Identifier
Mp00238:
Permutations
—Clarke-Steingrimsson-Zeng⟶
Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
=>
[1]=>[1]=>[1]=>
[1,2]=>[1,2]=>[1,2]=>0
[2,1]=>[2,1]=>[2,1]=>1
[1,2,3]=>[1,2,3]=>[1,2,3]=>00
[1,3,2]=>[1,3,2]=>[1,3,2]=>01
[2,1,3]=>[2,1,3]=>[2,1,3]=>10
[2,3,1]=>[3,2,1]=>[2,3,1]=>01
[3,1,2]=>[3,1,2]=>[3,2,1]=>11
[3,2,1]=>[2,3,1]=>[3,1,2]=>01
[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>000
[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>001
[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>010
[1,3,4,2]=>[1,4,3,2]=>[1,3,4,2]=>001
[1,4,2,3]=>[1,4,2,3]=>[1,4,3,2]=>011
[1,4,3,2]=>[1,3,4,2]=>[1,4,2,3]=>001
[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>100
[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>101
[2,3,1,4]=>[3,2,1,4]=>[2,3,1,4]=>010
[2,3,4,1]=>[4,2,3,1]=>[2,3,4,1]=>001
[2,4,1,3]=>[4,2,1,3]=>[2,4,3,1]=>011
[2,4,3,1]=>[3,2,4,1]=>[2,4,1,3]=>001
[3,1,2,4]=>[3,1,2,4]=>[3,2,1,4]=>110
[3,1,4,2]=>[4,3,1,2]=>[4,2,3,1]=>011
[3,2,1,4]=>[2,3,1,4]=>[3,1,2,4]=>010
[3,2,4,1]=>[4,3,2,1]=>[3,2,4,1]=>011
[3,4,1,2]=>[4,1,3,2]=>[3,4,2,1]=>101
[3,4,2,1]=>[2,4,3,1]=>[3,4,1,2]=>001
[4,1,2,3]=>[4,1,2,3]=>[4,3,2,1]=>111
[4,1,3,2]=>[3,4,1,2]=>[3,1,4,2]=>011
[4,2,1,3]=>[2,4,1,3]=>[4,3,1,2]=>011
[4,2,3,1]=>[3,4,2,1]=>[4,1,3,2]=>011
[4,3,1,2]=>[3,1,4,2]=>[4,2,1,3]=>101
[4,3,2,1]=>[2,3,4,1]=>[4,1,2,3]=>001
[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>0001
[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>0010
[1,2,4,5,3]=>[1,2,5,4,3]=>[1,2,4,5,3]=>0001
[1,2,5,3,4]=>[1,2,5,3,4]=>[1,2,5,4,3]=>0011
[1,2,5,4,3]=>[1,2,4,5,3]=>[1,2,5,3,4]=>0001
[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>0100
[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>0101
[1,3,4,2,5]=>[1,4,3,2,5]=>[1,3,4,2,5]=>0010
[1,3,4,5,2]=>[1,5,3,4,2]=>[1,3,4,5,2]=>0001
[1,3,5,2,4]=>[1,5,3,2,4]=>[1,3,5,4,2]=>0011
[1,3,5,4,2]=>[1,4,3,5,2]=>[1,3,5,2,4]=>0001
[1,4,2,3,5]=>[1,4,2,3,5]=>[1,4,3,2,5]=>0110
[1,4,2,5,3]=>[1,5,4,2,3]=>[1,5,3,4,2]=>0011
[1,4,3,2,5]=>[1,3,4,2,5]=>[1,4,2,3,5]=>0010
[1,4,3,5,2]=>[1,5,4,3,2]=>[1,4,3,5,2]=>0011
[1,4,5,2,3]=>[1,5,2,4,3]=>[1,4,5,3,2]=>0101
[1,4,5,3,2]=>[1,3,5,4,2]=>[1,4,5,2,3]=>0001
[1,5,2,3,4]=>[1,5,2,3,4]=>[1,5,4,3,2]=>0111
[1,5,2,4,3]=>[1,4,5,2,3]=>[1,4,2,5,3]=>0011
[1,5,3,2,4]=>[1,3,5,2,4]=>[1,5,4,2,3]=>0011
[1,5,3,4,2]=>[1,4,5,3,2]=>[1,5,2,4,3]=>0011
[1,5,4,2,3]=>[1,4,2,5,3]=>[1,5,3,2,4]=>0101
[1,5,4,3,2]=>[1,3,4,5,2]=>[1,5,2,3,4]=>0001
[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]=>1001
[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]=>1010
[2,1,4,5,3]=>[2,1,5,4,3]=>[2,1,4,5,3]=>1001
[2,1,5,3,4]=>[2,1,5,3,4]=>[2,1,5,4,3]=>1011
[2,1,5,4,3]=>[2,1,4,5,3]=>[2,1,5,3,4]=>1001
[2,3,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>0100
[2,3,1,5,4]=>[3,2,1,5,4]=>[2,3,1,5,4]=>0101
[2,3,4,1,5]=>[4,2,3,1,5]=>[2,3,4,1,5]=>0010
[2,3,4,5,1]=>[5,2,3,4,1]=>[2,3,4,5,1]=>0001
[2,3,5,1,4]=>[5,2,3,1,4]=>[2,3,5,4,1]=>0011
[2,3,5,4,1]=>[4,2,3,5,1]=>[2,3,5,1,4]=>0001
[2,4,1,3,5]=>[4,2,1,3,5]=>[2,4,3,1,5]=>0110
[2,4,1,5,3]=>[5,2,4,1,3]=>[2,5,3,4,1]=>0011
[2,4,3,1,5]=>[3,2,4,1,5]=>[2,4,1,3,5]=>0010
[2,4,3,5,1]=>[5,2,4,3,1]=>[2,4,3,5,1]=>0011
[2,4,5,1,3]=>[5,2,1,4,3]=>[2,4,5,3,1]=>0101
[2,4,5,3,1]=>[3,2,5,4,1]=>[2,4,5,1,3]=>0001
[2,5,1,3,4]=>[5,2,1,3,4]=>[2,5,4,3,1]=>0111
[2,5,1,4,3]=>[4,2,5,1,3]=>[2,4,1,5,3]=>0011
[2,5,3,1,4]=>[3,2,5,1,4]=>[2,5,4,1,3]=>0011
[2,5,3,4,1]=>[4,2,5,3,1]=>[2,5,1,4,3]=>0011
[2,5,4,1,3]=>[4,2,1,5,3]=>[2,5,3,1,4]=>0101
[2,5,4,3,1]=>[3,2,4,5,1]=>[2,5,1,3,4]=>0001
[3,1,2,4,5]=>[3,1,2,4,5]=>[3,2,1,4,5]=>1100
[3,1,2,5,4]=>[3,1,2,5,4]=>[3,2,1,5,4]=>1101
[3,1,4,2,5]=>[4,3,1,2,5]=>[4,2,3,1,5]=>0110
[3,1,4,5,2]=>[5,3,1,4,2]=>[4,5,2,3,1]=>0101
[3,1,5,2,4]=>[5,3,1,2,4]=>[5,4,2,3,1]=>0111
[3,1,5,4,2]=>[4,3,1,5,2]=>[5,2,3,1,4]=>0101
[3,2,1,4,5]=>[2,3,1,4,5]=>[3,1,2,4,5]=>0100
[3,2,1,5,4]=>[2,3,1,5,4]=>[3,1,2,5,4]=>0101
[3,2,4,1,5]=>[4,3,2,1,5]=>[3,2,4,1,5]=>0110
[3,2,4,5,1]=>[5,3,2,4,1]=>[3,2,4,5,1]=>0101
[3,2,5,1,4]=>[5,3,2,1,4]=>[3,2,5,4,1]=>0111
[3,2,5,4,1]=>[4,3,2,5,1]=>[3,2,5,1,4]=>0101
[3,4,1,2,5]=>[4,1,3,2,5]=>[3,4,2,1,5]=>1010
[3,4,1,5,2]=>[5,4,3,1,2]=>[3,5,2,4,1]=>0011
[3,4,2,1,5]=>[2,4,3,1,5]=>[3,4,1,2,5]=>0010
[3,4,2,5,1]=>[5,4,3,2,1]=>[3,4,2,5,1]=>0011
[3,4,5,1,2]=>[5,1,3,4,2]=>[3,4,5,2,1]=>1001
[3,4,5,2,1]=>[2,5,3,4,1]=>[3,4,5,1,2]=>0001
[3,5,1,2,4]=>[5,1,3,2,4]=>[3,5,4,2,1]=>1011
[3,5,1,4,2]=>[4,5,3,1,2]=>[3,4,1,5,2]=>0011
[3,5,2,1,4]=>[2,5,3,1,4]=>[3,5,4,1,2]=>0011
[3,5,2,4,1]=>[4,5,3,2,1]=>[3,5,1,4,2]=>0011
[3,5,4,1,2]=>[4,1,3,5,2]=>[3,5,2,1,4]=>1001
[3,5,4,2,1]=>[2,4,3,5,1]=>[3,5,1,2,4]=>0001
[4,1,2,3,5]=>[4,1,2,3,5]=>[4,3,2,1,5]=>1110
[4,1,2,5,3]=>[5,1,4,2,3]=>[5,3,4,2,1]=>1011
[4,1,3,2,5]=>[3,4,1,2,5]=>[3,1,4,2,5]=>0110
[4,1,3,5,2]=>[5,4,1,3,2]=>[5,2,4,3,1]=>0111
[4,1,5,2,3]=>[5,4,1,2,3]=>[4,2,5,3,1]=>0111
[4,1,5,3,2]=>[3,5,4,1,2]=>[4,1,3,5,2]=>0011
[4,2,1,3,5]=>[2,4,1,3,5]=>[4,3,1,2,5]=>0110
[4,2,1,5,3]=>[2,5,4,1,3]=>[5,3,4,1,2]=>0011
[4,2,3,1,5]=>[3,4,2,1,5]=>[4,1,3,2,5]=>0110
[4,2,3,5,1]=>[5,4,2,3,1]=>[4,3,2,5,1]=>0111
[4,2,5,1,3]=>[5,4,2,1,3]=>[5,3,2,4,1]=>0111
[4,2,5,3,1]=>[3,5,4,2,1]=>[5,1,3,4,2]=>0011
[4,3,1,2,5]=>[3,1,4,2,5]=>[4,2,1,3,5]=>1010
[4,3,1,5,2]=>[5,3,4,1,2]=>[5,2,3,4,1]=>0011
[4,3,2,1,5]=>[2,3,4,1,5]=>[4,1,2,3,5]=>0010
[4,3,2,5,1]=>[5,3,4,2,1]=>[4,2,3,5,1]=>0011
[4,3,5,1,2]=>[5,1,4,3,2]=>[4,3,5,2,1]=>1011
[4,3,5,2,1]=>[2,5,4,3,1]=>[4,3,5,1,2]=>0011
[4,5,1,2,3]=>[5,1,2,4,3]=>[4,5,3,2,1]=>1101
[4,5,1,3,2]=>[3,5,1,4,2]=>[3,1,4,5,2]=>0101
[4,5,2,1,3]=>[2,5,1,4,3]=>[4,5,3,1,2]=>0101
[4,5,2,3,1]=>[3,5,2,4,1]=>[4,5,1,3,2]=>0101
[4,5,3,1,2]=>[3,1,5,4,2]=>[4,5,2,1,3]=>1001
[4,5,3,2,1]=>[2,3,5,4,1]=>[4,5,1,2,3]=>0001
[5,1,2,3,4]=>[5,1,2,3,4]=>[5,4,3,2,1]=>1111
[5,1,2,4,3]=>[4,1,5,2,3]=>[4,2,1,5,3]=>1011
[5,1,3,2,4]=>[3,5,1,2,4]=>[3,1,5,4,2]=>0111
[5,1,3,4,2]=>[4,5,1,3,2]=>[4,3,1,5,2]=>0111
[5,1,4,2,3]=>[4,5,1,2,3]=>[5,3,1,4,2]=>0111
[5,1,4,3,2]=>[3,4,5,1,2]=>[5,2,4,1,3]=>0011
[5,2,1,3,4]=>[2,5,1,3,4]=>[5,4,3,1,2]=>0111
[5,2,1,4,3]=>[2,4,5,1,3]=>[4,1,2,5,3]=>0011
[5,2,3,1,4]=>[3,5,2,1,4]=>[5,4,1,3,2]=>0111
[5,2,3,4,1]=>[4,5,2,3,1]=>[5,1,4,3,2]=>0111
[5,2,4,1,3]=>[4,5,2,1,3]=>[4,1,5,3,2]=>0111
[5,2,4,3,1]=>[3,4,5,2,1]=>[4,2,5,1,3]=>0011
[5,3,1,2,4]=>[3,1,5,2,4]=>[5,4,2,1,3]=>1011
[5,3,1,4,2]=>[4,3,5,1,2]=>[4,1,5,2,3]=>0011
[5,3,2,1,4]=>[2,3,5,1,4]=>[5,4,1,2,3]=>0011
[5,3,2,4,1]=>[4,3,5,2,1]=>[5,1,4,2,3]=>0011
[5,3,4,1,2]=>[4,1,5,3,2]=>[5,2,1,4,3]=>1011
[5,3,4,2,1]=>[2,4,5,3,1]=>[5,1,2,4,3]=>0011
[5,4,1,2,3]=>[4,1,2,5,3]=>[5,3,2,1,4]=>1101
[5,4,1,3,2]=>[3,4,1,5,2]=>[3,1,5,2,4]=>0101
[5,4,2,1,3]=>[2,4,1,5,3]=>[5,3,1,2,4]=>0101
[5,4,2,3,1]=>[3,4,2,5,1]=>[5,1,3,2,4]=>0101
[5,4,3,1,2]=>[3,1,4,5,2]=>[5,2,1,3,4]=>1001
[5,4,3,2,1]=>[2,3,4,5,1]=>[5,1,2,3,4]=>0001
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>00001
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>00010
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>00001
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>00011
[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>00001
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>00100
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>00101
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>00010
[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>00001
[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>[1,2,4,6,5,3]=>00011
[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>[1,2,4,6,3,5]=>00001
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]=>00110
[1,2,5,3,6,4]=>[1,2,6,5,3,4]=>[1,2,6,4,5,3]=>00011
[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>00010
[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[1,2,5,4,6,3]=>00011
[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>00101
[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>[1,2,5,6,3,4]=>00001
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>00111
[1,2,6,3,5,4]=>[1,2,5,6,3,4]=>[1,2,5,3,6,4]=>00011
[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>[1,2,6,5,3,4]=>00011
[1,2,6,4,5,3]=>[1,2,5,6,4,3]=>[1,2,6,3,5,4]=>00011
[1,2,6,5,3,4]=>[1,2,5,3,6,4]=>[1,2,6,4,3,5]=>00101
[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>00001
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>01000
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>01001
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>01010
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>01001
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]=>01011
[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>01001
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>00100
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>00101
[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>00010
[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>00001
[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>[1,3,4,6,5,2]=>00011
[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>[1,3,4,6,2,5]=>00001
[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>[1,3,5,4,2,6]=>00110
[1,3,5,2,6,4]=>[1,6,3,5,2,4]=>[1,3,6,4,5,2]=>00011
[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>[1,3,5,2,4,6]=>00010
[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[1,3,5,4,6,2]=>00011
[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>[1,3,5,6,4,2]=>00101
[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>[1,3,5,6,2,4]=>00001
[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[1,3,6,5,4,2]=>00111
[1,3,6,2,5,4]=>[1,5,3,6,2,4]=>[1,3,5,2,6,4]=>00011
[1,3,6,4,2,5]=>[1,4,3,6,2,5]=>[1,3,6,5,2,4]=>00011
[1,3,6,4,5,2]=>[1,5,3,6,4,2]=>[1,3,6,2,5,4]=>00011
[1,3,6,5,2,4]=>[1,5,3,2,6,4]=>[1,3,6,4,2,5]=>00101
[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>[1,3,6,2,4,5]=>00001
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[1,4,3,2,5,6]=>01100
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[1,4,3,2,6,5]=>01101
[1,4,2,5,3,6]=>[1,5,4,2,3,6]=>[1,5,3,4,2,6]=>00110
[1,4,2,5,6,3]=>[1,6,4,2,5,3]=>[1,5,6,3,4,2]=>00101
[1,4,2,6,3,5]=>[1,6,4,2,3,5]=>[1,6,5,3,4,2]=>00111
[1,4,2,6,5,3]=>[1,5,4,2,6,3]=>[1,6,3,4,2,5]=>00101
[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>00100
[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>00101
[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[1,4,3,5,2,6]=>00110
[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[1,4,3,5,6,2]=>00101
[1,4,3,6,2,5]=>[1,6,4,3,2,5]=>[1,4,3,6,5,2]=>00111
[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>[1,4,3,6,2,5]=>00101
[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>01010
[1,4,5,2,6,3]=>[1,6,5,4,2,3]=>[1,4,6,3,5,2]=>00011
[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>[1,4,5,2,3,6]=>00010
[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[1,4,5,3,6,2]=>00011
[1,4,5,6,2,3]=>[1,6,2,4,5,3]=>[1,4,5,6,3,2]=>01001
[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>[1,4,5,6,2,3]=>00001
[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>[1,4,6,5,3,2]=>01011
[1,4,6,2,5,3]=>[1,5,6,4,2,3]=>[1,4,5,2,6,3]=>00011
[1,4,6,3,2,5]=>[1,3,6,4,2,5]=>[1,4,6,5,2,3]=>00011
[1,4,6,3,5,2]=>[1,5,6,4,3,2]=>[1,4,6,2,5,3]=>00011
[1,4,6,5,2,3]=>[1,5,2,4,6,3]=>[1,4,6,3,2,5]=>01001
[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>[1,4,6,2,3,5]=>00001
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>01110
[1,5,2,3,6,4]=>[1,6,2,5,3,4]=>[1,6,4,5,3,2]=>01011
[1,5,2,4,3,6]=>[1,4,5,2,3,6]=>[1,4,2,5,3,6]=>00110
[1,5,2,4,6,3]=>[1,6,5,2,4,3]=>[1,6,3,5,4,2]=>00111
[1,5,2,6,3,4]=>[1,6,5,2,3,4]=>[1,5,3,6,4,2]=>00111
[1,5,2,6,4,3]=>[1,4,6,5,2,3]=>[1,5,2,4,6,3]=>00011
[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>[1,5,4,2,3,6]=>00110
[1,5,3,2,6,4]=>[1,3,6,5,2,4]=>[1,6,4,5,2,3]=>00011
[1,5,3,4,2,6]=>[1,4,5,3,2,6]=>[1,5,2,4,3,6]=>00110
[1,5,3,4,6,2]=>[1,6,5,3,4,2]=>[1,5,4,3,6,2]=>00111
[1,5,3,6,2,4]=>[1,6,5,3,2,4]=>[1,6,4,3,5,2]=>00111
[1,5,3,6,4,2]=>[1,4,6,5,3,2]=>[1,6,2,4,5,3]=>00011
[1,5,4,2,3,6]=>[1,4,2,5,3,6]=>[1,5,3,2,4,6]=>01010
[1,5,4,2,6,3]=>[1,6,4,5,2,3]=>[1,6,3,4,5,2]=>00011
[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>00010
[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>[1,5,3,4,6,2]=>00011
[1,5,4,6,2,3]=>[1,6,2,5,4,3]=>[1,5,4,6,3,2]=>01011
[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>[1,5,4,6,2,3]=>00011
[1,5,6,2,3,4]=>[1,6,2,3,5,4]=>[1,5,6,4,3,2]=>01101
[1,5,6,2,4,3]=>[1,4,6,2,5,3]=>[1,4,2,5,6,3]=>00101
[1,5,6,3,2,4]=>[1,3,6,2,5,4]=>[1,5,6,4,2,3]=>00101
[1,5,6,3,4,2]=>[1,4,6,3,5,2]=>[1,5,6,2,4,3]=>00101
[1,5,6,4,2,3]=>[1,4,2,6,5,3]=>[1,5,6,3,2,4]=>01001
[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>[1,5,6,2,3,4]=>00001
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>01111
[1,6,2,3,5,4]=>[1,5,2,6,3,4]=>[1,5,3,2,6,4]=>01011
[1,6,2,4,3,5]=>[1,4,6,2,3,5]=>[1,4,2,6,5,3]=>00111
[1,6,2,4,5,3]=>[1,5,6,2,4,3]=>[1,5,4,2,6,3]=>00111
[1,6,2,5,3,4]=>[1,5,6,2,3,4]=>[1,6,4,2,5,3]=>00111
[1,6,2,5,4,3]=>[1,4,5,6,2,3]=>[1,6,3,5,2,4]=>00011
[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>[1,6,5,4,2,3]=>00111
[1,6,3,2,5,4]=>[1,3,5,6,2,4]=>[1,5,2,3,6,4]=>00011
[1,6,3,4,2,5]=>[1,4,6,3,2,5]=>[1,6,5,2,4,3]=>00111
[1,6,3,4,5,2]=>[1,5,6,3,4,2]=>[1,6,2,5,4,3]=>00111
[1,6,3,5,2,4]=>[1,5,6,3,2,4]=>[1,5,2,6,4,3]=>00111
[1,6,3,5,4,2]=>[1,4,5,6,3,2]=>[1,5,3,6,2,4]=>00011
[1,6,4,2,3,5]=>[1,4,2,6,3,5]=>[1,6,5,3,2,4]=>01011
[1,6,4,2,5,3]=>[1,5,4,6,2,3]=>[1,5,2,6,3,4]=>00011
[1,6,4,3,2,5]=>[1,3,4,6,2,5]=>[1,6,5,2,3,4]=>00011
[1,6,4,3,5,2]=>[1,5,4,6,3,2]=>[1,6,2,5,3,4]=>00011
[1,6,4,5,2,3]=>[1,5,2,6,4,3]=>[1,6,3,2,5,4]=>01011
[1,6,4,5,3,2]=>[1,3,5,6,4,2]=>[1,6,2,3,5,4]=>00011
[1,6,5,2,3,4]=>[1,5,2,3,6,4]=>[1,6,4,3,2,5]=>01101
[1,6,5,2,4,3]=>[1,4,5,2,6,3]=>[1,4,2,6,3,5]=>00101
[1,6,5,3,2,4]=>[1,3,5,2,6,4]=>[1,6,4,2,3,5]=>00101
[1,6,5,3,4,2]=>[1,4,5,3,6,2]=>[1,6,2,4,3,5]=>00101
[1,6,5,4,2,3]=>[1,4,2,5,6,3]=>[1,6,3,2,4,5]=>01001
[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>00001
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>10001
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>10010
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>10001
[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[2,1,3,6,5,4]=>10011
[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>10001
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>10100
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>10101
[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>10010
[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>10001
[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>[2,1,4,6,5,3]=>10011
[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>[2,1,4,6,3,5]=>10001
[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[2,1,5,4,3,6]=>10110
[2,1,5,3,6,4]=>[2,1,6,5,3,4]=>[2,1,6,4,5,3]=>10011
[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>10010
[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[2,1,5,4,6,3]=>10011
[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[2,1,5,6,4,3]=>10101
[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>[2,1,5,6,3,4]=>10001
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[2,1,6,5,4,3]=>10111
[2,1,6,3,5,4]=>[2,1,5,6,3,4]=>[2,1,5,3,6,4]=>10011
[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>[2,1,6,5,3,4]=>10011
[2,1,6,4,5,3]=>[2,1,5,6,4,3]=>[2,1,6,3,5,4]=>10011
[2,1,6,5,3,4]=>[2,1,5,3,6,4]=>[2,1,6,4,3,5]=>10101
[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>10001
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>01000
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>01001
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>01010
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>01001
[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[2,3,1,6,5,4]=>01011
[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>[2,3,1,6,4,5]=>01001
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>00100
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>00101
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>00010
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>00001
[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[2,3,4,6,5,1]=>00011
[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>[2,3,4,6,1,5]=>00001
[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[2,3,5,4,1,6]=>00110
[2,3,5,1,6,4]=>[6,2,3,5,1,4]=>[2,3,6,4,5,1]=>00011
[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>[2,3,5,1,4,6]=>00010
[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[2,3,5,4,6,1]=>00011
[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[2,3,5,6,4,1]=>00101
[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>[2,3,5,6,1,4]=>00001
[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[2,3,6,5,4,1]=>00111
[2,3,6,1,5,4]=>[5,2,3,6,1,4]=>[2,3,5,1,6,4]=>00011
[2,3,6,4,1,5]=>[4,2,3,6,1,5]=>[2,3,6,5,1,4]=>00011
[2,3,6,4,5,1]=>[5,2,3,6,4,1]=>[2,3,6,1,5,4]=>00011
[2,3,6,5,1,4]=>[5,2,3,1,6,4]=>[2,3,6,4,1,5]=>00101
[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>[2,3,6,1,4,5]=>00001
[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[2,4,3,1,5,6]=>01100
[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>[2,4,3,1,6,5]=>01101
[2,4,1,5,3,6]=>[5,2,4,1,3,6]=>[2,5,3,4,1,6]=>00110
[2,4,1,5,6,3]=>[6,2,4,1,5,3]=>[2,5,6,3,4,1]=>00101
[2,4,1,6,3,5]=>[6,2,4,1,3,5]=>[2,6,5,3,4,1]=>00111
[2,4,1,6,5,3]=>[5,2,4,1,6,3]=>[2,6,3,4,1,5]=>00101
[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>[2,4,1,3,5,6]=>00100
[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>[2,4,1,3,6,5]=>00101
[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[2,4,3,5,1,6]=>00110
[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[2,4,3,5,6,1]=>00101
[2,4,3,6,1,5]=>[6,2,4,3,1,5]=>[2,4,3,6,5,1]=>00111
[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>[2,4,3,6,1,5]=>00101
[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>[2,4,5,3,1,6]=>01010
[2,4,5,1,6,3]=>[6,2,5,4,1,3]=>[2,4,6,3,5,1]=>00011
[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>[2,4,5,1,3,6]=>00010
[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[2,4,5,3,6,1]=>00011
[2,4,5,6,1,3]=>[6,2,1,4,5,3]=>[2,4,5,6,3,1]=>01001
[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>[2,4,5,6,1,3]=>00001
[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[2,4,6,5,3,1]=>01011
[2,4,6,1,5,3]=>[5,2,6,4,1,3]=>[2,4,5,1,6,3]=>00011
[2,4,6,3,1,5]=>[3,2,6,4,1,5]=>[2,4,6,5,1,3]=>00011
[2,4,6,3,5,1]=>[5,2,6,4,3,1]=>[2,4,6,1,5,3]=>00011
[2,4,6,5,1,3]=>[5,2,1,4,6,3]=>[2,4,6,3,1,5]=>01001
[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>[2,4,6,1,3,5]=>00001
[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[2,5,4,3,1,6]=>01110
[2,5,1,3,6,4]=>[6,2,1,5,3,4]=>[2,6,4,5,3,1]=>01011
[2,5,1,4,3,6]=>[4,2,5,1,3,6]=>[2,4,1,5,3,6]=>00110
[2,5,1,4,6,3]=>[6,2,5,1,4,3]=>[2,6,3,5,4,1]=>00111
[2,5,1,6,3,4]=>[6,2,5,1,3,4]=>[2,5,3,6,4,1]=>00111
[2,5,1,6,4,3]=>[4,2,6,5,1,3]=>[2,5,1,4,6,3]=>00011
[2,5,3,1,4,6]=>[3,2,5,1,4,6]=>[2,5,4,1,3,6]=>00110
[2,5,3,1,6,4]=>[3,2,6,5,1,4]=>[2,6,4,5,1,3]=>00011
[2,5,3,4,1,6]=>[4,2,5,3,1,6]=>[2,5,1,4,3,6]=>00110
[2,5,3,4,6,1]=>[6,2,5,3,4,1]=>[2,5,4,3,6,1]=>00111
[2,5,3,6,1,4]=>[6,2,5,3,1,4]=>[2,6,4,3,5,1]=>00111
[2,5,3,6,4,1]=>[4,2,6,5,3,1]=>[2,6,1,4,5,3]=>00011
[2,5,4,1,3,6]=>[4,2,1,5,3,6]=>[2,5,3,1,4,6]=>01010
[2,5,4,1,6,3]=>[6,2,4,5,1,3]=>[2,6,3,4,5,1]=>00011
[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>[2,5,1,3,4,6]=>00010
[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>[2,5,3,4,6,1]=>00011
[2,5,4,6,1,3]=>[6,2,1,5,4,3]=>[2,5,4,6,3,1]=>01011
[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>[2,5,4,6,1,3]=>00011
[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[2,5,6,4,3,1]=>01101
[2,5,6,1,4,3]=>[4,2,6,1,5,3]=>[2,4,1,5,6,3]=>00101
[2,5,6,3,1,4]=>[3,2,6,1,5,4]=>[2,5,6,4,1,3]=>00101
[2,5,6,3,4,1]=>[4,2,6,3,5,1]=>[2,5,6,1,4,3]=>00101
[2,5,6,4,1,3]=>[4,2,1,6,5,3]=>[2,5,6,3,1,4]=>01001
[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>[2,5,6,1,3,4]=>00001
[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[2,6,5,4,3,1]=>01111
[2,6,1,3,5,4]=>[5,2,1,6,3,4]=>[2,5,3,1,6,4]=>01011
[2,6,1,4,3,5]=>[4,2,6,1,3,5]=>[2,4,1,6,5,3]=>00111
[2,6,1,4,5,3]=>[5,2,6,1,4,3]=>[2,5,4,1,6,3]=>00111
[2,6,1,5,3,4]=>[5,2,6,1,3,4]=>[2,6,4,1,5,3]=>00111
[2,6,1,5,4,3]=>[4,2,5,6,1,3]=>[2,6,3,5,1,4]=>00011
[2,6,3,1,4,5]=>[3,2,6,1,4,5]=>[2,6,5,4,1,3]=>00111
[2,6,3,1,5,4]=>[3,2,5,6,1,4]=>[2,5,1,3,6,4]=>00011
[2,6,3,4,1,5]=>[4,2,6,3,1,5]=>[2,6,5,1,4,3]=>00111
[2,6,3,4,5,1]=>[5,2,6,3,4,1]=>[2,6,1,5,4,3]=>00111
[2,6,3,5,1,4]=>[5,2,6,3,1,4]=>[2,5,1,6,4,3]=>00111
[2,6,3,5,4,1]=>[4,2,5,6,3,1]=>[2,5,3,6,1,4]=>00011
[2,6,4,1,3,5]=>[4,2,1,6,3,5]=>[2,6,5,3,1,4]=>01011
[2,6,4,1,5,3]=>[5,2,4,6,1,3]=>[2,5,1,6,3,4]=>00011
[2,6,4,3,1,5]=>[3,2,4,6,1,5]=>[2,6,5,1,3,4]=>00011
[2,6,4,3,5,1]=>[5,2,4,6,3,1]=>[2,6,1,5,3,4]=>00011
[2,6,4,5,1,3]=>[5,2,1,6,4,3]=>[2,6,3,1,5,4]=>01011
[2,6,4,5,3,1]=>[3,2,5,6,4,1]=>[2,6,1,3,5,4]=>00011
[2,6,5,1,3,4]=>[5,2,1,3,6,4]=>[2,6,4,3,1,5]=>01101
[2,6,5,1,4,3]=>[4,2,5,1,6,3]=>[2,4,1,6,3,5]=>00101
[2,6,5,3,1,4]=>[3,2,5,1,6,4]=>[2,6,4,1,3,5]=>00101
[2,6,5,3,4,1]=>[4,2,5,3,6,1]=>[2,6,1,4,3,5]=>00101
[2,6,5,4,1,3]=>[4,2,1,5,6,3]=>[2,6,3,1,4,5]=>01001
[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>[2,6,1,3,4,5]=>00001
[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>11000
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,2,1,4,6,5]=>11001
[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,2,1,5,4,6]=>11010
[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[3,2,1,5,6,4]=>11001
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,2,1,6,5,4]=>11011
[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>[3,2,1,6,4,5]=>11001
[3,1,4,2,5,6]=>[4,3,1,2,5,6]=>[4,2,3,1,5,6]=>01100
[3,1,4,2,6,5]=>[4,3,1,2,6,5]=>[4,2,3,1,6,5]=>01101
[3,1,4,5,2,6]=>[5,3,1,4,2,6]=>[4,5,2,3,1,6]=>01010
[3,1,4,5,6,2]=>[6,3,1,4,5,2]=>[4,5,6,2,3,1]=>01001
[3,1,4,6,2,5]=>[6,3,1,4,2,5]=>[4,6,5,2,3,1]=>01011
[3,1,4,6,5,2]=>[5,3,1,4,6,2]=>[4,6,2,3,1,5]=>01001
[3,1,5,2,4,6]=>[5,3,1,2,4,6]=>[5,4,2,3,1,6]=>01110
[3,1,5,2,6,4]=>[6,3,1,5,2,4]=>[6,4,5,2,3,1]=>01011
[3,1,5,4,2,6]=>[4,3,1,5,2,6]=>[5,2,3,1,4,6]=>01010
[3,1,5,4,6,2]=>[6,3,1,5,4,2]=>[5,4,6,2,3,1]=>01011
[3,1,5,6,2,4]=>[6,3,1,2,5,4]=>[5,6,4,2,3,1]=>01101
[3,1,5,6,4,2]=>[4,3,1,6,5,2]=>[5,6,2,3,1,4]=>01001
[3,1,6,2,4,5]=>[6,3,1,2,4,5]=>[6,5,4,2,3,1]=>01111
[3,1,6,2,5,4]=>[5,3,1,6,2,4]=>[5,2,3,1,6,4]=>01011
[3,1,6,4,2,5]=>[4,3,1,6,2,5]=>[6,5,2,3,1,4]=>01011
[3,1,6,4,5,2]=>[5,3,1,6,4,2]=>[6,2,3,1,5,4]=>01011
[3,1,6,5,2,4]=>[5,3,1,2,6,4]=>[6,4,2,3,1,5]=>01101
[3,1,6,5,4,2]=>[4,3,1,5,6,2]=>[6,2,3,1,4,5]=>01001
[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>01000
[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>01001
[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>01010
[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>[3,1,2,5,6,4]=>01001
[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>[3,1,2,6,5,4]=>01011
[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>01001
[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[3,2,4,1,5,6]=>01100
[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[3,2,4,1,6,5]=>01101
[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[3,2,4,5,1,6]=>01010
[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[3,2,4,5,6,1]=>01001
[3,2,4,6,1,5]=>[6,3,2,4,1,5]=>[3,2,4,6,5,1]=>01011
[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>[3,2,4,6,1,5]=>01001
[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[3,2,5,4,1,6]=>01110
[3,2,5,1,6,4]=>[6,3,2,5,1,4]=>[3,2,6,4,5,1]=>01011
[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>[3,2,5,1,4,6]=>01010
[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[3,2,5,4,6,1]=>01011
[3,2,5,6,1,4]=>[6,3,2,1,5,4]=>[3,2,5,6,4,1]=>01101
[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>[3,2,5,6,1,4]=>01001
[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[3,2,6,5,4,1]=>01111
[3,2,6,1,5,4]=>[5,3,2,6,1,4]=>[3,2,5,1,6,4]=>01011
[3,2,6,4,1,5]=>[4,3,2,6,1,5]=>[3,2,6,5,1,4]=>01011
[3,2,6,4,5,1]=>[5,3,2,6,4,1]=>[3,2,6,1,5,4]=>01011
[3,2,6,5,1,4]=>[5,3,2,1,6,4]=>[3,2,6,4,1,5]=>01101
[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>[3,2,6,1,4,5]=>01001
[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[3,4,2,1,5,6]=>10100
[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[3,4,2,1,6,5]=>10101
[3,4,1,5,2,6]=>[5,4,3,1,2,6]=>[3,5,2,4,1,6]=>00110
[3,4,1,5,6,2]=>[6,4,3,1,5,2]=>[3,5,6,2,4,1]=>00101
[3,4,1,6,2,5]=>[6,4,3,1,2,5]=>[3,6,5,2,4,1]=>00111
[3,4,1,6,5,2]=>[5,4,3,1,6,2]=>[3,6,2,4,1,5]=>00101
[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[3,4,1,2,5,6]=>00100
[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>[3,4,1,2,6,5]=>00101
[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[3,4,2,5,1,6]=>00110
[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[3,4,2,5,6,1]=>00101
[3,4,2,6,1,5]=>[6,4,3,2,1,5]=>[3,4,2,6,5,1]=>00111
[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>[3,4,2,6,1,5]=>00101
[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[3,4,5,2,1,6]=>10010
[3,4,5,1,6,2]=>[6,5,3,4,1,2]=>[3,4,6,2,5,1]=>00011
[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[3,4,5,1,2,6]=>00010
[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[3,4,5,2,6,1]=>00011
[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[3,4,5,6,2,1]=>10001
[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[3,4,5,6,1,2]=>00001
[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[3,4,6,5,2,1]=>10011
[3,4,6,1,5,2]=>[5,6,3,4,1,2]=>[3,4,5,1,6,2]=>00011
[3,4,6,2,1,5]=>[2,6,3,4,1,5]=>[3,4,6,5,1,2]=>00011
[3,4,6,2,5,1]=>[5,6,3,4,2,1]=>[3,4,6,1,5,2]=>00011
[3,4,6,5,1,2]=>[5,1,3,4,6,2]=>[3,4,6,2,1,5]=>10001
[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>[3,4,6,1,2,5]=>00001
[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[3,5,4,2,1,6]=>10110
[3,5,1,2,6,4]=>[6,1,3,5,2,4]=>[3,6,4,5,2,1]=>10011
[3,5,1,4,2,6]=>[4,5,3,1,2,6]=>[3,4,1,5,2,6]=>00110
[3,5,1,4,6,2]=>[6,5,3,1,4,2]=>[3,6,2,5,4,1]=>00111
[3,5,1,6,2,4]=>[6,5,3,1,2,4]=>[3,5,2,6,4,1]=>00111
[3,5,1,6,4,2]=>[4,6,3,5,1,2]=>[3,5,1,4,6,2]=>00011
[3,5,2,1,4,6]=>[2,5,3,1,4,6]=>[3,5,4,1,2,6]=>00110
[3,5,2,1,6,4]=>[2,6,3,5,1,4]=>[3,6,4,5,1,2]=>00011
[3,5,2,4,1,6]=>[4,5,3,2,1,6]=>[3,5,1,4,2,6]=>00110
[3,5,2,4,6,1]=>[6,5,3,2,4,1]=>[3,5,4,2,6,1]=>00111
[3,5,2,6,1,4]=>[6,5,3,2,1,4]=>[3,6,4,2,5,1]=>00111
[3,5,2,6,4,1]=>[4,6,3,5,2,1]=>[3,6,1,4,5,2]=>00011
[3,5,4,1,2,6]=>[4,1,3,5,2,6]=>[3,5,2,1,4,6]=>10010
[3,5,4,1,6,2]=>[6,4,3,5,1,2]=>[3,6,2,4,5,1]=>00011
[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>[3,5,1,2,4,6]=>00010
[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>[3,5,2,4,6,1]=>00011
[3,5,4,6,1,2]=>[6,1,3,5,4,2]=>[3,5,4,6,2,1]=>10011
[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>[3,5,4,6,1,2]=>00011
[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[3,5,6,4,2,1]=>10101
[3,5,6,1,4,2]=>[4,6,3,1,5,2]=>[3,4,1,5,6,2]=>00101
[3,5,6,2,1,4]=>[2,6,3,1,5,4]=>[3,5,6,4,1,2]=>00101
[3,5,6,2,4,1]=>[4,6,3,2,5,1]=>[3,5,6,1,4,2]=>00101
[3,5,6,4,1,2]=>[4,1,3,6,5,2]=>[3,5,6,2,1,4]=>10001
[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>[3,5,6,1,2,4]=>00001
[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[3,6,5,4,2,1]=>10111
[3,6,1,2,5,4]=>[5,1,3,6,2,4]=>[3,5,2,1,6,4]=>10011
[3,6,1,4,2,5]=>[4,6,3,1,2,5]=>[3,4,1,6,5,2]=>00111
[3,6,1,4,5,2]=>[5,6,3,1,4,2]=>[3,5,4,1,6,2]=>00111
[3,6,1,5,2,4]=>[5,6,3,1,2,4]=>[3,6,4,1,5,2]=>00111
[3,6,1,5,4,2]=>[4,5,3,6,1,2]=>[3,6,2,5,1,4]=>00011
[3,6,2,1,4,5]=>[2,6,3,1,4,5]=>[3,6,5,4,1,2]=>00111
[3,6,2,1,5,4]=>[2,5,3,6,1,4]=>[3,5,1,2,6,4]=>00011
[3,6,2,4,1,5]=>[4,6,3,2,1,5]=>[3,6,5,1,4,2]=>00111
[3,6,2,4,5,1]=>[5,6,3,2,4,1]=>[3,6,1,5,4,2]=>00111
[3,6,2,5,1,4]=>[5,6,3,2,1,4]=>[3,5,1,6,4,2]=>00111
[3,6,2,5,4,1]=>[4,5,3,6,2,1]=>[3,5,2,6,1,4]=>00011
[3,6,4,1,2,5]=>[4,1,3,6,2,5]=>[3,6,5,2,1,4]=>10011
[3,6,4,1,5,2]=>[5,4,3,6,1,2]=>[3,5,1,6,2,4]=>00011
[3,6,4,2,1,5]=>[2,4,3,6,1,5]=>[3,6,5,1,2,4]=>00011
[3,6,4,2,5,1]=>[5,4,3,6,2,1]=>[3,6,1,5,2,4]=>00011
[3,6,4,5,1,2]=>[5,1,3,6,4,2]=>[3,6,2,1,5,4]=>10011
[3,6,4,5,2,1]=>[2,5,3,6,4,1]=>[3,6,1,2,5,4]=>00011
[3,6,5,1,2,4]=>[5,1,3,2,6,4]=>[3,6,4,2,1,5]=>10101
[3,6,5,1,4,2]=>[4,5,3,1,6,2]=>[3,4,1,6,2,5]=>00101
[3,6,5,2,1,4]=>[2,5,3,1,6,4]=>[3,6,4,1,2,5]=>00101
[3,6,5,2,4,1]=>[4,5,3,2,6,1]=>[3,6,1,4,2,5]=>00101
[3,6,5,4,1,2]=>[4,1,3,5,6,2]=>[3,6,2,1,4,5]=>10001
[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>[3,6,1,2,4,5]=>00001
[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>11100
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[4,3,2,1,6,5]=>11101
[4,1,2,5,3,6]=>[5,1,4,2,3,6]=>[5,3,4,2,1,6]=>10110
[4,1,2,5,6,3]=>[6,1,4,2,5,3]=>[5,6,3,4,2,1]=>10101
[4,1,2,6,3,5]=>[6,1,4,2,3,5]=>[6,5,3,4,2,1]=>10111
[4,1,2,6,5,3]=>[5,1,4,2,6,3]=>[6,3,4,2,1,5]=>10101
[4,1,3,2,5,6]=>[3,4,1,2,5,6]=>[3,1,4,2,5,6]=>01100
[4,1,3,2,6,5]=>[3,4,1,2,6,5]=>[3,1,4,2,6,5]=>01101
[4,1,3,5,2,6]=>[5,4,1,3,2,6]=>[5,2,4,3,1,6]=>01110
[4,1,3,5,6,2]=>[6,4,1,3,5,2]=>[5,6,2,4,3,1]=>01101
[4,1,3,6,2,5]=>[6,4,1,3,2,5]=>[6,5,2,4,3,1]=>01111
[4,1,3,6,5,2]=>[5,4,1,3,6,2]=>[6,2,4,3,1,5]=>01101
[4,1,5,2,3,6]=>[5,4,1,2,3,6]=>[4,2,5,3,1,6]=>01110
[4,1,5,2,6,3]=>[6,5,4,1,2,3]=>[5,2,6,3,4,1]=>00111
[4,1,5,3,2,6]=>[3,5,4,1,2,6]=>[4,1,3,5,2,6]=>00110
[4,1,5,3,6,2]=>[6,5,4,1,3,2]=>[6,2,5,3,4,1]=>00111
[4,1,5,6,2,3]=>[6,4,1,2,5,3]=>[4,2,5,6,3,1]=>01101
[4,1,5,6,3,2]=>[3,6,4,1,5,2]=>[4,1,3,5,6,2]=>00101
[4,1,6,2,3,5]=>[6,4,1,2,3,5]=>[4,2,6,5,3,1]=>01111
[4,1,6,2,5,3]=>[5,6,4,1,2,3]=>[6,3,4,1,5,2]=>00111
[4,1,6,3,2,5]=>[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>00111
[4,1,6,3,5,2]=>[5,6,4,1,3,2]=>[5,3,4,1,6,2]=>00111
[4,1,6,5,2,3]=>[5,4,1,2,6,3]=>[4,2,6,3,1,5]=>01101
[4,1,6,5,3,2]=>[3,5,4,1,6,2]=>[4,1,3,6,2,5]=>00101
[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,3,1,2,5,6]=>01100
[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>[4,3,1,2,6,5]=>01101
[4,2,1,5,3,6]=>[2,5,4,1,3,6]=>[5,3,4,1,2,6]=>00110
[4,2,1,5,6,3]=>[2,6,4,1,5,3]=>[5,6,3,4,1,2]=>00101
[4,2,1,6,3,5]=>[2,6,4,1,3,5]=>[6,5,3,4,1,2]=>00111
[4,2,1,6,5,3]=>[2,5,4,1,6,3]=>[6,3,4,1,2,5]=>00101
[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>01100
[4,2,3,1,6,5]=>[3,4,2,1,6,5]=>[4,1,3,2,6,5]=>01101
[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[4,3,2,5,1,6]=>01110
[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[4,3,2,5,6,1]=>01101
[4,2,3,6,1,5]=>[6,4,2,3,1,5]=>[4,3,2,6,5,1]=>01111
[4,2,3,6,5,1]=>[5,4,2,3,6,1]=>[4,3,2,6,1,5]=>01101
[4,2,5,1,3,6]=>[5,4,2,1,3,6]=>[5,3,2,4,1,6]=>01110
[4,2,5,1,6,3]=>[6,5,4,2,1,3]=>[6,3,4,2,5,1]=>00111
[4,2,5,3,1,6]=>[3,5,4,2,1,6]=>[5,1,3,4,2,6]=>00110
[4,2,5,3,6,1]=>[6,5,4,2,3,1]=>[5,3,4,2,6,1]=>00111
[4,2,5,6,1,3]=>[6,4,2,1,5,3]=>[5,6,3,2,4,1]=>01101
[4,2,5,6,3,1]=>[3,6,4,2,5,1]=>[5,6,1,3,4,2]=>00101
[4,2,6,1,3,5]=>[6,4,2,1,3,5]=>[6,5,3,2,4,1]=>01111
[4,2,6,1,5,3]=>[5,6,4,2,1,3]=>[5,1,6,3,4,2]=>00111
[4,2,6,3,1,5]=>[3,6,4,2,1,5]=>[6,5,1,3,4,2]=>00111
[4,2,6,3,5,1]=>[5,6,4,2,3,1]=>[6,1,5,3,4,2]=>00111
[4,2,6,5,1,3]=>[5,4,2,1,6,3]=>[6,3,2,4,1,5]=>01101
[4,2,6,5,3,1]=>[3,5,4,2,6,1]=>[6,1,3,4,2,5]=>00101
[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[4,2,1,3,5,6]=>10100
[4,3,1,2,6,5]=>[3,1,4,2,6,5]=>[4,2,1,3,6,5]=>10101
[4,3,1,5,2,6]=>[5,3,4,1,2,6]=>[5,2,3,4,1,6]=>00110
[4,3,1,5,6,2]=>[6,3,4,1,5,2]=>[5,6,2,3,4,1]=>00101
[4,3,1,6,2,5]=>[6,3,4,1,2,5]=>[6,5,2,3,4,1]=>00111
[4,3,1,6,5,2]=>[5,3,4,1,6,2]=>[6,2,3,4,1,5]=>00101
[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>00100
[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>00101
[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[4,2,3,5,1,6]=>00110
[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[4,2,3,5,6,1]=>00101
[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>[4,2,3,6,5,1]=>00111
[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>[4,2,3,6,1,5]=>00101
[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[4,3,5,2,1,6]=>10110
[4,3,5,1,6,2]=>[6,5,4,3,1,2]=>[4,3,6,2,5,1]=>00111
[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[4,3,5,1,2,6]=>00110
[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[4,3,5,2,6,1]=>00111
[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[4,3,5,6,2,1]=>10101
[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[4,3,5,6,1,2]=>00101
[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>[4,3,6,5,2,1]=>10111
[4,3,6,1,5,2]=>[5,6,4,3,1,2]=>[4,3,5,1,6,2]=>00111
[4,3,6,2,1,5]=>[2,6,4,3,1,5]=>[4,3,6,5,1,2]=>00111
[4,3,6,2,5,1]=>[5,6,4,3,2,1]=>[4,3,6,1,5,2]=>00111
[4,3,6,5,1,2]=>[5,1,4,3,6,2]=>[4,3,6,2,1,5]=>10101
[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>[4,3,6,1,2,5]=>00101
[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[4,5,3,2,1,6]=>11010
[4,5,1,2,6,3]=>[6,1,5,4,2,3]=>[4,6,3,5,2,1]=>10011
[4,5,1,3,2,6]=>[3,5,1,4,2,6]=>[3,1,4,5,2,6]=>01010
[4,5,1,3,6,2]=>[6,5,1,4,3,2]=>[4,6,2,5,3,1]=>01011
[4,5,1,6,2,3]=>[6,5,1,4,2,3]=>[4,5,2,6,3,1]=>01011
[4,5,1,6,3,2]=>[3,6,5,4,1,2]=>[4,5,1,3,6,2]=>00011
[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>[4,5,3,1,2,6]=>01010
[4,5,2,1,6,3]=>[2,6,5,4,1,3]=>[4,6,3,5,1,2]=>00011
[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[4,5,1,3,2,6]=>01010
[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[4,5,3,2,6,1]=>01011
[4,5,2,6,1,3]=>[6,5,2,4,1,3]=>[4,6,3,2,5,1]=>01011
[4,5,2,6,3,1]=>[3,6,5,4,2,1]=>[4,6,1,3,5,2]=>00011
[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>[4,5,2,1,3,6]=>10010
[4,5,3,1,6,2]=>[6,3,5,4,1,2]=>[4,6,2,3,5,1]=>00011
[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[4,5,1,2,3,6]=>00010
[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[4,5,2,3,6,1]=>00011
[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[4,5,3,6,2,1]=>10011
[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[4,5,3,6,1,2]=>00011
[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[4,5,6,3,2,1]=>11001
[4,5,6,1,3,2]=>[3,6,1,4,5,2]=>[3,1,4,5,6,2]=>01001
[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[4,5,6,3,1,2]=>01001
[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[4,5,6,1,3,2]=>01001
[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[4,5,6,2,1,3]=>10001
[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[4,5,6,1,2,3]=>00001
[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[4,6,5,3,2,1]=>11011
[4,6,1,2,5,3]=>[5,1,6,4,2,3]=>[4,5,2,1,6,3]=>10011
[4,6,1,3,2,5]=>[3,6,1,4,2,5]=>[3,1,4,6,5,2]=>01011
[4,6,1,3,5,2]=>[5,6,1,4,3,2]=>[4,5,3,1,6,2]=>01011
[4,6,1,5,2,3]=>[5,6,1,4,2,3]=>[4,6,3,1,5,2]=>01011
[4,6,1,5,3,2]=>[3,5,6,4,1,2]=>[4,6,2,5,1,3]=>00011
[4,6,2,1,3,5]=>[2,6,1,4,3,5]=>[4,6,5,3,1,2]=>01011
[4,6,2,1,5,3]=>[2,5,6,4,1,3]=>[4,5,1,2,6,3]=>00011
[4,6,2,3,1,5]=>[3,6,2,4,1,5]=>[4,6,5,1,3,2]=>01011
[4,6,2,3,5,1]=>[5,6,2,4,3,1]=>[4,6,1,5,3,2]=>01011
[4,6,2,5,1,3]=>[5,6,2,4,1,3]=>[4,5,1,6,3,2]=>01011
[4,6,2,5,3,1]=>[3,5,6,4,2,1]=>[4,5,2,6,1,3]=>00011
[4,6,3,1,2,5]=>[3,1,6,4,2,5]=>[4,6,5,2,1,3]=>10011
[4,6,3,1,5,2]=>[5,3,6,4,1,2]=>[4,5,1,6,2,3]=>00011
[4,6,3,2,1,5]=>[2,3,6,4,1,5]=>[4,6,5,1,2,3]=>00011
[4,6,3,2,5,1]=>[5,3,6,4,2,1]=>[4,6,1,5,2,3]=>00011
[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>[4,6,2,1,5,3]=>10011
[4,6,3,5,2,1]=>[2,5,6,4,3,1]=>[4,6,1,2,5,3]=>00011
[4,6,5,1,2,3]=>[5,1,2,4,6,3]=>[4,6,3,2,1,5]=>11001
[4,6,5,1,3,2]=>[3,5,1,4,6,2]=>[3,1,4,6,2,5]=>01001
[4,6,5,2,1,3]=>[2,5,1,4,6,3]=>[4,6,3,1,2,5]=>01001
[4,6,5,2,3,1]=>[3,5,2,4,6,1]=>[4,6,1,3,2,5]=>01001
[4,6,5,3,1,2]=>[3,1,5,4,6,2]=>[4,6,2,1,3,5]=>10001
[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>[4,6,1,2,3,5]=>00001
[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>11110
[5,1,2,3,6,4]=>[6,1,2,5,3,4]=>[6,4,5,3,2,1]=>11011
[5,1,2,4,3,6]=>[4,1,5,2,3,6]=>[4,2,1,5,3,6]=>10110
[5,1,2,4,6,3]=>[6,1,5,2,4,3]=>[6,3,5,4,2,1]=>10111
[5,1,2,6,3,4]=>[6,1,5,2,3,4]=>[5,3,6,4,2,1]=>10111
[5,1,2,6,4,3]=>[4,1,6,5,2,3]=>[5,2,1,4,6,3]=>10011
[5,1,3,2,4,6]=>[3,5,1,2,4,6]=>[3,1,5,4,2,6]=>01110
[5,1,3,2,6,4]=>[3,6,1,5,2,4]=>[3,1,6,4,5,2]=>01011
[5,1,3,4,2,6]=>[4,5,1,3,2,6]=>[4,3,1,5,2,6]=>01110
[5,1,3,4,6,2]=>[6,5,1,3,4,2]=>[6,2,5,4,3,1]=>01111
[5,1,3,6,2,4]=>[6,5,1,3,2,4]=>[5,2,6,4,3,1]=>01111
[5,1,3,6,4,2]=>[4,6,1,5,3,2]=>[5,3,1,4,6,2]=>01011
[5,1,4,2,3,6]=>[4,5,1,2,3,6]=>[5,3,1,4,2,6]=>01110
[5,1,4,2,6,3]=>[6,4,5,1,2,3]=>[6,3,5,2,4,1]=>00111
[5,1,4,3,2,6]=>[3,4,5,1,2,6]=>[5,2,4,1,3,6]=>00110
[5,1,4,3,6,2]=>[6,4,5,1,3,2]=>[5,3,6,2,4,1]=>00111
[5,1,4,6,2,3]=>[6,5,1,2,4,3]=>[5,4,2,6,3,1]=>01111
[5,1,4,6,3,2]=>[3,6,5,1,4,2]=>[5,4,1,3,6,2]=>00111
[5,1,6,2,3,4]=>[6,5,1,2,3,4]=>[6,4,2,5,3,1]=>01111
[5,1,6,2,4,3]=>[4,6,5,1,2,3]=>[4,1,6,3,5,2]=>00111
[5,1,6,3,2,4]=>[3,6,5,1,2,4]=>[6,4,1,3,5,2]=>00111
[5,1,6,3,4,2]=>[4,6,5,1,3,2]=>[4,1,5,3,6,2]=>00111
[5,1,6,4,2,3]=>[4,6,1,5,2,3]=>[6,3,1,4,5,2]=>01011
[5,1,6,4,3,2]=>[3,4,6,5,1,2]=>[6,2,4,5,1,3]=>00011
[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[5,4,3,1,2,6]=>01110
[5,2,1,3,6,4]=>[2,6,1,5,3,4]=>[6,4,5,3,1,2]=>01011
[5,2,1,4,3,6]=>[2,4,5,1,3,6]=>[4,1,2,5,3,6]=>00110
[5,2,1,4,6,3]=>[2,6,5,1,4,3]=>[6,3,5,4,1,2]=>00111
[5,2,1,6,3,4]=>[2,6,5,1,3,4]=>[5,3,6,4,1,2]=>00111
[5,2,1,6,4,3]=>[2,4,6,5,1,3]=>[5,1,2,4,6,3]=>00011
[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[5,4,1,3,2,6]=>01110
[5,2,3,1,6,4]=>[3,6,2,5,1,4]=>[6,4,5,1,3,2]=>01011
[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,1,4,3,2,6]=>01110
[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[5,4,3,2,6,1]=>01111
[5,2,3,6,1,4]=>[6,5,2,3,1,4]=>[6,4,3,2,5,1]=>01111
[5,2,3,6,4,1]=>[4,6,2,5,3,1]=>[6,1,4,5,3,2]=>01011
[5,2,4,1,3,6]=>[4,5,2,1,3,6]=>[4,1,5,3,2,6]=>01110
[5,2,4,1,6,3]=>[6,4,5,2,1,3]=>[4,2,6,3,5,1]=>00111
[5,2,4,3,1,6]=>[3,4,5,2,1,6]=>[4,2,5,1,3,6]=>00110
[5,2,4,3,6,1]=>[6,4,5,2,3,1]=>[4,2,5,3,6,1]=>00111
[5,2,4,6,1,3]=>[6,5,2,1,4,3]=>[6,3,2,5,4,1]=>01111
[5,2,4,6,3,1]=>[3,6,5,2,4,1]=>[6,1,3,5,4,2]=>00111
[5,2,6,1,3,4]=>[6,5,2,1,3,4]=>[5,3,2,6,4,1]=>01111
[5,2,6,1,4,3]=>[4,6,5,2,1,3]=>[6,3,5,1,4,2]=>00111
[5,2,6,3,1,4]=>[3,6,5,2,1,4]=>[5,1,3,6,4,2]=>00111
[5,2,6,3,4,1]=>[4,6,5,2,3,1]=>[5,3,6,1,4,2]=>00111
[5,2,6,4,1,3]=>[4,6,2,5,1,3]=>[5,1,4,6,3,2]=>01011
[5,2,6,4,3,1]=>[3,4,6,5,2,1]=>[5,2,4,6,1,3]=>00011
[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[5,4,2,1,3,6]=>10110
[5,3,1,2,6,4]=>[3,1,6,5,2,4]=>[6,4,5,2,1,3]=>10011
[5,3,1,4,2,6]=>[4,3,5,1,2,6]=>[4,1,5,2,3,6]=>00110
[5,3,1,4,6,2]=>[6,3,5,1,4,2]=>[6,2,3,5,4,1]=>00111
[5,3,1,6,2,4]=>[6,3,5,1,2,4]=>[5,2,3,6,4,1]=>00111
[5,3,1,6,4,2]=>[4,3,6,5,1,2]=>[5,1,4,6,2,3]=>00011
[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[5,4,1,2,3,6]=>00110
[5,3,2,1,6,4]=>[2,3,6,5,1,4]=>[6,4,5,1,2,3]=>00011
[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[5,1,4,2,3,6]=>00110
[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[5,4,2,3,6,1]=>00111
[5,3,2,6,1,4]=>[6,3,5,2,1,4]=>[6,4,2,3,5,1]=>00111
[5,3,2,6,4,1]=>[4,3,6,5,2,1]=>[6,1,4,5,2,3]=>00011
[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[5,2,1,4,3,6]=>10110
[5,3,4,1,6,2]=>[6,4,5,3,1,2]=>[6,2,4,3,5,1]=>00111
[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[5,1,2,4,3,6]=>00110
[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[5,2,4,3,6,1]=>00111
[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[5,4,3,6,2,1]=>10111
[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[5,4,3,6,1,2]=>00111
[5,3,6,1,2,4]=>[6,1,5,3,2,4]=>[6,4,3,5,2,1]=>10111
[5,3,6,1,4,2]=>[4,6,5,3,1,2]=>[5,1,4,3,6,2]=>00111
[5,3,6,2,1,4]=>[2,6,5,3,1,4]=>[6,4,3,5,1,2]=>00111
[5,3,6,2,4,1]=>[4,6,5,3,2,1]=>[6,1,4,3,5,2]=>00111
[5,3,6,4,1,2]=>[4,1,6,5,3,2]=>[6,2,1,4,5,3]=>10011
[5,3,6,4,2,1]=>[2,4,6,5,3,1]=>[6,1,2,4,5,3]=>00011
[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[5,3,2,1,4,6]=>11010
[5,4,1,2,6,3]=>[6,1,4,5,2,3]=>[6,3,4,5,2,1]=>10011
[5,4,1,3,2,6]=>[3,4,1,5,2,6]=>[3,1,5,2,4,6]=>01010
[5,4,1,3,6,2]=>[6,4,1,5,3,2]=>[6,2,4,5,3,1]=>01011
[5,4,1,6,2,3]=>[6,4,1,5,2,3]=>[5,2,4,6,3,1]=>01011
[5,4,1,6,3,2]=>[3,6,4,5,1,2]=>[5,1,3,4,6,2]=>00011
[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[5,3,1,2,4,6]=>01010
[5,4,2,1,6,3]=>[2,6,4,5,1,3]=>[6,3,4,5,1,2]=>00011
[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[5,1,3,2,4,6]=>01010
[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[5,3,2,4,6,1]=>01011
[5,4,2,6,1,3]=>[6,4,2,5,1,3]=>[6,3,2,4,5,1]=>01011
[5,4,2,6,3,1]=>[3,6,4,5,2,1]=>[6,1,3,4,5,2]=>00011
[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[5,2,1,3,4,6]=>10010
[5,4,3,1,6,2]=>[6,3,4,5,1,2]=>[6,2,3,4,5,1]=>00011
[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>00010
[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[5,2,3,4,6,1]=>00011
[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[5,3,4,6,2,1]=>10011
[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[5,3,4,6,1,2]=>00011
[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[5,4,6,3,2,1]=>11011
[5,4,6,1,3,2]=>[3,6,1,5,4,2]=>[3,1,5,4,6,2]=>01011
[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[5,4,6,3,1,2]=>01011
[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[5,4,6,1,3,2]=>01011
[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[5,4,6,2,1,3]=>10011
[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[5,4,6,1,2,3]=>00011
[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[5,6,4,3,2,1]=>11101
[5,6,1,2,4,3]=>[4,1,6,2,5,3]=>[4,2,1,5,6,3]=>10101
[5,6,1,3,2,4]=>[3,6,1,2,5,4]=>[3,1,5,6,4,2]=>01101
[5,6,1,3,4,2]=>[4,6,1,3,5,2]=>[4,3,1,5,6,2]=>01101
[5,6,1,4,2,3]=>[4,6,1,2,5,3]=>[5,6,3,1,4,2]=>01101
[5,6,1,4,3,2]=>[3,4,6,1,5,2]=>[5,6,2,4,1,3]=>00101
[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[5,6,4,3,1,2]=>01101
[5,6,2,1,4,3]=>[2,4,6,1,5,3]=>[4,1,2,5,6,3]=>00101
[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[5,6,4,1,3,2]=>01101
[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[5,6,1,4,3,2]=>01101
[5,6,2,4,1,3]=>[4,6,2,1,5,3]=>[4,1,5,6,3,2]=>01101
[5,6,2,4,3,1]=>[3,4,6,2,5,1]=>[4,2,5,6,1,3]=>00101
[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[5,6,4,2,1,3]=>10101
[5,6,3,1,4,2]=>[4,3,6,1,5,2]=>[4,1,5,6,2,3]=>00101
[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[5,6,4,1,2,3]=>00101
[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[5,6,1,4,2,3]=>00101
[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[5,6,2,1,4,3]=>10101
[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[5,6,1,2,4,3]=>00101
[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[5,6,3,2,1,4]=>11001
[5,6,4,1,3,2]=>[3,4,1,6,5,2]=>[3,1,5,6,2,4]=>01001
[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[5,6,3,1,2,4]=>01001
[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[5,6,1,3,2,4]=>01001
[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[5,6,2,1,3,4]=>10001
[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[5,6,1,2,3,4]=>00001
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>11111
[6,1,2,3,5,4]=>[5,1,2,6,3,4]=>[5,3,2,1,6,4]=>11011
[6,1,2,4,3,5]=>[4,1,6,2,3,5]=>[4,2,1,6,5,3]=>10111
[6,1,2,4,5,3]=>[5,1,6,2,4,3]=>[5,4,2,1,6,3]=>10111
[6,1,2,5,3,4]=>[5,1,6,2,3,4]=>[6,4,2,1,5,3]=>10111
[6,1,2,5,4,3]=>[4,1,5,6,2,3]=>[6,3,5,2,1,4]=>10011
[6,1,3,2,4,5]=>[3,6,1,2,4,5]=>[3,1,6,5,4,2]=>01111
[6,1,3,2,5,4]=>[3,5,1,6,2,4]=>[3,1,5,2,6,4]=>01011
[6,1,3,4,2,5]=>[4,6,1,3,2,5]=>[4,3,1,6,5,2]=>01111
[6,1,3,4,5,2]=>[5,6,1,3,4,2]=>[5,4,3,1,6,2]=>01111
[6,1,3,5,2,4]=>[5,6,1,3,2,4]=>[6,4,3,1,5,2]=>01111
[6,1,3,5,4,2]=>[4,5,1,6,3,2]=>[6,2,5,3,1,4]=>01011
[6,1,4,2,3,5]=>[4,6,1,2,3,5]=>[6,5,3,1,4,2]=>01111
[6,1,4,2,5,3]=>[5,4,6,1,2,3]=>[5,2,4,1,6,3]=>00111
[6,1,4,3,2,5]=>[3,4,6,1,2,5]=>[6,5,2,4,1,3]=>00111
[6,1,4,3,5,2]=>[5,4,6,1,3,2]=>[6,2,4,1,5,3]=>00111
[6,1,4,5,2,3]=>[5,6,1,2,4,3]=>[6,3,1,5,4,2]=>01111
[6,1,4,5,3,2]=>[3,5,6,1,4,2]=>[6,2,5,4,1,3]=>00111
[6,1,5,2,3,4]=>[5,6,1,2,3,4]=>[5,3,1,6,4,2]=>01111
[6,1,5,2,4,3]=>[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>00111
[6,1,5,3,2,4]=>[3,5,6,1,2,4]=>[5,2,6,4,1,3]=>00111
[6,1,5,3,4,2]=>[4,5,6,1,3,2]=>[4,1,6,2,5,3]=>00111
[6,1,5,4,2,3]=>[4,5,1,6,2,3]=>[5,2,6,3,1,4]=>01011
[6,1,5,4,3,2]=>[3,4,5,6,1,2]=>[5,1,3,6,2,4]=>00011
[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[6,5,4,3,1,2]=>01111
[6,2,1,3,5,4]=>[2,5,1,6,3,4]=>[5,3,1,2,6,4]=>01011
[6,2,1,4,3,5]=>[2,4,6,1,3,5]=>[4,1,2,6,5,3]=>00111
[6,2,1,4,5,3]=>[2,5,6,1,4,3]=>[5,4,1,2,6,3]=>00111
[6,2,1,5,3,4]=>[2,5,6,1,3,4]=>[6,4,1,2,5,3]=>00111
[6,2,1,5,4,3]=>[2,4,5,6,1,3]=>[6,3,5,1,2,4]=>00011
[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[6,5,4,1,3,2]=>01111
[6,2,3,1,5,4]=>[3,5,2,6,1,4]=>[5,1,3,2,6,4]=>01011
[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[6,5,1,4,3,2]=>01111
[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6,1,5,4,3,2]=>01111
[6,2,3,5,1,4]=>[5,6,2,3,1,4]=>[5,1,6,4,3,2]=>01111
[6,2,3,5,4,1]=>[4,5,2,6,3,1]=>[5,3,2,6,1,4]=>01011
[6,2,4,1,3,5]=>[4,6,2,1,3,5]=>[4,1,6,5,3,2]=>01111
[6,2,4,1,5,3]=>[5,4,6,2,1,3]=>[4,2,5,1,6,3]=>00111
[6,2,4,3,1,5]=>[3,4,6,2,1,5]=>[4,2,6,5,1,3]=>00111
[6,2,4,3,5,1]=>[5,4,6,2,3,1]=>[4,2,6,1,5,3]=>00111
[6,2,4,5,1,3]=>[5,6,2,1,4,3]=>[5,4,1,6,3,2]=>01111
[6,2,4,5,3,1]=>[3,5,6,2,4,1]=>[5,4,2,6,1,3]=>00111
[6,2,5,1,3,4]=>[5,6,2,1,3,4]=>[6,4,1,5,3,2]=>01111
[6,2,5,1,4,3]=>[4,5,6,2,1,3]=>[5,1,4,2,6,3]=>00111
[6,2,5,3,1,4]=>[3,5,6,2,1,4]=>[6,4,2,5,1,3]=>00111
[6,2,5,3,4,1]=>[4,5,6,2,3,1]=>[6,1,4,2,5,3]=>00111
[6,2,5,4,1,3]=>[4,5,2,6,1,3]=>[6,3,2,5,1,4]=>01011
[6,2,5,4,3,1]=>[3,4,5,6,2,1]=>[6,1,3,5,2,4]=>00011
[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[6,5,4,2,1,3]=>10111
[6,3,1,2,5,4]=>[3,1,5,6,2,4]=>[5,2,1,3,6,4]=>10011
[6,3,1,4,2,5]=>[4,3,6,1,2,5]=>[4,1,6,5,2,3]=>00111
[6,3,1,4,5,2]=>[5,3,6,1,4,2]=>[5,4,1,6,2,3]=>00111
[6,3,1,5,2,4]=>[5,3,6,1,2,4]=>[6,4,1,5,2,3]=>00111
[6,3,1,5,4,2]=>[4,3,5,6,1,2]=>[6,2,3,5,1,4]=>00011
[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[6,5,4,1,2,3]=>00111
[6,3,2,1,5,4]=>[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>00011
[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[6,5,1,4,2,3]=>00111
[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[6,1,5,4,2,3]=>00111
[6,3,2,5,1,4]=>[5,3,6,2,1,4]=>[5,1,6,4,2,3]=>00111
[6,3,2,5,4,1]=>[4,3,5,6,2,1]=>[5,2,3,6,1,4]=>00011
[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[6,5,2,1,4,3]=>10111
[6,3,4,1,5,2]=>[5,4,6,3,1,2]=>[5,1,6,2,4,3]=>00111
[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[6,5,1,2,4,3]=>00111
[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[6,1,5,2,4,3]=>00111
[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[6,2,1,5,4,3]=>10111
[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[6,1,2,5,4,3]=>00111
[6,3,5,1,2,4]=>[5,1,6,3,2,4]=>[5,2,1,6,4,3]=>10111
[6,3,5,1,4,2]=>[4,5,6,3,1,2]=>[6,2,5,1,4,3]=>00111
[6,3,5,2,1,4]=>[2,5,6,3,1,4]=>[5,1,2,6,4,3]=>00111
[6,3,5,2,4,1]=>[4,5,6,3,2,1]=>[5,2,6,1,4,3]=>00111
[6,3,5,4,1,2]=>[4,1,5,6,3,2]=>[5,3,6,2,1,4]=>10011
[6,3,5,4,2,1]=>[2,4,5,6,3,1]=>[5,3,6,1,2,4]=>00011
[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[6,5,3,2,1,4]=>11011
[6,4,1,2,5,3]=>[5,1,4,6,2,3]=>[5,2,1,6,3,4]=>10011
[6,4,1,3,2,5]=>[3,4,1,6,2,5]=>[3,1,6,5,2,4]=>01011
[6,4,1,3,5,2]=>[5,4,1,6,3,2]=>[5,3,1,6,2,4]=>01011
[6,4,1,5,2,3]=>[5,4,1,6,2,3]=>[6,3,1,5,2,4]=>01011
[6,4,1,5,3,2]=>[3,5,4,6,1,2]=>[6,2,5,1,3,4]=>00011
[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[6,5,3,1,2,4]=>01011
[6,4,2,1,5,3]=>[2,5,4,6,1,3]=>[5,1,2,6,3,4]=>00011
[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[6,5,1,3,2,4]=>01011
[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[6,1,5,3,2,4]=>01011
[6,4,2,5,1,3]=>[5,4,2,6,1,3]=>[5,1,6,3,2,4]=>01011
[6,4,2,5,3,1]=>[3,5,4,6,2,1]=>[5,2,6,1,3,4]=>00011
[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[6,5,2,1,3,4]=>10011
[6,4,3,1,5,2]=>[5,3,4,6,1,2]=>[5,1,6,2,3,4]=>00011
[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[6,5,1,2,3,4]=>00011
[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[6,1,5,2,3,4]=>00011
[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[6,2,1,5,3,4]=>10011
[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[6,1,2,5,3,4]=>00011
[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[6,3,2,1,5,4]=>11011
[6,4,5,1,3,2]=>[3,5,1,6,4,2]=>[3,1,6,2,5,4]=>01011
[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[6,3,1,2,5,4]=>01011
[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[6,1,3,2,5,4]=>01011
[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[6,2,1,3,5,4]=>10011
[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[6,1,2,3,5,4]=>00011
[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[6,4,3,2,1,5]=>11101
[6,5,1,2,4,3]=>[4,1,5,2,6,3]=>[4,2,1,6,3,5]=>10101
[6,5,1,3,2,4]=>[3,5,1,2,6,4]=>[3,1,6,4,2,5]=>01101
[6,5,1,3,4,2]=>[4,5,1,3,6,2]=>[4,3,1,6,2,5]=>01101
[6,5,1,4,2,3]=>[4,5,1,2,6,3]=>[6,3,1,4,2,5]=>01101
[6,5,1,4,3,2]=>[3,4,5,1,6,2]=>[6,2,4,1,3,5]=>00101
[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[6,4,3,1,2,5]=>01101
[6,5,2,1,4,3]=>[2,4,5,1,6,3]=>[4,1,2,6,3,5]=>00101
[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[6,4,1,3,2,5]=>01101
[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[6,1,4,3,2,5]=>01101
[6,5,2,4,1,3]=>[4,5,2,1,6,3]=>[4,1,6,3,2,5]=>01101
[6,5,2,4,3,1]=>[3,4,5,2,6,1]=>[4,2,6,1,3,5]=>00101
[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[6,4,2,1,3,5]=>10101
[6,5,3,1,4,2]=>[4,3,5,1,6,2]=>[4,1,6,2,3,5]=>00101
[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[6,4,1,2,3,5]=>00101
[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[6,1,4,2,3,5]=>00101
[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[6,2,1,4,3,5]=>10101
[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,1,2,4,3,5]=>00101
[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[6,3,2,1,4,5]=>11001
[6,5,4,1,3,2]=>[3,4,1,5,6,2]=>[3,1,6,2,4,5]=>01001
[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[6,3,1,2,4,5]=>01001
[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[6,1,3,2,4,5]=>01001
[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[6,2,1,3,4,5]=>10001
[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>00001
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>000001
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>000010
[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>000001
[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]=>000011
[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>000001
[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>000100
[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>000101
[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>000010
[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[1,2,3,5,6,7,4]=>000001
[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>[1,2,3,5,7,6,4]=>000011
[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>[1,2,3,5,7,4,6]=>000001
[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]=>000110
[1,2,3,6,4,7,5]=>[1,2,3,7,6,4,5]=>[1,2,3,7,5,6,4]=>000011
[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>000010
[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>[1,2,3,6,5,7,4]=>000011
[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>000101
[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]=>[1,2,3,6,7,4,5]=>000001
[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]=>000111
[1,2,3,7,4,6,5]=>[1,2,3,6,7,4,5]=>[1,2,3,6,4,7,5]=>000011
[1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]=>[1,2,3,7,6,4,5]=>000011
[1,2,3,7,5,6,4]=>[1,2,3,6,7,5,4]=>[1,2,3,7,4,6,5]=>000011
[1,2,3,7,6,4,5]=>[1,2,3,6,4,7,5]=>[1,2,3,7,5,4,6]=>000101
[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>000001
[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000
[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>001001
[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>001010
[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>001001
[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]=>001011
[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>001001
[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>000100
[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>000101
[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[1,2,4,5,6,3,7]=>000010
[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[1,2,4,5,6,7,3]=>000001
[1,2,4,5,7,3,6]=>[1,2,7,4,5,3,6]=>[1,2,4,5,7,6,3]=>000011
[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>[1,2,4,5,7,3,6]=>000001
[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>[1,2,4,6,5,3,7]=>000110
[1,2,4,6,3,7,5]=>[1,2,7,4,6,3,5]=>[1,2,4,7,5,6,3]=>000011
[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>[1,2,4,6,3,5,7]=>000010
[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>[1,2,4,6,5,7,3]=>000011
[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>[1,2,4,6,7,5,3]=>000101
[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]=>[1,2,4,6,7,3,5]=>000001
[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>[1,2,4,7,6,5,3]=>000111
[1,2,4,7,3,6,5]=>[1,2,6,4,7,3,5]=>[1,2,4,6,3,7,5]=>000011
[1,2,4,7,5,3,6]=>[1,2,5,4,7,3,6]=>[1,2,4,7,6,3,5]=>000011
[1,2,4,7,5,6,3]=>[1,2,6,4,7,5,3]=>[1,2,4,7,3,6,5]=>000011
[1,2,4,7,6,3,5]=>[1,2,6,4,3,7,5]=>[1,2,4,7,5,3,6]=>000101
[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>[1,2,4,7,3,5,6]=>000001
[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[1,2,5,4,3,6,7]=>001100
[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]=>001101
[1,2,5,3,6,4,7]=>[1,2,6,5,3,4,7]=>[1,2,6,4,5,3,7]=>000110
[1,2,5,3,6,7,4]=>[1,2,7,5,3,6,4]=>[1,2,6,7,4,5,3]=>000101
[1,2,5,3,7,4,6]=>[1,2,7,5,3,4,6]=>[1,2,7,6,4,5,3]=>000111
[1,2,5,3,7,6,4]=>[1,2,6,5,3,7,4]=>[1,2,7,4,5,3,6]=>000101
[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>000100
[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>000101
[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[1,2,5,4,6,3,7]=>000110
[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>[1,2,5,4,6,7,3]=>000101
[1,2,5,4,7,3,6]=>[1,2,7,5,4,3,6]=>[1,2,5,4,7,6,3]=>000111
[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>[1,2,5,4,7,3,6]=>000101
[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>001010
[1,2,5,6,3,7,4]=>[1,2,7,6,5,3,4]=>[1,2,5,7,4,6,3]=>000011
[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]=>[1,2,5,6,3,4,7]=>000010
[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>[1,2,5,6,4,7,3]=>000011
[1,2,5,6,7,3,4]=>[1,2,7,3,5,6,4]=>[1,2,5,6,7,4,3]=>001001
[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]=>[1,2,5,6,7,3,4]=>000001
[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>[1,2,5,7,6,4,3]=>001011
[1,2,5,7,3,6,4]=>[1,2,6,7,5,3,4]=>[1,2,5,6,3,7,4]=>000011
[1,2,5,7,4,3,6]=>[1,2,4,7,5,3,6]=>[1,2,5,7,6,3,4]=>000011
[1,2,5,7,4,6,3]=>[1,2,6,7,5,4,3]=>[1,2,5,7,3,6,4]=>000011
[1,2,5,7,6,3,4]=>[1,2,6,3,5,7,4]=>[1,2,5,7,4,3,6]=>001001
[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]=>[1,2,5,7,3,4,6]=>000001
[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]=>001110
[1,2,6,3,4,7,5]=>[1,2,7,3,6,4,5]=>[1,2,7,5,6,4,3]=>001011
[1,2,6,3,5,4,7]=>[1,2,5,6,3,4,7]=>[1,2,5,3,6,4,7]=>000110
[1,2,6,3,5,7,4]=>[1,2,7,6,3,5,4]=>[1,2,7,4,6,5,3]=>000111
[1,2,6,3,7,4,5]=>[1,2,7,6,3,4,5]=>[1,2,6,4,7,5,3]=>000111
[1,2,6,3,7,5,4]=>[1,2,5,7,6,3,4]=>[1,2,6,3,5,7,4]=>000011
[1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]=>[1,2,6,5,3,4,7]=>000110
[1,2,6,4,3,7,5]=>[1,2,4,7,6,3,5]=>[1,2,7,5,6,3,4]=>000011
[1,2,6,4,5,3,7]=>[1,2,5,6,4,3,7]=>[1,2,6,3,5,4,7]=>000110
[1,2,6,4,5,7,3]=>[1,2,7,6,4,5,3]=>[1,2,6,5,4,7,3]=>000111
[1,2,6,4,7,3,5]=>[1,2,7,6,4,3,5]=>[1,2,7,5,4,6,3]=>000111
[1,2,6,4,7,5,3]=>[1,2,5,7,6,4,3]=>[1,2,7,3,5,6,4]=>000011
[1,2,6,5,3,4,7]=>[1,2,5,3,6,4,7]=>[1,2,6,4,3,5,7]=>001010
[1,2,6,5,3,7,4]=>[1,2,7,5,6,3,4]=>[1,2,7,4,5,6,3]=>000011
[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>000010
[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>[1,2,6,4,5,7,3]=>000011
[1,2,6,5,7,3,4]=>[1,2,7,3,6,5,4]=>[1,2,6,5,7,4,3]=>001011
[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]=>[1,2,6,5,7,3,4]=>000011
[1,2,6,7,3,4,5]=>[1,2,7,3,4,6,5]=>[1,2,6,7,5,4,3]=>001101
[1,2,6,7,3,5,4]=>[1,2,5,7,3,6,4]=>[1,2,5,3,6,7,4]=>000101
[1,2,6,7,4,3,5]=>[1,2,4,7,3,6,5]=>[1,2,6,7,5,3,4]=>000101
[1,2,6,7,4,5,3]=>[1,2,5,7,4,6,3]=>[1,2,6,7,3,5,4]=>000101
[1,2,6,7,5,3,4]=>[1,2,5,3,7,6,4]=>[1,2,6,7,4,3,5]=>001001
[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]=>[1,2,6,7,3,4,5]=>000001
[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]=>001111
[1,2,7,3,4,6,5]=>[1,2,6,3,7,4,5]=>[1,2,6,4,3,7,5]=>001011
[1,2,7,3,5,4,6]=>[1,2,5,7,3,4,6]=>[1,2,5,3,7,6,4]=>000111
[1,2,7,3,5,6,4]=>[1,2,6,7,3,5,4]=>[1,2,6,5,3,7,4]=>000111
[1,2,7,3,6,4,5]=>[1,2,6,7,3,4,5]=>[1,2,7,5,3,6,4]=>000111
[1,2,7,3,6,5,4]=>[1,2,5,6,7,3,4]=>[1,2,7,4,6,3,5]=>000011
[1,2,7,4,3,5,6]=>[1,2,4,7,3,5,6]=>[1,2,7,6,5,3,4]=>000111
[1,2,7,4,3,6,5]=>[1,2,4,6,7,3,5]=>[1,2,6,3,4,7,5]=>000011
[1,2,7,4,5,3,6]=>[1,2,5,7,4,3,6]=>[1,2,7,6,3,5,4]=>000111
[1,2,7,4,5,6,3]=>[1,2,6,7,4,5,3]=>[1,2,7,3,6,5,4]=>000111
[1,2,7,4,6,3,5]=>[1,2,6,7,4,3,5]=>[1,2,6,3,7,5,4]=>000111
[1,2,7,4,6,5,3]=>[1,2,5,6,7,4,3]=>[1,2,6,4,7,3,5]=>000011
[1,2,7,5,3,4,6]=>[1,2,5,3,7,4,6]=>[1,2,7,6,4,3,5]=>001011
[1,2,7,5,3,6,4]=>[1,2,6,5,7,3,4]=>[1,2,6,3,7,4,5]=>000011
[1,2,7,5,4,3,6]=>[1,2,4,5,7,3,6]=>[1,2,7,6,3,4,5]=>000011
[1,2,7,5,4,6,3]=>[1,2,6,5,7,4,3]=>[1,2,7,3,6,4,5]=>000011
[1,2,7,5,6,3,4]=>[1,2,6,3,7,5,4]=>[1,2,7,4,3,6,5]=>001011
[1,2,7,5,6,4,3]=>[1,2,4,6,7,5,3]=>[1,2,7,3,4,6,5]=>000011
[1,2,7,6,3,4,5]=>[1,2,6,3,4,7,5]=>[1,2,7,5,4,3,6]=>001101
[1,2,7,6,3,5,4]=>[1,2,5,6,3,7,4]=>[1,2,5,3,7,4,6]=>000101
[1,2,7,6,4,3,5]=>[1,2,4,6,3,7,5]=>[1,2,7,5,3,4,6]=>000101
[1,2,7,6,4,5,3]=>[1,2,5,6,4,7,3]=>[1,2,7,3,5,4,6]=>000101
[1,2,7,6,5,3,4]=>[1,2,5,3,6,7,4]=>[1,2,7,4,3,5,6]=>001001
[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>000001
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000
[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>010001
[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>010010
[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>010001
[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]=>010011
[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>010001
[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>010100
[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>010101
[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>010010
[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[1,3,2,5,6,7,4]=>010001
[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>[1,3,2,5,7,6,4]=>010011
[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>[1,3,2,5,7,4,6]=>010001
[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]=>010110
[1,3,2,6,4,7,5]=>[1,3,2,7,6,4,5]=>[1,3,2,7,5,6,4]=>010011
[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[1,3,2,6,4,5,7]=>010010
[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>[1,3,2,6,5,7,4]=>010011
[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>010101
[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]=>[1,3,2,6,7,4,5]=>010001
[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]=>010111
[1,3,2,7,4,6,5]=>[1,3,2,6,7,4,5]=>[1,3,2,6,4,7,5]=>010011
[1,3,2,7,5,4,6]=>[1,3,2,5,7,4,6]=>[1,3,2,7,6,4,5]=>010011
[1,3,2,7,5,6,4]=>[1,3,2,6,7,5,4]=>[1,3,2,7,4,6,5]=>010011
[1,3,2,7,6,4,5]=>[1,3,2,6,4,7,5]=>[1,3,2,7,5,4,6]=>010101
[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>010001
[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>001000
[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>001001
[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>001010
[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>001001
[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>[1,3,4,2,7,6,5]=>001011
[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,5,6]=>001001
[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[1,3,4,5,2,6,7]=>000100
[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[1,3,4,5,2,7,6]=>000101
[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[1,3,4,5,6,2,7]=>000010
[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[1,3,4,5,6,7,2]=>000001
[1,3,4,5,7,2,6]=>[1,7,3,4,5,2,6]=>[1,3,4,5,7,6,2]=>000011
[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>[1,3,4,5,7,2,6]=>000001
[1,3,4,6,2,5,7]=>[1,6,3,4,2,5,7]=>[1,3,4,6,5,2,7]=>000110
[1,3,4,6,2,7,5]=>[1,7,3,4,6,2,5]=>[1,3,4,7,5,6,2]=>000011
[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>[1,3,4,6,2,5,7]=>000010
[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>[1,3,4,6,5,7,2]=>000011
[1,3,4,6,7,2,5]=>[1,7,3,4,2,6,5]=>[1,3,4,6,7,5,2]=>000101
[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]=>[1,3,4,6,7,2,5]=>000001
[1,3,4,7,2,5,6]=>[1,7,3,4,2,5,6]=>[1,3,4,7,6,5,2]=>000111
[1,3,4,7,2,6,5]=>[1,6,3,4,7,2,5]=>[1,3,4,6,2,7,5]=>000011
[1,3,4,7,5,2,6]=>[1,5,3,4,7,2,6]=>[1,3,4,7,6,2,5]=>000011
[1,3,4,7,5,6,2]=>[1,6,3,4,7,5,2]=>[1,3,4,7,2,6,5]=>000011
[1,3,4,7,6,2,5]=>[1,6,3,4,2,7,5]=>[1,3,4,7,5,2,6]=>000101
[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>[1,3,4,7,2,5,6]=>000001
[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>[1,3,5,4,2,6,7]=>001100
[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>[1,3,5,4,2,7,6]=>001101
[1,3,5,2,6,4,7]=>[1,6,3,5,2,4,7]=>[1,3,6,4,5,2,7]=>000110
[1,3,5,2,6,7,4]=>[1,7,3,5,2,6,4]=>[1,3,6,7,4,5,2]=>000101
[1,3,5,2,7,4,6]=>[1,7,3,5,2,4,6]=>[1,3,7,6,4,5,2]=>000111
[1,3,5,2,7,6,4]=>[1,6,3,5,2,7,4]=>[1,3,7,4,5,2,6]=>000101
[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>[1,3,5,2,4,6,7]=>000100
[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>[1,3,5,2,4,7,6]=>000101
[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>[1,3,5,4,6,2,7]=>000110
[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>[1,3,5,4,6,7,2]=>000101
[1,3,5,4,7,2,6]=>[1,7,3,5,4,2,6]=>[1,3,5,4,7,6,2]=>000111
[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>[1,3,5,4,7,2,6]=>000101
[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>[1,3,5,6,4,2,7]=>001010
[1,3,5,6,2,7,4]=>[1,7,3,6,5,2,4]=>[1,3,5,7,4,6,2]=>000011
[1,3,5,6,4,2,7]=>[1,4,3,6,5,2,7]=>[1,3,5,6,2,4,7]=>000010
[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>[1,3,5,6,4,7,2]=>000011
[1,3,5,6,7,2,4]=>[1,7,3,2,5,6,4]=>[1,3,5,6,7,4,2]=>001001
[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]=>[1,3,5,6,7,2,4]=>000001
[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>[1,3,5,7,6,4,2]=>001011
[1,3,5,7,2,6,4]=>[1,6,3,7,5,2,4]=>[1,3,5,6,2,7,4]=>000011
[1,3,5,7,4,2,6]=>[1,4,3,7,5,2,6]=>[1,3,5,7,6,2,4]=>000011
[1,3,5,7,4,6,2]=>[1,6,3,7,5,4,2]=>[1,3,5,7,2,6,4]=>000011
[1,3,5,7,6,2,4]=>[1,6,3,2,5,7,4]=>[1,3,5,7,4,2,6]=>001001
[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]=>[1,3,5,7,2,4,6]=>000001
[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>[1,3,6,5,4,2,7]=>001110
[1,3,6,2,4,7,5]=>[1,7,3,2,6,4,5]=>[1,3,7,5,6,4,2]=>001011
[1,3,6,2,5,4,7]=>[1,5,3,6,2,4,7]=>[1,3,5,2,6,4,7]=>000110
[1,3,6,2,5,7,4]=>[1,7,3,6,2,5,4]=>[1,3,7,4,6,5,2]=>000111
[1,3,6,2,7,4,5]=>[1,7,3,6,2,4,5]=>[1,3,6,4,7,5,2]=>000111
[1,3,6,2,7,5,4]=>[1,5,3,7,6,2,4]=>[1,3,6,2,5,7,4]=>000011
[1,3,6,4,2,5,7]=>[1,4,3,6,2,5,7]=>[1,3,6,5,2,4,7]=>000110
[1,3,6,4,2,7,5]=>[1,4,3,7,6,2,5]=>[1,3,7,5,6,2,4]=>000011
[1,3,6,4,5,2,7]=>[1,5,3,6,4,2,7]=>[1,3,6,2,5,4,7]=>000110
[1,3,6,4,5,7,2]=>[1,7,3,6,4,5,2]=>[1,3,6,5,4,7,2]=>000111
[1,3,6,4,7,2,5]=>[1,7,3,6,4,2,5]=>[1,3,7,5,4,6,2]=>000111
[1,3,6,4,7,5,2]=>[1,5,3,7,6,4,2]=>[1,3,7,2,5,6,4]=>000011
[1,3,6,5,2,4,7]=>[1,5,3,2,6,4,7]=>[1,3,6,4,2,5,7]=>001010
[1,3,6,5,2,7,4]=>[1,7,3,5,6,2,4]=>[1,3,7,4,5,6,2]=>000011
[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]=>[1,3,6,2,4,5,7]=>000010
[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>[1,3,6,4,5,7,2]=>000011
[1,3,6,5,7,2,4]=>[1,7,3,2,6,5,4]=>[1,3,6,5,7,4,2]=>001011
[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]=>[1,3,6,5,7,2,4]=>000011
[1,3,6,7,2,4,5]=>[1,7,3,2,4,6,5]=>[1,3,6,7,5,4,2]=>001101
[1,3,6,7,2,5,4]=>[1,5,3,7,2,6,4]=>[1,3,5,2,6,7,4]=>000101
[1,3,6,7,4,2,5]=>[1,4,3,7,2,6,5]=>[1,3,6,7,5,2,4]=>000101
[1,3,6,7,4,5,2]=>[1,5,3,7,4,6,2]=>[1,3,6,7,2,5,4]=>000101
[1,3,6,7,5,2,4]=>[1,5,3,2,7,6,4]=>[1,3,6,7,4,2,5]=>001001
[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]=>[1,3,6,7,2,4,5]=>000001
[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>[1,3,7,6,5,4,2]=>001111
[1,3,7,2,4,6,5]=>[1,6,3,2,7,4,5]=>[1,3,6,4,2,7,5]=>001011
[1,3,7,2,5,4,6]=>[1,5,3,7,2,4,6]=>[1,3,5,2,7,6,4]=>000111
[1,3,7,2,5,6,4]=>[1,6,3,7,2,5,4]=>[1,3,6,5,2,7,4]=>000111
[1,3,7,2,6,4,5]=>[1,6,3,7,2,4,5]=>[1,3,7,5,2,6,4]=>000111
[1,3,7,2,6,5,4]=>[1,5,3,6,7,2,4]=>[1,3,7,4,6,2,5]=>000011
[1,3,7,4,2,5,6]=>[1,4,3,7,2,5,6]=>[1,3,7,6,5,2,4]=>000111
[1,3,7,4,2,6,5]=>[1,4,3,6,7,2,5]=>[1,3,6,2,4,7,5]=>000011
[1,3,7,4,5,2,6]=>[1,5,3,7,4,2,6]=>[1,3,7,6,2,5,4]=>000111
[1,3,7,4,5,6,2]=>[1,6,3,7,4,5,2]=>[1,3,7,2,6,5,4]=>000111
[1,3,7,4,6,2,5]=>[1,6,3,7,4,2,5]=>[1,3,6,2,7,5,4]=>000111
[1,3,7,4,6,5,2]=>[1,5,3,6,7,4,2]=>[1,3,6,4,7,2,5]=>000011
[1,3,7,5,2,4,6]=>[1,5,3,2,7,4,6]=>[1,3,7,6,4,2,5]=>001011
[1,3,7,5,2,6,4]=>[1,6,3,5,7,2,4]=>[1,3,6,2,7,4,5]=>000011
[1,3,7,5,4,2,6]=>[1,4,3,5,7,2,6]=>[1,3,7,6,2,4,5]=>000011
[1,3,7,5,4,6,2]=>[1,6,3,5,7,4,2]=>[1,3,7,2,6,4,5]=>000011
[1,3,7,5,6,2,4]=>[1,6,3,2,7,5,4]=>[1,3,7,4,2,6,5]=>001011
[1,3,7,5,6,4,2]=>[1,4,3,6,7,5,2]=>[1,3,7,2,4,6,5]=>000011
[1,3,7,6,2,4,5]=>[1,6,3,2,4,7,5]=>[1,3,7,5,4,2,6]=>001101
[1,3,7,6,2,5,4]=>[1,5,3,6,2,7,4]=>[1,3,5,2,7,4,6]=>000101
[1,3,7,6,4,2,5]=>[1,4,3,6,2,7,5]=>[1,3,7,5,2,4,6]=>000101
[1,3,7,6,4,5,2]=>[1,5,3,6,4,7,2]=>[1,3,7,2,5,4,6]=>000101
[1,3,7,6,5,2,4]=>[1,5,3,2,6,7,4]=>[1,3,7,4,2,5,6]=>001001
[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>[1,3,7,2,4,5,6]=>000001
[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[1,4,3,2,5,6,7]=>011000
[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]=>011001
[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]=>011010
[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>[1,4,3,2,6,7,5]=>011001
[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]=>011011
[1,4,2,3,7,6,5]=>[1,4,2,3,6,7,5]=>[1,4,3,2,7,5,6]=>011001
[1,4,2,5,3,6,7]=>[1,5,4,2,3,6,7]=>[1,5,3,4,2,6,7]=>001100
[1,4,2,5,3,7,6]=>[1,5,4,2,3,7,6]=>[1,5,3,4,2,7,6]=>001101
[1,4,2,5,6,3,7]=>[1,6,4,2,5,3,7]=>[1,5,6,3,4,2,7]=>001010
[1,4,2,5,6,7,3]=>[1,7,4,2,5,6,3]=>[1,5,6,7,3,4,2]=>001001
[1,4,2,5,7,3,6]=>[1,7,4,2,5,3,6]=>[1,5,7,6,3,4,2]=>001011
[1,4,2,5,7,6,3]=>[1,6,4,2,5,7,3]=>[1,5,7,3,4,2,6]=>001001
[1,4,2,6,3,5,7]=>[1,6,4,2,3,5,7]=>[1,6,5,3,4,2,7]=>001110
[1,4,2,6,3,7,5]=>[1,7,4,2,6,3,5]=>[1,7,5,6,3,4,2]=>001011
[1,4,2,6,5,3,7]=>[1,5,4,2,6,3,7]=>[1,6,3,4,2,5,7]=>001010
[1,4,2,6,5,7,3]=>[1,7,4,2,6,5,3]=>[1,6,5,7,3,4,2]=>001011
[1,4,2,6,7,3,5]=>[1,7,4,2,3,6,5]=>[1,6,7,5,3,4,2]=>001101
[1,4,2,6,7,5,3]=>[1,5,4,2,7,6,3]=>[1,6,7,3,4,2,5]=>001001
[1,4,2,7,3,5,6]=>[1,7,4,2,3,5,6]=>[1,7,6,5,3,4,2]=>001111
[1,4,2,7,3,6,5]=>[1,6,4,2,7,3,5]=>[1,6,3,4,2,7,5]=>001011
[1,4,2,7,5,3,6]=>[1,5,4,2,7,3,6]=>[1,7,6,3,4,2,5]=>001011
[1,4,2,7,5,6,3]=>[1,6,4,2,7,5,3]=>[1,7,3,4,2,6,5]=>001011
[1,4,2,7,6,3,5]=>[1,6,4,2,3,7,5]=>[1,7,5,3,4,2,6]=>001101
[1,4,2,7,6,5,3]=>[1,5,4,2,6,7,3]=>[1,7,3,4,2,5,6]=>001001
[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>001000
[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>001001
[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[1,4,2,3,6,5,7]=>001010
[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>[1,4,2,3,6,7,5]=>001001
[1,4,3,2,7,5,6]=>[1,3,4,2,7,5,6]=>[1,4,2,3,7,6,5]=>001011
[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>001001
[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[1,4,3,5,2,6,7]=>001100
[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>[1,4,3,5,2,7,6]=>001101
[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[1,4,3,5,6,2,7]=>001010
[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>[1,4,3,5,6,7,2]=>001001
[1,4,3,5,7,2,6]=>[1,7,4,3,5,2,6]=>[1,4,3,5,7,6,2]=>001011
[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>[1,4,3,5,7,2,6]=>001001
[1,4,3,6,2,5,7]=>[1,6,4,3,2,5,7]=>[1,4,3,6,5,2,7]=>001110
[1,4,3,6,2,7,5]=>[1,7,4,3,6,2,5]=>[1,4,3,7,5,6,2]=>001011
[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]=>[1,4,3,6,2,5,7]=>001010
[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>[1,4,3,6,5,7,2]=>001011
[1,4,3,6,7,2,5]=>[1,7,4,3,2,6,5]=>[1,4,3,6,7,5,2]=>001101
[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]=>[1,4,3,6,7,2,5]=>001001
[1,4,3,7,2,5,6]=>[1,7,4,3,2,5,6]=>[1,4,3,7,6,5,2]=>001111
[1,4,3,7,2,6,5]=>[1,6,4,3,7,2,5]=>[1,4,3,6,2,7,5]=>001011
[1,4,3,7,5,2,6]=>[1,5,4,3,7,2,6]=>[1,4,3,7,6,2,5]=>001011
[1,4,3,7,5,6,2]=>[1,6,4,3,7,5,2]=>[1,4,3,7,2,6,5]=>001011
[1,4,3,7,6,2,5]=>[1,6,4,3,2,7,5]=>[1,4,3,7,5,2,6]=>001101
[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>[1,4,3,7,2,5,6]=>001001
[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>010100
[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>010101
[1,4,5,2,6,3,7]=>[1,6,5,4,2,3,7]=>[1,4,6,3,5,2,7]=>000110
[1,4,5,2,6,7,3]=>[1,7,5,4,2,6,3]=>[1,4,6,7,3,5,2]=>000101
[1,4,5,2,7,3,6]=>[1,7,5,4,2,3,6]=>[1,4,7,6,3,5,2]=>000111
[1,4,5,2,7,6,3]=>[1,6,5,4,2,7,3]=>[1,4,7,3,5,2,6]=>000101
[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]=>[1,4,5,2,3,6,7]=>000100
[1,4,5,3,2,7,6]=>[1,3,5,4,2,7,6]=>[1,4,5,2,3,7,6]=>000101
[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>[1,4,5,3,6,2,7]=>000110
[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>[1,4,5,3,6,7,2]=>000101
[1,4,5,3,7,2,6]=>[1,7,5,4,3,2,6]=>[1,4,5,3,7,6,2]=>000111
[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]=>[1,4,5,3,7,2,6]=>000101
[1,4,5,6,2,3,7]=>[1,6,2,4,5,3,7]=>[1,4,5,6,3,2,7]=>010010
[1,4,5,6,2,7,3]=>[1,7,6,4,5,2,3]=>[1,4,5,7,3,6,2]=>000011
[1,4,5,6,3,2,7]=>[1,3,6,4,5,2,7]=>[1,4,5,6,2,3,7]=>000010
[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>[1,4,5,6,3,7,2]=>000011
[1,4,5,6,7,2,3]=>[1,7,2,4,5,6,3]=>[1,4,5,6,7,3,2]=>010001
[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]=>[1,4,5,6,7,2,3]=>000001
[1,4,5,7,2,3,6]=>[1,7,2,4,5,3,6]=>[1,4,5,7,6,3,2]=>010011
[1,4,5,7,2,6,3]=>[1,6,7,4,5,2,3]=>[1,4,5,6,2,7,3]=>000011
[1,4,5,7,3,2,6]=>[1,3,7,4,5,2,6]=>[1,4,5,7,6,2,3]=>000011
[1,4,5,7,3,6,2]=>[1,6,7,4,5,3,2]=>[1,4,5,7,2,6,3]=>000011
[1,4,5,7,6,2,3]=>[1,6,2,4,5,7,3]=>[1,4,5,7,3,2,6]=>010001
[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]=>[1,4,5,7,2,3,6]=>000001
[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>[1,4,6,5,3,2,7]=>010110
[1,4,6,2,3,7,5]=>[1,7,2,4,6,3,5]=>[1,4,7,5,6,3,2]=>010011
[1,4,6,2,5,3,7]=>[1,5,6,4,2,3,7]=>[1,4,5,2,6,3,7]=>000110
[1,4,6,2,5,7,3]=>[1,7,6,4,2,5,3]=>[1,4,7,3,6,5,2]=>000111
[1,4,6,2,7,3,5]=>[1,7,6,4,2,3,5]=>[1,4,6,3,7,5,2]=>000111
[1,4,6,2,7,5,3]=>[1,5,7,4,6,2,3]=>[1,4,6,2,5,7,3]=>000011
[1,4,6,3,2,5,7]=>[1,3,6,4,2,5,7]=>[1,4,6,5,2,3,7]=>000110
[1,4,6,3,2,7,5]=>[1,3,7,4,6,2,5]=>[1,4,7,5,6,2,3]=>000011
[1,4,6,3,5,2,7]=>[1,5,6,4,3,2,7]=>[1,4,6,2,5,3,7]=>000110
[1,4,6,3,5,7,2]=>[1,7,6,4,3,5,2]=>[1,4,6,5,3,7,2]=>000111
[1,4,6,3,7,2,5]=>[1,7,6,4,3,2,5]=>[1,4,7,5,3,6,2]=>000111
[1,4,6,3,7,5,2]=>[1,5,7,4,6,3,2]=>[1,4,7,2,5,6,3]=>000011
[1,4,6,5,2,3,7]=>[1,5,2,4,6,3,7]=>[1,4,6,3,2,5,7]=>010010
[1,4,6,5,2,7,3]=>[1,7,5,4,6,2,3]=>[1,4,7,3,5,6,2]=>000011
[1,4,6,5,3,2,7]=>[1,3,5,4,6,2,7]=>[1,4,6,2,3,5,7]=>000010
[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]=>[1,4,6,3,5,7,2]=>000011
[1,4,6,5,7,2,3]=>[1,7,2,4,6,5,3]=>[1,4,6,5,7,3,2]=>010011
[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]=>[1,4,6,5,7,2,3]=>000011
[1,4,6,7,2,3,5]=>[1,7,2,4,3,6,5]=>[1,4,6,7,5,3,2]=>010101
[1,4,6,7,2,5,3]=>[1,5,7,4,2,6,3]=>[1,4,5,2,6,7,3]=>000101
[1,4,6,7,3,2,5]=>[1,3,7,4,2,6,5]=>[1,4,6,7,5,2,3]=>000101
[1,4,6,7,3,5,2]=>[1,5,7,4,3,6,2]=>[1,4,6,7,2,5,3]=>000101
[1,4,6,7,5,2,3]=>[1,5,2,4,7,6,3]=>[1,4,6,7,3,2,5]=>010001
[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]=>[1,4,6,7,2,3,5]=>000001
[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>[1,4,7,6,5,3,2]=>010111
[1,4,7,2,3,6,5]=>[1,6,2,4,7,3,5]=>[1,4,6,3,2,7,5]=>010011
[1,4,7,2,5,3,6]=>[1,5,7,4,2,3,6]=>[1,4,5,2,7,6,3]=>000111
[1,4,7,2,5,6,3]=>[1,6,7,4,2,5,3]=>[1,4,6,5,2,7,3]=>000111
[1,4,7,2,6,3,5]=>[1,6,7,4,2,3,5]=>[1,4,7,5,2,6,3]=>000111
[1,4,7,2,6,5,3]=>[1,5,6,4,7,2,3]=>[1,4,7,3,6,2,5]=>000011
[1,4,7,3,2,5,6]=>[1,3,7,4,2,5,6]=>[1,4,7,6,5,2,3]=>000111
[1,4,7,3,2,6,5]=>[1,3,6,4,7,2,5]=>[1,4,6,2,3,7,5]=>000011
[1,4,7,3,5,2,6]=>[1,5,7,4,3,2,6]=>[1,4,7,6,2,5,3]=>000111
[1,4,7,3,5,6,2]=>[1,6,7,4,3,5,2]=>[1,4,7,2,6,5,3]=>000111
[1,4,7,3,6,2,5]=>[1,6,7,4,3,2,5]=>[1,4,6,2,7,5,3]=>000111
[1,4,7,3,6,5,2]=>[1,5,6,4,7,3,2]=>[1,4,6,3,7,2,5]=>000011
[1,4,7,5,2,3,6]=>[1,5,2,4,7,3,6]=>[1,4,7,6,3,2,5]=>010011
[1,4,7,5,2,6,3]=>[1,6,5,4,7,2,3]=>[1,4,6,2,7,3,5]=>000011
[1,4,7,5,3,2,6]=>[1,3,5,4,7,2,6]=>[1,4,7,6,2,3,5]=>000011
[1,4,7,5,3,6,2]=>[1,6,5,4,7,3,2]=>[1,4,7,2,6,3,5]=>000011
[1,4,7,5,6,2,3]=>[1,6,2,4,7,5,3]=>[1,4,7,3,2,6,5]=>010011
[1,4,7,5,6,3,2]=>[1,3,6,4,7,5,2]=>[1,4,7,2,3,6,5]=>000011
[1,4,7,6,2,3,5]=>[1,6,2,4,3,7,5]=>[1,4,7,5,3,2,6]=>010101
[1,4,7,6,2,5,3]=>[1,5,6,4,2,7,3]=>[1,4,5,2,7,3,6]=>000101
[1,4,7,6,3,2,5]=>[1,3,6,4,2,7,5]=>[1,4,7,5,2,3,6]=>000101
[1,4,7,6,3,5,2]=>[1,5,6,4,3,7,2]=>[1,4,7,2,5,3,6]=>000101
[1,4,7,6,5,2,3]=>[1,5,2,4,6,7,3]=>[1,4,7,3,2,5,6]=>010001
[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]=>[1,4,7,2,3,5,6]=>000001
[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[1,5,4,3,2,6,7]=>011100
[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]=>011101
[1,5,2,3,6,4,7]=>[1,6,2,5,3,4,7]=>[1,6,4,5,3,2,7]=>010110
[1,5,2,3,6,7,4]=>[1,7,2,5,3,6,4]=>[1,6,7,4,5,3,2]=>010101
[1,5,2,3,7,4,6]=>[1,7,2,5,3,4,6]=>[1,7,6,4,5,3,2]=>010111
[1,5,2,3,7,6,4]=>[1,6,2,5,3,7,4]=>[1,7,4,5,3,2,6]=>010101
[1,5,2,4,3,6,7]=>[1,4,5,2,3,6,7]=>[1,4,2,5,3,6,7]=>001100
[1,5,2,4,3,7,6]=>[1,4,5,2,3,7,6]=>[1,4,2,5,3,7,6]=>001101
[1,5,2,4,6,3,7]=>[1,6,5,2,4,3,7]=>[1,6,3,5,4,2,7]=>001110
[1,5,2,4,6,7,3]=>[1,7,5,2,4,6,3]=>[1,6,7,3,5,4,2]=>001101
[1,5,2,4,7,3,6]=>[1,7,5,2,4,3,6]=>[1,7,6,3,5,4,2]=>001111
[1,5,2,4,7,6,3]=>[1,6,5,2,4,7,3]=>[1,7,3,5,4,2,6]=>001101
[1,5,2,6,3,4,7]=>[1,6,5,2,3,4,7]=>[1,5,3,6,4,2,7]=>001110
[1,5,2,6,3,7,4]=>[1,7,6,5,2,3,4]=>[1,6,3,7,4,5,2]=>000111
[1,5,2,6,4,3,7]=>[1,4,6,5,2,3,7]=>[1,5,2,4,6,3,7]=>000110
[1,5,2,6,4,7,3]=>[1,7,6,5,2,4,3]=>[1,7,3,6,4,5,2]=>000111
[1,5,2,6,7,3,4]=>[1,7,5,2,3,6,4]=>[1,5,3,6,7,4,2]=>001101
[1,5,2,6,7,4,3]=>[1,4,7,5,2,6,3]=>[1,5,2,4,6,7,3]=>000101
[1,5,2,7,3,4,6]=>[1,7,5,2,3,4,6]=>[1,5,3,7,6,4,2]=>001111
[1,5,2,7,3,6,4]=>[1,6,7,5,2,3,4]=>[1,7,4,5,2,6,3]=>000111
[1,5,2,7,4,3,6]=>[1,4,7,5,2,3,6]=>[1,5,2,4,7,6,3]=>000111
[1,5,2,7,4,6,3]=>[1,6,7,5,2,4,3]=>[1,6,4,5,2,7,3]=>000111
[1,5,2,7,6,3,4]=>[1,6,5,2,3,7,4]=>[1,5,3,7,4,2,6]=>001101
[1,5,2,7,6,4,3]=>[1,4,6,5,2,7,3]=>[1,5,2,4,7,3,6]=>000101
[1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]=>[1,5,4,2,3,6,7]=>001100
[1,5,3,2,4,7,6]=>[1,3,5,2,4,7,6]=>[1,5,4,2,3,7,6]=>001101
[1,5,3,2,6,4,7]=>[1,3,6,5,2,4,7]=>[1,6,4,5,2,3,7]=>000110
[1,5,3,2,6,7,4]=>[1,3,7,5,2,6,4]=>[1,6,7,4,5,2,3]=>000101
[1,5,3,2,7,4,6]=>[1,3,7,5,2,4,6]=>[1,7,6,4,5,2,3]=>000111
[1,5,3,2,7,6,4]=>[1,3,6,5,2,7,4]=>[1,7,4,5,2,3,6]=>000101
[1,5,3,4,2,6,7]=>[1,4,5,3,2,6,7]=>[1,5,2,4,3,6,7]=>001100
[1,5,3,4,2,7,6]=>[1,4,5,3,2,7,6]=>[1,5,2,4,3,7,6]=>001101
[1,5,3,4,6,2,7]=>[1,6,5,3,4,2,7]=>[1,5,4,3,6,2,7]=>001110
[1,5,3,4,6,7,2]=>[1,7,5,3,4,6,2]=>[1,5,4,3,6,7,2]=>001101
[1,5,3,4,7,2,6]=>[1,7,5,3,4,2,6]=>[1,5,4,3,7,6,2]=>001111
[1,5,3,4,7,6,2]=>[1,6,5,3,4,7,2]=>[1,5,4,3,7,2,6]=>001101
[1,5,3,6,2,4,7]=>[1,6,5,3,2,4,7]=>[1,6,4,3,5,2,7]=>001110
[1,5,3,6,2,7,4]=>[1,7,6,5,3,2,4]=>[1,7,4,5,3,6,2]=>000111
[1,5,3,6,4,2,7]=>[1,4,6,5,3,2,7]=>[1,6,2,4,5,3,7]=>000110
[1,5,3,6,4,7,2]=>[1,7,6,5,3,4,2]=>[1,6,4,5,3,7,2]=>000111
[1,5,3,6,7,2,4]=>[1,7,5,3,2,6,4]=>[1,6,7,4,3,5,2]=>001101
[1,5,3,6,7,4,2]=>[1,4,7,5,3,6,2]=>[1,6,7,2,4,5,3]=>000101
[1,5,3,7,2,4,6]=>[1,7,5,3,2,4,6]=>[1,7,6,4,3,5,2]=>001111
[1,5,3,7,2,6,4]=>[1,6,7,5,3,2,4]=>[1,6,2,7,4,5,3]=>000111
[1,5,3,7,4,2,6]=>[1,4,7,5,3,2,6]=>[1,7,6,2,4,5,3]=>000111
[1,5,3,7,4,6,2]=>[1,6,7,5,3,4,2]=>[1,7,2,6,4,5,3]=>000111
[1,5,3,7,6,2,4]=>[1,6,5,3,2,7,4]=>[1,7,4,3,5,2,6]=>001101
[1,5,3,7,6,4,2]=>[1,4,6,5,3,7,2]=>[1,7,2,4,5,3,6]=>000101
[1,5,4,2,3,6,7]=>[1,4,2,5,3,6,7]=>[1,5,3,2,4,6,7]=>010100
[1,5,4,2,3,7,6]=>[1,4,2,5,3,7,6]=>[1,5,3,2,4,7,6]=>010101
[1,5,4,2,6,3,7]=>[1,6,4,5,2,3,7]=>[1,6,3,4,5,2,7]=>000110
[1,5,4,2,6,7,3]=>[1,7,4,5,2,6,3]=>[1,6,7,3,4,5,2]=>000101
[1,5,4,2,7,3,6]=>[1,7,4,5,2,3,6]=>[1,7,6,3,4,5,2]=>000111
[1,5,4,2,7,6,3]=>[1,6,4,5,2,7,3]=>[1,7,3,4,5,2,6]=>000101
[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>[1,5,2,3,4,6,7]=>000100
[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>000101
[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]=>[1,5,3,4,6,2,7]=>000110
[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>[1,5,3,4,6,7,2]=>000101
[1,5,4,3,7,2,6]=>[1,7,4,5,3,2,6]=>[1,5,3,4,7,6,2]=>000111
[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>[1,5,3,4,7,2,6]=>000101
[1,5,4,6,2,3,7]=>[1,6,2,5,4,3,7]=>[1,5,4,6,3,2,7]=>010110
[1,5,4,6,2,7,3]=>[1,7,6,5,4,2,3]=>[1,5,4,7,3,6,2]=>000111
[1,5,4,6,3,2,7]=>[1,3,6,5,4,2,7]=>[1,5,4,6,2,3,7]=>000110
[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>[1,5,4,6,3,7,2]=>000111
[1,5,4,6,7,2,3]=>[1,7,2,5,4,6,3]=>[1,5,4,6,7,3,2]=>010101
[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]=>[1,5,4,6,7,2,3]=>000101
[1,5,4,7,2,3,6]=>[1,7,2,5,4,3,6]=>[1,5,4,7,6,3,2]=>010111
[1,5,4,7,2,6,3]=>[1,6,7,5,4,2,3]=>[1,5,4,6,2,7,3]=>000111
[1,5,4,7,3,2,6]=>[1,3,7,5,4,2,6]=>[1,5,4,7,6,2,3]=>000111
[1,5,4,7,3,6,2]=>[1,6,7,5,4,3,2]=>[1,5,4,7,2,6,3]=>000111
[1,5,4,7,6,2,3]=>[1,6,2,5,4,7,3]=>[1,5,4,7,3,2,6]=>010101
[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]=>[1,5,4,7,2,3,6]=>000101
[1,5,6,2,3,4,7]=>[1,6,2,3,5,4,7]=>[1,5,6,4,3,2,7]=>011010
[1,5,6,2,3,7,4]=>[1,7,2,6,5,3,4]=>[1,5,7,4,6,3,2]=>010011
[1,5,6,2,4,3,7]=>[1,4,6,2,5,3,7]=>[1,4,2,5,6,3,7]=>001010
[1,5,6,2,4,7,3]=>[1,7,6,2,5,4,3]=>[1,5,7,3,6,4,2]=>001011
[1,5,6,2,7,3,4]=>[1,7,6,2,5,3,4]=>[1,5,6,3,7,4,2]=>001011
[1,5,6,2,7,4,3]=>[1,4,7,6,5,2,3]=>[1,5,6,2,4,7,3]=>000011
[1,5,6,3,2,4,7]=>[1,3,6,2,5,4,7]=>[1,5,6,4,2,3,7]=>001010
[1,5,6,3,2,7,4]=>[1,3,7,6,5,2,4]=>[1,5,7,4,6,2,3]=>000011
[1,5,6,3,4,2,7]=>[1,4,6,3,5,2,7]=>[1,5,6,2,4,3,7]=>001010
[1,5,6,3,4,7,2]=>[1,7,6,3,5,4,2]=>[1,5,6,4,3,7,2]=>001011
[1,5,6,3,7,2,4]=>[1,7,6,3,5,2,4]=>[1,5,7,4,3,6,2]=>001011
[1,5,6,3,7,4,2]=>[1,4,7,6,5,3,2]=>[1,5,7,2,4,6,3]=>000011
[1,5,6,4,2,3,7]=>[1,4,2,6,5,3,7]=>[1,5,6,3,2,4,7]=>010010
[1,5,6,4,2,7,3]=>[1,7,4,6,5,2,3]=>[1,5,7,3,4,6,2]=>000011
[1,5,6,4,3,2,7]=>[1,3,4,6,5,2,7]=>[1,5,6,2,3,4,7]=>000010
[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]=>[1,5,6,3,4,7,2]=>000011
[1,5,6,4,7,2,3]=>[1,7,2,6,5,4,3]=>[1,5,6,4,7,3,2]=>010011
[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]=>[1,5,6,4,7,2,3]=>000011
[1,5,6,7,2,3,4]=>[1,7,2,3,5,6,4]=>[1,5,6,7,4,3,2]=>011001
[1,5,6,7,2,4,3]=>[1,4,7,2,5,6,3]=>[1,4,2,5,6,7,3]=>001001
[1,5,6,7,3,2,4]=>[1,3,7,2,5,6,4]=>[1,5,6,7,4,2,3]=>001001
[1,5,6,7,3,4,2]=>[1,4,7,3,5,6,2]=>[1,5,6,7,2,4,3]=>001001
[1,5,6,7,4,2,3]=>[1,4,2,7,5,6,3]=>[1,5,6,7,3,2,4]=>010001
[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]=>[1,5,6,7,2,3,4]=>000001
[1,5,7,2,3,4,6]=>[1,7,2,3,5,4,6]=>[1,5,7,6,4,3,2]=>011011
[1,5,7,2,3,6,4]=>[1,6,2,7,5,3,4]=>[1,5,6,3,2,7,4]=>010011
[1,5,7,2,4,3,6]=>[1,4,7,2,5,3,6]=>[1,4,2,5,7,6,3]=>001011
[1,5,7,2,4,6,3]=>[1,6,7,2,5,4,3]=>[1,5,6,4,2,7,3]=>001011
[1,5,7,2,6,3,4]=>[1,6,7,2,5,3,4]=>[1,5,7,4,2,6,3]=>001011
[1,5,7,2,6,4,3]=>[1,4,6,7,5,2,3]=>[1,5,7,3,6,2,4]=>000011
[1,5,7,3,2,4,6]=>[1,3,7,2,5,4,6]=>[1,5,7,6,4,2,3]=>001011
[1,5,7,3,2,6,4]=>[1,3,6,7,5,2,4]=>[1,5,6,2,3,7,4]=>000011
[1,5,7,3,4,2,6]=>[1,4,7,3,5,2,6]=>[1,5,7,6,2,4,3]=>001011
[1,5,7,3,4,6,2]=>[1,6,7,3,5,4,2]=>[1,5,7,2,6,4,3]=>001011
[1,5,7,3,6,2,4]=>[1,6,7,3,5,2,4]=>[1,5,6,2,7,4,3]=>001011
[1,5,7,3,6,4,2]=>[1,4,6,7,5,3,2]=>[1,5,6,3,7,2,4]=>000011
[1,5,7,4,2,3,6]=>[1,4,2,7,5,3,6]=>[1,5,7,6,3,2,4]=>010011
[1,5,7,4,2,6,3]=>[1,6,4,7,5,2,3]=>[1,5,6,2,7,3,4]=>000011
[1,5,7,4,3,2,6]=>[1,3,4,7,5,2,6]=>[1,5,7,6,2,3,4]=>000011
[1,5,7,4,3,6,2]=>[1,6,4,7,5,3,2]=>[1,5,7,2,6,3,4]=>000011
[1,5,7,4,6,2,3]=>[1,6,2,7,5,4,3]=>[1,5,7,3,2,6,4]=>010011
[1,5,7,4,6,3,2]=>[1,3,6,7,5,4,2]=>[1,5,7,2,3,6,4]=>000011
[1,5,7,6,2,3,4]=>[1,6,2,3,5,7,4]=>[1,5,7,4,3,2,6]=>011001
[1,5,7,6,2,4,3]=>[1,4,6,2,5,7,3]=>[1,4,2,5,7,3,6]=>001001
[1,5,7,6,3,2,4]=>[1,3,6,2,5,7,4]=>[1,5,7,4,2,3,6]=>001001
[1,5,7,6,3,4,2]=>[1,4,6,3,5,7,2]=>[1,5,7,2,4,3,6]=>001001
[1,5,7,6,4,2,3]=>[1,4,2,6,5,7,3]=>[1,5,7,3,2,4,6]=>010001
[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]=>[1,5,7,2,3,4,6]=>000001
[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[1,6,5,4,3,2,7]=>011110
[1,6,2,3,4,7,5]=>[1,7,2,3,6,4,5]=>[1,7,5,6,4,3,2]=>011011
[1,6,2,3,5,4,7]=>[1,5,2,6,3,4,7]=>[1,5,3,2,6,4,7]=>010110
[1,6,2,3,5,7,4]=>[1,7,2,6,3,5,4]=>[1,7,4,6,5,3,2]=>010111
[1,6,2,3,7,4,5]=>[1,7,2,6,3,4,5]=>[1,6,4,7,5,3,2]=>010111
[1,6,2,3,7,5,4]=>[1,5,2,7,6,3,4]=>[1,6,3,2,5,7,4]=>010011
[1,6,2,4,3,5,7]=>[1,4,6,2,3,5,7]=>[1,4,2,6,5,3,7]=>001110
[1,6,2,4,3,7,5]=>[1,4,7,2,6,3,5]=>[1,4,2,7,5,6,3]=>001011
[1,6,2,4,5,3,7]=>[1,5,6,2,4,3,7]=>[1,5,4,2,6,3,7]=>001110
[1,6,2,4,5,7,3]=>[1,7,6,2,4,5,3]=>[1,7,3,6,5,4,2]=>001111
[1,6,2,4,7,3,5]=>[1,7,6,2,4,3,5]=>[1,6,3,7,5,4,2]=>001111
[1,6,2,4,7,5,3]=>[1,5,7,2,6,4,3]=>[1,6,4,2,5,7,3]=>001011
[1,6,2,5,3,4,7]=>[1,5,6,2,3,4,7]=>[1,6,4,2,5,3,7]=>001110
[1,6,2,5,3,7,4]=>[1,7,5,6,2,3,4]=>[1,7,4,6,3,5,2]=>000111
[1,6,2,5,4,3,7]=>[1,4,5,6,2,3,7]=>[1,6,3,5,2,4,7]=>000110
[1,6,2,5,4,7,3]=>[1,7,5,6,2,4,3]=>[1,6,4,7,3,5,2]=>000111
[1,6,2,5,7,3,4]=>[1,7,6,2,3,5,4]=>[1,6,5,3,7,4,2]=>001111
[1,6,2,5,7,4,3]=>[1,4,7,6,2,5,3]=>[1,6,5,2,4,7,3]=>000111
[1,6,2,7,3,4,5]=>[1,7,6,2,3,4,5]=>[1,7,5,3,6,4,2]=>001111
[1,6,2,7,3,5,4]=>[1,5,7,6,2,3,4]=>[1,5,2,7,4,6,3]=>000111
[1,6,2,7,4,3,5]=>[1,4,7,6,2,3,5]=>[1,7,5,2,4,6,3]=>000111
[1,6,2,7,4,5,3]=>[1,5,7,6,2,4,3]=>[1,5,2,6,4,7,3]=>000111
[1,6,2,7,5,3,4]=>[1,5,7,2,6,3,4]=>[1,7,4,2,5,6,3]=>001011
[1,6,2,7,5,4,3]=>[1,4,5,7,6,2,3]=>[1,7,3,5,6,2,4]=>000011
[1,6,3,2,4,5,7]=>[1,3,6,2,4,5,7]=>[1,6,5,4,2,3,7]=>001110
[1,6,3,2,4,7,5]=>[1,3,7,2,6,4,5]=>[1,7,5,6,4,2,3]=>001011
[1,6,3,2,5,4,7]=>[1,3,5,6,2,4,7]=>[1,5,2,3,6,4,7]=>000110
[1,6,3,2,5,7,4]=>[1,3,7,6,2,5,4]=>[1,7,4,6,5,2,3]=>000111
[1,6,3,2,7,4,5]=>[1,3,7,6,2,4,5]=>[1,6,4,7,5,2,3]=>000111
[1,6,3,2,7,5,4]=>[1,3,5,7,6,2,4]=>[1,6,2,3,5,7,4]=>000011
[1,6,3,4,2,5,7]=>[1,4,6,3,2,5,7]=>[1,6,5,2,4,3,7]=>001110
[1,6,3,4,2,7,5]=>[1,4,7,3,6,2,5]=>[1,7,5,6,2,4,3]=>001011
[1,6,3,4,5,2,7]=>[1,5,6,3,4,2,7]=>[1,6,2,5,4,3,7]=>001110
[1,6,3,4,5,7,2]=>[1,7,6,3,4,5,2]=>[1,6,5,4,3,7,2]=>001111
[1,6,3,4,7,2,5]=>[1,7,6,3,4,2,5]=>[1,7,5,4,3,6,2]=>001111
[1,6,3,4,7,5,2]=>[1,5,7,3,6,4,2]=>[1,7,2,5,6,4,3]=>001011
[1,6,3,5,2,4,7]=>[1,5,6,3,2,4,7]=>[1,5,2,6,4,3,7]=>001110
[1,6,3,5,2,7,4]=>[1,7,5,6,3,2,4]=>[1,5,3,7,4,6,2]=>000111
[1,6,3,5,4,2,7]=>[1,4,5,6,3,2,7]=>[1,5,3,6,2,4,7]=>000110
[1,6,3,5,4,7,2]=>[1,7,5,6,3,4,2]=>[1,5,3,6,4,7,2]=>000111
[1,6,3,5,7,2,4]=>[1,7,6,3,2,5,4]=>[1,7,4,3,6,5,2]=>001111
[1,6,3,5,7,4,2]=>[1,4,7,6,3,5,2]=>[1,7,2,4,6,5,3]=>000111
[1,6,3,7,2,4,5]=>[1,7,6,3,2,4,5]=>[1,6,4,3,7,5,2]=>001111
[1,6,3,7,2,5,4]=>[1,5,7,6,3,2,4]=>[1,7,4,6,2,5,3]=>000111
[1,6,3,7,4,2,5]=>[1,4,7,6,3,2,5]=>[1,6,2,4,7,5,3]=>000111
[1,6,3,7,4,5,2]=>[1,5,7,6,3,4,2]=>[1,6,4,7,2,5,3]=>000111
[1,6,3,7,5,2,4]=>[1,5,7,3,6,2,4]=>[1,6,2,5,7,4,3]=>001011
[1,6,3,7,5,4,2]=>[1,4,5,7,6,3,2]=>[1,6,3,5,7,2,4]=>000011
[1,6,4,2,3,5,7]=>[1,4,2,6,3,5,7]=>[1,6,5,3,2,4,7]=>010110
[1,6,4,2,3,7,5]=>[1,4,2,7,6,3,5]=>[1,7,5,6,3,2,4]=>010011
[1,6,4,2,5,3,7]=>[1,5,4,6,2,3,7]=>[1,5,2,6,3,4,7]=>000110
[1,6,4,2,5,7,3]=>[1,7,4,6,2,5,3]=>[1,7,3,4,6,5,2]=>000111
[1,6,4,2,7,3,5]=>[1,7,4,6,2,3,5]=>[1,6,3,4,7,5,2]=>000111
[1,6,4,2,7,5,3]=>[1,5,4,7,6,2,3]=>[1,6,2,5,7,3,4]=>000011
[1,6,4,3,2,5,7]=>[1,3,4,6,2,5,7]=>[1,6,5,2,3,4,7]=>000110
[1,6,4,3,2,7,5]=>[1,3,4,7,6,2,5]=>[1,7,5,6,2,3,4]=>000011
[1,6,4,3,5,2,7]=>[1,5,4,6,3,2,7]=>[1,6,2,5,3,4,7]=>000110
[1,6,4,3,5,7,2]=>[1,7,4,6,3,5,2]=>[1,6,5,3,4,7,2]=>000111
[1,6,4,3,7,2,5]=>[1,7,4,6,3,2,5]=>[1,7,5,3,4,6,2]=>000111
[1,6,4,3,7,5,2]=>[1,5,4,7,6,3,2]=>[1,7,2,5,6,3,4]=>000011
[1,6,4,5,2,3,7]=>[1,5,2,6,4,3,7]=>[1,6,3,2,5,4,7]=>010110
[1,6,4,5,2,7,3]=>[1,7,5,6,4,2,3]=>[1,7,3,5,4,6,2]=>000111
[1,6,4,5,3,2,7]=>[1,3,5,6,4,2,7]=>[1,6,2,3,5,4,7]=>000110
[1,6,4,5,3,7,2]=>[1,7,5,6,4,3,2]=>[1,6,3,5,4,7,2]=>000111
[1,6,4,5,7,2,3]=>[1,7,2,6,4,5,3]=>[1,6,5,4,7,3,2]=>010111
[1,6,4,5,7,3,2]=>[1,3,7,6,4,5,2]=>[1,6,5,4,7,2,3]=>000111
[1,6,4,7,2,3,5]=>[1,7,2,6,4,3,5]=>[1,7,5,4,6,3,2]=>010111
[1,6,4,7,2,5,3]=>[1,5,7,6,4,2,3]=>[1,6,2,5,4,7,3]=>000111
[1,6,4,7,3,2,5]=>[1,3,7,6,4,2,5]=>[1,7,5,4,6,2,3]=>000111
[1,6,4,7,3,5,2]=>[1,5,7,6,4,3,2]=>[1,7,2,5,4,6,3]=>000111
[1,6,4,7,5,2,3]=>[1,5,2,7,6,4,3]=>[1,7,3,2,5,6,4]=>010011
[1,6,4,7,5,3,2]=>[1,3,5,7,6,4,2]=>[1,7,2,3,5,6,4]=>000011
[1,6,5,2,3,4,7]=>[1,5,2,3,6,4,7]=>[1,6,4,3,2,5,7]=>011010
[1,6,5,2,3,7,4]=>[1,7,2,5,6,3,4]=>[1,7,4,5,6,3,2]=>010011
[1,6,5,2,4,3,7]=>[1,4,5,2,6,3,7]=>[1,4,2,6,3,5,7]=>001010
[1,6,5,2,4,7,3]=>[1,7,5,2,6,4,3]=>[1,7,3,5,6,4,2]=>001011
[1,6,5,2,7,3,4]=>[1,7,5,2,6,3,4]=>[1,6,3,5,7,4,2]=>001011
[1,6,5,2,7,4,3]=>[1,4,7,5,6,2,3]=>[1,6,2,4,5,7,3]=>000011
[1,6,5,3,2,4,7]=>[1,3,5,2,6,4,7]=>[1,6,4,2,3,5,7]=>001010
[1,6,5,3,2,7,4]=>[1,3,7,5,6,2,4]=>[1,7,4,5,6,2,3]=>000011
[1,6,5,3,4,2,7]=>[1,4,5,3,6,2,7]=>[1,6,2,4,3,5,7]=>001010
[1,6,5,3,4,7,2]=>[1,7,5,3,6,4,2]=>[1,6,4,3,5,7,2]=>001011
[1,6,5,3,7,2,4]=>[1,7,5,3,6,2,4]=>[1,7,4,3,5,6,2]=>001011
[1,6,5,3,7,4,2]=>[1,4,7,5,6,3,2]=>[1,7,2,4,5,6,3]=>000011
[1,6,5,4,2,3,7]=>[1,4,2,5,6,3,7]=>[1,6,3,2,4,5,7]=>010010
[1,6,5,4,2,7,3]=>[1,7,4,5,6,2,3]=>[1,7,3,4,5,6,2]=>000011
[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]=>[1,6,2,3,4,5,7]=>000010
[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>[1,6,3,4,5,7,2]=>000011
[1,6,5,4,7,2,3]=>[1,7,2,5,6,4,3]=>[1,6,4,5,7,3,2]=>010011
[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]=>[1,6,4,5,7,2,3]=>000011
[1,6,5,7,2,3,4]=>[1,7,2,3,6,5,4]=>[1,6,5,7,4,3,2]=>011011
[1,6,5,7,2,4,3]=>[1,4,7,2,6,5,3]=>[1,4,2,6,5,7,3]=>001011
[1,6,5,7,3,2,4]=>[1,3,7,2,6,5,4]=>[1,6,5,7,4,2,3]=>001011
[1,6,5,7,3,4,2]=>[1,4,7,3,6,5,2]=>[1,6,5,7,2,4,3]=>001011
[1,6,5,7,4,2,3]=>[1,4,2,7,6,5,3]=>[1,6,5,7,3,2,4]=>010011
[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]=>[1,6,5,7,2,3,4]=>000011
[1,6,7,2,3,4,5]=>[1,7,2,3,4,6,5]=>[1,6,7,5,4,3,2]=>011101
[1,6,7,2,3,5,4]=>[1,5,2,7,3,6,4]=>[1,5,3,2,6,7,4]=>010101
[1,6,7,2,4,3,5]=>[1,4,7,2,3,6,5]=>[1,4,2,6,7,5,3]=>001101
[1,6,7,2,4,5,3]=>[1,5,7,2,4,6,3]=>[1,5,4,2,6,7,3]=>001101
[1,6,7,2,5,3,4]=>[1,5,7,2,3,6,4]=>[1,6,7,4,2,5,3]=>001101
[1,6,7,2,5,4,3]=>[1,4,5,7,2,6,3]=>[1,6,7,3,5,2,4]=>000101
[1,6,7,3,2,4,5]=>[1,3,7,2,4,6,5]=>[1,6,7,5,4,2,3]=>001101
[1,6,7,3,2,5,4]=>[1,3,5,7,2,6,4]=>[1,5,2,3,6,7,4]=>000101
[1,6,7,3,4,2,5]=>[1,4,7,3,2,6,5]=>[1,6,7,5,2,4,3]=>001101
[1,6,7,3,4,5,2]=>[1,5,7,3,4,6,2]=>[1,6,7,2,5,4,3]=>001101
[1,6,7,3,5,2,4]=>[1,5,7,3,2,6,4]=>[1,5,2,6,7,4,3]=>001101
[1,6,7,3,5,4,2]=>[1,4,5,7,3,6,2]=>[1,5,3,6,7,2,4]=>000101
[1,6,7,4,2,3,5]=>[1,4,2,7,3,6,5]=>[1,6,7,5,3,2,4]=>010101
[1,6,7,4,2,5,3]=>[1,5,4,7,2,6,3]=>[1,5,2,6,7,3,4]=>000101
[1,6,7,4,3,2,5]=>[1,3,4,7,2,6,5]=>[1,6,7,5,2,3,4]=>000101
[1,6,7,4,3,5,2]=>[1,5,4,7,3,6,2]=>[1,6,7,2,5,3,4]=>000101
[1,6,7,4,5,2,3]=>[1,5,2,7,4,6,3]=>[1,6,7,3,2,5,4]=>010101
[1,6,7,4,5,3,2]=>[1,3,5,7,4,6,2]=>[1,6,7,2,3,5,4]=>000101
[1,6,7,5,2,3,4]=>[1,5,2,3,7,6,4]=>[1,6,7,4,3,2,5]=>011001
[1,6,7,5,2,4,3]=>[1,4,5,2,7,6,3]=>[1,4,2,6,7,3,5]=>001001
[1,6,7,5,3,2,4]=>[1,3,5,2,7,6,4]=>[1,6,7,4,2,3,5]=>001001
[1,6,7,5,3,4,2]=>[1,4,5,3,7,6,2]=>[1,6,7,2,4,3,5]=>001001
[1,6,7,5,4,2,3]=>[1,4,2,5,7,6,3]=>[1,6,7,3,2,4,5]=>010001
[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]=>[1,6,7,2,3,4,5]=>000001
[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>011111
[1,7,2,3,4,6,5]=>[1,6,2,3,7,4,5]=>[1,6,4,3,2,7,5]=>011011
[1,7,2,3,5,4,6]=>[1,5,2,7,3,4,6]=>[1,5,3,2,7,6,4]=>010111
[1,7,2,3,5,6,4]=>[1,6,2,7,3,5,4]=>[1,6,5,3,2,7,4]=>010111
[1,7,2,3,6,4,5]=>[1,6,2,7,3,4,5]=>[1,7,5,3,2,6,4]=>010111
[1,7,2,3,6,5,4]=>[1,5,2,6,7,3,4]=>[1,7,4,6,3,2,5]=>010011
[1,7,2,4,3,5,6]=>[1,4,7,2,3,5,6]=>[1,4,2,7,6,5,3]=>001111
[1,7,2,4,3,6,5]=>[1,4,6,2,7,3,5]=>[1,4,2,6,3,7,5]=>001011
[1,7,2,4,5,3,6]=>[1,5,7,2,4,3,6]=>[1,5,4,2,7,6,3]=>001111
[1,7,2,4,5,6,3]=>[1,6,7,2,4,5,3]=>[1,6,5,4,2,7,3]=>001111
[1,7,2,4,6,3,5]=>[1,6,7,2,4,3,5]=>[1,7,5,4,2,6,3]=>001111
[1,7,2,4,6,5,3]=>[1,5,6,2,7,4,3]=>[1,7,3,6,4,2,5]=>001011
[1,7,2,5,3,4,6]=>[1,5,7,2,3,4,6]=>[1,7,6,4,2,5,3]=>001111
[1,7,2,5,3,6,4]=>[1,6,5,7,2,3,4]=>[1,6,3,5,2,7,4]=>000111
[1,7,2,5,4,3,6]=>[1,4,5,7,2,3,6]=>[1,7,6,3,5,2,4]=>000111
[1,7,2,5,4,6,3]=>[1,6,5,7,2,4,3]=>[1,7,3,5,2,6,4]=>000111
[1,7,2,5,6,3,4]=>[1,6,7,2,3,5,4]=>[1,7,4,2,6,5,3]=>001111
[1,7,2,5,6,4,3]=>[1,4,6,7,2,5,3]=>[1,7,3,6,5,2,4]=>000111
[1,7,2,6,3,4,5]=>[1,6,7,2,3,4,5]=>[1,6,4,2,7,5,3]=>001111
[1,7,2,6,3,5,4]=>[1,5,6,7,2,3,4]=>[1,5,2,6,3,7,4]=>000111
[1,7,2,6,4,3,5]=>[1,4,6,7,2,3,5]=>[1,6,3,7,5,2,4]=>000111
[1,7,2,6,4,5,3]=>[1,5,6,7,2,4,3]=>[1,5,2,7,3,6,4]=>000111
[1,7,2,6,5,3,4]=>[1,5,6,2,7,3,4]=>[1,6,3,7,4,2,5]=>001011
[1,7,2,6,5,4,3]=>[1,4,5,6,7,2,3]=>[1,6,2,4,7,3,5]=>000011
[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]=>[1,7,6,5,4,2,3]=>001111
[1,7,3,2,4,6,5]=>[1,3,6,2,7,4,5]=>[1,6,4,2,3,7,5]=>001011
[1,7,3,2,5,4,6]=>[1,3,5,7,2,4,6]=>[1,5,2,3,7,6,4]=>000111
[1,7,3,2,5,6,4]=>[1,3,6,7,2,5,4]=>[1,6,5,2,3,7,4]=>000111
[1,7,3,2,6,4,5]=>[1,3,6,7,2,4,5]=>[1,7,5,2,3,6,4]=>000111
[1,7,3,2,6,5,4]=>[1,3,5,6,7,2,4]=>[1,7,4,6,2,3,5]=>000011
[1,7,3,4,2,5,6]=>[1,4,7,3,2,5,6]=>[1,7,6,5,2,4,3]=>001111
[1,7,3,4,2,6,5]=>[1,4,6,3,7,2,5]=>[1,6,2,4,3,7,5]=>001011
[1,7,3,4,5,2,6]=>[1,5,7,3,4,2,6]=>[1,7,6,2,5,4,3]=>001111
[1,7,3,4,5,6,2]=>[1,6,7,3,4,5,2]=>[1,7,2,6,5,4,3]=>001111
[1,7,3,4,6,2,5]=>[1,6,7,3,4,2,5]=>[1,6,2,7,5,4,3]=>001111
[1,7,3,4,6,5,2]=>[1,5,6,3,7,4,2]=>[1,6,4,3,7,2,5]=>001011
[1,7,3,5,2,4,6]=>[1,5,7,3,2,4,6]=>[1,5,2,7,6,4,3]=>001111
[1,7,3,5,2,6,4]=>[1,6,5,7,3,2,4]=>[1,5,3,6,2,7,4]=>000111
[1,7,3,5,4,2,6]=>[1,4,5,7,3,2,6]=>[1,5,3,7,6,2,4]=>000111
[1,7,3,5,4,6,2]=>[1,6,5,7,3,4,2]=>[1,5,3,7,2,6,4]=>000111
[1,7,3,5,6,2,4]=>[1,6,7,3,2,5,4]=>[1,6,5,2,7,4,3]=>001111
[1,7,3,5,6,4,2]=>[1,4,6,7,3,5,2]=>[1,6,5,3,7,2,4]=>000111
[1,7,3,6,2,4,5]=>[1,6,7,3,2,4,5]=>[1,7,5,2,6,4,3]=>001111
[1,7,3,6,2,5,4]=>[1,5,6,7,3,2,4]=>[1,6,2,5,3,7,4]=>000111
[1,7,3,6,4,2,5]=>[1,4,6,7,3,2,5]=>[1,7,5,3,6,2,4]=>000111
[1,7,3,6,4,5,2]=>[1,5,6,7,3,4,2]=>[1,7,2,5,3,6,4]=>000111
[1,7,3,6,5,2,4]=>[1,5,6,3,7,2,4]=>[1,7,4,3,6,2,5]=>001011
[1,7,3,6,5,4,2]=>[1,4,5,6,7,3,2]=>[1,7,2,4,6,3,5]=>000011
[1,7,4,2,3,5,6]=>[1,4,2,7,3,5,6]=>[1,7,6,5,3,2,4]=>010111
[1,7,4,2,3,6,5]=>[1,4,2,6,7,3,5]=>[1,6,3,2,4,7,5]=>010011
[1,7,4,2,5,3,6]=>[1,5,4,7,2,3,6]=>[1,5,2,7,6,3,4]=>000111
[1,7,4,2,5,6,3]=>[1,6,4,7,2,5,3]=>[1,6,5,2,7,3,4]=>000111
[1,7,4,2,6,3,5]=>[1,6,4,7,2,3,5]=>[1,7,5,2,6,3,4]=>000111
[1,7,4,2,6,5,3]=>[1,5,4,6,7,2,3]=>[1,7,3,4,6,2,5]=>000011
[1,7,4,3,2,5,6]=>[1,3,4,7,2,5,6]=>[1,7,6,5,2,3,4]=>000111
[1,7,4,3,2,6,5]=>[1,3,4,6,7,2,5]=>[1,6,2,3,4,7,5]=>000011
[1,7,4,3,5,2,6]=>[1,5,4,7,3,2,6]=>[1,7,6,2,5,3,4]=>000111
[1,7,4,3,5,6,2]=>[1,6,4,7,3,5,2]=>[1,7,2,6,5,3,4]=>000111
[1,7,4,3,6,2,5]=>[1,6,4,7,3,2,5]=>[1,6,2,7,5,3,4]=>000111
[1,7,4,3,6,5,2]=>[1,5,4,6,7,3,2]=>[1,6,3,4,7,2,5]=>000011
[1,7,4,5,2,3,6]=>[1,5,2,7,4,3,6]=>[1,7,6,3,2,5,4]=>010111
[1,7,4,5,2,6,3]=>[1,6,5,7,4,2,3]=>[1,6,2,7,3,5,4]=>000111
[1,7,4,5,3,2,6]=>[1,3,5,7,4,2,6]=>[1,7,6,2,3,5,4]=>000111
[1,7,4,5,3,6,2]=>[1,6,5,7,4,3,2]=>[1,7,2,6,3,5,4]=>000111
[1,7,4,5,6,2,3]=>[1,6,2,7,4,5,3]=>[1,7,3,2,6,5,4]=>010111
[1,7,4,5,6,3,2]=>[1,3,6,7,4,5,2]=>[1,7,2,3,6,5,4]=>000111
[1,7,4,6,2,3,5]=>[1,6,2,7,4,3,5]=>[1,6,3,2,7,5,4]=>010111
[1,7,4,6,2,5,3]=>[1,5,6,7,4,2,3]=>[1,7,3,6,2,5,4]=>000111
[1,7,4,6,3,2,5]=>[1,3,6,7,4,2,5]=>[1,6,2,3,7,5,4]=>000111
[1,7,4,6,3,5,2]=>[1,5,6,7,4,3,2]=>[1,6,3,7,2,5,4]=>000111
[1,7,4,6,5,2,3]=>[1,5,2,6,7,4,3]=>[1,6,4,7,3,2,5]=>010011
[1,7,4,6,5,3,2]=>[1,3,5,6,7,4,2]=>[1,6,4,7,2,3,5]=>000011
[1,7,5,2,3,4,6]=>[1,5,2,3,7,4,6]=>[1,7,6,4,3,2,5]=>011011
[1,7,5,2,3,6,4]=>[1,6,2,5,7,3,4]=>[1,6,3,2,7,4,5]=>010011
[1,7,5,2,4,3,6]=>[1,4,5,2,7,3,6]=>[1,4,2,7,6,3,5]=>001011
[1,7,5,2,4,6,3]=>[1,6,5,2,7,4,3]=>[1,6,4,2,7,3,5]=>001011
[1,7,5,2,6,3,4]=>[1,6,5,2,7,3,4]=>[1,7,4,2,6,3,5]=>001011
[1,7,5,2,6,4,3]=>[1,4,6,5,7,2,3]=>[1,7,3,6,2,4,5]=>000011
[1,7,5,3,2,4,6]=>[1,3,5,2,7,4,6]=>[1,7,6,4,2,3,5]=>001011
[1,7,5,3,2,6,4]=>[1,3,6,5,7,2,4]=>[1,6,2,3,7,4,5]=>000011
[1,7,5,3,4,2,6]=>[1,4,5,3,7,2,6]=>[1,7,6,2,4,3,5]=>001011
[1,7,5,3,4,6,2]=>[1,6,5,3,7,4,2]=>[1,7,2,6,4,3,5]=>001011
[1,7,5,3,6,2,4]=>[1,6,5,3,7,2,4]=>[1,6,2,7,4,3,5]=>001011
[1,7,5,3,6,4,2]=>[1,4,6,5,7,3,2]=>[1,6,3,7,2,4,5]=>000011
[1,7,5,4,2,3,6]=>[1,4,2,5,7,3,6]=>[1,7,6,3,2,4,5]=>010011
[1,7,5,4,2,6,3]=>[1,6,4,5,7,2,3]=>[1,6,2,7,3,4,5]=>000011
[1,7,5,4,3,2,6]=>[1,3,4,5,7,2,6]=>[1,7,6,2,3,4,5]=>000011
[1,7,5,4,3,6,2]=>[1,6,4,5,7,3,2]=>[1,7,2,6,3,4,5]=>000011
[1,7,5,4,6,2,3]=>[1,6,2,5,7,4,3]=>[1,7,3,2,6,4,5]=>010011
[1,7,5,4,6,3,2]=>[1,3,6,5,7,4,2]=>[1,7,2,3,6,4,5]=>000011
[1,7,5,6,2,3,4]=>[1,6,2,3,7,5,4]=>[1,7,4,3,2,6,5]=>011011
[1,7,5,6,2,4,3]=>[1,4,6,2,7,5,3]=>[1,4,2,7,3,6,5]=>001011
[1,7,5,6,3,2,4]=>[1,3,6,2,7,5,4]=>[1,7,4,2,3,6,5]=>001011
[1,7,5,6,3,4,2]=>[1,4,6,3,7,5,2]=>[1,7,2,4,3,6,5]=>001011
[1,7,5,6,4,2,3]=>[1,4,2,6,7,5,3]=>[1,7,3,2,4,6,5]=>010011
[1,7,5,6,4,3,2]=>[1,3,4,6,7,5,2]=>[1,7,2,3,4,6,5]=>000011
[1,7,6,2,3,4,5]=>[1,6,2,3,4,7,5]=>[1,7,5,4,3,2,6]=>011101
[1,7,6,2,3,5,4]=>[1,5,2,6,3,7,4]=>[1,5,3,2,7,4,6]=>010101
[1,7,6,2,4,3,5]=>[1,4,6,2,3,7,5]=>[1,4,2,7,5,3,6]=>001101
[1,7,6,2,4,5,3]=>[1,5,6,2,4,7,3]=>[1,5,4,2,7,3,6]=>001101
[1,7,6,2,5,3,4]=>[1,5,6,2,3,7,4]=>[1,7,4,2,5,3,6]=>001101
[1,7,6,2,5,4,3]=>[1,4,5,6,2,7,3]=>[1,7,3,5,2,4,6]=>000101
[1,7,6,3,2,4,5]=>[1,3,6,2,4,7,5]=>[1,7,5,4,2,3,6]=>001101
[1,7,6,3,2,5,4]=>[1,3,5,6,2,7,4]=>[1,5,2,3,7,4,6]=>000101
[1,7,6,3,4,2,5]=>[1,4,6,3,2,7,5]=>[1,7,5,2,4,3,6]=>001101
[1,7,6,3,4,5,2]=>[1,5,6,3,4,7,2]=>[1,7,2,5,4,3,6]=>001101
[1,7,6,3,5,2,4]=>[1,5,6,3,2,7,4]=>[1,5,2,7,4,3,6]=>001101
[1,7,6,3,5,4,2]=>[1,4,5,6,3,7,2]=>[1,5,3,7,2,4,6]=>000101
[1,7,6,4,2,3,5]=>[1,4,2,6,3,7,5]=>[1,7,5,3,2,4,6]=>010101
[1,7,6,4,2,5,3]=>[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>000101
[1,7,6,4,3,2,5]=>[1,3,4,6,2,7,5]=>[1,7,5,2,3,4,6]=>000101
[1,7,6,4,3,5,2]=>[1,5,4,6,3,7,2]=>[1,7,2,5,3,4,6]=>000101
[1,7,6,4,5,2,3]=>[1,5,2,6,4,7,3]=>[1,7,3,2,5,4,6]=>010101
[1,7,6,4,5,3,2]=>[1,3,5,6,4,7,2]=>[1,7,2,3,5,4,6]=>000101
[1,7,6,5,2,3,4]=>[1,5,2,3,6,7,4]=>[1,7,4,3,2,5,6]=>011001
[1,7,6,5,2,4,3]=>[1,4,5,2,6,7,3]=>[1,4,2,7,3,5,6]=>001001
[1,7,6,5,3,2,4]=>[1,3,5,2,6,7,4]=>[1,7,4,2,3,5,6]=>001001
[1,7,6,5,3,4,2]=>[1,4,5,3,6,7,2]=>[1,7,2,4,3,5,6]=>001001
[1,7,6,5,4,2,3]=>[1,4,2,5,6,7,3]=>[1,7,3,2,4,5,6]=>010001
[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>000001
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>100001
[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>100010
[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>100001
[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]=>100011
[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>100001
[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>100100
[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>100101
[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>100010
[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[2,1,3,5,6,7,4]=>100001
[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>[2,1,3,5,7,6,4]=>100011
[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>[2,1,3,5,7,4,6]=>100001
[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>[2,1,3,6,5,4,7]=>100110
[2,1,3,6,4,7,5]=>[2,1,3,7,6,4,5]=>[2,1,3,7,5,6,4]=>100011
[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[2,1,3,6,4,5,7]=>100010
[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>[2,1,3,6,5,7,4]=>100011
[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>[2,1,3,6,7,5,4]=>100101
[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]=>[2,1,3,6,7,4,5]=>100001
[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]=>100111
[2,1,3,7,4,6,5]=>[2,1,3,6,7,4,5]=>[2,1,3,6,4,7,5]=>100011
[2,1,3,7,5,4,6]=>[2,1,3,5,7,4,6]=>[2,1,3,7,6,4,5]=>100011
[2,1,3,7,5,6,4]=>[2,1,3,6,7,5,4]=>[2,1,3,7,4,6,5]=>100011
[2,1,3,7,6,4,5]=>[2,1,3,6,4,7,5]=>[2,1,3,7,5,4,6]=>100101
[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>100001
[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>101000
[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>101001
[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>101010
[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>101001
[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]=>101011
[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,5,6]=>101001
[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>100100
[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>100101
[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[2,1,4,5,6,3,7]=>100010
[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[2,1,4,5,6,7,3]=>100001
[2,1,4,5,7,3,6]=>[2,1,7,4,5,3,6]=>[2,1,4,5,7,6,3]=>100011
[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>[2,1,4,5,7,3,6]=>100001
[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>[2,1,4,6,5,3,7]=>100110
[2,1,4,6,3,7,5]=>[2,1,7,4,6,3,5]=>[2,1,4,7,5,6,3]=>100011
[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>[2,1,4,6,3,5,7]=>100010
[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>[2,1,4,6,5,7,3]=>100011
[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>[2,1,4,6,7,5,3]=>100101
[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]=>[2,1,4,6,7,3,5]=>100001
[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>[2,1,4,7,6,5,3]=>100111
[2,1,4,7,3,6,5]=>[2,1,6,4,7,3,5]=>[2,1,4,6,3,7,5]=>100011
[2,1,4,7,5,3,6]=>[2,1,5,4,7,3,6]=>[2,1,4,7,6,3,5]=>100011
[2,1,4,7,5,6,3]=>[2,1,6,4,7,5,3]=>[2,1,4,7,3,6,5]=>100011
[2,1,4,7,6,3,5]=>[2,1,6,4,3,7,5]=>[2,1,4,7,5,3,6]=>100101
[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>[2,1,4,7,3,5,6]=>100001
[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>[2,1,5,4,3,6,7]=>101100
[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]=>101101
[2,1,5,3,6,4,7]=>[2,1,6,5,3,4,7]=>[2,1,6,4,5,3,7]=>100110
[2,1,5,3,6,7,4]=>[2,1,7,5,3,6,4]=>[2,1,6,7,4,5,3]=>100101
[2,1,5,3,7,4,6]=>[2,1,7,5,3,4,6]=>[2,1,7,6,4,5,3]=>100111
[2,1,5,3,7,6,4]=>[2,1,6,5,3,7,4]=>[2,1,7,4,5,3,6]=>100101
[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[2,1,5,3,4,6,7]=>100100
[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[2,1,5,3,4,7,6]=>100101
[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[2,1,5,4,6,3,7]=>100110
[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>[2,1,5,4,6,7,3]=>100101
[2,1,5,4,7,3,6]=>[2,1,7,5,4,3,6]=>[2,1,5,4,7,6,3]=>100111
[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>[2,1,5,4,7,3,6]=>100101
[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>[2,1,5,6,4,3,7]=>101010
[2,1,5,6,3,7,4]=>[2,1,7,6,5,3,4]=>[2,1,5,7,4,6,3]=>100011
[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]=>[2,1,5,6,3,4,7]=>100010
[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>[2,1,5,6,4,7,3]=>100011
[2,1,5,6,7,3,4]=>[2,1,7,3,5,6,4]=>[2,1,5,6,7,4,3]=>101001
[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]=>[2,1,5,6,7,3,4]=>100001
[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>[2,1,5,7,6,4,3]=>101011
[2,1,5,7,3,6,4]=>[2,1,6,7,5,3,4]=>[2,1,5,6,3,7,4]=>100011
[2,1,5,7,4,3,6]=>[2,1,4,7,5,3,6]=>[2,1,5,7,6,3,4]=>100011
[2,1,5,7,4,6,3]=>[2,1,6,7,5,4,3]=>[2,1,5,7,3,6,4]=>100011
[2,1,5,7,6,3,4]=>[2,1,6,3,5,7,4]=>[2,1,5,7,4,3,6]=>101001
[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]=>[2,1,5,7,3,4,6]=>100001
[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>[2,1,6,5,4,3,7]=>101110
[2,1,6,3,4,7,5]=>[2,1,7,3,6,4,5]=>[2,1,7,5,6,4,3]=>101011
[2,1,6,3,5,4,7]=>[2,1,5,6,3,4,7]=>[2,1,5,3,6,4,7]=>100110
[2,1,6,3,5,7,4]=>[2,1,7,6,3,5,4]=>[2,1,7,4,6,5,3]=>100111
[2,1,6,3,7,4,5]=>[2,1,7,6,3,4,5]=>[2,1,6,4,7,5,3]=>100111
[2,1,6,3,7,5,4]=>[2,1,5,7,6,3,4]=>[2,1,6,3,5,7,4]=>100011
[2,1,6,4,3,5,7]=>[2,1,4,6,3,5,7]=>[2,1,6,5,3,4,7]=>100110
[2,1,6,4,3,7,5]=>[2,1,4,7,6,3,5]=>[2,1,7,5,6,3,4]=>100011
[2,1,6,4,5,3,7]=>[2,1,5,6,4,3,7]=>[2,1,6,3,5,4,7]=>100110
[2,1,6,4,5,7,3]=>[2,1,7,6,4,5,3]=>[2,1,6,5,4,7,3]=>100111
[2,1,6,4,7,3,5]=>[2,1,7,6,4,3,5]=>[2,1,7,5,4,6,3]=>100111
[2,1,6,4,7,5,3]=>[2,1,5,7,6,4,3]=>[2,1,7,3,5,6,4]=>100011
[2,1,6,5,3,4,7]=>[2,1,5,3,6,4,7]=>[2,1,6,4,3,5,7]=>101010
[2,1,6,5,3,7,4]=>[2,1,7,5,6,3,4]=>[2,1,7,4,5,6,3]=>100011
[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>100010
[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>[2,1,6,4,5,7,3]=>100011
[2,1,6,5,7,3,4]=>[2,1,7,3,6,5,4]=>[2,1,6,5,7,4,3]=>101011
[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]=>[2,1,6,5,7,3,4]=>100011
[2,1,6,7,3,4,5]=>[2,1,7,3,4,6,5]=>[2,1,6,7,5,4,3]=>101101
[2,1,6,7,3,5,4]=>[2,1,5,7,3,6,4]=>[2,1,5,3,6,7,4]=>100101
[2,1,6,7,4,3,5]=>[2,1,4,7,3,6,5]=>[2,1,6,7,5,3,4]=>100101
[2,1,6,7,4,5,3]=>[2,1,5,7,4,6,3]=>[2,1,6,7,3,5,4]=>100101
[2,1,6,7,5,3,4]=>[2,1,5,3,7,6,4]=>[2,1,6,7,4,3,5]=>101001
[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]=>[2,1,6,7,3,4,5]=>100001
[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>[2,1,7,6,5,4,3]=>101111
[2,1,7,3,4,6,5]=>[2,1,6,3,7,4,5]=>[2,1,6,4,3,7,5]=>101011
[2,1,7,3,5,4,6]=>[2,1,5,7,3,4,6]=>[2,1,5,3,7,6,4]=>100111
[2,1,7,3,5,6,4]=>[2,1,6,7,3,5,4]=>[2,1,6,5,3,7,4]=>100111
[2,1,7,3,6,4,5]=>[2,1,6,7,3,4,5]=>[2,1,7,5,3,6,4]=>100111
[2,1,7,3,6,5,4]=>[2,1,5,6,7,3,4]=>[2,1,7,4,6,3,5]=>100011
[2,1,7,4,3,5,6]=>[2,1,4,7,3,5,6]=>[2,1,7,6,5,3,4]=>100111
[2,1,7,4,3,6,5]=>[2,1,4,6,7,3,5]=>[2,1,6,3,4,7,5]=>100011
[2,1,7,4,5,3,6]=>[2,1,5,7,4,3,6]=>[2,1,7,6,3,5,4]=>100111
[2,1,7,4,5,6,3]=>[2,1,6,7,4,5,3]=>[2,1,7,3,6,5,4]=>100111
[2,1,7,4,6,3,5]=>[2,1,6,7,4,3,5]=>[2,1,6,3,7,5,4]=>100111
[2,1,7,4,6,5,3]=>[2,1,5,6,7,4,3]=>[2,1,6,4,7,3,5]=>100011
[2,1,7,5,3,4,6]=>[2,1,5,3,7,4,6]=>[2,1,7,6,4,3,5]=>101011
[2,1,7,5,3,6,4]=>[2,1,6,5,7,3,4]=>[2,1,6,3,7,4,5]=>100011
[2,1,7,5,4,3,6]=>[2,1,4,5,7,3,6]=>[2,1,7,6,3,4,5]=>100011
[2,1,7,5,4,6,3]=>[2,1,6,5,7,4,3]=>[2,1,7,3,6,4,5]=>100011
[2,1,7,5,6,3,4]=>[2,1,6,3,7,5,4]=>[2,1,7,4,3,6,5]=>101011
[2,1,7,5,6,4,3]=>[2,1,4,6,7,5,3]=>[2,1,7,3,4,6,5]=>100011
[2,1,7,6,3,4,5]=>[2,1,6,3,4,7,5]=>[2,1,7,5,4,3,6]=>101101
[2,1,7,6,3,5,4]=>[2,1,5,6,3,7,4]=>[2,1,5,3,7,4,6]=>100101
[2,1,7,6,4,3,5]=>[2,1,4,6,3,7,5]=>[2,1,7,5,3,4,6]=>100101
[2,1,7,6,4,5,3]=>[2,1,5,6,4,7,3]=>[2,1,7,3,5,4,6]=>100101
[2,1,7,6,5,3,4]=>[2,1,5,3,6,7,4]=>[2,1,7,4,3,5,6]=>101001
[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>100001
[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>010000
[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>010001
[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>010010
[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>010001
[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>[2,3,1,4,7,6,5]=>010011
[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,5,6]=>010001
[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>010100
[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>010101
[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>010010
[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[2,3,1,5,6,7,4]=>010001
[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>[2,3,1,5,7,6,4]=>010011
[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>[2,3,1,5,7,4,6]=>010001
[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>[2,3,1,6,5,4,7]=>010110
[2,3,1,6,4,7,5]=>[3,2,1,7,6,4,5]=>[2,3,1,7,5,6,4]=>010011
[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>[2,3,1,6,4,5,7]=>010010
[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>[2,3,1,6,5,7,4]=>010011
[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>[2,3,1,6,7,5,4]=>010101
[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]=>[2,3,1,6,7,4,5]=>010001
[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>[2,3,1,7,6,5,4]=>010111
[2,3,1,7,4,6,5]=>[3,2,1,6,7,4,5]=>[2,3,1,6,4,7,5]=>010011
[2,3,1,7,5,4,6]=>[3,2,1,5,7,4,6]=>[2,3,1,7,6,4,5]=>010011
[2,3,1,7,5,6,4]=>[3,2,1,6,7,5,4]=>[2,3,1,7,4,6,5]=>010011
[2,3,1,7,6,4,5]=>[3,2,1,6,4,7,5]=>[2,3,1,7,5,4,6]=>010101
[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>[2,3,1,7,4,5,6]=>010001
[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,3,4,1,5,6,7]=>001000
[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[2,3,4,1,5,7,6]=>001001
[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[2,3,4,1,6,5,7]=>001010
[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[2,3,4,1,6,7,5]=>001001
[2,3,4,1,7,5,6]=>[4,2,3,1,7,5,6]=>[2,3,4,1,7,6,5]=>001011
[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>[2,3,4,1,7,5,6]=>001001
[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,3,4,5,1,6,7]=>000100
[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[2,3,4,5,1,7,6]=>000101
[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,3,4,5,6,1,7]=>000010
[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,7,1]=>000001
[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[2,3,4,5,7,6,1]=>000011
[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>[2,3,4,5,7,1,6]=>000001
[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>[2,3,4,6,5,1,7]=>000110
[2,3,4,6,1,7,5]=>[7,2,3,4,6,1,5]=>[2,3,4,7,5,6,1]=>000011
[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>[2,3,4,6,1,5,7]=>000010
[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>[2,3,4,6,5,7,1]=>000011
[2,3,4,6,7,1,5]=>[7,2,3,4,1,6,5]=>[2,3,4,6,7,5,1]=>000101
[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]=>[2,3,4,6,7,1,5]=>000001
[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[2,3,4,7,6,5,1]=>000111
[2,3,4,7,1,6,5]=>[6,2,3,4,7,1,5]=>[2,3,4,6,1,7,5]=>000011
[2,3,4,7,5,1,6]=>[5,2,3,4,7,1,6]=>[2,3,4,7,6,1,5]=>000011
[2,3,4,7,5,6,1]=>[6,2,3,4,7,5,1]=>[2,3,4,7,1,6,5]=>000011
[2,3,4,7,6,1,5]=>[6,2,3,4,1,7,5]=>[2,3,4,7,5,1,6]=>000101
[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>[2,3,4,7,1,5,6]=>000001
[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>[2,3,5,4,1,6,7]=>001100
[2,3,5,1,4,7,6]=>[5,2,3,1,4,7,6]=>[2,3,5,4,1,7,6]=>001101
[2,3,5,1,6,4,7]=>[6,2,3,5,1,4,7]=>[2,3,6,4,5,1,7]=>000110
[2,3,5,1,6,7,4]=>[7,2,3,5,1,6,4]=>[2,3,6,7,4,5,1]=>000101
[2,3,5,1,7,4,6]=>[7,2,3,5,1,4,6]=>[2,3,7,6,4,5,1]=>000111
[2,3,5,1,7,6,4]=>[6,2,3,5,1,7,4]=>[2,3,7,4,5,1,6]=>000101
[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>[2,3,5,1,4,6,7]=>000100
[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>[2,3,5,1,4,7,6]=>000101
[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>[2,3,5,4,6,1,7]=>000110
[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>[2,3,5,4,6,7,1]=>000101
[2,3,5,4,7,1,6]=>[7,2,3,5,4,1,6]=>[2,3,5,4,7,6,1]=>000111
[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>[2,3,5,4,7,1,6]=>000101
[2,3,5,6,1,4,7]=>[6,2,3,1,5,4,7]=>[2,3,5,6,4,1,7]=>001010
[2,3,5,6,1,7,4]=>[7,2,3,6,5,1,4]=>[2,3,5,7,4,6,1]=>000011
[2,3,5,6,4,1,7]=>[4,2,3,6,5,1,7]=>[2,3,5,6,1,4,7]=>000010
[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>[2,3,5,6,4,7,1]=>000011
[2,3,5,6,7,1,4]=>[7,2,3,1,5,6,4]=>[2,3,5,6,7,4,1]=>001001
[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]=>[2,3,5,6,7,1,4]=>000001
[2,3,5,7,1,4,6]=>[7,2,3,1,5,4,6]=>[2,3,5,7,6,4,1]=>001011
[2,3,5,7,1,6,4]=>[6,2,3,7,5,1,4]=>[2,3,5,6,1,7,4]=>000011
[2,3,5,7,4,1,6]=>[4,2,3,7,5,1,6]=>[2,3,5,7,6,1,4]=>000011
[2,3,5,7,4,6,1]=>[6,2,3,7,5,4,1]=>[2,3,5,7,1,6,4]=>000011
[2,3,5,7,6,1,4]=>[6,2,3,1,5,7,4]=>[2,3,5,7,4,1,6]=>001001
[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]=>[2,3,5,7,1,4,6]=>000001
[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>[2,3,6,5,4,1,7]=>001110
[2,3,6,1,4,7,5]=>[7,2,3,1,6,4,5]=>[2,3,7,5,6,4,1]=>001011
[2,3,6,1,5,4,7]=>[5,2,3,6,1,4,7]=>[2,3,5,1,6,4,7]=>000110
[2,3,6,1,5,7,4]=>[7,2,3,6,1,5,4]=>[2,3,7,4,6,5,1]=>000111
[2,3,6,1,7,4,5]=>[7,2,3,6,1,4,5]=>[2,3,6,4,7,5,1]=>000111
[2,3,6,1,7,5,4]=>[5,2,3,7,6,1,4]=>[2,3,6,1,5,7,4]=>000011
[2,3,6,4,1,5,7]=>[4,2,3,6,1,5,7]=>[2,3,6,5,1,4,7]=>000110
[2,3,6,4,1,7,5]=>[4,2,3,7,6,1,5]=>[2,3,7,5,6,1,4]=>000011
[2,3,6,4,5,1,7]=>[5,2,3,6,4,1,7]=>[2,3,6,1,5,4,7]=>000110
[2,3,6,4,5,7,1]=>[7,2,3,6,4,5,1]=>[2,3,6,5,4,7,1]=>000111
[2,3,6,4,7,1,5]=>[7,2,3,6,4,1,5]=>[2,3,7,5,4,6,1]=>000111
[2,3,6,4,7,5,1]=>[5,2,3,7,6,4,1]=>[2,3,7,1,5,6,4]=>000011
[2,3,6,5,1,4,7]=>[5,2,3,1,6,4,7]=>[2,3,6,4,1,5,7]=>001010
[2,3,6,5,1,7,4]=>[7,2,3,5,6,1,4]=>[2,3,7,4,5,6,1]=>000011
[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]=>[2,3,6,1,4,5,7]=>000010
[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>[2,3,6,4,5,7,1]=>000011
[2,3,6,5,7,1,4]=>[7,2,3,1,6,5,4]=>[2,3,6,5,7,4,1]=>001011
[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]=>[2,3,6,5,7,1,4]=>000011
[2,3,6,7,1,4,5]=>[7,2,3,1,4,6,5]=>[2,3,6,7,5,4,1]=>001101
[2,3,6,7,1,5,4]=>[5,2,3,7,1,6,4]=>[2,3,5,1,6,7,4]=>000101
[2,3,6,7,4,1,5]=>[4,2,3,7,1,6,5]=>[2,3,6,7,5,1,4]=>000101
[2,3,6,7,4,5,1]=>[5,2,3,7,4,6,1]=>[2,3,6,7,1,5,4]=>000101
[2,3,6,7,5,1,4]=>[5,2,3,1,7,6,4]=>[2,3,6,7,4,1,5]=>001001
[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]=>[2,3,6,7,1,4,5]=>000001
[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[2,3,7,6,5,4,1]=>001111
[2,3,7,1,4,6,5]=>[6,2,3,1,7,4,5]=>[2,3,6,4,1,7,5]=>001011
[2,3,7,1,5,4,6]=>[5,2,3,7,1,4,6]=>[2,3,5,1,7,6,4]=>000111
[2,3,7,1,5,6,4]=>[6,2,3,7,1,5,4]=>[2,3,6,5,1,7,4]=>000111
[2,3,7,1,6,4,5]=>[6,2,3,7,1,4,5]=>[2,3,7,5,1,6,4]=>000111
[2,3,7,1,6,5,4]=>[5,2,3,6,7,1,4]=>[2,3,7,4,6,1,5]=>000011
[2,3,7,4,1,5,6]=>[4,2,3,7,1,5,6]=>[2,3,7,6,5,1,4]=>000111
[2,3,7,4,1,6,5]=>[4,2,3,6,7,1,5]=>[2,3,6,1,4,7,5]=>000011
[2,3,7,4,5,1,6]=>[5,2,3,7,4,1,6]=>[2,3,7,6,1,5,4]=>000111
[2,3,7,4,5,6,1]=>[6,2,3,7,4,5,1]=>[2,3,7,1,6,5,4]=>000111
[2,3,7,4,6,1,5]=>[6,2,3,7,4,1,5]=>[2,3,6,1,7,5,4]=>000111
[2,3,7,4,6,5,1]=>[5,2,3,6,7,4,1]=>[2,3,6,4,7,1,5]=>000011
[2,3,7,5,1,4,6]=>[5,2,3,1,7,4,6]=>[2,3,7,6,4,1,5]=>001011
[2,3,7,5,1,6,4]=>[6,2,3,5,7,1,4]=>[2,3,6,1,7,4,5]=>000011
[2,3,7,5,4,1,6]=>[4,2,3,5,7,1,6]=>[2,3,7,6,1,4,5]=>000011
[2,3,7,5,4,6,1]=>[6,2,3,5,7,4,1]=>[2,3,7,1,6,4,5]=>000011
[2,3,7,5,6,1,4]=>[6,2,3,1,7,5,4]=>[2,3,7,4,1,6,5]=>001011
[2,3,7,5,6,4,1]=>[4,2,3,6,7,5,1]=>[2,3,7,1,4,6,5]=>000011
[2,3,7,6,1,4,5]=>[6,2,3,1,4,7,5]=>[2,3,7,5,4,1,6]=>001101
[2,3,7,6,1,5,4]=>[5,2,3,6,1,7,4]=>[2,3,5,1,7,4,6]=>000101
[2,3,7,6,4,1,5]=>[4,2,3,6,1,7,5]=>[2,3,7,5,1,4,6]=>000101
[2,3,7,6,4,5,1]=>[5,2,3,6,4,7,1]=>[2,3,7,1,5,4,6]=>000101
[2,3,7,6,5,1,4]=>[5,2,3,1,6,7,4]=>[2,3,7,4,1,5,6]=>001001
[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>[2,3,7,1,4,5,6]=>000001
[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,3,1,5,6,7]=>011000
[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>[2,4,3,1,5,7,6]=>011001
[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>[2,4,3,1,6,5,7]=>011010
[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>[2,4,3,1,6,7,5]=>011001
[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>[2,4,3,1,7,6,5]=>011011
[2,4,1,3,7,6,5]=>[4,2,1,3,6,7,5]=>[2,4,3,1,7,5,6]=>011001
[2,4,1,5,3,6,7]=>[5,2,4,1,3,6,7]=>[2,5,3,4,1,6,7]=>001100
[2,4,1,5,3,7,6]=>[5,2,4,1,3,7,6]=>[2,5,3,4,1,7,6]=>001101
[2,4,1,5,6,3,7]=>[6,2,4,1,5,3,7]=>[2,5,6,3,4,1,7]=>001010
[2,4,1,5,6,7,3]=>[7,2,4,1,5,6,3]=>[2,5,6,7,3,4,1]=>001001
[2,4,1,5,7,3,6]=>[7,2,4,1,5,3,6]=>[2,5,7,6,3,4,1]=>001011
[2,4,1,5,7,6,3]=>[6,2,4,1,5,7,3]=>[2,5,7,3,4,1,6]=>001001
[2,4,1,6,3,5,7]=>[6,2,4,1,3,5,7]=>[2,6,5,3,4,1,7]=>001110
[2,4,1,6,3,7,5]=>[7,2,4,1,6,3,5]=>[2,7,5,6,3,4,1]=>001011
[2,4,1,6,5,3,7]=>[5,2,4,1,6,3,7]=>[2,6,3,4,1,5,7]=>001010
[2,4,1,6,5,7,3]=>[7,2,4,1,6,5,3]=>[2,6,5,7,3,4,1]=>001011
[2,4,1,6,7,3,5]=>[7,2,4,1,3,6,5]=>[2,6,7,5,3,4,1]=>001101
[2,4,1,6,7,5,3]=>[5,2,4,1,7,6,3]=>[2,6,7,3,4,1,5]=>001001
[2,4,1,7,3,5,6]=>[7,2,4,1,3,5,6]=>[2,7,6,5,3,4,1]=>001111
[2,4,1,7,3,6,5]=>[6,2,4,1,7,3,5]=>[2,6,3,4,1,7,5]=>001011
[2,4,1,7,5,3,6]=>[5,2,4,1,7,3,6]=>[2,7,6,3,4,1,5]=>001011
[2,4,1,7,5,6,3]=>[6,2,4,1,7,5,3]=>[2,7,3,4,1,6,5]=>001011
[2,4,1,7,6,3,5]=>[6,2,4,1,3,7,5]=>[2,7,5,3,4,1,6]=>001101
[2,4,1,7,6,5,3]=>[5,2,4,1,6,7,3]=>[2,7,3,4,1,5,6]=>001001
[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>[2,4,1,3,5,6,7]=>001000
[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>[2,4,1,3,5,7,6]=>001001
[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>[2,4,1,3,6,5,7]=>001010
[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>[2,4,1,3,6,7,5]=>001001
[2,4,3,1,7,5,6]=>[3,2,4,1,7,5,6]=>[2,4,1,3,7,6,5]=>001011
[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>[2,4,1,3,7,5,6]=>001001
[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[2,4,3,5,1,6,7]=>001100
[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>[2,4,3,5,1,7,6]=>001101
[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>[2,4,3,5,6,1,7]=>001010
[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>[2,4,3,5,6,7,1]=>001001
[2,4,3,5,7,1,6]=>[7,2,4,3,5,1,6]=>[2,4,3,5,7,6,1]=>001011
[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>[2,4,3,5,7,1,6]=>001001
[2,4,3,6,1,5,7]=>[6,2,4,3,1,5,7]=>[2,4,3,6,5,1,7]=>001110
[2,4,3,6,1,7,5]=>[7,2,4,3,6,1,5]=>[2,4,3,7,5,6,1]=>001011
[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]=>[2,4,3,6,1,5,7]=>001010
[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>[2,4,3,6,5,7,1]=>001011
[2,4,3,6,7,1,5]=>[7,2,4,3,1,6,5]=>[2,4,3,6,7,5,1]=>001101
[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]=>[2,4,3,6,7,1,5]=>001001
[2,4,3,7,1,5,6]=>[7,2,4,3,1,5,6]=>[2,4,3,7,6,5,1]=>001111
[2,4,3,7,1,6,5]=>[6,2,4,3,7,1,5]=>[2,4,3,6,1,7,5]=>001011
[2,4,3,7,5,1,6]=>[5,2,4,3,7,1,6]=>[2,4,3,7,6,1,5]=>001011
[2,4,3,7,5,6,1]=>[6,2,4,3,7,5,1]=>[2,4,3,7,1,6,5]=>001011
[2,4,3,7,6,1,5]=>[6,2,4,3,1,7,5]=>[2,4,3,7,5,1,6]=>001101
[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>[2,4,3,7,1,5,6]=>001001
[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>[2,4,5,3,1,6,7]=>010100
[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>[2,4,5,3,1,7,6]=>010101
[2,4,5,1,6,3,7]=>[6,2,5,4,1,3,7]=>[2,4,6,3,5,1,7]=>000110
[2,4,5,1,6,7,3]=>[7,2,5,4,1,6,3]=>[2,4,6,7,3,5,1]=>000101
[2,4,5,1,7,3,6]=>[7,2,5,4,1,3,6]=>[2,4,7,6,3,5,1]=>000111
[2,4,5,1,7,6,3]=>[6,2,5,4,1,7,3]=>[2,4,7,3,5,1,6]=>000101
[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]=>[2,4,5,1,3,6,7]=>000100
[2,4,5,3,1,7,6]=>[3,2,5,4,1,7,6]=>[2,4,5,1,3,7,6]=>000101
[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>[2,4,5,3,6,1,7]=>000110
[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>[2,4,5,3,6,7,1]=>000101
[2,4,5,3,7,1,6]=>[7,2,5,4,3,1,6]=>[2,4,5,3,7,6,1]=>000111
[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]=>[2,4,5,3,7,1,6]=>000101
[2,4,5,6,1,3,7]=>[6,2,1,4,5,3,7]=>[2,4,5,6,3,1,7]=>010010
[2,4,5,6,1,7,3]=>[7,2,6,4,5,1,3]=>[2,4,5,7,3,6,1]=>000011
[2,4,5,6,3,1,7]=>[3,2,6,4,5,1,7]=>[2,4,5,6,1,3,7]=>000010
[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>[2,4,5,6,3,7,1]=>000011
[2,4,5,6,7,1,3]=>[7,2,1,4,5,6,3]=>[2,4,5,6,7,3,1]=>010001
[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]=>[2,4,5,6,7,1,3]=>000001
[2,4,5,7,1,3,6]=>[7,2,1,4,5,3,6]=>[2,4,5,7,6,3,1]=>010011
[2,4,5,7,1,6,3]=>[6,2,7,4,5,1,3]=>[2,4,5,6,1,7,3]=>000011
[2,4,5,7,3,1,6]=>[3,2,7,4,5,1,6]=>[2,4,5,7,6,1,3]=>000011
[2,4,5,7,3,6,1]=>[6,2,7,4,5,3,1]=>[2,4,5,7,1,6,3]=>000011
[2,4,5,7,6,1,3]=>[6,2,1,4,5,7,3]=>[2,4,5,7,3,1,6]=>010001
[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]=>[2,4,5,7,1,3,6]=>000001
[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[2,4,6,5,3,1,7]=>010110
[2,4,6,1,3,7,5]=>[7,2,1,4,6,3,5]=>[2,4,7,5,6,3,1]=>010011
[2,4,6,1,5,3,7]=>[5,2,6,4,1,3,7]=>[2,4,5,1,6,3,7]=>000110
[2,4,6,1,5,7,3]=>[7,2,6,4,1,5,3]=>[2,4,7,3,6,5,1]=>000111
[2,4,6,1,7,3,5]=>[7,2,6,4,1,3,5]=>[2,4,6,3,7,5,1]=>000111
[2,4,6,1,7,5,3]=>[5,2,7,4,6,1,3]=>[2,4,6,1,5,7,3]=>000011
[2,4,6,3,1,5,7]=>[3,2,6,4,1,5,7]=>[2,4,6,5,1,3,7]=>000110
[2,4,6,3,1,7,5]=>[3,2,7,4,6,1,5]=>[2,4,7,5,6,1,3]=>000011
[2,4,6,3,5,1,7]=>[5,2,6,4,3,1,7]=>[2,4,6,1,5,3,7]=>000110
[2,4,6,3,5,7,1]=>[7,2,6,4,3,5,1]=>[2,4,6,5,3,7,1]=>000111
[2,4,6,3,7,1,5]=>[7,2,6,4,3,1,5]=>[2,4,7,5,3,6,1]=>000111
[2,4,6,3,7,5,1]=>[5,2,7,4,6,3,1]=>[2,4,7,1,5,6,3]=>000011
[2,4,6,5,1,3,7]=>[5,2,1,4,6,3,7]=>[2,4,6,3,1,5,7]=>010010
[2,4,6,5,1,7,3]=>[7,2,5,4,6,1,3]=>[2,4,7,3,5,6,1]=>000011
[2,4,6,5,3,1,7]=>[3,2,5,4,6,1,7]=>[2,4,6,1,3,5,7]=>000010
[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]=>[2,4,6,3,5,7,1]=>000011
[2,4,6,5,7,1,3]=>[7,2,1,4,6,5,3]=>[2,4,6,5,7,3,1]=>010011
[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]=>[2,4,6,5,7,1,3]=>000011
[2,4,6,7,1,3,5]=>[7,2,1,4,3,6,5]=>[2,4,6,7,5,3,1]=>010101
[2,4,6,7,1,5,3]=>[5,2,7,4,1,6,3]=>[2,4,5,1,6,7,3]=>000101
[2,4,6,7,3,1,5]=>[3,2,7,4,1,6,5]=>[2,4,6,7,5,1,3]=>000101
[2,4,6,7,3,5,1]=>[5,2,7,4,3,6,1]=>[2,4,6,7,1,5,3]=>000101
[2,4,6,7,5,1,3]=>[5,2,1,4,7,6,3]=>[2,4,6,7,3,1,5]=>010001
[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]=>[2,4,6,7,1,3,5]=>000001
[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[2,4,7,6,5,3,1]=>010111
[2,4,7,1,3,6,5]=>[6,2,1,4,7,3,5]=>[2,4,6,3,1,7,5]=>010011
[2,4,7,1,5,3,6]=>[5,2,7,4,1,3,6]=>[2,4,5,1,7,6,3]=>000111
[2,4,7,1,5,6,3]=>[6,2,7,4,1,5,3]=>[2,4,6,5,1,7,3]=>000111
[2,4,7,1,6,3,5]=>[6,2,7,4,1,3,5]=>[2,4,7,5,1,6,3]=>000111
[2,4,7,1,6,5,3]=>[5,2,6,4,7,1,3]=>[2,4,7,3,6,1,5]=>000011
[2,4,7,3,1,5,6]=>[3,2,7,4,1,5,6]=>[2,4,7,6,5,1,3]=>000111
[2,4,7,3,1,6,5]=>[3,2,6,4,7,1,5]=>[2,4,6,1,3,7,5]=>000011
[2,4,7,3,5,1,6]=>[5,2,7,4,3,1,6]=>[2,4,7,6,1,5,3]=>000111
[2,4,7,3,5,6,1]=>[6,2,7,4,3,5,1]=>[2,4,7,1,6,5,3]=>000111
[2,4,7,3,6,1,5]=>[6,2,7,4,3,1,5]=>[2,4,6,1,7,5,3]=>000111
[2,4,7,3,6,5,1]=>[5,2,6,4,7,3,1]=>[2,4,6,3,7,1,5]=>000011
[2,4,7,5,1,3,6]=>[5,2,1,4,7,3,6]=>[2,4,7,6,3,1,5]=>010011
[2,4,7,5,1,6,3]=>[6,2,5,4,7,1,3]=>[2,4,6,1,7,3,5]=>000011
[2,4,7,5,3,1,6]=>[3,2,5,4,7,1,6]=>[2,4,7,6,1,3,5]=>000011
[2,4,7,5,3,6,1]=>[6,2,5,4,7,3,1]=>[2,4,7,1,6,3,5]=>000011
[2,4,7,5,6,1,3]=>[6,2,1,4,7,5,3]=>[2,4,7,3,1,6,5]=>010011
[2,4,7,5,6,3,1]=>[3,2,6,4,7,5,1]=>[2,4,7,1,3,6,5]=>000011
[2,4,7,6,1,3,5]=>[6,2,1,4,3,7,5]=>[2,4,7,5,3,1,6]=>010101
[2,4,7,6,1,5,3]=>[5,2,6,4,1,7,3]=>[2,4,5,1,7,3,6]=>000101
[2,4,7,6,3,1,5]=>[3,2,6,4,1,7,5]=>[2,4,7,5,1,3,6]=>000101
[2,4,7,6,3,5,1]=>[5,2,6,4,3,7,1]=>[2,4,7,1,5,3,6]=>000101
[2,4,7,6,5,1,3]=>[5,2,1,4,6,7,3]=>[2,4,7,3,1,5,6]=>010001
[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]=>[2,4,7,1,3,5,6]=>000001
[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[2,5,4,3,1,6,7]=>011100
[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>[2,5,4,3,1,7,6]=>011101
[2,5,1,3,6,4,7]=>[6,2,1,5,3,4,7]=>[2,6,4,5,3,1,7]=>010110
[2,5,1,3,6,7,4]=>[7,2,1,5,3,6,4]=>[2,6,7,4,5,3,1]=>010101
[2,5,1,3,7,4,6]=>[7,2,1,5,3,4,6]=>[2,7,6,4,5,3,1]=>010111
[2,5,1,3,7,6,4]=>[6,2,1,5,3,7,4]=>[2,7,4,5,3,1,6]=>010101
[2,5,1,4,3,6,7]=>[4,2,5,1,3,6,7]=>[2,4,1,5,3,6,7]=>001100
[2,5,1,4,3,7,6]=>[4,2,5,1,3,7,6]=>[2,4,1,5,3,7,6]=>001101
[2,5,1,4,6,3,7]=>[6,2,5,1,4,3,7]=>[2,6,3,5,4,1,7]=>001110
[2,5,1,4,6,7,3]=>[7,2,5,1,4,6,3]=>[2,6,7,3,5,4,1]=>001101
[2,5,1,4,7,3,6]=>[7,2,5,1,4,3,6]=>[2,7,6,3,5,4,1]=>001111
[2,5,1,4,7,6,3]=>[6,2,5,1,4,7,3]=>[2,7,3,5,4,1,6]=>001101
[2,5,1,6,3,4,7]=>[6,2,5,1,3,4,7]=>[2,5,3,6,4,1,7]=>001110
[2,5,1,6,3,7,4]=>[7,2,6,5,1,3,4]=>[2,6,3,7,4,5,1]=>000111
[2,5,1,6,4,3,7]=>[4,2,6,5,1,3,7]=>[2,5,1,4,6,3,7]=>000110
[2,5,1,6,4,7,3]=>[7,2,6,5,1,4,3]=>[2,7,3,6,4,5,1]=>000111
[2,5,1,6,7,3,4]=>[7,2,5,1,3,6,4]=>[2,5,3,6,7,4,1]=>001101
[2,5,1,6,7,4,3]=>[4,2,7,5,1,6,3]=>[2,5,1,4,6,7,3]=>000101
[2,5,1,7,3,4,6]=>[7,2,5,1,3,4,6]=>[2,5,3,7,6,4,1]=>001111
[2,5,1,7,3,6,4]=>[6,2,7,5,1,3,4]=>[2,7,4,5,1,6,3]=>000111
[2,5,1,7,4,3,6]=>[4,2,7,5,1,3,6]=>[2,5,1,4,7,6,3]=>000111
[2,5,1,7,4,6,3]=>[6,2,7,5,1,4,3]=>[2,6,4,5,1,7,3]=>000111
[2,5,1,7,6,3,4]=>[6,2,5,1,3,7,4]=>[2,5,3,7,4,1,6]=>001101
[2,5,1,7,6,4,3]=>[4,2,6,5,1,7,3]=>[2,5,1,4,7,3,6]=>000101
[2,5,3,1,4,6,7]=>[3,2,5,1,4,6,7]=>[2,5,4,1,3,6,7]=>001100
[2,5,3,1,4,7,6]=>[3,2,5,1,4,7,6]=>[2,5,4,1,3,7,6]=>001101
[2,5,3,1,6,4,7]=>[3,2,6,5,1,4,7]=>[2,6,4,5,1,3,7]=>000110
[2,5,3,1,6,7,4]=>[3,2,7,5,1,6,4]=>[2,6,7,4,5,1,3]=>000101
[2,5,3,1,7,4,6]=>[3,2,7,5,1,4,6]=>[2,7,6,4,5,1,3]=>000111
[2,5,3,1,7,6,4]=>[3,2,6,5,1,7,4]=>[2,7,4,5,1,3,6]=>000101
[2,5,3,4,1,6,7]=>[4,2,5,3,1,6,7]=>[2,5,1,4,3,6,7]=>001100
[2,5,3,4,1,7,6]=>[4,2,5,3,1,7,6]=>[2,5,1,4,3,7,6]=>001101
[2,5,3,4,6,1,7]=>[6,2,5,3,4,1,7]=>[2,5,4,3,6,1,7]=>001110
[2,5,3,4,6,7,1]=>[7,2,5,3,4,6,1]=>[2,5,4,3,6,7,1]=>001101
[2,5,3,4,7,1,6]=>[7,2,5,3,4,1,6]=>[2,5,4,3,7,6,1]=>001111
[2,5,3,4,7,6,1]=>[6,2,5,3,4,7,1]=>[2,5,4,3,7,1,6]=>001101
[2,5,3,6,1,4,7]=>[6,2,5,3,1,4,7]=>[2,6,4,3,5,1,7]=>001110
[2,5,3,6,1,7,4]=>[7,2,6,5,3,1,4]=>[2,7,4,5,3,6,1]=>000111
[2,5,3,6,4,1,7]=>[4,2,6,5,3,1,7]=>[2,6,1,4,5,3,7]=>000110
[2,5,3,6,4,7,1]=>[7,2,6,5,3,4,1]=>[2,6,4,5,3,7,1]=>000111
[2,5,3,6,7,1,4]=>[7,2,5,3,1,6,4]=>[2,6,7,4,3,5,1]=>001101
[2,5,3,6,7,4,1]=>[4,2,7,5,3,6,1]=>[2,6,7,1,4,5,3]=>000101
[2,5,3,7,1,4,6]=>[7,2,5,3,1,4,6]=>[2,7,6,4,3,5,1]=>001111
[2,5,3,7,1,6,4]=>[6,2,7,5,3,1,4]=>[2,6,1,7,4,5,3]=>000111
[2,5,3,7,4,1,6]=>[4,2,7,5,3,1,6]=>[2,7,6,1,4,5,3]=>000111
[2,5,3,7,4,6,1]=>[6,2,7,5,3,4,1]=>[2,7,1,6,4,5,3]=>000111
[2,5,3,7,6,1,4]=>[6,2,5,3,1,7,4]=>[2,7,4,3,5,1,6]=>001101
[2,5,3,7,6,4,1]=>[4,2,6,5,3,7,1]=>[2,7,1,4,5,3,6]=>000101
[2,5,4,1,3,6,7]=>[4,2,1,5,3,6,7]=>[2,5,3,1,4,6,7]=>010100
[2,5,4,1,3,7,6]=>[4,2,1,5,3,7,6]=>[2,5,3,1,4,7,6]=>010101
[2,5,4,1,6,3,7]=>[6,2,4,5,1,3,7]=>[2,6,3,4,5,1,7]=>000110
[2,5,4,1,6,7,3]=>[7,2,4,5,1,6,3]=>[2,6,7,3,4,5,1]=>000101
[2,5,4,1,7,3,6]=>[7,2,4,5,1,3,6]=>[2,7,6,3,4,5,1]=>000111
[2,5,4,1,7,6,3]=>[6,2,4,5,1,7,3]=>[2,7,3,4,5,1,6]=>000101
[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>[2,5,1,3,4,6,7]=>000100
[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]=>[2,5,1,3,4,7,6]=>000101
[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]=>[2,5,3,4,6,1,7]=>000110
[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>[2,5,3,4,6,7,1]=>000101
[2,5,4,3,7,1,6]=>[7,2,4,5,3,1,6]=>[2,5,3,4,7,6,1]=>000111
[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>[2,5,3,4,7,1,6]=>000101
[2,5,4,6,1,3,7]=>[6,2,1,5,4,3,7]=>[2,5,4,6,3,1,7]=>010110
[2,5,4,6,1,7,3]=>[7,2,6,5,4,1,3]=>[2,5,4,7,3,6,1]=>000111
[2,5,4,6,3,1,7]=>[3,2,6,5,4,1,7]=>[2,5,4,6,1,3,7]=>000110
[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>[2,5,4,6,3,7,1]=>000111
[2,5,4,6,7,1,3]=>[7,2,1,5,4,6,3]=>[2,5,4,6,7,3,1]=>010101
[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]=>[2,5,4,6,7,1,3]=>000101
[2,5,4,7,1,3,6]=>[7,2,1,5,4,3,6]=>[2,5,4,7,6,3,1]=>010111
[2,5,4,7,1,6,3]=>[6,2,7,5,4,1,3]=>[2,5,4,6,1,7,3]=>000111
[2,5,4,7,3,1,6]=>[3,2,7,5,4,1,6]=>[2,5,4,7,6,1,3]=>000111
[2,5,4,7,3,6,1]=>[6,2,7,5,4,3,1]=>[2,5,4,7,1,6,3]=>000111
[2,5,4,7,6,1,3]=>[6,2,1,5,4,7,3]=>[2,5,4,7,3,1,6]=>010101
[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]=>[2,5,4,7,1,3,6]=>000101
[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[2,5,6,4,3,1,7]=>011010
[2,5,6,1,3,7,4]=>[7,2,1,6,5,3,4]=>[2,5,7,4,6,3,1]=>010011
[2,5,6,1,4,3,7]=>[4,2,6,1,5,3,7]=>[2,4,1,5,6,3,7]=>001010
[2,5,6,1,4,7,3]=>[7,2,6,1,5,4,3]=>[2,5,7,3,6,4,1]=>001011
[2,5,6,1,7,3,4]=>[7,2,6,1,5,3,4]=>[2,5,6,3,7,4,1]=>001011
[2,5,6,1,7,4,3]=>[4,2,7,6,5,1,3]=>[2,5,6,1,4,7,3]=>000011
[2,5,6,3,1,4,7]=>[3,2,6,1,5,4,7]=>[2,5,6,4,1,3,7]=>001010
[2,5,6,3,1,7,4]=>[3,2,7,6,5,1,4]=>[2,5,7,4,6,1,3]=>000011
[2,5,6,3,4,1,7]=>[4,2,6,3,5,1,7]=>[2,5,6,1,4,3,7]=>001010
[2,5,6,3,4,7,1]=>[7,2,6,3,5,4,1]=>[2,5,6,4,3,7,1]=>001011
[2,5,6,3,7,1,4]=>[7,2,6,3,5,1,4]=>[2,5,7,4,3,6,1]=>001011
[2,5,6,3,7,4,1]=>[4,2,7,6,5,3,1]=>[2,5,7,1,4,6,3]=>000011
[2,5,6,4,1,3,7]=>[4,2,1,6,5,3,7]=>[2,5,6,3,1,4,7]=>010010
[2,5,6,4,1,7,3]=>[7,2,4,6,5,1,3]=>[2,5,7,3,4,6,1]=>000011
[2,5,6,4,3,1,7]=>[3,2,4,6,5,1,7]=>[2,5,6,1,3,4,7]=>000010
[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]=>[2,5,6,3,4,7,1]=>000011
[2,5,6,4,7,1,3]=>[7,2,1,6,5,4,3]=>[2,5,6,4,7,3,1]=>010011
[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]=>[2,5,6,4,7,1,3]=>000011
[2,5,6,7,1,3,4]=>[7,2,1,3,5,6,4]=>[2,5,6,7,4,3,1]=>011001
[2,5,6,7,1,4,3]=>[4,2,7,1,5,6,3]=>[2,4,1,5,6,7,3]=>001001
[2,5,6,7,3,1,4]=>[3,2,7,1,5,6,4]=>[2,5,6,7,4,1,3]=>001001
[2,5,6,7,3,4,1]=>[4,2,7,3,5,6,1]=>[2,5,6,7,1,4,3]=>001001
[2,5,6,7,4,1,3]=>[4,2,1,7,5,6,3]=>[2,5,6,7,3,1,4]=>010001
[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]=>[2,5,6,7,1,3,4]=>000001
[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[2,5,7,6,4,3,1]=>011011
[2,5,7,1,3,6,4]=>[6,2,1,7,5,3,4]=>[2,5,6,3,1,7,4]=>010011
[2,5,7,1,4,3,6]=>[4,2,7,1,5,3,6]=>[2,4,1,5,7,6,3]=>001011
[2,5,7,1,4,6,3]=>[6,2,7,1,5,4,3]=>[2,5,6,4,1,7,3]=>001011
[2,5,7,1,6,3,4]=>[6,2,7,1,5,3,4]=>[2,5,7,4,1,6,3]=>001011
[2,5,7,1,6,4,3]=>[4,2,6,7,5,1,3]=>[2,5,7,3,6,1,4]=>000011
[2,5,7,3,1,4,6]=>[3,2,7,1,5,4,6]=>[2,5,7,6,4,1,3]=>001011
[2,5,7,3,1,6,4]=>[3,2,6,7,5,1,4]=>[2,5,6,1,3,7,4]=>000011
[2,5,7,3,4,1,6]=>[4,2,7,3,5,1,6]=>[2,5,7,6,1,4,3]=>001011
[2,5,7,3,4,6,1]=>[6,2,7,3,5,4,1]=>[2,5,7,1,6,4,3]=>001011
[2,5,7,3,6,1,4]=>[6,2,7,3,5,1,4]=>[2,5,6,1,7,4,3]=>001011
[2,5,7,3,6,4,1]=>[4,2,6,7,5,3,1]=>[2,5,6,3,7,1,4]=>000011
[2,5,7,4,1,3,6]=>[4,2,1,7,5,3,6]=>[2,5,7,6,3,1,4]=>010011
[2,5,7,4,1,6,3]=>[6,2,4,7,5,1,3]=>[2,5,6,1,7,3,4]=>000011
[2,5,7,4,3,1,6]=>[3,2,4,7,5,1,6]=>[2,5,7,6,1,3,4]=>000011
[2,5,7,4,3,6,1]=>[6,2,4,7,5,3,1]=>[2,5,7,1,6,3,4]=>000011
[2,5,7,4,6,1,3]=>[6,2,1,7,5,4,3]=>[2,5,7,3,1,6,4]=>010011
[2,5,7,4,6,3,1]=>[3,2,6,7,5,4,1]=>[2,5,7,1,3,6,4]=>000011
[2,5,7,6,1,3,4]=>[6,2,1,3,5,7,4]=>[2,5,7,4,3,1,6]=>011001
[2,5,7,6,1,4,3]=>[4,2,6,1,5,7,3]=>[2,4,1,5,7,3,6]=>001001
[2,5,7,6,3,1,4]=>[3,2,6,1,5,7,4]=>[2,5,7,4,1,3,6]=>001001
[2,5,7,6,3,4,1]=>[4,2,6,3,5,7,1]=>[2,5,7,1,4,3,6]=>001001
[2,5,7,6,4,1,3]=>[4,2,1,6,5,7,3]=>[2,5,7,3,1,4,6]=>010001
[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]=>[2,5,7,1,3,4,6]=>000001
[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[2,6,5,4,3,1,7]=>011110
[2,6,1,3,4,7,5]=>[7,2,1,3,6,4,5]=>[2,7,5,6,4,3,1]=>011011
[2,6,1,3,5,4,7]=>[5,2,1,6,3,4,7]=>[2,5,3,1,6,4,7]=>010110
[2,6,1,3,5,7,4]=>[7,2,1,6,3,5,4]=>[2,7,4,6,5,3,1]=>010111
[2,6,1,3,7,4,5]=>[7,2,1,6,3,4,5]=>[2,6,4,7,5,3,1]=>010111
[2,6,1,3,7,5,4]=>[5,2,1,7,6,3,4]=>[2,6,3,1,5,7,4]=>010011
[2,6,1,4,3,5,7]=>[4,2,6,1,3,5,7]=>[2,4,1,6,5,3,7]=>001110
[2,6,1,4,3,7,5]=>[4,2,7,1,6,3,5]=>[2,4,1,7,5,6,3]=>001011
[2,6,1,4,5,3,7]=>[5,2,6,1,4,3,7]=>[2,5,4,1,6,3,7]=>001110
[2,6,1,4,5,7,3]=>[7,2,6,1,4,5,3]=>[2,7,3,6,5,4,1]=>001111
[2,6,1,4,7,3,5]=>[7,2,6,1,4,3,5]=>[2,6,3,7,5,4,1]=>001111
[2,6,1,4,7,5,3]=>[5,2,7,1,6,4,3]=>[2,6,4,1,5,7,3]=>001011
[2,6,1,5,3,4,7]=>[5,2,6,1,3,4,7]=>[2,6,4,1,5,3,7]=>001110
[2,6,1,5,3,7,4]=>[7,2,5,6,1,3,4]=>[2,7,4,6,3,5,1]=>000111
[2,6,1,5,4,3,7]=>[4,2,5,6,1,3,7]=>[2,6,3,5,1,4,7]=>000110
[2,6,1,5,4,7,3]=>[7,2,5,6,1,4,3]=>[2,6,4,7,3,5,1]=>000111
[2,6,1,5,7,3,4]=>[7,2,6,1,3,5,4]=>[2,6,5,3,7,4,1]=>001111
[2,6,1,5,7,4,3]=>[4,2,7,6,1,5,3]=>[2,6,5,1,4,7,3]=>000111
[2,6,1,7,3,4,5]=>[7,2,6,1,3,4,5]=>[2,7,5,3,6,4,1]=>001111
[2,6,1,7,3,5,4]=>[5,2,7,6,1,3,4]=>[2,5,1,7,4,6,3]=>000111
[2,6,1,7,4,3,5]=>[4,2,7,6,1,3,5]=>[2,7,5,1,4,6,3]=>000111
[2,6,1,7,4,5,3]=>[5,2,7,6,1,4,3]=>[2,5,1,6,4,7,3]=>000111
[2,6,1,7,5,3,4]=>[5,2,7,1,6,3,4]=>[2,7,4,1,5,6,3]=>001011
[2,6,1,7,5,4,3]=>[4,2,5,7,6,1,3]=>[2,7,3,5,6,1,4]=>000011
[2,6,3,1,4,5,7]=>[3,2,6,1,4,5,7]=>[2,6,5,4,1,3,7]=>001110
[2,6,3,1,4,7,5]=>[3,2,7,1,6,4,5]=>[2,7,5,6,4,1,3]=>001011
[2,6,3,1,5,4,7]=>[3,2,5,6,1,4,7]=>[2,5,1,3,6,4,7]=>000110
[2,6,3,1,5,7,4]=>[3,2,7,6,1,5,4]=>[2,7,4,6,5,1,3]=>000111
[2,6,3,1,7,4,5]=>[3,2,7,6,1,4,5]=>[2,6,4,7,5,1,3]=>000111
[2,6,3,1,7,5,4]=>[3,2,5,7,6,1,4]=>[2,6,1,3,5,7,4]=>000011
[2,6,3,4,1,5,7]=>[4,2,6,3,1,5,7]=>[2,6,5,1,4,3,7]=>001110
[2,6,3,4,1,7,5]=>[4,2,7,3,6,1,5]=>[2,7,5,6,1,4,3]=>001011
[2,6,3,4,5,1,7]=>[5,2,6,3,4,1,7]=>[2,6,1,5,4,3,7]=>001110
[2,6,3,4,5,7,1]=>[7,2,6,3,4,5,1]=>[2,6,5,4,3,7,1]=>001111
[2,6,3,4,7,1,5]=>[7,2,6,3,4,1,5]=>[2,7,5,4,3,6,1]=>001111
[2,6,3,4,7,5,1]=>[5,2,7,3,6,4,1]=>[2,7,1,5,6,4,3]=>001011
[2,6,3,5,1,4,7]=>[5,2,6,3,1,4,7]=>[2,5,1,6,4,3,7]=>001110
[2,6,3,5,1,7,4]=>[7,2,5,6,3,1,4]=>[2,5,3,7,4,6,1]=>000111
[2,6,3,5,4,1,7]=>[4,2,5,6,3,1,7]=>[2,5,3,6,1,4,7]=>000110
[2,6,3,5,4,7,1]=>[7,2,5,6,3,4,1]=>[2,5,3,6,4,7,1]=>000111
[2,6,3,5,7,1,4]=>[7,2,6,3,1,5,4]=>[2,7,4,3,6,5,1]=>001111
[2,6,3,5,7,4,1]=>[4,2,7,6,3,5,1]=>[2,7,1,4,6,5,3]=>000111
[2,6,3,7,1,4,5]=>[7,2,6,3,1,4,5]=>[2,6,4,3,7,5,1]=>001111
[2,6,3,7,1,5,4]=>[5,2,7,6,3,1,4]=>[2,7,4,6,1,5,3]=>000111
[2,6,3,7,4,1,5]=>[4,2,7,6,3,1,5]=>[2,6,1,4,7,5,3]=>000111
[2,6,3,7,4,5,1]=>[5,2,7,6,3,4,1]=>[2,6,4,7,1,5,3]=>000111
[2,6,3,7,5,1,4]=>[5,2,7,3,6,1,4]=>[2,6,1,5,7,4,3]=>001011
[2,6,3,7,5,4,1]=>[4,2,5,7,6,3,1]=>[2,6,3,5,7,1,4]=>000011
[2,6,4,1,3,5,7]=>[4,2,1,6,3,5,7]=>[2,6,5,3,1,4,7]=>010110
[2,6,4,1,3,7,5]=>[4,2,1,7,6,3,5]=>[2,7,5,6,3,1,4]=>010011
[2,6,4,1,5,3,7]=>[5,2,4,6,1,3,7]=>[2,5,1,6,3,4,7]=>000110
[2,6,4,1,5,7,3]=>[7,2,4,6,1,5,3]=>[2,7,3,4,6,5,1]=>000111
[2,6,4,1,7,3,5]=>[7,2,4,6,1,3,5]=>[2,6,3,4,7,5,1]=>000111
[2,6,4,1,7,5,3]=>[5,2,4,7,6,1,3]=>[2,6,1,5,7,3,4]=>000011
[2,6,4,3,1,5,7]=>[3,2,4,6,1,5,7]=>[2,6,5,1,3,4,7]=>000110
[2,6,4,3,1,7,5]=>[3,2,4,7,6,1,5]=>[2,7,5,6,1,3,4]=>000011
[2,6,4,3,5,1,7]=>[5,2,4,6,3,1,7]=>[2,6,1,5,3,4,7]=>000110
[2,6,4,3,5,7,1]=>[7,2,4,6,3,5,1]=>[2,6,5,3,4,7,1]=>000111
[2,6,4,3,7,1,5]=>[7,2,4,6,3,1,5]=>[2,7,5,3,4,6,1]=>000111
[2,6,4,3,7,5,1]=>[5,2,4,7,6,3,1]=>[2,7,1,5,6,3,4]=>000011
[2,6,4,5,1,3,7]=>[5,2,1,6,4,3,7]=>[2,6,3,1,5,4,7]=>010110
[2,6,4,5,1,7,3]=>[7,2,5,6,4,1,3]=>[2,7,3,5,4,6,1]=>000111
[2,6,4,5,3,1,7]=>[3,2,5,6,4,1,7]=>[2,6,1,3,5,4,7]=>000110
[2,6,4,5,3,7,1]=>[7,2,5,6,4,3,1]=>[2,6,3,5,4,7,1]=>000111
[2,6,4,5,7,1,3]=>[7,2,1,6,4,5,3]=>[2,6,5,4,7,3,1]=>010111
[2,6,4,5,7,3,1]=>[3,2,7,6,4,5,1]=>[2,6,5,4,7,1,3]=>000111
[2,6,4,7,1,3,5]=>[7,2,1,6,4,3,5]=>[2,7,5,4,6,3,1]=>010111
[2,6,4,7,1,5,3]=>[5,2,7,6,4,1,3]=>[2,6,1,5,4,7,3]=>000111
[2,6,4,7,3,1,5]=>[3,2,7,6,4,1,5]=>[2,7,5,4,6,1,3]=>000111
[2,6,4,7,3,5,1]=>[5,2,7,6,4,3,1]=>[2,7,1,5,4,6,3]=>000111
[2,6,4,7,5,1,3]=>[5,2,1,7,6,4,3]=>[2,7,3,1,5,6,4]=>010011
[2,6,4,7,5,3,1]=>[3,2,5,7,6,4,1]=>[2,7,1,3,5,6,4]=>000011
[2,6,5,1,3,4,7]=>[5,2,1,3,6,4,7]=>[2,6,4,3,1,5,7]=>011010
[2,6,5,1,3,7,4]=>[7,2,1,5,6,3,4]=>[2,7,4,5,6,3,1]=>010011
[2,6,5,1,4,3,7]=>[4,2,5,1,6,3,7]=>[2,4,1,6,3,5,7]=>001010
[2,6,5,1,4,7,3]=>[7,2,5,1,6,4,3]=>[2,7,3,5,6,4,1]=>001011
[2,6,5,1,7,3,4]=>[7,2,5,1,6,3,4]=>[2,6,3,5,7,4,1]=>001011
[2,6,5,1,7,4,3]=>[4,2,7,5,6,1,3]=>[2,6,1,4,5,7,3]=>000011
[2,6,5,3,1,4,7]=>[3,2,5,1,6,4,7]=>[2,6,4,1,3,5,7]=>001010
[2,6,5,3,1,7,4]=>[3,2,7,5,6,1,4]=>[2,7,4,5,6,1,3]=>000011
[2,6,5,3,4,1,7]=>[4,2,5,3,6,1,7]=>[2,6,1,4,3,5,7]=>001010
[2,6,5,3,4,7,1]=>[7,2,5,3,6,4,1]=>[2,6,4,3,5,7,1]=>001011
[2,6,5,3,7,1,4]=>[7,2,5,3,6,1,4]=>[2,7,4,3,5,6,1]=>001011
[2,6,5,3,7,4,1]=>[4,2,7,5,6,3,1]=>[2,7,1,4,5,6,3]=>000011
[2,6,5,4,1,3,7]=>[4,2,1,5,6,3,7]=>[2,6,3,1,4,5,7]=>010010
[2,6,5,4,1,7,3]=>[7,2,4,5,6,1,3]=>[2,7,3,4,5,6,1]=>000011
[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]=>[2,6,1,3,4,5,7]=>000010
[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>[2,6,3,4,5,7,1]=>000011
[2,6,5,4,7,1,3]=>[7,2,1,5,6,4,3]=>[2,6,4,5,7,3,1]=>010011
[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]=>[2,6,4,5,7,1,3]=>000011
[2,6,5,7,1,3,4]=>[7,2,1,3,6,5,4]=>[2,6,5,7,4,3,1]=>011011
[2,6,5,7,1,4,3]=>[4,2,7,1,6,5,3]=>[2,4,1,6,5,7,3]=>001011
[2,6,5,7,3,1,4]=>[3,2,7,1,6,5,4]=>[2,6,5,7,4,1,3]=>001011
[2,6,5,7,3,4,1]=>[4,2,7,3,6,5,1]=>[2,6,5,7,1,4,3]=>001011
[2,6,5,7,4,1,3]=>[4,2,1,7,6,5,3]=>[2,6,5,7,3,1,4]=>010011
[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]=>[2,6,5,7,1,3,4]=>000011
[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[2,6,7,5,4,3,1]=>011101
[2,6,7,1,3,5,4]=>[5,2,1,7,3,6,4]=>[2,5,3,1,6,7,4]=>010101
[2,6,7,1,4,3,5]=>[4,2,7,1,3,6,5]=>[2,4,1,6,7,5,3]=>001101
[2,6,7,1,4,5,3]=>[5,2,7,1,4,6,3]=>[2,5,4,1,6,7,3]=>001101
[2,6,7,1,5,3,4]=>[5,2,7,1,3,6,4]=>[2,6,7,4,1,5,3]=>001101
[2,6,7,1,5,4,3]=>[4,2,5,7,1,6,3]=>[2,6,7,3,5,1,4]=>000101
[2,6,7,3,1,4,5]=>[3,2,7,1,4,6,5]=>[2,6,7,5,4,1,3]=>001101
[2,6,7,3,1,5,4]=>[3,2,5,7,1,6,4]=>[2,5,1,3,6,7,4]=>000101
[2,6,7,3,4,1,5]=>[4,2,7,3,1,6,5]=>[2,6,7,5,1,4,3]=>001101
[2,6,7,3,4,5,1]=>[5,2,7,3,4,6,1]=>[2,6,7,1,5,4,3]=>001101
[2,6,7,3,5,1,4]=>[5,2,7,3,1,6,4]=>[2,5,1,6,7,4,3]=>001101
[2,6,7,3,5,4,1]=>[4,2,5,7,3,6,1]=>[2,5,3,6,7,1,4]=>000101
[2,6,7,4,1,3,5]=>[4,2,1,7,3,6,5]=>[2,6,7,5,3,1,4]=>010101
[2,6,7,4,1,5,3]=>[5,2,4,7,1,6,3]=>[2,5,1,6,7,3,4]=>000101
[2,6,7,4,3,1,5]=>[3,2,4,7,1,6,5]=>[2,6,7,5,1,3,4]=>000101
[2,6,7,4,3,5,1]=>[5,2,4,7,3,6,1]=>[2,6,7,1,5,3,4]=>000101
[2,6,7,4,5,1,3]=>[5,2,1,7,4,6,3]=>[2,6,7,3,1,5,4]=>010101
[2,6,7,4,5,3,1]=>[3,2,5,7,4,6,1]=>[2,6,7,1,3,5,4]=>000101
[2,6,7,5,1,3,4]=>[5,2,1,3,7,6,4]=>[2,6,7,4,3,1,5]=>011001
[2,6,7,5,1,4,3]=>[4,2,5,1,7,6,3]=>[2,4,1,6,7,3,5]=>001001
[2,6,7,5,3,1,4]=>[3,2,5,1,7,6,4]=>[2,6,7,4,1,3,5]=>001001
[2,6,7,5,3,4,1]=>[4,2,5,3,7,6,1]=>[2,6,7,1,4,3,5]=>001001
[2,6,7,5,4,1,3]=>[4,2,1,5,7,6,3]=>[2,6,7,3,1,4,5]=>010001
[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]=>[2,6,7,1,3,4,5]=>000001
[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[2,7,6,5,4,3,1]=>011111
[2,7,1,3,4,6,5]=>[6,2,1,3,7,4,5]=>[2,6,4,3,1,7,5]=>011011
[2,7,1,3,5,4,6]=>[5,2,1,7,3,4,6]=>[2,5,3,1,7,6,4]=>010111
[2,7,1,3,5,6,4]=>[6,2,1,7,3,5,4]=>[2,6,5,3,1,7,4]=>010111
[2,7,1,3,6,4,5]=>[6,2,1,7,3,4,5]=>[2,7,5,3,1,6,4]=>010111
[2,7,1,3,6,5,4]=>[5,2,1,6,7,3,4]=>[2,7,4,6,3,1,5]=>010011
[2,7,1,4,3,5,6]=>[4,2,7,1,3,5,6]=>[2,4,1,7,6,5,3]=>001111
[2,7,1,4,3,6,5]=>[4,2,6,1,7,3,5]=>[2,4,1,6,3,7,5]=>001011
[2,7,1,4,5,3,6]=>[5,2,7,1,4,3,6]=>[2,5,4,1,7,6,3]=>001111
[2,7,1,4,5,6,3]=>[6,2,7,1,4,5,3]=>[2,6,5,4,1,7,3]=>001111
[2,7,1,4,6,3,5]=>[6,2,7,1,4,3,5]=>[2,7,5,4,1,6,3]=>001111
[2,7,1,4,6,5,3]=>[5,2,6,1,7,4,3]=>[2,7,3,6,4,1,5]=>001011
[2,7,1,5,3,4,6]=>[5,2,7,1,3,4,6]=>[2,7,6,4,1,5,3]=>001111
[2,7,1,5,3,6,4]=>[6,2,5,7,1,3,4]=>[2,6,3,5,1,7,4]=>000111
[2,7,1,5,4,3,6]=>[4,2,5,7,1,3,6]=>[2,7,6,3,5,1,4]=>000111
[2,7,1,5,4,6,3]=>[6,2,5,7,1,4,3]=>[2,7,3,5,1,6,4]=>000111
[2,7,1,5,6,3,4]=>[6,2,7,1,3,5,4]=>[2,7,4,1,6,5,3]=>001111
[2,7,1,5,6,4,3]=>[4,2,6,7,1,5,3]=>[2,7,3,6,5,1,4]=>000111
[2,7,1,6,3,4,5]=>[6,2,7,1,3,4,5]=>[2,6,4,1,7,5,3]=>001111
[2,7,1,6,3,5,4]=>[5,2,6,7,1,3,4]=>[2,5,1,6,3,7,4]=>000111
[2,7,1,6,4,3,5]=>[4,2,6,7,1,3,5]=>[2,6,3,7,5,1,4]=>000111
[2,7,1,6,4,5,3]=>[5,2,6,7,1,4,3]=>[2,5,1,7,3,6,4]=>000111
[2,7,1,6,5,3,4]=>[5,2,6,1,7,3,4]=>[2,6,3,7,4,1,5]=>001011
[2,7,1,6,5,4,3]=>[4,2,5,6,7,1,3]=>[2,6,1,4,7,3,5]=>000011
[2,7,3,1,4,5,6]=>[3,2,7,1,4,5,6]=>[2,7,6,5,4,1,3]=>001111
[2,7,3,1,4,6,5]=>[3,2,6,1,7,4,5]=>[2,6,4,1,3,7,5]=>001011
[2,7,3,1,5,4,6]=>[3,2,5,7,1,4,6]=>[2,5,1,3,7,6,4]=>000111
[2,7,3,1,5,6,4]=>[3,2,6,7,1,5,4]=>[2,6,5,1,3,7,4]=>000111
[2,7,3,1,6,4,5]=>[3,2,6,7,1,4,5]=>[2,7,5,1,3,6,4]=>000111
[2,7,3,1,6,5,4]=>[3,2,5,6,7,1,4]=>[2,7,4,6,1,3,5]=>000011
[2,7,3,4,1,5,6]=>[4,2,7,3,1,5,6]=>[2,7,6,5,1,4,3]=>001111
[2,7,3,4,1,6,5]=>[4,2,6,3,7,1,5]=>[2,6,1,4,3,7,5]=>001011
[2,7,3,4,5,1,6]=>[5,2,7,3,4,1,6]=>[2,7,6,1,5,4,3]=>001111
[2,7,3,4,5,6,1]=>[6,2,7,3,4,5,1]=>[2,7,1,6,5,4,3]=>001111
[2,7,3,4,6,1,5]=>[6,2,7,3,4,1,5]=>[2,6,1,7,5,4,3]=>001111
[2,7,3,4,6,5,1]=>[5,2,6,3,7,4,1]=>[2,6,4,3,7,1,5]=>001011
[2,7,3,5,1,4,6]=>[5,2,7,3,1,4,6]=>[2,5,1,7,6,4,3]=>001111
[2,7,3,5,1,6,4]=>[6,2,5,7,3,1,4]=>[2,5,3,6,1,7,4]=>000111
[2,7,3,5,4,1,6]=>[4,2,5,7,3,1,6]=>[2,5,3,7,6,1,4]=>000111
[2,7,3,5,4,6,1]=>[6,2,5,7,3,4,1]=>[2,5,3,7,1,6,4]=>000111
[2,7,3,5,6,1,4]=>[6,2,7,3,1,5,4]=>[2,6,5,1,7,4,3]=>001111
[2,7,3,5,6,4,1]=>[4,2,6,7,3,5,1]=>[2,6,5,3,7,1,4]=>000111
[2,7,3,6,1,4,5]=>[6,2,7,3,1,4,5]=>[2,7,5,1,6,4,3]=>001111
[2,7,3,6,1,5,4]=>[5,2,6,7,3,1,4]=>[2,6,1,5,3,7,4]=>000111
[2,7,3,6,4,1,5]=>[4,2,6,7,3,1,5]=>[2,7,5,3,6,1,4]=>000111
[2,7,3,6,4,5,1]=>[5,2,6,7,3,4,1]=>[2,7,1,5,3,6,4]=>000111
[2,7,3,6,5,1,4]=>[5,2,6,3,7,1,4]=>[2,7,4,3,6,1,5]=>001011
[2,7,3,6,5,4,1]=>[4,2,5,6,7,3,1]=>[2,7,1,4,6,3,5]=>000011
[2,7,4,1,3,5,6]=>[4,2,1,7,3,5,6]=>[2,7,6,5,3,1,4]=>010111
[2,7,4,1,3,6,5]=>[4,2,1,6,7,3,5]=>[2,6,3,1,4,7,5]=>010011
[2,7,4,1,5,3,6]=>[5,2,4,7,1,3,6]=>[2,5,1,7,6,3,4]=>000111
[2,7,4,1,5,6,3]=>[6,2,4,7,1,5,3]=>[2,6,5,1,7,3,4]=>000111
[2,7,4,1,6,3,5]=>[6,2,4,7,1,3,5]=>[2,7,5,1,6,3,4]=>000111
[2,7,4,1,6,5,3]=>[5,2,4,6,7,1,3]=>[2,7,3,4,6,1,5]=>000011
[2,7,4,3,1,5,6]=>[3,2,4,7,1,5,6]=>[2,7,6,5,1,3,4]=>000111
[2,7,4,3,1,6,5]=>[3,2,4,6,7,1,5]=>[2,6,1,3,4,7,5]=>000011
[2,7,4,3,5,1,6]=>[5,2,4,7,3,1,6]=>[2,7,6,1,5,3,4]=>000111
[2,7,4,3,5,6,1]=>[6,2,4,7,3,5,1]=>[2,7,1,6,5,3,4]=>000111
[2,7,4,3,6,1,5]=>[6,2,4,7,3,1,5]=>[2,6,1,7,5,3,4]=>000111
[2,7,4,3,6,5,1]=>[5,2,4,6,7,3,1]=>[2,6,3,4,7,1,5]=>000011
[2,7,4,5,1,3,6]=>[5,2,1,7,4,3,6]=>[2,7,6,3,1,5,4]=>010111
[2,7,4,5,1,6,3]=>[6,2,5,7,4,1,3]=>[2,6,1,7,3,5,4]=>000111
[2,7,4,5,3,1,6]=>[3,2,5,7,4,1,6]=>[2,7,6,1,3,5,4]=>000111
[2,7,4,5,3,6,1]=>[6,2,5,7,4,3,1]=>[2,7,1,6,3,5,4]=>000111
[2,7,4,5,6,1,3]=>[6,2,1,7,4,5,3]=>[2,7,3,1,6,5,4]=>010111
[2,7,4,5,6,3,1]=>[3,2,6,7,4,5,1]=>[2,7,1,3,6,5,4]=>000111
[2,7,4,6,1,3,5]=>[6,2,1,7,4,3,5]=>[2,6,3,1,7,5,4]=>010111
[2,7,4,6,1,5,3]=>[5,2,6,7,4,1,3]=>[2,7,3,6,1,5,4]=>000111
[2,7,4,6,3,1,5]=>[3,2,6,7,4,1,5]=>[2,6,1,3,7,5,4]=>000111
[2,7,4,6,3,5,1]=>[5,2,6,7,4,3,1]=>[2,6,3,7,1,5,4]=>000111
[2,7,4,6,5,1,3]=>[5,2,1,6,7,4,3]=>[2,6,4,7,3,1,5]=>010011
[2,7,4,6,5,3,1]=>[3,2,5,6,7,4,1]=>[2,6,4,7,1,3,5]=>000011
[2,7,5,1,3,4,6]=>[5,2,1,3,7,4,6]=>[2,7,6,4,3,1,5]=>011011
[2,7,5,1,3,6,4]=>[6,2,1,5,7,3,4]=>[2,6,3,1,7,4,5]=>010011
[2,7,5,1,4,3,6]=>[4,2,5,1,7,3,6]=>[2,4,1,7,6,3,5]=>001011
[2,7,5,1,4,6,3]=>[6,2,5,1,7,4,3]=>[2,6,4,1,7,3,5]=>001011
[2,7,5,1,6,3,4]=>[6,2,5,1,7,3,4]=>[2,7,4,1,6,3,5]=>001011
[2,7,5,1,6,4,3]=>[4,2,6,5,7,1,3]=>[2,7,3,6,1,4,5]=>000011
[2,7,5,3,1,4,6]=>[3,2,5,1,7,4,6]=>[2,7,6,4,1,3,5]=>001011
[2,7,5,3,1,6,4]=>[3,2,6,5,7,1,4]=>[2,6,1,3,7,4,5]=>000011
[2,7,5,3,4,1,6]=>[4,2,5,3,7,1,6]=>[2,7,6,1,4,3,5]=>001011
[2,7,5,3,4,6,1]=>[6,2,5,3,7,4,1]=>[2,7,1,6,4,3,5]=>001011
[2,7,5,3,6,1,4]=>[6,2,5,3,7,1,4]=>[2,6,1,7,4,3,5]=>001011
[2,7,5,3,6,4,1]=>[4,2,6,5,7,3,1]=>[2,6,3,7,1,4,5]=>000011
[2,7,5,4,1,3,6]=>[4,2,1,5,7,3,6]=>[2,7,6,3,1,4,5]=>010011
[2,7,5,4,1,6,3]=>[6,2,4,5,7,1,3]=>[2,6,1,7,3,4,5]=>000011
[2,7,5,4,3,1,6]=>[3,2,4,5,7,1,6]=>[2,7,6,1,3,4,5]=>000011
[2,7,5,4,3,6,1]=>[6,2,4,5,7,3,1]=>[2,7,1,6,3,4,5]=>000011
[2,7,5,4,6,1,3]=>[6,2,1,5,7,4,3]=>[2,7,3,1,6,4,5]=>010011
[2,7,5,4,6,3,1]=>[3,2,6,5,7,4,1]=>[2,7,1,3,6,4,5]=>000011
[2,7,5,6,1,3,4]=>[6,2,1,3,7,5,4]=>[2,7,4,3,1,6,5]=>011011
[2,7,5,6,1,4,3]=>[4,2,6,1,7,5,3]=>[2,4,1,7,3,6,5]=>001011
[2,7,5,6,3,1,4]=>[3,2,6,1,7,5,4]=>[2,7,4,1,3,6,5]=>001011
[2,7,5,6,3,4,1]=>[4,2,6,3,7,5,1]=>[2,7,1,4,3,6,5]=>001011
[2,7,5,6,4,1,3]=>[4,2,1,6,7,5,3]=>[2,7,3,1,4,6,5]=>010011
[2,7,5,6,4,3,1]=>[3,2,4,6,7,5,1]=>[2,7,1,3,4,6,5]=>000011
[2,7,6,1,3,4,5]=>[6,2,1,3,4,7,5]=>[2,7,5,4,3,1,6]=>011101
[2,7,6,1,3,5,4]=>[5,2,1,6,3,7,4]=>[2,5,3,1,7,4,6]=>010101
[2,7,6,1,4,3,5]=>[4,2,6,1,3,7,5]=>[2,4,1,7,5,3,6]=>001101
[2,7,6,1,4,5,3]=>[5,2,6,1,4,7,3]=>[2,5,4,1,7,3,6]=>001101
[2,7,6,1,5,3,4]=>[5,2,6,1,3,7,4]=>[2,7,4,1,5,3,6]=>001101
[2,7,6,1,5,4,3]=>[4,2,5,6,1,7,3]=>[2,7,3,5,1,4,6]=>000101
[2,7,6,3,1,4,5]=>[3,2,6,1,4,7,5]=>[2,7,5,4,1,3,6]=>001101
[2,7,6,3,1,5,4]=>[3,2,5,6,1,7,4]=>[2,5,1,3,7,4,6]=>000101
[2,7,6,3,4,1,5]=>[4,2,6,3,1,7,5]=>[2,7,5,1,4,3,6]=>001101
[2,7,6,3,4,5,1]=>[5,2,6,3,4,7,1]=>[2,7,1,5,4,3,6]=>001101
[2,7,6,3,5,1,4]=>[5,2,6,3,1,7,4]=>[2,5,1,7,4,3,6]=>001101
[2,7,6,3,5,4,1]=>[4,2,5,6,3,7,1]=>[2,5,3,7,1,4,6]=>000101
[2,7,6,4,1,3,5]=>[4,2,1,6,3,7,5]=>[2,7,5,3,1,4,6]=>010101
[2,7,6,4,1,5,3]=>[5,2,4,6,1,7,3]=>[2,5,1,7,3,4,6]=>000101
[2,7,6,4,3,1,5]=>[3,2,4,6,1,7,5]=>[2,7,5,1,3,4,6]=>000101
[2,7,6,4,3,5,1]=>[5,2,4,6,3,7,1]=>[2,7,1,5,3,4,6]=>000101
[2,7,6,4,5,1,3]=>[5,2,1,6,4,7,3]=>[2,7,3,1,5,4,6]=>010101
[2,7,6,4,5,3,1]=>[3,2,5,6,4,7,1]=>[2,7,1,3,5,4,6]=>000101
[2,7,6,5,1,3,4]=>[5,2,1,3,6,7,4]=>[2,7,4,3,1,5,6]=>011001
[2,7,6,5,1,4,3]=>[4,2,5,1,6,7,3]=>[2,4,1,7,3,5,6]=>001001
[2,7,6,5,3,1,4]=>[3,2,5,1,6,7,4]=>[2,7,4,1,3,5,6]=>001001
[2,7,6,5,3,4,1]=>[4,2,5,3,6,7,1]=>[2,7,1,4,3,5,6]=>001001
[2,7,6,5,4,1,3]=>[4,2,1,5,6,7,3]=>[2,7,3,1,4,5,6]=>010001
[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>[2,7,1,3,4,5,6]=>000001
[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>[3,2,1,4,5,7,6]=>110001
[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>[3,2,1,4,6,5,7]=>110010
[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>[3,2,1,4,6,7,5]=>110001
[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]=>110011
[3,1,2,4,7,6,5]=>[3,1,2,4,6,7,5]=>[3,2,1,4,7,5,6]=>110001
[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,2,1,5,4,6,7]=>110100
[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,2,1,5,4,7,6]=>110101
[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>[3,2,1,5,6,4,7]=>110010
[3,1,2,5,6,7,4]=>[3,1,2,7,5,6,4]=>[3,2,1,5,6,7,4]=>110001
[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>[3,2,1,5,7,6,4]=>110011
[3,1,2,5,7,6,4]=>[3,1,2,6,5,7,4]=>[3,2,1,5,7,4,6]=>110001
[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>[3,2,1,6,5,4,7]=>110110
[3,1,2,6,4,7,5]=>[3,1,2,7,6,4,5]=>[3,2,1,7,5,6,4]=>110011
[3,1,2,6,5,4,7]=>[3,1,2,5,6,4,7]=>[3,2,1,6,4,5,7]=>110010
[3,1,2,6,5,7,4]=>[3,1,2,7,6,5,4]=>[3,2,1,6,5,7,4]=>110011
[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>[3,2,1,6,7,5,4]=>110101
[3,1,2,6,7,5,4]=>[3,1,2,5,7,6,4]=>[3,2,1,6,7,4,5]=>110001
[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>[3,2,1,7,6,5,4]=>110111
[3,1,2,7,4,6,5]=>[3,1,2,6,7,4,5]=>[3,2,1,6,4,7,5]=>110011
[3,1,2,7,5,4,6]=>[3,1,2,5,7,4,6]=>[3,2,1,7,6,4,5]=>110011
[3,1,2,7,5,6,4]=>[3,1,2,6,7,5,4]=>[3,2,1,7,4,6,5]=>110011
[3,1,2,7,6,4,5]=>[3,1,2,6,4,7,5]=>[3,2,1,7,5,4,6]=>110101
[3,1,2,7,6,5,4]=>[3,1,2,5,6,7,4]=>[3,2,1,7,4,5,6]=>110001
[3,1,4,2,5,6,7]=>[4,3,1,2,5,6,7]=>[4,2,3,1,5,6,7]=>011000
[3,1,4,2,5,7,6]=>[4,3,1,2,5,7,6]=>[4,2,3,1,5,7,6]=>011001
[3,1,4,2,6,5,7]=>[4,3,1,2,6,5,7]=>[4,2,3,1,6,5,7]=>011010
[3,1,4,2,6,7,5]=>[4,3,1,2,7,6,5]=>[4,2,3,1,6,7,5]=>011001
[3,1,4,2,7,5,6]=>[4,3,1,2,7,5,6]=>[4,2,3,1,7,6,5]=>011011
[3,1,4,2,7,6,5]=>[4,3,1,2,6,7,5]=>[4,2,3,1,7,5,6]=>011001
[3,1,4,5,2,6,7]=>[5,3,1,4,2,6,7]=>[4,5,2,3,1,6,7]=>010100
[3,1,4,5,2,7,6]=>[5,3,1,4,2,7,6]=>[4,5,2,3,1,7,6]=>010101
[3,1,4,5,6,2,7]=>[6,3,1,4,5,2,7]=>[4,5,6,2,3,1,7]=>010010
[3,1,4,5,6,7,2]=>[7,3,1,4,5,6,2]=>[4,5,6,7,2,3,1]=>010001
[3,1,4,5,7,2,6]=>[7,3,1,4,5,2,6]=>[4,5,7,6,2,3,1]=>010011
[3,1,4,5,7,6,2]=>[6,3,1,4,5,7,2]=>[4,5,7,2,3,1,6]=>010001
[3,1,4,6,2,5,7]=>[6,3,1,4,2,5,7]=>[4,6,5,2,3,1,7]=>010110
[3,1,4,6,2,7,5]=>[7,3,1,4,6,2,5]=>[4,7,5,6,2,3,1]=>010011
[3,1,4,6,5,2,7]=>[5,3,1,4,6,2,7]=>[4,6,2,3,1,5,7]=>010010
[3,1,4,6,5,7,2]=>[7,3,1,4,6,5,2]=>[4,6,5,7,2,3,1]=>010011
[3,1,4,6,7,2,5]=>[7,3,1,4,2,6,5]=>[4,6,7,5,2,3,1]=>010101
[3,1,4,6,7,5,2]=>[5,3,1,4,7,6,2]=>[4,6,7,2,3,1,5]=>010001
[3,1,4,7,2,5,6]=>[7,3,1,4,2,5,6]=>[4,7,6,5,2,3,1]=>010111
[3,1,4,7,2,6,5]=>[6,3,1,4,7,2,5]=>[4,6,2,3,1,7,5]=>010011
[3,1,4,7,5,2,6]=>[5,3,1,4,7,2,6]=>[4,7,6,2,3,1,5]=>010011
[3,1,4,7,5,6,2]=>[6,3,1,4,7,5,2]=>[4,7,2,3,1,6,5]=>010011
[3,1,4,7,6,2,5]=>[6,3,1,4,2,7,5]=>[4,7,5,2,3,1,6]=>010101
[3,1,4,7,6,5,2]=>[5,3,1,4,6,7,2]=>[4,7,2,3,1,5,6]=>010001
[3,1,5,2,4,6,7]=>[5,3,1,2,4,6,7]=>[5,4,2,3,1,6,7]=>011100
[3,1,5,2,4,7,6]=>[5,3,1,2,4,7,6]=>[5,4,2,3,1,7,6]=>011101
[3,1,5,2,6,4,7]=>[6,3,1,5,2,4,7]=>[6,4,5,2,3,1,7]=>010110
[3,1,5,2,6,7,4]=>[7,3,1,5,2,6,4]=>[6,7,4,5,2,3,1]=>010101
[3,1,5,2,7,4,6]=>[7,3,1,5,2,4,6]=>[7,6,4,5,2,3,1]=>010111
[3,1,5,2,7,6,4]=>[6,3,1,5,2,7,4]=>[7,4,5,2,3,1,6]=>010101
[3,1,5,4,2,6,7]=>[4,3,1,5,2,6,7]=>[5,2,3,1,4,6,7]=>010100
[3,1,5,4,2,7,6]=>[4,3,1,5,2,7,6]=>[5,2,3,1,4,7,6]=>010101
[3,1,5,4,6,2,7]=>[6,3,1,5,4,2,7]=>[5,4,6,2,3,1,7]=>010110
[3,1,5,4,6,7,2]=>[7,3,1,5,4,6,2]=>[5,4,6,7,2,3,1]=>010101
[3,1,5,4,7,2,6]=>[7,3,1,5,4,2,6]=>[5,4,7,6,2,3,1]=>010111
[3,1,5,4,7,6,2]=>[6,3,1,5,4,7,2]=>[5,4,7,2,3,1,6]=>010101
[3,1,5,6,2,4,7]=>[6,3,1,2,5,4,7]=>[5,6,4,2,3,1,7]=>011010
[3,1,5,6,2,7,4]=>[7,3,1,6,5,2,4]=>[5,7,4,6,2,3,1]=>010011
[3,1,5,6,4,2,7]=>[4,3,1,6,5,2,7]=>[5,6,2,3,1,4,7]=>010010
[3,1,5,6,4,7,2]=>[7,3,1,6,5,4,2]=>[5,6,4,7,2,3,1]=>010011
[3,1,5,6,7,2,4]=>[7,3,1,2,5,6,4]=>[5,6,7,4,2,3,1]=>011001
[3,1,5,6,7,4,2]=>[4,3,1,7,5,6,2]=>[5,6,7,2,3,1,4]=>010001
[3,1,5,7,2,4,6]=>[7,3,1,2,5,4,6]=>[5,7,6,4,2,3,1]=>011011
[3,1,5,7,2,6,4]=>[6,3,1,7,5,2,4]=>[5,6,2,3,1,7,4]=>010011
[3,1,5,7,4,2,6]=>[4,3,1,7,5,2,6]=>[5,7,6,2,3,1,4]=>010011
[3,1,5,7,4,6,2]=>[6,3,1,7,5,4,2]=>[5,7,2,3,1,6,4]=>010011
[3,1,5,7,6,2,4]=>[6,3,1,2,5,7,4]=>[5,7,4,2,3,1,6]=>011001
[3,1,5,7,6,4,2]=>[4,3,1,6,5,7,2]=>[5,7,2,3,1,4,6]=>010001
[3,1,6,2,4,5,7]=>[6,3,1,2,4,5,7]=>[6,5,4,2,3,1,7]=>011110
[3,1,6,2,4,7,5]=>[7,3,1,2,6,4,5]=>[7,5,6,4,2,3,1]=>011011
[3,1,6,2,5,4,7]=>[5,3,1,6,2,4,7]=>[5,2,3,1,6,4,7]=>010110
[3,1,6,2,5,7,4]=>[7,3,1,6,2,5,4]=>[7,4,6,5,2,3,1]=>010111
[3,1,6,2,7,4,5]=>[7,3,1,6,2,4,5]=>[6,4,7,5,2,3,1]=>010111
[3,1,6,2,7,5,4]=>[5,3,1,7,6,2,4]=>[6,2,3,1,5,7,4]=>010011
[3,1,6,4,2,5,7]=>[4,3,1,6,2,5,7]=>[6,5,2,3,1,4,7]=>010110
[3,1,6,4,2,7,5]=>[4,3,1,7,6,2,5]=>[7,5,6,2,3,1,4]=>010011
[3,1,6,4,5,2,7]=>[5,3,1,6,4,2,7]=>[6,2,3,1,5,4,7]=>010110
[3,1,6,4,5,7,2]=>[7,3,1,6,4,5,2]=>[6,5,4,7,2,3,1]=>010111
[3,1,6,4,7,2,5]=>[7,3,1,6,4,2,5]=>[7,5,4,6,2,3,1]=>010111
[3,1,6,4,7,5,2]=>[5,3,1,7,6,4,2]=>[7,2,3,1,5,6,4]=>010011
[3,1,6,5,2,4,7]=>[5,3,1,2,6,4,7]=>[6,4,2,3,1,5,7]=>011010
[3,1,6,5,2,7,4]=>[7,3,1,5,6,2,4]=>[7,4,5,6,2,3,1]=>010011
[3,1,6,5,4,2,7]=>[4,3,1,5,6,2,7]=>[6,2,3,1,4,5,7]=>010010
[3,1,6,5,4,7,2]=>[7,3,1,5,6,4,2]=>[6,4,5,7,2,3,1]=>010011
[3,1,6,5,7,2,4]=>[7,3,1,2,6,5,4]=>[6,5,7,4,2,3,1]=>011011
[3,1,6,5,7,4,2]=>[4,3,1,7,6,5,2]=>[6,5,7,2,3,1,4]=>010011
[3,1,6,7,2,4,5]=>[7,3,1,2,4,6,5]=>[6,7,5,4,2,3,1]=>011101
[3,1,6,7,2,5,4]=>[5,3,1,7,2,6,4]=>[5,2,3,1,6,7,4]=>010101
[3,1,6,7,4,2,5]=>[4,3,1,7,2,6,5]=>[6,7,5,2,3,1,4]=>010101
[3,1,6,7,4,5,2]=>[5,3,1,7,4,6,2]=>[6,7,2,3,1,5,4]=>010101
[3,1,6,7,5,2,4]=>[5,3,1,2,7,6,4]=>[6,7,4,2,3,1,5]=>011001
[3,1,6,7,5,4,2]=>[4,3,1,5,7,6,2]=>[6,7,2,3,1,4,5]=>010001
[3,1,7,2,4,5,6]=>[7,3,1,2,4,5,6]=>[7,6,5,4,2,3,1]=>011111
[3,1,7,2,4,6,5]=>[6,3,1,2,7,4,5]=>[6,4,2,3,1,7,5]=>011011
[3,1,7,2,5,4,6]=>[5,3,1,7,2,4,6]=>[5,2,3,1,7,6,4]=>010111
[3,1,7,2,5,6,4]=>[6,3,1,7,2,5,4]=>[6,5,2,3,1,7,4]=>010111
[3,1,7,2,6,4,5]=>[6,3,1,7,2,4,5]=>[7,5,2,3,1,6,4]=>010111
[3,1,7,2,6,5,4]=>[5,3,1,6,7,2,4]=>[7,4,6,2,3,1,5]=>010011
[3,1,7,4,2,5,6]=>[4,3,1,7,2,5,6]=>[7,6,5,2,3,1,4]=>010111
[3,1,7,4,2,6,5]=>[4,3,1,6,7,2,5]=>[6,2,3,1,4,7,5]=>010011
[3,1,7,4,5,2,6]=>[5,3,1,7,4,2,6]=>[7,6,2,3,1,5,4]=>010111
[3,1,7,4,5,6,2]=>[6,3,1,7,4,5,2]=>[7,2,3,1,6,5,4]=>010111
[3,1,7,4,6,2,5]=>[6,3,1,7,4,2,5]=>[6,2,3,1,7,5,4]=>010111
[3,1,7,4,6,5,2]=>[5,3,1,6,7,4,2]=>[6,4,7,2,3,1,5]=>010011
[3,1,7,5,2,4,6]=>[5,3,1,2,7,4,6]=>[7,6,4,2,3,1,5]=>011011
[3,1,7,5,2,6,4]=>[6,3,1,5,7,2,4]=>[6,2,3,1,7,4,5]=>010011
[3,1,7,5,4,2,6]=>[4,3,1,5,7,2,6]=>[7,6,2,3,1,4,5]=>010011
[3,1,7,5,4,6,2]=>[6,3,1,5,7,4,2]=>[7,2,3,1,6,4,5]=>010011
[3,1,7,5,6,2,4]=>[6,3,1,2,7,5,4]=>[7,4,2,3,1,6,5]=>011011
[3,1,7,5,6,4,2]=>[4,3,1,6,7,5,2]=>[7,2,3,1,4,6,5]=>010011
[3,1,7,6,2,4,5]=>[6,3,1,2,4,7,5]=>[7,5,4,2,3,1,6]=>011101
[3,1,7,6,2,5,4]=>[5,3,1,6,2,7,4]=>[5,2,3,1,7,4,6]=>010101
[3,1,7,6,4,2,5]=>[4,3,1,6,2,7,5]=>[7,5,2,3,1,4,6]=>010101
[3,1,7,6,4,5,2]=>[5,3,1,6,4,7,2]=>[7,2,3,1,5,4,6]=>010101
[3,1,7,6,5,2,4]=>[5,3,1,2,6,7,4]=>[7,4,2,3,1,5,6]=>011001
[3,1,7,6,5,4,2]=>[4,3,1,5,6,7,2]=>[7,2,3,1,4,5,6]=>010001
[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>010000
[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>010001
[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>010010
[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>[3,1,2,4,6,7,5]=>010001
[3,2,1,4,7,5,6]=>[2,3,1,4,7,5,6]=>[3,1,2,4,7,6,5]=>010011
[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[3,1,2,4,7,5,6]=>010001
[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>010100
[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>010101
[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>[3,1,2,5,6,4,7]=>010010
[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>[3,1,2,5,6,7,4]=>010001
[3,2,1,5,7,4,6]=>[2,3,1,7,5,4,6]=>[3,1,2,5,7,6,4]=>010011
[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>[3,1,2,5,7,4,6]=>010001
[3,2,1,6,4,5,7]=>[2,3,1,6,4,5,7]=>[3,1,2,6,5,4,7]=>010110
[3,2,1,6,4,7,5]=>[2,3,1,7,6,4,5]=>[3,1,2,7,5,6,4]=>010011
[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[3,1,2,6,4,5,7]=>010010
[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>[3,1,2,6,5,7,4]=>010011
[3,2,1,6,7,4,5]=>[2,3,1,7,4,6,5]=>[3,1,2,6,7,5,4]=>010101
[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]=>[3,1,2,6,7,4,5]=>010001
[3,2,1,7,4,5,6]=>[2,3,1,7,4,5,6]=>[3,1,2,7,6,5,4]=>010111
[3,2,1,7,4,6,5]=>[2,3,1,6,7,4,5]=>[3,1,2,6,4,7,5]=>010011
[3,2,1,7,5,4,6]=>[2,3,1,5,7,4,6]=>[3,1,2,7,6,4,5]=>010011
[3,2,1,7,5,6,4]=>[2,3,1,6,7,5,4]=>[3,1,2,7,4,6,5]=>010011
[3,2,1,7,6,4,5]=>[2,3,1,6,4,7,5]=>[3,1,2,7,5,4,6]=>010101
[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>[3,1,2,7,4,5,6]=>010001
[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[3,2,4,1,5,6,7]=>011000
[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>[3,2,4,1,5,7,6]=>011001
[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[3,2,4,1,6,5,7]=>011010
[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>[3,2,4,1,6,7,5]=>011001
[3,2,4,1,7,5,6]=>[4,3,2,1,7,5,6]=>[3,2,4,1,7,6,5]=>011011
[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>[3,2,4,1,7,5,6]=>011001
[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[3,2,4,5,1,6,7]=>010100
[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>[3,2,4,5,1,7,6]=>010101
[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[3,2,4,5,6,1,7]=>010010
[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[3,2,4,5,6,7,1]=>010001
[3,2,4,5,7,1,6]=>[7,3,2,4,5,1,6]=>[3,2,4,5,7,6,1]=>010011
[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>[3,2,4,5,7,1,6]=>010001
[3,2,4,6,1,5,7]=>[6,3,2,4,1,5,7]=>[3,2,4,6,5,1,7]=>010110
[3,2,4,6,1,7,5]=>[7,3,2,4,6,1,5]=>[3,2,4,7,5,6,1]=>010011
[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]=>[3,2,4,6,1,5,7]=>010010
[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>[3,2,4,6,5,7,1]=>010011
[3,2,4,6,7,1,5]=>[7,3,2,4,1,6,5]=>[3,2,4,6,7,5,1]=>010101
[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]=>[3,2,4,6,7,1,5]=>010001
[3,2,4,7,1,5,6]=>[7,3,2,4,1,5,6]=>[3,2,4,7,6,5,1]=>010111
[3,2,4,7,1,6,5]=>[6,3,2,4,7,1,5]=>[3,2,4,6,1,7,5]=>010011
[3,2,4,7,5,1,6]=>[5,3,2,4,7,1,6]=>[3,2,4,7,6,1,5]=>010011
[3,2,4,7,5,6,1]=>[6,3,2,4,7,5,1]=>[3,2,4,7,1,6,5]=>010011
[3,2,4,7,6,1,5]=>[6,3,2,4,1,7,5]=>[3,2,4,7,5,1,6]=>010101
[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>[3,2,4,7,1,5,6]=>010001
[3,2,5,1,4,6,7]=>[5,3,2,1,4,6,7]=>[3,2,5,4,1,6,7]=>011100
[3,2,5,1,4,7,6]=>[5,3,2,1,4,7,6]=>[3,2,5,4,1,7,6]=>011101
[3,2,5,1,6,4,7]=>[6,3,2,5,1,4,7]=>[3,2,6,4,5,1,7]=>010110
[3,2,5,1,6,7,4]=>[7,3,2,5,1,6,4]=>[3,2,6,7,4,5,1]=>010101
[3,2,5,1,7,4,6]=>[7,3,2,5,1,4,6]=>[3,2,7,6,4,5,1]=>010111
[3,2,5,1,7,6,4]=>[6,3,2,5,1,7,4]=>[3,2,7,4,5,1,6]=>010101
[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>[3,2,5,1,4,6,7]=>010100
[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]=>[3,2,5,1,4,7,6]=>010101
[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>[3,2,5,4,6,1,7]=>010110
[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>[3,2,5,4,6,7,1]=>010101
[3,2,5,4,7,1,6]=>[7,3,2,5,4,1,6]=>[3,2,5,4,7,6,1]=>010111
[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>[3,2,5,4,7,1,6]=>010101
[3,2,5,6,1,4,7]=>[6,3,2,1,5,4,7]=>[3,2,5,6,4,1,7]=>011010
[3,2,5,6,1,7,4]=>[7,3,2,6,5,1,4]=>[3,2,5,7,4,6,1]=>010011
[3,2,5,6,4,1,7]=>[4,3,2,6,5,1,7]=>[3,2,5,6,1,4,7]=>010010
[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>[3,2,5,6,4,7,1]=>010011
[3,2,5,6,7,1,4]=>[7,3,2,1,5,6,4]=>[3,2,5,6,7,4,1]=>011001
[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]=>[3,2,5,6,7,1,4]=>010001
[3,2,5,7,1,4,6]=>[7,3,2,1,5,4,6]=>[3,2,5,7,6,4,1]=>011011
[3,2,5,7,1,6,4]=>[6,3,2,7,5,1,4]=>[3,2,5,6,1,7,4]=>010011
[3,2,5,7,4,1,6]=>[4,3,2,7,5,1,6]=>[3,2,5,7,6,1,4]=>010011
[3,2,5,7,4,6,1]=>[6,3,2,7,5,4,1]=>[3,2,5,7,1,6,4]=>010011
[3,2,5,7,6,1,4]=>[6,3,2,1,5,7,4]=>[3,2,5,7,4,1,6]=>011001
[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]=>[3,2,5,7,1,4,6]=>010001
[3,2,6,1,4,5,7]=>[6,3,2,1,4,5,7]=>[3,2,6,5,4,1,7]=>011110
[3,2,6,1,4,7,5]=>[7,3,2,1,6,4,5]=>[3,2,7,5,6,4,1]=>011011
[3,2,6,1,5,4,7]=>[5,3,2,6,1,4,7]=>[3,2,5,1,6,4,7]=>010110
[3,2,6,1,5,7,4]=>[7,3,2,6,1,5,4]=>[3,2,7,4,6,5,1]=>010111
[3,2,6,1,7,4,5]=>[7,3,2,6,1,4,5]=>[3,2,6,4,7,5,1]=>010111
[3,2,6,1,7,5,4]=>[5,3,2,7,6,1,4]=>[3,2,6,1,5,7,4]=>010011
[3,2,6,4,1,5,7]=>[4,3,2,6,1,5,7]=>[3,2,6,5,1,4,7]=>010110
[3,2,6,4,1,7,5]=>[4,3,2,7,6,1,5]=>[3,2,7,5,6,1,4]=>010011
[3,2,6,4,5,1,7]=>[5,3,2,6,4,1,7]=>[3,2,6,1,5,4,7]=>010110
[3,2,6,4,5,7,1]=>[7,3,2,6,4,5,1]=>[3,2,6,5,4,7,1]=>010111
[3,2,6,4,7,1,5]=>[7,3,2,6,4,1,5]=>[3,2,7,5,4,6,1]=>010111
[3,2,6,4,7,5,1]=>[5,3,2,7,6,4,1]=>[3,2,7,1,5,6,4]=>010011
[3,2,6,5,1,4,7]=>[5,3,2,1,6,4,7]=>[3,2,6,4,1,5,7]=>011010
[3,2,6,5,1,7,4]=>[7,3,2,5,6,1,4]=>[3,2,7,4,5,6,1]=>010011
[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]=>[3,2,6,1,4,5,7]=>010010
[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>[3,2,6,4,5,7,1]=>010011
[3,2,6,5,7,1,4]=>[7,3,2,1,6,5,4]=>[3,2,6,5,7,4,1]=>011011
[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]=>[3,2,6,5,7,1,4]=>010011
[3,2,6,7,1,4,5]=>[7,3,2,1,4,6,5]=>[3,2,6,7,5,4,1]=>011101
[3,2,6,7,1,5,4]=>[5,3,2,7,1,6,4]=>[3,2,5,1,6,7,4]=>010101
[3,2,6,7,4,1,5]=>[4,3,2,7,1,6,5]=>[3,2,6,7,5,1,4]=>010101
[3,2,6,7,4,5,1]=>[5,3,2,7,4,6,1]=>[3,2,6,7,1,5,4]=>010101
[3,2,6,7,5,1,4]=>[5,3,2,1,7,6,4]=>[3,2,6,7,4,1,5]=>011001
[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]=>[3,2,6,7,1,4,5]=>010001
[3,2,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>[3,2,7,6,5,4,1]=>011111
[3,2,7,1,4,6,5]=>[6,3,2,1,7,4,5]=>[3,2,6,4,1,7,5]=>011011
[3,2,7,1,5,4,6]=>[5,3,2,7,1,4,6]=>[3,2,5,1,7,6,4]=>010111
[3,2,7,1,5,6,4]=>[6,3,2,7,1,5,4]=>[3,2,6,5,1,7,4]=>010111
[3,2,7,1,6,4,5]=>[6,3,2,7,1,4,5]=>[3,2,7,5,1,6,4]=>010111
[3,2,7,1,6,5,4]=>[5,3,2,6,7,1,4]=>[3,2,7,4,6,1,5]=>010011
[3,2,7,4,1,5,6]=>[4,3,2,7,1,5,6]=>[3,2,7,6,5,1,4]=>010111
[3,2,7,4,1,6,5]=>[4,3,2,6,7,1,5]=>[3,2,6,1,4,7,5]=>010011
[3,2,7,4,5,1,6]=>[5,3,2,7,4,1,6]=>[3,2,7,6,1,5,4]=>010111
[3,2,7,4,5,6,1]=>[6,3,2,7,4,5,1]=>[3,2,7,1,6,5,4]=>010111
[3,2,7,4,6,1,5]=>[6,3,2,7,4,1,5]=>[3,2,6,1,7,5,4]=>010111
[3,2,7,4,6,5,1]=>[5,3,2,6,7,4,1]=>[3,2,6,4,7,1,5]=>010011
[3,2,7,5,1,4,6]=>[5,3,2,1,7,4,6]=>[3,2,7,6,4,1,5]=>011011
[3,2,7,5,1,6,4]=>[6,3,2,5,7,1,4]=>[3,2,6,1,7,4,5]=>010011
[3,2,7,5,4,1,6]=>[4,3,2,5,7,1,6]=>[3,2,7,6,1,4,5]=>010011
[3,2,7,5,4,6,1]=>[6,3,2,5,7,4,1]=>[3,2,7,1,6,4,5]=>010011
[3,2,7,5,6,1,4]=>[6,3,2,1,7,5,4]=>[3,2,7,4,1,6,5]=>011011
[3,2,7,5,6,4,1]=>[4,3,2,6,7,5,1]=>[3,2,7,1,4,6,5]=>010011
[3,2,7,6,1,4,5]=>[6,3,2,1,4,7,5]=>[3,2,7,5,4,1,6]=>011101
[3,2,7,6,1,5,4]=>[5,3,2,6,1,7,4]=>[3,2,5,1,7,4,6]=>010101
[3,2,7,6,4,1,5]=>[4,3,2,6,1,7,5]=>[3,2,7,5,1,4,6]=>010101
[3,2,7,6,4,5,1]=>[5,3,2,6,4,7,1]=>[3,2,7,1,5,4,6]=>010101
[3,2,7,6,5,1,4]=>[5,3,2,1,6,7,4]=>[3,2,7,4,1,5,6]=>011001
[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>[3,2,7,1,4,5,6]=>010001
[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>101000
[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>[3,4,2,1,5,7,6]=>101001
[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>[3,4,2,1,6,5,7]=>101010
[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>[3,4,2,1,6,7,5]=>101001
[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>[3,4,2,1,7,6,5]=>101011
[3,4,1,2,7,6,5]=>[4,1,3,2,6,7,5]=>[3,4,2,1,7,5,6]=>101001
[3,4,1,5,2,6,7]=>[5,4,3,1,2,6,7]=>[3,5,2,4,1,6,7]=>001100
[3,4,1,5,2,7,6]=>[5,4,3,1,2,7,6]=>[3,5,2,4,1,7,6]=>001101
[3,4,1,5,6,2,7]=>[6,4,3,1,5,2,7]=>[3,5,6,2,4,1,7]=>001010
[3,4,1,5,6,7,2]=>[7,4,3,1,5,6,2]=>[3,5,6,7,2,4,1]=>001001
[3,4,1,5,7,2,6]=>[7,4,3,1,5,2,6]=>[3,5,7,6,2,4,1]=>001011
[3,4,1,5,7,6,2]=>[6,4,3,1,5,7,2]=>[3,5,7,2,4,1,6]=>001001
[3,4,1,6,2,5,7]=>[6,4,3,1,2,5,7]=>[3,6,5,2,4,1,7]=>001110
[3,4,1,6,2,7,5]=>[7,4,3,1,6,2,5]=>[3,7,5,6,2,4,1]=>001011
[3,4,1,6,5,2,7]=>[5,4,3,1,6,2,7]=>[3,6,2,4,1,5,7]=>001010
[3,4,1,6,5,7,2]=>[7,4,3,1,6,5,2]=>[3,6,5,7,2,4,1]=>001011
[3,4,1,6,7,2,5]=>[7,4,3,1,2,6,5]=>[3,6,7,5,2,4,1]=>001101
[3,4,1,6,7,5,2]=>[5,4,3,1,7,6,2]=>[3,6,7,2,4,1,5]=>001001
[3,4,1,7,2,5,6]=>[7,4,3,1,2,5,6]=>[3,7,6,5,2,4,1]=>001111
[3,4,1,7,2,6,5]=>[6,4,3,1,7,2,5]=>[3,6,2,4,1,7,5]=>001011
[3,4,1,7,5,2,6]=>[5,4,3,1,7,2,6]=>[3,7,6,2,4,1,5]=>001011
[3,4,1,7,5,6,2]=>[6,4,3,1,7,5,2]=>[3,7,2,4,1,6,5]=>001011
[3,4,1,7,6,2,5]=>[6,4,3,1,2,7,5]=>[3,7,5,2,4,1,6]=>001101
[3,4,1,7,6,5,2]=>[5,4,3,1,6,7,2]=>[3,7,2,4,1,5,6]=>001001
[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[3,4,1,2,5,6,7]=>001000
[3,4,2,1,5,7,6]=>[2,4,3,1,5,7,6]=>[3,4,1,2,5,7,6]=>001001
[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]=>[3,4,1,2,6,5,7]=>001010
[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]=>[3,4,1,2,6,7,5]=>001001
[3,4,2,1,7,5,6]=>[2,4,3,1,7,5,6]=>[3,4,1,2,7,6,5]=>001011
[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]=>[3,4,1,2,7,5,6]=>001001
[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[3,4,2,5,1,6,7]=>001100
[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>[3,4,2,5,1,7,6]=>001101
[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[3,4,2,5,6,1,7]=>001010
[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[3,4,2,5,6,7,1]=>001001
[3,4,2,5,7,1,6]=>[7,4,3,2,5,1,6]=>[3,4,2,5,7,6,1]=>001011
[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]=>[3,4,2,5,7,1,6]=>001001
[3,4,2,6,1,5,7]=>[6,4,3,2,1,5,7]=>[3,4,2,6,5,1,7]=>001110
[3,4,2,6,1,7,5]=>[7,4,3,2,6,1,5]=>[3,4,2,7,5,6,1]=>001011
[3,4,2,6,5,1,7]=>[5,4,3,2,6,1,7]=>[3,4,2,6,1,5,7]=>001010
[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>[3,4,2,6,5,7,1]=>001011
[3,4,2,6,7,1,5]=>[7,4,3,2,1,6,5]=>[3,4,2,6,7,5,1]=>001101
[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]=>[3,4,2,6,7,1,5]=>001001
[3,4,2,7,1,5,6]=>[7,4,3,2,1,5,6]=>[3,4,2,7,6,5,1]=>001111
[3,4,2,7,1,6,5]=>[6,4,3,2,7,1,5]=>[3,4,2,6,1,7,5]=>001011
[3,4,2,7,5,1,6]=>[5,4,3,2,7,1,6]=>[3,4,2,7,6,1,5]=>001011
[3,4,2,7,5,6,1]=>[6,4,3,2,7,5,1]=>[3,4,2,7,1,6,5]=>001011
[3,4,2,7,6,1,5]=>[6,4,3,2,1,7,5]=>[3,4,2,7,5,1,6]=>001101
[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]=>[3,4,2,7,1,5,6]=>001001
[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[3,4,5,2,1,6,7]=>100100
[3,4,5,1,2,7,6]=>[5,1,3,4,2,7,6]=>[3,4,5,2,1,7,6]=>100101
[3,4,5,1,6,2,7]=>[6,5,3,4,1,2,7]=>[3,4,6,2,5,1,7]=>000110
[3,4,5,1,6,7,2]=>[7,5,3,4,1,6,2]=>[3,4,6,7,2,5,1]=>000101
[3,4,5,1,7,2,6]=>[7,5,3,4,1,2,6]=>[3,4,7,6,2,5,1]=>000111
[3,4,5,1,7,6,2]=>[6,5,3,4,1,7,2]=>[3,4,7,2,5,1,6]=>000101
[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[3,4,5,1,2,6,7]=>000100
[3,4,5,2,1,7,6]=>[2,5,3,4,1,7,6]=>[3,4,5,1,2,7,6]=>000101
[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[3,4,5,2,6,1,7]=>000110
[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[3,4,5,2,6,7,1]=>000101
[3,4,5,2,7,1,6]=>[7,5,3,4,2,1,6]=>[3,4,5,2,7,6,1]=>000111
[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]=>[3,4,5,2,7,1,6]=>000101
[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[3,4,5,6,2,1,7]=>100010
[3,4,5,6,1,7,2]=>[7,6,3,4,5,1,2]=>[3,4,5,7,2,6,1]=>000011
[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[3,4,5,6,1,2,7]=>000010
[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[3,4,5,6,2,7,1]=>000011
[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[3,4,5,6,7,2,1]=>100001
[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[3,4,5,6,7,1,2]=>000001
[3,4,5,7,1,2,6]=>[7,1,3,4,5,2,6]=>[3,4,5,7,6,2,1]=>100011
[3,4,5,7,1,6,2]=>[6,7,3,4,5,1,2]=>[3,4,5,6,1,7,2]=>000011
[3,4,5,7,2,1,6]=>[2,7,3,4,5,1,6]=>[3,4,5,7,6,1,2]=>000011
[3,4,5,7,2,6,1]=>[6,7,3,4,5,2,1]=>[3,4,5,7,1,6,2]=>000011
[3,4,5,7,6,1,2]=>[6,1,3,4,5,7,2]=>[3,4,5,7,2,1,6]=>100001
[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]=>[3,4,5,7,1,2,6]=>000001
[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[3,4,6,5,2,1,7]=>100110
[3,4,6,1,2,7,5]=>[7,1,3,4,6,2,5]=>[3,4,7,5,6,2,1]=>100011
[3,4,6,1,5,2,7]=>[5,6,3,4,1,2,7]=>[3,4,5,1,6,2,7]=>000110
[3,4,6,1,5,7,2]=>[7,6,3,4,1,5,2]=>[3,4,7,2,6,5,1]=>000111
[3,4,6,1,7,2,5]=>[7,6,3,4,1,2,5]=>[3,4,6,2,7,5,1]=>000111
[3,4,6,1,7,5,2]=>[5,7,3,4,6,1,2]=>[3,4,6,1,5,7,2]=>000011
[3,4,6,2,1,5,7]=>[2,6,3,4,1,5,7]=>[3,4,6,5,1,2,7]=>000110
[3,4,6,2,1,7,5]=>[2,7,3,4,6,1,5]=>[3,4,7,5,6,1,2]=>000011
[3,4,6,2,5,1,7]=>[5,6,3,4,2,1,7]=>[3,4,6,1,5,2,7]=>000110
[3,4,6,2,5,7,1]=>[7,6,3,4,2,5,1]=>[3,4,6,5,2,7,1]=>000111
[3,4,6,2,7,1,5]=>[7,6,3,4,2,1,5]=>[3,4,7,5,2,6,1]=>000111
[3,4,6,2,7,5,1]=>[5,7,3,4,6,2,1]=>[3,4,7,1,5,6,2]=>000011
[3,4,6,5,1,2,7]=>[5,1,3,4,6,2,7]=>[3,4,6,2,1,5,7]=>100010
[3,4,6,5,1,7,2]=>[7,5,3,4,6,1,2]=>[3,4,7,2,5,6,1]=>000011
[3,4,6,5,2,1,7]=>[2,5,3,4,6,1,7]=>[3,4,6,1,2,5,7]=>000010
[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]=>[3,4,6,2,5,7,1]=>000011
[3,4,6,5,7,1,2]=>[7,1,3,4,6,5,2]=>[3,4,6,5,7,2,1]=>100011
[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]=>[3,4,6,5,7,1,2]=>000011
[3,4,6,7,1,2,5]=>[7,1,3,4,2,6,5]=>[3,4,6,7,5,2,1]=>100101
[3,4,6,7,1,5,2]=>[5,7,3,4,1,6,2]=>[3,4,5,1,6,7,2]=>000101
[3,4,6,7,2,1,5]=>[2,7,3,4,1,6,5]=>[3,4,6,7,5,1,2]=>000101
[3,4,6,7,2,5,1]=>[5,7,3,4,2,6,1]=>[3,4,6,7,1,5,2]=>000101
[3,4,6,7,5,1,2]=>[5,1,3,4,7,6,2]=>[3,4,6,7,2,1,5]=>100001
[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]=>[3,4,6,7,1,2,5]=>000001
[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[3,4,7,6,5,2,1]=>100111
[3,4,7,1,2,6,5]=>[6,1,3,4,7,2,5]=>[3,4,6,2,1,7,5]=>100011
[3,4,7,1,5,2,6]=>[5,7,3,4,1,2,6]=>[3,4,5,1,7,6,2]=>000111
[3,4,7,1,5,6,2]=>[6,7,3,4,1,5,2]=>[3,4,6,5,1,7,2]=>000111
[3,4,7,1,6,2,5]=>[6,7,3,4,1,2,5]=>[3,4,7,5,1,6,2]=>000111
[3,4,7,1,6,5,2]=>[5,6,3,4,7,1,2]=>[3,4,7,2,6,1,5]=>000011
[3,4,7,2,1,5,6]=>[2,7,3,4,1,5,6]=>[3,4,7,6,5,1,2]=>000111
[3,4,7,2,1,6,5]=>[2,6,3,4,7,1,5]=>[3,4,6,1,2,7,5]=>000011
[3,4,7,2,5,1,6]=>[5,7,3,4,2,1,6]=>[3,4,7,6,1,5,2]=>000111
[3,4,7,2,5,6,1]=>[6,7,3,4,2,5,1]=>[3,4,7,1,6,5,2]=>000111
[3,4,7,2,6,1,5]=>[6,7,3,4,2,1,5]=>[3,4,6,1,7,5,2]=>000111
[3,4,7,2,6,5,1]=>[5,6,3,4,7,2,1]=>[3,4,6,2,7,1,5]=>000011
[3,4,7,5,1,2,6]=>[5,1,3,4,7,2,6]=>[3,4,7,6,2,1,5]=>100011
[3,4,7,5,1,6,2]=>[6,5,3,4,7,1,2]=>[3,4,6,1,7,2,5]=>000011
[3,4,7,5,2,1,6]=>[2,5,3,4,7,1,6]=>[3,4,7,6,1,2,5]=>000011
[3,4,7,5,2,6,1]=>[6,5,3,4,7,2,1]=>[3,4,7,1,6,2,5]=>000011
[3,4,7,5,6,1,2]=>[6,1,3,4,7,5,2]=>[3,4,7,2,1,6,5]=>100011
[3,4,7,5,6,2,1]=>[2,6,3,4,7,5,1]=>[3,4,7,1,2,6,5]=>000011
[3,4,7,6,1,2,5]=>[6,1,3,4,2,7,5]=>[3,4,7,5,2,1,6]=>100101
[3,4,7,6,1,5,2]=>[5,6,3,4,1,7,2]=>[3,4,5,1,7,2,6]=>000101
[3,4,7,6,2,1,5]=>[2,6,3,4,1,7,5]=>[3,4,7,5,1,2,6]=>000101
[3,4,7,6,2,5,1]=>[5,6,3,4,2,7,1]=>[3,4,7,1,5,2,6]=>000101
[3,4,7,6,5,1,2]=>[5,1,3,4,6,7,2]=>[3,4,7,2,1,5,6]=>100001
[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]=>[3,4,7,1,2,5,6]=>000001
[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[3,5,4,2,1,6,7]=>101100
[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>[3,5,4,2,1,7,6]=>101101
[3,5,1,2,6,4,7]=>[6,1,3,5,2,4,7]=>[3,6,4,5,2,1,7]=>100110
[3,5,1,2,6,7,4]=>[7,1,3,5,2,6,4]=>[3,6,7,4,5,2,1]=>100101
[3,5,1,2,7,4,6]=>[7,1,3,5,2,4,6]=>[3,7,6,4,5,2,1]=>100111
[3,5,1,2,7,6,4]=>[6,1,3,5,2,7,4]=>[3,7,4,5,2,1,6]=>100101
[3,5,1,4,2,6,7]=>[4,5,3,1,2,6,7]=>[3,4,1,5,2,6,7]=>001100
[3,5,1,4,2,7,6]=>[4,5,3,1,2,7,6]=>[3,4,1,5,2,7,6]=>001101
[3,5,1,4,6,2,7]=>[6,5,3,1,4,2,7]=>[3,6,2,5,4,1,7]=>001110
[3,5,1,4,6,7,2]=>[7,5,3,1,4,6,2]=>[3,6,7,2,5,4,1]=>001101
[3,5,1,4,7,2,6]=>[7,5,3,1,4,2,6]=>[3,7,6,2,5,4,1]=>001111
[3,5,1,4,7,6,2]=>[6,5,3,1,4,7,2]=>[3,7,2,5,4,1,6]=>001101
[3,5,1,6,2,4,7]=>[6,5,3,1,2,4,7]=>[3,5,2,6,4,1,7]=>001110
[3,5,1,6,2,7,4]=>[7,6,3,5,1,2,4]=>[3,6,2,7,4,5,1]=>000111
[3,5,1,6,4,2,7]=>[4,6,3,5,1,2,7]=>[3,5,1,4,6,2,7]=>000110
[3,5,1,6,4,7,2]=>[7,6,3,5,1,4,2]=>[3,7,2,6,4,5,1]=>000111
[3,5,1,6,7,2,4]=>[7,5,3,1,2,6,4]=>[3,5,2,6,7,4,1]=>001101
[3,5,1,6,7,4,2]=>[4,7,3,5,1,6,2]=>[3,5,1,4,6,7,2]=>000101
[3,5,1,7,2,4,6]=>[7,5,3,1,2,4,6]=>[3,5,2,7,6,4,1]=>001111
[3,5,1,7,2,6,4]=>[6,7,3,5,1,2,4]=>[3,7,4,5,1,6,2]=>000111
[3,5,1,7,4,2,6]=>[4,7,3,5,1,2,6]=>[3,5,1,4,7,6,2]=>000111
[3,5,1,7,4,6,2]=>[6,7,3,5,1,4,2]=>[3,6,4,5,1,7,2]=>000111
[3,5,1,7,6,2,4]=>[6,5,3,1,2,7,4]=>[3,5,2,7,4,1,6]=>001101
[3,5,1,7,6,4,2]=>[4,6,3,5,1,7,2]=>[3,5,1,4,7,2,6]=>000101
[3,5,2,1,4,6,7]=>[2,5,3,1,4,6,7]=>[3,5,4,1,2,6,7]=>001100
[3,5,2,1,4,7,6]=>[2,5,3,1,4,7,6]=>[3,5,4,1,2,7,6]=>001101
[3,5,2,1,6,4,7]=>[2,6,3,5,1,4,7]=>[3,6,4,5,1,2,7]=>000110
[3,5,2,1,6,7,4]=>[2,7,3,5,1,6,4]=>[3,6,7,4,5,1,2]=>000101
[3,5,2,1,7,4,6]=>[2,7,3,5,1,4,6]=>[3,7,6,4,5,1,2]=>000111
[3,5,2,1,7,6,4]=>[2,6,3,5,1,7,4]=>[3,7,4,5,1,2,6]=>000101
[3,5,2,4,1,6,7]=>[4,5,3,2,1,6,7]=>[3,5,1,4,2,6,7]=>001100
[3,5,2,4,1,7,6]=>[4,5,3,2,1,7,6]=>[3,5,1,4,2,7,6]=>001101
[3,5,2,4,6,1,7]=>[6,5,3,2,4,1,7]=>[3,5,4,2,6,1,7]=>001110
[3,5,2,4,6,7,1]=>[7,5,3,2,4,6,1]=>[3,5,4,2,6,7,1]=>001101
[3,5,2,4,7,1,6]=>[7,5,3,2,4,1,6]=>[3,5,4,2,7,6,1]=>001111
[3,5,2,4,7,6,1]=>[6,5,3,2,4,7,1]=>[3,5,4,2,7,1,6]=>001101
[3,5,2,6,1,4,7]=>[6,5,3,2,1,4,7]=>[3,6,4,2,5,1,7]=>001110
[3,5,2,6,1,7,4]=>[7,6,3,5,2,1,4]=>[3,7,4,5,2,6,1]=>000111
[3,5,2,6,4,1,7]=>[4,6,3,5,2,1,7]=>[3,6,1,4,5,2,7]=>000110
[3,5,2,6,4,7,1]=>[7,6,3,5,2,4,1]=>[3,6,4,5,2,7,1]=>000111
[3,5,2,6,7,1,4]=>[7,5,3,2,1,6,4]=>[3,6,7,4,2,5,1]=>001101
[3,5,2,6,7,4,1]=>[4,7,3,5,2,6,1]=>[3,6,7,1,4,5,2]=>000101
[3,5,2,7,1,4,6]=>[7,5,3,2,1,4,6]=>[3,7,6,4,2,5,1]=>001111
[3,5,2,7,1,6,4]=>[6,7,3,5,2,1,4]=>[3,6,1,7,4,5,2]=>000111
[3,5,2,7,4,1,6]=>[4,7,3,5,2,1,6]=>[3,7,6,1,4,5,2]=>000111
[3,5,2,7,4,6,1]=>[6,7,3,5,2,4,1]=>[3,7,1,6,4,5,2]=>000111
[3,5,2,7,6,1,4]=>[6,5,3,2,1,7,4]=>[3,7,4,2,5,1,6]=>001101
[3,5,2,7,6,4,1]=>[4,6,3,5,2,7,1]=>[3,7,1,4,5,2,6]=>000101
[3,5,4,1,2,6,7]=>[4,1,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>100100
[3,5,4,1,2,7,6]=>[4,1,3,5,2,7,6]=>[3,5,2,1,4,7,6]=>100101
[3,5,4,1,6,2,7]=>[6,4,3,5,1,2,7]=>[3,6,2,4,5,1,7]=>000110
[3,5,4,1,6,7,2]=>[7,4,3,5,1,6,2]=>[3,6,7,2,4,5,1]=>000101
[3,5,4,1,7,2,6]=>[7,4,3,5,1,2,6]=>[3,7,6,2,4,5,1]=>000111
[3,5,4,1,7,6,2]=>[6,4,3,5,1,7,2]=>[3,7,2,4,5,1,6]=>000101
[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]=>[3,5,1,2,4,6,7]=>000100
[3,5,4,2,1,7,6]=>[2,4,3,5,1,7,6]=>[3,5,1,2,4,7,6]=>000101
[3,5,4,2,6,1,7]=>[6,4,3,5,2,1,7]=>[3,5,2,4,6,1,7]=>000110
[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]=>[3,5,2,4,6,7,1]=>000101
[3,5,4,2,7,1,6]=>[7,4,3,5,2,1,6]=>[3,5,2,4,7,6,1]=>000111
[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]=>[3,5,2,4,7,1,6]=>000101
[3,5,4,6,1,2,7]=>[6,1,3,5,4,2,7]=>[3,5,4,6,2,1,7]=>100110
[3,5,4,6,1,7,2]=>[7,6,3,5,4,1,2]=>[3,5,4,7,2,6,1]=>000111
[3,5,4,6,2,1,7]=>[2,6,3,5,4,1,7]=>[3,5,4,6,1,2,7]=>000110
[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>[3,5,4,6,2,7,1]=>000111
[3,5,4,6,7,1,2]=>[7,1,3,5,4,6,2]=>[3,5,4,6,7,2,1]=>100101
[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]=>[3,5,4,6,7,1,2]=>000101
[3,5,4,7,1,2,6]=>[7,1,3,5,4,2,6]=>[3,5,4,7,6,2,1]=>100111
[3,5,4,7,1,6,2]=>[6,7,3,5,4,1,2]=>[3,5,4,6,1,7,2]=>000111
[3,5,4,7,2,1,6]=>[2,7,3,5,4,1,6]=>[3,5,4,7,6,1,2]=>000111
[3,5,4,7,2,6,1]=>[6,7,3,5,4,2,1]=>[3,5,4,7,1,6,2]=>000111
[3,5,4,7,6,1,2]=>[6,1,3,5,4,7,2]=>[3,5,4,7,2,1,6]=>100101
[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]=>[3,5,4,7,1,2,6]=>000101
[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[3,5,6,4,2,1,7]=>101010
[3,5,6,1,2,7,4]=>[7,1,3,6,5,2,4]=>[3,5,7,4,6,2,1]=>100011
[3,5,6,1,4,2,7]=>[4,6,3,1,5,2,7]=>[3,4,1,5,6,2,7]=>001010
[3,5,6,1,4,7,2]=>[7,6,3,1,5,4,2]=>[3,5,7,2,6,4,1]=>001011
[3,5,6,1,7,2,4]=>[7,6,3,1,5,2,4]=>[3,5,6,2,7,4,1]=>001011
[3,5,6,1,7,4,2]=>[4,7,3,6,5,1,2]=>[3,5,6,1,4,7,2]=>000011
[3,5,6,2,1,4,7]=>[2,6,3,1,5,4,7]=>[3,5,6,4,1,2,7]=>001010
[3,5,6,2,1,7,4]=>[2,7,3,6,5,1,4]=>[3,5,7,4,6,1,2]=>000011
[3,5,6,2,4,1,7]=>[4,6,3,2,5,1,7]=>[3,5,6,1,4,2,7]=>001010
[3,5,6,2,4,7,1]=>[7,6,3,2,5,4,1]=>[3,5,6,4,2,7,1]=>001011
[3,5,6,2,7,1,4]=>[7,6,3,2,5,1,4]=>[3,5,7,4,2,6,1]=>001011
[3,5,6,2,7,4,1]=>[4,7,3,6,5,2,1]=>[3,5,7,1,4,6,2]=>000011
[3,5,6,4,1,2,7]=>[4,1,3,6,5,2,7]=>[3,5,6,2,1,4,7]=>100010
[3,5,6,4,1,7,2]=>[7,4,3,6,5,1,2]=>[3,5,7,2,4,6,1]=>000011
[3,5,6,4,2,1,7]=>[2,4,3,6,5,1,7]=>[3,5,6,1,2,4,7]=>000010
[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]=>[3,5,6,2,4,7,1]=>000011
[3,5,6,4,7,1,2]=>[7,1,3,6,5,4,2]=>[3,5,6,4,7,2,1]=>100011
[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]=>[3,5,6,4,7,1,2]=>000011
[3,5,6,7,1,2,4]=>[7,1,3,2,5,6,4]=>[3,5,6,7,4,2,1]=>101001
[3,5,6,7,1,4,2]=>[4,7,3,1,5,6,2]=>[3,4,1,5,6,7,2]=>001001
[3,5,6,7,2,1,4]=>[2,7,3,1,5,6,4]=>[3,5,6,7,4,1,2]=>001001
[3,5,6,7,2,4,1]=>[4,7,3,2,5,6,1]=>[3,5,6,7,1,4,2]=>001001
[3,5,6,7,4,1,2]=>[4,1,3,7,5,6,2]=>[3,5,6,7,2,1,4]=>100001
[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]=>[3,5,6,7,1,2,4]=>000001
[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[3,5,7,6,4,2,1]=>101011
[3,5,7,1,2,6,4]=>[6,1,3,7,5,2,4]=>[3,5,6,2,1,7,4]=>100011
[3,5,7,1,4,2,6]=>[4,7,3,1,5,2,6]=>[3,4,1,5,7,6,2]=>001011
[3,5,7,1,4,6,2]=>[6,7,3,1,5,4,2]=>[3,5,6,4,1,7,2]=>001011
[3,5,7,1,6,2,4]=>[6,7,3,1,5,2,4]=>[3,5,7,4,1,6,2]=>001011
[3,5,7,1,6,4,2]=>[4,6,3,7,5,1,2]=>[3,5,7,2,6,1,4]=>000011
[3,5,7,2,1,4,6]=>[2,7,3,1,5,4,6]=>[3,5,7,6,4,1,2]=>001011
[3,5,7,2,1,6,4]=>[2,6,3,7,5,1,4]=>[3,5,6,1,2,7,4]=>000011
[3,5,7,2,4,1,6]=>[4,7,3,2,5,1,6]=>[3,5,7,6,1,4,2]=>001011
[3,5,7,2,4,6,1]=>[6,7,3,2,5,4,1]=>[3,5,7,1,6,4,2]=>001011
[3,5,7,2,6,1,4]=>[6,7,3,2,5,1,4]=>[3,5,6,1,7,4,2]=>001011
[3,5,7,2,6,4,1]=>[4,6,3,7,5,2,1]=>[3,5,6,2,7,1,4]=>000011
[3,5,7,4,1,2,6]=>[4,1,3,7,5,2,6]=>[3,5,7,6,2,1,4]=>100011
[3,5,7,4,1,6,2]=>[6,4,3,7,5,1,2]=>[3,5,6,1,7,2,4]=>000011
[3,5,7,4,2,1,6]=>[2,4,3,7,5,1,6]=>[3,5,7,6,1,2,4]=>000011
[3,5,7,4,2,6,1]=>[6,4,3,7,5,2,1]=>[3,5,7,1,6,2,4]=>000011
[3,5,7,4,6,1,2]=>[6,1,3,7,5,4,2]=>[3,5,7,2,1,6,4]=>100011
[3,5,7,4,6,2,1]=>[2,6,3,7,5,4,1]=>[3,5,7,1,2,6,4]=>000011
[3,5,7,6,1,2,4]=>[6,1,3,2,5,7,4]=>[3,5,7,4,2,1,6]=>101001
[3,5,7,6,1,4,2]=>[4,6,3,1,5,7,2]=>[3,4,1,5,7,2,6]=>001001
[3,5,7,6,2,1,4]=>[2,6,3,1,5,7,4]=>[3,5,7,4,1,2,6]=>001001
[3,5,7,6,2,4,1]=>[4,6,3,2,5,7,1]=>[3,5,7,1,4,2,6]=>001001
[3,5,7,6,4,1,2]=>[4,1,3,6,5,7,2]=>[3,5,7,2,1,4,6]=>100001
[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]=>[3,5,7,1,2,4,6]=>000001
[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[3,6,5,4,2,1,7]=>101110
[3,6,1,2,4,7,5]=>[7,1,3,2,6,4,5]=>[3,7,5,6,4,2,1]=>101011
[3,6,1,2,5,4,7]=>[5,1,3,6,2,4,7]=>[3,5,2,1,6,4,7]=>100110
[3,6,1,2,5,7,4]=>[7,1,3,6,2,5,4]=>[3,7,4,6,5,2,1]=>100111
[3,6,1,2,7,4,5]=>[7,1,3,6,2,4,5]=>[3,6,4,7,5,2,1]=>100111
[3,6,1,2,7,5,4]=>[5,1,3,7,6,2,4]=>[3,6,2,1,5,7,4]=>100011
[3,6,1,4,2,5,7]=>[4,6,3,1,2,5,7]=>[3,4,1,6,5,2,7]=>001110
[3,6,1,4,2,7,5]=>[4,7,3,1,6,2,5]=>[3,4,1,7,5,6,2]=>001011
[3,6,1,4,5,2,7]=>[5,6,3,1,4,2,7]=>[3,5,4,1,6,2,7]=>001110
[3,6,1,4,5,7,2]=>[7,6,3,1,4,5,2]=>[3,7,2,6,5,4,1]=>001111
[3,6,1,4,7,2,5]=>[7,6,3,1,4,2,5]=>[3,6,2,7,5,4,1]=>001111
[3,6,1,4,7,5,2]=>[5,7,3,1,6,4,2]=>[3,6,4,1,5,7,2]=>001011
[3,6,1,5,2,4,7]=>[5,6,3,1,2,4,7]=>[3,6,4,1,5,2,7]=>001110
[3,6,1,5,2,7,4]=>[7,5,3,6,1,2,4]=>[3,7,4,6,2,5,1]=>000111
[3,6,1,5,4,2,7]=>[4,5,3,6,1,2,7]=>[3,6,2,5,1,4,7]=>000110
[3,6,1,5,4,7,2]=>[7,5,3,6,1,4,2]=>[3,6,4,7,2,5,1]=>000111
[3,6,1,5,7,2,4]=>[7,6,3,1,2,5,4]=>[3,6,5,2,7,4,1]=>001111
[3,6,1,5,7,4,2]=>[4,7,3,6,1,5,2]=>[3,6,5,1,4,7,2]=>000111
[3,6,1,7,2,4,5]=>[7,6,3,1,2,4,5]=>[3,7,5,2,6,4,1]=>001111
[3,6,1,7,2,5,4]=>[5,7,3,6,1,2,4]=>[3,5,1,7,4,6,2]=>000111
[3,6,1,7,4,2,5]=>[4,7,3,6,1,2,5]=>[3,7,5,1,4,6,2]=>000111
[3,6,1,7,4,5,2]=>[5,7,3,6,1,4,2]=>[3,5,1,6,4,7,2]=>000111
[3,6,1,7,5,2,4]=>[5,7,3,1,6,2,4]=>[3,7,4,1,5,6,2]=>001011
[3,6,1,7,5,4,2]=>[4,5,3,7,6,1,2]=>[3,7,2,5,6,1,4]=>000011
[3,6,2,1,4,5,7]=>[2,6,3,1,4,5,7]=>[3,6,5,4,1,2,7]=>001110
[3,6,2,1,4,7,5]=>[2,7,3,1,6,4,5]=>[3,7,5,6,4,1,2]=>001011
[3,6,2,1,5,4,7]=>[2,5,3,6,1,4,7]=>[3,5,1,2,6,4,7]=>000110
[3,6,2,1,5,7,4]=>[2,7,3,6,1,5,4]=>[3,7,4,6,5,1,2]=>000111
[3,6,2,1,7,4,5]=>[2,7,3,6,1,4,5]=>[3,6,4,7,5,1,2]=>000111
[3,6,2,1,7,5,4]=>[2,5,3,7,6,1,4]=>[3,6,1,2,5,7,4]=>000011
[3,6,2,4,1,5,7]=>[4,6,3,2,1,5,7]=>[3,6,5,1,4,2,7]=>001110
[3,6,2,4,1,7,5]=>[4,7,3,2,6,1,5]=>[3,7,5,6,1,4,2]=>001011
[3,6,2,4,5,1,7]=>[5,6,3,2,4,1,7]=>[3,6,1,5,4,2,7]=>001110
[3,6,2,4,5,7,1]=>[7,6,3,2,4,5,1]=>[3,6,5,4,2,7,1]=>001111
[3,6,2,4,7,1,5]=>[7,6,3,2,4,1,5]=>[3,7,5,4,2,6,1]=>001111
[3,6,2,4,7,5,1]=>[5,7,3,2,6,4,1]=>[3,7,1,5,6,4,2]=>001011
[3,6,2,5,1,4,7]=>[5,6,3,2,1,4,7]=>[3,5,1,6,4,2,7]=>001110
[3,6,2,5,1,7,4]=>[7,5,3,6,2,1,4]=>[3,5,2,7,4,6,1]=>000111
[3,6,2,5,4,1,7]=>[4,5,3,6,2,1,7]=>[3,5,2,6,1,4,7]=>000110
[3,6,2,5,4,7,1]=>[7,5,3,6,2,4,1]=>[3,5,2,6,4,7,1]=>000111
[3,6,2,5,7,1,4]=>[7,6,3,2,1,5,4]=>[3,7,4,2,6,5,1]=>001111
[3,6,2,5,7,4,1]=>[4,7,3,6,2,5,1]=>[3,7,1,4,6,5,2]=>000111
[3,6,2,7,1,4,5]=>[7,6,3,2,1,4,5]=>[3,6,4,2,7,5,1]=>001111
[3,6,2,7,1,5,4]=>[5,7,3,6,2,1,4]=>[3,7,4,6,1,5,2]=>000111
[3,6,2,7,4,1,5]=>[4,7,3,6,2,1,5]=>[3,6,1,4,7,5,2]=>000111
[3,6,2,7,4,5,1]=>[5,7,3,6,2,4,1]=>[3,6,4,7,1,5,2]=>000111
[3,6,2,7,5,1,4]=>[5,7,3,2,6,1,4]=>[3,6,1,5,7,4,2]=>001011
[3,6,2,7,5,4,1]=>[4,5,3,7,6,2,1]=>[3,6,2,5,7,1,4]=>000011
[3,6,4,1,2,5,7]=>[4,1,3,6,2,5,7]=>[3,6,5,2,1,4,7]=>100110
[3,6,4,1,2,7,5]=>[4,1,3,7,6,2,5]=>[3,7,5,6,2,1,4]=>100011
[3,6,4,1,5,2,7]=>[5,4,3,6,1,2,7]=>[3,5,1,6,2,4,7]=>000110
[3,6,4,1,5,7,2]=>[7,4,3,6,1,5,2]=>[3,7,2,4,6,5,1]=>000111
[3,6,4,1,7,2,5]=>[7,4,3,6,1,2,5]=>[3,6,2,4,7,5,1]=>000111
[3,6,4,1,7,5,2]=>[5,4,3,7,6,1,2]=>[3,6,1,5,7,2,4]=>000011
[3,6,4,2,1,5,7]=>[2,4,3,6,1,5,7]=>[3,6,5,1,2,4,7]=>000110
[3,6,4,2,1,7,5]=>[2,4,3,7,6,1,5]=>[3,7,5,6,1,2,4]=>000011
[3,6,4,2,5,1,7]=>[5,4,3,6,2,1,7]=>[3,6,1,5,2,4,7]=>000110
[3,6,4,2,5,7,1]=>[7,4,3,6,2,5,1]=>[3,6,5,2,4,7,1]=>000111
[3,6,4,2,7,1,5]=>[7,4,3,6,2,1,5]=>[3,7,5,2,4,6,1]=>000111
[3,6,4,2,7,5,1]=>[5,4,3,7,6,2,1]=>[3,7,1,5,6,2,4]=>000011
[3,6,4,5,1,2,7]=>[5,1,3,6,4,2,7]=>[3,6,2,1,5,4,7]=>100110
[3,6,4,5,1,7,2]=>[7,5,3,6,4,1,2]=>[3,7,2,5,4,6,1]=>000111
[3,6,4,5,2,1,7]=>[2,5,3,6,4,1,7]=>[3,6,1,2,5,4,7]=>000110
[3,6,4,5,2,7,1]=>[7,5,3,6,4,2,1]=>[3,6,2,5,4,7,1]=>000111
[3,6,4,5,7,1,2]=>[7,1,3,6,4,5,2]=>[3,6,5,4,7,2,1]=>100111
[3,6,4,5,7,2,1]=>[2,7,3,6,4,5,1]=>[3,6,5,4,7,1,2]=>000111
[3,6,4,7,1,2,5]=>[7,1,3,6,4,2,5]=>[3,7,5,4,6,2,1]=>100111
[3,6,4,7,1,5,2]=>[5,7,3,6,4,1,2]=>[3,6,1,5,4,7,2]=>000111
[3,6,4,7,2,1,5]=>[2,7,3,6,4,1,5]=>[3,7,5,4,6,1,2]=>000111
[3,6,4,7,2,5,1]=>[5,7,3,6,4,2,1]=>[3,7,1,5,4,6,2]=>000111
[3,6,4,7,5,1,2]=>[5,1,3,7,6,4,2]=>[3,7,2,1,5,6,4]=>100011
[3,6,4,7,5,2,1]=>[2,5,3,7,6,4,1]=>[3,7,1,2,5,6,4]=>000011
[3,6,5,1,2,4,7]=>[5,1,3,2,6,4,7]=>[3,6,4,2,1,5,7]=>101010
[3,6,5,1,2,7,4]=>[7,1,3,5,6,2,4]=>[3,7,4,5,6,2,1]=>100011
[3,6,5,1,4,2,7]=>[4,5,3,1,6,2,7]=>[3,4,1,6,2,5,7]=>001010
[3,6,5,1,4,7,2]=>[7,5,3,1,6,4,2]=>[3,7,2,5,6,4,1]=>001011
[3,6,5,1,7,2,4]=>[7,5,3,1,6,2,4]=>[3,6,2,5,7,4,1]=>001011
[3,6,5,1,7,4,2]=>[4,7,3,5,6,1,2]=>[3,6,1,4,5,7,2]=>000011
[3,6,5,2,1,4,7]=>[2,5,3,1,6,4,7]=>[3,6,4,1,2,5,7]=>001010
[3,6,5,2,1,7,4]=>[2,7,3,5,6,1,4]=>[3,7,4,5,6,1,2]=>000011
[3,6,5,2,4,1,7]=>[4,5,3,2,6,1,7]=>[3,6,1,4,2,5,7]=>001010
[3,6,5,2,4,7,1]=>[7,5,3,2,6,4,1]=>[3,6,4,2,5,7,1]=>001011
[3,6,5,2,7,1,4]=>[7,5,3,2,6,1,4]=>[3,7,4,2,5,6,1]=>001011
[3,6,5,2,7,4,1]=>[4,7,3,5,6,2,1]=>[3,7,1,4,5,6,2]=>000011
[3,6,5,4,1,2,7]=>[4,1,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>100010
[3,6,5,4,1,7,2]=>[7,4,3,5,6,1,2]=>[3,7,2,4,5,6,1]=>000011
[3,6,5,4,2,1,7]=>[2,4,3,5,6,1,7]=>[3,6,1,2,4,5,7]=>000010
[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]=>[3,6,2,4,5,7,1]=>000011
[3,6,5,4,7,1,2]=>[7,1,3,5,6,4,2]=>[3,6,4,5,7,2,1]=>100011
[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]=>[3,6,4,5,7,1,2]=>000011
[3,6,5,7,1,2,4]=>[7,1,3,2,6,5,4]=>[3,6,5,7,4,2,1]=>101011
[3,6,5,7,1,4,2]=>[4,7,3,1,6,5,2]=>[3,4,1,6,5,7,2]=>001011
[3,6,5,7,2,1,4]=>[2,7,3,1,6,5,4]=>[3,6,5,7,4,1,2]=>001011
[3,6,5,7,2,4,1]=>[4,7,3,2,6,5,1]=>[3,6,5,7,1,4,2]=>001011
[3,6,5,7,4,1,2]=>[4,1,3,7,6,5,2]=>[3,6,5,7,2,1,4]=>100011
[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]=>[3,6,5,7,1,2,4]=>000011
[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[3,6,7,5,4,2,1]=>101101
[3,6,7,1,2,5,4]=>[5,1,3,7,2,6,4]=>[3,5,2,1,6,7,4]=>100101
[3,6,7,1,4,2,5]=>[4,7,3,1,2,6,5]=>[3,4,1,6,7,5,2]=>001101
[3,6,7,1,4,5,2]=>[5,7,3,1,4,6,2]=>[3,5,4,1,6,7,2]=>001101
[3,6,7,1,5,2,4]=>[5,7,3,1,2,6,4]=>[3,6,7,4,1,5,2]=>001101
[3,6,7,1,5,4,2]=>[4,5,3,7,1,6,2]=>[3,6,7,2,5,1,4]=>000101
[3,6,7,2,1,4,5]=>[2,7,3,1,4,6,5]=>[3,6,7,5,4,1,2]=>001101
[3,6,7,2,1,5,4]=>[2,5,3,7,1,6,4]=>[3,5,1,2,6,7,4]=>000101
[3,6,7,2,4,1,5]=>[4,7,3,2,1,6,5]=>[3,6,7,5,1,4,2]=>001101
[3,6,7,2,4,5,1]=>[5,7,3,2,4,6,1]=>[3,6,7,1,5,4,2]=>001101
[3,6,7,2,5,1,4]=>[5,7,3,2,1,6,4]=>[3,5,1,6,7,4,2]=>001101
[3,6,7,2,5,4,1]=>[4,5,3,7,2,6,1]=>[3,5,2,6,7,1,4]=>000101
[3,6,7,4,1,2,5]=>[4,1,3,7,2,6,5]=>[3,6,7,5,2,1,4]=>100101
[3,6,7,4,1,5,2]=>[5,4,3,7,1,6,2]=>[3,5,1,6,7,2,4]=>000101
[3,6,7,4,2,1,5]=>[2,4,3,7,1,6,5]=>[3,6,7,5,1,2,4]=>000101
[3,6,7,4,2,5,1]=>[5,4,3,7,2,6,1]=>[3,6,7,1,5,2,4]=>000101
[3,6,7,4,5,1,2]=>[5,1,3,7,4,6,2]=>[3,6,7,2,1,5,4]=>100101
[3,6,7,4,5,2,1]=>[2,5,3,7,4,6,1]=>[3,6,7,1,2,5,4]=>000101
[3,6,7,5,1,2,4]=>[5,1,3,2,7,6,4]=>[3,6,7,4,2,1,5]=>101001
[3,6,7,5,1,4,2]=>[4,5,3,1,7,6,2]=>[3,4,1,6,7,2,5]=>001001
[3,6,7,5,2,1,4]=>[2,5,3,1,7,6,4]=>[3,6,7,4,1,2,5]=>001001
[3,6,7,5,2,4,1]=>[4,5,3,2,7,6,1]=>[3,6,7,1,4,2,5]=>001001
[3,6,7,5,4,1,2]=>[4,1,3,5,7,6,2]=>[3,6,7,2,1,4,5]=>100001
[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]=>[3,6,7,1,2,4,5]=>000001
[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[3,7,6,5,4,2,1]=>101111
[3,7,1,2,4,6,5]=>[6,1,3,2,7,4,5]=>[3,6,4,2,1,7,5]=>101011
[3,7,1,2,5,4,6]=>[5,1,3,7,2,4,6]=>[3,5,2,1,7,6,4]=>100111
[3,7,1,2,5,6,4]=>[6,1,3,7,2,5,4]=>[3,6,5,2,1,7,4]=>100111
[3,7,1,2,6,4,5]=>[6,1,3,7,2,4,5]=>[3,7,5,2,1,6,4]=>100111
[3,7,1,2,6,5,4]=>[5,1,3,6,7,2,4]=>[3,7,4,6,2,1,5]=>100011
[3,7,1,4,2,5,6]=>[4,7,3,1,2,5,6]=>[3,4,1,7,6,5,2]=>001111
[3,7,1,4,2,6,5]=>[4,6,3,1,7,2,5]=>[3,4,1,6,2,7,5]=>001011
[3,7,1,4,5,2,6]=>[5,7,3,1,4,2,6]=>[3,5,4,1,7,6,2]=>001111
[3,7,1,4,5,6,2]=>[6,7,3,1,4,5,2]=>[3,6,5,4,1,7,2]=>001111
[3,7,1,4,6,2,5]=>[6,7,3,1,4,2,5]=>[3,7,5,4,1,6,2]=>001111
[3,7,1,4,6,5,2]=>[5,6,3,1,7,4,2]=>[3,7,2,6,4,1,5]=>001011
[3,7,1,5,2,4,6]=>[5,7,3,1,2,4,6]=>[3,7,6,4,1,5,2]=>001111
[3,7,1,5,2,6,4]=>[6,5,3,7,1,2,4]=>[3,6,2,5,1,7,4]=>000111
[3,7,1,5,4,2,6]=>[4,5,3,7,1,2,6]=>[3,7,6,2,5,1,4]=>000111
[3,7,1,5,4,6,2]=>[6,5,3,7,1,4,2]=>[3,7,2,5,1,6,4]=>000111
[3,7,1,5,6,2,4]=>[6,7,3,1,2,5,4]=>[3,7,4,1,6,5,2]=>001111
[3,7,1,5,6,4,2]=>[4,6,3,7,1,5,2]=>[3,7,2,6,5,1,4]=>000111
[3,7,1,6,2,4,5]=>[6,7,3,1,2,4,5]=>[3,6,4,1,7,5,2]=>001111
[3,7,1,6,2,5,4]=>[5,6,3,7,1,2,4]=>[3,5,1,6,2,7,4]=>000111
[3,7,1,6,4,2,5]=>[4,6,3,7,1,2,5]=>[3,6,2,7,5,1,4]=>000111
[3,7,1,6,4,5,2]=>[5,6,3,7,1,4,2]=>[3,5,1,7,2,6,4]=>000111
[3,7,1,6,5,2,4]=>[5,6,3,1,7,2,4]=>[3,6,2,7,4,1,5]=>001011
[3,7,1,6,5,4,2]=>[4,5,3,6,7,1,2]=>[3,6,1,4,7,2,5]=>000011
[3,7,2,1,4,5,6]=>[2,7,3,1,4,5,6]=>[3,7,6,5,4,1,2]=>001111
[3,7,2,1,4,6,5]=>[2,6,3,1,7,4,5]=>[3,6,4,1,2,7,5]=>001011
[3,7,2,1,5,4,6]=>[2,5,3,7,1,4,6]=>[3,5,1,2,7,6,4]=>000111
[3,7,2,1,5,6,4]=>[2,6,3,7,1,5,4]=>[3,6,5,1,2,7,4]=>000111
[3,7,2,1,6,4,5]=>[2,6,3,7,1,4,5]=>[3,7,5,1,2,6,4]=>000111
[3,7,2,1,6,5,4]=>[2,5,3,6,7,1,4]=>[3,7,4,6,1,2,5]=>000011
[3,7,2,4,1,5,6]=>[4,7,3,2,1,5,6]=>[3,7,6,5,1,4,2]=>001111
[3,7,2,4,1,6,5]=>[4,6,3,2,7,1,5]=>[3,6,1,4,2,7,5]=>001011
[3,7,2,4,5,1,6]=>[5,7,3,2,4,1,6]=>[3,7,6,1,5,4,2]=>001111
[3,7,2,4,5,6,1]=>[6,7,3,2,4,5,1]=>[3,7,1,6,5,4,2]=>001111
[3,7,2,4,6,1,5]=>[6,7,3,2,4,1,5]=>[3,6,1,7,5,4,2]=>001111
[3,7,2,4,6,5,1]=>[5,6,3,2,7,4,1]=>[3,6,4,2,7,1,5]=>001011
[3,7,2,5,1,4,6]=>[5,7,3,2,1,4,6]=>[3,5,1,7,6,4,2]=>001111
[3,7,2,5,1,6,4]=>[6,5,3,7,2,1,4]=>[3,5,2,6,1,7,4]=>000111
[3,7,2,5,4,1,6]=>[4,5,3,7,2,1,6]=>[3,5,2,7,6,1,4]=>000111
[3,7,2,5,4,6,1]=>[6,5,3,7,2,4,1]=>[3,5,2,7,1,6,4]=>000111
[3,7,2,5,6,1,4]=>[6,7,3,2,1,5,4]=>[3,6,5,1,7,4,2]=>001111
[3,7,2,5,6,4,1]=>[4,6,3,7,2,5,1]=>[3,6,5,2,7,1,4]=>000111
[3,7,2,6,1,4,5]=>[6,7,3,2,1,4,5]=>[3,7,5,1,6,4,2]=>001111
[3,7,2,6,1,5,4]=>[5,6,3,7,2,1,4]=>[3,6,1,5,2,7,4]=>000111
[3,7,2,6,4,1,5]=>[4,6,3,7,2,1,5]=>[3,7,5,2,6,1,4]=>000111
[3,7,2,6,4,5,1]=>[5,6,3,7,2,4,1]=>[3,7,1,5,2,6,4]=>000111
[3,7,2,6,5,1,4]=>[5,6,3,2,7,1,4]=>[3,7,4,2,6,1,5]=>001011
[3,7,2,6,5,4,1]=>[4,5,3,6,7,2,1]=>[3,7,1,4,6,2,5]=>000011
[3,7,4,1,2,5,6]=>[4,1,3,7,2,5,6]=>[3,7,6,5,2,1,4]=>100111
[3,7,4,1,2,6,5]=>[4,1,3,6,7,2,5]=>[3,6,2,1,4,7,5]=>100011
[3,7,4,1,5,2,6]=>[5,4,3,7,1,2,6]=>[3,5,1,7,6,2,4]=>000111
[3,7,4,1,5,6,2]=>[6,4,3,7,1,5,2]=>[3,6,5,1,7,2,4]=>000111
[3,7,4,1,6,2,5]=>[6,4,3,7,1,2,5]=>[3,7,5,1,6,2,4]=>000111
[3,7,4,1,6,5,2]=>[5,4,3,6,7,1,2]=>[3,7,2,4,6,1,5]=>000011
[3,7,4,2,1,5,6]=>[2,4,3,7,1,5,6]=>[3,7,6,5,1,2,4]=>000111
[3,7,4,2,1,6,5]=>[2,4,3,6,7,1,5]=>[3,6,1,2,4,7,5]=>000011
[3,7,4,2,5,1,6]=>[5,4,3,7,2,1,6]=>[3,7,6,1,5,2,4]=>000111
[3,7,4,2,5,6,1]=>[6,4,3,7,2,5,1]=>[3,7,1,6,5,2,4]=>000111
[3,7,4,2,6,1,5]=>[6,4,3,7,2,1,5]=>[3,6,1,7,5,2,4]=>000111
[3,7,4,2,6,5,1]=>[5,4,3,6,7,2,1]=>[3,6,2,4,7,1,5]=>000011
[3,7,4,5,1,2,6]=>[5,1,3,7,4,2,6]=>[3,7,6,2,1,5,4]=>100111
[3,7,4,5,1,6,2]=>[6,5,3,7,4,1,2]=>[3,6,1,7,2,5,4]=>000111
[3,7,4,5,2,1,6]=>[2,5,3,7,4,1,6]=>[3,7,6,1,2,5,4]=>000111
[3,7,4,5,2,6,1]=>[6,5,3,7,4,2,1]=>[3,7,1,6,2,5,4]=>000111
[3,7,4,5,6,1,2]=>[6,1,3,7,4,5,2]=>[3,7,2,1,6,5,4]=>100111
[3,7,4,5,6,2,1]=>[2,6,3,7,4,5,1]=>[3,7,1,2,6,5,4]=>000111
[3,7,4,6,1,2,5]=>[6,1,3,7,4,2,5]=>[3,6,2,1,7,5,4]=>100111
[3,7,4,6,1,5,2]=>[5,6,3,7,4,1,2]=>[3,7,2,6,1,5,4]=>000111
[3,7,4,6,2,1,5]=>[2,6,3,7,4,1,5]=>[3,6,1,2,7,5,4]=>000111
[3,7,4,6,2,5,1]=>[5,6,3,7,4,2,1]=>[3,6,2,7,1,5,4]=>000111
[3,7,4,6,5,1,2]=>[5,1,3,6,7,4,2]=>[3,6,4,7,2,1,5]=>100011
[3,7,4,6,5,2,1]=>[2,5,3,6,7,4,1]=>[3,6,4,7,1,2,5]=>000011
[3,7,5,1,2,4,6]=>[5,1,3,2,7,4,6]=>[3,7,6,4,2,1,5]=>101011
[3,7,5,1,2,6,4]=>[6,1,3,5,7,2,4]=>[3,6,2,1,7,4,5]=>100011
[3,7,5,1,4,2,6]=>[4,5,3,1,7,2,6]=>[3,4,1,7,6,2,5]=>001011
[3,7,5,1,4,6,2]=>[6,5,3,1,7,4,2]=>[3,6,4,1,7,2,5]=>001011
[3,7,5,1,6,2,4]=>[6,5,3,1,7,2,4]=>[3,7,4,1,6,2,5]=>001011
[3,7,5,1,6,4,2]=>[4,6,3,5,7,1,2]=>[3,7,2,6,1,4,5]=>000011
[3,7,5,2,1,4,6]=>[2,5,3,1,7,4,6]=>[3,7,6,4,1,2,5]=>001011
[3,7,5,2,1,6,4]=>[2,6,3,5,7,1,4]=>[3,6,1,2,7,4,5]=>000011
[3,7,5,2,4,1,6]=>[4,5,3,2,7,1,6]=>[3,7,6,1,4,2,5]=>001011
[3,7,5,2,4,6,1]=>[6,5,3,2,7,4,1]=>[3,7,1,6,4,2,5]=>001011
[3,7,5,2,6,1,4]=>[6,5,3,2,7,1,4]=>[3,6,1,7,4,2,5]=>001011
[3,7,5,2,6,4,1]=>[4,6,3,5,7,2,1]=>[3,6,2,7,1,4,5]=>000011
[3,7,5,4,1,2,6]=>[4,1,3,5,7,2,6]=>[3,7,6,2,1,4,5]=>100011
[3,7,5,4,1,6,2]=>[6,4,3,5,7,1,2]=>[3,6,1,7,2,4,5]=>000011
[3,7,5,4,2,1,6]=>[2,4,3,5,7,1,6]=>[3,7,6,1,2,4,5]=>000011
[3,7,5,4,2,6,1]=>[6,4,3,5,7,2,1]=>[3,7,1,6,2,4,5]=>000011
[3,7,5,4,6,1,2]=>[6,1,3,5,7,4,2]=>[3,7,2,1,6,4,5]=>100011
[3,7,5,4,6,2,1]=>[2,6,3,5,7,4,1]=>[3,7,1,2,6,4,5]=>000011
[3,7,5,6,1,2,4]=>[6,1,3,2,7,5,4]=>[3,7,4,2,1,6,5]=>101011
[3,7,5,6,1,4,2]=>[4,6,3,1,7,5,2]=>[3,4,1,7,2,6,5]=>001011
[3,7,5,6,2,1,4]=>[2,6,3,1,7,5,4]=>[3,7,4,1,2,6,5]=>001011
[3,7,5,6,2,4,1]=>[4,6,3,2,7,5,1]=>[3,7,1,4,2,6,5]=>001011
[3,7,5,6,4,1,2]=>[4,1,3,6,7,5,2]=>[3,7,2,1,4,6,5]=>100011
[3,7,5,6,4,2,1]=>[2,4,3,6,7,5,1]=>[3,7,1,2,4,6,5]=>000011
[3,7,6,1,2,4,5]=>[6,1,3,2,4,7,5]=>[3,7,5,4,2,1,6]=>101101
[3,7,6,1,2,5,4]=>[5,1,3,6,2,7,4]=>[3,5,2,1,7,4,6]=>100101
[3,7,6,1,4,2,5]=>[4,6,3,1,2,7,5]=>[3,4,1,7,5,2,6]=>001101
[3,7,6,1,4,5,2]=>[5,6,3,1,4,7,2]=>[3,5,4,1,7,2,6]=>001101
[3,7,6,1,5,2,4]=>[5,6,3,1,2,7,4]=>[3,7,4,1,5,2,6]=>001101
[3,7,6,1,5,4,2]=>[4,5,3,6,1,7,2]=>[3,7,2,5,1,4,6]=>000101
[3,7,6,2,1,4,5]=>[2,6,3,1,4,7,5]=>[3,7,5,4,1,2,6]=>001101
[3,7,6,2,1,5,4]=>[2,5,3,6,1,7,4]=>[3,5,1,2,7,4,6]=>000101
[3,7,6,2,4,1,5]=>[4,6,3,2,1,7,5]=>[3,7,5,1,4,2,6]=>001101
[3,7,6,2,4,5,1]=>[5,6,3,2,4,7,1]=>[3,7,1,5,4,2,6]=>001101
[3,7,6,2,5,1,4]=>[5,6,3,2,1,7,4]=>[3,5,1,7,4,2,6]=>001101
[3,7,6,2,5,4,1]=>[4,5,3,6,2,7,1]=>[3,5,2,7,1,4,6]=>000101
[3,7,6,4,1,2,5]=>[4,1,3,6,2,7,5]=>[3,7,5,2,1,4,6]=>100101
[3,7,6,4,1,5,2]=>[5,4,3,6,1,7,2]=>[3,5,1,7,2,4,6]=>000101
[3,7,6,4,2,1,5]=>[2,4,3,6,1,7,5]=>[3,7,5,1,2,4,6]=>000101
[3,7,6,4,2,5,1]=>[5,4,3,6,2,7,1]=>[3,7,1,5,2,4,6]=>000101
[3,7,6,4,5,1,2]=>[5,1,3,6,4,7,2]=>[3,7,2,1,5,4,6]=>100101
[3,7,6,4,5,2,1]=>[2,5,3,6,4,7,1]=>[3,7,1,2,5,4,6]=>000101
[3,7,6,5,1,2,4]=>[5,1,3,2,6,7,4]=>[3,7,4,2,1,5,6]=>101001
[3,7,6,5,1,4,2]=>[4,5,3,1,6,7,2]=>[3,4,1,7,2,5,6]=>001001
[3,7,6,5,2,1,4]=>[2,5,3,1,6,7,4]=>[3,7,4,1,2,5,6]=>001001
[3,7,6,5,2,4,1]=>[4,5,3,2,6,7,1]=>[3,7,1,4,2,5,6]=>001001
[3,7,6,5,4,1,2]=>[4,1,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>100001
[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]=>[3,7,1,2,4,5,6]=>000001
[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>[4,3,2,1,5,7,6]=>111001
[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>[4,3,2,1,6,5,7]=>111010
[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>[4,3,2,1,6,7,5]=>111001
[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>[4,3,2,1,7,6,5]=>111011
[4,1,2,3,7,6,5]=>[4,1,2,3,6,7,5]=>[4,3,2,1,7,5,6]=>111001
[4,1,2,5,3,6,7]=>[5,1,4,2,3,6,7]=>[5,3,4,2,1,6,7]=>101100
[4,1,2,5,3,7,6]=>[5,1,4,2,3,7,6]=>[5,3,4,2,1,7,6]=>101101
[4,1,2,5,6,3,7]=>[6,1,4,2,5,3,7]=>[5,6,3,4,2,1,7]=>101010
[4,1,2,5,6,7,3]=>[7,1,4,2,5,6,3]=>[5,6,7,3,4,2,1]=>101001
[4,1,2,5,7,3,6]=>[7,1,4,2,5,3,6]=>[5,7,6,3,4,2,1]=>101011
[4,1,2,5,7,6,3]=>[6,1,4,2,5,7,3]=>[5,7,3,4,2,1,6]=>101001
[4,1,2,6,3,5,7]=>[6,1,4,2,3,5,7]=>[6,5,3,4,2,1,7]=>101110
[4,1,2,6,3,7,5]=>[7,1,4,2,6,3,5]=>[7,5,6,3,4,2,1]=>101011
[4,1,2,6,5,3,7]=>[5,1,4,2,6,3,7]=>[6,3,4,2,1,5,7]=>101010
[4,1,2,6,5,7,3]=>[7,1,4,2,6,5,3]=>[6,5,7,3,4,2,1]=>101011
[4,1,2,6,7,3,5]=>[7,1,4,2,3,6,5]=>[6,7,5,3,4,2,1]=>101101
[4,1,2,6,7,5,3]=>[5,1,4,2,7,6,3]=>[6,7,3,4,2,1,5]=>101001
[4,1,2,7,3,5,6]=>[7,1,4,2,3,5,6]=>[7,6,5,3,4,2,1]=>101111
[4,1,2,7,3,6,5]=>[6,1,4,2,7,3,5]=>[6,3,4,2,1,7,5]=>101011
[4,1,2,7,5,3,6]=>[5,1,4,2,7,3,6]=>[7,6,3,4,2,1,5]=>101011
[4,1,2,7,5,6,3]=>[6,1,4,2,7,5,3]=>[7,3,4,2,1,6,5]=>101011
[4,1,2,7,6,3,5]=>[6,1,4,2,3,7,5]=>[7,5,3,4,2,1,6]=>101101
[4,1,2,7,6,5,3]=>[5,1,4,2,6,7,3]=>[7,3,4,2,1,5,6]=>101001
[4,1,3,2,5,6,7]=>[3,4,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>011000
[4,1,3,2,5,7,6]=>[3,4,1,2,5,7,6]=>[3,1,4,2,5,7,6]=>011001
[4,1,3,2,6,5,7]=>[3,4,1,2,6,5,7]=>[3,1,4,2,6,5,7]=>011010
[4,1,3,2,6,7,5]=>[3,4,1,2,7,6,5]=>[3,1,4,2,6,7,5]=>011001
[4,1,3,2,7,5,6]=>[3,4,1,2,7,5,6]=>[3,1,4,2,7,6,5]=>011011
[4,1,3,2,7,6,5]=>[3,4,1,2,6,7,5]=>[3,1,4,2,7,5,6]=>011001
[4,1,3,5,2,6,7]=>[5,4,1,3,2,6,7]=>[5,2,4,3,1,6,7]=>011100
[4,1,3,5,2,7,6]=>[5,4,1,3,2,7,6]=>[5,2,4,3,1,7,6]=>011101
[4,1,3,5,6,2,7]=>[6,4,1,3,5,2,7]=>[5,6,2,4,3,1,7]=>011010
[4,1,3,5,6,7,2]=>[7,4,1,3,5,6,2]=>[5,6,7,2,4,3,1]=>011001
[4,1,3,5,7,2,6]=>[7,4,1,3,5,2,6]=>[5,7,6,2,4,3,1]=>011011
[4,1,3,5,7,6,2]=>[6,4,1,3,5,7,2]=>[5,7,2,4,3,1,6]=>011001
[4,1,3,6,2,5,7]=>[6,4,1,3,2,5,7]=>[6,5,2,4,3,1,7]=>011110
[4,1,3,6,2,7,5]=>[7,4,1,3,6,2,5]=>[7,5,6,2,4,3,1]=>011011
[4,1,3,6,5,2,7]=>[5,4,1,3,6,2,7]=>[6,2,4,3,1,5,7]=>011010
[4,1,3,6,5,7,2]=>[7,4,1,3,6,5,2]=>[6,5,7,2,4,3,1]=>011011
[4,1,3,6,7,2,5]=>[7,4,1,3,2,6,5]=>[6,7,5,2,4,3,1]=>011101
[4,1,3,6,7,5,2]=>[5,4,1,3,7,6,2]=>[6,7,2,4,3,1,5]=>011001
[4,1,3,7,2,5,6]=>[7,4,1,3,2,5,6]=>[7,6,5,2,4,3,1]=>011111
[4,1,3,7,2,6,5]=>[6,4,1,3,7,2,5]=>[6,2,4,3,1,7,5]=>011011
[4,1,3,7,5,2,6]=>[5,4,1,3,7,2,6]=>[7,6,2,4,3,1,5]=>011011
[4,1,3,7,5,6,2]=>[6,4,1,3,7,5,2]=>[7,2,4,3,1,6,5]=>011011
[4,1,3,7,6,2,5]=>[6,4,1,3,2,7,5]=>[7,5,2,4,3,1,6]=>011101
[4,1,3,7,6,5,2]=>[5,4,1,3,6,7,2]=>[7,2,4,3,1,5,6]=>011001
[4,1,5,2,3,6,7]=>[5,4,1,2,3,6,7]=>[4,2,5,3,1,6,7]=>011100
[4,1,5,2,3,7,6]=>[5,4,1,2,3,7,6]=>[4,2,5,3,1,7,6]=>011101
[4,1,5,2,6,3,7]=>[6,5,4,1,2,3,7]=>[5,2,6,3,4,1,7]=>001110
[4,1,5,2,6,7,3]=>[7,5,4,1,2,6,3]=>[5,2,6,7,3,4,1]=>001101
[4,1,5,2,7,3,6]=>[7,5,4,1,2,3,6]=>[5,2,7,6,3,4,1]=>001111
[4,1,5,2,7,6,3]=>[6,5,4,1,2,7,3]=>[5,2,7,3,4,1,6]=>001101
[4,1,5,3,2,6,7]=>[3,5,4,1,2,6,7]=>[4,1,3,5,2,6,7]=>001100
[4,1,5,3,2,7,6]=>[3,5,4,1,2,7,6]=>[4,1,3,5,2,7,6]=>001101
[4,1,5,3,6,2,7]=>[6,5,4,1,3,2,7]=>[6,2,5,3,4,1,7]=>001110
[4,1,5,3,6,7,2]=>[7,5,4,1,3,6,2]=>[6,7,2,5,3,4,1]=>001101
[4,1,5,3,7,2,6]=>[7,5,4,1,3,2,6]=>[7,6,2,5,3,4,1]=>001111
[4,1,5,3,7,6,2]=>[6,5,4,1,3,7,2]=>[7,2,5,3,4,1,6]=>001101
[4,1,5,6,2,3,7]=>[6,4,1,2,5,3,7]=>[4,2,5,6,3,1,7]=>011010
[4,1,5,6,2,7,3]=>[7,6,4,1,5,2,3]=>[5,6,2,7,3,4,1]=>001011
[4,1,5,6,3,2,7]=>[3,6,4,1,5,2,7]=>[4,1,3,5,6,2,7]=>001010
[4,1,5,6,3,7,2]=>[7,6,4,1,5,3,2]=>[5,7,2,6,3,4,1]=>001011
[4,1,5,6,7,2,3]=>[7,4,1,2,5,6,3]=>[4,2,5,6,7,3,1]=>011001
[4,1,5,6,7,3,2]=>[3,7,4,1,5,6,2]=>[4,1,3,5,6,7,2]=>001001
[4,1,5,7,2,3,6]=>[7,4,1,2,5,3,6]=>[4,2,5,7,6,3,1]=>011011
[4,1,5,7,2,6,3]=>[6,7,4,1,5,2,3]=>[5,7,3,4,1,6,2]=>001011
[4,1,5,7,3,2,6]=>[3,7,4,1,5,2,6]=>[4,1,3,5,7,6,2]=>001011
[4,1,5,7,3,6,2]=>[6,7,4,1,5,3,2]=>[5,6,3,4,1,7,2]=>001011
[4,1,5,7,6,2,3]=>[6,4,1,2,5,7,3]=>[4,2,5,7,3,1,6]=>011001
[4,1,5,7,6,3,2]=>[3,6,4,1,5,7,2]=>[4,1,3,5,7,2,6]=>001001
[4,1,6,2,3,5,7]=>[6,4,1,2,3,5,7]=>[4,2,6,5,3,1,7]=>011110
[4,1,6,2,3,7,5]=>[7,4,1,2,6,3,5]=>[4,2,7,5,6,3,1]=>011011
[4,1,6,2,5,3,7]=>[5,6,4,1,2,3,7]=>[6,3,4,1,5,2,7]=>001110
[4,1,6,2,5,7,3]=>[7,6,4,1,2,5,3]=>[6,5,2,7,3,4,1]=>001111
[4,1,6,2,7,3,5]=>[7,6,4,1,2,3,5]=>[7,5,2,6,3,4,1]=>001111
[4,1,6,2,7,5,3]=>[5,7,4,1,6,2,3]=>[7,3,4,1,5,6,2]=>001011
[4,1,6,3,2,5,7]=>[3,6,4,1,2,5,7]=>[4,1,3,6,5,2,7]=>001110
[4,1,6,3,2,7,5]=>[3,7,4,1,6,2,5]=>[4,1,3,7,5,6,2]=>001011
[4,1,6,3,5,2,7]=>[5,6,4,1,3,2,7]=>[5,3,4,1,6,2,7]=>001110
[4,1,6,3,5,7,2]=>[7,6,4,1,3,5,2]=>[7,2,6,5,3,4,1]=>001111
[4,1,6,3,7,2,5]=>[7,6,4,1,3,2,5]=>[6,2,7,5,3,4,1]=>001111
[4,1,6,3,7,5,2]=>[5,7,4,1,6,3,2]=>[6,3,4,1,5,7,2]=>001011
[4,1,6,5,2,3,7]=>[5,4,1,2,6,3,7]=>[4,2,6,3,1,5,7]=>011010
[4,1,6,5,2,7,3]=>[7,5,4,1,6,2,3]=>[6,2,5,7,3,4,1]=>001011
[4,1,6,5,3,2,7]=>[3,5,4,1,6,2,7]=>[4,1,3,6,2,5,7]=>001010
[4,1,6,5,3,7,2]=>[7,5,4,1,6,3,2]=>[7,2,5,6,3,4,1]=>001011
[4,1,6,5,7,2,3]=>[7,4,1,2,6,5,3]=>[4,2,6,5,7,3,1]=>011011
[4,1,6,5,7,3,2]=>[3,7,4,1,6,5,2]=>[4,1,3,6,5,7,2]=>001011
[4,1,6,7,2,3,5]=>[7,4,1,2,3,6,5]=>[4,2,6,7,5,3,1]=>011101
[4,1,6,7,2,5,3]=>[5,7,4,1,2,6,3]=>[6,7,3,4,1,5,2]=>001101
[4,1,6,7,3,2,5]=>[3,7,4,1,2,6,5]=>[4,1,3,6,7,5,2]=>001101
[4,1,6,7,3,5,2]=>[5,7,4,1,3,6,2]=>[5,3,4,1,6,7,2]=>001101
[4,1,6,7,5,2,3]=>[5,4,1,2,7,6,3]=>[4,2,6,7,3,1,5]=>011001
[4,1,6,7,5,3,2]=>[3,5,4,1,7,6,2]=>[4,1,3,6,7,2,5]=>001001
[4,1,7,2,3,5,6]=>[7,4,1,2,3,5,6]=>[4,2,7,6,5,3,1]=>011111
[4,1,7,2,3,6,5]=>[6,4,1,2,7,3,5]=>[4,2,6,3,1,7,5]=>011011
[4,1,7,2,5,3,6]=>[5,7,4,1,2,3,6]=>[7,6,3,4,1,5,2]=>001111
[4,1,7,2,5,6,3]=>[6,7,4,1,2,5,3]=>[7,3,4,1,6,5,2]=>001111
[4,1,7,2,6,3,5]=>[6,7,4,1,2,3,5]=>[6,3,4,1,7,5,2]=>001111
[4,1,7,2,6,5,3]=>[5,6,4,1,7,2,3]=>[6,2,7,3,4,1,5]=>001011
[4,1,7,3,2,5,6]=>[3,7,4,1,2,5,6]=>[4,1,3,7,6,5,2]=>001111
[4,1,7,3,2,6,5]=>[3,6,4,1,7,2,5]=>[4,1,3,6,2,7,5]=>001011
[4,1,7,3,5,2,6]=>[5,7,4,1,3,2,6]=>[5,3,4,1,7,6,2]=>001111
[4,1,7,3,5,6,2]=>[6,7,4,1,3,5,2]=>[6,5,3,4,1,7,2]=>001111
[4,1,7,3,6,2,5]=>[6,7,4,1,3,2,5]=>[7,5,3,4,1,6,2]=>001111
[4,1,7,3,6,5,2]=>[5,6,4,1,7,3,2]=>[7,2,6,3,4,1,5]=>001011
[4,1,7,5,2,3,6]=>[5,4,1,2,7,3,6]=>[4,2,7,6,3,1,5]=>011011
[4,1,7,5,2,6,3]=>[6,5,4,1,7,2,3]=>[7,3,4,1,6,2,5]=>001011
[4,1,7,5,3,2,6]=>[3,5,4,1,7,2,6]=>[4,1,3,7,6,2,5]=>001011
[4,1,7,5,3,6,2]=>[6,5,4,1,7,3,2]=>[6,3,4,1,7,2,5]=>001011
[4,1,7,5,6,2,3]=>[6,4,1,2,7,5,3]=>[4,2,7,3,1,6,5]=>011011
[4,1,7,5,6,3,2]=>[3,6,4,1,7,5,2]=>[4,1,3,7,2,6,5]=>001011
[4,1,7,6,2,3,5]=>[6,4,1,2,3,7,5]=>[4,2,7,5,3,1,6]=>011101
[4,1,7,6,2,5,3]=>[5,6,4,1,2,7,3]=>[7,3,4,1,5,2,6]=>001101
[4,1,7,6,3,2,5]=>[3,6,4,1,2,7,5]=>[4,1,3,7,5,2,6]=>001101
[4,1,7,6,3,5,2]=>[5,6,4,1,3,7,2]=>[5,3,4,1,7,2,6]=>001101
[4,1,7,6,5,2,3]=>[5,4,1,2,6,7,3]=>[4,2,7,3,1,5,6]=>011001
[4,1,7,6,5,3,2]=>[3,5,4,1,6,7,2]=>[4,1,3,7,2,5,6]=>001001
[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[4,3,1,2,5,6,7]=>011000
[4,2,1,3,5,7,6]=>[2,4,1,3,5,7,6]=>[4,3,1,2,5,7,6]=>011001
[4,2,1,3,6,5,7]=>[2,4,1,3,6,5,7]=>[4,3,1,2,6,5,7]=>011010
[4,2,1,3,6,7,5]=>[2,4,1,3,7,6,5]=>[4,3,1,2,6,7,5]=>011001
[4,2,1,3,7,5,6]=>[2,4,1,3,7,5,6]=>[4,3,1,2,7,6,5]=>011011
[4,2,1,3,7,6,5]=>[2,4,1,3,6,7,5]=>[4,3,1,2,7,5,6]=>011001
[4,2,1,5,3,6,7]=>[2,5,4,1,3,6,7]=>[5,3,4,1,2,6,7]=>001100
[4,2,1,5,3,7,6]=>[2,5,4,1,3,7,6]=>[5,3,4,1,2,7,6]=>001101
[4,2,1,5,6,3,7]=>[2,6,4,1,5,3,7]=>[5,6,3,4,1,2,7]=>001010
[4,2,1,5,6,7,3]=>[2,7,4,1,5,6,3]=>[5,6,7,3,4,1,2]=>001001
[4,2,1,5,7,3,6]=>[2,7,4,1,5,3,6]=>[5,7,6,3,4,1,2]=>001011
[4,2,1,5,7,6,3]=>[2,6,4,1,5,7,3]=>[5,7,3,4,1,2,6]=>001001
[4,2,1,6,3,5,7]=>[2,6,4,1,3,5,7]=>[6,5,3,4,1,2,7]=>001110
[4,2,1,6,3,7,5]=>[2,7,4,1,6,3,5]=>[7,5,6,3,4,1,2]=>001011
[4,2,1,6,5,3,7]=>[2,5,4,1,6,3,7]=>[6,3,4,1,2,5,7]=>001010
[4,2,1,6,5,7,3]=>[2,7,4,1,6,5,3]=>[6,5,7,3,4,1,2]=>001011
[4,2,1,6,7,3,5]=>[2,7,4,1,3,6,5]=>[6,7,5,3,4,1,2]=>001101
[4,2,1,6,7,5,3]=>[2,5,4,1,7,6,3]=>[6,7,3,4,1,2,5]=>001001
[4,2,1,7,3,5,6]=>[2,7,4,1,3,5,6]=>[7,6,5,3,4,1,2]=>001111
[4,2,1,7,3,6,5]=>[2,6,4,1,7,3,5]=>[6,3,4,1,2,7,5]=>001011
[4,2,1,7,5,3,6]=>[2,5,4,1,7,3,6]=>[7,6,3,4,1,2,5]=>001011
[4,2,1,7,5,6,3]=>[2,6,4,1,7,5,3]=>[7,3,4,1,2,6,5]=>001011
[4,2,1,7,6,3,5]=>[2,6,4,1,3,7,5]=>[7,5,3,4,1,2,6]=>001101
[4,2,1,7,6,5,3]=>[2,5,4,1,6,7,3]=>[7,3,4,1,2,5,6]=>001001
[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>011000
[4,2,3,1,5,7,6]=>[3,4,2,1,5,7,6]=>[4,1,3,2,5,7,6]=>011001
[4,2,3,1,6,5,7]=>[3,4,2,1,6,5,7]=>[4,1,3,2,6,5,7]=>011010
[4,2,3,1,6,7,5]=>[3,4,2,1,7,6,5]=>[4,1,3,2,6,7,5]=>011001
[4,2,3,1,7,5,6]=>[3,4,2,1,7,5,6]=>[4,1,3,2,7,6,5]=>011011
[4,2,3,1,7,6,5]=>[3,4,2,1,6,7,5]=>[4,1,3,2,7,5,6]=>011001
[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[4,3,2,5,1,6,7]=>011100
[4,2,3,5,1,7,6]=>[5,4,2,3,1,7,6]=>[4,3,2,5,1,7,6]=>011101
[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[4,3,2,5,6,1,7]=>011010
[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[4,3,2,5,6,7,1]=>011001
[4,2,3,5,7,1,6]=>[7,4,2,3,5,1,6]=>[4,3,2,5,7,6,1]=>011011
[4,2,3,5,7,6,1]=>[6,4,2,3,5,7,1]=>[4,3,2,5,7,1,6]=>011001
[4,2,3,6,1,5,7]=>[6,4,2,3,1,5,7]=>[4,3,2,6,5,1,7]=>011110
[4,2,3,6,1,7,5]=>[7,4,2,3,6,1,5]=>[4,3,2,7,5,6,1]=>011011
[4,2,3,6,5,1,7]=>[5,4,2,3,6,1,7]=>[4,3,2,6,1,5,7]=>011010
[4,2,3,6,5,7,1]=>[7,4,2,3,6,5,1]=>[4,3,2,6,5,7,1]=>011011
[4,2,3,6,7,1,5]=>[7,4,2,3,1,6,5]=>[4,3,2,6,7,5,1]=>011101
[4,2,3,6,7,5,1]=>[5,4,2,3,7,6,1]=>[4,3,2,6,7,1,5]=>011001
[4,2,3,7,1,5,6]=>[7,4,2,3,1,5,6]=>[4,3,2,7,6,5,1]=>011111
[4,2,3,7,1,6,5]=>[6,4,2,3,7,1,5]=>[4,3,2,6,1,7,5]=>011011
[4,2,3,7,5,1,6]=>[5,4,2,3,7,1,6]=>[4,3,2,7,6,1,5]=>011011
[4,2,3,7,5,6,1]=>[6,4,2,3,7,5,1]=>[4,3,2,7,1,6,5]=>011011
[4,2,3,7,6,1,5]=>[6,4,2,3,1,7,5]=>[4,3,2,7,5,1,6]=>011101
[4,2,3,7,6,5,1]=>[5,4,2,3,6,7,1]=>[4,3,2,7,1,5,6]=>011001
[4,2,5,1,3,6,7]=>[5,4,2,1,3,6,7]=>[5,3,2,4,1,6,7]=>011100
[4,2,5,1,3,7,6]=>[5,4,2,1,3,7,6]=>[5,3,2,4,1,7,6]=>011101
[4,2,5,1,6,3,7]=>[6,5,4,2,1,3,7]=>[6,3,4,2,5,1,7]=>001110
[4,2,5,1,6,7,3]=>[7,5,4,2,1,6,3]=>[6,7,3,4,2,5,1]=>001101
[4,2,5,1,7,3,6]=>[7,5,4,2,1,3,6]=>[7,6,3,4,2,5,1]=>001111
[4,2,5,1,7,6,3]=>[6,5,4,2,1,7,3]=>[7,3,4,2,5,1,6]=>001101
[4,2,5,3,1,6,7]=>[3,5,4,2,1,6,7]=>[5,1,3,4,2,6,7]=>001100
[4,2,5,3,1,7,6]=>[3,5,4,2,1,7,6]=>[5,1,3,4,2,7,6]=>001101
[4,2,5,3,6,1,7]=>[6,5,4,2,3,1,7]=>[5,3,4,2,6,1,7]=>001110
[4,2,5,3,6,7,1]=>[7,5,4,2,3,6,1]=>[5,3,4,2,6,7,1]=>001101
[4,2,5,3,7,1,6]=>[7,5,4,2,3,1,6]=>[5,3,4,2,7,6,1]=>001111
[4,2,5,3,7,6,1]=>[6,5,4,2,3,7,1]=>[5,3,4,2,7,1,6]=>001101
[4,2,5,6,1,3,7]=>[6,4,2,1,5,3,7]=>[5,6,3,2,4,1,7]=>011010
[4,2,5,6,1,7,3]=>[7,6,4,2,5,1,3]=>[5,7,3,4,2,6,1]=>001011
[4,2,5,6,3,1,7]=>[3,6,4,2,5,1,7]=>[5,6,1,3,4,2,7]=>001010
[4,2,5,6,3,7,1]=>[7,6,4,2,5,3,1]=>[5,6,3,4,2,7,1]=>001011
[4,2,5,6,7,1,3]=>[7,4,2,1,5,6,3]=>[5,6,7,3,2,4,1]=>011001
[4,2,5,6,7,3,1]=>[3,7,4,2,5,6,1]=>[5,6,7,1,3,4,2]=>001001
[4,2,5,7,1,3,6]=>[7,4,2,1,5,3,6]=>[5,7,6,3,2,4,1]=>011011
[4,2,5,7,1,6,3]=>[6,7,4,2,5,1,3]=>[5,6,1,7,3,4,2]=>001011
[4,2,5,7,3,1,6]=>[3,7,4,2,5,1,6]=>[5,7,6,1,3,4,2]=>001011
[4,2,5,7,3,6,1]=>[6,7,4,2,5,3,1]=>[5,7,1,6,3,4,2]=>001011
[4,2,5,7,6,1,3]=>[6,4,2,1,5,7,3]=>[5,7,3,2,4,1,6]=>011001
[4,2,5,7,6,3,1]=>[3,6,4,2,5,7,1]=>[5,7,1,3,4,2,6]=>001001
[4,2,6,1,3,5,7]=>[6,4,2,1,3,5,7]=>[6,5,3,2,4,1,7]=>011110
[4,2,6,1,3,7,5]=>[7,4,2,1,6,3,5]=>[7,5,6,3,2,4,1]=>011011
[4,2,6,1,5,3,7]=>[5,6,4,2,1,3,7]=>[5,1,6,3,4,2,7]=>001110
[4,2,6,1,5,7,3]=>[7,6,4,2,1,5,3]=>[7,3,4,2,6,5,1]=>001111
[4,2,6,1,7,3,5]=>[7,6,4,2,1,3,5]=>[6,3,4,2,7,5,1]=>001111
[4,2,6,1,7,5,3]=>[5,7,4,2,6,1,3]=>[6,1,5,7,3,4,2]=>001011
[4,2,6,3,1,5,7]=>[3,6,4,2,1,5,7]=>[6,5,1,3,4,2,7]=>001110
[4,2,6,3,1,7,5]=>[3,7,4,2,6,1,5]=>[7,5,6,1,3,4,2]=>001011
[4,2,6,3,5,1,7]=>[5,6,4,2,3,1,7]=>[6,1,5,3,4,2,7]=>001110
[4,2,6,3,5,7,1]=>[7,6,4,2,3,5,1]=>[6,5,3,4,2,7,1]=>001111
[4,2,6,3,7,1,5]=>[7,6,4,2,3,1,5]=>[7,5,3,4,2,6,1]=>001111
[4,2,6,3,7,5,1]=>[5,7,4,2,6,3,1]=>[7,1,5,6,3,4,2]=>001011
[4,2,6,5,1,3,7]=>[5,4,2,1,6,3,7]=>[6,3,2,4,1,5,7]=>011010
[4,2,6,5,1,7,3]=>[7,5,4,2,6,1,3]=>[7,3,4,2,5,6,1]=>001011
[4,2,6,5,3,1,7]=>[3,5,4,2,6,1,7]=>[6,1,3,4,2,5,7]=>001010
[4,2,6,5,3,7,1]=>[7,5,4,2,6,3,1]=>[6,3,4,2,5,7,1]=>001011
[4,2,6,5,7,1,3]=>[7,4,2,1,6,5,3]=>[6,5,7,3,2,4,1]=>011011
[4,2,6,5,7,3,1]=>[3,7,4,2,6,5,1]=>[6,5,7,1,3,4,2]=>001011
[4,2,6,7,1,3,5]=>[7,4,2,1,3,6,5]=>[6,7,5,3,2,4,1]=>011101
[4,2,6,7,1,5,3]=>[5,7,4,2,1,6,3]=>[5,1,6,7,3,4,2]=>001101
[4,2,6,7,3,1,5]=>[3,7,4,2,1,6,5]=>[6,7,5,1,3,4,2]=>001101
[4,2,6,7,3,5,1]=>[5,7,4,2,3,6,1]=>[6,7,1,5,3,4,2]=>001101
[4,2,6,7,5,1,3]=>[5,4,2,1,7,6,3]=>[6,7,3,2,4,1,5]=>011001
[4,2,6,7,5,3,1]=>[3,5,4,2,7,6,1]=>[6,7,1,3,4,2,5]=>001001
[4,2,7,1,3,5,6]=>[7,4,2,1,3,5,6]=>[7,6,5,3,2,4,1]=>011111
[4,2,7,1,3,6,5]=>[6,4,2,1,7,3,5]=>[6,3,2,4,1,7,5]=>011011
[4,2,7,1,5,3,6]=>[5,7,4,2,1,3,6]=>[5,1,7,6,3,4,2]=>001111
[4,2,7,1,5,6,3]=>[6,7,4,2,1,5,3]=>[6,5,1,7,3,4,2]=>001111
[4,2,7,1,6,3,5]=>[6,7,4,2,1,3,5]=>[7,5,1,6,3,4,2]=>001111
[4,2,7,1,6,5,3]=>[5,6,4,2,7,1,3]=>[7,3,4,2,6,1,5]=>001011
[4,2,7,3,1,5,6]=>[3,7,4,2,1,5,6]=>[7,6,5,1,3,4,2]=>001111
[4,2,7,3,1,6,5]=>[3,6,4,2,7,1,5]=>[6,1,3,4,2,7,5]=>001011
[4,2,7,3,5,1,6]=>[5,7,4,2,3,1,6]=>[7,6,1,5,3,4,2]=>001111
[4,2,7,3,5,6,1]=>[6,7,4,2,3,5,1]=>[7,1,6,5,3,4,2]=>001111
[4,2,7,3,6,1,5]=>[6,7,4,2,3,1,5]=>[6,1,7,5,3,4,2]=>001111
[4,2,7,3,6,5,1]=>[5,6,4,2,7,3,1]=>[6,3,4,2,7,1,5]=>001011
[4,2,7,5,1,3,6]=>[5,4,2,1,7,3,6]=>[7,6,3,2,4,1,5]=>011011
[4,2,7,5,1,6,3]=>[6,5,4,2,7,1,3]=>[6,1,7,3,4,2,5]=>001011
[4,2,7,5,3,1,6]=>[3,5,4,2,7,1,6]=>[7,6,1,3,4,2,5]=>001011
[4,2,7,5,3,6,1]=>[6,5,4,2,7,3,1]=>[7,1,6,3,4,2,5]=>001011
[4,2,7,5,6,1,3]=>[6,4,2,1,7,5,3]=>[7,3,2,4,1,6,5]=>011011
[4,2,7,5,6,3,1]=>[3,6,4,2,7,5,1]=>[7,1,3,4,2,6,5]=>001011
[4,2,7,6,1,3,5]=>[6,4,2,1,3,7,5]=>[7,5,3,2,4,1,6]=>011101
[4,2,7,6,1,5,3]=>[5,6,4,2,1,7,3]=>[5,1,7,3,4,2,6]=>001101
[4,2,7,6,3,1,5]=>[3,6,4,2,1,7,5]=>[7,5,1,3,4,2,6]=>001101
[4,2,7,6,3,5,1]=>[5,6,4,2,3,7,1]=>[7,1,5,3,4,2,6]=>001101
[4,2,7,6,5,1,3]=>[5,4,2,1,6,7,3]=>[7,3,2,4,1,5,6]=>011001
[4,2,7,6,5,3,1]=>[3,5,4,2,6,7,1]=>[7,1,3,4,2,5,6]=>001001
[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[4,2,1,3,5,6,7]=>101000
[4,3,1,2,5,7,6]=>[3,1,4,2,5,7,6]=>[4,2,1,3,5,7,6]=>101001
[4,3,1,2,6,5,7]=>[3,1,4,2,6,5,7]=>[4,2,1,3,6,5,7]=>101010
[4,3,1,2,6,7,5]=>[3,1,4,2,7,6,5]=>[4,2,1,3,6,7,5]=>101001
[4,3,1,2,7,5,6]=>[3,1,4,2,7,5,6]=>[4,2,1,3,7,6,5]=>101011
[4,3,1,2,7,6,5]=>[3,1,4,2,6,7,5]=>[4,2,1,3,7,5,6]=>101001
[4,3,1,5,2,6,7]=>[5,3,4,1,2,6,7]=>[5,2,3,4,1,6,7]=>001100
[4,3,1,5,2,7,6]=>[5,3,4,1,2,7,6]=>[5,2,3,4,1,7,6]=>001101
[4,3,1,5,6,2,7]=>[6,3,4,1,5,2,7]=>[5,6,2,3,4,1,7]=>001010
[4,3,1,5,6,7,2]=>[7,3,4,1,5,6,2]=>[5,6,7,2,3,4,1]=>001001
[4,3,1,5,7,2,6]=>[7,3,4,1,5,2,6]=>[5,7,6,2,3,4,1]=>001011
[4,3,1,5,7,6,2]=>[6,3,4,1,5,7,2]=>[5,7,2,3,4,1,6]=>001001
[4,3,1,6,2,5,7]=>[6,3,4,1,2,5,7]=>[6,5,2,3,4,1,7]=>001110
[4,3,1,6,2,7,5]=>[7,3,4,1,6,2,5]=>[7,5,6,2,3,4,1]=>001011
[4,3,1,6,5,2,7]=>[5,3,4,1,6,2,7]=>[6,2,3,4,1,5,7]=>001010
[4,3,1,6,5,7,2]=>[7,3,4,1,6,5,2]=>[6,5,7,2,3,4,1]=>001011
[4,3,1,6,7,2,5]=>[7,3,4,1,2,6,5]=>[6,7,5,2,3,4,1]=>001101
[4,3,1,6,7,5,2]=>[5,3,4,1,7,6,2]=>[6,7,2,3,4,1,5]=>001001
[4,3,1,7,2,5,6]=>[7,3,4,1,2,5,6]=>[7,6,5,2,3,4,1]=>001111
[4,3,1,7,2,6,5]=>[6,3,4,1,7,2,5]=>[6,2,3,4,1,7,5]=>001011
[4,3,1,7,5,2,6]=>[5,3,4,1,7,2,6]=>[7,6,2,3,4,1,5]=>001011
[4,3,1,7,5,6,2]=>[6,3,4,1,7,5,2]=>[7,2,3,4,1,6,5]=>001011
[4,3,1,7,6,2,5]=>[6,3,4,1,2,7,5]=>[7,5,2,3,4,1,6]=>001101
[4,3,1,7,6,5,2]=>[5,3,4,1,6,7,2]=>[7,2,3,4,1,5,6]=>001001
[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>001000
[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>001001
[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>001010
[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>[4,1,2,3,6,7,5]=>001001
[4,3,2,1,7,5,6]=>[2,3,4,1,7,5,6]=>[4,1,2,3,7,6,5]=>001011
[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>[4,1,2,3,7,5,6]=>001001
[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[4,2,3,5,1,6,7]=>001100
[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]=>[4,2,3,5,1,7,6]=>001101
[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[4,2,3,5,6,1,7]=>001010
[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[4,2,3,5,6,7,1]=>001001
[4,3,2,5,7,1,6]=>[7,3,4,2,5,1,6]=>[4,2,3,5,7,6,1]=>001011
[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>[4,2,3,5,7,1,6]=>001001
[4,3,2,6,1,5,7]=>[6,3,4,2,1,5,7]=>[4,2,3,6,5,1,7]=>001110
[4,3,2,6,1,7,5]=>[7,3,4,2,6,1,5]=>[4,2,3,7,5,6,1]=>001011
[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]=>[4,2,3,6,1,5,7]=>001010
[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>[4,2,3,6,5,7,1]=>001011
[4,3,2,6,7,1,5]=>[7,3,4,2,1,6,5]=>[4,2,3,6,7,5,1]=>001101
[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]=>[4,2,3,6,7,1,5]=>001001
[4,3,2,7,1,5,6]=>[7,3,4,2,1,5,6]=>[4,2,3,7,6,5,1]=>001111
[4,3,2,7,1,6,5]=>[6,3,4,2,7,1,5]=>[4,2,3,6,1,7,5]=>001011
[4,3,2,7,5,1,6]=>[5,3,4,2,7,1,6]=>[4,2,3,7,6,1,5]=>001011
[4,3,2,7,5,6,1]=>[6,3,4,2,7,5,1]=>[4,2,3,7,1,6,5]=>001011
[4,3,2,7,6,1,5]=>[6,3,4,2,1,7,5]=>[4,2,3,7,5,1,6]=>001101
[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>[4,2,3,7,1,5,6]=>001001
[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[4,3,5,2,1,6,7]=>101100
[4,3,5,1,2,7,6]=>[5,1,4,3,2,7,6]=>[4,3,5,2,1,7,6]=>101101
[4,3,5,1,6,2,7]=>[6,5,4,3,1,2,7]=>[4,3,6,2,5,1,7]=>001110
[4,3,5,1,6,7,2]=>[7,5,4,3,1,6,2]=>[4,3,6,7,2,5,1]=>001101
[4,3,5,1,7,2,6]=>[7,5,4,3,1,2,6]=>[4,3,7,6,2,5,1]=>001111
[4,3,5,1,7,6,2]=>[6,5,4,3,1,7,2]=>[4,3,7,2,5,1,6]=>001101
[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[4,3,5,1,2,6,7]=>001100
[4,3,5,2,1,7,6]=>[2,5,4,3,1,7,6]=>[4,3,5,1,2,7,6]=>001101
[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[4,3,5,2,6,1,7]=>001110
[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[4,3,5,2,6,7,1]=>001101
[4,3,5,2,7,1,6]=>[7,5,4,3,2,1,6]=>[4,3,5,2,7,6,1]=>001111
[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]=>[4,3,5,2,7,1,6]=>001101
[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>[4,3,5,6,2,1,7]=>101010
[4,3,5,6,1,7,2]=>[7,6,4,3,5,1,2]=>[4,3,5,7,2,6,1]=>001011
[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[4,3,5,6,1,2,7]=>001010
[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[4,3,5,6,2,7,1]=>001011
[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>[4,3,5,6,7,2,1]=>101001
[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[4,3,5,6,7,1,2]=>001001
[4,3,5,7,1,2,6]=>[7,1,4,3,5,2,6]=>[4,3,5,7,6,2,1]=>101011
[4,3,5,7,1,6,2]=>[6,7,4,3,5,1,2]=>[4,3,5,6,1,7,2]=>001011
[4,3,5,7,2,1,6]=>[2,7,4,3,5,1,6]=>[4,3,5,7,6,1,2]=>001011
[4,3,5,7,2,6,1]=>[6,7,4,3,5,2,1]=>[4,3,5,7,1,6,2]=>001011
[4,3,5,7,6,1,2]=>[6,1,4,3,5,7,2]=>[4,3,5,7,2,1,6]=>101001
[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]=>[4,3,5,7,1,2,6]=>001001
[4,3,6,1,2,5,7]=>[6,1,4,3,2,5,7]=>[4,3,6,5,2,1,7]=>101110
[4,3,6,1,2,7,5]=>[7,1,4,3,6,2,5]=>[4,3,7,5,6,2,1]=>101011
[4,3,6,1,5,2,7]=>[5,6,4,3,1,2,7]=>[4,3,5,1,6,2,7]=>001110
[4,3,6,1,5,7,2]=>[7,6,4,3,1,5,2]=>[4,3,7,2,6,5,1]=>001111
[4,3,6,1,7,2,5]=>[7,6,4,3,1,2,5]=>[4,3,6,2,7,5,1]=>001111
[4,3,6,1,7,5,2]=>[5,7,4,3,6,1,2]=>[4,3,6,1,5,7,2]=>001011
[4,3,6,2,1,5,7]=>[2,6,4,3,1,5,7]=>[4,3,6,5,1,2,7]=>001110
[4,3,6,2,1,7,5]=>[2,7,4,3,6,1,5]=>[4,3,7,5,6,1,2]=>001011
[4,3,6,2,5,1,7]=>[5,6,4,3,2,1,7]=>[4,3,6,1,5,2,7]=>001110
[4,3,6,2,5,7,1]=>[7,6,4,3,2,5,1]=>[4,3,6,5,2,7,1]=>001111
[4,3,6,2,7,1,5]=>[7,6,4,3,2,1,5]=>[4,3,7,5,2,6,1]=>001111
[4,3,6,2,7,5,1]=>[5,7,4,3,6,2,1]=>[4,3,7,1,5,6,2]=>001011
[4,3,6,5,1,2,7]=>[5,1,4,3,6,2,7]=>[4,3,6,2,1,5,7]=>101010
[4,3,6,5,1,7,2]=>[7,5,4,3,6,1,2]=>[4,3,7,2,5,6,1]=>001011
[4,3,6,5,2,1,7]=>[2,5,4,3,6,1,7]=>[4,3,6,1,2,5,7]=>001010
[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]=>[4,3,6,2,5,7,1]=>001011
[4,3,6,5,7,1,2]=>[7,1,4,3,6,5,2]=>[4,3,6,5,7,2,1]=>101011
[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]=>[4,3,6,5,7,1,2]=>001011
[4,3,6,7,1,2,5]=>[7,1,4,3,2,6,5]=>[4,3,6,7,5,2,1]=>101101
[4,3,6,7,1,5,2]=>[5,7,4,3,1,6,2]=>[4,3,5,1,6,7,2]=>001101
[4,3,6,7,2,1,5]=>[2,7,4,3,1,6,5]=>[4,3,6,7,5,1,2]=>001101
[4,3,6,7,2,5,1]=>[5,7,4,3,2,6,1]=>[4,3,6,7,1,5,2]=>001101
[4,3,6,7,5,1,2]=>[5,1,4,3,7,6,2]=>[4,3,6,7,2,1,5]=>101001
[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]=>[4,3,6,7,1,2,5]=>001001
[4,3,7,1,2,5,6]=>[7,1,4,3,2,5,6]=>[4,3,7,6,5,2,1]=>101111
[4,3,7,1,2,6,5]=>[6,1,4,3,7,2,5]=>[4,3,6,2,1,7,5]=>101011
[4,3,7,1,5,2,6]=>[5,7,4,3,1,2,6]=>[4,3,5,1,7,6,2]=>001111
[4,3,7,1,5,6,2]=>[6,7,4,3,1,5,2]=>[4,3,6,5,1,7,2]=>001111
[4,3,7,1,6,2,5]=>[6,7,4,3,1,2,5]=>[4,3,7,5,1,6,2]=>001111
[4,3,7,1,6,5,2]=>[5,6,4,3,7,1,2]=>[4,3,7,2,6,1,5]=>001011
[4,3,7,2,1,5,6]=>[2,7,4,3,1,5,6]=>[4,3,7,6,5,1,2]=>001111
[4,3,7,2,1,6,5]=>[2,6,4,3,7,1,5]=>[4,3,6,1,2,7,5]=>001011
[4,3,7,2,5,1,6]=>[5,7,4,3,2,1,6]=>[4,3,7,6,1,5,2]=>001111
[4,3,7,2,5,6,1]=>[6,7,4,3,2,5,1]=>[4,3,7,1,6,5,2]=>001111
[4,3,7,2,6,1,5]=>[6,7,4,3,2,1,5]=>[4,3,6,1,7,5,2]=>001111
[4,3,7,2,6,5,1]=>[5,6,4,3,7,2,1]=>[4,3,6,2,7,1,5]=>001011
[4,3,7,5,1,2,6]=>[5,1,4,3,7,2,6]=>[4,3,7,6,2,1,5]=>101011
[4,3,7,5,1,6,2]=>[6,5,4,3,7,1,2]=>[4,3,6,1,7,2,5]=>001011
[4,3,7,5,2,1,6]=>[2,5,4,3,7,1,6]=>[4,3,7,6,1,2,5]=>001011
[4,3,7,5,2,6,1]=>[6,5,4,3,7,2,1]=>[4,3,7,1,6,2,5]=>001011
[4,3,7,5,6,1,2]=>[6,1,4,3,7,5,2]=>[4,3,7,2,1,6,5]=>101011
[4,3,7,5,6,2,1]=>[2,6,4,3,7,5,1]=>[4,3,7,1,2,6,5]=>001011
[4,3,7,6,1,2,5]=>[6,1,4,3,2,7,5]=>[4,3,7,5,2,1,6]=>101101
[4,3,7,6,1,5,2]=>[5,6,4,3,1,7,2]=>[4,3,5,1,7,2,6]=>001101
[4,3,7,6,2,1,5]=>[2,6,4,3,1,7,5]=>[4,3,7,5,1,2,6]=>001101
[4,3,7,6,2,5,1]=>[5,6,4,3,2,7,1]=>[4,3,7,1,5,2,6]=>001101
[4,3,7,6,5,1,2]=>[5,1,4,3,6,7,2]=>[4,3,7,2,1,5,6]=>101001
[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]=>[4,3,7,1,2,5,6]=>001001
[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[4,5,3,2,1,6,7]=>110100
[4,5,1,2,3,7,6]=>[5,1,2,4,3,7,6]=>[4,5,3,2,1,7,6]=>110101
[4,5,1,2,6,3,7]=>[6,1,5,4,2,3,7]=>[4,6,3,5,2,1,7]=>100110
[4,5,1,2,6,7,3]=>[7,1,5,4,2,6,3]=>[4,6,7,3,5,2,1]=>100101
[4,5,1,2,7,3,6]=>[7,1,5,4,2,3,6]=>[4,7,6,3,5,2,1]=>100111
[4,5,1,2,7,6,3]=>[6,1,5,4,2,7,3]=>[4,7,3,5,2,1,6]=>100101
[4,5,1,3,2,6,7]=>[3,5,1,4,2,6,7]=>[3,1,4,5,2,6,7]=>010100
[4,5,1,3,2,7,6]=>[3,5,1,4,2,7,6]=>[3,1,4,5,2,7,6]=>010101
[4,5,1,3,6,2,7]=>[6,5,1,4,3,2,7]=>[4,6,2,5,3,1,7]=>010110
[4,5,1,3,6,7,2]=>[7,5,1,4,3,6,2]=>[4,6,7,2,5,3,1]=>010101
[4,5,1,3,7,2,6]=>[7,5,1,4,3,2,6]=>[4,7,6,2,5,3,1]=>010111
[4,5,1,3,7,6,2]=>[6,5,1,4,3,7,2]=>[4,7,2,5,3,1,6]=>010101
[4,5,1,6,2,3,7]=>[6,5,1,4,2,3,7]=>[4,5,2,6,3,1,7]=>010110
[4,5,1,6,2,7,3]=>[7,6,5,4,1,2,3]=>[4,6,2,7,3,5,1]=>000111
[4,5,1,6,3,2,7]=>[3,6,5,4,1,2,7]=>[4,5,1,3,6,2,7]=>000110
[4,5,1,6,3,7,2]=>[7,6,5,4,1,3,2]=>[4,7,2,6,3,5,1]=>000111
[4,5,1,6,7,2,3]=>[7,5,1,4,2,6,3]=>[4,5,2,6,7,3,1]=>010101
[4,5,1,6,7,3,2]=>[3,7,5,4,1,6,2]=>[4,5,1,3,6,7,2]=>000101
[4,5,1,7,2,3,6]=>[7,5,1,4,2,3,6]=>[4,5,2,7,6,3,1]=>010111
[4,5,1,7,2,6,3]=>[6,7,5,4,1,2,3]=>[4,7,3,5,1,6,2]=>000111
[4,5,1,7,3,2,6]=>[3,7,5,4,1,2,6]=>[4,5,1,3,7,6,2]=>000111
[4,5,1,7,3,6,2]=>[6,7,5,4,1,3,2]=>[4,6,3,5,1,7,2]=>000111
[4,5,1,7,6,2,3]=>[6,5,1,4,2,7,3]=>[4,5,2,7,3,1,6]=>010101
[4,5,1,7,6,3,2]=>[3,6,5,4,1,7,2]=>[4,5,1,3,7,2,6]=>000101
[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>[4,5,3,1,2,6,7]=>010100
[4,5,2,1,3,7,6]=>[2,5,1,4,3,7,6]=>[4,5,3,1,2,7,6]=>010101
[4,5,2,1,6,3,7]=>[2,6,5,4,1,3,7]=>[4,6,3,5,1,2,7]=>000110
[4,5,2,1,6,7,3]=>[2,7,5,4,1,6,3]=>[4,6,7,3,5,1,2]=>000101
[4,5,2,1,7,3,6]=>[2,7,5,4,1,3,6]=>[4,7,6,3,5,1,2]=>000111
[4,5,2,1,7,6,3]=>[2,6,5,4,1,7,3]=>[4,7,3,5,1,2,6]=>000101
[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>[4,5,1,3,2,6,7]=>010100
[4,5,2,3,1,7,6]=>[3,5,2,4,1,7,6]=>[4,5,1,3,2,7,6]=>010101
[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>[4,5,3,2,6,1,7]=>010110
[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>[4,5,3,2,6,7,1]=>010101
[4,5,2,3,7,1,6]=>[7,5,2,4,3,1,6]=>[4,5,3,2,7,6,1]=>010111
[4,5,2,3,7,6,1]=>[6,5,2,4,3,7,1]=>[4,5,3,2,7,1,6]=>010101
[4,5,2,6,1,3,7]=>[6,5,2,4,1,3,7]=>[4,6,3,2,5,1,7]=>010110
[4,5,2,6,1,7,3]=>[7,6,5,4,2,1,3]=>[4,7,3,5,2,6,1]=>000111
[4,5,2,6,3,1,7]=>[3,6,5,4,2,1,7]=>[4,6,1,3,5,2,7]=>000110
[4,5,2,6,3,7,1]=>[7,6,5,4,2,3,1]=>[4,6,3,5,2,7,1]=>000111
[4,5,2,6,7,1,3]=>[7,5,2,4,1,6,3]=>[4,6,7,3,2,5,1]=>010101
[4,5,2,6,7,3,1]=>[3,7,5,4,2,6,1]=>[4,6,7,1,3,5,2]=>000101
[4,5,2,7,1,3,6]=>[7,5,2,4,1,3,6]=>[4,7,6,3,2,5,1]=>010111
[4,5,2,7,1,6,3]=>[6,7,5,4,2,1,3]=>[4,6,1,7,3,5,2]=>000111
[4,5,2,7,3,1,6]=>[3,7,5,4,2,1,6]=>[4,7,6,1,3,5,2]=>000111
[4,5,2,7,3,6,1]=>[6,7,5,4,2,3,1]=>[4,7,1,6,3,5,2]=>000111
[4,5,2,7,6,1,3]=>[6,5,2,4,1,7,3]=>[4,7,3,2,5,1,6]=>010101
[4,5,2,7,6,3,1]=>[3,6,5,4,2,7,1]=>[4,7,1,3,5,2,6]=>000101
[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>[4,5,2,1,3,6,7]=>100100
[4,5,3,1,2,7,6]=>[3,1,5,4,2,7,6]=>[4,5,2,1,3,7,6]=>100101
[4,5,3,1,6,2,7]=>[6,3,5,4,1,2,7]=>[4,6,2,3,5,1,7]=>000110
[4,5,3,1,6,7,2]=>[7,3,5,4,1,6,2]=>[4,6,7,2,3,5,1]=>000101
[4,5,3,1,7,2,6]=>[7,3,5,4,1,2,6]=>[4,7,6,2,3,5,1]=>000111
[4,5,3,1,7,6,2]=>[6,3,5,4,1,7,2]=>[4,7,2,3,5,1,6]=>000101
[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[4,5,1,2,3,6,7]=>000100
[4,5,3,2,1,7,6]=>[2,3,5,4,1,7,6]=>[4,5,1,2,3,7,6]=>000101
[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[4,5,2,3,6,1,7]=>000110
[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[4,5,2,3,6,7,1]=>000101
[4,5,3,2,7,1,6]=>[7,3,5,4,2,1,6]=>[4,5,2,3,7,6,1]=>000111
[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]=>[4,5,2,3,7,1,6]=>000101
[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>[4,5,3,6,2,1,7]=>100110
[4,5,3,6,1,7,2]=>[7,6,5,4,3,1,2]=>[4,5,3,7,2,6,1]=>000111
[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[4,5,3,6,1,2,7]=>000110
[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[4,5,3,6,2,7,1]=>000111
[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>[4,5,3,6,7,2,1]=>100101
[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[4,5,3,6,7,1,2]=>000101
[4,5,3,7,1,2,6]=>[7,1,5,4,3,2,6]=>[4,5,3,7,6,2,1]=>100111
[4,5,3,7,1,6,2]=>[6,7,5,4,3,1,2]=>[4,5,3,6,1,7,2]=>000111
[4,5,3,7,2,1,6]=>[2,7,5,4,3,1,6]=>[4,5,3,7,6,1,2]=>000111
[4,5,3,7,2,6,1]=>[6,7,5,4,3,2,1]=>[4,5,3,7,1,6,2]=>000111
[4,5,3,7,6,1,2]=>[6,1,5,4,3,7,2]=>[4,5,3,7,2,1,6]=>100101
[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]=>[4,5,3,7,1,2,6]=>000101
[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[4,5,6,3,2,1,7]=>110010
[4,5,6,1,2,7,3]=>[7,1,6,4,5,2,3]=>[4,5,7,3,6,2,1]=>100011
[4,5,6,1,3,2,7]=>[3,6,1,4,5,2,7]=>[3,1,4,5,6,2,7]=>010010
[4,5,6,1,3,7,2]=>[7,6,1,4,5,3,2]=>[4,5,7,2,6,3,1]=>010011
[4,5,6,1,7,2,3]=>[7,6,1,4,5,2,3]=>[4,5,6,2,7,3,1]=>010011
[4,5,6,1,7,3,2]=>[3,7,6,4,5,1,2]=>[4,5,6,1,3,7,2]=>000011
[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>[4,5,6,3,1,2,7]=>010010
[4,5,6,2,1,7,3]=>[2,7,6,4,5,1,3]=>[4,5,7,3,6,1,2]=>000011
[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>[4,5,6,1,3,2,7]=>010010
[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>[4,5,6,3,2,7,1]=>010011
[4,5,6,2,7,1,3]=>[7,6,2,4,5,1,3]=>[4,5,7,3,2,6,1]=>010011
[4,5,6,2,7,3,1]=>[3,7,6,4,5,2,1]=>[4,5,7,1,3,6,2]=>000011
[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>[4,5,6,2,1,3,7]=>100010
[4,5,6,3,1,7,2]=>[7,3,6,4,5,1,2]=>[4,5,7,2,3,6,1]=>000011
[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[4,5,6,1,2,3,7]=>000010
[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[4,5,6,2,3,7,1]=>000011
[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>[4,5,6,3,7,2,1]=>100011
[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[4,5,6,3,7,1,2]=>000011
[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[4,5,6,7,3,2,1]=>110001
[4,5,6,7,1,3,2]=>[3,7,1,4,5,6,2]=>[3,1,4,5,6,7,2]=>010001
[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>[4,5,6,7,3,1,2]=>010001
[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>[4,5,6,7,1,3,2]=>010001
[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>[4,5,6,7,2,1,3]=>100001
[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[4,5,6,7,1,2,3]=>000001
[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[4,5,7,6,3,2,1]=>110011
[4,5,7,1,2,6,3]=>[6,1,7,4,5,2,3]=>[4,5,6,2,1,7,3]=>100011
[4,5,7,1,3,2,6]=>[3,7,1,4,5,2,6]=>[3,1,4,5,7,6,2]=>010011
[4,5,7,1,3,6,2]=>[6,7,1,4,5,3,2]=>[4,5,6,3,1,7,2]=>010011
[4,5,7,1,6,2,3]=>[6,7,1,4,5,2,3]=>[4,5,7,3,1,6,2]=>010011
[4,5,7,1,6,3,2]=>[3,6,7,4,5,1,2]=>[4,5,7,2,6,1,3]=>000011
[4,5,7,2,1,3,6]=>[2,7,1,4,5,3,6]=>[4,5,7,6,3,1,2]=>010011
[4,5,7,2,1,6,3]=>[2,6,7,4,5,1,3]=>[4,5,6,1,2,7,3]=>000011
[4,5,7,2,3,1,6]=>[3,7,2,4,5,1,6]=>[4,5,7,6,1,3,2]=>010011
[4,5,7,2,3,6,1]=>[6,7,2,4,5,3,1]=>[4,5,7,1,6,3,2]=>010011
[4,5,7,2,6,1,3]=>[6,7,2,4,5,1,3]=>[4,5,6,1,7,3,2]=>010011
[4,5,7,2,6,3,1]=>[3,6,7,4,5,2,1]=>[4,5,6,2,7,1,3]=>000011
[4,5,7,3,1,2,6]=>[3,1,7,4,5,2,6]=>[4,5,7,6,2,1,3]=>100011
[4,5,7,3,1,6,2]=>[6,3,7,4,5,1,2]=>[4,5,6,1,7,2,3]=>000011
[4,5,7,3,2,1,6]=>[2,3,7,4,5,1,6]=>[4,5,7,6,1,2,3]=>000011
[4,5,7,3,2,6,1]=>[6,3,7,4,5,2,1]=>[4,5,7,1,6,2,3]=>000011
[4,5,7,3,6,1,2]=>[6,1,7,4,5,3,2]=>[4,5,7,2,1,6,3]=>100011
[4,5,7,3,6,2,1]=>[2,6,7,4,5,3,1]=>[4,5,7,1,2,6,3]=>000011
[4,5,7,6,1,2,3]=>[6,1,2,4,5,7,3]=>[4,5,7,3,2,1,6]=>110001
[4,5,7,6,1,3,2]=>[3,6,1,4,5,7,2]=>[3,1,4,5,7,2,6]=>010001
[4,5,7,6,2,1,3]=>[2,6,1,4,5,7,3]=>[4,5,7,3,1,2,6]=>010001
[4,5,7,6,2,3,1]=>[3,6,2,4,5,7,1]=>[4,5,7,1,3,2,6]=>010001
[4,5,7,6,3,1,2]=>[3,1,6,4,5,7,2]=>[4,5,7,2,1,3,6]=>100001
[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]=>[4,5,7,1,2,3,6]=>000001
[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[4,6,5,3,2,1,7]=>110110
[4,6,1,2,3,7,5]=>[7,1,2,4,6,3,5]=>[4,7,5,6,3,2,1]=>110011
[4,6,1,2,5,3,7]=>[5,1,6,4,2,3,7]=>[4,5,2,1,6,3,7]=>100110
[4,6,1,2,5,7,3]=>[7,1,6,4,2,5,3]=>[4,7,3,6,5,2,1]=>100111
[4,6,1,2,7,3,5]=>[7,1,6,4,2,3,5]=>[4,6,3,7,5,2,1]=>100111
[4,6,1,2,7,5,3]=>[5,1,7,4,6,2,3]=>[4,6,2,1,5,7,3]=>100011
[4,6,1,3,2,5,7]=>[3,6,1,4,2,5,7]=>[3,1,4,6,5,2,7]=>010110
[4,6,1,3,2,7,5]=>[3,7,1,4,6,2,5]=>[3,1,4,7,5,6,2]=>010011
[4,6,1,3,5,2,7]=>[5,6,1,4,3,2,7]=>[4,5,3,1,6,2,7]=>010110
[4,6,1,3,5,7,2]=>[7,6,1,4,3,5,2]=>[4,7,2,6,5,3,1]=>010111
[4,6,1,3,7,2,5]=>[7,6,1,4,3,2,5]=>[4,6,2,7,5,3,1]=>010111
[4,6,1,3,7,5,2]=>[5,7,1,4,6,3,2]=>[4,6,3,1,5,7,2]=>010011
[4,6,1,5,2,3,7]=>[5,6,1,4,2,3,7]=>[4,6,3,1,5,2,7]=>010110
[4,6,1,5,2,7,3]=>[7,5,6,4,1,2,3]=>[4,7,3,6,2,5,1]=>000111
[4,6,1,5,3,2,7]=>[3,5,6,4,1,2,7]=>[4,6,2,5,1,3,7]=>000110
[4,6,1,5,3,7,2]=>[7,5,6,4,1,3,2]=>[4,6,3,7,2,5,1]=>000111
[4,6,1,5,7,2,3]=>[7,6,1,4,2,5,3]=>[4,6,5,2,7,3,1]=>010111
[4,6,1,5,7,3,2]=>[3,7,6,4,1,5,2]=>[4,6,5,1,3,7,2]=>000111
[4,6,1,7,2,3,5]=>[7,6,1,4,2,3,5]=>[4,7,5,2,6,3,1]=>010111
[4,6,1,7,2,5,3]=>[5,7,6,4,1,2,3]=>[4,5,1,7,3,6,2]=>000111
[4,6,1,7,3,2,5]=>[3,7,6,4,1,2,5]=>[4,7,5,1,3,6,2]=>000111
[4,6,1,7,3,5,2]=>[5,7,6,4,1,3,2]=>[4,5,1,6,3,7,2]=>000111
[4,6,1,7,5,2,3]=>[5,7,1,4,6,2,3]=>[4,7,3,1,5,6,2]=>010011
[4,6,1,7,5,3,2]=>[3,5,7,4,6,1,2]=>[4,7,2,5,6,1,3]=>000011
[4,6,2,1,3,5,7]=>[2,6,1,4,3,5,7]=>[4,6,5,3,1,2,7]=>010110
[4,6,2,1,3,7,5]=>[2,7,1,4,6,3,5]=>[4,7,5,6,3,1,2]=>010011
[4,6,2,1,5,3,7]=>[2,5,6,4,1,3,7]=>[4,5,1,2,6,3,7]=>000110
[4,6,2,1,5,7,3]=>[2,7,6,4,1,5,3]=>[4,7,3,6,5,1,2]=>000111
[4,6,2,1,7,3,5]=>[2,7,6,4,1,3,5]=>[4,6,3,7,5,1,2]=>000111
[4,6,2,1,7,5,3]=>[2,5,7,4,6,1,3]=>[4,6,1,2,5,7,3]=>000011
[4,6,2,3,1,5,7]=>[3,6,2,4,1,5,7]=>[4,6,5,1,3,2,7]=>010110
[4,6,2,3,1,7,5]=>[3,7,2,4,6,1,5]=>[4,7,5,6,1,3,2]=>010011
[4,6,2,3,5,1,7]=>[5,6,2,4,3,1,7]=>[4,6,1,5,3,2,7]=>010110
[4,6,2,3,5,7,1]=>[7,6,2,4,3,5,1]=>[4,6,5,3,2,7,1]=>010111
[4,6,2,3,7,1,5]=>[7,6,2,4,3,1,5]=>[4,7,5,3,2,6,1]=>010111
[4,6,2,3,7,5,1]=>[5,7,2,4,6,3,1]=>[4,7,1,5,6,3,2]=>010011
[4,6,2,5,1,3,7]=>[5,6,2,4,1,3,7]=>[4,5,1,6,3,2,7]=>010110
[4,6,2,5,1,7,3]=>[7,5,6,4,2,1,3]=>[4,5,2,7,3,6,1]=>000111
[4,6,2,5,3,1,7]=>[3,5,6,4,2,1,7]=>[4,5,2,6,1,3,7]=>000110
[4,6,2,5,3,7,1]=>[7,5,6,4,2,3,1]=>[4,5,2,6,3,7,1]=>000111
[4,6,2,5,7,1,3]=>[7,6,2,4,1,5,3]=>[4,7,3,2,6,5,1]=>010111
[4,6,2,5,7,3,1]=>[3,7,6,4,2,5,1]=>[4,7,1,3,6,5,2]=>000111
[4,6,2,7,1,3,5]=>[7,6,2,4,1,3,5]=>[4,6,3,2,7,5,1]=>010111
[4,6,2,7,1,5,3]=>[5,7,6,4,2,1,3]=>[4,7,3,6,1,5,2]=>000111
[4,6,2,7,3,1,5]=>[3,7,6,4,2,1,5]=>[4,6,1,3,7,5,2]=>000111
[4,6,2,7,3,5,1]=>[5,7,6,4,2,3,1]=>[4,6,3,7,1,5,2]=>000111
[4,6,2,7,5,1,3]=>[5,7,2,4,6,1,3]=>[4,6,1,5,7,3,2]=>010011
[4,6,2,7,5,3,1]=>[3,5,7,4,6,2,1]=>[4,6,2,5,7,1,3]=>000011
[4,6,3,1,2,5,7]=>[3,1,6,4,2,5,7]=>[4,6,5,2,1,3,7]=>100110
[4,6,3,1,2,7,5]=>[3,1,7,4,6,2,5]=>[4,7,5,6,2,1,3]=>100011
[4,6,3,1,5,2,7]=>[5,3,6,4,1,2,7]=>[4,5,1,6,2,3,7]=>000110
[4,6,3,1,5,7,2]=>[7,3,6,4,1,5,2]=>[4,7,2,3,6,5,1]=>000111
[4,6,3,1,7,2,5]=>[7,3,6,4,1,2,5]=>[4,6,2,3,7,5,1]=>000111
[4,6,3,1,7,5,2]=>[5,3,7,4,6,1,2]=>[4,6,1,5,7,2,3]=>000011
[4,6,3,2,1,5,7]=>[2,3,6,4,1,5,7]=>[4,6,5,1,2,3,7]=>000110
[4,6,3,2,1,7,5]=>[2,3,7,4,6,1,5]=>[4,7,5,6,1,2,3]=>000011
[4,6,3,2,5,1,7]=>[5,3,6,4,2,1,7]=>[4,6,1,5,2,3,7]=>000110
[4,6,3,2,5,7,1]=>[7,3,6,4,2,5,1]=>[4,6,5,2,3,7,1]=>000111
[4,6,3,2,7,1,5]=>[7,3,6,4,2,1,5]=>[4,7,5,2,3,6,1]=>000111
[4,6,3,2,7,5,1]=>[5,3,7,4,6,2,1]=>[4,7,1,5,6,2,3]=>000011
[4,6,3,5,1,2,7]=>[5,1,6,4,3,2,7]=>[4,6,2,1,5,3,7]=>100110
[4,6,3,5,1,7,2]=>[7,5,6,4,3,1,2]=>[4,7,2,5,3,6,1]=>000111
[4,6,3,5,2,1,7]=>[2,5,6,4,3,1,7]=>[4,6,1,2,5,3,7]=>000110
[4,6,3,5,2,7,1]=>[7,5,6,4,3,2,1]=>[4,6,2,5,3,7,1]=>000111
[4,6,3,5,7,1,2]=>[7,1,6,4,3,5,2]=>[4,6,5,3,7,2,1]=>100111
[4,6,3,5,7,2,1]=>[2,7,6,4,3,5,1]=>[4,6,5,3,7,1,2]=>000111
[4,6,3,7,1,2,5]=>[7,1,6,4,3,2,5]=>[4,7,5,3,6,2,1]=>100111
[4,6,3,7,1,5,2]=>[5,7,6,4,3,1,2]=>[4,6,1,5,3,7,2]=>000111
[4,6,3,7,2,1,5]=>[2,7,6,4,3,1,5]=>[4,7,5,3,6,1,2]=>000111
[4,6,3,7,2,5,1]=>[5,7,6,4,3,2,1]=>[4,7,1,5,3,6,2]=>000111
[4,6,3,7,5,1,2]=>[5,1,7,4,6,3,2]=>[4,7,2,1,5,6,3]=>100011
[4,6,3,7,5,2,1]=>[2,5,7,4,6,3,1]=>[4,7,1,2,5,6,3]=>000011
[4,6,5,1,2,3,7]=>[5,1,2,4,6,3,7]=>[4,6,3,2,1,5,7]=>110010
[4,6,5,1,2,7,3]=>[7,1,5,4,6,2,3]=>[4,7,3,5,6,2,1]=>100011
[4,6,5,1,3,2,7]=>[3,5,1,4,6,2,7]=>[3,1,4,6,2,5,7]=>010010
[4,6,5,1,3,7,2]=>[7,5,1,4,6,3,2]=>[4,7,2,5,6,3,1]=>010011
[4,6,5,1,7,2,3]=>[7,5,1,4,6,2,3]=>[4,6,2,5,7,3,1]=>010011
[4,6,5,1,7,3,2]=>[3,7,5,4,6,1,2]=>[4,6,1,3,5,7,2]=>000011
[4,6,5,2,1,3,7]=>[2,5,1,4,6,3,7]=>[4,6,3,1,2,5,7]=>010010
[4,6,5,2,1,7,3]=>[2,7,5,4,6,1,3]=>[4,7,3,5,6,1,2]=>000011
[4,6,5,2,3,1,7]=>[3,5,2,4,6,1,7]=>[4,6,1,3,2,5,7]=>010010
[4,6,5,2,3,7,1]=>[7,5,2,4,6,3,1]=>[4,6,3,2,5,7,1]=>010011
[4,6,5,2,7,1,3]=>[7,5,2,4,6,1,3]=>[4,7,3,2,5,6,1]=>010011
[4,6,5,2,7,3,1]=>[3,7,5,4,6,2,1]=>[4,7,1,3,5,6,2]=>000011
[4,6,5,3,1,2,7]=>[3,1,5,4,6,2,7]=>[4,6,2,1,3,5,7]=>100010
[4,6,5,3,1,7,2]=>[7,3,5,4,6,1,2]=>[4,7,2,3,5,6,1]=>000011
[4,6,5,3,2,1,7]=>[2,3,5,4,6,1,7]=>[4,6,1,2,3,5,7]=>000010
[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]=>[4,6,2,3,5,7,1]=>000011
[4,6,5,3,7,1,2]=>[7,1,5,4,6,3,2]=>[4,6,3,5,7,2,1]=>100011
[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]=>[4,6,3,5,7,1,2]=>000011
[4,6,5,7,1,2,3]=>[7,1,2,4,6,5,3]=>[4,6,5,7,3,2,1]=>110011
[4,6,5,7,1,3,2]=>[3,7,1,4,6,5,2]=>[3,1,4,6,5,7,2]=>010011
[4,6,5,7,2,1,3]=>[2,7,1,4,6,5,3]=>[4,6,5,7,3,1,2]=>010011
[4,6,5,7,2,3,1]=>[3,7,2,4,6,5,1]=>[4,6,5,7,1,3,2]=>010011
[4,6,5,7,3,1,2]=>[3,1,7,4,6,5,2]=>[4,6,5,7,2,1,3]=>100011
[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]=>[4,6,5,7,1,2,3]=>000011
[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[4,6,7,5,3,2,1]=>110101
[4,6,7,1,2,5,3]=>[5,1,7,4,2,6,3]=>[4,5,2,1,6,7,3]=>100101
[4,6,7,1,3,2,5]=>[3,7,1,4,2,6,5]=>[3,1,4,6,7,5,2]=>010101
[4,6,7,1,3,5,2]=>[5,7,1,4,3,6,2]=>[4,5,3,1,6,7,2]=>010101
[4,6,7,1,5,2,3]=>[5,7,1,4,2,6,3]=>[4,6,7,3,1,5,2]=>010101
[4,6,7,1,5,3,2]=>[3,5,7,4,1,6,2]=>[4,6,7,2,5,1,3]=>000101
[4,6,7,2,1,3,5]=>[2,7,1,4,3,6,5]=>[4,6,7,5,3,1,2]=>010101
[4,6,7,2,1,5,3]=>[2,5,7,4,1,6,3]=>[4,5,1,2,6,7,3]=>000101
[4,6,7,2,3,1,5]=>[3,7,2,4,1,6,5]=>[4,6,7,5,1,3,2]=>010101
[4,6,7,2,3,5,1]=>[5,7,2,4,3,6,1]=>[4,6,7,1,5,3,2]=>010101
[4,6,7,2,5,1,3]=>[5,7,2,4,1,6,3]=>[4,5,1,6,7,3,2]=>010101
[4,6,7,2,5,3,1]=>[3,5,7,4,2,6,1]=>[4,5,2,6,7,1,3]=>000101
[4,6,7,3,1,2,5]=>[3,1,7,4,2,6,5]=>[4,6,7,5,2,1,3]=>100101
[4,6,7,3,1,5,2]=>[5,3,7,4,1,6,2]=>[4,5,1,6,7,2,3]=>000101
[4,6,7,3,2,1,5]=>[2,3,7,4,1,6,5]=>[4,6,7,5,1,2,3]=>000101
[4,6,7,3,2,5,1]=>[5,3,7,4,2,6,1]=>[4,6,7,1,5,2,3]=>000101
[4,6,7,3,5,1,2]=>[5,1,7,4,3,6,2]=>[4,6,7,2,1,5,3]=>100101
[4,6,7,3,5,2,1]=>[2,5,7,4,3,6,1]=>[4,6,7,1,2,5,3]=>000101
[4,6,7,5,1,2,3]=>[5,1,2,4,7,6,3]=>[4,6,7,3,2,1,5]=>110001
[4,6,7,5,1,3,2]=>[3,5,1,4,7,6,2]=>[3,1,4,6,7,2,5]=>010001
[4,6,7,5,2,1,3]=>[2,5,1,4,7,6,3]=>[4,6,7,3,1,2,5]=>010001
[4,6,7,5,2,3,1]=>[3,5,2,4,7,6,1]=>[4,6,7,1,3,2,5]=>010001
[4,6,7,5,3,1,2]=>[3,1,5,4,7,6,2]=>[4,6,7,2,1,3,5]=>100001
[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]=>[4,6,7,1,2,3,5]=>000001
[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[4,7,6,5,3,2,1]=>110111
[4,7,1,2,3,6,5]=>[6,1,2,4,7,3,5]=>[4,6,3,2,1,7,5]=>110011
[4,7,1,2,5,3,6]=>[5,1,7,4,2,3,6]=>[4,5,2,1,7,6,3]=>100111
[4,7,1,2,5,6,3]=>[6,1,7,4,2,5,3]=>[4,6,5,2,1,7,3]=>100111
[4,7,1,2,6,3,5]=>[6,1,7,4,2,3,5]=>[4,7,5,2,1,6,3]=>100111
[4,7,1,2,6,5,3]=>[5,1,6,4,7,2,3]=>[4,7,3,6,2,1,5]=>100011
[4,7,1,3,2,5,6]=>[3,7,1,4,2,5,6]=>[3,1,4,7,6,5,2]=>010111
[4,7,1,3,2,6,5]=>[3,6,1,4,7,2,5]=>[3,1,4,6,2,7,5]=>010011
[4,7,1,3,5,2,6]=>[5,7,1,4,3,2,6]=>[4,5,3,1,7,6,2]=>010111
[4,7,1,3,5,6,2]=>[6,7,1,4,3,5,2]=>[4,6,5,3,1,7,2]=>010111
[4,7,1,3,6,2,5]=>[6,7,1,4,3,2,5]=>[4,7,5,3,1,6,2]=>010111
[4,7,1,3,6,5,2]=>[5,6,1,4,7,3,2]=>[4,7,2,6,3,1,5]=>010011
[4,7,1,5,2,3,6]=>[5,7,1,4,2,3,6]=>[4,7,6,3,1,5,2]=>010111
[4,7,1,5,2,6,3]=>[6,5,7,4,1,2,3]=>[4,6,2,5,1,7,3]=>000111
[4,7,1,5,3,2,6]=>[3,5,7,4,1,2,6]=>[4,7,6,2,5,1,3]=>000111
[4,7,1,5,3,6,2]=>[6,5,7,4,1,3,2]=>[4,7,2,5,1,6,3]=>000111
[4,7,1,5,6,2,3]=>[6,7,1,4,2,5,3]=>[4,7,3,1,6,5,2]=>010111
[4,7,1,5,6,3,2]=>[3,6,7,4,1,5,2]=>[4,7,2,6,5,1,3]=>000111
[4,7,1,6,2,3,5]=>[6,7,1,4,2,3,5]=>[4,6,3,1,7,5,2]=>010111
[4,7,1,6,2,5,3]=>[5,6,7,4,1,2,3]=>[4,5,1,6,2,7,3]=>000111
[4,7,1,6,3,2,5]=>[3,6,7,4,1,2,5]=>[4,6,2,7,5,1,3]=>000111
[4,7,1,6,3,5,2]=>[5,6,7,4,1,3,2]=>[4,5,1,7,2,6,3]=>000111
[4,7,1,6,5,2,3]=>[5,6,1,4,7,2,3]=>[4,6,2,7,3,1,5]=>010011
[4,7,1,6,5,3,2]=>[3,5,6,4,7,1,2]=>[4,6,1,3,7,2,5]=>000011
[4,7,2,1,3,5,6]=>[2,7,1,4,3,5,6]=>[4,7,6,5,3,1,2]=>010111
[4,7,2,1,3,6,5]=>[2,6,1,4,7,3,5]=>[4,6,3,1,2,7,5]=>010011
[4,7,2,1,5,3,6]=>[2,5,7,4,1,3,6]=>[4,5,1,2,7,6,3]=>000111
[4,7,2,1,5,6,3]=>[2,6,7,4,1,5,3]=>[4,6,5,1,2,7,3]=>000111
[4,7,2,1,6,3,5]=>[2,6,7,4,1,3,5]=>[4,7,5,1,2,6,3]=>000111
[4,7,2,1,6,5,3]=>[2,5,6,4,7,1,3]=>[4,7,3,6,1,2,5]=>000011
[4,7,2,3,1,5,6]=>[3,7,2,4,1,5,6]=>[4,7,6,5,1,3,2]=>010111
[4,7,2,3,1,6,5]=>[3,6,2,4,7,1,5]=>[4,6,1,3,2,7,5]=>010011
[4,7,2,3,5,1,6]=>[5,7,2,4,3,1,6]=>[4,7,6,1,5,3,2]=>010111
[4,7,2,3,5,6,1]=>[6,7,2,4,3,5,1]=>[4,7,1,6,5,3,2]=>010111
[4,7,2,3,6,1,5]=>[6,7,2,4,3,1,5]=>[4,6,1,7,5,3,2]=>010111
[4,7,2,3,6,5,1]=>[5,6,2,4,7,3,1]=>[4,6,3,2,7,1,5]=>010011
[4,7,2,5,1,3,6]=>[5,7,2,4,1,3,6]=>[4,5,1,7,6,3,2]=>010111
[4,7,2,5,1,6,3]=>[6,5,7,4,2,1,3]=>[4,5,2,6,1,7,3]=>000111
[4,7,2,5,3,1,6]=>[3,5,7,4,2,1,6]=>[4,5,2,7,6,1,3]=>000111
[4,7,2,5,3,6,1]=>[6,5,7,4,2,3,1]=>[4,5,2,7,1,6,3]=>000111
[4,7,2,5,6,1,3]=>[6,7,2,4,1,5,3]=>[4,6,5,1,7,3,2]=>010111
[4,7,2,5,6,3,1]=>[3,6,7,4,2,5,1]=>[4,6,5,2,7,1,3]=>000111
[4,7,2,6,1,3,5]=>[6,7,2,4,1,3,5]=>[4,7,5,1,6,3,2]=>010111
[4,7,2,6,1,5,3]=>[5,6,7,4,2,1,3]=>[4,6,1,5,2,7,3]=>000111
[4,7,2,6,3,1,5]=>[3,6,7,4,2,1,5]=>[4,7,5,2,6,1,3]=>000111
[4,7,2,6,3,5,1]=>[5,6,7,4,2,3,1]=>[4,7,1,5,2,6,3]=>000111
[4,7,2,6,5,1,3]=>[5,6,2,4,7,1,3]=>[4,7,3,2,6,1,5]=>010011
[4,7,2,6,5,3,1]=>[3,5,6,4,7,2,1]=>[4,7,1,3,6,2,5]=>000011
[4,7,3,1,2,5,6]=>[3,1,7,4,2,5,6]=>[4,7,6,5,2,1,3]=>100111
[4,7,3,1,2,6,5]=>[3,1,6,4,7,2,5]=>[4,6,2,1,3,7,5]=>100011
[4,7,3,1,5,2,6]=>[5,3,7,4,1,2,6]=>[4,5,1,7,6,2,3]=>000111
[4,7,3,1,5,6,2]=>[6,3,7,4,1,5,2]=>[4,6,5,1,7,2,3]=>000111
[4,7,3,1,6,2,5]=>[6,3,7,4,1,2,5]=>[4,7,5,1,6,2,3]=>000111
[4,7,3,1,6,5,2]=>[5,3,6,4,7,1,2]=>[4,7,2,3,6,1,5]=>000011
[4,7,3,2,1,5,6]=>[2,3,7,4,1,5,6]=>[4,7,6,5,1,2,3]=>000111
[4,7,3,2,1,6,5]=>[2,3,6,4,7,1,5]=>[4,6,1,2,3,7,5]=>000011
[4,7,3,2,5,1,6]=>[5,3,7,4,2,1,6]=>[4,7,6,1,5,2,3]=>000111
[4,7,3,2,5,6,1]=>[6,3,7,4,2,5,1]=>[4,7,1,6,5,2,3]=>000111
[4,7,3,2,6,1,5]=>[6,3,7,4,2,1,5]=>[4,6,1,7,5,2,3]=>000111
[4,7,3,2,6,5,1]=>[5,3,6,4,7,2,1]=>[4,6,2,3,7,1,5]=>000011
[4,7,3,5,1,2,6]=>[5,1,7,4,3,2,6]=>[4,7,6,2,1,5,3]=>100111
[4,7,3,5,1,6,2]=>[6,5,7,4,3,1,2]=>[4,6,1,7,2,5,3]=>000111
[4,7,3,5,2,1,6]=>[2,5,7,4,3,1,6]=>[4,7,6,1,2,5,3]=>000111
[4,7,3,5,2,6,1]=>[6,5,7,4,3,2,1]=>[4,7,1,6,2,5,3]=>000111
[4,7,3,5,6,1,2]=>[6,1,7,4,3,5,2]=>[4,7,2,1,6,5,3]=>100111
[4,7,3,5,6,2,1]=>[2,6,7,4,3,5,1]=>[4,7,1,2,6,5,3]=>000111
[4,7,3,6,1,2,5]=>[6,1,7,4,3,2,5]=>[4,6,2,1,7,5,3]=>100111
[4,7,3,6,1,5,2]=>[5,6,7,4,3,1,2]=>[4,7,2,6,1,5,3]=>000111
[4,7,3,6,2,1,5]=>[2,6,7,4,3,1,5]=>[4,6,1,2,7,5,3]=>000111
[4,7,3,6,2,5,1]=>[5,6,7,4,3,2,1]=>[4,6,2,7,1,5,3]=>000111
[4,7,3,6,5,1,2]=>[5,1,6,4,7,3,2]=>[4,6,3,7,2,1,5]=>100011
[4,7,3,6,5,2,1]=>[2,5,6,4,7,3,1]=>[4,6,3,7,1,2,5]=>000011
[4,7,5,1,2,3,6]=>[5,1,2,4,7,3,6]=>[4,7,6,3,2,1,5]=>110011
[4,7,5,1,2,6,3]=>[6,1,5,4,7,2,3]=>[4,6,2,1,7,3,5]=>100011
[4,7,5,1,3,2,6]=>[3,5,1,4,7,2,6]=>[3,1,4,7,6,2,5]=>010011
[4,7,5,1,3,6,2]=>[6,5,1,4,7,3,2]=>[4,6,3,1,7,2,5]=>010011
[4,7,5,1,6,2,3]=>[6,5,1,4,7,2,3]=>[4,7,3,1,6,2,5]=>010011
[4,7,5,1,6,3,2]=>[3,6,5,4,7,1,2]=>[4,7,2,6,1,3,5]=>000011
[4,7,5,2,1,3,6]=>[2,5,1,4,7,3,6]=>[4,7,6,3,1,2,5]=>010011
[4,7,5,2,1,6,3]=>[2,6,5,4,7,1,3]=>[4,6,1,2,7,3,5]=>000011
[4,7,5,2,3,1,6]=>[3,5,2,4,7,1,6]=>[4,7,6,1,3,2,5]=>010011
[4,7,5,2,3,6,1]=>[6,5,2,4,7,3,1]=>[4,7,1,6,3,2,5]=>010011
[4,7,5,2,6,1,3]=>[6,5,2,4,7,1,3]=>[4,6,1,7,3,2,5]=>010011
[4,7,5,2,6,3,1]=>[3,6,5,4,7,2,1]=>[4,6,2,7,1,3,5]=>000011
[4,7,5,3,1,2,6]=>[3,1,5,4,7,2,6]=>[4,7,6,2,1,3,5]=>100011
[4,7,5,3,1,6,2]=>[6,3,5,4,7,1,2]=>[4,6,1,7,2,3,5]=>000011
[4,7,5,3,2,1,6]=>[2,3,5,4,7,1,6]=>[4,7,6,1,2,3,5]=>000011
[4,7,5,3,2,6,1]=>[6,3,5,4,7,2,1]=>[4,7,1,6,2,3,5]=>000011
[4,7,5,3,6,1,2]=>[6,1,5,4,7,3,2]=>[4,7,2,1,6,3,5]=>100011
[4,7,5,3,6,2,1]=>[2,6,5,4,7,3,1]=>[4,7,1,2,6,3,5]=>000011
[4,7,5,6,1,2,3]=>[6,1,2,4,7,5,3]=>[4,7,3,2,1,6,5]=>110011
[4,7,5,6,1,3,2]=>[3,6,1,4,7,5,2]=>[3,1,4,7,2,6,5]=>010011
[4,7,5,6,2,1,3]=>[2,6,1,4,7,5,3]=>[4,7,3,1,2,6,5]=>010011
[4,7,5,6,2,3,1]=>[3,6,2,4,7,5,1]=>[4,7,1,3,2,6,5]=>010011
[4,7,5,6,3,1,2]=>[3,1,6,4,7,5,2]=>[4,7,2,1,3,6,5]=>100011
[4,7,5,6,3,2,1]=>[2,3,6,4,7,5,1]=>[4,7,1,2,3,6,5]=>000011
[4,7,6,1,2,3,5]=>[6,1,2,4,3,7,5]=>[4,7,5,3,2,1,6]=>110101
[4,7,6,1,2,5,3]=>[5,1,6,4,2,7,3]=>[4,5,2,1,7,3,6]=>100101
[4,7,6,1,3,2,5]=>[3,6,1,4,2,7,5]=>[3,1,4,7,5,2,6]=>010101
[4,7,6,1,3,5,2]=>[5,6,1,4,3,7,2]=>[4,5,3,1,7,2,6]=>010101
[4,7,6,1,5,2,3]=>[5,6,1,4,2,7,3]=>[4,7,3,1,5,2,6]=>010101
[4,7,6,1,5,3,2]=>[3,5,6,4,1,7,2]=>[4,7,2,5,1,3,6]=>000101
[4,7,6,2,1,3,5]=>[2,6,1,4,3,7,5]=>[4,7,5,3,1,2,6]=>010101
[4,7,6,2,1,5,3]=>[2,5,6,4,1,7,3]=>[4,5,1,2,7,3,6]=>000101
[4,7,6,2,3,1,5]=>[3,6,2,4,1,7,5]=>[4,7,5,1,3,2,6]=>010101
[4,7,6,2,3,5,1]=>[5,6,2,4,3,7,1]=>[4,7,1,5,3,2,6]=>010101
[4,7,6,2,5,1,3]=>[5,6,2,4,1,7,3]=>[4,5,1,7,3,2,6]=>010101
[4,7,6,2,5,3,1]=>[3,5,6,4,2,7,1]=>[4,5,2,7,1,3,6]=>000101
[4,7,6,3,1,2,5]=>[3,1,6,4,2,7,5]=>[4,7,5,2,1,3,6]=>100101
[4,7,6,3,1,5,2]=>[5,3,6,4,1,7,2]=>[4,5,1,7,2,3,6]=>000101
[4,7,6,3,2,1,5]=>[2,3,6,4,1,7,5]=>[4,7,5,1,2,3,6]=>000101
[4,7,6,3,2,5,1]=>[5,3,6,4,2,7,1]=>[4,7,1,5,2,3,6]=>000101
[4,7,6,3,5,1,2]=>[5,1,6,4,3,7,2]=>[4,7,2,1,5,3,6]=>100101
[4,7,6,3,5,2,1]=>[2,5,6,4,3,7,1]=>[4,7,1,2,5,3,6]=>000101
[4,7,6,5,1,2,3]=>[5,1,2,4,6,7,3]=>[4,7,3,2,1,5,6]=>110001
[4,7,6,5,1,3,2]=>[3,5,1,4,6,7,2]=>[3,1,4,7,2,5,6]=>010001
[4,7,6,5,2,1,3]=>[2,5,1,4,6,7,3]=>[4,7,3,1,2,5,6]=>010001
[4,7,6,5,2,3,1]=>[3,5,2,4,6,7,1]=>[4,7,1,3,2,5,6]=>010001
[4,7,6,5,3,1,2]=>[3,1,5,4,6,7,2]=>[4,7,2,1,3,5,6]=>100001
[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]=>[4,7,1,2,3,5,6]=>000001
[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,4,3,2,1,6,7]=>111100
[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>[5,4,3,2,1,7,6]=>111101
[5,1,2,3,6,4,7]=>[6,1,2,5,3,4,7]=>[6,4,5,3,2,1,7]=>110110
[5,1,2,3,6,7,4]=>[7,1,2,5,3,6,4]=>[6,7,4,5,3,2,1]=>110101
[5,1,2,3,7,4,6]=>[7,1,2,5,3,4,6]=>[7,6,4,5,3,2,1]=>110111
[5,1,2,3,7,6,4]=>[6,1,2,5,3,7,4]=>[7,4,5,3,2,1,6]=>110101
[5,1,2,4,3,6,7]=>[4,1,5,2,3,6,7]=>[4,2,1,5,3,6,7]=>101100
[5,1,2,4,3,7,6]=>[4,1,5,2,3,7,6]=>[4,2,1,5,3,7,6]=>101101
[5,1,2,4,6,3,7]=>[6,1,5,2,4,3,7]=>[6,3,5,4,2,1,7]=>101110
[5,1,2,4,6,7,3]=>[7,1,5,2,4,6,3]=>[6,7,3,5,4,2,1]=>101101
[5,1,2,4,7,3,6]=>[7,1,5,2,4,3,6]=>[7,6,3,5,4,2,1]=>101111
[5,1,2,4,7,6,3]=>[6,1,5,2,4,7,3]=>[7,3,5,4,2,1,6]=>101101
[5,1,2,6,3,4,7]=>[6,1,5,2,3,4,7]=>[5,3,6,4,2,1,7]=>101110
[5,1,2,6,3,7,4]=>[7,1,6,5,2,3,4]=>[6,3,7,4,5,2,1]=>100111
[5,1,2,6,4,3,7]=>[4,1,6,5,2,3,7]=>[5,2,1,4,6,3,7]=>100110
[5,1,2,6,4,7,3]=>[7,1,6,5,2,4,3]=>[7,3,6,4,5,2,1]=>100111
[5,1,2,6,7,3,4]=>[7,1,5,2,3,6,4]=>[5,3,6,7,4,2,1]=>101101
[5,1,2,6,7,4,3]=>[4,1,7,5,2,6,3]=>[5,2,1,4,6,7,3]=>100101
[5,1,2,7,3,4,6]=>[7,1,5,2,3,4,6]=>[5,3,7,6,4,2,1]=>101111
[5,1,2,7,3,6,4]=>[6,1,7,5,2,3,4]=>[7,4,5,2,1,6,3]=>100111
[5,1,2,7,4,3,6]=>[4,1,7,5,2,3,6]=>[5,2,1,4,7,6,3]=>100111
[5,1,2,7,4,6,3]=>[6,1,7,5,2,4,3]=>[6,4,5,2,1,7,3]=>100111
[5,1,2,7,6,3,4]=>[6,1,5,2,3,7,4]=>[5,3,7,4,2,1,6]=>101101
[5,1,2,7,6,4,3]=>[4,1,6,5,2,7,3]=>[5,2,1,4,7,3,6]=>100101
[5,1,3,2,4,6,7]=>[3,5,1,2,4,6,7]=>[3,1,5,4,2,6,7]=>011100
[5,1,3,2,4,7,6]=>[3,5,1,2,4,7,6]=>[3,1,5,4,2,7,6]=>011101
[5,1,3,2,6,4,7]=>[3,6,1,5,2,4,7]=>[3,1,6,4,5,2,7]=>010110
[5,1,3,2,6,7,4]=>[3,7,1,5,2,6,4]=>[3,1,6,7,4,5,2]=>010101
[5,1,3,2,7,4,6]=>[3,7,1,5,2,4,6]=>[3,1,7,6,4,5,2]=>010111
[5,1,3,2,7,6,4]=>[3,6,1,5,2,7,4]=>[3,1,7,4,5,2,6]=>010101
[5,1,3,4,2,6,7]=>[4,5,1,3,2,6,7]=>[4,3,1,5,2,6,7]=>011100
[5,1,3,4,2,7,6]=>[4,5,1,3,2,7,6]=>[4,3,1,5,2,7,6]=>011101
[5,1,3,4,6,2,7]=>[6,5,1,3,4,2,7]=>[6,2,5,4,3,1,7]=>011110
[5,1,3,4,6,7,2]=>[7,5,1,3,4,6,2]=>[6,7,2,5,4,3,1]=>011101
[5,1,3,4,7,2,6]=>[7,5,1,3,4,2,6]=>[7,6,2,5,4,3,1]=>011111
[5,1,3,4,7,6,2]=>[6,5,1,3,4,7,2]=>[7,2,5,4,3,1,6]=>011101
[5,1,3,6,2,4,7]=>[6,5,1,3,2,4,7]=>[5,2,6,4,3,1,7]=>011110
[5,1,3,6,2,7,4]=>[7,6,1,5,3,2,4]=>[6,2,7,4,5,3,1]=>010111
[5,1,3,6,4,2,7]=>[4,6,1,5,3,2,7]=>[5,3,1,4,6,2,7]=>010110
[5,1,3,6,4,7,2]=>[7,6,1,5,3,4,2]=>[7,2,6,4,5,3,1]=>010111
[5,1,3,6,7,2,4]=>[7,5,1,3,2,6,4]=>[5,2,6,7,4,3,1]=>011101
[5,1,3,6,7,4,2]=>[4,7,1,5,3,6,2]=>[5,3,1,4,6,7,2]=>010101
[5,1,3,7,2,4,6]=>[7,5,1,3,2,4,6]=>[5,2,7,6,4,3,1]=>011111
[5,1,3,7,2,6,4]=>[6,7,1,5,3,2,4]=>[7,4,5,3,1,6,2]=>010111
[5,1,3,7,4,2,6]=>[4,7,1,5,3,2,6]=>[5,3,1,4,7,6,2]=>010111
[5,1,3,7,4,6,2]=>[6,7,1,5,3,4,2]=>[6,4,5,3,1,7,2]=>010111
[5,1,3,7,6,2,4]=>[6,5,1,3,2,7,4]=>[5,2,7,4,3,1,6]=>011101
[5,1,3,7,6,4,2]=>[4,6,1,5,3,7,2]=>[5,3,1,4,7,2,6]=>010101
[5,1,4,2,3,6,7]=>[4,5,1,2,3,6,7]=>[5,3,1,4,2,6,7]=>011100
[5,1,4,2,3,7,6]=>[4,5,1,2,3,7,6]=>[5,3,1,4,2,7,6]=>011101
[5,1,4,2,6,3,7]=>[6,4,5,1,2,3,7]=>[6,3,5,2,4,1,7]=>001110
[5,1,4,2,6,7,3]=>[7,4,5,1,2,6,3]=>[6,7,3,5,2,4,1]=>001101
[5,1,4,2,7,3,6]=>[7,4,5,1,2,3,6]=>[7,6,3,5,2,4,1]=>001111
[5,1,4,2,7,6,3]=>[6,4,5,1,2,7,3]=>[7,3,5,2,4,1,6]=>001101
[5,1,4,3,2,6,7]=>[3,4,5,1,2,6,7]=>[5,2,4,1,3,6,7]=>001100
[5,1,4,3,2,7,6]=>[3,4,5,1,2,7,6]=>[5,2,4,1,3,7,6]=>001101
[5,1,4,3,6,2,7]=>[6,4,5,1,3,2,7]=>[5,3,6,2,4,1,7]=>001110
[5,1,4,3,6,7,2]=>[7,4,5,1,3,6,2]=>[5,3,6,7,2,4,1]=>001101
[5,1,4,3,7,2,6]=>[7,4,5,1,3,2,6]=>[5,3,7,6,2,4,1]=>001111
[5,1,4,3,7,6,2]=>[6,4,5,1,3,7,2]=>[5,3,7,2,4,1,6]=>001101
[5,1,4,6,2,3,7]=>[6,5,1,2,4,3,7]=>[5,4,2,6,3,1,7]=>011110
[5,1,4,6,2,7,3]=>[7,6,5,1,4,2,3]=>[6,2,7,3,5,4,1]=>001111
[5,1,4,6,3,2,7]=>[3,6,5,1,4,2,7]=>[5,4,1,3,6,2,7]=>001110
[5,1,4,6,3,7,2]=>[7,6,5,1,4,3,2]=>[7,2,6,3,5,4,1]=>001111
[5,1,4,6,7,2,3]=>[7,5,1,2,4,6,3]=>[5,4,2,6,7,3,1]=>011101
[5,1,4,6,7,3,2]=>[3,7,5,1,4,6,2]=>[5,4,1,3,6,7,2]=>001101
[5,1,4,7,2,3,6]=>[7,5,1,2,4,3,6]=>[5,4,2,7,6,3,1]=>011111
[5,1,4,7,2,6,3]=>[6,7,5,1,4,2,3]=>[7,3,5,4,1,6,2]=>001111
[5,1,4,7,3,2,6]=>[3,7,5,1,4,2,6]=>[5,4,1,3,7,6,2]=>001111
[5,1,4,7,3,6,2]=>[6,7,5,1,4,3,2]=>[6,3,5,4,1,7,2]=>001111
[5,1,4,7,6,2,3]=>[6,5,1,2,4,7,3]=>[5,4,2,7,3,1,6]=>011101
[5,1,4,7,6,3,2]=>[3,6,5,1,4,7,2]=>[5,4,1,3,7,2,6]=>001101
[5,1,6,2,3,4,7]=>[6,5,1,2,3,4,7]=>[6,4,2,5,3,1,7]=>011110
[5,1,6,2,3,7,4]=>[7,6,1,5,2,3,4]=>[7,4,5,2,6,3,1]=>010111
[5,1,6,2,4,3,7]=>[4,6,5,1,2,3,7]=>[4,1,6,3,5,2,7]=>001110
[5,1,6,2,4,7,3]=>[7,6,5,1,2,4,3]=>[7,3,5,2,6,4,1]=>001111
[5,1,6,2,7,3,4]=>[7,6,5,1,2,3,4]=>[6,3,5,2,7,4,1]=>001111
[5,1,6,2,7,4,3]=>[4,7,6,5,1,2,3]=>[5,1,4,7,3,6,2]=>000111
[5,1,6,3,2,4,7]=>[3,6,5,1,2,4,7]=>[6,4,1,3,5,2,7]=>001110
[5,1,6,3,2,7,4]=>[3,7,6,5,1,2,4]=>[7,4,5,1,3,6,2]=>000111
[5,1,6,3,4,2,7]=>[4,6,5,1,3,2,7]=>[4,1,5,3,6,2,7]=>001110
[5,1,6,3,4,7,2]=>[7,6,5,1,3,4,2]=>[5,3,7,2,6,4,1]=>001111
[5,1,6,3,7,2,4]=>[7,6,5,1,3,2,4]=>[5,3,6,2,7,4,1]=>001111
[5,1,6,3,7,4,2]=>[4,7,6,5,1,3,2]=>[5,1,4,6,3,7,2]=>000111
[5,1,6,4,2,3,7]=>[4,6,1,5,2,3,7]=>[6,3,1,4,5,2,7]=>010110
[5,1,6,4,2,7,3]=>[7,4,6,5,1,2,3]=>[7,3,6,2,4,5,1]=>000111
[5,1,6,4,3,2,7]=>[3,4,6,5,1,2,7]=>[6,2,4,5,1,3,7]=>000110
[5,1,6,4,3,7,2]=>[7,4,6,5,1,3,2]=>[6,3,7,2,4,5,1]=>000111
[5,1,6,4,7,2,3]=>[7,6,1,5,2,4,3]=>[6,4,5,2,7,3,1]=>010111
[5,1,6,4,7,3,2]=>[3,7,6,5,1,4,2]=>[6,4,5,1,3,7,2]=>000111
[5,1,6,7,2,3,4]=>[7,5,1,2,3,6,4]=>[6,7,4,2,5,3,1]=>011101
[5,1,6,7,2,4,3]=>[4,7,5,1,2,6,3]=>[4,1,6,7,3,5,2]=>001101
[5,1,6,7,3,2,4]=>[3,7,5,1,2,6,4]=>[6,7,4,1,3,5,2]=>001101
[5,1,6,7,3,4,2]=>[4,7,5,1,3,6,2]=>[4,1,5,3,6,7,2]=>001101
[5,1,6,7,4,2,3]=>[4,7,1,5,2,6,3]=>[6,7,3,1,4,5,2]=>010101
[5,1,6,7,4,3,2]=>[3,4,7,5,1,6,2]=>[6,7,2,4,5,1,3]=>000101
[5,1,7,2,3,4,6]=>[7,5,1,2,3,4,6]=>[7,6,4,2,5,3,1]=>011111
[5,1,7,2,3,6,4]=>[6,7,1,5,2,3,4]=>[6,3,1,7,4,5,2]=>010111
[5,1,7,2,4,3,6]=>[4,7,5,1,2,3,6]=>[4,1,7,6,3,5,2]=>001111
[5,1,7,2,4,6,3]=>[6,7,5,1,2,4,3]=>[6,4,1,7,3,5,2]=>001111
[5,1,7,2,6,3,4]=>[6,7,5,1,2,3,4]=>[7,4,1,6,3,5,2]=>001111
[5,1,7,2,6,4,3]=>[4,6,7,5,1,2,3]=>[5,1,4,6,2,7,3]=>000111
[5,1,7,3,2,4,6]=>[3,7,5,1,2,4,6]=>[7,6,4,1,3,5,2]=>001111
[5,1,7,3,2,6,4]=>[3,6,7,5,1,2,4]=>[6,2,7,4,5,1,3]=>000111
[5,1,7,3,4,2,6]=>[4,7,5,1,3,2,6]=>[4,1,5,3,7,6,2]=>001111
[5,1,7,3,4,6,2]=>[6,7,5,1,3,4,2]=>[5,3,6,4,1,7,2]=>001111
[5,1,7,3,6,2,4]=>[6,7,5,1,3,2,4]=>[5,3,7,4,1,6,2]=>001111
[5,1,7,3,6,4,2]=>[4,6,7,5,1,3,2]=>[5,1,4,7,2,6,3]=>000111
[5,1,7,4,2,3,6]=>[4,7,1,5,2,3,6]=>[7,6,3,1,4,5,2]=>010111
[5,1,7,4,2,6,3]=>[6,4,7,5,1,2,3]=>[6,2,4,5,1,7,3]=>000111
[5,1,7,4,3,2,6]=>[3,4,7,5,1,2,6]=>[7,6,2,4,5,1,3]=>000111
[5,1,7,4,3,6,2]=>[6,4,7,5,1,3,2]=>[7,2,4,5,1,6,3]=>000111
[5,1,7,4,6,2,3]=>[6,7,1,5,2,4,3]=>[7,3,1,6,4,5,2]=>010111
[5,1,7,4,6,3,2]=>[3,6,7,5,1,4,2]=>[7,2,6,4,5,1,3]=>000111
[5,1,7,6,2,3,4]=>[6,5,1,2,3,7,4]=>[7,4,2,5,3,1,6]=>011101
[5,1,7,6,2,4,3]=>[4,6,5,1,2,7,3]=>[4,1,7,3,5,2,6]=>001101
[5,1,7,6,3,2,4]=>[3,6,5,1,2,7,4]=>[7,4,1,3,5,2,6]=>001101
[5,1,7,6,3,4,2]=>[4,6,5,1,3,7,2]=>[4,1,5,3,7,2,6]=>001101
[5,1,7,6,4,2,3]=>[4,6,1,5,2,7,3]=>[7,3,1,4,5,2,6]=>010101
[5,1,7,6,4,3,2]=>[3,4,6,5,1,7,2]=>[7,2,4,5,1,3,6]=>000101
[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,4,3,1,2,6,7]=>011100
[5,2,1,3,4,7,6]=>[2,5,1,3,4,7,6]=>[5,4,3,1,2,7,6]=>011101
[5,2,1,3,6,4,7]=>[2,6,1,5,3,4,7]=>[6,4,5,3,1,2,7]=>010110
[5,2,1,3,6,7,4]=>[2,7,1,5,3,6,4]=>[6,7,4,5,3,1,2]=>010101
[5,2,1,3,7,4,6]=>[2,7,1,5,3,4,6]=>[7,6,4,5,3,1,2]=>010111
[5,2,1,3,7,6,4]=>[2,6,1,5,3,7,4]=>[7,4,5,3,1,2,6]=>010101
[5,2,1,4,3,6,7]=>[2,4,5,1,3,6,7]=>[4,1,2,5,3,6,7]=>001100
[5,2,1,4,3,7,6]=>[2,4,5,1,3,7,6]=>[4,1,2,5,3,7,6]=>001101
[5,2,1,4,6,3,7]=>[2,6,5,1,4,3,7]=>[6,3,5,4,1,2,7]=>001110
[5,2,1,4,6,7,3]=>[2,7,5,1,4,6,3]=>[6,7,3,5,4,1,2]=>001101
[5,2,1,4,7,3,6]=>[2,7,5,1,4,3,6]=>[7,6,3,5,4,1,2]=>001111
[5,2,1,4,7,6,3]=>[2,6,5,1,4,7,3]=>[7,3,5,4,1,2,6]=>001101
[5,2,1,6,3,4,7]=>[2,6,5,1,3,4,7]=>[5,3,6,4,1,2,7]=>001110
[5,2,1,6,3,7,4]=>[2,7,6,5,1,3,4]=>[6,3,7,4,5,1,2]=>000111
[5,2,1,6,4,3,7]=>[2,4,6,5,1,3,7]=>[5,1,2,4,6,3,7]=>000110
[5,2,1,6,4,7,3]=>[2,7,6,5,1,4,3]=>[7,3,6,4,5,1,2]=>000111
[5,2,1,6,7,3,4]=>[2,7,5,1,3,6,4]=>[5,3,6,7,4,1,2]=>001101
[5,2,1,6,7,4,3]=>[2,4,7,5,1,6,3]=>[5,1,2,4,6,7,3]=>000101
[5,2,1,7,3,4,6]=>[2,7,5,1,3,4,6]=>[5,3,7,6,4,1,2]=>001111
[5,2,1,7,3,6,4]=>[2,6,7,5,1,3,4]=>[7,4,5,1,2,6,3]=>000111
[5,2,1,7,4,3,6]=>[2,4,7,5,1,3,6]=>[5,1,2,4,7,6,3]=>000111
[5,2,1,7,4,6,3]=>[2,6,7,5,1,4,3]=>[6,4,5,1,2,7,3]=>000111
[5,2,1,7,6,3,4]=>[2,6,5,1,3,7,4]=>[5,3,7,4,1,2,6]=>001101
[5,2,1,7,6,4,3]=>[2,4,6,5,1,7,3]=>[5,1,2,4,7,3,6]=>000101
[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[5,4,1,3,2,6,7]=>011100
[5,2,3,1,4,7,6]=>[3,5,2,1,4,7,6]=>[5,4,1,3,2,7,6]=>011101
[5,2,3,1,6,4,7]=>[3,6,2,5,1,4,7]=>[6,4,5,1,3,2,7]=>010110
[5,2,3,1,6,7,4]=>[3,7,2,5,1,6,4]=>[6,7,4,5,1,3,2]=>010101
[5,2,3,1,7,4,6]=>[3,7,2,5,1,4,6]=>[7,6,4,5,1,3,2]=>010111
[5,2,3,1,7,6,4]=>[3,6,2,5,1,7,4]=>[7,4,5,1,3,2,6]=>010101
[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>011100
[5,2,3,4,1,7,6]=>[4,5,2,3,1,7,6]=>[5,1,4,3,2,7,6]=>011101
[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[5,4,3,2,6,1,7]=>011110
[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[5,4,3,2,6,7,1]=>011101
[5,2,3,4,7,1,6]=>[7,5,2,3,4,1,6]=>[5,4,3,2,7,6,1]=>011111
[5,2,3,4,7,6,1]=>[6,5,2,3,4,7,1]=>[5,4,3,2,7,1,6]=>011101
[5,2,3,6,1,4,7]=>[6,5,2,3,1,4,7]=>[6,4,3,2,5,1,7]=>011110
[5,2,3,6,1,7,4]=>[7,6,2,5,3,1,4]=>[7,4,5,3,2,6,1]=>010111
[5,2,3,6,4,1,7]=>[4,6,2,5,3,1,7]=>[6,1,4,5,3,2,7]=>010110
[5,2,3,6,4,7,1]=>[7,6,2,5,3,4,1]=>[6,4,5,3,2,7,1]=>010111
[5,2,3,6,7,1,4]=>[7,5,2,3,1,6,4]=>[6,7,4,3,2,5,1]=>011101
[5,2,3,6,7,4,1]=>[4,7,2,5,3,6,1]=>[6,7,1,4,5,3,2]=>010101
[5,2,3,7,1,4,6]=>[7,5,2,3,1,4,6]=>[7,6,4,3,2,5,1]=>011111
[5,2,3,7,1,6,4]=>[6,7,2,5,3,1,4]=>[6,1,7,4,5,3,2]=>010111
[5,2,3,7,4,1,6]=>[4,7,2,5,3,1,6]=>[7,6,1,4,5,3,2]=>010111
[5,2,3,7,4,6,1]=>[6,7,2,5,3,4,1]=>[7,1,6,4,5,3,2]=>010111
[5,2,3,7,6,1,4]=>[6,5,2,3,1,7,4]=>[7,4,3,2,5,1,6]=>011101
[5,2,3,7,6,4,1]=>[4,6,2,5,3,7,1]=>[7,1,4,5,3,2,6]=>010101
[5,2,4,1,3,6,7]=>[4,5,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>011100
[5,2,4,1,3,7,6]=>[4,5,2,1,3,7,6]=>[4,1,5,3,2,7,6]=>011101
[5,2,4,1,6,3,7]=>[6,4,5,2,1,3,7]=>[4,2,6,3,5,1,7]=>001110
[5,2,4,1,6,7,3]=>[7,4,5,2,1,6,3]=>[4,2,6,7,3,5,1]=>001101
[5,2,4,1,7,3,6]=>[7,4,5,2,1,3,6]=>[4,2,7,6,3,5,1]=>001111
[5,2,4,1,7,6,3]=>[6,4,5,2,1,7,3]=>[4,2,7,3,5,1,6]=>001101
[5,2,4,3,1,6,7]=>[3,4,5,2,1,6,7]=>[4,2,5,1,3,6,7]=>001100
[5,2,4,3,1,7,6]=>[3,4,5,2,1,7,6]=>[4,2,5,1,3,7,6]=>001101
[5,2,4,3,6,1,7]=>[6,4,5,2,3,1,7]=>[4,2,5,3,6,1,7]=>001110
[5,2,4,3,6,7,1]=>[7,4,5,2,3,6,1]=>[4,2,5,3,6,7,1]=>001101
[5,2,4,3,7,1,6]=>[7,4,5,2,3,1,6]=>[4,2,5,3,7,6,1]=>001111
[5,2,4,3,7,6,1]=>[6,4,5,2,3,7,1]=>[4,2,5,3,7,1,6]=>001101
[5,2,4,6,1,3,7]=>[6,5,2,1,4,3,7]=>[6,3,2,5,4,1,7]=>011110
[5,2,4,6,1,7,3]=>[7,6,5,2,4,1,3]=>[7,3,5,4,2,6,1]=>001111
[5,2,4,6,3,1,7]=>[3,6,5,2,4,1,7]=>[6,1,3,5,4,2,7]=>001110
[5,2,4,6,3,7,1]=>[7,6,5,2,4,3,1]=>[6,3,5,4,2,7,1]=>001111
[5,2,4,6,7,1,3]=>[7,5,2,1,4,6,3]=>[6,7,3,2,5,4,1]=>011101
[5,2,4,6,7,3,1]=>[3,7,5,2,4,6,1]=>[6,7,1,3,5,4,2]=>001101
[5,2,4,7,1,3,6]=>[7,5,2,1,4,3,6]=>[7,6,3,2,5,4,1]=>011111
[5,2,4,7,1,6,3]=>[6,7,5,2,4,1,3]=>[6,1,7,3,5,4,2]=>001111
[5,2,4,7,3,1,6]=>[3,7,5,2,4,1,6]=>[7,6,1,3,5,4,2]=>001111
[5,2,4,7,3,6,1]=>[6,7,5,2,4,3,1]=>[7,1,6,3,5,4,2]=>001111
[5,2,4,7,6,1,3]=>[6,5,2,1,4,7,3]=>[7,3,2,5,4,1,6]=>011101
[5,2,4,7,6,3,1]=>[3,6,5,2,4,7,1]=>[7,1,3,5,4,2,6]=>001101
[5,2,6,1,3,4,7]=>[6,5,2,1,3,4,7]=>[5,3,2,6,4,1,7]=>011110
[5,2,6,1,3,7,4]=>[7,6,2,5,1,3,4]=>[6,3,2,7,4,5,1]=>010111
[5,2,6,1,4,3,7]=>[4,6,5,2,1,3,7]=>[6,3,5,1,4,2,7]=>001110
[5,2,6,1,4,7,3]=>[7,6,5,2,1,4,3]=>[6,4,2,7,3,5,1]=>001111
[5,2,6,1,7,3,4]=>[7,6,5,2,1,3,4]=>[7,4,2,6,3,5,1]=>001111
[5,2,6,1,7,4,3]=>[4,7,6,5,2,1,3]=>[7,3,6,1,4,5,2]=>000111
[5,2,6,3,1,4,7]=>[3,6,5,2,1,4,7]=>[5,1,3,6,4,2,7]=>001110
[5,2,6,3,1,7,4]=>[3,7,6,5,2,1,4]=>[6,1,3,7,4,5,2]=>000111
[5,2,6,3,4,1,7]=>[4,6,5,2,3,1,7]=>[5,3,6,1,4,2,7]=>001110
[5,2,6,3,4,7,1]=>[7,6,5,2,3,4,1]=>[5,3,6,4,2,7,1]=>001111
[5,2,6,3,7,1,4]=>[7,6,5,2,3,1,4]=>[5,3,7,4,2,6,1]=>001111
[5,2,6,3,7,4,1]=>[4,7,6,5,2,3,1]=>[6,3,7,1,4,5,2]=>000111
[5,2,6,4,1,3,7]=>[4,6,2,5,1,3,7]=>[5,1,4,6,3,2,7]=>010110
[5,2,6,4,1,7,3]=>[7,4,6,5,2,1,3]=>[5,2,4,7,3,6,1]=>000111
[5,2,6,4,3,1,7]=>[3,4,6,5,2,1,7]=>[5,2,4,6,1,3,7]=>000110
[5,2,6,4,3,7,1]=>[7,4,6,5,2,3,1]=>[5,2,4,6,3,7,1]=>000111
[5,2,6,4,7,1,3]=>[7,6,2,5,1,4,3]=>[7,3,2,6,4,5,1]=>010111
[5,2,6,4,7,3,1]=>[3,7,6,5,2,4,1]=>[7,1,3,6,4,5,2]=>000111
[5,2,6,7,1,3,4]=>[7,5,2,1,3,6,4]=>[5,3,2,6,7,4,1]=>011101
[5,2,6,7,1,4,3]=>[4,7,5,2,1,6,3]=>[6,7,3,5,1,4,2]=>001101
[5,2,6,7,3,1,4]=>[3,7,5,2,1,6,4]=>[5,1,3,6,7,4,2]=>001101
[5,2,6,7,3,4,1]=>[4,7,5,2,3,6,1]=>[5,3,6,7,1,4,2]=>001101
[5,2,6,7,4,1,3]=>[4,7,2,5,1,6,3]=>[5,1,4,6,7,3,2]=>010101
[5,2,6,7,4,3,1]=>[3,4,7,5,2,6,1]=>[5,2,4,6,7,1,3]=>000101
[5,2,7,1,3,4,6]=>[7,5,2,1,3,4,6]=>[5,3,2,7,6,4,1]=>011111
[5,2,7,1,3,6,4]=>[6,7,2,5,1,3,4]=>[7,4,5,1,6,3,2]=>010111
[5,2,7,1,4,3,6]=>[4,7,5,2,1,3,6]=>[7,6,3,5,1,4,2]=>001111
[5,2,7,1,4,6,3]=>[6,7,5,2,1,4,3]=>[7,3,5,1,6,4,2]=>001111
[5,2,7,1,6,3,4]=>[6,7,5,2,1,3,4]=>[6,3,5,1,7,4,2]=>001111
[5,2,7,1,6,4,3]=>[4,6,7,5,2,1,3]=>[6,1,4,5,2,7,3]=>000111
[5,2,7,3,1,4,6]=>[3,7,5,2,1,4,6]=>[5,1,3,7,6,4,2]=>001111
[5,2,7,3,1,6,4]=>[3,6,7,5,2,1,4]=>[7,4,5,2,6,1,3]=>000111
[5,2,7,3,4,1,6]=>[4,7,5,2,3,1,6]=>[5,3,7,6,1,4,2]=>001111
[5,2,7,3,4,6,1]=>[6,7,5,2,3,4,1]=>[5,3,7,1,6,4,2]=>001111
[5,2,7,3,6,1,4]=>[6,7,5,2,3,1,4]=>[5,3,6,1,7,4,2]=>001111
[5,2,7,3,6,4,1]=>[4,6,7,5,2,3,1]=>[7,1,4,5,2,6,3]=>000111
[5,2,7,4,1,3,6]=>[4,7,2,5,1,3,6]=>[5,1,4,7,6,3,2]=>010111
[5,2,7,4,1,6,3]=>[6,4,7,5,2,1,3]=>[5,2,4,6,1,7,3]=>000111
[5,2,7,4,3,1,6]=>[3,4,7,5,2,1,6]=>[5,2,4,7,6,1,3]=>000111
[5,2,7,4,3,6,1]=>[6,4,7,5,2,3,1]=>[5,2,4,7,1,6,3]=>000111
[5,2,7,4,6,1,3]=>[6,7,2,5,1,4,3]=>[6,4,5,1,7,3,2]=>010111
[5,2,7,4,6,3,1]=>[3,6,7,5,2,4,1]=>[6,4,5,2,7,1,3]=>000111
[5,2,7,6,1,3,4]=>[6,5,2,1,3,7,4]=>[5,3,2,7,4,1,6]=>011101
[5,2,7,6,1,4,3]=>[4,6,5,2,1,7,3]=>[7,3,5,1,4,2,6]=>001101
[5,2,7,6,3,1,4]=>[3,6,5,2,1,7,4]=>[5,1,3,7,4,2,6]=>001101
[5,2,7,6,3,4,1]=>[4,6,5,2,3,7,1]=>[5,3,7,1,4,2,6]=>001101
[5,2,7,6,4,1,3]=>[4,6,2,5,1,7,3]=>[5,1,4,7,3,2,6]=>010101
[5,2,7,6,4,3,1]=>[3,4,6,5,2,7,1]=>[5,2,4,7,1,3,6]=>000101
[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[5,4,2,1,3,6,7]=>101100
[5,3,1,2,4,7,6]=>[3,1,5,2,4,7,6]=>[5,4,2,1,3,7,6]=>101101
[5,3,1,2,6,4,7]=>[3,1,6,5,2,4,7]=>[6,4,5,2,1,3,7]=>100110
[5,3,1,2,6,7,4]=>[3,1,7,5,2,6,4]=>[6,7,4,5,2,1,3]=>100101
[5,3,1,2,7,4,6]=>[3,1,7,5,2,4,6]=>[7,6,4,5,2,1,3]=>100111
[5,3,1,2,7,6,4]=>[3,1,6,5,2,7,4]=>[7,4,5,2,1,3,6]=>100101
[5,3,1,4,2,6,7]=>[4,3,5,1,2,6,7]=>[4,1,5,2,3,6,7]=>001100
[5,3,1,4,2,7,6]=>[4,3,5,1,2,7,6]=>[4,1,5,2,3,7,6]=>001101
[5,3,1,4,6,2,7]=>[6,3,5,1,4,2,7]=>[6,2,3,5,4,1,7]=>001110
[5,3,1,4,6,7,2]=>[7,3,5,1,4,6,2]=>[6,7,2,3,5,4,1]=>001101
[5,3,1,4,7,2,6]=>[7,3,5,1,4,2,6]=>[7,6,2,3,5,4,1]=>001111
[5,3,1,4,7,6,2]=>[6,3,5,1,4,7,2]=>[7,2,3,5,4,1,6]=>001101
[5,3,1,6,2,4,7]=>[6,3,5,1,2,4,7]=>[5,2,3,6,4,1,7]=>001110
[5,3,1,6,2,7,4]=>[7,3,6,5,1,2,4]=>[6,2,3,7,4,5,1]=>000111
[5,3,1,6,4,2,7]=>[4,3,6,5,1,2,7]=>[5,1,4,6,2,3,7]=>000110
[5,3,1,6,4,7,2]=>[7,3,6,5,1,4,2]=>[7,2,3,6,4,5,1]=>000111
[5,3,1,6,7,2,4]=>[7,3,5,1,2,6,4]=>[5,2,3,6,7,4,1]=>001101
[5,3,1,6,7,4,2]=>[4,3,7,5,1,6,2]=>[5,1,4,6,7,2,3]=>000101
[5,3,1,7,2,4,6]=>[7,3,5,1,2,4,6]=>[5,2,3,7,6,4,1]=>001111
[5,3,1,7,2,6,4]=>[6,3,7,5,1,2,4]=>[7,4,5,1,6,2,3]=>000111
[5,3,1,7,4,2,6]=>[4,3,7,5,1,2,6]=>[5,1,4,7,6,2,3]=>000111
[5,3,1,7,4,6,2]=>[6,3,7,5,1,4,2]=>[6,4,5,1,7,2,3]=>000111
[5,3,1,7,6,2,4]=>[6,3,5,1,2,7,4]=>[5,2,3,7,4,1,6]=>001101
[5,3,1,7,6,4,2]=>[4,3,6,5,1,7,2]=>[5,1,4,7,2,3,6]=>000101
[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[5,4,1,2,3,6,7]=>001100
[5,3,2,1,4,7,6]=>[2,3,5,1,4,7,6]=>[5,4,1,2,3,7,6]=>001101
[5,3,2,1,6,4,7]=>[2,3,6,5,1,4,7]=>[6,4,5,1,2,3,7]=>000110
[5,3,2,1,6,7,4]=>[2,3,7,5,1,6,4]=>[6,7,4,5,1,2,3]=>000101
[5,3,2,1,7,4,6]=>[2,3,7,5,1,4,6]=>[7,6,4,5,1,2,3]=>000111
[5,3,2,1,7,6,4]=>[2,3,6,5,1,7,4]=>[7,4,5,1,2,3,6]=>000101
[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[5,1,4,2,3,6,7]=>001100
[5,3,2,4,1,7,6]=>[4,3,5,2,1,7,6]=>[5,1,4,2,3,7,6]=>001101
[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[5,4,2,3,6,1,7]=>001110
[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[5,4,2,3,6,7,1]=>001101
[5,3,2,4,7,1,6]=>[7,3,5,2,4,1,6]=>[5,4,2,3,7,6,1]=>001111
[5,3,2,4,7,6,1]=>[6,3,5,2,4,7,1]=>[5,4,2,3,7,1,6]=>001101
[5,3,2,6,1,4,7]=>[6,3,5,2,1,4,7]=>[6,4,2,3,5,1,7]=>001110
[5,3,2,6,1,7,4]=>[7,3,6,5,2,1,4]=>[7,4,5,2,3,6,1]=>000111
[5,3,2,6,4,1,7]=>[4,3,6,5,2,1,7]=>[6,1,4,5,2,3,7]=>000110
[5,3,2,6,4,7,1]=>[7,3,6,5,2,4,1]=>[6,4,5,2,3,7,1]=>000111
[5,3,2,6,7,1,4]=>[7,3,5,2,1,6,4]=>[6,7,4,2,3,5,1]=>001101
[5,3,2,6,7,4,1]=>[4,3,7,5,2,6,1]=>[6,7,1,4,5,2,3]=>000101
[5,3,2,7,1,4,6]=>[7,3,5,2,1,4,6]=>[7,6,4,2,3,5,1]=>001111
[5,3,2,7,1,6,4]=>[6,3,7,5,2,1,4]=>[6,1,7,4,5,2,3]=>000111
[5,3,2,7,4,1,6]=>[4,3,7,5,2,1,6]=>[7,6,1,4,5,2,3]=>000111
[5,3,2,7,4,6,1]=>[6,3,7,5,2,4,1]=>[7,1,6,4,5,2,3]=>000111
[5,3,2,7,6,1,4]=>[6,3,5,2,1,7,4]=>[7,4,2,3,5,1,6]=>001101
[5,3,2,7,6,4,1]=>[4,3,6,5,2,7,1]=>[7,1,4,5,2,3,6]=>000101
[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[5,2,1,4,3,6,7]=>101100
[5,3,4,1,2,7,6]=>[4,1,5,3,2,7,6]=>[5,2,1,4,3,7,6]=>101101
[5,3,4,1,6,2,7]=>[6,4,5,3,1,2,7]=>[6,2,4,3,5,1,7]=>001110
[5,3,4,1,6,7,2]=>[7,4,5,3,1,6,2]=>[6,7,2,4,3,5,1]=>001101
[5,3,4,1,7,2,6]=>[7,4,5,3,1,2,6]=>[7,6,2,4,3,5,1]=>001111
[5,3,4,1,7,6,2]=>[6,4,5,3,1,7,2]=>[7,2,4,3,5,1,6]=>001101
[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>[5,1,2,4,3,6,7]=>001100
[5,3,4,2,1,7,6]=>[2,4,5,3,1,7,6]=>[5,1,2,4,3,7,6]=>001101
[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[5,2,4,3,6,1,7]=>001110
[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[5,2,4,3,6,7,1]=>001101
[5,3,4,2,7,1,6]=>[7,4,5,3,2,1,6]=>[5,2,4,3,7,6,1]=>001111
[5,3,4,2,7,6,1]=>[6,4,5,3,2,7,1]=>[5,2,4,3,7,1,6]=>001101
[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>[5,4,3,6,2,1,7]=>101110
[5,3,4,6,1,7,2]=>[7,6,5,3,4,1,2]=>[5,4,3,7,2,6,1]=>001111
[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[5,4,3,6,1,2,7]=>001110
[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[5,4,3,6,2,7,1]=>001111
[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>[5,4,3,6,7,2,1]=>101101
[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[5,4,3,6,7,1,2]=>001101
[5,3,4,7,1,2,6]=>[7,1,5,3,4,2,6]=>[5,4,3,7,6,2,1]=>101111
[5,3,4,7,1,6,2]=>[6,7,5,3,4,1,2]=>[5,4,3,6,1,7,2]=>001111
[5,3,4,7,2,1,6]=>[2,7,5,3,4,1,6]=>[5,4,3,7,6,1,2]=>001111
[5,3,4,7,2,6,1]=>[6,7,5,3,4,2,1]=>[5,4,3,7,1,6,2]=>001111
[5,3,4,7,6,1,2]=>[6,1,5,3,4,7,2]=>[5,4,3,7,2,1,6]=>101101
[5,3,4,7,6,2,1]=>[2,6,5,3,4,7,1]=>[5,4,3,7,1,2,6]=>001101
[5,3,6,1,2,4,7]=>[6,1,5,3,2,4,7]=>[6,4,3,5,2,1,7]=>101110
[5,3,6,1,2,7,4]=>[7,1,6,5,3,2,4]=>[7,4,5,3,6,2,1]=>100111
[5,3,6,1,4,2,7]=>[4,6,5,3,1,2,7]=>[5,1,4,3,6,2,7]=>001110
[5,3,6,1,4,7,2]=>[7,6,5,3,1,4,2]=>[7,2,6,4,3,5,1]=>001111
[5,3,6,1,7,2,4]=>[7,6,5,3,1,2,4]=>[6,2,7,4,3,5,1]=>001111
[5,3,6,1,7,4,2]=>[4,7,6,5,3,1,2]=>[6,1,4,5,3,7,2]=>000111
[5,3,6,2,1,4,7]=>[2,6,5,3,1,4,7]=>[6,4,3,5,1,2,7]=>001110
[5,3,6,2,1,7,4]=>[2,7,6,5,3,1,4]=>[7,4,5,3,6,1,2]=>000111
[5,3,6,2,4,1,7]=>[4,6,5,3,2,1,7]=>[6,1,4,3,5,2,7]=>001110
[5,3,6,2,4,7,1]=>[7,6,5,3,2,4,1]=>[6,4,3,5,2,7,1]=>001111
[5,3,6,2,7,1,4]=>[7,6,5,3,2,1,4]=>[7,4,3,5,2,6,1]=>001111
[5,3,6,2,7,4,1]=>[4,7,6,5,3,2,1]=>[7,1,4,5,3,6,2]=>000111
[5,3,6,4,1,2,7]=>[4,1,6,5,3,2,7]=>[6,2,1,4,5,3,7]=>100110
[5,3,6,4,1,7,2]=>[7,4,6,5,3,1,2]=>[7,2,4,5,3,6,1]=>000111
[5,3,6,4,2,1,7]=>[2,4,6,5,3,1,7]=>[6,1,2,4,5,3,7]=>000110
[5,3,6,4,2,7,1]=>[7,4,6,5,3,2,1]=>[6,2,4,5,3,7,1]=>000111
[5,3,6,4,7,1,2]=>[7,1,6,5,3,4,2]=>[6,4,5,3,7,2,1]=>100111
[5,3,6,4,7,2,1]=>[2,7,6,5,3,4,1]=>[6,4,5,3,7,1,2]=>000111
[5,3,6,7,1,2,4]=>[7,1,5,3,2,6,4]=>[6,7,4,3,5,2,1]=>101101
[5,3,6,7,1,4,2]=>[4,7,5,3,1,6,2]=>[5,1,4,3,6,7,2]=>001101
[5,3,6,7,2,1,4]=>[2,7,5,3,1,6,4]=>[6,7,4,3,5,1,2]=>001101
[5,3,6,7,2,4,1]=>[4,7,5,3,2,6,1]=>[6,7,1,4,3,5,2]=>001101
[5,3,6,7,4,1,2]=>[4,1,7,5,3,6,2]=>[6,7,2,1,4,5,3]=>100101
[5,3,6,7,4,2,1]=>[2,4,7,5,3,6,1]=>[6,7,1,2,4,5,3]=>000101
[5,3,7,1,2,4,6]=>[7,1,5,3,2,4,6]=>[7,6,4,3,5,2,1]=>101111
[5,3,7,1,2,6,4]=>[6,1,7,5,3,2,4]=>[6,2,1,7,4,5,3]=>100111
[5,3,7,1,4,2,6]=>[4,7,5,3,1,2,6]=>[5,1,4,3,7,6,2]=>001111
[5,3,7,1,4,6,2]=>[6,7,5,3,1,4,2]=>[6,4,3,5,1,7,2]=>001111
[5,3,7,1,6,2,4]=>[6,7,5,3,1,2,4]=>[7,4,3,5,1,6,2]=>001111
[5,3,7,1,6,4,2]=>[4,6,7,5,3,1,2]=>[7,2,6,1,4,5,3]=>000111
[5,3,7,2,1,4,6]=>[2,7,5,3,1,4,6]=>[7,6,4,3,5,1,2]=>001111
[5,3,7,2,1,6,4]=>[2,6,7,5,3,1,4]=>[6,1,2,7,4,5,3]=>000111
[5,3,7,2,4,1,6]=>[4,7,5,3,2,1,6]=>[7,6,1,4,3,5,2]=>001111
[5,3,7,2,4,6,1]=>[6,7,5,3,2,4,1]=>[7,1,6,4,3,5,2]=>001111
[5,3,7,2,6,1,4]=>[6,7,5,3,2,1,4]=>[6,1,7,4,3,5,2]=>001111
[5,3,7,2,6,4,1]=>[4,6,7,5,3,2,1]=>[6,2,7,1,4,5,3]=>000111
[5,3,7,4,1,2,6]=>[4,1,7,5,3,2,6]=>[7,6,2,1,4,5,3]=>100111
[5,3,7,4,1,6,2]=>[6,4,7,5,3,1,2]=>[6,1,7,2,4,5,3]=>000111
[5,3,7,4,2,1,6]=>[2,4,7,5,3,1,6]=>[7,6,1,2,4,5,3]=>000111
[5,3,7,4,2,6,1]=>[6,4,7,5,3,2,1]=>[7,1,6,2,4,5,3]=>000111
[5,3,7,4,6,1,2]=>[6,1,7,5,3,4,2]=>[7,2,1,6,4,5,3]=>100111
[5,3,7,4,6,2,1]=>[2,6,7,5,3,4,1]=>[7,1,2,6,4,5,3]=>000111
[5,3,7,6,1,2,4]=>[6,1,5,3,2,7,4]=>[7,4,3,5,2,1,6]=>101101
[5,3,7,6,1,4,2]=>[4,6,5,3,1,7,2]=>[5,1,4,3,7,2,6]=>001101
[5,3,7,6,2,1,4]=>[2,6,5,3,1,7,4]=>[7,4,3,5,1,2,6]=>001101
[5,3,7,6,2,4,1]=>[4,6,5,3,2,7,1]=>[7,1,4,3,5,2,6]=>001101
[5,3,7,6,4,1,2]=>[4,1,6,5,3,7,2]=>[7,2,1,4,5,3,6]=>100101
[5,3,7,6,4,2,1]=>[2,4,6,5,3,7,1]=>[7,1,2,4,5,3,6]=>000101
[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[5,3,2,1,4,6,7]=>110100
[5,4,1,2,3,7,6]=>[4,1,2,5,3,7,6]=>[5,3,2,1,4,7,6]=>110101
[5,4,1,2,6,3,7]=>[6,1,4,5,2,3,7]=>[6,3,4,5,2,1,7]=>100110
[5,4,1,2,6,7,3]=>[7,1,4,5,2,6,3]=>[6,7,3,4,5,2,1]=>100101
[5,4,1,2,7,3,6]=>[7,1,4,5,2,3,6]=>[7,6,3,4,5,2,1]=>100111
[5,4,1,2,7,6,3]=>[6,1,4,5,2,7,3]=>[7,3,4,5,2,1,6]=>100101
[5,4,1,3,2,6,7]=>[3,4,1,5,2,6,7]=>[3,1,5,2,4,6,7]=>010100
[5,4,1,3,2,7,6]=>[3,4,1,5,2,7,6]=>[3,1,5,2,4,7,6]=>010101
[5,4,1,3,6,2,7]=>[6,4,1,5,3,2,7]=>[6,2,4,5,3,1,7]=>010110
[5,4,1,3,6,7,2]=>[7,4,1,5,3,6,2]=>[6,7,2,4,5,3,1]=>010101
[5,4,1,3,7,2,6]=>[7,4,1,5,3,2,6]=>[7,6,2,4,5,3,1]=>010111
[5,4,1,3,7,6,2]=>[6,4,1,5,3,7,2]=>[7,2,4,5,3,1,6]=>010101
[5,4,1,6,2,3,7]=>[6,4,1,5,2,3,7]=>[5,2,4,6,3,1,7]=>010110
[5,4,1,6,2,7,3]=>[7,6,4,5,1,2,3]=>[6,2,7,3,4,5,1]=>000111
[5,4,1,6,3,2,7]=>[3,6,4,5,1,2,7]=>[5,1,3,4,6,2,7]=>000110
[5,4,1,6,3,7,2]=>[7,6,4,5,1,3,2]=>[7,2,6,3,4,5,1]=>000111
[5,4,1,6,7,2,3]=>[7,4,1,5,2,6,3]=>[5,2,4,6,7,3,1]=>010101
[5,4,1,6,7,3,2]=>[3,7,4,5,1,6,2]=>[5,1,3,4,6,7,2]=>000101
[5,4,1,7,2,3,6]=>[7,4,1,5,2,3,6]=>[5,2,4,7,6,3,1]=>010111
[5,4,1,7,2,6,3]=>[6,7,4,5,1,2,3]=>[7,3,4,5,1,6,2]=>000111
[5,4,1,7,3,2,6]=>[3,7,4,5,1,2,6]=>[5,1,3,4,7,6,2]=>000111
[5,4,1,7,3,6,2]=>[6,7,4,5,1,3,2]=>[6,3,4,5,1,7,2]=>000111
[5,4,1,7,6,2,3]=>[6,4,1,5,2,7,3]=>[5,2,4,7,3,1,6]=>010101
[5,4,1,7,6,3,2]=>[3,6,4,5,1,7,2]=>[5,1,3,4,7,2,6]=>000101
[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[5,3,1,2,4,6,7]=>010100
[5,4,2,1,3,7,6]=>[2,4,1,5,3,7,6]=>[5,3,1,2,4,7,6]=>010101
[5,4,2,1,6,3,7]=>[2,6,4,5,1,3,7]=>[6,3,4,5,1,2,7]=>000110
[5,4,2,1,6,7,3]=>[2,7,4,5,1,6,3]=>[6,7,3,4,5,1,2]=>000101
[5,4,2,1,7,3,6]=>[2,7,4,5,1,3,6]=>[7,6,3,4,5,1,2]=>000111
[5,4,2,1,7,6,3]=>[2,6,4,5,1,7,3]=>[7,3,4,5,1,2,6]=>000101
[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>[5,1,3,2,4,6,7]=>010100
[5,4,2,3,1,7,6]=>[3,4,2,5,1,7,6]=>[5,1,3,2,4,7,6]=>010101
[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>[5,3,2,4,6,1,7]=>010110
[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>[5,3,2,4,6,7,1]=>010101
[5,4,2,3,7,1,6]=>[7,4,2,5,3,1,6]=>[5,3,2,4,7,6,1]=>010111
[5,4,2,3,7,6,1]=>[6,4,2,5,3,7,1]=>[5,3,2,4,7,1,6]=>010101
[5,4,2,6,1,3,7]=>[6,4,2,5,1,3,7]=>[6,3,2,4,5,1,7]=>010110
[5,4,2,6,1,7,3]=>[7,6,4,5,2,1,3]=>[7,3,4,5,2,6,1]=>000111
[5,4,2,6,3,1,7]=>[3,6,4,5,2,1,7]=>[6,1,3,4,5,2,7]=>000110
[5,4,2,6,3,7,1]=>[7,6,4,5,2,3,1]=>[6,3,4,5,2,7,1]=>000111
[5,4,2,6,7,1,3]=>[7,4,2,5,1,6,3]=>[6,7,3,2,4,5,1]=>010101
[5,4,2,6,7,3,1]=>[3,7,4,5,2,6,1]=>[6,7,1,3,4,5,2]=>000101
[5,4,2,7,1,3,6]=>[7,4,2,5,1,3,6]=>[7,6,3,2,4,5,1]=>010111
[5,4,2,7,1,6,3]=>[6,7,4,5,2,1,3]=>[6,1,7,3,4,5,2]=>000111
[5,4,2,7,3,1,6]=>[3,7,4,5,2,1,6]=>[7,6,1,3,4,5,2]=>000111
[5,4,2,7,3,6,1]=>[6,7,4,5,2,3,1]=>[7,1,6,3,4,5,2]=>000111
[5,4,2,7,6,1,3]=>[6,4,2,5,1,7,3]=>[7,3,2,4,5,1,6]=>010101
[5,4,2,7,6,3,1]=>[3,6,4,5,2,7,1]=>[7,1,3,4,5,2,6]=>000101
[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[5,2,1,3,4,6,7]=>100100
[5,4,3,1,2,7,6]=>[3,1,4,5,2,7,6]=>[5,2,1,3,4,7,6]=>100101
[5,4,3,1,6,2,7]=>[6,3,4,5,1,2,7]=>[6,2,3,4,5,1,7]=>000110
[5,4,3,1,6,7,2]=>[7,3,4,5,1,6,2]=>[6,7,2,3,4,5,1]=>000101
[5,4,3,1,7,2,6]=>[7,3,4,5,1,2,6]=>[7,6,2,3,4,5,1]=>000111
[5,4,3,1,7,6,2]=>[6,3,4,5,1,7,2]=>[7,2,3,4,5,1,6]=>000101
[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>000100
[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>000101
[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[5,2,3,4,6,1,7]=>000110
[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,7,1]=>000101
[5,4,3,2,7,1,6]=>[7,3,4,5,2,1,6]=>[5,2,3,4,7,6,1]=>000111
[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>[5,2,3,4,7,1,6]=>000101
[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[5,3,4,6,2,1,7]=>100110
[5,4,3,6,1,7,2]=>[7,6,4,5,3,1,2]=>[5,3,4,7,2,6,1]=>000111
[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[5,3,4,6,1,2,7]=>000110
[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[5,3,4,6,2,7,1]=>000111
[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>[5,3,4,6,7,2,1]=>100101
[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[5,3,4,6,7,1,2]=>000101
[5,4,3,7,1,2,6]=>[7,1,4,5,3,2,6]=>[5,3,4,7,6,2,1]=>100111
[5,4,3,7,1,6,2]=>[6,7,4,5,3,1,2]=>[5,3,4,6,1,7,2]=>000111
[5,4,3,7,2,1,6]=>[2,7,4,5,3,1,6]=>[5,3,4,7,6,1,2]=>000111
[5,4,3,7,2,6,1]=>[6,7,4,5,3,2,1]=>[5,3,4,7,1,6,2]=>000111
[5,4,3,7,6,1,2]=>[6,1,4,5,3,7,2]=>[5,3,4,7,2,1,6]=>100101
[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]=>[5,3,4,7,1,2,6]=>000101
[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[5,4,6,3,2,1,7]=>110110
[5,4,6,1,2,7,3]=>[7,1,6,5,4,2,3]=>[5,4,7,3,6,2,1]=>100111
[5,4,6,1,3,2,7]=>[3,6,1,5,4,2,7]=>[3,1,5,4,6,2,7]=>010110
[5,4,6,1,3,7,2]=>[7,6,1,5,4,3,2]=>[5,4,7,2,6,3,1]=>010111
[5,4,6,1,7,2,3]=>[7,6,1,5,4,2,3]=>[5,4,6,2,7,3,1]=>010111
[5,4,6,1,7,3,2]=>[3,7,6,5,4,1,2]=>[5,4,6,1,3,7,2]=>000111
[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>[5,4,6,3,1,2,7]=>010110
[5,4,6,2,1,7,3]=>[2,7,6,5,4,1,3]=>[5,4,7,3,6,1,2]=>000111
[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>[5,4,6,1,3,2,7]=>010110
[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>[5,4,6,3,2,7,1]=>010111
[5,4,6,2,7,1,3]=>[7,6,2,5,4,1,3]=>[5,4,7,3,2,6,1]=>010111
[5,4,6,2,7,3,1]=>[3,7,6,5,4,2,1]=>[5,4,7,1,3,6,2]=>000111
[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>[5,4,6,2,1,3,7]=>100110
[5,4,6,3,1,7,2]=>[7,3,6,5,4,1,2]=>[5,4,7,2,3,6,1]=>000111
[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[5,4,6,1,2,3,7]=>000110
[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[5,4,6,2,3,7,1]=>000111
[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>[5,4,6,3,7,2,1]=>100111
[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[5,4,6,3,7,1,2]=>000111
[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[5,4,6,7,3,2,1]=>110101
[5,4,6,7,1,3,2]=>[3,7,1,5,4,6,2]=>[3,1,5,4,6,7,2]=>010101
[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>[5,4,6,7,3,1,2]=>010101
[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>[5,4,6,7,1,3,2]=>010101
[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>[5,4,6,7,2,1,3]=>100101
[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[5,4,6,7,1,2,3]=>000101
[5,4,7,1,2,3,6]=>[7,1,2,5,4,3,6]=>[5,4,7,6,3,2,1]=>110111
[5,4,7,1,2,6,3]=>[6,1,7,5,4,2,3]=>[5,4,6,2,1,7,3]=>100111
[5,4,7,1,3,2,6]=>[3,7,1,5,4,2,6]=>[3,1,5,4,7,6,2]=>010111
[5,4,7,1,3,6,2]=>[6,7,1,5,4,3,2]=>[5,4,6,3,1,7,2]=>010111
[5,4,7,1,6,2,3]=>[6,7,1,5,4,2,3]=>[5,4,7,3,1,6,2]=>010111
[5,4,7,1,6,3,2]=>[3,6,7,5,4,1,2]=>[5,4,7,2,6,1,3]=>000111
[5,4,7,2,1,3,6]=>[2,7,1,5,4,3,6]=>[5,4,7,6,3,1,2]=>010111
[5,4,7,2,1,6,3]=>[2,6,7,5,4,1,3]=>[5,4,6,1,2,7,3]=>000111
[5,4,7,2,3,1,6]=>[3,7,2,5,4,1,6]=>[5,4,7,6,1,3,2]=>010111
[5,4,7,2,3,6,1]=>[6,7,2,5,4,3,1]=>[5,4,7,1,6,3,2]=>010111
[5,4,7,2,6,1,3]=>[6,7,2,5,4,1,3]=>[5,4,6,1,7,3,2]=>010111
[5,4,7,2,6,3,1]=>[3,6,7,5,4,2,1]=>[5,4,6,2,7,1,3]=>000111
[5,4,7,3,1,2,6]=>[3,1,7,5,4,2,6]=>[5,4,7,6,2,1,3]=>100111
[5,4,7,3,1,6,2]=>[6,3,7,5,4,1,2]=>[5,4,6,1,7,2,3]=>000111
[5,4,7,3,2,1,6]=>[2,3,7,5,4,1,6]=>[5,4,7,6,1,2,3]=>000111
[5,4,7,3,2,6,1]=>[6,3,7,5,4,2,1]=>[5,4,7,1,6,2,3]=>000111
[5,4,7,3,6,1,2]=>[6,1,7,5,4,3,2]=>[5,4,7,2,1,6,3]=>100111
[5,4,7,3,6,2,1]=>[2,6,7,5,4,3,1]=>[5,4,7,1,2,6,3]=>000111
[5,4,7,6,1,2,3]=>[6,1,2,5,4,7,3]=>[5,4,7,3,2,1,6]=>110101
[5,4,7,6,1,3,2]=>[3,6,1,5,4,7,2]=>[3,1,5,4,7,2,6]=>010101
[5,4,7,6,2,1,3]=>[2,6,1,5,4,7,3]=>[5,4,7,3,1,2,6]=>010101
[5,4,7,6,2,3,1]=>[3,6,2,5,4,7,1]=>[5,4,7,1,3,2,6]=>010101
[5,4,7,6,3,1,2]=>[3,1,6,5,4,7,2]=>[5,4,7,2,1,3,6]=>100101
[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]=>[5,4,7,1,2,3,6]=>000101
[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[5,6,4,3,2,1,7]=>111010
[5,6,1,2,3,7,4]=>[7,1,2,6,5,3,4]=>[5,7,4,6,3,2,1]=>110011
[5,6,1,2,4,3,7]=>[4,1,6,2,5,3,7]=>[4,2,1,5,6,3,7]=>101010
[5,6,1,2,4,7,3]=>[7,1,6,2,5,4,3]=>[5,7,3,6,4,2,1]=>101011
[5,6,1,2,7,3,4]=>[7,1,6,2,5,3,4]=>[5,6,3,7,4,2,1]=>101011
[5,6,1,2,7,4,3]=>[4,1,7,6,5,2,3]=>[5,6,2,1,4,7,3]=>100011
[5,6,1,3,2,4,7]=>[3,6,1,2,5,4,7]=>[3,1,5,6,4,2,7]=>011010
[5,6,1,3,2,7,4]=>[3,7,1,6,5,2,4]=>[3,1,5,7,4,6,2]=>010011
[5,6,1,3,4,2,7]=>[4,6,1,3,5,2,7]=>[4,3,1,5,6,2,7]=>011010
[5,6,1,3,4,7,2]=>[7,6,1,3,5,4,2]=>[5,7,2,6,4,3,1]=>011011
[5,6,1,3,7,2,4]=>[7,6,1,3,5,2,4]=>[5,6,2,7,4,3,1]=>011011
[5,6,1,3,7,4,2]=>[4,7,1,6,5,3,2]=>[5,6,3,1,4,7,2]=>010011
[5,6,1,4,2,3,7]=>[4,6,1,2,5,3,7]=>[5,6,3,1,4,2,7]=>011010
[5,6,1,4,2,7,3]=>[7,4,6,1,5,2,3]=>[5,7,3,6,2,4,1]=>001011
[5,6,1,4,3,2,7]=>[3,4,6,1,5,2,7]=>[5,6,2,4,1,3,7]=>001010
[5,6,1,4,3,7,2]=>[7,4,6,1,5,3,2]=>[5,6,3,7,2,4,1]=>001011
[5,6,1,4,7,2,3]=>[7,6,1,2,5,4,3]=>[5,6,4,2,7,3,1]=>011011
[5,6,1,4,7,3,2]=>[3,7,6,1,5,4,2]=>[5,6,4,1,3,7,2]=>001011
[5,6,1,7,2,3,4]=>[7,6,1,2,5,3,4]=>[5,7,4,2,6,3,1]=>011011
[5,6,1,7,2,4,3]=>[4,7,6,1,5,2,3]=>[4,1,5,7,3,6,2]=>001011
[5,6,1,7,3,2,4]=>[3,7,6,1,5,2,4]=>[5,7,4,1,3,6,2]=>001011
[5,6,1,7,3,4,2]=>[4,7,6,1,5,3,2]=>[4,1,5,6,3,7,2]=>001011
[5,6,1,7,4,2,3]=>[4,7,1,6,5,2,3]=>[5,7,3,1,4,6,2]=>010011
[5,6,1,7,4,3,2]=>[3,4,7,6,5,1,2]=>[5,7,2,4,6,1,3]=>000011
[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>[5,6,4,3,1,2,7]=>011010
[5,6,2,1,3,7,4]=>[2,7,1,6,5,3,4]=>[5,7,4,6,3,1,2]=>010011
[5,6,2,1,4,3,7]=>[2,4,6,1,5,3,7]=>[4,1,2,5,6,3,7]=>001010
[5,6,2,1,4,7,3]=>[2,7,6,1,5,4,3]=>[5,7,3,6,4,1,2]=>001011
[5,6,2,1,7,3,4]=>[2,7,6,1,5,3,4]=>[5,6,3,7,4,1,2]=>001011
[5,6,2,1,7,4,3]=>[2,4,7,6,5,1,3]=>[5,6,1,2,4,7,3]=>000011
[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>[5,6,4,1,3,2,7]=>011010
[5,6,2,3,1,7,4]=>[3,7,2,6,5,1,4]=>[5,7,4,6,1,3,2]=>010011
[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>[5,6,1,4,3,2,7]=>011010
[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>[5,6,4,3,2,7,1]=>011011
[5,6,2,3,7,1,4]=>[7,6,2,3,5,1,4]=>[5,7,4,3,2,6,1]=>011011
[5,6,2,3,7,4,1]=>[4,7,2,6,5,3,1]=>[5,7,1,4,6,3,2]=>010011
[5,6,2,4,1,3,7]=>[4,6,2,1,5,3,7]=>[4,1,5,6,3,2,7]=>011010
[5,6,2,4,1,7,3]=>[7,4,6,2,5,1,3]=>[4,2,5,7,3,6,1]=>001011
[5,6,2,4,3,1,7]=>[3,4,6,2,5,1,7]=>[4,2,5,6,1,3,7]=>001010
[5,6,2,4,3,7,1]=>[7,4,6,2,5,3,1]=>[4,2,5,6,3,7,1]=>001011
[5,6,2,4,7,1,3]=>[7,6,2,1,5,4,3]=>[5,7,3,2,6,4,1]=>011011
[5,6,2,4,7,3,1]=>[3,7,6,2,5,4,1]=>[5,7,1,3,6,4,2]=>001011
[5,6,2,7,1,3,4]=>[7,6,2,1,5,3,4]=>[5,6,3,2,7,4,1]=>011011
[5,6,2,7,1,4,3]=>[4,7,6,2,5,1,3]=>[5,7,3,6,1,4,2]=>001011
[5,6,2,7,3,1,4]=>[3,7,6,2,5,1,4]=>[5,6,1,3,7,4,2]=>001011
[5,6,2,7,3,4,1]=>[4,7,6,2,5,3,1]=>[5,6,3,7,1,4,2]=>001011
[5,6,2,7,4,1,3]=>[4,7,2,6,5,1,3]=>[5,6,1,4,7,3,2]=>010011
[5,6,2,7,4,3,1]=>[3,4,7,6,5,2,1]=>[5,6,2,4,7,1,3]=>000011
[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>[5,6,4,2,1,3,7]=>101010
[5,6,3,1,2,7,4]=>[3,1,7,6,5,2,4]=>[5,7,4,6,2,1,3]=>100011
[5,6,3,1,4,2,7]=>[4,3,6,1,5,2,7]=>[4,1,5,6,2,3,7]=>001010
[5,6,3,1,4,7,2]=>[7,3,6,1,5,4,2]=>[5,7,2,3,6,4,1]=>001011
[5,6,3,1,7,2,4]=>[7,3,6,1,5,2,4]=>[5,6,2,3,7,4,1]=>001011
[5,6,3,1,7,4,2]=>[4,3,7,6,5,1,2]=>[5,6,1,4,7,2,3]=>000011
[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>[5,6,4,1,2,3,7]=>001010
[5,6,3,2,1,7,4]=>[2,3,7,6,5,1,4]=>[5,7,4,6,1,2,3]=>000011
[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>[5,6,1,4,2,3,7]=>001010
[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>[5,6,4,2,3,7,1]=>001011
[5,6,3,2,7,1,4]=>[7,3,6,2,5,1,4]=>[5,7,4,2,3,6,1]=>001011
[5,6,3,2,7,4,1]=>[4,3,7,6,5,2,1]=>[5,7,1,4,6,2,3]=>000011
[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[5,6,2,1,4,3,7]=>101010
[5,6,3,4,1,7,2]=>[7,4,6,3,5,1,2]=>[5,7,2,4,3,6,1]=>001011
[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>[5,6,1,2,4,3,7]=>001010
[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>[5,6,2,4,3,7,1]=>001011
[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>[5,6,4,3,7,2,1]=>101011
[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>[5,6,4,3,7,1,2]=>001011
[5,6,3,7,1,2,4]=>[7,1,6,3,5,2,4]=>[5,7,4,3,6,2,1]=>101011
[5,6,3,7,1,4,2]=>[4,7,6,3,5,1,2]=>[5,6,1,4,3,7,2]=>001011
[5,6,3,7,2,1,4]=>[2,7,6,3,5,1,4]=>[5,7,4,3,6,1,2]=>001011
[5,6,3,7,2,4,1]=>[4,7,6,3,5,2,1]=>[5,7,1,4,3,6,2]=>001011
[5,6,3,7,4,1,2]=>[4,1,7,6,5,3,2]=>[5,7,2,1,4,6,3]=>100011
[5,6,3,7,4,2,1]=>[2,4,7,6,5,3,1]=>[5,7,1,2,4,6,3]=>000011
[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>[5,6,3,2,1,4,7]=>110010
[5,6,4,1,2,7,3]=>[7,1,4,6,5,2,3]=>[5,7,3,4,6,2,1]=>100011
[5,6,4,1,3,2,7]=>[3,4,1,6,5,2,7]=>[3,1,5,6,2,4,7]=>010010
[5,6,4,1,3,7,2]=>[7,4,1,6,5,3,2]=>[5,7,2,4,6,3,1]=>010011
[5,6,4,1,7,2,3]=>[7,4,1,6,5,2,3]=>[5,6,2,4,7,3,1]=>010011
[5,6,4,1,7,3,2]=>[3,7,4,6,5,1,2]=>[5,6,1,3,4,7,2]=>000011
[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>[5,6,3,1,2,4,7]=>010010
[5,6,4,2,1,7,3]=>[2,7,4,6,5,1,3]=>[5,7,3,4,6,1,2]=>000011
[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>[5,6,1,3,2,4,7]=>010010
[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>[5,6,3,2,4,7,1]=>010011
[5,6,4,2,7,1,3]=>[7,4,2,6,5,1,3]=>[5,7,3,2,4,6,1]=>010011
[5,6,4,2,7,3,1]=>[3,7,4,6,5,2,1]=>[5,7,1,3,4,6,2]=>000011
[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>[5,6,2,1,3,4,7]=>100010
[5,6,4,3,1,7,2]=>[7,3,4,6,5,1,2]=>[5,7,2,3,4,6,1]=>000011
[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[5,6,1,2,3,4,7]=>000010
[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[5,6,2,3,4,7,1]=>000011
[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>[5,6,3,4,7,2,1]=>100011
[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[5,6,3,4,7,1,2]=>000011
[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[5,6,4,7,3,2,1]=>110011
[5,6,4,7,1,3,2]=>[3,7,1,6,5,4,2]=>[3,1,5,6,4,7,2]=>010011
[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>[5,6,4,7,3,1,2]=>010011
[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>[5,6,4,7,1,3,2]=>010011
[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>[5,6,4,7,2,1,3]=>100011
[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[5,6,4,7,1,2,3]=>000011
[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[5,6,7,4,3,2,1]=>111001
[5,6,7,1,2,4,3]=>[4,1,7,2,5,6,3]=>[4,2,1,5,6,7,3]=>101001
[5,6,7,1,3,2,4]=>[3,7,1,2,5,6,4]=>[3,1,5,6,7,4,2]=>011001
[5,6,7,1,3,4,2]=>[4,7,1,3,5,6,2]=>[4,3,1,5,6,7,2]=>011001
[5,6,7,1,4,2,3]=>[4,7,1,2,5,6,3]=>[5,6,7,3,1,4,2]=>011001
[5,6,7,1,4,3,2]=>[3,4,7,1,5,6,2]=>[5,6,7,2,4,1,3]=>001001
[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[5,6,7,4,3,1,2]=>011001
[5,6,7,2,1,4,3]=>[2,4,7,1,5,6,3]=>[4,1,2,5,6,7,3]=>001001
[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[5,6,7,4,1,3,2]=>011001
[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>[5,6,7,1,4,3,2]=>011001
[5,6,7,2,4,1,3]=>[4,7,2,1,5,6,3]=>[4,1,5,6,7,3,2]=>011001
[5,6,7,2,4,3,1]=>[3,4,7,2,5,6,1]=>[4,2,5,6,7,1,3]=>001001
[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[5,6,7,4,2,1,3]=>101001
[5,6,7,3,1,4,2]=>[4,3,7,1,5,6,2]=>[4,1,5,6,7,2,3]=>001001
[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[5,6,7,4,1,2,3]=>001001
[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>[5,6,7,1,4,2,3]=>001001
[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>[5,6,7,2,1,4,3]=>101001
[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>[5,6,7,1,2,4,3]=>001001
[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>[5,6,7,3,2,1,4]=>110001
[5,6,7,4,1,3,2]=>[3,4,1,7,5,6,2]=>[3,1,5,6,7,2,4]=>010001
[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>[5,6,7,3,1,2,4]=>010001
[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>[5,6,7,1,3,2,4]=>010001
[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>[5,6,7,2,1,3,4]=>100001
[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[5,6,7,1,2,3,4]=>000001
[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[5,7,6,4,3,2,1]=>111011
[5,7,1,2,3,6,4]=>[6,1,2,7,5,3,4]=>[5,6,3,2,1,7,4]=>110011
[5,7,1,2,4,3,6]=>[4,1,7,2,5,3,6]=>[4,2,1,5,7,6,3]=>101011
[5,7,1,2,4,6,3]=>[6,1,7,2,5,4,3]=>[5,6,4,2,1,7,3]=>101011
[5,7,1,2,6,3,4]=>[6,1,7,2,5,3,4]=>[5,7,4,2,1,6,3]=>101011
[5,7,1,2,6,4,3]=>[4,1,6,7,5,2,3]=>[5,7,3,6,2,1,4]=>100011
[5,7,1,3,2,4,6]=>[3,7,1,2,5,4,6]=>[3,1,5,7,6,4,2]=>011011
[5,7,1,3,2,6,4]=>[3,6,1,7,5,2,4]=>[3,1,5,6,2,7,4]=>010011
[5,7,1,3,4,2,6]=>[4,7,1,3,5,2,6]=>[4,3,1,5,7,6,2]=>011011
[5,7,1,3,4,6,2]=>[6,7,1,3,5,4,2]=>[5,6,4,3,1,7,2]=>011011
[5,7,1,3,6,2,4]=>[6,7,1,3,5,2,4]=>[5,7,4,3,1,6,2]=>011011
[5,7,1,3,6,4,2]=>[4,6,1,7,5,3,2]=>[5,7,2,6,3,1,4]=>010011
[5,7,1,4,2,3,6]=>[4,7,1,2,5,3,6]=>[5,7,6,3,1,4,2]=>011011
[5,7,1,4,2,6,3]=>[6,4,7,1,5,2,3]=>[5,6,2,4,1,7,3]=>001011
[5,7,1,4,3,2,6]=>[3,4,7,1,5,2,6]=>[5,7,6,2,4,1,3]=>001011
[5,7,1,4,3,6,2]=>[6,4,7,1,5,3,2]=>[5,7,2,4,1,6,3]=>001011
[5,7,1,4,6,2,3]=>[6,7,1,2,5,4,3]=>[5,7,3,1,6,4,2]=>011011
[5,7,1,4,6,3,2]=>[3,6,7,1,5,4,2]=>[5,7,2,6,4,1,3]=>001011
[5,7,1,6,2,3,4]=>[6,7,1,2,5,3,4]=>[5,6,3,1,7,4,2]=>011011
[5,7,1,6,2,4,3]=>[4,6,7,1,5,2,3]=>[4,1,5,6,2,7,3]=>001011
[5,7,1,6,3,2,4]=>[3,6,7,1,5,2,4]=>[5,6,2,7,4,1,3]=>001011
[5,7,1,6,3,4,2]=>[4,6,7,1,5,3,2]=>[4,1,5,7,2,6,3]=>001011
[5,7,1,6,4,2,3]=>[4,6,1,7,5,2,3]=>[5,6,2,7,3,1,4]=>010011
[5,7,1,6,4,3,2]=>[3,4,6,7,5,1,2]=>[5,6,1,3,7,2,4]=>000011
[5,7,2,1,3,4,6]=>[2,7,1,3,5,4,6]=>[5,7,6,4,3,1,2]=>011011
[5,7,2,1,3,6,4]=>[2,6,1,7,5,3,4]=>[5,6,3,1,2,7,4]=>010011
[5,7,2,1,4,3,6]=>[2,4,7,1,5,3,6]=>[4,1,2,5,7,6,3]=>001011
[5,7,2,1,4,6,3]=>[2,6,7,1,5,4,3]=>[5,6,4,1,2,7,3]=>001011
[5,7,2,1,6,3,4]=>[2,6,7,1,5,3,4]=>[5,7,4,1,2,6,3]=>001011
[5,7,2,1,6,4,3]=>[2,4,6,7,5,1,3]=>[5,7,3,6,1,2,4]=>000011
[5,7,2,3,1,4,6]=>[3,7,2,1,5,4,6]=>[5,7,6,4,1,3,2]=>011011
[5,7,2,3,1,6,4]=>[3,6,2,7,5,1,4]=>[5,6,1,3,2,7,4]=>010011
[5,7,2,3,4,1,6]=>[4,7,2,3,5,1,6]=>[5,7,6,1,4,3,2]=>011011
[5,7,2,3,4,6,1]=>[6,7,2,3,5,4,1]=>[5,7,1,6,4,3,2]=>011011
[5,7,2,3,6,1,4]=>[6,7,2,3,5,1,4]=>[5,6,1,7,4,3,2]=>011011
[5,7,2,3,6,4,1]=>[4,6,2,7,5,3,1]=>[5,6,3,2,7,1,4]=>010011
[5,7,2,4,1,3,6]=>[4,7,2,1,5,3,6]=>[4,1,5,7,6,3,2]=>011011
[5,7,2,4,1,6,3]=>[6,4,7,2,5,1,3]=>[4,2,5,6,1,7,3]=>001011
[5,7,2,4,3,1,6]=>[3,4,7,2,5,1,6]=>[4,2,5,7,6,1,3]=>001011
[5,7,2,4,3,6,1]=>[6,4,7,2,5,3,1]=>[4,2,5,7,1,6,3]=>001011
[5,7,2,4,6,1,3]=>[6,7,2,1,5,4,3]=>[5,6,4,1,7,3,2]=>011011
[5,7,2,4,6,3,1]=>[3,6,7,2,5,4,1]=>[5,6,4,2,7,1,3]=>001011
[5,7,2,6,1,3,4]=>[6,7,2,1,5,3,4]=>[5,7,4,1,6,3,2]=>011011
[5,7,2,6,1,4,3]=>[4,6,7,2,5,1,3]=>[5,6,1,4,2,7,3]=>001011
[5,7,2,6,3,1,4]=>[3,6,7,2,5,1,4]=>[5,7,4,2,6,1,3]=>001011
[5,7,2,6,3,4,1]=>[4,6,7,2,5,3,1]=>[5,7,1,4,2,6,3]=>001011
[5,7,2,6,4,1,3]=>[4,6,2,7,5,1,3]=>[5,7,3,2,6,1,4]=>010011
[5,7,2,6,4,3,1]=>[3,4,6,7,5,2,1]=>[5,7,1,3,6,2,4]=>000011
[5,7,3,1,2,4,6]=>[3,1,7,2,5,4,6]=>[5,7,6,4,2,1,3]=>101011
[5,7,3,1,2,6,4]=>[3,1,6,7,5,2,4]=>[5,6,2,1,3,7,4]=>100011
[5,7,3,1,4,2,6]=>[4,3,7,1,5,2,6]=>[4,1,5,7,6,2,3]=>001011
[5,7,3,1,4,6,2]=>[6,3,7,1,5,4,2]=>[5,6,4,1,7,2,3]=>001011
[5,7,3,1,6,2,4]=>[6,3,7,1,5,2,4]=>[5,7,4,1,6,2,3]=>001011
[5,7,3,1,6,4,2]=>[4,3,6,7,5,1,2]=>[5,7,2,3,6,1,4]=>000011
[5,7,3,2,1,4,6]=>[2,3,7,1,5,4,6]=>[5,7,6,4,1,2,3]=>001011
[5,7,3,2,1,6,4]=>[2,3,6,7,5,1,4]=>[5,6,1,2,3,7,4]=>000011
[5,7,3,2,4,1,6]=>[4,3,7,2,5,1,6]=>[5,7,6,1,4,2,3]=>001011
[5,7,3,2,4,6,1]=>[6,3,7,2,5,4,1]=>[5,7,1,6,4,2,3]=>001011
[5,7,3,2,6,1,4]=>[6,3,7,2,5,1,4]=>[5,6,1,7,4,2,3]=>001011
[5,7,3,2,6,4,1]=>[4,3,6,7,5,2,1]=>[5,6,2,3,7,1,4]=>000011
[5,7,3,4,1,2,6]=>[4,1,7,3,5,2,6]=>[5,7,6,2,1,4,3]=>101011
[5,7,3,4,1,6,2]=>[6,4,7,3,5,1,2]=>[5,6,1,7,2,4,3]=>001011
[5,7,3,4,2,1,6]=>[2,4,7,3,5,1,6]=>[5,7,6,1,2,4,3]=>001011
[5,7,3,4,2,6,1]=>[6,4,7,3,5,2,1]=>[5,7,1,6,2,4,3]=>001011
[5,7,3,4,6,1,2]=>[6,1,7,3,5,4,2]=>[5,7,2,1,6,4,3]=>101011
[5,7,3,4,6,2,1]=>[2,6,7,3,5,4,1]=>[5,7,1,2,6,4,3]=>001011
[5,7,3,6,1,2,4]=>[6,1,7,3,5,2,4]=>[5,6,2,1,7,4,3]=>101011
[5,7,3,6,1,4,2]=>[4,6,7,3,5,1,2]=>[5,7,2,6,1,4,3]=>001011
[5,7,3,6,2,1,4]=>[2,6,7,3,5,1,4]=>[5,6,1,2,7,4,3]=>001011
[5,7,3,6,2,4,1]=>[4,6,7,3,5,2,1]=>[5,6,2,7,1,4,3]=>001011
[5,7,3,6,4,1,2]=>[4,1,6,7,5,3,2]=>[5,6,3,7,2,1,4]=>100011
[5,7,3,6,4,2,1]=>[2,4,6,7,5,3,1]=>[5,6,3,7,1,2,4]=>000011
[5,7,4,1,2,3,6]=>[4,1,2,7,5,3,6]=>[5,7,6,3,2,1,4]=>110011
[5,7,4,1,2,6,3]=>[6,1,4,7,5,2,3]=>[5,6,2,1,7,3,4]=>100011
[5,7,4,1,3,2,6]=>[3,4,1,7,5,2,6]=>[3,1,5,7,6,2,4]=>010011
[5,7,4,1,3,6,2]=>[6,4,1,7,5,3,2]=>[5,6,3,1,7,2,4]=>010011
[5,7,4,1,6,2,3]=>[6,4,1,7,5,2,3]=>[5,7,3,1,6,2,4]=>010011
[5,7,4,1,6,3,2]=>[3,6,4,7,5,1,2]=>[5,7,2,6,1,3,4]=>000011
[5,7,4,2,1,3,6]=>[2,4,1,7,5,3,6]=>[5,7,6,3,1,2,4]=>010011
[5,7,4,2,1,6,3]=>[2,6,4,7,5,1,3]=>[5,6,1,2,7,3,4]=>000011
[5,7,4,2,3,1,6]=>[3,4,2,7,5,1,6]=>[5,7,6,1,3,2,4]=>010011
[5,7,4,2,3,6,1]=>[6,4,2,7,5,3,1]=>[5,7,1,6,3,2,4]=>010011
[5,7,4,2,6,1,3]=>[6,4,2,7,5,1,3]=>[5,6,1,7,3,2,4]=>010011
[5,7,4,2,6,3,1]=>[3,6,4,7,5,2,1]=>[5,6,2,7,1,3,4]=>000011
[5,7,4,3,1,2,6]=>[3,1,4,7,5,2,6]=>[5,7,6,2,1,3,4]=>100011
[5,7,4,3,1,6,2]=>[6,3,4,7,5,1,2]=>[5,6,1,7,2,3,4]=>000011
[5,7,4,3,2,1,6]=>[2,3,4,7,5,1,6]=>[5,7,6,1,2,3,4]=>000011
[5,7,4,3,2,6,1]=>[6,3,4,7,5,2,1]=>[5,7,1,6,2,3,4]=>000011
[5,7,4,3,6,1,2]=>[6,1,4,7,5,3,2]=>[5,7,2,1,6,3,4]=>100011
[5,7,4,3,6,2,1]=>[2,6,4,7,5,3,1]=>[5,7,1,2,6,3,4]=>000011
[5,7,4,6,1,2,3]=>[6,1,2,7,5,4,3]=>[5,7,3,2,1,6,4]=>110011
[5,7,4,6,1,3,2]=>[3,6,1,7,5,4,2]=>[3,1,5,7,2,6,4]=>010011
[5,7,4,6,2,1,3]=>[2,6,1,7,5,4,3]=>[5,7,3,1,2,6,4]=>010011
[5,7,4,6,2,3,1]=>[3,6,2,7,5,4,1]=>[5,7,1,3,2,6,4]=>010011
[5,7,4,6,3,1,2]=>[3,1,6,7,5,4,2]=>[5,7,2,1,3,6,4]=>100011
[5,7,4,6,3,2,1]=>[2,3,6,7,5,4,1]=>[5,7,1,2,3,6,4]=>000011
[5,7,6,1,2,3,4]=>[6,1,2,3,5,7,4]=>[5,7,4,3,2,1,6]=>111001
[5,7,6,1,2,4,3]=>[4,1,6,2,5,7,3]=>[4,2,1,5,7,3,6]=>101001
[5,7,6,1,3,2,4]=>[3,6,1,2,5,7,4]=>[3,1,5,7,4,2,6]=>011001
[5,7,6,1,3,4,2]=>[4,6,1,3,5,7,2]=>[4,3,1,5,7,2,6]=>011001
[5,7,6,1,4,2,3]=>[4,6,1,2,5,7,3]=>[5,7,3,1,4,2,6]=>011001
[5,7,6,1,4,3,2]=>[3,4,6,1,5,7,2]=>[5,7,2,4,1,3,6]=>001001
[5,7,6,2,1,3,4]=>[2,6,1,3,5,7,4]=>[5,7,4,3,1,2,6]=>011001
[5,7,6,2,1,4,3]=>[2,4,6,1,5,7,3]=>[4,1,2,5,7,3,6]=>001001
[5,7,6,2,3,1,4]=>[3,6,2,1,5,7,4]=>[5,7,4,1,3,2,6]=>011001
[5,7,6,2,3,4,1]=>[4,6,2,3,5,7,1]=>[5,7,1,4,3,2,6]=>011001
[5,7,6,2,4,1,3]=>[4,6,2,1,5,7,3]=>[4,1,5,7,3,2,6]=>011001
[5,7,6,2,4,3,1]=>[3,4,6,2,5,7,1]=>[4,2,5,7,1,3,6]=>001001
[5,7,6,3,1,2,4]=>[3,1,6,2,5,7,4]=>[5,7,4,2,1,3,6]=>101001
[5,7,6,3,1,4,2]=>[4,3,6,1,5,7,2]=>[4,1,5,7,2,3,6]=>001001
[5,7,6,3,2,1,4]=>[2,3,6,1,5,7,4]=>[5,7,4,1,2,3,6]=>001001
[5,7,6,3,2,4,1]=>[4,3,6,2,5,7,1]=>[5,7,1,4,2,3,6]=>001001
[5,7,6,3,4,1,2]=>[4,1,6,3,5,7,2]=>[5,7,2,1,4,3,6]=>101001
[5,7,6,3,4,2,1]=>[2,4,6,3,5,7,1]=>[5,7,1,2,4,3,6]=>001001
[5,7,6,4,1,2,3]=>[4,1,2,6,5,7,3]=>[5,7,3,2,1,4,6]=>110001
[5,7,6,4,1,3,2]=>[3,4,1,6,5,7,2]=>[3,1,5,7,2,4,6]=>010001
[5,7,6,4,2,1,3]=>[2,4,1,6,5,7,3]=>[5,7,3,1,2,4,6]=>010001
[5,7,6,4,2,3,1]=>[3,4,2,6,5,7,1]=>[5,7,1,3,2,4,6]=>010001
[5,7,6,4,3,1,2]=>[3,1,4,6,5,7,2]=>[5,7,2,1,3,4,6]=>100001
[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]=>[5,7,1,2,3,4,6]=>000001
[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,5,4,3,2,1,7]=>111110
[6,1,2,3,4,7,5]=>[7,1,2,3,6,4,5]=>[7,5,6,4,3,2,1]=>111011
[6,1,2,3,5,4,7]=>[5,1,2,6,3,4,7]=>[5,3,2,1,6,4,7]=>110110
[6,1,2,3,5,7,4]=>[7,1,2,6,3,5,4]=>[7,4,6,5,3,2,1]=>110111
[6,1,2,3,7,4,5]=>[7,1,2,6,3,4,5]=>[6,4,7,5,3,2,1]=>110111
[6,1,2,3,7,5,4]=>[5,1,2,7,6,3,4]=>[6,3,2,1,5,7,4]=>110011
[6,1,2,4,3,5,7]=>[4,1,6,2,3,5,7]=>[4,2,1,6,5,3,7]=>101110
[6,1,2,4,3,7,5]=>[4,1,7,2,6,3,5]=>[4,2,1,7,5,6,3]=>101011
[6,1,2,4,5,3,7]=>[5,1,6,2,4,3,7]=>[5,4,2,1,6,3,7]=>101110
[6,1,2,4,5,7,3]=>[7,1,6,2,4,5,3]=>[7,3,6,5,4,2,1]=>101111
[6,1,2,4,7,3,5]=>[7,1,6,2,4,3,5]=>[6,3,7,5,4,2,1]=>101111
[6,1,2,4,7,5,3]=>[5,1,7,2,6,4,3]=>[6,4,2,1,5,7,3]=>101011
[6,1,2,5,3,4,7]=>[5,1,6,2,3,4,7]=>[6,4,2,1,5,3,7]=>101110
[6,1,2,5,3,7,4]=>[7,1,5,6,2,3,4]=>[7,4,6,3,5,2,1]=>100111
[6,1,2,5,4,3,7]=>[4,1,5,6,2,3,7]=>[6,3,5,2,1,4,7]=>100110
[6,1,2,5,4,7,3]=>[7,1,5,6,2,4,3]=>[6,4,7,3,5,2,1]=>100111
[6,1,2,5,7,3,4]=>[7,1,6,2,3,5,4]=>[6,5,3,7,4,2,1]=>101111
[6,1,2,5,7,4,3]=>[4,1,7,6,2,5,3]=>[6,5,2,1,4,7,3]=>100111
[6,1,2,7,3,4,5]=>[7,1,6,2,3,4,5]=>[7,5,3,6,4,2,1]=>101111
[6,1,2,7,3,5,4]=>[5,1,7,6,2,3,4]=>[5,2,1,7,4,6,3]=>100111
[6,1,2,7,4,3,5]=>[4,1,7,6,2,3,5]=>[7,5,2,1,4,6,3]=>100111
[6,1,2,7,4,5,3]=>[5,1,7,6,2,4,3]=>[5,2,1,6,4,7,3]=>100111
[6,1,2,7,5,3,4]=>[5,1,7,2,6,3,4]=>[7,4,2,1,5,6,3]=>101011
[6,1,2,7,5,4,3]=>[4,1,5,7,6,2,3]=>[7,3,5,6,2,1,4]=>100011
[6,1,3,2,4,5,7]=>[3,6,1,2,4,5,7]=>[3,1,6,5,4,2,7]=>011110
[6,1,3,2,4,7,5]=>[3,7,1,2,6,4,5]=>[3,1,7,5,6,4,2]=>011011
[6,1,3,2,5,4,7]=>[3,5,1,6,2,4,7]=>[3,1,5,2,6,4,7]=>010110
[6,1,3,2,5,7,4]=>[3,7,1,6,2,5,4]=>[3,1,7,4,6,5,2]=>010111
[6,1,3,2,7,4,5]=>[3,7,1,6,2,4,5]=>[3,1,6,4,7,5,2]=>010111
[6,1,3,2,7,5,4]=>[3,5,1,7,6,2,4]=>[3,1,6,2,5,7,4]=>010011
[6,1,3,4,2,5,7]=>[4,6,1,3,2,5,7]=>[4,3,1,6,5,2,7]=>011110
[6,1,3,4,2,7,5]=>[4,7,1,3,6,2,5]=>[4,3,1,7,5,6,2]=>011011
[6,1,3,4,5,2,7]=>[5,6,1,3,4,2,7]=>[5,4,3,1,6,2,7]=>011110
[6,1,3,4,5,7,2]=>[7,6,1,3,4,5,2]=>[7,2,6,5,4,3,1]=>011111
[6,1,3,4,7,2,5]=>[7,6,1,3,4,2,5]=>[6,2,7,5,4,3,1]=>011111
[6,1,3,4,7,5,2]=>[5,7,1,3,6,4,2]=>[6,4,3,1,5,7,2]=>011011
[6,1,3,5,2,4,7]=>[5,6,1,3,2,4,7]=>[6,4,3,1,5,2,7]=>011110
[6,1,3,5,2,7,4]=>[7,5,1,6,3,2,4]=>[7,4,6,2,5,3,1]=>010111
[6,1,3,5,4,2,7]=>[4,5,1,6,3,2,7]=>[6,2,5,3,1,4,7]=>010110
[6,1,3,5,4,7,2]=>[7,5,1,6,3,4,2]=>[6,4,7,2,5,3,1]=>010111
[6,1,3,5,7,2,4]=>[7,6,1,3,2,5,4]=>[6,5,2,7,4,3,1]=>011111
[6,1,3,5,7,4,2]=>[4,7,1,6,3,5,2]=>[6,5,3,1,4,7,2]=>010111
[6,1,3,7,2,4,5]=>[7,6,1,3,2,4,5]=>[7,5,2,6,4,3,1]=>011111
[6,1,3,7,2,5,4]=>[5,7,1,6,3,2,4]=>[5,3,1,7,4,6,2]=>010111
[6,1,3,7,4,2,5]=>[4,7,1,6,3,2,5]=>[7,5,3,1,4,6,2]=>010111
[6,1,3,7,4,5,2]=>[5,7,1,6,3,4,2]=>[5,3,1,6,4,7,2]=>010111
[6,1,3,7,5,2,4]=>[5,7,1,3,6,2,4]=>[7,4,3,1,5,6,2]=>011011
[6,1,3,7,5,4,2]=>[4,5,1,7,6,3,2]=>[7,2,5,6,3,1,4]=>010011
[6,1,4,2,3,5,7]=>[4,6,1,2,3,5,7]=>[6,5,3,1,4,2,7]=>011110
[6,1,4,2,3,7,5]=>[4,7,1,2,6,3,5]=>[7,5,6,3,1,4,2]=>011011
[6,1,4,2,5,3,7]=>[5,4,6,1,2,3,7]=>[5,2,4,1,6,3,7]=>001110
[6,1,4,2,5,7,3]=>[7,4,6,1,2,5,3]=>[7,3,6,5,2,4,1]=>001111
[6,1,4,2,7,3,5]=>[7,4,6,1,2,3,5]=>[6,3,7,5,2,4,1]=>001111
[6,1,4,2,7,5,3]=>[5,4,7,1,6,2,3]=>[6,2,4,1,5,7,3]=>001011
[6,1,4,3,2,5,7]=>[3,4,6,1,2,5,7]=>[6,5,2,4,1,3,7]=>001110
[6,1,4,3,2,7,5]=>[3,4,7,1,6,2,5]=>[7,5,6,2,4,1,3]=>001011
[6,1,4,3,5,2,7]=>[5,4,6,1,3,2,7]=>[6,2,4,1,5,3,7]=>001110
[6,1,4,3,5,7,2]=>[7,4,6,1,3,5,2]=>[6,5,3,7,2,4,1]=>001111
[6,1,4,3,7,2,5]=>[7,4,6,1,3,2,5]=>[7,5,3,6,2,4,1]=>001111
[6,1,4,3,7,5,2]=>[5,4,7,1,6,3,2]=>[7,2,4,1,5,6,3]=>001011
[6,1,4,5,2,3,7]=>[5,6,1,2,4,3,7]=>[6,3,1,5,4,2,7]=>011110
[6,1,4,5,2,7,3]=>[7,5,6,1,4,2,3]=>[7,3,6,2,5,4,1]=>001111
[6,1,4,5,3,2,7]=>[3,5,6,1,4,2,7]=>[6,2,5,4,1,3,7]=>001110
[6,1,4,5,3,7,2]=>[7,5,6,1,4,3,2]=>[6,3,7,2,5,4,1]=>001111
[6,1,4,5,7,2,3]=>[7,6,1,2,4,5,3]=>[6,5,4,2,7,3,1]=>011111
[6,1,4,5,7,3,2]=>[3,7,6,1,4,5,2]=>[6,5,4,1,3,7,2]=>001111
[6,1,4,7,2,3,5]=>[7,6,1,2,4,3,5]=>[7,5,4,2,6,3,1]=>011111
[6,1,4,7,2,5,3]=>[5,7,6,1,4,2,3]=>[5,4,1,7,3,6,2]=>001111
[6,1,4,7,3,2,5]=>[3,7,6,1,4,2,5]=>[7,5,4,1,3,6,2]=>001111
[6,1,4,7,3,5,2]=>[5,7,6,1,4,3,2]=>[5,4,1,6,3,7,2]=>001111
[6,1,4,7,5,2,3]=>[5,7,1,2,6,4,3]=>[7,3,1,5,6,4,2]=>011011
[6,1,4,7,5,3,2]=>[3,5,7,1,6,4,2]=>[7,2,5,6,4,1,3]=>001011
[6,1,5,2,3,4,7]=>[5,6,1,2,3,4,7]=>[5,3,1,6,4,2,7]=>011110
[6,1,5,2,3,7,4]=>[7,5,1,6,2,3,4]=>[5,2,7,4,6,3,1]=>010111
[6,1,5,2,4,3,7]=>[4,5,6,1,2,3,7]=>[4,1,5,2,6,3,7]=>001110
[6,1,5,2,4,7,3]=>[7,5,6,1,2,4,3]=>[5,2,7,3,6,4,1]=>001111
[6,1,5,2,7,3,4]=>[7,5,6,1,2,3,4]=>[5,2,6,3,7,4,1]=>001111
[6,1,5,2,7,4,3]=>[4,7,5,6,1,2,3]=>[7,3,5,1,4,6,2]=>000111
[6,1,5,3,2,4,7]=>[3,5,6,1,2,4,7]=>[5,2,6,4,1,3,7]=>001110
[6,1,5,3,2,7,4]=>[3,7,5,6,1,2,4]=>[5,1,3,7,4,6,2]=>000111
[6,1,5,3,4,2,7]=>[4,5,6,1,3,2,7]=>[4,1,6,2,5,3,7]=>001110
[6,1,5,3,4,7,2]=>[7,5,6,1,3,4,2]=>[7,2,5,3,6,4,1]=>001111
[6,1,5,3,7,2,4]=>[7,5,6,1,3,2,4]=>[6,2,5,3,7,4,1]=>001111
[6,1,5,3,7,4,2]=>[4,7,5,6,1,3,2]=>[6,3,5,1,4,7,2]=>000111
[6,1,5,4,2,3,7]=>[4,5,1,6,2,3,7]=>[5,2,6,3,1,4,7]=>010110
[6,1,5,4,2,7,3]=>[7,4,5,6,1,2,3]=>[6,2,4,7,3,5,1]=>000111
[6,1,5,4,3,2,7]=>[3,4,5,6,1,2,7]=>[5,1,3,6,2,4,7]=>000110
[6,1,5,4,3,7,2]=>[7,4,5,6,1,3,2]=>[7,2,4,6,3,5,1]=>000111
[6,1,5,4,7,2,3]=>[7,5,1,6,2,4,3]=>[5,2,6,4,7,3,1]=>010111
[6,1,5,4,7,3,2]=>[3,7,5,6,1,4,2]=>[5,1,3,6,4,7,2]=>000111
[6,1,5,7,2,3,4]=>[7,6,1,2,3,5,4]=>[7,4,2,6,5,3,1]=>011111
[6,1,5,7,2,4,3]=>[4,7,6,1,2,5,3]=>[4,1,7,3,6,5,2]=>001111
[6,1,5,7,3,2,4]=>[3,7,6,1,2,5,4]=>[7,4,1,3,6,5,2]=>001111
[6,1,5,7,3,4,2]=>[4,7,6,1,3,5,2]=>[4,1,6,5,3,7,2]=>001111
[6,1,5,7,4,2,3]=>[4,7,1,6,2,5,3]=>[7,3,1,4,6,5,2]=>010111
[6,1,5,7,4,3,2]=>[3,4,7,6,1,5,2]=>[7,2,4,6,5,1,3]=>000111
[6,1,7,2,3,4,5]=>[7,6,1,2,3,4,5]=>[6,4,2,7,5,3,1]=>011111
[6,1,7,2,3,5,4]=>[5,7,1,6,2,3,4]=>[7,4,6,3,1,5,2]=>010111
[6,1,7,2,4,3,5]=>[4,7,6,1,2,3,5]=>[4,1,6,3,7,5,2]=>001111
[6,1,7,2,4,5,3]=>[5,7,6,1,2,4,3]=>[7,3,6,4,1,5,2]=>001111
[6,1,7,2,5,3,4]=>[5,7,6,1,2,3,4]=>[6,3,7,4,1,5,2]=>001111
[6,1,7,2,5,4,3]=>[4,5,7,6,1,2,3]=>[6,2,5,1,4,7,3]=>000111
[6,1,7,3,2,4,5]=>[3,7,6,1,2,4,5]=>[6,4,1,3,7,5,2]=>001111
[6,1,7,3,2,5,4]=>[3,5,7,6,1,2,4]=>[7,4,6,2,5,1,3]=>000111
[6,1,7,3,4,2,5]=>[4,7,6,1,3,2,5]=>[4,1,7,5,3,6,2]=>001111
[6,1,7,3,4,5,2]=>[5,7,6,1,3,4,2]=>[6,4,1,5,3,7,2]=>001111
[6,1,7,3,5,2,4]=>[5,7,6,1,3,2,4]=>[7,4,1,5,3,6,2]=>001111
[6,1,7,3,5,4,2]=>[4,5,7,6,1,3,2]=>[7,2,5,1,4,6,3]=>000111
[6,1,7,4,2,3,5]=>[4,7,1,6,2,3,5]=>[6,3,1,4,7,5,2]=>010111
[6,1,7,4,2,5,3]=>[5,4,7,6,1,2,3]=>[5,1,6,2,4,7,3]=>000111
[6,1,7,4,3,2,5]=>[3,4,7,6,1,2,5]=>[6,2,4,7,5,1,3]=>000111
[6,1,7,4,3,5,2]=>[5,4,7,6,1,3,2]=>[5,1,7,2,4,6,3]=>000111
[6,1,7,4,5,2,3]=>[5,7,1,6,2,4,3]=>[6,4,7,3,1,5,2]=>010111
[6,1,7,4,5,3,2]=>[3,5,7,6,1,4,2]=>[6,4,7,2,5,1,3]=>000111
[6,1,7,5,2,3,4]=>[5,7,1,2,6,3,4]=>[6,3,1,5,7,4,2]=>011011
[6,1,7,5,2,4,3]=>[4,5,7,1,6,2,3]=>[4,1,6,2,5,7,3]=>001011
[6,1,7,5,3,2,4]=>[3,5,7,1,6,2,4]=>[6,2,5,7,4,1,3]=>001011
[6,1,7,5,3,4,2]=>[4,5,7,1,6,3,2]=>[4,1,7,2,5,6,3]=>001011
[6,1,7,5,4,2,3]=>[4,5,1,7,6,2,3]=>[6,2,5,7,3,1,4]=>010011
[6,1,7,5,4,3,2]=>[3,4,5,7,6,1,2]=>[6,1,3,5,7,2,4]=>000011
[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[6,5,4,3,1,2,7]=>011110
[6,2,1,3,4,7,5]=>[2,7,1,3,6,4,5]=>[7,5,6,4,3,1,2]=>011011
[6,2,1,3,5,4,7]=>[2,5,1,6,3,4,7]=>[5,3,1,2,6,4,7]=>010110
[6,2,1,3,5,7,4]=>[2,7,1,6,3,5,4]=>[7,4,6,5,3,1,2]=>010111
[6,2,1,3,7,4,5]=>[2,7,1,6,3,4,5]=>[6,4,7,5,3,1,2]=>010111
[6,2,1,3,7,5,4]=>[2,5,1,7,6,3,4]=>[6,3,1,2,5,7,4]=>010011
[6,2,1,4,3,5,7]=>[2,4,6,1,3,5,7]=>[4,1,2,6,5,3,7]=>001110
[6,2,1,4,3,7,5]=>[2,4,7,1,6,3,5]=>[4,1,2,7,5,6,3]=>001011
[6,2,1,4,5,3,7]=>[2,5,6,1,4,3,7]=>[5,4,1,2,6,3,7]=>001110
[6,2,1,4,5,7,3]=>[2,7,6,1,4,5,3]=>[7,3,6,5,4,1,2]=>001111
[6,2,1,4,7,3,5]=>[2,7,6,1,4,3,5]=>[6,3,7,5,4,1,2]=>001111
[6,2,1,4,7,5,3]=>[2,5,7,1,6,4,3]=>[6,4,1,2,5,7,3]=>001011
[6,2,1,5,3,4,7]=>[2,5,6,1,3,4,7]=>[6,4,1,2,5,3,7]=>001110
[6,2,1,5,3,7,4]=>[2,7,5,6,1,3,4]=>[7,4,6,3,5,1,2]=>000111
[6,2,1,5,4,3,7]=>[2,4,5,6,1,3,7]=>[6,3,5,1,2,4,7]=>000110
[6,2,1,5,4,7,3]=>[2,7,5,6,1,4,3]=>[6,4,7,3,5,1,2]=>000111
[6,2,1,5,7,3,4]=>[2,7,6,1,3,5,4]=>[6,5,3,7,4,1,2]=>001111
[6,2,1,5,7,4,3]=>[2,4,7,6,1,5,3]=>[6,5,1,2,4,7,3]=>000111
[6,2,1,7,3,4,5]=>[2,7,6,1,3,4,5]=>[7,5,3,6,4,1,2]=>001111
[6,2,1,7,3,5,4]=>[2,5,7,6,1,3,4]=>[5,1,2,7,4,6,3]=>000111
[6,2,1,7,4,3,5]=>[2,4,7,6,1,3,5]=>[7,5,1,2,4,6,3]=>000111
[6,2,1,7,4,5,3]=>[2,5,7,6,1,4,3]=>[5,1,2,6,4,7,3]=>000111
[6,2,1,7,5,3,4]=>[2,5,7,1,6,3,4]=>[7,4,1,2,5,6,3]=>001011
[6,2,1,7,5,4,3]=>[2,4,5,7,6,1,3]=>[7,3,5,6,1,2,4]=>000011
[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[6,5,4,1,3,2,7]=>011110
[6,2,3,1,4,7,5]=>[3,7,2,1,6,4,5]=>[7,5,6,4,1,3,2]=>011011
[6,2,3,1,5,4,7]=>[3,5,2,6,1,4,7]=>[5,1,3,2,6,4,7]=>010110
[6,2,3,1,5,7,4]=>[3,7,2,6,1,5,4]=>[7,4,6,5,1,3,2]=>010111
[6,2,3,1,7,4,5]=>[3,7,2,6,1,4,5]=>[6,4,7,5,1,3,2]=>010111
[6,2,3,1,7,5,4]=>[3,5,2,7,6,1,4]=>[6,1,3,2,5,7,4]=>010011
[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[6,5,1,4,3,2,7]=>011110
[6,2,3,4,1,7,5]=>[4,7,2,3,6,1,5]=>[7,5,6,1,4,3,2]=>011011
[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,1,5,4,3,2,7]=>011110
[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[6,5,4,3,2,7,1]=>011111
[6,2,3,4,7,1,5]=>[7,6,2,3,4,1,5]=>[7,5,4,3,2,6,1]=>011111
[6,2,3,4,7,5,1]=>[5,7,2,3,6,4,1]=>[7,1,5,6,4,3,2]=>011011
[6,2,3,5,1,4,7]=>[5,6,2,3,1,4,7]=>[5,1,6,4,3,2,7]=>011110
[6,2,3,5,1,7,4]=>[7,5,2,6,3,1,4]=>[5,3,2,7,4,6,1]=>010111
[6,2,3,5,4,1,7]=>[4,5,2,6,3,1,7]=>[5,3,2,6,1,4,7]=>010110
[6,2,3,5,4,7,1]=>[7,5,2,6,3,4,1]=>[5,3,2,6,4,7,1]=>010111
[6,2,3,5,7,1,4]=>[7,6,2,3,1,5,4]=>[7,4,3,2,6,5,1]=>011111
[6,2,3,5,7,4,1]=>[4,7,2,6,3,5,1]=>[7,1,4,6,5,3,2]=>010111
[6,2,3,7,1,4,5]=>[7,6,2,3,1,4,5]=>[6,4,3,2,7,5,1]=>011111
[6,2,3,7,1,5,4]=>[5,7,2,6,3,1,4]=>[7,4,6,1,5,3,2]=>010111
[6,2,3,7,4,1,5]=>[4,7,2,6,3,1,5]=>[6,1,4,7,5,3,2]=>010111
[6,2,3,7,4,5,1]=>[5,7,2,6,3,4,1]=>[6,4,7,1,5,3,2]=>010111
[6,2,3,7,5,1,4]=>[5,7,2,3,6,1,4]=>[6,1,5,7,4,3,2]=>011011
[6,2,3,7,5,4,1]=>[4,5,2,7,6,3,1]=>[6,3,2,5,7,1,4]=>010011
[6,2,4,1,3,5,7]=>[4,6,2,1,3,5,7]=>[4,1,6,5,3,2,7]=>011110
[6,2,4,1,3,7,5]=>[4,7,2,1,6,3,5]=>[4,1,7,5,6,3,2]=>011011
[6,2,4,1,5,3,7]=>[5,4,6,2,1,3,7]=>[4,2,5,1,6,3,7]=>001110
[6,2,4,1,5,7,3]=>[7,4,6,2,1,5,3]=>[4,2,7,3,6,5,1]=>001111
[6,2,4,1,7,3,5]=>[7,4,6,2,1,3,5]=>[4,2,6,3,7,5,1]=>001111
[6,2,4,1,7,5,3]=>[5,4,7,2,6,1,3]=>[4,2,6,1,5,7,3]=>001011
[6,2,4,3,1,5,7]=>[3,4,6,2,1,5,7]=>[4,2,6,5,1,3,7]=>001110
[6,2,4,3,1,7,5]=>[3,4,7,2,6,1,5]=>[4,2,7,5,6,1,3]=>001011
[6,2,4,3,5,1,7]=>[5,4,6,2,3,1,7]=>[4,2,6,1,5,3,7]=>001110
[6,2,4,3,5,7,1]=>[7,4,6,2,3,5,1]=>[4,2,6,5,3,7,1]=>001111
[6,2,4,3,7,1,5]=>[7,4,6,2,3,1,5]=>[4,2,7,5,3,6,1]=>001111
[6,2,4,3,7,5,1]=>[5,4,7,2,6,3,1]=>[4,2,7,1,5,6,3]=>001011
[6,2,4,5,1,3,7]=>[5,6,2,1,4,3,7]=>[5,4,1,6,3,2,7]=>011110
[6,2,4,5,1,7,3]=>[7,5,6,2,4,1,3]=>[5,4,2,7,3,6,1]=>001111
[6,2,4,5,3,1,7]=>[3,5,6,2,4,1,7]=>[5,4,2,6,1,3,7]=>001110
[6,2,4,5,3,7,1]=>[7,5,6,2,4,3,1]=>[5,4,2,6,3,7,1]=>001111
[6,2,4,5,7,1,3]=>[7,6,2,1,4,5,3]=>[7,3,2,6,5,4,1]=>011111
[6,2,4,5,7,3,1]=>[3,7,6,2,4,5,1]=>[7,1,3,6,5,4,2]=>001111
[6,2,4,7,1,3,5]=>[7,6,2,1,4,3,5]=>[6,3,2,7,5,4,1]=>011111
[6,2,4,7,1,5,3]=>[5,7,6,2,4,1,3]=>[7,3,6,1,5,4,2]=>001111
[6,2,4,7,3,1,5]=>[3,7,6,2,4,1,5]=>[6,1,3,7,5,4,2]=>001111
[6,2,4,7,3,5,1]=>[5,7,6,2,4,3,1]=>[6,3,7,1,5,4,2]=>001111
[6,2,4,7,5,1,3]=>[5,7,2,1,6,4,3]=>[6,4,1,5,7,3,2]=>011011
[6,2,4,7,5,3,1]=>[3,5,7,2,6,4,1]=>[6,4,2,5,7,1,3]=>001011
[6,2,5,1,3,4,7]=>[5,6,2,1,3,4,7]=>[6,4,1,5,3,2,7]=>011110
[6,2,5,1,3,7,4]=>[7,5,2,6,1,3,4]=>[7,4,6,3,2,5,1]=>010111
[6,2,5,1,4,3,7]=>[4,5,6,2,1,3,7]=>[5,1,4,2,6,3,7]=>001110
[6,2,5,1,4,7,3]=>[7,5,6,2,1,4,3]=>[7,3,6,4,2,5,1]=>001111
[6,2,5,1,7,3,4]=>[7,5,6,2,1,3,4]=>[6,3,7,4,2,5,1]=>001111
[6,2,5,1,7,4,3]=>[4,7,5,6,2,1,3]=>[6,1,4,7,3,5,2]=>000111
[6,2,5,3,1,4,7]=>[3,5,6,2,1,4,7]=>[6,4,2,5,1,3,7]=>001110
[6,2,5,3,1,7,4]=>[3,7,5,6,2,1,4]=>[7,4,6,1,3,5,2]=>000111
[6,2,5,3,4,1,7]=>[4,5,6,2,3,1,7]=>[6,1,4,2,5,3,7]=>001110
[6,2,5,3,4,7,1]=>[7,5,6,2,3,4,1]=>[6,4,2,5,3,7,1]=>001111
[6,2,5,3,7,1,4]=>[7,5,6,2,3,1,4]=>[7,4,2,5,3,6,1]=>001111
[6,2,5,3,7,4,1]=>[4,7,5,6,2,3,1]=>[7,1,4,6,3,5,2]=>000111
[6,2,5,4,1,3,7]=>[4,5,2,6,1,3,7]=>[6,3,2,5,1,4,7]=>010110
[6,2,5,4,1,7,3]=>[7,4,5,6,2,1,3]=>[7,3,5,2,4,6,1]=>000111
[6,2,5,4,3,1,7]=>[3,4,5,6,2,1,7]=>[6,1,3,5,2,4,7]=>000110
[6,2,5,4,3,7,1]=>[7,4,5,6,2,3,1]=>[6,3,5,2,4,7,1]=>000111
[6,2,5,4,7,1,3]=>[7,5,2,6,1,4,3]=>[6,4,7,3,2,5,1]=>010111
[6,2,5,4,7,3,1]=>[3,7,5,6,2,4,1]=>[6,4,7,1,3,5,2]=>000111
[6,2,5,7,1,3,4]=>[7,6,2,1,3,5,4]=>[6,5,3,2,7,4,1]=>011111
[6,2,5,7,1,4,3]=>[4,7,6,2,1,5,3]=>[7,3,6,5,1,4,2]=>001111
[6,2,5,7,3,1,4]=>[3,7,6,2,1,5,4]=>[6,5,1,3,7,4,2]=>001111
[6,2,5,7,3,4,1]=>[4,7,6,2,3,5,1]=>[6,5,3,7,1,4,2]=>001111
[6,2,5,7,4,1,3]=>[4,7,2,6,1,5,3]=>[6,5,1,4,7,3,2]=>010111
[6,2,5,7,4,3,1]=>[3,4,7,6,2,5,1]=>[6,5,2,4,7,1,3]=>000111
[6,2,7,1,3,4,5]=>[7,6,2,1,3,4,5]=>[7,5,3,2,6,4,1]=>011111
[6,2,7,1,3,5,4]=>[5,7,2,6,1,3,4]=>[5,1,7,4,6,3,2]=>010111
[6,2,7,1,4,3,5]=>[4,7,6,2,1,3,5]=>[6,3,7,5,1,4,2]=>001111
[6,2,7,1,4,5,3]=>[5,7,6,2,1,4,3]=>[5,1,7,3,6,4,2]=>001111
[6,2,7,1,5,3,4]=>[5,7,6,2,1,3,4]=>[5,1,6,3,7,4,2]=>001111
[6,2,7,1,5,4,3]=>[4,5,7,6,2,1,3]=>[5,2,6,1,4,7,3]=>000111
[6,2,7,3,1,4,5]=>[3,7,6,2,1,4,5]=>[7,5,1,3,6,4,2]=>001111
[6,2,7,3,1,5,4]=>[3,5,7,6,2,1,4]=>[5,2,7,4,6,1,3]=>000111
[6,2,7,3,4,1,5]=>[4,7,6,2,3,1,5]=>[7,5,3,6,1,4,2]=>001111
[6,2,7,3,4,5,1]=>[5,7,6,2,3,4,1]=>[7,1,5,3,6,4,2]=>001111
[6,2,7,3,5,1,4]=>[5,7,6,2,3,1,4]=>[6,1,5,3,7,4,2]=>001111
[6,2,7,3,5,4,1]=>[4,5,7,6,2,3,1]=>[5,2,7,1,4,6,3]=>000111
[6,2,7,4,1,3,5]=>[4,7,2,6,1,3,5]=>[7,5,1,4,6,3,2]=>010111
[6,2,7,4,1,5,3]=>[5,4,7,6,2,1,3]=>[6,1,5,2,4,7,3]=>000111
[6,2,7,4,3,1,5]=>[3,4,7,6,2,1,5]=>[7,5,2,4,6,1,3]=>000111
[6,2,7,4,3,5,1]=>[5,4,7,6,2,3,1]=>[7,1,5,2,4,6,3]=>000111
[6,2,7,4,5,1,3]=>[5,7,2,6,1,4,3]=>[5,1,6,4,7,3,2]=>010111
[6,2,7,4,5,3,1]=>[3,5,7,6,2,4,1]=>[5,2,6,4,7,1,3]=>000111
[6,2,7,5,1,3,4]=>[5,7,2,1,6,3,4]=>[7,4,1,5,6,3,2]=>011011
[6,2,7,5,1,4,3]=>[4,5,7,2,6,1,3]=>[6,1,4,2,5,7,3]=>001011
[6,2,7,5,3,1,4]=>[3,5,7,2,6,1,4]=>[7,4,2,5,6,1,3]=>001011
[6,2,7,5,3,4,1]=>[4,5,7,2,6,3,1]=>[7,1,4,2,5,6,3]=>001011
[6,2,7,5,4,1,3]=>[4,5,2,7,6,1,3]=>[7,3,2,5,6,1,4]=>010011
[6,2,7,5,4,3,1]=>[3,4,5,7,6,2,1]=>[7,1,3,5,6,2,4]=>000011
[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[6,5,4,2,1,3,7]=>101110
[6,3,1,2,4,7,5]=>[3,1,7,2,6,4,5]=>[7,5,6,4,2,1,3]=>101011
[6,3,1,2,5,4,7]=>[3,1,5,6,2,4,7]=>[5,2,1,3,6,4,7]=>100110
[6,3,1,2,5,7,4]=>[3,1,7,6,2,5,4]=>[7,4,6,5,2,1,3]=>100111
[6,3,1,2,7,4,5]=>[3,1,7,6,2,4,5]=>[6,4,7,5,2,1,3]=>100111
[6,3,1,2,7,5,4]=>[3,1,5,7,6,2,4]=>[6,2,1,3,5,7,4]=>100011
[6,3,1,4,2,5,7]=>[4,3,6,1,2,5,7]=>[4,1,6,5,2,3,7]=>001110
[6,3,1,4,2,7,5]=>[4,3,7,1,6,2,5]=>[4,1,7,5,6,2,3]=>001011
[6,3,1,4,5,2,7]=>[5,3,6,1,4,2,7]=>[5,4,1,6,2,3,7]=>001110
[6,3,1,4,5,7,2]=>[7,3,6,1,4,5,2]=>[7,2,3,6,5,4,1]=>001111
[6,3,1,4,7,2,5]=>[7,3,6,1,4,2,5]=>[6,2,3,7,5,4,1]=>001111
[6,3,1,4,7,5,2]=>[5,3,7,1,6,4,2]=>[6,4,1,5,7,2,3]=>001011
[6,3,1,5,2,4,7]=>[5,3,6,1,2,4,7]=>[6,4,1,5,2,3,7]=>001110
[6,3,1,5,2,7,4]=>[7,3,5,6,1,2,4]=>[7,4,6,2,3,5,1]=>000111
[6,3,1,5,4,2,7]=>[4,3,5,6,1,2,7]=>[6,2,3,5,1,4,7]=>000110
[6,3,1,5,4,7,2]=>[7,3,5,6,1,4,2]=>[6,4,7,2,3,5,1]=>000111
[6,3,1,5,7,2,4]=>[7,3,6,1,2,5,4]=>[6,5,2,3,7,4,1]=>001111
[6,3,1,5,7,4,2]=>[4,3,7,6,1,5,2]=>[6,5,1,4,7,2,3]=>000111
[6,3,1,7,2,4,5]=>[7,3,6,1,2,4,5]=>[7,5,2,3,6,4,1]=>001111
[6,3,1,7,2,5,4]=>[5,3,7,6,1,2,4]=>[5,1,7,4,6,2,3]=>000111
[6,3,1,7,4,2,5]=>[4,3,7,6,1,2,5]=>[7,5,1,4,6,2,3]=>000111
[6,3,1,7,4,5,2]=>[5,3,7,6,1,4,2]=>[5,1,6,4,7,2,3]=>000111
[6,3,1,7,5,2,4]=>[5,3,7,1,6,2,4]=>[7,4,1,5,6,2,3]=>001011
[6,3,1,7,5,4,2]=>[4,3,5,7,6,1,2]=>[7,2,3,5,6,1,4]=>000011
[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[6,5,4,1,2,3,7]=>001110
[6,3,2,1,4,7,5]=>[2,3,7,1,6,4,5]=>[7,5,6,4,1,2,3]=>001011
[6,3,2,1,5,4,7]=>[2,3,5,6,1,4,7]=>[5,1,2,3,6,4,7]=>000110
[6,3,2,1,5,7,4]=>[2,3,7,6,1,5,4]=>[7,4,6,5,1,2,3]=>000111
[6,3,2,1,7,4,5]=>[2,3,7,6,1,4,5]=>[6,4,7,5,1,2,3]=>000111
[6,3,2,1,7,5,4]=>[2,3,5,7,6,1,4]=>[6,1,2,3,5,7,4]=>000011
[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[6,5,1,4,2,3,7]=>001110
[6,3,2,4,1,7,5]=>[4,3,7,2,6,1,5]=>[7,5,6,1,4,2,3]=>001011
[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[6,1,5,4,2,3,7]=>001110
[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[6,5,4,2,3,7,1]=>001111
[6,3,2,4,7,1,5]=>[7,3,6,2,4,1,5]=>[7,5,4,2,3,6,1]=>001111
[6,3,2,4,7,5,1]=>[5,3,7,2,6,4,1]=>[7,1,5,6,4,2,3]=>001011
[6,3,2,5,1,4,7]=>[5,3,6,2,1,4,7]=>[5,1,6,4,2,3,7]=>001110
[6,3,2,5,1,7,4]=>[7,3,5,6,2,1,4]=>[5,2,3,7,4,6,1]=>000111
[6,3,2,5,4,1,7]=>[4,3,5,6,2,1,7]=>[5,2,3,6,1,4,7]=>000110
[6,3,2,5,4,7,1]=>[7,3,5,6,2,4,1]=>[5,2,3,6,4,7,1]=>000111
[6,3,2,5,7,1,4]=>[7,3,6,2,1,5,4]=>[7,4,2,3,6,5,1]=>001111
[6,3,2,5,7,4,1]=>[4,3,7,6,2,5,1]=>[7,1,4,6,5,2,3]=>000111
[6,3,2,7,1,4,5]=>[7,3,6,2,1,4,5]=>[6,4,2,3,7,5,1]=>001111
[6,3,2,7,1,5,4]=>[5,3,7,6,2,1,4]=>[7,4,6,1,5,2,3]=>000111
[6,3,2,7,4,1,5]=>[4,3,7,6,2,1,5]=>[6,1,4,7,5,2,3]=>000111
[6,3,2,7,4,5,1]=>[5,3,7,6,2,4,1]=>[6,4,7,1,5,2,3]=>000111
[6,3,2,7,5,1,4]=>[5,3,7,2,6,1,4]=>[6,1,5,7,4,2,3]=>001011
[6,3,2,7,5,4,1]=>[4,3,5,7,6,2,1]=>[6,2,3,5,7,1,4]=>000011
[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[6,5,2,1,4,3,7]=>101110
[6,3,4,1,2,7,5]=>[4,1,7,3,6,2,5]=>[7,5,6,2,1,4,3]=>101011
[6,3,4,1,5,2,7]=>[5,4,6,3,1,2,7]=>[5,1,6,2,4,3,7]=>001110
[6,3,4,1,5,7,2]=>[7,4,6,3,1,5,2]=>[7,2,4,3,6,5,1]=>001111
[6,3,4,1,7,2,5]=>[7,4,6,3,1,2,5]=>[6,2,4,3,7,5,1]=>001111
[6,3,4,1,7,5,2]=>[5,4,7,3,6,1,2]=>[6,1,5,7,2,4,3]=>001011
[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[6,5,1,2,4,3,7]=>001110
[6,3,4,2,1,7,5]=>[2,4,7,3,6,1,5]=>[7,5,6,1,2,4,3]=>001011
[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[6,1,5,2,4,3,7]=>001110
[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[6,5,2,4,3,7,1]=>001111
[6,3,4,2,7,1,5]=>[7,4,6,3,2,1,5]=>[7,5,2,4,3,6,1]=>001111
[6,3,4,2,7,5,1]=>[5,4,7,3,6,2,1]=>[7,1,5,6,2,4,3]=>001011
[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>[6,2,1,5,4,3,7]=>101110
[6,3,4,5,1,7,2]=>[7,5,6,3,4,1,2]=>[7,2,5,4,3,6,1]=>001111
[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[6,1,2,5,4,3,7]=>001110
[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[6,2,5,4,3,7,1]=>001111
[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>[6,5,4,3,7,2,1]=>101111
[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[6,5,4,3,7,1,2]=>001111
[6,3,4,7,1,2,5]=>[7,1,6,3,4,2,5]=>[7,5,4,3,6,2,1]=>101111
[6,3,4,7,1,5,2]=>[5,7,6,3,4,1,2]=>[6,1,5,4,3,7,2]=>001111
[6,3,4,7,2,1,5]=>[2,7,6,3,4,1,5]=>[7,5,4,3,6,1,2]=>001111
[6,3,4,7,2,5,1]=>[5,7,6,3,4,2,1]=>[7,1,5,4,3,6,2]=>001111
[6,3,4,7,5,1,2]=>[5,1,7,3,6,4,2]=>[7,2,1,5,6,4,3]=>101011
[6,3,4,7,5,2,1]=>[2,5,7,3,6,4,1]=>[7,1,2,5,6,4,3]=>001011
[6,3,5,1,2,4,7]=>[5,1,6,3,2,4,7]=>[5,2,1,6,4,3,7]=>101110
[6,3,5,1,2,7,4]=>[7,1,5,6,3,2,4]=>[5,3,7,4,6,2,1]=>100111
[6,3,5,1,4,2,7]=>[4,5,6,3,1,2,7]=>[6,2,5,1,4,3,7]=>001110
[6,3,5,1,4,7,2]=>[7,5,6,3,1,4,2]=>[6,4,3,7,2,5,1]=>001111
[6,3,5,1,7,2,4]=>[7,5,6,3,1,2,4]=>[7,4,3,6,2,5,1]=>001111
[6,3,5,1,7,4,2]=>[4,7,5,6,3,1,2]=>[5,3,6,1,4,7,2]=>000111
[6,3,5,2,1,4,7]=>[2,5,6,3,1,4,7]=>[5,1,2,6,4,3,7]=>001110
[6,3,5,2,1,7,4]=>[2,7,5,6,3,1,4]=>[5,3,7,4,6,1,2]=>000111
[6,3,5,2,4,1,7]=>[4,5,6,3,2,1,7]=>[5,2,6,1,4,3,7]=>001110
[6,3,5,2,4,7,1]=>[7,5,6,3,2,4,1]=>[5,2,6,4,3,7,1]=>001111
[6,3,5,2,7,1,4]=>[7,5,6,3,2,1,4]=>[5,2,7,4,3,6,1]=>001111
[6,3,5,2,7,4,1]=>[4,7,5,6,3,2,1]=>[5,3,7,1,4,6,2]=>000111
[6,3,5,4,1,2,7]=>[4,1,5,6,3,2,7]=>[5,3,6,2,1,4,7]=>100110
[6,3,5,4,1,7,2]=>[7,4,5,6,3,1,2]=>[5,3,7,2,4,6,1]=>000111
[6,3,5,4,2,1,7]=>[2,4,5,6,3,1,7]=>[5,3,6,1,2,4,7]=>000110
[6,3,5,4,2,7,1]=>[7,4,5,6,3,2,1]=>[5,3,6,2,4,7,1]=>000111
[6,3,5,4,7,1,2]=>[7,1,5,6,3,4,2]=>[5,3,6,4,7,2,1]=>100111
[6,3,5,4,7,2,1]=>[2,7,5,6,3,4,1]=>[5,3,6,4,7,1,2]=>000111
[6,3,5,7,1,2,4]=>[7,1,6,3,2,5,4]=>[7,4,3,6,5,2,1]=>101111
[6,3,5,7,1,4,2]=>[4,7,6,3,1,5,2]=>[6,5,1,4,3,7,2]=>001111
[6,3,5,7,2,1,4]=>[2,7,6,3,1,5,4]=>[7,4,3,6,5,1,2]=>001111
[6,3,5,7,2,4,1]=>[4,7,6,3,2,5,1]=>[7,1,4,3,6,5,2]=>001111
[6,3,5,7,4,1,2]=>[4,1,7,6,3,5,2]=>[7,2,1,4,6,5,3]=>100111
[6,3,5,7,4,2,1]=>[2,4,7,6,3,5,1]=>[7,1,2,4,6,5,3]=>000111
[6,3,7,1,2,4,5]=>[7,1,6,3,2,4,5]=>[6,4,3,7,5,2,1]=>101111
[6,3,7,1,2,5,4]=>[5,1,7,6,3,2,4]=>[7,4,6,2,1,5,3]=>100111
[6,3,7,1,4,2,5]=>[4,7,6,3,1,2,5]=>[7,5,1,4,3,6,2]=>001111
[6,3,7,1,4,5,2]=>[5,7,6,3,1,4,2]=>[5,1,6,4,3,7,2]=>001111
[6,3,7,1,5,2,4]=>[5,7,6,3,1,2,4]=>[5,1,7,4,3,6,2]=>001111
[6,3,7,1,5,4,2]=>[4,5,7,6,3,1,2]=>[6,1,4,7,2,5,3]=>000111
[6,3,7,2,1,4,5]=>[2,7,6,3,1,4,5]=>[6,4,3,7,5,1,2]=>001111
[6,3,7,2,1,5,4]=>[2,5,7,6,3,1,4]=>[7,4,6,1,2,5,3]=>000111
[6,3,7,2,4,1,5]=>[4,7,6,3,2,1,5]=>[6,1,4,3,7,5,2]=>001111
[6,3,7,2,4,5,1]=>[5,7,6,3,2,4,1]=>[6,4,3,7,1,5,2]=>001111
[6,3,7,2,5,1,4]=>[5,7,6,3,2,1,4]=>[7,4,3,6,1,5,2]=>001111
[6,3,7,2,5,4,1]=>[4,5,7,6,3,2,1]=>[7,1,4,6,2,5,3]=>000111
[6,3,7,4,1,2,5]=>[4,1,7,6,3,2,5]=>[6,2,1,4,7,5,3]=>100111
[6,3,7,4,1,5,2]=>[5,4,7,6,3,1,2]=>[7,2,4,6,1,5,3]=>000111
[6,3,7,4,2,1,5]=>[2,4,7,6,3,1,5]=>[6,1,2,4,7,5,3]=>000111
[6,3,7,4,2,5,1]=>[5,4,7,6,3,2,1]=>[6,2,4,7,1,5,3]=>000111
[6,3,7,4,5,1,2]=>[5,1,7,6,3,4,2]=>[6,4,7,2,1,5,3]=>100111
[6,3,7,4,5,2,1]=>[2,5,7,6,3,4,1]=>[6,4,7,1,2,5,3]=>000111
[6,3,7,5,1,2,4]=>[5,1,7,3,6,2,4]=>[6,2,1,5,7,4,3]=>101011
[6,3,7,5,1,4,2]=>[4,5,7,3,6,1,2]=>[7,2,5,6,1,4,3]=>001011
[6,3,7,5,2,1,4]=>[2,5,7,3,6,1,4]=>[6,1,2,5,7,4,3]=>001011
[6,3,7,5,2,4,1]=>[4,5,7,3,6,2,1]=>[6,2,5,7,1,4,3]=>001011
[6,3,7,5,4,1,2]=>[4,1,5,7,6,3,2]=>[6,3,5,7,2,1,4]=>100011
[6,3,7,5,4,2,1]=>[2,4,5,7,6,3,1]=>[6,3,5,7,1,2,4]=>000011
[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[6,5,3,2,1,4,7]=>110110
[6,4,1,2,3,7,5]=>[4,1,2,7,6,3,5]=>[7,5,6,3,2,1,4]=>110011
[6,4,1,2,5,3,7]=>[5,1,4,6,2,3,7]=>[5,2,1,6,3,4,7]=>100110
[6,4,1,2,5,7,3]=>[7,1,4,6,2,5,3]=>[7,3,4,6,5,2,1]=>100111
[6,4,1,2,7,3,5]=>[7,1,4,6,2,3,5]=>[6,3,4,7,5,2,1]=>100111
[6,4,1,2,7,5,3]=>[5,1,4,7,6,2,3]=>[6,2,1,5,7,3,4]=>100011
[6,4,1,3,2,5,7]=>[3,4,1,6,2,5,7]=>[3,1,6,5,2,4,7]=>010110
[6,4,1,3,2,7,5]=>[3,4,1,7,6,2,5]=>[3,1,7,5,6,2,4]=>010011
[6,4,1,3,5,2,7]=>[5,4,1,6,3,2,7]=>[5,3,1,6,2,4,7]=>010110
[6,4,1,3,5,7,2]=>[7,4,1,6,3,5,2]=>[7,2,4,6,5,3,1]=>010111
[6,4,1,3,7,2,5]=>[7,4,1,6,3,2,5]=>[6,2,4,7,5,3,1]=>010111
[6,4,1,3,7,5,2]=>[5,4,1,7,6,3,2]=>[6,3,1,5,7,2,4]=>010011
[6,4,1,5,2,3,7]=>[5,4,1,6,2,3,7]=>[6,3,1,5,2,4,7]=>010110
[6,4,1,5,2,7,3]=>[7,5,4,6,1,2,3]=>[7,3,4,6,2,5,1]=>000111
[6,4,1,5,3,2,7]=>[3,5,4,6,1,2,7]=>[6,2,5,1,3,4,7]=>000110
[6,4,1,5,3,7,2]=>[7,5,4,6,1,3,2]=>[6,3,4,7,2,5,1]=>000111
[6,4,1,5,7,2,3]=>[7,4,1,6,2,5,3]=>[6,5,2,4,7,3,1]=>010111
[6,4,1,5,7,3,2]=>[3,7,4,6,1,5,2]=>[6,5,1,3,4,7,2]=>000111
[6,4,1,7,2,3,5]=>[7,4,1,6,2,3,5]=>[7,5,2,4,6,3,1]=>010111
[6,4,1,7,2,5,3]=>[5,7,4,6,1,2,3]=>[5,1,7,3,4,6,2]=>000111
[6,4,1,7,3,2,5]=>[3,7,4,6,1,2,5]=>[7,5,1,3,4,6,2]=>000111
[6,4,1,7,3,5,2]=>[5,7,4,6,1,3,2]=>[5,1,6,3,4,7,2]=>000111
[6,4,1,7,5,2,3]=>[5,4,1,7,6,2,3]=>[7,3,1,5,6,2,4]=>010011
[6,4,1,7,5,3,2]=>[3,5,4,7,6,1,2]=>[7,2,5,6,1,3,4]=>000011
[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[6,5,3,1,2,4,7]=>010110
[6,4,2,1,3,7,5]=>[2,4,1,7,6,3,5]=>[7,5,6,3,1,2,4]=>010011
[6,4,2,1,5,3,7]=>[2,5,4,6,1,3,7]=>[5,1,2,6,3,4,7]=>000110
[6,4,2,1,5,7,3]=>[2,7,4,6,1,5,3]=>[7,3,4,6,5,1,2]=>000111
[6,4,2,1,7,3,5]=>[2,7,4,6,1,3,5]=>[6,3,4,7,5,1,2]=>000111
[6,4,2,1,7,5,3]=>[2,5,4,7,6,1,3]=>[6,1,2,5,7,3,4]=>000011
[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>[6,5,1,3,2,4,7]=>010110
[6,4,2,3,1,7,5]=>[3,4,2,7,6,1,5]=>[7,5,6,1,3,2,4]=>010011
[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>[6,1,5,3,2,4,7]=>010110
[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>[6,5,3,2,4,7,1]=>010111
[6,4,2,3,7,1,5]=>[7,4,2,6,3,1,5]=>[7,5,3,2,4,6,1]=>010111
[6,4,2,3,7,5,1]=>[5,4,2,7,6,3,1]=>[7,1,5,6,3,2,4]=>010011
[6,4,2,5,1,3,7]=>[5,4,2,6,1,3,7]=>[5,1,6,3,2,4,7]=>010110
[6,4,2,5,1,7,3]=>[7,5,4,6,2,1,3]=>[5,2,7,3,4,6,1]=>000111
[6,4,2,5,3,1,7]=>[3,5,4,6,2,1,7]=>[5,2,6,1,3,4,7]=>000110
[6,4,2,5,3,7,1]=>[7,5,4,6,2,3,1]=>[5,2,6,3,4,7,1]=>000111
[6,4,2,5,7,1,3]=>[7,4,2,6,1,5,3]=>[7,3,2,4,6,5,1]=>010111
[6,4,2,5,7,3,1]=>[3,7,4,6,2,5,1]=>[7,1,3,4,6,5,2]=>000111
[6,4,2,7,1,3,5]=>[7,4,2,6,1,3,5]=>[6,3,2,4,7,5,1]=>010111
[6,4,2,7,1,5,3]=>[5,7,4,6,2,1,3]=>[7,3,4,6,1,5,2]=>000111
[6,4,2,7,3,1,5]=>[3,7,4,6,2,1,5]=>[6,1,3,4,7,5,2]=>000111
[6,4,2,7,3,5,1]=>[5,7,4,6,2,3,1]=>[6,3,4,7,1,5,2]=>000111
[6,4,2,7,5,1,3]=>[5,4,2,7,6,1,3]=>[6,1,5,7,3,2,4]=>010011
[6,4,2,7,5,3,1]=>[3,5,4,7,6,2,1]=>[6,2,5,7,1,3,4]=>000011
[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[6,5,2,1,3,4,7]=>100110
[6,4,3,1,2,7,5]=>[3,1,4,7,6,2,5]=>[7,5,6,2,1,3,4]=>100011
[6,4,3,1,5,2,7]=>[5,3,4,6,1,2,7]=>[5,1,6,2,3,4,7]=>000110
[6,4,3,1,5,7,2]=>[7,3,4,6,1,5,2]=>[7,2,3,4,6,5,1]=>000111
[6,4,3,1,7,2,5]=>[7,3,4,6,1,2,5]=>[6,2,3,4,7,5,1]=>000111
[6,4,3,1,7,5,2]=>[5,3,4,7,6,1,2]=>[6,1,5,7,2,3,4]=>000011
[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[6,5,1,2,3,4,7]=>000110
[6,4,3,2,1,7,5]=>[2,3,4,7,6,1,5]=>[7,5,6,1,2,3,4]=>000011
[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[6,1,5,2,3,4,7]=>000110
[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[6,5,2,3,4,7,1]=>000111
[6,4,3,2,7,1,5]=>[7,3,4,6,2,1,5]=>[7,5,2,3,4,6,1]=>000111
[6,4,3,2,7,5,1]=>[5,3,4,7,6,2,1]=>[7,1,5,6,2,3,4]=>000011
[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[6,2,1,5,3,4,7]=>100110
[6,4,3,5,1,7,2]=>[7,5,4,6,3,1,2]=>[7,2,5,3,4,6,1]=>000111
[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[6,1,2,5,3,4,7]=>000110
[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[6,2,5,3,4,7,1]=>000111
[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>[6,5,3,4,7,2,1]=>100111
[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[6,5,3,4,7,1,2]=>000111
[6,4,3,7,1,2,5]=>[7,1,4,6,3,2,5]=>[7,5,3,4,6,2,1]=>100111
[6,4,3,7,1,5,2]=>[5,7,4,6,3,1,2]=>[6,1,5,3,4,7,2]=>000111
[6,4,3,7,2,1,5]=>[2,7,4,6,3,1,5]=>[7,5,3,4,6,1,2]=>000111
[6,4,3,7,2,5,1]=>[5,7,4,6,3,2,1]=>[7,1,5,3,4,6,2]=>000111
[6,4,3,7,5,1,2]=>[5,1,4,7,6,3,2]=>[7,2,1,5,6,3,4]=>100011
[6,4,3,7,5,2,1]=>[2,5,4,7,6,3,1]=>[7,1,2,5,6,3,4]=>000011
[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[6,3,2,1,5,4,7]=>110110
[6,4,5,1,2,7,3]=>[7,1,5,6,4,2,3]=>[7,3,5,4,6,2,1]=>100111
[6,4,5,1,3,2,7]=>[3,5,1,6,4,2,7]=>[3,1,6,2,5,4,7]=>010110
[6,4,5,1,3,7,2]=>[7,5,1,6,4,3,2]=>[7,2,5,4,6,3,1]=>010111
[6,4,5,1,7,2,3]=>[7,5,1,6,4,2,3]=>[6,2,5,4,7,3,1]=>010111
[6,4,5,1,7,3,2]=>[3,7,5,6,4,1,2]=>[6,1,3,5,4,7,2]=>000111
[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>[6,3,1,2,5,4,7]=>010110
[6,4,5,2,1,7,3]=>[2,7,5,6,4,1,3]=>[7,3,5,4,6,1,2]=>000111
[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>[6,1,3,2,5,4,7]=>010110
[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>[6,3,2,5,4,7,1]=>010111
[6,4,5,2,7,1,3]=>[7,5,2,6,4,1,3]=>[7,3,2,5,4,6,1]=>010111
[6,4,5,2,7,3,1]=>[3,7,5,6,4,2,1]=>[7,1,3,5,4,6,2]=>000111
[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>[6,2,1,3,5,4,7]=>100110
[6,4,5,3,1,7,2]=>[7,3,5,6,4,1,2]=>[7,2,3,5,4,6,1]=>000111
[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>[6,1,2,3,5,4,7]=>000110
[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[6,2,3,5,4,7,1]=>000111
[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>[6,3,5,4,7,2,1]=>100111
[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[6,3,5,4,7,1,2]=>000111
[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[6,5,4,7,3,2,1]=>110111
[6,4,5,7,1,3,2]=>[3,7,1,6,4,5,2]=>[3,1,6,5,4,7,2]=>010111
[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>[6,5,4,7,3,1,2]=>010111
[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>[6,5,4,7,1,3,2]=>010111
[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>[6,5,4,7,2,1,3]=>100111
[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[6,5,4,7,1,2,3]=>000111
[6,4,7,1,2,3,5]=>[7,1,2,6,4,3,5]=>[7,5,4,6,3,2,1]=>110111
[6,4,7,1,2,5,3]=>[5,1,7,6,4,2,3]=>[6,2,1,5,4,7,3]=>100111
[6,4,7,1,3,2,5]=>[3,7,1,6,4,2,5]=>[3,1,7,5,4,6,2]=>010111
[6,4,7,1,3,5,2]=>[5,7,1,6,4,3,2]=>[6,3,1,5,4,7,2]=>010111
[6,4,7,1,5,2,3]=>[5,7,1,6,4,2,3]=>[7,3,1,5,4,6,2]=>010111
[6,4,7,1,5,3,2]=>[3,5,7,6,4,1,2]=>[7,2,5,4,6,1,3]=>000111
[6,4,7,2,1,3,5]=>[2,7,1,6,4,3,5]=>[7,5,4,6,3,1,2]=>010111
[6,4,7,2,1,5,3]=>[2,5,7,6,4,1,3]=>[6,1,2,5,4,7,3]=>000111
[6,4,7,2,3,1,5]=>[3,7,2,6,4,1,5]=>[7,5,4,6,1,3,2]=>010111
[6,4,7,2,3,5,1]=>[5,7,2,6,4,3,1]=>[7,1,5,4,6,3,2]=>010111
[6,4,7,2,5,1,3]=>[5,7,2,6,4,1,3]=>[6,1,5,4,7,3,2]=>010111
[6,4,7,2,5,3,1]=>[3,5,7,6,4,2,1]=>[6,2,5,4,7,1,3]=>000111
[6,4,7,3,1,2,5]=>[3,1,7,6,4,2,5]=>[7,5,4,6,2,1,3]=>100111
[6,4,7,3,1,5,2]=>[5,3,7,6,4,1,2]=>[6,1,5,4,7,2,3]=>000111
[6,4,7,3,2,1,5]=>[2,3,7,6,4,1,5]=>[7,5,4,6,1,2,3]=>000111
[6,4,7,3,2,5,1]=>[5,3,7,6,4,2,1]=>[7,1,5,4,6,2,3]=>000111
[6,4,7,3,5,1,2]=>[5,1,7,6,4,3,2]=>[7,2,1,5,4,6,3]=>100111
[6,4,7,3,5,2,1]=>[2,5,7,6,4,3,1]=>[7,1,2,5,4,6,3]=>000111
[6,4,7,5,1,2,3]=>[5,1,2,7,6,4,3]=>[7,3,2,1,5,6,4]=>110011
[6,4,7,5,1,3,2]=>[3,5,1,7,6,4,2]=>[3,1,7,2,5,6,4]=>010011
[6,4,7,5,2,1,3]=>[2,5,1,7,6,4,3]=>[7,3,1,2,5,6,4]=>010011
[6,4,7,5,2,3,1]=>[3,5,2,7,6,4,1]=>[7,1,3,2,5,6,4]=>010011
[6,4,7,5,3,1,2]=>[3,1,5,7,6,4,2]=>[7,2,1,3,5,6,4]=>100011
[6,4,7,5,3,2,1]=>[2,3,5,7,6,4,1]=>[7,1,2,3,5,6,4]=>000011
[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[6,4,3,2,1,5,7]=>111010
[6,5,1,2,3,7,4]=>[7,1,2,5,6,3,4]=>[7,4,5,6,3,2,1]=>110011
[6,5,1,2,4,3,7]=>[4,1,5,2,6,3,7]=>[4,2,1,6,3,5,7]=>101010
[6,5,1,2,4,7,3]=>[7,1,5,2,6,4,3]=>[7,3,5,6,4,2,1]=>101011
[6,5,1,2,7,3,4]=>[7,1,5,2,6,3,4]=>[6,3,5,7,4,2,1]=>101011
[6,5,1,2,7,4,3]=>[4,1,7,5,6,2,3]=>[6,2,1,4,5,7,3]=>100011
[6,5,1,3,2,4,7]=>[3,5,1,2,6,4,7]=>[3,1,6,4,2,5,7]=>011010
[6,5,1,3,2,7,4]=>[3,7,1,5,6,2,4]=>[3,1,7,4,5,6,2]=>010011
[6,5,1,3,4,2,7]=>[4,5,1,3,6,2,7]=>[4,3,1,6,2,5,7]=>011010
[6,5,1,3,4,7,2]=>[7,5,1,3,6,4,2]=>[7,2,5,6,4,3,1]=>011011
[6,5,1,3,7,2,4]=>[7,5,1,3,6,2,4]=>[6,2,5,7,4,3,1]=>011011
[6,5,1,3,7,4,2]=>[4,7,1,5,6,3,2]=>[6,3,1,4,5,7,2]=>010011
[6,5,1,4,2,3,7]=>[4,5,1,2,6,3,7]=>[6,3,1,4,2,5,7]=>011010
[6,5,1,4,2,7,3]=>[7,4,5,1,6,2,3]=>[7,3,5,6,2,4,1]=>001011
[6,5,1,4,3,2,7]=>[3,4,5,1,6,2,7]=>[6,2,4,1,3,5,7]=>001010
[6,5,1,4,3,7,2]=>[7,4,5,1,6,3,2]=>[6,3,5,7,2,4,1]=>001011
[6,5,1,4,7,2,3]=>[7,5,1,2,6,4,3]=>[6,4,2,5,7,3,1]=>011011
[6,5,1,4,7,3,2]=>[3,7,5,1,6,4,2]=>[6,4,1,3,5,7,2]=>001011
[6,5,1,7,2,3,4]=>[7,5,1,2,6,3,4]=>[7,4,2,5,6,3,1]=>011011
[6,5,1,7,2,4,3]=>[4,7,5,1,6,2,3]=>[4,1,7,3,5,6,2]=>001011
[6,5,1,7,3,2,4]=>[3,7,5,1,6,2,4]=>[7,4,1,3,5,6,2]=>001011
[6,5,1,7,3,4,2]=>[4,7,5,1,6,3,2]=>[4,1,6,3,5,7,2]=>001011
[6,5,1,7,4,2,3]=>[4,7,1,5,6,2,3]=>[7,3,1,4,5,6,2]=>010011
[6,5,1,7,4,3,2]=>[3,4,7,5,6,1,2]=>[7,2,4,5,6,1,3]=>000011
[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[6,4,3,1,2,5,7]=>011010
[6,5,2,1,3,7,4]=>[2,7,1,5,6,3,4]=>[7,4,5,6,3,1,2]=>010011
[6,5,2,1,4,3,7]=>[2,4,5,1,6,3,7]=>[4,1,2,6,3,5,7]=>001010
[6,5,2,1,4,7,3]=>[2,7,5,1,6,4,3]=>[7,3,5,6,4,1,2]=>001011
[6,5,2,1,7,3,4]=>[2,7,5,1,6,3,4]=>[6,3,5,7,4,1,2]=>001011
[6,5,2,1,7,4,3]=>[2,4,7,5,6,1,3]=>[6,1,2,4,5,7,3]=>000011
[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>[6,4,1,3,2,5,7]=>011010
[6,5,2,3,1,7,4]=>[3,7,2,5,6,1,4]=>[7,4,5,6,1,3,2]=>010011
[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>011010
[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>[6,4,3,2,5,7,1]=>011011
[6,5,2,3,7,1,4]=>[7,5,2,3,6,1,4]=>[7,4,3,2,5,6,1]=>011011
[6,5,2,3,7,4,1]=>[4,7,2,5,6,3,1]=>[7,1,4,5,6,3,2]=>010011
[6,5,2,4,1,3,7]=>[4,5,2,1,6,3,7]=>[4,1,6,3,2,5,7]=>011010
[6,5,2,4,1,7,3]=>[7,4,5,2,6,1,3]=>[4,2,7,3,5,6,1]=>001011
[6,5,2,4,3,1,7]=>[3,4,5,2,6,1,7]=>[4,2,6,1,3,5,7]=>001010
[6,5,2,4,3,7,1]=>[7,4,5,2,6,3,1]=>[4,2,6,3,5,7,1]=>001011
[6,5,2,4,7,1,3]=>[7,5,2,1,6,4,3]=>[7,3,2,5,6,4,1]=>011011
[6,5,2,4,7,3,1]=>[3,7,5,2,6,4,1]=>[7,1,3,5,6,4,2]=>001011
[6,5,2,7,1,3,4]=>[7,5,2,1,6,3,4]=>[6,3,2,5,7,4,1]=>011011
[6,5,2,7,1,4,3]=>[4,7,5,2,6,1,3]=>[7,3,5,6,1,4,2]=>001011
[6,5,2,7,3,1,4]=>[3,7,5,2,6,1,4]=>[6,1,3,5,7,4,2]=>001011
[6,5,2,7,3,4,1]=>[4,7,5,2,6,3,1]=>[6,3,5,7,1,4,2]=>001011
[6,5,2,7,4,1,3]=>[4,7,2,5,6,1,3]=>[6,1,4,5,7,3,2]=>010011
[6,5,2,7,4,3,1]=>[3,4,7,5,6,2,1]=>[6,2,4,5,7,1,3]=>000011
[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[6,4,2,1,3,5,7]=>101010
[6,5,3,1,2,7,4]=>[3,1,7,5,6,2,4]=>[7,4,5,6,2,1,3]=>100011
[6,5,3,1,4,2,7]=>[4,3,5,1,6,2,7]=>[4,1,6,2,3,5,7]=>001010
[6,5,3,1,4,7,2]=>[7,3,5,1,6,4,2]=>[7,2,3,5,6,4,1]=>001011
[6,5,3,1,7,2,4]=>[7,3,5,1,6,2,4]=>[6,2,3,5,7,4,1]=>001011
[6,5,3,1,7,4,2]=>[4,3,7,5,6,1,2]=>[6,1,4,5,7,2,3]=>000011
[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[6,4,1,2,3,5,7]=>001010
[6,5,3,2,1,7,4]=>[2,3,7,5,6,1,4]=>[7,4,5,6,1,2,3]=>000011
[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>[6,1,4,2,3,5,7]=>001010
[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>[6,4,2,3,5,7,1]=>001011
[6,5,3,2,7,1,4]=>[7,3,5,2,6,1,4]=>[7,4,2,3,5,6,1]=>001011
[6,5,3,2,7,4,1]=>[4,3,7,5,6,2,1]=>[7,1,4,5,6,2,3]=>000011
[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[6,2,1,4,3,5,7]=>101010
[6,5,3,4,1,7,2]=>[7,4,5,3,6,1,2]=>[7,2,4,3,5,6,1]=>001011
[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,1,2,4,3,5,7]=>001010
[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>[6,2,4,3,5,7,1]=>001011
[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>[6,4,3,5,7,2,1]=>101011
[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>[6,4,3,5,7,1,2]=>001011
[6,5,3,7,1,2,4]=>[7,1,5,3,6,2,4]=>[7,4,3,5,6,2,1]=>101011
[6,5,3,7,1,4,2]=>[4,7,5,3,6,1,2]=>[6,1,4,3,5,7,2]=>001011
[6,5,3,7,2,1,4]=>[2,7,5,3,6,1,4]=>[7,4,3,5,6,1,2]=>001011
[6,5,3,7,2,4,1]=>[4,7,5,3,6,2,1]=>[7,1,4,3,5,6,2]=>001011
[6,5,3,7,4,1,2]=>[4,1,7,5,6,3,2]=>[7,2,1,4,5,6,3]=>100011
[6,5,3,7,4,2,1]=>[2,4,7,5,6,3,1]=>[7,1,2,4,5,6,3]=>000011
[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[6,3,2,1,4,5,7]=>110010
[6,5,4,1,2,7,3]=>[7,1,4,5,6,2,3]=>[7,3,4,5,6,2,1]=>100011
[6,5,4,1,3,2,7]=>[3,4,1,5,6,2,7]=>[3,1,6,2,4,5,7]=>010010
[6,5,4,1,3,7,2]=>[7,4,1,5,6,3,2]=>[7,2,4,5,6,3,1]=>010011
[6,5,4,1,7,2,3]=>[7,4,1,5,6,2,3]=>[6,2,4,5,7,3,1]=>010011
[6,5,4,1,7,3,2]=>[3,7,4,5,6,1,2]=>[6,1,3,4,5,7,2]=>000011
[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[6,3,1,2,4,5,7]=>010010
[6,5,4,2,1,7,3]=>[2,7,4,5,6,1,3]=>[7,3,4,5,6,1,2]=>000011
[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>[6,1,3,2,4,5,7]=>010010
[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>[6,3,2,4,5,7,1]=>010011
[6,5,4,2,7,1,3]=>[7,4,2,5,6,1,3]=>[7,3,2,4,5,6,1]=>010011
[6,5,4,2,7,3,1]=>[3,7,4,5,6,2,1]=>[7,1,3,4,5,6,2]=>000011
[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[6,2,1,3,4,5,7]=>100010
[6,5,4,3,1,7,2]=>[7,3,4,5,6,1,2]=>[7,2,3,4,5,6,1]=>000011
[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>000010
[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,7,1]=>000011
[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[6,3,4,5,7,2,1]=>100011
[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[6,3,4,5,7,1,2]=>000011
[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[6,4,5,7,3,2,1]=>110011
[6,5,4,7,1,3,2]=>[3,7,1,5,6,4,2]=>[3,1,6,4,5,7,2]=>010011
[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>[6,4,5,7,3,1,2]=>010011
[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>[6,4,5,7,1,3,2]=>010011
[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>[6,4,5,7,2,1,3]=>100011
[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[6,4,5,7,1,2,3]=>000011
[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[6,5,7,4,3,2,1]=>111011
[6,5,7,1,2,4,3]=>[4,1,7,2,6,5,3]=>[4,2,1,6,5,7,3]=>101011
[6,5,7,1,3,2,4]=>[3,7,1,2,6,5,4]=>[3,1,6,5,7,4,2]=>011011
[6,5,7,1,3,4,2]=>[4,7,1,3,6,5,2]=>[4,3,1,6,5,7,2]=>011011
[6,5,7,1,4,2,3]=>[4,7,1,2,6,5,3]=>[6,5,7,3,1,4,2]=>011011
[6,5,7,1,4,3,2]=>[3,4,7,1,6,5,2]=>[6,5,7,2,4,1,3]=>001011
[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[6,5,7,4,3,1,2]=>011011
[6,5,7,2,1,4,3]=>[2,4,7,1,6,5,3]=>[4,1,2,6,5,7,3]=>001011
[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[6,5,7,4,1,3,2]=>011011
[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>[6,5,7,1,4,3,2]=>011011
[6,5,7,2,4,1,3]=>[4,7,2,1,6,5,3]=>[4,1,6,5,7,3,2]=>011011
[6,5,7,2,4,3,1]=>[3,4,7,2,6,5,1]=>[4,2,6,5,7,1,3]=>001011
[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[6,5,7,4,2,1,3]=>101011
[6,5,7,3,1,4,2]=>[4,3,7,1,6,5,2]=>[4,1,6,5,7,2,3]=>001011
[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[6,5,7,4,1,2,3]=>001011
[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>[6,5,7,1,4,2,3]=>001011
[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[6,5,7,2,1,4,3]=>101011
[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>[6,5,7,1,2,4,3]=>001011
[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>[6,5,7,3,2,1,4]=>110011
[6,5,7,4,1,3,2]=>[3,4,1,7,6,5,2]=>[3,1,6,5,7,2,4]=>010011
[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>[6,5,7,3,1,2,4]=>010011
[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>[6,5,7,1,3,2,4]=>010011
[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>[6,5,7,2,1,3,4]=>100011
[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[6,5,7,1,2,3,4]=>000011
[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[6,7,5,4,3,2,1]=>111101
[6,7,1,2,3,5,4]=>[5,1,2,7,3,6,4]=>[5,3,2,1,6,7,4]=>110101
[6,7,1,2,4,3,5]=>[4,1,7,2,3,6,5]=>[4,2,1,6,7,5,3]=>101101
[6,7,1,2,4,5,3]=>[5,1,7,2,4,6,3]=>[5,4,2,1,6,7,3]=>101101
[6,7,1,2,5,3,4]=>[5,1,7,2,3,6,4]=>[6,7,4,2,1,5,3]=>101101
[6,7,1,2,5,4,3]=>[4,1,5,7,2,6,3]=>[6,7,3,5,2,1,4]=>100101
[6,7,1,3,2,4,5]=>[3,7,1,2,4,6,5]=>[3,1,6,7,5,4,2]=>011101
[6,7,1,3,2,5,4]=>[3,5,1,7,2,6,4]=>[3,1,5,2,6,7,4]=>010101
[6,7,1,3,4,2,5]=>[4,7,1,3,2,6,5]=>[4,3,1,6,7,5,2]=>011101
[6,7,1,3,4,5,2]=>[5,7,1,3,4,6,2]=>[5,4,3,1,6,7,2]=>011101
[6,7,1,3,5,2,4]=>[5,7,1,3,2,6,4]=>[6,7,4,3,1,5,2]=>011101
[6,7,1,3,5,4,2]=>[4,5,1,7,3,6,2]=>[6,7,2,5,3,1,4]=>010101
[6,7,1,4,2,3,5]=>[4,7,1,2,3,6,5]=>[6,7,5,3,1,4,2]=>011101
[6,7,1,4,2,5,3]=>[5,4,7,1,2,6,3]=>[5,2,4,1,6,7,3]=>001101
[6,7,1,4,3,2,5]=>[3,4,7,1,2,6,5]=>[6,7,5,2,4,1,3]=>001101
[6,7,1,4,3,5,2]=>[5,4,7,1,3,6,2]=>[6,7,2,4,1,5,3]=>001101
[6,7,1,4,5,2,3]=>[5,7,1,2,4,6,3]=>[6,7,3,1,5,4,2]=>011101
[6,7,1,4,5,3,2]=>[3,5,7,1,4,6,2]=>[6,7,2,5,4,1,3]=>001101
[6,7,1,5,2,3,4]=>[5,7,1,2,3,6,4]=>[5,3,1,6,7,4,2]=>011101
[6,7,1,5,2,4,3]=>[4,5,7,1,2,6,3]=>[4,1,5,2,6,7,3]=>001101
[6,7,1,5,3,2,4]=>[3,5,7,1,2,6,4]=>[5,2,6,7,4,1,3]=>001101
[6,7,1,5,3,4,2]=>[4,5,7,1,3,6,2]=>[4,1,6,7,2,5,3]=>001101
[6,7,1,5,4,2,3]=>[4,5,1,7,2,6,3]=>[5,2,6,7,3,1,4]=>010101
[6,7,1,5,4,3,2]=>[3,4,5,7,1,6,2]=>[5,1,3,6,7,2,4]=>000101
[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[6,7,5,4,3,1,2]=>011101
[6,7,2,1,3,5,4]=>[2,5,1,7,3,6,4]=>[5,3,1,2,6,7,4]=>010101
[6,7,2,1,4,3,5]=>[2,4,7,1,3,6,5]=>[4,1,2,6,7,5,3]=>001101
[6,7,2,1,4,5,3]=>[2,5,7,1,4,6,3]=>[5,4,1,2,6,7,3]=>001101
[6,7,2,1,5,3,4]=>[2,5,7,1,3,6,4]=>[6,7,4,1,2,5,3]=>001101
[6,7,2,1,5,4,3]=>[2,4,5,7,1,6,3]=>[6,7,3,5,1,2,4]=>000101
[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[6,7,5,4,1,3,2]=>011101
[6,7,2,3,1,5,4]=>[3,5,2,7,1,6,4]=>[5,1,3,2,6,7,4]=>010101
[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[6,7,5,1,4,3,2]=>011101
[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>[6,7,1,5,4,3,2]=>011101
[6,7,2,3,5,1,4]=>[5,7,2,3,1,6,4]=>[5,1,6,7,4,3,2]=>011101
[6,7,2,3,5,4,1]=>[4,5,2,7,3,6,1]=>[5,3,2,6,7,1,4]=>010101
[6,7,2,4,1,3,5]=>[4,7,2,1,3,6,5]=>[4,1,6,7,5,3,2]=>011101
[6,7,2,4,1,5,3]=>[5,4,7,2,1,6,3]=>[4,2,5,1,6,7,3]=>001101
[6,7,2,4,3,1,5]=>[3,4,7,2,1,6,5]=>[4,2,6,7,5,1,3]=>001101
[6,7,2,4,3,5,1]=>[5,4,7,2,3,6,1]=>[4,2,6,7,1,5,3]=>001101
[6,7,2,4,5,1,3]=>[5,7,2,1,4,6,3]=>[5,4,1,6,7,3,2]=>011101
[6,7,2,4,5,3,1]=>[3,5,7,2,4,6,1]=>[5,4,2,6,7,1,3]=>001101
[6,7,2,5,1,3,4]=>[5,7,2,1,3,6,4]=>[6,7,4,1,5,3,2]=>011101
[6,7,2,5,1,4,3]=>[4,5,7,2,1,6,3]=>[5,1,4,2,6,7,3]=>001101
[6,7,2,5,3,1,4]=>[3,5,7,2,1,6,4]=>[6,7,4,2,5,1,3]=>001101
[6,7,2,5,3,4,1]=>[4,5,7,2,3,6,1]=>[6,7,1,4,2,5,3]=>001101
[6,7,2,5,4,1,3]=>[4,5,2,7,1,6,3]=>[6,7,3,2,5,1,4]=>010101
[6,7,2,5,4,3,1]=>[3,4,5,7,2,6,1]=>[6,7,1,3,5,2,4]=>000101
[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[6,7,5,4,2,1,3]=>101101
[6,7,3,1,2,5,4]=>[3,1,5,7,2,6,4]=>[5,2,1,3,6,7,4]=>100101
[6,7,3,1,4,2,5]=>[4,3,7,1,2,6,5]=>[4,1,6,7,5,2,3]=>001101
[6,7,3,1,4,5,2]=>[5,3,7,1,4,6,2]=>[5,4,1,6,7,2,3]=>001101
[6,7,3,1,5,2,4]=>[5,3,7,1,2,6,4]=>[6,7,4,1,5,2,3]=>001101
[6,7,3,1,5,4,2]=>[4,3,5,7,1,6,2]=>[6,7,2,3,5,1,4]=>000101
[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[6,7,5,4,1,2,3]=>001101
[6,7,3,2,1,5,4]=>[2,3,5,7,1,6,4]=>[5,1,2,3,6,7,4]=>000101
[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[6,7,5,1,4,2,3]=>001101
[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>[6,7,1,5,4,2,3]=>001101
[6,7,3,2,5,1,4]=>[5,3,7,2,1,6,4]=>[5,1,6,7,4,2,3]=>001101
[6,7,3,2,5,4,1]=>[4,3,5,7,2,6,1]=>[5,2,3,6,7,1,4]=>000101
[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[6,7,5,2,1,4,3]=>101101
[6,7,3,4,1,5,2]=>[5,4,7,3,1,6,2]=>[5,1,6,7,2,4,3]=>001101
[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[6,7,5,1,2,4,3]=>001101
[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>[6,7,1,5,2,4,3]=>001101
[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>[6,7,2,1,5,4,3]=>101101
[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>[6,7,1,2,5,4,3]=>001101
[6,7,3,5,1,2,4]=>[5,1,7,3,2,6,4]=>[5,2,1,6,7,4,3]=>101101
[6,7,3,5,1,4,2]=>[4,5,7,3,1,6,2]=>[6,7,2,5,1,4,3]=>001101
[6,7,3,5,2,1,4]=>[2,5,7,3,1,6,4]=>[5,1,2,6,7,4,3]=>001101
[6,7,3,5,2,4,1]=>[4,5,7,3,2,6,1]=>[5,2,6,7,1,4,3]=>001101
[6,7,3,5,4,1,2]=>[4,1,5,7,3,6,2]=>[5,3,6,7,2,1,4]=>100101
[6,7,3,5,4,2,1]=>[2,4,5,7,3,6,1]=>[5,3,6,7,1,2,4]=>000101
[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[6,7,5,3,2,1,4]=>110101
[6,7,4,1,2,5,3]=>[5,1,4,7,2,6,3]=>[5,2,1,6,7,3,4]=>100101
[6,7,4,1,3,2,5]=>[3,4,1,7,2,6,5]=>[3,1,6,7,5,2,4]=>010101
[6,7,4,1,3,5,2]=>[5,4,1,7,3,6,2]=>[5,3,1,6,7,2,4]=>010101
[6,7,4,1,5,2,3]=>[5,4,1,7,2,6,3]=>[6,7,3,1,5,2,4]=>010101
[6,7,4,1,5,3,2]=>[3,5,4,7,1,6,2]=>[6,7,2,5,1,3,4]=>000101
[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[6,7,5,3,1,2,4]=>010101
[6,7,4,2,1,5,3]=>[2,5,4,7,1,6,3]=>[5,1,2,6,7,3,4]=>000101
[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[6,7,5,1,3,2,4]=>010101
[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>[6,7,1,5,3,2,4]=>010101
[6,7,4,2,5,1,3]=>[5,4,2,7,1,6,3]=>[5,1,6,7,3,2,4]=>010101
[6,7,4,2,5,3,1]=>[3,5,4,7,2,6,1]=>[5,2,6,7,1,3,4]=>000101
[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[6,7,5,2,1,3,4]=>100101
[6,7,4,3,1,5,2]=>[5,3,4,7,1,6,2]=>[5,1,6,7,2,3,4]=>000101
[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[6,7,5,1,2,3,4]=>000101
[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>[6,7,1,5,2,3,4]=>000101
[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>[6,7,2,1,5,3,4]=>100101
[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>[6,7,1,2,5,3,4]=>000101
[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[6,7,3,2,1,5,4]=>110101
[6,7,4,5,1,3,2]=>[3,5,1,7,4,6,2]=>[3,1,6,7,2,5,4]=>010101
[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>[6,7,3,1,2,5,4]=>010101
[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>[6,7,1,3,2,5,4]=>010101
[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>[6,7,2,1,3,5,4]=>100101
[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>[6,7,1,2,3,5,4]=>000101
[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[6,7,4,3,2,1,5]=>111001
[6,7,5,1,2,4,3]=>[4,1,5,2,7,6,3]=>[4,2,1,6,7,3,5]=>101001
[6,7,5,1,3,2,4]=>[3,5,1,2,7,6,4]=>[3,1,6,7,4,2,5]=>011001
[6,7,5,1,3,4,2]=>[4,5,1,3,7,6,2]=>[4,3,1,6,7,2,5]=>011001
[6,7,5,1,4,2,3]=>[4,5,1,2,7,6,3]=>[6,7,3,1,4,2,5]=>011001
[6,7,5,1,4,3,2]=>[3,4,5,1,7,6,2]=>[6,7,2,4,1,3,5]=>001001
[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[6,7,4,3,1,2,5]=>011001
[6,7,5,2,1,4,3]=>[2,4,5,1,7,6,3]=>[4,1,2,6,7,3,5]=>001001
[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[6,7,4,1,3,2,5]=>011001
[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>[6,7,1,4,3,2,5]=>011001
[6,7,5,2,4,1,3]=>[4,5,2,1,7,6,3]=>[4,1,6,7,3,2,5]=>011001
[6,7,5,2,4,3,1]=>[3,4,5,2,7,6,1]=>[4,2,6,7,1,3,5]=>001001
[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[6,7,4,2,1,3,5]=>101001
[6,7,5,3,1,4,2]=>[4,3,5,1,7,6,2]=>[4,1,6,7,2,3,5]=>001001
[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[6,7,4,1,2,3,5]=>001001
[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>[6,7,1,4,2,3,5]=>001001
[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>[6,7,2,1,4,3,5]=>101001
[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>[6,7,1,2,4,3,5]=>001001
[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>[6,7,3,2,1,4,5]=>110001
[6,7,5,4,1,3,2]=>[3,4,1,5,7,6,2]=>[3,1,6,7,2,4,5]=>010001
[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>[6,7,3,1,2,4,5]=>010001
[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>[6,7,1,3,2,4,5]=>010001
[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>[6,7,2,1,3,4,5]=>100001
[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[6,7,1,2,3,4,5]=>000001
[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,6,5,4,3,2,1]=>111111
[7,1,2,3,4,6,5]=>[6,1,2,3,7,4,5]=>[6,4,3,2,1,7,5]=>111011
[7,1,2,3,5,4,6]=>[5,1,2,7,3,4,6]=>[5,3,2,1,7,6,4]=>110111
[7,1,2,3,5,6,4]=>[6,1,2,7,3,5,4]=>[6,5,3,2,1,7,4]=>110111
[7,1,2,3,6,4,5]=>[6,1,2,7,3,4,5]=>[7,5,3,2,1,6,4]=>110111
[7,1,2,3,6,5,4]=>[5,1,2,6,7,3,4]=>[7,4,6,3,2,1,5]=>110011
[7,1,2,4,3,5,6]=>[4,1,7,2,3,5,6]=>[4,2,1,7,6,5,3]=>101111
[7,1,2,4,3,6,5]=>[4,1,6,2,7,3,5]=>[4,2,1,6,3,7,5]=>101011
[7,1,2,4,5,3,6]=>[5,1,7,2,4,3,6]=>[5,4,2,1,7,6,3]=>101111
[7,1,2,4,5,6,3]=>[6,1,7,2,4,5,3]=>[6,5,4,2,1,7,3]=>101111
[7,1,2,4,6,3,5]=>[6,1,7,2,4,3,5]=>[7,5,4,2,1,6,3]=>101111
[7,1,2,4,6,5,3]=>[5,1,6,2,7,4,3]=>[7,3,6,4,2,1,5]=>101011
[7,1,2,5,3,4,6]=>[5,1,7,2,3,4,6]=>[7,6,4,2,1,5,3]=>101111
[7,1,2,5,3,6,4]=>[6,1,5,7,2,3,4]=>[6,3,5,2,1,7,4]=>100111
[7,1,2,5,4,3,6]=>[4,1,5,7,2,3,6]=>[7,6,3,5,2,1,4]=>100111
[7,1,2,5,4,6,3]=>[6,1,5,7,2,4,3]=>[7,3,5,2,1,6,4]=>100111
[7,1,2,5,6,3,4]=>[6,1,7,2,3,5,4]=>[7,4,2,1,6,5,3]=>101111
[7,1,2,5,6,4,3]=>[4,1,6,7,2,5,3]=>[7,3,6,5,2,1,4]=>100111
[7,1,2,6,3,4,5]=>[6,1,7,2,3,4,5]=>[6,4,2,1,7,5,3]=>101111
[7,1,2,6,3,5,4]=>[5,1,6,7,2,3,4]=>[5,2,1,6,3,7,4]=>100111
[7,1,2,6,4,3,5]=>[4,1,6,7,2,3,5]=>[6,3,7,5,2,1,4]=>100111
[7,1,2,6,4,5,3]=>[5,1,6,7,2,4,3]=>[5,2,1,7,3,6,4]=>100111
[7,1,2,6,5,3,4]=>[5,1,6,2,7,3,4]=>[6,3,7,4,2,1,5]=>101011
[7,1,2,6,5,4,3]=>[4,1,5,6,7,2,3]=>[6,2,1,4,7,3,5]=>100011
[7,1,3,2,4,5,6]=>[3,7,1,2,4,5,6]=>[3,1,7,6,5,4,2]=>011111
[7,1,3,2,4,6,5]=>[3,6,1,2,7,4,5]=>[3,1,6,4,2,7,5]=>011011
[7,1,3,2,5,4,6]=>[3,5,1,7,2,4,6]=>[3,1,5,2,7,6,4]=>010111
[7,1,3,2,5,6,4]=>[3,6,1,7,2,5,4]=>[3,1,6,5,2,7,4]=>010111
[7,1,3,2,6,4,5]=>[3,6,1,7,2,4,5]=>[3,1,7,5,2,6,4]=>010111
[7,1,3,2,6,5,4]=>[3,5,1,6,7,2,4]=>[3,1,7,4,6,2,5]=>010011
[7,1,3,4,2,5,6]=>[4,7,1,3,2,5,6]=>[4,3,1,7,6,5,2]=>011111
[7,1,3,4,2,6,5]=>[4,6,1,3,7,2,5]=>[4,3,1,6,2,7,5]=>011011
[7,1,3,4,5,2,6]=>[5,7,1,3,4,2,6]=>[5,4,3,1,7,6,2]=>011111
[7,1,3,4,5,6,2]=>[6,7,1,3,4,5,2]=>[6,5,4,3,1,7,2]=>011111
[7,1,3,4,6,2,5]=>[6,7,1,3,4,2,5]=>[7,5,4,3,1,6,2]=>011111
[7,1,3,4,6,5,2]=>[5,6,1,3,7,4,2]=>[7,2,6,4,3,1,5]=>011011
[7,1,3,5,2,4,6]=>[5,7,1,3,2,4,6]=>[7,6,4,3,1,5,2]=>011111
[7,1,3,5,2,6,4]=>[6,5,1,7,3,2,4]=>[6,2,5,3,1,7,4]=>010111
[7,1,3,5,4,2,6]=>[4,5,1,7,3,2,6]=>[7,6,2,5,3,1,4]=>010111
[7,1,3,5,4,6,2]=>[6,5,1,7,3,4,2]=>[7,2,5,3,1,6,4]=>010111
[7,1,3,5,6,2,4]=>[6,7,1,3,2,5,4]=>[7,4,3,1,6,5,2]=>011111
[7,1,3,5,6,4,2]=>[4,6,1,7,3,5,2]=>[7,2,6,5,3,1,4]=>010111
[7,1,3,6,2,4,5]=>[6,7,1,3,2,4,5]=>[6,4,3,1,7,5,2]=>011111
[7,1,3,6,2,5,4]=>[5,6,1,7,3,2,4]=>[5,3,1,6,2,7,4]=>010111
[7,1,3,6,4,2,5]=>[4,6,1,7,3,2,5]=>[6,2,7,5,3,1,4]=>010111
[7,1,3,6,4,5,2]=>[5,6,1,7,3,4,2]=>[5,3,1,7,2,6,4]=>010111
[7,1,3,6,5,2,4]=>[5,6,1,3,7,2,4]=>[6,2,7,4,3,1,5]=>011011
[7,1,3,6,5,4,2]=>[4,5,1,6,7,3,2]=>[6,3,1,4,7,2,5]=>010011
[7,1,4,2,3,5,6]=>[4,7,1,2,3,5,6]=>[7,6,5,3,1,4,2]=>011111
[7,1,4,2,3,6,5]=>[4,6,1,2,7,3,5]=>[6,3,1,4,2,7,5]=>011011
[7,1,4,2,5,3,6]=>[5,4,7,1,2,3,6]=>[5,2,4,1,7,6,3]=>001111
[7,1,4,2,5,6,3]=>[6,4,7,1,2,5,3]=>[6,5,2,4,1,7,3]=>001111
[7,1,4,2,6,3,5]=>[6,4,7,1,2,3,5]=>[7,5,2,4,1,6,3]=>001111
[7,1,4,2,6,5,3]=>[5,4,6,1,7,2,3]=>[7,3,6,2,4,1,5]=>001011
[7,1,4,3,2,5,6]=>[3,4,7,1,2,5,6]=>[7,6,5,2,4,1,3]=>001111
[7,1,4,3,2,6,5]=>[3,4,6,1,7,2,5]=>[6,2,4,1,3,7,5]=>001011
[7,1,4,3,5,2,6]=>[5,4,7,1,3,2,6]=>[7,6,2,4,1,5,3]=>001111
[7,1,4,3,5,6,2]=>[6,4,7,1,3,5,2]=>[7,2,4,1,6,5,3]=>001111
[7,1,4,3,6,2,5]=>[6,4,7,1,3,2,5]=>[6,2,4,1,7,5,3]=>001111
[7,1,4,3,6,5,2]=>[5,4,6,1,7,3,2]=>[6,3,7,2,4,1,5]=>001011
[7,1,4,5,2,3,6]=>[5,7,1,2,4,3,6]=>[7,6,3,1,5,4,2]=>011111
[7,1,4,5,2,6,3]=>[6,5,7,1,4,2,3]=>[6,2,5,4,1,7,3]=>001111
[7,1,4,5,3,2,6]=>[3,5,7,1,4,2,6]=>[7,6,2,5,4,1,3]=>001111
[7,1,4,5,3,6,2]=>[6,5,7,1,4,3,2]=>[7,2,5,4,1,6,3]=>001111
[7,1,4,5,6,2,3]=>[6,7,1,2,4,5,3]=>[7,3,1,6,5,4,2]=>011111
[7,1,4,5,6,3,2]=>[3,6,7,1,4,5,2]=>[7,2,6,5,4,1,3]=>001111
[7,1,4,6,2,3,5]=>[6,7,1,2,4,3,5]=>[6,3,1,7,5,4,2]=>011111
[7,1,4,6,2,5,3]=>[5,6,7,1,4,2,3]=>[5,4,1,6,2,7,3]=>001111
[7,1,4,6,3,2,5]=>[3,6,7,1,4,2,5]=>[6,2,7,5,4,1,3]=>001111
[7,1,4,6,3,5,2]=>[5,6,7,1,4,3,2]=>[5,4,1,7,2,6,3]=>001111
[7,1,4,6,5,2,3]=>[5,6,1,2,7,4,3]=>[6,4,2,7,3,1,5]=>011011
[7,1,4,6,5,3,2]=>[3,5,6,1,7,4,2]=>[6,4,1,3,7,2,5]=>001011
[7,1,5,2,3,4,6]=>[5,7,1,2,3,4,6]=>[5,3,1,7,6,4,2]=>011111
[7,1,5,2,3,6,4]=>[6,5,1,7,2,3,4]=>[5,2,6,3,1,7,4]=>010111
[7,1,5,2,4,3,6]=>[4,5,7,1,2,3,6]=>[4,1,5,2,7,6,3]=>001111
[7,1,5,2,4,6,3]=>[6,5,7,1,2,4,3]=>[5,2,6,4,1,7,3]=>001111
[7,1,5,2,6,3,4]=>[6,5,7,1,2,3,4]=>[5,2,7,4,1,6,3]=>001111
[7,1,5,2,6,4,3]=>[4,6,5,7,1,2,3]=>[6,2,7,3,5,1,4]=>000111
[7,1,5,3,2,4,6]=>[3,5,7,1,2,4,6]=>[5,2,7,6,4,1,3]=>001111
[7,1,5,3,2,6,4]=>[3,6,5,7,1,2,4]=>[5,1,3,6,2,7,4]=>000111
[7,1,5,3,4,2,6]=>[4,5,7,1,3,2,6]=>[4,1,7,6,2,5,3]=>001111
[7,1,5,3,4,6,2]=>[6,5,7,1,3,4,2]=>[6,4,1,7,2,5,3]=>001111
[7,1,5,3,6,2,4]=>[6,5,7,1,3,2,4]=>[7,4,1,6,2,5,3]=>001111
[7,1,5,3,6,4,2]=>[4,6,5,7,1,3,2]=>[7,2,6,3,5,1,4]=>000111
[7,1,5,4,2,3,6]=>[4,5,1,7,2,3,6]=>[5,2,7,6,3,1,4]=>010111
[7,1,5,4,2,6,3]=>[6,4,5,7,1,2,3]=>[7,3,5,1,6,2,4]=>000111
[7,1,5,4,3,2,6]=>[3,4,5,7,1,2,6]=>[5,1,3,7,6,2,4]=>000111
[7,1,5,4,3,6,2]=>[6,4,5,7,1,3,2]=>[6,3,5,1,7,2,4]=>000111
[7,1,5,4,6,2,3]=>[6,5,1,7,2,4,3]=>[5,2,7,3,1,6,4]=>010111
[7,1,5,4,6,3,2]=>[3,6,5,7,1,4,2]=>[5,1,3,7,2,6,4]=>000111
[7,1,5,6,2,3,4]=>[6,7,1,2,3,5,4]=>[6,5,3,1,7,4,2]=>011111
[7,1,5,6,2,4,3]=>[4,6,7,1,2,5,3]=>[4,1,6,5,2,7,3]=>001111
[7,1,5,6,3,2,4]=>[3,6,7,1,2,5,4]=>[6,5,2,7,4,1,3]=>001111
[7,1,5,6,3,4,2]=>[4,6,7,1,3,5,2]=>[4,1,7,2,6,5,3]=>001111
[7,1,5,6,4,2,3]=>[4,6,1,7,2,5,3]=>[6,5,2,7,3,1,4]=>010111
[7,1,5,6,4,3,2]=>[3,4,6,7,1,5,2]=>[6,5,1,3,7,2,4]=>000111
[7,1,6,2,3,4,5]=>[6,7,1,2,3,4,5]=>[7,5,3,1,6,4,2]=>011111
[7,1,6,2,3,5,4]=>[5,6,1,7,2,3,4]=>[6,3,1,5,2,7,4]=>010111
[7,1,6,2,4,3,5]=>[4,6,7,1,2,3,5]=>[4,1,7,5,2,6,3]=>001111
[7,1,6,2,4,5,3]=>[5,6,7,1,2,4,3]=>[6,4,1,5,2,7,3]=>001111
[7,1,6,2,5,3,4]=>[5,6,7,1,2,3,4]=>[7,4,1,5,2,6,3]=>001111
[7,1,6,2,5,4,3]=>[4,5,6,7,1,2,3]=>[7,3,6,2,5,1,4]=>000111
[7,1,6,3,2,4,5]=>[3,6,7,1,2,4,5]=>[7,5,2,6,4,1,3]=>001111
[7,1,6,3,2,5,4]=>[3,5,6,7,1,2,4]=>[6,2,5,1,3,7,4]=>000111
[7,1,6,3,4,2,5]=>[4,6,7,1,3,2,5]=>[4,1,6,2,7,5,3]=>001111
[7,1,6,3,4,5,2]=>[5,6,7,1,3,4,2]=>[7,2,6,4,1,5,3]=>001111
[7,1,6,3,5,2,4]=>[5,6,7,1,3,2,4]=>[6,2,7,4,1,5,3]=>001111
[7,1,6,3,5,4,2]=>[4,5,6,7,1,3,2]=>[6,3,7,2,5,1,4]=>000111
[7,1,6,4,2,3,5]=>[4,6,1,7,2,3,5]=>[7,5,2,6,3,1,4]=>010111
[7,1,6,4,2,5,3]=>[5,4,6,7,1,2,3]=>[5,1,7,3,6,2,4]=>000111
[7,1,6,4,3,2,5]=>[3,4,6,7,1,2,5]=>[7,5,1,3,6,2,4]=>000111
[7,1,6,4,3,5,2]=>[5,4,6,7,1,3,2]=>[5,1,6,3,7,2,4]=>000111
[7,1,6,4,5,2,3]=>[5,6,1,7,2,4,3]=>[7,3,1,5,2,6,4]=>010111
[7,1,6,4,5,3,2]=>[3,5,6,7,1,4,2]=>[7,2,5,1,3,6,4]=>000111
[7,1,6,5,2,3,4]=>[5,6,1,2,7,3,4]=>[7,4,2,6,3,1,5]=>011011
[7,1,6,5,2,4,3]=>[4,5,6,1,7,2,3]=>[4,1,7,3,6,2,5]=>001011
[7,1,6,5,3,2,4]=>[3,5,6,1,7,2,4]=>[7,4,1,3,6,2,5]=>001011
[7,1,6,5,3,4,2]=>[4,5,6,1,7,3,2]=>[4,1,6,3,7,2,5]=>001011
[7,1,6,5,4,2,3]=>[4,5,1,6,7,2,3]=>[7,3,1,4,6,2,5]=>010011
[7,1,6,5,4,3,2]=>[3,4,5,6,7,1,2]=>[7,2,4,6,1,3,5]=>000011
[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[7,6,5,4,3,1,2]=>011111
[7,2,1,3,4,6,5]=>[2,6,1,3,7,4,5]=>[6,4,3,1,2,7,5]=>011011
[7,2,1,3,5,4,6]=>[2,5,1,7,3,4,6]=>[5,3,1,2,7,6,4]=>010111
[7,2,1,3,5,6,4]=>[2,6,1,7,3,5,4]=>[6,5,3,1,2,7,4]=>010111
[7,2,1,3,6,4,5]=>[2,6,1,7,3,4,5]=>[7,5,3,1,2,6,4]=>010111
[7,2,1,3,6,5,4]=>[2,5,1,6,7,3,4]=>[7,4,6,3,1,2,5]=>010011
[7,2,1,4,3,5,6]=>[2,4,7,1,3,5,6]=>[4,1,2,7,6,5,3]=>001111
[7,2,1,4,3,6,5]=>[2,4,6,1,7,3,5]=>[4,1,2,6,3,7,5]=>001011
[7,2,1,4,5,3,6]=>[2,5,7,1,4,3,6]=>[5,4,1,2,7,6,3]=>001111
[7,2,1,4,5,6,3]=>[2,6,7,1,4,5,3]=>[6,5,4,1,2,7,3]=>001111
[7,2,1,4,6,3,5]=>[2,6,7,1,4,3,5]=>[7,5,4,1,2,6,3]=>001111
[7,2,1,4,6,5,3]=>[2,5,6,1,7,4,3]=>[7,3,6,4,1,2,5]=>001011
[7,2,1,5,3,4,6]=>[2,5,7,1,3,4,6]=>[7,6,4,1,2,5,3]=>001111
[7,2,1,5,3,6,4]=>[2,6,5,7,1,3,4]=>[6,3,5,1,2,7,4]=>000111
[7,2,1,5,4,3,6]=>[2,4,5,7,1,3,6]=>[7,6,3,5,1,2,4]=>000111
[7,2,1,5,4,6,3]=>[2,6,5,7,1,4,3]=>[7,3,5,1,2,6,4]=>000111
[7,2,1,5,6,3,4]=>[2,6,7,1,3,5,4]=>[7,4,1,2,6,5,3]=>001111
[7,2,1,5,6,4,3]=>[2,4,6,7,1,5,3]=>[7,3,6,5,1,2,4]=>000111
[7,2,1,6,3,4,5]=>[2,6,7,1,3,4,5]=>[6,4,1,2,7,5,3]=>001111
[7,2,1,6,3,5,4]=>[2,5,6,7,1,3,4]=>[5,1,2,6,3,7,4]=>000111
[7,2,1,6,4,3,5]=>[2,4,6,7,1,3,5]=>[6,3,7,5,1,2,4]=>000111
[7,2,1,6,4,5,3]=>[2,5,6,7,1,4,3]=>[5,1,2,7,3,6,4]=>000111
[7,2,1,6,5,3,4]=>[2,5,6,1,7,3,4]=>[6,3,7,4,1,2,5]=>001011
[7,2,1,6,5,4,3]=>[2,4,5,6,7,1,3]=>[6,1,2,4,7,3,5]=>000011
[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[7,6,5,4,1,3,2]=>011111
[7,2,3,1,4,6,5]=>[3,6,2,1,7,4,5]=>[6,4,1,3,2,7,5]=>011011
[7,2,3,1,5,4,6]=>[3,5,2,7,1,4,6]=>[5,1,3,2,7,6,4]=>010111
[7,2,3,1,5,6,4]=>[3,6,2,7,1,5,4]=>[6,5,1,3,2,7,4]=>010111
[7,2,3,1,6,4,5]=>[3,6,2,7,1,4,5]=>[7,5,1,3,2,6,4]=>010111
[7,2,3,1,6,5,4]=>[3,5,2,6,7,1,4]=>[7,4,6,1,3,2,5]=>010011
[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[7,6,5,1,4,3,2]=>011111
[7,2,3,4,1,6,5]=>[4,6,2,3,7,1,5]=>[6,1,4,3,2,7,5]=>011011
[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[7,6,1,5,4,3,2]=>011111
[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7,1,6,5,4,3,2]=>011111
[7,2,3,4,6,1,5]=>[6,7,2,3,4,1,5]=>[6,1,7,5,4,3,2]=>011111
[7,2,3,4,6,5,1]=>[5,6,2,3,7,4,1]=>[6,4,3,2,7,1,5]=>011011
[7,2,3,5,1,4,6]=>[5,7,2,3,1,4,6]=>[5,1,7,6,4,3,2]=>011111
[7,2,3,5,1,6,4]=>[6,5,2,7,3,1,4]=>[5,3,2,6,1,7,4]=>010111
[7,2,3,5,4,1,6]=>[4,5,2,7,3,1,6]=>[5,3,2,7,6,1,4]=>010111
[7,2,3,5,4,6,1]=>[6,5,2,7,3,4,1]=>[5,3,2,7,1,6,4]=>010111
[7,2,3,5,6,1,4]=>[6,7,2,3,1,5,4]=>[6,5,1,7,4,3,2]=>011111
[7,2,3,5,6,4,1]=>[4,6,2,7,3,5,1]=>[6,5,3,2,7,1,4]=>010111
[7,2,3,6,1,4,5]=>[6,7,2,3,1,4,5]=>[7,5,1,6,4,3,2]=>011111
[7,2,3,6,1,5,4]=>[5,6,2,7,3,1,4]=>[6,1,5,3,2,7,4]=>010111
[7,2,3,6,4,1,5]=>[4,6,2,7,3,1,5]=>[7,5,3,2,6,1,4]=>010111
[7,2,3,6,4,5,1]=>[5,6,2,7,3,4,1]=>[7,1,5,3,2,6,4]=>010111
[7,2,3,6,5,1,4]=>[5,6,2,3,7,1,4]=>[7,4,3,2,6,1,5]=>011011
[7,2,3,6,5,4,1]=>[4,5,2,6,7,3,1]=>[7,1,4,6,3,2,5]=>010011
[7,2,4,1,3,5,6]=>[4,7,2,1,3,5,6]=>[4,1,7,6,5,3,2]=>011111
[7,2,4,1,3,6,5]=>[4,6,2,1,7,3,5]=>[4,1,6,3,2,7,5]=>011011
[7,2,4,1,5,3,6]=>[5,4,7,2,1,3,6]=>[4,2,5,1,7,6,3]=>001111
[7,2,4,1,5,6,3]=>[6,4,7,2,1,5,3]=>[4,2,6,5,1,7,3]=>001111
[7,2,4,1,6,3,5]=>[6,4,7,2,1,3,5]=>[4,2,7,5,1,6,3]=>001111
[7,2,4,1,6,5,3]=>[5,4,6,2,7,1,3]=>[4,2,7,3,6,1,5]=>001011
[7,2,4,3,1,5,6]=>[3,4,7,2,1,5,6]=>[4,2,7,6,5,1,3]=>001111
[7,2,4,3,1,6,5]=>[3,4,6,2,7,1,5]=>[4,2,6,1,3,7,5]=>001011
[7,2,4,3,5,1,6]=>[5,4,7,2,3,1,6]=>[4,2,7,6,1,5,3]=>001111
[7,2,4,3,5,6,1]=>[6,4,7,2,3,5,1]=>[4,2,7,1,6,5,3]=>001111
[7,2,4,3,6,1,5]=>[6,4,7,2,3,1,5]=>[4,2,6,1,7,5,3]=>001111
[7,2,4,3,6,5,1]=>[5,4,6,2,7,3,1]=>[4,2,6,3,7,1,5]=>001011
[7,2,4,5,1,3,6]=>[5,7,2,1,4,3,6]=>[5,4,1,7,6,3,2]=>011111
[7,2,4,5,1,6,3]=>[6,5,7,2,4,1,3]=>[5,4,2,6,1,7,3]=>001111
[7,2,4,5,3,1,6]=>[3,5,7,2,4,1,6]=>[5,4,2,7,6,1,3]=>001111
[7,2,4,5,3,6,1]=>[6,5,7,2,4,3,1]=>[5,4,2,7,1,6,3]=>001111
[7,2,4,5,6,1,3]=>[6,7,2,1,4,5,3]=>[6,5,4,1,7,3,2]=>011111
[7,2,4,5,6,3,1]=>[3,6,7,2,4,5,1]=>[6,5,4,2,7,1,3]=>001111
[7,2,4,6,1,3,5]=>[6,7,2,1,4,3,5]=>[7,5,4,1,6,3,2]=>011111
[7,2,4,6,1,5,3]=>[5,6,7,2,4,1,3]=>[6,1,5,4,2,7,3]=>001111
[7,2,4,6,3,1,5]=>[3,6,7,2,4,1,5]=>[7,5,4,2,6,1,3]=>001111
[7,2,4,6,3,5,1]=>[5,6,7,2,4,3,1]=>[7,1,5,4,2,6,3]=>001111
[7,2,4,6,5,1,3]=>[5,6,2,1,7,4,3]=>[7,3,2,6,4,1,5]=>011011
[7,2,4,6,5,3,1]=>[3,5,6,2,7,4,1]=>[7,1,3,6,4,2,5]=>001011
[7,2,5,1,3,4,6]=>[5,7,2,1,3,4,6]=>[7,6,4,1,5,3,2]=>011111
[7,2,5,1,3,6,4]=>[6,5,2,7,1,3,4]=>[6,3,2,5,1,7,4]=>010111
[7,2,5,1,4,3,6]=>[4,5,7,2,1,3,6]=>[5,1,4,2,7,6,3]=>001111
[7,2,5,1,4,6,3]=>[6,5,7,2,1,4,3]=>[6,4,2,5,1,7,3]=>001111
[7,2,5,1,6,3,4]=>[6,5,7,2,1,3,4]=>[7,4,2,5,1,6,3]=>001111
[7,2,5,1,6,4,3]=>[4,6,5,7,2,1,3]=>[7,3,5,2,6,1,4]=>000111
[7,2,5,3,1,4,6]=>[3,5,7,2,1,4,6]=>[7,6,4,2,5,1,3]=>001111
[7,2,5,3,1,6,4]=>[3,6,5,7,2,1,4]=>[6,1,3,5,2,7,4]=>000111
[7,2,5,3,4,1,6]=>[4,5,7,2,3,1,6]=>[7,6,1,4,2,5,3]=>001111
[7,2,5,3,4,6,1]=>[6,5,7,2,3,4,1]=>[7,1,6,4,2,5,3]=>001111
[7,2,5,3,6,1,4]=>[6,5,7,2,3,1,4]=>[6,1,7,4,2,5,3]=>001111
[7,2,5,3,6,4,1]=>[4,6,5,7,2,3,1]=>[6,3,5,2,7,1,4]=>000111
[7,2,5,4,1,3,6]=>[4,5,2,7,1,3,6]=>[7,6,3,2,5,1,4]=>010111
[7,2,5,4,1,6,3]=>[6,4,5,7,2,1,3]=>[6,1,7,3,5,2,4]=>000111
[7,2,5,4,3,1,6]=>[3,4,5,7,2,1,6]=>[7,6,1,3,5,2,4]=>000111
[7,2,5,4,3,6,1]=>[6,4,5,7,2,3,1]=>[7,1,6,3,5,2,4]=>000111
[7,2,5,4,6,1,3]=>[6,5,2,7,1,4,3]=>[7,3,2,5,1,6,4]=>010111
[7,2,5,4,6,3,1]=>[3,6,5,7,2,4,1]=>[7,1,3,5,2,6,4]=>000111
[7,2,5,6,1,3,4]=>[6,7,2,1,3,5,4]=>[7,4,1,6,5,3,2]=>011111
[7,2,5,6,1,4,3]=>[4,6,7,2,1,5,3]=>[6,5,1,4,2,7,3]=>001111
[7,2,5,6,3,1,4]=>[3,6,7,2,1,5,4]=>[7,4,2,6,5,1,3]=>001111
[7,2,5,6,3,4,1]=>[4,6,7,2,3,5,1]=>[7,1,4,2,6,5,3]=>001111
[7,2,5,6,4,1,3]=>[4,6,2,7,1,5,3]=>[7,3,2,6,5,1,4]=>010111
[7,2,5,6,4,3,1]=>[3,4,6,7,2,5,1]=>[7,1,3,6,5,2,4]=>000111
[7,2,6,1,3,4,5]=>[6,7,2,1,3,4,5]=>[6,4,1,7,5,3,2]=>011111
[7,2,6,1,3,5,4]=>[5,6,2,7,1,3,4]=>[5,1,6,3,2,7,4]=>010111
[7,2,6,1,4,3,5]=>[4,6,7,2,1,3,5]=>[7,5,1,4,2,6,3]=>001111
[7,2,6,1,4,5,3]=>[5,6,7,2,1,4,3]=>[5,1,6,4,2,7,3]=>001111
[7,2,6,1,5,3,4]=>[5,6,7,2,1,3,4]=>[5,1,7,4,2,6,3]=>001111
[7,2,6,1,5,4,3]=>[4,5,6,7,2,1,3]=>[5,2,7,3,6,1,4]=>000111
[7,2,6,3,1,4,5]=>[3,6,7,2,1,4,5]=>[6,4,2,7,5,1,3]=>001111
[7,2,6,3,1,5,4]=>[3,5,6,7,2,1,4]=>[5,2,6,1,3,7,4]=>000111
[7,2,6,3,4,1,5]=>[4,6,7,2,3,1,5]=>[6,1,4,2,7,5,3]=>001111
[7,2,6,3,4,5,1]=>[5,6,7,2,3,4,1]=>[6,4,2,7,1,5,3]=>001111
[7,2,6,3,5,1,4]=>[5,6,7,2,3,1,4]=>[7,4,2,6,1,5,3]=>001111
[7,2,6,3,5,4,1]=>[4,5,6,7,2,3,1]=>[5,2,6,3,7,1,4]=>000111
[7,2,6,4,1,3,5]=>[4,6,2,7,1,3,5]=>[6,3,2,7,5,1,4]=>010111
[7,2,6,4,1,5,3]=>[5,4,6,7,2,1,3]=>[7,3,6,1,5,2,4]=>000111
[7,2,6,4,3,1,5]=>[3,4,6,7,2,1,5]=>[6,1,3,7,5,2,4]=>000111
[7,2,6,4,3,5,1]=>[5,4,6,7,2,3,1]=>[6,3,7,1,5,2,4]=>000111
[7,2,6,4,5,1,3]=>[5,6,2,7,1,4,3]=>[5,1,7,3,2,6,4]=>010111
[7,2,6,4,5,3,1]=>[3,5,6,7,2,4,1]=>[5,2,7,1,3,6,4]=>000111
[7,2,6,5,1,3,4]=>[5,6,2,1,7,3,4]=>[6,3,2,7,4,1,5]=>011011
[7,2,6,5,1,4,3]=>[4,5,6,2,7,1,3]=>[7,3,6,1,4,2,5]=>001011
[7,2,6,5,3,1,4]=>[3,5,6,2,7,1,4]=>[6,1,3,7,4,2,5]=>001011
[7,2,6,5,3,4,1]=>[4,5,6,2,7,3,1]=>[6,3,7,1,4,2,5]=>001011
[7,2,6,5,4,1,3]=>[4,5,2,6,7,1,3]=>[6,1,4,7,3,2,5]=>010011
[7,2,6,5,4,3,1]=>[3,4,5,6,7,2,1]=>[6,2,4,7,1,3,5]=>000011
[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[7,6,5,4,2,1,3]=>101111
[7,3,1,2,4,6,5]=>[3,1,6,2,7,4,5]=>[6,4,2,1,3,7,5]=>101011
[7,3,1,2,5,4,6]=>[3,1,5,7,2,4,6]=>[5,2,1,3,7,6,4]=>100111
[7,3,1,2,5,6,4]=>[3,1,6,7,2,5,4]=>[6,5,2,1,3,7,4]=>100111
[7,3,1,2,6,4,5]=>[3,1,6,7,2,4,5]=>[7,5,2,1,3,6,4]=>100111
[7,3,1,2,6,5,4]=>[3,1,5,6,7,2,4]=>[7,4,6,2,1,3,5]=>100011
[7,3,1,4,2,5,6]=>[4,3,7,1,2,5,6]=>[4,1,7,6,5,2,3]=>001111
[7,3,1,4,2,6,5]=>[4,3,6,1,7,2,5]=>[4,1,6,2,3,7,5]=>001011
[7,3,1,4,5,2,6]=>[5,3,7,1,4,2,6]=>[5,4,1,7,6,2,3]=>001111
[7,3,1,4,5,6,2]=>[6,3,7,1,4,5,2]=>[6,5,4,1,7,2,3]=>001111
[7,3,1,4,6,2,5]=>[6,3,7,1,4,2,5]=>[7,5,4,1,6,2,3]=>001111
[7,3,1,4,6,5,2]=>[5,3,6,1,7,4,2]=>[7,2,3,6,4,1,5]=>001011
[7,3,1,5,2,4,6]=>[5,3,7,1,2,4,6]=>[7,6,4,1,5,2,3]=>001111
[7,3,1,5,2,6,4]=>[6,3,5,7,1,2,4]=>[6,2,3,5,1,7,4]=>000111
[7,3,1,5,4,2,6]=>[4,3,5,7,1,2,6]=>[7,6,2,3,5,1,4]=>000111
[7,3,1,5,4,6,2]=>[6,3,5,7,1,4,2]=>[7,2,3,5,1,6,4]=>000111
[7,3,1,5,6,2,4]=>[6,3,7,1,2,5,4]=>[7,4,1,6,5,2,3]=>001111
[7,3,1,5,6,4,2]=>[4,3,6,7,1,5,2]=>[7,2,3,6,5,1,4]=>000111
[7,3,1,6,2,4,5]=>[6,3,7,1,2,4,5]=>[6,4,1,7,5,2,3]=>001111
[7,3,1,6,2,5,4]=>[5,3,6,7,1,2,4]=>[5,1,6,2,3,7,4]=>000111
[7,3,1,6,4,2,5]=>[4,3,6,7,1,2,5]=>[6,2,3,7,5,1,4]=>000111
[7,3,1,6,4,5,2]=>[5,3,6,7,1,4,2]=>[5,1,7,2,3,6,4]=>000111
[7,3,1,6,5,2,4]=>[5,3,6,1,7,2,4]=>[6,2,3,7,4,1,5]=>001011
[7,3,1,6,5,4,2]=>[4,3,5,6,7,1,2]=>[6,1,4,7,2,3,5]=>000011
[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[7,6,5,4,1,2,3]=>001111
[7,3,2,1,4,6,5]=>[2,3,6,1,7,4,5]=>[6,4,1,2,3,7,5]=>001011
[7,3,2,1,5,4,6]=>[2,3,5,7,1,4,6]=>[5,1,2,3,7,6,4]=>000111
[7,3,2,1,5,6,4]=>[2,3,6,7,1,5,4]=>[6,5,1,2,3,7,4]=>000111
[7,3,2,1,6,4,5]=>[2,3,6,7,1,4,5]=>[7,5,1,2,3,6,4]=>000111
[7,3,2,1,6,5,4]=>[2,3,5,6,7,1,4]=>[7,4,6,1,2,3,5]=>000011
[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[7,6,5,1,4,2,3]=>001111
[7,3,2,4,1,6,5]=>[4,3,6,2,7,1,5]=>[6,1,4,2,3,7,5]=>001011
[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[7,6,1,5,4,2,3]=>001111
[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[7,1,6,5,4,2,3]=>001111
[7,3,2,4,6,1,5]=>[6,3,7,2,4,1,5]=>[6,1,7,5,4,2,3]=>001111
[7,3,2,4,6,5,1]=>[5,3,6,2,7,4,1]=>[6,4,2,3,7,1,5]=>001011
[7,3,2,5,1,4,6]=>[5,3,7,2,1,4,6]=>[5,1,7,6,4,2,3]=>001111
[7,3,2,5,1,6,4]=>[6,3,5,7,2,1,4]=>[5,2,3,6,1,7,4]=>000111
[7,3,2,5,4,1,6]=>[4,3,5,7,2,1,6]=>[5,2,3,7,6,1,4]=>000111
[7,3,2,5,4,6,1]=>[6,3,5,7,2,4,1]=>[5,2,3,7,1,6,4]=>000111
[7,3,2,5,6,1,4]=>[6,3,7,2,1,5,4]=>[6,5,1,7,4,2,3]=>001111
[7,3,2,5,6,4,1]=>[4,3,6,7,2,5,1]=>[6,5,2,3,7,1,4]=>000111
[7,3,2,6,1,4,5]=>[6,3,7,2,1,4,5]=>[7,5,1,6,4,2,3]=>001111
[7,3,2,6,1,5,4]=>[5,3,6,7,2,1,4]=>[6,1,5,2,3,7,4]=>000111
[7,3,2,6,4,1,5]=>[4,3,6,7,2,1,5]=>[7,5,2,3,6,1,4]=>000111
[7,3,2,6,4,5,1]=>[5,3,6,7,2,4,1]=>[7,1,5,2,3,6,4]=>000111
[7,3,2,6,5,1,4]=>[5,3,6,2,7,1,4]=>[7,4,2,3,6,1,5]=>001011
[7,3,2,6,5,4,1]=>[4,3,5,6,7,2,1]=>[7,1,4,6,2,3,5]=>000011
[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[7,6,5,2,1,4,3]=>101111
[7,3,4,1,2,6,5]=>[4,1,6,3,7,2,5]=>[6,2,1,4,3,7,5]=>101011
[7,3,4,1,5,2,6]=>[5,4,7,3,1,2,6]=>[5,1,7,6,2,4,3]=>001111
[7,3,4,1,5,6,2]=>[6,4,7,3,1,5,2]=>[6,5,1,7,2,4,3]=>001111
[7,3,4,1,6,2,5]=>[6,4,7,3,1,2,5]=>[7,5,1,6,2,4,3]=>001111
[7,3,4,1,6,5,2]=>[5,4,6,3,7,1,2]=>[7,2,4,3,6,1,5]=>001011
[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[7,6,5,1,2,4,3]=>001111
[7,3,4,2,1,6,5]=>[2,4,6,3,7,1,5]=>[6,1,2,4,3,7,5]=>001011
[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[7,6,1,5,2,4,3]=>001111
[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[7,1,6,5,2,4,3]=>001111
[7,3,4,2,6,1,5]=>[6,4,7,3,2,1,5]=>[6,1,7,5,2,4,3]=>001111
[7,3,4,2,6,5,1]=>[5,4,6,3,7,2,1]=>[6,2,4,3,7,1,5]=>001011
[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[7,6,2,1,5,4,3]=>101111
[7,3,4,5,1,6,2]=>[6,5,7,3,4,1,2]=>[6,1,7,2,5,4,3]=>001111
[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[7,6,1,2,5,4,3]=>001111
[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[7,1,6,2,5,4,3]=>001111
[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>[7,2,1,6,5,4,3]=>101111
[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[7,1,2,6,5,4,3]=>001111
[7,3,4,6,1,2,5]=>[6,1,7,3,4,2,5]=>[6,2,1,7,5,4,3]=>101111
[7,3,4,6,1,5,2]=>[5,6,7,3,4,1,2]=>[7,2,6,1,5,4,3]=>001111
[7,3,4,6,2,1,5]=>[2,6,7,3,4,1,5]=>[6,1,2,7,5,4,3]=>001111
[7,3,4,6,2,5,1]=>[5,6,7,3,4,2,1]=>[6,2,7,1,5,4,3]=>001111
[7,3,4,6,5,1,2]=>[5,1,6,3,7,4,2]=>[6,4,3,7,2,1,5]=>101011
[7,3,4,6,5,2,1]=>[2,5,6,3,7,4,1]=>[6,4,3,7,1,2,5]=>001011
[7,3,5,1,2,4,6]=>[5,1,7,3,2,4,6]=>[5,2,1,7,6,4,3]=>101111
[7,3,5,1,2,6,4]=>[6,1,5,7,3,2,4]=>[5,3,6,2,1,7,4]=>100111
[7,3,5,1,4,2,6]=>[4,5,7,3,1,2,6]=>[7,6,2,5,1,4,3]=>001111
[7,3,5,1,4,6,2]=>[6,5,7,3,1,4,2]=>[7,2,5,1,6,4,3]=>001111
[7,3,5,1,6,2,4]=>[6,5,7,3,1,2,4]=>[6,2,5,1,7,4,3]=>001111
[7,3,5,1,6,4,2]=>[4,6,5,7,3,1,2]=>[5,3,7,2,6,1,4]=>000111
[7,3,5,2,1,4,6]=>[2,5,7,3,1,4,6]=>[5,1,2,7,6,4,3]=>001111
[7,3,5,2,1,6,4]=>[2,6,5,7,3,1,4]=>[5,3,6,1,2,7,4]=>000111
[7,3,5,2,4,1,6]=>[4,5,7,3,2,1,6]=>[5,2,7,6,1,4,3]=>001111
[7,3,5,2,4,6,1]=>[6,5,7,3,2,4,1]=>[5,2,7,1,6,4,3]=>001111
[7,3,5,2,6,1,4]=>[6,5,7,3,2,1,4]=>[5,2,6,1,7,4,3]=>001111
[7,3,5,2,6,4,1]=>[4,6,5,7,3,2,1]=>[5,3,6,2,7,1,4]=>000111
[7,3,5,4,1,2,6]=>[4,1,5,7,3,2,6]=>[5,3,7,6,2,1,4]=>100111
[7,3,5,4,1,6,2]=>[6,4,5,7,3,1,2]=>[5,3,6,1,7,2,4]=>000111
[7,3,5,4,2,1,6]=>[2,4,5,7,3,1,6]=>[5,3,7,6,1,2,4]=>000111
[7,3,5,4,2,6,1]=>[6,4,5,7,3,2,1]=>[5,3,7,1,6,2,4]=>000111
[7,3,5,4,6,1,2]=>[6,1,5,7,3,4,2]=>[5,3,7,2,1,6,4]=>100111
[7,3,5,4,6,2,1]=>[2,6,5,7,3,4,1]=>[5,3,7,1,2,6,4]=>000111
[7,3,5,6,1,2,4]=>[6,1,7,3,2,5,4]=>[6,5,2,1,7,4,3]=>101111
[7,3,5,6,1,4,2]=>[4,6,7,3,1,5,2]=>[7,2,6,5,1,4,3]=>001111
[7,3,5,6,2,1,4]=>[2,6,7,3,1,5,4]=>[6,5,1,2,7,4,3]=>001111
[7,3,5,6,2,4,1]=>[4,6,7,3,2,5,1]=>[6,5,2,7,1,4,3]=>001111
[7,3,5,6,4,1,2]=>[4,1,6,7,3,5,2]=>[6,5,3,7,2,1,4]=>100111
[7,3,5,6,4,2,1]=>[2,4,6,7,3,5,1]=>[6,5,3,7,1,2,4]=>000111
[7,3,6,1,2,4,5]=>[6,1,7,3,2,4,5]=>[7,5,2,1,6,4,3]=>101111
[7,3,6,1,2,5,4]=>[5,1,6,7,3,2,4]=>[6,2,1,5,3,7,4]=>100111
[7,3,6,1,4,2,5]=>[4,6,7,3,1,2,5]=>[6,2,7,5,1,4,3]=>001111
[7,3,6,1,4,5,2]=>[5,6,7,3,1,4,2]=>[5,1,7,2,6,4,3]=>001111
[7,3,6,1,5,2,4]=>[5,6,7,3,1,2,4]=>[5,1,6,2,7,4,3]=>001111
[7,3,6,1,5,4,2]=>[4,5,6,7,3,1,2]=>[7,2,5,3,6,1,4]=>000111
[7,3,6,2,1,4,5]=>[2,6,7,3,1,4,5]=>[7,5,1,2,6,4,3]=>001111
[7,3,6,2,1,5,4]=>[2,5,6,7,3,1,4]=>[6,1,2,5,3,7,4]=>000111
[7,3,6,2,4,1,5]=>[4,6,7,3,2,1,5]=>[7,5,2,6,1,4,3]=>001111
[7,3,6,2,4,5,1]=>[5,6,7,3,2,4,1]=>[7,1,5,2,6,4,3]=>001111
[7,3,6,2,5,1,4]=>[5,6,7,3,2,1,4]=>[6,1,5,2,7,4,3]=>001111
[7,3,6,2,5,4,1]=>[4,5,6,7,3,2,1]=>[6,2,5,3,7,1,4]=>000111
[7,3,6,4,1,2,5]=>[4,1,6,7,3,2,5]=>[7,5,3,6,2,1,4]=>100111
[7,3,6,4,1,5,2]=>[5,4,6,7,3,1,2]=>[6,1,5,3,7,2,4]=>000111
[7,3,6,4,2,1,5]=>[2,4,6,7,3,1,5]=>[7,5,3,6,1,2,4]=>000111
[7,3,6,4,2,5,1]=>[5,4,6,7,3,2,1]=>[7,1,5,3,6,2,4]=>000111
[7,3,6,4,5,1,2]=>[5,1,6,7,3,4,2]=>[7,2,1,5,3,6,4]=>100111
[7,3,6,4,5,2,1]=>[2,5,6,7,3,4,1]=>[7,1,2,5,3,6,4]=>000111
[7,3,6,5,1,2,4]=>[5,1,6,3,7,2,4]=>[7,4,3,6,2,1,5]=>101011
[7,3,6,5,1,4,2]=>[4,5,6,3,7,1,2]=>[6,1,4,3,7,2,5]=>001011
[7,3,6,5,2,1,4]=>[2,5,6,3,7,1,4]=>[7,4,3,6,1,2,5]=>001011
[7,3,6,5,2,4,1]=>[4,5,6,3,7,2,1]=>[7,1,4,3,6,2,5]=>001011
[7,3,6,5,4,1,2]=>[4,1,5,6,7,3,2]=>[7,2,1,4,6,3,5]=>100011
[7,3,6,5,4,2,1]=>[2,4,5,6,7,3,1]=>[7,1,2,4,6,3,5]=>000011
[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[7,6,5,3,2,1,4]=>110111
[7,4,1,2,3,6,5]=>[4,1,2,6,7,3,5]=>[6,3,2,1,4,7,5]=>110011
[7,4,1,2,5,3,6]=>[5,1,4,7,2,3,6]=>[5,2,1,7,6,3,4]=>100111
[7,4,1,2,5,6,3]=>[6,1,4,7,2,5,3]=>[6,5,2,1,7,3,4]=>100111
[7,4,1,2,6,3,5]=>[6,1,4,7,2,3,5]=>[7,5,2,1,6,3,4]=>100111
[7,4,1,2,6,5,3]=>[5,1,4,6,7,2,3]=>[7,3,4,6,2,1,5]=>100011
[7,4,1,3,2,5,6]=>[3,4,1,7,2,5,6]=>[3,1,7,6,5,2,4]=>010111
[7,4,1,3,2,6,5]=>[3,4,1,6,7,2,5]=>[3,1,6,2,4,7,5]=>010011
[7,4,1,3,5,2,6]=>[5,4,1,7,3,2,6]=>[5,3,1,7,6,2,4]=>010111
[7,4,1,3,5,6,2]=>[6,4,1,7,3,5,2]=>[6,5,3,1,7,2,4]=>010111
[7,4,1,3,6,2,5]=>[6,4,1,7,3,2,5]=>[7,5,3,1,6,2,4]=>010111
[7,4,1,3,6,5,2]=>[5,4,1,6,7,3,2]=>[7,2,4,6,3,1,5]=>010011
[7,4,1,5,2,3,6]=>[5,4,1,7,2,3,6]=>[7,6,3,1,5,2,4]=>010111
[7,4,1,5,2,6,3]=>[6,5,4,7,1,2,3]=>[6,2,5,1,7,3,4]=>000111
[7,4,1,5,3,2,6]=>[3,5,4,7,1,2,6]=>[7,6,2,5,1,3,4]=>000111
[7,4,1,5,3,6,2]=>[6,5,4,7,1,3,2]=>[7,2,5,1,6,3,4]=>000111
[7,4,1,5,6,2,3]=>[6,4,1,7,2,5,3]=>[7,3,1,6,5,2,4]=>010111
[7,4,1,5,6,3,2]=>[3,6,4,7,1,5,2]=>[7,2,6,5,1,3,4]=>000111
[7,4,1,6,2,3,5]=>[6,4,1,7,2,3,5]=>[6,3,1,7,5,2,4]=>010111
[7,4,1,6,2,5,3]=>[5,6,4,7,1,2,3]=>[5,1,6,2,7,3,4]=>000111
[7,4,1,6,3,2,5]=>[3,6,4,7,1,2,5]=>[6,2,7,5,1,3,4]=>000111
[7,4,1,6,3,5,2]=>[5,6,4,7,1,3,2]=>[5,1,7,2,6,3,4]=>000111
[7,4,1,6,5,2,3]=>[5,4,1,6,7,2,3]=>[6,2,4,7,3,1,5]=>010011
[7,4,1,6,5,3,2]=>[3,5,4,6,7,1,2]=>[6,1,3,4,7,2,5]=>000011
[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[7,6,5,3,1,2,4]=>010111
[7,4,2,1,3,6,5]=>[2,4,1,6,7,3,5]=>[6,3,1,2,4,7,5]=>010011
[7,4,2,1,5,3,6]=>[2,5,4,7,1,3,6]=>[5,1,2,7,6,3,4]=>000111
[7,4,2,1,5,6,3]=>[2,6,4,7,1,5,3]=>[6,5,1,2,7,3,4]=>000111
[7,4,2,1,6,3,5]=>[2,6,4,7,1,3,5]=>[7,5,1,2,6,3,4]=>000111
[7,4,2,1,6,5,3]=>[2,5,4,6,7,1,3]=>[7,3,4,6,1,2,5]=>000011
[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[7,6,5,1,3,2,4]=>010111
[7,4,2,3,1,6,5]=>[3,4,2,6,7,1,5]=>[6,1,3,2,4,7,5]=>010011
[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[7,6,1,5,3,2,4]=>010111
[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>[7,1,6,5,3,2,4]=>010111
[7,4,2,3,6,1,5]=>[6,4,2,7,3,1,5]=>[6,1,7,5,3,2,4]=>010111
[7,4,2,3,6,5,1]=>[5,4,2,6,7,3,1]=>[6,3,2,4,7,1,5]=>010011
[7,4,2,5,1,3,6]=>[5,4,2,7,1,3,6]=>[5,1,7,6,3,2,4]=>010111
[7,4,2,5,1,6,3]=>[6,5,4,7,2,1,3]=>[5,2,6,1,7,3,4]=>000111
[7,4,2,5,3,1,6]=>[3,5,4,7,2,1,6]=>[5,2,7,6,1,3,4]=>000111
[7,4,2,5,3,6,1]=>[6,5,4,7,2,3,1]=>[5,2,7,1,6,3,4]=>000111
[7,4,2,5,6,1,3]=>[6,4,2,7,1,5,3]=>[6,5,1,7,3,2,4]=>010111
[7,4,2,5,6,3,1]=>[3,6,4,7,2,5,1]=>[6,5,2,7,1,3,4]=>000111
[7,4,2,6,1,3,5]=>[6,4,2,7,1,3,5]=>[7,5,1,6,3,2,4]=>010111
[7,4,2,6,1,5,3]=>[5,6,4,7,2,1,3]=>[6,1,5,2,7,3,4]=>000111
[7,4,2,6,3,1,5]=>[3,6,4,7,2,1,5]=>[7,5,2,6,1,3,4]=>000111
[7,4,2,6,3,5,1]=>[5,6,4,7,2,3,1]=>[7,1,5,2,6,3,4]=>000111
[7,4,2,6,5,1,3]=>[5,4,2,6,7,1,3]=>[7,3,2,4,6,1,5]=>010011
[7,4,2,6,5,3,1]=>[3,5,4,6,7,2,1]=>[7,1,3,4,6,2,5]=>000011
[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[7,6,5,2,1,3,4]=>100111
[7,4,3,1,2,6,5]=>[3,1,4,6,7,2,5]=>[6,2,1,3,4,7,5]=>100011
[7,4,3,1,5,2,6]=>[5,3,4,7,1,2,6]=>[5,1,7,6,2,3,4]=>000111
[7,4,3,1,5,6,2]=>[6,3,4,7,1,5,2]=>[6,5,1,7,2,3,4]=>000111
[7,4,3,1,6,2,5]=>[6,3,4,7,1,2,5]=>[7,5,1,6,2,3,4]=>000111
[7,4,3,1,6,5,2]=>[5,3,4,6,7,1,2]=>[7,2,3,4,6,1,5]=>000011
[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[7,6,5,1,2,3,4]=>000111
[7,4,3,2,1,6,5]=>[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>000011
[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[7,6,1,5,2,3,4]=>000111
[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[7,1,6,5,2,3,4]=>000111
[7,4,3,2,6,1,5]=>[6,3,4,7,2,1,5]=>[6,1,7,5,2,3,4]=>000111
[7,4,3,2,6,5,1]=>[5,3,4,6,7,2,1]=>[6,2,3,4,7,1,5]=>000011
[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[7,6,2,1,5,3,4]=>100111
[7,4,3,5,1,6,2]=>[6,5,4,7,3,1,2]=>[6,1,7,2,5,3,4]=>000111
[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[7,6,1,2,5,3,4]=>000111
[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[7,1,6,2,5,3,4]=>000111
[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>[7,2,1,6,5,3,4]=>100111
[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[7,1,2,6,5,3,4]=>000111
[7,4,3,6,1,2,5]=>[6,1,4,7,3,2,5]=>[6,2,1,7,5,3,4]=>100111
[7,4,3,6,1,5,2]=>[5,6,4,7,3,1,2]=>[7,2,6,1,5,3,4]=>000111
[7,4,3,6,2,1,5]=>[2,6,4,7,3,1,5]=>[6,1,2,7,5,3,4]=>000111
[7,4,3,6,2,5,1]=>[5,6,4,7,3,2,1]=>[6,2,7,1,5,3,4]=>000111
[7,4,3,6,5,1,2]=>[5,1,4,6,7,3,2]=>[6,3,4,7,2,1,5]=>100011
[7,4,3,6,5,2,1]=>[2,5,4,6,7,3,1]=>[6,3,4,7,1,2,5]=>000011
[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[7,6,3,2,1,5,4]=>110111
[7,4,5,1,2,6,3]=>[6,1,5,7,4,2,3]=>[6,2,1,7,3,5,4]=>100111
[7,4,5,1,3,2,6]=>[3,5,1,7,4,2,6]=>[3,1,7,6,2,5,4]=>010111
[7,4,5,1,3,6,2]=>[6,5,1,7,4,3,2]=>[6,3,1,7,2,5,4]=>010111
[7,4,5,1,6,2,3]=>[6,5,1,7,4,2,3]=>[7,3,1,6,2,5,4]=>010111
[7,4,5,1,6,3,2]=>[3,6,5,7,4,1,2]=>[7,2,6,1,3,5,4]=>000111
[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[7,6,3,1,2,5,4]=>010111
[7,4,5,2,1,6,3]=>[2,6,5,7,4,1,3]=>[6,1,2,7,3,5,4]=>000111
[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>[7,6,1,3,2,5,4]=>010111
[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>[7,1,6,3,2,5,4]=>010111
[7,4,5,2,6,1,3]=>[6,5,2,7,4,1,3]=>[6,1,7,3,2,5,4]=>010111
[7,4,5,2,6,3,1]=>[3,6,5,7,4,2,1]=>[6,2,7,1,3,5,4]=>000111
[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[7,6,2,1,3,5,4]=>100111
[7,4,5,3,1,6,2]=>[6,3,5,7,4,1,2]=>[6,1,7,2,3,5,4]=>000111
[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[7,6,1,2,3,5,4]=>000111
[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[7,1,6,2,3,5,4]=>000111
[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>[7,2,1,6,3,5,4]=>100111
[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[7,1,2,6,3,5,4]=>000111
[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[7,3,2,1,6,5,4]=>110111
[7,4,5,6,1,3,2]=>[3,6,1,7,4,5,2]=>[3,1,7,2,6,5,4]=>010111
[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>[7,3,1,2,6,5,4]=>010111
[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>[7,1,3,2,6,5,4]=>010111
[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>[7,2,1,3,6,5,4]=>100111
[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[7,1,2,3,6,5,4]=>000111
[7,4,6,1,2,3,5]=>[6,1,2,7,4,3,5]=>[6,3,2,1,7,5,4]=>110111
[7,4,6,1,2,5,3]=>[5,1,6,7,4,2,3]=>[7,3,6,2,1,5,4]=>100111
[7,4,6,1,3,2,5]=>[3,6,1,7,4,2,5]=>[3,1,6,2,7,5,4]=>010111
[7,4,6,1,3,5,2]=>[5,6,1,7,4,3,2]=>[7,2,6,3,1,5,4]=>010111
[7,4,6,1,5,2,3]=>[5,6,1,7,4,2,3]=>[6,2,7,3,1,5,4]=>010111
[7,4,6,1,5,3,2]=>[3,5,6,7,4,1,2]=>[6,1,3,7,2,5,4]=>000111
[7,4,6,2,1,3,5]=>[2,6,1,7,4,3,5]=>[6,3,1,2,7,5,4]=>010111
[7,4,6,2,1,5,3]=>[2,5,6,7,4,1,3]=>[7,3,6,1,2,5,4]=>000111
[7,4,6,2,3,1,5]=>[3,6,2,7,4,1,5]=>[6,1,3,2,7,5,4]=>010111
[7,4,6,2,3,5,1]=>[5,6,2,7,4,3,1]=>[6,3,2,7,1,5,4]=>010111
[7,4,6,2,5,1,3]=>[5,6,2,7,4,1,3]=>[7,3,2,6,1,5,4]=>010111
[7,4,6,2,5,3,1]=>[3,5,6,7,4,2,1]=>[7,1,3,6,2,5,4]=>000111
[7,4,6,3,1,2,5]=>[3,1,6,7,4,2,5]=>[6,2,1,3,7,5,4]=>100111
[7,4,6,3,1,5,2]=>[5,3,6,7,4,1,2]=>[7,2,3,6,1,5,4]=>000111
[7,4,6,3,2,1,5]=>[2,3,6,7,4,1,5]=>[6,1,2,3,7,5,4]=>000111
[7,4,6,3,2,5,1]=>[5,3,6,7,4,2,1]=>[6,2,3,7,1,5,4]=>000111
[7,4,6,3,5,1,2]=>[5,1,6,7,4,3,2]=>[6,3,7,2,1,5,4]=>100111
[7,4,6,3,5,2,1]=>[2,5,6,7,4,3,1]=>[6,3,7,1,2,5,4]=>000111
[7,4,6,5,1,2,3]=>[5,1,2,6,7,4,3]=>[6,4,7,3,2,1,5]=>110011
[7,4,6,5,1,3,2]=>[3,5,1,6,7,4,2]=>[3,1,6,4,7,2,5]=>010011
[7,4,6,5,2,1,3]=>[2,5,1,6,7,4,3]=>[6,4,7,3,1,2,5]=>010011
[7,4,6,5,2,3,1]=>[3,5,2,6,7,4,1]=>[6,4,7,1,3,2,5]=>010011
[7,4,6,5,3,1,2]=>[3,1,5,6,7,4,2]=>[6,4,7,2,1,3,5]=>100011
[7,4,6,5,3,2,1]=>[2,3,5,6,7,4,1]=>[6,4,7,1,2,3,5]=>000011
[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[7,6,4,3,2,1,5]=>111011
[7,5,1,2,3,6,4]=>[6,1,2,5,7,3,4]=>[6,3,2,1,7,4,5]=>110011
[7,5,1,2,4,3,6]=>[4,1,5,2,7,3,6]=>[4,2,1,7,6,3,5]=>101011
[7,5,1,2,4,6,3]=>[6,1,5,2,7,4,3]=>[6,4,2,1,7,3,5]=>101011
[7,5,1,2,6,3,4]=>[6,1,5,2,7,3,4]=>[7,4,2,1,6,3,5]=>101011
[7,5,1,2,6,4,3]=>[4,1,6,5,7,2,3]=>[7,3,6,2,1,4,5]=>100011
[7,5,1,3,2,4,6]=>[3,5,1,2,7,4,6]=>[3,1,7,6,4,2,5]=>011011
[7,5,1,3,2,6,4]=>[3,6,1,5,7,2,4]=>[3,1,6,2,7,4,5]=>010011
[7,5,1,3,4,2,6]=>[4,5,1,3,7,2,6]=>[4,3,1,7,6,2,5]=>011011
[7,5,1,3,4,6,2]=>[6,5,1,3,7,4,2]=>[6,4,3,1,7,2,5]=>011011
[7,5,1,3,6,2,4]=>[6,5,1,3,7,2,4]=>[7,4,3,1,6,2,5]=>011011
[7,5,1,3,6,4,2]=>[4,6,1,5,7,3,2]=>[7,2,6,3,1,4,5]=>010011
[7,5,1,4,2,3,6]=>[4,5,1,2,7,3,6]=>[7,6,3,1,4,2,5]=>011011
[7,5,1,4,2,6,3]=>[6,4,5,1,7,2,3]=>[6,2,4,1,7,3,5]=>001011
[7,5,1,4,3,2,6]=>[3,4,5,1,7,2,6]=>[7,6,2,4,1,3,5]=>001011
[7,5,1,4,3,6,2]=>[6,4,5,1,7,3,2]=>[7,2,4,1,6,3,5]=>001011
[7,5,1,4,6,2,3]=>[6,5,1,2,7,4,3]=>[7,3,1,6,4,2,5]=>011011
[7,5,1,4,6,3,2]=>[3,6,5,1,7,4,2]=>[7,2,6,4,1,3,5]=>001011
[7,5,1,6,2,3,4]=>[6,5,1,2,7,3,4]=>[6,3,1,7,4,2,5]=>011011
[7,5,1,6,2,4,3]=>[4,6,5,1,7,2,3]=>[4,1,6,2,7,3,5]=>001011
[7,5,1,6,3,2,4]=>[3,6,5,1,7,2,4]=>[6,2,7,4,1,3,5]=>001011
[7,5,1,6,3,4,2]=>[4,6,5,1,7,3,2]=>[4,1,7,2,6,3,5]=>001011
[7,5,1,6,4,2,3]=>[4,6,1,5,7,2,3]=>[6,2,7,3,1,4,5]=>010011
[7,5,1,6,4,3,2]=>[3,4,6,5,7,1,2]=>[6,1,3,7,2,4,5]=>000011
[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[7,6,4,3,1,2,5]=>011011
[7,5,2,1,3,6,4]=>[2,6,1,5,7,3,4]=>[6,3,1,2,7,4,5]=>010011
[7,5,2,1,4,3,6]=>[2,4,5,1,7,3,6]=>[4,1,2,7,6,3,5]=>001011
[7,5,2,1,4,6,3]=>[2,6,5,1,7,4,3]=>[6,4,1,2,7,3,5]=>001011
[7,5,2,1,6,3,4]=>[2,6,5,1,7,3,4]=>[7,4,1,2,6,3,5]=>001011
[7,5,2,1,6,4,3]=>[2,4,6,5,7,1,3]=>[7,3,6,1,2,4,5]=>000011
[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[7,6,4,1,3,2,5]=>011011
[7,5,2,3,1,6,4]=>[3,6,2,5,7,1,4]=>[6,1,3,2,7,4,5]=>010011
[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>[7,6,1,4,3,2,5]=>011011
[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>[7,1,6,4,3,2,5]=>011011
[7,5,2,3,6,1,4]=>[6,5,2,3,7,1,4]=>[6,1,7,4,3,2,5]=>011011
[7,5,2,3,6,4,1]=>[4,6,2,5,7,3,1]=>[6,3,2,7,1,4,5]=>010011
[7,5,2,4,1,3,6]=>[4,5,2,1,7,3,6]=>[4,1,7,6,3,2,5]=>011011
[7,5,2,4,1,6,3]=>[6,4,5,2,7,1,3]=>[4,2,6,1,7,3,5]=>001011
[7,5,2,4,3,1,6]=>[3,4,5,2,7,1,6]=>[4,2,7,6,1,3,5]=>001011
[7,5,2,4,3,6,1]=>[6,4,5,2,7,3,1]=>[4,2,7,1,6,3,5]=>001011
[7,5,2,4,6,1,3]=>[6,5,2,1,7,4,3]=>[6,4,1,7,3,2,5]=>011011
[7,5,2,4,6,3,1]=>[3,6,5,2,7,4,1]=>[6,4,2,7,1,3,5]=>001011
[7,5,2,6,1,3,4]=>[6,5,2,1,7,3,4]=>[7,4,1,6,3,2,5]=>011011
[7,5,2,6,1,4,3]=>[4,6,5,2,7,1,3]=>[6,1,4,2,7,3,5]=>001011
[7,5,2,6,3,1,4]=>[3,6,5,2,7,1,4]=>[7,4,2,6,1,3,5]=>001011
[7,5,2,6,3,4,1]=>[4,6,5,2,7,3,1]=>[7,1,4,2,6,3,5]=>001011
[7,5,2,6,4,1,3]=>[4,6,2,5,7,1,3]=>[7,3,2,6,1,4,5]=>010011
[7,5,2,6,4,3,1]=>[3,4,6,5,7,2,1]=>[7,1,3,6,2,4,5]=>000011
[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[7,6,4,2,1,3,5]=>101011
[7,5,3,1,2,6,4]=>[3,1,6,5,7,2,4]=>[6,2,1,3,7,4,5]=>100011
[7,5,3,1,4,2,6]=>[4,3,5,1,7,2,6]=>[4,1,7,6,2,3,5]=>001011
[7,5,3,1,4,6,2]=>[6,3,5,1,7,4,2]=>[6,4,1,7,2,3,5]=>001011
[7,5,3,1,6,2,4]=>[6,3,5,1,7,2,4]=>[7,4,1,6,2,3,5]=>001011
[7,5,3,1,6,4,2]=>[4,3,6,5,7,1,2]=>[7,2,3,6,1,4,5]=>000011
[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[7,6,4,1,2,3,5]=>001011
[7,5,3,2,1,6,4]=>[2,3,6,5,7,1,4]=>[6,1,2,3,7,4,5]=>000011
[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[7,6,1,4,2,3,5]=>001011
[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>[7,1,6,4,2,3,5]=>001011
[7,5,3,2,6,1,4]=>[6,3,5,2,7,1,4]=>[6,1,7,4,2,3,5]=>001011
[7,5,3,2,6,4,1]=>[4,3,6,5,7,2,1]=>[6,2,3,7,1,4,5]=>000011
[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[7,6,2,1,4,3,5]=>101011
[7,5,3,4,1,6,2]=>[6,4,5,3,7,1,2]=>[6,1,7,2,4,3,5]=>001011
[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[7,6,1,2,4,3,5]=>001011
[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[7,1,6,2,4,3,5]=>001011
[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>[7,2,1,6,4,3,5]=>101011
[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>[7,1,2,6,4,3,5]=>001011
[7,5,3,6,1,2,4]=>[6,1,5,3,7,2,4]=>[6,2,1,7,4,3,5]=>101011
[7,5,3,6,1,4,2]=>[4,6,5,3,7,1,2]=>[7,2,6,1,4,3,5]=>001011
[7,5,3,6,2,1,4]=>[2,6,5,3,7,1,4]=>[6,1,2,7,4,3,5]=>001011
[7,5,3,6,2,4,1]=>[4,6,5,3,7,2,1]=>[6,2,7,1,4,3,5]=>001011
[7,5,3,6,4,1,2]=>[4,1,6,5,7,3,2]=>[6,3,7,2,1,4,5]=>100011
[7,5,3,6,4,2,1]=>[2,4,6,5,7,3,1]=>[6,3,7,1,2,4,5]=>000011
[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[7,6,3,2,1,4,5]=>110011
[7,5,4,1,2,6,3]=>[6,1,4,5,7,2,3]=>[6,2,1,7,3,4,5]=>100011
[7,5,4,1,3,2,6]=>[3,4,1,5,7,2,6]=>[3,1,7,6,2,4,5]=>010011
[7,5,4,1,3,6,2]=>[6,4,1,5,7,3,2]=>[6,3,1,7,2,4,5]=>010011
[7,5,4,1,6,2,3]=>[6,4,1,5,7,2,3]=>[7,3,1,6,2,4,5]=>010011
[7,5,4,1,6,3,2]=>[3,6,4,5,7,1,2]=>[7,2,6,1,3,4,5]=>000011
[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[7,6,3,1,2,4,5]=>010011
[7,5,4,2,1,6,3]=>[2,6,4,5,7,1,3]=>[6,1,2,7,3,4,5]=>000011
[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[7,6,1,3,2,4,5]=>010011
[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>[7,1,6,3,2,4,5]=>010011
[7,5,4,2,6,1,3]=>[6,4,2,5,7,1,3]=>[6,1,7,3,2,4,5]=>010011
[7,5,4,2,6,3,1]=>[3,6,4,5,7,2,1]=>[6,2,7,1,3,4,5]=>000011
[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[7,6,2,1,3,4,5]=>100011
[7,5,4,3,1,6,2]=>[6,3,4,5,7,1,2]=>[6,1,7,2,3,4,5]=>000011
[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[7,6,1,2,3,4,5]=>000011
[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[7,1,6,2,3,4,5]=>000011
[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[7,2,1,6,3,4,5]=>100011
[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[7,1,2,6,3,4,5]=>000011
[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[7,3,2,1,6,4,5]=>110011
[7,5,4,6,1,3,2]=>[3,6,1,5,7,4,2]=>[3,1,7,2,6,4,5]=>010011
[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>[7,3,1,2,6,4,5]=>010011
[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>[7,1,3,2,6,4,5]=>010011
[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>[7,2,1,3,6,4,5]=>100011
[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[7,1,2,3,6,4,5]=>000011
[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[7,4,3,2,1,6,5]=>111011
[7,5,6,1,2,4,3]=>[4,1,6,2,7,5,3]=>[4,2,1,7,3,6,5]=>101011
[7,5,6,1,3,2,4]=>[3,6,1,2,7,5,4]=>[3,1,7,4,2,6,5]=>011011
[7,5,6,1,3,4,2]=>[4,6,1,3,7,5,2]=>[4,3,1,7,2,6,5]=>011011
[7,5,6,1,4,2,3]=>[4,6,1,2,7,5,3]=>[7,3,1,4,2,6,5]=>011011
[7,5,6,1,4,3,2]=>[3,4,6,1,7,5,2]=>[7,2,4,1,3,6,5]=>001011
[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[7,4,3,1,2,6,5]=>011011
[7,5,6,2,1,4,3]=>[2,4,6,1,7,5,3]=>[4,1,2,7,3,6,5]=>001011
[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[7,4,1,3,2,6,5]=>011011
[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>[7,1,4,3,2,6,5]=>011011
[7,5,6,2,4,1,3]=>[4,6,2,1,7,5,3]=>[4,1,7,3,2,6,5]=>011011
[7,5,6,2,4,3,1]=>[3,4,6,2,7,5,1]=>[4,2,7,1,3,6,5]=>001011
[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[7,4,2,1,3,6,5]=>101011
[7,5,6,3,1,4,2]=>[4,3,6,1,7,5,2]=>[4,1,7,2,3,6,5]=>001011
[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[7,4,1,2,3,6,5]=>001011
[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>[7,1,4,2,3,6,5]=>001011
[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[7,2,1,4,3,6,5]=>101011
[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>[7,1,2,4,3,6,5]=>001011
[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>[7,3,2,1,4,6,5]=>110011
[7,5,6,4,1,3,2]=>[3,4,1,6,7,5,2]=>[3,1,7,2,4,6,5]=>010011
[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>[7,3,1,2,4,6,5]=>010011
[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>[7,1,3,2,4,6,5]=>010011
[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>[7,2,1,3,4,6,5]=>100011
[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[7,1,2,3,4,6,5]=>000011
[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[7,5,4,3,2,1,6]=>111101
[7,6,1,2,3,5,4]=>[5,1,2,6,3,7,4]=>[5,3,2,1,7,4,6]=>110101
[7,6,1,2,4,3,5]=>[4,1,6,2,3,7,5]=>[4,2,1,7,5,3,6]=>101101
[7,6,1,2,4,5,3]=>[5,1,6,2,4,7,3]=>[5,4,2,1,7,3,6]=>101101
[7,6,1,2,5,3,4]=>[5,1,6,2,3,7,4]=>[7,4,2,1,5,3,6]=>101101
[7,6,1,2,5,4,3]=>[4,1,5,6,2,7,3]=>[7,3,5,2,1,4,6]=>100101
[7,6,1,3,2,4,5]=>[3,6,1,2,4,7,5]=>[3,1,7,5,4,2,6]=>011101
[7,6,1,3,2,5,4]=>[3,5,1,6,2,7,4]=>[3,1,5,2,7,4,6]=>010101
[7,6,1,3,4,2,5]=>[4,6,1,3,2,7,5]=>[4,3,1,7,5,2,6]=>011101
[7,6,1,3,4,5,2]=>[5,6,1,3,4,7,2]=>[5,4,3,1,7,2,6]=>011101
[7,6,1,3,5,2,4]=>[5,6,1,3,2,7,4]=>[7,4,3,1,5,2,6]=>011101
[7,6,1,3,5,4,2]=>[4,5,1,6,3,7,2]=>[7,2,5,3,1,4,6]=>010101
[7,6,1,4,2,3,5]=>[4,6,1,2,3,7,5]=>[7,5,3,1,4,2,6]=>011101
[7,6,1,4,2,5,3]=>[5,4,6,1,2,7,3]=>[5,2,4,1,7,3,6]=>001101
[7,6,1,4,3,2,5]=>[3,4,6,1,2,7,5]=>[7,5,2,4,1,3,6]=>001101
[7,6,1,4,3,5,2]=>[5,4,6,1,3,7,2]=>[7,2,4,1,5,3,6]=>001101
[7,6,1,4,5,2,3]=>[5,6,1,2,4,7,3]=>[7,3,1,5,4,2,6]=>011101
[7,6,1,4,5,3,2]=>[3,5,6,1,4,7,2]=>[7,2,5,4,1,3,6]=>001101
[7,6,1,5,2,3,4]=>[5,6,1,2,3,7,4]=>[5,3,1,7,4,2,6]=>011101
[7,6,1,5,2,4,3]=>[4,5,6,1,2,7,3]=>[4,1,5,2,7,3,6]=>001101
[7,6,1,5,3,2,4]=>[3,5,6,1,2,7,4]=>[5,2,7,4,1,3,6]=>001101
[7,6,1,5,3,4,2]=>[4,5,6,1,3,7,2]=>[4,1,7,2,5,3,6]=>001101
[7,6,1,5,4,2,3]=>[4,5,1,6,2,7,3]=>[5,2,7,3,1,4,6]=>010101
[7,6,1,5,4,3,2]=>[3,4,5,6,1,7,2]=>[5,1,3,7,2,4,6]=>000101
[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[7,5,4,3,1,2,6]=>011101
[7,6,2,1,3,5,4]=>[2,5,1,6,3,7,4]=>[5,3,1,2,7,4,6]=>010101
[7,6,2,1,4,3,5]=>[2,4,6,1,3,7,5]=>[4,1,2,7,5,3,6]=>001101
[7,6,2,1,4,5,3]=>[2,5,6,1,4,7,3]=>[5,4,1,2,7,3,6]=>001101
[7,6,2,1,5,3,4]=>[2,5,6,1,3,7,4]=>[7,4,1,2,5,3,6]=>001101
[7,6,2,1,5,4,3]=>[2,4,5,6,1,7,3]=>[7,3,5,1,2,4,6]=>000101
[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[7,5,4,1,3,2,6]=>011101
[7,6,2,3,1,5,4]=>[3,5,2,6,1,7,4]=>[5,1,3,2,7,4,6]=>010101
[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[7,5,1,4,3,2,6]=>011101
[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>[7,1,5,4,3,2,6]=>011101
[7,6,2,3,5,1,4]=>[5,6,2,3,1,7,4]=>[5,1,7,4,3,2,6]=>011101
[7,6,2,3,5,4,1]=>[4,5,2,6,3,7,1]=>[5,3,2,7,1,4,6]=>010101
[7,6,2,4,1,3,5]=>[4,6,2,1,3,7,5]=>[4,1,7,5,3,2,6]=>011101
[7,6,2,4,1,5,3]=>[5,4,6,2,1,7,3]=>[4,2,5,1,7,3,6]=>001101
[7,6,2,4,3,1,5]=>[3,4,6,2,1,7,5]=>[4,2,7,5,1,3,6]=>001101
[7,6,2,4,3,5,1]=>[5,4,6,2,3,7,1]=>[4,2,7,1,5,3,6]=>001101
[7,6,2,4,5,1,3]=>[5,6,2,1,4,7,3]=>[5,4,1,7,3,2,6]=>011101
[7,6,2,4,5,3,1]=>[3,5,6,2,4,7,1]=>[5,4,2,7,1,3,6]=>001101
[7,6,2,5,1,3,4]=>[5,6,2,1,3,7,4]=>[7,4,1,5,3,2,6]=>011101
[7,6,2,5,1,4,3]=>[4,5,6,2,1,7,3]=>[5,1,4,2,7,3,6]=>001101
[7,6,2,5,3,1,4]=>[3,5,6,2,1,7,4]=>[7,4,2,5,1,3,6]=>001101
[7,6,2,5,3,4,1]=>[4,5,6,2,3,7,1]=>[7,1,4,2,5,3,6]=>001101
[7,6,2,5,4,1,3]=>[4,5,2,6,1,7,3]=>[7,3,2,5,1,4,6]=>010101
[7,6,2,5,4,3,1]=>[3,4,5,6,2,7,1]=>[7,1,3,5,2,4,6]=>000101
[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[7,5,4,2,1,3,6]=>101101
[7,6,3,1,2,5,4]=>[3,1,5,6,2,7,4]=>[5,2,1,3,7,4,6]=>100101
[7,6,3,1,4,2,5]=>[4,3,6,1,2,7,5]=>[4,1,7,5,2,3,6]=>001101
[7,6,3,1,4,5,2]=>[5,3,6,1,4,7,2]=>[5,4,1,7,2,3,6]=>001101
[7,6,3,1,5,2,4]=>[5,3,6,1,2,7,4]=>[7,4,1,5,2,3,6]=>001101
[7,6,3,1,5,4,2]=>[4,3,5,6,1,7,2]=>[7,2,3,5,1,4,6]=>000101
[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[7,5,4,1,2,3,6]=>001101
[7,6,3,2,1,5,4]=>[2,3,5,6,1,7,4]=>[5,1,2,3,7,4,6]=>000101
[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[7,5,1,4,2,3,6]=>001101
[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>[7,1,5,4,2,3,6]=>001101
[7,6,3,2,5,1,4]=>[5,3,6,2,1,7,4]=>[5,1,7,4,2,3,6]=>001101
[7,6,3,2,5,4,1]=>[4,3,5,6,2,7,1]=>[5,2,3,7,1,4,6]=>000101
[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[7,5,2,1,4,3,6]=>101101
[7,6,3,4,1,5,2]=>[5,4,6,3,1,7,2]=>[5,1,7,2,4,3,6]=>001101
[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[7,5,1,2,4,3,6]=>001101
[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>[7,1,5,2,4,3,6]=>001101
[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[7,2,1,5,4,3,6]=>101101
[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,1,2,5,4,3,6]=>001101
[7,6,3,5,1,2,4]=>[5,1,6,3,2,7,4]=>[5,2,1,7,4,3,6]=>101101
[7,6,3,5,1,4,2]=>[4,5,6,3,1,7,2]=>[7,2,5,1,4,3,6]=>001101
[7,6,3,5,2,1,4]=>[2,5,6,3,1,7,4]=>[5,1,2,7,4,3,6]=>001101
[7,6,3,5,2,4,1]=>[4,5,6,3,2,7,1]=>[5,2,7,1,4,3,6]=>001101
[7,6,3,5,4,1,2]=>[4,1,5,6,3,7,2]=>[5,3,7,2,1,4,6]=>100101
[7,6,3,5,4,2,1]=>[2,4,5,6,3,7,1]=>[5,3,7,1,2,4,6]=>000101
[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[7,5,3,2,1,4,6]=>110101
[7,6,4,1,2,5,3]=>[5,1,4,6,2,7,3]=>[5,2,1,7,3,4,6]=>100101
[7,6,4,1,3,2,5]=>[3,4,1,6,2,7,5]=>[3,1,7,5,2,4,6]=>010101
[7,6,4,1,3,5,2]=>[5,4,1,6,3,7,2]=>[5,3,1,7,2,4,6]=>010101
[7,6,4,1,5,2,3]=>[5,4,1,6,2,7,3]=>[7,3,1,5,2,4,6]=>010101
[7,6,4,1,5,3,2]=>[3,5,4,6,1,7,2]=>[7,2,5,1,3,4,6]=>000101
[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[7,5,3,1,2,4,6]=>010101
[7,6,4,2,1,5,3]=>[2,5,4,6,1,7,3]=>[5,1,2,7,3,4,6]=>000101
[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[7,5,1,3,2,4,6]=>010101
[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>[7,1,5,3,2,4,6]=>010101
[7,6,4,2,5,1,3]=>[5,4,2,6,1,7,3]=>[5,1,7,3,2,4,6]=>010101
[7,6,4,2,5,3,1]=>[3,5,4,6,2,7,1]=>[5,2,7,1,3,4,6]=>000101
[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[7,5,2,1,3,4,6]=>100101
[7,6,4,3,1,5,2]=>[5,3,4,6,1,7,2]=>[5,1,7,2,3,4,6]=>000101
[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[7,5,1,2,3,4,6]=>000101
[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>[7,1,5,2,3,4,6]=>000101
[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[7,2,1,5,3,4,6]=>100101
[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[7,1,2,5,3,4,6]=>000101
[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[7,3,2,1,5,4,6]=>110101
[7,6,4,5,1,3,2]=>[3,5,1,6,4,7,2]=>[3,1,7,2,5,4,6]=>010101
[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>[7,3,1,2,5,4,6]=>010101
[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>[7,1,3,2,5,4,6]=>010101
[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>[7,2,1,3,5,4,6]=>100101
[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>[7,1,2,3,5,4,6]=>000101
[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[7,4,3,2,1,5,6]=>111001
[7,6,5,1,2,4,3]=>[4,1,5,2,6,7,3]=>[4,2,1,7,3,5,6]=>101001
[7,6,5,1,3,2,4]=>[3,5,1,2,6,7,4]=>[3,1,7,4,2,5,6]=>011001
[7,6,5,1,3,4,2]=>[4,5,1,3,6,7,2]=>[4,3,1,7,2,5,6]=>011001
[7,6,5,1,4,2,3]=>[4,5,1,2,6,7,3]=>[7,3,1,4,2,5,6]=>011001
[7,6,5,1,4,3,2]=>[3,4,5,1,6,7,2]=>[7,2,4,1,3,5,6]=>001001
[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[7,4,3,1,2,5,6]=>011001
[7,6,5,2,1,4,3]=>[2,4,5,1,6,7,3]=>[4,1,2,7,3,5,6]=>001001
[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[7,4,1,3,2,5,6]=>011001
[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>011001
[7,6,5,2,4,1,3]=>[4,5,2,1,6,7,3]=>[4,1,7,3,2,5,6]=>011001
[7,6,5,2,4,3,1]=>[3,4,5,2,6,7,1]=>[4,2,7,1,3,5,6]=>001001
[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[7,4,2,1,3,5,6]=>101001
[7,6,5,3,1,4,2]=>[4,3,5,1,6,7,2]=>[4,1,7,2,3,5,6]=>001001
[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[7,4,1,2,3,5,6]=>001001
[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>[7,1,4,2,3,5,6]=>001001
[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[7,2,1,4,3,5,6]=>101001
[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>[7,1,2,4,3,5,6]=>001001
[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[7,3,2,1,4,5,6]=>110001
[7,6,5,4,1,3,2]=>[3,4,1,5,6,7,2]=>[3,1,7,2,4,5,6]=>010001
[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[7,3,1,2,4,5,6]=>010001
[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>[7,1,3,2,4,5,6]=>010001
[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[7,2,1,3,4,5,6]=>100001
[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>000001
[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>0000001
[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>[7,8,1,2,3,4,5,6]=>0000001
[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>[7,6,8,1,2,3,4,5]=>0000011
[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>[6,7,8,1,2,3,4,5]=>0000001
[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]=>[7,8,1,2,3,4,6,5]=>0000101
[8,5,6,7,4,3,2,1]=>[2,3,4,7,8,5,6,1]=>[8,1,2,3,4,7,6,5]=>0000111
[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>[7,5,6,8,1,2,3,4]=>0000011
[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>[6,7,5,8,1,2,3,4]=>0000011
[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]=>[7,6,5,8,1,2,3,4]=>0000111
[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>[6,5,7,8,1,2,3,4]=>0000101
[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[5,6,7,8,1,2,3,4]=>0000001
[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,1,2,3,5,4,6,7]=>0001001
[7,6,8,4,5,3,2,1]=>[2,3,5,8,4,7,6,1]=>[7,6,8,1,2,3,5,4]=>0001011
[8,6,5,4,7,3,2,1]=>[2,3,7,5,6,8,4,1]=>[8,1,2,3,7,4,5,6]=>0000011
[8,6,4,5,7,3,2,1]=>[2,3,7,6,4,8,5,1]=>[8,1,2,3,7,5,4,6]=>0001011
[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]=>[7,4,5,6,8,1,2,3]=>0000011
[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>[6,7,4,5,8,1,2,3]=>0000011
[7,5,6,4,8,3,2,1]=>[2,3,8,6,7,5,4,1]=>[7,4,6,5,8,1,2,3]=>0000111
[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>[6,5,7,4,8,1,2,3]=>0000111
[5,6,7,4,8,3,2,1]=>[2,3,8,7,5,6,4,1]=>[5,6,7,4,8,1,2,3]=>0000011
[7,6,4,5,8,3,2,1]=>[2,3,8,6,4,7,5,1]=>[7,5,4,6,8,1,2,3]=>0001011
[6,7,4,5,8,3,2,1]=>[2,3,8,7,4,6,5,1]=>[6,7,5,4,8,1,2,3]=>0001011
[7,5,4,6,8,3,2,1]=>[2,3,8,5,7,4,6,1]=>[7,6,4,5,8,1,2,3]=>0000111
[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]=>[7,6,5,4,8,1,2,3]=>0001111
[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]=>[6,4,5,7,8,1,2,3]=>0000101
[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>[5,6,4,7,8,1,2,3]=>0000101
[6,4,5,7,8,3,2,1]=>[2,3,8,6,4,5,7,1]=>[6,5,4,7,8,1,2,3]=>0001101
[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]=>[5,4,6,7,8,1,2,3]=>0001001
[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>[4,5,6,7,8,1,2,3]=>0000001
[8,7,5,6,3,4,2,1]=>[2,4,6,3,7,5,8,1]=>[8,1,2,4,3,6,5,7]=>0010101
[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]=>[7,8,1,2,4,3,6,5]=>0010101
[6,7,5,8,3,4,2,1]=>[2,4,8,3,7,6,5,1]=>[6,7,5,8,1,2,4,3]=>0010011
[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>[5,6,7,8,1,2,4,3]=>0010001
[8,7,6,4,3,5,2,1]=>[2,5,4,6,3,7,8,1]=>[8,1,2,5,3,4,6,7]=>0001001
[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>[7,6,8,1,2,5,3,4]=>0001011
[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]=>[6,7,8,1,2,5,3,4]=>0001001
[8,7,6,3,4,5,2,1]=>[2,5,6,3,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>0011001
[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>[6,7,8,1,2,5,4,3]=>0011001
[7,8,5,4,3,6,2,1]=>[2,6,4,5,8,3,7,1]=>[7,8,1,2,6,3,4,5]=>0000101
[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[8,1,2,6,5,3,4,7]=>0001101
[6,4,5,7,3,8,2,1]=>[2,8,7,6,4,5,3,1]=>[6,5,4,7,3,8,1,2]=>0001111
[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>[5,4,6,7,3,8,1,2]=>0001011
[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]=>[4,5,6,7,3,8,1,2]=>0000011
[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]=>[7,5,6,8,1,3,2,4]=>0100011
[6,7,5,8,4,2,3,1]=>[3,4,2,8,7,6,5,1]=>[6,7,5,8,1,3,2,4]=>0100011
[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>[5,6,7,8,1,3,2,4]=>0100001
[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]=>[8,1,3,2,5,4,6,7]=>0101001
[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[8,1,3,2,5,4,7,6]=>0101011
[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>[7,6,8,1,3,2,5,4]=>0101011
[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>[6,7,8,1,3,2,5,4]=>0101001
[8,7,4,5,6,2,3,1]=>[3,6,2,7,4,5,8,1]=>[8,1,3,2,6,5,4,7]=>0101101
[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>[8,1,3,2,7,4,6,5]=>0100111
[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>[7,4,6,5,8,1,3,2]=>0100111
[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[6,5,7,4,8,1,3,2]=>0100111
[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]=>[4,5,6,7,8,1,3,2]=>0100001
[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>0010001
[7,6,8,5,3,2,4,1]=>[4,3,5,2,8,7,6,1]=>[7,6,8,1,4,2,3,5]=>0010011
[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>[6,7,8,1,4,2,3,5]=>0010001
[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>[8,1,4,2,3,7,6,5]=>0010111
[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>[6,7,5,8,1,4,2,3]=>0010011
[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[5,6,7,8,1,4,2,3]=>0010001
[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>0110001
[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>[6,7,8,1,4,3,2,5]=>0110001
[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>[8,1,4,3,2,6,5,7]=>0110101
[8,6,5,7,2,3,4,1]=>[4,7,2,3,6,8,5,1]=>[8,1,4,3,2,7,5,6]=>0110011
[8,5,6,7,2,3,4,1]=>[4,7,2,3,8,5,6,1]=>[8,1,4,3,2,7,6,5]=>0110111
[7,6,5,8,2,3,4,1]=>[4,8,2,3,6,7,5,1]=>[7,5,6,8,1,4,3,2]=>0110011
[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[5,6,7,8,1,4,3,2]=>0110001
[7,6,8,4,3,2,5,1]=>[5,3,4,8,2,7,6,1]=>[7,6,8,1,5,2,3,4]=>0001011
[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>[8,1,5,2,4,3,7,6]=>0011011
[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>[7,6,8,1,5,2,4,3]=>0011011
[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]=>[6,7,8,1,5,4,2,3]=>0011001
[7,6,8,2,3,4,5,1]=>[5,8,2,3,4,7,6,1]=>[7,6,8,1,5,4,3,2]=>0111011
[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>[8,1,6,2,4,3,5,7]=>0010101
[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>[7,8,1,6,2,4,3,5]=>0010101
[8,7,5,3,2,4,6,1]=>[6,3,5,2,7,4,8,1]=>[8,1,6,4,2,3,5,7]=>0010101
[7,8,4,3,2,5,6,1]=>[6,3,4,8,2,5,7,1]=>[7,8,1,6,5,2,3,4]=>0001101
[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>[8,1,7,2,4,3,6,5]=>0010111
[8,6,4,3,5,2,7,1]=>[7,5,4,6,3,8,2,1]=>[8,1,7,2,5,3,4,6]=>0001011
[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>[8,1,7,2,6,3,5,4]=>0001111
[8,6,4,2,3,5,7,1]=>[7,4,2,6,3,8,5,1]=>[8,1,7,5,3,2,4,6]=>0101011
[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[8,1,7,6,2,4,3,5]=>0010111
[6,4,5,7,3,2,8,1]=>[8,3,7,6,4,5,2,1]=>[6,5,4,7,2,3,8,1]=>0001111
[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>[4,5,6,7,2,3,8,1]=>0000011
[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>[7,2,4,3,6,5,8,1]=>0010111
[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>[6,3,5,4,7,2,8,1]=>0001111
[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[5,4,6,3,7,2,8,1]=>0001111
[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[4,5,6,3,7,2,8,1]=>0000111
[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]=>[6,7,3,2,4,5,8,1]=>0100011
[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>[6,7,3,2,5,4,8,1]=>0101011
[6,5,4,7,2,3,8,1]=>[8,7,2,5,6,4,3,1]=>[6,4,5,7,3,2,8,1]=>0100111
[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]=>[4,5,6,7,3,2,8,1]=>0100011
[6,5,7,3,2,4,8,1]=>[8,3,7,2,6,5,4,1]=>[6,5,7,4,2,3,8,1]=>0010111
[6,7,3,2,4,5,8,1]=>[8,3,7,2,4,6,5,1]=>[6,7,5,4,2,3,8,1]=>0011011
[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>[3,4,5,6,2,7,8,1]=>0000101
[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]=>[5,2,3,4,6,7,8,1]=>0001001
[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>[4,3,5,2,6,7,8,1]=>0011001
[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[3,4,2,5,6,7,8,1]=>0010001
[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]=>[7,8,2,1,3,4,5,6]=>1000001
[7,8,5,6,4,3,1,2]=>[3,1,4,6,8,5,7,2]=>[7,8,2,1,3,4,6,5]=>1000101
[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]=>[6,7,5,8,2,1,3,4]=>1000011
[7,5,6,8,4,3,1,2]=>[3,1,4,8,7,5,6,2]=>[7,6,5,8,2,1,3,4]=>1000111
[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>[5,6,7,8,2,1,3,4]=>1000001
[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]=>[7,8,2,1,3,6,5,4]=>1001101
[6,7,4,5,8,3,1,2]=>[3,1,8,7,4,6,5,2]=>[6,7,5,4,8,2,1,3]=>1001011
[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]=>[4,5,6,7,8,2,1,3]=>1000001
[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[8,2,1,4,3,6,5,7]=>1010101
[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[7,8,2,1,4,3,6,5]=>1010101
[7,6,5,8,3,4,1,2]=>[4,1,8,3,6,7,5,2]=>[7,5,6,8,2,1,4,3]=>1010011
[6,7,5,8,3,4,1,2]=>[4,1,8,3,7,6,5,2]=>[6,7,5,8,2,1,4,3]=>1010011
[7,5,6,8,3,4,1,2]=>[4,1,8,3,7,5,6,2]=>[7,6,5,8,2,1,4,3]=>1010111
[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>[6,5,7,8,2,1,4,3]=>1010101
[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[5,6,7,8,2,1,4,3]=>1010001
[7,8,5,4,3,6,1,2]=>[6,1,4,5,8,3,7,2]=>[7,8,2,1,6,3,4,5]=>1000101
[7,8,4,5,3,6,1,2]=>[6,1,5,8,4,3,7,2]=>[7,8,2,1,6,3,5,4]=>1001101
[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]=>[7,8,2,1,6,5,3,4]=>1001101
[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]=>[7,8,2,1,6,5,4,3]=>1011101
[8,5,4,3,6,7,1,2]=>[7,1,4,5,8,3,6,2]=>[8,2,1,7,6,3,4,5]=>1000111
[6,7,4,5,3,8,1,2]=>[8,1,5,7,4,6,3,2]=>[6,7,3,5,4,8,2,1]=>1001011
[7,5,4,6,3,8,1,2]=>[8,1,6,5,7,4,3,2]=>[7,3,6,4,5,8,2,1]=>1000111
[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]=>[6,4,5,7,3,8,2,1]=>1000111
[5,4,6,7,3,8,1,2]=>[8,1,7,5,4,6,3,2]=>[5,4,6,7,3,8,2,1]=>1001011
[4,5,6,7,3,8,1,2]=>[8,1,7,4,5,6,3,2]=>[4,5,6,7,3,8,2,1]=>1000011
[7,6,3,4,5,8,1,2]=>[8,1,6,3,4,7,5,2]=>[7,5,4,3,6,8,2,1]=>1011011
[7,5,4,3,6,8,1,2]=>[8,1,4,5,7,3,6,2]=>[7,6,3,4,5,8,2,1]=>1000111
[6,3,4,5,7,8,1,2]=>[8,1,6,3,4,5,7,2]=>[6,5,4,3,7,8,2,1]=>1011101
[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[8,3,1,2,4,5,6,7]=>0100001
[6,7,8,5,4,2,1,3]=>[2,4,1,5,8,6,7,3]=>[6,7,8,3,1,2,4,5]=>0100001
[8,7,5,6,4,2,1,3]=>[2,4,1,6,7,5,8,3]=>[8,3,1,2,4,6,5,7]=>0100101
[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>[7,8,3,1,2,4,6,5]=>0100101
[7,6,5,8,4,2,1,3]=>[2,4,1,8,6,7,5,3]=>[7,5,6,8,3,1,2,4]=>0100011
[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]=>[6,7,5,8,3,1,2,4]=>0100011
[6,5,7,8,4,2,1,3]=>[2,4,1,8,6,5,7,3]=>[6,5,7,8,3,1,2,4]=>0100101
[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[5,6,7,8,3,1,2,4]=>0100001
[7,6,8,4,5,2,1,3]=>[2,5,1,8,4,7,6,3]=>[7,6,8,3,1,2,5,4]=>0101011
[6,7,5,4,8,2,1,3]=>[2,8,1,5,7,6,4,3]=>[6,7,4,5,8,3,1,2]=>0100011
[4,5,6,7,8,2,1,3]=>[2,8,1,4,5,6,7,3]=>[4,5,6,7,8,3,1,2]=>0100001
[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[8,3,2,1,4,5,6,7]=>1100001
[6,7,8,5,4,1,2,3]=>[4,1,2,5,8,6,7,3]=>[6,7,8,3,2,1,4,5]=>1100001
[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>[7,8,3,2,1,4,6,5]=>1100101
[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>[8,3,2,1,4,7,6,5]=>1100111
[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>[6,7,5,8,3,2,1,4]=>1100011
[6,5,7,8,4,1,2,3]=>[4,1,2,8,6,5,7,3]=>[6,5,7,8,3,2,1,4]=>1100101
[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[5,6,7,8,3,2,1,4]=>1100001
[8,6,7,4,5,1,2,3]=>[5,1,2,7,4,8,6,3]=>[8,3,2,1,5,4,7,6]=>1101011
[8,6,5,4,7,1,2,3]=>[7,1,2,5,6,8,4,3]=>[8,3,2,1,7,4,5,6]=>1100011
[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>[8,3,2,1,7,4,6,5]=>1100111
[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[7,4,5,6,8,3,2,1]=>1100011
[6,7,5,4,8,1,2,3]=>[8,1,2,5,7,6,4,3]=>[6,7,4,5,8,3,2,1]=>1100011
[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>[7,4,6,5,8,3,2,1]=>1100111
[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>[6,5,7,4,8,3,2,1]=>1100111
[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]=>[7,5,4,6,8,3,2,1]=>1101011
[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[6,7,5,4,8,3,2,1]=>1101011
[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]=>[7,6,4,5,8,3,2,1]=>1100111
[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>[7,6,5,4,8,3,2,1]=>1101111
[6,5,4,7,8,1,2,3]=>[8,1,2,5,6,4,7,3]=>[6,4,5,7,8,3,2,1]=>1100101
[5,6,4,7,8,1,2,3]=>[8,1,2,6,5,4,7,3]=>[5,6,4,7,8,3,2,1]=>1100101
[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>[6,5,4,7,8,3,2,1]=>1101101
[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[4,5,6,7,8,3,2,1]=>1100001
[7,6,8,5,3,2,1,4]=>[2,3,5,1,8,7,6,4]=>[7,6,8,4,1,2,3,5]=>0010011
[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>[7,8,4,1,2,3,6,5]=>0010101
[7,6,5,8,3,2,1,4]=>[2,3,8,1,6,7,5,4]=>[7,5,6,8,4,1,2,3]=>0010011
[6,7,5,8,3,2,1,4]=>[2,3,8,1,7,6,5,4]=>[6,7,5,8,4,1,2,3]=>0010011
[6,5,7,8,3,2,1,4]=>[2,3,8,1,6,5,7,4]=>[6,5,7,8,4,1,2,3]=>0010101
[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[5,6,7,8,4,1,2,3]=>0010001
[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>[8,4,1,3,2,5,6,7]=>0110001
[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>[8,4,1,3,2,5,7,6]=>0110011
[7,6,8,5,2,3,1,4]=>[3,5,2,1,8,7,6,4]=>[7,6,8,4,1,3,2,5]=>0110011
[8,7,5,6,2,3,1,4]=>[3,6,2,1,7,5,8,4]=>[8,4,1,3,2,6,5,7]=>0110101
[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[6,7,5,8,4,1,3,2]=>0110011
[7,5,6,8,2,3,1,4]=>[3,8,2,1,7,5,6,4]=>[7,6,5,8,4,1,3,2]=>0110111
[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[5,6,7,8,4,1,3,2]=>0110001
[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[8,4,2,1,3,5,6,7]=>1010001
[7,8,6,5,3,1,2,4]=>[3,1,5,2,6,8,7,4]=>[7,8,4,2,1,3,5,6]=>1010001
[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>[7,8,4,2,1,3,6,5]=>1010101
[7,6,5,8,3,1,2,4]=>[3,1,8,2,6,7,5,4]=>[7,5,6,8,4,2,1,3]=>1010011
[6,7,5,8,3,1,2,4]=>[3,1,8,2,7,6,5,4]=>[6,7,5,8,4,2,1,3]=>1010011
[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>[7,6,5,8,4,2,1,3]=>1010111
[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>[6,5,7,8,4,2,1,3]=>1010101
[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[5,6,7,8,4,2,1,3]=>1010001
[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>[6,7,8,4,3,1,2,5]=>0110001
[7,6,5,8,2,1,3,4]=>[2,8,1,3,6,7,5,4]=>[7,5,6,8,4,3,1,2]=>0110011
[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>[6,7,5,8,4,3,1,2]=>0110011
[7,5,6,8,2,1,3,4]=>[2,8,1,3,7,5,6,4]=>[7,6,5,8,4,3,1,2]=>0110111
[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[5,6,7,8,4,3,1,2]=>0110001
[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[8,4,3,2,1,5,6,7]=>1110001
[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[7,8,4,3,2,1,5,6]=>1110001
[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>[8,4,3,2,1,5,7,6]=>1110011
[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>[7,6,8,4,3,2,1,5]=>1110011
[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[6,7,8,4,3,2,1,5]=>1110001
[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[8,4,3,2,1,6,5,7]=>1110101
[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[7,8,4,3,2,1,6,5]=>1110101
[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[8,4,3,2,1,7,5,6]=>1110011
[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[8,4,3,2,1,7,6,5]=>1110111
[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[7,5,6,8,4,3,2,1]=>1110011
[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>[6,7,5,8,4,3,2,1]=>1110011
[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[7,6,5,8,4,3,2,1]=>1110111
[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[6,5,7,8,4,3,2,1]=>1110101
[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[5,6,7,8,4,3,2,1]=>1110001
[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>[7,8,5,1,2,3,4,6]=>0001001
[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>[7,6,8,5,1,2,3,4]=>0001011
[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>[6,7,8,5,1,2,3,4]=>0001001
[8,7,6,3,4,2,1,5]=>[2,4,6,3,1,7,8,5]=>[8,5,1,2,4,3,6,7]=>0011001
[7,8,6,3,4,2,1,5]=>[2,4,6,3,1,8,7,5]=>[7,8,5,1,2,4,3,6]=>0011001
[6,7,8,3,4,2,1,5]=>[2,4,8,3,1,6,7,5]=>[6,7,8,5,1,2,4,3]=>0011001
[8,7,6,4,2,3,1,5]=>[3,4,2,6,1,7,8,5]=>[8,5,1,3,2,4,6,7]=>0101001
[6,7,8,4,2,3,1,5]=>[3,4,2,8,1,6,7,5]=>[6,7,8,5,1,3,2,4]=>0101001
[8,7,6,3,2,4,1,5]=>[4,3,6,2,1,7,8,5]=>[8,5,1,4,2,3,6,7]=>0011001
[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>[6,7,8,5,1,4,2,3]=>0011001
[6,7,8,2,3,4,1,5]=>[4,8,2,3,1,6,7,5]=>[6,7,8,5,1,4,3,2]=>0111001
[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>[6,7,8,5,2,1,3,4]=>1001001
[6,7,8,3,4,1,2,5]=>[4,1,8,3,2,6,7,5]=>[6,7,8,5,2,1,4,3]=>1011001
[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[8,5,3,1,2,4,6,7]=>0101001
[7,8,6,4,2,1,3,5]=>[2,4,1,6,3,8,7,5]=>[7,8,5,3,1,2,4,6]=>0101001
[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[8,5,3,2,1,4,6,7]=>1101001
[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[7,8,5,3,2,1,4,6]=>1101001
[7,6,8,4,1,2,3,5]=>[4,1,2,8,3,7,6,5]=>[7,6,8,5,3,2,1,4]=>1101011
[6,7,8,4,1,2,3,5]=>[4,1,2,8,3,6,7,5]=>[6,7,8,5,3,2,1,4]=>1101001
[6,7,8,3,2,1,4,5]=>[2,3,8,1,4,6,7,5]=>[6,7,8,5,4,1,2,3]=>0011001
[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>[8,5,4,2,1,3,6,7]=>1011001
[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[7,8,5,4,2,1,3,6]=>1011001
[6,7,8,3,1,2,4,5]=>[3,1,8,2,4,6,7,5]=>[6,7,8,5,4,2,1,3]=>1011001
[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>[7,8,5,4,3,2,1,6]=>1111001
[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[8,5,4,3,2,1,7,6]=>1111011
[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[7,6,8,5,4,3,2,1]=>1111011
[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[6,7,8,5,4,3,2,1]=>1111001
[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>[7,8,6,1,2,3,4,5]=>0000101
[8,7,3,4,5,2,1,6]=>[2,5,7,3,4,1,8,6]=>[8,6,1,2,5,4,3,7]=>0011101
[7,8,4,5,2,3,1,6]=>[3,5,2,8,4,1,7,6]=>[7,8,6,1,3,2,5,4]=>0101101
[8,7,5,3,2,4,1,6]=>[4,3,5,2,7,1,8,6]=>[8,6,1,4,2,3,5,7]=>0010101
[7,8,4,3,2,5,1,6]=>[5,3,4,8,2,1,7,6]=>[7,8,6,1,5,2,3,4]=>0001101
[7,8,5,4,3,1,2,6]=>[3,1,4,5,8,2,7,6]=>[7,8,6,2,1,3,4,5]=>1000101
[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[8,6,2,1,4,3,5,7]=>1010101
[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[7,8,6,2,1,4,3,5]=>1010101
[7,8,5,4,2,1,3,6]=>[2,4,1,5,8,3,7,6]=>[7,8,6,3,1,2,4,5]=>0100101
[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>[7,8,6,4,1,2,3,5]=>0010101
[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]=>[8,6,4,1,3,2,5,7]=>0110101
[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[7,8,6,4,2,1,3,5]=>1010101
[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[8,6,4,3,2,1,5,7]=>1110101
[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>[7,8,6,4,3,2,1,5]=>1110101
[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[8,6,5,1,2,3,4,7]=>0001101
[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>[7,8,6,5,1,2,3,4]=>0001101
[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]=>[8,6,5,1,2,4,3,7]=>0011101
[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>[7,8,6,5,1,4,2,3]=>0011101
[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>[7,8,6,5,1,4,3,2]=>0111101
[7,8,4,2,1,3,5,6]=>[2,4,1,8,3,5,7,6]=>[7,8,6,5,3,1,2,4]=>0101101
[7,8,4,1,2,3,5,6]=>[4,1,2,8,3,5,7,6]=>[7,8,6,5,3,2,1,4]=>1101101
[7,8,2,1,3,4,5,6]=>[2,8,1,3,4,5,7,6]=>[7,8,6,5,4,3,1,2]=>0111101
[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]=>[8,7,1,2,4,3,6,5]=>0010111
[8,5,6,4,2,3,1,7]=>[3,4,2,6,8,5,1,7]=>[8,7,1,3,2,4,6,5]=>0100111
[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>[8,7,2,1,4,3,6,5]=>1010111
[8,5,6,4,2,1,3,7]=>[2,4,1,6,8,5,3,7]=>[8,7,3,1,2,4,6,5]=>0100111
[8,5,6,4,1,2,3,7]=>[4,1,2,6,8,5,3,7]=>[8,7,3,2,1,4,6,5]=>1100111
[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]=>[8,7,4,1,2,3,6,5]=>0010111
[8,5,6,3,1,2,4,7]=>[3,1,6,2,8,5,4,7]=>[8,7,4,2,1,3,6,5]=>1010111
[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[8,7,4,3,2,1,5,6]=>1110011
[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>[8,7,5,1,2,3,4,6]=>0001011
[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>[8,7,5,1,2,4,3,6]=>0011011
[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]=>[8,7,5,1,4,2,3,6]=>0011011
[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[8,7,5,3,1,2,4,6]=>0101011
[8,4,5,3,2,1,6,7]=>[2,3,5,8,4,1,6,7]=>[8,7,6,1,2,3,5,4]=>0001111
[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]=>[8,7,6,1,2,5,3,4]=>0001111
[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]=>[8,7,6,1,2,5,4,3]=>0011111
[8,4,5,2,3,1,6,7]=>[3,5,2,8,4,1,6,7]=>[8,7,6,1,3,2,5,4]=>0101111
[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]=>[8,7,6,1,5,3,2,4]=>0101111
[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>[8,7,6,2,1,4,3,5]=>1010111
[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]=>[8,7,6,3,1,2,4,5]=>0100111
[8,5,1,2,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>[8,7,6,4,3,2,1,5]=>1110111
[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[8,7,6,5,1,2,3,4]=>0001111
[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>[8,7,6,5,2,1,4,3]=>1011111
[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>[8,7,6,5,3,1,2,4]=>0101111
[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[8,7,6,5,4,1,2,3]=>0011111
[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[8,7,6,5,4,2,1,3]=>1011111
[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[8,7,6,5,4,3,2,1]=>1111111
[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>0000010
[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>[6,5,7,1,2,3,4,8]=>0000110
[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>[5,6,7,1,2,3,4,8]=>0000010
[7,4,5,6,3,2,1,8]=>[2,3,6,7,4,5,1,8]=>[7,1,2,3,6,5,4,8]=>0001110
[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[5,6,4,7,1,2,3,8]=>0000110
[4,5,6,7,3,2,1,8]=>[2,3,7,4,5,6,1,8]=>[4,5,6,7,1,2,3,8]=>0000010
[7,4,5,3,6,2,1,8]=>[2,6,5,7,4,3,1,8]=>[7,1,2,6,3,5,4,8]=>0001110
[7,3,4,5,6,2,1,8]=>[2,6,7,3,4,5,1,8]=>[7,1,2,6,5,4,3,8]=>0011110
[7,6,4,5,2,3,1,8]=>[3,5,2,6,4,7,1,8]=>[7,1,3,2,5,4,6,8]=>0101010
[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>[6,7,1,3,2,5,4,8]=>0101010
[5,6,4,7,2,3,1,8]=>[3,7,2,6,5,4,1,8]=>[5,6,4,7,1,3,2,8]=>0100110
[4,5,6,7,2,3,1,8]=>[3,7,2,4,5,6,1,8]=>[4,5,6,7,1,3,2,8]=>0100010
[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]=>[7,1,4,3,2,5,6,8]=>0110010
[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[6,7,1,4,3,2,5,8]=>0110010
[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>[6,5,7,1,4,3,2,8]=>0110110
[7,6,4,2,3,5,1,8]=>[5,4,2,6,3,7,1,8]=>[7,1,5,3,2,4,6,8]=>0101010
[7,6,3,2,4,5,1,8]=>[5,3,6,2,4,7,1,8]=>[7,1,5,4,2,3,6,8]=>0011010
[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>[7,1,6,2,5,3,4,8]=>0001110
[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]=>[7,1,6,4,2,3,5,8]=>0010110
[5,6,3,4,2,7,1,8]=>[7,4,6,3,5,2,1,8]=>[5,6,2,4,3,7,1,8]=>0010110
[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[4,5,3,6,2,7,1,8]=>0001110
[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[3,4,5,6,2,7,1,8]=>0000110
[4,5,6,7,3,1,2,8]=>[3,1,7,4,5,6,2,8]=>[4,5,6,7,2,1,3,8]=>1000010
[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>[7,2,1,4,3,6,5,8]=>1010110
[4,5,6,7,2,1,3,8]=>[2,7,1,4,5,6,3,8]=>[4,5,6,7,3,1,2,8]=>0100010
[7,5,6,4,1,2,3,8]=>[4,1,2,6,7,5,3,8]=>[7,3,2,1,4,6,5,8]=>1100110
[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]=>[5,6,4,7,3,2,1,8]=>1100110
[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]=>[4,5,6,7,3,2,1,8]=>1100010
[7,6,5,2,3,1,4,8]=>[3,5,2,1,6,7,4,8]=>[7,4,1,3,2,5,6,8]=>0110010
[7,6,5,2,1,3,4,8]=>[2,5,1,3,6,7,4,8]=>[7,4,3,1,2,5,6,8]=>0110010
[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[7,4,3,2,1,5,6,8]=>1110010
[6,7,5,1,2,3,4,8]=>[5,1,2,3,7,6,4,8]=>[6,7,4,3,2,1,5,8]=>1110010
[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>[7,4,3,2,1,6,5,8]=>1110110
[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>[6,5,7,4,3,2,1,8]=>1110110
[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[5,6,7,4,3,2,1,8]=>1110010
[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]=>[7,5,1,2,3,4,6,8]=>0001010
[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]=>[6,7,5,1,2,3,4,8]=>0001010
[7,6,4,2,3,1,5,8]=>[3,4,2,6,1,7,5,8]=>[7,5,1,3,2,4,6,8]=>0101010
[7,6,3,2,4,1,5,8]=>[4,3,6,2,1,7,5,8]=>[7,5,1,4,2,3,6,8]=>0011010
[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[7,5,3,1,2,4,6,8]=>0101010
[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]=>[7,5,4,1,3,2,6,8]=>0111010
[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]=>[7,6,1,4,3,2,5,8]=>0110110
[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[7,6,4,2,1,3,5,8]=>1010110
[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>[7,6,5,1,2,3,4,8]=>0001110
[7,4,3,1,2,5,6,8]=>[3,1,4,7,2,5,6,8]=>[7,6,5,2,1,3,4,8]=>1001110
[7,3,4,1,2,5,6,8]=>[4,1,7,3,2,5,6,8]=>[7,6,5,2,1,4,3,8]=>1011110
[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,6,5,4,3,2,1,8]=>1111110
[5,4,6,2,3,1,7,8]=>[3,6,2,5,4,1,7,8]=>[5,4,6,1,3,2,7,8]=>0101100
[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>[5,6,1,4,2,3,7,8]=>0010100
[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]=>[5,4,6,2,1,3,7,8]=>1001100
[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>[5,6,2,1,4,3,7,8]=>1010100
[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]=>[5,4,6,3,1,2,7,8]=>0101100
[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>0001000
[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[4,5,1,2,3,6,7,8]=>0001000
[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>0011000
[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>0101000
[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>0011000
[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>0111000
[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>0011000
[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>0011000
[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>0111000
[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>0101000
[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>0001000
[5,3,4,1,2,6,7,8]=>[4,1,5,3,2,6,7,8]=>[5,2,1,4,3,6,7,8]=>1011000
[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[4,5,3,2,1,6,7,8]=>1101000
[5,2,3,1,4,6,7,8]=>[3,5,2,1,4,6,7,8]=>[5,4,1,3,2,6,7,8]=>0111000
[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>[5,4,3,1,2,6,7,8]=>0111000
[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>0010000
[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>0010000
[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>0110000
[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>0110000
[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>0010000
[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>1010000
[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>1010000
[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>0110000
[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>0100000
[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>0100000
[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[5,7,8,6,4,3,2,1]=>[2,3,4,6,5,8,7,1]=>[5,7,8,1,2,3,4,6]=>0000001
[6,5,8,7,4,3,2,1]=>[2,3,4,7,6,5,8,1]=>[6,5,8,1,2,3,4,7]=>0000101
[5,6,8,7,4,3,2,1]=>[2,3,4,7,5,6,8,1]=>[5,6,8,1,2,3,4,7]=>0000001
[5,7,6,8,4,3,2,1]=>[2,3,4,8,5,7,6,1]=>[5,7,6,8,1,2,3,4]=>0000011
[4,8,7,6,5,3,2,1]=>[2,3,5,4,6,7,8,1]=>[4,8,1,2,3,5,6,7]=>0000001
[4,6,8,7,5,3,2,1]=>[2,3,5,4,7,6,8,1]=>[4,6,8,1,2,3,5,7]=>0000001
[4,5,8,7,6,3,2,1]=>[2,3,6,4,5,7,8,1]=>[4,5,8,1,2,3,6,7]=>0000001
[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]=>[4,5,6,8,1,2,3,7]=>0000001
[5,7,6,4,8,3,2,1]=>[2,3,8,6,5,7,4,1]=>[5,7,4,6,8,1,2,3]=>0000011
[4,7,6,5,8,3,2,1]=>[2,3,8,4,6,7,5,1]=>[4,7,5,6,8,1,2,3]=>0000011
[4,6,7,5,8,3,2,1]=>[2,3,8,4,7,6,5,1]=>[4,6,7,5,8,1,2,3]=>0000011
[5,4,7,6,8,3,2,1]=>[2,3,8,5,4,7,6,1]=>[5,4,7,6,8,1,2,3]=>0001011
[4,5,7,6,8,3,2,1]=>[2,3,8,4,5,7,6,1]=>[4,5,7,6,8,1,2,3]=>0000011
[4,6,5,7,8,3,2,1]=>[2,3,8,4,6,5,7,1]=>[4,6,5,7,8,1,2,3]=>0000101
[3,5,7,8,6,4,2,1]=>[2,4,3,6,5,8,7,1]=>[3,5,7,8,1,2,4,6]=>0000001
[3,6,7,5,8,4,2,1]=>[2,4,3,8,7,6,5,1]=>[3,6,7,5,8,1,2,4]=>0000011
[3,5,6,7,8,4,2,1]=>[2,4,3,8,5,6,7,1]=>[3,5,6,7,8,1,2,4]=>0000001
[4,3,6,7,8,5,2,1]=>[2,5,4,3,8,6,7,1]=>[4,3,6,7,8,1,2,5]=>0010001
[3,4,8,7,6,5,2,1]=>[2,5,3,4,6,7,8,1]=>[3,4,8,1,2,5,6,7]=>0000001
[3,4,6,7,8,5,2,1]=>[2,5,3,4,8,6,7,1]=>[3,4,6,7,8,1,2,5]=>0000001
[4,5,3,7,8,6,2,1]=>[2,6,5,4,3,8,7,1]=>[4,5,3,7,8,1,2,6]=>0001001
[4,5,3,6,8,7,2,1]=>[2,7,5,4,3,6,8,1]=>[4,5,3,6,8,1,2,7]=>0001001
[4,5,3,7,6,8,2,1]=>[2,8,5,4,3,7,6,1]=>[4,5,3,7,6,8,1,2]=>0001011
[4,3,5,7,6,8,2,1]=>[2,8,4,3,5,7,6,1]=>[4,3,5,7,6,8,1,2]=>0010011
[2,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,1]=>[2,8,1,3,4,5,6,7]=>0000001
[2,5,6,7,8,4,3,1]=>[3,2,4,8,5,6,7,1]=>[2,5,6,7,8,1,3,4]=>0000001
[2,4,6,8,7,5,3,1]=>[3,2,5,4,7,6,8,1]=>[2,4,6,8,1,3,5,7]=>0000001
[2,4,6,7,8,5,3,1]=>[3,2,5,4,8,6,7,1]=>[2,4,6,7,8,1,3,5]=>0000001
[2,4,6,5,8,7,3,1]=>[3,2,7,4,6,5,8,1]=>[2,4,6,5,8,1,3,7]=>0000101
[2,7,6,5,4,8,3,1]=>[3,2,8,5,6,7,4,1]=>[2,7,4,5,6,8,1,3]=>0000011
[2,6,7,5,4,8,3,1]=>[3,2,8,5,7,6,4,1]=>[2,6,7,4,5,8,1,3]=>0000011
[3,2,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,1]=>[3,2,8,1,4,5,6,7]=>0100001
[3,2,6,8,7,5,4,1]=>[4,3,2,5,7,6,8,1]=>[3,2,6,8,1,4,5,7]=>0100001
[3,2,5,6,7,8,4,1]=>[4,3,2,8,5,6,7,1]=>[3,2,5,6,7,8,1,4]=>0100001
[2,3,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,1]=>[2,3,8,1,4,5,6,7]=>0000001
[2,3,7,6,5,8,4,1]=>[4,2,3,8,6,7,5,1]=>[2,3,7,5,6,8,1,4]=>0000011
[2,3,5,6,7,8,4,1]=>[4,2,3,8,5,6,7,1]=>[2,3,5,6,7,8,1,4]=>0000001
[4,3,2,6,8,7,5,1]=>[5,3,4,2,7,6,8,1]=>[4,2,3,6,8,1,5,7]=>0010001
[3,4,2,8,7,6,5,1]=>[5,4,3,2,6,7,8,1]=>[3,4,2,8,1,5,6,7]=>0010001
[3,4,2,7,8,6,5,1]=>[5,4,3,2,6,8,7,1]=>[3,4,2,7,8,1,5,6]=>0010001
[2,4,3,6,8,7,5,1]=>[5,2,4,3,7,6,8,1]=>[2,4,3,6,8,1,5,7]=>0010001
[3,2,4,8,7,6,5,1]=>[5,3,2,4,6,7,8,1]=>[3,2,4,8,1,5,6,7]=>0100001
[2,3,4,8,7,6,5,1]=>[5,2,3,4,6,7,8,1]=>[2,3,4,8,1,5,6,7]=>0000001
[2,3,4,6,7,8,5,1]=>[5,2,3,4,8,6,7,1]=>[2,3,4,6,7,8,1,5]=>0000001
[4,5,3,2,8,7,6,1]=>[6,3,5,4,2,7,8,1]=>[4,5,2,3,8,1,6,7]=>0001001
[4,5,6,3,2,8,7,1]=>[7,3,6,4,5,2,8,1]=>[4,5,6,2,3,8,1,7]=>0000101
[3,5,6,4,2,8,7,1]=>[7,4,3,6,5,2,8,1]=>[3,5,6,2,4,8,1,7]=>0000101
[4,3,6,5,2,8,7,1]=>[7,5,4,3,6,2,8,1]=>[4,3,6,2,5,8,1,7]=>0010101
[2,6,5,4,3,8,7,1]=>[7,2,4,5,6,3,8,1]=>[2,6,3,4,5,8,1,7]=>0000101
[3,4,2,6,5,8,7,1]=>[7,4,3,2,6,5,8,1]=>[3,4,2,6,5,8,1,7]=>0010101
[2,4,3,6,5,8,7,1]=>[7,2,4,3,6,5,8,1]=>[2,4,3,6,5,8,1,7]=>0010101
[2,3,4,6,5,8,7,1]=>[7,2,3,4,6,5,8,1]=>[2,3,4,6,5,8,1,7]=>0000101
[2,5,4,3,6,8,7,1]=>[7,2,4,5,3,6,8,1]=>[2,5,3,4,6,8,1,7]=>0001001
[4,6,5,3,7,2,8,1]=>[8,7,5,4,6,3,2,1]=>[4,6,3,5,7,2,8,1]=>0000111
[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[3,5,6,4,7,2,8,1]=>0000111
[3,5,4,6,7,2,8,1]=>[8,7,3,5,4,6,2,1]=>[3,5,4,6,7,2,8,1]=>0001011
[2,4,6,5,7,3,8,1]=>[8,2,7,4,6,5,3,1]=>[2,4,6,5,7,3,8,1]=>0000111
[2,4,5,6,7,3,8,1]=>[8,2,7,4,5,6,3,1]=>[2,4,5,6,7,3,8,1]=>0000011
[2,3,4,7,6,5,8,1]=>[8,2,3,4,6,7,5,1]=>[2,3,4,7,5,6,8,1]=>0000011
[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[3,2,5,4,7,6,8,1]=>0101011
[2,3,5,4,7,6,8,1]=>[8,2,3,5,4,7,6,1]=>[2,3,5,4,7,6,8,1]=>0001011
[3,2,4,5,7,6,8,1]=>[8,3,2,4,5,7,6,1]=>[3,2,4,5,7,6,8,1]=>0100011
[2,5,4,6,3,7,8,1]=>[8,2,6,5,4,3,7,1]=>[2,5,4,6,3,7,8,1]=>0001101
[3,4,2,6,5,7,8,1]=>[8,4,3,2,6,5,7,1]=>[3,4,2,6,5,7,8,1]=>0010101
[2,4,3,6,5,7,8,1]=>[8,2,4,3,6,5,7,1]=>[2,4,3,6,5,7,8,1]=>0010101
[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>0000001
[1,7,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,2]=>[1,7,8,2,3,4,5,6]=>0000001
[1,7,6,8,5,4,3,2]=>[1,3,4,5,8,7,6,2]=>[1,7,6,8,2,3,4,5]=>0000011
[1,6,7,8,5,4,3,2]=>[1,3,4,5,8,6,7,2]=>[1,6,7,8,2,3,4,5]=>0000001
[1,6,7,5,8,4,3,2]=>[1,3,4,8,7,6,5,2]=>[1,6,7,5,8,2,3,4]=>0000011
[1,5,6,7,8,4,3,2]=>[1,3,4,8,5,6,7,2]=>[1,5,6,7,8,2,3,4]=>0000001
[1,4,8,7,6,5,3,2]=>[1,3,5,4,6,7,8,2]=>[1,4,8,2,3,5,6,7]=>0000001
[1,4,6,8,7,5,3,2]=>[1,3,5,4,7,6,8,2]=>[1,4,6,8,2,3,5,7]=>0000001
[1,4,5,7,8,6,3,2]=>[1,3,6,4,5,8,7,2]=>[1,4,5,7,8,2,3,6]=>0000001
[1,3,5,8,7,6,4,2]=>[1,4,3,6,5,7,8,2]=>[1,3,5,8,2,4,6,7]=>0000001
[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>[1,3,5,7,8,2,4,6]=>0000001
[1,3,5,7,6,8,4,2]=>[1,4,3,8,5,7,6,2]=>[1,3,5,7,6,8,2,4]=>0000011
[1,3,5,6,7,8,4,2]=>[1,4,3,8,5,6,7,2]=>[1,3,5,6,7,8,2,4]=>0000001
[1,4,3,8,7,6,5,2]=>[1,5,4,3,6,7,8,2]=>[1,4,3,8,2,5,6,7]=>0010001
[1,4,3,6,8,7,5,2]=>[1,5,4,3,7,6,8,2]=>[1,4,3,6,8,2,5,7]=>0010001
[1,4,3,7,6,8,5,2]=>[1,5,4,3,8,7,6,2]=>[1,4,3,7,6,8,2,5]=>0010011
[1,3,4,8,7,6,5,2]=>[1,5,3,4,6,7,8,2]=>[1,3,4,8,2,5,6,7]=>0000001
[1,3,4,7,6,8,5,2]=>[1,5,3,4,8,7,6,2]=>[1,3,4,7,6,8,2,5]=>0000011
[1,3,5,4,7,8,6,2]=>[1,6,3,5,4,8,7,2]=>[1,3,5,4,7,8,2,6]=>0001001
[1,5,6,4,3,8,7,2]=>[1,7,4,6,5,3,8,2]=>[1,5,6,3,4,8,2,7]=>0000101
[1,5,4,3,6,8,7,2]=>[1,7,4,5,3,6,8,2]=>[1,5,3,4,6,8,2,7]=>0001001
[1,6,7,5,4,3,8,2]=>[1,8,4,5,7,6,3,2]=>[1,6,7,3,4,5,8,2]=>0000011
[1,3,5,7,6,4,8,2]=>[1,8,3,6,5,7,4,2]=>[1,3,5,7,4,6,8,2]=>0000011
[1,3,5,4,7,6,8,2]=>[1,8,3,5,4,7,6,2]=>[1,3,5,4,7,6,8,2]=>0001011
[1,4,3,6,5,7,8,2]=>[1,8,4,3,6,5,7,2]=>[1,4,3,6,5,7,8,2]=>0010101
[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>1000001
[2,1,7,8,6,5,4,3]=>[2,1,4,5,6,8,7,3]=>[2,1,7,8,3,4,5,6]=>1000001
[2,1,7,6,8,5,4,3]=>[2,1,4,5,8,7,6,3]=>[2,1,7,6,8,3,4,5]=>1000011
[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>[2,1,6,7,8,3,4,5]=>1000001
[2,1,5,7,8,6,4,3]=>[2,1,4,6,5,8,7,3]=>[2,1,5,7,8,3,4,6]=>1000001
[2,1,6,7,5,8,4,3]=>[2,1,4,8,7,6,5,3]=>[2,1,6,7,5,8,3,4]=>1000011
[2,1,6,5,7,8,4,3]=>[2,1,4,8,6,5,7,3]=>[2,1,6,5,7,8,3,4]=>1000101
[2,1,5,6,7,8,4,3]=>[2,1,4,8,5,6,7,3]=>[2,1,5,6,7,8,3,4]=>1000001
[2,1,4,8,7,6,5,3]=>[2,1,5,4,6,7,8,3]=>[2,1,4,8,3,5,6,7]=>1000001
[2,1,4,6,8,7,5,3]=>[2,1,5,4,7,6,8,3]=>[2,1,4,6,8,3,5,7]=>1000001
[2,1,4,5,8,7,6,3]=>[2,1,6,4,5,7,8,3]=>[2,1,4,5,8,3,6,7]=>1000001
[2,1,4,6,5,8,7,3]=>[2,1,7,4,6,5,8,3]=>[2,1,4,6,5,8,3,7]=>1000101
[2,1,5,7,6,4,8,3]=>[2,1,8,6,5,7,4,3]=>[2,1,5,7,4,6,8,3]=>1000011
[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[2,1,6,5,7,4,8,3]=>1000111
[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[2,1,5,6,7,4,8,3]=>1000011
[2,1,4,6,7,5,8,3]=>[2,1,8,4,7,6,5,3]=>[2,1,4,6,7,5,8,3]=>1000011
[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[2,1,5,4,7,6,8,3]=>1001011
[2,1,5,6,4,7,8,3]=>[2,1,8,6,5,4,7,3]=>[2,1,5,6,4,7,8,3]=>1000101
[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[2,1,4,5,6,7,8,3]=>1000001
[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]=>[1,2,8,3,4,5,6,7]=>0000001
[1,2,6,7,8,5,4,3]=>[1,2,4,5,8,6,7,3]=>[1,2,6,7,8,3,4,5]=>0000001
[1,2,6,5,8,7,4,3]=>[1,2,4,7,6,5,8,3]=>[1,2,6,5,8,3,4,7]=>0000101
[1,2,5,6,7,8,4,3]=>[1,2,4,8,5,6,7,3]=>[1,2,5,6,7,8,3,4]=>0000001
[1,2,4,8,7,6,5,3]=>[1,2,5,4,6,7,8,3]=>[1,2,4,8,3,5,6,7]=>0000001
[1,2,4,7,8,6,5,3]=>[1,2,5,4,6,8,7,3]=>[1,2,4,7,8,3,5,6]=>0000001
[1,2,5,4,8,7,6,3]=>[1,2,6,5,4,7,8,3]=>[1,2,5,4,8,3,6,7]=>0001001
[1,2,5,4,7,8,6,3]=>[1,2,6,5,4,8,7,3]=>[1,2,5,4,7,8,3,6]=>0001001
[1,2,6,5,4,8,7,3]=>[1,2,7,5,6,4,8,3]=>[1,2,6,4,5,8,3,7]=>0000101
[1,2,5,7,6,4,8,3]=>[1,2,8,6,5,7,4,3]=>[1,2,5,7,4,6,8,3]=>0000011
[1,2,5,6,7,4,8,3]=>[1,2,8,7,5,6,4,3]=>[1,2,5,6,7,4,8,3]=>0000011
[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]=>[3,1,2,8,4,5,6,7]=>0100001
[3,2,1,7,8,6,5,4]=>[2,3,1,5,6,8,7,4]=>[3,1,2,7,8,4,5,6]=>0100001
[3,2,1,5,8,7,6,4]=>[2,3,1,6,5,7,8,4]=>[3,1,2,5,8,4,6,7]=>0100001
[3,2,1,6,5,8,7,4]=>[2,3,1,7,6,5,8,4]=>[3,1,2,6,5,8,4,7]=>0100101
[3,2,1,5,6,8,7,4]=>[2,3,1,7,5,6,8,4]=>[3,1,2,5,6,8,4,7]=>0100001
[3,2,1,7,6,5,8,4]=>[2,3,1,8,6,7,5,4]=>[3,1,2,7,5,6,8,4]=>0100011
[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]=>[3,1,2,6,7,5,8,4]=>0100011
[3,2,1,5,7,6,8,4]=>[2,3,1,8,5,7,6,4]=>[3,1,2,5,7,6,8,4]=>0100011
[3,2,1,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]=>[3,1,2,5,6,7,8,4]=>0100001
[2,3,1,8,7,6,5,4]=>[3,2,1,5,6,7,8,4]=>[2,3,1,8,4,5,6,7]=>0100001
[2,3,1,6,8,7,5,4]=>[3,2,1,5,7,6,8,4]=>[2,3,1,6,8,4,5,7]=>0100001
[2,3,1,7,6,8,5,4]=>[3,2,1,5,8,7,6,4]=>[2,3,1,7,6,8,4,5]=>0100011
[2,3,1,6,7,8,5,4]=>[3,2,1,5,8,6,7,4]=>[2,3,1,6,7,8,4,5]=>0100001
[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[2,3,1,5,6,7,8,4]=>0100001
[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]=>[1,3,2,8,4,5,6,7]=>0100001
[1,3,2,5,7,8,6,4]=>[1,3,2,6,5,8,7,4]=>[1,3,2,5,7,8,4,6]=>0100001
[1,3,2,6,5,8,7,4]=>[1,3,2,7,6,5,8,4]=>[1,3,2,6,5,8,4,7]=>0100101
[1,3,2,7,6,5,8,4]=>[1,3,2,8,6,7,5,4]=>[1,3,2,7,5,6,8,4]=>0100011
[1,3,2,5,7,6,8,4]=>[1,3,2,8,5,7,6,4]=>[1,3,2,5,7,6,8,4]=>0100011
[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]=>[1,3,2,6,5,7,8,4]=>0100101
[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,4,5,6,7]=>1000001
[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>0000001
[1,2,3,7,8,6,5,4]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,8,4,5,6]=>0000001
[1,2,3,7,6,8,5,4]=>[1,2,3,5,8,7,6,4]=>[1,2,3,7,6,8,4,5]=>0000011
[1,2,3,6,7,8,5,4]=>[1,2,3,5,8,6,7,4]=>[1,2,3,6,7,8,4,5]=>0000001
[1,2,3,5,8,7,6,4]=>[1,2,3,6,5,7,8,4]=>[1,2,3,5,8,4,6,7]=>0000001
[1,2,3,5,7,8,6,4]=>[1,2,3,6,5,8,7,4]=>[1,2,3,5,7,8,4,6]=>0000001
[1,2,3,6,5,8,7,4]=>[1,2,3,7,6,5,8,4]=>[1,2,3,6,5,8,4,7]=>0000101
[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]=>[1,2,3,5,6,8,4,7]=>0000001
[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,7,5,4]=>[1,2,3,7,5,6,8,4]=>0000011
[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>[1,2,3,6,7,5,8,4]=>0000011
[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>[1,2,3,5,7,6,8,4]=>0000011
[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>[1,2,3,6,5,7,8,4]=>0000101
[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[1,2,3,5,6,7,8,4]=>0000001
[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>0010001
[4,3,2,1,7,8,6,5]=>[2,3,4,1,6,8,7,5]=>[4,1,2,3,7,8,5,6]=>0010001
[4,3,2,1,6,8,7,5]=>[2,3,4,1,7,6,8,5]=>[4,1,2,3,6,8,5,7]=>0010001
[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]=>[4,1,2,3,7,6,8,5]=>0010011
[4,3,2,1,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>[4,1,2,3,6,7,8,5]=>0010001
[3,4,2,1,8,7,6,5]=>[2,4,3,1,6,7,8,5]=>[3,4,1,2,8,5,6,7]=>0010001
[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>[3,4,1,2,7,8,5,6]=>0010001
[3,4,2,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]=>[3,4,1,2,6,8,5,7]=>0010001
[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>[3,4,1,2,7,6,8,5]=>0010011
[3,4,2,1,6,7,8,5]=>[2,4,3,1,8,6,7,5]=>[3,4,1,2,6,7,8,5]=>0010001
[2,4,3,1,8,7,6,5]=>[3,2,4,1,6,7,8,5]=>[2,4,1,3,8,5,6,7]=>0010001
[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>[2,4,1,3,6,8,5,7]=>0010001
[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>[2,4,1,3,7,6,8,5]=>0010011
[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>[2,4,1,3,6,7,8,5]=>0010001
[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>[3,2,4,1,8,5,6,7]=>0110001
[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>[3,2,4,1,7,8,5,6]=>0110001
[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>[3,2,4,1,6,8,5,7]=>0110001
[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[3,2,4,1,7,6,8,5]=>0110011
[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[3,2,4,1,6,7,8,5]=>0110001
[2,3,4,1,8,7,6,5]=>[4,2,3,1,6,7,8,5]=>[2,3,4,1,8,5,6,7]=>0010001
[2,3,4,1,7,8,6,5]=>[4,2,3,1,6,8,7,5]=>[2,3,4,1,7,8,5,6]=>0010001
[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]=>[2,3,4,1,6,8,5,7]=>0010001
[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>[2,3,4,1,7,6,8,5]=>0010011
[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[2,3,4,1,6,7,8,5]=>0010001
[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]=>[1,4,2,3,8,5,6,7]=>0010001
[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>[1,4,2,3,7,6,8,5]=>0010011
[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>[1,4,2,3,6,7,8,5]=>0010001
[1,3,4,2,8,7,6,5]=>[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,5,6,7]=>0010001
[1,3,4,2,7,8,6,5]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,8,5,6]=>0010001
[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,7,6,8,5]=>0010011
[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[1,3,4,2,6,7,8,5]=>0010001
[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>1010001
[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,8,5,6]=>1010001
[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,6,8,5,7]=>1010001
[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,8,5]=>1010011
[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,4,3,6,7,8,5]=>1010001
[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,5,6,7]=>0010001
[1,2,4,3,7,8,6,5]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,8,5,6]=>0010001
[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,6,8,5,7]=>0010001
[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,7,6,8,5]=>0010011
[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[1,2,4,3,6,7,8,5]=>0010001
[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]=>[3,1,2,4,8,5,6,7]=>0100001
[3,2,1,4,7,8,6,5]=>[2,3,1,4,6,8,7,5]=>[3,1,2,4,7,8,5,6]=>0100001
[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,6,8,5]=>[3,1,2,4,6,8,5,7]=>0100001
[3,2,1,4,7,6,8,5]=>[2,3,1,4,8,7,6,5]=>[3,1,2,4,7,6,8,5]=>0100011
[3,2,1,4,6,7,8,5]=>[2,3,1,4,8,6,7,5]=>[3,1,2,4,6,7,8,5]=>0100001
[2,3,1,4,8,7,6,5]=>[3,2,1,4,6,7,8,5]=>[2,3,1,4,8,5,6,7]=>0100001
[2,3,1,4,7,8,6,5]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,8,5,6]=>0100001
[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,7,6,8,5]=>0100011
[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[2,3,1,4,6,7,8,5]=>0100001
[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,5,6,7]=>0100001
[1,3,2,4,6,8,7,5]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,6,8,5,7]=>0100001
[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,7,6,8,5]=>0100011
[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>[1,3,2,4,6,7,8,5]=>0100001
[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,5,6,7]=>1000001
[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,7,6,8,5]=>1000011
[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[2,1,3,4,6,7,8,5]=>1000001
[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,5,6,7]=>0000001
[1,2,3,4,7,8,6,5]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,8,5,6]=>0000001
[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,6,8,5,7]=>0000001
[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,7,6,8,5]=>0000011
[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[1,2,3,4,6,7,8,5]=>0000001
[4,5,3,2,1,8,7,6]=>[2,3,5,4,1,7,8,6]=>[4,5,1,2,3,8,6,7]=>0001001
[3,5,4,2,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>[3,5,1,2,4,8,6,7]=>0001001
[3,5,4,2,1,7,8,6]=>[2,4,3,5,1,8,7,6]=>[3,5,1,2,4,7,8,6]=>0001001
[3,4,5,2,1,8,7,6]=>[2,5,3,4,1,7,8,6]=>[3,4,5,1,2,8,6,7]=>0001001
[3,2,5,4,1,7,8,6]=>[4,3,2,5,1,8,7,6]=>[3,2,5,1,4,7,8,6]=>0101001
[2,3,5,4,1,8,7,6]=>[4,2,3,5,1,7,8,6]=>[2,3,5,1,4,8,6,7]=>0001001
[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>[3,4,2,5,1,8,6,7]=>0011001
[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[3,4,2,5,1,7,8,6]=>0011001
[2,4,3,5,1,8,7,6]=>[5,2,4,3,1,7,8,6]=>[2,4,3,5,1,8,6,7]=>0011001
[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>0011001
[3,2,4,5,1,8,7,6]=>[5,3,2,4,1,7,8,6]=>[3,2,4,5,1,8,6,7]=>0101001
[1,3,5,4,2,7,8,6]=>[1,4,3,5,2,8,7,6]=>[1,3,5,2,4,7,8,6]=>0001001
[1,4,3,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>[1,4,3,5,2,7,8,6]=>0011001
[1,3,4,5,2,8,7,6]=>[1,5,3,4,2,7,8,6]=>[1,3,4,5,2,8,6,7]=>0001001
[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[1,3,4,5,2,7,8,6]=>0001001
[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,7,6]=>[1,2,5,3,4,7,8,6]=>0001001
[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,6,7]=>0001001
[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>0001001
[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,6,7]=>0101001
[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>0101001
[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,6,7]=>0001001
[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>0001001
[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>[4,1,2,3,5,8,6,7]=>0010001
[4,3,2,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>0010001
[3,4,2,1,5,8,7,6]=>[2,4,3,1,5,7,8,6]=>[3,4,1,2,5,8,6,7]=>0010001
[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>[3,2,4,1,5,8,6,7]=>0110001
[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[3,2,4,1,5,7,8,6]=>0110001
[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,7,8,6]=>[2,3,4,1,5,8,6,7]=>0010001
[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>0010001
[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>[1,4,2,3,5,8,6,7]=>0010001
[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,7,6]=>[1,4,2,3,5,7,8,6]=>0010001
[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,6,7]=>0010001
[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>0010001
[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>0100001
[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>0100001
[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>0100001
[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,6,7]=>0000001
[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>0000001
[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>0000101
[5,4,6,3,2,1,8,7]=>[2,3,6,5,4,1,8,7]=>[5,4,6,1,2,3,8,7]=>0001101
[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>[4,5,6,1,2,3,8,7]=>0000101
[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]=>[3,5,6,1,2,4,8,7]=>0000101
[4,5,3,6,2,1,8,7]=>[2,6,5,4,3,1,8,7]=>[4,5,3,6,1,2,8,7]=>0001101
[2,4,6,5,3,1,8,7]=>[3,2,5,4,6,1,8,7]=>[2,4,6,1,3,5,8,7]=>0000101
[2,3,6,5,4,1,8,7]=>[4,2,3,5,6,1,8,7]=>[2,3,6,1,4,5,8,7]=>0000101
[2,3,5,6,4,1,8,7]=>[4,2,3,6,5,1,8,7]=>[2,3,5,6,1,4,8,7]=>0000101
[2,4,3,6,5,1,8,7]=>[5,2,4,3,6,1,8,7]=>[2,4,3,6,1,5,8,7]=>0010101
[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[4,3,5,2,6,1,8,7]=>0011101
[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>[3,4,5,2,6,1,8,7]=>0001101
[2,4,5,3,6,1,8,7]=>[6,2,5,4,3,1,8,7]=>[2,4,5,3,6,1,8,7]=>0001101
[3,4,2,5,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[3,4,2,5,6,1,8,7]=>0010101
[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[2,3,4,5,6,1,8,7]=>0000101
[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>1000101
[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>[2,1,5,6,3,4,8,7]=>1000101
[2,1,4,6,5,3,8,7]=>[2,1,5,4,6,3,8,7]=>[2,1,4,6,3,5,8,7]=>1000101
[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,5,4,6,3,8,7]=>1001101
[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,4,5,6,3,8,7]=>1000101
[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,4,5,8,7]=>0000101
[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>0000101
[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>0010101
[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>0010101
[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>0010101
[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>0110101
[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>0010101
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>1010101
[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>0010101
[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>0100101
[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>1000101
[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>0000101
[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>[2,1,5,3,4,6,8,7]=>1001001
[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>1001001
[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>1001001
[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>0010001
[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>0110001
[2,3,4,1,5,6,8,7]=>[4,2,3,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>0010001
[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>0010001
[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>0010001
[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>1010001
[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>0010001
[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>1000001
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>0000001
[3,5,7,6,4,2,1,8]=>[2,4,3,6,5,7,1,8]=>[3,5,7,1,2,4,6,8]=>0000010
[4,5,3,7,6,2,1,8]=>[2,6,5,4,3,7,1,8]=>[4,5,3,7,1,2,6,8]=>0001010
[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>[2,4,6,7,1,3,5,8]=>0000010
[2,3,4,7,6,5,1,8]=>[5,2,3,4,6,7,1,8]=>[2,3,4,7,1,5,6,8]=>0000010
[4,5,3,2,7,6,1,8]=>[6,3,5,4,2,7,1,8]=>[4,5,2,3,7,1,6,8]=>0001010
[3,5,4,2,7,6,1,8]=>[6,4,3,5,2,7,1,8]=>[3,5,2,4,7,1,6,8]=>0001010
[3,2,5,4,7,6,1,8]=>[6,3,2,5,4,7,1,8]=>[3,2,5,4,7,1,6,8]=>0101010
[3,6,5,4,2,7,1,8]=>[7,4,3,5,6,2,1,8]=>[3,6,2,4,5,7,1,8]=>0000110
[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]=>[3,5,4,6,2,7,1,8]=>0001110
[2,5,4,6,3,7,1,8]=>[7,2,6,5,4,3,1,8]=>[2,5,4,6,3,7,1,8]=>0001110
[3,4,2,6,5,7,1,8]=>[7,4,3,2,6,5,1,8]=>[3,4,2,6,5,7,1,8]=>0010110
[2,4,3,6,5,7,1,8]=>[7,2,4,3,6,5,1,8]=>[2,4,3,6,5,7,1,8]=>0010110
[2,5,4,3,6,7,1,8]=>[7,2,4,5,3,6,1,8]=>[2,5,3,4,6,7,1,8]=>0001010
[1,4,6,5,7,3,2,8]=>[1,3,7,4,6,5,2,8]=>[1,4,6,5,7,2,3,8]=>0000110
[1,3,5,7,6,4,2,8]=>[1,4,3,6,5,7,2,8]=>[1,3,5,7,2,4,6,8]=>0000010
[1,3,5,6,7,4,2,8]=>[1,4,3,7,5,6,2,8]=>[1,3,5,6,7,2,4,8]=>0000010
[1,4,3,6,5,7,2,8]=>[1,7,4,3,6,5,2,8]=>[1,4,3,6,5,7,2,8]=>0010110
[1,2,5,6,4,7,3,8]=>[1,2,7,6,5,4,3,8]=>[1,2,5,6,4,7,3,8]=>0000110
[3,2,1,5,7,6,4,8]=>[2,3,1,6,5,7,4,8]=>[3,1,2,5,7,4,6,8]=>0100010
[2,3,1,6,5,7,4,8]=>[3,2,1,7,6,5,4,8]=>[2,3,1,6,5,7,4,8]=>0100110
[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[2,3,1,5,6,7,4,8]=>0100010
[1,3,2,5,7,6,4,8]=>[1,3,2,6,5,7,4,8]=>[1,3,2,5,7,4,6,8]=>0100010
[1,3,2,6,5,7,4,8]=>[1,3,2,7,6,5,4,8]=>[1,3,2,6,5,7,4,8]=>0100110
[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]=>[1,3,2,5,6,7,4,8]=>0100010
[1,2,3,7,6,5,4,8]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,4,5,6,8]=>0000010
[1,2,3,6,7,5,4,8]=>[1,2,3,5,7,6,4,8]=>[1,2,3,6,7,4,5,8]=>0000010
[1,2,3,5,7,6,4,8]=>[1,2,3,6,5,7,4,8]=>[1,2,3,5,7,4,6,8]=>0000010
[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]=>[1,2,3,6,5,7,4,8]=>0000110
[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[1,2,3,5,6,7,4,8]=>0000010
[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>[4,1,2,3,7,5,6,8]=>0010010
[4,3,2,1,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>0010010
[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>[3,2,4,1,7,5,6,8]=>0110010
[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[3,2,4,1,6,7,5,8]=>0110010
[2,3,4,1,7,6,5,8]=>[4,2,3,1,6,7,5,8]=>[2,3,4,1,7,5,6,8]=>0010010
[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>0010010
[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>0010010
[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>0010010
[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,6,7,5,8]=>0010010
[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>[3,1,2,4,7,5,6,8]=>0100010
[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>0100010
[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,5,6,8]=>0000010
[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>0000010
[4,5,3,2,1,7,6,8]=>[2,3,5,4,1,7,6,8]=>[4,5,1,2,3,7,6,8]=>0001010
[3,5,4,2,1,7,6,8]=>[2,4,3,5,1,7,6,8]=>[3,5,1,2,4,7,6,8]=>0001010
[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[3,4,2,5,1,7,6,8]=>0011010
[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[2,4,3,5,1,7,6,8]=>0011010
[1,3,5,4,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>[1,3,5,2,4,7,6,8]=>0001010
[1,4,3,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>0011010
[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]=>[1,3,4,5,2,7,6,8]=>0001010
[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>0101010
[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>0101010
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>0101010
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>0001010
[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>0010010
[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>0110010
[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>0010010
[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>0010010
[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>0010010
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>0100010
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>0000010
[2,4,5,6,3,1,7,8]=>[3,2,6,4,5,1,7,8]=>[2,4,5,6,1,3,7,8]=>0000100
[1,5,4,6,3,2,7,8]=>[1,3,6,5,4,2,7,8]=>[1,5,4,6,2,3,7,8]=>0001100
[1,3,5,6,4,2,7,8]=>[1,4,3,6,5,2,7,8]=>[1,3,5,6,2,4,7,8]=>0000100
[1,4,3,6,5,2,7,8]=>[1,5,4,3,6,2,7,8]=>[1,4,3,6,2,5,7,8]=>0010100
[2,1,5,6,4,3,7,8]=>[2,1,4,6,5,3,7,8]=>[2,1,5,6,3,4,7,8]=>1000100
[1,2,6,5,4,3,7,8]=>[1,2,4,5,6,3,7,8]=>[1,2,6,3,4,5,7,8]=>0000100
[1,2,5,6,4,3,7,8]=>[1,2,4,6,5,3,7,8]=>[1,2,5,6,3,4,7,8]=>0000100
[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[1,2,4,5,6,3,7,8]=>0000100
[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>0100100
[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>0000100
[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>0010100
[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>0110100
[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>0010100
[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>1010100
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>0010100
[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>0100100
[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>1000100
[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100
[3,5,4,2,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>[3,5,1,2,4,6,7,8]=>0001000
[2,5,4,3,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>[2,5,1,3,4,6,7,8]=>0001000
[3,2,5,4,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>[3,2,5,1,4,6,7,8]=>0101000
[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>0011000
[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>0001000
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>0101000
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000
[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>0010000
[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0010000
[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>0010000
[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>1010000
[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000
[1,2,3,4,8,6,7,5]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,5,7,6]=>0000011
[1,2,3,5,8,6,7,4]=>[1,2,3,7,5,8,6,4]=>[1,2,3,5,8,4,7,6]=>0000011
[1,2,3,7,5,6,4,8]=>[1,2,3,6,7,5,4,8]=>[1,2,3,7,4,6,5,8]=>0000110
[1,2,3,7,5,6,8,4]=>[1,2,3,8,7,5,6,4]=>[1,2,3,7,6,5,8,4]=>0000111
[1,2,3,8,5,6,7,4]=>[1,2,3,7,8,5,6,4]=>[1,2,3,8,4,7,6,5]=>0000111
[1,2,3,8,6,5,7,4]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,4,7,5,6]=>0000011
[1,2,3,8,6,7,5,4]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,4,5,7,6]=>0000011
[1,2,4,5,8,6,7,3]=>[1,2,7,4,5,8,6,3]=>[1,2,4,5,8,3,7,6]=>0000011
[1,2,4,8,5,6,7,3]=>[1,2,7,4,8,5,6,3]=>[1,2,4,8,3,7,6,5]=>0000111
[1,2,5,4,8,6,7,3]=>[1,2,7,5,4,8,6,3]=>[1,2,5,4,8,3,7,6]=>0001011
[1,2,8,4,5,6,7,3]=>[1,2,7,8,4,5,6,3]=>[1,2,8,3,7,6,5,4]=>0001111
[1,2,8,5,4,6,7,3]=>[1,2,7,5,8,4,6,3]=>[1,2,8,3,7,6,4,5]=>0000111
[1,2,8,6,5,4,7,3]=>[1,2,7,5,6,8,4,3]=>[1,2,8,3,7,4,5,6]=>0000011
[1,3,2,8,5,7,6,4]=>[1,3,2,6,7,8,5,4]=>[1,3,2,7,5,8,4,6]=>0100011
[1,3,8,4,5,6,7,2]=>[1,7,3,8,4,5,6,2]=>[1,3,8,2,7,6,5,4]=>0001111
[1,3,8,4,6,7,5,2]=>[1,5,3,7,8,4,6,2]=>[1,3,7,6,4,8,2,5]=>0000111
[1,3,8,5,4,6,7,2]=>[1,7,3,5,8,4,6,2]=>[1,3,8,2,7,6,4,5]=>0000111
[1,3,8,5,4,7,6,2]=>[1,6,3,5,7,8,4,2]=>[1,3,7,4,5,8,2,6]=>0000011
[1,3,8,5,6,7,4,2]=>[1,4,3,7,8,5,6,2]=>[1,3,8,2,4,7,6,5]=>0000111
[1,3,8,5,7,6,4,2]=>[1,4,3,6,7,8,5,2]=>[1,3,7,5,8,2,4,6]=>0000011
[1,4,3,8,5,7,6,2]=>[1,6,4,3,7,8,5,2]=>[1,4,3,7,5,8,2,6]=>0010011
[1,8,3,4,6,7,5,2]=>[1,5,7,3,8,4,6,2]=>[1,7,6,4,3,8,2,5]=>0010111
[1,6,3,5,4,2,7,8]=>[1,4,5,6,3,2,7,8]=>[1,5,3,6,2,4,7,8]=>0001100
[1,8,3,5,4,7,6,2]=>[1,6,5,7,3,8,4,2]=>[1,5,3,7,4,8,2,6]=>0001011
[1,8,4,3,5,7,6,2]=>[1,6,4,7,3,8,5,2]=>[1,7,5,3,4,8,2,6]=>0001011
[1,8,4,3,6,7,5,2]=>[1,5,4,7,8,3,6,2]=>[1,7,6,3,4,8,2,5]=>0000111
[1,8,4,5,6,3,7,2]=>[1,7,6,8,4,5,3,2]=>[1,8,2,7,3,6,5,4]=>0001111
[1,8,4,5,6,7,3,2]=>[1,3,7,8,4,5,6,2]=>[1,8,2,3,7,6,5,4]=>0001111
[1,8,4,7,6,5,3,2]=>[1,3,5,6,7,8,4,2]=>[1,8,2,3,5,7,4,6]=>0000011
[1,7,5,4,3,6,8,2]=>[1,8,4,5,7,3,6,2]=>[1,7,6,3,4,5,8,2]=>0000111
[1,8,5,4,3,6,7,2]=>[1,7,4,5,8,3,6,2]=>[1,8,2,7,6,3,4,5]=>0000111
[1,8,5,4,6,3,7,2]=>[1,7,6,5,8,4,3,2]=>[1,8,2,7,3,6,4,5]=>0000111
[1,8,6,4,5,7,3,2]=>[1,3,7,6,4,8,5,2]=>[1,8,2,3,7,5,4,6]=>0001011
[1,8,7,4,5,6,3,2]=>[1,3,6,7,4,5,8,2]=>[1,8,2,3,6,5,4,7]=>0001101
[2,1,4,3,8,6,7,5]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,5,7,6]=>1010011
[2,1,4,5,8,6,7,3]=>[2,1,7,4,5,8,6,3]=>[2,1,4,5,8,3,7,6]=>1000011
[2,1,4,8,5,7,6,3]=>[2,1,6,4,7,8,5,3]=>[2,1,4,7,5,8,3,6]=>1000011
[2,1,4,8,6,7,5,3]=>[2,1,5,4,7,8,6,3]=>[2,1,4,8,3,5,7,6]=>1000011
[2,1,5,4,8,6,7,3]=>[2,1,7,5,4,8,6,3]=>[2,1,5,4,8,3,7,6]=>1001011
[2,1,6,4,5,3,8,7]=>[2,1,5,6,4,3,8,7]=>[2,1,6,3,5,4,8,7]=>1001101
[2,1,6,4,5,8,7,3]=>[2,1,7,6,4,5,8,3]=>[2,1,6,5,4,8,3,7]=>1001101
[2,1,8,4,5,6,7,3]=>[2,1,7,8,4,5,6,3]=>[2,1,8,3,7,6,5,4]=>1001111
[2,1,8,4,5,7,6,3]=>[2,1,6,7,4,8,5,3]=>[2,1,7,5,4,8,3,6]=>1001011
[2,1,8,4,6,5,7,3]=>[2,1,7,6,8,4,5,3]=>[2,1,6,4,8,3,7,5]=>1000111
[2,1,8,4,7,6,5,3]=>[2,1,5,6,7,8,4,3]=>[2,1,8,3,5,7,4,6]=>1000011
[2,1,7,5,4,6,8,3]=>[2,1,8,5,7,4,6,3]=>[2,1,7,6,4,5,8,3]=>1000111
[2,1,8,5,4,6,7,3]=>[2,1,7,5,8,4,6,3]=>[2,1,8,3,7,6,4,5]=>1000111
[2,1,8,5,4,7,6,3]=>[2,1,6,5,7,8,4,3]=>[2,1,7,4,5,8,3,6]=>1000011
[2,1,8,5,6,4,7,3]=>[2,1,7,6,8,5,4,3]=>[2,1,8,3,7,4,6,5]=>1000111
[2,1,8,5,7,6,4,3]=>[2,1,4,6,7,8,5,3]=>[2,1,7,5,8,3,4,6]=>1000011
[2,3,1,5,8,6,7,4]=>[3,2,1,7,5,8,6,4]=>[2,3,1,5,8,4,7,6]=>0100011
[2,3,1,8,6,7,5,4]=>[3,2,1,5,7,8,6,4]=>[2,3,1,8,4,5,7,6]=>0100011
[2,3,4,1,8,6,7,5]=>[4,2,3,1,7,8,6,5]=>[2,3,4,1,8,5,7,6]=>0010011
[2,3,4,5,8,6,7,1]=>[7,2,3,4,5,8,6,1]=>[2,3,4,5,8,1,7,6]=>0000011
[2,3,4,7,5,6,8,1]=>[8,2,3,4,7,5,6,1]=>[2,3,4,7,6,5,8,1]=>0000111
[2,3,4,8,5,6,7,1]=>[7,2,3,4,8,5,6,1]=>[2,3,4,8,1,7,6,5]=>0000111
[2,3,4,8,6,5,7,1]=>[7,2,3,4,6,8,5,1]=>[2,3,4,8,1,7,5,6]=>0000011
[2,3,4,8,6,7,5,1]=>[5,2,3,4,7,8,6,1]=>[2,3,4,8,1,5,7,6]=>0000011
[2,3,6,4,5,1,8,7]=>[5,2,3,6,4,1,8,7]=>[2,3,6,1,5,4,8,7]=>0001101
[2,3,7,4,5,6,8,1]=>[8,2,3,7,4,5,6,1]=>[2,3,7,6,5,4,8,1]=>0001111
[2,3,8,4,5,6,7,1]=>[7,2,3,8,4,5,6,1]=>[2,3,8,1,7,6,5,4]=>0001111
[2,3,7,5,6,4,8,1]=>[8,2,3,6,7,5,4,1]=>[2,3,7,4,6,5,8,1]=>0000111
[2,3,8,5,7,6,4,1]=>[4,2,3,6,7,8,5,1]=>[2,3,7,5,8,1,4,6]=>0000011
[2,4,3,1,8,6,7,5]=>[3,2,4,1,7,8,6,5]=>[2,4,1,3,8,5,7,6]=>0010011
[2,5,3,4,6,7,1,8]=>[7,2,5,3,4,6,1,8]=>[2,5,4,3,6,7,1,8]=>0011010
[2,6,3,4,5,7,8,1]=>[8,2,6,3,4,5,7,1]=>[2,6,5,4,3,7,8,1]=>0011101
[2,6,3,4,5,8,7,1]=>[7,2,6,3,4,5,8,1]=>[2,6,5,4,3,8,1,7]=>0011101
[2,6,3,5,4,1,7,8]=>[4,2,5,6,3,1,7,8]=>[2,5,3,6,1,4,7,8]=>0001100
[2,7,3,5,4,6,8,1]=>[8,2,5,7,3,4,6,1]=>[2,5,3,7,6,4,8,1]=>0001111
[2,7,3,5,6,4,8,1]=>[8,2,6,7,3,5,4,1]=>[2,6,5,3,7,4,8,1]=>0001111
[2,8,3,7,5,6,4,1]=>[4,2,6,7,8,3,5,1]=>[2,6,3,8,1,4,7,5]=>0000111
[2,5,4,3,8,6,7,1]=>[7,2,4,5,3,8,6,1]=>[2,5,3,4,8,1,7,6]=>0001011
[2,7,5,4,3,6,8,1]=>[8,2,4,5,7,3,6,1]=>[2,7,6,3,4,5,8,1]=>0000111
[2,8,5,4,3,6,7,1]=>[7,2,4,5,8,3,6,1]=>[2,8,1,7,6,3,4,5]=>0000111
[2,8,5,4,7,6,3,1]=>[3,2,6,5,7,8,4,1]=>[2,7,4,5,8,1,3,6]=>0000011
[3,2,1,4,8,6,7,5]=>[2,3,1,4,7,8,6,5]=>[3,1,2,4,8,5,7,6]=>0100011
[3,2,1,7,5,6,8,4]=>[2,3,1,8,7,5,6,4]=>[3,1,2,7,6,5,8,4]=>0100111
[3,2,1,8,5,7,6,4]=>[2,3,1,6,7,8,5,4]=>[3,1,2,7,5,8,4,6]=>0100011
[3,2,1,8,6,5,7,4]=>[2,3,1,7,6,8,5,4]=>[3,1,2,8,4,7,5,6]=>0100011
[3,2,1,8,6,7,5,4]=>[2,3,1,5,7,8,6,4]=>[3,1,2,8,4,5,7,6]=>0100011
[3,2,4,1,8,6,7,5]=>[4,3,2,1,7,8,6,5]=>[3,2,4,1,8,5,7,6]=>0110011
[3,2,5,4,8,6,7,1]=>[7,3,2,5,4,8,6,1]=>[3,2,5,4,8,1,7,6]=>0101011
[3,2,6,4,5,1,7,8]=>[5,3,2,6,4,1,7,8]=>[3,2,6,1,5,4,7,8]=>0101100
[3,2,6,4,5,1,8,7]=>[5,3,2,6,4,1,8,7]=>[3,2,6,1,5,4,8,7]=>0101101
[3,2,7,4,6,5,8,1]=>[8,3,2,6,7,4,5,1]=>[3,2,6,4,7,5,8,1]=>0100111
[3,2,8,5,4,6,7,1]=>[7,3,2,5,8,4,6,1]=>[3,2,8,1,7,6,4,5]=>0100111
[3,2,7,5,6,4,8,1]=>[8,3,2,6,7,5,4,1]=>[3,2,7,4,6,5,8,1]=>0100111
[3,2,8,5,6,4,7,1]=>[7,3,2,6,8,5,4,1]=>[3,2,8,1,7,4,6,5]=>0100111
[4,2,3,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>0110101
[4,2,3,1,6,7,8,5]=>[3,4,2,1,8,6,7,5]=>[4,1,3,2,6,7,8,5]=>0110001
[4,2,3,1,7,6,8,5]=>[3,4,2,1,8,7,6,5]=>[4,1,3,2,7,6,8,5]=>0110011
[4,2,3,1,8,6,7,5]=>[3,4,2,1,7,8,6,5]=>[4,1,3,2,8,5,7,6]=>0110011
[4,2,3,1,8,7,6,5]=>[3,4,2,1,6,7,8,5]=>[4,1,3,2,8,5,6,7]=>0110001
[4,2,3,5,1,8,7,6]=>[5,4,2,3,1,7,8,6]=>[4,3,2,5,1,8,6,7]=>0111001
[4,2,3,6,5,1,7,8]=>[5,4,2,3,6,1,7,8]=>[4,3,2,6,1,5,7,8]=>0110100
[4,2,3,7,6,5,8,1]=>[8,4,2,3,6,7,5,1]=>[4,3,2,7,5,6,8,1]=>0110011
[4,2,3,8,7,6,5,1]=>[5,4,2,3,6,7,8,1]=>[4,3,2,8,1,5,6,7]=>0110001
[5,2,3,4,8,7,6,1]=>[6,5,2,3,4,7,8,1]=>[5,4,3,2,8,1,6,7]=>0111001
[6,2,3,5,4,1,7,8]=>[4,5,2,6,3,1,7,8]=>[5,3,2,6,1,4,7,8]=>0101100
[6,2,3,5,4,1,8,7]=>[4,5,2,6,3,1,8,7]=>[5,3,2,6,1,4,8,7]=>0101101
[7,2,3,5,6,4,1,8]=>[4,6,2,7,3,5,1,8]=>[6,5,3,2,7,1,4,8]=>0101110
[8,2,3,7,5,6,4,1]=>[4,6,2,7,8,3,5,1]=>[6,3,2,8,1,4,7,5]=>0100111
[5,2,4,3,1,8,7,6]=>[3,4,5,2,1,7,8,6]=>[4,2,5,1,3,8,6,7]=>0011001
[5,2,4,3,6,1,8,7]=>[6,4,5,2,3,1,8,7]=>[4,2,5,3,6,1,8,7]=>0011101
[5,2,4,3,7,6,8,1]=>[8,4,5,2,3,7,6,1]=>[4,2,5,3,7,6,8,1]=>0011011
[6,2,4,3,5,1,8,7]=>[5,4,6,2,3,1,8,7]=>[4,2,6,1,5,3,8,7]=>0011101
[7,2,4,3,6,5,8,1]=>[8,4,6,2,7,3,5,1]=>[4,2,6,3,7,5,8,1]=>0010111
[8,2,4,3,6,5,7,1]=>[7,4,6,2,8,3,5,1]=>[4,2,6,3,8,1,7,5]=>0010111
[8,2,4,3,7,6,5,1]=>[5,4,6,2,7,8,3,1]=>[4,2,8,1,5,7,3,6]=>0010011
[6,2,4,5,3,1,7,8]=>[3,5,6,2,4,1,7,8]=>[5,4,2,6,1,3,7,8]=>0011100
[7,2,4,5,3,6,8,1]=>[8,5,7,2,4,3,6,1]=>[5,4,2,7,6,3,8,1]=>0011111
[8,2,4,7,6,5,3,1]=>[3,5,6,2,7,8,4,1]=>[7,4,2,5,8,1,3,6]=>0010011
[8,2,5,4,3,7,6,1]=>[6,4,5,7,2,8,3,1]=>[7,3,5,2,4,8,1,6]=>0001011
[8,2,7,4,6,5,3,1]=>[3,5,6,7,8,2,4,1]=>[7,4,8,1,3,6,2,5]=>0000111
[4,3,2,1,8,6,7,5]=>[2,3,4,1,7,8,6,5]=>[4,1,2,3,8,5,7,6]=>0010011
[4,3,2,7,5,6,8,1]=>[8,3,4,2,7,5,6,1]=>[4,2,3,7,6,5,8,1]=>0010111
[5,3,2,4,1,8,7,6]=>[4,3,5,2,1,7,8,6]=>[5,1,4,2,3,8,6,7]=>0011001
[5,3,2,4,6,1,8,7]=>[6,3,5,2,4,1,8,7]=>[5,4,2,3,6,1,8,7]=>0011101
[6,3,2,5,4,1,7,8]=>[4,3,5,6,2,1,7,8]=>[5,2,3,6,1,4,7,8]=>0001100
[8,3,2,7,6,5,4,1]=>[4,3,5,6,7,8,2,1]=>[7,2,3,5,8,1,4,6]=>0000011
[5,3,4,2,1,6,8,7]=>[2,4,5,3,1,6,8,7]=>[5,1,2,4,3,6,8,7]=>0011001
[5,3,4,2,1,7,8,6]=>[2,4,5,3,1,8,7,6]=>[5,1,2,4,3,7,8,6]=>0011001
[5,3,4,2,6,1,8,7]=>[6,4,5,3,2,1,8,7]=>[5,2,4,3,6,1,8,7]=>0011101
[5,3,4,2,7,6,8,1]=>[8,4,5,3,2,7,6,1]=>[5,2,4,3,7,6,8,1]=>0011011
[6,3,4,2,5,1,8,7]=>[5,4,6,3,2,1,8,7]=>[6,1,5,2,4,3,8,7]=>0011101
[7,3,4,2,6,5,8,1]=>[8,4,6,3,7,2,5,1]=>[6,2,4,3,7,5,8,1]=>0010111
[7,3,4,6,5,2,1,8]=>[2,5,6,3,7,4,1,8]=>[6,4,3,7,1,2,5,8]=>0010110
[6,3,5,4,2,7,1,8]=>[7,4,5,6,3,2,1,8]=>[5,3,6,2,4,7,1,8]=>0001110
[8,4,3,2,6,7,5,1]=>[5,3,4,7,8,2,6,1]=>[7,6,2,3,4,8,1,5]=>0000111
[8,7,3,4,6,5,2,1]=>[2,5,6,3,7,4,8,1]=>[6,4,3,8,1,2,5,7]=>0010101
[8,6,3,5,4,2,7,1]=>[7,4,5,6,3,8,2,1]=>[5,3,8,1,7,2,4,6]=>0001011
[8,5,4,3,7,6,2,1]=>[2,6,4,5,7,8,3,1]=>[7,3,4,5,8,1,2,6]=>0000011
[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>0110101
[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>[2,1,4,6,5,3,8,7]=>1001101
[2,4,1,6,3,5,8,7]=>[6,2,4,1,3,5,8,7]=>[2,6,5,3,4,1,8,7]=>0011101
[2,4,6,1,3,5,8,7]=>[6,2,1,4,3,5,8,7]=>[2,4,6,5,3,1,8,7]=>0101101
[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,7,5]=>1010011
[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>[2,4,3,1,6,8,7,5]=>0110011
[2,4,6,1,3,8,5,7]=>[8,2,1,4,6,3,5,7]=>[2,4,8,7,5,6,3,1]=>0100111
[2,1,4,6,8,3,5,7]=>[2,1,8,4,3,6,5,7]=>[2,1,4,6,8,7,5,3]=>1001011
[2,4,6,1,8,3,5,7]=>[8,2,6,4,1,3,5,7]=>[2,4,6,3,8,7,5,1]=>0001111
[2,4,6,8,1,3,5,7]=>[8,2,1,4,3,6,5,7]=>[2,4,6,8,7,5,3,1]=>0101011
[2,4,6,7,1,3,5,8]=>[7,2,1,4,3,6,5,8]=>[2,4,6,7,5,3,1,8]=>0101010
[2,4,1,3,6,7,8,5]=>[4,2,1,3,8,6,7,5]=>[2,4,3,1,6,7,8,5]=>0110001
[2,1,4,6,3,7,8,5]=>[2,1,8,4,6,3,7,5]=>[2,1,4,7,8,5,6,3]=>1000101
[2,4,1,6,3,7,8,5]=>[8,2,4,1,6,3,7,5]=>[2,7,8,5,6,3,4,1]=>0010101
[2,4,6,1,3,7,8,5]=>[8,2,1,4,6,3,7,5]=>[2,4,7,8,5,6,3,1]=>0100101
[2,4,6,7,1,3,8,5]=>[8,2,1,4,7,6,3,5]=>[2,4,6,8,5,7,3,1]=>0100011
[2,4,1,6,7,8,3,5]=>[8,2,4,1,3,6,7,5]=>[2,6,7,8,5,3,4,1]=>0011001
[2,4,6,7,1,8,3,5]=>[8,2,7,4,1,6,3,5]=>[2,4,6,7,3,8,5,1]=>0001011
[2,1,4,3,7,5,8,6]=>[2,1,4,3,8,7,5,6]=>[2,1,4,3,8,6,7,5]=>1010011
[2,4,1,3,7,5,8,6]=>[4,2,1,3,8,7,5,6]=>[2,4,3,1,8,6,7,5]=>0110011
[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,7,8,6,5]=>1010101
[2,4,1,7,3,8,5,6]=>[8,2,4,1,7,3,5,6]=>[2,7,5,8,6,3,4,1]=>0010111
[2,4,7,1,8,3,5,6]=>[8,2,7,4,1,3,5,6]=>[2,4,8,6,3,7,5,1]=>0001111
[2,1,4,5,7,3,8,6]=>[2,1,8,4,5,7,3,6]=>[2,1,4,5,8,6,7,3]=>1000011
[2,4,1,5,7,3,8,6]=>[8,2,4,1,5,7,3,6]=>[2,5,8,6,7,3,4,1]=>0010011
[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,7,6,5]=>1010111
[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>[2,4,3,1,8,7,6,5]=>0110111
[2,1,4,8,3,5,6,7]=>[2,1,8,4,3,5,6,7]=>[2,1,4,8,7,6,5,3]=>1001111
[2,4,1,5,3,8,6,7]=>[5,2,4,1,3,8,6,7]=>[2,5,3,4,1,8,7,6]=>0011011
[2,1,4,5,8,3,6,7]=>[2,1,8,4,5,3,6,7]=>[2,1,4,5,8,7,6,3]=>1000111
[2,1,4,5,6,8,3,7]=>[2,1,8,4,5,6,3,7]=>[2,1,4,5,6,8,7,3]=>1000011
[2,4,5,1,6,8,3,7]=>[8,2,5,4,1,6,3,7]=>[2,4,6,8,7,3,5,1]=>0001011
[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>0110000
[2,4,5,6,1,3,7,8]=>[6,2,1,4,5,3,7,8]=>[2,4,5,6,3,1,7,8]=>0100100
[2,4,1,5,6,7,8,3]=>[8,2,4,1,5,6,7,3]=>[2,5,6,7,8,3,4,1]=>0010001
[2,1,5,3,6,4,8,7]=>[2,1,6,5,3,4,8,7]=>[2,1,6,4,5,3,8,7]=>1001101
[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>[2,1,5,6,4,3,8,7]=>1010101
[2,1,5,3,6,7,8,4]=>[2,1,8,5,3,6,7,4]=>[2,1,6,7,8,4,5,3]=>1001001
[2,1,5,6,7,3,8,4]=>[2,1,8,7,5,6,3,4]=>[2,1,5,6,8,4,7,3]=>1000011
[2,1,5,6,7,8,3,4]=>[2,1,8,3,5,6,7,4]=>[2,1,5,6,7,8,4,3]=>1010001
[2,5,6,7,8,1,3,4]=>[8,2,1,3,5,6,7,4]=>[2,5,6,7,8,4,3,1]=>0110001
[2,1,5,3,7,4,8,6]=>[2,1,8,5,3,7,4,6]=>[2,1,8,6,7,4,5,3]=>1001011
[2,5,1,3,7,4,8,6]=>[8,2,1,5,3,7,4,6]=>[2,8,6,7,4,5,3,1]=>0101011
[2,1,5,7,3,4,8,6]=>[2,1,8,3,5,7,4,6]=>[2,1,5,8,6,7,4,3]=>1010011
[2,5,1,7,3,4,8,6]=>[8,2,5,1,3,7,4,6]=>[2,5,3,8,6,7,4,1]=>0011011
[2,5,7,1,3,4,8,6]=>[8,2,1,3,5,7,4,6]=>[2,5,8,6,7,4,3,1]=>0110011
[2,1,5,7,3,8,4,6]=>[2,1,8,7,5,3,4,6]=>[2,1,5,7,4,8,6,3]=>1000111
[2,5,7,1,3,8,4,6]=>[8,2,1,7,5,3,4,6]=>[2,5,7,4,8,6,3,1]=>0100111
[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]=>[2,1,5,7,8,6,4,3]=>1010101
[2,3,5,1,4,8,6,7]=>[5,2,3,1,4,8,6,7]=>[2,3,5,4,1,8,7,6]=>0011011
[2,3,5,1,6,4,8,7]=>[6,2,3,5,1,4,8,7]=>[2,3,6,4,5,1,8,7]=>0001101
[2,3,5,6,1,4,8,7]=>[6,2,3,1,5,4,8,7]=>[2,3,5,6,4,1,8,7]=>0010101
[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>[2,5,4,3,1,6,7,8]=>0111000
[2,3,5,6,7,8,1,4]=>[8,2,3,1,5,6,7,4]=>[2,3,5,6,7,8,4,1]=>0010001
[2,6,7,1,3,4,8,5]=>[8,2,1,3,7,6,4,5]=>[2,6,8,5,7,4,3,1]=>0110011
[2,1,6,7,3,8,4,5]=>[2,1,8,7,3,6,4,5]=>[2,1,6,7,4,8,5,3]=>1001011
[2,6,1,7,3,8,4,5]=>[8,2,7,6,1,3,4,5]=>[2,7,4,6,3,8,5,1]=>0001111
[2,1,6,7,8,3,4,5]=>[2,1,8,3,4,6,7,5]=>[2,1,6,7,8,5,4,3]=>1011001
[2,1,6,3,4,7,8,5]=>[2,1,8,3,6,4,7,5]=>[2,1,7,8,5,6,4,3]=>1010101
[2,1,3,6,7,4,8,5]=>[2,1,3,8,7,6,4,5]=>[2,1,3,6,8,5,7,4]=>1000011
[2,3,1,6,7,8,4,5]=>[3,2,1,8,4,6,7,5]=>[2,3,1,6,7,8,5,4]=>0101001
[2,1,6,3,4,8,5,7]=>[2,1,8,3,6,4,5,7]=>[2,1,8,7,5,6,4,3]=>1010111
[2,3,1,6,4,8,5,7]=>[3,2,1,8,6,4,5,7]=>[2,3,1,8,7,5,6,4]=>0100111
[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]=>[2,3,1,6,8,7,5,4]=>0101011
[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>[2,1,6,5,4,3,8,7]=>1011101
[2,3,6,1,4,5,8,7]=>[6,2,3,1,4,5,8,7]=>[2,3,6,5,4,1,8,7]=>0011101
[2,3,4,1,6,8,5,7]=>[4,2,3,1,8,6,5,7]=>[2,3,4,1,6,8,7,5]=>0010011
[2,3,4,6,1,8,5,7]=>[8,2,3,4,6,1,5,7]=>[2,3,4,8,7,5,6,1]=>0000111
[2,3,4,6,7,8,1,5]=>[8,2,3,4,1,6,7,5]=>[2,3,4,6,7,8,5,1]=>0001001
[2,7,1,3,8,4,5,6]=>[8,2,1,7,3,4,5,6]=>[2,8,6,4,7,5,3,1]=>0101111
[2,1,7,8,3,4,5,6]=>[2,1,8,3,4,5,7,6]=>[2,1,7,8,6,5,4,3]=>1011101
[2,7,1,8,3,4,5,6]=>[8,2,7,1,3,4,5,6]=>[2,7,5,3,8,6,4,1]=>0011111
[2,1,7,3,4,8,5,6]=>[2,1,8,3,7,4,5,6]=>[2,1,7,5,8,6,4,3]=>1010111
[2,3,1,7,4,5,8,6]=>[3,2,1,8,4,7,5,6]=>[2,3,1,8,6,7,5,4]=>0101011
[2,3,7,1,4,5,8,6]=>[8,2,3,1,4,7,5,6]=>[2,3,8,6,7,5,4,1]=>0011011
[2,3,4,1,7,5,8,6]=>[4,2,3,1,8,7,5,6]=>[2,3,4,1,8,6,7,5]=>0010011
[2,3,4,7,1,5,8,6]=>[8,2,3,4,1,7,5,6]=>[2,3,4,8,6,7,5,1]=>0001011
[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,5,7,6]=>[2,3,1,4,7,8,6,5]=>0100101
[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>[2,3,4,1,7,8,6,5]=>0010101
[2,3,4,1,7,5,6,8]=>[4,2,3,1,7,5,6,8]=>[2,3,4,1,7,6,5,8]=>0010110
[2,3,4,7,1,5,6,8]=>[7,2,3,4,1,5,6,8]=>[2,3,4,7,6,5,1,8]=>0001110
[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>[2,1,8,7,6,5,4,3]=>1011111
[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,7,6,5,4]=>1001111
[2,3,1,8,4,5,6,7]=>[3,2,1,8,4,5,6,7]=>[2,3,1,8,7,6,5,4]=>0101111
[2,3,8,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>[2,3,8,7,6,5,4,1]=>0011111
[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,7,6,5]=>1000111
[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,7,6,5]=>0100111
[2,3,4,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>[2,3,4,1,8,7,6,5]=>0010111
[2,3,4,8,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>[2,3,4,8,7,6,5,1]=>0001111
[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,8,6,7]=>[2,3,4,1,5,8,7,6]=>0010011
[3,1,4,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>0110101
[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>1010101
[3,1,4,2,6,8,5,7]=>[4,3,1,2,8,6,5,7]=>[4,2,3,1,6,8,7,5]=>0110011
[3,4,1,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>[3,4,2,1,6,8,7,5]=>1010011
[3,1,4,6,8,2,5,7]=>[8,3,1,4,2,6,5,7]=>[4,6,8,7,5,2,3,1]=>0101011
[3,4,6,1,2,7,5,8]=>[7,1,3,4,6,2,5,8]=>[3,4,7,5,6,2,1,8]=>1000110
[3,1,4,2,6,7,8,5]=>[4,3,1,2,8,6,7,5]=>[4,2,3,1,6,7,8,5]=>0110001
[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[3,4,2,1,6,7,8,5]=>1010001
[3,4,6,1,7,2,8,5]=>[8,7,3,4,6,1,2,5]=>[3,4,7,2,8,5,6,1]=>0000111
[3,4,6,7,1,8,2,5]=>[8,7,3,4,1,6,2,5]=>[3,4,6,7,2,8,5,1]=>0001011
[3,1,4,2,7,5,8,6]=>[4,3,1,2,8,7,5,6]=>[4,2,3,1,8,6,7,5]=>0110011
[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>[3,4,2,1,7,8,6,5]=>1010101
[3,1,4,5,2,7,6,8]=>[5,3,1,4,2,7,6,8]=>[4,5,2,3,1,7,6,8]=>0101010
[3,4,1,5,2,7,6,8]=>[5,4,3,1,2,7,6,8]=>[3,5,2,4,1,7,6,8]=>0011010
[3,4,1,5,7,2,6,8]=>[7,4,3,1,5,2,6,8]=>[3,5,7,6,2,4,1,8]=>0010110
[3,1,4,5,2,7,8,6]=>[5,3,1,4,2,8,7,6]=>[4,5,2,3,1,7,8,6]=>0101001
[3,4,5,7,1,2,8,6]=>[8,1,3,4,5,7,2,6]=>[3,4,5,8,6,7,2,1]=>1000011
[3,4,5,1,7,8,2,6]=>[8,5,3,4,1,2,7,6]=>[3,4,7,8,6,2,5,1]=>0001101
[3,1,4,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]=>[4,2,3,1,8,7,6,5]=>0110111
[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[3,4,2,1,8,7,6,5]=>1010111
[3,1,4,8,2,5,6,7]=>[8,3,1,4,2,5,6,7]=>[4,8,7,6,5,2,3,1]=>0101111
[3,4,1,8,2,5,6,7]=>[8,4,3,1,2,5,6,7]=>[3,8,7,6,5,2,4,1]=>0011111
[3,4,1,2,5,8,6,7]=>[4,1,3,2,5,8,6,7]=>[3,4,2,1,5,8,7,6]=>1010011
[3,4,5,1,2,8,6,7]=>[5,1,3,4,2,8,6,7]=>[3,4,5,2,1,8,7,6]=>1001011
[3,1,4,5,6,2,8,7]=>[6,3,1,4,5,2,8,7]=>[4,5,6,2,3,1,8,7]=>0100101
[3,1,4,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>0110000
[3,4,1,5,6,2,7,8]=>[6,4,3,1,5,2,7,8]=>[3,5,6,2,4,1,7,8]=>0010100
[3,4,5,1,6,2,7,8]=>[6,5,3,4,1,2,7,8]=>[3,4,6,2,5,1,7,8]=>0001100
[3,4,1,5,6,7,2,8]=>[7,4,3,1,5,6,2,8]=>[3,5,6,7,2,4,1,8]=>0010010
[3,1,4,5,6,7,8,2]=>[8,3,1,4,5,6,7,2]=>[4,5,6,7,8,2,3,1]=>0100001
[3,1,5,2,6,4,8,7]=>[6,3,1,5,2,4,8,7]=>[6,4,5,2,3,1,8,7]=>0101101
[3,1,5,6,2,4,8,7]=>[6,3,1,2,5,4,8,7]=>[5,6,4,2,3,1,8,7]=>0110101
[3,5,1,6,2,4,8,7]=>[6,5,3,1,2,4,8,7]=>[3,5,2,6,4,1,8,7]=>0011101
[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>[3,5,6,4,2,1,8,7]=>1010101
[3,1,5,6,2,8,4,7]=>[8,3,1,6,5,2,4,7]=>[5,8,7,4,6,2,3,1]=>0100111
[3,5,6,1,2,8,4,7]=>[8,1,3,6,5,2,4,7]=>[3,5,8,7,4,6,2,1]=>1000111
[3,5,6,1,8,2,4,7]=>[8,6,3,1,5,2,4,7]=>[3,5,6,2,8,7,4,1]=>0010111
[3,5,6,1,2,7,4,8]=>[7,1,3,6,5,2,4,8]=>[3,5,7,4,6,2,1,8]=>1000110
[3,5,6,1,7,2,4,8]=>[7,6,3,1,5,2,4,8]=>[3,5,6,2,7,4,1,8]=>0010110
[3,1,5,2,6,7,8,4]=>[8,3,1,5,2,6,7,4]=>[6,7,8,4,5,2,3,1]=>0101001
[3,5,1,6,2,7,8,4]=>[8,6,3,5,1,2,7,4]=>[3,6,2,7,8,4,5,1]=>0001101
[3,5,6,1,2,7,8,4]=>[8,1,3,6,5,2,7,4]=>[3,5,7,8,4,6,2,1]=>1000101
[3,5,1,6,7,2,8,4]=>[8,7,3,5,1,6,2,4]=>[3,6,7,2,8,4,5,1]=>0001011
[3,5,6,1,7,2,8,4]=>[8,7,3,6,5,1,2,4]=>[3,5,7,2,8,4,6,1]=>0000111
[3,1,5,6,7,8,2,4]=>[8,3,1,2,5,6,7,4]=>[5,6,7,8,4,2,3,1]=>0110001
[3,5,6,1,7,8,2,4]=>[8,6,3,1,5,2,7,4]=>[3,5,6,2,7,8,4,1]=>0010101
[3,5,6,7,8,1,2,4]=>[8,1,3,2,5,6,7,4]=>[3,5,6,7,8,4,2,1]=>1010001
[3,1,5,2,7,4,8,6]=>[8,3,1,5,2,7,4,6]=>[8,6,7,4,5,2,3,1]=>0101011
[3,1,5,7,2,4,8,6]=>[8,3,1,2,5,7,4,6]=>[5,8,6,7,4,2,3,1]=>0110011
[3,5,1,7,2,4,8,6]=>[8,5,3,1,2,7,4,6]=>[3,5,2,8,6,7,4,1]=>0011011
[3,5,7,1,2,4,8,6]=>[8,1,3,2,5,7,4,6]=>[3,5,8,6,7,4,2,1]=>1010011
[3,1,5,7,8,2,4,6]=>[8,3,1,2,5,4,7,6]=>[5,7,8,6,4,2,3,1]=>0110101
[3,1,5,2,7,4,6,8]=>[7,3,1,5,2,4,6,8]=>[7,6,4,5,2,3,1,8]=>0101110
[3,1,5,7,2,4,6,8]=>[7,3,1,2,5,4,6,8]=>[5,7,6,4,2,3,1,8]=>0110110
[3,5,1,7,2,4,6,8]=>[7,5,3,1,2,4,6,8]=>[3,5,2,7,6,4,1,8]=>0011110
[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>[3,5,7,6,4,2,1,8]=>1010110
[3,5,1,2,4,7,6,8]=>[5,1,3,2,4,7,6,8]=>[3,5,4,2,1,7,6,8]=>1011010
[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>1101010
[1,3,5,2,4,7,6,8]=>[1,5,3,2,4,7,6,8]=>[1,3,5,4,2,7,6,8]=>0011010
[3,1,2,5,7,4,6,8]=>[3,1,2,7,5,4,6,8]=>[3,2,1,5,7,6,4,8]=>1100110
[1,3,2,5,7,4,6,8]=>[1,3,2,7,5,4,6,8]=>[1,3,2,5,7,6,4,8]=>0100110
[1,3,5,7,2,4,6,8]=>[1,7,3,2,5,4,6,8]=>[1,3,5,7,6,4,2,8]=>0010110
[3,5,1,2,4,7,8,6]=>[5,1,3,2,4,8,7,6]=>[3,5,4,2,1,7,8,6]=>1011001
[1,3,5,2,4,7,8,6]=>[1,5,3,2,4,8,7,6]=>[1,3,5,4,2,7,8,6]=>0011001
[3,1,2,5,7,4,8,6]=>[3,1,2,8,5,7,4,6]=>[3,2,1,5,8,6,7,4]=>1100011
[1,3,2,5,7,8,4,6]=>[1,3,2,8,5,4,7,6]=>[1,3,2,5,7,8,6,4]=>0100101
[1,3,5,7,2,8,4,6]=>[1,8,3,7,5,2,4,6]=>[1,3,5,7,4,8,6,2]=>0000111
[1,3,5,7,8,2,4,6]=>[1,8,3,2,5,4,7,6]=>[1,3,5,7,8,6,4,2]=>0010101
[3,1,5,2,8,4,6,7]=>[8,3,1,5,2,4,6,7]=>[8,7,6,4,5,2,3,1]=>0101111
[3,5,1,8,2,4,6,7]=>[8,5,3,1,2,4,6,7]=>[3,5,2,8,7,6,4,1]=>0011111
[3,1,5,2,4,8,6,7]=>[5,3,1,2,4,8,6,7]=>[5,4,2,3,1,8,7,6]=>0111011
[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[3,5,4,2,1,8,7,6]=>1011011
[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,7,6]=>0101011
[1,3,5,8,2,4,6,7]=>[1,8,3,2,5,4,6,7]=>[1,3,5,8,7,6,4,2]=>0010111
[3,5,1,2,4,6,8,7]=>[5,1,3,2,4,6,8,7]=>[3,5,4,2,1,6,8,7]=>1011001
[1,3,5,2,4,6,8,7]=>[1,5,3,2,4,6,8,7]=>[1,3,5,4,2,6,8,7]=>0011001
[3,1,2,5,6,8,4,7]=>[3,1,2,8,5,6,4,7]=>[3,2,1,5,6,8,7,4]=>1100011
[3,5,1,2,4,6,7,8]=>[5,1,3,2,4,6,7,8]=>[3,5,4,2,1,6,7,8]=>1011000
[1,3,5,2,4,6,7,8]=>[1,5,3,2,4,6,7,8]=>[1,3,5,4,2,6,7,8]=>0011000
[1,3,5,6,2,4,7,8]=>[1,6,3,2,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>0010100
[1,3,5,6,7,2,4,8]=>[1,7,3,2,5,6,4,8]=>[1,3,5,6,7,4,2,8]=>0010010
[3,1,2,5,6,7,8,4]=>[3,1,2,8,5,6,7,4]=>[3,2,1,5,6,7,8,4]=>1100001
[1,3,5,6,2,7,8,4]=>[1,8,3,6,5,2,7,4]=>[1,3,5,7,8,4,6,2]=>0000101
[1,3,5,6,7,8,2,4]=>[1,8,3,2,5,6,7,4]=>[1,3,5,6,7,8,4,2]=>0010001
[3,1,6,2,7,4,8,5]=>[8,3,1,7,6,2,4,5]=>[7,4,8,5,6,2,3,1]=>0100111
[3,6,1,2,7,4,8,5]=>[8,1,3,7,6,2,4,5]=>[3,7,4,8,5,6,2,1]=>1000111
[3,6,7,1,2,4,8,5]=>[8,1,3,2,7,6,4,5]=>[3,6,8,5,7,4,2,1]=>1010011
[3,6,7,1,2,8,4,5]=>[8,1,3,7,2,6,4,5]=>[3,6,7,4,8,5,2,1]=>1001011
[3,1,6,2,4,7,5,8]=>[7,3,1,2,6,4,5,8]=>[7,5,6,4,2,3,1,8]=>0110110
[3,6,1,2,4,7,5,8]=>[7,1,3,2,6,4,5,8]=>[3,7,5,6,4,2,1,8]=>1010110
[3,6,1,2,4,7,8,5]=>[8,1,3,2,6,4,7,5]=>[3,7,8,5,6,4,2,1]=>1010101
[1,3,6,2,4,7,8,5]=>[1,8,3,2,6,4,7,5]=>[1,3,7,8,5,6,4,2]=>0010101
[3,1,2,6,7,4,8,5]=>[3,1,2,8,7,6,4,5]=>[3,2,1,6,8,5,7,4]=>1100011
[3,1,6,2,8,4,5,7]=>[8,3,1,6,2,4,5,7]=>[6,4,8,7,5,2,3,1]=>0101111
[1,3,6,2,4,8,5,7]=>[1,8,3,2,6,4,5,7]=>[1,3,8,7,5,6,4,2]=>0010111
[3,1,6,2,4,5,8,7]=>[6,3,1,2,4,5,8,7]=>[6,5,4,2,3,1,8,7]=>0111101
[3,1,2,4,6,8,5,7]=>[3,1,2,4,8,6,5,7]=>[3,2,1,4,6,8,7,5]=>1100011
[1,3,2,4,6,8,5,7]=>[1,3,2,4,8,6,5,7]=>[1,3,2,4,6,8,7,5]=>0100011
[3,1,2,4,6,7,8,5]=>[3,1,2,4,8,6,7,5]=>[3,2,1,4,6,7,8,5]=>1100001
[3,1,2,7,4,8,5,6]=>[3,1,2,8,7,4,5,6]=>[3,2,1,7,5,8,6,4]=>1100111
[1,3,2,7,4,8,5,6]=>[1,3,2,8,7,4,5,6]=>[1,3,2,7,5,8,6,4]=>0100111
[3,1,2,7,8,4,5,6]=>[3,1,2,8,4,5,7,6]=>[3,2,1,7,8,6,5,4]=>1101101
[1,3,7,2,8,4,5,6]=>[1,8,3,7,2,4,5,6]=>[1,3,8,6,4,7,5,2]=>0001111
[3,1,2,4,7,5,8,6]=>[3,1,2,4,8,7,5,6]=>[3,2,1,4,8,6,7,5]=>1100011
[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,5,7,6]=>[3,2,1,4,7,8,6,5]=>1100101
[1,3,4,2,7,8,5,6]=>[1,4,3,2,8,5,7,6]=>[1,3,4,2,7,8,6,5]=>0010101
[3,1,8,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>[8,7,6,5,4,2,3,1]=>0111111
[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]=>[3,2,1,8,7,6,5,4]=>1101111
[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,7,6,5,4]=>0101111
[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]=>[1,3,8,7,6,5,4,2]=>0011111
[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>[3,2,1,4,8,7,6,5]=>1100111
[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,7,6,5]=>0100111
[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,7,6,5]=>0010111
[1,3,4,8,2,5,6,7]=>[1,8,3,4,2,5,6,7]=>[1,3,4,8,7,6,5,2]=>0001111
[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>[3,2,1,4,5,8,7,6]=>1100011
[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,6,7]=>[1,3,4,2,5,8,7,6]=>0010011
[4,5,1,6,2,3,8,7]=>[6,5,1,4,2,3,8,7]=>[4,5,2,6,3,1,8,7]=>0101101
[4,5,6,1,2,3,8,7]=>[6,1,2,4,5,3,8,7]=>[4,5,6,3,2,1,8,7]=>1100101
[4,1,5,6,8,2,3,7]=>[8,4,1,2,5,6,3,7]=>[4,2,5,6,8,7,3,1]=>0110011
[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[4,5,6,8,7,3,2,1]=>1100011
[4,5,1,6,2,7,3,8]=>[7,6,5,4,1,2,3,8]=>[4,6,2,7,3,5,1,8]=>0001110
[4,5,1,2,6,7,8,3]=>[8,1,5,4,2,6,7,3]=>[4,6,7,8,3,5,2,1]=>1001001
[4,5,1,6,2,7,8,3]=>[8,6,5,4,1,2,7,3]=>[4,6,2,7,8,3,5,1]=>0001101
[4,5,1,6,7,2,8,3]=>[8,7,5,4,1,6,2,3]=>[4,6,7,2,8,3,5,1]=>0001011
[4,5,6,7,1,2,8,3]=>[8,1,7,4,5,6,2,3]=>[4,5,6,8,3,7,2,1]=>1000011
[4,5,6,7,1,8,2,3]=>[8,7,1,4,5,6,2,3]=>[4,5,6,7,2,8,3,1]=>0100011
[4,1,5,2,7,3,8,6]=>[8,5,4,1,2,7,3,6]=>[5,2,8,6,7,3,4,1]=>0011011
[4,5,1,2,7,3,8,6]=>[8,1,5,4,2,7,3,6]=>[4,8,6,7,3,5,2,1]=>1001011
[4,5,1,2,7,8,3,6]=>[8,1,5,4,2,3,7,6]=>[4,7,8,6,3,5,2,1]=>1001101
[4,5,1,7,2,8,3,6]=>[8,7,5,4,1,2,3,6]=>[4,8,6,2,7,3,5,1]=>0001111
[4,5,7,1,2,8,3,6]=>[8,1,7,4,5,2,3,6]=>[4,5,7,3,8,6,2,1]=>1000111
[4,5,1,7,2,3,6,8]=>[7,5,1,4,2,3,6,8]=>[4,5,2,7,6,3,1,8]=>0101110
[4,5,1,2,3,7,6,8]=>[5,1,2,4,3,7,6,8]=>[4,5,3,2,1,7,6,8]=>1101010
[4,1,5,2,3,7,8,6]=>[5,4,1,2,3,8,7,6]=>[4,2,5,3,1,7,8,6]=>0111001
[4,1,2,5,3,7,8,6]=>[5,1,4,2,3,8,7,6]=>[5,3,4,2,1,7,8,6]=>1011001
[1,4,2,5,3,7,8,6]=>[1,5,4,2,3,8,7,6]=>[1,5,3,4,2,7,8,6]=>0011001
[1,4,2,5,7,3,8,6]=>[1,8,4,2,5,7,3,6]=>[1,5,8,6,7,3,4,2]=>0010011
[1,4,2,5,7,8,3,6]=>[1,8,4,2,5,3,7,6]=>[1,5,7,8,6,3,4,2]=>0010101
[1,4,5,7,8,2,3,6]=>[1,8,2,4,5,3,7,6]=>[1,4,5,7,8,6,3,2]=>0100101
[4,5,1,2,8,3,6,7]=>[8,1,5,4,2,3,6,7]=>[4,8,7,6,3,5,2,1]=>1001111
[4,5,8,1,2,3,6,7]=>[8,1,2,4,5,3,6,7]=>[4,5,8,7,6,3,2,1]=>1100111
[4,1,5,2,3,8,6,7]=>[5,4,1,2,3,8,6,7]=>[4,2,5,3,1,8,7,6]=>0111011
[4,5,1,2,3,8,6,7]=>[5,1,2,4,3,8,6,7]=>[4,5,3,2,1,8,7,6]=>1101011
[4,1,2,5,3,8,6,7]=>[5,1,4,2,3,8,6,7]=>[5,3,4,2,1,8,7,6]=>1011011
[1,4,2,5,3,8,6,7]=>[1,5,4,2,3,8,6,7]=>[1,5,3,4,2,8,7,6]=>0011011
[4,1,2,5,8,3,6,7]=>[8,1,4,2,5,3,6,7]=>[5,8,7,6,3,4,2,1]=>1010111
[1,4,2,5,8,3,6,7]=>[1,8,4,2,5,3,6,7]=>[1,5,8,7,6,3,4,2]=>0010111
[1,4,5,2,8,3,6,7]=>[1,8,5,4,2,3,6,7]=>[1,4,8,7,6,3,5,2]=>0001111
[4,1,2,5,6,3,8,7]=>[6,1,4,2,5,3,8,7]=>[5,6,3,4,2,1,8,7]=>1010101
[4,1,2,5,6,7,8,3]=>[8,1,4,2,5,6,7,3]=>[5,6,7,8,3,4,2,1]=>1010001
[1,4,5,2,6,7,8,3]=>[1,8,5,4,2,6,7,3]=>[1,4,6,7,8,3,5,2]=>0001001
[4,1,6,2,7,3,8,5]=>[8,7,4,1,6,2,3,5]=>[8,5,6,2,7,3,4,1]=>0010111
[4,1,6,7,2,3,8,5]=>[8,4,1,2,7,6,3,5]=>[4,2,6,8,5,7,3,1]=>0110011
[4,6,7,1,2,3,8,5]=>[8,1,2,4,7,6,3,5]=>[4,6,8,5,7,3,2,1]=>1100011
[4,6,1,2,7,8,3,5]=>[8,1,6,4,2,3,7,5]=>[4,6,3,7,8,5,2,1]=>1001101
[4,6,1,2,7,3,5,8]=>[7,1,6,4,2,3,5,8]=>[4,6,3,7,5,2,1,8]=>1001110
[4,6,1,7,2,3,5,8]=>[7,6,1,4,2,3,5,8]=>[4,7,5,2,6,3,1,8]=>0101110
[4,1,6,2,3,7,5,8]=>[7,4,1,2,6,3,5,8]=>[4,2,7,5,6,3,1,8]=>0110110
[4,6,1,2,3,7,5,8]=>[7,1,2,4,6,3,5,8]=>[4,7,5,6,3,2,1,8]=>1100110
[4,1,2,6,3,7,5,8]=>[7,1,4,2,6,3,5,8]=>[7,5,6,3,4,2,1,8]=>1010110
[1,4,6,2,7,3,5,8]=>[1,7,6,4,2,3,5,8]=>[1,4,6,3,7,5,2,8]=>0001110
[4,1,2,6,3,7,8,5]=>[8,1,4,2,6,3,7,5]=>[7,8,5,6,3,4,2,1]=>1010101
[1,4,2,6,7,8,3,5]=>[1,8,4,2,3,6,7,5]=>[1,6,7,8,5,3,4,2]=>0011001
[1,4,6,7,2,8,3,5]=>[1,8,7,4,2,6,3,5]=>[1,4,6,7,3,8,5,2]=>0001011
[4,1,6,2,8,3,5,7]=>[8,6,4,1,2,3,5,7]=>[8,7,5,2,6,3,4,1]=>0011111
[4,1,6,8,2,3,5,7]=>[8,4,1,2,3,6,5,7]=>[4,2,6,8,7,5,3,1]=>0111011
[4,6,1,8,2,3,5,7]=>[8,6,1,4,2,3,5,7]=>[4,8,7,5,2,6,3,1]=>0101111
[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]=>[4,6,8,7,5,3,2,1]=>1101011
[4,6,1,2,3,8,5,7]=>[8,1,2,4,6,3,5,7]=>[4,8,7,5,6,3,2,1]=>1100111
[4,1,2,6,3,8,5,7]=>[8,1,4,2,6,3,5,7]=>[8,7,5,6,3,4,2,1]=>1010111
[1,4,2,6,3,8,5,7]=>[1,8,4,2,6,3,5,7]=>[1,8,7,5,6,3,4,2]=>0010111
[1,4,2,6,8,3,5,7]=>[1,8,4,2,3,6,5,7]=>[1,6,8,7,5,3,4,2]=>0011011
[1,4,6,2,8,3,5,7]=>[1,8,6,4,2,3,5,7]=>[1,4,6,3,8,7,5,2]=>0001111
[1,4,6,8,2,3,5,7]=>[1,8,2,4,3,6,5,7]=>[1,4,6,8,7,5,3,2]=>0101011
[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>1110101
[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>[4,3,2,1,6,8,7,5]=>1110011
[1,2,4,3,6,8,5,7]=>[1,2,4,3,8,6,5,7]=>[1,2,4,3,6,8,7,5]=>0010011
[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>1110100
[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>1110010
[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>[4,3,2,1,6,7,8,5]=>1110001
[1,4,2,3,6,7,8,5]=>[1,4,2,3,8,6,7,5]=>[1,4,3,2,6,7,8,5]=>0110001
[1,2,4,6,7,3,8,5]=>[1,2,8,4,7,6,3,5]=>[1,2,4,6,8,5,7,3]=>0000011
[4,1,7,2,8,3,5,6]=>[8,7,4,1,2,3,5,6]=>[7,5,2,8,6,3,4,1]=>0011111
[4,7,1,2,8,3,5,6]=>[8,1,7,4,2,3,5,6]=>[4,8,6,3,7,5,2,1]=>1001111
[4,7,1,8,2,3,5,6]=>[8,7,1,4,2,3,5,6]=>[4,7,5,2,8,6,3,1]=>0101111
[4,1,7,2,3,8,5,6]=>[8,4,1,2,7,3,5,6]=>[4,2,7,5,8,6,3,1]=>0110111
[1,4,2,7,3,8,5,6]=>[1,8,4,2,7,3,5,6]=>[1,7,5,8,6,3,4,2]=>0010111
[4,1,2,7,8,3,5,6]=>[8,1,4,2,3,5,7,6]=>[7,8,6,5,3,4,2,1]=>1011101
[4,1,7,2,3,5,8,6]=>[8,4,1,2,3,7,5,6]=>[4,2,8,6,7,5,3,1]=>0111011
[1,4,2,7,3,5,8,6]=>[1,8,4,2,3,7,5,6]=>[1,8,6,7,5,3,4,2]=>0011011
[1,4,7,2,3,5,8,6]=>[1,8,2,4,3,7,5,6]=>[1,4,8,6,7,5,3,2]=>0101011
[4,1,2,3,7,5,8,6]=>[4,1,2,3,8,7,5,6]=>[4,3,2,1,8,6,7,5]=>1110011
[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]=>[4,3,2,1,7,8,6,5]=>1110101
[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,7,8,6,5]=>0010101
[1,2,4,7,3,8,5,6]=>[1,2,8,4,7,3,5,6]=>[1,2,4,7,5,8,6,3]=>0000111
[1,2,4,7,8,3,5,6]=>[1,2,8,4,3,5,7,6]=>[1,2,4,7,8,6,5,3]=>0001101
[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>[4,3,2,1,7,6,5,8]=>1110110
[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[1,4,3,2,7,6,5,8]=>0110110
[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>1110010
[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>0110010
[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>1110001
[1,4,2,3,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>[1,4,3,2,5,7,8,6]=>0110001
[1,2,4,5,7,3,8,6]=>[1,2,8,4,5,7,3,6]=>[1,2,4,5,8,6,7,3]=>0000011
[4,8,1,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>[4,8,7,6,5,3,2,1]=>1101111
[4,1,2,8,3,5,6,7]=>[8,1,4,2,3,5,6,7]=>[8,7,6,5,3,4,2,1]=>1011111
[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>[1,4,8,7,6,5,3,2]=>0101111
[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>[4,3,2,1,8,7,6,5]=>1110111
[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[1,4,3,2,8,7,6,5]=>0110111
[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,7,6,5]=>0010111
[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]=>[1,2,4,8,7,6,5,3]=>0001111
[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>[4,3,2,1,5,8,7,6]=>1110011
[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>[1,4,3,2,5,8,7,6]=>0110011
[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[1,2,4,5,3,8,7,6]=>0001011
[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>1110001
[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>0110001
[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000
[5,1,6,2,7,3,8,4]=>[8,7,6,5,1,2,3,4]=>[7,3,6,2,8,4,5,1]=>0001111
[5,6,1,2,7,3,8,4]=>[8,1,7,6,5,2,3,4]=>[5,7,3,8,4,6,2,1]=>1000111
[5,1,6,7,2,3,8,4]=>[8,7,1,5,2,6,3,4]=>[6,8,4,5,2,7,3,1]=>0101011
[5,6,7,1,2,8,3,4]=>[8,1,7,2,5,6,3,4]=>[5,6,7,3,8,4,2,1]=>1010011
[5,1,6,7,8,2,3,4]=>[8,5,1,2,3,6,7,4]=>[6,7,8,4,2,5,3,1]=>0111001
[5,6,1,7,8,2,3,4]=>[8,6,1,2,5,3,7,4]=>[5,7,8,4,2,6,3,1]=>0110101
[5,6,7,1,8,2,3,4]=>[8,7,1,2,5,6,3,4]=>[5,6,8,4,2,7,3,1]=>0110011
[5,1,6,2,7,3,4,8]=>[7,6,5,1,2,3,4,8]=>[6,3,5,2,7,4,1,8]=>0011110
[5,1,6,2,3,7,4,8]=>[7,6,1,5,2,3,4,8]=>[7,4,5,2,6,3,1,8]=>0101110
[1,5,2,6,7,3,4,8]=>[1,7,5,2,3,6,4,8]=>[1,5,3,6,7,4,2,8]=>0011010
[5,6,1,2,3,7,8,4]=>[8,1,2,6,5,3,7,4]=>[5,7,8,4,6,3,2,1]=>1100101
[5,1,2,6,3,7,8,4]=>[8,1,6,5,2,3,7,4]=>[6,3,7,8,4,5,2,1]=>1001101
[1,5,6,2,3,7,8,4]=>[1,8,2,6,5,3,7,4]=>[1,5,7,8,4,6,3,2]=>0100101
[5,1,2,6,7,3,8,4]=>[8,1,7,5,2,6,3,4]=>[6,7,3,8,4,5,2,1]=>1001011
[5,1,2,6,7,8,3,4]=>[8,1,5,2,3,6,7,4]=>[5,3,6,7,8,4,2,1]=>1011001
[1,5,6,7,8,2,3,4]=>[1,8,2,3,5,6,7,4]=>[1,5,6,7,8,4,3,2]=>0110001
[5,1,6,2,8,3,4,7]=>[8,6,5,1,2,3,4,7]=>[6,3,5,2,8,7,4,1]=>0011111
[5,6,8,1,2,3,4,7]=>[8,1,2,3,5,6,4,7]=>[5,6,8,7,4,3,2,1]=>1110011
[5,1,2,6,3,8,4,7]=>[8,1,6,5,2,3,4,7]=>[6,3,8,7,4,5,2,1]=>1001111
[1,5,2,6,3,8,4,7]=>[1,8,6,5,2,3,4,7]=>[1,6,3,8,7,4,5,2]=>0001111
[1,5,2,6,8,3,4,7]=>[1,8,5,2,3,6,4,7]=>[1,5,3,6,8,7,4,2]=>0011011
[1,5,2,3,6,8,4,7]=>[1,8,2,5,3,6,4,7]=>[1,6,8,7,4,5,3,2]=>0101011
[1,2,5,6,3,8,4,7]=>[1,2,8,6,5,3,4,7]=>[1,2,5,8,7,4,6,3]=>0000111
[5,1,6,2,3,4,7,8]=>[6,5,1,2,3,4,7,8]=>[6,4,2,5,3,1,7,8]=>0111100
[1,5,2,3,6,7,8,4]=>[1,8,2,5,3,6,7,4]=>[1,6,7,8,4,5,3,2]=>0101001
[1,2,5,6,3,7,8,4]=>[1,2,8,6,5,3,7,4]=>[1,2,5,7,8,4,6,3]=>0000101
[1,2,5,6,7,8,3,4]=>[1,2,8,3,5,6,7,4]=>[1,2,5,6,7,8,4,3]=>0010001
[5,1,7,2,8,3,4,6]=>[8,7,5,1,2,3,4,6]=>[8,6,3,5,2,7,4,1]=>0011111
[5,7,8,1,2,3,4,6]=>[8,1,2,3,5,4,7,6]=>[5,7,8,6,4,3,2,1]=>1110101
[1,5,2,7,3,8,4,6]=>[1,8,7,5,2,3,4,6]=>[1,8,6,3,7,4,5,2]=>0001111
[1,5,7,2,3,8,4,6]=>[1,8,2,7,5,3,4,6]=>[1,5,7,4,8,6,3,2]=>0100111
[1,5,7,2,8,3,4,6]=>[1,8,7,2,5,3,4,6]=>[1,5,8,6,3,7,4,2]=>0010111
[5,1,7,2,3,4,8,6]=>[8,5,1,2,3,7,4,6]=>[8,6,7,4,2,5,3,1]=>0111011
[1,5,2,7,3,4,8,6]=>[1,8,5,2,3,7,4,6]=>[1,5,3,8,6,7,4,2]=>0011011
[5,1,2,3,7,4,8,6]=>[8,1,2,5,3,7,4,6]=>[8,6,7,4,5,3,2,1]=>1101011
[1,5,2,3,7,4,8,6]=>[1,8,2,5,3,7,4,6]=>[1,8,6,7,4,5,3,2]=>0101011
[1,2,5,7,3,4,8,6]=>[1,2,8,3,5,7,4,6]=>[1,2,5,8,6,7,4,3]=>0010011
[1,5,2,3,7,8,4,6]=>[1,8,2,5,3,4,7,6]=>[1,7,8,6,4,5,3,2]=>0101101
[5,7,1,2,3,4,6,8]=>[7,1,2,3,5,4,6,8]=>[5,7,6,4,3,2,1,8]=>1110110
[1,2,3,5,7,4,6,8]=>[1,2,3,7,5,4,6,8]=>[1,2,3,5,7,6,4,8]=>0000110
[1,2,5,3,4,7,8,6]=>[1,2,5,3,4,8,7,6]=>[1,2,5,4,3,7,8,6]=>0011001
[1,2,3,5,7,4,8,6]=>[1,2,3,8,5,7,4,6]=>[1,2,3,5,8,6,7,4]=>0000011
[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,4,7,6]=>[1,2,3,5,7,8,6,4]=>0000101
[1,5,2,3,8,4,6,7]=>[1,8,2,5,3,4,6,7]=>[1,8,7,6,4,5,3,2]=>0101111
[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,7,6]=>0001011
[1,2,3,5,8,4,6,7]=>[1,2,3,8,5,4,6,7]=>[1,2,3,5,8,7,6,4]=>0000111
[1,2,3,5,6,8,4,7]=>[1,2,3,8,5,6,4,7]=>[1,2,3,5,6,8,7,4]=>0000011
[6,1,7,2,8,3,4,5]=>[8,7,6,1,2,3,4,5]=>[6,3,8,5,2,7,4,1]=>0011111
[6,1,7,8,2,3,4,5]=>[8,6,1,2,3,4,7,5]=>[6,4,2,7,8,5,3,1]=>0111101
[6,7,1,8,2,3,4,5]=>[8,7,1,2,3,6,4,5]=>[6,7,4,2,8,5,3,1]=>0111011
[6,1,7,2,3,8,4,5]=>[8,7,1,6,2,3,4,5]=>[8,5,2,7,4,6,3,1]=>0101111
[1,6,2,7,3,8,4,5]=>[1,8,7,6,2,3,4,5]=>[1,7,4,6,3,8,5,2]=>0001111
[1,6,7,2,3,8,4,5]=>[1,8,2,7,3,6,4,5]=>[1,6,7,4,8,5,3,2]=>0101011
[1,6,7,2,8,3,4,5]=>[1,8,7,2,3,6,4,5]=>[1,6,8,5,3,7,4,2]=>0011011
[1,6,7,8,2,3,4,5]=>[1,8,2,3,4,6,7,5]=>[1,6,7,8,5,4,3,2]=>0111001
[6,1,7,2,3,4,8,5]=>[8,7,1,2,6,3,4,5]=>[7,4,2,8,5,6,3,1]=>0110111
[6,1,2,7,3,4,8,5]=>[8,1,7,2,6,3,4,5]=>[8,5,6,3,7,4,2,1]=>1010111
[1,2,6,3,7,4,8,5]=>[1,2,8,7,6,3,4,5]=>[1,2,7,4,8,5,6,3]=>0000111
[1,2,6,7,3,4,8,5]=>[1,2,8,3,7,6,4,5]=>[1,2,6,8,5,7,4,3]=>0010011
[1,2,6,3,7,8,4,5]=>[1,2,8,6,3,4,7,5]=>[1,2,6,4,7,8,5,3]=>0001101
[1,2,6,7,8,3,4,5]=>[1,2,8,3,4,6,7,5]=>[1,2,6,7,8,5,4,3]=>0011001
[6,1,7,2,3,4,5,8]=>[7,6,1,2,3,4,5,8]=>[6,4,2,7,5,3,1,8]=>0111110
[1,2,3,6,4,7,5,8]=>[1,2,3,7,6,4,5,8]=>[1,2,3,7,5,6,4,8]=>0000110
[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,5,4,8]=>0001010
[1,2,3,6,4,7,8,5]=>[1,2,3,8,6,4,7,5]=>[1,2,3,7,8,5,6,4]=>0000101
[1,2,3,6,7,4,8,5]=>[1,2,3,8,7,6,4,5]=>[1,2,3,6,8,5,7,4]=>0000011
[1,2,3,6,7,8,4,5]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,7,8,5,4]=>0001001
[6,1,8,2,3,4,5,7]=>[8,6,1,2,3,4,5,7]=>[6,4,2,8,7,5,3,1]=>0111111
[6,1,2,8,3,4,5,7]=>[8,1,6,2,3,4,5,7]=>[8,7,5,3,6,4,2,1]=>1011111
[1,6,2,8,3,4,5,7]=>[1,8,6,2,3,4,5,7]=>[1,8,7,5,3,6,4,2]=>0011111
[1,6,2,3,8,4,5,7]=>[1,8,2,6,3,4,5,7]=>[1,6,4,8,7,5,3,2]=>0101111
[1,6,2,3,4,8,5,7]=>[1,8,2,3,6,4,5,7]=>[1,8,7,5,6,4,3,2]=>0110111
[1,2,6,3,4,8,5,7]=>[1,2,8,3,6,4,5,7]=>[1,2,8,7,5,6,4,3]=>0010111
[1,2,3,6,4,8,5,7]=>[1,2,3,8,6,4,5,7]=>[1,2,3,8,7,5,6,4]=>0000111
[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>[6,5,4,3,2,1,8,7]=>1111101
[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,5,4,8,7]=>0001101
[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,6,5,7]=>[1,2,3,4,6,8,7,5]=>0000011
[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]=>[1,2,6,5,4,3,7,8]=>0011100
[1,7,2,8,3,4,5,6]=>[1,8,7,2,3,4,5,6]=>[1,7,5,3,8,6,4,2]=>0011111
[1,7,8,2,3,4,5,6]=>[1,8,2,3,4,5,7,6]=>[1,7,8,6,5,4,3,2]=>0111101
[7,1,2,3,8,4,5,6]=>[8,1,2,7,3,4,5,6]=>[8,6,4,7,5,3,2,1]=>1101111
[1,2,7,3,4,8,5,6]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,8,6,4,3]=>0010111
[1,2,3,7,4,8,5,6]=>[1,2,3,8,7,4,5,6]=>[1,2,3,7,5,8,6,4]=>0000111
[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,5,7,6]=>[1,2,3,7,8,6,5,4]=>0001101
[1,2,3,7,4,5,8,6]=>[1,2,3,8,4,7,5,6]=>[1,2,3,8,6,7,5,4]=>0001011
[1,2,3,4,7,5,8,6]=>[1,2,3,4,8,7,5,6]=>[1,2,3,4,8,6,7,5]=>0000011
[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,6,5]=>0000101
[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,6,5,4,8]=>0001110
[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,6,5,8]=>0000110
[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>0111111
[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]=>0011111
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,7,6,5,4]=>0001111
[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]=>0000111
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]=>0000011
[8,4,5,2,3,7,6,1]=>[6,5,2,7,4,8,3,1]=>[7,3,2,5,4,8,1,6]=>0101011
[7,4,5,2,3,8,1,6]=>[8,5,2,7,4,3,1,6]=>[8,6,3,2,5,4,7,1]=>0101111
[6,4,5,2,3,1,8,7]=>[3,5,2,6,4,1,8,7]=>[6,1,3,2,5,4,8,7]=>0101101
[3,6,1,5,4,2,8,7]=>[4,5,3,6,1,2,8,7]=>[3,6,2,5,1,4,8,7]=>0001101
[7,6,4,3,8,2,1,5]=>[2,8,4,6,3,7,1,5]=>[8,5,3,4,6,7,1,2]=>0001011
[4,7,5,1,3,8,2,6]=>[8,5,1,4,7,3,2,6]=>[4,7,2,5,8,6,3,1]=>0100111
[6,8,4,3,7,1,5,2]=>[5,7,4,8,3,6,1,2]=>[6,8,2,7,1,5,3,4]=>0001011
[6,8,5,7,3,1,4,2]=>[4,3,7,1,8,6,5,2]=>[4,1,6,8,2,3,7,5]=>0010011
[5,8,6,7,1,3,4,2]=>[4,7,1,3,5,8,6,2]=>[4,3,1,5,8,2,7,6]=>0110011
[3,8,1,6,7,4,5,2]=>[5,7,3,8,1,4,6,2]=>[3,5,1,8,2,7,6,4]=>0001111
[2,1,8,6,7,4,5,3]=>[2,1,5,7,4,8,6,3]=>[2,1,8,3,5,4,7,6]=>1001011
[5,7,6,8,1,3,2,4]=>[3,8,1,2,5,7,6,4]=>[3,1,5,7,6,8,4,2]=>0110011
[5,4,7,2,1,8,3,6]=>[2,8,7,5,4,1,3,6]=>[5,4,7,3,8,6,1,2]=>0001111
[6,4,7,2,8,1,3,5]=>[8,7,2,6,4,1,3,5]=>[7,3,2,8,5,4,6,1]=>0101111
[8,3,2,6,7,4,5,1]=>[5,3,7,8,2,4,6,1]=>[8,1,5,2,3,7,6,4]=>0001111
[7,3,2,6,8,4,1,5]=>[4,3,8,7,2,1,6,5]=>[7,6,1,4,8,5,2,3]=>0001111
[5,3,2,7,1,8,4,6]=>[8,3,7,5,2,1,4,6]=>[7,4,5,2,3,8,6,1]=>0001111
[4,3,2,1,7,8,5,6]=>[2,3,4,1,8,5,7,6]=>[4,1,2,3,7,8,6,5]=>0010101
[3,4,1,2,8,7,6,5]=>[4,1,3,2,6,7,8,5]=>[3,4,2,1,8,5,6,7]=>1010001
[6,3,2,8,7,1,5,4]=>[5,3,7,6,2,1,8,4]=>[8,4,6,1,5,2,3,7]=>0001101
[8,4,7,2,6,5,3,1]=>[3,5,6,7,8,4,2,1]=>[8,1,3,6,4,7,2,5]=>0000111
[7,4,8,2,6,5,1,3]=>[5,6,2,8,7,4,1,3]=>[7,1,5,8,3,2,6,4]=>0100111
[2,1,5,8,3,7,6,4]=>[2,1,6,7,5,8,3,4]=>[2,1,5,8,4,7,3,6]=>1000011
[2,1,6,8,7,3,5,4]=>[2,1,5,7,3,6,8,4]=>[2,1,5,3,6,8,4,7]=>1001001
[4,6,8,1,7,2,5,3]=>[5,7,8,4,1,6,2,3]=>[4,5,1,6,7,2,8,3]=>0001011
[5,7,8,6,1,4,2,3]=>[4,6,1,2,5,8,7,3]=>[5,7,8,3,1,4,2,6]=>0110001
[2,1,7,8,6,5,3,4]=>[2,1,5,3,6,8,7,4]=>[2,1,7,8,4,3,5,6]=>1010001
[3,8,1,7,6,5,4,2]=>[4,5,3,6,7,8,1,2]=>[3,8,2,5,7,1,4,6]=>0000011
[6,8,7,5,4,1,3,2]=>[3,4,1,5,7,6,8,2]=>[3,1,6,8,2,4,5,7]=>0100001
[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>101010101
[3,2,5,1,4,6,7,8]=>[5,3,2,1,4,6,7,8]=>[3,2,5,4,1,6,7,8]=>0111000
[6,3,5,1,2,4,7,8]=>[5,1,6,3,2,4,7,8]=>[5,2,1,6,4,3,7,8]=>1011100
[7,3,5,1,2,4,6,8]=>[5,1,7,3,2,4,6,8]=>[5,2,1,7,6,4,3,8]=>1011110
[3,2,8,1,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>[3,2,8,7,6,5,4,1]=>0111111
[5,2,8,1,3,4,6,7]=>[8,5,2,1,3,4,6,7]=>[5,3,2,8,7,6,4,1]=>0111111
[6,5,8,1,2,3,4,7]=>[8,1,2,3,6,5,4,7]=>[6,5,8,7,4,3,2,1]=>1110111
[7,5,8,1,2,3,4,6]=>[8,1,2,3,7,5,4,6]=>[8,6,5,7,4,3,2,1]=>1110111
[8,3,6,1,2,4,5,7]=>[6,1,8,3,2,4,5,7]=>[8,7,5,2,1,6,4,3]=>1011111
[8,5,7,1,2,3,4,6]=>[7,1,2,3,8,5,4,6]=>[7,4,3,2,1,8,6,5]=>1110111
[4,3,5,7,1,2,6,8]=>[7,1,4,3,5,2,6,8]=>[4,3,5,7,6,2,1,8]=>1010110
[5,2,6,7,1,3,4,8]=>[7,5,2,1,3,6,4,8]=>[5,3,2,6,7,4,1,8]=>0111010
[4,2,5,8,1,3,6,7]=>[8,4,2,1,5,3,6,7]=>[5,8,7,6,3,2,4,1]=>0110111
[3,2,6,8,1,4,5,7]=>[8,3,2,1,4,6,5,7]=>[3,2,6,8,7,5,4,1]=>0111011
[4,2,6,8,1,3,5,7]=>[8,4,2,1,3,6,5,7]=>[6,8,7,5,3,2,4,1]=>0111011
[6,2,4,8,1,3,5,7]=>[8,6,2,1,4,3,5,7]=>[6,3,2,8,7,5,4,1]=>0111111
[6,3,5,8,1,2,4,7]=>[8,1,6,3,2,5,4,7]=>[8,7,4,3,6,5,2,1]=>1011111
[6,3,7,8,1,2,4,5]=>[8,1,6,3,2,4,7,5]=>[6,4,3,7,8,5,2,1]=>1011101
[7,4,5,8,1,2,3,6]=>[8,1,2,7,4,5,3,6]=>[8,6,5,4,7,3,2,1]=>1101111
[8,2,5,6,1,3,4,7]=>[6,8,2,1,3,5,4,7]=>[8,7,4,1,6,5,3,2]=>0111111
[8,2,4,7,1,3,5,6]=>[7,8,2,1,4,3,5,6]=>[7,5,4,1,8,6,3,2]=>0111111
[8,3,5,7,1,2,4,6]=>[7,1,8,3,2,5,4,6]=>[8,6,5,2,1,7,4,3]=>1011111
[8,2,6,7,1,3,4,5]=>[7,8,2,1,3,4,6,5]=>[7,6,4,1,8,5,3,2]=>0111111
[8,4,6,7,1,2,3,5]=>[7,1,2,8,4,3,6,5]=>[7,6,3,2,1,8,5,4]=>1101111
[4,6,2,5,1,3,7,8]=>[5,6,2,4,1,3,7,8]=>[4,5,1,6,3,2,7,8]=>0101100
[4,6,3,5,1,2,7,8]=>[5,1,6,4,3,2,7,8]=>[4,6,2,1,5,3,7,8]=>1001100
[5,6,2,4,1,3,7,8]=>[4,6,2,1,5,3,7,8]=>[4,1,5,6,3,2,7,8]=>0110100
[5,7,2,4,1,3,6,8]=>[4,7,2,1,5,3,6,8]=>[4,1,5,7,6,3,2,8]=>0110110
[5,7,2,6,1,3,4,8]=>[6,7,2,1,5,3,4,8]=>[5,7,4,1,6,3,2,8]=>0110110
[5,8,3,4,1,2,6,7]=>[4,1,8,3,5,2,6,7]=>[5,8,7,6,2,1,4,3]=>1010111
[6,8,2,4,1,3,5,7]=>[4,8,2,1,3,6,5,7]=>[4,1,6,8,7,5,3,2]=>0111011
[6,8,3,4,1,2,5,7]=>[4,1,8,3,2,6,5,7]=>[6,8,7,5,2,1,4,3]=>1011011
[6,8,4,5,1,2,3,7]=>[5,1,2,8,4,6,3,7]=>[6,8,7,3,2,1,5,4]=>1101011
[3,8,2,7,1,4,5,6]=>[7,8,3,2,1,4,5,6]=>[3,7,5,1,8,6,4,2]=>0011111
[4,8,2,7,1,3,5,6]=>[7,8,2,4,1,3,5,6]=>[4,7,5,1,8,6,3,2]=>0101111
[5,8,2,7,1,3,4,6]=>[7,8,2,1,5,3,4,6]=>[5,7,4,1,8,6,3,2]=>0110111
[6,8,2,7,1,3,4,5]=>[7,8,2,1,3,6,4,5]=>[6,7,4,1,8,5,3,2]=>0111011
[6,8,5,7,1,2,3,4]=>[7,1,2,3,8,6,5,4]=>[6,8,4,3,2,1,7,5]=>1110011
[7,8,4,6,1,2,3,5]=>[6,1,2,8,4,3,7,5]=>[6,3,2,1,7,8,5,4]=>1101101
[4,3,2,6,1,5,7,8]=>[6,3,4,2,1,5,7,8]=>[4,2,3,6,5,1,7,8]=>0011100
[6,4,2,5,1,3,7,8]=>[5,4,2,6,1,3,7,8]=>[5,1,6,3,2,4,7,8]=>0101100
[5,3,2,7,1,4,6,8]=>[7,3,5,2,1,4,6,8]=>[7,6,4,2,3,5,1,8]=>0011110
[5,4,3,7,1,2,6,8]=>[7,1,4,5,3,2,6,8]=>[5,3,4,7,6,2,1,8]=>1001110
[4,3,2,8,1,5,6,7]=>[8,3,4,2,1,5,6,7]=>[4,2,3,8,7,6,5,1]=>0011111
[6,3,2,8,1,4,5,7]=>[8,3,6,2,1,4,5,7]=>[6,4,2,3,8,7,5,1]=>0011111
[6,5,3,8,1,2,4,7]=>[8,1,5,3,6,2,4,7]=>[8,7,4,3,5,6,2,1]=>1010111
[7,3,2,8,1,4,5,6]=>[8,3,7,2,1,4,5,6]=>[8,6,4,2,3,7,5,1]=>0011111
[7,4,2,8,1,3,5,6]=>[8,4,2,7,1,3,5,6]=>[8,6,3,2,4,7,5,1]=>0101111
[7,5,3,8,1,2,4,6]=>[8,1,5,3,7,2,4,6]=>[7,4,3,5,8,6,2,1]=>1010111
[8,5,3,6,1,2,4,7]=>[6,1,5,3,8,2,4,7]=>[6,2,1,8,7,4,3,5]=>1010111
[8,4,2,7,1,3,5,6]=>[7,4,2,8,1,3,5,6]=>[7,5,1,8,6,3,2,4]=>0101111
[8,6,3,7,1,2,4,5]=>[7,1,6,3,2,8,4,5]=>[8,5,2,1,7,4,3,6]=>1011011
[8,7,2,4,1,3,5,6]=>[4,7,2,1,3,5,8,6]=>[4,1,8,6,5,3,2,7]=>0111101
[8,7,2,5,1,3,4,6]=>[5,7,2,1,3,4,8,6]=>[8,6,4,1,5,3,2,7]=>0111101
[8,7,2,6,1,3,4,5]=>[6,7,2,1,3,4,8,5]=>[6,4,1,8,5,3,2,7]=>0111101
[8,7,3,6,1,2,4,5]=>[6,1,7,3,2,4,8,5]=>[8,5,2,1,6,4,3,7]=>1011101
[5,6,2,4,8,1,3,7]=>[8,6,2,1,5,4,3,7]=>[5,8,7,3,2,6,4,1]=>0110111
[4,7,2,5,8,1,3,6]=>[8,7,2,4,1,5,3,6]=>[4,7,3,2,8,6,5,1]=>0101111
[3,7,2,6,8,1,4,5]=>[8,7,3,2,1,4,6,5]=>[3,7,6,4,2,8,5,1]=>0011111
[5,7,4,6,8,1,2,3]=>[8,1,2,7,5,4,6,3]=>[5,7,6,4,8,3,2,1]=>1100111
[6,7,3,5,8,1,2,4]=>[8,1,7,3,2,6,5,4]=>[6,8,4,3,7,5,2,1]=>1011011
[4,8,2,5,7,1,3,6]=>[7,8,2,4,1,5,3,6]=>[4,8,6,5,1,7,3,2]=>0101111
[3,8,2,6,7,1,4,5]=>[7,8,3,2,1,4,6,5]=>[3,8,5,1,7,6,4,2]=>0011111
[5,8,4,6,7,1,2,3]=>[7,1,2,8,5,4,6,3]=>[5,8,3,2,1,7,6,4]=>1100111
[6,8,2,5,7,1,3,4]=>[7,8,2,1,3,6,5,4]=>[6,8,4,1,7,5,3,2]=>0111011
[7,8,2,4,6,1,3,5]=>[6,8,2,1,4,3,7,5]=>[7,8,5,4,1,6,3,2]=>0111101
[7,8,3,4,6,1,2,5]=>[6,1,8,3,4,2,7,5]=>[6,2,1,7,8,5,4,3]=>1011101
[7,8,2,5,6,1,3,4]=>[6,8,2,1,3,5,7,4]=>[7,8,4,1,6,5,3,2]=>0111101
[4,3,2,6,8,1,5,7]=>[8,3,4,2,1,6,5,7]=>[4,2,3,6,8,7,5,1]=>0011011
[5,3,2,6,8,1,4,7]=>[8,3,5,2,1,6,4,7]=>[6,8,7,4,2,3,5,1]=>0011011
[6,3,2,5,8,1,4,7]=>[8,3,6,2,1,5,4,7]=>[8,7,4,2,3,6,5,1]=>0011111
[6,4,3,5,8,1,2,7]=>[8,1,4,6,3,5,2,7]=>[6,5,3,4,8,7,2,1]=>1001111
[6,5,2,4,8,1,3,7]=>[8,5,2,1,6,4,3,7]=>[8,7,3,2,5,6,4,1]=>0110111
[7,4,2,5,8,1,3,6]=>[8,4,2,7,1,5,3,6]=>[7,3,2,4,8,6,5,1]=>0101111
[7,3,2,6,8,1,4,5]=>[8,3,7,2,1,4,6,5]=>[7,6,4,2,3,8,5,1]=>0011111
[7,5,3,6,8,1,2,4]=>[8,1,5,3,7,2,6,4]=>[8,4,3,5,7,6,2,1]=>1010111
[8,4,2,5,7,1,3,6]=>[7,4,2,8,1,5,3,6]=>[8,6,5,1,7,3,2,4]=>0101111
[8,5,2,6,7,1,3,4]=>[7,5,2,1,8,3,6,4]=>[8,4,1,7,6,3,2,5]=>0110111
[8,5,3,6,7,1,2,4]=>[7,1,5,3,8,2,6,4]=>[7,6,2,1,8,4,3,5]=>1010111
[8,6,2,5,7,1,3,4]=>[7,6,2,1,3,8,5,4]=>[8,4,1,7,5,3,2,6]=>0111011
[8,7,2,4,6,1,3,5]=>[6,7,2,1,4,3,8,5]=>[8,5,4,1,6,3,2,7]=>0111101
[4,3,7,2,6,1,5,8]=>[6,7,4,3,2,1,5,8]=>[4,3,6,1,7,5,2,8]=>0011110
[4,3,8,2,6,1,5,7]=>[6,8,4,3,2,1,5,7]=>[4,3,6,1,8,7,5,2]=>0011111
[5,3,8,2,6,1,4,7]=>[6,8,5,3,2,1,4,7]=>[6,1,8,7,4,3,5,2]=>0011111
[6,5,8,3,4,1,2,7]=>[4,1,8,3,6,5,2,7]=>[6,5,8,7,2,1,4,3]=>1010111
[5,4,8,2,7,1,3,6]=>[7,8,2,5,4,1,3,6]=>[5,4,8,6,1,7,3,2]=>0101111
[7,5,8,3,4,1,2,6]=>[4,1,8,3,7,5,2,6]=>[8,6,5,7,2,1,4,3]=>1010111
[7,5,8,4,6,1,2,3]=>[6,1,2,8,7,5,4,3]=>[8,3,2,1,6,5,7,4]=>1100111
[8,3,6,2,5,1,4,7]=>[5,6,8,3,2,1,4,7]=>[6,1,5,2,8,7,4,3]=>0011111
[8,4,6,2,5,1,3,7]=>[5,6,2,8,4,1,3,7]=>[8,7,3,2,6,1,5,4]=>0101111
[8,3,7,2,5,1,4,6]=>[5,7,8,3,2,1,4,6]=>[8,6,1,5,2,7,4,3]=>0011111
[8,4,7,3,5,1,2,6]=>[5,1,7,8,4,3,2,6]=>[8,6,3,7,2,1,5,4]=>1001111
[8,3,7,2,6,1,4,5]=>[6,7,8,3,2,1,4,5]=>[6,1,8,5,2,7,4,3]=>0011111
[8,4,7,2,6,1,3,5]=>[6,7,2,8,4,1,3,5]=>[6,1,7,3,2,8,5,4]=>0101111
[8,4,7,3,6,1,2,5]=>[6,1,7,8,4,3,2,5]=>[7,2,1,6,3,8,5,4]=>1001111
[7,5,3,2,6,1,4,8]=>[6,3,5,2,7,1,4,8]=>[6,1,7,4,2,3,5,8]=>0010110
[5,4,3,2,8,1,6,7]=>[8,3,4,5,2,1,6,7]=>[5,2,3,4,8,7,6,1]=>0001111
[6,5,4,3,8,1,2,7]=>[8,1,4,5,6,3,2,7]=>[6,3,4,5,8,7,2,1]=>1000111
[8,5,3,2,6,1,4,7]=>[6,3,5,2,8,1,4,7]=>[6,1,8,7,4,2,3,5]=>0010111
[8,6,3,2,5,1,4,7]=>[5,3,6,2,1,8,4,7]=>[5,1,8,7,4,2,3,6]=>0011011
[8,5,3,2,7,1,4,6]=>[7,3,5,2,8,1,4,6]=>[8,6,1,7,4,2,3,5]=>0010111
[8,7,3,2,6,1,4,5]=>[6,3,7,2,1,4,8,5]=>[8,5,1,6,4,2,3,7]=>0011101
[4,8,3,7,2,6,1,5]=>[6,7,8,4,3,2,1,5]=>[4,7,1,6,2,8,5,3]=>0001111
[5,8,3,7,2,6,1,4]=>[6,7,8,3,5,2,1,4]=>[5,7,1,6,2,8,4,3]=>0010111
[5,8,4,7,2,6,1,3]=>[6,7,2,8,5,4,1,3]=>[5,8,3,2,7,1,6,4]=>0100111
[5,8,4,7,3,6,1,2]=>[6,1,7,8,5,4,3,2]=>[5,7,3,8,2,1,6,4]=>1000111
[6,8,3,7,2,5,1,4]=>[5,7,8,3,2,6,1,4]=>[6,7,1,5,2,8,4,3]=>0011011
[6,8,4,7,2,5,1,3]=>[5,7,2,8,4,6,1,3]=>[6,8,3,2,7,1,5,4]=>0101011
[6,8,4,7,3,5,1,2]=>[5,1,7,8,4,6,3,2]=>[6,7,3,8,2,1,5,4]=>1001011
[6,8,5,7,3,4,1,2]=>[4,1,7,3,8,6,5,2]=>[6,8,2,1,4,3,7,5]=>1010011
[7,8,3,6,2,5,1,4]=>[5,6,8,3,2,1,7,4]=>[6,1,5,2,7,8,4,3]=>0011101
[6,5,3,8,2,7,1,4]=>[7,8,5,3,6,2,1,4]=>[7,1,8,4,3,5,6,2]=>0010111
[7,5,4,8,2,6,1,3]=>[6,8,2,5,7,4,1,3]=>[7,1,6,4,5,8,3,2]=>0100111
[7,6,4,8,2,5,1,3]=>[5,8,2,6,4,7,1,3]=>[7,1,5,4,6,8,3,2]=>0101011
[8,6,4,7,2,5,1,3]=>[5,7,2,6,4,8,1,3]=>[8,3,2,7,1,5,4,6]=>0101011
[8,7,4,6,3,5,1,2]=>[5,1,6,7,4,3,8,2]=>[6,3,8,2,1,5,4,7]=>1001101
[8,5,4,3,2,7,1,6]=>[7,3,4,5,8,2,1,6]=>[7,1,8,6,2,3,4,5]=>0000111
[8,7,4,3,2,6,1,5]=>[6,3,4,7,2,1,8,5]=>[6,1,8,5,2,3,4,7]=>0001101
[8,7,5,3,2,6,1,4]=>[6,3,5,2,7,1,8,4]=>[6,1,8,4,2,3,5,7]=>0010101
[8,7,6,3,2,5,1,4]=>[5,3,6,2,1,7,8,4]=>[5,1,8,4,2,3,6,7]=>0011001
[8,7,6,5,2,4,1,3]=>[4,5,2,1,6,7,8,3]=>[4,1,8,3,2,5,6,7]=>0110001
[8,1,2,3,7,4,5,6]=>[7,1,2,8,3,4,5,6]=>[7,5,3,2,1,8,6,4]=>1101111
[4,1,2,8,7,3,5,6]=>[7,1,4,2,3,5,8,6]=>[8,6,5,3,4,2,1,7]=>1011101
[4,1,2,7,6,3,8,5]=>[8,1,4,2,6,7,3,5]=>[8,5,6,7,3,4,2,1]=>1010011
[7,1,2,5,6,3,8,4]=>[8,1,6,7,2,5,3,4]=>[8,4,7,3,6,5,2,1]=>1001111
[8,1,2,5,6,7,3,4]=>[7,1,8,2,3,5,6,4]=>[8,4,2,1,7,6,5,3]=>1011111
[3,1,8,2,6,4,5,7]=>[6,3,1,8,2,4,5,7]=>[8,7,5,2,3,1,6,4]=>0101111
[3,1,7,2,6,4,8,5]=>[8,3,1,6,7,2,4,5]=>[8,5,7,4,6,2,3,1]=>0100111
[3,1,8,2,6,7,4,5]=>[7,3,1,8,2,4,6,5]=>[8,5,2,3,1,7,6,4]=>0101111
[8,1,4,2,3,5,6,7]=>[4,8,1,2,3,5,6,7]=>[8,7,6,5,3,1,4,2]=>0111111
[7,1,4,2,3,5,8,6]=>[4,8,1,2,3,7,5,6]=>[8,6,7,5,3,1,4,2]=>0111011
[5,1,4,2,8,3,6,7]=>[8,4,5,1,2,3,6,7]=>[8,7,6,3,5,2,4,1]=>0011111
[5,1,4,2,7,3,8,6]=>[8,4,5,1,2,7,3,6]=>[8,6,7,3,5,2,4,1]=>0011011
[8,1,4,2,6,3,5,7]=>[6,4,8,1,2,3,5,7]=>[8,7,5,2,4,1,6,3]=>0011111
[7,1,4,2,6,3,8,5]=>[8,4,6,1,7,2,3,5]=>[8,5,7,3,6,2,4,1]=>0010111
[8,1,5,2,7,3,4,6]=>[7,5,8,1,2,3,4,6]=>[5,2,7,4,1,8,6,3]=>0011111
[7,1,5,2,6,3,8,4]=>[8,6,5,7,1,2,3,4]=>[6,2,8,4,7,3,5,1]=>0001111
[5,1,4,2,8,7,3,6]=>[7,4,5,1,2,3,8,6]=>[8,6,3,5,2,4,1,7]=>0011101
[3,1,8,5,2,7,4,6]=>[7,3,1,5,8,2,4,6]=>[8,6,2,3,1,7,4,5]=>0100111
[7,1,8,6,2,3,4,5]=>[6,8,1,2,3,7,4,5]=>[8,5,3,1,6,7,4,2]=>0111011
[3,1,4,8,6,2,5,7]=>[6,3,1,4,2,8,5,7]=>[4,8,7,5,2,3,1,6]=>0101011
[8,1,4,5,6,7,2,3]=>[7,8,1,2,4,5,6,3]=>[8,3,1,7,6,5,4,2]=>0111111
[2,6,1,5,3,8,4,7]=>[8,2,5,6,1,3,4,7]=>[2,8,7,4,6,3,5,1]=>0001111
[2,8,1,6,3,7,4,5]=>[7,2,6,8,1,3,4,5]=>[2,6,3,8,5,1,7,4]=>0001111
[2,4,1,8,6,3,5,7]=>[6,2,4,1,3,8,5,7]=>[2,8,7,5,3,4,1,6]=>0011011
[6,3,1,2,4,8,5,7]=>[3,1,8,2,6,4,5,7]=>[8,7,5,6,4,2,1,3]=>1010111
[7,3,1,2,6,4,8,5]=>[3,1,8,6,7,2,4,5]=>[8,5,7,4,6,2,1,3]=>1000111
[7,6,1,2,3,4,8,5]=>[8,1,2,3,6,7,4,5]=>[8,5,6,7,4,3,2,1]=>1110011
[5,4,1,2,8,3,6,7]=>[8,1,4,5,2,3,6,7]=>[8,7,6,3,4,5,2,1]=>1001111
[8,4,1,2,7,3,5,6]=>[7,1,4,8,2,3,5,6]=>[7,5,2,1,8,6,3,4]=>1001111
[8,7,1,2,6,3,4,5]=>[6,1,7,2,3,4,8,5]=>[6,4,2,1,8,5,3,7]=>1011101
[5,7,1,2,6,3,8,4]=>[8,1,6,7,5,2,3,4]=>[5,8,4,7,3,6,2,1]=>1000111
[5,4,1,2,6,7,8,3]=>[8,1,4,5,2,6,7,3]=>[6,7,8,3,4,5,2,1]=>1001001
[4,3,1,8,2,5,6,7]=>[8,3,4,1,2,5,6,7]=>[8,7,6,5,2,3,4,1]=>0011111
[4,3,1,7,2,5,8,6]=>[8,3,4,1,2,7,5,6]=>[8,6,7,5,2,3,4,1]=>0011011
[4,3,1,6,2,8,5,7]=>[8,3,4,1,6,2,5,7]=>[8,7,5,6,2,3,4,1]=>0010111
[8,3,1,5,2,4,6,7]=>[5,3,8,1,2,4,6,7]=>[8,7,6,4,1,5,2,3]=>0011111
[8,3,1,5,2,7,4,6]=>[7,3,5,8,1,2,4,6]=>[8,6,2,3,5,1,7,4]=>0001111
[8,3,1,6,2,7,4,5]=>[7,3,6,8,1,2,4,5]=>[6,2,3,8,5,1,7,4]=>0001111
[8,4,1,6,2,3,5,7]=>[6,4,1,8,2,3,5,7]=>[6,3,1,8,7,5,2,4]=>0101111
[7,4,1,8,2,3,5,6]=>[8,4,1,7,2,3,5,6]=>[7,5,2,4,8,6,3,1]=>0101111
[8,7,1,6,2,3,4,5]=>[6,7,1,2,3,4,8,5]=>[8,5,3,1,6,4,2,7]=>0111101
[8,4,1,6,2,7,3,5]=>[7,6,4,8,1,2,3,5]=>[6,2,8,5,1,7,3,4]=>0001111
[4,3,1,8,7,2,5,6]=>[7,3,4,1,2,5,8,6]=>[8,6,5,2,3,4,1,7]=>0011101
[4,3,1,7,6,2,8,5]=>[8,3,4,1,6,7,2,5]=>[8,5,6,7,2,3,4,1]=>0010011
[8,3,1,5,6,2,4,7]=>[6,3,8,1,2,5,4,7]=>[8,7,4,1,6,5,2,3]=>0011111
[8,3,1,7,6,2,4,5]=>[6,3,7,1,2,8,4,5]=>[8,5,2,3,7,4,1,6]=>0011011
[7,3,1,5,6,2,8,4]=>[8,3,6,7,1,5,2,4]=>[8,4,7,2,3,6,5,1]=>0001111
[7,8,1,5,6,2,3,4]=>[6,8,1,2,3,5,7,4]=>[6,5,3,1,7,8,4,2]=>0111101
[4,3,1,5,6,7,8,2]=>[8,3,4,1,5,6,7,2]=>[5,6,7,8,2,3,4,1]=>0010001
[2,7,5,1,3,4,8,6]=>[5,2,1,3,8,7,4,6]=>[2,8,6,7,4,3,1,5]=>0110011
[2,6,8,1,3,7,4,5]=>[7,2,1,8,3,6,4,5]=>[2,6,8,5,3,1,7,4]=>0101011
[2,6,5,1,3,7,8,4]=>[8,2,1,5,6,3,7,4]=>[2,7,8,4,5,6,3,1]=>0100101
[6,3,4,1,2,7,8,5]=>[4,1,8,3,6,2,7,5]=>[7,8,5,6,2,1,4,3]=>1010101
[7,3,5,1,2,4,8,6]=>[5,1,8,3,2,7,4,6]=>[5,2,1,8,6,7,4,3]=>1011011
[6,3,7,1,2,4,8,5]=>[8,1,7,3,6,2,4,5]=>[7,4,3,8,5,6,2,1]=>1010111
[6,8,5,1,2,3,4,7]=>[5,1,2,3,8,6,4,7]=>[6,8,7,4,3,2,1,5]=>1110011
[8,5,4,1,2,7,3,6]=>[7,1,4,5,8,2,3,6]=>[8,6,2,1,7,3,4,5]=>1000111
[6,8,4,1,2,7,3,5]=>[7,1,4,8,2,6,3,5]=>[6,8,5,2,1,7,3,4]=>1001011
[6,8,5,1,2,7,3,4]=>[7,1,5,2,8,6,3,4]=>[6,8,4,2,1,7,3,5]=>1010011
[8,3,4,1,7,2,5,6]=>[7,4,8,3,1,2,5,6]=>[7,5,1,8,6,2,4,3]=>0011111
[7,3,4,1,6,2,8,5]=>[8,4,6,3,7,1,2,5]=>[8,5,7,2,4,3,6,1]=>0010111
[7,8,4,1,6,2,3,5]=>[6,4,1,8,2,3,7,5]=>[6,3,1,7,8,5,2,4]=>0101101
[7,8,5,1,6,2,3,4]=>[6,5,1,2,8,3,7,4]=>[6,3,1,7,8,4,2,5]=>0110101
[5,3,4,1,6,7,8,2]=>[8,4,5,3,1,6,7,2]=>[6,7,8,2,4,3,5,1]=>0011001
[2,3,4,8,1,7,5,6]=>[7,2,3,4,8,1,5,6]=>[2,3,4,8,6,1,7,5]=>0000111
[2,3,6,5,1,8,4,7]=>[8,2,3,5,6,1,4,7]=>[2,3,8,7,4,5,6,1]=>0000111
[2,7,4,8,1,3,5,6]=>[8,2,1,7,4,3,5,6]=>[2,7,5,4,8,6,3,1]=>0101111
[7,3,8,5,1,2,4,6]=>[5,1,8,3,7,2,4,6]=>[8,6,2,1,5,7,4,3]=>1010111
[2,3,4,8,6,1,5,7]=>[6,2,3,4,1,8,5,7]=>[2,3,4,8,7,5,1,6]=>0001011
[2,3,4,8,7,1,5,6]=>[7,2,3,4,1,5,8,6]=>[2,3,4,8,6,5,1,7]=>0001101
[2,3,4,7,6,1,8,5]=>[8,2,3,4,6,7,1,5]=>[2,3,4,8,5,6,7,1]=>0000011
[2,3,8,5,7,1,4,6]=>[7,2,3,1,8,5,4,6]=>[2,3,7,4,1,8,6,5]=>0010111
[8,3,4,7,6,1,2,5]=>[6,1,7,3,4,8,2,5]=>[8,5,4,3,7,2,1,6]=>1011011
[8,3,7,5,6,1,2,4]=>[6,1,7,3,8,2,5,4]=>[6,2,1,8,4,3,7,5]=>1010111
[2,3,4,5,8,7,1,6]=>[7,2,3,4,5,1,8,6]=>[2,3,4,5,8,6,1,7]=>0000101
[2,3,4,8,6,7,1,5]=>[7,2,3,4,1,8,6,5]=>[2,3,4,8,5,1,7,6]=>0001011
[2,8,4,5,6,7,1,3]=>[7,2,1,8,4,5,6,3]=>[2,8,3,1,7,6,5,4]=>0101111
[1,6,7,4,5,2,3,8]=>[1,5,2,7,4,6,3,8]=>[1,6,7,3,2,5,4,8]=>0101010
[6,3,8,4,5,7,1,2]=>[7,1,8,6,3,4,5,2]=>[6,4,8,2,1,7,5,3]=>1001111
[3,2,5,6,1,8,7,4]=>[7,3,2,6,5,1,8,4]=>[3,2,5,8,4,6,1,7]=>0100101
[5,2,4,8,6,1,7,3]=>[7,6,5,2,4,8,1,3]=>[7,1,8,3,5,4,2,6]=>0011011
[7,8,1,3,2,5,4,6]=>[3,5,1,8,2,4,7,6]=>[3,1,5,2,7,8,6,4]=>0101101
[6,3,8,2,1,7,5,4]=>[2,5,7,8,6,3,1,4]=>[7,1,2,5,6,3,8,4]=>0000111
[7,8,3,2,1,6,5,4]=>[2,3,5,6,8,1,7,4]=>[7,8,4,6,1,2,3,5]=>0000101
[7,8,4,2,6,1,5,3]=>[5,6,4,8,2,1,7,3]=>[6,1,5,2,7,8,3,4]=>0001101
[4,5,2,7,8,1,6,3]=>[6,8,5,4,2,1,7,3]=>[4,6,1,7,8,3,5,2]=>0001101
[3,5,2,7,1,8,6,4]=>[6,8,3,5,2,7,1,4]=>[3,7,1,6,8,4,5,2]=>0001011
[1,5,3,7,2,6,4,8]=>[1,6,7,5,3,2,4,8]=>[1,6,2,7,4,5,3,8]=>0001110
[2,6,7,3,1,5,8,4]=>[3,2,8,7,1,6,5,4]=>[2,6,8,4,7,5,1,3]=>0001011
[4,6,7,2,8,1,5,3]=>[5,8,7,4,2,6,1,3]=>[4,6,8,3,7,1,5,2]=>0001011
[5,6,7,8,2,1,4,3]=>[2,4,8,1,5,6,7,3]=>[4,1,2,5,6,7,8,3]=>0010001
[7,8,5,6,2,1,4,3]=>[2,4,6,1,8,5,7,3]=>[4,1,2,7,8,3,6,5]=>0010101
[6,5,8,7,1,2,3,4]=>[7,1,2,3,6,5,8,4]=>[6,5,8,4,3,2,1,7]=>1110101
[5,3,1,8,2,7,4,6]=>[7,3,8,5,1,2,4,6]=>[7,4,5,1,8,6,2,3]=>0001111
[4,3,1,2,8,7,5,6]=>[3,1,4,2,7,5,8,6]=>[4,2,1,3,8,6,5,7]=>1010101
[5,2,1,8,3,4,7,6]=>[2,7,5,1,3,8,4,6]=>[5,3,7,4,1,2,8,6]=>0011011
[7,8,2,1,3,4,6,5]=>[2,6,1,3,8,4,7,5]=>[6,4,3,1,2,7,8,5]=>0110101
[4,5,2,3,7,6,1,8]=>[6,5,2,4,3,7,1,8]=>[4,5,3,2,7,1,6,8]=>0101010
[3,2,6,7,4,5,1,8]=>[5,3,2,7,4,6,1,8]=>[3,2,6,7,1,5,4,8]=>0101010
[8,7,5,4,1,3,2,6]=>[3,4,1,5,7,2,8,6]=>[3,1,8,6,2,4,5,7]=>0100101
[4,1,2,6,5,8,7,3]=>[7,1,4,2,6,5,8,3]=>[6,5,8,3,4,2,1,7]=>1010101
[7,1,5,4,8,2,6,3]=>[6,8,5,7,1,4,2,3]=>[8,3,5,1,6,4,7,2]=>0001111
[8,1,6,7,4,5,2,3]=>[5,7,1,8,2,4,6,3]=>[8,3,1,5,2,7,6,4]=>0101111
[6,1,7,8,2,4,5,3]=>[5,8,6,1,2,4,7,3]=>[7,8,3,6,4,1,5,2]=>0011101
[5,1,7,2,8,4,6,3]=>[6,8,7,5,1,2,4,3]=>[8,3,7,4,5,1,6,2]=>0001111
[4,1,2,7,8,5,6,3]=>[6,1,4,2,8,5,7,3]=>[7,8,3,4,2,1,6,5]=>1010101
[4,8,2,7,1,5,3,6]=>[5,7,8,4,2,1,3,6]=>[4,8,6,1,5,2,7,3]=>0001111
[6,8,7,1,2,4,3,5]=>[4,1,7,2,3,6,8,5]=>[4,2,1,6,8,5,3,7]=>1011001
[8,6,7,1,3,4,2,5]=>[4,7,1,3,2,8,6,5]=>[4,3,1,8,5,2,7,6]=>0111011
[4,6,2,8,3,1,5,7]=>[3,8,6,4,2,1,5,7]=>[4,6,1,3,8,7,5,2]=>0001111
[4,5,2,3,8,1,6,7]=>[8,5,2,4,3,1,6,7]=>[4,5,3,2,8,7,6,1]=>0101111
[4,5,2,3,1,8,7,6]=>[3,5,2,4,1,7,8,6]=>[4,5,1,3,2,8,6,7]=>0101001
[6,4,3,1,2,8,7,5]=>[3,1,4,7,6,2,8,5]=>[8,5,6,2,1,3,4,7]=>1000101
[1,5,8,3,7,6,4,2]=>[1,4,6,7,5,8,3,2]=>[1,5,8,2,4,7,3,6]=>0000011
[5,7,1,2,8,3,6,4]=>[6,1,8,7,5,2,3,4]=>[5,6,2,1,8,4,7,3]=>1000111
[6,7,1,8,2,3,5,4]=>[5,8,1,7,2,6,3,4]=>[6,8,4,7,3,1,5,2]=>0101011
[7,8,1,6,5,2,3,4]=>[5,6,1,2,8,3,7,4]=>[7,8,4,2,6,3,1,5]=>0110101
[6,8,1,7,2,5,3,4]=>[5,7,8,1,2,6,3,4]=>[6,8,4,1,5,2,7,3]=>0011011
[4,8,2,1,7,6,3,5]=>[2,6,7,4,1,8,3,5]=>[4,7,3,8,5,1,2,6]=>0001011
[3,2,8,1,7,6,4,5]=>[6,3,2,7,1,8,4,5]=>[3,2,7,4,8,5,1,6]=>0101011
[8,1,7,6,5,4,2,3]=>[4,5,1,6,7,8,2,3]=>[7,2,5,8,3,1,4,6]=>0100011
[4,1,5,3,6,2,8,7]=>[6,5,4,1,3,2,8,7]=>[6,2,5,3,4,1,8,7]=>0011101
[4,3,5,2,7,1,8,6]=>[8,5,4,3,2,7,1,6]=>[4,3,5,2,8,6,7,1]=>0011011
[4,1,5,3,7,2,8,6]=>[8,5,4,1,3,7,2,6]=>[8,6,7,2,5,3,4,1]=>0011011
[3,1,5,4,7,6,8,2]=>[8,3,1,5,4,7,6,2]=>[5,4,7,6,8,2,3,1]=>0101011
[4,1,5,3,7,6,8,2]=>[8,5,4,1,3,7,6,2]=>[7,6,8,2,5,3,4,1]=>0011011
[5,3,6,4,7,1,8,2]=>[8,7,6,5,3,4,1,2]=>[6,4,5,3,8,2,7,1]=>0001111
[4,1,6,3,7,5,8,2]=>[8,7,4,1,6,3,5,2]=>[8,2,7,5,6,3,4,1]=>0010111
[2,1,6,4,7,5,8,3]=>[2,1,8,7,6,4,5,3]=>[2,1,7,5,6,4,8,3]=>1000111
[3,1,6,4,7,2,8,5]=>[8,3,1,7,6,4,2,5]=>[8,5,6,4,7,2,3,1]=>0100111
[5,1,6,3,7,2,8,4]=>[8,7,6,5,1,3,2,4]=>[6,3,7,2,8,4,5,1]=>0001111
[5,2,6,3,7,1,8,4]=>[8,7,6,5,2,3,1,4]=>[6,3,8,4,5,2,7,1]=>0001111
[4,2,5,1,7,3,8,6]=>[8,5,4,2,1,7,3,6]=>[8,6,7,3,4,2,5,1]=>0011011
[4,2,6,1,7,3,8,5]=>[8,7,4,2,6,1,3,5]=>[7,3,4,2,8,5,6,1]=>0010111
[3,2,5,1,7,4,8,6]=>[8,3,2,5,1,7,4,6]=>[3,2,8,6,7,4,5,1]=>0101011
[3,2,4,1,7,5,8,6]=>[4,3,2,1,8,7,5,6]=>[3,2,4,1,8,6,7,5]=>0110011
[3,1,4,2,7,6,8,5]=>[4,3,1,2,8,7,6,5]=>[4,2,3,1,7,6,8,5]=>0110011
[4,2,6,1,7,5,8,3]=>[8,7,4,2,6,1,5,3]=>[8,3,4,2,7,5,6,1]=>0010111
[4,2,5,1,7,6,8,3]=>[8,5,4,2,1,7,6,3]=>[7,6,8,3,4,2,5,1]=>0011011
[3,1,5,2,7,6,8,4]=>[8,3,1,5,2,7,6,4]=>[7,6,8,4,5,2,3,1]=>0101011
[2,1,5,3,7,6,8,4]=>[2,1,8,5,3,7,6,4]=>[2,1,7,6,8,4,5,3]=>1001011
[2,1,6,3,7,5,8,4]=>[2,1,8,7,6,3,5,4]=>[2,1,8,4,7,5,6,3]=>1000111
[3,1,6,2,7,5,8,4]=>[8,3,1,7,6,2,5,4]=>[8,4,7,5,6,2,3,1]=>0100111
[4,1,6,2,7,5,8,3]=>[8,7,4,1,6,2,5,3]=>[7,5,6,2,8,3,4,1]=>0010111
[5,2,6,1,7,4,8,3]=>[8,7,6,5,2,1,4,3]=>[7,4,5,2,8,3,6,1]=>0001111
[5,1,6,4,7,2,8,3]=>[8,7,6,5,1,4,2,3]=>[7,2,8,3,6,4,5,1]=>0001111
[3,1,6,5,7,2,8,4]=>[8,3,1,7,6,5,2,4]=>[6,5,8,4,7,2,3,1]=>0100111
[3,1,6,5,7,4,8,2]=>[8,3,1,7,6,5,4,2]=>[6,5,7,4,8,2,3,1]=>0100111
[5,1,6,4,7,3,8,2]=>[8,7,6,5,1,4,3,2]=>[8,2,7,3,6,4,5,1]=>0001111
[8,6,1,3,4,2,5,7]=>[4,6,1,3,2,8,5,7]=>[4,3,1,8,7,5,2,6]=>0111011
[8,6,3,5,2,4,1,7]=>[4,5,6,3,2,8,1,7]=>[5,2,8,7,1,4,3,6]=>0011011
[8,3,7,5,2,4,6,1]=>[6,5,7,3,8,2,4,1]=>[7,4,3,8,1,6,2,5]=>0010111
[2,4,5,7,3,1,8,6]=>[3,2,8,4,5,7,1,6]=>[2,4,5,8,6,7,1,3]=>0000011
[8,5,7,4,3,2,6,1]=>[6,3,4,7,8,5,2,1]=>[7,2,3,4,8,1,6,5]=>0000111
[4,8,1,6,7,3,5,2]=>[5,7,8,4,1,3,6,2]=>[4,5,1,8,2,7,6,3]=>0001111
[3,7,6,5,8,2,1,4]=>[2,8,3,1,6,7,5,4]=>[3,7,5,6,8,4,1,2]=>0010011
[3,6,8,5,7,2,4,1]=>[4,7,3,2,8,6,5,1]=>[3,6,8,1,4,2,7,5]=>0010011
[2,1,6,5,7,8,3,4]=>[2,1,8,3,6,5,7,4]=>[2,1,6,5,7,8,4,3]=>1010101
[3,2,6,1,4,7,8,5]=>[8,3,2,1,6,4,7,5]=>[3,2,7,8,5,6,4,1]=>0110101
[4,7,2,1,3,5,8,6]=>[2,8,1,4,3,7,5,6]=>[4,8,6,7,5,3,1,2]=>0101011
[3,7,8,6,2,1,5,4]=>[2,5,3,6,1,8,7,4]=>[3,5,1,2,7,8,4,6]=>0001001
[2,7,4,8,1,6,5,3]=>[5,2,6,8,7,4,1,3]=>[2,7,1,5,8,3,6,4]=>0000111
[4,6,8,2,1,7,5,3]=>[2,5,7,4,8,6,1,3]=>[4,6,8,3,7,1,2,5]=>0000011
[8,5,7,2,1,3,6,4]=>[2,6,1,7,8,5,3,4]=>[8,4,7,3,1,2,6,5]=>0100111
[4,6,1,8,7,2,5,3]=>[5,7,6,4,1,2,8,3]=>[4,5,1,8,3,6,2,7]=>0001101
[2,1,7,8,5,6,4,3]=>[2,1,4,6,8,5,7,3]=>[2,1,7,8,3,4,6,5]=>1000101
[2,7,6,8,5,4,1,3]=>[4,2,1,5,8,7,6,3]=>[2,7,6,8,3,1,4,5]=>0100011
[1,7,2,5,8,6,4,3]=>[1,4,6,8,2,7,5,3]=>[1,8,3,6,7,5,2,4]=>0001011
[3,7,8,1,6,5,2,4]=>[5,6,3,1,8,2,7,4]=>[3,6,2,7,8,4,1,5]=>0010101
[8,4,7,6,5,1,3,2]=>[3,5,1,6,7,8,4,2]=>[3,1,8,2,5,7,4,6]=>0100011
[3,2,5,1,6,8,4,7]=>[8,3,2,5,1,6,4,7]=>[3,2,6,8,7,4,5,1]=>0101011
[3,6,2,5,4,8,1,7]=>[8,5,3,6,2,4,1,7]=>[3,5,2,6,4,8,7,1]=>0001111
[3,5,8,2,4,7,6,1]=>[6,7,3,2,5,8,4,1]=>[3,5,7,4,2,8,1,6]=>0010011
[5,4,3,8,2,7,6,1]=>[6,7,4,5,3,8,2,1]=>[5,3,4,7,2,8,1,6]=>0001011
[6,4,3,1,7,2,8,5]=>[8,3,4,7,6,1,2,5]=>[7,2,3,4,8,5,6,1]=>0000111
[1,4,7,5,8,3,2,6]=>[1,3,8,4,7,5,2,6]=>[1,4,8,6,5,7,2,3]=>0000111
[4,3,7,1,8,6,5,2]=>[5,6,4,3,8,7,1,2]=>[4,3,8,2,6,7,1,5]=>0010011
[6,5,2,1,7,3,8,4]=>[2,8,7,5,6,1,3,4]=>[7,3,8,4,5,6,1,2]=>0000111
[5,7,3,1,8,2,4,6]=>[8,3,7,1,5,2,4,6]=>[5,8,6,2,3,7,4,1]=>0010111
[4,7,1,5,2,8,3,6]=>[8,5,7,4,1,2,3,6]=>[4,7,3,8,6,2,5,1]=>0001111
[4,3,7,8,2,1,5,6]=>[2,8,4,3,1,5,7,6]=>[4,3,7,8,6,5,1,2]=>0011101
[8,3,7,1,4,6,2,5]=>[6,7,8,3,1,4,2,5]=>[7,2,8,5,1,6,4,3]=>0011111
[3,8,2,5,7,1,6,4]=>[6,7,3,8,2,5,1,4]=>[3,7,1,6,5,2,8,4]=>0001111
[5,8,3,7,1,6,2,4]=>[6,7,8,3,5,1,2,4]=>[5,6,1,7,2,8,4,3]=>0010111
[5,8,7,2,6,1,3,4]=>[6,7,2,1,5,3,8,4]=>[5,8,4,1,6,3,2,7]=>0110101
[5,2,7,1,8,6,4,3]=>[4,6,8,5,2,7,1,3]=>[7,1,4,5,2,6,8,3]=>0001011
[7,1,8,6,5,4,3,2]=>[3,4,5,6,8,7,1,2]=>[8,2,4,6,7,1,3,5]=>0000011
[4,1,3,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>0110101
[6,5,2,7,1,8,3,4]=>[8,7,5,2,6,1,3,4]=>[8,4,2,7,3,5,6,1]=>0010111
[3,5,2,6,4,1,8,7]=>[4,6,3,5,2,1,8,7]=>[3,6,1,4,5,2,8,7]=>0001101
[5,6,3,2,1,4,8,7]=>[2,3,6,1,5,4,8,7]=>[5,6,4,1,2,3,8,7]=>0010101
[2,1,6,3,5,4,8,7]=>[2,1,5,6,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>1001101
[5,3,1,4,6,2,8,7]=>[6,3,5,1,4,2,8,7]=>[6,2,3,5,4,1,8,7]=>0011101
[3,4,7,8,5,2,1,6]=>[2,5,3,4,8,1,7,6]=>[3,4,7,8,6,1,2,5]=>0000101
[2,4,6,3,7,5,8,1]=>[8,2,7,4,6,3,5,1]=>[2,4,7,5,6,3,8,1]=>0000111
[4,1,6,3,8,5,7,2]=>[7,8,4,1,6,3,5,2]=>[7,5,6,3,4,1,8,2]=>0010111
[2,1,5,7,4,8,6,3]=>[2,1,6,8,5,7,4,3]=>[2,1,5,8,3,6,7,4]=>1000011
[4,3,7,2,6,8,5,1]=>[5,8,4,3,7,2,6,1]=>[4,3,8,1,5,7,6,2]=>0010111
[7,8,2,4,3,6,1,5]=>[6,4,8,2,3,1,7,5]=>[4,2,6,1,7,8,5,3]=>0011101
[6,8,3,2,4,1,7,5]=>[4,3,7,2,8,6,1,5]=>[6,7,1,4,2,3,8,5]=>0010011
[2,1,7,8,5,4,3,6]=>[2,1,4,5,8,3,7,6]=>[2,1,7,8,6,3,4,5]=>1000101
[7,1,8,4,5,3,2,6]=>[3,5,8,7,1,4,2,6]=>[8,6,4,7,2,5,1,3]=>0001111
[5,3,8,7,4,2,6,1]=>[6,4,7,5,3,2,8,1]=>[8,1,6,2,4,5,3,7]=>0001101
[2,3,4,1,8,5,7,6]=>[4,2,3,1,7,8,5,6]=>[2,3,4,1,7,5,8,6]=>0010011
[4,1,3,2,8,5,7,6]=>[3,4,1,2,7,8,5,6]=>[3,1,4,2,7,5,8,6]=>0110011
[2,1,4,3,8,5,7,6]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,7,5,8,6]=>1010011
[4,1,3,2,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[3,1,4,2,6,7,8,5]=>0110001
[7,8,5,6,1,4,2,3]=>[4,6,1,2,8,5,7,3]=>[7,8,3,1,4,2,6,5]=>0110101
[2,1,8,6,5,7,3,4]=>[2,1,7,3,6,8,5,4]=>[2,1,8,4,3,7,5,6]=>1010011
[2,1,7,5,3,6,8,4]=>[2,1,8,5,7,3,6,4]=>[2,1,8,4,5,7,6,3]=>1000111
[7,1,4,2,5,6,8,3]=>[8,4,7,1,2,5,6,3]=>[8,3,7,6,5,2,4,1]=>0011111
[7,3,5,4,6,1,8,2]=>[8,6,5,7,3,4,1,2]=>[5,3,8,2,6,4,7,1]=>0001111
[6,5,2,7,4,8,3,1]=>[3,8,7,5,6,2,4,1]=>[8,1,3,7,4,5,6,2]=>0000111
[6,3,1,5,2,4,8,7]=>[5,3,6,1,2,4,8,7]=>[6,4,1,5,2,3,8,7]=>0011101
[5,6,3,2,4,1,8,7]=>[4,3,6,2,5,1,8,7]=>[5,6,1,4,2,3,8,7]=>0010101
[2,5,7,3,8,6,4,1]=>[4,2,6,8,5,7,3,1]=>[2,5,7,3,6,8,1,4]=>0000011
[5,8,3,7,4,2,6,1]=>[6,4,7,8,5,3,2,1]=>[5,8,1,6,3,7,2,4]=>0000111
[4,8,1,2,7,6,3,5]=>[6,1,7,4,2,8,3,5]=>[4,7,3,8,5,2,1,6]=>1001011
[2,1,8,5,3,7,4,6]=>[2,1,7,5,8,3,4,6]=>[2,1,8,6,3,7,4,5]=>1000111
[4,1,2,8,7,5,6,3]=>[6,1,4,2,7,5,8,3]=>[8,3,4,2,1,6,5,7]=>1010101
[4,3,1,8,6,7,5,2]=>[5,3,4,1,7,8,6,2]=>[8,2,3,4,1,5,7,6]=>0010011
[5,7,1,6,8,2,4,3]=>[4,8,7,1,5,2,6,3]=>[4,1,5,8,3,7,6,2]=>0010111
[8,6,2,5,1,7,4,3]=>[4,7,5,6,2,8,1,3]=>[8,3,5,2,7,1,4,6]=>0001011
[4,1,2,3,6,8,7,5]=>[4,1,2,3,7,6,8,5]=>[4,3,2,1,6,8,5,7]=>1110001
[2,4,3,1,8,5,6,7]=>[3,2,4,1,8,5,6,7]=>[2,4,1,3,8,7,6,5]=>0010111
[4,7,2,8,1,5,3,6]=>[5,8,7,4,2,1,3,6]=>[4,7,3,8,6,1,5,2]=>0001111
[3,6,8,7,1,5,4,2]=>[4,5,3,7,1,6,8,2]=>[3,6,8,2,5,1,4,7]=>0001001
[5,7,8,6,3,4,1,2]=>[4,1,6,3,5,8,7,2]=>[5,7,8,2,1,4,3,6]=>1010001
[2,1,7,8,5,4,6,3]=>[2,1,6,5,8,4,7,3]=>[2,1,7,8,3,6,4,5]=>1000101
[7,5,8,4,3,6,2,1]=>[2,6,4,8,7,5,3,1]=>[8,1,2,6,5,7,3,4]=>0000111
[2,4,8,3,5,6,1,7]=>[6,2,8,4,3,5,1,7]=>[2,4,8,7,1,6,5,3]=>0001111
[4,1,8,3,6,5,2,7]=>[5,6,4,1,8,3,2,7]=>[8,7,2,6,3,4,1,5]=>0010111
[6,8,2,4,3,5,1,7]=>[5,4,8,2,3,6,1,7]=>[4,2,6,8,7,1,5,3]=>0011011
[4,8,2,3,5,1,6,7]=>[5,8,2,4,3,1,6,7]=>[4,8,7,6,1,5,3,2]=>0101111
[7,8,5,6,1,4,3,2]=>[3,4,6,1,8,5,7,2]=>[7,8,2,4,1,3,6,5]=>0010101
[7,8,2,1,6,5,3,4]=>[2,5,6,1,8,3,7,4]=>[6,3,7,8,4,1,2,5]=>0010101
[4,3,8,1,7,2,5,6]=>[7,8,4,3,1,2,5,6]=>[4,3,7,5,1,8,6,2]=>0011111
[7,8,1,4,6,2,5,3]=>[5,6,8,1,4,2,7,3]=>[5,4,1,6,2,7,8,3]=>0011101
[7,8,4,1,2,3,6,5]=>[4,1,2,6,8,3,7,5]=>[6,3,2,1,4,7,8,5]=>1100101
[7,8,3,6,5,4,1,2]=>[4,1,5,6,8,3,7,2]=>[7,8,2,1,4,6,3,5]=>1000101
[7,8,2,6,4,1,3,5]=>[4,6,2,8,1,3,7,5]=>[6,3,2,7,8,5,1,4]=>0101101
[7,8,1,6,5,4,3,2]=>[3,4,5,6,8,1,7,2]=>[7,8,2,4,6,1,3,5]=>0000101
[5,3,7,1,6,4,8,2]=>[8,6,7,5,3,1,4,2]=>[7,4,5,3,8,2,6,1]=>0001111
[2,4,7,1,5,3,6,8]=>[5,2,7,4,1,3,6,8]=>[2,4,5,1,7,6,3,8]=>0001110
[3,8,1,7,6,4,5,2]=>[5,6,3,7,1,8,4,2]=>[3,5,1,7,4,8,2,6]=>0001011
[1,8,5,7,3,6,4,2]=>[1,4,6,7,8,5,3,2]=>[1,8,2,4,7,3,6,5]=>0000111
[5,1,6,3,4,2,8,7]=>[4,6,5,1,3,2,8,7]=>[4,1,5,3,6,2,8,7]=>0011101
[5,7,1,4,2,3,8,6]=>[4,8,1,2,5,7,3,6]=>[5,8,6,7,3,1,4,2]=>0110011
[5,7,6,4,3,8,1,2]=>[8,1,4,6,5,7,3,2]=>[5,7,3,4,6,8,2,1]=>1000011
[6,3,4,5,8,7,1,2]=>[7,1,6,3,4,5,8,2]=>[6,5,4,3,8,2,1,7]=>1011101
[6,2,3,5,4,8,1,7]=>[8,5,2,6,3,4,1,7]=>[5,3,2,6,4,8,7,1]=>0101111
[1,6,2,4,7,8,3,5]=>[1,8,6,2,4,3,7,5]=>[1,6,3,7,8,5,4,2]=>0011101
[6,7,5,8,1,4,3,2]=>[3,4,8,1,7,6,5,2]=>[6,7,5,8,2,4,1,3]=>0010011
[5,8,7,6,3,4,1,2]=>[4,1,6,3,5,7,8,2]=>[5,8,2,1,4,3,6,7]=>1010001
[4,2,7,8,1,6,3,5]=>[6,8,4,2,1,3,7,5]=>[7,8,5,1,6,3,4,2]=>0011101
[4,2,7,1,6,3,8,5]=>[8,6,4,2,7,1,3,5]=>[8,5,7,3,4,2,6,1]=>0010111
[3,7,8,5,1,2,4,6]=>[5,1,3,2,8,4,7,6]=>[3,7,8,6,4,2,1,5]=>1010101
[4,1,8,6,2,3,5,7]=>[6,4,1,2,3,8,5,7]=>[4,2,8,7,5,3,1,6]=>0111011
[3,8,7,6,5,4,1,2]=>[4,1,3,5,6,7,8,2]=>[3,8,2,1,4,5,6,7]=>1000001
[2,1,7,8,4,3,5,6]=>[2,1,4,8,3,5,7,6]=>[2,1,7,8,6,5,3,4]=>1001101
[2,6,8,3,1,4,7,5]=>[3,2,7,1,8,6,4,5]=>[2,6,7,4,1,3,8,5]=>0010011
[8,4,1,3,7,6,2,5]=>[6,4,1,7,3,8,2,5]=>[7,2,4,8,5,3,1,6]=>0101011
[4,7,2,8,1,3,6,5]=>[6,8,2,4,7,1,3,5]=>[4,6,1,8,5,7,3,2]=>0100111
[7,3,8,6,1,2,5,4]=>[5,1,6,8,3,7,2,4]=>[7,2,1,5,3,6,8,4]=>1001011
[1,8,2,4,3,5,6,7]=>[1,4,8,2,3,5,6,7]=>[1,4,2,8,7,6,5,3]=>0011111
[1,5,2,4,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>0011000
[1,7,2,5,3,4,6,8]=>[1,5,7,2,3,4,6,8]=>[1,7,6,4,2,5,3,8]=>0011110
[1,8,2,6,3,4,5,7]=>[1,6,8,2,3,4,5,7]=>[1,6,4,2,8,7,5,3]=>0011111
[1,8,2,7,3,4,5,6]=>[1,7,8,2,3,4,5,6]=>[1,8,6,4,2,7,5,3]=>0011111
[1,8,2,7,3,5,4,6]=>[1,5,7,8,2,3,4,6]=>[1,5,2,8,6,3,7,4]=>0001111
[1,7,2,8,3,5,4,6]=>[1,5,8,7,2,3,4,6]=>[1,5,2,7,4,8,6,3]=>0001111
[1,2,3,8,4,6,5,7]=>[1,2,3,6,8,4,5,7]=>[1,2,3,6,4,8,7,5]=>0000111
[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,4,5,8]=>[1,2,3,6,4,7,5,8]=>0000110
[1,3,2,7,4,6,5,8]=>[1,3,2,6,7,4,5,8]=>[1,3,2,6,4,7,5,8]=>0100110
[1,4,2,7,3,6,5,8]=>[1,6,4,2,7,3,5,8]=>[1,6,3,4,2,7,5,8]=>0010110
[1,7,2,6,3,5,4,8]=>[1,5,6,7,2,3,4,8]=>[1,5,2,6,3,7,4,8]=>0001110
[1,8,2,6,3,5,4,7]=>[1,5,6,8,2,3,4,7]=>[1,5,2,6,3,8,7,4]=>0001111
[1,8,2,5,3,6,4,7]=>[1,6,5,8,2,3,4,7]=>[1,6,3,5,2,8,7,4]=>0001111
[1,5,2,4,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>0011010
[1,7,2,4,3,6,5,8]=>[1,4,6,2,7,3,5,8]=>[1,4,2,6,3,7,5,8]=>0010110
[1,7,2,4,3,8,5,6]=>[1,4,8,2,7,3,5,6]=>[1,4,2,7,5,8,6,3]=>0010111
[1,7,2,5,3,8,4,6]=>[1,8,5,7,2,3,4,6]=>[1,7,4,8,6,3,5,2]=>0001111
[1,8,2,5,3,7,4,6]=>[1,7,5,8,2,3,4,6]=>[1,8,6,3,5,2,7,4]=>0001111
[1,8,2,6,3,7,4,5]=>[1,7,6,8,2,3,4,5]=>[1,6,3,8,5,2,7,4]=>0001111
[1,7,2,6,3,8,4,5]=>[1,8,6,7,2,3,4,5]=>[1,6,3,7,4,8,5,2]=>0001111
[1,2,3,8,4,7,5,6]=>[1,2,3,7,8,4,5,6]=>[1,2,3,8,6,4,7,5]=>0000111
[1,6,2,8,3,7,4,5]=>[1,7,8,6,2,3,4,5]=>[1,8,5,2,7,4,6,3]=>0001111
[1,7,2,8,3,6,4,5]=>[1,6,8,7,2,3,4,5]=>[1,7,4,8,5,2,6,3]=>0001111
[1,8,2,7,3,6,4,5]=>[1,6,7,8,2,3,4,5]=>[1,8,5,2,6,3,7,4]=>0001111
[2,8,4,1,6,5,3,7]=>[5,2,4,6,8,1,3,7]=>[2,8,7,3,4,6,1,5]=>0000111
[2,8,4,1,5,6,7,3]=>[7,2,4,8,1,5,6,3]=>[2,7,6,5,1,8,3,4]=>0001111
[7,2,8,5,4,1,6,3]=>[6,4,5,8,7,2,1,3]=>[8,3,5,7,1,6,2,4]=>0000111
[2,8,5,3,4,1,6,7]=>[4,2,5,3,8,1,6,7]=>[2,8,7,6,1,4,3,5]=>0010111
[6,3,2,8,5,1,4,7]=>[5,3,8,2,6,1,4,7]=>[6,1,5,8,7,4,2,3]=>0010111
[6,4,8,5,1,3,7,2]=>[7,5,1,8,6,4,3,2]=>[7,3,1,8,2,5,6,4]=>0100111
[4,3,7,1,5,6,8,2]=>[8,7,4,3,1,5,6,2]=>[4,3,8,2,7,6,5,1]=>0011111
[3,6,1,7,5,2,8,4]=>[8,5,3,7,6,1,2,4]=>[3,8,4,7,2,5,6,1]=>0000111
[3,4,1,2,7,6,8,5]=>[4,1,3,2,8,7,6,5]=>[3,4,2,1,7,6,8,5]=>1010011
[3,5,2,6,4,8,7,1]=>[7,6,3,5,2,4,8,1]=>[3,6,4,5,2,8,1,7]=>0001101
[6,3,5,8,2,7,4,1]=>[4,7,8,6,3,5,2,1]=>[7,2,8,1,4,6,5,3]=>0001111
[4,3,2,1,8,6,5,7]=>[2,3,4,1,6,8,5,7]=>[4,1,2,3,8,7,5,6]=>0010011
[4,2,1,3,8,7,6,5]=>[2,4,1,3,6,7,8,5]=>[4,3,1,2,8,5,6,7]=>0110001
[6,1,2,8,4,5,7,3]=>[7,1,8,6,2,4,5,3]=>[6,4,7,5,2,1,8,3]=>1001111
[5,6,8,2,3,1,7,4]=>[3,7,2,8,5,6,1,4]=>[5,6,7,1,3,2,8,4]=>0100011
[1,6,5,7,3,4,2,8]=>[1,4,7,3,6,5,2,8]=>[1,6,5,7,2,4,3,8]=>0010110
[5,2,1,8,7,6,3,4]=>[2,6,5,1,3,7,8,4]=>[5,3,8,4,1,2,6,7]=>0011001
[7,1,3,8,4,6,2,5]=>[6,8,1,7,3,4,2,5]=>[8,5,3,1,6,4,7,2]=>0101111
[5,7,8,4,3,6,2,1]=>[2,6,4,8,5,3,7,1]=>[5,7,8,1,2,6,3,4]=>0000101
[4,1,8,3,6,2,7,5]=>[7,6,4,1,8,3,2,5]=>[7,2,6,3,4,1,8,5]=>0010111
[2,3,4,8,6,5,1,7]=>[5,2,3,4,6,8,1,7]=>[2,3,4,8,7,1,5,6]=>0000011
[2,7,3,5,8,6,1,4]=>[6,2,8,3,1,7,5,4]=>[2,7,5,1,6,8,4,3]=>0011011
[5,2,4,7,1,8,3,6]=>[8,7,5,2,4,1,3,6]=>[7,3,5,4,2,8,6,1]=>0011111
[7,3,5,6,8,4,2,1]=>[2,4,8,7,3,5,6,1]=>[8,1,2,4,7,6,5,3]=>0001111
[5,7,1,6,3,8,4,2]=>[4,8,6,7,5,1,3,2]=>[5,7,3,6,1,4,8,2]=>0000111
[3,2,4,1,7,8,5,6]=>[4,3,2,1,8,5,7,6]=>[3,2,4,1,7,8,6,5]=>0110101
[1,8,3,2,5,4,7,6]=>[1,3,5,7,2,8,4,6]=>[1,5,2,3,7,4,8,6]=>0001011
[7,2,1,5,6,3,4,8]=>[2,6,7,1,3,5,4,8]=>[7,4,1,2,6,5,3,8]=>0011110
[2,3,8,1,5,4,7,6]=>[5,2,3,7,1,8,4,6]=>[2,3,5,1,7,4,8,6]=>0001011
[2,4,8,5,1,3,7,6]=>[5,2,1,4,7,8,3,6]=>[2,4,7,3,1,5,8,6]=>0100011
[2,6,8,4,3,7,1,5]=>[7,2,4,8,3,6,1,5]=>[2,6,7,1,8,5,3,4]=>0001011
[2,7,8,4,3,6,5,1]=>[5,2,4,6,8,3,7,1]=>[2,6,3,4,7,8,1,5]=>0000101
[1,8,7,5,6,3,4,2]=>[1,4,6,3,7,5,8,2]=>[1,8,2,4,3,6,5,7]=>0010101
[2,7,8,5,6,3,4,1]=>[4,2,6,3,8,5,7,1]=>[2,7,8,1,4,3,6,5]=>0010101
[1,8,5,6,7,2,3,4]=>[1,7,2,3,8,5,6,4]=>[1,8,4,3,2,7,6,5]=>0110111
[5,4,6,7,1,8,2,3]=>[8,7,1,5,4,6,2,3]=>[5,4,6,7,2,8,3,1]=>0101011
[6,3,5,1,7,2,8,4]=>[8,7,5,6,3,1,2,4]=>[5,3,7,2,8,4,6,1]=>0001111
[5,7,3,2,6,8,4,1]=>[4,3,8,7,5,2,6,1]=>[5,8,1,4,7,6,2,3]=>0000111
[6,4,3,2,1,7,8,5]=>[2,3,4,8,6,1,7,5]=>[7,8,5,6,1,2,3,4]=>0000101
[6,2,1,4,3,7,8,5]=>[2,4,8,1,6,3,7,5]=>[4,1,2,7,8,5,6,3]=>0010101
[5,2,1,4,3,8,7,6]=>[2,4,5,1,3,7,8,6]=>[4,1,2,5,3,8,6,7]=>0011001
[4,5,3,2,8,1,7,6]=>[7,3,5,4,2,8,1,6]=>[4,5,2,3,7,1,8,6]=>0001011
[4,6,3,2,8,7,1,5]=>[7,3,6,4,2,1,8,5]=>[4,8,5,2,3,6,1,7]=>0001101
[1,8,3,2,7,6,5,4]=>[1,3,5,6,7,8,2,4]=>[1,7,2,3,5,8,4,6]=>0000011
[1,8,4,7,2,6,5,3]=>[1,5,6,7,8,4,2,3]=>[1,8,3,6,4,7,2,5]=>0000111
[3,6,4,8,2,7,1,5]=>[7,8,3,6,4,2,1,5]=>[3,7,1,8,5,4,6,2]=>0001111
[3,4,5,8,1,2,7,6]=>[7,1,3,4,5,8,2,6]=>[3,4,5,7,2,1,8,6]=>1000011
[4,3,5,1,8,2,7,6]=>[7,5,4,3,1,8,2,6]=>[4,3,7,2,5,1,8,6]=>0011011
[4,2,1,6,8,7,3,5]=>[2,7,4,1,3,6,8,5]=>[6,8,5,3,4,1,2,7]=>0011001
[3,5,6,8,7,1,2,4]=>[7,1,3,2,5,6,8,4]=>[3,5,6,8,4,2,1,7]=>1010001
[3,6,7,8,5,4,1,2]=>[4,1,3,5,8,6,7,2]=>[3,6,7,8,2,1,4,5]=>1000001
[3,5,7,8,6,1,4,2]=>[4,6,3,1,5,8,7,2]=>[3,4,1,5,7,8,2,6]=>0010001
[2,4,8,7,1,6,5,3]=>[5,2,6,4,7,1,8,3]=>[2,4,8,3,6,1,5,7]=>0000101
[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101
[8,1,2,4,3,6,5,7]=>[4,1,6,2,8,3,5,7]=>[4,2,1,6,3,8,7,5]=>1010111
[8,1,5,3,7,2,6,4]=>[6,7,5,8,1,3,2,4]=>[6,3,5,1,7,2,8,4]=>0001111
[6,3,2,1,4,5,8,7]=>[2,3,6,1,4,5,8,7]=>[6,5,4,1,2,3,8,7]=>0011101
[4,7,8,5,6,1,2,3]=>[6,1,2,4,8,5,7,3]=>[4,7,8,3,2,1,6,5]=>1100101
[3,7,8,5,6,2,1,4]=>[2,6,3,1,8,5,7,4]=>[3,7,8,4,1,2,6,5]=>0010101
[3,7,8,4,2,6,1,5]=>[6,4,3,8,2,1,7,5]=>[3,6,1,7,8,5,2,4]=>0001101
[3,6,2,8,4,5,1,7]=>[5,8,3,6,2,4,1,7]=>[3,6,4,8,7,1,5,2]=>0001111
[3,5,2,4,8,6,1,7]=>[6,5,3,2,4,8,1,7]=>[3,5,4,2,8,7,1,6]=>0011011
[3,5,4,2,8,7,1,6]=>[7,4,3,5,2,1,8,6]=>[3,5,2,4,8,6,1,7]=>0001101
[4,6,5,8,7,1,2,3]=>[7,1,2,4,6,5,8,3]=>[4,6,5,8,3,2,1,7]=>1100101
[5,4,2,3,1,8,6,7]=>[3,4,2,5,1,8,6,7]=>[5,1,3,2,4,8,7,6]=>0101011
[6,5,4,1,8,7,2,3]=>[7,4,1,5,6,2,8,3]=>[6,2,4,5,8,3,1,7]=>0100101
[7,5,1,4,8,6,2,3]=>[6,5,1,2,8,7,4,3]=>[8,3,1,6,7,4,2,5]=>0110011
[7,4,1,2,3,8,5,6]=>[4,1,2,8,7,3,5,6]=>[7,5,8,6,3,2,1,4]=>1100111
[2,6,5,8,7,3,4,1]=>[4,2,7,3,6,5,8,1]=>[2,6,5,8,1,4,3,7]=>0010101
[7,5,1,2,8,3,4,6]=>[8,1,5,2,7,3,4,6]=>[8,6,3,5,7,4,2,1]=>1010111
[6,7,8,1,4,5,2,3]=>[5,8,1,2,4,6,7,3]=>[6,7,8,3,1,5,4,2]=>0111001
[6,7,8,1,3,2,5,4]=>[3,5,1,8,2,6,7,4]=>[3,1,5,2,6,7,8,4]=>0101001
[2,5,6,7,8,3,4,1]=>[4,2,8,3,5,6,7,1]=>[2,5,6,7,8,1,4,3]=>0010001
[5,7,8,4,1,6,2,3]=>[6,4,1,8,5,2,7,3]=>[5,7,8,3,1,6,2,4]=>0100101
[5,6,4,8,1,7,2,3]=>[7,8,1,6,5,4,2,3]=>[5,6,4,8,3,1,7,2]=>0100111
[4,6,3,8,2,1,7,5]=>[2,7,8,4,6,3,1,5]=>[4,7,1,2,8,5,6,3]=>0000111
[4,2,5,3,7,1,6,8]=>[7,5,4,2,3,1,6,8]=>[5,3,4,2,7,6,1,8]=>0011110
[3,5,6,7,8,2,1,4]=>[2,8,3,1,5,6,7,4]=>[3,5,6,7,8,4,1,2]=>0010001
[3,4,6,7,2,8,1,5]=>[8,7,3,4,2,6,1,5]=>[3,4,6,8,5,2,7,1]=>0001011
[4,5,7,3,1,8,6,2]=>[6,3,8,4,5,7,1,2]=>[4,5,7,1,6,8,2,3]=>0000011
[4,5,6,2,1,8,7,3]=>[2,7,6,4,5,1,8,3]=>[4,5,8,3,6,1,2,7]=>0000101
[7,4,3,1,8,6,5,2]=>[5,3,4,6,8,7,1,2]=>[8,2,3,4,6,7,1,5]=>0000011
[7,5,6,1,8,3,4,2]=>[4,8,6,1,7,5,3,2]=>[4,1,7,3,6,5,8,2]=>0010111
[6,4,2,1,8,7,5,3]=>[2,5,4,7,6,1,8,3]=>[6,1,2,5,8,3,4,7]=>0000101
[1,5,3,2,7,6,4,8]=>[1,3,6,5,2,7,4,8]=>[1,7,4,5,2,3,6,8]=>0001010
[4,3,1,2,8,6,5,7]=>[3,1,4,2,6,8,5,7]=>[4,2,1,3,8,7,5,6]=>1010011
[2,6,1,5,7,8,3,4]=>[8,2,6,1,3,5,7,4]=>[2,6,5,3,7,8,4,1]=>0011101
[7,6,1,5,8,3,2,4]=>[3,8,6,1,2,7,5,4]=>[8,4,1,3,6,7,5,2]=>0011011
[7,1,6,5,8,2,4,3]=>[4,8,6,1,7,2,5,3]=>[4,1,7,5,8,3,6,2]=>0010111
[5,2,3,1,8,6,7,4]=>[3,7,2,5,1,8,6,4]=>[8,4,5,1,3,2,7,6]=>0101011
[7,3,1,5,8,6,2,4]=>[6,3,8,1,2,7,5,4]=>[8,4,1,6,7,5,2,3]=>0011011
[6,2,4,1,8,5,7,3]=>[7,4,8,2,6,1,5,3]=>[4,2,7,5,6,1,8,3]=>0010111
[6,2,5,1,8,4,7,3]=>[7,8,5,6,2,1,4,3]=>[7,4,6,1,8,3,5,2]=>0001111
[7,1,6,4,8,2,5,3]=>[5,8,6,7,1,4,2,3]=>[5,1,8,3,6,4,7,2]=>0001111
[7,1,5,3,8,2,6,4]=>[6,8,5,7,1,3,2,4]=>[6,3,5,1,8,4,7,2]=>0001111
[6,1,5,2,8,3,7,4]=>[7,8,5,6,1,2,3,4]=>[7,3,5,1,8,4,6,2]=>0001111
[6,1,4,2,8,3,7,5]=>[7,4,8,1,6,2,3,5]=>[8,5,6,2,4,1,7,3]=>0010111
[7,6,1,4,8,3,2,5]=>[3,8,6,1,4,7,2,5]=>[8,5,4,1,3,6,7,2]=>0011011
[5,1,3,2,8,4,7,6]=>[3,7,1,5,2,8,4,6]=>[3,1,7,4,5,2,8,6]=>0101011
[4,2,1,3,8,7,5,6]=>[2,4,1,3,7,5,8,6]=>[4,3,1,2,8,6,5,7]=>0110101
[2,6,1,4,7,8,3,5]=>[8,2,6,1,4,3,7,5]=>[2,6,3,7,8,5,4,1]=>0011101
[7,8,5,6,1,3,4,2]=>[4,6,1,3,8,5,7,2]=>[4,3,1,7,8,2,6,5]=>0110101
[4,6,1,2,5,7,3,8]=>[7,1,6,4,2,5,3,8]=>[4,7,3,6,5,2,1,8]=>1001110
[7,8,4,2,5,1,3,6]=>[5,4,2,8,1,3,7,6]=>[5,1,7,8,6,3,2,4]=>0101101
[7,8,3,5,6,4,1,2]=>[4,1,6,8,3,5,7,2]=>[6,5,3,7,8,2,1,4]=>1001101
[1,4,6,8,3,7,5,2]=>[1,5,7,4,8,6,3,2]=>[1,4,6,7,3,8,2,5]=>0000011
[2,1,8,4,7,3,6,5]=>[2,1,6,7,8,4,3,5]=>[2,1,7,3,6,4,8,5]=>1000111
[3,5,8,4,7,6,1,2]=>[6,1,3,7,5,8,4,2]=>[3,5,7,4,8,2,1,6]=>1000011
[1,6,2,4,7,3,8,5]=>[1,8,7,2,6,4,3,5]=>[1,7,3,8,5,6,4,2]=>0010111
[5,6,2,1,4,7,8,3]=>[2,8,6,1,5,4,7,3]=>[5,7,8,3,6,4,1,2]=>0010101
[4,6,2,5,3,1,8,7]=>[3,5,6,4,2,1,8,7]=>[4,5,2,6,1,3,8,7]=>0001101
[5,7,3,6,1,4,8,2]=>[8,6,7,3,5,1,4,2]=>[5,7,4,3,8,2,6,1]=>0010111
[5,3,6,7,2,1,8,4]=>[2,8,7,5,3,6,1,4]=>[6,8,4,5,3,7,1,2]=>0001011
[6,3,1,2,4,5,8,7]=>[3,1,6,2,4,5,8,7]=>[6,5,4,2,1,3,8,7]=>1011101
[1,4,7,2,5,3,8,6]=>[1,5,8,4,2,7,3,6]=>[1,4,5,2,8,6,7,3]=>0001011
[5,2,7,6,1,4,3,8]=>[4,6,5,2,1,7,3,8]=>[7,3,5,1,4,2,6,8]=>0011010
[2,7,5,6,8,4,1,3]=>[4,2,1,8,7,5,6,3]=>[2,7,6,5,8,3,1,4]=>0100111
[2,1,6,8,4,5,3,7]=>[2,1,5,8,4,6,3,7]=>[2,1,6,8,7,3,5,4]=>1001011
[3,1,8,5,4,6,7,2]=>[7,3,1,5,8,4,6,2]=>[8,2,3,1,7,6,4,5]=>0100111
[5,7,8,6,3,2,1,4]=>[2,3,6,1,5,8,7,4]=>[5,7,8,4,1,2,3,6]=>0010001
[5,7,8,6,1,3,4,2]=>[4,6,1,3,5,8,7,2]=>[4,3,1,5,7,8,2,6]=>0110001
[7,6,5,8,1,3,4,2]=>[4,8,1,3,6,7,5,2]=>[4,3,1,7,5,6,8,2]=>0110011
[2,6,3,4,5,8,1,7]=>[8,2,6,3,4,5,1,7]=>[2,6,5,4,3,8,7,1]=>0011111
[2,6,4,1,8,3,7,5]=>[7,2,4,8,6,1,3,5]=>[2,8,5,6,1,7,3,4]=>0000111
[6,1,5,2,8,3,4,7]=>[8,5,6,1,2,3,4,7]=>[5,2,6,3,8,7,4,1]=>0011111
[7,4,2,6,5,1,3,8]=>[5,4,2,6,7,1,3,8]=>[7,3,2,4,6,1,5,8]=>0100110
[7,2,3,5,4,1,6,8]=>[4,5,2,7,3,1,6,8]=>[5,3,2,7,6,1,4,8]=>0101110
[3,5,7,4,1,6,2,8]=>[6,4,3,7,5,1,2,8]=>[3,5,6,1,7,2,4,8]=>0000110
[5,2,1,8,6,3,7,4]=>[2,7,6,5,1,8,3,4]=>[8,4,5,1,2,7,3,6]=>0001011
[1,4,2,7,5,8,6,3]=>[1,6,4,2,8,7,5,3]=>[1,8,3,4,2,6,7,5]=>0010011
[5,8,7,4,3,6,1,2]=>[6,1,4,7,5,3,8,2]=>[5,8,2,1,6,3,4,7]=>1000101
[6,4,2,8,7,1,3,5]=>[7,4,2,6,1,3,8,5]=>[6,3,2,4,8,5,1,7]=>0101101
[5,8,3,7,1,6,4,2]=>[4,6,7,8,5,3,1,2]=>[5,8,2,6,3,7,1,4]=>0000111
[5,1,8,4,6,2,7,3]=>[7,6,8,5,1,4,2,3]=>[7,2,6,4,5,1,8,3]=>0001111
[6,8,5,1,2,3,7,4]=>[7,1,2,5,8,6,3,4]=>[6,7,3,2,1,8,4,5]=>1100011
[6,8,5,2,4,3,7,1]=>[7,4,5,2,8,6,3,1]=>[4,2,6,8,1,7,3,5]=>0010011
[6,8,5,3,1,2,7,4]=>[3,1,7,5,8,6,2,4]=>[6,7,2,1,3,8,4,5]=>1000011
[3,5,6,1,8,4,7,2]=>[7,8,3,6,5,1,4,2]=>[3,5,7,4,6,1,8,2]=>0000111
[3,5,7,1,2,8,6,4]=>[6,1,3,8,5,7,2,4]=>[3,5,7,2,1,6,8,4]=>1000011
[3,5,2,7,8,1,6,4]=>[6,8,3,5,2,1,7,4]=>[3,6,1,7,8,4,5,2]=>0001101
[4,2,5,6,1,8,7,3]=>[7,6,4,2,5,1,8,3]=>[5,8,3,4,2,6,1,7]=>0010101
[2,1,7,5,8,6,4,3]=>[2,1,4,6,8,7,5,3]=>[2,1,8,3,4,6,7,5]=>1000011
[1,2,7,5,3,8,6,4]=>[1,2,6,5,8,7,3,4]=>[1,2,7,3,6,8,4,5]=>0000011
[6,1,3,7,5,2,4,8]=>[5,7,1,3,6,2,4,8]=>[7,4,3,1,5,6,2,8]=>0110110
[3,2,7,8,1,6,5,4]=>[5,3,2,6,8,1,7,4]=>[3,2,7,8,4,6,1,5]=>0100101
[2,6,8,3,1,5,7,4]=>[3,2,7,8,1,6,5,4]=>[2,6,7,5,1,3,8,4]=>0001011
[6,3,7,4,5,1,8,2]=>[8,5,7,6,3,4,1,2]=>[6,4,8,2,5,3,7,1]=>0001111
[6,4,7,5,2,8,1,3]=>[8,5,2,7,6,4,1,3]=>[8,3,2,5,6,4,7,1]=>0100111
[2,6,3,7,5,8,1,4]=>[8,2,7,3,6,1,5,4]=>[2,8,4,3,7,5,6,1]=>0010111
[5,2,8,4,7,1,6,3]=>[6,7,8,5,2,4,1,3]=>[7,1,6,4,5,2,8,3]=>0001111
[4,1,6,2,8,3,7,5]=>[7,8,4,1,6,2,3,5]=>[7,3,4,1,8,5,6,2]=>0010111
[8,4,5,1,2,6,3,7]=>[6,1,5,8,4,2,3,7]=>[6,2,1,8,7,3,5,4]=>1001111
[1,6,3,7,2,8,4,5]=>[1,8,7,6,3,2,4,5]=>[1,8,5,3,7,4,6,2]=>0001111
[6,4,7,2,8,1,5,3]=>[5,8,7,6,4,2,1,3]=>[8,3,7,1,5,4,6,2]=>0001111
[4,7,2,5,8,1,6,3]=>[6,8,7,4,2,5,1,3]=>[4,8,3,7,1,6,5,2]=>0001111
[5,7,3,8,2,6,1,4]=>[6,8,7,3,5,2,1,4]=>[5,8,4,3,7,1,6,2]=>0010111
[3,4,7,8,2,6,1,5]=>[6,8,3,4,2,1,7,5]=>[3,4,6,1,7,8,5,2]=>0001101
[8,1,3,4,6,2,5,7]=>[6,8,1,3,4,2,5,7]=>[8,7,5,4,3,1,6,2]=>0111111
[2,4,5,6,8,1,7,3]=>[7,2,8,4,5,6,1,3]=>[2,4,5,6,7,1,8,3]=>0000011
[4,8,3,5,6,1,7,2]=>[7,6,8,4,3,5,1,2]=>[4,7,1,8,2,6,5,3]=>0001111
[8,4,3,6,5,1,7,2]=>[7,5,4,6,8,3,1,2]=>[6,3,4,7,1,8,2,5]=>0000111
[7,8,5,4,1,3,6,2]=>[6,4,1,5,8,3,7,2]=>[6,3,1,7,8,2,4,5]=>0100101
[5,8,6,2,4,1,7,3]=>[7,4,6,2,5,8,1,3]=>[4,2,5,7,1,8,3,6]=>0010011
[3,2,8,6,5,1,7,4]=>[7,3,2,5,6,8,1,4]=>[3,2,7,1,8,4,5,6]=>0100011
[1,2,8,3,7,4,5,6]=>[1,2,7,8,3,4,5,6]=>[1,2,7,5,3,8,6,4]=>0001111
[8,1,7,2,6,3,5,4]=>[5,6,7,8,1,2,3,4]=>[5,1,6,2,7,3,8,4]=>0001111
[5,1,8,3,2,7,4,6]=>[3,7,8,5,1,2,4,6]=>[8,6,2,7,4,5,1,3]=>0001111
[5,8,7,2,1,6,4,3]=>[2,4,6,7,5,1,8,3]=>[5,8,3,6,1,2,4,7]=>0000101
[8,7,6,1,5,4,3,2]=>[3,4,5,6,1,7,8,2]=>[5,1,3,8,2,4,6,7]=>0001001
[8,6,7,1,4,5,3,2]=>[3,5,7,1,4,8,6,2]=>[8,2,5,4,1,3,7,6]=>0011011
[6,7,8,1,3,4,5,2]=>[5,8,1,3,4,6,7,2]=>[5,4,3,1,6,7,8,2]=>0111001
[4,7,2,8,1,5,6,3]=>[6,8,7,4,2,1,5,3]=>[4,6,1,8,3,7,5,2]=>0001111
[6,4,3,8,2,1,7,5]=>[2,7,4,8,6,3,1,5]=>[7,1,2,8,5,6,3,4]=>0000111
[4,5,2,3,8,1,7,6]=>[7,5,2,4,3,8,1,6]=>[4,5,3,2,7,1,8,6]=>0101011
[3,2,5,4,8,1,7,6]=>[7,3,2,5,4,8,1,6]=>[3,2,5,4,7,1,8,6]=>0101011
[6,4,3,1,5,2,7,8]=>[5,3,4,6,1,2,7,8]=>[5,1,6,2,3,4,7,8]=>0001100
[1,5,4,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[1,5,3,2,4,6,7,8]=>0101000
[7,5,1,4,2,6,3,8]=>[6,4,5,1,7,2,3,8]=>[6,2,4,1,7,3,5,8]=>0010110
[3,2,6,1,5,4,7,8]=>[5,3,2,6,1,4,7,8]=>[3,2,5,1,6,4,7,8]=>0101100
[6,7,1,2,4,5,3,8]=>[5,1,7,2,4,6,3,8]=>[5,4,2,1,6,7,3,8]=>1011010
[4,8,2,1,3,5,7,6]=>[2,7,1,4,3,8,5,6]=>[4,7,5,3,1,2,8,6]=>0101011
[4,1,3,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>0110000
[6,7,3,8,5,1,2,4]=>[5,1,8,3,7,6,2,4]=>[6,7,2,1,5,8,4,3]=>1010011
[4,3,8,7,6,1,2,5]=>[6,1,4,3,2,7,8,5]=>[4,3,8,5,2,1,6,7]=>1011001
[4,5,6,7,1,8,3,2]=>[3,8,7,4,5,6,1,2]=>[4,5,6,7,1,3,8,2]=>0000011
[3,5,6,1,7,8,4,2]=>[4,8,3,6,5,1,7,2]=>[3,5,6,1,4,7,8,2]=>0000101
[8,2,4,5,1,6,3,7]=>[6,5,8,2,4,1,3,7]=>[5,4,2,6,1,8,7,3]=>0011111
[8,1,3,2,5,4,6,7]=>[3,5,1,8,2,4,6,7]=>[3,1,5,2,8,7,6,4]=>0101111
[3,8,2,1,7,5,4,6]=>[2,5,3,7,8,1,4,6]=>[3,7,4,8,6,1,2,5]=>0000111
[8,3,2,1,6,5,4,7]=>[2,3,5,6,8,1,4,7]=>[8,7,4,6,1,2,3,5]=>0000111
[6,7,2,1,8,5,4,3]=>[2,4,5,8,7,6,1,3]=>[6,8,3,5,7,1,2,4]=>0000011
[6,7,2,8,1,5,3,4]=>[5,8,7,2,1,6,3,4]=>[5,1,6,7,3,8,4,2]=>0011011
[6,7,8,2,1,4,3,5]=>[2,4,8,1,3,6,7,5]=>[4,1,2,6,7,8,5,3]=>0011001
[8,5,6,2,1,4,3,7]=>[2,4,6,1,8,5,3,7]=>[4,1,2,8,7,3,6,5]=>0010111
[5,8,7,1,2,3,4,6]=>[7,1,2,3,5,4,8,6]=>[5,8,6,4,3,2,1,7]=>1110101
[6,7,1,3,4,8,5,2]=>[5,8,1,3,7,6,4,2]=>[6,7,4,3,1,5,8,2]=>0110011
[5,1,7,3,4,8,6,2]=>[6,8,5,1,3,7,4,2]=>[5,3,7,4,1,6,8,2]=>0011011
[5,1,7,8,2,3,6,4]=>[6,8,1,5,2,3,7,4]=>[6,3,1,7,8,4,5,2]=>0101101
[3,8,1,2,7,4,5,6]=>[7,1,3,8,2,4,5,6]=>[3,7,5,2,1,8,6,4]=>1001111
[3,1,2,8,7,5,6,4]=>[3,1,2,6,7,5,8,4]=>[3,2,1,8,4,6,5,7]=>1100101
[6,3,4,5,8,7,2,1]=>[2,7,6,3,4,5,8,1]=>[6,5,4,3,8,1,2,7]=>0011101
[5,8,1,4,7,2,3,6]=>[7,8,1,2,5,4,3,6]=>[5,7,3,1,8,6,4,2]=>0110111
[6,3,8,4,2,7,1,5]=>[7,4,8,6,3,2,1,5]=>[6,2,4,7,1,8,5,3]=>0001111
[4,6,1,2,7,8,5,3]=>[5,1,8,4,6,2,7,3]=>[4,6,2,1,5,7,8,3]=>1000101
[5,8,1,4,6,7,2,3]=>[7,8,1,2,5,4,6,3]=>[5,8,3,1,7,6,4,2]=>0110111
[6,3,7,4,2,8,5,1]=>[5,4,8,7,6,3,2,1]=>[7,2,4,8,1,5,6,3]=>0000111
[3,6,4,5,7,2,8,1]=>[8,7,3,6,4,5,2,1]=>[3,6,5,4,7,2,8,1]=>0001111
[6,4,1,5,3,8,2,7]=>[8,5,4,6,1,3,2,7]=>[6,3,4,8,7,2,5,1]=>0001111
[3,6,2,7,4,5,8,1]=>[8,7,3,6,2,4,5,1]=>[3,6,4,7,5,2,8,1]=>0001111
[6,8,3,1,7,2,5,4]=>[5,3,7,8,1,6,2,4]=>[5,1,6,7,2,3,8,4]=>0001011
[1,8,6,3,7,5,2,4]=>[1,5,7,3,6,8,2,4]=>[1,8,4,3,7,2,5,6]=>0010011
[8,7,5,2,6,4,3,1]=>[3,4,6,5,7,2,8,1]=>[8,1,3,6,2,4,5,7]=>0000101
[8,7,1,6,2,5,4,3]=>[4,5,6,7,1,2,8,3]=>[8,3,6,2,5,1,4,7]=>0001101
[2,8,1,7,3,5,6,4]=>[6,2,7,8,1,3,5,4]=>[2,7,5,1,6,3,8,4]=>0001111
[1,7,2,8,5,3,4,6]=>[1,5,8,2,7,3,4,6]=>[1,7,4,2,5,8,6,3]=>0010111
[4,2,5,7,1,8,3,6]=>[8,7,4,2,5,1,3,6]=>[5,7,3,4,2,8,6,1]=>0010111
[4,2,1,5,8,3,6,7]=>[2,8,4,1,5,3,6,7]=>[5,8,7,6,3,4,1,2]=>0010111
[5,4,3,1,6,8,2,7]=>[8,3,4,5,1,6,2,7]=>[6,8,7,2,3,4,5,1]=>0001011
[1,5,3,4,6,8,2,7]=>[1,8,5,3,4,6,2,7]=>[1,5,4,3,6,8,7,2]=>0011011
[4,7,5,6,8,3,2,1]=>[2,3,8,4,7,5,6,1]=>[4,7,6,5,8,1,2,3]=>0000111
[6,5,4,8,2,7,3,1]=>[3,7,8,5,6,4,2,1]=>[6,4,5,7,2,8,1,3]=>0000111
[5,1,8,3,7,6,2,4]=>[6,7,5,1,3,8,2,4]=>[5,3,7,2,8,4,1,6]=>0011011
[5,7,3,8,2,6,4,1]=>[4,6,8,7,5,3,2,1]=>[5,8,1,4,7,2,6,3]=>0000111
[5,4,6,8,2,7,3,1]=>[3,7,8,5,4,6,2,1]=>[5,4,6,7,2,8,1,3]=>0001011
[3,6,8,1,7,2,5,4]=>[5,7,3,8,1,6,2,4]=>[3,5,1,6,7,2,8,4]=>0001011
[7,1,8,6,5,3,2,4]=>[3,5,6,1,8,7,2,4]=>[8,4,1,3,6,7,2,5]=>0010011
[6,7,4,5,2,8,1,3]=>[8,5,2,7,4,6,1,3]=>[6,8,3,2,5,4,7,1]=>0101011
[5,7,4,6,2,3,1,8]=>[3,6,2,7,5,4,1,8]=>[5,7,1,3,2,6,4,8]=>0100110
[5,7,4,6,3,8,1,2]=>[8,1,6,7,5,4,3,2]=>[5,7,3,6,4,8,2,1]=>1000111
[6,8,4,5,3,7,1,2]=>[7,1,5,8,4,6,3,2]=>[6,8,2,1,7,3,5,4]=>1001011
[5,6,4,8,3,7,1,2]=>[7,1,8,6,5,4,3,2]=>[5,6,4,8,2,1,7,3]=>1000111
[5,6,3,7,2,8,1,4]=>[8,7,6,3,5,2,1,4]=>[5,8,4,3,6,2,7,1]=>0010111
[5,6,4,8,2,7,1,3]=>[7,8,2,6,5,4,1,3]=>[5,6,4,7,1,8,3,2]=>0100111
[6,8,4,5,2,7,1,3]=>[7,5,2,8,4,6,1,3]=>[6,7,1,8,3,2,5,4]=>0101011
[6,8,4,5,2,3,1,7]=>[3,5,2,8,4,6,1,7]=>[6,8,7,1,3,2,5,4]=>0101011
[4,6,3,5,2,8,1,7]=>[8,5,6,4,3,2,1,7]=>[4,6,2,5,3,8,7,1]=>0001111
[4,8,3,6,2,5,1,7]=>[5,6,8,4,3,2,1,7]=>[4,6,2,8,7,1,5,3]=>0001111
[5,8,3,6,2,4,1,7]=>[4,6,8,3,5,2,1,7]=>[5,6,2,8,7,1,4,3]=>0010111
[7,8,3,5,2,6,1,4]=>[6,5,8,3,2,1,7,4]=>[5,2,6,1,7,8,4,3]=>0011101
[6,8,3,5,2,7,1,4]=>[7,5,8,3,2,6,1,4]=>[5,2,6,7,1,8,4,3]=>0011011
[5,8,3,6,2,7,1,4]=>[7,6,8,3,5,2,1,4]=>[5,6,2,7,1,8,4,3]=>0010111
[4,8,3,6,2,7,1,5]=>[7,6,8,4,3,2,1,5]=>[4,6,2,7,1,8,5,3]=>0001111
[4,6,3,8,2,7,1,5]=>[7,8,6,4,3,2,1,5]=>[4,7,1,8,5,3,6,2]=>0001111
[4,6,3,7,2,8,1,5]=>[8,7,6,4,3,2,1,5]=>[4,8,5,3,6,2,7,1]=>0001111
[4,7,3,6,2,5,1,8]=>[5,6,7,4,3,2,1,8]=>[4,6,2,7,1,5,3,8]=>0001110
[4,7,3,6,2,8,1,5]=>[8,6,7,4,3,2,1,5]=>[4,6,2,8,5,3,7,1]=>0001111
[5,7,3,6,2,8,1,4]=>[8,6,7,3,5,2,1,4]=>[5,6,2,8,4,3,7,1]=>0010111
[6,7,3,8,2,5,1,4]=>[5,8,7,3,2,6,1,4]=>[6,8,4,3,7,1,5,2]=>0011011
[6,7,3,8,2,4,1,5]=>[4,8,7,3,2,6,1,5]=>[6,7,1,4,3,8,5,2]=>0011011
[5,7,3,4,2,6,1,8]=>[6,4,7,3,5,2,1,8]=>[5,7,1,6,2,4,3,8]=>0010110
[5,8,4,7,2,3,1,6]=>[3,7,2,8,5,4,1,6]=>[5,7,1,3,2,8,6,4]=>0100111
[6,8,4,7,2,3,1,5]=>[3,7,2,8,4,6,1,5]=>[6,7,1,3,2,8,5,4]=>0101011
[7,8,4,6,2,3,1,5]=>[3,6,2,8,4,1,7,5]=>[6,1,3,2,7,8,5,4]=>0101101
[6,8,3,7,2,4,1,5]=>[4,7,8,3,2,6,1,5]=>[6,8,5,2,7,1,4,3]=>0011011
[4,7,3,5,2,6,1,8]=>[6,5,7,4,3,2,1,8]=>[4,7,1,6,2,5,3,8]=>0001110
[4,5,3,7,2,8,1,6]=>[8,7,5,4,3,2,1,6]=>[4,5,3,8,6,2,7,1]=>0001111
[4,8,3,5,2,7,1,6]=>[7,5,8,4,3,2,1,6]=>[4,7,1,8,6,2,5,3]=>0001111
[6,8,3,4,2,7,1,5]=>[7,4,8,3,2,6,1,5]=>[6,7,1,8,5,2,4,3]=>0011011
[4,7,5,2,1,8,3,6]=>[2,8,5,4,7,1,3,6]=>[4,7,3,5,8,6,1,2]=>0000111
[7,4,8,1,6,5,3,2]=>[3,5,6,8,7,4,1,2]=>[8,2,5,7,1,3,6,4]=>0000111
[7,4,5,3,1,8,2,6]=>[8,3,5,7,4,1,2,6]=>[7,2,3,5,4,8,6,1]=>0001111
[8,5,7,6,4,2,1,3]=>[2,4,1,6,7,8,5,3]=>[7,5,8,3,1,2,4,6]=>0100011
[2,1,6,8,7,4,3,5]=>[2,1,4,7,3,6,8,5]=>[2,1,6,8,5,3,4,7]=>1001001
[8,4,7,3,6,2,5,1]=>[5,6,7,8,4,3,2,1]=>[7,2,6,3,8,1,5,4]=>0001111
[7,6,8,5,2,4,3,1]=>[3,4,5,2,8,7,6,1]=>[4,2,7,6,8,1,3,5]=>0010011
[5,7,8,6,2,3,1,4]=>[3,6,2,1,5,8,7,4]=>[5,7,8,4,1,3,2,6]=>0110001
[5,8,7,6,3,2,1,4]=>[2,3,6,1,5,7,8,4]=>[5,8,4,1,2,3,6,7]=>0010001
[6,8,7,5,3,2,4,1]=>[4,3,5,2,7,6,8,1]=>[6,8,1,4,2,3,5,7]=>0010001
[4,8,6,2,7,3,1,5]=>[3,7,6,4,2,8,1,5]=>[4,8,5,2,7,1,3,6]=>0001011
[4,7,6,2,8,1,3,5]=>[8,6,2,4,1,7,3,5]=>[4,7,3,2,6,8,5,1]=>0101011
[6,7,4,2,8,1,5,3]=>[5,8,4,7,2,6,1,3]=>[6,8,3,4,7,1,5,2]=>0001011
[6,8,4,2,7,5,1,3]=>[5,4,2,7,8,6,1,3]=>[6,8,3,2,4,7,1,5]=>0100011
[8,6,4,3,7,5,1,2]=>[5,1,4,7,6,8,3,2]=>[7,3,4,8,2,1,5,6]=>1000011
[5,8,6,7,3,1,2,4]=>[3,1,7,2,5,8,6,4]=>[5,8,4,2,1,3,7,6]=>1010011
[7,6,5,8,1,4,3,2]=>[3,4,8,1,6,7,5,2]=>[7,5,6,8,2,4,1,3]=>0010011
[2,1,7,6,8,3,5,4]=>[2,1,5,8,3,7,6,4]=>[2,1,5,3,7,6,8,4]=>1001011
[7,4,6,3,8,1,2,5]=>[8,1,6,7,4,3,2,5]=>[6,3,8,5,4,7,2,1]=>1001111
[7,5,6,8,1,4,2,3]=>[4,8,1,2,7,5,6,3]=>[7,6,5,8,3,1,4,2]=>0110111
[8,1,3,7,4,6,5,2]=>[5,6,1,7,8,3,4,2]=>[7,4,8,2,6,3,1,5]=>0100111
[6,1,4,5,3,7,8,2]=>[8,5,6,1,4,3,7,2]=>[6,3,7,8,2,5,4,1]=>0011101
[6,1,8,3,4,5,7,2]=>[7,8,6,1,3,4,5,2]=>[7,5,3,6,4,1,8,2]=>0011111
[8,5,2,1,4,3,7,6]=>[2,4,5,1,7,8,3,6]=>[4,1,2,7,3,5,8,6]=>0010011
[3,4,1,2,8,6,5,7]=>[4,1,3,2,6,8,5,7]=>[3,4,2,1,8,7,5,6]=>1010011
[6,3,8,5,2,1,4,7]=>[2,5,8,3,6,1,4,7]=>[6,1,2,5,8,7,4,3]=>0010111
[8,7,5,4,1,6,2,3]=>[6,4,1,5,7,2,8,3]=>[8,3,1,6,2,4,5,7]=>0100101
[7,1,2,3,6,5,8,4]=>[8,1,2,6,7,3,5,4]=>[7,5,8,4,6,3,2,1]=>1100111
[1,5,7,3,2,4,6,8]=>[1,3,7,2,5,4,6,8]=>[1,5,7,6,4,2,3,8]=>0010110
[8,7,2,6,3,4,1,5]=>[4,6,7,2,3,1,8,5]=>[6,1,4,2,8,5,3,7]=>0011101
[3,5,8,7,2,4,1,6]=>[4,7,3,2,5,1,8,6]=>[3,5,8,6,1,4,2,7]=>0010101
[4,2,1,3,7,8,5,6]=>[2,4,1,3,8,5,7,6]=>[4,3,1,2,7,8,6,5]=>0110101
[5,2,7,8,6,4,1,3]=>[4,6,2,5,1,8,7,3]=>[5,1,4,7,8,3,2,6]=>0101001
[1,7,3,2,8,6,4,5]=>[1,3,6,8,2,7,4,5]=>[1,8,5,2,3,6,7,4]=>0001011
[4,7,2,8,6,1,5,3]=>[5,6,8,4,2,7,1,3]=>[4,7,1,5,2,6,8,3]=>0001011
[4,2,5,7,8,6,1,3]=>[6,4,2,1,5,8,7,3]=>[5,7,8,3,2,4,1,6]=>0110001
[6,2,4,7,5,8,1,3]=>[8,7,2,1,6,4,5,3]=>[8,3,2,7,5,6,4,1]=>0110111
[7,2,5,1,8,3,4,6]=>[8,5,7,2,1,3,4,6]=>[8,6,3,7,4,2,5,1]=>0011111
[7,8,2,1,4,3,5,6]=>[2,4,8,1,3,5,7,6]=>[4,1,2,7,8,6,5,3]=>0011101
[8,2,5,4,6,7,1,3]=>[7,5,2,8,1,4,6,3]=>[8,3,2,5,1,7,6,4]=>0101111
[8,2,7,4,1,3,5,6]=>[4,7,2,8,1,3,5,6]=>[8,6,3,2,7,5,1,4]=>0101111
[1,8,7,5,4,3,6,2]=>[1,6,4,5,7,3,8,2]=>[1,8,2,6,3,4,5,7]=>0000101
[6,8,7,3,2,5,1,4]=>[5,3,7,2,1,6,8,4]=>[5,1,6,8,4,2,3,7]=>0011001
[5,1,8,3,2,6,4,7]=>[3,6,8,5,1,2,4,7]=>[6,2,8,7,4,5,1,3]=>0001111
[1,4,6,2,8,3,7,5]=>[1,7,8,4,6,2,3,5]=>[1,4,8,5,6,2,7,3]=>0000111
[1,6,3,2,7,8,4,5]=>[1,3,8,6,2,4,7,5]=>[1,6,4,7,8,5,2,3]=>0001101
[4,6,2,7,8,1,5,3]=>[5,8,6,4,2,1,7,3]=>[4,7,8,3,6,1,5,2]=>0001101
[4,5,7,2,1,8,6,3]=>[2,6,8,4,5,7,1,3]=>[4,5,7,1,2,6,8,3]=>0000011
[7,8,3,4,2,1,6,5]=>[2,4,6,3,8,1,7,5]=>[6,1,2,4,3,7,8,5]=>0010101
[6,3,4,1,2,5,8,7]=>[4,1,6,3,2,5,8,7]=>[6,5,2,1,4,3,8,7]=>1011101
[8,5,3,2,6,7,1,4]=>[7,3,5,2,8,1,6,4]=>[7,6,1,8,4,2,3,5]=>0010111
[4,2,5,6,7,8,1,3]=>[8,4,2,1,5,6,7,3]=>[5,6,7,8,3,2,4,1]=>0110001
[6,2,3,4,1,7,8,5]=>[4,8,2,3,6,1,7,5]=>[7,8,5,6,1,4,3,2]=>0110101
[7,2,3,1,4,5,8,6]=>[3,8,2,1,4,7,5,6]=>[8,6,7,5,4,1,3,2]=>0111011
[7,8,3,5,4,6,1,2]=>[6,1,5,8,3,4,7,2]=>[5,3,7,8,2,1,6,4]=>1001101
[6,8,3,7,5,1,4,2]=>[4,5,7,3,8,6,1,2]=>[6,7,1,4,3,8,2,5]=>0010011
[7,5,8,4,2,6,1,3]=>[6,4,2,8,7,5,1,3]=>[7,1,6,5,8,3,2,4]=>0100111
[8,6,3,7,5,2,4,1]=>[4,5,7,3,6,8,2,1]=>[8,1,4,3,7,2,5,6]=>0010011
[7,8,4,6,1,5,2,3]=>[5,6,1,8,4,2,7,3]=>[6,2,7,8,3,1,5,4]=>0101101
[6,8,1,7,4,5,2,3]=>[5,7,1,8,2,6,4,3]=>[6,8,3,1,5,2,7,4]=>0101011
[1,8,6,7,4,5,2,3]=>[1,5,2,7,4,8,6,3]=>[1,8,3,2,5,4,7,6]=>0101011
[6,8,1,7,3,5,2,4]=>[5,7,8,1,3,6,2,4]=>[6,7,2,8,4,1,5,3]=>0011011
[7,8,3,6,1,5,2,4]=>[5,6,8,3,1,2,7,4]=>[5,1,6,2,7,8,4,3]=>0011101
[7,8,3,6,4,5,1,2]=>[5,1,6,8,3,4,7,2]=>[7,8,2,1,5,3,6,4]=>1001101
[7,8,2,6,3,5,1,4]=>[5,6,8,2,3,1,7,4]=>[7,8,4,2,6,1,5,3]=>0011101
[1,8,6,7,2,5,3,4]=>[1,5,7,2,3,8,6,4]=>[1,8,4,2,5,3,7,6]=>0011011
[5,8,1,7,2,6,3,4]=>[6,7,8,1,5,2,3,4]=>[5,8,4,1,6,2,7,3]=>0010111
[6,8,2,7,1,5,3,4]=>[5,7,8,2,1,6,3,4]=>[5,1,6,8,4,2,7,3]=>0011011
[6,8,2,7,3,5,1,4]=>[5,7,8,2,3,6,1,4]=>[6,8,4,2,7,1,5,3]=>0011011
[6,8,3,7,4,5,1,2]=>[5,1,7,8,3,6,4,2]=>[6,8,2,1,5,3,7,4]=>1001011
[3,8,6,7,4,5,1,2]=>[5,1,3,7,4,8,6,2]=>[3,8,2,1,5,4,7,6]=>1001011
[2,8,6,7,3,5,1,4]=>[5,2,7,3,1,8,6,4]=>[2,5,1,8,4,3,7,6]=>0011011
[2,8,6,7,1,5,3,4]=>[5,2,7,1,3,8,6,4]=>[2,8,4,1,5,3,7,6]=>0011011
[2,8,1,7,5,6,3,4]=>[6,2,7,1,8,3,5,4]=>[2,8,4,1,6,3,7,5]=>0010111
[1,8,2,7,4,6,3,5]=>[1,6,7,8,2,4,3,5]=>[1,7,3,8,5,2,6,4]=>0001111
[2,8,1,7,4,6,3,5]=>[6,2,7,8,1,4,3,5]=>[2,7,3,8,5,1,6,4]=>0001111
[3,8,5,7,4,6,1,2]=>[6,1,3,7,8,5,4,2]=>[3,7,4,8,2,1,6,5]=>1000111
[5,8,2,7,3,6,1,4]=>[6,7,8,2,5,3,1,4]=>[5,8,4,2,7,1,6,3]=>0010111
[4,8,2,7,3,6,1,5]=>[6,7,8,4,2,3,1,5]=>[4,8,5,2,7,1,6,3]=>0001111
[1,8,4,7,2,6,3,5]=>[1,6,7,8,4,2,3,5]=>[1,6,2,7,3,8,5,4]=>0001111
[1,8,4,7,3,6,2,5]=>[1,6,7,8,4,3,2,5]=>[1,7,2,6,3,8,5,4]=>0001111
[4,8,1,7,3,6,2,5]=>[6,7,8,4,1,3,2,5]=>[4,7,2,8,5,1,6,3]=>0001111
[6,8,3,7,1,5,2,4]=>[5,7,8,3,1,6,2,4]=>[5,1,6,7,2,8,4,3]=>0011011
[5,8,1,7,3,6,2,4]=>[6,7,8,1,5,3,2,4]=>[5,7,2,8,4,1,6,3]=>0010111
[1,8,5,7,3,6,2,4]=>[1,6,7,3,8,5,2,4]=>[1,8,4,3,7,2,6,5]=>0010111
[5,8,1,7,4,6,2,3]=>[6,7,1,8,5,2,4,3]=>[5,8,3,1,6,2,7,4]=>0100111
[6,8,4,7,1,5,2,3]=>[5,7,1,8,4,6,2,3]=>[6,7,2,8,3,1,5,4]=>0101011
[6,8,5,7,1,4,2,3]=>[4,7,1,2,8,6,5,3]=>[6,8,3,1,4,2,7,5]=>0110011
[4,8,5,7,1,6,2,3]=>[6,7,1,4,8,5,2,3]=>[4,7,2,8,3,1,6,5]=>0100111
[1,8,3,7,5,6,2,4]=>[1,6,7,3,8,2,5,4]=>[1,6,2,8,4,3,7,5]=>0010111
[4,8,6,7,2,5,1,3]=>[5,7,2,4,1,8,6,3]=>[4,5,1,8,3,2,7,6]=>0101011
[3,8,4,7,2,6,1,5]=>[6,7,3,8,4,2,1,5]=>[3,7,1,6,2,8,5,4]=>0001111
[1,8,3,7,4,6,2,5]=>[1,6,7,8,3,4,2,5]=>[1,8,5,3,7,2,6,4]=>0001111
[1,8,3,7,2,6,4,5]=>[1,6,7,8,3,2,4,5]=>[1,6,2,8,5,3,7,4]=>0001111
[3,8,2,7,1,6,4,5]=>[6,7,3,8,2,1,4,5]=>[3,6,1,8,5,2,7,4]=>0001111
[4,8,2,7,5,6,1,3]=>[6,7,2,4,8,1,5,3]=>[4,6,1,8,3,2,7,5]=>0100111
[2,8,3,7,5,6,1,4]=>[6,2,7,3,8,1,5,4]=>[2,6,1,8,4,3,7,5]=>0010111
[7,1,8,4,5,2,6,3]=>[6,5,8,7,1,4,2,3]=>[7,2,5,1,6,4,8,3]=>0001111
[7,3,8,6,2,5,1,4]=>[5,6,8,3,2,7,1,4]=>[7,1,5,2,6,8,4,3]=>0011011
[6,8,1,7,2,3,4,5]=>[7,8,1,2,3,6,4,5]=>[6,8,5,3,1,7,4,2]=>0111011
[1,5,7,8,2,6,3,4]=>[1,6,8,2,5,3,7,4]=>[1,5,7,8,4,2,6,3]=>0010101
[2,5,4,1,3,7,8,6]=>[4,2,1,5,3,8,7,6]=>[2,5,3,1,4,7,8,6]=>0101001
[4,8,1,3,6,7,2,5]=>[7,8,1,4,3,2,6,5]=>[4,8,5,3,1,7,6,2]=>0101111
[5,3,8,2,4,7,1,6]=>[7,8,5,3,2,4,1,6]=>[7,1,8,6,4,3,5,2]=>0011111
[6,4,2,8,1,3,7,5]=>[7,4,2,8,6,1,3,5]=>[8,5,6,1,7,3,2,4]=>0100111
[6,3,8,1,4,7,2,5]=>[7,8,6,3,1,4,2,5]=>[6,4,3,8,5,1,7,2]=>0011111
[1,5,7,4,2,6,8,3]=>[1,8,4,7,5,2,6,3]=>[1,5,8,3,4,7,6,2]=>0000111
[6,5,1,2,8,7,3,4]=>[7,1,5,2,6,3,8,4]=>[6,3,5,8,4,2,1,7]=>1010101
[4,3,1,5,7,2,6,8]=>[7,3,4,1,5,2,6,8]=>[5,7,6,2,3,4,1,8]=>0010110
[3,4,7,2,8,6,1,5]=>[6,8,3,4,2,7,1,5]=>[3,4,7,1,6,8,5,2]=>0001011
[5,3,6,8,4,7,2,1]=>[2,7,8,5,3,6,4,1]=>[6,8,1,2,7,4,5,3]=>0001011
[4,1,6,5,8,3,2,7]=>[3,8,4,1,6,5,2,7]=>[4,1,3,6,5,8,7,2]=>0010111
[6,7,8,1,4,3,2,5]=>[3,4,8,1,2,6,7,5]=>[6,7,8,5,2,4,1,3]=>0011001
[4,7,1,5,8,3,2,6]=>[3,8,7,4,1,5,2,6]=>[4,8,6,5,1,3,7,2]=>0001111
[8,3,1,5,4,7,2,6]=>[7,3,5,8,1,4,2,6]=>[7,2,3,5,1,8,6,4]=>0001111
[8,4,1,5,7,3,2,6]=>[3,7,4,8,1,5,2,6]=>[7,2,8,6,5,1,3,4]=>0001111
[8,2,6,1,4,3,7,5]=>[4,7,6,2,8,1,3,5]=>[7,3,6,1,4,2,8,5]=>0010111
[3,7,6,1,4,8,2,5]=>[8,6,3,1,4,7,2,5]=>[3,7,2,6,8,5,4,1]=>0011011
[6,7,8,5,1,3,2,4]=>[3,5,1,2,8,6,7,4]=>[3,1,6,7,8,4,2,5]=>0110001
[6,7,8,2,4,3,5,1]=>[5,4,8,2,3,6,7,1]=>[4,2,6,7,8,1,5,3]=>0011001
[8,7,2,1,4,3,6,5]=>[2,4,6,1,7,3,8,5]=>[4,1,2,6,3,8,5,7]=>0010101
[8,7,2,5,1,3,6,4]=>[6,5,2,7,1,3,8,4]=>[6,3,2,5,1,8,4,7]=>0101101
[4,7,6,5,8,1,2,3]=>[8,1,2,4,6,7,5,3]=>[4,7,5,6,8,3,2,1]=>1100011
[8,7,6,5,2,1,4,3]=>[2,4,5,1,6,7,8,3]=>[4,1,2,8,3,5,6,7]=>0010001
[3,6,4,8,7,5,1,2]=>[5,1,3,7,6,4,8,2]=>[3,8,2,1,5,6,4,7]=>1000101
[5,6,4,3,8,7,1,2]=>[7,1,4,6,5,3,8,2]=>[5,6,3,4,8,2,1,7]=>1000101
[1,6,2,4,7,8,5,3]=>[1,5,8,2,6,4,7,3]=>[1,6,4,2,5,7,8,3]=>0010101
[1,4,7,2,5,8,6,3]=>[1,6,8,4,2,7,5,3]=>[1,4,7,5,2,6,8,3]=>0001011
[7,3,8,4,5,6,1,2]=>[6,1,8,7,3,4,5,2]=>[8,2,1,6,4,7,5,3]=>1001111
[4,3,6,7,8,5,1,2]=>[5,1,4,3,8,6,7,2]=>[4,3,6,7,8,2,1,5]=>1010001
[3,5,6,4,8,7,1,2]=>[7,1,3,6,5,4,8,2]=>[3,5,6,4,8,2,1,7]=>1000101
[6,5,2,1,4,7,8,3]=>[2,8,5,1,6,4,7,3]=>[7,8,3,5,6,4,1,2]=>0010101
[4,2,7,5,1,8,6,3]=>[6,5,4,2,8,7,1,3]=>[7,1,6,8,3,4,2,5]=>0010011
[5,8,3,6,1,4,2,7]=>[4,6,8,3,5,1,2,7]=>[5,8,7,2,6,1,4,3]=>0010111
[1,6,8,7,4,2,3,5]=>[1,4,2,7,3,6,8,5]=>[1,6,8,5,3,2,4,7]=>0101001
[7,6,1,8,3,2,4,5]=>[3,8,6,1,2,7,4,5]=>[7,4,1,3,6,8,5,2]=>0011011
[2,1,7,5,6,3,8,4]=>[2,1,8,6,7,5,3,4]=>[2,1,8,4,6,5,7,3]=>1000111
[3,1,6,7,5,8,2,4]=>[8,3,1,2,7,6,5,4]=>[6,7,5,8,4,2,3,1]=>0110011
[7,8,1,6,5,3,2,4]=>[3,5,6,1,8,2,7,4]=>[7,8,4,1,3,6,2,5]=>0010101
[4,2,6,1,8,5,7,3]=>[7,8,4,2,6,1,5,3]=>[7,5,6,1,8,3,4,2]=>0010111
[1,2,8,3,6,5,7,4]=>[1,2,7,6,8,3,5,4]=>[1,2,8,4,6,3,7,5]=>0000111
[4,6,3,8,1,2,7,5]=>[7,1,8,4,6,3,2,5]=>[4,7,2,1,8,5,6,3]=>1000111
[7,8,1,3,4,2,6,5]=>[4,6,1,3,8,2,7,5]=>[4,3,1,6,2,7,8,5]=>0110101
[5,3,8,7,1,2,6,4]=>[6,1,7,5,3,2,8,4]=>[6,2,1,8,4,5,3,7]=>1001101
[6,5,3,8,2,1,7,4]=>[2,7,8,5,6,3,1,4]=>[7,1,2,8,4,5,6,3]=>0000111
[7,6,3,5,4,8,1,2]=>[8,1,5,6,3,7,4,2]=>[5,3,7,4,6,8,2,1]=>1001011
[4,5,6,3,8,7,1,2]=>[7,1,6,4,5,3,8,2]=>[4,5,6,3,8,2,1,7]=>1000101
[4,8,2,6,1,5,3,7]=>[5,6,8,4,2,1,3,7]=>[4,6,1,5,2,8,7,3]=>0001111
[4,3,6,2,5,1,8,7]=>[5,6,4,3,2,1,8,7]=>[4,3,6,1,5,2,8,7]=>0011101
[7,8,1,2,5,6,3,4]=>[6,1,8,2,3,5,7,4]=>[7,8,4,2,1,6,5,3]=>1011101
[4,1,6,2,5,7,3,8]=>[7,6,4,1,2,5,3,8]=>[6,5,2,7,3,4,1,8]=>0011110
[2,1,8,6,4,7,3,5]=>[2,1,7,6,4,8,3,5]=>[2,1,7,3,8,5,4,6]=>1001011
[1,8,3,6,7,4,5,2]=>[1,5,7,8,3,4,6,2]=>[1,8,2,5,3,7,6,4]=>0001111
[5,8,7,1,2,4,3,6]=>[4,1,7,2,5,3,8,6]=>[4,2,1,5,8,6,3,7]=>1010101
[3,5,6,4,1,8,2,7]=>[8,4,3,6,5,1,2,7]=>[3,5,8,7,2,4,6,1]=>0000111
[4,2,6,3,8,1,7,5]=>[7,8,4,2,6,3,1,5]=>[7,1,8,5,6,3,4,2]=>0010111
[1,3,7,4,8,2,5,6]=>[1,8,3,7,4,2,5,6]=>[1,3,7,5,4,8,6,2]=>0001111
[2,4,7,3,6,1,8,5]=>[8,2,6,4,7,3,1,5]=>[2,4,6,3,8,5,7,1]=>0000111
[5,8,7,6,3,1,2,4]=>[3,1,6,2,5,7,8,4]=>[5,8,4,2,1,3,6,7]=>1010001
[7,5,6,8,1,4,3,2]=>[3,4,8,1,7,5,6,2]=>[7,6,5,8,2,4,1,3]=>0010111
[2,4,7,1,6,5,3,8]=>[5,2,6,4,7,1,3,8]=>[2,4,7,3,6,1,5,8]=>0000110
[4,2,1,3,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>0110101
[7,5,1,6,4,3,8,2]=>[8,4,6,5,7,1,3,2]=>[8,2,4,5,7,3,6,1]=>0000111
[6,8,1,7,5,2,3,4]=>[5,7,1,2,8,6,3,4]=>[6,8,4,2,7,3,1,5]=>0110011
[7,8,5,1,6,4,2,3]=>[4,6,1,5,8,2,7,3]=>[6,2,7,8,3,1,4,5]=>0100101
[1,3,7,4,6,8,2,5]=>[1,8,3,7,4,2,6,5]=>[1,3,8,5,4,7,6,2]=>0001111
[8,1,6,5,7,2,4,3]=>[4,7,6,1,8,2,5,3]=>[4,1,8,3,6,2,7,5]=>0010111
[7,1,6,5,8,3,2,4]=>[3,8,6,1,7,2,5,4]=>[7,5,8,4,1,3,6,2]=>0010111
[7,8,1,6,2,4,5,3]=>[5,6,8,1,2,4,7,3]=>[6,4,1,5,2,7,8,3]=>0011101
[6,1,2,8,4,3,5,7]=>[4,1,8,6,2,3,5,7]=>[8,7,5,2,1,4,6,3]=>1001111
[5,1,2,4,8,3,6,7]=>[8,1,5,2,4,3,6,7]=>[8,7,6,3,5,4,2,1]=>1011111
[4,1,3,2,8,5,6,7]=>[3,4,1,2,8,5,6,7]=>[3,1,4,2,8,7,6,5]=>0110111
[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,5,6,7]=>[3,1,2,4,8,7,6,5]=>0100111
[4,3,6,1,5,8,2,7]=>[8,6,4,3,1,5,2,7]=>[4,3,8,7,2,6,5,1]=>0011111
[8,4,2,1,7,3,6,5]=>[2,6,4,7,8,1,3,5]=>[6,1,2,7,3,4,8,5]=>0000111
[7,4,2,1,8,5,3,6]=>[2,5,4,8,7,1,3,6]=>[8,6,1,2,5,7,3,4]=>0000111
[1,5,4,2,8,3,6,7]=>[1,8,4,5,2,3,6,7]=>[1,8,7,6,3,4,5,2]=>0001111
[5,4,3,2,1,8,6,7]=>[2,3,4,5,1,8,6,7]=>[5,1,2,3,4,8,7,6]=>0001011
[3,7,6,8,4,5,2,1]=>[2,5,3,8,4,7,6,1]=>[3,7,6,8,1,2,5,4]=>0001011
[3,4,8,5,6,7,2,1]=>[2,7,3,4,8,5,6,1]=>[3,4,8,1,2,7,6,5]=>0000111
[6,3,5,8,4,7,2,1]=>[2,7,8,6,3,5,4,1]=>[8,1,2,7,4,6,5,3]=>0001111
[2,1,8,7,4,6,3,5]=>[2,1,6,7,4,3,8,5]=>[2,1,6,3,8,5,4,7]=>1001101
[5,8,6,7,4,3,2,1]=>[2,3,4,7,5,8,6,1]=>[5,8,1,2,3,4,7,6]=>0000011
[6,2,1,4,3,8,5,7]=>[2,4,8,1,6,3,5,7]=>[4,1,2,8,7,5,6,3]=>0010111
[8,2,1,4,3,6,5,7]=>[2,4,6,1,8,3,5,7]=>[4,1,2,6,3,8,7,5]=>0010111
[2,1,6,4,3,5,8,7]=>[2,1,4,6,3,5,8,7]=>[2,1,6,5,3,4,8,7]=>1001101
[6,4,2,1,3,5,8,7]=>[2,4,1,6,3,5,8,7]=>[6,5,3,1,2,4,8,7]=>0101101
[8,4,2,1,3,6,5,7]=>[2,4,1,6,8,3,5,7]=>[6,3,1,2,4,8,7,5]=>0100111
[8,4,2,1,6,3,5,7]=>[2,6,4,8,1,3,5,7]=>[8,7,5,1,2,6,3,4]=>0001111
[6,4,2,1,8,3,5,7]=>[2,8,4,6,1,3,5,7]=>[6,3,4,8,7,5,1,2]=>0001111
[4,8,2,1,3,6,5,7]=>[2,6,1,4,8,3,5,7]=>[4,6,3,1,2,8,7,5]=>0100111
[6,8,2,1,4,3,5,7]=>[2,4,8,1,3,6,5,7]=>[4,1,2,6,8,7,5,3]=>0011011
[8,6,2,1,4,3,5,7]=>[2,4,6,1,3,8,5,7]=>[4,1,2,8,7,5,3,6]=>0011011
[2,8,1,4,6,3,5,7]=>[6,2,8,1,4,3,5,7]=>[2,8,7,5,4,1,6,3]=>0011111
[2,6,4,8,1,3,5,7]=>[8,2,1,6,4,3,5,7]=>[2,8,7,5,4,6,3,1]=>0101111
[4,6,2,8,1,3,5,7]=>[8,6,2,4,1,3,5,7]=>[4,6,3,2,8,7,5,1]=>0101111
[4,2,6,1,8,3,5,7]=>[8,6,4,2,1,3,5,7]=>[6,3,4,2,8,7,5,1]=>0011111
[6,2,4,1,8,3,5,7]=>[8,4,6,2,1,3,5,7]=>[4,2,6,3,8,7,5,1]=>0011111
[4,2,1,6,3,8,5,7]=>[2,8,4,1,6,3,5,7]=>[8,7,5,6,3,4,1,2]=>0010111
[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,7,5,6]=>1010011
[4,2,1,3,8,6,5,7]=>[2,4,1,3,6,8,5,7]=>[4,3,1,2,8,7,5,6]=>0110011
[4,2,1,8,3,6,5,7]=>[2,6,4,1,8,3,5,7]=>[6,3,4,1,2,8,7,5]=>0010111
[4,2,1,8,6,3,5,7]=>[2,6,4,1,3,8,5,7]=>[8,7,5,3,4,1,2,6]=>0011011
[2,1,4,8,3,6,5,7]=>[2,1,6,4,8,3,5,7]=>[2,1,4,6,3,8,7,5]=>1000111
[2,4,8,6,1,3,5,7]=>[6,2,1,4,3,8,5,7]=>[2,4,8,7,5,3,1,6]=>0101011
[4,2,8,6,1,3,5,7]=>[6,4,2,1,3,8,5,7]=>[8,7,5,3,2,4,1,6]=>0111011
[2,1,8,6,4,3,5,7]=>[2,1,4,6,3,8,5,7]=>[2,1,8,7,5,3,4,6]=>1001011
[3,2,6,1,5,4,8,7]=>[5,3,2,6,1,4,8,7]=>[3,2,5,1,6,4,8,7]=>0101101
[6,1,5,2,4,3,8,7]=>[4,5,6,1,2,3,8,7]=>[4,1,5,2,6,3,8,7]=>0011101
[6,1,3,2,5,4,8,7]=>[3,5,1,6,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>0101101
[4,3,5,2,8,1,7,6]=>[7,5,4,3,2,8,1,6]=>[4,3,5,2,7,1,8,6]=>0011011
[4,3,8,1,5,2,7,6]=>[5,7,4,3,1,8,2,6]=>[4,3,5,1,7,2,8,6]=>0011011
[2,1,5,4,8,3,7,6]=>[2,1,7,5,4,8,3,6]=>[2,1,5,4,7,3,8,6]=>1001011
[4,3,6,5,8,1,7,2]=>[7,8,4,3,6,5,1,2]=>[4,3,6,5,7,1,8,2]=>0010111
[7,1,6,5,8,3,4,2]=>[4,8,6,1,7,3,5,2]=>[4,1,6,3,7,5,8,2]=>0010111
[8,4,6,1,3,2,7,5]=>[3,7,1,6,8,4,2,5]=>[3,1,6,4,7,2,8,5]=>0100111
[8,1,6,3,4,2,7,5]=>[4,7,6,1,8,3,2,5]=>[4,1,6,3,7,2,8,5]=>0010111
[7,3,5,2,6,4,8,1]=>[8,6,5,7,3,2,4,1]=>[5,3,6,2,7,4,8,1]=>0001111
[8,2,7,1,5,3,6,4]=>[6,5,7,8,2,1,3,4]=>[5,2,6,1,7,3,8,4]=>0001111
[2,1,8,3,7,4,6,5]=>[2,1,6,7,8,3,4,5]=>[2,1,6,3,7,4,8,5]=>1000111
[2,1,8,3,5,4,7,6]=>[2,1,5,7,3,8,4,6]=>[2,1,5,3,7,4,8,6]=>1001011
[8,1,3,2,5,4,7,6]=>[3,5,1,7,2,8,4,6]=>[3,1,5,2,7,4,8,6]=>0101011
[8,1,5,2,4,3,7,6]=>[4,5,7,1,2,8,3,6]=>[4,1,5,2,7,3,8,6]=>0011011
[3,2,8,4,6,1,7,5]=>[7,3,2,6,8,4,1,5]=>[3,2,6,4,7,1,8,5]=>0100111
[3,2,8,1,7,4,6,5]=>[6,3,2,7,8,1,4,5]=>[3,2,6,1,7,4,8,5]=>0100111
[3,2,8,1,5,4,7,6]=>[5,3,2,7,1,8,4,6]=>[3,2,5,1,7,4,8,6]=>0101011
[3,2,4,1,8,5,7,6]=>[4,3,2,1,7,8,5,6]=>[3,2,4,1,7,5,8,6]=>0110011
[4,1,3,2,7,6,8,5]=>[3,4,1,2,8,7,6,5]=>[3,1,4,2,7,6,8,5]=>0110011
[3,2,7,1,8,5,6,4]=>[6,3,2,8,7,1,5,4]=>[3,2,6,1,7,5,8,4]=>0100111
[7,2,4,1,8,5,6,3]=>[6,4,8,2,7,1,5,3]=>[4,2,6,1,7,5,8,3]=>0010111
[7,6,8,1,3,2,5,4]=>[3,5,1,8,2,7,6,4]=>[3,1,5,2,7,6,8,4]=>0101011
[7,1,8,2,6,4,5,3]=>[5,6,8,7,1,2,4,3]=>[5,1,6,2,7,4,8,3]=>0001111
[5,4,8,2,6,1,7,3]=>[7,6,8,5,4,2,1,3]=>[5,4,6,2,7,1,8,3]=>0001111
[6,1,8,4,7,2,5,3]=>[5,7,8,6,1,4,2,3]=>[5,1,6,4,7,2,8,3]=>0001111
[6,5,8,1,3,2,7,4]=>[3,7,1,8,6,5,2,4]=>[3,1,6,5,7,2,8,4]=>0100111
[6,5,7,4,8,1,3,2]=>[3,8,1,7,6,5,4,2]=>[3,1,6,5,7,4,8,2]=>0100111
[4,2,5,3,1,8,6,7]=>[3,5,4,2,1,8,6,7]=>[5,1,3,4,2,8,7,6]=>0011011
[1,8,4,2,5,3,6,7]=>[1,5,4,8,2,3,6,7]=>[1,5,2,8,7,6,3,4]=>0001111
[8,1,5,3,2,4,6,7]=>[3,5,8,1,2,4,6,7]=>[5,2,8,7,6,4,1,3]=>0011111
[1,5,7,3,8,4,2,6]=>[1,4,8,7,5,3,2,6]=>[1,5,7,2,4,8,6,3]=>0000111
[8,1,5,3,7,4,6,2]=>[6,7,5,8,1,3,4,2]=>[6,3,5,1,8,2,7,4]=>0001111
[1,4,3,8,7,5,6,2]=>[1,6,4,3,7,5,8,2]=>[1,4,3,8,2,6,5,7]=>0010101
[6,7,1,4,2,8,3,5]=>[8,4,7,1,2,6,3,5]=>[6,7,3,8,5,2,4,1]=>0011011
[6,3,7,1,4,8,2,5]=>[8,7,6,3,1,4,2,5]=>[6,4,3,7,2,8,5,1]=>0011111
[7,1,2,8,5,3,4,6]=>[5,1,8,2,7,3,4,6]=>[7,4,2,1,5,8,6,3]=>1010111
[1,7,2,8,4,5,3,6]=>[1,5,8,7,2,4,3,6]=>[1,5,2,8,6,4,7,3]=>0001111
[8,7,1,3,6,2,4,5]=>[6,7,1,3,2,4,8,5]=>[6,4,3,1,8,5,2,7]=>0111101
[2,7,8,4,1,6,5,3]=>[5,2,4,6,8,1,7,3]=>[2,7,8,3,4,6,1,5]=>0000101
[2,8,4,1,6,7,5,3]=>[5,2,4,7,8,1,6,3]=>[2,8,3,4,7,6,1,5]=>0000111
[2,1,8,4,7,5,6,3]=>[2,1,6,7,8,4,5,3]=>[2,1,8,3,6,4,7,5]=>1000111
[8,3,7,1,5,6,2,4]=>[6,7,8,3,1,2,5,4]=>[7,5,1,6,2,8,4,3]=>0011111
[8,6,1,2,7,5,3,4]=>[5,1,7,2,6,8,3,4]=>[7,3,8,4,2,1,5,6]=>1010011
[6,3,5,2,1,4,8,7]=>[2,5,6,3,1,4,8,7]=>[5,1,2,6,4,3,8,7]=>0011101
[8,3,5,7,2,4,1,6]=>[4,7,8,3,2,5,1,6]=>[8,6,5,2,7,1,4,3]=>0011111
[8,5,2,7,4,3,1,6]=>[3,4,7,5,8,2,1,6]=>[7,1,3,8,6,2,4,5]=>0000111
[6,5,3,1,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>[6,4,2,1,3,5,8,7]=>1010101
[4,5,3,6,1,2,8,7]=>[6,1,5,4,3,2,8,7]=>[4,5,3,6,2,1,8,7]=>1001101
[3,5,1,4,6,2,8,7]=>[6,5,3,1,4,2,8,7]=>[3,6,2,5,4,1,8,7]=>0011101
[8,1,4,7,3,6,2,5]=>[6,7,8,1,4,3,2,5]=>[7,2,8,5,4,1,6,3]=>0011111
[6,3,4,7,5,8,1,2]=>[8,1,7,3,6,4,5,2]=>[7,5,6,4,3,8,2,1]=>1010111
[4,8,3,7,1,2,6,5]=>[6,1,7,4,8,3,2,5]=>[4,7,2,1,6,3,8,5]=>1000111
[8,7,1,4,2,6,3,5]=>[6,4,7,1,2,3,8,5]=>[8,5,2,4,1,6,3,7]=>0011101
[2,1,8,7,5,3,4,6]=>[2,1,5,3,7,4,8,6]=>[2,1,8,6,4,3,5,7]=>1010101
[8,1,7,4,5,2,3,6]=>[5,7,1,8,2,4,3,6]=>[7,3,1,5,2,8,6,4]=>0101111
[2,8,7,5,4,1,3,6]=>[4,2,1,5,7,3,8,6]=>[2,8,6,3,1,4,5,7]=>0100101
[8,7,2,6,4,1,3,5]=>[4,6,2,7,1,3,8,5]=>[6,3,2,8,5,1,4,7]=>0101101
[5,7,8,6,4,2,1,3]=>[2,4,1,6,5,8,7,3]=>[5,7,8,3,1,2,4,6]=>0100001
[2,6,7,5,4,8,1,3]=>[8,2,1,5,7,6,4,3]=>[2,6,7,4,5,8,3,1]=>0100011
[2,1,6,7,5,8,3,4]=>[2,1,8,3,7,6,5,4]=>[2,1,6,7,5,8,4,3]=>1010011
[2,1,5,7,3,6,8,4]=>[2,1,8,7,5,3,6,4]=>[2,1,5,8,4,7,6,3]=>1000111
[4,1,7,2,5,6,8,3]=>[8,7,4,1,2,5,6,3]=>[7,6,5,2,8,3,4,1]=>0011111
[2,4,7,1,6,5,8,3]=>[8,2,6,4,7,1,5,3]=>[2,4,7,5,8,3,6,1]=>0000111
[3,5,6,4,7,1,8,2]=>[8,7,3,6,5,4,1,2]=>[3,5,6,4,8,2,7,1]=>0000111
[6,3,2,1,7,4,8,5]=>[2,3,8,7,6,1,4,5]=>[7,4,8,5,6,1,2,3]=>0000111
[7,2,5,1,4,3,8,6]=>[4,5,8,2,1,7,3,6]=>[5,1,4,2,8,6,7,3]=>0011011
[6,4,3,2,1,8,5,7]=>[2,3,4,8,6,1,5,7]=>[8,7,5,6,1,2,3,4]=>0000111
[5,8,3,2,7,1,6,4]=>[6,3,7,8,5,2,1,4]=>[5,7,1,6,2,3,8,4]=>0000111
[5,8,4,6,7,1,3,2]=>[3,7,1,8,5,4,6,2]=>[3,1,5,8,2,7,6,4]=>0100111
[7,2,8,5,6,1,4,3]=>[4,6,8,2,7,1,5,3]=>[6,1,4,2,7,5,8,3]=>0010111
[4,3,6,8,2,1,5,7]=>[2,8,4,3,1,6,5,7]=>[4,3,6,8,7,5,1,2]=>0011011
[2,5,7,4,8,1,3,6]=>[8,2,1,7,5,4,3,6]=>[2,5,8,6,4,7,3,1]=>0100111
[4,3,6,7,8,1,2,5]=>[8,1,4,3,2,6,7,5]=>[4,3,6,7,8,5,2,1]=>1011001
[3,5,7,1,4,8,2,6]=>[8,7,3,1,5,4,2,6]=>[3,5,7,2,8,6,4,1]=>0010111
[8,4,1,5,7,3,6,2]=>[6,7,4,8,1,5,3,2]=>[6,5,1,8,2,7,3,4]=>0001111
[6,3,1,8,4,7,5,2]=>[5,3,7,8,6,1,4,2]=>[6,1,5,8,2,3,7,4]=>0000111
[5,2,8,1,7,3,6,4]=>[6,7,8,5,2,1,3,4]=>[6,1,8,4,5,2,7,3]=>0001111
[5,7,3,8,1,6,4,2]=>[4,6,8,7,5,3,1,2]=>[5,7,1,4,8,2,6,3]=>0000111
[4,3,8,7,6,2,1,5]=>[2,6,4,3,1,7,8,5]=>[4,3,8,5,1,2,6,7]=>0011001
[3,5,8,7,2,6,1,4]=>[6,7,3,2,5,1,8,4]=>[3,5,6,1,8,4,2,7]=>0010101
[7,5,8,6,4,3,2,1]=>[2,3,4,6,8,7,5,1]=>[8,1,2,3,4,6,7,5]=>0000011
[3,8,7,6,5,1,4,2]=>[4,5,3,1,6,7,8,2]=>[3,4,1,8,2,5,6,7]=>0010001
[2,8,7,6,5,4,1,3]=>[4,2,1,5,6,7,8,3]=>[2,8,3,1,4,5,6,7]=>0100001
[7,8,5,6,3,1,4,2]=>[4,3,6,1,8,5,7,2]=>[4,1,7,8,2,3,6,5]=>0010101
[7,8,5,3,1,4,2,6]=>[4,3,5,1,8,2,7,6]=>[4,1,7,8,6,2,3,5]=>0010101
[7,8,5,3,1,6,2,4]=>[6,3,5,1,8,2,7,4]=>[7,8,4,1,6,2,3,5]=>0010101
[7,8,5,3,1,6,4,2]=>[4,3,6,5,8,1,7,2]=>[7,8,2,3,6,1,4,5]=>0000101
[7,8,5,3,6,4,1,2]=>[4,1,6,5,8,3,7,2]=>[6,3,7,8,2,1,4,5]=>1000101
[7,8,5,3,1,4,6,2]=>[6,3,5,1,8,4,7,2]=>[6,4,1,7,8,2,3,5]=>0010101
[7,5,8,3,4,1,6,2]=>[6,4,8,3,7,5,1,2]=>[7,1,6,5,8,2,4,3]=>0010111
[7,5,6,3,4,1,8,2]=>[8,4,6,3,7,5,1,2]=>[8,2,4,3,6,5,7,1]=>0010111
[7,5,3,6,4,1,8,2]=>[8,4,6,5,7,3,1,2]=>[6,3,8,2,4,5,7,1]=>0000111
[7,5,3,6,4,8,1,2]=>[8,1,6,5,7,3,4,2]=>[6,3,7,4,5,8,2,1]=>1000111
[7,5,3,8,4,1,6,2]=>[6,4,8,5,7,3,1,2]=>[8,2,4,5,7,1,6,3]=>0000111
[7,5,3,8,1,4,6,2]=>[6,8,5,3,7,1,4,2]=>[6,1,7,4,3,5,8,2]=>0010111
[7,5,3,1,8,2,6,4]=>[6,3,8,5,7,1,2,4]=>[6,1,8,4,5,7,2,3]=>0000111
[7,5,3,1,6,2,4,8]=>[6,3,5,1,7,2,4,8]=>[7,4,1,6,2,3,5,8]=>0010110
[7,5,3,1,8,4,2,6]=>[4,3,8,5,7,1,2,6]=>[8,6,1,4,5,7,2,3]=>0000111
[7,5,3,1,8,6,2,4]=>[6,3,5,1,8,7,2,4]=>[8,4,1,6,7,2,3,5]=>0010011
[7,5,8,3,6,4,1,2]=>[4,1,6,8,7,5,3,2]=>[7,3,6,5,8,2,1,4]=>1000111
[7,5,8,3,6,1,4,2]=>[4,6,8,3,7,5,1,2]=>[8,2,6,5,7,1,4,3]=>0010111
[7,5,8,3,1,6,4,2]=>[4,3,6,8,7,5,1,2]=>[8,2,3,6,5,7,1,4]=>0000111
[7,5,3,8,1,4,2,6]=>[4,8,5,3,7,1,2,6]=>[8,6,1,4,3,5,7,2]=>0010111
[7,5,3,6,4,1,2,8]=>[4,1,6,5,7,3,2,8]=>[6,3,7,2,1,4,5,8]=>1000110
[7,5,8,6,3,1,2,4]=>[3,1,6,2,8,7,5,4]=>[8,4,2,1,3,6,7,5]=>1010011
[7,5,8,6,3,1,4,2]=>[4,3,6,1,8,7,5,2]=>[4,1,8,2,3,6,7,5]=>0010011
[7,5,3,6,1,8,2,4]=>[8,6,5,3,7,1,2,4]=>[8,4,3,5,7,2,6,1]=>0010111
[7,5,6,3,1,8,4,2]=>[4,3,8,6,7,5,1,2]=>[7,1,4,6,5,8,2,3]=>0000111
[7,5,6,3,8,1,4,2]=>[4,8,6,3,7,5,1,2]=>[7,1,4,3,6,5,8,2]=>0010111
[7,5,6,3,8,4,1,2]=>[4,1,8,6,7,5,3,2]=>[8,2,1,4,6,5,7,3]=>1000111
[7,5,3,6,8,1,4,2]=>[4,8,5,3,7,1,6,2]=>[7,6,1,4,3,5,8,2]=>0010111
[7,5,3,1,2,8,6,4]=>[3,1,6,5,8,7,2,4]=>[7,2,1,3,6,8,4,5]=>1000011
[6,8,1,2,4,5,7,3]=>[7,1,8,2,4,6,5,3]=>[6,7,5,4,2,1,8,3]=>1011011
[3,6,8,2,5,7,1,4]=>[7,8,3,2,1,6,5,4]=>[3,6,7,5,1,8,4,2]=>0011011
[8,3,5,2,4,1,6,7]=>[4,5,8,3,2,1,6,7]=>[5,2,8,7,6,1,4,3]=>0011111
[2,1,6,8,4,7,3,5]=>[2,1,7,8,4,6,3,5]=>[2,1,6,7,3,8,5,4]=>1001011
[5,8,4,7,6,3,1,2]=>[3,1,6,7,5,8,4,2]=>[5,7,4,8,2,1,3,6]=>1000011
[5,8,7,1,4,2,6,3]=>[6,4,7,1,5,2,8,3]=>[5,6,2,4,1,8,3,7]=>0010101
[4,7,3,6,5,2,1,8]=>[2,5,6,4,7,3,1,8]=>[4,6,3,7,1,2,5,8]=>0000110
[1,3,8,5,4,2,7,6]=>[1,4,3,5,7,8,2,6]=>[1,3,7,2,4,5,8,6]=>0000011
[1,8,3,6,2,7,5,4]=>[1,5,7,6,8,3,2,4]=>[1,8,4,6,3,7,2,5]=>0000111
[1,6,8,7,4,2,5,3]=>[1,5,4,7,2,6,8,3]=>[1,5,2,6,8,3,4,7]=>0001001
[3,1,2,7,6,4,8,5]=>[3,1,2,8,6,7,4,5]=>[3,2,1,8,5,6,7,4]=>1100011
[2,1,7,3,8,5,4,6]=>[2,1,5,8,7,3,4,6]=>[2,1,8,6,3,5,7,4]=>1000111
[1,6,2,3,7,8,5,4]=>[1,5,2,8,6,3,7,4]=>[1,6,3,2,5,7,8,4]=>0100101
[6,3,7,4,8,5,1,2]=>[5,1,8,7,6,3,4,2]=>[7,4,8,2,1,5,6,3]=>1000111
[5,7,1,8,2,4,6,3]=>[6,8,7,1,5,2,4,3]=>[5,8,3,7,4,1,6,2]=>0010111
[4,2,1,7,3,8,5,6]=>[2,8,4,1,7,3,5,6]=>[7,5,8,6,3,4,1,2]=>0010111
[6,2,8,4,3,1,5,7]=>[3,4,8,6,2,1,5,7]=>[8,7,5,2,4,6,1,3]=>0001111
[7,3,2,1,8,4,5,6]=>[2,3,8,7,1,4,5,6]=>[8,6,4,7,5,1,2,3]=>0001111
[8,3,6,5,2,1,4,7]=>[2,5,6,3,8,1,4,7]=>[8,7,4,3,6,1,2,5]=>0010111
[8,2,4,1,7,6,3,5]=>[6,4,7,2,1,8,3,5]=>[4,2,7,3,8,5,1,6]=>0011011
[6,1,8,2,3,7,5,4]=>[5,7,1,8,6,2,3,4]=>[7,3,1,5,6,2,8,4]=>0100111
[2,8,1,7,5,4,3,6]=>[4,2,5,7,8,1,3,6]=>[2,8,6,1,4,7,3,5]=>0000111
[1,8,7,6,5,2,4,3]=>[1,4,5,2,6,7,8,3]=>[1,4,2,8,3,5,6,7]=>0010001
[4,3,1,2,8,7,6,5]=>[3,1,4,2,6,7,8,5]=>[4,2,1,3,8,5,6,7]=>1010001
[8,6,4,1,5,2,7,3]=>[7,5,4,6,1,8,2,3]=>[7,2,5,1,8,3,4,6]=>0001011
[8,6,5,3,2,1,7,4]=>[2,3,7,5,6,8,1,4]=>[7,1,2,3,8,4,5,6]=>0000011
[8,7,2,4,5,3,1,6]=>[3,5,7,2,4,1,8,6]=>[5,4,2,8,6,1,3,7]=>0011101
[8,5,1,2,6,7,3,4]=>[7,1,5,2,8,3,6,4]=>[8,4,2,1,7,6,3,5]=>1010111
[8,5,1,6,4,2,7,3]=>[7,4,6,5,8,1,2,3]=>[8,3,6,1,7,2,4,5]=>0000111
[8,5,1,3,6,4,7,2]=>[7,6,1,5,8,3,4,2]=>[8,2,6,3,1,7,4,5]=>0100111
[8,6,5,1,7,3,2,4]=>[3,7,5,1,6,8,2,4]=>[7,2,8,4,1,3,5,6]=>0010011
[8,5,7,4,6,1,3,2]=>[3,6,1,7,8,5,4,2]=>[3,1,7,4,8,2,6,5]=>0100111
[1,8,5,3,7,2,6,4]=>[1,6,7,5,8,3,2,4]=>[1,7,2,6,3,8,4,5]=>0000111
[1,6,3,8,7,2,5,4]=>[1,5,7,6,3,2,8,4]=>[1,8,4,6,2,5,3,7]=>0001101
[8,4,1,6,7,5,3,2]=>[3,5,4,7,8,1,6,2]=>[7,6,1,3,4,8,2,5]=>0000111
[7,3,6,8,5,1,2,4]=>[5,1,8,3,7,2,6,4]=>[7,6,2,1,5,8,4,3]=>1010111
[1,3,7,2,6,8,4,5]=>[1,8,3,7,2,4,6,5]=>[1,3,7,6,4,8,5,2]=>0001111
[6,1,2,7,8,5,3,4]=>[5,1,8,2,6,3,7,4]=>[7,8,4,2,1,5,6,3]=>1010101
[6,1,2,7,4,8,5,3]=>[5,1,8,7,6,2,4,3]=>[6,2,1,5,7,4,8,3]=>1000111
[5,7,1,8,4,2,6,3]=>[6,4,8,7,5,1,2,3]=>[5,6,1,7,2,4,8,3]=>0000111
[4,2,6,3,8,1,5,7]=>[8,6,4,2,3,1,5,7]=>[8,7,5,3,4,2,6,1]=>0011111
[3,6,2,4,1,8,5,7]=>[4,8,3,2,6,1,5,7]=>[3,8,7,5,6,1,4,2]=>0010111
[8,7,6,4,1,5,2,3]=>[5,4,1,6,2,7,8,3]=>[8,3,1,5,2,4,6,7]=>0101001
[3,6,8,2,1,5,4,7]=>[2,5,3,8,1,6,4,7]=>[3,5,1,2,6,8,7,4]=>0001011
[8,5,7,6,1,4,2,3]=>[4,6,1,2,7,8,5,3]=>[7,5,8,3,1,4,2,6]=>0110011
[1,8,2,4,6,7,3,5]=>[1,7,8,2,4,3,6,5]=>[1,8,5,4,2,7,6,3]=>0011111
[2,1,5,8,6,4,3,7]=>[2,1,4,6,5,8,3,7]=>[2,1,5,8,7,3,4,6]=>1000011
[1,2,5,7,8,4,3,6]=>[1,2,4,8,5,3,7,6]=>[1,2,5,7,8,6,3,4]=>0000101
[1,2,7,4,8,6,3,5]=>[1,2,6,8,4,7,3,5]=>[1,2,7,3,6,8,5,4]=>0001011
[1,6,8,5,4,3,2,7]=>[1,3,4,5,8,6,2,7]=>[1,6,8,7,2,3,4,5]=>0000011
[7,1,6,4,2,3,5,8]=>[4,6,1,7,2,3,5,8]=>[7,5,2,6,3,1,4,8]=>0101110
[7,1,3,4,2,6,8,5]=>[4,8,1,3,7,2,6,5]=>[4,3,1,8,5,7,6,2]=>0110111
[3,6,7,1,4,8,5,2]=>[5,8,3,1,7,6,4,2]=>[3,6,7,4,1,5,8,2]=>0010011
[3,4,7,2,5,8,1,6]=>[8,7,3,4,2,5,1,6]=>[3,4,8,6,5,2,7,1]=>0001111
[5,6,7,8,1,3,4,2]=>[4,8,1,3,5,6,7,2]=>[4,3,1,5,6,7,8,2]=>0110001
[5,7,8,6,1,2,3,4]=>[6,1,2,3,5,8,7,4]=>[5,7,8,4,3,2,1,6]=>1110001
[2,8,3,1,5,6,4,7]=>[3,2,6,8,1,5,4,7]=>[2,6,5,1,3,8,7,4]=>0001111
[4,3,1,7,6,8,2,5]=>[8,3,4,1,2,7,6,5]=>[7,6,8,5,2,3,4,1]=>0011011
[3,4,1,5,7,6,2,8]=>[6,4,3,1,5,7,2,8]=>[3,5,7,2,4,1,6,8]=>0010010
[2,4,6,1,7,5,8,3]=>[8,2,7,4,6,1,5,3]=>[2,4,8,3,7,5,6,1]=>0000111
[4,2,1,5,6,3,7,8]=>[2,6,4,1,5,3,7,8]=>[5,6,3,4,1,2,7,8]=>0010100
[5,8,1,6,3,7,2,4]=>[7,6,8,1,5,3,2,4]=>[5,8,4,1,7,2,6,3]=>0010111
[8,4,5,3,7,2,6,1]=>[6,7,5,8,4,3,2,1]=>[7,2,8,1,6,3,5,4]=>0001111
[4,6,3,8,5,1,7,2]=>[7,5,8,4,6,3,1,2]=>[4,7,1,8,2,5,6,3]=>0000111
[2,6,4,3,1,5,7,8]=>[3,2,4,6,1,5,7,8]=>[2,6,5,1,3,4,7,8]=>0001100
[7,3,8,4,1,5,2,6]=>[5,4,8,7,3,1,2,6]=>[7,2,4,8,6,1,5,3]=>0001111
[1,4,3,7,2,6,5,8]=>[1,6,4,3,7,2,5,8]=>[1,4,3,6,2,7,5,8]=>0010110
[1,6,5,7,2,4,3,8]=>[1,4,7,2,6,5,3,8]=>[1,4,2,6,5,7,3,8]=>0010110
[1,7,6,2,8,3,4,5]=>[1,8,6,2,3,7,4,5]=>[1,8,5,3,6,7,4,2]=>0011011
[1,4,2,3,5,8,7,6]=>[1,4,2,3,5,7,8,6]=>[1,4,3,2,5,8,6,7]=>0110001
[1,7,6,5,2,8,4,3]=>[1,4,8,5,6,7,2,3]=>[1,7,2,4,5,6,8,3]=>0000011
[1,6,5,2,3,8,4,7]=>[1,8,2,5,6,3,4,7]=>[1,8,7,4,5,6,3,2]=>0100111
[1,5,7,6,2,4,8,3]=>[1,8,6,2,5,7,4,3]=>[1,5,8,3,6,7,4,2]=>0010011
[1,4,7,6,2,5,8,3]=>[1,8,6,4,2,7,5,3]=>[1,4,8,3,6,7,5,2]=>0001011
[1,7,3,5,2,8,4,6]=>[1,8,5,7,3,2,4,6]=>[1,5,3,7,4,8,6,2]=>0001111
[1,3,7,4,2,6,8,5]=>[1,4,3,8,7,2,6,5]=>[1,3,8,5,7,6,2,4]=>0000111
[1,4,3,2,5,8,6,7]=>[1,3,4,2,5,8,6,7]=>[1,4,2,3,5,8,7,6]=>0010011
[1,5,3,2,4,8,6,7]=>[1,3,5,2,4,8,6,7]=>[1,5,4,2,3,8,7,6]=>0011011
[1,7,6,4,2,8,5,3]=>[1,5,4,8,6,7,2,3]=>[1,7,2,5,6,8,3,4]=>0000011
[1,7,5,3,2,8,6,4]=>[1,3,6,5,8,7,2,4]=>[1,7,2,3,6,8,4,5]=>0000011
[1,5,3,2,4,8,7,6]=>[1,3,5,2,4,7,8,6]=>[1,5,4,2,3,8,6,7]=>0011001
[6,8,5,4,3,2,1,7]=>[2,3,4,5,8,6,1,7]=>[6,8,7,1,2,3,4,5]=>0000011
[7,3,5,4,8,1,6,2]=>[6,8,5,7,3,4,1,2]=>[5,3,7,1,6,4,8,2]=>0001111
[5,6,8,4,3,1,7,2]=>[7,3,4,8,5,6,1,2]=>[5,6,7,1,8,2,3,4]=>0000011
[6,8,5,4,1,2,7,3]=>[7,1,4,5,8,6,2,3]=>[6,7,2,1,8,3,4,5]=>1000011
[7,5,8,4,3,2,1,6]=>[2,3,4,8,7,5,1,6]=>[8,6,5,7,1,2,3,4]=>0000111
[7,8,1,2,4,3,5,6]=>[4,1,8,2,3,5,7,6]=>[4,2,1,7,8,6,5,3]=>1011101
[7,8,2,1,4,3,6,5]=>[2,4,6,1,8,3,7,5]=>[4,1,2,6,3,7,8,5]=>0010101
[4,3,6,5,8,7,1,2]=>[7,1,4,3,6,5,8,2]=>[4,3,6,5,8,2,1,7]=>1010101
[4,2,6,1,8,3,7,5]=>[7,8,4,2,6,1,3,5]=>[8,5,6,1,7,3,4,2]=>0010111
[6,7,3,8,4,5,1,2]=>[5,1,8,7,3,6,4,2]=>[6,7,4,8,2,1,5,3]=>1001011
[4,7,5,6,1,8,2,3]=>[8,6,1,4,7,5,2,3]=>[4,7,2,6,5,8,3,1]=>0100111
[4,8,3,6,5,7,1,2]=>[7,1,6,4,8,3,5,2]=>[4,6,3,8,2,1,7,5]=>1000111
[7,8,4,5,1,6,2,3]=>[6,5,1,8,4,2,7,3]=>[7,8,3,1,6,2,5,4]=>0101101
[3,6,4,5,2,7,1,8]=>[7,5,3,6,4,2,1,8]=>[3,6,2,5,4,7,1,8]=>0001110
[3,6,4,5,1,8,2,7]=>[8,5,3,6,4,1,2,7]=>[3,8,7,2,5,4,6,1]=>0001111
[2,6,4,8,1,5,3,7]=>[5,2,8,6,4,1,3,7]=>[2,6,1,5,4,8,7,3]=>0001111
[2,8,3,4,1,6,5,7]=>[4,2,6,3,8,1,5,7]=>[2,6,1,4,3,8,7,5]=>0010111
[7,8,1,5,3,6,2,4]=>[6,5,8,1,3,2,7,4]=>[7,8,4,1,6,2,5,3]=>0011101
[1,6,4,7,3,8,2,5]=>[1,8,7,6,4,3,2,5]=>[1,8,5,4,6,3,7,2]=>0001111
[6,7,1,5,3,8,2,4]=>[8,5,7,1,3,6,2,4]=>[6,7,2,5,3,8,4,1]=>0011011
[6,7,1,8,2,5,3,4]=>[5,8,7,1,2,6,3,4]=>[6,7,3,8,4,1,5,2]=>0011011
[6,7,1,8,4,5,2,3]=>[5,8,1,7,2,6,4,3]=>[6,7,4,8,3,1,5,2]=>0101011
[6,7,5,8,1,4,2,3]=>[4,8,1,2,7,6,5,3]=>[6,7,5,8,3,1,4,2]=>0110011
[6,7,2,3,1,8,4,5]=>[3,8,2,7,1,6,4,5]=>[6,7,4,8,5,1,3,2]=>0101011
[6,7,2,8,1,4,3,5]=>[4,8,7,2,1,6,3,5]=>[6,7,3,8,5,1,4,2]=>0011011
[6,7,3,4,1,8,2,5]=>[8,4,7,3,1,6,2,5]=>[6,7,2,4,3,8,5,1]=>0011011
[2,3,1,8,4,7,5,6]=>[3,2,1,7,8,4,5,6]=>[2,3,1,8,6,4,7,5]=>0100111
[2,3,1,8,6,7,4,5]=>[3,2,1,7,4,8,6,5]=>[2,3,1,8,5,4,7,6]=>0101011
[2,8,1,4,3,7,5,6]=>[4,2,7,1,8,3,5,6]=>[2,4,1,8,6,3,7,5]=>0010111
[2,8,1,7,3,5,4,6]=>[5,2,7,8,1,3,4,6]=>[2,5,1,8,6,3,7,4]=>0001111
[3,4,2,5,1,8,6,7]=>[5,4,3,2,1,8,6,7]=>[3,4,2,5,1,8,7,6]=>0011011
[3,6,5,4,1,2,8,7]=>[4,1,3,5,6,2,8,7]=>[3,6,2,1,4,5,8,7]=>1000101
[3,6,5,1,2,4,8,7]=>[5,1,3,2,6,4,8,7]=>[3,6,4,2,1,5,8,7]=>1010101
[5,2,3,6,4,1,8,7]=>[4,6,2,5,3,1,8,7]=>[6,1,4,5,3,2,8,7]=>0101101
[5,6,7,8,1,4,3,2]=>[3,4,8,1,5,6,7,2]=>[5,6,7,8,2,4,1,3]=>0010001
[2,1,5,8,7,6,3,4]=>[2,1,6,3,5,7,8,4]=>[2,1,5,8,4,3,6,7]=>1010001
[2,1,4,7,6,3,8,5]=>[2,1,8,4,6,7,3,5]=>[2,1,4,8,5,6,7,3]=>1000011
[6,3,7,1,5,2,8,4]=>[8,5,7,6,3,1,2,4]=>[7,2,5,3,8,4,6,1]=>0001111
[4,7,5,8,1,6,3,2]=>[3,6,8,4,7,5,1,2]=>[4,8,2,6,5,7,1,3]=>0000111
[2,1,5,8,7,3,4,6]=>[2,1,7,3,5,4,8,6]=>[2,1,5,8,6,4,3,7]=>1010101
[8,5,7,3,6,1,4,2]=>[4,6,7,3,8,5,1,2]=>[7,1,4,3,8,2,6,5]=>0010111
[7,2,3,4,8,5,6,1]=>[6,8,2,3,7,4,5,1]=>[7,5,8,1,6,4,3,2]=>0110111
[2,1,7,4,5,8,6,3]=>[2,1,6,8,4,7,5,3]=>[2,1,8,3,6,7,5,4]=>1001011
[7,8,2,5,6,1,4,3]=>[4,6,8,2,1,5,7,3]=>[6,5,1,4,2,7,8,3]=>0011101
[6,1,2,3,7,5,8,4]=>[8,1,2,7,6,3,5,4]=>[8,4,7,5,6,3,2,1]=>1100111
[4,1,2,3,7,6,8,5]=>[4,1,2,3,8,7,6,5]=>[4,3,2,1,7,6,8,5]=>1110011
[3,2,4,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>[3,2,4,1,8,7,6,5]=>0110111
[3,4,8,6,5,2,1,7]=>[2,5,3,4,6,8,1,7]=>[3,4,8,7,1,2,5,6]=>0000011
[2,1,6,5,8,4,7,3]=>[2,1,7,8,6,5,4,3]=>[2,1,6,5,8,3,7,4]=>1000111
[4,1,8,5,6,2,3,7]=>[6,4,1,2,8,5,3,7]=>[4,2,8,7,3,1,6,5]=>0110111
[5,8,4,3,2,7,1,6]=>[7,3,4,8,5,2,1,6]=>[5,7,1,8,6,2,3,4]=>0000111
[2,1,8,4,3,7,5,6]=>[2,1,4,7,8,3,5,6]=>[2,1,8,6,3,4,7,5]=>1000111
[7,3,5,8,1,4,2,6]=>[4,8,7,3,1,5,2,6]=>[8,6,5,1,4,3,7,2]=>0011111
[1,6,8,4,7,5,2,3]=>[1,5,2,7,8,6,4,3]=>[1,6,7,4,8,3,2,5]=>0100011
[6,8,1,3,5,7,2,4]=>[7,8,1,3,2,6,5,4]=>[6,8,4,3,1,7,5,2]=>0111011
[1,8,6,2,5,3,4,7]=>[1,5,6,2,3,8,4,7]=>[1,8,7,4,2,5,3,6]=>0011011
[4,7,1,2,5,3,8,6]=>[5,1,8,4,2,7,3,6]=>[4,5,2,1,8,6,7,3]=>1001011
[5,7,8,6,2,1,4,3]=>[2,4,6,1,5,8,7,3]=>[4,1,2,5,7,8,3,6]=>0010001
[1,8,6,4,5,2,3,7]=>[1,5,2,6,4,8,3,7]=>[1,8,7,3,2,5,4,6]=>0101011
[4,3,7,8,5,1,6,2]=>[6,5,4,3,8,1,7,2]=>[4,3,6,1,7,8,2,5]=>0010101
[5,8,2,6,3,4,1,7]=>[4,6,8,2,5,3,1,7]=>[5,8,7,1,4,2,6,3]=>0010111
[4,1,7,5,8,6,2,3]=>[6,4,1,2,8,7,5,3]=>[4,2,8,3,1,6,7,5]=>0110011
[1,2,4,5,8,3,7,6]=>[1,2,7,4,5,8,3,6]=>[1,2,4,5,7,3,8,6]=>0000011
[4,8,1,5,2,3,7,6]=>[5,7,1,4,2,8,3,6]=>[4,7,3,1,5,2,8,6]=>0101011
[6,5,8,7,1,3,4,2]=>[4,7,1,3,6,5,8,2]=>[4,3,1,6,5,8,2,7]=>0110101
[1,5,2,7,4,3,8,6]=>[1,4,8,5,2,7,3,6]=>[1,5,2,4,8,6,7,3]=>0001011
[6,7,8,1,5,2,4,3]=>[4,5,8,1,2,6,7,3]=>[4,1,5,2,6,7,8,3]=>0011001
[5,7,8,4,1,2,6,3]=>[6,1,4,8,5,2,7,3]=>[5,6,2,1,7,8,3,4]=>1000101
[7,5,1,6,2,3,8,4]=>[8,6,1,5,7,2,3,4]=>[6,2,8,4,5,7,3,1]=>0100111
[4,5,6,7,8,1,3,2]=>[3,8,1,4,5,6,7,2]=>[3,1,4,5,6,7,8,2]=>0100001
[8,1,3,6,7,4,5,2]=>[5,7,1,8,3,4,6,2]=>[5,3,1,8,2,7,6,4]=>0101111
[8,1,5,4,3,2,6,7]=>[3,4,5,8,1,2,6,7]=>[5,1,3,8,7,6,2,4]=>0001111
[6,5,3,1,2,7,4,8]=>[3,1,7,5,6,2,4,8]=>[7,4,5,6,2,1,3,8]=>1000110
[5,6,3,8,1,4,2,7]=>[4,8,6,3,5,1,2,7]=>[5,6,1,4,3,8,7,2]=>0010111
[4,6,3,8,2,1,5,7]=>[2,8,6,4,3,1,5,7]=>[4,8,7,5,3,6,1,2]=>0001111
[4,7,8,3,2,1,5,6]=>[2,3,8,4,1,5,7,6]=>[4,7,8,6,5,1,2,3]=>0001101
[8,1,7,2,5,4,3,6]=>[4,5,7,8,1,2,3,6]=>[7,3,8,6,2,5,1,4]=>0001111
[8,1,7,2,4,5,6,3]=>[6,7,8,1,2,4,5,3]=>[6,4,1,7,5,2,8,3]=>0011111
[8,1,6,3,2,5,7,4]=>[3,7,6,8,1,2,5,4]=>[7,5,1,3,6,2,8,4]=>0001111
[5,4,2,3,1,6,8,7]=>[3,4,2,5,1,6,8,7]=>[5,1,3,2,4,6,8,7]=>0101001
[6,3,2,1,5,7,4,8]=>[2,3,7,6,1,5,4,8]=>[7,4,6,5,1,2,3,8]=>0001110
[3,6,5,8,2,4,1,7]=>[4,8,3,2,6,5,1,7]=>[3,6,5,8,7,1,4,2]=>0010111
[5,3,7,2,4,8,1,6]=>[8,7,5,3,2,4,1,6]=>[8,6,4,3,5,2,7,1]=>0011111
[6,2,4,5,8,3,1,7]=>[3,8,6,2,4,5,1,7]=>[8,7,1,3,6,5,4,2]=>0011111
[4,6,8,3,7,2,5,1]=>[5,7,8,4,3,6,2,1]=>[4,6,7,2,8,1,5,3]=>0001011
[1,4,3,6,2,7,8,5]=>[1,8,4,3,6,2,7,5]=>[1,4,3,7,8,5,6,2]=>0010101
[8,5,7,4,3,6,1,2]=>[6,1,4,7,8,5,3,2]=>[7,3,4,8,2,1,6,5]=>1000111
[4,7,8,3,6,1,5,2]=>[5,6,8,4,3,1,7,2]=>[4,7,8,2,6,1,5,3]=>0001101
[1,3,8,6,4,7,5,2]=>[1,5,3,7,6,8,4,2]=>[1,3,7,4,8,2,5,6]=>0000011
[7,6,2,1,4,3,8,5]=>[2,4,8,1,6,7,3,5]=>[4,1,2,8,5,6,7,3]=>0010011
[7,6,8,1,4,3,2,5]=>[3,4,8,1,2,7,6,5]=>[7,6,8,5,2,4,1,3]=>0011011
[1,5,7,3,2,6,8,4]=>[1,3,8,7,5,2,6,4]=>[1,5,8,4,7,6,2,3]=>0000111
[1,6,4,7,2,3,8,5]=>[1,8,2,7,6,4,3,5]=>[1,8,5,6,4,7,3,2]=>0100111
[3,2,6,8,7,4,5,1]=>[5,3,2,7,4,6,8,1]=>[3,2,6,8,1,5,4,7]=>0101001
[3,7,1,8,4,2,5,6]=>[4,8,3,7,1,2,5,6]=>[3,7,5,1,4,8,6,2]=>0001111
[4,2,1,3,7,5,8,6]=>[2,4,1,3,8,7,5,6]=>[4,3,1,2,8,6,7,5]=>0110011
[3,6,2,8,7,1,5,4]=>[5,7,3,6,2,1,8,4]=>[3,8,4,6,1,5,2,7]=>0001101
[4,2,7,8,6,1,5,3]=>[5,6,4,2,1,8,7,3]=>[5,1,7,8,3,4,2,6]=>0011001
[5,8,4,2,7,1,6,3]=>[6,7,4,8,5,2,1,3]=>[5,7,1,6,2,8,3,4]=>0000111
[8,5,3,1,7,2,6,4]=>[6,3,7,5,8,1,2,4]=>[6,1,7,2,3,8,4,5]=>0000111
[2,1,7,3,8,6,5,4]=>[2,1,5,6,8,7,3,4]=>[2,1,8,4,6,7,3,5]=>1000011
[8,2,1,7,6,5,4,3]=>[2,4,5,6,7,8,1,3]=>[8,3,5,7,1,2,4,6]=>0000011
[6,4,7,3,2,1,8,5]=>[2,3,8,7,6,4,1,5]=>[8,5,6,4,7,1,2,3]=>0000111
[4,8,7,3,2,1,6,5]=>[2,3,6,4,7,1,8,5]=>[4,6,1,2,3,8,5,7]=>0000101
[5,8,3,6,2,1,4,7]=>[2,6,8,3,5,1,4,7]=>[5,6,1,2,8,7,4,3]=>0010111
[6,3,7,8,2,1,4,5]=>[2,8,6,3,1,4,7,5]=>[6,4,3,7,8,5,1,2]=>0011101
[5,8,4,2,6,1,3,7]=>[6,4,2,8,5,1,3,7]=>[5,6,1,8,7,3,2,4]=>0100111
[6,4,2,7,5,1,3,8]=>[5,4,2,7,6,1,3,8]=>[6,1,5,7,3,2,4,8]=>0100110
[5,4,2,6,7,1,3,8]=>[7,4,2,5,1,6,3,8]=>[6,7,3,2,4,5,1,8]=>0101010
[6,2,7,8,5,1,3,4]=>[5,8,2,1,6,3,7,4]=>[7,8,4,1,5,6,3,2]=>0110101
[5,8,3,6,1,4,7,2]=>[7,6,8,3,5,1,4,2]=>[5,8,2,6,1,7,4,3]=>0010111
[5,8,3,2,1,4,7,6]=>[2,3,7,1,5,8,4,6]=>[5,7,4,1,2,3,8,6]=>0010011
[6,3,7,2,1,4,5,8]=>[2,7,6,3,1,4,5,8]=>[6,4,3,7,5,1,2,8]=>0011110
[5,8,4,1,6,7,3,2]=>[3,7,4,8,5,1,6,2]=>[5,8,2,7,6,1,3,4]=>0000111
[4,8,7,1,5,6,3,2]=>[3,6,7,4,1,5,8,2]=>[4,8,2,6,5,1,3,7]=>0001101
[5,8,3,1,6,4,7,2]=>[7,3,6,8,5,1,4,2]=>[5,8,2,3,6,1,7,4]=>0000111
[5,8,2,1,6,4,3,7]=>[2,4,6,8,5,1,3,7]=>[5,8,7,3,6,1,2,4]=>0000111
[5,4,1,6,7,8,3,2]=>[3,8,4,5,1,6,7,2]=>[5,1,3,4,6,7,8,2]=>0001001
[4,3,1,6,5,7,8,2]=>[8,3,4,1,6,5,7,2]=>[6,5,7,8,2,3,4,1]=>0010101
[4,2,1,6,5,7,3,8]=>[2,7,4,1,6,5,3,8]=>[6,5,7,3,4,1,2,8]=>0010110
[2,8,1,6,5,4,3,7]=>[4,2,5,6,8,1,3,7]=>[2,6,1,4,8,7,3,5]=>0000111
[5,1,7,6,8,4,3,2]=>[3,4,8,5,1,7,6,2]=>[7,6,8,2,4,5,1,3]=>0001011
[4,1,7,6,5,8,3,2]=>[3,8,4,1,6,7,5,2]=>[4,1,3,7,5,6,8,2]=>0010011
[4,5,8,1,7,2,3,6]=>[7,8,1,4,5,2,3,6]=>[4,5,7,3,1,8,6,2]=>0100111
[4,5,8,1,2,6,3,7]=>[6,1,8,4,5,2,3,7]=>[4,5,6,2,1,8,7,3]=>1000111
[8,1,3,5,7,2,4,6]=>[7,8,1,3,2,5,4,6]=>[7,4,3,1,8,6,5,2]=>0111111
[3,6,8,1,7,2,4,5]=>[7,8,3,1,2,6,4,5]=>[3,6,7,4,1,8,5,2]=>0011011
[8,2,3,5,6,7,1,4]=>[7,8,2,3,1,5,6,4]=>[7,6,5,1,8,4,3,2]=>0111111
[8,7,2,1,6,3,4,5]=>[2,6,7,1,3,4,8,5]=>[6,4,1,2,8,5,3,7]=>0011101
[8,7,2,1,3,5,4,6]=>[2,5,1,7,3,4,8,6]=>[5,3,1,2,8,6,4,7]=>0101101
[8,6,4,1,7,5,3,2]=>[3,5,4,7,6,8,1,2]=>[7,1,3,4,8,2,5,6]=>0000011
[2,3,6,7,8,1,5,4]=>[5,2,3,8,1,6,7,4]=>[2,3,5,1,6,7,8,4]=>0001001
[7,3,1,8,6,2,4,5]=>[6,3,8,1,2,7,4,5]=>[7,4,1,6,8,5,2,3]=>0011011
[7,1,8,2,5,3,6,4]=>[6,5,8,7,1,2,3,4]=>[6,2,5,1,8,4,7,3]=>0001111
[7,3,8,4,5,1,6,2]=>[6,5,8,7,3,4,1,2]=>[7,1,6,4,8,2,5,3]=>0001111
[8,3,7,4,6,1,5,2]=>[5,6,7,8,3,4,1,2]=>[7,1,5,3,8,2,6,4]=>0001111
[8,2,7,1,6,4,5,3]=>[5,6,7,8,2,1,4,3]=>[6,1,5,2,8,3,7,4]=>0001111
[8,1,7,5,4,2,3,6]=>[4,5,1,7,8,2,3,6]=>[7,3,1,4,8,6,2,5]=>0100111
[8,1,2,6,5,4,3,7]=>[4,1,5,6,8,2,3,7]=>[6,2,1,4,8,7,3,5]=>1000111
[8,1,7,6,3,2,4,5]=>[3,6,7,1,2,8,4,5]=>[7,4,1,3,8,5,2,6]=>0011011
[8,2,7,5,6,1,4,3]=>[4,6,7,2,8,1,5,3]=>[6,1,4,2,8,3,7,5]=>0010111
[3,6,8,1,7,5,4,2]=>[4,5,3,7,8,6,1,2]=>[3,6,7,1,4,8,2,5]=>0000011
[8,2,6,7,5,4,1,3]=>[4,5,2,7,8,1,6,3]=>[7,6,1,4,8,3,2,5]=>0100111
[8,6,7,2,3,1,5,4]=>[3,5,2,7,1,8,6,4]=>[5,1,3,2,8,4,7,6]=>0101011
[2,7,8,6,3,1,5,4]=>[3,2,5,6,1,8,7,4]=>[2,5,1,3,7,8,4,6]=>0001001
[8,1,7,6,5,4,3,2]=>[3,4,5,6,7,8,1,2]=>[7,1,3,5,8,2,4,6]=>0000011
[2,1,8,6,3,7,4,5]=>[2,1,7,6,3,8,4,5]=>[2,1,8,5,3,7,4,6]=>1001011
[8,5,1,7,4,2,6,3]=>[6,4,7,5,8,1,2,3]=>[6,1,8,3,7,2,4,5]=>0000111
[2,1,8,4,5,3,6,7]=>[2,1,5,8,4,3,6,7]=>[2,1,8,7,6,3,5,4]=>1001111
[6,4,1,5,2,3,8,7]=>[5,4,1,6,2,3,8,7]=>[6,3,1,5,2,4,8,7]=>0101101
[5,8,3,7,6,2,1,4]=>[2,6,7,3,5,8,1,4]=>[5,8,4,3,7,1,2,6]=>0010011
[8,3,2,4,1,7,5,6]=>[4,3,7,2,8,1,5,6]=>[8,6,1,4,2,3,7,5]=>0010111
[6,3,4,2,1,7,8,5]=>[2,4,8,3,6,1,7,5]=>[7,8,5,6,1,2,4,3]=>0010101
[6,2,3,1,4,5,8,7]=>[3,6,2,1,4,5,8,7]=>[6,5,4,1,3,2,8,7]=>0111101
[6,8,1,4,5,3,2,7]=>[3,5,8,1,4,6,2,7]=>[6,8,7,2,5,4,1,3]=>0011011
[4,2,1,3,6,7,8,5]=>[2,4,1,3,8,6,7,5]=>[4,3,1,2,6,7,8,5]=>0110001
[2,3,4,1,8,6,5,7]=>[4,2,3,1,6,8,5,7]=>[2,3,4,1,8,7,5,6]=>0010011
[8,7,3,6,5,1,4,2]=>[4,5,6,3,7,1,8,2]=>[6,1,4,3,8,2,5,7]=>0010101
[4,2,3,5,8,1,6,7]=>[8,4,2,3,5,1,6,7]=>[4,3,2,5,8,7,6,1]=>0110111
[3,4,6,2,8,5,1,7]=>[5,8,3,4,6,2,1,7]=>[3,4,8,7,1,5,6,2]=>0000111
[3,4,6,8,1,5,2,7]=>[5,8,3,4,1,6,2,7]=>[3,4,5,1,6,8,7,2]=>0001011
[3,4,8,2,1,5,6,7]=>[2,8,3,4,1,5,6,7]=>[3,4,8,7,6,5,1,2]=>0001111
[3,5,2,7,4,8,6,1]=>[6,8,3,5,2,7,4,1]=>[3,8,1,6,7,4,5,2]=>0001011
[3,5,6,2,8,4,1,7]=>[4,8,3,6,5,2,1,7]=>[3,5,8,7,1,4,6,2]=>0000111
[3,5,6,8,4,1,2,7]=>[4,1,3,8,5,6,2,7]=>[3,5,6,8,7,2,1,4]=>1000011
[3,5,7,2,8,4,6,1]=>[6,8,3,7,5,2,4,1]=>[3,5,7,4,8,1,6,2]=>0000111
[3,5,7,8,4,1,6,2]=>[6,4,3,8,5,1,7,2]=>[3,5,6,1,7,8,2,4]=>0000101
[3,6,2,7,8,5,4,1]=>[4,5,3,8,6,2,7,1]=>[3,6,2,5,7,8,1,4]=>0000101
[3,6,8,2,4,5,1,7]=>[5,8,3,2,4,6,1,7]=>[3,6,8,7,1,5,4,2]=>0011011
[3,8,2,1,4,5,6,7]=>[2,8,3,1,4,5,6,7]=>[3,8,7,6,5,4,1,2]=>0011111
[4,1,5,7,3,8,6,2]=>[6,8,4,1,5,7,3,2]=>[5,7,3,4,1,6,8,2]=>0010011
[4,1,5,8,3,2,6,7]=>[3,8,4,1,5,2,6,7]=>[4,1,3,5,8,7,6,2]=>0010111
[4,1,6,3,7,8,5,2]=>[5,8,4,1,6,3,7,2]=>[6,3,4,1,5,7,8,2]=>0010101
[4,1,8,3,2,5,6,7]=>[3,8,4,1,2,5,6,7]=>[4,1,3,8,7,6,5,2]=>0011111
[4,5,2,7,3,8,6,1]=>[6,8,5,4,2,7,3,1]=>[4,8,1,6,7,3,5,2]=>0001011
[4,5,8,3,2,1,6,7]=>[2,3,8,4,5,1,6,7]=>[4,5,8,7,6,1,2,3]=>0000111
[4,6,2,3,8,5,1,7]=>[5,8,2,4,6,3,1,7]=>[4,8,7,1,5,6,3,2]=>0100111
[4,6,7,3,2,8,5,1]=>[5,3,8,4,7,6,2,1]=>[4,6,8,1,5,7,2,3]=>0000011
[4,8,2,3,1,5,6,7]=>[3,8,2,4,1,5,6,7]=>[4,8,7,6,5,1,3,2]=>0101111
[5,1,6,3,7,8,2,4]=>[8,6,5,1,3,2,7,4]=>[5,3,6,2,7,8,4,1]=>0011101
[5,6,2,7,4,8,1,3]=>[8,7,2,6,5,1,4,3]=>[5,8,3,2,7,4,6,1]=>0100111
[5,6,8,3,4,2,1,7]=>[2,4,8,3,5,6,1,7]=>[5,6,8,7,1,2,4,3]=>0010011
[6,1,7,8,4,5,3,2]=>[3,5,8,6,1,4,7,2]=>[6,4,7,8,2,5,1,3]=>0001101
[7,1,2,3,4,8,6,5]=>[6,1,2,3,8,7,4,5]=>[7,4,3,2,1,6,8,5]=>1110011
[6,4,1,8,2,3,7,5]=>[7,4,1,8,6,2,3,5]=>[7,3,1,8,5,6,2,4]=>0100111
[5,8,1,2,4,3,7,6]=>[4,1,7,2,5,8,3,6]=>[4,2,1,5,7,3,8,6]=>1010011
[2,3,5,6,8,1,7,4]=>[7,2,3,8,5,6,1,4]=>[2,3,5,6,7,1,8,4]=>0000011
[7,1,8,6,3,4,5,2]=>[5,6,8,1,3,7,4,2]=>[8,2,6,7,4,1,5,3]=>0011011
[6,7,4,5,2,1,8,3]=>[2,8,5,7,4,6,1,3]=>[6,8,3,5,4,7,1,2]=>0001011
[5,1,7,8,6,4,3,2]=>[3,4,6,5,1,8,7,2]=>[7,8,2,4,5,1,3,6]=>0001001
[2,5,7,8,6,3,1,4]=>[3,2,6,1,5,8,7,4]=>[2,5,7,8,4,1,3,6]=>0010001
[8,4,1,2,5,6,3,7]=>[6,1,4,8,2,5,3,7]=>[6,5,2,1,8,7,3,4]=>1001111
[2,5,3,8,7,6,1,4]=>[6,2,5,3,1,7,8,4]=>[2,8,4,3,5,1,6,7]=>0011001
[1,8,7,6,5,2,3,4]=>[1,5,2,3,6,7,8,4]=>[1,8,4,3,2,5,6,7]=>0110001
[8,4,7,2,5,6,3,1]=>[3,6,7,8,4,2,5,1]=>[6,2,8,1,3,7,5,4]=>0001111
[6,8,5,4,3,1,7,2]=>[7,3,4,5,8,6,1,2]=>[6,7,1,8,2,3,4,5]=>0000011
[5,8,6,4,1,3,7,2]=>[7,4,1,6,5,8,3,2]=>[5,7,3,1,8,2,4,6]=>0100011
[3,6,1,8,5,2,7,4]=>[7,5,3,8,6,1,2,4]=>[3,7,2,5,6,1,8,4]=>0000111
[7,2,5,8,3,6,1,4]=>[6,8,7,2,3,5,1,4]=>[7,1,6,5,3,8,4,2]=>0011111
[6,8,3,4,5,1,7,2]=>[7,5,8,3,4,6,1,2]=>[6,7,1,8,2,5,4,3]=>0011011
[8,3,2,1,5,4,7,6]=>[2,3,5,7,1,8,4,6]=>[5,1,2,3,7,4,8,6]=>0001011
[2,5,1,8,4,3,7,6]=>[4,2,7,5,1,8,3,6]=>[2,5,1,4,7,3,8,6]=>0001011
[4,3,1,6,5,8,2,7]=>[8,3,4,1,6,5,2,7]=>[6,5,8,7,2,3,4,1]=>0010111
[7,5,8,2,4,6,1,3]=>[6,8,2,1,7,5,4,3]=>[7,4,1,6,5,8,3,2]=>0110111
[8,2,7,4,6,1,3,5]=>[6,7,2,8,1,4,3,5]=>[7,3,2,8,5,1,6,4]=>0101111
[4,7,3,2,8,1,6,5]=>[6,3,8,4,7,2,1,5]=>[4,8,5,7,1,6,2,3]=>0000111
[8,3,2,5,7,6,1,4]=>[6,3,7,2,1,8,5,4]=>[8,4,2,3,7,5,1,6]=>0011011
[2,8,6,1,5,7,3,4]=>[7,2,6,1,3,8,5,4]=>[2,8,4,1,7,5,3,6]=>0011011
[1,2,8,3,5,6,7,4]=>[1,2,7,8,3,5,6,4]=>[1,2,7,6,5,3,8,4]=>0001111
[4,2,3,7,1,8,6,5]=>[6,4,2,3,8,7,1,5]=>[4,3,2,7,1,6,8,5]=>0110011
[3,2,6,4,8,1,7,5]=>[7,3,2,8,6,4,1,5]=>[3,2,7,1,8,5,6,4]=>0100111
[2,7,8,5,4,1,3,6]=>[4,2,1,5,8,3,7,6]=>[2,7,8,6,3,1,4,5]=>0100101
[4,7,5,3,1,2,8,6]=>[3,1,5,4,8,7,2,6]=>[4,8,6,7,2,1,3,5]=>1000011
[5,6,7,3,8,4,2,1]=>[2,4,8,7,5,6,3,1]=>[5,6,8,1,2,4,7,3]=>0000011
[5,7,3,2,4,1,8,6]=>[4,3,8,2,5,7,1,6]=>[5,8,6,7,1,4,2,3]=>0010011
[8,4,1,3,7,2,5,6]=>[7,4,1,8,3,2,5,6]=>[7,5,3,1,8,6,2,4]=>0101111
[1,7,6,3,2,5,8,4]=>[1,3,8,6,2,7,5,4]=>[1,8,4,6,7,5,2,3]=>0001011
[4,3,5,6,7,1,8,2]=>[8,7,4,3,5,6,1,2]=>[4,3,5,6,8,2,7,1]=>0010011
[7,1,5,2,8,6,4,3]=>[4,6,5,8,1,7,2,3]=>[7,2,6,8,3,5,1,4]=>0001011
[1,8,5,3,6,2,7,4]=>[1,7,6,5,8,3,2,4]=>[1,6,3,7,2,8,4,5]=>0000111
[6,5,8,7,2,1,3,4]=>[2,7,1,3,6,5,8,4]=>[6,5,8,4,3,1,2,7]=>0110101
[3,6,2,1,7,5,8,4]=>[2,8,3,7,6,1,5,4]=>[3,8,4,7,5,6,1,2]=>0000111
[6,8,1,4,2,7,3,5]=>[7,4,8,1,2,6,3,5]=>[6,8,5,2,4,1,7,3]=>0011011
[1,8,2,4,5,6,7,3]=>[1,7,8,2,4,5,6,3]=>[1,7,6,5,4,2,8,3]=>0011111
[2,1,4,6,8,5,7,3]=>[2,1,7,4,8,6,5,3]=>[2,1,4,6,8,3,7,5]=>1000011
[1,2,3,4,8,6,5,7]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,7,5,6]=>0000011
[1,2,3,8,5,4,6,7]=>[1,2,3,5,8,4,6,7]=>[1,2,3,8,7,6,4,5]=>0000111
[1,2,3,8,5,6,4,7]=>[1,2,3,6,8,5,4,7]=>[1,2,3,8,7,4,6,5]=>0000111
[1,2,3,8,6,5,4,7]=>[1,2,3,5,6,8,4,7]=>[1,2,3,8,7,4,5,6]=>0000011
[1,8,3,4,2,5,6,7]=>[1,4,8,3,2,5,6,7]=>[1,8,7,6,5,2,4,3]=>0011111
[1,8,4,3,2,5,6,7]=>[1,3,4,8,2,5,6,7]=>[1,8,7,6,5,2,3,4]=>0001111
[8,5,7,6,4,3,2,1]=>[2,3,4,6,7,8,5,1]=>[7,5,8,1,2,3,4,6]=>0000011
[8,4,7,6,5,3,2,1]=>[2,3,5,6,7,8,4,1]=>[8,1,2,3,5,7,4,6]=>0000011
[8,6,7,3,5,4,2,1]=>[2,4,5,7,3,8,6,1]=>[5,3,8,1,2,4,7,6]=>0001011
[8,4,7,3,6,5,2,1]=>[2,5,6,7,8,4,3,1]=>[7,3,6,4,8,1,2,5]=>0000111
[8,1,7,4,6,5,3,2]=>[3,5,6,7,8,1,4,2]=>[6,1,3,7,4,8,2,5]=>0000111
[8,3,7,2,6,5,4,1]=>[4,5,6,7,8,3,2,1]=>[6,3,8,1,4,7,2,5]=>0000111
[8,4,7,1,6,5,3,2]=>[3,5,6,7,8,4,1,2]=>[7,1,3,6,4,8,2,5]=>0000111
[8,3,7,1,6,5,4,2]=>[4,5,6,7,8,3,1,2]=>[6,3,7,1,4,8,2,5]=>0000111
[8,1,7,2,6,5,4,3]=>[4,5,6,7,8,1,2,3]=>[8,3,6,1,4,7,2,5]=>0000111
[8,3,7,1,6,4,5,2]=>[5,6,7,8,3,1,4,2]=>[8,2,6,1,5,3,7,4]=>0001111
[8,7,6,2,5,3,4,1]=>[4,5,6,2,3,7,8,1]=>[8,1,4,2,5,3,6,7]=>0011001
[8,6,7,2,5,3,4,1]=>[4,5,7,2,3,8,6,1]=>[8,1,4,2,5,3,7,6]=>0011011
[8,5,7,2,6,3,4,1]=>[4,6,7,2,8,5,3,1]=>[7,3,8,1,4,2,6,5]=>0010111
[8,4,7,2,6,3,5,1]=>[5,6,7,8,4,2,3,1]=>[6,2,7,3,8,1,5,4]=>0001111
[8,3,7,2,6,4,5,1]=>[5,6,7,8,3,2,4,1]=>[6,2,8,1,5,3,7,4]=>0001111
[8,2,7,3,6,4,5,1]=>[5,6,7,8,2,3,4,1]=>[8,1,5,2,6,3,7,4]=>0001111
[8,3,7,4,6,2,5,1]=>[5,6,7,8,3,4,2,1]=>[8,1,5,3,7,2,6,4]=>0001111
[8,5,7,3,6,2,4,1]=>[4,6,7,3,8,5,2,1]=>[8,1,4,3,7,2,6,5]=>0010111
[8,6,7,3,5,2,4,1]=>[4,5,7,3,2,8,6,1]=>[5,2,8,1,4,3,7,6]=>0011011
[8,5,7,4,6,2,3,1]=>[3,6,2,7,8,5,4,1]=>[7,4,8,1,3,2,6,5]=>0100111
[8,4,7,5,6,2,3,1]=>[3,6,2,7,8,4,5,1]=>[8,1,3,2,6,4,7,5]=>0100111
[8,3,7,5,6,2,4,1]=>[4,6,7,3,8,2,5,1]=>[6,2,8,1,4,3,7,5]=>0010111
[8,2,7,5,6,3,4,1]=>[4,6,7,2,8,3,5,1]=>[8,1,4,2,6,3,7,5]=>0010111
[8,5,7,6,4,2,3,1]=>[3,4,2,6,7,8,5,1]=>[7,5,8,1,3,2,4,6]=>0100011
[8,7,6,5,4,1,3,2]=>[3,4,1,5,6,7,8,2]=>[3,1,8,2,4,5,6,7]=>0100001
[8,5,7,6,4,1,3,2]=>[3,4,1,6,7,8,5,2]=>[3,1,7,5,8,2,4,6]=>0100011
[8,3,7,5,6,1,4,2]=>[4,6,7,3,8,1,5,2]=>[8,2,6,1,4,3,7,5]=>0010111
[8,4,7,5,6,1,3,2]=>[3,6,1,7,8,4,5,2]=>[3,1,8,2,6,4,7,5]=>0100111
[8,6,7,4,5,1,3,2]=>[3,5,1,7,4,8,6,2]=>[3,1,8,2,5,4,7,6]=>0101011
[8,7,6,4,5,1,3,2]=>[3,5,1,6,4,7,8,2]=>[3,1,8,2,5,4,6,7]=>0101001
[8,6,7,3,5,1,4,2]=>[4,5,7,3,1,8,6,2]=>[8,2,5,1,4,3,7,6]=>0011011
[8,4,7,3,6,1,5,2]=>[5,6,7,8,4,3,1,2]=>[8,2,6,3,7,1,5,4]=>0001111
[8,1,7,3,6,2,5,4]=>[5,6,7,8,1,3,2,4]=>[5,1,7,2,6,3,8,4]=>0001111
[8,3,7,2,6,1,5,4]=>[5,6,7,8,3,2,1,4]=>[6,2,7,1,5,3,8,4]=>0001111
[8,4,7,2,6,1,5,3]=>[5,6,7,8,4,2,1,3]=>[6,2,8,3,7,1,5,4]=>0001111
[8,5,7,2,6,1,4,3]=>[4,6,7,2,8,5,1,3]=>[8,3,7,1,4,2,6,5]=>0010111
[8,6,7,2,5,1,4,3]=>[4,5,7,2,1,8,6,3]=>[5,1,4,2,8,3,7,6]=>0011011
[8,7,6,2,5,1,4,3]=>[4,5,6,2,1,7,8,3]=>[5,1,4,2,8,3,6,7]=>0011001
[8,7,6,1,5,2,4,3]=>[4,5,6,1,2,7,8,3]=>[4,1,5,2,8,3,6,7]=>0011001
[8,4,7,1,6,2,5,3]=>[5,6,7,8,4,1,2,3]=>[8,3,7,2,6,1,5,4]=>0001111
[1,4,8,2,6,3,5,7]=>[1,6,8,4,2,3,5,7]=>[1,4,8,7,5,2,6,3]=>0001111
[1,8,2,3,5,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,5,3,2,8,7,6,4]=>0101111
[1,5,8,2,3,7,4,6]=>[1,7,2,8,5,3,4,6]=>[1,5,8,6,3,2,7,4]=>0100111
[1,6,8,2,3,5,4,7]=>[1,5,2,8,3,6,4,7]=>[1,5,3,2,6,8,7,4]=>0101011
[5,7,1,6,8,4,3,2]=>[3,4,8,7,5,1,6,2]=>[5,8,2,4,7,6,1,3]=>0000111
[1,7,8,4,6,2,5,3]=>[1,5,6,8,4,2,7,3]=>[1,7,8,3,6,2,5,4]=>0001101
[3,7,4,8,5,1,6,2]=>[6,5,3,8,7,4,1,2]=>[3,8,2,5,7,1,6,4]=>0000111
[3,7,5,4,8,2,1,6]=>[2,8,3,5,7,4,1,6]=>[3,8,6,4,5,7,1,2]=>0000111
[4,3,2,1,5,8,6,7]=>[2,3,4,1,5,8,6,7]=>[4,1,2,3,5,8,7,6]=>0010011
[4,1,3,7,5,6,8,2]=>[8,4,1,3,7,5,6,2]=>[7,6,5,8,2,4,3,1]=>0110111
[6,8,5,7,1,2,4,3]=>[4,1,7,2,8,6,5,3]=>[4,2,1,6,8,3,7,5]=>1010011
[7,1,3,4,2,8,5,6]=>[4,8,1,3,7,2,5,6]=>[4,3,1,7,5,8,6,2]=>0110111
[2,4,8,3,6,1,7,5]=>[7,2,6,4,8,3,1,5]=>[2,4,6,3,7,1,8,5]=>0000111
[8,2,4,3,7,5,6,1]=>[6,4,7,2,8,3,5,1]=>[4,2,8,1,6,3,7,5]=>0010111
[7,1,5,6,8,4,3,2]=>[3,4,8,7,1,5,6,2]=>[8,2,4,7,6,5,1,3]=>0001111
[2,7,6,5,3,8,1,4]=>[8,2,5,3,6,7,1,4]=>[2,8,4,3,5,6,7,1]=>0010011
[2,7,8,1,4,6,3,5]=>[6,2,8,1,4,3,7,5]=>[2,7,8,5,4,1,6,3]=>0011101
[4,8,2,5,7,1,6,3]=>[6,7,8,4,2,5,1,3]=>[4,7,1,6,5,2,8,3]=>0001111
[4,1,6,8,5,3,7,2]=>[7,5,4,1,8,6,3,2]=>[6,7,3,4,1,8,2,5]=>0010011
[6,7,1,3,4,5,8,2]=>[8,7,1,3,4,6,5,2]=>[6,8,2,7,5,4,3,1]=>0111011
[1,7,3,2,4,8,5,6]=>[1,3,8,2,7,4,5,6]=>[1,7,5,8,6,4,2,3]=>0010111
[5,8,6,7,2,1,4,3]=>[2,4,7,1,5,8,6,3]=>[4,1,2,5,8,3,7,6]=>0010011
[6,3,4,2,8,7,5,1]=>[5,4,7,3,6,2,8,1]=>[8,1,5,6,2,4,3,7]=>0010101
[4,3,8,7,5,2,6,1]=>[6,5,4,3,7,2,8,1]=>[4,3,8,1,6,2,5,7]=>0010101
[8,6,1,3,5,4,2,7]=>[4,5,1,6,3,8,2,7]=>[8,7,2,5,3,1,4,6]=>0101011
[2,7,6,3,4,5,8,1]=>[8,2,6,3,4,7,5,1]=>[2,7,5,4,3,6,8,1]=>0011011
[2,4,8,7,3,5,6,1]=>[6,2,7,4,3,5,8,1]=>[2,4,8,1,6,5,3,7]=>0001101
[3,8,7,2,6,4,5,1]=>[5,6,3,7,2,4,8,1]=>[3,8,1,5,2,6,4,7]=>0001101
[8,5,2,7,1,4,3,6]=>[4,7,5,2,8,1,3,6]=>[8,6,1,4,2,7,3,5]=>0010111
[4,5,2,8,3,7,6,1]=>[6,7,5,4,2,8,3,1]=>[4,7,3,5,2,8,1,6]=>0001011
[4,1,3,8,2,6,7,5]=>[7,4,1,3,8,2,6,5]=>[7,6,2,4,3,1,8,5]=>0110111
[3,2,1,6,4,8,5,7]=>[2,3,1,8,6,4,5,7]=>[3,1,2,8,7,5,6,4]=>0100111
[2,1,8,5,4,3,6,7]=>[2,1,4,5,8,3,6,7]=>[2,1,8,7,6,3,4,5]=>1000111
[2,7,4,1,5,3,8,6]=>[5,2,4,8,1,7,3,6]=>[2,5,1,8,6,7,3,4]=>0001011
[7,3,2,4,8,6,1,5]=>[6,3,8,2,4,7,1,5]=>[7,1,6,8,5,4,2,3]=>0011011
[1,3,4,8,6,5,2,7]=>[1,5,3,4,6,8,2,7]=>[1,3,4,8,7,2,5,6]=>0000011
[4,8,5,3,6,2,7,1]=>[7,6,5,4,8,3,2,1]=>[4,8,1,7,2,6,3,5]=>0000111
[7,5,2,8,4,6,1,3]=>[6,8,2,5,7,1,4,3]=>[6,1,7,4,5,8,3,2]=>0100111
[7,6,2,4,5,8,3,1]=>[3,8,6,2,4,7,5,1]=>[8,1,3,6,7,5,4,2]=>0011011
[6,2,7,5,8,3,1,4]=>[3,8,7,2,6,1,5,4]=>[7,5,6,1,3,8,4,2]=>0010111
[2,1,5,6,8,3,7,4]=>[2,1,7,8,5,6,3,4]=>[2,1,5,6,7,3,8,4]=>1000011
[1,2,7,4,8,3,6,5]=>[1,2,6,8,7,4,3,5]=>[1,2,8,5,7,3,6,4]=>0000111
[1,6,8,3,2,7,4,5]=>[1,3,7,8,2,6,4,5]=>[1,6,8,5,2,3,7,4]=>0001011
[5,4,8,3,6,2,7,1]=>[7,6,8,5,4,3,2,1]=>[5,4,8,1,7,2,6,3]=>0001111
[5,7,3,8,2,4,6,1]=>[6,8,7,3,5,2,4,1]=>[5,7,4,3,8,1,6,2]=>0010111
[1,2,8,3,7,5,4,6]=>[1,2,5,7,8,3,4,6]=>[1,2,7,4,8,6,3,5]=>0000111
[1,6,3,8,7,4,2,5]=>[1,4,7,6,3,2,8,5]=>[1,6,2,4,8,5,3,7]=>0001101
[7,4,6,5,2,1,8,3]=>[2,8,5,6,7,4,1,3]=>[6,4,8,3,5,7,1,2]=>0000111
[3,8,5,7,1,4,2,6]=>[4,7,3,1,8,5,2,6]=>[3,4,1,7,2,8,6,5]=>0010111
[5,2,8,4,7,3,1,6]=>[3,7,8,5,2,4,1,6]=>[8,6,4,5,2,7,1,3]=>0001111
[6,3,2,1,4,8,7,5]=>[2,3,7,1,6,4,8,5]=>[8,5,6,4,1,2,3,7]=>0010101
[6,3,5,1,7,4,2,8]=>[4,7,5,6,3,1,2,8]=>[5,3,6,1,4,7,2,8]=>0001110
[4,6,3,7,5,8,1,2]=>[8,1,7,4,6,3,5,2]=>[4,7,5,6,3,8,2,1]=>1000111
[3,8,1,6,7,5,4,2]=>[4,5,3,7,8,1,6,2]=>[3,7,6,1,4,8,2,5]=>0000111
[3,7,2,6,8,5,1,4]=>[5,8,3,2,7,1,6,4]=>[3,7,6,1,5,8,4,2]=>0010111
[8,2,4,3,6,1,5,7]=>[6,4,8,2,3,1,5,7]=>[4,2,6,1,8,7,5,3]=>0011111
[7,3,8,1,4,2,6,5]=>[4,6,8,3,7,1,2,5]=>[8,5,7,2,6,1,4,3]=>0010111
[3,8,7,4,2,6,1,5]=>[6,4,3,7,2,1,8,5]=>[3,6,1,8,5,2,4,7]=>0001101
[3,7,8,1,2,6,5,4]=>[5,1,3,6,8,2,7,4]=>[3,7,8,4,6,2,1,5]=>1000101
[8,1,7,6,2,4,3,5]=>[4,6,7,1,2,8,3,5]=>[4,1,7,3,8,5,2,6]=>0011011
[1,7,5,3,6,8,4,2]=>[1,4,8,5,7,3,6,2]=>[1,8,2,4,5,7,6,3]=>0000111
[6,4,2,8,7,5,1,3]=>[5,4,2,7,6,1,8,3]=>[6,1,5,8,3,2,4,7]=>0100101
[3,5,4,6,1,8,2,7]=>[8,6,3,5,4,1,2,7]=>[3,5,4,8,7,2,6,1]=>0001111
[5,3,6,4,2,8,1,7]=>[8,4,6,5,3,2,1,7]=>[6,2,4,5,3,8,7,1]=>0001111
[2,5,7,3,6,8,1,4]=>[8,2,7,3,5,1,6,4]=>[2,5,8,4,3,7,6,1]=>0010111
[8,2,6,4,7,3,1,5]=>[3,7,6,8,2,4,1,5]=>[8,5,2,7,1,3,6,4]=>0001111
[8,6,1,7,4,5,2,3]=>[5,7,1,6,2,8,4,3]=>[8,3,1,5,2,7,4,6]=>0101011
[1,2,8,3,5,4,6,7]=>[1,2,5,8,3,4,6,7]=>[1,2,5,3,8,7,6,4]=>0001111
[6,2,7,1,8,4,5,3]=>[5,8,7,6,2,1,4,3]=>[8,3,7,4,6,1,5,2]=>0001111
[3,7,2,1,8,4,5,6]=>[2,8,3,7,1,4,5,6]=>[3,8,6,4,7,5,1,2]=>0001111
[4,3,1,6,8,2,7,5]=>[7,3,4,1,8,6,2,5]=>[6,7,2,3,4,1,8,5]=>0010011
[5,3,4,6,8,2,7,1]=>[7,8,5,3,4,6,2,1]=>[5,4,3,6,8,1,7,2]=>0011011
[3,5,1,6,8,2,7,4]=>[7,8,3,5,1,6,2,4]=>[3,6,8,4,5,1,7,2]=>0001011
[7,3,8,2,6,4,1,5]=>[4,6,8,7,3,2,1,5]=>[6,2,7,1,4,8,5,3]=>0001111
[3,8,7,4,5,6,1,2]=>[6,1,3,7,4,5,8,2]=>[3,8,2,1,6,5,4,7]=>1001101
[5,8,3,7,6,2,4,1]=>[4,6,7,3,5,8,2,1]=>[5,8,1,4,3,7,2,6]=>0010011
[8,7,2,5,4,3,1,6]=>[3,4,5,7,2,1,8,6]=>[8,6,1,3,5,2,4,7]=>0001101
[5,8,6,4,3,7,1,2]=>[7,1,4,6,5,8,3,2]=>[5,8,2,1,7,3,4,6]=>1000011
[6,5,8,4,3,1,7,2]=>[7,3,4,8,6,5,1,2]=>[6,5,7,1,8,2,3,4]=>0000111
[5,4,8,7,1,6,3,2]=>[3,6,7,5,4,1,8,2]=>[5,4,8,2,6,1,3,7]=>0001101
[4,8,5,6,7,1,2,3]=>[7,1,2,4,8,5,6,3]=>[4,8,3,2,1,7,6,5]=>1100111
[5,4,8,6,1,7,2,3]=>[7,6,1,5,4,8,2,3]=>[5,4,8,3,1,7,2,6]=>0101011
[5,2,1,8,6,7,3,4]=>[2,7,5,1,3,8,6,4]=>[5,3,8,4,1,2,7,6]=>0011011
[6,5,4,8,2,1,7,3]=>[2,7,8,5,6,4,1,3]=>[6,4,5,7,1,2,8,3]=>0000111
[6,4,3,2,1,8,7,5]=>[2,3,4,7,6,1,8,5]=>[8,5,6,1,2,3,4,7]=>0000101
[6,3,4,1,2,8,7,5]=>[4,1,7,3,6,2,8,5]=>[8,5,6,2,1,4,3,7]=>1010101
[4,3,6,1,5,2,7,8]=>[5,6,4,3,1,2,7,8]=>[4,3,5,1,6,2,7,8]=>0011100
[3,5,4,7,1,6,2,8]=>[6,7,3,5,4,1,2,8]=>[3,5,4,6,1,7,2,8]=>0001110
[2,1,7,3,5,4,8,6]=>[2,1,5,8,3,7,4,6]=>[2,1,5,3,8,6,7,4]=>1001011
[2,1,7,3,6,4,8,5]=>[2,1,8,6,7,3,4,5]=>[2,1,8,5,7,4,6,3]=>1000111
[2,1,7,3,8,4,6,5]=>[2,1,6,8,7,3,4,5]=>[2,1,6,3,8,5,7,4]=>1000111
[8,1,4,2,7,3,6,5]=>[6,4,7,1,8,2,3,5]=>[6,2,4,1,7,3,8,5]=>0010111
[4,1,7,2,8,3,6,5]=>[6,8,4,1,7,2,3,5]=>[8,5,7,3,4,1,6,2]=>0010111
[7,1,8,2,4,3,6,5]=>[4,6,8,1,7,2,3,5]=>[4,1,6,2,8,5,7,3]=>0010111
[7,1,5,2,8,3,6,4]=>[6,8,5,7,1,2,3,4]=>[8,4,7,3,5,1,6,2]=>0001111
[4,1,7,2,5,3,8,6]=>[5,8,4,1,2,7,3,6]=>[8,6,7,3,4,1,5,2]=>0011011
[4,1,7,2,6,3,8,5]=>[8,6,4,1,7,2,3,5]=>[6,2,8,5,7,3,4,1]=>0010111
[5,1,7,2,6,3,8,4]=>[8,6,7,5,1,2,3,4]=>[6,2,7,3,8,4,5,1]=>0001111
[5,1,7,2,8,3,6,4]=>[6,8,7,5,1,2,3,4]=>[7,3,8,4,5,1,6,2]=>0001111
[8,1,5,2,7,3,6,4]=>[6,7,5,8,1,2,3,4]=>[7,3,5,1,6,2,8,4]=>0001111
[5,1,8,2,6,3,7,4]=>[7,6,8,5,1,2,3,4]=>[6,2,8,4,5,1,7,3]=>0001111
[5,1,6,2,8,3,7,4]=>[7,8,6,5,1,2,3,4]=>[8,4,5,1,7,3,6,2]=>0001111
[3,1,6,2,8,4,7,5]=>[7,3,1,8,6,2,4,5]=>[8,5,6,2,3,1,7,4]=>0100111
[4,1,8,2,6,3,7,5]=>[7,6,4,1,8,2,3,5]=>[6,2,7,3,4,1,8,5]=>0010111
[4,1,5,2,8,3,7,6]=>[7,5,4,1,2,8,3,6]=>[5,2,7,3,4,1,8,6]=>0011011
[3,1,5,2,8,4,7,6]=>[7,3,1,5,2,8,4,6]=>[7,4,5,2,3,1,8,6]=>0101011
[6,1,3,2,8,4,7,5]=>[3,7,1,8,6,2,4,5]=>[3,1,8,5,6,2,7,4]=>0100111
[5,1,3,2,7,4,8,6]=>[3,8,1,5,2,7,4,6]=>[3,1,8,6,7,4,5,2]=>0101011
[5,1,3,2,6,4,8,7]=>[3,6,1,5,2,4,8,7]=>[3,1,6,4,5,2,8,7]=>0101101
[5,1,4,2,6,3,8,7]=>[6,4,5,1,2,3,8,7]=>[6,3,5,2,4,1,8,7]=>0011101
[6,1,4,2,7,3,8,5]=>[8,4,7,1,6,2,3,5]=>[7,3,8,5,6,2,4,1]=>0010111
[6,1,5,2,7,3,8,4]=>[8,7,5,6,1,2,3,4]=>[8,4,6,2,7,3,5,1]=>0001111
[6,1,7,2,8,3,5,4]=>[5,8,7,6,1,2,3,4]=>[5,1,7,3,8,4,6,2]=>0001111
[5,1,6,2,4,3,8,7]=>[4,6,5,1,2,3,8,7]=>[4,1,6,3,5,2,8,7]=>0011101
[6,2,8,1,3,5,4,7]=>[5,8,2,6,1,3,4,7]=>[5,1,8,7,4,6,3,2]=>0101111
[4,3,1,2,7,8,6,5]=>[3,1,4,2,6,8,7,5]=>[4,2,1,3,7,8,5,6]=>1010001
[5,3,4,7,8,6,1,2]=>[6,1,5,3,4,8,7,2]=>[5,4,3,7,8,2,1,6]=>1011001
[4,1,3,2,6,8,7,5]=>[3,4,1,2,7,6,8,5]=>[3,1,4,2,6,8,5,7]=>0110001
[5,1,3,7,2,6,8,4]=>[8,7,1,5,3,2,6,4]=>[7,6,2,8,4,5,3,1]=>0101111
[2,5,4,6,8,1,7,3]=>[7,2,8,5,4,6,1,3]=>[2,5,4,6,7,1,8,3]=>0001011
[4,2,5,7,6,1,8,3]=>[8,6,4,2,5,7,1,3]=>[5,8,3,4,2,6,7,1]=>0010011
[4,3,5,7,6,8,1,2]=>[8,1,4,3,5,7,6,2]=>[4,3,5,7,6,8,2,1]=>1010011
[4,2,1,3,7,6,8,5]=>[2,4,1,3,8,7,6,5]=>[4,3,1,2,7,6,8,5]=>0110011
[2,4,3,1,8,5,7,6]=>[3,2,4,1,7,8,5,6]=>[2,4,1,3,7,5,8,6]=>0010011
[3,2,4,1,8,6,5,7]=>[4,3,2,1,6,8,5,7]=>[3,2,4,1,8,7,5,6]=>0110011
[3,4,2,1,8,7,5,6]=>[2,4,3,1,7,5,8,6]=>[3,4,1,2,8,6,5,7]=>0010101
[7,6,4,3,2,1,8,5]=>[2,3,4,8,6,7,1,5]=>[8,5,6,7,1,2,3,4]=>0000011
[7,8,4,3,2,1,6,5]=>[2,3,4,6,8,1,7,5]=>[6,1,2,3,4,7,8,5]=>0000101
[7,4,8,3,2,1,6,5]=>[2,3,6,8,7,4,1,5]=>[8,5,7,1,2,3,6,4]=>0000111
[4,8,7,2,6,5,1,3]=>[5,6,2,4,7,1,8,3]=>[4,8,3,2,6,1,5,7]=>0100101
[4,7,8,2,6,1,5,3]=>[5,6,8,4,2,1,7,3]=>[4,6,1,5,2,7,8,3]=>0001101
[8,4,7,3,6,5,1,2]=>[5,1,6,7,8,4,3,2]=>[7,3,6,4,8,2,1,5]=>1000111
[7,4,8,3,6,1,5,2]=>[5,6,8,7,4,3,1,2]=>[7,1,5,4,8,2,6,3]=>0001111
[6,8,4,3,7,2,1,5]=>[2,7,4,8,3,6,1,5]=>[6,7,1,2,8,5,3,4]=>0001011
[6,7,4,2,8,3,1,5]=>[3,8,4,7,2,6,1,5]=>[6,7,1,3,4,8,5,2]=>0001011
[2,8,7,6,5,1,4,3]=>[4,2,5,1,6,7,8,3]=>[2,4,1,8,3,5,6,7]=>0010001
[7,3,2,5,4,1,6,8]=>[4,3,5,7,2,1,6,8]=>[5,2,3,7,6,1,4,8]=>0001110
[1,8,4,6,5,3,2,7]=>[1,3,5,6,8,4,2,7]=>[1,6,4,8,7,2,3,5]=>0000111
[3,6,2,1,4,8,5,7]=>[2,8,3,1,6,4,5,7]=>[3,8,7,5,6,4,1,2]=>0010111
[3,1,2,8,6,5,4,7]=>[3,1,2,5,6,8,4,7]=>[3,2,1,8,7,4,5,6]=>1100011
[5,4,8,6,1,2,3,7]=>[6,1,2,5,4,8,3,7]=>[5,4,8,7,3,2,1,6]=>1101011
[6,4,8,5,3,1,7,2]=>[7,3,5,8,6,4,1,2]=>[7,1,8,2,3,5,6,4]=>0000111
[5,7,8,6,1,3,2,4]=>[3,6,1,2,5,8,7,4]=>[3,1,5,7,8,4,2,6]=>0110001
[2,4,8,1,6,3,7,5]=>[7,2,6,4,8,1,3,5]=>[2,4,7,3,6,1,8,5]=>0000111
[3,7,5,4,6,8,2,1]=>[2,8,3,5,7,4,6,1]=>[3,7,6,4,5,8,1,2]=>0000111
[5,6,1,4,7,2,8,3]=>[8,7,6,1,5,4,2,3]=>[5,7,2,8,3,6,4,1]=>0010111
[4,3,1,7,5,6,8,2]=>[8,3,4,1,7,5,6,2]=>[7,6,5,8,2,3,4,1]=>0010111
[5,3,2,1,4,8,6,7]=>[2,3,5,1,4,8,6,7]=>[5,4,1,2,3,8,7,6]=>0011011
[3,4,7,8,1,2,6,5]=>[6,1,3,4,8,2,7,5]=>[3,4,6,2,1,7,8,5]=>1000101
[3,6,7,8,1,4,5,2]=>[5,8,3,1,4,6,7,2]=>[3,5,4,1,6,7,8,2]=>0011001
[3,1,6,4,8,2,5,7]=>[8,3,1,6,4,2,5,7]=>[8,7,5,4,6,2,3,1]=>0101111
[7,5,4,8,3,6,2,1]=>[2,6,8,5,7,4,3,1]=>[8,1,2,6,4,5,7,3]=>0000111
[7,3,2,5,8,4,6,1]=>[6,3,8,7,2,5,4,1]=>[7,4,8,1,6,5,2,3]=>0001111
[2,7,1,3,5,4,8,6]=>[5,2,1,8,3,7,4,6]=>[2,5,3,1,8,6,7,4]=>0101011
[1,2,7,3,4,8,6,5]=>[1,2,6,3,8,7,4,5]=>[1,2,7,4,3,6,8,5]=>0010011
[2,3,4,8,1,6,5,7]=>[6,2,3,4,8,1,5,7]=>[2,3,4,6,1,8,7,5]=>0000111
[3,1,4,8,2,6,7,5]=>[7,3,1,4,8,2,6,5]=>[4,7,6,2,3,1,8,5]=>0100111
[4,7,3,5,6,1,8,2]=>[8,6,7,4,3,5,1,2]=>[4,8,2,6,5,3,7,1]=>0001111
[1,2,5,8,3,7,4,6]=>[1,2,7,8,5,3,4,6]=>[1,2,5,8,6,3,7,4]=>0000111
[8,2,4,1,7,5,6,3]=>[6,4,7,2,8,1,5,3]=>[4,2,6,1,8,3,7,5]=>0010111
[2,1,8,6,7,3,5,4]=>[2,1,5,7,3,8,6,4]=>[2,1,5,3,8,4,7,6]=>1001011
[7,3,2,5,6,1,4,8]=>[6,3,7,2,1,5,4,8]=>[6,5,1,7,4,2,3,8]=>0011110
[1,5,2,8,6,3,7,4]=>[1,7,6,5,2,8,3,4]=>[1,8,4,5,2,7,3,6]=>0001011
[7,8,1,4,2,5,3,6]=>[5,4,8,1,2,3,7,6]=>[5,2,4,1,7,8,6,3]=>0011101
[5,6,2,7,1,3,4,8]=>[7,6,2,1,5,3,4,8]=>[5,6,3,2,7,4,1,8]=>0110110
[1,6,2,7,4,8,3,5]=>[1,8,7,6,2,4,3,5]=>[1,6,4,7,3,8,5,2]=>0001111
[2,1,7,8,6,3,4,5]=>[2,1,6,3,4,8,7,5]=>[2,1,7,8,5,4,3,6]=>1011001
[5,2,6,3,4,1,8,7]=>[4,6,5,2,3,1,8,7]=>[5,3,6,1,4,2,8,7]=>0011101
[4,1,2,6,5,3,8,7]=>[5,1,4,2,6,3,8,7]=>[6,3,4,2,1,5,8,7]=>1010101
[3,8,5,1,7,2,4,6]=>[7,5,3,1,8,2,4,6]=>[3,7,4,1,8,6,2,5]=>0010111
[2,1,7,4,8,5,6,3]=>[2,1,6,8,7,4,5,3]=>[2,1,7,5,8,3,6,4]=>1000111
[2,5,1,8,7,4,6,3]=>[6,2,7,5,1,4,8,3]=>[2,6,4,5,1,8,3,7]=>0001101
[2,1,6,3,4,8,7,5]=>[2,1,7,3,6,4,8,5]=>[2,1,8,5,6,4,3,7]=>1010101
[4,6,7,2,5,8,3,1]=>[3,8,7,4,2,6,5,1]=>[4,6,8,1,3,7,5,2]=>0001011
[8,1,3,2,5,6,7,4]=>[3,7,1,8,2,5,6,4]=>[3,1,7,6,5,2,8,4]=>0101111
[6,3,8,5,7,4,2,1]=>[2,4,7,8,6,3,5,1]=>[7,5,6,3,8,1,2,4]=>0000111
[2,8,5,3,6,7,1,4]=>[7,2,5,3,8,1,6,4]=>[2,7,6,1,8,4,3,5]=>0010111
[3,8,1,4,5,6,2,7]=>[6,8,3,1,4,5,2,7]=>[3,6,5,4,1,8,7,2]=>0011111
[5,8,7,3,6,1,4,2]=>[4,6,7,3,5,1,8,2]=>[5,8,2,6,1,4,3,7]=>0010101
[7,5,8,4,6,1,3,2]=>[3,6,1,8,7,5,4,2]=>[3,1,8,2,6,5,7,4]=>0100111
[2,4,8,1,3,7,6,5]=>[6,2,1,4,7,8,3,5]=>[2,4,8,5,7,3,1,6]=>0100011
[2,6,1,3,8,7,5,4]=>[5,2,1,7,6,3,8,4]=>[2,6,3,1,5,8,4,7]=>0100101
[8,5,2,1,6,3,7,4]=>[2,7,6,5,8,1,3,4]=>[7,3,6,1,2,8,4,5]=>0000111
[3,5,6,8,7,1,4,2]=>[4,7,3,1,5,6,8,2]=>[3,4,1,5,6,8,2,7]=>0010001
[3,6,1,7,4,8,2,5]=>[8,7,3,6,1,4,2,5]=>[3,6,4,7,2,8,5,1]=>0001111
[8,4,2,6,3,1,5,7]=>[3,6,4,8,2,1,5,7]=>[8,7,5,2,6,1,3,4]=>0001111
[4,1,8,5,7,3,6,2]=>[6,7,4,1,8,5,3,2]=>[8,2,7,3,4,1,6,5]=>0010111
[3,4,8,7,1,2,6,5]=>[6,1,3,4,7,2,8,5]=>[3,4,6,2,1,8,5,7]=>1000101
[3,4,6,8,5,7,1,2]=>[7,1,3,4,8,6,5,2]=>[3,4,6,8,2,1,7,5]=>1000011
[4,6,8,3,5,7,2,1]=>[2,7,8,4,3,6,5,1]=>[4,6,8,1,2,7,5,3]=>0001011
[5,6,8,3,7,2,1,4]=>[2,7,8,3,5,6,1,4]=>[5,6,7,1,2,8,4,3]=>0010011
[5,6,8,4,2,7,3,1]=>[3,7,4,8,5,6,2,1]=>[5,6,7,2,8,1,3,4]=>0000011
[6,5,4,1,7,2,8,3]=>[8,7,4,5,6,1,2,3]=>[7,2,8,3,4,5,6,1]=>0000111
[6,8,5,7,4,3,2,1]=>[2,3,4,7,8,6,5,1]=>[6,8,1,2,3,4,7,5]=>0000011
[7,4,2,6,3,5,1,8]=>[5,6,4,7,2,3,1,8]=>[7,1,5,2,6,3,4,8]=>0001110
[1,6,8,4,2,5,3,7]=>[1,5,4,8,2,6,3,7]=>[1,5,2,6,8,7,3,4]=>0001011
[3,6,8,4,1,7,5,2]=>[5,4,3,7,8,6,1,2]=>[3,6,8,2,4,7,1,5]=>0000011
[8,7,2,3,6,1,4,5]=>[6,7,2,3,1,4,8,5]=>[8,5,1,6,4,3,2,7]=>0111101
[1,4,8,5,2,6,7,3]=>[1,7,5,4,8,2,6,3]=>[1,4,7,6,2,8,3,5]=>0000111
[8,1,2,3,6,5,7,4]=>[7,1,2,6,8,3,5,4]=>[8,4,6,3,2,1,7,5]=>1100111
[6,1,8,4,3,7,2,5]=>[7,4,8,6,1,3,2,5]=>[8,5,1,7,2,4,6,3]=>0001111
[3,2,6,4,1,8,7,5]=>[4,3,2,7,6,1,8,5]=>[3,2,8,5,6,1,4,7]=>0100101
[8,4,6,5,1,7,2,3]=>[7,5,1,6,8,4,2,3]=>[6,4,8,3,1,7,2,5]=>0100111
[3,2,5,6,1,7,8,4]=>[8,3,2,6,5,1,7,4]=>[3,2,5,7,8,4,6,1]=>0100101
[8,2,7,6,5,1,3,4]=>[5,6,2,1,7,8,3,4]=>[8,4,1,5,7,3,2,6]=>0110011
[1,8,6,7,2,3,4,5]=>[1,7,2,3,4,8,6,5]=>[1,8,5,4,3,2,7,6]=>0111011
[7,6,3,2,1,8,5,4]=>[2,3,5,8,6,7,1,4]=>[7,1,2,3,5,6,8,4]=>0000011
[5,2,3,4,7,1,8,6]=>[8,5,2,3,4,7,1,6]=>[5,4,3,2,8,6,7,1]=>0111011
[8,6,3,1,4,5,7,2]=>[7,3,6,1,4,8,5,2]=>[7,5,4,1,8,2,3,6]=>0011011
[8,4,1,7,2,3,6,5]=>[6,4,1,7,8,2,3,5]=>[7,3,1,6,2,4,8,5]=>0100111
[3,2,6,1,5,7,4,8]=>[7,3,2,6,1,5,4,8]=>[3,2,7,4,6,5,1,8]=>0101110
[5,3,8,4,2,6,7,1]=>[7,4,8,5,3,2,6,1]=>[8,1,7,6,2,4,5,3]=>0001111
[2,4,6,3,5,8,1,7]=>[8,2,6,4,3,5,1,7]=>[2,4,6,5,3,8,7,1]=>0001111
[2,6,3,4,7,5,8,1]=>[8,2,7,3,6,4,5,1]=>[2,7,5,6,4,3,8,1]=>0010111
[2,3,1,7,6,4,8,5]=>[3,2,1,8,6,7,4,5]=>[2,3,1,8,5,6,7,4]=>0100011
[3,1,8,2,7,6,4,5]=>[6,3,1,7,2,8,4,5]=>[7,4,8,5,2,3,1,6]=>0101011
[3,6,4,7,2,5,1,8]=>[5,7,3,6,4,2,1,8]=>[3,7,1,5,4,6,2,8]=>0001110
[7,3,2,8,6,1,4,5]=>[6,3,8,2,1,7,4,5]=>[8,5,1,6,7,4,2,3]=>0011011
[1,2,5,8,4,7,3,6]=>[1,2,7,8,5,4,3,6]=>[1,2,5,7,3,8,6,4]=>0000111
[2,4,6,1,8,3,7,5]=>[7,2,8,4,6,1,3,5]=>[2,4,8,5,6,1,7,3]=>0000111
[1,4,2,5,8,7,3,6]=>[1,7,4,2,5,3,8,6]=>[1,5,8,6,3,4,2,7]=>0010101
[3,5,1,7,2,8,6,4]=>[6,8,3,5,1,7,2,4]=>[3,8,4,5,1,6,7,2]=>0001011
[5,3,1,6,7,8,4,2]=>[4,3,8,5,1,6,7,2]=>[5,1,4,6,7,8,2,3]=>0001001
[4,1,6,2,7,8,5,3]=>[5,8,4,1,6,2,7,3]=>[7,8,3,4,1,5,6,2]=>0010101
[4,8,7,3,6,5,1,2]=>[5,1,6,4,7,3,8,2]=>[4,6,3,8,2,1,5,7]=>1000101
[6,3,8,7,5,4,1,2]=>[4,1,5,7,6,3,8,2]=>[6,3,5,8,2,1,4,7]=>1000101
[4,3,8,7,6,5,1,2]=>[5,1,4,3,6,7,8,2]=>[4,3,8,2,1,5,6,7]=>1010001
[3,1,8,7,6,5,4,2]=>[4,3,1,5,6,7,8,2]=>[8,2,3,1,4,5,6,7]=>0100001
[4,2,8,1,7,6,5,3]=>[5,6,4,2,7,8,1,3]=>[7,1,5,8,3,4,2,6]=>0010011
[3,2,8,1,7,6,5,4]=>[5,3,2,6,7,8,1,4]=>[3,2,7,1,5,8,4,6]=>0100011
[3,8,2,7,1,6,5,4]=>[5,6,3,7,8,2,1,4]=>[3,6,2,8,4,7,1,5]=>0000111
[5,8,7,6,2,1,4,3]=>[2,4,6,1,5,7,8,3]=>[4,1,2,5,8,3,6,7]=>0010001
[4,8,1,7,6,5,3,2]=>[3,5,6,4,7,8,1,2]=>[4,8,2,5,7,1,3,6]=>0000011
[5,4,1,8,7,6,3,2]=>[3,6,4,5,1,7,8,2]=>[5,1,3,4,8,2,6,7]=>0001001
[7,8,3,1,6,5,4,2]=>[4,3,5,6,8,1,7,2]=>[6,1,4,7,8,2,3,5]=>0000101
[4,3,1,8,7,6,5,2]=>[5,3,4,1,6,7,8,2]=>[8,2,3,4,1,5,6,7]=>0010001
[4,2,1,8,7,6,5,3]=>[2,5,4,1,6,7,8,3]=>[8,3,4,1,2,5,6,7]=>0010001
[7,3,2,1,8,6,5,4]=>[2,3,5,6,8,7,1,4]=>[8,4,6,7,1,2,3,5]=>0000011
[6,2,3,8,4,1,5,7]=>[4,8,2,6,3,1,5,7]=>[6,1,4,8,7,5,3,2]=>0101111
[6,4,2,3,8,1,5,7]=>[8,4,2,6,3,1,5,7]=>[8,7,5,3,2,4,6,1]=>0101111
[2,6,3,8,4,1,5,7]=>[4,2,8,6,3,1,5,7]=>[2,6,1,4,8,7,5,3]=>0001111
[6,3,8,4,2,1,5,7]=>[2,4,8,6,3,1,5,7]=>[6,1,2,4,8,7,5,3]=>0001111
[2,4,8,3,6,1,5,7]=>[6,2,8,4,3,1,5,7]=>[2,4,6,1,8,7,5,3]=>0001111
[8,3,6,2,1,4,5,7]=>[2,6,8,3,1,4,5,7]=>[8,7,5,1,2,6,4,3]=>0011111
[2,1,8,3,6,4,5,7]=>[2,1,6,8,3,4,5,7]=>[2,1,8,7,5,3,6,4]=>1001111
[6,3,8,2,1,4,5,7]=>[2,8,6,3,1,4,5,7]=>[6,4,3,8,7,5,1,2]=>0011111
[3,4,6,8,7,5,1,2]=>[5,1,3,4,7,6,8,2]=>[3,4,6,8,2,1,5,7]=>1000001
[5,4,6,3,8,7,1,2]=>[7,1,6,5,4,3,8,2]=>[5,4,6,3,8,2,1,7]=>1001101
[6,4,8,5,3,7,1,2]=>[7,1,5,8,6,4,3,2]=>[8,2,1,7,3,5,6,4]=>1000111
[1,8,5,2,6,3,7,4]=>[1,7,6,5,8,2,3,4]=>[1,7,3,6,2,8,4,5]=>0000111
[7,8,1,4,2,5,6,3]=>[6,4,8,1,2,5,7,3]=>[6,5,2,4,1,7,8,3]=>0011101
[1,2,8,5,7,3,6,4]=>[1,2,6,7,8,5,3,4]=>[1,2,8,4,7,3,6,5]=>0000111
[7,8,1,2,4,6,5,3]=>[5,1,6,2,8,4,7,3]=>[7,8,3,6,4,2,1,5]=>1010101
[1,8,2,5,4,7,6,3]=>[1,6,5,7,2,8,4,3]=>[1,7,4,8,3,5,2,6]=>0001011
[4,6,2,1,7,5,3,8]=>[2,5,7,4,6,1,3,8]=>[4,6,1,2,5,7,3,8]=>0000110
[5,8,2,7,4,3,1,6]=>[3,4,7,8,5,2,1,6]=>[5,7,1,3,8,6,2,4]=>0000111
[6,5,8,4,2,3,1,7]=>[3,4,2,8,6,5,1,7]=>[6,5,8,7,1,3,2,4]=>0100111
[2,4,1,3,5,8,7,6]=>[4,2,1,3,5,7,8,6]=>[2,4,3,1,5,8,6,7]=>0110001
[1,4,6,3,5,8,7,2]=>[1,7,6,4,3,5,8,2]=>[1,4,6,5,3,8,2,7]=>0001101
[4,2,1,3,6,5,7,8]=>[2,4,1,3,6,5,7,8]=>[4,3,1,2,6,5,7,8]=>0110100
[6,2,1,8,3,5,7,4]=>[2,7,8,6,1,3,5,4]=>[7,5,1,2,8,4,6,3]=>0001111
[6,4,1,3,8,5,7,2]=>[7,4,1,8,6,3,5,2]=>[7,5,6,3,1,8,2,4]=>0100111
[6,1,4,3,8,5,7,2]=>[7,4,8,1,6,3,5,2]=>[8,2,4,1,7,5,6,3]=>0010111
[1,6,4,3,8,5,7,2]=>[1,7,4,8,6,3,5,2]=>[1,8,2,7,5,6,3,4]=>0000111
[8,1,4,3,6,5,7,2]=>[7,4,6,1,8,3,5,2]=>[6,3,8,2,4,1,7,5]=>0010111
[8,2,1,3,6,5,7,4]=>[2,7,1,6,8,3,5,4]=>[8,4,6,3,1,2,7,5]=>0100111
[1,4,6,8,3,5,7,2]=>[1,7,8,4,3,6,5,2]=>[1,4,6,8,2,7,5,3]=>0001011
[4,6,1,3,8,5,7,2]=>[7,8,1,4,6,3,5,2]=>[4,7,5,6,3,1,8,2]=>0100111
[2,6,1,8,3,5,7,4]=>[7,2,8,6,1,3,5,4]=>[2,7,5,1,8,4,6,3]=>0001111
[2,1,6,3,8,5,7,4]=>[2,1,7,8,6,3,5,4]=>[2,1,7,5,6,3,8,4]=>1000111
[2,8,4,1,3,5,7,6]=>[4,2,1,7,3,8,5,6]=>[2,7,5,3,1,4,8,6]=>0101011
[8,6,1,4,3,5,7,2]=>[7,4,6,1,3,8,5,2]=>[8,2,4,1,7,5,3,6]=>0011011
[8,5,7,4,3,2,1,6]=>[2,3,4,7,8,5,1,6]=>[7,1,2,3,4,8,6,5]=>0000111
[8,7,4,3,6,2,1,5]=>[2,6,4,7,3,1,8,5]=>[6,1,2,8,5,3,4,7]=>0001101
[6,5,8,4,3,2,1,7]=>[2,3,4,8,6,5,1,7]=>[6,5,8,7,1,2,3,4]=>0000111
[8,4,7,6,3,2,1,5]=>[2,3,6,7,4,8,1,5]=>[8,5,4,7,1,2,3,6]=>0001011
[5,8,7,4,3,2,1,6]=>[2,3,4,7,5,1,8,6]=>[5,8,6,1,2,3,4,7]=>0000101
[4,8,2,6,3,5,7,1]=>[7,6,8,4,2,3,5,1]=>[4,8,1,7,5,2,6,3]=>0001111
[8,6,1,2,7,4,3,5]=>[4,1,7,6,2,8,3,5]=>[7,3,8,5,2,1,4,6]=>1001011
[4,6,2,1,7,8,5,3]=>[2,5,8,4,6,1,7,3]=>[4,6,1,2,5,7,8,3]=>0000101
[2,3,8,7,4,1,6,5]=>[4,2,3,6,7,1,8,5]=>[2,3,6,1,4,8,5,7]=>0000101
[7,8,2,1,5,6,4,3]=>[2,4,6,8,1,5,7,3]=>[7,8,3,6,5,1,2,4]=>0001101
[5,2,7,1,8,6,3,4]=>[6,8,5,2,1,7,3,4]=>[7,3,5,1,6,8,4,2]=>0011011
[1,2,8,3,7,6,5,4]=>[1,2,5,6,7,8,3,4]=>[1,2,7,3,5,8,4,6]=>0000011
[5,4,2,8,6,1,7,3]=>[7,6,4,5,2,8,1,3]=>[7,1,8,3,4,5,2,6]=>0001011
[8,5,4,3,7,2,6,1]=>[6,7,4,5,8,3,2,1]=>[7,2,8,1,6,3,4,5]=>0000111
[8,3,7,4,2,6,5,1]=>[5,4,6,7,8,3,2,1]=>[6,3,7,2,4,8,1,5]=>0000111
[4,8,7,6,1,5,3,2]=>[3,5,6,4,1,7,8,2]=>[4,8,2,5,1,3,6,7]=>0001001
[7,3,8,4,2,1,6,5]=>[2,4,6,8,7,3,1,5]=>[6,3,8,5,7,1,2,4]=>0000111
[3,7,8,4,1,2,6,5]=>[4,1,3,6,8,2,7,5]=>[3,6,2,1,4,7,8,5]=>1000101
[6,5,8,7,3,1,4,2]=>[4,3,7,1,6,5,8,2]=>[4,1,6,5,8,2,3,7]=>0010101
[2,4,8,3,1,5,7,6]=>[3,2,7,4,1,8,5,6]=>[2,4,7,5,1,3,8,6]=>0001011
[2,4,3,8,1,6,5,7]=>[6,2,4,3,8,1,5,7]=>[2,4,3,6,1,8,7,5]=>0010111
[2,6,5,8,1,4,3,7]=>[4,2,8,1,6,5,3,7]=>[2,4,1,6,5,8,7,3]=>0010111
[2,5,8,3,1,4,7,6]=>[3,2,7,1,5,8,4,6]=>[2,5,7,4,1,3,8,6]=>0010011
[8,7,4,1,6,2,5,3]=>[5,6,4,7,1,2,8,3]=>[5,1,6,2,8,3,4,7]=>0001101
[6,3,7,4,5,8,2,1]=>[2,8,7,6,3,4,5,1]=>[6,4,7,5,3,8,1,2]=>0001111
[6,8,4,1,7,2,5,3]=>[5,7,4,8,1,6,2,3]=>[5,1,6,7,2,8,3,4]=>0001011
[6,8,3,4,5,7,2,1]=>[2,7,8,3,4,6,5,1]=>[6,8,1,2,7,5,4,3]=>0011011
[8,7,1,2,4,3,5,6]=>[4,1,7,2,3,5,8,6]=>[4,2,1,8,6,5,3,7]=>1011101
[6,8,3,1,4,7,2,5]=>[7,3,8,1,4,6,2,5]=>[6,8,5,4,1,7,2,3]=>0011011
[6,4,7,2,8,5,1,3]=>[5,8,2,7,6,4,1,3]=>[7,1,5,6,4,8,3,2]=>0100111
[8,7,1,4,5,3,2,6]=>[3,5,7,1,4,2,8,6]=>[8,6,2,5,4,1,3,7]=>0011101
[8,7,4,2,6,5,1,3]=>[5,4,2,6,7,1,8,3]=>[8,3,2,4,6,1,5,7]=>0100101
[8,7,3,2,4,6,5,1]=>[5,3,6,2,7,4,8,1]=>[6,4,2,3,8,1,5,7]=>0010101
[2,6,3,1,4,5,8,7]=>[3,2,6,1,4,5,8,7]=>[2,6,5,4,1,3,8,7]=>0011101
[6,3,7,2,8,4,5,1]=>[5,8,7,6,3,2,4,1]=>[8,1,5,3,7,4,6,2]=>0001111
[6,7,1,8,3,2,5,4]=>[3,5,8,7,1,6,2,4]=>[6,8,4,7,2,5,1,3]=>0001011
[8,7,6,1,3,2,5,4]=>[3,5,1,6,2,7,8,4]=>[3,1,5,2,8,4,6,7]=>0101001
[8,7,4,5,1,6,2,3]=>[6,5,1,7,4,2,8,3]=>[8,3,1,6,2,5,4,7]=>0101101
[8,4,6,2,3,1,7,5]=>[3,7,2,6,8,4,1,5]=>[6,4,7,1,3,2,8,5]=>0100111
[7,1,6,8,4,5,3,2]=>[3,5,8,7,1,4,6,2]=>[7,6,4,8,2,5,1,3]=>0001111
[1,8,4,6,7,5,3,2]=>[1,3,5,7,8,4,6,2]=>[1,7,6,4,8,2,3,5]=>0000111
[8,1,4,5,6,7,3,2]=>[3,7,8,1,4,5,6,2]=>[8,2,7,6,5,4,1,3]=>0011111
[5,1,8,4,2,6,3,7]=>[6,4,8,5,1,2,3,7]=>[6,2,4,5,1,8,7,3]=>0001111
[1,8,4,6,2,5,3,7]=>[1,5,6,8,4,2,3,7]=>[1,8,7,3,6,2,5,4]=>0001111
[2,8,3,1,5,6,7,4]=>[3,2,7,8,1,5,6,4]=>[2,7,6,5,1,3,8,4]=>0001111
[8,2,4,3,6,7,1,5]=>[7,4,8,2,3,1,6,5]=>[4,2,7,6,1,8,5,3]=>0011111
[6,2,1,8,4,7,5,3]=>[2,5,7,8,6,1,4,3]=>[6,1,2,5,8,3,7,4]=>0000111
[8,2,7,1,5,4,6,3]=>[6,5,7,8,2,1,4,3]=>[5,2,6,1,8,3,7,4]=>0001111
[7,2,8,1,6,4,5,3]=>[5,6,8,7,2,1,4,3]=>[6,1,5,2,7,4,8,3]=>0001111
[7,8,2,6,4,1,5,3]=>[5,4,6,8,2,1,7,3]=>[7,8,3,6,1,5,2,4]=>0001101
[8,7,2,4,1,6,5,3]=>[5,4,6,2,7,1,8,3]=>[4,2,8,3,6,1,5,7]=>0010101
[1,2,8,6,3,7,5,4]=>[1,2,5,7,6,8,3,4]=>[1,2,8,4,7,3,5,6]=>0000011
[1,6,2,8,4,3,7,5]=>[1,4,7,8,6,2,3,5]=>[1,7,3,8,5,6,2,4]=>0000111
[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,7,5,8,6]=>0000011
[3,7,2,5,6,4,1,8]=>[4,6,3,7,2,5,1,8]=>[3,6,5,2,7,1,4,8]=>0001110
[7,6,2,5,4,3,1,8]=>[3,4,5,6,2,7,1,8]=>[7,1,3,5,2,4,6,8]=>0001010
[5,6,7,2,4,3,1,8]=>[3,4,7,2,5,6,1,8]=>[4,2,5,6,7,1,3,8]=>0010010
[1,8,3,4,2,7,5,6]=>[1,4,7,3,8,2,5,6]=>[1,8,6,2,4,3,7,5]=>0010111
[7,8,2,4,3,1,6,5]=>[3,4,6,2,8,1,7,5]=>[4,2,6,1,3,7,8,5]=>0010101
[6,1,3,5,7,2,4,8]=>[7,6,1,3,2,5,4,8]=>[6,5,2,7,4,3,1,8]=>0111110
[6,1,5,8,2,7,3,4]=>[7,8,6,1,2,5,3,4]=>[8,4,1,7,3,6,5,2]=>0011111
[2,3,8,1,5,6,7,4]=>[7,2,3,8,1,5,6,4]=>[2,3,7,6,5,1,8,4]=>0001111
[2,8,7,1,6,4,5,3]=>[5,2,6,7,1,4,8,3]=>[2,5,1,8,3,6,4,7]=>0001101
[5,8,6,7,1,4,3,2]=>[3,4,7,1,5,8,6,2]=>[5,8,2,4,1,3,7,6]=>0010011
[6,7,8,5,1,4,3,2]=>[3,4,5,1,8,6,7,2]=>[6,7,8,2,4,1,3,5]=>0010001
[5,6,3,8,4,1,7,2]=>[7,4,8,6,5,3,1,2]=>[5,7,1,8,2,4,6,3]=>0000111
[7,3,8,5,4,1,6,2]=>[6,4,5,8,7,3,1,2]=>[7,1,6,3,5,8,2,4]=>0000111
[3,4,8,5,6,1,7,2]=>[7,6,3,4,8,5,1,2]=>[3,4,7,1,8,2,6,5]=>0000111
[3,6,4,1,5,2,7,8]=>[5,4,3,6,1,2,7,8]=>[3,5,1,6,2,4,7,8]=>0001100
[8,6,1,2,4,3,7,5]=>[4,1,7,2,6,8,3,5]=>[4,2,1,7,3,8,5,6]=>1010011
[6,8,1,4,2,3,7,5]=>[4,7,1,2,8,6,3,5]=>[6,7,3,1,4,2,8,5]=>0110011
[1,8,2,7,5,4,6,3]=>[1,6,5,7,8,2,4,3]=>[1,6,2,7,4,8,3,5]=>0000111
[1,8,6,3,7,2,4,5]=>[1,7,6,3,2,8,4,5]=>[1,8,5,2,7,4,3,6]=>0011011
[1,4,7,5,2,6,8,3]=>[1,8,5,4,7,2,6,3]=>[1,4,8,3,5,7,6,2]=>0000111
[4,6,5,3,7,1,8,2]=>[8,7,5,4,6,3,1,2]=>[4,6,3,5,8,2,7,1]=>0000111
[5,6,2,7,3,1,8,4]=>[3,8,7,6,5,2,1,4]=>[5,7,1,3,8,4,6,2]=>0000111
[1,6,3,7,5,8,2,4]=>[1,8,7,3,6,2,5,4]=>[1,8,4,3,7,5,6,2]=>0010111
[5,2,3,4,8,1,6,7]=>[8,5,2,3,4,1,6,7]=>[5,4,3,2,8,7,6,1]=>0111111
[3,5,2,4,7,1,6,8]=>[7,5,3,2,4,1,6,8]=>[3,5,4,2,7,6,1,8]=>0011110
[6,5,3,4,8,7,1,2]=>[7,1,5,3,6,4,8,2]=>[6,4,3,5,8,2,1,7]=>1010101
[6,2,4,8,5,1,3,7]=>[5,8,2,1,6,4,3,7]=>[6,4,1,5,8,7,3,2]=>0110111
[6,3,8,1,7,2,4,5]=>[7,8,6,3,1,2,4,5]=>[8,5,1,7,4,3,6,2]=>0011111
[1,3,7,2,8,6,4,5]=>[1,6,3,8,2,7,4,5]=>[1,3,8,5,2,6,7,4]=>0001011
[4,2,3,5,6,8,1,7]=>[8,4,2,3,5,6,1,7]=>[4,3,2,5,6,8,7,1]=>0110011
[4,2,3,6,8,1,5,7]=>[8,4,2,3,1,6,5,7]=>[4,3,2,6,8,7,5,1]=>0111011
[2,6,1,5,4,8,3,7]=>[8,2,5,6,1,4,3,7]=>[2,6,4,8,7,3,5,1]=>0001111
[2,3,4,8,1,7,6,5]=>[6,2,3,4,7,8,1,5]=>[2,3,4,8,5,7,1,6]=>0000011
[8,4,1,2,7,6,3,5]=>[6,1,4,7,2,8,3,5]=>[7,3,4,8,5,2,1,6]=>1001011
[3,8,4,7,2,5,6,1]=>[6,7,3,8,4,2,5,1]=>[3,8,1,6,2,7,5,4]=>0001111
[5,3,4,7,1,8,6,2]=>[6,8,5,3,4,7,1,2]=>[5,4,3,7,1,6,8,2]=>0011011
[5,3,7,1,6,2,8,4]=>[8,6,7,5,3,1,2,4]=>[8,4,5,3,7,2,6,1]=>0001111
[8,2,4,6,7,1,3,5]=>[7,8,2,1,4,3,6,5]=>[8,5,4,1,7,6,3,2]=>0111111
[5,7,4,3,8,6,2,1]=>[2,6,4,8,5,7,3,1]=>[5,8,1,2,6,7,3,4]=>0000011
[2,4,3,5,1,8,6,7]=>[5,2,4,3,1,8,6,7]=>[2,4,3,5,1,8,7,6]=>0011011
[8,3,5,7,6,2,1,4]=>[2,6,7,3,1,8,5,4]=>[8,4,3,7,5,1,2,6]=>0011011
[8,2,6,3,4,5,1,7]=>[5,6,8,2,3,4,1,7]=>[6,4,2,8,7,1,5,3]=>0011111
[8,2,3,4,7,6,1,5]=>[6,7,2,3,4,8,1,5]=>[8,5,4,3,2,7,1,6]=>0111011
[2,5,7,8,4,1,3,6]=>[4,2,1,8,5,3,7,6]=>[2,5,7,8,6,3,1,4]=>0100101
[6,3,5,8,7,2,4,1]=>[4,7,6,3,2,5,8,1]=>[8,1,4,3,6,5,2,7]=>0011101
[5,2,7,4,8,1,6,3]=>[6,8,7,5,2,4,1,3]=>[8,3,7,1,6,4,5,2]=>0001111
[8,3,7,4,2,5,6,1]=>[6,4,7,8,3,2,5,1]=>[7,5,3,8,1,6,2,4]=>0001111
[4,6,3,5,8,1,7,2]=>[7,8,6,4,3,5,1,2]=>[4,6,5,3,7,1,8,2]=>0001111
[2,1,7,6,4,5,8,3]=>[2,1,8,6,4,7,5,3]=>[2,1,7,5,4,6,8,3]=>1001011
[4,6,2,5,3,8,7,1]=>[7,5,6,4,2,3,8,1]=>[4,5,2,6,3,8,1,7]=>0001101
[8,6,4,2,3,1,7,5]=>[3,4,2,7,6,8,1,5]=>[7,1,3,2,4,8,5,6]=>0100011
[4,2,8,3,1,5,6,7]=>[3,8,4,2,1,5,6,7]=>[8,7,6,5,1,3,4,2]=>0011111
[2,5,7,3,8,4,6,1]=>[6,2,8,7,5,3,4,1]=>[2,5,7,4,8,1,6,3]=>0000111
[3,5,7,1,4,8,6,2]=>[6,8,3,1,5,7,4,2]=>[3,5,7,4,1,6,8,2]=>0010011
[7,3,8,2,5,4,1,6]=>[4,5,8,7,3,2,1,6]=>[7,1,4,8,6,2,5,3]=>0001111
[7,4,2,5,8,3,1,6]=>[3,8,4,7,2,5,1,6]=>[7,1,3,4,8,6,5,2]=>0001111
[3,1,2,8,5,6,4,7]=>[3,1,2,6,8,5,4,7]=>[3,2,1,8,7,4,6,5]=>1100111
[5,6,8,1,4,3,2,7]=>[3,4,8,1,5,6,2,7]=>[5,6,8,7,2,4,1,3]=>0010011
[6,4,8,3,7,2,5,1]=>[5,7,8,6,4,3,2,1]=>[7,2,8,1,5,4,6,3]=>0001111
[4,7,3,6,2,1,8,5]=>[2,8,6,4,7,3,1,5]=>[4,6,3,8,5,7,1,2]=>0000111
[7,8,4,1,5,3,2,6]=>[3,5,4,8,1,2,7,6]=>[7,8,6,2,5,1,3,4]=>0001101
[7,3,8,5,1,4,2,6]=>[4,5,8,3,7,1,2,6]=>[7,2,5,8,6,1,4,3]=>0010111
[6,7,1,3,2,8,4,5]=>[3,8,1,7,2,6,4,5]=>[3,1,6,7,4,8,5,2]=>0101011
[4,8,2,6,3,7,5,1]=>[5,7,6,4,8,2,3,1]=>[4,7,3,6,2,8,1,5]=>0000111
[3,7,2,4,6,1,8,5]=>[8,6,3,2,7,4,1,5]=>[3,6,4,2,8,5,7,1]=>0010111
[4,8,7,6,3,2,1,5]=>[2,3,6,4,1,7,8,5]=>[4,8,5,1,2,3,6,7]=>0001001
[7,8,2,4,6,1,5,3]=>[5,6,8,2,4,1,7,3]=>[6,1,5,4,2,7,8,3]=>0011101
[5,6,1,2,8,7,4,3]=>[4,1,7,6,5,2,8,3]=>[5,6,2,1,4,8,3,7]=>1000101
[6,7,8,1,2,5,4,3]=>[4,1,5,8,2,6,7,3]=>[6,7,8,3,5,2,1,4]=>1001001
[6,8,7,5,1,4,3,2]=>[3,4,5,1,7,6,8,2]=>[6,8,2,4,1,3,5,7]=>0010001
[6,5,4,3,8,2,7,1]=>[7,8,4,5,6,3,2,1]=>[6,3,4,5,8,1,7,2]=>0000111
[7,5,4,3,2,8,6,1]=>[6,3,4,5,8,7,2,1]=>[8,1,6,7,2,3,4,5]=>0000011
[8,4,3,2,1,7,6,5]=>[2,3,4,6,7,8,1,5]=>[8,5,7,1,2,3,4,6]=>0000011
[4,7,5,8,3,2,1,6]=>[2,3,8,4,7,5,1,6]=>[4,8,6,5,7,1,2,3]=>0000111
[5,7,2,3,6,1,8,4]=>[8,6,2,7,5,3,1,4]=>[5,6,3,2,8,4,7,1]=>0100111
[8,6,4,2,3,7,5,1]=>[5,4,2,7,6,8,3,1]=>[7,3,2,4,8,1,5,6]=>0100011
[3,1,2,4,8,7,6,5]=>[3,1,2,4,6,7,8,5]=>[3,2,1,4,8,5,6,7]=>1100001
[5,6,7,8,1,4,2,3]=>[4,8,1,2,5,6,7,3]=>[5,6,7,8,3,1,4,2]=>0110001
[4,6,1,3,7,2,5,8]=>[7,6,1,4,3,2,5,8]=>[4,6,2,7,5,3,1,8]=>0101110
[6,5,7,8,3,1,4,2]=>[4,3,8,1,6,5,7,2]=>[4,1,6,5,7,8,2,3]=>0010101
[7,5,8,6,2,1,3,4]=>[2,6,1,3,8,7,5,4]=>[8,4,3,1,2,6,7,5]=>0110011
[2,8,1,3,6,5,4,7]=>[5,2,1,6,8,3,4,7]=>[2,8,7,4,6,3,1,5]=>0100111
[7,3,8,4,1,2,6,5]=>[4,1,6,8,7,3,2,5]=>[6,3,8,5,7,2,1,4]=>1000111
[6,8,3,2,7,1,5,4]=>[5,3,7,8,2,6,1,4]=>[6,7,1,5,2,3,8,4]=>0001011
[4,1,8,2,6,3,5,7]=>[6,8,4,1,2,3,5,7]=>[6,3,4,1,8,7,5,2]=>0011111
[5,8,6,7,1,2,3,4]=>[7,1,2,3,5,8,6,4]=>[5,8,4,3,2,1,7,6]=>1110011
[4,8,1,5,7,2,3,6]=>[7,8,1,4,2,5,3,6]=>[4,7,3,1,8,6,5,2]=>0101111
[5,3,2,7,1,6,8,4]=>[8,3,7,5,2,1,6,4]=>[8,4,5,2,3,7,6,1]=>0001111
[4,5,7,1,2,6,8,3]=>[8,1,7,4,5,2,6,3]=>[4,5,8,3,7,6,2,1]=>1000111
[5,4,1,7,3,6,8,2]=>[8,7,4,5,1,3,6,2]=>[8,2,7,6,3,4,5,1]=>0001111
[4,8,3,6,5,2,1,7]=>[2,5,6,4,8,3,1,7]=>[4,6,3,8,7,1,2,5]=>0000111
[1,8,6,5,4,2,3,7]=>[1,4,2,5,6,8,3,7]=>[1,8,7,3,2,4,5,6]=>0100011
[3,1,4,6,7,8,5,2]=>[5,3,1,4,8,6,7,2]=>[4,6,7,8,2,3,1,5]=>0100001
[7,4,6,1,8,2,3,5]=>[8,6,1,7,4,2,3,5]=>[6,2,8,5,4,7,3,1]=>0101111
[5,1,6,8,4,2,7,3]=>[7,4,8,5,1,6,2,3]=>[6,7,2,4,5,1,8,3]=>0001011
[5,7,8,3,1,6,4,2]=>[4,3,6,8,5,1,7,2]=>[5,7,8,2,3,6,1,4]=>0000101
[7,5,8,3,2,4,1,6]=>[4,3,8,2,7,5,1,6]=>[8,6,5,7,1,4,2,3]=>0010111
[5,8,2,6,3,1,4,7]=>[3,6,8,2,5,1,4,7]=>[5,8,7,4,2,6,1,3]=>0010111
[8,2,7,5,4,1,3,6]=>[4,5,2,7,8,1,3,6]=>[8,6,1,4,7,3,2,5]=>0100111
[3,7,2,4,8,5,1,6]=>[5,8,3,2,7,4,1,6]=>[3,7,1,5,8,6,4,2]=>0010111
[8,3,6,2,5,4,1,7]=>[4,5,6,8,3,2,1,7]=>[6,2,5,3,8,7,1,4]=>0001111
[7,4,8,5,3,2,1,6]=>[2,3,5,8,7,4,1,6]=>[7,1,2,3,5,8,6,4]=>0000111
[6,1,2,7,3,8,5,4]=>[5,1,8,7,6,2,3,4]=>[6,2,1,5,8,4,7,3]=>1000111
[2,1,7,3,4,8,6,5]=>[2,1,6,3,8,7,4,5]=>[2,1,7,4,3,6,8,5]=>1010011
[4,8,3,7,1,5,2,6]=>[5,7,8,4,3,1,2,6]=>[4,7,2,8,6,1,5,3]=>0001111
[1,3,5,8,2,4,7,6]=>[1,7,3,2,5,8,4,6]=>[1,3,5,7,4,2,8,6]=>0010011
[4,6,8,2,5,1,3,7]=>[5,8,2,4,1,6,3,7]=>[4,5,1,6,8,7,3,2]=>0101011
[5,7,2,3,8,1,4,6]=>[8,7,2,3,5,1,4,6]=>[5,7,4,3,2,8,6,1]=>0110111
[6,4,7,5,8,1,2,3]=>[8,1,2,7,6,4,5,3]=>[7,5,6,4,8,3,2,1]=>1100111
[7,4,2,1,5,8,6,3]=>[2,6,4,8,1,7,5,3]=>[7,5,1,2,6,8,3,4]=>0001011
[1,6,4,8,7,5,3,2]=>[1,3,5,7,6,4,8,2]=>[1,8,2,3,5,6,4,7]=>0000101
[6,4,1,8,3,2,7,5]=>[3,7,4,8,6,1,2,5]=>[7,2,8,5,6,1,3,4]=>0000111
[8,6,1,7,5,4,3,2]=>[3,4,5,7,6,8,1,2]=>[8,2,4,7,1,3,5,6]=>0000011
[8,1,2,4,5,3,6,7]=>[5,1,8,2,4,3,6,7]=>[5,4,2,1,8,7,6,3]=>1011111
[1,8,7,6,4,5,3,2]=>[1,3,5,6,4,7,8,2]=>[1,8,2,3,5,4,6,7]=>0001001
[2,6,8,1,3,7,5,4]=>[5,2,1,7,8,6,3,4]=>[2,6,8,4,7,3,1,5]=>0100011
[4,2,3,8,5,1,6,7]=>[5,4,2,3,8,1,6,7]=>[4,3,2,8,7,6,1,5]=>0110111
[8,4,3,7,5,2,6,1]=>[6,5,4,7,8,3,2,1]=>[8,1,6,3,4,7,2,5]=>0000111
[3,5,2,8,4,6,1,7]=>[6,8,3,5,2,4,1,7]=>[3,8,7,1,6,4,5,2]=>0001111
[5,3,8,7,4,1,6,2]=>[6,4,7,5,3,1,8,2]=>[6,1,8,2,4,5,3,7]=>0001101
[6,4,2,8,5,3,1,7]=>[3,5,4,8,6,2,1,7]=>[6,2,5,8,7,1,3,4]=>0000111
[6,4,5,3,8,2,7,1]=>[7,8,5,6,4,3,2,1]=>[6,3,5,4,8,1,7,2]=>0001111
[7,4,5,3,8,2,6,1]=>[6,8,5,7,4,3,2,1]=>[8,1,6,3,5,4,7,2]=>0001111
[7,5,6,3,8,2,4,1]=>[4,8,6,3,7,5,2,1]=>[8,1,4,3,6,5,7,2]=>0010111
[8,5,6,3,7,2,4,1]=>[4,7,6,3,8,5,2,1]=>[7,2,8,1,4,3,6,5]=>0010111
[8,4,6,3,7,2,5,1]=>[5,7,6,8,4,3,2,1]=>[6,3,7,2,8,1,5,4]=>0001111
[7,4,6,3,5,2,8,1]=>[8,5,6,7,4,3,2,1]=>[6,3,7,2,5,4,8,1]=>0001111
[7,5,8,3,4,2,6,1]=>[6,4,8,3,7,5,2,1]=>[8,1,6,5,7,2,4,3]=>0010111
[7,5,8,4,6,2,3,1]=>[3,6,2,8,7,5,4,1]=>[8,1,3,2,6,5,7,4]=>0100111
[7,4,8,3,6,2,5,1]=>[5,6,8,7,4,3,2,1]=>[8,1,5,4,7,2,6,3]=>0001111
[6,4,8,3,5,2,7,1]=>[7,5,8,6,4,3,2,1]=>[8,1,7,2,5,4,6,3]=>0001111
[5,4,7,3,6,2,8,1]=>[8,6,7,5,4,3,2,1]=>[5,4,7,2,6,3,8,1]=>0001111
[5,4,8,3,7,2,6,1]=>[6,7,8,5,4,3,2,1]=>[5,4,7,2,8,1,6,3]=>0001111
[6,5,8,4,7,2,3,1]=>[3,7,2,8,6,5,4,1]=>[6,5,8,1,3,2,7,4]=>0100111
[6,5,7,3,8,2,4,1]=>[4,8,7,3,6,5,2,1]=>[6,5,8,1,4,3,7,2]=>0010111
[6,4,7,3,8,2,5,1]=>[5,8,7,6,4,3,2,1]=>[8,1,5,4,6,3,7,2]=>0001111
[5,4,6,3,8,2,7,1]=>[7,8,6,5,4,3,2,1]=>[5,4,6,3,8,1,7,2]=>0001111
[6,5,3,7,8,2,1,4]=>[2,8,5,3,6,1,7,4]=>[7,8,4,3,5,6,1,2]=>0010101
[4,8,2,6,3,7,1,5]=>[7,6,8,4,2,3,1,5]=>[4,7,1,8,5,2,6,3]=>0001111
[1,4,7,6,3,2,5,8]=>[1,3,6,4,2,7,5,8]=>[1,4,7,5,2,3,6,8]=>0001010
[4,8,7,3,6,2,1,5]=>[2,6,7,4,3,1,8,5]=>[4,6,1,2,8,5,3,7]=>0001101
[4,3,8,2,7,1,6,5]=>[6,7,4,3,8,2,1,5]=>[4,3,7,1,6,2,8,5]=>0010111
[4,7,5,1,2,8,3,6]=>[8,1,5,4,7,2,3,6]=>[4,7,3,5,8,6,2,1]=>1000111
[4,3,1,2,8,5,7,6]=>[3,1,4,2,7,8,5,6]=>[4,2,1,3,7,5,8,6]=>1010011
[4,7,1,8,5,2,3,6]=>[5,8,1,4,7,2,3,6]=>[4,7,3,1,5,8,6,2]=>0100111
[3,7,8,6,2,4,1,5]=>[4,6,3,2,1,8,7,5]=>[3,7,8,5,1,4,2,6]=>0011001
[3,7,8,2,6,4,1,5]=>[4,6,3,8,2,1,7,5]=>[3,7,8,5,2,6,1,4]=>0001101
[4,2,8,6,3,1,7,5]=>[3,7,4,2,6,8,1,5]=>[7,1,3,4,2,8,5,6]=>0010011
[2,6,8,4,7,3,1,5]=>[3,2,7,8,4,6,1,5]=>[2,6,7,1,3,8,5,4]=>0001011
[2,4,6,8,3,1,7,5]=>[3,2,7,4,8,6,1,5]=>[2,4,6,7,1,3,8,5]=>0000011
[3,7,2,4,8,6,1,5]=>[6,8,3,2,4,7,1,5]=>[3,7,1,6,8,5,4,2]=>0011011
[2,4,3,6,1,8,7,5]=>[7,2,4,3,6,1,8,5]=>[2,4,3,8,5,6,1,7]=>0010101
[2,6,3,7,4,8,1,5]=>[8,2,7,6,3,4,1,5]=>[2,6,4,8,5,3,7,1]=>0001111
[1,3,5,7,6,8,2,4]=>[1,8,3,2,5,7,6,4]=>[1,3,5,7,6,8,4,2]=>0010011
[1,3,5,7,6,2,8,4]=>[1,8,3,6,5,7,2,4]=>[1,3,5,8,4,6,7,2]=>0000011
[1,3,5,7,6,2,4,8]=>[1,6,3,2,5,7,4,8]=>[1,3,5,7,4,2,6,8]=>0010010
[1,3,5,7,4,6,8,2]=>[1,8,3,7,5,4,6,2]=>[1,3,5,7,6,4,8,2]=>0000111
[1,3,5,4,7,8,2,6]=>[1,8,3,5,4,2,7,6]=>[1,3,5,4,7,8,6,2]=>0001101
[1,3,5,7,8,4,6,2]=>[1,6,3,8,5,4,7,2]=>[1,3,5,7,8,2,6,4]=>0000101
[1,3,5,7,8,4,2,6]=>[1,4,3,8,5,2,7,6]=>[1,3,5,7,8,6,2,4]=>0000101
[1,3,5,7,2,8,6,4]=>[1,6,3,8,5,7,2,4]=>[1,3,5,7,2,6,8,4]=>0000011
[1,3,5,7,8,2,6,4]=>[1,6,3,8,5,2,7,4]=>[1,3,5,6,2,7,8,4]=>0000101
[1,3,5,7,8,6,2,4]=>[1,6,3,2,5,8,7,4]=>[1,3,5,7,8,4,2,6]=>0010001
[2,3,6,1,7,8,5,4]=>[5,2,3,8,6,1,7,4]=>[2,3,6,1,5,7,8,4]=>0000101
[2,3,7,1,4,8,6,5]=>[6,2,3,1,8,7,4,5]=>[2,3,7,4,1,6,8,5]=>0010011
[4,7,2,3,5,6,1,8]=>[6,7,2,4,3,5,1,8]=>[4,7,1,6,5,3,2,8]=>0101110
[4,6,1,2,5,8,3,7]=>[8,1,6,4,2,5,3,7]=>[4,8,7,3,6,5,2,1]=>1001111
[6,4,5,7,1,3,8,2]=>[8,7,1,6,4,5,3,2]=>[6,5,4,8,2,7,3,1]=>0101111
[4,1,6,2,8,5,7,3]=>[7,8,4,1,6,2,5,3]=>[8,3,4,1,7,5,6,2]=>0010111
[7,1,4,2,3,6,8,5]=>[4,8,1,2,7,3,6,5]=>[8,5,7,6,3,1,4,2]=>0110111
[6,4,2,1,3,8,7,5]=>[2,4,1,7,6,3,8,5]=>[8,5,6,3,1,2,4,7]=>0100101
[1,5,8,3,4,6,7,2]=>[1,7,8,3,5,4,6,2]=>[1,5,8,2,7,6,4,3]=>0010111
[8,7,1,4,3,5,2,6]=>[5,4,7,1,3,2,8,6]=>[8,6,2,4,1,5,3,7]=>0011101
[8,3,2,1,4,5,7,6]=>[2,3,7,1,4,8,5,6]=>[7,5,4,1,2,3,8,6]=>0011011
[3,8,6,4,2,1,5,7]=>[2,4,3,6,1,8,5,7]=>[3,8,7,5,1,2,4,6]=>0001011
[8,3,2,5,4,1,6,7]=>[4,3,5,8,2,1,6,7]=>[5,2,3,8,7,6,1,4]=>0001111
[2,7,8,4,6,3,1,5]=>[3,2,6,8,4,1,7,5]=>[2,6,1,3,7,8,5,4]=>0001101
[7,8,2,5,3,6,1,4]=>[6,5,8,2,3,1,7,4]=>[6,1,7,8,4,2,5,3]=>0011101
[8,1,6,3,5,7,2,4]=>[7,6,8,1,3,2,5,4]=>[6,2,8,4,1,7,5,3]=>0011111
[8,4,2,5,6,7,1,3]=>[7,4,2,8,1,5,6,3]=>[7,6,5,1,8,3,2,4]=>0101111
[2,5,8,7,3,6,1,4]=>[6,2,7,3,5,1,8,4]=>[2,5,6,1,8,4,3,7]=>0010101
[4,1,8,7,2,6,5,3]=>[5,6,4,1,7,2,8,3]=>[6,2,8,3,4,1,5,7]=>0010101
[1,5,8,7,3,2,6,4]=>[1,3,6,7,5,2,8,4]=>[1,5,6,2,3,8,4,7]=>0000101
[2,6,8,1,7,5,4,3]=>[4,2,5,7,8,6,1,3]=>[2,6,7,1,4,8,3,5]=>0000011
[2,6,8,3,7,5,1,4]=>[5,2,7,3,8,6,1,4]=>[2,6,8,4,3,7,1,5]=>0010011
[1,6,8,4,7,2,5,3]=>[1,5,7,8,4,6,2,3]=>[1,6,8,3,7,2,5,4]=>0001011
[1,5,8,4,7,2,6,3]=>[1,6,7,8,5,4,2,3]=>[1,5,8,3,7,2,6,4]=>0000111
[5,6,8,4,3,2,1,7]=>[2,3,4,8,5,6,1,7]=>[5,6,8,7,1,2,3,4]=>0000011
[7,3,1,8,6,2,5,4]=>[5,3,6,8,1,7,2,4]=>[5,1,7,2,3,6,8,4]=>0001011
[7,3,4,8,6,2,1,5]=>[2,6,8,3,4,7,1,5]=>[7,1,2,6,8,5,4,3]=>0011011
[1,6,4,8,7,2,5,3]=>[1,5,7,6,4,2,8,3]=>[1,6,2,5,4,8,3,7]=>0001101
[1,4,5,8,7,2,6,3]=>[1,6,7,4,5,2,8,3]=>[1,4,5,6,2,8,3,7]=>0000101
[1,6,4,8,2,7,5,3]=>[1,5,7,8,6,4,2,3]=>[1,8,3,7,2,5,6,4]=>0000111
[2,6,1,8,3,7,5,4]=>[5,2,7,8,6,1,3,4]=>[2,6,1,5,7,3,8,4]=>0000111
[1,4,5,8,3,2,7,6]=>[1,3,7,4,5,8,2,6]=>[1,4,5,7,2,3,8,6]=>0000011
[7,6,3,4,8,2,1,5]=>[2,8,6,3,4,7,1,5]=>[8,5,4,3,6,7,1,2]=>0011011
[1,3,5,4,8,2,7,6]=>[1,7,3,5,4,8,2,6]=>[1,3,5,4,7,2,8,6]=>0001011
[7,1,5,2,3,8,6,4]=>[6,5,1,8,2,7,3,4]=>[5,2,7,3,1,6,8,4]=>0101011
[1,6,2,4,3,8,7,5]=>[1,4,7,2,6,3,8,5]=>[1,4,2,8,5,6,3,7]=>0010101
[2,6,5,4,3,8,1,7]=>[8,2,4,5,6,3,1,7]=>[2,6,3,4,5,8,7,1]=>0000111
[7,6,5,1,3,2,8,4]=>[3,8,1,5,6,7,2,4]=>[3,1,8,4,5,6,7,2]=>0100011
[3,5,7,2,4,8,1,6]=>[8,7,3,2,5,4,1,6]=>[3,5,8,6,4,2,7,1]=>0010111
[3,5,7,2,4,6,8,1]=>[8,7,3,2,5,4,6,1]=>[3,5,7,6,4,2,8,1]=>0010111
[4,5,1,3,6,8,2,7]=>[8,5,1,4,3,6,2,7]=>[4,6,8,7,2,5,3,1]=>0101011
[4,3,5,1,7,8,2,6]=>[8,5,4,3,1,2,7,6]=>[4,3,7,8,6,2,5,1]=>0011101
[4,6,3,5,7,2,8,1]=>[8,7,6,4,3,5,2,1]=>[4,6,5,3,7,2,8,1]=>0001111
[1,6,7,3,4,5,8,2]=>[1,8,7,3,4,6,5,2]=>[1,6,7,5,4,3,8,2]=>0011011
[2,6,7,4,5,8,1,3]=>[8,2,1,7,4,6,5,3]=>[2,6,7,5,4,8,3,1]=>0101011
[2,6,7,4,8,1,3,5]=>[8,2,1,7,4,6,3,5]=>[2,6,8,5,4,7,3,1]=>0101011
[1,4,6,7,3,8,2,5]=>[1,8,7,4,3,6,2,5]=>[1,4,6,8,5,3,7,2]=>0001011
[6,3,1,7,8,2,4,5]=>[8,3,6,1,2,4,7,5]=>[7,8,5,2,3,6,4,1]=>0011101
[2,4,6,7,1,5,8,3]=>[8,2,7,4,1,6,5,3]=>[2,4,6,8,3,7,5,1]=>0001011
[2,4,7,1,5,6,8,3]=>[8,2,7,4,1,5,6,3]=>[2,4,8,3,7,6,5,1]=>0001111
[4,6,7,1,2,5,8,3]=>[8,1,7,4,2,6,5,3]=>[4,6,8,3,7,5,2,1]=>1001011
[5,6,4,7,1,3,8,2]=>[8,7,1,6,5,4,3,2]=>[5,6,4,8,2,7,3,1]=>0100111
[7,4,5,3,1,6,8,2]=>[8,3,5,7,4,1,6,2]=>[8,2,3,5,4,7,6,1]=>0001111
[5,6,3,7,4,1,8,2]=>[8,4,7,6,5,3,1,2]=>[5,8,2,4,6,3,7,1]=>0000111
[5,6,3,7,8,1,2,4]=>[8,1,6,3,5,2,7,4]=>[5,7,8,4,3,6,2,1]=>1010101
[5,6,3,7,2,4,8,1]=>[8,7,6,3,5,2,4,1]=>[5,7,4,3,6,2,8,1]=>0010111
[5,6,7,2,8,1,3,4]=>[8,7,2,1,5,6,3,4]=>[5,6,7,3,2,8,4,1]=>0110011
[7,6,3,4,1,2,8,5]=>[4,1,8,3,6,7,2,5]=>[8,5,6,7,2,1,4,3]=>1010011
[7,6,3,2,4,1,8,5]=>[4,3,8,2,6,7,1,5]=>[8,5,6,7,1,4,2,3]=>0010011
[6,4,7,2,5,1,8,3]=>[8,5,7,6,4,2,1,3]=>[6,2,5,4,8,3,7,1]=>0001111
[6,5,3,7,1,8,2,4]=>[8,7,5,3,6,1,2,4]=>[7,2,8,4,3,5,6,1]=>0010111
[3,7,8,5,6,4,1,2]=>[4,1,3,6,8,5,7,2]=>[3,7,8,2,1,4,6,5]=>1000101
[1,7,8,5,6,3,4,2]=>[1,4,6,3,8,5,7,2]=>[1,7,8,2,4,3,6,5]=>0010101
[3,7,5,8,6,4,1,2]=>[4,1,3,6,8,7,5,2]=>[3,8,2,1,4,6,7,5]=>1000011
[5,7,3,8,6,4,1,2]=>[4,1,6,8,5,7,3,2]=>[5,7,3,6,8,2,1,4]=>1000011
[7,3,5,8,6,4,1,2]=>[4,1,6,8,3,7,5,2]=>[7,5,3,6,8,2,1,4]=>1001011
[3,5,7,8,6,4,1,2]=>[4,1,3,6,5,8,7,2]=>[3,5,7,8,2,1,4,6]=>1000001
[1,5,7,8,6,3,4,2]=>[1,4,6,3,5,8,7,2]=>[1,5,7,8,2,4,3,6]=>0010001
[1,5,7,8,3,6,4,2]=>[1,4,6,8,5,3,7,2]=>[1,5,6,3,7,8,2,4]=>0000101
[7,3,8,5,6,1,4,2]=>[4,6,8,3,7,1,5,2]=>[7,5,8,2,6,1,4,3]=>0010111
[7,8,3,5,6,1,4,2]=>[4,6,8,3,1,5,7,2]=>[7,8,2,6,5,1,4,3]=>0011101
[7,8,1,5,6,3,4,2]=>[4,6,8,1,3,5,7,2]=>[4,1,7,8,2,6,5,3]=>0011101
[5,1,7,8,3,6,4,2]=>[4,6,8,5,1,3,7,2]=>[5,1,4,7,8,2,6,3]=>0001101
[5,1,7,3,8,6,4,2]=>[4,6,8,5,1,7,3,2]=>[5,1,4,8,2,6,7,3]=>0001011
[7,8,1,5,3,6,4,2]=>[4,6,5,8,1,3,7,2]=>[7,8,2,6,3,5,1,4]=>0001101
[5,3,7,1,8,6,4,2]=>[4,6,8,5,3,7,1,2]=>[8,2,6,7,1,4,5,3]=>0001011
[1,5,7,3,8,6,4,2]=>[1,4,6,8,5,7,3,2]=>[1,5,7,3,6,8,2,4]=>0000011
[3,7,5,1,8,6,4,2]=>[4,6,3,5,8,7,1,2]=>[3,8,2,6,7,1,4,5]=>0000011
[3,7,5,8,1,6,4,2]=>[4,6,3,8,7,5,1,2]=>[3,8,2,6,5,7,1,4]=>0000111
[1,7,8,5,3,6,4,2]=>[1,4,6,5,8,3,7,2]=>[1,6,3,7,8,2,4,5]=>0000101
[3,7,8,5,1,6,4,2]=>[4,6,3,5,8,1,7,2]=>[3,7,8,2,6,1,4,5]=>0000101
[7,5,8,6,1,3,4,2]=>[4,6,1,3,8,7,5,2]=>[4,3,1,8,2,6,7,5]=>0110011
[5,7,8,1,6,3,4,2]=>[4,6,8,1,5,3,7,2]=>[4,1,5,7,8,2,6,3]=>0010101
[3,7,1,8,5,6,4,2]=>[4,6,3,8,7,1,5,2]=>[3,7,5,8,2,6,1,4]=>0000111
[7,5,8,1,6,3,4,2]=>[4,6,8,1,7,5,3,2]=>[4,1,8,2,6,5,7,3]=>0010111
[3,7,1,5,8,6,4,2]=>[4,6,3,8,1,7,5,2]=>[3,8,2,6,7,5,1,4]=>0001011
[1,5,3,7,8,6,4,2]=>[1,4,6,5,3,8,7,2]=>[1,7,8,2,4,5,3,6]=>0001001
[7,3,1,5,8,6,4,2]=>[4,3,6,8,1,7,5,2]=>[8,2,3,6,7,5,1,4]=>0001011
[7,8,1,3,5,6,4,2]=>[4,6,1,8,3,5,7,2]=>[7,8,2,6,5,3,1,4]=>0101101
[7,1,3,5,8,6,4,2]=>[4,6,1,8,3,7,5,2]=>[8,2,6,7,5,3,1,4]=>0101011
[4,3,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>1010101
[4,6,3,5,1,2,8,7]=>[5,1,6,4,3,2,8,7]=>[4,6,2,1,5,3,8,7]=>1001101
[6,2,4,5,1,3,8,7]=>[5,6,2,1,4,3,8,7]=>[5,4,1,6,3,2,8,7]=>0111101
[2,3,6,1,5,4,8,7]=>[5,2,3,6,1,4,8,7]=>[2,3,5,1,6,4,8,7]=>0001101
[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>[2,1,6,4,3,5,8,7]=>1010101
[8,7,6,1,3,2,4,5]=>[3,6,1,2,4,7,8,5]=>[3,1,8,5,4,2,6,7]=>0111001
[2,1,8,4,6,7,3,5]=>[2,1,7,8,4,3,6,5]=>[2,1,7,6,3,8,5,4]=>1001111
[3,8,1,5,6,7,2,4]=>[7,8,3,1,2,5,6,4]=>[3,8,4,1,7,6,5,2]=>0011111
[6,8,4,2,1,3,7,5]=>[2,4,1,7,8,6,3,5]=>[6,7,3,1,2,4,8,5]=>0100011
[2,1,4,5,8,3,7,6]=>[2,1,7,4,5,8,3,6]=>[2,1,4,5,7,3,8,6]=>1000011
[2,4,8,3,5,6,7,1]=>[7,2,8,4,3,5,6,1]=>[2,4,8,1,7,6,5,3]=>0001111
[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,8,6,5,7]=>1010101
[4,3,1,2,8,6,7,5]=>[3,1,4,2,7,8,6,5]=>[4,2,1,3,8,5,7,6]=>1010011
[5,1,6,7,8,4,3,2]=>[3,4,8,5,1,6,7,2]=>[6,7,8,2,4,5,1,3]=>0001001
[3,7,1,4,5,6,8,2]=>[8,7,3,1,4,5,6,2]=>[3,8,2,7,6,5,4,1]=>0011111
[8,6,4,7,5,3,1,2]=>[3,1,5,7,6,8,4,2]=>[7,4,8,2,1,3,5,6]=>1000011
[1,6,3,7,5,8,4,2]=>[1,4,8,7,6,3,5,2]=>[1,8,2,4,7,5,6,3]=>0000111
[4,7,3,8,5,6,1,2]=>[6,1,8,4,7,3,5,2]=>[4,7,5,8,2,1,6,3]=>1000111
[6,8,4,7,5,3,1,2]=>[3,1,5,7,8,6,4,2]=>[6,7,4,8,2,1,3,5]=>1000011
[1,7,6,5,3,8,4,2]=>[1,4,8,5,6,7,3,2]=>[1,8,2,4,5,6,7,3]=>0000011
[2,7,6,3,1,4,5,8]=>[3,2,6,1,4,7,5,8]=>[2,7,5,4,1,3,6,8]=>0011010
[2,7,6,4,5,1,3,8]=>[5,2,1,6,4,7,3,8]=>[2,7,3,1,5,4,6,8]=>0101010
[1,8,2,7,3,6,5,4]=>[1,5,6,7,8,2,3,4]=>[1,8,4,7,3,6,2,5]=>0000111
[3,1,2,8,4,6,7,5]=>[3,1,2,7,8,4,6,5]=>[3,2,1,7,6,4,8,5]=>1100111
[4,1,7,2,8,5,6,3]=>[6,8,4,1,7,2,5,3]=>[7,5,8,3,4,1,6,2]=>0010111
[2,8,4,1,5,6,3,7]=>[6,2,4,8,1,5,3,7]=>[2,6,5,1,8,7,3,4]=>0001111
[1,2,3,8,4,5,7,6]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,5,4,8,6]=>0001011
[2,4,8,3,1,5,6,7]=>[3,2,8,4,1,5,6,7]=>[2,4,8,7,6,5,1,3]=>0001111
[7,4,8,3,2,1,5,6]=>[2,3,8,7,4,1,5,6]=>[7,5,4,8,6,1,2,3]=>0001111
[6,3,7,1,8,4,5,2]=>[5,8,7,6,3,1,4,2]=>[7,4,6,1,5,3,8,2]=>0001111
[4,7,1,2,8,3,6,5]=>[6,1,8,4,7,2,3,5]=>[4,6,2,1,8,5,7,3]=>1000111
[1,2,8,7,6,3,5,4]=>[1,2,5,6,3,7,8,4]=>[1,2,5,3,8,4,6,7]=>0001001
[2,3,1,8,7,4,5,6]=>[3,2,1,7,4,5,8,6]=>[2,3,1,8,6,5,4,7]=>0101101
[2,6,1,4,8,7,3,5]=>[7,2,6,1,4,3,8,5]=>[2,6,3,8,5,4,1,7]=>0011101
[5,8,2,1,7,6,3,4]=>[2,6,7,1,5,8,3,4]=>[5,7,3,8,4,1,2,6]=>0010011
[1,2,3,4,8,7,5,6]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,8,6,5,7]=>0000101
[1,2,3,8,6,4,5,7]=>[1,2,3,6,4,8,5,7]=>[1,2,3,8,7,5,4,6]=>0001011
[1,2,8,5,3,4,6,7]=>[1,2,5,3,8,4,6,7]=>[1,2,8,7,6,4,3,5]=>0010111
[2,4,7,5,6,8,3,1]=>[3,2,8,4,7,5,6,1]=>[2,4,7,6,5,8,1,3]=>0000111
[3,1,8,5,7,4,2,6]=>[4,3,1,7,8,5,2,6]=>[7,2,3,1,4,8,6,5]=>0100111
[2,7,6,4,5,8,3,1]=>[3,2,8,6,4,7,5,1]=>[2,7,5,4,6,8,1,3]=>0001011
[4,8,1,7,6,3,2,5]=>[3,6,7,4,1,8,2,5]=>[4,8,5,1,3,7,2,6]=>0001011
[7,3,6,4,2,8,5,1]=>[5,4,8,6,7,3,2,1]=>[8,1,5,7,2,4,6,3]=>0000111
[5,8,7,1,4,3,2,6]=>[3,4,7,1,5,2,8,6]=>[5,8,6,2,4,1,3,7]=>0010101
[5,6,1,2,4,3,8,7]=>[4,1,6,2,5,3,8,7]=>[4,2,1,5,6,3,8,7]=>1010101
[8,4,6,2,1,3,7,5]=>[2,7,1,6,8,4,3,5]=>[6,4,7,3,1,2,8,5]=>0100111
[5,4,8,7,3,1,2,6]=>[3,1,7,5,4,2,8,6]=>[5,4,8,6,2,1,3,7]=>1001101
[6,8,3,7,2,5,4,1]=>[4,5,7,8,3,6,2,1]=>[6,7,2,5,3,8,1,4]=>0001011
[5,7,4,2,8,3,6,1]=>[6,8,4,7,5,2,3,1]=>[5,7,3,4,8,1,6,2]=>0000111
[6,4,7,2,1,8,3,5]=>[2,8,7,6,4,1,3,5]=>[7,3,8,5,4,6,1,2]=>0001111
[6,5,3,1,4,7,2,8]=>[7,3,5,1,6,4,2,8]=>[7,2,3,5,6,4,1,8]=>0010110
[5,7,8,2,6,4,1,3]=>[4,6,2,8,5,1,7,3]=>[5,7,8,3,2,6,1,4]=>0100101
[2,6,8,4,5,7,1,3]=>[7,2,1,8,4,6,5,3]=>[2,6,8,3,1,7,5,4]=>0101011
[6,3,7,2,8,5,1,4]=>[5,8,7,3,6,2,1,4]=>[8,4,3,7,1,5,6,2]=>0010111
[5,3,6,7,1,8,4,2]=>[4,8,7,5,3,6,1,2]=>[6,7,1,4,5,3,8,2]=>0001011
[8,1,4,2,7,5,3,6]=>[5,4,7,1,8,2,3,6]=>[7,3,8,6,2,4,1,5]=>0010111
[2,7,1,4,3,8,5,6]=>[4,2,8,1,7,3,5,6]=>[2,4,1,7,5,8,6,3]=>0010111
[1,7,5,2,8,6,3,4]=>[1,6,5,2,8,7,3,4]=>[1,8,4,2,6,7,3,5]=>0010011
[4,5,3,2,7,1,8,6]=>[8,3,5,4,2,7,1,6]=>[4,5,2,3,8,6,7,1]=>0001011
[5,3,6,2,8,1,7,4]=>[7,8,6,5,3,2,1,4]=>[7,1,8,4,5,3,6,2]=>0001111
[1,8,4,7,2,5,3,6]=>[1,5,7,8,4,2,3,6]=>[1,7,3,8,6,2,5,4]=>0001111
[3,5,7,4,1,6,8,2]=>[8,4,3,7,5,1,6,2]=>[3,5,8,2,4,7,6,1]=>0000111
[4,5,8,3,1,7,6,2]=>[6,3,7,4,5,8,1,2]=>[4,5,8,2,3,7,1,6]=>0000011
[3,4,7,8,2,1,6,5]=>[2,6,3,4,8,1,7,5]=>[3,4,6,1,2,7,8,5]=>0000101
[5,2,6,1,3,4,8,7]=>[6,5,2,1,3,4,8,7]=>[5,3,2,6,4,1,8,7]=>0111101
[7,2,8,6,5,1,3,4]=>[5,6,2,1,8,7,3,4]=>[7,3,2,6,8,4,1,5]=>0110011
[6,2,7,8,5,4,1,3]=>[4,5,2,8,6,1,7,3]=>[7,8,3,2,5,6,1,4]=>0100101
[4,8,2,6,5,7,1,3]=>[7,6,2,4,8,1,5,3]=>[4,8,3,2,6,1,7,5]=>0100111
[5,7,1,4,6,3,2,8]=>[3,6,7,1,5,4,2,8]=>[5,7,2,6,4,1,3,8]=>0010110
[5,7,8,3,2,1,4,6]=>[2,3,8,1,5,4,7,6]=>[5,7,8,6,4,1,2,3]=>0010101
[8,3,2,1,4,7,6,5]=>[2,3,6,1,7,8,4,5]=>[8,5,7,4,1,2,3,6]=>0010011
[1,7,5,3,8,2,6,4]=>[1,6,8,5,7,3,2,4]=>[1,8,4,5,7,2,6,3]=>0000111
[8,6,3,2,7,5,1,4]=>[5,3,7,2,6,8,1,4]=>[8,4,2,3,7,1,5,6]=>0010011
[8,7,4,2,6,1,5,3]=>[5,6,4,7,2,1,8,3]=>[6,1,5,2,8,3,4,7]=>0001101
[5,2,6,1,8,7,4,3]=>[4,7,6,5,2,1,8,3]=>[8,3,6,1,4,5,2,7]=>0001101
[1,7,6,4,3,8,2,5]=>[1,8,4,6,3,7,2,5]=>[1,8,5,3,4,6,7,2]=>0001011
[5,1,4,3,2,7,8,6]=>[3,4,5,1,2,8,7,6]=>[5,2,4,1,3,7,8,6]=>0011001
[5,3,1,7,8,4,2,6]=>[4,3,8,5,1,2,7,6]=>[5,1,4,7,8,6,2,3]=>0001101
[4,1,6,8,5,7,3,2]=>[3,7,4,1,8,6,5,2]=>[4,1,3,6,8,2,7,5]=>0010011
[6,7,1,8,3,4,2,5]=>[4,8,7,1,3,6,2,5]=>[4,1,6,8,5,3,7,2]=>0011011
[7,8,2,5,1,6,3,4]=>[6,5,8,2,1,3,7,4]=>[7,8,4,2,5,1,6,3]=>0011101
[5,7,1,6,2,8,3,4]=>[8,6,7,1,5,2,3,4]=>[5,6,2,7,3,8,4,1]=>0010111
[6,7,2,5,1,8,3,4]=>[8,5,7,2,1,6,3,4]=>[6,7,3,8,4,2,5,1]=>0011011
[6,7,2,4,3,8,1,5]=>[8,4,7,2,3,6,1,5]=>[4,2,6,8,5,3,7,1]=>0011011
[1,8,2,7,4,5,3,6]=>[1,5,7,8,2,4,3,6]=>[1,5,2,7,3,8,6,4]=>0001111
[2,4,3,8,5,6,1,7]=>[6,2,4,3,8,5,1,7]=>[2,4,3,8,7,1,6,5]=>0010111
[4,7,1,6,2,5,3,8]=>[5,6,7,4,1,2,3,8]=>[4,5,1,6,2,7,3,8]=>0001110
[4,7,1,8,5,6,2,3]=>[6,8,1,4,7,2,5,3]=>[4,7,5,8,3,1,6,2]=>0100111
[3,7,1,6,2,8,4,5]=>[8,6,3,7,1,2,4,5]=>[3,6,2,7,4,8,5,1]=>0001111
[2,6,7,3,8,5,4,1]=>[4,2,5,8,7,6,3,1]=>[2,6,7,3,5,8,1,4]=>0000011
[4,2,1,6,5,3,8,7]=>[2,5,4,1,6,3,8,7]=>[6,3,4,1,2,5,8,7]=>0010101
[6,2,4,3,1,5,8,7]=>[3,4,6,2,1,5,8,7]=>[4,2,6,5,1,3,8,7]=>0011101
[4,6,2,1,5,3,8,7]=>[2,5,6,4,1,3,8,7]=>[4,5,1,2,6,3,8,7]=>0001101
[6,8,7,2,1,4,3,5]=>[2,4,7,1,3,6,8,5]=>[4,1,2,6,8,5,3,7]=>0011001
[6,8,2,1,7,4,3,5]=>[2,4,7,8,1,6,3,5]=>[6,7,3,8,5,1,2,4]=>0001011
[8,6,2,4,3,1,5,7]=>[3,4,6,2,1,8,5,7]=>[4,2,8,7,5,1,3,6]=>0011011
[6,8,2,4,3,1,7,5]=>[3,4,7,2,8,6,1,5]=>[4,2,6,7,1,3,8,5]=>0010011
[2,8,4,6,7,3,1,5]=>[3,2,7,8,4,1,6,5]=>[2,7,6,1,3,8,5,4]=>0001111
[6,8,7,2,4,3,1,5]=>[3,4,7,2,1,6,8,5]=>[4,2,6,8,5,1,3,7]=>0011001
[8,4,2,6,3,5,1,7]=>[5,6,4,8,2,3,1,7]=>[8,7,1,5,2,6,3,4]=>0001111
[8,2,4,3,6,5,1,7]=>[5,4,6,2,8,3,1,7]=>[4,2,6,3,8,7,1,5]=>0010111
[4,2,1,6,5,8,7,3]=>[2,7,4,1,6,5,8,3]=>[6,5,8,3,4,1,2,7]=>0010101
[6,2,1,8,4,3,7,5]=>[2,4,7,8,6,1,3,5]=>[7,3,8,5,6,1,2,4]=>0000111
[2,4,8,6,7,5,1,3]=>[5,2,1,4,7,8,6,3]=>[2,4,8,3,1,5,7,6]=>0100011
[4,2,8,6,5,7,1,3]=>[7,4,2,1,6,8,5,3]=>[8,3,2,4,1,7,5,6]=>0110011
[6,4,8,2,1,5,7,3]=>[2,7,8,6,4,1,5,3]=>[7,5,4,6,1,2,8,3]=>0001111
[2,6,8,4,7,1,5,3]=>[5,2,7,8,4,6,1,3]=>[2,6,8,3,7,1,5,4]=>0001011
[4,8,6,7,2,1,3,5]=>[2,7,1,4,3,8,6,5]=>[4,8,5,3,1,2,7,6]=>0101011
[6,2,3,5,1,4,8,7]=>[5,6,2,3,1,4,8,7]=>[5,1,6,4,3,2,8,7]=>0111101
[7,4,5,2,3,8,6,1]=>[6,5,2,8,4,7,3,1]=>[8,1,6,7,3,2,5,4]=>0101011
[7,3,2,5,4,8,6,1]=>[6,3,5,8,2,7,4,1]=>[5,2,3,8,1,6,7,4]=>0001011
[3,5,1,6,4,2,8,7]=>[4,6,3,5,1,2,8,7]=>[3,5,1,4,6,2,8,7]=>0001101
[3,6,2,4,5,1,8,7]=>[5,6,3,2,4,1,8,7]=>[3,6,1,5,4,2,8,7]=>0011101
[7,2,3,4,5,8,6,1]=>[6,8,2,3,4,7,5,1]=>[8,1,6,7,5,4,3,2]=>0111011
[8,2,3,4,5,7,1,6]=>[7,8,2,3,4,5,1,6]=>[7,1,8,6,5,4,3,2]=>0111111
[6,7,3,4,8,5,2,1]=>[2,5,8,3,7,6,4,1]=>[6,8,1,2,5,7,4,3]=>0010011
[5,7,1,3,8,6,2,4]=>[6,8,1,3,5,7,2,4]=>[5,8,4,3,1,6,7,2]=>0110011
[4,8,1,5,6,7,3,2]=>[3,7,8,4,1,5,6,2]=>[4,8,2,7,6,5,1,3]=>0001111
[6,8,2,5,1,7,3,4]=>[7,5,8,2,1,6,3,4]=>[6,8,4,2,5,1,7,3]=>0011011
[7,8,3,4,6,2,1,5]=>[2,6,8,3,4,1,7,5]=>[6,1,2,7,8,5,4,3]=>0011101
[4,8,2,5,1,6,7,3]=>[7,5,8,4,2,1,6,3]=>[4,5,2,7,6,1,8,3]=>0001111
[3,8,2,5,4,7,6,1]=>[6,5,3,7,2,8,4,1]=>[3,5,2,7,4,8,1,6]=>0001011
[3,7,6,1,8,5,2,4]=>[5,8,3,1,6,7,2,4]=>[3,8,4,1,5,6,7,2]=>0010011
[2,1,5,7,3,8,6,4]=>[2,1,6,8,5,7,3,4]=>[2,1,5,7,3,6,8,4]=>1000011
[5,4,7,1,2,8,6,3]=>[6,1,8,5,4,7,2,3]=>[5,4,7,2,1,6,8,3]=>1001011
[4,1,2,3,7,8,6,5]=>[4,1,2,3,6,8,7,5]=>[4,3,2,1,7,8,5,6]=>1110001
[3,4,2,1,8,5,6,7]=>[2,4,3,1,8,5,6,7]=>[3,4,1,2,8,7,6,5]=>0010111
[8,2,3,5,7,1,4,6]=>[7,8,2,3,1,5,4,6]=>[8,6,5,1,7,4,3,2]=>0111111
[5,4,8,3,6,7,1,2]=>[7,1,8,5,4,3,6,2]=>[5,4,8,2,1,7,6,3]=>1001111
[4,5,8,3,6,7,2,1]=>[2,7,8,4,5,3,6,1]=>[4,5,8,1,2,7,6,3]=>0000111
[2,1,5,8,4,6,7,3]=>[2,1,7,8,5,4,6,3]=>[2,1,5,8,3,7,6,4]=>1000111
[4,6,8,3,5,2,7,1]=>[7,5,8,4,3,6,2,1]=>[4,6,8,1,7,2,5,3]=>0001011
[5,7,8,3,2,4,1,6]=>[4,3,8,2,5,1,7,6]=>[5,7,8,6,1,4,2,3]=>0010101
[4,3,1,6,5,8,7,2]=>[7,3,4,1,6,5,8,2]=>[6,5,8,2,3,4,1,7]=>0010101
[8,2,7,4,1,3,6,5]=>[4,6,2,7,8,1,3,5]=>[7,3,2,6,1,4,8,5]=>0100111
[3,7,8,2,1,4,6,5]=>[2,6,3,1,8,4,7,5]=>[3,6,4,1,2,7,8,5]=>0010101
[3,1,5,2,4,8,7,6]=>[5,3,1,2,4,7,8,6]=>[5,4,2,3,1,8,6,7]=>0111001
[6,1,3,5,4,8,7,2]=>[7,5,1,6,3,4,8,2]=>[6,4,8,2,5,3,1,7]=>0101101
[1,6,7,4,8,5,3,2]=>[1,3,5,8,7,6,4,2]=>[1,6,8,2,3,5,7,4]=>0000011
[8,1,2,5,4,6,3,7]=>[6,1,5,8,2,4,3,7]=>[8,7,3,5,2,1,6,4]=>1001111
[1,8,5,3,7,4,6,2]=>[1,6,7,5,8,3,4,2]=>[1,8,2,6,3,7,4,5]=>0000111
[5,3,2,8,7,1,4,6]=>[7,3,5,2,1,4,8,6]=>[8,6,4,2,3,5,1,7]=>0011101
[4,2,8,5,7,6,1,3]=>[6,4,2,1,7,8,5,3]=>[7,5,8,3,2,4,1,6]=>0110011
[1,4,5,8,6,7,3,2]=>[1,3,7,4,5,8,6,2]=>[1,4,5,8,2,3,7,6]=>0000011
[1,6,5,4,8,2,3,7]=>[1,8,2,5,6,4,3,7]=>[1,6,4,5,8,7,3,2]=>0100111
[5,2,6,3,8,1,4,7]=>[8,6,5,2,3,1,4,7]=>[5,3,8,7,4,2,6,1]=>0011111
[6,2,8,4,3,1,7,5]=>[3,4,7,8,6,2,1,5]=>[7,1,3,8,5,6,2,4]=>0000111
[7,1,6,2,3,4,5,8]=>[6,7,1,2,3,4,5,8]=>[7,5,3,1,6,4,2,8]=>0111110
[1,8,5,4,3,6,2,7]=>[1,6,4,5,8,3,2,7]=>[1,8,7,2,6,3,4,5]=>0000111
[1,8,3,6,5,2,7,4]=>[1,7,5,6,8,3,2,4]=>[1,7,2,8,4,6,3,5]=>0000111
[6,1,5,2,4,7,8,3]=>[8,5,6,1,2,4,7,3]=>[5,2,7,8,3,6,4,1]=>0011101
[4,1,8,5,2,7,6,3]=>[6,5,4,1,7,8,2,3]=>[7,2,5,8,3,4,1,6]=>0010011
[4,3,8,5,1,2,6,7]=>[5,1,4,3,8,2,6,7]=>[4,3,8,7,6,2,1,5]=>1010111
[4,1,8,2,3,7,5,6]=>[7,4,1,2,8,3,5,6]=>[4,2,8,6,3,1,7,5]=>0110111
[4,6,3,1,5,2,7,8]=>[5,3,6,4,1,2,7,8]=>[4,5,1,6,2,3,7,8]=>0001100
[5,7,3,4,1,6,2,8]=>[6,4,7,3,5,1,2,8]=>[5,6,1,7,2,4,3,8]=>0010110
[4,2,8,1,5,6,7,3]=>[7,8,4,2,1,5,6,3]=>[7,6,5,1,8,3,4,2]=>0011111
[1,5,8,4,2,6,7,3]=>[1,7,4,8,5,2,6,3]=>[1,5,7,6,2,8,3,4]=>0000111
[1,7,3,8,5,6,2,4]=>[1,6,8,3,7,2,5,4]=>[1,6,2,7,5,8,4,3]=>0010111
[4,2,6,1,5,3,7,8]=>[5,6,4,2,1,3,7,8]=>[5,1,6,3,4,2,7,8]=>0011100
[1,2,7,8,5,6,3,4]=>[1,2,6,3,8,5,7,4]=>[1,2,7,8,4,3,6,5]=>0010101
[1,2,6,8,5,3,7,4]=>[1,2,7,5,8,6,3,4]=>[1,2,6,7,3,8,4,5]=>0000011
[1,2,6,4,8,3,7,5]=>[1,2,7,8,6,4,3,5]=>[1,2,7,3,8,5,6,4]=>0000111
[1,8,4,2,3,6,7,5]=>[1,4,2,7,8,3,6,5]=>[1,7,6,3,2,4,8,5]=>0100111
[4,1,7,2,3,6,8,5]=>[8,4,1,2,7,3,6,5]=>[4,2,8,5,7,6,3,1]=>0110111
[3,2,6,7,4,1,8,5]=>[4,3,2,8,7,6,1,5]=>[3,2,6,8,5,7,1,4]=>0100011
[5,6,2,7,1,4,8,3]=>[8,7,6,2,5,1,4,3]=>[5,7,4,2,8,3,6,1]=>0010111
[2,7,8,5,4,6,3,1]=>[3,2,6,5,8,4,7,1]=>[2,7,8,1,3,6,4,5]=>0000101
[2,1,3,7,8,5,6,4]=>[2,1,3,6,8,5,7,4]=>[2,1,3,7,8,4,6,5]=>1000101
[2,3,6,1,8,5,7,4]=>[7,2,3,8,6,1,5,4]=>[2,3,7,5,6,1,8,4]=>0000111
[5,2,3,4,8,7,1,6]=>[7,5,2,3,4,1,8,6]=>[5,4,3,2,8,6,1,7]=>0111101
[4,1,8,2,5,7,3,6]=>[7,8,4,1,2,5,3,6]=>[7,3,4,1,8,6,5,2]=>0011111
[3,1,8,4,7,2,5,6]=>[7,3,1,8,4,2,5,6]=>[8,6,2,3,1,7,5,4]=>0101111
[6,2,1,4,7,8,3,5]=>[2,8,6,1,4,3,7,5]=>[6,3,7,8,5,4,1,2]=>0011101
[8,3,4,2,1,6,5,7]=>[2,4,6,3,8,1,5,7]=>[6,1,2,4,3,8,7,5]=>0010111
[5,3,2,8,1,6,4,7]=>[6,3,8,5,2,1,4,7]=>[6,1,8,7,4,5,2,3]=>0001111
[2,4,5,8,3,6,1,7]=>[6,2,8,4,5,3,1,7]=>[2,4,5,8,7,1,6,3]=>0000111
[3,5,8,1,2,6,4,7]=>[6,1,3,8,5,2,4,7]=>[3,5,6,2,1,8,7,4]=>1000111
[8,6,1,3,5,2,4,7]=>[5,6,1,3,2,8,4,7]=>[8,7,4,3,1,5,2,6]=>0111011
[7,4,1,8,3,2,5,6]=>[3,8,4,7,1,2,5,6]=>[7,5,1,3,4,8,6,2]=>0001111
[2,4,6,5,1,7,8,3]=>[8,2,5,4,6,1,7,3]=>[2,4,7,8,3,5,6,1]=>0000101
[1,3,8,6,2,7,4,5]=>[1,7,3,6,2,8,4,5]=>[1,3,8,5,2,7,4,6]=>0001011
[4,3,7,5,6,1,8,2]=>[8,6,4,3,7,5,1,2]=>[4,3,8,2,6,5,7,1]=>0010111
[4,7,5,8,3,1,2,6]=>[3,1,8,4,7,5,2,6]=>[4,8,6,5,7,2,1,3]=>1000111
[4,6,7,2,8,3,1,5]=>[3,8,7,4,2,6,1,5]=>[4,6,7,1,3,8,5,2]=>0001011
[2,5,1,3,6,8,7,4]=>[7,2,1,5,3,6,8,4]=>[2,6,8,4,5,3,1,7]=>0101001
[5,8,3,6,4,7,1,2]=>[7,1,6,8,5,3,4,2]=>[5,6,3,8,2,1,7,4]=>1000111
[3,5,8,6,7,4,2,1]=>[2,4,3,7,5,8,6,1]=>[3,5,8,1,2,4,7,6]=>0000011
[8,6,1,7,2,5,4,3]=>[4,5,7,6,1,8,2,3]=>[8,3,7,2,5,1,4,6]=>0001011
[8,7,6,1,2,3,5,4]=>[5,1,2,6,3,7,8,4]=>[5,3,2,1,8,4,6,7]=>1101001
[4,6,2,8,5,1,3,7]=>[5,8,2,4,6,1,3,7]=>[4,6,1,5,8,7,3,2]=>0100111
[6,5,2,7,4,3,8,1]=>[8,4,7,5,6,2,3,1]=>[6,2,4,5,7,3,8,1]=>0000111
[4,6,5,2,7,3,8,1]=>[8,7,5,4,6,2,3,1]=>[4,7,3,5,6,2,8,1]=>0000111
[3,1,6,2,4,8,7,5]=>[7,3,1,2,6,4,8,5]=>[8,5,6,4,2,3,1,7]=>0110101
[8,7,5,1,2,6,4,3]=>[4,1,6,5,7,2,8,3]=>[8,3,6,2,1,4,5,7]=>1000101
[8,2,3,4,6,7,1,5]=>[7,8,2,3,4,1,6,5]=>[7,6,1,8,5,4,3,2]=>0111111
[7,8,5,3,6,4,2,1]=>[2,4,6,5,8,3,7,1]=>[6,3,7,8,1,2,4,5]=>0000101
[2,1,4,8,7,5,6,3]=>[2,1,6,4,7,5,8,3]=>[2,1,4,8,3,6,5,7]=>1000101
[7,4,6,8,5,1,3,2]=>[3,5,1,8,7,4,6,2]=>[3,1,8,2,5,7,6,4]=>0100111
[2,1,8,6,4,3,7,5]=>[2,1,4,7,6,8,3,5]=>[2,1,7,3,4,8,5,6]=>1000011
[8,4,2,5,6,1,7,3]=>[7,6,4,8,2,5,1,3]=>[6,5,2,7,1,8,3,4]=>0001111
[8,4,7,6,2,1,5,3]=>[2,5,6,7,4,8,1,3]=>[7,1,2,5,4,8,3,6]=>0001011
[3,5,7,6,4,1,8,2]=>[8,4,3,6,5,7,1,2]=>[3,5,8,2,4,6,7,1]=>0000011
[4,7,5,2,1,3,8,6]=>[2,5,1,4,8,7,3,6]=>[4,8,6,7,3,1,2,5]=>0100011
[7,1,2,3,5,8,4,6]=>[8,1,2,7,3,5,4,6]=>[7,4,8,6,5,3,2,1]=>1101111
[6,1,8,2,7,3,4,5]=>[7,8,6,1,2,3,4,5]=>[6,3,7,4,1,8,5,2]=>0011111
[7,8,6,1,3,2,5,4]=>[3,5,1,6,2,8,7,4]=>[3,1,5,2,7,8,4,6]=>0101001
[5,4,1,6,3,8,7,2]=>[7,6,4,5,1,3,8,2]=>[8,2,6,3,4,5,1,7]=>0001101
[5,4,1,2,8,7,6,3]=>[6,1,4,5,2,7,8,3]=>[8,3,4,5,2,1,6,7]=>1001001
[1,5,4,2,7,8,3,6]=>[1,8,4,5,2,3,7,6]=>[1,7,8,6,3,4,5,2]=>0001101
[5,1,3,8,4,2,7,6]=>[4,7,1,5,3,8,2,6]=>[5,3,1,4,7,2,8,6]=>0101011
[3,1,6,8,7,4,2,5]=>[4,3,1,7,2,6,8,5]=>[6,8,5,2,3,1,4,7]=>0101001
[3,6,5,8,4,7,1,2]=>[7,1,3,8,6,5,4,2]=>[3,6,5,8,2,1,7,4]=>1000111
[6,5,8,4,3,1,2,7]=>[3,1,4,8,6,5,2,7]=>[6,5,8,7,2,1,3,4]=>1000111
[8,5,1,3,7,4,6,2]=>[6,7,1,5,8,3,4,2]=>[6,3,1,8,2,7,4,5]=>0100111
[3,2,5,8,4,1,7,6]=>[4,3,2,7,5,8,1,6]=>[3,2,5,7,1,4,8,6]=>0100011
[2,1,7,8,3,4,6,5]=>[2,1,6,3,8,4,7,5]=>[2,1,6,4,3,7,8,5]=>1010101
[5,6,1,8,2,7,4,3]=>[4,7,8,6,5,1,2,3]=>[5,6,1,4,7,2,8,3]=>0000111
[3,6,8,5,2,7,4,1]=>[4,7,3,5,8,6,2,1]=>[3,6,7,2,8,1,4,5]=>0000011
[2,1,6,5,4,8,3,7]=>[2,1,8,5,6,4,3,7]=>[2,1,6,4,5,8,7,3]=>1000111
[2,1,7,3,5,8,6,4]=>[2,1,6,8,3,7,5,4]=>[2,1,7,5,3,6,8,4]=>1001011
[3,5,7,8,4,6,1,2]=>[6,1,3,8,5,4,7,2]=>[3,5,7,8,2,1,6,4]=>1000101
[7,5,2,8,4,6,3,1]=>[3,6,8,5,7,2,4,1]=>[6,2,7,4,5,8,1,3]=>0000111
[7,6,2,8,5,1,4,3]=>[4,5,8,2,6,7,1,3]=>[7,1,4,2,5,6,8,3]=>0010011
[4,7,5,6,3,8,2,1]=>[2,8,6,4,7,5,3,1]=>[4,7,3,6,5,8,1,2]=>0000111
[4,2,7,5,8,3,6,1]=>[6,8,4,2,7,5,3,1]=>[8,1,6,5,7,3,4,2]=>0010111
[7,8,1,2,3,4,6,5]=>[6,1,2,3,8,4,7,5]=>[6,4,3,2,1,7,8,5]=>1110101
[6,8,5,2,1,7,3,4]=>[2,7,5,1,8,6,3,4]=>[6,8,4,1,2,7,3,5]=>0010011
[7,1,2,4,8,5,6,3]=>[6,1,8,2,7,4,5,3]=>[6,4,2,1,7,5,8,3]=>1010111
[8,7,6,2,4,3,1,5]=>[3,4,6,2,1,7,8,5]=>[4,2,8,5,1,3,6,7]=>0011001
[6,5,8,7,4,1,3,2]=>[3,4,1,7,6,5,8,2]=>[3,1,6,5,8,2,4,7]=>0100101
[7,6,3,1,5,8,4,2]=>[4,3,8,6,1,7,5,2]=>[7,5,1,4,6,8,2,3]=>0001011
[4,6,3,7,5,2,1,8]=>[2,5,7,4,6,3,1,8]=>[4,7,1,2,5,6,3,8]=>0000110
[3,2,1,6,8,4,5,7]=>[2,3,1,8,4,6,5,7]=>[3,1,2,6,8,7,5,4]=>0101011
[6,2,5,1,7,4,8,3]=>[8,7,5,6,2,1,4,3]=>[8,3,5,2,7,4,6,1]=>0001111
[7,4,1,5,3,8,2,6]=>[8,5,4,7,1,3,2,6]=>[8,6,3,4,7,2,5,1]=>0001111
[3,4,1,2,7,8,6,5]=>[4,1,3,2,6,8,7,5]=>[3,4,2,1,7,8,5,6]=>1010001
[5,4,8,3,7,1,6,2]=>[6,7,8,5,4,3,1,2]=>[5,4,8,2,7,1,6,3]=>0001111
[3,1,2,4,7,6,8,5]=>[3,1,2,4,8,7,6,5]=>[3,2,1,4,7,6,8,5]=>1100011
[7,1,4,3,5,2,8,6]=>[5,4,8,1,3,7,2,6]=>[8,6,7,2,4,1,5,3]=>0011011
[8,2,1,5,6,4,3,7]=>[2,4,6,8,1,5,3,7]=>[8,7,3,6,5,1,2,4]=>0001111
[4,7,1,8,2,5,3,6]=>[5,8,7,4,1,2,3,6]=>[4,5,1,7,3,8,6,2]=>0001111
[8,4,7,6,2,3,1,5]=>[3,6,2,7,4,8,1,5]=>[8,5,4,7,1,3,2,6]=>0101011
[5,7,2,3,8,1,6,4]=>[6,8,2,7,5,3,1,4]=>[5,8,4,7,1,6,3,2]=>0100111
[3,2,5,6,7,8,1,4]=>[8,3,2,1,5,6,7,4]=>[3,2,5,6,7,8,4,1]=>0110001
[4,3,8,5,2,1,6,7]=>[2,5,4,3,8,1,6,7]=>[4,3,8,7,6,1,2,5]=>0010111
[5,6,3,1,8,2,7,4]=>[7,3,8,6,5,1,2,4]=>[5,8,4,6,1,7,2,3]=>0000111
[1,5,6,3,4,8,2,7]=>[1,8,6,3,5,4,2,7]=>[1,5,6,4,3,8,7,2]=>0010111
[2,1,4,5,8,6,3,7]=>[2,1,6,4,5,8,3,7]=>[2,1,4,5,8,7,3,6]=>1000011
[5,8,6,2,3,7,4,1]=>[4,7,2,6,5,8,3,1]=>[5,7,3,2,8,1,4,6]=>0100011
[1,8,3,4,7,6,2,5]=>[1,6,7,3,4,8,2,5]=>[1,8,5,4,3,7,2,6]=>0011011
[1,3,2,8,5,4,6,7]=>[1,3,2,5,8,4,6,7]=>[1,3,2,8,7,6,4,5]=>0100111
[3,2,1,8,6,5,4,7]=>[2,3,1,5,6,8,4,7]=>[3,1,2,8,7,4,5,6]=>0100011
[6,7,2,1,8,4,3,5]=>[2,4,8,7,1,6,3,5]=>[6,8,5,1,2,4,7,3]=>0001011
[5,4,7,6,1,8,2,3]=>[8,6,1,5,4,7,2,3]=>[5,4,7,2,6,8,3,1]=>0101011
[3,5,6,8,4,7,2,1]=>[2,7,3,8,5,6,4,1]=>[3,5,6,8,1,2,7,4]=>0000011
[6,7,3,8,4,5,2,1]=>[2,5,8,7,3,6,4,1]=>[6,7,4,8,1,2,5,3]=>0001011
[2,1,8,7,6,4,3,5]=>[2,1,4,6,3,7,8,5]=>[2,1,8,5,3,4,6,7]=>1001001
[2,5,3,7,6,8,1,4]=>[8,2,5,3,1,7,6,4]=>[2,7,6,8,4,3,5,1]=>0011011
[8,7,2,3,5,4,1,6]=>[4,5,2,7,3,1,8,6]=>[5,3,2,8,6,1,4,7]=>0101101
[8,1,4,2,3,6,7,5]=>[4,7,1,2,8,3,6,5]=>[7,6,3,1,4,2,8,5]=>0110111
[1,8,2,5,7,6,3,4]=>[1,6,7,2,3,8,5,4]=>[1,7,5,3,8,4,2,6]=>0011011
[4,1,6,8,2,3,7,5]=>[7,4,1,2,8,6,3,5]=>[4,2,6,7,3,1,8,5]=>0110011
[3,1,7,4,8,5,2,6]=>[5,3,1,8,7,4,2,6]=>[7,2,3,1,5,8,6,4]=>0100111
[6,4,2,8,5,1,3,7]=>[5,4,2,8,6,1,3,7]=>[6,1,5,8,7,3,2,4]=>0100111
[8,6,2,4,1,3,7,5]=>[4,7,2,1,6,8,3,5]=>[4,1,7,3,2,8,5,6]=>0110011
[6,7,5,1,4,2,8,3]=>[8,4,5,1,7,6,2,3]=>[6,8,3,5,7,2,4,1]=>0010011
[6,2,4,1,7,5,8,3]=>[8,4,7,2,6,1,5,3]=>[4,2,8,3,7,5,6,1]=>0010111
[3,1,5,4,2,8,6,7]=>[4,3,1,5,2,8,6,7]=>[5,2,3,1,4,8,7,6]=>0101011
[6,2,7,1,4,8,5,3]=>[5,8,7,2,6,1,4,3]=>[6,1,5,8,3,7,4,2]=>0010111
[4,3,2,1,8,5,7,6]=>[2,3,4,1,7,8,5,6]=>[4,1,2,3,7,5,8,6]=>0010011
[4,2,1,7,3,6,5,8]=>[2,6,4,1,7,3,5,8]=>[6,3,4,1,2,7,5,8]=>0010110
[7,4,3,2,8,1,6,5]=>[6,3,4,8,7,2,1,5]=>[8,5,7,1,6,2,3,4]=>0000111
[2,8,5,6,1,4,3,7]=>[4,2,6,1,8,5,3,7]=>[2,4,1,8,7,3,6,5]=>0010111
[5,7,4,8,1,3,6,2]=>[6,8,1,7,5,4,3,2]=>[5,7,3,1,6,4,8,2]=>0100111
[3,6,7,8,1,2,5,4]=>[5,1,3,8,2,6,7,4]=>[3,5,2,1,6,7,8,4]=>1001001
[2,7,4,1,8,3,6,5]=>[6,2,4,8,7,1,3,5]=>[2,6,1,8,5,7,3,4]=>0000111
[3,6,4,7,8,1,2,5]=>[8,1,3,6,4,2,7,5]=>[3,7,8,5,4,6,2,1]=>1001101
[3,7,4,8,5,2,1,6]=>[2,5,3,8,7,4,1,6]=>[3,7,1,2,5,8,6,4]=>0000111
[4,8,1,7,6,2,3,5]=>[6,7,1,4,2,8,3,5]=>[4,8,5,2,7,3,1,6]=>0101011
[5,8,7,1,3,6,4,2]=>[4,6,1,7,5,3,8,2]=>[5,8,2,6,3,1,4,7]=>0100101
[2,8,7,1,6,3,5,4]=>[5,2,6,7,1,3,8,4]=>[2,5,1,6,3,8,4,7]=>0001101
[3,8,7,6,2,1,5,4]=>[2,5,3,6,1,7,8,4]=>[3,5,1,2,8,4,6,7]=>0001001
[7,3,8,6,5,1,2,4]=>[5,1,6,3,8,7,2,4]=>[8,4,3,6,7,2,1,5]=>1010011
[5,8,6,4,3,2,1,7]=>[2,3,4,6,5,8,1,7]=>[5,8,7,1,2,3,4,6]=>0000011
[8,7,6,2,5,3,1,4]=>[3,5,6,2,1,7,8,4]=>[8,4,2,5,1,3,6,7]=>0011001
[8,1,2,3,4,7,6,5]=>[6,1,2,3,7,8,4,5]=>[8,5,7,4,3,2,1,6]=>1110011
[8,3,1,7,6,5,4,2]=>[4,3,5,6,7,8,1,2]=>[8,2,3,5,7,1,4,6]=>0000011
[8,3,2,1,7,6,5,4]=>[2,3,5,6,7,8,1,4]=>[7,1,2,3,5,8,4,6]=>0000011
[8,4,1,7,6,5,3,2]=>[3,5,4,6,7,8,1,2]=>[8,2,5,7,1,3,4,6]=>0000011
[2,5,8,6,3,1,4,7]=>[3,2,6,1,5,8,4,7]=>[2,5,8,7,4,1,3,6]=>0010011
[4,5,6,2,3,8,1,7]=>[8,6,2,4,5,3,1,7]=>[4,5,6,3,2,8,7,1]=>0100111
[5,4,6,1,3,8,2,7]=>[8,6,1,5,4,3,2,7]=>[5,4,8,7,2,6,3,1]=>0101111
[4,8,6,5,7,1,2,3]=>[7,1,2,4,6,8,5,3]=>[4,8,3,2,1,7,5,6]=>1100011
[3,1,2,7,8,6,4,5]=>[3,1,2,6,4,8,7,5]=>[3,2,1,7,8,5,4,6]=>1101001
[7,5,1,8,2,4,3,6]=>[4,8,5,1,7,2,3,6]=>[4,1,7,3,5,8,6,2]=>0010111
[3,5,8,1,2,4,7,6]=>[7,1,3,2,5,8,4,6]=>[3,5,7,4,2,1,8,6]=>1010011
[2,7,5,8,3,4,1,6]=>[4,2,8,3,7,5,1,6]=>[2,8,6,5,7,1,4,3]=>0010111
[6,4,1,3,2,7,8,5]=>[3,4,1,8,6,2,7,5]=>[3,1,7,8,5,6,2,4]=>0100101
[2,3,7,6,8,1,5,4]=>[5,2,3,8,1,7,6,4]=>[2,3,5,1,7,6,8,4]=>0001011
[4,2,1,5,8,7,6,3]=>[2,6,4,1,5,7,8,3]=>[5,8,3,4,1,2,6,7]=>0010001
[7,8,4,1,2,5,3,6]=>[5,1,4,8,2,3,7,6]=>[5,2,1,7,8,6,3,4]=>1001101
[1,2,8,3,6,4,7,5]=>[1,2,7,6,8,3,4,5]=>[1,2,7,4,6,3,8,5]=>0000111
[1,8,3,7,6,4,5,2]=>[1,5,6,7,3,8,4,2]=>[1,7,4,8,2,5,3,6]=>0001011
[5,6,2,1,7,3,8,4]=>[2,8,7,6,5,1,3,4]=>[5,7,3,8,4,6,1,2]=>0000111
[5,7,4,2,1,3,6,8]=>[2,4,1,7,5,3,6,8]=>[5,7,6,3,1,2,4,8]=>0100110
[6,4,2,1,5,3,7,8]=>[2,5,4,6,1,3,7,8]=>[5,1,2,6,3,4,7,8]=>0001100
[3,1,2,4,6,8,7,5]=>[3,1,2,4,7,6,8,5]=>[3,2,1,4,6,8,5,7]=>1100001
[3,8,6,5,2,7,1,4]=>[7,5,3,2,6,8,1,4]=>[3,7,1,8,4,2,5,6]=>0010011
[2,1,8,7,6,3,5,4]=>[2,1,5,6,3,7,8,4]=>[2,1,5,3,8,4,6,7]=>1001001
[4,6,2,5,1,3,8,7]=>[5,6,2,4,1,3,8,7]=>[4,5,1,6,3,2,8,7]=>0101101
[2,6,4,3,1,5,8,7]=>[3,2,4,6,1,5,8,7]=>[2,6,5,1,3,4,8,7]=>0001101
[5,1,7,2,8,6,4,3]=>[4,6,8,5,1,7,2,3]=>[5,1,4,7,2,6,8,3]=>0001011
[6,8,2,5,4,7,1,3]=>[7,5,2,8,1,6,4,3]=>[6,8,3,2,5,1,7,4]=>0101011
[2,1,7,6,3,8,5,4]=>[2,1,5,8,6,7,3,4]=>[2,1,7,3,5,6,8,4]=>1000011
[2,6,5,1,8,4,3,7]=>[4,2,8,5,6,1,3,7]=>[2,6,1,4,5,8,7,3]=>0000111
[4,2,1,6,3,8,7,5]=>[2,7,4,1,6,3,8,5]=>[8,5,6,3,4,1,2,7]=>0010101
[5,2,7,3,8,6,1,4]=>[6,8,5,2,3,7,1,4]=>[5,3,7,1,6,8,4,2]=>0011011
[5,8,3,2,7,6,1,4]=>[6,3,7,2,5,8,1,4]=>[5,8,4,2,3,7,1,6]=>0010011
[4,5,8,2,6,1,3,7]=>[6,8,2,4,5,1,3,7]=>[4,5,6,1,8,7,3,2]=>0100111
[2,6,8,3,7,1,4,5]=>[7,2,8,3,1,6,4,5]=>[2,6,8,5,1,7,4,3]=>0011011
[5,8,3,1,6,2,7,4]=>[7,3,6,8,5,1,2,4]=>[5,7,2,3,6,1,8,4]=>0000111
[4,3,2,1,6,8,5,7]=>[2,3,4,1,8,6,5,7]=>[4,1,2,3,6,8,7,5]=>0010011
[2,4,1,3,8,7,6,5]=>[4,2,1,3,6,7,8,5]=>[2,4,3,1,8,5,6,7]=>0110001
[4,8,6,5,1,7,3,2]=>[3,7,5,4,6,8,1,2]=>[4,8,2,7,1,3,5,6]=>0000011
[3,8,5,4,2,1,7,6]=>[2,4,3,5,7,8,1,6]=>[3,7,1,2,4,5,8,6]=>0000011
[4,3,2,8,7,6,1,5]=>[6,3,4,2,1,7,8,5]=>[4,2,3,8,5,1,6,7]=>0011001
[7,3,6,5,2,8,4,1]=>[4,8,5,6,7,3,2,1]=>[8,1,4,6,3,5,7,2]=>0000111
[5,6,3,1,2,4,8,7]=>[3,1,6,2,5,4,8,7]=>[5,6,4,2,1,3,8,7]=>1010101
[7,1,5,3,8,4,6,2]=>[6,8,5,7,1,3,4,2]=>[6,3,5,1,7,4,8,2]=>0001111
[3,7,6,4,2,8,5,1]=>[5,4,3,8,6,7,2,1]=>[3,8,1,5,6,7,2,4]=>0000011
[5,7,3,6,2,8,4,1]=>[4,8,6,7,5,3,2,1]=>[5,6,3,8,1,4,7,2]=>0000111
[3,8,4,1,5,7,2,6]=>[7,4,3,8,1,5,2,6]=>[3,8,6,5,1,7,2,4]=>0001111
[3,5,7,4,8,6,2,1]=>[2,6,3,8,5,7,4,1]=>[3,5,8,1,2,6,7,4]=>0000011
[2,6,7,4,5,8,3,1]=>[3,2,8,7,4,6,5,1]=>[2,6,7,5,4,8,1,3]=>0001011
[6,3,7,5,8,4,2,1]=>[2,4,8,7,6,3,5,1]=>[8,1,2,4,7,5,6,3]=>0000111
[2,1,7,8,5,3,4,6]=>[2,1,5,3,8,4,7,6]=>[2,1,7,8,6,4,3,5]=>1010101
[2,4,8,1,5,6,3,7]=>[6,2,8,4,1,5,3,7]=>[2,4,6,5,1,8,7,3]=>0001111
[4,7,3,8,1,2,6,5]=>[6,1,8,4,7,3,2,5]=>[4,8,5,7,2,1,6,3]=>1000111
[4,8,1,2,5,3,6,7]=>[5,1,8,4,2,3,6,7]=>[4,5,2,1,8,7,6,3]=>1001111
[4,8,7,3,6,5,2,1]=>[2,5,6,4,7,3,8,1]=>[4,6,3,8,1,2,5,7]=>0000101
[7,5,8,3,2,1,6,4]=>[2,3,6,8,7,5,1,4]=>[7,1,2,3,6,5,8,4]=>0000111
[2,3,7,8,4,1,6,5]=>[4,2,3,6,8,1,7,5]=>[2,3,6,1,4,7,8,5]=>0000101
[2,1,7,5,8,4,6,3]=>[2,1,6,8,7,5,4,3]=>[2,1,8,3,6,5,7,4]=>1000111
[8,6,4,1,3,2,5,7]=>[3,4,1,6,2,8,5,7]=>[3,1,8,7,5,2,4,6]=>0101011
[8,3,5,6,2,1,4,7]=>[2,6,8,3,1,5,4,7]=>[6,5,1,2,8,7,4,3]=>0011111
[8,4,2,1,5,6,3,7]=>[2,6,4,8,1,5,3,7]=>[6,5,1,2,8,7,3,4]=>0001111
[5,4,7,6,8,2,3,1]=>[3,8,2,5,4,7,6,1]=>[5,4,7,6,8,1,3,2]=>0101011
[5,4,1,6,8,2,7,3]=>[7,8,4,5,1,6,2,3]=>[6,8,3,4,5,1,7,2]=>0001011
[7,4,1,8,3,5,6,2]=>[6,8,4,7,1,3,5,2]=>[7,5,1,6,3,4,8,2]=>0001111
[7,4,3,2,6,8,5,1]=>[5,3,4,8,7,2,6,1]=>[8,1,5,7,6,2,3,4]=>0000111
[8,2,1,3,6,4,7,5]=>[2,7,1,6,8,3,4,5]=>[7,4,6,3,1,2,8,5]=>0100111
[8,3,1,6,7,4,2,5]=>[4,3,7,8,1,2,6,5]=>[7,6,2,3,8,5,1,4]=>0001111
[8,4,7,1,3,2,5,6]=>[3,7,1,8,4,2,5,6]=>[3,1,8,6,2,7,5,4]=>0101111
[6,4,2,1,3,7,8,5]=>[2,4,1,8,6,3,7,5]=>[7,8,5,6,3,1,2,4]=>0100101
[7,1,6,3,5,8,2,4]=>[8,6,7,1,3,2,5,4]=>[6,2,7,5,3,8,4,1]=>0011111
[1,4,2,8,6,5,7,3]=>[1,7,4,2,6,8,5,3]=>[1,8,3,4,2,7,5,6]=>0010011
[7,6,2,4,5,1,8,3]=>[8,5,6,2,4,7,1,3]=>[5,4,2,8,3,6,7,1]=>0011011
[3,5,7,2,1,6,8,4]=>[2,8,3,7,5,1,6,4]=>[3,5,8,4,7,6,1,2]=>0000111
[4,2,1,5,6,7,8,3]=>[2,8,4,1,5,6,7,3]=>[5,6,7,8,3,4,1,2]=>0010001
[3,7,5,4,6,8,1,2]=>[8,1,3,5,7,4,6,2]=>[3,7,6,4,5,8,2,1]=>1000111
[8,3,4,1,5,6,7,2]=>[7,4,8,3,1,5,6,2]=>[7,6,5,1,8,2,4,3]=>0011111
[3,5,2,4,7,6,1,8]=>[6,5,3,2,4,7,1,8]=>[3,5,4,2,7,1,6,8]=>0011010
[3,2,5,7,4,6,1,8]=>[6,3,2,7,5,4,1,8]=>[3,2,5,7,1,6,4,8]=>0100110
[3,7,2,5,4,1,6,8]=>[4,5,3,7,2,1,6,8]=>[3,5,2,7,6,1,4,8]=>0001110
[7,1,3,5,2,4,6,8]=>[5,7,1,3,2,4,6,8]=>[7,6,4,3,1,5,2,8]=>0111110
[3,2,5,7,4,1,6,8]=>[4,3,2,7,5,1,6,8]=>[3,2,5,7,6,1,4,8]=>0100110
[3,5,2,7,4,1,6,8]=>[4,7,3,5,2,1,6,8]=>[3,7,6,1,4,5,2,8]=>0001110
[3,5,7,2,4,1,6,8]=>[4,7,3,2,5,1,6,8]=>[3,5,7,6,1,4,2,8]=>0010110
[5,3,2,4,7,1,6,8]=>[7,3,5,2,4,1,6,8]=>[5,4,2,3,7,6,1,8]=>0011110
[3,2,5,4,7,1,6,8]=>[7,3,2,5,4,1,6,8]=>[3,2,5,4,7,6,1,8]=>0101110
[3,5,2,4,1,7,6,8]=>[4,5,3,2,1,7,6,8]=>[3,5,1,4,2,7,6,8]=>0011010
[1,3,7,2,5,4,6,8]=>[1,5,3,7,2,4,6,8]=>[1,3,5,2,7,6,4,8]=>0001110
[3,5,2,1,4,7,6,8]=>[2,5,3,1,4,7,6,8]=>[3,5,4,1,2,7,6,8]=>0011010
[3,2,5,1,7,4,6,8]=>[7,3,2,5,1,4,6,8]=>[3,2,7,6,4,5,1,8]=>0101110
[3,5,2,1,7,4,6,8]=>[2,7,3,5,1,4,6,8]=>[3,7,6,4,5,1,2,8]=>0001110
[1,3,7,5,2,4,6,8]=>[1,5,3,2,7,4,6,8]=>[1,3,7,6,4,2,5,8]=>0010110
[5,7,1,3,2,4,6,8]=>[3,7,1,2,5,4,6,8]=>[3,1,5,7,6,4,2,8]=>0110110
[3,7,1,5,2,4,6,8]=>[5,7,3,1,2,4,6,8]=>[3,7,6,4,1,5,2,8]=>0011110
[3,1,7,5,2,4,6,8]=>[5,3,1,2,7,4,6,8]=>[7,6,4,2,3,1,5,8]=>0110110
[1,7,5,3,2,4,6,8]=>[1,3,5,2,7,4,6,8]=>[1,7,6,4,2,3,5,8]=>0010110
[1,8,7,6,3,2,5,4]=>[1,3,5,6,2,7,8,4]=>[1,5,2,3,8,4,6,7]=>0001001
[1,6,7,5,8,2,3,4]=>[1,8,2,3,7,6,5,4]=>[1,6,7,5,8,4,3,2]=>0110011
[5,2,3,4,8,6,1,7]=>[6,5,2,3,4,8,1,7]=>[5,4,3,2,8,7,1,6]=>0111011
[5,3,8,2,4,1,7,6]=>[4,7,5,3,2,8,1,6]=>[7,1,4,3,5,2,8,6]=>0011011
[5,2,8,4,1,7,3,6]=>[7,4,8,5,2,1,3,6]=>[5,2,4,8,6,1,7,3]=>0001111
[6,4,3,5,8,2,1,7]=>[2,8,4,6,3,5,1,7]=>[6,5,3,4,8,7,1,2]=>0001111
[6,3,5,8,7,1,2,4]=>[7,1,6,3,2,5,8,4]=>[8,4,3,6,5,2,1,7]=>1011101
[5,8,4,1,3,7,6,2]=>[6,4,1,7,5,8,3,2]=>[5,8,2,4,7,3,1,6]=>0100011
[6,4,5,3,8,1,7,2]=>[7,8,5,6,4,3,1,2]=>[6,3,5,4,7,1,8,2]=>0001111
[3,5,4,7,2,6,1,8]=>[6,7,3,5,4,2,1,8]=>[3,5,4,7,1,6,2,8]=>0001110
[1,8,4,3,7,5,6,2]=>[1,6,4,7,8,3,5,2]=>[1,8,2,6,3,4,7,5]=>0000111
[1,5,7,2,4,6,8,3]=>[1,8,7,2,5,4,6,3]=>[1,5,8,3,7,6,4,2]=>0010111
[7,6,3,8,4,2,1,5]=>[2,4,8,6,3,7,1,5]=>[7,1,2,4,6,8,5,3]=>0001011
[7,4,3,8,5,2,6,1]=>[6,5,4,8,7,3,2,1]=>[7,2,5,8,1,6,3,4]=>0000111
[7,2,8,5,1,3,4,6]=>[5,8,2,1,7,3,4,6]=>[7,4,1,5,8,6,3,2]=>0110111
[1,2,6,4,5,8,3,7]=>[1,2,8,6,4,5,3,7]=>[1,2,6,5,4,8,7,3]=>0001111
[1,2,7,4,8,5,3,6]=>[1,2,5,8,7,4,3,6]=>[1,2,7,3,5,8,6,4]=>0000111
[1,6,3,7,8,2,4,5]=>[1,8,6,3,2,4,7,5]=>[1,6,4,3,7,8,5,2]=>0011101
[3,8,4,7,6,1,5,2]=>[5,6,3,7,4,8,1,2]=>[3,7,1,5,4,8,2,6]=>0001011
[5,7,4,2,6,3,1,8]=>[3,6,4,7,5,2,1,8]=>[5,6,2,7,1,3,4,8]=>0000110
[2,1,8,3,6,7,4,5]=>[2,1,7,8,3,4,6,5]=>[2,1,8,5,3,7,6,4]=>1001111
[5,1,8,6,2,7,3,4]=>[7,6,5,1,2,8,3,4]=>[8,4,1,7,3,5,2,6]=>0011011
[5,7,1,4,2,6,3,8]=>[6,4,7,1,5,2,3,8]=>[5,6,2,4,1,7,3,8]=>0010110
[7,6,8,3,1,5,4,2]=>[4,3,5,8,1,7,6,2]=>[7,6,8,2,3,5,1,4]=>0001011
[6,3,7,2,8,1,5,4]=>[5,8,7,6,3,2,1,4]=>[7,1,5,3,8,4,6,2]=>0001111
[7,5,2,8,6,1,4,3]=>[4,6,5,2,8,7,1,3]=>[7,1,4,2,6,8,3,5]=>0010011
[4,5,6,8,3,1,7,2]=>[7,3,8,4,5,6,1,2]=>[4,5,6,7,1,8,2,3]=>0000011
[8,4,6,5,3,1,7,2]=>[7,3,5,6,8,4,1,2]=>[6,4,7,1,8,2,3,5]=>0000111
[5,6,4,8,3,1,7,2]=>[7,3,8,6,5,4,1,2]=>[5,6,4,7,1,8,2,3]=>0000111
[6,3,1,7,5,2,4,8]=>[5,3,7,1,6,2,4,8]=>[7,4,1,5,6,2,3,8]=>0010110
[6,3,1,8,2,7,4,5]=>[7,3,8,6,1,2,4,5]=>[8,5,1,7,4,6,2,3]=>0001111
[3,2,1,6,4,7,8,5]=>[2,3,1,8,6,4,7,5]=>[3,1,2,7,8,5,6,4]=>0100101
[8,1,4,3,5,7,6,2]=>[6,4,7,1,3,8,5,2]=>[7,5,3,8,2,4,1,6]=>0011011
[5,2,4,1,3,7,8,6]=>[4,5,2,1,3,8,7,6]=>[4,1,5,3,2,7,8,6]=>0111001
[3,2,6,1,5,7,8,4]=>[8,3,2,6,1,5,7,4]=>[3,2,7,8,4,6,5,1]=>0101101
[8,7,1,3,6,5,4,2]=>[4,5,1,6,7,3,8,2]=>[6,3,1,4,8,2,5,7]=>0100101
[2,7,6,5,8,3,1,4]=>[3,2,8,1,6,7,5,4]=>[2,7,5,6,8,4,1,3]=>0010011
[3,5,7,4,8,1,2,6]=>[8,1,3,7,5,4,2,6]=>[3,5,8,6,4,7,2,1]=>1000111
[4,6,1,7,5,8,2,3]=>[8,7,1,4,6,2,5,3]=>[4,7,5,6,2,8,3,1]=>0100111
[1,2,6,7,4,8,3,5]=>[1,2,8,7,4,6,3,5]=>[1,2,6,8,5,4,7,3]=>0001011
[4,7,2,8,5,6,3,1]=>[3,6,8,4,7,2,5,1]=>[4,6,2,7,5,8,1,3]=>0000111
[1,4,8,7,3,5,6,2]=>[1,6,7,4,3,5,8,2]=>[1,4,8,2,6,5,3,7]=>0001101
[3,2,8,7,1,5,6,4]=>[6,3,2,7,1,5,8,4]=>[3,2,6,5,1,8,4,7]=>0101101
[1,7,8,3,5,2,4,6]=>[1,5,8,3,2,4,7,6]=>[1,5,2,7,8,6,4,3]=>0011101
[8,6,5,1,3,4,2,7]=>[4,5,1,3,6,8,2,7]=>[4,3,1,8,7,2,5,6]=>0110011
[1,7,8,5,4,3,2,6]=>[1,3,4,5,8,2,7,6]=>[1,7,8,6,2,3,4,5]=>0000101
[2,6,8,7,4,3,5,1]=>[5,2,4,7,3,6,8,1]=>[2,6,8,1,5,3,4,7]=>0001001
[1,2,6,7,8,4,3,5]=>[1,2,4,8,3,6,7,5]=>[1,2,6,7,8,5,3,4]=>0001001
[3,5,8,6,7,4,1,2]=>[4,1,3,7,5,8,6,2]=>[3,5,8,2,1,4,7,6]=>1000011
[3,1,6,5,8,7,4,2]=>[4,3,1,7,6,5,8,2]=>[6,5,8,2,3,1,4,7]=>0100101
[3,7,6,4,8,1,2,5]=>[8,1,3,6,4,7,2,5]=>[3,8,5,4,6,7,2,1]=>1001011
[2,3,6,4,1,7,8,5]=>[4,2,3,8,6,1,7,5]=>[2,3,7,8,5,6,1,4]=>0000101
[4,7,2,1,5,3,8,6]=>[2,5,8,4,1,7,3,6]=>[4,5,1,2,8,6,7,3]=>0001011
[3,1,7,4,5,2,8,6]=>[5,3,1,8,4,7,2,6]=>[8,6,7,2,3,1,5,4]=>0101011
[5,4,2,1,3,7,8,6]=>[2,4,1,5,3,8,7,6]=>[5,3,1,2,4,7,8,6]=>0101001
[1,7,8,2,6,4,5,3]=>[1,5,6,8,2,4,7,3]=>[1,5,2,7,8,3,6,4]=>0001101
[8,7,2,5,4,6,1,3]=>[6,5,2,7,1,4,8,3]=>[8,3,2,5,1,6,4,7]=>0101101
[8,7,2,5,3,1,6,4]=>[3,6,5,7,2,1,8,4]=>[6,1,3,5,2,8,4,7]=>0001101
[8,7,3,2,1,5,6,4]=>[2,3,6,7,1,5,8,4]=>[6,5,1,2,3,8,4,7]=>0001101
[8,7,6,5,1,3,4,2]=>[4,5,1,3,6,7,8,2]=>[4,3,1,8,2,5,6,7]=>0110001
[8,5,7,6,1,4,3,2]=>[3,4,6,1,7,8,5,2]=>[7,5,8,2,4,1,3,6]=>0010011
[8,7,4,6,5,1,3,2]=>[3,5,1,6,7,4,8,2]=>[3,1,6,4,8,2,5,7]=>0100101
[1,5,8,7,6,2,4,3]=>[1,4,6,2,5,7,8,3]=>[1,4,2,5,8,3,6,7]=>0010001
[7,5,8,4,1,6,3,2]=>[3,6,4,8,7,5,1,2]=>[8,2,6,5,7,1,3,4]=>0000111
[6,8,5,1,7,4,3,2]=>[3,4,7,5,8,6,1,2]=>[6,7,1,3,8,2,4,5]=>0000011
[4,8,5,7,1,6,3,2]=>[3,6,7,4,8,5,1,2]=>[4,7,1,3,8,2,6,5]=>0000111
[4,3,7,6,5,1,8,2]=>[8,5,4,3,6,7,1,2]=>[4,3,8,2,5,6,7,1]=>0010011
[5,4,3,6,7,1,8,2]=>[8,7,4,5,3,6,1,2]=>[5,3,4,6,8,2,7,1]=>0001011
[4,8,7,6,3,1,5,2]=>[5,3,6,4,1,7,8,2]=>[4,5,1,8,2,3,6,7]=>0001001
[2,4,6,3,1,7,8,5]=>[3,2,8,4,6,1,7,5]=>[2,4,7,8,5,6,1,3]=>0000101
[6,8,5,7,3,2,1,4]=>[2,3,7,1,8,6,5,4]=>[6,8,4,1,2,3,7,5]=>0010011
[6,8,5,3,7,2,1,4]=>[2,7,5,3,8,6,1,4]=>[6,7,1,2,8,4,3,5]=>0010011
[2,1,8,7,6,3,4,5]=>[2,1,6,3,4,7,8,5]=>[2,1,8,5,4,3,6,7]=>1011001
[5,8,7,6,2,4,1,3]=>[4,6,2,1,5,7,8,3]=>[4,1,5,8,3,2,6,7]=>0110001
[6,8,2,7,5,1,4,3]=>[4,5,7,2,8,6,1,3]=>[6,8,3,7,1,4,2,5]=>0010011
[5,8,7,2,6,4,1,3]=>[4,6,2,7,5,1,8,3]=>[5,8,3,2,6,1,4,7]=>0100101
[2,4,5,3,7,1,8,6]=>[8,2,5,4,3,7,1,6]=>[2,4,5,3,8,6,7,1]=>0001011
[2,4,5,7,3,8,6,1]=>[6,2,8,4,5,7,3,1]=>[2,4,5,8,1,6,7,3]=>0000011
[2,4,6,8,3,5,1,7]=>[5,2,8,4,3,6,1,7]=>[2,4,6,8,7,1,5,3]=>0001011
[2,4,7,3,1,8,6,5]=>[3,2,6,4,8,7,1,5]=>[2,4,7,1,3,6,8,5]=>0000011
[2,4,7,8,3,5,6,1]=>[6,2,8,4,3,5,7,1]=>[2,4,7,8,1,6,5,3]=>0001101
[2,5,1,6,7,4,8,3]=>[8,2,7,5,1,6,4,3]=>[2,6,8,3,7,4,5,1]=>0001011
[2,5,6,3,7,4,8,1]=>[8,2,7,6,5,3,4,1]=>[2,5,7,4,6,3,8,1]=>0000111
[2,5,6,7,8,4,1,3]=>[4,2,1,8,5,6,7,3]=>[2,5,6,7,8,3,1,4]=>0100001
[2,6,1,7,4,8,5,3]=>[5,2,8,7,6,1,4,3]=>[2,6,1,5,7,4,8,3]=>0000111
[7,6,5,2,8,4,1,3]=>[4,8,2,5,6,7,1,3]=>[7,1,4,5,6,8,3,2]=>0100011
[5,1,2,3,4,8,7,6]=>[5,1,2,3,4,7,8,6]=>[5,4,3,2,1,8,6,7]=>1111001
[4,1,2,3,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>[4,3,2,1,7,5,6,8]=>1110010
[6,8,7,4,5,2,3,1]=>[3,5,2,7,4,6,8,1]=>[6,8,1,3,2,5,4,7]=>0101001
[6,8,4,7,2,5,3,1]=>[3,5,7,8,4,6,2,1]=>[6,8,1,3,7,2,5,4]=>0001011
[6,4,8,7,5,2,3,1]=>[3,5,2,7,6,4,8,1]=>[8,1,3,2,5,6,4,7]=>0100101
[6,4,8,2,7,5,3,1]=>[3,5,7,8,6,4,2,1]=>[8,1,3,7,2,5,6,4]=>0000111
[6,8,4,2,7,1,5,3]=>[5,7,4,8,2,6,1,3]=>[6,7,1,5,2,8,3,4]=>0001011
[6,4,2,8,7,5,3,1]=>[3,5,4,7,6,2,8,1]=>[6,2,5,8,1,3,4,7]=>0000101
[6,8,5,7,1,4,3,2]=>[3,4,7,1,8,6,5,2]=>[6,8,2,4,1,3,7,5]=>0010011
[1,8,7,3,6,2,5,4]=>[1,5,6,7,3,2,8,4]=>[1,6,2,5,3,8,4,7]=>0001101
[6,8,2,7,5,4,1,3]=>[4,5,2,7,8,6,1,3]=>[6,7,1,4,8,3,2,5]=>0100011
[6,8,3,7,5,2,1,4]=>[2,5,7,3,8,6,1,4]=>[6,8,4,3,7,1,2,5]=>0010011
[1,8,4,7,6,2,5,3]=>[1,5,6,7,4,8,2,3]=>[1,7,2,5,4,8,3,6]=>0001011
[1,8,4,7,3,6,5,2]=>[1,5,6,7,8,4,3,2]=>[1,7,3,6,4,8,2,5]=>0000111
[4,8,5,7,1,2,6,3]=>[6,1,7,4,8,5,2,3]=>[4,8,3,7,2,1,6,5]=>1000111
[2,8,1,3,7,6,5,4]=>[5,2,1,6,7,8,3,4]=>[2,7,3,1,5,8,4,6]=>0100011
[6,8,1,4,3,7,5,2]=>[5,4,7,1,8,6,3,2]=>[6,7,3,8,2,4,1,5]=>0010011
[6,8,1,4,2,7,5,3]=>[5,4,7,1,8,6,2,3]=>[6,8,3,7,2,4,1,5]=>0010011
[3,1,6,7,4,8,5,2]=>[5,3,1,8,7,6,4,2]=>[6,8,2,3,1,5,7,4]=>0100011
[8,6,4,2,7,5,1,3]=>[5,4,2,7,6,8,1,3]=>[8,3,2,4,7,1,5,6]=>0100011
[3,4,6,7,8,5,1,2]=>[5,1,3,4,8,6,7,2]=>[3,4,6,7,8,2,1,5]=>1000001
[7,5,8,2,6,4,1,3]=>[4,6,2,8,7,5,1,3]=>[8,3,2,6,5,7,1,4]=>0100111
[5,4,7,2,6,8,1,3]=>[8,7,2,5,4,1,6,3]=>[5,4,8,3,2,7,6,1]=>0101111
[5,3,7,2,6,4,1,8]=>[4,6,7,5,3,2,1,8]=>[6,2,7,1,4,5,3,8]=>0001110
[7,5,2,6,8,4,1,3]=>[4,8,2,5,7,1,6,3]=>[7,6,1,4,5,8,3,2]=>0100111
[7,1,8,4,2,6,5,3]=>[5,4,6,8,7,1,2,3]=>[8,3,6,1,5,7,2,4]=>0000111
[7,1,8,3,6,2,5,4]=>[5,6,8,7,1,3,2,4]=>[5,1,8,4,7,2,6,3]=>0001111
[7,2,3,4,5,1,8,6]=>[5,8,2,3,4,7,1,6]=>[8,6,7,1,5,4,3,2]=>0111011
[2,8,3,4,5,1,6,7]=>[5,2,8,3,4,1,6,7]=>[2,8,7,6,1,5,4,3]=>0011111
[2,7,3,4,1,5,6,8]=>[4,2,7,3,1,5,6,8]=>[2,7,6,5,1,4,3,8]=>0011110
[5,3,6,1,2,7,4,8]=>[7,1,6,5,3,2,4,8]=>[7,4,5,3,6,2,1,8]=>1001110
[2,8,5,3,4,6,7,1]=>[7,2,5,3,8,4,6,1]=>[2,8,1,7,6,4,3,5]=>0010111
[4,5,3,1,2,8,7,6]=>[3,1,5,4,2,7,8,6]=>[4,5,2,1,3,8,6,7]=>1001001
[5,7,3,4,1,6,8,2]=>[8,4,7,3,5,1,6,2]=>[5,8,2,4,3,7,6,1]=>0010111
[6,5,3,2,1,8,7,4]=>[2,3,7,5,6,1,8,4]=>[8,4,5,6,1,2,3,7]=>0000101
[7,1,2,3,4,6,8,5]=>[8,1,2,3,7,4,6,5]=>[8,5,7,6,4,3,2,1]=>1110111
[8,6,3,5,2,7,4,1]=>[4,7,5,6,3,8,2,1]=>[5,3,7,2,8,1,4,6]=>0001011
[7,5,2,8,6,3,4,1]=>[4,6,5,2,8,7,3,1]=>[8,1,4,2,6,7,3,5]=>0010011
[5,2,8,6,7,3,4,1]=>[4,7,5,2,3,8,6,1]=>[5,3,8,1,4,2,7,6]=>0011011
[7,5,2,3,8,6,4,1]=>[4,6,2,5,8,7,3,1]=>[7,3,2,6,8,1,4,5]=>0100011
[5,2,3,8,6,7,4,1]=>[4,7,2,5,3,8,6,1]=>[8,1,4,5,3,2,7,6]=>0101011
[6,3,8,4,5,1,2,7]=>[5,1,8,6,3,4,2,7]=>[6,4,8,7,2,1,5,3]=>1001111
[7,4,5,1,8,6,2,3]=>[6,5,1,8,4,7,2,3]=>[8,3,1,6,7,2,5,4]=>0101011
[6,2,3,4,8,5,1,7]=>[5,8,2,3,6,4,1,7]=>[8,7,1,5,6,4,3,2]=>0110111
[7,4,8,5,6,1,2,3]=>[6,1,2,8,7,4,5,3]=>[7,5,8,3,2,1,6,4]=>1100111
[7,5,8,6,1,2,3,4]=>[6,1,2,3,8,7,5,4]=>[8,4,3,2,1,6,7,5]=>1110011
[7,3,4,8,5,6,1,2]=>[6,1,8,3,7,4,5,2]=>[7,5,8,2,1,6,4,3]=>1010111
[7,3,4,5,8,6,1,2]=>[6,1,8,3,4,7,5,2]=>[8,2,1,6,7,5,4,3]=>1011011
[8,6,3,1,7,5,2,4]=>[5,3,7,1,6,8,2,4]=>[7,2,3,8,4,1,5,6]=>0010011
[7,2,8,3,4,5,6,1]=>[6,8,7,2,3,4,5,1]=>[7,5,3,8,1,6,4,2]=>0011111
[3,5,4,6,1,7,8,2]=>[8,6,3,5,4,1,7,2]=>[3,5,4,7,8,2,6,1]=>0001101
[2,7,4,5,6,8,1,3]=>[8,2,1,7,4,5,6,3]=>[2,7,6,5,4,8,3,1]=>0101111
[4,1,2,8,7,5,3,6]=>[5,1,4,2,7,3,8,6]=>[8,6,3,4,2,1,5,7]=>1010101
[3,1,7,6,8,2,4,5]=>[8,3,1,2,4,7,6,5]=>[7,6,8,5,4,2,3,1]=>0111011
[7,3,5,1,8,2,4,6]=>[8,5,7,3,1,2,4,6]=>[7,4,3,8,6,2,5,1]=>0011111
[1,5,6,7,8,3,4,2]=>[1,4,8,3,5,6,7,2]=>[1,5,6,7,8,2,4,3]=>0010001
[6,1,2,3,4,8,7,5]=>[7,1,2,3,6,4,8,5]=>[8,5,6,4,3,2,1,7]=>1110101
[5,1,2,3,8,7,6,4]=>[6,1,2,5,3,7,8,4]=>[8,4,5,3,2,1,6,7]=>1101001
[5,1,2,3,8,6,7,4]=>[7,1,2,5,3,8,6,4]=>[8,4,5,3,2,1,7,6]=>1101011
[2,8,5,3,1,4,6,7]=>[3,2,5,1,8,4,6,7]=>[2,8,7,6,4,1,3,5]=>0010111
[2,6,3,7,8,1,4,5]=>[8,2,6,3,1,4,7,5]=>[2,6,4,3,7,8,5,1]=>0011101
[3,4,6,1,8,5,7,2]=>[7,8,3,4,6,1,5,2]=>[3,4,7,5,6,1,8,2]=>0000111
[3,5,6,4,8,1,7,2]=>[7,8,3,6,5,4,1,2]=>[3,5,6,4,7,1,8,2]=>0000111
[3,6,1,8,5,4,7,2]=>[7,5,3,8,6,1,4,2]=>[3,8,2,5,6,1,7,4]=>0000111
[3,6,8,4,5,1,7,2]=>[7,5,3,8,4,6,1,2]=>[3,6,7,1,8,2,5,4]=>0001011
[4,1,5,6,8,3,7,2]=>[7,8,4,1,5,6,3,2]=>[5,6,7,3,4,1,8,2]=>0010011
[4,1,5,7,8,6,3,2]=>[3,6,4,1,5,8,7,2]=>[4,1,3,5,7,8,2,6]=>0010001
[4,1,7,3,5,8,6,2]=>[6,8,4,1,3,7,5,2]=>[7,5,3,4,1,6,8,2]=>0011011
[4,5,7,3,8,6,1,2]=>[6,1,8,4,5,7,3,2]=>[4,5,8,2,1,6,7,3]=>1000011
[4,5,7,8,1,6,3,2]=>[3,6,8,4,5,1,7,2]=>[4,5,7,8,2,6,1,3]=>0000101
[4,5,8,3,1,6,7,2]=>[7,3,8,4,5,1,6,2]=>[4,5,7,6,1,8,2,3]=>0000111
[4,6,3,1,8,5,7,2]=>[7,3,8,4,6,1,5,2]=>[4,7,5,6,1,8,2,3]=>0000111
[4,6,7,8,5,1,3,2]=>[3,5,1,4,8,6,7,2]=>[3,1,4,6,7,8,2,5]=>0100001
[4,6,8,3,5,1,7,2]=>[7,5,8,4,3,6,1,2]=>[4,6,7,1,8,2,5,3]=>0001011
[4,7,3,1,8,6,5,2]=>[5,3,6,4,8,7,1,2]=>[4,8,2,3,6,7,1,5]=>0000011
[5,1,6,7,8,3,4,2]=>[4,8,5,1,3,6,7,2]=>[4,1,5,3,6,7,8,2]=>0011001
[5,6,7,8,4,1,3,2]=>[3,4,1,8,5,6,7,2]=>[3,1,5,6,7,8,2,4]=>0100001
[5,7,3,4,1,8,6,2]=>[6,4,8,3,5,7,1,2]=>[5,7,1,6,8,2,4,3]=>0010011
[5,7,3,8,4,6,1,2]=>[6,1,8,7,5,3,4,2]=>[5,7,4,8,2,1,6,3]=>1000111
[5,7,8,4,3,6,1,2]=>[6,1,4,8,5,3,7,2]=>[5,7,8,2,1,6,3,4]=>1000101
[6,1,7,4,5,8,3,2]=>[3,8,7,6,1,4,5,2]=>[6,4,7,5,1,3,8,2]=>0001111
[6,1,8,4,5,3,7,2]=>[7,5,8,6,1,4,3,2]=>[6,4,8,2,5,1,7,3]=>0001111
[8,4,1,3,2,5,6,7]=>[3,4,1,8,2,5,6,7]=>[3,1,8,7,6,5,2,4]=>0101111
[8,5,1,2,4,3,6,7]=>[4,1,5,2,8,3,6,7]=>[4,2,1,8,7,6,3,5]=>1010111
[8,7,1,2,3,4,6,5]=>[6,1,2,3,7,4,8,5]=>[6,4,3,2,1,8,5,7]=>1110101
[8,5,1,4,2,3,6,7]=>[4,5,1,2,8,3,6,7]=>[8,7,6,3,1,4,2,5]=>0110111
[8,6,1,2,5,3,4,7]=>[5,1,6,2,3,8,4,7]=>[8,7,4,2,1,5,3,6]=>1011011
[8,7,1,2,3,6,4,5]=>[6,1,2,7,3,4,8,5]=>[8,5,3,2,1,6,4,7]=>1101101
[8,6,1,2,5,4,3,7]=>[4,1,5,6,2,8,3,7]=>[8,7,3,5,2,1,4,6]=>1001011
[2,5,8,6,1,7,3,4]=>[7,2,6,1,5,8,3,4]=>[2,5,8,4,1,7,3,6]=>0010011
[5,6,8,7,2,3,1,4]=>[3,7,2,1,5,6,8,4]=>[5,6,8,4,1,3,2,7]=>0110001
[5,2,3,6,7,8,1,4]=>[8,5,2,3,1,6,7,4]=>[6,7,8,4,3,2,5,1]=>0111001
[4,2,8,7,5,3,1,6]=>[3,5,4,2,7,1,8,6]=>[8,6,1,3,4,2,5,7]=>0010101
[1,3,2,4,8,5,7,6]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,7,5,8,6]=>0100011
[7,6,2,1,4,8,3,5]=>[2,8,6,1,4,7,3,5]=>[7,3,6,8,5,4,1,2]=>0011011
[1,4,2,7,3,8,6,5]=>[1,6,4,2,8,7,3,5]=>[1,7,3,4,2,6,8,5]=>0010011
[3,8,1,6,5,2,7,4]=>[7,5,3,6,8,1,2,4]=>[3,8,4,6,1,7,2,5]=>0000111
[8,7,6,2,1,4,3,5]=>[2,4,6,1,3,7,8,5]=>[4,1,2,8,5,3,6,7]=>0011001
[1,3,8,6,2,4,7,5]=>[1,7,3,2,6,8,4,5]=>[1,3,7,4,2,8,5,6]=>0010011
[1,2,5,3,4,8,7,6]=>[1,2,5,3,4,7,8,6]=>[1,2,5,4,3,8,6,7]=>0011001
[1,2,3,8,4,7,6,5]=>[1,2,3,6,7,8,4,5]=>[1,2,3,8,5,7,4,6]=>0000011
[1,4,8,2,6,3,7,5]=>[1,7,6,4,8,2,3,5]=>[1,4,7,3,6,2,8,5]=>0000111
[1,8,7,3,2,4,6,5]=>[1,3,6,2,7,4,8,5]=>[1,6,4,2,3,8,5,7]=>0010101
[7,5,8,6,3,2,4,1]=>[4,3,6,2,8,7,5,1]=>[8,1,4,2,3,6,7,5]=>0010011
[5,8,7,6,3,2,4,1]=>[4,3,6,2,5,7,8,1]=>[5,8,1,4,2,3,6,7]=>0010001
[8,1,5,4,6,3,7,2]=>[7,6,5,8,1,4,3,2]=>[7,3,5,1,8,2,6,4]=>0001111
[2,1,5,8,3,7,4,6]=>[2,1,7,8,5,3,4,6]=>[2,1,5,8,6,3,7,4]=>1000111
[2,1,7,4,8,3,6,5]=>[2,1,6,8,7,4,3,5]=>[2,1,8,5,7,3,6,4]=>1000111
[1,2,3,5,8,7,4,6]=>[1,2,3,7,5,4,8,6]=>[1,2,3,5,8,6,4,7]=>0000101
[6,1,2,7,8,4,3,5]=>[4,1,8,6,2,3,7,5]=>[7,8,5,2,1,4,6,3]=>1001101
[5,1,4,8,2,7,3,6]=>[7,8,5,1,4,2,3,6]=>[7,3,5,4,1,8,6,2]=>0011111
[3,4,1,2,8,7,5,6]=>[4,1,3,2,7,5,8,6]=>[3,4,2,1,8,6,5,7]=>1010101
[1,2,5,7,8,6,3,4]=>[1,2,6,3,5,8,7,4]=>[1,2,5,7,8,4,3,6]=>0010001
[6,2,5,1,7,3,8,4]=>[8,7,5,6,2,1,3,4]=>[7,3,5,2,8,4,6,1]=>0001111
[2,4,8,1,3,7,5,6]=>[7,2,1,4,8,3,5,6]=>[2,4,8,6,3,1,7,5]=>0100111
[4,1,2,3,8,7,5,6]=>[4,1,2,3,7,5,8,6]=>[4,3,2,1,8,6,5,7]=>1110101
[2,3,1,8,5,4,7,6]=>[3,2,1,5,7,8,4,6]=>[2,3,1,7,4,5,8,6]=>0100011
[1,2,3,8,5,7,4,6]=>[1,2,3,7,8,5,4,6]=>[1,2,3,7,4,8,6,5]=>0000111
[6,1,7,2,5,8,3,4]=>[8,7,6,1,2,3,5,4]=>[6,3,7,5,2,8,4,1]=>0011111
[1,4,2,8,5,3,7,6]=>[1,5,4,2,7,8,3,6]=>[1,7,3,4,2,5,8,6]=>0010011
[3,1,5,2,8,6,7,4]=>[7,3,1,5,2,8,6,4]=>[8,4,5,2,3,1,7,6]=>0101011
[7,8,6,5,2,1,4,3]=>[2,4,5,1,6,8,7,3]=>[4,1,2,7,8,3,5,6]=>0010001
[6,7,8,2,1,5,4,3]=>[2,4,5,8,1,6,7,3]=>[6,7,8,3,5,1,2,4]=>0001001
[8,7,5,6,2,1,4,3]=>[2,4,6,1,7,5,8,3]=>[4,1,2,8,3,6,5,7]=>0010101
[3,2,8,5,6,7,1,4]=>[7,3,2,1,8,5,6,4]=>[3,2,8,4,1,7,6,5]=>0110111
[5,2,7,8,6,3,1,4]=>[3,6,5,2,1,8,7,4]=>[5,1,3,7,8,4,2,6]=>0011001
[7,2,4,5,8,3,6,1]=>[6,8,7,2,4,5,3,1]=>[7,3,8,1,6,5,4,2]=>0011111
[3,2,5,8,1,6,7,4]=>[7,3,2,8,5,1,6,4]=>[3,2,5,7,6,1,8,4]=>0100111
[8,1,4,3,2,5,6,7]=>[3,4,8,1,2,5,6,7]=>[8,7,6,5,2,4,1,3]=>0011111
[1,3,8,4,2,5,6,7]=>[1,4,3,8,2,5,6,7]=>[1,3,8,7,6,5,2,4]=>0001111
[6,2,5,1,8,3,4,7]=>[8,5,6,2,1,3,4,7]=>[6,3,8,7,4,2,5,1]=>0011111
[5,1,8,2,4,3,6,7]=>[4,8,5,1,2,3,6,7]=>[4,1,8,7,6,3,5,2]=>0011111
[8,2,3,1,5,6,7,4]=>[3,7,2,8,1,5,6,4]=>[7,6,5,1,3,2,8,4]=>0101111
[6,5,8,3,4,2,1,7]=>[2,4,8,3,6,5,1,7]=>[6,5,8,7,1,2,4,3]=>0010111
[6,5,8,2,3,4,1,7]=>[4,8,2,3,6,5,1,7]=>[6,5,8,7,1,4,3,2]=>0110111
[4,2,1,3,5,8,6,7]=>[2,4,1,3,5,8,6,7]=>[4,3,1,2,5,8,7,6]=>0110011
[6,1,2,7,4,3,8,5]=>[4,1,8,7,6,2,3,5]=>[8,5,6,2,1,4,7,3]=>1000111
[5,4,1,2,3,8,6,7]=>[4,1,2,5,3,8,6,7]=>[5,3,2,1,4,8,7,6]=>1101011
[7,6,8,5,2,4,1,3]=>[4,5,2,1,8,7,6,3]=>[4,1,7,6,8,3,2,5]=>0110011
[6,7,8,5,2,4,1,3]=>[4,5,2,1,8,6,7,3]=>[4,1,6,7,8,3,2,5]=>0110001
[3,4,5,8,2,1,7,6]=>[2,7,3,4,5,8,1,6]=>[3,4,5,7,1,2,8,6]=>0000011
[3,4,6,1,5,2,7,8]=>[5,6,3,4,1,2,7,8]=>[3,4,5,1,6,2,7,8]=>0001100
[3,4,7,2,1,6,5,8]=>[2,6,3,4,7,1,5,8]=>[3,4,6,1,2,7,5,8]=>0000110
[3,5,2,1,4,6,7,8]=>[2,5,3,1,4,6,7,8]=>[3,5,4,1,2,6,7,8]=>0011000
[3,5,6,4,1,2,7,8]=>[4,1,3,6,5,2,7,8]=>[3,5,6,2,1,4,7,8]=>1000100
[3,5,6,8,4,2,1,7]=>[2,4,3,8,5,6,1,7]=>[3,5,6,8,7,1,2,4]=>0000011
[3,5,6,1,4,2,7,8]=>[4,6,3,1,5,2,7,8]=>[3,4,1,5,6,2,7,8]=>0010100
[3,5,7,4,2,8,1,6]=>[8,4,3,7,5,2,1,6]=>[3,5,8,6,2,4,7,1]=>0000111
[3,5,7,8,1,6,2,4]=>[6,8,3,1,5,2,7,4]=>[3,5,7,8,4,1,6,2]=>0010101
[3,5,8,4,2,6,1,7]=>[6,4,3,8,5,2,1,7]=>[3,5,8,7,1,6,2,4]=>0000111
[3,5,8,1,4,6,7,2]=>[7,8,3,1,5,4,6,2]=>[3,5,7,6,4,1,8,2]=>0010111
[3,6,2,4,8,1,7,5]=>[7,8,3,2,6,4,1,5]=>[3,7,1,8,5,6,4,2]=>0010111
[3,6,2,7,8,5,1,4]=>[5,8,3,2,6,1,7,4]=>[3,6,1,5,7,8,4,2]=>0010101
[3,6,2,7,8,1,4,5]=>[8,6,3,2,1,4,7,5]=>[3,6,4,2,7,8,5,1]=>0011101
[3,6,7,8,5,1,2,4]=>[5,1,3,2,8,6,7,4]=>[3,6,7,8,4,2,1,5]=>1010001
[3,6,7,8,1,5,2,4]=>[5,8,3,1,2,6,7,4]=>[3,6,7,8,4,1,5,2]=>0011001
[3,7,2,4,8,1,6,5]=>[6,8,3,2,7,4,1,5]=>[3,8,5,7,1,6,4,2]=>0010111
[3,7,2,1,5,6,4,8]=>[2,6,3,7,1,5,4,8]=>[3,6,5,1,2,7,4,8]=>0001110
[3,7,8,4,5,1,6,2]=>[6,5,3,8,4,1,7,2]=>[3,6,1,7,8,2,5,4]=>0001101
[3,8,2,1,5,6,7,4]=>[2,7,3,8,1,5,6,4]=>[3,7,6,5,1,2,8,4]=>0001111
[4,1,3,6,7,8,5,2]=>[5,4,1,3,8,6,7,2]=>[6,7,8,2,4,3,1,5]=>0110001
[2,7,6,1,4,8,3,5]=>[8,2,6,1,4,7,3,5]=>[2,7,3,6,8,5,4,1]=>0011011
[6,7,8,1,4,2,5,3]=>[5,4,8,1,2,6,7,3]=>[5,2,4,1,6,7,8,3]=>0011001
[2,3,4,8,1,5,7,6]=>[7,2,3,4,1,8,5,6]=>[2,3,4,7,5,1,8,6]=>0001011
[2,7,8,5,1,4,6,3]=>[6,2,5,1,8,4,7,3]=>[2,6,4,1,7,8,3,5]=>0010101
[7,4,6,8,1,5,2,3]=>[5,8,1,7,4,2,6,3]=>[8,3,1,5,4,7,6,2]=>0101111
[2,7,4,6,5,8,3,1]=>[3,2,8,6,7,4,5,1]=>[2,6,4,7,5,8,1,3]=>0000111
[2,6,7,8,5,3,1,4]=>[3,2,5,1,8,6,7,4]=>[2,6,7,8,4,1,3,5]=>0010001
[2,5,6,1,4,8,3,7]=>[8,2,6,1,5,4,3,7]=>[2,5,8,7,3,6,4,1]=>0010111
[5,2,3,4,6,8,1,7]=>[8,5,2,3,4,6,1,7]=>[5,4,3,2,6,8,7,1]=>0111011
[3,2,5,7,8,1,6,4]=>[6,3,2,8,5,1,7,4]=>[3,2,5,6,1,7,8,4]=>0100101
[5,7,1,6,2,8,4,3]=>[4,8,6,7,5,1,2,3]=>[5,8,3,6,1,4,7,2]=>0000111
[7,3,5,1,6,8,4,2]=>[4,8,5,7,3,1,6,2]=>[5,3,7,6,1,4,8,2]=>0001111
[6,3,4,5,8,2,1,7]=>[2,8,6,3,4,5,1,7]=>[6,5,4,3,8,7,1,2]=>0011111
[4,7,1,3,8,2,6,5]=>[6,8,1,4,7,3,2,5]=>[4,6,3,1,8,5,7,2]=>0100111
[5,7,1,8,6,2,3,4]=>[6,8,1,2,5,7,3,4]=>[5,7,3,1,6,8,4,2]=>0110011
[4,8,1,3,5,6,7,2]=>[7,8,1,4,3,5,6,2]=>[4,7,6,5,3,1,8,2]=>0101111
[5,6,7,3,8,2,1,4]=>[2,8,7,3,5,6,1,4]=>[5,6,8,4,3,7,1,2]=>0010011
[5,6,8,3,1,2,7,4]=>[3,1,7,8,5,6,2,4]=>[5,6,7,2,1,3,8,4]=>1000011
[5,7,8,3,1,6,2,4]=>[6,3,8,1,5,2,7,4]=>[5,7,8,4,1,6,2,3]=>0010101
[5,8,3,2,1,6,7,4]=>[2,3,7,8,5,1,6,4]=>[5,7,6,1,2,3,8,4]=>0000111
[6,2,7,3,8,5,1,4]=>[5,8,7,2,6,3,1,4]=>[7,1,5,6,3,8,4,2]=>0010111
[6,2,3,7,8,5,1,4]=>[5,8,2,3,6,1,7,4]=>[6,1,5,7,8,4,3,2]=>0110101
[6,7,8,3,5,1,2,4]=>[5,1,8,3,2,6,7,4]=>[5,2,1,6,7,8,4,3]=>1011001
[1,5,6,7,8,3,2,4]=>[1,3,8,2,5,6,7,4]=>[1,5,6,7,8,4,2,3]=>0010001
[1,5,8,3,2,6,7,4]=>[1,3,7,8,5,2,6,4]=>[1,5,7,6,2,3,8,4]=>0000111
[1,6,7,8,5,2,3,4]=>[1,5,2,3,8,6,7,4]=>[1,6,7,8,4,3,2,5]=>0110001
[1,2,6,8,4,3,7,5]=>[1,2,4,7,8,6,3,5]=>[1,2,6,7,3,4,8,5]=>0000011
[1,8,3,4,2,6,7,5]=>[1,4,7,3,8,2,6,5]=>[1,7,6,2,4,3,8,5]=>0010111
[1,2,8,4,3,6,7,5]=>[1,2,4,7,8,3,6,5]=>[1,2,7,6,3,4,8,5]=>0000111
[6,2,7,8,4,1,3,5]=>[4,8,2,6,1,3,7,5]=>[7,8,5,1,4,6,3,2]=>0101101
[4,5,7,1,8,6,2,3]=>[6,8,1,4,5,7,2,3]=>[4,5,8,3,1,6,7,2]=>0100011
[4,5,7,8,2,6,1,3]=>[6,8,2,4,5,1,7,3]=>[4,5,6,1,7,8,3,2]=>0100101
[4,6,7,1,8,5,2,3]=>[5,8,1,4,7,6,2,3]=>[4,6,8,3,1,5,7,2]=>0100011
[4,7,2,8,5,6,1,3]=>[6,8,2,4,7,1,5,3]=>[4,6,1,7,5,8,3,2]=>0100111
[4,8,2,1,5,6,7,3]=>[2,7,8,4,1,5,6,3]=>[4,7,6,5,1,2,8,3]=>0001111
[1,2,8,4,5,3,7,6]=>[1,2,5,7,4,8,3,6]=>[1,2,7,3,5,4,8,6]=>0001011
[1,2,3,7,8,5,4,6]=>[1,2,3,5,8,4,7,6]=>[1,2,3,7,8,6,4,5]=>0000101
[1,2,3,8,5,4,7,6]=>[1,2,3,5,7,8,4,6]=>[1,2,3,7,4,5,8,6]=>0000011
[5,6,2,7,8,1,4,3]=>[4,8,6,2,5,1,7,3]=>[5,7,8,3,6,1,4,2]=>0010101
[5,8,2,4,1,6,7,3]=>[7,4,8,2,5,1,6,3]=>[4,2,5,7,6,1,8,3]=>0010111
[6,2,1,7,8,5,4,3]=>[2,4,5,8,6,1,7,3]=>[7,8,3,5,6,1,2,4]=>0000101
[6,7,2,4,8,5,1,3]=>[5,8,2,1,7,6,4,3]=>[6,7,4,1,5,8,3,2]=>0110011
[6,8,2,4,5,1,7,3]=>[7,5,8,2,4,6,1,3]=>[5,4,2,6,7,1,8,3]=>0011011
[7,1,3,2,8,4,5,6]=>[3,8,1,7,2,4,5,6]=>[3,1,8,6,4,7,5,2]=>0101111
[4,1,8,2,7,5,3,6]=>[5,7,4,1,8,2,3,6]=>[8,6,2,7,3,4,1,5]=>0010111
[4,1,7,2,5,8,3,6]=>[8,7,4,1,2,5,3,6]=>[8,6,5,2,7,3,4,1]=>0011111
[8,1,7,3,2,5,6,4]=>[3,6,7,8,1,2,5,4]=>[6,2,7,5,1,3,8,4]=>0001111
[3,8,1,2,7,5,4,6]=>[5,1,3,7,8,2,4,6]=>[3,7,4,8,6,2,1,5]=>1000111
[8,4,7,1,3,2,6,5]=>[3,6,1,7,8,4,2,5]=>[3,1,7,2,6,4,8,5]=>0100111
[8,5,7,3,1,2,6,4]=>[3,1,6,7,8,5,2,4]=>[8,4,7,2,1,3,6,5]=>1000111
[3,8,1,2,4,5,7,6]=>[7,1,3,2,4,8,5,6]=>[3,7,5,4,2,1,8,6]=>1011011
[7,6,2,1,8,4,3,5]=>[2,4,8,6,1,7,3,5]=>[8,5,1,2,4,6,7,3]=>0001011
[8,5,2,3,6,1,4,7]=>[6,5,2,3,8,1,4,7]=>[6,1,8,7,4,3,2,5]=>0110111
[7,6,8,1,4,5,2,3]=>[5,8,1,2,4,7,6,3]=>[7,6,8,3,1,5,4,2]=>0111011
[5,4,3,8,2,1,7,6]=>[2,7,4,5,3,8,1,6]=>[5,3,4,7,1,2,8,6]=>0001011
[5,8,7,3,2,1,6,4]=>[2,3,6,7,5,1,8,4]=>[5,6,1,2,3,8,4,7]=>0000101
[2,6,1,5,7,4,8,3]=>[8,2,7,6,1,5,4,3]=>[2,8,3,7,4,6,5,1]=>0001111
[8,7,1,4,5,6,3,2]=>[3,6,7,1,4,5,8,2]=>[8,2,6,5,4,1,3,7]=>0011101
[8,1,5,6,7,4,3,2]=>[3,4,7,8,1,5,6,2]=>[7,6,5,1,3,8,2,4]=>0001111
[1,5,2,6,7,8,4,3]=>[1,4,8,5,2,6,7,3]=>[1,5,2,4,6,7,8,3]=>0001001
[4,2,6,8,5,1,7,3]=>[7,5,4,2,8,6,1,3]=>[6,7,1,8,3,4,2,5]=>0010011
[4,2,7,8,5,6,1,3]=>[6,4,2,1,8,5,7,3]=>[7,8,3,2,4,1,6,5]=>0110101
[5,6,2,7,3,8,4,1]=>[4,8,7,6,5,2,3,1]=>[5,7,3,8,1,4,6,2]=>0000111
[3,7,2,8,4,1,5,6]=>[4,8,3,7,2,1,5,6]=>[3,8,6,1,4,7,5,2]=>0001111
[5,1,3,8,2,4,6,7]=>[8,5,1,3,2,4,6,7]=>[5,2,8,7,6,4,3,1]=>0111111
[4,2,1,3,8,5,6,7]=>[2,4,1,3,8,5,6,7]=>[4,3,1,2,8,7,6,5]=>0110111
[8,5,7,6,3,1,4,2]=>[4,3,6,1,7,8,5,2]=>[4,1,7,5,8,2,3,6]=>0010011
[7,8,1,4,5,6,3,2]=>[3,6,8,1,4,5,7,2]=>[7,8,2,6,5,4,1,3]=>0011101
[4,2,7,3,1,6,5,8]=>[3,6,4,2,7,1,5,8]=>[6,1,3,4,2,7,5,8]=>0010110
[2,3,4,8,1,6,7,5]=>[7,2,3,4,8,1,6,5]=>[2,3,4,7,6,1,8,5]=>0000111
[5,1,4,6,3,7,8,2]=>[8,6,5,1,4,3,7,2]=>[7,8,2,6,3,5,4,1]=>0011101
[5,1,6,3,4,7,8,2]=>[8,6,5,1,3,4,7,2]=>[5,3,7,8,2,6,4,1]=>0011101
[2,1,7,5,3,8,6,4]=>[2,1,6,5,8,7,3,4]=>[2,1,7,3,6,8,4,5]=>1000011
[7,5,3,2,1,8,6,4]=>[2,3,6,5,8,7,1,4]=>[7,1,2,3,6,8,4,5]=>0000011
[5,2,3,4,1,8,6,7]=>[4,5,2,3,1,8,6,7]=>[5,1,4,3,2,8,7,6]=>0111011
[7,4,6,8,5,3,2,1]=>[2,3,5,8,7,4,6,1]=>[8,1,2,3,5,7,6,4]=>0000111
[7,4,8,5,6,3,2,1]=>[2,3,6,8,7,4,5,1]=>[7,5,8,1,2,3,6,4]=>0000111
[7,5,8,6,4,2,1,3]=>[2,4,1,6,8,7,5,3]=>[8,3,1,2,4,6,7,5]=>0100011
[5,3,8,4,2,1,6,7]=>[2,4,8,5,3,1,6,7]=>[8,7,6,1,2,4,5,3]=>0001111
[7,5,2,1,8,6,3,4]=>[2,6,5,1,8,7,3,4]=>[8,4,1,2,6,7,3,5]=>0010011
[7,3,4,5,8,6,2,1]=>[2,6,8,3,4,7,5,1]=>[8,1,2,6,7,5,4,3]=>0011011
[1,8,7,2,6,5,4,3]=>[1,4,5,6,7,2,8,3]=>[1,6,2,4,8,3,5,7]=>0000101
[1,8,2,5,6,7,4,3]=>[1,4,7,8,2,5,6,3]=>[1,8,3,7,6,5,2,4]=>0001111
[1,2,8,3,4,5,7,6]=>[1,2,7,3,4,8,5,6]=>[1,2,7,5,4,3,8,6]=>0011011
[7,6,1,2,3,8,4,5]=>[8,1,2,6,3,7,4,5]=>[7,4,6,8,5,3,2,1]=>1101011
[1,8,5,2,3,7,4,6]=>[1,7,2,5,8,3,4,6]=>[1,8,6,3,2,7,4,5]=>0100111
[6,5,1,2,7,3,8,4]=>[8,1,7,5,6,2,3,4]=>[7,3,8,4,5,6,2,1]=>1000111
[1,2,8,5,3,7,4,6]=>[1,2,7,5,8,3,4,6]=>[1,2,8,6,3,7,4,5]=>0000111
[7,5,1,6,8,2,3,4]=>[8,5,1,2,7,3,6,4]=>[8,4,2,5,7,6,3,1]=>0110111
[5,4,1,6,2,7,8,3]=>[8,6,4,5,1,2,7,3]=>[6,2,7,8,3,4,5,1]=>0001101
[3,8,1,6,7,2,4,5]=>[7,8,3,1,2,4,6,5]=>[3,7,6,4,1,8,5,2]=>0011111
[7,1,4,2,8,5,3,6]=>[5,4,8,1,7,2,3,6]=>[8,6,2,4,1,5,7,3]=>0010111
[1,2,6,8,3,5,4,7]=>[1,2,5,8,3,6,4,7]=>[1,2,5,3,6,8,7,4]=>0001011
[1,2,3,7,8,6,4,5]=>[1,2,3,6,4,8,7,5]=>[1,2,3,7,8,5,4,6]=>0001001
[1,2,8,3,5,7,6,4]=>[1,2,6,7,3,8,5,4]=>[1,2,8,4,7,5,3,6]=>0001011
[6,1,8,2,7,5,3,4]=>[5,7,8,1,6,2,3,4]=>[8,4,1,5,6,2,7,3]=>0010111
[8,2,7,3,1,4,5,6]=>[3,7,8,2,1,4,5,6]=>[8,6,4,2,7,5,1,3]=>0011111
[5,4,8,7,3,2,1,6]=>[2,3,7,5,4,1,8,6]=>[5,4,8,6,1,2,3,7]=>0001101
[5,6,3,1,4,2,7,8]=>[4,3,6,1,5,2,7,8]=>[4,1,5,6,2,3,7,8]=>0010100
[5,8,3,1,4,6,7,2]=>[7,3,8,1,5,4,6,2]=>[5,7,6,4,1,8,2,3]=>0010111
[6,7,1,4,5,3,2,8]=>[3,5,7,1,4,6,2,8]=>[6,7,2,5,4,1,3,8]=>0011010
[7,2,3,8,5,1,6,4]=>[6,5,2,8,7,3,1,4]=>[7,1,6,3,2,5,8,4]=>0100111
[7,2,8,4,1,6,5,3]=>[5,4,6,8,7,2,1,3]=>[7,1,5,8,3,6,2,4]=>0000111
[7,8,3,4,1,6,5,2]=>[5,4,6,3,8,1,7,2]=>[7,8,2,4,3,6,1,5]=>0010101
[8,1,2,3,5,6,4,7]=>[6,1,2,8,3,5,4,7]=>[6,5,3,2,1,8,7,4]=>1101111
[4,1,8,2,3,5,7,6]=>[7,4,1,2,3,8,5,6]=>[4,2,7,5,3,1,8,6]=>0111011
[6,1,2,8,3,4,7,5]=>[7,1,8,2,6,3,4,5]=>[7,4,2,1,8,5,6,3]=>1010111
[1,5,2,8,3,4,7,6]=>[1,7,5,2,3,8,4,6]=>[1,5,3,7,4,2,8,6]=>0011011
[7,1,2,5,3,6,8,4]=>[8,1,5,7,2,3,6,4]=>[8,4,7,6,3,5,2,1]=>1001111
[1,8,2,5,6,3,7,4]=>[1,7,6,8,2,5,3,4]=>[1,7,3,6,5,2,8,4]=>0001111
[6,8,1,3,4,2,5,7]=>[4,8,1,3,2,6,5,7]=>[4,3,1,6,8,7,5,2]=>0111011
[1,7,3,2,8,4,5,6]=>[1,3,8,7,2,4,5,6]=>[1,8,6,4,7,5,2,3]=>0001111
[6,3,5,1,8,2,4,7]=>[8,5,6,3,1,2,4,7]=>[8,7,4,3,6,2,5,1]=>0011111
[1,7,4,2,3,6,8,5]=>[1,4,2,8,7,3,6,5]=>[1,8,5,7,6,3,2,4]=>0100111
[7,1,3,4,5,8,2,6]=>[8,7,1,3,4,5,2,6]=>[7,2,8,6,5,4,3,1]=>0111111
[1,8,7,6,3,2,4,5]=>[1,3,6,2,4,7,8,5]=>[1,8,5,4,2,3,6,7]=>0011001
[1,8,2,7,5,3,6,4]=>[1,6,5,7,8,2,3,4]=>[1,6,2,8,4,7,3,5]=>0000111
[1,7,4,5,2,6,8,3]=>[1,8,5,7,4,2,6,3]=>[1,8,3,5,4,7,6,2]=>0001111
[3,2,1,8,7,4,5,6]=>[2,3,1,7,4,5,8,6]=>[3,1,2,8,6,5,4,7]=>0101101
[3,2,1,8,4,7,6,5]=>[2,3,1,6,7,8,4,5]=>[3,1,2,8,5,7,4,6]=>0100011
[3,2,8,7,6,1,5,4]=>[5,3,2,6,1,7,8,4]=>[3,2,5,1,8,4,6,7]=>0101001
[6,5,8,7,3,2,1,4]=>[2,3,7,1,6,5,8,4]=>[6,5,8,4,1,2,3,7]=>0010101
[5,3,8,4,6,2,7,1]=>[7,6,8,5,3,4,2,1]=>[8,1,7,2,6,4,5,3]=>0001111
[5,7,8,4,3,2,1,6]=>[2,3,4,8,5,1,7,6]=>[5,7,8,6,1,2,3,4]=>0000101
[4,6,8,7,3,2,1,5]=>[2,3,7,4,1,6,8,5]=>[4,6,8,5,1,2,3,7]=>0001001
[2,4,8,7,6,5,1,3]=>[5,2,1,4,6,7,8,3]=>[2,4,8,3,1,5,6,7]=>0100001
[4,7,6,8,3,2,1,5]=>[2,3,8,4,1,7,6,5]=>[4,7,6,8,5,1,2,3]=>0001011
[4,6,7,8,3,2,1,5]=>[2,3,8,4,1,6,7,5]=>[4,6,7,8,5,1,2,3]=>0001001
[3,5,6,8,7,2,1,4]=>[2,7,3,1,5,6,8,4]=>[3,5,6,8,4,1,2,7]=>0010001
[2,4,7,1,8,3,6,5]=>[6,2,8,4,7,1,3,5]=>[2,4,6,1,8,5,7,3]=>0000111
[2,4,6,1,5,8,3,7]=>[8,2,6,4,1,5,3,7]=>[2,4,8,7,3,6,5,1]=>0001111
[2,5,4,8,6,7,3,1]=>[3,2,7,5,4,8,6,1]=>[2,5,4,8,1,3,7,6]=>0001011
[3,4,1,7,6,8,5,2]=>[5,4,3,1,8,7,6,2]=>[3,7,6,8,2,4,1,5]=>0010011
[3,5,1,7,2,6,8,4]=>[8,7,3,5,1,2,6,4]=>[3,7,6,2,8,4,5,1]=>0001111
[4,3,6,2,8,1,7,5]=>[7,8,4,3,6,2,1,5]=>[4,3,7,1,8,5,6,2]=>0010111
[5,3,4,7,2,8,1,6]=>[8,7,5,3,4,2,1,6]=>[5,4,3,8,6,2,7,1]=>0011111
[4,5,7,2,1,6,8,3]=>[2,8,7,4,5,1,6,3]=>[4,5,8,3,7,6,1,2]=>0000111
[3,4,1,5,6,8,7,2]=>[7,4,3,1,5,6,8,2]=>[3,5,6,8,2,4,1,7]=>0010001
[6,3,7,8,2,5,1,4]=>[5,8,6,3,2,1,7,4]=>[7,8,4,3,6,1,5,2]=>0011101
[4,3,7,5,6,2,8,1]=>[8,6,4,3,7,5,2,1]=>[4,3,7,2,6,5,8,1]=>0010111
[4,7,8,5,6,2,1,3]=>[2,6,1,4,8,5,7,3]=>[4,7,8,3,1,2,6,5]=>0100101
[4,2,6,3,7,8,1,5]=>[8,6,4,2,3,1,7,5]=>[7,8,5,3,4,2,6,1]=>0011101
[7,1,6,2,8,3,4,5]=>[8,6,7,1,2,3,4,5]=>[8,5,2,6,3,7,4,1]=>0011111
[8,2,1,7,4,6,3,5]=>[2,6,7,8,1,4,3,5]=>[7,3,8,5,1,2,6,4]=>0001111
[5,2,1,6,8,4,7,3]=>[2,7,8,5,1,6,4,3]=>[6,7,4,5,1,2,8,3]=>0001011
[8,2,1,7,3,5,4,6]=>[2,5,7,8,1,3,4,6]=>[5,1,2,8,6,3,7,4]=>0001111
[6,1,2,8,3,7,4,5]=>[7,1,8,6,2,3,4,5]=>[8,5,2,1,7,4,6,3]=>1001111
[4,1,7,6,8,3,2,5]=>[3,8,4,1,2,7,6,5]=>[4,1,3,7,6,8,5,2]=>0011011
[7,1,6,3,4,2,8,5]=>[4,8,6,1,7,3,2,5]=>[4,1,6,3,8,5,7,2]=>0010111
[7,1,6,8,5,2,3,4]=>[5,8,1,2,7,3,6,4]=>[7,6,3,1,5,8,4,2]=>0110111
[6,2,3,8,7,5,1,4]=>[5,7,2,3,6,1,8,4]=>[6,1,5,8,4,3,2,7]=>0110101
[3,8,5,7,2,4,1,6]=>[4,7,3,2,8,5,1,6]=>[3,7,1,4,2,8,6,5]=>0010111
[7,6,2,3,4,1,8,5]=>[4,8,2,3,6,7,1,5]=>[8,5,6,7,1,4,3,2]=>0110011
[8,5,7,3,1,6,2,4]=>[6,3,7,1,8,5,2,4]=>[7,2,3,8,4,1,6,5]=>0010111
[6,3,4,8,7,5,1,2]=>[5,1,7,3,6,4,8,2]=>[8,2,1,5,6,4,3,7]=>1010101
[7,3,5,6,8,1,4,2]=>[4,8,7,3,1,5,6,2]=>[7,6,5,1,4,3,8,2]=>0011111
[7,4,5,2,8,3,6,1]=>[6,8,5,7,4,2,3,1]=>[7,3,5,4,8,1,6,2]=>0001111
[4,3,1,2,6,7,8,5]=>[3,1,4,2,8,6,7,5]=>[4,2,1,3,6,7,8,5]=>1010001
[7,4,6,5,8,3,2,1]=>[2,3,8,6,7,4,5,1]=>[6,4,7,5,8,1,2,3]=>0000111
[4,8,5,2,6,7,3,1]=>[3,7,5,4,8,2,6,1]=>[4,7,6,2,8,1,3,5]=>0000111
[2,5,8,6,7,3,1,4]=>[3,2,7,1,5,8,6,4]=>[2,5,8,4,1,3,7,6]=>0010011
[3,7,4,8,6,2,5,1]=>[5,6,3,8,4,7,2,1]=>[3,7,2,6,8,1,5,4]=>0001011
[2,3,4,1,8,7,5,6]=>[4,2,3,1,7,5,8,6]=>[2,3,4,1,8,6,5,7]=>0010101
[6,5,4,1,3,2,8,7]=>[3,4,1,5,6,2,8,7]=>[3,1,6,2,4,5,8,7]=>0100101
[6,5,4,2,1,3,8,7]=>[2,4,1,5,6,3,8,7]=>[6,3,1,2,4,5,8,7]=>0100101
[7,8,4,2,1,5,6,3]=>[2,6,4,8,1,5,7,3]=>[6,5,1,2,7,8,3,4]=>0001101
[2,1,7,8,4,5,6,3]=>[2,1,6,8,4,5,7,3]=>[2,1,7,8,3,6,5,4]=>1001101
[8,6,2,7,1,3,5,4]=>[5,7,2,6,1,8,3,4]=>[5,1,7,3,2,8,4,6]=>0101011
[8,3,2,7,6,4,1,5]=>[4,3,6,7,2,8,1,5]=>[7,1,4,8,5,2,3,6]=>0001011
[8,5,4,1,3,7,6,2]=>[6,4,1,5,7,8,3,2]=>[8,2,4,5,7,3,1,6]=>0100011
[6,8,2,7,3,4,1,5]=>[4,7,8,2,3,6,1,5]=>[6,7,1,4,2,8,5,3]=>0011011
[5,6,1,4,7,2,3,8]=>[7,6,1,2,5,4,3,8]=>[5,6,4,2,7,3,1,8]=>0110110
[3,6,7,4,1,2,5,8]=>[4,1,3,7,2,6,5,8]=>[3,6,7,5,2,1,4,8]=>1001010
[2,5,1,4,3,7,6,8]=>[4,2,5,1,3,7,6,8]=>[2,4,1,5,3,7,6,8]=>0011010
[1,6,7,4,3,2,8,5]=>[1,3,4,8,7,6,2,5]=>[1,6,8,5,7,2,3,4]=>0000011
[2,6,4,3,1,8,5,7]=>[3,2,4,8,6,1,5,7]=>[2,8,7,5,6,1,3,4]=>0000111
[7,8,2,1,5,4,3,6]=>[2,4,5,8,1,3,7,6]=>[7,8,6,3,5,1,2,4]=>0001101
[7,8,1,2,3,6,4,5]=>[6,1,2,8,3,4,7,5]=>[7,8,5,3,2,1,6,4]=>1101101
[1,3,2,6,5,8,4,7]=>[1,3,2,8,6,5,4,7]=>[1,3,2,6,5,8,7,4]=>0100111
[3,1,7,2,6,5,8,4]=>[8,3,1,6,7,2,5,4]=>[7,5,8,4,6,2,3,1]=>0100111
[1,3,2,7,5,4,8,6]=>[1,3,2,5,8,7,4,6]=>[1,3,2,8,6,7,4,5]=>0100011
[1,6,7,2,3,5,8,4]=>[1,8,2,7,3,6,5,4]=>[1,6,8,4,7,5,3,2]=>0101011
[2,5,4,7,8,6,1,3]=>[6,2,1,5,4,8,7,3]=>[2,5,4,7,8,3,1,6]=>0101001
[3,1,7,8,6,4,5,2]=>[5,3,1,6,4,8,7,2]=>[7,8,2,3,1,5,4,6]=>0101001
[2,3,4,8,7,5,6,1]=>[6,2,3,4,7,5,8,1]=>[2,3,4,8,1,6,5,7]=>0000101
[5,1,6,3,7,8,4,2]=>[4,8,6,5,1,3,7,2]=>[5,1,4,6,3,7,8,2]=>0001101
[6,4,7,5,8,3,2,1]=>[2,3,8,7,6,4,5,1]=>[7,5,6,4,8,1,2,3]=>0000111
[3,8,4,5,6,7,2,1]=>[2,7,3,8,4,5,6,1]=>[3,8,1,2,7,6,5,4]=>0001111
[8,2,4,1,6,7,5,3]=>[5,4,7,2,8,1,6,3]=>[4,2,8,3,7,6,1,5]=>0010111
[3,7,8,5,6,4,2,1]=>[2,4,3,6,8,5,7,1]=>[3,7,8,1,2,4,6,5]=>0000101
[4,3,7,5,8,6,2,1]=>[2,6,4,3,8,7,5,1]=>[4,3,8,1,2,6,7,5]=>0010011
[5,4,6,2,3,1,8,7]=>[3,6,2,5,4,1,8,7]=>[5,4,6,1,3,2,8,7]=>0101101
[6,3,1,5,4,2,8,7]=>[4,3,5,6,1,2,8,7]=>[6,2,3,5,1,4,8,7]=>0001101
[2,7,5,6,8,3,4,1]=>[4,2,8,3,7,5,6,1]=>[2,7,6,5,8,1,4,3]=>0010111
[2,1,7,6,8,4,5,3]=>[2,1,5,8,4,7,6,3]=>[2,1,7,6,8,3,5,4]=>1001011
[2,6,5,3,7,4,8,1]=>[8,2,7,5,6,3,4,1]=>[2,7,4,5,6,3,8,1]=>0000111
[2,1,8,5,3,7,6,4]=>[2,1,6,5,7,8,3,4]=>[2,1,8,4,5,7,3,6]=>1000011
[2,5,3,1,6,4,7,8]=>[3,2,6,5,1,4,7,8]=>[2,6,4,5,1,3,7,8]=>0001100
[3,5,4,2,8,6,1,7]=>[6,4,3,5,2,8,1,7]=>[3,5,2,4,8,7,1,6]=>0001011
[7,4,1,3,2,6,8,5]=>[3,4,1,8,7,2,6,5]=>[3,1,8,5,7,6,2,4]=>0100111
[2,5,4,3,8,1,6,7]=>[8,2,4,5,3,1,6,7]=>[2,5,3,4,8,7,6,1]=>0001111
[7,6,5,8,1,2,4,3]=>[4,1,8,2,6,7,5,3]=>[4,2,1,7,5,6,8,3]=>1010011
[4,3,8,1,6,5,7,2]=>[7,6,4,3,8,1,5,2]=>[4,3,8,2,6,1,7,5]=>0010111
[4,3,8,2,5,6,7,1]=>[7,8,4,3,2,5,6,1]=>[4,3,8,1,7,6,5,2]=>0011111
[7,2,8,1,6,3,5,4]=>[5,6,8,7,2,1,3,4]=>[6,1,5,2,8,4,7,3]=>0001111
[6,3,4,5,8,2,7,1]=>[7,8,6,3,4,5,2,1]=>[6,5,4,3,8,1,7,2]=>0011111
[7,3,8,1,4,5,6,2]=>[6,8,7,3,1,4,5,2]=>[7,5,1,6,4,3,8,2]=>0011111
[2,8,1,3,5,6,7,4]=>[7,2,1,8,3,5,6,4]=>[2,7,6,5,3,1,8,4]=>0101111
[1,2,7,6,8,4,5,3]=>[1,2,5,8,4,7,6,3]=>[1,2,7,6,8,3,5,4]=>0001011
[1,2,6,7,8,3,5,4]=>[1,2,5,8,3,6,7,4]=>[1,2,5,3,6,7,8,4]=>0001001
[1,2,5,3,7,6,8,4]=>[1,2,8,5,3,7,6,4]=>[1,2,7,6,8,4,5,3]=>0001011
[3,7,8,1,5,6,2,4]=>[6,8,3,1,2,5,7,4]=>[3,7,8,4,1,6,5,2]=>0011101
[1,2,4,8,3,6,5,7]=>[1,2,6,4,8,3,5,7]=>[1,2,4,6,3,8,7,5]=>0000111
[4,8,2,7,5,1,3,6]=>[5,7,2,4,8,1,3,6]=>[4,7,3,2,8,6,1,5]=>0100111
[3,6,8,2,5,7,4,1]=>[4,7,3,8,2,6,5,1]=>[3,6,7,5,2,8,1,4]=>0001011
[4,8,7,5,2,6,3,1]=>[3,6,5,4,7,2,8,1]=>[4,6,2,8,1,3,5,7]=>0000101
[3,2,8,5,6,1,7,4]=>[7,3,2,6,8,5,1,4]=>[3,2,7,1,8,4,6,5]=>0100111
[3,5,8,7,4,6,2,1]=>[2,6,3,7,5,4,8,1]=>[3,5,8,1,2,6,4,7]=>0000101
[1,6,8,7,4,5,3,2]=>[1,3,5,7,4,6,8,2]=>[1,6,8,2,3,5,4,7]=>0001001
[1,3,5,6,8,7,2,4]=>[1,7,3,2,5,6,8,4]=>[1,3,5,6,8,4,2,7]=>0010001
[3,5,6,7,8,2,4,1]=>[4,8,3,2,5,6,7,1]=>[3,5,6,7,8,1,4,2]=>0010001
[5,2,4,1,6,7,8,3]=>[8,4,5,2,1,6,7,3]=>[4,2,6,7,8,3,5,1]=>0011001
[8,5,6,7,2,4,3,1]=>[3,4,7,2,8,5,6,1]=>[4,2,8,1,3,7,6,5]=>0010111
[4,8,6,7,5,2,3,1]=>[3,5,2,4,7,8,6,1]=>[4,8,1,3,2,5,7,6]=>0100011
[8,1,4,3,6,5,2,7]=>[5,4,6,1,8,3,2,7]=>[6,3,8,7,2,4,1,5]=>0010111
[6,1,2,5,4,3,8,7]=>[4,1,5,6,2,3,8,7]=>[6,3,5,2,1,4,8,7]=>1001101
[8,1,2,3,5,7,4,6]=>[7,1,2,8,3,5,4,6]=>[8,6,5,3,2,1,7,4]=>1101111
[8,1,2,3,5,4,7,6]=>[5,1,2,7,3,8,4,6]=>[5,3,2,1,7,4,8,6]=>1101011
[3,7,8,6,4,2,1,5]=>[2,4,3,6,1,8,7,5]=>[3,7,8,5,1,2,4,6]=>0001001
[4,5,2,8,6,7,1,3]=>[7,5,2,4,1,8,6,3]=>[4,8,3,2,5,1,7,6]=>0101011
[8,1,2,3,6,7,5,4]=>[5,1,2,7,8,3,6,4]=>[8,4,7,6,3,2,1,5]=>1100111
[5,4,1,3,2,8,7,6]=>[3,4,1,5,2,7,8,6]=>[3,1,5,2,4,8,6,7]=>0101001
[5,4,2,1,3,8,7,6]=>[2,4,1,5,3,7,8,6]=>[5,3,1,2,4,8,6,7]=>0101001
[3,2,7,4,1,6,5,8]=>[4,3,2,6,7,1,5,8]=>[3,2,6,1,4,7,5,8]=>0100110
[1,5,7,2,4,3,6,8]=>[1,4,7,2,5,3,6,8]=>[1,4,2,5,7,6,3,8]=>0010110
[5,2,8,1,4,3,7,6]=>[4,7,5,2,1,8,3,6]=>[7,3,5,1,4,2,8,6]=>0011011
[8,4,6,2,3,7,1,5]=>[7,6,2,8,4,3,1,5]=>[6,3,2,7,1,8,5,4]=>0101111
[8,6,1,3,7,5,2,4]=>[5,7,1,3,6,8,2,4]=>[7,2,8,4,3,1,5,6]=>0110011
[5,8,1,3,4,7,2,6]=>[7,8,1,3,5,4,2,6]=>[5,8,6,4,3,1,7,2]=>0110111
[8,2,6,3,1,4,7,5]=>[3,7,6,2,8,1,4,5]=>[6,1,3,7,4,2,8,5]=>0010111
[8,3,2,7,6,1,4,5]=>[6,3,7,2,1,8,4,5]=>[7,4,2,3,8,5,1,6]=>0011011
[3,6,7,5,8,2,1,4]=>[2,8,3,1,7,6,5,4]=>[3,6,7,5,8,4,1,2]=>0010011
[2,4,6,8,7,3,5,1]=>[5,2,7,4,3,6,8,1]=>[2,4,6,8,1,5,3,7]=>0001001
[3,5,6,8,7,2,4,1]=>[4,7,3,2,5,6,8,1]=>[3,5,6,8,1,4,2,7]=>0010001
[1,6,8,4,7,5,3,2]=>[1,3,5,7,8,6,4,2]=>[1,6,7,4,8,2,3,5]=>0000011
[6,4,7,8,3,5,2,1]=>[2,5,8,6,4,3,7,1]=>[7,8,1,2,5,4,6,3]=>0001101
[6,3,5,2,7,4,8,1]=>[8,7,5,6,3,2,4,1]=>[5,3,7,4,6,2,8,1]=>0001111
[7,5,4,2,6,3,8,1]=>[8,6,4,5,7,2,3,1]=>[6,2,7,3,4,5,8,1]=>0000111
[4,5,7,2,6,3,8,1]=>[8,6,7,4,5,2,3,1]=>[4,5,6,2,7,3,8,1]=>0000111
[5,4,7,2,6,1,8,3]=>[8,6,7,5,4,2,1,3]=>[5,4,6,2,8,3,7,1]=>0001111
[4,2,7,5,6,3,8,1]=>[8,6,4,2,7,5,3,1]=>[7,3,4,2,6,5,8,1]=>0010111
[6,2,4,3,7,5,8,1]=>[8,4,7,2,6,3,5,1]=>[4,2,7,5,6,3,8,1]=>0010111
[2,7,5,4,8,6,3,1]=>[3,2,6,5,8,7,4,1]=>[2,8,1,3,6,7,4,5]=>0000011
[4,3,7,5,8,6,1,2]=>[6,1,4,3,8,7,5,2]=>[4,3,8,2,1,6,7,5]=>1010011
[6,7,4,8,3,5,2,1]=>[2,5,8,7,4,6,3,1]=>[6,8,1,2,5,4,7,3]=>0001011
[3,6,8,5,4,7,1,2]=>[7,1,3,5,8,6,4,2]=>[3,6,8,2,1,7,4,5]=>1000011
[8,4,3,5,7,2,6,1]=>[6,7,4,8,3,5,2,1]=>[7,2,8,1,6,5,3,4]=>0001111
[1,6,8,3,2,4,7,5]=>[1,3,7,2,8,6,4,5]=>[1,6,7,4,2,3,8,5]=>0010011
[1,8,7,6,4,2,3,5]=>[1,4,2,6,3,7,8,5]=>[1,8,5,3,2,4,6,7]=>0101001
[8,1,7,3,5,4,6,2]=>[6,5,7,8,1,3,4,2]=>[8,2,5,1,6,3,7,4]=>0001111
[4,5,7,2,3,8,6,1]=>[6,8,2,4,5,7,3,1]=>[4,5,8,1,6,7,3,2]=>0100011
[4,5,7,2,3,8,1,6]=>[8,7,2,4,5,3,1,6]=>[4,5,8,6,3,2,7,1]=>0100111
[4,5,6,2,3,1,8,7]=>[3,6,2,4,5,1,8,7]=>[4,5,6,1,3,2,8,7]=>0100101
[4,5,6,2,1,3,8,7]=>[2,6,1,4,5,3,8,7]=>[4,5,6,3,1,2,8,7]=>0100101
[4,5,6,1,3,2,8,7]=>[3,6,1,4,5,2,8,7]=>[3,1,4,5,6,2,8,7]=>0100101
[4,5,6,3,1,2,8,7]=>[3,1,6,4,5,2,8,7]=>[4,5,6,2,1,3,8,7]=>1000101
[4,6,7,3,8,2,5,1]=>[5,8,7,4,3,6,2,1]=>[4,6,8,1,5,3,7,2]=>0001011
[4,6,7,3,8,2,1,5]=>[2,8,7,4,3,6,1,5]=>[4,6,8,5,3,7,1,2]=>0001011
[4,5,7,3,1,8,2,6]=>[8,3,7,4,5,1,2,6]=>[4,5,7,2,3,8,6,1]=>0000111
[3,5,1,7,4,8,2,6]=>[8,7,3,5,1,4,2,6]=>[3,7,2,8,6,4,5,1]=>0001111
[2,1,5,7,4,8,3,6]=>[2,1,8,7,5,4,3,6]=>[2,1,5,8,6,4,7,3]=>1000111
[4,5,7,1,3,8,6,2]=>[6,8,1,4,5,7,3,2]=>[4,5,7,3,1,6,8,2]=>0100011
[4,6,7,1,8,3,5,2]=>[5,8,7,4,1,6,3,2]=>[4,5,1,6,7,3,8,2]=>0001011
[3,6,1,7,8,4,5,2]=>[5,8,3,6,1,4,7,2]=>[3,5,1,6,4,7,8,2]=>0001101
[2,1,6,7,8,4,5,3]=>[2,1,5,8,4,6,7,3]=>[2,1,6,7,8,3,5,4]=>1001001
[2,1,6,7,8,4,3,5]=>[2,1,4,8,3,6,7,5]=>[2,1,6,7,8,5,3,4]=>1001001
[4,6,7,1,8,3,2,5]=>[3,8,7,4,1,6,2,5]=>[4,6,8,5,1,3,7,2]=>0001011
[5,6,7,8,1,3,2,4]=>[3,8,1,2,5,6,7,4]=>[3,1,5,6,7,8,4,2]=>0110001
[4,6,7,2,8,3,5,1]=>[5,8,7,4,2,6,3,1]=>[4,6,7,3,8,1,5,2]=>0001011
[3,6,2,7,8,4,5,1]=>[5,8,3,6,2,4,7,1]=>[3,6,4,7,8,1,5,2]=>0001101
[3,6,2,7,8,4,1,5]=>[4,8,3,6,2,1,7,5]=>[3,6,1,4,7,8,5,2]=>0001101
[3,4,2,1,7,8,5,6]=>[2,4,3,1,8,5,7,6]=>[3,4,1,2,7,8,6,5]=>0010101
[4,6,7,2,8,5,3,1]=>[3,5,8,4,7,6,2,1]=>[4,6,7,2,5,8,1,3]=>0000011
[4,6,7,2,8,5,1,3]=>[5,8,2,4,7,6,1,3]=>[4,6,7,1,5,8,3,2]=>0100011
[2,1,6,7,8,3,5,4]=>[2,1,5,8,3,6,7,4]=>[2,1,5,3,6,7,8,4]=>1001001
[2,1,6,7,8,5,3,4]=>[2,1,5,3,8,6,7,4]=>[2,1,6,7,8,4,3,5]=>1010001
[5,3,1,6,2,4,8,7]=>[6,3,5,1,2,4,8,7]=>[5,2,3,6,4,1,8,7]=>0011101
[7,4,5,1,2,8,3,6]=>[8,1,5,7,4,2,3,6]=>[7,3,5,4,8,6,2,1]=>1001111
[5,4,6,1,2,3,8,7]=>[6,1,2,5,4,3,8,7]=>[5,4,6,3,2,1,8,7]=>1101101
[5,6,4,1,2,3,8,7]=>[4,1,2,6,5,3,8,7]=>[5,6,3,2,1,4,8,7]=>1100101
[7,5,4,1,2,8,3,6]=>[8,1,4,5,7,2,3,6]=>[7,3,4,5,8,6,2,1]=>1000111
[3,7,1,5,2,8,4,6]=>[8,5,3,7,1,2,4,6]=>[3,7,4,8,6,2,5,1]=>0001111
[2,1,7,5,3,8,4,6]=>[2,1,8,5,7,3,4,6]=>[2,1,7,4,5,8,6,3]=>1000111
[6,8,4,1,7,2,3,5]=>[7,4,1,8,2,6,3,5]=>[6,7,3,1,8,5,2,4]=>0101011
[4,8,6,1,7,2,3,5]=>[7,6,1,4,2,8,3,5]=>[4,7,3,1,8,5,2,6]=>0101011
[2,1,8,6,7,3,4,5]=>[2,1,7,3,4,8,6,5]=>[2,1,8,5,4,3,7,6]=>1011011
[2,1,7,6,8,3,4,5]=>[2,1,8,3,4,7,6,5]=>[2,1,7,6,8,5,4,3]=>1011011
[4,7,6,1,8,2,3,5]=>[8,6,1,4,2,7,3,5]=>[4,8,5,2,6,7,3,1]=>0101011
[5,7,6,8,1,2,3,4]=>[8,1,2,3,5,7,6,4]=>[5,7,6,8,4,3,2,1]=>1110011
[8,4,6,1,7,2,3,5]=>[7,6,1,8,4,2,3,5]=>[6,2,7,3,1,8,5,4]=>0101111
[8,3,1,6,7,2,4,5]=>[7,3,8,1,2,4,6,5]=>[7,6,4,1,8,5,2,3]=>0011111
[4,3,1,2,7,8,5,6]=>[3,1,4,2,8,5,7,6]=>[4,2,1,3,7,8,6,5]=>1010101
[5,6,8,7,1,2,3,4]=>[7,1,2,3,5,6,8,4]=>[5,6,8,4,3,2,1,7]=>1110001
[8,5,7,6,1,2,3,4]=>[6,1,2,3,7,8,5,4]=>[7,5,8,4,3,2,1,6]=>1110011
[4,7,8,1,6,2,3,5]=>[6,8,1,4,2,3,7,5]=>[4,6,3,1,7,8,5,2]=>0101101
[6,8,7,5,1,2,3,4]=>[5,1,2,3,7,6,8,4]=>[6,8,4,3,2,1,5,7]=>1110001
[6,4,7,3,8,5,1,2]=>[5,1,8,7,6,4,3,2]=>[8,2,1,5,6,4,7,3]=>1000111
[5,4,3,7,8,6,1,2]=>[6,1,4,5,3,8,7,2]=>[5,3,4,7,8,2,1,6]=>1001001
[5,4,3,6,8,7,1,2]=>[7,1,4,5,3,6,8,2]=>[5,3,4,6,8,2,1,7]=>1001001
[5,3,2,6,1,7,4,8]=>[7,3,6,5,2,1,4,8]=>[7,4,5,2,3,6,1,8]=>0001110
[5,4,2,6,8,1,7,3]=>[7,8,4,5,2,6,1,3]=>[6,7,1,8,3,4,5,2]=>0001011
[7,8,3,2,1,5,4,6]=>[2,3,5,8,1,4,7,6]=>[5,1,2,3,7,8,6,4]=>0001101
[5,3,2,8,1,6,7,4]=>[7,3,8,5,2,1,6,4]=>[7,6,1,8,4,5,2,3]=>0001111
[5,3,2,7,1,6,4,8]=>[6,3,7,5,2,1,4,8]=>[6,1,7,4,5,2,3,8]=>0001110
[6,3,7,2,1,5,8,4]=>[2,8,7,6,3,1,5,4]=>[7,5,3,8,4,6,1,2]=>0001111
[6,3,7,2,1,8,5,4]=>[2,5,8,7,6,3,1,4]=>[8,4,7,1,2,5,6,3]=>0000111
[6,3,7,2,1,4,8,5]=>[2,8,7,3,6,1,4,5]=>[7,4,3,8,5,6,1,2]=>0010111
[5,4,2,8,7,1,3,6]=>[7,4,2,5,1,3,8,6]=>[8,6,3,2,4,5,1,7]=>0101101
[7,8,4,2,6,1,3,5]=>[6,4,2,8,1,3,7,5]=>[7,8,5,1,6,3,2,4]=>0101101
[4,3,2,1,8,7,5,6]=>[2,3,4,1,7,5,8,6]=>[4,1,2,3,8,6,5,7]=>0010101
[4,3,2,1,7,5,8,6]=>[2,3,4,1,8,7,5,6]=>[4,1,2,3,8,6,7,5]=>0010011
[4,3,2,1,7,5,6,8]=>[2,3,4,1,7,5,6,8]=>[4,1,2,3,7,6,5,8]=>0010110
[6,3,8,2,1,4,7,5]=>[2,7,8,3,6,1,4,5]=>[8,5,6,1,2,7,4,3]=>0010111
[4,3,2,1,8,5,6,7]=>[2,3,4,1,8,5,6,7]=>[4,1,2,3,8,7,6,5]=>0010111
[7,8,5,6,1,2,4,3]=>[4,1,6,2,8,5,7,3]=>[4,2,1,7,8,3,6,5]=>1010101
[1,6,8,3,2,7,5,4]=>[1,3,5,7,8,6,2,4]=>[1,6,8,4,7,2,3,5]=>0000011
[6,1,8,3,2,7,5,4]=>[3,5,7,8,6,1,2,4]=>[7,2,5,6,1,3,8,4]=>0000111
[7,8,1,3,2,6,5,4]=>[3,5,1,6,8,2,7,4]=>[3,1,7,8,4,6,2,5]=>0100101
[7,8,2,3,1,6,5,4]=>[3,5,2,6,8,1,7,4]=>[7,8,4,6,1,3,2,5]=>0100101
[1,5,2,8,3,7,6,4]=>[1,6,7,5,2,8,3,4]=>[1,7,3,8,4,5,2,6]=>0001011
[5,2,1,8,3,7,6,4]=>[2,6,7,5,1,8,3,4]=>[7,3,8,4,5,1,2,6]=>0001011
[6,2,8,4,7,1,5,3]=>[5,7,8,6,2,4,1,3]=>[6,4,7,1,5,2,8,3]=>0001111
[6,3,8,4,7,5,1,2]=>[5,1,7,8,6,3,4,2]=>[8,2,1,5,6,3,7,4]=>1000111
[1,2,5,8,3,7,6,4]=>[1,2,6,7,5,8,3,4]=>[1,2,5,8,4,7,3,6]=>0000011
[4,1,2,3,8,7,6,5]=>[4,1,2,3,6,7,8,5]=>[4,3,2,1,8,5,6,7]=>1110001
[1,4,2,3,8,7,6,5]=>[1,4,2,3,6,7,8,5]=>[1,4,3,2,8,5,6,7]=>0110001
[4,1,3,2,8,7,6,5]=>[3,4,1,2,6,7,8,5]=>[3,1,4,2,8,5,6,7]=>0110001
[6,3,8,1,2,7,5,4]=>[5,1,7,8,6,3,2,4]=>[7,2,1,5,6,3,8,4]=>1000111
[1,5,4,8,7,2,6,3]=>[1,6,7,5,4,2,8,3]=>[1,5,4,6,2,8,3,7]=>0001101
[6,5,8,7,1,2,4,3]=>[4,1,7,2,6,5,8,3]=>[4,2,1,6,5,8,3,7]=>1010101
[5,6,8,7,2,1,4,3]=>[2,4,7,1,5,6,8,3]=>[4,1,2,5,6,8,3,7]=>0010001
[4,5,1,8,7,2,6,3]=>[6,7,5,4,1,2,8,3]=>[4,8,3,5,1,6,2,7]=>0001101
[4,1,5,8,7,2,6,3]=>[6,7,4,1,5,2,8,3]=>[5,8,3,4,1,6,2,7]=>0010101
[1,3,5,8,2,7,6,4]=>[1,6,3,7,5,8,2,4]=>[1,3,5,8,4,7,2,6]=>0000011
[3,1,5,8,2,7,6,4]=>[6,3,1,7,5,8,2,4]=>[5,8,4,7,2,3,1,6]=>0100011
[4,6,8,3,7,5,1,2]=>[5,1,7,4,8,6,3,2]=>[4,6,7,3,8,2,1,5]=>1000011
[4,5,3,8,7,6,1,2]=>[6,1,5,4,3,7,8,2]=>[4,5,3,8,2,1,6,7]=>1001001
[3,1,4,2,8,7,6,5]=>[4,3,1,2,6,7,8,5]=>[4,2,3,1,8,5,6,7]=>0110001
[3,2,5,8,1,7,6,4]=>[6,3,2,7,5,8,1,4]=>[3,2,5,8,4,7,1,6]=>0100011
[4,3,5,8,7,6,1,2]=>[6,1,4,3,5,7,8,2]=>[4,3,5,8,2,1,6,7]=>1010001
[2,4,5,8,7,1,6,3]=>[6,2,7,4,5,1,8,3]=>[2,4,5,6,1,8,3,7]=>0000101
[6,2,5,1,4,3,8,7]=>[4,5,6,2,1,3,8,7]=>[5,1,4,2,6,3,8,7]=>0011101
[5,2,6,1,4,3,8,7]=>[4,6,5,2,1,3,8,7]=>[6,3,5,1,4,2,8,7]=>0011101
[5,2,7,1,4,3,8,6]=>[4,8,5,2,1,7,3,6]=>[8,6,7,3,5,1,4,2]=>0011011
[6,2,7,1,4,3,8,5]=>[4,8,7,2,6,1,3,5]=>[7,3,8,5,6,1,4,2]=>0010111
[7,2,6,1,4,3,8,5]=>[4,8,6,2,7,1,3,5]=>[8,5,7,3,6,1,4,2]=>0010111
[8,2,5,1,4,3,7,6]=>[4,5,7,2,1,8,3,6]=>[5,1,4,2,7,3,8,6]=>0011011
[6,2,8,1,5,3,7,4]=>[7,5,8,6,2,1,3,4]=>[5,2,8,4,6,1,7,3]=>0001111
[7,4,8,1,3,2,6,5]=>[3,6,1,8,7,4,2,5]=>[3,1,8,5,7,2,6,4]=>0100111
[8,3,7,1,4,2,6,5]=>[4,6,7,3,8,1,2,5]=>[7,2,6,1,4,3,8,5]=>0010111
[7,3,8,1,5,2,6,4]=>[6,5,8,7,3,1,2,4]=>[6,1,8,4,7,2,5,3]=>0001111
[6,2,8,3,7,1,5,4]=>[5,7,8,6,2,3,1,4]=>[7,1,5,2,8,4,6,3]=>0001111
[5,1,8,3,7,2,6,4]=>[6,7,8,5,1,3,2,4]=>[7,2,8,4,5,1,6,3]=>0001111
[4,1,8,3,7,2,6,5]=>[6,7,4,1,8,3,2,5]=>[6,3,4,1,7,2,8,5]=>0010111
[3,1,7,4,8,2,6,5]=>[6,3,1,8,7,4,2,5]=>[8,5,7,2,3,1,6,4]=>0100111
[7,3,8,2,6,1,5,4]=>[5,6,8,7,3,2,1,4]=>[6,2,8,4,7,1,5,3]=>0001111
[8,2,6,3,7,1,5,4]=>[5,7,6,8,2,3,1,4]=>[6,3,7,1,5,2,8,4]=>0001111
[4,5,2,6,3,8,1,7]=>[8,6,5,4,2,3,1,7]=>[4,6,3,5,2,8,7,1]=>0001111
[3,5,6,1,4,8,2,7]=>[8,6,3,1,5,4,2,7]=>[3,5,8,7,2,6,4,1]=>0010111
[4,1,5,6,3,8,2,7]=>[8,6,4,1,5,3,2,7]=>[5,8,7,2,6,3,4,1]=>0010111
[6,7,4,1,8,3,2,5]=>[3,8,4,7,1,6,2,5]=>[6,8,5,1,3,4,7,2]=>0001011
[5,3,7,8,1,4,2,6]=>[4,8,5,3,1,2,7,6]=>[5,1,4,3,7,8,6,2]=>0011101
[4,5,1,7,8,3,6,2]=>[6,8,5,4,1,3,7,2]=>[4,6,3,5,1,7,8,2]=>0001101
[5,6,1,7,3,8,4,2]=>[4,8,7,6,5,1,3,2]=>[5,6,1,4,7,3,8,2]=>0000111
[5,1,6,7,3,8,4,2]=>[4,8,7,5,1,6,3,2]=>[5,1,4,6,7,3,8,2]=>0001011
[6,4,7,1,8,3,5,2]=>[5,8,7,6,4,1,3,2]=>[6,1,5,4,7,3,8,2]=>0001111
[6,7,8,3,1,4,5,2]=>[5,3,8,1,4,6,7,2]=>[5,4,1,6,7,8,2,3]=>0011001
[6,7,2,8,4,5,1,3]=>[5,8,2,7,1,6,4,3]=>[5,1,6,7,4,8,3,2]=>0101011
[6,1,7,4,8,3,2,5]=>[3,8,7,6,1,4,2,5]=>[6,4,8,5,1,3,7,2]=>0001111
[3,6,7,2,8,4,5,1]=>[5,8,3,7,2,6,4,1]=>[3,6,7,4,8,1,5,2]=>0001011
[3,6,7,2,8,4,1,5]=>[4,8,3,7,2,6,1,5]=>[3,6,7,1,4,8,5,2]=>0001011
[3,6,7,2,1,8,4,5]=>[2,8,3,7,1,6,4,5]=>[3,6,7,4,8,5,1,2]=>0001011
[3,7,8,1,4,6,2,5]=>[6,8,3,1,4,2,7,5]=>[3,7,8,5,4,1,6,2]=>0011101
[3,6,7,8,5,2,1,4]=>[2,5,3,1,8,6,7,4]=>[3,6,7,8,4,1,2,5]=>0010001
[3,6,7,8,5,2,4,1]=>[4,5,3,2,8,6,7,1]=>[3,6,7,8,1,4,2,5]=>0010001
[6,4,7,8,2,5,3,1]=>[3,5,8,6,4,2,7,1]=>[6,2,5,4,7,8,1,3]=>0001101
[6,4,7,8,2,1,5,3]=>[2,5,8,6,4,1,7,3]=>[6,1,2,5,4,7,8,3]=>0001101
[6,7,2,8,5,1,3,4]=>[5,8,2,1,7,6,3,4]=>[6,8,4,1,5,7,3,2]=>0110011
[6,4,1,7,8,2,5,3]=>[5,8,4,6,1,2,7,3]=>[5,1,7,8,3,4,6,2]=>0001101
[5,1,6,2,7,8,4,3]=>[4,8,6,5,1,2,7,3]=>[5,1,4,7,8,3,6,2]=>0001101
[5,6,2,7,1,8,4,3]=>[4,8,7,6,5,2,1,3]=>[5,8,3,7,1,4,6,2]=>0000111
[5,6,2,7,8,4,3,1]=>[3,4,8,6,5,2,7,1]=>[5,6,2,4,7,8,1,3]=>0000101
[5,1,6,7,2,8,4,3]=>[4,8,7,5,1,6,2,3]=>[5,1,4,6,8,3,7,2]=>0001011
[5,6,7,1,8,4,3,2]=>[3,4,8,7,5,6,1,2]=>[5,6,8,2,4,7,1,3]=>0000011
[8,3,2,5,1,6,4,7]=>[6,3,5,8,2,1,4,7]=>[5,2,3,6,1,8,7,4]=>0001111
[7,5,3,8,2,4,6,1]=>[6,8,5,3,7,2,4,1]=>[7,4,3,5,8,1,6,2]=>0010111
[8,2,4,5,6,3,1,7]=>[3,6,8,2,4,5,1,7]=>[6,5,4,2,8,7,1,3]=>0011111
[8,2,4,5,6,1,3,7]=>[6,8,2,1,4,5,3,7]=>[6,5,4,1,8,7,3,2]=>0111111
[8,5,3,6,4,1,2,7]=>[4,1,6,5,8,3,2,7]=>[6,3,8,7,2,1,4,5]=>1000111
[8,4,1,5,6,3,2,7]=>[3,6,4,8,1,5,2,7]=>[8,7,2,6,5,1,3,4]=>0001111
[4,5,3,7,2,1,8,6]=>[2,8,5,4,3,7,1,6]=>[4,5,3,8,6,7,1,2]=>0001011
[4,3,6,7,2,8,5,1]=>[5,8,4,3,7,6,2,1]=>[4,3,6,8,1,5,7,2]=>0010011
[4,3,6,7,2,8,1,5]=>[8,7,4,3,2,6,1,5]=>[4,3,6,8,5,2,7,1]=>0011011
[1,4,3,6,7,2,8,5]=>[1,8,4,3,7,6,2,5]=>[1,4,3,6,8,5,7,2]=>0010011
[4,5,3,7,1,8,2,6]=>[8,7,5,4,3,1,2,6]=>[4,5,3,7,2,8,6,1]=>0001111
[5,3,4,7,1,2,8,6]=>[8,1,5,3,4,7,2,6]=>[5,4,3,8,6,7,2,1]=>1011011
[3,5,6,7,8,4,1,2]=>[4,1,3,8,5,6,7,2]=>[3,5,6,7,8,2,1,4]=>1000001
[3,1,5,6,7,8,4,2]=>[4,3,1,8,5,6,7,2]=>[5,6,7,8,2,3,1,4]=>0100001
[6,2,4,1,7,8,5,3]=>[5,4,8,2,6,1,7,3]=>[4,2,6,1,5,7,8,3]=>0010101
[2,6,7,1,4,8,3,5]=>[8,2,7,1,4,6,3,5]=>[2,6,7,3,8,5,4,1]=>0011011
[1,5,3,6,7,8,2,4]=>[1,8,5,3,2,6,7,4]=>[1,6,7,8,4,3,5,2]=>0011001
[4,2,6,7,8,3,5,1]=>[5,8,4,2,3,6,7,1]=>[6,7,8,1,5,3,4,2]=>0011001
[7,8,4,2,1,3,6,5]=>[2,4,1,6,8,3,7,5]=>[6,3,1,2,4,7,8,5]=>0100101
[6,4,7,8,5,2,3,1]=>[3,5,2,8,6,4,7,1]=>[7,8,1,3,2,5,6,4]=>0100101
[2,6,4,7,8,1,5,3]=>[5,2,8,6,4,1,7,3]=>[2,6,1,5,4,7,8,3]=>0001101
[7,4,1,5,8,6,2,3]=>[6,4,1,8,2,7,5,3]=>[8,3,1,6,7,5,2,4]=>0101011
[4,6,1,7,8,5,2,3]=>[5,8,1,4,6,2,7,3]=>[4,7,8,3,1,5,6,2]=>0100101
[5,1,2,6,7,8,4,3]=>[4,1,8,5,2,6,7,3]=>[5,2,1,4,6,7,8,3]=>1001001
[1,6,4,7,8,5,2,3]=>[1,5,2,8,6,4,7,3]=>[1,7,8,3,2,5,6,4]=>0100101
[2,6,7,1,3,8,5,4]=>[5,2,1,8,7,6,3,4]=>[2,6,7,3,1,5,8,4]=>0100011
[3,1,2,6,5,8,7,4]=>[3,1,2,7,6,5,8,4]=>[3,2,1,6,5,8,4,7]=>1100101
[4,5,1,2,3,8,7,6]=>[5,1,2,4,3,7,8,6]=>[4,5,3,2,1,8,6,7]=>1101001
[4,6,1,2,3,8,7,5]=>[7,1,2,4,6,3,8,5]=>[4,8,5,6,3,2,1,7]=>1100101
[6,1,5,2,4,8,7,3]=>[7,5,6,1,2,4,8,3]=>[5,2,8,3,6,4,1,7]=>0011101
[6,5,1,2,3,8,7,4]=>[7,1,2,5,6,3,8,4]=>[8,4,5,6,3,2,1,7]=>1100101
[6,4,1,2,3,8,7,5]=>[4,1,2,7,6,3,8,5]=>[8,5,6,3,2,1,4,7]=>1100101
[5,4,1,2,3,8,7,6]=>[4,1,2,5,3,7,8,6]=>[5,3,2,1,4,8,6,7]=>1101001
[5,4,1,2,7,3,6,8]=>[7,1,4,5,2,3,6,8]=>[7,6,3,4,5,2,1,8]=>1001110
[6,4,1,7,2,3,5,8]=>[7,4,1,6,2,3,5,8]=>[7,5,2,4,6,3,1,8]=>0101110
[6,4,1,8,2,3,5,7]=>[8,4,1,6,2,3,5,7]=>[8,7,5,2,4,6,3,1]=>0101111
[7,4,1,2,8,3,6,5]=>[6,1,4,8,7,2,3,5]=>[6,2,1,8,5,7,3,4]=>1000111
[8,4,1,2,7,3,6,5]=>[6,1,4,7,8,2,3,5]=>[6,2,1,7,3,4,8,5]=>1000111
[8,4,1,7,2,3,5,6]=>[7,4,1,8,2,3,5,6]=>[8,6,3,1,7,5,2,4]=>0101111
[7,4,1,6,2,3,5,8]=>[6,4,1,7,2,3,5,8]=>[6,3,1,7,5,2,4,8]=>0101110
[8,6,1,7,2,3,5,4]=>[5,7,1,6,2,8,3,4]=>[7,3,1,5,2,8,4,6]=>0101011
[8,1,6,7,2,4,5,3]=>[5,7,8,1,2,4,6,3]=>[7,6,4,1,5,2,8,3]=>0011111
[1,7,6,8,3,4,5,2]=>[1,5,8,3,4,7,6,2]=>[1,7,6,8,2,5,4,3]=>0011011
[3,1,8,7,2,4,5,6]=>[7,3,1,2,4,5,8,6]=>[8,6,5,4,2,3,1,7]=>0111101
[4,7,1,6,2,3,5,8]=>[6,7,1,4,2,3,5,8]=>[4,6,3,1,7,5,2,8]=>0101110
[4,8,1,6,2,3,5,7]=>[6,8,1,4,2,3,5,7]=>[4,6,3,1,8,7,5,2]=>0101111
[5,8,1,2,7,3,6,4]=>[6,1,7,8,5,2,3,4]=>[5,6,2,1,7,3,8,4]=>1000111
[5,1,8,2,7,4,6,3]=>[6,7,8,5,1,2,4,3]=>[7,4,5,1,6,2,8,3]=>0001111
[6,1,8,7,2,4,5,3]=>[5,7,6,1,2,4,8,3]=>[8,3,6,4,1,5,2,7]=>0011101
[6,8,1,7,2,3,5,4]=>[5,7,1,8,2,6,3,4]=>[6,7,3,1,5,2,8,4]=>0101011
[6,8,7,1,2,3,4,5]=>[7,1,2,3,4,6,8,5]=>[6,8,5,4,3,2,1,7]=>1111001
[5,8,6,1,2,3,4,7]=>[6,1,2,3,5,8,4,7]=>[5,8,7,4,3,2,1,6]=>1110011
[7,8,1,6,2,3,5,4]=>[5,6,1,8,2,3,7,4]=>[6,3,1,5,2,7,8,4]=>0101101
[7,1,8,6,2,4,5,3]=>[5,6,8,1,2,7,4,3]=>[7,4,1,5,2,6,8,3]=>0011011
[1,7,8,6,3,4,5,2]=>[1,5,6,3,4,8,7,2]=>[1,7,8,2,5,4,3,6]=>0011001
[8,1,7,6,2,4,5,3]=>[5,6,7,1,2,8,4,3]=>[8,3,7,4,1,5,2,6]=>0011011
[8,5,3,7,2,1,4,6]=>[2,7,5,3,8,1,4,6]=>[8,6,1,2,7,4,3,5]=>0010111
[6,8,1,4,5,7,3,2]=>[3,7,8,1,4,6,5,2]=>[6,8,2,7,5,4,1,3]=>0011011
[8,7,2,4,5,1,3,6]=>[5,7,2,1,4,3,8,6]=>[5,4,1,8,6,3,2,7]=>0111101
[2,6,1,4,5,3,8,7]=>[5,2,6,1,4,3,8,7]=>[2,5,4,1,6,3,8,7]=>0011101
[6,3,1,4,5,2,8,7]=>[5,3,6,1,4,2,8,7]=>[5,4,1,6,2,3,8,7]=>0011101
[3,1,6,4,5,2,8,7]=>[5,3,1,6,4,2,8,7]=>[6,2,3,1,5,4,8,7]=>0101101
[8,3,7,4,5,1,2,6]=>[5,1,7,8,3,4,2,6]=>[7,2,1,5,3,8,6,4]=>1001111
[5,8,7,4,2,6,3,1]=>[3,6,4,7,5,2,8,1]=>[5,6,2,8,1,3,4,7]=>0000101
[3,7,8,4,5,1,2,6]=>[5,1,3,8,4,2,7,6]=>[3,7,8,6,2,1,5,4]=>1001101
[5,6,3,8,1,7,2,4]=>[7,8,6,3,5,1,2,4]=>[5,8,4,3,6,1,7,2]=>0010111
[7,6,1,4,5,8,3,2]=>[3,8,6,1,4,7,5,2]=>[7,5,4,1,3,6,8,2]=>0011011
[3,7,6,4,5,8,2,1]=>[2,8,3,6,4,7,5,1]=>[3,7,5,4,6,8,1,2]=>0001011
[6,5,3,8,4,1,7,2]=>[7,4,8,5,6,3,1,2]=>[7,1,8,2,4,5,6,3]=>0000111
[2,1,4,8,3,6,7,5]=>[2,1,7,4,8,3,6,5]=>[2,1,4,7,6,3,8,5]=>1000111
[4,8,2,3,5,6,7,1]=>[7,8,2,4,3,5,6,1]=>[4,8,1,7,6,5,3,2]=>0101111
[8,7,1,4,3,6,2,5]=>[6,4,7,1,3,2,8,5]=>[6,2,4,1,8,5,3,7]=>0011101
[5,6,3,8,4,2,7,1]=>[7,4,8,6,5,3,2,1]=>[5,8,1,7,2,4,6,3]=>0000111
[8,6,3,1,4,2,7,5]=>[4,3,7,1,6,8,2,5]=>[4,1,7,2,3,8,5,6]=>0010011
[8,6,3,5,1,2,7,4]=>[7,1,5,6,3,8,2,4]=>[5,3,7,2,1,8,4,6]=>1001011
[3,5,8,4,7,6,2,1]=>[2,6,3,7,5,8,4,1]=>[3,5,7,4,8,1,2,6]=>0000011
[2,1,8,5,3,6,7,4]=>[2,1,7,5,8,3,6,4]=>[2,1,7,6,3,8,4,5]=>1000111
[6,8,3,5,2,1,7,4]=>[2,7,5,8,3,6,1,4]=>[5,3,6,7,1,2,8,4]=>0001011
[4,8,1,2,5,6,7,3]=>[7,1,8,4,2,5,6,3]=>[4,7,6,5,2,1,8,3]=>1001111
[8,4,2,1,5,6,7,3]=>[2,7,4,8,1,5,6,3]=>[7,6,5,1,2,8,3,4]=>0001111
[2,1,5,3,8,6,7,4]=>[2,1,7,5,3,8,6,4]=>[2,1,8,4,5,3,7,6]=>1001011
[6,5,3,7,2,8,4,1]=>[4,8,7,5,6,3,2,1]=>[8,1,4,5,6,3,7,2]=>0000111
[6,7,2,4,5,8,3,1]=>[3,8,7,2,4,6,5,1]=>[6,8,1,3,7,5,4,2]=>0011011
[5,6,3,7,1,8,4,2]=>[4,8,7,6,5,3,1,2]=>[5,7,1,4,6,3,8,2]=>0000111
[3,8,7,4,5,2,1,6]=>[2,5,3,7,4,1,8,6]=>[3,8,6,1,2,5,4,7]=>0001101
[4,6,3,5,8,2,7,1]=>[7,8,6,4,3,5,2,1]=>[4,6,5,3,8,1,7,2]=>0001111
[3,7,8,4,1,6,2,5]=>[6,4,3,8,1,2,7,5]=>[3,7,8,5,1,6,2,4]=>0001101
[5,4,2,3,7,6,1,8]=>[6,4,2,5,3,7,1,8]=>[5,3,2,4,7,1,6,8]=>0101010
[3,2,7,6,4,5,1,8]=>[5,3,2,6,4,7,1,8]=>[3,2,7,1,5,4,6,8]=>0101010
[4,7,2,6,3,5,1,8]=>[5,6,7,4,2,3,1,8]=>[4,7,1,5,2,6,3,8]=>0001110
[5,7,6,2,3,4,1,8]=>[4,6,2,3,5,7,1,8]=>[5,7,1,4,3,2,6,8]=>0110010
[1,7,5,2,8,3,4,6]=>[1,8,5,2,7,3,4,6]=>[1,8,6,3,5,7,4,2]=>0010111
[7,1,5,2,8,3,4,6]=>[8,5,7,1,2,3,4,6]=>[5,2,8,6,3,7,4,1]=>0011111
[1,8,5,2,7,3,4,6]=>[1,7,5,2,8,3,4,6]=>[1,7,4,2,8,6,3,5]=>0010111
[7,1,6,8,2,3,4,5]=>[8,7,1,2,3,4,6,5]=>[7,6,4,2,8,5,3,1]=>0111111
[3,2,8,7,1,4,5,6]=>[7,3,2,1,4,5,8,6]=>[3,2,8,6,5,4,1,7]=>0111101
[1,7,6,8,2,3,4,5]=>[1,8,2,3,4,7,6,5]=>[1,7,6,8,5,4,3,2]=>0111011
[6,5,8,2,3,1,4,7]=>[3,8,2,1,6,5,4,7]=>[6,5,8,7,4,1,3,2]=>0110111
[8,4,2,1,7,3,5,6]=>[2,7,4,8,1,3,5,6]=>[7,5,1,2,8,6,3,4]=>0001111
[1,5,8,2,7,3,4,6]=>[1,7,8,2,5,3,4,6]=>[1,5,7,4,2,8,6,3]=>0010111
[8,5,1,2,7,3,4,6]=>[7,1,5,2,8,3,4,6]=>[7,4,2,1,8,6,3,5]=>1010111
[4,7,2,1,8,3,5,6]=>[2,8,7,4,1,3,5,6]=>[4,8,6,3,7,5,1,2]=>0001111
[1,6,8,7,2,3,4,5]=>[1,7,2,3,4,6,8,5]=>[1,6,8,5,4,3,2,7]=>0111001
[1,7,8,6,2,3,4,5]=>[1,6,2,3,4,8,7,5]=>[1,7,8,5,4,3,2,6]=>0111001
[7,8,1,6,2,3,4,5]=>[6,8,1,2,3,4,7,5]=>[7,8,5,3,1,6,4,2]=>0111101
[4,8,2,1,7,3,5,6]=>[2,7,8,4,1,3,5,6]=>[4,7,5,1,2,8,6,3]=>0001111
[3,2,8,1,7,4,5,6]=>[7,3,2,8,1,4,5,6]=>[3,2,7,5,1,8,6,4]=>0101111
[5,1,8,2,7,3,4,6]=>[7,8,5,1,2,3,4,6]=>[7,4,1,8,6,3,5,2]=>0011111
[6,1,8,7,2,3,4,5]=>[7,6,1,2,3,4,8,5]=>[6,4,2,8,5,3,1,7]=>0111101
[6,5,2,8,3,1,4,7]=>[3,8,5,2,6,1,4,7]=>[6,1,3,5,8,7,4,2]=>0010111
[6,5,2,7,3,1,8,4]=>[3,8,7,5,6,2,1,4]=>[7,1,3,8,4,5,6,2]=>0000111
[4,5,2,6,3,1,7,8]=>[3,6,5,4,2,1,7,8]=>[4,6,1,3,5,2,7,8]=>0001100
[5,1,6,7,4,3,8,2]=>[8,4,7,5,1,6,3,2]=>[6,7,3,8,2,4,5,1]=>0001011
[6,5,2,8,3,7,4,1]=>[4,7,8,5,6,2,3,1]=>[8,1,4,5,6,2,7,3]=>0000111
[4,1,2,3,8,6,5,7]=>[4,1,2,3,6,8,5,7]=>[4,3,2,1,8,7,5,6]=>1110011
[4,1,2,3,8,6,7,5]=>[4,1,2,3,7,8,6,5]=>[4,3,2,1,8,5,7,6]=>1110011
[4,1,2,3,8,5,7,6]=>[4,1,2,3,7,8,5,6]=>[4,3,2,1,7,5,8,6]=>1110011
[6,5,8,2,4,3,7,1]=>[7,4,8,2,6,5,3,1]=>[4,2,6,5,8,1,7,3]=>0010111
[6,5,2,7,3,4,1,8]=>[4,7,5,2,6,3,1,8]=>[6,3,5,7,1,4,2,8]=>0010110
[5,7,8,6,3,4,2,1]=>[2,4,6,3,5,8,7,1]=>[5,7,8,1,2,4,3,6]=>0010001
[3,1,4,8,6,2,7,5]=>[7,3,1,4,6,8,2,5]=>[4,7,2,3,1,8,5,6]=>0100011
[4,1,6,7,8,3,2,5]=>[3,8,4,1,2,6,7,5]=>[4,1,3,6,7,8,5,2]=>0011001
[4,1,6,5,7,3,2,8]=>[3,7,4,1,6,5,2,8]=>[4,1,3,6,5,7,2,8]=>0010110
[4,5,2,6,3,7,1,8]=>[7,6,5,4,2,3,1,8]=>[4,6,3,5,2,7,1,8]=>0001110
[3,5,6,2,4,8,1,7]=>[8,6,3,2,5,4,1,7]=>[3,5,6,4,2,8,7,1]=>0010111
[3,7,5,6,8,4,1,2]=>[4,1,3,8,7,5,6,2]=>[3,7,6,5,8,2,1,4]=>1000111
[6,1,2,5,8,4,7,3]=>[7,1,8,6,2,5,4,3]=>[7,4,6,5,2,1,8,3]=>1001111
[4,1,2,3,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>[4,3,2,1,5,8,6,7]=>1110001
[4,1,6,7,8,3,5,2]=>[5,8,4,1,3,6,7,2]=>[5,3,4,1,6,7,8,2]=>0011001
[4,1,2,6,8,5,7,3]=>[7,1,4,2,8,6,5,3]=>[6,8,3,4,2,1,7,5]=>1010011
[4,1,2,5,6,8,7,3]=>[7,1,4,2,5,6,8,3]=>[5,6,8,3,4,2,1,7]=>1010001
[6,3,1,2,7,4,8,5]=>[3,1,8,7,6,2,4,5]=>[7,4,8,5,6,2,1,3]=>1000111
[4,7,1,5,2,3,8,6]=>[5,8,1,4,2,7,3,6]=>[4,8,6,7,3,1,5,2]=>0101011
[5,7,2,6,1,8,3,4]=>[8,6,7,2,5,1,3,4]=>[5,7,3,8,4,2,6,1]=>0010111
[6,8,4,3,7,1,2,5]=>[7,1,4,8,3,6,2,5]=>[6,7,2,1,8,5,3,4]=>1001011
[3,8,5,7,1,2,4,6]=>[7,1,3,2,8,5,4,6]=>[3,7,4,2,1,8,6,5]=>1010111
[7,3,8,5,6,1,2,4]=>[6,1,8,3,7,2,5,4]=>[6,2,1,7,5,8,4,3]=>1010111
[6,3,7,5,8,1,2,4]=>[8,1,7,3,6,2,5,4]=>[8,4,3,7,5,6,2,1]=>1010111
[5,4,7,3,8,1,2,6]=>[8,1,7,5,4,3,2,6]=>[5,4,8,6,3,7,2,1]=>1001111
[8,4,6,3,7,1,2,5]=>[7,1,6,8,4,3,2,5]=>[6,3,7,2,1,8,5,4]=>1001111
[8,4,1,6,7,2,3,5]=>[7,4,1,8,2,3,6,5]=>[7,6,3,1,8,5,2,4]=>0101111
[5,4,1,7,8,2,3,6]=>[8,4,1,5,2,3,7,6]=>[5,2,4,7,8,6,3,1]=>0101101
[6,5,1,2,7,8,3,4]=>[8,1,5,2,6,3,7,4]=>[6,3,5,7,8,4,2,1]=>1010101
[4,7,1,5,8,6,2,3]=>[6,8,1,4,2,7,5,3]=>[4,8,3,1,6,7,5,2]=>0101011
[3,6,8,2,7,1,4,5]=>[7,8,3,2,1,6,4,5]=>[3,6,8,5,1,7,4,2]=>0011011
[8,3,7,6,1,2,4,5]=>[6,1,7,3,2,8,4,5]=>[7,4,3,8,5,2,1,6]=>1011011
[3,5,8,7,1,2,4,6]=>[7,1,3,2,5,4,8,6]=>[3,5,8,6,4,2,1,7]=>1010101
[6,8,4,7,5,1,2,3]=>[5,1,2,7,8,6,4,3]=>[6,7,4,8,3,2,1,5]=>1100011
[2,8,7,6,1,3,4,5]=>[6,2,1,3,4,7,8,5]=>[2,8,5,4,3,1,6,7]=>0111001
[3,8,7,6,1,2,4,5]=>[6,1,3,2,4,7,8,5]=>[3,8,5,4,2,1,6,7]=>1011001
[5,6,3,1,4,2,8,7]=>[4,3,6,1,5,2,8,7]=>[4,1,5,6,2,3,8,7]=>0010101
[2,1,7,8,5,3,6,4]=>[2,1,6,5,8,3,7,4]=>[2,1,6,3,7,8,4,5]=>1000101
[5,7,3,8,1,2,6,4]=>[6,1,8,7,5,3,2,4]=>[5,8,4,7,2,1,6,3]=>1000111
[8,6,3,1,2,5,7,4]=>[3,1,7,6,2,8,5,4]=>[7,5,2,1,3,8,4,6]=>1001011
[8,7,1,4,2,6,5,3]=>[5,4,6,1,7,2,8,3]=>[8,3,6,2,4,1,5,7]=>0010101
[8,5,3,6,2,7,1,4]=>[7,6,5,3,8,2,1,4]=>[6,2,7,1,8,4,3,5]=>0010111
[7,2,6,3,4,5,8,1]=>[8,6,7,2,3,4,5,1]=>[6,4,2,7,5,3,8,1]=>0011111
[6,7,3,5,2,4,8,1]=>[8,5,7,3,2,6,4,1]=>[5,2,6,7,4,3,8,1]=>0011011
[6,5,3,1,2,8,4,7]=>[3,1,8,5,6,2,4,7]=>[8,7,4,5,6,2,1,3]=>1000111
[8,5,2,1,7,3,4,6]=>[2,7,5,1,8,3,4,6]=>[7,4,1,2,8,6,3,5]=>0010111
[1,6,3,2,8,4,5,7]=>[1,3,8,6,2,4,5,7]=>[1,6,4,8,7,5,2,3]=>0001111
[5,7,3,1,2,8,4,6]=>[3,1,8,7,5,2,4,6]=>[5,7,4,8,6,2,1,3]=>1000111
[7,8,5,2,3,6,1,4]=>[6,5,2,3,8,1,7,4]=>[6,1,7,8,4,3,2,5]=>0110101
[2,8,1,7,3,4,5,6]=>[7,2,8,1,3,4,5,6]=>[2,8,6,4,1,7,5,3]=>0011111
[3,8,6,1,7,2,4,5]=>[7,6,3,1,2,8,4,5]=>[3,7,4,1,8,5,2,6]=>0011011
[4,1,7,5,8,2,3,6]=>[8,4,1,2,7,5,3,6]=>[4,2,8,6,5,7,3,1]=>0110111
[8,1,2,7,3,4,5,6]=>[7,1,8,2,3,4,5,6]=>[8,6,4,2,1,7,5,3]=>1011111
[6,3,7,1,2,8,4,5]=>[8,1,7,6,3,2,4,5]=>[8,5,3,7,4,6,2,1]=>1001111
[8,2,6,1,7,3,4,5]=>[7,6,8,2,1,3,4,5]=>[8,5,1,7,4,2,6,3]=>0011111
[7,6,8,2,3,5,1,4]=>[5,8,2,3,1,7,6,4]=>[5,1,7,6,8,4,3,2]=>0111011
[3,7,8,2,4,6,1,5]=>[6,8,3,2,4,1,7,5]=>[3,6,1,7,8,5,4,2]=>0011101
[5,4,7,8,2,6,1,3]=>[6,8,2,5,4,1,7,3]=>[5,4,6,1,7,8,3,2]=>0101101
[3,7,8,1,6,2,4,5]=>[6,8,3,1,2,4,7,5]=>[3,6,4,1,7,8,5,2]=>0011101
[6,8,3,7,5,1,2,4]=>[5,1,7,3,8,6,2,4]=>[6,8,4,3,7,2,1,5]=>1010011
[7,8,6,2,5,1,3,4]=>[5,6,2,1,3,8,7,4]=>[7,8,4,1,5,3,2,6]=>0111001
[8,1,5,3,6,2,4,7]=>[6,5,8,1,3,2,4,7]=>[8,7,4,1,6,2,5,3]=>0011111
[8,1,4,3,2,7,5,6]=>[3,4,7,1,8,2,5,6]=>[8,6,2,4,1,3,7,5]=>0010111
[8,1,4,3,2,5,7,6]=>[3,4,7,1,2,8,5,6]=>[7,5,2,4,1,3,8,6]=>0011011
[7,5,1,3,6,2,8,4]=>[8,6,1,5,7,3,2,4]=>[8,4,5,7,2,6,3,1]=>0100111
[5,4,3,2,8,7,1,6]=>[7,3,4,5,2,1,8,6]=>[5,2,3,4,8,6,1,7]=>0001101
[6,4,3,1,2,7,8,5]=>[3,1,4,8,6,2,7,5]=>[7,8,5,6,2,1,3,4]=>1000101
[6,5,3,8,7,2,4,1]=>[4,7,5,3,6,2,8,1]=>[8,1,4,3,5,6,2,7]=>0010101
[7,5,1,3,8,2,4,6]=>[8,5,1,3,7,2,4,6]=>[8,6,2,5,7,4,3,1]=>0110111
[6,5,3,7,8,2,4,1]=>[4,8,5,3,6,2,7,1]=>[7,8,1,4,3,5,6,2]=>0010101
[6,4,3,7,2,1,5,8]=>[2,7,4,6,3,1,5,8]=>[7,5,3,4,6,1,2,8]=>0001110
[6,5,4,8,1,7,2,3]=>[7,8,1,5,6,4,2,3]=>[6,4,5,8,3,1,7,2]=>0100111
[4,6,3,8,5,1,2,7]=>[5,1,8,4,6,3,2,7]=>[4,8,7,2,1,5,6,3]=>1000111
[5,6,8,3,4,1,2,7]=>[4,1,8,3,5,6,2,7]=>[5,6,8,7,2,1,4,3]=>1010011
[5,7,8,4,1,3,6,2]=>[6,4,1,8,5,3,7,2]=>[5,6,3,1,7,8,2,4]=>0100101
[5,6,8,4,2,1,7,3]=>[2,7,4,8,5,6,1,3]=>[5,6,7,1,2,8,3,4]=>0000011
[3,2,6,8,5,1,4,7]=>[5,3,2,1,8,6,4,7]=>[3,2,6,8,7,4,1,5]=>0110011
[5,6,8,4,2,1,3,7]=>[2,4,1,8,5,6,3,7]=>[5,6,8,7,3,1,2,4]=>0100011
[5,7,8,4,1,2,3,6]=>[4,1,2,8,5,3,7,6]=>[5,7,8,6,3,2,1,4]=>1100101
[6,7,8,1,5,2,3,4]=>[5,8,1,2,3,6,7,4]=>[5,3,1,6,7,8,4,2]=>0111001
[6,7,8,1,5,3,2,4]=>[3,5,8,1,2,6,7,4]=>[5,2,6,7,8,4,1,3]=>0011001
[6,7,8,1,3,5,2,4]=>[5,8,1,3,2,6,7,4]=>[6,7,8,4,3,1,5,2]=>0111001
[5,7,8,2,1,6,3,4]=>[2,6,8,1,5,3,7,4]=>[5,7,8,4,1,2,6,3]=>0010101
[4,7,2,8,1,6,3,5]=>[6,8,7,4,2,1,3,5]=>[4,6,1,7,3,8,5,2]=>0001111
[5,7,8,2,1,6,4,3]=>[2,4,6,8,5,1,7,3]=>[5,7,8,3,6,1,2,4]=>0000101
[5,6,8,3,2,1,7,4]=>[2,3,7,8,5,6,1,4]=>[5,6,7,1,2,3,8,4]=>0000011
[4,7,3,8,1,6,2,5]=>[6,8,7,4,3,1,2,5]=>[4,6,1,8,5,3,7,2]=>0001111
[5,7,8,3,1,2,4,6]=>[3,1,8,2,5,4,7,6]=>[5,7,8,6,4,2,1,3]=>1010101
[5,6,8,3,2,1,4,7]=>[2,3,8,1,5,6,4,7]=>[5,6,8,7,4,1,2,3]=>0010011
[3,2,7,8,1,5,4,6]=>[5,3,2,8,1,4,7,6]=>[3,2,5,1,7,8,6,4]=>0101101
[6,7,8,1,3,4,2,5]=>[4,8,1,3,2,6,7,5]=>[4,3,1,6,7,8,5,2]=>0111001
[6,7,8,1,2,5,3,4]=>[5,1,8,2,3,6,7,4]=>[6,7,8,4,2,1,5,3]=>1011001
[6,7,8,1,2,4,5,3]=>[5,1,8,2,4,6,7,3]=>[5,4,2,1,6,7,8,3]=>1011001
[5,7,8,2,1,3,6,4]=>[2,6,1,8,5,3,7,4]=>[5,6,3,1,2,7,8,4]=>0100101
[3,2,7,8,1,4,6,5]=>[6,3,2,1,8,4,7,5]=>[3,2,6,4,1,7,8,5]=>0110101
[6,7,8,1,2,4,3,5]=>[4,1,8,2,3,6,7,5]=>[4,2,1,6,7,8,5,3]=>1011001
[6,7,8,1,2,3,5,4]=>[5,1,2,8,3,6,7,4]=>[5,3,2,1,6,7,8,4]=>1101001
[8,3,5,1,7,4,6,2]=>[6,7,5,8,3,1,4,2]=>[5,3,6,1,8,2,7,4]=>0001111
[4,8,3,1,7,5,6,2]=>[6,3,7,4,8,1,5,2]=>[4,6,1,8,2,3,7,5]=>0000111
[6,8,4,3,1,7,5,2]=>[5,3,4,7,8,6,1,2]=>[6,8,2,3,4,7,1,5]=>0000011
[6,7,5,1,8,4,3,2]=>[3,4,8,5,7,6,1,2]=>[6,8,2,4,5,7,1,3]=>0000011
[6,8,4,1,7,5,3,2]=>[3,5,4,7,8,6,1,2]=>[6,7,1,3,4,8,2,5]=>0000011
[6,7,5,3,1,8,4,2]=>[4,3,8,5,7,6,1,2]=>[6,7,1,4,5,8,2,3]=>0000011
[8,4,2,1,6,7,5,3]=>[2,5,4,7,8,1,6,3]=>[8,3,4,7,6,1,2,5]=>0000111
[1,5,3,2,7,6,8,4]=>[1,3,8,5,2,7,6,4]=>[1,7,6,8,4,5,2,3]=>0001011
[4,7,1,6,5,8,2,3]=>[8,6,1,4,7,2,5,3]=>[4,6,2,7,5,8,3,1]=>0100111
[4,6,1,2,7,5,8,3]=>[8,1,7,4,6,2,5,3]=>[4,8,3,7,5,6,2,1]=>1000111
[8,4,1,2,6,7,5,3]=>[5,1,4,7,8,2,6,3]=>[8,3,4,7,6,2,1,5]=>1000111
[5,3,1,2,7,6,8,4]=>[3,1,8,5,2,7,6,4]=>[7,6,8,4,5,2,1,3]=>1001011
[4,3,1,2,7,6,8,5]=>[3,1,4,2,8,7,6,5]=>[4,2,1,3,7,6,8,5]=>1010011
[3,5,1,2,7,6,8,4]=>[8,1,3,5,2,7,6,4]=>[3,7,6,8,4,5,2,1]=>1001011
[3,5,2,1,7,6,8,4]=>[2,8,3,5,1,7,6,4]=>[3,7,6,8,4,5,1,2]=>0001011
[7,6,2,1,5,8,3,4]=>[2,8,6,1,3,7,5,4]=>[7,5,3,6,8,4,1,2]=>0011011
[8,2,6,4,7,1,5,3]=>[5,7,6,8,2,4,1,3]=>[7,1,5,2,8,3,6,4]=>0001111
[1,5,2,3,7,6,8,4]=>[1,8,2,5,3,7,6,4]=>[1,7,6,8,4,5,3,2]=>0101011
[8,4,2,6,7,5,1,3]=>[5,4,2,7,8,1,6,3]=>[8,3,2,4,7,6,1,5]=>0100111
[6,1,4,2,7,5,8,3]=>[8,4,7,1,6,2,5,3]=>[8,3,7,5,6,2,4,1]=>0010111
[1,4,2,3,7,6,8,5]=>[1,4,2,3,8,7,6,5]=>[1,4,3,2,7,6,8,5]=>0110011
[2,4,1,3,7,6,8,5]=>[4,2,1,3,8,7,6,5]=>[2,4,3,1,7,6,8,5]=>0110011
[6,8,2,3,5,7,1,4]=>[7,8,2,3,1,6,5,4]=>[6,7,5,1,8,4,3,2]=>0111011
[8,3,5,7,6,1,2,4]=>[6,1,7,3,2,8,5,4]=>[8,4,3,7,5,2,1,6]=>1011011
[5,1,2,3,7,6,8,4]=>[8,1,2,5,3,7,6,4]=>[7,6,8,4,5,3,2,1]=>1101011
[6,8,7,1,5,3,2,4]=>[3,5,7,1,2,6,8,4]=>[5,2,6,8,4,1,3,7]=>0011001
[8,5,7,1,2,6,3,4]=>[6,1,7,2,8,5,3,4]=>[7,3,8,4,2,1,6,5]=>1010111
[6,8,2,7,1,3,5,4]=>[5,7,2,8,1,6,3,4]=>[5,1,6,7,3,2,8,4]=>0101011
[6,8,2,1,7,3,5,4]=>[2,5,7,8,1,6,3,4]=>[5,1,2,6,7,3,8,4]=>0001011
[8,5,7,2,1,6,3,4]=>[2,6,7,1,8,5,3,4]=>[7,3,8,4,1,2,6,5]=>0010111
[8,5,7,2,3,1,6,4]=>[3,6,2,7,8,5,1,4]=>[8,4,7,1,3,2,6,5]=>0100111
[8,5,7,1,3,2,6,4]=>[3,6,1,7,8,5,2,4]=>[3,1,8,4,7,2,6,5]=>0100111
[5,8,4,7,1,2,6,3]=>[6,1,7,8,5,4,2,3]=>[5,8,3,7,2,1,6,4]=>1000111
[8,2,5,6,7,4,1,3]=>[4,7,2,8,1,5,6,3]=>[8,3,2,7,6,5,1,4]=>0101111
[4,6,2,8,1,7,5,3]=>[5,7,8,4,6,2,1,3]=>[4,7,1,5,6,2,8,3]=>0000111
[1,8,7,4,5,3,6,2]=>[1,6,5,7,4,3,8,2]=>[1,8,2,6,3,5,4,7]=>0001101
[8,7,6,3,1,4,2,5]=>[4,3,6,1,2,7,8,5]=>[4,1,8,5,2,3,6,7]=>0011001
[1,8,7,4,3,5,6,2]=>[1,6,4,7,3,5,8,2]=>[1,8,2,6,5,3,4,7]=>0001101
[8,5,4,2,1,7,3,6]=>[2,7,4,5,8,1,3,6]=>[8,6,1,2,7,3,4,5]=>0000111
[6,3,2,5,1,4,8,7]=>[5,3,6,2,1,4,8,7]=>[5,1,6,4,2,3,8,7]=>0011101
[8,7,4,1,6,3,2,5]=>[3,6,4,7,1,2,8,5]=>[6,2,8,5,1,3,4,7]=>0001101
[8,7,4,1,6,3,5,2]=>[5,6,4,7,1,3,8,2]=>[5,1,8,2,6,3,4,7]=>0001101
[8,7,4,1,6,5,3,2]=>[3,5,4,6,7,1,8,2]=>[6,1,3,4,8,2,5,7]=>0000101
[8,5,4,3,1,7,6,2]=>[6,3,4,5,7,8,1,2]=>[8,2,3,4,5,7,1,6]=>0000011
[8,3,2,5,1,7,6,4]=>[6,3,5,7,2,8,1,4]=>[5,2,3,8,4,7,1,6]=>0001011
[8,5,4,3,1,7,2,6]=>[7,3,4,5,8,1,2,6]=>[8,6,1,7,2,3,4,5]=>0000111
[8,5,4,1,3,7,2,6]=>[7,4,1,5,8,3,2,6]=>[8,6,3,1,7,2,4,5]=>0100111
[8,3,2,7,6,4,5,1]=>[5,3,6,7,2,8,4,1]=>[7,4,8,1,5,2,3,6]=>0001011
[8,7,4,2,6,5,3,1]=>[3,5,4,6,7,2,8,1]=>[8,1,3,4,6,2,5,7]=>0000101
[8,7,4,2,6,3,5,1]=>[5,6,4,7,2,3,8,1]=>[8,1,5,2,6,3,4,7]=>0001101
[8,3,1,7,6,4,5,2]=>[5,3,6,7,1,8,4,2]=>[5,1,7,4,8,2,3,6]=>0001011
[8,3,1,5,4,7,6,2]=>[6,3,5,7,1,8,4,2]=>[7,4,8,2,3,5,1,6]=>0001011
[8,3,1,7,6,2,5,4]=>[5,3,6,7,1,8,2,4]=>[5,1,8,4,7,2,3,6]=>0001011
[8,5,4,2,3,7,1,6]=>[7,4,2,5,8,3,1,6]=>[7,1,8,6,3,2,4,5]=>0100111
[8,3,2,7,6,5,1,4]=>[5,3,6,2,7,8,1,4]=>[7,1,5,8,4,2,3,6]=>0010011
[8,3,2,7,6,1,5,4]=>[5,3,6,7,2,8,1,4]=>[8,4,7,1,5,2,3,6]=>0001011
[8,7,6,5,1,2,4,3]=>[4,1,5,2,6,7,8,3]=>[4,2,1,8,3,5,6,7]=>1010001
[5,2,3,1,6,4,8,7]=>[3,6,2,5,1,4,8,7]=>[6,4,5,1,3,2,8,7]=>0101101
[7,4,5,2,3,1,8,6]=>[3,5,2,8,4,7,1,6]=>[8,6,7,1,3,2,5,4]=>0101011
[6,3,5,2,4,1,8,7]=>[4,5,6,3,2,1,8,7]=>[5,2,6,1,4,3,8,7]=>0011101
[6,3,4,1,5,2,8,7]=>[5,4,6,3,1,2,8,7]=>[5,1,6,2,4,3,8,7]=>0011101
[2,1,7,4,5,3,8,6]=>[2,1,5,8,4,7,3,6]=>[2,1,8,6,7,3,5,4]=>1001011
[3,1,8,6,7,4,5,2]=>[5,3,1,7,4,8,6,2]=>[8,2,3,1,5,4,7,6]=>0101011
[4,1,8,6,7,3,5,2]=>[5,7,4,1,3,8,6,2]=>[5,3,4,1,8,2,7,6]=>0011011
[8,5,7,3,4,1,6,2]=>[6,4,7,3,8,5,1,2]=>[8,2,4,3,7,1,6,5]=>0010111
[2,1,8,5,7,4,6,3]=>[2,1,6,7,8,5,4,3]=>[2,1,7,4,8,3,6,5]=>1000111
[3,1,7,4,6,2,8,5]=>[8,3,1,6,7,4,2,5]=>[6,4,8,5,7,2,3,1]=>0100111
[4,1,7,3,6,2,8,5]=>[8,6,4,1,7,3,2,5]=>[8,5,7,2,6,3,4,1]=>0010111
[7,3,6,2,5,1,8,4]=>[8,5,6,7,3,2,1,4]=>[6,2,5,3,8,4,7,1]=>0001111
[5,2,4,1,7,3,8,6]=>[8,4,5,2,1,7,3,6]=>[4,2,8,6,7,3,5,1]=>0011011
[6,2,4,1,7,3,8,5]=>[8,4,7,2,6,1,3,5]=>[4,2,7,3,8,5,6,1]=>0010111
[6,2,3,1,7,4,8,5]=>[3,8,2,7,6,1,4,5]=>[7,4,8,5,6,1,3,2]=>0100111
[5,2,3,1,7,4,8,6]=>[3,8,2,5,1,7,4,6]=>[8,6,7,4,5,1,3,2]=>0101011
[4,2,3,1,7,5,8,6]=>[3,4,2,1,8,7,5,6]=>[4,1,3,2,8,6,7,5]=>0110011
[3,1,4,2,8,6,7,5]=>[4,3,1,2,7,8,6,5]=>[4,2,3,1,8,5,7,6]=>0110011
[8,5,6,2,4,1,7,3]=>[7,4,6,2,8,5,1,3]=>[4,2,7,1,8,3,6,5]=>0010111
[5,2,4,1,8,6,7,3]=>[7,4,5,2,1,8,6,3]=>[4,2,8,3,5,1,7,6]=>0011011
[4,1,5,2,8,6,7,3]=>[7,5,4,1,2,8,6,3]=>[5,2,8,3,4,1,7,6]=>0011011
[8,4,6,2,5,1,7,3]=>[7,5,6,8,4,2,1,3]=>[7,1,8,3,6,2,5,4]=>0001111
[6,2,7,3,8,4,5,1]=>[5,8,7,6,2,3,4,1]=>[7,4,6,3,8,1,5,2]=>0001111
[2,1,8,5,6,3,7,4]=>[2,1,7,6,8,5,3,4]=>[2,1,7,3,8,4,6,5]=>1000111
[5,3,8,7,6,1,2,4]=>[6,1,5,3,2,7,8,4]=>[8,4,3,5,2,1,6,7]=>1011001
[8,3,4,6,5,1,2,7]=>[5,1,6,3,8,4,2,7]=>[6,4,3,8,7,2,1,5]=>1010111
[4,5,8,7,6,1,2,3]=>[6,1,2,4,5,7,8,3]=>[4,5,8,3,2,1,6,7]=>1100001
[3,5,8,1,7,6,4,2]=>[4,6,3,7,5,8,1,2]=>[3,5,7,1,4,8,2,6]=>0000011
[2,5,8,7,1,6,3,4]=>[6,2,7,1,5,3,8,4]=>[2,5,8,4,1,6,3,7]=>0010101
[8,2,4,6,1,5,3,7]=>[5,6,8,2,4,1,3,7]=>[6,1,5,4,2,8,7,3]=>0011111
[1,4,8,7,2,6,3,5]=>[1,6,7,4,2,3,8,5]=>[1,4,8,5,2,6,3,7]=>0001101
[1,5,8,7,2,6,3,4]=>[1,6,7,2,5,3,8,4]=>[1,5,8,4,2,6,3,7]=>0010101
[1,3,8,2,7,6,4,5]=>[1,6,3,7,2,8,4,5]=>[1,3,7,4,8,5,2,6]=>0001011
[1,8,3,2,7,5,4,6]=>[1,3,5,7,8,2,4,6]=>[1,7,4,8,6,2,3,5]=>0000111
[6,8,3,2,7,5,4,1]=>[4,3,5,7,8,6,2,1]=>[6,8,1,4,7,2,3,5]=>0000011
[6,8,2,3,7,5,4,1]=>[4,5,2,7,8,6,3,1]=>[6,8,1,4,7,3,2,5]=>0100011
[5,2,8,3,7,6,4,1]=>[4,6,7,5,2,8,3,1]=>[7,3,8,1,4,5,2,6]=>0001011
[4,8,1,7,2,5,3,6]=>[5,7,8,4,1,2,3,6]=>[4,5,1,8,6,2,7,3]=>0001111
[8,4,1,6,2,5,3,7]=>[5,6,4,8,1,2,3,7]=>[5,1,6,2,8,7,3,4]=>0001111
[3,1,2,8,7,6,5,4]=>[3,1,2,5,6,7,8,4]=>[3,2,1,8,4,5,6,7]=>1100001
[3,1,4,8,7,6,5,2]=>[5,3,1,4,6,7,8,2]=>[4,8,2,3,1,5,6,7]=>0100001
[2,8,1,3,7,5,4,6]=>[5,2,1,7,8,3,4,6]=>[2,7,4,8,6,3,1,5]=>0100111
[1,8,2,3,7,5,4,6]=>[1,5,2,7,8,3,4,6]=>[1,7,4,8,6,3,2,5]=>0100111
[1,2,8,3,7,6,4,5]=>[1,2,6,7,3,8,4,5]=>[1,2,7,4,8,5,3,6]=>0001011
[1,4,3,6,8,2,5,7]=>[1,8,4,3,2,6,5,7]=>[1,4,3,6,8,7,5,2]=>0011011
[1,4,5,2,8,3,7,6]=>[1,7,5,4,2,8,3,6]=>[1,4,7,3,5,2,8,6]=>0001011
[1,4,2,6,5,8,3,7]=>[1,8,4,2,6,5,3,7]=>[1,6,5,8,7,3,4,2]=>0010111
[1,5,4,2,6,8,3,7]=>[1,8,4,5,2,6,3,7]=>[1,6,8,7,3,4,5,2]=>0001011
[3,1,6,5,8,2,4,7]=>[8,3,1,2,6,5,4,7]=>[6,5,8,7,4,2,3,1]=>0110111
[1,6,4,2,5,8,3,7]=>[1,8,4,6,2,5,3,7]=>[1,8,7,3,4,6,5,2]=>0001111
[1,5,2,6,4,8,3,7]=>[1,8,6,5,2,4,3,7]=>[1,8,7,3,6,4,5,2]=>0001111
[1,2,6,5,4,8,3,7]=>[1,2,8,5,6,4,3,7]=>[1,2,6,4,5,8,7,3]=>0000111
[1,2,5,4,7,3,8,6]=>[1,2,8,5,4,7,3,6]=>[1,2,5,4,8,6,7,3]=>0001011
[4,1,2,6,3,8,7,5]=>[7,1,4,2,6,3,8,5]=>[8,5,6,3,4,2,1,7]=>1010101
[7,1,3,5,2,8,4,6]=>[8,5,1,7,3,2,4,6]=>[7,4,8,6,2,5,3,1]=>0101111
[1,6,4,2,8,3,7,5]=>[1,7,4,8,6,2,3,5]=>[1,8,5,6,2,7,3,4]=>0000111
[1,4,2,8,3,7,6,5]=>[1,6,4,2,7,8,3,5]=>[1,8,5,7,3,4,2,6]=>0010011
[7,3,1,6,2,8,4,5]=>[8,3,6,7,1,2,4,5]=>[6,2,3,7,4,8,5,1]=>0001111
[1,7,6,4,2,8,3,5]=>[1,8,4,6,2,7,3,5]=>[1,7,3,4,6,8,5,2]=>0001011
[1,2,7,6,5,3,8,4]=>[1,2,8,5,6,7,3,4]=>[1,2,8,4,5,6,7,3]=>0000011
[1,6,5,2,7,3,8,4]=>[1,8,7,5,6,2,3,4]=>[1,7,3,8,4,5,6,2]=>0000111
[1,5,7,4,2,8,3,6]=>[1,8,4,7,5,2,3,6]=>[1,5,7,3,4,8,6,2]=>0000111
[8,3,1,6,2,4,7,5]=>[7,3,6,1,8,2,4,5]=>[6,2,3,7,4,1,8,5]=>0010111
[1,7,4,2,8,3,6,5]=>[1,6,4,8,7,2,3,5]=>[1,6,2,8,5,7,3,4]=>0000111
[8,1,5,4,2,7,3,6]=>[7,4,5,8,1,2,3,6]=>[7,3,5,1,8,6,2,4]=>0001111
[8,5,3,1,7,2,4,6]=>[7,3,5,1,8,2,4,6]=>[7,4,1,8,6,2,3,5]=>0010111
[8,6,2,1,7,3,4,5]=>[2,7,6,1,3,8,4,5]=>[7,4,1,2,8,5,3,6]=>0011011
[1,8,6,4,2,7,3,5]=>[1,7,4,6,2,8,3,5]=>[1,8,5,2,7,3,4,6]=>0001011
[1,5,2,7,3,8,6,4]=>[1,6,8,5,2,7,3,4]=>[1,8,4,5,2,6,7,3]=>0001011
[1,2,8,5,3,7,6,4]=>[1,2,6,5,7,8,3,4]=>[1,2,8,4,5,7,3,6]=>0000011
[7,2,1,8,6,3,4,5]=>[2,6,8,1,3,7,4,5]=>[7,4,1,2,6,8,5,3]=>0011011
[1,8,7,3,2,6,4,5]=>[1,3,6,7,2,4,8,5]=>[1,8,5,2,3,6,4,7]=>0001101
[1,2,8,7,5,3,6,4]=>[1,2,6,5,7,3,8,4]=>[1,2,6,3,8,4,5,7]=>0000101
[8,1,7,6,3,4,5,2]=>[5,6,7,1,3,8,4,2]=>[7,4,1,5,3,8,2,6]=>0011011
[5,7,8,6,2,4,1,3]=>[4,6,2,1,5,8,7,3]=>[4,1,5,7,8,3,2,6]=>0110001
[6,1,4,5,3,8,7,2]=>[7,5,6,1,4,3,8,2]=>[6,3,8,2,5,4,1,7]=>0011101
[6,4,5,8,3,7,2,1]=>[2,7,8,6,4,5,3,1]=>[6,5,4,8,1,2,7,3]=>0001111
[2,3,8,6,1,5,7,4]=>[7,2,3,6,1,8,5,4]=>[2,3,7,5,1,8,4,6]=>0001011
[8,3,5,7,2,1,6,4]=>[2,6,7,8,3,5,1,4]=>[7,1,2,6,5,3,8,4]=>0001111
[2,7,6,5,1,3,4,8]=>[5,2,1,3,6,7,4,8]=>[2,7,4,3,1,5,6,8]=>0110010
[2,7,6,8,1,3,5,4]=>[5,2,1,8,3,7,6,4]=>[2,5,3,1,7,6,8,4]=>0101011
[8,7,5,6,1,4,2,3]=>[4,6,1,2,7,5,8,3]=>[8,3,1,4,2,6,5,7]=>0110101
[2,7,6,1,4,3,5,8]=>[4,2,6,1,3,7,5,8]=>[2,4,1,7,5,3,6,8]=>0011010
[7,3,5,1,2,8,4,6]=>[8,1,5,7,3,2,4,6]=>[5,3,7,4,8,6,2,1]=>1001111
[2,3,8,1,6,4,7,5]=>[7,2,3,6,8,1,4,5]=>[2,3,7,4,6,1,8,5]=>0000111
[5,7,2,3,8,6,1,4]=>[6,8,2,3,5,7,1,4]=>[5,7,1,6,8,4,3,2]=>0110011
[5,1,6,4,2,8,7,3]=>[7,4,6,5,1,2,8,3]=>[8,3,6,2,4,5,1,7]=>0001101
[5,7,3,2,8,1,6,4]=>[6,3,8,7,5,2,1,4]=>[5,8,4,7,1,6,2,3]=>0000111
[6,7,3,8,1,2,5,4]=>[5,1,8,7,3,6,2,4]=>[6,8,4,7,2,1,5,3]=>1001011
[1,5,7,4,8,3,6,2]=>[1,6,8,7,5,4,3,2]=>[1,5,8,2,6,4,7,3]=>0000111
[5,7,3,1,8,6,2,4]=>[6,3,8,1,5,7,2,4]=>[5,8,4,1,6,7,2,3]=>0010011
[6,7,1,8,3,5,2,4]=>[5,8,7,1,3,6,2,4]=>[6,8,4,1,5,3,7,2]=>0011011
[6,1,7,8,4,5,2,3]=>[5,8,1,6,2,4,7,3]=>[6,4,7,8,3,1,5,2]=>0101101
[1,6,7,8,4,5,3,2]=>[1,3,5,8,4,6,7,2]=>[1,6,7,8,2,3,5,4]=>0001001
[1,6,7,8,4,3,5,2]=>[1,5,4,8,3,6,7,2]=>[1,6,7,8,2,5,3,4]=>0001001
[6,7,2,8,1,3,5,4]=>[5,8,2,7,1,6,3,4]=>[5,1,6,8,4,7,3,2]=>0101011
[6,2,7,8,1,4,5,3]=>[5,8,6,2,1,4,7,3]=>[5,1,7,8,3,6,4,2]=>0011101
[6,2,7,8,1,5,4,3]=>[4,5,8,6,2,1,7,3]=>[5,2,6,1,4,7,8,3]=>0001101
[5,7,2,1,8,6,3,4]=>[2,6,8,1,5,7,3,4]=>[5,8,4,1,2,6,7,3]=>0010011
[1,6,7,8,3,5,4,2]=>[1,4,5,8,3,6,7,2]=>[1,5,3,6,7,8,2,4]=>0001001
[6,7,1,8,5,2,3,4]=>[5,8,1,2,7,6,3,4]=>[6,7,3,1,5,8,4,2]=>0110011
[1,6,7,8,5,3,4,2]=>[1,4,5,3,8,6,7,2]=>[1,6,7,8,2,4,3,5]=>0010001
[2,7,3,8,5,6,1,4]=>[6,2,8,3,7,1,5,4]=>[2,6,1,7,5,8,4,3]=>0010111
[2,6,1,8,4,7,3,5]=>[7,2,8,6,1,4,3,5]=>[2,6,4,8,5,1,7,3]=>0001111
[3,7,2,6,1,8,4,5]=>[8,6,3,7,2,1,4,5]=>[3,7,4,8,5,2,6,1]=>0001111
[4,8,1,6,2,7,3,5]=>[7,6,8,4,1,2,3,5]=>[4,6,2,8,5,1,7,3]=>0001111
[4,8,2,6,1,7,3,5]=>[7,6,8,4,2,1,3,5]=>[4,8,5,2,6,1,7,3]=>0001111
[8,1,2,5,6,4,3,7]=>[4,1,6,8,2,5,3,7]=>[8,7,3,6,5,2,1,4]=>1001111
[3,7,5,1,2,8,4,6]=>[8,1,3,5,7,2,4,6]=>[3,7,4,5,8,6,2,1]=>1000111
[4,1,5,8,2,7,3,6]=>[7,8,4,1,5,2,3,6]=>[5,7,3,4,1,8,6,2]=>0010111
[1,4,6,2,8,7,3,5]=>[1,7,6,4,2,3,8,5]=>[1,4,6,3,8,5,2,7]=>0001101
[3,1,2,6,4,8,7,5]=>[3,1,2,7,6,4,8,5]=>[3,2,1,8,5,6,4,7]=>1100101
[3,1,2,7,4,6,8,5]=>[3,1,2,8,7,4,6,5]=>[3,2,1,8,5,7,6,4]=>1100111
[1,2,3,6,8,5,7,4]=>[1,2,3,7,8,6,5,4]=>[1,2,3,6,8,4,7,5]=>0000011
[1,4,2,6,8,3,7,5]=>[1,7,4,2,8,6,3,5]=>[1,6,7,3,4,2,8,5]=>0010011
[1,2,3,7,8,5,6,4]=>[1,2,3,6,8,5,7,4]=>[1,2,3,7,8,4,6,5]=>0000101
[1,2,3,7,5,8,6,4]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,4,6,7,5]=>0000011
[3,1,7,2,8,6,4,5]=>[6,3,1,8,2,7,4,5]=>[8,5,2,3,1,6,7,4]=>0101011
[1,2,3,8,7,5,6,4]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,4,6,5,7]=>0000101
[5,7,8,3,2,1,6,4]=>[2,3,6,8,5,1,7,4]=>[5,6,1,2,3,7,8,4]=>0000101
[2,7,8,4,3,5,6,1]=>[6,2,4,8,3,5,7,1]=>[2,7,8,1,6,5,3,4]=>0001101
[8,6,3,7,2,1,4,5]=>[2,7,6,3,1,8,4,5]=>[8,5,1,2,7,4,3,6]=>0011011
[5,6,3,8,2,1,4,7]=>[2,8,6,3,5,1,4,7]=>[5,8,7,4,3,6,1,2]=>0010111
[2,6,4,7,3,5,8,1]=>[8,2,7,6,4,3,5,1]=>[2,7,5,4,6,3,8,1]=>0001111
[8,4,3,2,1,6,5,7]=>[2,3,4,6,8,1,5,7]=>[6,1,2,3,4,8,7,5]=>0000111
[6,4,3,2,1,7,5,8]=>[2,3,4,7,6,1,5,8]=>[7,5,6,1,2,3,4,8]=>0000110
[4,5,3,2,7,1,6,8]=>[7,3,5,4,2,1,6,8]=>[4,5,2,3,7,6,1,8]=>0001110
[7,4,3,2,1,8,5,6]=>[2,3,4,8,7,1,5,6]=>[7,5,8,6,1,2,3,4]=>0000111
[8,4,3,2,1,7,5,6]=>[2,3,4,7,8,1,5,6]=>[8,6,1,2,3,4,7,5]=>0000111
[7,4,3,2,1,8,6,5]=>[2,3,4,6,8,7,1,5]=>[7,1,2,3,4,6,8,5]=>0000011
[8,5,4,2,7,6,1,3]=>[6,4,2,5,7,8,1,3]=>[8,3,2,4,5,7,1,6]=>0100011
[7,5,4,2,8,6,1,3]=>[6,4,2,5,8,7,1,3]=>[7,1,6,8,3,2,4,5]=>0100011
[6,5,4,2,7,8,1,3]=>[8,4,2,5,6,1,7,3]=>[7,8,3,2,4,5,6,1]=>0100101
[8,5,4,2,6,7,1,3]=>[7,4,2,5,8,1,6,3]=>[7,6,1,8,3,2,4,5]=>0100111
[5,6,3,7,2,1,8,4]=>[2,8,7,6,5,3,1,4]=>[5,8,4,6,3,7,1,2]=>0000111
[2,6,4,7,3,8,5,1]=>[5,2,8,7,6,4,3,1]=>[2,8,1,5,6,4,7,3]=>0000111
[3,5,4,2,7,8,1,6]=>[8,4,3,5,2,1,7,6]=>[3,5,2,4,7,8,6,1]=>0001101
[7,4,3,2,1,6,8,5]=>[2,3,4,8,7,1,6,5]=>[8,5,7,6,1,2,3,4]=>0000111
[8,4,3,2,1,6,7,5]=>[2,3,4,7,8,1,6,5]=>[7,6,1,2,3,4,8,5]=>0000111
[7,4,3,2,1,5,8,6]=>[2,3,4,8,1,7,5,6]=>[8,6,7,5,1,2,3,4]=>0001011
[6,4,3,2,1,5,8,7]=>[2,3,4,6,1,5,8,7]=>[6,5,1,2,3,4,8,7]=>0001101
[3,2,6,4,8,5,1,7]=>[5,3,2,8,6,4,1,7]=>[3,2,8,7,1,5,6,4]=>0100111
[3,2,5,8,4,6,1,7]=>[6,3,2,8,5,4,1,7]=>[3,2,5,8,7,1,6,4]=>0100111
[4,2,1,5,7,3,6,8]=>[2,7,4,1,5,3,6,8]=>[5,7,6,3,4,1,2,8]=>0010110
[4,5,2,3,7,1,6,8]=>[7,5,2,4,3,1,6,8]=>[4,5,3,2,7,6,1,8]=>0101110
[4,2,5,8,3,1,6,7]=>[3,8,4,2,5,1,6,7]=>[5,8,7,6,1,3,4,2]=>0010111
[4,1,5,3,8,2,6,7]=>[8,5,4,1,3,2,6,7]=>[8,7,6,2,5,3,4,1]=>0011111
[4,3,2,7,5,1,6,8]=>[5,3,4,2,7,1,6,8]=>[4,2,3,7,6,1,5,8]=>0010110
[4,3,6,2,5,1,7,8]=>[5,6,4,3,2,1,7,8]=>[4,3,6,1,5,2,7,8]=>0011100
[4,5,1,7,3,2,6,8]=>[3,7,5,4,1,2,6,8]=>[4,5,1,3,7,6,2,8]=>0001110
[3,5,1,4,2,7,6,8]=>[4,5,3,1,2,7,6,8]=>[3,4,1,5,2,7,6,8]=>0011010
[2,5,1,4,3,7,8,6]=>[4,2,5,1,3,8,7,6]=>[2,4,1,5,3,7,8,6]=>0011001
[5,2,1,4,3,7,8,6]=>[2,4,5,1,3,8,7,6]=>[4,1,2,5,3,7,8,6]=>0011001
[4,3,1,7,5,2,6,8]=>[5,3,4,1,7,2,6,8]=>[7,6,2,3,4,1,5,8]=>0010110
[4,3,6,1,7,2,5,8]=>[7,6,4,3,1,2,5,8]=>[4,3,6,2,7,5,1,8]=>0011110
[6,2,4,1,3,7,8,5]=>[4,8,2,1,6,3,7,5]=>[4,1,7,8,5,6,3,2]=>0110101
[3,6,4,1,2,7,5,8]=>[4,1,3,7,6,2,5,8]=>[3,7,5,6,2,1,4,8]=>1000110
[4,6,3,1,7,2,5,8]=>[7,3,6,4,1,2,5,8]=>[4,6,2,3,7,5,1,8]=>0001110
[5,3,6,2,1,4,7,8]=>[2,6,5,3,1,4,7,8]=>[6,4,3,5,1,2,7,8]=>0011100
[3,2,6,1,4,7,5,8]=>[7,3,2,1,6,4,5,8]=>[3,2,7,5,6,4,1,8]=>0110110
[7,3,1,4,6,8,2,5]=>[8,3,7,1,4,2,6,5]=>[7,6,2,3,8,5,4,1]=>0011111
[7,2,1,5,3,6,8,4]=>[2,8,5,7,1,3,6,4]=>[8,4,7,6,3,5,1,2]=>0001111
[2,4,1,5,3,8,7,6]=>[5,2,4,1,3,7,8,6]=>[2,5,3,4,1,8,6,7]=>0011001
[3,4,5,1,2,8,7,6]=>[5,1,3,4,2,7,8,6]=>[3,4,5,2,1,8,6,7]=>1001001
[1,8,4,5,3,2,7,6]=>[1,3,5,7,4,8,2,6]=>[1,7,2,3,5,4,8,6]=>0001011
[2,4,8,5,3,1,7,6]=>[3,2,5,4,7,8,1,6]=>[2,4,7,1,3,5,8,6]=>0000011
[3,4,6,8,2,7,1,5]=>[7,8,3,4,2,6,1,5]=>[3,4,6,7,1,8,5,2]=>0001011
[2,4,8,6,3,7,1,5]=>[7,2,6,4,3,8,1,5]=>[2,4,7,1,8,5,3,6]=>0001011
[1,8,4,6,3,7,5,2]=>[1,5,7,6,8,4,3,2]=>[1,6,4,7,3,8,2,5]=>0000111
[3,5,6,2,7,4,1,8]=>[4,7,3,6,5,2,1,8]=>[3,5,7,1,4,6,2,8]=>0000110
[1,8,5,6,7,3,2,4]=>[1,3,7,2,8,5,6,4]=>[1,8,4,2,3,7,6,5]=>0010111
[3,4,6,1,8,7,2,5]=>[7,6,3,4,1,2,8,5]=>[3,4,6,2,8,5,1,7]=>0001101
[3,5,6,1,7,4,8,2]=>[8,7,3,6,5,1,4,2]=>[3,5,8,2,7,4,6,1]=>0000111
[3,4,6,1,8,7,5,2]=>[5,7,3,4,6,1,8,2]=>[3,4,6,1,5,8,2,7]=>0000101
[3,4,6,8,1,7,5,2]=>[5,7,3,4,8,6,1,2]=>[3,4,6,8,2,7,1,5]=>0000011
[2,4,8,6,1,7,5,3]=>[5,2,7,4,6,8,1,3]=>[2,4,8,3,7,1,5,6]=>0000011
[1,8,5,6,7,2,4,3]=>[1,4,7,2,8,5,6,3]=>[1,4,2,8,3,7,6,5]=>0010111
[4,5,6,7,1,3,8,2]=>[8,7,1,4,5,6,3,2]=>[4,5,6,8,2,7,3,1]=>0100011
[2,5,8,6,7,4,1,3]=>[4,2,1,7,5,8,6,3]=>[2,5,8,3,1,4,7,6]=>0100011
[1,8,5,6,7,4,3,2]=>[1,3,4,7,8,5,6,2]=>[1,8,2,3,4,7,6,5]=>0000111
[2,5,8,6,7,4,3,1]=>[3,2,4,7,5,8,6,1]=>[2,5,8,1,3,4,7,6]=>0000011
[8,2,4,3,7,1,6,5]=>[6,4,7,2,8,3,1,5]=>[4,2,7,1,6,3,8,5]=>0010111
[4,2,5,6,1,8,3,7]=>[8,6,4,2,5,1,3,7]=>[5,8,7,3,4,2,6,1]=>0010111
[4,2,5,6,1,7,3,8]=>[7,6,4,2,5,1,3,8]=>[5,7,3,4,2,6,1,8]=>0010110
[6,1,5,7,3,2,4,8]=>[3,7,6,1,2,5,4,8]=>[7,4,1,3,6,5,2,8]=>0011110
[3,6,8,2,4,7,1,5]=>[7,8,3,2,4,6,1,5]=>[3,6,7,1,8,5,4,2]=>0011011
[7,8,3,2,4,6,1,5]=>[6,3,8,2,4,1,7,5]=>[6,1,7,8,5,4,2,3]=>0011101
[4,2,5,6,1,7,8,3]=>[8,6,4,2,5,1,7,3]=>[5,7,8,3,4,2,6,1]=>0010101
[5,8,6,1,7,3,4,2]=>[4,7,6,1,5,8,3,2]=>[4,1,5,8,2,7,3,6]=>0010011
[6,1,5,8,7,3,2,4]=>[3,7,6,1,2,5,8,4]=>[8,4,1,3,6,5,2,7]=>0011101
[3,2,4,1,8,7,5,6]=>[4,3,2,1,7,5,8,6]=>[3,2,4,1,8,6,5,7]=>0110101
[3,7,6,5,1,8,4,2]=>[4,8,3,5,6,7,1,2]=>[3,7,1,4,5,6,8,2]=>0000011
[3,2,4,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>[3,2,4,1,7,6,5,8]=>0110110
[3,2,4,1,6,8,5,7]=>[4,3,2,1,8,6,5,7]=>[3,2,4,1,6,8,7,5]=>0110011
[8,3,2,4,7,6,1,5]=>[6,3,7,2,4,8,1,5]=>[8,5,4,2,3,7,1,6]=>0011011
[3,2,5,1,6,7,4,8]=>[7,3,2,5,1,6,4,8]=>[3,2,6,7,4,5,1,8]=>0101010
[6,5,1,8,4,2,3,7]=>[4,8,1,5,6,2,3,7]=>[8,7,3,1,4,5,6,2]=>0100111
[8,4,2,3,7,5,1,6]=>[5,4,2,7,8,3,1,6]=>[8,6,3,2,4,7,1,5]=>0100111
[7,4,2,3,8,5,1,6]=>[5,4,2,8,7,3,1,6]=>[7,1,5,8,6,3,2,4]=>0100111
[3,2,5,1,8,6,4,7]=>[6,3,2,5,1,8,4,7]=>[3,2,8,7,4,5,1,6]=>0101011
[8,6,1,5,7,3,2,4]=>[3,7,6,1,2,8,5,4]=>[7,5,2,8,4,1,3,6]=>0011011
[3,6,8,5,1,7,4,2]=>[4,7,3,5,8,6,1,2]=>[3,6,8,2,7,1,4,5]=>0000011
[8,5,1,6,7,4,2,3]=>[4,7,1,5,8,2,6,3]=>[7,6,2,8,3,1,4,5]=>0100111
[3,2,4,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>[3,2,4,1,5,8,7,6]=>0110011
[4,3,7,5,1,8,6,2]=>[6,5,4,3,8,7,1,2]=>[4,3,7,1,6,8,2,5]=>0010011
[6,4,3,8,5,1,7,2]=>[7,5,4,8,6,3,1,2]=>[7,1,8,2,5,6,3,4]=>0000111
[2,4,1,7,5,8,6,3]=>[6,2,4,1,8,7,5,3]=>[2,8,3,4,1,6,7,5]=>0010011
[2,6,4,1,8,5,3,7]=>[5,2,4,8,6,1,3,7]=>[2,6,1,5,8,7,3,4]=>0000111
[2,5,8,4,1,6,3,7]=>[6,2,4,8,5,1,3,7]=>[2,5,6,1,8,7,3,4]=>0000111
[3,2,5,6,1,8,4,7]=>[8,3,2,6,5,1,4,7]=>[3,2,5,8,7,4,6,1]=>0100111
[4,8,3,2,6,1,5,7]=>[6,3,8,4,2,1,5,7]=>[4,6,1,8,7,5,2,3]=>0001111
[3,2,7,1,5,4,8,6]=>[5,3,2,8,1,7,4,6]=>[3,2,5,1,8,6,7,4]=>0101011
[3,2,7,1,5,8,6,4]=>[6,3,2,8,1,7,5,4]=>[3,2,7,5,1,6,8,4]=>0101011
[3,8,2,5,1,6,7,4]=>[7,5,3,8,2,1,6,4]=>[3,5,2,7,6,1,8,4]=>0001111
[4,3,7,8,2,6,1,5]=>[6,8,4,3,2,1,7,5]=>[4,3,6,1,7,8,5,2]=>0011101
[6,3,2,7,1,5,4,8]=>[5,3,7,6,2,1,4,8]=>[7,4,6,1,5,2,3,8]=>0001110
[6,5,2,1,7,8,4,3]=>[2,4,8,5,6,1,7,3]=>[6,1,2,4,5,7,8,3]=>0000101
[6,2,1,8,5,3,7,4]=>[2,7,5,8,6,1,3,4]=>[7,3,5,6,1,2,8,4]=>0000111
[6,3,2,1,4,7,8,5]=>[2,3,8,1,6,4,7,5]=>[7,8,5,6,4,1,2,3]=>0010101
[6,3,2,1,4,7,5,8]=>[2,3,7,1,6,4,5,8]=>[7,5,6,4,1,2,3,8]=>0010110
[4,8,3,2,7,1,5,6]=>[7,3,8,4,2,1,5,6]=>[4,8,6,1,7,5,2,3]=>0001111
[6,3,2,8,1,4,7,5]=>[7,3,8,2,6,1,4,5]=>[8,5,6,1,7,4,2,3]=>0010111
[3,2,1,4,7,5,8,6]=>[2,3,1,4,8,7,5,6]=>[3,1,2,4,8,6,7,5]=>0100011
[4,8,3,2,1,5,6,7]=>[2,3,8,4,1,5,6,7]=>[4,8,7,6,5,1,2,3]=>0001111
[4,3,8,2,1,5,6,7]=>[2,8,4,3,1,5,6,7]=>[4,3,8,7,6,5,1,2]=>0011111
[6,2,5,3,4,1,8,7]=>[4,5,6,2,3,1,8,7]=>[6,1,4,2,5,3,8,7]=>0011101
[8,3,7,2,4,1,6,5]=>[4,6,7,3,8,2,1,5]=>[6,2,7,1,4,3,8,5]=>0010111
[8,4,5,1,3,2,7,6]=>[3,5,1,7,4,8,2,6]=>[3,1,7,2,5,4,8,6]=>0101011
[8,1,7,3,4,2,6,5]=>[4,6,7,1,8,3,2,5]=>[4,1,7,2,6,3,8,5]=>0010111
[8,2,7,1,4,3,6,5]=>[4,6,7,2,8,1,3,5]=>[6,1,4,2,7,3,8,5]=>0010111
[8,2,3,1,5,4,7,6]=>[3,5,2,7,1,8,4,6]=>[5,1,3,2,7,4,8,6]=>0101011
[8,6,7,1,3,2,5,4]=>[3,5,1,7,2,8,6,4]=>[3,1,5,2,8,4,7,6]=>0101011
[2,1,8,5,7,3,6,4]=>[2,1,6,7,8,5,3,4]=>[2,1,8,4,7,3,6,5]=>1000111
[4,5,8,6,3,2,7,1]=>[7,3,6,4,5,8,2,1]=>[4,5,8,1,7,2,3,6]=>0000011
[1,5,8,7,3,6,2,4]=>[1,6,7,3,5,2,8,4]=>[1,5,6,2,8,4,3,7]=>0010101
[3,6,2,8,4,5,7,1]=>[7,8,3,6,2,4,5,1]=>[3,6,4,8,1,7,5,2]=>0001111
[2,8,4,6,1,5,7,3]=>[7,2,6,8,4,1,5,3]=>[2,8,3,6,1,7,5,4]=>0001111
[6,3,7,8,4,1,5,2]=>[5,4,8,6,3,1,7,2]=>[7,8,2,4,6,1,5,3]=>0001101
[1,3,7,8,4,6,5,2]=>[1,5,3,6,8,4,7,2]=>[1,3,6,4,7,8,2,5]=>0000101
[3,6,7,8,4,2,5,1]=>[5,4,3,8,2,6,7,1]=>[3,6,7,8,1,5,2,4]=>0001001
[7,6,1,8,4,2,5,3]=>[5,4,8,6,1,7,2,3]=>[5,1,7,2,4,6,8,3]=>0001011
[5,2,8,7,3,6,1,4]=>[6,7,5,2,3,1,8,4]=>[5,3,6,1,8,4,2,7]=>0011101
[5,2,7,8,1,4,6,3]=>[6,8,5,2,1,4,7,3]=>[7,8,3,5,1,6,4,2]=>0011101
[1,2,7,8,5,4,6,3]=>[1,2,6,5,8,4,7,3]=>[1,2,7,8,3,6,4,5]=>0000101
[6,2,8,5,4,3,1,7]=>[3,4,5,8,6,2,1,7]=>[8,7,1,3,5,6,2,4]=>0000111
[2,8,3,5,4,1,6,7]=>[4,2,5,8,3,1,6,7]=>[2,5,3,8,7,6,1,4]=>0001111
[7,3,5,8,2,4,6,1]=>[6,8,7,3,2,5,4,1]=>[7,4,3,8,1,6,5,2]=>0011111
[4,3,1,2,8,5,6,7]=>[3,1,4,2,8,5,6,7]=>[4,2,1,3,8,7,6,5]=>1010111
[2,7,6,8,4,3,5,1]=>[5,2,4,8,3,7,6,1]=>[2,7,6,8,1,5,3,4]=>0001011
[4,6,8,5,1,3,2,7]=>[3,5,1,4,8,6,2,7]=>[3,1,4,6,8,7,2,5]=>0100011
[2,4,8,3,6,5,1,7]=>[5,2,6,4,8,3,1,7]=>[2,4,6,3,8,7,1,5]=>0000111
[2,8,5,4,3,1,6,7]=>[3,2,4,5,8,1,6,7]=>[2,8,7,6,1,3,4,5]=>0000111
[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]=>[1,4,2,3,8,7,6,5]=>0010111
[7,3,2,8,5,4,6,1]=>[6,3,5,8,7,2,4,1]=>[8,1,6,2,3,5,7,4]=>0000111
[2,8,4,3,5,1,6,7]=>[5,2,4,8,3,1,6,7]=>[2,8,7,6,1,5,3,4]=>0001111
[6,2,8,4,5,3,1,7]=>[3,5,8,6,2,4,1,7]=>[5,2,6,4,8,7,1,3]=>0001111
[4,2,3,1,8,5,6,7]=>[3,4,2,1,8,5,6,7]=>[4,1,3,2,8,7,6,5]=>0110111
[2,8,1,5,3,4,7,6]=>[5,2,7,1,3,8,4,6]=>[2,7,4,1,5,3,8,6]=>0011011
[1,4,2,8,5,3,6,7]=>[1,5,4,2,8,3,6,7]=>[1,8,7,6,3,4,2,5]=>0010111
[1,5,2,8,4,3,6,7]=>[1,4,8,5,2,3,6,7]=>[1,5,2,4,8,7,6,3]=>0001111
[1,2,5,4,3,8,6,7]=>[1,2,4,5,3,8,6,7]=>[1,2,5,3,4,8,7,6]=>0001011
[1,2,8,5,7,4,3,6]=>[1,2,4,7,8,5,3,6]=>[1,2,7,3,4,8,6,5]=>0000111
[1,2,4,8,7,5,3,6]=>[1,2,5,4,7,3,8,6]=>[1,2,4,8,6,3,5,7]=>0000101
[7,6,1,4,2,8,3,5]=>[8,4,6,1,2,7,3,5]=>[7,3,6,8,5,2,4,1]=>0011011
[1,4,2,7,8,5,3,6]=>[1,5,4,2,8,3,7,6]=>[1,7,8,6,3,4,2,5]=>0010101
[6,1,2,8,4,3,7,5]=>[4,1,7,8,6,2,3,5]=>[7,3,8,5,6,2,1,4]=>1000111
[6,7,1,3,2,4,8,5]=>[3,8,1,2,7,6,4,5]=>[3,1,6,8,5,7,4,2]=>0110011
[1,2,7,3,5,8,4,6]=>[1,2,8,7,3,5,4,6]=>[1,2,7,4,8,6,5,3]=>0001111
[5,8,1,3,7,2,4,6]=>[7,8,1,3,5,2,4,6]=>[5,7,4,3,1,8,6,2]=>0110111
[4,2,8,1,7,3,6,5]=>[6,7,4,2,8,1,3,5]=>[6,1,7,3,4,2,8,5]=>0010111
[1,2,8,4,7,5,3,6]=>[1,2,5,7,8,4,3,6]=>[1,2,8,6,4,7,3,5]=>0000111
[8,3,7,1,5,2,4,6]=>[5,7,8,3,1,2,4,6]=>[5,1,8,6,2,7,4,3]=>0011111
[7,1,2,8,6,4,3,5]=>[4,1,6,8,2,7,3,5]=>[7,3,6,8,5,2,1,4]=>1001011
[3,7,4,8,1,6,2,5]=>[6,8,3,7,4,1,2,5]=>[3,6,1,8,5,4,7,2]=>0001111
[4,2,8,1,7,6,3,5]=>[6,7,4,2,1,8,3,5]=>[7,3,4,2,8,5,1,6]=>0011011
[5,8,3,4,1,7,2,6]=>[7,4,8,3,5,1,2,6]=>[5,8,6,1,7,2,4,3]=>0010111
[4,8,3,5,1,6,2,7]=>[6,5,8,4,3,1,2,7]=>[4,6,1,8,7,2,5,3]=>0001111
[5,6,2,7,3,8,1,4]=>[8,7,6,2,5,3,1,4]=>[5,6,3,8,4,2,7,1]=>0010111
[5,6,2,8,4,7,1,3]=>[7,8,2,6,5,1,4,3]=>[5,7,4,6,1,8,3,2]=>0100111
[4,6,2,8,3,7,1,5]=>[7,8,6,4,2,3,1,5]=>[4,6,3,7,1,8,5,2]=>0001111
[8,1,7,4,3,6,2,5]=>[6,4,7,8,1,3,2,5]=>[8,5,1,6,3,7,2,4]=>0001111
[6,8,3,5,1,7,4,2]=>[4,7,5,8,3,6,1,2]=>[5,3,6,8,2,7,1,4]=>0001011
[2,5,8,4,7,6,3,1]=>[3,2,6,7,5,8,4,1]=>[2,5,7,4,8,1,3,6]=>0000011
[4,3,8,1,5,6,7,2]=>[7,8,4,3,1,5,6,2]=>[4,3,7,6,5,1,8,2]=>0011111
[4,8,3,6,1,2,7,5]=>[7,1,6,4,8,3,2,5]=>[4,6,3,7,2,1,8,5]=>1000111
[3,8,1,2,5,6,7,4]=>[7,1,3,8,2,5,6,4]=>[3,7,6,5,2,1,8,4]=>1001111
[2,8,7,4,5,1,3,6]=>[5,2,1,7,4,3,8,6]=>[2,8,6,3,1,5,4,7]=>0101101
[8,7,2,4,1,6,3,5]=>[6,4,7,2,1,3,8,5]=>[4,2,8,5,1,6,3,7]=>0011101
[5,8,3,6,2,4,7,1]=>[7,6,8,3,5,2,4,1]=>[5,6,2,8,1,7,4,3]=>0010111
[8,6,3,2,1,4,7,5]=>[2,3,7,1,6,8,4,5]=>[7,4,1,2,3,8,5,6]=>0010011
[6,1,8,4,5,7,2,3]=>[7,8,1,6,2,4,5,3]=>[6,4,8,3,1,7,5,2]=>0101111
[5,8,3,6,1,2,7,4]=>[7,1,6,8,5,3,2,4]=>[5,6,3,7,2,1,8,4]=>1000111
[4,5,3,8,6,1,7,2]=>[7,6,5,4,3,8,1,2]=>[4,5,3,7,1,8,2,6]=>0001011
[3,5,7,2,6,4,8,1]=>[8,6,3,7,5,2,4,1]=>[3,5,6,2,7,4,8,1]=>0000111
[2,5,7,3,6,4,8,1]=>[8,2,6,7,5,3,4,1]=>[2,5,6,3,7,4,8,1]=>0000111
[8,4,3,7,6,1,5,2]=>[5,6,4,7,3,8,1,2]=>[7,1,5,3,4,8,2,6]=>0001011
[6,7,2,3,5,4,8,1]=>[8,5,2,7,3,6,4,1]=>[5,3,2,6,7,4,8,1]=>0101011
[2,8,4,7,1,6,5,3]=>[5,2,6,7,8,4,1,3]=>[2,8,3,6,4,7,1,5]=>0000111
[8,1,4,7,2,6,5,3]=>[5,6,7,1,8,4,2,3]=>[8,3,7,2,6,4,1,5]=>0010111
[8,2,3,1,7,6,5,4]=>[3,5,2,6,7,8,1,4]=>[7,1,3,2,5,8,4,6]=>0100011
[3,5,7,1,6,8,4,2]=>[4,8,3,7,5,1,6,2]=>[3,5,7,6,1,4,8,2]=>0000111
[8,4,1,7,2,6,5,3]=>[5,6,4,7,8,1,2,3]=>[8,3,4,7,2,6,1,5]=>0000111
[1,3,8,2,7,6,5,4]=>[1,5,3,6,7,8,2,4]=>[1,3,7,2,5,8,4,6]=>0000011
[8,3,1,2,7,6,5,4]=>[3,1,5,6,7,8,2,4]=>[7,2,1,3,5,8,4,6]=>1000011
[2,1,8,3,7,6,5,4]=>[2,1,5,6,7,8,3,4]=>[2,1,7,3,5,8,4,6]=>1000011
[4,8,1,7,2,6,5,3]=>[5,6,7,4,8,1,2,3]=>[4,8,3,7,2,6,1,5]=>0000111
[3,8,1,2,7,6,5,4]=>[5,1,3,6,7,8,2,4]=>[3,7,2,1,5,8,4,6]=>1000011
[3,7,1,5,8,2,6,4]=>[6,8,3,7,1,5,2,4]=>[3,6,5,1,8,4,7,2]=>0001111
[2,5,6,1,8,3,7,4]=>[7,2,8,6,5,1,3,4]=>[2,5,8,4,6,1,7,3]=>0000111
[2,4,6,1,3,8,7,5]=>[7,2,1,4,6,3,8,5]=>[2,4,8,5,6,3,1,7]=>0100101
[3,4,6,1,2,8,7,5]=>[7,1,3,4,6,2,8,5]=>[3,4,8,5,6,2,1,7]=>1000101
[5,3,6,1,8,2,7,4]=>[7,8,6,5,3,1,2,4]=>[8,4,5,3,6,1,7,2]=>0001111
[8,1,3,5,7,2,6,4]=>[6,7,1,8,3,5,2,4]=>[6,5,3,1,7,2,8,4]=>0101111
[8,1,2,5,7,3,6,4]=>[6,1,7,8,2,5,3,4]=>[6,5,2,1,7,3,8,4]=>1001111
[7,2,1,5,8,3,6,4]=>[2,6,8,7,1,5,3,4]=>[6,5,1,2,8,4,7,3]=>0001111
[6,2,5,1,8,3,7,4]=>[7,8,5,6,2,1,3,4]=>[8,4,6,1,7,3,5,2]=>0001111
[4,2,5,3,1,8,7,6]=>[3,5,4,2,1,7,8,6]=>[5,1,3,4,2,8,6,7]=>0011001
[6,2,4,1,3,8,7,5]=>[4,7,2,1,6,3,8,5]=>[4,1,8,5,6,3,2,7]=>0110101
[8,1,2,4,3,7,6,5]=>[4,1,6,2,7,8,3,5]=>[4,2,1,8,5,7,3,6]=>1010011
[7,3,1,4,2,8,6,5]=>[4,3,6,1,8,7,2,5]=>[4,1,7,2,3,6,8,5]=>0010011
[5,6,2,1,8,3,7,4]=>[2,7,8,6,5,1,3,4]=>[5,8,4,6,1,2,7,3]=>0000111
[8,1,4,2,3,7,6,5]=>[4,6,1,2,7,8,3,5]=>[8,5,7,3,1,4,2,6]=>0110011
[7,4,1,2,3,8,6,5]=>[4,1,2,6,8,7,3,5]=>[7,3,2,1,4,6,8,5]=>1100011
[5,4,2,3,1,8,7,6]=>[3,4,2,5,1,7,8,6]=>[5,1,3,2,4,8,6,7]=>0101001
[7,3,1,2,4,8,6,5]=>[3,1,6,2,8,7,4,5]=>[7,4,2,1,3,6,8,5]=>1010011
[2,4,3,6,1,5,8,7]=>[6,2,4,3,1,5,8,7]=>[2,4,3,6,5,1,8,7]=>0011101
[2,4,3,6,5,8,1,7]=>[8,2,4,3,6,5,1,7]=>[2,4,3,6,5,8,7,1]=>0010111
[2,4,6,3,5,8,7,1]=>[7,2,6,4,3,5,8,1]=>[2,4,6,5,3,8,1,7]=>0001101
[2,4,6,3,5,1,8,7]=>[5,2,6,4,3,1,8,7]=>[2,4,6,1,5,3,8,7]=>0001101
[2,4,6,3,1,5,8,7]=>[3,2,6,4,1,5,8,7]=>[2,4,6,5,1,3,8,7]=>0001101
[4,2,6,5,8,1,3,7]=>[8,4,2,1,6,5,3,7]=>[6,5,8,7,3,2,4,1]=>0110111
[2,4,1,6,5,8,3,7]=>[8,2,4,1,6,5,3,7]=>[2,6,5,8,7,3,4,1]=>0010111
[2,1,4,6,5,8,3,7]=>[2,1,8,4,6,5,3,7]=>[2,1,4,6,5,8,7,3]=>1000111
[2,4,1,6,5,8,7,3]=>[7,2,4,1,6,5,8,3]=>[2,6,5,8,3,4,1,7]=>0010101
[2,1,4,6,8,5,3,7]=>[2,1,5,4,8,6,3,7]=>[2,1,4,6,8,7,3,5]=>1000011
[2,4,6,1,8,5,3,7]=>[5,2,8,4,6,1,3,7]=>[2,4,6,1,5,8,7,3]=>0000111
[2,4,6,8,1,5,3,7]=>[5,2,8,4,1,6,3,7]=>[2,4,5,1,6,8,7,3]=>0001011
[2,4,6,8,3,5,7,1]=>[7,2,8,4,3,6,5,1]=>[2,4,6,8,1,7,5,3]=>0001011
[2,4,6,8,3,1,5,7]=>[3,2,8,4,1,6,5,7]=>[2,4,6,8,7,5,1,3]=>0001011
[2,4,3,6,8,5,7,1]=>[7,2,4,3,8,6,5,1]=>[2,4,3,6,8,1,7,5]=>0010011
[2,4,3,6,8,5,1,7]=>[5,2,4,3,8,6,1,7]=>[2,4,3,6,8,7,1,5]=>0010011
[2,4,3,6,8,1,5,7]=>[8,2,4,3,1,6,5,7]=>[2,4,3,6,8,7,5,1]=>0011011
[2,4,3,1,6,8,5,7]=>[3,2,4,1,8,6,5,7]=>[2,4,1,3,6,8,7,5]=>0010011
[2,4,1,3,6,8,7,5]=>[4,2,1,3,7,6,8,5]=>[2,4,3,1,6,8,5,7]=>0110001
[2,4,6,3,1,8,7,5]=>[3,2,7,4,6,1,8,5]=>[2,4,8,5,6,1,3,7]=>0000101
[2,4,1,6,8,3,7,5]=>[7,2,4,1,8,6,3,5]=>[2,6,7,3,4,1,8,5]=>0010011
[4,6,2,8,5,7,1,3]=>[7,8,2,4,6,1,5,3]=>[4,7,5,6,1,8,3,2]=>0100111
[6,2,4,8,7,1,3,5]=>[7,6,2,1,4,3,8,5]=>[6,3,2,8,5,4,1,7]=>0111101
[2,6,4,8,1,7,5,3]=>[5,2,7,8,6,4,1,3]=>[2,8,3,7,1,5,6,4]=>0000111
[2,6,4,1,8,7,5,3]=>[5,2,4,7,6,1,8,3]=>[2,6,1,5,8,3,4,7]=>0000101
[2,1,6,4,8,7,3,5]=>[2,1,7,6,4,3,8,5]=>[2,1,8,5,4,6,3,7]=>1001101
[1,7,6,3,4,8,2,5]=>[1,8,6,3,4,7,2,5]=>[1,8,5,4,3,6,7,2]=>0011011
[1,2,7,4,8,3,5,6]=>[1,2,8,7,4,3,5,6]=>[1,2,7,5,4,8,6,3]=>0001111
[4,3,1,7,5,8,2,6]=>[8,3,4,1,7,5,2,6]=>[8,6,5,7,2,3,4,1]=>0010111
[6,8,1,3,7,2,4,5]=>[7,8,1,3,2,6,4,5]=>[6,7,4,3,1,8,5,2]=>0111011
[5,8,2,1,7,3,4,6]=>[2,7,8,1,5,3,4,6]=>[5,7,4,1,2,8,6,3]=>0010111
[6,7,1,3,8,2,4,5]=>[8,7,1,3,2,6,4,5]=>[6,8,5,2,7,4,3,1]=>0111011
[8,5,1,3,7,2,4,6]=>[7,5,1,3,8,2,4,6]=>[7,4,3,1,8,6,2,5]=>0110111
[2,6,4,8,7,1,3,5]=>[7,2,1,6,4,3,8,5]=>[2,8,5,4,6,3,1,7]=>0101101
[1,6,4,8,7,2,3,5]=>[1,7,2,6,4,3,8,5]=>[1,8,5,4,6,3,2,7]=>0101101
[6,2,8,3,7,1,4,5]=>[7,8,6,2,3,1,4,5]=>[8,5,3,6,1,7,4,2]=>0011111
[3,8,2,1,5,4,7,6]=>[2,5,3,7,1,8,4,6]=>[3,5,1,2,7,4,8,6]=>0001011
[8,3,2,1,5,4,6,7]=>[2,3,5,8,1,4,6,7]=>[5,1,2,3,8,7,6,4]=>0001111
[8,3,2,1,6,4,5,7]=>[2,3,6,8,1,4,5,7]=>[8,7,5,1,2,3,6,4]=>0001111
[8,3,2,1,4,6,5,7]=>[2,3,6,1,8,4,5,7]=>[6,4,1,2,3,8,7,5]=>0010111
[3,2,7,1,4,6,8,5]=>[8,3,2,1,7,4,6,5]=>[3,2,8,5,7,6,4,1]=>0110111
[4,7,2,5,1,8,3,6]=>[8,5,7,4,2,1,3,6]=>[4,5,2,7,3,8,6,1]=>0001111
[3,7,2,1,5,8,4,6]=>[2,8,3,7,1,5,4,6]=>[3,7,4,8,6,5,1,2]=>0001111
[3,7,2,1,4,8,5,6]=>[2,8,3,1,7,4,5,6]=>[3,7,5,8,6,4,1,2]=>0010111
[3,2,1,7,5,8,6,4]=>[2,3,1,6,8,7,5,4]=>[3,1,2,8,4,6,7,5]=>0100011
[4,2,7,6,1,8,3,5]=>[8,6,4,2,1,7,3,5]=>[7,3,4,2,6,8,5,1]=>0011011
[3,8,2,1,7,4,5,6]=>[2,7,3,8,1,4,5,6]=>[3,7,5,1,2,8,6,4]=>0001111
[3,2,8,1,6,4,7,5]=>[7,3,2,6,8,1,4,5]=>[3,2,7,4,6,1,8,5]=>0100111
[3,2,7,1,6,4,8,5]=>[8,3,2,6,7,1,4,5]=>[3,2,8,5,7,4,6,1]=>0100111
[4,2,7,6,1,3,8,5]=>[8,4,2,1,6,7,3,5]=>[8,5,6,7,3,2,4,1]=>0110011
[5,7,8,3,4,1,2,6]=>[4,1,8,3,5,2,7,6]=>[5,7,8,6,2,1,4,3]=>1010101
[4,2,6,8,1,3,7,5]=>[7,4,2,1,8,6,3,5]=>[6,7,3,2,4,1,8,5]=>0110011
[3,2,6,1,8,4,7,5]=>[7,3,2,8,6,1,4,5]=>[3,2,8,5,6,1,7,4]=>0100111
[4,7,3,8,5,1,2,6]=>[5,1,8,4,7,3,2,6]=>[4,7,2,1,5,8,6,3]=>1000111
[4,3,7,8,6,1,2,5]=>[6,1,4,3,2,8,7,5]=>[4,3,7,8,5,2,1,6]=>1011001
[3,2,7,1,8,6,4,5]=>[6,3,2,8,1,7,4,5]=>[3,2,8,5,1,6,7,4]=>0101011
[3,2,1,6,8,5,7,4]=>[2,3,1,7,8,6,5,4]=>[3,1,2,6,8,4,7,5]=>0100011
[3,2,6,1,8,7,4,5]=>[7,3,2,6,1,4,8,5]=>[3,2,6,4,8,5,1,7]=>0101101
[4,2,6,8,1,7,3,5]=>[7,8,4,2,1,6,3,5]=>[6,8,5,1,7,3,4,2]=>0011011
[4,3,6,8,7,1,2,5]=>[7,1,4,3,2,6,8,5]=>[4,3,6,8,5,2,1,7]=>1011001
[3,2,6,1,7,8,4,5]=>[8,3,2,6,1,4,7,5]=>[3,2,6,4,7,8,5,1]=>0101101
[5,3,6,4,8,7,1,2]=>[7,1,6,5,3,4,8,2]=>[6,4,5,3,8,2,1,7]=>1001101
[1,8,2,5,7,3,6,4]=>[1,6,7,8,2,5,3,4]=>[1,6,5,2,7,3,8,4]=>0001111
[7,8,3,1,4,2,6,5]=>[4,3,6,1,8,2,7,5]=>[4,1,6,2,3,7,8,5]=>0010101
[4,3,6,1,8,2,7,5]=>[7,8,4,3,6,1,2,5]=>[4,3,8,5,6,1,7,2]=>0010111
[1,5,8,6,4,3,2,7]=>[1,3,4,6,5,8,2,7]=>[1,5,8,7,2,3,4,6]=>0000011
[7,8,5,1,6,3,2,4]=>[3,6,5,1,8,2,7,4]=>[6,2,7,8,4,1,3,5]=>0010101
[6,8,1,7,4,3,2,5]=>[3,4,7,8,1,6,2,5]=>[6,8,5,1,3,7,2,4]=>0001011
[5,1,7,6,4,3,2,8]=>[3,4,6,5,1,7,2,8]=>[7,2,4,5,1,3,6,8]=>0001010
[1,2,8,5,6,3,7,4]=>[1,2,7,6,8,5,3,4]=>[1,2,7,3,8,4,6,5]=>0000111
[4,1,7,5,2,3,8,6]=>[5,4,1,2,8,7,3,6]=>[4,2,8,6,7,3,1,5]=>0110011
[7,8,1,4,6,3,2,5]=>[3,6,8,1,4,2,7,5]=>[6,2,7,8,5,4,1,3]=>0011101
[1,5,7,8,4,3,2,6]=>[1,3,4,8,5,2,7,6]=>[1,5,7,8,6,2,3,4]=>0000101
[2,4,7,5,1,3,8,6]=>[5,2,1,4,8,7,3,6]=>[2,4,8,6,7,3,1,5]=>0100011
[1,6,5,8,4,3,2,7]=>[1,3,4,8,6,5,2,7]=>[1,6,5,8,7,2,3,4]=>0000111
[3,6,2,5,4,1,7,8]=>[4,5,3,6,2,1,7,8]=>[3,5,2,6,1,4,7,8]=>0001100
[4,3,6,2,8,1,5,7]=>[8,6,4,3,2,1,5,7]=>[4,3,8,7,5,2,6,1]=>0011111
[6,1,2,5,4,7,8,3]=>[8,1,5,6,2,4,7,3]=>[6,4,7,8,3,5,2,1]=>1001101
[6,2,4,5,1,3,7,8]=>[5,6,2,1,4,3,7,8]=>[5,4,1,6,3,2,7,8]=>0111100
[1,5,8,4,3,6,7,2]=>[1,7,4,8,5,3,6,2]=>[1,5,8,2,7,6,3,4]=>0000111
[2,5,4,1,6,7,3,8]=>[7,2,4,5,1,6,3,8]=>[2,6,7,3,4,5,1,8]=>0001010
[6,8,4,3,2,1,5,7]=>[2,3,4,8,1,6,5,7]=>[6,8,7,5,1,2,3,4]=>0001011
[5,3,8,2,1,6,4,7]=>[2,6,8,5,3,1,4,7]=>[6,1,2,8,7,4,5,3]=>0001111
[7,3,2,8,5,1,6,4]=>[6,3,5,8,7,2,1,4]=>[7,1,6,2,3,5,8,4]=>0000111
[6,3,7,2,5,1,8,4]=>[8,5,7,6,3,2,1,4]=>[8,4,6,2,5,3,7,1]=>0001111
[6,7,8,3,5,2,1,4]=>[2,5,8,3,1,6,7,4]=>[5,1,2,6,7,8,4,3]=>0011001
[2,1,5,7,8,6,3,4]=>[2,1,6,3,5,8,7,4]=>[2,1,5,7,8,4,3,6]=>1010001
[3,2,6,1,7,4,5,8]=>[7,3,2,6,1,4,5,8]=>[3,2,6,4,7,5,1,8]=>0101110
[2,5,8,4,1,3,7,6]=>[4,2,1,7,5,8,3,6]=>[2,5,7,3,1,4,8,6]=>0100011
[3,6,8,2,1,7,4,5]=>[2,7,3,8,1,6,4,5]=>[3,6,8,5,1,2,7,4]=>0001011
[4,8,7,3,2,1,5,6]=>[2,3,7,4,1,5,8,6]=>[4,8,6,5,1,2,3,7]=>0001101
[2,3,6,5,1,4,8,7]=>[5,2,3,1,6,4,8,7]=>[2,3,6,4,1,5,8,7]=>0010101
[2,3,6,4,1,5,8,7]=>[4,2,3,6,1,5,8,7]=>[2,3,6,5,1,4,8,7]=>0001101
[2,3,4,8,7,6,1,5]=>[6,2,3,4,1,7,8,5]=>[2,3,4,8,5,1,6,7]=>0001001
[7,3,5,4,8,1,2,6]=>[8,1,5,7,3,4,2,6]=>[5,3,8,6,4,7,2,1]=>1001111
[2,1,4,5,8,7,3,6]=>[2,1,7,4,5,3,8,6]=>[2,1,4,5,8,6,3,7]=>1000101
[6,4,3,5,8,7,1,2]=>[7,1,4,6,3,5,8,2]=>[6,5,3,4,8,2,1,7]=>1001101
[2,3,4,8,7,5,1,6]=>[5,2,3,4,7,1,8,6]=>[2,3,4,8,6,1,5,7]=>0000101
[2,7,6,5,4,8,1,3]=>[8,2,1,5,6,7,4,3]=>[2,7,4,5,6,8,3,1]=>0100011
[6,3,5,7,8,2,1,4]=>[2,8,6,3,1,5,7,4]=>[7,8,4,3,6,5,1,2]=>0011101
[2,3,4,8,5,6,1,7]=>[6,2,3,4,8,5,1,7]=>[2,3,4,8,7,1,6,5]=>0000111
[2,3,4,8,7,1,6,5]=>[6,2,3,4,7,1,8,5]=>[2,3,4,6,1,8,5,7]=>0000101
[2,3,4,8,5,1,7,6]=>[5,2,3,4,7,8,1,6]=>[2,3,4,7,1,5,8,6]=>0000011
[7,4,3,5,8,2,6,1]=>[6,8,4,7,3,5,2,1]=>[8,1,6,5,3,4,7,2]=>0001111
[2,3,4,8,5,1,6,7]=>[5,2,3,4,8,1,6,7]=>[2,3,4,8,7,6,1,5]=>0000111
[6,1,4,2,8,5,7,3]=>[7,4,8,1,6,2,5,3]=>[7,5,6,2,4,1,8,3]=>0010111
[4,8,6,5,3,2,7,1]=>[7,3,5,4,6,8,2,1]=>[4,8,1,7,2,3,5,6]=>0000011
[8,6,5,1,2,4,7,3]=>[7,1,5,2,6,8,4,3]=>[7,4,2,1,8,3,5,6]=>1010011
[6,3,8,5,7,1,2,4]=>[7,1,8,3,6,2,5,4]=>[7,5,6,2,1,8,4,3]=>1010111
[8,1,2,5,6,3,7,4]=>[7,1,6,8,2,5,3,4]=>[7,3,6,5,2,1,8,4]=>1001111
[8,6,1,5,7,2,3,4]=>[7,6,1,2,3,8,5,4]=>[7,5,3,1,8,4,2,6]=>0111011
[7,2,5,8,1,6,4,3]=>[4,6,8,7,2,5,1,3]=>[6,5,2,7,1,4,8,3]=>0001111
[8,2,1,5,7,6,3,4]=>[2,6,7,1,3,8,5,4]=>[7,5,3,8,4,1,2,6]=>0011011
[5,2,8,6,1,7,3,4]=>[7,6,5,2,1,8,3,4]=>[7,3,5,1,8,4,2,6]=>0011011
[1,2,8,6,5,7,3,4]=>[1,2,7,3,6,8,5,4]=>[1,2,8,4,3,7,5,6]=>0010011
[8,2,5,6,3,7,1,4]=>[7,6,8,2,3,5,1,4]=>[7,1,8,4,2,6,5,3]=>0011111
[8,5,2,6,3,7,1,4]=>[7,6,5,2,8,3,1,4]=>[7,1,8,4,2,6,3,5]=>0010111
[8,1,6,5,7,3,2,4]=>[3,7,6,1,8,2,5,4]=>[8,4,1,3,6,2,7,5]=>0010111
[3,5,8,6,2,7,1,4]=>[7,6,3,2,5,8,1,4]=>[3,5,7,1,8,4,2,6]=>0010011
[7,1,4,2,6,5,8,3]=>[8,4,6,1,7,2,5,3]=>[7,5,8,3,6,2,4,1]=>0010111
[4,7,6,1,5,2,8,3]=>[8,5,6,4,1,7,2,3]=>[4,8,3,6,7,2,5,1]=>0001011
[8,1,3,5,7,6,2,4]=>[6,7,1,3,2,8,5,4]=>[7,5,2,8,4,3,1,6]=>0111011
[6,1,4,3,5,7,8,2]=>[8,4,6,1,3,5,7,2]=>[6,5,3,7,8,2,4,1]=>0011101
[3,8,2,7,6,1,5,4]=>[5,6,3,7,2,8,1,4]=>[3,8,4,7,1,5,2,6]=>0001011
[4,8,7,3,2,6,5,1]=>[5,3,6,4,7,2,8,1]=>[4,6,2,3,8,1,5,7]=>0000101
[4,8,7,3,6,1,5,2]=>[5,6,7,4,3,1,8,2]=>[4,8,2,6,1,5,3,7]=>0001101
[5,8,7,6,3,1,4,2]=>[4,3,6,1,5,7,8,2]=>[4,1,5,8,2,3,6,7]=>0010001
[5,8,7,6,2,4,3,1]=>[3,4,6,2,5,7,8,1]=>[4,2,5,8,1,3,6,7]=>0010001
[5,8,7,6,4,1,3,2]=>[3,4,1,6,5,7,8,2]=>[3,1,5,8,2,4,6,7]=>0100001
[7,3,5,2,6,4,1,8]=>[4,6,5,7,3,2,1,8]=>[5,3,6,2,7,1,4,8]=>0001110
[2,5,6,7,8,3,1,4]=>[3,2,8,1,5,6,7,4]=>[2,5,6,7,8,4,1,3]=>0010001
[3,2,1,6,7,8,4,5]=>[2,3,1,8,4,6,7,5]=>[3,1,2,6,7,8,5,4]=>0101001
[5,2,1,6,7,8,4,3]=>[2,4,8,5,1,6,7,3]=>[5,1,2,4,6,7,8,3]=>0001001
[5,3,6,1,7,8,4,2]=>[4,8,6,5,3,1,7,2]=>[6,1,4,5,3,7,8,2]=>0001101
[5,3,6,2,7,8,4,1]=>[4,8,6,5,3,2,7,1]=>[7,8,1,4,5,3,6,2]=>0001101
[5,3,6,2,7,8,1,4]=>[8,6,5,3,2,1,7,4]=>[7,8,4,3,5,2,6,1]=>0011101
[6,3,5,2,7,1,8,4]=>[8,7,5,6,3,2,1,4]=>[5,3,8,4,6,2,7,1]=>0001111
[5,3,4,1,2,7,8,6]=>[4,1,5,3,2,8,7,6]=>[5,2,1,4,3,7,8,6]=>1011001
[3,4,5,7,2,1,8,6]=>[2,8,3,4,5,7,1,6]=>[3,4,5,8,6,7,1,2]=>0000011
[4,2,1,6,7,8,3,5]=>[2,8,4,1,3,6,7,5]=>[6,7,8,5,3,4,1,2]=>0011001
[4,3,6,1,7,8,2,5]=>[8,6,4,3,1,2,7,5]=>[4,3,6,2,7,8,5,1]=>0011101
[1,5,6,7,8,4,2,3]=>[1,4,2,8,5,6,7,3]=>[1,5,6,7,8,3,2,4]=>0100001
[4,3,6,1,7,8,5,2]=>[5,8,4,3,6,1,7,2]=>[4,3,6,1,5,7,8,2]=>0010101
[4,2,1,6,7,8,5,3]=>[2,5,4,1,8,6,7,3]=>[6,7,8,3,4,1,2,5]=>0010001
[2,4,6,7,1,8,5,3]=>[5,2,8,4,7,6,1,3]=>[2,4,6,7,1,5,8,3]=>0000011
[2,5,6,7,8,1,4,3]=>[4,2,8,1,5,6,7,3]=>[2,4,1,5,6,7,8,3]=>0010001
[1,4,3,6,2,5,7,8]=>[1,6,4,3,2,5,7,8]=>[1,4,3,6,5,2,7,8]=>0011100
[1,4,3,7,6,8,2,5]=>[1,8,4,3,2,7,6,5]=>[1,4,3,7,6,8,5,2]=>0011011
[1,5,4,8,2,6,3,7]=>[1,6,8,5,4,2,3,7]=>[1,5,4,6,2,8,7,3]=>0001111
[1,2,3,6,5,8,4,7]=>[1,2,3,8,6,5,4,7]=>[1,2,3,6,5,8,7,4]=>0000111
[6,8,2,4,5,7,1,3]=>[7,8,2,1,4,6,5,3]=>[6,7,5,4,1,8,3,2]=>0111011
[7,8,1,4,5,3,6,2]=>[6,5,8,1,4,3,7,2]=>[7,8,2,5,4,1,6,3]=>0011101
[7,5,1,8,6,2,4,3]=>[4,6,5,1,8,7,2,3]=>[4,1,7,2,6,8,3,5]=>0010011
[7,4,1,8,2,6,3,5]=>[6,8,4,7,1,2,3,5]=>[7,3,4,8,5,1,6,2]=>0001111
[7,2,8,3,6,1,5,4]=>[5,6,8,7,2,3,1,4]=>[8,4,7,1,5,2,6,3]=>0001111
[6,1,2,8,3,5,4,7]=>[5,1,8,6,2,3,4,7]=>[5,2,1,8,7,4,6,3]=>1001111
[6,2,4,1,8,7,3,5]=>[7,4,6,2,1,3,8,5]=>[4,2,6,3,8,5,1,7]=>0011101
[1,2,4,8,3,7,6,5]=>[1,2,6,4,7,8,3,5]=>[1,2,4,8,5,7,3,6]=>0000011
[2,5,3,8,1,7,4,6]=>[7,2,8,5,3,1,4,6]=>[2,8,6,1,7,4,5,3]=>0001111
[5,3,1,4,8,2,7,6]=>[7,3,5,1,4,8,2,6]=>[7,2,3,5,4,1,8,6]=>0011011
[4,8,2,3,7,6,1,5]=>[6,7,2,4,3,8,1,5]=>[4,8,5,3,2,7,1,6]=>0101011
[4,8,2,3,7,1,6,5]=>[6,7,2,4,8,3,1,5]=>[4,7,1,6,3,2,8,5]=>0100111
[4,8,1,2,3,7,6,5]=>[6,1,2,4,7,8,3,5]=>[4,8,5,7,3,2,1,6]=>1100011
[6,3,8,1,5,2,4,7]=>[5,8,6,3,1,2,4,7]=>[5,1,8,7,4,3,6,2]=>0011111
[1,5,3,8,2,4,7,6]=>[1,7,5,3,2,8,4,6]=>[1,7,4,3,5,2,8,6]=>0011011
[3,5,1,2,8,7,4,6]=>[7,1,3,5,2,4,8,6]=>[3,8,6,4,5,2,1,7]=>1001101
[3,4,8,7,2,6,1,5]=>[6,7,3,4,2,1,8,5]=>[3,4,6,1,8,5,2,7]=>0001101
[3,4,8,1,7,2,6,5]=>[6,7,3,4,8,1,2,5]=>[3,4,6,1,7,2,8,5]=>0000111
[1,3,4,8,2,7,6,5]=>[1,6,3,4,7,8,2,5]=>[1,3,4,8,5,7,2,6]=>0000011
[3,4,8,1,2,7,6,5]=>[6,1,3,4,7,8,2,5]=>[3,4,8,5,7,2,1,6]=>1000011
[3,4,8,2,7,1,6,5]=>[6,7,3,4,8,2,1,5]=>[3,4,7,1,6,2,8,5]=>0000111
[4,2,5,8,1,7,6,3]=>[6,7,4,2,5,8,1,3]=>[5,8,3,4,2,7,1,6]=>0010011
[4,3,1,2,5,8,7,6]=>[3,1,4,2,5,7,8,6]=>[4,2,1,3,5,8,6,7]=>1010001
[3,1,4,2,5,8,7,6]=>[4,3,1,2,5,7,8,6]=>[4,2,3,1,5,8,6,7]=>0110001
[7,8,3,5,4,1,6,2]=>[6,4,5,8,3,1,7,2]=>[5,3,6,1,7,8,2,4]=>0001101
[6,4,2,1,7,3,8,5]=>[2,8,4,7,6,1,3,5]=>[7,3,4,8,5,6,1,2]=>0000111
[3,7,6,4,8,5,1,2]=>[5,1,3,8,6,7,4,2]=>[3,8,2,1,5,6,7,4]=>1000011
[1,7,6,5,3,2,8,4]=>[1,3,8,5,6,7,2,4]=>[1,8,4,5,6,7,2,3]=>0000011
[4,7,6,5,1,2,8,3]=>[8,1,5,4,6,7,2,3]=>[4,8,3,5,6,7,2,1]=>1000011
[4,7,6,5,3,1,8,2]=>[8,3,5,4,6,7,1,2]=>[4,8,2,3,5,6,7,1]=>0000011
[4,7,2,1,5,3,6,8]=>[2,5,7,4,1,3,6,8]=>[4,5,1,2,7,6,3,8]=>0001110
[4,7,1,6,2,3,8,5]=>[8,6,1,4,7,2,3,5]=>[4,6,2,8,5,7,3,1]=>0100111
[3,2,8,5,4,6,1,7]=>[6,3,2,5,8,4,1,7]=>[3,2,8,7,1,6,4,5]=>0100111
[3,7,6,5,8,1,4,2]=>[4,8,3,1,6,7,5,2]=>[3,4,1,7,5,6,8,2]=>0010011
[3,7,6,5,1,2,4,8]=>[5,1,3,2,6,7,4,8]=>[3,7,4,2,1,5,6,8]=>1010010
[3,1,6,8,4,2,5,7]=>[4,3,1,8,2,6,5,7]=>[6,8,7,5,2,3,1,4]=>0101011
[4,7,6,8,3,5,1,2]=>[5,1,8,4,3,7,6,2]=>[4,7,6,8,2,1,5,3]=>1001011
[2,7,6,5,8,1,3,4]=>[8,2,1,3,6,7,5,4]=>[2,7,5,6,8,4,3,1]=>0110011
[2,7,6,5,8,4,1,3]=>[4,2,1,8,6,7,5,3]=>[2,7,5,6,8,3,1,4]=>0100011
[5,1,2,4,6,3,8,7]=>[6,1,5,2,4,3,8,7]=>[6,3,5,4,2,1,8,7]=>1011101
[4,1,7,8,5,2,3,6]=>[5,4,1,2,8,3,7,6]=>[4,2,7,8,6,3,1,5]=>0110101
[5,1,8,4,7,2,3,6]=>[7,8,1,5,2,4,3,6]=>[7,3,1,8,6,4,5,2]=>0101111
[4,1,8,7,5,2,3,6]=>[5,4,1,2,7,3,8,6]=>[4,2,8,6,3,1,5,7]=>0110101
[4,7,1,6,3,2,8,5]=>[3,8,6,4,7,1,2,5]=>[4,6,1,3,8,5,7,2]=>0000111
[6,8,1,4,3,7,2,5]=>[7,4,8,1,3,6,2,5]=>[6,7,2,4,1,8,5,3]=>0011011
[8,7,3,2,4,1,6,5]=>[4,3,6,2,7,1,8,5]=>[6,1,4,2,3,8,5,7]=>0010101
[6,7,1,4,3,8,2,5]=>[8,4,7,1,3,6,2,5]=>[6,8,5,3,7,2,4,1]=>0011011
[7,1,8,5,4,3,2,6]=>[3,4,5,8,7,1,2,6]=>[8,6,1,3,5,7,2,4]=>0000111
[3,5,7,8,2,4,1,6]=>[4,8,3,2,5,1,7,6]=>[3,5,7,8,6,1,4,2]=>0010101
[8,1,7,5,4,3,2,6]=>[3,4,5,7,8,1,2,6]=>[7,2,4,8,6,1,3,5]=>0000111
[2,1,7,3,4,6,8,5]=>[2,1,8,3,7,4,6,5]=>[2,1,8,5,7,6,4,3]=>1010111
[6,7,3,2,4,1,8,5]=>[4,3,8,2,7,6,1,5]=>[6,8,5,7,1,4,2,3]=>0010011
[8,7,2,4,3,6,1,5]=>[6,4,7,2,3,1,8,5]=>[4,2,6,1,8,5,3,7]=>0011101
[7,1,2,3,5,6,8,4]=>[8,1,2,7,3,5,6,4]=>[8,4,7,6,5,3,2,1]=>1101111
[8,6,2,4,3,1,7,5]=>[3,4,7,2,6,8,1,5]=>[4,2,7,1,3,8,5,6]=>0010011
[7,6,3,2,4,8,1,5]=>[8,3,6,2,4,7,1,5]=>[8,5,4,2,3,6,7,1]=>0011011
[8,6,3,2,4,7,1,5]=>[7,3,6,2,4,8,1,5]=>[7,1,8,5,4,2,3,6]=>0011011
[7,6,2,4,3,1,8,5]=>[3,4,8,2,6,7,1,5]=>[4,2,8,5,6,7,1,3]=>0010011
[1,4,8,2,7,3,5,6]=>[1,7,8,4,2,3,5,6]=>[1,4,7,5,2,8,6,3]=>0001111
[1,2,8,5,4,7,3,6]=>[1,2,7,5,8,4,3,6]=>[1,2,7,3,8,6,4,5]=>0000111
[2,4,8,1,7,3,6,5]=>[6,2,7,4,8,1,3,5]=>[2,4,6,1,7,3,8,5]=>0000111
[1,2,6,8,4,5,7,3]=>[1,2,7,8,4,6,5,3]=>[1,2,6,8,3,7,5,4]=>0001011
[7,4,6,1,5,2,3,8]=>[5,6,1,7,4,2,3,8]=>[6,2,7,3,1,5,4,8]=>0101110
[6,8,1,4,7,2,3,5]=>[7,8,1,2,4,6,3,5]=>[6,7,3,1,8,5,4,2]=>0111011
[7,1,3,6,5,4,2,8]=>[4,5,1,6,7,3,2,8]=>[6,3,1,4,7,2,5,8]=>0100110
[1,6,2,3,8,5,4,7]=>[1,5,2,8,6,3,4,7]=>[1,6,3,2,5,8,7,4]=>0100111
[1,5,8,2,7,6,3,4]=>[1,6,7,2,5,8,3,4]=>[1,5,7,3,8,4,2,6]=>0010011
[5,8,2,7,6,3,4,1]=>[4,6,7,2,5,8,3,1]=>[5,7,3,8,1,4,2,6]=>0010011
[2,5,1,8,7,6,3,4]=>[6,2,5,1,3,7,8,4]=>[2,5,3,8,4,1,6,7]=>0011001
[1,2,5,3,8,7,4,6]=>[1,2,7,5,3,4,8,6]=>[1,2,8,6,4,5,3,7]=>0001101
[2,5,3,8,7,1,6,4]=>[6,2,7,5,3,1,8,4]=>[2,6,1,8,4,5,3,7]=>0001101
[4,2,8,7,6,3,5,1]=>[5,6,4,2,3,7,8,1]=>[8,1,5,3,4,2,6,7]=>0011001
[6,3,1,8,7,2,5,4]=>[5,3,7,6,1,2,8,4]=>[5,1,8,4,6,2,3,7]=>0001101
[5,8,7,4,6,1,2,3]=>[6,1,2,7,5,4,8,3]=>[5,8,3,2,1,6,4,7]=>1100101
[6,8,5,1,2,4,7,3]=>[7,1,5,2,8,6,4,3]=>[6,7,4,2,1,8,3,5]=>1010011
[1,3,2,5,8,7,4,6]=>[1,3,2,7,5,4,8,6]=>[1,3,2,5,8,6,4,7]=>0100101
[3,5,1,8,7,4,6,2]=>[6,7,3,5,1,4,8,2]=>[3,6,4,5,1,8,2,7]=>0001101
[3,2,5,8,7,1,6,4]=>[6,3,2,7,5,1,8,4]=>[3,2,5,6,1,8,4,7]=>0100101
[3,4,8,7,6,2,5,1]=>[5,6,3,4,2,7,8,1]=>[3,4,8,1,5,2,6,7]=>0001001
[1,2,7,5,8,6,4,3]=>[1,2,4,6,8,7,5,3]=>[1,2,8,3,4,6,7,5]=>0000011
[6,8,1,3,7,5,2,4]=>[5,7,1,3,8,6,2,4]=>[6,7,2,8,4,3,1,5]=>0110011
[1,3,7,8,2,6,5,4]=>[1,5,3,6,8,2,7,4]=>[1,3,7,8,4,6,2,5]=>0000101
[2,7,8,1,3,6,5,4]=>[5,2,1,6,8,3,7,4]=>[2,7,8,4,6,3,1,5]=>0100101
[8,1,2,6,7,3,5,4]=>[5,1,7,8,2,3,6,4]=>[5,2,1,7,6,3,8,4]=>1001111
[8,1,2,6,7,5,3,4]=>[5,1,7,2,8,3,6,4]=>[7,6,3,8,4,2,1,5]=>1010111
[6,8,3,4,1,7,5,2]=>[5,4,7,3,8,6,1,2]=>[6,8,2,4,3,7,1,5]=>0010011
[6,8,3,7,4,1,5,2]=>[5,4,7,8,3,6,1,2]=>[6,7,1,5,3,8,2,4]=>0001011
[8,5,7,4,2,6,1,3]=>[6,4,2,7,8,5,1,3]=>[8,3,2,4,7,1,6,5]=>0100111
[8,2,7,1,4,6,3,5]=>[6,7,8,2,1,4,3,5]=>[8,5,1,6,4,2,7,3]=>0011111
[8,4,7,1,3,6,2,5]=>[6,7,1,8,4,3,2,5]=>[6,3,1,7,2,8,5,4]=>0101111
[1,6,8,3,7,5,2,4]=>[1,5,7,3,8,6,2,4]=>[1,6,8,4,3,7,2,5]=>0010011
[8,4,5,7,3,1,6,2]=>[6,3,7,8,4,5,1,2]=>[8,2,3,7,1,6,5,4]=>0001111
[8,3,7,2,4,6,1,5]=>[6,7,8,3,2,4,1,5]=>[8,5,2,7,1,6,4,3]=>0011111
[2,8,4,5,7,1,6,3]=>[6,2,7,8,4,5,1,3]=>[2,8,3,7,1,6,5,4]=>0001111
[8,7,4,5,2,6,1,3]=>[6,5,2,7,4,1,8,3]=>[6,1,8,3,2,5,4,7]=>0101101
[8,7,3,1,5,2,4,6]=>[5,3,7,1,2,4,8,6]=>[8,6,4,1,5,2,3,7]=>0011101
[5,1,4,2,3,8,6,7]=>[4,5,1,2,3,8,6,7]=>[5,3,1,4,2,8,7,6]=>0111011
[5,8,1,7,3,4,6,2]=>[6,7,8,1,5,3,4,2]=>[5,8,2,7,4,1,6,3]=>0010111
[8,1,5,7,2,4,6,3]=>[6,7,8,1,2,5,4,3]=>[7,4,1,6,5,2,8,3]=>0011111
[1,4,2,3,8,7,5,6]=>[1,4,2,3,7,5,8,6]=>[1,4,3,2,8,6,5,7]=>0110101
[6,1,2,8,7,5,3,4]=>[5,1,7,2,6,3,8,4]=>[8,4,2,1,5,6,3,7]=>1010101
[6,1,2,4,8,7,5,3]=>[5,1,7,2,6,4,8,3]=>[6,4,2,1,5,8,3,7]=>1010101
[3,1,8,4,6,7,5,2]=>[5,3,1,7,8,4,6,2]=>[7,6,4,8,2,3,1,5]=>0100111
[7,1,2,4,6,8,5,3]=>[5,1,8,2,7,4,6,3]=>[7,6,4,2,1,5,8,3]=>1010111
[7,1,5,3,2,8,6,4]=>[3,6,5,8,1,7,2,4]=>[5,1,3,7,2,6,8,4]=>0001011
[3,1,2,8,4,7,5,6]=>[3,1,2,7,8,4,5,6]=>[3,2,1,8,6,4,7,5]=>1100111
[1,4,2,3,8,5,7,6]=>[1,4,2,3,7,8,5,6]=>[1,4,3,2,7,5,8,6]=>0110011
[5,8,1,7,2,4,6,3]=>[6,7,8,1,5,2,4,3]=>[5,7,4,1,6,2,8,3]=>0010111
[5,8,1,3,4,7,6,2]=>[6,7,1,3,5,8,4,2]=>[5,8,2,7,4,3,1,6]=>0110011
[3,1,8,6,4,7,5,2]=>[5,3,1,7,6,8,4,2]=>[7,4,8,2,3,1,5,6]=>0100011
[8,1,2,6,7,4,5,3]=>[5,1,7,8,2,4,6,3]=>[5,2,1,8,3,7,6,4]=>1001111
[1,2,3,5,8,4,7,6]=>[1,2,3,7,5,8,4,6]=>[1,2,3,5,7,4,8,6]=>0000011
[1,2,3,5,8,6,4,7]=>[1,2,3,6,5,8,4,7]=>[1,2,3,5,8,7,4,6]=>0000011
[7,1,2,8,6,4,5,3]=>[5,1,6,8,2,7,4,3]=>[5,2,1,8,3,6,7,4]=>1001011
[3,1,7,8,4,6,5,2]=>[5,3,1,6,8,4,7,2]=>[6,4,7,8,2,3,1,5]=>0100101
[8,1,2,7,4,6,5,3]=>[5,1,6,7,8,2,4,3]=>[7,4,8,3,6,2,1,5]=>1000111
[8,1,2,7,3,6,5,4]=>[5,1,6,7,8,2,3,4]=>[8,4,7,3,6,2,1,5]=>1000111
[1,2,3,6,8,5,4,7]=>[1,2,3,5,8,6,4,7]=>[1,2,3,6,8,7,4,5]=>0000011
[3,6,2,5,4,1,8,7]=>[4,5,3,6,2,1,8,7]=>[3,5,2,6,1,4,8,7]=>0001101
[4,5,8,3,2,7,6,1]=>[6,3,7,4,5,8,2,1]=>[4,5,7,2,3,8,1,6]=>0000011
[4,7,6,3,8,5,2,1]=>[2,5,8,4,6,7,3,1]=>[4,8,1,2,5,6,7,3]=>0000011
[5,3,2,8,4,7,6,1]=>[6,3,7,5,2,8,4,1]=>[7,4,5,2,3,8,1,6]=>0001011
[2,1,5,8,4,7,6,3]=>[2,1,6,7,5,8,4,3]=>[2,1,5,7,4,8,3,6]=>1000011
[5,3,2,7,4,8,6,1]=>[6,3,8,5,2,7,4,1]=>[8,1,6,7,4,5,2,3]=>0001011
[4,6,8,3,7,5,2,1]=>[2,5,7,4,8,6,3,1]=>[4,6,7,3,8,1,2,5]=>0000011
[7,6,4,3,8,5,2,1]=>[2,5,4,8,6,7,3,1]=>[8,1,2,5,6,7,3,4]=>0000011
[8,4,5,3,2,7,6,1]=>[6,3,5,7,4,8,2,1]=>[7,2,3,5,4,8,1,6]=>0001011
[8,4,6,3,7,5,2,1]=>[2,5,7,6,8,4,3,1]=>[6,4,7,3,8,1,2,5]=>0000111
[3,7,2,8,6,5,4,1]=>[4,5,3,6,8,7,2,1]=>[3,8,1,4,6,7,2,5]=>0000011
[7,4,5,3,2,8,6,1]=>[6,3,5,8,4,7,2,1]=>[8,1,6,7,2,3,5,4]=>0001011
[2,1,7,5,4,8,6,3]=>[2,1,6,5,8,7,4,3]=>[2,1,8,3,6,7,4,5]=>1000011
[1,6,4,8,2,5,3,7]=>[1,5,8,6,4,2,3,7]=>[1,6,2,5,4,8,7,3]=>0001111
[1,6,2,4,3,7,8,5]=>[1,4,8,2,6,3,7,5]=>[1,4,2,7,8,5,6,3]=>0010101
[1,5,6,2,4,7,8,3]=>[1,8,6,2,5,4,7,3]=>[1,5,7,8,3,6,4,2]=>0010101
[1,6,7,2,4,3,8,5]=>[1,4,8,2,7,6,3,5]=>[1,4,2,6,8,5,7,3]=>0010011
[1,5,7,8,3,2,4,6]=>[1,3,8,2,5,4,7,6]=>[1,5,7,8,6,4,2,3]=>0010101
[1,5,8,7,3,2,4,6]=>[1,3,7,2,5,4,8,6]=>[1,5,8,6,4,2,3,7]=>0010101
[1,5,8,3,2,4,7,6]=>[1,3,7,2,5,8,4,6]=>[1,5,7,4,2,3,8,6]=>0010011
[1,6,8,5,2,3,7,4]=>[1,7,2,5,8,6,3,4]=>[1,6,7,3,2,8,4,5]=>0100011
[1,6,4,2,3,7,5,8]=>[1,4,2,7,6,3,5,8]=>[1,7,5,6,3,2,4,8]=>0100110
[1,5,8,6,2,4,7,3]=>[1,7,6,2,5,8,4,3]=>[1,5,7,4,2,8,3,6]=>0010011
[1,7,5,2,8,6,4,3]=>[1,4,6,5,8,7,2,3]=>[1,8,3,6,7,2,4,5]=>0000011
[8,6,1,4,2,7,5,3]=>[5,4,7,1,6,8,2,3]=>[8,3,7,2,4,1,5,6]=>0010011
[6,7,1,4,3,5,8,2]=>[8,4,7,1,3,6,5,2]=>[6,7,5,3,8,2,4,1]=>0011011
[1,7,6,4,3,5,8,2]=>[1,8,4,6,3,7,5,2]=>[1,7,5,3,4,6,8,2]=>0001011
[8,1,6,4,2,7,5,3]=>[5,4,7,6,8,1,2,3]=>[8,3,7,2,4,6,1,5]=>0000111
[4,7,1,3,8,2,5,6]=>[8,7,1,4,3,2,5,6]=>[4,8,6,2,7,5,3,1]=>0101111
[7,4,1,3,8,2,5,6]=>[8,4,1,7,3,2,5,6]=>[8,6,2,4,7,5,3,1]=>0101111
[1,8,6,4,2,7,5,3]=>[1,5,4,7,6,8,2,3]=>[1,8,3,4,7,2,5,6]=>0000011
[8,7,1,3,6,2,5,4]=>[5,6,1,7,3,2,8,4]=>[5,3,1,6,2,8,4,7]=>0101101
[6,1,4,3,8,2,5,7]=>[8,4,6,1,3,2,5,7]=>[8,7,5,3,6,2,4,1]=>0011111
[7,2,5,6,8,4,1,3]=>[4,8,2,7,1,5,6,3]=>[7,6,5,1,4,8,3,2]=>0101111
[6,1,8,3,7,2,5,4]=>[5,7,8,6,1,3,2,4]=>[5,1,7,2,8,4,6,3]=>0001111
[1,4,8,3,6,2,5,7]=>[1,6,8,4,3,2,5,7]=>[1,4,6,2,8,7,5,3]=>0001111
[3,7,5,8,6,2,1,4]=>[2,6,3,1,8,7,5,4]=>[3,8,4,1,2,6,7,5]=>0010011
[5,7,6,8,3,4,1,2]=>[4,1,8,3,5,7,6,2]=>[5,7,6,8,2,1,4,3]=>1010011
[3,7,6,8,4,5,1,2]=>[5,1,3,8,4,7,6,2]=>[3,7,6,8,2,1,5,4]=>1001011
[3,7,4,6,5,8,1,2]=>[8,1,3,6,7,4,5,2]=>[3,6,4,7,5,8,2,1]=>1000111
[1,6,2,7,5,8,3,4]=>[1,8,7,2,6,3,5,4]=>[1,7,5,6,3,8,4,2]=>0010111
[1,6,4,8,5,7,2,3]=>[1,7,2,8,6,4,5,3]=>[1,8,3,2,7,5,6,4]=>0100111
[1,7,6,8,4,5,2,3]=>[1,5,2,8,4,7,6,3]=>[1,7,6,8,3,2,5,4]=>0101011
[7,8,1,3,2,6,4,5]=>[3,6,1,8,2,4,7,5]=>[3,1,7,8,5,2,6,4]=>0101101
[1,8,6,7,2,4,3,5]=>[1,4,7,2,3,8,6,5]=>[1,4,2,8,5,3,7,6]=>0011011
[7,8,1,4,2,6,3,5]=>[6,4,8,1,2,3,7,5]=>[7,8,5,2,4,1,6,3]=>0011101
[4,8,7,5,6,1,3,2]=>[3,6,1,4,7,5,8,2]=>[3,1,4,8,2,6,5,7]=>0100101
[2,7,5,1,8,4,3,6]=>[4,2,8,5,7,1,3,6]=>[2,8,6,1,4,5,7,3]=>0000111
[5,7,1,2,4,3,8,6]=>[4,1,8,2,5,7,3,6]=>[4,2,1,5,8,6,7,3]=>1010011
[4,3,7,6,8,2,5,1]=>[5,8,4,3,2,7,6,1]=>[4,3,7,6,8,1,5,2]=>0011011
[3,2,6,8,5,7,1,4]=>[7,3,2,1,8,6,5,4]=>[3,2,6,8,4,1,7,5]=>0110011
[7,4,8,6,5,2,1,3]=>[2,5,1,6,8,7,4,3]=>[7,4,6,8,3,1,2,5]=>0100011
[8,4,7,1,2,5,6,3]=>[6,1,7,8,4,2,5,3]=>[6,2,1,8,3,7,5,4]=>1001111
[7,4,3,2,8,5,6,1]=>[6,3,4,8,7,2,5,1]=>[7,5,8,1,6,2,3,4]=>0000111
[7,6,2,1,5,8,4,3]=>[2,4,8,6,1,7,5,3]=>[7,5,1,2,4,6,8,3]=>0001011
[7,6,4,1,2,3,8,5]=>[4,1,2,8,6,7,3,5]=>[8,5,6,7,3,2,1,4]=>1100011
[4,7,8,1,3,5,6,2]=>[6,8,1,4,3,5,7,2]=>[4,6,5,3,1,7,8,2]=>0101101
[4,8,2,7,3,5,6,1]=>[6,7,8,4,2,3,5,1]=>[4,7,5,2,8,1,6,3]=>0001111
[8,2,3,7,1,5,6,4]=>[6,7,2,8,3,1,5,4]=>[6,1,7,5,3,2,8,4]=>0101111
[7,8,2,4,3,5,6,1]=>[6,4,8,2,3,5,7,1]=>[4,2,7,8,1,6,5,3]=>0011101
[4,6,5,2,8,3,1,7]=>[3,8,5,4,6,2,1,7]=>[4,8,7,1,3,5,6,2]=>0000111
[6,8,5,2,7,4,3,1]=>[3,4,7,5,8,6,2,1]=>[6,8,1,3,7,2,4,5]=>0000011
[6,8,1,2,4,5,3,7]=>[5,1,8,2,4,6,3,7]=>[5,4,2,1,6,8,7,3]=>1011011
[4,1,6,5,8,2,3,7]=>[8,4,1,2,6,5,3,7]=>[4,2,6,5,8,7,3,1]=>0110111
[8,3,6,1,4,5,2,7]=>[5,6,8,3,1,4,2,7]=>[5,1,8,7,2,6,4,3]=>0011111
[6,3,8,7,4,2,5,1]=>[5,4,7,6,3,2,8,1]=>[6,2,4,8,1,5,3,7]=>0001101
[2,8,6,1,7,4,5,3]=>[5,2,7,6,1,8,4,3]=>[2,5,1,8,3,7,4,6]=>0001011
[4,8,3,2,5,6,7,1]=>[7,3,8,4,2,5,6,1]=>[4,8,1,7,6,5,2,3]=>0001111
[6,8,5,1,7,2,3,4]=>[7,5,1,2,8,6,3,4]=>[6,7,3,1,8,4,2,5]=>0110011
[7,3,6,5,8,2,1,4]=>[2,8,6,3,7,1,5,4]=>[7,5,8,4,3,6,1,2]=>0010111
[8,6,5,4,1,2,7,3]=>[7,1,4,5,6,8,2,3]=>[7,2,1,8,3,4,5,6]=>1000011
[6,1,5,3,8,7,2,4]=>[7,5,6,1,3,2,8,4]=>[6,2,5,3,8,4,1,7]=>0011101
[7,6,1,5,8,2,3,4]=>[8,6,1,2,3,7,5,4]=>[8,4,2,6,7,5,3,1]=>0111011
[3,6,8,5,1,2,7,4]=>[7,1,3,5,8,6,2,4]=>[3,6,7,2,1,8,4,5]=>1000011
[6,5,2,4,8,1,7,3]=>[7,8,5,2,6,4,1,3]=>[7,1,8,3,5,6,4,2]=>0010111
[3,4,8,5,2,6,7,1]=>[7,5,3,4,8,2,6,1]=>[3,4,8,1,7,6,2,5]=>0000111
[7,2,1,5,8,6,3,4]=>[2,6,8,1,3,7,5,4]=>[8,4,1,2,6,7,5,3]=>0011011
[5,4,8,3,7,6,1,2]=>[6,1,7,5,4,8,3,2]=>[5,4,7,3,8,2,1,6]=>1001011
[6,5,4,8,1,2,7,3]=>[7,1,8,5,6,4,2,3]=>[6,4,5,7,2,1,8,3]=>1000111
[6,5,4,7,1,2,8,3]=>[8,1,7,5,6,4,2,3]=>[6,4,5,8,3,7,2,1]=>1000111
[8,1,5,4,3,7,2,6]=>[7,4,5,8,1,3,2,6]=>[8,6,3,5,1,7,2,4]=>0001111
[8,1,7,2,5,4,6,3]=>[6,5,7,8,1,2,4,3]=>[6,2,5,1,8,3,7,4]=>0001111
[7,4,1,5,3,2,8,6]=>[3,5,4,8,1,7,2,6]=>[8,6,7,2,5,1,3,4]=>0001011
[7,1,5,8,4,6,2,3]=>[6,8,1,7,2,5,4,3]=>[7,4,8,3,1,6,5,2]=>0101111
[7,6,1,3,8,5,2,4]=>[5,8,1,3,6,7,2,4]=>[8,4,3,1,5,6,7,2]=>0110011
[7,6,8,2,4,5,1,3]=>[5,8,2,1,4,7,6,3]=>[5,4,1,7,6,8,3,2]=>0111011
[8,7,1,5,2,6,3,4]=>[6,5,7,1,2,3,8,4]=>[5,2,8,4,1,6,3,7]=>0011101
[8,6,2,7,3,1,5,4]=>[3,5,7,6,2,8,1,4]=>[5,2,7,1,3,8,4,6]=>0001011
[8,6,7,2,4,1,5,3]=>[5,4,7,2,1,8,6,3]=>[4,2,5,1,8,3,7,6]=>0011011
[6,8,7,3,4,1,5,2]=>[5,4,7,3,1,6,8,2]=>[5,1,6,8,2,4,3,7]=>0011001
[8,7,2,1,4,6,3,5]=>[2,6,7,1,4,3,8,5]=>[8,5,4,1,2,6,3,7]=>0011101
[8,5,7,2,1,4,3,6]=>[2,4,7,1,8,5,3,6]=>[4,1,2,7,3,8,6,5]=>0010111
[5,8,7,3,1,4,2,6]=>[4,3,7,1,5,2,8,6]=>[4,1,5,8,6,2,3,7]=>0010101
[8,7,4,1,2,3,6,5]=>[4,1,2,6,7,3,8,5]=>[6,3,2,1,4,8,5,7]=>1100101
[8,4,3,1,7,2,6,5]=>[6,3,4,7,8,1,2,5]=>[6,1,7,2,3,4,8,5]=>0000111
[8,4,3,1,2,7,6,5]=>[3,1,4,6,7,8,2,5]=>[8,5,7,2,1,3,4,6]=>1000011
[8,6,1,3,7,2,5,4]=>[5,7,1,6,3,8,2,4]=>[5,3,1,7,2,8,4,6]=>0101011
[8,1,6,4,7,2,5,3]=>[5,7,6,8,1,4,2,3]=>[5,1,7,2,8,3,6,4]=>0001111
[8,4,7,5,1,6,2,3]=>[6,5,1,7,8,4,2,3]=>[8,3,1,6,4,7,2,5]=>0100111
[8,3,2,6,5,1,4,7]=>[5,3,6,2,8,1,4,7]=>[8,7,4,2,3,6,1,5]=>0010111
[8,4,7,2,1,5,3,6]=>[2,5,7,8,4,1,3,6]=>[7,3,8,6,1,2,5,4]=>0001111
[8,7,3,1,2,4,6,5]=>[3,1,6,2,7,4,8,5]=>[6,4,2,1,3,8,5,7]=>1010101
[8,7,2,1,3,4,6,5]=>[2,6,1,3,7,4,8,5]=>[6,4,3,1,2,8,5,7]=>0110101
[1,2,7,3,5,4,8,6]=>[1,2,5,8,3,7,4,6]=>[1,2,5,3,8,6,7,4]=>0001011
[1,3,8,2,4,5,7,6]=>[1,7,3,2,4,8,5,6]=>[1,3,7,5,4,2,8,6]=>0011011
[1,2,3,8,4,6,7,5]=>[1,2,3,7,8,4,6,5]=>[1,2,3,7,6,4,8,5]=>0000111
[1,2,7,8,3,6,4,5]=>[1,2,6,8,3,4,7,5]=>[1,2,7,8,5,3,6,4]=>0001101
[7,6,3,1,5,2,4,8]=>[5,3,6,1,2,7,4,8]=>[7,4,1,5,2,3,6,8]=>0011010
[6,8,4,5,1,2,7,3]=>[7,1,5,8,4,6,2,3]=>[6,7,2,1,8,3,5,4]=>1001011
[7,3,6,1,5,2,4,8]=>[5,6,7,3,1,2,4,8]=>[5,1,6,2,7,4,3,8]=>0011110
[6,7,5,4,1,2,8,3]=>[8,1,4,5,7,6,2,3]=>[6,8,3,4,5,7,2,1]=>1000011
[5,6,7,4,1,8,2,3]=>[8,4,1,7,5,6,2,3]=>[5,6,7,2,4,8,3,1]=>0100011
[6,3,8,1,5,2,7,4]=>[7,5,8,6,3,1,2,4]=>[8,4,6,1,7,2,5,3]=>0001111
[4,6,8,5,7,1,2,3]=>[7,1,2,4,8,6,5,3]=>[4,6,8,3,2,1,7,5]=>1100011
[4,6,7,5,8,1,2,3]=>[8,1,2,4,7,6,5,3]=>[4,6,7,5,8,3,2,1]=>1100011
[4,7,5,6,8,1,2,3]=>[8,1,2,4,7,5,6,3]=>[4,7,6,5,8,3,2,1]=>1100111
[5,8,3,1,6,7,2,4]=>[7,3,8,1,5,2,6,4]=>[5,8,4,1,7,6,2,3]=>0010111
[5,7,3,1,6,8,2,4]=>[8,3,7,1,5,2,6,4]=>[5,7,6,2,3,8,4,1]=>0010111
[5,7,4,8,1,6,2,3]=>[6,8,1,7,5,4,2,3]=>[5,8,3,1,6,4,7,2]=>0100111
[5,4,6,8,1,7,2,3]=>[7,8,1,5,4,6,2,3]=>[5,4,6,8,3,1,7,2]=>0101011
[4,5,6,8,7,1,2,3]=>[7,1,2,4,5,6,8,3]=>[4,5,6,8,3,2,1,7]=>1100001
[4,7,6,8,5,1,2,3]=>[5,1,2,4,8,7,6,3]=>[4,7,6,8,3,2,1,5]=>1100011
[4,6,7,8,5,1,2,3]=>[5,1,2,4,8,6,7,3]=>[4,6,7,8,3,2,1,5]=>1100001
[5,4,7,8,1,6,2,3]=>[6,8,1,5,4,2,7,3]=>[5,4,7,8,3,1,6,2]=>0101101
[5,2,1,7,8,6,3,4]=>[2,6,5,1,3,8,7,4]=>[5,3,7,8,4,1,2,6]=>0011001
[4,7,8,6,5,1,2,3]=>[5,1,2,4,6,8,7,3]=>[4,7,8,3,2,1,5,6]=>1100001
[4,8,7,6,5,1,2,3]=>[5,1,2,4,6,7,8,3]=>[4,8,3,2,1,5,6,7]=>1100001
[4,2,6,3,1,5,8,7]=>[3,6,4,2,1,5,8,7]=>[6,5,1,3,4,2,8,7]=>0011101
[2,5,3,1,6,4,8,7]=>[3,2,6,5,1,4,8,7]=>[2,6,4,5,1,3,8,7]=>0001101
[2,7,5,3,6,4,1,8]=>[4,2,6,5,7,3,1,8]=>[2,6,3,7,1,4,5,8]=>0000110
[2,1,3,7,5,4,8,6]=>[2,1,3,5,8,7,4,6]=>[2,1,3,8,6,7,4,5]=>1000011
[2,3,1,8,6,5,4,7]=>[3,2,1,5,6,8,4,7]=>[2,3,1,8,7,4,5,6]=>0100011
[2,5,3,1,8,6,4,7]=>[3,2,6,5,1,8,4,7]=>[2,8,7,4,5,1,3,6]=>0001011
[4,2,8,3,1,6,5,7]=>[3,6,4,2,8,1,5,7]=>[6,1,3,4,2,8,7,5]=>0010111
[1,2,3,8,6,4,7,5]=>[1,2,3,7,6,8,4,5]=>[1,2,3,7,4,8,5,6]=>0000011
[1,2,3,7,4,8,6,5]=>[1,2,3,6,8,7,4,5]=>[1,2,3,7,4,6,8,5]=>0000011
[1,2,7,6,3,8,4,5]=>[1,2,8,6,3,7,4,5]=>[1,2,7,4,6,8,5,3]=>0001011
[1,2,3,6,4,8,7,5]=>[1,2,3,7,6,4,8,5]=>[1,2,3,8,5,6,4,7]=>0000101
[1,2,3,7,6,4,8,5]=>[1,2,3,8,6,7,4,5]=>[1,2,3,8,5,6,7,4]=>0000011
[7,1,8,4,2,3,5,6]=>[4,8,1,7,2,3,5,6]=>[8,6,3,1,4,7,5,2]=>0101111
[4,2,6,3,1,8,5,7]=>[3,8,4,2,6,1,5,7]=>[8,7,5,6,1,3,4,2]=>0010111
[5,4,2,8,3,1,6,7]=>[3,8,4,5,2,1,6,7]=>[8,7,6,1,3,4,5,2]=>0001111
[1,2,8,6,3,7,4,5]=>[1,2,7,6,3,8,4,5]=>[1,2,8,5,3,7,4,6]=>0001011
[1,2,6,3,8,4,7,5]=>[1,2,7,8,6,3,4,5]=>[1,2,8,5,6,3,7,4]=>0000111
[1,2,3,8,7,4,6,5]=>[1,2,3,6,7,4,8,5]=>[1,2,3,6,4,8,5,7]=>0000101
[1,2,3,8,7,6,4,5]=>[1,2,3,6,4,7,8,5]=>[1,2,3,8,5,4,6,7]=>0001001
[2,6,5,7,1,4,3,8]=>[4,2,7,1,6,5,3,8]=>[2,4,1,6,5,7,3,8]=>0010110
[3,4,8,6,1,2,5,7]=>[6,1,3,4,2,8,5,7]=>[3,4,8,7,5,2,1,6]=>1001011
[2,5,7,1,4,8,6,3]=>[6,2,8,1,5,7,4,3]=>[2,5,7,4,1,6,8,3]=>0010011
[4,8,6,7,1,3,5,2]=>[5,7,1,4,3,8,6,2]=>[4,5,3,1,8,2,7,6]=>0101011
[4,8,6,7,2,1,5,3]=>[2,5,7,4,1,8,6,3]=>[4,5,1,2,8,3,7,6]=>0001011
[5,8,6,7,2,4,3,1]=>[3,4,7,2,5,8,6,1]=>[4,2,5,8,1,3,7,6]=>0010011
[3,2,5,7,6,1,4,8]=>[6,3,2,1,5,7,4,8]=>[3,2,5,7,4,1,6,8]=>0110010
[4,8,6,7,1,2,5,3]=>[5,1,7,4,2,8,6,3]=>[4,5,2,1,8,3,7,6]=>1001011
[3,8,4,7,1,5,2,6]=>[5,7,3,8,4,1,2,6]=>[3,7,2,8,6,1,5,4]=>0001111
[4,1,3,8,5,2,6,7]=>[5,4,1,3,8,2,6,7]=>[8,7,6,2,4,3,1,5]=>0110111
[4,8,6,7,3,2,5,1]=>[5,3,7,4,2,8,6,1]=>[4,8,1,5,2,3,7,6]=>0001011
[4,8,6,7,3,1,2,5]=>[3,1,7,4,2,8,6,5]=>[4,8,5,2,1,3,7,6]=>1001011
[3,1,5,7,6,2,4,8]=>[6,3,1,2,5,7,4,8]=>[5,7,4,2,3,1,6,8]=>0110010
[5,8,6,7,3,2,4,1]=>[4,3,7,2,5,8,6,1]=>[5,8,1,4,2,3,7,6]=>0010011
[1,7,3,5,8,6,2,4]=>[1,6,8,3,2,7,5,4]=>[1,7,5,2,6,8,4,3]=>0011011
[7,3,5,8,6,1,2,4]=>[6,1,8,3,2,7,5,4]=>[7,5,2,1,6,8,4,3]=>1011011
[2,7,1,5,8,6,3,4]=>[6,2,8,1,3,7,5,4]=>[2,8,4,1,6,7,5,3]=>0011011
[2,4,7,1,8,5,6,3]=>[6,2,8,4,7,1,5,3]=>[2,4,6,1,7,5,8,3]=>0000111
[4,7,5,8,3,1,6,2]=>[6,3,8,4,7,5,1,2]=>[4,7,1,6,5,8,2,3]=>0000111
[7,3,5,8,6,2,1,4]=>[2,6,8,3,1,7,5,4]=>[7,5,1,2,6,8,4,3]=>0011011
[1,2,7,6,8,3,5,4]=>[1,2,5,8,3,7,6,4]=>[1,2,5,3,7,6,8,4]=>0001011
[6,7,4,1,8,5,3,2]=>[3,5,4,8,7,6,1,2]=>[6,8,2,5,7,1,3,4]=>0000011
[7,1,4,2,8,5,6,3]=>[6,4,8,1,7,2,5,3]=>[6,2,4,1,7,5,8,3]=>0010111
[7,2,6,8,5,4,1,3]=>[4,5,2,8,7,1,6,3]=>[8,3,2,5,7,6,1,4]=>0100111
[2,7,6,8,3,1,5,4]=>[3,2,5,8,1,7,6,4]=>[2,5,1,3,7,6,8,4]=>0001011
[6,7,3,1,8,5,4,2]=>[4,3,5,8,7,6,1,2]=>[6,8,2,3,5,7,1,4]=>0000011
[6,7,1,8,5,4,3,2]=>[3,4,5,8,7,6,1,2]=>[6,7,1,3,5,8,2,4]=>0000011
[7,8,4,2,1,6,5,3]=>[2,5,4,6,8,1,7,3]=>[7,8,3,4,6,1,2,5]=>0000101
[7,8,3,6,4,2,1,5]=>[2,4,6,8,3,1,7,5]=>[7,8,5,3,6,1,2,4]=>0001101
[7,8,3,5,6,2,1,4]=>[2,6,8,3,1,5,7,4]=>[6,5,1,2,7,8,4,3]=>0011101
[5,2,6,3,8,1,7,4]=>[7,8,6,5,2,3,1,4]=>[6,3,7,1,8,4,5,2]=>0001111
[6,3,2,8,4,7,1,5]=>[7,3,8,6,2,4,1,5]=>[6,4,7,1,8,5,2,3]=>0001111
[4,5,6,8,3,2,1,7]=>[2,3,8,4,5,6,1,7]=>[4,5,6,8,7,1,2,3]=>0000011
[5,6,1,4,2,3,7,8]=>[4,6,1,2,5,3,7,8]=>[5,6,3,1,4,2,7,8]=>0110100
[5,6,1,4,2,3,8,7]=>[4,6,1,2,5,3,8,7]=>[5,6,3,1,4,2,8,7]=>0110101
[5,1,4,3,6,2,8,7]=>[6,4,5,1,3,2,8,7]=>[5,3,6,2,4,1,8,7]=>0011101
[5,1,4,3,8,2,7,6]=>[7,4,5,1,3,8,2,6]=>[5,3,7,2,4,1,8,6]=>0011011
[5,7,2,4,1,8,6,3]=>[6,4,8,2,5,7,1,3]=>[4,2,5,7,1,6,8,3]=>0010011
[5,4,1,3,7,2,6,8]=>[7,4,1,5,3,2,6,8]=>[7,6,2,4,5,3,1,8]=>0101110
[4,8,3,1,6,7,5,2]=>[5,3,7,4,8,1,6,2]=>[4,8,2,3,7,6,1,5]=>0000111
[4,3,8,1,6,2,5,7]=>[6,8,4,3,1,2,5,7]=>[4,3,8,7,5,1,6,2]=>0011111
[5,8,1,4,7,2,6,3]=>[6,7,8,1,5,4,2,3]=>[5,6,4,1,7,2,8,3]=>0010111
[4,3,8,2,7,5,6,1]=>[6,7,4,3,8,2,5,1]=>[4,3,8,1,6,2,7,5]=>0010111
[1,4,8,3,7,5,6,2]=>[1,6,7,4,8,3,5,2]=>[1,4,8,2,6,3,7,5]=>0000111
[3,4,8,1,6,2,5,7]=>[6,8,3,4,1,2,5,7]=>[3,4,8,7,5,1,6,2]=>0001111
[3,4,2,1,8,6,5,7]=>[2,4,3,1,6,8,5,7]=>[3,4,1,2,8,7,5,6]=>0010011
[3,4,1,8,2,6,5,7]=>[6,4,3,1,8,2,5,7]=>[3,6,2,4,1,8,7,5]=>0010111
[3,6,7,8,4,1,2,5]=>[4,1,3,8,2,6,7,5]=>[3,6,7,8,5,2,1,4]=>1001001
[4,1,2,8,3,6,5,7]=>[6,1,4,2,8,3,5,7]=>[6,3,4,2,1,8,7,5]=>1010111
[1,4,3,2,8,6,5,7]=>[1,3,4,2,6,8,5,7]=>[1,4,2,3,8,7,5,6]=>0010011
[3,7,8,2,6,4,5,1]=>[5,6,3,8,2,4,7,1]=>[3,7,8,1,5,2,6,4]=>0001101
[2,4,8,6,3,1,5,7]=>[3,2,6,4,1,8,5,7]=>[2,4,8,7,5,1,3,6]=>0001011
[6,2,8,7,4,3,5,1]=>[5,4,7,6,2,3,8,1]=>[8,1,5,2,4,6,3,7]=>0001101
[7,4,1,8,5,2,6,3]=>[6,5,4,8,7,1,2,3]=>[6,1,7,2,5,8,3,4]=>0000111
[3,2,1,4,8,6,5,7]=>[2,3,1,4,6,8,5,7]=>[3,1,2,4,8,7,5,6]=>0100011
[3,1,2,4,8,6,5,7]=>[3,1,2,4,6,8,5,7]=>[3,2,1,4,8,7,5,6]=>1100011
[3,1,4,2,8,6,5,7]=>[4,3,1,2,6,8,5,7]=>[4,2,3,1,8,7,5,6]=>0110011
[2,1,3,4,8,6,5,7]=>[2,1,3,4,6,8,5,7]=>[2,1,3,4,8,7,5,6]=>1000011
[3,1,5,6,8,2,7,4]=>[7,3,1,8,5,6,2,4]=>[5,6,7,2,3,1,8,4]=>0100011
[5,1,6,3,8,4,7,2]=>[7,8,6,5,1,3,4,2]=>[6,3,7,4,5,1,8,2]=>0001111
[2,5,1,6,8,3,7,4]=>[7,2,8,5,1,6,3,4]=>[2,6,8,4,5,1,7,3]=>0001011
[5,1,2,6,8,3,7,4]=>[7,1,8,5,2,6,3,4]=>[6,8,4,5,2,1,7,3]=>1001011
[1,5,2,7,8,6,3,4]=>[1,6,5,2,3,8,7,4]=>[1,5,3,7,8,4,2,6]=>0011001
[5,7,2,8,6,1,3,4]=>[6,8,2,1,5,7,3,4]=>[5,8,4,1,6,7,3,2]=>0110011
[3,5,7,8,6,2,1,4]=>[2,6,3,1,5,8,7,4]=>[3,5,7,8,4,1,2,6]=>0010001
[5,7,8,6,4,1,2,3]=>[4,1,2,6,5,8,7,3]=>[5,7,8,3,2,1,4,6]=>1100001
[6,3,1,7,5,8,2,4]=>[8,3,7,1,6,2,5,4]=>[7,5,6,2,3,8,4,1]=>0010111
[2,5,3,7,8,6,1,4]=>[6,2,5,3,1,8,7,4]=>[2,7,8,4,3,5,1,6]=>0011001
[6,3,2,7,5,8,1,4]=>[8,3,7,2,6,1,5,4]=>[8,4,2,3,7,5,6,1]=>0010111
[6,7,4,2,5,1,8,3]=>[8,5,4,7,2,6,1,3]=>[5,2,6,8,3,4,7,1]=>0001011
[6,2,7,4,5,1,8,3]=>[8,5,7,6,2,4,1,3]=>[5,2,6,4,8,3,7,1]=>0001111
[6,2,3,7,5,8,1,4]=>[8,7,2,3,6,1,5,4]=>[8,4,3,2,7,5,6,1]=>0110111
[2,7,6,1,3,8,4,5]=>[8,2,1,6,3,7,4,5]=>[2,7,4,6,8,5,3,1]=>0101011
[2,7,6,1,3,8,5,4]=>[5,2,1,8,6,7,3,4]=>[2,7,3,1,5,6,8,4]=>0100011
[2,6,7,1,5,8,3,4]=>[8,2,7,1,3,6,5,4]=>[2,6,7,5,3,8,4,1]=>0011011
[2,6,7,4,1,8,5,3]=>[5,2,4,8,7,6,1,3]=>[2,6,7,1,5,8,3,4]=>0000011
[4,6,1,5,8,7,2,3]=>[7,6,1,4,2,5,8,3]=>[4,6,5,2,8,3,1,7]=>0101101
[4,6,1,5,8,2,7,3]=>[7,8,6,4,1,5,2,3]=>[4,8,3,6,5,1,7,2]=>0001111
[4,6,1,5,8,2,3,7]=>[8,6,1,4,2,5,3,7]=>[4,6,5,2,8,7,3,1]=>0101111
[4,2,5,6,8,3,1,7]=>[3,8,4,2,5,6,1,7]=>[5,6,8,7,1,3,4,2]=>0010011
[4,5,6,8,1,3,2,7]=>[3,8,1,4,5,6,2,7]=>[3,1,4,5,6,8,7,2]=>0100011
[5,1,7,3,8,4,2,6]=>[4,8,7,5,1,3,2,6]=>[5,1,4,8,6,3,7,2]=>0001111
[5,6,3,1,2,7,8,4]=>[3,1,8,6,5,2,7,4]=>[5,7,8,4,6,2,1,3]=>1000101
[5,6,1,3,2,7,8,4]=>[3,8,1,6,5,2,7,4]=>[3,1,5,7,8,4,6,2]=>0100101
[6,3,2,7,1,8,4,5]=>[8,3,7,6,2,1,4,5]=>[8,5,2,3,7,4,6,1]=>0001111
[4,7,2,1,3,8,6,5]=>[2,6,1,4,8,7,3,5]=>[4,7,3,1,2,6,8,5]=>0100011
[5,7,3,8,2,1,6,4]=>[2,6,8,7,5,3,1,4]=>[5,8,4,7,1,2,6,3]=>0000111
[2,5,1,7,3,8,6,4]=>[6,2,8,5,1,7,3,4]=>[2,8,4,5,1,6,7,3]=>0001011
[6,2,1,7,3,8,5,4]=>[2,5,8,7,6,1,3,4]=>[6,1,2,5,8,4,7,3]=>0000111
[5,3,2,1,8,4,7,6]=>[2,3,7,5,1,8,4,6]=>[7,4,5,1,2,3,8,6]=>0001011
[4,5,2,1,3,8,7,6]=>[2,5,1,4,3,7,8,6]=>[4,5,3,1,2,8,6,7]=>0101001
[1,6,3,4,5,8,2,7]=>[1,8,6,3,4,5,2,7]=>[1,6,5,4,3,8,7,2]=>0011111
[1,5,3,2,8,7,4,6]=>[1,3,7,5,2,4,8,6]=>[1,8,6,4,5,2,3,7]=>0001101
[1,7,6,4,5,8,3,2]=>[1,3,8,6,4,7,5,2]=>[1,7,5,4,6,8,2,3]=>0001011
[2,4,8,6,7,1,3,5]=>[7,2,1,4,3,8,6,5]=>[2,4,8,5,3,1,7,6]=>0101011
[3,7,4,8,2,1,6,5]=>[2,6,3,8,7,4,1,5]=>[3,8,5,7,1,2,6,4]=>0000111
[3,5,2,7,6,1,8,4]=>[8,6,3,5,2,7,1,4]=>[3,8,4,5,2,6,7,1]=>0001011
[5,8,2,7,4,1,6,3]=>[6,4,7,8,5,2,1,3]=>[5,8,3,7,1,6,2,4]=>0000111
[5,2,6,8,7,1,3,4]=>[7,5,2,1,3,6,8,4]=>[5,3,2,6,8,4,1,7]=>0111001
[6,3,2,1,8,5,7,4]=>[2,3,7,8,6,1,5,4]=>[7,5,6,1,2,3,8,4]=>0000111
[1,8,4,2,5,6,7,3]=>[1,7,4,8,2,5,6,3]=>[1,7,6,5,2,8,3,4]=>0001111
[5,1,3,2,8,6,7,4]=>[3,7,1,5,2,8,6,4]=>[3,1,8,4,5,2,7,6]=>0101011
[1,8,4,3,7,2,6,5]=>[1,6,4,7,8,3,2,5]=>[1,7,2,6,3,4,8,5]=>0000111
[8,4,7,2,3,1,5,6]=>[3,7,2,8,4,1,5,6]=>[8,6,1,3,2,7,5,4]=>0101111
[2,8,1,5,4,7,6,3]=>[6,2,5,7,1,8,4,3]=>[2,7,4,8,3,5,1,6]=>0001011
[1,7,2,4,6,5,8,3]=>[1,8,6,2,7,4,5,3]=>[1,7,5,8,3,6,4,2]=>0010111
[6,3,5,8,7,2,1,4]=>[2,7,6,3,1,5,8,4]=>[8,4,3,6,5,1,2,7]=>0011101
[2,5,7,8,4,1,6,3]=>[6,2,4,8,5,1,7,3]=>[2,5,6,1,7,8,3,4]=>0000101
[2,7,1,8,5,4,6,3]=>[6,2,5,8,7,1,4,3]=>[2,6,1,8,3,5,7,4]=>0000111
[5,8,6,2,1,3,7,4]=>[2,7,1,6,5,8,3,4]=>[5,7,3,1,2,8,4,6]=>0100011
[1,3,2,7,5,8,6,4]=>[1,3,2,6,8,7,5,4]=>[1,3,2,8,4,6,7,5]=>0100011
[1,4,2,5,8,3,7,6]=>[1,7,4,2,5,8,3,6]=>[1,5,7,3,4,2,8,6]=>0010011
[5,1,2,6,8,4,7,3]=>[7,1,8,5,2,6,4,3]=>[6,7,4,5,2,1,8,3]=>1001011
[3,1,2,6,5,8,4,7]=>[3,1,2,8,6,5,4,7]=>[3,2,1,6,5,8,7,4]=>1100111
[1,2,7,4,8,6,5,3]=>[1,2,5,6,8,7,4,3]=>[1,2,7,4,6,8,3,5]=>0000011
[2,3,1,7,5,4,8,6]=>[3,2,1,5,8,7,4,6]=>[2,3,1,8,6,7,4,5]=>0100011
[1,3,2,8,5,7,4,6]=>[1,3,2,7,8,5,4,6]=>[1,3,2,7,4,8,6,5]=>0100111
[1,2,6,4,8,7,3,5]=>[1,2,7,6,4,3,8,5]=>[1,2,8,5,4,6,3,7]=>0001101
[1,2,6,8,5,7,3,4]=>[1,2,7,3,8,6,5,4]=>[1,2,6,8,4,3,7,5]=>0010011
[1,5,6,8,2,7,3,4]=>[1,7,8,2,5,6,3,4]=>[1,5,6,8,4,2,7,3]=>0010011
[1,4,7,2,8,6,3,5]=>[1,6,8,4,2,7,3,5]=>[1,4,8,5,2,6,7,3]=>0001011
[1,6,7,8,2,5,3,4]=>[1,5,8,2,3,6,7,4]=>[1,6,7,8,4,2,5,3]=>0011001
[1,2,6,8,3,7,5,4]=>[1,2,5,7,8,6,3,4]=>[1,2,6,8,4,7,3,5]=>0000011
[1,5,7,8,2,3,6,4]=>[1,6,2,8,5,3,7,4]=>[1,5,6,3,2,7,8,4]=>0100101
[1,4,7,2,8,3,6,5]=>[1,6,8,4,7,2,3,5]=>[1,4,6,2,8,5,7,3]=>0000111
[1,2,8,4,7,3,6,5]=>[1,2,6,7,8,4,3,5]=>[1,2,7,3,6,4,8,5]=>0000111
[1,8,4,5,7,2,3,6]=>[1,7,2,8,4,5,3,6]=>[1,7,3,2,8,6,5,4]=>0101111
[2,8,3,5,1,4,7,6]=>[5,2,7,3,1,8,4,6]=>[2,5,1,7,4,3,8,6]=>0011011
[1,2,5,8,7,3,6,4]=>[1,2,6,7,5,3,8,4]=>[1,2,5,6,3,8,4,7]=>0000101
[1,2,7,8,6,3,5,4]=>[1,2,5,6,3,8,7,4]=>[1,2,5,3,7,8,4,6]=>0001001
[1,5,7,8,6,2,3,4]=>[1,6,2,3,5,8,7,4]=>[1,5,7,8,4,3,2,6]=>0110001
[1,3,7,6,2,8,4,5]=>[1,8,3,6,2,7,4,5]=>[1,3,7,4,6,8,5,2]=>0001011
[1,2,8,4,7,6,3,5]=>[1,2,6,7,4,8,3,5]=>[1,2,8,5,4,7,3,6]=>0001011
[1,2,6,8,7,5,3,4]=>[1,2,5,3,7,6,8,4]=>[1,2,6,8,4,3,5,7]=>0010001
[1,2,7,8,6,5,3,4]=>[1,2,5,3,6,8,7,4]=>[1,2,7,8,4,3,5,6]=>0010001
[5,6,2,1,4,8,7,3]=>[2,7,6,1,5,4,8,3]=>[5,8,3,6,4,1,2,7]=>0010101
[2,6,1,7,5,8,3,4]=>[8,2,7,1,6,3,5,4]=>[2,7,5,6,3,8,4,1]=>0010111
[2,6,1,7,4,8,3,5]=>[8,2,7,6,1,4,3,5]=>[2,6,4,7,3,8,5,1]=>0001111
[5,4,6,1,7,8,2,3]=>[8,6,1,5,4,2,7,3]=>[5,4,6,2,7,8,3,1]=>0101101
[2,6,1,4,7,8,5,3]=>[5,2,8,1,6,4,7,3]=>[2,6,4,1,5,7,8,3]=>0010101
[5,1,2,4,8,7,6,3]=>[6,1,5,2,4,7,8,3]=>[8,3,5,4,2,1,6,7]=>1011001
[5,4,6,3,1,8,7,2]=>[7,3,6,5,4,1,8,2]=>[5,4,8,2,3,6,1,7]=>0001101
[1,2,3,8,6,7,4,5]=>[1,2,3,7,4,8,6,5]=>[1,2,3,8,5,4,7,6]=>0001011
[1,2,3,8,7,5,4,6]=>[1,2,3,5,7,4,8,6]=>[1,2,3,8,6,4,5,7]=>0000101
[1,2,3,8,7,4,5,6]=>[1,2,3,7,4,5,8,6]=>[1,2,3,8,6,5,4,7]=>0001101
[7,8,1,4,3,6,2,5]=>[6,4,8,1,3,2,7,5]=>[6,2,4,1,7,8,5,3]=>0011101
[5,8,1,4,3,7,2,6]=>[7,4,8,1,5,3,2,6]=>[5,7,2,4,1,8,6,3]=>0010111
[2,6,1,4,3,7,5,8]=>[4,2,7,1,6,3,5,8]=>[2,4,1,7,5,6,3,8]=>0010110
[5,8,2,6,4,7,1,3]=>[7,6,2,8,5,1,4,3]=>[5,8,3,2,6,1,7,4]=>0100111
[5,8,1,3,2,6,4,7]=>[3,6,1,8,5,2,4,7]=>[3,1,5,6,2,8,7,4]=>0100111
[5,8,4,7,1,3,2,6]=>[3,7,1,8,5,4,2,6]=>[3,1,5,7,2,8,6,4]=>0100111
[3,7,1,4,2,6,5,8]=>[4,6,3,1,7,2,5,8]=>[3,4,1,6,2,7,5,8]=>0010110
[3,7,6,8,1,4,2,5]=>[4,8,3,1,2,7,6,5]=>[3,4,1,7,6,8,5,2]=>0011011
[4,7,5,8,2,6,1,3]=>[6,8,2,4,7,5,1,3]=>[4,7,1,6,5,8,3,2]=>0100111
[2,6,5,8,4,7,1,3]=>[7,2,1,8,6,5,4,3]=>[2,6,5,8,3,1,7,4]=>0100111
[7,6,4,8,5,2,3,1]=>[3,5,2,8,6,7,4,1]=>[8,1,3,2,5,6,7,4]=>0100011
[6,7,3,5,4,8,2,1]=>[2,8,5,7,3,6,4,1]=>[5,3,6,7,4,8,1,2]=>0001011
[6,8,3,7,5,2,4,1]=>[4,5,7,3,8,6,2,1]=>[6,8,1,4,3,7,2,5]=>0010011
[7,6,2,8,4,1,5,3]=>[5,4,8,6,2,7,1,3]=>[7,1,5,2,4,6,8,3]=>0001011
[7,6,3,4,8,2,5,1]=>[5,8,6,3,4,7,2,1]=>[8,1,5,4,3,6,7,2]=>0011011
[5,7,8,3,6,2,1,4]=>[2,6,8,3,5,1,7,4]=>[5,6,1,2,7,8,4,3]=>0010101
[4,6,7,8,3,5,2,1]=>[2,5,8,4,3,6,7,1]=>[4,6,7,8,1,2,5,3]=>0001001
[5,3,4,7,8,2,1,6]=>[2,8,5,3,4,1,7,6]=>[5,4,3,7,8,6,1,2]=>0011101
[5,3,8,2,4,1,6,7]=>[4,8,5,3,2,1,6,7]=>[8,7,6,1,4,3,5,2]=>0011111
[4,8,3,6,2,5,7,1]=>[7,6,8,4,3,2,5,1]=>[4,6,2,8,1,7,5,3]=>0001111
[4,8,3,5,7,2,6,1]=>[6,7,8,4,3,5,2,1]=>[4,7,2,8,1,6,5,3]=>0001111
[4,8,3,5,6,7,2,1]=>[2,7,8,4,3,5,6,1]=>[4,8,1,2,7,6,5,3]=>0001111
[4,7,8,3,5,6,2,1]=>[2,6,8,4,3,5,7,1]=>[4,7,8,1,2,6,5,3]=>0001101
[4,7,8,3,6,2,5,1]=>[5,6,8,4,3,2,7,1]=>[4,6,2,7,8,1,5,3]=>0001101
[5,8,3,7,2,6,4,1]=>[4,6,7,8,5,3,2,1]=>[5,7,2,6,3,8,1,4]=>0000111
[5,7,3,4,8,2,1,6]=>[2,8,7,3,5,4,1,6]=>[5,8,6,4,3,7,1,2]=>0010111
[5,8,4,2,3,1,6,7]=>[3,4,2,8,5,1,6,7]=>[5,8,7,6,1,3,2,4]=>0100111
[6,4,8,5,3,7,2,1]=>[2,7,5,8,6,4,3,1]=>[8,1,2,7,3,5,6,4]=>0000111
[6,4,3,7,8,5,2,1]=>[2,5,4,8,6,3,7,1]=>[7,8,1,2,5,6,3,4]=>0000101
[6,4,5,3,7,1,8,2]=>[8,7,5,6,4,3,1,2]=>[6,3,5,4,8,2,7,1]=>0001111
[5,7,4,2,3,1,6,8]=>[3,4,2,7,5,1,6,8]=>[5,7,6,1,3,2,4,8]=>0100110
[5,6,3,4,8,2,1,7]=>[2,8,6,3,5,4,1,7]=>[5,6,4,3,8,7,1,2]=>0010111
[6,3,5,4,7,8,2,1]=>[2,8,5,6,3,4,7,1]=>[5,3,6,4,7,8,1,2]=>0001101
[5,3,4,7,2,6,1,8]=>[6,7,5,3,4,2,1,8]=>[5,4,3,7,1,6,2,8]=>0011110
[4,7,3,6,8,2,5,1]=>[5,8,7,4,3,2,6,1]=>[4,8,1,5,3,7,6,2]=>0001111
[5,3,4,6,8,2,1,7]=>[2,8,5,3,4,6,1,7]=>[5,4,3,6,8,7,1,2]=>0011011
[5,3,4,6,7,1,8,2]=>[8,7,5,3,4,6,1,2]=>[5,4,3,6,8,2,7,1]=>0011011
[7,1,5,4,8,2,3,6]=>[8,5,1,7,2,4,3,6]=>[5,2,8,6,4,7,3,1]=>0101111
[7,1,4,8,5,2,3,6]=>[5,8,1,2,7,4,3,6]=>[7,3,1,5,8,6,4,2]=>0110111
[7,8,3,1,2,4,6,5]=>[3,1,6,2,8,4,7,5]=>[6,4,2,1,3,7,8,5]=>1010101
[7,3,8,1,2,4,6,5]=>[6,1,8,3,7,2,4,5]=>[6,2,1,8,5,7,4,3]=>1010111
[8,3,7,1,2,4,6,5]=>[6,1,7,3,8,2,4,5]=>[6,2,1,7,4,3,8,5]=>1010111
[8,3,6,1,2,4,7,5]=>[7,1,6,3,8,2,4,5]=>[7,4,3,6,2,1,8,5]=>1010111
[8,3,7,5,1,2,4,6]=>[5,1,7,3,8,2,4,6]=>[7,4,3,8,6,2,1,5]=>1010111
[7,3,6,1,2,4,8,5]=>[8,1,6,3,7,2,4,5]=>[8,5,7,4,3,6,2,1]=>1010111
[6,7,1,8,4,2,3,5]=>[4,8,1,7,2,6,3,5]=>[6,7,3,1,4,8,5,2]=>0101011
[6,7,1,4,2,3,8,5]=>[4,8,1,2,7,6,3,5]=>[6,8,5,7,3,1,4,2]=>0110011
[4,3,6,8,5,7,1,2]=>[7,1,4,3,8,6,5,2]=>[4,3,6,8,2,1,7,5]=>1010011
[6,1,2,5,4,8,3,7]=>[8,1,5,6,2,4,3,7]=>[6,4,8,7,3,5,2,1]=>1001111
[3,2,8,5,4,1,7,6]=>[4,3,2,5,7,8,1,6]=>[3,2,7,1,4,5,8,6]=>0100011
[7,8,2,1,4,6,3,5]=>[2,6,8,1,4,3,7,5]=>[7,8,5,4,1,2,6,3]=>0011101
[1,2,8,5,7,3,4,6]=>[1,2,7,3,8,5,4,6]=>[1,2,7,4,3,8,6,5]=>0010111
[1,3,6,2,5,7,8,4]=>[1,8,3,6,2,5,7,4]=>[1,3,7,8,4,6,5,2]=>0001101
[1,2,6,4,3,8,5,7]=>[1,2,4,8,6,3,5,7]=>[1,2,8,7,5,6,3,4]=>0000111
[1,2,7,4,6,8,3,5]=>[1,2,8,7,4,3,6,5]=>[1,2,8,5,4,7,6,3]=>0001111
[1,2,7,6,4,8,5,3]=>[1,2,5,8,6,7,4,3]=>[1,2,8,3,5,6,7,4]=>0000011
[1,2,6,8,5,4,7,3]=>[1,2,7,5,8,6,4,3]=>[1,2,6,8,3,7,4,5]=>0000011
[1,2,5,8,4,3,7,6]=>[1,2,4,7,5,8,3,6]=>[1,2,5,7,3,4,8,6]=>0000011
[2,3,6,5,8,1,7,4]=>[7,2,3,8,6,5,1,4]=>[2,3,6,5,7,1,8,4]=>0000111
[1,2,4,7,5,8,3,6]=>[1,2,8,4,7,5,3,6]=>[1,2,4,8,6,5,7,3]=>0000111
[1,2,5,7,3,8,6,4]=>[1,2,6,8,5,7,3,4]=>[1,2,5,7,3,6,8,4]=>0000011
[3,1,5,7,6,8,4,2]=>[4,3,1,8,5,7,6,2]=>[5,7,6,8,2,3,1,4]=>0100011
[1,2,7,4,6,8,5,3]=>[1,2,5,8,7,4,6,3]=>[1,2,8,3,5,7,6,4]=>0000111
[3,1,6,7,5,8,4,2]=>[4,3,1,8,7,6,5,2]=>[6,7,5,8,2,3,1,4]=>0100011
[4,6,2,7,5,8,3,1]=>[3,8,7,4,6,2,5,1]=>[4,8,1,3,7,5,6,2]=>0000111
[1,3,6,8,2,5,7,4]=>[1,7,3,8,2,6,5,4]=>[1,3,6,7,5,2,8,4]=>0001011
[1,2,4,8,7,3,6,5]=>[1,2,6,4,7,3,8,5]=>[1,2,4,6,3,8,5,7]=>0000101
[3,1,7,6,8,5,4,2]=>[4,3,1,5,8,7,6,2]=>[7,6,8,2,3,1,4,5]=>0100011
[1,2,6,8,5,7,4,3]=>[1,2,4,7,8,6,5,3]=>[1,2,6,8,3,4,7,5]=>0000011
[5,3,6,2,7,1,4,8]=>[7,6,5,3,2,1,4,8]=>[7,4,3,5,2,6,1,8]=>0011110
[7,6,2,4,5,8,1,3]=>[8,6,2,1,4,7,5,3]=>[8,3,2,6,7,5,4,1]=>0111011
[5,2,1,7,3,4,6,8]=>[2,7,5,1,3,4,6,8]=>[5,3,7,6,4,1,2,8]=>0011110
[6,3,2,8,4,5,7,1]=>[7,3,8,6,2,4,5,1]=>[6,4,8,1,7,5,2,3]=>0001111
[8,2,1,7,3,4,5,6]=>[2,7,8,1,3,4,5,6]=>[8,6,4,1,2,7,5,3]=>0011111
[8,6,3,7,2,4,5,1]=>[5,7,6,3,2,8,4,1]=>[8,1,5,2,7,4,3,6]=>0011011
[8,2,7,3,4,5,6,1]=>[6,7,8,2,3,4,5,1]=>[8,1,6,4,2,7,5,3]=>0011111
[8,1,6,2,3,4,5,7]=>[6,8,1,2,3,4,5,7]=>[8,7,5,3,1,6,4,2]=>0111111
[8,1,7,3,4,5,6,2]=>[6,7,8,1,3,4,5,2]=>[6,4,1,8,2,7,5,3]=>0011111
[7,2,1,8,3,4,5,6]=>[2,8,7,1,3,4,5,6]=>[7,5,3,8,6,4,1,2]=>0011111
[3,2,8,7,1,4,6,5]=>[6,3,2,1,7,4,8,5]=>[3,2,6,4,1,8,5,7]=>0110101
[3,8,1,7,2,4,5,6]=>[7,8,3,1,2,4,5,6]=>[3,8,6,4,1,7,5,2]=>0011111
[1,8,6,2,3,4,5,7]=>[1,6,2,3,4,8,5,7]=>[1,8,7,5,4,3,2,6]=>0111011
[2,8,7,3,4,5,6,1]=>[6,2,7,3,4,5,8,1]=>[2,8,1,6,5,4,3,7]=>0011101
[1,5,8,7,2,3,6,4]=>[1,6,2,7,5,3,8,4]=>[1,5,6,3,2,8,4,7]=>0100101
[6,2,3,7,5,4,1,8]=>[4,5,2,7,6,3,1,8]=>[6,3,2,5,7,1,4,8]=>0100110
[1,3,4,7,6,2,8,5]=>[1,8,3,4,6,7,2,5]=>[1,3,4,8,5,6,7,2]=>0000011
[3,8,2,6,5,1,7,4]=>[7,5,3,6,8,2,1,4]=>[3,7,1,8,4,6,2,5]=>0000111
[4,8,5,2,6,1,7,3]=>[7,6,5,4,8,2,1,3]=>[4,6,2,7,1,8,3,5]=>0000111
[4,5,1,3,7,2,8,6]=>[8,5,1,4,3,7,2,6]=>[4,8,6,7,2,5,3,1]=>0101011
[6,1,3,7,5,2,8,4]=>[8,5,1,7,6,3,2,4]=>[8,4,7,2,5,6,3,1]=>0100111
[3,4,8,6,5,1,7,2]=>[7,5,3,4,6,8,1,2]=>[3,4,7,1,8,2,5,6]=>0000011
[3,4,6,5,1,2,8,7]=>[5,1,3,4,6,2,8,7]=>[3,4,6,2,1,5,8,7]=>1000101
[2,7,1,3,8,6,5,4]=>[5,2,1,6,8,7,3,4]=>[2,8,4,6,7,3,1,5]=>0100011
[8,6,1,2,7,5,4,3]=>[4,1,5,7,6,8,2,3]=>[7,2,1,4,8,3,5,6]=>1000011
[3,8,1,6,2,7,5,4]=>[5,7,3,6,8,1,2,4]=>[3,7,2,8,4,6,1,5]=>0000111
[1,8,2,7,4,3,5,6]=>[1,4,7,8,2,3,5,6]=>[1,8,6,3,7,5,2,4]=>0001111
[1,8,4,2,6,3,5,7]=>[1,6,4,8,2,3,5,7]=>[1,8,7,5,2,6,3,4]=>0001111
[5,1,7,4,3,6,2,8]=>[6,4,7,5,1,3,2,8]=>[7,2,4,5,1,6,3,8]=>0001110
[1,8,5,4,3,7,2,6]=>[1,7,4,5,8,3,2,6]=>[1,7,2,8,6,3,4,5]=>0000111
[3,1,7,2,6,8,4,5]=>[8,3,1,7,2,4,6,5]=>[7,6,4,8,5,2,3,1]=>0101111
[5,1,7,4,2,6,8,3]=>[8,4,7,5,1,2,6,3]=>[8,3,7,6,2,4,5,1]=>0001111
[6,5,4,3,7,1,8,2]=>[8,7,4,5,6,3,1,2]=>[6,3,4,5,8,2,7,1]=>0000111
[6,3,2,8,5,7,1,4]=>[7,3,8,2,6,1,5,4]=>[7,5,6,1,8,4,2,3]=>0010111
[6,5,4,2,8,3,7,1]=>[7,8,4,5,6,2,3,1]=>[8,1,7,3,4,5,6,2]=>0000111
[7,2,8,6,3,1,4,5]=>[3,6,8,2,1,7,4,5]=>[7,4,2,6,8,5,1,3]=>0011011
[2,1,7,8,3,6,4,5]=>[2,1,6,8,3,4,7,5]=>[2,1,7,8,5,3,6,4]=>1001101
[5,4,2,7,3,8,1,6]=>[8,7,4,5,2,3,1,6]=>[8,6,3,4,5,2,7,1]=>0001111
[3,1,6,2,8,7,4,5]=>[7,3,1,6,2,4,8,5]=>[6,4,8,5,2,3,1,7]=>0101101
[6,3,1,7,8,5,2,4]=>[5,3,8,1,6,2,7,4]=>[7,8,4,1,5,6,2,3]=>0010101
[5,4,3,1,6,7,8,2]=>[8,3,4,5,1,6,7,2]=>[6,7,8,2,3,4,5,1]=>0001001
[4,6,7,2,5,1,3,8]=>[5,7,2,4,1,6,3,8]=>[4,5,1,6,7,3,2,8]=>0101010
[5,2,3,6,1,4,7,8]=>[6,5,2,3,1,4,7,8]=>[6,4,3,2,5,1,7,8]=>0111100
[1,5,3,6,2,4,7,8]=>[1,6,5,3,2,4,7,8]=>[1,6,4,3,5,2,7,8]=>0011100
[4,2,5,6,7,1,3,8]=>[7,4,2,1,5,6,3,8]=>[5,6,7,3,2,4,1,8]=>0110010
[5,2,1,6,3,4,7,8]=>[2,6,5,1,3,4,7,8]=>[5,3,6,4,1,2,7,8]=>0011100
[1,3,6,7,5,2,8,4]=>[1,8,3,5,7,6,2,4]=>[1,3,6,8,4,5,7,2]=>0000011
[1,3,6,7,2,5,8,4]=>[1,8,3,7,2,6,5,4]=>[1,3,6,8,4,7,5,2]=>0001011
[4,3,1,7,2,6,8,5]=>[8,3,4,1,7,2,6,5]=>[8,5,7,6,2,3,4,1]=>0010111
[5,3,2,1,7,4,8,6]=>[2,3,8,5,1,7,4,6]=>[8,6,7,4,5,1,2,3]=>0001011
[1,3,4,5,8,7,2,6]=>[1,7,3,4,5,2,8,6]=>[1,3,4,5,8,6,2,7]=>0000101
[6,3,4,5,8,1,7,2]=>[7,8,6,3,4,5,1,2]=>[6,5,4,3,7,1,8,2]=>0011111
[2,4,5,1,6,8,7,3]=>[7,2,5,4,1,6,8,3]=>[2,4,6,8,3,5,1,7]=>0001001
[3,1,2,5,6,8,7,4]=>[3,1,2,7,5,6,8,4]=>[3,2,1,5,6,8,4,7]=>1100001
[3,1,4,6,5,8,2,7]=>[8,3,1,4,6,5,2,7]=>[4,6,5,8,7,2,3,1]=>0100111
[2,3,4,5,8,6,1,7]=>[6,2,3,4,5,8,1,7]=>[2,3,4,5,8,7,1,6]=>0000011
[5,6,1,2,7,4,8,3]=>[8,1,7,6,5,2,4,3]=>[5,8,3,7,4,6,2,1]=>1000111
[5,3,1,4,2,7,8,6]=>[4,3,5,1,2,8,7,6]=>[4,1,5,2,3,7,8,6]=>0011001
[5,3,1,2,4,7,8,6]=>[3,1,5,2,4,8,7,6]=>[5,4,2,1,3,7,8,6]=>1011001
[2,3,6,7,1,5,8,4]=>[8,2,3,7,1,6,5,4]=>[2,3,6,8,4,7,5,1]=>0001011
[1,3,4,5,8,6,2,7]=>[1,6,3,4,5,8,2,7]=>[1,3,4,5,8,7,2,6]=>0000011
[7,3,2,5,6,8,4,1]=>[4,3,8,7,2,5,6,1]=>[8,1,4,7,6,5,2,3]=>0001111
[4,2,1,8,3,6,7,5]=>[2,7,4,1,8,3,6,5]=>[7,6,3,4,1,2,8,5]=>0010111
[6,2,1,7,3,5,8,4]=>[2,8,7,6,1,3,5,4]=>[8,4,6,3,7,5,1,2]=>0001111
[2,7,3,1,4,8,5,6]=>[3,2,8,1,7,4,5,6]=>[2,7,5,8,6,4,1,3]=>0010111
[3,2,1,5,7,8,4,6]=>[2,3,1,8,5,4,7,6]=>[3,1,2,5,7,8,6,4]=>0100101
[2,4,7,5,1,6,8,3]=>[8,2,5,4,7,1,6,3]=>[2,4,8,3,5,7,6,1]=>0000111
[2,1,6,8,3,7,4,5]=>[2,1,7,8,3,6,4,5]=>[2,1,6,8,5,3,7,4]=>1001011
[3,2,1,5,6,8,4,7]=>[2,3,1,8,5,6,4,7]=>[3,1,2,5,6,8,7,4]=>0100011
[2,6,1,8,3,5,4,7]=>[5,2,8,6,1,3,4,7]=>[2,5,1,8,7,4,6,3]=>0001111
[2,7,3,1,5,6,4,8]=>[3,2,6,7,1,5,4,8]=>[2,6,5,1,3,7,4,8]=>0001110
[2,4,8,5,1,6,3,7]=>[6,2,5,4,8,1,3,7]=>[2,4,6,1,8,7,3,5]=>0000111
[2,1,8,3,7,4,5,6]=>[2,1,7,8,3,4,5,6]=>[2,1,7,5,3,8,6,4]=>1001111
[3,2,1,8,4,5,6,7]=>[2,3,1,8,4,5,6,7]=>[3,1,2,8,7,6,5,4]=>0101111
[3,8,1,5,7,2,4,6]=>[7,8,3,1,2,5,4,6]=>[3,7,4,1,8,6,5,2]=>0011111
[1,2,6,8,4,7,3,5]=>[1,2,7,8,4,6,3,5]=>[1,2,6,7,3,8,5,4]=>0001011
[1,2,4,8,3,6,7,5]=>[1,2,7,4,8,3,6,5]=>[1,2,4,7,6,3,8,5]=>0000111
[4,1,2,7,8,3,6,5]=>[6,1,4,2,8,3,7,5]=>[6,3,4,2,1,7,8,5]=>1010101
[5,3,8,4,7,6,1,2]=>[6,1,7,5,3,8,4,2]=>[7,4,5,3,8,2,1,6]=>1001011
[8,7,1,2,5,4,6,3]=>[6,1,5,7,2,4,8,3]=>[8,3,5,2,1,6,4,7]=>1001101
[7,1,6,2,8,4,5,3]=>[5,8,6,7,1,2,4,3]=>[5,1,7,4,8,3,6,2]=>0001111
[1,2,8,5,3,6,4,7]=>[1,2,6,5,8,3,4,7]=>[1,2,6,3,8,7,4,5]=>0000111
[1,2,7,3,8,5,4,6]=>[1,2,5,8,7,3,4,6]=>[1,2,8,6,3,5,7,4]=>0000111
[1,6,2,8,4,3,5,7]=>[1,4,8,6,2,3,5,7]=>[1,8,7,5,2,4,6,3]=>0001111
[1,3,2,8,7,4,5,6]=>[1,3,2,7,4,5,8,6]=>[1,3,2,8,6,5,4,7]=>0101101
[1,2,8,4,3,7,5,6]=>[1,2,4,7,8,3,5,6]=>[1,2,8,6,3,4,7,5]=>0000111
[1,2,3,7,5,4,8,6]=>[1,2,3,5,8,7,4,6]=>[1,2,3,8,6,7,4,5]=>0000011
[7,4,6,3,8,5,1,2]=>[5,1,8,6,7,4,3,2]=>[6,4,8,2,1,5,7,3]=>1000111
[3,5,6,8,2,4,1,7]=>[4,8,3,2,5,6,1,7]=>[3,5,6,8,7,1,4,2]=>0010011
[2,6,7,8,1,4,5,3]=>[5,2,8,1,4,6,7,3]=>[2,5,4,1,6,7,8,3]=>0011001
[3,5,7,8,2,1,4,6]=>[2,8,3,1,5,4,7,6]=>[3,5,7,8,6,4,1,2]=>0010101
[6,4,7,3,8,1,5,2]=>[5,8,7,6,4,3,1,2]=>[7,1,5,4,6,3,8,2]=>0001111
[7,4,6,3,8,2,1,5]=>[2,8,6,7,4,3,1,5]=>[6,3,8,5,4,7,1,2]=>0001111
[2,5,7,8,3,1,6,4]=>[3,2,6,8,5,1,7,4]=>[2,5,6,1,3,7,8,4]=>0000101
[4,5,7,8,3,1,2,6]=>[3,1,8,4,5,2,7,6]=>[4,5,7,8,6,2,1,3]=>1000101
[5,4,7,2,8,1,3,6]=>[8,7,2,5,4,1,3,6]=>[5,4,7,3,2,8,6,1]=>0101111
[4,6,7,8,1,3,5,2]=>[5,8,1,4,3,6,7,2]=>[4,5,3,1,6,7,8,2]=>0101001
[4,6,7,8,1,5,2,3]=>[5,8,1,4,2,6,7,3]=>[4,6,7,8,3,1,5,2]=>0101001
[5,3,2,7,8,1,6,4]=>[6,3,8,5,2,1,7,4]=>[6,1,7,8,4,5,2,3]=>0001101
[3,5,7,8,2,1,6,4]=>[2,6,3,8,5,1,7,4]=>[3,5,6,1,2,7,8,4]=>0000101
[4,5,8,3,6,7,1,2]=>[7,1,8,4,5,3,6,2]=>[4,5,8,2,1,7,6,3]=>1000111
[4,2,8,3,7,1,6,5]=>[6,7,4,2,8,3,1,5]=>[7,1,6,3,4,2,8,5]=>0010111
[7,2,3,4,8,1,5,6]=>[8,7,2,3,4,1,5,6]=>[7,5,4,3,2,8,6,1]=>0111111
[7,6,3,4,8,5,1,2]=>[5,1,8,3,6,7,4,2]=>[8,2,1,5,6,7,4,3]=>1010011
[7,8,2,3,6,1,4,5]=>[6,8,2,3,1,4,7,5]=>[7,8,5,1,6,4,3,2]=>0111101
[4,2,6,3,7,1,5,8]=>[7,6,4,2,3,1,5,8]=>[7,5,3,4,2,6,1,8]=>0011110
[7,2,3,5,8,1,6,4]=>[6,8,2,7,3,5,1,4]=>[8,4,7,1,6,5,3,2]=>0101111
[3,5,8,4,1,2,7,6]=>[4,1,3,7,5,8,2,6]=>[3,5,7,2,1,4,8,6]=>1000011
[2,5,8,4,1,7,3,6]=>[7,2,4,8,5,1,3,6]=>[2,5,8,6,1,7,3,4]=>0000111
[2,6,4,5,1,3,7,8]=>[5,2,1,6,4,3,7,8]=>[2,6,3,1,5,4,7,8]=>0101100
[7,6,5,1,2,8,3,4]=>[8,1,5,2,6,7,3,4]=>[7,3,5,6,8,4,2,1]=>1010011
[7,6,5,1,8,2,4,3]=>[4,8,5,1,6,7,2,3]=>[4,1,8,3,5,6,7,2]=>0010011
[7,6,5,1,8,3,2,4]=>[3,8,5,1,6,7,2,4]=>[8,4,1,3,5,6,7,2]=>0010011
[7,6,5,1,8,3,4,2]=>[4,8,5,1,6,7,3,2]=>[4,1,7,3,5,6,8,2]=>0010011
[7,6,5,1,8,4,2,3]=>[4,8,1,5,6,7,2,3]=>[8,3,1,4,5,6,7,2]=>0100011
[6,7,4,2,5,3,1,8]=>[3,5,4,7,2,6,1,8]=>[5,2,6,7,1,3,4,8]=>0001010
[6,2,8,5,1,7,4,3]=>[4,7,5,8,6,2,1,3]=>[8,3,5,6,2,7,1,4]=>0000111
[3,2,7,8,6,1,5,4]=>[5,3,2,6,1,8,7,4]=>[3,2,5,1,7,8,4,6]=>0101001
[6,8,4,1,2,3,7,5]=>[4,1,2,7,8,6,3,5]=>[6,7,3,2,1,4,8,5]=>1100011
[3,8,1,5,2,7,6,4]=>[6,5,3,7,1,8,2,4]=>[3,8,4,7,2,5,1,6]=>0001011
[8,1,6,5,3,7,2,4]=>[7,5,6,1,8,3,2,4]=>[6,3,8,4,1,7,2,5]=>0010111
[7,1,4,6,3,2,8,5]=>[3,8,6,1,7,4,2,5]=>[6,4,1,3,8,5,7,2]=>0010111
[7,6,4,3,1,2,8,5]=>[3,1,4,8,6,7,2,5]=>[8,5,6,7,2,1,3,4]=>1000011
[1,8,2,5,3,7,6,4]=>[1,6,5,7,2,8,3,4]=>[1,8,4,7,3,5,2,6]=>0001011
[3,8,1,5,6,4,2,7]=>[4,6,3,8,1,5,2,7]=>[3,8,7,2,6,5,1,4]=>0001111
[7,5,4,1,3,2,8,6]=>[3,4,1,5,8,7,2,6]=>[3,1,8,6,7,2,4,5]=>0100011
[3,2,5,1,4,7,8,6]=>[5,3,2,1,4,8,7,6]=>[3,2,5,4,1,7,8,6]=>0111001
[5,1,3,4,6,7,8,2]=>[8,5,1,3,4,6,7,2]=>[6,7,8,2,5,4,3,1]=>0111001
[3,6,8,4,5,7,2,1]=>[2,7,3,8,4,6,5,1]=>[3,6,8,1,2,7,5,4]=>0001011
[3,7,8,4,5,6,2,1]=>[2,6,3,8,4,5,7,1]=>[3,7,8,1,2,6,5,4]=>0001101
[6,7,1,4,5,3,8,2]=>[8,5,7,1,4,6,3,2]=>[6,7,3,8,2,5,4,1]=>0011011
[5,7,1,4,6,3,8,2]=>[8,6,7,1,5,4,3,2]=>[5,7,3,8,2,6,4,1]=>0010111
[5,6,4,2,8,3,1,7]=>[3,8,4,6,5,2,1,7]=>[5,8,7,1,3,4,6,2]=>0000111
[5,8,1,4,6,3,2,7]=>[3,6,8,1,5,4,2,7]=>[5,8,7,2,6,4,1,3]=>0010111
[3,6,1,5,4,8,2,7]=>[8,5,3,6,1,4,2,7]=>[3,6,4,8,7,2,5,1]=>0001111
[3,8,1,5,4,7,2,6]=>[7,5,3,8,1,4,2,6]=>[3,7,2,5,1,8,6,4]=>0001111
[3,6,1,5,4,8,7,2]=>[7,5,3,6,1,4,8,2]=>[3,6,4,8,2,5,1,7]=>0001101
[3,6,1,5,4,7,2,8]=>[7,5,3,6,1,4,2,8]=>[3,6,4,7,2,5,1,8]=>0001110
[6,8,3,1,4,2,7,5]=>[4,3,7,1,8,6,2,5]=>[4,1,6,7,2,3,8,5]=>0010011
[7,8,4,2,6,5,1,3]=>[5,4,2,6,8,1,7,3]=>[7,8,3,2,4,6,1,5]=>0100101
[3,8,1,5,4,2,7,6]=>[4,5,3,7,1,8,2,6]=>[3,7,2,5,1,4,8,6]=>0001011
[5,8,1,4,7,3,6,2]=>[6,7,8,1,5,4,3,2]=>[5,6,4,1,8,2,7,3]=>0010111
[6,7,3,1,4,5,8,2]=>[8,3,7,1,4,6,5,2]=>[6,8,2,3,7,5,4,1]=>0011011
[3,8,1,5,4,2,6,7]=>[4,5,3,8,1,2,6,7]=>[3,8,7,6,2,5,1,4]=>0001111
[2,3,5,4,1,8,6,7]=>[4,2,3,5,1,8,6,7]=>[2,3,5,1,4,8,7,6]=>0001011
[2,3,6,4,8,1,5,7]=>[8,2,3,6,4,1,5,7]=>[2,3,8,7,5,4,6,1]=>0001111
[1,8,4,6,3,5,2,7]=>[1,5,6,8,4,3,2,7]=>[1,6,3,8,7,2,5,4]=>0001111
[5,4,8,6,2,1,3,7]=>[2,6,1,5,4,8,3,7]=>[5,4,8,7,3,1,2,6]=>0101011
[2,7,6,1,8,5,4,3]=>[4,2,5,8,6,7,1,3]=>[2,8,3,5,6,7,1,4]=>0000011
[2,3,4,7,6,1,5,8]=>[6,2,3,4,1,7,5,8]=>[2,3,4,7,5,1,6,8]=>0001010
[7,3,5,8,4,1,2,6]=>[4,1,8,7,3,5,2,6]=>[7,2,1,4,8,6,5,3]=>1001111
[7,3,5,8,4,1,6,2]=>[6,4,8,7,3,5,1,2]=>[8,2,4,7,1,6,5,3]=>0001111
[2,7,6,4,8,5,1,3]=>[5,2,1,8,6,7,4,3]=>[2,8,3,1,5,6,7,4]=>0100011
[1,8,4,3,6,2,5,7]=>[1,6,4,8,3,2,5,7]=>[1,6,2,8,7,5,3,4]=>0001111
[2,3,1,8,6,4,5,7]=>[3,2,1,6,4,8,5,7]=>[2,3,1,8,7,5,4,6]=>0101011
[2,7,6,4,8,5,3,1]=>[3,2,5,8,6,7,4,1]=>[2,8,1,3,5,6,7,4]=>0000011
[2,3,4,7,5,1,8,6]=>[5,2,3,4,8,7,1,6]=>[2,3,4,8,6,7,1,5]=>0000011
[2,3,4,7,5,1,6,8]=>[5,2,3,4,7,1,6,8]=>[2,3,4,7,6,1,5,8]=>0000110
[2,3,4,7,1,6,8,5]=>[8,2,3,4,7,1,6,5]=>[2,3,4,8,5,7,6,1]=>0000111
[2,3,4,6,1,8,7,5]=>[7,2,3,4,6,1,8,5]=>[2,3,4,8,5,6,1,7]=>0000101
[1,8,4,5,2,3,6,7]=>[1,5,2,8,4,3,6,7]=>[1,8,7,6,3,2,5,4]=>0101111
[7,4,8,5,3,2,6,1]=>[6,3,5,8,7,4,2,1]=>[7,2,3,5,8,1,6,4]=>0000111
[3,4,8,7,5,2,6,1]=>[6,5,3,4,7,2,8,1]=>[3,4,8,1,6,2,5,7]=>0000101
[3,2,8,6,1,5,4,7]=>[5,3,2,6,1,8,4,7]=>[3,2,5,1,8,7,4,6]=>0101011
[3,8,7,2,5,4,6,1]=>[6,5,3,7,2,4,8,1]=>[3,5,2,8,1,6,4,7]=>0001101
[3,7,2,5,1,4,8,6]=>[5,8,3,2,1,7,4,6]=>[3,5,1,8,6,7,4,2]=>0011011
[5,1,8,6,2,3,4,7]=>[6,5,1,2,3,8,4,7]=>[8,7,4,2,5,3,1,6]=>0111011
[2,5,4,1,8,6,3,7]=>[6,2,4,5,1,8,3,7]=>[2,8,7,3,4,5,1,6]=>0001011
[1,8,2,6,3,4,7,5]=>[1,7,6,2,8,3,4,5]=>[1,6,3,7,4,2,8,5]=>0010111
[7,2,3,6,1,4,8,5]=>[8,6,2,3,7,1,4,5]=>[8,5,7,4,3,2,6,1]=>0110111
[7,4,8,1,3,6,2,5]=>[6,8,1,7,4,3,2,5]=>[6,3,1,8,5,4,7,2]=>0101111
[8,6,1,4,7,3,2,5]=>[3,7,6,1,4,8,2,5]=>[7,2,8,5,4,1,3,6]=>0011011
[8,5,4,7,1,3,2,6]=>[3,7,1,5,8,4,2,6]=>[3,1,7,2,8,6,4,5]=>0100111
[2,3,1,8,5,4,6,7]=>[3,2,1,5,8,4,6,7]=>[2,3,1,8,7,6,4,5]=>0100111
[8,4,7,5,1,3,2,6]=>[3,5,1,7,8,4,2,6]=>[3,1,8,6,4,7,2,5]=>0100111
[6,8,3,1,7,2,4,5]=>[7,3,8,1,2,6,4,5]=>[6,7,4,1,8,5,2,3]=>0011011
[8,3,1,4,7,2,6,5]=>[6,3,7,1,8,4,2,5]=>[6,4,1,7,2,3,8,5]=>0010111
[8,3,7,1,6,5,2,4]=>[5,6,7,3,8,1,2,4]=>[8,4,3,7,2,6,1,5]=>0010111
[4,2,8,6,5,1,7,3]=>[7,5,4,2,6,8,1,3]=>[7,1,8,3,4,2,5,6]=>0010011
[5,1,6,4,2,3,8,7]=>[4,6,1,5,2,3,8,7]=>[6,3,1,4,5,2,8,7]=>0101101
[6,4,7,8,1,5,2,3]=>[5,8,1,6,4,2,7,3]=>[7,8,3,1,5,4,6,2]=>0101101
[5,8,7,6,1,4,2,3]=>[4,6,1,2,5,7,8,3]=>[5,8,3,1,4,2,6,7]=>0110001
[5,1,6,7,4,2,3,8]=>[4,7,1,5,2,6,3,8]=>[6,7,3,1,4,5,2,8]=>0101010
[8,4,7,6,1,5,2,3]=>[5,6,1,7,4,8,2,3]=>[8,3,1,5,4,7,2,6]=>0101011
[2,4,7,1,5,8,6,3]=>[6,2,8,4,1,7,5,3]=>[2,4,7,5,1,6,8,3]=>0001011
[6,8,7,5,1,4,2,3]=>[4,5,1,2,7,6,8,3]=>[6,8,3,1,4,2,5,7]=>0110001
[6,7,8,5,1,4,2,3]=>[4,5,1,2,8,6,7,3]=>[6,7,8,3,1,4,2,5]=>0110001
[7,8,6,5,1,4,2,3]=>[4,5,1,2,6,8,7,3]=>[7,8,3,1,4,2,5,6]=>0110001
[4,1,8,5,2,3,6,7]=>[5,4,1,2,8,3,6,7]=>[4,2,8,7,6,3,1,5]=>0110111
[5,4,1,3,6,7,2,8]=>[7,4,1,5,3,6,2,8]=>[6,7,2,4,5,3,1,8]=>0101010
[8,2,7,1,5,3,4,6]=>[5,7,8,2,1,3,4,6]=>[5,1,7,4,2,8,6,3]=>0011111
[7,3,8,1,5,4,2,6]=>[4,5,8,7,3,1,2,6]=>[8,6,1,4,7,2,5,3]=>0001111
[6,7,2,1,5,3,4,8]=>[2,5,7,1,3,6,4,8]=>[6,7,4,1,2,5,3,8]=>0011010
[5,6,8,7,1,4,3,2]=>[3,4,7,1,5,6,8,2]=>[5,6,8,2,4,1,3,7]=>0010001
[5,3,1,4,8,6,7,2]=>[7,3,5,1,4,8,6,2]=>[8,2,3,5,4,1,7,6]=>0011011
[5,8,1,6,4,3,7,2]=>[7,4,6,8,5,1,3,2]=>[5,7,3,6,1,8,2,4]=>0000111
[5,3,1,8,4,6,7,2]=>[7,3,8,5,1,4,6,2]=>[7,6,4,5,1,8,2,3]=>0001111
[8,3,1,5,4,6,7,2]=>[7,3,5,8,1,4,6,2]=>[8,2,3,5,1,7,6,4]=>0001111
[8,2,6,1,4,5,3,7]=>[5,6,8,2,1,4,3,7]=>[5,1,6,4,2,8,7,3]=>0011111
[7,2,6,1,5,3,4,8]=>[5,6,7,2,1,3,4,8]=>[5,1,7,4,2,6,3,8]=>0011110
[4,2,1,5,6,3,8,7]=>[2,6,4,1,5,3,8,7]=>[5,6,3,4,1,2,8,7]=>0010101
[5,7,6,8,1,4,3,2]=>[3,4,8,1,5,7,6,2]=>[5,7,6,8,2,4,1,3]=>0010011
[7,8,6,5,1,4,3,2]=>[3,4,5,1,6,8,7,2]=>[7,8,2,4,1,3,5,6]=>0010001
[5,3,6,2,1,8,7,4]=>[2,7,6,5,3,1,8,4]=>[8,4,5,3,6,1,2,7]=>0001101
[5,3,7,2,8,4,1,6]=>[4,8,7,5,3,2,1,6]=>[7,1,4,5,3,8,6,2]=>0001111
[6,2,4,5,1,8,7,3]=>[7,5,6,2,4,1,8,3]=>[5,4,2,8,3,6,1,7]=>0011101
[3,1,4,5,2,8,7,6]=>[5,3,1,4,2,7,8,6]=>[4,5,2,3,1,8,6,7]=>0101001
[6,3,7,1,8,4,2,5]=>[4,8,7,6,3,1,2,5]=>[6,1,4,8,5,3,7,2]=>0001111
[4,8,3,5,6,7,1,2]=>[7,1,8,4,3,5,6,2]=>[4,8,2,1,7,6,5,3]=>1001111
[1,8,3,5,6,7,2,4]=>[1,7,8,3,2,5,6,4]=>[1,7,6,5,2,8,4,3]=>0011111
[4,8,1,5,6,7,2,3]=>[7,8,1,4,2,5,6,3]=>[4,8,3,1,7,6,5,2]=>0101111
[5,3,8,4,1,7,2,6]=>[7,4,8,5,3,1,2,6]=>[8,6,1,7,2,4,5,3]=>0001111
[1,4,8,3,6,7,5,2]=>[1,5,7,4,8,3,6,2]=>[1,4,7,6,3,8,2,5]=>0000111
[3,8,1,5,6,7,4,2]=>[4,7,3,8,1,5,6,2]=>[3,8,2,7,6,5,1,4]=>0001111
[3,8,2,5,6,7,1,4]=>[7,8,3,2,1,5,6,4]=>[3,7,6,5,1,8,4,2]=>0011111
[7,8,4,3,6,2,1,5]=>[2,6,4,8,3,1,7,5]=>[6,1,2,7,8,5,3,4]=>0001101
[7,1,4,8,6,2,3,5]=>[6,8,1,2,4,7,3,5]=>[7,3,1,6,8,5,4,2]=>0111011
[8,3,5,2,1,7,4,6]=>[2,7,5,8,3,1,4,6]=>[5,3,8,6,1,2,7,4]=>0001111
[1,2,8,5,6,7,3,4]=>[1,2,7,3,8,5,6,4]=>[1,2,8,4,3,7,6,5]=>0010111
[1,4,8,5,6,7,2,3]=>[1,7,2,4,8,5,6,3]=>[1,4,8,3,2,7,6,5]=>0100111
[6,2,4,3,8,7,5,1]=>[5,4,7,2,6,3,8,1]=>[4,2,8,1,5,6,3,7]=>0010101
[7,3,5,4,1,8,6,2]=>[6,4,5,8,3,7,1,2]=>[5,3,7,1,6,8,2,4]=>0001011
[5,2,7,1,3,4,8,6]=>[8,5,2,1,3,7,4,6]=>[5,3,2,8,6,7,4,1]=>0111011
[2,6,5,7,3,1,8,4]=>[3,2,8,7,6,5,1,4]=>[2,6,5,8,4,7,1,3]=>0000111
[6,3,1,4,7,8,5,2]=>[5,3,8,1,6,4,7,2]=>[6,4,1,5,7,8,2,3]=>0010101
[3,7,1,8,4,5,2,6]=>[5,8,3,7,1,4,2,6]=>[3,5,1,8,6,4,7,2]=>0001111
[6,3,2,4,7,5,8,1]=>[8,3,7,2,6,4,5,1]=>[7,5,6,4,2,3,8,1]=>0010111
[4,2,1,6,3,7,5,8]=>[2,7,4,1,6,3,5,8]=>[7,5,6,3,4,1,2,8]=>0010110
[4,2,1,6,3,7,8,5]=>[2,8,4,1,6,3,7,5]=>[7,8,5,6,3,4,1,2]=>0010101
[2,7,6,8,3,1,4,5]=>[3,2,8,1,4,7,6,5]=>[2,7,6,8,5,4,1,3]=>0011011
[7,4,3,5,8,6,2,1]=>[2,6,4,8,3,7,5,1]=>[8,1,2,6,7,5,3,4]=>0001011
[4,2,1,7,3,8,6,5]=>[2,6,4,1,8,7,3,5]=>[7,3,4,1,2,6,8,5]=>0010011
[4,2,1,3,7,8,6,5]=>[2,4,1,3,6,8,7,5]=>[4,3,1,2,7,8,5,6]=>0110001
[4,2,1,8,3,5,6,7]=>[2,8,4,1,3,5,6,7]=>[8,7,6,5,3,4,1,2]=>0011111
[3,6,7,5,2,1,4,8]=>[2,5,3,1,7,6,4,8]=>[3,6,7,4,1,2,5,8]=>0010010
[3,6,7,5,2,1,8,4]=>[2,8,3,5,7,6,1,4]=>[3,6,8,4,5,7,1,2]=>0000011
[3,6,7,5,2,4,1,8]=>[4,5,3,2,7,6,1,8]=>[3,6,7,1,4,2,5,8]=>0010010
[4,2,1,3,8,6,7,5]=>[2,4,1,3,7,8,6,5]=>[4,3,1,2,8,5,7,6]=>0110011
[4,2,1,3,5,7,6,8]=>[2,4,1,3,5,7,6,8]=>[4,3,1,2,5,7,6,8]=>0110010
[4,8,1,7,3,6,5,2]=>[5,6,7,4,8,1,3,2]=>[4,7,3,8,2,6,1,5]=>0000111
[7,8,2,4,1,3,6,5]=>[4,6,2,1,8,3,7,5]=>[4,1,6,3,2,7,8,5]=>0110101
[2,6,1,5,4,7,8,3]=>[8,2,5,6,1,4,7,3]=>[2,6,4,7,8,3,5,1]=>0001101
[4,6,3,5,8,7,1,2]=>[7,1,6,4,3,5,8,2]=>[4,6,5,3,8,2,1,7]=>1001101
[2,3,6,8,4,1,5,7]=>[4,2,3,8,1,6,5,7]=>[2,3,6,8,7,5,1,4]=>0001011
[3,5,6,2,4,1,7,8]=>[4,6,3,2,5,1,7,8]=>[3,5,6,1,4,2,7,8]=>0010100
[2,5,3,8,4,7,6,1]=>[6,2,7,5,3,8,4,1]=>[2,7,4,5,3,8,1,6]=>0001011
[2,8,6,3,4,5,7,1]=>[7,2,6,3,4,8,5,1]=>[2,8,1,7,5,4,3,6]=>0011011
[2,7,8,5,3,6,4,1]=>[4,2,6,5,8,3,7,1]=>[2,6,3,7,8,1,4,5]=>0000101
[8,3,7,6,1,4,5,2]=>[5,6,7,3,1,8,4,2]=>[5,1,7,4,3,8,2,6]=>0011011
[4,1,7,2,3,6,5,8]=>[6,4,1,2,7,3,5,8]=>[4,2,6,3,1,7,5,8]=>0110110
[3,7,1,8,2,6,4,5]=>[6,8,3,7,1,2,4,5]=>[3,7,4,8,5,1,6,2]=>0001111
[3,1,7,8,2,5,6,4]=>[6,3,1,8,2,5,7,4]=>[6,5,2,3,1,7,8,4]=>0101101
[7,4,8,1,2,3,6,5]=>[6,1,2,8,7,4,3,5]=>[8,5,7,3,2,1,6,4]=>1100111
[8,7,4,6,1,2,5,3]=>[5,1,6,7,4,2,8,3]=>[8,3,6,2,1,5,4,7]=>1001101
[7,5,1,2,3,4,8,6]=>[5,1,2,3,8,7,4,6]=>[8,6,7,4,3,2,1,5]=>1110011
[3,1,4,8,7,5,2,6]=>[5,3,1,4,7,2,8,6]=>[4,8,6,2,3,1,5,7]=>0100101
[5,4,1,8,2,7,6,3]=>[6,7,4,5,1,8,2,3]=>[7,2,8,3,4,5,1,6]=>0001011
[8,6,7,4,1,2,5,3]=>[5,1,4,7,2,8,6,3]=>[5,2,1,8,3,4,7,6]=>1001011
[6,7,4,1,2,8,3,5]=>[8,1,4,7,2,6,3,5]=>[6,7,3,4,8,5,2,1]=>1001011
[8,6,5,1,2,3,7,4]=>[7,1,2,5,6,8,3,4]=>[7,3,2,1,8,4,5,6]=>1100011
[6,5,1,2,3,7,4,8]=>[7,1,2,5,6,3,4,8]=>[7,4,5,6,3,2,1,8]=>1100110
[7,8,6,4,1,2,5,3]=>[5,1,4,6,2,8,7,3]=>[5,2,1,7,8,3,4,6]=>1001001
[1,4,8,3,2,5,7,6]=>[1,3,7,4,2,8,5,6]=>[1,4,7,5,2,3,8,6]=>0001011
[1,3,8,4,2,6,7,5]=>[1,4,3,7,8,2,6,5]=>[1,3,7,6,2,4,8,5]=>0000111
[4,2,6,7,5,8,3,1]=>[3,8,4,2,7,6,5,1]=>[6,7,5,8,1,3,4,2]=>0010011
[6,7,5,2,1,8,4,3]=>[2,4,8,5,7,6,1,3]=>[6,7,1,2,4,5,8,3]=>0000011
[5,6,8,3,1,7,2,4]=>[7,3,8,1,5,6,2,4]=>[5,6,8,4,1,7,2,3]=>0010011
[3,4,7,1,8,6,2,5]=>[6,8,3,4,1,7,2,5]=>[3,4,8,5,1,6,7,2]=>0001011
[3,4,6,8,2,1,5,7]=>[2,8,3,4,1,6,5,7]=>[3,4,6,8,7,5,1,2]=>0001011
[3,5,2,8,6,4,1,7]=>[4,6,3,5,2,8,1,7]=>[3,8,7,1,4,5,2,6]=>0001011
[4,5,7,3,8,2,6,1]=>[6,8,7,4,5,3,2,1]=>[4,5,8,1,6,3,7,2]=>0000111
[7,5,2,8,1,4,3,6]=>[4,8,5,2,7,1,3,6]=>[7,3,5,8,6,1,4,2]=>0010111
[6,7,2,4,8,1,5,3]=>[5,8,7,2,4,6,1,3]=>[6,8,3,7,1,5,4,2]=>0011011
[6,7,3,8,2,4,5,1]=>[5,8,7,3,2,6,4,1]=>[6,7,4,3,8,1,5,2]=>0011011
[3,6,2,7,4,1,8,5]=>[4,8,3,7,6,2,1,5]=>[3,7,1,4,8,5,6,2]=>0000111
[6,7,3,2,1,4,8,5]=>[2,3,8,1,7,6,4,5]=>[6,8,5,7,4,1,2,3]=>0010011
[6,3,7,8,2,5,4,1]=>[4,5,8,6,3,2,7,1]=>[7,8,1,4,6,2,5,3]=>0001101
[1,3,7,8,5,2,6,4]=>[1,6,3,5,8,2,7,4]=>[1,3,6,2,7,8,4,5]=>0000101
[2,5,7,8,1,6,3,4]=>[6,2,8,1,5,3,7,4]=>[2,5,7,8,4,1,6,3]=>0010101
[2,5,6,1,7,8,4,3]=>[4,2,8,6,5,1,7,3]=>[2,5,6,1,4,7,8,3]=>0000101
[6,4,2,5,3,1,8,7]=>[3,5,4,6,2,1,8,7]=>[5,2,6,1,3,4,8,7]=>0001101
[8,6,2,4,7,5,3,1]=>[3,5,7,2,6,8,4,1]=>[8,1,3,7,4,2,5,6]=>0010011
[4,8,2,6,7,5,3,1]=>[3,5,7,4,8,2,6,1]=>[4,8,1,3,7,6,2,5]=>0000111
[2,8,4,6,7,5,3,1]=>[3,2,5,7,8,4,6,1]=>[2,7,6,4,8,1,3,5]=>0000111
[2,8,6,7,4,5,3,1]=>[3,2,5,7,4,8,6,1]=>[2,8,1,3,5,4,7,6]=>0001011
[6,8,7,2,4,5,3,1]=>[3,5,7,2,4,6,8,1]=>[5,4,2,6,8,1,3,7]=>0011001
[8,2,4,6,7,5,3,1]=>[3,5,7,2,8,4,6,1]=>[8,1,3,7,6,4,2,5]=>0010111
[6,2,4,5,8,7,3,1]=>[3,7,6,2,4,5,8,1]=>[8,1,3,6,5,4,2,7]=>0011101
[8,2,6,7,4,5,3,1]=>[3,5,7,8,2,4,6,1]=>[5,2,8,1,3,7,6,4]=>0001111
[8,6,7,2,4,5,3,1]=>[3,5,7,2,4,8,6,1]=>[5,4,2,8,1,3,7,6]=>0011011
[4,6,5,8,2,7,3,1]=>[3,7,8,4,6,5,2,1]=>[4,6,5,7,2,8,1,3]=>0000111
[2,1,6,8,4,7,5,3]=>[2,1,5,7,8,6,4,3]=>[2,1,6,7,4,8,3,5]=>1000011
[2,1,8,6,4,7,5,3]=>[2,1,5,7,6,8,4,3]=>[2,1,7,4,8,3,5,6]=>1000011
[2,8,6,4,7,5,3,1]=>[3,2,5,7,6,8,4,1]=>[2,7,4,8,1,3,5,6]=>0000011
[4,8,6,2,7,5,3,1]=>[3,5,7,4,6,8,2,1]=>[4,8,1,3,7,2,5,6]=>0000011
[3,7,8,5,6,1,2,4]=>[6,1,3,2,8,5,7,4]=>[3,7,8,4,2,1,6,5]=>1010101
[3,6,1,8,4,7,2,5]=>[7,8,3,6,1,4,2,5]=>[3,6,4,8,5,1,7,2]=>0001111
[4,6,1,8,3,2,7,5]=>[3,7,8,4,6,1,2,5]=>[4,7,2,8,5,6,1,3]=>0000111
[4,7,8,3,1,2,6,5]=>[3,1,6,4,8,2,7,5]=>[4,6,2,1,3,7,8,5]=>1000101
[4,7,8,2,1,3,6,5]=>[2,6,1,4,8,3,7,5]=>[4,6,3,1,2,7,8,5]=>0100101
[4,6,1,8,2,3,7,5]=>[7,8,1,4,6,2,3,5]=>[4,7,3,1,8,5,6,2]=>0100111
[4,5,2,1,8,3,7,6]=>[2,7,5,4,1,8,3,6]=>[4,7,3,5,1,2,8,6]=>0001011
[4,6,2,8,1,3,7,5]=>[7,8,2,4,6,1,3,5]=>[4,8,5,6,1,7,3,2]=>0100111
[3,6,2,8,4,7,1,5]=>[7,8,3,6,2,4,1,5]=>[3,6,4,7,1,8,5,2]=>0001111
[3,2,6,8,4,7,1,5]=>[7,3,2,8,4,6,1,5]=>[3,2,6,7,1,8,5,4]=>0101011
[4,2,5,3,8,1,7,6]=>[7,5,4,2,3,8,1,6]=>[5,3,4,2,7,1,8,6]=>0011011
[3,2,5,4,8,7,1,6]=>[7,3,2,5,4,1,8,6]=>[3,2,5,4,8,6,1,7]=>0101101
[3,5,2,4,8,7,1,6]=>[7,5,3,2,4,1,8,6]=>[3,5,4,2,8,6,1,7]=>0011101
[3,1,5,4,8,7,2,6]=>[7,3,1,5,4,2,8,6]=>[5,4,8,6,2,3,1,7]=>0101101
[2,4,6,8,3,7,5,1]=>[5,2,7,4,8,6,3,1]=>[2,4,6,7,3,8,1,5]=>0000011
[5,3,1,4,2,8,7,6]=>[4,3,5,1,2,7,8,6]=>[4,1,5,2,3,8,6,7]=>0011001
[5,1,3,2,4,8,7,6]=>[3,5,1,2,4,7,8,6]=>[3,1,5,4,2,8,6,7]=>0111001
[5,3,2,1,4,8,7,6]=>[2,3,5,1,4,7,8,6]=>[5,4,1,2,3,8,6,7]=>0011001
[3,2,4,5,8,7,1,6]=>[7,3,2,4,5,1,8,6]=>[3,2,4,5,8,6,1,7]=>0100101
[5,2,3,1,4,8,7,6]=>[3,5,2,1,4,7,8,6]=>[5,4,1,3,2,8,6,7]=>0111001
[3,7,4,1,2,5,8,6]=>[4,1,3,8,2,7,5,6]=>[3,8,6,7,5,2,1,4]=>1001011
[4,3,7,1,6,8,5,2]=>[5,8,4,3,7,1,6,2]=>[4,3,7,6,1,5,8,2]=>0010111
[4,1,6,7,5,8,2,3]=>[8,4,1,2,7,6,5,3]=>[4,2,6,7,5,8,3,1]=>0110011
[2,8,7,4,5,3,1,6]=>[3,2,5,7,4,1,8,6]=>[2,8,6,1,3,5,4,7]=>0001101
[5,8,7,6,1,2,4,3]=>[4,1,6,2,5,7,8,3]=>[4,2,1,5,8,3,6,7]=>1010001
[3,8,5,6,2,4,1,7]=>[4,6,3,2,8,5,1,7]=>[3,8,7,1,4,2,6,5]=>0010111
[3,8,2,5,4,6,7,1]=>[7,5,3,8,2,4,6,1]=>[3,5,2,8,1,7,6,4]=>0001111
[2,8,7,5,3,4,1,6]=>[4,2,5,3,7,1,8,6]=>[2,8,6,1,4,3,5,7]=>0010101
[8,1,7,2,4,5,3,6]=>[5,7,8,1,2,4,3,6]=>[8,6,4,1,5,2,7,3]=>0011111
[2,7,1,6,3,5,4,8]=>[5,2,6,7,1,3,4,8]=>[2,5,1,6,3,7,4,8]=>0001110
[8,1,5,6,2,3,7,4]=>[7,6,1,8,2,5,3,4]=>[6,5,2,7,3,1,8,4]=>0101111
[7,3,1,5,4,2,6,8]=>[4,3,5,7,1,2,6,8]=>[7,6,2,3,5,1,4,8]=>0001110
[7,3,1,6,2,5,4,8]=>[5,3,6,7,1,2,4,8]=>[5,1,6,2,3,7,4,8]=>0001110
[3,7,1,6,2,5,4,8]=>[5,6,3,7,1,2,4,8]=>[3,5,1,6,2,7,4,8]=>0001110
[6,3,4,1,5,2,7,8]=>[5,4,6,3,1,2,7,8]=>[5,1,6,2,4,3,7,8]=>0011100
[6,2,4,1,5,3,7,8]=>[5,4,6,2,1,3,7,8]=>[4,2,5,1,6,3,7,8]=>0011100
[6,5,2,1,3,7,4,8]=>[2,7,1,5,6,3,4,8]=>[7,4,5,6,3,1,2,8]=>0100110
[6,7,1,2,8,3,5,4]=>[5,1,8,7,2,6,3,4]=>[5,2,1,6,8,4,7,3]=>1001011
[2,4,6,1,5,3,7,8]=>[5,2,6,4,1,3,7,8]=>[2,4,5,1,6,3,7,8]=>0001100
[4,2,5,3,1,6,7,8]=>[3,5,4,2,1,6,7,8]=>[5,1,3,4,2,6,7,8]=>0011000
[4,7,6,1,5,3,8,2]=>[8,5,6,4,1,7,3,2]=>[4,7,3,6,8,2,5,1]=>0001011
[6,1,7,5,3,8,4,2]=>[4,8,5,7,6,1,3,2]=>[7,3,5,6,1,4,8,2]=>0000111
[8,6,7,5,3,1,4,2]=>[4,3,5,1,7,8,6,2]=>[4,1,8,2,3,5,7,6]=>0010011
[5,6,2,4,7,8,1,3]=>[8,6,2,1,5,4,7,3]=>[5,7,8,3,2,6,4,1]=>0110101
[3,4,8,6,7,1,5,2]=>[5,7,3,4,1,8,6,2]=>[3,4,5,1,8,2,7,6]=>0001011
[5,8,6,4,1,2,7,3]=>[7,1,4,6,5,8,2,3]=>[5,7,2,1,8,3,4,6]=>1000011
[5,8,1,7,2,6,4,3]=>[4,6,7,8,5,1,2,3]=>[5,8,3,7,2,6,1,4]=>0000111
[8,1,5,7,2,6,4,3]=>[4,6,7,8,1,5,2,3]=>[8,3,7,2,6,5,1,4]=>0001111
[8,1,7,2,5,6,3,4]=>[6,7,8,1,2,3,5,4]=>[7,5,2,8,4,1,6,3]=>0011111
[3,7,8,5,1,6,2,4]=>[6,5,3,1,8,2,7,4]=>[3,7,8,4,1,6,2,5]=>0010101
[6,5,2,7,8,1,4,3]=>[4,8,5,2,6,1,7,3]=>[7,8,3,5,6,1,4,2]=>0010101
[8,7,2,1,5,6,3,4]=>[2,6,7,1,3,5,8,4]=>[8,4,1,2,6,5,3,7]=>0011101
[8,7,5,2,1,6,4,3]=>[2,4,6,5,7,1,8,3]=>[8,3,6,1,2,4,5,7]=>0000101
[8,5,1,6,3,4,7,2]=>[7,6,5,1,8,3,4,2]=>[7,4,1,8,2,6,3,5]=>0010111
[6,4,5,8,3,2,7,1]=>[7,3,8,6,4,5,2,1]=>[6,5,4,8,1,7,2,3]=>0001111
[3,6,4,8,7,1,5,2]=>[5,7,3,6,4,1,8,2]=>[3,6,1,5,4,8,2,7]=>0001101
[7,8,2,3,5,6,1,4]=>[6,8,2,3,1,5,7,4]=>[6,5,1,7,8,4,3,2]=>0111101
[8,6,5,1,4,3,7,2]=>[7,4,5,1,6,8,3,2]=>[8,2,4,1,7,3,5,6]=>0010011
[2,7,8,6,1,4,3,5]=>[4,2,6,1,3,8,7,5]=>[2,4,1,7,8,5,3,6]=>0011001
[7,6,5,2,8,3,4,1]=>[4,8,5,2,6,7,3,1]=>[7,3,5,6,8,1,4,2]=>0010011
[2,4,7,6,5,8,1,3]=>[8,2,1,4,6,7,5,3]=>[2,4,7,5,6,8,3,1]=>0100011
[7,8,6,1,3,5,2,4]=>[5,6,1,3,2,8,7,4]=>[7,8,4,3,1,5,2,6]=>0111001
[2,5,1,8,6,7,4,3]=>[4,2,7,5,1,8,6,3]=>[2,5,1,4,8,3,7,6]=>0001011
[3,5,1,8,6,7,4,2]=>[4,7,3,5,1,8,6,2]=>[3,5,1,4,8,2,7,6]=>0001011
[8,3,5,4,6,7,1,2]=>[7,1,5,8,3,4,6,2]=>[5,3,8,2,1,7,6,4]=>1001111
[5,1,3,8,6,7,4,2]=>[4,7,1,5,3,8,6,2]=>[5,3,1,4,8,2,7,6]=>0101011
[8,1,6,3,5,2,7,4]=>[7,5,6,8,1,3,2,4]=>[6,3,7,2,5,1,8,4]=>0001111
[4,7,6,8,3,2,5,1]=>[5,3,8,4,2,7,6,1]=>[4,7,6,8,1,5,2,3]=>0001011
[3,6,8,2,4,1,7,5]=>[4,7,3,2,8,6,1,5]=>[3,6,7,1,4,2,8,5]=>0010011
[8,4,3,2,6,7,1,5]=>[7,3,4,8,2,1,6,5]=>[7,6,1,8,5,2,3,4]=>0001111
[4,2,8,1,6,7,3,5]=>[7,8,4,2,1,3,6,5]=>[8,5,1,7,6,3,4,2]=>0011111
[5,8,4,1,6,7,2,3]=>[7,4,1,8,5,2,6,3]=>[5,8,3,1,7,6,2,4]=>0100111
[1,6,3,5,2,4,7,8]=>[1,5,6,3,2,4,7,8]=>[1,5,2,6,4,3,7,8]=>0011100
[1,7,3,4,2,6,5,8]=>[1,4,6,3,7,2,5,8]=>[1,6,2,4,3,7,5,8]=>0010110
[1,4,2,8,5,7,3,6]=>[1,7,4,2,8,5,3,6]=>[1,7,3,4,2,8,6,5]=>0010111
[1,7,3,5,2,6,4,8]=>[1,6,5,7,3,2,4,8]=>[1,5,3,6,2,7,4,8]=>0001110
[1,7,4,6,2,3,5,8]=>[1,6,2,7,4,3,5,8]=>[1,6,3,2,7,5,4,8]=>0101110
[1,8,5,6,2,4,3,7]=>[1,4,6,2,8,5,3,7]=>[1,4,2,8,7,3,6,5]=>0010111
[1,3,2,8,5,6,4,7]=>[1,3,2,6,8,5,4,7]=>[1,3,2,8,7,4,6,5]=>0100111
[1,6,4,7,2,8,3,5]=>[1,8,7,6,4,2,3,5]=>[1,7,3,8,5,4,6,2]=>0001111
[5,4,8,2,3,6,1,7]=>[6,8,2,5,4,3,1,7]=>[5,4,8,7,1,6,3,2]=>0101111
[1,7,5,3,4,8,2,6]=>[1,8,5,3,7,4,2,6]=>[1,8,6,4,3,5,7,2]=>0010111
[5,8,7,4,1,2,3,6]=>[4,1,2,7,5,3,8,6]=>[5,8,6,3,2,1,4,7]=>1100101
[8,5,1,6,3,7,2,4]=>[7,6,5,1,8,3,2,4]=>[8,4,1,7,2,6,3,5]=>0010111
[6,1,3,7,4,8,2,5]=>[8,7,1,6,3,4,2,5]=>[6,4,7,2,8,5,3,1]=>0101111
[6,1,5,7,8,2,3,4]=>[8,6,1,2,3,5,7,4]=>[7,8,4,2,6,5,3,1]=>0111101
[3,8,7,5,1,2,4,6]=>[5,1,3,2,7,4,8,6]=>[3,8,6,4,2,1,5,7]=>1010101
[6,5,8,4,1,2,3,7]=>[4,1,2,8,6,5,3,7]=>[6,5,8,7,3,2,1,4]=>1100111
[8,5,7,4,1,2,3,6]=>[4,1,2,7,8,5,3,6]=>[7,3,2,1,4,8,6,5]=>1100111
[7,6,2,3,8,1,4,5]=>[8,6,2,3,1,7,4,5]=>[7,4,3,2,6,8,5,1]=>0111011
[8,6,4,1,2,7,3,5]=>[7,1,4,6,2,8,3,5]=>[8,5,2,1,7,3,4,6]=>1001011
[1,7,2,8,6,3,4,5]=>[1,6,8,2,3,7,4,5]=>[1,7,4,2,6,8,5,3]=>0011011
[1,5,8,7,2,3,4,6]=>[1,7,2,3,5,4,8,6]=>[1,5,8,6,4,3,2,7]=>0110101
[7,1,5,8,6,2,3,4]=>[6,8,1,2,3,7,5,4]=>[7,5,3,1,6,8,4,2]=>0111011
[7,1,5,8,3,4,2,6]=>[4,8,7,1,3,5,2,6]=>[4,1,8,6,5,3,7,2]=>0011111
[7,1,4,6,5,8,2,3]=>[8,6,1,2,7,4,5,3]=>[6,4,2,7,5,8,3,1]=>0110111
[7,1,4,6,3,8,2,5]=>[8,6,7,1,4,3,2,5]=>[7,2,6,3,8,5,4,1]=>0011111
[7,1,4,6,5,3,8,2]=>[8,5,6,1,7,4,3,2]=>[8,2,5,7,3,6,4,1]=>0010111
[6,4,2,3,8,5,1,7]=>[5,4,2,8,6,3,1,7]=>[8,7,1,5,6,3,2,4]=>0100111
[4,8,3,1,2,6,5,7]=>[3,1,6,4,8,2,5,7]=>[4,6,2,1,3,8,7,5]=>1000111
[4,8,3,1,2,6,7,5]=>[3,1,7,4,8,2,6,5]=>[4,7,6,2,1,3,8,5]=>1000111
[5,8,1,6,3,4,2,7]=>[4,6,8,1,5,3,2,7]=>[4,1,5,8,7,2,6,3]=>0010111
[6,8,5,1,3,7,2,4]=>[7,5,1,3,8,6,2,4]=>[6,8,4,3,1,7,2,5]=>0110011
[6,8,5,1,3,4,7,2]=>[7,5,1,3,8,6,4,2]=>[6,7,4,3,1,8,2,5]=>0110011
[2,4,7,3,6,1,5,8]=>[6,2,7,4,3,1,5,8]=>[2,4,6,1,7,5,3,8]=>0001110
[5,8,3,2,1,6,4,7]=>[2,3,6,8,5,1,4,7]=>[5,6,1,2,3,8,7,4]=>0000111
[5,3,6,1,4,8,7,2]=>[7,6,5,3,1,4,8,2]=>[8,2,6,4,3,5,1,7]=>0011101
[4,2,1,5,8,6,3,7]=>[2,6,4,1,5,8,3,7]=>[5,8,7,3,4,1,2,6]=>0010011
[4,3,1,5,7,8,2,6]=>[8,3,4,1,5,2,7,6]=>[5,7,8,6,2,3,4,1]=>0010101
[3,2,1,8,5,4,6,7]=>[2,3,1,5,8,4,6,7]=>[3,1,2,8,7,6,4,5]=>0100111
[6,7,2,1,8,4,5,3]=>[2,5,8,7,1,6,4,3]=>[5,1,2,6,7,4,8,3]=>0001011
[3,2,1,8,5,6,4,7]=>[2,3,1,6,8,5,4,7]=>[3,1,2,8,7,4,6,5]=>0100111
[4,3,1,6,7,8,5,2]=>[5,3,4,1,8,6,7,2]=>[6,7,8,2,3,4,1,5]=>0010001
[4,2,1,6,8,5,3,7]=>[2,5,4,1,8,6,3,7]=>[6,8,7,3,4,1,2,5]=>0010011
[5,2,6,1,8,7,3,4]=>[7,6,5,2,1,3,8,4]=>[8,4,2,6,3,5,1,7]=>0011101
[5,2,6,1,8,3,4,7]=>[8,6,5,2,1,3,4,7]=>[8,7,4,2,6,3,5,1]=>0011111
[4,3,1,6,7,8,2,5]=>[8,3,4,1,2,6,7,5]=>[6,7,8,5,2,3,4,1]=>0011001
[4,2,1,7,8,6,3,5]=>[2,6,4,1,3,8,7,5]=>[7,8,5,3,4,1,2,6]=>0011001
[3,2,1,8,6,4,7,5]=>[2,3,1,7,6,8,4,5]=>[3,1,2,7,4,8,5,6]=>0100011
[3,2,1,8,6,4,5,7]=>[2,3,1,6,4,8,5,7]=>[3,1,2,8,7,5,4,6]=>0101011
[3,2,1,8,4,6,5,7]=>[2,3,1,6,8,4,5,7]=>[3,1,2,6,4,8,7,5]=>0100111
[3,2,1,8,4,6,7,5]=>[2,3,1,7,8,4,6,5]=>[3,1,2,7,6,4,8,5]=>0100111
[4,2,1,7,8,3,6,5]=>[2,6,4,1,8,3,7,5]=>[6,3,4,1,2,7,8,5]=>0010101
[5,2,7,1,8,3,6,4]=>[6,8,7,5,2,1,3,4]=>[6,1,7,3,8,4,5,2]=>0001111
[6,7,2,1,8,3,5,4]=>[2,5,8,7,1,6,3,4]=>[5,1,2,6,8,4,7,3]=>0001011
[5,2,7,1,8,3,4,6]=>[8,7,5,2,1,3,4,6]=>[7,4,2,8,6,3,5,1]=>0011111
[4,2,1,7,8,3,5,6]=>[2,8,4,1,3,5,7,6]=>[7,8,6,5,3,4,1,2]=>0011101
[3,2,1,8,4,5,7,6]=>[2,3,1,7,4,8,5,6]=>[3,1,2,7,5,4,8,6]=>0101011
[6,3,8,2,5,7,4,1]=>[4,7,8,6,3,2,5,1]=>[8,1,4,6,2,7,5,3]=>0001111
[5,7,4,2,6,8,1,3]=>[8,4,2,7,5,1,6,3]=>[5,8,3,2,4,7,6,1]=>0100111
[6,3,7,2,5,8,4,1]=>[4,8,7,6,3,2,5,1]=>[7,5,3,8,1,4,6,2]=>0001111
[5,3,6,7,8,2,4,1]=>[4,8,5,3,2,6,7,1]=>[6,7,8,1,4,3,5,2]=>0011001
[3,6,4,2,1,5,8,7]=>[2,4,3,6,1,5,8,7]=>[3,6,5,1,2,4,8,7]=>0001101
[3,5,8,6,4,2,1,7]=>[2,4,3,6,5,8,1,7]=>[3,5,8,7,1,2,4,6]=>0000011
[5,8,6,3,4,2,1,7]=>[2,4,6,3,5,8,1,7]=>[5,8,7,1,2,4,3,6]=>0010011
[5,6,3,4,2,1,8,7]=>[2,4,6,3,5,1,8,7]=>[5,6,1,2,4,3,8,7]=>0010101
[6,3,4,2,1,5,8,7]=>[2,4,6,3,1,5,8,7]=>[6,5,1,2,4,3,8,7]=>0011101
[5,6,4,2,1,3,8,7]=>[2,4,1,6,5,3,8,7]=>[5,6,3,1,2,4,8,7]=>0100101
[2,7,8,5,4,1,6,3]=>[6,2,4,5,8,1,7,3]=>[2,6,1,7,8,3,4,5]=>0000101
[2,6,3,8,5,4,1,7]=>[4,2,5,8,6,3,1,7]=>[2,6,3,5,8,7,1,4]=>0000111
[5,8,6,4,2,1,3,7]=>[2,4,1,6,5,8,3,7]=>[5,8,7,3,1,2,4,6]=>0100011
[4,2,1,5,7,8,6,3]=>[2,6,4,1,5,8,7,3]=>[5,7,8,3,4,1,2,6]=>0010001
[2,1,8,5,6,4,3,7]=>[2,1,4,6,8,5,3,7]=>[2,1,8,7,3,4,6,5]=>1000111
[3,8,5,6,4,2,1,7]=>[2,4,3,6,8,5,1,7]=>[3,8,7,1,2,4,6,5]=>0000111
[3,6,4,2,1,8,5,7]=>[2,4,3,8,6,1,5,7]=>[3,8,7,5,6,1,2,4]=>0000111
[7,6,2,4,1,8,5,3]=>[5,4,8,2,6,7,1,3]=>[4,2,7,1,5,6,8,3]=>0010011
[8,5,4,1,7,6,2,3]=>[6,4,1,5,7,8,2,3]=>[7,2,4,5,8,3,1,6]=>0100011
[7,6,2,3,8,5,4,1]=>[4,5,2,8,6,7,3,1]=>[7,3,2,5,6,8,1,4]=>0100011
[2,1,7,8,6,4,3,5]=>[2,1,4,6,3,8,7,5]=>[2,1,7,8,5,3,4,6]=>1001001
[2,1,6,4,3,7,8,5]=>[2,1,4,8,6,3,7,5]=>[2,1,7,8,5,6,3,4]=>1000101
[7,8,4,2,1,6,3,5]=>[2,6,4,8,1,3,7,5]=>[7,8,5,1,2,6,3,4]=>0001101
[2,6,1,8,4,3,7,5]=>[4,2,7,8,6,1,3,5]=>[2,7,3,8,5,6,1,4]=>0000111
[8,4,2,3,7,5,6,1]=>[6,4,2,7,8,3,5,1]=>[8,1,6,3,2,4,7,5]=>0100111
[8,5,7,6,2,1,4,3]=>[2,4,6,1,7,8,5,3]=>[4,1,2,7,5,8,3,6]=>0010011
[4,8,5,7,6,2,1,3]=>[2,6,1,4,7,8,5,3]=>[4,7,5,8,3,1,2,6]=>0100011
[4,7,6,2,1,3,8,5]=>[2,8,1,4,6,7,3,5]=>[4,8,5,6,7,3,1,2]=>0100011
[2,7,5,8,4,3,6,1]=>[6,2,4,8,7,5,3,1]=>[2,8,1,6,5,7,3,4]=>0000111
[8,4,2,6,3,1,7,5]=>[3,7,4,6,8,2,1,5]=>[7,1,3,4,6,2,8,5]=>0000111
[8,6,5,2,3,1,7,4]=>[3,7,2,5,6,8,1,4]=>[7,1,3,2,8,4,5,6]=>0100011
[1,8,6,3,2,5,7,4]=>[1,3,7,6,2,8,5,4]=>[1,7,5,2,3,8,4,6]=>0001011
[8,7,5,2,1,4,6,3]=>[2,6,5,1,7,4,8,3]=>[6,4,1,2,8,3,5,7]=>0010101
[7,8,5,2,1,4,6,3]=>[2,6,5,1,8,4,7,3]=>[6,4,1,2,7,8,3,5]=>0010101
[5,8,6,2,3,1,7,4]=>[3,7,2,6,5,8,1,4]=>[5,7,1,3,2,8,4,6]=>0100011
[3,2,8,6,4,1,7,5]=>[4,3,2,7,6,8,1,5]=>[3,2,7,1,4,8,5,6]=>0100011
[4,8,2,7,1,5,6,3]=>[6,7,8,4,2,1,5,3]=>[4,6,1,7,5,2,8,3]=>0001111
[6,8,7,1,3,4,5,2]=>[5,7,1,3,4,6,8,2]=>[5,4,3,1,6,8,2,7]=>0111001
[1,6,8,3,2,5,7,4]=>[1,3,7,8,2,6,5,4]=>[1,6,7,5,2,3,8,4]=>0001011
[8,4,2,7,1,5,6,3]=>[6,7,4,8,2,1,5,3]=>[6,1,7,5,2,8,3,4]=>0001111
[7,4,2,8,1,5,6,3]=>[6,8,4,7,2,1,5,3]=>[6,1,8,3,4,7,5,2]=>0001111
[5,4,2,3,8,1,7,6]=>[7,4,2,5,3,8,1,6]=>[5,3,2,4,7,1,8,6]=>0101011
[8,4,2,1,3,6,7,5]=>[2,4,1,7,8,3,6,5]=>[7,6,3,1,2,4,8,5]=>0100111
[1,5,3,2,4,7,8,6]=>[1,3,5,2,4,8,7,6]=>[1,5,4,2,3,7,8,6]=>0011001
[5,6,1,3,4,2,8,7]=>[4,6,1,3,5,2,8,7]=>[4,3,1,5,6,2,8,7]=>0110101
[4,1,3,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[3,1,4,2,5,7,8,6]=>0110001
[5,1,2,4,3,7,8,6]=>[4,1,5,2,3,8,7,6]=>[4,2,1,5,3,7,8,6]=>1011001
[8,7,5,2,6,3,4,1]=>[4,6,5,2,7,3,8,1]=>[8,1,4,2,6,3,5,7]=>0010101
[3,1,7,5,4,2,6,8]=>[4,3,1,5,7,2,6,8]=>[7,6,2,3,1,4,5,8]=>0100110
[6,3,8,5,4,7,1,2]=>[7,1,5,8,6,3,4,2]=>[6,3,5,8,2,1,7,4]=>1000111
[1,6,2,5,4,7,8,3]=>[1,8,5,6,2,4,7,3]=>[1,6,4,7,8,3,5,2]=>0001101
[7,8,3,1,4,2,5,6]=>[4,3,8,1,2,5,7,6]=>[4,1,7,8,6,5,2,3]=>0011101
[4,8,1,5,2,3,6,7]=>[5,8,1,4,2,3,6,7]=>[4,8,7,6,3,1,5,2]=>0101111
[7,4,1,5,2,3,6,8]=>[5,4,1,7,2,3,6,8]=>[7,6,3,1,5,2,4,8]=>0101110
[5,6,1,8,4,3,2,7]=>[3,4,8,6,5,1,2,7]=>[5,8,7,2,4,6,1,3]=>0000111
[5,1,8,6,4,3,2,7]=>[3,4,6,5,1,8,2,7]=>[8,7,2,4,5,1,3,6]=>0001011
[6,1,8,7,4,3,2,5]=>[3,4,7,6,1,2,8,5]=>[6,2,4,8,5,1,3,7]=>0001101
[1,2,7,5,8,3,6,4]=>[1,2,6,8,7,5,3,4]=>[1,2,7,3,6,5,8,4]=>0000111
[1,2,6,4,7,8,5,3]=>[1,2,5,8,6,4,7,3]=>[1,2,7,8,3,5,6,4]=>0000101
[6,5,8,1,4,3,2,7]=>[3,4,8,1,6,5,2,7]=>[6,5,8,7,2,4,1,3]=>0010111
[1,6,3,2,7,4,8,5]=>[1,3,8,7,6,2,4,5]=>[1,7,4,8,5,6,2,3]=>0000111
[2,6,1,7,4,3,8,5]=>[4,2,8,7,6,1,3,5]=>[2,8,5,6,1,4,7,3]=>0000111
[2,5,7,4,3,8,1,6]=>[8,2,4,7,5,3,1,6]=>[2,5,8,6,3,4,7,1]=>0000111
[1,4,6,3,8,2,7,5]=>[1,7,8,4,6,3,2,5]=>[1,4,7,2,8,5,6,3]=>0000111
[3,2,6,7,8,1,5,4]=>[5,3,2,8,1,6,7,4]=>[3,2,5,1,6,7,8,4]=>0101001
[2,5,1,6,8,4,7,3]=>[7,2,8,5,1,6,4,3]=>[2,6,7,4,5,1,8,3]=>0001011
[1,3,6,2,8,7,5,4]=>[1,5,3,7,6,2,8,4]=>[1,3,6,2,5,8,4,7]=>0000101
[1,5,7,2,4,8,6,3]=>[1,6,8,2,5,7,4,3]=>[1,5,7,4,2,6,8,3]=>0010011
[4,3,6,7,8,2,5,1]=>[5,8,4,3,2,6,7,1]=>[4,3,6,7,8,1,5,2]=>0011001
[8,2,4,7,3,1,5,6]=>[3,7,8,2,4,1,5,6]=>[7,5,4,2,8,6,1,3]=>0011111
[3,2,4,8,1,5,6,7]=>[8,3,2,4,1,5,6,7]=>[3,2,4,8,7,6,5,1]=>0101111
[4,6,7,8,2,3,1,5]=>[3,8,2,4,1,6,7,5]=>[4,6,7,8,5,1,3,2]=>0101001
[7,4,6,8,2,3,1,5]=>[3,8,2,7,4,1,6,5]=>[8,5,4,7,6,1,3,2]=>0101111
[4,6,8,7,2,3,1,5]=>[3,7,2,4,1,6,8,5]=>[4,6,8,5,1,3,2,7]=>0101001
[5,7,6,8,2,3,1,4]=>[3,8,2,1,5,7,6,4]=>[5,7,6,8,4,1,3,2]=>0110011
[4,7,6,8,2,3,1,5]=>[3,8,2,4,1,7,6,5]=>[4,7,6,8,5,1,3,2]=>0101011
[8,6,4,7,2,3,1,5]=>[3,7,2,6,4,8,1,5]=>[7,1,3,2,8,5,4,6]=>0101011
[8,2,3,7,4,1,6,5]=>[4,6,2,7,8,3,1,5]=>[6,3,2,7,1,4,8,5]=>0100111
[3,7,4,8,2,5,1,6]=>[5,8,3,7,4,2,1,6]=>[3,7,1,5,4,8,6,2]=>0001111
[6,3,1,7,4,2,8,5]=>[4,3,8,7,6,1,2,5]=>[8,5,6,1,4,7,2,3]=>0000111
[8,5,7,6,2,3,1,4]=>[3,6,2,1,7,8,5,4]=>[7,5,8,4,1,3,2,6]=>0110011
[3,1,7,6,4,2,8,5]=>[4,3,1,8,6,7,2,5]=>[8,5,6,7,2,3,1,4]=>0100011
[4,8,7,6,2,3,1,5]=>[3,6,2,4,1,7,8,5]=>[4,8,5,1,3,2,6,7]=>0101001
[4,6,8,1,5,7,3,2]=>[3,7,8,4,1,6,5,2]=>[4,6,8,2,7,5,1,3]=>0001011
[1,4,6,8,5,7,3,2]=>[1,3,7,4,8,6,5,2]=>[1,4,6,8,2,3,7,5]=>0000011
[1,4,6,8,5,3,7,2]=>[1,7,5,4,8,6,3,2]=>[1,4,6,8,2,7,3,5]=>0000011
[4,3,6,1,8,5,7,2]=>[7,8,4,3,6,1,5,2]=>[4,3,7,5,6,1,8,2]=>0010111
[4,3,1,6,8,5,7,2]=>[7,3,4,1,8,6,5,2]=>[6,8,2,3,4,1,7,5]=>0010011
[4,1,3,6,8,7,5,2]=>[5,4,1,3,7,6,8,2]=>[6,8,2,4,3,1,5,7]=>0110001
[4,3,6,1,8,7,5,2]=>[5,7,4,3,6,1,8,2]=>[4,3,6,1,5,8,2,7]=>0010101
[4,3,6,8,1,7,5,2]=>[5,7,4,3,8,6,1,2]=>[4,3,6,8,2,7,1,5]=>0010011
[6,5,2,8,7,1,3,4]=>[7,5,2,1,6,3,8,4]=>[6,3,2,5,8,4,1,7]=>0110101
[6,2,5,8,7,3,1,4]=>[3,7,6,2,1,5,8,4]=>[6,5,1,3,8,4,2,7]=>0011101
[4,6,3,1,8,7,5,2]=>[5,3,7,4,6,1,8,2]=>[4,6,1,5,8,2,3,7]=>0000101
[1,4,6,3,8,7,5,2]=>[1,5,7,4,6,3,8,2]=>[1,4,8,2,5,6,3,7]=>0000101
[4,1,6,8,3,7,5,2]=>[5,7,4,1,8,6,3,2]=>[6,8,2,7,3,4,1,5]=>0010011
[6,2,8,5,7,3,1,4]=>[3,7,8,2,6,1,5,4]=>[8,4,2,7,5,6,1,3]=>0010111
[6,4,1,8,7,5,3,2]=>[3,5,4,7,6,1,8,2]=>[8,2,5,6,1,3,4,7]=>0000101
[1,5,3,2,6,4,7,8]=>[1,3,6,5,2,4,7,8]=>[1,6,4,5,2,3,7,8]=>0001100
[1,5,3,2,6,7,4,8]=>[1,3,7,5,2,6,4,8]=>[1,6,7,4,5,2,3,8]=>0001010
[3,6,4,8,2,1,5,7]=>[2,8,3,6,4,1,5,7]=>[3,8,7,5,4,6,1,2]=>0001111
[1,5,7,2,8,4,3,6]=>[1,4,8,7,5,2,3,6]=>[1,5,8,6,2,4,7,3]=>0000111
[2,3,1,8,4,5,7,6]=>[3,2,1,7,4,8,5,6]=>[2,3,1,7,5,4,8,6]=>0101011
[3,8,2,1,6,5,4,7]=>[2,5,3,6,8,1,4,7]=>[3,8,7,4,6,1,2,5]=>0000111
[7,4,1,8,3,5,2,6]=>[5,8,4,7,1,3,2,6]=>[5,1,8,6,3,4,7,2]=>0001111
[8,4,2,5,3,1,6,7]=>[3,5,4,8,2,1,6,7]=>[5,2,8,7,6,1,3,4]=>0001111
[4,3,2,5,1,8,6,7]=>[5,3,4,2,1,8,6,7]=>[4,2,3,5,1,8,7,6]=>0011011
[3,5,2,4,1,8,6,7]=>[4,5,3,2,1,8,6,7]=>[3,5,1,4,2,8,7,6]=>0011011
[6,3,2,1,8,4,5,7]=>[2,3,8,6,1,4,5,7]=>[6,4,8,7,5,1,2,3]=>0001111
[7,3,2,8,4,5,1,6]=>[5,3,8,7,2,4,1,6]=>[8,6,4,7,1,5,2,3]=>0001111
[7,8,2,3,4,6,1,5]=>[6,8,2,3,4,1,7,5]=>[6,1,7,8,5,4,3,2]=>0111101
[6,8,1,3,4,7,2,5]=>[7,8,1,3,4,6,2,5]=>[6,8,5,4,3,1,7,2]=>0111011
[8,3,2,7,4,5,1,6]=>[5,3,7,8,2,4,1,6]=>[7,1,5,2,3,8,6,4]=>0001111
[6,7,2,3,4,1,8,5]=>[4,8,2,3,7,6,1,5]=>[6,8,5,7,1,4,3,2]=>0110011
[8,6,2,3,4,7,1,5]=>[7,6,2,3,4,8,1,5]=>[7,1,8,5,4,3,2,6]=>0111011
[5,8,7,3,4,6,1,2]=>[6,1,7,3,5,4,8,2]=>[5,8,2,1,6,4,3,7]=>1010101
[5,3,7,2,6,1,8,4]=>[8,6,7,5,3,2,1,4]=>[6,2,8,4,5,3,7,1]=>0001111
[5,2,8,1,6,3,7,4]=>[7,6,8,5,2,1,3,4]=>[8,4,5,2,6,1,7,3]=>0001111
[7,8,4,1,2,6,5,3]=>[5,1,4,6,8,2,7,3]=>[7,8,3,4,6,2,1,5]=>1000101
[4,8,1,5,2,7,6,3]=>[6,5,7,4,1,8,2,3]=>[4,8,3,7,2,5,1,6]=>0001011
[2,8,7,6,4,1,3,5]=>[4,2,1,6,3,7,8,5]=>[2,8,5,3,1,4,6,7]=>0101001
[7,8,2,6,5,1,3,4]=>[5,6,2,1,8,3,7,4]=>[6,3,2,7,8,4,1,5]=>0110101
[1,8,7,6,2,4,3,5]=>[1,4,6,2,3,7,8,5]=>[1,4,2,8,5,3,6,7]=>0011001
[2,1,7,3,6,5,8,4]=>[2,1,8,6,7,3,5,4]=>[2,1,7,5,8,4,6,3]=>1000111
[6,1,2,8,5,7,3,4]=>[7,1,8,2,6,3,5,4]=>[8,4,2,1,7,5,6,3]=>1010111
[6,3,1,8,5,7,2,4]=>[7,3,8,1,6,2,5,4]=>[8,4,1,7,5,6,2,3]=>0010111
[7,8,3,6,5,1,2,4]=>[5,1,6,3,8,2,7,4]=>[7,8,4,3,6,2,1,5]=>1010101
[2,3,7,5,6,8,1,4]=>[8,2,3,1,7,5,6,4]=>[2,3,7,6,5,8,4,1]=>0010111
[3,8,7,6,4,2,1,5]=>[2,4,3,6,1,7,8,5]=>[3,8,5,1,2,4,6,7]=>0001001
[3,1,4,2,6,8,7,5]=>[4,3,1,2,7,6,8,5]=>[4,2,3,1,6,8,5,7]=>0110001
[2,7,8,3,5,4,1,6]=>[4,2,5,8,3,1,7,6]=>[2,5,3,7,8,6,1,4]=>0001101
[4,8,1,2,7,5,3,6]=>[5,1,7,4,8,2,3,6]=>[4,7,3,8,6,2,1,5]=>1000111
[7,4,1,2,8,5,3,6]=>[5,1,4,8,7,2,3,6]=>[8,6,2,1,5,7,3,4]=>1000111
[7,4,1,2,6,5,3,8]=>[5,1,4,6,7,2,3,8]=>[7,3,4,6,2,1,5,8]=>1000110
[7,4,3,1,5,6,8,2]=>[8,3,4,7,1,5,6,2]=>[8,2,3,4,7,6,5,1]=>0001111
[4,5,3,1,7,6,8,2]=>[8,3,5,4,1,7,6,2]=>[4,7,6,8,2,3,5,1]=>0001011
[5,4,3,8,1,6,7,2]=>[7,8,4,5,3,1,6,2]=>[5,3,4,7,6,1,8,2]=>0001111
[5,7,1,4,6,8,3,2]=>[3,8,7,1,5,4,6,2]=>[5,7,6,4,1,3,8,2]=>0010111
[7,6,4,2,1,5,3,8]=>[2,5,4,6,1,7,3,8]=>[5,1,2,7,3,4,6,8]=>0001010
[7,8,1,5,3,2,4,6]=>[3,5,8,1,2,4,7,6]=>[5,2,7,8,6,4,1,3]=>0011101
[8,6,1,4,5,2,3,7]=>[5,6,1,2,4,8,3,7]=>[8,7,3,1,5,4,2,6]=>0111011
[8,6,3,1,5,2,4,7]=>[5,3,6,1,2,8,4,7]=>[8,7,4,1,5,2,3,6]=>0011011
[8,6,2,1,5,4,3,7]=>[2,4,5,6,1,8,3,7]=>[8,7,3,5,1,2,4,6]=>0001011
[8,5,2,6,1,4,3,7]=>[4,6,5,2,8,1,3,7]=>[6,1,4,2,8,7,3,5]=>0010111
[8,2,7,5,1,3,4,6]=>[5,7,2,1,8,3,4,6]=>[8,6,3,2,7,4,1,5]=>0110111
[8,4,1,7,5,2,3,6]=>[5,4,1,7,8,2,3,6]=>[8,6,2,4,7,3,1,5]=>0100111
[5,7,8,1,3,2,6,4]=>[3,6,1,8,5,2,7,4]=>[3,1,5,6,2,7,8,4]=>0100101
[8,2,6,1,5,7,3,4]=>[7,6,8,2,1,3,5,4]=>[7,5,1,8,4,2,6,3]=>0011111
[5,8,1,6,7,2,3,4]=>[7,8,1,2,5,3,6,4]=>[5,7,6,3,1,8,4,2]=>0110111
[7,1,8,4,3,6,2,5]=>[6,4,8,7,1,3,2,5]=>[7,2,4,8,5,1,6,3]=>0001111
[7,3,1,8,5,6,2,4]=>[6,3,8,1,7,2,5,4]=>[7,5,8,4,1,6,2,3]=>0010111
[6,2,7,8,3,1,5,4]=>[3,5,8,6,2,1,7,4]=>[5,2,7,8,4,6,1,3]=>0001101
[8,4,1,7,3,2,6,5]=>[3,6,4,7,8,1,2,5]=>[7,2,6,1,3,4,8,5]=>0000111
[7,4,8,2,1,3,6,5]=>[2,6,1,8,7,4,3,5]=>[8,5,7,3,1,2,6,4]=>0100111
[2,6,8,7,1,5,4,3]=>[4,2,5,7,1,6,8,3]=>[2,6,8,3,5,1,4,7]=>0001001
[6,8,5,2,3,4,7,1]=>[7,5,2,3,8,6,4,1]=>[6,8,1,7,4,3,2,5]=>0110011
[5,7,3,4,6,8,1,2]=>[8,1,7,3,5,4,6,2]=>[5,7,6,4,3,8,2,1]=>1010111
[7,3,8,5,1,2,6,4]=>[6,1,5,8,7,3,2,4]=>[7,2,1,6,3,5,8,4]=>1000111
[7,3,5,8,1,2,6,4]=>[6,1,8,7,3,5,2,4]=>[8,4,7,2,1,6,5,3]=>1001111
[3,7,5,1,2,6,4,8]=>[6,1,3,5,7,2,4,8]=>[3,6,2,1,7,4,5,8]=>1000110
[3,5,7,2,8,6,1,4]=>[6,8,3,2,5,7,1,4]=>[3,5,7,1,6,8,4,2]=>0010011
[2,5,7,4,8,6,1,3]=>[6,2,1,8,5,7,4,3]=>[2,5,8,3,1,6,7,4]=>0100011
[2,6,4,8,7,5,1,3]=>[5,2,1,7,6,4,8,3]=>[2,8,3,1,5,6,4,7]=>0100101
[2,3,5,7,6,1,8,4]=>[8,2,3,6,5,7,1,4]=>[2,3,5,8,4,6,7,1]=>0000011
[1,3,4,6,2,8,7,5]=>[1,7,3,4,6,2,8,5]=>[1,3,4,8,5,6,2,7]=>0000101
[4,2,7,3,8,1,6,5]=>[6,8,4,2,7,3,1,5]=>[8,5,7,1,6,3,4,2]=>0010111
[3,1,5,6,2,8,7,4]=>[7,3,1,6,5,2,8,4]=>[5,8,4,6,2,3,1,7]=>0100101
[5,1,3,7,2,8,6,4]=>[6,8,1,5,3,7,2,4]=>[8,4,5,3,1,6,7,2]=>0101011
[2,6,1,4,3,8,7,5]=>[4,2,7,1,6,3,8,5]=>[2,4,1,8,5,6,3,7]=>0010101
[7,2,3,5,1,8,6,4]=>[6,5,2,8,3,7,1,4]=>[5,3,2,7,1,6,8,4]=>0101011
[7,3,4,1,8,6,5,2]=>[5,4,6,3,8,7,1,2]=>[8,2,4,3,6,7,1,5]=>0010011
[1,6,4,2,8,7,5,3]=>[1,5,4,7,6,2,8,3]=>[1,6,2,5,8,3,4,7]=>0000101
[2,5,8,3,1,7,6,4]=>[3,2,6,7,5,8,1,4]=>[2,5,8,4,7,1,3,6]=>0000011
[3,6,2,5,1,4,8,7]=>[5,6,3,2,1,4,8,7]=>[3,5,1,6,4,2,8,7]=>0011101
[2,4,8,7,1,3,6,5]=>[6,2,1,4,7,3,8,5]=>[2,4,6,3,1,8,5,7]=>0100101
[2,5,8,1,3,7,6,4]=>[6,2,1,7,5,8,3,4]=>[2,5,8,4,7,3,1,6]=>0100011
[3,5,2,1,7,4,8,6]=>[2,8,3,5,1,7,4,6]=>[3,8,6,7,4,5,1,2]=>0001011
[1,6,2,3,8,7,5,4]=>[1,5,2,7,6,3,8,4]=>[1,6,3,2,5,8,4,7]=>0100101
[4,5,1,2,8,7,6,3]=>[6,1,5,4,2,7,8,3]=>[4,8,3,5,2,1,6,7]=>1001001
[5,2,8,1,3,7,6,4]=>[6,7,2,5,1,8,3,4]=>[7,3,2,8,4,5,1,6]=>0101011
[3,5,8,7,2,6,4,1]=>[4,6,3,7,5,2,8,1]=>[3,5,6,2,8,1,4,7]=>0000101
[5,8,2,7,1,6,4,3]=>[4,6,7,8,5,2,1,3]=>[5,6,2,8,3,7,1,4]=>0000111
[8,6,3,7,5,2,1,4]=>[2,5,7,3,6,8,1,4]=>[8,4,3,7,1,2,5,6]=>0010011
[4,6,3,8,5,2,1,7]=>[2,5,8,4,6,3,1,7]=>[4,8,7,1,2,5,6,3]=>0000111
[4,6,3,7,5,2,8,1]=>[8,5,7,4,6,3,2,1]=>[4,7,2,5,6,3,8,1]=>0000111
[3,5,7,8,2,6,1,4]=>[6,8,3,2,5,1,7,4]=>[3,5,6,1,7,8,4,2]=>0010101
[5,6,2,4,1,3,8,7]=>[4,6,2,1,5,3,8,7]=>[4,1,5,6,3,2,8,7]=>0110101
[8,2,3,4,6,1,5,7]=>[6,8,2,3,4,1,5,7]=>[6,1,8,7,5,4,3,2]=>0111111
[4,7,3,6,5,8,2,1]=>[2,8,6,4,7,3,5,1]=>[4,6,3,7,5,8,1,2]=>0000111
[5,8,1,7,3,6,4,2]=>[4,6,7,8,5,1,3,2]=>[5,7,3,8,2,6,1,4]=>0000111
[8,2,7,3,1,6,4,5]=>[3,6,7,8,2,1,4,5]=>[8,5,2,6,1,3,7,4]=>0001111
[6,2,3,4,1,8,5,7]=>[4,8,2,3,6,1,5,7]=>[8,7,5,6,1,4,3,2]=>0110111
[6,2,3,4,8,7,5,1]=>[5,7,2,3,6,4,8,1]=>[8,1,5,6,4,3,2,7]=>0110101
[8,5,7,1,4,6,3,2]=>[3,6,7,1,8,5,4,2]=>[7,4,1,3,8,2,6,5]=>0010111
[8,7,5,1,4,6,2,3]=>[6,5,1,2,7,4,8,3]=>[8,3,1,6,4,2,5,7]=>0110101
[8,7,2,5,1,4,6,3]=>[6,5,7,2,1,4,8,3]=>[6,4,2,5,1,8,3,7]=>0011101
[8,7,1,4,2,5,6,3]=>[6,4,7,1,2,5,8,3]=>[6,5,2,4,1,8,3,7]=>0011101
[8,7,5,1,2,4,6,3]=>[6,1,5,2,7,4,8,3]=>[6,4,2,1,8,3,5,7]=>1010101
[3,5,8,7,1,2,6,4]=>[6,1,3,7,5,2,8,4]=>[3,5,6,2,1,8,4,7]=>1000101
[2,3,8,5,7,1,6,4]=>[6,2,3,7,8,5,1,4]=>[2,3,8,4,7,1,6,5]=>0000111
[3,8,7,1,5,6,2,4]=>[6,7,3,1,2,5,8,4]=>[3,8,4,1,6,5,2,7]=>0011101
[3,5,8,7,1,6,2,4]=>[6,7,3,1,5,2,8,4]=>[3,5,8,4,1,6,2,7]=>0010101
[8,7,4,1,2,6,5,3]=>[5,1,4,6,7,2,8,3]=>[8,3,4,6,2,1,5,7]=>1000101
[5,7,1,8,2,6,3,4]=>[6,8,7,1,5,2,3,4]=>[5,7,3,8,4,1,6,2]=>0010111
[2,8,7,1,5,6,3,4]=>[6,2,7,1,3,5,8,4]=>[2,8,4,1,6,5,3,7]=>0011101
[1,8,3,7,2,5,6,4]=>[1,6,7,8,3,2,5,4]=>[1,6,2,7,5,3,8,4]=>0001111
[5,7,1,8,2,3,6,4]=>[6,8,1,7,5,2,3,4]=>[5,8,4,7,3,1,6,2]=>0100111
[7,1,8,2,3,5,6,4]=>[6,8,1,7,2,3,5,4]=>[6,3,1,8,4,7,5,2]=>0101111
[8,3,7,4,5,1,6,2]=>[6,5,7,8,3,4,1,2]=>[8,2,5,3,7,1,6,4]=>0001111
[8,7,2,4,1,5,6,3]=>[6,4,7,2,1,5,8,3]=>[4,2,6,5,1,8,3,7]=>0011101
[4,8,6,1,7,2,5,3]=>[5,7,6,4,1,8,2,3]=>[4,5,1,7,2,8,3,6]=>0001011
[8,7,4,1,2,5,6,3]=>[6,1,4,7,2,5,8,3]=>[6,5,2,1,8,3,4,7]=>1001101
[8,7,2,1,3,5,6,4]=>[2,6,1,7,3,5,8,4]=>[6,5,3,1,2,8,4,7]=>0101101
[1,8,7,2,6,3,4,5]=>[1,6,7,2,3,4,8,5]=>[1,6,4,2,8,5,3,7]=>0011101
[8,2,7,3,6,1,4,5]=>[6,7,8,2,3,1,4,5]=>[6,1,7,4,2,8,5,3]=>0011111
[8,2,7,4,1,5,6,3]=>[6,4,7,8,2,1,5,3]=>[6,1,8,3,7,5,2,4]=>0001111
[8,7,3,1,5,6,2,4]=>[6,3,7,1,2,5,8,4]=>[8,4,1,6,5,2,3,7]=>0011101
[2,8,7,3,5,6,1,4]=>[6,2,7,3,1,5,8,4]=>[2,6,5,1,8,4,3,7]=>0011101
[8,5,2,1,6,7,4,3]=>[2,4,7,5,8,1,6,3]=>[8,3,7,6,1,2,4,5]=>0000111
[1,5,2,8,6,7,4,3]=>[1,4,7,5,2,8,6,3]=>[1,5,2,4,8,3,7,6]=>0001011
[1,2,8,6,7,5,3,4]=>[1,2,5,3,7,8,6,4]=>[1,2,8,4,3,5,7,6]=>0010011
[1,8,3,6,7,5,2,4]=>[1,5,7,3,8,2,6,4]=>[1,8,4,3,7,6,2,5]=>0010111
[8,2,3,6,7,5,1,4]=>[5,7,2,3,8,1,6,4]=>[8,4,3,2,7,6,1,5]=>0110111
[8,3,7,2,5,6,1,4]=>[6,7,8,3,2,1,5,4]=>[6,1,7,5,2,8,4,3]=>0011111
[1,2,8,6,7,3,5,4]=>[1,2,5,7,3,8,6,4]=>[1,2,5,3,8,4,7,6]=>0001011
[8,1,2,7,3,6,4,5]=>[6,1,7,8,2,3,4,5]=>[8,5,2,1,6,3,7,4]=>1001111
[8,1,7,3,6,2,4,5]=>[6,7,8,1,3,2,4,5]=>[7,4,1,6,2,8,5,3]=>0011111
[8,1,7,2,6,3,4,5]=>[6,7,8,1,2,3,4,5]=>[8,5,2,7,4,1,6,3]=>0011111
[8,1,7,2,3,6,4,5]=>[6,7,1,8,2,3,4,5]=>[6,3,1,8,5,2,7,4]=>0101111
[1,7,8,2,3,6,5,4]=>[1,5,2,6,8,3,7,4]=>[1,7,8,4,6,3,2,5]=>0100101
[7,4,2,6,1,5,3,8]=>[5,6,4,7,2,1,3,8]=>[6,1,5,2,7,3,4,8]=>0001110
[5,3,8,2,6,7,4,1]=>[4,7,8,5,3,2,6,1]=>[7,6,2,8,1,4,5,3]=>0001111
[6,3,8,2,5,4,7,1]=>[7,5,8,6,3,2,4,1]=>[8,1,7,4,6,2,5,3]=>0001111
[5,3,7,8,2,6,4,1]=>[4,6,8,5,3,2,7,1]=>[6,2,7,8,1,4,5,3]=>0001101
[5,3,7,6,8,2,4,1]=>[4,8,5,3,2,7,6,1]=>[7,6,8,1,4,3,5,2]=>0011011
[5,7,8,4,6,2,1,3]=>[2,6,1,8,5,4,7,3]=>[5,7,8,3,1,2,6,4]=>0100101
[5,3,8,6,7,2,4,1]=>[4,7,5,3,2,8,6,1]=>[8,1,4,3,5,2,7,6]=>0011011
[5,3,7,8,6,2,4,1]=>[4,6,5,3,2,8,7,1]=>[7,8,1,4,3,5,2,6]=>0011001
[6,7,4,3,1,8,2,5]=>[8,3,4,7,1,6,2,5]=>[6,7,2,3,4,8,5,1]=>0001011
[5,4,6,8,2,7,1,3]=>[7,8,2,5,4,6,1,3]=>[5,4,6,7,1,8,3,2]=>0101011
[7,8,2,4,3,5,1,6]=>[5,4,8,2,3,1,7,6]=>[4,2,7,8,6,1,5,3]=>0011101
[1,4,2,6,5,7,3,8]=>[1,7,4,2,6,5,3,8]=>[1,6,5,7,3,4,2,8]=>0010110
[5,6,1,4,2,7,3,8]=>[7,4,6,1,5,2,3,8]=>[5,7,3,6,2,4,1,8]=>0010110
[6,7,3,5,4,8,1,2]=>[8,1,5,7,3,6,4,2]=>[5,3,6,7,4,8,2,1]=>1001011
[2,4,1,6,5,7,3,8]=>[7,2,4,1,6,5,3,8]=>[2,6,5,7,3,4,1,8]=>0010110
[4,5,1,6,3,7,2,8]=>[7,6,5,4,1,3,2,8]=>[4,7,2,6,3,5,1,8]=>0001110
[5,6,1,4,3,7,2,8]=>[7,4,6,1,5,3,2,8]=>[5,6,3,7,2,4,1,8]=>0010110
[6,7,5,8,1,3,2,4]=>[3,8,1,2,7,6,5,4]=>[3,1,6,7,5,8,4,2]=>0110011
[4,5,1,3,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[3,1,4,5,2,7,6,8]=>0101010
[4,5,2,3,1,7,6,8]=>[3,5,2,4,1,7,6,8]=>[4,5,1,3,2,7,6,8]=>0101010
[4,5,3,7,6,8,1,2]=>[8,1,5,4,3,7,6,2]=>[4,5,3,7,6,8,2,1]=>1001011
[3,5,4,6,1,7,2,8]=>[7,6,3,5,4,1,2,8]=>[3,5,4,7,2,6,1,8]=>0001110
[4,6,2,7,3,5,8,1]=>[8,7,6,4,2,3,5,1]=>[4,6,3,7,5,2,8,1]=>0001111
[4,6,1,7,3,8,2,5]=>[8,7,6,4,1,3,2,5]=>[4,6,3,7,2,8,5,1]=>0001111
[1,5,7,4,3,8,2,6]=>[1,8,4,7,5,3,2,6]=>[1,5,8,6,3,4,7,2]=>0000111
[1,5,7,2,8,3,6,4]=>[1,6,8,7,5,2,3,4]=>[1,5,6,2,8,4,7,3]=>0000111
[1,5,7,3,4,8,2,6]=>[1,8,7,3,5,4,2,6]=>[1,5,8,6,4,3,7,2]=>0010111
[2,1,5,6,8,4,3,7]=>[2,1,4,8,5,6,3,7]=>[2,1,5,6,8,7,3,4]=>1000011
[2,3,1,6,8,5,4,7]=>[3,2,1,5,8,6,4,7]=>[2,3,1,6,8,7,4,5]=>0100011
[1,3,6,2,8,7,4,5]=>[1,7,3,6,2,4,8,5]=>[1,3,6,4,8,5,2,7]=>0001101
[2,1,5,6,8,4,7,3]=>[2,1,7,8,5,6,4,3]=>[2,1,5,6,8,3,7,4]=>1000011
[2,1,5,6,8,7,3,4]=>[2,1,7,3,5,6,8,4]=>[2,1,5,6,8,4,3,7]=>1010001
[6,2,4,7,5,8,3,1]=>[3,8,7,2,6,4,5,1]=>[8,1,3,7,5,6,4,2]=>0010111
[3,7,4,1,8,6,2,5]=>[6,4,3,8,1,7,2,5]=>[3,8,5,1,6,7,2,4]=>0001011
[5,3,1,6,2,7,4,8]=>[7,3,6,5,1,2,4,8]=>[6,2,3,7,4,5,1,8]=>0001110
[5,2,6,3,1,7,4,8]=>[3,7,6,5,2,1,4,8]=>[6,1,3,7,4,5,2,8]=>0001110
[4,2,6,3,1,7,8,5]=>[3,8,4,2,6,1,7,5]=>[7,8,5,6,1,3,4,2]=>0010101
[5,4,1,6,2,7,3,8]=>[7,6,4,5,1,2,3,8]=>[6,2,7,3,4,5,1,8]=>0001110
[5,1,6,4,3,2,7,8]=>[3,4,6,5,1,2,7,8]=>[6,2,4,5,1,3,7,8]=>0001100
[1,2,8,7,4,6,3,5]=>[1,2,6,7,4,3,8,5]=>[1,2,6,3,8,5,4,7]=>0001101
[4,5,1,8,7,6,2,3]=>[6,5,1,4,2,7,8,3]=>[4,5,2,8,3,1,6,7]=>0101001
[5,1,2,8,7,6,3,4]=>[6,1,5,2,3,7,8,4]=>[5,3,8,4,2,1,6,7]=>1011001
[4,5,6,8,2,7,3,1]=>[3,7,8,4,5,6,2,1]=>[4,5,6,7,2,8,1,3]=>0000011
[6,8,3,5,7,1,4,2]=>[4,7,8,3,1,6,5,2]=>[6,8,2,7,5,1,4,3]=>0011011
[7,5,8,4,2,6,3,1]=>[3,6,4,8,7,5,2,1]=>[7,2,6,5,8,1,3,4]=>0000111
[6,8,4,5,2,7,3,1]=>[3,7,5,8,4,6,2,1]=>[6,7,2,8,1,3,5,4]=>0001011
[3,4,7,5,8,6,2,1]=>[2,6,3,4,8,7,5,1]=>[3,4,8,1,2,6,7,5]=>0000011
[3,6,7,4,8,5,2,1]=>[2,5,3,8,7,6,4,1]=>[3,6,8,1,2,5,7,4]=>0000011
[5,6,8,3,2,7,4,1]=>[4,3,7,8,5,6,2,1]=>[5,6,7,2,3,8,1,4]=>0000011
[3,6,8,4,2,7,5,1]=>[5,4,3,7,8,6,2,1]=>[3,6,7,2,4,8,1,5]=>0000011
[5,8,4,7,2,3,6,1]=>[6,7,2,8,5,4,3,1]=>[5,7,3,2,8,1,6,4]=>0100111
[1,7,4,8,6,2,5,3]=>[1,5,6,8,4,7,2,3]=>[1,8,3,6,7,2,5,4]=>0001011
[7,4,2,8,6,1,5,3]=>[5,6,4,8,2,7,1,3]=>[7,1,5,2,6,8,3,4]=>0001011
[6,8,5,2,3,7,4,1]=>[4,7,2,5,8,6,3,1]=>[6,7,3,2,8,1,4,5]=>0100011
[6,1,8,3,4,7,5,2]=>[5,7,8,1,6,3,4,2]=>[8,2,7,4,1,5,6,3]=>0010111
[7,5,8,3,4,6,2,1]=>[2,6,8,3,7,5,4,1]=>[8,1,2,6,5,7,4,3]=>0010111
[3,6,8,4,5,7,1,2]=>[7,1,3,8,4,6,5,2]=>[3,6,8,2,1,7,5,4]=>1001011
[1,4,5,8,7,2,3,6]=>[1,7,2,4,5,3,8,6]=>[1,4,5,8,6,3,2,7]=>0100101
[1,2,5,8,3,6,4,7]=>[1,2,6,8,5,3,4,7]=>[1,2,5,6,3,8,7,4]=>0000111
[7,8,1,4,6,2,3,5]=>[6,8,1,2,4,3,7,5]=>[6,3,1,7,8,5,4,2]=>0111101
[1,4,5,6,8,2,7,3]=>[1,7,8,4,5,6,2,3]=>[1,4,5,6,7,2,8,3]=>0000011
[1,2,5,8,3,4,7,6]=>[1,2,7,3,5,8,4,6]=>[1,2,5,7,4,3,8,6]=>0010011
[1,6,7,2,3,5,4,8]=>[1,5,2,7,3,6,4,8]=>[1,5,3,2,6,7,4,8]=>0101010
[1,2,5,7,3,6,4,8]=>[1,2,6,7,5,3,4,8]=>[1,2,5,6,3,7,4,8]=>0000110
[1,2,5,7,3,6,8,4]=>[1,2,8,7,5,3,6,4]=>[1,2,5,8,4,7,6,3]=>0000111
[1,6,8,2,3,4,7,5]=>[1,7,2,3,8,6,4,5]=>[1,6,7,4,3,2,8,5]=>0110011
[1,4,5,7,6,2,8,3]=>[1,8,6,4,5,7,2,3]=>[1,4,5,8,3,6,7,2]=>0000011
[7,8,1,4,5,2,6,3]=>[6,5,8,1,4,2,7,3]=>[6,2,5,4,1,7,8,3]=>0011101
[1,2,5,6,3,8,7,4]=>[1,2,7,6,5,3,8,4]=>[1,2,5,8,4,6,3,7]=>0000101
[2,7,4,8,3,5,1,6]=>[5,2,8,7,4,3,1,6]=>[2,7,1,5,4,8,6,3]=>0001111
[8,4,1,5,3,2,6,7]=>[3,5,4,8,1,2,6,7]=>[8,7,6,2,5,1,3,4]=>0001111
[6,7,3,8,4,2,5,1]=>[5,4,8,7,3,6,2,1]=>[6,7,2,4,8,1,5,3]=>0001011
[6,7,3,1,8,4,5,2]=>[5,3,8,7,1,6,4,2]=>[5,1,6,7,4,8,2,3]=>0001011
[1,6,7,8,4,3,2,5]=>[1,3,4,8,2,6,7,5]=>[1,6,7,8,5,2,3,4]=>0001001
[6,2,7,8,4,3,5,1]=>[5,4,8,6,2,3,7,1]=>[7,8,1,5,2,4,6,3]=>0001101
[2,6,7,1,8,5,3,4]=>[5,2,8,1,7,6,3,4]=>[2,6,8,4,1,5,7,3]=>0010011
[2,6,7,8,5,3,4,1]=>[4,2,5,3,8,6,7,1]=>[2,6,7,8,1,4,3,5]=>0010001
[6,7,1,2,8,5,3,4]=>[5,1,8,2,7,6,3,4]=>[6,8,4,2,1,5,7,3]=>1010011
[1,7,5,3,6,4,8,2]=>[1,8,6,5,7,3,4,2]=>[1,6,3,7,4,5,8,2]=>0000111
[4,6,1,8,3,2,5,7]=>[3,8,6,4,1,2,5,7]=>[4,8,7,5,1,3,6,2]=>0001111
[4,1,7,8,6,2,3,5]=>[6,4,1,2,3,8,7,5]=>[4,2,7,8,5,3,1,6]=>0111001
[1,6,5,7,8,3,4,2]=>[1,4,8,3,6,5,7,2]=>[1,6,5,7,8,2,4,3]=>0010101
[1,6,5,8,7,3,4,2]=>[1,4,7,3,6,5,8,2]=>[1,6,5,8,2,4,3,7]=>0010101
[4,8,1,7,3,5,2,6]=>[5,7,8,4,1,3,2,6]=>[4,5,1,7,2,8,6,3]=>0001111
[4,8,1,6,3,2,5,7]=>[3,6,8,4,1,2,5,7]=>[4,6,2,8,7,5,1,3]=>0001111
[6,1,2,3,7,5,4,8]=>[5,1,2,7,6,3,4,8]=>[6,3,2,1,5,7,4,8]=>1100110
[6,8,1,5,3,7,2,4]=>[7,5,8,1,3,6,2,4]=>[6,8,4,1,7,2,5,3]=>0011011
[1,5,8,3,4,7,6,2]=>[1,6,7,3,5,8,4,2]=>[1,5,7,4,3,8,2,6]=>0010011
[6,7,2,4,3,1,5,8]=>[3,4,7,2,1,6,5,8]=>[4,2,6,7,5,1,3,8]=>0011010
[3,7,1,8,6,4,2,5]=>[4,6,3,8,1,7,2,5]=>[3,7,2,6,8,5,1,4]=>0001011
[3,1,2,6,7,5,8,4]=>[3,1,2,8,7,6,5,4]=>[3,2,1,6,7,5,8,4]=>1100011
[8,1,7,6,5,3,2,4]=>[3,5,6,1,7,8,2,4]=>[7,2,5,8,4,1,3,6]=>0010011
[7,1,2,3,5,4,8,6]=>[5,1,2,8,3,7,4,6]=>[5,3,2,1,8,6,7,4]=>1101011
[8,6,5,2,4,7,1,3]=>[7,5,2,1,6,8,4,3]=>[7,4,1,8,3,2,5,6]=>0110011
[5,7,8,4,2,6,3,1]=>[3,6,4,8,5,2,7,1]=>[5,6,2,7,8,1,3,4]=>0000101
[6,8,4,5,7,1,3,2]=>[3,7,1,8,4,6,5,2]=>[3,1,6,8,2,7,5,4]=>0101011
[5,8,4,6,1,7,3,2]=>[3,7,6,8,5,4,1,2]=>[5,8,2,7,1,3,6,4]=>0000111
[5,3,6,7,4,8,2,1]=>[2,8,7,5,3,6,4,1]=>[6,7,4,5,3,8,1,2]=>0001011
[5,4,8,2,6,7,3,1]=>[3,7,8,5,4,2,6,1]=>[5,4,7,6,2,8,1,3]=>0001111
[5,4,8,6,2,7,3,1]=>[3,7,6,5,4,8,2,1]=>[5,4,7,2,8,1,3,6]=>0001011
[6,4,8,5,7,2,3,1]=>[3,7,2,8,6,4,5,1]=>[8,1,3,2,7,5,6,4]=>0100111
[4,3,7,2,8,6,5,1]=>[5,6,4,3,8,7,2,1]=>[4,3,7,2,6,8,1,5]=>0010011
[5,3,2,7,6,8,4,1]=>[4,3,8,5,2,7,6,1]=>[7,6,8,1,4,5,2,3]=>0001011
[6,7,3,8,5,2,4,1]=>[4,5,8,3,7,6,2,1]=>[6,7,2,5,8,1,4,3]=>0010011
[6,2,7,5,1,4,8,3]=>[8,5,7,2,6,1,4,3]=>[8,3,7,4,2,5,6,1]=>0010111
[2,6,8,4,7,3,5,1]=>[5,2,7,8,4,6,3,1]=>[2,6,7,3,8,1,5,4]=>0001011
[6,3,1,8,7,5,4,2]=>[4,3,5,7,6,1,8,2]=>[8,2,3,5,6,1,4,7]=>0000101
[7,5,4,1,8,6,3,2]=>[3,6,4,5,8,7,1,2]=>[8,2,6,7,1,3,4,5]=>0000011
[2,6,8,4,3,5,7,1]=>[7,2,4,8,3,6,5,1]=>[2,6,8,1,7,5,3,4]=>0001011
[2,6,5,7,3,4,1,8]=>[4,2,7,3,6,5,1,8]=>[2,6,5,7,1,4,3,8]=>0010110
[6,2,5,7,4,1,3,8]=>[4,7,2,6,1,5,3,8]=>[6,5,1,4,7,3,2,8]=>0101110
[1,6,2,4,8,7,3,5]=>[1,7,6,2,4,3,8,5]=>[1,6,3,8,5,4,2,7]=>0011101
[6,5,2,1,8,7,3,4]=>[2,7,5,1,6,3,8,4]=>[6,3,5,8,4,1,2,7]=>0010101
[2,6,5,3,7,8,4,1]=>[4,2,8,5,6,3,7,1]=>[2,7,8,1,4,5,6,3]=>0000101
[5,1,4,2,3,7,8,6]=>[4,5,1,2,3,8,7,6]=>[5,3,1,4,2,7,8,6]=>0111001
[5,1,6,3,8,2,7,4]=>[7,8,6,5,1,3,2,4]=>[6,3,8,4,5,1,7,2]=>0001111
[6,4,2,7,8,5,1,3]=>[5,4,2,8,6,1,7,3]=>[6,1,5,7,8,3,2,4]=>0100101
[1,6,4,8,7,5,2,3]=>[1,5,2,7,6,4,8,3]=>[1,8,3,2,5,6,4,7]=>0100101
[1,8,6,2,4,7,3,5]=>[1,7,6,2,4,8,3,5]=>[1,8,5,4,2,7,3,6]=>0011011
[6,4,1,7,8,5,2,3]=>[5,4,1,8,6,2,7,3]=>[7,8,3,1,5,6,2,4]=>0100101
[1,8,6,3,4,7,2,5]=>[1,7,6,3,4,8,2,5]=>[1,7,2,8,5,4,3,6]=>0011011
[7,2,1,5,4,8,3,6]=>[2,8,5,7,1,4,3,6]=>[8,6,4,7,3,5,1,2]=>0001111
[1,2,7,5,4,8,3,6]=>[1,2,8,5,7,4,3,6]=>[1,2,8,6,4,5,7,3]=>0000111
[2,5,8,4,7,3,1,6]=>[3,2,7,8,5,4,1,6]=>[2,5,7,1,3,8,6,4]=>0000111
[3,7,2,5,4,8,1,6]=>[8,5,3,7,2,4,1,6]=>[3,5,2,8,6,4,7,1]=>0001111
[8,1,5,4,7,3,2,6]=>[3,7,5,8,1,4,2,6]=>[5,1,3,7,2,8,6,4]=>0001111
[8,6,4,1,7,2,5,3]=>[5,7,4,6,1,8,2,3]=>[5,1,7,2,8,3,4,6]=>0001011
[7,3,6,5,2,1,4,8]=>[2,5,6,3,7,1,4,8]=>[7,4,3,6,1,2,5,8]=>0010110
[5,4,2,8,1,3,7,6]=>[7,4,2,5,1,8,3,6]=>[7,3,2,4,5,1,8,6]=>0101011
[5,8,2,6,4,1,3,7]=>[4,6,2,8,5,1,3,7]=>[5,8,7,3,2,6,1,4]=>0100111
[2,3,6,8,1,5,7,4]=>[7,2,3,8,1,6,5,4]=>[2,3,6,7,5,1,8,4]=>0001011
[2,5,7,6,3,1,4,8]=>[3,2,6,1,5,7,4,8]=>[2,5,7,4,1,3,6,8]=>0010010
[2,8,7,3,6,1,4,5]=>[6,2,7,3,1,4,8,5]=>[2,8,5,1,6,4,3,7]=>0011101
[2,3,6,8,1,4,7,5]=>[7,2,3,1,8,6,4,5]=>[2,3,6,7,4,1,8,5]=>0010011
[2,7,8,6,3,1,4,5]=>[3,2,6,1,4,8,7,5]=>[2,7,8,5,4,1,3,6]=>0011001
[2,8,6,3,1,4,5,7]=>[3,2,6,1,4,8,5,7]=>[2,8,7,5,4,1,3,6]=>0011011
[2,6,8,1,5,7,3,4]=>[7,2,8,1,3,6,5,4]=>[2,6,8,4,1,7,5,3]=>0011011
[6,8,4,5,1,7,2,3]=>[7,5,1,8,4,6,2,3]=>[6,8,3,1,7,2,5,4]=>0101011
[5,1,8,7,6,2,3,4]=>[6,5,1,2,3,7,8,4]=>[8,4,2,5,3,1,6,7]=>0111001
[8,5,1,6,2,7,3,4]=>[7,6,5,1,8,2,3,4]=>[6,2,8,4,1,7,3,5]=>0010111
[8,4,6,1,7,5,2,3]=>[5,7,1,6,8,4,2,3]=>[6,4,7,2,8,3,1,5]=>0100111
[4,8,5,1,7,2,3,6]=>[7,5,1,4,8,2,3,6]=>[4,7,3,1,8,6,2,5]=>0100111
[3,4,8,7,1,2,5,6]=>[7,1,3,4,2,5,8,6]=>[3,4,8,6,5,2,1,7]=>1001101
[6,5,1,8,2,7,3,4]=>[7,8,5,1,6,2,3,4]=>[8,4,1,7,3,5,6,2]=>0010111
[8,6,5,1,2,7,3,4]=>[7,1,5,2,6,8,3,4]=>[8,4,2,1,7,3,5,6]=>1010011
[6,8,5,7,4,1,2,3]=>[4,1,2,7,8,6,5,3]=>[6,8,3,2,1,4,7,5]=>1100011
[5,8,2,1,4,7,3,6]=>[2,7,8,1,5,4,3,6]=>[5,8,6,4,1,2,7,3]=>0010111
[6,8,4,2,1,5,7,3]=>[2,7,4,8,1,6,5,3]=>[6,7,5,1,2,8,3,4]=>0001011
[6,8,3,2,1,4,5,7]=>[2,3,8,1,4,6,5,7]=>[6,8,7,5,4,1,2,3]=>0011011
[5,4,7,2,1,6,8,3]=>[2,8,7,5,4,1,6,3]=>[5,4,8,3,7,6,1,2]=>0001111
[3,2,1,7,6,4,8,5]=>[2,3,1,8,6,7,4,5]=>[3,1,2,8,5,6,7,4]=>0100011
[4,2,1,6,5,8,3,7]=>[2,8,4,1,6,5,3,7]=>[6,5,8,7,3,4,1,2]=>0010111
[7,4,3,1,8,5,6,2]=>[6,3,4,8,7,1,5,2]=>[6,1,7,5,8,2,3,4]=>0000111
[5,3,2,7,6,1,4,8]=>[6,3,5,2,1,7,4,8]=>[7,4,2,3,5,1,6,8]=>0011010
[6,3,2,8,7,1,4,5]=>[7,3,6,2,1,4,8,5]=>[6,4,2,3,8,5,1,7]=>0011101
[4,2,8,1,7,3,5,6]=>[7,8,4,2,1,3,5,6]=>[7,5,1,8,6,3,4,2]=>0011111
[2,1,5,8,4,7,3,6]=>[2,1,7,8,5,4,3,6]=>[2,1,5,7,3,8,6,4]=>1000111
[4,3,1,6,2,7,5,8]=>[7,3,4,1,6,2,5,8]=>[7,5,6,2,3,4,1,8]=>0010110
[5,4,1,7,2,8,6,3]=>[6,8,4,5,1,7,2,3]=>[8,3,4,5,1,6,7,2]=>0001011
[5,3,2,6,8,1,7,4]=>[7,3,8,5,2,6,1,4]=>[6,7,1,8,4,5,2,3]=>0001011
[3,2,1,4,6,8,5,7]=>[2,3,1,4,8,6,5,7]=>[3,1,2,4,6,8,7,5]=>0100011
[8,6,1,4,5,7,2,3]=>[7,6,1,2,4,8,5,3]=>[8,3,1,7,5,4,2,6]=>0111011
[3,8,6,4,5,7,1,2]=>[7,1,3,6,4,8,5,2]=>[3,8,2,1,7,5,4,6]=>1001011
[6,2,8,5,4,7,3,1]=>[3,7,5,8,6,2,4,1]=>[8,1,3,5,6,2,7,4]=>0000111
[6,5,3,8,4,7,2,1]=>[2,7,8,5,6,3,4,1]=>[8,1,2,7,4,5,6,3]=>0000111
[5,2,8,4,3,7,1,6]=>[7,4,8,5,2,3,1,6]=>[5,2,4,7,1,8,6,3]=>0001111
[5,4,2,7,3,1,8,6]=>[3,8,4,5,2,7,1,6]=>[8,6,7,1,3,4,5,2]=>0001011
[7,2,8,4,3,1,5,6]=>[3,4,8,7,2,1,5,6]=>[7,5,2,4,8,6,1,3]=>0001111
[5,4,1,7,3,8,2,6]=>[8,7,4,5,1,3,2,6]=>[7,2,8,6,3,4,5,1]=>0001111
[8,1,6,5,7,3,4,2]=>[4,7,6,1,8,3,5,2]=>[4,1,6,3,8,2,7,5]=>0010111
[8,4,1,5,7,6,2,3]=>[6,4,1,7,2,8,5,3]=>[7,5,2,4,8,3,1,6]=>0101011
[7,8,6,2,5,3,1,4]=>[3,5,6,2,1,8,7,4]=>[7,8,4,2,5,1,3,6]=>0011001
[2,7,6,4,8,3,5,1]=>[5,2,8,6,4,7,3,1]=>[2,8,1,5,4,6,7,3]=>0001011
[8,4,7,6,3,1,5,2]=>[5,3,6,7,4,8,1,2]=>[7,1,5,4,8,2,3,6]=>0001011
[2,7,6,1,3,4,8,5]=>[8,2,1,3,6,7,4,5]=>[2,8,5,6,7,4,3,1]=>0110011
[5,7,2,1,6,3,8,4]=>[2,8,6,7,5,1,3,4]=>[5,8,4,7,3,6,1,2]=>0000111
[4,7,2,5,6,3,8,1]=>[8,6,7,4,2,5,3,1]=>[4,6,5,2,7,3,8,1]=>0001111
[1,8,5,6,2,4,7,3]=>[1,7,6,2,8,5,4,3]=>[1,7,4,2,8,3,6,5]=>0010111
[6,4,8,1,3,2,7,5]=>[3,7,1,8,6,4,2,5]=>[3,1,7,2,8,5,6,4]=>0100111
[5,4,1,2,8,6,7,3]=>[7,1,4,5,2,8,6,3]=>[8,3,4,5,2,1,7,6]=>1001011
[8,4,5,2,1,6,7,3]=>[2,7,5,8,4,1,6,3]=>[7,6,1,2,8,3,5,4]=>0001111
[3,1,2,6,8,4,7,5]=>[3,1,2,7,8,6,4,5]=>[3,2,1,6,7,4,8,5]=>1100011
[5,1,3,2,7,8,4,6]=>[3,8,1,5,2,4,7,6]=>[3,1,7,8,6,4,5,2]=>0101101
[4,6,7,8,3,1,5,2]=>[5,3,8,4,1,6,7,2]=>[4,5,1,6,7,8,2,3]=>0001001
[5,6,8,4,3,2,7,1]=>[7,3,4,8,5,6,2,1]=>[5,6,8,1,7,2,3,4]=>0000011
[3,6,7,8,4,2,1,5]=>[2,4,3,8,1,6,7,5]=>[3,6,7,8,5,1,2,4]=>0001001
[5,1,8,3,4,6,7,2]=>[7,8,5,1,3,4,6,2]=>[5,3,7,6,4,1,8,2]=>0011111
[2,8,1,6,3,4,7,5]=>[7,2,6,1,8,3,4,5]=>[2,6,3,7,4,1,8,5]=>0010111
[1,4,5,8,2,3,7,6]=>[1,7,2,4,5,8,3,6]=>[1,4,5,7,3,2,8,6]=>0100011
[2,5,1,8,4,7,3,6]=>[7,2,8,5,1,4,3,6]=>[2,8,6,4,5,1,7,3]=>0001111
[2,7,1,4,3,6,8,5]=>[4,2,8,1,7,3,6,5]=>[2,4,1,8,5,7,6,3]=>0010111
[1,3,7,5,8,2,4,6]=>[1,8,3,2,7,5,4,6]=>[1,3,8,6,5,7,4,2]=>0010111
[8,2,1,5,7,3,4,6]=>[2,7,8,1,3,5,4,6]=>[7,4,1,2,8,6,5,3]=>0011111
[2,4,1,3,8,6,7,5]=>[4,2,1,3,7,8,6,5]=>[2,4,3,1,8,5,7,6]=>0110011
[1,7,3,5,8,2,6,4]=>[1,6,8,7,3,5,2,4]=>[1,8,4,7,2,6,5,3]=>0001111
[7,2,1,6,3,5,8,4]=>[2,8,6,7,1,3,5,4]=>[6,3,8,4,7,5,1,2]=>0001111
[8,1,3,2,4,6,7,5]=>[3,7,1,2,8,4,6,5]=>[3,1,7,6,4,2,8,5]=>0110111
[7,3,1,2,4,6,8,5]=>[3,1,8,2,7,4,6,5]=>[8,5,7,6,4,2,1,3]=>1010111
[1,3,7,4,8,2,6,5]=>[1,6,3,8,7,4,2,5]=>[1,3,8,5,7,2,6,4]=>0000111
[2,6,8,1,7,3,4,5]=>[7,2,8,1,3,6,4,5]=>[2,6,7,4,1,8,5,3]=>0011011
[2,6,7,3,8,1,5,4]=>[5,2,8,7,3,6,1,4]=>[2,6,8,4,7,1,5,3]=>0001011
[8,4,1,7,3,6,2,5]=>[6,7,4,8,1,3,2,5]=>[7,2,8,5,1,6,3,4]=>0001111
[5,1,8,7,4,2,6,3]=>[6,4,7,5,1,2,8,3]=>[6,2,4,5,1,8,3,7]=>0001101
[4,7,2,6,3,5,8,1]=>[8,6,7,4,2,3,5,1]=>[4,7,5,2,6,3,8,1]=>0001111
[1,2,6,4,7,8,3,5]=>[1,2,8,6,4,3,7,5]=>[1,2,7,8,5,4,6,3]=>0001101
[3,6,4,7,8,1,5,2]=>[5,8,3,6,4,1,7,2]=>[3,6,1,5,4,7,8,2]=>0001101
[4,3,6,7,1,8,2,5]=>[8,7,4,3,1,6,2,5]=>[4,3,6,7,2,8,5,1]=>0011011
[1,6,7,3,8,2,5,4]=>[1,5,8,7,3,6,2,4]=>[1,6,8,4,7,2,5,3]=>0001011
[4,8,6,1,5,3,2,7]=>[3,5,6,4,1,8,2,7]=>[4,8,7,2,5,1,3,6]=>0001011
[5,8,6,4,1,3,2,7]=>[3,4,1,6,5,8,2,7]=>[3,1,5,8,7,2,4,6]=>0100011
[4,3,7,8,1,6,2,5]=>[6,8,4,3,1,2,7,5]=>[4,3,7,8,5,1,6,2]=>0011101
[3,5,8,7,4,1,2,6]=>[4,1,3,7,5,2,8,6]=>[3,5,8,6,2,1,4,7]=>1000101
[4,8,1,2,7,3,5,6]=>[7,1,8,4,2,3,5,6]=>[4,7,5,2,1,8,6,3]=>1001111
[5,6,8,4,1,3,7,2]=>[7,4,1,8,5,6,3,2]=>[5,6,7,3,1,8,2,4]=>0100011
[8,5,4,7,1,6,3,2]=>[3,6,7,5,8,4,1,2]=>[7,1,3,8,2,6,4,5]=>0000111
[2,5,8,7,3,6,4,1]=>[4,2,6,7,5,3,8,1]=>[2,5,6,3,8,1,4,7]=>0000101
[3,7,4,8,5,6,2,1]=>[2,6,3,8,7,4,5,1]=>[3,7,5,8,1,2,6,4]=>0000111
[3,8,5,2,4,6,7,1]=>[7,5,3,2,8,4,6,1]=>[3,8,1,7,6,4,2,5]=>0010111
[2,3,7,8,5,6,1,4]=>[6,2,3,1,8,5,7,4]=>[2,3,7,8,4,1,6,5]=>0010101
[5,4,7,8,2,6,3,1]=>[3,6,8,5,4,2,7,1]=>[5,4,6,2,7,8,1,3]=>0001101
[6,8,3,4,1,2,7,5]=>[4,1,7,3,8,6,2,5]=>[6,7,2,1,4,3,8,5]=>1010011
[4,5,3,2,8,6,7,1]=>[7,3,5,4,2,8,6,1]=>[4,5,2,3,8,1,7,6]=>0001011
[2,8,5,6,1,4,7,3]=>[7,2,6,1,8,5,4,3]=>[2,7,4,1,8,3,6,5]=>0010111
[4,6,8,5,3,2,7,1]=>[7,3,5,4,8,6,2,1]=>[4,6,8,1,7,2,3,5]=>0000011
[7,6,4,8,5,2,1,3]=>[2,5,1,8,6,7,4,3]=>[8,3,1,2,5,6,7,4]=>0100011
[5,1,6,4,3,2,8,7]=>[3,4,6,5,1,2,8,7]=>[6,2,4,5,1,3,8,7]=>0001101
[8,3,7,1,4,6,5,2]=>[5,6,7,3,8,1,4,2]=>[7,4,3,8,2,6,1,5]=>0010111
[2,8,3,6,4,7,5,1]=>[5,2,7,6,8,3,4,1]=>[2,7,4,6,3,8,1,5]=>0000111
[6,2,1,7,5,8,3,4]=>[2,8,7,1,6,3,5,4]=>[7,5,6,3,8,4,1,2]=>0010111
[1,8,3,5,6,2,4,7]=>[1,6,8,3,2,5,4,7]=>[1,6,5,2,8,7,4,3]=>0011111
[5,7,4,1,2,3,8,6]=>[4,1,2,8,5,7,3,6]=>[5,8,6,7,3,2,1,4]=>1100011
[1,7,4,2,5,3,8,6]=>[1,5,4,8,2,7,3,6]=>[1,5,2,8,6,7,3,4]=>0001011
[6,4,3,8,5,7,1,2]=>[7,1,4,8,6,3,5,2]=>[8,2,1,7,5,6,3,4]=>1000111
[8,3,7,4,5,6,1,2]=>[6,1,7,8,3,4,5,2]=>[7,5,3,8,2,1,6,4]=>1001111
[2,7,4,3,1,5,6,8]=>[3,2,4,7,1,5,6,8]=>[2,7,6,5,1,3,4,8]=>0001110
[6,8,4,2,3,1,5,7]=>[3,4,2,8,1,6,5,7]=>[6,8,7,5,1,3,2,4]=>0101011
[2,1,7,4,8,3,5,6]=>[2,1,8,7,4,3,5,6]=>[2,1,7,5,4,8,6,3]=>1001111
[2,8,3,1,4,5,6,7]=>[3,2,8,1,4,5,6,7]=>[2,8,7,6,5,4,1,3]=>0011111
[4,2,7,3,1,5,6,8]=>[3,7,4,2,1,5,6,8]=>[7,6,5,1,3,4,2,8]=>0011110
[8,3,7,2,1,4,5,6]=>[2,7,8,3,1,4,5,6]=>[7,5,1,2,8,6,4,3]=>0011111
[7,8,4,1,3,6,2,5]=>[6,4,1,8,3,2,7,5]=>[7,8,5,3,1,6,2,4]=>0101101
[6,5,8,1,3,7,2,4]=>[7,8,1,3,6,5,2,4]=>[6,5,8,4,3,1,7,2]=>0110111
[5,3,6,1,8,2,4,7]=>[8,6,5,3,1,2,4,7]=>[6,2,8,7,4,3,5,1]=>0011111
[4,7,3,1,8,2,5,6]=>[8,3,7,4,1,2,5,6]=>[4,8,6,2,3,7,5,1]=>0001111
[4,1,5,8,3,7,6,2]=>[6,7,4,1,5,8,3,2]=>[5,8,2,7,3,4,1,6]=>0010011
[4,8,6,3,7,1,5,2]=>[5,7,6,4,3,8,1,2]=>[4,8,2,7,1,5,3,6]=>0001011
[5,6,2,7,4,1,8,3]=>[8,4,7,6,5,2,1,3]=>[5,6,2,4,8,3,7,1]=>0000111
[5,6,7,2,1,8,3,4]=>[2,8,7,1,5,6,3,4]=>[5,6,7,3,8,4,1,2]=>0010011
[5,6,1,7,8,4,2,3]=>[4,8,1,6,5,2,7,3]=>[5,7,8,3,1,4,6,2]=>0100101
[4,6,8,1,7,5,2,3]=>[5,7,1,4,8,6,2,3]=>[4,6,7,2,8,3,1,5]=>0100011
[4,8,6,1,7,5,3,2]=>[3,5,7,4,6,8,1,2]=>[4,7,1,3,8,2,5,6]=>0000011
[5,6,7,1,8,3,2,4]=>[3,8,7,1,5,6,2,4]=>[5,6,8,4,1,3,7,2]=>0010011
[5,6,7,1,3,8,2,4]=>[8,7,1,3,5,6,2,4]=>[5,6,7,2,8,4,3,1]=>0110011
[7,8,3,1,5,6,2,4]=>[6,3,8,1,2,5,7,4]=>[7,8,4,1,6,5,2,3]=>0011101
[1,5,7,8,3,4,6,2]=>[1,6,8,3,5,4,7,2]=>[1,5,7,8,2,6,4,3]=>0010101
[3,7,1,5,8,6,2,4]=>[6,8,3,1,2,7,5,4]=>[3,8,4,1,6,7,5,2]=>0011011
[1,3,7,5,8,2,6,4]=>[1,6,3,8,7,5,2,4]=>[1,3,7,2,6,5,8,4]=>0000111
[3,5,7,1,8,4,6,2]=>[6,8,3,7,5,1,4,2]=>[3,5,6,1,7,4,8,2]=>0000111
[5,3,7,8,4,1,6,2]=>[6,4,8,5,3,1,7,2]=>[6,1,7,8,2,4,5,3]=>0001101
[2,5,8,1,7,3,4,6]=>[7,2,8,1,5,3,4,6]=>[2,5,7,4,1,8,6,3]=>0010111
[6,8,2,3,7,1,4,5]=>[7,8,2,3,1,6,4,5]=>[6,8,5,1,7,4,3,2]=>0111011
[8,6,2,7,4,5,1,3]=>[5,7,2,6,1,8,4,3]=>[5,1,8,3,2,7,4,6]=>0101011
[5,2,8,1,7,3,4,6]=>[7,8,5,2,1,3,4,6]=>[8,6,3,5,1,7,4,2]=>0011111
[4,2,3,8,1,5,6,7]=>[8,4,2,3,1,5,6,7]=>[4,3,2,8,7,6,5,1]=>0111111
[2,1,5,8,4,3,6,7]=>[2,1,4,8,5,3,6,7]=>[2,1,5,8,7,6,3,4]=>1000111
[3,1,8,4,2,5,6,7]=>[4,3,1,8,2,5,6,7]=>[8,7,6,5,2,3,1,4]=>0101111
[3,8,4,2,1,5,6,7]=>[2,4,3,8,1,5,6,7]=>[3,8,7,6,5,1,2,4]=>0001111
[2,3,8,4,1,5,6,7]=>[4,2,3,8,1,5,6,7]=>[2,3,8,7,6,5,1,4]=>0001111
[3,4,2,8,1,5,6,7]=>[8,4,3,2,1,5,6,7]=>[3,4,2,8,7,6,5,1]=>0011111
[2,1,4,8,5,3,6,7]=>[2,1,5,4,8,3,6,7]=>[2,1,4,8,7,6,3,5]=>1000111
[3,2,8,4,1,5,6,7]=>[4,3,2,8,1,5,6,7]=>[3,2,8,7,6,5,1,4]=>0101111
[2,8,4,3,1,5,6,7]=>[3,2,4,8,1,5,6,7]=>[2,8,7,6,5,1,3,4]=>0001111
[4,1,7,5,6,2,8,3]=>[8,6,4,1,7,5,2,3]=>[7,2,6,5,8,3,4,1]=>0010111
[5,7,4,3,8,2,6,1]=>[6,8,4,7,5,3,2,1]=>[5,8,1,6,3,4,7,2]=>0000111
[3,8,4,2,6,7,5,1]=>[5,4,3,7,8,2,6,1]=>[3,7,6,2,4,8,1,5]=>0000111
[6,1,7,5,2,8,4,3]=>[4,8,5,7,6,1,2,3]=>[8,3,5,6,1,4,7,2]=>0000111
[2,6,7,5,3,8,4,1]=>[4,2,8,5,7,6,3,1]=>[2,6,8,1,4,5,7,3]=>0000011
[6,1,3,4,8,2,5,7]=>[8,6,1,3,4,2,5,7]=>[6,2,8,7,5,4,3,1]=>0111111
[6,7,5,8,3,1,4,2]=>[4,3,8,1,7,6,5,2]=>[4,1,6,7,5,8,2,3]=>0010011
[6,7,4,8,2,3,5,1]=>[5,8,2,7,4,6,3,1]=>[6,8,1,5,4,7,3,2]=>0101011
[2,6,7,5,1,3,8,4]=>[8,2,1,5,7,6,3,4]=>[2,6,8,4,5,7,3,1]=>0100011
[6,7,4,8,1,3,2,5]=>[3,8,1,7,4,6,2,5]=>[3,1,6,8,5,4,7,2]=>0101011
[6,7,5,8,4,1,3,2]=>[3,4,1,8,7,6,5,2]=>[3,1,6,7,5,8,2,4]=>0100011
[7,8,3,2,6,1,4,5]=>[6,3,8,2,1,4,7,5]=>[7,8,5,1,6,4,2,3]=>0011101
[7,8,5,1,4,6,3,2]=>[3,6,5,1,8,4,7,2]=>[7,8,2,6,4,1,3,5]=>0010101
[6,2,4,8,1,5,3,7]=>[5,8,6,2,4,1,3,7]=>[8,7,3,6,1,5,4,2]=>0011111
[4,2,6,8,1,5,3,7]=>[5,8,4,2,1,6,3,7]=>[5,1,6,8,7,3,4,2]=>0011011
[1,2,7,8,5,3,4,6]=>[1,2,5,3,8,4,7,6]=>[1,2,7,8,6,4,3,5]=>0010101
[6,1,5,7,8,4,3,2]=>[3,4,8,6,1,5,7,2]=>[7,8,2,4,6,5,1,3]=>0001101
[3,1,8,4,5,6,7,2]=>[7,3,1,8,4,5,6,2]=>[8,2,3,1,7,6,5,4]=>0101111
[3,2,7,8,5,1,4,6]=>[5,3,2,1,8,4,7,6]=>[3,2,7,8,6,4,1,5]=>0110101
[2,7,3,8,5,1,4,6]=>[5,2,8,3,7,1,4,6]=>[2,8,6,1,5,7,4,3]=>0010111
[1,4,2,8,7,5,3,6]=>[1,5,4,2,7,3,8,6]=>[1,8,6,3,4,2,5,7]=>0010101
[1,2,6,8,4,5,3,7]=>[1,2,5,8,4,6,3,7]=>[1,2,6,8,7,3,5,4]=>0001011
[7,1,6,5,8,4,3,2]=>[3,4,8,6,7,1,5,2]=>[7,5,8,2,4,6,1,3]=>0000111
[6,7,1,5,8,4,3,2]=>[3,4,8,7,1,6,5,2]=>[6,8,2,4,7,5,1,3]=>0001011
[7,1,6,5,3,2,4,8]=>[3,5,6,1,7,2,4,8]=>[7,4,1,3,6,2,5,8]=>0010110
[1,8,7,5,3,2,4,6]=>[1,3,5,2,7,4,8,6]=>[1,8,6,4,2,3,5,7]=>0010101
[1,8,7,4,2,5,3,6]=>[1,5,4,7,2,3,8,6]=>[1,5,2,8,6,3,4,7]=>0001101
[7,1,6,4,2,5,3,8]=>[5,4,6,7,1,2,3,8]=>[5,1,7,3,6,2,4,8]=>0001110
[7,1,5,3,6,4,2,8]=>[4,6,5,7,1,3,2,8]=>[7,2,6,3,5,1,4,8]=>0001110
[7,4,2,8,6,3,5,1]=>[5,6,4,8,2,7,3,1]=>[8,1,5,2,6,7,3,4]=>0001011
[2,3,1,8,7,5,4,6]=>[3,2,1,5,7,4,8,6]=>[2,3,1,8,6,4,5,7]=>0100101
[7,4,2,1,8,6,3,5]=>[2,6,4,8,1,7,3,5]=>[8,5,1,2,6,7,3,4]=>0001011
[1,8,6,3,5,7,4,2]=>[1,4,7,6,3,8,5,2]=>[1,7,5,3,8,2,4,6]=>0001011
[8,6,3,7,4,2,1,5]=>[2,4,7,6,3,8,1,5]=>[8,5,3,7,1,2,4,6]=>0001011
[5,1,8,6,3,7,4,2]=>[4,7,6,5,1,8,3,2]=>[5,1,4,8,2,7,3,6]=>0001011
[6,3,7,4,1,8,5,2]=>[5,4,8,7,6,3,1,2]=>[8,2,4,7,1,5,6,3]=>0000111
[6,1,8,7,5,3,2,4]=>[3,5,7,1,6,2,8,4]=>[6,2,5,8,4,1,3,7]=>0010101
[2,4,5,1,3,8,7,6]=>[5,2,1,4,3,7,8,6]=>[2,4,5,3,1,8,6,7]=>0101001
[1,7,5,8,6,3,2,4]=>[1,3,6,2,8,7,5,4]=>[1,8,4,2,3,6,7,5]=>0010011
[8,6,3,1,7,4,2,5]=>[4,3,7,6,1,8,2,5]=>[7,2,3,8,5,1,4,6]=>0001011
[8,7,4,2,5,3,1,6]=>[3,5,4,7,2,1,8,6]=>[5,2,8,6,1,3,4,7]=>0001101
[5,3,1,8,7,4,2,6]=>[4,3,7,5,1,2,8,6]=>[5,1,4,8,6,2,3,7]=>0001101
[7,4,2,8,6,3,1,5]=>[3,6,4,8,2,7,1,5]=>[8,5,2,6,7,1,3,4]=>0001011
[7,4,8,5,2,6,3,1]=>[3,6,5,8,7,4,2,1]=>[8,1,3,5,7,2,6,4]=>0000111
[1,8,5,2,7,4,6,3]=>[1,6,7,5,8,2,4,3]=>[1,6,2,8,3,7,4,5]=>0000111
[4,1,7,5,8,6,3,2]=>[3,6,4,1,8,7,5,2]=>[4,1,3,8,2,6,7,5]=>0010011
[2,3,1,7,5,8,6,4]=>[3,2,1,6,8,7,5,4]=>[2,3,1,8,4,6,7,5]=>0100011
[3,6,5,2,1,4,8,7]=>[2,5,3,1,6,4,8,7]=>[3,6,4,1,2,5,8,7]=>0010101
[5,1,7,4,8,3,2,6]=>[3,8,7,5,1,4,2,6]=>[8,6,4,5,1,3,7,2]=>0001111
[4,6,2,7,3,1,8,5]=>[3,8,7,4,6,2,1,5]=>[4,7,1,3,8,5,6,2]=>0000111
[3,7,8,2,4,1,6,5]=>[4,6,3,2,8,1,7,5]=>[3,6,1,4,2,7,8,5]=>0010101
[3,8,7,2,4,1,6,5]=>[4,6,3,2,7,1,8,5]=>[3,6,1,4,2,8,5,7]=>0010101
[1,8,5,4,2,3,7,6]=>[1,4,2,5,7,8,3,6]=>[1,7,3,2,4,5,8,6]=>0100011
[3,5,4,8,1,2,7,6]=>[7,1,3,5,4,8,2,6]=>[3,5,4,7,2,1,8,6]=>1001011
[4,5,3,8,1,2,7,6]=>[7,1,5,4,3,8,2,6]=>[4,5,3,7,2,1,8,6]=>1001011
[4,6,3,8,1,7,2,5]=>[7,8,6,4,3,1,2,5]=>[4,8,5,3,6,1,7,2]=>0001111
[1,8,7,4,2,6,3,5]=>[1,6,4,7,2,3,8,5]=>[1,8,5,2,6,3,4,7]=>0001101
[7,2,8,5,6,1,3,4]=>[6,8,2,1,7,3,5,4]=>[7,5,8,4,1,6,3,2]=>0110111
[1,8,3,2,7,6,4,5]=>[1,3,6,7,2,8,4,5]=>[1,7,4,8,5,2,3,6]=>0001011
[6,2,8,7,5,1,3,4]=>[5,7,2,1,6,3,8,4]=>[8,4,1,5,6,3,2,7]=>0110101
[1,8,5,7,6,2,3,4]=>[1,6,2,3,7,8,5,4]=>[1,7,5,8,4,3,2,6]=>0110011
[7,4,6,5,8,1,2,3]=>[8,1,2,6,7,4,5,3]=>[6,4,7,5,8,3,2,1]=>1100111
[5,7,6,4,8,1,2,3]=>[8,1,2,6,5,7,4,3]=>[5,7,4,6,8,3,2,1]=>1100011
[8,7,1,5,4,2,3,6]=>[4,5,1,7,2,3,8,6]=>[5,2,8,6,3,1,4,7]=>0101101
[7,1,6,2,8,5,3,4]=>[5,8,6,1,7,2,3,4]=>[8,4,1,5,7,3,6,2]=>0010111
[7,2,4,3,5,1,8,6]=>[5,4,8,2,3,7,1,6]=>[4,2,8,6,7,1,5,3]=>0011011
[7,6,3,1,4,8,2,5]=>[8,3,6,1,4,7,2,5]=>[7,2,3,6,8,5,4,1]=>0011011
[5,1,7,4,3,8,2,6]=>[8,4,7,5,1,3,2,6]=>[8,6,3,7,2,4,5,1]=>0001111
[5,3,1,7,4,8,2,6]=>[8,3,7,5,1,4,2,6]=>[7,2,3,8,6,4,5,1]=>0001111
[8,2,4,1,6,3,7,5]=>[7,4,6,2,8,1,3,5]=>[4,2,7,3,6,1,8,5]=>0010111
[6,2,1,5,3,8,4,7]=>[2,8,5,6,1,3,4,7]=>[8,7,4,6,3,5,1,2]=>0001111
[7,4,3,8,1,5,2,6]=>[5,8,4,7,3,1,2,6]=>[8,6,1,5,3,4,7,2]=>0001111
[7,4,8,1,5,3,2,6]=>[3,5,8,7,4,1,2,6]=>[7,2,5,4,8,6,1,3]=>0001111
[6,1,5,3,2,8,4,7]=>[3,8,5,6,1,2,4,7]=>[5,1,3,8,7,4,6,2]=>0001111
[6,3,2,8,4,1,5,7]=>[4,3,8,6,2,1,5,7]=>[6,1,4,8,7,5,2,3]=>0001111
[8,5,1,3,7,4,2,6]=>[4,7,1,5,8,3,2,6]=>[7,2,8,6,3,1,4,5]=>0100111
[3,8,6,1,5,2,7,4]=>[7,5,3,6,1,8,2,4]=>[3,7,2,5,1,8,4,6]=>0001011
[4,8,5,6,1,7,3,2]=>[3,7,6,4,8,5,1,2]=>[4,8,2,7,1,3,6,5]=>0000111
[6,7,1,3,8,5,2,4]=>[5,8,1,3,7,6,2,4]=>[6,8,4,3,1,5,7,2]=>0110011
[7,1,3,8,4,2,6,5]=>[4,6,1,8,7,3,2,5]=>[8,5,7,2,6,3,1,4]=>0100111
[5,6,2,7,1,3,8,4]=>[8,7,2,6,5,1,3,4]=>[5,7,3,2,8,4,6,1]=>0100111
[5,6,2,8,1,3,7,4]=>[7,8,2,6,5,1,3,4]=>[5,8,4,6,1,7,3,2]=>0100111
[6,1,8,3,7,5,2,4]=>[5,7,8,1,6,3,2,4]=>[7,2,8,4,1,5,6,3]=>0010111
[7,4,2,1,5,8,3,6]=>[2,8,4,7,1,5,3,6]=>[7,3,4,8,6,5,1,2]=>0001111
[7,4,1,5,8,3,2,6]=>[3,8,4,7,1,5,2,6]=>[8,6,5,1,3,4,7,2]=>0001111
[6,1,8,4,5,2,7,3]=>[7,5,8,6,1,4,2,3]=>[6,4,7,2,5,1,8,3]=>0001111
[4,5,7,2,8,1,3,6]=>[8,7,2,4,5,1,3,6]=>[4,5,7,3,2,8,6,1]=>0100111
[4,6,7,2,1,5,8,3]=>[2,8,7,4,1,6,5,3]=>[4,6,8,3,7,5,1,2]=>0001011
[1,3,7,5,4,2,8,6]=>[1,4,3,5,8,7,2,6]=>[1,3,8,6,7,2,4,5]=>0000011
[5,2,6,3,4,7,1,8]=>[7,6,5,2,3,4,1,8]=>[5,3,6,4,2,7,1,8]=>0011110
[2,7,6,5,3,1,8,4]=>[3,2,8,5,6,7,1,4]=>[2,8,4,5,6,7,1,3]=>0000011
[4,7,6,5,2,1,8,3]=>[2,8,5,4,6,7,1,3]=>[4,8,3,5,6,7,1,2]=>0000011
[6,3,1,5,4,7,8,2]=>[8,3,5,6,1,4,7,2]=>[6,4,7,8,2,3,5,1]=>0001101
[5,3,6,1,4,2,7,8]=>[4,6,5,3,1,2,7,8]=>[5,1,4,3,6,2,7,8]=>0011100
[6,4,1,2,5,3,7,8]=>[5,1,4,6,2,3,7,8]=>[5,2,1,6,3,4,7,8]=>1001100
[4,7,6,3,8,5,1,2]=>[5,1,8,4,6,7,3,2]=>[4,8,2,1,5,6,7,3]=>1000011
[3,7,6,5,2,8,1,4]=>[8,5,3,2,6,7,1,4]=>[3,8,4,2,5,6,7,1]=>0010011
[3,7,6,5,1,2,8,4]=>[8,1,3,5,6,7,2,4]=>[3,8,4,5,6,7,2,1]=>1000011
[1,2,3,7,4,6,8,5]=>[1,2,3,8,7,4,6,5]=>[1,2,3,8,5,7,6,4]=>0000111
[1,2,3,7,6,8,4,5]=>[1,2,3,8,4,7,6,5]=>[1,2,3,7,6,8,5,4]=>0001011
[1,2,3,6,8,7,4,5]=>[1,2,3,7,4,6,8,5]=>[1,2,3,6,8,5,4,7]=>0001001
[1,2,3,7,8,4,6,5]=>[1,2,3,6,8,4,7,5]=>[1,2,3,6,4,7,8,5]=>0000101
[1,2,3,6,8,4,7,5]=>[1,2,3,7,8,6,4,5]=>[1,2,3,6,7,4,8,5]=>0000011
[6,2,8,3,7,5,1,4]=>[5,7,8,2,6,3,1,4]=>[8,4,2,7,1,5,6,3]=>0010111
[4,2,8,3,7,5,6,1]=>[6,7,4,2,8,3,5,1]=>[8,1,6,3,4,2,7,5]=>0010111
[2,6,8,3,7,4,5,1]=>[5,2,7,8,3,6,4,1]=>[2,6,8,1,5,3,7,4]=>0001011
[3,5,4,8,7,2,6,1]=>[6,7,3,5,4,2,8,1]=>[3,5,4,8,1,6,2,7]=>0001101
[4,5,3,8,6,7,2,1]=>[2,7,5,4,3,8,6,1]=>[4,5,3,8,1,2,7,6]=>0001011
[3,6,7,8,4,5,2,1]=>[2,5,3,8,4,6,7,1]=>[3,6,7,8,1,2,5,4]=>0001001
[6,3,7,8,4,5,2,1]=>[2,5,8,6,3,4,7,1]=>[6,4,7,8,1,2,5,3]=>0001101
[3,2,8,6,7,4,5,1]=>[5,3,2,7,4,8,6,1]=>[3,2,8,1,5,4,7,6]=>0101011
[1,8,2,7,4,5,6,3]=>[1,6,7,8,2,4,5,3]=>[1,8,3,7,5,2,6,4]=>0001111
[6,2,8,4,5,7,3,1]=>[3,7,8,6,2,4,5,1]=>[6,4,7,5,2,8,1,3]=>0001111
[2,7,8,4,5,6,3,1]=>[3,2,6,8,4,5,7,1]=>[2,7,8,1,3,6,5,4]=>0001101
[5,7,4,6,8,3,2,1]=>[2,3,8,7,5,4,6,1]=>[5,7,6,4,8,1,2,3]=>0000111
[2,6,8,4,5,7,3,1]=>[3,2,7,8,4,6,5,1]=>[2,6,8,1,3,7,5,4]=>0001011
[4,2,7,1,3,8,5,6]=>[8,4,2,1,7,3,5,6]=>[7,5,8,6,3,2,4,1]=>0110111
[6,4,2,3,7,1,5,8]=>[7,4,2,6,3,1,5,8]=>[7,5,3,2,4,6,1,8]=>0101110
[7,4,2,3,8,1,6,5]=>[6,4,2,8,7,3,1,5]=>[8,5,7,1,6,3,2,4]=>0100111
[4,7,5,2,8,1,3,6]=>[8,5,2,4,7,1,3,6]=>[4,7,3,2,5,8,6,1]=>0100111
[8,4,7,1,2,3,6,5]=>[6,1,2,7,8,4,3,5]=>[7,3,2,1,6,4,8,5]=>1100111
[3,6,8,1,2,5,7,4]=>[7,1,3,8,2,6,5,4]=>[3,6,7,5,2,1,8,4]=>1001011
[4,1,7,8,2,3,6,5]=>[6,4,1,2,8,3,7,5]=>[4,2,6,3,1,7,8,5]=>0110101
[5,1,2,8,6,3,4,7]=>[6,1,5,2,3,8,4,7]=>[5,3,8,7,4,2,1,6]=>1011011
[6,8,2,7,1,4,5,3]=>[5,7,8,2,1,6,4,3]=>[5,1,6,7,4,2,8,3]=>0011011
[3,8,7,1,2,4,6,5]=>[6,1,3,2,7,4,8,5]=>[3,6,4,2,1,8,5,7]=>1010101
[5,8,7,1,3,4,6,2]=>[6,7,1,3,5,4,8,2]=>[5,6,4,3,1,8,2,7]=>0110101
[8,2,4,1,7,3,5,6]=>[7,4,8,2,1,3,5,6]=>[4,2,7,5,1,8,6,3]=>0011111
[3,1,4,7,8,5,2,6]=>[5,3,1,4,8,2,7,6]=>[4,7,8,6,2,3,1,5]=>0100101
[7,4,1,3,8,2,6,5]=>[6,4,1,8,7,3,2,5]=>[6,3,1,8,5,7,2,4]=>0100111
[4,8,6,2,1,3,7,5]=>[2,7,1,4,6,8,3,5]=>[4,7,3,1,2,8,5,6]=>0100011
[1,4,7,3,6,2,8,5]=>[1,8,6,4,7,3,2,5]=>[1,4,6,3,8,5,7,2]=>0000111
[2,8,5,7,3,4,1,6]=>[4,2,7,3,8,5,1,6]=>[2,7,1,4,3,8,6,5]=>0010111
[7,2,5,8,4,3,1,6]=>[3,4,8,7,2,5,1,6]=>[8,6,5,2,4,7,1,3]=>0001111
[8,2,3,5,4,7,1,6]=>[7,5,2,8,3,4,1,6]=>[5,3,2,7,1,8,6,4]=>0101111
[6,1,8,3,4,2,7,5]=>[4,7,8,1,6,3,2,5]=>[4,1,7,2,8,5,6,3]=>0010111
[1,8,6,4,2,3,7,5]=>[1,4,2,7,6,8,3,5]=>[1,7,3,2,4,8,5,6]=>0100011
[6,3,1,4,2,8,7,5]=>[4,3,7,1,6,2,8,5]=>[4,1,8,5,6,2,3,7]=>0010101
[5,3,1,8,4,7,2,6]=>[7,3,8,5,1,4,2,6]=>[8,6,4,5,1,7,2,3]=>0001111
[3,8,4,1,6,5,2,7]=>[5,4,3,6,8,1,2,7]=>[3,8,7,2,4,6,1,5]=>0000111
[7,5,3,6,4,8,2,1]=>[2,8,6,5,7,3,4,1]=>[6,3,7,4,5,8,1,2]=>0000111
[5,8,3,7,4,1,6,2]=>[6,4,7,8,5,3,1,2]=>[5,7,1,6,3,8,2,4]=>0000111
[8,5,3,6,1,4,7,2]=>[7,6,5,3,8,1,4,2]=>[8,2,6,1,7,4,3,5]=>0010111
[8,5,1,7,2,6,4,3]=>[4,6,7,5,8,1,2,3]=>[8,3,7,2,6,1,4,5]=>0000111
[8,7,1,4,5,2,6,3]=>[6,5,7,1,4,2,8,3]=>[6,2,5,4,1,8,3,7]=>0011101
[7,6,3,1,5,2,8,4]=>[8,3,5,6,1,7,2,4]=>[8,4,6,7,2,3,5,1]=>0001011
[7,5,1,8,2,6,3,4]=>[6,8,5,1,7,2,3,4]=>[7,3,5,8,4,1,6,2]=>0010111
[3,5,7,4,6,2,1,8]=>[2,6,3,7,5,4,1,8]=>[3,5,7,1,2,6,4,8]=>0000110
[3,5,2,7,6,4,1,8]=>[4,6,3,5,2,7,1,8]=>[3,7,1,4,5,2,6,8]=>0001010
[3,5,7,2,6,4,1,8]=>[4,6,3,7,5,2,1,8]=>[3,5,6,2,7,1,4,8]=>0000110
[3,5,7,2,6,1,4,8]=>[6,7,3,2,5,1,4,8]=>[3,5,6,1,7,4,2,8]=>0010110
[3,7,5,4,1,8,6,2]=>[6,4,3,5,8,7,1,2]=>[3,7,1,6,8,2,4,5]=>0000011
[3,7,5,1,4,8,2,6]=>[8,5,3,1,7,4,2,6]=>[3,7,2,5,8,6,4,1]=>0010111
[3,5,7,1,2,6,8,4]=>[8,1,3,7,5,2,6,4]=>[3,5,8,4,7,6,2,1]=>1000111
[3,5,7,4,1,2,6,8]=>[4,1,3,7,5,2,6,8]=>[3,5,7,6,2,1,4,8]=>1000110
[3,5,4,7,1,6,8,2]=>[8,7,3,5,4,1,6,2]=>[3,5,4,8,2,7,6,1]=>0001111
[3,5,4,7,1,2,6,8]=>[7,1,3,5,4,2,6,8]=>[3,5,4,7,6,2,1,8]=>1001110
[3,5,4,2,7,1,6,8]=>[7,4,3,5,2,1,6,8]=>[3,5,2,4,7,6,1,8]=>0001110
[3,5,4,7,2,1,8,6]=>[2,8,3,5,4,7,1,6]=>[3,5,4,8,6,7,1,2]=>0001011
[5,7,6,3,1,8,4,2]=>[4,3,8,6,5,7,1,2]=>[5,7,1,4,6,8,2,3]=>0000011
[3,2,5,7,1,4,8,6]=>[8,3,2,1,5,7,4,6]=>[3,2,5,8,6,7,4,1]=>0110011
[3,5,7,2,1,4,8,6]=>[2,8,3,1,5,7,4,6]=>[3,5,8,6,7,4,1,2]=>0010011
[3,7,2,5,1,8,6,4]=>[6,5,3,8,2,7,1,4]=>[3,5,2,7,1,6,8,4]=>0001011
[3,2,7,5,1,8,6,4]=>[6,3,2,5,8,7,1,4]=>[3,2,7,1,6,8,4,5]=>0100011
[3,7,2,5,1,8,4,6]=>[8,5,3,7,2,1,4,6]=>[3,5,2,7,4,8,6,1]=>0001111
[5,8,3,4,1,7,6,2]=>[6,4,7,3,5,8,1,2]=>[5,8,2,4,3,7,1,6]=>0010011
[5,8,7,2,4,1,6,3]=>[6,4,7,2,5,1,8,3]=>[4,2,5,6,1,8,3,7]=>0010101
[3,8,6,4,1,7,5,2]=>[5,4,3,7,6,8,1,2]=>[3,8,2,4,7,1,5,6]=>0000011
[3,7,6,4,1,8,5,2]=>[5,4,3,8,6,7,1,2]=>[3,7,1,5,6,8,2,4]=>0000011
[3,8,4,1,7,6,5,2]=>[5,4,3,6,7,8,1,2]=>[3,7,1,5,8,2,4,6]=>0000011
[5,8,2,4,1,6,3,7]=>[6,4,8,2,5,1,3,7]=>[4,2,5,6,1,8,7,3]=>0010111
[3,2,6,8,1,5,4,7]=>[5,3,2,8,1,6,4,7]=>[3,2,5,1,6,8,7,4]=>0101011
[3,2,6,8,7,1,5,4]=>[5,3,2,7,1,6,8,4]=>[3,2,5,1,6,8,4,7]=>0101001
[8,7,3,2,5,6,1,4]=>[6,3,7,2,1,5,8,4]=>[6,5,1,8,4,2,3,7]=>0011101
[7,2,4,1,8,3,6,5]=>[6,4,8,2,7,1,3,5]=>[4,2,6,1,8,5,7,3]=>0010111
[8,5,6,2,7,4,3,1]=>[3,4,7,6,8,5,2,1]=>[8,1,3,7,2,4,6,5]=>0000111
[1,7,2,3,6,8,5,4]=>[1,5,2,8,7,3,6,4]=>[1,7,6,3,2,5,8,4]=>0100111
[2,7,5,4,8,6,1,3]=>[6,2,1,5,8,7,4,3]=>[2,8,3,1,6,7,4,5]=>0100011
[2,5,1,4,8,7,3,6]=>[7,2,5,1,4,3,8,6]=>[2,8,6,3,5,4,1,7]=>0011101
[3,6,4,2,8,7,1,5]=>[7,4,3,6,2,1,8,5]=>[3,8,5,2,4,6,1,7]=>0001101
[3,6,4,5,8,7,2,1]=>[2,7,3,6,4,5,8,1]=>[3,6,5,4,8,1,2,7]=>0001101
[7,1,3,2,5,8,4,6]=>[3,8,1,7,2,5,4,6]=>[3,1,7,4,8,6,5,2]=>0101111
[2,6,4,3,8,1,7,5]=>[7,2,4,8,6,3,1,5]=>[2,7,1,8,5,6,3,4]=>0000111
[2,6,4,3,8,5,7,1]=>[7,2,4,8,6,3,5,1]=>[2,8,1,7,5,6,3,4]=>0000111
[7,1,5,6,3,8,4,2]=>[4,8,6,7,1,5,3,2]=>[7,3,6,5,1,4,8,2]=>0001111
[7,3,6,5,1,4,8,2]=>[8,5,6,3,7,1,4,2]=>[8,2,5,7,4,3,6,1]=>0010111
[7,2,3,5,4,8,6,1]=>[6,5,2,8,3,7,4,1]=>[5,3,2,8,1,6,7,4]=>0101011
[1,5,6,4,8,3,7,2]=>[1,7,8,6,5,4,3,2]=>[1,5,6,4,8,2,7,3]=>0000111
[7,1,3,2,4,8,5,6]=>[3,8,1,2,7,4,5,6]=>[3,1,7,5,8,6,4,2]=>0110111
[4,2,1,5,3,7,8,6]=>[2,5,4,1,3,8,7,6]=>[5,3,4,1,2,7,8,6]=>0011001
[4,2,5,6,3,1,8,7]=>[3,6,4,2,5,1,8,7]=>[5,6,1,3,4,2,8,7]=>0010101
[3,5,6,8,1,7,2,4]=>[7,8,3,1,5,6,2,4]=>[3,5,6,8,4,1,7,2]=>0010011
[4,1,5,6,3,2,8,7]=>[3,6,4,1,5,2,8,7]=>[4,1,3,5,6,2,8,7]=>0010101
[2,5,4,7,3,8,6,1]=>[6,2,8,5,4,7,3,1]=>[2,5,4,8,1,6,7,3]=>0001011
[3,5,7,1,8,4,2,6]=>[4,8,3,7,5,1,2,6]=>[3,5,8,6,1,4,7,2]=>0000111
[4,1,5,3,2,7,8,6]=>[3,5,4,1,2,8,7,6]=>[4,1,3,5,2,7,8,6]=>0011001
[4,5,3,7,1,2,8,6]=>[8,1,5,4,3,7,2,6]=>[4,5,3,8,6,7,2,1]=>1001011
[3,6,1,7,4,5,2,8]=>[5,7,3,6,1,4,2,8]=>[3,5,1,6,4,7,2,8]=>0001110
[4,5,2,3,7,1,8,6]=>[8,5,2,4,3,7,1,6]=>[4,5,3,2,8,6,7,1]=>0101011
[3,6,2,1,7,4,8,5]=>[2,8,3,7,6,1,4,5]=>[3,7,4,8,5,6,1,2]=>0000111
[3,5,7,1,8,2,6,4]=>[6,8,3,7,5,1,2,4]=>[3,5,6,1,8,4,7,2]=>0000111
[5,1,4,2,3,6,7,8]=>[4,5,1,2,3,6,7,8]=>[5,3,1,4,2,6,7,8]=>0111000
[5,1,4,3,2,6,7,8]=>[3,4,5,1,2,6,7,8]=>[5,2,4,1,3,6,7,8]=>0011000
[8,2,6,7,1,4,5,3]=>[5,7,8,2,1,4,6,3]=>[5,1,7,6,4,2,8,3]=>0011111
[4,6,2,3,5,8,1,7]=>[8,6,2,4,3,5,1,7]=>[4,6,5,3,2,8,7,1]=>0101111
[2,8,1,6,7,4,5,3]=>[5,2,7,8,1,4,6,3]=>[2,5,1,8,3,7,6,4]=>0001111
[4,2,3,1,6,8,5,7]=>[3,4,2,1,8,6,5,7]=>[4,1,3,2,6,8,7,5]=>0110011
[6,4,8,5,2,3,7,1]=>[7,5,2,8,6,4,3,1]=>[8,1,7,3,2,5,6,4]=>0100111
[2,4,1,8,3,6,7,5]=>[7,2,4,1,8,3,6,5]=>[2,7,6,3,4,1,8,5]=>0010111
[2,8,1,4,6,7,3,5]=>[7,2,8,1,4,3,6,5]=>[2,8,5,4,1,7,6,3]=>0011111
[8,4,2,6,7,3,1,5]=>[3,7,4,8,2,1,6,5]=>[8,5,2,7,6,1,3,4]=>0001111
[5,1,3,8,7,6,4,2]=>[4,6,1,5,3,7,8,2]=>[5,3,1,4,8,2,6,7]=>0101001
[4,7,6,8,5,1,3,2]=>[3,5,1,4,8,7,6,2]=>[3,1,4,7,6,8,2,5]=>0100011
[4,3,6,8,7,1,5,2]=>[5,7,4,3,1,6,8,2]=>[4,3,5,1,6,8,2,7]=>0011001
[6,2,8,4,3,7,5,1]=>[5,4,7,8,6,2,3,1]=>[7,3,8,1,5,6,2,4]=>0000111
[4,6,3,8,2,7,5,1]=>[5,7,8,4,6,3,2,1]=>[4,7,2,8,1,5,6,3]=>0000111
[6,5,8,1,3,7,4,2]=>[4,7,1,8,6,5,3,2]=>[6,5,8,2,7,3,1,4]=>0100111
[6,5,3,8,2,7,4,1]=>[4,7,8,5,6,3,2,1]=>[7,2,8,1,4,5,6,3]=>0000111
[6,4,8,1,3,7,5,2]=>[5,7,1,8,6,4,3,2]=>[8,2,7,3,1,5,6,4]=>0100111
[7,6,3,1,4,2,5,8]=>[4,3,6,1,2,7,5,8]=>[4,1,7,5,2,3,6,8]=>0011010
[1,5,4,3,7,8,2,6]=>[1,8,4,5,3,2,7,6]=>[1,5,3,4,7,8,6,2]=>0001101
[4,2,5,3,1,7,8,6]=>[3,5,4,2,1,8,7,6]=>[5,1,3,4,2,7,8,6]=>0011001
[6,3,1,8,7,5,2,4]=>[5,3,7,1,6,2,8,4]=>[8,4,1,5,6,2,3,7]=>0010101
[7,5,2,1,8,3,6,4]=>[2,6,8,5,7,1,3,4]=>[6,1,2,8,4,5,7,3]=>0000111
[8,7,4,1,5,2,6,3]=>[6,5,4,7,1,2,8,3]=>[6,2,5,1,8,3,4,7]=>0001101
[7,6,3,1,4,2,8,5]=>[4,3,8,1,6,7,2,5]=>[4,1,8,5,6,7,2,3]=>0010011
[8,7,5,2,1,3,6,4]=>[2,6,1,5,7,3,8,4]=>[6,3,1,2,8,4,5,7]=>0100101
[1,3,7,6,5,8,2,4]=>[1,8,3,2,6,7,5,4]=>[1,3,7,5,6,8,4,2]=>0010011
[7,5,2,1,6,4,8,3]=>[2,8,6,5,7,1,4,3]=>[7,4,5,8,3,6,1,2]=>0000111
[6,3,8,7,4,1,5,2]=>[5,4,7,6,3,1,8,2]=>[8,2,4,6,1,5,3,7]=>0001101
[7,4,1,6,3,5,2,8]=>[5,6,4,7,1,3,2,8]=>[5,1,7,2,6,3,4,8]=>0001110
[4,6,7,2,5,3,1,8]=>[3,5,7,4,2,6,1,8]=>[4,5,2,6,7,1,3,8]=>0001010
[3,6,7,4,8,1,5,2]=>[5,8,3,7,4,6,1,2]=>[3,6,7,1,5,4,8,2]=>0001011
[4,6,7,1,2,8,5,3]=>[5,1,8,4,7,6,2,3]=>[4,6,7,2,1,5,8,3]=>1000011
[6,2,1,8,3,7,5,4]=>[2,5,7,8,6,1,3,4]=>[6,1,2,5,7,3,8,4]=>0000111
[1,8,5,4,6,2,3,7]=>[1,6,2,5,8,4,3,7]=>[1,8,7,3,2,6,4,5]=>0100111
[3,8,5,1,6,4,2,7]=>[4,6,3,5,8,1,2,7]=>[3,8,7,2,6,1,4,5]=>0000111
[2,8,5,4,6,3,1,7]=>[3,2,6,5,8,4,1,7]=>[2,8,7,1,3,6,4,5]=>0000111
[3,6,4,2,7,8,5,1]=>[5,4,3,8,6,2,7,1]=>[3,7,8,1,5,6,2,4]=>0000101
[7,6,1,3,8,4,2,5]=>[4,8,1,6,3,7,2,5]=>[8,5,3,1,4,6,7,2]=>0101011
[2,6,4,1,7,8,3,5]=>[8,2,4,6,1,3,7,5]=>[2,6,3,4,7,8,5,1]=>0001101
[7,2,3,1,8,6,4,5]=>[3,6,2,8,1,7,4,5]=>[8,5,1,3,2,6,7,4]=>0101011
[7,2,3,4,1,6,8,5]=>[4,8,2,3,7,1,6,5]=>[8,5,7,6,1,4,3,2]=>0110111
[1,2,4,3,8,5,7,6]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,7,5,8,6]=>0010011
[7,3,8,6,1,4,2,5]=>[4,6,8,3,1,7,2,5]=>[7,2,6,8,5,1,4,3]=>0011011
[7,2,3,1,5,6,8,4]=>[3,8,2,7,1,5,6,4]=>[8,4,7,6,5,1,3,2]=>0101111
[2,6,4,8,7,1,5,3]=>[5,2,7,6,4,1,8,3]=>[2,6,1,5,4,8,3,7]=>0001101
[1,5,8,4,7,6,2,3]=>[1,6,2,7,5,8,4,3]=>[1,5,7,4,8,3,2,6]=>0100011
[4,1,6,5,8,2,7,3]=>[7,8,4,1,6,5,2,3]=>[6,5,8,3,4,1,7,2]=>0010111
[3,1,6,5,8,4,7,2]=>[7,3,1,8,6,5,4,2]=>[6,5,8,2,3,1,7,4]=>0100111
[3,2,6,5,8,4,7,1]=>[7,3,2,8,6,5,4,1]=>[3,2,6,5,8,1,7,4]=>0100111
[4,3,7,5,8,1,6,2]=>[6,8,4,3,7,5,1,2]=>[4,3,7,1,6,5,8,2]=>0010111
[4,3,7,5,8,2,6,1]=>[6,8,4,3,7,5,2,1]=>[4,3,8,1,6,5,7,2]=>0010111
[5,4,8,1,6,2,7,3]=>[7,6,8,5,4,1,2,3]=>[5,4,7,2,6,1,8,3]=>0001111
[4,3,7,1,5,2,8,6]=>[5,8,4,3,1,7,2,6]=>[4,3,5,1,8,6,7,2]=>0011011
[5,4,8,2,6,3,7,1]=>[7,6,8,5,4,2,3,1]=>[5,4,6,2,8,1,7,3]=>0001111
[4,1,7,8,6,3,2,5]=>[3,6,4,1,2,8,7,5]=>[4,1,3,7,8,5,2,6]=>0011001
[1,2,6,8,3,7,4,5]=>[1,2,7,8,3,6,4,5]=>[1,2,6,8,5,3,7,4]=>0001011
[6,8,3,2,1,4,7,5]=>[2,3,7,1,8,6,4,5]=>[6,7,4,1,2,3,8,5]=>0010011
[4,5,2,6,8,3,7,1]=>[7,8,5,4,2,6,3,1]=>[4,6,8,1,7,3,5,2]=>0001011
[8,4,7,6,2,3,5,1]=>[5,6,2,7,4,8,3,1]=>[8,1,5,4,7,3,2,6]=>0101011
[6,8,4,1,5,3,7,2]=>[7,5,4,8,1,6,3,2]=>[6,8,2,5,1,7,3,4]=>0001011
[6,5,3,8,4,2,7,1]=>[7,4,8,5,6,3,2,1]=>[8,1,7,2,4,5,6,3]=>0000111
[3,1,6,8,4,7,5,2]=>[5,3,1,7,8,6,4,2]=>[6,7,4,8,2,3,1,5]=>0100011
[2,4,6,8,1,7,5,3]=>[5,2,7,4,8,6,1,3]=>[2,4,6,8,3,7,1,5]=>0000011
[7,4,3,8,6,2,1,5]=>[2,6,4,8,3,7,1,5]=>[7,1,2,6,8,5,3,4]=>0001011
[4,3,6,2,1,8,5,7]=>[2,8,4,3,6,1,5,7]=>[4,3,8,7,5,6,1,2]=>0010111
[8,4,5,3,2,1,7,6]=>[2,3,5,7,4,8,1,6]=>[7,1,2,3,5,4,8,6]=>0001011
[5,8,3,7,2,1,6,4]=>[2,6,7,8,5,3,1,4]=>[5,7,1,2,6,3,8,4]=>0000111
[2,5,4,8,1,6,7,3]=>[7,2,8,5,4,1,6,3]=>[2,5,4,7,6,1,8,3]=>0001111
[8,6,1,2,3,4,7,5]=>[7,1,2,3,6,8,4,5]=>[7,4,3,2,1,8,5,6]=>1110011
[8,6,2,3,5,1,4,7]=>[5,6,2,3,1,8,4,7]=>[5,1,8,7,4,3,2,6]=>0111011
[8,2,3,7,5,4,1,6]=>[4,5,2,7,8,3,1,6]=>[7,1,4,8,6,3,2,5]=>0100111
[8,2,6,3,5,4,1,7]=>[4,5,6,8,2,3,1,7]=>[5,2,6,3,8,7,1,4]=>0001111
[8,6,2,4,1,5,3,7]=>[5,4,6,2,1,8,3,7]=>[4,2,5,1,8,7,3,6]=>0011011
[3,6,1,8,7,5,4,2]=>[4,5,3,7,6,1,8,2]=>[3,8,2,5,6,1,4,7]=>0000101
[3,8,1,5,7,6,4,2]=>[4,6,3,7,1,8,5,2]=>[3,7,5,1,4,8,2,6]=>0001011
[8,1,7,3,4,6,2,5]=>[6,7,8,1,3,4,2,5]=>[6,4,1,7,2,8,5,3]=>0011111
[8,3,1,7,2,6,5,4]=>[5,3,6,7,8,1,2,4]=>[8,4,7,2,3,6,1,5]=>0000111
[2,8,3,7,4,6,5,1]=>[5,2,6,7,8,3,4,1]=>[2,6,3,7,4,8,1,5]=>0000111
[8,2,3,7,1,6,5,4]=>[5,6,2,7,8,3,1,4]=>[6,3,2,8,4,7,1,5]=>0100111
[8,1,7,2,6,4,3,5]=>[4,6,7,8,1,2,3,5]=>[6,2,7,3,8,5,1,4]=>0001111
[8,2,3,7,4,6,1,5]=>[6,7,2,8,3,4,1,5]=>[8,5,3,2,7,1,6,4]=>0101111
[2,4,8,5,7,6,3,1]=>[3,2,6,4,7,8,5,1]=>[2,4,7,5,8,1,3,6]=>0000011
[8,2,7,4,3,1,5,6]=>[3,4,7,8,2,1,5,6]=>[8,6,1,3,7,5,2,4]=>0001111
[6,1,8,2,7,5,4,3]=>[4,5,7,8,6,1,2,3]=>[8,3,7,2,5,6,1,4]=>0000111
[8,2,4,1,7,6,5,3]=>[5,4,6,2,7,8,1,3]=>[4,2,7,1,5,8,3,6]=>0010011
[8,2,5,4,1,7,6,3]=>[6,4,5,7,2,8,1,3]=>[8,3,5,2,4,7,1,6]=>0001011
[5,1,4,8,7,6,3,2]=>[3,6,5,1,4,7,8,2]=>[5,4,1,3,8,2,6,7]=>0011001
[6,2,8,1,5,7,3,4]=>[7,8,6,2,1,3,5,4]=>[6,3,7,5,1,8,4,2]=>0011111
[4,1,2,8,5,3,6,7]=>[5,1,4,2,8,3,6,7]=>[8,7,6,3,4,2,1,5]=>1010111
[3,5,8,2,6,1,7,4]=>[7,6,3,8,5,2,1,4]=>[3,5,6,2,7,1,8,4]=>0000111
[7,2,6,3,4,5,1,8]=>[5,6,7,2,3,4,1,8]=>[6,4,2,7,1,5,3,8]=>0011110
[4,1,2,7,8,5,3,6]=>[5,1,4,2,8,3,7,6]=>[7,8,6,3,4,2,1,5]=>1010101
[4,7,3,1,2,6,8,5]=>[3,1,8,4,7,2,6,5]=>[4,8,5,7,6,2,1,3]=>1000111
[3,2,6,4,7,8,5,1]=>[5,3,2,8,6,4,7,1]=>[3,2,7,8,1,5,6,4]=>0100101
[1,5,8,6,4,2,3,7]=>[1,4,2,6,5,8,3,7]=>[1,5,8,7,3,2,4,6]=>0100011
[1,6,2,3,5,8,7,4]=>[1,7,2,6,3,5,8,4]=>[1,8,4,6,5,3,2,7]=>0101101
[7,4,6,2,8,3,5,1]=>[5,8,6,7,4,2,3,1]=>[8,1,5,4,7,3,6,2]=>0001111
[4,3,8,2,5,7,1,6]=>[7,8,4,3,2,5,1,6]=>[4,3,7,1,8,6,5,2]=>0011111
[4,2,6,1,5,3,8,7]=>[5,6,4,2,1,3,8,7]=>[5,1,6,3,4,2,8,7]=>0011101
[6,7,2,3,1,5,8,4]=>[3,8,2,7,1,6,5,4]=>[6,8,4,7,5,1,3,2]=>0101011
[2,1,5,7,8,3,6,4]=>[2,1,6,8,5,3,7,4]=>[2,1,5,6,3,7,8,4]=>1000101
[4,7,5,8,6,3,1,2]=>[3,1,6,4,8,7,5,2]=>[4,8,2,1,3,6,7,5]=>1000011
[2,4,8,3,7,1,5,6]=>[7,2,8,4,3,1,5,6]=>[2,4,8,6,1,7,5,3]=>0001111
[7,6,5,2,1,8,4,3]=>[2,4,8,5,6,7,1,3]=>[7,1,2,4,5,6,8,3]=>0000011
[2,7,5,1,8,3,6,4]=>[6,2,8,5,7,1,3,4]=>[2,6,1,8,4,5,7,3]=>0000111
[5,1,8,7,4,3,6,2]=>[6,4,7,5,1,3,8,2]=>[8,2,4,5,1,6,3,7]=>0001101
[5,7,1,3,2,4,8,6]=>[3,8,1,2,5,7,4,6]=>[3,1,5,8,6,7,4,2]=>0110011
[8,1,7,4,2,3,5,6]=>[4,7,1,8,2,3,5,6]=>[7,5,2,8,6,3,1,4]=>0101111
[5,1,6,8,3,7,4,2]=>[4,7,8,5,1,6,3,2]=>[5,1,4,6,8,2,7,3]=>0001011
[7,6,4,1,3,5,8,2]=>[8,4,1,6,3,7,5,2]=>[8,2,4,6,7,5,3,1]=>0101011
[8,2,3,7,1,4,5,6]=>[7,8,2,3,1,4,5,6]=>[7,5,1,8,6,4,3,2]=>0111111
[3,7,8,2,6,1,4,5]=>[6,8,3,2,1,4,7,5]=>[3,7,8,5,1,6,4,2]=>0011101
[4,8,6,5,1,2,7,3]=>[7,1,5,4,6,8,2,3]=>[4,7,2,1,8,3,5,6]=>1000011
[4,8,6,5,1,2,3,7]=>[5,1,2,4,6,8,3,7]=>[4,8,7,3,2,1,5,6]=>1100011
[3,8,7,6,5,1,2,4]=>[5,1,3,2,6,7,8,4]=>[3,8,4,2,1,5,6,7]=>1010001
[3,8,7,5,6,1,4,2]=>[4,6,3,1,7,5,8,2]=>[3,4,1,8,2,6,5,7]=>0010101
[4,6,3,8,7,5,1,2]=>[5,1,7,4,6,3,8,2]=>[4,8,2,1,5,6,3,7]=>1000101
[2,5,8,3,7,1,6,4]=>[6,2,7,8,5,3,1,4]=>[2,5,7,1,6,3,8,4]=>0000111
[2,4,6,1,8,7,5,3]=>[5,2,7,4,6,1,8,3]=>[2,4,6,1,5,8,3,7]=>0000101
[3,5,8,1,7,6,2,4]=>[6,7,3,1,5,8,2,4]=>[3,5,7,2,8,4,1,6]=>0010011
[1,6,3,8,7,5,2,4]=>[1,5,7,3,6,2,8,4]=>[1,6,2,5,8,4,3,7]=>0010101
[3,2,8,1,5,7,6,4]=>[6,3,2,7,1,8,5,4]=>[3,2,8,4,7,5,1,6]=>0101011
[3,1,8,2,5,7,6,4]=>[6,3,1,7,2,8,5,4]=>[8,4,7,5,2,3,1,6]=>0101011
[2,3,6,8,7,5,1,4]=>[5,2,3,1,7,6,8,4]=>[2,3,6,8,4,1,5,7]=>0010001
[3,8,4,5,1,6,2,7]=>[6,5,3,8,4,1,2,7]=>[3,6,1,8,7,2,5,4]=>0001111
[5,3,8,6,2,7,1,4]=>[7,6,5,3,2,8,1,4]=>[7,1,8,4,3,5,2,6]=>0011011
[8,4,6,3,1,2,5,7]=>[3,1,6,8,4,2,5,7]=>[6,2,1,3,8,7,5,4]=>1001111
[6,8,1,4,5,2,3,7]=>[5,8,1,2,4,6,3,7]=>[6,8,7,3,1,5,4,2]=>0111011
[1,5,8,4,6,2,3,7]=>[1,6,2,8,5,4,3,7]=>[1,5,8,7,3,2,6,4]=>0100111
[5,7,4,8,1,2,3,6]=>[8,1,2,7,5,4,3,6]=>[5,8,6,4,7,3,2,1]=>1100111
[8,7,1,5,6,2,3,4]=>[6,7,1,2,3,5,8,4]=>[6,5,3,1,8,4,2,7]=>0111101
[1,6,5,8,7,2,3,4]=>[1,7,2,3,6,5,8,4]=>[1,6,5,8,4,3,2,7]=>0110101
[1,7,6,5,8,2,3,4]=>[1,8,2,3,6,7,5,4]=>[1,7,5,6,8,4,3,2]=>0110011
[5,1,2,6,8,7,3,4]=>[7,1,5,2,3,6,8,4]=>[5,3,6,8,4,2,1,7]=>1011001
[1,8,6,2,5,7,3,4]=>[1,7,6,2,3,8,5,4]=>[1,8,4,2,7,5,3,6]=>0011011
[8,1,5,7,6,2,3,4]=>[6,7,1,2,3,8,5,4]=>[8,4,2,7,5,3,1,6]=>0111011
[7,8,6,1,5,2,3,4]=>[5,6,1,2,3,8,7,4]=>[5,3,1,7,8,4,2,6]=>0111001
[4,5,7,2,3,1,8,6]=>[3,8,2,4,5,7,1,6]=>[4,5,8,6,7,1,3,2]=>0100011
[3,7,8,1,4,6,5,2]=>[5,6,3,1,8,4,7,2]=>[3,7,8,2,6,4,1,5]=>0010101
[2,5,8,7,4,1,3,6]=>[4,2,1,7,5,3,8,6]=>[2,5,8,6,3,1,4,7]=>0100101
[2,6,4,7,5,3,8,1]=>[8,2,5,7,6,4,3,1]=>[2,7,3,5,6,4,8,1]=>0000111
[7,3,5,1,4,2,8,6]=>[4,5,8,3,1,7,2,6]=>[8,6,7,2,5,1,4,3]=>0011011
[6,1,4,7,5,3,8,2]=>[8,5,7,1,6,4,3,2]=>[7,3,8,2,5,6,4,1]=>0010111
[8,7,1,4,3,5,6,2]=>[6,4,7,1,3,5,8,2]=>[8,2,4,1,6,5,3,7]=>0011101
[6,1,8,4,7,3,2,5]=>[3,7,8,6,1,4,2,5]=>[6,4,7,2,8,5,1,3]=>0001111
[4,7,3,6,1,2,8,5]=>[8,1,6,4,7,3,2,5]=>[4,6,3,8,5,7,2,1]=>1000111
[4,7,6,2,3,1,8,5]=>[3,8,2,4,6,7,1,5]=>[4,8,5,6,7,1,3,2]=>0100011
[2,3,6,1,8,7,5,4]=>[5,2,3,7,6,1,8,4]=>[2,3,6,1,5,8,4,7]=>0000101
[6,4,1,7,5,2,8,3]=>[8,5,4,7,6,1,2,3]=>[8,3,4,7,2,5,6,1]=>0000111
[5,7,8,2,3,6,1,4]=>[6,8,2,3,5,1,7,4]=>[5,6,1,7,8,4,3,2]=>0110101
[8,6,2,1,5,7,4,3]=>[2,4,7,6,1,8,5,3]=>[8,3,7,5,1,2,4,6]=>0001011
[1,3,8,6,7,2,4,5]=>[1,7,3,2,4,8,6,5]=>[1,3,8,5,4,2,7,6]=>0011011
[2,8,3,7,6,1,4,5]=>[6,2,7,3,1,8,4,5]=>[2,7,4,3,8,5,1,6]=>0011011
[1,3,8,7,6,2,4,5]=>[1,6,3,2,4,7,8,5]=>[1,3,8,5,4,2,6,7]=>0011001
[7,6,4,8,5,1,3,2]=>[3,5,1,8,6,7,4,2]=>[3,1,8,2,5,6,7,4]=>0100011
[2,8,6,1,7,4,3,5]=>[4,2,7,6,1,8,3,5]=>[2,7,3,8,5,1,4,6]=>0001011
[7,1,2,5,4,6,3,8]=>[6,1,5,7,2,4,3,8]=>[7,3,5,2,1,6,4,8]=>1001110
[4,1,2,7,5,6,3,8]=>[6,1,4,2,7,5,3,8]=>[7,3,4,2,1,6,5,8]=>1010110
[5,4,1,3,2,8,6,7]=>[3,4,1,5,2,8,6,7]=>[3,1,5,2,4,8,7,6]=>0101011
[4,2,7,3,8,5,1,6]=>[5,8,4,2,7,3,1,6]=>[7,1,5,8,6,3,4,2]=>0010111
[5,3,1,2,4,8,6,7]=>[3,1,5,2,4,8,6,7]=>[5,4,2,1,3,8,7,6]=>1011011
[1,3,2,6,4,8,7,5]=>[1,3,2,7,6,4,8,5]=>[1,3,2,8,5,6,4,7]=>0100101
[1,6,2,5,3,8,7,4]=>[1,7,5,6,2,3,8,4]=>[1,8,4,6,3,5,2,7]=>0001101
[1,8,2,6,3,7,5,4]=>[1,5,7,6,8,2,3,4]=>[1,7,3,8,4,6,2,5]=>0000111
[1,5,2,7,4,8,6,3]=>[1,6,8,5,2,7,4,3]=>[1,7,4,5,2,6,8,3]=>0001011
[4,8,1,3,2,6,5,7]=>[3,6,1,4,8,2,5,7]=>[3,1,4,6,2,8,7,5]=>0100111
[2,6,3,8,1,5,4,7]=>[5,2,8,6,3,1,4,7]=>[2,8,7,4,6,1,5,3]=>0001111
[8,3,5,1,2,6,4,7]=>[6,1,5,8,3,2,4,7]=>[5,3,6,2,1,8,7,4]=>1001111
[8,6,3,1,5,4,2,7]=>[4,3,5,6,1,8,2,7]=>[8,7,2,3,5,1,4,6]=>0001011
[8,6,4,1,5,3,2,7]=>[3,5,4,6,1,8,2,7]=>[8,7,2,5,1,3,4,6]=>0001011
[8,6,5,4,1,3,2,7]=>[3,4,1,5,6,8,2,7]=>[3,1,8,7,2,4,5,6]=>0100011
[2,3,8,7,4,6,1,5]=>[6,2,3,7,4,1,8,5]=>[2,3,6,1,8,5,4,7]=>0001101
[4,8,5,3,1,2,7,6]=>[3,1,5,4,7,8,2,6]=>[4,7,2,1,3,5,8,6]=>1000011
[6,8,7,3,1,5,4,2]=>[4,3,5,7,1,6,8,2]=>[6,8,2,3,5,1,4,7]=>0001001
[6,8,5,4,1,3,7,2]=>[7,4,1,5,8,6,3,2]=>[6,7,3,1,8,2,4,5]=>0100011
[4,8,7,6,5,1,3,2]=>[3,5,1,4,6,7,8,2]=>[3,1,4,8,2,5,6,7]=>0100001
[2,8,7,1,3,6,4,5]=>[6,2,1,7,3,4,8,5]=>[2,8,5,3,1,6,4,7]=>0101101
[8,5,4,7,2,1,3,6]=>[2,7,1,5,8,4,3,6]=>[7,3,1,2,8,6,4,5]=>0100111
[6,8,4,1,5,2,7,3]=>[7,5,4,8,1,6,2,3]=>[6,7,2,5,1,8,3,4]=>0001011
[6,8,2,1,7,5,3,4]=>[2,5,7,1,8,6,3,4]=>[6,7,3,8,4,1,2,5]=>0010011
[5,8,4,6,1,2,7,3]=>[7,1,6,8,5,4,2,3]=>[5,7,2,1,8,3,6,4]=>1000111
[2,4,8,6,5,1,7,3]=>[7,2,5,4,6,8,1,3]=>[2,4,7,1,8,3,5,6]=>0000011
[4,6,1,2,5,7,8,3]=>[8,1,6,4,2,5,7,3]=>[4,7,8,3,6,5,2,1]=>1001101
[2,6,4,1,5,7,8,3]=>[8,2,4,6,1,5,7,3]=>[2,7,8,3,4,6,5,1]=>0001101
[5,3,2,1,8,6,4,7]=>[2,3,6,5,1,8,4,7]=>[8,7,4,5,1,2,3,6]=>0001011
[3,8,6,4,5,7,2,1]=>[2,7,3,6,4,8,5,1]=>[3,8,1,2,7,5,4,6]=>0001011
[5,3,6,4,8,2,1,7]=>[2,8,6,5,3,4,1,7]=>[6,4,5,3,8,7,1,2]=>0001111
[6,3,1,8,4,7,2,5]=>[7,3,8,6,1,4,2,5]=>[6,4,8,5,1,7,2,3]=>0001111
[7,1,4,8,6,3,2,5]=>[3,6,8,1,4,7,2,5]=>[7,2,6,8,5,4,1,3]=>0011011
[5,3,6,8,2,7,1,4]=>[7,8,5,3,2,6,1,4]=>[6,7,1,8,4,3,5,2]=>0011011
[6,3,7,4,8,2,1,5]=>[2,8,7,6,3,4,1,5]=>[6,4,8,5,3,7,1,2]=>0001111
[5,3,8,4,1,6,2,7]=>[6,4,8,5,3,1,2,7]=>[6,1,8,7,2,4,5,3]=>0001111
[5,8,4,1,6,3,2,7]=>[3,6,4,8,5,1,2,7]=>[5,8,7,2,6,1,3,4]=>0000111
[4,5,1,8,6,7,3,2]=>[3,7,5,4,1,8,6,2]=>[4,5,1,3,8,2,7,6]=>0001011
[3,4,5,8,7,1,2,6]=>[7,1,3,4,5,2,8,6]=>[3,4,5,8,6,2,1,7]=>1000101
[3,8,6,5,2,7,4,1]=>[4,7,3,5,6,8,2,1]=>[3,7,2,8,1,4,5,6]=>0000011
[5,1,4,6,7,2,8,3]=>[8,7,5,1,4,6,2,3]=>[6,7,2,8,3,5,4,1]=>0011011
[6,5,4,7,1,3,8,2]=>[8,7,1,5,6,4,3,2]=>[6,4,5,8,2,7,3,1]=>0100111
[2,1,6,5,3,7,8,4]=>[2,1,8,5,6,3,7,4]=>[2,1,7,8,4,5,6,3]=>1000101
[1,6,2,5,4,8,3,7]=>[1,8,5,6,2,4,3,7]=>[1,6,4,8,7,3,5,2]=>0001111
[6,7,2,3,8,4,5,1]=>[5,8,2,7,3,6,4,1]=>[6,7,4,8,1,5,3,2]=>0101011
[4,1,7,5,8,3,6,2]=>[6,8,4,1,7,5,3,2]=>[7,3,4,1,6,5,8,2]=>0010111
[6,1,7,4,2,8,5,3]=>[5,4,8,7,6,1,2,3]=>[6,1,5,7,2,4,8,3]=>0000111
[2,1,6,7,4,3,8,5]=>[2,1,4,8,7,6,3,5]=>[2,1,6,8,5,7,3,4]=>1000011
[6,7,3,2,1,8,4,5]=>[2,3,8,7,1,6,4,5]=>[6,7,4,8,5,1,2,3]=>0001011
[6,7,3,2,8,4,5,1]=>[5,3,8,7,2,6,4,1]=>[6,7,4,8,1,5,2,3]=>0001011
[1,2,6,7,4,3,8,5]=>[1,2,4,8,7,6,3,5]=>[1,2,6,8,5,7,3,4]=>0000011
[1,7,5,8,2,4,3,6]=>[1,4,8,2,7,5,3,6]=>[1,4,2,8,6,5,7,3]=>0010111
[6,7,1,8,4,5,3,2]=>[3,5,8,7,1,6,4,2]=>[6,7,4,8,2,5,1,3]=>0001011
[1,3,7,6,4,8,5,2]=>[1,5,3,8,6,7,4,2]=>[1,3,8,2,5,6,7,4]=>0000011
[5,4,1,8,6,3,2,7]=>[3,6,4,5,1,8,2,7]=>[5,1,3,4,8,7,2,6]=>0001011
[6,4,1,8,5,3,2,7]=>[3,5,4,8,6,1,2,7]=>[8,7,2,5,6,1,3,4]=>0000111
[5,7,6,1,4,3,2,8]=>[3,4,6,1,5,7,2,8]=>[5,7,2,4,1,3,6,8]=>0010010
[5,8,6,1,4,3,2,7]=>[3,4,6,1,5,8,2,7]=>[5,8,7,2,4,1,3,6]=>0010011
[8,6,5,1,4,3,2,7]=>[3,4,5,1,6,8,2,7]=>[8,7,2,4,1,3,5,6]=>0010011
[3,1,6,4,5,7,2,8]=>[7,3,1,6,4,5,2,8]=>[6,5,4,7,2,3,1,8]=>0101110
[8,2,7,6,1,4,3,5]=>[4,6,7,2,1,8,3,5]=>[7,3,8,5,1,4,2,6]=>0011011
[5,2,3,7,1,6,8,4]=>[8,7,2,5,3,1,6,4]=>[8,4,5,3,2,7,6,1]=>0101111
[5,2,3,4,7,8,1,6]=>[8,5,2,3,4,1,7,6]=>[5,4,3,2,7,8,6,1]=>0111101
[1,2,5,7,8,4,6,3]=>[1,2,6,8,5,4,7,3]=>[1,2,5,7,8,3,6,4]=>0000101
[6,7,4,1,3,2,8,5]=>[3,4,1,8,7,6,2,5]=>[3,1,6,8,5,7,2,4]=>0100011
[1,7,2,8,4,3,5,6]=>[1,4,8,7,2,3,5,6]=>[1,7,5,2,4,8,6,3]=>0001111
[1,6,3,5,7,8,2,4]=>[1,8,6,3,2,5,7,4]=>[1,7,8,4,3,6,5,2]=>0011101
[7,6,4,1,8,3,2,5]=>[3,8,4,6,1,7,2,5]=>[8,5,1,3,4,6,7,2]=>0001011
[4,2,1,5,7,8,3,6]=>[2,8,4,1,5,3,7,6]=>[5,7,8,6,3,4,1,2]=>0010101
[7,1,5,4,6,3,2,8]=>[3,6,5,7,1,4,2,8]=>[5,1,3,7,2,6,4,8]=>0001110
[8,2,1,6,7,5,4,3]=>[2,4,5,7,8,1,6,3]=>[7,6,1,2,4,8,3,5]=>0000111
[1,2,4,7,6,3,8,5]=>[1,2,8,4,6,7,3,5]=>[1,2,4,8,5,6,7,3]=>0000011
[6,1,5,4,8,3,2,7]=>[3,8,5,6,1,4,2,7]=>[5,1,3,6,4,8,7,2]=>0001111
[1,2,8,7,4,3,6,5]=>[1,2,4,6,7,3,8,5]=>[1,2,6,3,4,8,5,7]=>0000101
[3,2,1,7,5,8,4,6]=>[2,3,1,8,7,5,4,6]=>[3,1,2,8,6,5,7,4]=>0100111
[1,3,6,4,7,8,2,5]=>[1,8,3,6,4,2,7,5]=>[1,3,7,8,5,4,6,2]=>0001101
[8,4,6,5,1,2,7,3]=>[7,1,5,6,8,4,2,3]=>[6,4,7,2,1,8,3,5]=>1000111
[3,5,1,7,8,2,6,4]=>[6,8,3,5,1,2,7,4]=>[3,7,8,4,5,1,6,2]=>0001101
[5,3,6,1,8,4,2,7]=>[4,8,6,5,3,1,2,7]=>[6,1,4,5,3,8,7,2]=>0001111
[3,4,6,2,1,8,5,7]=>[2,8,3,4,6,1,5,7]=>[3,4,8,7,5,6,1,2]=>0000111
[4,7,5,8,2,1,6,3]=>[2,6,8,4,7,5,1,3]=>[4,7,1,2,6,5,8,3]=>0000111
[7,1,2,6,3,8,5,4]=>[5,1,8,6,7,2,3,4]=>[8,4,6,2,1,5,7,3]=>1000111
[8,1,2,6,3,7,5,4]=>[5,1,7,6,8,2,3,4]=>[7,3,8,4,6,2,1,5]=>1000111
[7,4,3,1,8,6,2,5]=>[6,3,4,8,1,7,2,5]=>[8,5,1,6,7,2,3,4]=>0001011
[4,3,7,2,8,6,1,5]=>[6,8,4,3,2,7,1,5]=>[4,3,7,1,6,8,5,2]=>0011011
[5,1,2,6,3,8,7,4]=>[7,1,6,5,2,3,8,4]=>[6,3,8,4,5,2,1,7]=>1001101
[5,1,2,7,3,8,6,4]=>[6,1,8,5,2,7,3,4]=>[8,4,5,2,1,6,7,3]=>1001011
[6,1,2,7,3,5,8,4]=>[8,1,7,6,2,3,5,4]=>[8,4,6,3,7,5,2,1]=>1001111
[1,5,8,4,7,6,3,2]=>[1,3,6,7,5,8,4,2]=>[1,5,7,4,8,2,3,6]=>0000011
[7,4,3,2,8,6,1,5]=>[6,3,4,8,2,7,1,5]=>[7,1,6,8,5,2,3,4]=>0001011
[8,2,5,4,7,6,1,3]=>[6,5,2,7,1,8,4,3]=>[7,4,8,3,2,5,1,6]=>0101011
[6,2,8,7,5,4,1,3]=>[4,5,2,7,6,1,8,3]=>[8,3,2,5,6,1,4,7]=>0100101
[4,5,3,2,8,6,1,7]=>[6,3,5,4,2,8,1,7]=>[4,5,2,3,8,7,1,6]=>0001011
[3,2,5,4,8,6,1,7]=>[6,3,2,5,4,8,1,7]=>[3,2,5,4,8,7,1,6]=>0101011
[3,2,8,6,5,4,1,7]=>[4,3,2,5,6,8,1,7]=>[3,2,8,7,1,4,5,6]=>0100011
[3,2,7,8,5,4,1,6]=>[4,3,2,5,8,1,7,6]=>[3,2,7,8,6,1,4,5]=>0100101
[6,8,7,4,3,2,1,5]=>[2,3,4,7,1,6,8,5]=>[6,8,5,1,2,3,4,7]=>0001001
[3,4,8,1,7,5,6,2]=>[6,7,3,4,8,1,5,2]=>[3,4,6,1,8,2,7,5]=>0000111
[7,2,1,5,8,4,6,3]=>[2,6,8,7,1,5,4,3]=>[6,5,1,2,7,4,8,3]=>0001111
[7,1,6,4,8,3,5,2]=>[5,8,6,7,1,4,3,2]=>[5,1,7,3,6,4,8,2]=>0001111
[4,6,7,1,5,3,8,2]=>[8,5,7,4,1,6,3,2]=>[4,6,7,3,8,2,5,1]=>0001011
[3,6,1,5,7,8,2,4]=>[8,6,3,1,2,5,7,4]=>[3,6,5,2,7,8,4,1]=>0011101
[2,1,5,8,6,3,7,4]=>[2,1,7,6,5,8,3,4]=>[2,1,5,7,3,8,4,6]=>1000011
[3,7,8,5,2,6,1,4]=>[6,5,3,2,8,1,7,4]=>[3,6,1,7,8,4,2,5]=>0010101
[3,7,8,5,4,1,6,2]=>[6,4,3,5,8,1,7,2]=>[3,6,1,7,8,2,4,5]=>0000101
[5,7,3,1,2,4,8,6]=>[3,1,8,2,5,7,4,6]=>[5,8,6,7,4,2,1,3]=>1010011
[6,3,2,5,1,7,4,8]=>[7,3,5,6,2,1,4,8]=>[5,2,3,7,4,6,1,8]=>0001110
[3,7,2,8,5,1,4,6]=>[5,8,3,2,7,1,4,6]=>[3,8,6,1,5,7,4,2]=>0010111
[6,8,4,3,1,7,2,5]=>[7,3,4,8,1,6,2,5]=>[6,8,5,1,7,2,3,4]=>0001011
[8,4,1,3,7,5,6,2]=>[6,4,1,7,8,3,5,2]=>[6,3,1,8,2,4,7,5]=>0100111
[1,8,5,7,4,2,3,6]=>[1,4,2,7,8,5,3,6]=>[1,7,3,2,4,8,6,5]=>0100111
[2,1,6,8,5,3,4,7]=>[2,1,5,3,8,6,4,7]=>[2,1,6,8,7,4,3,5]=>1010011
[1,2,6,8,5,3,4,7]=>[1,2,5,3,8,6,4,7]=>[1,2,6,8,7,4,3,5]=>0010011
[6,3,2,4,7,1,8,5]=>[8,3,7,2,6,4,1,5]=>[8,5,6,4,2,3,7,1]=>0010111
[1,5,6,8,4,2,3,7]=>[1,4,2,8,5,6,3,7]=>[1,5,6,8,7,3,2,4]=>0100011
[5,7,8,3,6,1,2,4]=>[6,1,8,3,5,2,7,4]=>[5,6,2,1,7,8,4,3]=>1010101
[1,5,8,6,2,4,3,7]=>[1,4,6,2,5,8,3,7]=>[1,4,2,5,8,7,3,6]=>0010011
[5,7,6,3,8,1,2,4]=>[8,1,6,3,5,7,2,4]=>[5,8,4,3,6,7,2,1]=>1010011
[1,2,5,3,6,8,7,4]=>[1,2,7,5,3,6,8,4]=>[1,2,6,8,4,5,3,7]=>0001001
[7,1,5,6,2,3,8,4]=>[8,6,1,7,2,5,3,4]=>[6,5,2,8,4,7,3,1]=>0101111
[7,2,6,1,3,4,8,5]=>[8,6,2,1,7,3,4,5]=>[6,3,2,8,5,7,4,1]=>0110111
[6,2,7,5,1,3,8,4]=>[8,5,2,7,6,1,3,4]=>[8,4,7,3,2,5,6,1]=>0100111
[1,7,5,6,2,3,8,4]=>[1,8,2,6,7,5,3,4]=>[1,8,4,6,5,7,3,2]=>0100111
[7,8,4,1,5,6,2,3]=>[6,4,1,8,2,5,7,3]=>[7,8,3,1,6,5,2,4]=>0101101
[5,8,1,3,6,7,2,4]=>[7,8,1,3,5,2,6,4]=>[5,8,4,3,1,7,6,2]=>0110111
[2,8,4,3,7,1,5,6]=>[7,2,4,8,3,1,5,6]=>[2,8,6,1,7,5,3,4]=>0001111
[1,2,5,4,8,3,6,7]=>[1,2,8,5,4,3,6,7]=>[1,2,5,4,8,7,6,3]=>0001111
[2,5,8,4,7,1,3,6]=>[7,2,1,8,5,4,3,6]=>[2,5,7,3,1,8,6,4]=>0100111
[4,5,8,7,1,2,3,6]=>[7,1,2,4,5,3,8,6]=>[4,5,8,6,3,2,1,7]=>1100101
[1,8,7,4,6,2,3,5]=>[1,6,2,7,4,3,8,5]=>[1,6,3,2,8,5,4,7]=>0101101
[2,6,5,4,1,8,3,7]=>[8,2,4,5,6,1,3,7]=>[2,8,7,3,4,5,6,1]=>0000111
[3,8,4,5,1,6,7,2]=>[7,5,3,8,4,1,6,2]=>[3,7,6,1,8,2,5,4]=>0001111
[8,5,4,1,3,6,7,2]=>[7,4,1,5,8,3,6,2]=>[7,6,3,1,8,2,4,5]=>0100111
[8,4,7,6,5,3,1,2]=>[3,1,5,6,7,8,4,2]=>[8,2,1,3,5,7,4,6]=>1000011
[2,4,1,8,5,7,6,3]=>[6,2,4,1,7,8,5,3]=>[2,7,5,8,3,4,1,6]=>0010011
[8,2,7,3,1,6,5,4]=>[3,5,6,7,8,2,1,4]=>[8,4,7,1,3,6,2,5]=>0000111
[1,8,4,2,3,7,6,5]=>[1,4,2,6,7,8,3,5]=>[1,8,5,7,3,2,4,6]=>0100011
[2,3,1,8,7,6,4,5]=>[3,2,1,6,4,7,8,5]=>[2,3,1,8,5,4,6,7]=>0101001
[8,2,7,5,6,4,1,3]=>[4,6,2,7,8,1,5,3]=>[8,3,2,6,1,4,7,5]=>0100111
[8,4,7,6,5,1,2,3]=>[5,1,2,6,7,8,4,3]=>[8,3,2,1,5,7,4,6]=>1100011
[8,4,7,2,1,6,5,3]=>[2,5,6,7,8,4,1,3]=>[8,3,6,4,7,1,2,5]=>0000111
[1,8,4,7,6,5,2,3]=>[1,5,2,6,7,8,4,3]=>[1,8,3,2,5,7,4,6]=>0100011
[8,2,5,7,1,4,6,3]=>[6,7,8,2,1,5,4,3]=>[6,5,1,7,4,2,8,3]=>0011111
[5,3,6,1,4,2,8,7]=>[4,6,5,3,1,2,8,7]=>[5,1,4,3,6,2,8,7]=>0011101
[2,1,7,5,8,3,6,4]=>[2,1,6,8,7,5,3,4]=>[2,1,7,3,6,5,8,4]=>1000111
[7,3,8,5,6,2,1,4]=>[2,6,8,3,7,1,5,4]=>[6,1,2,7,5,8,4,3]=>0010111
[6,8,1,2,5,7,4,3]=>[4,1,7,8,2,6,5,3]=>[6,8,3,7,5,2,1,4]=>1001011
[7,3,1,8,2,5,6,4]=>[6,3,8,7,1,2,5,4]=>[8,4,7,5,1,6,2,3]=>0001111
[7,2,3,8,1,5,6,4]=>[6,8,2,7,3,1,5,4]=>[6,1,8,4,7,5,3,2]=>0101111
[2,7,4,8,6,3,1,5]=>[3,2,6,8,4,7,1,5]=>[2,7,1,3,6,8,5,4]=>0001011
[7,2,1,8,3,5,6,4]=>[2,6,8,7,1,3,5,4]=>[8,4,7,5,1,2,6,3]=>0001111
[5,1,6,3,8,2,4,7]=>[8,6,5,1,3,2,4,7]=>[5,3,6,2,8,7,4,1]=>0011111
[4,3,5,8,2,1,6,7]=>[2,8,4,3,5,1,6,7]=>[4,3,5,8,7,6,1,2]=>0010111
[7,8,6,3,1,4,2,5]=>[4,3,6,1,2,8,7,5]=>[4,1,7,8,5,2,3,6]=>0011001
[3,1,2,4,8,5,7,6]=>[3,1,2,4,7,8,5,6]=>[3,2,1,4,7,5,8,6]=>1100011
[5,1,2,4,6,7,8,3]=>[8,1,5,2,4,6,7,3]=>[6,7,8,3,5,4,2,1]=>1011001
[5,3,2,6,8,4,7,1]=>[7,3,8,5,2,6,4,1]=>[6,8,1,7,4,5,2,3]=>0001011
[5,4,3,8,6,2,7,1]=>[7,6,4,5,3,8,2,1]=>[5,3,4,8,1,7,2,6]=>0001011
[5,4,2,8,6,3,7,1]=>[7,6,4,5,2,8,3,1]=>[8,1,7,3,4,5,2,6]=>0001011
[5,7,4,2,6,3,8,1]=>[8,6,4,7,5,2,3,1]=>[5,6,2,7,3,4,8,1]=>0000111
[6,4,7,8,2,3,5,1]=>[5,8,2,6,4,3,7,1]=>[7,8,1,5,4,6,3,2]=>0101101
[4,7,5,2,3,8,6,1]=>[6,5,2,4,8,7,3,1]=>[4,8,1,6,7,3,2,5]=>0100011
[5,7,3,2,8,4,6,1]=>[6,3,8,7,5,2,4,1]=>[5,7,4,8,1,6,2,3]=>0000111
[5,3,7,2,8,4,6,1]=>[6,8,7,5,3,2,4,1]=>[7,4,5,3,8,1,6,2]=>0001111
[7,5,3,2,6,4,8,1]=>[8,3,6,5,7,2,4,1]=>[6,2,3,7,4,5,8,1]=>0000111
[5,3,2,8,6,4,7,1]=>[7,3,6,5,2,8,4,1]=>[8,1,7,4,5,2,3,6]=>0001011
[7,4,6,2,3,8,5,1]=>[5,8,2,6,7,4,3,1]=>[6,4,8,1,5,7,3,2]=>0100111
[6,3,7,5,2,4,8,1]=>[8,5,7,3,6,2,4,1]=>[6,2,5,7,4,3,8,1]=>0010111
[4,7,6,2,3,8,5,1]=>[5,8,2,4,6,7,3,1]=>[4,8,1,5,6,7,3,2]=>0100011
[7,6,3,2,5,8,1,4]=>[8,3,6,2,1,7,5,4]=>[8,4,2,3,6,7,5,1]=>0011011
[5,8,3,2,1,7,6,4]=>[2,3,6,7,5,8,1,4]=>[5,8,4,7,1,2,3,6]=>0000011
[4,8,2,7,6,5,3,1]=>[3,5,6,4,7,8,2,1]=>[4,7,2,5,8,1,3,6]=>0000011
[4,8,3,7,2,1,6,5]=>[2,6,7,4,8,3,1,5]=>[4,7,1,2,6,3,8,5]=>0000111
[8,4,2,1,7,6,5,3]=>[2,5,4,6,7,8,1,3]=>[7,1,2,5,8,3,4,6]=>0000011
[1,6,4,2,5,3,7,8]=>[1,5,4,6,2,3,7,8]=>[1,5,2,6,3,4,7,8]=>0001100
[1,8,6,2,7,3,4,5]=>[1,7,6,2,3,8,4,5]=>[1,7,4,2,8,5,3,6]=>0011011
[1,5,2,6,4,3,7,8]=>[1,4,6,5,2,3,7,8]=>[1,5,2,4,6,3,7,8]=>0001100
[1,8,6,2,3,7,4,5]=>[1,7,2,6,3,8,4,5]=>[1,8,5,3,2,7,4,6]=>0101011
[1,5,2,8,6,3,4,7]=>[1,6,5,2,3,8,4,7]=>[1,5,3,8,7,4,2,6]=>0011011
[1,3,6,8,2,7,4,5]=>[1,7,3,8,2,6,4,5]=>[1,3,6,8,5,2,7,4]=>0001011
[1,4,3,8,2,5,6,7]=>[1,8,4,3,2,5,6,7]=>[1,4,3,8,7,6,5,2]=>0011111
[1,7,2,3,8,5,4,6]=>[1,5,2,8,7,3,4,6]=>[1,8,6,3,2,5,7,4]=>0100111
[1,6,2,8,5,4,3,7]=>[1,4,5,8,6,2,3,7]=>[1,8,7,3,5,6,2,4]=>0000111
[1,7,2,3,8,6,4,5]=>[1,6,2,8,3,7,4,5]=>[1,8,5,3,2,6,7,4]=>0101011
[1,2,7,3,6,8,4,5]=>[1,2,8,7,3,4,6,5]=>[1,2,7,6,4,8,5,3]=>0001111
[1,7,5,6,8,3,4,2]=>[1,4,8,3,7,5,6,2]=>[1,7,6,5,8,2,4,3]=>0010111
[1,3,7,2,5,8,6,4]=>[1,6,3,8,2,7,5,4]=>[1,3,7,5,2,6,8,4]=>0001011
[1,3,7,5,6,2,8,4]=>[1,8,3,6,7,5,2,4]=>[1,3,8,4,6,5,7,2]=>0000111
[2,5,7,4,1,3,8,6]=>[4,2,1,8,5,7,3,6]=>[2,5,8,6,7,3,1,4]=>0100011
[6,7,3,1,8,5,2,4]=>[5,3,8,1,7,6,2,4]=>[6,8,4,1,5,7,2,3]=>0010011
[3,5,6,1,8,7,2,4]=>[7,6,3,1,5,2,8,4]=>[3,5,6,2,8,4,1,7]=>0010101
[2,4,6,8,7,3,1,5]=>[3,2,7,4,1,6,8,5]=>[2,4,6,8,5,1,3,7]=>0001001
[7,2,4,8,6,3,1,5]=>[3,6,8,2,4,7,1,5]=>[8,5,4,2,6,7,1,3]=>0011011
[8,5,3,6,2,1,7,4]=>[2,7,6,5,8,3,1,4]=>[6,3,7,1,2,8,4,5]=>0000111
[4,5,1,8,3,2,7,6]=>[3,7,5,4,1,8,2,6]=>[4,5,1,3,7,2,8,6]=>0001011
[5,8,2,1,4,6,7,3]=>[2,7,8,1,5,4,6,3]=>[5,7,6,4,1,2,8,3]=>0010111
[3,7,8,4,2,6,5,1]=>[5,4,3,6,8,2,7,1]=>[3,6,2,4,7,8,1,5]=>0000101
[7,1,3,8,4,5,6,2]=>[6,8,1,7,3,4,5,2]=>[7,5,3,1,6,4,8,2]=>0101111
[7,8,1,4,3,5,6,2]=>[6,4,8,1,3,5,7,2]=>[7,8,2,4,1,6,5,3]=>0011101
[3,2,5,7,1,8,6,4]=>[6,3,2,8,5,7,1,4]=>[3,2,5,7,1,6,8,4]=>0100011
[2,1,4,6,8,7,3,5]=>[2,1,7,4,3,6,8,5]=>[2,1,4,6,8,5,3,7]=>1001001
[7,8,5,2,4,1,3,6]=>[4,5,2,1,8,3,7,6]=>[4,1,7,8,6,3,2,5]=>0110101
[7,6,2,3,1,8,4,5]=>[3,8,2,6,1,7,4,5]=>[7,4,6,8,5,1,3,2]=>0101011
[3,1,8,5,4,2,7,6]=>[4,3,1,5,7,8,2,6]=>[7,2,3,1,4,5,8,6]=>0100011
[1,3,8,5,2,6,7,4]=>[1,7,3,5,8,2,6,4]=>[1,3,7,6,2,8,4,5]=>0000111
[8,5,3,2,1,6,7,4]=>[2,3,7,5,8,1,6,4]=>[7,6,1,2,3,8,4,5]=>0000111
[5,8,3,1,2,6,4,7]=>[3,1,6,8,5,2,4,7]=>[5,6,2,1,3,8,7,4]=>1000111
[8,5,3,2,1,6,4,7]=>[2,3,6,5,8,1,4,7]=>[6,1,2,3,8,7,4,5]=>0000111
[8,1,5,4,2,6,3,7]=>[6,4,5,8,1,2,3,7]=>[8,7,3,5,1,6,2,4]=>0001111
[4,8,7,1,5,2,6,3]=>[6,5,7,4,1,2,8,3]=>[4,6,2,5,1,8,3,7]=>0001101
[3,8,7,5,4,1,2,6]=>[4,1,3,5,7,2,8,6]=>[3,8,6,2,1,4,5,7]=>1000101
[8,6,2,5,3,4,7,1]=>[7,5,6,2,3,8,4,1]=>[8,1,7,4,2,5,3,6]=>0011011
[8,6,5,1,3,4,7,2]=>[7,5,1,3,6,8,4,2]=>[7,4,3,1,8,2,5,6]=>0110011
[8,7,1,5,3,6,2,4]=>[6,5,7,1,3,2,8,4]=>[8,4,1,6,2,5,3,7]=>0011101
[8,6,1,3,5,4,7,2]=>[7,5,1,6,3,8,4,2]=>[8,2,5,3,1,7,4,6]=>0101011
[8,1,6,3,5,4,7,2]=>[7,5,6,8,1,3,4,2]=>[6,3,8,2,5,1,7,4]=>0001111
[8,3,2,7,4,6,5,1]=>[5,3,6,7,8,2,4,1]=>[6,2,3,7,4,8,1,5]=>0000111
[7,8,5,2,4,3,6,1]=>[6,4,5,2,8,3,7,1]=>[4,2,7,8,1,6,3,5]=>0010101
[4,8,1,5,3,7,6,2]=>[6,5,7,4,1,8,3,2]=>[4,7,3,8,2,5,1,6]=>0001011
[6,4,1,7,8,5,3,2]=>[3,5,4,8,6,1,7,2]=>[7,8,2,5,6,1,3,4]=>0000101
[8,7,3,1,6,2,5,4]=>[5,3,6,7,1,2,8,4]=>[5,1,6,2,3,8,4,7]=>0001101
[8,1,7,3,5,6,2,4]=>[6,7,8,1,3,2,5,4]=>[8,4,1,6,2,7,5,3]=>0011111
[8,7,3,2,6,1,5,4]=>[5,3,6,7,2,1,8,4]=>[6,1,5,2,3,8,4,7]=>0001101
[8,7,2,6,5,1,3,4]=>[5,6,2,1,7,3,8,4]=>[6,3,2,8,4,1,5,7]=>0110101
[1,4,8,6,7,5,3,2]=>[1,3,5,4,7,8,6,2]=>[1,4,8,2,3,5,7,6]=>0000011
[6,5,7,2,8,3,4,1]=>[4,8,7,2,6,5,3,1]=>[6,5,7,3,8,1,4,2]=>0010111
[6,7,2,5,8,1,4,3]=>[4,8,7,2,1,6,5,3]=>[6,8,3,7,5,1,4,2]=>0011011
[6,3,7,5,8,2,4,1]=>[4,8,7,3,6,2,5,1]=>[8,1,4,3,7,5,6,2]=>0010111
[6,5,7,3,8,1,4,2]=>[4,8,7,3,6,5,1,2]=>[6,5,7,1,4,3,8,2]=>0010111
[6,3,7,4,8,2,5,1]=>[5,8,7,6,3,4,2,1]=>[6,4,8,1,5,3,7,2]=>0001111
[6,3,7,4,8,1,5,2]=>[5,8,7,6,3,4,1,2]=>[6,4,7,1,5,3,8,2]=>0001111
[6,2,7,4,8,1,5,3]=>[5,8,7,6,2,4,1,3]=>[6,4,8,3,7,1,5,2]=>0001111
[8,7,6,4,2,5,3,1]=>[3,5,4,6,2,7,8,1]=>[5,2,8,1,3,4,6,7]=>0001001
[1,5,7,3,6,8,2,4]=>[1,8,7,3,5,2,6,4]=>[1,5,8,4,3,7,6,2]=>0010111
[1,3,4,7,6,8,2,5]=>[1,8,3,4,2,7,6,5]=>[1,3,4,7,6,8,5,2]=>0001011
[4,1,3,7,6,8,2,5]=>[8,4,1,3,2,7,6,5]=>[7,6,8,5,2,4,3,1]=>0111011
[6,7,8,2,4,5,1,3]=>[5,8,2,1,4,6,7,3]=>[5,4,1,6,7,8,3,2]=>0111001
[5,8,6,2,4,7,1,3]=>[7,6,2,1,5,8,4,3]=>[5,7,4,1,8,3,2,6]=>0110011
[8,7,2,5,6,3,1,4]=>[3,6,7,2,1,5,8,4]=>[8,4,2,6,5,1,3,7]=>0011101
[1,8,2,7,5,4,3,6]=>[1,4,5,7,8,2,3,6]=>[1,8,6,2,4,7,3,5]=>0000111
[3,8,1,7,5,4,2,6]=>[4,5,3,7,8,1,2,6]=>[3,8,6,1,4,7,2,5]=>0000111
[5,8,6,1,7,3,2,4]=>[3,7,6,1,5,8,2,4]=>[5,7,2,8,4,1,3,6]=>0010011
[6,7,1,2,8,4,3,5]=>[4,1,8,7,2,6,3,5]=>[6,8,5,2,1,4,7,3]=>1001011
[8,2,1,7,5,4,3,6]=>[2,4,5,7,8,1,3,6]=>[8,6,1,2,4,7,3,5]=>0000111
[1,3,2,8,6,5,4,7]=>[1,3,2,5,6,8,4,7]=>[1,3,2,8,7,4,5,6]=>0100011
[3,5,7,1,6,8,2,4]=>[8,7,3,1,5,2,6,4]=>[3,5,7,6,2,8,4,1]=>0010111
[1,5,7,8,6,3,2,4]=>[1,3,6,2,5,8,7,4]=>[1,5,7,8,4,2,3,6]=>0010001
[8,4,6,7,5,2,1,3]=>[2,5,1,7,8,4,6,3]=>[7,6,4,8,3,1,2,5]=>0100111
[8,3,7,5,6,2,1,4]=>[2,6,7,3,8,1,5,4]=>[6,1,2,8,4,3,7,5]=>0010111
[1,4,8,6,7,3,2,5]=>[1,3,7,4,2,8,6,5]=>[1,4,8,5,2,3,7,6]=>0001011
[2,4,8,6,7,3,1,5]=>[3,2,7,4,1,8,6,5]=>[2,4,8,5,1,3,7,6]=>0001011
[1,3,8,7,5,4,2,6]=>[1,4,3,5,7,2,8,6]=>[1,3,8,6,2,4,5,7]=>0000101
[4,8,7,5,6,2,1,3]=>[2,6,1,4,7,5,8,3]=>[4,8,3,1,2,6,5,7]=>0100101
[8,1,7,2,5,6,4,3]=>[4,6,7,8,1,2,5,3]=>[6,2,8,3,7,5,1,4]=>0001111
[8,1,3,5,2,7,6,4]=>[6,5,1,7,3,8,2,4]=>[8,4,7,2,5,3,1,6]=>0101011
[8,1,7,4,3,6,5,2]=>[5,4,6,7,8,1,3,2]=>[8,2,4,7,3,6,1,5]=>0000111
[8,1,4,5,6,2,7,3]=>[7,6,8,1,4,5,2,3]=>[7,2,6,5,4,1,8,3]=>0011111
[2,5,1,7,8,6,4,3]=>[4,2,6,5,1,8,7,3]=>[2,5,1,4,7,8,3,6]=>0001001
[3,5,6,1,8,7,4,2]=>[4,7,3,6,5,1,8,2]=>[3,5,6,1,4,8,2,7]=>0000101
[8,4,5,3,7,6,2,1]=>[2,6,5,7,4,8,3,1]=>[7,3,5,4,8,1,2,6]=>0001011
[7,2,1,6,3,4,8,5]=>[2,8,6,1,7,3,4,5]=>[6,3,8,5,7,4,1,2]=>0010111
[2,3,5,1,4,8,7,6]=>[5,2,3,1,4,7,8,6]=>[2,3,5,4,1,8,6,7]=>0011001
[2,7,1,3,6,8,5,4]=>[5,2,1,8,7,3,6,4]=>[2,7,6,3,1,5,8,4]=>0100111
[4,8,5,7,2,6,3,1]=>[3,6,7,4,8,5,2,1]=>[4,8,1,3,7,2,6,5]=>0000111
[8,4,5,7,3,2,6,1]=>[6,3,7,8,4,5,2,1]=>[7,2,3,8,1,6,5,4]=>0001111
[8,3,7,2,4,1,5,6]=>[4,7,8,3,2,1,5,6]=>[7,5,2,8,6,1,4,3]=>0011111
[8,6,7,2,1,4,3,5]=>[2,4,7,1,3,8,6,5]=>[4,1,2,8,5,3,7,6]=>0011011
[8,3,7,5,1,2,6,4]=>[6,1,5,7,8,3,2,4]=>[8,4,7,2,1,6,3,5]=>1000111
[3,7,4,6,1,5,2,8]=>[5,6,3,7,4,1,2,8]=>[3,7,2,6,1,5,4,8]=>0001110
[3,4,7,6,1,2,8,5]=>[8,1,3,4,6,7,2,5]=>[3,4,8,5,6,7,2,1]=>1000011
[7,6,3,8,1,4,5,2]=>[5,8,6,3,1,7,4,2]=>[5,1,7,4,3,6,8,2]=>0011011
[7,6,4,8,1,2,5,3]=>[5,1,8,6,4,7,2,3]=>[7,2,1,5,4,6,8,3]=>1001011
[8,7,4,1,5,6,2,3]=>[6,4,1,7,2,5,8,3]=>[8,3,1,6,5,2,4,7]=>0101101
[8,5,3,7,1,6,4,2]=>[4,6,7,5,8,3,1,2]=>[8,2,6,3,7,1,4,5]=>0000111
[8,5,3,1,6,4,2,7]=>[4,3,6,5,8,1,2,7]=>[8,7,2,3,6,1,4,5]=>0000111
[8,7,4,1,5,2,3,6]=>[5,4,1,7,2,3,8,6]=>[8,6,3,1,5,2,4,7]=>0101101
[8,7,5,1,2,6,3,4]=>[6,1,5,2,7,3,8,4]=>[8,4,2,1,6,3,5,7]=>1010101
[8,7,5,1,2,3,6,4]=>[6,1,2,5,7,3,8,4]=>[6,3,2,1,8,4,5,7]=>1100101
[1,8,6,3,2,7,4,5]=>[1,3,7,6,2,8,4,5]=>[1,8,5,2,3,7,4,6]=>0001011
[1,5,6,2,8,4,3,7]=>[1,4,8,6,5,2,3,7]=>[1,5,6,2,4,8,7,3]=>0000111
[1,2,5,3,8,6,7,4]=>[1,2,7,5,3,8,6,4]=>[1,2,8,4,5,3,7,6]=>0001011
[2,3,8,6,7,1,5,4]=>[5,2,3,7,1,8,6,4]=>[2,3,5,1,8,4,7,6]=>0001011
[1,2,5,7,4,6,8,3]=>[1,2,8,7,5,4,6,3]=>[1,2,5,7,6,4,8,3]=>0000111
[2,3,6,8,1,7,4,5]=>[7,2,3,8,1,6,4,5]=>[2,3,6,8,5,1,7,4]=>0001011
[3,6,4,2,5,1,8,7]=>[5,4,3,6,2,1,8,7]=>[3,6,1,5,2,4,8,7]=>0001101
[2,1,5,8,6,4,7,3]=>[2,1,7,6,5,8,4,3]=>[2,1,5,8,3,7,4,6]=>1000011
[5,8,7,2,6,3,4,1]=>[4,6,7,2,5,3,8,1]=>[5,8,1,4,2,6,3,7]=>0010101
[7,6,2,4,8,1,5,3]=>[5,8,6,2,4,7,1,3]=>[8,3,6,7,1,5,4,2]=>0011011
[5,3,8,2,1,7,6,4]=>[2,6,7,5,3,8,1,4]=>[8,4,5,3,7,1,2,6]=>0001011
[3,8,7,2,6,5,1,4]=>[5,6,3,2,7,1,8,4]=>[3,8,4,2,6,1,5,7]=>0010101
[5,8,4,7,1,6,3,2]=>[3,6,7,8,5,4,1,2]=>[5,7,1,3,8,2,6,4]=>0000111
[8,5,6,1,4,7,2,3]=>[7,6,1,2,8,5,4,3]=>[8,3,1,7,4,2,6,5]=>0110111
[3,6,7,5,8,1,2,4]=>[8,1,3,2,7,6,5,4]=>[3,6,7,5,8,4,2,1]=>1010011
[6,5,8,7,4,2,3,1]=>[3,4,2,7,6,5,8,1]=>[6,5,8,1,3,2,4,7]=>0100101
[2,5,6,3,1,4,8,7]=>[3,2,6,1,5,4,8,7]=>[2,5,6,4,1,3,8,7]=>0010101
[4,8,5,6,7,3,1,2]=>[3,1,7,4,8,5,6,2]=>[4,8,2,1,3,7,6,5]=>1000111
[5,8,6,2,7,4,1,3]=>[4,7,2,6,5,8,1,3]=>[5,8,3,2,7,1,4,6]=>0100011
[8,5,6,1,7,2,4,3]=>[4,7,6,1,8,5,2,3]=>[4,1,7,2,8,3,6,5]=>0010111
[7,4,5,1,3,8,6,2]=>[6,5,1,8,4,7,3,2]=>[7,3,1,6,8,2,5,4]=>0101011
[5,8,7,4,6,2,3,1]=>[3,6,2,7,5,4,8,1]=>[5,8,1,3,2,6,4,7]=>0100101
[2,7,8,4,6,5,1,3]=>[5,2,1,6,8,4,7,3]=>[2,6,4,7,8,3,1,5]=>0100101
[1,8,7,3,6,4,5,2]=>[1,5,6,7,3,4,8,2]=>[1,8,2,5,3,6,4,7]=>0001101
[2,8,7,4,6,1,5,3]=>[5,2,6,7,4,1,8,3]=>[2,8,3,6,1,5,4,7]=>0001101
[4,5,8,6,3,7,2,1]=>[2,7,6,4,5,8,3,1]=>[4,5,8,1,2,7,3,6]=>0000011
[6,1,2,8,4,7,5,3]=>[5,1,7,8,6,2,4,3]=>[6,2,1,5,8,3,7,4]=>1000111
[4,7,1,8,5,6,3,2]=>[3,6,8,4,7,1,5,2]=>[4,7,5,8,2,6,1,3]=>0000111
[2,5,8,1,7,4,6,3]=>[6,2,7,8,5,1,4,3]=>[2,5,6,1,8,3,7,4]=>0000111
[2,4,8,5,7,6,1,3]=>[6,2,1,4,7,8,5,3]=>[2,4,7,5,8,3,1,6]=>0100011
[4,1,5,8,6,7,3,2]=>[3,7,4,1,5,8,6,2]=>[4,1,3,5,8,2,7,6]=>0010011
[2,8,7,1,4,3,6,5]=>[4,2,6,1,7,3,8,5]=>[2,4,1,6,3,8,5,7]=>0010101
[1,2,7,8,4,3,6,5]=>[1,2,4,6,8,3,7,5]=>[1,2,6,3,4,7,8,5]=>0000101
[2,8,5,4,1,3,7,6]=>[4,2,1,5,7,8,3,6]=>[2,7,3,1,4,5,8,6]=>0100011
[1,5,6,8,7,3,2,4]=>[1,3,7,2,5,6,8,4]=>[1,5,6,8,4,2,3,7]=>0010001
[1,4,8,3,6,5,2,7]=>[1,5,6,4,8,3,2,7]=>[1,4,6,3,8,7,2,5]=>0000111
[1,2,8,6,4,3,7,5]=>[1,2,4,7,6,8,3,5]=>[1,2,7,3,4,8,5,6]=>0000011
[6,5,1,8,7,3,2,4]=>[3,7,5,1,6,2,8,4]=>[8,4,1,3,5,6,2,7]=>0010101
[6,5,1,8,7,4,3,2]=>[3,4,7,5,6,1,8,2]=>[8,2,4,5,6,1,3,7]=>0000101
[7,5,1,8,6,4,3,2]=>[3,4,6,5,8,7,1,2]=>[7,1,3,6,8,2,4,5]=>0000011
[2,7,5,8,1,4,6,3]=>[6,2,8,1,7,5,4,3]=>[2,7,4,1,6,5,8,3]=>0010111
[8,5,6,1,7,3,2,4]=>[3,7,6,1,8,5,2,4]=>[7,2,8,4,1,3,6,5]=>0010111
[3,4,6,7,8,2,1,5]=>[2,8,3,4,1,6,7,5]=>[3,4,6,7,8,5,1,2]=>0001001
[1,2,6,7,8,5,3,4]=>[1,2,5,3,8,6,7,4]=>[1,2,6,7,8,4,3,5]=>0010001
[8,6,1,2,7,3,4,5]=>[7,1,6,2,3,8,4,5]=>[7,4,2,1,8,5,3,6]=>1011011
[3,6,8,2,7,1,5,4]=>[5,7,3,8,2,6,1,4]=>[3,6,7,1,5,2,8,4]=>0001011
[6,8,7,2,5,4,1,3]=>[4,5,2,7,1,6,8,3]=>[6,8,3,2,5,1,4,7]=>0101001
[4,7,2,8,6,5,1,3]=>[5,6,2,4,8,7,1,3]=>[4,8,3,2,6,7,1,5]=>0100011
[4,3,8,1,5,7,6,2]=>[6,7,4,3,1,8,5,2]=>[4,3,8,2,7,5,1,6]=>0011011
[4,2,3,6,8,7,1,5]=>[7,4,2,3,1,6,8,5]=>[4,3,2,6,8,5,1,7]=>0111001
[4,2,8,3,5,7,6,1]=>[6,7,4,2,3,8,5,1]=>[7,5,3,4,2,8,1,6]=>0011011
[3,4,7,1,5,6,8,2]=>[8,7,3,4,1,5,6,2]=>[3,4,8,2,7,6,5,1]=>0001111
[7,3,2,8,1,6,4,5]=>[6,3,8,7,2,1,4,5]=>[6,1,7,4,8,5,2,3]=>0001111
[4,3,5,2,8,6,7,1]=>[7,5,4,3,2,8,6,1]=>[4,3,5,2,8,1,7,6]=>0011011
[4,5,2,3,8,6,7,1]=>[7,5,2,4,3,8,6,1]=>[4,5,3,2,8,1,7,6]=>0101011
[4,8,5,3,2,6,7,1]=>[7,3,5,4,8,2,6,1]=>[4,8,1,7,6,2,3,5]=>0000111
[3,8,4,5,2,6,7,1]=>[7,5,3,8,4,2,6,1]=>[3,8,1,7,6,2,5,4]=>0001111
[4,1,2,7,5,6,8,3]=>[8,1,4,2,7,5,6,3]=>[7,6,5,8,3,4,2,1]=>1010111
[4,8,1,6,5,2,7,3]=>[7,5,6,4,8,1,2,3]=>[4,8,3,6,1,7,2,5]=>0000111
[5,6,7,4,2,8,3,1]=>[3,8,4,7,5,6,2,1]=>[5,6,8,1,3,4,7,2]=>0000011
[7,3,5,4,2,8,6,1]=>[6,4,5,8,3,7,2,1]=>[5,3,8,1,6,7,2,4]=>0001011
[7,5,2,4,3,8,6,1]=>[6,4,5,2,8,7,3,1]=>[4,2,8,1,6,7,3,5]=>0010011
[6,8,1,2,5,4,7,3]=>[7,1,5,8,2,6,4,3]=>[6,8,3,5,2,1,7,4]=>1001011
[7,1,2,8,5,6,4,3]=>[4,1,6,8,7,2,5,3]=>[7,5,8,3,6,2,1,4]=>1000111
[3,7,6,4,8,5,2,1]=>[2,5,3,8,6,7,4,1]=>[3,8,1,2,5,6,7,4]=>0000011
[3,1,6,8,5,4,7,2]=>[7,3,1,5,8,6,4,2]=>[6,8,2,3,1,7,4,5]=>0100011
[2,3,5,8,4,6,7,1]=>[7,2,3,8,5,4,6,1]=>[2,3,5,8,1,7,6,4]=>0000111
[5,3,4,8,2,6,7,1]=>[7,8,5,3,4,2,6,1]=>[5,4,3,8,1,7,6,2]=>0011111
[5,4,8,3,2,6,7,1]=>[7,3,8,5,4,2,6,1]=>[5,4,8,1,7,6,2,3]=>0001111
[5,8,2,3,4,6,7,1]=>[7,8,2,3,5,4,6,1]=>[5,8,1,7,6,4,3,2]=>0110111
[1,5,7,6,3,2,8,4]=>[1,3,8,6,5,7,2,4]=>[1,5,8,4,6,7,2,3]=>0000011
[3,4,5,2,1,8,6,7]=>[2,5,3,4,1,8,6,7]=>[3,4,5,1,2,8,7,6]=>0001011
[3,2,7,8,6,1,4,5]=>[6,3,2,1,4,8,7,5]=>[3,2,7,8,5,4,1,6]=>0111001
[5,7,4,1,6,8,2,3]=>[8,4,1,7,5,2,6,3]=>[5,7,6,2,4,8,3,1]=>0100111
[5,6,8,1,3,7,2,4]=>[7,8,1,3,5,6,2,4]=>[5,6,8,4,3,1,7,2]=>0110011
[4,1,6,8,7,3,2,5]=>[3,7,4,1,2,6,8,5]=>[4,1,3,6,8,5,2,7]=>0011001
[5,1,4,6,7,3,8,2]=>[8,7,5,1,4,6,3,2]=>[6,8,2,7,3,5,4,1]=>0011011
[7,1,3,4,6,2,8,5]=>[8,6,1,3,7,4,2,5]=>[8,5,7,2,6,4,3,1]=>0110111
[5,8,7,4,2,1,3,6]=>[2,4,1,7,5,3,8,6]=>[5,8,6,3,1,2,4,7]=>0100101
[3,1,5,2,7,8,6,4]=>[6,3,1,5,2,8,7,4]=>[7,8,4,5,2,3,1,6]=>0101001
[1,2,5,4,8,7,3,6]=>[1,2,7,5,4,3,8,6]=>[1,2,5,4,8,6,3,7]=>0001101
[1,2,4,8,6,3,5,7]=>[1,2,6,4,3,8,5,7]=>[1,2,4,8,7,5,3,6]=>0001011
[1,2,5,8,4,6,3,7]=>[1,2,6,8,5,4,3,7]=>[1,2,5,8,7,3,6,4]=>0000111
[1,2,7,8,4,5,3,6]=>[1,2,5,8,4,3,7,6]=>[1,2,7,8,6,3,5,4]=>0001101
[1,8,5,7,6,3,2,4]=>[1,3,6,2,7,8,5,4]=>[1,7,5,8,4,2,3,6]=>0010011
[1,8,4,7,5,3,2,6]=>[1,3,5,7,8,4,2,6]=>[1,8,6,4,7,2,3,5]=>0000111
[7,6,2,3,5,4,1,8]=>[4,5,2,6,3,7,1,8]=>[5,3,2,7,1,4,6,8]=>0101010
[8,4,2,7,1,6,3,5]=>[6,7,4,8,2,1,3,5]=>[6,1,8,5,2,7,3,4]=>0001111
[4,6,3,2,8,1,7,5]=>[7,3,8,4,6,2,1,5]=>[4,7,1,8,5,6,2,3]=>0000111
[4,5,3,8,2,1,6,7]=>[2,8,5,4,3,1,6,7]=>[4,5,3,8,7,6,1,2]=>0001111
[8,3,5,4,2,1,6,7]=>[2,4,5,8,3,1,6,7]=>[5,3,8,7,6,1,2,4]=>0001111
[7,8,4,3,1,5,2,6]=>[5,3,4,8,1,2,7,6]=>[5,1,7,8,6,2,3,4]=>0001101
[8,6,3,7,1,5,2,4]=>[5,7,6,3,1,8,2,4]=>[5,1,7,2,8,4,3,6]=>0011011
[8,7,6,1,2,5,3,4]=>[5,1,6,2,3,7,8,4]=>[8,4,2,1,5,3,6,7]=>1011001
[5,7,6,4,2,3,1,8]=>[3,4,2,6,5,7,1,8]=>[5,7,1,3,2,4,6,8]=>0100010
[4,1,2,8,5,3,7,6]=>[5,1,4,2,7,8,3,6]=>[7,3,4,2,1,5,8,6]=>1010011
[2,4,6,8,5,1,7,3]=>[7,2,5,4,8,6,1,3]=>[2,4,6,7,1,8,3,5]=>0000011
[3,1,6,8,5,2,7,4]=>[7,3,1,5,8,6,2,4]=>[6,7,2,3,1,8,4,5]=>0100011
[5,8,2,1,3,7,6,4]=>[2,6,1,7,5,8,3,4]=>[5,8,4,7,3,1,2,6]=>0100011
[8,4,1,6,5,2,3,7]=>[5,4,1,6,8,2,3,7]=>[6,2,4,8,7,3,1,5]=>0100111
[1,2,7,4,6,3,8,5]=>[1,2,8,6,7,4,3,5]=>[1,2,6,4,8,5,7,3]=>0000111
[5,3,2,6,7,4,8,1]=>[8,3,7,5,2,6,4,1]=>[6,7,4,5,2,3,8,1]=>0001011
[3,2,7,5,4,8,6,1]=>[6,3,2,5,8,7,4,1]=>[3,2,8,1,6,7,4,5]=>0100011
[2,3,7,5,4,8,6,1]=>[6,2,3,5,8,7,4,1]=>[2,3,8,1,6,7,4,5]=>0000011
[2,4,8,7,5,1,3,6]=>[5,2,1,4,7,3,8,6]=>[2,4,8,6,3,1,5,7]=>0100101
[3,5,7,6,1,8,4,2]=>[4,8,3,6,5,7,1,2]=>[3,5,7,1,4,6,8,2]=>0000011
[1,5,3,2,8,7,6,4]=>[1,3,6,5,2,7,8,4]=>[1,8,4,5,2,3,6,7]=>0001001
[6,2,3,8,7,5,4,1]=>[4,5,2,7,6,3,8,1]=>[6,3,2,5,8,1,4,7]=>0100101
[4,1,3,5,8,7,6,2]=>[6,4,1,3,5,7,8,2]=>[5,8,2,4,3,1,6,7]=>0110001
[7,2,5,3,6,4,1,8]=>[4,6,5,7,2,3,1,8]=>[6,3,5,2,7,1,4,8]=>0001110
[5,2,1,4,8,6,3,7]=>[2,6,5,1,4,8,3,7]=>[8,7,3,5,4,1,2,6]=>0011011
[5,2,8,3,7,4,1,6]=>[4,7,8,5,2,3,1,6]=>[7,1,4,5,2,8,6,3]=>0001111
[1,3,7,4,8,5,2,6]=>[1,5,3,8,7,4,2,6]=>[1,3,7,2,5,8,6,4]=>0000111
[8,2,6,3,7,4,1,5]=>[4,7,6,8,2,3,1,5]=>[6,3,8,5,2,7,1,4]=>0001111
[7,2,6,3,8,4,1,5]=>[4,8,6,7,2,3,1,5]=>[6,3,7,1,4,8,5,2]=>0001111
[3,2,7,4,8,5,1,6]=>[5,3,2,8,7,4,1,6]=>[3,2,7,1,5,8,6,4]=>0100111
[7,2,5,3,8,4,1,6]=>[4,8,5,7,2,3,1,6]=>[7,1,4,8,6,3,5,2]=>0001111
[1,3,6,4,8,5,2,7]=>[1,5,3,8,6,4,2,7]=>[1,3,8,7,2,5,6,4]=>0000111
[5,2,4,3,8,6,1,7]=>[6,4,5,2,3,8,1,7]=>[4,2,5,3,8,7,1,6]=>0011011
[4,2,5,3,1,7,6,8]=>[3,5,4,2,1,7,6,8]=>[5,1,3,4,2,7,6,8]=>0011010
[7,2,4,3,1,6,5,8]=>[3,4,6,2,7,1,5,8]=>[4,2,6,1,3,7,5,8]=>0010110
[6,2,5,3,1,7,4,8]=>[3,7,5,6,2,1,4,8]=>[7,4,6,1,3,5,2,8]=>0001110
[5,2,7,3,1,6,4,8]=>[3,6,7,5,2,1,4,8]=>[7,4,5,2,6,1,3,8]=>0001110
[6,2,7,3,1,5,4,8]=>[3,5,7,6,2,1,4,8]=>[5,2,7,4,6,1,3,8]=>0001110
[1,5,2,4,8,6,3,7]=>[1,6,5,2,4,8,3,7]=>[1,8,7,3,5,4,2,6]=>0011011
[8,4,1,3,7,5,2,6]=>[5,4,1,7,8,3,2,6]=>[7,2,4,8,6,3,1,5]=>0100111
[3,2,8,5,1,6,4,7]=>[6,3,2,5,8,1,4,7]=>[3,2,6,1,8,7,4,5]=>0100111
[6,2,8,4,1,5,3,7]=>[5,4,8,6,2,1,3,7]=>[6,1,5,2,4,8,7,3]=>0001111
[1,4,8,5,2,6,3,7]=>[1,6,5,4,8,2,3,7]=>[1,4,6,2,8,7,3,5]=>0000111
[8,3,7,4,1,5,2,6]=>[5,4,7,8,3,1,2,6]=>[8,6,1,5,3,7,2,4]=>0001111
[1,5,2,8,7,4,3,6]=>[1,4,7,5,2,3,8,6]=>[1,5,2,4,8,6,3,7]=>0001101
[5,7,2,8,1,4,3,6]=>[4,8,7,2,5,1,3,6]=>[5,7,3,8,6,1,4,2]=>0010111
[7,1,5,3,2,6,8,4]=>[3,8,5,7,1,2,6,4]=>[5,1,3,8,4,7,6,2]=>0001111
[1,7,3,4,5,2,8,6]=>[1,5,8,3,4,7,2,6]=>[1,8,6,7,2,5,4,3]=>0011011
[3,2,1,7,8,5,4,6]=>[2,3,1,5,8,4,7,6]=>[3,1,2,7,8,6,4,5]=>0100101
[1,7,6,3,2,4,8,5]=>[1,3,8,2,6,7,4,5]=>[1,8,5,6,7,4,2,3]=>0010011
[1,8,5,3,2,4,7,6]=>[1,3,5,2,7,8,4,6]=>[1,7,4,2,3,5,8,6]=>0010011
[1,2,8,4,6,3,5,7]=>[1,2,6,8,4,3,5,7]=>[1,2,6,3,8,7,5,4]=>0001111
[1,3,6,8,4,5,7,2]=>[1,7,3,8,4,6,5,2]=>[1,3,6,8,2,7,5,4]=>0001011
[2,3,6,8,4,1,7,5]=>[4,2,3,7,8,6,1,5]=>[2,3,6,7,1,4,8,5]=>0000011
[1,2,6,8,4,7,5,3]=>[1,2,5,7,8,6,4,3]=>[1,2,6,7,4,8,3,5]=>0000011
[1,2,8,4,7,3,5,6]=>[1,2,7,8,4,3,5,6]=>[1,2,8,6,3,7,5,4]=>0001111
[7,1,5,2,6,4,3,8]=>[4,6,5,7,1,2,3,8]=>[6,2,7,3,5,1,4,8]=>0001110
[1,8,5,6,2,7,4,3]=>[1,4,7,6,8,5,2,3]=>[1,8,3,7,2,4,6,5]=>0000111
[6,7,2,4,3,5,8,1]=>[8,4,7,2,3,6,5,1]=>[4,2,6,7,5,3,8,1]=>0011011
[4,3,8,2,1,5,7,6]=>[2,7,4,3,1,8,5,6]=>[4,3,7,5,1,2,8,6]=>0011011
[4,5,8,3,2,7,1,6]=>[7,3,8,4,5,2,1,6]=>[4,5,7,1,8,6,2,3]=>0000111
[4,6,7,2,5,3,8,1]=>[8,5,7,4,2,6,3,1]=>[4,5,2,6,7,3,8,1]=>0001011
[8,4,7,3,1,5,6,2]=>[6,3,7,8,4,1,5,2]=>[6,1,8,2,3,7,5,4]=>0001111
[2,3,7,6,5,1,8,4]=>[8,2,3,5,6,7,1,4]=>[2,3,8,4,5,6,7,1]=>0000011
[3,7,2,6,8,1,5,4]=>[5,8,3,7,2,1,6,4]=>[3,8,4,7,6,1,5,2]=>0001111
[7,3,1,6,8,2,5,4]=>[5,3,8,7,1,2,6,4]=>[5,1,8,4,7,6,2,3]=>0001111
[3,6,2,1,4,7,8,5]=>[2,8,3,1,6,4,7,5]=>[3,7,8,5,6,4,1,2]=>0010101
[8,4,7,1,5,3,6,2]=>[6,5,7,8,4,1,3,2]=>[6,1,7,3,8,2,5,4]=>0001111
[8,2,7,4,5,1,6,3]=>[6,5,7,8,2,4,1,3]=>[5,2,8,3,7,1,6,4]=>0001111
[4,7,6,1,5,8,3,2]=>[3,8,6,4,1,7,5,2]=>[4,7,5,1,3,6,8,2]=>0001011
[5,4,7,3,8,2,1,6]=>[2,8,7,5,4,3,1,6]=>[5,4,8,6,3,7,1,2]=>0001111
[1,7,2,8,5,4,3,6]=>[1,4,5,8,7,2,3,6]=>[1,7,3,5,8,6,2,4]=>0000111
[6,8,3,5,7,2,4,1]=>[4,7,8,3,2,6,5,1]=>[6,7,5,2,8,1,4,3]=>0011011
[7,3,4,8,2,1,6,5]=>[2,6,8,3,7,4,1,5]=>[8,5,7,1,2,6,4,3]=>0010111
[4,3,8,2,7,5,1,6]=>[5,7,4,3,8,2,1,6]=>[4,3,8,6,2,7,1,5]=>0010111
[4,5,7,8,3,2,1,6]=>[2,3,8,4,5,1,7,6]=>[4,5,7,8,6,1,2,3]=>0000101
[5,4,3,7,2,1,6,8]=>[2,7,4,5,3,1,6,8]=>[5,3,4,7,6,1,2,8]=>0001110
[5,4,3,7,8,2,6,1]=>[6,8,4,5,3,2,7,1]=>[5,3,4,7,8,1,6,2]=>0001101
[5,4,3,7,8,2,1,6]=>[2,8,4,5,3,1,7,6]=>[5,3,4,7,8,6,1,2]=>0001101
[6,8,5,7,3,4,2,1]=>[2,4,7,3,8,6,5,1]=>[6,8,1,2,4,3,7,5]=>0010011
[5,1,6,8,4,7,3,2]=>[3,7,8,5,1,6,4,2]=>[6,8,2,7,4,5,1,3]=>0001011
[2,4,1,8,7,6,3,5]=>[6,2,4,1,3,7,8,5]=>[2,8,5,3,4,1,6,7]=>0011001
[1,3,5,8,4,7,2,6]=>[1,7,3,8,5,4,2,6]=>[1,3,5,7,2,8,6,4]=>0000111
[4,1,3,5,6,2,8,7]=>[6,4,1,3,5,2,8,7]=>[5,6,2,4,3,1,8,7]=>0110101
[6,3,8,5,1,7,4,2]=>[4,7,5,8,6,3,1,2]=>[6,3,5,8,2,7,1,4]=>0000111
[5,2,4,6,1,3,8,7]=>[6,5,2,1,4,3,8,7]=>[6,3,2,5,4,1,8,7]=>0111101
[6,4,8,7,3,5,2,1]=>[2,5,7,6,4,3,8,1]=>[8,1,2,5,4,6,3,7]=>0001101
[8,2,3,5,6,1,4,7]=>[6,8,2,3,1,5,4,7]=>[6,5,1,8,7,4,3,2]=>0111111
[4,3,5,6,8,2,7,1]=>[7,8,4,3,5,6,2,1]=>[4,3,5,6,8,1,7,2]=>0010011
[1,7,4,3,5,2,8,6]=>[1,5,4,8,3,7,2,6]=>[1,8,6,7,2,5,3,4]=>0001011
[3,2,4,5,1,8,6,7]=>[5,3,2,4,1,8,6,7]=>[3,2,4,5,1,8,7,6]=>0101011
[8,3,4,5,1,6,7,2]=>[7,5,8,3,4,1,6,2]=>[7,6,1,8,2,5,4,3]=>0011111
[7,8,1,3,5,4,2,6]=>[4,5,1,8,3,2,7,6]=>[7,8,6,2,5,3,1,4]=>0101101
[1,3,7,8,5,2,4,6]=>[1,5,3,2,8,4,7,6]=>[1,3,7,8,6,4,2,5]=>0010101
[1,7,8,3,2,5,6,4]=>[1,3,6,8,2,5,7,4]=>[1,6,5,2,3,7,8,4]=>0001101
[3,5,7,6,4,8,1,2]=>[8,1,3,6,5,7,4,2]=>[3,5,7,4,6,8,2,1]=>1000011
[1,3,7,8,5,4,6,2]=>[1,6,3,5,8,4,7,2]=>[1,3,7,8,2,6,4,5]=>0000101
[1,3,7,8,2,5,4,6]=>[1,5,3,8,2,4,7,6]=>[1,3,5,2,7,8,6,4]=>0001101
[1,7,8,5,6,3,2,4]=>[1,3,6,2,8,5,7,4]=>[1,7,8,4,2,3,6,5]=>0010101
[1,5,7,6,8,3,2,4]=>[1,3,8,2,5,7,6,4]=>[1,5,7,6,8,4,2,3]=>0010011
[4,2,7,5,3,1,8,6]=>[3,5,4,2,8,7,1,6]=>[8,6,7,1,3,4,2,5]=>0010011
[3,6,4,1,8,2,7,5]=>[7,4,3,8,6,1,2,5]=>[3,8,5,6,1,7,2,4]=>0000111
[4,3,5,1,8,7,2,6]=>[7,5,4,3,1,2,8,6]=>[4,3,8,6,2,5,1,7]=>0011101
[8,4,3,2,7,5,1,6]=>[5,3,4,7,8,2,1,6]=>[8,6,2,3,4,7,1,5]=>0000111
[8,3,5,6,1,4,7,2]=>[7,6,8,3,1,5,4,2]=>[8,2,6,5,1,7,4,3]=>0011111
[1,6,4,7,5,2,3,8]=>[1,5,2,7,6,4,3,8]=>[1,7,3,2,5,6,4,8]=>0100110
[2,5,4,7,8,3,1,6]=>[3,2,8,5,4,1,7,6]=>[2,5,4,7,8,6,1,3]=>0001101
[6,4,5,8,2,3,1,7]=>[3,8,2,6,4,5,1,7]=>[6,5,4,8,7,1,3,2]=>0101111
[8,6,1,3,2,5,7,4]=>[3,7,1,6,2,8,5,4]=>[3,1,7,5,2,8,4,6]=>0101011
[7,5,8,1,4,6,3,2]=>[3,6,8,1,7,5,4,2]=>[8,2,6,5,7,4,1,3]=>0010111
[4,2,6,7,8,1,5,3]=>[5,8,4,2,1,6,7,3]=>[5,1,6,7,8,3,4,2]=>0011001
[4,8,5,3,2,6,1,7]=>[6,3,5,4,8,2,1,7]=>[4,8,7,1,6,2,3,5]=>0000111
[2,8,4,5,3,6,1,7]=>[6,2,5,8,4,3,1,7]=>[2,8,7,1,6,3,5,4]=>0001111
[8,1,4,5,3,2,7,6]=>[3,5,7,1,4,8,2,6]=>[7,2,5,4,1,3,8,6]=>0011011
[8,6,1,3,2,7,4,5]=>[3,7,1,6,2,8,4,5]=>[3,1,8,5,2,7,4,6]=>0101011
[1,3,6,4,2,5,7,8]=>[1,4,3,6,2,5,7,8]=>[1,3,6,5,2,4,7,8]=>0001100
[1,7,6,4,2,3,5,8]=>[1,4,2,6,3,7,5,8]=>[1,7,5,3,2,4,6,8]=>0101010
[1,2,3,7,6,4,5,8]=>[1,2,3,6,4,7,5,8]=>[1,2,3,7,5,4,6,8]=>0001010
[1,3,2,5,8,6,4,7]=>[1,3,2,6,5,8,4,7]=>[1,3,2,5,8,7,4,6]=>0100011
[4,8,2,7,1,3,6,5]=>[6,7,2,4,8,1,3,5]=>[4,6,1,7,3,2,8,5]=>0100111
[1,7,4,6,8,3,5,2]=>[1,5,8,7,4,3,6,2]=>[1,8,2,5,4,7,6,3]=>0001111
[2,8,7,1,4,6,3,5]=>[6,2,7,1,4,3,8,5]=>[2,8,5,4,1,6,3,7]=>0011101
[1,6,5,3,2,4,7,8]=>[1,3,5,2,6,4,7,8]=>[1,6,4,2,3,5,7,8]=>0010100
[1,3,7,2,4,6,5,8]=>[1,6,3,2,7,4,5,8]=>[1,3,6,4,2,7,5,8]=>0010110
[1,2,6,8,7,4,3,5]=>[1,2,4,7,3,6,8,5]=>[1,2,6,8,5,3,4,7]=>0001001
[1,2,7,4,3,5,8,6]=>[1,2,4,8,3,7,5,6]=>[1,2,8,6,7,5,3,4]=>0001011
[1,3,8,7,5,4,6,2]=>[1,6,3,5,7,4,8,2]=>[1,3,8,2,6,4,5,7]=>0000101
[1,2,8,6,3,5,7,4]=>[1,2,7,6,3,8,5,4]=>[1,2,7,5,3,8,4,6]=>0001011
[1,4,7,5,8,6,3,2]=>[1,3,6,4,8,7,5,2]=>[1,4,8,2,3,6,7,5]=>0000011
[1,6,3,7,4,2,8,5]=>[1,4,8,7,6,3,2,5]=>[1,7,2,4,8,5,6,3]=>0000111
[1,4,8,6,3,2,7,5]=>[1,3,7,4,6,8,2,5]=>[1,4,7,2,3,8,5,6]=>0000011
[1,4,8,7,5,3,2,6]=>[1,3,5,4,7,2,8,6]=>[1,4,8,6,2,3,5,7]=>0000101
[1,2,5,8,6,3,7,4]=>[1,2,7,6,5,8,3,4]=>[1,2,5,7,3,8,4,6]=>0000011
[1,2,4,7,5,8,6,3]=>[1,2,6,4,8,7,5,3]=>[1,2,4,8,3,6,7,5]=>0000011
[1,5,3,2,6,8,7,4]=>[1,3,7,5,2,6,8,4]=>[1,6,8,4,5,2,3,7]=>0001001
[1,5,8,6,3,2,7,4]=>[1,3,7,6,5,8,2,4]=>[1,5,7,2,3,8,4,6]=>0000011
[1,8,5,2,6,3,4,7]=>[1,6,5,2,8,3,4,7]=>[1,8,7,4,2,6,3,5]=>0010111
[1,6,3,2,8,5,4,7]=>[1,3,5,8,6,2,4,7]=>[1,6,2,3,5,8,7,4]=>0000111
[1,3,8,6,4,2,5,7]=>[1,4,3,6,2,8,5,7]=>[1,3,8,7,5,2,4,6]=>0001011
[5,4,2,3,6,1,8,7]=>[6,4,2,5,3,1,8,7]=>[5,3,2,4,6,1,8,7]=>0101101
[8,7,2,6,3,1,4,5]=>[3,6,7,2,1,4,8,5]=>[6,4,2,8,5,1,3,7]=>0011101
[5,4,1,3,7,2,8,6]=>[8,4,1,5,3,7,2,6]=>[8,6,7,2,4,5,3,1]=>0101011
[3,1,8,7,5,2,4,6]=>[5,3,1,2,7,4,8,6]=>[8,6,4,2,3,1,5,7]=>0110101
[6,5,8,7,2,4,3,1]=>[3,4,7,2,6,5,8,1]=>[4,2,6,5,8,1,3,7]=>0010101
[3,2,6,8,7,1,4,5]=>[7,3,2,1,4,6,8,5]=>[3,2,6,8,5,4,1,7]=>0111001
[5,1,7,8,6,2,3,4]=>[6,5,1,2,3,8,7,4]=>[7,8,4,2,5,3,1,6]=>0111001
[8,5,1,6,7,2,3,4]=>[7,5,1,2,8,3,6,4]=>[7,6,3,1,8,4,2,5]=>0110111
[1,8,3,6,4,5,7,2]=>[1,7,6,8,3,4,5,2]=>[1,8,2,7,5,3,6,4]=>0001111
[7,1,6,2,5,3,4,8]=>[5,6,7,1,2,3,4,8]=>[7,4,1,5,2,6,3,8]=>0011110
[8,1,7,2,5,3,4,6]=>[5,7,8,1,2,3,4,6]=>[7,4,1,5,2,8,6,3]=>0011111
[8,1,6,7,5,2,3,4]=>[5,7,1,2,8,3,6,4]=>[8,4,2,7,6,3,1,5]=>0110111
[8,1,6,4,2,3,5,7]=>[4,6,1,8,2,3,5,7]=>[8,7,5,2,6,3,1,4]=>0101111
[8,3,1,2,4,6,7,5]=>[3,1,7,2,8,4,6,5]=>[7,6,4,2,1,3,8,5]=>1010111
[7,1,8,2,5,3,4,6]=>[5,8,7,1,2,3,4,6]=>[8,6,3,7,4,1,5,2]=>0011111
[5,1,7,2,6,3,4,8]=>[6,7,5,1,2,3,4,8]=>[7,4,1,6,3,5,2,8]=>0011110
[1,6,3,8,4,5,7,2]=>[1,7,8,6,3,4,5,2]=>[1,6,4,8,2,7,5,3]=>0001111
[2,7,4,3,8,5,1,6]=>[5,2,4,8,7,3,1,6]=>[2,7,1,5,8,6,3,4]=>0000111
[2,5,8,4,6,3,1,7]=>[3,2,6,8,5,4,1,7]=>[2,5,8,7,1,3,6,4]=>0000111
[3,4,6,2,1,5,8,7]=>[2,6,3,4,1,5,8,7]=>[3,4,6,5,1,2,8,7]=>0001101
[2,3,7,1,6,5,8,4]=>[8,2,3,6,7,1,5,4]=>[2,3,7,5,8,4,6,1]=>0000111
[2,4,7,1,3,6,8,5]=>[8,2,1,4,7,3,6,5]=>[2,4,8,5,7,6,3,1]=>0100111
[2,5,7,1,4,6,3,8]=>[6,2,7,1,5,4,3,8]=>[2,5,6,4,1,7,3,8]=>0010110
[5,7,3,2,8,1,4,6]=>[8,3,7,2,5,1,4,6]=>[5,7,4,2,3,8,6,1]=>0010111
[2,5,7,1,4,6,8,3]=>[8,2,7,1,5,4,6,3]=>[2,5,8,3,7,6,4,1]=>0010111
[2,4,7,1,6,3,8,5]=>[8,2,6,4,7,1,3,5]=>[2,4,8,5,7,3,6,1]=>0000111
[7,5,4,8,3,2,6,1]=>[6,3,8,5,7,4,2,1]=>[8,1,6,4,5,7,2,3]=>0000111
[8,4,1,2,5,3,6,7]=>[5,1,4,8,2,3,6,7]=>[5,2,1,8,7,6,3,4]=>1001111
[8,7,5,2,4,3,6,1]=>[6,4,5,2,7,3,8,1]=>[4,2,8,1,6,3,5,7]=>0010101
[8,2,4,5,3,1,6,7]=>[3,5,8,2,4,1,6,7]=>[5,4,2,8,7,6,1,3]=>0011111
[1,4,5,7,3,2,6,8]=>[1,3,7,4,5,2,6,8]=>[1,4,5,7,6,2,3,8]=>0000110
[2,5,1,4,7,8,3,6]=>[8,2,5,1,4,3,7,6]=>[2,7,8,6,3,5,4,1]=>0011101
[6,3,2,7,4,5,1,8]=>[5,3,7,6,2,4,1,8]=>[6,4,7,1,5,2,3,8]=>0001110
[7,2,4,1,3,6,8,5]=>[4,8,2,1,7,3,6,5]=>[4,1,8,5,7,6,3,2]=>0110111
[1,7,3,2,5,6,4,8]=>[1,3,6,7,2,5,4,8]=>[1,6,5,2,3,7,4,8]=>0001110
[5,6,2,1,4,3,7,8]=>[2,4,6,1,5,3,7,8]=>[4,1,2,5,6,3,7,8]=>0010100
[4,6,1,5,2,7,3,8]=>[7,5,6,4,1,2,3,8]=>[4,7,3,6,2,5,1,8]=>0001110
[2,6,1,8,5,4,3,7]=>[4,2,5,8,6,1,3,7]=>[2,8,7,3,5,6,1,4]=>0000111
[5,8,6,2,3,4,1,7]=>[4,6,2,3,5,8,1,7]=>[5,8,7,1,4,3,2,6]=>0110011
[4,5,8,6,2,1,3,7]=>[2,6,1,4,5,8,3,7]=>[4,5,8,7,3,1,2,6]=>0100011
[7,5,6,2,4,3,8,1]=>[8,4,6,2,7,5,3,1]=>[4,2,7,3,6,5,8,1]=>0010111
[5,6,3,2,8,1,7,4]=>[7,3,8,6,5,2,1,4]=>[5,7,1,8,4,6,2,3]=>0000111
[8,2,6,3,1,5,7,4]=>[3,7,6,8,2,1,5,4]=>[6,1,3,7,5,2,8,4]=>0001111
[8,2,5,3,4,7,6,1]=>[6,5,7,2,3,8,4,1]=>[7,4,2,5,3,8,1,6]=>0011011
[3,1,8,4,6,5,7,2]=>[7,3,1,6,8,4,5,2]=>[6,4,8,2,3,1,7,5]=>0100111
[8,3,7,6,4,5,1,2]=>[5,1,6,7,3,8,4,2]=>[7,4,8,2,1,5,3,6]=>1001011
[3,8,2,5,1,7,4,6]=>[7,5,3,8,2,1,4,6]=>[3,5,2,8,6,1,7,4]=>0001111
[8,5,7,6,1,2,4,3]=>[4,1,6,2,7,8,5,3]=>[4,2,1,7,5,8,3,6]=>1010011
[5,7,6,8,4,1,3,2]=>[3,4,1,8,5,7,6,2]=>[3,1,5,7,6,8,2,4]=>0100011
[5,3,1,7,4,8,6,2]=>[6,3,8,5,1,7,4,2]=>[7,4,5,1,6,8,2,3]=>0001011
[5,7,2,4,3,6,8,1]=>[8,4,7,2,5,3,6,1]=>[4,2,5,7,6,3,8,1]=>0010111
[8,3,1,2,6,4,7,5]=>[3,1,7,6,8,2,4,5]=>[7,4,6,2,1,3,8,5]=>1000111
[1,7,8,2,4,3,5,6]=>[1,4,8,2,3,5,7,6]=>[1,4,2,7,8,6,5,3]=>0011101
[3,6,4,7,1,2,8,5]=>[8,1,3,7,6,4,2,5]=>[3,8,5,6,4,7,2,1]=>1000111
[5,7,4,8,1,3,2,6]=>[3,8,1,7,5,4,2,6]=>[3,1,5,8,6,4,7,2]=>0100111
[3,2,6,8,7,4,1,5]=>[4,3,2,7,1,6,8,5]=>[3,2,6,8,5,1,4,7]=>0101001
[7,2,1,5,3,8,4,6]=>[2,8,5,7,1,3,4,6]=>[7,4,8,6,3,5,1,2]=>0001111
[1,5,8,2,4,3,6,7]=>[1,4,8,2,5,3,6,7]=>[1,4,2,5,8,7,6,3]=>0010111
[4,3,6,8,1,5,2,7]=>[5,8,4,3,1,6,2,7]=>[4,3,5,1,6,8,7,2]=>0011011
[2,4,6,8,5,1,3,7]=>[5,2,1,4,8,6,3,7]=>[2,4,6,8,7,3,1,5]=>0100011
[1,6,8,2,4,3,5,7]=>[1,4,8,2,3,6,5,7]=>[1,4,2,6,8,7,5,3]=>0011011
[5,4,6,8,3,1,7,2]=>[7,3,8,5,4,6,1,2]=>[5,4,6,7,1,8,2,3]=>0001011
[3,2,7,8,6,4,1,5]=>[4,3,2,6,1,8,7,5]=>[3,2,7,8,5,1,4,6]=>0101001
[6,2,8,3,1,4,7,5]=>[3,7,8,2,6,1,4,5]=>[7,4,2,8,5,6,1,3]=>0010111
[3,1,2,8,7,4,5,6]=>[3,1,2,7,4,5,8,6]=>[3,2,1,8,6,5,4,7]=>1101101
[2,1,3,8,7,4,5,6]=>[2,1,3,7,4,5,8,6]=>[2,1,3,8,6,5,4,7]=>1001101
[1,3,2,8,7,6,4,5]=>[1,3,2,6,4,7,8,5]=>[1,3,2,8,5,4,6,7]=>0101001
[3,5,8,2,4,1,7,6]=>[4,7,3,2,5,8,1,6]=>[3,5,7,1,4,2,8,6]=>0010011
[1,4,2,6,8,5,3,7]=>[1,5,4,2,8,6,3,7]=>[1,6,8,7,3,4,2,5]=>0010011
[1,5,4,2,3,6,8,7]=>[1,4,2,5,3,6,8,7]=>[1,5,3,2,4,6,8,7]=>0101001
[1,5,3,2,4,6,8,7]=>[1,3,5,2,4,6,8,7]=>[1,5,4,2,3,6,8,7]=>0011001
[1,5,8,7,6,3,2,4]=>[1,3,6,2,5,7,8,4]=>[1,5,8,4,2,3,6,7]=>0010001
[1,5,7,6,3,2,4,8]=>[1,3,6,2,5,7,4,8]=>[1,5,7,4,2,3,6,8]=>0010010
[1,6,3,2,4,8,7,5]=>[1,3,7,2,6,4,8,5]=>[1,8,5,6,4,2,3,7]=>0010101
[1,8,7,5,2,4,6,3]=>[1,6,5,2,7,4,8,3]=>[1,6,4,2,8,3,5,7]=>0010101
[1,7,5,2,4,6,3,8]=>[1,6,5,2,7,4,3,8]=>[1,6,4,2,7,3,5,8]=>0010110
[1,7,5,2,6,3,4,8]=>[1,6,5,2,7,3,4,8]=>[1,7,4,2,6,3,5,8]=>0010110
[1,6,3,7,4,2,5,8]=>[1,4,7,6,3,2,5,8]=>[1,6,2,4,7,5,3,8]=>0001110
[1,4,8,7,5,2,6,3]=>[1,6,5,4,7,2,8,3]=>[1,4,6,2,8,3,5,7]=>0000101
[1,3,7,6,4,2,5,8]=>[1,4,3,6,2,7,5,8]=>[1,3,7,5,2,4,6,8]=>0001010
[1,3,8,7,5,2,4,6]=>[1,5,3,2,7,4,8,6]=>[1,3,8,6,4,2,5,7]=>0010101
[1,4,6,3,2,8,7,5]=>[1,3,7,4,6,2,8,5]=>[1,4,8,5,6,2,3,7]=>0000101
[1,5,7,6,4,2,3,8]=>[1,4,2,6,5,7,3,8]=>[1,5,7,3,2,4,6,8]=>0100010
[1,5,2,7,4,3,6,8]=>[1,4,7,5,2,3,6,8]=>[1,5,2,4,7,6,3,8]=>0001110
[1,6,3,5,2,7,4,8]=>[1,7,5,6,3,2,4,8]=>[1,5,3,7,4,6,2,8]=>0001110
[1,8,3,7,5,2,4,6]=>[1,5,7,3,8,2,4,6]=>[1,7,4,3,8,6,2,5]=>0010111
[1,8,4,6,3,2,7,5]=>[1,3,7,6,8,4,2,5]=>[1,6,4,7,2,3,8,5]=>0000111
[6,4,7,1,5,3,8,2]=>[8,5,7,6,4,1,3,2]=>[7,3,8,2,5,4,6,1]=>0001111
[5,3,8,2,6,4,7,1]=>[7,6,8,5,3,2,4,1]=>[6,2,8,1,7,4,5,3]=>0001111
[4,3,8,2,6,5,7,1]=>[7,6,4,3,8,2,5,1]=>[4,3,6,2,8,1,7,5]=>0010111
[6,5,7,1,4,3,8,2]=>[8,4,7,1,6,5,3,2]=>[6,5,7,3,8,2,4,1]=>0010111
[4,8,3,5,7,6,1,2]=>[6,1,7,4,3,8,5,2]=>[4,7,5,3,8,2,1,6]=>1001011
[4,8,3,5,7,6,2,1]=>[2,6,7,4,3,8,5,1]=>[4,7,5,3,8,1,2,6]=>0001011
[6,7,5,2,3,8,4,1]=>[4,8,2,5,7,6,3,1]=>[6,8,1,4,5,7,3,2]=>0100011
[6,7,5,3,8,4,2,1]=>[2,4,8,5,7,6,3,1]=>[6,8,1,2,4,5,7,3]=>0000011
[3,2,1,4,8,5,7,6]=>[2,3,1,4,7,8,5,6]=>[3,1,2,4,7,5,8,6]=>0100011
[7,3,1,4,2,6,5,8]=>[4,3,6,1,7,2,5,8]=>[4,1,6,2,3,7,5,8]=>0010110
[7,4,1,6,2,5,3,8]=>[5,6,4,7,1,2,3,8]=>[5,1,6,2,7,3,4,8]=>0001110
[5,4,1,8,2,6,3,7]=>[6,8,4,5,1,2,3,7]=>[8,7,3,4,5,1,6,2]=>0001111
[4,8,6,2,3,1,7,5]=>[3,7,2,4,6,8,1,5]=>[4,7,1,3,2,8,5,6]=>0100011
[2,8,6,4,5,1,7,3]=>[7,2,5,6,4,8,1,3]=>[2,7,1,8,3,5,4,6]=>0001011
[2,8,3,1,4,5,7,6]=>[3,2,7,1,4,8,5,6]=>[2,7,5,4,1,3,8,6]=>0011011
[6,1,7,2,8,4,5,3]=>[5,8,7,6,1,2,4,3]=>[5,1,8,3,7,4,6,2]=>0001111
[8,3,2,1,5,6,7,4]=>[2,3,7,8,1,5,6,4]=>[7,6,5,1,2,3,8,4]=>0001111
[7,5,2,1,6,8,3,4]=>[2,8,5,1,7,3,6,4]=>[7,6,3,5,8,4,1,2]=>0010111
[7,6,3,2,1,8,4,5]=>[2,3,8,6,1,7,4,5]=>[7,4,6,8,5,1,2,3]=>0001011
[2,8,7,3,4,6,1,5]=>[6,2,7,3,4,1,8,5]=>[2,6,1,8,5,4,3,7]=>0011101
[6,5,1,3,7,2,8,4]=>[8,7,1,5,6,3,2,4]=>[7,2,8,4,5,6,3,1]=>0100111
[1,7,8,3,4,5,2,6]=>[1,5,8,3,4,2,7,6]=>[1,7,8,6,2,5,4,3]=>0011101
[7,1,3,6,4,5,8,2]=>[8,6,1,7,3,4,5,2]=>[8,2,6,4,7,5,3,1]=>0101111
[5,7,1,3,2,8,6,4]=>[3,6,1,8,5,7,2,4]=>[3,1,5,7,2,6,8,4]=>0100011
[5,8,7,1,2,6,3,4]=>[6,1,7,2,5,3,8,4]=>[5,8,4,2,1,6,3,7]=>1010101
[6,8,2,3,4,7,1,5]=>[7,8,2,3,4,6,1,5]=>[6,7,1,8,5,4,3,2]=>0111011
[5,1,7,3,8,6,2,4]=>[6,8,5,1,3,7,2,4]=>[5,3,8,4,1,6,7,2]=>0011011
[6,1,3,2,4,7,8,5]=>[3,8,1,2,6,4,7,5]=>[3,1,7,8,5,6,4,2]=>0110101
[3,2,5,8,7,4,1,6]=>[4,3,2,7,5,1,8,6]=>[3,2,5,8,6,1,4,7]=>0100101
[8,3,4,1,6,5,2,7]=>[5,4,6,3,8,1,2,7]=>[8,7,2,4,3,6,1,5]=>0010111
[5,8,4,7,3,6,2,1]=>[2,6,7,8,5,4,3,1]=>[5,7,3,8,1,2,6,4]=>0000111
[4,2,8,7,3,1,6,5]=>[3,6,4,2,7,1,8,5]=>[6,1,3,4,2,8,5,7]=>0010101
[6,1,4,3,8,7,2,5]=>[7,4,6,1,3,2,8,5]=>[8,5,3,6,2,4,1,7]=>0011101
[6,1,3,8,7,2,4,5]=>[7,6,1,3,2,4,8,5]=>[8,5,2,6,4,3,1,7]=>0111101
[1,2,8,4,5,7,3,6]=>[1,2,7,8,4,5,3,6]=>[1,2,7,3,8,6,5,4]=>0001111
[4,2,1,8,7,6,3,5]=>[2,6,4,1,3,7,8,5]=>[8,5,3,4,1,2,6,7]=>0011001
[2,5,8,4,7,1,6,3]=>[6,2,7,8,5,4,1,3]=>[2,5,8,3,7,1,6,4]=>0000111
[1,4,6,2,5,3,7,8]=>[1,5,6,4,2,3,7,8]=>[1,4,5,2,6,3,7,8]=>0001100
[1,3,8,7,6,5,2,4]=>[1,5,3,2,6,7,8,4]=>[1,3,8,4,2,5,6,7]=>0010001
[1,8,7,2,6,3,5,4]=>[1,5,6,7,2,3,8,4]=>[1,5,2,6,3,8,4,7]=>0001101
[2,8,7,1,6,3,4,5]=>[6,2,7,1,3,4,8,5]=>[2,6,4,1,8,5,3,7]=>0011101
[6,2,1,8,7,5,3,4]=>[2,5,7,1,6,3,8,4]=>[8,4,1,2,5,6,3,7]=>0010101
[2,6,5,3,8,4,1,7]=>[4,2,8,5,6,3,1,7]=>[2,8,7,1,4,5,6,3]=>0000111
[1,7,6,4,8,2,5,3]=>[1,5,8,6,4,7,2,3]=>[1,7,2,5,4,6,8,3]=>0001011
[6,3,8,7,2,4,5,1]=>[5,7,6,3,2,4,8,1]=>[6,4,3,8,1,5,2,7]=>0011101
[2,4,3,8,7,1,6,5]=>[6,2,4,3,7,1,8,5]=>[2,4,3,6,1,8,5,7]=>0010101
[2,8,7,6,1,5,3,4]=>[5,2,6,1,3,7,8,4]=>[2,8,4,1,5,3,6,7]=>0011001
[3,6,4,8,1,5,2,7]=>[5,8,3,6,4,1,2,7]=>[3,6,1,5,4,8,7,2]=>0001111
[3,8,4,6,1,5,2,7]=>[5,6,3,8,4,1,2,7]=>[3,8,7,2,6,1,5,4]=>0001111
[8,3,7,2,1,6,5,4]=>[2,5,6,7,8,3,1,4]=>[6,3,8,4,7,1,2,5]=>0000111
[8,4,7,3,6,2,1,5]=>[2,6,7,8,4,3,1,5]=>[7,1,2,6,3,8,5,4]=>0001111
[3,8,7,5,6,2,4,1]=>[4,6,3,2,7,5,8,1]=>[3,8,1,4,2,6,5,7]=>0010101
[2,6,3,5,7,8,1,4]=>[8,2,6,3,1,5,7,4]=>[2,7,8,4,3,6,5,1]=>0011101
[1,5,8,3,4,2,7,6]=>[1,4,7,3,5,8,2,6]=>[1,5,7,2,4,3,8,6]=>0010011
[1,4,5,3,8,2,7,6]=>[1,7,5,4,3,8,2,6]=>[1,4,5,3,7,2,8,6]=>0001011
[1,4,8,2,6,5,3,7]=>[1,5,6,4,8,2,3,7]=>[1,4,8,7,3,6,2,5]=>0000111
[1,5,6,8,2,7,4,3]=>[1,4,7,8,5,6,2,3]=>[1,5,6,8,3,7,2,4]=>0000011
[1,5,8,6,7,3,4,2]=>[1,4,7,3,5,8,6,2]=>[1,5,8,2,4,3,7,6]=>0010011
[1,6,5,8,7,2,4,3]=>[1,4,7,2,6,5,8,3]=>[1,4,2,6,5,8,3,7]=>0010101
[1,5,7,6,2,8,3,4]=>[1,8,6,2,5,7,3,4]=>[1,5,7,3,6,8,4,2]=>0010011
[1,2,5,8,6,7,4,3]=>[1,2,4,7,5,8,6,3]=>[1,2,5,8,3,4,7,6]=>0000011
[3,8,7,4,2,6,5,1]=>[5,4,3,6,7,2,8,1]=>[3,6,2,4,8,1,5,7]=>0000101
[5,8,3,2,4,7,6,1]=>[6,3,7,2,5,8,4,1]=>[5,7,4,2,3,8,1,6]=>0010011
[4,5,8,3,2,6,1,7]=>[6,3,8,4,5,2,1,7]=>[4,5,8,7,1,6,2,3]=>0000111
[4,1,5,8,6,2,3,7]=>[6,4,1,2,5,8,3,7]=>[4,2,5,8,7,3,1,6]=>0110011
[5,8,2,1,6,3,4,7]=>[2,6,8,1,5,3,4,7]=>[5,8,7,4,1,2,6,3]=>0010111
[2,6,7,8,4,1,3,5]=>[4,2,1,8,3,6,7,5]=>[2,6,7,8,5,3,1,4]=>0101001
[1,8,4,3,2,7,6,5]=>[1,3,4,6,7,8,2,5]=>[1,8,5,7,2,3,4,6]=>0000011
[3,5,1,4,6,2,7,8]=>[6,5,3,1,4,2,7,8]=>[3,6,2,5,4,1,7,8]=>0011100
[2,5,1,4,6,7,3,8]=>[7,2,5,1,4,6,3,8]=>[2,6,7,3,5,4,1,8]=>0011010
[8,6,3,5,4,1,2,7]=>[4,1,5,6,3,8,2,7]=>[5,3,8,7,2,1,4,6]=>1001011
[8,1,6,5,4,3,2,7]=>[3,4,5,6,8,1,2,7]=>[8,7,2,4,6,1,3,5]=>0000111
[4,8,1,7,6,3,5,2]=>[5,6,7,4,1,8,3,2]=>[4,5,1,7,3,8,2,6]=>0001011
[8,5,1,7,4,3,6,2]=>[6,4,7,5,8,1,3,2]=>[6,1,7,3,8,2,4,5]=>0000111
[5,4,8,3,1,7,2,6]=>[7,3,8,5,4,1,2,6]=>[5,4,8,6,1,7,2,3]=>0001111
[5,1,4,8,3,2,7,6]=>[3,7,5,1,4,8,2,6]=>[5,4,1,3,7,2,8,6]=>0011011
[4,3,8,7,2,6,1,5]=>[6,7,4,3,2,1,8,5]=>[4,3,6,1,8,5,2,7]=>0011101
[8,2,7,6,4,1,5,3]=>[5,4,6,7,2,8,1,3]=>[7,1,5,2,4,8,3,6]=>0001011
[4,3,8,7,2,6,5,1]=>[5,6,4,3,7,2,8,1]=>[4,3,6,2,8,1,5,7]=>0010101
[8,2,5,7,4,3,6,1]=>[6,4,7,8,2,5,3,1]=>[7,3,8,1,6,5,2,4]=>0001111
[3,8,7,4,6,1,2,5]=>[6,1,3,7,4,2,8,5]=>[3,6,2,1,8,5,4,7]=>1001101
[1,8,3,7,6,5,2,4]=>[1,5,6,3,7,8,2,4]=>[1,7,2,5,8,4,3,6]=>0010011
[7,5,8,1,6,2,4,3]=>[4,6,8,1,7,5,2,3]=>[4,1,7,2,6,5,8,3]=>0010111
[6,7,8,4,2,1,5,3]=>[2,5,4,8,1,6,7,3]=>[5,1,2,6,7,8,3,4]=>0001001
[7,5,2,4,8,3,1,6]=>[3,8,5,2,7,4,1,6]=>[7,1,3,5,8,6,4,2]=>0010111
[7,8,3,1,6,2,5,4]=>[5,3,6,8,1,2,7,4]=>[5,1,6,2,3,7,8,4]=>0001101
[6,7,8,4,3,1,5,2]=>[5,3,4,8,1,6,7,2]=>[5,1,6,7,8,2,3,4]=>0001001
[7,8,3,6,4,1,5,2]=>[5,4,6,8,3,1,7,2]=>[6,1,5,3,7,8,2,4]=>0001101
[7,5,2,4,8,3,6,1]=>[6,8,5,2,7,4,3,1]=>[7,3,5,8,1,6,4,2]=>0010111
[3,7,8,2,6,5,1,4]=>[5,6,3,2,8,1,7,4]=>[3,7,8,4,2,6,1,5]=>0010101
[7,8,1,6,2,5,4,3]=>[4,5,6,8,1,2,7,3]=>[7,8,3,6,2,5,1,4]=>0001101
[5,6,1,4,3,8,2,7]=>[8,4,6,1,5,3,2,7]=>[5,6,3,8,7,2,4,1]=>0010111
[1,6,7,4,2,8,3,5]=>[1,8,4,7,2,6,3,5]=>[1,6,7,3,4,8,5,2]=>0001011
[1,5,8,7,4,3,2,6]=>[1,3,4,7,5,2,8,6]=>[1,5,8,6,2,3,4,7]=>0000101
[1,4,7,2,3,6,8,5]=>[1,8,2,4,7,3,6,5]=>[1,4,8,5,7,6,3,2]=>0100111
[1,6,3,4,7,8,2,5]=>[1,8,6,3,4,2,7,5]=>[1,7,8,5,4,3,6,2]=>0011101
[2,4,3,7,6,1,8,5]=>[8,2,4,3,6,7,1,5]=>[2,4,3,8,5,6,7,1]=>0010011
[7,2,1,5,6,3,8,4]=>[2,8,6,7,1,5,3,4]=>[8,4,7,3,6,5,1,2]=>0001111
[3,1,5,2,8,7,6,4]=>[6,3,1,5,2,7,8,4]=>[8,4,5,2,3,1,6,7]=>0101001
[1,2,8,4,3,7,6,5]=>[1,2,4,6,7,8,3,5]=>[1,2,8,5,7,3,4,6]=>0000011
[1,8,5,4,2,7,3,6]=>[1,7,4,5,8,2,3,6]=>[1,8,6,2,7,3,4,5]=>0000111
[3,1,8,5,4,7,2,6]=>[7,3,1,5,8,4,2,6]=>[7,2,3,1,8,6,4,5]=>0100111
[7,5,1,8,3,2,6,4]=>[3,6,8,5,7,1,2,4]=>[8,4,5,7,2,6,1,3]=>0000111
[5,3,1,8,6,2,4,7]=>[6,3,5,1,2,8,4,7]=>[5,2,3,8,7,4,1,6]=>0011011
[1,5,4,2,8,6,3,7]=>[1,6,4,5,2,8,3,7]=>[1,8,7,3,4,5,2,6]=>0001011
[8,3,1,6,4,2,5,7]=>[4,3,6,8,1,2,5,7]=>[6,2,3,8,7,5,1,4]=>0001111
[5,7,8,1,4,2,6,3]=>[6,4,8,1,5,2,7,3]=>[5,6,2,4,1,7,8,3]=>0010101
[5,7,1,2,3,8,6,4]=>[6,1,2,8,5,7,3,4]=>[5,7,3,2,1,6,8,4]=>1100011
[7,2,8,1,4,3,6,5]=>[4,6,8,2,7,1,3,5]=>[6,1,4,2,8,5,7,3]=>0010111
[1,8,3,6,4,7,2,5]=>[1,7,6,8,3,4,2,5]=>[1,7,2,8,5,3,6,4]=>0001111
[2,8,1,7,5,3,6,4]=>[6,2,5,7,8,1,3,4]=>[2,6,1,8,4,7,3,5]=>0000111
[1,2,8,7,6,4,3,5]=>[1,2,4,6,3,7,8,5]=>[1,2,8,5,3,4,6,7]=>0001001
[4,8,2,6,3,5,1,7]=>[5,6,8,4,2,3,1,7]=>[4,8,7,1,5,2,6,3]=>0001111
[6,2,1,5,4,3,7,8]=>[2,4,5,6,1,3,7,8]=>[6,3,5,1,2,4,7,8]=>0001100
[3,1,8,5,4,6,2,7]=>[6,3,1,5,8,4,2,7]=>[8,7,2,3,1,6,4,5]=>0100111
[6,3,8,4,5,1,7,2]=>[7,5,8,6,3,4,1,2]=>[6,4,7,1,8,2,5,3]=>0001111
[2,6,1,8,5,7,4,3]=>[4,2,7,8,6,1,5,3]=>[2,8,3,7,5,6,1,4]=>0000111
[6,5,8,7,2,3,4,1]=>[4,7,2,3,6,5,8,1]=>[6,5,8,1,4,3,2,7]=>0110101
[6,3,8,4,5,2,7,1]=>[7,5,8,6,3,4,2,1]=>[6,4,8,1,7,2,5,3]=>0001111
[2,1,6,8,5,3,7,4]=>[2,1,7,5,8,6,3,4]=>[2,1,6,7,3,8,4,5]=>1000011
[6,5,8,7,2,4,1,3]=>[4,7,2,1,6,5,8,3]=>[4,1,6,5,8,3,2,7]=>0110101
[3,5,1,8,4,7,6,2]=>[6,7,3,5,1,8,4,2]=>[3,8,2,7,4,5,1,6]=>0001011
[3,6,8,2,5,4,7,1]=>[7,5,3,8,2,6,4,1]=>[3,5,2,6,8,1,7,4]=>0001011
[4,6,8,3,2,5,7,1]=>[7,3,8,4,2,6,5,1]=>[4,6,8,1,7,5,2,3]=>0001011
[4,6,2,8,3,5,7,1]=>[7,8,6,4,2,3,5,1]=>[4,6,3,8,1,7,5,2]=>0001111
[3,6,1,8,5,7,4,2]=>[4,7,3,8,6,1,5,2]=>[3,8,2,7,5,6,1,4]=>0000111
[2,4,8,7,3,6,5,1]=>[5,2,6,4,7,3,8,1]=>[2,4,6,3,8,1,5,7]=>0000101
[6,1,2,8,7,3,4,5]=>[7,1,6,2,3,4,8,5]=>[8,5,3,6,4,2,1,7]=>1011101
[4,5,2,1,7,8,3,6]=>[2,8,5,4,1,3,7,6]=>[4,7,8,6,3,5,1,2]=>0001101
[2,3,7,8,5,1,6,4]=>[6,2,3,5,8,1,7,4]=>[2,3,6,1,7,8,4,5]=>0000101
[8,1,3,2,5,6,4,7]=>[3,6,1,8,2,5,4,7]=>[3,1,6,5,2,8,7,4]=>0101111
[3,2,5,8,4,7,1,6]=>[7,3,2,8,5,4,1,6]=>[3,2,5,7,1,8,6,4]=>0100111
[8,6,4,1,5,2,3,7]=>[5,4,1,6,2,8,3,7]=>[8,7,3,1,5,2,4,6]=>0101011
[3,5,1,8,7,4,2,6]=>[4,7,3,5,1,2,8,6]=>[3,5,1,4,8,6,2,7]=>0001101
[4,6,1,3,8,2,7,5]=>[7,8,1,4,6,3,2,5]=>[4,8,5,6,3,1,7,2]=>0100111
[8,1,5,2,3,7,6,4]=>[6,5,1,7,2,8,3,4]=>[5,2,8,4,7,3,1,6]=>0101011
[6,2,1,8,5,7,4,3]=>[2,4,7,8,6,1,5,3]=>[8,3,7,5,6,1,2,4]=>0000111
[1,8,4,3,7,6,2,5]=>[1,6,4,7,3,8,2,5]=>[1,8,5,3,4,7,2,6]=>0001011
[4,3,8,7,1,2,6,5]=>[6,1,4,3,7,2,8,5]=>[4,3,6,2,1,8,5,7]=>1010101
[4,3,8,5,7,1,6,2]=>[6,7,4,3,8,5,1,2]=>[4,3,8,2,7,1,6,5]=>0010111
[5,2,8,7,1,4,6,3]=>[6,7,5,2,1,4,8,3]=>[8,3,5,1,6,4,2,7]=>0011101
[3,2,8,7,1,6,4,5]=>[6,3,2,7,1,4,8,5]=>[3,2,8,5,1,6,4,7]=>0101101
[3,5,8,7,4,1,6,2]=>[6,4,3,7,5,1,8,2]=>[3,5,6,1,8,2,4,7]=>0000101
[4,5,7,8,6,3,1,2]=>[3,1,6,4,5,8,7,2]=>[4,5,7,8,2,1,3,6]=>1000001
[3,7,6,8,2,4,1,5]=>[4,8,3,2,1,7,6,5]=>[3,7,6,8,5,1,4,2]=>0011011
[5,4,7,8,6,3,1,2]=>[3,1,6,5,4,8,7,2]=>[5,4,7,8,2,1,3,6]=>1001001
[3,6,7,8,2,1,4,5]=>[2,8,3,1,4,6,7,5]=>[3,6,7,8,5,4,1,2]=>0011001
[5,3,6,2,4,1,8,7]=>[4,6,5,3,2,1,8,7]=>[6,1,4,3,5,2,8,7]=>0011101
[4,8,2,3,7,5,6,1]=>[6,7,2,4,8,3,5,1]=>[4,8,1,6,3,2,7,5]=>0100111
[2,8,4,3,7,5,6,1]=>[6,2,4,7,8,3,5,1]=>[2,8,1,6,3,4,7,5]=>0000111
[7,6,3,8,5,4,2,1]=>[2,4,5,8,6,7,3,1]=>[7,3,5,6,8,1,2,4]=>0000011
[3,8,5,7,6,4,2,1]=>[2,4,3,6,7,8,5,1]=>[3,7,5,8,1,2,4,6]=>0000011
[7,4,2,5,6,3,8,1]=>[8,6,4,7,2,5,3,1]=>[6,5,2,7,3,4,8,1]=>0001111
[2,4,8,3,7,5,6,1]=>[6,2,7,4,8,3,5,1]=>[2,4,8,1,6,3,7,5]=>0000111
[4,7,3,8,2,5,6,1]=>[6,8,7,4,3,2,5,1]=>[4,7,5,3,8,1,6,2]=>0001111
[4,5,8,1,3,7,2,6]=>[7,8,1,4,5,3,2,6]=>[4,5,8,6,3,1,7,2]=>0100111
[3,6,2,8,7,4,5,1]=>[5,7,3,6,2,4,8,1]=>[3,6,4,8,1,5,2,7]=>0001101
[3,6,2,8,4,7,5,1]=>[5,7,3,8,6,2,4,1]=>[3,8,1,5,6,2,7,4]=>0000111
[1,5,8,6,3,4,2,7]=>[1,4,6,3,5,8,2,7]=>[1,5,8,7,2,4,3,6]=>0010011
[3,7,8,5,2,6,4,1]=>[4,6,3,5,8,2,7,1]=>[3,6,2,7,8,1,4,5]=>0000101
[5,3,7,8,4,2,6,1]=>[6,4,8,5,3,2,7,1]=>[7,8,1,6,2,4,5,3]=>0001101
[5,1,6,4,3,8,7,2]=>[7,4,6,5,1,3,8,2]=>[6,3,8,2,4,5,1,7]=>0001101
[4,7,6,8,3,1,5,2]=>[5,3,8,4,1,7,6,2]=>[4,5,1,7,6,8,2,3]=>0001011
[5,4,8,6,1,7,3,2]=>[3,7,6,5,4,8,1,2]=>[5,4,8,2,7,1,3,6]=>0001011
[3,5,4,7,1,8,6,2]=>[6,8,3,5,4,7,1,2]=>[3,5,4,7,1,6,8,2]=>0001011
[1,8,5,4,2,3,6,7]=>[1,4,2,5,8,3,6,7]=>[1,8,7,6,3,2,4,5]=>0100111
[6,1,3,8,4,5,2,7]=>[5,8,1,6,3,4,2,7]=>[5,3,1,6,4,8,7,2]=>0101111
[5,8,2,7,1,3,6,4]=>[6,7,2,8,5,1,3,4]=>[5,6,1,7,3,2,8,4]=>0100111
[5,3,8,2,7,1,6,4]=>[6,7,8,5,3,2,1,4]=>[7,1,6,2,8,4,5,3]=>0001111
[6,3,4,2,1,8,7,5]=>[2,4,7,3,6,1,8,5]=>[8,5,6,1,2,4,3,7]=>0010101
[4,5,1,7,6,3,2,8]=>[3,6,5,4,1,7,2,8]=>[4,5,1,3,7,2,6,8]=>0001010
[1,5,4,2,3,8,7,6]=>[1,4,2,5,3,7,8,6]=>[1,5,3,2,4,8,6,7]=>0101001
[1,5,4,2,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>[1,5,3,2,4,8,7,6]=>0101011
[1,5,3,2,4,6,7,8]=>[1,3,5,2,4,6,7,8]=>[1,5,4,2,3,6,7,8]=>0011000
[1,5,4,2,3,7,8,6]=>[1,4,2,5,3,8,7,6]=>[1,5,3,2,4,7,8,6]=>0101001
[4,6,7,2,5,1,8,3]=>[8,5,7,4,2,6,1,3]=>[4,5,2,6,8,3,7,1]=>0001011
[3,6,2,5,1,7,8,4]=>[8,5,3,6,2,1,7,4]=>[3,5,2,7,8,4,6,1]=>0001101
[3,4,2,7,8,1,5,6]=>[8,4,3,2,1,5,7,6]=>[3,4,2,7,8,6,5,1]=>0011101
[3,8,5,2,4,7,1,6]=>[7,5,3,2,8,4,1,6]=>[3,7,1,8,6,4,2,5]=>0010111
[6,4,3,2,8,1,7,5]=>[7,3,4,8,6,2,1,5]=>[7,1,8,5,6,2,3,4]=>0000111
[6,2,4,3,8,1,7,5]=>[7,4,8,2,6,3,1,5]=>[4,2,7,1,8,5,6,3]=>0010111
[8,7,3,6,2,1,5,4]=>[2,5,6,7,3,1,8,4]=>[6,1,2,5,3,8,4,7]=>0001101
[7,3,5,4,1,2,6,8]=>[4,1,5,7,3,2,6,8]=>[5,3,7,6,2,1,4,8]=>1001110
[7,1,3,8,2,5,4,6]=>[5,8,1,7,3,2,4,6]=>[5,3,1,7,4,8,6,2]=>0101111
[6,7,1,8,3,4,5,2]=>[5,8,7,1,3,6,4,2]=>[6,7,4,1,5,3,8,2]=>0011011
[8,6,7,2,5,3,1,4]=>[3,5,7,2,1,8,6,4]=>[8,4,2,5,1,3,7,6]=>0011011
[1,8,2,6,5,3,4,7]=>[1,5,6,2,8,3,4,7]=>[1,6,3,8,7,4,2,5]=>0010111
[8,6,1,5,2,3,4,7]=>[5,6,1,2,3,8,4,7]=>[5,3,1,8,7,4,2,6]=>0111011
[8,5,1,6,2,3,4,7]=>[6,5,1,2,8,3,4,7]=>[6,3,1,8,7,4,2,5]=>0110111
[2,7,8,4,1,3,5,6]=>[4,2,1,8,3,5,7,6]=>[2,7,8,6,5,3,1,4]=>0101101
[1,2,8,6,4,5,3,7]=>[1,2,5,6,4,8,3,7]=>[1,2,8,7,3,5,4,6]=>0001011
[1,5,8,7,6,3,4,2]=>[1,4,6,3,5,7,8,2]=>[1,5,8,2,4,3,6,7]=>0010001
[1,2,7,8,4,3,5,6]=>[1,2,4,8,3,5,7,6]=>[1,2,7,8,6,5,3,4]=>0001101
[1,5,7,8,4,2,3,6]=>[1,4,2,8,5,3,7,6]=>[1,5,7,8,6,3,2,4]=>0100101
[1,2,3,7,5,4,6,8]=>[1,2,3,5,7,4,6,8]=>[1,2,3,7,6,4,5,8]=>0000110
[1,3,4,8,5,2,7,6]=>[1,5,3,4,7,8,2,6]=>[1,3,4,7,2,5,8,6]=>0000011
[2,3,6,4,7,5,1,8]=>[5,2,3,7,6,4,1,8]=>[2,3,7,1,5,6,4,8]=>0000110
[3,7,2,5,8,4,6,1]=>[6,8,3,7,2,5,4,1]=>[3,7,4,8,1,6,5,2]=>0001111
[4,6,5,2,1,7,8,3]=>[2,8,5,4,6,1,7,3]=>[4,7,8,3,5,6,1,2]=>0000101
[4,2,6,5,1,7,8,3]=>[8,5,4,2,6,1,7,3]=>[7,8,3,4,2,5,6,1]=>0010101
[3,5,6,2,1,4,7,8]=>[2,6,3,1,5,4,7,8]=>[3,5,6,4,1,2,7,8]=>0010100
[4,2,5,7,6,8,3,1]=>[3,8,4,2,5,7,6,1]=>[5,7,6,8,1,3,4,2]=>0010011
[3,5,6,4,2,8,1,7]=>[8,4,3,6,5,2,1,7]=>[3,5,6,2,4,8,7,1]=>0000111
[5,1,3,4,8,2,6,7]=>[8,5,1,3,4,2,6,7]=>[8,7,6,2,5,4,3,1]=>0111111
[5,8,1,4,2,3,6,7]=>[4,8,1,2,5,3,6,7]=>[5,8,7,6,3,1,4,2]=>0110111
[3,5,4,8,1,7,2,6]=>[7,8,3,5,4,1,2,6]=>[3,5,4,8,6,1,7,2]=>0001111
[5,3,6,8,1,4,7,2]=>[7,8,5,3,1,6,4,2]=>[6,7,4,3,5,1,8,2]=>0011011
[4,7,2,8,3,1,6,5]=>[3,6,8,4,7,2,1,5]=>[4,6,2,8,5,7,1,3]=>0000111
[1,5,6,8,3,7,2,4]=>[1,7,8,3,5,6,2,4]=>[1,5,6,7,2,8,4,3]=>0010011
[5,6,8,1,2,3,7,4]=>[7,1,2,8,5,6,3,4]=>[5,6,7,3,2,1,8,4]=>1100011
[1,2,5,6,8,4,7,3]=>[1,2,7,8,5,6,4,3]=>[1,2,5,6,8,3,7,4]=>0000011
[6,8,1,4,5,7,2,3]=>[7,8,1,2,4,6,5,3]=>[6,8,3,1,7,5,4,2]=>0111011
[5,6,8,1,3,4,7,2]=>[7,8,1,3,5,6,4,2]=>[5,6,7,4,3,1,8,2]=>0110011
[5,7,8,3,2,6,1,4]=>[6,3,8,2,5,1,7,4]=>[5,6,1,7,8,4,2,3]=>0010101
[2,3,1,7,6,8,4,5]=>[3,2,1,8,4,7,6,5]=>[2,3,1,7,6,8,5,4]=>0101011
[3,7,6,1,4,5,2,8]=>[5,6,3,1,4,7,2,8]=>[3,5,4,1,7,2,6,8]=>0011010
[4,1,6,2,7,5,3,8]=>[5,7,4,1,6,2,3,8]=>[7,3,4,1,5,6,2,8]=>0010110
[7,6,2,5,3,1,4,8]=>[3,5,6,2,1,7,4,8]=>[7,4,2,5,1,3,6,8]=>0011010
[4,3,1,7,6,2,5,8]=>[6,3,4,1,2,7,5,8]=>[7,5,2,3,4,1,6,8]=>0011010
[4,5,3,1,2,8,6,7]=>[3,1,5,4,2,8,6,7]=>[4,5,2,1,3,8,7,6]=>1001011
[2,4,5,3,1,8,6,7]=>[3,2,5,4,1,8,6,7]=>[2,4,5,1,3,8,7,6]=>0001011
[5,7,6,2,3,1,4,8]=>[3,6,2,1,5,7,4,8]=>[5,7,4,1,3,2,6,8]=>0110010
[4,1,3,7,5,2,6,8]=>[5,4,1,3,7,2,6,8]=>[7,6,2,4,3,1,5,8]=>0110110
[4,1,6,3,2,7,5,8]=>[3,7,4,1,6,2,5,8]=>[4,1,3,7,5,6,2,8]=>0010110
[2,7,5,4,1,3,6,8]=>[4,2,1,5,7,3,6,8]=>[2,7,6,3,1,4,5,8]=>0100110
[7,5,4,1,3,2,6,8]=>[3,4,1,5,7,2,6,8]=>[3,1,7,6,2,4,5,8]=>0100110
[2,4,8,5,6,3,1,7]=>[3,2,6,4,8,5,1,7]=>[2,4,8,7,1,3,6,5]=>0000111
[2,5,7,4,1,3,6,8]=>[4,2,1,7,5,3,6,8]=>[2,5,7,6,3,1,4,8]=>0100110
[5,7,4,1,3,2,6,8]=>[3,4,1,7,5,2,6,8]=>[3,1,5,7,6,2,4,8]=>0100110
[6,2,4,5,7,3,1,8]=>[3,7,6,2,4,5,1,8]=>[7,1,3,6,5,4,2,8]=>0011110
[2,6,8,4,5,3,1,7]=>[3,2,5,8,4,6,1,7]=>[2,6,8,7,1,3,5,4]=>0001011
[4,3,5,1,6,2,7,8]=>[6,5,4,3,1,2,7,8]=>[4,3,6,2,5,1,7,8]=>0011100
[6,2,1,7,5,8,4,3]=>[2,4,8,7,6,1,5,3]=>[7,5,6,1,2,4,8,3]=>0000111
[1,5,7,8,6,4,2,3]=>[1,4,2,6,5,8,7,3]=>[1,5,7,8,3,2,4,6]=>0100001
[3,5,6,2,8,7,1,4]=>[7,6,3,2,5,1,8,4]=>[3,5,8,4,2,6,1,7]=>0010101
[4,2,6,7,8,1,3,5]=>[8,4,2,1,3,6,7,5]=>[6,7,8,5,3,2,4,1]=>0111001
[6,8,5,2,7,3,1,4]=>[3,7,5,2,8,6,1,4]=>[6,8,4,2,7,1,3,5]=>0010011
[7,1,2,4,6,3,8,5]=>[8,1,6,2,7,4,3,5]=>[8,5,7,3,6,4,2,1]=>1010111
[7,1,2,6,5,3,8,4]=>[8,1,5,6,7,2,3,4]=>[7,3,5,8,4,6,2,1]=>1000111
[7,5,6,1,2,4,8,3]=>[8,1,6,2,7,5,4,3]=>[8,3,6,5,7,4,2,1]=>1010111
[6,1,8,5,7,2,3,4]=>[7,8,1,2,6,3,5,4]=>[7,5,6,3,1,8,4,2]=>0110111
[6,8,7,5,1,2,4,3]=>[4,1,5,2,7,6,8,3]=>[4,2,1,6,8,3,5,7]=>1010001
[8,3,1,2,4,6,5,7]=>[3,1,6,2,8,4,5,7]=>[6,4,2,1,3,8,7,5]=>1010111
[6,7,8,5,1,2,4,3]=>[4,1,5,2,8,6,7,3]=>[4,2,1,6,7,8,3,5]=>1010001
[3,5,1,6,4,8,2,7]=>[8,6,3,5,1,4,2,7]=>[3,8,7,2,6,4,5,1]=>0001111
[3,5,8,6,2,1,4,7]=>[2,6,3,1,5,8,4,7]=>[3,5,8,7,4,1,2,6]=>0010011
[3,7,8,5,1,4,2,6]=>[4,5,3,1,8,2,7,6]=>[3,4,1,7,8,6,2,5]=>0010101
[8,7,2,4,6,3,1,5]=>[3,6,7,2,4,1,8,5]=>[8,5,4,2,6,1,3,7]=>0011101
[7,8,3,4,6,5,2,1]=>[2,5,6,3,8,4,7,1]=>[6,4,3,7,8,1,2,5]=>0010101
[3,1,2,8,6,5,7,4]=>[3,1,2,7,6,8,5,4]=>[3,2,1,8,4,7,5,6]=>1100011
[3,8,2,7,5,4,6,1]=>[6,5,3,7,8,2,4,1]=>[3,7,4,8,1,6,2,5]=>0000111
[8,7,1,4,5,3,6,2]=>[6,5,7,1,4,3,8,2]=>[8,2,5,4,1,6,3,7]=>0011101
[2,8,7,4,6,3,5,1]=>[5,2,6,7,4,3,8,1]=>[2,6,3,8,1,5,4,7]=>0001101
[8,3,4,1,2,5,7,6]=>[4,1,7,3,2,8,5,6]=>[7,5,2,1,4,3,8,6]=>1011011
[7,4,8,2,3,5,1,6]=>[5,8,2,7,4,3,1,6]=>[7,1,5,4,8,6,3,2]=>0101111
[7,2,8,4,6,5,1,3]=>[5,6,2,8,7,1,4,3]=>[8,3,2,6,1,5,7,4]=>0100111
[8,2,7,3,4,6,1,5]=>[6,7,8,2,3,4,1,5]=>[7,1,6,4,2,8,5,3]=>0011111
[2,5,7,1,6,3,8,4]=>[8,2,6,7,5,1,3,4]=>[2,5,8,4,7,3,6,1]=>0000111
[3,5,6,2,8,1,7,4]=>[7,8,3,6,5,2,1,4]=>[3,5,7,1,8,4,6,2]=>0000111
[3,6,5,2,1,4,7,8]=>[2,5,3,1,6,4,7,8]=>[3,6,4,1,2,5,7,8]=>0010100
[4,5,2,7,6,1,3,8]=>[6,5,2,4,1,7,3,8]=>[4,7,3,2,5,1,6,8]=>0101010
[3,6,5,1,4,7,2,8]=>[7,5,3,1,6,4,2,8]=>[3,7,2,5,6,4,1,8]=>0010110
[5,4,2,6,3,7,1,8]=>[7,6,4,5,2,3,1,8]=>[6,3,4,5,2,7,1,8]=>0001110
[1,5,8,4,2,3,6,7]=>[1,4,2,8,5,3,6,7]=>[1,5,8,7,6,3,2,4]=>0100111
[5,8,2,4,3,6,1,7]=>[6,4,8,2,5,3,1,7]=>[4,2,5,8,7,1,6,3]=>0010111
[1,5,8,4,6,7,2,3]=>[1,7,2,8,5,4,6,3]=>[1,5,8,3,2,7,6,4]=>0100111
[1,8,6,4,5,7,2,3]=>[1,7,2,6,4,8,5,3]=>[1,8,3,2,7,5,4,6]=>0101011
[8,6,2,4,5,3,1,7]=>[3,5,6,2,4,8,1,7]=>[5,4,2,8,7,1,3,6]=>0011011
[1,8,6,4,2,3,5,7]=>[1,4,2,6,3,8,5,7]=>[1,8,7,5,3,2,4,6]=>0101011
[1,3,8,6,2,4,5,7]=>[1,6,3,2,4,8,5,7]=>[1,3,8,7,5,4,2,6]=>0011011
[3,8,6,2,1,4,5,7]=>[2,6,3,1,4,8,5,7]=>[3,8,7,5,4,1,2,6]=>0011011
[2,5,8,4,6,1,7,3]=>[7,2,6,8,5,4,1,3]=>[2,5,7,1,8,3,6,4]=>0000111
[8,2,6,4,5,1,7,3]=>[7,5,6,8,2,4,1,3]=>[5,2,7,1,8,3,6,4]=>0001111
[8,4,6,1,7,2,5,3]=>[5,7,6,8,4,1,2,3]=>[7,2,8,3,6,1,5,4]=>0001111
[8,1,4,6,7,5,2,3]=>[5,7,1,2,8,4,6,3]=>[7,6,4,2,8,3,1,5]=>0110111
[8,4,7,2,1,3,6,5]=>[2,6,1,7,8,4,3,5]=>[7,3,1,2,6,4,8,5]=>0100111
[8,4,2,1,5,3,7,6]=>[2,5,4,7,1,8,3,6]=>[5,1,2,7,3,4,8,6]=>0001011
[4,7,3,1,8,6,2,5]=>[6,3,8,4,1,7,2,5]=>[4,8,5,1,6,7,2,3]=>0001011
[3,2,1,6,7,4,8,5]=>[2,3,1,8,7,6,4,5]=>[3,1,2,6,8,5,7,4]=>0100011
[5,8,2,6,4,3,7,1]=>[7,4,6,8,5,2,3,1]=>[5,8,1,7,3,6,2,4]=>0000111
[1,2,8,6,4,7,3,5]=>[1,2,7,6,4,8,3,5]=>[1,2,7,3,8,5,4,6]=>0001011
[2,8,3,7,1,4,6,5]=>[6,2,7,3,8,1,4,5]=>[2,6,1,7,4,3,8,5]=>0010111
[3,8,4,2,7,6,5,1]=>[5,4,3,6,7,8,2,1]=>[3,8,1,5,7,2,4,6]=>0000011
[3,2,4,8,7,5,6,1]=>[6,3,2,4,7,5,8,1]=>[3,2,4,8,1,6,5,7]=>0100101
[8,1,5,2,4,6,3,7]=>[6,5,8,1,2,4,3,7]=>[5,2,6,4,1,8,7,3]=>0011111
[3,8,1,6,4,5,2,7]=>[5,6,3,8,1,4,2,7]=>[3,5,1,8,7,2,6,4]=>0001111
[1,2,4,8,6,3,7,5]=>[1,2,7,4,6,8,3,5]=>[1,2,4,7,3,8,5,6]=>0000011
[5,7,2,3,1,4,8,6]=>[3,8,2,1,5,7,4,6]=>[5,8,6,7,4,1,3,2]=>0110011
[7,1,5,2,4,6,8,3]=>[8,5,7,1,2,4,6,3]=>[5,2,8,3,7,6,4,1]=>0011111
[7,4,1,5,8,6,3,2]=>[3,6,4,8,1,7,5,2]=>[8,2,6,7,5,1,3,4]=>0001011
[4,5,8,7,3,1,2,6]=>[3,1,7,4,5,2,8,6]=>[4,5,8,6,2,1,3,7]=>1000101
[1,3,8,7,6,4,2,5]=>[1,4,3,6,2,7,8,5]=>[1,3,8,5,2,4,6,7]=>0001001
[1,2,8,6,4,7,5,3]=>[1,2,5,7,6,8,4,3]=>[1,2,7,4,8,3,5,6]=>0000011
[8,6,2,1,5,7,3,4]=>[2,7,6,1,3,8,5,4]=>[8,4,1,2,7,5,3,6]=>0011011
[3,2,5,7,8,4,1,6]=>[4,3,2,8,5,1,7,6]=>[3,2,5,7,8,6,1,4]=>0100101
[5,1,8,4,3,2,6,7]=>[3,4,8,5,1,2,6,7]=>[8,7,6,2,4,5,1,3]=>0001111
[3,1,5,7,8,4,2,6]=>[4,3,1,8,5,2,7,6]=>[5,7,8,6,2,3,1,4]=>0100101
[1,2,8,6,4,5,7,3]=>[1,2,7,6,4,8,5,3]=>[1,2,8,3,7,5,4,6]=>0001011
[6,2,3,7,4,1,8,5]=>[4,8,2,7,6,3,1,5]=>[7,1,4,8,5,6,3,2]=>0100111
[6,2,3,7,4,8,5,1]=>[5,8,2,7,6,3,4,1]=>[7,4,8,1,5,6,3,2]=>0100111
[6,1,3,7,4,5,8,2]=>[8,7,1,6,3,4,5,2]=>[6,4,8,2,7,5,3,1]=>0101111
[1,8,5,3,2,6,7,4]=>[1,3,7,5,8,2,6,4]=>[1,7,6,2,3,8,4,5]=>0000111
[6,5,2,4,1,3,8,7]=>[4,5,2,1,6,3,8,7]=>[4,1,6,3,2,5,8,7]=>0110101
[7,2,3,4,6,8,1,5]=>[8,7,2,3,4,1,6,5]=>[8,5,4,3,2,7,6,1]=>0111111
[4,2,5,8,7,6,3,1]=>[3,6,4,2,5,7,8,1]=>[5,8,1,3,4,2,6,7]=>0010001
[6,7,2,4,5,1,8,3]=>[8,5,7,2,4,6,1,3]=>[5,4,2,6,8,3,7,1]=>0011011
[5,2,7,8,3,6,1,4]=>[6,8,5,2,3,1,7,4]=>[5,3,6,1,7,8,4,2]=>0011101
[8,2,3,4,7,1,5,6]=>[7,8,2,3,4,1,5,6]=>[8,6,1,7,5,4,3,2]=>0111111
[6,7,3,2,5,8,1,4]=>[8,3,7,2,1,6,5,4]=>[6,8,4,2,3,7,5,1]=>0011011
[7,2,8,3,1,6,4,5]=>[3,6,8,7,2,1,4,5]=>[7,4,8,5,2,6,1,3]=>0001111
[2,7,8,5,6,1,4,3]=>[4,2,6,1,8,5,7,3]=>[2,4,1,7,8,3,6,5]=>0010101
[2,4,7,8,1,3,6,5]=>[6,2,1,4,8,3,7,5]=>[2,4,6,3,1,7,8,5]=>0100101
[8,3,5,1,2,4,7,6]=>[5,1,7,3,2,8,4,6]=>[5,2,1,7,4,3,8,6]=>1011011
[8,3,6,5,4,1,2,7]=>[4,1,5,6,8,3,2,7]=>[8,7,2,1,4,6,3,5]=>1000111
[8,4,3,7,5,1,2,6]=>[5,1,4,7,8,3,2,6]=>[8,6,3,4,7,2,1,5]=>1000111
[8,5,7,6,4,3,1,2]=>[3,1,4,6,7,8,5,2]=>[7,5,8,2,1,3,4,6]=>1000011
[8,4,7,6,5,2,1,3]=>[2,5,1,6,7,8,4,3]=>[8,3,1,2,5,7,4,6]=>0100011
[8,3,1,4,7,6,2,5]=>[6,3,7,1,4,8,2,5]=>[7,2,3,8,5,4,1,6]=>0011011
[1,5,2,6,8,3,7,4]=>[1,7,8,5,2,6,3,4]=>[1,6,8,4,5,2,7,3]=>0001011
[7,2,8,4,1,3,5,6]=>[4,8,2,7,1,3,5,6]=>[7,5,1,4,8,6,3,2]=>0101111
[8,5,6,7,2,1,4,3]=>[2,4,7,1,8,5,6,3]=>[4,1,2,8,3,7,6,5]=>0010111
[8,5,6,7,3,1,4,2]=>[4,3,7,1,8,5,6,2]=>[4,1,8,2,3,7,6,5]=>0010111
[1,8,3,2,5,4,6,7]=>[1,3,5,8,2,4,6,7]=>[1,5,2,3,8,7,6,4]=>0001111
[5,1,7,3,2,8,4,6]=>[3,8,7,5,1,2,4,6]=>[7,4,5,1,3,8,6,2]=>0001111
[8,2,5,3,1,7,4,6]=>[3,7,5,8,2,1,4,6]=>[8,6,1,3,5,2,7,4]=>0001111
[5,8,3,1,4,2,6,7]=>[4,3,8,1,5,2,6,7]=>[4,1,5,8,7,6,2,3]=>0010111
[5,7,8,1,3,2,4,6]=>[3,8,1,2,5,4,7,6]=>[3,1,5,7,8,6,4,2]=>0110101
[8,2,4,1,6,7,3,5]=>[7,4,8,2,1,3,6,5]=>[4,2,8,5,1,7,6,3]=>0011111
[8,7,3,6,2,4,1,5]=>[4,6,7,3,2,1,8,5]=>[8,5,2,6,1,4,3,7]=>0011101
[1,7,4,8,3,6,2,5]=>[1,6,8,7,4,3,2,5]=>[1,8,5,4,7,2,6,3]=>0001111
[1,7,5,8,4,3,2,6]=>[1,3,4,8,7,5,2,6]=>[1,8,6,5,7,2,3,4]=>0000111
[8,4,7,2,6,3,1,5]=>[3,6,7,8,4,2,1,5]=>[6,2,7,1,3,8,5,4]=>0001111
[1,2,5,7,8,3,6,4]=>[1,2,6,8,5,3,7,4]=>[1,2,5,6,3,7,8,4]=>0000101
[4,3,8,6,7,5,1,2]=>[5,1,4,3,7,8,6,2]=>[4,3,8,2,1,5,7,6]=>1010011
[4,5,1,6,7,8,3,2]=>[3,8,5,4,1,6,7,2]=>[4,5,1,3,6,7,8,2]=>0001001
[8,6,4,3,7,2,1,5]=>[2,7,4,6,3,8,1,5]=>[7,1,2,8,5,3,4,6]=>0001011
[5,8,1,4,3,2,7,6]=>[3,4,7,1,5,8,2,6]=>[5,7,2,4,1,3,8,6]=>0010011
[1,6,4,3,8,2,7,5]=>[1,7,4,8,6,3,2,5]=>[1,7,2,8,5,6,3,4]=>0000111
[8,1,7,4,3,5,6,2]=>[6,4,7,8,1,3,5,2]=>[7,5,1,6,3,8,2,4]=>0001111
[5,2,3,7,4,1,8,6]=>[4,8,2,5,3,7,1,6]=>[8,6,7,1,4,5,3,2]=>0101011
[8,5,3,1,4,6,7,2]=>[7,3,5,1,8,4,6,2]=>[7,6,4,1,8,2,3,5]=>0010111
[6,5,3,4,1,7,8,2]=>[8,4,5,3,6,1,7,2]=>[7,8,2,4,3,5,6,1]=>0010101
[2,5,3,1,4,7,8,6]=>[3,2,5,1,4,8,7,6]=>[2,5,4,1,3,7,8,6]=>0011001
[2,6,1,4,3,7,8,5]=>[4,2,8,1,6,3,7,5]=>[2,4,1,7,8,5,6,3]=>0010101
[7,2,1,3,5,6,8,4]=>[2,8,1,7,3,5,6,4]=>[8,4,7,6,5,3,1,2]=>0101111
[6,4,3,7,5,8,2,1]=>[2,8,4,7,6,3,5,1]=>[7,5,6,3,4,8,1,2]=>0000111
[4,8,6,2,3,1,5,7]=>[3,6,2,4,1,8,5,7]=>[4,8,7,5,1,3,2,6]=>0101011
[2,5,6,8,3,4,7,1]=>[7,2,8,3,5,6,4,1]=>[2,5,6,8,1,7,4,3]=>0010011
[4,1,3,6,5,2,7,8]=>[5,4,1,3,6,2,7,8]=>[6,2,4,3,1,5,7,8]=>0110100
[3,6,2,4,5,7,1,8]=>[7,6,3,2,4,5,1,8]=>[3,6,5,4,2,7,1,8]=>0011110
[3,6,2,5,4,7,1,8]=>[7,5,3,6,2,4,1,8]=>[3,5,2,6,4,7,1,8]=>0001110
[3,5,1,7,6,4,2,8]=>[4,6,3,5,1,7,2,8]=>[3,5,1,4,7,2,6,8]=>0001010
[3,6,1,4,5,7,2,8]=>[7,6,3,1,4,5,2,8]=>[3,7,2,6,5,4,1,8]=>0011110
[3,6,4,2,5,7,1,8]=>[7,4,3,6,2,5,1,8]=>[3,6,5,2,4,7,1,8]=>0001110
[5,8,7,1,4,6,3,2]=>[3,6,7,1,5,4,8,2]=>[5,8,2,6,4,1,3,7]=>0010101
[2,6,5,1,3,4,8,7]=>[5,2,1,3,6,4,8,7]=>[2,6,4,3,1,5,8,7]=>0110101
[6,4,5,1,2,7,3,8]=>[7,1,5,6,4,2,3,8]=>[7,3,5,4,6,2,1,8]=>1001110
[5,7,3,8,1,2,4,6]=>[8,1,7,3,5,2,4,6]=>[5,7,4,3,8,6,2,1]=>1010111
[4,5,2,7,6,3,1,8]=>[3,6,5,4,2,7,1,8]=>[4,7,1,3,5,2,6,8]=>0001010
[4,5,2,1,7,6,3,8]=>[2,6,5,4,1,7,3,8]=>[4,7,3,5,1,2,6,8]=>0001010
[5,4,6,2,7,8,3,1]=>[3,8,6,5,4,2,7,1]=>[5,4,7,8,1,3,6,2]=>0001101
[2,4,5,8,1,7,6,3]=>[6,2,7,4,5,8,1,3]=>[2,4,5,8,3,7,1,6]=>0000011
[2,6,8,1,4,3,7,5]=>[4,2,7,1,8,6,3,5]=>[2,4,1,6,7,3,8,5]=>0010011
[4,1,8,2,6,7,3,5]=>[7,8,4,1,2,3,6,5]=>[7,6,3,4,1,8,5,2]=>0011111
[6,7,5,3,2,8,4,1]=>[4,3,8,5,7,6,2,1]=>[6,8,1,4,5,7,2,3]=>0000011
[1,3,5,4,8,7,2,6]=>[1,7,3,5,4,2,8,6]=>[1,3,5,4,8,6,2,7]=>0001101
[1,7,3,2,4,6,5,8]=>[1,3,6,2,7,4,5,8]=>[1,6,4,2,3,7,5,8]=>0010110
[8,1,3,2,6,5,7,4]=>[3,7,1,6,8,2,5,4]=>[3,1,8,4,6,2,7,5]=>0100111
[1,5,2,8,6,4,7,3]=>[1,7,6,5,2,8,4,3]=>[1,7,4,5,2,8,3,6]=>0001011
[5,8,4,1,6,2,7,3]=>[7,6,4,8,5,1,2,3]=>[5,7,2,6,1,8,3,4]=>0000111
[3,1,2,6,8,7,5,4]=>[3,1,2,5,7,6,8,4]=>[3,2,1,6,8,4,5,7]=>1100001
[4,6,8,2,5,7,1,3]=>[7,8,2,4,1,6,5,3]=>[4,6,7,5,1,8,3,2]=>0101011
[6,8,2,4,7,3,5,1]=>[5,7,8,2,4,6,3,1]=>[6,8,1,5,4,2,7,3]=>0011011
[8,6,2,4,5,1,3,7]=>[5,6,2,1,4,8,3,7]=>[5,4,1,8,7,3,2,6]=>0111011
[6,8,2,4,1,7,3,5]=>[7,4,8,2,1,6,3,5]=>[4,2,6,8,5,1,7,3]=>0011011
[5,7,2,3,4,1,6,8]=>[4,7,2,3,5,1,6,8]=>[5,7,6,1,4,3,2,8]=>0110110
[7,2,6,3,5,1,4,8]=>[5,6,7,2,3,1,4,8]=>[7,4,2,6,1,5,3,8]=>0011110
[8,2,6,3,1,7,4,5]=>[3,7,6,8,2,1,4,5]=>[6,1,3,8,5,2,7,4]=>0001111
[1,7,2,4,5,6,8,3]=>[1,8,7,2,4,5,6,3]=>[1,8,3,7,6,5,4,2]=>0011111
[1,8,3,2,5,6,4,7]=>[1,3,6,8,2,5,4,7]=>[1,6,5,2,3,8,7,4]=>0001111
[7,2,8,1,4,6,3,5]=>[6,8,7,2,1,4,3,5]=>[7,3,8,5,1,6,4,2]=>0011111
[2,7,8,1,5,6,3,4]=>[6,2,8,1,3,5,7,4]=>[2,7,8,4,1,6,5,3]=>0011101
[6,8,2,3,1,5,4,7]=>[3,5,2,8,1,6,4,7]=>[5,1,3,2,6,8,7,4]=>0101011
[5,8,2,3,1,6,4,7]=>[3,6,2,8,5,1,4,7]=>[5,6,1,3,2,8,7,4]=>0100111
[4,2,1,5,3,7,6,8]=>[2,5,4,1,3,7,6,8]=>[5,3,4,1,2,7,6,8]=>0011010
[5,1,3,2,6,7,8,4]=>[3,8,1,5,2,6,7,4]=>[3,1,6,7,8,4,5,2]=>0101001
[5,1,3,4,2,7,6,8]=>[4,5,1,3,2,7,6,8]=>[4,3,1,5,2,7,6,8]=>0111010
[7,2,1,3,5,8,4,6]=>[2,8,1,7,3,5,4,6]=>[7,4,8,6,5,3,1,2]=>0101111
[3,7,2,8,1,4,5,6]=>[8,7,3,2,1,4,5,6]=>[3,8,6,4,2,7,5,1]=>0011111
[6,2,7,3,4,5,1,8]=>[5,7,6,2,3,4,1,8]=>[7,1,5,3,6,4,2,8]=>0011110
[6,2,8,3,5,1,4,7]=>[5,8,6,2,3,1,4,7]=>[6,1,5,3,8,7,4,2]=>0011111
[3,8,4,5,2,1,6,7]=>[2,5,3,8,4,1,6,7]=>[3,8,7,6,1,2,5,4]=>0001111
[8,2,6,3,5,1,4,7]=>[5,6,8,2,3,1,4,7]=>[8,7,4,2,6,1,5,3]=>0011111
[2,7,6,3,4,5,1,8]=>[5,2,6,3,4,7,1,8]=>[2,7,1,5,4,3,6,8]=>0011010
[1,6,5,7,2,8,3,4]=>[1,8,7,2,6,5,3,4]=>[1,6,5,7,3,8,4,2]=>0010111
[7,5,2,6,1,8,4,3]=>[4,8,6,5,7,2,1,3]=>[7,1,4,5,8,3,6,2]=>0000111
[4,2,6,5,3,1,7,8]=>[3,5,4,2,6,1,7,8]=>[6,1,3,4,2,5,7,8]=>0010100
[4,3,7,5,1,6,2,8]=>[6,5,4,3,7,1,2,8]=>[4,3,6,1,7,2,5,8]=>0010110
[5,3,7,4,2,8,6,1]=>[6,4,8,5,3,7,2,1]=>[8,1,6,7,2,4,5,3]=>0001011
[7,2,5,8,6,1,4,3]=>[4,6,8,2,1,7,5,3]=>[7,5,1,4,2,6,8,3]=>0011011
[4,3,6,1,5,7,8,2]=>[8,6,4,3,1,5,7,2]=>[4,3,7,8,2,6,5,1]=>0011101
[3,5,4,1,2,6,7,8]=>[4,1,3,5,2,6,7,8]=>[3,5,2,1,4,6,7,8]=>1001000
[5,3,1,4,6,7,8,2]=>[8,3,5,1,4,6,7,2]=>[6,7,8,2,3,5,4,1]=>0011001
[3,2,6,7,4,8,5,1]=>[5,3,2,8,7,6,4,1]=>[3,2,6,8,1,5,7,4]=>0100011
[4,2,6,1,5,7,3,8]=>[7,6,4,2,1,5,3,8]=>[7,3,4,2,6,5,1,8]=>0011110
[6,7,4,3,1,5,8,2]=>[8,3,4,7,1,6,5,2]=>[6,8,2,3,4,7,5,1]=>0001011
[6,4,1,2,7,8,3,5]=>[8,1,4,6,2,3,7,5]=>[6,3,4,7,8,5,2,1]=>1001101
[5,1,8,3,4,6,2,7]=>[6,8,5,1,3,4,2,7]=>[5,3,6,4,1,8,7,2]=>0011111
[5,1,4,7,2,6,8,3]=>[8,7,5,1,4,2,6,3]=>[7,6,2,8,3,5,4,1]=>0011111
[5,8,2,6,7,4,3,1]=>[3,4,7,8,5,2,6,1]=>[5,8,1,3,7,6,2,4]=>0000111
[5,2,6,8,3,7,1,4]=>[7,8,5,2,3,6,1,4]=>[5,3,6,7,1,8,4,2]=>0011011
[6,1,3,8,7,4,5,2]=>[5,7,1,6,3,4,8,2]=>[5,3,1,6,4,8,2,7]=>0101101
[2,3,8,4,1,7,6,5]=>[4,2,3,6,7,8,1,5]=>[2,3,8,5,7,1,4,6]=>0000011
[4,1,7,3,8,6,2,5]=>[6,8,4,1,3,7,2,5]=>[8,5,3,4,1,6,7,2]=>0011011
[4,8,2,7,6,5,1,3]=>[5,6,2,4,7,8,1,3]=>[4,7,1,5,8,3,2,6]=>0100011
[6,8,5,2,7,1,4,3]=>[4,7,5,2,8,6,1,3]=>[6,7,1,4,2,8,3,5]=>0010011
[3,2,1,6,5,8,4,7]=>[2,3,1,8,6,5,4,7]=>[3,1,2,6,5,8,7,4]=>0100111
[3,4,8,5,2,1,7,6]=>[2,5,3,4,7,8,1,6]=>[3,4,7,1,2,5,8,6]=>0000011
[4,8,7,1,3,2,6,5]=>[3,6,1,4,7,2,8,5]=>[3,1,4,6,2,8,5,7]=>0100101
[4,2,5,8,6,7,1,3]=>[7,4,2,1,5,8,6,3]=>[5,8,3,2,4,1,7,6]=>0110011
[2,4,5,8,1,3,7,6]=>[7,2,1,4,5,8,3,6]=>[2,4,5,7,3,1,8,6]=>0100011
[7,1,4,3,8,5,6,2]=>[6,4,8,1,7,3,5,2]=>[7,5,8,2,4,1,6,3]=>0010111
[6,3,2,5,8,4,1,7]=>[4,3,8,6,2,5,1,7]=>[8,7,1,4,6,5,2,3]=>0001111
[8,7,1,4,6,3,2,5]=>[3,6,7,1,4,2,8,5]=>[6,2,8,5,4,1,3,7]=>0011101
[8,4,1,3,7,6,5,2]=>[5,4,1,6,7,8,3,2]=>[7,3,1,5,8,2,4,6]=>0100011
[2,7,8,6,5,3,1,4]=>[3,2,5,1,6,8,7,4]=>[2,7,8,4,1,3,5,6]=>0010001
[1,3,6,4,2,7,5,8]=>[1,4,3,7,6,2,5,8]=>[1,3,7,5,6,2,4,8]=>0000110
[5,4,7,8,2,1,3,6]=>[2,8,1,5,4,3,7,6]=>[5,4,7,8,6,3,1,2]=>0101101
[4,7,5,8,1,2,3,6]=>[8,1,2,4,7,5,3,6]=>[4,8,6,5,7,3,2,1]=>1100111
[2,4,7,5,8,3,1,6]=>[3,2,8,4,7,5,1,6]=>[2,4,8,6,5,7,1,3]=>0000111
[3,7,8,4,2,1,6,5]=>[2,4,3,6,8,1,7,5]=>[3,6,1,2,4,7,8,5]=>0000101
[2,4,6,8,3,7,1,5]=>[7,2,8,4,3,6,1,5]=>[2,4,6,7,1,8,5,3]=>0001011
[4,8,3,7,6,2,1,5]=>[2,6,7,4,3,8,1,5]=>[4,8,5,3,7,1,2,6]=>0001011
[3,6,5,1,7,2,8,4]=>[8,7,3,5,6,1,2,4]=>[3,7,2,8,4,5,6,1]=>0000111
[1,3,6,8,2,4,7,5]=>[1,7,3,2,8,6,4,5]=>[1,3,6,7,4,2,8,5]=>0010011
[8,5,4,1,6,2,7,3]=>[7,6,4,5,8,1,2,3]=>[7,2,6,1,8,3,4,5]=>0000111
[4,5,2,6,7,1,8,3]=>[8,7,5,4,2,6,1,3]=>[4,6,8,3,5,2,7,1]=>0001011
[4,7,5,2,6,3,8,1]=>[8,6,5,4,7,2,3,1]=>[4,6,2,7,3,5,8,1]=>0000111
[5,7,2,1,8,4,3,6]=>[2,4,8,7,5,1,3,6]=>[5,8,6,1,2,4,7,3]=>0000111
[1,6,8,2,5,3,4,7]=>[1,5,8,2,3,6,4,7]=>[1,6,8,7,4,2,5,3]=>0011011
[7,4,6,1,3,5,2,8]=>[5,6,1,7,4,3,2,8]=>[7,2,6,3,1,5,4,8]=>0101110
[5,2,1,8,7,4,6,3]=>[2,6,7,5,1,4,8,3]=>[6,4,5,1,2,8,3,7]=>0001101
[6,8,3,5,1,2,7,4]=>[7,1,5,8,3,6,2,4]=>[5,3,6,7,2,1,8,4]=>1001011
[5,8,2,7,4,6,3,1]=>[3,6,7,8,5,2,4,1]=>[5,6,2,8,1,3,7,4]=>0000111
[4,6,8,3,2,1,7,5]=>[2,3,7,4,8,6,1,5]=>[4,6,7,1,2,3,8,5]=>0000011
[1,4,6,3,7,5,2,8]=>[1,5,7,4,6,3,2,8]=>[1,4,7,2,5,6,3,8]=>0000110
[3,2,8,7,4,5,6,1]=>[6,3,2,7,4,5,8,1]=>[3,2,8,1,6,5,4,7]=>0101101
[1,3,2,8,7,4,6,5]=>[1,3,2,6,7,4,8,5]=>[1,3,2,6,4,8,5,7]=>0100101
[7,5,2,8,3,1,6,4]=>[3,6,8,5,7,2,1,4]=>[6,2,8,4,5,7,1,3]=>0000111
[6,7,1,3,2,5,8,4]=>[3,8,1,7,2,6,5,4]=>[3,1,6,8,4,7,5,2]=>0101011
[8,3,5,4,7,1,2,6]=>[7,1,5,8,3,4,2,6]=>[5,3,7,2,1,8,6,4]=>1001111
[4,1,5,6,3,8,7,2]=>[7,6,4,1,5,3,8,2]=>[5,8,2,6,3,4,1,7]=>0010101
[8,1,5,4,6,7,3,2]=>[3,7,5,8,1,4,6,2]=>[5,1,3,8,2,7,6,4]=>0001111
[6,1,3,5,4,8,2,7]=>[8,5,1,6,3,4,2,7]=>[6,4,8,7,2,5,3,1]=>0101111
[1,4,8,3,2,7,6,5]=>[1,3,6,4,7,8,2,5]=>[1,4,8,5,7,2,3,6]=>0000011
[3,5,8,2,1,4,7,6]=>[2,7,3,1,5,8,4,6]=>[3,5,7,4,1,2,8,6]=>0010011
[8,4,1,2,7,6,5,3]=>[5,1,4,6,7,8,2,3]=>[7,2,1,5,8,3,4,6]=>1000011
[4,8,3,2,7,6,5,1]=>[5,3,6,4,7,8,2,1]=>[4,8,1,5,7,2,3,6]=>0000011
[1,4,8,5,2,3,7,6]=>[1,5,2,4,7,8,3,6]=>[1,4,7,3,2,5,8,6]=>0100011
[1,5,8,7,2,4,3,6]=>[1,4,7,2,5,3,8,6]=>[1,4,2,5,8,6,3,7]=>0010101
[1,2,8,7,3,5,4,6]=>[1,2,5,7,3,4,8,6]=>[1,2,5,3,8,6,4,7]=>0001101
[6,8,4,3,2,7,5,1]=>[5,3,4,7,8,6,2,1]=>[6,7,2,3,4,8,1,5]=>0000011
[8,1,3,7,2,4,6,5]=>[6,7,1,3,8,2,4,5]=>[7,4,3,1,6,2,8,5]=>0110111
[2,1,4,7,5,8,6,3]=>[2,1,6,4,8,7,5,3]=>[2,1,4,8,3,6,7,5]=>1000011
[6,8,3,1,2,5,4,7]=>[3,1,5,8,2,6,4,7]=>[5,2,1,3,6,8,7,4]=>1001011
[6,8,1,7,5,4,2,3]=>[4,5,1,7,8,6,2,3]=>[6,8,3,1,4,7,2,5]=>0100011
[4,8,2,7,5,3,6,1]=>[6,5,7,4,8,2,3,1]=>[4,7,3,8,1,6,2,5]=>0000111
[5,8,4,3,1,6,7,2]=>[7,3,4,8,5,1,6,2]=>[5,7,6,1,8,2,3,4]=>0000111
[2,3,1,8,7,5,6,4]=>[3,2,1,6,7,5,8,4]=>[2,3,1,8,4,6,5,7]=>0100101
[8,5,1,2,7,4,3,6]=>[4,1,7,5,8,2,3,6]=>[7,3,8,6,2,1,4,5]=>1000111
[4,5,7,8,6,2,1,3]=>[2,6,1,4,5,8,7,3]=>[4,5,7,8,3,1,2,6]=>0100001
[2,1,5,7,4,6,8,3]=>[2,1,8,7,5,4,6,3]=>[2,1,5,7,6,4,8,3]=>1000111
[2,3,5,7,8,1,6,4]=>[6,2,3,8,5,1,7,4]=>[2,3,5,6,1,7,8,4]=>0000101
[1,6,4,2,3,5,7,8]=>[1,4,2,6,3,5,7,8]=>[1,6,5,3,2,4,7,8]=>0101100
[8,1,7,2,4,6,3,5]=>[6,7,8,1,2,4,3,5]=>[6,4,1,8,5,2,7,3]=>0011111
[1,5,7,2,3,6,8,4]=>[1,8,2,7,5,3,6,4]=>[1,5,8,4,7,6,3,2]=>0100111
[2,4,7,8,3,5,1,6]=>[5,2,8,4,3,1,7,6]=>[2,4,7,8,6,1,5,3]=>0001101
[2,8,5,1,4,3,7,6]=>[4,2,5,1,7,8,3,6]=>[2,4,1,7,3,5,8,6]=>0010011
[1,8,6,2,4,3,7,5]=>[1,4,7,2,6,8,3,5]=>[1,4,2,7,3,8,5,6]=>0010011
[4,8,5,1,3,2,6,7]=>[3,5,1,4,8,2,6,7]=>[3,1,4,8,7,6,2,5]=>0100111
[7,4,1,2,3,6,8,5]=>[4,1,2,8,7,3,6,5]=>[8,5,7,6,3,2,1,4]=>1100111
[1,3,5,8,4,6,7,2]=>[1,7,3,8,5,4,6,2]=>[1,3,5,8,2,7,6,4]=>0000111
[3,4,5,8,2,1,6,7]=>[2,8,3,4,5,1,6,7]=>[3,4,5,8,7,6,1,2]=>0000111
[1,8,3,7,4,2,5,6]=>[1,4,7,8,3,2,5,6]=>[1,7,5,3,8,6,2,4]=>0001111
[8,5,7,2,4,3,6,1]=>[6,4,7,2,8,5,3,1]=>[4,2,7,3,8,1,6,5]=>0010111
[7,8,6,2,4,1,3,5]=>[4,6,2,1,3,8,7,5]=>[4,1,7,8,5,3,2,6]=>0111001
[7,2,8,3,4,5,1,6]=>[5,8,7,2,3,4,1,6]=>[7,1,5,3,8,6,4,2]=>0011111
[6,1,8,3,4,2,5,7]=>[4,8,6,1,3,2,5,7]=>[4,1,8,7,5,3,6,2]=>0011111
[5,8,2,1,7,4,3,6]=>[2,4,7,8,5,1,3,6]=>[5,7,3,8,6,1,2,4]=>0000111
[6,3,5,2,1,8,4,7]=>[2,8,5,6,3,1,4,7]=>[5,3,8,7,4,6,1,2]=>0001111
[2,1,3,8,4,5,7,6]=>[2,1,3,7,4,8,5,6]=>[2,1,3,7,5,4,8,6]=>1001011
[1,4,7,5,2,3,8,6]=>[1,5,2,4,8,7,3,6]=>[1,4,8,6,7,3,2,5]=>0100011
[3,1,2,8,4,5,7,6]=>[3,1,2,7,4,8,5,6]=>[3,2,1,7,5,4,8,6]=>1101011
[6,4,5,1,2,8,3,7]=>[8,1,5,6,4,2,3,7]=>[8,7,3,5,4,6,2,1]=>1001111
[4,6,5,2,1,8,3,7]=>[2,8,5,4,6,1,3,7]=>[4,8,7,3,5,6,1,2]=>0000111
[3,2,6,5,1,8,4,7]=>[8,3,2,5,6,1,4,7]=>[3,2,8,7,4,5,6,1]=>0100111
[6,4,5,1,8,3,2,7]=>[3,8,5,6,4,1,2,7]=>[6,1,3,5,4,8,7,2]=>0001111
[5,1,8,4,6,7,3,2]=>[3,7,8,5,1,4,6,2]=>[8,2,7,6,4,5,1,3]=>0001111
[3,7,2,5,8,6,4,1]=>[4,6,3,8,2,7,5,1]=>[3,7,5,2,6,8,1,4]=>0001011
[5,4,3,7,2,8,6,1]=>[6,8,4,5,3,7,2,1]=>[5,3,4,8,1,6,7,2]=>0001011
[6,3,2,7,4,5,8,1]=>[8,3,7,6,2,4,5,1]=>[6,4,7,5,2,3,8,1]=>0001111
[7,4,3,8,5,6,1,2]=>[6,1,4,8,7,3,5,2]=>[7,5,8,2,1,6,3,4]=>1000111
[7,3,2,8,4,6,1,5]=>[6,3,8,7,2,4,1,5]=>[7,1,6,4,8,5,2,3]=>0001111
[5,2,1,7,6,3,4,8]=>[2,6,5,1,3,7,4,8]=>[5,3,7,4,1,2,6,8]=>0011010
[7,4,3,8,5,6,2,1]=>[2,6,4,8,7,3,5,1]=>[7,5,8,1,2,6,3,4]=>0000111
[4,2,6,8,5,7,1,3]=>[7,4,2,1,8,6,5,3]=>[6,8,3,2,4,1,7,5]=>0110011
[4,2,1,6,5,7,8,3]=>[2,8,4,1,6,5,7,3]=>[6,5,7,8,3,4,1,2]=>0010101
[8,6,1,4,3,5,2,7]=>[5,4,6,1,3,8,2,7]=>[8,7,2,4,1,5,3,6]=>0011011
[5,1,6,4,8,2,3,7]=>[8,6,1,5,2,4,3,7]=>[6,4,5,2,8,7,3,1]=>0101111
[2,8,4,1,5,3,6,7]=>[5,2,4,8,1,3,6,7]=>[2,5,1,8,7,6,3,4]=>0001111
[3,4,8,1,5,2,6,7]=>[5,8,3,4,1,2,6,7]=>[3,4,5,1,8,7,6,2]=>0001111
[8,3,1,2,5,4,6,7]=>[3,1,5,8,2,4,6,7]=>[5,2,1,3,8,7,6,4]=>1001111
[6,3,7,5,1,4,8,2]=>[8,5,7,3,6,1,4,2]=>[7,4,3,8,2,5,6,1]=>0010111
[5,3,7,2,4,1,8,6]=>[4,8,5,3,2,7,1,6]=>[8,6,7,1,4,3,5,2]=>0011011
[6,1,5,7,8,4,2,3]=>[4,8,1,6,2,5,7,3]=>[7,8,3,1,4,6,5,2]=>0101101
[1,8,4,5,6,7,2,3]=>[1,7,2,8,4,5,6,3]=>[1,8,3,2,7,6,5,4]=>0101111
[6,4,2,7,1,5,8,3]=>[8,7,4,6,2,1,5,3]=>[7,5,2,8,3,4,6,1]=>0001111
[1,7,3,2,4,8,6,5]=>[1,3,6,2,8,7,4,5]=>[1,7,4,2,3,6,8,5]=>0010011
[6,4,1,3,8,7,5,2]=>[5,4,1,7,6,3,8,2]=>[6,3,1,5,8,2,4,7]=>0100101
[4,3,1,8,2,6,7,5]=>[7,3,4,1,8,2,6,5]=>[7,6,2,3,4,1,8,5]=>0010111
[4,2,5,8,1,3,7,6]=>[7,4,2,1,5,8,3,6]=>[5,7,3,2,4,1,8,6]=>0110011
[1,5,8,2,6,4,3,7]=>[1,4,6,8,5,2,3,7]=>[1,5,8,7,3,6,2,4]=>0000111
[3,1,8,2,6,5,4,7]=>[5,3,1,6,8,2,4,7]=>[8,7,4,6,2,3,1,5]=>0100111
[4,5,2,6,1,3,8,7]=>[6,5,2,4,1,3,8,7]=>[4,6,3,2,5,1,8,7]=>0101101
[2,7,8,1,4,3,6,5]=>[4,2,6,1,8,3,7,5]=>[2,4,1,6,3,7,8,5]=>0010101
[6,5,8,1,3,2,4,7]=>[3,8,1,2,6,5,4,7]=>[3,1,6,5,8,7,4,2]=>0110111
[2,1,8,5,3,4,6,7]=>[2,1,5,3,8,4,6,7]=>[2,1,8,7,6,4,3,5]=>1010111
[7,8,1,5,2,4,6,3]=>[6,5,8,1,2,4,7,3]=>[5,2,6,4,1,7,8,3]=>0011101
[5,8,6,3,2,1,4,7]=>[2,3,6,1,5,8,4,7]=>[5,8,7,4,1,2,3,6]=>0010011
[2,5,6,3,8,1,4,7]=>[8,2,6,3,5,1,4,7]=>[2,5,8,7,4,3,6,1]=>0010111
[7,3,5,6,1,8,4,2]=>[4,8,6,7,3,5,1,2]=>[6,5,3,7,1,4,8,2]=>0001111
[2,8,1,7,4,5,3,6]=>[5,2,7,8,1,4,3,6]=>[2,5,1,7,3,8,6,4]=>0001111
[7,3,6,2,5,4,8,1]=>[8,5,6,7,3,2,4,1]=>[6,2,5,3,7,4,8,1]=>0001111
[1,6,5,3,8,4,7,2]=>[1,7,8,5,6,3,4,2]=>[1,8,2,7,4,5,6,3]=>0000111
[7,6,2,3,5,4,8,1]=>[8,5,2,6,3,7,4,1]=>[5,3,2,7,4,6,8,1]=>0101011
[6,1,5,2,3,4,8,7]=>[5,6,1,2,3,4,8,7]=>[5,3,1,6,4,2,8,7]=>0111101
[6,2,5,3,4,8,1,7]=>[8,5,6,2,3,4,1,7]=>[6,4,2,5,3,8,7,1]=>0011111
[2,5,1,4,8,3,7,6]=>[7,2,5,1,4,8,3,6]=>[2,7,3,5,4,1,8,6]=>0011011
[1,2,5,4,8,3,7,6]=>[1,2,7,5,4,8,3,6]=>[1,2,5,4,7,3,8,6]=>0001011
[5,1,3,8,4,7,6,2]=>[6,7,1,5,3,8,4,2]=>[8,2,7,4,5,3,1,6]=>0101011
[3,6,5,4,8,1,2,7]=>[8,1,3,5,6,4,2,7]=>[3,6,4,5,8,7,2,1]=>1000111
[4,2,8,5,1,3,6,7]=>[5,4,2,1,8,3,6,7]=>[8,7,6,3,2,4,1,5]=>0110111
[8,1,3,6,2,5,7,4]=>[7,6,1,8,3,2,5,4]=>[6,2,7,5,3,1,8,4]=>0101111
[1,4,6,5,7,2,3,8]=>[1,7,2,4,6,5,3,8]=>[1,4,6,5,7,3,2,8]=>0100110
[3,5,2,1,7,8,6,4]=>[2,6,3,5,1,8,7,4]=>[3,7,8,4,5,1,2,6]=>0001001
[1,2,7,8,6,4,5,3]=>[1,2,5,6,4,8,7,3]=>[1,2,7,8,3,5,4,6]=>0001001
[8,5,1,2,3,6,7,4]=>[7,1,2,5,8,3,6,4]=>[7,6,3,2,1,8,4,5]=>1100111
[6,4,8,1,2,3,7,5]=>[7,1,2,8,6,4,3,5]=>[7,3,2,1,8,5,6,4]=>1100111
[4,3,5,1,7,8,6,2]=>[6,5,4,3,1,8,7,2]=>[4,3,7,8,2,5,1,6]=>0011001
[4,6,7,2,3,8,5,1]=>[5,8,2,4,7,6,3,1]=>[4,6,8,1,5,7,3,2]=>0100011
[4,5,3,7,8,1,2,6]=>[8,1,5,4,3,2,7,6]=>[4,5,3,7,8,6,2,1]=>1001101
[4,6,7,5,2,8,3,1]=>[3,8,5,4,7,6,2,1]=>[4,6,8,1,3,5,7,2]=>0000011
[8,1,5,2,4,7,3,6]=>[7,5,8,1,2,4,3,6]=>[5,2,8,6,4,1,7,3]=>0011111
[7,4,6,8,3,1,2,5]=>[3,1,8,7,4,2,6,5]=>[8,5,4,7,6,2,1,3]=>1001111
[2,5,6,4,8,1,3,7]=>[8,2,1,6,5,4,3,7]=>[2,5,6,4,8,7,3,1]=>0100111
[1,3,6,5,2,4,7,8]=>[1,5,3,2,6,4,7,8]=>[1,3,6,4,2,5,7,8]=>0010100
[1,5,6,3,2,4,7,8]=>[1,3,6,2,5,4,7,8]=>[1,5,6,4,2,3,7,8]=>0010100
[2,5,1,4,6,3,8,7]=>[6,2,5,1,4,3,8,7]=>[2,6,3,5,4,1,8,7]=>0011101
[8,3,4,1,2,6,7,5]=>[4,1,7,3,8,2,6,5]=>[7,6,2,1,4,3,8,5]=>1010111
[2,1,4,7,3,6,8,5]=>[2,1,8,4,7,3,6,5]=>[2,1,4,8,5,7,6,3]=>1000111
[8,1,4,3,7,5,6,2]=>[6,4,7,1,8,3,5,2]=>[8,2,4,1,6,3,7,5]=>0010111
[8,3,7,6,2,4,5,1]=>[5,6,7,3,2,8,4,1]=>[7,4,3,8,1,5,2,6]=>0011011
[8,1,2,7,6,4,5,3]=>[5,1,6,7,2,8,4,3]=>[5,2,1,7,4,8,3,6]=>1001011
[8,1,5,7,3,6,4,2]=>[4,6,7,8,1,5,3,2]=>[7,3,8,2,6,5,1,4]=>0001111
[4,2,8,3,7,6,1,5]=>[6,7,4,2,3,8,1,5]=>[8,5,3,4,2,7,1,6]=>0011011
[1,2,4,6,8,3,7,5]=>[1,2,7,4,8,6,3,5]=>[1,2,4,6,7,3,8,5]=>0000011
[5,4,8,6,3,7,2,1]=>[2,7,6,5,4,8,3,1]=>[5,4,8,1,2,7,3,6]=>0001011
[5,4,8,6,3,7,1,2]=>[7,1,6,5,4,8,3,2]=>[5,4,8,2,1,7,3,6]=>1001011
[6,4,5,8,3,1,7,2]=>[7,3,8,6,4,5,1,2]=>[6,5,4,7,1,8,2,3]=>0001111
[6,3,5,1,8,4,7,2]=>[7,8,5,6,3,1,4,2]=>[5,3,7,4,6,1,8,2]=>0001111
[1,2,5,4,8,6,3,7]=>[1,2,6,5,4,8,3,7]=>[1,2,5,4,8,7,3,6]=>0001011
[2,4,8,5,6,7,3,1]=>[3,2,7,4,8,5,6,1]=>[2,4,8,1,3,7,6,5]=>0000111
[6,4,5,8,2,1,7,3]=>[2,7,8,6,4,5,1,3]=>[6,5,4,7,1,2,8,3]=>0001111
[6,3,5,2,8,1,7,4]=>[7,8,5,6,3,2,1,4]=>[5,3,7,1,8,4,6,2]=>0001111
[4,3,5,1,8,6,2,7]=>[6,5,4,3,1,8,2,7]=>[4,3,8,7,2,5,1,6]=>0011011
[3,5,4,8,1,6,7,2]=>[7,8,3,5,4,1,6,2]=>[3,5,4,7,6,1,8,2]=>0001111
[2,4,3,1,5,8,6,7]=>[3,2,4,1,5,8,6,7]=>[2,4,1,3,5,8,7,6]=>0010011
[1,7,6,2,5,4,8,3]=>[1,8,5,6,2,7,4,3]=>[1,7,4,6,8,3,5,2]=>0001011
[1,3,7,8,2,6,4,5]=>[1,6,3,8,2,4,7,5]=>[1,3,7,8,5,2,6,4]=>0001101
[4,5,8,1,6,7,2,3]=>[7,8,1,4,5,2,6,3]=>[4,5,8,3,1,7,6,2]=>0100111
[3,7,4,5,1,6,8,2]=>[8,5,3,7,4,1,6,2]=>[3,8,2,5,4,7,6,1]=>0001111
[3,7,8,5,1,4,6,2]=>[6,5,3,1,8,4,7,2]=>[3,6,4,1,7,8,2,5]=>0010101
[4,6,8,5,2,7,3,1]=>[3,7,5,4,8,6,2,1]=>[4,6,7,2,8,1,3,5]=>0000011
[3,8,6,2,7,4,5,1]=>[5,7,3,6,2,8,4,1]=>[3,8,1,5,2,7,4,6]=>0001011
[4,6,8,3,7,1,5,2]=>[5,7,8,4,3,6,1,2]=>[4,6,8,2,7,1,5,3]=>0001011
[3,5,1,7,8,4,6,2]=>[6,8,3,5,1,4,7,2]=>[3,6,4,5,1,7,8,2]=>0001101
[4,8,3,6,1,5,2,7]=>[5,6,8,4,3,1,2,7]=>[4,8,7,2,6,1,5,3]=>0001111
[8,3,2,4,7,1,6,5]=>[6,3,7,2,8,4,1,5]=>[7,1,6,4,2,3,8,5]=>0010111
[7,3,2,4,8,1,6,5]=>[6,3,8,2,7,4,1,5]=>[8,5,7,1,6,4,2,3]=>0010111
[3,6,7,2,4,1,8,5]=>[4,8,3,2,7,6,1,5]=>[3,6,8,5,7,1,4,2]=>0010011
[4,3,6,1,8,5,2,7]=>[5,8,4,3,6,1,2,7]=>[4,3,6,1,5,8,7,2]=>0010111
[4,3,7,5,8,2,1,6]=>[2,8,4,3,7,5,1,6]=>[4,3,8,6,5,7,1,2]=>0010111
[1,5,2,7,6,4,8,3]=>[1,8,6,5,2,7,4,3]=>[1,8,3,6,7,4,5,2]=>0001011
[1,4,6,8,7,2,5,3]=>[1,5,7,4,2,6,8,3]=>[1,4,5,2,6,8,3,7]=>0001001
[1,3,6,8,7,2,5,4]=>[1,5,3,7,2,6,8,4]=>[1,3,5,2,6,8,4,7]=>0001001
[1,6,3,7,2,4,5,8]=>[1,7,6,3,2,4,5,8]=>[1,6,4,3,7,5,2,8]=>0011110
[1,6,3,2,7,4,5,8]=>[1,3,7,6,2,4,5,8]=>[1,6,4,7,5,2,3,8]=>0001110
[1,3,7,2,6,4,5,8]=>[1,6,3,7,2,4,5,8]=>[1,3,7,5,2,6,4,8]=>0001110
[1,7,3,2,8,5,6,4]=>[1,3,6,8,7,2,5,4]=>[1,6,2,3,7,5,8,4]=>0000111
[1,6,2,4,7,5,8,3]=>[1,8,7,2,6,4,5,3]=>[1,8,3,7,5,6,4,2]=>0010111
[1,6,2,7,4,3,8,5]=>[1,4,8,7,6,2,3,5]=>[1,8,5,6,2,4,7,3]=>0000111
[1,5,8,2,3,6,4,7]=>[1,6,2,8,5,3,4,7]=>[1,5,6,3,2,8,7,4]=>0100111
[2,6,7,3,4,8,1,5]=>[8,2,7,3,4,6,1,5]=>[2,6,8,5,4,3,7,1]=>0011011
[4,1,3,8,7,5,2,6]=>[5,4,1,3,7,2,8,6]=>[8,6,2,4,3,1,5,7]=>0110101
[3,6,7,2,1,5,8,4]=>[2,8,3,7,1,6,5,4]=>[3,6,8,4,7,5,1,2]=>0001011
[2,5,6,1,3,8,7,4]=>[7,2,1,6,5,3,8,4]=>[2,5,8,4,6,3,1,7]=>0100101
[2,1,3,8,6,7,4,5]=>[2,1,3,7,4,8,6,5]=>[2,1,3,8,5,4,7,6]=>1001011
[5,4,7,8,1,6,3,2]=>[3,6,8,5,4,1,7,2]=>[5,4,7,8,2,6,1,3]=>0001101
[3,2,7,6,8,4,5,1]=>[5,3,2,8,4,7,6,1]=>[3,2,7,6,8,1,5,4]=>0101011
[4,3,8,6,7,2,5,1]=>[5,7,4,3,2,8,6,1]=>[4,3,8,1,5,2,7,6]=>0011011
[4,3,8,5,6,2,7,1]=>[7,6,4,3,8,5,2,1]=>[4,3,8,1,7,2,6,5]=>0010111
[7,3,4,2,8,5,6,1]=>[6,4,8,3,7,2,5,1]=>[7,5,8,1,6,2,4,3]=>0010111
[4,3,6,5,8,2,7,1]=>[7,8,4,3,6,5,2,1]=>[4,3,6,5,8,1,7,2]=>0010111
[3,2,8,4,7,5,6,1]=>[6,3,2,7,8,4,5,1]=>[3,2,8,1,6,4,7,5]=>0100111
[8,3,6,2,7,4,5,1]=>[5,7,6,8,3,2,4,1]=>[8,1,5,3,6,2,7,4]=>0001111
[1,7,8,4,3,6,5,2]=>[1,5,4,6,8,3,7,2]=>[1,6,3,4,7,8,2,5]=>0000101
[1,8,4,2,3,7,5,6]=>[1,4,2,7,8,3,5,6]=>[1,8,6,3,2,4,7,5]=>0100111
[6,4,2,3,8,7,5,1]=>[5,4,2,7,6,3,8,1]=>[8,1,5,6,3,2,4,7]=>0100101
[6,1,4,2,7,8,3,5]=>[8,4,6,1,2,3,7,5]=>[6,3,7,8,5,2,4,1]=>0011101
[6,4,2,3,7,8,5,1]=>[5,4,2,8,6,3,7,1]=>[7,8,1,5,6,3,2,4]=>0100101
[5,1,3,2,6,8,4,7]=>[3,8,1,5,2,6,4,7]=>[3,1,6,8,7,4,5,2]=>0101011
[1,6,7,2,4,8,3,5]=>[1,8,7,2,4,6,3,5]=>[1,6,7,3,8,5,4,2]=>0011011
[1,6,7,8,2,4,3,5]=>[1,4,8,2,3,6,7,5]=>[1,4,2,6,7,8,5,3]=>0011001
[3,1,6,7,8,4,2,5]=>[4,3,1,8,2,6,7,5]=>[6,7,8,5,2,3,1,4]=>0101001
[5,3,4,1,7,8,6,2]=>[6,4,5,3,1,8,7,2]=>[7,8,2,4,3,5,1,6]=>0011001
[1,2,6,8,4,3,5,7]=>[1,2,4,8,3,6,5,7]=>[1,2,6,8,7,5,3,4]=>0001011
[2,4,7,5,8,3,6,1]=>[6,2,8,4,7,5,3,1]=>[2,4,8,1,6,5,7,3]=>0000111
[7,6,3,1,2,8,5,4]=>[3,1,5,8,6,7,2,4]=>[7,2,1,3,5,6,8,4]=>1000011
[2,3,7,5,8,4,6,1]=>[6,2,3,8,7,5,4,1]=>[2,3,8,1,6,5,7,4]=>0000111
[4,8,2,6,5,3,7,1]=>[7,5,6,4,8,2,3,1]=>[4,8,1,7,3,6,2,5]=>0000111
[8,3,5,2,1,6,7,4]=>[2,7,5,8,3,1,6,4]=>[5,3,7,6,1,2,8,4]=>0001111
[2,8,6,1,5,4,7,3]=>[7,2,5,6,1,8,4,3]=>[2,8,3,5,1,7,4,6]=>0001011
[3,8,6,4,7,1,2,5]=>[7,1,3,6,4,8,2,5]=>[3,7,2,1,8,5,4,6]=>1001011
[3,8,6,2,5,4,7,1]=>[7,5,3,6,2,8,4,1]=>[3,5,2,8,1,7,4,6]=>0001011
[8,3,5,4,2,7,1,6]=>[7,4,5,8,3,2,1,6]=>[5,3,7,1,8,6,2,4]=>0001111
[8,1,7,4,2,5,3,6]=>[5,4,7,8,1,2,3,6]=>[5,1,7,3,8,6,2,4]=>0001111
[8,3,2,5,1,4,7,6]=>[5,3,7,2,1,8,4,6]=>[5,1,7,4,2,3,8,6]=>0011011
[2,8,1,6,5,3,7,4]=>[7,2,5,6,8,1,3,4]=>[2,8,4,6,1,7,3,5]=>0000111
[2,1,8,5,4,3,7,6]=>[2,1,4,5,7,8,3,6]=>[2,1,7,3,4,5,8,6]=>1000011
[7,2,8,5,4,1,3,6]=>[4,5,2,8,7,1,3,6]=>[7,3,2,5,8,6,1,4]=>0100111
[1,7,6,2,8,5,3,4]=>[1,5,8,2,6,7,3,4]=>[1,8,4,2,5,6,7,3]=>0010011
[5,6,2,8,1,7,3,4]=>[7,8,6,2,5,1,3,4]=>[5,7,3,6,1,8,4,2]=>0010111
[3,1,2,4,8,6,7,5]=>[3,1,2,4,7,8,6,5]=>[3,2,1,4,8,5,7,6]=>1100011
[8,6,4,2,5,3,7,1]=>[7,5,4,6,2,8,3,1]=>[5,2,8,1,7,3,4,6]=>0001011
[8,4,5,2,6,3,7,1]=>[7,6,5,8,4,2,3,1]=>[6,2,8,1,7,3,5,4]=>0001111
[7,3,6,4,8,2,5,1]=>[5,8,6,7,3,4,2,1]=>[8,1,5,3,6,4,7,2]=>0001111
[3,7,5,2,8,1,4,6]=>[8,5,3,2,7,1,4,6]=>[3,7,4,2,5,8,6,1]=>0010111
[1,2,7,4,8,5,6,3]=>[1,2,6,8,7,4,5,3]=>[1,2,7,5,8,3,6,4]=>0000111
[2,6,7,1,8,4,5,3]=>[5,2,8,7,1,6,4,3]=>[2,5,1,6,7,4,8,3]=>0001011
[5,6,3,4,2,8,7,1]=>[7,4,6,3,5,2,8,1]=>[5,6,2,4,3,8,1,7]=>0010101
[2,7,1,8,5,6,4,3]=>[4,2,6,8,7,1,5,3]=>[2,7,5,8,3,6,1,4]=>0000111
[4,5,3,2,1,8,6,7]=>[2,3,5,4,1,8,6,7]=>[4,5,1,2,3,8,7,6]=>0001011
[4,1,6,8,5,2,3,7]=>[5,4,1,2,8,6,3,7]=>[4,2,6,8,7,3,1,5]=>0110011
[3,2,4,5,8,6,1,7]=>[6,3,2,4,5,8,1,7]=>[3,2,4,5,8,7,1,6]=>0100011
[3,4,5,8,6,2,1,7]=>[2,6,3,4,5,8,1,7]=>[3,4,5,8,7,1,2,6]=>0000011
[3,4,5,8,6,2,7,1]=>[7,6,3,4,5,8,2,1]=>[3,4,5,8,1,7,2,6]=>0000011
[4,5,2,1,3,8,6,7]=>[2,5,1,4,3,8,6,7]=>[4,5,3,1,2,8,7,6]=>0101011
[3,1,4,5,8,6,2,7]=>[6,3,1,4,5,8,2,7]=>[4,5,8,7,2,3,1,6]=>0100011
[8,2,6,4,1,3,7,5]=>[4,7,2,6,8,1,3,5]=>[6,1,4,7,3,2,8,5]=>0100111
[1,5,8,2,4,3,7,6]=>[1,4,7,2,5,8,3,6]=>[1,4,2,5,7,3,8,6]=>0010011
[4,3,7,8,2,6,5,1]=>[5,6,4,3,8,2,7,1]=>[4,3,6,2,7,8,1,5]=>0010101
[8,6,7,1,4,3,2,5]=>[3,4,7,1,2,8,6,5]=>[8,5,2,4,1,3,7,6]=>0011011
[5,4,7,8,3,6,1,2]=>[6,1,8,5,4,3,7,2]=>[5,4,7,8,2,1,6,3]=>1001101
[6,8,1,3,2,5,7,4]=>[3,7,1,8,2,6,5,4]=>[3,1,6,7,5,2,8,4]=>0101011
[1,8,7,3,2,4,5,6]=>[1,3,7,2,4,5,8,6]=>[1,8,6,5,4,2,3,7]=>0011101
[5,6,2,7,8,3,1,4]=>[3,8,6,2,5,1,7,4]=>[5,6,1,3,7,8,4,2]=>0010101
[8,6,2,7,3,4,1,5]=>[4,7,6,2,3,8,1,5]=>[7,1,4,2,8,5,3,6]=>0011011
[8,6,2,7,3,4,5,1]=>[5,7,6,2,3,8,4,1]=>[7,4,2,8,1,5,3,6]=>0011011
[6,8,5,3,1,7,2,4]=>[7,3,5,1,8,6,2,4]=>[6,8,4,1,7,2,3,5]=>0010011
[5,1,6,7,8,3,2,4]=>[3,8,5,1,2,6,7,4]=>[6,7,8,4,1,3,5,2]=>0011001
[8,6,1,7,3,4,5,2]=>[5,7,6,1,3,8,4,2]=>[8,2,7,4,1,5,3,6]=>0011011
[6,8,5,1,7,4,2,3]=>[4,7,1,5,8,6,2,3]=>[6,7,2,8,3,1,4,5]=>0100011
[5,8,2,7,3,6,4,1]=>[4,6,7,8,5,2,3,1]=>[5,6,2,7,3,8,1,4]=>0000111
[4,8,2,5,6,3,7,1]=>[7,6,8,4,2,5,3,1]=>[4,6,5,2,8,1,7,3]=>0001111
[4,5,7,1,6,3,8,2]=>[8,6,7,4,5,1,3,2]=>[4,5,7,3,8,2,6,1]=>0000111
[5,6,8,3,7,4,2,1]=>[2,4,7,8,5,6,3,1]=>[5,6,7,3,8,1,2,4]=>0000011
[4,5,7,2,6,8,1,3]=>[8,7,2,4,5,1,6,3]=>[4,5,8,3,2,7,6,1]=>0100111
[2,3,1,8,7,4,6,5]=>[3,2,1,6,7,4,8,5]=>[2,3,1,6,4,8,5,7]=>0100101
[4,6,8,2,1,5,3,7]=>[2,5,8,4,1,6,3,7]=>[4,5,1,2,6,8,7,3]=>0001011
[4,5,8,2,6,1,7,3]=>[7,6,8,4,5,2,1,3]=>[4,5,6,2,7,1,8,3]=>0000111
[3,5,7,6,8,2,1,4]=>[2,8,3,1,5,7,6,4]=>[3,5,7,6,8,4,1,2]=>0010011
[3,5,7,6,8,1,4,2]=>[4,8,3,1,5,7,6,2]=>[3,4,1,5,7,6,8,2]=>0010011
[3,5,7,8,4,2,1,6]=>[2,4,3,8,5,1,7,6]=>[3,5,7,8,6,1,2,4]=>0000101
[4,6,5,3,7,8,1,2]=>[8,1,5,4,6,3,7,2]=>[4,6,3,5,7,8,2,1]=>1000101
[3,7,5,2,8,6,1,4]=>[6,5,3,2,8,7,1,4]=>[3,7,1,6,8,4,2,5]=>0010011
[5,6,2,4,7,8,3,1]=>[3,8,6,2,5,4,7,1]=>[5,7,8,1,3,6,4,2]=>0010101
[3,7,4,8,1,6,5,2]=>[5,6,3,8,7,4,1,2]=>[3,7,1,5,8,2,6,4]=>0000111
[5,2,6,4,8,7,3,1]=>[3,7,6,5,2,4,8,1]=>[8,1,3,6,4,5,2,7]=>0001101
[8,6,3,7,2,4,1,5]=>[4,7,6,3,2,8,1,5]=>[8,5,2,7,1,4,3,6]=>0011011
[8,4,5,3,1,7,2,6]=>[7,3,5,8,4,1,2,6]=>[8,6,1,7,2,3,5,4]=>0001111
[5,7,8,6,4,2,3,1]=>[3,4,2,6,5,8,7,1]=>[5,7,8,1,3,2,4,6]=>0100001
[6,8,7,5,1,3,2,4]=>[3,5,1,2,7,6,8,4]=>[3,1,6,8,4,2,5,7]=>0110001
[6,7,4,1,8,2,5,3]=>[5,8,4,7,1,6,2,3]=>[5,1,6,8,3,4,7,2]=>0001011
[5,7,6,8,3,2,4,1]=>[4,3,8,2,5,7,6,1]=>[5,7,6,8,1,4,2,3]=>0010011
[1,8,5,6,4,2,3,7]=>[1,4,2,6,8,5,3,7]=>[1,8,7,3,2,4,6,5]=>0100111
[1,7,6,2,3,5,8,4]=>[1,8,2,6,3,7,5,4]=>[1,8,4,6,7,5,3,2]=>0101011
[7,2,4,5,6,8,1,3]=>[8,7,2,1,4,5,6,3]=>[8,3,2,7,6,5,4,1]=>0111111
[3,5,7,2,8,4,1,6]=>[4,8,3,7,5,2,1,6]=>[3,5,7,1,4,8,6,2]=>0000111
[7,3,2,1,4,8,6,5]=>[2,3,6,1,8,7,4,5]=>[7,4,1,2,3,6,8,5]=>0010011
[8,3,7,2,6,5,1,4]=>[5,6,7,3,8,2,1,4]=>[6,2,8,4,3,7,1,5]=>0010111
[7,5,8,2,6,1,4,3]=>[4,6,8,2,7,5,1,3]=>[7,1,4,2,6,5,8,3]=>0010111
[8,5,1,3,2,4,6,7]=>[3,5,1,2,8,4,6,7]=>[3,1,8,7,6,4,2,5]=>0110111
[3,8,5,1,2,4,6,7]=>[5,1,3,2,8,4,6,7]=>[3,8,7,6,4,2,1,5]=>1010111
[5,8,4,1,2,3,6,7]=>[4,1,2,8,5,3,6,7]=>[5,8,7,6,3,2,1,4]=>1100111
[3,5,8,1,4,2,7,6]=>[4,7,3,1,5,8,2,6]=>[3,4,1,5,7,2,8,6]=>0010011
[2,8,5,7,1,4,3,6]=>[4,2,7,1,8,5,3,6]=>[2,4,1,7,3,8,6,5]=>0010111
[8,1,2,4,6,3,7,5]=>[7,1,6,2,8,4,3,5]=>[7,3,6,4,2,1,8,5]=>1010111
[7,6,1,4,2,3,8,5]=>[4,8,1,2,6,7,3,5]=>[8,5,6,7,3,1,4,2]=>0110011
[1,8,4,7,5,2,3,6]=>[1,5,2,7,8,4,3,6]=>[1,8,6,4,7,3,2,5]=>0100111
[8,4,7,2,1,6,3,5]=>[2,6,7,8,4,1,3,5]=>[6,1,2,7,3,8,5,4]=>0001111
[7,1,5,3,6,8,2,4]=>[8,5,7,1,3,2,6,4]=>[7,6,2,5,3,8,4,1]=>0011111
[3,6,5,2,4,7,8,1]=>[8,5,3,2,6,4,7,1]=>[3,6,4,2,5,7,8,1]=>0010101
[1,7,5,4,6,8,2,3]=>[1,8,2,5,7,4,6,3]=>[1,7,6,4,5,8,3,2]=>0100111
[4,2,7,6,8,1,3,5]=>[8,4,2,1,3,7,6,5]=>[7,6,8,5,3,2,4,1]=>0111011
[1,3,8,5,6,7,2,4]=>[1,7,3,2,8,5,6,4]=>[1,3,8,4,2,7,6,5]=>0010111
[3,4,7,8,6,1,2,5]=>[6,1,3,4,2,8,7,5]=>[3,4,7,8,5,2,1,6]=>1001001
[6,8,3,2,4,1,5,7]=>[4,3,8,2,1,6,5,7]=>[6,8,7,5,1,4,2,3]=>0011011
[5,2,3,7,1,8,4,6]=>[8,7,2,5,3,1,4,6]=>[7,4,5,3,2,8,6,1]=>0101111
[1,7,5,4,8,6,2,3]=>[1,6,2,5,8,7,4,3]=>[1,8,3,2,6,7,4,5]=>0100011
[4,5,1,6,8,2,7,3]=>[7,8,5,4,1,6,2,3]=>[4,6,8,3,5,1,7,2]=>0001011
[4,3,1,6,7,2,5,8]=>[7,3,4,1,2,6,5,8]=>[6,7,5,2,3,4,1,8]=>0011010
[8,2,7,4,1,6,5,3]=>[5,4,6,7,8,2,1,3]=>[8,3,6,2,4,7,1,5]=>0000111
[4,6,8,1,7,3,5,2]=>[5,7,8,4,1,6,3,2]=>[4,5,1,6,8,2,7,3]=>0001011
[2,8,4,6,3,1,5,7]=>[3,2,6,8,4,1,5,7]=>[2,6,1,3,8,7,5,4]=>0001111
[2,8,3,1,6,7,4,5]=>[3,2,7,8,1,4,6,5]=>[2,8,5,1,3,7,6,4]=>0001111
[7,8,6,1,4,3,2,5]=>[3,4,6,1,2,8,7,5]=>[7,8,5,2,4,1,3,6]=>0011001
[7,4,8,3,6,2,1,5]=>[2,6,8,7,4,3,1,5]=>[8,5,4,7,1,2,6,3]=>0001111
[1,5,7,4,8,6,2,3]=>[1,6,2,8,5,7,4,3]=>[1,5,8,3,2,6,7,4]=>0100011
[1,2,7,8,6,4,3,5]=>[1,2,4,6,3,8,7,5]=>[1,2,7,8,5,3,4,6]=>0001001
[3,5,1,7,8,6,2,4]=>[6,5,3,1,2,8,7,4]=>[3,5,2,7,8,4,1,6]=>0011001
[1,8,6,7,4,2,3,5]=>[1,4,2,7,3,8,6,5]=>[1,8,5,3,2,4,7,6]=>0101011
[2,4,6,5,8,3,1,7]=>[3,2,8,4,6,5,1,7]=>[2,4,6,5,8,7,1,3]=>0000111
[2,4,6,5,8,1,7,3]=>[7,2,8,4,6,5,1,3]=>[2,4,6,5,7,1,8,3]=>0000111
[2,5,6,4,1,3,8,7]=>[4,2,1,6,5,3,8,7]=>[2,5,6,3,1,4,8,7]=>0100101
[1,4,8,3,2,7,5,6]=>[1,3,7,4,8,2,5,6]=>[1,4,8,6,2,3,7,5]=>0000111
[4,8,2,1,5,7,3,6]=>[2,7,8,4,1,5,3,6]=>[4,8,6,5,1,2,7,3]=>0001111
[5,8,3,2,4,1,7,6]=>[4,3,7,2,5,8,1,6]=>[5,7,1,4,2,3,8,6]=>0010011
[6,1,4,3,7,5,8,2]=>[8,4,7,1,6,3,5,2]=>[7,5,6,3,8,2,4,1]=>0010111
[6,4,1,8,2,7,5,3]=>[5,7,4,8,6,1,2,3]=>[6,1,5,7,2,8,3,4]=>0000111
[7,8,5,3,2,1,6,4]=>[2,3,6,5,8,1,7,4]=>[6,1,2,3,7,8,4,5]=>0000101
[8,7,3,5,2,1,6,4]=>[2,6,5,7,3,1,8,4]=>[5,3,6,1,2,8,4,7]=>0001101
[7,5,2,4,1,3,8,6]=>[4,5,2,1,8,7,3,6]=>[4,1,8,6,7,3,2,5]=>0110011
[3,1,7,4,2,6,8,5]=>[4,3,1,8,7,2,6,5]=>[8,5,7,6,2,3,1,4]=>0100111
[7,3,5,2,1,6,4,8]=>[2,6,5,7,3,1,4,8]=>[5,3,6,1,2,7,4,8]=>0001110
[2,5,6,1,4,3,7,8]=>[4,2,6,1,5,3,7,8]=>[2,4,1,5,6,3,7,8]=>0010100
[6,1,5,3,7,2,4,8]=>[7,5,6,1,3,2,4,8]=>[6,2,5,3,7,4,1,8]=>0011110
[1,4,2,6,7,8,5,3]=>[1,5,4,2,8,6,7,3]=>[1,6,7,8,3,4,2,5]=>0010001
[4,1,2,6,7,8,5,3]=>[5,1,4,2,8,6,7,3]=>[6,7,8,3,4,2,1,5]=>1010001
[3,7,8,1,5,2,6,4]=>[6,5,3,8,1,2,7,4]=>[3,6,2,5,1,7,8,4]=>0001101
[5,6,4,1,7,3,8,2]=>[8,7,4,6,5,1,3,2]=>[5,8,2,7,3,4,6,1]=>0000111
[4,3,7,8,2,5,1,6]=>[5,8,4,3,2,1,7,6]=>[4,3,7,8,6,1,5,2]=>0011101
[2,7,1,6,5,8,3,4]=>[8,2,6,1,7,3,5,4]=>[2,6,3,7,5,8,4,1]=>0010111
[2,7,4,5,6,8,3,1]=>[3,2,8,7,4,5,6,1]=>[2,7,6,5,4,8,1,3]=>0001111
[2,4,7,8,3,1,6,5]=>[3,2,6,4,8,1,7,5]=>[2,4,6,1,3,7,8,5]=>0000101
[5,4,3,6,8,1,7,2]=>[7,8,4,5,3,6,1,2]=>[5,3,4,6,7,1,8,2]=>0001011
[1,7,3,6,4,2,8,5]=>[1,4,8,6,7,3,2,5]=>[1,8,5,7,2,4,6,3]=>0000111
[1,3,7,6,2,4,8,5]=>[1,8,3,2,6,7,4,5]=>[1,3,8,5,6,7,4,2]=>0010011
[4,7,3,5,1,2,8,6]=>[5,1,8,4,3,7,2,6]=>[4,8,6,7,2,1,5,3]=>1001011
[3,8,4,1,7,5,2,6]=>[5,4,3,7,8,1,2,6]=>[3,7,2,4,8,6,1,5]=>0000111
[7,8,5,3,6,2,1,4]=>[2,6,5,3,8,1,7,4]=>[6,1,2,7,8,4,3,5]=>0010101
[4,7,5,2,3,6,1,8]=>[6,5,2,4,7,3,1,8]=>[4,7,1,6,3,2,5,8]=>0100110
[4,3,7,8,2,1,6,5]=>[2,6,4,3,8,1,7,5]=>[4,3,6,1,2,7,8,5]=>0010101
[7,3,8,2,5,1,6,4]=>[6,5,8,7,3,2,1,4]=>[8,4,7,1,6,2,5,3]=>0001111
[4,5,3,8,2,1,7,6]=>[2,7,5,4,3,8,1,6]=>[4,5,3,7,1,2,8,6]=>0001011
[4,8,7,5,1,3,2,6]=>[3,5,1,4,7,2,8,6]=>[3,1,4,8,6,2,5,7]=>0100101
[7,8,4,6,1,3,5,2]=>[5,6,1,8,4,3,7,2]=>[7,8,2,6,3,1,5,4]=>0101101
[4,5,3,6,8,1,2,7]=>[8,1,5,4,3,6,2,7]=>[4,5,3,6,8,7,2,1]=>1001011
[7,8,6,2,1,4,3,5]=>[2,4,6,1,3,8,7,5]=>[4,1,2,7,8,5,3,6]=>0011001
[5,1,8,2,4,6,3,7]=>[6,8,5,1,2,4,3,7]=>[6,4,1,8,7,3,5,2]=>0011111
[5,8,4,7,1,3,6,2]=>[6,7,1,8,5,4,3,2]=>[5,8,2,7,3,1,6,4]=>0100111
[3,6,7,5,8,4,1,2]=>[4,1,3,8,7,6,5,2]=>[3,6,7,5,8,2,1,4]=>1000011
[3,2,6,1,5,8,7,4]=>[7,3,2,6,1,5,8,4]=>[3,2,8,4,6,5,1,7]=>0101101
[3,7,6,4,1,5,2,8]=>[5,4,3,6,1,7,2,8]=>[3,5,1,7,2,4,6,8]=>0001010
[8,7,1,4,5,2,3,6]=>[5,7,1,2,4,3,8,6]=>[8,6,3,1,5,4,2,7]=>0111101
[4,8,7,3,1,2,6,5]=>[3,1,6,4,7,2,8,5]=>[4,6,2,1,3,8,5,7]=>1000101
[4,6,3,5,7,1,8,2]=>[8,7,6,4,3,5,1,2]=>[4,6,5,3,8,2,7,1]=>0001111
[4,8,3,5,7,1,6,2]=>[6,7,8,4,3,5,1,2]=>[4,8,2,7,1,6,5,3]=>0001111
[4,7,2,5,6,8,1,3]=>[8,7,2,4,1,5,6,3]=>[4,8,3,2,7,6,5,1]=>0101111
[4,8,2,5,6,7,1,3]=>[7,8,2,4,1,5,6,3]=>[4,7,6,5,1,8,3,2]=>0101111
[4,2,8,1,6,5,7,3]=>[7,6,4,2,8,1,5,3]=>[8,3,4,2,6,1,7,5]=>0010111
[3,1,8,2,6,5,7,4]=>[7,3,1,6,8,2,5,4]=>[8,4,6,2,3,1,7,5]=>0100111
[7,8,3,1,6,4,5,2]=>[5,3,6,8,1,4,7,2]=>[5,1,7,8,2,3,6,4]=>0001101
[8,1,4,6,2,5,7,3]=>[7,6,8,1,4,2,5,3]=>[6,2,7,5,4,1,8,3]=>0011111
[2,4,8,6,3,1,7,5]=>[3,2,7,4,6,8,1,5]=>[2,4,7,1,3,8,5,6]=>0000011
[3,6,7,8,4,1,5,2]=>[5,4,3,8,1,6,7,2]=>[3,5,1,6,7,8,2,4]=>0001001
[2,3,7,8,4,6,1,5]=>[6,2,3,8,4,1,7,5]=>[2,3,6,1,7,8,5,4]=>0001101
[1,3,7,8,4,6,2,5]=>[1,6,3,8,4,2,7,5]=>[1,3,6,2,7,8,5,4]=>0001101
[5,8,4,3,7,1,2,6]=>[7,1,4,8,5,3,2,6]=>[5,7,2,1,8,6,3,4]=>1000111
[4,1,8,3,7,5,2,6]=>[5,7,4,1,8,3,2,6]=>[7,2,8,6,3,4,1,5]=>0010111
[2,4,8,6,5,7,1,3]=>[7,2,1,4,6,8,5,3]=>[2,4,8,3,1,7,5,6]=>0100011
[7,2,6,8,3,5,1,4]=>[5,8,7,2,3,1,6,4]=>[7,6,1,5,3,8,4,2]=>0011111
[7,2,8,6,5,3,1,4]=>[3,5,6,2,8,7,1,4]=>[7,1,3,6,8,4,2,5]=>0010011
[4,8,3,7,6,1,2,5]=>[6,1,7,4,3,8,2,5]=>[4,8,5,3,7,2,1,6]=>1001011
[2,1,8,7,3,5,4,6]=>[2,1,5,7,3,4,8,6]=>[2,1,5,3,8,6,4,7]=>1001101
[1,8,5,3,2,7,4,6]=>[1,3,7,5,8,2,4,6]=>[1,8,6,2,3,7,4,5]=>0000111
[7,2,3,8,6,4,5,1]=>[5,6,2,8,3,7,4,1]=>[8,1,5,3,2,6,7,4]=>0101011
[3,5,8,1,7,4,2,6]=>[4,7,3,8,5,1,2,6]=>[3,5,7,2,8,6,1,4]=>0000111
[1,3,8,5,2,4,6,7]=>[1,5,3,2,8,4,6,7]=>[1,3,8,7,6,4,2,5]=>0010111
[7,8,6,1,3,2,4,5]=>[3,6,1,2,4,8,7,5]=>[3,1,7,8,5,4,2,6]=>0111001
[1,2,6,8,3,4,7,5]=>[1,2,7,3,8,6,4,5]=>[1,2,6,7,4,3,8,5]=>0010011
[5,8,2,7,6,1,4,3]=>[4,6,7,2,5,8,1,3]=>[5,8,3,7,1,4,2,6]=>0010011
[6,8,7,3,5,1,4,2]=>[4,5,7,3,1,6,8,2]=>[6,8,2,5,1,4,3,7]=>0011001
[1,8,6,4,7,3,2,5]=>[1,3,7,6,4,8,2,5]=>[1,7,2,3,8,5,4,6]=>0001011
[8,6,7,2,3,5,4,1]=>[4,5,2,7,3,8,6,1]=>[5,3,2,8,1,4,7,6]=>0101011
[5,4,8,6,7,3,1,2]=>[3,1,7,5,4,8,6,2]=>[5,4,8,2,1,3,7,6]=>1001011
[7,2,6,8,5,1,3,4]=>[5,8,2,1,7,3,6,4]=>[8,4,1,5,7,6,3,2]=>0110111
[7,3,6,4,2,1,8,5]=>[2,4,8,6,7,3,1,5]=>[8,5,7,1,2,4,6,3]=>0000111
[4,8,5,2,7,3,1,6]=>[3,7,5,4,8,2,1,6]=>[4,8,6,2,7,1,3,5]=>0000111
[7,4,3,1,5,8,6,2]=>[6,3,4,8,1,7,5,2]=>[7,5,1,6,8,2,3,4]=>0001011
[7,3,2,1,8,5,6,4]=>[2,3,6,8,7,1,5,4]=>[6,1,2,3,7,5,8,4]=>0000111
[1,2,7,5,8,4,3,6]=>[1,2,4,8,7,5,3,6]=>[1,2,8,6,5,7,3,4]=>0000111
[5,1,3,8,2,7,4,6]=>[7,8,1,5,3,2,4,6]=>[7,4,5,3,1,8,6,2]=>0101111
[8,7,1,3,2,4,6,5]=>[3,6,1,2,7,4,8,5]=>[3,1,6,4,2,8,5,7]=>0110101
[1,8,2,7,6,3,5,4]=>[1,5,6,7,2,8,3,4]=>[1,5,2,8,4,7,3,6]=>0001011
[1,8,6,2,7,4,3,5]=>[1,4,7,6,2,8,3,5]=>[1,7,3,8,5,2,4,6]=>0001011
[8,7,2,3,5,1,4,6]=>[5,7,2,3,1,4,8,6]=>[5,1,8,6,4,3,2,7]=>0111101
[6,4,5,3,1,7,8,2]=>[8,3,5,6,4,1,7,2]=>[7,8,2,3,5,4,6,1]=>0001101
[2,8,1,3,5,6,4,7]=>[6,2,1,8,3,5,4,7]=>[2,6,5,3,1,8,7,4]=>0101111
[7,6,3,1,8,5,2,4]=>[5,3,8,1,6,7,2,4]=>[8,4,1,5,6,7,2,3]=>0010011
[1,2,4,6,8,5,7,3]=>[1,2,7,4,8,6,5,3]=>[1,2,4,6,8,3,7,5]=>0000011
[8,5,2,3,7,4,1,6]=>[4,7,2,5,8,3,1,6]=>[8,6,3,2,7,1,4,5]=>0100111
[6,1,3,2,8,5,7,4]=>[3,7,1,8,6,2,5,4]=>[3,1,7,5,6,2,8,4]=>0100111
[3,8,5,1,2,4,7,6]=>[5,1,3,2,7,8,4,6]=>[3,7,4,2,1,5,8,6]=>1010011
[1,8,3,7,5,2,6,4]=>[1,6,5,7,8,3,2,4]=>[1,8,4,7,2,6,3,5]=>0000111
[7,1,3,8,5,2,6,4]=>[6,5,1,8,7,3,2,4]=>[6,3,1,7,2,5,8,4]=>0100111
[4,7,1,5,2,6,8,3]=>[8,5,7,4,1,2,6,3]=>[4,8,3,7,6,2,5,1]=>0001111
[7,4,1,5,2,6,8,3]=>[8,5,4,7,1,2,6,3]=>[8,3,4,7,6,2,5,1]=>0001111
[3,1,6,7,5,2,8,4]=>[8,3,1,5,7,6,2,4]=>[6,8,4,5,7,2,3,1]=>0100011
[8,6,2,4,5,1,7,3]=>[7,5,6,2,4,8,1,3]=>[5,4,2,7,1,8,3,6]=>0011011
[5,6,4,7,1,8,3,2]=>[3,8,7,6,5,4,1,2]=>[5,6,4,7,1,3,8,2]=>0000111
[3,6,7,5,1,4,8,2]=>[8,5,3,1,7,6,4,2]=>[3,6,8,2,5,7,4,1]=>0010011
[6,3,7,1,2,5,8,4]=>[8,1,7,6,3,2,5,4]=>[7,5,3,8,4,6,2,1]=>1001111
[6,3,7,5,1,2,8,4]=>[8,1,5,7,6,3,2,4]=>[6,3,5,8,4,7,2,1]=>1000111
[5,3,7,4,6,1,8,2]=>[8,6,7,5,3,4,1,2]=>[8,2,6,4,5,3,7,1]=>0001111
[5,4,1,7,6,8,3,2]=>[3,8,4,5,1,7,6,2]=>[5,1,3,4,7,6,8,2]=>0001011
[4,5,1,3,6,7,8,2]=>[8,5,1,4,3,6,7,2]=>[4,6,7,8,2,5,3,1]=>0101001
[2,5,6,7,1,8,4,3]=>[4,2,8,7,5,6,1,3]=>[2,5,6,7,1,4,8,3]=>0000011
[4,8,1,3,5,2,7,6]=>[5,7,1,4,3,8,2,6]=>[4,5,3,1,7,2,8,6]=>0101011
[4,5,1,6,2,8,7,3]=>[7,6,5,4,1,2,8,3]=>[4,6,2,8,3,5,1,7]=>0001101
[3,2,5,8,6,1,7,4]=>[7,3,2,6,5,8,1,4]=>[3,2,5,7,1,8,4,6]=>0100011
[5,2,6,7,4,3,1,8]=>[3,4,7,5,2,6,1,8]=>[5,2,4,6,7,1,3,8]=>0001010
[8,5,1,6,4,3,2,7]=>[3,4,6,5,8,1,2,7]=>[6,1,3,8,7,2,4,5]=>0000111
[8,5,1,6,4,3,7,2]=>[7,4,6,5,8,1,3,2]=>[7,3,6,1,8,2,4,5]=>0000111
[8,5,2,1,6,4,3,7]=>[2,4,6,5,8,1,3,7]=>[8,7,3,6,1,2,4,5]=>0000111
[6,7,1,4,3,2,8,5]=>[3,4,8,1,7,6,2,5]=>[6,8,5,7,2,4,1,3]=>0010011
[4,1,7,3,2,8,5,6]=>[3,8,4,1,7,2,5,6]=>[4,1,3,7,5,8,6,2]=>0010111
[8,3,5,2,4,7,1,6]=>[7,5,8,3,2,4,1,6]=>[5,2,7,1,8,6,4,3]=>0011111
[2,6,4,7,5,3,1,8]=>[3,2,5,7,6,4,1,8]=>[2,7,1,3,5,6,4,8]=>0000110
[5,6,3,7,2,8,4,1]=>[4,8,7,6,5,3,2,1]=>[5,8,1,4,6,3,7,2]=>0000111
[4,5,1,8,6,2,7,3]=>[7,6,5,4,1,8,2,3]=>[4,8,3,5,1,7,2,6]=>0001011
[2,4,6,3,5,1,7,8]=>[5,2,6,4,3,1,7,8]=>[2,4,6,1,5,3,7,8]=>0001100
[4,5,6,3,1,7,2,8]=>[7,3,6,4,5,1,2,8]=>[4,5,7,2,3,6,1,8]=>0000110
[3,4,6,2,5,1,7,8]=>[5,6,3,4,2,1,7,8]=>[3,4,6,1,5,2,7,8]=>0001100
[1,4,7,5,2,3,6,8]=>[1,5,2,4,7,3,6,8]=>[1,4,7,6,3,2,5,8]=>0100110
[1,4,6,5,8,2,3,7]=>[1,8,2,4,6,5,3,7]=>[1,4,6,5,8,7,3,2]=>0100111
[1,5,8,6,2,3,4,7]=>[1,6,2,3,5,8,4,7]=>[1,5,8,7,4,3,2,6]=>0110011
[1,4,8,7,3,6,2,5]=>[1,6,7,4,3,2,8,5]=>[1,4,6,2,8,5,3,7]=>0001101
[2,3,8,4,7,1,6,5]=>[6,2,3,7,8,4,1,5]=>[2,3,7,1,6,4,8,5]=>0000111
[1,8,7,5,2,6,3,4]=>[1,6,5,2,7,3,8,4]=>[1,8,4,2,6,3,5,7]=>0010101
[1,8,7,5,4,3,2,6]=>[1,3,4,5,7,2,8,6]=>[1,8,6,2,3,4,5,7]=>0000101
[1,7,6,3,4,5,8,2]=>[1,8,6,3,4,7,5,2]=>[1,7,5,4,3,6,8,2]=>0011011
[1,8,7,2,4,6,3,5]=>[1,6,7,2,4,3,8,5]=>[1,8,5,4,2,6,3,7]=>0011101
[1,7,6,4,2,5,3,8]=>[1,5,4,6,2,7,3,8]=>[1,5,2,7,3,4,6,8]=>0001010
[1,4,7,5,8,2,6,3]=>[1,6,8,4,7,5,2,3]=>[1,4,7,2,6,5,8,3]=>0000111
[1,7,2,5,6,3,4,8]=>[1,6,7,2,3,5,4,8]=>[1,7,4,2,6,5,3,8]=>0011110
[1,5,8,3,6,4,7,2]=>[1,7,6,8,5,3,4,2]=>[1,5,6,3,8,2,7,4]=>0000111
[1,6,8,2,7,3,4,5]=>[1,7,8,2,3,6,4,5]=>[1,6,7,4,2,8,5,3]=>0011011
[6,4,7,5,2,3,1,8]=>[3,5,2,7,6,4,1,8]=>[7,1,3,2,5,6,4,8]=>0100110
[8,5,3,2,4,1,7,6]=>[4,3,5,2,7,8,1,6]=>[7,1,4,2,3,5,8,6]=>0010011
[6,8,4,1,7,3,2,5]=>[3,7,4,8,1,6,2,5]=>[6,7,2,8,5,1,3,4]=>0001011
[1,8,3,5,2,6,4,7]=>[1,6,5,8,3,2,4,7]=>[1,5,3,6,2,8,7,4]=>0001111
[1,8,4,5,6,2,7,3]=>[1,7,6,8,4,5,2,3]=>[1,7,2,8,3,6,5,4]=>0001111
[2,4,8,5,7,3,1,6]=>[3,2,7,4,8,5,1,6]=>[2,4,7,1,3,8,6,5]=>0000111
[2,5,8,4,6,7,1,3]=>[7,2,1,8,5,4,6,3]=>[2,5,8,3,1,7,6,4]=>0100111
[3,5,6,8,4,7,1,2]=>[7,1,3,8,5,6,4,2]=>[3,5,6,8,2,1,7,4]=>1000011
[3,5,6,8,4,2,7,1]=>[7,4,3,8,5,6,2,1]=>[3,5,6,8,1,7,2,4]=>0000011
[2,5,8,4,6,3,7,1]=>[7,2,6,8,5,4,3,1]=>[2,5,8,1,7,3,6,4]=>0000111
[7,2,5,3,4,6,1,8]=>[6,5,7,2,3,4,1,8]=>[7,1,6,4,2,5,3,8]=>0011110
[7,1,2,6,4,3,5,8]=>[4,1,6,7,2,3,5,8]=>[6,3,7,5,2,1,4,8]=>1001110
[7,1,2,6,3,4,5,8]=>[6,1,7,2,3,4,5,8]=>[6,4,2,1,7,5,3,8]=>1011110
[5,3,1,4,7,2,8,6]=>[8,3,5,1,4,7,2,6]=>[8,6,7,2,3,5,4,1]=>0011011
[1,8,3,7,2,4,6,5]=>[1,6,7,3,8,2,4,5]=>[1,6,2,7,4,3,8,5]=>0010111
[2,7,5,6,4,8,1,3]=>[8,2,1,6,7,5,4,3]=>[2,7,4,6,5,8,3,1]=>0100111
[1,5,2,4,3,8,7,6]=>[1,4,5,2,3,7,8,6]=>[1,4,2,5,3,8,6,7]=>0011001
[3,1,2,4,8,7,5,6]=>[3,1,2,4,7,5,8,6]=>[3,2,1,4,8,6,5,7]=>1100101
[5,2,1,6,3,8,7,4]=>[2,7,6,5,1,3,8,4]=>[6,3,8,4,5,1,2,7]=>0001101
[4,6,2,7,5,8,1,3]=>[8,7,2,4,6,1,5,3]=>[4,8,3,2,7,5,6,1]=>0100111
[5,8,3,6,4,1,7,2]=>[7,4,6,8,5,3,1,2]=>[5,6,3,7,1,8,2,4]=>0000111
[4,6,8,5,1,2,3,7]=>[5,1,2,4,8,6,3,7]=>[4,6,8,7,3,2,1,5]=>1100011
[4,6,5,7,1,3,8,2]=>[8,7,1,4,6,5,3,2]=>[4,6,5,8,2,7,3,1]=>0100111
[3,4,7,6,1,8,2,5]=>[8,6,3,4,1,7,2,5]=>[3,4,7,2,6,8,5,1]=>0001011
[8,1,4,6,7,2,5,3]=>[5,7,8,1,4,2,6,3]=>[5,4,1,7,6,2,8,3]=>0011111
[8,6,1,3,2,7,5,4]=>[3,5,1,7,6,8,2,4]=>[3,1,8,4,7,2,5,6]=>0100011
[8,2,1,6,7,4,5,3]=>[2,5,7,8,1,4,6,3]=>[5,1,2,8,3,7,6,4]=>0001111
[8,6,1,2,7,3,5,4]=>[5,1,7,6,2,8,3,4]=>[5,2,1,7,3,8,4,6]=>1001011
[5,2,6,7,4,8,3,1]=>[3,8,7,5,2,6,4,1]=>[6,8,1,3,7,4,5,2]=>0001011
[4,3,7,1,2,8,5,6]=>[8,1,4,3,7,2,5,6]=>[4,3,7,5,8,6,2,1]=>1010111
[8,5,7,1,4,2,6,3]=>[6,4,7,1,8,5,2,3]=>[8,3,7,2,4,1,6,5]=>0010111
[2,6,7,1,4,3,8,5]=>[4,2,8,1,7,6,3,5]=>[2,4,1,6,8,5,7,3]=>0010011
[4,5,2,1,6,3,8,7]=>[2,6,5,4,1,3,8,7]=>[4,6,3,5,1,2,8,7]=>0001101
[2,5,1,6,4,3,8,7]=>[4,2,6,5,1,3,8,7]=>[2,5,1,4,6,3,8,7]=>0001101
[3,6,2,8,5,7,1,4]=>[7,8,3,2,6,1,5,4]=>[3,7,5,6,1,8,4,2]=>0010111
[4,6,8,1,5,7,2,3]=>[7,8,1,4,2,6,5,3]=>[4,6,8,3,1,7,5,2]=>0101011
[5,2,3,8,7,1,6,4]=>[6,7,2,5,3,1,8,4]=>[6,1,8,4,5,3,2,7]=>0101101
[3,2,8,1,7,5,4,6]=>[5,3,2,7,8,1,4,6]=>[3,2,7,4,8,6,1,5]=>0100111
[4,8,2,1,6,7,5,3]=>[2,5,7,4,8,1,6,3]=>[4,8,3,7,6,1,2,5]=>0000111
[4,8,1,2,7,5,6,3]=>[6,1,7,4,8,2,5,3]=>[4,6,2,1,8,3,7,5]=>1000111
[4,5,1,6,8,7,2,3]=>[7,5,1,4,2,6,8,3]=>[4,5,2,6,8,3,1,7]=>0101001
[4,3,8,6,1,2,5,7]=>[6,1,4,3,2,8,5,7]=>[4,3,8,7,5,2,1,6]=>1011011
[4,8,1,5,3,6,7,2]=>[7,5,8,4,1,3,6,2]=>[4,8,2,5,1,7,6,3]=>0001111
[8,3,4,2,7,6,1,5]=>[6,4,7,3,2,8,1,5]=>[8,5,2,4,3,7,1,6]=>0011011
[8,4,2,3,7,6,5,1]=>[5,4,2,6,7,8,3,1]=>[8,1,5,7,3,2,4,6]=>0100011
[8,6,4,7,5,1,3,2]=>[3,5,1,7,6,8,4,2]=>[3,1,7,4,8,2,5,6]=>0100011
[5,3,4,7,8,1,6,2]=>[6,8,5,3,4,1,7,2]=>[5,4,3,6,1,7,8,2]=>0011101
[5,1,4,8,2,3,7,6]=>[7,5,1,2,4,8,3,6]=>[5,4,2,7,3,1,8,6]=>0111011
[5,8,6,3,1,2,4,7]=>[3,1,6,2,5,8,4,7]=>[5,8,7,4,2,1,3,6]=>1010011
[6,4,7,5,1,3,2,8]=>[3,5,1,7,6,4,2,8]=>[3,1,7,2,5,6,4,8]=>0100110
[6,7,2,4,1,8,3,5]=>[8,4,7,2,1,6,3,5]=>[4,2,6,7,3,8,5,1]=>0011011
[7,4,5,1,2,6,8,3]=>[8,1,5,7,4,2,6,3]=>[8,3,5,4,7,6,2,1]=>1001111
[6,7,2,5,4,1,3,8]=>[4,5,2,7,1,6,3,8]=>[6,7,3,2,5,1,4,8]=>0101010
[8,5,7,6,2,3,4,1]=>[4,6,2,3,7,8,5,1]=>[7,5,8,1,4,3,2,6]=>0110011
[8,4,2,3,6,7,5,1]=>[5,4,2,7,8,3,6,1]=>[7,6,3,2,4,8,1,5]=>0100111
[2,4,7,5,8,6,3,1]=>[3,2,6,4,8,7,5,1]=>[2,4,8,1,3,6,7,5]=>0000011
[4,1,7,6,2,8,3,5]=>[8,6,4,1,2,7,3,5]=>[8,5,2,6,7,3,4,1]=>0011011
[7,1,4,3,6,5,8,2]=>[8,4,6,1,7,3,5,2]=>[6,3,7,5,8,2,4,1]=>0010111
[7,1,6,3,5,4,8,2]=>[8,5,6,7,1,3,4,2]=>[6,3,7,4,8,2,5,1]=>0001111
[5,7,3,2,8,4,1,6]=>[4,3,8,7,5,2,1,6]=>[5,7,1,4,8,6,2,3]=>0000111
[2,8,7,1,6,5,3,4]=>[5,2,6,1,7,3,8,4]=>[2,6,3,8,4,1,5,7]=>0010101
[8,1,5,2,7,4,3,6]=>[4,7,5,8,1,2,3,6]=>[8,6,2,7,3,5,1,4]=>0001111
[2,6,8,1,7,5,3,4]=>[5,2,7,1,8,6,3,4]=>[2,6,7,3,8,4,1,5]=>0010011
[1,4,6,5,3,8,2,7]=>[1,8,5,4,6,3,2,7]=>[1,4,6,3,5,8,7,2]=>0000111
[3,1,6,8,7,5,4,2]=>[4,3,1,5,7,6,8,2]=>[6,8,2,3,1,4,5,7]=>0100001
[5,1,8,7,6,3,4,2]=>[4,6,5,1,3,7,8,2]=>[4,1,5,3,8,2,6,7]=>0011001
[1,3,8,4,7,2,6,5]=>[1,6,3,7,8,4,2,5]=>[1,3,7,2,6,4,8,5]=>0000111
[1,8,2,4,7,3,6,5]=>[1,6,7,2,8,4,3,5]=>[1,6,4,2,7,3,8,5]=>0010111
[1,2,8,6,7,5,4,3]=>[1,2,4,5,7,8,6,3]=>[1,2,8,3,4,5,7,6]=>0000011
[1,8,7,2,6,4,5,3]=>[1,5,6,7,2,4,8,3]=>[1,5,2,8,3,6,4,7]=>0001101
[8,7,2,4,3,6,5,1]=>[5,4,6,2,7,3,8,1]=>[4,2,6,3,8,1,5,7]=>0010101
[8,7,1,6,4,3,5,2]=>[5,4,6,7,1,3,8,2]=>[5,1,6,3,8,2,4,7]=>0001101
[2,8,6,7,5,3,1,4]=>[3,2,5,1,7,8,6,4]=>[2,8,4,1,3,5,7,6]=>0010011
[8,6,3,4,5,1,7,2]=>[7,5,6,3,4,8,1,2]=>[7,1,8,2,5,4,3,6]=>0011011
[8,4,7,3,1,2,5,6]=>[3,1,7,8,4,2,5,6]=>[8,6,2,1,3,7,5,4]=>1001111
[8,6,2,3,5,1,7,4]=>[7,5,2,6,3,8,1,4]=>[5,3,2,7,1,8,4,6]=>0101011
[3,6,2,5,7,8,4,1]=>[4,8,3,6,2,5,7,1]=>[3,7,8,1,4,6,5,2]=>0001101
[3,7,5,6,8,2,4,1]=>[4,8,3,2,7,5,6,1]=>[3,7,6,5,8,1,4,2]=>0010111
[1,5,7,6,8,4,2,3]=>[1,4,2,8,5,7,6,3]=>[1,5,7,6,8,3,2,4]=>0100011
[2,7,5,6,8,4,3,1]=>[3,2,4,8,7,5,6,1]=>[2,7,6,5,8,1,3,4]=>0000111
[3,7,6,8,5,1,4,2]=>[4,5,3,1,8,7,6,2]=>[3,4,1,7,6,8,2,5]=>0010011
[5,3,4,7,6,2,1,8]=>[2,6,5,3,4,7,1,8]=>[5,4,3,7,1,2,6,8]=>0011010
[8,7,2,6,4,5,1,3]=>[5,6,2,7,1,4,8,3]=>[5,1,8,3,2,6,4,7]=>0101101
[3,1,2,8,7,5,4,6]=>[3,1,2,5,7,4,8,6]=>[3,2,1,8,6,4,5,7]=>1100101
[3,1,2,8,7,6,4,5]=>[3,1,2,6,4,7,8,5]=>[3,2,1,8,5,4,6,7]=>1101001
[7,2,5,1,6,4,8,3]=>[8,6,5,7,2,1,4,3]=>[7,4,8,3,5,2,6,1]=>0001111
[1,5,7,8,4,6,3,2]=>[1,3,6,8,5,4,7,2]=>[1,5,7,8,2,3,6,4]=>0000101
[2,8,5,1,6,4,3,7]=>[4,2,6,5,8,1,3,7]=>[2,8,7,3,6,1,4,5]=>0000111
[8,7,2,1,3,6,5,4]=>[2,5,1,6,7,3,8,4]=>[8,4,6,3,1,2,5,7]=>0100101
[6,4,1,2,5,7,8,3]=>[8,1,4,6,2,5,7,3]=>[7,8,3,4,6,5,2,1]=>1001101
[6,4,2,3,1,7,5,8]=>[3,4,2,7,6,1,5,8]=>[7,5,6,1,3,2,4,8]=>0100110
[3,4,6,1,8,2,7,5]=>[7,8,3,4,6,1,2,5]=>[3,4,8,5,6,1,7,2]=>0000111
[2,6,1,3,5,4,7,8]=>[5,2,1,6,3,4,7,8]=>[2,5,3,1,6,4,7,8]=>0101100
[7,1,5,4,2,6,3,8]=>[6,4,5,7,1,2,3,8]=>[7,3,5,1,6,2,4,8]=>0001110
[5,1,8,6,2,7,4,3]=>[4,7,6,5,1,8,2,3]=>[5,1,4,7,2,8,3,6]=>0001011
[5,6,4,1,7,2,8,3]=>[8,7,4,6,5,1,2,3]=>[5,7,2,8,3,4,6,1]=>0000111
[5,4,3,1,7,2,8,6]=>[8,3,4,5,1,7,2,6]=>[8,6,7,2,3,4,5,1]=>0001011
[6,5,2,4,1,7,8,3]=>[8,4,5,2,6,1,7,3]=>[4,2,7,8,3,5,6,1]=>0010101
[1,6,2,7,8,4,5,3]=>[1,5,8,6,2,4,7,3]=>[1,5,2,6,4,7,8,3]=>0001101
[5,4,2,3,1,7,8,6]=>[3,4,2,5,1,8,7,6]=>[5,1,3,2,4,7,8,6]=>0101001
[4,6,5,3,8,2,1,7]=>[2,8,5,4,6,3,1,7]=>[4,6,3,5,8,7,1,2]=>0000111
[5,8,4,3,7,6,2,1]=>[2,6,4,7,5,8,3,1]=>[5,7,3,4,8,1,2,6]=>0000011
[8,1,5,3,4,7,2,6]=>[7,5,8,1,3,4,2,6]=>[8,6,4,1,7,2,5,3]=>0011111
[6,1,8,7,4,5,3,2]=>[3,5,7,6,1,4,8,2]=>[6,4,8,2,5,1,3,7]=>0001101
[1,5,8,6,4,3,7,2]=>[1,7,4,6,5,8,3,2]=>[1,5,8,2,7,3,4,6]=>0000011
[8,5,4,1,2,3,7,6]=>[4,1,2,5,7,8,3,6]=>[7,3,2,1,4,5,8,6]=>1100011
[5,8,6,4,2,1,7,3]=>[2,7,4,6,5,8,1,3]=>[5,7,1,2,8,3,4,6]=>0000011
[5,3,8,6,1,2,7,4]=>[7,1,6,5,3,8,2,4]=>[7,2,1,8,4,5,3,6]=>1001011
[5,4,7,2,1,3,8,6]=>[2,8,1,5,4,7,3,6]=>[5,4,8,6,7,3,1,2]=>0101011
[8,4,6,5,2,7,3,1]=>[3,7,5,6,8,4,2,1]=>[6,4,7,2,8,1,3,5]=>0000111
[6,4,7,5,8,3,1,2]=>[3,1,8,7,6,4,5,2]=>[7,5,6,4,8,2,1,3]=>1000111
[6,4,7,1,2,3,8,5]=>[8,1,2,7,6,4,3,5]=>[8,5,6,4,7,3,2,1]=>1100111
[8,2,3,1,6,4,7,5]=>[3,7,2,6,8,1,4,5]=>[7,4,6,1,3,2,8,5]=>0100111
[3,1,8,5,7,2,6,4]=>[6,3,1,7,8,5,2,4]=>[8,4,7,2,3,1,6,5]=>0100111
[5,7,6,3,1,2,8,4]=>[3,1,8,6,5,7,2,4]=>[5,8,4,6,7,2,1,3]=>1000011
[1,2,4,8,5,7,3,6]=>[1,2,7,4,8,5,3,6]=>[1,2,4,7,3,8,6,5]=>0000111
[1,2,7,5,8,6,3,4]=>[1,2,6,3,8,7,5,4]=>[1,2,8,4,3,6,7,5]=>0010011
[6,2,1,5,3,7,8,4]=>[2,8,5,6,1,3,7,4]=>[7,8,4,6,3,5,1,2]=>0001101
[2,7,3,8,5,6,4,1]=>[4,2,6,8,7,3,5,1]=>[2,6,3,7,5,8,1,4]=>0000111
[1,5,3,7,8,4,6,2]=>[1,6,8,5,3,4,7,2]=>[1,7,8,2,6,4,5,3]=>0001101
[1,6,3,7,8,5,4,2]=>[1,4,5,8,6,3,7,2]=>[1,6,3,5,7,8,2,4]=>0000101
[6,1,4,8,2,7,5,3]=>[5,7,8,1,6,4,2,3]=>[6,4,1,5,7,2,8,3]=>0010111
[8,6,4,2,7,3,5,1]=>[5,7,4,6,2,8,3,1]=>[8,1,5,2,7,3,4,6]=>0001011
[7,6,1,5,2,3,8,4]=>[8,5,1,6,2,7,3,4]=>[5,2,8,4,6,7,3,1]=>0101011
[5,1,7,6,8,2,3,4]=>[8,5,1,2,3,7,6,4]=>[7,6,8,4,2,5,3,1]=>0111011
[6,1,5,7,2,8,3,4]=>[8,7,6,1,2,5,3,4]=>[7,3,6,5,2,8,4,1]=>0011111
[8,4,5,1,6,7,2,3]=>[7,5,1,8,4,2,6,3]=>[8,3,1,7,6,2,5,4]=>0101111
[4,1,6,5,2,3,8,7]=>[5,4,1,2,6,3,8,7]=>[4,2,6,3,1,5,8,7]=>0110101
[8,3,1,4,6,2,7,5]=>[7,3,6,1,8,4,2,5]=>[7,2,3,6,4,1,8,5]=>0010111
[8,3,6,1,5,2,4,7]=>[5,6,8,3,1,2,4,7]=>[5,1,6,2,8,7,4,3]=>0011111
[6,7,3,1,8,2,4,5]=>[8,3,7,1,2,6,4,5]=>[6,8,5,2,3,7,4,1]=>0011011
[6,4,1,2,5,8,3,7]=>[8,1,4,6,2,5,3,7]=>[8,7,3,4,6,5,2,1]=>1001111
[4,3,1,2,6,5,7,8]=>[3,1,4,2,6,5,7,8]=>[4,2,1,3,6,5,7,8]=>1010100
[4,3,1,2,5,7,6,8]=>[3,1,4,2,5,7,6,8]=>[4,2,1,3,5,7,6,8]=>1010010
[4,7,3,1,5,2,8,6]=>[5,3,8,4,1,7,2,6]=>[4,5,1,8,6,7,2,3]=>0001011
[8,3,6,5,7,4,2,1]=>[2,4,7,6,8,3,5,1]=>[8,1,2,4,6,3,7,5]=>0000111
[8,1,4,2,6,5,7,3]=>[7,4,6,1,8,2,5,3]=>[8,3,6,2,4,1,7,5]=>0010111
[8,4,7,1,5,2,6,3]=>[6,5,7,8,4,1,2,3]=>[6,1,8,3,7,2,5,4]=>0001111
[8,2,6,3,7,4,5,1]=>[5,7,6,8,2,3,4,1]=>[6,3,8,1,5,2,7,4]=>0001111
[8,6,7,1,4,3,5,2]=>[5,4,7,1,3,8,6,2]=>[8,2,4,1,5,3,7,6]=>0011011
[8,5,7,1,4,3,6,2]=>[6,4,7,1,8,5,3,2]=>[7,3,8,2,4,1,6,5]=>0010111
[6,5,1,2,7,4,8,3]=>[8,1,7,5,6,2,4,3]=>[8,3,7,4,5,6,2,1]=>1000111
[6,5,3,4,1,8,2,7]=>[8,4,5,3,6,1,2,7]=>[8,7,2,4,3,5,6,1]=>0010111
[2,8,7,4,1,3,6,5]=>[4,2,1,6,7,3,8,5]=>[2,6,3,1,4,8,5,7]=>0100101
[8,2,3,1,6,7,4,5]=>[3,7,2,8,1,4,6,5]=>[8,5,1,3,2,7,6,4]=>0101111
[7,2,8,3,1,4,5,6]=>[3,8,7,2,1,4,5,6]=>[7,5,1,3,8,6,4,2]=>0011111
[8,2,5,4,1,6,7,3]=>[7,4,5,8,2,1,6,3]=>[7,6,1,8,3,5,2,4]=>0001111
[7,2,4,6,8,1,5,3]=>[5,8,7,2,4,1,6,3]=>[8,3,7,6,1,5,4,2]=>0011111
[6,2,5,4,7,8,1,3]=>[8,5,2,6,1,4,7,3]=>[6,4,7,8,3,2,5,1]=>0101101
[6,3,5,2,7,1,4,8]=>[7,5,6,3,2,1,4,8]=>[5,2,7,4,3,6,1,8]=>0011110
[8,5,6,3,7,2,1,4]=>[2,7,6,3,8,5,1,4]=>[7,1,2,8,4,3,6,5]=>0010111
[3,6,4,1,2,5,7,8]=>[4,1,3,6,2,5,7,8]=>[3,6,5,2,1,4,7,8]=>1001100
[3,6,4,1,2,5,8,7]=>[4,1,3,6,2,5,8,7]=>[3,6,5,2,1,4,8,7]=>1001101
[6,8,2,5,7,3,1,4]=>[3,7,8,2,1,6,5,4]=>[6,8,4,2,7,5,1,3]=>0011011
[3,6,5,1,8,2,4,7]=>[8,5,3,1,6,2,4,7]=>[3,6,2,5,8,7,4,1]=>0010111
[5,8,7,3,4,2,6,1]=>[6,4,7,3,5,2,8,1]=>[5,8,1,6,2,4,3,7]=>0010101
[4,8,6,2,5,7,3,1]=>[3,7,6,4,2,8,5,1]=>[4,7,5,2,8,1,3,6]=>0001011
[3,4,8,5,7,2,6,1]=>[6,7,3,4,8,5,2,1]=>[3,4,7,2,8,1,6,5]=>0000111
[4,3,6,1,2,7,8,5]=>[8,1,4,3,6,2,7,5]=>[4,3,7,8,5,6,2,1]=>1010101
[5,7,3,6,4,2,1,8]=>[2,4,6,7,5,3,1,8]=>[5,6,3,7,1,2,4,8]=>0000110
[5,7,3,6,4,1,8,2]=>[8,4,6,7,5,3,1,2]=>[5,6,3,8,2,4,7,1]=>0000111
[2,4,6,5,1,8,7,3]=>[7,2,5,4,6,1,8,3]=>[2,4,8,3,5,6,1,7]=>0000101
[2,4,6,5,1,8,3,7]=>[8,2,5,4,6,1,3,7]=>[2,4,8,7,3,5,6,1]=>0000111
[2,4,6,1,8,7,3,5]=>[7,2,6,4,1,3,8,5]=>[2,4,6,3,8,5,1,7]=>0001101
[2,4,6,5,8,3,7,1]=>[7,2,8,4,6,5,3,1]=>[2,4,6,5,8,1,7,3]=>0000111
[2,4,6,8,5,3,1,7]=>[3,2,5,4,8,6,1,7]=>[2,4,6,8,7,1,3,5]=>0000011
[2,4,6,8,5,7,3,1]=>[3,2,7,4,8,6,5,1]=>[2,4,6,8,1,3,7,5]=>0000011
[2,4,6,8,7,5,1,3]=>[5,2,1,4,7,6,8,3]=>[2,4,6,8,3,1,5,7]=>0100001
[2,4,6,8,5,7,1,3]=>[7,2,1,4,8,6,5,3]=>[2,4,6,8,3,1,7,5]=>0100011
[2,4,6,8,7,1,5,3]=>[5,2,7,4,1,6,8,3]=>[2,4,5,1,6,8,3,7]=>0001001
[2,4,6,8,1,7,3,5]=>[7,2,8,4,1,6,3,5]=>[2,4,6,8,5,1,7,3]=>0001011
[2,6,7,5,3,8,1,4]=>[8,2,5,3,7,6,1,4]=>[2,6,8,4,3,5,7,1]=>0010011
[3,6,7,5,8,2,4,1]=>[4,8,3,2,7,6,5,1]=>[3,6,7,5,8,1,4,2]=>0010011
[3,1,2,7,5,8,4,6]=>[3,1,2,8,7,5,4,6]=>[3,2,1,8,6,5,7,4]=>1100111
[4,8,1,6,2,5,3,7]=>[5,6,8,4,1,2,3,7]=>[4,5,1,6,2,8,7,3]=>0001111
[1,5,8,3,4,6,2,7]=>[1,6,8,3,5,4,2,7]=>[1,5,8,7,2,6,4,3]=>0010111
[7,5,8,2,4,3,6,1]=>[6,4,8,2,7,5,3,1]=>[4,2,8,1,6,5,7,3]=>0010111
[2,7,3,8,4,5,6,1]=>[6,2,8,7,3,4,5,1]=>[2,8,1,6,4,7,5,3]=>0001111
[1,8,2,4,7,5,6,3]=>[1,6,7,2,8,4,5,3]=>[1,6,4,2,8,3,7,5]=>0010111
[7,8,2,3,5,4,6,1]=>[6,5,2,8,3,4,7,1]=>[5,3,2,7,8,1,6,4]=>0101101
[8,4,1,3,2,6,5,7]=>[3,4,1,6,8,2,5,7]=>[3,1,6,2,4,8,7,5]=>0100111
[8,7,2,3,5,4,6,1]=>[6,5,2,7,3,4,8,1]=>[5,3,2,8,1,6,4,7]=>0101101
[1,7,6,8,4,5,3,2]=>[1,3,5,8,4,7,6,2]=>[1,7,6,8,2,3,5,4]=>0001011
[7,4,1,3,8,5,6,2]=>[6,4,1,8,7,3,5,2]=>[6,3,1,7,5,8,2,4]=>0100111
[8,3,5,1,7,6,4,2]=>[4,6,5,7,3,8,1,2]=>[5,3,7,1,4,8,2,6]=>0001011
[8,3,5,4,7,1,6,2]=>[6,7,5,8,3,4,1,2]=>[5,3,8,2,7,1,6,4]=>0001111
[1,8,5,3,2,4,6,7]=>[1,3,5,2,8,4,6,7]=>[1,8,7,6,4,2,3,5]=>0010111
[4,8,5,1,2,3,6,7]=>[5,1,2,4,8,3,6,7]=>[4,8,7,6,3,2,1,5]=>1100111
[8,7,2,4,3,5,6,1]=>[6,4,7,2,3,5,8,1]=>[4,2,8,1,6,5,3,7]=>0011101
[4,8,3,2,5,1,6,7]=>[5,3,8,4,2,1,6,7]=>[4,8,7,6,1,5,2,3]=>0001111
[5,8,4,2,1,3,7,6]=>[2,4,1,7,5,8,3,6]=>[5,7,3,1,2,4,8,6]=>0100011
[4,5,2,3,8,7,1,6]=>[7,5,2,4,3,1,8,6]=>[4,5,3,2,8,6,1,7]=>0101101
[4,6,7,5,2,3,1,8]=>[3,5,2,4,7,6,1,8]=>[4,6,7,1,3,2,5,8]=>0100010
[1,6,4,5,8,7,3,2]=>[1,3,7,6,4,5,8,2]=>[1,6,5,4,8,2,3,7]=>0001101
[8,2,7,4,5,3,1,6]=>[3,5,7,8,2,4,1,6]=>[5,2,7,1,3,8,6,4]=>0001111
[8,2,6,7,5,3,1,4]=>[3,5,7,2,8,1,6,4]=>[7,6,1,3,8,4,2,5]=>0010111
[8,4,6,7,5,3,1,2]=>[3,1,5,7,8,4,6,2]=>[7,6,4,8,2,1,3,5]=>1000111
[2,4,8,7,5,3,1,6]=>[3,2,5,4,7,1,8,6]=>[2,4,8,6,1,3,5,7]=>0000101
[6,7,2,4,5,3,1,8]=>[3,5,7,2,4,6,1,8]=>[5,4,2,6,7,1,3,8]=>0011010
[6,8,7,4,5,3,1,2]=>[3,1,5,7,4,6,8,2]=>[6,8,2,1,3,5,4,7]=>1001001
[3,7,4,6,2,1,8,5]=>[2,8,3,6,7,4,1,5]=>[3,6,4,8,5,7,1,2]=>0000111
[2,3,6,5,8,4,7,1]=>[7,2,3,8,6,5,4,1]=>[2,3,6,5,8,1,7,4]=>0000111
[2,4,7,3,8,5,1,6]=>[5,2,8,4,7,3,1,6]=>[2,4,7,1,5,8,6,3]=>0000111
[1,2,8,3,5,4,7,6]=>[1,2,5,7,3,8,4,6]=>[1,2,5,3,7,4,8,6]=>0001011
[5,6,2,1,8,3,4,7]=>[2,8,6,1,5,3,4,7]=>[5,6,3,8,7,4,1,2]=>0010111
[6,4,1,3,7,8,2,5]=>[8,4,1,6,3,2,7,5]=>[6,2,4,7,8,5,3,1]=>0101101
[1,6,2,8,7,3,4,5]=>[1,7,6,2,3,4,8,5]=>[1,8,5,3,6,4,2,7]=>0011101
[3,8,7,2,6,1,4,5]=>[6,7,3,2,1,4,8,5]=>[3,8,5,1,6,4,2,7]=>0011101
[2,5,1,8,3,6,4,7]=>[6,2,8,5,1,3,4,7]=>[2,8,7,4,5,1,6,3]=>0001111
[2,3,8,1,4,6,5,7]=>[6,2,3,1,8,4,5,7]=>[2,3,6,4,1,8,7,5]=>0010111
[1,3,8,2,5,4,7,6]=>[1,5,3,7,2,8,4,6]=>[1,3,5,2,7,4,8,6]=>0001011
[1,4,8,6,2,3,5,7]=>[1,6,2,4,3,8,5,7]=>[1,4,8,7,5,3,2,6]=>0101011
[1,6,2,7,4,5,3,8]=>[1,5,7,6,2,4,3,8]=>[1,5,2,6,4,7,3,8]=>0001110
[6,2,7,5,3,1,4,8]=>[3,5,7,2,6,1,4,8]=>[7,4,2,5,6,1,3,8]=>0010110
[6,1,7,4,8,5,2,3]=>[5,8,1,7,6,2,4,3]=>[7,4,8,3,1,5,6,2]=>0100111
[1,2,4,8,6,7,3,5]=>[1,2,7,4,3,8,6,5]=>[1,2,4,8,5,3,7,6]=>0001011
[8,1,2,6,5,7,3,4]=>[7,1,6,2,8,3,5,4]=>[6,3,8,4,2,1,7,5]=>1010111
[7,1,2,6,5,8,3,4]=>[8,1,6,2,7,3,5,4]=>[6,3,7,5,8,4,2,1]=>1010111
[2,6,1,4,7,5,8,3]=>[8,2,7,1,6,4,5,3]=>[2,8,3,7,5,6,4,1]=>0010111
[5,1,4,3,7,8,6,2]=>[6,4,5,1,3,8,7,2]=>[5,3,7,8,2,4,1,6]=>0011001
[3,1,5,7,2,6,8,4]=>[8,3,1,7,5,2,6,4]=>[5,8,4,7,6,2,3,1]=>0100111
[4,6,3,1,2,7,8,5]=>[3,1,8,4,6,2,7,5]=>[4,7,8,5,6,2,1,3]=>1000101
[6,7,3,1,2,4,8,5]=>[3,1,8,2,7,6,4,5]=>[6,8,5,7,4,2,1,3]=>1010011
[5,3,8,4,6,7,2,1]=>[2,7,8,5,3,4,6,1]=>[8,1,2,7,6,4,5,3]=>0001111
[4,7,3,8,5,6,2,1]=>[2,6,8,4,7,3,5,1]=>[4,7,5,8,1,2,6,3]=>0000111
[7,1,4,8,5,6,3,2]=>[3,6,8,1,7,4,5,2]=>[7,5,8,2,6,4,1,3]=>0010111
[1,2,6,8,7,4,5,3]=>[1,2,5,7,4,6,8,3]=>[1,2,6,8,3,5,4,7]=>0001001
[1,6,3,8,7,4,5,2]=>[1,5,7,6,3,4,8,2]=>[1,6,4,8,2,5,3,7]=>0001101
[3,5,6,7,1,8,4,2]=>[4,8,3,7,5,6,1,2]=>[3,5,6,7,1,4,8,2]=>0000011
[1,7,3,8,2,5,4,6]=>[1,5,8,7,3,2,4,6]=>[1,7,4,8,6,2,5,3]=>0001111
[3,4,7,5,8,2,1,6]=>[2,8,3,4,7,5,1,6]=>[3,4,8,6,5,7,1,2]=>0000111
[7,4,8,5,3,6,1,2]=>[6,1,5,8,7,4,3,2]=>[7,3,5,8,2,1,6,4]=>1000111
[8,4,6,5,1,3,7,2]=>[7,5,1,6,8,4,3,2]=>[6,4,7,3,1,8,2,5]=>0100111
[7,3,6,1,5,8,4,2]=>[4,8,6,7,3,1,5,2]=>[7,5,3,6,1,4,8,2]=>0001111
[2,3,7,8,1,4,6,5]=>[6,2,3,1,8,4,7,5]=>[2,3,6,4,1,7,8,5]=>0010101
[8,2,3,5,4,1,7,6]=>[4,5,2,7,3,8,1,6]=>[5,3,2,7,1,4,8,6]=>0101011
[7,1,3,8,2,4,6,5]=>[6,8,1,3,7,2,4,5]=>[8,5,7,4,3,1,6,2]=>0110111
[6,5,2,4,1,8,3,7]=>[8,4,5,2,6,1,3,7]=>[4,2,8,7,3,5,6,1]=>0010111
[5,7,2,4,1,3,8,6]=>[4,8,2,1,5,7,3,6]=>[4,1,5,8,6,7,3,2]=>0110011
[8,1,2,5,3,7,6,4]=>[6,1,5,7,2,8,3,4]=>[8,4,7,3,5,2,1,6]=>1001011
[1,8,5,4,2,6,3,7]=>[1,6,4,5,8,2,3,7]=>[1,6,2,8,7,3,4,5]=>0000111
[5,6,8,4,2,7,1,3]=>[7,4,2,8,5,6,1,3]=>[5,6,7,1,8,3,2,4]=>0100011
[6,8,7,3,2,1,5,4]=>[2,3,5,7,1,6,8,4]=>[5,1,2,3,6,8,4,7]=>0001001
[3,7,6,4,2,8,1,5]=>[8,4,3,6,2,7,1,5]=>[3,8,5,2,4,6,7,1]=>0001011
[5,7,3,6,2,1,8,4]=>[2,8,6,7,5,3,1,4]=>[5,6,3,8,4,7,1,2]=>0000111
[7,1,5,4,6,3,8,2]=>[8,6,5,7,1,4,3,2]=>[8,2,6,4,7,3,5,1]=>0001111
[2,5,4,7,1,8,3,6]=>[8,2,7,5,4,1,3,6]=>[2,5,4,7,3,8,6,1]=>0001111
[1,5,4,7,3,8,2,6]=>[1,8,7,5,4,3,2,6]=>[1,5,4,8,6,3,7,2]=>0001111
[1,5,6,7,2,4,3,8]=>[1,4,7,2,5,6,3,8]=>[1,4,2,5,6,7,3,8]=>0010010
[1,7,2,5,6,8,3,4]=>[1,8,7,2,3,5,6,4]=>[1,7,6,5,3,8,4,2]=>0011111
[7,3,8,4,2,6,5,1]=>[5,4,6,8,7,3,2,1]=>[6,3,8,1,5,7,2,4]=>0000111
[8,5,7,3,2,4,6,1]=>[6,3,7,2,8,5,4,1]=>[7,4,2,3,8,1,6,5]=>0010111
[6,2,8,3,7,4,5,1]=>[5,7,8,6,2,3,4,1]=>[8,1,5,2,7,4,6,3]=>0001111
[1,5,8,3,2,7,4,6]=>[1,3,7,8,5,2,4,6]=>[1,5,8,6,2,3,7,4]=>0000111
[7,6,4,2,5,3,1,8]=>[3,5,4,6,2,7,1,8]=>[5,2,7,1,3,4,6,8]=>0001010
[1,8,6,5,2,7,4,3]=>[1,4,7,5,6,8,2,3]=>[1,8,3,7,2,4,5,6]=>0000011
[6,8,2,5,1,7,4,3]=>[4,7,5,8,2,6,1,3]=>[6,8,3,5,2,7,1,4]=>0001011
[1,5,6,3,2,8,7,4]=>[1,3,7,6,5,2,8,4]=>[1,5,8,4,6,2,3,7]=>0000101
[7,2,6,3,8,5,4,1]=>[4,5,8,6,7,2,3,1]=>[8,1,4,6,2,5,7,3]=>0000111
[1,4,2,3,7,8,6,5]=>[1,4,2,3,6,8,7,5]=>[1,4,3,2,7,8,5,6]=>0110001
[1,8,4,2,3,6,5,7]=>[1,4,2,6,8,3,5,7]=>[1,6,3,2,4,8,7,5]=>0100111
[1,6,3,7,8,4,2,5]=>[1,4,8,6,3,2,7,5]=>[1,6,2,4,7,8,5,3]=>0001101
[1,6,3,8,4,2,5,7]=>[1,4,8,6,3,2,5,7]=>[1,6,2,4,8,7,5,3]=>0001111
[1,5,7,6,2,3,8,4]=>[1,8,2,6,5,7,3,4]=>[1,5,8,4,6,7,3,2]=>0100011
[1,3,7,6,2,4,5,8]=>[1,6,3,2,4,7,5,8]=>[1,3,7,5,4,2,6,8]=>0011010
[1,5,8,4,3,7,6,2]=>[1,6,4,7,5,8,3,2]=>[1,5,7,3,4,8,2,6]=>0000011
[1,7,5,8,4,3,6,2]=>[1,6,4,8,7,5,3,2]=>[1,8,2,6,5,7,3,4]=>0000111
[1,3,7,4,6,8,5,2]=>[1,5,3,8,7,4,6,2]=>[1,3,8,2,5,7,6,4]=>0000111
[1,5,2,6,8,7,4,3]=>[1,4,7,5,2,6,8,3]=>[1,5,2,4,6,8,3,7]=>0001001
[1,3,7,6,4,8,2,5]=>[1,8,3,6,4,7,2,5]=>[1,3,8,5,4,6,7,2]=>0001011
[5,6,1,4,3,8,7,2]=>[7,4,6,1,5,3,8,2]=>[5,6,3,8,2,4,1,7]=>0010101
[4,1,3,7,8,6,5,2]=>[5,4,1,3,6,8,7,2]=>[7,8,2,4,3,1,5,6]=>0110001
Map
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
- $des$ is the number of descents, St000021The number of descents of a permutation.,
- $exc$ is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
- $Dbot$ is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
- $Ebot$ is the sum of the excedance bottoms,
- $Ddif$ is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
- $Edif$ is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
- $Res$ is the sum of the (right) embracing numbers,
- $Ine$ is the sum of the side numbers.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
searching the database
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