Identifier
Mp00326:
Permutations
—weak order rowmotion⟶
Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00109: Permutations —descent word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
[1]=>[1]=>=>
[1,2]=>[2,1]=>1=>1
[2,1]=>[1,2]=>0=>0
[1,2,3]=>[3,2,1]=>11=>11
[1,3,2]=>[2,3,1]=>01=>10
[2,1,3]=>[3,1,2]=>10=>01
[2,3,1]=>[2,1,3]=>10=>01
[3,1,2]=>[1,3,2]=>01=>10
[3,2,1]=>[1,2,3]=>00=>00
[1,2,3,4]=>[4,3,2,1]=>111=>111
[1,2,4,3]=>[3,4,2,1]=>011=>110
[1,3,2,4]=>[4,2,3,1]=>101=>101
[1,3,4,2]=>[3,2,4,1]=>101=>101
[1,4,2,3]=>[2,4,3,1]=>011=>110
[1,4,3,2]=>[2,3,4,1]=>001=>100
[2,1,3,4]=>[4,3,1,2]=>110=>011
[2,1,4,3]=>[3,4,1,2]=>010=>010
[2,3,1,4]=>[4,2,1,3]=>110=>011
[2,3,4,1]=>[3,2,1,4]=>110=>011
[2,4,1,3]=>[2,1,4,3]=>101=>101
[2,4,3,1]=>[2,1,3,4]=>100=>001
[3,1,2,4]=>[4,1,3,2]=>101=>101
[3,1,4,2]=>[1,3,2,4]=>010=>010
[3,2,1,4]=>[4,1,2,3]=>100=>001
[3,2,4,1]=>[2,3,1,4]=>010=>010
[3,4,1,2]=>[3,1,4,2]=>101=>101
[3,4,2,1]=>[3,1,2,4]=>100=>001
[4,1,2,3]=>[1,4,3,2]=>011=>110
[4,1,3,2]=>[1,4,2,3]=>010=>010
[4,2,1,3]=>[1,2,4,3]=>001=>100
[4,2,3,1]=>[2,4,1,3]=>010=>010
[4,3,1,2]=>[1,3,4,2]=>001=>100
[4,3,2,1]=>[1,2,3,4]=>000=>000
[1,2,3,4,5]=>[5,4,3,2,1]=>1111=>1111
[1,2,3,5,4]=>[4,5,3,2,1]=>0111=>1110
[1,2,4,3,5]=>[5,3,4,2,1]=>1011=>1101
[1,2,4,5,3]=>[4,3,5,2,1]=>1011=>1101
[1,2,5,3,4]=>[3,5,4,2,1]=>0111=>1110
[1,2,5,4,3]=>[3,4,5,2,1]=>0011=>1100
[1,3,2,4,5]=>[5,4,2,3,1]=>1101=>1011
[1,3,2,5,4]=>[4,5,2,3,1]=>0101=>1010
[1,3,4,2,5]=>[5,3,2,4,1]=>1101=>1011
[1,3,4,5,2]=>[4,3,2,5,1]=>1101=>1011
[1,3,5,2,4]=>[3,2,5,4,1]=>1011=>1101
[1,3,5,4,2]=>[3,2,4,5,1]=>1001=>1001
[1,4,2,3,5]=>[5,2,4,3,1]=>1011=>1101
[1,4,2,5,3]=>[2,4,3,5,1]=>0101=>1010
[1,4,3,2,5]=>[5,2,3,4,1]=>1001=>1001
[1,4,3,5,2]=>[3,4,2,5,1]=>0101=>1010
[1,4,5,2,3]=>[4,2,5,3,1]=>1011=>1101
[1,4,5,3,2]=>[4,2,3,5,1]=>1001=>1001
[1,5,2,3,4]=>[2,5,4,3,1]=>0111=>1110
[1,5,2,4,3]=>[2,5,3,4,1]=>0101=>1010
[1,5,3,2,4]=>[2,3,5,4,1]=>0011=>1100
[1,5,3,4,2]=>[3,5,2,4,1]=>0101=>1010
[1,5,4,2,3]=>[2,4,5,3,1]=>0011=>1100
[1,5,4,3,2]=>[2,3,4,5,1]=>0001=>1000
[2,1,3,4,5]=>[5,4,3,1,2]=>1110=>0111
[2,1,3,5,4]=>[4,5,3,1,2]=>0110=>0110
[2,1,4,3,5]=>[5,3,4,1,2]=>1010=>0101
[2,1,4,5,3]=>[4,3,5,1,2]=>1010=>0101
[2,1,5,3,4]=>[3,5,4,1,2]=>0110=>0110
[2,1,5,4,3]=>[3,4,5,1,2]=>0010=>0100
[2,3,1,4,5]=>[5,4,2,1,3]=>1110=>0111
[2,3,1,5,4]=>[4,5,2,1,3]=>0110=>0110
[2,3,4,1,5]=>[5,3,2,1,4]=>1110=>0111
[2,3,4,5,1]=>[4,3,2,1,5]=>1110=>0111
[2,3,5,1,4]=>[3,2,1,5,4]=>1101=>1011
[2,3,5,4,1]=>[3,2,1,4,5]=>1100=>0011
[2,4,1,3,5]=>[5,2,1,4,3]=>1101=>1011
[2,4,1,5,3]=>[2,1,4,3,5]=>1010=>0101
[2,4,3,1,5]=>[5,2,1,3,4]=>1100=>0011
[2,4,3,5,1]=>[3,4,2,1,5]=>0110=>0110
[2,4,5,1,3]=>[4,2,1,5,3]=>1101=>1011
[2,4,5,3,1]=>[4,2,1,3,5]=>1100=>0011
[2,5,1,3,4]=>[2,1,5,4,3]=>1011=>1101
[2,5,1,4,3]=>[2,1,5,3,4]=>1010=>0101
[2,5,3,1,4]=>[2,1,3,5,4]=>1001=>1001
[2,5,3,4,1]=>[3,5,2,1,4]=>0110=>0110
[2,5,4,1,3]=>[2,1,4,5,3]=>1001=>1001
[2,5,4,3,1]=>[2,1,3,4,5]=>1000=>0001
[3,1,2,4,5]=>[5,4,1,3,2]=>1101=>1011
[3,1,2,5,4]=>[4,5,1,3,2]=>0101=>1010
[3,1,4,2,5]=>[5,1,3,2,4]=>1010=>0101
[3,1,4,5,2]=>[4,1,3,2,5]=>1010=>0101
[3,1,5,2,4]=>[1,3,2,5,4]=>0101=>1010
[3,1,5,4,2]=>[1,3,2,4,5]=>0100=>0010
[3,2,1,4,5]=>[5,4,1,2,3]=>1100=>0011
[3,2,1,5,4]=>[4,5,1,2,3]=>0100=>0010
[3,2,4,1,5]=>[5,2,3,1,4]=>1010=>0101
[3,2,4,5,1]=>[4,2,3,1,5]=>1010=>0101
[3,2,5,1,4]=>[2,3,1,5,4]=>0101=>1010
[3,2,5,4,1]=>[2,3,1,4,5]=>0100=>0010
[3,4,1,2,5]=>[5,3,1,4,2]=>1101=>1011
[3,4,1,5,2]=>[3,1,4,2,5]=>1010=>0101
[3,4,2,1,5]=>[5,3,1,2,4]=>1100=>0011
[3,4,2,5,1]=>[3,2,4,1,5]=>1010=>0101
[3,4,5,1,2]=>[4,3,1,5,2]=>1101=>1011
[3,4,5,2,1]=>[4,3,1,2,5]=>1100=>0011
[3,5,1,2,4]=>[3,1,5,4,2]=>1011=>1101
[3,5,1,4,2]=>[3,1,5,2,4]=>1010=>0101
[3,5,2,1,4]=>[3,1,2,5,4]=>1001=>1001
[3,5,2,4,1]=>[3,2,5,1,4]=>1010=>0101
[3,5,4,1,2]=>[3,1,4,5,2]=>1001=>1001
[3,5,4,2,1]=>[3,1,2,4,5]=>1000=>0001
[4,1,2,3,5]=>[5,1,4,3,2]=>1011=>1101
[4,1,2,5,3]=>[1,4,3,5,2]=>0101=>1010
[4,1,3,2,5]=>[5,1,4,2,3]=>1010=>0101
[4,1,3,5,2]=>[1,4,3,2,5]=>0110=>0110
[4,1,5,2,3]=>[1,4,2,5,3]=>0101=>1010
[4,1,5,3,2]=>[1,4,2,3,5]=>0100=>0010
[4,2,1,3,5]=>[5,1,2,4,3]=>1001=>1001
[4,2,1,5,3]=>[1,2,4,3,5]=>0010=>0100
[4,2,3,1,5]=>[5,2,4,1,3]=>1010=>0101
[4,2,3,5,1]=>[2,4,3,1,5]=>0110=>0110
[4,2,5,1,3]=>[2,4,1,5,3]=>0101=>1010
[4,2,5,3,1]=>[2,4,1,3,5]=>0100=>0010
[4,3,1,2,5]=>[5,1,3,4,2]=>1001=>1001
[4,3,1,5,2]=>[1,3,4,2,5]=>0010=>0100
[4,3,2,1,5]=>[5,1,2,3,4]=>1000=>0001
[4,3,2,5,1]=>[2,3,4,1,5]=>0010=>0100
[4,3,5,1,2]=>[3,4,1,5,2]=>0101=>1010
[4,3,5,2,1]=>[3,4,1,2,5]=>0100=>0010
[4,5,1,2,3]=>[4,1,5,3,2]=>1011=>1101
[4,5,1,3,2]=>[4,1,5,2,3]=>1010=>0101
[4,5,2,1,3]=>[4,1,2,5,3]=>1001=>1001
[4,5,2,3,1]=>[4,2,5,1,3]=>1010=>0101
[4,5,3,1,2]=>[4,1,3,5,2]=>1001=>1001
[4,5,3,2,1]=>[4,1,2,3,5]=>1000=>0001
[5,1,2,3,4]=>[1,5,4,3,2]=>0111=>1110
[5,1,2,4,3]=>[1,5,3,4,2]=>0101=>1010
[5,1,3,2,4]=>[1,5,4,2,3]=>0110=>0110
[5,1,3,4,2]=>[1,5,3,2,4]=>0110=>0110
[5,1,4,2,3]=>[1,5,2,4,3]=>0101=>1010
[5,1,4,3,2]=>[1,5,2,3,4]=>0100=>0010
[5,2,1,3,4]=>[1,2,5,4,3]=>0011=>1100
[5,2,1,4,3]=>[1,2,5,3,4]=>0010=>0100
[5,2,3,1,4]=>[2,5,4,1,3]=>0110=>0110
[5,2,3,4,1]=>[2,5,3,1,4]=>0110=>0110
[5,2,4,1,3]=>[2,5,1,4,3]=>0101=>1010
[5,2,4,3,1]=>[2,5,1,3,4]=>0100=>0010
[5,3,1,2,4]=>[1,3,5,4,2]=>0011=>1100
[5,3,1,4,2]=>[1,3,5,2,4]=>0010=>0100
[5,3,2,1,4]=>[1,2,3,5,4]=>0001=>1000
[5,3,2,4,1]=>[2,3,5,1,4]=>0010=>0100
[5,3,4,1,2]=>[3,5,1,4,2]=>0101=>1010
[5,3,4,2,1]=>[3,5,1,2,4]=>0100=>0010
[5,4,1,2,3]=>[1,4,5,3,2]=>0011=>1100
[5,4,1,3,2]=>[1,4,5,2,3]=>0010=>0100
[5,4,2,1,3]=>[1,2,4,5,3]=>0001=>1000
[5,4,2,3,1]=>[2,4,5,1,3]=>0010=>0100
[5,4,3,1,2]=>[1,3,4,5,2]=>0001=>1000
[5,4,3,2,1]=>[1,2,3,4,5]=>0000=>0000
[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>11111=>11111
[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>01111=>11110
[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>10111=>11101
[1,2,3,5,6,4]=>[5,4,6,3,2,1]=>10111=>11101
[1,2,3,6,4,5]=>[4,6,5,3,2,1]=>01111=>11110
[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>00111=>11100
[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>11011=>11011
[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>01011=>11010
[1,2,4,5,3,6]=>[6,4,3,5,2,1]=>11011=>11011
[1,2,4,5,6,3]=>[5,4,3,6,2,1]=>11011=>11011
[1,2,4,6,3,5]=>[4,3,6,5,2,1]=>10111=>11101
[1,2,4,6,5,3]=>[4,3,5,6,2,1]=>10011=>11001
[1,2,5,3,4,6]=>[6,3,5,4,2,1]=>10111=>11101
[1,2,5,3,6,4]=>[3,5,4,6,2,1]=>01011=>11010
[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>10011=>11001
[1,2,5,4,6,3]=>[4,5,3,6,2,1]=>01011=>11010
[1,2,5,6,3,4]=>[5,3,6,4,2,1]=>10111=>11101
[1,2,5,6,4,3]=>[5,3,4,6,2,1]=>10011=>11001
[1,2,6,3,4,5]=>[3,6,5,4,2,1]=>01111=>11110
[1,2,6,3,5,4]=>[3,6,4,5,2,1]=>01011=>11010
[1,2,6,4,3,5]=>[3,4,6,5,2,1]=>00111=>11100
[1,2,6,4,5,3]=>[4,6,3,5,2,1]=>01011=>11010
[1,2,6,5,3,4]=>[3,5,6,4,2,1]=>00111=>11100
[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>00011=>11000
[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>11101=>10111
[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>01101=>10110
[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>10101=>10101
[1,3,2,5,6,4]=>[5,4,6,2,3,1]=>10101=>10101
[1,3,2,6,4,5]=>[4,6,5,2,3,1]=>01101=>10110
[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>00101=>10100
[1,3,4,2,5,6]=>[6,5,3,2,4,1]=>11101=>10111
[1,3,4,2,6,5]=>[5,6,3,2,4,1]=>01101=>10110
[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>11101=>10111
[1,3,4,5,6,2]=>[5,4,3,2,6,1]=>11101=>10111
[1,3,4,6,2,5]=>[4,3,2,6,5,1]=>11011=>11011
[1,3,4,6,5,2]=>[4,3,2,5,6,1]=>11001=>10011
[1,3,5,2,4,6]=>[6,3,2,5,4,1]=>11011=>11011
[1,3,5,2,6,4]=>[3,2,5,4,6,1]=>10101=>10101
[1,3,5,4,2,6]=>[6,3,2,4,5,1]=>11001=>10011
[1,3,5,4,6,2]=>[4,5,3,2,6,1]=>01101=>10110
[1,3,5,6,2,4]=>[5,3,2,6,4,1]=>11011=>11011
[1,3,5,6,4,2]=>[5,3,2,4,6,1]=>11001=>10011
[1,3,6,2,4,5]=>[3,2,6,5,4,1]=>10111=>11101
[1,3,6,2,5,4]=>[3,2,6,4,5,1]=>10101=>10101
[1,3,6,4,2,5]=>[3,2,4,6,5,1]=>10011=>11001
[1,3,6,4,5,2]=>[4,6,3,2,5,1]=>01101=>10110
[1,3,6,5,2,4]=>[3,2,5,6,4,1]=>10011=>11001
[1,3,6,5,4,2]=>[3,2,4,5,6,1]=>10001=>10001
[1,4,2,3,5,6]=>[6,5,2,4,3,1]=>11011=>11011
[1,4,2,3,6,5]=>[5,6,2,4,3,1]=>01011=>11010
[1,4,2,5,3,6]=>[6,2,4,3,5,1]=>10101=>10101
[1,4,2,5,6,3]=>[5,2,4,3,6,1]=>10101=>10101
[1,4,2,6,3,5]=>[2,4,3,6,5,1]=>01011=>11010
[1,4,2,6,5,3]=>[2,4,3,5,6,1]=>01001=>10010
[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>11001=>10011
[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>01001=>10010
[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>10101=>10101
[1,4,3,5,6,2]=>[5,3,4,2,6,1]=>10101=>10101
[1,4,3,6,2,5]=>[3,4,2,6,5,1]=>01011=>11010
[1,4,3,6,5,2]=>[3,4,2,5,6,1]=>01001=>10010
[1,4,5,2,3,6]=>[6,4,2,5,3,1]=>11011=>11011
[1,4,5,2,6,3]=>[4,2,5,3,6,1]=>10101=>10101
[1,4,5,3,2,6]=>[6,4,2,3,5,1]=>11001=>10011
[1,4,5,3,6,2]=>[4,3,5,2,6,1]=>10101=>10101
[1,4,5,6,2,3]=>[5,4,2,6,3,1]=>11011=>11011
[1,4,5,6,3,2]=>[5,4,2,3,6,1]=>11001=>10011
[1,4,6,2,3,5]=>[4,2,6,5,3,1]=>10111=>11101
[1,4,6,2,5,3]=>[4,2,6,3,5,1]=>10101=>10101
[1,4,6,3,2,5]=>[4,2,3,6,5,1]=>10011=>11001
[1,4,6,3,5,2]=>[4,3,6,2,5,1]=>10101=>10101
[1,4,6,5,2,3]=>[4,2,5,6,3,1]=>10011=>11001
[1,4,6,5,3,2]=>[4,2,3,5,6,1]=>10001=>10001
[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>10111=>11101
[1,5,2,3,6,4]=>[2,5,4,6,3,1]=>01011=>11010
[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>10101=>10101
[1,5,2,4,6,3]=>[2,5,4,3,6,1]=>01101=>10110
[1,5,2,6,3,4]=>[2,5,3,6,4,1]=>01011=>11010
[1,5,2,6,4,3]=>[2,5,3,4,6,1]=>01001=>10010
[1,5,3,2,4,6]=>[6,2,3,5,4,1]=>10011=>11001
[1,5,3,2,6,4]=>[2,3,5,4,6,1]=>00101=>10100
[1,5,3,4,2,6]=>[6,3,5,2,4,1]=>10101=>10101
[1,5,3,4,6,2]=>[3,5,4,2,6,1]=>01101=>10110
[1,5,3,6,2,4]=>[3,5,2,6,4,1]=>01011=>11010
[1,5,3,6,4,2]=>[3,5,2,4,6,1]=>01001=>10010
[1,5,4,2,3,6]=>[6,2,4,5,3,1]=>10011=>11001
[1,5,4,2,6,3]=>[2,4,5,3,6,1]=>00101=>10100
[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>10001=>10001
[1,5,4,3,6,2]=>[3,4,5,2,6,1]=>00101=>10100
[1,5,4,6,2,3]=>[4,5,2,6,3,1]=>01011=>11010
[1,5,4,6,3,2]=>[4,5,2,3,6,1]=>01001=>10010
[1,5,6,2,3,4]=>[5,2,6,4,3,1]=>10111=>11101
[1,5,6,2,4,3]=>[5,2,6,3,4,1]=>10101=>10101
[1,5,6,3,2,4]=>[5,2,3,6,4,1]=>10011=>11001
[1,5,6,3,4,2]=>[5,3,6,2,4,1]=>10101=>10101
[1,5,6,4,2,3]=>[5,2,4,6,3,1]=>10011=>11001
[1,5,6,4,3,2]=>[5,2,3,4,6,1]=>10001=>10001
[1,6,2,3,4,5]=>[2,6,5,4,3,1]=>01111=>11110
[1,6,2,3,5,4]=>[2,6,4,5,3,1]=>01011=>11010
[1,6,2,4,3,5]=>[2,6,5,3,4,1]=>01101=>10110
[1,6,2,4,5,3]=>[2,6,4,3,5,1]=>01101=>10110
[1,6,2,5,3,4]=>[2,6,3,5,4,1]=>01011=>11010
[1,6,2,5,4,3]=>[2,6,3,4,5,1]=>01001=>10010
[1,6,3,2,4,5]=>[2,3,6,5,4,1]=>00111=>11100
[1,6,3,2,5,4]=>[2,3,6,4,5,1]=>00101=>10100
[1,6,3,4,2,5]=>[3,6,5,2,4,1]=>01101=>10110
[1,6,3,4,5,2]=>[3,6,4,2,5,1]=>01101=>10110
[1,6,3,5,2,4]=>[3,6,2,5,4,1]=>01011=>11010
[1,6,3,5,4,2]=>[3,6,2,4,5,1]=>01001=>10010
[1,6,4,2,3,5]=>[2,4,6,5,3,1]=>00111=>11100
[1,6,4,2,5,3]=>[2,4,6,3,5,1]=>00101=>10100
[1,6,4,3,2,5]=>[2,3,4,6,5,1]=>00011=>11000
[1,6,4,3,5,2]=>[3,4,6,2,5,1]=>00101=>10100
[1,6,4,5,2,3]=>[4,6,2,5,3,1]=>01011=>11010
[1,6,4,5,3,2]=>[4,6,2,3,5,1]=>01001=>10010
[1,6,5,2,3,4]=>[2,5,6,4,3,1]=>00111=>11100
[1,6,5,2,4,3]=>[2,5,6,3,4,1]=>00101=>10100
[1,6,5,3,2,4]=>[2,3,5,6,4,1]=>00011=>11000
[1,6,5,3,4,2]=>[3,5,6,2,4,1]=>00101=>10100
[1,6,5,4,2,3]=>[2,4,5,6,3,1]=>00011=>11000
[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>00001=>10000
[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>11110=>01111
[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>01110=>01110
[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>10110=>01101
[2,1,3,5,6,4]=>[5,4,6,3,1,2]=>10110=>01101
[2,1,3,6,4,5]=>[4,6,5,3,1,2]=>01110=>01110
[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>00110=>01100
[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>11010=>01011
[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>01010=>01010
[2,1,4,5,3,6]=>[6,4,3,5,1,2]=>11010=>01011
[2,1,4,5,6,3]=>[5,4,3,6,1,2]=>11010=>01011
[2,1,4,6,3,5]=>[4,3,6,5,1,2]=>10110=>01101
[2,1,4,6,5,3]=>[4,3,5,6,1,2]=>10010=>01001
[2,1,5,3,4,6]=>[6,3,5,4,1,2]=>10110=>01101
[2,1,5,3,6,4]=>[3,5,4,6,1,2]=>01010=>01010
[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>10010=>01001
[2,1,5,4,6,3]=>[4,5,3,6,1,2]=>01010=>01010
[2,1,5,6,3,4]=>[5,3,6,4,1,2]=>10110=>01101
[2,1,5,6,4,3]=>[5,3,4,6,1,2]=>10010=>01001
[2,1,6,3,4,5]=>[3,6,5,4,1,2]=>01110=>01110
[2,1,6,3,5,4]=>[3,6,4,5,1,2]=>01010=>01010
[2,1,6,4,3,5]=>[3,4,6,5,1,2]=>00110=>01100
[2,1,6,4,5,3]=>[4,6,3,5,1,2]=>01010=>01010
[2,1,6,5,3,4]=>[3,5,6,4,1,2]=>00110=>01100
[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>00010=>01000
[2,3,1,4,5,6]=>[6,5,4,2,1,3]=>11110=>01111
[2,3,1,4,6,5]=>[5,6,4,2,1,3]=>01110=>01110
[2,3,1,5,4,6]=>[6,4,5,2,1,3]=>10110=>01101
[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>10110=>01101
[2,3,1,6,4,5]=>[4,6,5,2,1,3]=>01110=>01110
[2,3,1,6,5,4]=>[4,5,6,2,1,3]=>00110=>01100
[2,3,4,1,5,6]=>[6,5,3,2,1,4]=>11110=>01111
[2,3,4,1,6,5]=>[5,6,3,2,1,4]=>01110=>01110
[2,3,4,5,1,6]=>[6,4,3,2,1,5]=>11110=>01111
[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>11110=>01111
[2,3,4,6,1,5]=>[4,3,2,1,6,5]=>11101=>10111
[2,3,4,6,5,1]=>[4,3,2,1,5,6]=>11100=>00111
[2,3,5,1,4,6]=>[6,3,2,1,5,4]=>11101=>10111
[2,3,5,1,6,4]=>[3,2,1,5,4,6]=>11010=>01011
[2,3,5,4,1,6]=>[6,3,2,1,4,5]=>11100=>00111
[2,3,5,4,6,1]=>[4,5,3,2,1,6]=>01110=>01110
[2,3,5,6,1,4]=>[5,3,2,1,6,4]=>11101=>10111
[2,3,5,6,4,1]=>[5,3,2,1,4,6]=>11100=>00111
[2,3,6,1,4,5]=>[3,2,1,6,5,4]=>11011=>11011
[2,3,6,1,5,4]=>[3,2,1,6,4,5]=>11010=>01011
[2,3,6,4,1,5]=>[3,2,1,4,6,5]=>11001=>10011
[2,3,6,4,5,1]=>[4,6,3,2,1,5]=>01110=>01110
[2,3,6,5,1,4]=>[3,2,1,5,6,4]=>11001=>10011
[2,3,6,5,4,1]=>[3,2,1,4,5,6]=>11000=>00011
[2,4,1,3,5,6]=>[6,5,2,1,4,3]=>11101=>10111
[2,4,1,3,6,5]=>[5,6,2,1,4,3]=>01101=>10110
[2,4,1,5,3,6]=>[6,2,1,4,3,5]=>11010=>01011
[2,4,1,5,6,3]=>[5,2,1,4,3,6]=>11010=>01011
[2,4,1,6,3,5]=>[2,1,4,3,6,5]=>10101=>10101
[2,4,1,6,5,3]=>[2,1,4,3,5,6]=>10100=>00101
[2,4,3,1,5,6]=>[6,5,2,1,3,4]=>11100=>00111
[2,4,3,1,6,5]=>[5,6,2,1,3,4]=>01100=>00110
[2,4,3,5,1,6]=>[6,3,4,2,1,5]=>10110=>01101
[2,4,3,5,6,1]=>[5,3,4,2,1,6]=>10110=>01101
[2,4,3,6,1,5]=>[3,4,2,1,6,5]=>01101=>10110
[2,4,3,6,5,1]=>[3,4,2,1,5,6]=>01100=>00110
[2,4,5,1,3,6]=>[6,4,2,1,5,3]=>11101=>10111
[2,4,5,1,6,3]=>[4,2,1,5,3,6]=>11010=>01011
[2,4,5,3,1,6]=>[6,4,2,1,3,5]=>11100=>00111
[2,4,5,3,6,1]=>[4,3,5,2,1,6]=>10110=>01101
[2,4,5,6,1,3]=>[5,4,2,1,6,3]=>11101=>10111
[2,4,5,6,3,1]=>[5,4,2,1,3,6]=>11100=>00111
[2,4,6,1,3,5]=>[4,2,1,6,5,3]=>11011=>11011
[2,4,6,1,5,3]=>[4,2,1,6,3,5]=>11010=>01011
[2,4,6,3,1,5]=>[4,2,1,3,6,5]=>11001=>10011
[2,4,6,3,5,1]=>[4,3,6,2,1,5]=>10110=>01101
[2,4,6,5,1,3]=>[4,2,1,5,6,3]=>11001=>10011
[2,4,6,5,3,1]=>[4,2,1,3,5,6]=>11000=>00011
[2,5,1,3,4,6]=>[6,2,1,5,4,3]=>11011=>11011
[2,5,1,3,6,4]=>[2,1,5,4,6,3]=>10101=>10101
[2,5,1,4,3,6]=>[6,2,1,5,3,4]=>11010=>01011
[2,5,1,4,6,3]=>[2,1,5,4,3,6]=>10110=>01101
[2,5,1,6,3,4]=>[2,1,5,3,6,4]=>10101=>10101
[2,5,1,6,4,3]=>[2,1,5,3,4,6]=>10100=>00101
[2,5,3,1,4,6]=>[6,2,1,3,5,4]=>11001=>10011
[2,5,3,1,6,4]=>[2,1,3,5,4,6]=>10010=>01001
[2,5,3,4,1,6]=>[6,3,5,2,1,4]=>10110=>01101
[2,5,3,4,6,1]=>[3,5,4,2,1,6]=>01110=>01110
[2,5,3,6,1,4]=>[3,5,2,1,6,4]=>01101=>10110
[2,5,3,6,4,1]=>[3,5,2,1,4,6]=>01100=>00110
[2,5,4,1,3,6]=>[6,2,1,4,5,3]=>11001=>10011
[2,5,4,1,6,3]=>[2,1,4,5,3,6]=>10010=>01001
[2,5,4,3,1,6]=>[6,2,1,3,4,5]=>11000=>00011
[2,5,4,3,6,1]=>[3,4,5,2,1,6]=>00110=>01100
[2,5,4,6,1,3]=>[4,5,2,1,6,3]=>01101=>10110
[2,5,4,6,3,1]=>[4,5,2,1,3,6]=>01100=>00110
[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>11011=>11011
[2,5,6,1,4,3]=>[5,2,1,6,3,4]=>11010=>01011
[2,5,6,3,1,4]=>[5,2,1,3,6,4]=>11001=>10011
[2,5,6,3,4,1]=>[5,3,6,2,1,4]=>10110=>01101
[2,5,6,4,1,3]=>[5,2,1,4,6,3]=>11001=>10011
[2,5,6,4,3,1]=>[5,2,1,3,4,6]=>11000=>00011
[2,6,1,3,4,5]=>[2,1,6,5,4,3]=>10111=>11101
[2,6,1,3,5,4]=>[2,1,6,4,5,3]=>10101=>10101
[2,6,1,4,3,5]=>[2,1,6,5,3,4]=>10110=>01101
[2,6,1,4,5,3]=>[2,1,6,4,3,5]=>10110=>01101
[2,6,1,5,3,4]=>[2,1,6,3,5,4]=>10101=>10101
[2,6,1,5,4,3]=>[2,1,6,3,4,5]=>10100=>00101
[2,6,3,1,4,5]=>[2,1,3,6,5,4]=>10011=>11001
[2,6,3,1,5,4]=>[2,1,3,6,4,5]=>10010=>01001
[2,6,3,4,1,5]=>[3,6,5,2,1,4]=>01110=>01110
[2,6,3,4,5,1]=>[3,6,4,2,1,5]=>01110=>01110
[2,6,3,5,1,4]=>[3,6,2,1,5,4]=>01101=>10110
[2,6,3,5,4,1]=>[3,6,2,1,4,5]=>01100=>00110
[2,6,4,1,3,5]=>[2,1,4,6,5,3]=>10011=>11001
[2,6,4,1,5,3]=>[2,1,4,6,3,5]=>10010=>01001
[2,6,4,3,1,5]=>[2,1,3,4,6,5]=>10001=>10001
[2,6,4,3,5,1]=>[3,4,6,2,1,5]=>00110=>01100
[2,6,4,5,1,3]=>[4,6,2,1,5,3]=>01101=>10110
[2,6,4,5,3,1]=>[4,6,2,1,3,5]=>01100=>00110
[2,6,5,1,3,4]=>[2,1,5,6,4,3]=>10011=>11001
[2,6,5,1,4,3]=>[2,1,5,6,3,4]=>10010=>01001
[2,6,5,3,1,4]=>[2,1,3,5,6,4]=>10001=>10001
[2,6,5,3,4,1]=>[3,5,6,2,1,4]=>00110=>01100
[2,6,5,4,1,3]=>[2,1,4,5,6,3]=>10001=>10001
[2,6,5,4,3,1]=>[2,1,3,4,5,6]=>10000=>00001
[3,1,2,4,5,6]=>[6,5,4,1,3,2]=>11101=>10111
[3,1,2,4,6,5]=>[5,6,4,1,3,2]=>01101=>10110
[3,1,2,5,4,6]=>[6,4,5,1,3,2]=>10101=>10101
[3,1,2,5,6,4]=>[5,4,6,1,3,2]=>10101=>10101
[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>01101=>10110
[3,1,2,6,5,4]=>[4,5,6,1,3,2]=>00101=>10100
[3,1,4,2,5,6]=>[6,5,1,3,2,4]=>11010=>01011
[3,1,4,2,6,5]=>[5,6,1,3,2,4]=>01010=>01010
[3,1,4,5,2,6]=>[6,4,1,3,2,5]=>11010=>01011
[3,1,4,5,6,2]=>[5,4,1,3,2,6]=>11010=>01011
[3,1,4,6,2,5]=>[4,1,3,2,6,5]=>10101=>10101
[3,1,4,6,5,2]=>[4,1,3,2,5,6]=>10100=>00101
[3,1,5,2,4,6]=>[6,1,3,2,5,4]=>10101=>10101
[3,1,5,2,6,4]=>[1,3,2,5,4,6]=>01010=>01010
[3,1,5,4,2,6]=>[6,1,3,2,4,5]=>10100=>00101
[3,1,5,4,6,2]=>[4,5,1,3,2,6]=>01010=>01010
[3,1,5,6,2,4]=>[5,1,3,2,6,4]=>10101=>10101
[3,1,5,6,4,2]=>[5,1,3,2,4,6]=>10100=>00101
[3,1,6,2,4,5]=>[1,3,2,6,5,4]=>01011=>11010
[3,1,6,2,5,4]=>[1,3,2,6,4,5]=>01010=>01010
[3,1,6,4,2,5]=>[1,3,2,4,6,5]=>01001=>10010
[3,1,6,4,5,2]=>[4,6,1,3,2,5]=>01010=>01010
[3,1,6,5,2,4]=>[1,3,2,5,6,4]=>01001=>10010
[3,1,6,5,4,2]=>[1,3,2,4,5,6]=>01000=>00010
[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>11100=>00111
[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>01100=>00110
[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>10100=>00101
[3,2,1,5,6,4]=>[5,4,6,1,2,3]=>10100=>00101
[3,2,1,6,4,5]=>[4,6,5,1,2,3]=>01100=>00110
[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>00100=>00100
[3,2,4,1,5,6]=>[6,5,2,3,1,4]=>11010=>01011
[3,2,4,1,6,5]=>[5,6,2,3,1,4]=>01010=>01010
[3,2,4,5,1,6]=>[6,4,2,3,1,5]=>11010=>01011
[3,2,4,5,6,1]=>[5,4,2,3,1,6]=>11010=>01011
[3,2,4,6,1,5]=>[4,2,3,1,6,5]=>10101=>10101
[3,2,4,6,5,1]=>[4,2,3,1,5,6]=>10100=>00101
[3,2,5,1,4,6]=>[6,2,3,1,5,4]=>10101=>10101
[3,2,5,1,6,4]=>[2,3,1,5,4,6]=>01010=>01010
[3,2,5,4,1,6]=>[6,2,3,1,4,5]=>10100=>00101
[3,2,5,4,6,1]=>[4,5,2,3,1,6]=>01010=>01010
[3,2,5,6,1,4]=>[5,2,3,1,6,4]=>10101=>10101
[3,2,5,6,4,1]=>[5,2,3,1,4,6]=>10100=>00101
[3,2,6,1,4,5]=>[2,3,1,6,5,4]=>01011=>11010
[3,2,6,1,5,4]=>[2,3,1,6,4,5]=>01010=>01010
[3,2,6,4,1,5]=>[2,3,1,4,6,5]=>01001=>10010
[3,2,6,4,5,1]=>[4,6,2,3,1,5]=>01010=>01010
[3,2,6,5,1,4]=>[2,3,1,5,6,4]=>01001=>10010
[3,2,6,5,4,1]=>[2,3,1,4,5,6]=>01000=>00010
[3,4,1,2,5,6]=>[6,5,3,1,4,2]=>11101=>10111
[3,4,1,2,6,5]=>[5,6,3,1,4,2]=>01101=>10110
[3,4,1,5,2,6]=>[6,3,1,4,2,5]=>11010=>01011
[3,4,1,5,6,2]=>[5,3,1,4,2,6]=>11010=>01011
[3,4,1,6,2,5]=>[3,1,4,2,6,5]=>10101=>10101
[3,4,1,6,5,2]=>[3,1,4,2,5,6]=>10100=>00101
[3,4,2,1,5,6]=>[6,5,3,1,2,4]=>11100=>00111
[3,4,2,1,6,5]=>[5,6,3,1,2,4]=>01100=>00110
[3,4,2,5,1,6]=>[6,3,2,4,1,5]=>11010=>01011
[3,4,2,5,6,1]=>[5,3,2,4,1,6]=>11010=>01011
[3,4,2,6,1,5]=>[3,2,4,1,6,5]=>10101=>10101
[3,4,2,6,5,1]=>[3,2,4,1,5,6]=>10100=>00101
[3,4,5,1,2,6]=>[6,4,3,1,5,2]=>11101=>10111
[3,4,5,1,6,2]=>[4,3,1,5,2,6]=>11010=>01011
[3,4,5,2,1,6]=>[6,4,3,1,2,5]=>11100=>00111
[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>11010=>01011
[3,4,5,6,1,2]=>[5,4,3,1,6,2]=>11101=>10111
[3,4,5,6,2,1]=>[5,4,3,1,2,6]=>11100=>00111
[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>11011=>11011
[3,4,6,1,5,2]=>[4,3,1,6,2,5]=>11010=>01011
[3,4,6,2,1,5]=>[4,3,1,2,6,5]=>11001=>10011
[3,4,6,2,5,1]=>[4,3,2,6,1,5]=>11010=>01011
[3,4,6,5,1,2]=>[4,3,1,5,6,2]=>11001=>10011
[3,4,6,5,2,1]=>[4,3,1,2,5,6]=>11000=>00011
[3,5,1,2,4,6]=>[6,3,1,5,4,2]=>11011=>11011
[3,5,1,2,6,4]=>[3,1,5,4,6,2]=>10101=>10101
[3,5,1,4,2,6]=>[6,3,1,5,2,4]=>11010=>01011
[3,5,1,4,6,2]=>[3,1,5,4,2,6]=>10110=>01101
[3,5,1,6,2,4]=>[3,1,5,2,6,4]=>10101=>10101
[3,5,1,6,4,2]=>[3,1,5,2,4,6]=>10100=>00101
[3,5,2,1,4,6]=>[6,3,1,2,5,4]=>11001=>10011
[3,5,2,1,6,4]=>[3,1,2,5,4,6]=>10010=>01001
[3,5,2,4,1,6]=>[6,3,2,5,1,4]=>11010=>01011
[3,5,2,4,6,1]=>[3,2,5,4,1,6]=>10110=>01101
[3,5,2,6,1,4]=>[3,2,5,1,6,4]=>10101=>10101
[3,5,2,6,4,1]=>[3,2,5,1,4,6]=>10100=>00101
[3,5,4,1,2,6]=>[6,3,1,4,5,2]=>11001=>10011
[3,5,4,1,6,2]=>[3,1,4,5,2,6]=>10010=>01001
[3,5,4,2,1,6]=>[6,3,1,2,4,5]=>11000=>00011
[3,5,4,2,6,1]=>[3,2,4,5,1,6]=>10010=>01001
[3,5,4,6,1,2]=>[4,5,3,1,6,2]=>01101=>10110
[3,5,4,6,2,1]=>[4,5,3,1,2,6]=>01100=>00110
[3,5,6,1,2,4]=>[5,3,1,6,4,2]=>11011=>11011
[3,5,6,1,4,2]=>[5,3,1,6,2,4]=>11010=>01011
[3,5,6,2,1,4]=>[5,3,1,2,6,4]=>11001=>10011
[3,5,6,2,4,1]=>[5,3,2,6,1,4]=>11010=>01011
[3,5,6,4,1,2]=>[5,3,1,4,6,2]=>11001=>10011
[3,5,6,4,2,1]=>[5,3,1,2,4,6]=>11000=>00011
[3,6,1,2,4,5]=>[3,1,6,5,4,2]=>10111=>11101
[3,6,1,2,5,4]=>[3,1,6,4,5,2]=>10101=>10101
[3,6,1,4,2,5]=>[3,1,6,5,2,4]=>10110=>01101
[3,6,1,4,5,2]=>[3,1,6,4,2,5]=>10110=>01101
[3,6,1,5,2,4]=>[3,1,6,2,5,4]=>10101=>10101
[3,6,1,5,4,2]=>[3,1,6,2,4,5]=>10100=>00101
[3,6,2,1,4,5]=>[3,1,2,6,5,4]=>10011=>11001
[3,6,2,1,5,4]=>[3,1,2,6,4,5]=>10010=>01001
[3,6,2,4,1,5]=>[3,2,6,5,1,4]=>10110=>01101
[3,6,2,4,5,1]=>[3,2,6,4,1,5]=>10110=>01101
[3,6,2,5,1,4]=>[3,2,6,1,5,4]=>10101=>10101
[3,6,2,5,4,1]=>[3,2,6,1,4,5]=>10100=>00101
[3,6,4,1,2,5]=>[3,1,4,6,5,2]=>10011=>11001
[3,6,4,1,5,2]=>[3,1,4,6,2,5]=>10010=>01001
[3,6,4,2,1,5]=>[3,1,2,4,6,5]=>10001=>10001
[3,6,4,2,5,1]=>[3,2,4,6,1,5]=>10010=>01001
[3,6,4,5,1,2]=>[4,6,3,1,5,2]=>01101=>10110
[3,6,4,5,2,1]=>[4,6,3,1,2,5]=>01100=>00110
[3,6,5,1,2,4]=>[3,1,5,6,4,2]=>10011=>11001
[3,6,5,1,4,2]=>[3,1,5,6,2,4]=>10010=>01001
[3,6,5,2,1,4]=>[3,1,2,5,6,4]=>10001=>10001
[3,6,5,2,4,1]=>[3,2,5,6,1,4]=>10010=>01001
[3,6,5,4,1,2]=>[3,1,4,5,6,2]=>10001=>10001
[3,6,5,4,2,1]=>[3,1,2,4,5,6]=>10000=>00001
[4,1,2,3,5,6]=>[6,5,1,4,3,2]=>11011=>11011
[4,1,2,3,6,5]=>[5,6,1,4,3,2]=>01011=>11010
[4,1,2,5,3,6]=>[6,1,4,3,5,2]=>10101=>10101
[4,1,2,5,6,3]=>[5,1,4,3,6,2]=>10101=>10101
[4,1,2,6,3,5]=>[1,4,3,6,5,2]=>01011=>11010
[4,1,2,6,5,3]=>[1,4,3,5,6,2]=>01001=>10010
[4,1,3,2,5,6]=>[6,5,1,4,2,3]=>11010=>01011
[4,1,3,2,6,5]=>[5,6,1,4,2,3]=>01010=>01010
[4,1,3,5,2,6]=>[6,1,4,3,2,5]=>10110=>01101
[4,1,3,5,6,2]=>[5,1,4,3,2,6]=>10110=>01101
[4,1,3,6,2,5]=>[1,4,3,2,6,5]=>01101=>10110
[4,1,3,6,5,2]=>[1,4,3,2,5,6]=>01100=>00110
[4,1,5,2,3,6]=>[6,1,4,2,5,3]=>10101=>10101
[4,1,5,2,6,3]=>[1,4,2,5,3,6]=>01010=>01010
[4,1,5,3,2,6]=>[6,1,4,2,3,5]=>10100=>00101
[4,1,5,3,6,2]=>[1,4,3,5,2,6]=>01010=>01010
[4,1,5,6,2,3]=>[5,1,4,2,6,3]=>10101=>10101
[4,1,5,6,3,2]=>[5,1,4,2,3,6]=>10100=>00101
[4,1,6,2,3,5]=>[1,4,2,6,5,3]=>01011=>11010
[4,1,6,2,5,3]=>[1,4,2,6,3,5]=>01010=>01010
[4,1,6,3,2,5]=>[1,4,2,3,6,5]=>01001=>10010
[4,1,6,3,5,2]=>[1,4,3,6,2,5]=>01010=>01010
[4,1,6,5,2,3]=>[1,4,2,5,6,3]=>01001=>10010
[4,1,6,5,3,2]=>[1,4,2,3,5,6]=>01000=>00010
[4,2,1,3,5,6]=>[6,5,1,2,4,3]=>11001=>10011
[4,2,1,3,6,5]=>[5,6,1,2,4,3]=>01001=>10010
[4,2,1,5,3,6]=>[6,1,2,4,3,5]=>10010=>01001
[4,2,1,5,6,3]=>[5,1,2,4,3,6]=>10010=>01001
[4,2,1,6,3,5]=>[1,2,4,3,6,5]=>00101=>10100
[4,2,1,6,5,3]=>[1,2,4,3,5,6]=>00100=>00100
[4,2,3,1,5,6]=>[6,5,2,4,1,3]=>11010=>01011
[4,2,3,1,6,5]=>[5,6,2,4,1,3]=>01010=>01010
[4,2,3,5,1,6]=>[6,2,4,3,1,5]=>10110=>01101
[4,2,3,5,6,1]=>[5,2,4,3,1,6]=>10110=>01101
[4,2,3,6,1,5]=>[2,4,3,1,6,5]=>01101=>10110
[4,2,3,6,5,1]=>[2,4,3,1,5,6]=>01100=>00110
[4,2,5,1,3,6]=>[6,2,4,1,5,3]=>10101=>10101
[4,2,5,1,6,3]=>[2,4,1,5,3,6]=>01010=>01010
[4,2,5,3,1,6]=>[6,2,4,1,3,5]=>10100=>00101
[4,2,5,3,6,1]=>[2,4,3,5,1,6]=>01010=>01010
[4,2,5,6,1,3]=>[5,2,4,1,6,3]=>10101=>10101
[4,2,5,6,3,1]=>[5,2,4,1,3,6]=>10100=>00101
[4,2,6,1,3,5]=>[2,4,1,6,5,3]=>01011=>11010
[4,2,6,1,5,3]=>[2,4,1,6,3,5]=>01010=>01010
[4,2,6,3,1,5]=>[2,4,1,3,6,5]=>01001=>10010
[4,2,6,3,5,1]=>[2,4,3,6,1,5]=>01010=>01010
[4,2,6,5,1,3]=>[2,4,1,5,6,3]=>01001=>10010
[4,2,6,5,3,1]=>[2,4,1,3,5,6]=>01000=>00010
[4,3,1,2,5,6]=>[6,5,1,3,4,2]=>11001=>10011
[4,3,1,2,6,5]=>[5,6,1,3,4,2]=>01001=>10010
[4,3,1,5,2,6]=>[6,1,3,4,2,5]=>10010=>01001
[4,3,1,5,6,2]=>[5,1,3,4,2,6]=>10010=>01001
[4,3,1,6,2,5]=>[1,3,4,2,6,5]=>00101=>10100
[4,3,1,6,5,2]=>[1,3,4,2,5,6]=>00100=>00100
[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>11000=>00011
[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>01000=>00010
[4,3,2,5,1,6]=>[6,2,3,4,1,5]=>10010=>01001
[4,3,2,5,6,1]=>[5,2,3,4,1,6]=>10010=>01001
[4,3,2,6,1,5]=>[2,3,4,1,6,5]=>00101=>10100
[4,3,2,6,5,1]=>[2,3,4,1,5,6]=>00100=>00100
[4,3,5,1,2,6]=>[6,3,4,1,5,2]=>10101=>10101
[4,3,5,1,6,2]=>[3,4,1,5,2,6]=>01010=>01010
[4,3,5,2,1,6]=>[6,3,4,1,2,5]=>10100=>00101
[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>01010=>01010
[4,3,5,6,1,2]=>[5,3,4,1,6,2]=>10101=>10101
[4,3,5,6,2,1]=>[5,3,4,1,2,6]=>10100=>00101
[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>01011=>11010
[4,3,6,1,5,2]=>[3,4,1,6,2,5]=>01010=>01010
[4,3,6,2,1,5]=>[3,4,1,2,6,5]=>01001=>10010
[4,3,6,2,5,1]=>[3,4,2,6,1,5]=>01010=>01010
[4,3,6,5,1,2]=>[3,4,1,5,6,2]=>01001=>10010
[4,3,6,5,2,1]=>[3,4,1,2,5,6]=>01000=>00010
[4,5,1,2,3,6]=>[6,4,1,5,3,2]=>11011=>11011
[4,5,1,2,6,3]=>[4,1,5,3,6,2]=>10101=>10101
[4,5,1,3,2,6]=>[6,4,1,5,2,3]=>11010=>01011
[4,5,1,3,6,2]=>[4,1,5,3,2,6]=>10110=>01101
[4,5,1,6,2,3]=>[4,1,5,2,6,3]=>10101=>10101
[4,5,1,6,3,2]=>[4,1,5,2,3,6]=>10100=>00101
[4,5,2,1,3,6]=>[6,4,1,2,5,3]=>11001=>10011
[4,5,2,1,6,3]=>[4,1,2,5,3,6]=>10010=>01001
[4,5,2,3,1,6]=>[6,4,2,5,1,3]=>11010=>01011
[4,5,2,3,6,1]=>[4,2,5,3,1,6]=>10110=>01101
[4,5,2,6,1,3]=>[4,2,5,1,6,3]=>10101=>10101
[4,5,2,6,3,1]=>[4,2,5,1,3,6]=>10100=>00101
[4,5,3,1,2,6]=>[6,4,1,3,5,2]=>11001=>10011
[4,5,3,1,6,2]=>[4,1,3,5,2,6]=>10010=>01001
[4,5,3,2,1,6]=>[6,4,1,2,3,5]=>11000=>00011
[4,5,3,2,6,1]=>[4,2,3,5,1,6]=>10010=>01001
[4,5,3,6,1,2]=>[4,3,5,1,6,2]=>10101=>10101
[4,5,3,6,2,1]=>[4,3,5,1,2,6]=>10100=>00101
[4,5,6,1,2,3]=>[5,4,1,6,3,2]=>11011=>11011
[4,5,6,1,3,2]=>[5,4,1,6,2,3]=>11010=>01011
[4,5,6,2,1,3]=>[5,4,1,2,6,3]=>11001=>10011
[4,5,6,2,3,1]=>[5,4,2,6,1,3]=>11010=>01011
[4,5,6,3,1,2]=>[5,4,1,3,6,2]=>11001=>10011
[4,5,6,3,2,1]=>[5,4,1,2,3,6]=>11000=>00011
[4,6,1,2,3,5]=>[4,1,6,5,3,2]=>10111=>11101
[4,6,1,2,5,3]=>[4,1,6,3,5,2]=>10101=>10101
[4,6,1,3,2,5]=>[4,1,6,5,2,3]=>10110=>01101
[4,6,1,3,5,2]=>[4,1,6,3,2,5]=>10110=>01101
[4,6,1,5,2,3]=>[4,1,6,2,5,3]=>10101=>10101
[4,6,1,5,3,2]=>[4,1,6,2,3,5]=>10100=>00101
[4,6,2,1,3,5]=>[4,1,2,6,5,3]=>10011=>11001
[4,6,2,1,5,3]=>[4,1,2,6,3,5]=>10010=>01001
[4,6,2,3,1,5]=>[4,2,6,5,1,3]=>10110=>01101
[4,6,2,3,5,1]=>[4,2,6,3,1,5]=>10110=>01101
[4,6,2,5,1,3]=>[4,2,6,1,5,3]=>10101=>10101
[4,6,2,5,3,1]=>[4,2,6,1,3,5]=>10100=>00101
[4,6,3,1,2,5]=>[4,1,3,6,5,2]=>10011=>11001
[4,6,3,1,5,2]=>[4,1,3,6,2,5]=>10010=>01001
[4,6,3,2,1,5]=>[4,1,2,3,6,5]=>10001=>10001
[4,6,3,2,5,1]=>[4,2,3,6,1,5]=>10010=>01001
[4,6,3,5,1,2]=>[4,3,6,1,5,2]=>10101=>10101
[4,6,3,5,2,1]=>[4,3,6,1,2,5]=>10100=>00101
[4,6,5,1,2,3]=>[4,1,5,6,3,2]=>10011=>11001
[4,6,5,1,3,2]=>[4,1,5,6,2,3]=>10010=>01001
[4,6,5,2,1,3]=>[4,1,2,5,6,3]=>10001=>10001
[4,6,5,2,3,1]=>[4,2,5,6,1,3]=>10010=>01001
[4,6,5,3,1,2]=>[4,1,3,5,6,2]=>10001=>10001
[4,6,5,3,2,1]=>[4,1,2,3,5,6]=>10000=>00001
[5,1,2,3,4,6]=>[6,1,5,4,3,2]=>10111=>11101
[5,1,2,3,6,4]=>[1,5,4,6,3,2]=>01011=>11010
[5,1,2,4,3,6]=>[6,1,5,3,4,2]=>10101=>10101
[5,1,2,4,6,3]=>[1,5,4,3,6,2]=>01101=>10110
[5,1,2,6,3,4]=>[1,5,3,6,4,2]=>01011=>11010
[5,1,2,6,4,3]=>[1,5,3,4,6,2]=>01001=>10010
[5,1,3,2,4,6]=>[6,1,5,4,2,3]=>10110=>01101
[5,1,3,2,6,4]=>[1,5,4,6,2,3]=>01010=>01010
[5,1,3,4,2,6]=>[6,1,5,3,2,4]=>10110=>01101
[5,1,3,4,6,2]=>[1,5,4,3,2,6]=>01110=>01110
[5,1,3,6,2,4]=>[1,5,3,2,6,4]=>01101=>10110
[5,1,3,6,4,2]=>[1,5,3,2,4,6]=>01100=>00110
[5,1,4,2,3,6]=>[6,1,5,2,4,3]=>10101=>10101
[5,1,4,2,6,3]=>[1,5,2,4,3,6]=>01010=>01010
[5,1,4,3,2,6]=>[6,1,5,2,3,4]=>10100=>00101
[5,1,4,3,6,2]=>[1,5,3,4,2,6]=>01010=>01010
[5,1,4,6,2,3]=>[1,5,4,2,6,3]=>01101=>10110
[5,1,4,6,3,2]=>[1,5,4,2,3,6]=>01100=>00110
[5,1,6,2,3,4]=>[1,5,2,6,4,3]=>01011=>11010
[5,1,6,2,4,3]=>[1,5,2,6,3,4]=>01010=>01010
[5,1,6,3,2,4]=>[1,5,2,3,6,4]=>01001=>10010
[5,1,6,3,4,2]=>[1,5,3,6,2,4]=>01010=>01010
[5,1,6,4,2,3]=>[1,5,2,4,6,3]=>01001=>10010
[5,1,6,4,3,2]=>[1,5,2,3,4,6]=>01000=>00010
[5,2,1,3,4,6]=>[6,1,2,5,4,3]=>10011=>11001
[5,2,1,3,6,4]=>[1,2,5,4,6,3]=>00101=>10100
[5,2,1,4,3,6]=>[6,1,2,5,3,4]=>10010=>01001
[5,2,1,4,6,3]=>[1,2,5,4,3,6]=>00110=>01100
[5,2,1,6,3,4]=>[1,2,5,3,6,4]=>00101=>10100
[5,2,1,6,4,3]=>[1,2,5,3,4,6]=>00100=>00100
[5,2,3,1,4,6]=>[6,2,5,4,1,3]=>10110=>01101
[5,2,3,1,6,4]=>[2,5,4,6,1,3]=>01010=>01010
[5,2,3,4,1,6]=>[6,2,5,3,1,4]=>10110=>01101
[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>01110=>01110
[5,2,3,6,1,4]=>[2,5,3,1,6,4]=>01101=>10110
[5,2,3,6,4,1]=>[2,5,3,1,4,6]=>01100=>00110
[5,2,4,1,3,6]=>[6,2,5,1,4,3]=>10101=>10101
[5,2,4,1,6,3]=>[2,5,1,4,3,6]=>01010=>01010
[5,2,4,3,1,6]=>[6,2,5,1,3,4]=>10100=>00101
[5,2,4,3,6,1]=>[2,5,3,4,1,6]=>01010=>01010
[5,2,4,6,1,3]=>[2,5,4,1,6,3]=>01101=>10110
[5,2,4,6,3,1]=>[2,5,4,1,3,6]=>01100=>00110
[5,2,6,1,3,4]=>[2,5,1,6,4,3]=>01011=>11010
[5,2,6,1,4,3]=>[2,5,1,6,3,4]=>01010=>01010
[5,2,6,3,1,4]=>[2,5,1,3,6,4]=>01001=>10010
[5,2,6,3,4,1]=>[2,5,3,6,1,4]=>01010=>01010
[5,2,6,4,1,3]=>[2,5,1,4,6,3]=>01001=>10010
[5,2,6,4,3,1]=>[2,5,1,3,4,6]=>01000=>00010
[5,3,1,2,4,6]=>[6,1,3,5,4,2]=>10011=>11001
[5,3,1,2,6,4]=>[1,3,5,4,6,2]=>00101=>10100
[5,3,1,4,2,6]=>[6,1,3,5,2,4]=>10010=>01001
[5,3,1,4,6,2]=>[1,3,5,4,2,6]=>00110=>01100
[5,3,1,6,2,4]=>[1,3,5,2,6,4]=>00101=>10100
[5,3,1,6,4,2]=>[1,3,5,2,4,6]=>00100=>00100
[5,3,2,1,4,6]=>[6,1,2,3,5,4]=>10001=>10001
[5,3,2,1,6,4]=>[1,2,3,5,4,6]=>00010=>01000
[5,3,2,4,1,6]=>[6,2,3,5,1,4]=>10010=>01001
[5,3,2,4,6,1]=>[2,3,5,4,1,6]=>00110=>01100
[5,3,2,6,1,4]=>[2,3,5,1,6,4]=>00101=>10100
[5,3,2,6,4,1]=>[2,3,5,1,4,6]=>00100=>00100
[5,3,4,1,2,6]=>[6,3,5,1,4,2]=>10101=>10101
[5,3,4,1,6,2]=>[3,5,1,4,2,6]=>01010=>01010
[5,3,4,2,1,6]=>[6,3,5,1,2,4]=>10100=>00101
[5,3,4,2,6,1]=>[3,5,2,4,1,6]=>01010=>01010
[5,3,4,6,1,2]=>[3,5,4,1,6,2]=>01101=>10110
[5,3,4,6,2,1]=>[3,5,4,1,2,6]=>01100=>00110
[5,3,6,1,2,4]=>[3,5,1,6,4,2]=>01011=>11010
[5,3,6,1,4,2]=>[3,5,1,6,2,4]=>01010=>01010
[5,3,6,2,1,4]=>[3,5,1,2,6,4]=>01001=>10010
[5,3,6,2,4,1]=>[3,5,2,6,1,4]=>01010=>01010
[5,3,6,4,1,2]=>[3,5,1,4,6,2]=>01001=>10010
[5,3,6,4,2,1]=>[3,5,1,2,4,6]=>01000=>00010
[5,4,1,2,3,6]=>[6,1,4,5,3,2]=>10011=>11001
[5,4,1,2,6,3]=>[1,4,5,3,6,2]=>00101=>10100
[5,4,1,3,2,6]=>[6,1,4,5,2,3]=>10010=>01001
[5,4,1,3,6,2]=>[1,4,5,3,2,6]=>00110=>01100
[5,4,1,6,2,3]=>[1,4,5,2,6,3]=>00101=>10100
[5,4,1,6,3,2]=>[1,4,5,2,3,6]=>00100=>00100
[5,4,2,1,3,6]=>[6,1,2,4,5,3]=>10001=>10001
[5,4,2,1,6,3]=>[1,2,4,5,3,6]=>00010=>01000
[5,4,2,3,1,6]=>[6,2,4,5,1,3]=>10010=>01001
[5,4,2,3,6,1]=>[2,4,5,3,1,6]=>00110=>01100
[5,4,2,6,1,3]=>[2,4,5,1,6,3]=>00101=>10100
[5,4,2,6,3,1]=>[2,4,5,1,3,6]=>00100=>00100
[5,4,3,1,2,6]=>[6,1,3,4,5,2]=>10001=>10001
[5,4,3,1,6,2]=>[1,3,4,5,2,6]=>00010=>01000
[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>10000=>00001
[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>00010=>01000
[5,4,3,6,1,2]=>[3,4,5,1,6,2]=>00101=>10100
[5,4,3,6,2,1]=>[3,4,5,1,2,6]=>00100=>00100
[5,4,6,1,2,3]=>[4,5,1,6,3,2]=>01011=>11010
[5,4,6,1,3,2]=>[4,5,1,6,2,3]=>01010=>01010
[5,4,6,2,1,3]=>[4,5,1,2,6,3]=>01001=>10010
[5,4,6,2,3,1]=>[4,5,2,6,1,3]=>01010=>01010
[5,4,6,3,1,2]=>[4,5,1,3,6,2]=>01001=>10010
[5,4,6,3,2,1]=>[4,5,1,2,3,6]=>01000=>00010
[5,6,1,2,3,4]=>[5,1,6,4,3,2]=>10111=>11101
[5,6,1,2,4,3]=>[5,1,6,3,4,2]=>10101=>10101
[5,6,1,3,2,4]=>[5,1,6,4,2,3]=>10110=>01101
[5,6,1,3,4,2]=>[5,1,6,3,2,4]=>10110=>01101
[5,6,1,4,2,3]=>[5,1,6,2,4,3]=>10101=>10101
[5,6,1,4,3,2]=>[5,1,6,2,3,4]=>10100=>00101
[5,6,2,1,3,4]=>[5,1,2,6,4,3]=>10011=>11001
[5,6,2,1,4,3]=>[5,1,2,6,3,4]=>10010=>01001
[5,6,2,3,1,4]=>[5,2,6,4,1,3]=>10110=>01101
[5,6,2,3,4,1]=>[5,2,6,3,1,4]=>10110=>01101
[5,6,2,4,1,3]=>[5,2,6,1,4,3]=>10101=>10101
[5,6,2,4,3,1]=>[5,2,6,1,3,4]=>10100=>00101
[5,6,3,1,2,4]=>[5,1,3,6,4,2]=>10011=>11001
[5,6,3,1,4,2]=>[5,1,3,6,2,4]=>10010=>01001
[5,6,3,2,1,4]=>[5,1,2,3,6,4]=>10001=>10001
[5,6,3,2,4,1]=>[5,2,3,6,1,4]=>10010=>01001
[5,6,3,4,1,2]=>[5,3,6,1,4,2]=>10101=>10101
[5,6,3,4,2,1]=>[5,3,6,1,2,4]=>10100=>00101
[5,6,4,1,2,3]=>[5,1,4,6,3,2]=>10011=>11001
[5,6,4,1,3,2]=>[5,1,4,6,2,3]=>10010=>01001
[5,6,4,2,1,3]=>[5,1,2,4,6,3]=>10001=>10001
[5,6,4,2,3,1]=>[5,2,4,6,1,3]=>10010=>01001
[5,6,4,3,1,2]=>[5,1,3,4,6,2]=>10001=>10001
[5,6,4,3,2,1]=>[5,1,2,3,4,6]=>10000=>00001
[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>01111=>11110
[6,1,2,3,5,4]=>[1,6,4,5,3,2]=>01011=>11010
[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>01101=>10110
[6,1,2,4,5,3]=>[1,6,4,3,5,2]=>01101=>10110
[6,1,2,5,3,4]=>[1,6,3,5,4,2]=>01011=>11010
[6,1,2,5,4,3]=>[1,6,3,4,5,2]=>01001=>10010
[6,1,3,2,4,5]=>[1,6,5,4,2,3]=>01110=>01110
[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>01010=>01010
[6,1,3,4,2,5]=>[1,6,5,3,2,4]=>01110=>01110
[6,1,3,4,5,2]=>[1,6,4,3,2,5]=>01110=>01110
[6,1,3,5,2,4]=>[1,6,3,2,5,4]=>01101=>10110
[6,1,3,5,4,2]=>[1,6,3,2,4,5]=>01100=>00110
[6,1,4,2,3,5]=>[1,6,5,2,4,3]=>01101=>10110
[6,1,4,2,5,3]=>[1,6,2,4,3,5]=>01010=>01010
[6,1,4,3,2,5]=>[1,6,5,2,3,4]=>01100=>00110
[6,1,4,3,5,2]=>[1,6,3,4,2,5]=>01010=>01010
[6,1,4,5,2,3]=>[1,6,4,2,5,3]=>01101=>10110
[6,1,4,5,3,2]=>[1,6,4,2,3,5]=>01100=>00110
[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>01011=>11010
[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>01010=>01010
[6,1,5,3,2,4]=>[1,6,2,3,5,4]=>01001=>10010
[6,1,5,3,4,2]=>[1,6,3,5,2,4]=>01010=>01010
[6,1,5,4,2,3]=>[1,6,2,4,5,3]=>01001=>10010
[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>01000=>00010
[6,2,1,3,4,5]=>[1,2,6,5,4,3]=>00111=>11100
[6,2,1,3,5,4]=>[1,2,6,4,5,3]=>00101=>10100
[6,2,1,4,3,5]=>[1,2,6,5,3,4]=>00110=>01100
[6,2,1,4,5,3]=>[1,2,6,4,3,5]=>00110=>01100
[6,2,1,5,3,4]=>[1,2,6,3,5,4]=>00101=>10100
[6,2,1,5,4,3]=>[1,2,6,3,4,5]=>00100=>00100
[6,2,3,1,4,5]=>[2,6,5,4,1,3]=>01110=>01110
[6,2,3,1,5,4]=>[2,6,4,5,1,3]=>01010=>01010
[6,2,3,4,1,5]=>[2,6,5,3,1,4]=>01110=>01110
[6,2,3,4,5,1]=>[2,6,4,3,1,5]=>01110=>01110
[6,2,3,5,1,4]=>[2,6,3,1,5,4]=>01101=>10110
[6,2,3,5,4,1]=>[2,6,3,1,4,5]=>01100=>00110
[6,2,4,1,3,5]=>[2,6,5,1,4,3]=>01101=>10110
[6,2,4,1,5,3]=>[2,6,1,4,3,5]=>01010=>01010
[6,2,4,3,1,5]=>[2,6,5,1,3,4]=>01100=>00110
[6,2,4,3,5,1]=>[2,6,3,4,1,5]=>01010=>01010
[6,2,4,5,1,3]=>[2,6,4,1,5,3]=>01101=>10110
[6,2,4,5,3,1]=>[2,6,4,1,3,5]=>01100=>00110
[6,2,5,1,3,4]=>[2,6,1,5,4,3]=>01011=>11010
[6,2,5,1,4,3]=>[2,6,1,5,3,4]=>01010=>01010
[6,2,5,3,1,4]=>[2,6,1,3,5,4]=>01001=>10010
[6,2,5,3,4,1]=>[2,6,3,5,1,4]=>01010=>01010
[6,2,5,4,1,3]=>[2,6,1,4,5,3]=>01001=>10010
[6,2,5,4,3,1]=>[2,6,1,3,4,5]=>01000=>00010
[6,3,1,2,4,5]=>[1,3,6,5,4,2]=>00111=>11100
[6,3,1,2,5,4]=>[1,3,6,4,5,2]=>00101=>10100
[6,3,1,4,2,5]=>[1,3,6,5,2,4]=>00110=>01100
[6,3,1,4,5,2]=>[1,3,6,4,2,5]=>00110=>01100
[6,3,1,5,2,4]=>[1,3,6,2,5,4]=>00101=>10100
[6,3,1,5,4,2]=>[1,3,6,2,4,5]=>00100=>00100
[6,3,2,1,4,5]=>[1,2,3,6,5,4]=>00011=>11000
[6,3,2,1,5,4]=>[1,2,3,6,4,5]=>00010=>01000
[6,3,2,4,1,5]=>[2,3,6,5,1,4]=>00110=>01100
[6,3,2,4,5,1]=>[2,3,6,4,1,5]=>00110=>01100
[6,3,2,5,1,4]=>[2,3,6,1,5,4]=>00101=>10100
[6,3,2,5,4,1]=>[2,3,6,1,4,5]=>00100=>00100
[6,3,4,1,2,5]=>[3,6,5,1,4,2]=>01101=>10110
[6,3,4,1,5,2]=>[3,6,1,4,2,5]=>01010=>01010
[6,3,4,2,1,5]=>[3,6,5,1,2,4]=>01100=>00110
[6,3,4,2,5,1]=>[3,6,2,4,1,5]=>01010=>01010
[6,3,4,5,1,2]=>[3,6,4,1,5,2]=>01101=>10110
[6,3,4,5,2,1]=>[3,6,4,1,2,5]=>01100=>00110
[6,3,5,1,2,4]=>[3,6,1,5,4,2]=>01011=>11010
[6,3,5,1,4,2]=>[3,6,1,5,2,4]=>01010=>01010
[6,3,5,2,1,4]=>[3,6,1,2,5,4]=>01001=>10010
[6,3,5,2,4,1]=>[3,6,2,5,1,4]=>01010=>01010
[6,3,5,4,1,2]=>[3,6,1,4,5,2]=>01001=>10010
[6,3,5,4,2,1]=>[3,6,1,2,4,5]=>01000=>00010
[6,4,1,2,3,5]=>[1,4,6,5,3,2]=>00111=>11100
[6,4,1,2,5,3]=>[1,4,6,3,5,2]=>00101=>10100
[6,4,1,3,2,5]=>[1,4,6,5,2,3]=>00110=>01100
[6,4,1,3,5,2]=>[1,4,6,3,2,5]=>00110=>01100
[6,4,1,5,2,3]=>[1,4,6,2,5,3]=>00101=>10100
[6,4,1,5,3,2]=>[1,4,6,2,3,5]=>00100=>00100
[6,4,2,1,3,5]=>[1,2,4,6,5,3]=>00011=>11000
[6,4,2,1,5,3]=>[1,2,4,6,3,5]=>00010=>01000
[6,4,2,3,1,5]=>[2,4,6,5,1,3]=>00110=>01100
[6,4,2,3,5,1]=>[2,4,6,3,1,5]=>00110=>01100
[6,4,2,5,1,3]=>[2,4,6,1,5,3]=>00101=>10100
[6,4,2,5,3,1]=>[2,4,6,1,3,5]=>00100=>00100
[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>00011=>11000
[6,4,3,1,5,2]=>[1,3,4,6,2,5]=>00010=>01000
[6,4,3,2,1,5]=>[1,2,3,4,6,5]=>00001=>10000
[6,4,3,2,5,1]=>[2,3,4,6,1,5]=>00010=>01000
[6,4,3,5,1,2]=>[3,4,6,1,5,2]=>00101=>10100
[6,4,3,5,2,1]=>[3,4,6,1,2,5]=>00100=>00100
[6,4,5,1,2,3]=>[4,6,1,5,3,2]=>01011=>11010
[6,4,5,1,3,2]=>[4,6,1,5,2,3]=>01010=>01010
[6,4,5,2,1,3]=>[4,6,1,2,5,3]=>01001=>10010
[6,4,5,2,3,1]=>[4,6,2,5,1,3]=>01010=>01010
[6,4,5,3,1,2]=>[4,6,1,3,5,2]=>01001=>10010
[6,4,5,3,2,1]=>[4,6,1,2,3,5]=>01000=>00010
[6,5,1,2,3,4]=>[1,5,6,4,3,2]=>00111=>11100
[6,5,1,2,4,3]=>[1,5,6,3,4,2]=>00101=>10100
[6,5,1,3,2,4]=>[1,5,6,4,2,3]=>00110=>01100
[6,5,1,3,4,2]=>[1,5,6,3,2,4]=>00110=>01100
[6,5,1,4,2,3]=>[1,5,6,2,4,3]=>00101=>10100
[6,5,1,4,3,2]=>[1,5,6,2,3,4]=>00100=>00100
[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>00011=>11000
[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>00010=>01000
[6,5,2,3,1,4]=>[2,5,6,4,1,3]=>00110=>01100
[6,5,2,3,4,1]=>[2,5,6,3,1,4]=>00110=>01100
[6,5,2,4,1,3]=>[2,5,6,1,4,3]=>00101=>10100
[6,5,2,4,3,1]=>[2,5,6,1,3,4]=>00100=>00100
[6,5,3,1,2,4]=>[1,3,5,6,4,2]=>00011=>11000
[6,5,3,1,4,2]=>[1,3,5,6,2,4]=>00010=>01000
[6,5,3,2,1,4]=>[1,2,3,5,6,4]=>00001=>10000
[6,5,3,2,4,1]=>[2,3,5,6,1,4]=>00010=>01000
[6,5,3,4,1,2]=>[3,5,6,1,4,2]=>00101=>10100
[6,5,3,4,2,1]=>[3,5,6,1,2,4]=>00100=>00100
[6,5,4,1,2,3]=>[1,4,5,6,3,2]=>00011=>11000
[6,5,4,1,3,2]=>[1,4,5,6,2,3]=>00010=>01000
[6,5,4,2,1,3]=>[1,2,4,5,6,3]=>00001=>10000
[6,5,4,2,3,1]=>[2,4,5,6,1,3]=>00010=>01000
[6,5,4,3,1,2]=>[1,3,4,5,6,2]=>00001=>10000
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>00000=>00000
[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>111111=>111111
[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>011111=>111110
[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>101111=>111101
[1,2,3,4,6,7,5]=>[6,5,7,4,3,2,1]=>101111=>111101
[1,2,3,4,7,5,6]=>[5,7,6,4,3,2,1]=>011111=>111110
[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>001111=>111100
[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>110111=>111011
[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>010111=>111010
[1,2,3,5,6,4,7]=>[7,5,4,6,3,2,1]=>110111=>111011
[1,2,3,5,6,7,4]=>[6,5,4,7,3,2,1]=>110111=>111011
[1,2,3,5,7,4,6]=>[5,4,7,6,3,2,1]=>101111=>111101
[1,2,3,5,7,6,4]=>[5,4,6,7,3,2,1]=>100111=>111001
[1,2,3,6,4,5,7]=>[7,4,6,5,3,2,1]=>101111=>111101
[1,2,3,6,4,7,5]=>[4,6,5,7,3,2,1]=>010111=>111010
[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>100111=>111001
[1,2,3,6,5,7,4]=>[5,6,4,7,3,2,1]=>010111=>111010
[1,2,3,6,7,4,5]=>[6,4,7,5,3,2,1]=>101111=>111101
[1,2,3,6,7,5,4]=>[6,4,5,7,3,2,1]=>100111=>111001
[1,2,3,7,4,5,6]=>[4,7,6,5,3,2,1]=>011111=>111110
[1,2,3,7,4,6,5]=>[4,7,5,6,3,2,1]=>010111=>111010
[1,2,3,7,5,4,6]=>[4,5,7,6,3,2,1]=>001111=>111100
[1,2,3,7,5,6,4]=>[5,7,4,6,3,2,1]=>010111=>111010
[1,2,3,7,6,4,5]=>[4,6,7,5,3,2,1]=>001111=>111100
[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>000111=>111000
[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>111011=>110111
[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>011011=>110110
[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>101011=>110101
[1,2,4,3,6,7,5]=>[6,5,7,3,4,2,1]=>101011=>110101
[1,2,4,3,7,5,6]=>[5,7,6,3,4,2,1]=>011011=>110110
[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>001011=>110100
[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>111011=>110111
[1,2,4,5,3,7,6]=>[6,7,4,3,5,2,1]=>011011=>110110
[1,2,4,5,6,3,7]=>[7,5,4,3,6,2,1]=>111011=>110111
[1,2,4,5,6,7,3]=>[6,5,4,3,7,2,1]=>111011=>110111
[1,2,4,5,7,3,6]=>[5,4,3,7,6,2,1]=>110111=>111011
[1,2,4,5,7,6,3]=>[5,4,3,6,7,2,1]=>110011=>110011
[1,2,4,6,3,5,7]=>[7,4,3,6,5,2,1]=>110111=>111011
[1,2,4,6,3,7,5]=>[4,3,6,5,7,2,1]=>101011=>110101
[1,2,4,6,5,3,7]=>[7,4,3,5,6,2,1]=>110011=>110011
[1,2,4,6,5,7,3]=>[5,6,4,3,7,2,1]=>011011=>110110
[1,2,4,6,7,3,5]=>[6,4,3,7,5,2,1]=>110111=>111011
[1,2,4,6,7,5,3]=>[6,4,3,5,7,2,1]=>110011=>110011
[1,2,4,7,3,5,6]=>[4,3,7,6,5,2,1]=>101111=>111101
[1,2,4,7,3,6,5]=>[4,3,7,5,6,2,1]=>101011=>110101
[1,2,4,7,5,3,6]=>[4,3,5,7,6,2,1]=>100111=>111001
[1,2,4,7,5,6,3]=>[5,7,4,3,6,2,1]=>011011=>110110
[1,2,4,7,6,3,5]=>[4,3,6,7,5,2,1]=>100111=>111001
[1,2,4,7,6,5,3]=>[4,3,5,6,7,2,1]=>100011=>110001
[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>110111=>111011
[1,2,5,3,4,7,6]=>[6,7,3,5,4,2,1]=>010111=>111010
[1,2,5,3,6,4,7]=>[7,3,5,4,6,2,1]=>101011=>110101
[1,2,5,3,6,7,4]=>[6,3,5,4,7,2,1]=>101011=>110101
[1,2,5,3,7,4,6]=>[3,5,4,7,6,2,1]=>010111=>111010
[1,2,5,3,7,6,4]=>[3,5,4,6,7,2,1]=>010011=>110010
[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>110011=>110011
[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>010011=>110010
[1,2,5,4,6,3,7]=>[7,4,5,3,6,2,1]=>101011=>110101
[1,2,5,4,6,7,3]=>[6,4,5,3,7,2,1]=>101011=>110101
[1,2,5,4,7,3,6]=>[4,5,3,7,6,2,1]=>010111=>111010
[1,2,5,4,7,6,3]=>[4,5,3,6,7,2,1]=>010011=>110010
[1,2,5,6,3,4,7]=>[7,5,3,6,4,2,1]=>110111=>111011
[1,2,5,6,3,7,4]=>[5,3,6,4,7,2,1]=>101011=>110101
[1,2,5,6,4,3,7]=>[7,5,3,4,6,2,1]=>110011=>110011
[1,2,5,6,4,7,3]=>[5,4,6,3,7,2,1]=>101011=>110101
[1,2,5,6,7,3,4]=>[6,5,3,7,4,2,1]=>110111=>111011
[1,2,5,6,7,4,3]=>[6,5,3,4,7,2,1]=>110011=>110011
[1,2,5,7,3,4,6]=>[5,3,7,6,4,2,1]=>101111=>111101
[1,2,5,7,3,6,4]=>[5,3,7,4,6,2,1]=>101011=>110101
[1,2,5,7,4,3,6]=>[5,3,4,7,6,2,1]=>100111=>111001
[1,2,5,7,4,6,3]=>[5,4,7,3,6,2,1]=>101011=>110101
[1,2,5,7,6,3,4]=>[5,3,6,7,4,2,1]=>100111=>111001
[1,2,5,7,6,4,3]=>[5,3,4,6,7,2,1]=>100011=>110001
[1,2,6,3,4,5,7]=>[7,3,6,5,4,2,1]=>101111=>111101
[1,2,6,3,4,7,5]=>[3,6,5,7,4,2,1]=>010111=>111010
[1,2,6,3,5,4,7]=>[7,3,6,4,5,2,1]=>101011=>110101
[1,2,6,3,5,7,4]=>[3,6,5,4,7,2,1]=>011011=>110110
[1,2,6,3,7,4,5]=>[3,6,4,7,5,2,1]=>010111=>111010
[1,2,6,3,7,5,4]=>[3,6,4,5,7,2,1]=>010011=>110010
[1,2,6,4,3,5,7]=>[7,3,4,6,5,2,1]=>100111=>111001
[1,2,6,4,3,7,5]=>[3,4,6,5,7,2,1]=>001011=>110100
[1,2,6,4,5,3,7]=>[7,4,6,3,5,2,1]=>101011=>110101
[1,2,6,4,5,7,3]=>[4,6,5,3,7,2,1]=>011011=>110110
[1,2,6,4,7,3,5]=>[4,6,3,7,5,2,1]=>010111=>111010
[1,2,6,4,7,5,3]=>[4,6,3,5,7,2,1]=>010011=>110010
[1,2,6,5,3,4,7]=>[7,3,5,6,4,2,1]=>100111=>111001
[1,2,6,5,3,7,4]=>[3,5,6,4,7,2,1]=>001011=>110100
[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>100011=>110001
[1,2,6,5,4,7,3]=>[4,5,6,3,7,2,1]=>001011=>110100
[1,2,6,5,7,3,4]=>[5,6,3,7,4,2,1]=>010111=>111010
[1,2,6,5,7,4,3]=>[5,6,3,4,7,2,1]=>010011=>110010
[1,2,6,7,3,4,5]=>[6,3,7,5,4,2,1]=>101111=>111101
[1,2,6,7,3,5,4]=>[6,3,7,4,5,2,1]=>101011=>110101
[1,2,6,7,4,3,5]=>[6,3,4,7,5,2,1]=>100111=>111001
[1,2,6,7,4,5,3]=>[6,4,7,3,5,2,1]=>101011=>110101
[1,2,6,7,5,3,4]=>[6,3,5,7,4,2,1]=>100111=>111001
[1,2,6,7,5,4,3]=>[6,3,4,5,7,2,1]=>100011=>110001
[1,2,7,3,4,5,6]=>[3,7,6,5,4,2,1]=>011111=>111110
[1,2,7,3,4,6,5]=>[3,7,5,6,4,2,1]=>010111=>111010
[1,2,7,3,5,4,6]=>[3,7,6,4,5,2,1]=>011011=>110110
[1,2,7,3,5,6,4]=>[3,7,5,4,6,2,1]=>011011=>110110
[1,2,7,3,6,4,5]=>[3,7,4,6,5,2,1]=>010111=>111010
[1,2,7,3,6,5,4]=>[3,7,4,5,6,2,1]=>010011=>110010
[1,2,7,4,3,5,6]=>[3,4,7,6,5,2,1]=>001111=>111100
[1,2,7,4,3,6,5]=>[3,4,7,5,6,2,1]=>001011=>110100
[1,2,7,4,5,3,6]=>[4,7,6,3,5,2,1]=>011011=>110110
[1,2,7,4,5,6,3]=>[4,7,5,3,6,2,1]=>011011=>110110
[1,2,7,4,6,3,5]=>[4,7,3,6,5,2,1]=>010111=>111010
[1,2,7,4,6,5,3]=>[4,7,3,5,6,2,1]=>010011=>110010
[1,2,7,5,3,4,6]=>[3,5,7,6,4,2,1]=>001111=>111100
[1,2,7,5,3,6,4]=>[3,5,7,4,6,2,1]=>001011=>110100
[1,2,7,5,4,3,6]=>[3,4,5,7,6,2,1]=>000111=>111000
[1,2,7,5,4,6,3]=>[4,5,7,3,6,2,1]=>001011=>110100
[1,2,7,5,6,3,4]=>[5,7,3,6,4,2,1]=>010111=>111010
[1,2,7,5,6,4,3]=>[5,7,3,4,6,2,1]=>010011=>110010
[1,2,7,6,3,4,5]=>[3,6,7,5,4,2,1]=>001111=>111100
[1,2,7,6,3,5,4]=>[3,6,7,4,5,2,1]=>001011=>110100
[1,2,7,6,4,3,5]=>[3,4,6,7,5,2,1]=>000111=>111000
[1,2,7,6,4,5,3]=>[4,6,7,3,5,2,1]=>001011=>110100
[1,2,7,6,5,3,4]=>[3,5,6,7,4,2,1]=>000111=>111000
[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>000011=>110000
[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>111101=>101111
[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>011101=>101110
[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>101101=>101101
[1,3,2,4,6,7,5]=>[6,5,7,4,2,3,1]=>101101=>101101
[1,3,2,4,7,5,6]=>[5,7,6,4,2,3,1]=>011101=>101110
[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>001101=>101100
[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>110101=>101011
[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>010101=>101010
[1,3,2,5,6,4,7]=>[7,5,4,6,2,3,1]=>110101=>101011
[1,3,2,5,6,7,4]=>[6,5,4,7,2,3,1]=>110101=>101011
[1,3,2,5,7,4,6]=>[5,4,7,6,2,3,1]=>101101=>101101
[1,3,2,5,7,6,4]=>[5,4,6,7,2,3,1]=>100101=>101001
[1,3,2,6,4,5,7]=>[7,4,6,5,2,3,1]=>101101=>101101
[1,3,2,6,4,7,5]=>[4,6,5,7,2,3,1]=>010101=>101010
[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>100101=>101001
[1,3,2,6,5,7,4]=>[5,6,4,7,2,3,1]=>010101=>101010
[1,3,2,6,7,4,5]=>[6,4,7,5,2,3,1]=>101101=>101101
[1,3,2,6,7,5,4]=>[6,4,5,7,2,3,1]=>100101=>101001
[1,3,2,7,4,5,6]=>[4,7,6,5,2,3,1]=>011101=>101110
[1,3,2,7,4,6,5]=>[4,7,5,6,2,3,1]=>010101=>101010
[1,3,2,7,5,4,6]=>[4,5,7,6,2,3,1]=>001101=>101100
[1,3,2,7,5,6,4]=>[5,7,4,6,2,3,1]=>010101=>101010
[1,3,2,7,6,4,5]=>[4,6,7,5,2,3,1]=>001101=>101100
[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>000101=>101000
[1,3,4,2,5,6,7]=>[7,6,5,3,2,4,1]=>111101=>101111
[1,3,4,2,5,7,6]=>[6,7,5,3,2,4,1]=>011101=>101110
[1,3,4,2,6,5,7]=>[7,5,6,3,2,4,1]=>101101=>101101
[1,3,4,2,6,7,5]=>[6,5,7,3,2,4,1]=>101101=>101101
[1,3,4,2,7,5,6]=>[5,7,6,3,2,4,1]=>011101=>101110
[1,3,4,2,7,6,5]=>[5,6,7,3,2,4,1]=>001101=>101100
[1,3,4,5,2,6,7]=>[7,6,4,3,2,5,1]=>111101=>101111
[1,3,4,5,2,7,6]=>[6,7,4,3,2,5,1]=>011101=>101110
[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>111101=>101111
[1,3,4,5,6,7,2]=>[6,5,4,3,2,7,1]=>111101=>101111
[1,3,4,5,7,2,6]=>[5,4,3,2,7,6,1]=>111011=>110111
[1,3,4,5,7,6,2]=>[5,4,3,2,6,7,1]=>111001=>100111
[1,3,4,6,2,5,7]=>[7,4,3,2,6,5,1]=>111011=>110111
[1,3,4,6,2,7,5]=>[4,3,2,6,5,7,1]=>110101=>101011
[1,3,4,6,5,2,7]=>[7,4,3,2,5,6,1]=>111001=>100111
[1,3,4,6,5,7,2]=>[5,6,4,3,2,7,1]=>011101=>101110
[1,3,4,6,7,2,5]=>[6,4,3,2,7,5,1]=>111011=>110111
[1,3,4,6,7,5,2]=>[6,4,3,2,5,7,1]=>111001=>100111
[1,3,4,7,2,5,6]=>[4,3,2,7,6,5,1]=>110111=>111011
[1,3,4,7,2,6,5]=>[4,3,2,7,5,6,1]=>110101=>101011
[1,3,4,7,5,2,6]=>[4,3,2,5,7,6,1]=>110011=>110011
[1,3,4,7,5,6,2]=>[5,7,4,3,2,6,1]=>011101=>101110
[1,3,4,7,6,2,5]=>[4,3,2,6,7,5,1]=>110011=>110011
[1,3,4,7,6,5,2]=>[4,3,2,5,6,7,1]=>110001=>100011
[1,3,5,2,4,6,7]=>[7,6,3,2,5,4,1]=>111011=>110111
[1,3,5,2,4,7,6]=>[6,7,3,2,5,4,1]=>011011=>110110
[1,3,5,2,6,4,7]=>[7,3,2,5,4,6,1]=>110101=>101011
[1,3,5,2,6,7,4]=>[6,3,2,5,4,7,1]=>110101=>101011
[1,3,5,2,7,4,6]=>[3,2,5,4,7,6,1]=>101011=>110101
[1,3,5,2,7,6,4]=>[3,2,5,4,6,7,1]=>101001=>100101
[1,3,5,4,2,6,7]=>[7,6,3,2,4,5,1]=>111001=>100111
[1,3,5,4,2,7,6]=>[6,7,3,2,4,5,1]=>011001=>100110
[1,3,5,4,6,2,7]=>[7,4,5,3,2,6,1]=>101101=>101101
[1,3,5,4,6,7,2]=>[6,4,5,3,2,7,1]=>101101=>101101
[1,3,5,4,7,2,6]=>[4,5,3,2,7,6,1]=>011011=>110110
[1,3,5,4,7,6,2]=>[4,5,3,2,6,7,1]=>011001=>100110
[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>111011=>110111
[1,3,5,6,2,7,4]=>[5,3,2,6,4,7,1]=>110101=>101011
[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>111001=>100111
[1,3,5,6,4,7,2]=>[5,4,6,3,2,7,1]=>101101=>101101
[1,3,5,6,7,2,4]=>[6,5,3,2,7,4,1]=>111011=>110111
[1,3,5,6,7,4,2]=>[6,5,3,2,4,7,1]=>111001=>100111
[1,3,5,7,2,4,6]=>[5,3,2,7,6,4,1]=>110111=>111011
[1,3,5,7,2,6,4]=>[5,3,2,7,4,6,1]=>110101=>101011
[1,3,5,7,4,2,6]=>[5,3,2,4,7,6,1]=>110011=>110011
[1,3,5,7,4,6,2]=>[5,4,7,3,2,6,1]=>101101=>101101
[1,3,5,7,6,2,4]=>[5,3,2,6,7,4,1]=>110011=>110011
[1,3,5,7,6,4,2]=>[5,3,2,4,6,7,1]=>110001=>100011
[1,3,6,2,4,5,7]=>[7,3,2,6,5,4,1]=>110111=>111011
[1,3,6,2,4,7,5]=>[3,2,6,5,7,4,1]=>101011=>110101
[1,3,6,2,5,4,7]=>[7,3,2,6,4,5,1]=>110101=>101011
[1,3,6,2,5,7,4]=>[3,2,6,5,4,7,1]=>101101=>101101
[1,3,6,2,7,4,5]=>[3,2,6,4,7,5,1]=>101011=>110101
[1,3,6,2,7,5,4]=>[3,2,6,4,5,7,1]=>101001=>100101
[1,3,6,4,2,5,7]=>[7,3,2,4,6,5,1]=>110011=>110011
[1,3,6,4,2,7,5]=>[3,2,4,6,5,7,1]=>100101=>101001
[1,3,6,4,5,2,7]=>[7,4,6,3,2,5,1]=>101101=>101101
[1,3,6,4,5,7,2]=>[4,6,5,3,2,7,1]=>011101=>101110
[1,3,6,4,7,2,5]=>[4,6,3,2,7,5,1]=>011011=>110110
[1,3,6,4,7,5,2]=>[4,6,3,2,5,7,1]=>011001=>100110
[1,3,6,5,2,4,7]=>[7,3,2,5,6,4,1]=>110011=>110011
[1,3,6,5,2,7,4]=>[3,2,5,6,4,7,1]=>100101=>101001
[1,3,6,5,4,2,7]=>[7,3,2,4,5,6,1]=>110001=>100011
[1,3,6,5,4,7,2]=>[4,5,6,3,2,7,1]=>001101=>101100
[1,3,6,5,7,2,4]=>[5,6,3,2,7,4,1]=>011011=>110110
[1,3,6,5,7,4,2]=>[5,6,3,2,4,7,1]=>011001=>100110
[1,3,6,7,2,4,5]=>[6,3,2,7,5,4,1]=>110111=>111011
[1,3,6,7,2,5,4]=>[6,3,2,7,4,5,1]=>110101=>101011
[1,3,6,7,4,2,5]=>[6,3,2,4,7,5,1]=>110011=>110011
[1,3,6,7,4,5,2]=>[6,4,7,3,2,5,1]=>101101=>101101
[1,3,6,7,5,2,4]=>[6,3,2,5,7,4,1]=>110011=>110011
[1,3,6,7,5,4,2]=>[6,3,2,4,5,7,1]=>110001=>100011
[1,3,7,2,4,5,6]=>[3,2,7,6,5,4,1]=>101111=>111101
[1,3,7,2,4,6,5]=>[3,2,7,5,6,4,1]=>101011=>110101
[1,3,7,2,5,4,6]=>[3,2,7,6,4,5,1]=>101101=>101101
[1,3,7,2,5,6,4]=>[3,2,7,5,4,6,1]=>101101=>101101
[1,3,7,2,6,4,5]=>[3,2,7,4,6,5,1]=>101011=>110101
[1,3,7,2,6,5,4]=>[3,2,7,4,5,6,1]=>101001=>100101
[1,3,7,4,2,5,6]=>[3,2,4,7,6,5,1]=>100111=>111001
[1,3,7,4,2,6,5]=>[3,2,4,7,5,6,1]=>100101=>101001
[1,3,7,4,5,2,6]=>[4,7,6,3,2,5,1]=>011101=>101110
[1,3,7,4,5,6,2]=>[4,7,5,3,2,6,1]=>011101=>101110
[1,3,7,4,6,2,5]=>[4,7,3,2,6,5,1]=>011011=>110110
[1,3,7,4,6,5,2]=>[4,7,3,2,5,6,1]=>011001=>100110
[1,3,7,5,2,4,6]=>[3,2,5,7,6,4,1]=>100111=>111001
[1,3,7,5,2,6,4]=>[3,2,5,7,4,6,1]=>100101=>101001
[1,3,7,5,4,2,6]=>[3,2,4,5,7,6,1]=>100011=>110001
[1,3,7,5,4,6,2]=>[4,5,7,3,2,6,1]=>001101=>101100
[1,3,7,5,6,2,4]=>[5,7,3,2,6,4,1]=>011011=>110110
[1,3,7,5,6,4,2]=>[5,7,3,2,4,6,1]=>011001=>100110
[1,3,7,6,2,4,5]=>[3,2,6,7,5,4,1]=>100111=>111001
[1,3,7,6,2,5,4]=>[3,2,6,7,4,5,1]=>100101=>101001
[1,3,7,6,4,2,5]=>[3,2,4,6,7,5,1]=>100011=>110001
[1,3,7,6,4,5,2]=>[4,6,7,3,2,5,1]=>001101=>101100
[1,3,7,6,5,2,4]=>[3,2,5,6,7,4,1]=>100011=>110001
[1,3,7,6,5,4,2]=>[3,2,4,5,6,7,1]=>100001=>100001
[1,4,2,3,5,6,7]=>[7,6,5,2,4,3,1]=>111011=>110111
[1,4,2,3,5,7,6]=>[6,7,5,2,4,3,1]=>011011=>110110
[1,4,2,3,6,5,7]=>[7,5,6,2,4,3,1]=>101011=>110101
[1,4,2,3,6,7,5]=>[6,5,7,2,4,3,1]=>101011=>110101
[1,4,2,3,7,5,6]=>[5,7,6,2,4,3,1]=>011011=>110110
[1,4,2,3,7,6,5]=>[5,6,7,2,4,3,1]=>001011=>110100
[1,4,2,5,3,6,7]=>[7,6,2,4,3,5,1]=>110101=>101011
[1,4,2,5,3,7,6]=>[6,7,2,4,3,5,1]=>010101=>101010
[1,4,2,5,6,3,7]=>[7,5,2,4,3,6,1]=>110101=>101011
[1,4,2,5,6,7,3]=>[6,5,2,4,3,7,1]=>110101=>101011
[1,4,2,5,7,3,6]=>[5,2,4,3,7,6,1]=>101011=>110101
[1,4,2,5,7,6,3]=>[5,2,4,3,6,7,1]=>101001=>100101
[1,4,2,6,3,5,7]=>[7,2,4,3,6,5,1]=>101011=>110101
[1,4,2,6,3,7,5]=>[2,4,3,6,5,7,1]=>010101=>101010
[1,4,2,6,5,3,7]=>[7,2,4,3,5,6,1]=>101001=>100101
[1,4,2,6,5,7,3]=>[5,6,2,4,3,7,1]=>010101=>101010
[1,4,2,6,7,3,5]=>[6,2,4,3,7,5,1]=>101011=>110101
[1,4,2,6,7,5,3]=>[6,2,4,3,5,7,1]=>101001=>100101
[1,4,2,7,3,5,6]=>[2,4,3,7,6,5,1]=>010111=>111010
[1,4,2,7,3,6,5]=>[2,4,3,7,5,6,1]=>010101=>101010
[1,4,2,7,5,3,6]=>[2,4,3,5,7,6,1]=>010011=>110010
[1,4,2,7,5,6,3]=>[5,7,2,4,3,6,1]=>010101=>101010
[1,4,2,7,6,3,5]=>[2,4,3,6,7,5,1]=>010011=>110010
[1,4,2,7,6,5,3]=>[2,4,3,5,6,7,1]=>010001=>100010
[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>111001=>100111
[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>011001=>100110
[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>101001=>100101
[1,4,3,2,6,7,5]=>[6,5,7,2,3,4,1]=>101001=>100101
[1,4,3,2,7,5,6]=>[5,7,6,2,3,4,1]=>011001=>100110
[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>001001=>100100
[1,4,3,5,2,6,7]=>[7,6,3,4,2,5,1]=>110101=>101011
[1,4,3,5,2,7,6]=>[6,7,3,4,2,5,1]=>010101=>101010
[1,4,3,5,6,2,7]=>[7,5,3,4,2,6,1]=>110101=>101011
[1,4,3,5,6,7,2]=>[6,5,3,4,2,7,1]=>110101=>101011
[1,4,3,5,7,2,6]=>[5,3,4,2,7,6,1]=>101011=>110101
[1,4,3,5,7,6,2]=>[5,3,4,2,6,7,1]=>101001=>100101
[1,4,3,6,2,5,7]=>[7,3,4,2,6,5,1]=>101011=>110101
[1,4,3,6,2,7,5]=>[3,4,2,6,5,7,1]=>010101=>101010
[1,4,3,6,5,2,7]=>[7,3,4,2,5,6,1]=>101001=>100101
[1,4,3,6,5,7,2]=>[5,6,3,4,2,7,1]=>010101=>101010
[1,4,3,6,7,2,5]=>[6,3,4,2,7,5,1]=>101011=>110101
[1,4,3,6,7,5,2]=>[6,3,4,2,5,7,1]=>101001=>100101
[1,4,3,7,2,5,6]=>[3,4,2,7,6,5,1]=>010111=>111010
[1,4,3,7,2,6,5]=>[3,4,2,7,5,6,1]=>010101=>101010
[1,4,3,7,5,2,6]=>[3,4,2,5,7,6,1]=>010011=>110010
[1,4,3,7,5,6,2]=>[5,7,3,4,2,6,1]=>010101=>101010
[1,4,3,7,6,2,5]=>[3,4,2,6,7,5,1]=>010011=>110010
[1,4,3,7,6,5,2]=>[3,4,2,5,6,7,1]=>010001=>100010
[1,4,5,2,3,6,7]=>[7,6,4,2,5,3,1]=>111011=>110111
[1,4,5,2,3,7,6]=>[6,7,4,2,5,3,1]=>011011=>110110
[1,4,5,2,6,3,7]=>[7,4,2,5,3,6,1]=>110101=>101011
[1,4,5,2,6,7,3]=>[6,4,2,5,3,7,1]=>110101=>101011
[1,4,5,2,7,3,6]=>[4,2,5,3,7,6,1]=>101011=>110101
[1,4,5,2,7,6,3]=>[4,2,5,3,6,7,1]=>101001=>100101
[1,4,5,3,2,6,7]=>[7,6,4,2,3,5,1]=>111001=>100111
[1,4,5,3,2,7,6]=>[6,7,4,2,3,5,1]=>011001=>100110
[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>110101=>101011
[1,4,5,3,6,7,2]=>[6,4,3,5,2,7,1]=>110101=>101011
[1,4,5,3,7,2,6]=>[4,3,5,2,7,6,1]=>101011=>110101
[1,4,5,3,7,6,2]=>[4,3,5,2,6,7,1]=>101001=>100101
[1,4,5,6,2,3,7]=>[7,5,4,2,6,3,1]=>111011=>110111
[1,4,5,6,2,7,3]=>[5,4,2,6,3,7,1]=>110101=>101011
[1,4,5,6,3,2,7]=>[7,5,4,2,3,6,1]=>111001=>100111
[1,4,5,6,3,7,2]=>[5,4,3,6,2,7,1]=>110101=>101011
[1,4,5,6,7,2,3]=>[6,5,4,2,7,3,1]=>111011=>110111
[1,4,5,6,7,3,2]=>[6,5,4,2,3,7,1]=>111001=>100111
[1,4,5,7,2,3,6]=>[5,4,2,7,6,3,1]=>110111=>111011
[1,4,5,7,2,6,3]=>[5,4,2,7,3,6,1]=>110101=>101011
[1,4,5,7,3,2,6]=>[5,4,2,3,7,6,1]=>110011=>110011
[1,4,5,7,3,6,2]=>[5,4,3,7,2,6,1]=>110101=>101011
[1,4,5,7,6,2,3]=>[5,4,2,6,7,3,1]=>110011=>110011
[1,4,5,7,6,3,2]=>[5,4,2,3,6,7,1]=>110001=>100011
[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>110111=>111011
[1,4,6,2,3,7,5]=>[4,2,6,5,7,3,1]=>101011=>110101
[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>110101=>101011
[1,4,6,2,5,7,3]=>[4,2,6,5,3,7,1]=>101101=>101101
[1,4,6,2,7,3,5]=>[4,2,6,3,7,5,1]=>101011=>110101
[1,4,6,2,7,5,3]=>[4,2,6,3,5,7,1]=>101001=>100101
[1,4,6,3,2,5,7]=>[7,4,2,3,6,5,1]=>110011=>110011
[1,4,6,3,2,7,5]=>[4,2,3,6,5,7,1]=>100101=>101001
[1,4,6,3,5,2,7]=>[7,4,3,6,2,5,1]=>110101=>101011
[1,4,6,3,5,7,2]=>[4,3,6,5,2,7,1]=>101101=>101101
[1,4,6,3,7,2,5]=>[4,3,6,2,7,5,1]=>101011=>110101
[1,4,6,3,7,5,2]=>[4,3,6,2,5,7,1]=>101001=>100101
[1,4,6,5,2,3,7]=>[7,4,2,5,6,3,1]=>110011=>110011
[1,4,6,5,2,7,3]=>[4,2,5,6,3,7,1]=>100101=>101001
[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>110001=>100011
[1,4,6,5,3,7,2]=>[4,3,5,6,2,7,1]=>100101=>101001
[1,4,6,5,7,2,3]=>[5,6,4,2,7,3,1]=>011011=>110110
[1,4,6,5,7,3,2]=>[5,6,4,2,3,7,1]=>011001=>100110
[1,4,6,7,2,3,5]=>[6,4,2,7,5,3,1]=>110111=>111011
[1,4,6,7,2,5,3]=>[6,4,2,7,3,5,1]=>110101=>101011
[1,4,6,7,3,2,5]=>[6,4,2,3,7,5,1]=>110011=>110011
[1,4,6,7,3,5,2]=>[6,4,3,7,2,5,1]=>110101=>101011
[1,4,6,7,5,2,3]=>[6,4,2,5,7,3,1]=>110011=>110011
[1,4,6,7,5,3,2]=>[6,4,2,3,5,7,1]=>110001=>100011
[1,4,7,2,3,5,6]=>[4,2,7,6,5,3,1]=>101111=>111101
[1,4,7,2,3,6,5]=>[4,2,7,5,6,3,1]=>101011=>110101
[1,4,7,2,5,3,6]=>[4,2,7,6,3,5,1]=>101101=>101101
[1,4,7,2,5,6,3]=>[4,2,7,5,3,6,1]=>101101=>101101
[1,4,7,2,6,3,5]=>[4,2,7,3,6,5,1]=>101011=>110101
[1,4,7,2,6,5,3]=>[4,2,7,3,5,6,1]=>101001=>100101
[1,4,7,3,2,5,6]=>[4,2,3,7,6,5,1]=>100111=>111001
[1,4,7,3,2,6,5]=>[4,2,3,7,5,6,1]=>100101=>101001
[1,4,7,3,5,2,6]=>[4,3,7,6,2,5,1]=>101101=>101101
[1,4,7,3,5,6,2]=>[4,3,7,5,2,6,1]=>101101=>101101
[1,4,7,3,6,2,5]=>[4,3,7,2,6,5,1]=>101011=>110101
[1,4,7,3,6,5,2]=>[4,3,7,2,5,6,1]=>101001=>100101
[1,4,7,5,2,3,6]=>[4,2,5,7,6,3,1]=>100111=>111001
[1,4,7,5,2,6,3]=>[4,2,5,7,3,6,1]=>100101=>101001
[1,4,7,5,3,2,6]=>[4,2,3,5,7,6,1]=>100011=>110001
[1,4,7,5,3,6,2]=>[4,3,5,7,2,6,1]=>100101=>101001
[1,4,7,5,6,2,3]=>[5,7,4,2,6,3,1]=>011011=>110110
[1,4,7,5,6,3,2]=>[5,7,4,2,3,6,1]=>011001=>100110
[1,4,7,6,2,3,5]=>[4,2,6,7,5,3,1]=>100111=>111001
[1,4,7,6,2,5,3]=>[4,2,6,7,3,5,1]=>100101=>101001
[1,4,7,6,3,2,5]=>[4,2,3,6,7,5,1]=>100011=>110001
[1,4,7,6,3,5,2]=>[4,3,6,7,2,5,1]=>100101=>101001
[1,4,7,6,5,2,3]=>[4,2,5,6,7,3,1]=>100011=>110001
[1,4,7,6,5,3,2]=>[4,2,3,5,6,7,1]=>100001=>100001
[1,5,2,3,4,6,7]=>[7,6,2,5,4,3,1]=>110111=>111011
[1,5,2,3,4,7,6]=>[6,7,2,5,4,3,1]=>010111=>111010
[1,5,2,3,6,4,7]=>[7,2,5,4,6,3,1]=>101011=>110101
[1,5,2,3,6,7,4]=>[6,2,5,4,7,3,1]=>101011=>110101
[1,5,2,3,7,4,6]=>[2,5,4,7,6,3,1]=>010111=>111010
[1,5,2,3,7,6,4]=>[2,5,4,6,7,3,1]=>010011=>110010
[1,5,2,4,3,6,7]=>[7,6,2,5,3,4,1]=>110101=>101011
[1,5,2,4,3,7,6]=>[6,7,2,5,3,4,1]=>010101=>101010
[1,5,2,4,6,3,7]=>[7,2,5,4,3,6,1]=>101101=>101101
[1,5,2,4,6,7,3]=>[6,2,5,4,3,7,1]=>101101=>101101
[1,5,2,4,7,3,6]=>[2,5,4,3,7,6,1]=>011011=>110110
[1,5,2,4,7,6,3]=>[2,5,4,3,6,7,1]=>011001=>100110
[1,5,2,6,3,4,7]=>[7,2,5,3,6,4,1]=>101011=>110101
[1,5,2,6,3,7,4]=>[2,5,3,6,4,7,1]=>010101=>101010
[1,5,2,6,4,3,7]=>[7,2,5,3,4,6,1]=>101001=>100101
[1,5,2,6,4,7,3]=>[2,5,4,6,3,7,1]=>010101=>101010
[1,5,2,6,7,3,4]=>[6,2,5,3,7,4,1]=>101011=>110101
[1,5,2,6,7,4,3]=>[6,2,5,3,4,7,1]=>101001=>100101
[1,5,2,7,3,4,6]=>[2,5,3,7,6,4,1]=>010111=>111010
[1,5,2,7,3,6,4]=>[2,5,3,7,4,6,1]=>010101=>101010
[1,5,2,7,4,3,6]=>[2,5,3,4,7,6,1]=>010011=>110010
[1,5,2,7,4,6,3]=>[2,5,4,7,3,6,1]=>010101=>101010
[1,5,2,7,6,3,4]=>[2,5,3,6,7,4,1]=>010011=>110010
[1,5,2,7,6,4,3]=>[2,5,3,4,6,7,1]=>010001=>100010
[1,5,3,2,4,6,7]=>[7,6,2,3,5,4,1]=>110011=>110011
[1,5,3,2,4,7,6]=>[6,7,2,3,5,4,1]=>010011=>110010
[1,5,3,2,6,4,7]=>[7,2,3,5,4,6,1]=>100101=>101001
[1,5,3,2,6,7,4]=>[6,2,3,5,4,7,1]=>100101=>101001
[1,5,3,2,7,4,6]=>[2,3,5,4,7,6,1]=>001011=>110100
[1,5,3,2,7,6,4]=>[2,3,5,4,6,7,1]=>001001=>100100
[1,5,3,4,2,6,7]=>[7,6,3,5,2,4,1]=>110101=>101011
[1,5,3,4,2,7,6]=>[6,7,3,5,2,4,1]=>010101=>101010
[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>101101=>101101
[1,5,3,4,6,7,2]=>[6,3,5,4,2,7,1]=>101101=>101101
[1,5,3,4,7,2,6]=>[3,5,4,2,7,6,1]=>011011=>110110
[1,5,3,4,7,6,2]=>[3,5,4,2,6,7,1]=>011001=>100110
[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>101011=>110101
[1,5,3,6,2,7,4]=>[3,5,2,6,4,7,1]=>010101=>101010
[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>101001=>100101
[1,5,3,6,4,7,2]=>[3,5,4,6,2,7,1]=>010101=>101010
[1,5,3,6,7,2,4]=>[6,3,5,2,7,4,1]=>101011=>110101
[1,5,3,6,7,4,2]=>[6,3,5,2,4,7,1]=>101001=>100101
[1,5,3,7,2,4,6]=>[3,5,2,7,6,4,1]=>010111=>111010
[1,5,3,7,2,6,4]=>[3,5,2,7,4,6,1]=>010101=>101010
[1,5,3,7,4,2,6]=>[3,5,2,4,7,6,1]=>010011=>110010
[1,5,3,7,4,6,2]=>[3,5,4,7,2,6,1]=>010101=>101010
[1,5,3,7,6,2,4]=>[3,5,2,6,7,4,1]=>010011=>110010
[1,5,3,7,6,4,2]=>[3,5,2,4,6,7,1]=>010001=>100010
[1,5,4,2,3,6,7]=>[7,6,2,4,5,3,1]=>110011=>110011
[1,5,4,2,3,7,6]=>[6,7,2,4,5,3,1]=>010011=>110010
[1,5,4,2,6,3,7]=>[7,2,4,5,3,6,1]=>100101=>101001
[1,5,4,2,6,7,3]=>[6,2,4,5,3,7,1]=>100101=>101001
[1,5,4,2,7,3,6]=>[2,4,5,3,7,6,1]=>001011=>110100
[1,5,4,2,7,6,3]=>[2,4,5,3,6,7,1]=>001001=>100100
[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>110001=>100011
[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>010001=>100010
[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>100101=>101001
[1,5,4,3,6,7,2]=>[6,3,4,5,2,7,1]=>100101=>101001
[1,5,4,3,7,2,6]=>[3,4,5,2,7,6,1]=>001011=>110100
[1,5,4,3,7,6,2]=>[3,4,5,2,6,7,1]=>001001=>100100
[1,5,4,6,2,3,7]=>[7,4,5,2,6,3,1]=>101011=>110101
[1,5,4,6,2,7,3]=>[4,5,2,6,3,7,1]=>010101=>101010
[1,5,4,6,3,2,7]=>[7,4,5,2,3,6,1]=>101001=>100101
[1,5,4,6,3,7,2]=>[4,5,3,6,2,7,1]=>010101=>101010
[1,5,4,6,7,2,3]=>[6,4,5,2,7,3,1]=>101011=>110101
[1,5,4,6,7,3,2]=>[6,4,5,2,3,7,1]=>101001=>100101
[1,5,4,7,2,3,6]=>[4,5,2,7,6,3,1]=>010111=>111010
[1,5,4,7,2,6,3]=>[4,5,2,7,3,6,1]=>010101=>101010
[1,5,4,7,3,2,6]=>[4,5,2,3,7,6,1]=>010011=>110010
[1,5,4,7,3,6,2]=>[4,5,3,7,2,6,1]=>010101=>101010
[1,5,4,7,6,2,3]=>[4,5,2,6,7,3,1]=>010011=>110010
[1,5,4,7,6,3,2]=>[4,5,2,3,6,7,1]=>010001=>100010
[1,5,6,2,3,4,7]=>[7,5,2,6,4,3,1]=>110111=>111011
[1,5,6,2,3,7,4]=>[5,2,6,4,7,3,1]=>101011=>110101
[1,5,6,2,4,3,7]=>[7,5,2,6,3,4,1]=>110101=>101011
[1,5,6,2,4,7,3]=>[5,2,6,4,3,7,1]=>101101=>101101
[1,5,6,2,7,3,4]=>[5,2,6,3,7,4,1]=>101011=>110101
[1,5,6,2,7,4,3]=>[5,2,6,3,4,7,1]=>101001=>100101
[1,5,6,3,2,4,7]=>[7,5,2,3,6,4,1]=>110011=>110011
[1,5,6,3,2,7,4]=>[5,2,3,6,4,7,1]=>100101=>101001
[1,5,6,3,4,2,7]=>[7,5,3,6,2,4,1]=>110101=>101011
[1,5,6,3,4,7,2]=>[5,3,6,4,2,7,1]=>101101=>101101
[1,5,6,3,7,2,4]=>[5,3,6,2,7,4,1]=>101011=>110101
[1,5,6,3,7,4,2]=>[5,3,6,2,4,7,1]=>101001=>100101
[1,5,6,4,2,3,7]=>[7,5,2,4,6,3,1]=>110011=>110011
[1,5,6,4,2,7,3]=>[5,2,4,6,3,7,1]=>100101=>101001
[1,5,6,4,3,2,7]=>[7,5,2,3,4,6,1]=>110001=>100011
[1,5,6,4,3,7,2]=>[5,3,4,6,2,7,1]=>100101=>101001
[1,5,6,4,7,2,3]=>[5,4,6,2,7,3,1]=>101011=>110101
[1,5,6,4,7,3,2]=>[5,4,6,2,3,7,1]=>101001=>100101
[1,5,6,7,2,3,4]=>[6,5,2,7,4,3,1]=>110111=>111011
[1,5,6,7,2,4,3]=>[6,5,2,7,3,4,1]=>110101=>101011
[1,5,6,7,3,2,4]=>[6,5,2,3,7,4,1]=>110011=>110011
[1,5,6,7,3,4,2]=>[6,5,3,7,2,4,1]=>110101=>101011
[1,5,6,7,4,2,3]=>[6,5,2,4,7,3,1]=>110011=>110011
[1,5,6,7,4,3,2]=>[6,5,2,3,4,7,1]=>110001=>100011
[1,5,7,2,3,4,6]=>[5,2,7,6,4,3,1]=>101111=>111101
[1,5,7,2,3,6,4]=>[5,2,7,4,6,3,1]=>101011=>110101
[1,5,7,2,4,3,6]=>[5,2,7,6,3,4,1]=>101101=>101101
[1,5,7,2,4,6,3]=>[5,2,7,4,3,6,1]=>101101=>101101
[1,5,7,2,6,3,4]=>[5,2,7,3,6,4,1]=>101011=>110101
[1,5,7,2,6,4,3]=>[5,2,7,3,4,6,1]=>101001=>100101
[1,5,7,3,2,4,6]=>[5,2,3,7,6,4,1]=>100111=>111001
[1,5,7,3,2,6,4]=>[5,2,3,7,4,6,1]=>100101=>101001
[1,5,7,3,4,2,6]=>[5,3,7,6,2,4,1]=>101101=>101101
[1,5,7,3,4,6,2]=>[5,3,7,4,2,6,1]=>101101=>101101
[1,5,7,3,6,2,4]=>[5,3,7,2,6,4,1]=>101011=>110101
[1,5,7,3,6,4,2]=>[5,3,7,2,4,6,1]=>101001=>100101
[1,5,7,4,2,3,6]=>[5,2,4,7,6,3,1]=>100111=>111001
[1,5,7,4,2,6,3]=>[5,2,4,7,3,6,1]=>100101=>101001
[1,5,7,4,3,2,6]=>[5,2,3,4,7,6,1]=>100011=>110001
[1,5,7,4,3,6,2]=>[5,3,4,7,2,6,1]=>100101=>101001
[1,5,7,4,6,2,3]=>[5,4,7,2,6,3,1]=>101011=>110101
[1,5,7,4,6,3,2]=>[5,4,7,2,3,6,1]=>101001=>100101
[1,5,7,6,2,3,4]=>[5,2,6,7,4,3,1]=>100111=>111001
[1,5,7,6,2,4,3]=>[5,2,6,7,3,4,1]=>100101=>101001
[1,5,7,6,3,2,4]=>[5,2,3,6,7,4,1]=>100011=>110001
[1,5,7,6,3,4,2]=>[5,3,6,7,2,4,1]=>100101=>101001
[1,5,7,6,4,2,3]=>[5,2,4,6,7,3,1]=>100011=>110001
[1,5,7,6,4,3,2]=>[5,2,3,4,6,7,1]=>100001=>100001
[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>101111=>111101
[1,6,2,3,4,7,5]=>[2,6,5,7,4,3,1]=>010111=>111010
[1,6,2,3,5,4,7]=>[7,2,6,4,5,3,1]=>101011=>110101
[1,6,2,3,5,7,4]=>[2,6,5,4,7,3,1]=>011011=>110110
[1,6,2,3,7,4,5]=>[2,6,4,7,5,3,1]=>010111=>111010
[1,6,2,3,7,5,4]=>[2,6,4,5,7,3,1]=>010011=>110010
[1,6,2,4,3,5,7]=>[7,2,6,5,3,4,1]=>101101=>101101
[1,6,2,4,3,7,5]=>[2,6,5,7,3,4,1]=>010101=>101010
[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>101101=>101101
[1,6,2,4,5,7,3]=>[2,6,5,4,3,7,1]=>011101=>101110
[1,6,2,4,7,3,5]=>[2,6,4,3,7,5,1]=>011011=>110110
[1,6,2,4,7,5,3]=>[2,6,4,3,5,7,1]=>011001=>100110
[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>101011=>110101
[1,6,2,5,3,7,4]=>[2,6,3,5,4,7,1]=>010101=>101010
[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>101001=>100101
[1,6,2,5,4,7,3]=>[2,6,4,5,3,7,1]=>010101=>101010
[1,6,2,5,7,3,4]=>[2,6,5,3,7,4,1]=>011011=>110110
[1,6,2,5,7,4,3]=>[2,6,5,3,4,7,1]=>011001=>100110
[1,6,2,7,3,4,5]=>[2,6,3,7,5,4,1]=>010111=>111010
[1,6,2,7,3,5,4]=>[2,6,3,7,4,5,1]=>010101=>101010
[1,6,2,7,4,3,5]=>[2,6,3,4,7,5,1]=>010011=>110010
[1,6,2,7,4,5,3]=>[2,6,4,7,3,5,1]=>010101=>101010
[1,6,2,7,5,3,4]=>[2,6,3,5,7,4,1]=>010011=>110010
[1,6,2,7,5,4,3]=>[2,6,3,4,5,7,1]=>010001=>100010
[1,6,3,2,4,5,7]=>[7,2,3,6,5,4,1]=>100111=>111001
[1,6,3,2,4,7,5]=>[2,3,6,5,7,4,1]=>001011=>110100
[1,6,3,2,5,4,7]=>[7,2,3,6,4,5,1]=>100101=>101001
[1,6,3,2,5,7,4]=>[2,3,6,5,4,7,1]=>001101=>101100
[1,6,3,2,7,4,5]=>[2,3,6,4,7,5,1]=>001011=>110100
[1,6,3,2,7,5,4]=>[2,3,6,4,5,7,1]=>001001=>100100
[1,6,3,4,2,5,7]=>[7,3,6,5,2,4,1]=>101101=>101101
[1,6,3,4,2,7,5]=>[3,6,5,7,2,4,1]=>010101=>101010
[1,6,3,4,5,2,7]=>[7,3,6,4,2,5,1]=>101101=>101101
[1,6,3,4,5,7,2]=>[3,6,5,4,2,7,1]=>011101=>101110
[1,6,3,4,7,2,5]=>[3,6,4,2,7,5,1]=>011011=>110110
[1,6,3,4,7,5,2]=>[3,6,4,2,5,7,1]=>011001=>100110
[1,6,3,5,2,4,7]=>[7,3,6,2,5,4,1]=>101011=>110101
[1,6,3,5,2,7,4]=>[3,6,2,5,4,7,1]=>010101=>101010
[1,6,3,5,4,2,7]=>[7,3,6,2,4,5,1]=>101001=>100101
[1,6,3,5,4,7,2]=>[3,6,4,5,2,7,1]=>010101=>101010
[1,6,3,5,7,2,4]=>[3,6,5,2,7,4,1]=>011011=>110110
[1,6,3,5,7,4,2]=>[3,6,5,2,4,7,1]=>011001=>100110
[1,6,3,7,2,4,5]=>[3,6,2,7,5,4,1]=>010111=>111010
[1,6,3,7,2,5,4]=>[3,6,2,7,4,5,1]=>010101=>101010
[1,6,3,7,4,2,5]=>[3,6,2,4,7,5,1]=>010011=>110010
[1,6,3,7,4,5,2]=>[3,6,4,7,2,5,1]=>010101=>101010
[1,6,3,7,5,2,4]=>[3,6,2,5,7,4,1]=>010011=>110010
[1,6,3,7,5,4,2]=>[3,6,2,4,5,7,1]=>010001=>100010
[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>100111=>111001
[1,6,4,2,3,7,5]=>[2,4,6,5,7,3,1]=>001011=>110100
[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>100101=>101001
[1,6,4,2,5,7,3]=>[2,4,6,5,3,7,1]=>001101=>101100
[1,6,4,2,7,3,5]=>[2,4,6,3,7,5,1]=>001011=>110100
[1,6,4,2,7,5,3]=>[2,4,6,3,5,7,1]=>001001=>100100
[1,6,4,3,2,5,7]=>[7,2,3,4,6,5,1]=>100011=>110001
[1,6,4,3,2,7,5]=>[2,3,4,6,5,7,1]=>000101=>101000
[1,6,4,3,5,2,7]=>[7,3,4,6,2,5,1]=>100101=>101001
[1,6,4,3,5,7,2]=>[3,4,6,5,2,7,1]=>001101=>101100
[1,6,4,3,7,2,5]=>[3,4,6,2,7,5,1]=>001011=>110100
[1,6,4,3,7,5,2]=>[3,4,6,2,5,7,1]=>001001=>100100
[1,6,4,5,2,3,7]=>[7,4,6,2,5,3,1]=>101011=>110101
[1,6,4,5,2,7,3]=>[4,6,2,5,3,7,1]=>010101=>101010
[1,6,4,5,3,2,7]=>[7,4,6,2,3,5,1]=>101001=>100101
[1,6,4,5,3,7,2]=>[4,6,3,5,2,7,1]=>010101=>101010
[1,6,4,5,7,2,3]=>[4,6,5,2,7,3,1]=>011011=>110110
[1,6,4,5,7,3,2]=>[4,6,5,2,3,7,1]=>011001=>100110
[1,6,4,7,2,3,5]=>[4,6,2,7,5,3,1]=>010111=>111010
[1,6,4,7,2,5,3]=>[4,6,2,7,3,5,1]=>010101=>101010
[1,6,4,7,3,2,5]=>[4,6,2,3,7,5,1]=>010011=>110010
[1,6,4,7,3,5,2]=>[4,6,3,7,2,5,1]=>010101=>101010
[1,6,4,7,5,2,3]=>[4,6,2,5,7,3,1]=>010011=>110010
[1,6,4,7,5,3,2]=>[4,6,2,3,5,7,1]=>010001=>100010
[1,6,5,2,3,4,7]=>[7,2,5,6,4,3,1]=>100111=>111001
[1,6,5,2,3,7,4]=>[2,5,6,4,7,3,1]=>001011=>110100
[1,6,5,2,4,3,7]=>[7,2,5,6,3,4,1]=>100101=>101001
[1,6,5,2,4,7,3]=>[2,5,6,4,3,7,1]=>001101=>101100
[1,6,5,2,7,3,4]=>[2,5,6,3,7,4,1]=>001011=>110100
[1,6,5,2,7,4,3]=>[2,5,6,3,4,7,1]=>001001=>100100
[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>100011=>110001
[1,6,5,3,2,7,4]=>[2,3,5,6,4,7,1]=>000101=>101000
[1,6,5,3,4,2,7]=>[7,3,5,6,2,4,1]=>100101=>101001
[1,6,5,3,4,7,2]=>[3,5,6,4,2,7,1]=>001101=>101100
[1,6,5,3,7,2,4]=>[3,5,6,2,7,4,1]=>001011=>110100
[1,6,5,3,7,4,2]=>[3,5,6,2,4,7,1]=>001001=>100100
[1,6,5,4,2,3,7]=>[7,2,4,5,6,3,1]=>100011=>110001
[1,6,5,4,2,7,3]=>[2,4,5,6,3,7,1]=>000101=>101000
[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>100001=>100001
[1,6,5,4,3,7,2]=>[3,4,5,6,2,7,1]=>000101=>101000
[1,6,5,4,7,2,3]=>[4,5,6,2,7,3,1]=>001011=>110100
[1,6,5,4,7,3,2]=>[4,5,6,2,3,7,1]=>001001=>100100
[1,6,5,7,2,3,4]=>[5,6,2,7,4,3,1]=>010111=>111010
[1,6,5,7,2,4,3]=>[5,6,2,7,3,4,1]=>010101=>101010
[1,6,5,7,3,2,4]=>[5,6,2,3,7,4,1]=>010011=>110010
[1,6,5,7,3,4,2]=>[5,6,3,7,2,4,1]=>010101=>101010
[1,6,5,7,4,2,3]=>[5,6,2,4,7,3,1]=>010011=>110010
[1,6,5,7,4,3,2]=>[5,6,2,3,4,7,1]=>010001=>100010
[1,6,7,2,3,4,5]=>[6,2,7,5,4,3,1]=>101111=>111101
[1,6,7,2,3,5,4]=>[6,2,7,4,5,3,1]=>101011=>110101
[1,6,7,2,4,3,5]=>[6,2,7,5,3,4,1]=>101101=>101101
[1,6,7,2,4,5,3]=>[6,2,7,4,3,5,1]=>101101=>101101
[1,6,7,2,5,3,4]=>[6,2,7,3,5,4,1]=>101011=>110101
[1,6,7,2,5,4,3]=>[6,2,7,3,4,5,1]=>101001=>100101
[1,6,7,3,2,4,5]=>[6,2,3,7,5,4,1]=>100111=>111001
[1,6,7,3,2,5,4]=>[6,2,3,7,4,5,1]=>100101=>101001
[1,6,7,3,4,2,5]=>[6,3,7,5,2,4,1]=>101101=>101101
[1,6,7,3,4,5,2]=>[6,3,7,4,2,5,1]=>101101=>101101
[1,6,7,3,5,2,4]=>[6,3,7,2,5,4,1]=>101011=>110101
[1,6,7,3,5,4,2]=>[6,3,7,2,4,5,1]=>101001=>100101
[1,6,7,4,2,3,5]=>[6,2,4,7,5,3,1]=>100111=>111001
[1,6,7,4,2,5,3]=>[6,2,4,7,3,5,1]=>100101=>101001
[1,6,7,4,3,2,5]=>[6,2,3,4,7,5,1]=>100011=>110001
[1,6,7,4,3,5,2]=>[6,3,4,7,2,5,1]=>100101=>101001
[1,6,7,4,5,2,3]=>[6,4,7,2,5,3,1]=>101011=>110101
[1,6,7,4,5,3,2]=>[6,4,7,2,3,5,1]=>101001=>100101
[1,6,7,5,2,3,4]=>[6,2,5,7,4,3,1]=>100111=>111001
[1,6,7,5,2,4,3]=>[6,2,5,7,3,4,1]=>100101=>101001
[1,6,7,5,3,2,4]=>[6,2,3,5,7,4,1]=>100011=>110001
[1,6,7,5,3,4,2]=>[6,3,5,7,2,4,1]=>100101=>101001
[1,6,7,5,4,2,3]=>[6,2,4,5,7,3,1]=>100011=>110001
[1,6,7,5,4,3,2]=>[6,2,3,4,5,7,1]=>100001=>100001
[1,7,2,3,4,5,6]=>[2,7,6,5,4,3,1]=>011111=>111110
[1,7,2,3,4,6,5]=>[2,7,5,6,4,3,1]=>010111=>111010
[1,7,2,3,5,4,6]=>[2,7,6,4,5,3,1]=>011011=>110110
[1,7,2,3,5,6,4]=>[2,7,5,4,6,3,1]=>011011=>110110
[1,7,2,3,6,4,5]=>[2,7,4,6,5,3,1]=>010111=>111010
[1,7,2,3,6,5,4]=>[2,7,4,5,6,3,1]=>010011=>110010
[1,7,2,4,3,5,6]=>[2,7,6,5,3,4,1]=>011101=>101110
[1,7,2,4,3,6,5]=>[2,7,5,6,3,4,1]=>010101=>101010
[1,7,2,4,5,3,6]=>[2,7,6,4,3,5,1]=>011101=>101110
[1,7,2,4,5,6,3]=>[2,7,5,4,3,6,1]=>011101=>101110
[1,7,2,4,6,3,5]=>[2,7,4,3,6,5,1]=>011011=>110110
[1,7,2,4,6,5,3]=>[2,7,4,3,5,6,1]=>011001=>100110
[1,7,2,5,3,4,6]=>[2,7,6,3,5,4,1]=>011011=>110110
[1,7,2,5,3,6,4]=>[2,7,3,5,4,6,1]=>010101=>101010
[1,7,2,5,4,3,6]=>[2,7,6,3,4,5,1]=>011001=>100110
[1,7,2,5,4,6,3]=>[2,7,4,5,3,6,1]=>010101=>101010
[1,7,2,5,6,3,4]=>[2,7,5,3,6,4,1]=>011011=>110110
[1,7,2,5,6,4,3]=>[2,7,5,3,4,6,1]=>011001=>100110
[1,7,2,6,3,4,5]=>[2,7,3,6,5,4,1]=>010111=>111010
[1,7,2,6,3,5,4]=>[2,7,3,6,4,5,1]=>010101=>101010
[1,7,2,6,4,3,5]=>[2,7,3,4,6,5,1]=>010011=>110010
[1,7,2,6,4,5,3]=>[2,7,4,6,3,5,1]=>010101=>101010
[1,7,2,6,5,3,4]=>[2,7,3,5,6,4,1]=>010011=>110010
[1,7,2,6,5,4,3]=>[2,7,3,4,5,6,1]=>010001=>100010
[1,7,3,2,4,5,6]=>[2,3,7,6,5,4,1]=>001111=>111100
[1,7,3,2,4,6,5]=>[2,3,7,5,6,4,1]=>001011=>110100
[1,7,3,2,5,4,6]=>[2,3,7,6,4,5,1]=>001101=>101100
[1,7,3,2,5,6,4]=>[2,3,7,5,4,6,1]=>001101=>101100
[1,7,3,2,6,4,5]=>[2,3,7,4,6,5,1]=>001011=>110100
[1,7,3,2,6,5,4]=>[2,3,7,4,5,6,1]=>001001=>100100
[1,7,3,4,2,5,6]=>[3,7,6,5,2,4,1]=>011101=>101110
[1,7,3,4,2,6,5]=>[3,7,5,6,2,4,1]=>010101=>101010
[1,7,3,4,5,2,6]=>[3,7,6,4,2,5,1]=>011101=>101110
[1,7,3,4,5,6,2]=>[3,7,5,4,2,6,1]=>011101=>101110
[1,7,3,4,6,2,5]=>[3,7,4,2,6,5,1]=>011011=>110110
[1,7,3,4,6,5,2]=>[3,7,4,2,5,6,1]=>011001=>100110
[1,7,3,5,2,4,6]=>[3,7,6,2,5,4,1]=>011011=>110110
[1,7,3,5,2,6,4]=>[3,7,2,5,4,6,1]=>010101=>101010
[1,7,3,5,4,2,6]=>[3,7,6,2,4,5,1]=>011001=>100110
[1,7,3,5,4,6,2]=>[3,7,4,5,2,6,1]=>010101=>101010
[1,7,3,5,6,2,4]=>[3,7,5,2,6,4,1]=>011011=>110110
[1,7,3,5,6,4,2]=>[3,7,5,2,4,6,1]=>011001=>100110
[1,7,3,6,2,4,5]=>[3,7,2,6,5,4,1]=>010111=>111010
[1,7,3,6,2,5,4]=>[3,7,2,6,4,5,1]=>010101=>101010
[1,7,3,6,4,2,5]=>[3,7,2,4,6,5,1]=>010011=>110010
[1,7,3,6,4,5,2]=>[3,7,4,6,2,5,1]=>010101=>101010
[1,7,3,6,5,2,4]=>[3,7,2,5,6,4,1]=>010011=>110010
[1,7,3,6,5,4,2]=>[3,7,2,4,5,6,1]=>010001=>100010
[1,7,4,2,3,5,6]=>[2,4,7,6,5,3,1]=>001111=>111100
[1,7,4,2,3,6,5]=>[2,4,7,5,6,3,1]=>001011=>110100
[1,7,4,2,5,3,6]=>[2,4,7,6,3,5,1]=>001101=>101100
[1,7,4,2,5,6,3]=>[2,4,7,5,3,6,1]=>001101=>101100
[1,7,4,2,6,3,5]=>[2,4,7,3,6,5,1]=>001011=>110100
[1,7,4,2,6,5,3]=>[2,4,7,3,5,6,1]=>001001=>100100
[1,7,4,3,2,5,6]=>[2,3,4,7,6,5,1]=>000111=>111000
[1,7,4,3,2,6,5]=>[2,3,4,7,5,6,1]=>000101=>101000
[1,7,4,3,5,2,6]=>[3,4,7,6,2,5,1]=>001101=>101100
[1,7,4,3,5,6,2]=>[3,4,7,5,2,6,1]=>001101=>101100
[1,7,4,3,6,2,5]=>[3,4,7,2,6,5,1]=>001011=>110100
[1,7,4,3,6,5,2]=>[3,4,7,2,5,6,1]=>001001=>100100
[1,7,4,5,2,3,6]=>[4,7,6,2,5,3,1]=>011011=>110110
[1,7,4,5,2,6,3]=>[4,7,2,5,3,6,1]=>010101=>101010
[1,7,4,5,3,2,6]=>[4,7,6,2,3,5,1]=>011001=>100110
[1,7,4,5,3,6,2]=>[4,7,3,5,2,6,1]=>010101=>101010
[1,7,4,5,6,2,3]=>[4,7,5,2,6,3,1]=>011011=>110110
[1,7,4,5,6,3,2]=>[4,7,5,2,3,6,1]=>011001=>100110
[1,7,4,6,2,3,5]=>[4,7,2,6,5,3,1]=>010111=>111010
[1,7,4,6,2,5,3]=>[4,7,2,6,3,5,1]=>010101=>101010
[1,7,4,6,3,2,5]=>[4,7,2,3,6,5,1]=>010011=>110010
[1,7,4,6,3,5,2]=>[4,7,3,6,2,5,1]=>010101=>101010
[1,7,4,6,5,2,3]=>[4,7,2,5,6,3,1]=>010011=>110010
[1,7,4,6,5,3,2]=>[4,7,2,3,5,6,1]=>010001=>100010
[1,7,5,2,3,4,6]=>[2,5,7,6,4,3,1]=>001111=>111100
[1,7,5,2,3,6,4]=>[2,5,7,4,6,3,1]=>001011=>110100
[1,7,5,2,4,3,6]=>[2,5,7,6,3,4,1]=>001101=>101100
[1,7,5,2,4,6,3]=>[2,5,7,4,3,6,1]=>001101=>101100
[1,7,5,2,6,3,4]=>[2,5,7,3,6,4,1]=>001011=>110100
[1,7,5,2,6,4,3]=>[2,5,7,3,4,6,1]=>001001=>100100
[1,7,5,3,2,4,6]=>[2,3,5,7,6,4,1]=>000111=>111000
[1,7,5,3,2,6,4]=>[2,3,5,7,4,6,1]=>000101=>101000
[1,7,5,3,4,2,6]=>[3,5,7,6,2,4,1]=>001101=>101100
[1,7,5,3,4,6,2]=>[3,5,7,4,2,6,1]=>001101=>101100
[1,7,5,3,6,2,4]=>[3,5,7,2,6,4,1]=>001011=>110100
[1,7,5,3,6,4,2]=>[3,5,7,2,4,6,1]=>001001=>100100
[1,7,5,4,2,3,6]=>[2,4,5,7,6,3,1]=>000111=>111000
[1,7,5,4,2,6,3]=>[2,4,5,7,3,6,1]=>000101=>101000
[1,7,5,4,3,2,6]=>[2,3,4,5,7,6,1]=>000011=>110000
[1,7,5,4,3,6,2]=>[3,4,5,7,2,6,1]=>000101=>101000
[1,7,5,4,6,2,3]=>[4,5,7,2,6,3,1]=>001011=>110100
[1,7,5,4,6,3,2]=>[4,5,7,2,3,6,1]=>001001=>100100
[1,7,5,6,2,3,4]=>[5,7,2,6,4,3,1]=>010111=>111010
[1,7,5,6,2,4,3]=>[5,7,2,6,3,4,1]=>010101=>101010
[1,7,5,6,3,2,4]=>[5,7,2,3,6,4,1]=>010011=>110010
[1,7,5,6,3,4,2]=>[5,7,3,6,2,4,1]=>010101=>101010
[1,7,5,6,4,2,3]=>[5,7,2,4,6,3,1]=>010011=>110010
[1,7,5,6,4,3,2]=>[5,7,2,3,4,6,1]=>010001=>100010
[1,7,6,2,3,4,5]=>[2,6,7,5,4,3,1]=>001111=>111100
[1,7,6,2,3,5,4]=>[2,6,7,4,5,3,1]=>001011=>110100
[1,7,6,2,4,3,5]=>[2,6,7,5,3,4,1]=>001101=>101100
[1,7,6,2,4,5,3]=>[2,6,7,4,3,5,1]=>001101=>101100
[1,7,6,2,5,3,4]=>[2,6,7,3,5,4,1]=>001011=>110100
[1,7,6,2,5,4,3]=>[2,6,7,3,4,5,1]=>001001=>100100
[1,7,6,3,2,4,5]=>[2,3,6,7,5,4,1]=>000111=>111000
[1,7,6,3,2,5,4]=>[2,3,6,7,4,5,1]=>000101=>101000
[1,7,6,3,4,2,5]=>[3,6,7,5,2,4,1]=>001101=>101100
[1,7,6,3,4,5,2]=>[3,6,7,4,2,5,1]=>001101=>101100
[1,7,6,3,5,2,4]=>[3,6,7,2,5,4,1]=>001011=>110100
[1,7,6,3,5,4,2]=>[3,6,7,2,4,5,1]=>001001=>100100
[1,7,6,4,2,3,5]=>[2,4,6,7,5,3,1]=>000111=>111000
[1,7,6,4,2,5,3]=>[2,4,6,7,3,5,1]=>000101=>101000
[1,7,6,4,3,2,5]=>[2,3,4,6,7,5,1]=>000011=>110000
[1,7,6,4,3,5,2]=>[3,4,6,7,2,5,1]=>000101=>101000
[1,7,6,4,5,2,3]=>[4,6,7,2,5,3,1]=>001011=>110100
[1,7,6,4,5,3,2]=>[4,6,7,2,3,5,1]=>001001=>100100
[1,7,6,5,2,3,4]=>[2,5,6,7,4,3,1]=>000111=>111000
[1,7,6,5,2,4,3]=>[2,5,6,7,3,4,1]=>000101=>101000
[1,7,6,5,3,2,4]=>[2,3,5,6,7,4,1]=>000011=>110000
[1,7,6,5,3,4,2]=>[3,5,6,7,2,4,1]=>000101=>101000
[1,7,6,5,4,2,3]=>[2,4,5,6,7,3,1]=>000011=>110000
[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>000001=>100000
[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>111110=>011111
[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>011110=>011110
[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>101110=>011101
[2,1,3,4,6,7,5]=>[6,5,7,4,3,1,2]=>101110=>011101
[2,1,3,4,7,5,6]=>[5,7,6,4,3,1,2]=>011110=>011110
[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>001110=>011100
[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>110110=>011011
[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>010110=>011010
[2,1,3,5,6,4,7]=>[7,5,4,6,3,1,2]=>110110=>011011
[2,1,3,5,6,7,4]=>[6,5,4,7,3,1,2]=>110110=>011011
[2,1,3,5,7,4,6]=>[5,4,7,6,3,1,2]=>101110=>011101
[2,1,3,5,7,6,4]=>[5,4,6,7,3,1,2]=>100110=>011001
[2,1,3,6,4,5,7]=>[7,4,6,5,3,1,2]=>101110=>011101
[2,1,3,6,4,7,5]=>[4,6,5,7,3,1,2]=>010110=>011010
[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>100110=>011001
[2,1,3,6,5,7,4]=>[5,6,4,7,3,1,2]=>010110=>011010
[2,1,3,6,7,4,5]=>[6,4,7,5,3,1,2]=>101110=>011101
[2,1,3,6,7,5,4]=>[6,4,5,7,3,1,2]=>100110=>011001
[2,1,3,7,4,5,6]=>[4,7,6,5,3,1,2]=>011110=>011110
[2,1,3,7,4,6,5]=>[4,7,5,6,3,1,2]=>010110=>011010
[2,1,3,7,5,4,6]=>[4,5,7,6,3,1,2]=>001110=>011100
[2,1,3,7,5,6,4]=>[5,7,4,6,3,1,2]=>010110=>011010
[2,1,3,7,6,4,5]=>[4,6,7,5,3,1,2]=>001110=>011100
[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>000110=>011000
[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>111010=>010111
[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>011010=>010110
[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>101010=>010101
[2,1,4,3,6,7,5]=>[6,5,7,3,4,1,2]=>101010=>010101
[2,1,4,3,7,5,6]=>[5,7,6,3,4,1,2]=>011010=>010110
[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>001010=>010100
[2,1,4,5,3,6,7]=>[7,6,4,3,5,1,2]=>111010=>010111
[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]=>011010=>010110
[2,1,4,5,6,3,7]=>[7,5,4,3,6,1,2]=>111010=>010111
[2,1,4,5,6,7,3]=>[6,5,4,3,7,1,2]=>111010=>010111
[2,1,4,5,7,3,6]=>[5,4,3,7,6,1,2]=>110110=>011011
[2,1,4,5,7,6,3]=>[5,4,3,6,7,1,2]=>110010=>010011
[2,1,4,6,3,5,7]=>[7,4,3,6,5,1,2]=>110110=>011011
[2,1,4,6,3,7,5]=>[4,3,6,5,7,1,2]=>101010=>010101
[2,1,4,6,5,3,7]=>[7,4,3,5,6,1,2]=>110010=>010011
[2,1,4,6,5,7,3]=>[5,6,4,3,7,1,2]=>011010=>010110
[2,1,4,6,7,3,5]=>[6,4,3,7,5,1,2]=>110110=>011011
[2,1,4,6,7,5,3]=>[6,4,3,5,7,1,2]=>110010=>010011
[2,1,4,7,3,5,6]=>[4,3,7,6,5,1,2]=>101110=>011101
[2,1,4,7,3,6,5]=>[4,3,7,5,6,1,2]=>101010=>010101
[2,1,4,7,5,3,6]=>[4,3,5,7,6,1,2]=>100110=>011001
[2,1,4,7,5,6,3]=>[5,7,4,3,6,1,2]=>011010=>010110
[2,1,4,7,6,3,5]=>[4,3,6,7,5,1,2]=>100110=>011001
[2,1,4,7,6,5,3]=>[4,3,5,6,7,1,2]=>100010=>010001
[2,1,5,3,4,6,7]=>[7,6,3,5,4,1,2]=>110110=>011011
[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>010110=>011010
[2,1,5,3,6,4,7]=>[7,3,5,4,6,1,2]=>101010=>010101
[2,1,5,3,6,7,4]=>[6,3,5,4,7,1,2]=>101010=>010101
[2,1,5,3,7,4,6]=>[3,5,4,7,6,1,2]=>010110=>011010
[2,1,5,3,7,6,4]=>[3,5,4,6,7,1,2]=>010010=>010010
[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>110010=>010011
[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>010010=>010010
[2,1,5,4,6,3,7]=>[7,4,5,3,6,1,2]=>101010=>010101
[2,1,5,4,6,7,3]=>[6,4,5,3,7,1,2]=>101010=>010101
[2,1,5,4,7,3,6]=>[4,5,3,7,6,1,2]=>010110=>011010
[2,1,5,4,7,6,3]=>[4,5,3,6,7,1,2]=>010010=>010010
[2,1,5,6,3,4,7]=>[7,5,3,6,4,1,2]=>110110=>011011
[2,1,5,6,3,7,4]=>[5,3,6,4,7,1,2]=>101010=>010101
[2,1,5,6,4,3,7]=>[7,5,3,4,6,1,2]=>110010=>010011
[2,1,5,6,4,7,3]=>[5,4,6,3,7,1,2]=>101010=>010101
[2,1,5,6,7,3,4]=>[6,5,3,7,4,1,2]=>110110=>011011
[2,1,5,6,7,4,3]=>[6,5,3,4,7,1,2]=>110010=>010011
[2,1,5,7,3,4,6]=>[5,3,7,6,4,1,2]=>101110=>011101
[2,1,5,7,3,6,4]=>[5,3,7,4,6,1,2]=>101010=>010101
[2,1,5,7,4,3,6]=>[5,3,4,7,6,1,2]=>100110=>011001
[2,1,5,7,4,6,3]=>[5,4,7,3,6,1,2]=>101010=>010101
[2,1,5,7,6,3,4]=>[5,3,6,7,4,1,2]=>100110=>011001
[2,1,5,7,6,4,3]=>[5,3,4,6,7,1,2]=>100010=>010001
[2,1,6,3,4,5,7]=>[7,3,6,5,4,1,2]=>101110=>011101
[2,1,6,3,4,7,5]=>[3,6,5,7,4,1,2]=>010110=>011010
[2,1,6,3,5,4,7]=>[7,3,6,4,5,1,2]=>101010=>010101
[2,1,6,3,5,7,4]=>[3,6,5,4,7,1,2]=>011010=>010110
[2,1,6,3,7,4,5]=>[3,6,4,7,5,1,2]=>010110=>011010
[2,1,6,3,7,5,4]=>[3,6,4,5,7,1,2]=>010010=>010010
[2,1,6,4,3,5,7]=>[7,3,4,6,5,1,2]=>100110=>011001
[2,1,6,4,3,7,5]=>[3,4,6,5,7,1,2]=>001010=>010100
[2,1,6,4,5,3,7]=>[7,4,6,3,5,1,2]=>101010=>010101
[2,1,6,4,5,7,3]=>[4,6,5,3,7,1,2]=>011010=>010110
[2,1,6,4,7,3,5]=>[4,6,3,7,5,1,2]=>010110=>011010
[2,1,6,4,7,5,3]=>[4,6,3,5,7,1,2]=>010010=>010010
[2,1,6,5,3,4,7]=>[7,3,5,6,4,1,2]=>100110=>011001
[2,1,6,5,3,7,4]=>[3,5,6,4,7,1,2]=>001010=>010100
[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>100010=>010001
[2,1,6,5,4,7,3]=>[4,5,6,3,7,1,2]=>001010=>010100
[2,1,6,5,7,3,4]=>[5,6,3,7,4,1,2]=>010110=>011010
[2,1,6,5,7,4,3]=>[5,6,3,4,7,1,2]=>010010=>010010
[2,1,6,7,3,4,5]=>[6,3,7,5,4,1,2]=>101110=>011101
[2,1,6,7,3,5,4]=>[6,3,7,4,5,1,2]=>101010=>010101
[2,1,6,7,4,3,5]=>[6,3,4,7,5,1,2]=>100110=>011001
[2,1,6,7,4,5,3]=>[6,4,7,3,5,1,2]=>101010=>010101
[2,1,6,7,5,3,4]=>[6,3,5,7,4,1,2]=>100110=>011001
[2,1,6,7,5,4,3]=>[6,3,4,5,7,1,2]=>100010=>010001
[2,1,7,3,4,5,6]=>[3,7,6,5,4,1,2]=>011110=>011110
[2,1,7,3,4,6,5]=>[3,7,5,6,4,1,2]=>010110=>011010
[2,1,7,3,5,4,6]=>[3,7,6,4,5,1,2]=>011010=>010110
[2,1,7,3,5,6,4]=>[3,7,5,4,6,1,2]=>011010=>010110
[2,1,7,3,6,4,5]=>[3,7,4,6,5,1,2]=>010110=>011010
[2,1,7,3,6,5,4]=>[3,7,4,5,6,1,2]=>010010=>010010
[2,1,7,4,3,5,6]=>[3,4,7,6,5,1,2]=>001110=>011100
[2,1,7,4,3,6,5]=>[3,4,7,5,6,1,2]=>001010=>010100
[2,1,7,4,5,3,6]=>[4,7,6,3,5,1,2]=>011010=>010110
[2,1,7,4,5,6,3]=>[4,7,5,3,6,1,2]=>011010=>010110
[2,1,7,4,6,3,5]=>[4,7,3,6,5,1,2]=>010110=>011010
[2,1,7,4,6,5,3]=>[4,7,3,5,6,1,2]=>010010=>010010
[2,1,7,5,3,4,6]=>[3,5,7,6,4,1,2]=>001110=>011100
[2,1,7,5,3,6,4]=>[3,5,7,4,6,1,2]=>001010=>010100
[2,1,7,5,4,3,6]=>[3,4,5,7,6,1,2]=>000110=>011000
[2,1,7,5,4,6,3]=>[4,5,7,3,6,1,2]=>001010=>010100
[2,1,7,5,6,3,4]=>[5,7,3,6,4,1,2]=>010110=>011010
[2,1,7,5,6,4,3]=>[5,7,3,4,6,1,2]=>010010=>010010
[2,1,7,6,3,4,5]=>[3,6,7,5,4,1,2]=>001110=>011100
[2,1,7,6,3,5,4]=>[3,6,7,4,5,1,2]=>001010=>010100
[2,1,7,6,4,3,5]=>[3,4,6,7,5,1,2]=>000110=>011000
[2,1,7,6,4,5,3]=>[4,6,7,3,5,1,2]=>001010=>010100
[2,1,7,6,5,3,4]=>[3,5,6,7,4,1,2]=>000110=>011000
[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>000010=>010000
[2,3,1,4,5,6,7]=>[7,6,5,4,2,1,3]=>111110=>011111
[2,3,1,4,5,7,6]=>[6,7,5,4,2,1,3]=>011110=>011110
[2,3,1,4,6,5,7]=>[7,5,6,4,2,1,3]=>101110=>011101
[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]=>101110=>011101
[2,3,1,4,7,5,6]=>[5,7,6,4,2,1,3]=>011110=>011110
[2,3,1,4,7,6,5]=>[5,6,7,4,2,1,3]=>001110=>011100
[2,3,1,5,4,6,7]=>[7,6,4,5,2,1,3]=>110110=>011011
[2,3,1,5,4,7,6]=>[6,7,4,5,2,1,3]=>010110=>011010
[2,3,1,5,6,4,7]=>[7,5,4,6,2,1,3]=>110110=>011011
[2,3,1,5,6,7,4]=>[6,5,4,7,2,1,3]=>110110=>011011
[2,3,1,5,7,4,6]=>[5,4,7,6,2,1,3]=>101110=>011101
[2,3,1,5,7,6,4]=>[5,4,6,7,2,1,3]=>100110=>011001
[2,3,1,6,4,5,7]=>[7,4,6,5,2,1,3]=>101110=>011101
[2,3,1,6,4,7,5]=>[4,6,5,7,2,1,3]=>010110=>011010
[2,3,1,6,5,4,7]=>[7,4,5,6,2,1,3]=>100110=>011001
[2,3,1,6,5,7,4]=>[5,6,4,7,2,1,3]=>010110=>011010
[2,3,1,6,7,4,5]=>[6,4,7,5,2,1,3]=>101110=>011101
[2,3,1,6,7,5,4]=>[6,4,5,7,2,1,3]=>100110=>011001
[2,3,1,7,4,5,6]=>[4,7,6,5,2,1,3]=>011110=>011110
[2,3,1,7,4,6,5]=>[4,7,5,6,2,1,3]=>010110=>011010
[2,3,1,7,5,4,6]=>[4,5,7,6,2,1,3]=>001110=>011100
[2,3,1,7,5,6,4]=>[5,7,4,6,2,1,3]=>010110=>011010
[2,3,1,7,6,4,5]=>[4,6,7,5,2,1,3]=>001110=>011100
[2,3,1,7,6,5,4]=>[4,5,6,7,2,1,3]=>000110=>011000
[2,3,4,1,5,6,7]=>[7,6,5,3,2,1,4]=>111110=>011111
[2,3,4,1,5,7,6]=>[6,7,5,3,2,1,4]=>011110=>011110
[2,3,4,1,6,5,7]=>[7,5,6,3,2,1,4]=>101110=>011101
[2,3,4,1,6,7,5]=>[6,5,7,3,2,1,4]=>101110=>011101
[2,3,4,1,7,5,6]=>[5,7,6,3,2,1,4]=>011110=>011110
[2,3,4,1,7,6,5]=>[5,6,7,3,2,1,4]=>001110=>011100
[2,3,4,5,1,6,7]=>[7,6,4,3,2,1,5]=>111110=>011111
[2,3,4,5,1,7,6]=>[6,7,4,3,2,1,5]=>011110=>011110
[2,3,4,5,6,1,7]=>[7,5,4,3,2,1,6]=>111110=>011111
[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>111110=>011111
[2,3,4,5,7,1,6]=>[5,4,3,2,1,7,6]=>111101=>101111
[2,3,4,5,7,6,1]=>[5,4,3,2,1,6,7]=>111100=>001111
[2,3,4,6,1,5,7]=>[7,4,3,2,1,6,5]=>111101=>101111
[2,3,4,6,1,7,5]=>[4,3,2,1,6,5,7]=>111010=>010111
[2,3,4,6,5,1,7]=>[7,4,3,2,1,5,6]=>111100=>001111
[2,3,4,6,5,7,1]=>[5,6,4,3,2,1,7]=>011110=>011110
[2,3,4,6,7,1,5]=>[6,4,3,2,1,7,5]=>111101=>101111
[2,3,4,6,7,5,1]=>[6,4,3,2,1,5,7]=>111100=>001111
[2,3,4,7,1,5,6]=>[4,3,2,1,7,6,5]=>111011=>110111
[2,3,4,7,1,6,5]=>[4,3,2,1,7,5,6]=>111010=>010111
[2,3,4,7,5,1,6]=>[4,3,2,1,5,7,6]=>111001=>100111
[2,3,4,7,5,6,1]=>[5,7,4,3,2,1,6]=>011110=>011110
[2,3,4,7,6,1,5]=>[4,3,2,1,6,7,5]=>111001=>100111
[2,3,4,7,6,5,1]=>[4,3,2,1,5,6,7]=>111000=>000111
[2,3,5,1,4,6,7]=>[7,6,3,2,1,5,4]=>111101=>101111
[2,3,5,1,4,7,6]=>[6,7,3,2,1,5,4]=>011101=>101110
[2,3,5,1,6,4,7]=>[7,3,2,1,5,4,6]=>111010=>010111
[2,3,5,1,6,7,4]=>[6,3,2,1,5,4,7]=>111010=>010111
[2,3,5,1,7,4,6]=>[3,2,1,5,4,7,6]=>110101=>101011
[2,3,5,1,7,6,4]=>[3,2,1,5,4,6,7]=>110100=>001011
[2,3,5,4,1,6,7]=>[7,6,3,2,1,4,5]=>111100=>001111
[2,3,5,4,1,7,6]=>[6,7,3,2,1,4,5]=>011100=>001110
[2,3,5,4,6,1,7]=>[7,4,5,3,2,1,6]=>101110=>011101
[2,3,5,4,6,7,1]=>[6,4,5,3,2,1,7]=>101110=>011101
[2,3,5,4,7,1,6]=>[4,5,3,2,1,7,6]=>011101=>101110
[2,3,5,4,7,6,1]=>[4,5,3,2,1,6,7]=>011100=>001110
[2,3,5,6,1,4,7]=>[7,5,3,2,1,6,4]=>111101=>101111
[2,3,5,6,1,7,4]=>[5,3,2,1,6,4,7]=>111010=>010111
[2,3,5,6,4,1,7]=>[7,5,3,2,1,4,6]=>111100=>001111
[2,3,5,6,4,7,1]=>[5,4,6,3,2,1,7]=>101110=>011101
[2,3,5,6,7,1,4]=>[6,5,3,2,1,7,4]=>111101=>101111
[2,3,5,6,7,4,1]=>[6,5,3,2,1,4,7]=>111100=>001111
[2,3,5,7,1,4,6]=>[5,3,2,1,7,6,4]=>111011=>110111
[2,3,5,7,1,6,4]=>[5,3,2,1,7,4,6]=>111010=>010111
[2,3,5,7,4,1,6]=>[5,3,2,1,4,7,6]=>111001=>100111
[2,3,5,7,4,6,1]=>[5,4,7,3,2,1,6]=>101110=>011101
[2,3,5,7,6,1,4]=>[5,3,2,1,6,7,4]=>111001=>100111
[2,3,5,7,6,4,1]=>[5,3,2,1,4,6,7]=>111000=>000111
[2,3,6,1,4,5,7]=>[7,3,2,1,6,5,4]=>111011=>110111
[2,3,6,1,4,7,5]=>[3,2,1,6,5,7,4]=>110101=>101011
[2,3,6,1,5,4,7]=>[7,3,2,1,6,4,5]=>111010=>010111
[2,3,6,1,5,7,4]=>[3,2,1,6,5,4,7]=>110110=>011011
[2,3,6,1,7,4,5]=>[3,2,1,6,4,7,5]=>110101=>101011
[2,3,6,1,7,5,4]=>[3,2,1,6,4,5,7]=>110100=>001011
[2,3,6,4,1,5,7]=>[7,3,2,1,4,6,5]=>111001=>100111
[2,3,6,4,1,7,5]=>[3,2,1,4,6,5,7]=>110010=>010011
[2,3,6,4,5,1,7]=>[7,4,6,3,2,1,5]=>101110=>011101
[2,3,6,4,5,7,1]=>[4,6,5,3,2,1,7]=>011110=>011110
[2,3,6,4,7,1,5]=>[4,6,3,2,1,7,5]=>011101=>101110
[2,3,6,4,7,5,1]=>[4,6,3,2,1,5,7]=>011100=>001110
[2,3,6,5,1,4,7]=>[7,3,2,1,5,6,4]=>111001=>100111
[2,3,6,5,1,7,4]=>[3,2,1,5,6,4,7]=>110010=>010011
[2,3,6,5,4,1,7]=>[7,3,2,1,4,5,6]=>111000=>000111
[2,3,6,5,4,7,1]=>[4,5,6,3,2,1,7]=>001110=>011100
[2,3,6,5,7,1,4]=>[5,6,3,2,1,7,4]=>011101=>101110
[2,3,6,5,7,4,1]=>[5,6,3,2,1,4,7]=>011100=>001110
[2,3,6,7,1,4,5]=>[6,3,2,1,7,5,4]=>111011=>110111
[2,3,6,7,1,5,4]=>[6,3,2,1,7,4,5]=>111010=>010111
[2,3,6,7,4,1,5]=>[6,3,2,1,4,7,5]=>111001=>100111
[2,3,6,7,4,5,1]=>[6,4,7,3,2,1,5]=>101110=>011101
[2,3,6,7,5,1,4]=>[6,3,2,1,5,7,4]=>111001=>100111
[2,3,6,7,5,4,1]=>[6,3,2,1,4,5,7]=>111000=>000111
[2,3,7,1,4,5,6]=>[3,2,1,7,6,5,4]=>110111=>111011
[2,3,7,1,4,6,5]=>[3,2,1,7,5,6,4]=>110101=>101011
[2,3,7,1,5,4,6]=>[3,2,1,7,6,4,5]=>110110=>011011
[2,3,7,1,5,6,4]=>[3,2,1,7,5,4,6]=>110110=>011011
[2,3,7,1,6,4,5]=>[3,2,1,7,4,6,5]=>110101=>101011
[2,3,7,1,6,5,4]=>[3,2,1,7,4,5,6]=>110100=>001011
[2,3,7,4,1,5,6]=>[3,2,1,4,7,6,5]=>110011=>110011
[2,3,7,4,1,6,5]=>[3,2,1,4,7,5,6]=>110010=>010011
[2,3,7,4,5,1,6]=>[4,7,6,3,2,1,5]=>011110=>011110
[2,3,7,4,5,6,1]=>[4,7,5,3,2,1,6]=>011110=>011110
[2,3,7,4,6,1,5]=>[4,7,3,2,1,6,5]=>011101=>101110
[2,3,7,4,6,5,1]=>[4,7,3,2,1,5,6]=>011100=>001110
[2,3,7,5,1,4,6]=>[3,2,1,5,7,6,4]=>110011=>110011
[2,3,7,5,1,6,4]=>[3,2,1,5,7,4,6]=>110010=>010011
[2,3,7,5,4,1,6]=>[3,2,1,4,5,7,6]=>110001=>100011
[2,3,7,5,4,6,1]=>[4,5,7,3,2,1,6]=>001110=>011100
[2,3,7,5,6,1,4]=>[5,7,3,2,1,6,4]=>011101=>101110
[2,3,7,5,6,4,1]=>[5,7,3,2,1,4,6]=>011100=>001110
[2,3,7,6,1,4,5]=>[3,2,1,6,7,5,4]=>110011=>110011
[2,3,7,6,1,5,4]=>[3,2,1,6,7,4,5]=>110010=>010011
[2,3,7,6,4,1,5]=>[3,2,1,4,6,7,5]=>110001=>100011
[2,3,7,6,4,5,1]=>[4,6,7,3,2,1,5]=>001110=>011100
[2,3,7,6,5,1,4]=>[3,2,1,5,6,7,4]=>110001=>100011
[2,3,7,6,5,4,1]=>[3,2,1,4,5,6,7]=>110000=>000011
[2,4,1,3,5,6,7]=>[7,6,5,2,1,4,3]=>111101=>101111
[2,4,1,3,5,7,6]=>[6,7,5,2,1,4,3]=>011101=>101110
[2,4,1,3,6,5,7]=>[7,5,6,2,1,4,3]=>101101=>101101
[2,4,1,3,6,7,5]=>[6,5,7,2,1,4,3]=>101101=>101101
[2,4,1,3,7,5,6]=>[5,7,6,2,1,4,3]=>011101=>101110
[2,4,1,3,7,6,5]=>[5,6,7,2,1,4,3]=>001101=>101100
[2,4,1,5,3,6,7]=>[7,6,2,1,4,3,5]=>111010=>010111
[2,4,1,5,3,7,6]=>[6,7,2,1,4,3,5]=>011010=>010110
[2,4,1,5,6,3,7]=>[7,5,2,1,4,3,6]=>111010=>010111
[2,4,1,5,6,7,3]=>[6,5,2,1,4,3,7]=>111010=>010111
[2,4,1,5,7,3,6]=>[5,2,1,4,3,7,6]=>110101=>101011
[2,4,1,5,7,6,3]=>[5,2,1,4,3,6,7]=>110100=>001011
[2,4,1,6,3,5,7]=>[7,2,1,4,3,6,5]=>110101=>101011
[2,4,1,6,3,7,5]=>[2,1,4,3,6,5,7]=>101010=>010101
[2,4,1,6,5,3,7]=>[7,2,1,4,3,5,6]=>110100=>001011
[2,4,1,6,5,7,3]=>[5,6,2,1,4,3,7]=>011010=>010110
[2,4,1,6,7,3,5]=>[6,2,1,4,3,7,5]=>110101=>101011
[2,4,1,6,7,5,3]=>[6,2,1,4,3,5,7]=>110100=>001011
[2,4,1,7,3,5,6]=>[2,1,4,3,7,6,5]=>101011=>110101
[2,4,1,7,3,6,5]=>[2,1,4,3,7,5,6]=>101010=>010101
[2,4,1,7,5,3,6]=>[2,1,4,3,5,7,6]=>101001=>100101
[2,4,1,7,5,6,3]=>[5,7,2,1,4,3,6]=>011010=>010110
[2,4,1,7,6,3,5]=>[2,1,4,3,6,7,5]=>101001=>100101
[2,4,1,7,6,5,3]=>[2,1,4,3,5,6,7]=>101000=>000101
[2,4,3,1,5,6,7]=>[7,6,5,2,1,3,4]=>111100=>001111
[2,4,3,1,5,7,6]=>[6,7,5,2,1,3,4]=>011100=>001110
[2,4,3,1,6,5,7]=>[7,5,6,2,1,3,4]=>101100=>001101
[2,4,3,1,6,7,5]=>[6,5,7,2,1,3,4]=>101100=>001101
[2,4,3,1,7,5,6]=>[5,7,6,2,1,3,4]=>011100=>001110
[2,4,3,1,7,6,5]=>[5,6,7,2,1,3,4]=>001100=>001100
[2,4,3,5,1,6,7]=>[7,6,3,4,2,1,5]=>110110=>011011
[2,4,3,5,1,7,6]=>[6,7,3,4,2,1,5]=>010110=>011010
[2,4,3,5,6,1,7]=>[7,5,3,4,2,1,6]=>110110=>011011
[2,4,3,5,6,7,1]=>[6,5,3,4,2,1,7]=>110110=>011011
[2,4,3,5,7,1,6]=>[5,3,4,2,1,7,6]=>101101=>101101
[2,4,3,5,7,6,1]=>[5,3,4,2,1,6,7]=>101100=>001101
[2,4,3,6,1,5,7]=>[7,3,4,2,1,6,5]=>101101=>101101
[2,4,3,6,1,7,5]=>[3,4,2,1,6,5,7]=>011010=>010110
[2,4,3,6,5,1,7]=>[7,3,4,2,1,5,6]=>101100=>001101
[2,4,3,6,5,7,1]=>[5,6,3,4,2,1,7]=>010110=>011010
[2,4,3,6,7,1,5]=>[6,3,4,2,1,7,5]=>101101=>101101
[2,4,3,6,7,5,1]=>[6,3,4,2,1,5,7]=>101100=>001101
[2,4,3,7,1,5,6]=>[3,4,2,1,7,6,5]=>011011=>110110
[2,4,3,7,1,6,5]=>[3,4,2,1,7,5,6]=>011010=>010110
[2,4,3,7,5,1,6]=>[3,4,2,1,5,7,6]=>011001=>100110
[2,4,3,7,5,6,1]=>[5,7,3,4,2,1,6]=>010110=>011010
[2,4,3,7,6,1,5]=>[3,4,2,1,6,7,5]=>011001=>100110
[2,4,3,7,6,5,1]=>[3,4,2,1,5,6,7]=>011000=>000110
[2,4,5,1,3,6,7]=>[7,6,4,2,1,5,3]=>111101=>101111
[2,4,5,1,3,7,6]=>[6,7,4,2,1,5,3]=>011101=>101110
[2,4,5,1,6,3,7]=>[7,4,2,1,5,3,6]=>111010=>010111
[2,4,5,1,6,7,3]=>[6,4,2,1,5,3,7]=>111010=>010111
[2,4,5,1,7,3,6]=>[4,2,1,5,3,7,6]=>110101=>101011
[2,4,5,1,7,6,3]=>[4,2,1,5,3,6,7]=>110100=>001011
[2,4,5,3,1,6,7]=>[7,6,4,2,1,3,5]=>111100=>001111
[2,4,5,3,1,7,6]=>[6,7,4,2,1,3,5]=>011100=>001110
[2,4,5,3,6,1,7]=>[7,4,3,5,2,1,6]=>110110=>011011
[2,4,5,3,6,7,1]=>[6,4,3,5,2,1,7]=>110110=>011011
[2,4,5,3,7,1,6]=>[4,3,5,2,1,7,6]=>101101=>101101
[2,4,5,3,7,6,1]=>[4,3,5,2,1,6,7]=>101100=>001101
[2,4,5,6,1,3,7]=>[7,5,4,2,1,6,3]=>111101=>101111
[2,4,5,6,1,7,3]=>[5,4,2,1,6,3,7]=>111010=>010111
[2,4,5,6,3,1,7]=>[7,5,4,2,1,3,6]=>111100=>001111
[2,4,5,6,3,7,1]=>[5,4,3,6,2,1,7]=>110110=>011011
[2,4,5,6,7,1,3]=>[6,5,4,2,1,7,3]=>111101=>101111
[2,4,5,6,7,3,1]=>[6,5,4,2,1,3,7]=>111100=>001111
[2,4,5,7,1,3,6]=>[5,4,2,1,7,6,3]=>111011=>110111
[2,4,5,7,1,6,3]=>[5,4,2,1,7,3,6]=>111010=>010111
[2,4,5,7,3,1,6]=>[5,4,2,1,3,7,6]=>111001=>100111
[2,4,5,7,3,6,1]=>[5,4,3,7,2,1,6]=>110110=>011011
[2,4,5,7,6,1,3]=>[5,4,2,1,6,7,3]=>111001=>100111
[2,4,5,7,6,3,1]=>[5,4,2,1,3,6,7]=>111000=>000111
[2,4,6,1,3,5,7]=>[7,4,2,1,6,5,3]=>111011=>110111
[2,4,6,1,3,7,5]=>[4,2,1,6,5,7,3]=>110101=>101011
[2,4,6,1,5,3,7]=>[7,4,2,1,6,3,5]=>111010=>010111
[2,4,6,1,5,7,3]=>[4,2,1,6,5,3,7]=>110110=>011011
[2,4,6,1,7,3,5]=>[4,2,1,6,3,7,5]=>110101=>101011
[2,4,6,1,7,5,3]=>[4,2,1,6,3,5,7]=>110100=>001011
[2,4,6,3,1,5,7]=>[7,4,2,1,3,6,5]=>111001=>100111
[2,4,6,3,1,7,5]=>[4,2,1,3,6,5,7]=>110010=>010011
[2,4,6,3,5,1,7]=>[7,4,3,6,2,1,5]=>110110=>011011
[2,4,6,3,5,7,1]=>[4,3,6,5,2,1,7]=>101110=>011101
[2,4,6,3,7,1,5]=>[4,3,6,2,1,7,5]=>101101=>101101
[2,4,6,3,7,5,1]=>[4,3,6,2,1,5,7]=>101100=>001101
[2,4,6,5,1,3,7]=>[7,4,2,1,5,6,3]=>111001=>100111
[2,4,6,5,1,7,3]=>[4,2,1,5,6,3,7]=>110010=>010011
[2,4,6,5,3,1,7]=>[7,4,2,1,3,5,6]=>111000=>000111
[2,4,6,5,3,7,1]=>[4,3,5,6,2,1,7]=>100110=>011001
[2,4,6,5,7,1,3]=>[5,6,4,2,1,7,3]=>011101=>101110
[2,4,6,5,7,3,1]=>[5,6,4,2,1,3,7]=>011100=>001110
[2,4,6,7,1,3,5]=>[6,4,2,1,7,5,3]=>111011=>110111
[2,4,6,7,1,5,3]=>[6,4,2,1,7,3,5]=>111010=>010111
[2,4,6,7,3,1,5]=>[6,4,2,1,3,7,5]=>111001=>100111
[2,4,6,7,3,5,1]=>[6,4,3,7,2,1,5]=>110110=>011011
[2,4,6,7,5,1,3]=>[6,4,2,1,5,7,3]=>111001=>100111
[2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>111000=>000111
[2,4,7,1,3,5,6]=>[4,2,1,7,6,5,3]=>110111=>111011
[2,4,7,1,3,6,5]=>[4,2,1,7,5,6,3]=>110101=>101011
[2,4,7,1,5,3,6]=>[4,2,1,7,6,3,5]=>110110=>011011
[2,4,7,1,5,6,3]=>[4,2,1,7,5,3,6]=>110110=>011011
[2,4,7,1,6,3,5]=>[4,2,1,7,3,6,5]=>110101=>101011
[2,4,7,1,6,5,3]=>[4,2,1,7,3,5,6]=>110100=>001011
[2,4,7,3,1,5,6]=>[4,2,1,3,7,6,5]=>110011=>110011
[2,4,7,3,1,6,5]=>[4,2,1,3,7,5,6]=>110010=>010011
[2,4,7,3,5,1,6]=>[4,3,7,6,2,1,5]=>101110=>011101
[2,4,7,3,5,6,1]=>[4,3,7,5,2,1,6]=>101110=>011101
[2,4,7,3,6,1,5]=>[4,3,7,2,1,6,5]=>101101=>101101
[2,4,7,3,6,5,1]=>[4,3,7,2,1,5,6]=>101100=>001101
[2,4,7,5,1,3,6]=>[4,2,1,5,7,6,3]=>110011=>110011
[2,4,7,5,1,6,3]=>[4,2,1,5,7,3,6]=>110010=>010011
[2,4,7,5,3,1,6]=>[4,2,1,3,5,7,6]=>110001=>100011
[2,4,7,5,3,6,1]=>[4,3,5,7,2,1,6]=>100110=>011001
[2,4,7,5,6,1,3]=>[5,7,4,2,1,6,3]=>011101=>101110
[2,4,7,5,6,3,1]=>[5,7,4,2,1,3,6]=>011100=>001110
[2,4,7,6,1,3,5]=>[4,2,1,6,7,5,3]=>110011=>110011
[2,4,7,6,1,5,3]=>[4,2,1,6,7,3,5]=>110010=>010011
[2,4,7,6,3,1,5]=>[4,2,1,3,6,7,5]=>110001=>100011
[2,4,7,6,3,5,1]=>[4,3,6,7,2,1,5]=>100110=>011001
[2,4,7,6,5,1,3]=>[4,2,1,5,6,7,3]=>110001=>100011
[2,4,7,6,5,3,1]=>[4,2,1,3,5,6,7]=>110000=>000011
[2,5,1,3,4,6,7]=>[7,6,2,1,5,4,3]=>111011=>110111
[2,5,1,3,4,7,6]=>[6,7,2,1,5,4,3]=>011011=>110110
[2,5,1,3,6,4,7]=>[7,2,1,5,4,6,3]=>110101=>101011
[2,5,1,3,6,7,4]=>[6,2,1,5,4,7,3]=>110101=>101011
[2,5,1,3,7,4,6]=>[2,1,5,4,7,6,3]=>101011=>110101
[2,5,1,3,7,6,4]=>[2,1,5,4,6,7,3]=>101001=>100101
[2,5,1,4,3,6,7]=>[7,6,2,1,5,3,4]=>111010=>010111
[2,5,1,4,3,7,6]=>[6,7,2,1,5,3,4]=>011010=>010110
[2,5,1,4,6,3,7]=>[7,2,1,5,4,3,6]=>110110=>011011
[2,5,1,4,6,7,3]=>[6,2,1,5,4,3,7]=>110110=>011011
[2,5,1,4,7,3,6]=>[2,1,5,4,3,7,6]=>101101=>101101
[2,5,1,4,7,6,3]=>[2,1,5,4,3,6,7]=>101100=>001101
[2,5,1,6,3,4,7]=>[7,2,1,5,3,6,4]=>110101=>101011
[2,5,1,6,3,7,4]=>[2,1,5,3,6,4,7]=>101010=>010101
[2,5,1,6,4,3,7]=>[7,2,1,5,3,4,6]=>110100=>001011
[2,5,1,6,4,7,3]=>[2,1,5,4,6,3,7]=>101010=>010101
[2,5,1,6,7,3,4]=>[6,2,1,5,3,7,4]=>110101=>101011
[2,5,1,6,7,4,3]=>[6,2,1,5,3,4,7]=>110100=>001011
[2,5,1,7,3,4,6]=>[2,1,5,3,7,6,4]=>101011=>110101
[2,5,1,7,3,6,4]=>[2,1,5,3,7,4,6]=>101010=>010101
[2,5,1,7,4,3,6]=>[2,1,5,3,4,7,6]=>101001=>100101
[2,5,1,7,4,6,3]=>[2,1,5,4,7,3,6]=>101010=>010101
[2,5,1,7,6,3,4]=>[2,1,5,3,6,7,4]=>101001=>100101
[2,5,1,7,6,4,3]=>[2,1,5,3,4,6,7]=>101000=>000101
[2,5,3,1,4,6,7]=>[7,6,2,1,3,5,4]=>111001=>100111
[2,5,3,1,4,7,6]=>[6,7,2,1,3,5,4]=>011001=>100110
[2,5,3,1,6,4,7]=>[7,2,1,3,5,4,6]=>110010=>010011
[2,5,3,1,6,7,4]=>[6,2,1,3,5,4,7]=>110010=>010011
[2,5,3,1,7,4,6]=>[2,1,3,5,4,7,6]=>100101=>101001
[2,5,3,1,7,6,4]=>[2,1,3,5,4,6,7]=>100100=>001001
[2,5,3,4,1,6,7]=>[7,6,3,5,2,1,4]=>110110=>011011
[2,5,3,4,1,7,6]=>[6,7,3,5,2,1,4]=>010110=>011010
[2,5,3,4,6,1,7]=>[7,3,5,4,2,1,6]=>101110=>011101
[2,5,3,4,6,7,1]=>[6,3,5,4,2,1,7]=>101110=>011101
[2,5,3,4,7,1,6]=>[3,5,4,2,1,7,6]=>011101=>101110
[2,5,3,4,7,6,1]=>[3,5,4,2,1,6,7]=>011100=>001110
[2,5,3,6,1,4,7]=>[7,3,5,2,1,6,4]=>101101=>101101
[2,5,3,6,1,7,4]=>[3,5,2,1,6,4,7]=>011010=>010110
[2,5,3,6,4,1,7]=>[7,3,5,2,1,4,6]=>101100=>001101
[2,5,3,6,4,7,1]=>[3,5,4,6,2,1,7]=>010110=>011010
[2,5,3,6,7,1,4]=>[6,3,5,2,1,7,4]=>101101=>101101
[2,5,3,6,7,4,1]=>[6,3,5,2,1,4,7]=>101100=>001101
[2,5,3,7,1,4,6]=>[3,5,2,1,7,6,4]=>011011=>110110
[2,5,3,7,1,6,4]=>[3,5,2,1,7,4,6]=>011010=>010110
[2,5,3,7,4,1,6]=>[3,5,2,1,4,7,6]=>011001=>100110
[2,5,3,7,4,6,1]=>[3,5,4,7,2,1,6]=>010110=>011010
[2,5,3,7,6,1,4]=>[3,5,2,1,6,7,4]=>011001=>100110
[2,5,3,7,6,4,1]=>[3,5,2,1,4,6,7]=>011000=>000110
[2,5,4,1,3,6,7]=>[7,6,2,1,4,5,3]=>111001=>100111
[2,5,4,1,3,7,6]=>[6,7,2,1,4,5,3]=>011001=>100110
[2,5,4,1,6,3,7]=>[7,2,1,4,5,3,6]=>110010=>010011
[2,5,4,1,6,7,3]=>[6,2,1,4,5,3,7]=>110010=>010011
[2,5,4,1,7,3,6]=>[2,1,4,5,3,7,6]=>100101=>101001
[2,5,4,1,7,6,3]=>[2,1,4,5,3,6,7]=>100100=>001001
[2,5,4,3,1,6,7]=>[7,6,2,1,3,4,5]=>111000=>000111
[2,5,4,3,1,7,6]=>[6,7,2,1,3,4,5]=>011000=>000110
[2,5,4,3,6,1,7]=>[7,3,4,5,2,1,6]=>100110=>011001
[2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>100110=>011001
[2,5,4,3,7,1,6]=>[3,4,5,2,1,7,6]=>001101=>101100
[2,5,4,3,7,6,1]=>[3,4,5,2,1,6,7]=>001100=>001100
[2,5,4,6,1,3,7]=>[7,4,5,2,1,6,3]=>101101=>101101
[2,5,4,6,1,7,3]=>[4,5,2,1,6,3,7]=>011010=>010110
[2,5,4,6,3,1,7]=>[7,4,5,2,1,3,6]=>101100=>001101
[2,5,4,6,3,7,1]=>[4,5,3,6,2,1,7]=>010110=>011010
[2,5,4,6,7,1,3]=>[6,4,5,2,1,7,3]=>101101=>101101
[2,5,4,6,7,3,1]=>[6,4,5,2,1,3,7]=>101100=>001101
[2,5,4,7,1,3,6]=>[4,5,2,1,7,6,3]=>011011=>110110
[2,5,4,7,1,6,3]=>[4,5,2,1,7,3,6]=>011010=>010110
[2,5,4,7,3,1,6]=>[4,5,2,1,3,7,6]=>011001=>100110
[2,5,4,7,3,6,1]=>[4,5,3,7,2,1,6]=>010110=>011010
[2,5,4,7,6,1,3]=>[4,5,2,1,6,7,3]=>011001=>100110
[2,5,4,7,6,3,1]=>[4,5,2,1,3,6,7]=>011000=>000110
[2,5,6,1,3,4,7]=>[7,5,2,1,6,4,3]=>111011=>110111
[2,5,6,1,3,7,4]=>[5,2,1,6,4,7,3]=>110101=>101011
[2,5,6,1,4,3,7]=>[7,5,2,1,6,3,4]=>111010=>010111
[2,5,6,1,4,7,3]=>[5,2,1,6,4,3,7]=>110110=>011011
[2,5,6,1,7,3,4]=>[5,2,1,6,3,7,4]=>110101=>101011
[2,5,6,1,7,4,3]=>[5,2,1,6,3,4,7]=>110100=>001011
[2,5,6,3,1,4,7]=>[7,5,2,1,3,6,4]=>111001=>100111
[2,5,6,3,1,7,4]=>[5,2,1,3,6,4,7]=>110010=>010011
[2,5,6,3,4,1,7]=>[7,5,3,6,2,1,4]=>110110=>011011
[2,5,6,3,4,7,1]=>[5,3,6,4,2,1,7]=>101110=>011101
[2,5,6,3,7,1,4]=>[5,3,6,2,1,7,4]=>101101=>101101
[2,5,6,3,7,4,1]=>[5,3,6,2,1,4,7]=>101100=>001101
[2,5,6,4,1,3,7]=>[7,5,2,1,4,6,3]=>111001=>100111
[2,5,6,4,1,7,3]=>[5,2,1,4,6,3,7]=>110010=>010011
[2,5,6,4,3,1,7]=>[7,5,2,1,3,4,6]=>111000=>000111
[2,5,6,4,3,7,1]=>[5,3,4,6,2,1,7]=>100110=>011001
[2,5,6,4,7,1,3]=>[5,4,6,2,1,7,3]=>101101=>101101
[2,5,6,4,7,3,1]=>[5,4,6,2,1,3,7]=>101100=>001101
[2,5,6,7,1,3,4]=>[6,5,2,1,7,4,3]=>111011=>110111
[2,5,6,7,1,4,3]=>[6,5,2,1,7,3,4]=>111010=>010111
[2,5,6,7,3,1,4]=>[6,5,2,1,3,7,4]=>111001=>100111
[2,5,6,7,3,4,1]=>[6,5,3,7,2,1,4]=>110110=>011011
[2,5,6,7,4,1,3]=>[6,5,2,1,4,7,3]=>111001=>100111
[2,5,6,7,4,3,1]=>[6,5,2,1,3,4,7]=>111000=>000111
[2,5,7,1,3,4,6]=>[5,2,1,7,6,4,3]=>110111=>111011
[2,5,7,1,3,6,4]=>[5,2,1,7,4,6,3]=>110101=>101011
[2,5,7,1,4,3,6]=>[5,2,1,7,6,3,4]=>110110=>011011
[2,5,7,1,4,6,3]=>[5,2,1,7,4,3,6]=>110110=>011011
[2,5,7,1,6,3,4]=>[5,2,1,7,3,6,4]=>110101=>101011
[2,5,7,1,6,4,3]=>[5,2,1,7,3,4,6]=>110100=>001011
[2,5,7,3,1,4,6]=>[5,2,1,3,7,6,4]=>110011=>110011
[2,5,7,3,1,6,4]=>[5,2,1,3,7,4,6]=>110010=>010011
[2,5,7,3,4,1,6]=>[5,3,7,6,2,1,4]=>101110=>011101
[2,5,7,3,4,6,1]=>[5,3,7,4,2,1,6]=>101110=>011101
[2,5,7,3,6,1,4]=>[5,3,7,2,1,6,4]=>101101=>101101
[2,5,7,3,6,4,1]=>[5,3,7,2,1,4,6]=>101100=>001101
[2,5,7,4,1,3,6]=>[5,2,1,4,7,6,3]=>110011=>110011
[2,5,7,4,1,6,3]=>[5,2,1,4,7,3,6]=>110010=>010011
[2,5,7,4,3,1,6]=>[5,2,1,3,4,7,6]=>110001=>100011
[2,5,7,4,3,6,1]=>[5,3,4,7,2,1,6]=>100110=>011001
[2,5,7,4,6,1,3]=>[5,4,7,2,1,6,3]=>101101=>101101
[2,5,7,4,6,3,1]=>[5,4,7,2,1,3,6]=>101100=>001101
[2,5,7,6,1,3,4]=>[5,2,1,6,7,4,3]=>110011=>110011
[2,5,7,6,1,4,3]=>[5,2,1,6,7,3,4]=>110010=>010011
[2,5,7,6,3,1,4]=>[5,2,1,3,6,7,4]=>110001=>100011
[2,5,7,6,3,4,1]=>[5,3,6,7,2,1,4]=>100110=>011001
[2,5,7,6,4,1,3]=>[5,2,1,4,6,7,3]=>110001=>100011
[2,5,7,6,4,3,1]=>[5,2,1,3,4,6,7]=>110000=>000011
[2,6,1,3,4,5,7]=>[7,2,1,6,5,4,3]=>110111=>111011
[2,6,1,3,4,7,5]=>[2,1,6,5,7,4,3]=>101011=>110101
[2,6,1,3,5,4,7]=>[7,2,1,6,4,5,3]=>110101=>101011
[2,6,1,3,5,7,4]=>[2,1,6,5,4,7,3]=>101101=>101101
[2,6,1,3,7,4,5]=>[2,1,6,4,7,5,3]=>101011=>110101
[2,6,1,3,7,5,4]=>[2,1,6,4,5,7,3]=>101001=>100101
[2,6,1,4,3,5,7]=>[7,2,1,6,5,3,4]=>110110=>011011
[2,6,1,4,3,7,5]=>[2,1,6,5,7,3,4]=>101010=>010101
[2,6,1,4,5,3,7]=>[7,2,1,6,4,3,5]=>110110=>011011
[2,6,1,4,5,7,3]=>[2,1,6,5,4,3,7]=>101110=>011101
[2,6,1,4,7,3,5]=>[2,1,6,4,3,7,5]=>101101=>101101
[2,6,1,4,7,5,3]=>[2,1,6,4,3,5,7]=>101100=>001101
[2,6,1,5,3,4,7]=>[7,2,1,6,3,5,4]=>110101=>101011
[2,6,1,5,3,7,4]=>[2,1,6,3,5,4,7]=>101010=>010101
[2,6,1,5,4,3,7]=>[7,2,1,6,3,4,5]=>110100=>001011
[2,6,1,5,4,7,3]=>[2,1,6,4,5,3,7]=>101010=>010101
[2,6,1,5,7,3,4]=>[2,1,6,5,3,7,4]=>101101=>101101
[2,6,1,5,7,4,3]=>[2,1,6,5,3,4,7]=>101100=>001101
[2,6,1,7,3,4,5]=>[2,1,6,3,7,5,4]=>101011=>110101
[2,6,1,7,3,5,4]=>[2,1,6,3,7,4,5]=>101010=>010101
[2,6,1,7,4,3,5]=>[2,1,6,3,4,7,5]=>101001=>100101
[2,6,1,7,4,5,3]=>[2,1,6,4,7,3,5]=>101010=>010101
[2,6,1,7,5,3,4]=>[2,1,6,3,5,7,4]=>101001=>100101
[2,6,1,7,5,4,3]=>[2,1,6,3,4,5,7]=>101000=>000101
[2,6,3,1,4,5,7]=>[7,2,1,3,6,5,4]=>110011=>110011
[2,6,3,1,4,7,5]=>[2,1,3,6,5,7,4]=>100101=>101001
[2,6,3,1,5,4,7]=>[7,2,1,3,6,4,5]=>110010=>010011
[2,6,3,1,5,7,4]=>[2,1,3,6,5,4,7]=>100110=>011001
[2,6,3,1,7,4,5]=>[2,1,3,6,4,7,5]=>100101=>101001
[2,6,3,1,7,5,4]=>[2,1,3,6,4,5,7]=>100100=>001001
[2,6,3,4,1,5,7]=>[7,3,6,5,2,1,4]=>101110=>011101
[2,6,3,4,1,7,5]=>[3,6,5,7,2,1,4]=>010110=>011010
[2,6,3,4,5,1,7]=>[7,3,6,4,2,1,5]=>101110=>011101
[2,6,3,4,5,7,1]=>[3,6,5,4,2,1,7]=>011110=>011110
[2,6,3,4,7,1,5]=>[3,6,4,2,1,7,5]=>011101=>101110
[2,6,3,4,7,5,1]=>[3,6,4,2,1,5,7]=>011100=>001110
[2,6,3,5,1,4,7]=>[7,3,6,2,1,5,4]=>101101=>101101
[2,6,3,5,1,7,4]=>[3,6,2,1,5,4,7]=>011010=>010110
[2,6,3,5,4,1,7]=>[7,3,6,2,1,4,5]=>101100=>001101
[2,6,3,5,4,7,1]=>[3,6,4,5,2,1,7]=>010110=>011010
[2,6,3,5,7,1,4]=>[3,6,5,2,1,7,4]=>011101=>101110
[2,6,3,5,7,4,1]=>[3,6,5,2,1,4,7]=>011100=>001110
[2,6,3,7,1,4,5]=>[3,6,2,1,7,5,4]=>011011=>110110
[2,6,3,7,1,5,4]=>[3,6,2,1,7,4,5]=>011010=>010110
[2,6,3,7,4,1,5]=>[3,6,2,1,4,7,5]=>011001=>100110
[2,6,3,7,4,5,1]=>[3,6,4,7,2,1,5]=>010110=>011010
[2,6,3,7,5,1,4]=>[3,6,2,1,5,7,4]=>011001=>100110
[2,6,3,7,5,4,1]=>[3,6,2,1,4,5,7]=>011000=>000110
[2,6,4,1,3,5,7]=>[7,2,1,4,6,5,3]=>110011=>110011
[2,6,4,1,3,7,5]=>[2,1,4,6,5,7,3]=>100101=>101001
[2,6,4,1,5,3,7]=>[7,2,1,4,6,3,5]=>110010=>010011
[2,6,4,1,5,7,3]=>[2,1,4,6,5,3,7]=>100110=>011001
[2,6,4,1,7,3,5]=>[2,1,4,6,3,7,5]=>100101=>101001
[2,6,4,1,7,5,3]=>[2,1,4,6,3,5,7]=>100100=>001001
[2,6,4,3,1,5,7]=>[7,2,1,3,4,6,5]=>110001=>100011
[2,6,4,3,1,7,5]=>[2,1,3,4,6,5,7]=>100010=>010001
[2,6,4,3,5,1,7]=>[7,3,4,6,2,1,5]=>100110=>011001
[2,6,4,3,5,7,1]=>[3,4,6,5,2,1,7]=>001110=>011100
[2,6,4,3,7,1,5]=>[3,4,6,2,1,7,5]=>001101=>101100
[2,6,4,3,7,5,1]=>[3,4,6,2,1,5,7]=>001100=>001100
[2,6,4,5,1,3,7]=>[7,4,6,2,1,5,3]=>101101=>101101
[2,6,4,5,1,7,3]=>[4,6,2,1,5,3,7]=>011010=>010110
[2,6,4,5,3,1,7]=>[7,4,6,2,1,3,5]=>101100=>001101
[2,6,4,5,3,7,1]=>[4,6,3,5,2,1,7]=>010110=>011010
[2,6,4,5,7,1,3]=>[4,6,5,2,1,7,3]=>011101=>101110
[2,6,4,5,7,3,1]=>[4,6,5,2,1,3,7]=>011100=>001110
[2,6,4,7,1,3,5]=>[4,6,2,1,7,5,3]=>011011=>110110
[2,6,4,7,1,5,3]=>[4,6,2,1,7,3,5]=>011010=>010110
[2,6,4,7,3,1,5]=>[4,6,2,1,3,7,5]=>011001=>100110
[2,6,4,7,3,5,1]=>[4,6,3,7,2,1,5]=>010110=>011010
[2,6,4,7,5,1,3]=>[4,6,2,1,5,7,3]=>011001=>100110
[2,6,4,7,5,3,1]=>[4,6,2,1,3,5,7]=>011000=>000110
[2,6,5,1,3,4,7]=>[7,2,1,5,6,4,3]=>110011=>110011
[2,6,5,1,3,7,4]=>[2,1,5,6,4,7,3]=>100101=>101001
[2,6,5,1,4,3,7]=>[7,2,1,5,6,3,4]=>110010=>010011
[2,6,5,1,4,7,3]=>[2,1,5,6,4,3,7]=>100110=>011001
[2,6,5,1,7,3,4]=>[2,1,5,6,3,7,4]=>100101=>101001
[2,6,5,1,7,4,3]=>[2,1,5,6,3,4,7]=>100100=>001001
[2,6,5,3,1,4,7]=>[7,2,1,3,5,6,4]=>110001=>100011
[2,6,5,3,1,7,4]=>[2,1,3,5,6,4,7]=>100010=>010001
[2,6,5,3,4,1,7]=>[7,3,5,6,2,1,4]=>100110=>011001
[2,6,5,3,4,7,1]=>[3,5,6,4,2,1,7]=>001110=>011100
[2,6,5,3,7,1,4]=>[3,5,6,2,1,7,4]=>001101=>101100
[2,6,5,3,7,4,1]=>[3,5,6,2,1,4,7]=>001100=>001100
[2,6,5,4,1,3,7]=>[7,2,1,4,5,6,3]=>110001=>100011
[2,6,5,4,1,7,3]=>[2,1,4,5,6,3,7]=>100010=>010001
[2,6,5,4,3,1,7]=>[7,2,1,3,4,5,6]=>110000=>000011
[2,6,5,4,3,7,1]=>[3,4,5,6,2,1,7]=>000110=>011000
[2,6,5,4,7,1,3]=>[4,5,6,2,1,7,3]=>001101=>101100
[2,6,5,4,7,3,1]=>[4,5,6,2,1,3,7]=>001100=>001100
[2,6,5,7,1,3,4]=>[5,6,2,1,7,4,3]=>011011=>110110
[2,6,5,7,1,4,3]=>[5,6,2,1,7,3,4]=>011010=>010110
[2,6,5,7,3,1,4]=>[5,6,2,1,3,7,4]=>011001=>100110
[2,6,5,7,3,4,1]=>[5,6,3,7,2,1,4]=>010110=>011010
[2,6,5,7,4,1,3]=>[5,6,2,1,4,7,3]=>011001=>100110
[2,6,5,7,4,3,1]=>[5,6,2,1,3,4,7]=>011000=>000110
[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>110111=>111011
[2,6,7,1,3,5,4]=>[6,2,1,7,4,5,3]=>110101=>101011
[2,6,7,1,4,3,5]=>[6,2,1,7,5,3,4]=>110110=>011011
[2,6,7,1,4,5,3]=>[6,2,1,7,4,3,5]=>110110=>011011
[2,6,7,1,5,3,4]=>[6,2,1,7,3,5,4]=>110101=>101011
[2,6,7,1,5,4,3]=>[6,2,1,7,3,4,5]=>110100=>001011
[2,6,7,3,1,4,5]=>[6,2,1,3,7,5,4]=>110011=>110011
[2,6,7,3,1,5,4]=>[6,2,1,3,7,4,5]=>110010=>010011
[2,6,7,3,4,1,5]=>[6,3,7,5,2,1,4]=>101110=>011101
[2,6,7,3,4,5,1]=>[6,3,7,4,2,1,5]=>101110=>011101
[2,6,7,3,5,1,4]=>[6,3,7,2,1,5,4]=>101101=>101101
[2,6,7,3,5,4,1]=>[6,3,7,2,1,4,5]=>101100=>001101
[2,6,7,4,1,3,5]=>[6,2,1,4,7,5,3]=>110011=>110011
[2,6,7,4,1,5,3]=>[6,2,1,4,7,3,5]=>110010=>010011
[2,6,7,4,3,1,5]=>[6,2,1,3,4,7,5]=>110001=>100011
[2,6,7,4,3,5,1]=>[6,3,4,7,2,1,5]=>100110=>011001
[2,6,7,4,5,1,3]=>[6,4,7,2,1,5,3]=>101101=>101101
[2,6,7,4,5,3,1]=>[6,4,7,2,1,3,5]=>101100=>001101
[2,6,7,5,1,3,4]=>[6,2,1,5,7,4,3]=>110011=>110011
[2,6,7,5,1,4,3]=>[6,2,1,5,7,3,4]=>110010=>010011
[2,6,7,5,3,1,4]=>[6,2,1,3,5,7,4]=>110001=>100011
[2,6,7,5,3,4,1]=>[6,3,5,7,2,1,4]=>100110=>011001
[2,6,7,5,4,1,3]=>[6,2,1,4,5,7,3]=>110001=>100011
[2,6,7,5,4,3,1]=>[6,2,1,3,4,5,7]=>110000=>000011
[2,7,1,3,4,5,6]=>[2,1,7,6,5,4,3]=>101111=>111101
[2,7,1,3,4,6,5]=>[2,1,7,5,6,4,3]=>101011=>110101
[2,7,1,3,5,4,6]=>[2,1,7,6,4,5,3]=>101101=>101101
[2,7,1,3,5,6,4]=>[2,1,7,5,4,6,3]=>101101=>101101
[2,7,1,3,6,4,5]=>[2,1,7,4,6,5,3]=>101011=>110101
[2,7,1,3,6,5,4]=>[2,1,7,4,5,6,3]=>101001=>100101
[2,7,1,4,3,5,6]=>[2,1,7,6,5,3,4]=>101110=>011101
[2,7,1,4,3,6,5]=>[2,1,7,5,6,3,4]=>101010=>010101
[2,7,1,4,5,3,6]=>[2,1,7,6,4,3,5]=>101110=>011101
[2,7,1,4,5,6,3]=>[2,1,7,5,4,3,6]=>101110=>011101
[2,7,1,4,6,3,5]=>[2,1,7,4,3,6,5]=>101101=>101101
[2,7,1,4,6,5,3]=>[2,1,7,4,3,5,6]=>101100=>001101
[2,7,1,5,3,4,6]=>[2,1,7,6,3,5,4]=>101101=>101101
[2,7,1,5,3,6,4]=>[2,1,7,3,5,4,6]=>101010=>010101
[2,7,1,5,4,3,6]=>[2,1,7,6,3,4,5]=>101100=>001101
[2,7,1,5,4,6,3]=>[2,1,7,4,5,3,6]=>101010=>010101
[2,7,1,5,6,3,4]=>[2,1,7,5,3,6,4]=>101101=>101101
[2,7,1,5,6,4,3]=>[2,1,7,5,3,4,6]=>101100=>001101
[2,7,1,6,3,4,5]=>[2,1,7,3,6,5,4]=>101011=>110101
[2,7,1,6,3,5,4]=>[2,1,7,3,6,4,5]=>101010=>010101
[2,7,1,6,4,3,5]=>[2,1,7,3,4,6,5]=>101001=>100101
[2,7,1,6,4,5,3]=>[2,1,7,4,6,3,5]=>101010=>010101
[2,7,1,6,5,3,4]=>[2,1,7,3,5,6,4]=>101001=>100101
[2,7,1,6,5,4,3]=>[2,1,7,3,4,5,6]=>101000=>000101
[2,7,3,1,4,5,6]=>[2,1,3,7,6,5,4]=>100111=>111001
[2,7,3,1,4,6,5]=>[2,1,3,7,5,6,4]=>100101=>101001
[2,7,3,1,5,4,6]=>[2,1,3,7,6,4,5]=>100110=>011001
[2,7,3,1,5,6,4]=>[2,1,3,7,5,4,6]=>100110=>011001
[2,7,3,1,6,4,5]=>[2,1,3,7,4,6,5]=>100101=>101001
[2,7,3,1,6,5,4]=>[2,1,3,7,4,5,6]=>100100=>001001
[2,7,3,4,1,5,6]=>[3,7,6,5,2,1,4]=>011110=>011110
[2,7,3,4,1,6,5]=>[3,7,5,6,2,1,4]=>010110=>011010
[2,7,3,4,5,1,6]=>[3,7,6,4,2,1,5]=>011110=>011110
[2,7,3,4,5,6,1]=>[3,7,5,4,2,1,6]=>011110=>011110
[2,7,3,4,6,1,5]=>[3,7,4,2,1,6,5]=>011101=>101110
[2,7,3,4,6,5,1]=>[3,7,4,2,1,5,6]=>011100=>001110
[2,7,3,5,1,4,6]=>[3,7,6,2,1,5,4]=>011101=>101110
[2,7,3,5,1,6,4]=>[3,7,2,1,5,4,6]=>011010=>010110
[2,7,3,5,4,1,6]=>[3,7,6,2,1,4,5]=>011100=>001110
[2,7,3,5,4,6,1]=>[3,7,4,5,2,1,6]=>010110=>011010
[2,7,3,5,6,1,4]=>[3,7,5,2,1,6,4]=>011101=>101110
[2,7,3,5,6,4,1]=>[3,7,5,2,1,4,6]=>011100=>001110
[2,7,3,6,1,4,5]=>[3,7,2,1,6,5,4]=>011011=>110110
[2,7,3,6,1,5,4]=>[3,7,2,1,6,4,5]=>011010=>010110
[2,7,3,6,4,1,5]=>[3,7,2,1,4,6,5]=>011001=>100110
[2,7,3,6,4,5,1]=>[3,7,4,6,2,1,5]=>010110=>011010
[2,7,3,6,5,1,4]=>[3,7,2,1,5,6,4]=>011001=>100110
[2,7,3,6,5,4,1]=>[3,7,2,1,4,5,6]=>011000=>000110
[2,7,4,1,3,5,6]=>[2,1,4,7,6,5,3]=>100111=>111001
[2,7,4,1,3,6,5]=>[2,1,4,7,5,6,3]=>100101=>101001
[2,7,4,1,5,3,6]=>[2,1,4,7,6,3,5]=>100110=>011001
[2,7,4,1,5,6,3]=>[2,1,4,7,5,3,6]=>100110=>011001
[2,7,4,1,6,3,5]=>[2,1,4,7,3,6,5]=>100101=>101001
[2,7,4,1,6,5,3]=>[2,1,4,7,3,5,6]=>100100=>001001
[2,7,4,3,1,5,6]=>[2,1,3,4,7,6,5]=>100011=>110001
[2,7,4,3,1,6,5]=>[2,1,3,4,7,5,6]=>100010=>010001
[2,7,4,3,5,1,6]=>[3,4,7,6,2,1,5]=>001110=>011100
[2,7,4,3,5,6,1]=>[3,4,7,5,2,1,6]=>001110=>011100
[2,7,4,3,6,1,5]=>[3,4,7,2,1,6,5]=>001101=>101100
[2,7,4,3,6,5,1]=>[3,4,7,2,1,5,6]=>001100=>001100
[2,7,4,5,1,3,6]=>[4,7,6,2,1,5,3]=>011101=>101110
[2,7,4,5,1,6,3]=>[4,7,2,1,5,3,6]=>011010=>010110
[2,7,4,5,3,1,6]=>[4,7,6,2,1,3,5]=>011100=>001110
[2,7,4,5,3,6,1]=>[4,7,3,5,2,1,6]=>010110=>011010
[2,7,4,5,6,1,3]=>[4,7,5,2,1,6,3]=>011101=>101110
[2,7,4,5,6,3,1]=>[4,7,5,2,1,3,6]=>011100=>001110
[2,7,4,6,1,3,5]=>[4,7,2,1,6,5,3]=>011011=>110110
[2,7,4,6,1,5,3]=>[4,7,2,1,6,3,5]=>011010=>010110
[2,7,4,6,3,1,5]=>[4,7,2,1,3,6,5]=>011001=>100110
[2,7,4,6,3,5,1]=>[4,7,3,6,2,1,5]=>010110=>011010
[2,7,4,6,5,1,3]=>[4,7,2,1,5,6,3]=>011001=>100110
[2,7,4,6,5,3,1]=>[4,7,2,1,3,5,6]=>011000=>000110
[2,7,5,1,3,4,6]=>[2,1,5,7,6,4,3]=>100111=>111001
[2,7,5,1,3,6,4]=>[2,1,5,7,4,6,3]=>100101=>101001
[2,7,5,1,4,3,6]=>[2,1,5,7,6,3,4]=>100110=>011001
[2,7,5,1,4,6,3]=>[2,1,5,7,4,3,6]=>100110=>011001
[2,7,5,1,6,3,4]=>[2,1,5,7,3,6,4]=>100101=>101001
[2,7,5,1,6,4,3]=>[2,1,5,7,3,4,6]=>100100=>001001
[2,7,5,3,1,4,6]=>[2,1,3,5,7,6,4]=>100011=>110001
[2,7,5,3,1,6,4]=>[2,1,3,5,7,4,6]=>100010=>010001
[2,7,5,3,4,1,6]=>[3,5,7,6,2,1,4]=>001110=>011100
[2,7,5,3,4,6,1]=>[3,5,7,4,2,1,6]=>001110=>011100
[2,7,5,3,6,1,4]=>[3,5,7,2,1,6,4]=>001101=>101100
[2,7,5,3,6,4,1]=>[3,5,7,2,1,4,6]=>001100=>001100
[2,7,5,4,1,3,6]=>[2,1,4,5,7,6,3]=>100011=>110001
[2,7,5,4,1,6,3]=>[2,1,4,5,7,3,6]=>100010=>010001
[2,7,5,4,3,1,6]=>[2,1,3,4,5,7,6]=>100001=>100001
[2,7,5,4,3,6,1]=>[3,4,5,7,2,1,6]=>000110=>011000
[2,7,5,4,6,1,3]=>[4,5,7,2,1,6,3]=>001101=>101100
[2,7,5,4,6,3,1]=>[4,5,7,2,1,3,6]=>001100=>001100
[2,7,5,6,1,3,4]=>[5,7,2,1,6,4,3]=>011011=>110110
[2,7,5,6,1,4,3]=>[5,7,2,1,6,3,4]=>011010=>010110
[2,7,5,6,3,1,4]=>[5,7,2,1,3,6,4]=>011001=>100110
[2,7,5,6,3,4,1]=>[5,7,3,6,2,1,4]=>010110=>011010
[2,7,5,6,4,1,3]=>[5,7,2,1,4,6,3]=>011001=>100110
[2,7,5,6,4,3,1]=>[5,7,2,1,3,4,6]=>011000=>000110
[2,7,6,1,3,4,5]=>[2,1,6,7,5,4,3]=>100111=>111001
[2,7,6,1,3,5,4]=>[2,1,6,7,4,5,3]=>100101=>101001
[2,7,6,1,4,3,5]=>[2,1,6,7,5,3,4]=>100110=>011001
[2,7,6,1,4,5,3]=>[2,1,6,7,4,3,5]=>100110=>011001
[2,7,6,1,5,3,4]=>[2,1,6,7,3,5,4]=>100101=>101001
[2,7,6,1,5,4,3]=>[2,1,6,7,3,4,5]=>100100=>001001
[2,7,6,3,1,4,5]=>[2,1,3,6,7,5,4]=>100011=>110001
[2,7,6,3,1,5,4]=>[2,1,3,6,7,4,5]=>100010=>010001
[2,7,6,3,4,1,5]=>[3,6,7,5,2,1,4]=>001110=>011100
[2,7,6,3,4,5,1]=>[3,6,7,4,2,1,5]=>001110=>011100
[2,7,6,3,5,1,4]=>[3,6,7,2,1,5,4]=>001101=>101100
[2,7,6,3,5,4,1]=>[3,6,7,2,1,4,5]=>001100=>001100
[2,7,6,4,1,3,5]=>[2,1,4,6,7,5,3]=>100011=>110001
[2,7,6,4,1,5,3]=>[2,1,4,6,7,3,5]=>100010=>010001
[2,7,6,4,3,1,5]=>[2,1,3,4,6,7,5]=>100001=>100001
[2,7,6,4,3,5,1]=>[3,4,6,7,2,1,5]=>000110=>011000
[2,7,6,4,5,1,3]=>[4,6,7,2,1,5,3]=>001101=>101100
[2,7,6,4,5,3,1]=>[4,6,7,2,1,3,5]=>001100=>001100
[2,7,6,5,1,3,4]=>[2,1,5,6,7,4,3]=>100011=>110001
[2,7,6,5,1,4,3]=>[2,1,5,6,7,3,4]=>100010=>010001
[2,7,6,5,3,1,4]=>[2,1,3,5,6,7,4]=>100001=>100001
[2,7,6,5,3,4,1]=>[3,5,6,7,2,1,4]=>000110=>011000
[2,7,6,5,4,1,3]=>[2,1,4,5,6,7,3]=>100001=>100001
[2,7,6,5,4,3,1]=>[2,1,3,4,5,6,7]=>100000=>000001
[3,1,2,4,5,6,7]=>[7,6,5,4,1,3,2]=>111101=>101111
[3,1,2,4,5,7,6]=>[6,7,5,4,1,3,2]=>011101=>101110
[3,1,2,4,6,5,7]=>[7,5,6,4,1,3,2]=>101101=>101101
[3,1,2,4,6,7,5]=>[6,5,7,4,1,3,2]=>101101=>101101
[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>011101=>101110
[3,1,2,4,7,6,5]=>[5,6,7,4,1,3,2]=>001101=>101100
[3,1,2,5,4,6,7]=>[7,6,4,5,1,3,2]=>110101=>101011
[3,1,2,5,4,7,6]=>[6,7,4,5,1,3,2]=>010101=>101010
[3,1,2,5,6,4,7]=>[7,5,4,6,1,3,2]=>110101=>101011
[3,1,2,5,6,7,4]=>[6,5,4,7,1,3,2]=>110101=>101011
[3,1,2,5,7,4,6]=>[5,4,7,6,1,3,2]=>101101=>101101
[3,1,2,5,7,6,4]=>[5,4,6,7,1,3,2]=>100101=>101001
[3,1,2,6,4,5,7]=>[7,4,6,5,1,3,2]=>101101=>101101
[3,1,2,6,4,7,5]=>[4,6,5,7,1,3,2]=>010101=>101010
[3,1,2,6,5,4,7]=>[7,4,5,6,1,3,2]=>100101=>101001
[3,1,2,6,5,7,4]=>[5,6,4,7,1,3,2]=>010101=>101010
[3,1,2,6,7,4,5]=>[6,4,7,5,1,3,2]=>101101=>101101
[3,1,2,6,7,5,4]=>[6,4,5,7,1,3,2]=>100101=>101001
[3,1,2,7,4,5,6]=>[4,7,6,5,1,3,2]=>011101=>101110
[3,1,2,7,4,6,5]=>[4,7,5,6,1,3,2]=>010101=>101010
[3,1,2,7,5,4,6]=>[4,5,7,6,1,3,2]=>001101=>101100
[3,1,2,7,5,6,4]=>[5,7,4,6,1,3,2]=>010101=>101010
[3,1,2,7,6,4,5]=>[4,6,7,5,1,3,2]=>001101=>101100
[3,1,2,7,6,5,4]=>[4,5,6,7,1,3,2]=>000101=>101000
[3,1,4,2,5,6,7]=>[7,6,5,1,3,2,4]=>111010=>010111
[3,1,4,2,5,7,6]=>[6,7,5,1,3,2,4]=>011010=>010110
[3,1,4,2,6,5,7]=>[7,5,6,1,3,2,4]=>101010=>010101
[3,1,4,2,6,7,5]=>[6,5,7,1,3,2,4]=>101010=>010101
[3,1,4,2,7,5,6]=>[5,7,6,1,3,2,4]=>011010=>010110
[3,1,4,2,7,6,5]=>[5,6,7,1,3,2,4]=>001010=>010100
[3,1,4,5,2,6,7]=>[7,6,4,1,3,2,5]=>111010=>010111
[3,1,4,5,2,7,6]=>[6,7,4,1,3,2,5]=>011010=>010110
[3,1,4,5,6,2,7]=>[7,5,4,1,3,2,6]=>111010=>010111
[3,1,4,5,6,7,2]=>[6,5,4,1,3,2,7]=>111010=>010111
[3,1,4,5,7,2,6]=>[5,4,1,3,2,7,6]=>110101=>101011
[3,1,4,5,7,6,2]=>[5,4,1,3,2,6,7]=>110100=>001011
[3,1,4,6,2,5,7]=>[7,4,1,3,2,6,5]=>110101=>101011
[3,1,4,6,2,7,5]=>[4,1,3,2,6,5,7]=>101010=>010101
[3,1,4,6,5,2,7]=>[7,4,1,3,2,5,6]=>110100=>001011
[3,1,4,6,5,7,2]=>[5,6,4,1,3,2,7]=>011010=>010110
[3,1,4,6,7,2,5]=>[6,4,1,3,2,7,5]=>110101=>101011
[3,1,4,6,7,5,2]=>[6,4,1,3,2,5,7]=>110100=>001011
[3,1,4,7,2,5,6]=>[4,1,3,2,7,6,5]=>101011=>110101
[3,1,4,7,2,6,5]=>[4,1,3,2,7,5,6]=>101010=>010101
[3,1,4,7,5,2,6]=>[4,1,3,2,5,7,6]=>101001=>100101
[3,1,4,7,5,6,2]=>[5,7,4,1,3,2,6]=>011010=>010110
[3,1,4,7,6,2,5]=>[4,1,3,2,6,7,5]=>101001=>100101
[3,1,4,7,6,5,2]=>[4,1,3,2,5,6,7]=>101000=>000101
[3,1,5,2,4,6,7]=>[7,6,1,3,2,5,4]=>110101=>101011
[3,1,5,2,4,7,6]=>[6,7,1,3,2,5,4]=>010101=>101010
[3,1,5,2,6,4,7]=>[7,1,3,2,5,4,6]=>101010=>010101
[3,1,5,2,6,7,4]=>[6,1,3,2,5,4,7]=>101010=>010101
[3,1,5,2,7,4,6]=>[1,3,2,5,4,7,6]=>010101=>101010
[3,1,5,2,7,6,4]=>[1,3,2,5,4,6,7]=>010100=>001010
[3,1,5,4,2,6,7]=>[7,6,1,3,2,4,5]=>110100=>001011
[3,1,5,4,2,7,6]=>[6,7,1,3,2,4,5]=>010100=>001010
[3,1,5,4,6,2,7]=>[7,4,5,1,3,2,6]=>101010=>010101
[3,1,5,4,6,7,2]=>[6,4,5,1,3,2,7]=>101010=>010101
[3,1,5,4,7,2,6]=>[4,5,1,3,2,7,6]=>010101=>101010
[3,1,5,4,7,6,2]=>[4,5,1,3,2,6,7]=>010100=>001010
[3,1,5,6,2,4,7]=>[7,5,1,3,2,6,4]=>110101=>101011
[3,1,5,6,2,7,4]=>[5,1,3,2,6,4,7]=>101010=>010101
[3,1,5,6,4,2,7]=>[7,5,1,3,2,4,6]=>110100=>001011
[3,1,5,6,4,7,2]=>[5,4,6,1,3,2,7]=>101010=>010101
[3,1,5,6,7,2,4]=>[6,5,1,3,2,7,4]=>110101=>101011
[3,1,5,6,7,4,2]=>[6,5,1,3,2,4,7]=>110100=>001011
[3,1,5,7,2,4,6]=>[5,1,3,2,7,6,4]=>101011=>110101
[3,1,5,7,2,6,4]=>[5,1,3,2,7,4,6]=>101010=>010101
[3,1,5,7,4,2,6]=>[5,1,3,2,4,7,6]=>101001=>100101
[3,1,5,7,4,6,2]=>[5,4,7,1,3,2,6]=>101010=>010101
[3,1,5,7,6,2,4]=>[5,1,3,2,6,7,4]=>101001=>100101
[3,1,5,7,6,4,2]=>[5,1,3,2,4,6,7]=>101000=>000101
[3,1,6,2,4,5,7]=>[7,1,3,2,6,5,4]=>101011=>110101
[3,1,6,2,4,7,5]=>[1,3,2,6,5,7,4]=>010101=>101010
[3,1,6,2,5,4,7]=>[7,1,3,2,6,4,5]=>101010=>010101
[3,1,6,2,5,7,4]=>[1,3,2,6,5,4,7]=>010110=>011010
[3,1,6,2,7,4,5]=>[1,3,2,6,4,7,5]=>010101=>101010
[3,1,6,2,7,5,4]=>[1,3,2,6,4,5,7]=>010100=>001010
[3,1,6,4,2,5,7]=>[7,1,3,2,4,6,5]=>101001=>100101
[3,1,6,4,2,7,5]=>[1,3,2,4,6,5,7]=>010010=>010010
[3,1,6,4,5,2,7]=>[7,4,6,1,3,2,5]=>101010=>010101
[3,1,6,4,5,7,2]=>[4,6,5,1,3,2,7]=>011010=>010110
[3,1,6,4,7,2,5]=>[4,6,1,3,2,7,5]=>010101=>101010
[3,1,6,4,7,5,2]=>[4,6,1,3,2,5,7]=>010100=>001010
[3,1,6,5,2,4,7]=>[7,1,3,2,5,6,4]=>101001=>100101
[3,1,6,5,2,7,4]=>[1,3,2,5,6,4,7]=>010010=>010010
[3,1,6,5,4,2,7]=>[7,1,3,2,4,5,6]=>101000=>000101
[3,1,6,5,4,7,2]=>[4,5,6,1,3,2,7]=>001010=>010100
[3,1,6,5,7,2,4]=>[5,6,1,3,2,7,4]=>010101=>101010
[3,1,6,5,7,4,2]=>[5,6,1,3,2,4,7]=>010100=>001010
[3,1,6,7,2,4,5]=>[6,1,3,2,7,5,4]=>101011=>110101
[3,1,6,7,2,5,4]=>[6,1,3,2,7,4,5]=>101010=>010101
[3,1,6,7,4,2,5]=>[6,1,3,2,4,7,5]=>101001=>100101
[3,1,6,7,4,5,2]=>[6,4,7,1,3,2,5]=>101010=>010101
[3,1,6,7,5,2,4]=>[6,1,3,2,5,7,4]=>101001=>100101
[3,1,6,7,5,4,2]=>[6,1,3,2,4,5,7]=>101000=>000101
[3,1,7,2,4,5,6]=>[1,3,2,7,6,5,4]=>010111=>111010
[3,1,7,2,4,6,5]=>[1,3,2,7,5,6,4]=>010101=>101010
[3,1,7,2,5,4,6]=>[1,3,2,7,6,4,5]=>010110=>011010
[3,1,7,2,5,6,4]=>[1,3,2,7,5,4,6]=>010110=>011010
[3,1,7,2,6,4,5]=>[1,3,2,7,4,6,5]=>010101=>101010
[3,1,7,2,6,5,4]=>[1,3,2,7,4,5,6]=>010100=>001010
[3,1,7,4,2,5,6]=>[1,3,2,4,7,6,5]=>010011=>110010
[3,1,7,4,2,6,5]=>[1,3,2,4,7,5,6]=>010010=>010010
[3,1,7,4,5,2,6]=>[4,7,6,1,3,2,5]=>011010=>010110
[3,1,7,4,5,6,2]=>[4,7,5,1,3,2,6]=>011010=>010110
[3,1,7,4,6,2,5]=>[4,7,1,3,2,6,5]=>010101=>101010
[3,1,7,4,6,5,2]=>[4,7,1,3,2,5,6]=>010100=>001010
[3,1,7,5,2,4,6]=>[1,3,2,5,7,6,4]=>010011=>110010
[3,1,7,5,2,6,4]=>[1,3,2,5,7,4,6]=>010010=>010010
[3,1,7,5,4,2,6]=>[1,3,2,4,5,7,6]=>010001=>100010
[3,1,7,5,4,6,2]=>[4,5,7,1,3,2,6]=>001010=>010100
[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]=>010101=>101010
[3,1,7,5,6,4,2]=>[5,7,1,3,2,4,6]=>010100=>001010
[3,1,7,6,2,4,5]=>[1,3,2,6,7,5,4]=>010011=>110010
[3,1,7,6,2,5,4]=>[1,3,2,6,7,4,5]=>010010=>010010
[3,1,7,6,4,2,5]=>[1,3,2,4,6,7,5]=>010001=>100010
[3,1,7,6,4,5,2]=>[4,6,7,1,3,2,5]=>001010=>010100
[3,1,7,6,5,2,4]=>[1,3,2,5,6,7,4]=>010001=>100010
[3,1,7,6,5,4,2]=>[1,3,2,4,5,6,7]=>010000=>000010
[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>111100=>001111
[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>011100=>001110
[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>101100=>001101
[3,2,1,4,6,7,5]=>[6,5,7,4,1,2,3]=>101100=>001101
[3,2,1,4,7,5,6]=>[5,7,6,4,1,2,3]=>011100=>001110
[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>001100=>001100
[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>110100=>001011
[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>010100=>001010
[3,2,1,5,6,4,7]=>[7,5,4,6,1,2,3]=>110100=>001011
[3,2,1,5,6,7,4]=>[6,5,4,7,1,2,3]=>110100=>001011
[3,2,1,5,7,4,6]=>[5,4,7,6,1,2,3]=>101100=>001101
[3,2,1,5,7,6,4]=>[5,4,6,7,1,2,3]=>100100=>001001
[3,2,1,6,4,5,7]=>[7,4,6,5,1,2,3]=>101100=>001101
[3,2,1,6,4,7,5]=>[4,6,5,7,1,2,3]=>010100=>001010
[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>100100=>001001
[3,2,1,6,5,7,4]=>[5,6,4,7,1,2,3]=>010100=>001010
[3,2,1,6,7,4,5]=>[6,4,7,5,1,2,3]=>101100=>001101
[3,2,1,6,7,5,4]=>[6,4,5,7,1,2,3]=>100100=>001001
[3,2,1,7,4,5,6]=>[4,7,6,5,1,2,3]=>011100=>001110
[3,2,1,7,4,6,5]=>[4,7,5,6,1,2,3]=>010100=>001010
[3,2,1,7,5,4,6]=>[4,5,7,6,1,2,3]=>001100=>001100
[3,2,1,7,5,6,4]=>[5,7,4,6,1,2,3]=>010100=>001010
[3,2,1,7,6,4,5]=>[4,6,7,5,1,2,3]=>001100=>001100
[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>000100=>001000
[3,2,4,1,5,6,7]=>[7,6,5,2,3,1,4]=>111010=>010111
[3,2,4,1,5,7,6]=>[6,7,5,2,3,1,4]=>011010=>010110
[3,2,4,1,6,5,7]=>[7,5,6,2,3,1,4]=>101010=>010101
[3,2,4,1,6,7,5]=>[6,5,7,2,3,1,4]=>101010=>010101
[3,2,4,1,7,5,6]=>[5,7,6,2,3,1,4]=>011010=>010110
[3,2,4,1,7,6,5]=>[5,6,7,2,3,1,4]=>001010=>010100
[3,2,4,5,1,6,7]=>[7,6,4,2,3,1,5]=>111010=>010111
[3,2,4,5,1,7,6]=>[6,7,4,2,3,1,5]=>011010=>010110
[3,2,4,5,6,1,7]=>[7,5,4,2,3,1,6]=>111010=>010111
[3,2,4,5,6,7,1]=>[6,5,4,2,3,1,7]=>111010=>010111
[3,2,4,5,7,1,6]=>[5,4,2,3,1,7,6]=>110101=>101011
[3,2,4,5,7,6,1]=>[5,4,2,3,1,6,7]=>110100=>001011
[3,2,4,6,1,5,7]=>[7,4,2,3,1,6,5]=>110101=>101011
[3,2,4,6,1,7,5]=>[4,2,3,1,6,5,7]=>101010=>010101
[3,2,4,6,5,1,7]=>[7,4,2,3,1,5,6]=>110100=>001011
[3,2,4,6,5,7,1]=>[5,6,4,2,3,1,7]=>011010=>010110
[3,2,4,6,7,1,5]=>[6,4,2,3,1,7,5]=>110101=>101011
[3,2,4,6,7,5,1]=>[6,4,2,3,1,5,7]=>110100=>001011
[3,2,4,7,1,5,6]=>[4,2,3,1,7,6,5]=>101011=>110101
[3,2,4,7,1,6,5]=>[4,2,3,1,7,5,6]=>101010=>010101
[3,2,4,7,5,1,6]=>[4,2,3,1,5,7,6]=>101001=>100101
[3,2,4,7,5,6,1]=>[5,7,4,2,3,1,6]=>011010=>010110
[3,2,4,7,6,1,5]=>[4,2,3,1,6,7,5]=>101001=>100101
[3,2,4,7,6,5,1]=>[4,2,3,1,5,6,7]=>101000=>000101
[3,2,5,1,4,6,7]=>[7,6,2,3,1,5,4]=>110101=>101011
[3,2,5,1,4,7,6]=>[6,7,2,3,1,5,4]=>010101=>101010
[3,2,5,1,6,4,7]=>[7,2,3,1,5,4,6]=>101010=>010101
[3,2,5,1,6,7,4]=>[6,2,3,1,5,4,7]=>101010=>010101
[3,2,5,1,7,4,6]=>[2,3,1,5,4,7,6]=>010101=>101010
[3,2,5,1,7,6,4]=>[2,3,1,5,4,6,7]=>010100=>001010
[3,2,5,4,1,6,7]=>[7,6,2,3,1,4,5]=>110100=>001011
[3,2,5,4,1,7,6]=>[6,7,2,3,1,4,5]=>010100=>001010
[3,2,5,4,6,1,7]=>[7,4,5,2,3,1,6]=>101010=>010101
[3,2,5,4,6,7,1]=>[6,4,5,2,3,1,7]=>101010=>010101
[3,2,5,4,7,1,6]=>[4,5,2,3,1,7,6]=>010101=>101010
[3,2,5,4,7,6,1]=>[4,5,2,3,1,6,7]=>010100=>001010
[3,2,5,6,1,4,7]=>[7,5,2,3,1,6,4]=>110101=>101011
[3,2,5,6,1,7,4]=>[5,2,3,1,6,4,7]=>101010=>010101
[3,2,5,6,4,1,7]=>[7,5,2,3,1,4,6]=>110100=>001011
[3,2,5,6,4,7,1]=>[5,4,6,2,3,1,7]=>101010=>010101
[3,2,5,6,7,1,4]=>[6,5,2,3,1,7,4]=>110101=>101011
[3,2,5,6,7,4,1]=>[6,5,2,3,1,4,7]=>110100=>001011
[3,2,5,7,1,4,6]=>[5,2,3,1,7,6,4]=>101011=>110101
[3,2,5,7,1,6,4]=>[5,2,3,1,7,4,6]=>101010=>010101
[3,2,5,7,4,1,6]=>[5,2,3,1,4,7,6]=>101001=>100101
[3,2,5,7,4,6,1]=>[5,4,7,2,3,1,6]=>101010=>010101
[3,2,5,7,6,1,4]=>[5,2,3,1,6,7,4]=>101001=>100101
[3,2,5,7,6,4,1]=>[5,2,3,1,4,6,7]=>101000=>000101
[3,2,6,1,4,5,7]=>[7,2,3,1,6,5,4]=>101011=>110101
[3,2,6,1,4,7,5]=>[2,3,1,6,5,7,4]=>010101=>101010
[3,2,6,1,5,4,7]=>[7,2,3,1,6,4,5]=>101010=>010101
[3,2,6,1,5,7,4]=>[2,3,1,6,5,4,7]=>010110=>011010
[3,2,6,1,7,4,5]=>[2,3,1,6,4,7,5]=>010101=>101010
[3,2,6,1,7,5,4]=>[2,3,1,6,4,5,7]=>010100=>001010
[3,2,6,4,1,5,7]=>[7,2,3,1,4,6,5]=>101001=>100101
[3,2,6,4,1,7,5]=>[2,3,1,4,6,5,7]=>010010=>010010
[3,2,6,4,5,1,7]=>[7,4,6,2,3,1,5]=>101010=>010101
[3,2,6,4,5,7,1]=>[4,6,5,2,3,1,7]=>011010=>010110
[3,2,6,4,7,1,5]=>[4,6,2,3,1,7,5]=>010101=>101010
[3,2,6,4,7,5,1]=>[4,6,2,3,1,5,7]=>010100=>001010
[3,2,6,5,1,4,7]=>[7,2,3,1,5,6,4]=>101001=>100101
[3,2,6,5,1,7,4]=>[2,3,1,5,6,4,7]=>010010=>010010
[3,2,6,5,4,1,7]=>[7,2,3,1,4,5,6]=>101000=>000101
[3,2,6,5,4,7,1]=>[4,5,6,2,3,1,7]=>001010=>010100
[3,2,6,5,7,1,4]=>[5,6,2,3,1,7,4]=>010101=>101010
[3,2,6,5,7,4,1]=>[5,6,2,3,1,4,7]=>010100=>001010
[3,2,6,7,1,4,5]=>[6,2,3,1,7,5,4]=>101011=>110101
[3,2,6,7,1,5,4]=>[6,2,3,1,7,4,5]=>101010=>010101
[3,2,6,7,4,1,5]=>[6,2,3,1,4,7,5]=>101001=>100101
[3,2,6,7,4,5,1]=>[6,4,7,2,3,1,5]=>101010=>010101
[3,2,6,7,5,1,4]=>[6,2,3,1,5,7,4]=>101001=>100101
[3,2,6,7,5,4,1]=>[6,2,3,1,4,5,7]=>101000=>000101
[3,2,7,1,4,5,6]=>[2,3,1,7,6,5,4]=>010111=>111010
[3,2,7,1,4,6,5]=>[2,3,1,7,5,6,4]=>010101=>101010
[3,2,7,1,5,4,6]=>[2,3,1,7,6,4,5]=>010110=>011010
[3,2,7,1,5,6,4]=>[2,3,1,7,5,4,6]=>010110=>011010
[3,2,7,1,6,4,5]=>[2,3,1,7,4,6,5]=>010101=>101010
[3,2,7,1,6,5,4]=>[2,3,1,7,4,5,6]=>010100=>001010
[3,2,7,4,1,5,6]=>[2,3,1,4,7,6,5]=>010011=>110010
[3,2,7,4,1,6,5]=>[2,3,1,4,7,5,6]=>010010=>010010
[3,2,7,4,5,1,6]=>[4,7,6,2,3,1,5]=>011010=>010110
[3,2,7,4,5,6,1]=>[4,7,5,2,3,1,6]=>011010=>010110
[3,2,7,4,6,1,5]=>[4,7,2,3,1,6,5]=>010101=>101010
[3,2,7,4,6,5,1]=>[4,7,2,3,1,5,6]=>010100=>001010
[3,2,7,5,1,4,6]=>[2,3,1,5,7,6,4]=>010011=>110010
[3,2,7,5,1,6,4]=>[2,3,1,5,7,4,6]=>010010=>010010
[3,2,7,5,4,1,6]=>[2,3,1,4,5,7,6]=>010001=>100010
[3,2,7,5,4,6,1]=>[4,5,7,2,3,1,6]=>001010=>010100
[3,2,7,5,6,1,4]=>[5,7,2,3,1,6,4]=>010101=>101010
[3,2,7,5,6,4,1]=>[5,7,2,3,1,4,6]=>010100=>001010
[3,2,7,6,1,4,5]=>[2,3,1,6,7,5,4]=>010011=>110010
[3,2,7,6,1,5,4]=>[2,3,1,6,7,4,5]=>010010=>010010
[3,2,7,6,4,1,5]=>[2,3,1,4,6,7,5]=>010001=>100010
[3,2,7,6,4,5,1]=>[4,6,7,2,3,1,5]=>001010=>010100
[3,2,7,6,5,1,4]=>[2,3,1,5,6,7,4]=>010001=>100010
[3,2,7,6,5,4,1]=>[2,3,1,4,5,6,7]=>010000=>000010
[3,4,1,2,5,6,7]=>[7,6,5,3,1,4,2]=>111101=>101111
[3,4,1,2,5,7,6]=>[6,7,5,3,1,4,2]=>011101=>101110
[3,4,1,2,6,5,7]=>[7,5,6,3,1,4,2]=>101101=>101101
[3,4,1,2,6,7,5]=>[6,5,7,3,1,4,2]=>101101=>101101
[3,4,1,2,7,5,6]=>[5,7,6,3,1,4,2]=>011101=>101110
[3,4,1,2,7,6,5]=>[5,6,7,3,1,4,2]=>001101=>101100
[3,4,1,5,2,6,7]=>[7,6,3,1,4,2,5]=>111010=>010111
[3,4,1,5,2,7,6]=>[6,7,3,1,4,2,5]=>011010=>010110
[3,4,1,5,6,2,7]=>[7,5,3,1,4,2,6]=>111010=>010111
[3,4,1,5,6,7,2]=>[6,5,3,1,4,2,7]=>111010=>010111
[3,4,1,5,7,2,6]=>[5,3,1,4,2,7,6]=>110101=>101011
[3,4,1,5,7,6,2]=>[5,3,1,4,2,6,7]=>110100=>001011
[3,4,1,6,2,5,7]=>[7,3,1,4,2,6,5]=>110101=>101011
[3,4,1,6,2,7,5]=>[3,1,4,2,6,5,7]=>101010=>010101
[3,4,1,6,5,2,7]=>[7,3,1,4,2,5,6]=>110100=>001011
[3,4,1,6,5,7,2]=>[5,6,3,1,4,2,7]=>011010=>010110
[3,4,1,6,7,2,5]=>[6,3,1,4,2,7,5]=>110101=>101011
[3,4,1,6,7,5,2]=>[6,3,1,4,2,5,7]=>110100=>001011
[3,4,1,7,2,5,6]=>[3,1,4,2,7,6,5]=>101011=>110101
[3,4,1,7,2,6,5]=>[3,1,4,2,7,5,6]=>101010=>010101
[3,4,1,7,5,2,6]=>[3,1,4,2,5,7,6]=>101001=>100101
[3,4,1,7,5,6,2]=>[5,7,3,1,4,2,6]=>011010=>010110
[3,4,1,7,6,2,5]=>[3,1,4,2,6,7,5]=>101001=>100101
[3,4,1,7,6,5,2]=>[3,1,4,2,5,6,7]=>101000=>000101
[3,4,2,1,5,6,7]=>[7,6,5,3,1,2,4]=>111100=>001111
[3,4,2,1,5,7,6]=>[6,7,5,3,1,2,4]=>011100=>001110
[3,4,2,1,6,5,7]=>[7,5,6,3,1,2,4]=>101100=>001101
[3,4,2,1,6,7,5]=>[6,5,7,3,1,2,4]=>101100=>001101
[3,4,2,1,7,5,6]=>[5,7,6,3,1,2,4]=>011100=>001110
[3,4,2,1,7,6,5]=>[5,6,7,3,1,2,4]=>001100=>001100
[3,4,2,5,1,6,7]=>[7,6,3,2,4,1,5]=>111010=>010111
[3,4,2,5,1,7,6]=>[6,7,3,2,4,1,5]=>011010=>010110
[3,4,2,5,6,1,7]=>[7,5,3,2,4,1,6]=>111010=>010111
[3,4,2,5,6,7,1]=>[6,5,3,2,4,1,7]=>111010=>010111
[3,4,2,5,7,1,6]=>[5,3,2,4,1,7,6]=>110101=>101011
[3,4,2,5,7,6,1]=>[5,3,2,4,1,6,7]=>110100=>001011
[3,4,2,6,1,5,7]=>[7,3,2,4,1,6,5]=>110101=>101011
[3,4,2,6,1,7,5]=>[3,2,4,1,6,5,7]=>101010=>010101
[3,4,2,6,5,1,7]=>[7,3,2,4,1,5,6]=>110100=>001011
[3,4,2,6,5,7,1]=>[5,6,3,2,4,1,7]=>011010=>010110
[3,4,2,6,7,1,5]=>[6,3,2,4,1,7,5]=>110101=>101011
[3,4,2,6,7,5,1]=>[6,3,2,4,1,5,7]=>110100=>001011
[3,4,2,7,1,5,6]=>[3,2,4,1,7,6,5]=>101011=>110101
[3,4,2,7,1,6,5]=>[3,2,4,1,7,5,6]=>101010=>010101
[3,4,2,7,5,1,6]=>[3,2,4,1,5,7,6]=>101001=>100101
[3,4,2,7,5,6,1]=>[5,7,3,2,4,1,6]=>011010=>010110
[3,4,2,7,6,1,5]=>[3,2,4,1,6,7,5]=>101001=>100101
[3,4,2,7,6,5,1]=>[3,2,4,1,5,6,7]=>101000=>000101
[3,4,5,1,2,6,7]=>[7,6,4,3,1,5,2]=>111101=>101111
[3,4,5,1,2,7,6]=>[6,7,4,3,1,5,2]=>011101=>101110
[3,4,5,1,6,2,7]=>[7,4,3,1,5,2,6]=>111010=>010111
[3,4,5,1,6,7,2]=>[6,4,3,1,5,2,7]=>111010=>010111
[3,4,5,1,7,2,6]=>[4,3,1,5,2,7,6]=>110101=>101011
[3,4,5,1,7,6,2]=>[4,3,1,5,2,6,7]=>110100=>001011
[3,4,5,2,1,6,7]=>[7,6,4,3,1,2,5]=>111100=>001111
[3,4,5,2,1,7,6]=>[6,7,4,3,1,2,5]=>011100=>001110
[3,4,5,2,6,1,7]=>[7,4,3,2,5,1,6]=>111010=>010111
[3,4,5,2,6,7,1]=>[6,4,3,2,5,1,7]=>111010=>010111
[3,4,5,2,7,1,6]=>[4,3,2,5,1,7,6]=>110101=>101011
[3,4,5,2,7,6,1]=>[4,3,2,5,1,6,7]=>110100=>001011
[3,4,5,6,1,2,7]=>[7,5,4,3,1,6,2]=>111101=>101111
[3,4,5,6,1,7,2]=>[5,4,3,1,6,2,7]=>111010=>010111
[3,4,5,6,2,1,7]=>[7,5,4,3,1,2,6]=>111100=>001111
[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>111010=>010111
[3,4,5,6,7,1,2]=>[6,5,4,3,1,7,2]=>111101=>101111
[3,4,5,6,7,2,1]=>[6,5,4,3,1,2,7]=>111100=>001111
[3,4,5,7,1,2,6]=>[5,4,3,1,7,6,2]=>111011=>110111
[3,4,5,7,1,6,2]=>[5,4,3,1,7,2,6]=>111010=>010111
[3,4,5,7,2,1,6]=>[5,4,3,1,2,7,6]=>111001=>100111
[3,4,5,7,2,6,1]=>[5,4,3,2,7,1,6]=>111010=>010111
[3,4,5,7,6,1,2]=>[5,4,3,1,6,7,2]=>111001=>100111
[3,4,5,7,6,2,1]=>[5,4,3,1,2,6,7]=>111000=>000111
[3,4,6,1,2,5,7]=>[7,4,3,1,6,5,2]=>111011=>110111
[3,4,6,1,2,7,5]=>[4,3,1,6,5,7,2]=>110101=>101011
[3,4,6,1,5,2,7]=>[7,4,3,1,6,2,5]=>111010=>010111
[3,4,6,1,5,7,2]=>[4,3,1,6,5,2,7]=>110110=>011011
[3,4,6,1,7,2,5]=>[4,3,1,6,2,7,5]=>110101=>101011
[3,4,6,1,7,5,2]=>[4,3,1,6,2,5,7]=>110100=>001011
[3,4,6,2,1,5,7]=>[7,4,3,1,2,6,5]=>111001=>100111
[3,4,6,2,1,7,5]=>[4,3,1,2,6,5,7]=>110010=>010011
[3,4,6,2,5,1,7]=>[7,4,3,2,6,1,5]=>111010=>010111
[3,4,6,2,5,7,1]=>[4,3,2,6,5,1,7]=>110110=>011011
[3,4,6,2,7,1,5]=>[4,3,2,6,1,7,5]=>110101=>101011
[3,4,6,2,7,5,1]=>[4,3,2,6,1,5,7]=>110100=>001011
[3,4,6,5,1,2,7]=>[7,4,3,1,5,6,2]=>111001=>100111
[3,4,6,5,1,7,2]=>[4,3,1,5,6,2,7]=>110010=>010011
[3,4,6,5,2,1,7]=>[7,4,3,1,2,5,6]=>111000=>000111
[3,4,6,5,2,7,1]=>[4,3,2,5,6,1,7]=>110010=>010011
[3,4,6,5,7,1,2]=>[5,6,4,3,1,7,2]=>011101=>101110
[3,4,6,5,7,2,1]=>[5,6,4,3,1,2,7]=>011100=>001110
[3,4,6,7,1,2,5]=>[6,4,3,1,7,5,2]=>111011=>110111
[3,4,6,7,1,5,2]=>[6,4,3,1,7,2,5]=>111010=>010111
[3,4,6,7,2,1,5]=>[6,4,3,1,2,7,5]=>111001=>100111
[3,4,6,7,2,5,1]=>[6,4,3,2,7,1,5]=>111010=>010111
[3,4,6,7,5,1,2]=>[6,4,3,1,5,7,2]=>111001=>100111
[3,4,6,7,5,2,1]=>[6,4,3,1,2,5,7]=>111000=>000111
[3,4,7,1,2,5,6]=>[4,3,1,7,6,5,2]=>110111=>111011
[3,4,7,1,2,6,5]=>[4,3,1,7,5,6,2]=>110101=>101011
[3,4,7,1,5,2,6]=>[4,3,1,7,6,2,5]=>110110=>011011
[3,4,7,1,5,6,2]=>[4,3,1,7,5,2,6]=>110110=>011011
[3,4,7,1,6,2,5]=>[4,3,1,7,2,6,5]=>110101=>101011
[3,4,7,1,6,5,2]=>[4,3,1,7,2,5,6]=>110100=>001011
[3,4,7,2,1,5,6]=>[4,3,1,2,7,6,5]=>110011=>110011
[3,4,7,2,1,6,5]=>[4,3,1,2,7,5,6]=>110010=>010011
[3,4,7,2,5,1,6]=>[4,3,2,7,6,1,5]=>110110=>011011
[3,4,7,2,5,6,1]=>[4,3,2,7,5,1,6]=>110110=>011011
[3,4,7,2,6,1,5]=>[4,3,2,7,1,6,5]=>110101=>101011
[3,4,7,2,6,5,1]=>[4,3,2,7,1,5,6]=>110100=>001011
[3,4,7,5,1,2,6]=>[4,3,1,5,7,6,2]=>110011=>110011
[3,4,7,5,1,6,2]=>[4,3,1,5,7,2,6]=>110010=>010011
[3,4,7,5,2,1,6]=>[4,3,1,2,5,7,6]=>110001=>100011
[3,4,7,5,2,6,1]=>[4,3,2,5,7,1,6]=>110010=>010011
[3,4,7,5,6,1,2]=>[5,7,4,3,1,6,2]=>011101=>101110
[3,4,7,5,6,2,1]=>[5,7,4,3,1,2,6]=>011100=>001110
[3,4,7,6,1,2,5]=>[4,3,1,6,7,5,2]=>110011=>110011
[3,4,7,6,1,5,2]=>[4,3,1,6,7,2,5]=>110010=>010011
[3,4,7,6,2,1,5]=>[4,3,1,2,6,7,5]=>110001=>100011
[3,4,7,6,2,5,1]=>[4,3,2,6,7,1,5]=>110010=>010011
[3,4,7,6,5,1,2]=>[4,3,1,5,6,7,2]=>110001=>100011
[3,4,7,6,5,2,1]=>[4,3,1,2,5,6,7]=>110000=>000011
[3,5,1,2,4,6,7]=>[7,6,3,1,5,4,2]=>111011=>110111
[3,5,1,2,4,7,6]=>[6,7,3,1,5,4,2]=>011011=>110110
[3,5,1,2,6,4,7]=>[7,3,1,5,4,6,2]=>110101=>101011
[3,5,1,2,6,7,4]=>[6,3,1,5,4,7,2]=>110101=>101011
[3,5,1,2,7,4,6]=>[3,1,5,4,7,6,2]=>101011=>110101
[3,5,1,2,7,6,4]=>[3,1,5,4,6,7,2]=>101001=>100101
[3,5,1,4,2,6,7]=>[7,6,3,1,5,2,4]=>111010=>010111
[3,5,1,4,2,7,6]=>[6,7,3,1,5,2,4]=>011010=>010110
[3,5,1,4,6,2,7]=>[7,3,1,5,4,2,6]=>110110=>011011
[3,5,1,4,6,7,2]=>[6,3,1,5,4,2,7]=>110110=>011011
[3,5,1,4,7,2,6]=>[3,1,5,4,2,7,6]=>101101=>101101
[3,5,1,4,7,6,2]=>[3,1,5,4,2,6,7]=>101100=>001101
[3,5,1,6,2,4,7]=>[7,3,1,5,2,6,4]=>110101=>101011
[3,5,1,6,2,7,4]=>[3,1,5,2,6,4,7]=>101010=>010101
[3,5,1,6,4,2,7]=>[7,3,1,5,2,4,6]=>110100=>001011
[3,5,1,6,4,7,2]=>[3,1,5,4,6,2,7]=>101010=>010101
[3,5,1,6,7,2,4]=>[6,3,1,5,2,7,4]=>110101=>101011
[3,5,1,6,7,4,2]=>[6,3,1,5,2,4,7]=>110100=>001011
[3,5,1,7,2,4,6]=>[3,1,5,2,7,6,4]=>101011=>110101
[3,5,1,7,2,6,4]=>[3,1,5,2,7,4,6]=>101010=>010101
[3,5,1,7,4,2,6]=>[3,1,5,2,4,7,6]=>101001=>100101
[3,5,1,7,4,6,2]=>[3,1,5,4,7,2,6]=>101010=>010101
[3,5,1,7,6,2,4]=>[3,1,5,2,6,7,4]=>101001=>100101
[3,5,1,7,6,4,2]=>[3,1,5,2,4,6,7]=>101000=>000101
[3,5,2,1,4,6,7]=>[7,6,3,1,2,5,4]=>111001=>100111
[3,5,2,1,4,7,6]=>[6,7,3,1,2,5,4]=>011001=>100110
[3,5,2,1,6,4,7]=>[7,3,1,2,5,4,6]=>110010=>010011
[3,5,2,1,6,7,4]=>[6,3,1,2,5,4,7]=>110010=>010011
[3,5,2,1,7,4,6]=>[3,1,2,5,4,7,6]=>100101=>101001
[3,5,2,1,7,6,4]=>[3,1,2,5,4,6,7]=>100100=>001001
[3,5,2,4,1,6,7]=>[7,6,3,2,5,1,4]=>111010=>010111
[3,5,2,4,1,7,6]=>[6,7,3,2,5,1,4]=>011010=>010110
[3,5,2,4,6,1,7]=>[7,3,2,5,4,1,6]=>110110=>011011
[3,5,2,4,6,7,1]=>[6,3,2,5,4,1,7]=>110110=>011011
[3,5,2,4,7,1,6]=>[3,2,5,4,1,7,6]=>101101=>101101
[3,5,2,4,7,6,1]=>[3,2,5,4,1,6,7]=>101100=>001101
[3,5,2,6,1,4,7]=>[7,3,2,5,1,6,4]=>110101=>101011
[3,5,2,6,1,7,4]=>[3,2,5,1,6,4,7]=>101010=>010101
[3,5,2,6,4,1,7]=>[7,3,2,5,1,4,6]=>110100=>001011
[3,5,2,6,4,7,1]=>[3,2,5,4,6,1,7]=>101010=>010101
[3,5,2,6,7,1,4]=>[6,3,2,5,1,7,4]=>110101=>101011
[3,5,2,6,7,4,1]=>[6,3,2,5,1,4,7]=>110100=>001011
[3,5,2,7,1,4,6]=>[3,2,5,1,7,6,4]=>101011=>110101
[3,5,2,7,1,6,4]=>[3,2,5,1,7,4,6]=>101010=>010101
[3,5,2,7,4,1,6]=>[3,2,5,1,4,7,6]=>101001=>100101
[3,5,2,7,4,6,1]=>[3,2,5,4,7,1,6]=>101010=>010101
[3,5,2,7,6,1,4]=>[3,2,5,1,6,7,4]=>101001=>100101
[3,5,2,7,6,4,1]=>[3,2,5,1,4,6,7]=>101000=>000101
[3,5,4,1,2,6,7]=>[7,6,3,1,4,5,2]=>111001=>100111
[3,5,4,1,2,7,6]=>[6,7,3,1,4,5,2]=>011001=>100110
[3,5,4,1,6,2,7]=>[7,3,1,4,5,2,6]=>110010=>010011
[3,5,4,1,6,7,2]=>[6,3,1,4,5,2,7]=>110010=>010011
[3,5,4,1,7,2,6]=>[3,1,4,5,2,7,6]=>100101=>101001
[3,5,4,1,7,6,2]=>[3,1,4,5,2,6,7]=>100100=>001001
[3,5,4,2,1,6,7]=>[7,6,3,1,2,4,5]=>111000=>000111
[3,5,4,2,1,7,6]=>[6,7,3,1,2,4,5]=>011000=>000110
[3,5,4,2,6,1,7]=>[7,3,2,4,5,1,6]=>110010=>010011
[3,5,4,2,6,7,1]=>[6,3,2,4,5,1,7]=>110010=>010011
[3,5,4,2,7,1,6]=>[3,2,4,5,1,7,6]=>100101=>101001
[3,5,4,2,7,6,1]=>[3,2,4,5,1,6,7]=>100100=>001001
[3,5,4,6,1,2,7]=>[7,4,5,3,1,6,2]=>101101=>101101
[3,5,4,6,1,7,2]=>[4,5,3,1,6,2,7]=>011010=>010110
[3,5,4,6,2,1,7]=>[7,4,5,3,1,2,6]=>101100=>001101
[3,5,4,6,2,7,1]=>[4,5,3,2,6,1,7]=>011010=>010110
[3,5,4,6,7,1,2]=>[6,4,5,3,1,7,2]=>101101=>101101
[3,5,4,6,7,2,1]=>[6,4,5,3,1,2,7]=>101100=>001101
[3,5,4,7,1,2,6]=>[4,5,3,1,7,6,2]=>011011=>110110
[3,5,4,7,1,6,2]=>[4,5,3,1,7,2,6]=>011010=>010110
[3,5,4,7,2,1,6]=>[4,5,3,1,2,7,6]=>011001=>100110
[3,5,4,7,2,6,1]=>[4,5,3,2,7,1,6]=>011010=>010110
[3,5,4,7,6,1,2]=>[4,5,3,1,6,7,2]=>011001=>100110
[3,5,4,7,6,2,1]=>[4,5,3,1,2,6,7]=>011000=>000110
[3,5,6,1,2,4,7]=>[7,5,3,1,6,4,2]=>111011=>110111
[3,5,6,1,2,7,4]=>[5,3,1,6,4,7,2]=>110101=>101011
[3,5,6,1,4,2,7]=>[7,5,3,1,6,2,4]=>111010=>010111
[3,5,6,1,4,7,2]=>[5,3,1,6,4,2,7]=>110110=>011011
[3,5,6,1,7,2,4]=>[5,3,1,6,2,7,4]=>110101=>101011
[3,5,6,1,7,4,2]=>[5,3,1,6,2,4,7]=>110100=>001011
[3,5,6,2,1,4,7]=>[7,5,3,1,2,6,4]=>111001=>100111
[3,5,6,2,1,7,4]=>[5,3,1,2,6,4,7]=>110010=>010011
[3,5,6,2,4,1,7]=>[7,5,3,2,6,1,4]=>111010=>010111
[3,5,6,2,4,7,1]=>[5,3,2,6,4,1,7]=>110110=>011011
[3,5,6,2,7,1,4]=>[5,3,2,6,1,7,4]=>110101=>101011
[3,5,6,2,7,4,1]=>[5,3,2,6,1,4,7]=>110100=>001011
[3,5,6,4,1,2,7]=>[7,5,3,1,4,6,2]=>111001=>100111
[3,5,6,4,1,7,2]=>[5,3,1,4,6,2,7]=>110010=>010011
[3,5,6,4,2,1,7]=>[7,5,3,1,2,4,6]=>111000=>000111
[3,5,6,4,2,7,1]=>[5,3,2,4,6,1,7]=>110010=>010011
[3,5,6,4,7,1,2]=>[5,4,6,3,1,7,2]=>101101=>101101
[3,5,6,4,7,2,1]=>[5,4,6,3,1,2,7]=>101100=>001101
[3,5,6,7,1,2,4]=>[6,5,3,1,7,4,2]=>111011=>110111
[3,5,6,7,1,4,2]=>[6,5,3,1,7,2,4]=>111010=>010111
[3,5,6,7,2,1,4]=>[6,5,3,1,2,7,4]=>111001=>100111
[3,5,6,7,2,4,1]=>[6,5,3,2,7,1,4]=>111010=>010111
[3,5,6,7,4,1,2]=>[6,5,3,1,4,7,2]=>111001=>100111
[3,5,6,7,4,2,1]=>[6,5,3,1,2,4,7]=>111000=>000111
[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]=>110111=>111011
[3,5,7,1,2,6,4]=>[5,3,1,7,4,6,2]=>110101=>101011
[3,5,7,1,4,2,6]=>[5,3,1,7,6,2,4]=>110110=>011011
[3,5,7,1,4,6,2]=>[5,3,1,7,4,2,6]=>110110=>011011
[3,5,7,1,6,2,4]=>[5,3,1,7,2,6,4]=>110101=>101011
[3,5,7,1,6,4,2]=>[5,3,1,7,2,4,6]=>110100=>001011
[3,5,7,2,1,4,6]=>[5,3,1,2,7,6,4]=>110011=>110011
[3,5,7,2,1,6,4]=>[5,3,1,2,7,4,6]=>110010=>010011
[3,5,7,2,4,1,6]=>[5,3,2,7,6,1,4]=>110110=>011011
[3,5,7,2,4,6,1]=>[5,3,2,7,4,1,6]=>110110=>011011
[3,5,7,2,6,1,4]=>[5,3,2,7,1,6,4]=>110101=>101011
[3,5,7,2,6,4,1]=>[5,3,2,7,1,4,6]=>110100=>001011
[3,5,7,4,1,2,6]=>[5,3,1,4,7,6,2]=>110011=>110011
[3,5,7,4,1,6,2]=>[5,3,1,4,7,2,6]=>110010=>010011
[3,5,7,4,2,1,6]=>[5,3,1,2,4,7,6]=>110001=>100011
[3,5,7,4,2,6,1]=>[5,3,2,4,7,1,6]=>110010=>010011
[3,5,7,4,6,1,2]=>[5,4,7,3,1,6,2]=>101101=>101101
[3,5,7,4,6,2,1]=>[5,4,7,3,1,2,6]=>101100=>001101
[3,5,7,6,1,2,4]=>[5,3,1,6,7,4,2]=>110011=>110011
[3,5,7,6,1,4,2]=>[5,3,1,6,7,2,4]=>110010=>010011
[3,5,7,6,2,1,4]=>[5,3,1,2,6,7,4]=>110001=>100011
[3,5,7,6,2,4,1]=>[5,3,2,6,7,1,4]=>110010=>010011
[3,5,7,6,4,1,2]=>[5,3,1,4,6,7,2]=>110001=>100011
[3,5,7,6,4,2,1]=>[5,3,1,2,4,6,7]=>110000=>000011
[3,6,1,2,4,5,7]=>[7,3,1,6,5,4,2]=>110111=>111011
[3,6,1,2,4,7,5]=>[3,1,6,5,7,4,2]=>101011=>110101
[3,6,1,2,5,4,7]=>[7,3,1,6,4,5,2]=>110101=>101011
[3,6,1,2,5,7,4]=>[3,1,6,5,4,7,2]=>101101=>101101
[3,6,1,2,7,4,5]=>[3,1,6,4,7,5,2]=>101011=>110101
[3,6,1,2,7,5,4]=>[3,1,6,4,5,7,2]=>101001=>100101
[3,6,1,4,2,5,7]=>[7,3,1,6,5,2,4]=>110110=>011011
[3,6,1,4,2,7,5]=>[3,1,6,5,7,2,4]=>101010=>010101
[3,6,1,4,5,2,7]=>[7,3,1,6,4,2,5]=>110110=>011011
[3,6,1,4,5,7,2]=>[3,1,6,5,4,2,7]=>101110=>011101
[3,6,1,4,7,2,5]=>[3,1,6,4,2,7,5]=>101101=>101101
[3,6,1,4,7,5,2]=>[3,1,6,4,2,5,7]=>101100=>001101
[3,6,1,5,2,4,7]=>[7,3,1,6,2,5,4]=>110101=>101011
[3,6,1,5,2,7,4]=>[3,1,6,2,5,4,7]=>101010=>010101
[3,6,1,5,4,2,7]=>[7,3,1,6,2,4,5]=>110100=>001011
[3,6,1,5,4,7,2]=>[3,1,6,4,5,2,7]=>101010=>010101
[3,6,1,5,7,2,4]=>[3,1,6,5,2,7,4]=>101101=>101101
[3,6,1,5,7,4,2]=>[3,1,6,5,2,4,7]=>101100=>001101
[3,6,1,7,2,4,5]=>[3,1,6,2,7,5,4]=>101011=>110101
[3,6,1,7,2,5,4]=>[3,1,6,2,7,4,5]=>101010=>010101
[3,6,1,7,4,2,5]=>[3,1,6,2,4,7,5]=>101001=>100101
[3,6,1,7,4,5,2]=>[3,1,6,4,7,2,5]=>101010=>010101
[3,6,1,7,5,2,4]=>[3,1,6,2,5,7,4]=>101001=>100101
[3,6,1,7,5,4,2]=>[3,1,6,2,4,5,7]=>101000=>000101
[3,6,2,1,4,5,7]=>[7,3,1,2,6,5,4]=>110011=>110011
[3,6,2,1,4,7,5]=>[3,1,2,6,5,7,4]=>100101=>101001
[3,6,2,1,5,4,7]=>[7,3,1,2,6,4,5]=>110010=>010011
[3,6,2,1,5,7,4]=>[3,1,2,6,5,4,7]=>100110=>011001
[3,6,2,1,7,4,5]=>[3,1,2,6,4,7,5]=>100101=>101001
[3,6,2,1,7,5,4]=>[3,1,2,6,4,5,7]=>100100=>001001
[3,6,2,4,1,5,7]=>[7,3,2,6,5,1,4]=>110110=>011011
[3,6,2,4,1,7,5]=>[3,2,6,5,7,1,4]=>101010=>010101
[3,6,2,4,5,1,7]=>[7,3,2,6,4,1,5]=>110110=>011011
[3,6,2,4,5,7,1]=>[3,2,6,5,4,1,7]=>101110=>011101
[3,6,2,4,7,1,5]=>[3,2,6,4,1,7,5]=>101101=>101101
[3,6,2,4,7,5,1]=>[3,2,6,4,1,5,7]=>101100=>001101
[3,6,2,5,1,4,7]=>[7,3,2,6,1,5,4]=>110101=>101011
[3,6,2,5,1,7,4]=>[3,2,6,1,5,4,7]=>101010=>010101
[3,6,2,5,4,1,7]=>[7,3,2,6,1,4,5]=>110100=>001011
[3,6,2,5,4,7,1]=>[3,2,6,4,5,1,7]=>101010=>010101
[3,6,2,5,7,1,4]=>[3,2,6,5,1,7,4]=>101101=>101101
[3,6,2,5,7,4,1]=>[3,2,6,5,1,4,7]=>101100=>001101
[3,6,2,7,1,4,5]=>[3,2,6,1,7,5,4]=>101011=>110101
[3,6,2,7,1,5,4]=>[3,2,6,1,7,4,5]=>101010=>010101
[3,6,2,7,4,1,5]=>[3,2,6,1,4,7,5]=>101001=>100101
[3,6,2,7,4,5,1]=>[3,2,6,4,7,1,5]=>101010=>010101
[3,6,2,7,5,1,4]=>[3,2,6,1,5,7,4]=>101001=>100101
[3,6,2,7,5,4,1]=>[3,2,6,1,4,5,7]=>101000=>000101
[3,6,4,1,2,5,7]=>[7,3,1,4,6,5,2]=>110011=>110011
[3,6,4,1,2,7,5]=>[3,1,4,6,5,7,2]=>100101=>101001
[3,6,4,1,5,2,7]=>[7,3,1,4,6,2,5]=>110010=>010011
[3,6,4,1,5,7,2]=>[3,1,4,6,5,2,7]=>100110=>011001
[3,6,4,1,7,2,5]=>[3,1,4,6,2,7,5]=>100101=>101001
[3,6,4,1,7,5,2]=>[3,1,4,6,2,5,7]=>100100=>001001
[3,6,4,2,1,5,7]=>[7,3,1,2,4,6,5]=>110001=>100011
[3,6,4,2,1,7,5]=>[3,1,2,4,6,5,7]=>100010=>010001
[3,6,4,2,5,1,7]=>[7,3,2,4,6,1,5]=>110010=>010011
[3,6,4,2,5,7,1]=>[3,2,4,6,5,1,7]=>100110=>011001
[3,6,4,2,7,1,5]=>[3,2,4,6,1,7,5]=>100101=>101001
[3,6,4,2,7,5,1]=>[3,2,4,6,1,5,7]=>100100=>001001
[3,6,4,5,1,2,7]=>[7,4,6,3,1,5,2]=>101101=>101101
[3,6,4,5,1,7,2]=>[4,6,3,1,5,2,7]=>011010=>010110
[3,6,4,5,2,1,7]=>[7,4,6,3,1,2,5]=>101100=>001101
[3,6,4,5,2,7,1]=>[4,6,3,2,5,1,7]=>011010=>010110
[3,6,4,5,7,1,2]=>[4,6,5,3,1,7,2]=>011101=>101110
[3,6,4,5,7,2,1]=>[4,6,5,3,1,2,7]=>011100=>001110
[3,6,4,7,1,2,5]=>[4,6,3,1,7,5,2]=>011011=>110110
[3,6,4,7,1,5,2]=>[4,6,3,1,7,2,5]=>011010=>010110
[3,6,4,7,2,1,5]=>[4,6,3,1,2,7,5]=>011001=>100110
[3,6,4,7,2,5,1]=>[4,6,3,2,7,1,5]=>011010=>010110
[3,6,4,7,5,1,2]=>[4,6,3,1,5,7,2]=>011001=>100110
[3,6,4,7,5,2,1]=>[4,6,3,1,2,5,7]=>011000=>000110
[3,6,5,1,2,4,7]=>[7,3,1,5,6,4,2]=>110011=>110011
[3,6,5,1,2,7,4]=>[3,1,5,6,4,7,2]=>100101=>101001
[3,6,5,1,4,2,7]=>[7,3,1,5,6,2,4]=>110010=>010011
[3,6,5,1,4,7,2]=>[3,1,5,6,4,2,7]=>100110=>011001
[3,6,5,1,7,2,4]=>[3,1,5,6,2,7,4]=>100101=>101001
[3,6,5,1,7,4,2]=>[3,1,5,6,2,4,7]=>100100=>001001
[3,6,5,2,1,4,7]=>[7,3,1,2,5,6,4]=>110001=>100011
[3,6,5,2,1,7,4]=>[3,1,2,5,6,4,7]=>100010=>010001
[3,6,5,2,4,1,7]=>[7,3,2,5,6,1,4]=>110010=>010011
[3,6,5,2,4,7,1]=>[3,2,5,6,4,1,7]=>100110=>011001
[3,6,5,2,7,1,4]=>[3,2,5,6,1,7,4]=>100101=>101001
[3,6,5,2,7,4,1]=>[3,2,5,6,1,4,7]=>100100=>001001
[3,6,5,4,1,2,7]=>[7,3,1,4,5,6,2]=>110001=>100011
[3,6,5,4,1,7,2]=>[3,1,4,5,6,2,7]=>100010=>010001
[3,6,5,4,2,1,7]=>[7,3,1,2,4,5,6]=>110000=>000011
[3,6,5,4,2,7,1]=>[3,2,4,5,6,1,7]=>100010=>010001
[3,6,5,4,7,1,2]=>[4,5,6,3,1,7,2]=>001101=>101100
[3,6,5,4,7,2,1]=>[4,5,6,3,1,2,7]=>001100=>001100
[3,6,5,7,1,2,4]=>[5,6,3,1,7,4,2]=>011011=>110110
[3,6,5,7,1,4,2]=>[5,6,3,1,7,2,4]=>011010=>010110
[3,6,5,7,2,1,4]=>[5,6,3,1,2,7,4]=>011001=>100110
[3,6,5,7,2,4,1]=>[5,6,3,2,7,1,4]=>011010=>010110
[3,6,5,7,4,1,2]=>[5,6,3,1,4,7,2]=>011001=>100110
[3,6,5,7,4,2,1]=>[5,6,3,1,2,4,7]=>011000=>000110
[3,6,7,1,2,4,5]=>[6,3,1,7,5,4,2]=>110111=>111011
[3,6,7,1,2,5,4]=>[6,3,1,7,4,5,2]=>110101=>101011
[3,6,7,1,4,2,5]=>[6,3,1,7,5,2,4]=>110110=>011011
[3,6,7,1,4,5,2]=>[6,3,1,7,4,2,5]=>110110=>011011
[3,6,7,1,5,2,4]=>[6,3,1,7,2,5,4]=>110101=>101011
[3,6,7,1,5,4,2]=>[6,3,1,7,2,4,5]=>110100=>001011
[3,6,7,2,1,4,5]=>[6,3,1,2,7,5,4]=>110011=>110011
[3,6,7,2,1,5,4]=>[6,3,1,2,7,4,5]=>110010=>010011
[3,6,7,2,4,1,5]=>[6,3,2,7,5,1,4]=>110110=>011011
[3,6,7,2,4,5,1]=>[6,3,2,7,4,1,5]=>110110=>011011
[3,6,7,2,5,1,4]=>[6,3,2,7,1,5,4]=>110101=>101011
[3,6,7,2,5,4,1]=>[6,3,2,7,1,4,5]=>110100=>001011
[3,6,7,4,1,2,5]=>[6,3,1,4,7,5,2]=>110011=>110011
[3,6,7,4,1,5,2]=>[6,3,1,4,7,2,5]=>110010=>010011
[3,6,7,4,2,1,5]=>[6,3,1,2,4,7,5]=>110001=>100011
[3,6,7,4,2,5,1]=>[6,3,2,4,7,1,5]=>110010=>010011
[3,6,7,4,5,1,2]=>[6,4,7,3,1,5,2]=>101101=>101101
[3,6,7,4,5,2,1]=>[6,4,7,3,1,2,5]=>101100=>001101
[3,6,7,5,1,2,4]=>[6,3,1,5,7,4,2]=>110011=>110011
[3,6,7,5,1,4,2]=>[6,3,1,5,7,2,4]=>110010=>010011
[3,6,7,5,2,1,4]=>[6,3,1,2,5,7,4]=>110001=>100011
[3,6,7,5,2,4,1]=>[6,3,2,5,7,1,4]=>110010=>010011
[3,6,7,5,4,1,2]=>[6,3,1,4,5,7,2]=>110001=>100011
[3,6,7,5,4,2,1]=>[6,3,1,2,4,5,7]=>110000=>000011
[3,7,1,2,4,5,6]=>[3,1,7,6,5,4,2]=>101111=>111101
[3,7,1,2,4,6,5]=>[3,1,7,5,6,4,2]=>101011=>110101
[3,7,1,2,5,4,6]=>[3,1,7,6,4,5,2]=>101101=>101101
[3,7,1,2,5,6,4]=>[3,1,7,5,4,6,2]=>101101=>101101
[3,7,1,2,6,4,5]=>[3,1,7,4,6,5,2]=>101011=>110101
[3,7,1,2,6,5,4]=>[3,1,7,4,5,6,2]=>101001=>100101
[3,7,1,4,2,5,6]=>[3,1,7,6,5,2,4]=>101110=>011101
[3,7,1,4,2,6,5]=>[3,1,7,5,6,2,4]=>101010=>010101
[3,7,1,4,5,2,6]=>[3,1,7,6,4,2,5]=>101110=>011101
[3,7,1,4,5,6,2]=>[3,1,7,5,4,2,6]=>101110=>011101
[3,7,1,4,6,2,5]=>[3,1,7,4,2,6,5]=>101101=>101101
[3,7,1,4,6,5,2]=>[3,1,7,4,2,5,6]=>101100=>001101
[3,7,1,5,2,4,6]=>[3,1,7,6,2,5,4]=>101101=>101101
[3,7,1,5,2,6,4]=>[3,1,7,2,5,4,6]=>101010=>010101
[3,7,1,5,4,2,6]=>[3,1,7,6,2,4,5]=>101100=>001101
[3,7,1,5,4,6,2]=>[3,1,7,4,5,2,6]=>101010=>010101
[3,7,1,5,6,2,4]=>[3,1,7,5,2,6,4]=>101101=>101101
[3,7,1,5,6,4,2]=>[3,1,7,5,2,4,6]=>101100=>001101
[3,7,1,6,2,4,5]=>[3,1,7,2,6,5,4]=>101011=>110101
[3,7,1,6,2,5,4]=>[3,1,7,2,6,4,5]=>101010=>010101
[3,7,1,6,4,2,5]=>[3,1,7,2,4,6,5]=>101001=>100101
[3,7,1,6,4,5,2]=>[3,1,7,4,6,2,5]=>101010=>010101
[3,7,1,6,5,2,4]=>[3,1,7,2,5,6,4]=>101001=>100101
[3,7,1,6,5,4,2]=>[3,1,7,2,4,5,6]=>101000=>000101
[3,7,2,1,4,5,6]=>[3,1,2,7,6,5,4]=>100111=>111001
[3,7,2,1,4,6,5]=>[3,1,2,7,5,6,4]=>100101=>101001
[3,7,2,1,5,4,6]=>[3,1,2,7,6,4,5]=>100110=>011001
[3,7,2,1,5,6,4]=>[3,1,2,7,5,4,6]=>100110=>011001
[3,7,2,1,6,4,5]=>[3,1,2,7,4,6,5]=>100101=>101001
[3,7,2,1,6,5,4]=>[3,1,2,7,4,5,6]=>100100=>001001
[3,7,2,4,1,5,6]=>[3,2,7,6,5,1,4]=>101110=>011101
[3,7,2,4,1,6,5]=>[3,2,7,5,6,1,4]=>101010=>010101
[3,7,2,4,5,1,6]=>[3,2,7,6,4,1,5]=>101110=>011101
[3,7,2,4,5,6,1]=>[3,2,7,5,4,1,6]=>101110=>011101
[3,7,2,4,6,1,5]=>[3,2,7,4,1,6,5]=>101101=>101101
[3,7,2,4,6,5,1]=>[3,2,7,4,1,5,6]=>101100=>001101
[3,7,2,5,1,4,6]=>[3,2,7,6,1,5,4]=>101101=>101101
[3,7,2,5,1,6,4]=>[3,2,7,1,5,4,6]=>101010=>010101
[3,7,2,5,4,1,6]=>[3,2,7,6,1,4,5]=>101100=>001101
[3,7,2,5,4,6,1]=>[3,2,7,4,5,1,6]=>101010=>010101
[3,7,2,5,6,1,4]=>[3,2,7,5,1,6,4]=>101101=>101101
[3,7,2,5,6,4,1]=>[3,2,7,5,1,4,6]=>101100=>001101
[3,7,2,6,1,4,5]=>[3,2,7,1,6,5,4]=>101011=>110101
[3,7,2,6,1,5,4]=>[3,2,7,1,6,4,5]=>101010=>010101
[3,7,2,6,4,1,5]=>[3,2,7,1,4,6,5]=>101001=>100101
[3,7,2,6,4,5,1]=>[3,2,7,4,6,1,5]=>101010=>010101
[3,7,2,6,5,1,4]=>[3,2,7,1,5,6,4]=>101001=>100101
[3,7,2,6,5,4,1]=>[3,2,7,1,4,5,6]=>101000=>000101
[3,7,4,1,2,5,6]=>[3,1,4,7,6,5,2]=>100111=>111001
[3,7,4,1,2,6,5]=>[3,1,4,7,5,6,2]=>100101=>101001
[3,7,4,1,5,2,6]=>[3,1,4,7,6,2,5]=>100110=>011001
[3,7,4,1,5,6,2]=>[3,1,4,7,5,2,6]=>100110=>011001
[3,7,4,1,6,2,5]=>[3,1,4,7,2,6,5]=>100101=>101001
[3,7,4,1,6,5,2]=>[3,1,4,7,2,5,6]=>100100=>001001
[3,7,4,2,1,5,6]=>[3,1,2,4,7,6,5]=>100011=>110001
[3,7,4,2,1,6,5]=>[3,1,2,4,7,5,6]=>100010=>010001
[3,7,4,2,5,1,6]=>[3,2,4,7,6,1,5]=>100110=>011001
[3,7,4,2,5,6,1]=>[3,2,4,7,5,1,6]=>100110=>011001
[3,7,4,2,6,1,5]=>[3,2,4,7,1,6,5]=>100101=>101001
[3,7,4,2,6,5,1]=>[3,2,4,7,1,5,6]=>100100=>001001
[3,7,4,5,1,2,6]=>[4,7,6,3,1,5,2]=>011101=>101110
[3,7,4,5,1,6,2]=>[4,7,3,1,5,2,6]=>011010=>010110
[3,7,4,5,2,1,6]=>[4,7,6,3,1,2,5]=>011100=>001110
[3,7,4,5,2,6,1]=>[4,7,3,2,5,1,6]=>011010=>010110
[3,7,4,5,6,1,2]=>[4,7,5,3,1,6,2]=>011101=>101110
[3,7,4,5,6,2,1]=>[4,7,5,3,1,2,6]=>011100=>001110
[3,7,4,6,1,2,5]=>[4,7,3,1,6,5,2]=>011011=>110110
[3,7,4,6,1,5,2]=>[4,7,3,1,6,2,5]=>011010=>010110
[3,7,4,6,2,1,5]=>[4,7,3,1,2,6,5]=>011001=>100110
[3,7,4,6,2,5,1]=>[4,7,3,2,6,1,5]=>011010=>010110
[3,7,4,6,5,1,2]=>[4,7,3,1,5,6,2]=>011001=>100110
[3,7,4,6,5,2,1]=>[4,7,3,1,2,5,6]=>011000=>000110
[3,7,5,1,2,4,6]=>[3,1,5,7,6,4,2]=>100111=>111001
[3,7,5,1,2,6,4]=>[3,1,5,7,4,6,2]=>100101=>101001
[3,7,5,1,4,2,6]=>[3,1,5,7,6,2,4]=>100110=>011001
[3,7,5,1,4,6,2]=>[3,1,5,7,4,2,6]=>100110=>011001
[3,7,5,1,6,2,4]=>[3,1,5,7,2,6,4]=>100101=>101001
[3,7,5,1,6,4,2]=>[3,1,5,7,2,4,6]=>100100=>001001
[3,7,5,2,1,4,6]=>[3,1,2,5,7,6,4]=>100011=>110001
[3,7,5,2,1,6,4]=>[3,1,2,5,7,4,6]=>100010=>010001
[3,7,5,2,4,1,6]=>[3,2,5,7,6,1,4]=>100110=>011001
[3,7,5,2,4,6,1]=>[3,2,5,7,4,1,6]=>100110=>011001
[3,7,5,2,6,1,4]=>[3,2,5,7,1,6,4]=>100101=>101001
[3,7,5,2,6,4,1]=>[3,2,5,7,1,4,6]=>100100=>001001
[3,7,5,4,1,2,6]=>[3,1,4,5,7,6,2]=>100011=>110001
[3,7,5,4,1,6,2]=>[3,1,4,5,7,2,6]=>100010=>010001
[3,7,5,4,2,1,6]=>[3,1,2,4,5,7,6]=>100001=>100001
[3,7,5,4,2,6,1]=>[3,2,4,5,7,1,6]=>100010=>010001
[3,7,5,4,6,1,2]=>[4,5,7,3,1,6,2]=>001101=>101100
[3,7,5,4,6,2,1]=>[4,5,7,3,1,2,6]=>001100=>001100
[3,7,5,6,1,2,4]=>[5,7,3,1,6,4,2]=>011011=>110110
[3,7,5,6,1,4,2]=>[5,7,3,1,6,2,4]=>011010=>010110
[3,7,5,6,2,1,4]=>[5,7,3,1,2,6,4]=>011001=>100110
[3,7,5,6,2,4,1]=>[5,7,3,2,6,1,4]=>011010=>010110
[3,7,5,6,4,1,2]=>[5,7,3,1,4,6,2]=>011001=>100110
[3,7,5,6,4,2,1]=>[5,7,3,1,2,4,6]=>011000=>000110
[3,7,6,1,2,4,5]=>[3,1,6,7,5,4,2]=>100111=>111001
[3,7,6,1,2,5,4]=>[3,1,6,7,4,5,2]=>100101=>101001
[3,7,6,1,4,2,5]=>[3,1,6,7,5,2,4]=>100110=>011001
[3,7,6,1,4,5,2]=>[3,1,6,7,4,2,5]=>100110=>011001
[3,7,6,1,5,2,4]=>[3,1,6,7,2,5,4]=>100101=>101001
[3,7,6,1,5,4,2]=>[3,1,6,7,2,4,5]=>100100=>001001
[3,7,6,2,1,4,5]=>[3,1,2,6,7,5,4]=>100011=>110001
[3,7,6,2,1,5,4]=>[3,1,2,6,7,4,5]=>100010=>010001
[3,7,6,2,4,1,5]=>[3,2,6,7,5,1,4]=>100110=>011001
[3,7,6,2,4,5,1]=>[3,2,6,7,4,1,5]=>100110=>011001
[3,7,6,2,5,1,4]=>[3,2,6,7,1,5,4]=>100101=>101001
[3,7,6,2,5,4,1]=>[3,2,6,7,1,4,5]=>100100=>001001
[3,7,6,4,1,2,5]=>[3,1,4,6,7,5,2]=>100011=>110001
[3,7,6,4,1,5,2]=>[3,1,4,6,7,2,5]=>100010=>010001
[3,7,6,4,2,1,5]=>[3,1,2,4,6,7,5]=>100001=>100001
[3,7,6,4,2,5,1]=>[3,2,4,6,7,1,5]=>100010=>010001
[3,7,6,4,5,1,2]=>[4,6,7,3,1,5,2]=>001101=>101100
[3,7,6,4,5,2,1]=>[4,6,7,3,1,2,5]=>001100=>001100
[3,7,6,5,1,2,4]=>[3,1,5,6,7,4,2]=>100011=>110001
[3,7,6,5,1,4,2]=>[3,1,5,6,7,2,4]=>100010=>010001
[3,7,6,5,2,1,4]=>[3,1,2,5,6,7,4]=>100001=>100001
[3,7,6,5,2,4,1]=>[3,2,5,6,7,1,4]=>100010=>010001
[3,7,6,5,4,1,2]=>[3,1,4,5,6,7,2]=>100001=>100001
[3,7,6,5,4,2,1]=>[3,1,2,4,5,6,7]=>100000=>000001
[4,1,2,3,5,6,7]=>[7,6,5,1,4,3,2]=>111011=>110111
[4,1,2,3,5,7,6]=>[6,7,5,1,4,3,2]=>011011=>110110
[4,1,2,3,6,5,7]=>[7,5,6,1,4,3,2]=>101011=>110101
[4,1,2,3,6,7,5]=>[6,5,7,1,4,3,2]=>101011=>110101
[4,1,2,3,7,5,6]=>[5,7,6,1,4,3,2]=>011011=>110110
[4,1,2,3,7,6,5]=>[5,6,7,1,4,3,2]=>001011=>110100
[4,1,2,5,3,6,7]=>[7,6,1,4,3,5,2]=>110101=>101011
[4,1,2,5,3,7,6]=>[6,7,1,4,3,5,2]=>010101=>101010
[4,1,2,5,6,3,7]=>[7,5,1,4,3,6,2]=>110101=>101011
[4,1,2,5,6,7,3]=>[6,5,1,4,3,7,2]=>110101=>101011
[4,1,2,5,7,3,6]=>[5,1,4,3,7,6,2]=>101011=>110101
[4,1,2,5,7,6,3]=>[5,1,4,3,6,7,2]=>101001=>100101
[4,1,2,6,3,5,7]=>[7,1,4,3,6,5,2]=>101011=>110101
[4,1,2,6,3,7,5]=>[1,4,3,6,5,7,2]=>010101=>101010
[4,1,2,6,5,3,7]=>[7,1,4,3,5,6,2]=>101001=>100101
[4,1,2,6,5,7,3]=>[5,6,1,4,3,7,2]=>010101=>101010
[4,1,2,6,7,3,5]=>[6,1,4,3,7,5,2]=>101011=>110101
[4,1,2,6,7,5,3]=>[6,1,4,3,5,7,2]=>101001=>100101
[4,1,2,7,3,5,6]=>[1,4,3,7,6,5,2]=>010111=>111010
[4,1,2,7,3,6,5]=>[1,4,3,7,5,6,2]=>010101=>101010
[4,1,2,7,5,3,6]=>[1,4,3,5,7,6,2]=>010011=>110010
[4,1,2,7,5,6,3]=>[5,7,1,4,3,6,2]=>010101=>101010
[4,1,2,7,6,3,5]=>[1,4,3,6,7,5,2]=>010011=>110010
[4,1,2,7,6,5,3]=>[1,4,3,5,6,7,2]=>010001=>100010
[4,1,3,2,5,6,7]=>[7,6,5,1,4,2,3]=>111010=>010111
[4,1,3,2,5,7,6]=>[6,7,5,1,4,2,3]=>011010=>010110
[4,1,3,2,6,5,7]=>[7,5,6,1,4,2,3]=>101010=>010101
[4,1,3,2,6,7,5]=>[6,5,7,1,4,2,3]=>101010=>010101
[4,1,3,2,7,5,6]=>[5,7,6,1,4,2,3]=>011010=>010110
[4,1,3,2,7,6,5]=>[5,6,7,1,4,2,3]=>001010=>010100
[4,1,3,5,2,6,7]=>[7,6,1,4,3,2,5]=>110110=>011011
[4,1,3,5,2,7,6]=>[6,7,1,4,3,2,5]=>010110=>011010
[4,1,3,5,6,2,7]=>[7,5,1,4,3,2,6]=>110110=>011011
[4,1,3,5,6,7,2]=>[6,5,1,4,3,2,7]=>110110=>011011
[4,1,3,5,7,2,6]=>[5,1,4,3,2,7,6]=>101101=>101101
[4,1,3,5,7,6,2]=>[5,1,4,3,2,6,7]=>101100=>001101
[4,1,3,6,2,5,7]=>[7,1,4,3,2,6,5]=>101101=>101101
[4,1,3,6,2,7,5]=>[1,4,3,2,6,5,7]=>011010=>010110
[4,1,3,6,5,2,7]=>[7,1,4,3,2,5,6]=>101100=>001101
[4,1,3,6,5,7,2]=>[5,6,1,4,3,2,7]=>010110=>011010
[4,1,3,6,7,2,5]=>[6,1,4,3,2,7,5]=>101101=>101101
[4,1,3,6,7,5,2]=>[6,1,4,3,2,5,7]=>101100=>001101
[4,1,3,7,2,5,6]=>[1,4,3,2,7,6,5]=>011011=>110110
[4,1,3,7,2,6,5]=>[1,4,3,2,7,5,6]=>011010=>010110
[4,1,3,7,5,2,6]=>[1,4,3,2,5,7,6]=>011001=>100110
[4,1,3,7,5,6,2]=>[5,7,1,4,3,2,6]=>010110=>011010
[4,1,3,7,6,2,5]=>[1,4,3,2,6,7,5]=>011001=>100110
[4,1,3,7,6,5,2]=>[1,4,3,2,5,6,7]=>011000=>000110
[4,1,5,2,3,6,7]=>[7,6,1,4,2,5,3]=>110101=>101011
[4,1,5,2,3,7,6]=>[6,7,1,4,2,5,3]=>010101=>101010
[4,1,5,2,6,3,7]=>[7,1,4,2,5,3,6]=>101010=>010101
[4,1,5,2,6,7,3]=>[6,1,4,2,5,3,7]=>101010=>010101
[4,1,5,2,7,3,6]=>[1,4,2,5,3,7,6]=>010101=>101010
[4,1,5,2,7,6,3]=>[1,4,2,5,3,6,7]=>010100=>001010
[4,1,5,3,2,6,7]=>[7,6,1,4,2,3,5]=>110100=>001011
[4,1,5,3,2,7,6]=>[6,7,1,4,2,3,5]=>010100=>001010
[4,1,5,3,6,2,7]=>[7,1,4,3,5,2,6]=>101010=>010101
[4,1,5,3,6,7,2]=>[6,1,4,3,5,2,7]=>101010=>010101
[4,1,5,3,7,2,6]=>[1,4,3,5,2,7,6]=>010101=>101010
[4,1,5,3,7,6,2]=>[1,4,3,5,2,6,7]=>010100=>001010
[4,1,5,6,2,3,7]=>[7,5,1,4,2,6,3]=>110101=>101011
[4,1,5,6,2,7,3]=>[5,1,4,2,6,3,7]=>101010=>010101
[4,1,5,6,3,2,7]=>[7,5,1,4,2,3,6]=>110100=>001011
[4,1,5,6,3,7,2]=>[5,1,4,3,6,2,7]=>101010=>010101
[4,1,5,6,7,2,3]=>[6,5,1,4,2,7,3]=>110101=>101011
[4,1,5,6,7,3,2]=>[6,5,1,4,2,3,7]=>110100=>001011
[4,1,5,7,2,3,6]=>[5,1,4,2,7,6,3]=>101011=>110101
[4,1,5,7,2,6,3]=>[5,1,4,2,7,3,6]=>101010=>010101
[4,1,5,7,3,2,6]=>[5,1,4,2,3,7,6]=>101001=>100101
[4,1,5,7,3,6,2]=>[5,1,4,3,7,2,6]=>101010=>010101
[4,1,5,7,6,2,3]=>[5,1,4,2,6,7,3]=>101001=>100101
[4,1,5,7,6,3,2]=>[5,1,4,2,3,6,7]=>101000=>000101
[4,1,6,2,3,5,7]=>[7,1,4,2,6,5,3]=>101011=>110101
[4,1,6,2,3,7,5]=>[1,4,2,6,5,7,3]=>010101=>101010
[4,1,6,2,5,3,7]=>[7,1,4,2,6,3,5]=>101010=>010101
[4,1,6,2,5,7,3]=>[1,4,2,6,5,3,7]=>010110=>011010
[4,1,6,2,7,3,5]=>[1,4,2,6,3,7,5]=>010101=>101010
[4,1,6,2,7,5,3]=>[1,4,2,6,3,5,7]=>010100=>001010
[4,1,6,3,2,5,7]=>[7,1,4,2,3,6,5]=>101001=>100101
[4,1,6,3,2,7,5]=>[1,4,2,3,6,5,7]=>010010=>010010
[4,1,6,3,5,2,7]=>[7,1,4,3,6,2,5]=>101010=>010101
[4,1,6,3,5,7,2]=>[1,4,3,6,5,2,7]=>010110=>011010
[4,1,6,3,7,2,5]=>[1,4,3,6,2,7,5]=>010101=>101010
[4,1,6,3,7,5,2]=>[1,4,3,6,2,5,7]=>010100=>001010
[4,1,6,5,2,3,7]=>[7,1,4,2,5,6,3]=>101001=>100101
[4,1,6,5,2,7,3]=>[1,4,2,5,6,3,7]=>010010=>010010
[4,1,6,5,3,2,7]=>[7,1,4,2,3,5,6]=>101000=>000101
[4,1,6,5,3,7,2]=>[1,4,3,5,6,2,7]=>010010=>010010
[4,1,6,5,7,2,3]=>[5,6,1,4,2,7,3]=>010101=>101010
[4,1,6,5,7,3,2]=>[5,6,1,4,2,3,7]=>010100=>001010
[4,1,6,7,2,3,5]=>[6,1,4,2,7,5,3]=>101011=>110101
[4,1,6,7,2,5,3]=>[6,1,4,2,7,3,5]=>101010=>010101
[4,1,6,7,3,2,5]=>[6,1,4,2,3,7,5]=>101001=>100101
[4,1,6,7,3,5,2]=>[6,1,4,3,7,2,5]=>101010=>010101
[4,1,6,7,5,2,3]=>[6,1,4,2,5,7,3]=>101001=>100101
[4,1,6,7,5,3,2]=>[6,1,4,2,3,5,7]=>101000=>000101
[4,1,7,2,3,5,6]=>[1,4,2,7,6,5,3]=>010111=>111010
[4,1,7,2,3,6,5]=>[1,4,2,7,5,6,3]=>010101=>101010
[4,1,7,2,5,3,6]=>[1,4,2,7,6,3,5]=>010110=>011010
[4,1,7,2,5,6,3]=>[1,4,2,7,5,3,6]=>010110=>011010
[4,1,7,2,6,3,5]=>[1,4,2,7,3,6,5]=>010101=>101010
[4,1,7,2,6,5,3]=>[1,4,2,7,3,5,6]=>010100=>001010
[4,1,7,3,2,5,6]=>[1,4,2,3,7,6,5]=>010011=>110010
[4,1,7,3,2,6,5]=>[1,4,2,3,7,5,6]=>010010=>010010
[4,1,7,3,5,2,6]=>[1,4,3,7,6,2,5]=>010110=>011010
[4,1,7,3,5,6,2]=>[1,4,3,7,5,2,6]=>010110=>011010
[4,1,7,3,6,2,5]=>[1,4,3,7,2,6,5]=>010101=>101010
[4,1,7,3,6,5,2]=>[1,4,3,7,2,5,6]=>010100=>001010
[4,1,7,5,2,3,6]=>[1,4,2,5,7,6,3]=>010011=>110010
[4,1,7,5,2,6,3]=>[1,4,2,5,7,3,6]=>010010=>010010
[4,1,7,5,3,2,6]=>[1,4,2,3,5,7,6]=>010001=>100010
[4,1,7,5,3,6,2]=>[1,4,3,5,7,2,6]=>010010=>010010
[4,1,7,5,6,2,3]=>[5,7,1,4,2,6,3]=>010101=>101010
[4,1,7,5,6,3,2]=>[5,7,1,4,2,3,6]=>010100=>001010
[4,1,7,6,2,3,5]=>[1,4,2,6,7,5,3]=>010011=>110010
[4,1,7,6,2,5,3]=>[1,4,2,6,7,3,5]=>010010=>010010
[4,1,7,6,3,2,5]=>[1,4,2,3,6,7,5]=>010001=>100010
[4,1,7,6,3,5,2]=>[1,4,3,6,7,2,5]=>010010=>010010
[4,1,7,6,5,2,3]=>[1,4,2,5,6,7,3]=>010001=>100010
[4,1,7,6,5,3,2]=>[1,4,2,3,5,6,7]=>010000=>000010
[4,2,1,3,5,6,7]=>[7,6,5,1,2,4,3]=>111001=>100111
[4,2,1,3,5,7,6]=>[6,7,5,1,2,4,3]=>011001=>100110
[4,2,1,3,6,5,7]=>[7,5,6,1,2,4,3]=>101001=>100101
[4,2,1,3,6,7,5]=>[6,5,7,1,2,4,3]=>101001=>100101
[4,2,1,3,7,5,6]=>[5,7,6,1,2,4,3]=>011001=>100110
[4,2,1,3,7,6,5]=>[5,6,7,1,2,4,3]=>001001=>100100
[4,2,1,5,3,6,7]=>[7,6,1,2,4,3,5]=>110010=>010011
[4,2,1,5,3,7,6]=>[6,7,1,2,4,3,5]=>010010=>010010
[4,2,1,5,6,3,7]=>[7,5,1,2,4,3,6]=>110010=>010011
[4,2,1,5,6,7,3]=>[6,5,1,2,4,3,7]=>110010=>010011
[4,2,1,5,7,3,6]=>[5,1,2,4,3,7,6]=>100101=>101001
[4,2,1,5,7,6,3]=>[5,1,2,4,3,6,7]=>100100=>001001
[4,2,1,6,3,5,7]=>[7,1,2,4,3,6,5]=>100101=>101001
[4,2,1,6,3,7,5]=>[1,2,4,3,6,5,7]=>001010=>010100
[4,2,1,6,5,3,7]=>[7,1,2,4,3,5,6]=>100100=>001001
[4,2,1,6,5,7,3]=>[5,6,1,2,4,3,7]=>010010=>010010
[4,2,1,6,7,3,5]=>[6,1,2,4,3,7,5]=>100101=>101001
[4,2,1,6,7,5,3]=>[6,1,2,4,3,5,7]=>100100=>001001
[4,2,1,7,3,5,6]=>[1,2,4,3,7,6,5]=>001011=>110100
[4,2,1,7,3,6,5]=>[1,2,4,3,7,5,6]=>001010=>010100
[4,2,1,7,5,3,6]=>[1,2,4,3,5,7,6]=>001001=>100100
[4,2,1,7,5,6,3]=>[5,7,1,2,4,3,6]=>010010=>010010
[4,2,1,7,6,3,5]=>[1,2,4,3,6,7,5]=>001001=>100100
[4,2,1,7,6,5,3]=>[1,2,4,3,5,6,7]=>001000=>000100
[4,2,3,1,5,6,7]=>[7,6,5,2,4,1,3]=>111010=>010111
[4,2,3,1,5,7,6]=>[6,7,5,2,4,1,3]=>011010=>010110
[4,2,3,1,6,5,7]=>[7,5,6,2,4,1,3]=>101010=>010101
[4,2,3,1,6,7,5]=>[6,5,7,2,4,1,3]=>101010=>010101
[4,2,3,1,7,5,6]=>[5,7,6,2,4,1,3]=>011010=>010110
[4,2,3,1,7,6,5]=>[5,6,7,2,4,1,3]=>001010=>010100
[4,2,3,5,1,6,7]=>[7,6,2,4,3,1,5]=>110110=>011011
[4,2,3,5,1,7,6]=>[6,7,2,4,3,1,5]=>010110=>011010
[4,2,3,5,6,1,7]=>[7,5,2,4,3,1,6]=>110110=>011011
[4,2,3,5,6,7,1]=>[6,5,2,4,3,1,7]=>110110=>011011
[4,2,3,5,7,1,6]=>[5,2,4,3,1,7,6]=>101101=>101101
[4,2,3,5,7,6,1]=>[5,2,4,3,1,6,7]=>101100=>001101
[4,2,3,6,1,5,7]=>[7,2,4,3,1,6,5]=>101101=>101101
[4,2,3,6,1,7,5]=>[2,4,3,1,6,5,7]=>011010=>010110
[4,2,3,6,5,1,7]=>[7,2,4,3,1,5,6]=>101100=>001101
[4,2,3,6,5,7,1]=>[5,6,2,4,3,1,7]=>010110=>011010
[4,2,3,6,7,1,5]=>[6,2,4,3,1,7,5]=>101101=>101101
[4,2,3,6,7,5,1]=>[6,2,4,3,1,5,7]=>101100=>001101
[4,2,3,7,1,5,6]=>[2,4,3,1,7,6,5]=>011011=>110110
[4,2,3,7,1,6,5]=>[2,4,3,1,7,5,6]=>011010=>010110
[4,2,3,7,5,1,6]=>[2,4,3,1,5,7,6]=>011001=>100110
[4,2,3,7,5,6,1]=>[5,7,2,4,3,1,6]=>010110=>011010
[4,2,3,7,6,1,5]=>[2,4,3,1,6,7,5]=>011001=>100110
[4,2,3,7,6,5,1]=>[2,4,3,1,5,6,7]=>011000=>000110
[4,2,5,1,3,6,7]=>[7,6,2,4,1,5,3]=>110101=>101011
[4,2,5,1,3,7,6]=>[6,7,2,4,1,5,3]=>010101=>101010
[4,2,5,1,6,3,7]=>[7,2,4,1,5,3,6]=>101010=>010101
[4,2,5,1,6,7,3]=>[6,2,4,1,5,3,7]=>101010=>010101
[4,2,5,1,7,3,6]=>[2,4,1,5,3,7,6]=>010101=>101010
[4,2,5,1,7,6,3]=>[2,4,1,5,3,6,7]=>010100=>001010
[4,2,5,3,1,6,7]=>[7,6,2,4,1,3,5]=>110100=>001011
[4,2,5,3,1,7,6]=>[6,7,2,4,1,3,5]=>010100=>001010
[4,2,5,3,6,1,7]=>[7,2,4,3,5,1,6]=>101010=>010101
[4,2,5,3,6,7,1]=>[6,2,4,3,5,1,7]=>101010=>010101
[4,2,5,3,7,1,6]=>[2,4,3,5,1,7,6]=>010101=>101010
[4,2,5,3,7,6,1]=>[2,4,3,5,1,6,7]=>010100=>001010
[4,2,5,6,1,3,7]=>[7,5,2,4,1,6,3]=>110101=>101011
[4,2,5,6,1,7,3]=>[5,2,4,1,6,3,7]=>101010=>010101
[4,2,5,6,3,1,7]=>[7,5,2,4,1,3,6]=>110100=>001011
[4,2,5,6,3,7,1]=>[5,2,4,3,6,1,7]=>101010=>010101
[4,2,5,6,7,1,3]=>[6,5,2,4,1,7,3]=>110101=>101011
[4,2,5,6,7,3,1]=>[6,5,2,4,1,3,7]=>110100=>001011
[4,2,5,7,1,3,6]=>[5,2,4,1,7,6,3]=>101011=>110101
[4,2,5,7,1,6,3]=>[5,2,4,1,7,3,6]=>101010=>010101
[4,2,5,7,3,1,6]=>[5,2,4,1,3,7,6]=>101001=>100101
[4,2,5,7,3,6,1]=>[5,2,4,3,7,1,6]=>101010=>010101
[4,2,5,7,6,1,3]=>[5,2,4,1,6,7,3]=>101001=>100101
[4,2,5,7,6,3,1]=>[5,2,4,1,3,6,7]=>101000=>000101
[4,2,6,1,3,5,7]=>[7,2,4,1,6,5,3]=>101011=>110101
[4,2,6,1,3,7,5]=>[2,4,1,6,5,7,3]=>010101=>101010
[4,2,6,1,5,3,7]=>[7,2,4,1,6,3,5]=>101010=>010101
[4,2,6,1,5,7,3]=>[2,4,1,6,5,3,7]=>010110=>011010
[4,2,6,1,7,3,5]=>[2,4,1,6,3,7,5]=>010101=>101010
[4,2,6,1,7,5,3]=>[2,4,1,6,3,5,7]=>010100=>001010
[4,2,6,3,1,5,7]=>[7,2,4,1,3,6,5]=>101001=>100101
[4,2,6,3,1,7,5]=>[2,4,1,3,6,5,7]=>010010=>010010
[4,2,6,3,5,1,7]=>[7,2,4,3,6,1,5]=>101010=>010101
[4,2,6,3,5,7,1]=>[2,4,3,6,5,1,7]=>010110=>011010
[4,2,6,3,7,1,5]=>[2,4,3,6,1,7,5]=>010101=>101010
[4,2,6,3,7,5,1]=>[2,4,3,6,1,5,7]=>010100=>001010
[4,2,6,5,1,3,7]=>[7,2,4,1,5,6,3]=>101001=>100101
[4,2,6,5,1,7,3]=>[2,4,1,5,6,3,7]=>010010=>010010
[4,2,6,5,3,1,7]=>[7,2,4,1,3,5,6]=>101000=>000101
[4,2,6,5,3,7,1]=>[2,4,3,5,6,1,7]=>010010=>010010
[4,2,6,5,7,1,3]=>[5,6,2,4,1,7,3]=>010101=>101010
[4,2,6,5,7,3,1]=>[5,6,2,4,1,3,7]=>010100=>001010
[4,2,6,7,1,3,5]=>[6,2,4,1,7,5,3]=>101011=>110101
[4,2,6,7,1,5,3]=>[6,2,4,1,7,3,5]=>101010=>010101
[4,2,6,7,3,1,5]=>[6,2,4,1,3,7,5]=>101001=>100101
[4,2,6,7,3,5,1]=>[6,2,4,3,7,1,5]=>101010=>010101
[4,2,6,7,5,1,3]=>[6,2,4,1,5,7,3]=>101001=>100101
[4,2,6,7,5,3,1]=>[6,2,4,1,3,5,7]=>101000=>000101
[4,2,7,1,3,5,6]=>[2,4,1,7,6,5,3]=>010111=>111010
[4,2,7,1,3,6,5]=>[2,4,1,7,5,6,3]=>010101=>101010
[4,2,7,1,5,3,6]=>[2,4,1,7,6,3,5]=>010110=>011010
[4,2,7,1,5,6,3]=>[2,4,1,7,5,3,6]=>010110=>011010
[4,2,7,1,6,3,5]=>[2,4,1,7,3,6,5]=>010101=>101010
[4,2,7,1,6,5,3]=>[2,4,1,7,3,5,6]=>010100=>001010
[4,2,7,3,1,5,6]=>[2,4,1,3,7,6,5]=>010011=>110010
[4,2,7,3,1,6,5]=>[2,4,1,3,7,5,6]=>010010=>010010
[4,2,7,3,5,1,6]=>[2,4,3,7,6,1,5]=>010110=>011010
[4,2,7,3,5,6,1]=>[2,4,3,7,5,1,6]=>010110=>011010
[4,2,7,3,6,1,5]=>[2,4,3,7,1,6,5]=>010101=>101010
[4,2,7,3,6,5,1]=>[2,4,3,7,1,5,6]=>010100=>001010
[4,2,7,5,1,3,6]=>[2,4,1,5,7,6,3]=>010011=>110010
[4,2,7,5,1,6,3]=>[2,4,1,5,7,3,6]=>010010=>010010
[4,2,7,5,3,1,6]=>[2,4,1,3,5,7,6]=>010001=>100010
[4,2,7,5,3,6,1]=>[2,4,3,5,7,1,6]=>010010=>010010
[4,2,7,5,6,1,3]=>[5,7,2,4,1,6,3]=>010101=>101010
[4,2,7,5,6,3,1]=>[5,7,2,4,1,3,6]=>010100=>001010
[4,2,7,6,1,3,5]=>[2,4,1,6,7,5,3]=>010011=>110010
[4,2,7,6,1,5,3]=>[2,4,1,6,7,3,5]=>010010=>010010
[4,2,7,6,3,1,5]=>[2,4,1,3,6,7,5]=>010001=>100010
[4,2,7,6,3,5,1]=>[2,4,3,6,7,1,5]=>010010=>010010
[4,2,7,6,5,1,3]=>[2,4,1,5,6,7,3]=>010001=>100010
[4,2,7,6,5,3,1]=>[2,4,1,3,5,6,7]=>010000=>000010
[4,3,1,2,5,6,7]=>[7,6,5,1,3,4,2]=>111001=>100111
[4,3,1,2,5,7,6]=>[6,7,5,1,3,4,2]=>011001=>100110
[4,3,1,2,6,5,7]=>[7,5,6,1,3,4,2]=>101001=>100101
[4,3,1,2,6,7,5]=>[6,5,7,1,3,4,2]=>101001=>100101
[4,3,1,2,7,5,6]=>[5,7,6,1,3,4,2]=>011001=>100110
[4,3,1,2,7,6,5]=>[5,6,7,1,3,4,2]=>001001=>100100
[4,3,1,5,2,6,7]=>[7,6,1,3,4,2,5]=>110010=>010011
[4,3,1,5,2,7,6]=>[6,7,1,3,4,2,5]=>010010=>010010
[4,3,1,5,6,2,7]=>[7,5,1,3,4,2,6]=>110010=>010011
[4,3,1,5,6,7,2]=>[6,5,1,3,4,2,7]=>110010=>010011
[4,3,1,5,7,2,6]=>[5,1,3,4,2,7,6]=>100101=>101001
[4,3,1,5,7,6,2]=>[5,1,3,4,2,6,7]=>100100=>001001
[4,3,1,6,2,5,7]=>[7,1,3,4,2,6,5]=>100101=>101001
[4,3,1,6,2,7,5]=>[1,3,4,2,6,5,7]=>001010=>010100
[4,3,1,6,5,2,7]=>[7,1,3,4,2,5,6]=>100100=>001001
[4,3,1,6,5,7,2]=>[5,6,1,3,4,2,7]=>010010=>010010
[4,3,1,6,7,2,5]=>[6,1,3,4,2,7,5]=>100101=>101001
[4,3,1,6,7,5,2]=>[6,1,3,4,2,5,7]=>100100=>001001
[4,3,1,7,2,5,6]=>[1,3,4,2,7,6,5]=>001011=>110100
[4,3,1,7,2,6,5]=>[1,3,4,2,7,5,6]=>001010=>010100
[4,3,1,7,5,2,6]=>[1,3,4,2,5,7,6]=>001001=>100100
[4,3,1,7,5,6,2]=>[5,7,1,3,4,2,6]=>010010=>010010
[4,3,1,7,6,2,5]=>[1,3,4,2,6,7,5]=>001001=>100100
[4,3,1,7,6,5,2]=>[1,3,4,2,5,6,7]=>001000=>000100
[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>111000=>000111
[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>011000=>000110
[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>101000=>000101
[4,3,2,1,6,7,5]=>[6,5,7,1,2,3,4]=>101000=>000101
[4,3,2,1,7,5,6]=>[5,7,6,1,2,3,4]=>011000=>000110
[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>001000=>000100
[4,3,2,5,1,6,7]=>[7,6,2,3,4,1,5]=>110010=>010011
[4,3,2,5,1,7,6]=>[6,7,2,3,4,1,5]=>010010=>010010
[4,3,2,5,6,1,7]=>[7,5,2,3,4,1,6]=>110010=>010011
[4,3,2,5,6,7,1]=>[6,5,2,3,4,1,7]=>110010=>010011
[4,3,2,5,7,1,6]=>[5,2,3,4,1,7,6]=>100101=>101001
[4,3,2,5,7,6,1]=>[5,2,3,4,1,6,7]=>100100=>001001
[4,3,2,6,1,5,7]=>[7,2,3,4,1,6,5]=>100101=>101001
[4,3,2,6,1,7,5]=>[2,3,4,1,6,5,7]=>001010=>010100
[4,3,2,6,5,1,7]=>[7,2,3,4,1,5,6]=>100100=>001001
[4,3,2,6,5,7,1]=>[5,6,2,3,4,1,7]=>010010=>010010
[4,3,2,6,7,1,5]=>[6,2,3,4,1,7,5]=>100101=>101001
[4,3,2,6,7,5,1]=>[6,2,3,4,1,5,7]=>100100=>001001
[4,3,2,7,1,5,6]=>[2,3,4,1,7,6,5]=>001011=>110100
[4,3,2,7,1,6,5]=>[2,3,4,1,7,5,6]=>001010=>010100
[4,3,2,7,5,1,6]=>[2,3,4,1,5,7,6]=>001001=>100100
[4,3,2,7,5,6,1]=>[5,7,2,3,4,1,6]=>010010=>010010
[4,3,2,7,6,1,5]=>[2,3,4,1,6,7,5]=>001001=>100100
[4,3,2,7,6,5,1]=>[2,3,4,1,5,6,7]=>001000=>000100
[4,3,5,1,2,6,7]=>[7,6,3,4,1,5,2]=>110101=>101011
[4,3,5,1,2,7,6]=>[6,7,3,4,1,5,2]=>010101=>101010
[4,3,5,1,6,2,7]=>[7,3,4,1,5,2,6]=>101010=>010101
[4,3,5,1,6,7,2]=>[6,3,4,1,5,2,7]=>101010=>010101
[4,3,5,1,7,2,6]=>[3,4,1,5,2,7,6]=>010101=>101010
[4,3,5,1,7,6,2]=>[3,4,1,5,2,6,7]=>010100=>001010
[4,3,5,2,1,6,7]=>[7,6,3,4,1,2,5]=>110100=>001011
[4,3,5,2,1,7,6]=>[6,7,3,4,1,2,5]=>010100=>001010
[4,3,5,2,6,1,7]=>[7,3,4,2,5,1,6]=>101010=>010101
[4,3,5,2,6,7,1]=>[6,3,4,2,5,1,7]=>101010=>010101
[4,3,5,2,7,1,6]=>[3,4,2,5,1,7,6]=>010101=>101010
[4,3,5,2,7,6,1]=>[3,4,2,5,1,6,7]=>010100=>001010
[4,3,5,6,1,2,7]=>[7,5,3,4,1,6,2]=>110101=>101011
[4,3,5,6,1,7,2]=>[5,3,4,1,6,2,7]=>101010=>010101
[4,3,5,6,2,1,7]=>[7,5,3,4,1,2,6]=>110100=>001011
[4,3,5,6,2,7,1]=>[5,3,4,2,6,1,7]=>101010=>010101
[4,3,5,6,7,1,2]=>[6,5,3,4,1,7,2]=>110101=>101011
[4,3,5,6,7,2,1]=>[6,5,3,4,1,2,7]=>110100=>001011
[4,3,5,7,1,2,6]=>[5,3,4,1,7,6,2]=>101011=>110101
[4,3,5,7,1,6,2]=>[5,3,4,1,7,2,6]=>101010=>010101
[4,3,5,7,2,1,6]=>[5,3,4,1,2,7,6]=>101001=>100101
[4,3,5,7,2,6,1]=>[5,3,4,2,7,1,6]=>101010=>010101
[4,3,5,7,6,1,2]=>[5,3,4,1,6,7,2]=>101001=>100101
[4,3,5,7,6,2,1]=>[5,3,4,1,2,6,7]=>101000=>000101
[4,3,6,1,2,5,7]=>[7,3,4,1,6,5,2]=>101011=>110101
[4,3,6,1,2,7,5]=>[3,4,1,6,5,7,2]=>010101=>101010
[4,3,6,1,5,2,7]=>[7,3,4,1,6,2,5]=>101010=>010101
[4,3,6,1,5,7,2]=>[3,4,1,6,5,2,7]=>010110=>011010
[4,3,6,1,7,2,5]=>[3,4,1,6,2,7,5]=>010101=>101010
[4,3,6,1,7,5,2]=>[3,4,1,6,2,5,7]=>010100=>001010
[4,3,6,2,1,5,7]=>[7,3,4,1,2,6,5]=>101001=>100101
[4,3,6,2,1,7,5]=>[3,4,1,2,6,5,7]=>010010=>010010
[4,3,6,2,5,1,7]=>[7,3,4,2,6,1,5]=>101010=>010101
[4,3,6,2,5,7,1]=>[3,4,2,6,5,1,7]=>010110=>011010
[4,3,6,2,7,1,5]=>[3,4,2,6,1,7,5]=>010101=>101010
[4,3,6,2,7,5,1]=>[3,4,2,6,1,5,7]=>010100=>001010
[4,3,6,5,1,2,7]=>[7,3,4,1,5,6,2]=>101001=>100101
[4,3,6,5,1,7,2]=>[3,4,1,5,6,2,7]=>010010=>010010
[4,3,6,5,2,1,7]=>[7,3,4,1,2,5,6]=>101000=>000101
[4,3,6,5,2,7,1]=>[3,4,2,5,6,1,7]=>010010=>010010
[4,3,6,5,7,1,2]=>[5,6,3,4,1,7,2]=>010101=>101010
[4,3,6,5,7,2,1]=>[5,6,3,4,1,2,7]=>010100=>001010
[4,3,6,7,1,2,5]=>[6,3,4,1,7,5,2]=>101011=>110101
[4,3,6,7,1,5,2]=>[6,3,4,1,7,2,5]=>101010=>010101
[4,3,6,7,2,1,5]=>[6,3,4,1,2,7,5]=>101001=>100101
[4,3,6,7,2,5,1]=>[6,3,4,2,7,1,5]=>101010=>010101
[4,3,6,7,5,1,2]=>[6,3,4,1,5,7,2]=>101001=>100101
[4,3,6,7,5,2,1]=>[6,3,4,1,2,5,7]=>101000=>000101
[4,3,7,1,2,5,6]=>[3,4,1,7,6,5,2]=>010111=>111010
[4,3,7,1,2,6,5]=>[3,4,1,7,5,6,2]=>010101=>101010
[4,3,7,1,5,2,6]=>[3,4,1,7,6,2,5]=>010110=>011010
[4,3,7,1,5,6,2]=>[3,4,1,7,5,2,6]=>010110=>011010
[4,3,7,1,6,2,5]=>[3,4,1,7,2,6,5]=>010101=>101010
[4,3,7,1,6,5,2]=>[3,4,1,7,2,5,6]=>010100=>001010
[4,3,7,2,1,5,6]=>[3,4,1,2,7,6,5]=>010011=>110010
[4,3,7,2,1,6,5]=>[3,4,1,2,7,5,6]=>010010=>010010
[4,3,7,2,5,1,6]=>[3,4,2,7,6,1,5]=>010110=>011010
[4,3,7,2,5,6,1]=>[3,4,2,7,5,1,6]=>010110=>011010
[4,3,7,2,6,1,5]=>[3,4,2,7,1,6,5]=>010101=>101010
[4,3,7,2,6,5,1]=>[3,4,2,7,1,5,6]=>010100=>001010
[4,3,7,5,1,2,6]=>[3,4,1,5,7,6,2]=>010011=>110010
[4,3,7,5,1,6,2]=>[3,4,1,5,7,2,6]=>010010=>010010
[4,3,7,5,2,1,6]=>[3,4,1,2,5,7,6]=>010001=>100010
[4,3,7,5,2,6,1]=>[3,4,2,5,7,1,6]=>010010=>010010
[4,3,7,5,6,1,2]=>[5,7,3,4,1,6,2]=>010101=>101010
[4,3,7,5,6,2,1]=>[5,7,3,4,1,2,6]=>010100=>001010
[4,3,7,6,1,2,5]=>[3,4,1,6,7,5,2]=>010011=>110010
[4,3,7,6,1,5,2]=>[3,4,1,6,7,2,5]=>010010=>010010
[4,3,7,6,2,1,5]=>[3,4,1,2,6,7,5]=>010001=>100010
[4,3,7,6,2,5,1]=>[3,4,2,6,7,1,5]=>010010=>010010
[4,3,7,6,5,1,2]=>[3,4,1,5,6,7,2]=>010001=>100010
[4,3,7,6,5,2,1]=>[3,4,1,2,5,6,7]=>010000=>000010
[4,5,1,2,3,6,7]=>[7,6,4,1,5,3,2]=>111011=>110111
[4,5,1,2,3,7,6]=>[6,7,4,1,5,3,2]=>011011=>110110
[4,5,1,2,6,3,7]=>[7,4,1,5,3,6,2]=>110101=>101011
[4,5,1,2,6,7,3]=>[6,4,1,5,3,7,2]=>110101=>101011
[4,5,1,2,7,3,6]=>[4,1,5,3,7,6,2]=>101011=>110101
[4,5,1,2,7,6,3]=>[4,1,5,3,6,7,2]=>101001=>100101
[4,5,1,3,2,6,7]=>[7,6,4,1,5,2,3]=>111010=>010111
[4,5,1,3,2,7,6]=>[6,7,4,1,5,2,3]=>011010=>010110
[4,5,1,3,6,2,7]=>[7,4,1,5,3,2,6]=>110110=>011011
[4,5,1,3,6,7,2]=>[6,4,1,5,3,2,7]=>110110=>011011
[4,5,1,3,7,2,6]=>[4,1,5,3,2,7,6]=>101101=>101101
[4,5,1,3,7,6,2]=>[4,1,5,3,2,6,7]=>101100=>001101
[4,5,1,6,2,3,7]=>[7,4,1,5,2,6,3]=>110101=>101011
[4,5,1,6,2,7,3]=>[4,1,5,2,6,3,7]=>101010=>010101
[4,5,1,6,3,2,7]=>[7,4,1,5,2,3,6]=>110100=>001011
[4,5,1,6,3,7,2]=>[4,1,5,3,6,2,7]=>101010=>010101
[4,5,1,6,7,2,3]=>[6,4,1,5,2,7,3]=>110101=>101011
[4,5,1,6,7,3,2]=>[6,4,1,5,2,3,7]=>110100=>001011
[4,5,1,7,2,3,6]=>[4,1,5,2,7,6,3]=>101011=>110101
[4,5,1,7,2,6,3]=>[4,1,5,2,7,3,6]=>101010=>010101
[4,5,1,7,3,2,6]=>[4,1,5,2,3,7,6]=>101001=>100101
[4,5,1,7,3,6,2]=>[4,1,5,3,7,2,6]=>101010=>010101
[4,5,1,7,6,2,3]=>[4,1,5,2,6,7,3]=>101001=>100101
[4,5,1,7,6,3,2]=>[4,1,5,2,3,6,7]=>101000=>000101
[4,5,2,1,3,6,7]=>[7,6,4,1,2,5,3]=>111001=>100111
[4,5,2,1,3,7,6]=>[6,7,4,1,2,5,3]=>011001=>100110
[4,5,2,1,6,3,7]=>[7,4,1,2,5,3,6]=>110010=>010011
[4,5,2,1,6,7,3]=>[6,4,1,2,5,3,7]=>110010=>010011
[4,5,2,1,7,3,6]=>[4,1,2,5,3,7,6]=>100101=>101001
[4,5,2,1,7,6,3]=>[4,1,2,5,3,6,7]=>100100=>001001
[4,5,2,3,1,6,7]=>[7,6,4,2,5,1,3]=>111010=>010111
[4,5,2,3,1,7,6]=>[6,7,4,2,5,1,3]=>011010=>010110
[4,5,2,3,6,1,7]=>[7,4,2,5,3,1,6]=>110110=>011011
[4,5,2,3,6,7,1]=>[6,4,2,5,3,1,7]=>110110=>011011
[4,5,2,3,7,1,6]=>[4,2,5,3,1,7,6]=>101101=>101101
[4,5,2,3,7,6,1]=>[4,2,5,3,1,6,7]=>101100=>001101
[4,5,2,6,1,3,7]=>[7,4,2,5,1,6,3]=>110101=>101011
[4,5,2,6,1,7,3]=>[4,2,5,1,6,3,7]=>101010=>010101
[4,5,2,6,3,1,7]=>[7,4,2,5,1,3,6]=>110100=>001011
[4,5,2,6,3,7,1]=>[4,2,5,3,6,1,7]=>101010=>010101
[4,5,2,6,7,1,3]=>[6,4,2,5,1,7,3]=>110101=>101011
[4,5,2,6,7,3,1]=>[6,4,2,5,1,3,7]=>110100=>001011
[4,5,2,7,1,3,6]=>[4,2,5,1,7,6,3]=>101011=>110101
[4,5,2,7,1,6,3]=>[4,2,5,1,7,3,6]=>101010=>010101
[4,5,2,7,3,1,6]=>[4,2,5,1,3,7,6]=>101001=>100101
[4,5,2,7,3,6,1]=>[4,2,5,3,7,1,6]=>101010=>010101
[4,5,2,7,6,1,3]=>[4,2,5,1,6,7,3]=>101001=>100101
[4,5,2,7,6,3,1]=>[4,2,5,1,3,6,7]=>101000=>000101
[4,5,3,1,2,6,7]=>[7,6,4,1,3,5,2]=>111001=>100111
[4,5,3,1,2,7,6]=>[6,7,4,1,3,5,2]=>011001=>100110
[4,5,3,1,6,2,7]=>[7,4,1,3,5,2,6]=>110010=>010011
[4,5,3,1,6,7,2]=>[6,4,1,3,5,2,7]=>110010=>010011
[4,5,3,1,7,2,6]=>[4,1,3,5,2,7,6]=>100101=>101001
[4,5,3,1,7,6,2]=>[4,1,3,5,2,6,7]=>100100=>001001
[4,5,3,2,1,6,7]=>[7,6,4,1,2,3,5]=>111000=>000111
[4,5,3,2,1,7,6]=>[6,7,4,1,2,3,5]=>011000=>000110
[4,5,3,2,6,1,7]=>[7,4,2,3,5,1,6]=>110010=>010011
[4,5,3,2,6,7,1]=>[6,4,2,3,5,1,7]=>110010=>010011
[4,5,3,2,7,1,6]=>[4,2,3,5,1,7,6]=>100101=>101001
[4,5,3,2,7,6,1]=>[4,2,3,5,1,6,7]=>100100=>001001
[4,5,3,6,1,2,7]=>[7,4,3,5,1,6,2]=>110101=>101011
[4,5,3,6,1,7,2]=>[4,3,5,1,6,2,7]=>101010=>010101
[4,5,3,6,2,1,7]=>[7,4,3,5,1,2,6]=>110100=>001011
[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>101010=>010101
[4,5,3,6,7,1,2]=>[6,4,3,5,1,7,2]=>110101=>101011
[4,5,3,6,7,2,1]=>[6,4,3,5,1,2,7]=>110100=>001011
[4,5,3,7,1,2,6]=>[4,3,5,1,7,6,2]=>101011=>110101
[4,5,3,7,1,6,2]=>[4,3,5,1,7,2,6]=>101010=>010101
[4,5,3,7,2,1,6]=>[4,3,5,1,2,7,6]=>101001=>100101
[4,5,3,7,2,6,1]=>[4,3,5,2,7,1,6]=>101010=>010101
[4,5,3,7,6,1,2]=>[4,3,5,1,6,7,2]=>101001=>100101
[4,5,3,7,6,2,1]=>[4,3,5,1,2,6,7]=>101000=>000101
[4,5,6,1,2,3,7]=>[7,5,4,1,6,3,2]=>111011=>110111
[4,5,6,1,2,7,3]=>[5,4,1,6,3,7,2]=>110101=>101011
[4,5,6,1,3,2,7]=>[7,5,4,1,6,2,3]=>111010=>010111
[4,5,6,1,3,7,2]=>[5,4,1,6,3,2,7]=>110110=>011011
[4,5,6,1,7,2,3]=>[5,4,1,6,2,7,3]=>110101=>101011
[4,5,6,1,7,3,2]=>[5,4,1,6,2,3,7]=>110100=>001011
[4,5,6,2,1,3,7]=>[7,5,4,1,2,6,3]=>111001=>100111
[4,5,6,2,1,7,3]=>[5,4,1,2,6,3,7]=>110010=>010011
[4,5,6,2,3,1,7]=>[7,5,4,2,6,1,3]=>111010=>010111
[4,5,6,2,3,7,1]=>[5,4,2,6,3,1,7]=>110110=>011011
[4,5,6,2,7,1,3]=>[5,4,2,6,1,7,3]=>110101=>101011
[4,5,6,2,7,3,1]=>[5,4,2,6,1,3,7]=>110100=>001011
[4,5,6,3,1,2,7]=>[7,5,4,1,3,6,2]=>111001=>100111
[4,5,6,3,1,7,2]=>[5,4,1,3,6,2,7]=>110010=>010011
[4,5,6,3,2,1,7]=>[7,5,4,1,2,3,6]=>111000=>000111
[4,5,6,3,2,7,1]=>[5,4,2,3,6,1,7]=>110010=>010011
[4,5,6,3,7,1,2]=>[5,4,3,6,1,7,2]=>110101=>101011
[4,5,6,3,7,2,1]=>[5,4,3,6,1,2,7]=>110100=>001011
[4,5,6,7,1,2,3]=>[6,5,4,1,7,3,2]=>111011=>110111
[4,5,6,7,1,3,2]=>[6,5,4,1,7,2,3]=>111010=>010111
[4,5,6,7,2,1,3]=>[6,5,4,1,2,7,3]=>111001=>100111
[4,5,6,7,2,3,1]=>[6,5,4,2,7,1,3]=>111010=>010111
[4,5,6,7,3,1,2]=>[6,5,4,1,3,7,2]=>111001=>100111
[4,5,6,7,3,2,1]=>[6,5,4,1,2,3,7]=>111000=>000111
[4,5,7,1,2,3,6]=>[5,4,1,7,6,3,2]=>110111=>111011
[4,5,7,1,2,6,3]=>[5,4,1,7,3,6,2]=>110101=>101011
[4,5,7,1,3,2,6]=>[5,4,1,7,6,2,3]=>110110=>011011
[4,5,7,1,3,6,2]=>[5,4,1,7,3,2,6]=>110110=>011011
[4,5,7,1,6,2,3]=>[5,4,1,7,2,6,3]=>110101=>101011
[4,5,7,1,6,3,2]=>[5,4,1,7,2,3,6]=>110100=>001011
[4,5,7,2,1,3,6]=>[5,4,1,2,7,6,3]=>110011=>110011
[4,5,7,2,1,6,3]=>[5,4,1,2,7,3,6]=>110010=>010011
[4,5,7,2,3,1,6]=>[5,4,2,7,6,1,3]=>110110=>011011
[4,5,7,2,3,6,1]=>[5,4,2,7,3,1,6]=>110110=>011011
[4,5,7,2,6,1,3]=>[5,4,2,7,1,6,3]=>110101=>101011
[4,5,7,2,6,3,1]=>[5,4,2,7,1,3,6]=>110100=>001011
[4,5,7,3,1,2,6]=>[5,4,1,3,7,6,2]=>110011=>110011
[4,5,7,3,1,6,2]=>[5,4,1,3,7,2,6]=>110010=>010011
[4,5,7,3,2,1,6]=>[5,4,1,2,3,7,6]=>110001=>100011
[4,5,7,3,2,6,1]=>[5,4,2,3,7,1,6]=>110010=>010011
[4,5,7,3,6,1,2]=>[5,4,3,7,1,6,2]=>110101=>101011
[4,5,7,3,6,2,1]=>[5,4,3,7,1,2,6]=>110100=>001011
[4,5,7,6,1,2,3]=>[5,4,1,6,7,3,2]=>110011=>110011
[4,5,7,6,1,3,2]=>[5,4,1,6,7,2,3]=>110010=>010011
[4,5,7,6,2,1,3]=>[5,4,1,2,6,7,3]=>110001=>100011
[4,5,7,6,2,3,1]=>[5,4,2,6,7,1,3]=>110010=>010011
[4,5,7,6,3,1,2]=>[5,4,1,3,6,7,2]=>110001=>100011
[4,5,7,6,3,2,1]=>[5,4,1,2,3,6,7]=>110000=>000011
[4,6,1,2,3,5,7]=>[7,4,1,6,5,3,2]=>110111=>111011
[4,6,1,2,3,7,5]=>[4,1,6,5,7,3,2]=>101011=>110101
[4,6,1,2,5,3,7]=>[7,4,1,6,3,5,2]=>110101=>101011
[4,6,1,2,5,7,3]=>[4,1,6,5,3,7,2]=>101101=>101101
[4,6,1,2,7,3,5]=>[4,1,6,3,7,5,2]=>101011=>110101
[4,6,1,2,7,5,3]=>[4,1,6,3,5,7,2]=>101001=>100101
[4,6,1,3,2,5,7]=>[7,4,1,6,5,2,3]=>110110=>011011
[4,6,1,3,2,7,5]=>[4,1,6,5,7,2,3]=>101010=>010101
[4,6,1,3,5,2,7]=>[7,4,1,6,3,2,5]=>110110=>011011
[4,6,1,3,5,7,2]=>[4,1,6,5,3,2,7]=>101110=>011101
[4,6,1,3,7,2,5]=>[4,1,6,3,2,7,5]=>101101=>101101
[4,6,1,3,7,5,2]=>[4,1,6,3,2,5,7]=>101100=>001101
[4,6,1,5,2,3,7]=>[7,4,1,6,2,5,3]=>110101=>101011
[4,6,1,5,2,7,3]=>[4,1,6,2,5,3,7]=>101010=>010101
[4,6,1,5,3,2,7]=>[7,4,1,6,2,3,5]=>110100=>001011
[4,6,1,5,3,7,2]=>[4,1,6,3,5,2,7]=>101010=>010101
[4,6,1,5,7,2,3]=>[4,1,6,5,2,7,3]=>101101=>101101
[4,6,1,5,7,3,2]=>[4,1,6,5,2,3,7]=>101100=>001101
[4,6,1,7,2,3,5]=>[4,1,6,2,7,5,3]=>101011=>110101
[4,6,1,7,2,5,3]=>[4,1,6,2,7,3,5]=>101010=>010101
[4,6,1,7,3,2,5]=>[4,1,6,2,3,7,5]=>101001=>100101
[4,6,1,7,3,5,2]=>[4,1,6,3,7,2,5]=>101010=>010101
[4,6,1,7,5,2,3]=>[4,1,6,2,5,7,3]=>101001=>100101
[4,6,1,7,5,3,2]=>[4,1,6,2,3,5,7]=>101000=>000101
[4,6,2,1,3,5,7]=>[7,4,1,2,6,5,3]=>110011=>110011
[4,6,2,1,3,7,5]=>[4,1,2,6,5,7,3]=>100101=>101001
[4,6,2,1,5,3,7]=>[7,4,1,2,6,3,5]=>110010=>010011
[4,6,2,1,5,7,3]=>[4,1,2,6,5,3,7]=>100110=>011001
[4,6,2,1,7,3,5]=>[4,1,2,6,3,7,5]=>100101=>101001
[4,6,2,1,7,5,3]=>[4,1,2,6,3,5,7]=>100100=>001001
[4,6,2,3,1,5,7]=>[7,4,2,6,5,1,3]=>110110=>011011
[4,6,2,3,1,7,5]=>[4,2,6,5,7,1,3]=>101010=>010101
[4,6,2,3,5,1,7]=>[7,4,2,6,3,1,5]=>110110=>011011
[4,6,2,3,5,7,1]=>[4,2,6,5,3,1,7]=>101110=>011101
[4,6,2,3,7,1,5]=>[4,2,6,3,1,7,5]=>101101=>101101
[4,6,2,3,7,5,1]=>[4,2,6,3,1,5,7]=>101100=>001101
[4,6,2,5,1,3,7]=>[7,4,2,6,1,5,3]=>110101=>101011
[4,6,2,5,1,7,3]=>[4,2,6,1,5,3,7]=>101010=>010101
[4,6,2,5,3,1,7]=>[7,4,2,6,1,3,5]=>110100=>001011
[4,6,2,5,3,7,1]=>[4,2,6,3,5,1,7]=>101010=>010101
[4,6,2,5,7,1,3]=>[4,2,6,5,1,7,3]=>101101=>101101
[4,6,2,5,7,3,1]=>[4,2,6,5,1,3,7]=>101100=>001101
[4,6,2,7,1,3,5]=>[4,2,6,1,7,5,3]=>101011=>110101
[4,6,2,7,1,5,3]=>[4,2,6,1,7,3,5]=>101010=>010101
[4,6,2,7,3,1,5]=>[4,2,6,1,3,7,5]=>101001=>100101
[4,6,2,7,3,5,1]=>[4,2,6,3,7,1,5]=>101010=>010101
[4,6,2,7,5,1,3]=>[4,2,6,1,5,7,3]=>101001=>100101
[4,6,2,7,5,3,1]=>[4,2,6,1,3,5,7]=>101000=>000101
[4,6,3,1,2,5,7]=>[7,4,1,3,6,5,2]=>110011=>110011
[4,6,3,1,2,7,5]=>[4,1,3,6,5,7,2]=>100101=>101001
[4,6,3,1,5,2,7]=>[7,4,1,3,6,2,5]=>110010=>010011
[4,6,3,1,5,7,2]=>[4,1,3,6,5,2,7]=>100110=>011001
[4,6,3,1,7,2,5]=>[4,1,3,6,2,7,5]=>100101=>101001
[4,6,3,1,7,5,2]=>[4,1,3,6,2,5,7]=>100100=>001001
[4,6,3,2,1,5,7]=>[7,4,1,2,3,6,5]=>110001=>100011
[4,6,3,2,1,7,5]=>[4,1,2,3,6,5,7]=>100010=>010001
[4,6,3,2,5,1,7]=>[7,4,2,3,6,1,5]=>110010=>010011
[4,6,3,2,5,7,1]=>[4,2,3,6,5,1,7]=>100110=>011001
[4,6,3,2,7,1,5]=>[4,2,3,6,1,7,5]=>100101=>101001
[4,6,3,2,7,5,1]=>[4,2,3,6,1,5,7]=>100100=>001001
[4,6,3,5,1,2,7]=>[7,4,3,6,1,5,2]=>110101=>101011
[4,6,3,5,1,7,2]=>[4,3,6,1,5,2,7]=>101010=>010101
[4,6,3,5,2,1,7]=>[7,4,3,6,1,2,5]=>110100=>001011
[4,6,3,5,2,7,1]=>[4,3,6,2,5,1,7]=>101010=>010101
[4,6,3,5,7,1,2]=>[4,3,6,5,1,7,2]=>101101=>101101
[4,6,3,5,7,2,1]=>[4,3,6,5,1,2,7]=>101100=>001101
[4,6,3,7,1,2,5]=>[4,3,6,1,7,5,2]=>101011=>110101
[4,6,3,7,1,5,2]=>[4,3,6,1,7,2,5]=>101010=>010101
[4,6,3,7,2,1,5]=>[4,3,6,1,2,7,5]=>101001=>100101
[4,6,3,7,2,5,1]=>[4,3,6,2,7,1,5]=>101010=>010101
[4,6,3,7,5,1,2]=>[4,3,6,1,5,7,2]=>101001=>100101
[4,6,3,7,5,2,1]=>[4,3,6,1,2,5,7]=>101000=>000101
[4,6,5,1,2,3,7]=>[7,4,1,5,6,3,2]=>110011=>110011
[4,6,5,1,2,7,3]=>[4,1,5,6,3,7,2]=>100101=>101001
[4,6,5,1,3,2,7]=>[7,4,1,5,6,2,3]=>110010=>010011
[4,6,5,1,3,7,2]=>[4,1,5,6,3,2,7]=>100110=>011001
[4,6,5,1,7,2,3]=>[4,1,5,6,2,7,3]=>100101=>101001
[4,6,5,1,7,3,2]=>[4,1,5,6,2,3,7]=>100100=>001001
[4,6,5,2,1,3,7]=>[7,4,1,2,5,6,3]=>110001=>100011
[4,6,5,2,1,7,3]=>[4,1,2,5,6,3,7]=>100010=>010001
[4,6,5,2,3,1,7]=>[7,4,2,5,6,1,3]=>110010=>010011
[4,6,5,2,3,7,1]=>[4,2,5,6,3,1,7]=>100110=>011001
[4,6,5,2,7,1,3]=>[4,2,5,6,1,7,3]=>100101=>101001
[4,6,5,2,7,3,1]=>[4,2,5,6,1,3,7]=>100100=>001001
[4,6,5,3,1,2,7]=>[7,4,1,3,5,6,2]=>110001=>100011
[4,6,5,3,1,7,2]=>[4,1,3,5,6,2,7]=>100010=>010001
[4,6,5,3,2,1,7]=>[7,4,1,2,3,5,6]=>110000=>000011
[4,6,5,3,2,7,1]=>[4,2,3,5,6,1,7]=>100010=>010001
[4,6,5,3,7,1,2]=>[4,3,5,6,1,7,2]=>100101=>101001
[4,6,5,3,7,2,1]=>[4,3,5,6,1,2,7]=>100100=>001001
[4,6,5,7,1,2,3]=>[5,6,4,1,7,3,2]=>011011=>110110
[4,6,5,7,1,3,2]=>[5,6,4,1,7,2,3]=>011010=>010110
[4,6,5,7,2,1,3]=>[5,6,4,1,2,7,3]=>011001=>100110
[4,6,5,7,2,3,1]=>[5,6,4,2,7,1,3]=>011010=>010110
[4,6,5,7,3,1,2]=>[5,6,4,1,3,7,2]=>011001=>100110
[4,6,5,7,3,2,1]=>[5,6,4,1,2,3,7]=>011000=>000110
[4,6,7,1,2,3,5]=>[6,4,1,7,5,3,2]=>110111=>111011
[4,6,7,1,2,5,3]=>[6,4,1,7,3,5,2]=>110101=>101011
[4,6,7,1,3,2,5]=>[6,4,1,7,5,2,3]=>110110=>011011
[4,6,7,1,3,5,2]=>[6,4,1,7,3,2,5]=>110110=>011011
[4,6,7,1,5,2,3]=>[6,4,1,7,2,5,3]=>110101=>101011
[4,6,7,1,5,3,2]=>[6,4,1,7,2,3,5]=>110100=>001011
[4,6,7,2,1,3,5]=>[6,4,1,2,7,5,3]=>110011=>110011
[4,6,7,2,1,5,3]=>[6,4,1,2,7,3,5]=>110010=>010011
[4,6,7,2,3,1,5]=>[6,4,2,7,5,1,3]=>110110=>011011
[4,6,7,2,3,5,1]=>[6,4,2,7,3,1,5]=>110110=>011011
[4,6,7,2,5,1,3]=>[6,4,2,7,1,5,3]=>110101=>101011
[4,6,7,2,5,3,1]=>[6,4,2,7,1,3,5]=>110100=>001011
[4,6,7,3,1,2,5]=>[6,4,1,3,7,5,2]=>110011=>110011
[4,6,7,3,1,5,2]=>[6,4,1,3,7,2,5]=>110010=>010011
[4,6,7,3,2,1,5]=>[6,4,1,2,3,7,5]=>110001=>100011
[4,6,7,3,2,5,1]=>[6,4,2,3,7,1,5]=>110010=>010011
[4,6,7,3,5,1,2]=>[6,4,3,7,1,5,2]=>110101=>101011
[4,6,7,3,5,2,1]=>[6,4,3,7,1,2,5]=>110100=>001011
[4,6,7,5,1,2,3]=>[6,4,1,5,7,3,2]=>110011=>110011
[4,6,7,5,1,3,2]=>[6,4,1,5,7,2,3]=>110010=>010011
[4,6,7,5,2,1,3]=>[6,4,1,2,5,7,3]=>110001=>100011
[4,6,7,5,2,3,1]=>[6,4,2,5,7,1,3]=>110010=>010011
[4,6,7,5,3,1,2]=>[6,4,1,3,5,7,2]=>110001=>100011
[4,6,7,5,3,2,1]=>[6,4,1,2,3,5,7]=>110000=>000011
[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]=>101111=>111101
[4,7,1,2,3,6,5]=>[4,1,7,5,6,3,2]=>101011=>110101
[4,7,1,2,5,3,6]=>[4,1,7,6,3,5,2]=>101101=>101101
[4,7,1,2,5,6,3]=>[4,1,7,5,3,6,2]=>101101=>101101
[4,7,1,2,6,3,5]=>[4,1,7,3,6,5,2]=>101011=>110101
[4,7,1,2,6,5,3]=>[4,1,7,3,5,6,2]=>101001=>100101
[4,7,1,3,2,5,6]=>[4,1,7,6,5,2,3]=>101110=>011101
[4,7,1,3,2,6,5]=>[4,1,7,5,6,2,3]=>101010=>010101
[4,7,1,3,5,2,6]=>[4,1,7,6,3,2,5]=>101110=>011101
[4,7,1,3,5,6,2]=>[4,1,7,5,3,2,6]=>101110=>011101
[4,7,1,3,6,2,5]=>[4,1,7,3,2,6,5]=>101101=>101101
[4,7,1,3,6,5,2]=>[4,1,7,3,2,5,6]=>101100=>001101
[4,7,1,5,2,3,6]=>[4,1,7,6,2,5,3]=>101101=>101101
[4,7,1,5,2,6,3]=>[4,1,7,2,5,3,6]=>101010=>010101
[4,7,1,5,3,2,6]=>[4,1,7,6,2,3,5]=>101100=>001101
[4,7,1,5,3,6,2]=>[4,1,7,3,5,2,6]=>101010=>010101
[4,7,1,5,6,2,3]=>[4,1,7,5,2,6,3]=>101101=>101101
[4,7,1,5,6,3,2]=>[4,1,7,5,2,3,6]=>101100=>001101
[4,7,1,6,2,3,5]=>[4,1,7,2,6,5,3]=>101011=>110101
[4,7,1,6,2,5,3]=>[4,1,7,2,6,3,5]=>101010=>010101
[4,7,1,6,3,2,5]=>[4,1,7,2,3,6,5]=>101001=>100101
[4,7,1,6,3,5,2]=>[4,1,7,3,6,2,5]=>101010=>010101
[4,7,1,6,5,2,3]=>[4,1,7,2,5,6,3]=>101001=>100101
[4,7,1,6,5,3,2]=>[4,1,7,2,3,5,6]=>101000=>000101
[4,7,2,1,3,5,6]=>[4,1,2,7,6,5,3]=>100111=>111001
[4,7,2,1,3,6,5]=>[4,1,2,7,5,6,3]=>100101=>101001
[4,7,2,1,5,3,6]=>[4,1,2,7,6,3,5]=>100110=>011001
[4,7,2,1,5,6,3]=>[4,1,2,7,5,3,6]=>100110=>011001
[4,7,2,1,6,3,5]=>[4,1,2,7,3,6,5]=>100101=>101001
[4,7,2,1,6,5,3]=>[4,1,2,7,3,5,6]=>100100=>001001
[4,7,2,3,1,5,6]=>[4,2,7,6,5,1,3]=>101110=>011101
[4,7,2,3,1,6,5]=>[4,2,7,5,6,1,3]=>101010=>010101
[4,7,2,3,5,1,6]=>[4,2,7,6,3,1,5]=>101110=>011101
[4,7,2,3,5,6,1]=>[4,2,7,5,3,1,6]=>101110=>011101
[4,7,2,3,6,1,5]=>[4,2,7,3,1,6,5]=>101101=>101101
[4,7,2,3,6,5,1]=>[4,2,7,3,1,5,6]=>101100=>001101
[4,7,2,5,1,3,6]=>[4,2,7,6,1,5,3]=>101101=>101101
[4,7,2,5,1,6,3]=>[4,2,7,1,5,3,6]=>101010=>010101
[4,7,2,5,3,1,6]=>[4,2,7,6,1,3,5]=>101100=>001101
[4,7,2,5,3,6,1]=>[4,2,7,3,5,1,6]=>101010=>010101
[4,7,2,5,6,1,3]=>[4,2,7,5,1,6,3]=>101101=>101101
[4,7,2,5,6,3,1]=>[4,2,7,5,1,3,6]=>101100=>001101
[4,7,2,6,1,3,5]=>[4,2,7,1,6,5,3]=>101011=>110101
[4,7,2,6,1,5,3]=>[4,2,7,1,6,3,5]=>101010=>010101
[4,7,2,6,3,1,5]=>[4,2,7,1,3,6,5]=>101001=>100101
[4,7,2,6,3,5,1]=>[4,2,7,3,6,1,5]=>101010=>010101
[4,7,2,6,5,1,3]=>[4,2,7,1,5,6,3]=>101001=>100101
[4,7,2,6,5,3,1]=>[4,2,7,1,3,5,6]=>101000=>000101
[4,7,3,1,2,5,6]=>[4,1,3,7,6,5,2]=>100111=>111001
[4,7,3,1,2,6,5]=>[4,1,3,7,5,6,2]=>100101=>101001
[4,7,3,1,5,2,6]=>[4,1,3,7,6,2,5]=>100110=>011001
[4,7,3,1,5,6,2]=>[4,1,3,7,5,2,6]=>100110=>011001
[4,7,3,1,6,2,5]=>[4,1,3,7,2,6,5]=>100101=>101001
[4,7,3,1,6,5,2]=>[4,1,3,7,2,5,6]=>100100=>001001
[4,7,3,2,1,5,6]=>[4,1,2,3,7,6,5]=>100011=>110001
[4,7,3,2,1,6,5]=>[4,1,2,3,7,5,6]=>100010=>010001
[4,7,3,2,5,1,6]=>[4,2,3,7,6,1,5]=>100110=>011001
[4,7,3,2,5,6,1]=>[4,2,3,7,5,1,6]=>100110=>011001
[4,7,3,2,6,1,5]=>[4,2,3,7,1,6,5]=>100101=>101001
[4,7,3,2,6,5,1]=>[4,2,3,7,1,5,6]=>100100=>001001
[4,7,3,5,1,2,6]=>[4,3,7,6,1,5,2]=>101101=>101101
[4,7,3,5,1,6,2]=>[4,3,7,1,5,2,6]=>101010=>010101
[4,7,3,5,2,1,6]=>[4,3,7,6,1,2,5]=>101100=>001101
[4,7,3,5,2,6,1]=>[4,3,7,2,5,1,6]=>101010=>010101
[4,7,3,5,6,1,2]=>[4,3,7,5,1,6,2]=>101101=>101101
[4,7,3,5,6,2,1]=>[4,3,7,5,1,2,6]=>101100=>001101
[4,7,3,6,1,2,5]=>[4,3,7,1,6,5,2]=>101011=>110101
[4,7,3,6,1,5,2]=>[4,3,7,1,6,2,5]=>101010=>010101
[4,7,3,6,2,1,5]=>[4,3,7,1,2,6,5]=>101001=>100101
[4,7,3,6,2,5,1]=>[4,3,7,2,6,1,5]=>101010=>010101
[4,7,3,6,5,1,2]=>[4,3,7,1,5,6,2]=>101001=>100101
[4,7,3,6,5,2,1]=>[4,3,7,1,2,5,6]=>101000=>000101
[4,7,5,1,2,3,6]=>[4,1,5,7,6,3,2]=>100111=>111001
[4,7,5,1,2,6,3]=>[4,1,5,7,3,6,2]=>100101=>101001
[4,7,5,1,3,2,6]=>[4,1,5,7,6,2,3]=>100110=>011001
[4,7,5,1,3,6,2]=>[4,1,5,7,3,2,6]=>100110=>011001
[4,7,5,1,6,2,3]=>[4,1,5,7,2,6,3]=>100101=>101001
[4,7,5,1,6,3,2]=>[4,1,5,7,2,3,6]=>100100=>001001
[4,7,5,2,1,3,6]=>[4,1,2,5,7,6,3]=>100011=>110001
[4,7,5,2,1,6,3]=>[4,1,2,5,7,3,6]=>100010=>010001
[4,7,5,2,3,1,6]=>[4,2,5,7,6,1,3]=>100110=>011001
[4,7,5,2,3,6,1]=>[4,2,5,7,3,1,6]=>100110=>011001
[4,7,5,2,6,1,3]=>[4,2,5,7,1,6,3]=>100101=>101001
[4,7,5,2,6,3,1]=>[4,2,5,7,1,3,6]=>100100=>001001
[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>100011=>110001
[4,7,5,3,1,6,2]=>[4,1,3,5,7,2,6]=>100010=>010001
[4,7,5,3,2,1,6]=>[4,1,2,3,5,7,6]=>100001=>100001
[4,7,5,3,2,6,1]=>[4,2,3,5,7,1,6]=>100010=>010001
[4,7,5,3,6,1,2]=>[4,3,5,7,1,6,2]=>100101=>101001
[4,7,5,3,6,2,1]=>[4,3,5,7,1,2,6]=>100100=>001001
[4,7,5,6,1,2,3]=>[5,7,4,1,6,3,2]=>011011=>110110
[4,7,5,6,1,3,2]=>[5,7,4,1,6,2,3]=>011010=>010110
[4,7,5,6,2,1,3]=>[5,7,4,1,2,6,3]=>011001=>100110
[4,7,5,6,2,3,1]=>[5,7,4,2,6,1,3]=>011010=>010110
[4,7,5,6,3,1,2]=>[5,7,4,1,3,6,2]=>011001=>100110
[4,7,5,6,3,2,1]=>[5,7,4,1,2,3,6]=>011000=>000110
[4,7,6,1,2,3,5]=>[4,1,6,7,5,3,2]=>100111=>111001
[4,7,6,1,2,5,3]=>[4,1,6,7,3,5,2]=>100101=>101001
[4,7,6,1,3,2,5]=>[4,1,6,7,5,2,3]=>100110=>011001
[4,7,6,1,3,5,2]=>[4,1,6,7,3,2,5]=>100110=>011001
[4,7,6,1,5,2,3]=>[4,1,6,7,2,5,3]=>100101=>101001
[4,7,6,1,5,3,2]=>[4,1,6,7,2,3,5]=>100100=>001001
[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>100011=>110001
[4,7,6,2,1,5,3]=>[4,1,2,6,7,3,5]=>100010=>010001
[4,7,6,2,3,1,5]=>[4,2,6,7,5,1,3]=>100110=>011001
[4,7,6,2,3,5,1]=>[4,2,6,7,3,1,5]=>100110=>011001
[4,7,6,2,5,1,3]=>[4,2,6,7,1,5,3]=>100101=>101001
[4,7,6,2,5,3,1]=>[4,2,6,7,1,3,5]=>100100=>001001
[4,7,6,3,1,2,5]=>[4,1,3,6,7,5,2]=>100011=>110001
[4,7,6,3,1,5,2]=>[4,1,3,6,7,2,5]=>100010=>010001
[4,7,6,3,2,1,5]=>[4,1,2,3,6,7,5]=>100001=>100001
[4,7,6,3,2,5,1]=>[4,2,3,6,7,1,5]=>100010=>010001
[4,7,6,3,5,1,2]=>[4,3,6,7,1,5,2]=>100101=>101001
[4,7,6,3,5,2,1]=>[4,3,6,7,1,2,5]=>100100=>001001
[4,7,6,5,1,2,3]=>[4,1,5,6,7,3,2]=>100011=>110001
[4,7,6,5,1,3,2]=>[4,1,5,6,7,2,3]=>100010=>010001
[4,7,6,5,2,1,3]=>[4,1,2,5,6,7,3]=>100001=>100001
[4,7,6,5,2,3,1]=>[4,2,5,6,7,1,3]=>100010=>010001
[4,7,6,5,3,1,2]=>[4,1,3,5,6,7,2]=>100001=>100001
[4,7,6,5,3,2,1]=>[4,1,2,3,5,6,7]=>100000=>000001
[5,1,2,3,4,6,7]=>[7,6,1,5,4,3,2]=>110111=>111011
[5,1,2,3,4,7,6]=>[6,7,1,5,4,3,2]=>010111=>111010
[5,1,2,3,6,4,7]=>[7,1,5,4,6,3,2]=>101011=>110101
[5,1,2,3,6,7,4]=>[6,1,5,4,7,3,2]=>101011=>110101
[5,1,2,3,7,4,6]=>[1,5,4,7,6,3,2]=>010111=>111010
[5,1,2,3,7,6,4]=>[1,5,4,6,7,3,2]=>010011=>110010
[5,1,2,4,3,6,7]=>[7,6,1,5,3,4,2]=>110101=>101011
[5,1,2,4,3,7,6]=>[6,7,1,5,3,4,2]=>010101=>101010
[5,1,2,4,6,3,7]=>[7,1,5,4,3,6,2]=>101101=>101101
[5,1,2,4,6,7,3]=>[6,1,5,4,3,7,2]=>101101=>101101
[5,1,2,4,7,3,6]=>[1,5,4,3,7,6,2]=>011011=>110110
[5,1,2,4,7,6,3]=>[1,5,4,3,6,7,2]=>011001=>100110
[5,1,2,6,3,4,7]=>[7,1,5,3,6,4,2]=>101011=>110101
[5,1,2,6,3,7,4]=>[1,5,3,6,4,7,2]=>010101=>101010
[5,1,2,6,4,3,7]=>[7,1,5,3,4,6,2]=>101001=>100101
[5,1,2,6,4,7,3]=>[1,5,4,6,3,7,2]=>010101=>101010
[5,1,2,6,7,3,4]=>[6,1,5,3,7,4,2]=>101011=>110101
[5,1,2,6,7,4,3]=>[6,1,5,3,4,7,2]=>101001=>100101
[5,1,2,7,3,4,6]=>[1,5,3,7,6,4,2]=>010111=>111010
[5,1,2,7,3,6,4]=>[1,5,3,7,4,6,2]=>010101=>101010
[5,1,2,7,4,3,6]=>[1,5,3,4,7,6,2]=>010011=>110010
[5,1,2,7,4,6,3]=>[1,5,4,7,3,6,2]=>010101=>101010
[5,1,2,7,6,3,4]=>[1,5,3,6,7,4,2]=>010011=>110010
[5,1,2,7,6,4,3]=>[1,5,3,4,6,7,2]=>010001=>100010
[5,1,3,2,4,6,7]=>[7,6,1,5,4,2,3]=>110110=>011011
[5,1,3,2,4,7,6]=>[6,7,1,5,4,2,3]=>010110=>011010
[5,1,3,2,6,4,7]=>[7,1,5,4,6,2,3]=>101010=>010101
[5,1,3,2,6,7,4]=>[6,1,5,4,7,2,3]=>101010=>010101
[5,1,3,2,7,4,6]=>[1,5,4,7,6,2,3]=>010110=>011010
[5,1,3,2,7,6,4]=>[1,5,4,6,7,2,3]=>010010=>010010
[5,1,3,4,2,6,7]=>[7,6,1,5,3,2,4]=>110110=>011011
[5,1,3,4,2,7,6]=>[6,7,1,5,3,2,4]=>010110=>011010
[5,1,3,4,6,2,7]=>[7,1,5,4,3,2,6]=>101110=>011101
[5,1,3,4,6,7,2]=>[6,1,5,4,3,2,7]=>101110=>011101
[5,1,3,4,7,2,6]=>[1,5,4,3,2,7,6]=>011101=>101110
[5,1,3,4,7,6,2]=>[1,5,4,3,2,6,7]=>011100=>001110
[5,1,3,6,2,4,7]=>[7,1,5,3,2,6,4]=>101101=>101101
[5,1,3,6,2,7,4]=>[1,5,3,2,6,4,7]=>011010=>010110
[5,1,3,6,4,2,7]=>[7,1,5,3,2,4,6]=>101100=>001101
[5,1,3,6,4,7,2]=>[1,5,4,6,3,2,7]=>010110=>011010
[5,1,3,6,7,2,4]=>[6,1,5,3,2,7,4]=>101101=>101101
[5,1,3,6,7,4,2]=>[6,1,5,3,2,4,7]=>101100=>001101
[5,1,3,7,2,4,6]=>[1,5,3,2,7,6,4]=>011011=>110110
[5,1,3,7,2,6,4]=>[1,5,3,2,7,4,6]=>011010=>010110
[5,1,3,7,4,2,6]=>[1,5,3,2,4,7,6]=>011001=>100110
[5,1,3,7,4,6,2]=>[1,5,4,7,3,2,6]=>010110=>011010
[5,1,3,7,6,2,4]=>[1,5,3,2,6,7,4]=>011001=>100110
[5,1,3,7,6,4,2]=>[1,5,3,2,4,6,7]=>011000=>000110
[5,1,4,2,3,6,7]=>[7,6,1,5,2,4,3]=>110101=>101011
[5,1,4,2,3,7,6]=>[6,7,1,5,2,4,3]=>010101=>101010
[5,1,4,2,6,3,7]=>[7,1,5,2,4,3,6]=>101010=>010101
[5,1,4,2,6,7,3]=>[6,1,5,2,4,3,7]=>101010=>010101
[5,1,4,2,7,3,6]=>[1,5,2,4,3,7,6]=>010101=>101010
[5,1,4,2,7,6,3]=>[1,5,2,4,3,6,7]=>010100=>001010
[5,1,4,3,2,6,7]=>[7,6,1,5,2,3,4]=>110100=>001011
[5,1,4,3,2,7,6]=>[6,7,1,5,2,3,4]=>010100=>001010
[5,1,4,3,6,2,7]=>[7,1,5,3,4,2,6]=>101010=>010101
[5,1,4,3,6,7,2]=>[6,1,5,3,4,2,7]=>101010=>010101
[5,1,4,3,7,2,6]=>[1,5,3,4,2,7,6]=>010101=>101010
[5,1,4,3,7,6,2]=>[1,5,3,4,2,6,7]=>010100=>001010
[5,1,4,6,2,3,7]=>[7,1,5,4,2,6,3]=>101101=>101101
[5,1,4,6,2,7,3]=>[1,5,4,2,6,3,7]=>011010=>010110
[5,1,4,6,3,2,7]=>[7,1,5,4,2,3,6]=>101100=>001101
[5,1,4,6,3,7,2]=>[1,5,4,3,6,2,7]=>011010=>010110
[5,1,4,6,7,2,3]=>[6,1,5,4,2,7,3]=>101101=>101101
[5,1,4,6,7,3,2]=>[6,1,5,4,2,3,7]=>101100=>001101
[5,1,4,7,2,3,6]=>[1,5,4,2,7,6,3]=>011011=>110110
[5,1,4,7,2,6,3]=>[1,5,4,2,7,3,6]=>011010=>010110
[5,1,4,7,3,2,6]=>[1,5,4,2,3,7,6]=>011001=>100110
[5,1,4,7,3,6,2]=>[1,5,4,3,7,2,6]=>011010=>010110
[5,1,4,7,6,2,3]=>[1,5,4,2,6,7,3]=>011001=>100110
[5,1,4,7,6,3,2]=>[1,5,4,2,3,6,7]=>011000=>000110
[5,1,6,2,3,4,7]=>[7,1,5,2,6,4,3]=>101011=>110101
[5,1,6,2,3,7,4]=>[1,5,2,6,4,7,3]=>010101=>101010
[5,1,6,2,4,3,7]=>[7,1,5,2,6,3,4]=>101010=>010101
[5,1,6,2,4,7,3]=>[1,5,2,6,4,3,7]=>010110=>011010
[5,1,6,2,7,3,4]=>[1,5,2,6,3,7,4]=>010101=>101010
[5,1,6,2,7,4,3]=>[1,5,2,6,3,4,7]=>010100=>001010
[5,1,6,3,2,4,7]=>[7,1,5,2,3,6,4]=>101001=>100101
[5,1,6,3,2,7,4]=>[1,5,2,3,6,4,7]=>010010=>010010
[5,1,6,3,4,2,7]=>[7,1,5,3,6,2,4]=>101010=>010101
[5,1,6,3,4,7,2]=>[1,5,3,6,4,2,7]=>010110=>011010
[5,1,6,3,7,2,4]=>[1,5,3,6,2,7,4]=>010101=>101010
[5,1,6,3,7,4,2]=>[1,5,3,6,2,4,7]=>010100=>001010
[5,1,6,4,2,3,7]=>[7,1,5,2,4,6,3]=>101001=>100101
[5,1,6,4,2,7,3]=>[1,5,2,4,6,3,7]=>010010=>010010
[5,1,6,4,3,2,7]=>[7,1,5,2,3,4,6]=>101000=>000101
[5,1,6,4,3,7,2]=>[1,5,3,4,6,2,7]=>010010=>010010
[5,1,6,4,7,2,3]=>[1,5,4,6,2,7,3]=>010101=>101010
[5,1,6,4,7,3,2]=>[1,5,4,6,2,3,7]=>010100=>001010
[5,1,6,7,2,3,4]=>[6,1,5,2,7,4,3]=>101011=>110101
[5,1,6,7,2,4,3]=>[6,1,5,2,7,3,4]=>101010=>010101
[5,1,6,7,3,2,4]=>[6,1,5,2,3,7,4]=>101001=>100101
[5,1,6,7,3,4,2]=>[6,1,5,3,7,2,4]=>101010=>010101
[5,1,6,7,4,2,3]=>[6,1,5,2,4,7,3]=>101001=>100101
[5,1,6,7,4,3,2]=>[6,1,5,2,3,4,7]=>101000=>000101
[5,1,7,2,3,4,6]=>[1,5,2,7,6,4,3]=>010111=>111010
[5,1,7,2,3,6,4]=>[1,5,2,7,4,6,3]=>010101=>101010
[5,1,7,2,4,3,6]=>[1,5,2,7,6,3,4]=>010110=>011010
[5,1,7,2,4,6,3]=>[1,5,2,7,4,3,6]=>010110=>011010
[5,1,7,2,6,3,4]=>[1,5,2,7,3,6,4]=>010101=>101010
[5,1,7,2,6,4,3]=>[1,5,2,7,3,4,6]=>010100=>001010
[5,1,7,3,2,4,6]=>[1,5,2,3,7,6,4]=>010011=>110010
[5,1,7,3,2,6,4]=>[1,5,2,3,7,4,6]=>010010=>010010
[5,1,7,3,4,2,6]=>[1,5,3,7,6,2,4]=>010110=>011010
[5,1,7,3,4,6,2]=>[1,5,3,7,4,2,6]=>010110=>011010
[5,1,7,3,6,2,4]=>[1,5,3,7,2,6,4]=>010101=>101010
[5,1,7,3,6,4,2]=>[1,5,3,7,2,4,6]=>010100=>001010
[5,1,7,4,2,3,6]=>[1,5,2,4,7,6,3]=>010011=>110010
[5,1,7,4,2,6,3]=>[1,5,2,4,7,3,6]=>010010=>010010
[5,1,7,4,3,2,6]=>[1,5,2,3,4,7,6]=>010001=>100010
[5,1,7,4,3,6,2]=>[1,5,3,4,7,2,6]=>010010=>010010
[5,1,7,4,6,2,3]=>[1,5,4,7,2,6,3]=>010101=>101010
[5,1,7,4,6,3,2]=>[1,5,4,7,2,3,6]=>010100=>001010
[5,1,7,6,2,3,4]=>[1,5,2,6,7,4,3]=>010011=>110010
[5,1,7,6,2,4,3]=>[1,5,2,6,7,3,4]=>010010=>010010
[5,1,7,6,3,2,4]=>[1,5,2,3,6,7,4]=>010001=>100010
[5,1,7,6,3,4,2]=>[1,5,3,6,7,2,4]=>010010=>010010
[5,1,7,6,4,2,3]=>[1,5,2,4,6,7,3]=>010001=>100010
[5,1,7,6,4,3,2]=>[1,5,2,3,4,6,7]=>010000=>000010
[5,2,1,3,4,6,7]=>[7,6,1,2,5,4,3]=>110011=>110011
[5,2,1,3,4,7,6]=>[6,7,1,2,5,4,3]=>010011=>110010
[5,2,1,3,6,4,7]=>[7,1,2,5,4,6,3]=>100101=>101001
[5,2,1,3,6,7,4]=>[6,1,2,5,4,7,3]=>100101=>101001
[5,2,1,3,7,4,6]=>[1,2,5,4,7,6,3]=>001011=>110100
[5,2,1,3,7,6,4]=>[1,2,5,4,6,7,3]=>001001=>100100
[5,2,1,4,3,6,7]=>[7,6,1,2,5,3,4]=>110010=>010011
[5,2,1,4,3,7,6]=>[6,7,1,2,5,3,4]=>010010=>010010
[5,2,1,4,6,3,7]=>[7,1,2,5,4,3,6]=>100110=>011001
[5,2,1,4,6,7,3]=>[6,1,2,5,4,3,7]=>100110=>011001
[5,2,1,4,7,3,6]=>[1,2,5,4,3,7,6]=>001101=>101100
[5,2,1,4,7,6,3]=>[1,2,5,4,3,6,7]=>001100=>001100
[5,2,1,6,3,4,7]=>[7,1,2,5,3,6,4]=>100101=>101001
[5,2,1,6,3,7,4]=>[1,2,5,3,6,4,7]=>001010=>010100
[5,2,1,6,4,3,7]=>[7,1,2,5,3,4,6]=>100100=>001001
[5,2,1,6,4,7,3]=>[1,2,5,4,6,3,7]=>001010=>010100
[5,2,1,6,7,3,4]=>[6,1,2,5,3,7,4]=>100101=>101001
[5,2,1,6,7,4,3]=>[6,1,2,5,3,4,7]=>100100=>001001
[5,2,1,7,3,4,6]=>[1,2,5,3,7,6,4]=>001011=>110100
[5,2,1,7,3,6,4]=>[1,2,5,3,7,4,6]=>001010=>010100
[5,2,1,7,4,3,6]=>[1,2,5,3,4,7,6]=>001001=>100100
[5,2,1,7,4,6,3]=>[1,2,5,4,7,3,6]=>001010=>010100
[5,2,1,7,6,3,4]=>[1,2,5,3,6,7,4]=>001001=>100100
[5,2,1,7,6,4,3]=>[1,2,5,3,4,6,7]=>001000=>000100
[5,2,3,1,4,6,7]=>[7,6,2,5,4,1,3]=>110110=>011011
[5,2,3,1,4,7,6]=>[6,7,2,5,4,1,3]=>010110=>011010
[5,2,3,1,6,4,7]=>[7,2,5,4,6,1,3]=>101010=>010101
[5,2,3,1,6,7,4]=>[6,2,5,4,7,1,3]=>101010=>010101
[5,2,3,1,7,4,6]=>[2,5,4,7,6,1,3]=>010110=>011010
[5,2,3,1,7,6,4]=>[2,5,4,6,7,1,3]=>010010=>010010
[5,2,3,4,1,6,7]=>[7,6,2,5,3,1,4]=>110110=>011011
[5,2,3,4,1,7,6]=>[6,7,2,5,3,1,4]=>010110=>011010
[5,2,3,4,6,1,7]=>[7,2,5,4,3,1,6]=>101110=>011101
[5,2,3,4,6,7,1]=>[6,2,5,4,3,1,7]=>101110=>011101
[5,2,3,4,7,1,6]=>[2,5,4,3,1,7,6]=>011101=>101110
[5,2,3,4,7,6,1]=>[2,5,4,3,1,6,7]=>011100=>001110
[5,2,3,6,1,4,7]=>[7,2,5,3,1,6,4]=>101101=>101101
[5,2,3,6,1,7,4]=>[2,5,3,1,6,4,7]=>011010=>010110
[5,2,3,6,4,1,7]=>[7,2,5,3,1,4,6]=>101100=>001101
[5,2,3,6,4,7,1]=>[2,5,4,6,3,1,7]=>010110=>011010
[5,2,3,6,7,1,4]=>[6,2,5,3,1,7,4]=>101101=>101101
[5,2,3,6,7,4,1]=>[6,2,5,3,1,4,7]=>101100=>001101
[5,2,3,7,1,4,6]=>[2,5,3,1,7,6,4]=>011011=>110110
[5,2,3,7,1,6,4]=>[2,5,3,1,7,4,6]=>011010=>010110
[5,2,3,7,4,1,6]=>[2,5,3,1,4,7,6]=>011001=>100110
[5,2,3,7,4,6,1]=>[2,5,4,7,3,1,6]=>010110=>011010
[5,2,3,7,6,1,4]=>[2,5,3,1,6,7,4]=>011001=>100110
[5,2,3,7,6,4,1]=>[2,5,3,1,4,6,7]=>011000=>000110
[5,2,4,1,3,6,7]=>[7,6,2,5,1,4,3]=>110101=>101011
[5,2,4,1,3,7,6]=>[6,7,2,5,1,4,3]=>010101=>101010
[5,2,4,1,6,3,7]=>[7,2,5,1,4,3,6]=>101010=>010101
[5,2,4,1,6,7,3]=>[6,2,5,1,4,3,7]=>101010=>010101
[5,2,4,1,7,3,6]=>[2,5,1,4,3,7,6]=>010101=>101010
[5,2,4,1,7,6,3]=>[2,5,1,4,3,6,7]=>010100=>001010
[5,2,4,3,1,6,7]=>[7,6,2,5,1,3,4]=>110100=>001011
[5,2,4,3,1,7,6]=>[6,7,2,5,1,3,4]=>010100=>001010
[5,2,4,3,6,1,7]=>[7,2,5,3,4,1,6]=>101010=>010101
[5,2,4,3,6,7,1]=>[6,2,5,3,4,1,7]=>101010=>010101
[5,2,4,3,7,1,6]=>[2,5,3,4,1,7,6]=>010101=>101010
[5,2,4,3,7,6,1]=>[2,5,3,4,1,6,7]=>010100=>001010
[5,2,4,6,1,3,7]=>[7,2,5,4,1,6,3]=>101101=>101101
[5,2,4,6,1,7,3]=>[2,5,4,1,6,3,7]=>011010=>010110
[5,2,4,6,3,1,7]=>[7,2,5,4,1,3,6]=>101100=>001101
[5,2,4,6,3,7,1]=>[2,5,4,3,6,1,7]=>011010=>010110
[5,2,4,6,7,1,3]=>[6,2,5,4,1,7,3]=>101101=>101101
[5,2,4,6,7,3,1]=>[6,2,5,4,1,3,7]=>101100=>001101
[5,2,4,7,1,3,6]=>[2,5,4,1,7,6,3]=>011011=>110110
[5,2,4,7,1,6,3]=>[2,5,4,1,7,3,6]=>011010=>010110
[5,2,4,7,3,1,6]=>[2,5,4,1,3,7,6]=>011001=>100110
[5,2,4,7,3,6,1]=>[2,5,4,3,7,1,6]=>011010=>010110
[5,2,4,7,6,1,3]=>[2,5,4,1,6,7,3]=>011001=>100110
[5,2,4,7,6,3,1]=>[2,5,4,1,3,6,7]=>011000=>000110
[5,2,6,1,3,4,7]=>[7,2,5,1,6,4,3]=>101011=>110101
[5,2,6,1,3,7,4]=>[2,5,1,6,4,7,3]=>010101=>101010
[5,2,6,1,4,3,7]=>[7,2,5,1,6,3,4]=>101010=>010101
[5,2,6,1,4,7,3]=>[2,5,1,6,4,3,7]=>010110=>011010
[5,2,6,1,7,3,4]=>[2,5,1,6,3,7,4]=>010101=>101010
[5,2,6,1,7,4,3]=>[2,5,1,6,3,4,7]=>010100=>001010
[5,2,6,3,1,4,7]=>[7,2,5,1,3,6,4]=>101001=>100101
[5,2,6,3,1,7,4]=>[2,5,1,3,6,4,7]=>010010=>010010
[5,2,6,3,4,1,7]=>[7,2,5,3,6,1,4]=>101010=>010101
[5,2,6,3,4,7,1]=>[2,5,3,6,4,1,7]=>010110=>011010
[5,2,6,3,7,1,4]=>[2,5,3,6,1,7,4]=>010101=>101010
[5,2,6,3,7,4,1]=>[2,5,3,6,1,4,7]=>010100=>001010
[5,2,6,4,1,3,7]=>[7,2,5,1,4,6,3]=>101001=>100101
[5,2,6,4,1,7,3]=>[2,5,1,4,6,3,7]=>010010=>010010
[5,2,6,4,3,1,7]=>[7,2,5,1,3,4,6]=>101000=>000101
[5,2,6,4,3,7,1]=>[2,5,3,4,6,1,7]=>010010=>010010
[5,2,6,4,7,1,3]=>[2,5,4,6,1,7,3]=>010101=>101010
[5,2,6,4,7,3,1]=>[2,5,4,6,1,3,7]=>010100=>001010
[5,2,6,7,1,3,4]=>[6,2,5,1,7,4,3]=>101011=>110101
[5,2,6,7,1,4,3]=>[6,2,5,1,7,3,4]=>101010=>010101
[5,2,6,7,3,1,4]=>[6,2,5,1,3,7,4]=>101001=>100101
[5,2,6,7,3,4,1]=>[6,2,5,3,7,1,4]=>101010=>010101
[5,2,6,7,4,1,3]=>[6,2,5,1,4,7,3]=>101001=>100101
[5,2,6,7,4,3,1]=>[6,2,5,1,3,4,7]=>101000=>000101
[5,2,7,1,3,4,6]=>[2,5,1,7,6,4,3]=>010111=>111010
[5,2,7,1,3,6,4]=>[2,5,1,7,4,6,3]=>010101=>101010
[5,2,7,1,4,3,6]=>[2,5,1,7,6,3,4]=>010110=>011010
[5,2,7,1,4,6,3]=>[2,5,1,7,4,3,6]=>010110=>011010
[5,2,7,1,6,3,4]=>[2,5,1,7,3,6,4]=>010101=>101010
[5,2,7,1,6,4,3]=>[2,5,1,7,3,4,6]=>010100=>001010
[5,2,7,3,1,4,6]=>[2,5,1,3,7,6,4]=>010011=>110010
[5,2,7,3,1,6,4]=>[2,5,1,3,7,4,6]=>010010=>010010
[5,2,7,3,4,1,6]=>[2,5,3,7,6,1,4]=>010110=>011010
[5,2,7,3,4,6,1]=>[2,5,3,7,4,1,6]=>010110=>011010
[5,2,7,3,6,1,4]=>[2,5,3,7,1,6,4]=>010101=>101010
[5,2,7,3,6,4,1]=>[2,5,3,7,1,4,6]=>010100=>001010
[5,2,7,4,1,3,6]=>[2,5,1,4,7,6,3]=>010011=>110010
[5,2,7,4,1,6,3]=>[2,5,1,4,7,3,6]=>010010=>010010
[5,2,7,4,3,1,6]=>[2,5,1,3,4,7,6]=>010001=>100010
[5,2,7,4,3,6,1]=>[2,5,3,4,7,1,6]=>010010=>010010
[5,2,7,4,6,1,3]=>[2,5,4,7,1,6,3]=>010101=>101010
[5,2,7,4,6,3,1]=>[2,5,4,7,1,3,6]=>010100=>001010
[5,2,7,6,1,3,4]=>[2,5,1,6,7,4,3]=>010011=>110010
[5,2,7,6,1,4,3]=>[2,5,1,6,7,3,4]=>010010=>010010
[5,2,7,6,3,1,4]=>[2,5,1,3,6,7,4]=>010001=>100010
[5,2,7,6,3,4,1]=>[2,5,3,6,7,1,4]=>010010=>010010
[5,2,7,6,4,1,3]=>[2,5,1,4,6,7,3]=>010001=>100010
[5,2,7,6,4,3,1]=>[2,5,1,3,4,6,7]=>010000=>000010
[5,3,1,2,4,6,7]=>[7,6,1,3,5,4,2]=>110011=>110011
[5,3,1,2,4,7,6]=>[6,7,1,3,5,4,2]=>010011=>110010
[5,3,1,2,6,4,7]=>[7,1,3,5,4,6,2]=>100101=>101001
[5,3,1,2,6,7,4]=>[6,1,3,5,4,7,2]=>100101=>101001
[5,3,1,2,7,4,6]=>[1,3,5,4,7,6,2]=>001011=>110100
[5,3,1,2,7,6,4]=>[1,3,5,4,6,7,2]=>001001=>100100
[5,3,1,4,2,6,7]=>[7,6,1,3,5,2,4]=>110010=>010011
[5,3,1,4,2,7,6]=>[6,7,1,3,5,2,4]=>010010=>010010
[5,3,1,4,6,2,7]=>[7,1,3,5,4,2,6]=>100110=>011001
[5,3,1,4,6,7,2]=>[6,1,3,5,4,2,7]=>100110=>011001
[5,3,1,4,7,2,6]=>[1,3,5,4,2,7,6]=>001101=>101100
[5,3,1,4,7,6,2]=>[1,3,5,4,2,6,7]=>001100=>001100
[5,3,1,6,2,4,7]=>[7,1,3,5,2,6,4]=>100101=>101001
[5,3,1,6,2,7,4]=>[1,3,5,2,6,4,7]=>001010=>010100
[5,3,1,6,4,2,7]=>[7,1,3,5,2,4,6]=>100100=>001001
[5,3,1,6,4,7,2]=>[1,3,5,4,6,2,7]=>001010=>010100
[5,3,1,6,7,2,4]=>[6,1,3,5,2,7,4]=>100101=>101001
[5,3,1,6,7,4,2]=>[6,1,3,5,2,4,7]=>100100=>001001
[5,3,1,7,2,4,6]=>[1,3,5,2,7,6,4]=>001011=>110100
[5,3,1,7,2,6,4]=>[1,3,5,2,7,4,6]=>001010=>010100
[5,3,1,7,4,2,6]=>[1,3,5,2,4,7,6]=>001001=>100100
[5,3,1,7,4,6,2]=>[1,3,5,4,7,2,6]=>001010=>010100
[5,3,1,7,6,2,4]=>[1,3,5,2,6,7,4]=>001001=>100100
[5,3,1,7,6,4,2]=>[1,3,5,2,4,6,7]=>001000=>000100
[5,3,2,1,4,6,7]=>[7,6,1,2,3,5,4]=>110001=>100011
[5,3,2,1,4,7,6]=>[6,7,1,2,3,5,4]=>010001=>100010
[5,3,2,1,6,4,7]=>[7,1,2,3,5,4,6]=>100010=>010001
[5,3,2,1,6,7,4]=>[6,1,2,3,5,4,7]=>100010=>010001
[5,3,2,1,7,4,6]=>[1,2,3,5,4,7,6]=>000101=>101000
[5,3,2,1,7,6,4]=>[1,2,3,5,4,6,7]=>000100=>001000
[5,3,2,4,1,6,7]=>[7,6,2,3,5,1,4]=>110010=>010011
[5,3,2,4,1,7,6]=>[6,7,2,3,5,1,4]=>010010=>010010
[5,3,2,4,6,1,7]=>[7,2,3,5,4,1,6]=>100110=>011001
[5,3,2,4,6,7,1]=>[6,2,3,5,4,1,7]=>100110=>011001
[5,3,2,4,7,1,6]=>[2,3,5,4,1,7,6]=>001101=>101100
[5,3,2,4,7,6,1]=>[2,3,5,4,1,6,7]=>001100=>001100
[5,3,2,6,1,4,7]=>[7,2,3,5,1,6,4]=>100101=>101001
[5,3,2,6,1,7,4]=>[2,3,5,1,6,4,7]=>001010=>010100
[5,3,2,6,4,1,7]=>[7,2,3,5,1,4,6]=>100100=>001001
[5,3,2,6,4,7,1]=>[2,3,5,4,6,1,7]=>001010=>010100
[5,3,2,6,7,1,4]=>[6,2,3,5,1,7,4]=>100101=>101001
[5,3,2,6,7,4,1]=>[6,2,3,5,1,4,7]=>100100=>001001
[5,3,2,7,1,4,6]=>[2,3,5,1,7,6,4]=>001011=>110100
[5,3,2,7,1,6,4]=>[2,3,5,1,7,4,6]=>001010=>010100
[5,3,2,7,4,1,6]=>[2,3,5,1,4,7,6]=>001001=>100100
[5,3,2,7,4,6,1]=>[2,3,5,4,7,1,6]=>001010=>010100
[5,3,2,7,6,1,4]=>[2,3,5,1,6,7,4]=>001001=>100100
[5,3,2,7,6,4,1]=>[2,3,5,1,4,6,7]=>001000=>000100
[5,3,4,1,2,6,7]=>[7,6,3,5,1,4,2]=>110101=>101011
[5,3,4,1,2,7,6]=>[6,7,3,5,1,4,2]=>010101=>101010
[5,3,4,1,6,2,7]=>[7,3,5,1,4,2,6]=>101010=>010101
[5,3,4,1,6,7,2]=>[6,3,5,1,4,2,7]=>101010=>010101
[5,3,4,1,7,2,6]=>[3,5,1,4,2,7,6]=>010101=>101010
[5,3,4,1,7,6,2]=>[3,5,1,4,2,6,7]=>010100=>001010
[5,3,4,2,1,6,7]=>[7,6,3,5,1,2,4]=>110100=>001011
[5,3,4,2,1,7,6]=>[6,7,3,5,1,2,4]=>010100=>001010
[5,3,4,2,6,1,7]=>[7,3,5,2,4,1,6]=>101010=>010101
[5,3,4,2,6,7,1]=>[6,3,5,2,4,1,7]=>101010=>010101
[5,3,4,2,7,1,6]=>[3,5,2,4,1,7,6]=>010101=>101010
[5,3,4,2,7,6,1]=>[3,5,2,4,1,6,7]=>010100=>001010
[5,3,4,6,1,2,7]=>[7,3,5,4,1,6,2]=>101101=>101101
[5,3,4,6,1,7,2]=>[3,5,4,1,6,2,7]=>011010=>010110
[5,3,4,6,2,1,7]=>[7,3,5,4,1,2,6]=>101100=>001101
[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>011010=>010110
[5,3,4,6,7,1,2]=>[6,3,5,4,1,7,2]=>101101=>101101
[5,3,4,6,7,2,1]=>[6,3,5,4,1,2,7]=>101100=>001101
[5,3,4,7,1,2,6]=>[3,5,4,1,7,6,2]=>011011=>110110
[5,3,4,7,1,6,2]=>[3,5,4,1,7,2,6]=>011010=>010110
[5,3,4,7,2,1,6]=>[3,5,4,1,2,7,6]=>011001=>100110
[5,3,4,7,2,6,1]=>[3,5,4,2,7,1,6]=>011010=>010110
[5,3,4,7,6,1,2]=>[3,5,4,1,6,7,2]=>011001=>100110
[5,3,4,7,6,2,1]=>[3,5,4,1,2,6,7]=>011000=>000110
[5,3,6,1,2,4,7]=>[7,3,5,1,6,4,2]=>101011=>110101
[5,3,6,1,2,7,4]=>[3,5,1,6,4,7,2]=>010101=>101010
[5,3,6,1,4,2,7]=>[7,3,5,1,6,2,4]=>101010=>010101
[5,3,6,1,4,7,2]=>[3,5,1,6,4,2,7]=>010110=>011010
[5,3,6,1,7,2,4]=>[3,5,1,6,2,7,4]=>010101=>101010
[5,3,6,1,7,4,2]=>[3,5,1,6,2,4,7]=>010100=>001010
[5,3,6,2,1,4,7]=>[7,3,5,1,2,6,4]=>101001=>100101
[5,3,6,2,1,7,4]=>[3,5,1,2,6,4,7]=>010010=>010010
[5,3,6,2,4,1,7]=>[7,3,5,2,6,1,4]=>101010=>010101
[5,3,6,2,4,7,1]=>[3,5,2,6,4,1,7]=>010110=>011010
[5,3,6,2,7,1,4]=>[3,5,2,6,1,7,4]=>010101=>101010
[5,3,6,2,7,4,1]=>[3,5,2,6,1,4,7]=>010100=>001010
[5,3,6,4,1,2,7]=>[7,3,5,1,4,6,2]=>101001=>100101
[5,3,6,4,1,7,2]=>[3,5,1,4,6,2,7]=>010010=>010010
[5,3,6,4,2,1,7]=>[7,3,5,1,2,4,6]=>101000=>000101
[5,3,6,4,2,7,1]=>[3,5,2,4,6,1,7]=>010010=>010010
[5,3,6,4,7,1,2]=>[3,5,4,6,1,7,2]=>010101=>101010
[5,3,6,4,7,2,1]=>[3,5,4,6,1,2,7]=>010100=>001010
[5,3,6,7,1,2,4]=>[6,3,5,1,7,4,2]=>101011=>110101
[5,3,6,7,1,4,2]=>[6,3,5,1,7,2,4]=>101010=>010101
[5,3,6,7,2,1,4]=>[6,3,5,1,2,7,4]=>101001=>100101
[5,3,6,7,2,4,1]=>[6,3,5,2,7,1,4]=>101010=>010101
[5,3,6,7,4,1,2]=>[6,3,5,1,4,7,2]=>101001=>100101
[5,3,6,7,4,2,1]=>[6,3,5,1,2,4,7]=>101000=>000101
[5,3,7,1,2,4,6]=>[3,5,1,7,6,4,2]=>010111=>111010
[5,3,7,1,2,6,4]=>[3,5,1,7,4,6,2]=>010101=>101010
[5,3,7,1,4,2,6]=>[3,5,1,7,6,2,4]=>010110=>011010
[5,3,7,1,4,6,2]=>[3,5,1,7,4,2,6]=>010110=>011010
[5,3,7,1,6,2,4]=>[3,5,1,7,2,6,4]=>010101=>101010
[5,3,7,1,6,4,2]=>[3,5,1,7,2,4,6]=>010100=>001010
[5,3,7,2,1,4,6]=>[3,5,1,2,7,6,4]=>010011=>110010
[5,3,7,2,1,6,4]=>[3,5,1,2,7,4,6]=>010010=>010010
[5,3,7,2,4,1,6]=>[3,5,2,7,6,1,4]=>010110=>011010
[5,3,7,2,4,6,1]=>[3,5,2,7,4,1,6]=>010110=>011010
[5,3,7,2,6,1,4]=>[3,5,2,7,1,6,4]=>010101=>101010
[5,3,7,2,6,4,1]=>[3,5,2,7,1,4,6]=>010100=>001010
[5,3,7,4,1,2,6]=>[3,5,1,4,7,6,2]=>010011=>110010
[5,3,7,4,1,6,2]=>[3,5,1,4,7,2,6]=>010010=>010010
[5,3,7,4,2,1,6]=>[3,5,1,2,4,7,6]=>010001=>100010
[5,3,7,4,2,6,1]=>[3,5,2,4,7,1,6]=>010010=>010010
[5,3,7,4,6,1,2]=>[3,5,4,7,1,6,2]=>010101=>101010
[5,3,7,4,6,2,1]=>[3,5,4,7,1,2,6]=>010100=>001010
[5,3,7,6,1,2,4]=>[3,5,1,6,7,4,2]=>010011=>110010
[5,3,7,6,1,4,2]=>[3,5,1,6,7,2,4]=>010010=>010010
[5,3,7,6,2,1,4]=>[3,5,1,2,6,7,4]=>010001=>100010
[5,3,7,6,2,4,1]=>[3,5,2,6,7,1,4]=>010010=>010010
[5,3,7,6,4,1,2]=>[3,5,1,4,6,7,2]=>010001=>100010
[5,3,7,6,4,2,1]=>[3,5,1,2,4,6,7]=>010000=>000010
[5,4,1,2,3,6,7]=>[7,6,1,4,5,3,2]=>110011=>110011
[5,4,1,2,3,7,6]=>[6,7,1,4,5,3,2]=>010011=>110010
[5,4,1,2,6,3,7]=>[7,1,4,5,3,6,2]=>100101=>101001
[5,4,1,2,6,7,3]=>[6,1,4,5,3,7,2]=>100101=>101001
[5,4,1,2,7,3,6]=>[1,4,5,3,7,6,2]=>001011=>110100
[5,4,1,2,7,6,3]=>[1,4,5,3,6,7,2]=>001001=>100100
[5,4,1,3,2,6,7]=>[7,6,1,4,5,2,3]=>110010=>010011
[5,4,1,3,2,7,6]=>[6,7,1,4,5,2,3]=>010010=>010010
[5,4,1,3,6,2,7]=>[7,1,4,5,3,2,6]=>100110=>011001
[5,4,1,3,6,7,2]=>[6,1,4,5,3,2,7]=>100110=>011001
[5,4,1,3,7,2,6]=>[1,4,5,3,2,7,6]=>001101=>101100
[5,4,1,3,7,6,2]=>[1,4,5,3,2,6,7]=>001100=>001100
[5,4,1,6,2,3,7]=>[7,1,4,5,2,6,3]=>100101=>101001
[5,4,1,6,2,7,3]=>[1,4,5,2,6,3,7]=>001010=>010100
[5,4,1,6,3,2,7]=>[7,1,4,5,2,3,6]=>100100=>001001
[5,4,1,6,3,7,2]=>[1,4,5,3,6,2,7]=>001010=>010100
[5,4,1,6,7,2,3]=>[6,1,4,5,2,7,3]=>100101=>101001
[5,4,1,6,7,3,2]=>[6,1,4,5,2,3,7]=>100100=>001001
[5,4,1,7,2,3,6]=>[1,4,5,2,7,6,3]=>001011=>110100
[5,4,1,7,2,6,3]=>[1,4,5,2,7,3,6]=>001010=>010100
[5,4,1,7,3,2,6]=>[1,4,5,2,3,7,6]=>001001=>100100
[5,4,1,7,3,6,2]=>[1,4,5,3,7,2,6]=>001010=>010100
[5,4,1,7,6,2,3]=>[1,4,5,2,6,7,3]=>001001=>100100
[5,4,1,7,6,3,2]=>[1,4,5,2,3,6,7]=>001000=>000100
[5,4,2,1,3,6,7]=>[7,6,1,2,4,5,3]=>110001=>100011
[5,4,2,1,3,7,6]=>[6,7,1,2,4,5,3]=>010001=>100010
[5,4,2,1,6,3,7]=>[7,1,2,4,5,3,6]=>100010=>010001
[5,4,2,1,6,7,3]=>[6,1,2,4,5,3,7]=>100010=>010001
[5,4,2,1,7,3,6]=>[1,2,4,5,3,7,6]=>000101=>101000
[5,4,2,1,7,6,3]=>[1,2,4,5,3,6,7]=>000100=>001000
[5,4,2,3,1,6,7]=>[7,6,2,4,5,1,3]=>110010=>010011
[5,4,2,3,1,7,6]=>[6,7,2,4,5,1,3]=>010010=>010010
[5,4,2,3,6,1,7]=>[7,2,4,5,3,1,6]=>100110=>011001
[5,4,2,3,6,7,1]=>[6,2,4,5,3,1,7]=>100110=>011001
[5,4,2,3,7,1,6]=>[2,4,5,3,1,7,6]=>001101=>101100
[5,4,2,3,7,6,1]=>[2,4,5,3,1,6,7]=>001100=>001100
[5,4,2,6,1,3,7]=>[7,2,4,5,1,6,3]=>100101=>101001
[5,4,2,6,1,7,3]=>[2,4,5,1,6,3,7]=>001010=>010100
[5,4,2,6,3,1,7]=>[7,2,4,5,1,3,6]=>100100=>001001
[5,4,2,6,3,7,1]=>[2,4,5,3,6,1,7]=>001010=>010100
[5,4,2,6,7,1,3]=>[6,2,4,5,1,7,3]=>100101=>101001
[5,4,2,6,7,3,1]=>[6,2,4,5,1,3,7]=>100100=>001001
[5,4,2,7,1,3,6]=>[2,4,5,1,7,6,3]=>001011=>110100
[5,4,2,7,1,6,3]=>[2,4,5,1,7,3,6]=>001010=>010100
[5,4,2,7,3,1,6]=>[2,4,5,1,3,7,6]=>001001=>100100
[5,4,2,7,3,6,1]=>[2,4,5,3,7,1,6]=>001010=>010100
[5,4,2,7,6,1,3]=>[2,4,5,1,6,7,3]=>001001=>100100
[5,4,2,7,6,3,1]=>[2,4,5,1,3,6,7]=>001000=>000100
[5,4,3,1,2,6,7]=>[7,6,1,3,4,5,2]=>110001=>100011
[5,4,3,1,2,7,6]=>[6,7,1,3,4,5,2]=>010001=>100010
[5,4,3,1,6,2,7]=>[7,1,3,4,5,2,6]=>100010=>010001
[5,4,3,1,6,7,2]=>[6,1,3,4,5,2,7]=>100010=>010001
[5,4,3,1,7,2,6]=>[1,3,4,5,2,7,6]=>000101=>101000
[5,4,3,1,7,6,2]=>[1,3,4,5,2,6,7]=>000100=>001000
[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>110000=>000011
[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>010000=>000010
[5,4,3,2,6,1,7]=>[7,2,3,4,5,1,6]=>100010=>010001
[5,4,3,2,6,7,1]=>[6,2,3,4,5,1,7]=>100010=>010001
[5,4,3,2,7,1,6]=>[2,3,4,5,1,7,6]=>000101=>101000
[5,4,3,2,7,6,1]=>[2,3,4,5,1,6,7]=>000100=>001000
[5,4,3,6,1,2,7]=>[7,3,4,5,1,6,2]=>100101=>101001
[5,4,3,6,1,7,2]=>[3,4,5,1,6,2,7]=>001010=>010100
[5,4,3,6,2,1,7]=>[7,3,4,5,1,2,6]=>100100=>001001
[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>001010=>010100
[5,4,3,6,7,1,2]=>[6,3,4,5,1,7,2]=>100101=>101001
[5,4,3,6,7,2,1]=>[6,3,4,5,1,2,7]=>100100=>001001
[5,4,3,7,1,2,6]=>[3,4,5,1,7,6,2]=>001011=>110100
[5,4,3,7,1,6,2]=>[3,4,5,1,7,2,6]=>001010=>010100
[5,4,3,7,2,1,6]=>[3,4,5,1,2,7,6]=>001001=>100100
[5,4,3,7,2,6,1]=>[3,4,5,2,7,1,6]=>001010=>010100
[5,4,3,7,6,1,2]=>[3,4,5,1,6,7,2]=>001001=>100100
[5,4,3,7,6,2,1]=>[3,4,5,1,2,6,7]=>001000=>000100
[5,4,6,1,2,3,7]=>[7,4,5,1,6,3,2]=>101011=>110101
[5,4,6,1,2,7,3]=>[4,5,1,6,3,7,2]=>010101=>101010
[5,4,6,1,3,2,7]=>[7,4,5,1,6,2,3]=>101010=>010101
[5,4,6,1,3,7,2]=>[4,5,1,6,3,2,7]=>010110=>011010
[5,4,6,1,7,2,3]=>[4,5,1,6,2,7,3]=>010101=>101010
[5,4,6,1,7,3,2]=>[4,5,1,6,2,3,7]=>010100=>001010
[5,4,6,2,1,3,7]=>[7,4,5,1,2,6,3]=>101001=>100101
[5,4,6,2,1,7,3]=>[4,5,1,2,6,3,7]=>010010=>010010
[5,4,6,2,3,1,7]=>[7,4,5,2,6,1,3]=>101010=>010101
[5,4,6,2,3,7,1]=>[4,5,2,6,3,1,7]=>010110=>011010
[5,4,6,2,7,1,3]=>[4,5,2,6,1,7,3]=>010101=>101010
[5,4,6,2,7,3,1]=>[4,5,2,6,1,3,7]=>010100=>001010
[5,4,6,3,1,2,7]=>[7,4,5,1,3,6,2]=>101001=>100101
[5,4,6,3,1,7,2]=>[4,5,1,3,6,2,7]=>010010=>010010
[5,4,6,3,2,1,7]=>[7,4,5,1,2,3,6]=>101000=>000101
[5,4,6,3,2,7,1]=>[4,5,2,3,6,1,7]=>010010=>010010
[5,4,6,3,7,1,2]=>[4,5,3,6,1,7,2]=>010101=>101010
[5,4,6,3,7,2,1]=>[4,5,3,6,1,2,7]=>010100=>001010
[5,4,6,7,1,2,3]=>[6,4,5,1,7,3,2]=>101011=>110101
[5,4,6,7,1,3,2]=>[6,4,5,1,7,2,3]=>101010=>010101
[5,4,6,7,2,1,3]=>[6,4,5,1,2,7,3]=>101001=>100101
[5,4,6,7,2,3,1]=>[6,4,5,2,7,1,3]=>101010=>010101
[5,4,6,7,3,1,2]=>[6,4,5,1,3,7,2]=>101001=>100101
[5,4,6,7,3,2,1]=>[6,4,5,1,2,3,7]=>101000=>000101
[5,4,7,1,2,3,6]=>[4,5,1,7,6,3,2]=>010111=>111010
[5,4,7,1,2,6,3]=>[4,5,1,7,3,6,2]=>010101=>101010
[5,4,7,1,3,2,6]=>[4,5,1,7,6,2,3]=>010110=>011010
[5,4,7,1,3,6,2]=>[4,5,1,7,3,2,6]=>010110=>011010
[5,4,7,1,6,2,3]=>[4,5,1,7,2,6,3]=>010101=>101010
[5,4,7,1,6,3,2]=>[4,5,1,7,2,3,6]=>010100=>001010
[5,4,7,2,1,3,6]=>[4,5,1,2,7,6,3]=>010011=>110010
[5,4,7,2,1,6,3]=>[4,5,1,2,7,3,6]=>010010=>010010
[5,4,7,2,3,1,6]=>[4,5,2,7,6,1,3]=>010110=>011010
[5,4,7,2,3,6,1]=>[4,5,2,7,3,1,6]=>010110=>011010
[5,4,7,2,6,1,3]=>[4,5,2,7,1,6,3]=>010101=>101010
[5,4,7,2,6,3,1]=>[4,5,2,7,1,3,6]=>010100=>001010
[5,4,7,3,1,2,6]=>[4,5,1,3,7,6,2]=>010011=>110010
[5,4,7,3,1,6,2]=>[4,5,1,3,7,2,6]=>010010=>010010
[5,4,7,3,2,1,6]=>[4,5,1,2,3,7,6]=>010001=>100010
[5,4,7,3,2,6,1]=>[4,5,2,3,7,1,6]=>010010=>010010
[5,4,7,3,6,1,2]=>[4,5,3,7,1,6,2]=>010101=>101010
[5,4,7,3,6,2,1]=>[4,5,3,7,1,2,6]=>010100=>001010
[5,4,7,6,1,2,3]=>[4,5,1,6,7,3,2]=>010011=>110010
[5,4,7,6,1,3,2]=>[4,5,1,6,7,2,3]=>010010=>010010
[5,4,7,6,2,1,3]=>[4,5,1,2,6,7,3]=>010001=>100010
[5,4,7,6,2,3,1]=>[4,5,2,6,7,1,3]=>010010=>010010
[5,4,7,6,3,1,2]=>[4,5,1,3,6,7,2]=>010001=>100010
[5,4,7,6,3,2,1]=>[4,5,1,2,3,6,7]=>010000=>000010
[5,6,1,2,3,4,7]=>[7,5,1,6,4,3,2]=>110111=>111011
[5,6,1,2,3,7,4]=>[5,1,6,4,7,3,2]=>101011=>110101
[5,6,1,2,4,3,7]=>[7,5,1,6,3,4,2]=>110101=>101011
[5,6,1,2,4,7,3]=>[5,1,6,4,3,7,2]=>101101=>101101
[5,6,1,2,7,3,4]=>[5,1,6,3,7,4,2]=>101011=>110101
[5,6,1,2,7,4,3]=>[5,1,6,3,4,7,2]=>101001=>100101
[5,6,1,3,2,4,7]=>[7,5,1,6,4,2,3]=>110110=>011011
[5,6,1,3,2,7,4]=>[5,1,6,4,7,2,3]=>101010=>010101
[5,6,1,3,4,2,7]=>[7,5,1,6,3,2,4]=>110110=>011011
[5,6,1,3,4,7,2]=>[5,1,6,4,3,2,7]=>101110=>011101
[5,6,1,3,7,2,4]=>[5,1,6,3,2,7,4]=>101101=>101101
[5,6,1,3,7,4,2]=>[5,1,6,3,2,4,7]=>101100=>001101
[5,6,1,4,2,3,7]=>[7,5,1,6,2,4,3]=>110101=>101011
[5,6,1,4,2,7,3]=>[5,1,6,2,4,3,7]=>101010=>010101
[5,6,1,4,3,2,7]=>[7,5,1,6,2,3,4]=>110100=>001011
[5,6,1,4,3,7,2]=>[5,1,6,3,4,2,7]=>101010=>010101
[5,6,1,4,7,2,3]=>[5,1,6,4,2,7,3]=>101101=>101101
[5,6,1,4,7,3,2]=>[5,1,6,4,2,3,7]=>101100=>001101
[5,6,1,7,2,3,4]=>[5,1,6,2,7,4,3]=>101011=>110101
[5,6,1,7,2,4,3]=>[5,1,6,2,7,3,4]=>101010=>010101
[5,6,1,7,3,2,4]=>[5,1,6,2,3,7,4]=>101001=>100101
[5,6,1,7,3,4,2]=>[5,1,6,3,7,2,4]=>101010=>010101
[5,6,1,7,4,2,3]=>[5,1,6,2,4,7,3]=>101001=>100101
[5,6,1,7,4,3,2]=>[5,1,6,2,3,4,7]=>101000=>000101
[5,6,2,1,3,4,7]=>[7,5,1,2,6,4,3]=>110011=>110011
[5,6,2,1,3,7,4]=>[5,1,2,6,4,7,3]=>100101=>101001
[5,6,2,1,4,3,7]=>[7,5,1,2,6,3,4]=>110010=>010011
[5,6,2,1,4,7,3]=>[5,1,2,6,4,3,7]=>100110=>011001
[5,6,2,1,7,3,4]=>[5,1,2,6,3,7,4]=>100101=>101001
[5,6,2,1,7,4,3]=>[5,1,2,6,3,4,7]=>100100=>001001
[5,6,2,3,1,4,7]=>[7,5,2,6,4,1,3]=>110110=>011011
[5,6,2,3,1,7,4]=>[5,2,6,4,7,1,3]=>101010=>010101
[5,6,2,3,4,1,7]=>[7,5,2,6,3,1,4]=>110110=>011011
[5,6,2,3,4,7,1]=>[5,2,6,4,3,1,7]=>101110=>011101
[5,6,2,3,7,1,4]=>[5,2,6,3,1,7,4]=>101101=>101101
[5,6,2,3,7,4,1]=>[5,2,6,3,1,4,7]=>101100=>001101
[5,6,2,4,1,3,7]=>[7,5,2,6,1,4,3]=>110101=>101011
[5,6,2,4,1,7,3]=>[5,2,6,1,4,3,7]=>101010=>010101
[5,6,2,4,3,1,7]=>[7,5,2,6,1,3,4]=>110100=>001011
[5,6,2,4,3,7,1]=>[5,2,6,3,4,1,7]=>101010=>010101
[5,6,2,4,7,1,3]=>[5,2,6,4,1,7,3]=>101101=>101101
[5,6,2,4,7,3,1]=>[5,2,6,4,1,3,7]=>101100=>001101
[5,6,2,7,1,3,4]=>[5,2,6,1,7,4,3]=>101011=>110101
[5,6,2,7,1,4,3]=>[5,2,6,1,7,3,4]=>101010=>010101
[5,6,2,7,3,1,4]=>[5,2,6,1,3,7,4]=>101001=>100101
[5,6,2,7,3,4,1]=>[5,2,6,3,7,1,4]=>101010=>010101
[5,6,2,7,4,1,3]=>[5,2,6,1,4,7,3]=>101001=>100101
[5,6,2,7,4,3,1]=>[5,2,6,1,3,4,7]=>101000=>000101
[5,6,3,1,2,4,7]=>[7,5,1,3,6,4,2]=>110011=>110011
[5,6,3,1,2,7,4]=>[5,1,3,6,4,7,2]=>100101=>101001
[5,6,3,1,4,2,7]=>[7,5,1,3,6,2,4]=>110010=>010011
[5,6,3,1,4,7,2]=>[5,1,3,6,4,2,7]=>100110=>011001
[5,6,3,1,7,2,4]=>[5,1,3,6,2,7,4]=>100101=>101001
[5,6,3,1,7,4,2]=>[5,1,3,6,2,4,7]=>100100=>001001
[5,6,3,2,1,4,7]=>[7,5,1,2,3,6,4]=>110001=>100011
[5,6,3,2,1,7,4]=>[5,1,2,3,6,4,7]=>100010=>010001
[5,6,3,2,4,1,7]=>[7,5,2,3,6,1,4]=>110010=>010011
[5,6,3,2,4,7,1]=>[5,2,3,6,4,1,7]=>100110=>011001
[5,6,3,2,7,1,4]=>[5,2,3,6,1,7,4]=>100101=>101001
[5,6,3,2,7,4,1]=>[5,2,3,6,1,4,7]=>100100=>001001
[5,6,3,4,1,2,7]=>[7,5,3,6,1,4,2]=>110101=>101011
[5,6,3,4,1,7,2]=>[5,3,6,1,4,2,7]=>101010=>010101
[5,6,3,4,2,1,7]=>[7,5,3,6,1,2,4]=>110100=>001011
[5,6,3,4,2,7,1]=>[5,3,6,2,4,1,7]=>101010=>010101
[5,6,3,4,7,1,2]=>[5,3,6,4,1,7,2]=>101101=>101101
[5,6,3,4,7,2,1]=>[5,3,6,4,1,2,7]=>101100=>001101
[5,6,3,7,1,2,4]=>[5,3,6,1,7,4,2]=>101011=>110101
[5,6,3,7,1,4,2]=>[5,3,6,1,7,2,4]=>101010=>010101
[5,6,3,7,2,1,4]=>[5,3,6,1,2,7,4]=>101001=>100101
[5,6,3,7,2,4,1]=>[5,3,6,2,7,1,4]=>101010=>010101
[5,6,3,7,4,1,2]=>[5,3,6,1,4,7,2]=>101001=>100101
[5,6,3,7,4,2,1]=>[5,3,6,1,2,4,7]=>101000=>000101
[5,6,4,1,2,3,7]=>[7,5,1,4,6,3,2]=>110011=>110011
[5,6,4,1,2,7,3]=>[5,1,4,6,3,7,2]=>100101=>101001
[5,6,4,1,3,2,7]=>[7,5,1,4,6,2,3]=>110010=>010011
[5,6,4,1,3,7,2]=>[5,1,4,6,3,2,7]=>100110=>011001
[5,6,4,1,7,2,3]=>[5,1,4,6,2,7,3]=>100101=>101001
[5,6,4,1,7,3,2]=>[5,1,4,6,2,3,7]=>100100=>001001
[5,6,4,2,1,3,7]=>[7,5,1,2,4,6,3]=>110001=>100011
[5,6,4,2,1,7,3]=>[5,1,2,4,6,3,7]=>100010=>010001
[5,6,4,2,3,1,7]=>[7,5,2,4,6,1,3]=>110010=>010011
[5,6,4,2,3,7,1]=>[5,2,4,6,3,1,7]=>100110=>011001
[5,6,4,2,7,1,3]=>[5,2,4,6,1,7,3]=>100101=>101001
[5,6,4,2,7,3,1]=>[5,2,4,6,1,3,7]=>100100=>001001
[5,6,4,3,1,2,7]=>[7,5,1,3,4,6,2]=>110001=>100011
[5,6,4,3,1,7,2]=>[5,1,3,4,6,2,7]=>100010=>010001
[5,6,4,3,2,1,7]=>[7,5,1,2,3,4,6]=>110000=>000011
[5,6,4,3,2,7,1]=>[5,2,3,4,6,1,7]=>100010=>010001
[5,6,4,3,7,1,2]=>[5,3,4,6,1,7,2]=>100101=>101001
[5,6,4,3,7,2,1]=>[5,3,4,6,1,2,7]=>100100=>001001
[5,6,4,7,1,2,3]=>[5,4,6,1,7,3,2]=>101011=>110101
[5,6,4,7,1,3,2]=>[5,4,6,1,7,2,3]=>101010=>010101
[5,6,4,7,2,1,3]=>[5,4,6,1,2,7,3]=>101001=>100101
[5,6,4,7,2,3,1]=>[5,4,6,2,7,1,3]=>101010=>010101
[5,6,4,7,3,1,2]=>[5,4,6,1,3,7,2]=>101001=>100101
[5,6,4,7,3,2,1]=>[5,4,6,1,2,3,7]=>101000=>000101
[5,6,7,1,2,3,4]=>[6,5,1,7,4,3,2]=>110111=>111011
[5,6,7,1,2,4,3]=>[6,5,1,7,3,4,2]=>110101=>101011
[5,6,7,1,3,2,4]=>[6,5,1,7,4,2,3]=>110110=>011011
[5,6,7,1,3,4,2]=>[6,5,1,7,3,2,4]=>110110=>011011
[5,6,7,1,4,2,3]=>[6,5,1,7,2,4,3]=>110101=>101011
[5,6,7,1,4,3,2]=>[6,5,1,7,2,3,4]=>110100=>001011
[5,6,7,2,1,3,4]=>[6,5,1,2,7,4,3]=>110011=>110011
[5,6,7,2,1,4,3]=>[6,5,1,2,7,3,4]=>110010=>010011
[5,6,7,2,3,1,4]=>[6,5,2,7,4,1,3]=>110110=>011011
[5,6,7,2,3,4,1]=>[6,5,2,7,3,1,4]=>110110=>011011
[5,6,7,2,4,1,3]=>[6,5,2,7,1,4,3]=>110101=>101011
[5,6,7,2,4,3,1]=>[6,5,2,7,1,3,4]=>110100=>001011
[5,6,7,3,1,2,4]=>[6,5,1,3,7,4,2]=>110011=>110011
[5,6,7,3,1,4,2]=>[6,5,1,3,7,2,4]=>110010=>010011
[5,6,7,3,2,1,4]=>[6,5,1,2,3,7,4]=>110001=>100011
[5,6,7,3,2,4,1]=>[6,5,2,3,7,1,4]=>110010=>010011
[5,6,7,3,4,1,2]=>[6,5,3,7,1,4,2]=>110101=>101011
[5,6,7,3,4,2,1]=>[6,5,3,7,1,2,4]=>110100=>001011
[5,6,7,4,1,2,3]=>[6,5,1,4,7,3,2]=>110011=>110011
[5,6,7,4,1,3,2]=>[6,5,1,4,7,2,3]=>110010=>010011
[5,6,7,4,2,1,3]=>[6,5,1,2,4,7,3]=>110001=>100011
[5,6,7,4,2,3,1]=>[6,5,2,4,7,1,3]=>110010=>010011
[5,6,7,4,3,1,2]=>[6,5,1,3,4,7,2]=>110001=>100011
[5,6,7,4,3,2,1]=>[6,5,1,2,3,4,7]=>110000=>000011
[5,7,1,2,3,4,6]=>[5,1,7,6,4,3,2]=>101111=>111101
[5,7,1,2,3,6,4]=>[5,1,7,4,6,3,2]=>101011=>110101
[5,7,1,2,4,3,6]=>[5,1,7,6,3,4,2]=>101101=>101101
[5,7,1,2,4,6,3]=>[5,1,7,4,3,6,2]=>101101=>101101
[5,7,1,2,6,3,4]=>[5,1,7,3,6,4,2]=>101011=>110101
[5,7,1,2,6,4,3]=>[5,1,7,3,4,6,2]=>101001=>100101
[5,7,1,3,2,4,6]=>[5,1,7,6,4,2,3]=>101110=>011101
[5,7,1,3,2,6,4]=>[5,1,7,4,6,2,3]=>101010=>010101
[5,7,1,3,4,2,6]=>[5,1,7,6,3,2,4]=>101110=>011101
[5,7,1,3,4,6,2]=>[5,1,7,4,3,2,6]=>101110=>011101
[5,7,1,3,6,2,4]=>[5,1,7,3,2,6,4]=>101101=>101101
[5,7,1,3,6,4,2]=>[5,1,7,3,2,4,6]=>101100=>001101
[5,7,1,4,2,3,6]=>[5,1,7,6,2,4,3]=>101101=>101101
[5,7,1,4,2,6,3]=>[5,1,7,2,4,3,6]=>101010=>010101
[5,7,1,4,3,2,6]=>[5,1,7,6,2,3,4]=>101100=>001101
[5,7,1,4,3,6,2]=>[5,1,7,3,4,2,6]=>101010=>010101
[5,7,1,4,6,2,3]=>[5,1,7,4,2,6,3]=>101101=>101101
[5,7,1,4,6,3,2]=>[5,1,7,4,2,3,6]=>101100=>001101
[5,7,1,6,2,3,4]=>[5,1,7,2,6,4,3]=>101011=>110101
[5,7,1,6,2,4,3]=>[5,1,7,2,6,3,4]=>101010=>010101
[5,7,1,6,3,2,4]=>[5,1,7,2,3,6,4]=>101001=>100101
[5,7,1,6,3,4,2]=>[5,1,7,3,6,2,4]=>101010=>010101
[5,7,1,6,4,2,3]=>[5,1,7,2,4,6,3]=>101001=>100101
[5,7,1,6,4,3,2]=>[5,1,7,2,3,4,6]=>101000=>000101
[5,7,2,1,3,4,6]=>[5,1,2,7,6,4,3]=>100111=>111001
[5,7,2,1,3,6,4]=>[5,1,2,7,4,6,3]=>100101=>101001
[5,7,2,1,4,3,6]=>[5,1,2,7,6,3,4]=>100110=>011001
[5,7,2,1,4,6,3]=>[5,1,2,7,4,3,6]=>100110=>011001
[5,7,2,1,6,3,4]=>[5,1,2,7,3,6,4]=>100101=>101001
[5,7,2,1,6,4,3]=>[5,1,2,7,3,4,6]=>100100=>001001
[5,7,2,3,1,4,6]=>[5,2,7,6,4,1,3]=>101110=>011101
[5,7,2,3,1,6,4]=>[5,2,7,4,6,1,3]=>101010=>010101
[5,7,2,3,4,1,6]=>[5,2,7,6,3,1,4]=>101110=>011101
[5,7,2,3,4,6,1]=>[5,2,7,4,3,1,6]=>101110=>011101
[5,7,2,3,6,1,4]=>[5,2,7,3,1,6,4]=>101101=>101101
[5,7,2,3,6,4,1]=>[5,2,7,3,1,4,6]=>101100=>001101
[5,7,2,4,1,3,6]=>[5,2,7,6,1,4,3]=>101101=>101101
[5,7,2,4,1,6,3]=>[5,2,7,1,4,3,6]=>101010=>010101
[5,7,2,4,3,1,6]=>[5,2,7,6,1,3,4]=>101100=>001101
[5,7,2,4,3,6,1]=>[5,2,7,3,4,1,6]=>101010=>010101
[5,7,2,4,6,1,3]=>[5,2,7,4,1,6,3]=>101101=>101101
[5,7,2,4,6,3,1]=>[5,2,7,4,1,3,6]=>101100=>001101
[5,7,2,6,1,3,4]=>[5,2,7,1,6,4,3]=>101011=>110101
[5,7,2,6,1,4,3]=>[5,2,7,1,6,3,4]=>101010=>010101
[5,7,2,6,3,1,4]=>[5,2,7,1,3,6,4]=>101001=>100101
[5,7,2,6,3,4,1]=>[5,2,7,3,6,1,4]=>101010=>010101
[5,7,2,6,4,1,3]=>[5,2,7,1,4,6,3]=>101001=>100101
[5,7,2,6,4,3,1]=>[5,2,7,1,3,4,6]=>101000=>000101
[5,7,3,1,2,4,6]=>[5,1,3,7,6,4,2]=>100111=>111001
[5,7,3,1,2,6,4]=>[5,1,3,7,4,6,2]=>100101=>101001
[5,7,3,1,4,2,6]=>[5,1,3,7,6,2,4]=>100110=>011001
[5,7,3,1,4,6,2]=>[5,1,3,7,4,2,6]=>100110=>011001
[5,7,3,1,6,2,4]=>[5,1,3,7,2,6,4]=>100101=>101001
[5,7,3,1,6,4,2]=>[5,1,3,7,2,4,6]=>100100=>001001
[5,7,3,2,1,4,6]=>[5,1,2,3,7,6,4]=>100011=>110001
[5,7,3,2,1,6,4]=>[5,1,2,3,7,4,6]=>100010=>010001
[5,7,3,2,4,1,6]=>[5,2,3,7,6,1,4]=>100110=>011001
[5,7,3,2,4,6,1]=>[5,2,3,7,4,1,6]=>100110=>011001
[5,7,3,2,6,1,4]=>[5,2,3,7,1,6,4]=>100101=>101001
[5,7,3,2,6,4,1]=>[5,2,3,7,1,4,6]=>100100=>001001
[5,7,3,4,1,2,6]=>[5,3,7,6,1,4,2]=>101101=>101101
[5,7,3,4,1,6,2]=>[5,3,7,1,4,2,6]=>101010=>010101
[5,7,3,4,2,1,6]=>[5,3,7,6,1,2,4]=>101100=>001101
[5,7,3,4,2,6,1]=>[5,3,7,2,4,1,6]=>101010=>010101
[5,7,3,4,6,1,2]=>[5,3,7,4,1,6,2]=>101101=>101101
[5,7,3,4,6,2,1]=>[5,3,7,4,1,2,6]=>101100=>001101
[5,7,3,6,1,2,4]=>[5,3,7,1,6,4,2]=>101011=>110101
[5,7,3,6,1,4,2]=>[5,3,7,1,6,2,4]=>101010=>010101
[5,7,3,6,2,1,4]=>[5,3,7,1,2,6,4]=>101001=>100101
[5,7,3,6,2,4,1]=>[5,3,7,2,6,1,4]=>101010=>010101
[5,7,3,6,4,1,2]=>[5,3,7,1,4,6,2]=>101001=>100101
[5,7,3,6,4,2,1]=>[5,3,7,1,2,4,6]=>101000=>000101
[5,7,4,1,2,3,6]=>[5,1,4,7,6,3,2]=>100111=>111001
[5,7,4,1,2,6,3]=>[5,1,4,7,3,6,2]=>100101=>101001
[5,7,4,1,3,2,6]=>[5,1,4,7,6,2,3]=>100110=>011001
[5,7,4,1,3,6,2]=>[5,1,4,7,3,2,6]=>100110=>011001
[5,7,4,1,6,2,3]=>[5,1,4,7,2,6,3]=>100101=>101001
[5,7,4,1,6,3,2]=>[5,1,4,7,2,3,6]=>100100=>001001
[5,7,4,2,1,3,6]=>[5,1,2,4,7,6,3]=>100011=>110001
[5,7,4,2,1,6,3]=>[5,1,2,4,7,3,6]=>100010=>010001
[5,7,4,2,3,1,6]=>[5,2,4,7,6,1,3]=>100110=>011001
[5,7,4,2,3,6,1]=>[5,2,4,7,3,1,6]=>100110=>011001
[5,7,4,2,6,1,3]=>[5,2,4,7,1,6,3]=>100101=>101001
[5,7,4,2,6,3,1]=>[5,2,4,7,1,3,6]=>100100=>001001
[5,7,4,3,1,2,6]=>[5,1,3,4,7,6,2]=>100011=>110001
[5,7,4,3,1,6,2]=>[5,1,3,4,7,2,6]=>100010=>010001
[5,7,4,3,2,1,6]=>[5,1,2,3,4,7,6]=>100001=>100001
[5,7,4,3,2,6,1]=>[5,2,3,4,7,1,6]=>100010=>010001
[5,7,4,3,6,1,2]=>[5,3,4,7,1,6,2]=>100101=>101001
[5,7,4,3,6,2,1]=>[5,3,4,7,1,2,6]=>100100=>001001
[5,7,4,6,1,2,3]=>[5,4,7,1,6,3,2]=>101011=>110101
[5,7,4,6,1,3,2]=>[5,4,7,1,6,2,3]=>101010=>010101
[5,7,4,6,2,1,3]=>[5,4,7,1,2,6,3]=>101001=>100101
[5,7,4,6,2,3,1]=>[5,4,7,2,6,1,3]=>101010=>010101
[5,7,4,6,3,1,2]=>[5,4,7,1,3,6,2]=>101001=>100101
[5,7,4,6,3,2,1]=>[5,4,7,1,2,3,6]=>101000=>000101
[5,7,6,1,2,3,4]=>[5,1,6,7,4,3,2]=>100111=>111001
[5,7,6,1,2,4,3]=>[5,1,6,7,3,4,2]=>100101=>101001
[5,7,6,1,3,2,4]=>[5,1,6,7,4,2,3]=>100110=>011001
[5,7,6,1,3,4,2]=>[5,1,6,7,3,2,4]=>100110=>011001
[5,7,6,1,4,2,3]=>[5,1,6,7,2,4,3]=>100101=>101001
[5,7,6,1,4,3,2]=>[5,1,6,7,2,3,4]=>100100=>001001
[5,7,6,2,1,3,4]=>[5,1,2,6,7,4,3]=>100011=>110001
[5,7,6,2,1,4,3]=>[5,1,2,6,7,3,4]=>100010=>010001
[5,7,6,2,3,1,4]=>[5,2,6,7,4,1,3]=>100110=>011001
[5,7,6,2,3,4,1]=>[5,2,6,7,3,1,4]=>100110=>011001
[5,7,6,2,4,1,3]=>[5,2,6,7,1,4,3]=>100101=>101001
[5,7,6,2,4,3,1]=>[5,2,6,7,1,3,4]=>100100=>001001
[5,7,6,3,1,2,4]=>[5,1,3,6,7,4,2]=>100011=>110001
[5,7,6,3,1,4,2]=>[5,1,3,6,7,2,4]=>100010=>010001
[5,7,6,3,2,1,4]=>[5,1,2,3,6,7,4]=>100001=>100001
[5,7,6,3,2,4,1]=>[5,2,3,6,7,1,4]=>100010=>010001
[5,7,6,3,4,1,2]=>[5,3,6,7,1,4,2]=>100101=>101001
[5,7,6,3,4,2,1]=>[5,3,6,7,1,2,4]=>100100=>001001
[5,7,6,4,1,2,3]=>[5,1,4,6,7,3,2]=>100011=>110001
[5,7,6,4,1,3,2]=>[5,1,4,6,7,2,3]=>100010=>010001
[5,7,6,4,2,1,3]=>[5,1,2,4,6,7,3]=>100001=>100001
[5,7,6,4,2,3,1]=>[5,2,4,6,7,1,3]=>100010=>010001
[5,7,6,4,3,1,2]=>[5,1,3,4,6,7,2]=>100001=>100001
[5,7,6,4,3,2,1]=>[5,1,2,3,4,6,7]=>100000=>000001
[6,1,2,3,4,5,7]=>[7,1,6,5,4,3,2]=>101111=>111101
[6,1,2,3,4,7,5]=>[1,6,5,7,4,3,2]=>010111=>111010
[6,1,2,3,5,4,7]=>[7,1,6,4,5,3,2]=>101011=>110101
[6,1,2,3,5,7,4]=>[1,6,5,4,7,3,2]=>011011=>110110
[6,1,2,3,7,4,5]=>[1,6,4,7,5,3,2]=>010111=>111010
[6,1,2,3,7,5,4]=>[1,6,4,5,7,3,2]=>010011=>110010
[6,1,2,4,3,5,7]=>[7,1,6,5,3,4,2]=>101101=>101101
[6,1,2,4,3,7,5]=>[1,6,5,7,3,4,2]=>010101=>101010
[6,1,2,4,5,3,7]=>[7,1,6,4,3,5,2]=>101101=>101101
[6,1,2,4,5,7,3]=>[1,6,5,4,3,7,2]=>011101=>101110
[6,1,2,4,7,3,5]=>[1,6,4,3,7,5,2]=>011011=>110110
[6,1,2,4,7,5,3]=>[1,6,4,3,5,7,2]=>011001=>100110
[6,1,2,5,3,4,7]=>[7,1,6,3,5,4,2]=>101011=>110101
[6,1,2,5,3,7,4]=>[1,6,3,5,4,7,2]=>010101=>101010
[6,1,2,5,4,3,7]=>[7,1,6,3,4,5,2]=>101001=>100101
[6,1,2,5,4,7,3]=>[1,6,4,5,3,7,2]=>010101=>101010
[6,1,2,5,7,3,4]=>[1,6,5,3,7,4,2]=>011011=>110110
[6,1,2,5,7,4,3]=>[1,6,5,3,4,7,2]=>011001=>100110
[6,1,2,7,3,4,5]=>[1,6,3,7,5,4,2]=>010111=>111010
[6,1,2,7,3,5,4]=>[1,6,3,7,4,5,2]=>010101=>101010
[6,1,2,7,4,3,5]=>[1,6,3,4,7,5,2]=>010011=>110010
[6,1,2,7,4,5,3]=>[1,6,4,7,3,5,2]=>010101=>101010
[6,1,2,7,5,3,4]=>[1,6,3,5,7,4,2]=>010011=>110010
[6,1,2,7,5,4,3]=>[1,6,3,4,5,7,2]=>010001=>100010
[6,1,3,2,4,5,7]=>[7,1,6,5,4,2,3]=>101110=>011101
[6,1,3,2,4,7,5]=>[1,6,5,7,4,2,3]=>010110=>011010
[6,1,3,2,5,4,7]=>[7,1,6,4,5,2,3]=>101010=>010101
[6,1,3,2,5,7,4]=>[1,6,5,4,7,2,3]=>011010=>010110
[6,1,3,2,7,4,5]=>[1,6,4,7,5,2,3]=>010110=>011010
[6,1,3,2,7,5,4]=>[1,6,4,5,7,2,3]=>010010=>010010
[6,1,3,4,2,5,7]=>[7,1,6,5,3,2,4]=>101110=>011101
[6,1,3,4,2,7,5]=>[1,6,5,7,3,2,4]=>010110=>011010
[6,1,3,4,5,2,7]=>[7,1,6,4,3,2,5]=>101110=>011101
[6,1,3,4,5,7,2]=>[1,6,5,4,3,2,7]=>011110=>011110
[6,1,3,4,7,2,5]=>[1,6,4,3,2,7,5]=>011101=>101110
[6,1,3,4,7,5,2]=>[1,6,4,3,2,5,7]=>011100=>001110
[6,1,3,5,2,4,7]=>[7,1,6,3,2,5,4]=>101101=>101101
[6,1,3,5,2,7,4]=>[1,6,3,2,5,4,7]=>011010=>010110
[6,1,3,5,4,2,7]=>[7,1,6,3,2,4,5]=>101100=>001101
[6,1,3,5,4,7,2]=>[1,6,4,5,3,2,7]=>010110=>011010
[6,1,3,5,7,2,4]=>[1,6,5,3,2,7,4]=>011101=>101110
[6,1,3,5,7,4,2]=>[1,6,5,3,2,4,7]=>011100=>001110
[6,1,3,7,2,4,5]=>[1,6,3,2,7,5,4]=>011011=>110110
[6,1,3,7,2,5,4]=>[1,6,3,2,7,4,5]=>011010=>010110
[6,1,3,7,4,2,5]=>[1,6,3,2,4,7,5]=>011001=>100110
[6,1,3,7,4,5,2]=>[1,6,4,7,3,2,5]=>010110=>011010
[6,1,3,7,5,2,4]=>[1,6,3,2,5,7,4]=>011001=>100110
[6,1,3,7,5,4,2]=>[1,6,3,2,4,5,7]=>011000=>000110
[6,1,4,2,3,5,7]=>[7,1,6,5,2,4,3]=>101101=>101101
[6,1,4,2,3,7,5]=>[1,6,5,7,2,4,3]=>010101=>101010
[6,1,4,2,5,3,7]=>[7,1,6,2,4,3,5]=>101010=>010101
[6,1,4,2,5,7,3]=>[1,6,5,2,4,3,7]=>011010=>010110
[6,1,4,2,7,3,5]=>[1,6,2,4,3,7,5]=>010101=>101010
[6,1,4,2,7,5,3]=>[1,6,2,4,3,5,7]=>010100=>001010
[6,1,4,3,2,5,7]=>[7,1,6,5,2,3,4]=>101100=>001101
[6,1,4,3,2,7,5]=>[1,6,5,7,2,3,4]=>010100=>001010
[6,1,4,3,5,2,7]=>[7,1,6,3,4,2,5]=>101010=>010101
[6,1,4,3,5,7,2]=>[1,6,5,3,4,2,7]=>011010=>010110
[6,1,4,3,7,2,5]=>[1,6,3,4,2,7,5]=>010101=>101010
[6,1,4,3,7,5,2]=>[1,6,3,4,2,5,7]=>010100=>001010
[6,1,4,5,2,3,7]=>[7,1,6,4,2,5,3]=>101101=>101101
[6,1,4,5,2,7,3]=>[1,6,4,2,5,3,7]=>011010=>010110
[6,1,4,5,3,2,7]=>[7,1,6,4,2,3,5]=>101100=>001101
[6,1,4,5,3,7,2]=>[1,6,4,3,5,2,7]=>011010=>010110
[6,1,4,5,7,2,3]=>[1,6,5,4,2,7,3]=>011101=>101110
[6,1,4,5,7,3,2]=>[1,6,5,4,2,3,7]=>011100=>001110
[6,1,4,7,2,3,5]=>[1,6,4,2,7,5,3]=>011011=>110110
[6,1,4,7,2,5,3]=>[1,6,4,2,7,3,5]=>011010=>010110
[6,1,4,7,3,2,5]=>[1,6,4,2,3,7,5]=>011001=>100110
[6,1,4,7,3,5,2]=>[1,6,4,3,7,2,5]=>011010=>010110
[6,1,4,7,5,2,3]=>[1,6,4,2,5,7,3]=>011001=>100110
[6,1,4,7,5,3,2]=>[1,6,4,2,3,5,7]=>011000=>000110
[6,1,5,2,3,4,7]=>[7,1,6,2,5,4,3]=>101011=>110101
[6,1,5,2,3,7,4]=>[1,6,2,5,4,7,3]=>010101=>101010
[6,1,5,2,4,3,7]=>[7,1,6,2,5,3,4]=>101010=>010101
[6,1,5,2,4,7,3]=>[1,6,2,5,4,3,7]=>010110=>011010
[6,1,5,2,7,3,4]=>[1,6,2,5,3,7,4]=>010101=>101010
[6,1,5,2,7,4,3]=>[1,6,2,5,3,4,7]=>010100=>001010
[6,1,5,3,2,4,7]=>[7,1,6,2,3,5,4]=>101001=>100101
[6,1,5,3,2,7,4]=>[1,6,2,3,5,4,7]=>010010=>010010
[6,1,5,3,4,2,7]=>[7,1,6,3,5,2,4]=>101010=>010101
[6,1,5,3,4,7,2]=>[1,6,3,5,4,2,7]=>010110=>011010
[6,1,5,3,7,2,4]=>[1,6,3,5,2,7,4]=>010101=>101010
[6,1,5,3,7,4,2]=>[1,6,3,5,2,4,7]=>010100=>001010
[6,1,5,4,2,3,7]=>[7,1,6,2,4,5,3]=>101001=>100101
[6,1,5,4,2,7,3]=>[1,6,2,4,5,3,7]=>010010=>010010
[6,1,5,4,3,2,7]=>[7,1,6,2,3,4,5]=>101000=>000101
[6,1,5,4,3,7,2]=>[1,6,3,4,5,2,7]=>010010=>010010
[6,1,5,4,7,2,3]=>[1,6,4,5,2,7,3]=>010101=>101010
[6,1,5,4,7,3,2]=>[1,6,4,5,2,3,7]=>010100=>001010
[6,1,5,7,2,3,4]=>[1,6,5,2,7,4,3]=>011011=>110110
[6,1,5,7,2,4,3]=>[1,6,5,2,7,3,4]=>011010=>010110
[6,1,5,7,3,2,4]=>[1,6,5,2,3,7,4]=>011001=>100110
[6,1,5,7,3,4,2]=>[1,6,5,3,7,2,4]=>011010=>010110
[6,1,5,7,4,2,3]=>[1,6,5,2,4,7,3]=>011001=>100110
[6,1,5,7,4,3,2]=>[1,6,5,2,3,4,7]=>011000=>000110
[6,1,7,2,3,4,5]=>[1,6,2,7,5,4,3]=>010111=>111010
[6,1,7,2,3,5,4]=>[1,6,2,7,4,5,3]=>010101=>101010
[6,1,7,2,4,3,5]=>[1,6,2,7,5,3,4]=>010110=>011010
[6,1,7,2,4,5,3]=>[1,6,2,7,4,3,5]=>010110=>011010
[6,1,7,2,5,3,4]=>[1,6,2,7,3,5,4]=>010101=>101010
[6,1,7,2,5,4,3]=>[1,6,2,7,3,4,5]=>010100=>001010
[6,1,7,3,2,4,5]=>[1,6,2,3,7,5,4]=>010011=>110010
[6,1,7,3,2,5,4]=>[1,6,2,3,7,4,5]=>010010=>010010
[6,1,7,3,4,2,5]=>[1,6,3,7,5,2,4]=>010110=>011010
[6,1,7,3,4,5,2]=>[1,6,3,7,4,2,5]=>010110=>011010
[6,1,7,3,5,2,4]=>[1,6,3,7,2,5,4]=>010101=>101010
[6,1,7,3,5,4,2]=>[1,6,3,7,2,4,5]=>010100=>001010
[6,1,7,4,2,3,5]=>[1,6,2,4,7,5,3]=>010011=>110010
[6,1,7,4,2,5,3]=>[1,6,2,4,7,3,5]=>010010=>010010
[6,1,7,4,3,2,5]=>[1,6,2,3,4,7,5]=>010001=>100010
[6,1,7,4,3,5,2]=>[1,6,3,4,7,2,5]=>010010=>010010
[6,1,7,4,5,2,3]=>[1,6,4,7,2,5,3]=>010101=>101010
[6,1,7,4,5,3,2]=>[1,6,4,7,2,3,5]=>010100=>001010
[6,1,7,5,2,3,4]=>[1,6,2,5,7,4,3]=>010011=>110010
[6,1,7,5,2,4,3]=>[1,6,2,5,7,3,4]=>010010=>010010
[6,1,7,5,3,2,4]=>[1,6,2,3,5,7,4]=>010001=>100010
[6,1,7,5,3,4,2]=>[1,6,3,5,7,2,4]=>010010=>010010
[6,1,7,5,4,2,3]=>[1,6,2,4,5,7,3]=>010001=>100010
[6,1,7,5,4,3,2]=>[1,6,2,3,4,5,7]=>010000=>000010
[6,2,1,3,4,5,7]=>[7,1,2,6,5,4,3]=>100111=>111001
[6,2,1,3,4,7,5]=>[1,2,6,5,7,4,3]=>001011=>110100
[6,2,1,3,5,4,7]=>[7,1,2,6,4,5,3]=>100101=>101001
[6,2,1,3,5,7,4]=>[1,2,6,5,4,7,3]=>001101=>101100
[6,2,1,3,7,4,5]=>[1,2,6,4,7,5,3]=>001011=>110100
[6,2,1,3,7,5,4]=>[1,2,6,4,5,7,3]=>001001=>100100
[6,2,1,4,3,5,7]=>[7,1,2,6,5,3,4]=>100110=>011001
[6,2,1,4,3,7,5]=>[1,2,6,5,7,3,4]=>001010=>010100
[6,2,1,4,5,3,7]=>[7,1,2,6,4,3,5]=>100110=>011001
[6,2,1,4,5,7,3]=>[1,2,6,5,4,3,7]=>001110=>011100
[6,2,1,4,7,3,5]=>[1,2,6,4,3,7,5]=>001101=>101100
[6,2,1,4,7,5,3]=>[1,2,6,4,3,5,7]=>001100=>001100
[6,2,1,5,3,4,7]=>[7,1,2,6,3,5,4]=>100101=>101001
[6,2,1,5,3,7,4]=>[1,2,6,3,5,4,7]=>001010=>010100
[6,2,1,5,4,3,7]=>[7,1,2,6,3,4,5]=>100100=>001001
[6,2,1,5,4,7,3]=>[1,2,6,4,5,3,7]=>001010=>010100
[6,2,1,5,7,3,4]=>[1,2,6,5,3,7,4]=>001101=>101100
[6,2,1,5,7,4,3]=>[1,2,6,5,3,4,7]=>001100=>001100
[6,2,1,7,3,4,5]=>[1,2,6,3,7,5,4]=>001011=>110100
[6,2,1,7,3,5,4]=>[1,2,6,3,7,4,5]=>001010=>010100
[6,2,1,7,4,3,5]=>[1,2,6,3,4,7,5]=>001001=>100100
[6,2,1,7,4,5,3]=>[1,2,6,4,7,3,5]=>001010=>010100
[6,2,1,7,5,3,4]=>[1,2,6,3,5,7,4]=>001001=>100100
[6,2,1,7,5,4,3]=>[1,2,6,3,4,5,7]=>001000=>000100
[6,2,3,1,4,5,7]=>[7,2,6,5,4,1,3]=>101110=>011101
[6,2,3,1,4,7,5]=>[2,6,5,7,4,1,3]=>010110=>011010
[6,2,3,1,5,4,7]=>[7,2,6,4,5,1,3]=>101010=>010101
[6,2,3,1,5,7,4]=>[2,6,5,4,7,1,3]=>011010=>010110
[6,2,3,1,7,4,5]=>[2,6,4,7,5,1,3]=>010110=>011010
[6,2,3,1,7,5,4]=>[2,6,4,5,7,1,3]=>010010=>010010
[6,2,3,4,1,5,7]=>[7,2,6,5,3,1,4]=>101110=>011101
[6,2,3,4,1,7,5]=>[2,6,5,7,3,1,4]=>010110=>011010
[6,2,3,4,5,1,7]=>[7,2,6,4,3,1,5]=>101110=>011101
[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>011110=>011110
[6,2,3,4,7,1,5]=>[2,6,4,3,1,7,5]=>011101=>101110
[6,2,3,4,7,5,1]=>[2,6,4,3,1,5,7]=>011100=>001110
[6,2,3,5,1,4,7]=>[7,2,6,3,1,5,4]=>101101=>101101
[6,2,3,5,1,7,4]=>[2,6,3,1,5,4,7]=>011010=>010110
[6,2,3,5,4,1,7]=>[7,2,6,3,1,4,5]=>101100=>001101
[6,2,3,5,4,7,1]=>[2,6,4,5,3,1,7]=>010110=>011010
[6,2,3,5,7,1,4]=>[2,6,5,3,1,7,4]=>011101=>101110
[6,2,3,5,7,4,1]=>[2,6,5,3,1,4,7]=>011100=>001110
[6,2,3,7,1,4,5]=>[2,6,3,1,7,5,4]=>011011=>110110
[6,2,3,7,1,5,4]=>[2,6,3,1,7,4,5]=>011010=>010110
[6,2,3,7,4,1,5]=>[2,6,3,1,4,7,5]=>011001=>100110
[6,2,3,7,4,5,1]=>[2,6,4,7,3,1,5]=>010110=>011010
[6,2,3,7,5,1,4]=>[2,6,3,1,5,7,4]=>011001=>100110
[6,2,3,7,5,4,1]=>[2,6,3,1,4,5,7]=>011000=>000110
[6,2,4,1,3,5,7]=>[7,2,6,5,1,4,3]=>101101=>101101
[6,2,4,1,3,7,5]=>[2,6,5,7,1,4,3]=>010101=>101010
[6,2,4,1,5,3,7]=>[7,2,6,1,4,3,5]=>101010=>010101
[6,2,4,1,5,7,3]=>[2,6,5,1,4,3,7]=>011010=>010110
[6,2,4,1,7,3,5]=>[2,6,1,4,3,7,5]=>010101=>101010
[6,2,4,1,7,5,3]=>[2,6,1,4,3,5,7]=>010100=>001010
[6,2,4,3,1,5,7]=>[7,2,6,5,1,3,4]=>101100=>001101
[6,2,4,3,1,7,5]=>[2,6,5,7,1,3,4]=>010100=>001010
[6,2,4,3,5,1,7]=>[7,2,6,3,4,1,5]=>101010=>010101
[6,2,4,3,5,7,1]=>[2,6,5,3,4,1,7]=>011010=>010110
[6,2,4,3,7,1,5]=>[2,6,3,4,1,7,5]=>010101=>101010
[6,2,4,3,7,5,1]=>[2,6,3,4,1,5,7]=>010100=>001010
[6,2,4,5,1,3,7]=>[7,2,6,4,1,5,3]=>101101=>101101
[6,2,4,5,1,7,3]=>[2,6,4,1,5,3,7]=>011010=>010110
[6,2,4,5,3,1,7]=>[7,2,6,4,1,3,5]=>101100=>001101
[6,2,4,5,3,7,1]=>[2,6,4,3,5,1,7]=>011010=>010110
[6,2,4,5,7,1,3]=>[2,6,5,4,1,7,3]=>011101=>101110
[6,2,4,5,7,3,1]=>[2,6,5,4,1,3,7]=>011100=>001110
[6,2,4,7,1,3,5]=>[2,6,4,1,7,5,3]=>011011=>110110
[6,2,4,7,1,5,3]=>[2,6,4,1,7,3,5]=>011010=>010110
[6,2,4,7,3,1,5]=>[2,6,4,1,3,7,5]=>011001=>100110
[6,2,4,7,3,5,1]=>[2,6,4,3,7,1,5]=>011010=>010110
[6,2,4,7,5,1,3]=>[2,6,4,1,5,7,3]=>011001=>100110
[6,2,4,7,5,3,1]=>[2,6,4,1,3,5,7]=>011000=>000110
[6,2,5,1,3,4,7]=>[7,2,6,1,5,4,3]=>101011=>110101
[6,2,5,1,3,7,4]=>[2,6,1,5,4,7,3]=>010101=>101010
[6,2,5,1,4,3,7]=>[7,2,6,1,5,3,4]=>101010=>010101
[6,2,5,1,4,7,3]=>[2,6,1,5,4,3,7]=>010110=>011010
[6,2,5,1,7,3,4]=>[2,6,1,5,3,7,4]=>010101=>101010
[6,2,5,1,7,4,3]=>[2,6,1,5,3,4,7]=>010100=>001010
[6,2,5,3,1,4,7]=>[7,2,6,1,3,5,4]=>101001=>100101
[6,2,5,3,1,7,4]=>[2,6,1,3,5,4,7]=>010010=>010010
[6,2,5,3,4,1,7]=>[7,2,6,3,5,1,4]=>101010=>010101
[6,2,5,3,4,7,1]=>[2,6,3,5,4,1,7]=>010110=>011010
[6,2,5,3,7,1,4]=>[2,6,3,5,1,7,4]=>010101=>101010
[6,2,5,3,7,4,1]=>[2,6,3,5,1,4,7]=>010100=>001010
[6,2,5,4,1,3,7]=>[7,2,6,1,4,5,3]=>101001=>100101
[6,2,5,4,1,7,3]=>[2,6,1,4,5,3,7]=>010010=>010010
[6,2,5,4,3,1,7]=>[7,2,6,1,3,4,5]=>101000=>000101
[6,2,5,4,3,7,1]=>[2,6,3,4,5,1,7]=>010010=>010010
[6,2,5,4,7,1,3]=>[2,6,4,5,1,7,3]=>010101=>101010
[6,2,5,4,7,3,1]=>[2,6,4,5,1,3,7]=>010100=>001010
[6,2,5,7,1,3,4]=>[2,6,5,1,7,4,3]=>011011=>110110
[6,2,5,7,1,4,3]=>[2,6,5,1,7,3,4]=>011010=>010110
[6,2,5,7,3,1,4]=>[2,6,5,1,3,7,4]=>011001=>100110
[6,2,5,7,3,4,1]=>[2,6,5,3,7,1,4]=>011010=>010110
[6,2,5,7,4,1,3]=>[2,6,5,1,4,7,3]=>011001=>100110
[6,2,5,7,4,3,1]=>[2,6,5,1,3,4,7]=>011000=>000110
[6,2,7,1,3,4,5]=>[2,6,1,7,5,4,3]=>010111=>111010
[6,2,7,1,3,5,4]=>[2,6,1,7,4,5,3]=>010101=>101010
[6,2,7,1,4,3,5]=>[2,6,1,7,5,3,4]=>010110=>011010
[6,2,7,1,4,5,3]=>[2,6,1,7,4,3,5]=>010110=>011010
[6,2,7,1,5,3,4]=>[2,6,1,7,3,5,4]=>010101=>101010
[6,2,7,1,5,4,3]=>[2,6,1,7,3,4,5]=>010100=>001010
[6,2,7,3,1,4,5]=>[2,6,1,3,7,5,4]=>010011=>110010
[6,2,7,3,1,5,4]=>[2,6,1,3,7,4,5]=>010010=>010010
[6,2,7,3,4,1,5]=>[2,6,3,7,5,1,4]=>010110=>011010
[6,2,7,3,4,5,1]=>[2,6,3,7,4,1,5]=>010110=>011010
[6,2,7,3,5,1,4]=>[2,6,3,7,1,5,4]=>010101=>101010
[6,2,7,3,5,4,1]=>[2,6,3,7,1,4,5]=>010100=>001010
[6,2,7,4,1,3,5]=>[2,6,1,4,7,5,3]=>010011=>110010
[6,2,7,4,1,5,3]=>[2,6,1,4,7,3,5]=>010010=>010010
[6,2,7,4,3,1,5]=>[2,6,1,3,4,7,5]=>010001=>100010
[6,2,7,4,3,5,1]=>[2,6,3,4,7,1,5]=>010010=>010010
[6,2,7,4,5,1,3]=>[2,6,4,7,1,5,3]=>010101=>101010
[6,2,7,4,5,3,1]=>[2,6,4,7,1,3,5]=>010100=>001010
[6,2,7,5,1,3,4]=>[2,6,1,5,7,4,3]=>010011=>110010
[6,2,7,5,1,4,3]=>[2,6,1,5,7,3,4]=>010010=>010010
[6,2,7,5,3,1,4]=>[2,6,1,3,5,7,4]=>010001=>100010
[6,2,7,5,3,4,1]=>[2,6,3,5,7,1,4]=>010010=>010010
[6,2,7,5,4,1,3]=>[2,6,1,4,5,7,3]=>010001=>100010
[6,2,7,5,4,3,1]=>[2,6,1,3,4,5,7]=>010000=>000010
[6,3,1,2,4,5,7]=>[7,1,3,6,5,4,2]=>100111=>111001
[6,3,1,2,4,7,5]=>[1,3,6,5,7,4,2]=>001011=>110100
[6,3,1,2,5,4,7]=>[7,1,3,6,4,5,2]=>100101=>101001
[6,3,1,2,5,7,4]=>[1,3,6,5,4,7,2]=>001101=>101100
[6,3,1,2,7,4,5]=>[1,3,6,4,7,5,2]=>001011=>110100
[6,3,1,2,7,5,4]=>[1,3,6,4,5,7,2]=>001001=>100100
[6,3,1,4,2,5,7]=>[7,1,3,6,5,2,4]=>100110=>011001
[6,3,1,4,2,7,5]=>[1,3,6,5,7,2,4]=>001010=>010100
[6,3,1,4,5,2,7]=>[7,1,3,6,4,2,5]=>100110=>011001
[6,3,1,4,5,7,2]=>[1,3,6,5,4,2,7]=>001110=>011100
[6,3,1,4,7,2,5]=>[1,3,6,4,2,7,5]=>001101=>101100
[6,3,1,4,7,5,2]=>[1,3,6,4,2,5,7]=>001100=>001100
[6,3,1,5,2,4,7]=>[7,1,3,6,2,5,4]=>100101=>101001
[6,3,1,5,2,7,4]=>[1,3,6,2,5,4,7]=>001010=>010100
[6,3,1,5,4,2,7]=>[7,1,3,6,2,4,5]=>100100=>001001
[6,3,1,5,4,7,2]=>[1,3,6,4,5,2,7]=>001010=>010100
[6,3,1,5,7,2,4]=>[1,3,6,5,2,7,4]=>001101=>101100
[6,3,1,5,7,4,2]=>[1,3,6,5,2,4,7]=>001100=>001100
[6,3,1,7,2,4,5]=>[1,3,6,2,7,5,4]=>001011=>110100
[6,3,1,7,2,5,4]=>[1,3,6,2,7,4,5]=>001010=>010100
[6,3,1,7,4,2,5]=>[1,3,6,2,4,7,5]=>001001=>100100
[6,3,1,7,4,5,2]=>[1,3,6,4,7,2,5]=>001010=>010100
[6,3,1,7,5,2,4]=>[1,3,6,2,5,7,4]=>001001=>100100
[6,3,1,7,5,4,2]=>[1,3,6,2,4,5,7]=>001000=>000100
[6,3,2,1,4,5,7]=>[7,1,2,3,6,5,4]=>100011=>110001
[6,3,2,1,4,7,5]=>[1,2,3,6,5,7,4]=>000101=>101000
[6,3,2,1,5,4,7]=>[7,1,2,3,6,4,5]=>100010=>010001
[6,3,2,1,5,7,4]=>[1,2,3,6,5,4,7]=>000110=>011000
[6,3,2,1,7,4,5]=>[1,2,3,6,4,7,5]=>000101=>101000
[6,3,2,1,7,5,4]=>[1,2,3,6,4,5,7]=>000100=>001000
[6,3,2,4,1,5,7]=>[7,2,3,6,5,1,4]=>100110=>011001
[6,3,2,4,1,7,5]=>[2,3,6,5,7,1,4]=>001010=>010100
[6,3,2,4,5,1,7]=>[7,2,3,6,4,1,5]=>100110=>011001
[6,3,2,4,5,7,1]=>[2,3,6,5,4,1,7]=>001110=>011100
[6,3,2,4,7,1,5]=>[2,3,6,4,1,7,5]=>001101=>101100
[6,3,2,4,7,5,1]=>[2,3,6,4,1,5,7]=>001100=>001100
[6,3,2,5,1,4,7]=>[7,2,3,6,1,5,4]=>100101=>101001
[6,3,2,5,1,7,4]=>[2,3,6,1,5,4,7]=>001010=>010100
[6,3,2,5,4,1,7]=>[7,2,3,6,1,4,5]=>100100=>001001
[6,3,2,5,4,7,1]=>[2,3,6,4,5,1,7]=>001010=>010100
[6,3,2,5,7,1,4]=>[2,3,6,5,1,7,4]=>001101=>101100
[6,3,2,5,7,4,1]=>[2,3,6,5,1,4,7]=>001100=>001100
[6,3,2,7,1,4,5]=>[2,3,6,1,7,5,4]=>001011=>110100
[6,3,2,7,1,5,4]=>[2,3,6,1,7,4,5]=>001010=>010100
[6,3,2,7,4,1,5]=>[2,3,6,1,4,7,5]=>001001=>100100
[6,3,2,7,4,5,1]=>[2,3,6,4,7,1,5]=>001010=>010100
[6,3,2,7,5,1,4]=>[2,3,6,1,5,7,4]=>001001=>100100
[6,3,2,7,5,4,1]=>[2,3,6,1,4,5,7]=>001000=>000100
[6,3,4,1,2,5,7]=>[7,3,6,5,1,4,2]=>101101=>101101
[6,3,4,1,2,7,5]=>[3,6,5,7,1,4,2]=>010101=>101010
[6,3,4,1,5,2,7]=>[7,3,6,1,4,2,5]=>101010=>010101
[6,3,4,1,5,7,2]=>[3,6,5,1,4,2,7]=>011010=>010110
[6,3,4,1,7,2,5]=>[3,6,1,4,2,7,5]=>010101=>101010
[6,3,4,1,7,5,2]=>[3,6,1,4,2,5,7]=>010100=>001010
[6,3,4,2,1,5,7]=>[7,3,6,5,1,2,4]=>101100=>001101
[6,3,4,2,1,7,5]=>[3,6,5,7,1,2,4]=>010100=>001010
[6,3,4,2,5,1,7]=>[7,3,6,2,4,1,5]=>101010=>010101
[6,3,4,2,5,7,1]=>[3,6,5,2,4,1,7]=>011010=>010110
[6,3,4,2,7,1,5]=>[3,6,2,4,1,7,5]=>010101=>101010
[6,3,4,2,7,5,1]=>[3,6,2,4,1,5,7]=>010100=>001010
[6,3,4,5,1,2,7]=>[7,3,6,4,1,5,2]=>101101=>101101
[6,3,4,5,1,7,2]=>[3,6,4,1,5,2,7]=>011010=>010110
[6,3,4,5,2,1,7]=>[7,3,6,4,1,2,5]=>101100=>001101
[6,3,4,5,2,7,1]=>[3,6,4,2,5,1,7]=>011010=>010110
[6,3,4,5,7,1,2]=>[3,6,5,4,1,7,2]=>011101=>101110
[6,3,4,5,7,2,1]=>[3,6,5,4,1,2,7]=>011100=>001110
[6,3,4,7,1,2,5]=>[3,6,4,1,7,5,2]=>011011=>110110
[6,3,4,7,1,5,2]=>[3,6,4,1,7,2,5]=>011010=>010110
[6,3,4,7,2,1,5]=>[3,6,4,1,2,7,5]=>011001=>100110
[6,3,4,7,2,5,1]=>[3,6,4,2,7,1,5]=>011010=>010110
[6,3,4,7,5,1,2]=>[3,6,4,1,5,7,2]=>011001=>100110
[6,3,4,7,5,2,1]=>[3,6,4,1,2,5,7]=>011000=>000110
[6,3,5,1,2,4,7]=>[7,3,6,1,5,4,2]=>101011=>110101
[6,3,5,1,2,7,4]=>[3,6,1,5,4,7,2]=>010101=>101010
[6,3,5,1,4,2,7]=>[7,3,6,1,5,2,4]=>101010=>010101
[6,3,5,1,4,7,2]=>[3,6,1,5,4,2,7]=>010110=>011010
[6,3,5,1,7,2,4]=>[3,6,1,5,2,7,4]=>010101=>101010
[6,3,5,1,7,4,2]=>[3,6,1,5,2,4,7]=>010100=>001010
[6,3,5,2,1,4,7]=>[7,3,6,1,2,5,4]=>101001=>100101
[6,3,5,2,1,7,4]=>[3,6,1,2,5,4,7]=>010010=>010010
[6,3,5,2,4,1,7]=>[7,3,6,2,5,1,4]=>101010=>010101
[6,3,5,2,4,7,1]=>[3,6,2,5,4,1,7]=>010110=>011010
[6,3,5,2,7,1,4]=>[3,6,2,5,1,7,4]=>010101=>101010
[6,3,5,2,7,4,1]=>[3,6,2,5,1,4,7]=>010100=>001010
[6,3,5,4,1,2,7]=>[7,3,6,1,4,5,2]=>101001=>100101
[6,3,5,4,1,7,2]=>[3,6,1,4,5,2,7]=>010010=>010010
[6,3,5,4,2,1,7]=>[7,3,6,1,2,4,5]=>101000=>000101
[6,3,5,4,2,7,1]=>[3,6,2,4,5,1,7]=>010010=>010010
[6,3,5,4,7,1,2]=>[3,6,4,5,1,7,2]=>010101=>101010
[6,3,5,4,7,2,1]=>[3,6,4,5,1,2,7]=>010100=>001010
[6,3,5,7,1,2,4]=>[3,6,5,1,7,4,2]=>011011=>110110
[6,3,5,7,1,4,2]=>[3,6,5,1,7,2,4]=>011010=>010110
[6,3,5,7,2,1,4]=>[3,6,5,1,2,7,4]=>011001=>100110
[6,3,5,7,2,4,1]=>[3,6,5,2,7,1,4]=>011010=>010110
[6,3,5,7,4,1,2]=>[3,6,5,1,4,7,2]=>011001=>100110
[6,3,5,7,4,2,1]=>[3,6,5,1,2,4,7]=>011000=>000110
[6,3,7,1,2,4,5]=>[3,6,1,7,5,4,2]=>010111=>111010
[6,3,7,1,2,5,4]=>[3,6,1,7,4,5,2]=>010101=>101010
[6,3,7,1,4,2,5]=>[3,6,1,7,5,2,4]=>010110=>011010
[6,3,7,1,4,5,2]=>[3,6,1,7,4,2,5]=>010110=>011010
[6,3,7,1,5,2,4]=>[3,6,1,7,2,5,4]=>010101=>101010
[6,3,7,1,5,4,2]=>[3,6,1,7,2,4,5]=>010100=>001010
[6,3,7,2,1,4,5]=>[3,6,1,2,7,5,4]=>010011=>110010
[6,3,7,2,1,5,4]=>[3,6,1,2,7,4,5]=>010010=>010010
[6,3,7,2,4,1,5]=>[3,6,2,7,5,1,4]=>010110=>011010
[6,3,7,2,4,5,1]=>[3,6,2,7,4,1,5]=>010110=>011010
[6,3,7,2,5,1,4]=>[3,6,2,7,1,5,4]=>010101=>101010
[6,3,7,2,5,4,1]=>[3,6,2,7,1,4,5]=>010100=>001010
[6,3,7,4,1,2,5]=>[3,6,1,4,7,5,2]=>010011=>110010
[6,3,7,4,1,5,2]=>[3,6,1,4,7,2,5]=>010010=>010010
[6,3,7,4,2,1,5]=>[3,6,1,2,4,7,5]=>010001=>100010
[6,3,7,4,2,5,1]=>[3,6,2,4,7,1,5]=>010010=>010010
[6,3,7,4,5,1,2]=>[3,6,4,7,1,5,2]=>010101=>101010
[6,3,7,4,5,2,1]=>[3,6,4,7,1,2,5]=>010100=>001010
[6,3,7,5,1,2,4]=>[3,6,1,5,7,4,2]=>010011=>110010
[6,3,7,5,1,4,2]=>[3,6,1,5,7,2,4]=>010010=>010010
[6,3,7,5,2,1,4]=>[3,6,1,2,5,7,4]=>010001=>100010
[6,3,7,5,2,4,1]=>[3,6,2,5,7,1,4]=>010010=>010010
[6,3,7,5,4,1,2]=>[3,6,1,4,5,7,2]=>010001=>100010
[6,3,7,5,4,2,1]=>[3,6,1,2,4,5,7]=>010000=>000010
[6,4,1,2,3,5,7]=>[7,1,4,6,5,3,2]=>100111=>111001
[6,4,1,2,3,7,5]=>[1,4,6,5,7,3,2]=>001011=>110100
[6,4,1,2,5,3,7]=>[7,1,4,6,3,5,2]=>100101=>101001
[6,4,1,2,5,7,3]=>[1,4,6,5,3,7,2]=>001101=>101100
[6,4,1,2,7,3,5]=>[1,4,6,3,7,5,2]=>001011=>110100
[6,4,1,2,7,5,3]=>[1,4,6,3,5,7,2]=>001001=>100100
[6,4,1,3,2,5,7]=>[7,1,4,6,5,2,3]=>100110=>011001
[6,4,1,3,2,7,5]=>[1,4,6,5,7,2,3]=>001010=>010100
[6,4,1,3,5,2,7]=>[7,1,4,6,3,2,5]=>100110=>011001
[6,4,1,3,5,7,2]=>[1,4,6,5,3,2,7]=>001110=>011100
[6,4,1,3,7,2,5]=>[1,4,6,3,2,7,5]=>001101=>101100
[6,4,1,3,7,5,2]=>[1,4,6,3,2,5,7]=>001100=>001100
[6,4,1,5,2,3,7]=>[7,1,4,6,2,5,3]=>100101=>101001
[6,4,1,5,2,7,3]=>[1,4,6,2,5,3,7]=>001010=>010100
[6,4,1,5,3,2,7]=>[7,1,4,6,2,3,5]=>100100=>001001
[6,4,1,5,3,7,2]=>[1,4,6,3,5,2,7]=>001010=>010100
[6,4,1,5,7,2,3]=>[1,4,6,5,2,7,3]=>001101=>101100
[6,4,1,5,7,3,2]=>[1,4,6,5,2,3,7]=>001100=>001100
[6,4,1,7,2,3,5]=>[1,4,6,2,7,5,3]=>001011=>110100
[6,4,1,7,2,5,3]=>[1,4,6,2,7,3,5]=>001010=>010100
[6,4,1,7,3,2,5]=>[1,4,6,2,3,7,5]=>001001=>100100
[6,4,1,7,3,5,2]=>[1,4,6,3,7,2,5]=>001010=>010100
[6,4,1,7,5,2,3]=>[1,4,6,2,5,7,3]=>001001=>100100
[6,4,1,7,5,3,2]=>[1,4,6,2,3,5,7]=>001000=>000100
[6,4,2,1,3,5,7]=>[7,1,2,4,6,5,3]=>100011=>110001
[6,4,2,1,3,7,5]=>[1,2,4,6,5,7,3]=>000101=>101000
[6,4,2,1,5,3,7]=>[7,1,2,4,6,3,5]=>100010=>010001
[6,4,2,1,5,7,3]=>[1,2,4,6,5,3,7]=>000110=>011000
[6,4,2,1,7,3,5]=>[1,2,4,6,3,7,5]=>000101=>101000
[6,4,2,1,7,5,3]=>[1,2,4,6,3,5,7]=>000100=>001000
[6,4,2,3,1,5,7]=>[7,2,4,6,5,1,3]=>100110=>011001
[6,4,2,3,1,7,5]=>[2,4,6,5,7,1,3]=>001010=>010100
[6,4,2,3,5,1,7]=>[7,2,4,6,3,1,5]=>100110=>011001
[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>001110=>011100
[6,4,2,3,7,1,5]=>[2,4,6,3,1,7,5]=>001101=>101100
[6,4,2,3,7,5,1]=>[2,4,6,3,1,5,7]=>001100=>001100
[6,4,2,5,1,3,7]=>[7,2,4,6,1,5,3]=>100101=>101001
[6,4,2,5,1,7,3]=>[2,4,6,1,5,3,7]=>001010=>010100
[6,4,2,5,3,1,7]=>[7,2,4,6,1,3,5]=>100100=>001001
[6,4,2,5,3,7,1]=>[2,4,6,3,5,1,7]=>001010=>010100
[6,4,2,5,7,1,3]=>[2,4,6,5,1,7,3]=>001101=>101100
[6,4,2,5,7,3,1]=>[2,4,6,5,1,3,7]=>001100=>001100
[6,4,2,7,1,3,5]=>[2,4,6,1,7,5,3]=>001011=>110100
[6,4,2,7,1,5,3]=>[2,4,6,1,7,3,5]=>001010=>010100
[6,4,2,7,3,1,5]=>[2,4,6,1,3,7,5]=>001001=>100100
[6,4,2,7,3,5,1]=>[2,4,6,3,7,1,5]=>001010=>010100
[6,4,2,7,5,1,3]=>[2,4,6,1,5,7,3]=>001001=>100100
[6,4,2,7,5,3,1]=>[2,4,6,1,3,5,7]=>001000=>000100
[6,4,3,1,2,5,7]=>[7,1,3,4,6,5,2]=>100011=>110001
[6,4,3,1,2,7,5]=>[1,3,4,6,5,7,2]=>000101=>101000
[6,4,3,1,5,2,7]=>[7,1,3,4,6,2,5]=>100010=>010001
[6,4,3,1,5,7,2]=>[1,3,4,6,5,2,7]=>000110=>011000
[6,4,3,1,7,2,5]=>[1,3,4,6,2,7,5]=>000101=>101000
[6,4,3,1,7,5,2]=>[1,3,4,6,2,5,7]=>000100=>001000
[6,4,3,2,1,5,7]=>[7,1,2,3,4,6,5]=>100001=>100001
[6,4,3,2,1,7,5]=>[1,2,3,4,6,5,7]=>000010=>010000
[6,4,3,2,5,1,7]=>[7,2,3,4,6,1,5]=>100010=>010001
[6,4,3,2,5,7,1]=>[2,3,4,6,5,1,7]=>000110=>011000
[6,4,3,2,7,1,5]=>[2,3,4,6,1,7,5]=>000101=>101000
[6,4,3,2,7,5,1]=>[2,3,4,6,1,5,7]=>000100=>001000
[6,4,3,5,1,2,7]=>[7,3,4,6,1,5,2]=>100101=>101001
[6,4,3,5,1,7,2]=>[3,4,6,1,5,2,7]=>001010=>010100
[6,4,3,5,2,1,7]=>[7,3,4,6,1,2,5]=>100100=>001001
[6,4,3,5,2,7,1]=>[3,4,6,2,5,1,7]=>001010=>010100
[6,4,3,5,7,1,2]=>[3,4,6,5,1,7,2]=>001101=>101100
[6,4,3,5,7,2,1]=>[3,4,6,5,1,2,7]=>001100=>001100
[6,4,3,7,1,2,5]=>[3,4,6,1,7,5,2]=>001011=>110100
[6,4,3,7,1,5,2]=>[3,4,6,1,7,2,5]=>001010=>010100
[6,4,3,7,2,1,5]=>[3,4,6,1,2,7,5]=>001001=>100100
[6,4,3,7,2,5,1]=>[3,4,6,2,7,1,5]=>001010=>010100
[6,4,3,7,5,1,2]=>[3,4,6,1,5,7,2]=>001001=>100100
[6,4,3,7,5,2,1]=>[3,4,6,1,2,5,7]=>001000=>000100
[6,4,5,1,2,3,7]=>[7,4,6,1,5,3,2]=>101011=>110101
[6,4,5,1,2,7,3]=>[4,6,1,5,3,7,2]=>010101=>101010
[6,4,5,1,3,2,7]=>[7,4,6,1,5,2,3]=>101010=>010101
[6,4,5,1,3,7,2]=>[4,6,1,5,3,2,7]=>010110=>011010
[6,4,5,1,7,2,3]=>[4,6,1,5,2,7,3]=>010101=>101010
[6,4,5,1,7,3,2]=>[4,6,1,5,2,3,7]=>010100=>001010
[6,4,5,2,1,3,7]=>[7,4,6,1,2,5,3]=>101001=>100101
[6,4,5,2,1,7,3]=>[4,6,1,2,5,3,7]=>010010=>010010
[6,4,5,2,3,1,7]=>[7,4,6,2,5,1,3]=>101010=>010101
[6,4,5,2,3,7,1]=>[4,6,2,5,3,1,7]=>010110=>011010
[6,4,5,2,7,1,3]=>[4,6,2,5,1,7,3]=>010101=>101010
[6,4,5,2,7,3,1]=>[4,6,2,5,1,3,7]=>010100=>001010
[6,4,5,3,1,2,7]=>[7,4,6,1,3,5,2]=>101001=>100101
[6,4,5,3,1,7,2]=>[4,6,1,3,5,2,7]=>010010=>010010
[6,4,5,3,2,1,7]=>[7,4,6,1,2,3,5]=>101000=>000101
[6,4,5,3,2,7,1]=>[4,6,2,3,5,1,7]=>010010=>010010
[6,4,5,3,7,1,2]=>[4,6,3,5,1,7,2]=>010101=>101010
[6,4,5,3,7,2,1]=>[4,6,3,5,1,2,7]=>010100=>001010
[6,4,5,7,1,2,3]=>[4,6,5,1,7,3,2]=>011011=>110110
[6,4,5,7,1,3,2]=>[4,6,5,1,7,2,3]=>011010=>010110
[6,4,5,7,2,1,3]=>[4,6,5,1,2,7,3]=>011001=>100110
[6,4,5,7,2,3,1]=>[4,6,5,2,7,1,3]=>011010=>010110
[6,4,5,7,3,1,2]=>[4,6,5,1,3,7,2]=>011001=>100110
[6,4,5,7,3,2,1]=>[4,6,5,1,2,3,7]=>011000=>000110
[6,4,7,1,2,3,5]=>[4,6,1,7,5,3,2]=>010111=>111010
[6,4,7,1,2,5,3]=>[4,6,1,7,3,5,2]=>010101=>101010
[6,4,7,1,3,2,5]=>[4,6,1,7,5,2,3]=>010110=>011010
[6,4,7,1,3,5,2]=>[4,6,1,7,3,2,5]=>010110=>011010
[6,4,7,1,5,2,3]=>[4,6,1,7,2,5,3]=>010101=>101010
[6,4,7,1,5,3,2]=>[4,6,1,7,2,3,5]=>010100=>001010
[6,4,7,2,1,3,5]=>[4,6,1,2,7,5,3]=>010011=>110010
[6,4,7,2,1,5,3]=>[4,6,1,2,7,3,5]=>010010=>010010
[6,4,7,2,3,1,5]=>[4,6,2,7,5,1,3]=>010110=>011010
[6,4,7,2,3,5,1]=>[4,6,2,7,3,1,5]=>010110=>011010
[6,4,7,2,5,1,3]=>[4,6,2,7,1,5,3]=>010101=>101010
[6,4,7,2,5,3,1]=>[4,6,2,7,1,3,5]=>010100=>001010
[6,4,7,3,1,2,5]=>[4,6,1,3,7,5,2]=>010011=>110010
[6,4,7,3,1,5,2]=>[4,6,1,3,7,2,5]=>010010=>010010
[6,4,7,3,2,1,5]=>[4,6,1,2,3,7,5]=>010001=>100010
[6,4,7,3,2,5,1]=>[4,6,2,3,7,1,5]=>010010=>010010
[6,4,7,3,5,1,2]=>[4,6,3,7,1,5,2]=>010101=>101010
[6,4,7,3,5,2,1]=>[4,6,3,7,1,2,5]=>010100=>001010
[6,4,7,5,1,2,3]=>[4,6,1,5,7,3,2]=>010011=>110010
[6,4,7,5,1,3,2]=>[4,6,1,5,7,2,3]=>010010=>010010
[6,4,7,5,2,1,3]=>[4,6,1,2,5,7,3]=>010001=>100010
[6,4,7,5,2,3,1]=>[4,6,2,5,7,1,3]=>010010=>010010
[6,4,7,5,3,1,2]=>[4,6,1,3,5,7,2]=>010001=>100010
[6,4,7,5,3,2,1]=>[4,6,1,2,3,5,7]=>010000=>000010
[6,5,1,2,3,4,7]=>[7,1,5,6,4,3,2]=>100111=>111001
[6,5,1,2,3,7,4]=>[1,5,6,4,7,3,2]=>001011=>110100
[6,5,1,2,4,3,7]=>[7,1,5,6,3,4,2]=>100101=>101001
[6,5,1,2,4,7,3]=>[1,5,6,4,3,7,2]=>001101=>101100
[6,5,1,2,7,3,4]=>[1,5,6,3,7,4,2]=>001011=>110100
[6,5,1,2,7,4,3]=>[1,5,6,3,4,7,2]=>001001=>100100
[6,5,1,3,2,4,7]=>[7,1,5,6,4,2,3]=>100110=>011001
[6,5,1,3,2,7,4]=>[1,5,6,4,7,2,3]=>001010=>010100
[6,5,1,3,4,2,7]=>[7,1,5,6,3,2,4]=>100110=>011001
[6,5,1,3,4,7,2]=>[1,5,6,4,3,2,7]=>001110=>011100
[6,5,1,3,7,2,4]=>[1,5,6,3,2,7,4]=>001101=>101100
[6,5,1,3,7,4,2]=>[1,5,6,3,2,4,7]=>001100=>001100
[6,5,1,4,2,3,7]=>[7,1,5,6,2,4,3]=>100101=>101001
[6,5,1,4,2,7,3]=>[1,5,6,2,4,3,7]=>001010=>010100
[6,5,1,4,3,2,7]=>[7,1,5,6,2,3,4]=>100100=>001001
[6,5,1,4,3,7,2]=>[1,5,6,3,4,2,7]=>001010=>010100
[6,5,1,4,7,2,3]=>[1,5,6,4,2,7,3]=>001101=>101100
[6,5,1,4,7,3,2]=>[1,5,6,4,2,3,7]=>001100=>001100
[6,5,1,7,2,3,4]=>[1,5,6,2,7,4,3]=>001011=>110100
[6,5,1,7,2,4,3]=>[1,5,6,2,7,3,4]=>001010=>010100
[6,5,1,7,3,2,4]=>[1,5,6,2,3,7,4]=>001001=>100100
[6,5,1,7,3,4,2]=>[1,5,6,3,7,2,4]=>001010=>010100
[6,5,1,7,4,2,3]=>[1,5,6,2,4,7,3]=>001001=>100100
[6,5,1,7,4,3,2]=>[1,5,6,2,3,4,7]=>001000=>000100
[6,5,2,1,3,4,7]=>[7,1,2,5,6,4,3]=>100011=>110001
[6,5,2,1,3,7,4]=>[1,2,5,6,4,7,3]=>000101=>101000
[6,5,2,1,4,3,7]=>[7,1,2,5,6,3,4]=>100010=>010001
[6,5,2,1,4,7,3]=>[1,2,5,6,4,3,7]=>000110=>011000
[6,5,2,1,7,3,4]=>[1,2,5,6,3,7,4]=>000101=>101000
[6,5,2,1,7,4,3]=>[1,2,5,6,3,4,7]=>000100=>001000
[6,5,2,3,1,4,7]=>[7,2,5,6,4,1,3]=>100110=>011001
[6,5,2,3,1,7,4]=>[2,5,6,4,7,1,3]=>001010=>010100
[6,5,2,3,4,1,7]=>[7,2,5,6,3,1,4]=>100110=>011001
[6,5,2,3,4,7,1]=>[2,5,6,4,3,1,7]=>001110=>011100
[6,5,2,3,7,1,4]=>[2,5,6,3,1,7,4]=>001101=>101100
[6,5,2,3,7,4,1]=>[2,5,6,3,1,4,7]=>001100=>001100
[6,5,2,4,1,3,7]=>[7,2,5,6,1,4,3]=>100101=>101001
[6,5,2,4,1,7,3]=>[2,5,6,1,4,3,7]=>001010=>010100
[6,5,2,4,3,1,7]=>[7,2,5,6,1,3,4]=>100100=>001001
[6,5,2,4,3,7,1]=>[2,5,6,3,4,1,7]=>001010=>010100
[6,5,2,4,7,1,3]=>[2,5,6,4,1,7,3]=>001101=>101100
[6,5,2,4,7,3,1]=>[2,5,6,4,1,3,7]=>001100=>001100
[6,5,2,7,1,3,4]=>[2,5,6,1,7,4,3]=>001011=>110100
[6,5,2,7,1,4,3]=>[2,5,6,1,7,3,4]=>001010=>010100
[6,5,2,7,3,1,4]=>[2,5,6,1,3,7,4]=>001001=>100100
[6,5,2,7,3,4,1]=>[2,5,6,3,7,1,4]=>001010=>010100
[6,5,2,7,4,1,3]=>[2,5,6,1,4,7,3]=>001001=>100100
[6,5,2,7,4,3,1]=>[2,5,6,1,3,4,7]=>001000=>000100
[6,5,3,1,2,4,7]=>[7,1,3,5,6,4,2]=>100011=>110001
[6,5,3,1,2,7,4]=>[1,3,5,6,4,7,2]=>000101=>101000
[6,5,3,1,4,2,7]=>[7,1,3,5,6,2,4]=>100010=>010001
[6,5,3,1,4,7,2]=>[1,3,5,6,4,2,7]=>000110=>011000
[6,5,3,1,7,2,4]=>[1,3,5,6,2,7,4]=>000101=>101000
[6,5,3,1,7,4,2]=>[1,3,5,6,2,4,7]=>000100=>001000
[6,5,3,2,1,4,7]=>[7,1,2,3,5,6,4]=>100001=>100001
[6,5,3,2,1,7,4]=>[1,2,3,5,6,4,7]=>000010=>010000
[6,5,3,2,4,1,7]=>[7,2,3,5,6,1,4]=>100010=>010001
[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>000110=>011000
[6,5,3,2,7,1,4]=>[2,3,5,6,1,7,4]=>000101=>101000
[6,5,3,2,7,4,1]=>[2,3,5,6,1,4,7]=>000100=>001000
[6,5,3,4,1,2,7]=>[7,3,5,6,1,4,2]=>100101=>101001
[6,5,3,4,1,7,2]=>[3,5,6,1,4,2,7]=>001010=>010100
[6,5,3,4,2,1,7]=>[7,3,5,6,1,2,4]=>100100=>001001
[6,5,3,4,2,7,1]=>[3,5,6,2,4,1,7]=>001010=>010100
[6,5,3,4,7,1,2]=>[3,5,6,4,1,7,2]=>001101=>101100
[6,5,3,4,7,2,1]=>[3,5,6,4,1,2,7]=>001100=>001100
[6,5,3,7,1,2,4]=>[3,5,6,1,7,4,2]=>001011=>110100
[6,5,3,7,1,4,2]=>[3,5,6,1,7,2,4]=>001010=>010100
[6,5,3,7,2,1,4]=>[3,5,6,1,2,7,4]=>001001=>100100
[6,5,3,7,2,4,1]=>[3,5,6,2,7,1,4]=>001010=>010100
[6,5,3,7,4,1,2]=>[3,5,6,1,4,7,2]=>001001=>100100
[6,5,3,7,4,2,1]=>[3,5,6,1,2,4,7]=>001000=>000100
[6,5,4,1,2,3,7]=>[7,1,4,5,6,3,2]=>100011=>110001
[6,5,4,1,2,7,3]=>[1,4,5,6,3,7,2]=>000101=>101000
[6,5,4,1,3,2,7]=>[7,1,4,5,6,2,3]=>100010=>010001
[6,5,4,1,3,7,2]=>[1,4,5,6,3,2,7]=>000110=>011000
[6,5,4,1,7,2,3]=>[1,4,5,6,2,7,3]=>000101=>101000
[6,5,4,1,7,3,2]=>[1,4,5,6,2,3,7]=>000100=>001000
[6,5,4,2,1,3,7]=>[7,1,2,4,5,6,3]=>100001=>100001
[6,5,4,2,1,7,3]=>[1,2,4,5,6,3,7]=>000010=>010000
[6,5,4,2,3,1,7]=>[7,2,4,5,6,1,3]=>100010=>010001
[6,5,4,2,3,7,1]=>[2,4,5,6,3,1,7]=>000110=>011000
[6,5,4,2,7,1,3]=>[2,4,5,6,1,7,3]=>000101=>101000
[6,5,4,2,7,3,1]=>[2,4,5,6,1,3,7]=>000100=>001000
[6,5,4,3,1,2,7]=>[7,1,3,4,5,6,2]=>100001=>100001
[6,5,4,3,1,7,2]=>[1,3,4,5,6,2,7]=>000010=>010000
[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>100000=>000001
[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>000010=>010000
[6,5,4,3,7,1,2]=>[3,4,5,6,1,7,2]=>000101=>101000
[6,5,4,3,7,2,1]=>[3,4,5,6,1,2,7]=>000100=>001000
[6,5,4,7,1,2,3]=>[4,5,6,1,7,3,2]=>001011=>110100
[6,5,4,7,1,3,2]=>[4,5,6,1,7,2,3]=>001010=>010100
[6,5,4,7,2,1,3]=>[4,5,6,1,2,7,3]=>001001=>100100
[6,5,4,7,2,3,1]=>[4,5,6,2,7,1,3]=>001010=>010100
[6,5,4,7,3,1,2]=>[4,5,6,1,3,7,2]=>001001=>100100
[6,5,4,7,3,2,1]=>[4,5,6,1,2,3,7]=>001000=>000100
[6,5,7,1,2,3,4]=>[5,6,1,7,4,3,2]=>010111=>111010
[6,5,7,1,2,4,3]=>[5,6,1,7,3,4,2]=>010101=>101010
[6,5,7,1,3,2,4]=>[5,6,1,7,4,2,3]=>010110=>011010
[6,5,7,1,3,4,2]=>[5,6,1,7,3,2,4]=>010110=>011010
[6,5,7,1,4,2,3]=>[5,6,1,7,2,4,3]=>010101=>101010
[6,5,7,1,4,3,2]=>[5,6,1,7,2,3,4]=>010100=>001010
[6,5,7,2,1,3,4]=>[5,6,1,2,7,4,3]=>010011=>110010
[6,5,7,2,1,4,3]=>[5,6,1,2,7,3,4]=>010010=>010010
[6,5,7,2,3,1,4]=>[5,6,2,7,4,1,3]=>010110=>011010
[6,5,7,2,3,4,1]=>[5,6,2,7,3,1,4]=>010110=>011010
[6,5,7,2,4,1,3]=>[5,6,2,7,1,4,3]=>010101=>101010
[6,5,7,2,4,3,1]=>[5,6,2,7,1,3,4]=>010100=>001010
[6,5,7,3,1,2,4]=>[5,6,1,3,7,4,2]=>010011=>110010
[6,5,7,3,1,4,2]=>[5,6,1,3,7,2,4]=>010010=>010010
[6,5,7,3,2,1,4]=>[5,6,1,2,3,7,4]=>010001=>100010
[6,5,7,3,2,4,1]=>[5,6,2,3,7,1,4]=>010010=>010010
[6,5,7,3,4,1,2]=>[5,6,3,7,1,4,2]=>010101=>101010
[6,5,7,3,4,2,1]=>[5,6,3,7,1,2,4]=>010100=>001010
[6,5,7,4,1,2,3]=>[5,6,1,4,7,3,2]=>010011=>110010
[6,5,7,4,1,3,2]=>[5,6,1,4,7,2,3]=>010010=>010010
[6,5,7,4,2,1,3]=>[5,6,1,2,4,7,3]=>010001=>100010
[6,5,7,4,2,3,1]=>[5,6,2,4,7,1,3]=>010010=>010010
[6,5,7,4,3,1,2]=>[5,6,1,3,4,7,2]=>010001=>100010
[6,5,7,4,3,2,1]=>[5,6,1,2,3,4,7]=>010000=>000010
[6,7,1,2,3,4,5]=>[6,1,7,5,4,3,2]=>101111=>111101
[6,7,1,2,3,5,4]=>[6,1,7,4,5,3,2]=>101011=>110101
[6,7,1,2,4,3,5]=>[6,1,7,5,3,4,2]=>101101=>101101
[6,7,1,2,4,5,3]=>[6,1,7,4,3,5,2]=>101101=>101101
[6,7,1,2,5,3,4]=>[6,1,7,3,5,4,2]=>101011=>110101
[6,7,1,2,5,4,3]=>[6,1,7,3,4,5,2]=>101001=>100101
[6,7,1,3,2,4,5]=>[6,1,7,5,4,2,3]=>101110=>011101
[6,7,1,3,2,5,4]=>[6,1,7,4,5,2,3]=>101010=>010101
[6,7,1,3,4,2,5]=>[6,1,7,5,3,2,4]=>101110=>011101
[6,7,1,3,4,5,2]=>[6,1,7,4,3,2,5]=>101110=>011101
[6,7,1,3,5,2,4]=>[6,1,7,3,2,5,4]=>101101=>101101
[6,7,1,3,5,4,2]=>[6,1,7,3,2,4,5]=>101100=>001101
[6,7,1,4,2,3,5]=>[6,1,7,5,2,4,3]=>101101=>101101
[6,7,1,4,2,5,3]=>[6,1,7,2,4,3,5]=>101010=>010101
[6,7,1,4,3,2,5]=>[6,1,7,5,2,3,4]=>101100=>001101
[6,7,1,4,3,5,2]=>[6,1,7,3,4,2,5]=>101010=>010101
[6,7,1,4,5,2,3]=>[6,1,7,4,2,5,3]=>101101=>101101
[6,7,1,4,5,3,2]=>[6,1,7,4,2,3,5]=>101100=>001101
[6,7,1,5,2,3,4]=>[6,1,7,2,5,4,3]=>101011=>110101
[6,7,1,5,2,4,3]=>[6,1,7,2,5,3,4]=>101010=>010101
[6,7,1,5,3,2,4]=>[6,1,7,2,3,5,4]=>101001=>100101
[6,7,1,5,3,4,2]=>[6,1,7,3,5,2,4]=>101010=>010101
[6,7,1,5,4,2,3]=>[6,1,7,2,4,5,3]=>101001=>100101
[6,7,1,5,4,3,2]=>[6,1,7,2,3,4,5]=>101000=>000101
[6,7,2,1,3,4,5]=>[6,1,2,7,5,4,3]=>100111=>111001
[6,7,2,1,3,5,4]=>[6,1,2,7,4,5,3]=>100101=>101001
[6,7,2,1,4,3,5]=>[6,1,2,7,5,3,4]=>100110=>011001
[6,7,2,1,4,5,3]=>[6,1,2,7,4,3,5]=>100110=>011001
[6,7,2,1,5,3,4]=>[6,1,2,7,3,5,4]=>100101=>101001
[6,7,2,1,5,4,3]=>[6,1,2,7,3,4,5]=>100100=>001001
[6,7,2,3,1,4,5]=>[6,2,7,5,4,1,3]=>101110=>011101
[6,7,2,3,1,5,4]=>[6,2,7,4,5,1,3]=>101010=>010101
[6,7,2,3,4,1,5]=>[6,2,7,5,3,1,4]=>101110=>011101
[6,7,2,3,4,5,1]=>[6,2,7,4,3,1,5]=>101110=>011101
[6,7,2,3,5,1,4]=>[6,2,7,3,1,5,4]=>101101=>101101
[6,7,2,3,5,4,1]=>[6,2,7,3,1,4,5]=>101100=>001101
[6,7,2,4,1,3,5]=>[6,2,7,5,1,4,3]=>101101=>101101
[6,7,2,4,1,5,3]=>[6,2,7,1,4,3,5]=>101010=>010101
[6,7,2,4,3,1,5]=>[6,2,7,5,1,3,4]=>101100=>001101
[6,7,2,4,3,5,1]=>[6,2,7,3,4,1,5]=>101010=>010101
[6,7,2,4,5,1,3]=>[6,2,7,4,1,5,3]=>101101=>101101
[6,7,2,4,5,3,1]=>[6,2,7,4,1,3,5]=>101100=>001101
[6,7,2,5,1,3,4]=>[6,2,7,1,5,4,3]=>101011=>110101
[6,7,2,5,1,4,3]=>[6,2,7,1,5,3,4]=>101010=>010101
[6,7,2,5,3,1,4]=>[6,2,7,1,3,5,4]=>101001=>100101
[6,7,2,5,3,4,1]=>[6,2,7,3,5,1,4]=>101010=>010101
[6,7,2,5,4,1,3]=>[6,2,7,1,4,5,3]=>101001=>100101
[6,7,2,5,4,3,1]=>[6,2,7,1,3,4,5]=>101000=>000101
[6,7,3,1,2,4,5]=>[6,1,3,7,5,4,2]=>100111=>111001
[6,7,3,1,2,5,4]=>[6,1,3,7,4,5,2]=>100101=>101001
[6,7,3,1,4,2,5]=>[6,1,3,7,5,2,4]=>100110=>011001
[6,7,3,1,4,5,2]=>[6,1,3,7,4,2,5]=>100110=>011001
[6,7,3,1,5,2,4]=>[6,1,3,7,2,5,4]=>100101=>101001
[6,7,3,1,5,4,2]=>[6,1,3,7,2,4,5]=>100100=>001001
[6,7,3,2,1,4,5]=>[6,1,2,3,7,5,4]=>100011=>110001
[6,7,3,2,1,5,4]=>[6,1,2,3,7,4,5]=>100010=>010001
[6,7,3,2,4,1,5]=>[6,2,3,7,5,1,4]=>100110=>011001
[6,7,3,2,4,5,1]=>[6,2,3,7,4,1,5]=>100110=>011001
[6,7,3,2,5,1,4]=>[6,2,3,7,1,5,4]=>100101=>101001
[6,7,3,2,5,4,1]=>[6,2,3,7,1,4,5]=>100100=>001001
[6,7,3,4,1,2,5]=>[6,3,7,5,1,4,2]=>101101=>101101
[6,7,3,4,1,5,2]=>[6,3,7,1,4,2,5]=>101010=>010101
[6,7,3,4,2,1,5]=>[6,3,7,5,1,2,4]=>101100=>001101
[6,7,3,4,2,5,1]=>[6,3,7,2,4,1,5]=>101010=>010101
[6,7,3,4,5,1,2]=>[6,3,7,4,1,5,2]=>101101=>101101
[6,7,3,4,5,2,1]=>[6,3,7,4,1,2,5]=>101100=>001101
[6,7,3,5,1,2,4]=>[6,3,7,1,5,4,2]=>101011=>110101
[6,7,3,5,1,4,2]=>[6,3,7,1,5,2,4]=>101010=>010101
[6,7,3,5,2,1,4]=>[6,3,7,1,2,5,4]=>101001=>100101
[6,7,3,5,2,4,1]=>[6,3,7,2,5,1,4]=>101010=>010101
[6,7,3,5,4,1,2]=>[6,3,7,1,4,5,2]=>101001=>100101
[6,7,3,5,4,2,1]=>[6,3,7,1,2,4,5]=>101000=>000101
[6,7,4,1,2,3,5]=>[6,1,4,7,5,3,2]=>100111=>111001
[6,7,4,1,2,5,3]=>[6,1,4,7,3,5,2]=>100101=>101001
[6,7,4,1,3,2,5]=>[6,1,4,7,5,2,3]=>100110=>011001
[6,7,4,1,3,5,2]=>[6,1,4,7,3,2,5]=>100110=>011001
[6,7,4,1,5,2,3]=>[6,1,4,7,2,5,3]=>100101=>101001
[6,7,4,1,5,3,2]=>[6,1,4,7,2,3,5]=>100100=>001001
[6,7,4,2,1,3,5]=>[6,1,2,4,7,5,3]=>100011=>110001
[6,7,4,2,1,5,3]=>[6,1,2,4,7,3,5]=>100010=>010001
[6,7,4,2,3,1,5]=>[6,2,4,7,5,1,3]=>100110=>011001
[6,7,4,2,3,5,1]=>[6,2,4,7,3,1,5]=>100110=>011001
[6,7,4,2,5,1,3]=>[6,2,4,7,1,5,3]=>100101=>101001
[6,7,4,2,5,3,1]=>[6,2,4,7,1,3,5]=>100100=>001001
[6,7,4,3,1,2,5]=>[6,1,3,4,7,5,2]=>100011=>110001
[6,7,4,3,1,5,2]=>[6,1,3,4,7,2,5]=>100010=>010001
[6,7,4,3,2,1,5]=>[6,1,2,3,4,7,5]=>100001=>100001
[6,7,4,3,2,5,1]=>[6,2,3,4,7,1,5]=>100010=>010001
[6,7,4,3,5,1,2]=>[6,3,4,7,1,5,2]=>100101=>101001
[6,7,4,3,5,2,1]=>[6,3,4,7,1,2,5]=>100100=>001001
[6,7,4,5,1,2,3]=>[6,4,7,1,5,3,2]=>101011=>110101
[6,7,4,5,1,3,2]=>[6,4,7,1,5,2,3]=>101010=>010101
[6,7,4,5,2,1,3]=>[6,4,7,1,2,5,3]=>101001=>100101
[6,7,4,5,2,3,1]=>[6,4,7,2,5,1,3]=>101010=>010101
[6,7,4,5,3,1,2]=>[6,4,7,1,3,5,2]=>101001=>100101
[6,7,4,5,3,2,1]=>[6,4,7,1,2,3,5]=>101000=>000101
[6,7,5,1,2,3,4]=>[6,1,5,7,4,3,2]=>100111=>111001
[6,7,5,1,2,4,3]=>[6,1,5,7,3,4,2]=>100101=>101001
[6,7,5,1,3,2,4]=>[6,1,5,7,4,2,3]=>100110=>011001
[6,7,5,1,3,4,2]=>[6,1,5,7,3,2,4]=>100110=>011001
[6,7,5,1,4,2,3]=>[6,1,5,7,2,4,3]=>100101=>101001
[6,7,5,1,4,3,2]=>[6,1,5,7,2,3,4]=>100100=>001001
[6,7,5,2,1,3,4]=>[6,1,2,5,7,4,3]=>100011=>110001
[6,7,5,2,1,4,3]=>[6,1,2,5,7,3,4]=>100010=>010001
[6,7,5,2,3,1,4]=>[6,2,5,7,4,1,3]=>100110=>011001
[6,7,5,2,3,4,1]=>[6,2,5,7,3,1,4]=>100110=>011001
[6,7,5,2,4,1,3]=>[6,2,5,7,1,4,3]=>100101=>101001
[6,7,5,2,4,3,1]=>[6,2,5,7,1,3,4]=>100100=>001001
[6,7,5,3,1,2,4]=>[6,1,3,5,7,4,2]=>100011=>110001
[6,7,5,3,1,4,2]=>[6,1,3,5,7,2,4]=>100010=>010001
[6,7,5,3,2,1,4]=>[6,1,2,3,5,7,4]=>100001=>100001
[6,7,5,3,2,4,1]=>[6,2,3,5,7,1,4]=>100010=>010001
[6,7,5,3,4,1,2]=>[6,3,5,7,1,4,2]=>100101=>101001
[6,7,5,3,4,2,1]=>[6,3,5,7,1,2,4]=>100100=>001001
[6,7,5,4,1,2,3]=>[6,1,4,5,7,3,2]=>100011=>110001
[6,7,5,4,1,3,2]=>[6,1,4,5,7,2,3]=>100010=>010001
[6,7,5,4,2,1,3]=>[6,1,2,4,5,7,3]=>100001=>100001
[6,7,5,4,2,3,1]=>[6,2,4,5,7,1,3]=>100010=>010001
[6,7,5,4,3,1,2]=>[6,1,3,4,5,7,2]=>100001=>100001
[6,7,5,4,3,2,1]=>[6,1,2,3,4,5,7]=>100000=>000001
[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>011111=>111110
[7,1,2,3,4,6,5]=>[1,7,5,6,4,3,2]=>010111=>111010
[7,1,2,3,5,4,6]=>[1,7,6,4,5,3,2]=>011011=>110110
[7,1,2,3,5,6,4]=>[1,7,5,4,6,3,2]=>011011=>110110
[7,1,2,3,6,4,5]=>[1,7,4,6,5,3,2]=>010111=>111010
[7,1,2,3,6,5,4]=>[1,7,4,5,6,3,2]=>010011=>110010
[7,1,2,4,3,5,6]=>[1,7,6,5,3,4,2]=>011101=>101110
[7,1,2,4,3,6,5]=>[1,7,5,6,3,4,2]=>010101=>101010
[7,1,2,4,5,3,6]=>[1,7,6,4,3,5,2]=>011101=>101110
[7,1,2,4,5,6,3]=>[1,7,5,4,3,6,2]=>011101=>101110
[7,1,2,4,6,3,5]=>[1,7,4,3,6,5,2]=>011011=>110110
[7,1,2,4,6,5,3]=>[1,7,4,3,5,6,2]=>011001=>100110
[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>011011=>110110
[7,1,2,5,3,6,4]=>[1,7,3,5,4,6,2]=>010101=>101010
[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>011001=>100110
[7,1,2,5,4,6,3]=>[1,7,4,5,3,6,2]=>010101=>101010
[7,1,2,5,6,3,4]=>[1,7,5,3,6,4,2]=>011011=>110110
[7,1,2,5,6,4,3]=>[1,7,5,3,4,6,2]=>011001=>100110
[7,1,2,6,3,4,5]=>[1,7,3,6,5,4,2]=>010111=>111010
[7,1,2,6,3,5,4]=>[1,7,3,6,4,5,2]=>010101=>101010
[7,1,2,6,4,3,5]=>[1,7,3,4,6,5,2]=>010011=>110010
[7,1,2,6,4,5,3]=>[1,7,4,6,3,5,2]=>010101=>101010
[7,1,2,6,5,3,4]=>[1,7,3,5,6,4,2]=>010011=>110010
[7,1,2,6,5,4,3]=>[1,7,3,4,5,6,2]=>010001=>100010
[7,1,3,2,4,5,6]=>[1,7,6,5,4,2,3]=>011110=>011110
[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>010110=>011010
[7,1,3,2,5,4,6]=>[1,7,6,4,5,2,3]=>011010=>010110
[7,1,3,2,5,6,4]=>[1,7,5,4,6,2,3]=>011010=>010110
[7,1,3,2,6,4,5]=>[1,7,4,6,5,2,3]=>010110=>011010
[7,1,3,2,6,5,4]=>[1,7,4,5,6,2,3]=>010010=>010010
[7,1,3,4,2,5,6]=>[1,7,6,5,3,2,4]=>011110=>011110
[7,1,3,4,2,6,5]=>[1,7,5,6,3,2,4]=>010110=>011010
[7,1,3,4,5,2,6]=>[1,7,6,4,3,2,5]=>011110=>011110
[7,1,3,4,5,6,2]=>[1,7,5,4,3,2,6]=>011110=>011110
[7,1,3,4,6,2,5]=>[1,7,4,3,2,6,5]=>011101=>101110
[7,1,3,4,6,5,2]=>[1,7,4,3,2,5,6]=>011100=>001110
[7,1,3,5,2,4,6]=>[1,7,6,3,2,5,4]=>011101=>101110
[7,1,3,5,2,6,4]=>[1,7,3,2,5,4,6]=>011010=>010110
[7,1,3,5,4,2,6]=>[1,7,6,3,2,4,5]=>011100=>001110
[7,1,3,5,4,6,2]=>[1,7,4,5,3,2,6]=>010110=>011010
[7,1,3,5,6,2,4]=>[1,7,5,3,2,6,4]=>011101=>101110
[7,1,3,5,6,4,2]=>[1,7,5,3,2,4,6]=>011100=>001110
[7,1,3,6,2,4,5]=>[1,7,3,2,6,5,4]=>011011=>110110
[7,1,3,6,2,5,4]=>[1,7,3,2,6,4,5]=>011010=>010110
[7,1,3,6,4,2,5]=>[1,7,3,2,4,6,5]=>011001=>100110
[7,1,3,6,4,5,2]=>[1,7,4,6,3,2,5]=>010110=>011010
[7,1,3,6,5,2,4]=>[1,7,3,2,5,6,4]=>011001=>100110
[7,1,3,6,5,4,2]=>[1,7,3,2,4,5,6]=>011000=>000110
[7,1,4,2,3,5,6]=>[1,7,6,5,2,4,3]=>011101=>101110
[7,1,4,2,3,6,5]=>[1,7,5,6,2,4,3]=>010101=>101010
[7,1,4,2,5,3,6]=>[1,7,6,2,4,3,5]=>011010=>010110
[7,1,4,2,5,6,3]=>[1,7,5,2,4,3,6]=>011010=>010110
[7,1,4,2,6,3,5]=>[1,7,2,4,3,6,5]=>010101=>101010
[7,1,4,2,6,5,3]=>[1,7,2,4,3,5,6]=>010100=>001010
[7,1,4,3,2,5,6]=>[1,7,6,5,2,3,4]=>011100=>001110
[7,1,4,3,2,6,5]=>[1,7,5,6,2,3,4]=>010100=>001010
[7,1,4,3,5,2,6]=>[1,7,6,3,4,2,5]=>011010=>010110
[7,1,4,3,5,6,2]=>[1,7,5,3,4,2,6]=>011010=>010110
[7,1,4,3,6,2,5]=>[1,7,3,4,2,6,5]=>010101=>101010
[7,1,4,3,6,5,2]=>[1,7,3,4,2,5,6]=>010100=>001010
[7,1,4,5,2,3,6]=>[1,7,6,4,2,5,3]=>011101=>101110
[7,1,4,5,2,6,3]=>[1,7,4,2,5,3,6]=>011010=>010110
[7,1,4,5,3,2,6]=>[1,7,6,4,2,3,5]=>011100=>001110
[7,1,4,5,3,6,2]=>[1,7,4,3,5,2,6]=>011010=>010110
[7,1,4,5,6,2,3]=>[1,7,5,4,2,6,3]=>011101=>101110
[7,1,4,5,6,3,2]=>[1,7,5,4,2,3,6]=>011100=>001110
[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]=>011011=>110110
[7,1,4,6,2,5,3]=>[1,7,4,2,6,3,5]=>011010=>010110
[7,1,4,6,3,2,5]=>[1,7,4,2,3,6,5]=>011001=>100110
[7,1,4,6,3,5,2]=>[1,7,4,3,6,2,5]=>011010=>010110
[7,1,4,6,5,2,3]=>[1,7,4,2,5,6,3]=>011001=>100110
[7,1,4,6,5,3,2]=>[1,7,4,2,3,5,6]=>011000=>000110
[7,1,5,2,3,4,6]=>[1,7,6,2,5,4,3]=>011011=>110110
[7,1,5,2,3,6,4]=>[1,7,2,5,4,6,3]=>010101=>101010
[7,1,5,2,4,3,6]=>[1,7,6,2,5,3,4]=>011010=>010110
[7,1,5,2,4,6,3]=>[1,7,2,5,4,3,6]=>010110=>011010
[7,1,5,2,6,3,4]=>[1,7,2,5,3,6,4]=>010101=>101010
[7,1,5,2,6,4,3]=>[1,7,2,5,3,4,6]=>010100=>001010
[7,1,5,3,2,4,6]=>[1,7,6,2,3,5,4]=>011001=>100110
[7,1,5,3,2,6,4]=>[1,7,2,3,5,4,6]=>010010=>010010
[7,1,5,3,4,2,6]=>[1,7,6,3,5,2,4]=>011010=>010110
[7,1,5,3,4,6,2]=>[1,7,3,5,4,2,6]=>010110=>011010
[7,1,5,3,6,2,4]=>[1,7,3,5,2,6,4]=>010101=>101010
[7,1,5,3,6,4,2]=>[1,7,3,5,2,4,6]=>010100=>001010
[7,1,5,4,2,3,6]=>[1,7,6,2,4,5,3]=>011001=>100110
[7,1,5,4,2,6,3]=>[1,7,2,4,5,3,6]=>010010=>010010
[7,1,5,4,3,2,6]=>[1,7,6,2,3,4,5]=>011000=>000110
[7,1,5,4,3,6,2]=>[1,7,3,4,5,2,6]=>010010=>010010
[7,1,5,4,6,2,3]=>[1,7,4,5,2,6,3]=>010101=>101010
[7,1,5,4,6,3,2]=>[1,7,4,5,2,3,6]=>010100=>001010
[7,1,5,6,2,3,4]=>[1,7,5,2,6,4,3]=>011011=>110110
[7,1,5,6,2,4,3]=>[1,7,5,2,6,3,4]=>011010=>010110
[7,1,5,6,3,2,4]=>[1,7,5,2,3,6,4]=>011001=>100110
[7,1,5,6,3,4,2]=>[1,7,5,3,6,2,4]=>011010=>010110
[7,1,5,6,4,2,3]=>[1,7,5,2,4,6,3]=>011001=>100110
[7,1,5,6,4,3,2]=>[1,7,5,2,3,4,6]=>011000=>000110
[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>010111=>111010
[7,1,6,2,3,5,4]=>[1,7,2,6,4,5,3]=>010101=>101010
[7,1,6,2,4,3,5]=>[1,7,2,6,5,3,4]=>010110=>011010
[7,1,6,2,4,5,3]=>[1,7,2,6,4,3,5]=>010110=>011010
[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>010101=>101010
[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>010100=>001010
[7,1,6,3,2,4,5]=>[1,7,2,3,6,5,4]=>010011=>110010
[7,1,6,3,2,5,4]=>[1,7,2,3,6,4,5]=>010010=>010010
[7,1,6,3,4,2,5]=>[1,7,3,6,5,2,4]=>010110=>011010
[7,1,6,3,4,5,2]=>[1,7,3,6,4,2,5]=>010110=>011010
[7,1,6,3,5,2,4]=>[1,7,3,6,2,5,4]=>010101=>101010
[7,1,6,3,5,4,2]=>[1,7,3,6,2,4,5]=>010100=>001010
[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>010011=>110010
[7,1,6,4,2,5,3]=>[1,7,2,4,6,3,5]=>010010=>010010
[7,1,6,4,3,2,5]=>[1,7,2,3,4,6,5]=>010001=>100010
[7,1,6,4,3,5,2]=>[1,7,3,4,6,2,5]=>010010=>010010
[7,1,6,4,5,2,3]=>[1,7,4,6,2,5,3]=>010101=>101010
[7,1,6,4,5,3,2]=>[1,7,4,6,2,3,5]=>010100=>001010
[7,1,6,5,2,3,4]=>[1,7,2,5,6,4,3]=>010011=>110010
[7,1,6,5,2,4,3]=>[1,7,2,5,6,3,4]=>010010=>010010
[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>010001=>100010
[7,1,6,5,3,4,2]=>[1,7,3,5,6,2,4]=>010010=>010010
[7,1,6,5,4,2,3]=>[1,7,2,4,5,6,3]=>010001=>100010
[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>010000=>000010
[7,2,1,3,4,5,6]=>[1,2,7,6,5,4,3]=>001111=>111100
[7,2,1,3,4,6,5]=>[1,2,7,5,6,4,3]=>001011=>110100
[7,2,1,3,5,4,6]=>[1,2,7,6,4,5,3]=>001101=>101100
[7,2,1,3,5,6,4]=>[1,2,7,5,4,6,3]=>001101=>101100
[7,2,1,3,6,4,5]=>[1,2,7,4,6,5,3]=>001011=>110100
[7,2,1,3,6,5,4]=>[1,2,7,4,5,6,3]=>001001=>100100
[7,2,1,4,3,5,6]=>[1,2,7,6,5,3,4]=>001110=>011100
[7,2,1,4,3,6,5]=>[1,2,7,5,6,3,4]=>001010=>010100
[7,2,1,4,5,3,6]=>[1,2,7,6,4,3,5]=>001110=>011100
[7,2,1,4,5,6,3]=>[1,2,7,5,4,3,6]=>001110=>011100
[7,2,1,4,6,3,5]=>[1,2,7,4,3,6,5]=>001101=>101100
[7,2,1,4,6,5,3]=>[1,2,7,4,3,5,6]=>001100=>001100
[7,2,1,5,3,4,6]=>[1,2,7,6,3,5,4]=>001101=>101100
[7,2,1,5,3,6,4]=>[1,2,7,3,5,4,6]=>001010=>010100
[7,2,1,5,4,3,6]=>[1,2,7,6,3,4,5]=>001100=>001100
[7,2,1,5,4,6,3]=>[1,2,7,4,5,3,6]=>001010=>010100
[7,2,1,5,6,3,4]=>[1,2,7,5,3,6,4]=>001101=>101100
[7,2,1,5,6,4,3]=>[1,2,7,5,3,4,6]=>001100=>001100
[7,2,1,6,3,4,5]=>[1,2,7,3,6,5,4]=>001011=>110100
[7,2,1,6,3,5,4]=>[1,2,7,3,6,4,5]=>001010=>010100
[7,2,1,6,4,3,5]=>[1,2,7,3,4,6,5]=>001001=>100100
[7,2,1,6,4,5,3]=>[1,2,7,4,6,3,5]=>001010=>010100
[7,2,1,6,5,3,4]=>[1,2,7,3,5,6,4]=>001001=>100100
[7,2,1,6,5,4,3]=>[1,2,7,3,4,5,6]=>001000=>000100
[7,2,3,1,4,5,6]=>[2,7,6,5,4,1,3]=>011110=>011110
[7,2,3,1,4,6,5]=>[2,7,5,6,4,1,3]=>010110=>011010
[7,2,3,1,5,4,6]=>[2,7,6,4,5,1,3]=>011010=>010110
[7,2,3,1,5,6,4]=>[2,7,5,4,6,1,3]=>011010=>010110
[7,2,3,1,6,4,5]=>[2,7,4,6,5,1,3]=>010110=>011010
[7,2,3,1,6,5,4]=>[2,7,4,5,6,1,3]=>010010=>010010
[7,2,3,4,1,5,6]=>[2,7,6,5,3,1,4]=>011110=>011110
[7,2,3,4,1,6,5]=>[2,7,5,6,3,1,4]=>010110=>011010
[7,2,3,4,5,1,6]=>[2,7,6,4,3,1,5]=>011110=>011110
[7,2,3,4,5,6,1]=>[2,7,5,4,3,1,6]=>011110=>011110
[7,2,3,4,6,1,5]=>[2,7,4,3,1,6,5]=>011101=>101110
[7,2,3,4,6,5,1]=>[2,7,4,3,1,5,6]=>011100=>001110
[7,2,3,5,1,4,6]=>[2,7,6,3,1,5,4]=>011101=>101110
[7,2,3,5,1,6,4]=>[2,7,3,1,5,4,6]=>011010=>010110
[7,2,3,5,4,1,6]=>[2,7,6,3,1,4,5]=>011100=>001110
[7,2,3,5,4,6,1]=>[2,7,4,5,3,1,6]=>010110=>011010
[7,2,3,5,6,1,4]=>[2,7,5,3,1,6,4]=>011101=>101110
[7,2,3,5,6,4,1]=>[2,7,5,3,1,4,6]=>011100=>001110
[7,2,3,6,1,4,5]=>[2,7,3,1,6,5,4]=>011011=>110110
[7,2,3,6,1,5,4]=>[2,7,3,1,6,4,5]=>011010=>010110
[7,2,3,6,4,1,5]=>[2,7,3,1,4,6,5]=>011001=>100110
[7,2,3,6,4,5,1]=>[2,7,4,6,3,1,5]=>010110=>011010
[7,2,3,6,5,1,4]=>[2,7,3,1,5,6,4]=>011001=>100110
[7,2,3,6,5,4,1]=>[2,7,3,1,4,5,6]=>011000=>000110
[7,2,4,1,3,5,6]=>[2,7,6,5,1,4,3]=>011101=>101110
[7,2,4,1,3,6,5]=>[2,7,5,6,1,4,3]=>010101=>101010
[7,2,4,1,5,3,6]=>[2,7,6,1,4,3,5]=>011010=>010110
[7,2,4,1,5,6,3]=>[2,7,5,1,4,3,6]=>011010=>010110
[7,2,4,1,6,3,5]=>[2,7,1,4,3,6,5]=>010101=>101010
[7,2,4,1,6,5,3]=>[2,7,1,4,3,5,6]=>010100=>001010
[7,2,4,3,1,5,6]=>[2,7,6,5,1,3,4]=>011100=>001110
[7,2,4,3,1,6,5]=>[2,7,5,6,1,3,4]=>010100=>001010
[7,2,4,3,5,1,6]=>[2,7,6,3,4,1,5]=>011010=>010110
[7,2,4,3,5,6,1]=>[2,7,5,3,4,1,6]=>011010=>010110
[7,2,4,3,6,1,5]=>[2,7,3,4,1,6,5]=>010101=>101010
[7,2,4,3,6,5,1]=>[2,7,3,4,1,5,6]=>010100=>001010
[7,2,4,5,1,3,6]=>[2,7,6,4,1,5,3]=>011101=>101110
[7,2,4,5,1,6,3]=>[2,7,4,1,5,3,6]=>011010=>010110
[7,2,4,5,3,1,6]=>[2,7,6,4,1,3,5]=>011100=>001110
[7,2,4,5,3,6,1]=>[2,7,4,3,5,1,6]=>011010=>010110
[7,2,4,5,6,1,3]=>[2,7,5,4,1,6,3]=>011101=>101110
[7,2,4,5,6,3,1]=>[2,7,5,4,1,3,6]=>011100=>001110
[7,2,4,6,1,3,5]=>[2,7,4,1,6,5,3]=>011011=>110110
[7,2,4,6,1,5,3]=>[2,7,4,1,6,3,5]=>011010=>010110
[7,2,4,6,3,1,5]=>[2,7,4,1,3,6,5]=>011001=>100110
[7,2,4,6,3,5,1]=>[2,7,4,3,6,1,5]=>011010=>010110
[7,2,4,6,5,1,3]=>[2,7,4,1,5,6,3]=>011001=>100110
[7,2,4,6,5,3,1]=>[2,7,4,1,3,5,6]=>011000=>000110
[7,2,5,1,3,4,6]=>[2,7,6,1,5,4,3]=>011011=>110110
[7,2,5,1,3,6,4]=>[2,7,1,5,4,6,3]=>010101=>101010
[7,2,5,1,4,3,6]=>[2,7,6,1,5,3,4]=>011010=>010110
[7,2,5,1,4,6,3]=>[2,7,1,5,4,3,6]=>010110=>011010
[7,2,5,1,6,3,4]=>[2,7,1,5,3,6,4]=>010101=>101010
[7,2,5,1,6,4,3]=>[2,7,1,5,3,4,6]=>010100=>001010
[7,2,5,3,1,4,6]=>[2,7,6,1,3,5,4]=>011001=>100110
[7,2,5,3,1,6,4]=>[2,7,1,3,5,4,6]=>010010=>010010
[7,2,5,3,4,1,6]=>[2,7,6,3,5,1,4]=>011010=>010110
[7,2,5,3,4,6,1]=>[2,7,3,5,4,1,6]=>010110=>011010
[7,2,5,3,6,1,4]=>[2,7,3,5,1,6,4]=>010101=>101010
[7,2,5,3,6,4,1]=>[2,7,3,5,1,4,6]=>010100=>001010
[7,2,5,4,1,3,6]=>[2,7,6,1,4,5,3]=>011001=>100110
[7,2,5,4,1,6,3]=>[2,7,1,4,5,3,6]=>010010=>010010
[7,2,5,4,3,1,6]=>[2,7,6,1,3,4,5]=>011000=>000110
[7,2,5,4,3,6,1]=>[2,7,3,4,5,1,6]=>010010=>010010
[7,2,5,4,6,1,3]=>[2,7,4,5,1,6,3]=>010101=>101010
[7,2,5,4,6,3,1]=>[2,7,4,5,1,3,6]=>010100=>001010
[7,2,5,6,1,3,4]=>[2,7,5,1,6,4,3]=>011011=>110110
[7,2,5,6,1,4,3]=>[2,7,5,1,6,3,4]=>011010=>010110
[7,2,5,6,3,1,4]=>[2,7,5,1,3,6,4]=>011001=>100110
[7,2,5,6,3,4,1]=>[2,7,5,3,6,1,4]=>011010=>010110
[7,2,5,6,4,1,3]=>[2,7,5,1,4,6,3]=>011001=>100110
[7,2,5,6,4,3,1]=>[2,7,5,1,3,4,6]=>011000=>000110
[7,2,6,1,3,4,5]=>[2,7,1,6,5,4,3]=>010111=>111010
[7,2,6,1,3,5,4]=>[2,7,1,6,4,5,3]=>010101=>101010
[7,2,6,1,4,3,5]=>[2,7,1,6,5,3,4]=>010110=>011010
[7,2,6,1,4,5,3]=>[2,7,1,6,4,3,5]=>010110=>011010
[7,2,6,1,5,3,4]=>[2,7,1,6,3,5,4]=>010101=>101010
[7,2,6,1,5,4,3]=>[2,7,1,6,3,4,5]=>010100=>001010
[7,2,6,3,1,4,5]=>[2,7,1,3,6,5,4]=>010011=>110010
[7,2,6,3,1,5,4]=>[2,7,1,3,6,4,5]=>010010=>010010
[7,2,6,3,4,1,5]=>[2,7,3,6,5,1,4]=>010110=>011010
[7,2,6,3,4,5,1]=>[2,7,3,6,4,1,5]=>010110=>011010
[7,2,6,3,5,1,4]=>[2,7,3,6,1,5,4]=>010101=>101010
[7,2,6,3,5,4,1]=>[2,7,3,6,1,4,5]=>010100=>001010
[7,2,6,4,1,3,5]=>[2,7,1,4,6,5,3]=>010011=>110010
[7,2,6,4,1,5,3]=>[2,7,1,4,6,3,5]=>010010=>010010
[7,2,6,4,3,1,5]=>[2,7,1,3,4,6,5]=>010001=>100010
[7,2,6,4,3,5,1]=>[2,7,3,4,6,1,5]=>010010=>010010
[7,2,6,4,5,1,3]=>[2,7,4,6,1,5,3]=>010101=>101010
[7,2,6,4,5,3,1]=>[2,7,4,6,1,3,5]=>010100=>001010
[7,2,6,5,1,3,4]=>[2,7,1,5,6,4,3]=>010011=>110010
[7,2,6,5,1,4,3]=>[2,7,1,5,6,3,4]=>010010=>010010
[7,2,6,5,3,1,4]=>[2,7,1,3,5,6,4]=>010001=>100010
[7,2,6,5,3,4,1]=>[2,7,3,5,6,1,4]=>010010=>010010
[7,2,6,5,4,1,3]=>[2,7,1,4,5,6,3]=>010001=>100010
[7,2,6,5,4,3,1]=>[2,7,1,3,4,5,6]=>010000=>000010
[7,3,1,2,4,5,6]=>[1,3,7,6,5,4,2]=>001111=>111100
[7,3,1,2,4,6,5]=>[1,3,7,5,6,4,2]=>001011=>110100
[7,3,1,2,5,4,6]=>[1,3,7,6,4,5,2]=>001101=>101100
[7,3,1,2,5,6,4]=>[1,3,7,5,4,6,2]=>001101=>101100
[7,3,1,2,6,4,5]=>[1,3,7,4,6,5,2]=>001011=>110100
[7,3,1,2,6,5,4]=>[1,3,7,4,5,6,2]=>001001=>100100
[7,3,1,4,2,5,6]=>[1,3,7,6,5,2,4]=>001110=>011100
[7,3,1,4,2,6,5]=>[1,3,7,5,6,2,4]=>001010=>010100
[7,3,1,4,5,2,6]=>[1,3,7,6,4,2,5]=>001110=>011100
[7,3,1,4,5,6,2]=>[1,3,7,5,4,2,6]=>001110=>011100
[7,3,1,4,6,2,5]=>[1,3,7,4,2,6,5]=>001101=>101100
[7,3,1,4,6,5,2]=>[1,3,7,4,2,5,6]=>001100=>001100
[7,3,1,5,2,4,6]=>[1,3,7,6,2,5,4]=>001101=>101100
[7,3,1,5,2,6,4]=>[1,3,7,2,5,4,6]=>001010=>010100
[7,3,1,5,4,2,6]=>[1,3,7,6,2,4,5]=>001100=>001100
[7,3,1,5,4,6,2]=>[1,3,7,4,5,2,6]=>001010=>010100
[7,3,1,5,6,2,4]=>[1,3,7,5,2,6,4]=>001101=>101100
[7,3,1,5,6,4,2]=>[1,3,7,5,2,4,6]=>001100=>001100
[7,3,1,6,2,4,5]=>[1,3,7,2,6,5,4]=>001011=>110100
[7,3,1,6,2,5,4]=>[1,3,7,2,6,4,5]=>001010=>010100
[7,3,1,6,4,2,5]=>[1,3,7,2,4,6,5]=>001001=>100100
[7,3,1,6,4,5,2]=>[1,3,7,4,6,2,5]=>001010=>010100
[7,3,1,6,5,2,4]=>[1,3,7,2,5,6,4]=>001001=>100100
[7,3,1,6,5,4,2]=>[1,3,7,2,4,5,6]=>001000=>000100
[7,3,2,1,4,5,6]=>[1,2,3,7,6,5,4]=>000111=>111000
[7,3,2,1,4,6,5]=>[1,2,3,7,5,6,4]=>000101=>101000
[7,3,2,1,5,4,6]=>[1,2,3,7,6,4,5]=>000110=>011000
[7,3,2,1,5,6,4]=>[1,2,3,7,5,4,6]=>000110=>011000
[7,3,2,1,6,4,5]=>[1,2,3,7,4,6,5]=>000101=>101000
[7,3,2,1,6,5,4]=>[1,2,3,7,4,5,6]=>000100=>001000
[7,3,2,4,1,5,6]=>[2,3,7,6,5,1,4]=>001110=>011100
[7,3,2,4,1,6,5]=>[2,3,7,5,6,1,4]=>001010=>010100
[7,3,2,4,5,1,6]=>[2,3,7,6,4,1,5]=>001110=>011100
[7,3,2,4,5,6,1]=>[2,3,7,5,4,1,6]=>001110=>011100
[7,3,2,4,6,1,5]=>[2,3,7,4,1,6,5]=>001101=>101100
[7,3,2,4,6,5,1]=>[2,3,7,4,1,5,6]=>001100=>001100
[7,3,2,5,1,4,6]=>[2,3,7,6,1,5,4]=>001101=>101100
[7,3,2,5,1,6,4]=>[2,3,7,1,5,4,6]=>001010=>010100
[7,3,2,5,4,1,6]=>[2,3,7,6,1,4,5]=>001100=>001100
[7,3,2,5,4,6,1]=>[2,3,7,4,5,1,6]=>001010=>010100
[7,3,2,5,6,1,4]=>[2,3,7,5,1,6,4]=>001101=>101100
[7,3,2,5,6,4,1]=>[2,3,7,5,1,4,6]=>001100=>001100
[7,3,2,6,1,4,5]=>[2,3,7,1,6,5,4]=>001011=>110100
[7,3,2,6,1,5,4]=>[2,3,7,1,6,4,5]=>001010=>010100
[7,3,2,6,4,1,5]=>[2,3,7,1,4,6,5]=>001001=>100100
[7,3,2,6,4,5,1]=>[2,3,7,4,6,1,5]=>001010=>010100
[7,3,2,6,5,1,4]=>[2,3,7,1,5,6,4]=>001001=>100100
[7,3,2,6,5,4,1]=>[2,3,7,1,4,5,6]=>001000=>000100
[7,3,4,1,2,5,6]=>[3,7,6,5,1,4,2]=>011101=>101110
[7,3,4,1,2,6,5]=>[3,7,5,6,1,4,2]=>010101=>101010
[7,3,4,1,5,2,6]=>[3,7,6,1,4,2,5]=>011010=>010110
[7,3,4,1,5,6,2]=>[3,7,5,1,4,2,6]=>011010=>010110
[7,3,4,1,6,2,5]=>[3,7,1,4,2,6,5]=>010101=>101010
[7,3,4,1,6,5,2]=>[3,7,1,4,2,5,6]=>010100=>001010
[7,3,4,2,1,5,6]=>[3,7,6,5,1,2,4]=>011100=>001110
[7,3,4,2,1,6,5]=>[3,7,5,6,1,2,4]=>010100=>001010
[7,3,4,2,5,1,6]=>[3,7,6,2,4,1,5]=>011010=>010110
[7,3,4,2,5,6,1]=>[3,7,5,2,4,1,6]=>011010=>010110
[7,3,4,2,6,1,5]=>[3,7,2,4,1,6,5]=>010101=>101010
[7,3,4,2,6,5,1]=>[3,7,2,4,1,5,6]=>010100=>001010
[7,3,4,5,1,2,6]=>[3,7,6,4,1,5,2]=>011101=>101110
[7,3,4,5,1,6,2]=>[3,7,4,1,5,2,6]=>011010=>010110
[7,3,4,5,2,1,6]=>[3,7,6,4,1,2,5]=>011100=>001110
[7,3,4,5,2,6,1]=>[3,7,4,2,5,1,6]=>011010=>010110
[7,3,4,5,6,1,2]=>[3,7,5,4,1,6,2]=>011101=>101110
[7,3,4,5,6,2,1]=>[3,7,5,4,1,2,6]=>011100=>001110
[7,3,4,6,1,2,5]=>[3,7,4,1,6,5,2]=>011011=>110110
[7,3,4,6,1,5,2]=>[3,7,4,1,6,2,5]=>011010=>010110
[7,3,4,6,2,1,5]=>[3,7,4,1,2,6,5]=>011001=>100110
[7,3,4,6,2,5,1]=>[3,7,4,2,6,1,5]=>011010=>010110
[7,3,4,6,5,1,2]=>[3,7,4,1,5,6,2]=>011001=>100110
[7,3,4,6,5,2,1]=>[3,7,4,1,2,5,6]=>011000=>000110
[7,3,5,1,2,4,6]=>[3,7,6,1,5,4,2]=>011011=>110110
[7,3,5,1,2,6,4]=>[3,7,1,5,4,6,2]=>010101=>101010
[7,3,5,1,4,2,6]=>[3,7,6,1,5,2,4]=>011010=>010110
[7,3,5,1,4,6,2]=>[3,7,1,5,4,2,6]=>010110=>011010
[7,3,5,1,6,2,4]=>[3,7,1,5,2,6,4]=>010101=>101010
[7,3,5,1,6,4,2]=>[3,7,1,5,2,4,6]=>010100=>001010
[7,3,5,2,1,4,6]=>[3,7,6,1,2,5,4]=>011001=>100110
[7,3,5,2,1,6,4]=>[3,7,1,2,5,4,6]=>010010=>010010
[7,3,5,2,4,1,6]=>[3,7,6,2,5,1,4]=>011010=>010110
[7,3,5,2,4,6,1]=>[3,7,2,5,4,1,6]=>010110=>011010
[7,3,5,2,6,1,4]=>[3,7,2,5,1,6,4]=>010101=>101010
[7,3,5,2,6,4,1]=>[3,7,2,5,1,4,6]=>010100=>001010
[7,3,5,4,1,2,6]=>[3,7,6,1,4,5,2]=>011001=>100110
[7,3,5,4,1,6,2]=>[3,7,1,4,5,2,6]=>010010=>010010
[7,3,5,4,2,1,6]=>[3,7,6,1,2,4,5]=>011000=>000110
[7,3,5,4,2,6,1]=>[3,7,2,4,5,1,6]=>010010=>010010
[7,3,5,4,6,1,2]=>[3,7,4,5,1,6,2]=>010101=>101010
[7,3,5,4,6,2,1]=>[3,7,4,5,1,2,6]=>010100=>001010
[7,3,5,6,1,2,4]=>[3,7,5,1,6,4,2]=>011011=>110110
[7,3,5,6,1,4,2]=>[3,7,5,1,6,2,4]=>011010=>010110
[7,3,5,6,2,1,4]=>[3,7,5,1,2,6,4]=>011001=>100110
[7,3,5,6,2,4,1]=>[3,7,5,2,6,1,4]=>011010=>010110
[7,3,5,6,4,1,2]=>[3,7,5,1,4,6,2]=>011001=>100110
[7,3,5,6,4,2,1]=>[3,7,5,1,2,4,6]=>011000=>000110
[7,3,6,1,2,4,5]=>[3,7,1,6,5,4,2]=>010111=>111010
[7,3,6,1,2,5,4]=>[3,7,1,6,4,5,2]=>010101=>101010
[7,3,6,1,4,2,5]=>[3,7,1,6,5,2,4]=>010110=>011010
[7,3,6,1,4,5,2]=>[3,7,1,6,4,2,5]=>010110=>011010
[7,3,6,1,5,2,4]=>[3,7,1,6,2,5,4]=>010101=>101010
[7,3,6,1,5,4,2]=>[3,7,1,6,2,4,5]=>010100=>001010
[7,3,6,2,1,4,5]=>[3,7,1,2,6,5,4]=>010011=>110010
[7,3,6,2,1,5,4]=>[3,7,1,2,6,4,5]=>010010=>010010
[7,3,6,2,4,1,5]=>[3,7,2,6,5,1,4]=>010110=>011010
[7,3,6,2,4,5,1]=>[3,7,2,6,4,1,5]=>010110=>011010
[7,3,6,2,5,1,4]=>[3,7,2,6,1,5,4]=>010101=>101010
[7,3,6,2,5,4,1]=>[3,7,2,6,1,4,5]=>010100=>001010
[7,3,6,4,1,2,5]=>[3,7,1,4,6,5,2]=>010011=>110010
[7,3,6,4,1,5,2]=>[3,7,1,4,6,2,5]=>010010=>010010
[7,3,6,4,2,1,5]=>[3,7,1,2,4,6,5]=>010001=>100010
[7,3,6,4,2,5,1]=>[3,7,2,4,6,1,5]=>010010=>010010
[7,3,6,4,5,1,2]=>[3,7,4,6,1,5,2]=>010101=>101010
[7,3,6,4,5,2,1]=>[3,7,4,6,1,2,5]=>010100=>001010
[7,3,6,5,1,2,4]=>[3,7,1,5,6,4,2]=>010011=>110010
[7,3,6,5,1,4,2]=>[3,7,1,5,6,2,4]=>010010=>010010
[7,3,6,5,2,1,4]=>[3,7,1,2,5,6,4]=>010001=>100010
[7,3,6,5,2,4,1]=>[3,7,2,5,6,1,4]=>010010=>010010
[7,3,6,5,4,1,2]=>[3,7,1,4,5,6,2]=>010001=>100010
[7,3,6,5,4,2,1]=>[3,7,1,2,4,5,6]=>010000=>000010
[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>001111=>111100
[7,4,1,2,3,6,5]=>[1,4,7,5,6,3,2]=>001011=>110100
[7,4,1,2,5,3,6]=>[1,4,7,6,3,5,2]=>001101=>101100
[7,4,1,2,5,6,3]=>[1,4,7,5,3,6,2]=>001101=>101100
[7,4,1,2,6,3,5]=>[1,4,7,3,6,5,2]=>001011=>110100
[7,4,1,2,6,5,3]=>[1,4,7,3,5,6,2]=>001001=>100100
[7,4,1,3,2,5,6]=>[1,4,7,6,5,2,3]=>001110=>011100
[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>001010=>010100
[7,4,1,3,5,2,6]=>[1,4,7,6,3,2,5]=>001110=>011100
[7,4,1,3,5,6,2]=>[1,4,7,5,3,2,6]=>001110=>011100
[7,4,1,3,6,2,5]=>[1,4,7,3,2,6,5]=>001101=>101100
[7,4,1,3,6,5,2]=>[1,4,7,3,2,5,6]=>001100=>001100
[7,4,1,5,2,3,6]=>[1,4,7,6,2,5,3]=>001101=>101100
[7,4,1,5,2,6,3]=>[1,4,7,2,5,3,6]=>001010=>010100
[7,4,1,5,3,2,6]=>[1,4,7,6,2,3,5]=>001100=>001100
[7,4,1,5,3,6,2]=>[1,4,7,3,5,2,6]=>001010=>010100
[7,4,1,5,6,2,3]=>[1,4,7,5,2,6,3]=>001101=>101100
[7,4,1,5,6,3,2]=>[1,4,7,5,2,3,6]=>001100=>001100
[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]=>001011=>110100
[7,4,1,6,2,5,3]=>[1,4,7,2,6,3,5]=>001010=>010100
[7,4,1,6,3,2,5]=>[1,4,7,2,3,6,5]=>001001=>100100
[7,4,1,6,3,5,2]=>[1,4,7,3,6,2,5]=>001010=>010100
[7,4,1,6,5,2,3]=>[1,4,7,2,5,6,3]=>001001=>100100
[7,4,1,6,5,3,2]=>[1,4,7,2,3,5,6]=>001000=>000100
[7,4,2,1,3,5,6]=>[1,2,4,7,6,5,3]=>000111=>111000
[7,4,2,1,3,6,5]=>[1,2,4,7,5,6,3]=>000101=>101000
[7,4,2,1,5,3,6]=>[1,2,4,7,6,3,5]=>000110=>011000
[7,4,2,1,5,6,3]=>[1,2,4,7,5,3,6]=>000110=>011000
[7,4,2,1,6,3,5]=>[1,2,4,7,3,6,5]=>000101=>101000
[7,4,2,1,6,5,3]=>[1,2,4,7,3,5,6]=>000100=>001000
[7,4,2,3,1,5,6]=>[2,4,7,6,5,1,3]=>001110=>011100
[7,4,2,3,1,6,5]=>[2,4,7,5,6,1,3]=>001010=>010100
[7,4,2,3,5,1,6]=>[2,4,7,6,3,1,5]=>001110=>011100
[7,4,2,3,5,6,1]=>[2,4,7,5,3,1,6]=>001110=>011100
[7,4,2,3,6,1,5]=>[2,4,7,3,1,6,5]=>001101=>101100
[7,4,2,3,6,5,1]=>[2,4,7,3,1,5,6]=>001100=>001100
[7,4,2,5,1,3,6]=>[2,4,7,6,1,5,3]=>001101=>101100
[7,4,2,5,1,6,3]=>[2,4,7,1,5,3,6]=>001010=>010100
[7,4,2,5,3,1,6]=>[2,4,7,6,1,3,5]=>001100=>001100
[7,4,2,5,3,6,1]=>[2,4,7,3,5,1,6]=>001010=>010100
[7,4,2,5,6,1,3]=>[2,4,7,5,1,6,3]=>001101=>101100
[7,4,2,5,6,3,1]=>[2,4,7,5,1,3,6]=>001100=>001100
[7,4,2,6,1,3,5]=>[2,4,7,1,6,5,3]=>001011=>110100
[7,4,2,6,1,5,3]=>[2,4,7,1,6,3,5]=>001010=>010100
[7,4,2,6,3,1,5]=>[2,4,7,1,3,6,5]=>001001=>100100
[7,4,2,6,3,5,1]=>[2,4,7,3,6,1,5]=>001010=>010100
[7,4,2,6,5,1,3]=>[2,4,7,1,5,6,3]=>001001=>100100
[7,4,2,6,5,3,1]=>[2,4,7,1,3,5,6]=>001000=>000100
[7,4,3,1,2,5,6]=>[1,3,4,7,6,5,2]=>000111=>111000
[7,4,3,1,2,6,5]=>[1,3,4,7,5,6,2]=>000101=>101000
[7,4,3,1,5,2,6]=>[1,3,4,7,6,2,5]=>000110=>011000
[7,4,3,1,5,6,2]=>[1,3,4,7,5,2,6]=>000110=>011000
[7,4,3,1,6,2,5]=>[1,3,4,7,2,6,5]=>000101=>101000
[7,4,3,1,6,5,2]=>[1,3,4,7,2,5,6]=>000100=>001000
[7,4,3,2,1,5,6]=>[1,2,3,4,7,6,5]=>000011=>110000
[7,4,3,2,1,6,5]=>[1,2,3,4,7,5,6]=>000010=>010000
[7,4,3,2,5,1,6]=>[2,3,4,7,6,1,5]=>000110=>011000
[7,4,3,2,5,6,1]=>[2,3,4,7,5,1,6]=>000110=>011000
[7,4,3,2,6,1,5]=>[2,3,4,7,1,6,5]=>000101=>101000
[7,4,3,2,6,5,1]=>[2,3,4,7,1,5,6]=>000100=>001000
[7,4,3,5,1,2,6]=>[3,4,7,6,1,5,2]=>001101=>101100
[7,4,3,5,1,6,2]=>[3,4,7,1,5,2,6]=>001010=>010100
[7,4,3,5,2,1,6]=>[3,4,7,6,1,2,5]=>001100=>001100
[7,4,3,5,2,6,1]=>[3,4,7,2,5,1,6]=>001010=>010100
[7,4,3,5,6,1,2]=>[3,4,7,5,1,6,2]=>001101=>101100
[7,4,3,5,6,2,1]=>[3,4,7,5,1,2,6]=>001100=>001100
[7,4,3,6,1,2,5]=>[3,4,7,1,6,5,2]=>001011=>110100
[7,4,3,6,1,5,2]=>[3,4,7,1,6,2,5]=>001010=>010100
[7,4,3,6,2,1,5]=>[3,4,7,1,2,6,5]=>001001=>100100
[7,4,3,6,2,5,1]=>[3,4,7,2,6,1,5]=>001010=>010100
[7,4,3,6,5,1,2]=>[3,4,7,1,5,6,2]=>001001=>100100
[7,4,3,6,5,2,1]=>[3,4,7,1,2,5,6]=>001000=>000100
[7,4,5,1,2,3,6]=>[4,7,6,1,5,3,2]=>011011=>110110
[7,4,5,1,2,6,3]=>[4,7,1,5,3,6,2]=>010101=>101010
[7,4,5,1,3,2,6]=>[4,7,6,1,5,2,3]=>011010=>010110
[7,4,5,1,3,6,2]=>[4,7,1,5,3,2,6]=>010110=>011010
[7,4,5,1,6,2,3]=>[4,7,1,5,2,6,3]=>010101=>101010
[7,4,5,1,6,3,2]=>[4,7,1,5,2,3,6]=>010100=>001010
[7,4,5,2,1,3,6]=>[4,7,6,1,2,5,3]=>011001=>100110
[7,4,5,2,1,6,3]=>[4,7,1,2,5,3,6]=>010010=>010010
[7,4,5,2,3,1,6]=>[4,7,6,2,5,1,3]=>011010=>010110
[7,4,5,2,3,6,1]=>[4,7,2,5,3,1,6]=>010110=>011010
[7,4,5,2,6,1,3]=>[4,7,2,5,1,6,3]=>010101=>101010
[7,4,5,2,6,3,1]=>[4,7,2,5,1,3,6]=>010100=>001010
[7,4,5,3,1,2,6]=>[4,7,6,1,3,5,2]=>011001=>100110
[7,4,5,3,1,6,2]=>[4,7,1,3,5,2,6]=>010010=>010010
[7,4,5,3,2,1,6]=>[4,7,6,1,2,3,5]=>011000=>000110
[7,4,5,3,2,6,1]=>[4,7,2,3,5,1,6]=>010010=>010010
[7,4,5,3,6,1,2]=>[4,7,3,5,1,6,2]=>010101=>101010
[7,4,5,3,6,2,1]=>[4,7,3,5,1,2,6]=>010100=>001010
[7,4,5,6,1,2,3]=>[4,7,5,1,6,3,2]=>011011=>110110
[7,4,5,6,1,3,2]=>[4,7,5,1,6,2,3]=>011010=>010110
[7,4,5,6,2,1,3]=>[4,7,5,1,2,6,3]=>011001=>100110
[7,4,5,6,2,3,1]=>[4,7,5,2,6,1,3]=>011010=>010110
[7,4,5,6,3,1,2]=>[4,7,5,1,3,6,2]=>011001=>100110
[7,4,5,6,3,2,1]=>[4,7,5,1,2,3,6]=>011000=>000110
[7,4,6,1,2,3,5]=>[4,7,1,6,5,3,2]=>010111=>111010
[7,4,6,1,2,5,3]=>[4,7,1,6,3,5,2]=>010101=>101010
[7,4,6,1,3,2,5]=>[4,7,1,6,5,2,3]=>010110=>011010
[7,4,6,1,3,5,2]=>[4,7,1,6,3,2,5]=>010110=>011010
[7,4,6,1,5,2,3]=>[4,7,1,6,2,5,3]=>010101=>101010
[7,4,6,1,5,3,2]=>[4,7,1,6,2,3,5]=>010100=>001010
[7,4,6,2,1,3,5]=>[4,7,1,2,6,5,3]=>010011=>110010
[7,4,6,2,1,5,3]=>[4,7,1,2,6,3,5]=>010010=>010010
[7,4,6,2,3,1,5]=>[4,7,2,6,5,1,3]=>010110=>011010
[7,4,6,2,3,5,1]=>[4,7,2,6,3,1,5]=>010110=>011010
[7,4,6,2,5,1,3]=>[4,7,2,6,1,5,3]=>010101=>101010
[7,4,6,2,5,3,1]=>[4,7,2,6,1,3,5]=>010100=>001010
[7,4,6,3,1,2,5]=>[4,7,1,3,6,5,2]=>010011=>110010
[7,4,6,3,1,5,2]=>[4,7,1,3,6,2,5]=>010010=>010010
[7,4,6,3,2,1,5]=>[4,7,1,2,3,6,5]=>010001=>100010
[7,4,6,3,2,5,1]=>[4,7,2,3,6,1,5]=>010010=>010010
[7,4,6,3,5,1,2]=>[4,7,3,6,1,5,2]=>010101=>101010
[7,4,6,3,5,2,1]=>[4,7,3,6,1,2,5]=>010100=>001010
[7,4,6,5,1,2,3]=>[4,7,1,5,6,3,2]=>010011=>110010
[7,4,6,5,1,3,2]=>[4,7,1,5,6,2,3]=>010010=>010010
[7,4,6,5,2,1,3]=>[4,7,1,2,5,6,3]=>010001=>100010
[7,4,6,5,2,3,1]=>[4,7,2,5,6,1,3]=>010010=>010010
[7,4,6,5,3,1,2]=>[4,7,1,3,5,6,2]=>010001=>100010
[7,4,6,5,3,2,1]=>[4,7,1,2,3,5,6]=>010000=>000010
[7,5,1,2,3,4,6]=>[1,5,7,6,4,3,2]=>001111=>111100
[7,5,1,2,3,6,4]=>[1,5,7,4,6,3,2]=>001011=>110100
[7,5,1,2,4,3,6]=>[1,5,7,6,3,4,2]=>001101=>101100
[7,5,1,2,4,6,3]=>[1,5,7,4,3,6,2]=>001101=>101100
[7,5,1,2,6,3,4]=>[1,5,7,3,6,4,2]=>001011=>110100
[7,5,1,2,6,4,3]=>[1,5,7,3,4,6,2]=>001001=>100100
[7,5,1,3,2,4,6]=>[1,5,7,6,4,2,3]=>001110=>011100
[7,5,1,3,2,6,4]=>[1,5,7,4,6,2,3]=>001010=>010100
[7,5,1,3,4,2,6]=>[1,5,7,6,3,2,4]=>001110=>011100
[7,5,1,3,4,6,2]=>[1,5,7,4,3,2,6]=>001110=>011100
[7,5,1,3,6,2,4]=>[1,5,7,3,2,6,4]=>001101=>101100
[7,5,1,3,6,4,2]=>[1,5,7,3,2,4,6]=>001100=>001100
[7,5,1,4,2,3,6]=>[1,5,7,6,2,4,3]=>001101=>101100
[7,5,1,4,2,6,3]=>[1,5,7,2,4,3,6]=>001010=>010100
[7,5,1,4,3,2,6]=>[1,5,7,6,2,3,4]=>001100=>001100
[7,5,1,4,3,6,2]=>[1,5,7,3,4,2,6]=>001010=>010100
[7,5,1,4,6,2,3]=>[1,5,7,4,2,6,3]=>001101=>101100
[7,5,1,4,6,3,2]=>[1,5,7,4,2,3,6]=>001100=>001100
[7,5,1,6,2,3,4]=>[1,5,7,2,6,4,3]=>001011=>110100
[7,5,1,6,2,4,3]=>[1,5,7,2,6,3,4]=>001010=>010100
[7,5,1,6,3,2,4]=>[1,5,7,2,3,6,4]=>001001=>100100
[7,5,1,6,3,4,2]=>[1,5,7,3,6,2,4]=>001010=>010100
[7,5,1,6,4,2,3]=>[1,5,7,2,4,6,3]=>001001=>100100
[7,5,1,6,4,3,2]=>[1,5,7,2,3,4,6]=>001000=>000100
[7,5,2,1,3,4,6]=>[1,2,5,7,6,4,3]=>000111=>111000
[7,5,2,1,3,6,4]=>[1,2,5,7,4,6,3]=>000101=>101000
[7,5,2,1,4,3,6]=>[1,2,5,7,6,3,4]=>000110=>011000
[7,5,2,1,4,6,3]=>[1,2,5,7,4,3,6]=>000110=>011000
[7,5,2,1,6,3,4]=>[1,2,5,7,3,6,4]=>000101=>101000
[7,5,2,1,6,4,3]=>[1,2,5,7,3,4,6]=>000100=>001000
[7,5,2,3,1,4,6]=>[2,5,7,6,4,1,3]=>001110=>011100
[7,5,2,3,1,6,4]=>[2,5,7,4,6,1,3]=>001010=>010100
[7,5,2,3,4,1,6]=>[2,5,7,6,3,1,4]=>001110=>011100
[7,5,2,3,4,6,1]=>[2,5,7,4,3,1,6]=>001110=>011100
[7,5,2,3,6,1,4]=>[2,5,7,3,1,6,4]=>001101=>101100
[7,5,2,3,6,4,1]=>[2,5,7,3,1,4,6]=>001100=>001100
[7,5,2,4,1,3,6]=>[2,5,7,6,1,4,3]=>001101=>101100
[7,5,2,4,1,6,3]=>[2,5,7,1,4,3,6]=>001010=>010100
[7,5,2,4,3,1,6]=>[2,5,7,6,1,3,4]=>001100=>001100
[7,5,2,4,3,6,1]=>[2,5,7,3,4,1,6]=>001010=>010100
[7,5,2,4,6,1,3]=>[2,5,7,4,1,6,3]=>001101=>101100
[7,5,2,4,6,3,1]=>[2,5,7,4,1,3,6]=>001100=>001100
[7,5,2,6,1,3,4]=>[2,5,7,1,6,4,3]=>001011=>110100
[7,5,2,6,1,4,3]=>[2,5,7,1,6,3,4]=>001010=>010100
[7,5,2,6,3,1,4]=>[2,5,7,1,3,6,4]=>001001=>100100
[7,5,2,6,3,4,1]=>[2,5,7,3,6,1,4]=>001010=>010100
[7,5,2,6,4,1,3]=>[2,5,7,1,4,6,3]=>001001=>100100
[7,5,2,6,4,3,1]=>[2,5,7,1,3,4,6]=>001000=>000100
[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>000111=>111000
[7,5,3,1,2,6,4]=>[1,3,5,7,4,6,2]=>000101=>101000
[7,5,3,1,4,2,6]=>[1,3,5,7,6,2,4]=>000110=>011000
[7,5,3,1,4,6,2]=>[1,3,5,7,4,2,6]=>000110=>011000
[7,5,3,1,6,2,4]=>[1,3,5,7,2,6,4]=>000101=>101000
[7,5,3,1,6,4,2]=>[1,3,5,7,2,4,6]=>000100=>001000
[7,5,3,2,1,4,6]=>[1,2,3,5,7,6,4]=>000011=>110000
[7,5,3,2,1,6,4]=>[1,2,3,5,7,4,6]=>000010=>010000
[7,5,3,2,4,1,6]=>[2,3,5,7,6,1,4]=>000110=>011000
[7,5,3,2,4,6,1]=>[2,3,5,7,4,1,6]=>000110=>011000
[7,5,3,2,6,1,4]=>[2,3,5,7,1,6,4]=>000101=>101000
[7,5,3,2,6,4,1]=>[2,3,5,7,1,4,6]=>000100=>001000
[7,5,3,4,1,2,6]=>[3,5,7,6,1,4,2]=>001101=>101100
[7,5,3,4,1,6,2]=>[3,5,7,1,4,2,6]=>001010=>010100
[7,5,3,4,2,1,6]=>[3,5,7,6,1,2,4]=>001100=>001100
[7,5,3,4,2,6,1]=>[3,5,7,2,4,1,6]=>001010=>010100
[7,5,3,4,6,1,2]=>[3,5,7,4,1,6,2]=>001101=>101100
[7,5,3,4,6,2,1]=>[3,5,7,4,1,2,6]=>001100=>001100
[7,5,3,6,1,2,4]=>[3,5,7,1,6,4,2]=>001011=>110100
[7,5,3,6,1,4,2]=>[3,5,7,1,6,2,4]=>001010=>010100
[7,5,3,6,2,1,4]=>[3,5,7,1,2,6,4]=>001001=>100100
[7,5,3,6,2,4,1]=>[3,5,7,2,6,1,4]=>001010=>010100
[7,5,3,6,4,1,2]=>[3,5,7,1,4,6,2]=>001001=>100100
[7,5,3,6,4,2,1]=>[3,5,7,1,2,4,6]=>001000=>000100
[7,5,4,1,2,3,6]=>[1,4,5,7,6,3,2]=>000111=>111000
[7,5,4,1,2,6,3]=>[1,4,5,7,3,6,2]=>000101=>101000
[7,5,4,1,3,2,6]=>[1,4,5,7,6,2,3]=>000110=>011000
[7,5,4,1,3,6,2]=>[1,4,5,7,3,2,6]=>000110=>011000
[7,5,4,1,6,2,3]=>[1,4,5,7,2,6,3]=>000101=>101000
[7,5,4,1,6,3,2]=>[1,4,5,7,2,3,6]=>000100=>001000
[7,5,4,2,1,3,6]=>[1,2,4,5,7,6,3]=>000011=>110000
[7,5,4,2,1,6,3]=>[1,2,4,5,7,3,6]=>000010=>010000
[7,5,4,2,3,1,6]=>[2,4,5,7,6,1,3]=>000110=>011000
[7,5,4,2,3,6,1]=>[2,4,5,7,3,1,6]=>000110=>011000
[7,5,4,2,6,1,3]=>[2,4,5,7,1,6,3]=>000101=>101000
[7,5,4,2,6,3,1]=>[2,4,5,7,1,3,6]=>000100=>001000
[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>000011=>110000
[7,5,4,3,1,6,2]=>[1,3,4,5,7,2,6]=>000010=>010000
[7,5,4,3,2,1,6]=>[1,2,3,4,5,7,6]=>000001=>100000
[7,5,4,3,2,6,1]=>[2,3,4,5,7,1,6]=>000010=>010000
[7,5,4,3,6,1,2]=>[3,4,5,7,1,6,2]=>000101=>101000
[7,5,4,3,6,2,1]=>[3,4,5,7,1,2,6]=>000100=>001000
[7,5,4,6,1,2,3]=>[4,5,7,1,6,3,2]=>001011=>110100
[7,5,4,6,1,3,2]=>[4,5,7,1,6,2,3]=>001010=>010100
[7,5,4,6,2,1,3]=>[4,5,7,1,2,6,3]=>001001=>100100
[7,5,4,6,2,3,1]=>[4,5,7,2,6,1,3]=>001010=>010100
[7,5,4,6,3,1,2]=>[4,5,7,1,3,6,2]=>001001=>100100
[7,5,4,6,3,2,1]=>[4,5,7,1,2,3,6]=>001000=>000100
[7,5,6,1,2,3,4]=>[5,7,1,6,4,3,2]=>010111=>111010
[7,5,6,1,2,4,3]=>[5,7,1,6,3,4,2]=>010101=>101010
[7,5,6,1,3,2,4]=>[5,7,1,6,4,2,3]=>010110=>011010
[7,5,6,1,3,4,2]=>[5,7,1,6,3,2,4]=>010110=>011010
[7,5,6,1,4,2,3]=>[5,7,1,6,2,4,3]=>010101=>101010
[7,5,6,1,4,3,2]=>[5,7,1,6,2,3,4]=>010100=>001010
[7,5,6,2,1,3,4]=>[5,7,1,2,6,4,3]=>010011=>110010
[7,5,6,2,1,4,3]=>[5,7,1,2,6,3,4]=>010010=>010010
[7,5,6,2,3,1,4]=>[5,7,2,6,4,1,3]=>010110=>011010
[7,5,6,2,3,4,1]=>[5,7,2,6,3,1,4]=>010110=>011010
[7,5,6,2,4,1,3]=>[5,7,2,6,1,4,3]=>010101=>101010
[7,5,6,2,4,3,1]=>[5,7,2,6,1,3,4]=>010100=>001010
[7,5,6,3,1,2,4]=>[5,7,1,3,6,4,2]=>010011=>110010
[7,5,6,3,1,4,2]=>[5,7,1,3,6,2,4]=>010010=>010010
[7,5,6,3,2,1,4]=>[5,7,1,2,3,6,4]=>010001=>100010
[7,5,6,3,2,4,1]=>[5,7,2,3,6,1,4]=>010010=>010010
[7,5,6,3,4,1,2]=>[5,7,3,6,1,4,2]=>010101=>101010
[7,5,6,3,4,2,1]=>[5,7,3,6,1,2,4]=>010100=>001010
[7,5,6,4,1,2,3]=>[5,7,1,4,6,3,2]=>010011=>110010
[7,5,6,4,1,3,2]=>[5,7,1,4,6,2,3]=>010010=>010010
[7,5,6,4,2,1,3]=>[5,7,1,2,4,6,3]=>010001=>100010
[7,5,6,4,2,3,1]=>[5,7,2,4,6,1,3]=>010010=>010010
[7,5,6,4,3,1,2]=>[5,7,1,3,4,6,2]=>010001=>100010
[7,5,6,4,3,2,1]=>[5,7,1,2,3,4,6]=>010000=>000010
[7,6,1,2,3,4,5]=>[1,6,7,5,4,3,2]=>001111=>111100
[7,6,1,2,3,5,4]=>[1,6,7,4,5,3,2]=>001011=>110100
[7,6,1,2,4,3,5]=>[1,6,7,5,3,4,2]=>001101=>101100
[7,6,1,2,4,5,3]=>[1,6,7,4,3,5,2]=>001101=>101100
[7,6,1,2,5,3,4]=>[1,6,7,3,5,4,2]=>001011=>110100
[7,6,1,2,5,4,3]=>[1,6,7,3,4,5,2]=>001001=>100100
[7,6,1,3,2,4,5]=>[1,6,7,5,4,2,3]=>001110=>011100
[7,6,1,3,2,5,4]=>[1,6,7,4,5,2,3]=>001010=>010100
[7,6,1,3,4,2,5]=>[1,6,7,5,3,2,4]=>001110=>011100
[7,6,1,3,4,5,2]=>[1,6,7,4,3,2,5]=>001110=>011100
[7,6,1,3,5,2,4]=>[1,6,7,3,2,5,4]=>001101=>101100
[7,6,1,3,5,4,2]=>[1,6,7,3,2,4,5]=>001100=>001100
[7,6,1,4,2,3,5]=>[1,6,7,5,2,4,3]=>001101=>101100
[7,6,1,4,2,5,3]=>[1,6,7,2,4,3,5]=>001010=>010100
[7,6,1,4,3,2,5]=>[1,6,7,5,2,3,4]=>001100=>001100
[7,6,1,4,3,5,2]=>[1,6,7,3,4,2,5]=>001010=>010100
[7,6,1,4,5,2,3]=>[1,6,7,4,2,5,3]=>001101=>101100
[7,6,1,4,5,3,2]=>[1,6,7,4,2,3,5]=>001100=>001100
[7,6,1,5,2,3,4]=>[1,6,7,2,5,4,3]=>001011=>110100
[7,6,1,5,2,4,3]=>[1,6,7,2,5,3,4]=>001010=>010100
[7,6,1,5,3,2,4]=>[1,6,7,2,3,5,4]=>001001=>100100
[7,6,1,5,3,4,2]=>[1,6,7,3,5,2,4]=>001010=>010100
[7,6,1,5,4,2,3]=>[1,6,7,2,4,5,3]=>001001=>100100
[7,6,1,5,4,3,2]=>[1,6,7,2,3,4,5]=>001000=>000100
[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>000111=>111000
[7,6,2,1,3,5,4]=>[1,2,6,7,4,5,3]=>000101=>101000
[7,6,2,1,4,3,5]=>[1,2,6,7,5,3,4]=>000110=>011000
[7,6,2,1,4,5,3]=>[1,2,6,7,4,3,5]=>000110=>011000
[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>000101=>101000
[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>000100=>001000
[7,6,2,3,1,4,5]=>[2,6,7,5,4,1,3]=>001110=>011100
[7,6,2,3,1,5,4]=>[2,6,7,4,5,1,3]=>001010=>010100
[7,6,2,3,4,1,5]=>[2,6,7,5,3,1,4]=>001110=>011100
[7,6,2,3,4,5,1]=>[2,6,7,4,3,1,5]=>001110=>011100
[7,6,2,3,5,1,4]=>[2,6,7,3,1,5,4]=>001101=>101100
[7,6,2,3,5,4,1]=>[2,6,7,3,1,4,5]=>001100=>001100
[7,6,2,4,1,3,5]=>[2,6,7,5,1,4,3]=>001101=>101100
[7,6,2,4,1,5,3]=>[2,6,7,1,4,3,5]=>001010=>010100
[7,6,2,4,3,1,5]=>[2,6,7,5,1,3,4]=>001100=>001100
[7,6,2,4,3,5,1]=>[2,6,7,3,4,1,5]=>001010=>010100
[7,6,2,4,5,1,3]=>[2,6,7,4,1,5,3]=>001101=>101100
[7,6,2,4,5,3,1]=>[2,6,7,4,1,3,5]=>001100=>001100
[7,6,2,5,1,3,4]=>[2,6,7,1,5,4,3]=>001011=>110100
[7,6,2,5,1,4,3]=>[2,6,7,1,5,3,4]=>001010=>010100
[7,6,2,5,3,1,4]=>[2,6,7,1,3,5,4]=>001001=>100100
[7,6,2,5,3,4,1]=>[2,6,7,3,5,1,4]=>001010=>010100
[7,6,2,5,4,1,3]=>[2,6,7,1,4,5,3]=>001001=>100100
[7,6,2,5,4,3,1]=>[2,6,7,1,3,4,5]=>001000=>000100
[7,6,3,1,2,4,5]=>[1,3,6,7,5,4,2]=>000111=>111000
[7,6,3,1,2,5,4]=>[1,3,6,7,4,5,2]=>000101=>101000
[7,6,3,1,4,2,5]=>[1,3,6,7,5,2,4]=>000110=>011000
[7,6,3,1,4,5,2]=>[1,3,6,7,4,2,5]=>000110=>011000
[7,6,3,1,5,2,4]=>[1,3,6,7,2,5,4]=>000101=>101000
[7,6,3,1,5,4,2]=>[1,3,6,7,2,4,5]=>000100=>001000
[7,6,3,2,1,4,5]=>[1,2,3,6,7,5,4]=>000011=>110000
[7,6,3,2,1,5,4]=>[1,2,3,6,7,4,5]=>000010=>010000
[7,6,3,2,4,1,5]=>[2,3,6,7,5,1,4]=>000110=>011000
[7,6,3,2,4,5,1]=>[2,3,6,7,4,1,5]=>000110=>011000
[7,6,3,2,5,1,4]=>[2,3,6,7,1,5,4]=>000101=>101000
[7,6,3,2,5,4,1]=>[2,3,6,7,1,4,5]=>000100=>001000
[7,6,3,4,1,2,5]=>[3,6,7,5,1,4,2]=>001101=>101100
[7,6,3,4,1,5,2]=>[3,6,7,1,4,2,5]=>001010=>010100
[7,6,3,4,2,1,5]=>[3,6,7,5,1,2,4]=>001100=>001100
[7,6,3,4,2,5,1]=>[3,6,7,2,4,1,5]=>001010=>010100
[7,6,3,4,5,1,2]=>[3,6,7,4,1,5,2]=>001101=>101100
[7,6,3,4,5,2,1]=>[3,6,7,4,1,2,5]=>001100=>001100
[7,6,3,5,1,2,4]=>[3,6,7,1,5,4,2]=>001011=>110100
[7,6,3,5,1,4,2]=>[3,6,7,1,5,2,4]=>001010=>010100
[7,6,3,5,2,1,4]=>[3,6,7,1,2,5,4]=>001001=>100100
[7,6,3,5,2,4,1]=>[3,6,7,2,5,1,4]=>001010=>010100
[7,6,3,5,4,1,2]=>[3,6,7,1,4,5,2]=>001001=>100100
[7,6,3,5,4,2,1]=>[3,6,7,1,2,4,5]=>001000=>000100
[7,6,4,1,2,3,5]=>[1,4,6,7,5,3,2]=>000111=>111000
[7,6,4,1,2,5,3]=>[1,4,6,7,3,5,2]=>000101=>101000
[7,6,4,1,3,2,5]=>[1,4,6,7,5,2,3]=>000110=>011000
[7,6,4,1,3,5,2]=>[1,4,6,7,3,2,5]=>000110=>011000
[7,6,4,1,5,2,3]=>[1,4,6,7,2,5,3]=>000101=>101000
[7,6,4,1,5,3,2]=>[1,4,6,7,2,3,5]=>000100=>001000
[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>000011=>110000
[7,6,4,2,1,5,3]=>[1,2,4,6,7,3,5]=>000010=>010000
[7,6,4,2,3,1,5]=>[2,4,6,7,5,1,3]=>000110=>011000
[7,6,4,2,3,5,1]=>[2,4,6,7,3,1,5]=>000110=>011000
[7,6,4,2,5,1,3]=>[2,4,6,7,1,5,3]=>000101=>101000
[7,6,4,2,5,3,1]=>[2,4,6,7,1,3,5]=>000100=>001000
[7,6,4,3,1,2,5]=>[1,3,4,6,7,5,2]=>000011=>110000
[7,6,4,3,1,5,2]=>[1,3,4,6,7,2,5]=>000010=>010000
[7,6,4,3,2,1,5]=>[1,2,3,4,6,7,5]=>000001=>100000
[7,6,4,3,2,5,1]=>[2,3,4,6,7,1,5]=>000010=>010000
[7,6,4,3,5,1,2]=>[3,4,6,7,1,5,2]=>000101=>101000
[7,6,4,3,5,2,1]=>[3,4,6,7,1,2,5]=>000100=>001000
[7,6,4,5,1,2,3]=>[4,6,7,1,5,3,2]=>001011=>110100
[7,6,4,5,1,3,2]=>[4,6,7,1,5,2,3]=>001010=>010100
[7,6,4,5,2,1,3]=>[4,6,7,1,2,5,3]=>001001=>100100
[7,6,4,5,2,3,1]=>[4,6,7,2,5,1,3]=>001010=>010100
[7,6,4,5,3,1,2]=>[4,6,7,1,3,5,2]=>001001=>100100
[7,6,4,5,3,2,1]=>[4,6,7,1,2,3,5]=>001000=>000100
[7,6,5,1,2,3,4]=>[1,5,6,7,4,3,2]=>000111=>111000
[7,6,5,1,2,4,3]=>[1,5,6,7,3,4,2]=>000101=>101000
[7,6,5,1,3,2,4]=>[1,5,6,7,4,2,3]=>000110=>011000
[7,6,5,1,3,4,2]=>[1,5,6,7,3,2,4]=>000110=>011000
[7,6,5,1,4,2,3]=>[1,5,6,7,2,4,3]=>000101=>101000
[7,6,5,1,4,3,2]=>[1,5,6,7,2,3,4]=>000100=>001000
[7,6,5,2,1,3,4]=>[1,2,5,6,7,4,3]=>000011=>110000
[7,6,5,2,1,4,3]=>[1,2,5,6,7,3,4]=>000010=>010000
[7,6,5,2,3,1,4]=>[2,5,6,7,4,1,3]=>000110=>011000
[7,6,5,2,3,4,1]=>[2,5,6,7,3,1,4]=>000110=>011000
[7,6,5,2,4,1,3]=>[2,5,6,7,1,4,3]=>000101=>101000
[7,6,5,2,4,3,1]=>[2,5,6,7,1,3,4]=>000100=>001000
[7,6,5,3,1,2,4]=>[1,3,5,6,7,4,2]=>000011=>110000
[7,6,5,3,1,4,2]=>[1,3,5,6,7,2,4]=>000010=>010000
[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>000001=>100000
[7,6,5,3,2,4,1]=>[2,3,5,6,7,1,4]=>000010=>010000
[7,6,5,3,4,1,2]=>[3,5,6,7,1,4,2]=>000101=>101000
[7,6,5,3,4,2,1]=>[3,5,6,7,1,2,4]=>000100=>001000
[7,6,5,4,1,2,3]=>[1,4,5,6,7,3,2]=>000011=>110000
[7,6,5,4,1,3,2]=>[1,4,5,6,7,2,3]=>000010=>010000
[7,6,5,4,2,1,3]=>[1,2,4,5,6,7,3]=>000001=>100000
[7,6,5,4,2,3,1]=>[2,4,5,6,7,1,3]=>000010=>010000
[7,6,5,4,3,1,2]=>[1,3,4,5,6,7,2]=>000001=>100000
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>000000=>000000
Map
weak order rowmotion
Description
Return the reversal of the permutation obtained by inverting the corresponding Laguerre heap.
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
Map
reverse
Description
Return the reversal of a binary word.
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