5,1,3,2,8,7]=>[7,8,2,3,1,5,4,6]=>0000000=>0000000
[6,1,5,3,4,2,8,7]=>[7,8,2,4,3,5,1,6]=>0000000=>0000000
[8,3,7,2,4,1,6,5]=>[5,6,1,4,2,7,3,8]=>0000001=>1000000
[8,3,5,1,4,2,7,6]=>[6,7,2,4,1,5,3,8]=>0000001=>1000000
[8,4,5,1,3,2,7,6]=>[6,7,2,3,1,5,4,8]=>0000001=>1000000
[2,1,8,4,5,3,7,6]=>[6,7,3,5,4,8,1,2]=>0000000=>0000000
[8,1,7,3,4,2,6,5]=>[5,6,2,4,3,7,1,8]=>0000001=>1000000
[8,2,7,1,4,3,6,5]=>[5,6,3,4,1,7,2,8]=>0000001=>1000000
[8,2,7,3,4,1,6,5]=>[5,6,1,4,3,7,2,8]=>0000001=>1000000
[8,4,7,2,3,1,6,5]=>[5,6,1,3,2,7,4,8]=>0000001=>1000000
[8,2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2,8]=>0000001=>1000000
[4,2,3,1,8,5,7,6]=>[6,7,5,8,1,3,2,4]=>0000000=>0000000
[8,2,3,1,7,5,6,4]=>[4,6,5,7,1,3,2,8]=>0000001=>1000000
[8,6,7,1,3,2,5,4]=>[4,5,2,3,1,7,6,8]=>0000101=>1010000
[8,1,3,2,7,5,6,4]=>[4,6,5,7,2,3,1,8]=>0000001=>1000000
[2,1,8,5,7,3,6,4]=>[4,6,3,7,5,8,1,2]=>0000000=>0000000
[4,5,8,6,3,2,7,1]=>[1,7,2,3,6,8,5,4]=>1000000=>0000001
[1,5,8,7,3,6,2,4]=>[4,2,6,3,7,8,5,1]=>0000000=>0000000
[1,7,2,8,4,6,5,3]=>[3,5,6,4,8,2,7,1]=>0000000=>0000000
[6,7,2,8,4,1,5,3]=>[3,5,1,4,8,2,7,6]=>0000000=>0000000
[3,6,2,8,4,5,7,1]=>[1,7,5,4,8,2,6,3]=>1000000=>0000001
[2,6,1,8,4,5,7,3]=>[3,7,5,4,8,1,6,2]=>0000000=>0000000
[2,8,4,6,1,5,7,3]=>[3,7,5,1,6,4,8,2]=>0000000=>0000000
[6,3,1,8,4,5,7,2]=>[2,7,5,4,8,1,3,6]=>0000000=>0000000
[2,3,6,8,4,5,7,1]=>[1,7,5,4,8,6,3,2]=>1000000=>0000001
[6,3,7,8,4,1,5,2]=>[2,5,1,4,8,7,3,6]=>0000000=>0000000
[1,3,7,8,4,6,5,2]=>[2,5,6,4,8,7,3,1]=>0000000=>0000000
[3,6,7,8,4,2,5,1]=>[1,5,2,4,8,7,6,3]=>1000000=>0000001
[7,6,1,8,4,2,5,3]=>[3,5,2,4,8,1,6,7]=>0000000=>0000000
[2,8,3,7,1,6,5,4]=>[4,5,6,1,7,3,8,2]=>0000000=>0000000
[5,2,8,7,3,6,1,4]=>[4,1,6,3,7,8,2,5]=>0000000=>0000000
[7,2,1,8,4,6,5,3]=>[3,5,6,4,8,1,2,7]=>0000000=>0000000
[3,2,7,8,4,6,5,1]=>[1,5,6,4,8,7,2,3]=>1000000=>0000001
[5,2,7,8,1,4,6,3]=>[3,6,4,1,8,7,2,5]=>0000000=>0000000
[1,2,7,8,5,4,6,3]=>[3,6,4,5,8,7,2,1]=>0000000=>0000000
[7,2,5,8,3,4,6,1]=>[1,6,4,3,8,5,2,7]=>1000000=>0000001
[6,2,8,5,4,3,1,7]=>[7,1,3,4,5,8,2,6]=>0000000=>0000000
[2,8,3,5,4,1,6,7]=>[7,6,1,4,5,3,8,2]=>0000000=>0000000
[2,8,4,5,3,1,6,7]=>[7,6,1,3,5,4,8,2]=>0000000=>0000000
[7,3,5,8,2,4,6,1]=>[1,6,4,2,8,5,3,7]=>1000000=>0000001
[4,3,1,2,8,5,6,7]=>[7,6,5,8,2,1,3,4]=>0000000=>0000000
[2,7,6,8,4,3,5,1]=>[1,5,3,4,8,6,7,2]=>1000000=>0000001
[1,7,5,8,3,4,6,2]=>[2,6,4,3,8,5,7,1]=>0000000=>0000000
[4,6,8,5,1,3,2,7]=>[7,2,3,1,5,8,6,4]=>0000000=>0000000
[2,4,8,3,6,5,1,7]=>[7,1,5,6,3,8,4,2]=>0000000=>0000000
[4,1,8,3,5,6,2,7]=>[7,2,6,5,3,8,1,4]=>0000000=>0000000
[5,6,8,4,1,3,2,7]=>[7,2,3,1,4,8,6,5]=>0000000=>0000000
[4,6,8,1,5,3,2,7]=>[7,2,3,5,1,8,6,4]=>0000000=>0000000
[1,6,8,4,5,3,2,7]=>[7,2,3,5,4,8,6,1]=>0000000=>0000000
[1,7,3,8,5,4,6,2]=>[2,6,4,5,8,3,7,1]=>0000000=>0000000
[3,7,1,8,5,4,6,2]=>[2,6,4,5,8,1,7,3]=>0000000=>0000000
[2,7,3,8,4,6,5,1]=>[1,5,6,4,8,3,7,2]=>1000000=>0000001
[2,8,7,4,1,6,5,3]=>[3,5,6,1,4,7,8,2]=>0000000=>0000000
[2,8,5,4,3,1,6,7]=>[7,6,1,3,4,5,8,2]=>0000000=>0000000
[1,4,3,2,8,5,6,7]=>[7,6,5,8,2,3,4,1]=>0000000=>0000000
[7,3,2,8,5,4,6,1]=>[1,6,4,5,8,2,3,7]=>1000000=>0000001
[6,4,8,2,5,3,1,7]=>[7,1,3,5,2,8,4,6]=>0000000=>0000000
[2,8,4,3,5,1,6,7]=>[7,6,1,5,3,4,8,2]=>0000000=>0000000
[6,2,8,4,5,3,1,7]=>[7,1,3,5,4,8,2,6]=>0000000=>0000000
[7,2,3,8,5,4,6,1]=>[1,6,4,5,8,3,2,7]=>1000000=>0000001
[4,2,3,1,8,5,6,7]=>[7,6,5,8,1,3,2,4]=>0000000=>0000000
[5,1,3,2,4,8,6,7]=>[7,6,8,4,2,3,1,5]=>0000000=>0000000
[2,8,1,5,3,4,7,6]=>[6,7,4,3,5,1,8,2]=>0000000=>0000000
[1,4,2,8,5,3,6,7]=>[7,6,3,5,8,2,4,1]=>0000000=>0000000
[3,5,1,4,8,2,6,7]=>[7,6,2,8,4,1,5,3]=>0000000=>0000000
[1,5,2,8,4,3,6,7]=>[7,6,3,4,8,2,5,1]=>0000000=>0000000
[1,2,5,4,3,8,6,7]=>[7,6,8,3,4,5,2,1]=>0000000=>0000000
[1,2,4,8,5,3,7,6]=>[6,7,3,5,8,4,2,1]=>0000000=>0000000
[1,5,2,7,8,4,3,6]=>[6,3,4,8,7,2,5,1]=>0000000=>0000000
[5,1,2,7,4,8,3,6]=>[6,3,8,4,7,2,1,5]=>0000000=>0000000
[8,3,5,1,4,7,2,6]=>[6,2,7,4,1,5,3,8]=>0000001=>1000000
[1,2,8,5,7,4,3,6]=>[6,3,4,7,5,8,2,1]=>0000000=>0000000
[1,2,4,8,7,5,3,6]=>[6,3,5,7,8,4,2,1]=>0000000=>0000000
[2,8,1,4,3,7,6,5]=>[5,6,7,3,4,1,8,2]=>0000000=>0000000
[7,6,1,4,2,8,3,5]=>[5,3,8,2,4,1,6,7]=>0000000=>0000000
[7,1,6,2,8,4,3,5]=>[5,3,4,8,2,6,1,7]=>0000000=>0000000
[1,4,2,7,8,5,3,6]=>[6,3,5,8,7,2,4,1]=>0000000=>0000000
[6,1,2,8,4,3,7,5]=>[5,7,3,4,8,2,1,6]=>0000000=>0000000
[6,4,1,2,8,3,7,5]=>[5,7,3,8,2,1,4,6]=>0000000=>0000000
[7,6,1,3,2,4,8,5]=>[5,8,4,2,3,1,6,7]=>0000000=>0000000
[6,7,1,3,2,4,8,5]=>[5,8,4,2,3,1,7,6]=>0000000=>0000000
[1,2,7,3,5,8,4,6]=>[6,4,8,5,3,7,2,1]=>0000000=>0000000
[5,8,1,3,7,2,4,6]=>[6,4,2,7,3,1,8,5]=>0000000=>0000000
[1,2,5,8,7,3,4,6]=>[6,4,3,7,8,5,2,1]=>0000000=>0000000
[8,6,1,3,2,4,7,5]=>[5,7,4,2,3,1,6,8]=>0000001=>1000000
[4,2,8,1,7,3,6,5]=>[5,6,3,7,1,8,2,4]=>0000000=>0000000
[7,1,2,8,4,3,6,5]=>[5,6,3,4,8,2,1,7]=>0000000=>0000000
[1,2,8,4,7,5,3,6]=>[6,3,5,7,4,8,2,1]=>0000000=>0000000
[1,2,8,7,4,5,3,6]=>[6,3,5,4,7,8,2,1]=>0000000=>0000000
[2,8,1,7,5,3,4,6]=>[6,4,3,5,7,1,8,2]=>0000000=>0000000
[8,3,7,1,5,2,4,6]=>[6,4,2,5,1,7,3,8]=>0000001=>1000000
[8,6,1,4,2,7,3,5]=>[5,3,7,2,4,1,6,8]=>0000001=>1000000
[7,1,2,8,6,4,3,5]=>[5,3,4,6,8,2,1,7]=>0000000=>0000000
[3,7,4,8,1,6,2,5]=>[5,2,6,1,8,4,7,3]=>0000000=>0000000
[3,4,8,7,1,6,2,5]=>[5,2,6,1,7,8,4,3]=>0000000=>0000000
[4,2,8,1,7,6,3,5]=>[5,3,6,7,1,8,2,4]=>0000000=>0000000
[2,8,1,7,6,4,3,5]=>[5,3,4,6,7,1,8,2]=>0000000=>0000000
[6,8,3,4,1,7,2,5]=>[5,2,7,1,4,3,8,6]=>0000000=>0000000
[5,7,3,4,1,8,2,6]=>[6,2,8,1,4,3,7,5]=>0000000=>0000000
[5,8,3,4,1,7,2,6]=>[6,2,7,1,4,3,8,5]=>0000000=>0000000
[4,8,3,5,1,7,2,6]=>[6,2,7,1,5,3,8,4]=>0000000=>0000000
[5,6,2,3,1,7,4,8]=>[8,4,7,1,3,2,6,5]=>0000000=>0000000
[5,6,2,4,1,8,3,7]=>[7,3,8,1,4,2,6,5]=>0000000=>0000000
[5,6,2,4,1,7,3,8]=>[8,3,7,1,4,2,6,5]=>0000000=>0000000
[4,5,1,8,3,7,2,6]=>[6,2,7,3,8,1,5,4]=>0000000=>0000000
[4,6,2,7,3,8,1,5]=>[5,1,8,3,7,2,6,4]=>0000000=>0000000
[5,6,2,7,3,8,1,4]=>[4,1,8,3,7,2,6,5]=>0000000=>0000000
[5,6,2,8,4,7,1,3]=>[3,1,7,4,8,2,6,5]=>0000000=>0000000
[4,6,2,8,3,7,1,5]=>[5,1,7,3,8,2,6,4]=>0000000=>0000000
[4,5,1,8,3,6,2,7]=>[7,2,6,3,8,1,5,4]=>0000000=>0000000
[6,5,3,2,1,4,8,7]=>[7,8,4,1,2,3,5,6]=>0000000=>0000000
[8,7,3,5,2,4,1,6]=>[6,1,4,2,5,3,7,8]=>0000011=>1100000
[6,8,2,4,5,7,3,1]=>[1,3,7,5,4,2,8,6]=>1000000=>0000001
[3,6,1,4,5,2,8,7]=>[7,8,2,5,4,1,6,3]=>0000000=>0000000
[8,3,7,4,5,2,1,6]=>[6,1,2,5,4,7,3,8]=>0000001=>1000000
[6,3,8,4,5,7,2,1]=>[1,2,7,5,4,8,3,6]=>1100000=>0000011
[8,1,7,4,3,6,2,5]=>[5,2,6,3,4,7,1,8]=>0000001=>1000000
[8,7,3,5,1,4,2,6]=>[6,2,4,1,5,3,7,8]=>0000011=>1100000
[2,1,6,8,5,7,4,3]=>[3,4,7,5,8,6,1,2]=>0000000=>0000000
[6,8,3,5,1,7,4,2]=>[2,4,7,1,5,3,8,6]=>0000000=>0000000
[2,5,8,4,7,6,3,1]=>[1,3,6,7,4,8,5,2]=>1000000=>0000001
[4,3,8,1,5,6,7,2]=>[2,7,6,5,1,8,3,4]=>0000000=>0000000
[4,8,3,6,1,2,7,5]=>[5,7,2,1,6,3,8,4]=>0000000=>0000000
[3,8,7,4,1,6,2,5]=>[5,2,6,1,4,7,8,3]=>0000000=>0000000
[3,8,1,2,5,6,7,4]=>[4,7,6,5,2,1,8,3]=>0000000=>0000000
[2,8,7,4,5,1,3,6]=>[6,3,1,5,4,7,8,2]=>0000000=>0000000
[8,7,2,4,1,6,3,5]=>[5,3,6,1,4,2,7,8]=>0000011=>1100000
[5,8,3,6,2,4,7,1]=>[1,7,4,2,6,3,8,5]=>1000000=>0000001
[8,6,3,2,1,4,7,5]=>[5,7,4,1,2,3,6,8]=>0000001=>1000000
[8,7,3,5,2,1,4,6]=>[6,4,1,2,5,3,7,8]=>0000011=>1100000
[5,8,3,6,2,1,7,4]=>[4,7,1,2,6,3,8,5]=>0000000=>0000000
[6,1,8,4,5,7,2,3]=>[3,2,7,5,4,8,1,6]=>0000000=>0000000
[6,8,3,5,1,7,2,4]=>[4,2,7,1,5,3,8,6]=>0000000=>0000000
[5,8,3,6,1,2,7,4]=>[4,7,2,1,6,3,8,5]=>0000000=>0000000
[5,8,1,4,7,6,2,3]=>[3,2,6,7,4,1,8,5]=>0000000=>0000000
[4,5,3,8,6,1,7,2]=>[2,7,1,6,8,3,5,4]=>0000000=>0000000
[4,5,7,6,2,3,8,1]=>[1,8,3,2,6,7,5,4]=>1000000=>0000001
[5,2,7,3,6,4,8,1]=>[1,8,4,6,3,7,2,5]=>1000000=>0000001
[5,1,7,3,6,8,4,2]=>[2,4,8,6,3,7,1,5]=>0000000=>0000000
[6,7,1,2,8,5,4,3]=>[3,4,5,8,2,1,7,6]=>0000000=>0000000
[3,5,7,1,6,8,4,2]=>[2,4,8,6,1,7,5,3]=>0000000=>0000000
[6,7,4,5,8,1,3,2]=>[2,3,1,8,5,4,7,6]=>0010000=>0000100
[4,2,8,7,1,6,5,3]=>[3,5,6,1,7,8,2,4]=>0000000=>0000000
[1,3,8,2,7,6,5,4]=>[4,5,6,7,2,8,3,1]=>0000000=>0000000
[2,1,8,3,7,6,5,4]=>[4,5,6,7,3,8,1,2]=>0000000=>0000000
[6,7,1,8,2,5,4,3]=>[3,4,5,2,8,1,7,6]=>0000000=>0000000
[3,8,1,2,7,6,5,4]=>[4,5,6,7,2,1,8,3]=>0000000=>0000000
[1,8,2,3,7,6,5,4]=>[4,5,6,7,3,2,8,1]=>0000000=>0000000
[3,7,1,5,8,2,6,4]=>[4,6,2,8,5,1,7,3]=>0000000=>0000000
[2,6,5,1,8,3,7,4]=>[4,7,3,8,1,5,6,2]=>0000000=>0000000
[5,6,4,1,8,7,2,3]=>[3,2,7,8,1,4,6,5]=>0000000=>0000000
[8,1,4,5,7,6,2,3]=>[3,2,6,7,5,4,1,8]=>0000001=>1000000
[6,4,5,1,8,7,2,3]=>[3,2,7,8,1,5,4,6]=>0000000=>0000000
[5,4,6,1,8,7,2,3]=>[3,2,7,8,1,6,4,5]=>0000000=>0000000
[3,5,6,1,8,2,7,4]=>[4,7,2,8,1,6,5,3]=>0000000=>0000000
[2,5,6,1,8,3,7,4]=>[4,7,3,8,1,6,5,2]=>0000000=>0000000
[2,4,6,1,3,8,7,5]=>[5,7,8,3,1,6,4,2]=>0000000=>0000000
[3,4,6,1,2,8,7,5]=>[5,7,8,2,1,6,4,3]=>0000000=>0000000
[5,3,6,1,8,2,7,4]=>[4,7,2,8,1,6,3,5]=>0000000=>0000000
[7,3,1,5,8,2,6,4]=>[4,6,2,8,5,1,3,7]=>0000000=>0000000
[8,1,3,5,7,2,6,4]=>[4,6,2,7,5,3,1,8]=>0000001=>1000000
[8,1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1,8]=>0000001=>1000000
[7,2,1,5,8,3,6,4]=>[4,6,3,8,5,1,2,7]=>0000000=>0000000
[6,2,5,1,8,3,7,4]=>[4,7,3,8,1,5,2,6]=>0000000=>0000000
[4,2,6,1,3,8,7,5]=>[5,7,8,3,1,6,2,4]=>0000000=>0000000
[4,2,5,3,1,8,7,6]=>[6,7,8,1,3,5,2,4]=>0000000=>0000000
[6,2,4,1,3,8,7,5]=>[5,7,8,3,1,4,2,6]=>0000000=>0000000
[7,2,1,4,3,8,6,5]=>[5,6,8,3,4,1,2,7]=>0000000=>0000000
[8,1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1,8]=>0000001=>1000000
[8,1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1,8]=>0000001=>1000000
[4,6,3,1,2,8,7,5]=>[5,7,8,2,1,3,6,4]=>0000000=>0000000
[2,6,4,1,3,8,7,5]=>[5,7,8,3,1,4,6,2]=>0000000=>0000000
[2,7,1,4,3,8,6,5]=>[5,6,8,3,4,1,7,2]=>0000000=>0000000
[8,1,6,7,2,3,5,4]=>[4,5,3,2,7,6,1,8]=>0000001=>1000000
[4,7,1,2,3,8,6,5]=>[5,6,8,3,2,1,7,4]=>0000000=>0000000
[3,7,1,2,4,8,6,5]=>[5,6,8,4,2,1,7,3]=>0000000=>0000000
[2,6,3,1,4,8,7,5]=>[5,7,8,4,1,3,6,2]=>0000000=>0000000
[3,6,2,1,4,8,7,5]=>[5,7,8,4,1,2,6,3]=>0000000=>0000000
[5,6,2,1,8,3,7,4]=>[4,7,3,8,1,2,6,5]=>0000000=>0000000
[6,5,2,1,8,3,7,4]=>[4,7,3,8,1,2,5,6]=>0000000=>0000000
[8,1,4,2,3,7,6,5]=>[5,6,7,3,2,4,1,8]=>0000001=>1000000
[5,4,2,3,1,8,7,6]=>[6,7,8,1,3,2,4,5]=>0000000=>0000000
[3,5,2,4,1,8,7,6]=>[6,7,8,1,4,2,5,3]=>0000000=>0000000
[7,3,1,2,4,8,6,5]=>[5,6,8,4,2,1,3,7]=>0000000=>0000000
[8,1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1,8]=>0000001=>1000000
[7,2,1,3,4,8,6,5]=>[5,6,8,4,3,1,2,7]=>0000000=>0000000
[2,4,3,6,5,8,1,7]=>[7,1,8,5,6,3,4,2]=>0000000=>0000000
[2,4,6,3,5,8,7,1]=>[1,7,8,5,3,6,4,2]=>1000000=>0000001
[2,4,1,6,5,3,8,7]=>[7,8,3,5,6,1,4,2]=>0000000=>0000000
[4,2,6,5,8,1,7,3]=>[3,7,1,8,5,6,2,4]=>0000000=>0000000
[4,2,6,5,8,1,3,7]=>[7,3,1,8,5,6,2,4]=>0000000=>0000000
[2,4,1,6,5,8,7,3]=>[3,7,8,5,6,1,4,2]=>0000000=>0000000
[2,4,6,8,1,5,7,3]=>[3,7,5,1,8,6,4,2]=>0000000=>0000000
[2,4,6,1,8,5,3,7]=>[7,3,5,8,1,6,4,2]=>0000000=>0000000
[2,4,6,8,1,5,3,7]=>[7,3,5,1,8,6,4,2]=>0000000=>0000000
[2,4,6,8,3,5,7,1]=>[1,7,5,3,8,6,4,2]=>1000000=>0000001
[2,4,6,8,3,1,5,7]=>[7,5,1,3,8,6,4,2]=>0000000=>0000000
[2,4,6,3,8,5,7,1]=>[1,7,5,8,3,6,4,2]=>1000000=>0000001
[2,4,3,6,8,5,7,1]=>[1,7,5,8,6,3,4,2]=>1000000=>0000001
[2,4,3,6,8,5,1,7]=>[7,1,5,8,6,3,4,2]=>0000000=>0000000
[2,4,3,6,8,1,5,7]=>[7,5,1,8,6,3,4,2]=>0000000=>0000000
[2,4,3,6,1,8,5,7]=>[7,5,8,1,6,3,4,2]=>0000000=>0000000
[2,4,3,1,6,8,5,7]=>[7,5,8,6,1,3,4,2]=>0000000=>0000000
[2,4,1,3,6,8,7,5]=>[5,7,8,6,3,1,4,2]=>0000000=>0000000
[2,4,3,6,8,1,7,5]=>[5,7,1,8,6,3,4,2]=>0000000=>0000000
[4,6,2,5,8,7,3,1]=>[1,3,7,8,5,2,6,4]=>1000000=>0000001
[2,4,1,6,8,3,7,5]=>[5,7,3,8,6,1,4,2]=>0000000=>0000000
[2,4,6,8,1,3,7,5]=>[5,7,3,1,8,6,4,2]=>0000000=>0000000
[4,6,2,8,5,7,3,1]=>[1,3,7,5,8,2,6,4]=>1000000=>0000001
[4,6,2,8,5,7,1,3]=>[3,1,7,5,8,2,6,4]=>0000000=>0000000
[2,6,4,8,1,7,5,3]=>[3,5,7,1,8,4,6,2]=>0000000=>0000000
[1,3,7,4,5,8,2,6]=>[6,2,8,5,4,7,3,1]=>0000000=>0000000
[1,7,6,3,4,8,2,5]=>[5,2,8,4,3,6,7,1]=>0000000=>0000000
[8,1,6,3,7,2,4,5]=>[5,4,2,7,3,6,1,8]=>0000001=>1000000
[1,2,7,4,8,3,5,6]=>[6,5,3,8,4,7,2,1]=>0000000=>0000000
[6,1,7,3,4,8,2,5]=>[5,2,8,4,3,7,1,6]=>0000000=>0000000
[2,1,7,4,5,8,3,6]=>[6,3,8,5,4,7,1,2]=>0000000=>0000000
[5,1,4,7,3,8,2,6]=>[6,2,8,3,7,4,1,5]=>0000000=>0000000
[4,3,1,7,5,8,2,6]=>[6,2,8,5,7,1,3,4]=>0000000=>0000000
[2,8,6,3,7,1,4,5]=>[5,4,1,7,3,6,8,2]=>0000000=>0000000
[6,8,1,3,7,2,4,5]=>[5,4,2,7,3,1,8,6]=>0000000=>0000000
[5,8,2,1,7,3,4,6]=>[6,4,3,7,1,2,8,5]=>0000000=>0000000
[5,7,2,1,8,3,4,6]=>[6,4,3,8,1,2,7,5]=>0000000=>0000000
[6,7,1,3,8,2,4,5]=>[5,4,2,8,3,1,7,6]=>0000000=>0000000
[8,5,1,3,7,2,4,6]=>[6,4,2,7,3,1,5,8]=>0000001=>1000000
[1,5,3,2,8,4,6,7]=>[7,6,4,8,2,3,5,1]=>0000000=>0000000
[2,6,4,8,7,1,3,5]=>[5,3,1,7,8,4,6,2]=>0000000=>0000000
[1,6,4,8,7,2,3,5]=>[5,3,2,7,8,4,6,1]=>0000000=>0000000
[4,3,2,8,7,1,5,6]=>[6,5,1,7,8,2,3,4]=>0000000=>0000000
[5,2,4,8,7,1,3,6]=>[6,3,1,7,8,4,2,5]=>0000000=>0000000
[6,2,8,3,7,1,4,5]=>[5,4,1,7,3,8,2,6]=>0000000=>0000000
[5,1,4,8,7,2,3,6]=>[6,3,2,7,8,4,1,5]=>0000000=>0000000
[8,4,2,5,1,6,3,7]=>[7,3,6,1,5,2,4,8]=>0000001=>1000000
[3,2,8,1,6,4,7,5]=>[5,7,4,6,1,8,2,3]=>0000000=>0000000
[4,2,8,6,1,3,7,5]=>[5,7,3,1,6,8,2,4]=>0000000=>0000000
[4,2,6,8,1,3,7,5]=>[5,7,3,1,8,6,2,4]=>0000000=>0000000
[4,7,3,8,5,1,2,6]=>[6,2,1,5,8,3,7,4]=>0000000=>0000000
[3,1,8,5,4,2,6,7]=>[7,6,2,4,5,8,1,3]=>0000000=>0000000
[1,8,2,5,7,3,6,4]=>[4,6,3,7,5,2,8,1]=>0000000=>0000000
[6,2,1,5,4,8,7,3]=>[3,7,8,4,5,1,2,6]=>0000000=>0000000
[4,3,6,1,8,2,7,5]=>[5,7,2,8,1,6,3,4]=>0000000=>0000000
[6,1,2,5,7,3,8,4]=>[4,8,3,7,5,2,1,6]=>0000000=>0000000
[1,3,6,8,5,7,2,4]=>[4,2,7,5,8,6,3,1]=>0000000=>0000000
[4,1,6,7,3,8,2,5]=>[5,2,8,3,7,6,1,4]=>0000000=>0000000
[5,4,6,1,3,7,2,8]=>[8,2,7,3,1,6,4,5]=>0000000=>0000000
[2,8,3,5,4,1,7,6]=>[6,7,1,4,5,3,8,2]=>0000000=>0000000
[5,1,8,7,4,3,2,6]=>[6,2,3,4,7,8,1,5]=>0000000=>0000000
[6,5,1,8,4,3,2,7]=>[7,2,3,4,8,1,5,6]=>0000000=>0000000
[6,1,2,5,4,7,8,3]=>[3,8,7,4,5,2,1,6]=>0000000=>0000000
[6,2,4,5,1,3,7,8]=>[8,7,3,1,5,4,2,6]=>0000000=>0000000
[4,3,6,8,1,7,2,5]=>[5,2,7,1,8,6,3,4]=>0000000=>0000000
[5,3,6,4,1,7,2,8]=>[8,2,7,1,4,6,3,5]=>0000000=>0000000
[4,6,7,2,5,8,1,3]=>[3,1,8,5,2,7,6,4]=>0000000=>0000000
[6,3,7,2,5,1,8,4]=>[4,8,1,5,2,7,3,6]=>0000000=>0000000
[6,7,8,3,5,2,1,4]=>[4,1,2,5,3,8,7,6]=>0000100=>0010000
[2,1,5,7,8,6,3,4]=>[4,3,6,8,7,5,1,2]=>0000000=>0000000
[3,2,6,1,7,4,5,8]=>[8,5,4,7,1,6,2,3]=>0000000=>0000000
[8,3,5,2,1,4,7,6]=>[6,7,4,1,2,5,3,8]=>0000001=>1000000
[2,7,6,5,1,8,3,4]=>[4,3,8,1,5,6,7,2]=>0000000=>0000000
[2,7,6,5,1,8,4,3]=>[3,4,8,1,5,6,7,2]=>0000000=>0000000
[2,3,6,5,1,4,8,7]=>[7,8,4,1,5,6,3,2]=>0000000=>0000000
[2,3,6,4,1,5,8,7]=>[7,8,5,1,4,6,3,2]=>0000000=>0000000
[2,7,6,1,4,8,5,3]=>[3,5,8,4,1,6,7,2]=>0000000=>0000000
[7,3,5,1,8,4,2,6]=>[6,2,4,8,1,5,3,7]=>0000000=>0000000
[2,7,6,1,5,8,4,3]=>[3,4,8,5,1,6,7,2]=>0000000=>0000000
[2,7,6,4,1,8,5,3]=>[3,5,8,1,4,6,7,2]=>0000000=>0000000
[2,7,6,4,1,8,3,5]=>[5,3,8,1,4,6,7,2]=>0000000=>0000000
[7,3,5,1,8,6,2,4]=>[4,2,6,8,1,5,3,7]=>0000000=>0000000
[2,3,4,8,7,6,1,5]=>[5,1,6,7,8,4,3,2]=>0000000=>0000000
[2,3,4,8,5,7,1,6]=>[6,1,7,5,8,4,3,2]=>0000000=>0000000
[7,3,5,4,8,1,2,6]=>[6,2,1,8,4,5,3,7]=>0000000=>0000000
[6,4,3,5,8,7,2,1]=>[1,2,7,8,5,3,4,6]=>1100000=>0000011
[2,1,4,5,8,7,3,6]=>[6,3,7,8,5,4,1,2]=>0000000=>0000000
[6,4,3,5,8,7,1,2]=>[2,1,7,8,5,3,4,6]=>0100000=>0000010
[2,3,4,8,7,5,1,6]=>[6,1,5,7,8,4,3,2]=>0000000=>0000000
[2,7,6,5,4,8,1,3]=>[3,1,8,4,5,6,7,2]=>0000000=>0000000
[7,3,5,6,8,1,2,4]=>[4,2,1,8,6,5,3,7]=>0000000=>0000000
[6,4,1,5,8,7,2,3]=>[3,2,7,8,5,1,4,6]=>0000000=>0000000
[6,4,1,5,8,7,3,2]=>[2,3,7,8,5,1,4,6]=>0000000=>0000000
[6,4,1,5,8,3,7,2]=>[2,7,3,8,5,1,4,6]=>0000000=>0000000
[5,7,1,6,3,8,2,4]=>[4,2,8,3,6,1,7,5]=>0000000=>0000000
[6,4,1,5,8,3,2,7]=>[7,2,3,8,5,1,4,6]=>0000000=>0000000
[6,3,5,7,8,2,1,4]=>[4,1,2,8,7,5,3,6]=>0000000=>0000000
[5,7,3,6,1,8,4,2]=>[2,4,8,1,6,3,7,5]=>0000000=>0000000
[7,3,5,4,8,6,2,1]=>[1,2,6,8,4,5,3,7]=>1100000=>0000011
[2,3,4,8,5,6,1,7]=>[7,1,6,5,8,4,3,2]=>0000000=>0000000
[2,3,4,8,7,1,6,5]=>[5,6,1,7,8,4,3,2]=>0000000=>0000000
[2,3,4,8,5,1,7,6]=>[6,7,1,5,8,4,3,2]=>0000000=>0000000
[7,4,3,5,8,2,1,6]=>[6,1,2,8,5,3,4,7]=>0000000=>0000000
[7,4,3,5,8,2,6,1]=>[1,6,2,8,5,3,4,7]=>1000000=>0000001
[6,3,5,4,8,2,1,7]=>[7,1,2,8,4,5,3,6]=>0000000=>0000000
[2,3,4,8,5,1,6,7]=>[7,6,1,5,8,4,3,2]=>0000000=>0000000
[6,1,4,2,8,5,7,3]=>[3,7,5,8,2,4,1,6]=>0000000=>0000000
[4,8,6,5,3,2,7,1]=>[1,7,2,3,5,6,8,4]=>1000000=>0000001
[8,6,5,1,2,4,7,3]=>[3,7,4,2,1,5,6,8]=>0000001=>1000000
[1,7,5,8,2,6,4,3]=>[3,4,6,2,8,5,7,1]=>0000000=>0000000
[1,3,8,5,7,6,2,4]=>[4,2,6,7,5,8,3,1]=>0000000=>0000000
[6,3,8,5,7,1,2,4]=>[4,2,1,7,5,8,3,6]=>0000000=>0000000
[6,8,5,2,1,4,7,3]=>[3,7,4,1,2,5,8,6]=>0000000=>0000000
[3,8,2,5,6,1,7,4]=>[4,7,1,6,5,2,8,3]=>0000000=>0000000
[8,1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1,8]=>0000001=>1000000
[8,6,1,5,7,2,3,4]=>[4,3,2,7,5,1,6,8]=>0000001=>1000000
[3,8,6,5,7,1,2,4]=>[4,2,1,7,5,6,8,3]=>0000000=>0000000
[5,1,7,6,8,4,2,3]=>[3,2,4,8,6,7,1,5]=>0000000=>0000000
[5,1,3,7,8,6,2,4]=>[4,2,6,8,7,3,1,5]=>0000000=>0000000
[7,2,5,8,1,6,4,3]=>[3,4,6,1,8,5,2,7]=>0000000=>0000000
[3,2,8,5,7,6,1,4]=>[4,1,6,7,5,8,2,3]=>0000000=>0000000
[8,2,1,5,7,6,3,4]=>[4,3,6,7,5,1,2,8]=>0000001=>1000000
[5,2,8,6,1,7,3,4]=>[4,3,7,1,6,8,2,5]=>0000000=>0000000
[1,2,8,6,5,7,3,4]=>[4,3,7,5,6,8,2,1]=>0000000=>0000000
[8,2,5,6,3,7,1,4]=>[4,1,7,3,6,5,2,8]=>0000001=>1000000
[7,2,6,5,4,1,8,3]=>[3,8,1,4,5,6,2,7]=>0000000=>0000000
[6,1,3,5,4,7,8,2]=>[2,8,7,4,5,3,1,6]=>0000000=>0000000
[6,1,5,3,4,7,8,2]=>[2,8,7,4,3,5,1,6]=>0000000=>0000000
[7,5,6,2,4,1,8,3]=>[3,8,1,4,2,6,5,7]=>0000000=>0000000
[8,5,2,6,3,7,1,4]=>[4,1,7,3,6,2,5,8]=>0000001=>1000000
[8,1,6,5,7,3,2,4]=>[4,2,3,7,5,6,1,8]=>0000001=>1000000
[3,5,8,6,2,7,1,4]=>[4,1,7,2,6,8,5,3]=>0000000=>0000000
[1,8,5,6,3,7,2,4]=>[4,2,7,3,6,5,8,1]=>0000000=>0000000
[1,7,6,5,4,2,8,3]=>[3,8,2,4,5,6,7,1]=>0000000=>0000000
[5,7,6,1,4,2,8,3]=>[3,8,2,4,1,6,7,5]=>0000000=>0000000
[7,1,4,2,6,5,8,3]=>[3,8,5,6,2,4,1,7]=>0000000=>0000000
[2,7,4,1,5,6,8,3]=>[3,8,6,5,1,4,7,2]=>0000000=>0000000
[5,7,6,4,1,2,8,3]=>[3,8,2,1,4,6,7,5]=>0000000=>0000000
[4,7,6,1,5,2,8,3]=>[3,8,2,5,1,6,7,4]=>0000000=>0000000
[1,7,6,4,5,2,8,3]=>[3,8,2,5,4,6,7,1]=>0000000=>0000000
[3,8,1,6,5,7,2,4]=>[4,2,7,5,6,1,8,3]=>0000000=>0000000
[8,1,3,5,7,6,2,4]=>[4,2,6,7,5,3,1,8]=>0000001=>1000000
[7,8,5,4,1,6,2,3]=>[3,2,6,1,4,5,8,7]=>0000010=>0100000
[6,1,5,4,3,7,8,2]=>[2,8,7,3,4,5,1,6]=>0000000=>0000000
[7,5,6,4,2,1,8,3]=>[3,8,1,2,4,6,5,7]=>0000000=>0000000
[8,3,2,6,5,7,1,4]=>[4,1,7,5,6,2,3,8]=>0000001=>1000000
[7,4,6,2,5,1,8,3]=>[3,8,1,5,2,6,4,7]=>0000000=>0000000
[6,1,4,3,5,7,8,2]=>[2,8,7,5,3,4,1,6]=>0000000=>0000000
[6,1,3,4,5,7,8,2]=>[2,8,7,5,4,3,1,6]=>0000000=>0000000
[7,2,6,4,5,1,8,3]=>[3,8,1,5,4,6,2,7]=>0000000=>0000000
[8,2,3,6,5,7,1,4]=>[4,1,7,5,6,3,2,8]=>0000001=>1000000
[2,1,4,3,6,5,8,7,11,12,10,9]=>[9,10,12,11,7,8,5,6,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,6,5,9,10,8,7,12,11]=>[11,12,7,8,10,9,5,6,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,6,5,9,11,8,12,10,7]=>[7,10,12,8,11,9,5,6,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,6,5,10,11,12,9,8,7]=>[7,8,9,12,11,10,5,6,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,7,8,6,5,10,9,12,11]=>[11,12,9,10,5,6,8,7,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,7,8,6,5,11,12,10,9]=>[9,10,12,11,5,6,8,7,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,7,9,6,10,8,5,12,11]=>[11,12,5,8,10,6,9,7,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,7,9,6,11,8,12,10,5]=>[5,10,12,8,11,6,9,7,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,7,10,6,11,12,9,8,5]=>[5,8,9,12,11,6,10,7,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,8,9,10,7,6,5,12,11]=>[11,12,5,6,7,10,9,8,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,8,9,11,7,6,12,10,5]=>[5,10,12,6,7,11,9,8,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,8,10,11,7,12,9,6,5]=>[5,6,9,12,7,11,10,8,3,4,1,2]=>00000000000=>00000000000
[2,1,4,3,9,10,11,12,8,7,6,5]=>[5,6,7,8,12,11,10,9,3,4,1,2]=>00000000000=>00000000000
[2,1,5,6,4,3,8,7,10,9,12,11]=>[11,12,9,10,7,8,3,4,6,5,1,2]=>00000000000=>00000000000
[2,1,5,6,4,3,8,7,11,12,10,9]=>[9,10,12,11,7,8,3,4,6,5,1,2]=>00000000000=>00000000000
[2,1,5,6,4,3,9,10,8,7,12,11]=>[11,12,7,8,10,9,3,4,6,5,1,2]=>00000000000=>00000000000
[2,1,5,6,4,3,9,11,8,12,10,7]=>[7,10,12,8,11,9,3,4,6,5,1,2]=>00000000000=>00000000000
[2,1,5,6,4,3,10,11,12,9,8,7]=>[7,8,9,12,11,10,3,4,6,5,1,2]=>00000000000=>00000000000
[2,1,5,7,4,8,6,3,10,9,12,11]=>[11,12,9,10,3,6,8,4,7,5,1,2]=>00000000000=>00000000000
[2,1,5,7,4,8,6,3,11,12,10,9]=>[9,10,12,11,3,6,8,4,7,5,1,2]=>00000000000=>00000000000
[2,1,5,7,4,9,6,10,8,3,12,11]=>[11,12,3,8,10,6,9,4,7,5,1,2]=>00000000000=>00000000000
[2,1,5,7,4,9,6,11,8,12,10,3]=>[3,10,12,8,11,6,9,4,7,5,1,2]=>00000000000=>00000000000
[2,1,5,7,4,10,6,11,12,9,8,3]=>[3,8,9,12,11,6,10,4,7,5,1,2]=>00000000000=>00000000000
[2,1,5,8,4,9,10,7,6,3,12,11]=>[11,12,3,6,7,10,9,4,8,5,1,2]=>00000000000=>00000000000
[2,1,5,8,4,9,11,7,6,12,10,3]=>[3,10,12,6,7,11,9,4,8,5,1,2]=>00000000000=>00000000000
[2,1,5,8,4,10,11,7,12,9,6,3]=>[3,6,9,12,7,11,10,4,8,5,1,2]=>00000000000=>00000000000
[2,1,5,9,4,10,11,12,8,7,6,3]=>[3,6,7,8,12,11,10,4,9,5,1,2]=>00000000000=>00000000000
[2,1,6,7,8,5,4,3,10,9,12,11]=>[11,12,9,10,3,4,5,8,7,6,1,2]=>00000000000=>00000000000
[2,1,6,7,8,5,4,3,11,12,10,9]=>[9,10,12,11,3,4,5,8,7,6,1,2]=>00000000000=>00000000000
[2,1,6,7,9,5,4,10,8,3,12,11]=>[11,12,3,8,10,4,5,9,7,6,1,2]=>00000000000=>00000000000
[2,1,6,7,9,5,4,11,8,12,10,3]=>[3,10,12,8,11,4,5,9,7,6,1,2]=>00000000000=>00000000000
[2,1,6,7,10,5,4,11,12,9,8,3]=>[3,8,9,12,11,4,5,10,7,6,1,2]=>00000000000=>00000000000
[2,1,6,8,9,5,10,7,4,3,12,11]=>[11,12,3,4,7,10,5,9,8,6,1,2]=>00000000000=>00000000000
[2,1,6,8,9,5,11,7,4,12,10,3]=>[3,10,12,4,7,11,5,9,8,6,1,2]=>00000000000=>00000000000
[2,1,6,8,10,5,11,7,12,9,4,3]=>[3,4,9,12,7,11,5,10,8,6,1,2]=>00000000000=>00000000000
[2,1,6,9,10,5,11,12,8,7,4,3]=>[3,4,7,8,12,11,5,10,9,6,1,2]=>00000000000=>00000000000
[2,1,7,8,9,10,6,5,4,3,12,11]=>[11,12,3,4,5,6,10,9,8,7,1,2]=>00000000000=>00000000000
[2,1,7,8,9,11,6,5,4,12,10,3]=>[3,10,12,4,5,6,11,9,8,7,1,2]=>00000000000=>00000000000
[2,1,7,8,10,11,6,5,12,9,4,3]=>[3,4,9,12,5,6,11,10,8,7,1,2]=>00000000000=>00000000000
[2,1,7,9,10,11,6,12,8,5,4,3]=>[3,4,5,8,12,6,11,10,9,7,1,2]=>00000000000=>00000000000
[2,1,8,9,10,11,12,7,6,5,4,3]=>[3,4,5,6,7,12,11,10,9,8,1,2]=>00000000000=>00000000000
[3,4,2,1,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,6,5,8,7,11,12,10,9]=>[9,10,12,11,7,8,5,6,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,6,5,9,10,8,7,12,11]=>[11,12,7,8,10,9,5,6,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,6,5,9,11,8,12,10,7]=>[7,10,12,8,11,9,5,6,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,6,5,10,11,12,9,8,7]=>[7,8,9,12,11,10,5,6,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,7,8,6,5,10,9,12,11]=>[11,12,9,10,5,6,8,7,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,7,8,6,5,11,12,10,9]=>[9,10,12,11,5,6,8,7,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,7,9,6,10,8,5,12,11]=>[11,12,5,8,10,6,9,7,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,7,9,6,11,8,12,10,5]=>[5,10,12,8,11,6,9,7,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,7,10,6,11,12,9,8,5]=>[5,8,9,12,11,6,10,7,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,8,9,10,7,6,5,12,11]=>[11,12,5,6,7,10,9,8,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,8,9,11,7,6,12,10,5]=>[5,10,12,6,7,11,9,8,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,8,10,11,7,12,9,6,5]=>[5,6,9,12,7,11,10,8,1,2,4,3]=>00000000000=>00000000000
[3,4,2,1,9,10,11,12,8,7,6,5]=>[5,6,7,8,12,11,10,9,1,2,4,3]=>00000000000=>00000000000
[3,5,2,6,4,1,8,7,10,9,12,11]=>[11,12,9,10,7,8,1,4,6,2,5,3]=>00000000000=>00000000000
[3,5,2,6,4,1,8,7,11,12,10,9]=>[9,10,12,11,7,8,1,4,6,2,5,3]=>00000000000=>00000000000
[3,5,2,6,4,1,9,10,8,7,12,11]=>[11,12,7,8,10,9,1,4,6,2,5,3]=>00000000000=>00000000000
[3,5,2,6,4,1,9,11,8,12,10,7]=>[7,10,12,8,11,9,1,4,6,2,5,3]=>00000000000=>00000000000
[3,5,2,6,4,1,10,11,12,9,8,7]=>[7,8,9,12,11,10,1,4,6,2,5,3]=>00000000000=>00000000000
[3,5,2,7,4,8,6,1,10,9,12,11]=>[11,12,9,10,1,6,8,4,7,2,5,3]=>00000000000=>00000000000
[3,5,2,7,4,8,6,1,11,12,10,9]=>[9,10,12,11,1,6,8,4,7,2,5,3]=>00000000000=>00000000000
[3,5,2,7,4,9,6,10,8,1,12,11]=>[11,12,1,8,10,6,9,4,7,2,5,3]=>00000000000=>00000000000
[3,5,2,7,4,9,6,11,8,12,10,1]=>[1,10,12,8,11,6,9,4,7,2,5,3]=>10000000000=>00000000001
[3,5,2,7,4,10,6,11,12,9,8,1]=>[1,8,9,12,11,6,10,4,7,2,5,3]=>10000000000=>00000000001
[3,5,2,8,4,9,10,7,6,1,12,11]=>[11,12,1,6,7,10,9,4,8,2,5,3]=>00000000000=>00000000000
[3,5,2,8,4,9,11,7,6,12,10,1]=>[1,10,12,6,7,11,9,4,8,2,5,3]=>10000000000=>00000000001
[3,5,2,8,4,10,11,7,12,9,6,1]=>[1,6,9,12,7,11,10,4,8,2,5,3]=>10000000000=>00000000001
[3,5,2,9,4,10,11,12,8,7,6,1]=>[1,6,7,8,12,11,10,4,9,2,5,3]=>10000000000=>00000000001
[3,6,2,7,8,5,4,1,10,9,12,11]=>[11,12,9,10,1,4,5,8,7,2,6,3]=>00000000000=>00000000000
[3,6,2,7,8,5,4,1,11,12,10,9]=>[9,10,12,11,1,4,5,8,7,2,6,3]=>00000000000=>00000000000
[3,6,2,7,9,5,4,10,8,1,12,11]=>[11,12,1,8,10,4,5,9,7,2,6,3]=>00000000000=>00000000000
[3,6,2,7,9,5,4,11,8,12,10,1]=>[1,10,12,8,11,4,5,9,7,2,6,3]=>10000000000=>00000000001
[3,6,2,7,10,5,4,11,12,9,8,1]=>[1,8,9,12,11,4,5,10,7,2,6,3]=>10000000000=>00000000001
[3,6,2,8,9,5,10,7,4,1,12,11]=>[11,12,1,4,7,10,5,9,8,2,6,3]=>00000000000=>00000000000
[3,6,2,8,9,5,11,7,4,12,10,1]=>[1,10,12,4,7,11,5,9,8,2,6,3]=>10000000000=>00000000001
[3,6,2,8,10,5,11,7,12,9,4,1]=>[1,4,9,12,7,11,5,10,8,2,6,3]=>10000000000=>00000000001
[3,6,2,9,10,5,11,12,8,7,4,1]=>[1,4,7,8,12,11,5,10,9,2,6,3]=>10000000000=>00000000001
[3,7,2,8,9,10,6,5,4,1,12,11]=>[11,12,1,4,5,6,10,9,8,2,7,3]=>00000000000=>00000000000
[3,7,2,8,9,11,6,5,4,12,10,1]=>[1,10,12,4,5,6,11,9,8,2,7,3]=>10000000000=>00000000001
[3,7,2,8,10,11,6,5,12,9,4,1]=>[1,4,9,12,5,6,11,10,8,2,7,3]=>10000000000=>00000000001
[3,7,2,9,10,11,6,12,8,5,4,1]=>[1,4,5,8,12,6,11,10,9,2,7,3]=>10000000000=>00000000001
[3,8,2,9,10,11,12,7,6,5,4,1]=>[1,4,5,6,7,12,11,10,9,2,8,3]=>10000000000=>00000000001
[4,5,6,3,2,1,8,7,10,9,12,11]=>[11,12,9,10,7,8,1,2,3,6,5,4]=>00000000000=>00000000000
[4,5,6,3,2,1,8,7,11,12,10,9]=>[9,10,12,11,7,8,1,2,3,6,5,4]=>00000000000=>00000000000
[4,5,6,3,2,1,9,10,8,7,12,11]=>[11,12,7,8,10,9,1,2,3,6,5,4]=>00000000000=>00000000000
[4,5,6,3,2,1,9,11,8,12,10,7]=>[7,10,12,8,11,9,1,2,3,6,5,4]=>00000000000=>00000000000
[4,5,6,3,2,1,10,11,12,9,8,7]=>[7,8,9,12,11,10,1,2,3,6,5,4]=>00000000000=>00000000000
[4,5,7,3,2,8,6,1,10,9,12,11]=>[11,12,9,10,1,6,8,2,3,7,5,4]=>00000000000=>00000000000
[4,5,7,3,2,8,6,1,11,12,10,9]=>[9,10,12,11,1,6,8,2,3,7,5,4]=>00000000000=>00000000000
[4,5,7,3,2,9,6,10,8,1,12,11]=>[11,12,1,8,10,6,9,2,3,7,5,4]=>00000000000=>00000000000
[4,5,7,3,2,9,6,11,8,12,10,1]=>[1,10,12,8,11,6,9,2,3,7,5,4]=>10000000000=>00000000001
[4,5,7,3,2,10,6,11,12,9,8,1]=>[1,8,9,12,11,6,10,2,3,7,5,4]=>10000000000=>00000000001
[4,5,8,3,2,9,10,7,6,1,12,11]=>[11,12,1,6,7,10,9,2,3,8,5,4]=>00000000000=>00000000000
[4,5,8,3,2,9,11,7,6,12,10,1]=>[1,10,12,6,7,11,9,2,3,8,5,4]=>10000000000=>00000000001
[4,5,8,3,2,10,11,7,12,9,6,1]=>[1,6,9,12,7,11,10,2,3,8,5,4]=>10000000000=>00000000001
[4,5,9,3,2,10,11,12,8,7,6,1]=>[1,6,7,8,12,11,10,2,3,9,5,4]=>10000000000=>00000000001
[4,6,7,3,8,5,2,1,10,9,12,11]=>[11,12,9,10,1,2,5,8,3,7,6,4]=>00000000000=>00000000000
[4,6,7,3,8,5,2,1,11,12,10,9]=>[9,10,12,11,1,2,5,8,3,7,6,4]=>00000000000=>00000000000
[4,6,7,3,9,5,2,10,8,1,12,11]=>[11,12,1,8,10,2,5,9,3,7,6,4]=>00000000000=>00000000000
[4,6,7,3,9,5,2,11,8,12,10,1]=>[1,10,12,8,11,2,5,9,3,7,6,4]=>10000000000=>00000000001
[4,6,7,3,10,5,2,11,12,9,8,1]=>[1,8,9,12,11,2,5,10,3,7,6,4]=>10000000000=>00000000001
[4,6,8,3,9,5,10,7,2,1,12,11]=>[11,12,1,2,7,10,5,9,3,8,6,4]=>00000000000=>00000000000
[4,6,8,3,9,5,11,7,2,12,10,1]=>[1,10,12,2,7,11,5,9,3,8,6,4]=>10000000000=>00000000001
[4,6,8,3,10,5,11,7,12,9,2,1]=>[1,2,9,12,7,11,5,10,3,8,6,4]=>11000000000=>00000000011
[4,6,9,3,10,5,11,12,8,7,2,1]=>[1,2,7,8,12,11,5,10,3,9,6,4]=>11000000000=>00000000011
[4,7,8,3,9,10,6,5,2,1,12,11]=>[11,12,1,2,5,6,10,9,3,8,7,4]=>00000000000=>00000000000
[4,7,8,3,9,11,6,5,2,12,10,1]=>[1,10,12,2,5,6,11,9,3,8,7,4]=>10000000000=>00000000001
[4,7,8,3,10,11,6,5,12,9,2,1]=>[1,2,9,12,5,6,11,10,3,8,7,4]=>11000000000=>00000000011
[4,7,9,3,10,11,6,12,8,5,2,1]=>[1,2,5,8,12,6,11,10,3,9,7,4]=>11000000000=>00000000011
[4,8,9,3,10,11,12,7,6,5,2,1]=>[1,2,5,6,7,12,11,10,3,9,8,4]=>11000000000=>00000000011
[5,6,7,8,4,3,2,1,10,9,12,11]=>[11,12,9,10,1,2,3,4,8,7,6,5]=>00000000000=>00000000000
[5,6,7,8,4,3,2,1,11,12,10,9]=>[9,10,12,11,1,2,3,4,8,7,6,5]=>00000000000=>00000000000
[5,6,7,9,4,3,2,10,8,1,12,11]=>[11,12,1,8,10,2,3,4,9,7,6,5]=>00000000000=>00000000000
[5,6,7,9,4,3,2,11,8,12,10,1]=>[1,10,12,8,11,2,3,4,9,7,6,5]=>10000000000=>00000000001
[5,6,7,10,4,3,2,11,12,9,8,1]=>[1,8,9,12,11,2,3,4,10,7,6,5]=>10000000000=>00000000001
[5,6,8,9,4,3,10,7,2,1,12,11]=>[11,12,1,2,7,10,3,4,9,8,6,5]=>00000000000=>00000000000
[5,6,8,9,4,3,11,7,2,12,10,1]=>[1,10,12,2,7,11,3,4,9,8,6,5]=>10000000000=>00000000001
[5,6,8,10,4,3,11,7,12,9,2,1]=>[1,2,9,12,7,11,3,4,10,8,6,5]=>11000000000=>00000000011
[5,6,9,10,4,3,11,12,8,7,2,1]=>[1,2,7,8,12,11,3,4,10,9,6,5]=>11000000000=>00000000011
[5,7,8,9,4,10,6,3,2,1,12,11]=>[11,12,1,2,3,6,10,4,9,8,7,5]=>00000000000=>00000000000
[5,7,8,9,4,11,6,3,2,12,10,1]=>[1,10,12,2,3,6,11,4,9,8,7,5]=>10000000000=>00000000001
[5,7,8,10,4,11,6,3,12,9,2,1]=>[1,2,9,12,3,6,11,4,10,8,7,5]=>11000000000=>00000000011
[6,7,8,9,10,5,4,3,2,1,12,11]=>[11,12,1,2,3,4,5,10,9,8,7,6]=>00000000000=>00000000000
[6,7,8,9,11,5,4,3,2,12,10,1]=>[1,10,12,2,3,4,5,11,9,8,7,6]=>10000000000=>00000000001
[6,7,8,10,11,5,4,3,12,9,2,1]=>[1,2,9,12,3,4,5,11,10,8,7,6]=>11000000000=>00000000011
[7,8,9,10,11,12,6,5,4,3,2,1]=>[1,2,3,4,5,6,12,11,10,9,8,7]=>11111100000=>00000111111
[3,8,2,7,6,1,5,4]=>[4,5,1,6,7,2,8,3]=>0000000=>0000000
[4,8,7,3,1,6,5,2]=>[2,5,6,1,3,7,8,4]=>0000000=>0000000
[4,8,7,3,2,6,5,1]=>[1,5,6,2,3,7,8,4]=>1000000=>0000001
[4,8,7,3,6,2,5,1]=>[1,5,2,6,3,7,8,4]=>1000000=>0000001
[5,8,7,6,3,4,2,1]=>[1,2,4,3,6,7,8,5]=>1101000=>0001011
[5,8,7,6,4,2,1,3]=>[3,1,2,4,6,7,8,5]=>0011000=>0001100
[5,8,7,6,4,3,1,2]=>[2,1,3,4,6,7,8,5]=>0111000=>0001110
[7,3,4,2,1,6,5,8]=>[8,5,6,1,2,4,3,7]=>0000000=>0000000
[7,3,5,2,6,1,4,8]=>[8,4,1,6,2,5,3,7]=>0000000=>0000000
[7,3,5,2,6,4,1,8]=>[8,1,4,6,2,5,3,7]=>0000000=>0000000
[7,2,1,5,6,4,3,8]=>[8,3,4,6,5,1,2,7]=>0000000=>0000000
[7,3,5,1,6,4,2,8]=>[8,2,4,6,1,5,3,7]=>0000000=>0000000
[7,4,5,6,1,3,2,8]=>[8,2,3,1,6,5,4,7]=>0000000=>0000000
[1,4,5,7,3,2,8,6]=>[6,8,2,3,7,5,4,1]=>0000000=>0000000
[6,4,5,7,3,1,8,2]=>[2,8,1,3,7,5,4,6]=>0000000=>0000000
[6,3,5,1,7,4,8,2]=>[2,8,4,7,1,5,3,6]=>0000000=>0000000
[6,2,1,5,7,4,8,3]=>[3,8,4,7,5,1,2,6]=>0000000=>0000000
[3,2,1,5,7,4,8,6]=>[6,8,4,7,5,1,2,3]=>0000000=>0000000
[2,4,6,7,3,8,1,5]=>[5,1,8,3,7,6,4,2]=>0000000=>0000000
[1,4,6,7,3,8,5,2]=>[2,5,8,3,7,6,4,1]=>0000000=>0000000
[2,5,6,7,8,3,1,4]=>[4,1,3,8,7,6,5,2]=>0000000=>0000000
[3,2,1,6,7,8,4,5]=>[5,4,8,7,6,1,2,3]=>0000000=>0000000
[5,2,1,6,7,8,4,3]=>[3,4,8,7,6,1,2,5]=>0000000=>0000000
[5,3,6,1,7,8,4,2]=>[2,4,8,7,1,6,3,5]=>0000000=>0000000
[5,4,6,7,1,8,3,2]=>[2,3,8,1,7,6,4,5]=>0000000=>0000000
[6,4,5,7,2,1,8,3]=>[3,8,1,2,7,5,4,6]=>0000000=>0000000
[5,4,6,7,2,8,3,1]=>[1,3,8,2,7,6,4,5]=>1000000=>0000001
[5,3,6,2,7,8,4,1]=>[1,4,8,7,2,6,3,5]=>1000000=>0000001
[5,3,6,2,7,8,1,4]=>[4,1,8,7,2,6,3,5]=>0000000=>0000000
[6,3,5,2,7,1,8,4]=>[4,8,1,7,2,5,3,6]=>0000000=>0000000
[5,3,4,1,2,7,8,6]=>[6,8,7,2,1,4,3,5]=>0000000=>0000000
[4,3,6,2,7,8,1,5]=>[5,1,8,7,2,6,3,4]=>0000000=>0000000
[4,3,6,2,7,8,5,1]=>[1,5,8,7,2,6,3,4]=>1000000=>0000001
[1,3,6,2,7,8,5,4]=>[4,5,8,7,2,6,3,1]=>0000000=>0000000
[1,4,6,7,2,8,5,3]=>[3,5,8,2,7,6,4,1]=>0000000=>0000000
[3,4,6,7,2,8,5,1]=>[1,5,8,2,7,6,4,3]=>1000000=>0000001
[3,4,5,7,2,1,8,6]=>[6,8,1,2,7,5,4,3]=>0000000=>0000000
[4,2,1,5,7,3,8,6]=>[6,8,3,7,5,1,2,4]=>0000000=>0000000
[4,2,1,6,7,8,3,5]=>[5,3,8,7,6,1,2,4]=>0000000=>0000000
[4,3,6,1,7,8,2,5]=>[5,2,8,7,1,6,3,4]=>0000000=>0000000
[1,5,6,7,8,2,4,3]=>[3,4,2,8,7,6,5,1]=>0000000=>0000000
[1,5,6,7,8,4,2,3]=>[3,2,4,8,7,6,5,1]=>0000000=>0000000
[4,3,6,1,7,8,5,2]=>[2,5,8,7,1,6,3,4]=>0000000=>0000000
[4,2,1,6,7,8,5,3]=>[3,5,8,7,6,1,2,4]=>0000000=>0000000
[2,4,6,7,1,8,5,3]=>[3,5,8,1,7,6,4,2]=>0000000=>0000000
[2,5,6,7,8,1,4,3]=>[3,4,1,8,7,6,5,2]=>0000000=>0000000
[6,8,2,4,5,7,1,3]=>[3,1,7,5,4,2,8,6]=>0000000=>0000000
[3,7,8,4,5,2,6,1]=>[1,6,2,5,4,8,7,3]=>1000000=>0000001
[7,8,1,4,5,3,6,2]=>[2,6,3,5,4,1,8,7]=>0000010=>0100000
[5,8,1,4,7,6,3,2]=>[2,3,6,7,4,1,8,5]=>0000000=>0000000
[7,5,1,8,6,2,4,3]=>[3,4,2,6,8,1,5,7]=>0000000=>0000000
[7,4,1,8,2,6,3,5]=>[5,3,6,2,8,1,4,7]=>0000000=>0000000
[7,1,8,4,2,6,3,5]=>[5,3,6,2,4,8,1,7]=>0000000=>0000000
[7,3,1,8,4,2,6,5]=>[5,6,2,4,8,1,3,7]=>0000000=>0000000
[7,2,8,3,6,5,1,4]=>[4,1,5,6,3,8,2,7]=>0000000=>0000000
[7,2,8,3,6,1,5,4]=>[4,5,1,6,3,8,2,7]=>0000000=>0000000
[6,1,2,8,3,5,4,7]=>[7,4,5,3,8,2,1,6]=>0000000=>0000000
[5,2,3,8,1,4,7,6]=>[6,7,4,1,8,3,2,5]=>0000000=>0000000
[6,2,4,1,8,7,3,5]=>[5,3,7,8,1,4,2,6]=>0000000=>0000000
[3,1,6,4,2,8,5,7]=>[7,5,8,2,4,6,1,3]=>0000000=>0000000
[2,6,3,8,7,1,5,4]=>[4,5,1,7,8,3,6,2]=>0000000=>0000000
[2,6,3,8,5,1,4,7]=>[7,4,1,5,8,3,6,2]=>0000000=>0000000
[2,5,1,8,3,4,7,6]=>[6,7,4,3,8,1,5,2]=>0000000=>0000000
[1,2,5,3,8,4,7,6]=>[6,7,4,8,3,5,2,1]=>0000000=>0000000
[1,2,4,8,3,7,6,5]=>[5,6,7,3,8,4,2,1]=>0000000=>0000000
[2,4,8,3,7,1,6,5]=>[5,6,1,7,3,8,4,2]=>0000000=>0000000
[2,4,8,3,7,6,1,5]=>[5,1,6,7,3,8,4,2]=>0000000=>0000000
[2,5,3,8,1,7,4,6]=>[6,4,7,1,8,3,5,2]=>0000000=>0000000
[2,5,4,1,3,8,7,6]=>[6,7,8,3,1,4,5,2]=>0000000=>0000000
[3,1,5,4,8,2,7,6]=>[6,7,2,8,4,5,1,3]=>0000000=>0000000
[5,2,3,8,4,7,1,6]=>[6,1,7,4,8,3,2,5]=>0000000=>0000000
[4,8,2,3,7,6,1,5]=>[5,1,6,7,3,2,8,4]=>0000000=>0000000
[4,8,2,3,7,1,6,5]=>[5,6,1,7,3,2,8,4]=>0000000=>0000000
[4,8,1,2,3,7,6,5]=>[5,6,7,3,2,1,8,4]=>0000000=>0000000
[1,4,8,3,7,2,6,5]=>[5,6,2,7,3,8,4,1]=>0000000=>0000000
[6,3,8,1,5,2,4,7]=>[7,4,2,5,1,8,3,6]=>0000000=>0000000
[5,3,8,1,2,4,7,6]=>[6,7,4,2,1,8,3,5]=>0000000=>0000000
[5,1,3,8,2,4,7,6]=>[6,7,4,2,8,3,1,5]=>0000000=>0000000
[1,5,3,8,2,4,7,6]=>[6,7,4,2,8,3,5,1]=>0000000=>0000000
[1,5,4,8,2,7,6,3]=>[3,6,7,2,8,4,5,1]=>0000000=>0000000
[5,1,4,8,2,7,6,3]=>[3,6,7,2,8,4,1,5]=>0000000=>0000000
[5,4,8,1,2,7,6,3]=>[3,6,7,2,1,8,4,5]=>0000000=>0000000
[6,5,1,2,8,7,4,3]=>[3,4,7,8,2,1,5,6]=>0000000=>0000000
[4,1,5,8,2,7,6,3]=>[3,6,7,2,8,5,1,4]=>0000000=>0000000
[4,1,2,5,8,7,6,3]=>[3,6,7,8,5,2,1,4]=>0000000=>0000000
[1,4,2,5,8,7,6,3]=>[3,6,7,8,5,2,4,1]=>0000000=>0000000
[1,3,5,2,8,7,4,6]=>[6,4,7,8,2,5,3,1]=>0000000=>0000000
[3,5,1,2,8,7,4,6]=>[6,4,7,8,2,1,5,3]=>0000000=>0000000
[4,2,6,1,8,7,3,5]=>[5,3,7,8,1,6,2,4]=>0000000=>0000000
[4,3,1,5,8,2,7,6]=>[6,7,2,8,5,1,3,4]=>0000000=>0000000
[3,5,2,8,7,1,4,6]=>[6,4,1,7,8,2,5,3]=>0000000=>0000000
[3,4,8,1,7,2,6,5]=>[5,6,2,7,1,8,4,3]=>0000000=>0000000
[1,3,4,8,7,2,6,5]=>[5,6,2,7,8,4,3,1]=>0000000=>0000000
[1,3,4,8,2,7,6,5]=>[5,6,7,2,8,4,3,1]=>0000000=>0000000
[3,4,8,1,2,7,6,5]=>[5,6,7,2,1,8,4,3]=>0000000=>0000000
[3,4,8,2,7,6,1,5]=>[5,1,6,7,2,8,4,3]=>0000000=>0000000
[4,2,5,8,1,7,6,3]=>[3,6,7,1,8,5,2,4]=>0000000=>0000000
[4,3,1,2,5,8,7,6]=>[6,7,8,5,2,1,3,4]=>0000000=>0000000
[3,1,4,2,5,8,7,6]=>[6,7,8,5,2,4,1,3]=>0000000=>0000000
[6,4,1,2,7,3,5,8]=>[8,5,3,7,2,1,4,6]=>0000000=>0000000
[7,8,2,5,4,6,1,3]=>[3,1,6,4,5,2,8,7]=>0000010=>0100000
[3,7,6,4,8,5,1,2]=>[2,1,5,8,4,6,7,3]=>0100000=>0000010
[5,1,6,2,4,8,3,7]=>[7,3,8,4,2,6,1,5]=>0000000=>0000000
[1,7,2,4,8,3,6,5]=>[5,6,3,8,4,2,7,1]=>0000000=>0000000
[4,7,2,1,5,3,6,8]=>[8,6,3,5,1,2,7,4]=>0000000=>0000000
[3,7,6,5,2,4,1,8]=>[8,1,4,2,5,6,7,3]=>0000000=>0000000
[1,7,6,5,8,2,4,3]=>[3,4,2,8,5,6,7,1]=>0000000=>0000000
[3,7,6,5,1,2,4,8]=>[8,4,2,1,5,6,7,3]=>0000000=>0000000
[2,7,6,5,8,1,3,4]=>[4,3,1,8,5,6,7,2]=>0000000=>0000000
[3,7,5,8,2,4,1,6]=>[6,1,4,2,8,5,7,3]=>0000000=>0000000
[5,1,7,8,4,3,2,6]=>[6,2,3,4,8,7,1,5]=>0000000=>0000000
[5,1,2,6,4,3,8,7]=>[7,8,3,4,6,2,1,5]=>0000000=>0000000
[5,1,2,4,6,3,8,7]=>[7,8,3,6,4,2,1,5]=>0000000=>0000000
[4,1,5,7,8,3,2,6]=>[6,2,3,8,7,5,1,4]=>0000000=>0000000
[4,7,1,8,3,6,2,5]=>[5,2,6,3,8,1,7,4]=>0000000=>0000000
[4,1,7,8,5,2,3,6]=>[6,3,2,5,8,7,1,4]=>0000000=>0000000
[5,1,7,4,8,2,3,6]=>[6,3,2,8,4,7,1,5]=>0000000=>0000000
[5,1,8,4,7,2,3,6]=>[6,3,2,7,4,8,1,5]=>0000000=>0000000
[4,1,8,7,5,2,3,6]=>[6,3,2,5,7,8,1,4]=>0000000=>0000000
[4,7,1,6,3,2,8,5]=>[5,8,2,3,6,1,7,4]=>0000000=>0000000
[7,1,2,3,8,6,5,4]=>[4,5,6,8,3,2,1,7]=>0000000=>0000000
[6,8,1,4,3,7,2,5]=>[5,2,7,3,4,1,8,6]=>0000000=>0000000
[8,7,3,2,4,1,6,5]=>[5,6,1,4,2,3,7,8]=>0000011=>1100000
[6,7,1,4,3,8,2,5]=>[5,2,8,3,4,1,7,6]=>0000000=>0000000
[8,1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1,8]=>0000001=>1000000
[7,1,2,3,6,8,5,4]=>[4,5,8,6,3,2,1,7]=>0000000=>0000000
[7,1,8,5,4,3,2,6]=>[6,2,3,4,5,8,1,7]=>0000000=>0000000
[7,8,2,6,3,4,1,5]=>[5,1,4,3,6,2,8,7]=>0000010=>0100000
[6,7,2,8,3,4,1,5]=>[5,1,4,3,8,2,7,6]=>0000000=>0000000
[3,8,7,1,4,2,6,5]=>[5,6,2,4,1,7,8,3]=>0000000=>0000000
[3,7,8,1,4,2,6,5]=>[5,6,2,4,1,8,7,3]=>0000000=>0000000
[3,6,8,1,4,2,7,5]=>[5,7,2,4,1,8,6,3]=>0000000=>0000000
[3,5,7,8,2,4,1,6]=>[6,1,4,2,8,7,5,3]=>0000000=>0000000
[3,6,7,1,4,2,8,5]=>[5,8,2,4,1,7,6,3]=>0000000=>0000000
[8,6,2,7,3,1,4,5]=>[5,4,1,3,7,2,6,8]=>0000001=>1000000
[8,1,7,5,4,3,2,6]=>[6,2,3,4,5,7,1,8]=>0000001=>1000000
[8,1,7,4,5,3,2,6]=>[6,2,3,5,4,7,1,8]=>0000001=>1000000
[5,8,3,7,1,4,2,6]=>[6,2,4,1,7,3,8,5]=>0000000=>0000000
[2,1,7,3,4,6,8,5]=>[5,8,6,4,3,7,1,2]=>0000000=>0000000
[6,7,3,2,4,1,8,5]=>[5,8,1,4,2,3,7,6]=>0000000=>0000000
[8,7,2,4,3,6,1,5]=>[5,1,6,3,4,2,7,8]=>0000011=>1100000
[7,1,2,3,5,6,8,4]=>[4,8,6,5,3,2,1,7]=>0000000=>0000000
[6,1,2,3,8,7,4,5]=>[5,4,7,8,3,2,1,6]=>0000000=>0000000
[5,1,2,3,7,8,6,4]=>[4,6,8,7,3,2,1,5]=>0000000=>0000000
[8,6,2,4,3,1,7,5]=>[5,7,1,3,4,2,6,8]=>0000001=>1000000
[7,6,3,2,4,8,1,5]=>[5,1,8,4,2,3,6,7]=>0000000=>0000000
[8,6,3,2,4,7,1,5]=>[5,1,7,4,2,3,6,8]=>0000001=>1000000
[7,6,2,4,3,1,8,5]=>[5,8,1,3,4,2,6,7]=>0000000=>0000000
[2,3,6,8,4,7,1,5]=>[5,1,7,4,8,6,3,2]=>0000000=>0000000
[7,4,6,1,5,2,3,8]=>[8,3,2,5,1,6,4,7]=>0000000=>0000000
[6,8,1,4,7,2,3,5]=>[5,3,2,7,4,1,8,6]=>0000000=>0000000
[1,6,4,2,8,3,5,7]=>[7,5,3,8,2,4,6,1]=>0000000=>0000000
[1,6,3,8,5,4,2,7]=>[7,2,4,5,8,3,6,1]=>0000000=>0000000
[7,1,3,6,5,4,2,8]=>[8,2,4,5,6,3,1,7]=>0000000=>0000000
[7,2,1,4,6,3,5,8]=>[8,5,3,6,4,1,2,7]=>0000000=>0000000
[7,1,2,3,6,5,4,8]=>[8,4,5,6,3,2,1,7]=>0000000=>0000000
[6,8,1,2,7,3,5,4]=>[4,5,3,7,2,1,8,6]=>0000000=>0000000
[1,6,2,3,8,5,4,7]=>[7,4,5,8,3,2,6,1]=>0000000=>0000000
[6,2,8,1,7,3,5,4]=>[4,5,3,7,1,8,2,6]=>0000000=>0000000
[3,6,4,1,2,8,5,7]=>[7,5,8,2,1,4,6,3]=>0000000=>0000000
[2,5,1,8,7,6,3,4]=>[4,3,6,7,8,1,5,2]=>0000000=>0000000
[1,2,5,3,8,7,4,6]=>[6,4,7,8,3,5,2,1]=>0000000=>0000000
[2,5,3,8,7,1,6,4]=>[4,6,1,7,8,3,5,2]=>0000000=>0000000
[2,5,8,4,1,7,6,3]=>[3,6,7,1,4,8,5,2]=>0000000=>0000000
[3,5,8,7,1,4,2,6]=>[6,2,4,1,7,8,5,3]=>0000000=>0000000
[5,3,8,4,1,7,6,2]=>[2,6,7,1,4,8,3,5]=>0000000=>0000000
[4,2,8,7,6,3,5,1]=>[1,5,3,6,7,8,2,4]=>1000000=>0000001
[6,3,1,8,7,2,5,4]=>[4,5,2,7,8,1,3,6]=>0000000=>0000000
[5,1,3,8,7,6,2,4]=>[4,2,6,7,8,3,1,5]=>0000000=>0000000
[1,5,3,8,7,6,2,4]=>[4,2,6,7,8,3,5,1]=>0000000=>0000000
[5,1,8,4,7,2,6,3]=>[3,6,2,7,4,8,1,5]=>0000000=>0000000
[5,8,7,4,6,1,2,3]=>[3,2,1,6,4,7,8,5]=>0010000=>0000100
[6,8,5,1,2,4,7,3]=>[3,7,4,2,1,5,8,6]=>0000000=>0000000
[4,5,8,1,7,2,6,3]=>[3,6,2,7,1,8,5,4]=>0000000=>0000000
[1,3,2,5,8,7,4,6]=>[6,4,7,8,5,2,3,1]=>0000000=>0000000
[3,5,1,8,7,4,6,2]=>[2,6,4,7,8,1,5,3]=>0000000=>0000000
[4,3,6,1,2,8,5,7]=>[7,5,8,2,1,6,3,4]=>0000000=>0000000
[4,5,8,3,1,7,2,6]=>[6,2,7,1,3,8,5,4]=>0000000=>0000000
[4,5,2,8,7,1,3,6]=>[6,3,1,7,8,2,5,4]=>0000000=>0000000
[3,4,8,7,6,2,1,5]=>[5,1,2,6,7,8,4,3]=>0000000=>0000000
[3,4,8,7,6,5,1,2]=>[2,1,5,6,7,8,4,3]=>0100000=>0000010
[1,3,4,8,7,6,2,5]=>[5,2,6,7,8,4,3,1]=>0000000=>0000000
[3,2,5,8,7,4,6,1]=>[1,6,4,7,8,5,2,3]=>1000000=>0000001
[2,1,3,5,8,7,4,6]=>[6,4,7,8,5,3,1,2]=>0000000=>0000000
[1,2,7,5,8,6,4,3]=>[3,4,6,8,5,7,2,1]=>0000000=>0000000
[6,8,1,3,7,5,2,4]=>[4,2,5,7,3,1,8,6]=>0000000=>0000000
[1,3,7,8,2,6,5,4]=>[4,5,6,2,8,7,3,1]=>0000000=>0000000
[2,7,8,1,3,6,5,4]=>[4,5,6,3,1,8,7,2]=>0000000=>0000000
[8,1,2,6,7,3,5,4]=>[4,5,3,7,6,2,1,8]=>0000001=>1000000
[8,1,2,6,7,5,3,4]=>[4,3,5,7,6,2,1,8]=>0000001=>1000000
[8,2,5,7,1,3,6,4]=>[4,6,3,1,7,5,2,8]=>0000001=>1000000
[2,8,1,6,7,3,5,4]=>[4,5,3,7,6,1,8,2]=>0000000=>0000000
[2,6,8,3,7,1,5,4]=>[4,5,1,7,3,8,6,2]=>0000000=>0000000
[2,8,6,4,7,1,5,3]=>[3,5,1,7,4,6,8,2]=>0000000=>0000000
[6,8,3,4,1,7,5,2]=>[2,5,7,1,4,3,8,6]=>0000000=>0000000
[6,8,3,7,4,1,5,2]=>[2,5,1,4,7,3,8,6]=>0000000=>0000000
[8,2,5,7,1,6,3,4]=>[4,3,6,1,7,5,2,8]=>0000001=>1000000
[8,4,7,2,3,6,1,5]=>[5,1,6,3,2,7,4,8]=>0000001=>1000000
[8,5,7,4,2,6,1,3]=>[3,1,6,2,4,7,5,8]=>0000001=>1000000
[8,3,5,7,4,1,6,2]=>[2,6,1,4,7,5,3,8]=>0000001=>1000000
[8,5,2,4,7,1,6,3]=>[3,6,1,7,4,2,5,8]=>0000001=>1000000
[8,2,4,7,3,6,1,5]=>[5,1,6,3,7,4,2,8]=>0000001=>1000000
[8,2,7,1,4,6,3,5]=>[5,3,6,4,1,7,2,8]=>0000001=>1000000
[8,7,1,2,4,6,3,5]=>[5,3,6,4,2,1,7,8]=>0000011=>1100000
[8,7,1,4,6,2,3,5]=>[5,3,2,6,4,1,7,8]=>0000011=>1100000
[8,4,7,1,3,6,2,5]=>[5,2,6,3,1,7,4,8]=>0000001=>1000000
[8,3,5,7,1,2,6,4]=>[4,6,2,1,7,5,3,8]=>0000001=>1000000
[5,8,7,1,3,6,2,4]=>[4,2,6,3,1,7,8,5]=>0000000=>0000000
[8,5,4,7,1,6,2,3]=>[3,2,6,1,7,4,5,8]=>0000001=>1000000
[8,5,4,7,1,2,6,3]=>[3,6,2,1,7,4,5,8]=>0000001=>1000000
[8,5,1,4,7,2,6,3]=>[3,6,2,7,4,1,5,8]=>0000001=>1000000
[8,5,6,3,1,7,4,2]=>[2,4,7,1,3,6,5,8]=>0000001=>1000000
[1,8,4,5,7,2,6,3]=>[3,6,2,7,5,4,8,1]=>0000000=>0000000
[5,8,7,3,6,1,2,4]=>[4,2,1,6,3,7,8,5]=>0000000=>0000000
[8,3,5,7,1,6,2,4]=>[4,2,6,1,7,5,3,8]=>0000001=>1000000
[1,6,8,3,7,5,2,4]=>[4,2,5,7,3,8,6,1]=>0000000=>0000000
[6,3,8,2,7,5,1,4]=>[4,1,5,7,2,8,3,6]=>0000000=>0000000
[8,6,4,7,3,1,5,2]=>[2,5,1,3,7,4,6,8]=>0000001=>1000000
[8,4,5,7,3,1,6,2]=>[2,6,1,3,7,5,4,8]=>0000001=>1000000
[8,3,4,7,2,6,1,5]=>[5,1,6,2,7,4,3,8]=>0000001=>1000000
[8,7,1,3,4,6,2,5]=>[5,2,6,4,3,1,7,8]=>0000011=>1100000
[8,3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3,8]=>0000001=>1000000
[2,8,4,5,7,1,6,3]=>[3,6,1,7,5,4,8,2]=>0000000=>0000000
[8,7,3,4,5,1,6,2]=>[2,6,1,5,4,3,7,8]=>0000011=>1100000
[8,7,4,5,2,6,1,3]=>[3,1,6,2,5,4,7,8]=>0000011=>1100000
[8,7,2,3,4,6,1,5]=>[5,1,6,4,3,2,7,8]=>0000011=>1100000
[8,6,1,2,5,7,3,4]=>[4,3,7,5,2,1,6,8]=>0000001=>1000000
[5,1,4,2,7,3,6,8]=>[8,6,3,7,2,4,1,5]=>0000000=>0000000
[5,7,8,1,3,4,6,2]=>[2,6,4,3,1,8,7,5]=>0000000=>0000000
[5,8,1,7,3,4,6,2]=>[2,6,4,3,7,1,8,5]=>0000000=>0000000
[6,1,2,4,8,7,5,3]=>[3,5,7,8,4,2,1,6]=>0000000=>0000000
[1,4,2,3,8,5,7,6]=>[6,7,5,8,3,2,4,1]=>0000000=>0000000
[3,1,8,6,4,7,5,2]=>[2,5,7,4,6,8,1,3]=>0000000=>0000000
[8,1,2,6,7,4,5,3]=>[3,5,4,7,6,2,1,8]=>0000001=>1000000
[7,1,2,8,3,6,5,4]=>[4,5,6,3,8,2,1,7]=>0000000=>0000000
[3,6,2,5,4,1,8,7]=>[7,8,1,4,5,2,6,3]=>0000000=>0000000
[3,5,2,8,4,7,6,1]=>[1,6,7,4,8,2,5,3]=>1000000=>0000001
[5,4,7,3,2,8,6,1]=>[1,6,8,2,3,7,4,5]=>1000000=>0000001
[5,4,8,3,2,7,6,1]=>[1,6,7,2,3,8,4,5]=>1000000=>0000001
[5,3,2,6,4,1,8,7]=>[7,8,1,4,6,2,3,5]=>0000000=>0000000
[4,5,8,3,2,7,6,1]=>[1,6,7,2,3,8,5,4]=>1000000=>0000001
[4,7,6,3,8,5,2,1]=>[1,2,5,8,3,6,7,4]=>1100000=>0000011
[4,8,6,3,7,5,2,1]=>[1,2,5,7,3,6,8,4]=>1100000=>0000011
[5,3,2,8,4,7,6,1]=>[1,6,7,4,8,2,3,5]=>1000000=>0000001
[2,1,5,8,4,7,6,3]=>[3,6,7,4,8,5,1,2]=>0000000=>0000000
[5,3,2,7,4,8,6,1]=>[1,6,8,4,7,2,3,5]=>1000000=>0000001
[5,7,4,3,2,8,6,1]=>[1,6,8,2,3,4,7,5]=>1000000=>0000001
[4,7,5,3,2,8,6,1]=>[1,6,8,2,3,5,7,4]=>1000000=>0000001
[4,7,8,3,6,5,2,1]=>[1,2,5,6,3,8,7,4]=>1100000=>0000011
[4,6,8,3,7,5,2,1]=>[1,2,5,7,3,8,6,4]=>1100000=>0000011
[7,6,4,3,8,5,2,1]=>[1,2,5,8,3,4,6,7]=>1100000=>0000011
[8,3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3,8]=>1000001=>1000001
[8,6,4,3,7,5,2,1]=>[1,2,5,7,3,4,6,8]=>1100001=>1000011
[8,4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4,8]=>1000001=>1000001
[8,4,6,3,7,5,2,1]=>[1,2,5,7,3,6,4,8]=>1100001=>1000011
[7,4,6,3,8,5,2,1]=>[1,2,5,8,3,6,4,7]=>1100000=>0000011
[3,7,2,6,8,5,4,1]=>[1,4,5,8,6,2,7,3]=>1000000=>0000001
[3,8,2,6,7,5,4,1]=>[1,4,5,7,6,2,8,3]=>1000000=>0000001
[3,7,2,8,6,5,4,1]=>[1,4,5,6,8,2,7,3]=>1000000=>0000001
[3,6,2,8,7,5,4,1]=>[1,4,5,7,8,2,6,3]=>1000000=>0000001
[7,4,5,3,2,8,6,1]=>[1,6,8,2,3,5,4,7]=>1000000=>0000001
[2,1,7,5,4,8,6,3]=>[3,6,8,4,5,7,1,2]=>0000000=>0000000
[7,3,2,8,6,5,4,1]=>[1,4,5,6,8,2,3,7]=>1000000=>0000001
[7,8,4,3,6,5,2,1]=>[1,2,5,6,3,4,8,7]=>1100010=>0100011
[6,3,2,8,7,5,4,1]=>[1,4,5,7,8,2,3,6]=>1000000=>0000001
[6,3,2,7,8,5,4,1]=>[1,4,5,8,7,2,3,6]=>1000000=>0000001
[1,5,6,2,4,7,3,8]=>[8,3,7,4,2,6,5,1]=>0000000=>0000000
[1,6,8,5,2,3,7,4]=>[4,7,3,2,5,8,6,1]=>0000000=>0000000
[3,7,5,6,1,4,8,2]=>[2,8,4,1,6,5,7,3]=>0000000=>0000000
[8,6,1,4,2,7,5,3]=>[3,5,7,2,4,1,6,8]=>0000001=>1000000
[8,1,6,4,2,7,5,3]=>[3,5,7,2,4,6,1,8]=>0000001=>1000000
[1,3,6,4,2,8,5,7]=>[7,5,8,2,4,6,3,1]=>0000000=>0000000
[1,8,4,3,7,2,5,6]=>[6,5,2,7,3,4,8,1]=>0000000=>0000000
[5,7,6,8,3,2,1,4]=>[4,1,2,3,8,6,7,5]=>0001000=>0001000
[6,1,4,3,8,2,5,7]=>[7,5,2,8,3,4,1,6]=>0000000=>0000000
[3,7,5,8,6,2,1,4]=>[4,1,2,6,8,5,7,3]=>0000000=>0000000
[6,8,7,5,3,2,1,4]=>[4,1,2,3,5,7,8,6]=>0001100=>0011000
[1,5,4,7,6,8,2,3]=>[3,2,8,6,7,4,5,1]=>0000000=>0000000
[3,5,4,8,6,7,1,2]=>[2,1,7,6,8,4,5,3]=>0100000=>0000010
[3,8,4,6,5,7,1,2]=>[2,1,7,5,6,4,8,3]=>0100000=>0000010
[3,6,4,7,5,8,1,2]=>[2,1,8,5,7,4,6,3]=>0100000=>0000010
[7,8,1,4,2,6,3,5]=>[5,3,6,2,4,1,8,7]=>0000010=>0100000
[3,8,7,1,4,6,5,2]=>[2,5,6,4,1,7,8,3]=>0000000=>0000000
[4,3,7,6,8,2,5,1]=>[1,5,2,8,6,7,3,4]=>1000000=>0000001
[5,3,6,8,1,7,2,4]=>[4,2,7,1,8,6,3,5]=>0000000=>0000000
[7,4,8,6,5,2,1,3]=>[3,1,2,5,6,8,4,7]=>0010000=>0000100
[7,4,3,2,8,5,6,1]=>[1,6,5,8,2,3,4,7]=>1000000=>0000001
[4,7,8,3,1,5,6,2]=>[2,6,5,1,3,8,7,4]=>0000000=>0000000
[4,8,7,5,6,1,2,3]=>[3,2,1,6,5,7,8,4]=>0010000=>0000100
[4,7,8,1,3,5,6,2]=>[2,6,5,3,1,8,7,4]=>0000000=>0000000
[6,4,8,7,1,3,2,5]=>[5,2,3,1,7,8,4,6]=>0000000=>0000000
[2,8,3,7,1,5,6,4]=>[4,6,5,1,7,3,8,2]=>0000000=>0000000
[5,3,8,6,2,1,4,7]=>[7,4,1,2,6,8,3,5]=>0000000=>0000000
[4,3,7,5,1,8,2,6]=>[6,2,8,1,5,7,3,4]=>0000000=>0000000
[6,8,5,2,7,4,3,1]=>[1,3,4,7,2,5,8,6]=>1000000=>0000001
[4,1,6,5,8,2,3,7]=>[7,3,2,8,5,6,1,4]=>0000000=>0000000
[4,3,8,6,2,5,1,7]=>[7,1,5,2,6,8,3,4]=>0000000=>0000000
[1,7,4,3,8,6,2,5]=>[5,2,6,8,3,4,7,1]=>0000000=>0000000
[2,8,6,1,7,4,5,3]=>[3,5,4,7,1,6,8,2]=>0000000=>0000000
[8,5,4,3,1,6,7,2]=>[2,7,6,1,3,4,5,8]=>0000001=>1000000
[5,8,3,6,7,4,1,2]=>[2,1,4,7,6,3,8,5]=>0100000=>0000010
[3,6,8,5,1,2,7,4]=>[4,7,2,1,5,8,6,3]=>0000000=>0000000
[6,5,2,4,8,1,7,3]=>[3,7,1,8,4,2,5,6]=>0000000=>0000000
[1,5,4,8,2,6,7,3]=>[3,7,6,2,8,4,5,1]=>0000000=>0000000
[7,2,1,5,8,6,3,4]=>[4,3,6,8,5,1,2,7]=>0000000=>0000000
[6,3,4,8,5,1,7,2]=>[2,7,1,5,8,4,3,6]=>0000000=>0000000
[6,5,4,8,1,2,7,3]=>[3,7,2,1,8,4,5,6]=>0000000=>0000000
[6,5,4,7,1,2,8,3]=>[3,8,2,1,7,4,5,6]=>0000000=>0000000
[6,5,4,7,8,1,3,2]=>[2,3,1,8,7,4,5,6]=>0010000=>0000100
[6,5,3,7,1,4,2,8]=>[8,2,4,1,7,3,5,6]=>0000000=>0000000
[6,5,3,8,1,4,2,7]=>[7,2,4,1,8,3,5,6]=>0000000=>0000000
[6,5,3,8,1,4,7,2]=>[2,7,4,1,8,3,5,6]=>0000000=>0000000
[6,5,3,1,2,7,8,4]=>[4,8,7,2,1,3,5,6]=>0000000=>0000000
[7,4,1,5,3,2,8,6]=>[6,8,2,3,5,1,4,7]=>0000000=>0000000
[6,4,3,1,5,2,8,7]=>[7,8,2,5,1,3,4,6]=>0000000=>0000000
[6,4,3,1,5,7,2,8]=>[8,2,7,5,1,3,4,6]=>0000000=>0000000
[6,4,3,1,5,7,8,2]=>[2,8,7,5,1,3,4,6]=>0000000=>0000000
[7,1,5,8,4,6,2,3]=>[3,2,6,4,8,5,1,7]=>0000000=>0000000
[8,6,7,1,4,2,5,3]=>[3,5,2,4,1,7,6,8]=>0000101=>1010000
[8,6,3,7,5,1,2,4]=>[4,2,1,5,7,3,6,8]=>0000001=>1000000
[8,6,1,7,3,2,5,4]=>[4,5,2,3,7,1,6,8]=>0000001=>1000000
[7,6,1,8,3,5,2,4]=>[4,2,5,3,8,1,6,7]=>0000000=>0000000
[7,6,1,3,8,5,2,4]=>[4,2,5,8,3,1,6,7]=>0000000=>0000000
[7,6,2,8,3,5,1,4]=>[4,1,5,3,8,2,6,7]=>0000000=>0000000
[8,7,1,5,2,6,3,4]=>[4,3,6,2,5,1,7,8]=>0000011=>1100000
[8,7,1,5,2,3,6,4]=>[4,6,3,2,5,1,7,8]=>0000011=>1100000
[8,5,2,3,1,7,6,4]=>[4,6,7,1,3,2,5,8]=>0000001=>1000000
[8,6,2,3,7,1,5,4]=>[4,5,1,7,3,2,6,8]=>0000001=>1000000
[8,6,2,7,3,1,5,4]=>[4,5,1,3,7,2,6,8]=>0000001=>1000000
[8,6,7,2,4,1,5,3]=>[3,5,1,4,2,7,6,8]=>0000101=>1010000
[6,8,7,3,4,1,5,2]=>[2,5,1,4,3,7,8,6]=>0000100=>0010000
[8,7,2,5,1,6,3,4]=>[4,3,6,1,5,2,7,8]=>0000011=>1100000
[8,7,2,1,4,6,3,5]=>[5,3,6,4,1,2,7,8]=>0000011=>1100000
[8,4,2,1,7,6,3,5]=>[5,3,6,7,1,2,4,8]=>0000001=>1000000
[8,5,2,7,1,6,3,4]=>[4,3,6,1,7,2,5,8]=>0000001=>1000000
[8,5,7,2,1,4,3,6]=>[6,3,4,1,2,7,5,8]=>0000001=>1000000
[5,8,7,3,1,4,2,6]=>[6,2,4,1,3,7,8,5]=>0000000=>0000000
[8,5,7,2,1,4,6,3]=>[3,6,4,1,2,7,5,8]=>0000001=>1000000
[8,5,2,7,1,3,6,4]=>[4,6,3,1,7,2,5,8]=>0000001=>1000000
[8,7,4,1,2,3,6,5]=>[5,6,3,2,1,4,7,8]=>0000011=>1100000
[8,7,4,1,2,6,3,5]=>[5,3,6,2,1,4,7,8]=>0000011=>1100000
[8,4,3,1,7,2,6,5]=>[5,6,2,7,1,3,4,8]=>0000001=>1000000
[8,4,3,1,2,7,6,5]=>[5,6,7,2,1,3,4,8]=>0000001=>1000000
[8,6,1,3,7,2,5,4]=>[4,5,2,7,3,1,6,8]=>0000001=>1000000
[8,5,1,3,2,7,6,4]=>[4,6,7,2,3,1,5,8]=>0000001=>1000000
[8,5,7,4,1,6,2,3]=>[3,2,6,1,4,7,5,8]=>0000001=>1000000
[8,5,7,4,1,2,6,3]=>[3,6,2,1,4,7,5,8]=>0000001=>1000000
[8,1,5,4,2,7,6,3]=>[3,6,7,2,4,5,1,8]=>0000001=>1000000
[8,1,6,4,7,2,5,3]=>[3,5,2,7,4,6,1,8]=>0000001=>1000000
[6,1,5,8,4,2,7,3]=>[3,7,2,4,8,5,1,6]=>0000000=>0000000
[5,8,3,6,4,1,2,7]=>[7,2,1,4,6,3,8,5]=>0000000=>0000000
[8,4,7,5,1,6,2,3]=>[3,2,6,1,5,7,4,8]=>0000001=>1000000
[8,4,7,5,1,2,6,3]=>[3,6,2,1,5,7,4,8]=>0000001=>1000000
[8,4,7,5,1,2,3,6]=>[6,3,2,1,5,7,4,8]=>0000001=>1000000
[8,3,2,6,5,1,4,7]=>[7,4,1,5,6,2,3,8]=>0000001=>1000000
[4,8,7,3,1,5,2,6]=>[6,2,5,1,3,7,8,4]=>0000000=>0000000
[8,4,7,2,1,5,3,6]=>[6,3,5,1,2,7,4,8]=>0000001=>1000000
[8,3,2,7,1,5,4,6]=>[6,4,5,1,7,2,3,8]=>0000001=>1000000
[8,7,3,1,6,2,4,5]=>[5,4,2,6,1,3,7,8]=>0000011=>1100000
[8,7,3,1,2,4,6,5]=>[5,6,4,2,1,3,7,8]=>0000011=>1100000
[8,3,2,1,7,4,6,5]=>[5,6,4,7,1,2,3,8]=>0000001=>1000000
[8,4,7,2,1,5,6,3]=>[3,6,5,1,2,7,4,8]=>0000001=>1000000
[8,7,2,1,3,6,4,5]=>[5,4,6,3,1,2,7,8]=>0000011=>1100000
[8,7,2,1,3,4,6,5]=>[5,6,4,3,1,2,7,8]=>0000011=>1100000
[1,2,3,8,4,6,7,5]=>[5,7,6,4,8,3,2,1]=>0000000=>0000000
[1,7,8,2,3,6,4,5]=>[5,4,6,3,2,8,7,1]=>0000000=>0000000
[1,6,7,8,2,3,5,4]=>[4,5,3,2,8,7,6,1]=>0000000=>0000000
[1,7,8,2,5,3,6,4]=>[4,6,3,5,2,8,7,1]=>0000000=>0000000
[1,7,8,2,4,3,6,5]=>[5,6,3,4,2,8,7,1]=>0000000=>0000000
[7,6,3,1,5,2,4,8]=>[8,4,2,5,1,3,6,7]=>0000000=>0000000
[6,7,3,1,5,2,8,4]=>[4,8,2,5,1,3,7,6]=>0000000=>0000000
[6,8,3,1,5,2,7,4]=>[4,7,2,5,1,3,8,6]=>0000000=>0000000
[6,8,4,5,1,2,7,3]=>[3,7,2,1,5,4,8,6]=>0000000=>0000000
[6,7,4,5,1,2,8,3]=>[3,8,2,1,5,4,7,6]=>0000000=>0000000
[7,2,1,6,5,3,4,8]=>[8,4,3,5,6,1,2,7]=>0000000=>0000000
[7,3,6,1,5,2,4,8]=>[8,4,2,5,1,6,3,7]=>0000000=>0000000
[7,4,6,5,1,2,3,8]=>[8,3,2,1,5,6,4,7]=>0000000=>0000000
[6,7,5,4,1,2,8,3]=>[3,8,2,1,4,5,7,6]=>0000000=>0000000
[5,8,6,4,1,7,2,3]=>[3,2,7,1,4,6,8,5]=>0000000=>0000000
[5,7,6,4,1,8,2,3]=>[3,2,8,1,4,6,7,5]=>0000000=>0000000
[5,6,7,4,1,8,2,3]=>[3,2,8,1,4,7,6,5]=>0000000=>0000000
[6,5,7,4,1,2,8,3]=>[3,8,2,1,4,7,5,6]=>0000000=>0000000
[6,2,1,7,5,3,8,4]=>[4,8,3,5,7,1,2,6]=>0000000=>0000000
[6,3,8,1,5,2,7,4]=>[4,7,2,5,1,8,3,6]=>0000000=>0000000
[6,4,8,5,1,2,7,3]=>[3,7,2,1,5,8,4,6]=>0000000=>0000000
[6,5,8,4,1,2,7,3]=>[3,7,2,1,4,8,5,6]=>0000000=>0000000
[5,6,8,4,1,7,2,3]=>[3,2,7,1,4,8,6,5]=>0000000=>0000000
[4,6,8,5,7,1,2,3]=>[3,2,1,7,5,8,6,4]=>0010000=>0000100
[4,5,8,6,7,1,2,3]=>[3,2,1,7,6,8,5,4]=>0010000=>0000100
[5,2,1,7,6,8,3,4]=>[4,3,8,6,7,1,2,5]=>0000000=>0000000
[4,5,7,6,8,1,2,3]=>[3,2,1,8,6,7,5,4]=>0010000=>0000100
[4,6,7,5,8,1,2,3]=>[3,2,1,8,5,7,6,4]=>0010000=>0000100
[4,7,5,6,8,1,2,3]=>[3,2,1,8,6,5,7,4]=>0010000=>0000100
[4,6,5,7,8,1,2,3]=>[3,2,1,8,7,5,6,4]=>0010000=>0000100
[5,7,4,6,1,8,2,3]=>[3,2,8,1,6,4,7,5]=>0000000=>0000000
[5,8,3,1,6,7,2,4]=>[4,2,7,6,1,3,8,5]=>0000000=>0000000
[5,7,3,1,6,8,2,4]=>[4,2,8,6,1,3,7,5]=>0000000=>0000000
[5,6,3,1,7,8,2,4]=>[4,2,8,7,1,3,6,5]=>0000000=>0000000
[5,8,3,1,7,6,2,4]=>[4,2,6,7,1,3,8,5]=>0000000=>0000000
[5,7,4,8,1,6,2,3]=>[3,2,6,1,8,4,7,5]=>0000000=>0000000
[5,2,1,6,8,7,3,4]=>[4,3,7,8,6,1,2,5]=>0000000=>0000000
[5,4,6,8,1,7,2,3]=>[3,2,7,1,8,6,4,5]=>0000000=>0000000
[4,5,6,8,7,1,2,3]=>[3,2,1,7,8,6,5,4]=>0010000=>0000100
[4,7,5,8,6,1,2,3]=>[3,2,1,6,8,5,7,4]=>0010000=>0000100
[4,8,5,7,6,1,2,3]=>[3,2,1,6,7,5,8,4]=>0010000=>0000100
[4,8,6,7,5,1,2,3]=>[3,2,1,5,7,6,8,4]=>0010000=>0000100
[4,7,6,8,5,1,2,3]=>[3,2,1,5,8,6,7,4]=>0010000=>0000100
[4,6,7,8,5,1,2,3]=>[3,2,1,5,8,7,6,4]=>0010000=>0000100
[4,5,7,8,6,1,2,3]=>[3,2,1,6,8,7,5,4]=>0010000=>0000100
[5,4,7,8,1,6,2,3]=>[3,2,6,1,8,7,4,5]=>0000000=>0000000
[5,3,7,1,8,6,2,4]=>[4,2,6,8,1,7,3,5]=>0000000=>0000000
[5,2,1,7,8,6,3,4]=>[4,3,6,8,7,1,2,5]=>0000000=>0000000
[5,3,8,1,7,6,2,4]=>[4,2,6,7,1,8,3,5]=>0000000=>0000000
[5,4,8,7,1,6,2,3]=>[3,2,6,1,7,8,4,5]=>0000000=>0000000
[4,6,8,7,5,1,2,3]=>[3,2,1,5,7,8,6,4]=>0010000=>0000100
[4,7,8,6,5,1,2,3]=>[3,2,1,5,6,8,7,4]=>0010000=>0000100
[4,8,7,6,5,1,2,3]=>[3,2,1,5,6,7,8,4]=>0010000=>0000100
[2,5,3,1,6,4,8,7]=>[7,8,4,6,1,3,5,2]=>0000000=>0000000
[2,7,5,3,6,4,1,8]=>[8,1,4,6,3,5,7,2]=>0000000=>0000000
[2,3,1,8,6,5,4,7]=>[7,4,5,6,8,1,3,2]=>0000000=>0000000
[1,2,6,3,8,7,4,5]=>[5,4,7,8,3,6,2,1]=>0000000=>0000000
[1,2,3,8,6,4,7,5]=>[5,7,4,6,8,3,2,1]=>0000000=>0000000
[2,1,3,8,5,4,7,6]=>[6,7,4,5,8,3,1,2]=>0000000=>0000000
[7,1,8,4,2,3,5,6]=>[6,5,3,2,4,8,1,7]=>0000000=>0000000
[4,2,6,3,1,8,5,7]=>[7,5,8,1,3,6,2,4]=>0000000=>0000000
[5,4,2,8,3,1,6,7]=>[7,6,1,3,8,2,4,5]=>0000000=>0000000
[1,5,2,8,7,3,4,6]=>[6,4,3,7,8,2,5,1]=>0000000=>0000000
[1,2,8,6,3,7,4,5]=>[5,4,7,3,6,8,2,1]=>0000000=>0000000
[1,2,3,8,7,4,6,5]=>[5,6,4,7,8,3,2,1]=>0000000=>0000000
[1,2,3,8,7,6,4,5]=>[5,4,6,7,8,3,2,1]=>0000000=>0000000
[3,8,5,7,1,6,4,2]=>[2,4,6,1,7,5,8,3]=>0000000=>0000000
[3,8,5,7,2,1,6,4]=>[4,6,1,2,7,5,8,3]=>0000000=>0000000
[4,3,2,8,5,1,7,6]=>[6,7,1,5,8,2,3,4]=>0000000=>0000000
[3,2,5,7,6,1,4,8]=>[8,4,1,6,7,5,2,3]=>0000000=>0000000
[4,2,6,7,5,1,3,8]=>[8,3,1,5,7,6,2,4]=>0000000=>0000000
[4,8,6,7,3,1,5,2]=>[2,5,1,3,7,6,8,4]=>0000000=>0000000
[5,8,6,7,4,2,1,3]=>[3,1,2,4,7,6,8,5]=>0011000=>0001100
[6,1,5,2,8,4,7,3]=>[3,7,4,8,2,5,1,6]=>0000000=>0000000
[4,6,1,8,5,7,2,3]=>[3,2,7,5,8,1,6,4]=>0000000=>0000000
[4,7,1,2,8,5,6,3]=>[3,6,5,8,2,1,7,4]=>0000000=>0000000
[1,4,7,2,8,5,6,3]=>[3,6,5,8,2,7,4,1]=>0000000=>0000000
[1,7,3,5,8,6,2,4]=>[4,2,6,8,5,3,7,1]=>0000000=>0000000
[7,3,5,8,6,1,2,4]=>[4,2,1,6,8,5,3,7]=>0000000=>0000000
[6,8,1,5,7,2,3,4]=>[4,3,2,7,5,1,8,6]=>0000000=>0000000
[7,1,2,5,8,6,3,4]=>[4,3,6,8,5,2,1,7]=>0000000=>0000000
[1,7,2,5,8,6,3,4]=>[4,3,6,8,5,2,7,1]=>0000000=>0000000
[1,7,6,8,2,3,5,4]=>[4,5,3,2,8,6,7,1]=>0000000=>0000000
[7,6,8,1,2,3,5,4]=>[4,5,3,2,1,8,6,7]=>0000100=>0010000
[2,7,1,5,8,6,3,4]=>[4,3,6,8,5,1,7,2]=>0000000=>0000000
[2,4,7,1,8,5,6,3]=>[3,6,5,8,1,7,4,2]=>0000000=>0000000
[4,7,5,8,3,1,6,2]=>[2,6,1,3,8,5,7,4]=>0000000=>0000000
[4,7,2,1,8,5,6,3]=>[3,6,5,8,1,2,7,4]=>0000000=>0000000
[7,3,5,8,6,2,1,4]=>[4,1,2,6,8,5,3,7]=>0000000=>0000000
[7,6,8,2,1,3,5,4]=>[4,5,3,1,2,8,6,7]=>0000100=>0010000
[1,2,7,6,8,3,5,4]=>[4,5,3,8,6,7,2,1]=>0000000=>0000000
[3,7,6,8,2,1,5,4]=>[4,5,1,2,8,6,7,3]=>0000000=>0000000
[6,7,4,1,8,5,3,2]=>[2,3,5,8,1,4,7,6]=>0000000=>0000000
[6,7,4,3,1,8,5,2]=>[2,5,8,1,3,4,7,6]=>0000000=>0000000
[2,7,4,1,6,8,5,3]=>[3,5,8,6,1,4,7,2]=>0000000=>0000000
[3,1,7,6,8,2,5,4]=>[4,5,2,8,6,7,1,3]=>0000000=>0000000
[1,3,7,6,8,2,5,4]=>[4,5,2,8,6,7,3,1]=>0000000=>0000000
[1,7,4,2,6,8,5,3]=>[3,5,8,6,2,4,7,1]=>0000000=>0000000
[7,1,4,2,8,5,6,3]=>[3,6,5,8,2,4,1,7]=>0000000=>0000000
[7,1,8,2,5,4,6,3]=>[3,6,4,5,2,8,1,7]=>0000000=>0000000
[7,1,6,8,5,4,2,3]=>[3,2,4,5,8,6,1,7]=>0000000=>0000000
[7,1,2,6,8,5,4,3]=>[3,4,5,8,6,2,1,7]=>0000000=>0000000
[1,7,2,6,8,5,4,3]=>[3,4,5,8,6,2,7,1]=>0000000=>0000000
[1,7,6,8,3,2,5,4]=>[4,5,2,3,8,6,7,1]=>0000000=>0000000
[7,6,8,3,1,2,5,4]=>[4,5,2,1,3,8,6,7]=>0000100=>0010000
[7,1,5,8,6,3,2,4]=>[4,2,3,6,8,5,1,7]=>0000000=>0000000
[3,6,7,1,8,5,4,2]=>[2,4,5,8,1,7,6,3]=>0000000=>0000000
[7,2,6,8,5,4,1,3]=>[3,1,4,5,8,6,2,7]=>0000000=>0000000
[7,6,8,2,3,1,5,4]=>[4,5,1,3,2,8,6,7]=>0000100=>0010000
[2,7,6,8,3,1,5,4]=>[4,5,1,3,8,6,7,2]=>0000000=>0000000
[2,7,1,6,8,5,4,3]=>[3,4,5,8,6,1,7,2]=>0000000=>0000000
[6,7,3,1,8,5,4,2]=>[2,4,5,8,1,3,7,6]=>0000000=>0000000
[6,7,1,8,5,4,3,2]=>[2,3,4,5,8,1,7,6]=>0000000=>0000000
[7,2,1,6,8,5,4,3]=>[3,4,5,8,6,1,2,7]=>0000000=>0000000
[6,2,3,4,8,7,1,5]=>[5,1,7,8,4,3,2,6]=>0000000=>0000000
[6,2,3,4,7,8,1,5]=>[5,1,8,7,4,3,2,6]=>0000000=>0000000
[5,2,6,3,8,1,7,4]=>[4,7,1,8,3,6,2,5]=>0000000=>0000000
[6,4,3,8,7,5,1,2]=>[2,1,5,7,8,3,4,6]=>0100000=>0000010
[6,4,3,7,8,5,1,2]=>[2,1,5,8,7,3,4,6]=>0100000=>0000010
[4,5,6,8,3,2,1,7]=>[7,1,2,3,8,6,5,4]=>0000000=>0000000
[5,6,1,4,2,3,7,8]=>[8,7,3,2,4,1,6,5]=>0000000=>0000000
[5,6,8,4,3,7,1,2]=>[2,1,7,3,4,8,6,5]=>0100000=>0000010
[5,6,1,4,2,3,8,7]=>[7,8,3,2,4,1,6,5]=>0000000=>0000000
[4,5,8,6,3,2,1,7]=>[7,1,2,3,6,8,5,4]=>0000000=>0000000
[4,8,6,5,3,2,1,7]=>[7,1,2,3,5,6,8,4]=>0000000=>0000000
[5,1,7,4,2,3,6,8]=>[8,6,3,2,4,7,1,5]=>0000000=>0000000
[4,8,7,5,3,2,1,6]=>[6,1,2,3,5,7,8,4]=>0000000=>0000000
[4,7,8,6,3,2,1,5]=>[5,1,2,3,6,8,7,4]=>0000000=>0000000
[4,8,2,3,6,7,5,1]=>[1,5,7,6,3,2,8,4]=>1000000=>0000001
[4,3,8,7,2,5,1,6]=>[6,1,5,2,7,8,3,4]=>0000000=>0000000
[5,8,1,4,7,2,6,3]=>[3,6,2,7,4,1,8,5]=>0000000=>0000000
[4,8,7,6,3,1,2,5]=>[5,2,1,3,6,7,8,4]=>0000000=>0000000
[1,4,3,8,2,6,5,7]=>[7,5,6,2,8,3,4,1]=>0000000=>0000000
[7,3,6,8,4,2,1,5]=>[5,1,2,4,8,6,3,7]=>0000000=>0000000
[6,2,8,7,4,3,5,1]=>[1,5,3,4,7,8,2,6]=>1000000=>0000001
[3,1,2,4,8,6,5,7]=>[7,5,6,8,4,2,1,3]=>0000000=>0000000
[3,1,4,2,8,6,5,7]=>[7,5,6,8,2,4,1,3]=>0000000=>0000000
[6,7,2,8,3,5,4,1]=>[1,4,5,3,8,2,7,6]=>1000000=>0000001
[2,1,3,4,8,6,5,7]=>[7,5,6,8,4,3,1,2]=>0000000=>0000000
[3,5,7,8,6,1,2,4]=>[4,2,1,6,8,7,5,3]=>0000000=>0000000
[3,1,5,6,8,2,7,4]=>[4,7,2,8,6,5,1,3]=>0000000=>0000000
[5,1,6,3,8,4,7,2]=>[2,7,4,8,3,6,1,5]=>0000000=>0000000
[2,5,1,6,8,3,7,4]=>[4,7,3,8,6,1,5,2]=>0000000=>0000000
[5,1,2,6,8,3,7,4]=>[4,7,3,8,6,2,1,5]=>0000000=>0000000
[1,5,2,7,8,6,3,4]=>[4,3,6,8,7,2,5,1]=>0000000=>0000000
[6,1,7,5,2,8,3,4]=>[4,3,8,2,5,7,1,6]=>0000000=>0000000
[2,6,7,5,1,8,3,4]=>[4,3,8,1,5,7,6,2]=>0000000=>0000000
[5,7,2,8,6,1,3,4]=>[4,3,1,6,8,2,7,5]=>0000000=>0000000
[3,5,7,8,6,2,1,4]=>[4,1,2,6,8,7,5,3]=>0000000=>0000000
[3,2,5,7,8,6,1,4]=>[4,1,6,8,7,5,2,3]=>0000000=>0000000
[6,2,7,5,1,8,3,4]=>[4,3,8,1,5,7,2,6]=>0000000=>0000000
[1,2,6,7,5,8,3,4]=>[4,3,8,5,7,6,2,1]=>0000000=>0000000
[6,2,7,5,4,1,8,3]=>[3,8,1,4,5,7,2,6]=>0000000=>0000000
[6,7,5,2,4,1,8,3]=>[3,8,1,4,2,5,7,6]=>0000000=>0000000
[6,7,2,5,3,8,1,4]=>[4,1,8,3,5,2,7,6]=>0000000=>0000000
[5,1,7,8,6,3,2,4]=>[4,2,3,6,8,7,1,5]=>0000000=>0000000
[1,6,7,5,3,8,2,4]=>[4,2,8,3,5,7,6,1]=>0000000=>0000000
[1,6,7,5,4,2,8,3]=>[3,8,2,4,5,7,6,1]=>0000000=>0000000
[5,7,8,6,4,1,2,3]=>[3,2,1,4,6,8,7,5]=>0011000=>0001100
[6,7,4,1,5,2,8,3]=>[3,8,2,5,1,4,7,6]=>0000000=>0000000
[1,6,7,4,5,2,8,3]=>[3,8,2,5,4,7,6,1]=>0000000=>0000000
[6,3,1,7,5,8,2,4]=>[4,2,8,5,7,1,3,6]=>0000000=>0000000
[2,5,3,7,8,6,1,4]=>[4,1,6,8,7,3,5,2]=>0000000=>0000000
[6,3,2,7,5,8,1,4]=>[4,1,8,5,7,2,3,6]=>0000000=>0000000
[6,7,4,2,5,1,8,3]=>[3,8,1,5,2,4,7,6]=>0000000=>0000000
[6,2,7,4,5,1,8,3]=>[3,8,1,5,4,7,2,6]=>0000000=>0000000
[6,2,3,7,5,8,1,4]=>[4,1,8,5,7,3,2,6]=>0000000=>0000000
[7,5,1,6,3,8,2,4]=>[4,2,8,3,6,1,5,7]=>0000000=>0000000
[7,5,1,6,3,8,4,2]=>[2,4,8,3,6,1,5,7]=>0000000=>0000000
[2,6,7,4,1,8,3,5]=>[5,3,8,1,4,7,6,2]=>0000000=>0000000
[2,1,6,7,3,8,5,4]=>[4,5,8,3,7,6,1,2]=>0000000=>0000000
[4,6,1,5,8,7,3,2]=>[2,3,7,8,5,1,6,4]=>0000000=>0000000
[7,5,1,6,2,8,3,4]=>[4,3,8,2,6,1,5,7]=>0000000=>0000000
[4,6,1,5,8,2,3,7]=>[7,3,2,8,5,1,6,4]=>0000000=>0000000
[7,5,3,2,8,4,1,6]=>[6,1,4,8,2,3,5,7]=>0000000=>0000000
[6,4,7,3,2,8,5,1]=>[1,5,8,2,3,7,4,6]=>1000000=>0000001
[5,1,7,3,8,4,2,6]=>[6,2,4,8,3,7,1,5]=>0000000=>0000000
[5,3,7,1,4,8,6,2]=>[2,6,8,4,1,7,3,5]=>0000000=>0000000
[6,4,3,1,7,8,5,2]=>[2,5,8,7,1,3,4,6]=>0000000=>0000000
[5,6,1,7,8,3,4,2]=>[2,4,3,8,7,1,6,5]=>0000000=>0000000
[1,6,3,7,4,8,5,2]=>[2,5,8,4,7,3,6,1]=>0000000=>0000000
[6,7,2,4,1,8,5,3]=>[3,5,8,1,4,2,7,6]=>0000000=>0000000
[5,6,3,2,1,7,8,4]=>[4,8,7,1,2,3,6,5]=>0000000=>0000000
[6,3,7,2,8,4,1,5]=>[5,1,4,8,2,7,3,6]=>0000000=>0000000
[6,7,2,1,3,8,5,4]=>[4,5,8,3,1,2,7,6]=>0000000=>0000000
[6,2,7,1,8,5,4,3]=>[3,4,5,8,1,7,2,6]=>0000000=>0000000
[6,3,1,7,8,5,4,2]=>[2,4,5,8,7,1,3,6]=>0000000=>0000000
[5,3,2,1,8,4,7,6]=>[6,7,4,8,1,2,3,5]=>0000000=>0000000
[2,4,6,5,8,1,3,7]=>[7,3,1,8,5,6,4,2]=>0000000=>0000000
[3,4,1,8,5,2,7,6]=>[6,7,2,5,8,1,4,3]=>0000000=>0000000
[1,5,3,2,8,7,4,6]=>[6,4,7,8,2,3,5,1]=>0000000=>0000000
[5,8,7,4,6,2,1,3]=>[3,1,2,6,4,7,8,5]=>0010000=>0000100
[3,2,5,6,8,7,1,4]=>[4,1,7,8,6,5,2,3]=>0000000=>0000000
[4,8,3,1,2,7,6,5]=>[5,6,7,2,1,3,8,4]=>0000000=>0000000
[5,8,2,7,4,1,6,3]=>[3,6,1,4,7,2,8,5]=>0000000=>0000000
[5,1,4,2,8,7,6,3]=>[3,6,7,8,2,4,1,5]=>0000000=>0000000
[6,3,2,1,8,5,7,4]=>[4,7,5,8,1,2,3,6]=>0000000=>0000000
[8,1,3,6,5,2,4,7]=>[7,4,2,5,6,3,1,8]=>0000001=>1000000
[1,3,5,2,4,8,7,6]=>[6,7,8,4,2,5,3,1]=>0000000=>0000000
[5,1,3,2,8,6,7,4]=>[4,7,6,8,2,3,1,5]=>0000000=>0000000
[1,8,4,3,7,2,6,5]=>[5,6,2,7,3,4,8,1]=>0000000=>0000000
[3,4,8,7,2,1,6,5]=>[5,6,1,2,7,8,4,3]=>0000000=>0000000
[5,4,7,8,3,6,2,1]=>[1,2,6,3,8,7,4,5]=>1100000=>0000011
[6,3,8,7,4,1,2,5]=>[5,2,1,4,7,8,3,6]=>0000000=>0000000
[1,7,2,4,6,5,8,3]=>[3,8,5,6,4,2,7,1]=>0000000=>0000000
[5,8,6,2,1,3,7,4]=>[4,7,3,1,2,6,8,5]=>0000000=>0000000
[1,3,2,7,5,8,6,4]=>[4,6,8,5,7,2,3,1]=>0000000=>0000000
[1,4,2,5,8,3,7,6]=>[6,7,3,8,5,2,4,1]=>0000000=>0000000
[1,4,2,7,8,5,6,3]=>[3,6,5,8,7,2,4,1]=>0000000=>0000000
[5,1,2,6,8,4,7,3]=>[3,7,4,8,6,2,1,5]=>0000000=>0000000
[4,1,2,6,8,5,3,7]=>[7,3,5,8,6,2,1,4]=>0000000=>0000000
[1,5,2,4,8,7,6,3]=>[3,6,7,8,4,2,5,1]=>0000000=>0000000
[1,2,7,4,8,6,5,3]=>[3,5,6,8,4,7,2,1]=>0000000=>0000000
[1,3,2,7,5,8,4,6]=>[6,4,8,5,7,2,3,1]=>0000000=>0000000
[1,3,2,8,5,7,4,6]=>[6,4,7,5,8,2,3,1]=>0000000=>0000000
[1,2,6,4,8,7,3,5]=>[5,3,7,8,4,6,2,1]=>0000000=>0000000
[1,2,6,8,5,7,3,4]=>[4,3,7,5,8,6,2,1]=>0000000=>0000000
[1,5,6,8,2,7,3,4]=>[4,3,7,2,8,6,5,1]=>0000000=>0000000
[1,3,8,2,6,7,4,5]=>[5,4,7,6,2,8,3,1]=>0000000=>0000000
[1,4,7,2,8,6,3,5]=>[5,3,6,8,2,7,4,1]=>0000000=>0000000
[1,6,7,8,2,5,3,4]=>[4,3,5,2,8,7,6,1]=>0000000=>0000000
[1,2,6,8,3,7,5,4]=>[4,5,7,3,8,6,2,1]=>0000000=>0000000
[1,5,7,8,2,3,6,4]=>[4,6,3,2,8,7,5,1]=>0000000=>0000000
[1,4,7,2,8,3,6,5]=>[5,6,3,8,2,7,4,1]=>0000000=>0000000
[1,6,7,3,4,8,5,2]=>[2,5,8,4,3,7,6,1]=>0000000=>0000000
[1,5,3,7,4,8,6,2]=>[2,6,8,4,7,3,5,1]=>0000000=>0000000
[1,3,6,4,2,8,7,5]=>[5,7,8,2,4,6,3,1]=>0000000=>0000000
[1,3,7,4,2,8,6,5]=>[5,6,8,2,4,7,3,1]=>0000000=>0000000
[1,2,8,4,7,3,6,5]=>[5,6,3,7,4,8,2,1]=>0000000=>0000000
[1,5,2,4,8,3,7,6]=>[6,7,3,8,4,2,5,1]=>0000000=>0000000
[1,8,4,5,7,2,3,6]=>[6,3,2,7,5,4,8,1]=>0000000=>0000000
[1,8,3,5,2,7,4,6]=>[6,4,7,2,5,3,8,1]=>0000000=>0000000
[2,8,3,5,1,4,7,6]=>[6,7,4,1,5,3,8,2]=>0000000=>0000000
[2,3,8,6,1,4,7,5]=>[5,7,4,1,6,8,3,2]=>0000000=>0000000
[1,4,8,6,7,2,3,5]=>[5,3,2,7,6,8,4,1]=>0000000=>0000000
[1,5,6,8,7,2,3,4]=>[4,3,2,7,8,6,5,1]=>0000000=>0000000
[1,2,7,8,5,3,6,4]=>[4,6,3,5,8,7,2,1]=>0000000=>0000000
[1,2,5,8,7,3,6,4]=>[4,6,3,7,8,5,2,1]=>0000000=>0000000
[1,2,6,8,7,3,5,4]=>[4,5,3,7,8,6,2,1]=>0000000=>0000000
[1,2,7,8,6,3,5,4]=>[4,5,3,6,8,7,2,1]=>0000000=>0000000
[1,5,7,8,6,2,3,4]=>[4,3,2,6,8,7,5,1]=>0000000=>0000000
[1,3,7,6,2,8,4,5]=>[5,4,8,2,6,7,3,1]=>0000000=>0000000
[1,2,8,4,7,6,3,5]=>[5,3,6,7,4,8,2,1]=>0000000=>0000000
[1,2,5,8,7,6,3,4]=>[4,3,6,7,8,5,2,1]=>0000000=>0000000
[1,2,6,8,7,5,3,4]=>[4,3,5,7,8,6,2,1]=>0000000=>0000000
[1,2,7,8,6,5,3,4]=>[4,3,5,6,8,7,2,1]=>0000000=>0000000
[5,2,6,7,3,4,8,1]=>[1,8,4,3,7,6,2,5]=>1000000=>0000001
[5,6,2,1,7,8,3,4]=>[4,3,8,7,1,2,6,5]=>0000000=>0000000
[5,6,2,1,4,8,7,3]=>[3,7,8,4,1,2,6,5]=>0000000=>0000000
[2,6,1,4,5,8,7,3]=>[3,7,8,5,4,1,6,2]=>0000000=>0000000
[5,4,2,7,6,3,8,1]=>[1,8,3,6,7,2,4,5]=>1000000=>0000001
[2,3,7,6,4,5,8,1]=>[1,8,5,4,6,7,3,2]=>1000000=>0000001
[2,6,1,7,5,8,3,4]=>[4,3,8,5,7,1,6,2]=>0000000=>0000000
[5,1,2,7,8,4,3,6]=>[6,3,4,8,7,2,1,5]=>0000000=>0000000
[2,6,1,7,4,8,3,5]=>[5,3,8,4,7,1,6,2]=>0000000=>0000000
[3,6,4,1,7,8,2,5]=>[5,2,8,7,1,4,6,3]=>0000000=>0000000
[5,4,6,1,7,8,2,3]=>[3,2,8,7,1,6,4,5]=>0000000=>0000000
[5,4,6,1,3,8,7,2]=>[2,7,8,3,1,6,4,5]=>0000000=>0000000
[3,6,4,1,5,8,7,2]=>[2,7,8,5,1,4,6,3]=>0000000=>0000000
[2,6,1,5,4,8,7,3]=>[3,7,8,4,5,1,6,2]=>0000000=>0000000
[2,6,1,4,7,8,5,3]=>[3,5,8,7,4,1,6,2]=>0000000=>0000000
[5,1,2,4,8,7,6,3]=>[3,6,7,8,4,2,1,5]=>0000000=>0000000
[2,1,5,3,8,6,4,7]=>[7,4,6,8,3,5,1,2]=>0000000=>0000000
[5,1,2,4,8,6,3,7]=>[7,3,6,8,4,2,1,5]=>0000000=>0000000
[5,6,3,1,4,8,2,7]=>[7,2,8,4,1,3,6,5]=>0000000=>0000000
[2,5,4,3,1,8,6,7]=>[7,6,8,1,3,4,5,2]=>0000000=>0000000
[5,4,6,3,1,8,7,2]=>[2,7,8,1,3,6,4,5]=>0000000=>0000000
[2,1,3,7,8,6,4,5]=>[5,4,6,8,7,3,1,2]=>0000000=>0000000
[5,1,4,2,8,6,7,3]=>[3,7,6,8,2,4,1,5]=>0000000=>0000000
[1,2,3,8,6,7,4,5]=>[5,4,7,6,8,3,2,1]=>0000000=>0000000
[1,2,3,8,7,5,4,6]=>[6,4,5,7,8,3,2,1]=>0000000=>0000000
[1,2,3,8,7,4,5,6]=>[6,5,4,7,8,3,2,1]=>0000000=>0000000
[2,1,3,6,8,7,4,5]=>[5,4,7,8,6,3,1,2]=>0000000=>0000000
[3,1,6,2,8,7,5,4]=>[4,5,7,8,2,6,1,3]=>0000000=>0000000
[6,8,1,3,2,5,4,7]=>[7,4,5,2,3,1,8,6]=>0000000=>0000000
[5,8,1,4,3,7,2,6]=>[6,2,7,3,4,1,8,5]=>0000000=>0000000
[2,5,4,7,6,8,1,3]=>[3,1,8,6,7,4,5,2]=>0000000=>0000000
[2,6,1,4,3,7,5,8]=>[8,5,7,3,4,1,6,2]=>0000000=>0000000
[2,6,1,5,3,7,4,8]=>[8,4,7,3,5,1,6,2]=>0000000=>0000000
[4,7,1,3,2,6,5,8]=>[8,5,6,2,3,1,7,4]=>0000000=>0000000
[4,7,5,8,2,6,1,3]=>[3,1,6,2,8,5,7,4]=>0000000=>0000000
[3,7,4,8,2,6,1,5]=>[5,1,6,2,8,4,7,3]=>0000000=>0000000
[3,7,2,6,5,8,1,4]=>[4,1,8,5,6,2,7,3]=>0000000=>0000000
[7,6,4,8,5,2,3,1]=>[1,3,2,5,8,4,6,7]=>1010000=>0000101
[6,7,4,3,5,1,8,2]=>[2,8,1,5,3,4,7,6]=>0000000=>0000000
[6,7,3,5,4,8,2,1]=>[1,2,8,4,5,3,7,6]=>1100000=>0000011
[6,8,3,7,5,2,4,1]=>[1,4,2,5,7,3,8,6]=>1000000=>0000001
[7,6,3,5,8,2,4,1]=>[1,4,2,8,5,3,6,7]=>1000000=>0000001
[7,6,2,8,4,1,5,3]=>[3,5,1,4,8,2,6,7]=>0000000=>0000000
[7,6,3,4,8,2,5,1]=>[1,5,2,8,4,3,6,7]=>1000000=>0000001
[6,8,3,7,4,5,2,1]=>[1,2,5,4,7,3,8,6]=>1100000=>0000011
[6,7,3,5,8,4,2,1]=>[1,2,4,8,5,3,7,6]=>1100000=>0000011
[5,7,8,3,6,2,1,4]=>[4,1,2,6,3,8,7,5]=>0000000=>0000000
[6,3,8,4,7,2,1,5]=>[5,1,2,7,4,8,3,6]=>0000000=>0000000
[6,3,4,7,5,8,2,1]=>[1,2,8,5,7,4,3,6]=>1100000=>0000011
[6,3,5,7,8,4,2,1]=>[1,2,4,8,7,5,3,6]=>1100000=>0000011
[5,7,3,6,8,2,1,4]=>[4,1,2,8,6,3,7,5]=>0000000=>0000000
[5,6,7,3,4,1,8,2]=>[2,8,1,4,3,7,6,5]=>0000000=>0000000
[4,6,7,8,3,5,2,1]=>[1,2,5,3,8,7,6,4]=>1100000=>0000011
[4,7,3,5,6,8,2,1]=>[1,2,8,6,5,3,7,4]=>1100000=>0000011
[5,3,4,7,8,2,1,6]=>[6,1,2,8,7,4,3,5]=>0000000=>0000000
[5,3,8,2,4,1,6,7]=>[7,6,1,4,2,8,3,5]=>0000000=>0000000
[5,3,4,8,2,6,1,7]=>[7,1,6,2,8,4,3,5]=>0000000=>0000000
[4,8,3,6,2,5,7,1]=>[1,7,5,2,6,3,8,4]=>1000000=>0000001
[4,8,3,5,7,2,6,1]=>[1,6,2,7,5,3,8,4]=>1000000=>0000001
[4,8,3,5,6,7,2,1]=>[1,2,7,6,5,3,8,4]=>1100000=>0000011
[4,7,8,3,5,6,2,1]=>[1,2,6,5,3,8,7,4]=>1100000=>0000011
[4,7,8,3,6,2,5,1]=>[1,5,2,6,3,8,7,4]=>1000000=>0000001
[4,8,3,6,7,2,5,1]=>[1,5,2,7,6,3,8,4]=>1000000=>0000001
[4,8,3,7,2,5,6,1]=>[1,6,5,2,7,3,8,4]=>1000000=>0000001
[5,8,3,7,2,6,4,1]=>[1,4,6,2,7,3,8,5]=>1000000=>0000001
[5,7,3,4,8,2,1,6]=>[6,1,2,8,4,3,7,5]=>0000000=>0000000
[5,8,4,2,3,1,6,7]=>[7,6,1,3,2,4,8,5]=>0000000=>0000000
[5,8,4,2,3,1,7,6]=>[6,7,1,3,2,4,8,5]=>0000000=>0000000
[6,4,8,5,3,7,2,1]=>[1,2,7,3,5,8,4,6]=>1100000=>0000011
[6,4,2,7,3,1,8,5]=>[5,8,1,3,7,2,4,6]=>0000000=>0000000
[6,4,3,7,8,5,2,1]=>[1,2,5,8,7,3,4,6]=>1100000=>0000011
[6,4,5,3,7,1,8,2]=>[2,8,1,7,3,5,4,6]=>0000000=>0000000
[5,7,4,2,3,1,6,8]=>[8,6,1,3,2,4,7,5]=>0000000=>0000000
[5,6,3,7,1,8,2,4]=>[4,2,8,1,7,3,6,5]=>0000000=>0000000
[5,6,3,4,8,2,1,7]=>[7,1,2,8,4,3,6,5]=>0000000=>0000000
[6,3,5,7,4,8,2,1]=>[1,2,8,4,7,5,3,6]=>1100000=>0000011
[6,3,5,4,7,8,2,1]=>[1,2,8,7,4,5,3,6]=>1100000=>0000011
[6,4,3,5,7,1,8,2]=>[2,8,1,7,5,3,4,6]=>0000000=>0000000
[6,4,2,5,1,7,3,8]=>[8,3,7,1,5,2,4,6]=>0000000=>0000000
[5,3,4,7,2,6,1,8]=>[8,1,6,2,7,4,3,5]=>0000000=>0000000
[4,7,3,6,2,5,8,1]=>[1,8,5,2,6,3,7,4]=>1000000=>0000001
[4,7,3,6,8,2,5,1]=>[1,5,2,8,6,3,7,4]=>1000000=>0000001
[4,6,7,3,5,8,2,1]=>[1,2,8,5,3,7,6,4]=>1100000=>0000011
[4,5,7,8,3,6,2,1]=>[1,2,6,3,8,7,5,4]=>1100000=>0000011
[4,5,8,3,7,2,6,1]=>[1,6,2,7,3,8,5,4]=>1000000=>0000001
[5,3,4,6,8,2,1,7]=>[7,1,2,8,6,4,3,5]=>0000000=>0000000
[5,3,6,7,1,8,2,4]=>[4,2,8,1,7,6,3,5]=>0000000=>0000000
[5,3,4,6,7,1,8,2]=>[2,8,1,7,6,4,3,5]=>0000000=>0000000
[4,6,3,5,7,8,2,1]=>[1,2,8,7,5,3,6,4]=>1100000=>0000011
[4,5,7,3,6,8,2,1]=>[1,2,8,6,3,7,5,4]=>1100000=>0000011
[7,1,5,8,4,2,3,6]=>[6,3,2,4,8,5,1,7]=>0000000=>0000000
[8,1,5,7,4,2,3,6]=>[6,3,2,4,7,5,1,8]=>0000001=>1000000
[7,1,4,5,8,2,3,6]=>[6,3,2,8,5,4,1,7]=>0000000=>0000000
[7,4,1,6,2,8,3,5]=>[5,3,8,2,6,1,4,7]=>0000000=>0000000
[8,4,1,7,2,6,3,5]=>[5,3,6,2,7,1,4,8]=>0000001=>1000000
[8,1,4,7,5,2,3,6]=>[6,3,2,5,7,4,1,8]=>0000001=>1000000
[8,1,5,4,7,2,3,6]=>[6,3,2,7,4,5,1,8]=>0000001=>1000000
[2,1,7,5,8,3,4,6]=>[6,4,3,8,5,7,1,2]=>0000000=>0000000
[7,1,5,4,8,2,3,6]=>[6,3,2,8,4,5,1,7]=>0000000=>0000000
[7,1,4,8,5,2,3,6]=>[6,3,2,5,8,4,1,7]=>0000000=>0000000
[7,8,3,1,2,4,6,5]=>[5,6,4,2,1,3,8,7]=>0000010=>0100000
[8,7,1,6,4,2,3,5]=>[5,3,2,4,6,1,7,8]=>0000011=>1100000
[8,6,1,7,4,2,3,5]=>[5,3,2,4,7,1,6,8]=>0000001=>1000000
[7,6,1,8,4,2,3,5]=>[5,3,2,4,8,1,6,7]=>0000000=>0000000
[7,3,8,1,2,4,6,5]=>[5,6,4,2,1,8,3,7]=>0000000=>0000000
[8,3,7,1,2,4,6,5]=>[5,6,4,2,1,7,3,8]=>0000001=>1000000
[8,3,6,1,2,4,7,5]=>[5,7,4,2,1,6,3,8]=>0000001=>1000000
[8,3,7,5,1,2,4,6]=>[6,4,2,1,5,7,3,8]=>0000001=>1000000
[7,3,6,1,2,4,8,5]=>[5,8,4,2,1,6,3,7]=>0000000=>0000000
[6,7,1,8,4,2,3,5]=>[5,3,2,4,8,1,7,6]=>0000000=>0000000
[6,8,1,7,4,2,3,5]=>[5,3,2,4,7,1,8,6]=>0000000=>0000000
[7,1,8,4,5,2,3,6]=>[6,3,2,5,4,8,1,7]=>0000000=>0000000
[7,6,3,1,2,4,8,5]=>[5,8,4,2,1,3,6,7]=>0000000=>0000000
[6,1,2,3,8,7,5,4]=>[4,5,7,8,3,2,1,6]=>0000000=>0000000
[6,8,3,1,2,7,4,5]=>[5,4,7,2,1,3,8,6]=>0000000=>0000000
[6,7,3,1,2,8,4,5]=>[5,4,8,2,1,3,7,6]=>0000000=>0000000
[6,7,1,4,2,3,8,5]=>[5,8,3,2,4,1,7,6]=>0000000=>0000000
[1,3,6,8,7,4,2,5]=>[5,2,4,7,8,6,3,1]=>0000000=>0000000
[2,3,5,1,8,4,7,6]=>[6,7,4,8,1,5,3,2]=>0000000=>0000000
[2,3,7,5,1,8,4,6]=>[6,4,8,1,5,7,3,2]=>0000000=>0000000
[3,5,4,6,8,2,1,7]=>[7,1,2,8,6,4,5,3]=>0000000=>0000000
[1,2,7,5,6,8,4,3]=>[3,4,8,6,5,7,2,1]=>0000000=>0000000
[4,6,2,7,5,8,3,1]=>[1,3,8,5,7,2,6,4]=>1000000=>0000001
[3,5,7,4,8,2,6,1]=>[1,6,2,8,4,7,5,3]=>1000000=>0000001
[1,2,4,8,7,3,6,5]=>[5,6,3,7,8,4,2,1]=>0000000=>0000000
[5,7,1,2,8,6,4,3]=>[3,4,6,8,2,1,7,5]=>0000000=>0000000
[1,2,5,8,7,4,6,3]=>[3,6,4,7,8,5,2,1]=>0000000=>0000000
[1,2,4,8,7,6,3,5]=>[5,3,6,7,8,4,2,1]=>0000000=>0000000
[2,6,3,4,7,1,5,8]=>[8,5,1,7,4,3,6,2]=>0000000=>0000000
[4,7,6,2,3,8,1,5]=>[5,1,8,3,2,6,7,4]=>0000000=>0000000
[7,6,2,4,5,8,1,3]=>[3,1,8,5,4,2,6,7]=>0000000=>0000000
[5,3,1,2,8,4,7,6]=>[6,7,4,8,2,1,3,5]=>0000000=>0000000
[6,5,2,3,7,1,4,8]=>[8,4,1,7,3,2,5,6]=>0000000=>0000000
[5,2,1,8,3,4,6,7]=>[7,6,4,3,8,1,2,5]=>0000000=>0000000
[6,2,3,1,8,4,7,5]=>[5,7,4,8,1,3,2,6]=>0000000=>0000000
[8,6,1,7,2,4,5,3]=>[3,5,4,2,7,1,6,8]=>0000001=>1000000
[6,4,5,8,7,1,2,3]=>[3,2,1,7,8,5,4,6]=>0010000=>0000100
[6,8,2,3,5,1,4,7]=>[7,4,1,5,3,2,8,6]=>0000000=>0000000
[7,8,3,6,2,4,5,1]=>[1,5,4,2,6,3,8,7]=>1000010=>0100001
[1,2,3,4,5,6,12,11,10,9,8,7]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>00000000000=>00000000000
[8,6,2,5,4,1,7,3]=>[3,7,1,4,5,2,6,8]=>0000001=>1000000
[8,7,2,5,1,6,4,3]=>[3,4,6,1,5,2,7,8]=>0000011=>1100000
[7,1,8,2,6,5,4,3]=>[3,4,5,6,2,8,1,7]=>0000000=>0000000
[3,4,6,5,1,2,8,7]=>[7,8,2,1,5,6,4,3]=>0000000=>0000000
[7,2,1,6,3,8,5,4]=>[4,5,8,3,6,1,2,7]=>0000000=>0000000
[8,7,1,2,6,5,4,3]=>[3,4,5,6,2,1,7,8]=>0000011=>1100000
[7,8,1,2,6,5,4,3]=>[3,4,5,6,2,1,8,7]=>0000010=>0100000
[12,11,10,9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9,10,11,12]=>00000111111=>11111100000
[1,8,2,7,4,3,5,6]=>[6,5,3,4,7,2,8,1]=>0000000=>0000000
[1,8,6,4,7,2,3,5]=>[5,3,2,7,4,6,8,1]=>0000000=>0000000
[1,8,4,2,6,3,5,7]=>[7,5,3,6,2,4,8,1]=>0000000=>0000000
[7,4,8,1,5,2,3,6]=>[6,3,2,5,1,8,4,7]=>0000000=>0000000
[4,1,7,2,6,3,5,8]=>[8,5,3,6,2,7,1,4]=>0000000=>0000000
[1,8,5,4,3,7,2,6]=>[6,2,7,3,4,5,8,1]=>0000000=>0000000
[1,8,4,2,5,3,7,6]=>[6,7,3,5,2,4,8,1]=>0000000=>0000000
[1,8,5,4,2,6,7,3]=>[3,7,6,2,4,5,8,1]=>0000000=>0000000
[7,4,8,2,1,3,5,6]=>[6,5,3,1,2,8,4,7]=>0000000=>0000000
[4,1,7,3,2,5,6,8]=>[8,6,5,2,3,7,1,4]=>0000000=>0000000
[7,5,4,8,2,3,6,1]=>[1,6,3,2,8,4,5,7]=>1000000=>0000001
[3,1,7,2,6,8,4,5]=>[5,4,8,6,2,7,1,3]=>0000000=>0000000
[5,1,7,4,2,6,8,3]=>[3,8,6,2,4,7,1,5]=>0000000=>0000000
[4,3,1,6,2,5,7,8]=>[8,7,5,2,6,1,3,4]=>0000000=>0000000
[6,5,4,3,7,1,8,2]=>[2,8,1,7,3,4,5,6]=>0000000=>0000000
[6,5,1,7,3,8,2,4]=>[4,2,8,3,7,1,5,6]=>0000000=>0000000
[5,4,3,8,1,6,2,7]=>[7,2,6,1,8,3,4,5]=>0000000=>0000000
[7,2,8,6,3,1,4,5]=>[5,4,1,3,6,8,2,7]=>0000000=>0000000
[2,1,7,8,3,6,4,5]=>[5,4,6,3,8,7,1,2]=>0000000=>0000000
[4,2,1,6,7,3,5,8]=>[8,5,3,7,6,1,2,4]=>0000000=>0000000
[4,3,1,5,2,7,6,8]=>[8,6,7,2,5,1,3,4]=>0000000=>0000000
[5,4,2,7,3,8,1,6]=>[6,1,8,3,7,2,4,5]=>0000000=>0000000
[3,1,6,2,8,7,4,5]=>[5,4,7,8,2,6,1,3]=>0000000=>0000000
[6,3,1,7,8,5,2,4]=>[4,2,5,8,7,1,3,6]=>0000000=>0000000
[6,5,4,1,7,8,3,2]=>[2,3,8,7,1,4,5,6]=>0000000=>0000000
[5,4,3,1,6,7,2,8]=>[8,2,7,6,1,3,4,5]=>0000000=>0000000
[5,4,2,6,3,8,7,1]=>[1,7,8,3,6,2,4,5]=>1000000=>0000001
[4,3,1,5,2,6,8,7]=>[7,8,6,2,5,1,3,4]=>0000000=>0000000
[5,4,2,1,6,7,8,3]=>[3,8,7,6,1,2,4,5]=>0000000=>0000000
[5,4,3,1,6,7,8,2]=>[2,8,7,6,1,3,4,5]=>0000000=>0000000
[4,6,7,2,5,1,3,8]=>[8,3,1,5,2,7,6,4]=>0000000=>0000000
[5,2,3,6,1,4,7,8]=>[8,7,4,1,6,3,2,5]=>0000000=>0000000
[2,5,3,6,1,4,7,8]=>[8,7,4,1,6,3,5,2]=>0000000=>0000000
[1,5,4,6,7,2,3,8]=>[8,3,2,7,6,4,5,1]=>0000000=>0000000
[1,6,7,3,2,4,5,8]=>[8,5,4,2,3,7,6,1]=>0000000=>0000000
[1,5,3,6,2,4,7,8]=>[8,7,4,2,6,3,5,1]=>0000000=>0000000
[5,1,3,6,2,4,7,8]=>[8,7,4,2,6,3,1,5]=>0000000=>0000000
[6,1,7,4,5,2,3,8]=>[8,3,2,5,4,7,1,6]=>0000000=>0000000
[7,3,4,1,6,2,5,8]=>[8,5,2,6,1,4,3,7]=>0000000=>0000000
[1,3,6,7,2,5,8,4]=>[4,8,5,2,7,6,3,1]=>0000000=>0000000
[2,3,4,5,8,6,1,7]=>[7,1,6,8,5,4,3,2]=>0000000=>0000000
[6,3,5,2,4,7,8,1]=>[1,8,7,4,2,5,3,6]=>1000000=>0000001
[4,3,2,6,7,1,8,5]=>[5,8,1,7,6,2,3,4]=>0000000=>0000000
[5,7,4,6,1,8,3,2]=>[2,3,8,1,6,4,7,5]=>0000000=>0000000
[7,3,4,5,8,2,6,1]=>[1,6,2,8,5,4,3,7]=>1000000=>0000001
[6,2,1,7,3,5,4,8]=>[8,4,5,3,7,1,2,6]=>0000000=>0000000
[2,1,8,6,3,5,4,7]=>[7,4,5,3,6,8,1,2]=>0000000=>0000000
[2,7,3,1,5,4,6,8]=>[8,6,4,5,1,3,7,2]=>0000000=>0000000
[2,6,3,1,4,8,5,7]=>[7,5,8,4,1,3,6,2]=>0000000=>0000000
[4,2,1,8,3,6,7,5]=>[5,7,6,3,8,1,2,4]=>0000000=>0000000
[6,2,1,7,3,5,8,4]=>[4,8,5,3,7,1,2,6]=>0000000=>0000000
[2,7,3,1,4,8,5,6]=>[6,5,8,4,1,3,7,2]=>0000000=>0000000
[3,2,1,5,7,8,4,6]=>[6,4,8,7,5,1,2,3]=>0000000=>0000000
[2,4,7,5,1,6,8,3]=>[3,8,6,1,5,7,4,2]=>0000000=>0000000
[4,3,6,8,5,1,7,2]=>[2,7,1,5,8,6,3,4]=>0000000=>0000000
[2,1,6,8,3,7,4,5]=>[5,4,7,3,8,6,1,2]=>0000000=>0000000
[3,2,1,5,6,8,4,7]=>[7,4,8,6,5,1,2,3]=>0000000=>0000000
[2,1,7,3,6,4,5,8]=>[8,5,4,6,3,7,1,2]=>0000000=>0000000
[2,1,6,3,5,8,4,7]=>[7,4,8,5,3,6,1,2]=>0000000=>0000000
[2,6,1,8,3,5,4,7]=>[7,4,5,3,8,1,6,2]=>0000000=>0000000
[2,7,3,1,5,6,4,8]=>[8,4,6,5,1,3,7,2]=>0000000=>0000000
[2,4,7,5,1,6,3,8]=>[8,3,6,1,5,7,4,2]=>0000000=>0000000
[8,2,4,1,7,5,3,6]=>[6,3,5,7,1,4,2,8]=>0000001=>1000000
[2,4,7,1,8,5,3,6]=>[6,3,5,8,1,7,4,2]=>0000000=>0000000
[2,4,8,5,1,6,3,7]=>[7,3,6,1,5,8,4,2]=>0000000=>0000000
[6,2,1,7,3,4,8,5]=>[5,8,4,3,7,1,2,6]=>0000000=>0000000
[6,2,1,7,8,3,5,4]=>[4,5,3,8,7,1,2,6]=>0000000=>0000000
[2,7,1,8,3,5,6,4]=>[4,6,5,3,8,1,7,2]=>0000000=>0000000
[3,2,1,6,7,4,5,8]=>[8,5,4,7,6,1,2,3]=>0000000=>0000000
[3,2,1,7,4,5,6,8]=>[8,6,5,4,7,1,2,3]=>0000000=>0000000
[2,1,8,3,7,4,5,6]=>[6,5,4,7,3,8,1,2]=>0000000=>0000000
[2,4,8,5,1,6,7,3]=>[3,7,6,1,5,8,4,2]=>0000000=>0000000
[4,3,8,5,6,1,7,2]=>[2,7,1,6,5,8,3,4]=>0000000=>0000000
[3,2,1,8,4,5,6,7]=>[7,6,5,4,8,1,2,3]=>0000000=>0000000
[6,1,5,8,2,4,7,3]=>[3,7,4,2,8,5,1,6]=>0000000=>0000000
[4,1,2,7,8,3,6,5]=>[5,6,3,8,7,2,1,4]=>0000000=>0000000
[3,8,6,4,7,5,1,2]=>[2,1,5,7,4,6,8,3]=>0100000=>0000010
[3,7,4,8,6,5,1,2]=>[2,1,5,6,8,4,7,3]=>0100000=>0000010
[4,3,2,6,8,5,1,7]=>[7,1,5,8,6,2,3,4]=>0000000=>0000000
[2,5,7,8,3,1,4,6]=>[6,4,1,3,8,7,5,2]=>0000000=>0000000
[6,4,7,3,8,1,5,2]=>[2,5,1,8,3,7,4,6]=>0000000=>0000000
[6,3,2,5,4,8,1,7]=>[7,1,8,4,5,2,3,6]=>0000000=>0000000
[2,5,7,8,3,1,6,4]=>[4,6,1,3,8,7,5,2]=>0000000=>0000000
[4,5,7,8,3,1,2,6]=>[6,2,1,3,8,7,5,4]=>0000000=>0000000
[5,4,6,2,8,3,1,7]=>[7,1,3,8,2,6,4,5]=>0000000=>0000000
[5,3,2,6,8,4,1,7]=>[7,1,4,8,6,2,3,5]=>0000000=>0000000
[5,4,7,2,8,1,3,6]=>[6,3,1,8,2,7,4,5]=>0000000=>0000000
[4,3,2,7,8,1,6,5]=>[5,6,1,8,7,2,3,4]=>0000000=>0000000
[4,5,8,3,7,6,1,2]=>[2,1,6,7,3,8,5,4]=>0100000=>0000010
[7,2,3,4,8,1,5,6]=>[6,5,1,8,4,3,2,7]=>0000000=>0000000
[2,6,4,8,1,5,7,3]=>[3,7,5,1,8,4,6,2]=>0000000=>0000000
[7,6,5,1,2,3,8,4]=>[4,8,3,2,1,5,6,7]=>0000000=>0000000
[3,5,6,4,1,2,8,7]=>[7,8,2,1,4,6,5,3]=>0000000=>0000000
[2,6,4,3,1,8,7,5]=>[5,7,8,1,3,4,6,2]=>0000000=>0000000
[3,6,4,2,1,7,5,8]=>[8,5,7,1,2,4,6,3]=>0000000=>0000000
[7,6,5,1,2,8,3,4]=>[4,3,8,2,1,5,6,7]=>0000000=>0000000
[7,6,5,1,8,2,3,4]=>[4,3,2,8,1,5,6,7]=>0000000=>0000000
[3,6,4,5,1,7,2,8]=>[8,2,7,1,5,4,6,3]=>0000000=>0000000
[7,6,5,1,8,4,2,3]=>[3,2,4,8,1,5,6,7]=>0000000=>0000000
[7,4,2,5,6,3,1,8]=>[8,1,3,6,5,2,4,7]=>0000000=>0000000
[1,6,8,5,2,7,4,3]=>[3,4,7,2,5,8,6,1]=>0000000=>0000000
[6,2,8,5,1,7,4,3]=>[3,4,7,1,5,8,2,6]=>0000000=>0000000
[3,2,7,8,6,1,5,4]=>[4,5,1,6,8,7,2,3]=>0000000=>0000000
[3,8,1,5,2,7,6,4]=>[4,6,7,2,5,1,8,3]=>0000000=>0000000
[5,2,3,1,6,7,8,4]=>[4,8,7,6,1,3,2,5]=>0000000=>0000000
[7,6,4,2,1,5,8,3]=>[3,8,5,1,2,4,6,7]=>0000000=>0000000
[6,7,4,1,5,3,8,2]=>[2,8,3,5,1,4,7,6]=>0000000=>0000000
[7,5,4,1,2,6,8,3]=>[3,8,6,2,1,4,5,7]=>0000000=>0000000
[5,2,1,4,6,7,8,3]=>[3,8,7,6,4,1,2,5]=>0000000=>0000000
[5,4,1,3,6,7,8,2]=>[2,8,7,6,3,1,4,5]=>0000000=>0000000
[8,4,1,5,3,7,2,6]=>[6,2,7,3,5,1,4,8]=>0000001=>1000000
[5,1,3,4,6,7,8,2]=>[2,8,7,6,4,3,1,5]=>0000000=>0000000
[3,8,1,7,5,6,4,2]=>[2,4,6,5,7,1,8,3]=>0000000=>0000000
[8,2,5,7,3,6,4,1]=>[1,4,6,3,7,5,2,8]=>1000001=>1000001
[1,8,6,7,5,3,4,2]=>[2,4,3,5,7,6,8,1]=>0000000=>0000000
[8,2,6,7,5,3,4,1]=>[1,4,3,5,7,6,2,8]=>1000001=>1000001
[5,4,8,6,2,3,7,1]=>[1,7,3,2,6,8,4,5]=>1000000=>0000001
[2,7,6,1,3,5,4,8]=>[8,4,5,3,1,6,7,2]=>0000000=>0000000
[2,8,6,1,3,5,4,7]=>[7,4,5,3,1,6,8,2]=>0000000=>0000000
[5,7,4,1,8,6,3,2]=>[2,3,6,8,1,4,7,5]=>0000000=>0000000
[5,6,4,2,8,3,7,1]=>[1,7,3,8,2,4,6,5]=>1000000=>0000001
[5,6,4,2,7,3,1,8]=>[8,1,3,7,2,4,6,5]=>0000000=>0000000
[5,8,1,4,6,3,7,2]=>[2,7,3,6,4,1,8,5]=>0000000=>0000000
[3,6,7,4,5,8,2,1]=>[1,2,8,5,4,7,6,3]=>1100000=>0000011
[5,4,6,1,7,8,3,2]=>[2,3,8,7,1,6,4,5]=>0000000=>0000000
[5,6,4,1,8,7,3,2]=>[2,3,7,8,1,4,6,5]=>0000000=>0000000
[3,5,8,4,6,7,2,1]=>[1,2,7,6,4,8,5,3]=>1100000=>0000011
[3,6,8,4,5,7,2,1]=>[1,2,7,5,4,8,6,3]=>1100000=>0000011
[3,7,8,4,5,6,2,1]=>[1,2,6,5,4,8,7,3]=>1100000=>0000011
[3,7,1,5,4,6,2,8]=>[8,2,6,4,5,1,7,3]=>0000000=>0000000
[3,8,1,5,4,6,7,2]=>[2,7,6,4,5,1,8,3]=>0000000=>0000000
[3,7,1,5,4,6,8,2]=>[2,8,6,4,5,1,7,3]=>0000000=>0000000
[6,7,1,4,5,3,8,2]=>[2,8,3,5,4,1,7,6]=>0000000=>0000000
[5,7,1,4,6,3,8,2]=>[2,8,3,6,4,1,7,5]=>0000000=>0000000
[5,4,7,2,8,3,1,6]=>[6,1,3,8,2,7,4,5]=>0000000=>0000000
[5,4,7,2,8,3,6,1]=>[1,6,3,8,2,7,4,5]=>1000000=>0000001
[5,6,4,2,8,3,1,7]=>[7,1,3,8,2,4,6,5]=>0000000=>0000000
[5,8,1,4,6,3,2,7]=>[7,2,3,6,4,1,8,5]=>0000000=>0000000
[3,8,1,5,4,6,2,7]=>[7,2,6,4,5,1,8,3]=>0000000=>0000000
[3,6,1,5,4,2,7,8]=>[8,7,2,4,5,1,6,3]=>0000000=>0000000
[3,6,1,5,4,8,2,7]=>[7,2,8,4,5,1,6,3]=>0000000=>0000000
[6,8,3,1,4,2,5,7]=>[7,5,2,4,1,3,8,6]=>0000000=>0000000
[7,3,8,1,4,2,5,6]=>[6,5,2,4,1,8,3,7]=>0000000=>0000000
[3,6,1,5,4,7,8,2]=>[2,8,7,4,5,1,6,3]=>0000000=>0000000
[3,4,1,2,7,6,5,8]=>[8,5,6,7,2,1,4,3]=>0000000=>0000000
[3,4,1,2,6,8,7,5]=>[5,7,8,6,2,1,4,3]=>0000000=>0000000
[7,8,1,4,5,3,2,6]=>[6,2,3,5,4,1,8,7]=>0000010=>0100000
[3,8,1,5,4,7,2,6]=>[6,2,7,4,5,1,8,3]=>0000000=>0000000
[3,6,1,5,4,8,7,2]=>[2,7,8,4,5,1,6,3]=>0000000=>0000000
[3,6,1,5,4,7,2,8]=>[8,2,7,4,5,1,6,3]=>0000000=>0000000
[6,7,3,1,4,2,5,8]=>[8,5,2,4,1,3,7,6]=>0000000=>0000000
[6,8,3,1,4,2,7,5]=>[5,7,2,4,1,3,8,6]=>0000000=>0000000
[7,8,3,1,4,6,2,5]=>[5,2,6,4,1,3,8,7]=>0000010=>0100000
[7,8,4,2,6,5,1,3]=>[3,1,5,6,2,4,8,7]=>0000010=>0100000
[6,5,8,7,3,4,2,1]=>[1,2,4,3,7,8,5,6]=>1101000=>0001011
[7,8,3,1,4,6,5,2]=>[2,5,6,4,1,3,8,7]=>0000010=>0100000
[6,7,3,1,4,5,2,8]=>[8,2,5,4,1,3,7,6]=>0000000=>0000000
[3,7,1,5,4,2,6,8]=>[8,6,2,4,5,1,7,3]=>0000000=>0000000
[3,8,1,5,4,2,7,6]=>[6,7,2,4,5,1,8,3]=>0000000=>0000000
[5,8,1,4,7,3,6,2]=>[2,6,3,7,4,1,8,5]=>0000000=>0000000
[6,3,7,1,4,8,5,2]=>[2,5,8,4,1,7,3,6]=>0000000=>0000000
[3,7,1,5,4,8,6,2]=>[2,6,8,4,5,1,7,3]=>0000000=>0000000
[3,7,1,5,4,2,8,6]=>[6,8,2,4,5,1,7,3]=>0000000=>0000000
[6,7,3,1,4,5,8,2]=>[2,8,5,4,1,3,7,6]=>0000000=>0000000
[7,3,8,1,4,5,2,6]=>[6,2,5,4,1,8,3,7]=>0000000=>0000000
[6,8,3,1,4,5,2,7]=>[7,2,5,4,1,3,8,6]=>0000000=>0000000
[3,8,1,5,4,2,6,7]=>[7,6,2,4,5,1,8,3]=>0000000=>0000000
[2,3,6,4,8,1,5,7]=>[7,5,1,8,4,6,3,2]=>0000000=>0000000
[2,5,6,1,4,7,3,8]=>[8,3,7,4,1,6,5,2]=>0000000=>0000000
[7,3,5,8,4,1,2,6]=>[6,2,1,4,8,5,3,7]=>0000000=>0000000
[6,3,5,4,7,1,8,2]=>[2,8,1,7,4,5,3,6]=>0000000=>0000000
[7,3,5,4,6,8,2,1]=>[1,2,8,6,4,5,3,7]=>1100000=>0000011
[6,4,8,5,3,1,2,7]=>[7,2,1,3,5,8,4,6]=>0000000=>0000000
[3,2,8,6,1,5,4,7]=>[7,4,5,1,6,8,2,3]=>0000000=>0000000
[8,7,3,6,4,2,5,1]=>[1,5,2,4,6,3,7,8]=>1000011=>1100001
[5,3,6,2,4,8,7,1]=>[1,7,8,4,2,6,3,5]=>1000000=>0000001
[3,5,2,8,6,1,4,7]=>[7,4,1,6,8,2,5,3]=>0000000=>0000000
[3,7,2,5,1,4,8,6]=>[6,8,4,1,5,2,7,3]=>0000000=>0000000
[8,2,3,6,1,4,7,5]=>[5,7,4,1,6,3,2,8]=>0000001=>1000000
[1,8,2,6,3,4,7,5]=>[5,7,4,3,6,2,8,1]=>0000000=>0000000
[7,2,3,6,1,4,8,5]=>[5,8,4,1,6,3,2,7]=>0000000=>0000000
[2,3,1,8,5,4,6,7]=>[7,6,4,5,8,1,3,2]=>0000000=>0000000
[8,5,1,7,6,3,4,2]=>[2,4,3,6,7,1,5,8]=>0000001=>1000000
[1,8,3,2,5,7,4,6]=>[6,4,7,5,2,3,8,1]=>0000000=>0000000
[4,2,8,6,5,1,7,3]=>[3,7,1,5,6,8,2,4]=>0000000=>0000000
[2,4,3,8,1,6,7,5]=>[5,7,6,1,8,3,4,2]=>0000000=>0000000
[8,7,4,6,1,5,2,3]=>[3,2,5,1,6,4,7,8]=>0000011=>1100000
[4,8,7,6,1,5,2,3]=>[3,2,5,1,6,7,8,4]=>0000000=>0000000
[6,7,4,8,1,5,2,3]=>[3,2,5,1,8,4,7,6]=>0000000=>0000000
[8,4,7,6,1,5,2,3]=>[3,2,5,1,6,7,4,8]=>0000001=>1000000
[5,1,6,8,4,2,3,7]=>[7,3,2,4,8,6,1,5]=>0000000=>0000000
[2,4,7,1,5,8,6,3]=>[3,6,8,5,1,7,4,2]=>0000000=>0000000
[4,7,6,8,1,5,2,3]=>[3,2,5,1,8,6,7,4]=>0000000=>0000000
[5,6,8,7,1,4,2,3]=>[3,2,4,1,7,8,6,5]=>0001000=>0001000
[4,6,8,7,1,5,2,3]=>[3,2,5,1,7,8,6,4]=>0000000=>0000000
[6,7,8,5,1,4,2,3]=>[3,2,4,1,5,8,7,6]=>0001100=>0011000
[4,1,8,5,2,3,6,7]=>[7,6,3,2,5,8,1,4]=>0000000=>0000000
[2,7,4,1,6,5,3,8]=>[8,3,5,6,1,4,7,2]=>0000000=>0000000
[6,2,4,1,8,5,3,7]=>[7,3,5,8,1,4,2,6]=>0000000=>0000000
[7,5,1,6,3,4,8,2]=>[2,8,4,3,6,1,5,7]=>0000000=>0000000
[8,3,1,5,4,6,7,2]=>[2,7,6,4,5,1,3,8]=>0000001=>1000000
[4,2,1,5,6,3,8,7]=>[7,8,3,6,5,1,2,4]=>0000000=>0000000
[7,1,2,5,8,3,4,6]=>[6,4,3,8,5,2,1,7]=>0000000=>0000000
[3,5,1,7,4,6,8,2]=>[2,8,6,4,7,1,5,3]=>0000000=>0000000
[5,3,1,2,4,8,7,6]=>[6,7,8,4,2,1,3,5]=>0000000=>0000000
[5,3,6,2,1,8,7,4]=>[4,7,8,1,2,6,3,5]=>0000000=>0000000
[5,8,4,3,6,1,2,7]=>[7,2,1,6,3,4,8,5]=>0000000=>0000000
[4,3,8,2,1,7,5,6]=>[6,5,7,1,2,8,3,4]=>0000000=>0000000
[3,8,2,5,6,7,1,4]=>[4,1,7,6,5,2,8,3]=>0000000=>0000000
[7,1,4,8,6,2,3,5]=>[5,3,2,6,8,4,1,7]=>0000000=>0000000
[8,3,5,2,1,7,4,6]=>[6,4,7,1,2,5,3,8]=>0000001=>1000000
[4,1,8,5,6,7,3,2]=>[2,3,7,6,5,8,1,4]=>0000000=>0000000
[5,2,7,1,3,4,8,6]=>[6,8,4,3,1,7,2,5]=>0000000=>0000000
[2,6,5,7,3,1,8,4]=>[4,8,1,3,7,5,6,2]=>0000000=>0000000
[4,2,1,6,3,7,8,5]=>[5,8,7,3,6,1,2,4]=>0000000=>0000000
[7,4,3,5,8,6,1,2]=>[2,1,6,8,5,3,4,7]=>0100000=>0000010
[3,6,7,5,2,4,8,1]=>[1,8,4,2,5,7,6,3]=>1000000=>0000001
[5,8,1,7,4,2,6,3]=>[3,6,2,4,7,1,8,5]=>0000000=>0000000
[4,2,1,8,3,7,6,5]=>[5,6,7,3,8,1,2,4]=>0000000=>0000000
[2,6,1,5,4,7,8,3]=>[3,8,7,4,5,1,6,2]=>0000000=>0000000
[2,3,6,8,4,1,5,7]=>[7,5,1,4,8,6,3,2]=>0000000=>0000000
[2,5,3,8,4,7,6,1]=>[1,6,7,4,8,3,5,2]=>1000000=>0000001
[2,8,5,7,3,6,4,1]=>[1,4,6,3,7,5,8,2]=>1000000=>0000001
[3,1,8,5,2,7,6,4]=>[4,6,7,2,5,8,1,3]=>0000000=>0000000
[8,3,5,7,1,6,4,2]=>[2,4,6,1,7,5,3,8]=>0000001=>1000000
[8,3,6,1,4,5,7,2]=>[2,7,5,4,1,6,3,8]=>0000001=>1000000
[2,8,6,3,4,5,7,1]=>[1,7,5,4,3,6,8,2]=>1000000=>0000001
[2,6,8,3,4,5,7,1]=>[1,7,5,4,3,8,6,2]=>1000000=>0000001
[2,7,8,5,3,6,4,1]=>[1,4,6,3,5,8,7,2]=>1000000=>0000001
[2,7,6,3,4,8,5,1]=>[1,5,8,4,3,6,7,2]=>1000000=>0000001
[8,3,7,6,1,4,5,2]=>[2,5,4,1,6,7,3,8]=>0000001=>1000000
[4,8,1,7,2,3,6,5]=>[5,6,3,2,7,1,8,4]=>0000000=>0000000
[4,1,7,2,3,6,5,8]=>[8,5,6,3,2,7,1,4]=>0000000=>0000000
[3,7,1,8,2,6,4,5]=>[5,4,6,2,8,1,7,3]=>0000000=>0000000
[3,1,7,8,2,5,6,4]=>[4,6,5,2,8,7,1,3]=>0000000=>0000000
[3,1,6,5,8,2,7,4]=>[4,7,2,8,5,6,1,3]=>0000000=>0000000
[6,3,5,8,7,1,4,2]=>[2,4,1,7,8,5,3,6]=>0000000=>0000000
[7,3,6,1,4,8,5,2]=>[2,5,8,4,1,6,3,7]=>0000000=>0000000
[7,8,3,6,1,4,5,2]=>[2,5,4,1,6,3,8,7]=>0000010=>0100000
[7,4,8,1,2,3,6,5]=>[5,6,3,2,1,8,4,7]=>0000000=>0000000
[8,7,4,6,1,2,5,3]=>[3,5,2,1,6,4,7,8]=>0000011=>1100000
[7,5,1,2,3,4,8,6]=>[6,8,4,3,2,1,5,7]=>0000000=>0000000
[7,4,6,1,2,8,3,5]=>[5,3,8,2,1,6,4,7]=>0000000=>0000000
[6,4,1,2,8,5,7,3]=>[3,7,5,8,2,1,4,6]=>0000000=>0000000
[5,7,1,2,3,6,4,8]=>[8,4,6,3,2,1,7,5]=>0000000=>0000000
[3,6,8,1,2,7,4,5]=>[5,4,7,2,1,8,6,3]=>0000000=>0000000
[4,8,6,1,2,3,7,5]=>[5,7,3,2,1,6,8,4]=>0000000=>0000000
[8,4,6,1,2,3,7,5]=>[5,7,3,2,1,6,4,8]=>0000001=>1000000
[4,8,1,5,2,7,3,6]=>[6,3,7,2,5,1,8,4]=>0000000=>0000000
[4,1,2,5,3,8,7,6]=>[6,7,8,3,5,2,1,4]=>0000000=>0000000
[3,1,4,8,7,5,2,6]=>[6,2,5,7,8,4,1,3]=>0000000=>0000000
[4,3,6,8,7,5,1,2]=>[2,1,5,7,8,6,3,4]=>0100000=>0000010
[5,4,1,8,2,7,6,3]=>[3,6,7,2,8,1,4,5]=>0000000=>0000000
[5,4,1,8,2,7,3,6]=>[6,3,7,2,8,1,4,5]=>0000000=>0000000
[8,6,7,4,1,2,5,3]=>[3,5,2,1,4,7,6,8]=>0000101=>1010000
[6,4,8,1,2,5,3,7]=>[7,3,5,2,1,8,4,6]=>0000000=>0000000
[6,7,3,1,4,8,5,2]=>[2,5,8,4,1,3,7,6]=>0000000=>0000000
[5,6,3,8,7,1,4,2]=>[2,4,1,7,8,3,6,5]=>0000000=>0000000
[6,7,4,1,2,8,3,5]=>[5,3,8,2,1,4,7,6]=>0000000=>0000000
[6,5,1,2,3,7,8,4]=>[4,8,7,3,2,1,5,6]=>0000000=>0000000
[6,5,1,2,3,4,8,7]=>[7,8,4,3,2,1,5,6]=>0000000=>0000000
[8,6,5,1,2,3,7,4]=>[4,7,3,2,1,5,6,8]=>0000001=>1000000
[6,5,1,2,3,7,4,8]=>[8,4,7,3,2,1,5,6]=>0000000=>0000000
[6,7,4,1,2,5,3,8]=>[8,3,5,2,1,4,7,6]=>0000000=>0000000
[7,8,6,4,1,2,5,3]=>[3,5,2,1,4,6,8,7]=>0000110=>0110000
[4,2,6,7,5,8,3,1]=>[1,3,8,5,7,6,2,4]=>1000000=>0000001
[6,7,5,2,1,8,4,3]=>[3,4,8,1,2,5,7,6]=>0000000=>0000000
[5,6,8,3,1,7,2,4]=>[4,2,7,1,3,8,6,5]=>0000000=>0000000
[3,4,6,8,2,1,5,7]=>[7,5,1,2,8,6,4,3]=>0000000=>0000000
[4,2,5,7,3,8,6,1]=>[1,6,8,3,7,5,2,4]=>1000000=>0000001
[6,4,3,7,8,2,5,1]=>[1,5,2,8,7,3,4,6]=>1000000=>0000001
[6,4,3,1,7,8,2,5]=>[5,2,8,7,1,3,4,6]=>0000000=>0000000
[7,1,3,5,4,8,2,6]=>[6,2,8,4,5,3,1,7]=>0000000=>0000000
[4,6,3,7,8,5,2,1]=>[1,2,5,8,7,3,6,4]=>1100000=>0000011
[1,5,3,6,7,8,4,2]=>[2,4,8,7,6,3,5,1]=>0000000=>0000000
[4,6,1,7,3,8,5,2]=>[2,5,8,3,7,1,6,4]=>0000000=>0000000
[3,5,7,2,1,8,6,4]=>[4,6,8,1,2,7,5,3]=>0000000=>0000000
[6,7,8,3,2,5,1,4]=>[4,1,5,2,3,8,7,6]=>0000100=>0010000
[6,3,7,8,2,5,4,1]=>[1,4,5,2,8,7,3,6]=>1000000=>0000001
[6,2,4,7,1,8,5,3]=>[3,5,8,1,7,4,2,6]=>0000000=>0000000
[2,5,7,8,1,6,3,4]=>[4,3,6,1,8,7,5,2]=>0000000=>0000000
[2,5,6,1,7,8,4,3]=>[3,4,8,7,1,6,5,2]=>0000000=>0000000
[5,6,1,2,7,8,4,3]=>[3,4,8,7,2,1,6,5]=>0000000=>0000000
[8,6,2,7,4,5,3,1]=>[1,3,5,4,7,2,6,8]=>1000001=>1000001
[6,8,2,7,4,5,3,1]=>[1,3,5,4,7,2,8,6]=>1000000=>0000001
[2,6,4,5,8,7,3,1]=>[1,3,7,8,5,4,6,2]=>1000000=>0000001
[8,2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2,8]=>1000001=>1000001
[4,2,6,5,8,7,3,1]=>[1,3,7,8,5,6,2,4]=>1000000=>0000001
[8,2,6,7,4,5,3,1]=>[1,3,5,4,7,6,2,8]=>1000001=>1000001
[6,4,5,8,7,2,3,1]=>[1,3,2,7,8,5,4,6]=>1010000=>0000101
[6,4,8,7,2,5,3,1]=>[1,3,5,2,7,8,4,6]=>1000000=>0000001
[4,6,5,8,7,2,3,1]=>[1,3,2,7,8,5,6,4]=>1010000=>0000101
[2,1,6,8,4,7,5,3]=>[3,5,7,4,8,6,1,2]=>0000000=>0000000
[2,8,6,4,7,5,3,1]=>[1,3,5,7,4,6,8,2]=>1000000=>0000001
[3,7,8,5,6,1,2,4]=>[4,2,1,6,5,8,7,3]=>0000000=>0000000
[3,6,1,8,4,7,2,5]=>[5,2,7,4,8,1,6,3]=>0000000=>0000000
[3,1,6,8,4,7,2,5]=>[5,2,7,4,8,6,1,3]=>0000000=>0000000
[4,1,6,8,3,2,7,5]=>[5,7,2,3,8,6,1,4]=>0000000=>0000000
[4,6,1,8,3,2,7,5]=>[5,7,2,3,8,1,6,4]=>0000000=>0000000
[4,7,8,1,3,2,6,5]=>[5,6,2,3,1,8,7,4]=>0000000=>0000000
[4,7,8,3,1,2,6,5]=>[5,6,2,1,3,8,7,4]=>0000000=>0000000
[2,7,8,3,4,6,5,1]=>[1,5,6,4,3,8,7,2]=>1000000=>0000001
[4,7,8,2,1,3,6,5]=>[5,6,3,1,2,8,7,4]=>0000000=>0000000
[4,6,1,8,2,3,7,5]=>[5,7,3,2,8,1,6,4]=>0000000=>0000000
[4,5,2,1,8,3,7,6]=>[6,7,3,8,1,2,5,4]=>0000000=>0000000
[4,6,2,8,1,3,7,5]=>[5,7,3,1,8,2,6,4]=>0000000=>0000000
[3,6,2,8,4,7,1,5]=>[5,1,7,4,8,2,6,3]=>0000000=>0000000
[2,3,6,8,4,7,5,1]=>[1,5,7,4,8,6,3,2]=>1000000=>0000001
[3,2,6,8,4,7,1,5]=>[5,1,7,4,8,6,2,3]=>0000000=>0000000
[4,2,6,8,3,1,7,5]=>[5,7,1,3,8,6,2,4]=>0000000=>0000000
[4,2,5,1,8,3,7,6]=>[6,7,3,8,1,5,2,4]=>0000000=>0000000
[5,1,2,4,3,8,7,6]=>[6,7,8,3,4,2,1,5]=>0000000=>0000000
[5,2,4,1,3,8,7,6]=>[6,7,8,3,1,4,2,5]=>0000000=>0000000
[4,2,5,3,8,1,7,6]=>[6,7,1,8,3,5,2,4]=>0000000=>0000000
[3,2,5,4,8,7,1,6]=>[6,1,7,8,4,5,2,3]=>0000000=>0000000
[3,5,2,4,8,7,1,6]=>[6,1,7,8,4,2,5,3]=>0000000=>0000000
[5,1,4,2,3,8,7,6]=>[6,7,8,3,2,4,1,5]=>0000000=>0000000
[5,4,3,1,2,8,7,6]=>[6,7,8,2,1,3,4,5]=>0000000=>0000000
[4,5,3,1,8,2,7,6]=>[6,7,2,8,1,3,5,4]=>0000000=>0000000
[4,5,1,3,8,2,7,6]=>[6,7,2,8,3,1,5,4]=>0000000=>0000000
[3,1,5,4,8,7,2,6]=>[6,2,7,8,4,5,1,3]=>0000000=>0000000
[3,5,4,1,8,7,2,6]=>[6,2,7,8,1,4,5,3]=>0000000=>0000000
[3,6,5,8,7,1,2,4]=>[4,2,1,7,8,5,6,3]=>0000000=>0000000
[3,4,1,5,8,7,2,6]=>[6,2,7,8,5,1,4,3]=>0000000=>0000000
[4,1,3,5,8,2,7,6]=>[6,7,2,8,5,3,1,4]=>0000000=>0000000
[4,3,6,8,2,1,7,5]=>[5,7,1,2,8,6,3,4]=>0000000=>0000000
[2,4,6,8,3,7,5,1]=>[1,5,7,3,8,6,4,2]=>1000000=>0000001
[3,4,5,2,8,7,1,6]=>[6,1,7,8,2,5,4,3]=>0000000=>0000000
[5,3,1,4,2,8,7,6]=>[6,7,8,2,4,1,3,5]=>0000000=>0000000
[5,1,3,4,2,8,7,6]=>[6,7,8,2,4,3,1,5]=>0000000=>0000000
[5,1,3,2,4,8,7,6]=>[6,7,8,4,2,3,1,5]=>0000000=>0000000
[5,3,2,1,4,8,7,6]=>[6,7,8,4,1,2,3,5]=>0000000=>0000000
[4,3,2,5,8,1,7,6]=>[6,7,1,8,5,2,3,4]=>0000000=>0000000
[3,4,2,5,8,7,1,6]=>[6,1,7,8,5,2,4,3]=>0000000=>0000000
[3,2,4,5,8,7,1,6]=>[6,1,7,8,5,4,2,3]=>0000000=>0000000
[4,2,3,5,8,1,7,6]=>[6,7,1,8,5,3,2,4]=>0000000=>0000000
[5,2,3,1,4,8,7,6]=>[6,7,8,4,1,3,2,5]=>0000000=>0000000
[5,2,1,3,4,8,7,6]=>[6,7,8,4,3,1,2,5]=>0000000=>0000000
[4,1,6,7,5,8,2,3]=>[3,2,8,5,7,6,1,4]=>0000000=>0000000
[5,8,7,6,1,2,4,3]=>[3,4,2,1,6,7,8,5]=>0001000=>0001000
[4,2,7,3,6,1,8,5]=>[5,8,1,6,3,7,2,4]=>0000000=>0000000
[2,8,6,5,3,7,1,4]=>[4,1,7,3,5,6,8,2]=>0000000=>0000000
[3,2,6,1,4,5,8,7]=>[7,8,5,4,1,6,2,3]=>0000000=>0000000
[5,8,7,6,2,3,4,1]=>[1,4,3,2,6,7,8,5]=>1001000=>0001001
[8,1,7,2,4,5,3,6]=>[6,3,5,4,2,7,1,8]=>0000001=>1000000
[8,1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1,8]=>0000001=>1000000
[8,1,5,3,4,2,6,7]=>[7,6,2,4,3,5,1,8]=>0000001=>1000000
[8,1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1,8]=>0000001=>1000000
[8,1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1,8]=>0000001=>1000000
[8,1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1,8]=>0000001=>1000000
[7,2,1,4,5,3,6,8]=>[8,6,3,5,4,1,2,7]=>0000000=>0000000
[3,7,1,4,5,2,6,8]=>[8,6,2,5,4,1,7,3]=>0000000=>0000000
[6,7,1,2,8,3,5,4]=>[4,5,3,8,2,1,7,6]=>0000000=>0000000
[5,6,3,1,2,7,4,8]=>[8,4,7,2,1,3,6,5]=>0000000=>0000000
[4,2,5,3,1,6,7,8]=>[8,7,6,1,3,5,2,4]=>0000000=>0000000
[6,1,7,5,3,8,4,2]=>[2,4,8,3,5,7,1,6]=>0000000=>0000000
[5,8,7,3,2,6,4,1]=>[1,4,6,2,3,7,8,5]=>1000000=>0000001
[6,8,7,2,5,1,3,4]=>[4,3,1,5,2,7,8,6]=>0000100=>0010000
[5,8,7,2,1,6,3,4]=>[4,3,6,1,2,7,8,5]=>0000000=>0000000
[7,1,2,8,5,6,3,4]=>[4,3,6,5,8,2,1,7]=>0000000=>0000000
[8,7,2,1,5,6,3,4]=>[4,3,6,5,1,2,7,8]=>0000011=>1100000
[6,4,5,8,3,2,7,1]=>[1,7,2,3,8,5,4,6]=>1000000=>0000001
[6,1,8,3,5,2,7,4]=>[4,7,2,5,3,8,1,6]=>0000000=>0000000
[7,6,8,3,5,2,1,4]=>[4,1,2,5,3,8,6,7]=>0000100=>0010000
[8,7,1,3,5,6,2,4]=>[4,2,6,5,3,1,7,8]=>0000011=>1100000
[5,8,2,4,3,6,7,1]=>[1,7,6,3,4,2,8,5]=>1000000=>0000001
[8,6,5,1,4,3,7,2]=>[2,7,3,4,1,5,6,8]=>0000001=>1000000
[2,4,8,6,1,3,7,5]=>[5,7,3,1,6,8,4,2]=>0000000=>0000000
[6,7,1,8,4,3,5,2]=>[2,5,3,4,8,1,7,6]=>0000000=>0000000
[4,1,7,6,3,8,2,5]=>[5,2,8,3,6,7,1,4]=>0000000=>0000000
[4,8,2,5,7,6,3,1]=>[1,3,6,7,5,2,8,4]=>1000000=>0000001
[2,6,7,5,1,8,4,3]=>[3,4,8,1,5,7,6,2]=>0000000=>0000000
[7,6,5,2,8,3,4,1]=>[1,4,3,8,2,5,6,7]=>1000000=>0000001
[8,1,3,5,7,4,6,2]=>[2,6,4,7,5,3,1,8]=>0000001=>1000000
[2,5,8,4,6,7,3,1]=>[1,3,7,6,4,8,5,2]=>1000000=>0000001
[2,4,8,1,6,7,3,5]=>[5,3,7,6,1,8,4,2]=>0000000=>0000000
[1,8,5,6,2,4,3,7]=>[7,3,4,2,6,5,8,1]=>0000000=>0000000
[5,4,8,2,3,6,1,7]=>[7,1,6,3,2,8,4,5]=>0000000=>0000000
[5,8,7,4,1,2,3,6]=>[6,3,2,1,4,7,8,5]=>0000000=>0000000
[7,4,8,6,1,2,3,5]=>[5,3,2,1,6,8,4,7]=>0000000=>0000000
[4,7,6,1,2,3,5,8]=>[8,5,3,2,1,6,7,4]=>0000000=>0000000
[8,5,7,4,1,2,3,6]=>[6,3,2,1,4,7,5,8]=>0000001=>1000000
[7,4,8,5,1,6,2,3]=>[3,2,6,1,5,8,4,7]=>0000000=>0000000
[8,6,4,1,2,7,3,5]=>[5,3,7,2,1,4,6,8]=>0000001=>1000000
[7,5,8,1,3,6,2,4]=>[4,2,6,3,1,8,5,7]=>0000000=>0000000
[5,7,1,3,8,2,4,6]=>[6,4,2,8,3,1,7,5]=>0000000=>0000000
[7,1,5,8,6,2,3,4]=>[4,3,2,6,8,5,1,7]=>0000000=>0000000
[4,1,8,7,2,3,5,6]=>[6,5,3,2,7,8,1,4]=>0000000=>0000000
[7,1,5,8,3,4,2,6]=>[6,2,4,3,8,5,1,7]=>0000000=>0000000
[7,1,4,3,2,5,6,8]=>[8,6,5,2,3,4,1,7]=>0000000=>0000000
[7,1,4,6,3,8,2,5]=>[5,2,8,3,6,4,1,7]=>0000000=>0000000
[3,4,7,2,6,8,5,1]=>[1,5,8,6,2,7,4,3]=>1000000=>0000001
[6,4,2,3,8,5,1,7]=>[7,1,5,8,3,2,4,6]=>0000000=>0000000
[6,4,2,7,5,3,1,8]=>[8,1,3,5,7,2,4,6]=>0000000=>0000000
[5,4,7,3,6,8,2,1]=>[1,2,8,6,3,7,4,5]=>1100000=>0000011
[4,8,7,3,5,1,2,6]=>[6,2,1,5,3,7,8,4]=>0000000=>0000000
[3,4,7,1,6,2,8,5]=>[5,8,2,6,1,7,4,3]=>0000000=>0000000
[5,8,3,4,2,6,7,1]=>[1,7,6,2,4,3,8,5]=>1000000=>0000001
[6,4,3,7,5,1,2,8]=>[8,2,1,5,7,3,4,6]=>0000000=>0000000
[5,3,6,2,4,7,8,1]=>[1,8,7,4,2,6,3,5]=>1000000=>0000001
[5,3,7,2,4,6,8,1]=>[1,8,6,4,2,7,3,5]=>1000000=>0000001
[4,3,1,5,7,8,2,6]=>[6,2,8,7,5,1,3,4]=>0000000=>0000000
[3,2,1,8,5,7,4,6]=>[6,4,7,5,8,1,2,3]=>0000000=>0000000
[6,7,2,1,8,4,5,3]=>[3,5,4,8,1,2,7,6]=>0000000=>0000000
[4,2,1,7,8,3,6,5]=>[5,6,3,8,7,1,2,4]=>0000000=>0000000
[7,4,8,6,2,5,3,1]=>[1,3,5,2,6,8,4,7]=>1000000=>0000001
[7,3,8,6,2,4,5,1]=>[1,5,4,2,6,8,3,7]=>1000000=>0000001
[7,4,3,1,8,2,5,6]=>[6,5,2,8,1,3,4,7]=>0000000=>0000000
[7,4,2,8,5,6,1,3]=>[3,1,6,5,8,2,4,7]=>0000000=>0000000
[7,3,8,5,2,4,6,1]=>[1,6,4,2,5,8,3,7]=>1000000=>0000001
[6,3,8,2,4,5,1,7]=>[7,1,5,4,2,8,3,6]=>0000000=>0000000
[6,3,8,2,5,7,4,1]=>[1,4,7,5,2,8,3,6]=>1000000=>0000001
[5,6,7,3,8,2,4,1]=>[1,4,2,8,3,7,6,5]=>1000000=>0000001
[5,3,8,2,4,6,7,1]=>[1,7,6,4,2,8,3,5]=>1000000=>0000001
[6,3,8,2,4,7,5,1]=>[1,5,7,4,2,8,3,6]=>1000000=>0000001
[5,7,4,2,6,8,1,3]=>[3,1,8,6,2,4,7,5]=>0000000=>0000000
[6,5,3,1,4,2,7,8]=>[8,7,2,4,1,3,5,6]=>0000000=>0000000
[5,7,4,2,6,1,3,8]=>[8,3,1,6,2,4,7,5]=>0000000=>0000000
[5,6,4,2,3,8,1,7]=>[7,1,8,3,2,4,6,5]=>0000000=>0000000
[5,6,3,7,8,2,4,1]=>[1,4,2,8,7,3,6,5]=>1000000=>0000001
[5,6,3,8,2,4,7,1]=>[1,7,4,2,8,3,6,5]=>1000000=>0000001
[6,3,7,2,4,5,1,8]=>[8,1,5,4,2,7,3,6]=>0000000=>0000000
[6,3,7,2,5,8,4,1]=>[1,4,8,5,2,7,3,6]=>1000000=>0000001
[5,3,6,8,2,4,7,1]=>[1,7,4,2,8,6,3,5]=>1000000=>0000001
[5,3,6,7,8,2,4,1]=>[1,4,2,8,7,6,3,5]=>1000000=>0000001
[3,5,8,6,4,2,1,7]=>[7,1,2,4,6,8,5,3]=>0000000=>0000000
[5,8,6,4,2,1,3,7]=>[7,3,1,2,4,6,8,5]=>0000000=>0000000
[4,3,8,5,7,6,2,1]=>[1,2,6,7,5,8,3,4]=>1100000=>0000011
[8,5,3,7,6,2,4,1]=>[1,4,2,6,7,3,5,8]=>1000001=>1000001
[2,1,6,4,3,7,8,5]=>[5,8,7,3,4,6,1,2]=>0000000=>0000000
[6,3,7,8,4,2,1,5]=>[5,1,2,4,8,7,3,6]=>0000000=>0000000
[1,7,6,3,4,2,8,5]=>[5,8,2,4,3,6,7,1]=>0000000=>0000000
[5,1,8,3,2,6,7,4]=>[4,7,6,2,3,8,1,5]=>0000000=>0000000
[5,8,7,2,1,4,6,3]=>[3,6,4,1,2,7,8,5]=>0000000=>0000000
[7,8,6,1,3,4,5,2]=>[2,5,4,3,1,6,8,7]=>0000110=>0110000
[7,6,8,1,3,4,5,2]=>[2,5,4,3,1,8,6,7]=>0000100=>0010000
[1,6,8,3,2,5,7,4]=>[4,7,5,2,3,8,6,1]=>0000000=>0000000
[8,4,2,7,1,5,6,3]=>[3,6,5,1,7,2,4,8]=>0000001=>1000000
[6,4,2,8,3,1,7,5]=>[5,7,1,3,8,2,4,6]=>0000000=>0000000
[4,1,3,2,5,7,8,6]=>[6,8,7,5,2,3,1,4]=>0000000=>0000000
[8,7,5,2,6,3,4,1]=>[1,4,3,6,2,5,7,8]=>1000011=>1100001
[8,6,5,2,7,3,4,1]=>[1,4,3,7,2,5,6,8]=>1000001=>1000001
[6,3,8,5,4,7,1,2]=>[2,1,7,4,5,8,3,6]=>0100000=>0000010
[5,6,1,8,4,3,2,7]=>[7,2,3,4,8,1,6,5]=>0000000=>0000000
[6,1,2,5,8,3,7,4]=>[4,7,3,8,5,2,1,6]=>0000000=>0000000
[1,2,7,5,8,3,6,4]=>[4,6,3,8,5,7,2,1]=>0000000=>0000000
[1,2,6,4,7,8,5,3]=>[3,5,8,7,4,6,2,1]=>0000000=>0000000
[4,1,6,3,8,7,2,5]=>[5,2,7,8,3,6,1,4]=>0000000=>0000000
[7,5,1,8,4,3,2,6]=>[6,2,3,4,8,1,5,7]=>0000000=>0000000
[3,2,6,7,8,1,5,4]=>[4,5,1,8,7,6,2,3]=>0000000=>0000000
[2,5,7,4,3,8,6,1]=>[1,6,8,3,4,7,5,2]=>1000000=>0000001
[4,6,3,7,2,8,5,1]=>[1,5,8,2,7,3,6,4]=>1000000=>0000001
[5,3,7,8,2,4,1,6]=>[6,1,4,2,8,7,3,5]=>0000000=>0000000
[3,2,4,8,1,5,6,7]=>[7,6,5,1,8,4,2,3]=>0000000=>0000000
[7,2,4,8,3,1,5,6]=>[6,5,1,3,8,4,2,7]=>0000000=>0000000
[5,3,8,7,2,4,1,6]=>[6,1,4,2,7,8,3,5]=>0000000=>0000000
[2,4,8,7,3,1,5,6]=>[6,5,1,3,7,8,4,2]=>0000000=>0000000
[3,1,7,4,2,8,6,5]=>[5,6,8,2,4,7,1,3]=>0000000=>0000000
[4,7,6,8,2,3,1,5]=>[5,1,3,2,8,6,7,4]=>0000000=>0000000
[8,1,6,4,2,3,7,5]=>[5,7,3,2,4,6,1,8]=>0000001=>1000000
[4,7,8,6,2,3,1,5]=>[5,1,3,2,6,8,7,4]=>0000000=>0000000
[7,1,6,4,2,3,8,5]=>[5,8,3,2,4,6,1,7]=>0000000=>0000000
[4,8,7,6,2,3,1,5]=>[5,1,3,2,6,7,8,4]=>0000000=>0000000
[6,8,7,5,2,3,1,4]=>[4,1,3,2,5,7,8,6]=>0001100=>0011000
[4,3,6,5,1,8,7,2]=>[2,7,8,1,5,6,3,4]=>0000000=>0000000
[2,6,5,8,3,1,7,4]=>[4,7,1,3,8,5,6,2]=>0000000=>0000000
[4,6,1,5,8,3,7,2]=>[2,7,3,8,5,1,6,4]=>0000000=>0000000
[4,1,6,5,8,3,7,2]=>[2,7,3,8,5,6,1,4]=>0000000=>0000000
[6,4,3,8,7,1,5,2]=>[2,5,1,7,8,3,4,6]=>0000000=>0000000
[2,6,8,5,3,7,1,4]=>[4,1,7,3,5,8,6,2]=>0000000=>0000000
[4,6,8,1,5,7,3,2]=>[2,3,7,5,1,8,6,4]=>0000000=>0000000
[4,6,3,8,5,7,1,2]=>[2,1,7,5,8,3,6,4]=>0100000=>0000010
[4,3,6,1,8,5,7,2]=>[2,7,5,8,1,6,3,4]=>0000000=>0000000
[4,1,3,6,8,7,5,2]=>[2,5,7,8,6,3,1,4]=>0000000=>0000000
[4,3,6,1,8,7,5,2]=>[2,5,7,8,1,6,3,4]=>0000000=>0000000
[4,3,6,8,1,7,5,2]=>[2,5,7,1,8,6,3,4]=>0000000=>0000000
[6,2,5,8,7,1,3,4]=>[4,3,1,7,8,5,2,6]=>0000000=>0000000
[4,6,3,8,1,7,5,2]=>[2,5,7,1,8,3,6,4]=>0000000=>0000000
[6,2,8,5,7,1,3,4]=>[4,3,1,7,5,8,2,6]=>0000000=>0000000
[1,6,4,8,7,3,5,2]=>[2,5,3,7,8,4,6,1]=>0000000=>0000000
[4,6,2,3,7,5,1,8]=>[8,1,5,7,3,2,6,4]=>0000000=>0000000
[5,3,2,6,4,7,1,8]=>[8,1,7,4,6,2,3,5]=>0000000=>0000000
[3,6,8,4,2,1,5,7]=>[7,5,1,2,4,8,6,3]=>0000000=>0000000
[4,3,2,6,1,8,5,7]=>[7,5,8,1,6,2,3,4]=>0000000=>0000000
[7,8,1,4,3,5,2,6]=>[6,2,5,3,4,1,8,7]=>0000010=>0100000
[8,4,2,5,3,1,6,7]=>[7,6,1,3,5,2,4,8]=>0000001=>1000000
[4,3,2,5,1,8,6,7]=>[7,6,8,1,5,2,3,4]=>0000000=>0000000
[7,1,8,3,5,4,2,6]=>[6,2,4,5,3,8,1,7]=>0000000=>0000000
[8,6,2,3,4,1,7,5]=>[5,7,1,4,3,2,6,8]=>0000001=>1000000
[4,8,7,5,3,6,1,2]=>[2,1,6,3,5,7,8,4]=>0100000=>0000010
[5,8,4,2,1,6,7,3]=>[3,7,6,1,2,4,8,5]=>0000000=>0000000
[5,3,7,2,6,1,8,4]=>[4,8,1,6,2,7,3,5]=>0000000=>0000000
[2,8,7,6,4,1,3,5]=>[5,3,1,4,6,7,8,2]=>0000000=>0000000
[7,8,2,6,5,3,1,4]=>[4,1,3,5,6,2,8,7]=>0000010=>0100000
[2,8,7,6,4,3,1,5]=>[5,1,3,4,6,7,8,2]=>0000000=>0000000
[3,8,7,6,1,2,5,4]=>[4,5,2,1,6,7,8,3]=>0000000=>0000000
[4,8,7,6,1,3,2,5]=>[5,2,3,1,6,7,8,4]=>0000000=>0000000
[3,8,7,6,4,1,2,5]=>[5,2,1,4,6,7,8,3]=>0000000=>0000000
[7,8,3,6,5,1,2,4]=>[4,2,1,5,6,3,8,7]=>0000010=>0100000
[8,3,4,2,6,1,7,5]=>[5,7,1,6,2,4,3,8]=>0000001=>1000000
[2,7,8,3,5,4,1,6]=>[6,1,4,5,3,8,7,2]=>0000000=>0000000
[4,7,1,2,8,5,3,6]=>[6,3,5,8,2,1,7,4]=>0000000=>0000000
[2,1,6,3,7,5,4,8]=>[8,4,5,7,3,6,1,2]=>0000000=>0000000
[7,4,1,2,6,5,3,8]=>[8,3,5,6,2,1,4,7]=>0000000=>0000000
[6,8,3,2,5,1,4,7]=>[7,4,1,5,2,3,8,6]=>0000000=>0000000
[8,6,1,4,5,2,3,7]=>[7,3,2,5,4,1,6,8]=>0000001=>1000000
[8,6,3,1,5,2,4,7]=>[7,4,2,5,1,3,6,8]=>0000001=>1000000
[8,4,6,1,5,2,3,7]=>[7,3,2,5,1,6,4,8]=>0000001=>1000000
[8,2,7,5,1,3,4,6]=>[6,4,3,1,5,7,2,8]=>0000001=>1000000
[8,4,1,7,5,2,3,6]=>[6,3,2,5,7,1,4,8]=>0000001=>1000000
[8,2,6,1,5,7,3,4]=>[4,3,7,5,1,6,2,8]=>0000001=>1000000
[5,7,6,1,8,2,3,4]=>[4,3,2,8,1,6,7,5]=>0000000=>0000000
[8,1,6,4,7,2,3,5]=>[5,3,2,7,4,6,1,8]=>0000001=>1000000
[8,5,1,7,3,2,4,6]=>[6,4,2,3,7,1,5,8]=>0000001=>1000000
[8,4,5,1,7,2,3,6]=>[6,3,2,7,1,5,4,8]=>0000001=>1000000
[7,3,1,8,5,6,2,4]=>[4,2,6,5,8,1,3,7]=>0000000=>0000000
[7,4,3,8,1,2,6,5]=>[5,6,2,1,8,3,4,7]=>0000000=>0000000
[8,2,3,6,7,1,5,4]=>[4,5,1,7,6,3,2,8]=>0000001=>1000000
[6,8,5,2,3,4,7,1]=>[1,7,4,3,2,5,8,6]=>1000000=>0000001
[5,7,3,4,6,8,1,2]=>[2,1,8,6,4,3,7,5]=>0100000=>0000010
[5,7,3,1,4,8,6,2]=>[2,6,8,4,1,3,7,5]=>0000000=>0000000
[5,3,7,1,4,2,8,6]=>[6,8,2,4,1,7,3,5]=>0000000=>0000000
[7,8,3,5,1,2,6,4]=>[4,6,2,1,5,3,8,7]=>0000010=>0100000
[3,7,5,1,2,6,4,8]=>[8,4,6,2,1,5,7,3]=>0000000=>0000000
[2,6,4,8,7,5,1,3]=>[3,1,5,7,8,4,6,2]=>0000000=>0000000
[6,2,4,8,7,5,1,3]=>[3,1,5,7,8,4,2,6]=>0000000=>0000000
[2,5,1,4,7,3,8,6]=>[6,8,3,7,4,1,5,2]=>0000000=>0000000
[7,1,4,2,8,6,5,3]=>[3,5,6,8,2,4,1,7]=>0000000=>0000000
[3,6,2,4,1,8,7,5]=>[5,7,8,1,4,2,6,3]=>0000000=>0000000
[3,4,5,1,8,7,6,2]=>[2,6,7,8,1,5,4,3]=>0000000=>0000000
[1,5,8,3,2,7,6,4]=>[4,6,7,2,3,8,5,1]=>0000000=>0000000
[7,5,1,2,8,6,4,3]=>[3,4,6,8,2,1,5,7]=>0000000=>0000000
[4,6,1,2,8,7,5,3]=>[3,5,7,8,2,1,6,4]=>0000000=>0000000
[6,4,1,2,8,7,5,3]=>[3,5,7,8,2,1,4,6]=>0000000=>0000000
[4,1,2,8,3,7,6,5]=>[5,6,7,3,8,2,1,4]=>0000000=>0000000
[2,1,7,8,4,6,3,5]=>[5,3,6,4,8,7,1,2]=>0000000=>0000000
[3,5,8,7,2,6,4,1]=>[1,4,6,2,7,8,5,3]=>1000000=>0000001
[5,8,2,7,1,6,4,3]=>[3,4,6,1,7,2,8,5]=>0000000=>0000000
[2,1,6,4,5,8,3,7]=>[7,3,8,5,4,6,1,2]=>0000000=>0000000
[8,6,3,7,5,2,1,4]=>[4,1,2,5,7,3,6,8]=>0000001=>1000000
[4,6,3,8,5,2,1,7]=>[7,1,2,5,8,3,6,4]=>0000000=>0000000
[4,6,3,7,5,2,8,1]=>[1,8,2,5,7,3,6,4]=>1000000=>0000001
[3,5,7,8,2,6,1,4]=>[4,1,6,2,8,7,5,3]=>0000000=>0000000
[5,6,2,4,1,3,8,7]=>[7,8,3,1,4,2,6,5]=>0000000=>0000000
[7,6,3,8,5,2,4,1]=>[1,4,2,5,8,3,6,7]=>1000000=>0000001
[8,2,3,4,6,1,5,7]=>[7,5,1,6,4,3,2,8]=>0000001=>1000000
[7,2,3,4,6,1,8,5]=>[5,8,1,6,4,3,2,7]=>0000000=>0000000
[8,2,3,4,7,5,1,6]=>[6,1,5,7,4,3,2,8]=>0000001=>1000000
[7,8,3,6,5,1,4,2]=>[2,4,1,5,6,3,8,7]=>0000010=>0100000
[4,2,3,6,1,5,8,7]=>[7,8,5,1,6,3,2,4]=>0000000=>0000000
[4,8,3,7,5,1,6,2]=>[2,6,1,5,7,3,8,4]=>0000000=>0000000
[8,2,3,4,7,1,6,5]=>[5,6,1,7,4,3,2,8]=>0000001=>1000000
[3,8,6,4,5,1,2,7]=>[7,2,1,5,4,6,8,3]=>0000000=>0000000
[4,7,3,6,5,8,2,1]=>[1,2,8,5,6,3,7,4]=>1100000=>0000011
[4,8,3,7,5,2,1,6]=>[6,1,2,5,7,3,8,4]=>0000000=>0000000
[8,7,3,6,5,1,2,4]=>[4,2,1,5,6,3,7,8]=>0000011=>1100000
[8,2,7,5,1,6,3,4]=>[4,3,6,1,5,7,2,8]=>0000001=>1000000
[5,8,1,7,3,6,4,2]=>[2,4,6,3,7,1,8,5]=>0000000=>0000000
[5,2,7,8,4,6,3,1]=>[1,3,6,4,8,7,2,5]=>1000000=>0000001
[5,2,8,3,7,6,1,4]=>[4,1,6,7,3,8,2,5]=>0000000=>0000000
[8,2,7,3,1,6,4,5]=>[5,4,6,1,3,7,2,8]=>0000001=>1000000
[6,8,3,2,5,7,1,4]=>[4,1,7,5,2,3,8,6]=>0000000=>0000000
[6,7,3,8,5,4,2,1]=>[1,2,4,5,8,3,7,6]=>1100000=>0000011
[6,2,3,4,7,5,8,1]=>[1,8,5,7,4,3,2,6]=>1000000=>0000001
[8,2,3,4,1,7,5,6]=>[6,5,7,1,4,3,2,8]=>0000001=>1000000
[6,2,3,4,1,8,5,7]=>[7,5,8,1,4,3,2,6]=>0000000=>0000000
[6,2,3,4,8,7,5,1]=>[1,5,7,8,4,3,2,6]=>1000000=>0000001
[6,8,3,1,5,7,4,2]=>[2,4,7,5,1,3,8,6]=>0000000=>0000000
[8,7,2,5,1,4,6,3]=>[3,6,4,1,5,2,7,8]=>0000011=>1100000
[4,8,7,2,5,1,6,3]=>[3,6,1,5,2,7,8,4]=>0000000=>0000000
[8,7,1,4,2,5,6,3]=>[3,6,5,2,4,1,7,8]=>0000011=>1100000
[3,5,8,7,1,2,6,4]=>[4,6,2,1,7,8,5,3]=>0000000=>0000000
[3,5,8,7,1,6,2,4]=>[4,2,6,1,7,8,5,3]=>0000000=>0000000
[8,7,4,1,2,6,5,3]=>[3,5,6,2,1,4,7,8]=>0000011=>1100000
[5,7,1,8,2,6,3,4]=>[4,3,6,2,8,1,7,5]=>0000000=>0000000
[2,8,7,1,5,6,3,4]=>[4,3,6,5,1,7,8,2]=>0000000=>0000000
[1,6,2,8,4,7,5,3]=>[3,5,7,4,8,2,6,1]=>0000000=>0000000
[1,3,8,5,7,2,6,4]=>[4,6,2,7,5,8,3,1]=>0000000=>0000000
[1,8,3,7,2,5,6,4]=>[4,6,5,2,7,3,8,1]=>0000000=>0000000
[2,8,7,1,3,5,6,4]=>[4,6,5,3,1,7,8,2]=>0000000=>0000000
[8,6,3,7,4,1,5,2]=>[2,5,1,4,7,3,6,8]=>0000001=>1000000
[4,2,8,6,7,5,1,3]=>[3,1,5,7,6,8,2,4]=>0000000=>0000000
[8,4,2,7,5,6,1,3]=>[3,1,6,5,7,2,4,8]=>0000001=>1000000
[4,8,3,6,1,7,5,2]=>[2,5,7,1,6,3,8,4]=>0000000=>0000000
[8,3,4,7,5,1,6,2]=>[2,6,1,5,7,4,3,8]=>0000001=>1000000
[8,3,7,4,5,1,6,2]=>[2,6,1,5,4,7,3,8]=>0000001=>1000000
[8,7,4,2,5,6,1,3]=>[3,1,6,5,2,4,7,8]=>0000011=>1100000
[8,7,5,1,6,2,3,4]=>[4,3,2,6,1,5,7,8]=>0000011=>1100000
[8,7,2,4,1,5,6,3]=>[3,6,5,1,4,2,7,8]=>0000011=>1100000
[4,8,6,1,7,2,5,3]=>[3,5,2,7,1,6,8,4]=>0000000=>0000000
[4,2,8,6,7,1,5,3]=>[3,5,1,7,6,8,2,4]=>0000000=>0000000
[8,7,4,1,2,5,6,3]=>[3,6,5,2,1,4,7,8]=>0000011=>1100000
[8,2,7,1,6,3,4,5]=>[5,4,3,6,1,7,2,8]=>0000001=>1000000
[8,2,7,1,3,6,4,5]=>[5,4,6,3,1,7,2,8]=>0000001=>1000000
[2,8,3,6,7,1,5,4]=>[4,5,1,7,6,3,8,2]=>0000000=>0000000
[8,7,2,1,3,5,6,4]=>[4,6,5,3,1,2,7,8]=>0000011=>1100000
[1,8,7,2,3,6,4,5]=>[5,4,6,3,2,7,8,1]=>0000000=>0000000
[1,8,7,2,6,3,4,5]=>[5,4,3,6,2,7,8,1]=>0000000=>0000000
[8,2,7,3,6,1,4,5]=>[5,4,1,6,3,7,2,8]=>0000001=>1000000
[1,8,7,3,6,2,4,5]=>[5,4,2,6,3,7,8,1]=>0000000=>0000000
[1,8,2,7,6,3,4,5]=>[5,4,3,6,7,2,8,1]=>0000000=>0000000
[8,2,7,4,1,5,6,3]=>[3,6,5,1,4,7,2,8]=>0000001=>1000000
[8,2,1,7,5,6,3,4]=>[4,3,6,5,7,1,2,8]=>0000001=>1000000
[8,7,3,1,5,6,2,4]=>[4,2,6,5,1,3,7,8]=>0000011=>1100000
[2,8,7,3,5,6,1,4]=>[4,1,6,5,3,7,8,2]=>0000000=>0000000
[8,3,1,6,7,5,2,4]=>[4,2,5,7,6,1,3,8]=>0000001=>1000000
[8,5,2,1,6,7,4,3]=>[3,4,7,6,1,2,5,8]=>0000001=>1000000
[1,5,2,8,6,7,4,3]=>[3,4,7,6,8,2,5,1]=>0000000=>0000000
[1,2,8,6,7,5,3,4]=>[4,3,5,7,6,8,2,1]=>0000000=>0000000
[1,8,3,6,7,5,2,4]=>[4,2,5,7,6,3,8,1]=>0000000=>0000000
[8,2,3,6,7,5,1,4]=>[4,1,5,7,6,3,2,8]=>0000001=>1000000
[8,3,7,2,5,6,1,4]=>[4,1,6,5,2,7,3,8]=>0000001=>1000000
[8,1,3,7,5,6,2,4]=>[4,2,6,5,7,3,1,8]=>0000001=>1000000
[8,4,1,2,7,5,6,3]=>[3,6,5,7,2,1,4,8]=>0000001=>1000000
[8,1,4,2,6,7,5,3]=>[3,5,7,6,2,4,1,8]=>0000001=>1000000
[1,2,8,6,7,3,5,4]=>[4,5,3,7,6,8,2,1]=>0000000=>0000000
[8,1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1,8]=>0000001=>1000000
[8,1,7,3,6,2,4,5]=>[5,4,2,6,3,7,1,8]=>0000001=>1000000
[8,1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1,8]=>0000001=>1000000
[8,1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1,8]=>0000001=>1000000
[8,1,3,7,2,5,6,4]=>[4,6,5,2,7,3,1,8]=>0000001=>1000000
[1,8,3,6,7,2,5,4]=>[4,5,2,7,6,3,8,1]=>0000000=>0000000
[1,7,8,2,3,6,5,4]=>[4,5,6,3,2,8,7,1]=>0000000=>0000000
[8,3,7,1,2,5,6,4]=>[4,6,5,2,1,7,3,8]=>0000001=>1000000
[7,4,2,6,1,5,3,8]=>[8,3,5,1,6,2,4,7]=>0000000=>0000000
[7,4,2,5,6,1,3,8]=>[8,3,1,6,5,2,4,7]=>0000000=>0000000
[7,3,5,6,4,2,1,8]=>[8,1,2,4,6,5,3,7]=>0000000=>0000000
[7,4,3,1,5,6,2,8]=>[8,2,6,5,1,3,4,7]=>0000000=>0000000
[7,4,5,2,6,1,3,8]=>[8,3,1,6,2,5,4,7]=>0000000=>0000000
[5,3,7,2,8,6,4,1]=>[1,4,6,8,2,7,3,5]=>1000000=>0000001
[5,3,8,2,6,7,4,1]=>[1,4,7,6,2,8,3,5]=>1000000=>0000001
[6,4,3,1,8,2,7,5]=>[5,7,2,8,1,3,4,6]=>0000000=>0000000
[5,3,7,8,2,6,4,1]=>[1,4,6,2,8,7,3,5]=>1000000=>0000001
[4,7,8,5,6,3,2,1]=>[1,2,3,6,5,8,7,4]=>1110000=>0000111
[5,3,7,6,8,2,4,1]=>[1,4,2,8,6,7,3,5]=>1000000=>0000001
[5,7,8,4,6,2,1,3]=>[3,1,2,6,4,8,7,5]=>0010000=>0000100
[5,8,4,3,6,7,1,2]=>[2,1,7,6,3,4,8,5]=>0100000=>0000010
[5,8,6,4,7,2,1,3]=>[3,1,2,7,4,6,8,5]=>0010000=>0000100
[5,3,8,6,2,7,4,1]=>[1,4,7,2,6,8,3,5]=>1000000=>0000001
[4,7,5,8,6,3,2,1]=>[1,2,3,6,8,5,7,4]=>1110000=>0000111
[6,3,8,7,2,4,1,5]=>[5,1,4,2,7,8,3,6]=>0000000=>0000000
[5,3,8,7,2,6,4,1]=>[1,4,6,2,7,8,3,5]=>1000000=>0000001
[5,3,8,6,7,2,4,1]=>[1,4,2,7,6,8,3,5]=>1000000=>0000001
[5,3,7,8,6,2,4,1]=>[1,4,2,6,8,7,3,5]=>1000000=>0000001
[5,7,6,4,8,2,1,3]=>[3,1,2,8,4,6,7,5]=>0010000=>0000100
[5,8,4,6,7,2,1,3]=>[3,1,2,7,6,4,8,5]=>0010000=>0000100
[6,4,2,8,1,7,3,5]=>[5,3,7,1,8,2,4,6]=>0000000=>0000000
[6,5,2,4,3,7,8,1]=>[1,8,7,3,4,2,5,6]=>1000000=>0000001
[5,4,6,2,8,7,1,3]=>[3,1,7,8,2,6,4,5]=>0000000=>0000000
[5,6,3,8,7,2,4,1]=>[1,4,2,7,8,3,6,5]=>1000000=>0000001
[5,7,4,3,6,8,1,2]=>[2,1,8,6,3,4,7,5]=>0100000=>0000010
[5,7,3,8,6,2,4,1]=>[1,4,2,6,8,3,7,5]=>1000000=>0000001
[4,5,8,6,7,3,2,1]=>[1,2,3,7,6,8,5,4]=>1110000=>0000111
[4,6,8,5,7,3,2,1]=>[1,2,3,7,5,8,6,4]=>1110000=>0000111
[5,6,8,3,7,2,4,1]=>[1,4,2,7,3,8,6,5]=>1000000=>0000001
[5,4,6,8,2,7,1,3]=>[3,1,7,2,8,6,4,5]=>0000000=>0000000
[5,6,2,4,3,7,1,8]=>[8,1,7,3,4,2,6,5]=>0000000=>0000000
[5,6,3,4,1,7,2,8]=>[8,2,7,1,4,3,6,5]=>0000000=>0000000
[4,5,1,3,2,7,6,8]=>[8,6,7,2,3,1,5,4]=>0000000=>0000000
[4,6,1,3,2,7,5,8]=>[8,5,7,2,3,1,6,4]=>0000000=>0000000
[4,5,3,7,6,8,1,2]=>[2,1,8,6,7,3,5,4]=>0100000=>0000010
[1,5,3,6,2,7,4,8]=>[8,4,7,2,6,3,5,1]=>0000000=>0000000
[4,6,2,3,1,7,5,8]=>[8,5,7,1,3,2,6,4]=>0000000=>0000000
[3,6,2,7,5,4,8,1]=>[1,8,4,5,7,2,6,3]=>1000000=>0000001
[2,4,7,1,3,8,6,5]=>[5,6,8,3,1,7,4,2]=>0000000=>0000000
[5,2,6,7,4,3,8,1]=>[1,8,3,4,7,6,2,5]=>1000000=>0000001
[2,5,7,3,1,8,6,4]=>[4,6,8,1,3,7,5,2]=>0000000=>0000000
[2,5,7,3,1,8,4,6]=>[6,4,8,1,3,7,5,2]=>0000000=>0000000
[2,3,1,5,8,4,7,6]=>[6,7,4,8,5,1,3,2]=>0000000=>0000000
[2,1,5,6,8,4,3,7]=>[7,3,4,8,6,5,1,2]=>0000000=>0000000
[4,6,2,7,1,8,3,5]=>[5,3,8,1,7,2,6,4]=>0000000=>0000000
[1,5,4,3,6,8,2,7]=>[7,2,8,6,3,4,5,1]=>0000000=>0000000
[1,6,4,5,7,8,3,2]=>[2,3,8,7,5,4,6,1]=>0000000=>0000000
[2,1,5,6,8,4,7,3]=>[3,7,4,8,6,5,1,2]=>0000000=>0000000
[3,4,6,8,5,7,2,1]=>[1,2,7,5,8,6,4,3]=>1100000=>0000011
[4,5,6,2,8,7,3,1]=>[1,3,7,8,2,6,5,4]=>1000000=>0000001
[4,5,6,1,8,7,3,2]=>[2,3,7,8,1,6,5,4]=>0000000=>0000000
[4,5,6,3,1,8,7,2]=>[2,7,8,1,3,6,5,4]=>0000000=>0000000
[4,3,6,2,1,7,5,8]=>[8,5,7,1,2,6,3,4]=>0000000=>0000000
[4,6,3,1,7,5,2,8]=>[8,2,5,7,1,3,6,4]=>0000000=>0000000
[4,5,3,7,6,1,8,2]=>[2,8,1,6,7,3,5,4]=>0000000=>0000000
[4,5,1,7,3,8,6,2]=>[2,6,8,3,7,1,5,4]=>0000000=>0000000
[2,5,7,1,4,3,8,6]=>[6,8,3,4,1,7,5,2]=>0000000=>0000000
[4,3,5,7,6,1,8,2]=>[2,8,1,6,7,5,3,4]=>0000000=>0000000
[4,3,2,6,1,7,5,8]=>[8,5,7,1,6,2,3,4]=>0000000=>0000000
[5,3,2,1,6,4,7,8]=>[8,7,4,6,1,2,3,5]=>0000000=>0000000
[5,3,1,6,2,7,4,8]=>[8,4,7,2,6,1,3,5]=>0000000=>0000000
[5,1,6,3,2,7,4,8]=>[8,4,7,2,3,6,1,5]=>0000000=>0000000
[2,6,1,4,7,5,3,8]=>[8,3,5,7,4,1,6,2]=>0000000=>0000000
[3,6,1,7,4,2,5,8]=>[8,5,2,4,7,1,6,3]=>0000000=>0000000
[4,6,1,7,5,3,2,8]=>[8,2,3,5,7,1,6,4]=>0000000=>0000000
[5,1,6,3,7,4,2,8]=>[8,2,4,7,3,6,1,5]=>0000000=>0000000
[5,3,6,4,2,1,7,8]=>[8,7,1,2,4,6,3,5]=>0000000=>0000000
[5,3,2,6,4,1,7,8]=>[8,7,1,4,6,2,3,5]=>0000000=>0000000
[5,2,1,6,3,7,4,8]=>[8,4,7,3,6,1,2,5]=>0000000=>0000000
[5,2,6,3,1,7,4,8]=>[8,4,7,1,3,6,2,5]=>0000000=>0000000
[4,2,6,3,1,7,8,5]=>[5,8,7,1,3,6,2,4]=>0000000=>0000000
[3,6,2,7,4,1,5,8]=>[8,5,1,4,7,2,6,3]=>0000000=>0000000
[3,5,7,2,8,6,4,1]=>[1,4,6,8,2,7,5,3]=>1000000=>0000001
[2,6,1,3,7,5,4,8]=>[8,4,5,7,3,1,6,2]=>0000000=>0000000
[3,6,1,7,5,2,4,8]=>[8,4,2,5,7,1,6,3]=>0000000=>0000000
[5,1,6,2,7,4,3,8]=>[8,3,4,7,2,6,1,5]=>0000000=>0000000
[5,2,6,4,3,1,7,8]=>[8,7,1,3,4,6,2,5]=>0000000=>0000000
[5,2,1,6,4,3,7,8]=>[8,7,3,4,6,1,2,5]=>0000000=>0000000
[5,4,2,1,6,3,7,8]=>[8,7,3,6,1,2,4,5]=>0000000=>0000000
[5,4,1,6,2,7,3,8]=>[8,3,7,2,6,1,4,5]=>0000000=>0000000
[5,1,6,4,2,7,3,8]=>[8,3,7,2,4,6,1,5]=>0000000=>0000000
[3,6,1,7,5,4,8,2]=>[2,8,4,5,7,1,6,3]=>0000000=>0000000
[2,6,1,5,4,3,7,8]=>[8,7,3,4,5,1,6,2]=>0000000=>0000000
[3,1,6,2,5,4,7,8]=>[8,7,4,5,2,6,1,3]=>0000000=>0000000
[4,1,6,3,2,7,8,5]=>[5,8,7,2,3,6,1,4]=>0000000=>0000000
[5,1,6,4,3,2,7,8]=>[8,7,2,3,4,6,1,5]=>0000000=>0000000
[5,4,1,6,3,2,7,8]=>[8,7,2,3,6,1,4,5]=>0000000=>0000000
[5,4,3,1,6,2,7,8]=>[8,7,2,6,1,3,4,5]=>0000000=>0000000
[4,5,1,8,7,6,2,3]=>[3,2,6,7,8,1,5,4]=>0000000=>0000000
[5,2,6,8,3,7,4,1]=>[1,4,7,3,8,6,2,5]=>1000000=>0000001
[6,1,4,8,7,2,5,3]=>[3,5,2,7,8,4,1,6]=>0000000=>0000000
[6,1,8,4,7,3,5,2]=>[2,5,3,7,4,8,1,6]=>0000000=>0000000
[6,8,3,5,7,1,4,2]=>[2,4,1,7,5,3,8,6]=>0000000=>0000000
[7,5,8,4,2,6,3,1]=>[1,3,6,2,4,8,5,7]=>1000000=>0000001
[3,6,7,4,8,5,2,1]=>[1,2,5,8,4,7,6,3]=>1100000=>0000011
[5,7,8,3,2,6,4,1]=>[1,4,6,2,3,8,7,5]=>1000000=>0000001
[1,5,8,2,7,3,6,4]=>[4,6,3,7,2,8,5,1]=>0000000=>0000000
[5,8,4,7,2,3,6,1]=>[1,6,3,2,7,4,8,5]=>1000000=>0000001
[6,7,4,8,1,5,3,2]=>[2,3,5,1,8,4,7,6]=>0000000=>0000000
[1,7,4,8,6,2,5,3]=>[3,5,2,6,8,4,7,1]=>0000000=>0000000
[6,8,5,3,7,2,4,1]=>[1,4,2,7,3,5,8,6]=>1000000=>0000001
[6,8,5,2,3,7,4,1]=>[1,4,7,3,2,5,8,6]=>1000000=>0000001
[6,8,4,2,5,7,3,1]=>[1,3,7,5,2,4,8,6]=>1000000=>0000001
[7,4,5,8,1,6,3,2]=>[2,3,6,1,8,5,4,7]=>0000000=>0000000
[6,3,4,7,8,5,2,1]=>[1,2,5,8,7,4,3,6]=>1100000=>0000011
[1,4,5,7,8,2,6,3]=>[3,6,2,8,7,5,4,1]=>0000000=>0000000
[1,6,7,2,3,5,4,8]=>[8,4,5,3,2,7,6,1]=>0000000=>0000000
[1,4,5,7,6,2,3,8]=>[8,3,2,6,7,5,4,1]=>0000000=>0000000
[1,2,5,7,3,6,4,8]=>[8,4,6,3,7,5,2,1]=>0000000=>0000000
[2,7,4,8,3,5,1,6]=>[6,1,5,3,8,4,7,2]=>0000000=>0000000
[2,7,4,8,3,5,6,1]=>[1,6,5,3,8,4,7,2]=>1000000=>0000001
[7,2,8,4,3,5,1,6]=>[6,1,5,3,4,8,2,7]=>0000000=>0000000
[8,4,2,1,5,3,6,7]=>[7,6,3,5,1,2,4,8]=>0000001=>1000000
[8,4,1,5,3,2,6,7]=>[7,6,2,3,5,1,4,8]=>0000001=>1000000
[6,7,3,8,4,2,5,1]=>[1,5,2,4,8,3,7,6]=>1000000=>0000001
[6,7,3,8,4,2,1,5]=>[5,1,2,4,8,3,7,6]=>0000000=>0000000
[7,1,8,4,3,5,2,6]=>[6,2,5,3,4,8,1,7]=>0000000=>0000000
[1,7,8,4,3,5,2,6]=>[6,2,5,3,4,8,7,1]=>0000000=>0000000
[7,1,4,8,3,5,2,6]=>[6,2,5,3,8,4,1,7]=>0000000=>0000000
[7,1,8,4,3,5,6,2]=>[2,6,5,3,4,8,1,7]=>0000000=>0000000
[6,7,3,1,8,4,5,2]=>[2,5,4,8,1,3,7,6]=>0000000=>0000000
[6,7,1,4,8,3,5,2]=>[2,5,3,8,4,1,7,6]=>0000000=>0000000
[6,7,4,1,3,8,2,5]=>[5,2,8,3,1,4,7,6]=>0000000=>0000000
[1,6,7,8,4,3,2,5]=>[5,2,3,4,8,7,6,1]=>0000000=>0000000
[7,2,1,8,4,5,3,6]=>[6,3,5,4,8,1,2,7]=>0000000=>0000000
[6,2,7,1,8,4,3,5]=>[5,3,4,8,1,7,2,6]=>0000000=>0000000
[6,2,7,8,4,3,1,5]=>[5,1,3,4,8,7,2,6]=>0000000=>0000000
[6,2,7,8,4,3,5,1]=>[1,5,3,4,8,7,2,6]=>1000000=>0000001
[2,6,7,4,8,3,5,1]=>[1,5,3,8,4,7,6,2]=>1000000=>0000001
[2,6,7,4,8,3,1,5]=>[5,1,3,8,4,7,6,2]=>0000000=>0000000
[7,8,1,3,6,2,4,5]=>[5,4,2,6,3,1,8,7]=>0000010=>0100000
[1,2,7,8,6,3,4,5]=>[5,4,3,6,8,7,2,1]=>0000000=>0000000
[2,6,7,1,8,5,3,4]=>[4,3,5,8,1,7,6,2]=>0000000=>0000000
[2,6,7,8,5,3,4,1]=>[1,4,3,5,8,7,6,2]=>1000000=>0000001
[6,2,7,8,4,5,3,1]=>[1,3,5,4,8,7,2,6]=>1000000=>0000001
[1,7,2,8,4,5,6,3]=>[3,6,5,4,8,2,7,1]=>0000000=>0000000
[6,3,7,8,1,5,2,4]=>[4,2,5,1,8,7,3,6]=>0000000=>0000000
[6,7,1,2,8,5,3,4]=>[4,3,5,8,2,1,7,6]=>0000000=>0000000
[1,6,7,8,4,2,5,3]=>[3,5,2,4,8,7,6,1]=>0000000=>0000000
[4,6,1,7,3,2,5,8]=>[8,5,2,3,7,1,6,4]=>0000000=>0000000
[1,5,8,3,4,7,6,2]=>[2,6,7,4,3,8,5,1]=>0000000=>0000000
[3,1,2,6,7,5,8,4]=>[4,8,5,7,6,2,1,3]=>0000000=>0000000
[6,7,3,5,1,4,8,2]=>[2,8,4,1,5,3,7,6]=>0000000=>0000000
[5,7,8,4,2,6,3,1]=>[1,3,6,2,4,8,7,5]=>1000000=>0000001
[5,4,7,6,2,8,3,1]=>[1,3,8,2,6,7,4,5]=>1000000=>0000001
[5,7,4,1,6,8,3,2]=>[2,3,8,6,1,4,7,5]=>0000000=>0000000
[6,8,4,5,7,1,3,2]=>[2,3,1,7,5,4,8,6]=>0010000=>0000100
[5,8,4,6,1,7,3,2]=>[2,3,7,1,6,4,8,5]=>0000000=>0000000
[5,6,1,4,7,8,3,2]=>[2,3,8,7,4,1,6,5]=>0000000=>0000000
[5,3,6,7,4,8,2,1]=>[1,2,8,4,7,6,3,5]=>1100000=>0000011
[5,3,2,8,6,7,4,1]=>[1,4,7,6,8,2,3,5]=>1000000=>0000001
[5,4,8,2,6,7,3,1]=>[1,3,7,6,2,8,4,5]=>1000000=>0000001
[5,4,8,6,2,7,3,1]=>[1,3,7,2,6,8,4,5]=>1000000=>0000001
[6,4,8,5,7,2,3,1]=>[1,3,2,7,5,8,4,6]=>1010000=>0000101
[4,6,8,5,7,2,3,1]=>[1,3,2,7,5,8,6,4]=>1010000=>0000101
[5,6,3,8,4,7,2,1]=>[1,2,7,4,8,3,6,5]=>1100000=>0000011
[4,6,3,5,8,7,2,1]=>[1,2,7,8,5,3,6,4]=>1100000=>0000011
[4,6,3,2,8,7,5,1]=>[1,5,7,8,2,3,6,4]=>1000000=>0000001
[5,6,3,8,2,7,4,1]=>[1,4,7,2,8,3,6,5]=>1000000=>0000001
[3,6,5,8,7,2,4,1]=>[1,4,2,7,8,5,6,3]=>1000000=>0000001
[5,3,6,8,2,7,4,1]=>[1,4,7,2,8,6,3,5]=>1000000=>0000001
[4,3,7,2,8,6,5,1]=>[1,5,6,8,2,7,3,4]=>1000000=>0000001
[5,4,7,2,6,8,3,1]=>[1,3,8,6,2,7,4,5]=>1000000=>0000001
[5,3,2,7,6,8,4,1]=>[1,4,8,6,7,2,3,5]=>1000000=>0000001
[6,7,3,8,5,2,4,1]=>[1,4,2,5,8,3,7,6]=>1000000=>0000001
[6,3,2,7,5,4,8,1]=>[1,8,4,5,7,2,3,6]=>1000000=>0000001
[6,4,7,2,5,3,8,1]=>[1,8,3,5,2,7,4,6]=>1000000=>0000001
[6,2,7,5,1,4,8,3]=>[3,8,4,1,5,7,2,6]=>0000000=>0000000
[2,7,8,5,3,6,1,4]=>[4,1,6,3,5,8,7,2]=>0000000=>0000000
[3,5,7,8,4,6,2,1]=>[1,2,6,4,8,7,5,3]=>1100000=>0000011
[5,7,8,2,4,6,3,1]=>[1,3,6,4,2,8,7,5]=>1000000=>0000001
[2,5,8,4,3,7,6,1]=>[1,6,7,3,4,8,5,2]=>1000000=>0000001
[2,6,8,4,7,3,5,1]=>[1,5,3,7,4,8,6,2]=>1000000=>0000001
[3,7,4,8,6,2,1,5]=>[5,1,2,6,8,4,7,3]=>0000000=>0000000
[3,6,4,8,7,2,5,1]=>[1,5,2,7,8,4,6,3]=>1000000=>0000001
[3,5,4,8,2,7,6,1]=>[1,6,7,2,8,4,5,3]=>1000000=>0000001
[4,5,7,3,8,6,2,1]=>[1,2,6,8,3,7,5,4]=>1100000=>0000011
[1,8,2,5,6,3,4,7]=>[7,4,3,6,5,2,8,1]=>0000000=>0000000
[7,2,8,4,5,1,3,6]=>[6,3,1,5,4,8,2,7]=>0000000=>0000000
[1,3,7,5,6,2,4,8]=>[8,4,2,6,5,7,3,1]=>0000000=>0000000
[1,6,7,4,3,5,2,8]=>[8,2,5,3,4,7,6,1]=>0000000=>0000000
[1,8,2,5,3,6,7,4]=>[4,7,6,3,5,2,8,1]=>0000000=>0000000
[2,6,8,4,3,5,7,1]=>[1,7,5,3,4,8,6,2]=>1000000=>0000001
[7,2,8,4,1,5,6,3]=>[3,6,5,1,4,8,2,7]=>0000000=>0000000
[7,5,8,1,2,6,3,4]=>[4,3,6,2,1,8,5,7]=>0000000=>0000000
[1,5,2,6,4,7,8,3]=>[3,8,7,4,6,2,5,1]=>0000000=>0000000
[1,5,4,6,2,3,7,8]=>[8,7,3,2,6,4,5,1]=>0000000=>0000000
[6,2,5,7,1,4,8,3]=>[3,8,4,1,7,5,2,6]=>0000000=>0000000
[6,5,4,3,8,1,7,2]=>[2,7,1,8,3,4,5,6]=>0000000=>0000000
[2,6,5,8,3,4,1,7]=>[7,1,4,3,8,5,6,2]=>0000000=>0000000
[2,6,5,7,3,4,1,8]=>[8,1,4,3,7,5,6,2]=>0000000=>0000000
[6,2,5,7,4,1,3,8]=>[8,3,1,4,7,5,2,6]=>0000000=>0000000
[6,2,5,8,4,1,3,7]=>[7,3,1,4,8,5,2,6]=>0000000=>0000000
[2,7,8,4,6,1,3,5]=>[5,3,1,6,4,8,7,2]=>0000000=>0000000
[6,1,2,8,5,4,7,3]=>[3,7,4,5,8,2,1,6]=>0000000=>0000000
[6,2,5,7,8,1,3,4]=>[4,3,1,8,7,5,2,6]=>0000000=>0000000
[1,5,4,2,6,7,3,8]=>[8,3,7,6,2,4,5,1]=>0000000=>0000000
[2,6,5,7,3,8,1,4]=>[4,1,8,3,7,5,6,2]=>0000000=>0000000
[1,6,2,7,5,8,4,3]=>[3,4,8,5,7,2,6,1]=>0000000=>0000000
[1,3,2,7,8,5,6,4]=>[4,6,5,8,7,2,3,1]=>0000000=>0000000
[1,6,2,4,8,7,3,5]=>[5,3,7,8,4,2,6,1]=>0000000=>0000000
[6,5,2,1,8,7,3,4]=>[4,3,7,8,1,2,5,6]=>0000000=>0000000
[2,6,5,3,7,8,4,1]=>[1,4,8,7,3,5,6,2]=>1000000=>0000001
[6,5,2,3,8,7,1,4]=>[4,1,7,8,3,2,5,6]=>0000000=>0000000
[5,1,4,2,3,7,8,6]=>[6,8,7,3,2,4,1,5]=>0000000=>0000000
[1,5,4,2,6,3,8,7]=>[7,8,3,6,2,4,5,1]=>0000000=>0000000
[5,1,6,3,8,2,7,4]=>[4,7,2,8,3,6,1,5]=>0000000=>0000000
[6,5,8,7,4,3,1,2]=>[2,1,3,4,7,8,5,6]=>0111000=>0001110
[6,4,2,7,8,5,1,3]=>[3,1,5,8,7,2,4,6]=>0000000=>0000000
[6,1,4,8,7,5,2,3]=>[3,2,5,7,8,4,1,6]=>0000000=>0000000
[1,6,4,8,7,5,2,3]=>[3,2,5,7,8,4,6,1]=>0000000=>0000000
[1,8,6,2,4,7,3,5]=>[5,3,7,4,2,6,8,1]=>0000000=>0000000
[8,1,6,2,4,7,3,5]=>[5,3,7,4,2,6,1,8]=>0000001=>1000000
[6,4,1,7,8,5,2,3]=>[3,2,5,8,7,1,4,6]=>0000000=>0000000
[7,6,1,2,4,8,3,5]=>[5,3,8,4,2,1,6,7]=>0000000=>0000000
[1,8,6,3,4,7,2,5]=>[5,2,7,4,3,6,8,1]=>0000000=>0000000
[1,7,2,5,4,8,3,6]=>[6,3,8,4,5,2,7,1]=>0000000=>0000000
[7,1,2,5,4,8,3,6]=>[6,3,8,4,5,2,1,7]=>0000000=>0000000
[2,7,1,5,4,8,3,6]=>[6,3,8,4,5,1,7,2]=>0000000=>0000000
[2,8,6,1,4,7,3,5]=>[5,3,7,4,1,6,8,2]=>0000000=>0000000
[7,2,1,5,4,8,3,6]=>[6,3,8,4,5,1,2,7]=>0000000=>0000000
[1,2,7,5,4,8,3,6]=>[6,3,8,4,5,7,2,1]=>0000000=>0000000
[3,2,7,5,4,8,1,6]=>[6,1,8,4,5,7,2,3]=>0000000=>0000000
[2,5,8,4,7,3,1,6]=>[6,1,3,7,4,8,5,2]=>0000000=>0000000
[2,3,7,5,4,8,1,6]=>[6,1,8,4,5,7,3,2]=>0000000=>0000000
[6,8,3,2,4,7,1,5]=>[5,1,7,4,2,3,8,6]=>0000000=>0000000
[3,7,2,5,4,8,1,6]=>[6,1,8,4,5,2,7,3]=>0000000=>0000000
[3,1,7,5,4,8,2,6]=>[6,2,8,4,5,7,1,3]=>0000000=>0000000
[1,3,7,5,4,8,2,6]=>[6,2,8,4,5,7,3,1]=>0000000=>0000000
[1,5,8,4,7,3,2,6]=>[6,2,3,7,4,8,5,1]=>0000000=>0000000
[5,1,8,4,7,3,2,6]=>[6,2,3,7,4,8,1,5]=>0000000=>0000000
[5,8,2,4,7,3,1,6]=>[6,1,3,7,4,2,8,5]=>0000000=>0000000
[6,8,4,3,7,5,1,2]=>[2,1,5,7,3,4,8,6]=>0100000=>0000010
[8,5,2,4,7,3,1,6]=>[6,1,3,7,4,2,5,8]=>0000001=>1000000
[8,1,5,4,7,3,2,6]=>[6,2,3,7,4,5,1,8]=>0000001=>1000000
[1,8,5,4,7,3,2,6]=>[6,2,3,7,4,5,8,1]=>0000000=>0000000
[1,7,3,5,4,8,2,6]=>[6,2,8,4,5,3,7,1]=>0000000=>0000000
[8,6,3,1,4,7,2,5]=>[5,2,7,4,1,3,6,8]=>0000001=>1000000
[8,6,4,1,7,2,5,3]=>[3,5,2,7,1,4,6,8]=>0000001=>1000000
[5,3,7,4,6,8,2,1]=>[1,2,8,6,4,7,3,5]=>1100000=>0000011
[4,1,3,2,7,8,5,6]=>[6,5,8,7,2,3,1,4]=>0000000=>0000000
[1,4,3,2,7,8,5,6]=>[6,5,8,7,2,3,4,1]=>0000000=>0000000
[2,4,3,1,7,8,5,6]=>[6,5,8,7,1,3,4,2]=>0000000=>0000000
[2,7,3,5,4,8,1,6]=>[6,1,8,4,5,3,7,2]=>0000000=>0000000
[2,8,5,4,7,3,1,6]=>[6,1,3,7,4,5,8,2]=>0000000=>0000000
[5,7,3,4,6,8,2,1]=>[1,2,8,6,4,3,7,5]=>1100000=>0000011
[8,2,5,4,7,3,1,6]=>[6,1,3,7,4,5,2,8]=>0000001=>1000000
[7,2,3,5,4,8,1,6]=>[6,1,8,4,5,3,2,7]=>0000000=>0000000
[3,2,1,4,7,8,5,6]=>[6,5,8,7,4,1,2,3]=>0000000=>0000000
[8,1,7,6,4,3,5,2]=>[2,5,3,4,6,7,1,8]=>0000001=>1000000
[8,6,4,5,2,7,1,3]=>[3,1,7,2,5,4,6,8]=>0000001=>1000000
[7,1,8,6,4,3,5,2]=>[2,5,3,4,6,8,1,7]=>0000000=>0000000
[7,4,2,5,1,6,3,8]=>[8,3,6,1,5,2,4,7]=>0000000=>0000000
[7,3,6,5,2,1,4,8]=>[8,4,1,2,5,6,3,7]=>0000000=>0000000
[8,3,6,5,2,1,7,4]=>[4,7,1,2,5,6,3,8]=>0000001=>1000000
[7,3,6,5,2,1,8,4]=>[4,8,1,2,5,6,3,7]=>0000000=>0000000
[5,4,2,8,1,3,7,6]=>[6,7,3,1,8,2,4,5]=>0000000=>0000000
[5,8,2,6,4,1,3,7]=>[7,3,1,4,6,2,8,5]=>0000000=>0000000
[6,4,2,5,1,8,3,7]=>[7,3,8,1,5,2,4,6]=>0000000=>0000000
[6,3,5,2,1,4,7,8]=>[8,7,4,1,2,5,3,6]=>0000000=>0000000
[2,3,5,8,1,4,7,6]=>[6,7,4,1,8,5,3,2]=>0000000=>0000000
[2,3,6,8,1,5,7,4]=>[4,7,5,1,8,6,3,2]=>0000000=>0000000
[6,3,8,5,2,7,1,4]=>[4,1,7,2,5,8,3,6]=>0000000=>0000000
[6,3,7,5,2,1,4,8]=>[8,4,1,2,5,7,3,6]=>0000000=>0000000
[2,5,7,6,3,1,4,8]=>[8,4,1,3,6,7,5,2]=>0000000=>0000000
[2,8,7,6,3,1,5,4]=>[4,5,1,3,6,7,8,2]=>0000000=>0000000
[2,5,8,7,6,3,1,4]=>[4,1,3,6,7,8,5,2]=>0000000=>0000000
[2,4,8,1,6,5,7,3]=>[3,7,5,6,1,8,4,2]=>0000000=>0000000
[2,8,7,3,6,1,4,5]=>[5,4,1,6,3,7,8,2]=>0000000=>0000000
[8,4,2,5,1,3,7,6]=>[6,7,3,1,5,2,4,8]=>0000001=>1000000
[2,3,6,8,1,4,7,5]=>[5,7,4,1,8,6,3,2]=>0000000=>0000000
[2,7,8,6,3,1,4,5]=>[5,4,1,3,6,8,7,2]=>0000000=>0000000
[2,8,6,3,1,4,5,7]=>[7,5,4,1,3,6,8,2]=>0000000=>0000000
[8,3,5,2,1,4,6,7]=>[7,6,4,1,2,5,3,8]=>0000001=>1000000
[2,5,8,1,7,3,6,4]=>[4,6,3,7,1,8,5,2]=>0000000=>0000000
[2,8,1,5,7,3,6,4]=>[4,6,3,7,5,1,8,2]=>0000000=>0000000
[8,3,6,1,4,7,5,2]=>[2,5,7,4,1,6,3,8]=>0000001=>1000000
[2,6,8,1,5,7,3,4]=>[4,3,7,5,1,8,6,2]=>0000000=>0000000
[2,7,1,5,8,3,4,6]=>[6,4,3,8,5,1,7,2]=>0000000=>0000000
[2,7,1,6,3,8,4,5]=>[5,4,8,3,6,1,7,2]=>0000000=>0000000
[4,7,6,1,8,5,2,3]=>[3,2,5,8,1,6,7,4]=>0000000=>0000000
[7,3,6,1,2,8,4,5]=>[5,4,8,2,1,6,3,7]=>0000000=>0000000
[7,4,8,1,6,5,2,3]=>[3,2,5,6,1,8,4,7]=>0000000=>0000000
[7,4,6,1,8,2,5,3]=>[3,5,2,8,1,6,4,7]=>0000000=>0000000
[4,6,8,5,1,7,2,3]=>[3,2,7,1,5,8,6,4]=>0000000=>0000000
[5,1,7,6,2,3,8,4]=>[4,8,3,2,6,7,1,5]=>0000000=>0000000
[5,1,7,6,2,8,3,4]=>[4,3,8,2,6,7,1,5]=>0000000=>0000000
[5,1,8,7,6,2,3,4]=>[4,3,2,6,7,8,1,5]=>0000000=>0000000
[8,5,1,7,6,2,3,4]=>[4,3,2,6,7,1,5,8]=>0000001=>1000000
[8,5,1,6,2,7,3,4]=>[4,3,7,2,6,1,5,8]=>0000001=>1000000
[3,6,1,8,4,7,5,2]=>[2,5,7,4,8,1,6,3]=>0000000=>0000000
[4,6,1,8,7,5,2,3]=>[3,2,5,7,8,1,6,4]=>0000000=>0000000
[8,4,6,1,7,5,2,3]=>[3,2,5,7,1,6,4,8]=>0000001=>1000000
[4,8,5,1,7,2,3,6]=>[6,3,2,7,1,5,8,4]=>0000000=>0000000
[3,4,8,7,1,2,5,6]=>[6,5,2,1,7,8,4,3]=>0000000=>0000000
[5,8,4,1,7,2,3,6]=>[6,3,2,7,1,4,8,5]=>0000000=>0000000
[8,6,4,7,1,2,5,3]=>[3,5,2,1,7,4,6,8]=>0000001=>1000000
[6,4,8,7,1,2,5,3]=>[3,5,2,1,7,8,4,6]=>0000000=>0000000
[5,6,8,3,7,1,4,2]=>[2,4,1,7,3,8,6,5]=>0000000=>0000000
[6,5,1,8,2,7,3,4]=>[4,3,7,2,8,1,5,6]=>0000000=>0000000
[8,6,5,1,2,7,3,4]=>[4,3,7,2,1,5,6,8]=>0000001=>1000000
[8,6,5,1,7,2,3,4]=>[4,3,2,7,1,5,6,8]=>0000001=>1000000
[6,5,1,8,7,2,3,4]=>[4,3,2,7,8,1,5,6]=>0000000=>0000000
[6,5,1,7,2,8,3,4]=>[4,3,8,2,7,1,5,6]=>0000000=>0000000
[6,5,1,7,2,3,8,4]=>[4,8,3,2,7,1,5,6]=>0000000=>0000000
[5,7,4,1,8,2,3,6]=>[6,3,2,8,1,4,7,5]=>0000000=>0000000
[5,6,8,7,4,1,2,3]=>[3,2,1,4,7,8,6,5]=>0011000=>0001100
[6,8,5,7,4,1,2,3]=>[3,2,1,4,7,5,8,6]=>0011000=>0001100
[4,2,7,1,6,3,5,8]=>[8,5,3,6,1,7,2,4]=>0000000=>0000000
[6,8,4,2,1,5,3,7]=>[7,3,5,1,2,4,8,6]=>0000000=>0000000
[6,8,4,2,1,5,7,3]=>[3,7,5,1,2,4,8,6]=>0000000=>0000000
[7,4,3,1,8,5,6,2]=>[2,6,5,8,1,3,4,7]=>0000000=>0000000
[6,2,1,8,3,7,4,5]=>[5,4,7,3,8,1,2,6]=>0000000=>0000000
[5,3,2,7,6,1,4,8]=>[8,4,1,6,7,2,3,5]=>0000000=>0000000
[2,1,5,8,4,7,3,6]=>[6,3,7,4,8,5,1,2]=>0000000=>0000000
[4,3,2,5,7,1,6,8]=>[8,6,1,7,5,2,3,4]=>0000000=>0000000
[4,3,1,6,2,7,5,8]=>[8,5,7,2,6,1,3,4]=>0000000=>0000000
[6,5,3,1,7,8,4,2]=>[2,4,8,7,1,3,5,6]=>0000000=>0000000
[5,4,2,1,6,7,3,8]=>[8,3,7,6,1,2,4,5]=>0000000=>0000000
[5,3,2,1,6,7,4,8]=>[8,4,7,6,1,2,3,5]=>0000000=>0000000
[6,4,2,1,7,8,5,3]=>[3,5,8,7,1,2,4,6]=>0000000=>0000000
[3,2,1,4,8,7,5,6]=>[6,5,7,8,4,1,2,3]=>0000000=>0000000
[4,3,2,6,1,7,8,5]=>[5,8,7,1,6,2,3,4]=>0000000=>0000000
[5,3,2,1,6,7,8,4]=>[4,8,7,6,1,2,3,5]=>0000000=>0000000
[8,6,1,4,5,7,2,3]=>[3,2,7,5,4,1,6,8]=>0000001=>1000000
[5,2,8,3,7,4,6,1]=>[1,6,4,7,3,8,2,5]=>1000000=>0000001
[6,2,8,5,4,7,3,1]=>[1,3,7,4,5,8,2,6]=>1000000=>0000001
[5,2,8,4,3,6,7,1]=>[1,7,6,3,4,8,2,5]=>1000000=>0000001
[5,4,2,7,3,6,1,8]=>[8,1,6,3,7,2,4,5]=>0000000=>0000000
[5,4,2,8,3,6,1,7]=>[7,1,6,3,8,2,4,5]=>0000000=>0000000
[6,5,3,8,4,7,2,1]=>[1,2,7,4,8,3,5,6]=>1100000=>0000011
[5,2,8,4,3,7,1,6]=>[6,1,7,3,4,8,2,5]=>0000000=>0000000
[6,2,8,3,7,4,1,5]=>[5,1,4,7,3,8,2,6]=>0000000=>0000000
[5,4,2,7,3,1,8,6]=>[6,8,1,3,7,2,4,5]=>0000000=>0000000
[6,4,3,7,1,2,8,5]=>[5,8,2,1,7,3,4,6]=>0000000=>0000000
[6,4,3,8,1,2,7,5]=>[5,7,2,1,8,3,4,6]=>0000000=>0000000
[7,2,8,4,3,1,5,6]=>[6,5,1,3,4,8,2,7]=>0000000=>0000000
[7,5,3,8,4,2,6,1]=>[1,6,2,4,8,3,5,7]=>1000000=>0000001
[6,4,2,7,3,1,5,8]=>[8,5,1,3,7,2,4,6]=>0000000=>0000000
[7,6,4,8,2,3,5,1]=>[1,5,3,2,8,4,6,7]=>1000000=>0000001
[5,3,1,7,8,4,6,2]=>[2,6,4,8,7,1,3,5]=>0000000=>0000000
[5,3,2,7,8,4,6,1]=>[1,6,4,8,7,2,3,5]=>1000000=>0000001
[6,5,1,7,8,2,3,4]=>[4,3,2,8,7,1,5,6]=>0000000=>0000000
[6,3,1,7,8,4,2,5]=>[5,2,4,8,7,1,3,6]=>0000000=>0000000
[6,3,2,7,8,4,1,5]=>[5,1,4,8,7,2,3,6]=>0000000=>0000000
[8,7,6,1,3,5,2,4]=>[4,2,5,3,1,6,7,8]=>0000111=>1110000
[7,4,6,1,3,2,8,5]=>[5,8,2,3,1,6,4,7]=>0000000=>0000000
[4,7,2,5,6,3,8,1]=>[1,8,3,6,5,2,7,4]=>1000000=>0000001
[2,8,6,5,7,1,4,3]=>[3,4,1,7,5,6,8,2]=>0000000=>0000000
[3,1,2,6,8,4,7,5]=>[5,7,4,8,6,2,1,3]=>0000000=>0000000
[5,1,3,2,7,8,4,6]=>[6,4,8,7,2,3,1,5]=>0000000=>0000000
[5,3,8,1,7,2,4,6]=>[6,4,2,7,1,8,3,5]=>0000000=>0000000
[3,6,7,8,4,2,1,5]=>[5,1,2,4,8,7,6,3]=>0000000=>0000000
[2,5,1,8,4,7,3,6]=>[6,3,7,4,8,1,5,2]=>0000000=>0000000
[8,2,1,5,7,3,4,6]=>[6,4,3,7,5,1,2,8]=>0000001=>1000000
[2,5,4,8,1,3,7,6]=>[6,7,3,1,8,4,5,2]=>0000000=>0000000
[1,7,3,5,8,2,6,4]=>[4,6,2,8,5,3,7,1]=>0000000=>0000000
[3,1,6,8,7,2,4,5]=>[5,4,2,7,8,6,1,3]=>0000000=>0000000
[4,1,7,2,6,8,3,5]=>[5,3,8,6,2,7,1,4]=>0000000=>0000000
[4,1,3,8,7,2,6,5]=>[5,6,2,7,8,3,1,4]=>0000000=>0000000
[1,8,3,2,7,5,6,4]=>[4,6,5,7,2,3,8,1]=>0000000=>0000000
[5,1,7,8,4,2,6,3]=>[3,6,2,4,8,7,1,5]=>0000000=>0000000
[5,1,8,7,4,2,6,3]=>[3,6,2,4,7,8,1,5]=>0000000=>0000000
[4,7,2,8,3,6,5,1]=>[1,5,6,3,8,2,7,4]=>1000000=>0000001
[4,1,7,8,5,3,6,2]=>[2,6,3,5,8,7,1,4]=>0000000=>0000000
[5,1,7,4,8,3,6,2]=>[2,6,3,8,4,7,1,5]=>0000000=>0000000
[4,1,8,7,5,3,6,2]=>[2,6,3,5,7,8,1,4]=>0000000=>0000000
[4,8,2,7,3,6,5,1]=>[1,5,6,3,7,2,8,4]=>1000000=>0000001
[4,7,2,6,3,5,8,1]=>[1,8,5,3,6,2,7,4]=>1000000=>0000001
[6,8,2,4,3,7,5,1]=>[1,5,7,3,4,2,8,6]=>1000000=>0000001
[6,7,2,4,3,8,5,1]=>[1,5,8,3,4,2,7,6]=>1000000=>0000001
[3,8,7,2,4,1,5,6]=>[6,5,1,4,2,7,8,3]=>0000000=>0000000
[3,7,8,2,4,1,5,6]=>[6,5,1,4,2,8,7,3]=>0000000=>0000000
[3,6,8,2,4,5,7,1]=>[1,7,5,4,2,8,6,3]=>1000000=>0000001
[3,6,7,2,4,5,8,1]=>[1,8,5,4,2,7,6,3]=>1000000=>0000001
[4,3,6,7,1,8,2,5]=>[5,2,8,1,7,6,3,4]=>0000000=>0000000
[6,1,7,3,8,2,5,4]=>[4,5,2,8,3,7,1,6]=>0000000=>0000000
[6,1,4,7,8,5,2,3]=>[3,2,5,8,7,4,1,6]=>0000000=>0000000
[6,3,2,1,7,8,5,4]=>[4,5,8,7,1,2,3,6]=>0000000=>0000000
[6,4,7,8,3,2,5,1]=>[1,5,2,3,8,7,4,6]=>1000000=>0000001
[6,8,5,7,4,2,3,1]=>[1,3,2,4,7,5,8,6]=>1011000=>0001101
[2,3,8,7,1,6,4,5]=>[5,4,6,1,7,8,3,2]=>0000000=>0000000
[6,8,1,2,7,4,5,3]=>[3,5,4,7,2,1,8,6]=>0000000=>0000000
[6,4,8,7,5,1,2,3]=>[3,2,1,5,7,8,4,6]=>0010000=>0000100
[5,7,1,8,4,6,2,3]=>[3,2,6,4,8,1,7,5]=>0000000=>0000000
[6,3,8,7,2,1,4,5]=>[5,4,1,2,7,8,3,6]=>0000000=>0000000
[2,3,7,8,5,6,1,4]=>[4,1,6,5,8,7,3,2]=>0000000=>0000000
[7,6,4,8,5,2,1,3]=>[3,1,2,5,8,4,6,7]=>0010000=>0000100
[7,5,3,2,8,6,1,4]=>[4,1,6,8,2,3,5,7]=>0000000=>0000000
[2,5,1,3,8,6,7,4]=>[4,7,6,8,3,1,5,2]=>0000000=>0000000
[8,3,5,4,1,6,7,2]=>[2,7,6,1,4,5,3,8]=>0000001=>1000000
[8,3,7,1,4,6,5,2]=>[2,5,6,4,1,7,3,8]=>0000001=>1000000
[1,6,4,8,3,2,5,7]=>[7,5,2,3,8,4,6,1]=>0000000=>0000000
[6,1,4,8,2,3,5,7]=>[7,5,3,2,8,4,1,6]=>0000000=>0000000
[6,4,3,8,5,7,1,2]=>[2,1,7,5,8,3,4,6]=>0100000=>0000010
[2,1,7,4,8,3,5,6]=>[6,5,3,8,4,7,1,2]=>0000000=>0000000
[4,5,2,8,1,7,6,3]=>[3,6,7,1,8,2,5,4]=>0000000=>0000000
[4,6,2,8,7,1,5,3]=>[3,5,1,7,8,2,6,4]=>0000000=>0000000
[4,6,8,2,7,5,1,3]=>[3,1,5,7,2,8,6,4]=>0000000=>0000000
[5,6,7,2,1,3,8,4]=>[4,8,3,1,2,7,6,5]=>0000000=>0000000
[5,6,1,7,8,4,2,3]=>[3,2,4,8,7,1,6,5]=>0000000=>0000000
[4,6,8,1,7,5,2,3]=>[3,2,5,7,1,8,6,4]=>0000000=>0000000
[5,6,7,1,3,8,2,4]=>[4,2,8,3,1,7,6,5]=>0000000=>0000000
[5,6,7,3,1,2,8,4]=>[4,8,2,1,3,7,6,5]=>0000000=>0000000
[1,5,7,8,3,4,6,2]=>[2,6,4,3,8,7,5,1]=>0000000=>0000000
[3,5,7,8,1,4,6,2]=>[2,6,4,1,8,7,5,3]=>0000000=>0000000
[3,6,2,1,4,5,8,7]=>[7,8,5,4,1,2,6,3]=>0000000=>0000000
[6,4,2,5,1,3,8,7]=>[7,8,3,1,5,2,4,6]=>0000000=>0000000
[6,8,2,7,3,1,4,5]=>[5,4,1,3,7,2,8,6]=>0000000=>0000000
[4,2,3,8,1,5,6,7]=>[7,6,5,1,8,3,2,4]=>0000000=>0000000
[2,1,5,8,4,3,6,7]=>[7,6,3,4,8,5,1,2]=>0000000=>0000000
[5,8,4,1,6,2,3,7]=>[7,3,2,6,1,4,8,5]=>0000000=>0000000
[2,1,5,4,8,3,6,7]=>[7,6,3,8,4,5,1,2]=>0000000=>0000000
[2,4,3,8,1,5,6,7]=>[7,6,5,1,8,3,4,2]=>0000000=>0000000
[3,8,4,2,1,5,6,7]=>[7,6,5,1,2,4,8,3]=>0000000=>0000000
[2,3,8,4,1,5,6,7]=>[7,6,5,1,4,8,3,2]=>0000000=>0000000
[3,4,2,8,1,5,6,7]=>[7,6,5,1,8,2,4,3]=>0000000=>0000000
[2,1,4,8,5,3,6,7]=>[7,6,3,5,8,4,1,2]=>0000000=>0000000
[3,2,8,4,1,5,6,7]=>[7,6,5,1,4,8,2,3]=>0000000=>0000000
[2,8,4,3,1,5,6,7]=>[7,6,5,1,3,4,8,2]=>0000000=>0000000
[3,8,4,2,6,7,5,1]=>[1,5,7,6,2,4,8,3]=>1000000=>0000001
[3,8,4,1,6,7,5,2]=>[2,5,7,6,1,4,8,3]=>0000000=>0000000
[2,6,7,5,3,8,4,1]=>[1,4,8,3,5,7,6,2]=>1000000=>0000001
[6,1,3,4,8,2,5,7]=>[7,5,2,8,4,3,1,6]=>0000000=>0000000
[6,2,3,4,8,1,5,7]=>[7,5,1,8,4,3,2,6]=>0000000=>0000000
[6,7,5,8,3,1,4,2]=>[2,4,1,3,8,5,7,6]=>0001000=>0001000
[2,5,7,6,1,4,8,3]=>[3,8,4,1,6,7,5,2]=>0000000=>0000000
[6,7,4,8,2,3,5,1]=>[1,5,3,2,8,4,7,6]=>1000000=>0000001
[6,7,4,8,2,1,3,5]=>[5,3,1,2,8,4,7,6]=>0000000=>0000000
[6,7,4,8,1,2,3,5]=>[5,3,2,1,8,4,7,6]=>0000000=>0000000
[7,8,3,2,6,1,4,5]=>[5,4,1,6,2,3,8,7]=>0000010=>0100000
[6,2,4,8,1,5,3,7]=>[7,3,5,1,8,4,2,6]=>0000000=>0000000
[6,3,7,8,5,4,1,2]=>[2,1,4,5,8,7,3,6]=>0100000=>0000010
[7,3,6,8,5,4,1,2]=>[2,1,4,5,8,6,3,7]=>0100000=>0000010
[8,7,4,2,5,3,6,1]=>[1,6,3,5,2,4,7,8]=>1000011=>1100001
[5,3,6,4,2,7,1,8]=>[8,1,7,2,4,6,3,5]=>0000000=>0000000
[7,4,2,8,6,3,5,1]=>[1,5,3,6,8,2,4,7]=>1000000=>0000001
[6,1,5,3,8,7,4,2]=>[2,4,7,8,3,5,1,6]=>0000000=>0000000
[2,8,6,4,7,5,1,3]=>[3,1,5,7,4,6,8,2]=>0000000=>0000000
[5,1,8,6,3,7,4,2]=>[2,4,7,3,6,8,1,5]=>0000000=>0000000
[8,6,3,2,4,7,5,1]=>[1,5,7,4,2,3,6,8]=>1000001=>1000001
[7,5,1,8,6,3,2,4]=>[4,2,3,6,8,1,5,7]=>0000000=>0000000
[2,4,5,1,3,8,7,6]=>[6,7,8,3,1,5,4,2]=>0000000=>0000000
[1,7,4,2,5,8,6,3]=>[3,6,8,5,2,4,7,1]=>0000000=>0000000
[7,4,8,5,2,6,3,1]=>[1,3,6,2,5,8,4,7]=>1000000=>0000001
[6,3,1,7,4,8,5,2]=>[2,5,8,4,7,1,3,6]=>0000000=>0000000
[7,4,8,5,2,1,6,3]=>[3,6,1,2,5,8,4,7]=>0000000=>0000000
[3,5,6,2,1,4,8,7]=>[7,8,4,1,2,6,5,3]=>0000000=>0000000
[4,3,5,8,1,2,7,6]=>[6,7,2,1,8,5,3,4]=>0000000=>0000000
[3,5,4,8,1,2,7,6]=>[6,7,2,1,8,4,5,3]=>0000000=>0000000
[7,4,3,8,1,6,2,5]=>[5,2,6,1,8,3,4,7]=>0000000=>0000000
[6,5,3,8,7,1,2,4]=>[4,2,1,7,8,3,5,6]=>0000000=>0000000
[2,6,8,4,1,7,3,5]=>[5,3,7,1,4,8,6,2]=>0000000=>0000000
[2,7,8,5,6,1,3,4]=>[4,3,1,6,5,8,7,2]=>0000000=>0000000
[1,8,7,5,6,2,3,4]=>[4,3,2,6,5,7,8,1]=>0000000=>0000000
[5,3,6,8,7,1,2,4]=>[4,2,1,7,8,6,3,5]=>0000000=>0000000
[5,2,8,6,7,1,3,4]=>[4,3,1,7,6,8,2,5]=>0000000=>0000000
[1,8,3,2,7,6,4,5]=>[5,4,6,7,2,3,8,1]=>0000000=>0000000
[2,5,8,7,6,1,3,4]=>[4,3,1,6,7,8,5,2]=>0000000=>0000000
[5,7,6,4,8,1,2,3]=>[3,2,1,8,4,6,7,5]=>0010000=>0000100
[8,1,6,2,7,5,3,4]=>[4,3,5,7,2,6,1,8]=>0000001=>1000000
[5,3,1,7,4,8,2,6]=>[6,2,8,4,7,1,3,5]=>0000000=>0000000
[6,2,1,5,3,8,4,7]=>[7,4,8,3,5,1,2,6]=>0000000=>0000000
[4,8,5,6,1,7,3,2]=>[2,3,7,1,6,5,8,4]=>0000000=>0000000
[3,6,7,1,5,2,8,4]=>[4,8,2,5,1,7,6,3]=>0000000=>0000000
[7,3,2,6,4,8,1,5]=>[5,1,8,4,6,2,3,7]=>0000000=>0000000
[6,4,2,7,3,8,1,5]=>[5,1,8,3,7,2,4,6]=>0000000=>0000000
[5,2,1,7,4,8,3,6]=>[6,3,8,4,7,1,2,5]=>0000000=>0000000
[6,1,8,4,5,2,7,3]=>[3,7,2,5,4,8,1,6]=>0000000=>0000000
[3,5,2,7,1,6,8,4]=>[4,8,6,1,7,2,5,3]=>0000000=>0000000
[4,5,7,2,8,6,1,3]=>[3,1,6,8,2,7,5,4]=>0000000=>0000000
[6,1,3,5,4,2,7,8]=>[8,7,2,4,5,3,1,6]=>0000000=>0000000
[2,3,6,7,4,8,1,5]=>[5,1,8,4,7,6,3,2]=>0000000=>0000000
[1,3,6,7,4,8,5,2]=>[2,5,8,4,7,6,3,1]=>0000000=>0000000
[5,2,6,1,4,7,8,3]=>[3,8,7,4,1,6,2,5]=>0000000=>0000000
[3,7,6,5,2,8,1,4]=>[4,1,8,2,5,6,7,3]=>0000000=>0000000
[2,1,5,3,8,7,4,6]=>[6,4,7,8,3,5,1,2]=>0000000=>0000000
[5,8,3,2,4,1,6,7]=>[7,6,1,4,2,3,8,5]=>0000000=>0000000
[6,2,8,3,7,5,1,4]=>[4,1,5,7,3,8,2,6]=>0000000=>0000000
[4,2,8,3,7,5,6,1]=>[1,6,5,7,3,8,2,4]=>1000000=>0000001
[7,3,4,8,6,5,1,2]=>[2,1,5,6,8,4,3,7]=>0100000=>0000010
[5,3,4,8,7,2,6,1]=>[1,6,2,7,8,4,3,5]=>1000000=>0000001
[4,6,3,8,5,7,2,1]=>[1,2,7,5,8,3,6,4]=>1100000=>0000011
[7,5,3,8,6,2,4,1]=>[1,4,2,6,8,3,5,7]=>1000000=>0000001
[2,6,8,3,7,4,5,1]=>[1,5,4,7,3,8,6,2]=>1000000=>0000001
[2,5,8,3,7,4,6,1]=>[1,6,4,7,3,8,5,2]=>1000000=>0000001
[7,4,3,8,6,2,5,1]=>[1,5,2,6,8,3,4,7]=>1000000=>0000001
[3,5,4,8,7,2,6,1]=>[1,6,2,7,8,4,5,3]=>1000000=>0000001
[4,5,3,8,6,7,2,1]=>[1,2,7,6,8,3,5,4]=>1100000=>0000011
[3,6,7,8,4,5,2,1]=>[1,2,5,4,8,7,6,3]=>1100000=>0000011
[1,8,5,6,4,7,3,2]=>[2,3,7,4,6,5,8,1]=>0000000=>0000000
[2,5,8,6,4,7,3,1]=>[1,3,7,4,6,8,5,2]=>1000000=>0000001
[6,3,7,8,4,5,2,1]=>[1,2,5,4,8,7,3,6]=>1100000=>0000011
[4,3,7,8,5,6,2,1]=>[1,2,6,5,8,7,3,4]=>1100000=>0000011
[4,2,8,6,5,7,3,1]=>[1,3,7,5,6,8,2,4]=>1000000=>0000001
[3,2,8,6,7,4,5,1]=>[1,5,4,7,6,8,2,3]=>1000000=>0000001
[2,3,8,7,5,4,6,1]=>[1,6,4,5,7,8,3,2]=>1000000=>0000001
[1,8,2,7,4,5,6,3]=>[3,6,5,4,7,2,8,1]=>0000000=>0000000
[7,2,8,6,3,4,5,1]=>[1,5,4,3,6,8,2,7]=>1000000=>0000001
[6,2,8,4,5,7,3,1]=>[1,3,7,5,4,8,2,6]=>1000000=>0000001
[5,2,8,4,6,7,3,1]=>[1,3,7,6,4,8,2,5]=>1000000=>0000001
[4,3,6,8,5,7,2,1]=>[1,2,7,5,8,6,3,4]=>1100000=>0000011
[3,4,6,8,7,2,5,1]=>[1,5,2,7,8,6,4,3]=>1000000=>0000001
[7,3,5,8,6,2,4,1]=>[1,4,2,6,8,5,3,7]=>1000000=>0000001
[1,8,3,5,7,4,6,2]=>[2,6,4,7,5,3,8,1]=>0000000=>0000000
[2,7,8,4,5,6,3,1]=>[1,3,6,5,4,8,7,2]=>1000000=>0000001
[3,7,5,8,4,6,2,1]=>[1,2,6,4,8,5,7,3]=>1100000=>0000011
[5,7,4,6,8,3,2,1]=>[1,2,3,8,6,4,7,5]=>1110000=>0000111
[3,6,5,8,4,7,2,1]=>[1,2,7,4,8,5,6,3]=>1100000=>0000011
[2,6,8,4,5,7,3,1]=>[1,3,7,5,4,8,6,2]=>1000000=>0000001
[5,3,6,1,7,2,4,8]=>[8,4,2,7,1,6,3,5]=>0000000=>0000000
[6,4,2,3,7,1,5,8]=>[8,5,1,7,3,2,4,6]=>0000000=>0000000
[8,6,1,2,7,4,5,3]=>[3,5,4,7,2,1,6,8]=>0000001=>1000000
[8,5,7,1,2,4,6,3]=>[3,6,4,2,1,7,5,8]=>0000001=>1000000
[4,1,7,8,2,3,6,5]=>[5,6,3,2,8,7,1,4]=>0000000=>0000000
[6,1,7,5,2,3,4,8]=>[8,4,3,2,5,7,1,6]=>0000000=>0000000
[4,8,7,1,2,3,6,5]=>[5,6,3,2,1,7,8,4]=>0000000=>0000000
[5,8,7,1,2,4,6,3]=>[3,6,4,2,1,7,8,5]=>0000000=>0000000
[5,8,6,4,1,2,3,7]=>[7,3,2,1,4,6,8,5]=>0000000=>0000000
[8,2,4,1,7,3,5,6]=>[6,5,3,7,1,4,2,8]=>0000001=>1000000
[2,7,4,1,8,3,5,6]=>[6,5,3,8,1,4,7,2]=>0000000=>0000000
[5,8,2,6,4,3,1,7]=>[7,1,3,4,6,2,8,5]=>0000000=>0000000
[3,8,6,5,4,2,1,7]=>[7,1,2,4,5,6,8,3]=>0000000=>0000000
[8,7,2,4,5,1,6,3]=>[3,6,1,5,4,2,7,8]=>0000011=>1100000
[5,8,3,7,4,1,6,2]=>[2,6,1,4,7,3,8,5]=>0000000=>0000000
[5,7,1,4,8,6,3,2]=>[2,3,6,8,4,1,7,5]=>0000000=>0000000
[5,3,7,4,8,6,2,1]=>[1,2,6,8,4,7,3,5]=>1100000=>0000011
[5,4,3,6,8,2,7,1]=>[1,7,2,8,6,3,4,5]=>1000000=>0000001
[8,5,1,7,2,6,4,3]=>[3,4,6,2,7,1,5,8]=>0000001=>1000000
[8,7,1,4,5,2,6,3]=>[3,6,2,5,4,1,7,8]=>0000011=>1100000
[7,6,3,1,5,2,8,4]=>[4,8,2,5,1,3,6,7]=>0000000=>0000000
[7,5,1,8,2,6,3,4]=>[4,3,6,2,8,1,5,7]=>0000000=>0000000
[8,7,3,1,5,4,2,6]=>[6,2,4,5,1,3,7,8]=>0000011=>1100000
[5,3,7,6,4,1,2,8]=>[8,2,1,4,6,7,3,5]=>0000000=>0000000
[3,5,7,1,4,6,8,2]=>[2,8,6,4,1,7,5,3]=>0000000=>0000000
[3,5,4,7,1,6,8,2]=>[2,8,6,1,7,4,5,3]=>0000000=>0000000
[3,5,4,7,2,1,6,8]=>[8,6,1,2,7,4,5,3]=>0000000=>0000000
[3,5,4,2,7,1,6,8]=>[8,6,1,7,2,4,5,3]=>0000000=>0000000
[3,2,7,5,1,8,6,4]=>[4,6,8,1,5,7,2,3]=>0000000=>0000000
[3,2,7,5,1,8,4,6]=>[6,4,8,1,5,7,2,3]=>0000000=>0000000
[5,8,3,4,1,7,6,2]=>[2,6,7,1,4,3,8,5]=>0000000=>0000000
[5,8,7,2,4,1,6,3]=>[3,6,1,4,2,7,8,5]=>0000000=>0000000
[3,8,6,4,1,7,5,2]=>[2,5,7,1,4,6,8,3]=>0000000=>0000000
[4,3,5,6,8,1,7,2]=>[2,7,1,8,6,5,3,4]=>0000000=>0000000
[3,7,6,4,1,8,5,2]=>[2,5,8,1,4,6,7,3]=>0000000=>0000000
[3,7,4,1,8,6,5,2]=>[2,5,6,8,1,4,7,3]=>0000000=>0000000
[3,8,4,1,7,6,5,2]=>[2,5,6,7,1,4,8,3]=>0000000=>0000000
[3,2,7,6,1,5,4,8]=>[8,4,5,1,6,7,2,3]=>0000000=>0000000
[5,7,8,2,4,1,6,3]=>[3,6,1,4,2,8,7,5]=>0000000=>0000000
[4,2,5,8,1,6,7,3]=>[3,7,6,1,8,5,2,4]=>0000000=>0000000
[5,8,2,4,1,6,3,7]=>[7,3,6,1,4,2,8,5]=>0000000=>0000000
[8,4,2,6,5,1,3,7]=>[7,3,1,5,6,2,4,8]=>0000001=>1000000
[3,2,6,8,1,5,4,7]=>[7,4,5,1,8,6,2,3]=>0000000=>0000000
[8,3,2,5,6,1,4,7]=>[7,4,1,6,5,2,3,8]=>0000001=>1000000
[3,2,8,6,7,1,5,4]=>[4,5,1,7,6,8,2,3]=>0000000=>0000000
[3,2,6,8,7,1,5,4]=>[4,5,1,7,8,6,2,3]=>0000000=>0000000
[3,2,6,7,1,5,4,8]=>[8,4,5,1,7,6,2,3]=>0000000=>0000000
[8,7,3,2,5,6,1,4]=>[4,1,6,5,2,3,7,8]=>0000011=>1100000
[7,2,8,1,5,3,6,4]=>[4,6,3,5,1,8,2,7]=>0000000=>0000000
[8,4,2,7,5,1,3,6]=>[6,3,1,5,7,2,4,8]=>0000001=>1000000
[7,4,2,8,5,1,3,6]=>[6,3,1,5,8,2,4,7]=>0000000=>0000000
[7,2,4,1,8,3,6,5]=>[5,6,3,8,1,4,2,7]=>0000000=>0000000
[8,5,3,6,2,4,7,1]=>[1,7,4,2,6,3,5,8]=>1000001=>1000001
[2,7,5,4,8,6,1,3]=>[3,1,6,8,4,5,7,2]=>0000000=>0000000
[3,6,4,2,8,7,1,5]=>[5,1,7,8,2,4,6,3]=>0000000=>0000000
[3,6,4,1,8,7,2,5]=>[5,2,7,8,1,4,6,3]=>0000000=>0000000
[7,6,1,3,5,4,8,2]=>[2,8,4,5,3,1,6,7]=>0000000=>0000000
[7,6,5,8,3,1,4,2]=>[2,4,1,3,8,5,6,7]=>0001000=>0001000
[7,2,3,1,5,8,6,4]=>[4,6,8,5,1,3,2,7]=>0000000=>0000000
[7,1,5,6,3,8,4,2]=>[2,4,8,3,6,5,1,7]=>0000000=>0000000
[7,6,1,3,4,5,8,2]=>[2,8,5,4,3,1,6,7]=>0000000=>0000000
[3,4,6,8,7,2,1,5]=>[5,1,2,7,8,6,4,3]=>0000000=>0000000
[3,5,6,8,2,1,7,4]=>[4,7,1,2,8,6,5,3]=>0000000=>0000000
[4,2,1,5,3,7,8,6]=>[6,8,7,3,5,1,2,4]=>0000000=>0000000
[4,2,5,6,3,1,8,7]=>[7,8,1,3,6,5,2,4]=>0000000=>0000000
[3,5,6,8,1,7,2,4]=>[4,2,7,1,8,6,5,3]=>0000000=>0000000
[4,1,5,6,3,2,8,7]=>[7,8,2,3,6,5,1,4]=>0000000=>0000000
[4,5,3,1,7,2,8,6]=>[6,8,2,7,1,3,5,4]=>0000000=>0000000
[2,5,4,7,3,8,6,1]=>[1,6,8,3,7,4,5,2]=>1000000=>0000001
[3,5,7,1,8,4,2,6]=>[6,2,4,8,1,7,5,3]=>0000000=>0000000
[4,1,5,3,2,7,8,6]=>[6,8,7,2,3,5,1,4]=>0000000=>0000000
[4,5,3,7,1,2,8,6]=>[6,8,2,1,7,3,5,4]=>0000000=>0000000
[4,3,6,1,2,7,5,8]=>[8,5,7,2,1,6,3,4]=>0000000=>0000000
[5,1,3,2,4,6,7,8]=>[8,7,6,4,2,3,1,5]=>0000000=>0000000
[3,6,1,7,4,5,2,8]=>[8,2,5,4,7,1,6,3]=>0000000=>0000000
[5,3,1,4,2,6,7,8]=>[8,7,6,2,4,1,3,5]=>0000000=>0000000
[4,5,2,3,7,1,8,6]=>[6,8,1,7,3,2,5,4]=>0000000=>0000000
[4,2,6,1,3,7,5,8]=>[8,5,7,3,1,6,2,4]=>0000000=>0000000
[4,6,2,1,3,7,5,8]=>[8,5,7,3,1,2,6,4]=>0000000=>0000000
[3,6,2,1,7,4,8,5]=>[5,8,4,7,1,2,6,3]=>0000000=>0000000
[3,1,4,7,6,5,2,8]=>[8,2,5,6,7,4,1,3]=>0000000=>0000000
[3,6,2,7,1,5,8,4]=>[4,8,5,1,7,2,6,3]=>0000000=>0000000
[4,6,2,7,1,3,5,8]=>[8,5,3,1,7,2,6,4]=>0000000=>0000000
[3,5,7,1,8,2,6,4]=>[4,6,2,8,1,7,5,3]=>0000000=>0000000
[5,1,4,2,3,6,7,8]=>[8,7,6,3,2,4,1,5]=>0000000=>0000000
[2,6,5,3,4,7,8,1]=>[1,8,7,4,3,5,6,2]=>1000000=>0000001
[5,1,4,3,2,6,7,8]=>[8,7,6,2,3,4,1,5]=>0000000=>0000000
[5,4,1,3,2,6,7,8]=>[8,7,6,2,3,1,4,5]=>0000000=>0000000
[6,2,4,5,1,8,3,7]=>[7,3,8,1,5,4,2,6]=>0000000=>0000000
[2,8,1,6,7,4,5,3]=>[3,5,4,7,6,1,8,2]=>0000000=>0000000
[2,8,6,1,4,7,5,3]=>[3,5,7,4,1,6,8,2]=>0000000=>0000000
[2,8,1,6,4,7,5,3]=>[3,5,7,4,6,1,8,2]=>0000000=>0000000
[6,4,5,2,8,3,1,7]=>[7,1,3,8,2,5,4,6]=>0000000=>0000000
[6,4,5,8,2,3,7,1]=>[1,7,3,2,8,5,4,6]=>1000000=>0000001
[2,4,8,1,3,6,7,5]=>[5,7,6,3,1,8,4,2]=>0000000=>0000000
[6,4,8,2,5,3,7,1]=>[1,7,3,5,2,8,4,6]=>1000000=>0000001
[2,8,1,4,6,7,3,5]=>[5,3,7,6,4,1,8,2]=>0000000=>0000000
[5,1,8,3,6,4,7,2]=>[2,7,4,6,3,8,1,5]=>0000000=>0000000
[1,8,4,6,7,2,5,3]=>[3,5,2,7,6,4,8,1]=>0000000=>0000000
[5,3,8,1,7,2,6,4]=>[4,6,2,7,1,8,3,5]=>0000000=>0000000
[6,3,4,8,2,7,5,1]=>[1,5,7,2,8,4,3,6]=>1000000=>0000001
[4,2,7,6,3,1,8,5]=>[5,8,1,3,6,7,2,4]=>0000000=>0000000
[7,6,3,1,8,4,2,5]=>[5,2,4,8,1,3,6,7]=>0000000=>0000000
[8,7,5,2,4,6,3,1]=>[1,3,6,4,2,5,7,8]=>1000011=>1100001
[7,5,2,1,8,3,6,4]=>[4,6,3,8,1,2,5,7]=>0000000=>0000000
[7,5,2,8,6,3,1,4]=>[4,1,3,6,8,2,5,7]=>0000000=>0000000
[8,7,5,2,1,3,6,4]=>[4,6,3,1,2,5,7,8]=>0000011=>1100000
[1,3,7,6,5,8,2,4]=>[4,2,8,5,6,7,3,1]=>0000000=>0000000
[6,4,7,5,2,1,3,8]=>[8,3,1,2,5,7,4,6]=>0000000=>0000000
[6,3,1,4,8,7,5,2]=>[2,5,7,8,4,1,3,6]=>0000000=>0000000
[6,3,8,7,4,1,5,2]=>[2,5,1,4,7,8,3,6]=>0000000=>0000000
[4,6,7,2,5,3,1,8]=>[8,1,3,5,2,7,6,4]=>0000000=>0000000
[3,6,7,4,8,1,5,2]=>[2,5,1,8,4,7,6,3]=>0000000=>0000000
[3,4,6,8,7,1,5,2]=>[2,5,1,7,8,6,4,3]=>0000000=>0000000
[1,4,7,8,2,6,5,3]=>[3,5,6,2,8,7,4,1]=>0000000=>0000000
[2,4,7,8,1,6,5,3]=>[3,5,6,1,8,7,4,2]=>0000000=>0000000
[4,2,6,8,7,1,5,3]=>[3,5,1,7,8,6,2,4]=>0000000=>0000000
[6,8,3,7,1,5,4,2]=>[2,4,5,1,7,3,8,6]=>0000000=>0000000
[2,6,8,4,1,7,5,3]=>[3,5,7,1,4,8,6,2]=>0000000=>0000000
[4,5,8,6,3,1,7,2]=>[2,7,1,3,6,8,5,4]=>0000000=>0000000
[2,5,8,4,7,3,6,1]=>[1,6,3,7,4,8,5,2]=>1000000=>0000001
[4,5,8,1,7,6,2,3]=>[3,2,6,7,1,8,5,4]=>0000000=>0000000
[3,5,8,4,7,1,6,2]=>[2,6,1,7,4,8,5,3]=>0000000=>0000000
[3,6,4,8,7,5,2,1]=>[1,2,5,7,8,4,6,3]=>1100000=>0000011
[2,6,4,3,7,1,8,5]=>[5,8,1,7,3,4,6,2]=>0000000=>0000000
[7,2,3,4,1,6,8,5]=>[5,8,6,1,4,3,2,7]=>0000000=>0000000
[1,2,4,3,8,5,7,6]=>[6,7,5,8,3,4,2,1]=>0000000=>0000000
[7,3,8,6,1,4,2,5]=>[5,2,4,1,6,8,3,7]=>0000000=>0000000
[1,5,8,4,7,6,2,3]=>[3,2,6,7,4,8,5,1]=>0000000=>0000000
[3,5,8,1,6,7,2,4]=>[4,2,7,6,1,8,5,3]=>0000000=>0000000
[4,1,6,5,8,2,7,3]=>[3,7,2,8,5,6,1,4]=>0000000=>0000000
[3,1,6,5,8,4,7,2]=>[2,7,4,8,5,6,1,3]=>0000000=>0000000
[3,2,6,5,8,4,7,1]=>[1,7,4,8,5,6,2,3]=>1000000=>0000001
[4,3,7,1,6,5,8,2]=>[2,8,5,6,1,7,3,4]=>0000000=>0000000
[5,1,6,4,8,2,7,3]=>[3,7,2,8,4,6,1,5]=>0000000=>0000000
[5,2,6,4,8,1,7,3]=>[3,7,1,8,4,6,2,5]=>0000000=>0000000
[4,3,7,5,8,1,6,2]=>[2,6,1,8,5,7,3,4]=>0000000=>0000000
[4,3,7,5,8,2,6,1]=>[1,6,2,8,5,7,3,4]=>1000000=>0000001
[5,3,7,4,8,2,6,1]=>[1,6,2,8,4,7,3,5]=>1000000=>0000001
[5,3,7,4,8,1,6,2]=>[2,6,1,8,4,7,3,5]=>0000000=>0000000
[5,4,8,1,6,2,7,3]=>[3,7,2,6,1,8,4,5]=>0000000=>0000000
[4,3,7,1,5,2,8,6]=>[6,8,2,5,1,7,3,4]=>0000000=>0000000
[5,4,8,2,6,3,7,1]=>[1,7,3,6,2,8,4,5]=>1000000=>0000001
[4,1,8,7,6,3,2,5]=>[5,2,3,6,7,8,1,4]=>0000000=>0000000
[6,8,3,2,1,4,7,5]=>[5,7,4,1,2,3,8,6]=>0000000=>0000000
[8,4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4,8]=>1110001=>1000111
[6,1,2,7,5,8,4,3]=>[3,4,8,5,7,2,1,6]=>0000000=>0000000
[6,2,5,7,3,8,4,1]=>[1,4,8,3,7,5,2,6]=>1000000=>0000001
[7,3,4,6,2,8,5,1]=>[1,5,8,2,6,4,3,7]=>1000000=>0000001
[4,5,2,6,8,3,7,1]=>[1,7,3,8,6,2,5,4]=>1000000=>0000001
[4,8,3,2,5,7,6,1]=>[1,6,7,5,2,3,8,4]=>1000000=>0000001
[6,8,5,3,4,7,2,1]=>[1,2,7,4,3,5,8,6]=>1100000=>0000011
[6,1,7,5,8,4,2,3]=>[3,2,4,8,5,7,1,6]=>0000000=>0000000
[6,8,3,4,7,2,5,1]=>[1,5,2,7,4,3,8,6]=>1000000=>0000001
[8,3,4,7,6,2,5,1]=>[1,5,2,6,7,4,3,8]=>1000001=>1000001
[4,7,6,2,5,8,3,1]=>[1,3,8,5,2,6,7,4]=>1000000=>0000001
[6,8,3,5,1,4,7,2]=>[2,7,4,1,5,3,8,6]=>0000000=>0000000
[7,5,3,4,8,2,6,1]=>[1,6,2,8,4,3,5,7]=>1000000=>0000001
[5,3,8,2,4,7,6,1]=>[1,6,7,4,2,8,3,5]=>1000000=>0000001
[3,7,4,6,2,8,5,1]=>[1,5,8,2,6,4,7,3]=>1000000=>0000001
[5,8,2,4,3,7,6,1]=>[1,6,7,3,4,2,8,5]=>1000000=>0000001
[3,4,5,8,2,7,6,1]=>[1,6,7,2,8,5,4,3]=>1000000=>0000001
[6,8,3,4,5,2,7,1]=>[1,7,2,5,4,3,8,6]=>1000000=>0000001
[7,4,6,3,2,8,5,1]=>[1,5,8,2,3,6,4,7]=>1000000=>0000001
[6,5,3,8,4,2,7,1]=>[1,7,2,4,8,3,5,6]=>1000000=>0000001
[3,1,6,8,4,7,5,2]=>[2,5,7,4,8,6,1,3]=>0000000=>0000000
[8,3,6,1,5,7,4,2]=>[2,4,7,5,1,6,3,8]=>0000001=>1000000
[2,7,3,5,8,6,4,1]=>[1,4,6,8,5,3,7,2]=>1000000=>0000001
[2,4,7,5,8,6,1,3]=>[3,1,6,8,5,7,4,2]=>0000000=>0000000
[2,4,6,8,1,7,5,3]=>[3,5,7,1,8,6,4,2]=>0000000=>0000000
[7,4,3,8,6,2,1,5]=>[5,1,2,6,8,3,4,7]=>0000000=>0000000
[4,3,6,2,1,8,5,7]=>[7,5,8,1,2,6,3,4]=>0000000=>0000000
[3,6,4,2,7,5,1,8]=>[8,1,5,7,2,4,6,3]=>0000000=>0000000
[5,8,4,2,3,6,7,1]=>[1,7,6,3,2,4,8,5]=>1000000=>0000001
[6,8,4,2,3,7,5,1]=>[1,5,7,3,2,4,8,6]=>1000000=>0000001
[3,6,4,2,1,8,7,5]=>[5,7,8,1,2,4,6,3]=>0000000=>0000000
[2,8,6,5,4,1,7,3]=>[3,7,1,4,5,6,8,2]=>0000000=>0000000
[3,8,6,2,5,7,1,4]=>[4,1,7,5,2,6,8,3]=>0000000=>0000000
[2,6,5,4,1,7,8,3]=>[3,8,7,1,4,5,6,2]=>0000000=>0000000
[6,5,7,3,2,8,1,4]=>[4,1,8,2,3,7,5,6]=>0000000=>0000000
[3,6,4,2,7,1,8,5]=>[5,8,1,7,2,4,6,3]=>0000000=>0000000
[1,2,6,5,8,7,3,4]=>[4,3,7,8,5,6,2,1]=>0000000=>0000000
[5,6,3,4,8,7,2,1]=>[1,2,7,8,4,3,6,5]=>1100000=>0000011
[8,5,3,7,4,6,2,1]=>[1,2,6,4,7,3,5,8]=>1100001=>1000011
[7,1,2,8,3,6,4,5]=>[5,4,6,3,8,2,1,7]=>0000000=>0000000
[7,1,6,2,3,5,8,4]=>[4,8,5,3,2,6,1,7]=>0000000=>0000000
[6,8,7,3,4,5,2,1]=>[1,2,5,4,3,7,8,6]=>1100100=>0010011
[8,1,6,2,3,5,4,7]=>[7,4,5,3,2,6,1,8]=>0000001=>1000000
[8,6,2,3,5,1,4,7]=>[7,4,1,5,3,2,6,8]=>0000001=>1000000
[8,6,2,4,1,5,3,7]=>[7,3,5,1,4,2,6,8]=>0000001=>1000000
[8,3,6,1,5,4,2,7]=>[7,2,4,5,1,6,3,8]=>0000001=>1000000
[3,4,8,7,1,6,5,2]=>[2,5,6,1,7,8,4,3]=>0000000=>0000000
[8,1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1,8]=>0000001=>1000000
[8,2,7,1,4,5,6,3]=>[3,6,5,4,1,7,2,8]=>0000001=>1000000
[8,2,3,7,1,6,5,4]=>[4,5,6,1,7,3,2,8]=>0000001=>1000000
[8,2,4,3,7,6,1,5]=>[5,1,6,7,3,4,2,8]=>0000001=>1000000
[4,2,8,3,7,6,5,1]=>[1,5,6,7,3,8,2,4]=>1000000=>0000001
[7,3,2,8,5,6,1,4]=>[4,1,6,5,8,2,3,7]=>0000000=>0000000
[7,2,5,4,1,6,3,8]=>[8,3,6,1,4,5,2,7]=>0000000=>0000000
[4,7,6,3,2,5,8,1]=>[1,8,5,2,3,6,7,4]=>1000000=>0000001
[4,7,6,5,1,3,8,2]=>[2,8,3,1,5,6,7,4]=>0000000=>0000000
[1,7,6,5,2,3,8,4]=>[4,8,3,2,5,6,7,1]=>0000000=>0000000
[1,7,6,5,8,3,2,4]=>[4,2,3,8,5,6,7,1]=>0000000=>0000000
[5,7,6,2,1,4,8,3]=>[3,8,4,1,2,6,7,5]=>0000000=>0000000
[6,5,8,3,4,1,7,2]=>[2,7,1,4,3,8,5,6]=>0000000=>0000000
[4,7,1,6,8,2,5,3]=>[3,5,2,8,6,1,7,4]=>0000000=>0000000
[4,3,2,8,5,1,6,7]=>[7,6,1,5,8,2,3,4]=>0000000=>0000000
[3,7,6,5,8,1,2,4]=>[4,2,1,8,5,6,7,3]=>0000000=>0000000
[7,1,2,6,3,5,4,8]=>[8,4,5,3,6,2,1,7]=>0000000=>0000000
[6,2,7,5,8,4,3,1]=>[1,3,4,8,5,7,2,6]=>1000000=>0000001
[7,2,5,1,4,6,3,8]=>[8,3,6,4,1,5,2,7]=>0000000=>0000000
[7,2,6,3,4,5,1,8]=>[8,1,5,4,3,6,2,7]=>0000000=>0000000
[7,4,3,1,5,2,6,8]=>[8,6,2,5,1,3,4,7]=>0000000=>0000000
[6,7,8,4,2,5,3,1]=>[1,3,5,2,4,8,7,6]=>1000100=>0010001
[6,1,2,5,7,8,4,3]=>[3,4,8,7,5,2,1,6]=>0000000=>0000000
[3,7,8,6,2,5,1,4]=>[4,1,5,2,6,8,7,3]=>0000000=>0000000
[3,6,1,4,8,7,5,2]=>[2,5,7,8,4,1,6,3]=>0000000=>0000000
[4,1,2,7,8,5,3,6]=>[6,3,5,8,7,2,1,4]=>0000000=>0000000
[4,7,3,1,2,6,8,5]=>[5,8,6,2,1,3,7,4]=>0000000=>0000000
[3,6,4,5,8,1,7,2]=>[2,7,1,8,5,4,6,3]=>0000000=>0000000
[3,7,6,1,5,8,2,4]=>[4,2,8,5,1,6,7,3]=>0000000=>0000000
[3,7,6,5,1,4,2,8]=>[8,2,4,1,5,6,7,3]=>0000000=>0000000
[3,8,5,4,6,7,1,2]=>[2,1,7,6,4,5,8,3]=>0100000=>0000010
[3,8,5,6,4,2,7,1]=>[1,7,2,4,6,5,8,3]=>1000000=>0000001
[1,2,6,4,3,5,8,7]=>[7,8,5,3,4,6,2,1]=>0000000=>0000000
[3,2,6,4,7,8,5,1]=>[1,5,8,7,4,6,2,3]=>1000000=>0000001
[4,2,7,5,8,3,1,6]=>[6,1,3,8,5,7,2,4]=>0000000=>0000000
[4,8,1,6,2,7,5,3]=>[3,5,7,2,6,1,8,4]=>0000000=>0000000
[5,7,2,3,1,4,6,8]=>[8,6,4,1,3,2,7,5]=>0000000=>0000000
[6,5,1,3,2,7,4,8]=>[8,4,7,2,3,1,5,6]=>0000000=>0000000
[6,5,2,3,1,7,4,8]=>[8,4,7,1,3,2,5,6]=>0000000=>0000000
[6,1,8,4,2,7,5,3]=>[3,5,7,2,4,8,1,6]=>0000000=>0000000
[5,7,2,3,8,4,1,6]=>[6,1,4,8,3,2,7,5]=>0000000=>0000000
[5,2,1,4,7,8,3,6]=>[6,3,8,7,4,1,2,5]=>0000000=>0000000
[5,6,2,7,3,4,8,1]=>[1,8,4,3,7,2,6,5]=>1000000=>0000001
[5,2,6,8,1,7,4,3]=>[3,4,7,1,8,6,2,5]=>0000000=>0000000
[3,7,8,6,1,2,4,5]=>[5,4,2,1,6,8,7,3]=>0000000=>0000000
[2,7,6,8,5,1,3,4]=>[4,3,1,5,8,6,7,2]=>0000000=>0000000
[2,7,8,6,1,5,4,3]=>[3,4,5,1,6,8,7,2]=>0000000=>0000000
[2,7,6,8,5,3,1,4]=>[4,1,3,5,8,6,7,2]=>0000000=>0000000
[4,7,6,8,2,1,3,5]=>[5,3,1,2,8,6,7,4]=>0000000=>0000000
[4,7,8,6,1,3,2,5]=>[5,2,3,1,6,8,7,4]=>0000000=>0000000
[1,7,8,6,5,2,3,4]=>[4,3,2,5,6,8,7,1]=>0000000=>0000000
[5,6,1,8,3,7,4,2]=>[2,4,7,3,8,1,6,5]=>0000000=>0000000
[4,7,6,8,1,2,3,5]=>[5,3,2,1,8,6,7,4]=>0000000=>0000000
[1,4,6,2,5,7,8,3]=>[3,8,7,5,2,6,4,1]=>0000000=>0000000
[2,4,6,1,5,7,3,8]=>[8,3,7,5,1,6,4,2]=>0000000=>0000000
[4,7,2,3,1,5,6,8]=>[8,6,5,1,3,2,7,4]=>0000000=>0000000
[7,4,6,2,8,3,5,1]=>[1,5,3,8,2,6,4,7]=>1000000=>0000001
[7,3,5,1,4,8,2,6]=>[6,2,8,4,1,5,3,7]=>0000000=>0000000
[2,4,1,8,6,7,5,3]=>[3,5,7,6,8,1,4,2]=>0000000=>0000000
[4,3,8,2,5,7,1,6]=>[6,1,7,5,2,8,3,4]=>0000000=>0000000
[3,5,6,1,4,2,8,7]=>[7,8,2,4,1,6,5,3]=>0000000=>0000000
[2,1,5,7,8,3,6,4]=>[4,6,3,8,7,5,1,2]=>0000000=>0000000
[4,7,5,8,6,3,1,2]=>[2,1,3,6,8,5,7,4]=>0110000=>0000110
[4,7,1,8,3,5,6,2]=>[2,6,5,3,8,1,7,4]=>0000000=>0000000
[2,7,5,1,8,3,6,4]=>[4,6,3,8,1,5,7,2]=>0000000=>0000000
[5,1,8,7,4,3,6,2]=>[2,6,3,4,7,8,1,5]=>0000000=>0000000
[8,4,7,6,3,5,1,2]=>[2,1,5,3,6,7,4,8]=>0100001=>1000010
[6,5,1,3,8,7,4,2]=>[2,4,7,8,3,1,5,6]=>0000000=>0000000
[6,1,8,5,3,7,2,4]=>[4,2,7,3,5,8,1,6]=>0000000=>0000000
[7,6,4,1,3,5,8,2]=>[2,8,5,3,1,4,6,7]=>0000000=>0000000
[3,4,7,2,5,6,1,8]=>[8,1,6,5,2,7,4,3]=>0000000=>0000000
[3,7,8,2,6,1,5,4]=>[4,5,1,6,2,8,7,3]=>0000000=>0000000
[4,8,6,5,1,2,7,3]=>[3,7,2,1,5,6,8,4]=>0000000=>0000000
[7,4,6,8,1,3,5,2]=>[2,5,3,1,8,6,4,7]=>0000000=>0000000
[3,2,5,6,1,4,8,7]=>[7,8,4,1,6,5,2,3]=>0000000=>0000000
[1,8,4,2,5,7,6,3]=>[3,6,7,5,2,4,8,1]=>0000000=>0000000
[2,5,8,3,7,1,6,4]=>[4,6,1,7,3,8,5,2]=>0000000=>0000000
[7,8,2,1,4,6,5,3]=>[3,5,6,4,1,2,8,7]=>0000010=>0100000
[5,3,8,6,2,7,1,4]=>[4,1,7,2,6,8,3,5]=>0000000=>0000000
[6,8,1,4,5,2,3,7]=>[7,3,2,5,4,1,8,6]=>0000000=>0000000
[5,3,7,1,2,4,8,6]=>[6,8,4,2,1,7,3,5]=>0000000=>0000000
[4,7,8,1,2,6,3,5]=>[5,3,6,2,1,8,7,4]=>0000000=>0000000
[8,7,1,5,6,2,3,4]=>[4,3,2,6,5,1,7,8]=>0000011=>1100000
[1,7,6,5,8,2,3,4]=>[4,3,2,8,5,6,7,1]=>0000000=>0000000
[5,7,8,1,2,6,3,4]=>[4,3,6,2,1,8,7,5]=>0000000=>0000000
[3,7,1,2,8,4,6,5]=>[5,6,4,8,2,1,7,3]=>0000000=>0000000
[2,6,4,7,5,3,8,1]=>[1,8,3,5,7,4,6,2]=>1000000=>0000001
[5,4,7,1,3,2,8,6]=>[6,8,2,3,1,7,4,5]=>0000000=>0000000
[4,7,6,2,3,1,8,5]=>[5,8,1,3,2,6,7,4]=>0000000=>0000000
[4,7,3,1,8,5,6,2]=>[2,6,5,8,1,3,7,4]=>0000000=>0000000
[1,5,7,6,8,2,3,4]=>[4,3,2,8,6,7,5,1]=>0000000=>0000000
[5,2,4,8,1,7,3,6]=>[6,3,7,1,8,4,2,5]=>0000000=>0000000
[6,2,7,5,8,1,3,4]=>[4,3,1,8,5,7,2,6]=>0000000=>0000000
[5,4,6,7,8,1,3,2]=>[2,3,1,8,7,6,4,5]=>0010000=>0000100
[5,3,6,7,8,1,4,2]=>[2,4,1,8,7,6,3,5]=>0000000=>0000000
[6,3,7,5,4,8,2,1]=>[1,2,8,4,5,7,3,6]=>1100000=>0000011
[6,3,2,8,5,4,1,7]=>[7,1,4,5,8,2,3,6]=>0000000=>0000000
[5,3,4,2,7,1,6,8]=>[8,6,1,7,2,4,3,5]=>0000000=>0000000
[7,1,5,3,2,6,4,8]=>[8,4,6,2,3,5,1,7]=>0000000=>0000000
[3,7,5,4,2,1,6,8]=>[8,6,1,2,4,5,7,3]=>0000000=>0000000
[2,7,6,4,1,3,5,8]=>[8,5,3,1,4,6,7,2]=>0000000=>0000000
[5,8,3,2,7,4,1,6]=>[6,1,4,7,2,3,8,5]=>0000000=>0000000
[2,5,6,4,1,3,7,8]=>[8,7,3,1,4,6,5,2]=>0000000=>0000000
[6,4,1,7,2,5,3,8]=>[8,3,5,2,7,1,4,6]=>0000000=>0000000
[2,4,1,6,5,3,7,8]=>[8,7,3,5,6,1,4,2]=>0000000=>0000000
[7,1,2,6,5,4,3,8]=>[8,3,4,5,6,2,1,7]=>0000000=>0000000
[7,5,1,4,6,2,3,8]=>[8,3,2,6,4,1,5,7]=>0000000=>0000000
[5,4,1,3,2,8,6,7]=>[7,6,8,2,3,1,4,5]=>0000000=>0000000
[4,7,3,2,8,5,1,6]=>[6,1,5,8,2,3,7,4]=>0000000=>0000000
[1,6,2,7,4,8,5,3]=>[3,5,8,4,7,2,6,1]=>0000000=>0000000
[1,5,3,8,4,7,6,2]=>[2,6,7,4,8,3,5,1]=>0000000=>0000000
[1,6,3,8,4,7,5,2]=>[2,5,7,4,8,3,6,1]=>0000000=>0000000
[1,6,2,8,3,7,5,4]=>[4,5,7,3,8,2,6,1]=>0000000=>0000000
[8,6,3,1,5,4,2,7]=>[7,2,4,5,1,3,6,8]=>0000001=>1000000
[5,3,8,7,4,6,2,1]=>[1,2,6,4,7,8,3,5]=>1100000=>0000011
[6,8,7,3,1,5,4,2]=>[2,4,5,1,3,7,8,6]=>0000100=>0010000
[6,8,5,4,1,3,7,2]=>[2,7,3,1,4,5,8,6]=>0000000=>0000000
[4,8,7,6,5,1,3,2]=>[2,3,1,5,6,7,8,4]=>0010000=>0000100
[3,8,7,5,1,6,2,4]=>[4,2,6,1,5,7,8,3]=>0000000=>0000000
[6,8,7,3,5,2,1,4]=>[4,1,2,5,3,7,8,6]=>0000100=>0010000
[4,8,7,6,5,2,1,3]=>[3,1,2,5,6,7,8,4]=>0010000=>0000100
[4,8,7,5,1,6,2,3]=>[3,2,6,1,5,7,8,4]=>0000000=>0000000
[2,4,6,3,5,7,8,1]=>[1,8,7,5,3,6,4,2]=>1000000=>0000001
[3,6,4,2,5,7,8,1]=>[1,8,7,5,2,4,6,3]=>1000000=>0000001
[2,3,6,1,5,7,8,4]=>[4,8,7,5,1,6,3,2]=>0000000=>0000000
[4,3,6,2,5,7,8,1]=>[1,8,7,5,2,6,3,4]=>1000000=>0000001
[2,4,1,6,5,7,8,3]=>[3,8,7,5,6,1,4,2]=>0000000=>0000000
[7,4,6,1,3,2,5,8]=>[8,5,2,3,1,6,4,7]=>0000000=>0000000
[1,4,5,8,6,3,2,7]=>[7,2,3,6,8,5,4,1]=>0000000=>0000000
[7,1,2,5,6,3,4,8]=>[8,4,3,6,5,2,1,7]=>0000000=>0000000
[5,1,4,3,6,7,8,2]=>[2,8,7,6,3,4,1,5]=>0000000=>0000000
[1,7,6,8,5,2,4,3]=>[3,4,2,5,8,6,7,1]=>0000000=>0000000
[3,8,6,4,5,7,2,1]=>[1,2,7,5,4,6,8,3]=>1100000=>0000011
[4,3,6,2,1,8,7,5]=>[5,7,8,1,2,6,3,4]=>0000000=>0000000
[7,2,4,5,1,6,3,8]=>[8,3,6,1,5,4,2,7]=>0000000=>0000000
[1,8,7,5,3,6,4,2]=>[2,4,6,3,5,7,8,1]=>0000000=>0000000
[7,3,8,4,1,6,2,5]=>[5,2,6,1,4,8,3,7]=>0000000=>0000000
[2,4,5,8,7,3,1,6]=>[6,1,3,7,8,5,4,2]=>0000000=>0000000
[4,3,1,5,6,2,8,7]=>[7,8,2,6,5,1,3,4]=>0000000=>0000000
[3,4,5,8,7,1,2,6]=>[6,2,1,7,8,5,4,3]=>0000000=>0000000
[4,7,1,5,6,2,8,3]=>[3,8,2,6,5,1,7,4]=>0000000=>0000000
[5,1,4,6,7,2,8,3]=>[3,8,2,7,6,4,1,5]=>0000000=>0000000
[2,1,6,5,3,7,8,4]=>[4,8,7,3,5,6,1,2]=>0000000=>0000000
[6,7,1,3,8,4,5,2]=>[2,5,4,8,3,1,7,6]=>0000000=>0000000
[6,7,3,2,1,8,4,5]=>[5,4,8,1,2,3,7,6]=>0000000=>0000000
[2,5,7,3,1,4,8,6]=>[6,8,4,1,3,7,5,2]=>0000000=>0000000
[2,7,5,8,1,6,3,4]=>[4,3,6,1,8,5,7,2]=>0000000=>0000000
[1,6,7,3,8,5,4,2]=>[2,4,5,8,3,7,6,1]=>0000000=>0000000
[2,3,8,7,1,6,5,4]=>[4,5,6,1,7,8,3,2]=>0000000=>0000000
[8,5,1,7,3,6,2,4]=>[4,2,6,3,7,1,5,8]=>0000001=>1000000
[8,6,1,5,4,3,2,7]=>[7,2,3,4,5,1,6,8]=>0000001=>1000000
[8,7,3,1,5,4,6,2]=>[2,6,4,5,1,3,7,8]=>0000011=>1100000
[6,2,5,4,8,3,1,7]=>[7,1,3,8,4,5,2,6]=>0000000=>0000000
[5,4,7,6,3,1,8,2]=>[2,8,1,3,6,7,4,5]=>0000000=>0000000
[1,5,6,7,3,8,2,4]=>[4,2,8,3,7,6,5,1]=>0000000=>0000000
[8,2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2,8]=>0000001=>1000000
[8,7,5,1,3,4,6,2]=>[2,6,4,3,1,5,7,8]=>0000011=>1100000
[8,7,2,1,4,6,5,3]=>[3,5,6,4,1,2,7,8]=>0000011=>1100000
[3,7,1,5,8,4,6,2]=>[2,6,4,8,5,1,7,3]=>0000000=>0000000
[3,2,7,6,4,8,5,1]=>[1,5,8,4,6,7,2,3]=>1000000=>0000001
[1,3,7,6,4,8,5,2]=>[2,5,8,4,6,7,3,1]=>0000000=>0000000
[1,2,7,5,8,4,6,3]=>[3,6,4,8,5,7,2,1]=>0000000=>0000000
[6,4,1,8,5,3,2,7]=>[7,2,3,5,8,1,4,6]=>0000000=>0000000
[7,4,1,6,5,3,2,8]=>[8,2,3,5,6,1,4,7]=>0000000=>0000000
[5,8,6,1,4,3,2,7]=>[7,2,3,4,1,6,8,5]=>0000000=>0000000
[6,7,5,1,4,3,2,8]=>[8,2,3,4,1,5,7,6]=>0000000=>0000000
[3,1,6,4,5,2,7,8]=>[8,7,2,5,4,6,1,3]=>0000000=>0000000
[1,8,6,3,4,2,7,5]=>[5,7,2,4,3,6,8,1]=>0000000=>0000000
[4,6,7,3,2,1,8,5]=>[5,8,1,2,3,7,6,4]=>0000000=>0000000
[5,6,3,7,4,2,8,1]=>[1,8,2,4,7,3,6,5]=>1000000=>0000001
[6,2,3,1,7,5,8,4]=>[4,8,5,7,1,3,2,6]=>0000000=>0000000
[7,6,3,8,4,5,2,1]=>[1,2,5,4,8,3,6,7]=>1100000=>0000011
[6,2,7,8,5,4,3,1]=>[1,3,4,5,8,7,2,6]=>1000000=>0000001
[6,8,1,7,4,5,3,2]=>[2,3,5,4,7,1,8,6]=>0000000=>0000000
[4,6,7,3,5,1,2,8]=>[8,2,1,5,3,7,6,4]=>0000000=>0000000
[5,2,3,4,7,8,1,6]=>[6,1,8,7,4,3,2,5]=>0000000=>0000000
[1,2,5,7,8,4,6,3]=>[3,6,4,8,7,5,2,1]=>0000000=>0000000
[8,1,4,6,5,2,7,3]=>[3,7,2,5,6,4,1,8]=>0000001=>1000000
[5,2,4,3,7,1,6,8]=>[8,6,1,7,3,4,2,5]=>0000000=>0000000
[8,4,6,5,1,2,7,3]=>[3,7,2,1,5,6,4,8]=>0000001=>1000000
[1,5,6,3,7,8,2,4]=>[4,2,8,7,3,6,5,1]=>0000000=>0000000
[1,6,4,7,2,8,5,3]=>[3,5,8,2,7,4,6,1]=>0000000=>0000000
[7,4,2,8,1,6,3,5]=>[5,3,6,1,8,2,4,7]=>0000000=>0000000
[5,2,8,6,1,4,3,7]=>[7,3,4,1,6,8,2,5]=>0000000=>0000000
[3,2,7,4,8,6,5,1]=>[1,5,6,8,4,7,2,3]=>1000000=>0000001
[7,2,3,8,6,5,4,1]=>[1,4,5,6,8,3,2,7]=>1000000=>0000001
[3,5,1,7,8,2,6,4]=>[4,6,2,8,7,1,5,3]=>0000000=>0000000
[6,4,5,8,3,2,1,7]=>[7,1,2,3,8,5,4,6]=>0000000=>0000000
[8,4,3,1,6,2,7,5]=>[5,7,2,6,1,3,4,8]=>0000001=>1000000
[7,4,3,1,8,6,2,5]=>[5,2,6,8,1,3,4,7]=>0000000=>0000000
[6,1,2,8,3,5,7,4]=>[4,7,5,3,8,2,1,6]=>0000000=>0000000
[6,4,3,8,5,2,1,7]=>[7,1,2,5,8,3,4,6]=>0000000=>0000000
[6,2,8,7,5,4,1,3]=>[3,1,4,5,7,8,2,6]=>0000000=>0000000
[6,3,2,1,8,7,4,5]=>[5,4,7,8,1,2,3,6]=>0000000=>0000000
[6,2,3,1,8,7,4,5]=>[5,4,7,8,1,3,2,6]=>0000000=>0000000
[7,1,4,6,8,2,5,3]=>[3,5,2,8,6,4,1,7]=>0000000=>0000000
[8,4,6,1,2,7,5,3]=>[3,5,7,2,1,6,4,8]=>0000001=>1000000
[8,6,1,5,3,7,4,2]=>[2,4,7,3,5,1,6,8]=>0000001=>1000000
[8,3,6,4,1,7,5,2]=>[2,5,7,1,4,6,3,8]=>0000001=>1000000
[7,3,1,5,2,8,6,4]=>[4,6,8,2,5,1,3,7]=>0000000=>0000000
[7,1,6,4,2,8,5,3]=>[3,5,8,2,4,6,1,7]=>0000000=>0000000
[5,8,6,1,2,7,4,3]=>[3,4,7,2,1,6,8,5]=>0000000=>0000000
[6,1,5,8,3,4,7,2]=>[2,7,4,3,8,5,1,6]=>0000000=>0000000
[6,8,1,2,4,7,5,3]=>[3,5,7,4,2,1,8,6]=>0000000=>0000000
[7,8,5,1,2,6,4,3]=>[3,4,6,2,1,5,8,7]=>0000010=>0100000
[8,6,4,1,3,7,5,2]=>[2,5,7,3,1,4,6,8]=>0000001=>1000000
[8,6,3,4,1,7,5,2]=>[2,5,7,1,4,3,6,8]=>0000001=>1000000
[8,5,3,6,1,7,4,2]=>[2,4,7,1,6,3,5,8]=>0000001=>1000000
[8,6,2,1,4,7,5,3]=>[3,5,7,4,1,2,6,8]=>0000001=>1000000
[7,1,5,3,6,8,4,2]=>[2,4,8,6,3,5,1,7]=>0000000=>0000000
[8,6,1,4,5,7,3,2]=>[2,3,7,5,4,1,6,8]=>0000001=>1000000
[8,5,6,1,2,7,4,3]=>[3,4,7,2,1,6,5,8]=>0000001=>1000000
[8,4,5,6,1,7,3,2]=>[2,3,7,1,6,5,4,8]=>0000001=>1000000
[4,5,8,6,2,7,3,1]=>[1,3,7,2,6,8,5,4]=>1000000=>0000001
[4,5,8,3,7,1,2,6]=>[6,2,1,7,3,8,5,4]=>0000000=>0000000
[4,5,8,3,7,2,1,6]=>[6,1,2,7,3,8,5,4]=>0000000=>0000000
[3,8,6,2,5,1,7,4]=>[4,7,1,5,2,6,8,3]=>0000000=>0000000
[3,7,8,5,4,1,6,2]=>[2,6,1,4,5,8,7,3]=>0000000=>0000000
[5,1,3,2,6,7,4,8]=>[8,4,7,6,2,3,1,5]=>0000000=>0000000
[4,6,5,1,7,3,8,2]=>[2,8,3,7,1,5,6,4]=>0000000=>0000000
[1,6,5,3,7,8,2,4]=>[4,2,8,7,3,5,6,1]=>0000000=>0000000
[3,6,5,2,4,7,1,8]=>[8,1,7,4,2,5,6,3]=>0000000=>0000000
[3,6,5,8,2,7,1,4]=>[4,1,7,2,8,5,6,3]=>0000000=>0000000
[4,8,1,3,7,5,6,2]=>[2,6,5,7,3,1,8,4]=>0000000=>0000000
[5,6,8,7,3,1,2,4]=>[4,2,1,3,7,8,6,5]=>0001000=>0001000
[6,7,5,3,8,1,2,4]=>[4,2,1,8,3,5,7,6]=>0000000=>0000000
[6,2,3,4,7,1,8,5]=>[5,8,1,7,4,3,2,6]=>0000000=>0000000
[6,8,5,7,3,1,2,4]=>[4,2,1,3,7,5,8,6]=>0001000=>0001000
[6,8,7,5,3,1,2,4]=>[4,2,1,3,5,7,8,6]=>0001100=>0011000
[6,5,7,3,8,1,2,4]=>[4,2,1,8,3,7,5,6]=>0000000=>0000000
[2,5,6,3,7,1,8,4]=>[4,8,1,7,3,6,5,2]=>0000000=>0000000
[8,2,1,4,6,7,3,5]=>[5,3,7,6,4,1,2,8]=>0000001=>1000000
[3,7,6,1,2,4,8,5]=>[5,8,4,2,1,6,7,3]=>0000000=>0000000
[6,1,5,3,4,8,2,7]=>[7,2,8,4,3,5,1,6]=>0000000=>0000000
[8,3,1,4,7,2,5,6]=>[6,5,2,7,4,1,3,8]=>0000001=>1000000
[1,3,7,8,5,6,2,4]=>[4,2,6,5,8,7,3,1]=>0000000=>0000000
[7,5,4,8,6,1,2,3]=>[3,2,1,6,8,4,5,7]=>0010000=>0000100
[6,2,5,1,4,8,3,7]=>[7,3,8,4,1,5,2,6]=>0000000=>0000000
[6,5,4,1,3,8,2,7]=>[7,2,8,3,1,4,5,6]=>0000000=>0000000
[1,3,8,7,4,2,6,5]=>[5,6,2,4,7,8,3,1]=>0000000=>0000000
[8,1,4,5,7,6,3,2]=>[2,3,6,7,5,4,1,8]=>0000001=>1000000
[2,4,1,8,5,7,6,3]=>[3,6,7,5,8,1,4,2]=>0000000=>0000000
[8,5,1,2,4,3,7,6]=>[6,7,3,4,2,1,5,8]=>0000001=>1000000
[6,8,5,4,1,7,2,3]=>[3,2,7,1,4,5,8,6]=>0000000=>0000000
[3,1,8,2,7,5,6,4]=>[4,6,5,7,2,8,1,3]=>0000000=>0000000
[8,4,7,2,1,6,5,3]=>[3,5,6,1,2,7,4,8]=>0000001=>1000000
[3,1,6,2,5,7,4,8]=>[8,4,7,5,2,6,1,3]=>0000000=>0000000
[3,7,1,2,8,6,4,5]=>[5,4,6,8,2,1,7,3]=>0000000=>0000000
[2,1,7,5,8,3,6,4]=>[4,6,3,8,5,7,1,2]=>0000000=>0000000
[6,1,5,8,3,7,4,2]=>[2,4,7,3,8,5,1,6]=>0000000=>0000000
[4,8,5,3,7,2,1,6]=>[6,1,2,7,3,5,8,4]=>0000000=>0000000
[7,4,8,6,5,3,2,1]=>[1,2,3,5,6,8,4,7]=>1110000=>0000111
[6,4,8,2,3,1,7,5]=>[5,7,1,3,2,8,4,6]=>0000000=>0000000
[7,6,1,3,8,4,5,2]=>[2,5,4,8,3,1,6,7]=>0000000=>0000000
[6,7,4,1,8,3,5,2]=>[2,5,3,8,1,4,7,6]=>0000000=>0000000
[7,3,6,2,8,1,4,5]=>[5,4,1,8,2,6,3,7]=>0000000=>0000000
[1,6,7,3,8,4,5,2]=>[2,5,4,8,3,7,6,1]=>0000000=>0000000
[7,5,1,8,6,4,2,3]=>[3,2,4,6,8,1,5,7]=>0000000=>0000000
[4,3,5,8,7,2,1,6]=>[6,1,2,7,8,5,3,4]=>0000000=>0000000
[4,3,5,8,7,1,2,6]=>[6,2,1,7,8,5,3,4]=>0000000=>0000000
[1,4,5,8,6,3,7,2]=>[2,7,3,6,8,5,4,1]=>0000000=>0000000
[3,5,4,8,2,7,1,6]=>[6,1,7,2,8,4,5,3]=>0000000=>0000000
[6,5,3,7,2,4,8,1]=>[1,8,4,2,7,3,5,6]=>1000000=>0000001
[5,7,6,8,4,3,1,2]=>[2,1,3,4,8,6,7,5]=>0111000=>0001110
[7,1,6,2,5,8,3,4]=>[4,3,8,5,2,6,1,7]=>0000000=>0000000
[5,7,4,3,6,8,2,1]=>[1,2,8,6,3,4,7,5]=>1100000=>0000011
[7,5,3,6,2,8,4,1]=>[1,4,8,2,6,3,5,7]=>1000000=>0000001
[3,1,2,4,8,5,7,6]=>[6,7,5,8,4,2,1,3]=>0000000=>0000000
[5,1,2,4,6,7,8,3]=>[3,8,7,6,4,2,1,5]=>0000000=>0000000
[4,6,3,5,2,8,7,1]=>[1,7,8,2,5,3,6,4]=>1000000=>0000001
[5,3,2,6,8,4,7,1]=>[1,7,4,8,6,2,3,5]=>1000000=>0000001
[5,3,6,4,1,7,8,2]=>[2,8,7,1,4,6,3,5]=>0000000=>0000000
[6,4,7,8,2,3,5,1]=>[1,5,3,2,8,7,4,6]=>1000000=>0000001
[4,7,5,2,3,8,6,1]=>[1,6,8,3,2,5,7,4]=>1000000=>0000001
[6,4,7,3,2,5,8,1]=>[1,8,5,2,3,7,4,6]=>1000000=>0000001
[4,3,7,2,5,8,6,1]=>[1,6,8,5,2,7,3,4]=>1000000=>0000001
[4,7,3,2,5,8,6,1]=>[1,6,8,5,2,3,7,4]=>1000000=>0000001
[8,5,2,6,7,3,4,1]=>[1,4,3,7,6,2,5,8]=>1000001=>1000001
[7,5,6,2,8,3,4,1]=>[1,4,3,8,2,6,5,7]=>1000000=>0000001
[4,7,6,2,3,8,5,1]=>[1,5,8,3,2,6,7,4]=>1000000=>0000001
[7,6,3,2,5,8,1,4]=>[4,1,8,5,2,3,6,7]=>0000000=>0000000
[5,8,3,2,1,7,6,4]=>[4,6,7,1,2,3,8,5]=>0000000=>0000000
[6,5,3,8,7,1,4,2]=>[2,4,1,7,8,3,5,6]=>0000000=>0000000
[3,8,7,6,2,5,1,4]=>[4,1,5,2,6,7,8,3]=>0000000=>0000000
[1,5,6,3,4,2,7,8]=>[8,7,2,4,3,6,5,1]=>0000000=>0000000
[6,7,3,1,8,5,2,4]=>[4,2,5,8,1,3,7,6]=>0000000=>0000000
[4,7,3,6,1,8,2,5]=>[5,2,8,1,6,3,7,4]=>0000000=>0000000
[3,5,6,1,8,7,2,4]=>[4,2,7,8,1,6,5,3]=>0000000=>0000000
[2,4,6,8,7,3,1,5]=>[5,1,3,7,8,6,4,2]=>0000000=>0000000
[6,3,4,7,2,1,8,5]=>[5,8,1,2,7,4,3,6]=>0000000=>0000000
[5,3,6,8,7,2,1,4]=>[4,1,2,7,8,6,3,5]=>0000000=>0000000
[2,7,5,3,1,8,6,4]=>[4,6,8,1,3,5,7,2]=>0000000=>0000000
[4,7,5,2,1,8,6,3]=>[3,6,8,1,2,5,7,4]=>0000000=>0000000
[2,5,3,8,4,1,7,6]=>[6,7,1,4,8,3,5,2]=>0000000=>0000000
[6,8,7,4,1,3,5,2]=>[2,5,3,1,4,7,8,6]=>0000100=>0010000
[5,7,3,1,2,6,8,4]=>[4,8,6,2,1,3,7,5]=>0000000=>0000000
[3,7,8,4,2,6,5,1]=>[1,5,6,2,4,8,7,3]=>1000000=>0000001
[5,6,2,8,7,1,3,4]=>[4,3,1,7,8,2,6,5]=>0000000=>0000000
[2,6,7,3,8,5,1,4]=>[4,1,5,8,3,7,6,2]=>0000000=>0000000
[2,6,7,8,3,5,1,4]=>[4,1,5,3,8,7,6,2]=>0000000=>0000000
[3,6,7,8,2,1,5,4]=>[4,5,1,2,8,7,6,3]=>0000000=>0000000
[3,6,7,2,8,1,5,4]=>[4,5,1,8,2,7,6,3]=>0000000=>0000000
[2,6,7,1,3,5,8,4]=>[4,8,5,3,1,7,6,2]=>0000000=>0000000
[3,6,7,1,2,8,5,4]=>[4,5,8,2,1,7,6,3]=>0000000=>0000000
[3,6,7,1,8,2,5,4]=>[4,5,2,8,1,7,6,3]=>0000000=>0000000
[3,4,1,8,7,2,6,5]=>[5,6,2,7,8,1,4,3]=>0000000=>0000000
[3,1,5,7,2,8,6,4]=>[4,6,8,2,7,5,1,3]=>0000000=>0000000
[3,1,5,7,8,2,6,4]=>[4,6,2,8,7,5,1,3]=>0000000=>0000000
[3,8,1,4,7,2,6,5]=>[5,6,2,7,4,1,8,3]=>0000000=>0000000
[4,8,1,3,2,7,6,5]=>[5,6,7,2,3,1,8,4]=>0000000=>0000000
[4,1,8,3,2,7,6,5]=>[5,6,7,2,3,8,1,4]=>0000000=>0000000
[4,1,3,8,2,7,6,5]=>[5,6,7,2,8,3,1,4]=>0000000=>0000000
[1,4,2,3,7,6,5,8]=>[8,5,6,7,3,2,4,1]=>0000000=>0000000
[4,3,1,8,2,7,6,5]=>[5,6,7,2,8,1,3,4]=>0000000=>0000000
[4,3,8,1,2,7,6,5]=>[5,6,7,2,1,8,3,4]=>0000000=>0000000
[4,3,8,2,1,7,6,5]=>[5,6,7,1,2,8,3,4]=>0000000=>0000000
[3,4,2,8,7,1,6,5]=>[5,6,1,7,8,2,4,3]=>0000000=>0000000
[3,8,4,2,7,1,6,5]=>[5,6,1,7,2,4,8,3]=>0000000=>0000000
[2,8,4,3,7,6,1,5]=>[5,1,6,7,3,4,8,2]=>0000000=>0000000
[2,4,3,8,7,6,1,5]=>[5,1,6,7,8,3,4,2]=>0000000=>0000000
[2,3,5,7,8,6,1,4]=>[4,1,6,8,7,5,3,2]=>0000000=>0000000
[2,3,8,4,7,6,1,5]=>[5,1,6,7,4,8,3,2]=>0000000=>0000000
[3,8,2,4,7,1,6,5]=>[5,6,1,7,4,2,8,3]=>0000000=>0000000
[3,2,4,8,7,1,6,5]=>[5,6,1,7,8,4,2,3]=>0000000=>0000000
[3,2,5,7,1,8,6,4]=>[4,6,8,1,7,5,2,3]=>0000000=>0000000
[4,2,3,8,1,7,6,5]=>[5,6,7,1,8,3,2,4]=>0000000=>0000000
[4,2,8,3,1,7,6,5]=>[5,6,7,1,3,8,2,4]=>0000000=>0000000
[4,8,2,3,1,7,6,5]=>[5,6,7,1,3,2,8,4]=>0000000=>0000000
[4,8,2,1,3,7,6,5]=>[5,6,7,3,1,2,8,4]=>0000000=>0000000
[4,2,8,1,3,7,6,5]=>[5,6,7,3,1,8,2,4]=>0000000=>0000000
[3,1,2,4,7,8,6,5]=>[5,6,8,7,4,2,1,3]=>0000000=>0000000
[3,5,4,7,2,8,1,6]=>[6,1,8,2,7,4,5,3]=>0000000=>0000000
[2,5,7,8,6,1,3,4]=>[4,3,1,6,8,7,5,2]=>0000000=>0000000
[4,6,7,5,8,2,3,1]=>[1,3,2,8,5,7,6,4]=>1010000=>0000101
[4,8,5,2,3,1,7,6]=>[6,7,1,3,2,5,8,4]=>0000000=>0000000
[4,1,3,7,8,5,2,6]=>[6,2,5,8,7,3,1,4]=>0000000=>0000000
[1,7,5,8,4,2,6,3]=>[3,6,2,4,8,5,7,1]=>0000000=>0000000
[8,5,3,2,1,6,7,4]=>[4,7,6,1,2,3,5,8]=>0000001=>1000000
[2,6,4,3,1,7,8,5]=>[5,8,7,1,3,4,6,2]=>0000000=>0000000
[5,8,3,1,2,6,4,7]=>[7,4,6,2,1,3,8,5]=>0000000=>0000000
[8,5,3,2,1,6,4,7]=>[7,4,6,1,2,3,5,8]=>0000001=>1000000
[4,8,7,1,5,2,6,3]=>[3,6,2,5,1,7,8,4]=>0000000=>0000000
[4,8,7,1,5,2,3,6]=>[6,3,2,5,1,7,8,4]=>0000000=>0000000
[7,6,8,4,1,3,2,5]=>[5,2,3,1,4,8,6,7]=>0000100=>0010000
[8,7,6,1,5,2,3,4]=>[4,3,2,5,1,6,7,8]=>0000111=>1110000
[8,6,5,1,3,4,7,2]=>[2,7,4,3,1,5,6,8]=>0000001=>1000000
[8,7,1,5,3,6,2,4]=>[4,2,6,3,5,1,7,8]=>0000011=>1100000
[7,8,5,2,4,3,6,1]=>[1,6,3,4,2,5,8,7]=>1000010=>0100001
[8,7,3,1,6,4,5,2]=>[2,5,4,6,1,3,7,8]=>0000011=>1100000
[8,7,3,1,4,6,5,2]=>[2,5,6,4,1,3,7,8]=>0000011=>1100000
[6,7,2,5,8,1,4,3]=>[3,4,1,8,5,2,7,6]=>0000000=>0000000
[6,7,3,5,8,2,4,1]=>[1,4,2,8,5,3,7,6]=>1000000=>0000001
[6,3,7,5,8,2,4,1]=>[1,4,2,8,5,7,3,6]=>1000000=>0000001
[6,5,7,3,8,1,4,2]=>[2,4,1,8,3,7,5,6]=>0000000=>0000000
[6,3,7,4,8,2,5,1]=>[1,5,2,8,4,7,3,6]=>1000000=>0000001
[6,3,7,4,8,1,5,2]=>[2,5,1,8,4,7,3,6]=>0000000=>0000000
[6,4,7,2,8,3,5,1]=>[1,5,3,8,2,7,4,6]=>1000000=>0000001
[8,7,4,6,2,3,5,1]=>[1,5,3,2,6,4,7,8]=>1000011=>1100001
[6,8,4,5,7,3,2,1]=>[1,2,3,7,5,4,8,6]=>1110000=>0000111
[5,6,4,2,1,7,8,3]=>[3,8,7,1,2,4,6,5]=>0000000=>0000000
[6,7,5,1,4,3,8,2]=>[2,8,3,4,1,5,7,6]=>0000000=>0000000
[3,6,8,7,4,5,2,1]=>[1,2,5,4,7,8,6,3]=>1100000=>0000011
[8,6,7,1,3,5,2,4]=>[4,2,5,3,1,7,6,8]=>0000101=>1010000
[7,2,1,8,6,3,5,4]=>[4,5,3,6,8,1,2,7]=>0000000=>0000000
[3,2,4,8,1,7,6,5]=>[5,6,7,1,8,4,2,3]=>0000000=>0000000
[6,2,7,1,4,8,3,5]=>[5,3,8,4,1,7,2,6]=>0000000=>0000000
[8,2,3,6,7,1,4,5]=>[5,4,1,7,6,3,2,8]=>0000001=>1000000
[2,1,4,7,8,5,3,6]=>[6,3,5,8,7,4,1,2]=>0000000=>0000000
[5,8,6,2,4,7,1,3]=>[3,1,7,4,2,6,8,5]=>0000000=>0000000
[3,8,2,6,5,7,1,4]=>[4,1,7,5,6,2,8,3]=>0000000=>0000000
[1,8,3,6,7,4,2,5]=>[5,2,4,7,6,3,8,1]=>0000000=>0000000
[8,2,7,6,4,3,1,5]=>[5,1,3,4,6,7,2,8]=>0000001=>1000000
[8,1,7,2,5,6,4,3]=>[3,4,6,5,2,7,1,8]=>0000001=>1000000
[8,1,3,5,2,7,6,4]=>[4,6,7,2,5,3,1,8]=>0000001=>1000000
[2,7,1,5,4,8,6,3]=>[3,6,8,4,5,1,7,2]=>0000000=>0000000
[8,1,4,5,6,3,7,2]=>[2,7,3,6,5,4,1,8]=>0000001=>1000000
[8,1,4,5,6,2,7,3]=>[3,7,2,6,5,4,1,8]=>0000001=>1000000
[3,4,5,6,2,8,1,7]=>[7,1,8,2,6,5,4,3]=>0000000=>0000000
[3,7,4,2,8,5,1,6]=>[6,1,5,8,2,4,7,3]=>0000000=>0000000
[7,2,1,6,3,4,8,5]=>[5,8,4,3,6,1,2,7]=>0000000=>0000000
[7,3,4,1,6,5,8,2]=>[2,8,5,6,1,4,3,7]=>0000000=>0000000
[2,3,5,1,4,8,7,6]=>[6,7,8,4,1,5,3,2]=>0000000=>0000000
[3,8,7,1,4,5,2,6]=>[6,2,5,4,1,7,8,3]=>0000000=>0000000
[3,7,4,2,1,8,6,5]=>[5,6,8,1,2,4,7,3]=>0000000=>0000000
[4,5,8,7,6,1,3,2]=>[2,3,1,6,7,8,5,4]=>0010000=>0000100
[8,3,6,7,2,5,1,4]=>[4,1,5,2,7,6,3,8]=>0000001=>1000000
[8,5,2,7,6,1,3,4]=>[4,3,1,6,7,2,5,8]=>0000001=>1000000
[8,6,4,1,7,5,2,3]=>[3,2,5,7,1,4,6,8]=>0000001=>1000000
[7,6,3,8,1,4,2,5]=>[5,2,4,1,8,3,6,7]=>0000000=>0000000
[5,6,3,2,1,7,4,8]=>[8,4,7,1,2,3,6,5]=>0000000=>0000000
[8,6,4,1,2,7,5,3]=>[3,5,7,2,1,4,6,8]=>0000001=>1000000
[8,7,4,1,2,5,3,6]=>[6,3,5,2,1,4,7,8]=>0000011=>1100000
[3,6,1,7,4,8,5,2]=>[2,5,8,4,7,1,6,3]=>0000000=>0000000
[2,3,6,1,8,7,4,5]=>[5,4,7,8,1,6,3,2]=>0000000=>0000000
[1,7,4,8,5,6,3,2]=>[2,3,6,5,8,4,7,1]=>0000000=>0000000
[8,5,2,7,6,3,1,4]=>[4,1,3,6,7,2,5,8]=>0000001=>1000000
[8,2,3,5,6,1,7,4]=>[4,7,1,6,5,3,2,8]=>0000001=>1000000
[5,4,2,7,8,6,1,3]=>[3,1,6,8,7,2,4,5]=>0000000=>0000000
[6,7,1,8,3,2,4,5]=>[5,4,2,3,8,1,7,6]=>0000000=>0000000
[6,7,2,8,1,3,4,5]=>[5,4,3,1,8,2,7,6]=>0000000=>0000000
[7,8,6,1,3,4,2,5]=>[5,2,4,3,1,6,8,7]=>0000110=>0110000
[7,6,1,2,5,3,8,4]=>[4,8,3,5,2,1,6,7]=>0000000=>0000000
[4,3,2,8,7,1,6,5]=>[5,6,1,7,8,2,3,4]=>0000000=>0000000
[7,4,1,8,6,5,3,2]=>[2,3,5,6,8,1,4,7]=>0000000=>0000000
[5,8,4,2,1,7,6,3]=>[3,6,7,1,2,4,8,5]=>0000000=>0000000
[6,1,8,5,4,3,7,2]=>[2,7,3,4,5,8,1,6]=>0000000=>0000000
[6,5,1,7,3,4,8,2]=>[2,8,4,3,7,1,5,6]=>0000000=>0000000
[7,3,4,8,1,6,5,2]=>[2,5,6,1,8,4,3,7]=>0000000=>0000000
[6,1,5,8,4,7,2,3]=>[3,2,7,4,8,5,1,6]=>0000000=>0000000
[8,5,6,1,4,7,2,3]=>[3,2,7,4,1,6,5,8]=>0000001=>1000000
[5,8,7,2,3,4,6,1]=>[1,6,4,3,2,7,8,5]=>1000000=>0000001
[7,2,5,6,1,4,8,3]=>[3,8,4,1,6,5,2,7]=>0000000=>0000000
[5,2,6,8,1,4,7,3]=>[3,7,4,1,8,6,2,5]=>0000000=>0000000
[1,6,8,5,2,4,7,3]=>[3,7,4,2,5,8,6,1]=>0000000=>0000000
[5,7,6,2,8,3,1,4]=>[4,1,3,8,2,6,7,5]=>0000000=>0000000
[2,5,6,3,1,4,8,7]=>[7,8,4,1,3,6,5,2]=>0000000=>0000000
[7,1,8,3,2,5,4,6]=>[6,4,5,2,3,8,1,7]=>0000000=>0000000
[2,5,6,8,7,3,1,4]=>[4,1,3,7,8,6,5,2]=>0000000=>0000000
[4,6,5,8,7,3,1,2]=>[2,1,3,7,8,5,6,4]=>0110000=>0000110
[8,3,1,7,2,6,4,5]=>[5,4,6,2,7,1,3,8]=>0000001=>1000000
[8,6,5,1,7,2,4,3]=>[3,4,2,7,1,5,6,8]=>0000001=>1000000
[6,7,5,1,3,8,4,2]=>[2,4,8,3,1,5,7,6]=>0000000=>0000000
[6,7,1,4,2,8,5,3]=>[3,5,8,2,4,1,7,6]=>0000000=>0000000
[5,7,1,4,2,8,6,3]=>[3,6,8,2,4,1,7,5]=>0000000=>0000000
[6,7,4,1,3,8,5,2]=>[2,5,8,3,1,4,7,6]=>0000000=>0000000
[2,1,6,4,8,3,7,5]=>[5,7,3,8,4,6,1,2]=>0000000=>0000000
[4,7,8,5,3,6,2,1]=>[1,2,6,3,5,8,7,4]=>1100000=>0000011
[4,5,8,6,3,7,2,1]=>[1,2,7,3,6,8,5,4]=>1100000=>0000011
[4,5,8,3,7,6,2,1]=>[1,2,6,7,3,8,5,4]=>1100000=>0000011
[4,8,2,5,7,3,1,6]=>[6,1,3,7,5,2,8,4]=>0000000=>0000000
[4,5,8,2,6,3,1,7]=>[7,1,3,6,2,8,5,4]=>0000000=>0000000
[6,3,5,2,4,7,1,8]=>[8,1,7,4,2,5,3,6]=>0000000=>0000000
[5,2,6,3,4,8,1,7]=>[7,1,8,4,3,6,2,5]=>0000000=>0000000
[6,5,1,3,2,8,4,7]=>[7,4,8,2,3,1,5,6]=>0000000=>0000000
[2,8,7,1,4,3,6,5]=>[5,6,3,4,1,7,8,2]=>0000000=>0000000
[1,2,7,8,4,3,6,5]=>[5,6,3,4,8,7,2,1]=>0000000=>0000000
[2,8,5,4,1,3,7,6]=>[6,7,3,1,4,5,8,2]=>0000000=>0000000
[4,8,6,5,3,1,2,7]=>[7,2,1,3,5,6,8,4]=>0000000=>0000000
[5,4,6,3,1,7,2,8]=>[8,2,7,1,3,6,4,5]=>0000000=>0000000
[3,8,1,6,4,7,2,5]=>[5,2,7,4,6,1,8,3]=>0000000=>0000000
[8,1,4,5,7,3,2,6]=>[6,2,3,7,5,4,1,8]=>0000001=>1000000
[7,6,5,2,8,4,3,1]=>[1,3,4,8,2,5,6,7]=>1000000=>0000001
[2,7,3,5,8,1,6,4]=>[4,6,1,8,5,3,7,2]=>0000000=>0000000
[8,5,1,6,7,3,2,4]=>[4,2,3,7,6,1,5,8]=>0000001=>1000000
[3,2,6,7,1,8,5,4]=>[4,5,8,1,7,6,2,3]=>0000000=>0000000
[6,1,3,7,8,2,5,4]=>[4,5,2,8,7,3,1,6]=>0000000=>0000000
[5,7,2,8,1,4,6,3]=>[3,6,4,1,8,2,7,5]=>0000000=>0000000
[2,7,5,8,6,1,3,4]=>[4,3,1,6,8,5,7,2]=>0000000=>0000000
[1,6,2,7,8,5,3,4]=>[4,3,5,8,7,2,6,1]=>0000000=>0000000
[8,6,1,2,7,3,4,5]=>[5,4,3,7,2,1,6,8]=>0000001=>1000000
[6,8,7,2,5,4,1,3]=>[3,1,4,5,2,7,8,6]=>0000100=>0010000
[2,7,4,8,3,6,1,5]=>[5,1,6,3,8,4,7,2]=>0000000=>0000000
[4,7,3,8,6,1,5,2]=>[2,5,1,6,8,3,7,4]=>0000000=>0000000
[4,7,3,8,6,2,1,5]=>[5,1,2,6,8,3,7,4]=>0000000=>0000000
[2,4,3,6,8,7,1,5]=>[5,1,7,8,6,3,4,2]=>0000000=>0000000
[3,6,7,4,1,2,8,5]=>[5,8,2,1,4,7,6,3]=>0000000=>0000000
[4,3,2,7,1,6,8,5]=>[5,8,6,1,7,2,3,4]=>0000000=>0000000
[7,4,8,1,5,6,3,2]=>[2,3,6,5,1,8,4,7]=>0000000=>0000000
[6,8,2,1,5,3,7,4]=>[4,7,3,5,1,2,8,6]=>0000000=>0000000
[5,7,8,4,6,3,2,1]=>[1,2,3,6,4,8,7,5]=>1110000=>0000111
[4,3,5,2,8,6,7,1]=>[1,7,6,8,2,5,3,4]=>1000000=>0000001
[4,8,5,3,2,6,7,1]=>[1,7,6,2,3,5,8,4]=>1000000=>0000001
[3,8,4,5,2,6,7,1]=>[1,7,6,2,5,4,8,3]=>1000000=>0000001
[2,5,7,4,6,8,3,1]=>[1,3,8,6,4,7,5,2]=>1000000=>0000001
[7,5,2,4,3,8,6,1]=>[1,6,8,3,4,2,5,7]=>1000000=>0000001
[3,4,5,8,2,6,7,1]=>[1,7,6,2,8,5,4,3]=>1000000=>0000001
[6,3,2,5,8,4,7,1]=>[1,7,4,8,5,2,3,6]=>1000000=>0000001
[5,4,8,3,2,6,7,1]=>[1,7,6,2,3,8,4,5]=>1000000=>0000001
[3,4,5,2,7,1,6,8]=>[8,6,1,7,2,5,4,3]=>0000000=>0000000
[8,4,6,2,3,1,5,7]=>[7,5,1,3,2,6,4,8]=>0000001=>1000000
[8,5,2,6,3,4,1,7]=>[7,1,4,3,6,2,5,8]=>0000001=>1000000
[3,4,5,2,8,6,1,7]=>[7,1,6,8,2,5,4,3]=>0000000=>0000000
[3,4,5,2,8,6,7,1]=>[1,7,6,8,2,5,4,3]=>1000000=>0000001
[3,4,5,2,6,8,1,7]=>[7,1,8,6,2,5,4,3]=>0000000=>0000000
[6,8,2,5,1,3,7,4]=>[4,7,3,1,5,2,8,6]=>0000000=>0000000
[6,7,4,2,1,5,3,8]=>[8,3,5,1,2,4,7,6]=>0000000=>0000000
[6,5,1,2,8,3,4,7]=>[7,4,3,8,2,1,5,6]=>0000000=>0000000
[6,4,2,8,3,7,1,5]=>[5,1,7,3,8,2,4,6]=>0000000=>0000000
[5,2,1,8,3,7,4,6]=>[6,4,7,3,8,1,2,5]=>0000000=>0000000
[7,2,8,4,6,1,3,5]=>[5,3,1,6,4,8,2,7]=>0000000=>0000000
[4,8,6,1,5,7,2,3]=>[3,2,7,5,1,6,8,4]=>0000000=>0000000
[3,4,8,2,5,7,1,6]=>[6,1,7,5,2,8,4,3]=>0000000=>0000000
[7,1,3,4,6,2,8,5]=>[5,8,2,6,4,3,1,7]=>0000000=>0000000
[1,7,3,4,6,2,8,5]=>[5,8,2,6,4,3,7,1]=>0000000=>0000000
[5,2,1,3,8,6,4,7]=>[7,4,6,8,3,1,2,5]=>0000000=>0000000
[6,2,1,3,8,7,4,5]=>[5,4,7,8,3,1,2,6]=>0000000=>0000000
[1,2,5,4,8,7,3,6]=>[6,3,7,8,4,5,2,1]=>0000000=>0000000
[2,7,4,1,8,6,3,5]=>[5,3,6,8,1,4,7,2]=>0000000=>0000000
[7,6,2,5,3,4,1,8]=>[8,1,4,3,5,2,6,7]=>0000000=>0000000
[7,6,2,4,5,3,1,8]=>[8,1,3,5,4,2,6,7]=>0000000=>0000000
[7,6,2,4,3,5,1,8]=>[8,1,5,3,4,2,6,7]=>0000000=>0000000
[7,6,2,3,5,4,1,8]=>[8,1,4,5,3,2,6,7]=>0000000=>0000000
[8,4,2,7,1,6,3,5]=>[5,3,6,1,7,2,4,8]=>0000001=>1000000
[4,6,3,2,8,1,7,5]=>[5,7,1,8,2,3,6,4]=>0000000=>0000000
[8,7,6,1,5,3,2,4]=>[4,2,3,5,1,6,7,8]=>0000111=>1110000
[7,8,4,3,1,5,6,2]=>[2,6,5,1,3,4,8,7]=>0000010=>0100000
[8,7,6,1,3,5,4,2]=>[2,4,5,3,1,6,7,8]=>0000111=>1110000
[8,7,6,1,5,4,2,3]=>[3,2,4,5,1,6,7,8]=>0000111=>1110000
[4,5,3,8,2,1,6,7]=>[7,6,1,2,8,3,5,4]=>0000000=>0000000
[8,3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3,8]=>0000001=>1000000
[7,8,4,3,1,5,2,6]=>[6,2,5,1,3,4,8,7]=>0000010=>0100000
[8,7,6,1,2,5,3,4]=>[4,3,5,2,1,6,7,8]=>0000111=>1110000
[8,7,6,1,2,5,4,3]=>[3,4,5,2,1,6,7,8]=>0000111=>1110000
[5,7,6,4,2,3,1,8]=>[8,1,3,2,4,6,7,5]=>0000000=>0000000
[2,4,6,8,5,1,7,3]=>[3,7,1,5,8,6,4,2]=>0000000=>0000000
[6,8,7,4,2,1,5,3]=>[3,5,1,2,4,7,8,6]=>0000100=>0010000
[4,3,2,7,8,6,1,5]=>[5,1,6,8,7,2,3,4]=>0000000=>0000000
[5,6,8,4,7,3,1,2]=>[2,1,3,7,4,8,6,5]=>0110000=>0000110
[4,8,1,5,7,6,3,2]=>[2,3,6,7,5,1,8,4]=>0000000=>0000000
[8,2,3,6,4,5,1,7]=>[7,1,5,4,6,3,2,8]=>0000001=>1000000
[5,8,4,2,6,7,3,1]=>[1,3,7,6,2,4,8,5]=>1000000=>0000001
[1,4,3,2,8,5,7,6]=>[6,7,5,8,2,3,4,1]=>0000000=>0000000
[5,1,8,3,6,7,4,2]=>[2,4,7,6,3,8,1,5]=>0000000=>0000000
[8,4,1,6,5,2,3,7]=>[7,3,2,5,6,1,4,8]=>0000001=>1000000
[3,2,7,5,6,8,4,1]=>[1,4,8,6,5,7,2,3]=>1000000=>0000001
[6,1,8,7,5,3,4,2]=>[2,4,3,5,7,8,1,6]=>0000000=>0000000
[6,8,7,3,2,4,1,5]=>[5,1,4,2,3,7,8,6]=>0000100=>0010000
[3,8,7,6,4,2,5,1]=>[1,5,2,4,6,7,8,3]=>1000000=>0000001
[5,3,2,6,4,7,8,1]=>[1,8,7,4,6,2,3,5]=>1000000=>0000001
[7,3,5,2,8,4,6,1]=>[1,6,4,8,2,5,3,7]=>1000000=>0000001
[2,3,5,7,4,6,8,1]=>[1,8,6,4,7,5,3,2]=>1000000=>0000001
[7,5,3,2,8,6,4,1]=>[1,4,6,8,2,3,5,7]=>1000000=>0000001
[3,8,6,2,5,1,4,7]=>[7,4,1,5,2,6,8,3]=>0000000=>0000000
[2,4,6,3,8,7,5,1]=>[1,5,7,8,3,6,4,2]=>1000000=>0000001
[2,5,3,8,7,6,4,1]=>[1,4,6,7,8,3,5,2]=>1000000=>0000001
[6,3,1,8,7,4,2,5]=>[5,2,4,7,8,1,3,6]=>0000000=>0000000
[5,8,3,1,7,6,4,2]=>[2,4,6,7,1,3,8,5]=>0000000=>0000000
[6,3,5,2,1,8,7,4]=>[4,7,8,1,2,5,3,6]=>0000000=>0000000
[4,8,7,1,3,6,5,2]=>[2,5,6,3,1,7,8,4]=>0000000=>0000000
[4,2,7,3,8,6,5,1]=>[1,5,6,8,3,7,2,4]=>1000000=>0000001
[2,8,1,3,7,6,4,5]=>[5,4,6,7,3,1,8,2]=>0000000=>0000000
[4,1,3,5,8,7,6,2]=>[2,6,7,8,5,3,1,4]=>0000000=>0000000
[5,2,7,3,6,4,1,8]=>[8,1,4,6,3,7,2,5]=>0000000=>0000000
[5,2,8,3,6,4,1,7]=>[7,1,4,6,3,8,2,5]=>0000000=>0000000
[7,3,1,4,8,5,2,6]=>[6,2,5,8,4,1,3,7]=>0000000=>0000000
[6,2,5,3,8,4,1,7]=>[7,1,4,8,3,5,2,6]=>0000000=>0000000
[1,3,5,4,8,6,2,7]=>[7,2,6,8,4,5,3,1]=>0000000=>0000000
[6,2,4,3,8,5,1,7]=>[7,1,5,8,3,4,2,6]=>0000000=>0000000
[5,2,4,3,8,6,1,7]=>[7,1,6,8,3,4,2,5]=>0000000=>0000000
[5,2,7,3,1,6,4,8]=>[8,4,6,1,3,7,2,5]=>0000000=>0000000
[6,2,1,5,3,7,4,8]=>[8,4,7,3,5,1,2,6]=>0000000=>0000000
[7,5,1,2,6,4,3,8]=>[8,3,4,6,2,1,5,7]=>0000000=>0000000
[7,3,6,4,1,2,8,5]=>[5,8,2,1,4,6,3,7]=>0000000=>0000000
[7,3,5,1,4,6,2,8]=>[8,2,6,4,1,5,3,7]=>0000000=>0000000
[6,1,8,2,7,4,3,5]=>[5,3,4,7,2,8,1,6]=>0000000=>0000000
[7,1,5,3,2,6,8,4]=>[4,8,6,2,3,5,1,7]=>0000000=>0000000
[7,3,5,2,1,4,8,6]=>[6,8,4,1,2,5,3,7]=>0000000=>0000000
[6,4,5,8,7,3,2,1]=>[1,2,3,7,8,5,4,6]=>1110000=>0000111
[3,2,1,7,8,5,4,6]=>[6,4,5,8,7,1,2,3]=>0000000=>0000000
[2,6,1,5,4,7,3,8]=>[8,3,7,4,5,1,6,2]=>0000000=>0000000
[1,2,8,4,6,3,7,5]=>[5,7,3,6,4,8,2,1]=>0000000=>0000000
[2,7,6,5,1,4,8,3]=>[3,8,4,1,5,6,7,2]=>0000000=>0000000
[2,3,6,8,4,1,7,5]=>[5,7,1,4,8,6,3,2]=>0000000=>0000000
[1,2,8,4,7,3,5,6]=>[6,5,3,7,4,8,2,1]=>0000000=>0000000
[2,3,5,8,7,1,6,4]=>[4,6,1,7,8,5,3,2]=>0000000=>0000000
[1,6,8,3,2,5,4,7]=>[7,4,5,2,3,8,6,1]=>0000000=>0000000
[6,5,7,3,1,2,8,4]=>[4,8,2,1,3,7,5,6]=>0000000=>0000000
[8,3,5,2,6,1,4,7]=>[7,4,1,6,2,5,3,8]=>0000001=>1000000
[1,8,5,6,2,7,4,3]=>[3,4,7,2,6,5,8,1]=>0000000=>0000000
[3,7,2,4,6,1,5,8]=>[8,5,1,6,4,2,7,3]=>0000000=>0000000
[3,8,2,4,1,5,6,7]=>[7,6,5,1,4,2,8,3]=>0000000=>0000000
[4,2,7,6,1,8,5,3]=>[3,5,8,1,6,7,2,4]=>0000000=>0000000
[3,5,2,1,8,4,7,6]=>[6,7,4,8,1,2,5,3]=>0000000=>0000000
[6,3,8,4,2,5,1,7]=>[7,1,5,2,4,8,3,6]=>0000000=>0000000
[4,3,8,2,1,5,7,6]=>[6,7,5,1,2,8,3,4]=>0000000=>0000000
[4,3,2,8,1,6,7,5]=>[5,7,6,1,8,2,3,4]=>0000000=>0000000
[5,8,3,4,7,2,1,6]=>[6,1,2,7,4,3,8,5]=>0000000=>0000000
[4,3,8,2,1,6,7,5]=>[5,7,6,1,2,8,3,4]=>0000000=>0000000
[4,5,3,2,6,8,1,7]=>[7,1,8,6,2,3,5,4]=>0000000=>0000000
[3,6,7,4,5,2,8,1]=>[1,8,2,5,4,7,6,3]=>1000000=>0000001
[6,3,5,1,7,8,4,2]=>[2,4,8,7,1,5,3,6]=>0000000=>0000000
[5,3,7,6,2,4,8,1]=>[1,8,4,2,6,7,3,5]=>1000000=>0000001
[4,6,7,3,5,2,8,1]=>[1,8,2,5,3,7,6,4]=>1000000=>0000001
[5,3,7,6,4,2,8,1]=>[1,8,2,4,6,7,3,5]=>1000000=>0000001
[8,4,7,3,1,5,6,2]=>[2,6,5,1,3,7,4,8]=>0000001=>1000000
[6,1,3,5,7,8,4,2]=>[2,4,8,7,5,3,1,6]=>0000000=>0000000
[6,1,5,3,7,8,4,2]=>[2,4,8,7,3,5,1,6]=>0000000=>0000000
[8,2,7,6,5,3,1,4]=>[4,1,3,5,6,7,2,8]=>0000001=>1000000
[8,3,7,6,5,1,2,4]=>[4,2,1,5,6,7,3,8]=>0000001=>1000000
[2,3,7,6,5,8,1,4]=>[4,1,8,5,6,7,3,2]=>0000000=>0000000
[7,1,2,5,6,4,8,3]=>[3,8,4,6,5,2,1,7]=>0000000=>0000000
[3,2,7,6,5,8,1,4]=>[4,1,8,5,6,7,2,3]=>0000000=>0000000
[2,3,7,6,5,1,8,4]=>[4,8,1,5,6,7,3,2]=>0000000=>0000000
[8,3,7,6,5,2,1,4]=>[4,1,2,5,6,7,3,8]=>0000001=>1000000
[3,5,8,7,6,4,1,2]=>[2,1,4,6,7,8,5,3]=>0100000=>0000010
[7,8,6,2,4,1,5,3]=>[3,5,1,4,2,6,8,7]=>0000110=>0110000
[3,6,2,1,4,7,8,5]=>[5,8,7,4,1,2,6,3]=>0000000=>0000000
[8,3,7,2,5,4,6,1]=>[1,6,4,5,2,7,3,8]=>1000001=>1000001
[6,2,5,1,4,7,3,8]=>[8,3,7,4,1,5,2,6]=>0000000=>0000000
[2,7,6,5,4,1,3,8]=>[8,3,1,4,5,6,7,2]=>0000000=>0000000
[8,4,2,1,6,7,3,5]=>[5,3,7,6,1,2,4,8]=>0000001=>1000000
[4,3,7,2,1,8,5,6]=>[6,5,8,1,2,7,3,4]=>0000000=>0000000
[4,7,3,8,6,2,5,1]=>[1,5,2,6,8,3,7,4]=>1000000=>0000001
[5,4,7,3,8,2,1,6]=>[6,1,2,8,3,7,4,5]=>0000000=>0000000
[8,7,2,4,6,3,5,1]=>[1,5,3,6,4,2,7,8]=>1000011=>1100001
[1,3,6,8,5,7,4,2]=>[2,4,7,5,8,6,3,1]=>0000000=>0000000
[7,3,6,2,8,5,4,1]=>[1,4,5,8,2,6,3,7]=>1000000=>0000001
[5,4,6,8,3,7,2,1]=>[1,2,7,3,8,6,4,5]=>1100000=>0000011
[3,7,5,2,6,4,1,8]=>[8,1,4,6,2,5,7,3]=>0000000=>0000000
[5,8,4,2,7,3,6,1]=>[1,6,3,7,2,4,8,5]=>1000000=>0000001
[6,2,5,1,4,7,8,3]=>[3,8,7,4,1,5,2,6]=>0000000=>0000000
[6,2,5,8,7,4,1,3]=>[3,1,4,7,8,5,2,6]=>0000000=>0000000
[3,8,5,6,7,4,2,1]=>[1,2,4,7,6,5,8,3]=>1100000=>0000011
[6,3,4,1,8,7,2,5]=>[5,2,7,8,1,4,3,6]=>0000000=>0000000
[8,7,3,2,5,4,6,1]=>[1,6,4,5,2,3,7,8]=>1000011=>1100001
[7,5,6,1,8,3,2,4]=>[4,2,3,8,1,6,5,7]=>0000000=>0000000
[5,3,4,7,1,6,2,8]=>[8,2,6,1,7,4,3,5]=>0000000=>0000000
[4,8,1,7,6,2,5,3]=>[3,5,2,6,7,1,8,4]=>0000000=>0000000
[7,4,8,6,5,1,2,3]=>[3,2,1,5,6,8,4,7]=>0010000=>0000100
[4,5,8,2,7,3,1,6]=>[6,1,3,7,2,8,5,4]=>0000000=>0000000
[5,4,8,6,1,3,2,7]=>[7,2,3,1,6,8,4,5]=>0000000=>0000000
[7,8,3,1,6,4,2,5]=>[5,2,4,6,1,3,8,7]=>0000010=>0100000
[4,3,8,2,7,5,1,6]=>[6,1,5,7,2,8,3,4]=>0000000=>0000000
[4,5,7,8,3,2,1,6]=>[6,1,2,3,8,7,5,4]=>0000000=>0000000
[4,6,3,2,8,5,7,1]=>[1,7,5,8,2,3,6,4]=>1000000=>0000001
[5,4,3,7,2,6,8,1]=>[1,8,6,2,7,3,4,5]=>1000000=>0000001
[1,3,6,5,8,2,7,4]=>[4,7,2,8,5,6,3,1]=>0000000=>0000000
[7,6,4,1,2,8,5,3]=>[3,5,8,2,1,4,6,7]=>0000000=>0000000
[1,6,5,3,2,8,4,7]=>[7,4,8,2,3,5,6,1]=>0000000=>0000000
[5,4,3,7,8,2,6,1]=>[1,6,2,8,7,3,4,5]=>1000000=>0000001
[5,4,3,8,2,6,7,1]=>[1,7,6,2,8,3,4,5]=>1000000=>0000001
[3,6,5,7,2,1,8,4]=>[4,8,1,2,7,5,6,3]=>0000000=>0000000
[5,4,3,7,8,2,1,6]=>[6,1,2,8,7,3,4,5]=>0000000=>0000000
[5,4,3,8,2,6,1,7]=>[7,1,6,2,8,3,4,5]=>0000000=>0000000
[6,8,5,7,3,4,2,1]=>[1,2,4,3,7,5,8,6]=>1101000=>0001011
[2,4,1,8,7,6,3,5]=>[5,3,6,7,8,1,4,2]=>0000000=>0000000
[5,8,7,2,4,1,3,6]=>[6,3,1,4,2,7,8,5]=>0000000=>0000000
[4,1,3,5,6,2,8,7]=>[7,8,2,6,5,3,1,4]=>0000000=>0000000
[6,4,8,7,3,5,2,1]=>[1,2,5,3,7,8,4,6]=>1100000=>0000011
[8,2,3,5,6,1,4,7]=>[7,4,1,6,5,3,2,8]=>0000001=>1000000
[1,7,8,3,5,2,6,4]=>[4,6,2,5,3,8,7,1]=>0000000=>0000000
[1,3,7,8,5,4,6,2]=>[2,6,4,5,8,7,3,1]=>0000000=>0000000
[4,2,7,3,1,8,6,5]=>[5,6,8,1,3,7,2,4]=>0000000=>0000000
[4,2,7,5,3,1,8,6]=>[6,8,1,3,5,7,2,4]=>0000000=>0000000
[7,3,2,5,4,1,8,6]=>[6,8,1,4,5,2,3,7]=>0000000=>0000000
[7,3,2,4,1,8,6,5]=>[5,6,8,1,4,2,3,7]=>0000000=>0000000
[4,8,6,5,3,1,7,2]=>[2,7,1,3,5,6,8,4]=>0000000=>0000000
[6,4,7,5,3,1,8,2]=>[2,8,1,3,5,7,4,6]=>0000000=>0000000
[6,4,2,7,5,1,8,3]=>[3,8,1,5,7,2,4,6]=>0000000=>0000000
[4,6,3,8,7,2,1,5]=>[5,1,2,7,8,3,6,4]=>0000000=>0000000
[4,8,3,2,6,5,1,7]=>[7,1,5,6,2,3,8,4]=>0000000=>0000000
[7,5,4,2,6,3,1,8]=>[8,1,3,6,2,4,5,7]=>0000000=>0000000
[5,4,2,8,6,3,1,7]=>[7,1,3,6,8,2,4,5]=>0000000=>0000000
[7,5,2,8,4,3,1,6]=>[6,1,3,4,8,2,5,7]=>0000000=>0000000
[2,5,3,6,1,8,4,7]=>[7,4,8,1,6,3,5,2]=>0000000=>0000000
[6,4,2,7,1,8,5,3]=>[3,5,8,1,7,2,4,6]=>0000000=>0000000
[4,6,2,1,5,7,3,8]=>[8,3,7,5,1,2,6,4]=>0000000=>0000000
[7,1,4,5,3,6,2,8]=>[8,2,6,3,5,4,1,7]=>0000000=>0000000
[8,3,5,6,1,4,7,2]=>[2,7,4,1,6,5,3,8]=>0000001=>1000000
[5,6,4,8,2,1,3,7]=>[7,3,1,2,8,4,6,5]=>0000000=>0000000
[2,5,3,7,8,1,4,6]=>[6,4,1,8,7,3,5,2]=>0000000=>0000000
[2,6,3,7,8,1,5,4]=>[4,5,1,8,7,3,6,2]=>0000000=>0000000
[7,4,3,2,5,8,1,6]=>[6,1,8,5,2,3,4,7]=>0000000=>0000000
[1,5,4,2,3,7,6,8]=>[8,6,7,3,2,4,5,1]=>0000000=>0000000
[8,4,6,3,5,7,2,1]=>[1,2,7,5,3,6,4,8]=>1100001=>1000011
[1,8,3,5,7,2,4,6]=>[6,4,2,7,5,3,8,1]=>0000000=>0000000
[4,3,6,8,2,5,7,1]=>[1,7,5,2,8,6,3,4]=>1000000=>0000001
[4,1,5,8,3,7,2,6]=>[6,2,7,3,8,5,1,4]=>0000000=>0000000
[4,1,5,2,3,8,7,6]=>[6,7,8,3,2,5,1,4]=>0000000=>0000000
[7,4,6,3,5,8,2,1]=>[1,2,8,5,3,6,4,7]=>1100000=>0000011
[3,7,2,6,1,8,5,4]=>[4,5,8,1,6,2,7,3]=>0000000=>0000000
[6,3,5,8,2,4,7,1]=>[1,7,4,2,8,5,3,6]=>1000000=>0000001
[1,4,7,5,2,8,6,3]=>[3,6,8,2,5,7,4,1]=>0000000=>0000000
[6,1,3,4,7,2,8,5]=>[5,8,2,7,4,3,1,6]=>0000000=>0000000
[8,3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3,8]=>0000001=>1000000
[6,3,4,7,2,1,5,8]=>[8,5,1,2,7,4,3,6]=>0000000=>0000000
[5,3,6,7,2,4,8,1]=>[1,8,4,2,7,6,3,5]=>1000000=>0000001
[8,6,1,4,7,5,2,3]=>[3,2,5,7,4,1,6,8]=>0000001=>1000000
[6,1,8,5,4,7,2,3]=>[3,2,7,4,5,8,1,6]=>0000000=>0000000
[2,1,7,6,3,5,8,4]=>[4,8,5,3,6,7,1,2]=>0000000=>0000000
[3,2,8,1,4,7,5,6]=>[6,5,7,4,1,8,2,3]=>0000000=>0000000
[8,1,5,7,6,4,2,3]=>[3,2,4,6,7,5,1,8]=>0000001=>1000000
[5,4,2,3,7,1,8,6]=>[6,8,1,7,3,2,4,5]=>0000000=>0000000
[8,6,3,7,2,5,4,1]=>[1,4,5,2,7,3,6,8]=>1000001=>1000001
[4,3,6,5,8,2,1,7]=>[7,1,2,8,5,6,3,4]=>0000000=>0000000
[3,8,2,7,6,1,4,5]=>[5,4,1,6,7,2,8,3]=>0000000=>0000000
[7,4,2,6,1,8,3,5]=>[5,3,8,1,6,2,4,7]=>0000000=>0000000
[3,8,7,2,5,6,1,4]=>[4,1,6,5,2,7,8,3]=>0000000=>0000000
[7,3,6,2,5,8,1,4]=>[4,1,8,5,2,6,3,7]=>0000000=>0000000
[7,4,2,1,6,8,3,5]=>[5,3,8,6,1,2,4,7]=>0000000=>0000000
[7,3,1,8,5,4,2,6]=>[6,2,4,5,8,1,3,7]=>0000000=>0000000
[3,6,7,2,5,8,1,4]=>[4,1,8,5,2,7,6,3]=>0000000=>0000000
[7,5,1,4,2,3,6,8]=>[8,6,3,2,4,1,5,7]=>0000000=>0000000
[7,8,6,1,2,4,5,3]=>[3,5,4,2,1,6,8,7]=>0000110=>0110000
[7,5,1,2,4,6,8,3]=>[3,8,6,4,2,1,5,7]=>0000000=>0000000
[7,1,2,6,4,5,8,3]=>[3,8,5,4,6,2,1,7]=>0000000=>0000000
[1,8,3,6,4,5,7,2]=>[2,7,5,4,6,3,8,1]=>0000000=>0000000
[8,1,6,2,5,3,4,7]=>[7,4,3,5,2,6,1,8]=>0000001=>1000000
[8,1,6,4,2,3,5,7]=>[7,5,3,2,4,6,1,8]=>0000001=>1000000
[3,1,2,8,5,6,7,4]=>[4,7,6,5,8,2,1,3]=>0000000=>0000000
[7,1,8,2,5,3,4,6]=>[6,4,3,5,2,8,1,7]=>0000000=>0000000
[2,3,8,6,5,4,1,7]=>[7,1,4,5,6,8,3,2]=>0000000=>0000000
[2,6,8,3,5,1,4,7]=>[7,4,1,5,3,8,6,2]=>0000000=>0000000
[2,5,8,3,4,1,7,6]=>[6,7,1,4,3,8,5,2]=>0000000=>0000000
[2,4,7,1,3,6,8,5]=>[5,8,6,3,1,7,4,2]=>0000000=>0000000
[5,4,7,8,1,3,2,6]=>[6,2,3,1,8,7,4,5]=>0000000=>0000000
[2,4,7,1,6,3,5,8]=>[8,5,3,6,1,7,4,2]=>0000000=>0000000
[2,6,5,7,1,8,4,3]=>[3,4,8,1,7,5,6,2]=>0000000=>0000000
[5,3,6,4,7,1,2,8]=>[8,2,1,7,4,6,3,5]=>0000000=>0000000
[6,5,1,4,8,3,2,7]=>[7,2,3,8,4,1,5,6]=>0000000=>0000000
[7,5,4,8,3,2,6,1]=>[1,6,2,3,8,4,5,7]=>1000000=>0000001
[7,6,5,3,8,4,1,2]=>[2,1,4,8,3,5,6,7]=>0100000=>0000010
[7,6,5,2,4,8,3,1]=>[1,3,8,4,2,5,6,7]=>1000000=>0000001
[8,7,1,4,3,2,5,6]=>[6,5,2,3,4,1,7,8]=>0000011=>1100000
[7,3,8,4,2,5,1,6]=>[6,1,5,2,4,8,3,7]=>0000000=>0000000
[7,3,8,4,2,5,6,1]=>[1,6,5,2,4,8,3,7]=>1000000=>0000001
[8,7,1,4,3,2,6,5]=>[5,6,2,3,4,1,7,8]=>0000011=>1100000
[8,7,6,3,1,4,5,2]=>[2,5,4,1,3,6,7,8]=>0000111=>1110000
[8,7,5,2,4,3,1,6]=>[6,1,3,4,2,5,7,8]=>0000011=>1100000
[8,7,5,2,4,3,6,1]=>[1,6,3,4,2,5,7,8]=>1000011=>1100001
[4,3,7,5,2,1,6,8]=>[8,6,1,2,5,7,3,4]=>0000000=>0000000
[6,4,3,1,7,2,5,8]=>[8,5,2,7,1,3,4,6]=>0000000=>0000000
[6,3,2,5,7,1,4,8]=>[8,4,1,7,5,2,3,6]=>0000000=>0000000
[2,1,6,3,5,7,8,4]=>[4,8,7,5,3,6,1,2]=>0000000=>0000000
[5,4,2,3,8,6,1,7]=>[7,1,6,8,3,2,4,5]=>0000000=>0000000
[2,7,4,5,8,1,6,3]=>[3,6,1,8,5,4,7,2]=>0000000=>0000000
[6,4,7,5,8,2,1,3]=>[3,1,2,8,5,7,4,6]=>0010000=>0000100
[4,6,2,5,7,3,8,1]=>[1,8,3,7,5,2,6,4]=>1000000=>0000001
[4,2,8,5,3,6,1,7]=>[7,1,6,3,5,8,2,4]=>0000000=>0000000
[2,3,6,4,1,8,5,7]=>[7,5,8,1,4,6,3,2]=>0000000=>0000000
[8,1,7,4,5,6,2,3]=>[3,2,6,5,4,7,1,8]=>0000001=>1000000
[2,7,8,3,4,1,6,5]=>[5,6,1,4,3,8,7,2]=>0000000=>0000000
[4,2,5,7,8,3,6,1]=>[1,6,3,8,7,5,2,4]=>1000000=>0000001
[8,4,6,2,5,3,7,1]=>[1,7,3,5,2,6,4,8]=>1000001=>1000001
[5,1,6,4,7,3,2,8]=>[8,2,3,7,4,6,1,5]=>0000000=>0000000
[8,2,5,3,4,7,6,1]=>[1,6,7,4,3,5,2,8]=>1000001=>1000001
[7,5,3,2,4,1,8,6]=>[6,8,1,4,2,3,5,7]=>0000000=>0000000
[6,5,3,2,4,8,1,7]=>[7,1,8,4,2,3,5,6]=>0000000=>0000000
[3,7,8,6,5,4,1,2]=>[2,1,4,5,6,8,7,3]=>0100000=>0000010
[7,6,2,8,3,1,5,4]=>[4,5,1,3,8,2,6,7]=>0000000=>0000000
[6,5,3,2,4,8,7,1]=>[1,7,8,4,2,3,5,6]=>1000000=>0000001
[5,7,4,2,3,8,6,1]=>[1,6,8,3,2,4,7,5]=>1000000=>0000001
[3,8,2,5,1,7,4,6]=>[6,4,7,1,5,2,8,3]=>0000000=>0000000
[6,4,8,3,7,2,1,5]=>[5,1,2,7,3,8,4,6]=>0000000=>0000000
[5,7,4,8,1,3,2,6]=>[6,2,3,1,8,4,7,5]=>0000000=>0000000
[3,2,6,8,7,4,1,5]=>[5,1,4,7,8,6,2,3]=>0000000=>0000000
[2,3,7,5,1,8,6,4]=>[4,6,8,1,5,7,3,2]=>0000000=>0000000
[6,3,1,2,8,7,4,5]=>[5,4,7,8,2,1,3,6]=>0000000=>0000000
[7,2,1,5,3,8,4,6]=>[6,4,8,3,5,1,2,7]=>0000000=>0000000
[2,4,6,8,5,1,3,7]=>[7,3,1,5,8,6,4,2]=>0000000=>0000000
[3,5,8,2,4,1,7,6]=>[6,7,1,4,2,8,5,3]=>0000000=>0000000
[2,6,8,3,1,5,4,7]=>[7,4,5,1,3,8,6,2]=>0000000=>0000000
[2,4,8,3,1,6,7,5]=>[5,7,6,1,3,8,4,2]=>0000000=>0000000
[3,4,2,7,1,6,5,8]=>[8,5,6,1,7,2,4,3]=>0000000=>0000000
[1,4,2,6,8,5,3,7]=>[7,3,5,8,6,2,4,1]=>0000000=>0000000
[1,4,8,7,5,2,6,3]=>[3,6,2,5,7,8,4,1]=>0000000=>0000000
[1,8,4,6,3,2,7,5]=>[5,7,2,3,6,4,8,1]=>0000000=>0000000
[6,4,7,1,5,3,8,2]=>[2,8,3,5,1,7,4,6]=>0000000=>0000000
[5,3,8,2,6,4,7,1]=>[1,7,4,6,2,8,3,5]=>1000000=>0000001
[4,3,8,2,6,5,7,1]=>[1,7,5,6,2,8,3,4]=>1000000=>0000001
[2,6,1,8,3,4,7,5]=>[5,7,4,3,8,1,6,2]=>0000000=>0000000
[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>0000000=>0000000
[6,5,7,1,4,3,8,2]=>[2,8,3,4,1,7,5,6]=>0000000=>0000000
[7,1,8,2,3,4,6,5]=>[5,6,4,3,2,8,1,7]=>0000000=>0000000
[4,8,3,5,7,6,1,2]=>[2,1,6,7,5,3,8,4]=>0100000=>0000010
[5,7,6,1,2,4,8,3]=>[3,8,4,2,1,6,7,5]=>0000000=>0000000
[4,8,3,5,7,6,2,1]=>[1,2,6,7,5,3,8,4]=>1100000=>0000011
[3,4,2,1,8,5,7,6]=>[6,7,5,8,1,2,4,3]=>0000000=>0000000
[6,7,5,1,2,8,4,3]=>[3,4,8,2,1,5,7,6]=>0000000=>0000000
[1,3,4,2,8,5,7,6]=>[6,7,5,8,2,4,3,1]=>0000000=>0000000
[7,5,1,8,4,2,3,6]=>[6,3,2,4,8,1,5,7]=>0000000=>0000000
[5,7,6,1,4,8,3,2]=>[2,3,8,4,1,6,7,5]=>0000000=>0000000
[1,6,7,5,2,8,4,3]=>[3,4,8,2,5,7,6,1]=>0000000=>0000000
[2,5,3,1,8,4,7,6]=>[6,7,4,8,1,3,5,2]=>0000000=>0000000
[4,8,3,1,5,7,6,2]=>[2,6,7,5,1,3,8,4]=>0000000=>0000000
[5,7,6,2,4,8,3,1]=>[1,3,8,4,2,6,7,5]=>1000000=>0000001
[6,7,5,2,3,8,4,1]=>[1,4,8,3,2,5,7,6]=>1000000=>0000001
[2,3,1,4,8,5,7,6]=>[6,7,5,8,4,1,3,2]=>0000000=>0000000
[6,7,5,3,8,4,2,1]=>[1,2,4,8,3,5,7,6]=>1100000=>0000011
[3,2,1,4,8,5,7,6]=>[6,7,5,8,4,1,2,3]=>0000000=>0000000
[7,6,1,4,2,5,3,8]=>[8,3,5,2,4,1,6,7]=>0000000=>0000000
[6,7,2,5,1,4,3,8]=>[8,3,4,1,5,2,7,6]=>0000000=>0000000
[6,4,1,8,2,5,3,7]=>[7,3,5,2,8,1,4,6]=>0000000=>0000000
[6,5,1,4,2,7,3,8]=>[8,3,7,2,4,1,5,6]=>0000000=>0000000
[5,6,1,4,2,8,3,7]=>[7,3,8,2,4,1,6,5]=>0000000=>0000000
[6,5,1,4,2,8,3,7]=>[7,3,8,2,4,1,5,6]=>0000000=>0000000
[5,4,1,8,3,7,2,6]=>[6,2,7,3,8,1,4,5]=>0000000=>0000000
[6,4,2,3,5,1,8,7]=>[7,8,1,5,3,2,4,6]=>0000000=>0000000
[4,8,6,2,3,1,7,5]=>[5,7,1,3,2,6,8,4]=>0000000=>0000000
[4,6,2,3,1,8,7,5]=>[5,7,8,1,3,2,6,4]=>0000000=>0000000
[6,4,2,3,1,8,5,7]=>[7,5,8,1,3,2,4,6]=>0000000=>0000000
[2,8,6,4,5,1,7,3]=>[3,7,1,5,4,6,8,2]=>0000000=>0000000
[2,8,6,7,4,1,5,3]=>[3,5,1,4,7,6,8,2]=>0000000=>0000000
[4,3,2,6,1,8,7,5]=>[5,7,8,1,6,2,3,4]=>0000000=>0000000
[5,6,8,4,1,7,3,2]=>[2,3,7,1,4,8,6,5]=>0000000=>0000000
[5,8,4,3,1,7,2,6]=>[6,2,7,1,3,4,8,5]=>0000000=>0000000
[7,2,6,3,5,8,1,4]=>[4,1,8,5,3,6,2,7]=>0000000=>0000000
[4,5,3,1,8,7,6,2]=>[2,6,7,8,1,3,5,4]=>0000000=>0000000
[6,3,4,2,7,8,5,1]=>[1,5,8,7,2,4,3,6]=>1000000=>0000001
[8,7,4,5,1,6,3,2]=>[2,3,6,1,5,4,7,8]=>0000011=>1100000
[7,2,8,1,3,4,6,5]=>[5,6,4,3,1,8,2,7]=>0000000=>0000000
[8,5,7,2,3,6,4,1]=>[1,4,6,3,2,7,5,8]=>1000001=>1000001
[7,6,3,2,1,8,4,5]=>[5,4,8,1,2,3,6,7]=>0000000=>0000000
[7,2,1,4,8,5,3,6]=>[6,3,5,8,4,1,2,7]=>0000000=>0000000
[6,8,7,3,4,2,1,5]=>[5,1,2,4,3,7,8,6]=>0000100=>0010000
[5,8,4,3,1,6,2,7]=>[7,2,6,1,3,4,8,5]=>0000000=>0000000
[7,1,3,6,4,5,8,2]=>[2,8,5,4,6,3,1,7]=>0000000=>0000000
[6,2,1,3,4,7,8,5]=>[5,8,7,4,3,1,2,6]=>0000000=>0000000
[3,2,5,8,7,4,1,6]=>[6,1,4,7,8,5,2,3]=>0000000=>0000000
[3,4,8,5,7,2,1,6]=>[6,1,2,7,5,8,4,3]=>0000000=>0000000
[5,8,4,7,3,6,2,1]=>[1,2,6,3,7,4,8,5]=>1100000=>0000011
[5,1,3,2,6,8,7,4]=>[4,7,8,6,2,3,1,5]=>0000000=>0000000
[5,6,3,8,7,2,1,4]=>[4,1,2,7,8,3,6,5]=>0000000=>0000000
[3,1,6,5,8,7,2,4]=>[4,2,7,8,5,6,1,3]=>0000000=>0000000
[8,3,2,7,5,4,6,1]=>[1,6,4,5,7,2,3,8]=>1000001=>1000001
[4,3,6,5,1,2,7,8]=>[8,7,2,1,5,6,3,4]=>0000000=>0000000
[8,7,3,4,1,2,6,5]=>[5,6,2,1,4,3,7,8]=>0000011=>1100000
[2,8,7,1,6,3,4,5]=>[5,4,3,6,1,7,8,2]=>0000000=>0000000
[4,1,8,7,6,5,2,3]=>[3,2,5,6,7,8,1,4]=>0000000=>0000000
[1,4,8,7,6,5,2,3]=>[3,2,5,6,7,8,4,1]=>0000000=>0000000
[1,5,8,7,4,2,6,3]=>[3,6,2,4,7,8,5,1]=>0000000=>0000000
[4,6,5,3,2,8,1,7]=>[7,1,8,2,3,5,6,4]=>0000000=>0000000
[2,8,3,4,1,5,6,7]=>[7,6,5,1,4,3,8,2]=>0000000=>0000000
[1,3,7,5,4,8,6,2]=>[2,6,8,4,5,7,3,1]=>0000000=>0000000
[5,8,6,3,1,4,2,7]=>[7,2,4,1,3,6,8,5]=>0000000=>0000000
[5,7,3,8,4,2,6,1]=>[1,6,2,4,8,3,7,5]=>1000000=>0000001
[3,7,5,4,8,2,6,1]=>[1,6,2,8,4,5,7,3]=>1000000=>0000001
[5,3,7,1,2,8,4,6]=>[6,4,8,2,1,7,3,5]=>0000000=>0000000
[6,3,8,7,1,2,5,4]=>[4,5,2,1,7,8,3,6]=>0000000=>0000000
[2,8,7,6,1,3,5,4]=>[4,5,3,1,6,7,8,2]=>0000000=>0000000
[7,6,4,8,2,5,3,1]=>[1,3,5,2,8,4,6,7]=>1000000=>0000001
[6,3,8,7,2,4,5,1]=>[1,5,4,2,7,8,3,6]=>1000000=>0000001
[6,3,8,7,2,5,4,1]=>[1,4,5,2,7,8,3,6]=>1000000=>0000001
[2,4,3,8,7,1,6,5]=>[5,6,1,7,8,3,4,2]=>0000000=>0000000
[6,3,8,7,1,5,2,4]=>[4,2,5,1,7,8,3,6]=>0000000=>0000000
[6,3,8,7,1,2,4,5]=>[5,4,2,1,7,8,3,6]=>0000000=>0000000
[3,8,4,6,1,5,2,7]=>[7,2,5,1,6,4,8,3]=>0000000=>0000000
[1,7,5,3,6,2,8,4]=>[4,8,2,6,3,5,7,1]=>0000000=>0000000
[6,5,1,4,2,8,7,3]=>[3,7,8,2,4,1,5,6]=>0000000=>0000000
[4,8,1,6,7,5,2,3]=>[3,2,5,7,6,1,8,4]=>0000000=>0000000
[3,8,5,2,1,4,7,6]=>[6,7,4,1,2,5,8,3]=>0000000=>0000000
[5,8,3,2,1,7,4,6]=>[6,4,7,1,2,3,8,5]=>0000000=>0000000
[1,5,6,7,2,8,4,3]=>[3,4,8,2,7,6,5,1]=>0000000=>0000000
[3,6,1,2,8,7,5,4]=>[4,5,7,8,2,1,6,3]=>0000000=>0000000
[2,7,5,4,3,1,6,8]=>[8,6,1,3,4,5,7,2]=>0000000=>0000000
[4,3,7,6,5,1,2,8]=>[8,2,1,5,6,7,3,4]=>0000000=>0000000
[7,6,1,2,3,5,4,8]=>[8,4,5,3,2,1,6,7]=>0000000=>0000000
[6,2,8,7,1,3,5,4]=>[4,5,3,1,7,8,2,6]=>0000000=>0000000
[6,1,3,8,4,2,5,7]=>[7,5,2,4,8,3,1,6]=>0000000=>0000000
[2,8,7,5,1,6,3,4]=>[4,3,6,1,5,7,8,2]=>0000000=>0000000
[8,7,6,4,2,1,5,3]=>[3,5,1,2,4,6,7,8]=>0000111=>1110000
[3,8,7,4,2,6,5,1]=>[1,5,6,2,4,7,8,3]=>1000000=>0000001
[5,8,3,2,4,7,6,1]=>[1,6,7,4,2,3,8,5]=>1000000=>0000001
[4,5,8,3,6,1,2,7]=>[7,2,1,6,3,8,5,4]=>0000000=>0000000
[6,1,7,8,3,5,2,4]=>[4,2,5,3,8,7,1,6]=>0000000=>0000000
[1,6,3,4,7,8,5,2]=>[2,5,8,7,4,3,6,1]=>0000000=>0000000
[4,1,5,8,6,2,3,7]=>[7,3,2,6,8,5,1,4]=>0000000=>0000000
[1,8,4,3,2,7,6,5]=>[5,6,7,2,3,4,8,1]=>0000000=>0000000
[2,6,4,8,3,1,7,5]=>[5,7,1,3,8,4,6,2]=>0000000=>0000000
[7,6,5,2,3,8,4,1]=>[1,4,8,3,2,5,6,7]=>1000000=>0000001
[3,5,1,4,6,2,7,8]=>[8,7,2,6,4,1,5,3]=>0000000=>0000000
[7,6,5,2,4,3,8,1]=>[1,8,3,4,2,5,6,7]=>1000000=>0000001
[7,5,1,8,3,6,2,4]=>[4,2,6,3,8,1,5,7]=>0000000=>0000000
[8,1,5,6,3,7,2,4]=>[4,2,7,3,6,5,1,8]=>0000001=>1000000
[6,2,8,3,1,4,5,7]=>[7,5,4,1,3,8,2,6]=>0000000=>0000000
[3,6,4,5,2,7,8,1]=>[1,8,7,2,5,4,6,3]=>1000000=>0000001
[7,6,5,4,1,3,8,2]=>[2,8,3,1,4,5,6,7]=>0000000=>0000000
[7,6,5,4,1,8,2,3]=>[3,2,8,1,4,5,6,7]=>0000000=>0000000
[8,6,3,5,4,1,2,7]=>[7,2,1,4,5,3,6,8]=>0000001=>1000000
[8,5,1,7,4,3,6,2]=>[2,6,3,4,7,1,5,8]=>0000001=>1000000
[2,5,4,8,3,1,7,6]=>[6,7,1,3,8,4,5,2]=>0000000=>0000000
[5,4,8,2,1,3,7,6]=>[6,7,3,1,2,8,4,5]=>0000000=>0000000
[3,8,7,2,6,1,5,4]=>[4,5,1,6,2,7,8,3]=>0000000=>0000000
[1,4,3,8,7,2,6,5]=>[5,6,2,7,8,3,4,1]=>0000000=>0000000
[6,7,8,3,5,4,2,1]=>[1,2,4,5,3,8,7,6]=>1100100=>0010011
[7,8,3,6,4,1,5,2]=>[2,5,1,4,6,3,8,7]=>0000010=>0100000
[7,5,2,4,8,3,6,1]=>[1,6,3,8,4,2,5,7]=>1000000=>0000001
[2,7,4,3,5,1,6,8]=>[8,6,1,5,3,4,7,2]=>0000000=>0000000
[3,6,4,2,5,1,7,8]=>[8,7,1,5,2,4,6,3]=>0000000=>0000000
[6,2,4,8,3,5,1,7]=>[7,1,5,3,8,4,2,6]=>0000000=>0000000
[5,3,7,4,2,1,6,8]=>[8,6,1,2,4,7,3,5]=>0000000=>0000000
[1,4,5,7,8,3,2,6]=>[6,2,3,8,7,5,4,1]=>0000000=>0000000
[8,7,1,3,5,4,2,6]=>[6,2,4,5,3,1,7,8]=>0000011=>1100000
[7,5,1,3,2,4,8,6]=>[6,8,4,2,3,1,5,7]=>0000000=>0000000
[8,1,5,7,3,4,2,6]=>[6,2,4,3,7,5,1,8]=>0000001=>1000000
[6,3,1,4,2,7,8,5]=>[5,8,7,2,4,1,3,6]=>0000000=>0000000
[3,1,8,5,4,7,2,6]=>[6,2,7,4,5,8,1,3]=>0000000=>0000000
[7,5,1,8,3,2,6,4]=>[4,6,2,3,8,1,5,7]=>0000000=>0000000
[1,7,4,8,3,5,2,6]=>[6,2,5,3,8,4,7,1]=>0000000=>0000000
[7,2,8,1,4,3,6,5]=>[5,6,3,4,1,8,2,7]=>0000000=>0000000
[1,6,5,7,8,4,2,3]=>[3,2,4,8,7,5,6,1]=>0000000=>0000000
[3,1,5,8,2,7,4,6]=>[6,4,7,2,8,5,1,3]=>0000000=>0000000
[6,5,8,7,3,2,4,1]=>[1,4,2,3,7,8,5,6]=>1001000=>0001001
[6,5,8,7,2,4,1,3]=>[3,1,4,2,7,8,5,6]=>0001000=>0001000
[3,6,8,5,2,4,7,1]=>[1,7,4,2,5,8,6,3]=>1000000=>0000001
[3,6,8,2,5,4,7,1]=>[1,7,4,5,2,8,6,3]=>1000000=>0000001
[4,6,2,8,3,5,7,1]=>[1,7,5,3,8,2,6,4]=>1000000=>0000001
[5,4,6,8,7,1,3,2]=>[2,3,1,7,8,6,4,5]=>0010000=>0000100
[4,6,3,8,7,2,5,1]=>[1,5,2,7,8,3,6,4]=>1000000=>0000001
[2,4,8,7,3,6,5,1]=>[1,5,6,3,7,8,4,2]=>1000000=>0000001
[2,5,8,7,4,3,6,1]=>[1,6,3,4,7,8,5,2]=>1000000=>0000001
[2,4,8,7,6,3,5,1]=>[1,5,3,6,7,8,4,2]=>1000000=>0000001
[4,7,2,5,6,3,1,8]=>[8,1,3,6,5,2,7,4]=>0000000=>0000000
[6,1,2,8,7,3,4,5]=>[5,4,3,7,8,2,1,6]=>0000000=>0000000
[5,1,3,6,7,8,2,4]=>[4,2,8,7,6,3,1,5]=>0000000=>0000000
[6,1,5,8,3,7,2,4]=>[4,2,7,3,8,5,1,6]=>0000000=>0000000
[4,1,3,5,7,8,2,6]=>[6,2,8,7,5,3,1,4]=>0000000=>0000000
[7,2,1,6,8,3,5,4]=>[4,5,3,8,6,1,2,7]=>0000000=>0000000
[3,2,6,1,5,8,4,7]=>[7,4,8,5,1,6,2,3]=>0000000=>0000000
[6,1,5,8,3,4,2,7]=>[7,2,4,3,8,5,1,6]=>0000000=>0000000
[7,2,5,6,3,4,1,8]=>[8,1,4,3,6,5,2,7]=>0000000=>0000000
[4,7,8,1,2,5,6,3]=>[3,6,5,2,1,8,7,4]=>0000000=>0000000
[2,3,7,8,5,1,6,4]=>[4,6,1,5,8,7,3,2]=>0000000=>0000000
[6,2,8,5,7,4,3,1]=>[1,3,4,7,5,8,2,6]=>1000000=>0000001
[4,1,7,6,2,3,8,5]=>[5,8,3,2,6,7,1,4]=>0000000=>0000000
[1,7,2,6,3,5,8,4]=>[4,8,5,3,6,2,7,1]=>0000000=>0000000
[1,2,6,7,4,3,5,8]=>[8,5,3,4,7,6,2,1]=>0000000=>0000000
[3,6,7,4,5,1,8,2]=>[2,8,1,5,4,7,6,3]=>0000000=>0000000
[2,3,7,4,8,6,1,5]=>[5,1,6,8,4,7,3,2]=>0000000=>0000000
[3,5,1,8,4,7,2,6]=>[6,2,7,4,8,1,5,3]=>0000000=>0000000
[5,4,7,2,3,8,6,1]=>[1,6,8,3,2,7,4,5]=>1000000=>0000001
[6,5,7,8,1,3,2,4]=>[4,2,3,1,8,7,5,6]=>0001000=>0001000
[6,4,7,2,8,3,1,5]=>[5,1,3,8,2,7,4,6]=>0000000=>0000000
[3,6,1,5,2,7,8,4]=>[4,8,7,2,5,1,6,3]=>0000000=>0000000
[7,1,6,8,3,4,2,5]=>[5,2,4,3,8,6,1,7]=>0000000=>0000000
[7,4,8,1,2,6,3,5]=>[5,3,6,2,1,8,4,7]=>0000000=>0000000
[1,8,4,3,7,6,2,5]=>[5,2,6,7,3,4,8,1]=>0000000=>0000000
[4,3,8,7,1,2,6,5]=>[5,6,2,1,7,8,3,4]=>0000000=>0000000
[1,8,3,6,7,2,4,5]=>[5,4,2,7,6,3,8,1]=>0000000=>0000000
[1,8,4,5,7,6,2,3]=>[3,2,6,7,5,4,8,1]=>0000000=>0000000
[4,3,8,5,7,1,6,2]=>[2,6,1,7,5,8,3,4]=>0000000=>0000000
[6,3,4,8,7,2,1,5]=>[5,1,2,7,8,4,3,6]=>0000000=>0000000
[5,2,8,7,1,4,6,3]=>[3,6,4,1,7,8,2,5]=>0000000=>0000000
[3,2,8,7,1,6,4,5]=>[5,4,6,1,7,8,2,3]=>0000000=>0000000
[2,7,8,3,1,6,4,5]=>[5,4,6,1,3,8,7,2]=>0000000=>0000000
[3,5,8,7,4,1,6,2]=>[2,6,1,4,7,8,5,3]=>0000000=>0000000
[7,4,6,8,3,5,1,2]=>[2,1,5,3,8,6,4,7]=>0100000=>0000010
[7,2,8,4,1,3,6,5]=>[5,6,3,1,4,8,2,7]=>0000000=>0000000
[2,7,8,1,3,6,4,5]=>[5,4,6,3,1,8,7,2]=>0000000=>0000000
[2,7,8,1,5,4,6,3]=>[3,6,4,5,1,8,7,2]=>0000000=>0000000
[2,7,8,1,4,5,6,3]=>[3,6,5,4,1,8,7,2]=>0000000=>0000000
[3,6,7,8,2,4,1,5]=>[5,1,4,2,8,7,6,3]=>0000000=>0000000
[4,5,7,8,6,3,1,2]=>[2,1,3,6,8,7,5,4]=>0110000=>0000110
[5,4,6,8,7,3,1,2]=>[2,1,3,7,8,6,4,5]=>0110000=>0000110
[4,5,8,6,7,1,3,2]=>[2,3,1,7,6,8,5,4]=>0010000=>0000100
[5,7,6,8,2,1,3,4]=>[4,3,1,2,8,6,7,5]=>0001000=>0001000
[3,7,6,8,2,4,1,5]=>[5,1,4,2,8,6,7,3]=>0000000=>0000000
[5,4,7,8,6,3,1,2]=>[2,1,3,6,8,7,4,5]=>0110000=>0000110
[3,6,7,8,2,1,4,5]=>[5,4,1,2,8,7,6,3]=>0000000=>0000000
[4,5,6,8,7,3,1,2]=>[2,1,3,7,8,6,5,4]=>0110000=>0000110
[5,3,6,2,4,1,8,7]=>[7,8,1,4,2,6,3,5]=>0000000=>0000000
[5,8,2,6,3,7,4,1]=>[1,4,7,3,6,2,8,5]=>1000000=>0000001
[2,7,6,3,8,5,4,1]=>[1,4,5,8,3,6,7,2]=>1000000=>0000001
[8,2,5,6,3,7,4,1]=>[1,4,7,3,6,5,2,8]=>1000001=>1000001
[5,2,6,3,7,1,4,8]=>[8,4,1,7,3,6,2,5]=>0000000=>0000000
[6,7,3,2,8,4,1,5]=>[5,1,4,8,2,3,7,6]=>0000000=>0000000
[7,2,8,5,3,1,4,6]=>[6,4,1,3,5,8,2,7]=>0000000=>0000000
[4,5,8,2,1,3,6,7]=>[7,6,3,1,2,8,5,4]=>0000000=>0000000
[8,1,3,5,2,4,6,7]=>[7,6,4,2,5,3,1,8]=>0000001=>1000000
[3,7,6,4,5,8,1,2]=>[2,1,8,5,4,6,7,3]=>0100000=>0000010
[5,7,2,8,3,4,6,1]=>[1,6,4,3,8,2,7,5]=>1000000=>0000001
[5,7,3,4,8,2,6,1]=>[1,6,2,8,4,3,7,5]=>1000000=>0000001
[2,3,8,6,4,7,5,1]=>[1,5,7,4,6,8,3,2]=>1000000=>0000001
[4,6,1,7,8,3,2,5]=>[5,2,3,8,7,1,6,4]=>0000000=>0000000
[3,5,2,8,7,4,6,1]=>[1,6,4,7,8,2,5,3]=>1000000=>0000001
[2,3,8,7,6,4,5,1]=>[1,5,4,6,7,8,3,2]=>1000000=>0000001
[8,5,6,1,3,4,2,7]=>[7,2,4,3,1,6,5,8]=>0000001=>1000000
[3,7,5,8,2,6,4,1]=>[1,4,6,2,8,5,7,3]=>1000000=>0000001
[3,5,7,8,2,4,6,1]=>[1,6,4,2,8,7,5,3]=>1000000=>0000001
[5,3,7,8,4,2,6,1]=>[1,6,2,4,8,7,3,5]=>1000000=>0000001
[7,2,4,5,1,3,8,6]=>[6,8,3,1,5,4,2,7]=>0000000=>0000000
[5,2,1,4,8,3,7,6]=>[6,7,3,8,4,1,2,5]=>0000000=>0000000
[7,4,1,8,5,6,3,2]=>[2,3,6,5,8,1,4,7]=>0000000=>0000000
[6,3,2,4,1,8,5,7]=>[7,5,8,1,4,2,3,6]=>0000000=>0000000
[5,8,6,3,1,2,7,4]=>[4,7,2,1,3,6,8,5]=>0000000=>0000000
[4,1,5,7,6,3,2,8]=>[8,2,3,6,7,5,1,4]=>0000000=>0000000
[4,5,1,7,6,3,2,8]=>[8,2,3,6,7,1,5,4]=>0000000=>0000000
[3,5,4,7,8,2,1,6]=>[6,1,2,8,7,4,5,3]=>0000000=>0000000
[7,3,6,1,4,5,2,8]=>[8,2,5,4,1,6,3,7]=>0000000=>0000000
[7,1,4,5,2,8,3,6]=>[6,3,8,2,5,4,1,7]=>0000000=>0000000
[5,4,2,1,8,7,3,6]=>[6,3,7,8,1,2,4,5]=>0000000=>0000000
[5,1,4,8,3,6,2,7]=>[7,2,6,3,8,4,1,5]=>0000000=>0000000
[1,5,4,2,3,8,7,6]=>[6,7,8,3,2,4,5,1]=>0000000=>0000000
[3,6,5,2,4,1,7,8]=>[8,7,1,4,2,5,6,3]=>0000000=>0000000
[3,7,1,6,2,5,8,4]=>[4,8,5,2,6,1,7,3]=>0000000=>0000000
[3,7,4,1,6,2,5,8]=>[8,5,2,6,1,4,7,3]=>0000000=>0000000
[4,6,7,2,5,1,8,3]=>[3,8,1,5,2,7,6,4]=>0000000=>0000000
[3,6,2,5,1,8,4,7]=>[7,4,8,1,5,2,6,3]=>0000000=>0000000
[5,7,6,3,1,2,4,8]=>[8,4,2,1,3,6,7,5]=>0000000=>0000000
[5,3,4,1,2,7,6,8]=>[8,6,7,2,1,4,3,5]=>0000000=>0000000
[7,8,5,1,3,6,2,4]=>[4,2,6,3,1,5,8,7]=>0000010=>0100000
[5,1,7,6,3,2,8,4]=>[4,8,2,3,6,7,1,5]=>0000000=>0000000
[7,5,1,3,8,6,2,4]=>[4,2,6,8,3,1,5,7]=>0000000=>0000000
[5,7,6,8,3,1,4,2]=>[2,4,1,3,8,6,7,5]=>0001000=>0001000
[5,3,1,7,6,4,2,8]=>[8,2,4,6,7,1,3,5]=>0000000=>0000000
[5,3,4,7,1,6,8,2]=>[2,8,6,1,7,4,3,5]=>0000000=>0000000
[3,7,1,6,4,8,5,2]=>[2,5,8,4,6,1,7,3]=>0000000=>0000000
[4,5,1,8,7,3,2,6]=>[6,2,3,7,8,1,5,4]=>0000000=>0000000
[5,2,8,7,3,1,4,6]=>[6,4,1,3,7,8,2,5]=>0000000=>0000000
[1,6,4,8,5,7,3,2]=>[2,3,7,5,8,4,6,1]=>0000000=>0000000
[1,2,7,8,4,3,5,6]=>[6,5,3,4,8,7,2,1]=>0000000=>0000000
[1,7,4,5,8,6,2,3]=>[3,2,6,8,5,4,7,1]=>0000000=>0000000
[3,2,5,6,4,8,1,7]=>[7,1,8,4,6,5,2,3]=>0000000=>0000000
[2,3,6,4,1,7,5,8]=>[8,5,7,1,4,6,3,2]=>0000000=>0000000
[2,3,5,7,4,8,1,6]=>[6,1,8,4,7,5,3,2]=>0000000=>0000000
[2,3,7,1,5,8,4,6]=>[6,4,8,5,1,7,3,2]=>0000000=>0000000
[2,3,6,5,1,7,4,8]=>[8,4,7,1,5,6,3,2]=>0000000=>0000000
[3,2,6,4,1,5,7,8]=>[8,7,5,1,4,6,2,3]=>0000000=>0000000
[3,7,2,5,8,4,6,1]=>[1,6,4,8,5,2,7,3]=>1000000=>0000001
[3,6,4,2,1,5,7,8]=>[8,7,5,1,2,4,6,3]=>0000000=>0000000
[4,3,2,6,5,8,1,7]=>[7,1,8,5,6,2,3,4]=>0000000=>0000000
[4,6,5,2,1,7,8,3]=>[3,8,7,1,2,5,6,4]=>0000000=>0000000
[4,6,1,7,5,8,3,2]=>[2,3,8,5,7,1,6,4]=>0000000=>0000000
[4,7,1,5,8,2,6,3]=>[3,6,2,8,5,1,7,4]=>0000000=>0000000
[4,2,6,5,1,7,8,3]=>[3,8,7,1,5,6,2,4]=>0000000=>0000000
[4,1,5,7,6,8,3,2]=>[2,3,8,6,7,5,1,4]=>0000000=>0000000
[4,1,5,7,6,8,2,3]=>[3,2,8,6,7,5,1,4]=>0000000=>0000000
[3,5,6,2,1,4,7,8]=>[8,7,4,1,2,6,5,3]=>0000000=>0000000
[4,2,5,7,6,8,3,1]=>[1,3,8,6,7,5,2,4]=>1000000=>0000001
[4,3,6,5,2,8,1,7]=>[7,1,8,2,5,6,3,4]=>0000000=>0000000
[4,3,6,5,1,7,8,2]=>[2,8,7,1,5,6,3,4]=>0000000=>0000000
[3,6,4,5,2,1,7,8]=>[8,7,1,2,5,4,6,3]=>0000000=>0000000
[3,5,6,4,2,8,1,7]=>[7,1,8,2,4,6,5,3]=>0000000=>0000000
[4,6,5,3,1,7,8,2]=>[2,8,7,1,3,5,6,4]=>0000000=>0000000
[3,5,4,8,1,7,2,6]=>[6,2,7,1,8,4,5,3]=>0000000=>0000000
[6,4,8,1,5,7,2,3]=>[3,2,7,5,1,8,4,6]=>0000000=>0000000
[6,3,7,8,4,5,1,2]=>[2,1,5,4,8,7,3,6]=>0100000=>0000010
[1,3,5,8,4,7,6,2]=>[2,6,7,4,8,5,3,1]=>0000000=>0000000
[6,8,7,3,2,4,5,1]=>[1,5,4,2,3,7,8,6]=>1000100=>0010001
[2,3,1,6,5,8,4,7]=>[7,4,8,5,6,1,3,2]=>0000000=>0000000
[4,3,1,7,6,2,5,8]=>[8,5,2,6,7,1,3,4]=>0000000=>0000000
[3,5,6,2,8,7,1,4]=>[4,1,7,8,2,6,5,3]=>0000000=>0000000
[4,5,1,7,6,3,8,2]=>[2,8,3,6,7,1,5,4]=>0000000=>0000000
[2,5,1,8,7,6,4,3]=>[3,4,6,7,8,1,5,2]=>0000000=>0000000
[6,5,4,1,3,7,8,2]=>[2,8,7,3,1,4,5,6]=>0000000=>0000000
[5,2,1,7,6,4,8,3]=>[3,8,4,6,7,1,2,5]=>0000000=>0000000
[6,8,5,2,7,3,1,4]=>[4,1,3,7,2,5,8,6]=>0000000=>0000000
[8,4,2,6,1,7,3,5]=>[5,3,7,1,6,2,4,8]=>0000001=>1000000
[7,1,2,8,5,4,6,3]=>[3,6,4,5,8,2,1,7]=>0000000=>0000000
[8,1,6,7,2,4,3,5]=>[5,3,4,2,7,6,1,8]=>0000001=>1000000
[5,1,7,2,6,8,3,4]=>[4,3,8,6,2,7,1,5]=>0000000=>0000000
[7,2,1,4,3,5,8,6]=>[6,8,5,3,4,1,2,7]=>0000000=>0000000
[8,1,5,4,2,3,6,7]=>[7,6,3,2,4,5,1,8]=>0000001=>1000000
[6,1,8,5,7,2,3,4]=>[4,3,2,7,5,8,1,6]=>0000000=>0000000
[6,1,8,7,5,2,3,4]=>[4,3,2,5,7,8,1,6]=>0000000=>0000000
[6,7,1,4,2,3,5,8]=>[8,5,3,2,4,1,7,6]=>0000000=>0000000
[4,6,8,2,3,5,1,7]=>[7,1,5,3,2,8,6,4]=>0000000=>0000000
[5,3,8,4,2,7,6,1]=>[1,6,7,2,4,8,3,5]=>1000000=>0000001
[3,6,8,5,7,4,2,1]=>[1,2,4,7,5,8,6,3]=>1100000=>0000011
[8,7,2,4,6,1,5,3]=>[3,5,1,6,4,2,7,8]=>0000011=>1100000
[6,7,5,4,8,1,3,2]=>[2,3,1,8,4,5,7,6]=>0010000=>0000100
[2,5,1,4,7,3,6,8]=>[8,6,3,7,4,1,5,2]=>0000000=>0000000
[3,1,6,5,7,2,4,8]=>[8,4,2,7,5,6,1,3]=>0000000=>0000000
[2,5,7,1,6,3,8,4]=>[4,8,3,6,1,7,5,2]=>0000000=>0000000
[2,6,1,5,7,4,3,8]=>[8,3,4,7,5,1,6,2]=>0000000=>0000000
[3,1,6,5,2,4,7,8]=>[8,7,4,2,5,6,1,3]=>0000000=>0000000
[3,6,5,1,4,2,7,8]=>[8,7,2,4,1,5,6,3]=>0000000=>0000000
[3,5,6,2,8,1,7,4]=>[4,7,1,8,2,6,5,3]=>0000000=>0000000
[3,6,5,1,7,2,4,8]=>[8,4,2,7,1,5,6,3]=>0000000=>0000000
[3,6,5,2,1,4,7,8]=>[8,7,4,1,2,5,6,3]=>0000000=>0000000
[4,5,2,7,6,1,3,8]=>[8,3,1,6,7,2,5,4]=>0000000=>0000000
[4,6,5,3,1,2,7,8]=>[8,7,2,1,3,5,6,4]=>0000000=>0000000
[5,4,1,6,3,7,2,8]=>[8,2,7,3,6,1,4,5]=>0000000=>0000000
[5,4,2,6,3,7,8,1]=>[1,8,7,3,6,2,4,5]=>1000000=>0000001
[3,6,5,7,1,4,2,8]=>[8,2,4,1,7,5,6,3]=>0000000=>0000000
[3,6,5,1,4,7,2,8]=>[8,2,7,4,1,5,6,3]=>0000000=>0000000
[4,3,6,5,7,1,2,8]=>[8,2,1,7,5,6,3,4]=>0000000=>0000000
[4,2,6,5,1,3,7,8]=>[8,7,3,1,5,6,2,4]=>0000000=>0000000
[4,1,6,5,3,7,8,2]=>[2,8,7,3,5,6,1,4]=>0000000=>0000000
[4,1,5,7,6,3,8,2]=>[2,8,3,6,7,5,1,4]=>0000000=>0000000
[4,2,5,7,6,1,3,8]=>[8,3,1,6,7,5,2,4]=>0000000=>0000000
[3,4,7,6,1,2,5,8]=>[8,5,2,1,6,7,4,3]=>0000000=>0000000
[3,4,7,6,8,2,5,1]=>[1,5,2,8,6,7,4,3]=>1000000=>0000001
[4,2,5,7,6,3,8,1]=>[1,8,3,6,7,5,2,4]=>1000000=>0000001
[4,1,6,5,2,7,3,8]=>[8,3,7,2,5,6,1,4]=>0000000=>0000000
[4,2,6,5,7,3,1,8]=>[8,1,3,7,5,6,2,4]=>0000000=>0000000
[3,5,7,6,2,4,1,8]=>[8,1,4,2,6,7,5,3]=>0000000=>0000000
[5,4,2,6,3,7,1,8]=>[8,1,7,3,6,2,4,5]=>0000000=>0000000
[4,6,5,2,7,3,1,8]=>[8,1,3,7,2,5,6,4]=>0000000=>0000000
[4,5,2,7,6,3,8,1]=>[1,8,3,6,7,2,5,4]=>1000000=>0000001
[4,6,5,2,1,7,3,8]=>[8,3,7,1,2,5,6,4]=>0000000=>0000000
[3,5,8,2,4,6,7,1]=>[1,7,6,4,2,8,5,3]=>1000000=>0000001
[5,8,2,4,6,3,7,1]=>[1,7,3,6,4,2,8,5]=>1000000=>0000001
[3,8,4,6,7,2,5,1]=>[1,5,2,7,6,4,8,3]=>1000000=>0000001
[3,8,6,2,1,4,5,7]=>[7,5,4,1,2,6,8,3]=>0000000=>0000000
[3,8,6,2,4,1,5,7]=>[7,5,1,4,2,6,8,3]=>0000000=>0000000
[1,8,3,6,2,4,5,7]=>[7,5,4,2,6,3,8,1]=>0000000=>0000000
[8,4,6,1,7,2,5,3]=>[3,5,2,7,1,6,4,8]=>0000001=>1000000
[8,1,4,6,7,5,2,3]=>[3,2,5,7,6,4,1,8]=>0000001=>1000000
[8,4,6,1,3,7,2,5]=>[5,2,7,3,1,6,4,8]=>0000001=>1000000
[8,1,4,6,3,7,2,5]=>[5,2,7,3,6,4,1,8]=>0000001=>1000000
[8,4,6,2,3,7,5,1]=>[1,5,7,3,2,6,4,8]=>1000001=>1000001
[8,4,7,3,1,6,2,5]=>[5,2,6,1,3,7,4,8]=>0000001=>1000000
[8,4,7,2,1,3,6,5]=>[5,6,3,1,2,7,4,8]=>0000001=>1000000
[2,7,1,6,3,5,8,4]=>[4,8,5,3,6,1,7,2]=>0000000=>0000000
[1,6,2,5,8,4,7,3]=>[3,7,4,8,5,2,6,1]=>0000000=>0000000
[1,7,4,2,6,8,3,5]=>[5,3,8,6,2,4,7,1]=>0000000=>0000000
[3,2,7,6,1,4,8,5]=>[5,8,4,1,6,7,2,3]=>0000000=>0000000
[3,2,8,6,1,4,7,5]=>[5,7,4,1,6,8,2,3]=>0000000=>0000000
[4,1,7,2,8,6,3,5]=>[5,3,6,8,2,7,1,4]=>0000000=>0000000
[4,3,1,7,8,5,2,6]=>[6,2,5,8,7,1,3,4]=>0000000=>0000000
[5,6,8,2,4,3,7,1]=>[1,7,3,4,2,8,6,5]=>1000000=>0000001
[5,3,2,7,8,6,4,1]=>[1,4,6,8,7,2,3,5]=>1000000=>0000001
[1,4,8,7,2,5,6,3]=>[3,6,5,2,7,8,4,1]=>0000000=>0000000
[2,8,3,7,1,4,6,5]=>[5,6,4,1,7,3,8,2]=>0000000=>0000000
[1,7,2,8,3,5,6,4]=>[4,6,5,3,8,2,7,1]=>0000000=>0000000
[3,8,4,2,7,6,5,1]=>[1,5,6,7,2,4,8,3]=>1000000=>0000001
[7,3,2,6,4,1,8,5]=>[5,8,1,4,6,2,3,7]=>0000000=>0000000
[4,8,3,2,7,5,6,1]=>[1,6,5,7,2,3,8,4]=>1000000=>0000001
[1,8,2,3,7,5,6,4]=>[4,6,5,7,3,2,8,1]=>0000000=>0000000
[8,4,2,7,3,5,6,1]=>[1,6,5,3,7,2,4,8]=>1000001=>1000001
[7,4,1,5,8,6,3,2]=>[2,3,6,8,5,1,4,7]=>0000000=>0000000
[8,6,4,7,5,1,2,3]=>[3,2,1,5,7,4,6,8]=>0010001=>1000100
[2,7,4,6,3,8,5,1]=>[1,5,8,3,6,4,7,2]=>1000000=>0000001
[4,1,8,6,3,7,5,2]=>[2,5,7,3,6,8,1,4]=>0000000=>0000000
[6,1,8,4,2,5,3,7]=>[7,3,5,2,4,8,1,6]=>0000000=>0000000
[7,1,8,4,3,2,5,6]=>[6,5,2,3,4,8,1,7]=>0000000=>0000000
[1,7,5,4,8,2,3,6]=>[6,3,2,8,4,5,7,1]=>0000000=>0000000
[2,7,5,8,3,1,4,6]=>[6,4,1,3,8,5,7,2]=>0000000=>0000000
[7,4,1,6,3,2,5,8]=>[8,5,2,3,6,1,4,7]=>0000000=>0000000
[1,5,4,2,7,3,6,8]=>[8,6,3,7,2,4,5,1]=>0000000=>0000000
[8,4,3,1,6,2,5,7]=>[7,5,2,6,1,3,4,8]=>0000001=>1000000
[1,6,5,4,2,8,3,7]=>[7,3,8,2,4,5,6,1]=>0000000=>0000000
[1,6,5,4,3,8,2,7]=>[7,2,8,3,4,5,6,1]=>0000000=>0000000
[7,5,4,3,8,1,6,2]=>[2,6,1,8,3,4,5,7]=>0000000=>0000000
[8,5,4,3,7,1,6,2]=>[2,6,1,7,3,4,5,8]=>0000001=>1000000
[7,6,4,2,8,5,1,3]=>[3,1,5,8,2,4,6,7]=>0000000=>0000000
[5,7,2,8,6,3,1,4]=>[4,1,3,6,8,2,7,5]=>0000000=>0000000
[1,7,2,8,6,4,3,5]=>[5,3,4,6,8,2,7,1]=>0000000=>0000000
[5,6,4,1,7,8,2,3]=>[3,2,8,7,1,4,6,5]=>0000000=>0000000
[6,5,4,2,7,3,8,1]=>[1,8,3,7,2,4,5,6]=>1000000=>0000001
[6,5,4,2,7,1,8,3]=>[3,8,1,7,2,4,5,6]=>0000000=>0000000
[3,5,4,1,7,8,2,6]=>[6,2,8,7,1,4,5,3]=>0000000=>0000000
[4,6,3,2,7,8,5,1]=>[1,5,8,7,2,3,6,4]=>1000000=>0000001
[5,2,7,4,3,6,1,8]=>[8,1,6,3,4,7,2,5]=>0000000=>0000000
[1,8,6,3,5,4,2,7]=>[7,2,4,5,3,6,8,1]=>0000000=>0000000
[2,5,7,8,4,6,3,1]=>[1,3,6,4,8,7,5,2]=>1000000=>0000001
[2,4,1,5,8,6,7,3]=>[3,7,6,8,5,1,4,2]=>0000000=>0000000
[7,4,2,8,3,6,1,5]=>[5,1,6,3,8,2,4,7]=>0000000=>0000000
[5,3,2,8,4,1,6,7]=>[7,6,1,4,8,2,3,5]=>0000000=>0000000
[8,5,4,6,1,7,2,3]=>[3,2,7,1,6,4,5,8]=>0000001=>1000000
[5,3,2,4,8,1,7,6]=>[6,7,1,8,4,2,3,5]=>0000000=>0000000
[5,3,2,4,7,8,1,6]=>[6,1,8,7,4,2,3,5]=>0000000=>0000000
[5,3,2,4,7,1,8,6]=>[6,8,1,7,4,2,3,5]=>0000000=>0000000
[5,3,2,8,4,6,7,1]=>[1,7,6,4,8,2,3,5]=>1000000=>0000001
[8,4,5,3,7,1,2,6]=>[6,2,1,7,3,5,4,8]=>0000001=>1000000
[5,3,2,8,4,7,1,6]=>[6,1,7,4,8,2,3,5]=>0000000=>0000000
[5,3,2,4,6,8,1,7]=>[7,1,8,6,4,2,3,5]=>0000000=>0000000
[5,1,2,8,4,7,3,6]=>[6,3,7,4,8,2,1,5]=>0000000=>0000000
[8,7,1,2,5,6,3,4]=>[4,3,6,5,2,1,7,8]=>0000011=>1100000
[8,6,2,5,1,7,3,4]=>[4,3,7,1,5,2,6,8]=>0000001=>1000000
[1,2,6,5,7,8,3,4]=>[4,3,8,7,5,6,2,1]=>0000000=>0000000
[7,6,4,2,8,3,1,5]=>[5,1,3,8,2,4,6,7]=>0000000=>0000000
[1,2,6,4,7,3,8,5]=>[5,8,3,7,4,6,2,1]=>0000000=>0000000
[1,2,6,4,7,3,5,8]=>[8,5,3,7,4,6,2,1]=>0000000=>0000000
[8,5,2,4,3,7,1,6]=>[6,1,7,3,4,2,5,8]=>0000001=>1000000
[8,5,1,4,3,2,7,6]=>[6,7,2,3,4,1,5,8]=>0000001=>1000000
[3,8,5,7,4,6,2,1]=>[1,2,6,4,7,5,8,3]=>1100000=>0000011
[8,6,2,4,5,7,1,3]=>[3,1,7,5,4,2,6,8]=>0000001=>1000000
[3,8,7,4,5,2,6,1]=>[1,6,2,5,4,7,8,3]=>1000000=>0000001
[4,7,3,6,5,2,8,1]=>[1,8,2,5,6,3,7,4]=>1000000=>0000001
[6,5,2,4,1,3,8,7]=>[7,8,3,1,4,2,5,6]=>0000000=>0000000
[7,6,3,2,5,1,8,4]=>[4,8,1,5,2,3,6,7]=>0000000=>0000000
[7,2,3,4,6,8,1,5]=>[5,1,8,6,4,3,2,7]=>0000000=>0000000
[4,2,7,8,3,6,1,5]=>[5,1,6,3,8,7,2,4]=>0000000=>0000000
[4,6,3,7,5,8,2,1]=>[1,2,8,5,7,3,6,4]=>1100000=>0000011
[4,2,5,7,8,6,3,1]=>[1,3,6,8,7,5,2,4]=>1000000=>0000001
[8,2,5,7,3,6,1,4]=>[4,1,6,3,7,5,2,8]=>0000001=>1000000
[4,2,5,8,7,6,3,1]=>[1,3,6,7,8,5,2,4]=>1000000=>0000001
[6,7,2,4,5,1,8,3]=>[3,8,1,5,4,2,7,6]=>0000000=>0000000
[5,2,3,6,1,4,8,7]=>[7,8,4,1,6,3,2,5]=>0000000=>0000000
[5,2,7,8,3,6,1,4]=>[4,1,6,3,8,7,2,5]=>0000000=>0000000
[8,2,3,4,7,1,5,6]=>[6,5,1,7,4,3,2,8]=>0000001=>1000000
[6,7,3,2,5,8,1,4]=>[4,1,8,5,2,3,7,6]=>0000000=>0000000
[7,2,8,3,1,6,4,5]=>[5,4,6,1,3,8,2,7]=>0000000=>0000000
[7,2,3,4,1,8,5,6]=>[6,5,8,1,4,3,2,7]=>0000000=>0000000
[5,2,8,3,1,4,7,6]=>[6,7,4,1,3,8,2,5]=>0000000=>0000000
[8,7,2,5,1,4,3,6]=>[6,3,4,1,5,2,7,8]=>0000011=>1100000
[8,1,3,5,2,4,7,6]=>[6,7,4,2,5,3,1,8]=>0000001=>1000000
[8,3,5,1,2,4,7,6]=>[6,7,4,2,1,5,3,8]=>0000001=>1000000
[8,7,4,5,1,2,6,3]=>[3,6,2,1,5,4,7,8]=>0000011=>1100000
[8,4,3,5,1,2,7,6]=>[6,7,2,1,5,3,4,8]=>0000001=>1000000
[3,4,8,2,1,7,6,5]=>[5,6,7,1,2,8,4,3]=>0000000=>0000000
[8,3,5,2,7,4,6,1]=>[1,6,4,7,2,5,3,8]=>1000001=>1000001
[8,3,4,2,7,5,6,1]=>[1,6,5,7,2,4,3,8]=>1000001=>1000001
[8,4,2,7,5,3,1,6]=>[6,1,3,5,7,2,4,8]=>0000001=>1000000
[8,4,3,7,5,1,2,6]=>[6,2,1,5,7,3,4,8]=>0000001=>1000000
[8,4,7,6,5,2,1,3]=>[3,1,2,5,6,7,4,8]=>0010001=>1000100
[3,6,2,8,1,4,7,5]=>[5,7,4,1,8,2,6,3]=>0000000=>0000000
[1,7,4,8,3,2,5,6]=>[6,5,2,3,8,4,7,1]=>0000000=>0000000
[5,8,2,1,3,4,6,7]=>[7,6,4,3,1,2,8,5]=>0000000=>0000000
[4,2,5,1,8,3,6,7]=>[7,6,3,8,1,5,2,4]=>0000000=>0000000
[1,6,2,7,8,4,3,5]=>[5,3,4,8,7,2,6,1]=>0000000=>0000000
[8,6,7,1,4,5,2,3]=>[3,2,5,4,1,7,6,8]=>0000101=>1010000
[2,5,7,3,8,1,6,4]=>[4,6,1,8,3,7,5,2]=>0000000=>0000000
[4,3,8,6,5,2,7,1]=>[1,7,2,5,6,8,3,4]=>1000000=>0000001
[8,4,1,6,5,7,2,3]=>[3,2,7,5,6,1,4,8]=>0000001=>1000000
[8,7,4,6,5,1,2,3]=>[3,2,1,5,6,4,7,8]=>0010011=>1100100
[2,1,3,6,8,4,7,5]=>[5,7,4,8,6,3,1,2]=>0000000=>0000000
[7,2,3,6,5,8,1,4]=>[4,1,8,5,6,3,2,7]=>0000000=>0000000
[3,4,1,6,5,2,7,8]=>[8,7,2,5,6,1,4,3]=>0000000=>0000000
[3,5,2,6,7,4,1,8]=>[8,1,4,7,6,2,5,3]=>0000000=>0000000
[4,5,7,2,6,1,3,8]=>[8,3,1,6,2,7,5,4]=>0000000=>0000000
[7,3,5,6,2,4,8,1]=>[1,8,4,2,6,5,3,7]=>1000000=>0000001
[4,2,7,5,8,1,3,6]=>[6,3,1,8,5,7,2,4]=>0000000=>0000000
[7,6,8,2,5,4,3,1]=>[1,3,4,5,2,8,6,7]=>1000100=>0010001
[2,7,6,1,5,4,3,8]=>[8,3,4,5,1,6,7,2]=>0000000=>0000000
[6,3,1,7,4,8,2,5]=>[5,2,8,4,7,1,3,6]=>0000000=>0000000
[8,4,7,1,2,5,3,6]=>[6,3,5,2,1,7,4,8]=>0000001=>1000000
[8,2,5,3,1,7,4,6]=>[6,4,7,1,3,5,2,8]=>0000001=>1000000
[1,5,4,8,2,3,7,6]=>[6,7,3,2,8,4,5,1]=>0000000=>0000000
[8,2,4,1,6,7,3,5]=>[5,3,7,6,1,4,2,8]=>0000001=>1000000
[7,8,6,1,3,5,4,2]=>[2,4,5,3,1,6,8,7]=>0000110=>0110000
[6,3,1,2,8,7,5,4]=>[4,5,7,8,2,1,3,6]=>0000000=>0000000
[8,2,4,6,3,7,1,5]=>[5,1,7,3,6,4,2,8]=>0000001=>1000000
[3,4,5,8,1,7,2,6]=>[6,2,7,1,8,5,4,3]=>0000000=>0000000
[6,3,4,2,7,1,5,8]=>[8,5,1,7,2,4,3,6]=>0000000=>0000000
[5,6,3,1,7,2,4,8]=>[8,4,2,7,1,3,6,5]=>0000000=>0000000
[5,3,6,7,1,4,8,2]=>[2,8,4,1,7,6,3,5]=>0000000=>0000000
[4,5,1,6,7,3,8,2]=>[2,8,3,7,6,1,5,4]=>0000000=>0000000
[4,5,6,1,7,3,2,8]=>[8,2,3,7,1,6,5,4]=>0000000=>0000000
[1,7,5,8,3,6,2,4]=>[4,2,6,3,8,5,7,1]=>0000000=>0000000
[1,6,5,3,8,7,2,4]=>[4,2,7,8,3,5,6,1]=>0000000=>0000000
[3,6,5,4,1,7,8,2]=>[2,8,7,1,4,5,6,3]=>0000000=>0000000
[4,7,5,1,3,6,2,8]=>[8,2,6,3,1,5,7,4]=>0000000=>0000000
[1,6,4,3,7,2,5,8]=>[8,5,2,7,3,4,6,1]=>0000000=>0000000
[5,8,1,4,3,2,6,7]=>[7,6,2,3,4,1,8,5]=>0000000=>0000000
[5,8,1,4,3,2,7,6]=>[6,7,2,3,4,1,8,5]=>0000000=>0000000
[1,6,4,3,8,2,7,5]=>[5,7,2,8,3,4,6,1]=>0000000=>0000000
[1,7,4,8,3,2,6,5]=>[5,6,2,3,8,4,7,1]=>0000000=>0000000
[1,5,4,3,2,8,6,7]=>[7,6,8,2,3,4,5,1]=>0000000=>0000000
[7,1,8,4,5,3,6,2]=>[2,6,3,5,4,8,1,7]=>0000000=>0000000
[7,1,2,4,5,6,8,3]=>[3,8,6,5,4,2,1,7]=>0000000=>0000000
[5,6,3,4,1,7,8,2]=>[2,8,7,1,4,3,6,5]=>0000000=>0000000
[2,6,1,4,3,7,8,5]=>[5,8,7,3,4,1,6,2]=>0000000=>0000000
[6,4,3,7,5,8,2,1]=>[1,2,8,5,7,3,4,6]=>1100000=>0000011
[5,2,4,7,8,6,3,1]=>[1,3,6,8,7,4,2,5]=>1000000=>0000001
[8,1,6,4,7,5,2,3]=>[3,2,5,7,4,6,1,8]=>0000001=>1000000
[6,8,4,5,7,2,1,3]=>[3,1,2,7,5,4,8,6]=>0010000=>0000100
[8,4,6,2,7,3,1,5]=>[5,1,3,7,2,6,4,8]=>0000001=>1000000
[8,6,1,4,2,5,7,3]=>[3,7,5,2,4,1,6,8]=>0000001=>1000000
[8,6,1,4,7,2,5,3]=>[3,5,2,7,4,1,6,8]=>0000001=>1000000
[8,1,6,7,4,2,5,3]=>[3,5,2,4,7,6,1,8]=>0000001=>1000000
[4,8,6,2,3,1,5,7]=>[7,5,1,3,2,6,8,4]=>0000000=>0000000
[3,6,2,4,5,7,1,8]=>[8,1,7,5,4,2,6,3]=>0000000=>0000000
[3,6,2,5,4,7,1,8]=>[8,1,7,4,5,2,6,3]=>0000000=>0000000
[4,3,1,6,5,2,7,8]=>[8,7,2,5,6,1,3,4]=>0000000=>0000000
[3,4,7,6,5,1,2,8]=>[8,2,1,5,6,7,4,3]=>0000000=>0000000
[2,6,3,7,4,8,5,1]=>[1,5,8,4,7,3,6,2]=>1000000=>0000001
[1,3,5,8,6,4,7,2]=>[2,7,4,6,8,5,3,1]=>0000000=>0000000
[8,1,5,6,2,4,3,7]=>[7,3,4,2,6,5,1,8]=>0000001=>1000000
[5,4,6,1,3,2,7,8]=>[8,7,2,3,1,6,4,5]=>0000000=>0000000
[6,3,2,5,7,4,8,1]=>[1,8,4,7,5,2,3,6]=>1000000=>0000001
[2,7,8,1,6,5,3,4]=>[4,3,5,6,1,8,7,2]=>0000000=>0000000
[6,2,8,7,1,5,3,4]=>[4,3,5,1,7,8,2,6]=>0000000=>0000000
[1,8,2,4,7,6,3,5]=>[5,3,6,7,4,2,8,1]=>0000000=>0000000
[1,4,8,7,6,3,2,5]=>[5,2,3,6,7,8,4,1]=>0000000=>0000000
[3,5,1,8,7,6,2,4]=>[4,2,6,7,8,1,5,3]=>0000000=>0000000
[6,4,8,7,2,1,5,3]=>[3,5,1,2,7,8,4,6]=>0000000=>0000000
[3,2,8,7,6,4,1,5]=>[5,1,4,6,7,8,2,3]=>0000000=>0000000
[1,8,2,4,6,7,5,3]=>[3,5,7,6,4,2,8,1]=>0000000=>0000000
[1,7,3,8,2,5,6,4]=>[4,6,5,2,8,3,7,1]=>0000000=>0000000
[1,7,3,8,4,2,6,5]=>[5,6,2,4,8,3,7,1]=>0000000=>0000000
[1,8,3,5,2,7,6,4]=>[4,6,7,2,5,3,8,1]=>0000000=>0000000
[1,6,2,5,8,7,4,3]=>[3,4,7,8,5,2,6,1]=>0000000=>0000000
[1,4,8,2,6,7,5,3]=>[3,5,7,6,2,8,4,1]=>0000000=>0000000
[2,6,1,5,8,7,3,4]=>[4,3,7,8,5,1,6,2]=>0000000=>0000000
[7,4,8,5,1,2,6,3]=>[3,6,2,1,5,8,4,7]=>0000000=>0000000
[7,6,1,3,5,2,4,8]=>[8,4,2,5,3,1,6,7]=>0000000=>0000000
[6,3,5,1,8,7,4,2]=>[2,4,7,8,1,5,3,6]=>0000000=>0000000
[6,8,5,3,2,7,4,1]=>[1,4,7,2,3,5,8,6]=>1000000=>0000001
[5,2,7,4,3,1,8,6]=>[6,8,1,3,4,7,2,5]=>0000000=>0000000
[6,8,5,3,2,7,1,4]=>[4,1,7,2,3,5,8,6]=>0000000=>0000000
[7,6,5,3,1,4,8,2]=>[2,8,4,1,3,5,6,7]=>0000000=>0000000
[1,8,5,4,6,7,2,3]=>[3,2,7,6,4,5,8,1]=>0000000=>0000000
[7,2,4,8,3,6,5,1]=>[1,5,6,3,8,4,2,7]=>1000000=>0000001
[2,3,5,4,8,1,7,6]=>[6,7,1,8,4,5,3,2]=>0000000=>0000000
[1,3,5,4,8,7,2,6]=>[6,2,7,8,4,5,3,1]=>0000000=>0000000
[7,6,5,3,2,8,4,1]=>[1,4,8,2,3,5,6,7]=>1000000=>0000001
[1,3,6,2,7,5,8,4]=>[4,8,5,7,2,6,3,1]=>0000000=>0000000
[1,5,7,3,2,6,4,8]=>[8,4,6,2,3,7,5,1]=>0000000=>0000000
[4,1,7,8,5,2,6,3]=>[3,6,2,5,8,7,1,4]=>0000000=>0000000
[5,6,1,8,4,2,7,3]=>[3,7,2,4,8,1,6,5]=>0000000=>0000000
[6,4,8,2,3,5,7,1]=>[1,7,5,3,2,8,4,6]=>1000000=>0000001
[6,2,4,1,5,8,3,7]=>[7,3,8,5,1,4,2,6]=>0000000=>0000000
[6,4,8,2,5,7,1,3]=>[3,1,7,5,2,8,4,6]=>0000000=>0000000
[6,8,2,4,7,3,5,1]=>[1,5,3,7,4,2,8,6]=>1000000=>0000001
[8,6,2,4,5,1,3,7]=>[7,3,1,5,4,2,6,8]=>0000001=>1000000
[4,8,2,6,7,5,1,3]=>[3,1,5,7,6,2,8,4]=>0000000=>0000000
[6,8,2,4,1,7,3,5]=>[5,3,7,1,4,2,8,6]=>0000000=>0000000
[4,2,7,3,5,1,6,8]=>[8,6,1,5,3,7,2,4]=>0000000=>0000000
[5,6,2,3,1,7,8,4]=>[4,8,7,1,3,2,6,5]=>0000000=>0000000
[5,7,2,3,4,1,6,8]=>[8,6,1,4,3,2,7,5]=>0000000=>0000000
[6,2,7,3,5,1,4,8]=>[8,4,1,5,3,7,2,6]=>0000000=>0000000
[2,7,8,1,5,6,3,4]=>[4,3,6,5,1,8,7,2]=>0000000=>0000000
[2,5,4,8,1,7,3,6]=>[6,3,7,1,8,4,5,2]=>0000000=>0000000
[5,1,3,2,6,7,8,4]=>[4,8,7,6,2,3,1,5]=>0000000=>0000000
[3,7,2,8,1,4,5,6]=>[6,5,4,1,8,2,7,3]=>0000000=>0000000
[5,2,3,7,4,6,1,8]=>[8,1,6,4,7,3,2,5]=>0000000=>0000000
[6,2,7,3,4,5,1,8]=>[8,1,5,4,3,7,2,6]=>0000000=>0000000
[6,2,8,3,5,1,4,7]=>[7,4,1,5,3,8,2,6]=>0000000=>0000000
[3,8,4,5,2,1,6,7]=>[7,6,1,2,5,4,8,3]=>0000000=>0000000
[8,2,6,3,5,1,4,7]=>[7,4,1,5,3,6,2,8]=>0000001=>1000000
[2,7,6,3,4,5,1,8]=>[8,1,5,4,3,6,7,2]=>0000000=>0000000
[2,8,6,3,5,1,4,7]=>[7,4,1,5,3,6,8,2]=>0000000=>0000000
[2,8,7,5,1,3,4,6]=>[6,4,3,1,5,7,8,2]=>0000000=>0000000
[5,2,1,4,8,7,6,3]=>[3,6,7,8,4,1,2,5]=>0000000=>0000000
[1,5,4,6,2,8,7,3]=>[3,7,8,2,6,4,5,1]=>0000000=>0000000
[6,2,1,5,8,4,7,3]=>[3,7,4,8,5,1,2,6]=>0000000=>0000000
[4,3,7,5,1,6,2,8]=>[8,2,6,1,5,7,3,4]=>0000000=>0000000
[5,3,1,4,6,7,8,2]=>[2,8,7,6,4,1,3,5]=>0000000=>0000000
[3,2,6,7,4,8,5,1]=>[1,5,8,4,7,6,2,3]=>1000000=>0000001
[6,3,2,7,5,8,4,1]=>[1,4,8,5,7,2,3,6]=>1000000=>0000001
[2,7,5,8,6,3,4,1]=>[1,4,3,6,8,5,7,2]=>1000000=>0000001
[6,5,2,7,4,1,3,8]=>[8,3,1,4,7,2,5,6]=>0000000=>0000000
[6,3,4,1,7,8,2,5]=>[5,2,8,7,1,4,3,6]=>0000000=>0000000
[4,5,8,2,3,7,1,6]=>[6,1,7,3,2,8,5,4]=>0000000=>0000000
[4,2,5,7,3,8,1,6]=>[6,1,8,3,7,5,2,4]=>0000000=>0000000
[5,1,4,6,2,8,3,7]=>[7,3,8,2,6,4,1,5]=>0000000=>0000000
[5,8,2,6,7,4,3,1]=>[1,3,4,7,6,2,8,5]=>1000000=>0000001
[5,2,6,8,3,7,1,4]=>[4,1,7,3,8,6,2,5]=>0000000=>0000000
[3,7,5,8,6,4,2,1]=>[1,2,4,6,8,5,7,3]=>1100000=>0000011
[7,4,5,8,2,3,6,1]=>[1,6,3,2,8,5,4,7]=>1000000=>0000001
[6,1,3,8,7,4,5,2]=>[2,5,4,7,8,3,1,6]=>0000000=>0000000
[3,1,4,8,2,7,6,5]=>[5,6,7,2,8,4,1,3]=>0000000=>0000000
[3,6,5,1,4,8,2,7]=>[7,2,8,4,1,5,6,3]=>0000000=>0000000
[1,5,8,7,3,4,6,2]=>[2,6,4,3,7,8,5,1]=>0000000=>0000000
[3,6,4,1,2,7,8,5]=>[5,8,7,2,1,4,6,3]=>0000000=>0000000
[4,1,7,3,8,6,2,5]=>[5,2,6,8,3,7,1,4]=>0000000=>0000000
[5,6,1,4,8,3,2,7]=>[7,2,3,8,4,1,6,5]=>0000000=>0000000
[5,3,6,4,1,8,2,7]=>[7,2,8,1,4,6,3,5]=>0000000=>0000000
[4,8,2,7,6,5,1,3]=>[3,1,5,6,7,2,8,4]=>0000000=>0000000
[7,4,2,8,6,5,1,3]=>[3,1,5,6,8,2,4,7]=>0000000=>0000000
[7,8,5,2,1,6,4,3]=>[3,4,6,1,2,5,8,7]=>0000010=>0100000
[3,2,1,6,5,8,4,7]=>[7,4,8,5,6,1,2,3]=>0000000=>0000000
[4,8,7,1,3,2,6,5]=>[5,6,2,3,1,7,8,4]=>0000000=>0000000
[8,1,5,7,4,2,6,3]=>[3,6,2,4,7,5,1,8]=>0000001=>1000000
[5,8,7,3,4,1,6,2]=>[2,6,1,4,3,7,8,5]=>0000000=>0000000
[3,6,2,1,8,5,7,4]=>[4,7,5,8,1,2,6,3]=>0000000=>0000000
[4,1,6,8,2,5,7,3]=>[3,7,5,2,8,6,1,4]=>0000000=>0000000
[2,4,5,8,1,3,7,6]=>[6,7,3,1,8,5,4,2]=>0000000=>0000000
[7,1,4,3,8,5,6,2]=>[2,6,5,8,3,4,1,7]=>0000000=>0000000
[2,7,8,6,5,3,1,4]=>[4,1,3,5,6,8,7,2]=>0000000=>0000000
[5,2,4,6,7,8,1,3]=>[3,1,8,7,6,4,2,5]=>0000000=>0000000
[8,1,4,6,5,7,3,2]=>[2,3,7,5,6,4,1,8]=>0000001=>1000000
[5,4,7,8,2,1,3,6]=>[6,3,1,2,8,7,4,5]=>0000000=>0000000
[4,7,5,8,1,2,3,6]=>[6,3,2,1,8,5,7,4]=>0000000=>0000000
[3,2,4,5,8,1,6,7]=>[7,6,1,8,5,4,2,3]=>0000000=>0000000
[2,4,6,8,3,7,1,5]=>[5,1,7,3,8,6,4,2]=>0000000=>0000000
[4,6,8,3,7,2,1,5]=>[5,1,2,7,3,8,6,4]=>0000000=>0000000
[3,6,5,1,7,2,8,4]=>[4,8,2,7,1,5,6,3]=>0000000=>0000000
[7,4,2,8,5,1,6,3]=>[3,6,1,5,8,2,4,7]=>0000000=>0000000
[6,1,8,5,4,2,7,3]=>[3,7,2,4,5,8,1,6]=>0000000=>0000000
[8,5,4,1,6,2,7,3]=>[3,7,2,6,1,4,5,8]=>0000001=>1000000
[5,6,3,1,7,2,8,4]=>[4,8,2,7,1,3,6,5]=>0000000=>0000000
[2,7,1,3,4,6,8,5]=>[5,8,6,4,3,1,7,2]=>0000000=>0000000
[2,8,1,3,4,7,6,5]=>[5,6,7,4,3,1,8,2]=>0000000=>0000000
[4,3,5,8,6,2,1,7]=>[7,1,2,6,8,5,3,4]=>0000000=>0000000
[7,6,8,4,2,1,5,3]=>[3,5,1,2,4,8,6,7]=>0000100=>0010000
[7,6,8,4,2,5,1,3]=>[3,1,5,2,4,8,6,7]=>0000100=>0010000
[8,6,7,2,3,5,1,4]=>[4,1,5,3,2,7,6,8]=>0000101=>1010000
[6,7,2,1,4,8,5,3]=>[3,5,8,4,1,2,7,6]=>0000000=>0000000
[1,8,6,3,4,5,7,2]=>[2,7,5,4,3,6,8,1]=>0000000=>0000000
[5,2,7,3,4,8,6,1]=>[1,6,8,4,3,7,2,5]=>1000000=>0000001
[5,7,3,2,4,8,6,1]=>[1,6,8,4,2,3,7,5]=>1000000=>0000001
[5,7,3,8,6,4,2,1]=>[1,2,4,6,8,3,7,5]=>1100000=>0000011
[7,3,5,2,4,8,6,1]=>[1,6,8,4,2,5,3,7]=>1000000=>0000001
[4,5,2,6,7,1,8,3]=>[3,8,1,7,6,2,5,4]=>0000000=>0000000
[5,7,1,2,6,8,4,3]=>[3,4,8,6,2,1,7,5]=>0000000=>0000000
[2,7,4,6,1,3,5,8]=>[8,5,3,1,6,4,7,2]=>0000000=>0000000
[7,6,1,3,5,4,2,8]=>[8,2,4,5,3,1,6,7]=>0000000=>0000000
[7,6,2,3,1,5,4,8]=>[8,4,5,1,3,2,6,7]=>0000000=>0000000
[3,6,4,1,8,2,5,7]=>[7,5,2,8,1,4,6,3]=>0000000=>0000000
[8,7,3,5,1,4,6,2]=>[2,6,4,1,5,3,7,8]=>0000011=>1100000
[8,7,3,5,2,4,6,1]=>[1,6,4,2,5,3,7,8]=>1000011=>1100001
[5,2,8,7,6,4,1,3]=>[3,1,4,6,7,8,2,5]=>0000000=>0000000
[7,5,3,4,2,8,6,1]=>[1,6,8,2,4,3,5,7]=>1000000=>0000001
[7,1,2,4,5,6,3,8]=>[8,3,6,5,4,2,1,7]=>0000000=>0000000
[6,3,8,5,4,2,7,1]=>[1,7,2,4,5,8,3,6]=>1000000=>0000001
[6,2,3,8,5,4,7,1]=>[1,7,4,5,8,3,2,6]=>1000000=>0000001
[1,5,3,8,7,4,6,2]=>[2,6,4,7,8,3,5,1]=>0000000=>0000000
[2,5,3,8,7,4,1,6]=>[6,1,4,7,8,3,5,2]=>0000000=>0000000
[5,2,1,8,7,4,6,3]=>[3,6,4,7,8,1,2,5]=>0000000=>0000000
[6,8,3,5,1,2,7,4]=>[4,7,2,1,5,3,8,6]=>0000000=>0000000
[4,5,8,3,1,2,7,6]=>[6,7,2,1,3,8,5,4]=>0000000=>0000000
[4,6,8,3,2,1,7,5]=>[5,7,1,2,3,8,6,4]=>0000000=>0000000
[4,6,8,3,5,1,2,7]=>[7,2,1,5,3,8,6,4]=>0000000=>0000000
[8,5,7,1,3,6,2,4]=>[4,2,6,3,1,7,5,8]=>0000001=>1000000
[4,6,7,3,5,2,1,8]=>[8,1,2,5,3,7,6,4]=>0000000=>0000000
[5,6,8,4,1,2,3,7]=>[7,3,2,1,4,8,6,5]=>0000000=>0000000
[1,3,8,7,4,5,6,2]=>[2,6,5,4,7,8,3,1]=>0000000=>0000000
[7,6,8,3,2,5,1,4]=>[4,1,5,2,3,8,6,7]=>0000100=>0010000
[4,6,7,3,2,5,1,8]=>[8,1,5,2,3,7,6,4]=>0000000=>0000000
[5,4,2,7,3,8,6,1]=>[1,6,8,3,7,2,4,5]=>1000000=>0000001
[6,3,5,4,8,1,2,7]=>[7,2,1,8,4,5,3,6]=>0000000=>0000000
[6,2,5,4,1,7,8,3]=>[3,8,7,1,4,5,2,6]=>0000000=>0000000
[4,1,5,6,3,8,7,2]=>[2,7,8,3,6,5,1,4]=>0000000=>0000000
[6,8,7,4,3,2,5,1]=>[1,5,2,3,4,7,8,6]=>1000100=>0010001
[2,4,5,8,3,7,6,1]=>[1,6,7,3,8,5,4,2]=>1000000=>0000001
[8,3,5,4,1,7,6,2]=>[2,6,7,1,4,5,3,8]=>0000001=>1000000
[8,2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2,8]=>0000001=>1000000
[1,3,8,7,2,5,6,4]=>[4,6,5,2,7,8,3,1]=>0000000=>0000000
[5,1,4,8,3,7,6,2]=>[2,6,7,3,8,4,1,5]=>0000000=>0000000
[4,8,3,2,7,6,5,1]=>[1,5,6,7,2,3,8,4]=>1000000=>0000001
[2,4,8,1,7,6,5,3]=>[3,5,6,7,1,8,4,2]=>0000000=>0000000
[1,8,4,2,5,7,3,6]=>[6,3,7,5,2,4,8,1]=>0000000=>0000000
[5,8,3,1,2,4,6,7]=>[7,6,4,2,1,3,8,5]=>0000000=>0000000
[6,1,4,2,8,7,3,5]=>[5,3,7,8,2,4,1,6]=>0000000=>0000000
[6,1,4,8,2,7,3,5]=>[5,3,7,2,8,4,1,6]=>0000000=>0000000
[4,7,5,6,2,8,3,1]=>[1,3,8,2,6,5,7,4]=>1000000=>0000001
[8,4,3,6,7,5,2,1]=>[1,2,5,7,6,3,4,8]=>1100001=>1000011
[6,7,5,2,8,4,3,1]=>[1,3,4,8,2,5,7,6]=>1000000=>0000001
[6,8,4,3,2,7,5,1]=>[1,5,7,2,3,4,8,6]=>1000000=>0000001
[8,1,4,2,7,6,5,3]=>[3,5,6,7,2,4,1,8]=>0000001=>1000000
[2,8,7,6,4,1,5,3]=>[3,5,1,4,6,7,8,2]=>0000000=>0000000
[5,3,1,6,4,8,2,7]=>[7,2,8,4,6,1,3,5]=>0000000=>0000000
[2,5,6,7,1,4,8,3]=>[3,8,4,1,7,6,5,2]=>0000000=>0000000
[2,7,3,5,8,4,6,1]=>[1,6,4,8,5,3,7,2]=>1000000=>0000001
[1,3,4,7,5,8,6,2]=>[2,6,8,5,7,4,3,1]=>0000000=>0000000
[5,2,3,6,8,4,1,7]=>[7,1,4,8,6,3,2,5]=>0000000=>0000000
[3,6,2,4,8,7,5,1]=>[1,5,7,8,4,2,6,3]=>1000000=>0000001
[4,3,2,7,5,8,6,1]=>[1,6,8,5,7,2,3,4]=>1000000=>0000001
[4,8,6,1,2,7,5,3]=>[3,5,7,2,1,6,8,4]=>0000000=>0000000
[2,3,7,1,5,6,8,4]=>[4,8,6,5,1,7,3,2]=>0000000=>0000000
[2,7,1,4,6,8,3,5]=>[5,3,8,6,4,1,7,2]=>0000000=>0000000
[5,7,1,4,2,8,3,6]=>[6,3,8,2,4,1,7,5]=>0000000=>0000000
[6,1,4,8,3,5,2,7]=>[7,2,5,3,8,4,1,6]=>0000000=>0000000
[5,4,8,6,3,1,2,7]=>[7,2,1,3,6,8,4,5]=>0000000=>0000000
[5,6,1,2,4,8,3,7]=>[7,3,8,4,2,1,6,5]=>0000000=>0000000
[8,7,4,5,1,3,2,6]=>[6,2,3,1,5,4,7,8]=>0000011=>1100000
[7,8,6,1,2,3,5,4]=>[4,5,3,2,1,6,8,7]=>0000110=>0110000
[1,7,8,2,3,5,6,4]=>[4,6,5,3,2,8,7,1]=>0000000=>0000000
[1,3,7,6,8,4,2,5]=>[5,2,4,8,6,7,3,1]=>0000000=>0000000
[4,8,5,1,3,2,7,6]=>[6,7,2,3,1,5,8,4]=>0000000=>0000000
[4,5,7,8,6,2,1,3]=>[3,1,2,6,8,7,5,4]=>0010000=>0000100
[2,3,6,8,5,7,4,1]=>[1,4,7,5,8,6,3,2]=>1000000=>0000001
[2,1,5,7,4,6,8,3]=>[3,8,6,4,7,5,1,2]=>0000000=>0000000
[5,7,2,3,6,8,4,1]=>[1,4,8,6,3,2,7,5]=>1000000=>0000001
[8,2,3,5,6,4,1,7]=>[7,1,4,6,5,3,2,8]=>0000001=>1000000
[2,4,7,5,3,6,8,1]=>[1,8,6,3,5,7,4,2]=>1000000=>0000001
[8,2,4,6,1,7,3,5]=>[5,3,7,1,6,4,2,8]=>0000001=>1000000
[2,4,7,8,6,3,5,1]=>[1,5,3,6,8,7,4,2]=>1000000=>0000001
[2,3,5,7,8,4,1,6]=>[6,1,4,8,7,5,3,2]=>0000000=>0000000
[3,6,2,5,8,4,7,1]=>[1,7,4,8,5,2,6,3]=>1000000=>0000001
[2,5,8,3,6,4,7,1]=>[1,7,4,6,3,8,5,2]=>1000000=>0000001
[3,6,4,7,2,5,8,1]=>[1,8,5,2,7,4,6,3]=>1000000=>0000001
[1,8,7,2,5,3,6,4]=>[4,6,3,5,2,7,8,1]=>0000000=>0000000
[2,8,3,1,7,4,6,5]=>[5,6,4,7,1,3,8,2]=>0000000=>0000000
[3,6,7,2,5,4,8,1]=>[1,8,4,5,2,7,6,3]=>1000000=>0000001
[4,1,6,5,2,3,7,8]=>[8,7,3,2,5,6,1,4]=>0000000=>0000000
[4,6,1,2,8,3,7,5]=>[5,7,3,8,2,1,6,4]=>0000000=>0000000
[2,7,5,8,1,3,6,4]=>[4,6,3,1,8,5,7,2]=>0000000=>0000000
[2,1,8,4,7,6,3,5]=>[5,3,6,7,4,8,1,2]=>0000000=>0000000
[7,2,4,3,8,6,5,1]=>[1,5,6,8,3,4,2,7]=>1000000=>0000001
[5,4,8,6,3,2,1,7]=>[7,1,2,3,6,8,4,5]=>0000000=>0000000
[7,8,2,4,5,6,3,1]=>[1,3,6,5,4,2,8,7]=>1000010=>0100001
[6,4,1,5,3,7,2,8]=>[8,2,7,3,5,1,4,6]=>0000000=>0000000
[2,1,6,4,7,8,3,5]=>[5,3,8,7,4,6,1,2]=>0000000=>0000000
[5,4,2,6,7,8,3,1]=>[1,3,8,7,6,2,4,5]=>1000000=>0000001
[1,3,5,8,4,6,7,2]=>[2,7,6,4,8,5,3,1]=>0000000=>0000000
[3,4,5,8,2,1,6,7]=>[7,6,1,2,8,5,4,3]=>0000000=>0000000
[8,5,7,2,4,3,6,1]=>[1,6,3,4,2,7,5,8]=>1000001=>1000001
[3,4,8,2,7,1,5,6]=>[6,5,1,7,2,8,4,3]=>0000000=>0000000
[7,2,6,1,4,8,3,5]=>[5,3,8,4,1,6,2,7]=>0000000=>0000000
[7,2,8,3,4,5,1,6]=>[6,1,5,4,3,8,2,7]=>0000000=>0000000
[1,7,2,6,3,4,8,5]=>[5,8,4,3,6,2,7,1]=>0000000=>0000000
[1,4,5,2,3,8,7,6]=>[6,7,8,3,2,5,4,1]=>0000000=>0000000
[7,2,1,8,5,4,3,6]=>[6,3,4,5,8,1,2,7]=>0000000=>0000000
[3,1,7,6,8,5,2,4]=>[4,2,5,8,6,7,1,3]=>0000000=>0000000
[2,6,1,8,7,3,4,5]=>[5,4,3,7,8,1,6,2]=>0000000=>0000000
[2,1,7,8,3,5,6,4]=>[4,6,5,3,8,7,1,2]=>0000000=>0000000
[5,8,4,3,6,7,2,1]=>[1,2,7,6,3,4,8,5]=>1100000=>0000011
[3,2,6,5,1,8,4,7]=>[7,4,8,1,5,6,2,3]=>0000000=>0000000
[4,5,8,1,6,7,3,2]=>[2,3,7,6,1,8,5,4]=>0000000=>0000000
[8,4,3,6,2,7,1,5]=>[5,1,7,2,6,3,4,8]=>0000001=>1000000
[1,7,6,4,5,8,2,3]=>[3,2,8,5,4,6,7,1]=>0000000=>0000000
[6,5,3,8,1,7,2,4]=>[4,2,7,1,8,3,5,6]=>0000000=>0000000
[7,3,2,6,4,8,5,1]=>[1,5,8,4,6,2,3,7]=>1000000=>0000001
[3,7,6,2,5,4,8,1]=>[1,8,4,5,2,6,7,3]=>1000000=>0000001
[4,7,2,6,5,3,8,1]=>[1,8,3,5,6,2,7,4]=>1000000=>0000001
[2,8,3,7,6,1,5,4]=>[4,5,1,6,7,3,8,2]=>0000000=>0000000
[5,4,3,7,2,8,6,1]=>[1,6,8,2,7,3,4,5]=>1000000=>0000001
[4,6,5,3,8,1,7,2]=>[2,7,1,8,3,5,6,4]=>0000000=>0000000
[7,2,3,8,4,6,5,1]=>[1,5,6,4,8,3,2,7]=>1000000=>0000001
[4,7,8,6,5,2,1,3]=>[3,1,2,5,6,8,7,4]=>0010000=>0000100
[2,5,8,7,6,4,1,3]=>[3,1,4,6,7,8,5,2]=>0000000=>0000000
[7,3,8,6,2,5,4,1]=>[1,4,5,2,6,8,3,7]=>1000000=>0000001
[5,8,1,7,6,2,3,4]=>[4,3,2,6,7,1,8,5]=>0000000=>0000000
[2,3,8,6,4,5,1,7]=>[7,1,5,4,6,8,3,2]=>0000000=>0000000
[6,4,8,5,1,7,2,3]=>[3,2,7,1,5,8,4,6]=>0000000=>0000000
[5,2,8,1,3,6,7,4]=>[4,7,6,3,1,8,2,5]=>0000000=>0000000
[6,3,7,2,5,4,8,1]=>[1,8,4,5,2,7,3,6]=>1000000=>0000001
[6,2,1,8,7,4,5,3]=>[3,5,4,7,8,1,2,6]=>0000000=>0000000
[7,4,3,8,5,6,2,1]=>[1,2,6,5,8,3,4,7]=>1100000=>0000011
[4,2,1,6,5,7,8,3]=>[3,8,7,5,6,1,2,4]=>0000000=>0000000
[8,6,1,4,3,5,2,7]=>[7,2,5,3,4,1,6,8]=>0000001=>1000000
[8,1,3,2,5,7,4,6]=>[6,4,7,5,2,3,1,8]=>0000001=>1000000
[4,6,7,2,1,5,3,8]=>[8,3,5,1,2,7,6,4]=>0000000=>0000000
[1,7,6,2,4,3,8,5]=>[5,8,3,4,2,6,7,1]=>0000000=>0000000
[2,3,6,7,4,5,1,8]=>[8,1,5,4,7,6,3,2]=>0000000=>0000000
[7,5,4,1,8,6,2,3]=>[3,2,6,8,1,4,5,7]=>0000000=>0000000
[8,2,5,6,3,1,4,7]=>[7,4,1,3,6,5,2,8]=>0000001=>1000000
[5,3,7,2,4,1,8,6]=>[6,8,1,4,2,7,3,5]=>0000000=>0000000
[6,1,4,7,8,5,3,2]=>[2,3,5,8,7,4,1,6]=>0000000=>0000000
[7,8,1,3,4,5,2,6]=>[6,2,5,4,3,1,8,7]=>0000010=>0100000
[8,2,4,5,6,7,1,3]=>[3,1,7,6,5,4,2,8]=>0000001=>1000000
[2,6,3,1,8,4,7,5]=>[5,7,4,8,1,3,6,2]=>0000000=>0000000
[5,2,1,6,8,7,4,3]=>[3,4,7,8,6,1,2,5]=>0000000=>0000000
[5,6,2,7,4,8,3,1]=>[1,3,8,4,7,2,6,5]=>1000000=>0000001
[6,4,1,3,8,7,5,2]=>[2,5,7,8,3,1,4,6]=>0000000=>0000000
[7,5,2,3,8,4,6,1]=>[1,6,4,8,3,2,5,7]=>1000000=>0000001
[2,7,3,8,5,1,6,4]=>[4,6,1,5,8,3,7,2]=>0000000=>0000000
[8,2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2,8]=>0000001=>1000000
[4,5,2,6,1,3,8,7]=>[7,8,3,1,6,2,5,4]=>0000000=>0000000
[2,1,6,7,4,8,3,5]=>[5,3,8,4,7,6,1,2]=>0000000=>0000000
[5,8,6,3,2,1,4,7]=>[7,4,1,2,3,6,8,5]=>0000000=>0000000
[7,4,5,6,8,1,3,2]=>[2,3,1,8,6,5,4,7]=>0010000=>0000100
[7,5,2,6,3,4,8,1]=>[1,8,4,3,6,2,5,7]=>1000000=>0000001
[7,3,6,2,5,4,8,1]=>[1,8,4,5,2,6,3,7]=>1000000=>0000001
[1,2,6,4,8,5,3,7]=>[7,3,5,8,4,6,2,1]=>0000000=>0000000
[6,1,5,3,8,4,7,2]=>[2,7,4,8,3,5,1,6]=>0000000=>0000000
[1,6,5,3,8,4,7,2]=>[2,7,4,8,3,5,6,1]=>0000000=>0000000
[7,6,2,3,5,1,4,8]=>[8,4,1,5,3,2,6,7]=>0000000=>0000000
[6,1,5,2,3,4,8,7]=>[7,8,4,3,2,5,1,6]=>0000000=>0000000
[6,2,5,3,4,8,1,7]=>[7,1,8,4,3,5,2,6]=>0000000=>0000000
[6,2,5,3,4,8,7,1]=>[1,7,8,4,3,5,2,6]=>1000000=>0000001
[2,6,5,3,4,8,7,1]=>[1,7,8,4,3,5,6,2]=>1000000=>0000001
[2,6,5,3,4,8,1,7]=>[7,1,8,4,3,5,6,2]=>0000000=>0000000
[2,5,1,4,8,3,7,6]=>[6,7,3,8,4,1,5,2]=>0000000=>0000000
[1,2,5,4,8,3,7,6]=>[6,7,3,8,4,5,2,1]=>0000000=>0000000
[5,3,4,8,1,7,2,6]=>[6,2,7,1,8,4,3,5]=>0000000=>0000000
[5,1,3,4,8,7,2,6]=>[6,2,7,8,4,3,1,5]=>0000000=>0000000
[1,5,3,4,8,7,2,6]=>[6,2,7,8,4,3,5,1]=>0000000=>0000000
[5,1,3,8,4,7,6,2]=>[2,6,7,4,8,3,1,5]=>0000000=>0000000
[5,3,8,1,4,7,6,2]=>[2,6,7,4,1,8,3,5]=>0000000=>0000000
[4,3,5,8,1,7,6,2]=>[2,6,7,1,8,5,3,4]=>0000000=>0000000
[3,6,5,4,8,1,2,7]=>[7,2,1,8,4,5,6,3]=>0000000=>0000000
[3,6,5,4,8,2,7,1]=>[1,7,2,8,4,5,6,3]=>1000000=>0000001
[3,5,2,4,8,7,6,1]=>[1,6,7,8,4,2,5,3]=>1000000=>0000001
[2,6,3,1,5,7,8,4]=>[4,8,7,5,1,3,6,2]=>0000000=>0000000
[6,2,5,3,1,7,8,4]=>[4,8,7,1,3,5,2,6]=>0000000=>0000000
[2,3,5,1,7,6,4,8]=>[8,4,6,7,1,5,3,2]=>0000000=>0000000
[4,7,5,1,3,2,8,6]=>[6,8,2,3,1,5,7,4]=>0000000=>0000000
[2,6,3,8,7,4,1,5]=>[5,1,4,7,8,3,6,2]=>0000000=>0000000
[6,1,3,5,2,7,8,4]=>[4,8,7,2,5,3,1,6]=>0000000=>0000000
[4,2,8,1,3,6,7,5]=>[5,7,6,3,1,8,2,4]=>0000000=>0000000
[8,1,3,6,2,5,7,4]=>[4,7,5,2,6,3,1,8]=>0000001=>1000000
[1,7,4,6,3,5,8,2]=>[2,8,5,3,6,4,7,1]=>0000000=>0000000
[7,1,4,8,3,6,2,5]=>[5,2,6,3,8,4,1,7]=>0000000=>0000000
[5,2,7,1,4,8,3,6]=>[6,3,8,4,1,7,2,5]=>0000000=>0000000
[5,2,7,3,6,1,4,8]=>[8,4,1,6,3,7,2,5]=>0000000=>0000000
[8,2,5,7,4,1,3,6]=>[6,3,1,4,7,5,2,8]=>0000001=>1000000
[6,4,8,1,2,5,7,3]=>[3,7,5,2,1,8,4,6]=>0000000=>0000000
[5,4,1,2,8,3,7,6]=>[6,7,3,8,2,1,4,5]=>0000000=>0000000
[4,7,1,8,2,3,6,5]=>[5,6,3,2,8,1,7,4]=>0000000=>0000000
[2,3,5,8,7,4,6,1]=>[1,6,4,7,8,5,3,2]=>1000000=>0000001
[5,4,2,7,8,3,1,6]=>[6,1,3,8,7,2,4,5]=>0000000=>0000000
[1,8,4,5,7,3,6,2]=>[2,6,3,7,5,4,8,1]=>0000000=>0000000
[2,8,3,1,7,4,5,6]=>[6,5,4,7,1,3,8,2]=>0000000=>0000000
[2,3,7,6,5,1,4,8]=>[8,4,1,5,6,7,3,2]=>0000000=>0000000
[4,6,7,5,2,8,3,1]=>[1,3,8,2,5,7,6,4]=>1000000=>0000001
[6,2,4,7,3,5,1,8]=>[8,1,5,3,7,4,2,6]=>0000000=>0000000
[6,1,8,3,5,2,4,7]=>[7,4,2,5,3,8,1,6]=>0000000=>0000000
[4,3,1,5,6,7,2,8]=>[8,2,7,6,5,1,3,4]=>0000000=>0000000
[5,4,6,2,1,7,3,8]=>[8,3,7,1,2,6,4,5]=>0000000=>0000000
[1,5,6,4,2,3,7,8]=>[8,7,3,2,4,6,5,1]=>0000000=>0000000
[5,8,1,4,2,6,7,3]=>[3,7,6,2,4,1,8,5]=>0000000=>0000000
[6,5,1,2,4,3,8,7]=>[7,8,3,4,2,1,5,6]=>0000000=>0000000
[2,5,1,4,6,3,8,7]=>[7,8,3,6,4,1,5,2]=>0000000=>0000000
[5,8,7,3,1,2,4,6]=>[6,4,2,1,3,7,8,5]=>0000000=>0000000
[2,5,6,3,8,7,1,4]=>[4,1,7,8,3,6,5,2]=>0000000=>0000000
[8,7,5,1,2,4,3,6]=>[6,3,4,2,1,5,7,8]=>0000011=>1100000
[8,6,2,3,5,4,1,7]=>[7,1,4,5,3,2,6,8]=>0000001=>1000000
[5,3,4,1,8,2,7,6]=>[6,7,2,8,1,4,3,5]=>0000000=>0000000
[8,2,4,5,1,7,3,6]=>[6,3,7,1,5,4,2,8]=>0000001=>1000000
[8,1,4,3,7,5,6,2]=>[2,6,5,7,3,4,1,8]=>0000001=>1000000
[8,3,7,6,2,4,5,1]=>[1,5,4,2,6,7,3,8]=>1000001=>1000001
[8,2,7,6,3,1,4,5]=>[5,4,1,3,6,7,2,8]=>0000001=>1000000
[6,8,1,4,7,3,2,5]=>[5,2,3,7,4,1,8,6]=>0000000=>0000000
[8,4,1,7,5,6,2,3]=>[3,2,6,5,7,1,4,8]=>0000001=>1000000
[8,1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1,8]=>0000001=>1000000
[8,1,5,7,3,6,4,2]=>[2,4,6,3,7,5,1,8]=>0000001=>1000000
[1,7,3,8,6,2,5,4]=>[4,5,2,6,8,3,7,1]=>0000000=>0000000
[7,3,8,6,2,1,5,4]=>[4,5,1,2,6,8,3,7]=>0000000=>0000000
[5,8,2,7,3,1,4,6]=>[6,4,1,3,7,2,8,5]=>0000000=>0000000
[8,5,1,3,4,7,2,6]=>[6,2,7,4,3,1,5,8]=>0000001=>1000000
[5,8,2,3,7,4,1,6]=>[6,1,4,7,3,2,8,5]=>0000000=>0000000
[8,3,6,7,5,2,1,4]=>[4,1,2,5,7,6,3,8]=>0000001=>1000000
[8,5,4,2,6,7,3,1]=>[1,3,7,6,2,4,5,8]=>1000001=>1000001
[5,4,2,8,3,7,1,6]=>[6,1,7,3,8,2,4,5]=>0000000=>0000000
[5,4,3,7,2,1,8,6]=>[6,8,1,2,7,3,4,5]=>0000000=>0000000
[1,5,3,2,8,6,7,4]=>[4,7,6,8,2,3,5,1]=>0000000=>0000000
[4,3,1,6,7,2,8,5]=>[5,8,2,7,6,1,3,4]=>0000000=>0000000
[6,5,2,4,3,8,1,7]=>[7,1,8,3,4,2,5,6]=>0000000=>0000000
[1,5,6,8,4,3,2,7]=>[7,2,3,4,8,6,5,1]=>0000000=>0000000
[6,3,5,7,1,4,2,8]=>[8,2,4,1,7,5,3,6]=>0000000=>0000000
[6,3,2,1,5,7,8,4]=>[4,8,7,5,1,2,3,6]=>0000000=>0000000
[8,4,1,6,7,3,2,5]=>[5,2,3,7,6,1,4,8]=>0000001=>1000000
[6,3,5,2,8,4,7,1]=>[1,7,4,8,2,5,3,6]=>1000000=>0000001
[5,4,8,6,3,7,2,1]=>[1,2,7,3,6,8,4,5]=>1100000=>0000011
[5,4,8,6,3,7,1,2]=>[2,1,7,3,6,8,4,5]=>0100000=>0000010
[6,4,5,8,1,3,7,2]=>[2,7,3,1,8,5,4,6]=>0000000=>0000000
[6,3,5,2,8,1,7,4]=>[4,7,1,8,2,5,3,6]=>0000000=>0000000
[5,3,4,1,2,6,8,7]=>[7,8,6,2,1,4,3,5]=>0000000=>0000000
[3,5,4,8,2,6,1,7]=>[7,1,6,2,8,4,5,3]=>0000000=>0000000
[3,7,2,1,5,6,8,4]=>[4,8,6,5,1,2,7,3]=>0000000=>0000000
[7,5,1,6,3,4,2,8]=>[8,2,4,3,6,1,5,7]=>0000000=>0000000
[8,1,6,4,3,5,2,7]=>[7,2,5,3,4,6,1,8]=>0000001=>1000000
[4,1,3,7,8,2,5,6]=>[6,5,2,8,7,3,1,4]=>0000000=>0000000
[1,4,3,2,8,7,5,6]=>[6,5,7,8,2,3,4,1]=>0000000=>0000000
[1,3,7,8,6,2,4,5]=>[5,4,2,6,8,7,3,1]=>0000000=>0000000
[4,7,8,1,3,5,2,6]=>[6,2,5,3,1,8,7,4]=>0000000=>0000000
[3,8,6,4,5,2,7,1]=>[1,7,2,5,4,6,8,3]=>1000000=>0000001
[4,6,8,5,3,7,2,1]=>[1,2,7,3,5,8,6,4]=>1100000=>0000011
[4,5,7,2,8,6,3,1]=>[1,3,6,8,2,7,5,4]=>1000000=>0000001
[4,6,8,1,2,5,7,3]=>[3,7,5,2,1,8,6,4]=>0000000=>0000000
[4,6,8,3,7,1,5,2]=>[2,5,1,7,3,8,6,4]=>0000000=>0000000
[3,5,1,7,8,4,6,2]=>[2,6,4,8,7,1,5,3]=>0000000=>0000000
[8,3,6,2,4,1,7,5]=>[5,7,1,4,2,6,3,8]=>0000001=>1000000
[7,4,5,3,8,6,2,1]=>[1,2,6,8,3,5,4,7]=>1100000=>0000011
[5,2,3,8,4,7,6,1]=>[1,6,7,4,8,3,2,5]=>1000000=>0000001
[7,2,5,4,8,3,1,6]=>[6,1,3,8,4,5,2,7]=>0000000=>0000000
[5,2,8,7,4,6,3,1]=>[1,3,6,4,7,8,2,5]=>1000000=>0000001
[4,3,6,1,8,5,2,7]=>[7,2,5,8,1,6,3,4]=>0000000=>0000000
[2,5,4,7,3,1,8,6]=>[6,8,1,3,7,4,5,2]=>0000000=>0000000
[7,4,2,3,6,8,1,5]=>[5,1,8,6,3,2,4,7]=>0000000=>0000000
[5,3,6,4,8,2,7,1]=>[1,7,2,8,4,6,3,5]=>1000000=>0000001
[4,8,7,1,3,6,2,5]=>[5,2,6,3,1,7,8,4]=>0000000=>0000000
[4,6,1,8,5,2,3,7]=>[7,3,2,5,8,1,6,4]=>0000000=>0000000
[4,3,7,5,8,2,1,6]=>[6,1,2,8,5,7,3,4]=>0000000=>0000000
[1,5,2,7,6,4,8,3]=>[3,8,4,6,7,2,5,1]=>0000000=>0000000
[1,5,8,6,2,7,4,3]=>[3,4,7,2,6,8,5,1]=>0000000=>0000000
[2,6,5,3,4,7,1,8]=>[8,1,7,4,3,5,6,2]=>0000000=>0000000
[5,4,2,7,6,3,1,8]=>[8,1,3,6,7,2,4,5]=>0000000=>0000000
[1,3,5,8,7,2,6,4]=>[4,6,2,7,8,5,3,1]=>0000000=>0000000
[6,5,3,1,7,4,8,2]=>[2,8,4,7,1,3,5,6]=>0000000=>0000000
[6,4,1,8,5,7,3,2]=>[2,3,7,5,8,1,4,6]=>0000000=>0000000
[6,5,8,2,1,4,7,3]=>[3,7,4,1,2,8,5,6]=>0000000=>0000000
[3,6,7,2,1,5,8,4]=>[4,8,5,1,2,7,6,3]=>0000000=>0000000
[2,5,6,1,3,8,7,4]=>[4,7,8,3,1,6,5,2]=>0000000=>0000000
[2,4,8,7,3,6,1,5]=>[5,1,6,3,7,8,4,2]=>0000000=>0000000
[3,2,7,6,8,4,5,1]=>[1,5,4,8,6,7,2,3]=>1000000=>0000001
[4,3,8,6,7,2,5,1]=>[1,5,2,7,6,8,3,4]=>1000000=>0000001
[4,3,8,5,6,2,7,1]=>[1,7,2,6,5,8,3,4]=>1000000=>0000001
[5,4,8,6,7,2,3,1]=>[1,3,2,7,6,8,4,5]=>1010000=>0000101
[7,3,4,2,8,5,6,1]=>[1,6,5,8,2,4,3,7]=>1000000=>0000001
[4,3,6,5,8,2,7,1]=>[1,7,2,8,5,6,3,4]=>1000000=>0000001
[3,2,6,8,4,5,7,1]=>[1,7,5,4,8,6,2,3]=>1000000=>0000001
[6,2,5,8,4,7,3,1]=>[1,3,7,4,8,5,2,6]=>1000000=>0000001
[4,6,7,8,3,1,2,5]=>[5,2,1,3,8,7,6,4]=>0000000=>0000000
[1,8,4,2,3,7,5,6]=>[6,5,7,3,2,4,8,1]=>0000000=>0000000
[7,3,4,2,8,6,1,5]=>[5,1,6,8,2,4,3,7]=>0000000=>0000000
[7,1,8,2,4,3,5,6]=>[6,5,3,4,2,8,1,7]=>0000000=>0000000
[7,6,1,8,3,4,2,5]=>[5,2,4,3,8,1,6,7]=>0000000=>0000000
[6,4,2,3,8,7,5,1]=>[1,5,7,8,3,2,4,6]=>1000000=>0000001
[5,1,3,2,7,6,4,8]=>[8,4,6,7,2,3,1,5]=>0000000=>0000000
[5,1,3,2,8,7,6,4]=>[4,6,7,8,2,3,1,5]=>0000000=>0000000
[5,1,3,2,8,6,4,7]=>[7,4,6,8,2,3,1,5]=>0000000=>0000000
[6,5,1,3,8,4,2,7]=>[7,2,4,8,3,1,5,6]=>0000000=>0000000
[6,1,4,2,7,8,3,5]=>[5,3,8,7,2,4,1,6]=>0000000=>0000000
[6,5,1,3,7,8,4,2]=>[2,4,8,7,3,1,5,6]=>0000000=>0000000
[5,1,3,2,7,8,6,4]=>[4,6,8,7,2,3,1,5]=>0000000=>0000000
[4,1,3,2,6,5,7,8]=>[8,7,5,6,2,3,1,4]=>0000000=>0000000
[4,1,3,2,7,8,6,5]=>[5,6,8,7,2,3,1,4]=>0000000=>0000000
[5,6,8,2,4,7,1,3]=>[3,1,7,4,2,8,6,5]=>0000000=>0000000
[5,6,7,1,4,8,2,3]=>[3,2,8,4,1,7,6,5]=>0000000=>0000000
[4,1,3,2,7,6,5,8]=>[8,5,6,7,2,3,1,4]=>0000000=>0000000
[4,1,3,2,7,5,6,8]=>[8,6,5,7,2,3,1,4]=>0000000=>0000000
[6,7,4,2,3,8,5,1]=>[1,5,8,3,2,4,7,6]=>1000000=>0000001
[5,6,1,4,7,3,2,8]=>[8,2,3,7,4,1,6,5]=>0000000=>0000000
[5,8,6,1,4,7,3,2]=>[2,3,7,4,1,6,8,5]=>0000000=>0000000
[4,1,3,2,6,7,5,8]=>[8,5,7,6,2,3,1,4]=>0000000=>0000000
[4,1,3,2,5,8,7,6]=>[6,7,8,5,2,3,1,4]=>0000000=>0000000
[4,1,3,2,5,8,6,7]=>[7,6,8,5,2,3,1,4]=>0000000=>0000000
[4,1,3,2,6,8,5,7]=>[7,5,8,6,2,3,1,4]=>0000000=>0000000
[5,1,3,2,6,8,4,7]=>[7,4,8,6,2,3,1,5]=>0000000=>0000000
[5,7,1,4,6,8,2,3]=>[3,2,8,6,4,1,7,5]=>0000000=>0000000
[5,7,8,3,2,4,6,1]=>[1,6,4,2,3,8,7,5]=>1000000=>0000001
[4,1,3,2,5,6,8,7]=>[7,8,6,5,2,3,1,4]=>0000000=>0000000
[6,2,7,4,1,8,3,5]=>[5,3,8,1,4,7,2,6]=>0000000=>0000000
[1,4,7,8,2,6,3,5]=>[5,3,6,2,8,7,4,1]=>0000000=>0000000
[6,5,2,3,8,1,4,7]=>[7,4,1,8,3,2,5,6]=>0000000=>0000000
[3,6,1,5,8,2,7,4]=>[4,7,2,8,5,1,6,3]=>0000000=>0000000
[5,3,4,7,8,6,2,1]=>[1,2,6,8,7,4,3,5]=>1100000=>0000011
[2,3,8,4,5,6,1,7]=>[7,1,6,5,4,8,3,2]=>0000000=>0000000
[6,4,1,8,2,7,3,5]=>[5,3,7,2,8,1,4,6]=>0000000=>0000000
[7,2,4,6,5,8,3,1]=>[1,3,8,5,6,4,2,7]=>1000000=>0000001
[2,6,8,4,3,1,5,7]=>[7,5,1,3,4,8,6,2]=>0000000=>0000000
[5,8,6,4,7,3,2,1]=>[1,2,3,7,4,6,8,5]=>1110000=>0000111
[8,5,4,2,1,6,7,3]=>[3,7,6,1,2,4,5,8]=>0000001=>1000000
[3,8,6,2,5,4,7,1]=>[1,7,4,5,2,6,8,3]=>1000000=>0000001
[5,2,6,4,1,3,8,7]=>[7,8,3,1,4,6,2,5]=>0000000=>0000000
[7,2,8,5,4,1,3,6]=>[6,3,1,4,5,8,2,7]=>0000000=>0000000
[6,4,8,5,3,2,7,1]=>[1,7,2,3,5,8,4,6]=>1000000=>0000001
[4,7,8,5,3,2,6,1]=>[1,6,2,3,5,8,7,4]=>1000000=>0000001
[5,7,6,3,8,4,2,1]=>[1,2,4,8,3,6,7,5]=>1100000=>0000011
[5,2,7,3,4,8,1,6]=>[6,1,8,4,3,7,2,5]=>0000000=>0000000
[2,7,5,1,3,4,6,8]=>[8,6,4,3,1,5,7,2]=>0000000=>0000000
[6,4,7,3,5,8,2,1]=>[1,2,8,5,3,7,4,6]=>1100000=>0000011
[2,5,3,7,4,1,6,8]=>[8,6,1,4,7,3,5,2]=>0000000=>0000000
[5,1,3,7,4,2,6,8]=>[8,6,2,4,7,3,1,5]=>0000000=>0000000
[5,2,3,8,1,4,6,7]=>[7,6,4,1,8,3,2,5]=>0000000=>0000000
[1,8,7,2,3,4,5,6]=>[6,5,4,3,2,7,8,1]=>0000000=>0000000
[2,5,3,1,8,4,6,7]=>[7,6,4,8,1,3,5,2]=>0000000=>0000000
[8,6,3,2,5,4,7,1]=>[1,7,4,5,2,3,6,8]=>1000001=>1000001
[8,6,4,2,5,3,7,1]=>[1,7,3,5,2,4,6,8]=>1000001=>1000001
[8,6,5,2,4,3,7,1]=>[1,7,3,4,2,5,6,8]=>1000001=>1000001
[8,5,6,2,4,3,7,1]=>[1,7,3,4,2,6,5,8]=>1000001=>1000001
[6,2,5,3,7,4,8,1]=>[1,8,4,7,3,5,2,6]=>1000000=>0000001
[8,4,5,2,6,3,7,1]=>[1,7,3,6,2,5,4,8]=>1000001=>1000001
[8,5,4,2,6,3,7,1]=>[1,7,3,6,2,4,5,8]=>1000001=>1000001
[7,4,6,5,8,2,3,1]=>[1,3,2,8,5,6,4,7]=>1010000=>0000101
[7,3,6,4,8,2,5,1]=>[1,5,2,8,4,6,3,7]=>1000000=>0000001
[7,3,5,4,8,2,6,1]=>[1,6,2,8,4,5,3,7]=>1000000=>0000001
[3,4,6,7,2,1,8,5]=>[5,8,1,2,7,6,4,3]=>0000000=>0000000
[7,6,1,2,8,5,3,4]=>[4,3,5,8,2,1,6,7]=>0000000=>0000000
[1,2,7,4,8,5,6,3]=>[3,6,5,8,4,7,2,1]=>0000000=>0000000
[7,2,5,6,3,8,4,1]=>[1,4,8,3,6,5,2,7]=>1000000=>0000001
[2,6,3,4,8,5,1,7]=>[7,1,5,8,4,3,6,2]=>0000000=>0000000
[3,2,7,5,8,4,6,1]=>[1,6,4,8,5,7,2,3]=>1000000=>0000001
[6,8,4,5,3,7,2,1]=>[1,2,7,3,5,4,8,6]=>1100000=>0000011
[7,8,4,3,2,6,5,1]=>[1,5,6,2,3,4,8,7]=>1000010=>0100001
[7,5,4,6,2,8,3,1]=>[1,3,8,2,6,4,5,7]=>1000000=>0000001
[6,8,4,5,3,2,7,1]=>[1,7,2,3,5,4,8,6]=>1000000=>0000001
[6,7,5,4,2,8,3,1]=>[1,3,8,2,4,5,7,6]=>1000000=>0000001
[5,7,6,4,8,2,3,1]=>[1,3,2,8,4,6,7,5]=>1010000=>0000101
[5,6,3,4,2,8,7,1]=>[1,7,8,2,4,3,6,5]=>1000000=>0000001
[3,6,5,8,1,7,4,2]=>[2,4,7,1,8,5,6,3]=>0000000=>0000000
[5,2,6,3,1,4,8,7]=>[7,8,4,1,3,6,2,5]=>0000000=>0000000
[4,2,7,3,1,5,8,6]=>[6,8,5,1,3,7,2,4]=>0000000=>0000000
[7,3,8,4,1,5,6,2]=>[2,6,5,1,4,8,3,7]=>0000000=>0000000
[3,7,8,2,5,4,6,1]=>[1,6,4,5,2,8,7,3]=>1000000=>0000001
[1,4,8,5,7,2,3,6]=>[6,3,2,7,5,8,4,1]=>0000000=>0000000
[5,6,2,7,8,3,1,4]=>[4,1,3,8,7,2,6,5]=>0000000=>0000000
[5,6,2,7,8,3,4,1]=>[1,4,3,8,7,2,6,5]=>1000000=>0000001
[5,6,3,2,8,7,1,4]=>[4,1,7,8,2,3,6,5]=>0000000=>0000000
[8,6,1,7,3,4,2,5]=>[5,2,4,3,7,1,6,8]=>0000001=>1000000
[6,2,4,8,3,7,1,5]=>[5,1,7,3,8,4,2,6]=>0000000=>0000000
[5,1,6,7,3,4,2,8]=>[8,2,4,3,7,6,1,5]=>0000000=>0000000
[6,1,8,7,4,5,2,3]=>[3,2,5,4,7,8,1,6]=>0000000=>0000000
[5,8,2,7,3,6,4,1]=>[1,4,6,3,7,2,8,5]=>1000000=>0000001
[4,8,2,5,6,3,7,1]=>[1,7,3,6,5,2,8,4]=>1000000=>0000001
[8,1,5,7,4,6,2,3]=>[3,2,6,4,7,5,1,8]=>0000001=>1000000
[4,7,1,5,6,3,2,8]=>[8,2,3,6,5,1,7,4]=>0000000=>0000000
[4,5,7,1,6,3,8,2]=>[2,8,3,6,1,7,5,4]=>0000000=>0000000
[6,8,2,7,3,1,5,4]=>[4,5,1,3,7,2,8,6]=>0000000=>0000000
[5,6,8,3,7,4,2,1]=>[1,2,4,7,3,8,6,5]=>1100000=>0000011
[4,5,7,2,6,8,1,3]=>[3,1,8,6,2,7,5,4]=>0000000=>0000000
[2,7,1,4,8,3,6,5]=>[5,6,3,8,4,1,7,2]=>0000000=>0000000
[3,5,7,2,6,8,4,1]=>[1,4,8,6,2,7,5,3]=>1000000=>0000001
[2,3,1,8,7,4,6,5]=>[5,6,4,7,8,1,3,2]=>0000000=>0000000
[4,6,8,2,1,5,3,7]=>[7,3,5,1,2,8,6,4]=>0000000=>0000000
[5,6,8,4,7,2,3,1]=>[1,3,2,7,4,8,6,5]=>1010000=>0000101
[6,8,3,7,1,2,5,4]=>[4,5,2,1,7,3,8,6]=>0000000=>0000000
[4,5,8,2,6,1,7,3]=>[3,7,1,6,2,8,5,4]=>0000000=>0000000
[4,5,6,8,3,2,7,1]=>[1,7,2,3,8,6,5,4]=>1000000=>0000001
[4,6,5,7,2,3,8,1]=>[1,8,3,2,7,5,6,4]=>1000000=>0000001
[3,5,7,8,4,2,1,6]=>[6,1,2,4,8,7,5,3]=>0000000=>0000000
[4,6,5,2,7,8,3,1]=>[1,3,8,7,2,5,6,4]=>1000000=>0000001
[5,2,6,4,8,7,3,1]=>[1,3,7,8,4,6,2,5]=>1000000=>0000001
[8,6,3,7,2,4,1,5]=>[5,1,4,2,7,3,6,8]=>0000001=>1000000
[8,5,7,3,6,2,1,4]=>[4,1,2,6,3,7,5,8]=>0000001=>1000000
[8,4,6,7,3,5,2,1]=>[1,2,5,3,7,6,4,8]=>1100001=>1000011
[7,8,4,6,3,5,2,1]=>[1,2,5,3,6,4,8,7]=>1100010=>0100011
[5,8,4,6,7,3,2,1]=>[1,2,3,7,6,4,8,5]=>1110000=>0000111
[7,4,5,8,3,6,2,1]=>[1,2,6,3,8,5,4,7]=>1100000=>0000011
[8,4,7,3,5,6,2,1]=>[1,2,6,5,3,7,4,8]=>1100001=>1000011
[4,5,8,7,3,2,6,1]=>[1,6,2,3,7,8,5,4]=>1000000=>0000001
[6,5,4,8,2,3,7,1]=>[1,7,3,2,8,4,5,6]=>1000000=>0000001
[2,1,6,5,3,4,7,8]=>[8,7,4,3,5,6,1,2]=>0000000=>0000000
[5,6,8,7,2,4,3,1]=>[1,3,4,2,7,8,6,5]=>1001000=>0001001
[5,7,8,6,4,2,3,1]=>[1,3,2,4,6,8,7,5]=>1011000=>0001101
[6,8,4,1,7,5,2,3]=>[3,2,5,7,1,4,8,6]=>0000000=>0000000
[7,6,4,2,8,1,5,3]=>[3,5,1,8,2,4,6,7]=>0000000=>0000000
[7,4,6,3,8,1,5,2]=>[2,5,1,8,3,6,4,7]=>0000000=>0000000
[3,4,6,8,2,5,7,1]=>[1,7,5,2,8,6,4,3]=>1000000=>0000001
[6,4,1,8,7,2,3,5]=>[5,3,2,7,8,1,4,6]=>0000000=>0000000
[2,6,8,3,7,5,4,1]=>[1,4,5,7,3,8,6,2]=>1000000=>0000001
[1,7,6,2,3,5,8,4]=>[4,8,5,3,2,6,7,1]=>0000000=>0000000
[1,7,2,6,8,3,4,5]=>[5,4,3,8,6,2,7,1]=>0000000=>0000000
[6,3,1,7,2,8,4,5]=>[5,4,8,2,7,1,3,6]=>0000000=>0000000
[7,2,6,4,5,8,1,3]=>[3,1,8,5,4,6,2,7]=>0000000=>0000000
[4,1,2,7,6,8,3,5]=>[5,3,8,6,7,2,1,4]=>0000000=>0000000
[6,2,1,5,8,7,4,3]=>[3,4,7,8,5,1,2,6]=>0000000=>0000000
[7,2,6,5,4,8,1,3]=>[3,1,8,4,5,6,2,7]=>0000000=>0000000
[7,2,4,5,6,8,1,3]=>[3,1,8,6,5,4,2,7]=>0000000=>0000000
[5,7,8,3,6,4,2,1]=>[1,2,4,6,3,8,7,5]=>1100000=>0000011
[2,7,1,5,3,8,6,4]=>[4,6,8,3,5,1,7,2]=>0000000=>0000000
[7,4,6,5,2,3,1,8]=>[8,1,3,2,5,6,4,7]=>0000000=>0000000
[3,5,7,2,8,4,1,6]=>[6,1,4,8,2,7,5,3]=>0000000=>0000000
[4,3,7,2,8,5,1,6]=>[6,1,5,8,2,7,3,4]=>0000000=>0000000
[5,6,3,2,8,4,1,7]=>[7,1,4,8,2,3,6,5]=>0000000=>0000000
[7,2,4,6,3,5,8,1]=>[1,8,5,3,6,4,2,7]=>1000000=>0000001
[7,3,6,2,4,5,8,1]=>[1,8,5,4,2,6,3,7]=>1000000=>0000001
[8,7,2,3,6,5,1,4]=>[4,1,5,6,3,2,7,8]=>0000011=>1100000
[7,8,6,1,4,5,2,3]=>[3,2,5,4,1,6,8,7]=>0000110=>0110000
[4,6,7,5,1,8,2,3]=>[3,2,8,1,5,7,6,4]=>0000000=>0000000
[8,5,1,3,2,4,6,7]=>[7,6,4,2,3,1,5,8]=>0000001=>1000000
[3,8,5,1,2,4,6,7]=>[7,6,4,2,1,5,8,3]=>0000000=>0000000
[5,1,7,8,4,2,3,6]=>[6,3,2,4,8,7,1,5]=>0000000=>0000000
[3,5,8,1,4,2,7,6]=>[6,7,2,4,1,8,5,3]=>0000000=>0000000
[8,1,2,4,6,3,7,5]=>[5,7,3,6,4,2,1,8]=>0000001=>1000000
[7,6,1,4,2,3,8,5]=>[5,8,3,2,4,1,6,7]=>0000000=>0000000
[7,8,1,2,5,3,4,6]=>[6,4,3,5,2,1,8,7]=>0000010=>0100000
[1,8,4,7,5,2,3,6]=>[6,3,2,5,7,4,8,1]=>0000000=>0000000
[7,3,4,1,8,6,2,5]=>[5,2,6,8,1,4,3,7]=>0000000=>0000000
[8,4,7,2,1,6,3,5]=>[5,3,6,1,2,7,4,8]=>0000001=>1000000
[8,1,5,3,6,7,2,4]=>[4,2,7,6,3,5,1,8]=>0000001=>1000000
[4,7,8,2,5,6,1,3]=>[3,1,6,5,2,8,7,4]=>0000000=>0000000
[4,7,5,3,8,1,2,6]=>[6,2,1,8,3,5,7,4]=>0000000=>0000000
[3,2,4,7,1,6,5,8]=>[8,5,6,1,7,4,2,3]=>0000000=>0000000
[7,1,5,6,8,3,4,2]=>[2,4,3,8,6,5,1,7]=>0000000=>0000000
[1,5,7,6,8,2,4,3]=>[3,4,2,8,6,7,5,1]=>0000000=>0000000
[8,5,3,2,1,7,4,6]=>[6,4,7,1,2,3,5,8]=>0000001=>1000000
[8,7,3,5,6,4,1,2]=>[2,1,4,6,5,3,7,8]=>0100011=>1100010
[7,4,3,1,5,8,2,6]=>[6,2,8,5,1,3,4,7]=>0000000=>0000000
[6,5,1,4,2,3,7,8]=>[8,7,3,2,4,1,5,6]=>0000000=>0000000
[6,7,4,1,2,8,5,3]=>[3,5,8,2,1,4,7,6]=>0000000=>0000000
[4,6,7,8,2,5,1,3]=>[3,1,5,2,8,7,6,4]=>0000000=>0000000
[5,4,2,8,1,6,3,7]=>[7,3,6,1,8,2,4,5]=>0000000=>0000000
[3,1,6,7,4,5,2,8]=>[8,2,5,4,7,6,1,3]=>0000000=>0000000
[8,3,7,6,4,5,2,1]=>[1,2,5,4,6,7,3,8]=>1100001=>1000011
[3,7,8,6,4,5,2,1]=>[1,2,5,4,6,8,7,3]=>1100000=>0000011
[8,2,7,4,1,6,3,5]=>[5,3,6,1,4,7,2,8]=>0000001=>1000000
[4,8,6,5,1,3,7,2]=>[2,7,3,1,5,6,8,4]=>0000000=>0000000
[5,8,3,4,7,6,1,2]=>[2,1,6,7,4,3,8,5]=>0100000=>0000010
[8,7,3,4,1,6,2,5]=>[5,2,6,1,4,3,7,8]=>0000011=>1100000
[2,4,5,1,8,6,7,3]=>[3,7,6,8,1,5,4,2]=>0000000=>0000000
[7,5,2,8,6,4,3,1]=>[1,3,4,6,8,2,5,7]=>1000000=>0000001
[6,7,3,2,8,5,4,1]=>[1,4,5,8,2,3,7,6]=>1000000=>0000001
[6,8,7,3,2,5,4,1]=>[1,4,5,2,3,7,8,6]=>1000100=>0010001
[7,3,8,6,4,2,5,1]=>[1,5,2,4,6,8,3,7]=>1000000=>0000001
[6,4,2,8,5,7,3,1]=>[1,3,7,5,8,2,4,6]=>1000000=>0000001
[5,6,2,1,7,3,4,8]=>[8,4,3,7,1,2,6,5]=>0000000=>0000000
[4,7,5,6,3,1,2,8]=>[8,2,1,3,6,5,7,4]=>0000000=>0000000
[5,4,3,8,6,1,2,7]=>[7,2,1,6,8,3,4,5]=>0000000=>0000000
[4,8,6,3,2,7,1,5]=>[5,1,7,2,3,6,8,4]=>0000000=>0000000
[4,8,5,3,6,1,2,7]=>[7,2,1,6,3,5,8,4]=>0000000=>0000000
[4,8,5,3,7,1,6,2]=>[2,6,1,7,3,5,8,4]=>0000000=>0000000
[4,8,6,3,5,2,1,7]=>[7,1,2,5,3,6,8,4]=>0000000=>0000000
[5,8,6,3,2,7,1,4]=>[4,1,7,2,3,6,8,5]=>0000000=>0000000
[5,7,6,3,2,4,8,1]=>[1,8,4,2,3,6,7,5]=>1000000=>0000001
[6,4,7,2,1,8,5,3]=>[3,5,8,1,2,7,4,6]=>0000000=>0000000
[5,7,4,2,1,8,6,3]=>[3,6,8,1,2,4,7,5]=>0000000=>0000000
[5,6,2,8,4,7,3,1]=>[1,3,7,4,8,2,6,5]=>1000000=>0000001
[5,7,3,2,8,6,4,1]=>[1,4,6,8,2,3,7,5]=>1000000=>0000001
[5,4,3,7,1,8,6,2]=>[2,6,8,1,7,3,4,5]=>0000000=>0000000
[4,5,1,8,3,7,6,2]=>[2,6,7,3,8,1,5,4]=>0000000=>0000000
[5,3,1,6,8,4,2,7]=>[7,2,4,8,6,1,3,5]=>0000000=>0000000
[4,5,1,6,8,2,7,3]=>[3,7,2,8,6,1,5,4]=>0000000=>0000000
[4,5,1,7,8,3,2,6]=>[6,2,3,8,7,1,5,4]=>0000000=>0000000
[5,8,4,1,2,3,7,6]=>[6,7,3,2,1,4,8,5]=>0000000=>0000000
[3,8,5,1,2,7,4,6]=>[6,4,7,2,1,5,8,3]=>0000000=>0000000
[4,3,7,1,6,2,5,8]=>[8,5,2,6,1,7,3,4]=>0000000=>0000000
[4,3,1,6,7,2,5,8]=>[8,5,2,7,6,1,3,4]=>0000000=>0000000
[6,1,5,8,4,2,3,7]=>[7,3,2,4,8,5,1,6]=>0000000=>0000000
[5,2,1,3,7,4,6,8]=>[8,6,4,7,3,1,2,5]=>0000000=>0000000
[7,3,1,8,5,4,6,2]=>[2,6,4,5,8,1,3,7]=>0000000=>0000000
[7,2,8,4,3,6,5,1]=>[1,5,6,3,4,8,2,7]=>1000000=>0000001
[7,1,2,4,8,6,3,5]=>[5,3,6,8,4,2,1,7]=>0000000=>0000000
[7,1,8,5,4,6,2,3]=>[3,2,6,4,5,8,1,7]=>0000000=>0000000
[6,3,5,4,1,2,7,8]=>[8,7,2,1,4,5,3,6]=>0000000=>0000000
[3,7,6,2,5,4,1,8]=>[8,1,4,5,2,6,7,3]=>0000000=>0000000
[2,3,7,5,8,6,1,4]=>[4,1,6,8,5,7,3,2]=>0000000=>0000000
[7,8,3,4,6,1,5,2]=>[2,5,1,6,4,3,8,7]=>0000010=>0100000
[8,1,5,7,3,6,2,4]=>[4,2,6,3,7,5,1,8]=>0000001=>1000000
[8,1,4,5,7,3,6,2]=>[2,6,3,7,5,4,1,8]=>0000001=>1000000
[8,1,4,7,3,5,6,2]=>[2,6,5,3,7,4,1,8]=>0000001=>1000000
[3,6,8,1,7,4,2,5]=>[5,2,4,7,1,8,6,3]=>0000000=>0000000
[2,4,7,8,5,3,1,6]=>[6,1,3,5,8,7,4,2]=>0000000=>0000000
[8,1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1,8]=>0000001=>1000000
[8,1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1,8]=>0000001=>1000000
[8,3,6,7,4,1,2,5]=>[5,2,1,4,7,6,3,8]=>0000001=>1000000
[5,7,6,2,8,1,3,4]=>[4,3,1,8,2,6,7,5]=>0000000=>0000000
[6,5,2,3,4,1,8,7]=>[7,8,1,4,3,2,5,6]=>0000000=>0000000
[5,8,2,3,1,4,7,6]=>[6,7,4,1,3,2,8,5]=>0000000=>0000000
[6,5,8,3,1,7,2,4]=>[4,2,7,1,3,8,5,6]=>0000000=>0000000
[6,7,4,3,8,2,5,1]=>[1,5,2,8,3,4,7,6]=>1000000=>0000001
[7,4,8,3,6,2,1,5]=>[5,1,2,6,3,8,4,7]=>0000000=>0000000
[6,1,5,7,3,8,2,4]=>[4,2,8,3,7,5,1,6]=>0000000=>0000000
[7,6,2,3,1,8,5,4]=>[4,5,8,1,3,2,6,7]=>0000000=>0000000
[2,4,6,7,5,1,8,3]=>[3,8,1,5,7,6,4,2]=>0000000=>0000000
[3,5,1,7,8,6,2,4]=>[4,2,6,8,7,1,5,3]=>0000000=>0000000
[8,5,7,6,2,4,1,3]=>[3,1,4,2,6,7,5,8]=>0001001=>1001000
[2,4,5,7,8,3,1,6]=>[6,1,3,8,7,5,4,2]=>0000000=>0000000
[2,4,6,5,8,3,1,7]=>[7,1,3,8,5,6,4,2]=>0000000=>0000000
[2,4,6,5,8,1,7,3]=>[3,7,1,8,5,6,4,2]=>0000000=>0000000
[2,5,6,7,3,4,1,8]=>[8,1,4,3,7,6,5,2]=>0000000=>0000000
[4,3,2,7,6,1,8,5]=>[5,8,1,6,7,2,3,4]=>0000000=>0000000
[4,3,2,5,8,7,1,6]=>[6,1,7,8,5,2,3,4]=>0000000=>0000000
[2,5,4,6,8,3,1,7]=>[7,1,3,8,6,4,5,2]=>0000000=>0000000
[2,4,6,3,8,7,1,5]=>[5,1,7,8,3,6,4,2]=>0000000=>0000000
[5,2,6,4,7,1,3,8]=>[8,3,1,7,4,6,2,5]=>0000000=>0000000
[1,5,4,7,3,8,6,2]=>[2,6,8,3,7,4,5,1]=>0000000=>0000000
[4,3,2,7,1,8,6,5]=>[5,6,8,1,7,2,3,4]=>0000000=>0000000
[2,5,6,1,8,4,7,3]=>[3,7,4,8,1,6,5,2]=>0000000=>0000000
[5,7,8,6,2,4,3,1]=>[1,3,4,2,6,8,7,5]=>1001000=>0001001
[4,1,8,2,5,7,6,3]=>[3,6,7,5,2,8,1,4]=>0000000=>0000000
[6,3,2,4,7,8,5,1]=>[1,5,8,7,4,2,3,6]=>1000000=>0000001
[1,5,4,3,8,7,2,6]=>[6,2,7,8,3,4,5,1]=>0000000=>0000000
[1,5,4,3,7,2,6,8]=>[8,6,2,7,3,4,5,1]=>0000000=>0000000
[1,5,3,8,7,2,6,4]=>[4,6,2,7,8,3,5,1]=>0000000=>0000000
[1,6,3,8,2,7,4,5]=>[5,4,7,2,8,3,6,1]=>0000000=>0000000
[1,4,2,5,8,6,3,7]=>[7,3,6,8,5,2,4,1]=>0000000=>0000000
[1,4,8,5,2,7,6,3]=>[3,6,7,2,5,8,4,1]=>0000000=>0000000
[6,2,5,7,8,4,3,1]=>[1,3,4,8,7,5,2,6]=>1000000=>0000001
[5,2,6,3,4,7,8,1]=>[1,8,7,4,3,6,2,5]=>1000000=>0000001
[6,7,5,1,3,2,8,4]=>[4,8,2,3,1,5,7,6]=>0000000=>0000000
[5,8,3,2,4,1,7,6]=>[6,7,1,4,2,3,8,5]=>0000000=>0000000
[5,6,3,2,4,8,7,1]=>[1,7,8,4,2,3,6,5]=>1000000=>0000001
[5,6,2,8,3,1,7,4]=>[4,7,1,3,8,2,6,5]=>0000000=>0000000
[5,6,2,4,3,1,7,8]=>[8,7,1,3,4,2,6,5]=>0000000=>0000000
[5,8,2,6,3,4,7,1]=>[1,7,4,3,6,2,8,5]=>1000000=>0000001
[7,1,2,5,4,6,8,3]=>[3,8,6,4,5,2,1,7]=>0000000=>0000000
[6,1,8,5,7,3,4,2]=>[2,4,3,7,5,8,1,6]=>0000000=>0000000
[5,8,6,2,4,3,1,7]=>[7,1,3,4,2,6,8,5]=>0000000=>0000000
[5,7,6,2,4,3,8,1]=>[1,8,3,4,2,6,7,5]=>1000000=>0000001
[6,1,7,5,8,3,2,4]=>[4,2,3,8,5,7,1,6]=>0000000=>0000000
[6,1,4,3,7,5,8,2]=>[2,8,5,7,3,4,1,6]=>0000000=>0000000
[7,1,4,3,6,2,8,5]=>[5,8,2,6,3,4,1,7]=>0000000=>0000000
[6,1,3,4,8,5,2,7]=>[7,2,5,8,4,3,1,6]=>0000000=>0000000
[6,1,7,8,5,3,2,4]=>[4,2,3,5,8,7,1,6]=>0000000=>0000000
[6,1,7,4,5,3,2,8]=>[8,2,3,5,4,7,1,6]=>0000000=>0000000
[5,7,3,2,4,6,8,1]=>[1,8,6,4,2,3,7,5]=>1000000=>0000001
[7,1,2,6,5,4,8,3]=>[3,8,4,5,6,2,1,7]=>0000000=>0000000
[7,1,2,4,6,5,8,3]=>[3,8,5,6,4,2,1,7]=>0000000=>0000000
[6,4,7,5,1,8,3,2]=>[2,3,8,1,5,7,4,6]=>0000000=>0000000
[6,5,7,1,2,3,8,4]=>[4,8,3,2,1,7,5,6]=>0000000=>0000000
[3,2,5,8,4,1,6,7]=>[7,6,1,4,8,5,2,3]=>0000000=>0000000
[8,6,2,4,1,7,5,3]=>[3,5,7,1,4,2,6,8]=>0000001=>1000000
[8,5,3,7,6,2,1,4]=>[4,1,2,6,7,3,5,8]=>0000001=>1000000
[5,2,8,6,1,7,4,3]=>[3,4,7,1,6,8,2,5]=>0000000=>0000000
[8,5,3,1,7,6,2,4]=>[4,2,6,7,1,3,5,8]=>0000001=>1000000
[6,2,7,1,3,8,4,5]=>[5,4,8,3,1,7,2,6]=>0000000=>0000000
[1,4,6,8,5,2,7,3]=>[3,7,2,5,8,6,4,1]=>0000000=>0000000
[5,8,2,3,4,7,1,6]=>[6,1,7,4,3,2,8,5]=>0000000=>0000000
[2,6,1,5,8,3,7,4]=>[4,7,3,8,5,1,6,2]=>0000000=>0000000
[2,5,4,8,3,7,1,6]=>[6,1,7,3,8,4,5,2]=>0000000=>0000000
[7,3,2,1,4,6,8,5]=>[5,8,6,4,1,2,3,7]=>0000000=>0000000
[4,5,2,1,8,7,3,6]=>[6,3,7,8,1,2,5,4]=>0000000=>0000000
[4,2,7,5,1,8,3,6]=>[6,3,8,1,5,7,2,4]=>0000000=>0000000
[8,3,7,2,1,4,6,5]=>[5,6,4,1,2,7,3,8]=>0000001=>1000000
[3,6,8,1,4,7,2,5]=>[5,2,7,4,1,8,6,3]=>0000000=>0000000
[7,3,5,1,4,2,6,8]=>[8,6,2,4,1,5,3,7]=>0000000=>0000000
[4,6,5,2,1,3,7,8]=>[8,7,3,1,2,5,6,4]=>0000000=>0000000
[3,6,5,4,1,7,2,8]=>[8,2,7,1,4,5,6,3]=>0000000=>0000000
[8,5,4,2,7,3,6,1]=>[1,6,3,7,2,4,5,8]=>1000001=>1000001
[6,8,4,3,7,2,5,1]=>[1,5,2,7,3,4,8,6]=>1000000=>0000001
[8,4,3,7,6,2,5,1]=>[1,5,2,6,7,3,4,8]=>1000001=>1000001
[3,7,6,2,5,8,4,1]=>[1,4,8,5,2,6,7,3]=>1000000=>0000001
[7,2,8,5,4,3,6,1]=>[1,6,3,4,5,8,2,7]=>1000000=>0000001
[6,4,3,8,5,2,7,1]=>[1,7,2,5,8,3,4,6]=>1000000=>0000001
[6,8,5,7,2,1,4,3]=>[3,4,1,2,7,5,8,6]=>0001000=>0001000
[2,5,6,3,7,1,4,8]=>[8,4,1,7,3,6,5,2]=>0000000=>0000000
[4,2,3,6,7,8,5,1]=>[1,5,8,7,6,3,2,4]=>1000000=>0000001
[7,6,4,1,2,8,3,5]=>[5,3,8,2,1,4,6,7]=>0000000=>0000000
[4,6,1,5,8,3,2,7]=>[7,2,3,8,5,1,6,4]=>0000000=>0000000
[4,6,1,8,5,3,2,7]=>[7,2,3,5,8,1,6,4]=>0000000=>0000000
[2,5,7,1,8,4,6,3]=>[3,6,4,8,1,7,5,2]=>0000000=>0000000
[6,8,1,5,4,3,2,7]=>[7,2,3,4,5,1,8,6]=>0000000=>0000000
[7,8,5,1,3,4,6,2]=>[2,6,4,3,1,5,8,7]=>0000010=>0100000
[7,6,2,1,4,8,5,3]=>[3,5,8,4,1,2,6,7]=>0000000=>0000000
[2,7,8,1,4,6,5,3]=>[3,5,6,4,1,8,7,2]=>0000000=>0000000
[2,8,7,1,5,4,6,3]=>[3,6,4,5,1,7,8,2]=>0000000=>0000000
[1,4,6,5,2,3,7,8]=>[8,7,3,2,5,6,4,1]=>0000000=>0000000
[3,8,6,4,7,5,2,1]=>[1,2,5,7,4,6,8,3]=>1100000=>0000011
[5,2,4,7,8,3,6,1]=>[1,6,3,8,7,4,2,5]=>1000000=>0000001
[6,1,7,2,3,8,5,4]=>[4,5,8,3,2,7,1,6]=>0000000=>0000000
[6,1,4,3,7,2,8,5]=>[5,8,2,7,3,4,1,6]=>0000000=>0000000
[5,6,4,1,7,3,8,2]=>[2,8,3,7,1,4,6,5]=>0000000=>0000000
[2,7,1,6,5,8,3,4]=>[4,3,8,5,6,1,7,2]=>0000000=>0000000
[2,8,3,5,6,4,1,7]=>[7,1,4,6,5,3,8,2]=>0000000=>0000000
[3,7,4,5,8,1,6,2]=>[2,6,1,8,5,4,7,3]=>0000000=>0000000
[1,7,3,6,4,2,8,5]=>[5,8,2,4,6,3,7,1]=>0000000=>0000000
[2,5,1,8,3,7,4,6]=>[6,4,7,3,8,1,5,2]=>0000000=>0000000
[8,7,3,1,5,2,6,4]=>[4,6,2,5,1,3,7,8]=>0000011=>1100000
[3,8,4,1,7,5,2,6]=>[6,2,5,7,1,4,8,3]=>0000000=>0000000
[8,7,3,6,1,4,5,2]=>[2,5,4,1,6,3,7,8]=>0000011=>1100000
[8,7,3,4,6,2,5,1]=>[1,5,2,6,4,3,7,8]=>1000011=>1100001
[8,7,2,6,1,4,5,3]=>[3,5,4,1,6,2,7,8]=>0000011=>1100000
[5,8,7,2,1,3,6,4]=>[4,6,3,1,2,7,8,5]=>0000000=>0000000
[6,8,2,1,3,7,5,4]=>[4,5,7,3,1,2,8,6]=>0000000=>0000000
[2,7,6,4,8,3,1,5]=>[5,1,3,8,4,6,7,2]=>0000000=>0000000
[6,2,4,7,8,3,5,1]=>[1,5,3,8,7,4,2,6]=>1000000=>0000001
[6,1,3,5,2,4,7,8]=>[8,7,4,2,5,3,1,6]=>0000000=>0000000
[4,7,3,2,6,5,1,8]=>[8,1,5,6,2,3,7,4]=>0000000=>0000000
[7,8,4,6,1,3,5,2]=>[2,5,3,1,6,4,8,7]=>0000010=>0100000
[4,1,3,5,7,2,8,6]=>[6,8,2,7,5,3,1,4]=>0000000=>0000000
[5,8,3,2,7,4,6,1]=>[1,6,4,7,2,3,8,5]=>1000000=>0000001
[3,1,5,8,6,7,2,4]=>[4,2,7,6,8,5,1,3]=>0000000=>0000000
[3,6,8,7,1,4,5,2]=>[2,5,4,1,7,8,6,3]=>0000000=>0000000
[1,4,8,7,3,6,5,2]=>[2,5,6,3,7,8,4,1]=>0000000=>0000000
[5,4,1,8,7,3,6,2]=>[2,6,3,7,8,1,4,5]=>0000000=>0000000
[4,5,2,1,6,7,8,3]=>[3,8,7,6,1,2,5,4]=>0000000=>0000000
[5,4,6,7,1,3,2,8]=>[8,2,3,1,7,6,4,5]=>0000000=>0000000
[6,5,1,3,4,7,2,8]=>[8,2,7,4,3,1,5,6]=>0000000=>0000000
[6,5,1,2,4,3,7,8]=>[8,7,3,4,2,1,5,6]=>0000000=>0000000
[8,7,1,4,5,2,3,6]=>[6,3,2,5,4,1,7,8]=>0000011=>1100000
[4,6,3,5,7,1,8,2]=>[2,8,1,7,5,3,6,4]=>0000000=>0000000
[4,7,3,5,8,6,1,2]=>[2,1,6,8,5,3,7,4]=>0100000=>0000010
[4,7,2,5,6,8,1,3]=>[3,1,8,6,5,2,7,4]=>0000000=>0000000
[4,8,2,5,6,7,1,3]=>[3,1,7,6,5,2,8,4]=>0000000=>0000000
[8,4,7,3,1,2,6,5]=>[5,6,2,1,3,7,4,8]=>0000001=>1000000
[7,4,5,8,1,3,6,2]=>[2,6,3,1,8,5,4,7]=>0000000=>0000000
[7,2,4,6,1,5,8,3]=>[3,8,5,1,6,4,2,7]=>0000000=>0000000
[5,8,2,6,1,7,4,3]=>[3,4,7,1,6,2,8,5]=>0000000=>0000000
[5,2,6,8,1,4,3,7]=>[7,3,4,1,8,6,2,5]=>0000000=>0000000
[8,7,3,1,2,5,6,4]=>[4,6,5,2,1,3,7,8]=>0000011=>1100000
[3,7,6,1,2,8,5,4]=>[4,5,8,2,1,6,7,3]=>0000000=>0000000
[2,7,3,6,1,8,5,4]=>[4,5,8,1,6,3,7,2]=>0000000=>0000000
[6,1,3,7,2,8,5,4]=>[4,5,8,2,7,3,1,6]=>0000000=>0000000
[6,1,8,2,5,7,4,3]=>[3,4,7,5,2,8,1,6]=>0000000=>0000000
[5,4,3,6,1,7,8,2]=>[2,8,7,1,6,3,4,5]=>0000000=>0000000
[4,3,8,6,2,1,5,7]=>[7,5,1,2,6,8,3,4]=>0000000=>0000000
[4,3,8,6,7,2,1,5]=>[5,1,2,7,6,8,3,4]=>0000000=>0000000
[7,4,3,6,8,2,1,5]=>[5,1,2,8,6,3,4,7]=>0000000=>0000000
[4,7,6,1,5,8,2,3]=>[3,2,8,5,1,6,7,4]=>0000000=>0000000
[2,6,7,5,3,4,8,1]=>[1,8,4,3,5,7,6,2]=>1000000=>0000001
[2,1,4,7,8,3,6,5]=>[5,6,3,8,7,4,1,2]=>0000000=>0000000
[1,4,5,7,8,6,2,3]=>[3,2,6,8,7,5,4,1]=>0000000=>0000000
[1,3,7,8,4,6,2,5]=>[5,2,6,4,8,7,3,1]=>0000000=>0000000
[3,1,7,8,4,6,2,5]=>[5,2,6,4,8,7,1,3]=>0000000=>0000000
[5,8,4,3,7,1,2,6]=>[6,2,1,7,3,4,8,5]=>0000000=>0000000
[6,7,8,3,1,2,5,4]=>[4,5,2,1,3,8,7,6]=>0000100=>0010000
[7,3,8,5,4,2,6,1]=>[1,6,2,4,5,8,3,7]=>1000000=>0000001
[7,2,8,5,6,4,3,1]=>[1,3,4,6,5,8,2,7]=>1000000=>0000001
[2,6,8,1,3,4,7,5]=>[5,7,4,3,1,8,6,2]=>0000000=>0000000
[5,3,1,7,6,8,4,2]=>[2,4,8,6,7,1,3,5]=>0000000=>0000000
[5,6,1,2,8,4,7,3]=>[3,7,4,8,2,1,6,5]=>0000000=>0000000
[1,7,6,8,5,3,4,2]=>[2,4,3,5,8,6,7,1]=>0000000=>0000000
[4,1,7,8,6,5,2,3]=>[3,2,5,6,8,7,1,4]=>0000000=>0000000
[6,2,4,8,3,5,7,1]=>[1,7,5,3,8,4,2,6]=>1000000=>0000001
[6,1,3,5,8,4,2,7]=>[7,2,4,8,5,3,1,6]=>0000000=>0000000
[6,5,1,7,3,2,4,8]=>[8,4,2,3,7,1,5,6]=>0000000=>0000000
[4,7,6,1,2,3,8,5]=>[5,8,3,2,1,6,7,4]=>0000000=>0000000
[4,3,1,7,8,6,2,5]=>[5,2,6,8,7,1,3,4]=>0000000=>0000000
[3,6,8,1,4,5,7,2]=>[2,7,5,4,1,8,6,3]=>0000000=>0000000
[3,1,7,8,6,5,2,4]=>[4,2,5,6,8,7,1,3]=>0000000=>0000000
[3,7,6,5,2,4,8,1]=>[1,8,4,2,5,6,7,3]=>1000000=>0000001
[2,6,8,1,7,4,3,5]=>[5,3,4,7,1,8,6,2]=>0000000=>0000000
[5,3,2,7,8,4,1,6]=>[6,1,4,8,7,2,3,5]=>0000000=>0000000
[3,5,8,1,7,4,2,6]=>[6,2,4,7,1,8,5,3]=>0000000=>0000000
[5,7,2,6,8,4,3,1]=>[1,3,4,8,6,2,7,5]=>1000000=>0000001
[7,5,6,2,4,3,1,8]=>[8,1,3,4,2,6,5,7]=>0000000=>0000000
[1,3,8,5,2,4,6,7]=>[7,6,4,2,5,8,3,1]=>0000000=>0000000
[7,8,6,1,3,2,4,5]=>[5,4,2,3,1,6,8,7]=>0000110=>0110000
[6,5,1,7,3,8,4,2]=>[2,4,8,3,7,1,5,6]=>0000000=>0000000
[7,1,6,3,8,5,4,2]=>[2,4,5,8,3,6,1,7]=>0000000=>0000000
[1,6,4,7,3,8,5,2]=>[2,5,8,3,7,4,6,1]=>0000000=>0000000
[5,4,1,7,3,8,6,2]=>[2,6,8,3,7,1,4,5]=>0000000=>0000000
[7,5,6,1,3,4,8,2]=>[2,8,4,3,1,6,5,7]=>0000000=>0000000
[6,8,3,4,7,5,2,1]=>[1,2,5,7,4,3,8,6]=>1100000=>0000011
[6,7,5,1,4,8,3,2]=>[2,3,8,4,1,5,7,6]=>0000000=>0000000
[6,1,4,7,3,8,2,5]=>[5,2,8,3,7,4,1,6]=>0000000=>0000000
[7,4,1,6,5,2,8,3]=>[3,8,2,5,6,1,4,7]=>0000000=>0000000
[6,4,2,8,1,5,3,7]=>[7,3,5,1,8,2,4,6]=>0000000=>0000000
[6,8,7,3,5,1,4,2]=>[2,4,1,5,3,7,8,6]=>0000100=>0010000
[7,3,6,4,2,1,8,5]=>[5,8,1,2,4,6,3,7]=>0000000=>0000000
[7,8,5,2,6,4,3,1]=>[1,3,4,6,2,5,8,7]=>1000010=>0100001
[5,1,3,8,2,7,4,6]=>[6,4,7,2,8,3,1,5]=>0000000=>0000000
[7,1,6,3,2,8,4,5]=>[5,4,8,2,3,6,1,7]=>0000000=>0000000
[6,3,8,5,7,2,1,4]=>[4,1,2,7,5,8,3,6]=>0000000=>0000000
[5,2,7,4,6,1,3,8]=>[8,3,1,6,4,7,2,5]=>0000000=>0000000
[8,7,2,3,5,1,4,6]=>[6,4,1,5,3,2,7,8]=>0000011=>1100000
[4,7,6,5,2,3,1,8]=>[8,1,3,2,5,6,7,4]=>0000000=>0000000
[5,7,2,3,1,8,4,6]=>[6,4,8,1,3,2,7,5]=>0000000=>0000000
[4,7,6,5,3,1,2,8]=>[8,2,1,3,5,6,7,4]=>0000000=>0000000
[7,2,3,6,8,5,4,1]=>[1,4,5,8,6,3,2,7]=>1000000=>0000001
[7,6,3,1,8,5,2,4]=>[4,2,5,8,1,3,6,7]=>0000000=>0000000
[1,6,4,7,8,5,3,2]=>[2,3,5,8,7,4,6,1]=>0000000=>0000000
[6,7,3,8,1,4,5,2]=>[2,5,4,1,8,3,7,6]=>0000000=>0000000
[6,3,5,2,1,7,8,4]=>[4,8,7,1,2,5,3,6]=>0000000=>0000000
[8,6,3,2,5,7,4,1]=>[1,4,7,5,2,3,6,8]=>1000001=>1000001
[8,5,7,4,1,3,6,2]=>[2,6,3,1,4,7,5,8]=>0000001=>1000000
[2,7,3,5,1,4,8,6]=>[6,8,4,1,5,3,7,2]=>0000000=>0000000
[3,8,5,1,2,4,7,6]=>[6,7,4,2,1,5,8,3]=>0000000=>0000000
[8,1,3,6,5,2,7,4]=>[4,7,2,5,6,3,1,8]=>0000001=>1000000
[8,6,2,4,5,1,7,3]=>[3,7,1,5,4,2,6,8]=>0000001=>1000000
[3,6,7,5,1,4,8,2]=>[2,8,4,1,5,7,6,3]=>0000000=>0000000
[6,3,7,5,1,2,8,4]=>[4,8,2,1,5,7,3,6]=>0000000=>0000000
[3,6,7,1,5,4,8,2]=>[2,8,4,5,1,7,6,3]=>0000000=>0000000
[5,6,1,7,4,8,3,2]=>[2,3,8,4,7,1,6,5]=>0000000=>0000000
[6,4,7,1,5,2,8,3]=>[3,8,2,5,1,7,4,6]=>0000000=>0000000
[5,3,4,7,8,2,6,1]=>[1,6,2,8,7,4,3,5]=>1000000=>0000001
[3,5,6,7,2,1,8,4]=>[4,8,1,2,7,6,5,3]=>0000000=>0000000
[3,6,4,7,1,8,2,5]=>[5,2,8,1,7,4,6,3]=>0000000=>0000000
[5,2,3,6,7,4,1,8]=>[8,1,4,7,6,3,2,5]=>0000000=>0000000
[5,7,3,1,4,2,8,6]=>[6,8,2,4,1,3,7,5]=>0000000=>0000000
[4,8,6,1,2,5,3,7]=>[7,3,5,2,1,6,8,4]=>0000000=>0000000
[7,1,3,6,5,8,2,4]=>[4,2,8,5,6,3,1,7]=>0000000=>0000000
[6,1,4,2,3,8,7,5]=>[5,7,8,3,2,4,1,6]=>0000000=>0000000
[2,3,5,4,8,6,1,7]=>[7,1,6,8,4,5,3,2]=>0000000=>0000000
[6,1,3,2,7,8,5,4]=>[4,5,8,7,2,3,1,6]=>0000000=>0000000
[6,3,4,2,8,7,1,5]=>[5,1,7,8,2,4,3,6]=>0000000=>0000000
[5,6,1,8,7,2,3,4]=>[4,3,2,7,8,1,6,5]=>0000000=>0000000
[4,5,6,3,1,7,2,8]=>[8,2,7,1,3,6,5,4]=>0000000=>0000000
[1,5,7,3,6,2,4,8]=>[8,4,2,6,3,7,5,1]=>0000000=>0000000
[1,5,8,6,2,3,4,7]=>[7,4,3,2,6,8,5,1]=>0000000=>0000000
[1,4,8,7,3,6,2,5]=>[5,2,6,3,7,8,4,1]=>0000000=>0000000
[2,5,7,3,8,6,1,4]=>[4,1,6,8,3,7,5,2]=>0000000=>0000000
[2,5,7,6,8,3,4,1]=>[1,4,3,8,6,7,5,2]=>1000000=>0000001
[6,7,4,8,5,3,2,1]=>[1,2,3,5,8,4,7,6]=>1110000=>0000111
[6,5,1,8,3,4,7,2]=>[2,7,4,3,8,1,5,6]=>0000000=>0000000
[3,8,4,6,5,1,7,2]=>[2,7,1,5,6,4,8,3]=>0000000=>0000000
[7,3,1,2,6,8,5,4]=>[4,5,8,6,2,1,3,7]=>0000000=>0000000
[4,8,5,6,1,7,2,3]=>[3,2,7,1,6,5,8,4]=>0000000=>0000000
[4,8,3,1,5,7,2,6]=>[6,2,7,5,1,3,8,4]=>0000000=>0000000
[4,5,2,7,8,6,3,1]=>[1,3,6,8,7,2,5,4]=>1000000=>0000001
[7,4,1,2,5,3,6,8]=>[8,6,3,5,2,1,4,7]=>0000000=>0000000
[6,7,3,5,4,2,1,8]=>[8,1,2,4,5,3,7,6]=>0000000=>0000000
[4,3,1,8,7,2,6,5]=>[5,6,2,7,8,1,3,4]=>0000000=>0000000
[1,4,7,5,8,2,3,6]=>[6,3,2,8,5,7,4,1]=>0000000=>0000000
[1,5,8,3,6,4,7,2]=>[2,7,4,6,3,8,5,1]=>0000000=>0000000
[1,6,8,2,7,3,4,5]=>[5,4,3,7,2,8,6,1]=>0000000=>0000000
[5,1,4,7,8,6,2,3]=>[3,2,6,8,7,4,1,5]=>0000000=>0000000
[2,5,7,1,8,6,3,4]=>[4,3,6,8,1,7,5,2]=>0000000=>0000000
[4,3,7,1,5,8,6,2]=>[2,6,8,5,1,7,3,4]=>0000000=>0000000
[4,8,7,2,6,1,3,5]=>[5,3,1,6,2,7,8,4]=>0000000=>0000000
[4,5,8,2,1,7,3,6]=>[6,3,7,1,2,8,5,4]=>0000000=>0000000
[5,8,2,1,7,4,6,3]=>[3,6,4,7,1,2,8,5]=>0000000=>0000000
[7,8,6,2,3,1,5,4]=>[4,5,1,3,2,6,8,7]=>0000110=>0110000
[5,3,7,6,8,4,2,1]=>[1,2,4,8,6,7,3,5]=>1100000=>0000011
[5,6,1,2,8,7,3,4]=>[4,3,7,8,2,1,6,5]=>0000000=>0000000
[7,4,6,1,3,5,8,2]=>[2,8,5,3,1,6,4,7]=>0000000=>0000000
[7,1,5,6,4,8,2,3]=>[3,2,8,4,6,5,1,7]=>0000000=>0000000
[1,8,3,6,2,5,7,4]=>[4,7,5,2,6,3,8,1]=>0000000=>0000000
[2,8,3,1,7,5,6,4]=>[4,6,5,7,1,3,8,2]=>0000000=>0000000
[2,5,8,4,6,7,1,3]=>[3,1,7,6,4,8,5,2]=>0000000=>0000000
[7,2,5,3,4,6,1,8]=>[8,1,6,4,3,5,2,7]=>0000000=>0000000
[4,2,1,5,6,8,3,7]=>[7,3,8,6,5,1,2,4]=>0000000=>0000000
[4,7,8,6,2,3,5,1]=>[1,5,3,2,6,8,7,4]=>1000000=>0000001
[7,1,4,3,8,6,5,2]=>[2,5,6,8,3,4,1,7]=>0000000=>0000000
[2,3,1,4,8,7,5,6]=>[6,5,7,8,4,1,3,2]=>0000000=>0000000
[7,1,2,4,8,6,5,3]=>[3,5,6,8,4,2,1,7]=>0000000=>0000000
[5,3,4,1,8,7,6,2]=>[2,6,7,8,1,4,3,5]=>0000000=>0000000
[6,5,1,8,3,7,4,2]=>[2,4,7,3,8,1,5,6]=>0000000=>0000000
[7,1,3,2,8,6,5,4]=>[4,5,6,8,2,3,1,7]=>0000000=>0000000
[7,1,3,8,2,6,4,5]=>[5,4,6,2,8,3,1,7]=>0000000=>0000000
[5,2,3,1,8,7,6,4]=>[4,6,7,8,1,3,2,5]=>0000000=>0000000
[2,5,3,1,8,7,6,4]=>[4,6,7,8,1,3,5,2]=>0000000=>0000000
[4,3,5,1,8,7,6,2]=>[2,6,7,8,1,5,3,4]=>0000000=>0000000
[4,6,1,8,7,2,3,5]=>[5,3,2,7,8,1,6,4]=>0000000=>0000000
[4,2,5,1,8,7,6,3]=>[3,6,7,8,1,5,2,4]=>0000000=>0000000
[2,4,5,1,8,7,6,3]=>[3,6,7,8,1,5,4,2]=>0000000=>0000000
[2,7,5,6,4,8,1,3]=>[3,1,8,4,6,5,7,2]=>0000000=>0000000
[7,1,2,6,3,8,4,5]=>[5,4,8,3,6,2,1,7]=>0000000=>0000000
[8,2,4,1,3,7,5,6]=>[6,5,7,3,1,4,2,8]=>0000001=>1000000
[3,4,6,7,2,1,5,8]=>[8,5,1,2,7,6,4,3]=>0000000=>0000000
[2,5,7,4,6,8,1,3]=>[3,1,8,6,4,7,5,2]=>0000000=>0000000
[4,6,2,7,5,8,1,3]=>[3,1,8,5,7,2,6,4]=>0000000=>0000000
[2,4,7,6,3,8,1,5]=>[5,1,8,3,6,7,4,2]=>0000000=>0000000
[5,6,2,1,8,7,4,3]=>[3,4,7,8,1,2,6,5]=>0000000=>0000000
[1,6,5,7,3,8,2,4]=>[4,2,8,3,7,5,6,1]=>0000000=>0000000
[8,1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1,8]=>0000001=>1000000
[8,1,4,6,2,7,5,3]=>[3,5,7,2,6,4,1,8]=>0000001=>1000000
[8,2,1,6,7,4,5,3]=>[3,5,4,7,6,1,2,8]=>0000001=>1000000
[8,7,2,1,5,3,6,4]=>[4,6,3,5,1,2,7,8]=>0000011=>1100000
[8,1,6,2,4,7,5,3]=>[3,5,7,4,2,6,1,8]=>0000001=>1000000
[6,3,5,1,4,2,7,8]=>[8,7,2,4,1,5,3,6]=>0000000=>0000000
[1,5,8,7,4,3,6,2]=>[2,6,3,4,7,8,5,1]=>0000000=>0000000
[7,5,8,1,4,2,6,3]=>[3,6,2,4,1,8,5,7]=>0000000=>0000000
[8,5,7,1,4,2,6,3]=>[3,6,2,4,1,7,5,8]=>0000001=>1000000
[3,8,4,2,7,5,1,6]=>[6,1,5,7,2,4,8,3]=>0000000=>0000000
[2,7,5,8,6,3,1,4]=>[4,1,3,6,8,5,7,2]=>0000000=>0000000
[7,4,2,8,5,3,1,6]=>[6,1,3,5,8,2,4,7]=>0000000=>0000000
[5,8,3,4,6,2,1,7]=>[7,1,2,6,4,3,8,5]=>0000000=>0000000
[6,8,1,7,3,4,2,5]=>[5,2,4,3,7,1,8,6]=>0000000=>0000000
[5,7,3,1,6,4,2,8]=>[8,2,4,6,1,3,7,5]=>0000000=>0000000
[5,8,3,1,4,7,6,2]=>[2,6,7,4,1,3,8,5]=>0000000=>0000000
[6,3,1,8,2,5,7,4]=>[4,7,5,2,8,1,3,6]=>0000000=>0000000
[4,6,8,1,5,7,2,3]=>[3,2,7,5,1,8,6,4]=>0000000=>0000000
[5,7,4,8,1,2,6,3]=>[3,6,2,1,8,4,7,5]=>0000000=>0000000
[8,1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1,8]=>0000001=>1000000
[7,4,2,6,5,3,8,1]=>[1,8,3,5,6,2,4,7]=>1000000=>0000001
[8,1,4,6,5,3,2,7]=>[7,2,3,5,6,4,1,8]=>0000001=>1000000
[8,1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1,8]=>0000001=>1000000
[8,1,3,6,5,7,2,4]=>[4,2,7,5,6,3,1,8]=>0000001=>1000000
[7,3,2,6,5,8,4,1]=>[1,4,8,5,6,2,3,7]=>1000000=>0000001
[2,4,7,3,5,8,1,6]=>[6,1,8,5,3,7,4,2]=>0000000=>0000000
[4,5,1,6,8,7,2,3]=>[3,2,7,8,6,1,5,4]=>0000000=>0000000
[3,4,7,2,5,8,6,1]=>[1,6,8,5,2,7,4,3]=>1000000=>0000001
[3,4,7,1,5,8,2,6]=>[6,2,8,5,1,7,4,3]=>0000000=>0000000
[3,2,7,4,5,1,6,8]=>[8,6,1,5,4,7,2,3]=>0000000=>0000000
[6,2,7,4,5,3,1,8]=>[8,1,3,5,4,7,2,6]=>0000000=>0000000
[6,8,2,5,3,4,1,7]=>[7,1,4,3,5,2,8,6]=>0000000=>0000000
[7,3,4,6,5,1,2,8]=>[8,2,1,5,6,4,3,7]=>0000000=>0000000
[2,3,7,4,5,1,8,6]=>[6,8,1,5,4,7,3,2]=>0000000=>0000000
[6,8,3,5,2,4,7,1]=>[1,7,4,2,5,3,8,6]=>1000000=>0000001
[7,2,5,3,1,4,6,8]=>[8,6,4,1,3,5,2,7]=>0000000=>0000000
[5,8,3,2,6,4,7,1]=>[1,7,4,6,2,3,8,5]=>1000000=>0000001
[4,2,7,3,5,6,1,8]=>[8,1,6,5,3,7,2,4]=>0000000=>0000000
[4,2,7,1,5,3,6,8]=>[8,6,3,5,1,7,2,4]=>0000000=>0000000
[4,8,7,1,6,5,2,3]=>[3,2,5,6,1,7,8,4]=>0000000=>0000000
[3,2,7,1,5,6,4,8]=>[8,4,6,5,1,7,2,3]=>0000000=>0000000
[3,8,7,6,1,5,2,4]=>[4,2,5,1,6,7,8,3]=>0000000=>0000000
[2,1,7,5,8,6,3,4]=>[4,3,6,8,5,7,1,2]=>0000000=>0000000
[5,3,4,7,8,1,6,2]=>[2,6,1,8,7,4,3,5]=>0000000=>0000000
[5,1,4,8,2,3,7,6]=>[6,7,3,2,8,4,1,5]=>0000000=>0000000
[5,8,6,3,1,2,4,7]=>[7,4,2,1,3,6,8,5]=>0000000=>0000000
[2,3,7,8,5,4,6,1]=>[1,6,4,5,8,7,3,2]=>1000000=>0000001
[6,7,2,3,8,1,5,4]=>[4,5,1,8,3,2,7,6]=>0000000=>0000000
[7,4,8,6,3,5,1,2]=>[2,1,5,3,6,8,4,7]=>0100000=>0000010
[7,4,8,6,2,3,5,1]=>[1,5,3,2,6,8,4,7]=>1000000=>0000001
[7,1,5,4,2,3,8,6]=>[6,8,3,2,4,5,1,7]=>0000000=>0000000
[3,6,7,2,5,1,8,4]=>[4,8,1,5,2,7,6,3]=>0000000=>0000000
[6,1,8,4,2,5,7,3]=>[3,7,5,2,4,8,1,6]=>0000000=>0000000
[8,1,2,6,4,7,5,3]=>[3,5,7,4,6,2,1,8]=>0000001=>1000000
[8,4,1,6,2,7,5,3]=>[3,5,7,2,6,1,4,8]=>0000001=>1000000
[8,4,1,6,7,2,5,3]=>[3,5,2,7,6,1,4,8]=>0000001=>1000000
[6,2,8,1,4,5,7,3]=>[3,7,5,4,1,8,2,6]=>0000000=>0000000
[8,4,6,2,1,7,5,3]=>[3,5,7,1,2,6,4,8]=>0000001=>1000000
[8,2,6,4,1,7,5,3]=>[3,5,7,1,4,6,2,8]=>0000001=>1000000
[8,6,1,2,4,7,5,3]=>[3,5,7,4,2,1,6,8]=>0000001=>1000000
[8,2,6,1,7,4,5,3]=>[3,5,4,7,1,6,2,8]=>0000001=>1000000
[8,6,2,1,7,4,5,3]=>[3,5,4,7,1,2,6,8]=>0000001=>1000000
[6,8,2,1,4,7,5,3]=>[3,5,7,4,1,2,8,6]=>0000000=>0000000
[6,8,2,4,1,7,5,3]=>[3,5,7,1,4,2,8,6]=>0000000=>0000000
[6,4,8,1,5,2,7,3]=>[3,7,2,5,1,8,4,6]=>0000000=>0000000
[8,5,7,6,2,3,4,1]=>[1,4,3,2,6,7,5,8]=>1001001=>1001001
[8,4,2,3,6,7,5,1]=>[1,5,7,6,3,2,4,8]=>1000001=>1000001
[7,4,1,8,3,6,5,2]=>[2,5,6,3,8,1,4,7]=>0000000=>0000000
[2,7,4,5,8,6,1,3]=>[3,1,6,8,5,4,7,2]=>0000000=>0000000
[2,7,4,6,8,1,5,3]=>[3,5,1,8,6,4,7,2]=>0000000=>0000000
[4,1,7,2,8,5,3,6]=>[6,3,5,8,2,7,1,4]=>0000000=>0000000
[7,1,6,3,5,4,8,2]=>[2,8,4,5,3,6,1,7]=>0000000=>0000000
[2,8,6,1,7,5,3,4]=>[4,3,5,7,1,6,8,2]=>0000000=>0000000
[2,4,5,8,7,1,3,6]=>[6,3,1,7,8,5,4,2]=>0000000=>0000000
[8,7,2,4,3,6,5,1]=>[1,5,6,3,4,2,7,8]=>1000011=>1100001
[4,2,8,7,3,6,5,1]=>[1,5,6,3,7,8,2,4]=>1000000=>0000001
[4,7,2,3,6,8,5,1]=>[1,5,8,6,3,2,7,4]=>1000000=>0000001
[8,5,2,3,4,7,6,1]=>[1,6,7,4,3,2,5,8]=>1000001=>1000001
[4,5,1,8,7,3,6,2]=>[2,6,3,7,8,1,5,4]=>0000000=>0000000
[6,4,2,5,7,8,1,3]=>[3,1,8,7,5,2,4,6]=>0000000=>0000000
[5,4,1,6,7,3,8,2]=>[2,8,3,7,6,1,4,5]=>0000000=>0000000
[3,6,5,4,1,8,2,7]=>[7,2,8,1,4,5,6,3]=>0000000=>0000000
[4,3,8,5,2,7,1,6]=>[6,1,7,2,5,8,3,4]=>0000000=>0000000
[2,6,7,4,3,1,8,5]=>[5,8,1,3,4,7,6,2]=>0000000=>0000000
[6,3,1,5,2,8,7,4]=>[4,7,8,2,5,1,3,6]=>0000000=>0000000
[3,7,8,6,5,2,4,1]=>[1,4,2,5,6,8,7,3]=>1000000=>0000001
[7,4,5,2,6,3,1,8]=>[8,1,3,6,2,5,4,7]=>0000000=>0000000
[8,4,5,3,6,1,7,2]=>[2,7,1,6,3,5,4,8]=>0000001=>1000000
[8,6,3,4,5,1,7,2]=>[2,7,1,5,4,3,6,8]=>0000001=>1000000
[8,6,3,5,4,1,7,2]=>[2,7,1,4,5,3,6,8]=>0000001=>1000000
[8,7,4,5,1,3,6,2]=>[2,6,3,1,5,4,7,8]=>0000011=>1100000
[8,4,5,2,6,1,7,3]=>[3,7,1,6,2,5,4,8]=>0000001=>1000000
[8,6,2,5,3,1,4,7]=>[7,4,1,3,5,2,6,8]=>0000001=>1000000
[8,4,7,3,1,2,5,6]=>[6,5,2,1,3,7,4,8]=>0000001=>1000000
[8,7,3,5,1,6,4,2]=>[2,4,6,1,5,3,7,8]=>0000011=>1100000
[8,6,2,3,5,1,7,4]=>[4,7,1,5,3,2,6,8]=>0000001=>1000000
[4,8,3,2,6,1,7,5]=>[5,7,1,6,2,3,8,4]=>0000000=>0000000
[3,6,2,5,7,8,4,1]=>[1,4,8,7,5,2,6,3]=>1000000=>0000001
[6,1,3,5,7,4,8,2]=>[2,8,4,7,5,3,1,6]=>0000000=>0000000
[5,4,1,7,2,3,6,8]=>[8,6,3,2,7,1,4,5]=>0000000=>0000000
[4,1,7,2,5,3,6,8]=>[8,6,3,5,2,7,1,4]=>0000000=>0000000
[5,3,4,1,6,7,2,8]=>[8,2,7,6,1,4,3,5]=>0000000=>0000000
[5,2,1,6,4,3,8,7]=>[7,8,3,4,6,1,2,5]=>0000000=>0000000
[3,2,5,7,4,8,6,1]=>[1,6,8,4,7,5,2,3]=>1000000=>0000001
[6,5,8,4,2,1,7,3]=>[3,7,1,2,4,8,5,6]=>0000000=>0000000
[5,1,2,7,6,4,8,3]=>[3,8,4,6,7,2,1,5]=>0000000=>0000000
[4,3,2,6,8,7,1,5]=>[5,1,7,8,6,2,3,4]=>0000000=>0000000
[4,3,2,7,8,5,6,1]=>[1,6,5,8,7,2,3,4]=>1000000=>0000001
[7,5,6,4,1,8,3,2]=>[2,3,8,1,4,6,5,7]=>0000000=>0000000
[2,5,4,3,8,1,7,6]=>[6,7,1,8,3,4,5,2]=>0000000=>0000000
[6,4,5,2,8,3,7,1]=>[1,7,3,8,2,5,4,6]=>1000000=>0000001
[3,1,2,8,5,4,6,7]=>[7,6,4,5,8,2,1,3]=>0000000=>0000000
[3,6,2,1,8,4,7,5]=>[5,7,4,8,1,2,6,3]=>0000000=>0000000
[3,5,1,6,7,4,8,2]=>[2,8,4,7,6,1,5,3]=>0000000=>0000000
[2,4,5,7,3,6,1,8]=>[8,1,6,3,7,5,4,2]=>0000000=>0000000
[6,4,3,7,1,8,2,5]=>[5,2,8,1,7,3,4,6]=>0000000=>0000000
[5,1,2,7,6,3,4,8]=>[8,4,3,6,7,2,1,5]=>0000000=>0000000
[7,1,5,4,2,6,3,8]=>[8,3,6,2,4,5,1,7]=>0000000=>0000000
[4,6,1,5,2,8,7,3]=>[3,7,8,2,5,1,6,4]=>0000000=>0000000
[5,1,8,6,2,7,4,3]=>[3,4,7,2,6,8,1,5]=>0000000=>0000000
[3,8,6,1,5,7,4,2]=>[2,4,7,5,1,6,8,3]=>0000000=>0000000
[8,6,7,1,3,5,4,2]=>[2,4,5,3,1,7,6,8]=>0000101=>1010000
[3,4,1,6,8,7,5,2]=>[2,5,7,8,6,1,4,3]=>0000000=>0000000
[6,1,3,8,5,7,4,2]=>[2,4,7,5,8,3,1,6]=>0000000=>0000000
[7,3,1,6,2,5,8,4]=>[4,8,5,2,6,1,3,7]=>0000000=>0000000
[7,3,1,6,2,4,5,8]=>[8,5,4,2,6,1,3,7]=>0000000=>0000000
[5,4,3,1,7,2,8,6]=>[6,8,2,7,1,3,4,5]=>0000000=>0000000
[5,3,1,6,4,7,2,8]=>[8,2,7,4,6,1,3,5]=>0000000=>0000000
[1,6,2,7,8,4,5,3]=>[3,5,4,8,7,2,6,1]=>0000000=>0000000
[5,8,1,6,4,2,7,3]=>[3,7,2,4,6,1,8,5]=>0000000=>0000000
[6,8,7,4,1,3,2,5]=>[5,2,3,1,4,7,8,6]=>0000100=>0010000
[7,6,3,2,8,1,5,4]=>[4,5,1,8,2,3,6,7]=>0000000=>0000000
[7,8,3,6,1,2,5,4]=>[4,5,2,1,6,3,8,7]=>0000010=>0100000
[7,4,3,1,6,8,2,5]=>[5,2,8,6,1,3,4,7]=>0000000=>0000000
[7,1,3,2,6,8,4,5]=>[5,4,8,6,2,3,1,7]=>0000000=>0000000
[5,8,4,3,7,6,2,1]=>[1,2,6,7,3,4,8,5]=>1100000=>0000011
[8,5,4,1,2,3,7,6]=>[6,7,3,2,1,4,5,8]=>0000001=>1000000
[4,5,8,7,3,6,2,1]=>[1,2,6,3,7,8,5,4]=>1100000=>0000011
[2,6,1,8,4,7,5,3]=>[3,5,7,4,8,1,6,2]=>0000000=>0000000
[3,7,6,2,1,4,8,5]=>[5,8,4,1,2,6,7,3]=>0000000=>0000000
[3,6,7,4,2,1,8,5]=>[5,8,1,2,4,7,6,3]=>0000000=>0000000
[3,7,6,5,4,1,8,2]=>[2,8,1,4,5,6,7,3]=>0000000=>0000000
[4,3,7,5,8,1,2,6]=>[6,2,1,8,5,7,3,4]=>0000000=>0000000
[3,8,5,7,2,1,4,6]=>[6,4,1,2,7,5,8,3]=>0000000=>0000000
[4,8,5,6,3,7,2,1]=>[1,2,7,3,6,5,8,4]=>1100000=>0000011
[4,1,8,5,7,6,2,3]=>[3,2,6,7,5,8,1,4]=>0000000=>0000000
[4,8,3,6,5,7,2,1]=>[1,2,7,5,6,3,8,4]=>1100000=>0000011
[4,1,8,6,5,7,3,2]=>[2,3,7,5,6,8,1,4]=>0000000=>0000000
[7,6,3,2,1,4,8,5]=>[5,8,4,1,2,3,6,7]=>0000000=>0000000
[6,1,3,2,5,8,4,7]=>[7,4,8,5,2,3,1,6]=>0000000=>0000000
[7,1,5,4,2,6,8,3]=>[3,8,6,2,4,5,1,7]=>0000000=>0000000
[4,2,7,3,6,1,5,8]=>[8,5,1,6,3,7,2,4]=>0000000=>0000000
[6,5,8,3,2,7,1,4]=>[4,1,7,2,3,8,5,6]=>0000000=>0000000
[6,2,8,5,3,7,1,4]=>[4,1,7,3,5,8,2,6]=>0000000=>0000000
[4,3,2,8,7,5,1,6]=>[6,1,5,7,8,2,3,4]=>0000000=>0000000
[6,4,2,1,5,7,8,3]=>[3,8,7,5,1,2,4,6]=>0000000=>0000000
[7,3,2,1,4,8,5,6]=>[6,5,8,4,1,2,3,7]=>0000000=>0000000
[6,3,2,8,4,7,5,1]=>[1,5,7,4,8,2,3,6]=>1000000=>0000001
[5,4,7,2,1,3,8,6]=>[6,8,3,1,2,7,4,5]=>0000000=>0000000
[6,5,3,2,7,8,4,1]=>[1,4,8,7,2,3,5,6]=>1000000=>0000001
[6,4,3,2,7,8,5,1]=>[1,5,8,7,2,3,4,6]=>1000000=>0000001
[7,5,4,2,8,1,6,3]=>[3,6,1,8,2,4,5,7]=>0000000=>0000000
[4,6,7,5,1,8,3,2]=>[2,3,8,1,5,7,6,4]=>0000000=>0000000
[4,1,7,6,5,2,8,3]=>[3,8,2,5,6,7,1,4]=>0000000=>0000000
[3,7,4,6,1,5,8,2]=>[2,8,5,1,6,4,7,3]=>0000000=>0000000
[3,6,8,5,4,2,7,1]=>[1,7,2,4,5,8,6,3]=>1000000=>0000001
[2,4,1,3,7,6,5,8]=>[8,5,6,7,3,1,4,2]=>0000000=>0000000
[6,4,7,2,5,8,3,1]=>[1,3,8,5,2,7,4,6]=>1000000=>0000001
[8,3,5,6,4,1,7,2]=>[2,7,1,4,6,5,3,8]=>0000001=>1000000
[7,2,8,3,5,6,4,1]=>[1,4,6,5,3,8,2,7]=>1000000=>0000001
[2,7,6,8,4,1,3,5]=>[5,3,1,4,8,6,7,2]=>0000000=>0000000
[7,1,3,8,6,5,2,4]=>[4,2,5,6,8,3,1,7]=>0000000=>0000000
[7,4,6,5,8,2,1,3]=>[3,1,2,8,5,6,4,7]=>0010000=>0000100
[7,4,3,8,6,1,2,5]=>[5,2,1,6,8,3,4,7]=>0000000=>0000000
[7,2,3,6,1,8,5,4]=>[4,5,8,1,6,3,2,7]=>0000000=>0000000
[6,3,4,1,8,2,5,7]=>[7,5,2,8,1,4,3,6]=>0000000=>0000000
[5,4,8,2,3,1,7,6]=>[6,7,1,3,2,8,4,5]=>0000000=>0000000
[5,1,8,7,3,6,2,4]=>[4,2,6,3,7,8,1,5]=>0000000=>0000000
[2,3,5,8,4,7,6,1]=>[1,6,7,4,8,5,3,2]=>1000000=>0000001
[2,7,8,6,3,4,5,1]=>[1,5,4,3,6,8,7,2]=>1000000=>0000001
[6,7,1,2,5,8,4,3]=>[3,4,8,5,2,1,7,6]=>0000000=>0000000
[3,1,8,5,7,2,6,4]=>[4,6,2,7,5,8,1,3]=>0000000=>0000000
[5,8,4,6,2,7,3,1]=>[1,3,7,2,6,4,8,5]=>1000000=>0000001
[6,8,7,1,4,5,2,3]=>[3,2,5,4,1,7,8,6]=>0000100=>0010000
[6,1,3,8,5,4,2,7]=>[7,2,4,5,8,3,1,6]=>0000000=>0000000
[2,7,8,3,5,6,4,1]=>[1,4,6,5,3,8,7,2]=>1000000=>0000001
[6,7,8,2,5,4,1,3]=>[3,1,4,5,2,8,7,6]=>0000100=>0010000
[8,6,2,1,5,4,7,3]=>[3,7,4,5,1,2,6,8]=>0000001=>1000000
[3,6,1,2,5,4,7,8]=>[8,7,4,5,2,1,6,3]=>0000000=>0000000
[5,6,4,2,1,7,3,8]=>[8,3,7,1,2,4,6,5]=>0000000=>0000000
[4,2,7,6,5,3,8,1]=>[1,8,3,5,6,7,2,4]=>1000000=>0000001
[2,3,7,6,4,8,5,1]=>[1,5,8,4,6,7,3,2]=>1000000=>0000001
[2,4,7,6,5,1,8,3]=>[3,8,1,5,6,7,4,2]=>0000000=>0000000
[4,5,7,8,6,2,3,1]=>[1,3,2,6,8,7,5,4]=>1010000=>0000101
[6,4,7,1,2,5,3,8]=>[8,3,5,2,1,7,4,6]=>0000000=>0000000
[3,1,7,6,5,2,4,8]=>[8,4,2,5,6,7,1,3]=>0000000=>0000000
[1,3,8,5,7,4,2,6]=>[6,2,4,7,5,8,3,1]=>0000000=>0000000
[5,7,6,3,1,2,8,4]=>[4,8,2,1,3,6,7,5]=>0000000=>0000000
[8,1,3,5,7,4,2,6]=>[6,2,4,7,5,3,1,8]=>0000001=>1000000
[1,2,7,5,8,6,3,4]=>[4,3,6,8,5,7,2,1]=>0000000=>0000000
[6,4,2,3,7,5,8,1]=>[1,8,5,7,3,2,4,6]=>1000000=>0000001
[6,1,5,7,4,8,2,3]=>[3,2,8,4,7,5,1,6]=>0000000=>0000000
[5,4,2,7,1,3,8,6]=>[6,8,3,1,7,2,4,5]=>0000000=>0000000
[6,4,7,5,3,8,1,2]=>[2,1,8,3,5,7,4,6]=>0100000=>0000010
[6,4,7,5,3,8,2,1]=>[1,2,8,3,5,7,4,6]=>1100000=>0000011
[1,7,5,8,3,2,4,6]=>[6,4,2,3,8,5,7,1]=>0000000=>0000000
[1,3,8,5,7,2,4,6]=>[6,4,2,7,5,8,3,1]=>0000000=>0000000
[6,3,8,5,7,1,4,2]=>[2,4,1,7,5,8,3,6]=>0000000=>0000000
[8,3,2,5,6,4,1,7]=>[7,1,4,6,5,2,3,8]=>0000001=>1000000
[3,2,8,5,6,4,1,7]=>[7,1,4,6,5,8,2,3]=>0000000=>0000000
[2,3,8,5,6,4,1,7]=>[7,1,4,6,5,8,3,2]=>0000000=>0000000
[3,8,2,5,6,4,1,7]=>[7,1,4,6,5,2,8,3]=>0000000=>0000000
[2,5,8,6,1,7,4,3]=>[3,4,7,1,6,8,5,2]=>0000000=>0000000
[5,2,6,8,7,1,4,3]=>[3,4,1,7,8,6,2,5]=>0000000=>0000000
[8,1,5,6,2,7,4,3]=>[3,4,7,2,6,5,1,8]=>0000001=>1000000
[6,2,1,5,3,7,8,4]=>[4,8,7,3,5,1,2,6]=>0000000=>0000000
[2,7,4,3,1,5,8,6]=>[6,8,5,1,3,4,7,2]=>0000000=>0000000
[5,7,6,1,4,3,8,2]=>[2,8,3,4,1,6,7,5]=>0000000=>0000000
[3,8,1,6,2,7,4,5]=>[5,4,7,2,6,1,8,3]=>0000000=>0000000
[7,8,5,1,3,4,2,6]=>[6,2,4,3,1,5,8,7]=>0000010=>0100000
[7,5,6,1,4,3,8,2]=>[2,8,3,4,1,6,5,7]=>0000000=>0000000
[8,5,1,6,3,7,4,2]=>[2,4,7,3,6,1,5,8]=>0000001=>1000000
[7,4,6,1,2,3,8,5]=>[5,8,3,2,1,6,4,7]=>0000000=>0000000
[6,4,2,1,7,3,5,8]=>[8,5,3,7,1,2,4,6]=>0000000=>0000000
[6,1,4,5,7,8,2,3]=>[3,2,8,7,5,4,1,6]=>0000000=>0000000
[6,4,2,5,7,8,3,1]=>[1,3,8,7,5,2,4,6]=>1000000=>0000001
[2,7,8,5,6,3,1,4]=>[4,1,3,6,5,8,7,2]=>0000000=>0000000
[2,7,8,5,1,6,3,4]=>[4,3,6,1,5,8,7,2]=>0000000=>0000000
[2,7,8,1,5,3,6,4]=>[4,6,3,5,1,8,7,2]=>0000000=>0000000
[2,7,8,5,3,1,6,4]=>[4,6,1,3,5,8,7,2]=>0000000=>0000000
[2,7,8,3,5,1,6,4]=>[4,6,1,5,3,8,7,2]=>0000000=>0000000
[2,7,3,8,5,6,4,1]=>[1,4,6,5,8,3,7,2]=>1000000=>0000001
[2,3,7,8,5,6,4,1]=>[1,4,6,5,8,7,3,2]=>1000000=>0000001
[2,3,7,5,8,1,6,4]=>[4,6,1,8,5,7,3,2]=>0000000=>0000000
[2,3,7,5,8,6,4,1]=>[1,4,6,8,5,7,3,2]=>1000000=>0000001
[2,7,3,5,1,8,6,4]=>[4,6,8,1,5,3,7,2]=>0000000=>0000000
[2,7,5,3,8,6,1,4]=>[4,1,6,8,3,5,7,2]=>0000000=>0000000
[2,7,5,8,3,6,4,1]=>[1,4,6,3,8,5,7,2]=>1000000=>0000001
[2,7,5,8,3,1,6,4]=>[4,6,1,3,8,5,7,2]=>0000000=>0000000
[4,3,1,7,8,2,5,6]=>[6,5,2,8,7,1,3,4]=>0000000=>0000000
[2,5,7,8,1,3,6,4]=>[4,6,3,1,8,7,5,2]=>0000000=>0000000
[2,5,7,8,3,6,4,1]=>[1,4,6,3,8,7,5,2]=>1000000=>0000001
[6,1,3,5,7,8,2,4]=>[4,2,8,7,5,3,1,6]=>0000000=>0000000
[4,2,7,8,6,5,3,1]=>[1,3,5,6,8,7,2,4]=>1000000=>0000001
[4,2,7,1,6,5,3,8]=>[8,3,5,6,1,7,2,4]=>0000000=>0000000
[5,7,1,6,8,4,2,3]=>[3,2,4,8,6,1,7,5]=>0000000=>0000000
[5,8,6,3,2,4,7,1]=>[1,7,4,2,3,6,8,5]=>1000000=>0000001
[7,1,2,3,8,4,6,5]=>[5,6,4,8,3,2,1,7]=>0000000=>0000000
[4,1,3,5,2,7,6,8]=>[8,6,7,2,5,3,1,4]=>0000000=>0000000
[6,7,4,5,2,8,3,1]=>[1,3,8,2,5,4,7,6]=>1000000=>0000001
[3,7,4,8,6,5,2,1]=>[1,2,5,6,8,4,7,3]=>1100000=>0000011
[3,8,6,5,4,2,7,1]=>[1,7,2,4,5,6,8,3]=>1000000=>0000001
[4,8,5,7,3,2,6,1]=>[1,6,2,3,7,5,8,4]=>1000000=>0000001
[2,6,7,4,8,1,5,3]=>[3,5,1,8,4,7,6,2]=>0000000=>0000000
[7,4,8,1,2,6,5,3]=>[3,5,6,2,1,8,4,7]=>0000000=>0000000
[1,6,4,8,2,3,5,7]=>[7,5,3,2,8,4,6,1]=>0000000=>0000000
[1,6,8,3,7,5,4,2]=>[2,4,5,7,3,8,6,1]=>0000000=>0000000
[7,3,6,5,1,8,2,4]=>[4,2,8,1,5,6,3,7]=>0000000=>0000000
[7,2,4,1,8,6,3,5]=>[5,3,6,8,1,4,2,7]=>0000000=>0000000
[1,6,8,2,7,3,5,4]=>[4,5,3,7,2,8,6,1]=>0000000=>0000000
[2,5,8,3,7,1,4,6]=>[6,4,1,7,3,8,5,2]=>0000000=>0000000
[2,4,8,7,3,1,6,5]=>[5,6,1,3,7,8,4,2]=>0000000=>0000000
[5,8,3,4,1,2,7,6]=>[6,7,2,1,4,3,8,5]=>0000000=>0000000
[5,8,2,1,3,7,4,6]=>[6,4,7,3,1,2,8,5]=>0000000=>0000000
[4,8,7,2,1,3,6,5]=>[5,6,3,1,2,7,8,4]=>0000000=>0000000
[4,8,7,2,3,1,6,5]=>[5,6,1,3,2,7,8,4]=>0000000=>0000000
[1,4,8,7,2,3,6,5]=>[5,6,3,2,7,8,4,1]=>0000000=>0000000
[5,8,1,3,7,4,6,2]=>[2,6,4,7,3,1,8,5]=>0000000=>0000000
[5,4,8,1,7,2,3,6]=>[6,3,2,7,1,8,4,5]=>0000000=>0000000
[1,5,3,7,8,4,6,2]=>[2,6,4,8,7,3,5,1]=>0000000=>0000000
[8,6,1,4,3,2,7,5]=>[5,7,2,3,4,1,6,8]=>0000001=>1000000
[8,6,1,5,3,7,2,4]=>[4,2,7,3,5,1,6,8]=>0000001=>1000000
[2,8,4,6,1,3,7,5]=>[5,7,3,1,6,4,8,2]=>0000000=>0000000
[4,5,8,3,6,2,1,7]=>[7,1,2,6,3,8,5,4]=>0000000=>0000000
[4,5,1,7,8,6,2,3]=>[3,2,6,8,7,1,5,4]=>0000000=>0000000
[7,4,1,2,5,6,3,8]=>[8,3,6,5,2,1,4,7]=>0000000=>0000000
[6,4,1,2,5,8,3,7]=>[7,3,8,5,2,1,4,6]=>0000000=>0000000
[5,7,3,4,6,2,1,8]=>[8,1,2,6,4,3,7,5]=>0000000=>0000000
[7,3,5,6,2,4,1,8]=>[8,1,4,2,6,5,3,7]=>0000000=>0000000
[3,7,2,5,6,1,4,8]=>[8,4,1,6,5,2,7,3]=>0000000=>0000000
[5,3,4,7,2,1,6,8]=>[8,6,1,2,7,4,3,5]=>0000000=>0000000
[4,7,3,1,5,2,8,6]=>[6,8,2,5,1,3,7,4]=>0000000=>0000000
[5,4,1,6,8,7,2,3]=>[3,2,7,8,6,1,4,5]=>0000000=>0000000
[4,5,1,7,8,2,6,3]=>[3,6,2,8,7,1,5,4]=>0000000=>0000000
[4,2,6,7,1,8,5,3]=>[3,5,8,1,7,6,2,4]=>0000000=>0000000
[4,1,6,7,2,8,5,3]=>[3,5,8,2,7,6,1,4]=>0000000=>0000000
[3,5,7,8,4,2,6,1]=>[1,6,2,4,8,7,5,3]=>1000000=>0000001
[4,1,5,7,8,3,6,2]=>[2,6,3,8,7,5,1,4]=>0000000=>0000000
[3,6,7,1,4,5,8,2]=>[2,8,5,4,1,7,6,3]=>0000000=>0000000
[5,4,2,7,6,8,3,1]=>[1,3,8,6,7,2,4,5]=>1000000=>0000001
[4,7,8,2,6,5,1,3]=>[3,1,5,6,2,8,7,4]=>0000000=>0000000
[3,8,1,5,7,2,6,4]=>[4,6,2,7,5,1,8,3]=>0000000=>0000000
[4,7,8,2,6,3,5,1]=>[1,5,3,6,2,8,7,4]=>1000000=>0000001
[4,5,8,2,7,1,3,6]=>[6,3,1,7,2,8,5,4]=>0000000=>0000000
[6,7,8,5,3,1,4,2]=>[2,4,1,3,5,8,7,6]=>0001100=>0011000
[6,7,5,1,8,3,4,2]=>[2,4,3,8,1,5,7,6]=>0000000=>0000000
[5,3,8,1,4,2,7,6]=>[6,7,2,4,1,8,3,5]=>0000000=>0000000
[5,2,4,1,6,8,3,7]=>[7,3,8,6,1,4,2,5]=>0000000=>0000000
[8,7,2,3,1,6,4,5]=>[5,4,6,1,3,2,7,8]=>0000011=>1100000
[2,5,8,7,3,1,4,6]=>[6,4,1,3,7,8,5,2]=>0000000=>0000000
[1,4,6,7,8,2,5,3]=>[3,5,2,8,7,6,4,1]=>0000000=>0000000
[5,6,1,7,4,2,3,8]=>[8,3,2,4,7,1,6,5]=>0000000=>0000000
[5,6,1,8,4,2,3,7]=>[7,3,2,4,8,1,6,5]=>0000000=>0000000
[5,7,1,3,6,2,4,8]=>[8,4,2,6,3,1,7,5]=>0000000=>0000000
[3,6,4,1,2,5,7,8]=>[8,7,5,2,1,4,6,3]=>0000000=>0000000
[3,6,4,1,2,5,8,7]=>[7,8,5,2,1,4,6,3]=>0000000=>0000000
[4,7,1,3,2,5,8,6]=>[6,8,5,2,3,1,7,4]=>0000000=>0000000
[4,7,1,3,2,6,8,5]=>[5,8,6,2,3,1,7,4]=>0000000=>0000000
[5,7,1,3,6,2,8,4]=>[4,8,2,6,3,1,7,5]=>0000000=>0000000
[6,8,2,5,7,3,1,4]=>[4,1,3,7,5,2,8,6]=>0000000=>0000000
[5,8,6,3,4,7,2,1]=>[1,2,7,4,3,6,8,5]=>1100000=>0000011
[4,7,1,3,2,8,5,6]=>[6,5,8,2,3,1,7,4]=>0000000=>0000000
[3,6,5,1,8,2,4,7]=>[7,4,2,8,1,5,6,3]=>0000000=>0000000
[5,8,7,3,4,2,6,1]=>[1,6,2,4,3,7,8,5]=>1000000=>0000001
[5,4,8,3,1,2,7,6]=>[6,7,2,1,3,8,4,5]=>0000000=>0000000
[5,2,8,1,6,7,4,3]=>[3,4,7,6,1,8,2,5]=>0000000=>0000000
[6,4,3,8,7,5,2,1]=>[1,2,5,7,8,3,4,6]=>1100000=>0000011
[6,3,1,5,4,8,2,7]=>[7,2,8,4,5,1,3,6]=>0000000=>0000000
[8,4,2,6,5,7,3,1]=>[1,3,7,5,6,2,4,8]=>1000001=>1000001
[4,7,6,3,5,2,8,1]=>[1,8,2,5,3,6,7,4]=>1000000=>0000001
[8,7,3,2,6,4,5,1]=>[1,5,4,6,2,3,7,8]=>1000011=>1100001
[8,3,1,4,7,5,2,6]=>[6,2,5,7,4,1,3,8]=>0000001=>1000000
[5,3,1,6,4,8,7,2]=>[2,7,8,4,6,1,3,5]=>0000000=>0000000
[3,4,8,5,7,2,6,1]=>[1,6,2,7,5,8,4,3]=>1000000=>0000001
[6,3,5,8,1,7,2,4]=>[4,2,7,1,8,5,3,6]=>0000000=>0000000
[5,7,8,2,4,1,3,6]=>[6,3,1,4,2,8,7,5]=>0000000=>0000000
[5,4,6,2,1,8,3,7]=>[7,3,8,1,2,6,4,5]=>0000000=>0000000
[8,2,4,5,7,1,3,6]=>[6,3,1,7,5,4,2,8]=>0000001=>1000000
[3,7,6,2,5,1,8,4]=>[4,8,1,5,2,6,7,3]=>0000000=>0000000
[3,4,6,8,2,5,1,7]=>[7,1,5,2,8,6,4,3]=>0000000=>0000000
[2,7,4,3,1,8,5,6]=>[6,5,8,1,3,4,7,2]=>0000000=>0000000
[6,5,7,3,2,1,8,4]=>[4,8,1,2,3,7,5,6]=>0000000=>0000000
[7,2,3,6,4,5,8,1]=>[1,8,5,4,6,3,2,7]=>1000000=>0000001
[1,5,8,7,2,4,6,3]=>[3,6,4,2,7,8,5,1]=>0000000=>0000000
[5,1,8,7,2,4,6,3]=>[3,6,4,2,7,8,1,5]=>0000000=>0000000
[7,2,8,6,3,1,5,4]=>[4,5,1,3,6,8,2,7]=>0000000=>0000000
[2,5,8,7,1,4,6,3]=>[3,6,4,1,7,8,5,2]=>0000000=>0000000
[5,4,6,8,2,3,1,7]=>[7,1,3,2,8,6,4,5]=>0000000=>0000000
[5,3,8,7,1,4,6,2]=>[2,6,4,1,7,8,3,5]=>0000000=>0000000
[5,4,6,8,1,3,2,7]=>[7,2,3,1,8,6,4,5]=>0000000=>0000000
[5,1,4,3,6,8,2,7]=>[7,2,8,6,3,4,1,5]=>0000000=>0000000
[4,8,6,5,1,3,2,7]=>[7,2,3,1,5,6,8,4]=>0000000=>0000000
[4,5,6,1,8,3,2,7]=>[7,2,3,8,1,6,5,4]=>0000000=>0000000
[1,4,6,5,8,3,2,7]=>[7,2,3,8,5,6,4,1]=>0000000=>0000000
[4,8,6,5,2,3,1,7]=>[7,1,3,2,5,6,8,4]=>0000000=>0000000
[3,8,5,7,2,4,6,1]=>[1,6,4,2,7,5,8,3]=>1000000=>0000001
[4,5,6,2,8,3,1,7]=>[7,1,3,8,2,6,5,4]=>0000000=>0000000
[5,7,3,6,4,2,1,8]=>[8,1,2,4,6,3,7,5]=>0000000=>0000000
[2,4,6,1,8,7,3,5]=>[5,3,7,8,1,6,4,2]=>0000000=>0000000
[2,4,6,5,8,3,7,1]=>[1,7,3,8,5,6,4,2]=>1000000=>0000001
[2,4,6,8,5,3,1,7]=>[7,1,3,5,8,6,4,2]=>0000000=>0000000
[2,4,6,8,5,3,7,1]=>[1,7,3,5,8,6,4,2]=>1000000=>0000001
[2,4,6,8,5,7,3,1]=>[1,3,7,5,8,6,4,2]=>1000000=>0000001
[2,4,6,5,3,8,1,7]=>[7,1,8,3,5,6,4,2]=>0000000=>0000000
[2,4,6,5,8,7,1,3]=>[3,1,7,8,5,6,4,2]=>0000000=>0000000
[2,4,6,8,7,5,1,3]=>[3,1,5,7,8,6,4,2]=>0000000=>0000000
[2,4,6,8,5,7,1,3]=>[3,1,7,5,8,6,4,2]=>0000000=>0000000
[2,4,6,8,7,1,5,3]=>[3,5,1,7,8,6,4,2]=>0000000=>0000000
[2,4,6,8,7,1,3,5]=>[5,3,1,7,8,6,4,2]=>0000000=>0000000
[2,4,6,8,1,7,3,5]=>[5,3,7,1,8,6,4,2]=>0000000=>0000000
[4,8,3,5,7,2,1,6]=>[6,1,2,7,5,3,8,4]=>0000000=>0000000
[7,5,1,3,4,2,6,8]=>[8,6,2,4,3,1,5,7]=>0000000=>0000000
[5,2,3,6,4,7,1,8]=>[8,1,7,4,6,3,2,5]=>0000000=>0000000
[3,6,7,5,8,2,4,1]=>[1,4,2,8,5,7,6,3]=>1000000=>0000001
[5,7,3,4,8,6,2,1]=>[1,2,6,8,4,3,7,5]=>1100000=>0000011
[2,7,3,6,4,5,8,1]=>[1,8,5,4,6,3,7,2]=>1000000=>0000001
[1,8,5,3,2,4,6,7]=>[7,6,4,2,3,5,8,1]=>0000000=>0000000
[7,1,8,6,4,2,3,5]=>[5,3,2,4,6,8,1,7]=>0000000=>0000000
[8,6,5,1,3,7,2,4]=>[4,2,7,3,1,5,6,8]=>0000001=>1000000
[6,5,4,1,2,7,3,8]=>[8,3,7,2,1,4,5,6]=>0000000=>0000000
[6,5,3,7,4,1,8,2]=>[2,8,1,4,7,3,5,6]=>0000000=>0000000
[7,2,4,5,3,8,6,1]=>[1,6,8,3,5,4,2,7]=>1000000=>0000001
[2,8,1,4,6,5,7,3]=>[3,7,5,6,4,1,8,2]=>0000000=>0000000
[6,3,5,7,8,4,1,2]=>[2,1,4,8,7,5,3,6]=>0100000=>0000010
[4,3,5,7,8,6,1,2]=>[2,1,6,8,7,5,3,4]=>0100000=>0000010
[3,6,2,1,5,7,8,4]=>[4,8,7,5,1,2,6,3]=>0000000=>0000000
[3,8,1,5,7,6,2,4]=>[4,2,6,7,5,1,8,3]=>0000000=>0000000
[5,2,7,1,6,3,8,4]=>[4,8,3,6,1,7,2,5]=>0000000=>0000000
[5,4,7,1,8,2,3,6]=>[6,3,2,8,1,7,4,5]=>0000000=>0000000
[5,1,3,6,2,4,8,7]=>[7,8,4,2,6,3,1,5]=>0000000=>0000000
[4,3,2,7,6,8,1,5]=>[5,1,8,6,7,2,3,4]=>0000000=>0000000
[4,3,1,2,7,5,8,6]=>[6,8,5,7,2,1,3,4]=>0000000=>0000000
[4,8,3,2,1,6,5,7]=>[7,5,6,1,2,3,8,4]=>0000000=>0000000
[4,8,3,2,5,1,6,7]=>[7,6,1,5,2,3,8,4]=>0000000=>0000000
[4,3,2,8,6,7,1,5]=>[5,1,7,6,8,2,3,4]=>0000000=>0000000
[4,3,1,2,5,7,8,6]=>[6,8,7,5,2,1,3,4]=>0000000=>0000000
[5,3,2,1,8,7,4,6]=>[6,4,7,8,1,2,3,5]=>0000000=>0000000
[5,8,4,2,1,3,7,6]=>[6,7,3,1,2,4,8,5]=>0000000=>0000000
[6,5,2,3,1,8,7,4]=>[4,7,8,1,3,2,5,6]=>0000000=>0000000
[1,6,4,5,8,7,3,2]=>[2,3,7,8,5,4,6,1]=>0000000=>0000000
[4,5,8,7,2,3,1,6]=>[6,1,3,2,7,8,5,4]=>0000000=>0000000
[6,4,2,5,7,3,8,1]=>[1,8,3,7,5,2,4,6]=>1000000=>0000001
[6,4,7,2,3,8,5,1]=>[1,5,8,3,2,7,4,6]=>1000000=>0000001
[6,4,2,8,5,7,1,3]=>[3,1,7,5,8,2,4,6]=>0000000=>0000000
[5,1,7,2,8,6,3,4]=>[4,3,6,8,2,7,1,5]=>0000000=>0000000
[1,3,6,7,4,5,8,2]=>[2,8,5,4,7,6,3,1]=>0000000=>0000000
[5,6,2,1,8,3,4,7]=>[7,4,3,8,1,2,6,5]=>0000000=>0000000
[3,8,7,2,6,1,4,5]=>[5,4,1,6,2,7,8,3]=>0000000=>0000000
[6,3,2,4,8,7,1,5]=>[5,1,7,8,4,2,3,6]=>0000000=>0000000
[5,2,8,6,3,1,4,7]=>[7,4,1,3,6,8,2,5]=>0000000=>0000000
[6,1,7,4,8,5,2,3]=>[3,2,5,8,4,7,1,6]=>0000000=>0000000
[4,7,5,1,8,6,2,3]=>[3,2,6,8,1,5,7,4]=>0000000=>0000000
[6,4,1,3,7,8,5,2]=>[2,5,8,7,3,1,4,6]=>0000000=>0000000
[6,1,7,5,3,4,8,2]=>[2,8,4,3,5,7,1,6]=>0000000=>0000000
[6,3,4,1,7,5,8,2]=>[2,8,5,7,1,4,3,6]=>0000000=>0000000
[8,7,1,3,5,6,4,2]=>[2,4,6,5,3,1,7,8]=>0000011=>1100000
[8,1,4,6,7,5,3,2]=>[2,3,5,7,6,4,1,8]=>0000001=>1000000
[8,1,4,7,5,6,3,2]=>[2,3,6,5,7,4,1,8]=>0000001=>1000000
[4,2,6,7,8,5,3,1]=>[1,3,5,8,7,6,2,4]=>1000000=>0000001
[7,1,4,8,5,6,3,2]=>[2,3,6,5,8,4,1,7]=>0000000=>0000000
[6,4,7,8,3,5,1,2]=>[2,1,5,3,8,7,4,6]=>0100000=>0000010
[3,5,6,7,1,8,4,2]=>[2,4,8,1,7,6,5,3]=>0000000=>0000000
[1,7,4,5,2,8,6,3]=>[3,6,8,2,5,4,7,1]=>0000000=>0000000
[6,8,3,2,1,5,4,7]=>[7,4,5,1,2,3,8,6]=>0000000=>0000000
[5,1,2,8,7,6,4,3]=>[3,4,6,7,8,2,1,5]=>0000000=>0000000
[8,6,4,5,1,3,7,2]=>[2,7,3,1,5,4,6,8]=>0000001=>1000000
[7,5,8,4,1,3,6,2]=>[2,6,3,1,4,8,5,7]=>0000000=>0000000
[4,7,5,3,6,8,1,2]=>[2,1,8,6,3,5,7,4]=>0100000=>0000010
[4,8,5,3,7,1,2,6]=>[6,2,1,7,3,5,8,4]=>0000000=>0000000
[2,8,1,6,5,7,3,4]=>[4,3,7,5,6,1,8,2]=>0000000=>0000000
[7,4,8,5,3,6,1,2]=>[2,1,6,3,5,8,4,7]=>0100000=>0000010
[7,4,5,3,8,1,6,2]=>[2,6,1,8,3,5,4,7]=>0000000=>0000000
[8,4,6,5,1,3,7,2]=>[2,7,3,1,5,6,4,8]=>0000001=>1000000
[6,3,5,8,1,7,4,2]=>[2,4,7,1,8,5,3,6]=>0000000=>0000000
[7,3,6,1,5,8,4,2]=>[2,4,8,5,1,6,3,7]=>0000000=>0000000
[4,5,3,8,7,1,2,6]=>[6,2,1,7,8,3,5,4]=>0000000=>0000000
[8,5,4,7,6,1,2,3]=>[3,2,1,6,7,4,5,8]=>0010001=>1000100
[3,7,6,1,5,8,4,2]=>[2,4,8,5,1,6,7,3]=>0000000=>0000000
[4,6,2,1,8,5,3,7]=>[7,3,5,8,1,2,6,4]=>0000000=>0000000
[1,3,7,8,6,5,2,4]=>[4,2,5,6,8,7,3,1]=>0000000=>0000000
[4,2,1,8,7,3,6,5]=>[5,6,3,7,8,1,2,4]=>0000000=>0000000
[5,2,4,8,1,7,6,3]=>[3,6,7,1,8,4,2,5]=>0000000=>0000000
[5,1,8,7,3,2,6,4]=>[4,6,2,3,7,8,1,5]=>0000000=>0000000
[7,4,2,8,3,6,5,1]=>[1,5,6,3,8,2,4,7]=>1000000=>0000001
[6,1,8,3,7,4,5,2]=>[2,5,4,7,3,8,1,6]=>0000000=>0000000
[5,4,2,6,8,3,1,7]=>[7,1,3,8,6,2,4,5]=>0000000=>0000000
[5,4,2,7,1,8,6,3]=>[3,6,8,1,7,2,4,5]=>0000000=>0000000
[5,2,7,6,8,1,4,3]=>[3,4,1,8,6,7,2,5]=>0000000=>0000000
[5,7,3,6,2,1,4,8]=>[8,4,1,2,6,3,7,5]=>0000000=>0000000
[6,4,3,5,1,7,2,8]=>[8,2,7,1,5,3,4,6]=>0000000=>0000000
[8,2,4,5,1,3,6,7]=>[7,6,3,1,5,4,2,8]=>0000001=>1000000
[6,4,3,5,1,8,7,2]=>[2,7,8,1,5,3,4,6]=>0000000=>0000000
[6,3,5,8,1,2,7,4]=>[4,7,2,1,8,5,3,6]=>0000000=>0000000
[2,3,8,5,4,6,1,7]=>[7,1,6,4,5,8,3,2]=>0000000=>0000000
[8,3,5,7,1,4,6,2]=>[2,6,4,1,7,5,3,8]=>0000001=>1000000
[8,4,6,5,1,3,2,7]=>[7,2,3,1,5,6,4,8]=>0000001=>1000000
[7,3,5,6,1,4,2,8]=>[8,2,4,1,6,5,3,7]=>0000000=>0000000
[8,7,5,6,3,1,4,2]=>[2,4,1,3,6,5,7,8]=>0001011=>1101000
[2,7,3,4,6,1,8,5]=>[5,8,1,6,4,3,7,2]=>0000000=>0000000
[7,3,5,4,1,6,2,8]=>[8,2,6,1,4,5,3,7]=>0000000=>0000000
[7,3,5,4,1,8,2,6]=>[6,2,8,1,4,5,3,7]=>0000000=>0000000
[2,3,8,4,6,5,1,7]=>[7,1,5,6,4,8,3,2]=>0000000=>0000000
[7,1,3,5,4,2,6,8]=>[8,6,2,4,5,3,1,7]=>0000000=>0000000
[5,2,4,8,7,6,1,3]=>[3,1,6,7,8,4,2,5]=>0000000=>0000000
[6,5,1,8,2,3,7,4]=>[4,7,3,2,8,1,5,6]=>0000000=>0000000
[5,6,3,1,2,8,4,7]=>[7,4,8,2,1,3,6,5]=>0000000=>0000000
[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>0000000=>0000000
[5,1,3,4,8,6,2,7]=>[7,2,6,8,4,3,1,5]=>0000000=>0000000
[6,8,2,7,4,1,5,3]=>[3,5,1,4,7,2,8,6]=>0000000=>0000000
[8,6,4,5,1,2,7,3]=>[3,7,2,1,5,4,6,8]=>0000001=>1000000
[5,8,4,2,6,1,7,3]=>[3,7,1,6,2,4,8,5]=>0000000=>0000000
[2,7,6,3,5,8,1,4]=>[4,1,8,5,3,6,7,2]=>0000000=>0000000
[6,5,8,3,7,1,4,2]=>[2,4,1,7,3,8,5,6]=>0000000=>0000000
[4,8,6,5,3,7,1,2]=>[2,1,7,3,5,6,8,4]=>0100000=>0000010
[3,2,4,7,1,5,8,6]=>[6,8,5,1,7,4,2,3]=>0000000=>0000000
[2,7,5,6,1,8,3,4]=>[4,3,8,1,6,5,7,2]=>0000000=>0000000
[4,2,3,5,7,8,6,1]=>[1,6,8,7,5,3,2,4]=>1000000=>0000001
[1,6,2,8,5,7,4,3]=>[3,4,7,5,8,2,6,1]=>0000000=>0000000
[8,1,6,3,7,5,2,4]=>[4,2,5,7,3,6,1,8]=>0000001=>1000000
[8,1,6,3,7,4,5,2]=>[2,5,4,7,3,6,1,8]=>0000001=>1000000
[6,8,4,5,7,3,1,2]=>[2,1,3,7,5,4,8,6]=>0110000=>0000110
[7,5,4,1,2,8,6,3]=>[3,6,8,2,1,4,5,7]=>0000000=>0000000
[5,4,8,3,6,7,2,1]=>[1,2,7,6,3,8,4,5]=>1100000=>0000011
[6,4,5,8,3,7,1,2]=>[2,1,7,3,8,5,4,6]=>0100000=>0000010
[7,5,1,3,4,8,2,6]=>[6,2,8,4,3,1,5,7]=>0000000=>0000000
[5,8,4,6,3,7,2,1]=>[1,2,7,3,6,4,8,5]=>1100000=>0000011
[5,6,8,4,3,7,2,1]=>[1,2,7,3,4,8,6,5]=>1100000=>0000011
[8,5,2,6,3,1,4,7]=>[7,4,1,3,6,2,5,8]=>0000001=>1000000
[5,8,1,4,3,7,6,2]=>[2,6,7,3,4,1,8,5]=>0000000=>0000000
[7,6,2,4,1,8,3,5]=>[5,3,8,1,4,2,6,7]=>0000000=>0000000
[4,7,8,1,6,2,5,3]=>[3,5,2,6,1,8,7,4]=>0000000=>0000000
[6,7,3,4,8,1,5,2]=>[2,5,1,8,4,3,7,6]=>0000000=>0000000
[7,1,8,5,2,6,3,4]=>[4,3,6,2,5,8,1,7]=>0000000=>0000000
[1,2,6,7,3,5,4,8]=>[8,4,5,3,7,6,2,1]=>0000000=>0000000
[7,6,5,3,1,2,8,4]=>[4,8,2,1,3,5,6,7]=>0000000=>0000000
[8,1,2,4,6,3,5,7]=>[7,5,3,6,4,2,1,8]=>0000001=>1000000
[1,7,2,5,6,8,3,4]=>[4,3,8,6,5,2,7,1]=>0000000=>0000000
[7,5,1,8,3,2,4,6]=>[6,4,2,3,8,1,5,7]=>0000000=>0000000
[4,5,2,1,8,3,6,7]=>[7,6,3,8,1,2,5,4]=>0000000=>0000000
[5,6,1,8,3,2,4,7]=>[7,4,2,3,8,1,6,5]=>0000000=>0000000
[5,4,1,7,3,6,2,8]=>[8,2,6,3,7,1,4,5]=>0000000=>0000000
[2,6,4,3,1,7,5,8]=>[8,5,7,1,3,4,6,2]=>0000000=>0000000
[7,4,2,1,6,5,8,3]=>[3,8,5,6,1,2,4,7]=>0000000=>0000000
[3,6,2,8,4,1,7,5]=>[5,7,1,4,8,2,6,3]=>0000000=>0000000
[8,5,2,1,7,3,6,4]=>[4,6,3,7,1,2,5,8]=>0000001=>1000000
[4,5,3,8,7,2,1,6]=>[6,1,2,7,8,3,5,4]=>0000000=>0000000
[5,4,3,6,1,8,2,7]=>[7,2,8,1,6,3,4,5]=>0000000=>0000000
[3,5,4,1,7,2,8,6]=>[6,8,2,7,1,4,5,3]=>0000000=>0000000
[5,7,3,4,2,8,6,1]=>[1,6,8,2,4,3,7,5]=>1000000=>0000001
[5,8,3,4,2,7,6,1]=>[1,6,7,2,4,3,8,5]=>1000000=>0000001
[7,6,4,2,3,8,5,1]=>[1,5,8,3,2,4,6,7]=>1000000=>0000001
[7,3,8,4,2,6,5,1]=>[1,5,6,2,4,8,3,7]=>1000000=>0000001
[3,5,6,8,2,4,7,1]=>[1,7,4,2,8,6,5,3]=>1000000=>0000001
[8,4,7,3,2,5,6,1]=>[1,6,5,2,3,7,4,8]=>1000001=>1000001
[3,7,4,2,6,8,5,1]=>[1,5,8,6,2,4,7,3]=>1000000=>0000001
[2,7,4,6,3,1,5,8]=>[8,5,1,3,6,4,7,2]=>0000000=>0000000
[3,7,4,2,5,1,6,8]=>[8,6,1,5,2,4,7,3]=>0000000=>0000000
[4,3,6,2,8,5,1,7]=>[7,1,5,8,2,6,3,4]=>0000000=>0000000
[5,3,6,7,2,1,4,8]=>[8,4,1,2,7,6,3,5]=>0000000=>0000000
[4,3,5,7,8,2,1,6]=>[6,1,2,8,7,5,3,4]=>0000000=>0000000
[3,6,8,2,5,4,1,7]=>[7,1,4,5,2,8,6,3]=>0000000=>0000000
[4,5,3,7,8,2,1,6]=>[6,1,2,8,7,3,5,4]=>0000000=>0000000
[8,3,6,7,5,1,2,4]=>[4,2,1,5,7,6,3,8]=>0000001=>1000000
[7,2,8,4,6,5,3,1]=>[1,3,5,6,4,8,2,7]=>1000000=>0000001
[7,5,8,1,4,6,2,3]=>[3,2,6,4,1,8,5,7]=>0000000=>0000000
[7,3,8,4,6,5,1,2]=>[2,1,5,6,4,8,3,7]=>0100000=>0000010
[5,6,1,2,4,8,7,3]=>[3,7,8,4,2,1,6,5]=>0000000=>0000000
[8,1,5,3,7,6,2,4]=>[4,2,6,7,3,5,1,8]=>0000001=>1000000
[8,1,5,4,2,6,7,3]=>[3,7,6,2,4,5,1,8]=>0000001=>1000000
[7,4,1,6,8,5,3,2]=>[2,3,5,8,6,1,4,7]=>0000000=>0000000
[7,5,1,6,8,3,2,4]=>[4,2,3,8,6,1,5,7]=>0000000=>0000000
[7,5,3,8,2,1,4,6]=>[6,4,1,2,8,3,5,7]=>0000000=>0000000
[6,4,8,7,3,5,1,2]=>[2,1,5,3,7,8,4,6]=>0100000=>0000010
[6,5,3,7,2,8,1,4]=>[4,1,8,2,7,3,5,6]=>0000000=>0000000
[6,4,8,3,5,7,2,1]=>[1,2,7,5,3,8,4,6]=>1100000=>0000011
[6,5,8,4,1,7,2,3]=>[3,2,7,1,4,8,5,6]=>0000000=>0000000
[6,4,8,7,3,2,5,1]=>[1,5,2,3,7,8,4,6]=>1000000=>0000001
[5,4,8,6,7,3,2,1]=>[1,2,3,7,6,8,4,5]=>1110000=>0000111
[8,3,5,7,4,6,2,1]=>[1,2,6,4,7,5,3,8]=>1100001=>1000011
[6,2,8,7,3,5,1,4]=>[4,1,5,3,7,8,2,6]=>0000000=>0000000
[7,4,1,8,2,6,5,3]=>[3,5,6,2,8,1,4,7]=>0000000=>0000000
[3,8,6,4,1,2,5,7]=>[7,5,2,1,4,6,8,3]=>0000000=>0000000
[8,2,3,5,1,7,4,6]=>[6,4,7,1,5,3,2,8]=>0000001=>1000000
[5,2,1,4,8,7,3,6]=>[6,3,7,8,4,1,2,5]=>0000000=>0000000
[4,7,3,6,5,1,2,8]=>[8,2,1,5,6,3,7,4]=>0000000=>0000000
[1,7,2,3,8,5,6,4]=>[4,6,5,8,3,2,7,1]=>0000000=>0000000
[1,6,5,2,8,7,4,3]=>[3,4,7,8,2,5,6,1]=>0000000=>0000000
[5,2,4,6,7,3,1,8]=>[8,1,3,7,6,4,2,5]=>0000000=>0000000
[1,6,3,8,4,2,5,7]=>[7,5,2,4,8,3,6,1]=>0000000=>0000000
[1,4,3,7,6,2,5,8]=>[8,5,2,6,7,3,4,1]=>0000000=>0000000
[4,1,5,7,3,8,2,6]=>[6,2,8,3,7,5,1,4]=>0000000=>0000000
[1,5,2,6,8,7,4,3]=>[3,4,7,8,6,2,5,1]=>0000000=>0000000
[1,3,7,6,4,8,2,5]=>[5,2,8,4,6,7,3,1]=>0000000=>0000000
[7,4,2,3,1,6,5,8]=>[8,5,6,1,3,2,4,7]=>0000000=>0000000
[7,4,2,1,6,3,5,8]=>[8,5,3,6,1,2,4,7]=>0000000=>0000000
[6,3,4,5,1,7,2,8]=>[8,2,7,1,5,4,3,6]=>0000000=>0000000
[5,4,2,7,1,6,3,8]=>[8,3,6,1,7,2,4,5]=>0000000=>0000000
[5,4,3,1,7,6,2,8]=>[8,2,6,7,1,3,4,5]=>0000000=>0000000
[4,3,2,8,6,1,5,7]=>[7,5,1,6,8,2,3,4]=>0000000=>0000000
[4,3,2,8,1,7,5,6]=>[6,5,7,1,8,2,3,4]=>0000000=>0000000
[6,5,2,3,1,4,8,7]=>[7,8,4,1,3,2,5,6]=>0000000=>0000000
[6,5,2,1,4,7,3,8]=>[8,3,7,4,1,2,5,6]=>0000000=>0000000
[4,6,2,3,7,1,8,5]=>[5,8,1,7,3,2,6,4]=>0000000=>0000000
[5,6,2,3,7,1,4,8]=>[8,4,1,7,3,2,6,5]=>0000000=>0000000
[5,6,2,1,7,4,3,8]=>[8,3,4,7,1,2,6,5]=>0000000=>0000000
[5,6,3,1,4,7,2,8]=>[8,2,7,4,1,3,6,5]=>0000000=>0000000
[4,7,1,5,8,6,3,2]=>[2,3,6,8,5,1,7,4]=>0000000=>0000000
[6,1,7,8,3,5,4,2]=>[2,4,5,3,8,7,1,6]=>0000000=>0000000
[2,5,4,8,7,6,1,3]=>[3,1,6,7,8,4,5,2]=>0000000=>0000000
[8,7,6,2,1,4,5,3]=>[3,5,4,1,2,6,7,8]=>0000111=>1110000
[6,1,7,8,3,2,5,4]=>[4,5,2,3,8,7,1,6]=>0000000=>0000000
[5,3,4,6,1,8,2,7]=>[7,2,8,1,6,4,3,5]=>0000000=>0000000
[8,5,4,2,1,3,7,6]=>[6,7,3,1,2,4,5,8]=>0000001=>1000000
[3,2,8,7,4,6,1,5]=>[5,1,6,4,7,8,2,3]=>0000000=>0000000
[3,2,8,7,5,6,1,4]=>[4,1,6,5,7,8,2,3]=>0000000=>0000000
[5,8,1,4,2,7,6,3]=>[3,6,7,2,4,1,8,5]=>0000000=>0000000
[5,4,7,6,1,3,2,8]=>[8,2,3,1,6,7,4,5]=>0000000=>0000000
[8,4,2,7,6,5,3,1]=>[1,3,5,6,7,2,4,8]=>1000001=>1000001
[4,7,1,6,8,5,2,3]=>[3,2,5,8,6,1,7,4]=>0000000=>0000000
[1,4,7,8,5,2,6,3]=>[3,6,2,5,8,7,4,1]=>0000000=>0000000
[8,7,1,3,5,2,6,4]=>[4,6,2,5,3,1,7,8]=>0000011=>1100000
[4,7,8,1,5,6,3,2]=>[2,3,6,5,1,8,7,4]=>0000000=>0000000
[3,5,7,8,2,6,4,1]=>[1,4,6,2,8,7,5,3]=>1000000=>0000001
[3,5,7,8,6,2,4,1]=>[1,4,2,6,8,7,5,3]=>1000000=>0000001
[3,5,2,7,8,6,4,1]=>[1,4,6,8,7,2,5,3]=>1000000=>0000001
[2,3,6,4,8,5,7,1]=>[1,7,5,8,4,6,3,2]=>1000000=>0000001
[2,3,6,4,8,7,5,1]=>[1,5,7,8,4,6,3,2]=>1000000=>0000001
[5,2,7,4,8,1,3,6]=>[6,3,1,8,4,7,2,5]=>0000000=>0000000
[2,7,5,3,1,4,6,8]=>[8,6,4,1,3,5,7,2]=>0000000=>0000000
[1,7,5,4,2,6,8,3]=>[3,8,6,2,4,5,7,1]=>0000000=>0000000
[7,4,2,1,5,3,8,6]=>[6,8,3,5,1,2,4,7]=>0000000=>0000000
[6,4,5,1,3,7,2,8]=>[8,2,7,3,1,5,4,6]=>0000000=>0000000
[5,6,1,3,8,2,7,4]=>[4,7,2,8,3,1,6,5]=>0000000=>0000000
[8,4,5,1,3,7,2,6]=>[6,2,7,3,1,5,4,8]=>0000001=>1000000
[8,7,2,3,5,6,4,1]=>[1,4,6,5,3,2,7,8]=>1000011=>1100001
[5,1,7,4,6,2,3,8]=>[8,3,2,6,4,7,1,5]=>0000000=>0000000
[2,6,7,4,3,5,8,1]=>[1,8,5,3,4,7,6,2]=>1000000=>0000001
[6,1,4,5,8,7,3,2]=>[2,3,7,8,5,4,1,6]=>0000000=>0000000
[3,7,4,6,5,1,2,8]=>[8,2,1,5,6,4,7,3]=>0000000=>0000000
[3,8,7,1,4,6,2,5]=>[5,2,6,4,1,7,8,3]=>0000000=>0000000
[3,8,7,1,2,6,5,4]=>[4,5,6,2,1,7,8,3]=>0000000=>0000000
[3,5,8,7,6,2,4,1]=>[1,4,2,6,7,8,5,3]=>1000000=>0000001
[8,1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1,8]=>0000001=>1000000
[8,3,5,6,4,2,7,1]=>[1,7,2,4,6,5,3,8]=>1000001=>1000001
[8,4,2,6,5,7,1,3]=>[3,1,7,5,6,2,4,8]=>0000001=>1000000
[4,7,3,6,8,5,2,1]=>[1,2,5,8,6,3,7,4]=>1100000=>0000011
[4,6,3,8,7,5,2,1]=>[1,2,5,7,8,3,6,4]=>1100000=>0000011
[5,1,3,7,2,8,4,6]=>[6,4,8,2,7,3,1,5]=>0000000=>0000000
[5,2,4,6,3,1,8,7]=>[7,8,1,3,6,4,2,5]=>0000000=>0000000
[1,5,8,3,2,6,4,7]=>[7,4,6,2,3,8,5,1]=>0000000=>0000000
[3,4,7,5,8,1,6,2]=>[2,6,1,8,5,7,4,3]=>0000000=>0000000
[7,1,2,8,4,6,3,5]=>[5,3,6,4,8,2,1,7]=>0000000=>0000000
[6,2,7,4,8,5,3,1]=>[1,3,5,8,4,7,2,6]=>1000000=>0000001
[8,1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1,8]=>0000001=>1000000
[7,1,2,8,4,6,5,3]=>[3,5,6,4,8,2,1,7]=>0000000=>0000000
[8,3,7,6,4,1,5,2]=>[2,5,1,4,6,7,3,8]=>0000001=>1000000
[3,5,4,6,1,2,7,8]=>[8,7,2,1,6,4,5,3]=>0000000=>0000000
[1,5,3,8,6,4,7,2]=>[2,7,4,6,8,3,5,1]=>0000000=>0000000
[3,5,1,8,4,2,6,7]=>[7,6,2,4,8,1,5,3]=>0000000=>0000000
[5,3,4,6,2,8,7,1]=>[1,7,8,2,6,4,3,5]=>1000000=>0000001
[6,8,4,3,5,2,7,1]=>[1,7,2,5,3,4,8,6]=>1000000=>0000001
[4,7,5,8,3,2,6,1]=>[1,6,2,3,8,5,7,4]=>1000000=>0000001
[6,2,3,8,1,4,7,5]=>[5,7,4,1,8,3,2,6]=>0000000=>0000000
[5,8,4,3,7,2,1,6]=>[6,1,2,7,3,4,8,5]=>0000000=>0000000
[6,7,2,3,8,4,1,5]=>[5,1,4,8,3,2,7,6]=>0000000=>0000000
[6,2,4,5,7,1,3,8]=>[8,3,1,7,5,4,2,6]=>0000000=>0000000
[6,1,4,7,5,2,3,8]=>[8,3,2,5,7,4,1,6]=>0000000=>0000000
[1,7,8,5,6,2,3,4]=>[4,3,2,6,5,8,7,1]=>0000000=>0000000
[5,1,8,4,2,6,7,3]=>[3,7,6,2,4,8,1,5]=>0000000=>0000000
[1,8,4,6,2,3,5,7]=>[7,5,3,2,6,4,8,1]=>0000000=>0000000
[1,8,4,6,2,3,7,5]=>[5,7,3,2,6,4,8,1]=>0000000=>0000000
[1,8,3,6,2,4,7,5]=>[5,7,4,2,6,3,8,1]=>0000000=>0000000
[1,6,4,8,2,3,7,5]=>[5,7,3,2,8,4,6,1]=>0000000=>0000000
[1,7,2,8,4,3,6,5]=>[5,6,3,4,8,2,7,1]=>0000000=>0000000
[1,5,4,2,8,7,3,6]=>[6,3,7,8,2,4,5,1]=>0000000=>0000000
[1,7,3,8,6,2,4,5]=>[5,4,2,6,8,3,7,1]=>0000000=>0000000
[1,7,4,6,8,2,3,5]=>[5,3,2,8,6,4,7,1]=>0000000=>0000000
[1,7,3,6,8,2,4,5]=>[5,4,2,8,6,3,7,1]=>0000000=>0000000
[1,7,3,4,8,2,6,5]=>[5,6,2,8,4,3,7,1]=>0000000=>0000000
[7,4,3,5,2,8,6,1]=>[1,6,8,2,5,3,4,7]=>1000000=>0000001
[5,4,8,6,3,2,7,1]=>[1,7,2,3,6,8,4,5]=>1000000=>0000001
[7,6,4,8,5,3,2,1]=>[1,2,3,5,8,4,6,7]=>1110000=>0000111
[8,6,3,2,1,5,4,7]=>[7,4,5,1,2,3,6,8]=>0000001=>1000000
[5,6,4,8,7,3,1,2]=>[2,1,3,7,8,4,6,5]=>0110000=>0000110
[5,7,8,4,6,3,1,2]=>[2,1,3,6,4,8,7,5]=>0110000=>0000110
[1,5,2,7,6,3,4,8]=>[8,4,3,6,7,2,5,1]=>0000000=>0000000
[2,3,6,7,4,1,5,8]=>[8,5,1,4,7,6,3,2]=>0000000=>0000000
[6,2,1,3,7,4,5,8]=>[8,5,4,7,3,1,2,6]=>0000000=>0000000
[2,4,3,8,1,7,6,5]=>[5,6,7,1,8,3,4,2]=>0000000=>0000000
[3,2,5,8,1,7,4,6]=>[6,4,7,1,8,5,2,3]=>0000000=>0000000
[8,2,3,1,6,4,5,7]=>[7,5,4,6,1,3,2,8]=>0000001=>1000000
[5,4,2,1,3,6,8,7]=>[7,8,6,3,1,2,4,5]=>0000000=>0000000
[6,2,5,3,8,7,4,1]=>[1,4,7,8,3,5,2,6]=>1000000=>0000001
[4,5,7,3,6,2,1,8]=>[8,1,2,6,3,7,5,4]=>0000000=>0000000
[2,7,1,4,8,6,5,3]=>[3,5,6,8,4,1,7,2]=>0000000=>0000000
[7,3,6,8,4,1,2,5]=>[5,2,1,4,8,6,3,7]=>0000000=>0000000
[8,4,6,1,2,5,3,7]=>[7,3,5,2,1,6,4,8]=>0000001=>1000000
[5,1,4,2,3,7,6,8]=>[8,6,7,3,2,4,1,5]=>0000000=>0000000
[3,8,5,2,1,4,6,7]=>[7,6,4,1,2,5,8,3]=>0000000=>0000000
[6,1,3,7,5,4,2,8]=>[8,2,4,5,7,3,1,6]=>0000000=>0000000
[5,4,1,2,7,6,8,3]=>[3,8,6,7,2,1,4,5]=>0000000=>0000000
[3,7,6,1,4,2,8,5]=>[5,8,2,4,1,6,7,3]=>0000000=>0000000
[3,7,6,4,1,2,8,5]=>[5,8,2,1,4,6,7,3]=>0000000=>0000000
[1,7,2,6,4,8,3,5]=>[5,3,8,4,6,2,7,1]=>0000000=>0000000
[1,7,4,8,2,3,6,5]=>[5,6,3,2,8,4,7,1]=>0000000=>0000000
[2,5,4,6,1,8,3,7]=>[7,3,8,1,6,4,5,2]=>0000000=>0000000
[3,6,1,2,8,5,7,4]=>[4,7,5,8,2,1,6,3]=>0000000=>0000000
[4,7,8,3,5,2,6,1]=>[1,6,2,5,3,8,7,4]=>1000000=>0000001
[6,5,7,3,4,1,8,2]=>[2,8,1,4,3,7,5,6]=>0000000=>0000000
[5,3,4,6,8,7,2,1]=>[1,2,7,8,6,4,3,5]=>1100000=>0000011
[5,4,1,3,8,7,2,6]=>[6,2,7,8,3,1,4,5]=>0000000=>0000000
[6,3,5,1,4,7,2,8]=>[8,2,7,4,1,5,3,6]=>0000000=>0000000
[3,7,5,1,4,2,6,8]=>[8,6,2,4,1,5,7,3]=>0000000=>0000000
[2,1,6,3,5,4,7,8]=>[8,7,4,5,3,6,1,2]=>0000000=>0000000
[5,1,4,6,2,7,3,8]=>[8,3,7,2,6,4,1,5]=>0000000=>0000000
[3,4,1,6,8,5,2,7]=>[7,2,5,8,6,1,4,3]=>0000000=>0000000
[5,8,6,3,2,4,1,7]=>[7,1,4,2,3,6,8,5]=>0000000=>0000000
[4,7,8,5,2,6,3,1]=>[1,3,6,2,5,8,7,4]=>1000000=>0000001
[4,1,3,8,5,7,2,6]=>[6,2,7,5,8,3,1,4]=>0000000=>0000000
[1,8,2,7,3,5,6,4]=>[4,6,5,3,7,2,8,1]=>0000000=>0000000
[2,7,8,1,3,5,6,4]=>[4,6,5,3,1,8,7,2]=>0000000=>0000000
[7,1,6,8,2,3,5,4]=>[4,5,3,2,8,6,1,7]=>0000000=>0000000
[5,4,2,1,7,3,8,6]=>[6,8,3,7,1,2,4,5]=>0000000=>0000000
[5,4,3,1,2,6,8,7]=>[7,8,6,2,1,3,4,5]=>0000000=>0000000
[5,4,1,3,8,2,7,6]=>[6,7,2,8,3,1,4,5]=>0000000=>0000000
[1,4,7,8,5,3,6,2]=>[2,6,3,5,8,7,4,1]=>0000000=>0000000
[5,2,6,1,3,8,7,4]=>[4,7,8,3,1,6,2,5]=>0000000=>0000000
[8,6,2,1,7,3,5,4]=>[4,5,3,7,1,2,6,8]=>0000001=>1000000
[7,4,1,3,6,2,8,5]=>[5,8,2,6,3,1,4,7]=>0000000=>0000000
[6,8,7,5,2,4,3,1]=>[1,3,4,2,5,7,8,6]=>1001100=>0011001
[6,1,3,2,5,8,7,4]=>[4,7,8,5,2,3,1,6]=>0000000=>0000000
[7,2,5,1,8,6,3,4]=>[4,3,6,8,1,5,2,7]=>0000000=>0000000
[3,8,5,7,4,1,6,2]=>[2,6,1,4,7,5,8,3]=>0000000=>0000000
[7,5,3,6,8,2,4,1]=>[1,4,2,8,6,3,5,7]=>1000000=>0000001
[5,3,4,7,2,6,8,1]=>[1,8,6,2,7,4,3,5]=>1000000=>0000001
[2,6,3,8,5,4,7,1]=>[1,7,4,5,8,3,6,2]=>1000000=>0000001
[5,7,4,2,8,6,3,1]=>[1,3,6,8,2,4,7,5]=>1000000=>0000001
[5,8,4,2,7,6,3,1]=>[1,3,6,7,2,4,8,5]=>1000000=>0000001
[6,3,4,8,5,2,7,1]=>[1,7,2,5,8,4,3,6]=>1000000=>0000001
[5,4,7,2,8,6,3,1]=>[1,3,6,8,2,7,4,5]=>1000000=>0000001
[5,8,6,2,4,3,7,1]=>[1,7,3,4,2,6,8,5]=>1000000=>0000001
[6,8,4,2,3,1,7,5]=>[5,7,1,3,2,4,8,6]=>0000000=>0000000
[5,2,7,4,6,3,8,1]=>[1,8,3,6,4,7,2,5]=>1000000=>0000001
[5,4,6,8,3,2,7,1]=>[1,7,2,3,8,6,4,5]=>1000000=>0000001
[1,7,2,8,6,5,3,4]=>[4,3,5,6,8,2,7,1]=>0000000=>0000000
[1,5,6,8,7,2,4,3]=>[3,4,2,7,8,6,5,1]=>0000000=>0000000
[3,2,6,8,1,7,5,4]=>[4,5,7,1,8,6,2,3]=>0000000=>0000000
[4,2,8,7,5,1,6,3]=>[3,6,1,5,7,8,2,4]=>0000000=>0000000
[5,1,8,2,3,7,6,4]=>[4,6,7,3,2,8,1,5]=>0000000=>0000000
[6,3,1,5,8,7,4,2]=>[2,4,7,8,5,1,3,6]=>0000000=>0000000
[1,4,3,8,5,6,2,7]=>[7,2,6,5,8,3,4,1]=>0000000=>0000000
[2,5,6,3,4,7,1,8]=>[8,1,7,4,3,6,5,2]=>0000000=>0000000
[4,3,1,2,6,7,5,8]=>[8,5,7,6,2,1,3,4]=>0000000=>0000000
[5,8,3,4,7,6,2,1]=>[1,2,6,7,4,3,8,5]=>1100000=>0000011
[4,6,8,1,2,7,3,5]=>[5,3,7,2,1,8,6,4]=>0000000=>0000000
[2,6,3,8,5,7,1,4]=>[4,1,7,5,8,3,6,2]=>0000000=>0000000
[6,7,2,4,3,1,8,5]=>[5,8,1,3,4,2,7,6]=>0000000=>0000000
[7,4,2,5,8,6,1,3]=>[3,1,6,8,5,2,4,7]=>0000000=>0000000
[4,6,2,5,3,7,1,8]=>[8,1,7,3,5,2,6,4]=>0000000=>0000000
[3,1,4,7,8,6,2,5]=>[5,2,6,8,7,4,1,3]=>0000000=>0000000
[8,2,7,4,3,1,6,5]=>[5,6,1,3,4,7,2,8]=>0000001=>1000000
[8,3,1,4,5,2,7,6]=>[6,7,2,5,4,1,3,8]=>0000001=>1000000
[3,8,1,4,7,6,2,5]=>[5,2,6,7,4,1,8,3]=>0000000=>0000000
[2,8,1,4,6,5,3,7]=>[7,3,5,6,4,1,8,2]=>0000000=>0000000
[2,8,1,4,6,7,5,3]=>[3,5,7,6,4,1,8,2]=>0000000=>0000000
[4,8,6,1,5,2,3,7]=>[7,3,2,5,1,6,8,4]=>0000000=>0000000
[6,4,1,5,8,2,3,7]=>[7,3,2,8,5,1,4,6]=>0000000=>0000000
[3,2,5,8,1,4,7,6]=>[6,7,4,1,8,5,2,3]=>0000000=>0000000
[2,4,5,8,3,1,7,6]=>[6,7,1,3,8,5,4,2]=>0000000=>0000000
[2,4,6,7,3,1,5,8]=>[8,5,1,3,7,6,4,2]=>0000000=>0000000
[8,6,7,1,2,4,5,3]=>[3,5,4,2,1,7,6,8]=>0000101=>1010000
[6,7,1,2,3,5,4,8]=>[8,4,5,3,2,1,7,6]=>0000000=>0000000
[1,3,7,6,8,4,5,2]=>[2,5,4,8,6,7,3,1]=>0000000=>0000000
[5,7,3,4,2,6,8,1]=>[1,8,6,2,4,3,7,5]=>1000000=>0000001
[1,3,7,5,8,4,6,2]=>[2,6,4,8,5,7,3,1]=>0000000=>0000000
[4,3,1,6,7,5,8,2]=>[2,8,5,7,6,1,3,4]=>0000000=>0000000
[3,4,2,6,1,8,5,7]=>[7,5,8,1,6,2,4,3]=>0000000=>0000000
[6,7,2,3,5,4,1,8]=>[8,1,4,5,3,2,7,6]=>0000000=>0000000
[2,3,5,8,6,4,1,7]=>[7,1,4,6,8,5,3,2]=>0000000=>0000000
[5,4,1,2,7,6,3,8]=>[8,3,6,7,2,1,4,5]=>0000000=>0000000
[5,3,7,1,4,6,8,2]=>[2,8,6,4,1,7,3,5]=>0000000=>0000000
[6,1,3,2,5,4,7,8]=>[8,7,4,5,2,3,1,6]=>0000000=>0000000
[5,2,1,6,4,7,8,3]=>[3,8,7,4,6,1,2,5]=>0000000=>0000000
[3,5,2,1,8,7,4,6]=>[6,4,7,8,1,2,5,3]=>0000000=>0000000
[7,3,2,1,5,8,6,4]=>[4,6,8,5,1,2,3,7]=>0000000=>0000000
[7,3,2,1,5,6,8,4]=>[4,8,6,5,1,2,3,7]=>0000000=>0000000
[4,7,1,5,6,2,3,8]=>[8,3,2,6,5,1,7,4]=>0000000=>0000000
[4,8,3,1,6,5,2,7]=>[7,2,5,6,1,3,8,4]=>0000000=>0000000
[1,4,6,3,5,7,2,8]=>[8,2,7,5,3,6,4,1]=>0000000=>0000000
[6,8,5,3,2,4,7,1]=>[1,7,4,2,3,5,8,6]=>1000000=>0000001
[2,4,5,8,6,3,1,7]=>[7,1,3,6,8,5,4,2]=>0000000=>0000000
[8,4,2,7,3,5,1,6]=>[6,1,5,3,7,2,4,8]=>0000001=>1000000
[6,8,5,3,4,2,7,1]=>[1,7,2,4,3,5,8,6]=>1000000=>0000001
[7,2,6,5,8,4,3,1]=>[1,3,4,8,5,6,2,7]=>1000000=>0000001
[7,2,1,6,5,8,4,3]=>[3,4,8,5,6,1,2,7]=>0000000=>0000000
[1,7,3,4,5,8,6,2]=>[2,6,8,5,4,3,7,1]=>0000000=>0000000
[5,7,3,2,1,8,4,6]=>[6,4,8,1,2,3,7,5]=>0000000=>0000000
[4,3,7,1,8,2,6,5]=>[5,6,2,8,1,7,3,4]=>0000000=>0000000
[7,2,3,8,4,5,1,6]=>[6,1,5,4,8,3,2,7]=>0000000=>0000000
[6,2,8,7,4,3,1,5]=>[5,1,3,4,7,8,2,6]=>0000000=>0000000
[6,2,8,7,3,1,5,4]=>[4,5,1,3,7,8,2,6]=>0000000=>0000000
[2,5,6,8,1,3,7,4]=>[4,7,3,1,8,6,5,2]=>0000000=>0000000
[2,5,3,6,4,8,1,7]=>[7,1,8,4,6,3,5,2]=>0000000=>0000000
[5,6,4,1,8,2,3,7]=>[7,3,2,8,1,4,6,5]=>0000000=>0000000
[6,5,8,3,2,7,4,1]=>[1,4,7,2,3,8,5,6]=>1000000=>0000001
[1,5,4,6,8,3,2,7]=>[7,2,3,8,6,4,5,1]=>0000000=>0000000
[8,6,2,3,5,4,7,1]=>[1,7,4,5,3,2,6,8]=>1000001=>1000001
[8,2,5,3,7,4,6,1]=>[1,6,4,7,3,5,2,8]=>1000001=>1000001
[8,3,2,5,7,4,6,1]=>[1,6,4,7,5,2,3,8]=>1000001=>1000001
[2,1,7,8,3,5,4,6]=>[6,4,5,3,8,7,1,2]=>0000000=>0000000
[5,2,4,1,3,6,8,7]=>[7,8,6,3,1,4,2,5]=>0000000=>0000000
[5,8,4,3,1,2,7,6]=>[6,7,2,1,3,4,8,5]=>0000000=>0000000
[7,4,3,1,8,5,2,6]=>[6,2,5,8,1,3,4,7]=>0000000=>0000000
[1,6,4,2,7,8,5,3]=>[3,5,8,7,2,4,6,1]=>0000000=>0000000
[7,3,6,8,4,2,5,1]=>[1,5,2,4,8,6,3,7]=>1000000=>0000001
[3,8,7,4,2,5,1,6]=>[6,1,5,2,4,7,8,3]=>0000000=>0000000
[6,8,7,1,2,4,5,3]=>[3,5,4,2,1,7,8,6]=>0000100=>0010000
[6,1,2,5,7,3,4,8]=>[8,4,3,7,5,2,1,6]=>0000000=>0000000
[6,2,3,5,7,1,4,8]=>[8,4,1,7,5,3,2,6]=>0000000=>0000000
[6,2,5,7,3,1,4,8]=>[8,4,1,3,7,5,2,6]=>0000000=>0000000
[7,3,6,1,5,2,8,4]=>[4,8,2,5,1,6,3,7]=>0000000=>0000000
[4,3,2,5,8,6,1,7]=>[7,1,6,8,5,2,3,4]=>0000000=>0000000
[2,5,6,7,3,1,4,8]=>[8,4,1,3,7,6,5,2]=>0000000=>0000000
[8,1,2,6,7,4,3,5]=>[5,3,4,7,6,2,1,8]=>0000001=>1000000
[8,2,4,6,3,7,5,1]=>[1,5,7,3,6,4,2,8]=>1000001=>1000001
[7,2,3,6,1,4,5,8]=>[8,5,4,1,6,3,2,7]=>0000000=>0000000
[2,3,7,5,1,4,6,8]=>[8,6,4,1,5,7,3,2]=>0000000=>0000000
[3,4,1,5,8,6,2,7]=>[7,2,6,8,5,1,4,3]=>0000000=>0000000
[2,3,7,1,4,6,5,8]=>[8,5,6,4,1,7,3,2]=>0000000=>0000000
[4,7,8,3,6,1,2,5]=>[5,2,1,6,3,8,7,4]=>0000000=>0000000
[5,6,8,4,2,3,7,1]=>[1,7,3,2,4,8,6,5]=>1000000=>0000001
[2,3,8,7,6,1,5,4]=>[4,5,1,6,7,8,3,2]=>0000000=>0000000
[8,5,7,4,2,3,6,1]=>[1,6,3,2,4,7,5,8]=>1000001=>1000001
[1,7,5,8,6,2,4,3]=>[3,4,2,6,8,5,7,1]=>0000000=>0000000
[4,1,2,8,6,7,5,3]=>[3,5,7,6,8,2,1,4]=>0000000=>0000000
[4,7,3,6,8,5,1,2]=>[2,1,5,8,6,3,7,4]=>0100000=>0000010
[6,2,3,5,7,8,4,1]=>[1,4,8,7,5,3,2,6]=>1000000=>0000001
[8,7,1,3,5,2,4,6]=>[6,4,2,5,3,1,7,8]=>0000011=>1100000
[3,5,1,6,8,7,4,2]=>[2,4,7,8,6,1,5,3]=>0000000=>0000000
[3,5,2,6,8,7,4,1]=>[1,4,7,8,6,2,5,3]=>1000000=>0000001
[3,6,2,8,5,7,4,1]=>[1,4,7,5,8,2,6,3]=>1000000=>0000001
[1,3,8,7,2,6,5,4]=>[4,5,6,2,7,8,3,1]=>0000000=>0000000
[2,8,1,4,7,3,6,5]=>[5,6,3,7,4,1,8,2]=>0000000=>0000000
[2,6,8,7,5,3,4,1]=>[1,4,3,5,7,8,6,2]=>1000000=>0000001
[4,6,3,1,8,5,2,7]=>[7,2,5,8,1,3,6,4]=>0000000=>0000000
[7,2,4,6,3,1,5,8]=>[8,5,1,3,6,4,2,7]=>0000000=>0000000
[6,2,1,5,4,8,3,7]=>[7,3,8,4,5,1,2,6]=>0000000=>0000000
[8,5,6,1,3,7,2,4]=>[4,2,7,3,1,6,5,8]=>0000001=>1000000
[8,2,1,4,3,7,5,6]=>[6,5,7,3,4,1,2,8]=>0000001=>1000000
[2,7,3,1,5,8,6,4]=>[4,6,8,5,1,3,7,2]=>0000000=>0000000
[6,5,4,1,3,7,2,8]=>[8,2,7,3,1,4,5,6]=>0000000=>0000000
[6,2,4,1,5,7,3,8]=>[8,3,7,5,1,4,2,6]=>0000000=>0000000
[5,8,7,3,1,6,2,4]=>[4,2,6,1,3,7,8,5]=>0000000=>0000000
[5,7,8,2,3,6,4,1]=>[1,4,6,3,2,8,7,5]=>1000000=>0000001
[2,7,5,3,4,6,8,1]=>[1,8,6,4,3,5,7,2]=>1000000=>0000001
[5,8,3,6,7,4,2,1]=>[1,2,4,7,6,3,8,5]=>1100000=>0000011
[7,6,3,2,1,5,8,4]=>[4,8,5,1,2,3,6,7]=>0000000=>0000000
[8,5,7,1,3,4,2,6]=>[6,2,4,3,1,7,5,8]=>0000001=>1000000
[8,2,6,1,7,5,3,4]=>[4,3,5,7,1,6,2,8]=>0000001=>1000000
[6,1,4,5,7,3,2,8]=>[8,2,3,7,5,4,1,6]=>0000000=>0000000
[7,2,3,5,6,1,4,8]=>[8,4,1,6,5,3,2,7]=>0000000=>0000000
[7,2,4,5,3,1,6,8]=>[8,6,1,3,5,4,2,7]=>0000000=>0000000
[7,1,4,5,6,2,3,8]=>[8,3,2,6,5,4,1,7]=>0000000=>0000000
[1,4,6,7,5,8,2,3]=>[3,2,8,5,7,6,4,1]=>0000000=>0000000
[5,2,6,4,3,7,1,8]=>[8,1,7,3,4,6,2,5]=>0000000=>0000000
[1,5,6,7,4,2,8,3]=>[3,8,2,4,7,6,5,1]=>0000000=>0000000
[1,3,6,7,8,4,5,2]=>[2,5,4,8,7,6,3,1]=>0000000=>0000000
[3,4,6,7,2,5,1,8]=>[8,1,5,2,7,6,4,3]=>0000000=>0000000
[3,6,7,1,4,5,2,8]=>[8,2,5,4,1,7,6,3]=>0000000=>0000000
[7,2,5,8,4,6,3,1]=>[1,3,6,4,8,5,2,7]=>1000000=>0000001
[5,6,8,4,7,1,3,2]=>[2,3,1,7,4,8,6,5]=>0010000=>0000100
[4,7,8,5,1,6,2,3]=>[3,2,6,1,5,8,7,4]=>0000000=>0000000
[5,3,1,4,8,7,6,2]=>[2,6,7,8,4,1,3,5]=>0000000=>0000000
[4,5,7,3,6,8,1,2]=>[2,1,8,6,3,7,5,4]=>0100000=>0000010
[8,6,7,3,1,2,5,4]=>[4,5,2,1,3,7,6,8]=>0000101=>1010000
[1,8,2,6,4,7,3,5]=>[5,3,7,4,6,2,8,1]=>0000000=>0000000
[8,1,2,4,7,3,6,5]=>[5,6,3,7,4,2,1,8]=>0000001=>1000000
[8,4,6,3,2,5,7,1]=>[1,7,5,2,3,6,4,8]=>1000001=>1000001
[8,4,5,7,6,3,1,2]=>[2,1,3,6,7,5,4,8]=>0110001=>1000110
[8,4,6,5,2,3,1,7]=>[7,1,3,2,5,6,4,8]=>0000001=>1000000
[3,8,5,6,2,7,4,1]=>[1,4,7,2,6,5,8,3]=>1000000=>0000001
[5,6,8,7,4,1,3,2]=>[2,3,1,4,7,8,6,5]=>0011000=>0001100
[3,4,6,7,2,5,8,1]=>[1,8,5,2,7,6,4,3]=>1000000=>0000001
[3,4,7,8,2,5,1,6]=>[6,1,5,2,8,7,4,3]=>0000000=>0000000
[8,5,7,3,1,4,6,2]=>[2,6,4,1,3,7,5,8]=>0000001=>1000000
[8,5,3,7,1,4,6,2]=>[2,6,4,1,7,3,5,8]=>0000001=>1000000
[6,3,1,8,5,7,4,2]=>[2,4,7,5,8,1,3,6]=>0000000=>0000000
[5,2,8,7,4,3,6,1]=>[1,6,3,4,7,8,2,5]=>1000000=>0000001
[7,4,3,8,6,5,2,1]=>[1,2,5,6,8,3,4,7]=>1100000=>0000011
[7,8,6,3,5,2,4,1]=>[1,4,2,5,3,6,8,7]=>1000110=>0110001
[5,4,7,2,3,1,6,8]=>[8,6,1,3,2,7,4,5]=>0000000=>0000000
[3,4,1,6,5,2,8,7]=>[7,8,2,5,6,1,4,3]=>0000000=>0000000
[6,1,8,2,4,7,5,3]=>[3,5,7,4,2,8,1,6]=>0000000=>0000000
[7,8,4,3,1,6,2,5]=>[5,2,6,1,3,4,8,7]=>0000010=>0100000
[2,7,8,6,1,5,3,4]=>[4,3,5,1,6,8,7,2]=>0000000=>0000000
[2,4,8,7,5,3,6,1]=>[1,6,3,5,7,8,4,2]=>1000000=>0000001
[8,1,6,2,5,7,3,4]=>[4,3,7,5,2,6,1,8]=>0000001=>1000000
[3,4,8,5,7,1,2,6]=>[6,2,1,7,5,8,4,3]=>0000000=>0000000
[5,3,1,8,7,6,2,4]=>[4,2,6,7,8,1,3,5]=>0000000=>0000000
[3,2,4,6,1,8,5,7]=>[7,5,8,1,6,4,2,3]=>0000000=>0000000
[7,4,5,1,6,2,3,8]=>[8,3,2,6,1,5,4,7]=>0000000=>0000000
[6,5,1,4,8,2,7,3]=>[3,7,2,8,4,1,5,6]=>0000000=>0000000
[4,5,8,7,6,2,1,3]=>[3,1,2,6,7,8,5,4]=>0010000=>0000100
[4,6,8,7,1,2,5,3]=>[3,5,2,1,7,8,6,4]=>0000000=>0000000
[8,6,1,5,2,3,7,4]=>[4,7,3,2,5,1,6,8]=>0000001=>1000000
[1,5,6,4,7,2,3,8]=>[8,3,2,7,4,6,5,1]=>0000000=>0000000
[7,3,4,8,5,2,6,1]=>[1,6,2,5,8,4,3,7]=>1000000=>0000001
[6,4,1,3,7,5,2,8]=>[8,2,5,7,3,1,4,6]=>0000000=>0000000
[8,5,6,3,2,7,4,1]=>[1,4,7,2,3,6,5,8]=>1000001=>1000001
[4,2,3,8,7,6,1,5]=>[5,1,6,7,8,3,2,4]=>0000000=>0000000
[1,7,3,5,4,2,6,8]=>[8,6,2,4,5,3,7,1]=>0000000=>0000000
[5,1,6,8,2,3,7,4]=>[4,7,3,2,8,6,1,5]=>0000000=>0000000
[5,7,8,1,2,3,6,4]=>[4,6,3,2,1,8,7,5]=>0000000=>0000000
[3,1,4,5,7,6,2,8]=>[8,2,6,7,5,4,1,3]=>0000000=>0000000
[7,1,6,8,4,5,2,3]=>[3,2,5,4,8,6,1,7]=>0000000=>0000000
[6,1,4,5,8,7,2,3]=>[3,2,7,8,5,4,1,6]=>0000000=>0000000
[7,2,5,6,3,1,4,8]=>[8,4,1,3,6,5,2,7]=>0000000=>0000000
[4,6,7,5,2,8,1,3]=>[3,1,8,2,5,7,6,4]=>0000000=>0000000
[4,6,7,5,3,8,1,2]=>[2,1,8,3,5,7,6,4]=>0100000=>0000010
[2,4,5,7,8,6,1,3]=>[3,1,6,8,7,5,4,2]=>0000000=>0000000
[4,5,8,6,3,1,2,7]=>[7,2,1,3,6,8,5,4]=>0000000=>0000000
[6,8,4,7,5,2,1,3]=>[3,1,2,5,7,4,8,6]=>0010000=>0000100
[8,3,6,7,1,2,5,4]=>[4,5,2,1,7,6,3,8]=>0000001=>1000000
[5,8,7,2,4,3,1,6]=>[6,1,3,4,2,7,8,5]=>0000000=>0000000
[7,2,5,1,3,4,8,6]=>[6,8,4,3,1,5,2,7]=>0000000=>0000000
[2,7,3,4,6,1,5,8]=>[8,5,1,6,4,3,7,2]=>0000000=>0000000
[3,6,4,5,8,2,7,1]=>[1,7,2,8,5,4,6,3]=>1000000=>0000001
[2,5,1,6,8,7,3,4]=>[4,3,7,8,6,1,5,2]=>0000000=>0000000
[4,2,3,7,1,6,5,8]=>[8,5,6,1,7,3,2,4]=>0000000=>0000000
[7,3,5,8,2,6,4,1]=>[1,4,6,2,8,5,3,7]=>1000000=>0000001
[4,2,6,8,3,7,1,5]=>[5,1,7,3,8,6,2,4]=>0000000=>0000000
[6,3,8,5,7,2,4,1]=>[1,4,2,7,5,8,3,6]=>1000000=>0000001
[5,2,4,6,1,8,3,7]=>[7,3,8,1,6,4,2,5]=>0000000=>0000000
[5,4,7,6,1,3,8,2]=>[2,8,3,1,6,7,4,5]=>0000000=>0000000
[2,7,1,4,8,5,6,3]=>[3,6,5,8,4,1,7,2]=>0000000=>0000000
[7,2,8,1,4,3,5,6]=>[6,5,3,4,1,8,2,7]=>0000000=>0000000
[1,8,5,3,6,7,2,4]=>[4,2,7,6,3,5,8,1]=>0000000=>0000000
[2,1,5,7,6,8,3,4]=>[4,3,8,6,7,5,1,2]=>0000000=>0000000
[8,3,7,1,2,6,5,4]=>[4,5,6,2,1,7,3,8]=>0000001=>1000000
[8,2,3,7,6,1,5,4]=>[4,5,1,6,7,3,2,8]=>0000001=>1000000
[4,8,6,2,7,5,1,3]=>[3,1,5,7,2,6,8,4]=>0000000=>0000000
[7,8,2,3,6,4,5,1]=>[1,5,4,6,3,2,8,7]=>1000010=>0100001
[7,8,6,2,4,5,3,1]=>[1,3,5,4,2,6,8,7]=>1000110=>0110001
[8,4,6,7,5,1,2,3]=>[3,2,1,5,7,6,4,8]=>0010001=>1000100
[2,6,3,1,5,4,8,7]=>[7,8,4,5,1,3,6,2]=>0000000=>0000000
[3,8,7,5,4,2,1,6]=>[6,1,2,4,5,7,8,3]=>0000000=>0000000
[7,1,6,4,2,5,8,3]=>[3,8,5,2,4,6,1,7]=>0000000=>0000000
[3,8,5,2,7,4,6,1]=>[1,6,4,7,2,5,8,3]=>1000000=>0000001
[2,6,8,1,7,4,5,3]=>[3,5,4,7,1,8,6,2]=>0000000=>0000000
[6,1,2,5,3,8,7,4]=>[4,7,8,3,5,2,1,6]=>0000000=>0000000
[8,1,3,5,4,2,7,6]=>[6,7,2,4,5,3,1,8]=>0000001=>1000000
[2,7,8,3,5,4,6,1]=>[1,6,4,5,3,8,7,2]=>1000000=>0000001
[7,5,2,6,4,8,1,3]=>[3,1,8,4,6,2,5,7]=>0000000=>0000000
[5,7,4,2,8,6,1,3]=>[3,1,6,8,2,4,7,5]=>0000000=>0000000
[5,6,8,7,3,4,2,1]=>[1,2,4,3,7,8,6,5]=>1101000=>0001011
[6,3,1,8,7,4,5,2]=>[2,5,4,7,8,1,3,6]=>0000000=>0000000
[8,1,3,6,7,2,5,4]=>[4,5,2,7,6,3,1,8]=>0000001=>1000000
[3,5,6,7,2,1,4,8]=>[8,4,1,2,7,6,5,3]=>0000000=>0000000
[7,3,5,6,2,8,4,1]=>[1,4,8,2,6,5,3,7]=>1000000=>0000001
[2,7,4,3,8,6,1,5]=>[5,1,6,8,3,4,7,2]=>0000000=>0000000
[1,7,6,5,3,4,8,2]=>[2,8,4,3,5,6,7,1]=>0000000=>0000000
[1,6,2,3,7,5,4,8]=>[8,4,5,7,3,2,6,1]=>0000000=>0000000
[3,2,6,4,7,1,5,8]=>[8,5,1,7,4,6,2,3]=>0000000=>0000000
[1,6,8,5,3,7,2,4]=>[4,2,7,3,5,8,6,1]=>0000000=>0000000
[1,3,8,7,2,6,4,5]=>[5,4,6,2,7,8,3,1]=>0000000=>0000000
[1,4,7,5,8,6,2,3]=>[3,2,6,8,5,7,4,1]=>0000000=>0000000
[6,1,3,5,2,7,4,8]=>[8,4,7,2,5,3,1,6]=>0000000=>0000000
[4,8,5,2,3,6,7,1]=>[1,7,6,3,2,5,8,4]=>1000000=>0000001
[4,5,8,3,2,6,7,1]=>[1,7,6,2,3,8,5,4]=>1000000=>0000001
[5,8,6,2,4,7,3,1]=>[1,3,7,4,2,6,8,5]=>1000000=>0000001
[7,4,1,8,5,3,2,6]=>[6,2,3,5,8,1,4,7]=>0000000=>0000000
[2,7,5,6,8,1,3,4]=>[4,3,1,8,6,5,7,2]=>0000000=>0000000
[1,4,7,6,8,2,5,3]=>[3,5,2,8,6,7,4,1]=>0000000=>0000000
[4,6,5,2,3,7,1,8]=>[8,1,7,3,2,5,6,4]=>0000000=>0000000
[4,1,7,8,3,5,2,6]=>[6,2,5,3,8,7,1,4]=>0000000=>0000000
[7,1,3,6,4,2,8,5]=>[5,8,2,4,6,3,1,7]=>0000000=>0000000
[6,7,8,2,4,1,5,3]=>[3,5,1,4,2,8,7,6]=>0000100=>0010000
[8,5,4,6,2,7,3,1]=>[1,3,7,2,6,4,5,8]=>1000001=>1000001
[8,5,3,2,6,7,4,1]=>[1,4,7,6,2,3,5,8]=>1000001=>1000001
[6,5,2,4,8,3,7,1]=>[1,7,3,8,4,2,5,6]=>1000000=>0000001
[3,8,5,7,4,2,6,1]=>[1,6,2,4,7,5,8,3]=>1000000=>0000001
[7,2,6,1,5,4,8,3]=>[3,8,4,5,1,6,2,7]=>0000000=>0000000
[4,6,1,8,7,5,3,2]=>[2,3,5,7,8,1,6,4]=>0000000=>0000000
[3,6,4,5,7,8,2,1]=>[1,2,8,7,5,4,6,3]=>1100000=>0000011
[4,2,1,8,5,7,6,3]=>[3,6,7,5,8,1,2,4]=>0000000=>0000000
[1,6,8,2,4,7,3,5]=>[5,3,7,4,2,8,6,1]=>0000000=>0000000
[1,5,6,3,8,7,2,4]=>[4,2,7,8,3,6,5,1]=>0000000=>0000000
[4,1,2,8,7,6,3,5]=>[5,3,6,7,8,2,1,4]=>0000000=>0000000
[6,1,2,8,4,7,3,5]=>[5,3,7,4,8,2,1,6]=>0000000=>0000000
[5,3,1,2,8,7,6,4]=>[4,6,7,8,2,1,3,5]=>0000000=>0000000
[2,5,1,8,7,3,6,4]=>[4,6,3,7,8,1,5,2]=>0000000=>0000000
[5,1,2,8,7,3,6,4]=>[4,6,3,7,8,2,1,5]=>0000000=>0000000
[2,1,8,7,3,5,6,4]=>[4,6,5,3,7,8,1,2]=>0000000=>0000000
[4,1,5,8,6,2,7,3]=>[3,7,2,6,8,5,1,4]=>0000000=>0000000
[1,7,4,3,8,2,6,5]=>[5,6,2,8,3,4,7,1]=>0000000=>0000000
[3,4,6,7,8,2,5,1]=>[1,5,2,8,7,6,4,3]=>1000000=>0000001
[1,8,6,2,7,5,3,4]=>[4,3,5,7,2,6,8,1]=>0000000=>0000000
[7,8,3,2,6,5,1,4]=>[4,1,5,6,2,3,8,7]=>0000010=>0100000
[6,1,2,5,8,4,3,7]=>[7,3,4,8,5,2,1,6]=>0000000=>0000000
[3,7,2,6,5,1,4,8]=>[8,4,1,5,6,2,7,3]=>0000000=>0000000
[8,3,1,6,7,4,5,2]=>[2,5,4,7,6,1,3,8]=>0000001=>1000000
[5,4,6,8,2,1,3,7]=>[7,3,1,2,8,6,4,5]=>0000000=>0000000
[2,7,5,3,4,1,8,6]=>[6,8,1,4,3,5,7,2]=>0000000=>0000000
[8,6,2,1,5,3,7,4]=>[4,7,3,5,1,2,6,8]=>0000001=>1000000
[4,1,5,6,2,8,7,3]=>[3,7,8,2,6,5,1,4]=>0000000=>0000000
[1,4,8,7,6,2,5,3]=>[3,5,2,6,7,8,4,1]=>0000000=>0000000
[5,6,2,3,7,4,8,1]=>[1,8,4,7,3,2,6,5]=>1000000=>0000001
[5,8,7,2,3,1,4,6]=>[6,4,1,3,2,7,8,5]=>0000000=>0000000
[2,4,7,6,3,8,5,1]=>[1,5,8,3,6,7,4,2]=>1000000=>0000001
[7,3,6,2,4,8,5,1]=>[1,5,8,4,2,6,3,7]=>1000000=>0000001
[2,6,8,7,1,4,5,3]=>[3,5,4,1,7,8,6,2]=>0000000=>0000000
[4,8,7,1,2,6,5,3]=>[3,5,6,2,1,7,8,4]=>0000000=>0000000
[5,2,6,4,3,8,1,7]=>[7,1,8,3,4,6,2,5]=>0000000=>0000000
[7,4,3,6,1,2,8,5]=>[5,8,2,1,6,3,4,7]=>0000000=>0000000
[7,6,4,8,2,1,5,3]=>[3,5,1,2,8,4,6,7]=>0000000=>0000000
[4,7,8,6,2,1,5,3]=>[3,5,1,2,6,8,7,4]=>0000000=>0000000
[3,5,7,1,6,4,2,8]=>[8,2,4,6,1,7,5,3]=>0000000=>0000000
[6,3,8,4,1,5,7,2]=>[2,7,5,1,4,8,3,6]=>0000000=>0000000
[8,1,6,7,3,5,2,4]=>[4,2,5,3,7,6,1,8]=>0000001=>1000000
[7,1,5,6,3,4,2,8]=>[8,2,4,3,6,5,1,7]=>0000000=>0000000
[8,2,5,6,4,1,3,7]=>[7,3,1,4,6,5,2,8]=>0000001=>1000000
[6,1,4,5,2,7,3,8]=>[8,3,7,2,5,4,1,6]=>0000000=>0000000
[7,1,4,5,2,6,3,8]=>[8,3,6,2,5,4,1,7]=>0000000=>0000000
[5,1,4,7,3,6,2,8]=>[8,2,6,3,7,4,1,5]=>0000000=>0000000
[6,1,4,8,3,7,2,5]=>[5,2,7,3,8,4,1,6]=>0000000=>0000000
[6,1,4,7,3,5,2,8]=>[8,2,5,3,7,4,1,6]=>0000000=>0000000
[8,3,6,7,4,2,5,1]=>[1,5,2,4,7,6,3,8]=>1000001=>1000001
[8,5,7,1,4,6,2,3]=>[3,2,6,4,1,7,5,8]=>0000001=>1000000
[5,6,7,2,3,8,4,1]=>[1,4,8,3,2,7,6,5]=>1000000=>0000001
[1,7,8,5,6,2,4,3]=>[3,4,2,6,5,8,7,1]=>0000000=>0000000
[4,6,1,5,7,8,3,2]=>[2,3,8,7,5,1,6,4]=>0000000=>0000000
[6,8,1,7,2,4,3,5]=>[5,3,4,2,7,1,8,6]=>0000000=>0000000
[5,3,6,8,2,4,1,7]=>[7,1,4,2,8,6,3,5]=>0000000=>0000000
[5,1,3,6,8,7,2,4]=>[4,2,7,8,6,3,1,5]=>0000000=>0000000
[7,2,6,1,3,5,8,4]=>[4,8,5,3,1,6,2,7]=>0000000=>0000000
[7,2,5,1,6,3,8,4]=>[4,8,3,6,1,5,2,7]=>0000000=>0000000
[5,2,6,1,3,8,4,7]=>[7,4,8,3,1,6,2,5]=>0000000=>0000000
[6,1,8,5,7,4,2,3]=>[3,2,4,7,5,8,1,6]=>0000000=>0000000
[5,8,1,6,4,7,2,3]=>[3,2,7,4,6,1,8,5]=>0000000=>0000000
[5,7,1,6,4,2,3,8]=>[8,3,2,4,6,1,7,5]=>0000000=>0000000
[6,1,7,5,4,2,3,8]=>[8,3,2,4,5,7,1,6]=>0000000=>0000000
[6,1,8,4,7,5,2,3]=>[3,2,5,7,4,8,1,6]=>0000000=>0000000
[4,2,3,6,1,8,7,5]=>[5,7,8,1,6,3,2,4]=>0000000=>0000000
[5,7,4,1,3,8,2,6]=>[6,2,8,3,1,4,7,5]=>0000000=>0000000
[6,7,5,4,1,3,8,2]=>[2,8,3,1,4,5,7,6]=>0000000=>0000000
[4,7,6,5,1,2,3,8]=>[8,3,2,1,5,6,7,4]=>0000000=>0000000
[5,7,8,4,2,3,6,1]=>[1,6,3,2,4,8,7,5]=>1000000=>0000001
[5,2,1,3,8,4,6,7]=>[7,6,4,8,3,1,2,5]=>0000000=>0000000
[4,1,3,5,7,6,8,2]=>[2,8,6,7,5,3,1,4]=>0000000=>0000000
[3,7,8,6,1,5,2,4]=>[4,2,5,1,6,8,7,3]=>0000000=>0000000
[2,5,4,6,1,3,8,7]=>[7,8,3,1,6,4,5,2]=>0000000=>0000000
[4,5,1,7,6,8,3,2]=>[2,3,8,6,7,1,5,4]=>0000000=>0000000
[8,6,7,2,4,3,1,5]=>[5,1,3,4,2,7,6,8]=>0000101=>1010000
[7,1,6,8,3,2,5,4]=>[4,5,2,3,8,6,1,7]=>0000000=>0000000
[8,5,7,6,3,4,2,1]=>[1,2,4,3,6,7,5,8]=>1101001=>1001011
[3,7,2,5,8,4,1,6]=>[6,1,4,8,5,2,7,3]=>0000000=>0000000
[4,3,5,7,8,1,6,2]=>[2,6,1,8,7,5,3,4]=>0000000=>0000000
[4,8,7,2,3,6,1,5]=>[5,1,6,3,2,7,8,4]=>0000000=>0000000
[3,7,1,6,2,4,5,8]=>[8,5,4,2,6,1,7,3]=>0000000=>0000000
[1,5,7,3,4,2,6,8]=>[8,6,2,4,3,7,5,1]=>0000000=>0000000
[4,8,6,5,7,2,3,1]=>[1,3,2,7,5,6,8,4]=>1010000=>0000101
[8,1,4,6,5,7,2,3]=>[3,2,7,5,6,4,1,8]=>0000001=>1000000
[8,4,6,5,2,3,7,1]=>[1,7,3,2,5,6,4,8]=>1000001=>1000001
[7,4,2,1,6,3,8,5]=>[5,8,3,6,1,2,4,7]=>0000000=>0000000
[8,7,2,4,1,3,6,5]=>[5,6,3,1,4,2,7,8]=>0000011=>1100000
[3,7,4,6,5,1,8,2]=>[2,8,1,5,6,4,7,3]=>0000000=>0000000
[5,3,7,1,4,6,2,8]=>[8,2,6,4,1,7,3,5]=>0000000=>0000000
[6,5,4,1,7,3,2,8]=>[8,2,3,7,1,4,5,6]=>0000000=>0000000
[2,7,8,3,4,1,5,6]=>[6,5,1,4,3,8,7,2]=>0000000=>0000000
[2,1,3,7,8,5,4,6]=>[6,4,5,8,7,3,1,2]=>0000000=>0000000
[6,5,3,1,4,8,2,7]=>[7,2,8,4,1,3,5,6]=>0000000=>0000000
[6,5,1,3,2,4,8,7]=>[7,8,4,2,3,1,5,6]=>0000000=>0000000
[6,5,2,4,8,7,1,3]=>[3,1,7,8,4,2,5,6]=>0000000=>0000000
[3,4,7,2,5,6,8,1]=>[1,8,6,5,2,7,4,3]=>1000000=>0000001
[4,5,2,6,1,3,7,8]=>[8,7,3,1,6,2,5,4]=>0000000=>0000000
[4,5,2,6,1,7,8,3]=>[3,8,7,1,6,2,5,4]=>0000000=>0000000
[6,7,4,3,2,8,1,5]=>[5,1,8,2,3,4,7,6]=>0000000=>0000000
[4,1,3,5,7,2,6,8]=>[8,6,2,7,5,3,1,4]=>0000000=>0000000
[6,5,2,3,7,4,1,8]=>[8,1,4,7,3,2,5,6]=>0000000=>0000000
[5,3,1,7,6,4,8,2]=>[2,8,4,6,7,1,3,5]=>0000000=>0000000
[5,1,3,4,8,7,6,2]=>[2,6,7,8,4,3,1,5]=>0000000=>0000000
[6,5,4,1,2,8,7,3]=>[3,7,8,2,1,4,5,6]=>0000000=>0000000
[8,6,2,5,3,7,4,1]=>[1,4,7,3,5,2,6,8]=>1000001=>1000001
[1,3,5,8,7,4,6,2]=>[2,6,4,7,8,5,3,1]=>0000000=>0000000
[7,4,6,5,3,2,8,1]=>[1,8,2,3,5,6,4,7]=>1000000=>0000001
[5,8,6,3,4,7,1,2]=>[2,1,7,4,3,6,8,5]=>0100000=>0000010
[7,2,6,3,8,5,1,4]=>[4,1,5,8,3,6,2,7]=>0000000=>0000000
[6,7,3,4,2,8,5,1]=>[1,5,8,2,4,3,7,6]=>1000000=>0000001
[5,2,1,7,8,6,4,3]=>[3,4,6,8,7,1,2,5]=>0000000=>0000000
[7,2,4,3,6,8,5,1]=>[1,5,8,6,3,4,2,7]=>1000000=>0000001
[8,3,6,7,5,2,4,1]=>[1,4,2,5,7,6,3,8]=>1000001=>1000001
[7,2,6,5,8,3,1,4]=>[4,1,3,8,5,6,2,7]=>0000000=>0000000
[2,5,7,8,4,6,1,3]=>[3,1,6,4,8,7,5,2]=>0000000=>0000000
[4,6,5,1,8,2,7,3]=>[3,7,2,8,1,5,6,4]=>0000000=>0000000
[8,1,3,2,5,7,6,4]=>[4,6,7,5,2,3,1,8]=>0000001=>1000000
[3,2,7,6,4,8,1,5]=>[5,1,8,4,6,7,2,3]=>0000000=>0000000
[7,3,1,8,4,6,5,2]=>[2,5,6,4,8,1,3,7]=>0000000=>0000000
[4,7,6,2,3,5,8,1]=>[1,8,5,3,2,6,7,4]=>1000000=>0000001
[7,2,3,5,6,1,8,4]=>[4,8,1,6,5,3,2,7]=>0000000=>0000000
[5,3,2,8,7,4,6,1]=>[1,6,4,7,8,2,3,5]=>1000000=>0000001
[3,5,7,6,1,2,8,4]=>[4,8,2,1,6,7,5,3]=>0000000=>0000000
[4,5,6,8,1,7,2,3]=>[3,2,7,1,8,6,5,4]=>0000000=>0000000
[4,7,3,6,8,1,5,2]=>[2,5,1,8,6,3,7,4]=>0000000=>0000000
[1,6,3,8,5,7,4,2]=>[2,4,7,5,8,3,6,1]=>0000000=>0000000
[7,8,6,4,2,1,5,3]=>[3,5,1,2,4,6,8,7]=>0000110=>0110000
[2,7,5,3,4,1,6,8]=>[8,6,1,4,3,5,7,2]=>0000000=>0000000
[3,1,5,7,4,8,6,2]=>[2,6,8,4,7,5,1,3]=>0000000=>0000000
[7,5,1,4,3,8,2,6]=>[6,2,8,3,4,1,5,7]=>0000000=>0000000
[5,7,3,6,4,1,2,8]=>[8,2,1,4,6,3,7,5]=>0000000=>0000000
[4,7,3,6,1,5,2,8]=>[8,2,5,1,6,3,7,4]=>0000000=>0000000
[4,2,7,1,3,5,8,6]=>[6,8,5,3,1,7,2,4]=>0000000=>0000000
[2,7,3,4,1,6,5,8]=>[8,5,6,1,4,3,7,2]=>0000000=>0000000
[6,3,4,2,8,5,7,1]=>[1,7,5,8,2,4,3,6]=>1000000=>0000001
[5,4,6,1,2,8,7,3]=>[3,7,8,2,1,6,4,5]=>0000000=>0000000
[7,2,8,3,4,1,6,5]=>[5,6,1,4,3,8,2,7]=>0000000=>0000000
[3,8,7,5,2,4,6,1]=>[1,6,4,2,5,7,8,3]=>1000000=>0000001
[8,6,4,2,5,7,3,1]=>[1,3,7,5,2,4,6,8]=>1000001=>1000001
[1,8,5,3,4,2,7,6]=>[6,7,2,4,3,5,8,1]=>0000000=>0000000
[2,6,3,5,8,1,7,4]=>[4,7,1,8,5,3,6,2]=>0000000=>0000000
[6,3,4,8,5,7,2,1]=>[1,2,7,5,8,4,3,6]=>1100000=>0000011
[3,8,6,2,1,5,4,7]=>[7,4,5,1,2,6,8,3]=>0000000=>0000000
[4,7,5,6,1,2,3,8]=>[8,3,2,1,6,5,7,4]=>0000000=>0000000
[3,8,6,2,5,4,1,7]=>[7,1,4,5,2,6,8,3]=>0000000=>0000000
[4,2,7,5,8,6,1,3]=>[3,1,6,8,5,7,2,4]=>0000000=>0000000
[6,1,3,7,8,5,2,4]=>[4,2,5,8,7,3,1,6]=>0000000=>0000000
[6,1,3,2,5,7,4,8]=>[8,4,7,5,2,3,1,6]=>0000000=>0000000
[6,1,3,5,4,7,2,8]=>[8,2,7,4,5,3,1,6]=>0000000=>0000000
[8,1,3,5,2,7,4,6]=>[6,4,7,2,5,3,1,8]=>0000001=>1000000
[4,1,3,5,7,6,2,8]=>[8,2,6,7,5,3,1,4]=>0000000=>0000000
[4,1,3,7,8,5,6,2]=>[2,6,5,8,7,3,1,4]=>0000000=>0000000
[8,1,4,5,2,3,7,6]=>[6,7,3,2,5,4,1,8]=>0000001=>1000000
[8,6,7,2,1,5,3,4]=>[4,3,5,1,2,7,6,8]=>0000101=>1010000
[4,7,2,5,3,6,8,1]=>[1,8,6,3,5,2,7,4]=>1000000=>0000001
[2,4,8,1,6,7,5,3]=>[3,5,7,6,1,8,4,2]=>0000000=>0000000
[2,8,1,4,3,6,7,5]=>[5,7,6,3,4,1,8,2]=>0000000=>0000000
[8,5,2,4,7,3,6,1]=>[1,6,3,7,4,2,5,8]=>1000001=>1000001
[6,8,3,4,2,7,5,1]=>[1,5,7,2,4,3,8,6]=>1000000=>0000001
[6,5,4,1,3,8,7,2]=>[2,7,8,3,1,4,5,6]=>0000000=>0000000
[7,6,1,3,2,8,5,4]=>[4,5,8,2,3,1,6,7]=>0000000=>0000000
[3,2,7,8,6,5,1,4]=>[4,1,5,6,8,7,2,3]=>0000000=>0000000
[2,7,4,8,6,5,3,1]=>[1,3,5,6,8,4,7,2]=>1000000=>0000001
[4,5,7,1,3,2,8,6]=>[6,8,2,3,1,7,5,4]=>0000000=>0000000
[8,1,6,3,2,7,5,4]=>[4,5,7,2,3,6,1,8]=>0000001=>1000000
[2,8,1,4,6,3,7,5]=>[5,7,3,6,4,1,8,2]=>0000000=>0000000
[4,6,8,7,1,2,3,5]=>[5,3,2,1,7,8,6,4]=>0000000=>0000000
[6,7,1,3,5,4,2,8]=>[8,2,4,5,3,1,7,6]=>0000000=>0000000
[3,8,4,7,6,5,1,2]=>[2,1,5,6,7,4,8,3]=>0100000=>0000010
[2,3,6,4,7,8,1,5]=>[5,1,8,7,4,6,3,2]=>0000000=>0000000
[4,7,8,6,3,1,5,2]=>[2,5,1,3,6,8,7,4]=>0000000=>0000000
[7,4,5,1,3,2,8,6]=>[6,8,2,3,1,5,4,7]=>0000000=>0000000
[7,4,1,6,5,8,2,3]=>[3,2,8,5,6,1,4,7]=>0000000=>0000000
[4,7,5,2,3,1,6,8]=>[8,6,1,3,2,5,7,4]=>0000000=>0000000
[3,6,4,1,8,5,2,7]=>[7,2,5,8,1,4,6,3]=>0000000=>0000000
[3,6,4,1,8,5,7,2]=>[2,7,5,8,1,4,6,3]=>0000000=>0000000
[5,8,2,3,7,1,6,4]=>[4,6,1,7,3,2,8,5]=>0000000=>0000000
[7,1,8,3,2,6,5,4]=>[4,5,6,2,3,8,1,7]=>0000000=>0000000
[4,2,1,7,6,3,5,8]=>[8,5,3,6,7,1,2,4]=>0000000=>0000000
[5,1,4,6,8,7,2,3]=>[3,2,7,8,6,4,1,5]=>0000000=>0000000
[8,6,3,5,2,4,7,1]=>[1,7,4,2,5,3,6,8]=>1000001=>1000001
[5,1,3,6,7,4,8,2]=>[2,8,4,7,6,3,1,5]=>0000000=>0000000
[6,3,8,5,1,4,7,2]=>[2,7,4,1,5,8,3,6]=>0000000=>0000000
[8,7,3,4,6,1,5,2]=>[2,5,1,6,4,3,7,8]=>0000011=>1100000
[3,7,2,6,5,8,4,1]=>[1,4,8,5,6,2,7,3]=>1000000=>0000001
[8,7,2,5,6,3,4,1]=>[1,4,3,6,5,2,7,8]=>1000011=>1100001
[8,7,2,3,6,4,5,1]=>[1,5,4,6,3,2,7,8]=>1000011=>1100001
[4,8,3,6,5,1,2,7]=>[7,2,1,5,6,3,8,4]=>0000000=>0000000
[7,3,6,8,2,4,5,1]=>[1,5,4,2,8,6,3,7]=>1000000=>0000001
[5,3,4,8,7,6,2,1]=>[1,2,6,7,8,4,3,5]=>1100000=>0000011
[4,5,7,1,8,3,6,2]=>[2,6,3,8,1,7,5,4]=>0000000=>0000000
[4,8,2,5,6,3,1,7]=>[7,1,3,6,5,2,8,4]=>0000000=>0000000
[4,6,2,5,8,3,1,7]=>[7,1,3,8,5,2,6,4]=>0000000=>0000000
[7,4,8,2,1,6,5,3]=>[3,5,6,1,2,8,4,7]=>0000000=>0000000
[5,6,1,8,4,7,3,2]=>[2,3,7,4,8,1,6,5]=>0000000=>0000000
[4,3,2,7,6,1,5,8]=>[8,5,1,6,7,2,3,4]=>0000000=>0000000
[2,8,5,1,3,4,7,6]=>[6,7,4,3,1,5,8,2]=>0000000=>0000000
[4,6,1,3,8,2,5,7]=>[7,5,2,8,3,1,6,4]=>0000000=>0000000
[2,8,1,6,7,4,3,5]=>[5,3,4,7,6,1,8,2]=>0000000=>0000000
[6,5,7,1,8,3,2,4]=>[4,2,3,8,1,7,5,6]=>0000000=>0000000
[7,1,3,8,5,4,2,6]=>[6,2,4,5,8,3,1,7]=>0000000=>0000000
[8,4,5,7,2,3,6,1]=>[1,6,3,2,7,5,4,8]=>1000001=>1000001
[5,2,4,8,6,3,7,1]=>[1,7,3,6,8,4,2,5]=>1000000=>0000001
[5,4,8,6,7,1,3,2]=>[2,3,1,7,6,8,4,5]=>0010000=>0000100
[5,8,6,3,1,4,7,2]=>[2,7,4,1,3,6,8,5]=>0000000=>0000000
[1,4,2,6,5,7,8,3]=>[3,8,7,5,6,2,4,1]=>0000000=>0000000
[3,8,6,2,1,4,7,5]=>[5,7,4,1,2,6,8,3]=>0000000=>0000000
[7,4,2,3,5,8,6,1]=>[1,6,8,5,3,2,4,7]=>1000000=>0000001
[5,2,3,6,8,7,1,4]=>[4,1,7,8,6,3,2,5]=>0000000=>0000000
[7,4,5,1,3,2,6,8]=>[8,6,2,3,1,5,4,7]=>0000000=>0000000
[2,5,8,3,4,7,6,1]=>[1,6,7,4,3,8,5,2]=>1000000=>0000001
[5,3,6,4,8,1,7,2]=>[2,7,1,8,4,6,3,5]=>0000000=>0000000
[5,3,6,4,2,7,8,1]=>[1,8,7,2,4,6,3,5]=>1000000=>0000001
[3,8,5,7,4,1,2,6]=>[6,2,1,4,7,5,8,3]=>0000000=>0000000
[8,3,2,1,7,5,6,4]=>[4,6,5,7,1,2,3,8]=>0000001=>1000000
[6,4,1,7,8,3,2,5]=>[5,2,3,8,7,1,4,6]=>0000000=>0000000
[4,2,7,5,1,6,3,8]=>[8,3,6,1,5,7,2,4]=>0000000=>0000000
[8,7,3,4,6,5,1,2]=>[2,1,5,6,4,3,7,8]=>0100011=>1100010
[4,2,8,7,5,3,6,1]=>[1,6,3,5,7,8,2,4]=>1000000=>0000001
[3,4,2,5,7,1,6,8]=>[8,6,1,7,5,2,4,3]=>0000000=>0000000
[5,2,8,7,3,4,6,1]=>[1,6,4,3,7,8,2,5]=>1000000=>0000001
[3,2,7,5,1,4,8,6]=>[6,8,4,1,5,7,2,3]=>0000000=>0000000
[1,3,6,4,7,8,5,2]=>[2,5,8,7,4,6,3,1]=>0000000=>0000000
[3,8,6,7,1,4,2,5]=>[5,2,4,1,7,6,8,3]=>0000000=>0000000
[5,7,4,8,6,2,3,1]=>[1,3,2,6,8,4,7,5]=>1010000=>0000101
[5,6,3,1,4,7,8,2]=>[2,8,7,4,1,3,6,5]=>0000000=>0000000
[5,4,8,1,3,2,6,7]=>[7,6,2,3,1,8,4,5]=>0000000=>0000000
[3,6,7,4,2,5,8,1]=>[1,8,5,2,4,7,6,3]=>1000000=>0000001
[5,8,6,3,2,7,4,1]=>[1,4,7,2,3,6,8,5]=>1000000=>0000001
[3,1,6,4,2,7,8,5]=>[5,8,7,2,4,6,1,3]=>0000000=>0000000
[8,3,7,6,1,2,5,4]=>[4,5,2,1,6,7,3,8]=>0000001=>1000000
[2,7,1,6,3,8,5,4]=>[4,5,8,3,6,1,7,2]=>0000000=>0000000
[5,7,4,2,3,6,1,8]=>[8,1,6,3,2,4,7,5]=>0000000=>0000000
[4,8,6,2,5,7,1,3]=>[3,1,7,5,2,6,8,4]=>0000000=>0000000
[6,3,4,5,1,8,7,2]=>[2,7,8,1,5,4,3,6]=>0000000=>0000000
[1,6,3,4,7,5,2,8]=>[8,2,5,7,4,3,6,1]=>0000000=>0000000
[1,8,6,5,2,3,7,4]=>[4,7,3,2,5,6,8,1]=>0000000=>0000000
[2,7,1,3,8,6,4,5]=>[5,4,6,8,3,1,7,2]=>0000000=>0000000
[7,4,6,3,2,5,8,1]=>[1,8,5,2,3,6,4,7]=>1000000=>0000001
[5,3,4,8,7,2,1,6]=>[6,1,2,7,8,4,3,5]=>0000000=>0000000
[6,2,3,5,7,1,8,4]=>[4,8,1,7,5,3,2,6]=>0000000=>0000000
[8,3,6,1,7,2,5,4]=>[4,5,2,7,1,6,3,8]=>0000001=>1000000
[3,5,4,1,8,2,6,7]=>[7,6,2,8,1,4,5,3]=>0000000=>0000000
[6,3,2,1,7,5,8,4]=>[4,8,5,7,1,2,3,6]=>0000000=>0000000
[7,8,2,5,4,6,3,1]=>[1,3,6,4,5,2,8,7]=>1000010=>0100001
[4,8,3,2,6,5,7,1]=>[1,7,5,6,2,3,8,4]=>1000000=>0000001
[8,4,2,7,3,6,5,1]=>[1,5,6,3,7,2,4,8]=>1000001=>1000001
[6,1,4,7,8,3,2,5]=>[5,2,3,8,7,4,1,6]=>0000000=>0000000
[8,5,7,2,4,3,1,6]=>[6,1,3,4,2,7,5,8]=>0000001=>1000000
[3,7,8,2,5,4,1,6]=>[6,1,4,5,2,8,7,3]=>0000000=>0000000
[7,5,4,1,2,6,3,8]=>[8,3,6,2,1,4,5,7]=>0000000=>0000000
[7,4,5,6,2,8,1,3]=>[3,1,8,2,6,5,4,7]=>0000000=>0000000
[1,7,8,2,3,5,4,6]=>[6,4,5,3,2,8,7,1]=>0000000=>0000000
[4,6,5,1,3,2,7,8]=>[8,7,2,3,1,5,6,4]=>0000000=>0000000
[4,3,6,2,8,5,7,1]=>[1,7,5,8,2,6,3,4]=>1000000=>0000001
[6,7,8,2,1,3,5,4]=>[4,5,3,1,2,8,7,6]=>0000100=>0010000
[6,5,2,3,8,7,4,1]=>[1,4,7,8,3,2,5,6]=>1000000=>0000001
[5,4,7,2,3,6,1,8]=>[8,1,6,3,2,7,4,5]=>0000000=>0000000
[5,4,7,3,8,6,2,1]=>[1,2,6,8,3,7,4,5]=>1100000=>0000011
[8,3,6,5,2,7,4,1]=>[1,4,7,2,5,6,3,8]=>1000001=>1000001
[3,7,5,8,4,2,6,1]=>[1,6,2,4,8,5,7,3]=>1000000=>0000001
[8,2,3,1,5,7,4,6]=>[6,4,7,5,1,3,2,8]=>0000001=>1000000
[4,2,7,6,5,1,8,3]=>[3,8,1,5,6,7,2,4]=>0000000=>0000000
[7,8,4,6,3,2,5,1]=>[1,5,2,3,6,4,8,7]=>1000010=>0100001
[6,3,1,4,5,7,2,8]=>[8,2,7,5,4,1,3,6]=>0000000=>0000000
[7,6,3,2,4,8,5,1]=>[1,5,8,4,2,3,6,7]=>1000000=>0000001
[5,1,8,7,3,2,4,6]=>[6,4,2,3,7,8,1,5]=>0000000=>0000000
[2,7,1,6,8,4,5,3]=>[3,5,4,8,6,1,7,2]=>0000000=>0000000
[8,3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3,8]=>0000001=>1000000
[1,7,4,6,5,2,3,8]=>[8,3,2,5,6,4,7,1]=>0000000=>0000000
[8,4,1,5,3,6,2,7]=>[7,2,6,3,5,1,4,8]=>0000001=>1000000
[3,6,8,4,2,5,7,1]=>[1,7,5,2,4,8,6,3]=>1000000=>0000001
[3,6,2,5,7,4,8,1]=>[1,8,4,7,5,2,6,3]=>1000000=>0000001
[8,4,3,6,2,5,7,1]=>[1,7,5,2,6,3,4,8]=>1000001=>1000001
[2,6,8,5,3,7,4,1]=>[1,4,7,3,5,8,6,2]=>1000000=>0000001
[7,8,6,4,2,5,3,1]=>[1,3,5,2,4,6,8,7]=>1000110=>0110001
[4,8,7,1,3,2,5,6]=>[6,5,2,3,1,7,8,4]=>0000000=>0000000
[4,3,8,5,6,2,1,7]=>[7,1,2,6,5,8,3,4]=>0000000=>0000000
[6,1,2,5,3,7,4,8]=>[8,4,7,3,5,2,1,6]=>0000000=>0000000
[8,2,5,1,6,4,7,3]=>[3,7,4,6,1,5,2,8]=>0000001=>1000000
[4,2,8,5,3,7,1,6]=>[6,1,7,3,5,8,2,4]=>0000000=>0000000
[5,6,8,7,3,2,4,1]=>[1,4,2,3,7,8,6,5]=>1001000=>0001001
[5,4,7,1,3,6,2,8]=>[8,2,6,3,1,7,4,5]=>0000000=>0000000
[3,8,6,1,7,5,2,4]=>[4,2,5,7,1,6,8,3]=>0000000=>0000000
[5,2,4,8,7,3,6,1]=>[1,6,3,7,8,4,2,5]=>1000000=>0000001
[4,3,1,5,7,6,2,8]=>[8,2,6,7,5,1,3,4]=>0000000=>0000000
[4,3,7,5,6,2,1,8]=>[8,1,2,6,5,7,3,4]=>0000000=>0000000
[7,8,4,6,2,5,3,1]=>[1,3,5,2,6,4,8,7]=>1000010=>0100001
[4,8,6,1,3,7,2,5]=>[5,2,7,3,1,6,8,4]=>0000000=>0000000
[6,3,7,4,2,5,1,8]=>[8,1,5,2,4,7,3,6]=>0000000=>0000000
[8,2,7,5,3,6,1,4]=>[4,1,6,3,5,7,2,8]=>0000001=>1000000
[5,8,7,3,1,2,6,4]=>[4,6,2,1,3,7,8,5]=>0000000=>0000000
[8,4,7,5,6,1,2,3]=>[3,2,1,6,5,7,4,8]=>0010001=>1000100
[5,2,3,6,7,1,4,8]=>[8,4,1,7,6,3,2,5]=>0000000=>0000000
[8,7,2,6,3,4,5,1]=>[1,5,4,3,6,2,7,8]=>1000011=>1100001
[3,7,6,8,2,4,5,1]=>[1,5,4,2,8,6,7,3]=>1000000=>0000001
[5,7,3,4,2,1,6,8]=>[8,6,1,2,4,3,7,5]=>0000000=>0000000
[7,3,4,6,5,1,8,2]=>[2,8,1,5,6,4,3,7]=>0000000=>0000000
[2,4,5,8,7,3,6,1]=>[1,6,3,7,8,5,4,2]=>1000000=>0000001
[4,7,1,3,6,2,8,5]=>[5,8,2,6,3,1,7,4]=>0000000=>0000000
[1,5,8,6,3,2,4,7]=>[7,4,2,3,6,8,5,1]=>0000000=>0000000
[7,3,2,4,6,8,5,1]=>[1,5,8,6,4,2,3,7]=>1000000=>0000001
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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
reverse
Description
Return the reversal of a binary word.
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