Identifier
Mp00326:
Permutations
—weak order rowmotion⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00069: Permutations —complement⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Images
=>
[1]=>[1]=>[1]=>
[1,2]=>[2,1]=>[1,2]=>0
[2,1]=>[1,2]=>[2,1]=>1
[1,2,3]=>[3,2,1]=>[1,2,3]=>00
[1,3,2]=>[2,3,1]=>[2,1,3]=>10
[2,1,3]=>[3,1,2]=>[1,3,2]=>01
[2,3,1]=>[2,1,3]=>[2,3,1]=>10
[3,1,2]=>[1,3,2]=>[3,1,2]=>10
[3,2,1]=>[1,2,3]=>[3,2,1]=>11
[1,2,3,4]=>[4,3,2,1]=>[1,2,3,4]=>000
[1,2,4,3]=>[3,4,2,1]=>[2,1,3,4]=>100
[1,3,2,4]=>[4,2,3,1]=>[1,3,2,4]=>010
[1,3,4,2]=>[3,2,4,1]=>[2,3,1,4]=>100
[1,4,2,3]=>[2,4,3,1]=>[3,1,2,4]=>100
[1,4,3,2]=>[2,3,4,1]=>[3,2,1,4]=>110
[2,1,3,4]=>[4,3,1,2]=>[1,2,4,3]=>001
[2,1,4,3]=>[3,4,1,2]=>[2,1,4,3]=>101
[2,3,1,4]=>[4,2,1,3]=>[1,3,4,2]=>010
[2,3,4,1]=>[3,2,1,4]=>[2,3,4,1]=>100
[2,4,1,3]=>[2,1,4,3]=>[3,4,1,2]=>100
[2,4,3,1]=>[2,1,3,4]=>[3,4,2,1]=>110
[3,1,2,4]=>[4,1,3,2]=>[1,4,2,3]=>010
[3,1,4,2]=>[1,3,2,4]=>[4,2,3,1]=>110
[3,2,1,4]=>[4,1,2,3]=>[1,4,3,2]=>011
[3,2,4,1]=>[2,3,1,4]=>[3,2,4,1]=>110
[3,4,1,2]=>[3,1,4,2]=>[2,4,1,3]=>100
[3,4,2,1]=>[3,1,2,4]=>[2,4,3,1]=>101
[4,1,2,3]=>[1,4,3,2]=>[4,1,2,3]=>100
[4,1,3,2]=>[1,4,2,3]=>[4,1,3,2]=>110
[4,2,1,3]=>[1,2,4,3]=>[4,3,1,2]=>101
[4,2,3,1]=>[2,4,1,3]=>[3,1,4,2]=>110
[4,3,1,2]=>[1,3,4,2]=>[4,2,1,3]=>110
[4,3,2,1]=>[1,2,3,4]=>[4,3,2,1]=>111
[1,2,3,4,5]=>[5,4,3,2,1]=>[1,2,3,4,5]=>0000
[1,2,3,5,4]=>[4,5,3,2,1]=>[2,1,3,4,5]=>1000
[1,2,4,3,5]=>[5,3,4,2,1]=>[1,3,2,4,5]=>0100
[1,2,4,5,3]=>[4,3,5,2,1]=>[2,3,1,4,5]=>1000
[1,2,5,3,4]=>[3,5,4,2,1]=>[3,1,2,4,5]=>1000
[1,2,5,4,3]=>[3,4,5,2,1]=>[3,2,1,4,5]=>1100
[1,3,2,4,5]=>[5,4,2,3,1]=>[1,2,4,3,5]=>0010
[1,3,2,5,4]=>[4,5,2,3,1]=>[2,1,4,3,5]=>1010
[1,3,4,2,5]=>[5,3,2,4,1]=>[1,3,4,2,5]=>0100
[1,3,4,5,2]=>[4,3,2,5,1]=>[2,3,4,1,5]=>1000
[1,3,5,2,4]=>[3,2,5,4,1]=>[3,4,1,2,5]=>1000
[1,3,5,4,2]=>[3,2,4,5,1]=>[3,4,2,1,5]=>1100
[1,4,2,3,5]=>[5,2,4,3,1]=>[1,4,2,3,5]=>0100
[1,4,2,5,3]=>[2,4,3,5,1]=>[4,2,3,1,5]=>1100
[1,4,3,2,5]=>[5,2,3,4,1]=>[1,4,3,2,5]=>0110
[1,4,3,5,2]=>[3,4,2,5,1]=>[3,2,4,1,5]=>1100
[1,4,5,2,3]=>[4,2,5,3,1]=>[2,4,1,3,5]=>1000
[1,4,5,3,2]=>[4,2,3,5,1]=>[2,4,3,1,5]=>1010
[1,5,2,3,4]=>[2,5,4,3,1]=>[4,1,2,3,5]=>1000
[1,5,2,4,3]=>[2,5,3,4,1]=>[4,1,3,2,5]=>1100
[1,5,3,2,4]=>[2,3,5,4,1]=>[4,3,1,2,5]=>1010
[1,5,3,4,2]=>[3,5,2,4,1]=>[3,1,4,2,5]=>1100
[1,5,4,2,3]=>[2,4,5,3,1]=>[4,2,1,3,5]=>1100
[1,5,4,3,2]=>[2,3,4,5,1]=>[4,3,2,1,5]=>1110
[2,1,3,4,5]=>[5,4,3,1,2]=>[1,2,3,5,4]=>0001
[2,1,3,5,4]=>[4,5,3,1,2]=>[2,1,3,5,4]=>1001
[2,1,4,3,5]=>[5,3,4,1,2]=>[1,3,2,5,4]=>0101
[2,1,4,5,3]=>[4,3,5,1,2]=>[2,3,1,5,4]=>1001
[2,1,5,3,4]=>[3,5,4,1,2]=>[3,1,2,5,4]=>1001
[2,1,5,4,3]=>[3,4,5,1,2]=>[3,2,1,5,4]=>1101
[2,3,1,4,5]=>[5,4,2,1,3]=>[1,2,4,5,3]=>0010
[2,3,1,5,4]=>[4,5,2,1,3]=>[2,1,4,5,3]=>1010
[2,3,4,1,5]=>[5,3,2,1,4]=>[1,3,4,5,2]=>0100
[2,3,4,5,1]=>[4,3,2,1,5]=>[2,3,4,5,1]=>1000
[2,3,5,1,4]=>[3,2,1,5,4]=>[3,4,5,1,2]=>1000
[2,3,5,4,1]=>[3,2,1,4,5]=>[3,4,5,2,1]=>1100
[2,4,1,3,5]=>[5,2,1,4,3]=>[1,4,5,2,3]=>0100
[2,4,1,5,3]=>[2,1,4,3,5]=>[4,5,2,3,1]=>1100
[2,4,3,1,5]=>[5,2,1,3,4]=>[1,4,5,3,2]=>0110
[2,4,3,5,1]=>[3,4,2,1,5]=>[3,2,4,5,1]=>1100
[2,4,5,1,3]=>[4,2,1,5,3]=>[2,4,5,1,3]=>1000
[2,4,5,3,1]=>[4,2,1,3,5]=>[2,4,5,3,1]=>1010
[2,5,1,3,4]=>[2,1,5,4,3]=>[4,5,1,2,3]=>1000
[2,5,1,4,3]=>[2,1,5,3,4]=>[4,5,1,3,2]=>1100
[2,5,3,1,4]=>[2,1,3,5,4]=>[4,5,3,1,2]=>1010
[2,5,3,4,1]=>[3,5,2,1,4]=>[3,1,4,5,2]=>1100
[2,5,4,1,3]=>[2,1,4,5,3]=>[4,5,2,1,3]=>1100
[2,5,4,3,1]=>[2,1,3,4,5]=>[4,5,3,2,1]=>1110
[3,1,2,4,5]=>[5,4,1,3,2]=>[1,2,5,3,4]=>0010
[3,1,2,5,4]=>[4,5,1,3,2]=>[2,1,5,3,4]=>1010
[3,1,4,2,5]=>[5,1,3,2,4]=>[1,5,3,4,2]=>0110
[3,1,4,5,2]=>[4,1,3,2,5]=>[2,5,3,4,1]=>1010
[3,1,5,2,4]=>[1,3,2,5,4]=>[5,3,4,1,2]=>1010
[3,1,5,4,2]=>[1,3,2,4,5]=>[5,3,4,2,1]=>1110
[3,2,1,4,5]=>[5,4,1,2,3]=>[1,2,5,4,3]=>0011
[3,2,1,5,4]=>[4,5,1,2,3]=>[2,1,5,4,3]=>1011
[3,2,4,1,5]=>[5,2,3,1,4]=>[1,4,3,5,2]=>0110
[3,2,4,5,1]=>[4,2,3,1,5]=>[2,4,3,5,1]=>1010
[3,2,5,1,4]=>[2,3,1,5,4]=>[4,3,5,1,2]=>1010
[3,2,5,4,1]=>[2,3,1,4,5]=>[4,3,5,2,1]=>1110
[3,4,1,2,5]=>[5,3,1,4,2]=>[1,3,5,2,4]=>0100
[3,4,1,5,2]=>[3,1,4,2,5]=>[3,5,2,4,1]=>1100
[3,4,2,1,5]=>[5,3,1,2,4]=>[1,3,5,4,2]=>0101
[3,4,2,5,1]=>[3,2,4,1,5]=>[3,4,2,5,1]=>1100
[3,4,5,1,2]=>[4,3,1,5,2]=>[2,3,5,1,4]=>1000
[3,4,5,2,1]=>[4,3,1,2,5]=>[2,3,5,4,1]=>1001
[3,5,1,2,4]=>[3,1,5,4,2]=>[3,5,1,2,4]=>1000
[3,5,1,4,2]=>[3,1,5,2,4]=>[3,5,1,4,2]=>1100
[3,5,2,1,4]=>[3,1,2,5,4]=>[3,5,4,1,2]=>1001
[3,5,2,4,1]=>[3,2,5,1,4]=>[3,4,1,5,2]=>1100
[3,5,4,1,2]=>[3,1,4,5,2]=>[3,5,2,1,4]=>1100
[3,5,4,2,1]=>[3,1,2,4,5]=>[3,5,4,2,1]=>1101
[4,1,2,3,5]=>[5,1,4,3,2]=>[1,5,2,3,4]=>0100
[4,1,2,5,3]=>[1,4,3,5,2]=>[5,2,3,1,4]=>1100
[4,1,3,2,5]=>[5,1,4,2,3]=>[1,5,2,4,3]=>0110
[4,1,3,5,2]=>[1,4,3,2,5]=>[5,2,3,4,1]=>1100
[4,1,5,2,3]=>[1,4,2,5,3]=>[5,2,4,1,3]=>1100
[4,1,5,3,2]=>[1,4,2,3,5]=>[5,2,4,3,1]=>1110
[4,2,1,3,5]=>[5,1,2,4,3]=>[1,5,4,2,3]=>0101
[4,2,1,5,3]=>[1,2,4,3,5]=>[5,4,2,3,1]=>1101
[4,2,3,1,5]=>[5,2,4,1,3]=>[1,4,2,5,3]=>0110
[4,2,3,5,1]=>[2,4,3,1,5]=>[4,2,3,5,1]=>1100
[4,2,5,1,3]=>[2,4,1,5,3]=>[4,2,5,1,3]=>1100
[4,2,5,3,1]=>[2,4,1,3,5]=>[4,2,5,3,1]=>1110
[4,3,1,2,5]=>[5,1,3,4,2]=>[1,5,3,2,4]=>0110
[4,3,1,5,2]=>[1,3,4,2,5]=>[5,3,2,4,1]=>1110
[4,3,2,1,5]=>[5,1,2,3,4]=>[1,5,4,3,2]=>0111
[4,3,2,5,1]=>[2,3,4,1,5]=>[4,3,2,5,1]=>1110
[4,3,5,1,2]=>[3,4,1,5,2]=>[3,2,5,1,4]=>1100
[4,3,5,2,1]=>[3,4,1,2,5]=>[3,2,5,4,1]=>1101
[4,5,1,2,3]=>[4,1,5,3,2]=>[2,5,1,3,4]=>1000
[4,5,1,3,2]=>[4,1,5,2,3]=>[2,5,1,4,3]=>1010
[4,5,2,1,3]=>[4,1,2,5,3]=>[2,5,4,1,3]=>1001
[4,5,2,3,1]=>[4,2,5,1,3]=>[2,4,1,5,3]=>1010
[4,5,3,1,2]=>[4,1,3,5,2]=>[2,5,3,1,4]=>1010
[4,5,3,2,1]=>[4,1,2,3,5]=>[2,5,4,3,1]=>1011
[5,1,2,3,4]=>[1,5,4,3,2]=>[5,1,2,3,4]=>1000
[5,1,2,4,3]=>[1,5,3,4,2]=>[5,1,3,2,4]=>1100
[5,1,3,2,4]=>[1,5,4,2,3]=>[5,1,2,4,3]=>1010
[5,1,3,4,2]=>[1,5,3,2,4]=>[5,1,3,4,2]=>1100
[5,1,4,2,3]=>[1,5,2,4,3]=>[5,1,4,2,3]=>1100
[5,1,4,3,2]=>[1,5,2,3,4]=>[5,1,4,3,2]=>1110
[5,2,1,3,4]=>[1,2,5,4,3]=>[5,4,1,2,3]=>1001
[5,2,1,4,3]=>[1,2,5,3,4]=>[5,4,1,3,2]=>1101
[5,2,3,1,4]=>[2,5,4,1,3]=>[4,1,2,5,3]=>1010
[5,2,3,4,1]=>[2,5,3,1,4]=>[4,1,3,5,2]=>1100
[5,2,4,1,3]=>[2,5,1,4,3]=>[4,1,5,2,3]=>1100
[5,2,4,3,1]=>[2,5,1,3,4]=>[4,1,5,3,2]=>1110
[5,3,1,2,4]=>[1,3,5,4,2]=>[5,3,1,2,4]=>1010
[5,3,1,4,2]=>[1,3,5,2,4]=>[5,3,1,4,2]=>1110
[5,3,2,1,4]=>[1,2,3,5,4]=>[5,4,3,1,2]=>1011
[5,3,2,4,1]=>[2,3,5,1,4]=>[4,3,1,5,2]=>1110
[5,3,4,1,2]=>[3,5,1,4,2]=>[3,1,5,2,4]=>1100
[5,3,4,2,1]=>[3,5,1,2,4]=>[3,1,5,4,2]=>1101
[5,4,1,2,3]=>[1,4,5,3,2]=>[5,2,1,3,4]=>1100
[5,4,1,3,2]=>[1,4,5,2,3]=>[5,2,1,4,3]=>1110
[5,4,2,1,3]=>[1,2,4,5,3]=>[5,4,2,1,3]=>1101
[5,4,2,3,1]=>[2,4,5,1,3]=>[4,2,1,5,3]=>1110
[5,4,3,1,2]=>[1,3,4,5,2]=>[5,3,2,1,4]=>1110
[5,4,3,2,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>1111
[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>00000
[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>10000
[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>01000
[1,2,3,5,6,4]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>10000
[1,2,3,6,4,5]=>[4,6,5,3,2,1]=>[3,1,2,4,5,6]=>10000
[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>11000
[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>00100
[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>10100
[1,2,4,5,3,6]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>01000
[1,2,4,5,6,3]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>10000
[1,2,4,6,3,5]=>[4,3,6,5,2,1]=>[3,4,1,2,5,6]=>10000
[1,2,4,6,5,3]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>11000
[1,2,5,3,4,6]=>[6,3,5,4,2,1]=>[1,4,2,3,5,6]=>01000
[1,2,5,3,6,4]=>[3,5,4,6,2,1]=>[4,2,3,1,5,6]=>11000
[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>01100
[1,2,5,4,6,3]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>11000
[1,2,5,6,3,4]=>[5,3,6,4,2,1]=>[2,4,1,3,5,6]=>10000
[1,2,5,6,4,3]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>10100
[1,2,6,3,4,5]=>[3,6,5,4,2,1]=>[4,1,2,3,5,6]=>10000
[1,2,6,3,5,4]=>[3,6,4,5,2,1]=>[4,1,3,2,5,6]=>11000
[1,2,6,4,3,5]=>[3,4,6,5,2,1]=>[4,3,1,2,5,6]=>10100
[1,2,6,4,5,3]=>[4,6,3,5,2,1]=>[3,1,4,2,5,6]=>11000
[1,2,6,5,3,4]=>[3,5,6,4,2,1]=>[4,2,1,3,5,6]=>11000
[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>11100
[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>00010
[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>10010
[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[1,3,2,5,6,4]=>[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>10010
[1,3,2,6,4,5]=>[4,6,5,2,3,1]=>[3,1,2,5,4,6]=>10010
[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>11010
[1,3,4,2,5,6]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>00100
[1,3,4,2,6,5]=>[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>10100
[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>01000
[1,3,4,5,6,2]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>10000
[1,3,4,6,2,5]=>[4,3,2,6,5,1]=>[3,4,5,1,2,6]=>10000
[1,3,4,6,5,2]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>11000
[1,3,5,2,4,6]=>[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>01000
[1,3,5,2,6,4]=>[3,2,5,4,6,1]=>[4,5,2,3,1,6]=>11000
[1,3,5,4,2,6]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>01100
[1,3,5,4,6,2]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>11000
[1,3,5,6,2,4]=>[5,3,2,6,4,1]=>[2,4,5,1,3,6]=>10000
[1,3,5,6,4,2]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>10100
[1,3,6,2,4,5]=>[3,2,6,5,4,1]=>[4,5,1,2,3,6]=>10000
[1,3,6,2,5,4]=>[3,2,6,4,5,1]=>[4,5,1,3,2,6]=>11000
[1,3,6,4,2,5]=>[3,2,4,6,5,1]=>[4,5,3,1,2,6]=>10100
[1,3,6,4,5,2]=>[4,6,3,2,5,1]=>[3,1,4,5,2,6]=>11000
[1,3,6,5,2,4]=>[3,2,5,6,4,1]=>[4,5,2,1,3,6]=>11000
[1,3,6,5,4,2]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>11100
[1,4,2,3,5,6]=>[6,5,2,4,3,1]=>[1,2,5,3,4,6]=>00100
[1,4,2,3,6,5]=>[5,6,2,4,3,1]=>[2,1,5,3,4,6]=>10100
[1,4,2,5,3,6]=>[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>01100
[1,4,2,5,6,3]=>[5,2,4,3,6,1]=>[2,5,3,4,1,6]=>10100
[1,4,2,6,3,5]=>[2,4,3,6,5,1]=>[5,3,4,1,2,6]=>10100
[1,4,2,6,5,3]=>[2,4,3,5,6,1]=>[5,3,4,2,1,6]=>11100
[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>00110
[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[2,1,5,4,3,6]=>10110
[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>01100
[1,4,3,5,6,2]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>10100
[1,4,3,6,2,5]=>[3,4,2,6,5,1]=>[4,3,5,1,2,6]=>10100
[1,4,3,6,5,2]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>11100
[1,4,5,2,3,6]=>[6,4,2,5,3,1]=>[1,3,5,2,4,6]=>01000
[1,4,5,2,6,3]=>[4,2,5,3,6,1]=>[3,5,2,4,1,6]=>11000
[1,4,5,3,2,6]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>01010
[1,4,5,3,6,2]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>11000
[1,4,5,6,2,3]=>[5,4,2,6,3,1]=>[2,3,5,1,4,6]=>10000
[1,4,5,6,3,2]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>10010
[1,4,6,2,3,5]=>[4,2,6,5,3,1]=>[3,5,1,2,4,6]=>10000
[1,4,6,2,5,3]=>[4,2,6,3,5,1]=>[3,5,1,4,2,6]=>11000
[1,4,6,3,2,5]=>[4,2,3,6,5,1]=>[3,5,4,1,2,6]=>10010
[1,4,6,3,5,2]=>[4,3,6,2,5,1]=>[3,4,1,5,2,6]=>11000
[1,4,6,5,2,3]=>[4,2,5,6,3,1]=>[3,5,2,1,4,6]=>11000
[1,4,6,5,3,2]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>11010
[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[1,5,2,3,4,6]=>01000
[1,5,2,3,6,4]=>[2,5,4,6,3,1]=>[5,2,3,1,4,6]=>11000
[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[1,5,2,4,3,6]=>01100
[1,5,2,4,6,3]=>[2,5,4,3,6,1]=>[5,2,3,4,1,6]=>11000
[1,5,2,6,3,4]=>[2,5,3,6,4,1]=>[5,2,4,1,3,6]=>11000
[1,5,2,6,4,3]=>[2,5,3,4,6,1]=>[5,2,4,3,1,6]=>11100
[1,5,3,2,4,6]=>[6,2,3,5,4,1]=>[1,5,4,2,3,6]=>01010
[1,5,3,2,6,4]=>[2,3,5,4,6,1]=>[5,4,2,3,1,6]=>11010
[1,5,3,4,2,6]=>[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>01100
[1,5,3,4,6,2]=>[3,5,4,2,6,1]=>[4,2,3,5,1,6]=>11000
[1,5,3,6,2,4]=>[3,5,2,6,4,1]=>[4,2,5,1,3,6]=>11000
[1,5,3,6,4,2]=>[3,5,2,4,6,1]=>[4,2,5,3,1,6]=>11100
[1,5,4,2,3,6]=>[6,2,4,5,3,1]=>[1,5,3,2,4,6]=>01100
[1,5,4,2,6,3]=>[2,4,5,3,6,1]=>[5,3,2,4,1,6]=>11100
[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110
[1,5,4,3,6,2]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>11100
[1,5,4,6,2,3]=>[4,5,2,6,3,1]=>[3,2,5,1,4,6]=>11000
[1,5,4,6,3,2]=>[4,5,2,3,6,1]=>[3,2,5,4,1,6]=>11010
[1,5,6,2,3,4]=>[5,2,6,4,3,1]=>[2,5,1,3,4,6]=>10000
[1,5,6,2,4,3]=>[5,2,6,3,4,1]=>[2,5,1,4,3,6]=>10100
[1,5,6,3,2,4]=>[5,2,3,6,4,1]=>[2,5,4,1,3,6]=>10010
[1,5,6,3,4,2]=>[5,3,6,2,4,1]=>[2,4,1,5,3,6]=>10100
[1,5,6,4,2,3]=>[5,2,4,6,3,1]=>[2,5,3,1,4,6]=>10100
[1,5,6,4,3,2]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>10110
[1,6,2,3,4,5]=>[2,6,5,4,3,1]=>[5,1,2,3,4,6]=>10000
[1,6,2,3,5,4]=>[2,6,4,5,3,1]=>[5,1,3,2,4,6]=>11000
[1,6,2,4,3,5]=>[2,6,5,3,4,1]=>[5,1,2,4,3,6]=>10100
[1,6,2,4,5,3]=>[2,6,4,3,5,1]=>[5,1,3,4,2,6]=>11000
[1,6,2,5,3,4]=>[2,6,3,5,4,1]=>[5,1,4,2,3,6]=>11000
[1,6,2,5,4,3]=>[2,6,3,4,5,1]=>[5,1,4,3,2,6]=>11100
[1,6,3,2,4,5]=>[2,3,6,5,4,1]=>[5,4,1,2,3,6]=>10010
[1,6,3,2,5,4]=>[2,3,6,4,5,1]=>[5,4,1,3,2,6]=>11010
[1,6,3,4,2,5]=>[3,6,5,2,4,1]=>[4,1,2,5,3,6]=>10100
[1,6,3,4,5,2]=>[3,6,4,2,5,1]=>[4,1,3,5,2,6]=>11000
[1,6,3,5,2,4]=>[3,6,2,5,4,1]=>[4,1,5,2,3,6]=>11000
[1,6,3,5,4,2]=>[3,6,2,4,5,1]=>[4,1,5,3,2,6]=>11100
[1,6,4,2,3,5]=>[2,4,6,5,3,1]=>[5,3,1,2,4,6]=>10100
[1,6,4,2,5,3]=>[2,4,6,3,5,1]=>[5,3,1,4,2,6]=>11100
[1,6,4,3,2,5]=>[2,3,4,6,5,1]=>[5,4,3,1,2,6]=>10110
[1,6,4,3,5,2]=>[3,4,6,2,5,1]=>[4,3,1,5,2,6]=>11100
[1,6,4,5,2,3]=>[4,6,2,5,3,1]=>[3,1,5,2,4,6]=>11000
[1,6,4,5,3,2]=>[4,6,2,3,5,1]=>[3,1,5,4,2,6]=>11010
[1,6,5,2,3,4]=>[2,5,6,4,3,1]=>[5,2,1,3,4,6]=>11000
[1,6,5,2,4,3]=>[2,5,6,3,4,1]=>[5,2,1,4,3,6]=>11100
[1,6,5,3,2,4]=>[2,3,5,6,4,1]=>[5,4,2,1,3,6]=>11010
[1,6,5,3,4,2]=>[3,5,6,2,4,1]=>[4,2,1,5,3,6]=>11100
[1,6,5,4,2,3]=>[2,4,5,6,3,1]=>[5,3,2,1,4,6]=>11100
[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>11110
[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>00001
[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001
[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>01001
[2,1,3,5,6,4]=>[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>10001
[2,1,3,6,4,5]=>[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>10001
[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>11001
[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>00101
[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[2,1,4,5,3,6]=>[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>01001
[2,1,4,5,6,3]=>[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>10001
[2,1,4,6,3,5]=>[4,3,6,5,1,2]=>[3,4,1,2,6,5]=>10001
[2,1,4,6,5,3]=>[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>11001
[2,1,5,3,4,6]=>[6,3,5,4,1,2]=>[1,4,2,3,6,5]=>01001
[2,1,5,3,6,4]=>[3,5,4,6,1,2]=>[4,2,3,1,6,5]=>11001
[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>01101
[2,1,5,4,6,3]=>[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>11001
[2,1,5,6,3,4]=>[5,3,6,4,1,2]=>[2,4,1,3,6,5]=>10001
[2,1,5,6,4,3]=>[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>10101
[2,1,6,3,4,5]=>[3,6,5,4,1,2]=>[4,1,2,3,6,5]=>10001
[2,1,6,3,5,4]=>[3,6,4,5,1,2]=>[4,1,3,2,6,5]=>11001
[2,1,6,4,3,5]=>[3,4,6,5,1,2]=>[4,3,1,2,6,5]=>10101
[2,1,6,4,5,3]=>[4,6,3,5,1,2]=>[3,1,4,2,6,5]=>11001
[2,1,6,5,3,4]=>[3,5,6,4,1,2]=>[4,2,1,3,6,5]=>11001
[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>11101
[2,3,1,4,5,6]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>00010
[2,3,1,4,6,5]=>[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>10010
[2,3,1,5,4,6]=>[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>01010
[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>10010
[2,3,1,6,4,5]=>[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>10010
[2,3,1,6,5,4]=>[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>11010
[2,3,4,1,5,6]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>00100
[2,3,4,1,6,5]=>[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>10100
[2,3,4,5,1,6]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>01000
[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>10000
[2,3,4,6,1,5]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>10000
[2,3,4,6,5,1]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>11000
[2,3,5,1,4,6]=>[6,3,2,1,5,4]=>[1,4,5,6,2,3]=>01000
[2,3,5,1,6,4]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>11000
[2,3,5,4,1,6]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>01100
[2,3,5,4,6,1]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>11000
[2,3,5,6,1,4]=>[5,3,2,1,6,4]=>[2,4,5,6,1,3]=>10000
[2,3,5,6,4,1]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>10100
[2,3,6,1,4,5]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>10000
[2,3,6,1,5,4]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>11000
[2,3,6,4,1,5]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>10100
[2,3,6,4,5,1]=>[4,6,3,2,1,5]=>[3,1,4,5,6,2]=>11000
[2,3,6,5,1,4]=>[3,2,1,5,6,4]=>[4,5,6,2,1,3]=>11000
[2,3,6,5,4,1]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>11100
[2,4,1,3,5,6]=>[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>00100
[2,4,1,3,6,5]=>[5,6,2,1,4,3]=>[2,1,5,6,3,4]=>10100
[2,4,1,5,3,6]=>[6,2,1,4,3,5]=>[1,5,6,3,4,2]=>01100
[2,4,1,5,6,3]=>[5,2,1,4,3,6]=>[2,5,6,3,4,1]=>10100
[2,4,1,6,3,5]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>10100
[2,4,1,6,5,3]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>11100
[2,4,3,1,5,6]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>00110
[2,4,3,1,6,5]=>[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>10110
[2,4,3,5,1,6]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>01100
[2,4,3,5,6,1]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>10100
[2,4,3,6,1,5]=>[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>10100
[2,4,3,6,5,1]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>11100
[2,4,5,1,3,6]=>[6,4,2,1,5,3]=>[1,3,5,6,2,4]=>01000
[2,4,5,1,6,3]=>[4,2,1,5,3,6]=>[3,5,6,2,4,1]=>11000
[2,4,5,3,1,6]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>01010
[2,4,5,3,6,1]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>11000
[2,4,5,6,1,3]=>[5,4,2,1,6,3]=>[2,3,5,6,1,4]=>10000
[2,4,5,6,3,1]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>10010
[2,4,6,1,3,5]=>[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>10000
[2,4,6,1,5,3]=>[4,2,1,6,3,5]=>[3,5,6,1,4,2]=>11000
[2,4,6,3,1,5]=>[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>10010
[2,4,6,3,5,1]=>[4,3,6,2,1,5]=>[3,4,1,5,6,2]=>11000
[2,4,6,5,1,3]=>[4,2,1,5,6,3]=>[3,5,6,2,1,4]=>11000
[2,4,6,5,3,1]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>11010
[2,5,1,3,4,6]=>[6,2,1,5,4,3]=>[1,5,6,2,3,4]=>01000
[2,5,1,3,6,4]=>[2,1,5,4,6,3]=>[5,6,2,3,1,4]=>11000
[2,5,1,4,3,6]=>[6,2,1,5,3,4]=>[1,5,6,2,4,3]=>01100
[2,5,1,4,6,3]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>11000
[2,5,1,6,3,4]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>11000
[2,5,1,6,4,3]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>11100
[2,5,3,1,4,6]=>[6,2,1,3,5,4]=>[1,5,6,4,2,3]=>01010
[2,5,3,1,6,4]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>11010
[2,5,3,4,1,6]=>[6,3,5,2,1,4]=>[1,4,2,5,6,3]=>01100
[2,5,3,4,6,1]=>[3,5,4,2,1,6]=>[4,2,3,5,6,1]=>11000
[2,5,3,6,1,4]=>[3,5,2,1,6,4]=>[4,2,5,6,1,3]=>11000
[2,5,3,6,4,1]=>[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>11100
[2,5,4,1,3,6]=>[6,2,1,4,5,3]=>[1,5,6,3,2,4]=>01100
[2,5,4,1,6,3]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>11100
[2,5,4,3,1,6]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>01110
[2,5,4,3,6,1]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>11100
[2,5,4,6,1,3]=>[4,5,2,1,6,3]=>[3,2,5,6,1,4]=>11000
[2,5,4,6,3,1]=>[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>11010
[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>[2,5,6,1,3,4]=>10000
[2,5,6,1,4,3]=>[5,2,1,6,3,4]=>[2,5,6,1,4,3]=>10100
[2,5,6,3,1,4]=>[5,2,1,3,6,4]=>[2,5,6,4,1,3]=>10010
[2,5,6,3,4,1]=>[5,3,6,2,1,4]=>[2,4,1,5,6,3]=>10100
[2,5,6,4,1,3]=>[5,2,1,4,6,3]=>[2,5,6,3,1,4]=>10100
[2,5,6,4,3,1]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>10110
[2,6,1,3,4,5]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>10000
[2,6,1,3,5,4]=>[2,1,6,4,5,3]=>[5,6,1,3,2,4]=>11000
[2,6,1,4,3,5]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>10100
[2,6,1,4,5,3]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>11000
[2,6,1,5,3,4]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>11000
[2,6,1,5,4,3]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>11100
[2,6,3,1,4,5]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>10010
[2,6,3,1,5,4]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>11010
[2,6,3,4,1,5]=>[3,6,5,2,1,4]=>[4,1,2,5,6,3]=>10100
[2,6,3,4,5,1]=>[3,6,4,2,1,5]=>[4,1,3,5,6,2]=>11000
[2,6,3,5,1,4]=>[3,6,2,1,5,4]=>[4,1,5,6,2,3]=>11000
[2,6,3,5,4,1]=>[3,6,2,1,4,5]=>[4,1,5,6,3,2]=>11100
[2,6,4,1,3,5]=>[2,1,4,6,5,3]=>[5,6,3,1,2,4]=>10100
[2,6,4,1,5,3]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>11100
[2,6,4,3,1,5]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>10110
[2,6,4,3,5,1]=>[3,4,6,2,1,5]=>[4,3,1,5,6,2]=>11100
[2,6,4,5,1,3]=>[4,6,2,1,5,3]=>[3,1,5,6,2,4]=>11000
[2,6,4,5,3,1]=>[4,6,2,1,3,5]=>[3,1,5,6,4,2]=>11010
[2,6,5,1,3,4]=>[2,1,5,6,4,3]=>[5,6,2,1,3,4]=>11000
[2,6,5,1,4,3]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>11100
[2,6,5,3,1,4]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>11010
[2,6,5,3,4,1]=>[3,5,6,2,1,4]=>[4,2,1,5,6,3]=>11100
[2,6,5,4,1,3]=>[2,1,4,5,6,3]=>[5,6,3,2,1,4]=>11100
[2,6,5,4,3,1]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>11110
[3,1,2,4,5,6]=>[6,5,4,1,3,2]=>[1,2,3,6,4,5]=>00010
[3,1,2,4,6,5]=>[5,6,4,1,3,2]=>[2,1,3,6,4,5]=>10010
[3,1,2,5,4,6]=>[6,4,5,1,3,2]=>[1,3,2,6,4,5]=>01010
[3,1,2,5,6,4]=>[5,4,6,1,3,2]=>[2,3,1,6,4,5]=>10010
[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[3,1,2,6,4,5]=>10010
[3,1,2,6,5,4]=>[4,5,6,1,3,2]=>[3,2,1,6,4,5]=>11010
[3,1,4,2,5,6]=>[6,5,1,3,2,4]=>[1,2,6,4,5,3]=>00110
[3,1,4,2,6,5]=>[5,6,1,3,2,4]=>[2,1,6,4,5,3]=>10110
[3,1,4,5,2,6]=>[6,4,1,3,2,5]=>[1,3,6,4,5,2]=>01010
[3,1,4,5,6,2]=>[5,4,1,3,2,6]=>[2,3,6,4,5,1]=>10010
[3,1,4,6,2,5]=>[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>10010
[3,1,4,6,5,2]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>11010
[3,1,5,2,4,6]=>[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>01010
[3,1,5,2,6,4]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>11010
[3,1,5,4,2,6]=>[6,1,3,2,4,5]=>[1,6,4,5,3,2]=>01110
[3,1,5,4,6,2]=>[4,5,1,3,2,6]=>[3,2,6,4,5,1]=>11010
[3,1,5,6,2,4]=>[5,1,3,2,6,4]=>[2,6,4,5,1,3]=>10010
[3,1,5,6,4,2]=>[5,1,3,2,4,6]=>[2,6,4,5,3,1]=>10110
[3,1,6,2,4,5]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>10010
[3,1,6,2,5,4]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>11010
[3,1,6,4,2,5]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>10110
[3,1,6,4,5,2]=>[4,6,1,3,2,5]=>[3,1,6,4,5,2]=>11010
[3,1,6,5,2,4]=>[1,3,2,5,6,4]=>[6,4,5,2,1,3]=>11010
[3,1,6,5,4,2]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>11110
[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>00011
[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>10011
[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>01011
[3,2,1,5,6,4]=>[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>10011
[3,2,1,6,4,5]=>[4,6,5,1,2,3]=>[3,1,2,6,5,4]=>10011
[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[3,2,4,1,5,6]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>00110
[3,2,4,1,6,5]=>[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>10110
[3,2,4,5,1,6]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>01010
[3,2,4,5,6,1]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>10010
[3,2,4,6,1,5]=>[4,2,3,1,6,5]=>[3,5,4,6,1,2]=>10010
[3,2,4,6,5,1]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>11010
[3,2,5,1,4,6]=>[6,2,3,1,5,4]=>[1,5,4,6,2,3]=>01010
[3,2,5,1,6,4]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>11010
[3,2,5,4,1,6]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>01110
[3,2,5,4,6,1]=>[4,5,2,3,1,6]=>[3,2,5,4,6,1]=>11010
[3,2,5,6,1,4]=>[5,2,3,1,6,4]=>[2,5,4,6,1,3]=>10010
[3,2,5,6,4,1]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>10110
[3,2,6,1,4,5]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>10010
[3,2,6,1,5,4]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>11010
[3,2,6,4,1,5]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>10110
[3,2,6,4,5,1]=>[4,6,2,3,1,5]=>[3,1,5,4,6,2]=>11010
[3,2,6,5,1,4]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>11010
[3,2,6,5,4,1]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>11110
[3,4,1,2,5,6]=>[6,5,3,1,4,2]=>[1,2,4,6,3,5]=>00100
[3,4,1,2,6,5]=>[5,6,3,1,4,2]=>[2,1,4,6,3,5]=>10100
[3,4,1,5,2,6]=>[6,3,1,4,2,5]=>[1,4,6,3,5,2]=>01100
[3,4,1,5,6,2]=>[5,3,1,4,2,6]=>[2,4,6,3,5,1]=>10100
[3,4,1,6,2,5]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>10100
[3,4,1,6,5,2]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>11100
[3,4,2,1,5,6]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>00101
[3,4,2,1,6,5]=>[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>10101
[3,4,2,5,1,6]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>01100
[3,4,2,5,6,1]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>10100
[3,4,2,6,1,5]=>[3,2,4,1,6,5]=>[4,5,3,6,1,2]=>10100
[3,4,2,6,5,1]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>11100
[3,4,5,1,2,6]=>[6,4,3,1,5,2]=>[1,3,4,6,2,5]=>01000
[3,4,5,1,6,2]=>[4,3,1,5,2,6]=>[3,4,6,2,5,1]=>11000
[3,4,5,2,1,6]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>01001
[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>11000
[3,4,5,6,1,2]=>[5,4,3,1,6,2]=>[2,3,4,6,1,5]=>10000
[3,4,5,6,2,1]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>10001
[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>[3,4,6,1,2,5]=>10000
[3,4,6,1,5,2]=>[4,3,1,6,2,5]=>[3,4,6,1,5,2]=>11000
[3,4,6,2,1,5]=>[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>10001
[3,4,6,2,5,1]=>[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>11000
[3,4,6,5,1,2]=>[4,3,1,5,6,2]=>[3,4,6,2,1,5]=>11000
[3,4,6,5,2,1]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>11001
[3,5,1,2,4,6]=>[6,3,1,5,4,2]=>[1,4,6,2,3,5]=>01000
[3,5,1,2,6,4]=>[3,1,5,4,6,2]=>[4,6,2,3,1,5]=>11000
[3,5,1,4,2,6]=>[6,3,1,5,2,4]=>[1,4,6,2,5,3]=>01100
[3,5,1,4,6,2]=>[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>11000
[3,5,1,6,2,4]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>11000
[3,5,1,6,4,2]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>11100
[3,5,2,1,4,6]=>[6,3,1,2,5,4]=>[1,4,6,5,2,3]=>01001
[3,5,2,1,6,4]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>11001
[3,5,2,4,1,6]=>[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>01100
[3,5,2,4,6,1]=>[3,2,5,4,1,6]=>[4,5,2,3,6,1]=>11000
[3,5,2,6,1,4]=>[3,2,5,1,6,4]=>[4,5,2,6,1,3]=>11000
[3,5,2,6,4,1]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>11100
[3,5,4,1,2,6]=>[6,3,1,4,5,2]=>[1,4,6,3,2,5]=>01100
[3,5,4,1,6,2]=>[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>11100
[3,5,4,2,1,6]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>01101
[3,5,4,2,6,1]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>11100
[3,5,4,6,1,2]=>[4,5,3,1,6,2]=>[3,2,4,6,1,5]=>11000
[3,5,4,6,2,1]=>[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>11001
[3,5,6,1,2,4]=>[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>10000
[3,5,6,1,4,2]=>[5,3,1,6,2,4]=>[2,4,6,1,5,3]=>10100
[3,5,6,2,1,4]=>[5,3,1,2,6,4]=>[2,4,6,5,1,3]=>10001
[3,5,6,2,4,1]=>[5,3,2,6,1,4]=>[2,4,5,1,6,3]=>10100
[3,5,6,4,1,2]=>[5,3,1,4,6,2]=>[2,4,6,3,1,5]=>10100
[3,5,6,4,2,1]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>10101
[3,6,1,2,4,5]=>[3,1,6,5,4,2]=>[4,6,1,2,3,5]=>10000
[3,6,1,2,5,4]=>[3,1,6,4,5,2]=>[4,6,1,3,2,5]=>11000
[3,6,1,4,2,5]=>[3,1,6,5,2,4]=>[4,6,1,2,5,3]=>10100
[3,6,1,4,5,2]=>[3,1,6,4,2,5]=>[4,6,1,3,5,2]=>11000
[3,6,1,5,2,4]=>[3,1,6,2,5,4]=>[4,6,1,5,2,3]=>11000
[3,6,1,5,4,2]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>11100
[3,6,2,1,4,5]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>10001
[3,6,2,1,5,4]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>11001
[3,6,2,4,1,5]=>[3,2,6,5,1,4]=>[4,5,1,2,6,3]=>10100
[3,6,2,4,5,1]=>[3,2,6,4,1,5]=>[4,5,1,3,6,2]=>11000
[3,6,2,5,1,4]=>[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>11000
[3,6,2,5,4,1]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>11100
[3,6,4,1,2,5]=>[3,1,4,6,5,2]=>[4,6,3,1,2,5]=>10100
[3,6,4,1,5,2]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>11100
[3,6,4,2,1,5]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>10101
[3,6,4,2,5,1]=>[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>11100
[3,6,4,5,1,2]=>[4,6,3,1,5,2]=>[3,1,4,6,2,5]=>11000
[3,6,4,5,2,1]=>[4,6,3,1,2,5]=>[3,1,4,6,5,2]=>11001
[3,6,5,1,2,4]=>[3,1,5,6,4,2]=>[4,6,2,1,3,5]=>11000
[3,6,5,1,4,2]=>[3,1,5,6,2,4]=>[4,6,2,1,5,3]=>11100
[3,6,5,2,1,4]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>11001
[3,6,5,2,4,1]=>[3,2,5,6,1,4]=>[4,5,2,1,6,3]=>11100
[3,6,5,4,1,2]=>[3,1,4,5,6,2]=>[4,6,3,2,1,5]=>11100
[3,6,5,4,2,1]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>11101
[4,1,2,3,5,6]=>[6,5,1,4,3,2]=>[1,2,6,3,4,5]=>00100
[4,1,2,3,6,5]=>[5,6,1,4,3,2]=>[2,1,6,3,4,5]=>10100
[4,1,2,5,3,6]=>[6,1,4,3,5,2]=>[1,6,3,4,2,5]=>01100
[4,1,2,5,6,3]=>[5,1,4,3,6,2]=>[2,6,3,4,1,5]=>10100
[4,1,2,6,3,5]=>[1,4,3,6,5,2]=>[6,3,4,1,2,5]=>10100
[4,1,2,6,5,3]=>[1,4,3,5,6,2]=>[6,3,4,2,1,5]=>11100
[4,1,3,2,5,6]=>[6,5,1,4,2,3]=>[1,2,6,3,5,4]=>00110
[4,1,3,2,6,5]=>[5,6,1,4,2,3]=>[2,1,6,3,5,4]=>10110
[4,1,3,5,2,6]=>[6,1,4,3,2,5]=>[1,6,3,4,5,2]=>01100
[4,1,3,5,6,2]=>[5,1,4,3,2,6]=>[2,6,3,4,5,1]=>10100
[4,1,3,6,2,5]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>10100
[4,1,3,6,5,2]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>11100
[4,1,5,2,3,6]=>[6,1,4,2,5,3]=>[1,6,3,5,2,4]=>01100
[4,1,5,2,6,3]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>11100
[4,1,5,3,2,6]=>[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>01110
[4,1,5,3,6,2]=>[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>11100
[4,1,5,6,2,3]=>[5,1,4,2,6,3]=>[2,6,3,5,1,4]=>10100
[4,1,5,6,3,2]=>[5,1,4,2,3,6]=>[2,6,3,5,4,1]=>10110
[4,1,6,2,3,5]=>[1,4,2,6,5,3]=>[6,3,5,1,2,4]=>10100
[4,1,6,2,5,3]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>11100
[4,1,6,3,2,5]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>10110
[4,1,6,3,5,2]=>[1,4,3,6,2,5]=>[6,3,4,1,5,2]=>11100
[4,1,6,5,2,3]=>[1,4,2,5,6,3]=>[6,3,5,2,1,4]=>11100
[4,1,6,5,3,2]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>11110
[4,2,1,3,5,6]=>[6,5,1,2,4,3]=>[1,2,6,5,3,4]=>00101
[4,2,1,3,6,5]=>[5,6,1,2,4,3]=>[2,1,6,5,3,4]=>10101
[4,2,1,5,3,6]=>[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>01101
[4,2,1,5,6,3]=>[5,1,2,4,3,6]=>[2,6,5,3,4,1]=>10101
[4,2,1,6,3,5]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>10101
[4,2,1,6,5,3]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>11101
[4,2,3,1,5,6]=>[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>00110
[4,2,3,1,6,5]=>[5,6,2,4,1,3]=>[2,1,5,3,6,4]=>10110
[4,2,3,5,1,6]=>[6,2,4,3,1,5]=>[1,5,3,4,6,2]=>01100
[4,2,3,5,6,1]=>[5,2,4,3,1,6]=>[2,5,3,4,6,1]=>10100
[4,2,3,6,1,5]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>10100
[4,2,3,6,5,1]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>11100
[4,2,5,1,3,6]=>[6,2,4,1,5,3]=>[1,5,3,6,2,4]=>01100
[4,2,5,1,6,3]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>11100
[4,2,5,3,1,6]=>[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>01110
[4,2,5,3,6,1]=>[2,4,3,5,1,6]=>[5,3,4,2,6,1]=>11100
[4,2,5,6,1,3]=>[5,2,4,1,6,3]=>[2,5,3,6,1,4]=>10100
[4,2,5,6,3,1]=>[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>10110
[4,2,6,1,3,5]=>[2,4,1,6,5,3]=>[5,3,6,1,2,4]=>10100
[4,2,6,1,5,3]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>11100
[4,2,6,3,1,5]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>10110
[4,2,6,3,5,1]=>[2,4,3,6,1,5]=>[5,3,4,1,6,2]=>11100
[4,2,6,5,1,3]=>[2,4,1,5,6,3]=>[5,3,6,2,1,4]=>11100
[4,2,6,5,3,1]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>11110
[4,3,1,2,5,6]=>[6,5,1,3,4,2]=>[1,2,6,4,3,5]=>00110
[4,3,1,2,6,5]=>[5,6,1,3,4,2]=>[2,1,6,4,3,5]=>10110
[4,3,1,5,2,6]=>[6,1,3,4,2,5]=>[1,6,4,3,5,2]=>01110
[4,3,1,5,6,2]=>[5,1,3,4,2,6]=>[2,6,4,3,5,1]=>10110
[4,3,1,6,2,5]=>[1,3,4,2,6,5]=>[6,4,3,5,1,2]=>10110
[4,3,1,6,5,2]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>11110
[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>00111
[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>10111
[4,3,2,5,1,6]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>01110
[4,3,2,5,6,1]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>10110
[4,3,2,6,1,5]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>10110
[4,3,2,6,5,1]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>11110
[4,3,5,1,2,6]=>[6,3,4,1,5,2]=>[1,4,3,6,2,5]=>01100
[4,3,5,1,6,2]=>[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>11100
[4,3,5,2,1,6]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>01101
[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>11100
[4,3,5,6,1,2]=>[5,3,4,1,6,2]=>[2,4,3,6,1,5]=>10100
[4,3,5,6,2,1]=>[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>10101
[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>[4,3,6,1,2,5]=>10100
[4,3,6,1,5,2]=>[3,4,1,6,2,5]=>[4,3,6,1,5,2]=>11100
[4,3,6,2,1,5]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>10101
[4,3,6,2,5,1]=>[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>11100
[4,3,6,5,1,2]=>[3,4,1,5,6,2]=>[4,3,6,2,1,5]=>11100
[4,3,6,5,2,1]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>11101
[4,5,1,2,3,6]=>[6,4,1,5,3,2]=>[1,3,6,2,4,5]=>01000
[4,5,1,2,6,3]=>[4,1,5,3,6,2]=>[3,6,2,4,1,5]=>11000
[4,5,1,3,2,6]=>[6,4,1,5,2,3]=>[1,3,6,2,5,4]=>01010
[4,5,1,3,6,2]=>[4,1,5,3,2,6]=>[3,6,2,4,5,1]=>11000
[4,5,1,6,2,3]=>[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>11000
[4,5,1,6,3,2]=>[4,1,5,2,3,6]=>[3,6,2,5,4,1]=>11010
[4,5,2,1,3,6]=>[6,4,1,2,5,3]=>[1,3,6,5,2,4]=>01001
[4,5,2,1,6,3]=>[4,1,2,5,3,6]=>[3,6,5,2,4,1]=>11001
[4,5,2,3,1,6]=>[6,4,2,5,1,3]=>[1,3,5,2,6,4]=>01010
[4,5,2,3,6,1]=>[4,2,5,3,1,6]=>[3,5,2,4,6,1]=>11000
[4,5,2,6,1,3]=>[4,2,5,1,6,3]=>[3,5,2,6,1,4]=>11000
[4,5,2,6,3,1]=>[4,2,5,1,3,6]=>[3,5,2,6,4,1]=>11010
[4,5,3,1,2,6]=>[6,4,1,3,5,2]=>[1,3,6,4,2,5]=>01010
[4,5,3,1,6,2]=>[4,1,3,5,2,6]=>[3,6,4,2,5,1]=>11010
[4,5,3,2,1,6]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>01011
[4,5,3,2,6,1]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>11010
[4,5,3,6,1,2]=>[4,3,5,1,6,2]=>[3,4,2,6,1,5]=>11000
[4,5,3,6,2,1]=>[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>11001
[4,5,6,1,2,3]=>[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>10000
[4,5,6,1,3,2]=>[5,4,1,6,2,3]=>[2,3,6,1,5,4]=>10010
[4,5,6,2,1,3]=>[5,4,1,2,6,3]=>[2,3,6,5,1,4]=>10001
[4,5,6,2,3,1]=>[5,4,2,6,1,3]=>[2,3,5,1,6,4]=>10010
[4,5,6,3,1,2]=>[5,4,1,3,6,2]=>[2,3,6,4,1,5]=>10010
[4,5,6,3,2,1]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>10011
[4,6,1,2,3,5]=>[4,1,6,5,3,2]=>[3,6,1,2,4,5]=>10000
[4,6,1,2,5,3]=>[4,1,6,3,5,2]=>[3,6,1,4,2,5]=>11000
[4,6,1,3,2,5]=>[4,1,6,5,2,3]=>[3,6,1,2,5,4]=>10010
[4,6,1,3,5,2]=>[4,1,6,3,2,5]=>[3,6,1,4,5,2]=>11000
[4,6,1,5,2,3]=>[4,1,6,2,5,3]=>[3,6,1,5,2,4]=>11000
[4,6,1,5,3,2]=>[4,1,6,2,3,5]=>[3,6,1,5,4,2]=>11010
[4,6,2,1,3,5]=>[4,1,2,6,5,3]=>[3,6,5,1,2,4]=>10001
[4,6,2,1,5,3]=>[4,1,2,6,3,5]=>[3,6,5,1,4,2]=>11001
[4,6,2,3,1,5]=>[4,2,6,5,1,3]=>[3,5,1,2,6,4]=>10010
[4,6,2,3,5,1]=>[4,2,6,3,1,5]=>[3,5,1,4,6,2]=>11000
[4,6,2,5,1,3]=>[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>11000
[4,6,2,5,3,1]=>[4,2,6,1,3,5]=>[3,5,1,6,4,2]=>11010
[4,6,3,1,2,5]=>[4,1,3,6,5,2]=>[3,6,4,1,2,5]=>10010
[4,6,3,1,5,2]=>[4,1,3,6,2,5]=>[3,6,4,1,5,2]=>11010
[4,6,3,2,1,5]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>10011
[4,6,3,2,5,1]=>[4,2,3,6,1,5]=>[3,5,4,1,6,2]=>11010
[4,6,3,5,1,2]=>[4,3,6,1,5,2]=>[3,4,1,6,2,5]=>11000
[4,6,3,5,2,1]=>[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>11001
[4,6,5,1,2,3]=>[4,1,5,6,3,2]=>[3,6,2,1,4,5]=>11000
[4,6,5,1,3,2]=>[4,1,5,6,2,3]=>[3,6,2,1,5,4]=>11010
[4,6,5,2,1,3]=>[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>11001
[4,6,5,2,3,1]=>[4,2,5,6,1,3]=>[3,5,2,1,6,4]=>11010
[4,6,5,3,1,2]=>[4,1,3,5,6,2]=>[3,6,4,2,1,5]=>11010
[4,6,5,3,2,1]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>11011
[5,1,2,3,4,6]=>[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>01000
[5,1,2,3,6,4]=>[1,5,4,6,3,2]=>[6,2,3,1,4,5]=>11000
[5,1,2,4,3,6]=>[6,1,5,3,4,2]=>[1,6,2,4,3,5]=>01100
[5,1,2,4,6,3]=>[1,5,4,3,6,2]=>[6,2,3,4,1,5]=>11000
[5,1,2,6,3,4]=>[1,5,3,6,4,2]=>[6,2,4,1,3,5]=>11000
[5,1,2,6,4,3]=>[1,5,3,4,6,2]=>[6,2,4,3,1,5]=>11100
[5,1,3,2,4,6]=>[6,1,5,4,2,3]=>[1,6,2,3,5,4]=>01010
[5,1,3,2,6,4]=>[1,5,4,6,2,3]=>[6,2,3,1,5,4]=>11010
[5,1,3,4,2,6]=>[6,1,5,3,2,4]=>[1,6,2,4,5,3]=>01100
[5,1,3,4,6,2]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>11000
[5,1,3,6,2,4]=>[1,5,3,2,6,4]=>[6,2,4,5,1,3]=>11000
[5,1,3,6,4,2]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>11100
[5,1,4,2,3,6]=>[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>01100
[5,1,4,2,6,3]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>11100
[5,1,4,3,2,6]=>[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>01110
[5,1,4,3,6,2]=>[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>11100
[5,1,4,6,2,3]=>[1,5,4,2,6,3]=>[6,2,3,5,1,4]=>11000
[5,1,4,6,3,2]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>11010
[5,1,6,2,3,4]=>[1,5,2,6,4,3]=>[6,2,5,1,3,4]=>11000
[5,1,6,2,4,3]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>11100
[5,1,6,3,2,4]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>11010
[5,1,6,3,4,2]=>[1,5,3,6,2,4]=>[6,2,4,1,5,3]=>11100
[5,1,6,4,2,3]=>[1,5,2,4,6,3]=>[6,2,5,3,1,4]=>11100
[5,1,6,4,3,2]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>11110
[5,2,1,3,4,6]=>[6,1,2,5,4,3]=>[1,6,5,2,3,4]=>01001
[5,2,1,3,6,4]=>[1,2,5,4,6,3]=>[6,5,2,3,1,4]=>11001
[5,2,1,4,3,6]=>[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>01101
[5,2,1,4,6,3]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>11001
[5,2,1,6,3,4]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>11001
[5,2,1,6,4,3]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>11101
[5,2,3,1,4,6]=>[6,2,5,4,1,3]=>[1,5,2,3,6,4]=>01010
[5,2,3,1,6,4]=>[2,5,4,6,1,3]=>[5,2,3,1,6,4]=>11010
[5,2,3,4,1,6]=>[6,2,5,3,1,4]=>[1,5,2,4,6,3]=>01100
[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>[5,2,3,4,6,1]=>11000
[5,2,3,6,1,4]=>[2,5,3,1,6,4]=>[5,2,4,6,1,3]=>11000
[5,2,3,6,4,1]=>[2,5,3,1,4,6]=>[5,2,4,6,3,1]=>11100
[5,2,4,1,3,6]=>[6,2,5,1,4,3]=>[1,5,2,6,3,4]=>01100
[5,2,4,1,6,3]=>[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>11100
[5,2,4,3,1,6]=>[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>01110
[5,2,4,3,6,1]=>[2,5,3,4,1,6]=>[5,2,4,3,6,1]=>11100
[5,2,4,6,1,3]=>[2,5,4,1,6,3]=>[5,2,3,6,1,4]=>11000
[5,2,4,6,3,1]=>[2,5,4,1,3,6]=>[5,2,3,6,4,1]=>11010
[5,2,6,1,3,4]=>[2,5,1,6,4,3]=>[5,2,6,1,3,4]=>11000
[5,2,6,1,4,3]=>[2,5,1,6,3,4]=>[5,2,6,1,4,3]=>11100
[5,2,6,3,1,4]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>11010
[5,2,6,3,4,1]=>[2,5,3,6,1,4]=>[5,2,4,1,6,3]=>11100
[5,2,6,4,1,3]=>[2,5,1,4,6,3]=>[5,2,6,3,1,4]=>11100
[5,2,6,4,3,1]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>11110
[5,3,1,2,4,6]=>[6,1,3,5,4,2]=>[1,6,4,2,3,5]=>01010
[5,3,1,2,6,4]=>[1,3,5,4,6,2]=>[6,4,2,3,1,5]=>11010
[5,3,1,4,2,6]=>[6,1,3,5,2,4]=>[1,6,4,2,5,3]=>01110
[5,3,1,4,6,2]=>[1,3,5,4,2,6]=>[6,4,2,3,5,1]=>11010
[5,3,1,6,2,4]=>[1,3,5,2,6,4]=>[6,4,2,5,1,3]=>11010
[5,3,1,6,4,2]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>11110
[5,3,2,1,4,6]=>[6,1,2,3,5,4]=>[1,6,5,4,2,3]=>01011
[5,3,2,1,6,4]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>11011
[5,3,2,4,1,6]=>[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>01110
[5,3,2,4,6,1]=>[2,3,5,4,1,6]=>[5,4,2,3,6,1]=>11010
[5,3,2,6,1,4]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>11010
[5,3,2,6,4,1]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>11110
[5,3,4,1,2,6]=>[6,3,5,1,4,2]=>[1,4,2,6,3,5]=>01100
[5,3,4,1,6,2]=>[3,5,1,4,2,6]=>[4,2,6,3,5,1]=>11100
[5,3,4,2,1,6]=>[6,3,5,1,2,4]=>[1,4,2,6,5,3]=>01101
[5,3,4,2,6,1]=>[3,5,2,4,1,6]=>[4,2,5,3,6,1]=>11100
[5,3,4,6,1,2]=>[3,5,4,1,6,2]=>[4,2,3,6,1,5]=>11000
[5,3,4,6,2,1]=>[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>11001
[5,3,6,1,2,4]=>[3,5,1,6,4,2]=>[4,2,6,1,3,5]=>11000
[5,3,6,1,4,2]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>11100
[5,3,6,2,1,4]=>[3,5,1,2,6,4]=>[4,2,6,5,1,3]=>11001
[5,3,6,2,4,1]=>[3,5,2,6,1,4]=>[4,2,5,1,6,3]=>11100
[5,3,6,4,1,2]=>[3,5,1,4,6,2]=>[4,2,6,3,1,5]=>11100
[5,3,6,4,2,1]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>11101
[5,4,1,2,3,6]=>[6,1,4,5,3,2]=>[1,6,3,2,4,5]=>01100
[5,4,1,2,6,3]=>[1,4,5,3,6,2]=>[6,3,2,4,1,5]=>11100
[5,4,1,3,2,6]=>[6,1,4,5,2,3]=>[1,6,3,2,5,4]=>01110
[5,4,1,3,6,2]=>[1,4,5,3,2,6]=>[6,3,2,4,5,1]=>11100
[5,4,1,6,2,3]=>[1,4,5,2,6,3]=>[6,3,2,5,1,4]=>11100
[5,4,1,6,3,2]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>11110
[5,4,2,1,3,6]=>[6,1,2,4,5,3]=>[1,6,5,3,2,4]=>01101
[5,4,2,1,6,3]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>11101
[5,4,2,3,1,6]=>[6,2,4,5,1,3]=>[1,5,3,2,6,4]=>01110
[5,4,2,3,6,1]=>[2,4,5,3,1,6]=>[5,3,2,4,6,1]=>11100
[5,4,2,6,1,3]=>[2,4,5,1,6,3]=>[5,3,2,6,1,4]=>11100
[5,4,2,6,3,1]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>11110
[5,4,3,1,2,6]=>[6,1,3,4,5,2]=>[1,6,4,3,2,5]=>01110
[5,4,3,1,6,2]=>[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>11110
[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>01111
[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>11110
[5,4,3,6,1,2]=>[3,4,5,1,6,2]=>[4,3,2,6,1,5]=>11100
[5,4,3,6,2,1]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>11101
[5,4,6,1,2,3]=>[4,5,1,6,3,2]=>[3,2,6,1,4,5]=>11000
[5,4,6,1,3,2]=>[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>11010
[5,4,6,2,1,3]=>[4,5,1,2,6,3]=>[3,2,6,5,1,4]=>11001
[5,4,6,2,3,1]=>[4,5,2,6,1,3]=>[3,2,5,1,6,4]=>11010
[5,4,6,3,1,2]=>[4,5,1,3,6,2]=>[3,2,6,4,1,5]=>11010
[5,4,6,3,2,1]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>11011
[5,6,1,2,3,4]=>[5,1,6,4,3,2]=>[2,6,1,3,4,5]=>10000
[5,6,1,2,4,3]=>[5,1,6,3,4,2]=>[2,6,1,4,3,5]=>10100
[5,6,1,3,2,4]=>[5,1,6,4,2,3]=>[2,6,1,3,5,4]=>10010
[5,6,1,3,4,2]=>[5,1,6,3,2,4]=>[2,6,1,4,5,3]=>10100
[5,6,1,4,2,3]=>[5,1,6,2,4,3]=>[2,6,1,5,3,4]=>10100
[5,6,1,4,3,2]=>[5,1,6,2,3,4]=>[2,6,1,5,4,3]=>10110
[5,6,2,1,3,4]=>[5,1,2,6,4,3]=>[2,6,5,1,3,4]=>10001
[5,6,2,1,4,3]=>[5,1,2,6,3,4]=>[2,6,5,1,4,3]=>10101
[5,6,2,3,1,4]=>[5,2,6,4,1,3]=>[2,5,1,3,6,4]=>10010
[5,6,2,3,4,1]=>[5,2,6,3,1,4]=>[2,5,1,4,6,3]=>10100
[5,6,2,4,1,3]=>[5,2,6,1,4,3]=>[2,5,1,6,3,4]=>10100
[5,6,2,4,3,1]=>[5,2,6,1,3,4]=>[2,5,1,6,4,3]=>10110
[5,6,3,1,2,4]=>[5,1,3,6,4,2]=>[2,6,4,1,3,5]=>10010
[5,6,3,1,4,2]=>[5,1,3,6,2,4]=>[2,6,4,1,5,3]=>10110
[5,6,3,2,1,4]=>[5,1,2,3,6,4]=>[2,6,5,4,1,3]=>10011
[5,6,3,2,4,1]=>[5,2,3,6,1,4]=>[2,5,4,1,6,3]=>10110
[5,6,3,4,1,2]=>[5,3,6,1,4,2]=>[2,4,1,6,3,5]=>10100
[5,6,3,4,2,1]=>[5,3,6,1,2,4]=>[2,4,1,6,5,3]=>10101
[5,6,4,1,2,3]=>[5,1,4,6,3,2]=>[2,6,3,1,4,5]=>10100
[5,6,4,1,3,2]=>[5,1,4,6,2,3]=>[2,6,3,1,5,4]=>10110
[5,6,4,2,1,3]=>[5,1,2,4,6,3]=>[2,6,5,3,1,4]=>10101
[5,6,4,2,3,1]=>[5,2,4,6,1,3]=>[2,5,3,1,6,4]=>10110
[5,6,4,3,1,2]=>[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>10110
[5,6,4,3,2,1]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>10111
[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>10000
[6,1,2,3,5,4]=>[1,6,4,5,3,2]=>[6,1,3,2,4,5]=>11000
[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>[6,1,2,4,3,5]=>10100
[6,1,2,4,5,3]=>[1,6,4,3,5,2]=>[6,1,3,4,2,5]=>11000
[6,1,2,5,3,4]=>[1,6,3,5,4,2]=>[6,1,4,2,3,5]=>11000
[6,1,2,5,4,3]=>[1,6,3,4,5,2]=>[6,1,4,3,2,5]=>11100
[6,1,3,2,4,5]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>10010
[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>[6,1,3,2,5,4]=>11010
[6,1,3,4,2,5]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>10100
[6,1,3,4,5,2]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>11000
[6,1,3,5,2,4]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>11000
[6,1,3,5,4,2]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>11100
[6,1,4,2,3,5]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>10100
[6,1,4,2,5,3]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>11100
[6,1,4,3,2,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>10110
[6,1,4,3,5,2]=>[1,6,3,4,2,5]=>[6,1,4,3,5,2]=>11100
[6,1,4,5,2,3]=>[1,6,4,2,5,3]=>[6,1,3,5,2,4]=>11000
[6,1,4,5,3,2]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>11010
[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>11000
[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>11100
[6,1,5,3,2,4]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>11010
[6,1,5,3,4,2]=>[1,6,3,5,2,4]=>[6,1,4,2,5,3]=>11100
[6,1,5,4,2,3]=>[1,6,2,4,5,3]=>[6,1,5,3,2,4]=>11100
[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>11110
[6,2,1,3,4,5]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>10001
[6,2,1,3,5,4]=>[1,2,6,4,5,3]=>[6,5,1,3,2,4]=>11001
[6,2,1,4,3,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>10101
[6,2,1,4,5,3]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>11001
[6,2,1,5,3,4]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>11001
[6,2,1,5,4,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>11101
[6,2,3,1,4,5]=>[2,6,5,4,1,3]=>[5,1,2,3,6,4]=>10010
[6,2,3,1,5,4]=>[2,6,4,5,1,3]=>[5,1,3,2,6,4]=>11010
[6,2,3,4,1,5]=>[2,6,5,3,1,4]=>[5,1,2,4,6,3]=>10100
[6,2,3,4,5,1]=>[2,6,4,3,1,5]=>[5,1,3,4,6,2]=>11000
[6,2,3,5,1,4]=>[2,6,3,1,5,4]=>[5,1,4,6,2,3]=>11000
[6,2,3,5,4,1]=>[2,6,3,1,4,5]=>[5,1,4,6,3,2]=>11100
[6,2,4,1,3,5]=>[2,6,5,1,4,3]=>[5,1,2,6,3,4]=>10100
[6,2,4,1,5,3]=>[2,6,1,4,3,5]=>[5,1,6,3,4,2]=>11100
[6,2,4,3,1,5]=>[2,6,5,1,3,4]=>[5,1,2,6,4,3]=>10110
[6,2,4,3,5,1]=>[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>11100
[6,2,4,5,1,3]=>[2,6,4,1,5,3]=>[5,1,3,6,2,4]=>11000
[6,2,4,5,3,1]=>[2,6,4,1,3,5]=>[5,1,3,6,4,2]=>11010
[6,2,5,1,3,4]=>[2,6,1,5,4,3]=>[5,1,6,2,3,4]=>11000
[6,2,5,1,4,3]=>[2,6,1,5,3,4]=>[5,1,6,2,4,3]=>11100
[6,2,5,3,1,4]=>[2,6,1,3,5,4]=>[5,1,6,4,2,3]=>11010
[6,2,5,3,4,1]=>[2,6,3,5,1,4]=>[5,1,4,2,6,3]=>11100
[6,2,5,4,1,3]=>[2,6,1,4,5,3]=>[5,1,6,3,2,4]=>11100
[6,2,5,4,3,1]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>11110
[6,3,1,2,4,5]=>[1,3,6,5,4,2]=>[6,4,1,2,3,5]=>10010
[6,3,1,2,5,4]=>[1,3,6,4,5,2]=>[6,4,1,3,2,5]=>11010
[6,3,1,4,2,5]=>[1,3,6,5,2,4]=>[6,4,1,2,5,3]=>10110
[6,3,1,4,5,2]=>[1,3,6,4,2,5]=>[6,4,1,3,5,2]=>11010
[6,3,1,5,2,4]=>[1,3,6,2,5,4]=>[6,4,1,5,2,3]=>11010
[6,3,1,5,4,2]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>11110
[6,3,2,1,4,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>10011
[6,3,2,1,5,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>11011
[6,3,2,4,1,5]=>[2,3,6,5,1,4]=>[5,4,1,2,6,3]=>10110
[6,3,2,4,5,1]=>[2,3,6,4,1,5]=>[5,4,1,3,6,2]=>11010
[6,3,2,5,1,4]=>[2,3,6,1,5,4]=>[5,4,1,6,2,3]=>11010
[6,3,2,5,4,1]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>11110
[6,3,4,1,2,5]=>[3,6,5,1,4,2]=>[4,1,2,6,3,5]=>10100
[6,3,4,1,5,2]=>[3,6,1,4,2,5]=>[4,1,6,3,5,2]=>11100
[6,3,4,2,1,5]=>[3,6,5,1,2,4]=>[4,1,2,6,5,3]=>10101
[6,3,4,2,5,1]=>[3,6,2,4,1,5]=>[4,1,5,3,6,2]=>11100
[6,3,4,5,1,2]=>[3,6,4,1,5,2]=>[4,1,3,6,2,5]=>11000
[6,3,4,5,2,1]=>[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>11001
[6,3,5,1,2,4]=>[3,6,1,5,4,2]=>[4,1,6,2,3,5]=>11000
[6,3,5,1,4,2]=>[3,6,1,5,2,4]=>[4,1,6,2,5,3]=>11100
[6,3,5,2,1,4]=>[3,6,1,2,5,4]=>[4,1,6,5,2,3]=>11001
[6,3,5,2,4,1]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>11100
[6,3,5,4,1,2]=>[3,6,1,4,5,2]=>[4,1,6,3,2,5]=>11100
[6,3,5,4,2,1]=>[3,6,1,2,4,5]=>[4,1,6,5,3,2]=>11101
[6,4,1,2,3,5]=>[1,4,6,5,3,2]=>[6,3,1,2,4,5]=>10100
[6,4,1,2,5,3]=>[1,4,6,3,5,2]=>[6,3,1,4,2,5]=>11100
[6,4,1,3,2,5]=>[1,4,6,5,2,3]=>[6,3,1,2,5,4]=>10110
[6,4,1,3,5,2]=>[1,4,6,3,2,5]=>[6,3,1,4,5,2]=>11100
[6,4,1,5,2,3]=>[1,4,6,2,5,3]=>[6,3,1,5,2,4]=>11100
[6,4,1,5,3,2]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>11110
[6,4,2,1,3,5]=>[1,2,4,6,5,3]=>[6,5,3,1,2,4]=>10101
[6,4,2,1,5,3]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>11101
[6,4,2,3,1,5]=>[2,4,6,5,1,3]=>[5,3,1,2,6,4]=>10110
[6,4,2,3,5,1]=>[2,4,6,3,1,5]=>[5,3,1,4,6,2]=>11100
[6,4,2,5,1,3]=>[2,4,6,1,5,3]=>[5,3,1,6,2,4]=>11100
[6,4,2,5,3,1]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>11110
[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[6,4,3,1,2,5]=>10110
[6,4,3,1,5,2]=>[1,3,4,6,2,5]=>[6,4,3,1,5,2]=>11110
[6,4,3,2,1,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>10111
[6,4,3,2,5,1]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>11110
[6,4,3,5,1,2]=>[3,4,6,1,5,2]=>[4,3,1,6,2,5]=>11100
[6,4,3,5,2,1]=>[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>11101
[6,4,5,1,2,3]=>[4,6,1,5,3,2]=>[3,1,6,2,4,5]=>11000
[6,4,5,1,3,2]=>[4,6,1,5,2,3]=>[3,1,6,2,5,4]=>11010
[6,4,5,2,1,3]=>[4,6,1,2,5,3]=>[3,1,6,5,2,4]=>11001
[6,4,5,2,3,1]=>[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>11010
[6,4,5,3,1,2]=>[4,6,1,3,5,2]=>[3,1,6,4,2,5]=>11010
[6,4,5,3,2,1]=>[4,6,1,2,3,5]=>[3,1,6,5,4,2]=>11011
[6,5,1,2,3,4]=>[1,5,6,4,3,2]=>[6,2,1,3,4,5]=>11000
[6,5,1,2,4,3]=>[1,5,6,3,4,2]=>[6,2,1,4,3,5]=>11100
[6,5,1,3,2,4]=>[1,5,6,4,2,3]=>[6,2,1,3,5,4]=>11010
[6,5,1,3,4,2]=>[1,5,6,3,2,4]=>[6,2,1,4,5,3]=>11100
[6,5,1,4,2,3]=>[1,5,6,2,4,3]=>[6,2,1,5,3,4]=>11100
[6,5,1,4,3,2]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>11110
[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[6,5,2,1,3,4]=>11001
[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>11101
[6,5,2,3,1,4]=>[2,5,6,4,1,3]=>[5,2,1,3,6,4]=>11010
[6,5,2,3,4,1]=>[2,5,6,3,1,4]=>[5,2,1,4,6,3]=>11100
[6,5,2,4,1,3]=>[2,5,6,1,4,3]=>[5,2,1,6,3,4]=>11100
[6,5,2,4,3,1]=>[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>11110
[6,5,3,1,2,4]=>[1,3,5,6,4,2]=>[6,4,2,1,3,5]=>11010
[6,5,3,1,4,2]=>[1,3,5,6,2,4]=>[6,4,2,1,5,3]=>11110
[6,5,3,2,1,4]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>11011
[6,5,3,2,4,1]=>[2,3,5,6,1,4]=>[5,4,2,1,6,3]=>11110
[6,5,3,4,1,2]=>[3,5,6,1,4,2]=>[4,2,1,6,3,5]=>11100
[6,5,3,4,2,1]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>11101
[6,5,4,1,2,3]=>[1,4,5,6,3,2]=>[6,3,2,1,4,5]=>11100
[6,5,4,1,3,2]=>[1,4,5,6,2,3]=>[6,3,2,1,5,4]=>11110
[6,5,4,2,1,3]=>[1,2,4,5,6,3]=>[6,5,3,2,1,4]=>11101
[6,5,4,2,3,1]=>[2,4,5,6,1,3]=>[5,3,2,1,6,4]=>11110
[6,5,4,3,1,2]=>[1,3,4,5,6,2]=>[6,4,3,2,1,5]=>11110
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>11111
[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>000000
[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>100000
[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>010000
[1,2,3,4,6,7,5]=>[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>100000
[1,2,3,4,7,5,6]=>[5,7,6,4,3,2,1]=>[3,1,2,4,5,6,7]=>100000
[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>110000
[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>001000
[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[2,1,4,3,5,6,7]=>101000
[1,2,3,5,6,4,7]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>010000
[1,2,3,5,6,7,4]=>[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>100000
[1,2,3,5,7,4,6]=>[5,4,7,6,3,2,1]=>[3,4,1,2,5,6,7]=>100000
[1,2,3,5,7,6,4]=>[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>110000
[1,2,3,6,4,5,7]=>[7,4,6,5,3,2,1]=>[1,4,2,3,5,6,7]=>010000
[1,2,3,6,4,7,5]=>[4,6,5,7,3,2,1]=>[4,2,3,1,5,6,7]=>110000
[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>011000
[1,2,3,6,5,7,4]=>[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>110000
[1,2,3,6,7,4,5]=>[6,4,7,5,3,2,1]=>[2,4,1,3,5,6,7]=>100000
[1,2,3,6,7,5,4]=>[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>101000
[1,2,3,7,4,5,6]=>[4,7,6,5,3,2,1]=>[4,1,2,3,5,6,7]=>100000
[1,2,3,7,4,6,5]=>[4,7,5,6,3,2,1]=>[4,1,3,2,5,6,7]=>110000
[1,2,3,7,5,4,6]=>[4,5,7,6,3,2,1]=>[4,3,1,2,5,6,7]=>101000
[1,2,3,7,5,6,4]=>[5,7,4,6,3,2,1]=>[3,1,4,2,5,6,7]=>110000
[1,2,3,7,6,4,5]=>[4,6,7,5,3,2,1]=>[4,2,1,3,5,6,7]=>110000
[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>111000
[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>000100
[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[2,1,3,5,4,6,7]=>100100
[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[1,3,2,5,4,6,7]=>010100
[1,2,4,3,6,7,5]=>[6,5,7,3,4,2,1]=>[2,3,1,5,4,6,7]=>100100
[1,2,4,3,7,5,6]=>[5,7,6,3,4,2,1]=>[3,1,2,5,4,6,7]=>100100
[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>[3,2,1,5,4,6,7]=>110100
[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>001000
[1,2,4,5,3,7,6]=>[6,7,4,3,5,2,1]=>[2,1,4,5,3,6,7]=>101000
[1,2,4,5,6,3,7]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>010000
[1,2,4,5,6,7,3]=>[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>100000
[1,2,4,5,7,3,6]=>[5,4,3,7,6,2,1]=>[3,4,5,1,2,6,7]=>100000
[1,2,4,5,7,6,3]=>[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>110000
[1,2,4,6,3,5,7]=>[7,4,3,6,5,2,1]=>[1,4,5,2,3,6,7]=>010000
[1,2,4,6,3,7,5]=>[4,3,6,5,7,2,1]=>[4,5,2,3,1,6,7]=>110000
[1,2,4,6,5,3,7]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>011000
[1,2,4,6,5,7,3]=>[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>110000
[1,2,4,6,7,3,5]=>[6,4,3,7,5,2,1]=>[2,4,5,1,3,6,7]=>100000
[1,2,4,6,7,5,3]=>[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>101000
[1,2,4,7,3,5,6]=>[4,3,7,6,5,2,1]=>[4,5,1,2,3,6,7]=>100000
[1,2,4,7,3,6,5]=>[4,3,7,5,6,2,1]=>[4,5,1,3,2,6,7]=>110000
[1,2,4,7,5,3,6]=>[4,3,5,7,6,2,1]=>[4,5,3,1,2,6,7]=>101000
[1,2,4,7,5,6,3]=>[5,7,4,3,6,2,1]=>[3,1,4,5,2,6,7]=>110000
[1,2,4,7,6,3,5]=>[4,3,6,7,5,2,1]=>[4,5,2,1,3,6,7]=>110000
[1,2,4,7,6,5,3]=>[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>111000
[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[1,2,5,3,4,6,7]=>001000
[1,2,5,3,4,7,6]=>[6,7,3,5,4,2,1]=>[2,1,5,3,4,6,7]=>101000
[1,2,5,3,6,4,7]=>[7,3,5,4,6,2,1]=>[1,5,3,4,2,6,7]=>011000
[1,2,5,3,6,7,4]=>[6,3,5,4,7,2,1]=>[2,5,3,4,1,6,7]=>101000
[1,2,5,3,7,4,6]=>[3,5,4,7,6,2,1]=>[5,3,4,1,2,6,7]=>101000
[1,2,5,3,7,6,4]=>[3,5,4,6,7,2,1]=>[5,3,4,2,1,6,7]=>111000
[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100
[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>[2,1,5,4,3,6,7]=>101100
[1,2,5,4,6,3,7]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>011000
[1,2,5,4,6,7,3]=>[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>101000
[1,2,5,4,7,3,6]=>[4,5,3,7,6,2,1]=>[4,3,5,1,2,6,7]=>101000
[1,2,5,4,7,6,3]=>[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>111000
[1,2,5,6,3,4,7]=>[7,5,3,6,4,2,1]=>[1,3,5,2,4,6,7]=>010000
[1,2,5,6,3,7,4]=>[5,3,6,4,7,2,1]=>[3,5,2,4,1,6,7]=>110000
[1,2,5,6,4,3,7]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>010100
[1,2,5,6,4,7,3]=>[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>110000
[1,2,5,6,7,3,4]=>[6,5,3,7,4,2,1]=>[2,3,5,1,4,6,7]=>100000
[1,2,5,6,7,4,3]=>[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>100100
[1,2,5,7,3,4,6]=>[5,3,7,6,4,2,1]=>[3,5,1,2,4,6,7]=>100000
[1,2,5,7,3,6,4]=>[5,3,7,4,6,2,1]=>[3,5,1,4,2,6,7]=>110000
[1,2,5,7,4,3,6]=>[5,3,4,7,6,2,1]=>[3,5,4,1,2,6,7]=>100100
[1,2,5,7,4,6,3]=>[5,4,7,3,6,2,1]=>[3,4,1,5,2,6,7]=>110000
[1,2,5,7,6,3,4]=>[5,3,6,7,4,2,1]=>[3,5,2,1,4,6,7]=>110000
[1,2,5,7,6,4,3]=>[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>110100
[1,2,6,3,4,5,7]=>[7,3,6,5,4,2,1]=>[1,5,2,3,4,6,7]=>010000
[1,2,6,3,4,7,5]=>[3,6,5,7,4,2,1]=>[5,2,3,1,4,6,7]=>110000
[1,2,6,3,5,4,7]=>[7,3,6,4,5,2,1]=>[1,5,2,4,3,6,7]=>011000
[1,2,6,3,5,7,4]=>[3,6,5,4,7,2,1]=>[5,2,3,4,1,6,7]=>110000
[1,2,6,3,7,4,5]=>[3,6,4,7,5,2,1]=>[5,2,4,1,3,6,7]=>110000
[1,2,6,3,7,5,4]=>[3,6,4,5,7,2,1]=>[5,2,4,3,1,6,7]=>111000
[1,2,6,4,3,5,7]=>[7,3,4,6,5,2,1]=>[1,5,4,2,3,6,7]=>010100
[1,2,6,4,3,7,5]=>[3,4,6,5,7,2,1]=>[5,4,2,3,1,6,7]=>110100
[1,2,6,4,5,3,7]=>[7,4,6,3,5,2,1]=>[1,4,2,5,3,6,7]=>011000
[1,2,6,4,5,7,3]=>[4,6,5,3,7,2,1]=>[4,2,3,5,1,6,7]=>110000
[1,2,6,4,7,3,5]=>[4,6,3,7,5,2,1]=>[4,2,5,1,3,6,7]=>110000
[1,2,6,4,7,5,3]=>[4,6,3,5,7,2,1]=>[4,2,5,3,1,6,7]=>111000
[1,2,6,5,3,4,7]=>[7,3,5,6,4,2,1]=>[1,5,3,2,4,6,7]=>011000
[1,2,6,5,3,7,4]=>[3,5,6,4,7,2,1]=>[5,3,2,4,1,6,7]=>111000
[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>011100
[1,2,6,5,4,7,3]=>[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>111000
[1,2,6,5,7,3,4]=>[5,6,3,7,4,2,1]=>[3,2,5,1,4,6,7]=>110000
[1,2,6,5,7,4,3]=>[5,6,3,4,7,2,1]=>[3,2,5,4,1,6,7]=>110100
[1,2,6,7,3,4,5]=>[6,3,7,5,4,2,1]=>[2,5,1,3,4,6,7]=>100000
[1,2,6,7,3,5,4]=>[6,3,7,4,5,2,1]=>[2,5,1,4,3,6,7]=>101000
[1,2,6,7,4,3,5]=>[6,3,4,7,5,2,1]=>[2,5,4,1,3,6,7]=>100100
[1,2,6,7,4,5,3]=>[6,4,7,3,5,2,1]=>[2,4,1,5,3,6,7]=>101000
[1,2,6,7,5,3,4]=>[6,3,5,7,4,2,1]=>[2,5,3,1,4,6,7]=>101000
[1,2,6,7,5,4,3]=>[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>101100
[1,2,7,3,4,5,6]=>[3,7,6,5,4,2,1]=>[5,1,2,3,4,6,7]=>100000
[1,2,7,3,4,6,5]=>[3,7,5,6,4,2,1]=>[5,1,3,2,4,6,7]=>110000
[1,2,7,3,5,4,6]=>[3,7,6,4,5,2,1]=>[5,1,2,4,3,6,7]=>101000
[1,2,7,3,5,6,4]=>[3,7,5,4,6,2,1]=>[5,1,3,4,2,6,7]=>110000
[1,2,7,3,6,4,5]=>[3,7,4,6,5,2,1]=>[5,1,4,2,3,6,7]=>110000
[1,2,7,3,6,5,4]=>[3,7,4,5,6,2,1]=>[5,1,4,3,2,6,7]=>111000
[1,2,7,4,3,5,6]=>[3,4,7,6,5,2,1]=>[5,4,1,2,3,6,7]=>100100
[1,2,7,4,3,6,5]=>[3,4,7,5,6,2,1]=>[5,4,1,3,2,6,7]=>110100
[1,2,7,4,5,3,6]=>[4,7,6,3,5,2,1]=>[4,1,2,5,3,6,7]=>101000
[1,2,7,4,5,6,3]=>[4,7,5,3,6,2,1]=>[4,1,3,5,2,6,7]=>110000
[1,2,7,4,6,3,5]=>[4,7,3,6,5,2,1]=>[4,1,5,2,3,6,7]=>110000
[1,2,7,4,6,5,3]=>[4,7,3,5,6,2,1]=>[4,1,5,3,2,6,7]=>111000
[1,2,7,5,3,4,6]=>[3,5,7,6,4,2,1]=>[5,3,1,2,4,6,7]=>101000
[1,2,7,5,3,6,4]=>[3,5,7,4,6,2,1]=>[5,3,1,4,2,6,7]=>111000
[1,2,7,5,4,3,6]=>[3,4,5,7,6,2,1]=>[5,4,3,1,2,6,7]=>101100
[1,2,7,5,4,6,3]=>[4,5,7,3,6,2,1]=>[4,3,1,5,2,6,7]=>111000
[1,2,7,5,6,3,4]=>[5,7,3,6,4,2,1]=>[3,1,5,2,4,6,7]=>110000
[1,2,7,5,6,4,3]=>[5,7,3,4,6,2,1]=>[3,1,5,4,2,6,7]=>110100
[1,2,7,6,3,4,5]=>[3,6,7,5,4,2,1]=>[5,2,1,3,4,6,7]=>110000
[1,2,7,6,3,5,4]=>[3,6,7,4,5,2,1]=>[5,2,1,4,3,6,7]=>111000
[1,2,7,6,4,3,5]=>[3,4,6,7,5,2,1]=>[5,4,2,1,3,6,7]=>110100
[1,2,7,6,4,5,3]=>[4,6,7,3,5,2,1]=>[4,2,1,5,3,6,7]=>111000
[1,2,7,6,5,3,4]=>[3,5,6,7,4,2,1]=>[5,3,2,1,4,6,7]=>111000
[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>111100
[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>000010
[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[2,1,3,4,6,5,7]=>100010
[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,3,2,4,6,7,5]=>[6,5,7,4,2,3,1]=>[2,3,1,4,6,5,7]=>100010
[1,3,2,4,7,5,6]=>[5,7,6,4,2,3,1]=>[3,1,2,4,6,5,7]=>100010
[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>[3,2,1,4,6,5,7]=>110010
[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[1,2,4,3,6,5,7]=>001010
[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[2,1,4,3,6,5,7]=>101010
[1,3,2,5,6,4,7]=>[7,5,4,6,2,3,1]=>[1,3,4,2,6,5,7]=>010010
[1,3,2,5,6,7,4]=>[6,5,4,7,2,3,1]=>[2,3,4,1,6,5,7]=>100010
[1,3,2,5,7,4,6]=>[5,4,7,6,2,3,1]=>[3,4,1,2,6,5,7]=>100010
[1,3,2,5,7,6,4]=>[5,4,6,7,2,3,1]=>[3,4,2,1,6,5,7]=>110010
[1,3,2,6,4,5,7]=>[7,4,6,5,2,3,1]=>[1,4,2,3,6,5,7]=>010010
[1,3,2,6,4,7,5]=>[4,6,5,7,2,3,1]=>[4,2,3,1,6,5,7]=>110010
[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>[1,4,3,2,6,5,7]=>011010
[1,3,2,6,5,7,4]=>[5,6,4,7,2,3,1]=>[3,2,4,1,6,5,7]=>110010
[1,3,2,6,7,4,5]=>[6,4,7,5,2,3,1]=>[2,4,1,3,6,5,7]=>100010
[1,3,2,6,7,5,4]=>[6,4,5,7,2,3,1]=>[2,4,3,1,6,5,7]=>101010
[1,3,2,7,4,5,6]=>[4,7,6,5,2,3,1]=>[4,1,2,3,6,5,7]=>100010
[1,3,2,7,4,6,5]=>[4,7,5,6,2,3,1]=>[4,1,3,2,6,5,7]=>110010
[1,3,2,7,5,4,6]=>[4,5,7,6,2,3,1]=>[4,3,1,2,6,5,7]=>101010
[1,3,2,7,5,6,4]=>[5,7,4,6,2,3,1]=>[3,1,4,2,6,5,7]=>110010
[1,3,2,7,6,4,5]=>[4,6,7,5,2,3,1]=>[4,2,1,3,6,5,7]=>110010
[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>[4,3,2,1,6,5,7]=>111010
[1,3,4,2,5,6,7]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>000100
[1,3,4,2,5,7,6]=>[6,7,5,3,2,4,1]=>[2,1,3,5,6,4,7]=>100100
[1,3,4,2,6,5,7]=>[7,5,6,3,2,4,1]=>[1,3,2,5,6,4,7]=>010100
[1,3,4,2,6,7,5]=>[6,5,7,3,2,4,1]=>[2,3,1,5,6,4,7]=>100100
[1,3,4,2,7,5,6]=>[5,7,6,3,2,4,1]=>[3,1,2,5,6,4,7]=>100100
[1,3,4,2,7,6,5]=>[5,6,7,3,2,4,1]=>[3,2,1,5,6,4,7]=>110100
[1,3,4,5,2,6,7]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>001000
[1,3,4,5,2,7,6]=>[6,7,4,3,2,5,1]=>[2,1,4,5,6,3,7]=>101000
[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>010000
[1,3,4,5,6,7,2]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>100000
[1,3,4,5,7,2,6]=>[5,4,3,2,7,6,1]=>[3,4,5,6,1,2,7]=>100000
[1,3,4,5,7,6,2]=>[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>110000
[1,3,4,6,2,5,7]=>[7,4,3,2,6,5,1]=>[1,4,5,6,2,3,7]=>010000
[1,3,4,6,2,7,5]=>[4,3,2,6,5,7,1]=>[4,5,6,2,3,1,7]=>110000
[1,3,4,6,5,2,7]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>011000
[1,3,4,6,5,7,2]=>[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>110000
[1,3,4,6,7,2,5]=>[6,4,3,2,7,5,1]=>[2,4,5,6,1,3,7]=>100000
[1,3,4,6,7,5,2]=>[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>101000
[1,3,4,7,2,5,6]=>[4,3,2,7,6,5,1]=>[4,5,6,1,2,3,7]=>100000
[1,3,4,7,2,6,5]=>[4,3,2,7,5,6,1]=>[4,5,6,1,3,2,7]=>110000
[1,3,4,7,5,2,6]=>[4,3,2,5,7,6,1]=>[4,5,6,3,1,2,7]=>101000
[1,3,4,7,5,6,2]=>[5,7,4,3,2,6,1]=>[3,1,4,5,6,2,7]=>110000
[1,3,4,7,6,2,5]=>[4,3,2,6,7,5,1]=>[4,5,6,2,1,3,7]=>110000
[1,3,4,7,6,5,2]=>[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>111000
[1,3,5,2,4,6,7]=>[7,6,3,2,5,4,1]=>[1,2,5,6,3,4,7]=>001000
[1,3,5,2,4,7,6]=>[6,7,3,2,5,4,1]=>[2,1,5,6,3,4,7]=>101000
[1,3,5,2,6,4,7]=>[7,3,2,5,4,6,1]=>[1,5,6,3,4,2,7]=>011000
[1,3,5,2,6,7,4]=>[6,3,2,5,4,7,1]=>[2,5,6,3,4,1,7]=>101000
[1,3,5,2,7,4,6]=>[3,2,5,4,7,6,1]=>[5,6,3,4,1,2,7]=>101000
[1,3,5,2,7,6,4]=>[3,2,5,4,6,7,1]=>[5,6,3,4,2,1,7]=>111000
[1,3,5,4,2,6,7]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>001100
[1,3,5,4,2,7,6]=>[6,7,3,2,4,5,1]=>[2,1,5,6,4,3,7]=>101100
[1,3,5,4,6,2,7]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>011000
[1,3,5,4,6,7,2]=>[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>101000
[1,3,5,4,7,2,6]=>[4,5,3,2,7,6,1]=>[4,3,5,6,1,2,7]=>101000
[1,3,5,4,7,6,2]=>[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>111000
[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[1,3,5,6,2,4,7]=>010000
[1,3,5,6,2,7,4]=>[5,3,2,6,4,7,1]=>[3,5,6,2,4,1,7]=>110000
[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>010100
[1,3,5,6,4,7,2]=>[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>110000
[1,3,5,6,7,2,4]=>[6,5,3,2,7,4,1]=>[2,3,5,6,1,4,7]=>100000
[1,3,5,6,7,4,2]=>[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>100100
[1,3,5,7,2,4,6]=>[5,3,2,7,6,4,1]=>[3,5,6,1,2,4,7]=>100000
[1,3,5,7,2,6,4]=>[5,3,2,7,4,6,1]=>[3,5,6,1,4,2,7]=>110000
[1,3,5,7,4,2,6]=>[5,3,2,4,7,6,1]=>[3,5,6,4,1,2,7]=>100100
[1,3,5,7,4,6,2]=>[5,4,7,3,2,6,1]=>[3,4,1,5,6,2,7]=>110000
[1,3,5,7,6,2,4]=>[5,3,2,6,7,4,1]=>[3,5,6,2,1,4,7]=>110000
[1,3,5,7,6,4,2]=>[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>110100
[1,3,6,2,4,5,7]=>[7,3,2,6,5,4,1]=>[1,5,6,2,3,4,7]=>010000
[1,3,6,2,4,7,5]=>[3,2,6,5,7,4,1]=>[5,6,2,3,1,4,7]=>110000
[1,3,6,2,5,4,7]=>[7,3,2,6,4,5,1]=>[1,5,6,2,4,3,7]=>011000
[1,3,6,2,5,7,4]=>[3,2,6,5,4,7,1]=>[5,6,2,3,4,1,7]=>110000
[1,3,6,2,7,4,5]=>[3,2,6,4,7,5,1]=>[5,6,2,4,1,3,7]=>110000
[1,3,6,2,7,5,4]=>[3,2,6,4,5,7,1]=>[5,6,2,4,3,1,7]=>111000
[1,3,6,4,2,5,7]=>[7,3,2,4,6,5,1]=>[1,5,6,4,2,3,7]=>010100
[1,3,6,4,2,7,5]=>[3,2,4,6,5,7,1]=>[5,6,4,2,3,1,7]=>110100
[1,3,6,4,5,2,7]=>[7,4,6,3,2,5,1]=>[1,4,2,5,6,3,7]=>011000
[1,3,6,4,5,7,2]=>[4,6,5,3,2,7,1]=>[4,2,3,5,6,1,7]=>110000
[1,3,6,4,7,2,5]=>[4,6,3,2,7,5,1]=>[4,2,5,6,1,3,7]=>110000
[1,3,6,4,7,5,2]=>[4,6,3,2,5,7,1]=>[4,2,5,6,3,1,7]=>111000
[1,3,6,5,2,4,7]=>[7,3,2,5,6,4,1]=>[1,5,6,3,2,4,7]=>011000
[1,3,6,5,2,7,4]=>[3,2,5,6,4,7,1]=>[5,6,3,2,4,1,7]=>111000
[1,3,6,5,4,2,7]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>011100
[1,3,6,5,4,7,2]=>[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>111000
[1,3,6,5,7,2,4]=>[5,6,3,2,7,4,1]=>[3,2,5,6,1,4,7]=>110000
[1,3,6,5,7,4,2]=>[5,6,3,2,4,7,1]=>[3,2,5,6,4,1,7]=>110100
[1,3,6,7,2,4,5]=>[6,3,2,7,5,4,1]=>[2,5,6,1,3,4,7]=>100000
[1,3,6,7,2,5,4]=>[6,3,2,7,4,5,1]=>[2,5,6,1,4,3,7]=>101000
[1,3,6,7,4,2,5]=>[6,3,2,4,7,5,1]=>[2,5,6,4,1,3,7]=>100100
[1,3,6,7,4,5,2]=>[6,4,7,3,2,5,1]=>[2,4,1,5,6,3,7]=>101000
[1,3,6,7,5,2,4]=>[6,3,2,5,7,4,1]=>[2,5,6,3,1,4,7]=>101000
[1,3,6,7,5,4,2]=>[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>101100
[1,3,7,2,4,5,6]=>[3,2,7,6,5,4,1]=>[5,6,1,2,3,4,7]=>100000
[1,3,7,2,4,6,5]=>[3,2,7,5,6,4,1]=>[5,6,1,3,2,4,7]=>110000
[1,3,7,2,5,4,6]=>[3,2,7,6,4,5,1]=>[5,6,1,2,4,3,7]=>101000
[1,3,7,2,5,6,4]=>[3,2,7,5,4,6,1]=>[5,6,1,3,4,2,7]=>110000
[1,3,7,2,6,4,5]=>[3,2,7,4,6,5,1]=>[5,6,1,4,2,3,7]=>110000
[1,3,7,2,6,5,4]=>[3,2,7,4,5,6,1]=>[5,6,1,4,3,2,7]=>111000
[1,3,7,4,2,5,6]=>[3,2,4,7,6,5,1]=>[5,6,4,1,2,3,7]=>100100
[1,3,7,4,2,6,5]=>[3,2,4,7,5,6,1]=>[5,6,4,1,3,2,7]=>110100
[1,3,7,4,5,2,6]=>[4,7,6,3,2,5,1]=>[4,1,2,5,6,3,7]=>101000
[1,3,7,4,5,6,2]=>[4,7,5,3,2,6,1]=>[4,1,3,5,6,2,7]=>110000
[1,3,7,4,6,2,5]=>[4,7,3,2,6,5,1]=>[4,1,5,6,2,3,7]=>110000
[1,3,7,4,6,5,2]=>[4,7,3,2,5,6,1]=>[4,1,5,6,3,2,7]=>111000
[1,3,7,5,2,4,6]=>[3,2,5,7,6,4,1]=>[5,6,3,1,2,4,7]=>101000
[1,3,7,5,2,6,4]=>[3,2,5,7,4,6,1]=>[5,6,3,1,4,2,7]=>111000
[1,3,7,5,4,2,6]=>[3,2,4,5,7,6,1]=>[5,6,4,3,1,2,7]=>101100
[1,3,7,5,4,6,2]=>[4,5,7,3,2,6,1]=>[4,3,1,5,6,2,7]=>111000
[1,3,7,5,6,2,4]=>[5,7,3,2,6,4,1]=>[3,1,5,6,2,4,7]=>110000
[1,3,7,5,6,4,2]=>[5,7,3,2,4,6,1]=>[3,1,5,6,4,2,7]=>110100
[1,3,7,6,2,4,5]=>[3,2,6,7,5,4,1]=>[5,6,2,1,3,4,7]=>110000
[1,3,7,6,2,5,4]=>[3,2,6,7,4,5,1]=>[5,6,2,1,4,3,7]=>111000
[1,3,7,6,4,2,5]=>[3,2,4,6,7,5,1]=>[5,6,4,2,1,3,7]=>110100
[1,3,7,6,4,5,2]=>[4,6,7,3,2,5,1]=>[4,2,1,5,6,3,7]=>111000
[1,3,7,6,5,2,4]=>[3,2,5,6,7,4,1]=>[5,6,3,2,1,4,7]=>111000
[1,3,7,6,5,4,2]=>[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>111100
[1,4,2,3,5,6,7]=>[7,6,5,2,4,3,1]=>[1,2,3,6,4,5,7]=>000100
[1,4,2,3,5,7,6]=>[6,7,5,2,4,3,1]=>[2,1,3,6,4,5,7]=>100100
[1,4,2,3,6,5,7]=>[7,5,6,2,4,3,1]=>[1,3,2,6,4,5,7]=>010100
[1,4,2,3,6,7,5]=>[6,5,7,2,4,3,1]=>[2,3,1,6,4,5,7]=>100100
[1,4,2,3,7,5,6]=>[5,7,6,2,4,3,1]=>[3,1,2,6,4,5,7]=>100100
[1,4,2,3,7,6,5]=>[5,6,7,2,4,3,1]=>[3,2,1,6,4,5,7]=>110100
[1,4,2,5,3,6,7]=>[7,6,2,4,3,5,1]=>[1,2,6,4,5,3,7]=>001100
[1,4,2,5,3,7,6]=>[6,7,2,4,3,5,1]=>[2,1,6,4,5,3,7]=>101100
[1,4,2,5,6,3,7]=>[7,5,2,4,3,6,1]=>[1,3,6,4,5,2,7]=>010100
[1,4,2,5,6,7,3]=>[6,5,2,4,3,7,1]=>[2,3,6,4,5,1,7]=>100100
[1,4,2,5,7,3,6]=>[5,2,4,3,7,6,1]=>[3,6,4,5,1,2,7]=>100100
[1,4,2,5,7,6,3]=>[5,2,4,3,6,7,1]=>[3,6,4,5,2,1,7]=>110100
[1,4,2,6,3,5,7]=>[7,2,4,3,6,5,1]=>[1,6,4,5,2,3,7]=>010100
[1,4,2,6,3,7,5]=>[2,4,3,6,5,7,1]=>[6,4,5,2,3,1,7]=>110100
[1,4,2,6,5,3,7]=>[7,2,4,3,5,6,1]=>[1,6,4,5,3,2,7]=>011100
[1,4,2,6,5,7,3]=>[5,6,2,4,3,7,1]=>[3,2,6,4,5,1,7]=>110100
[1,4,2,6,7,3,5]=>[6,2,4,3,7,5,1]=>[2,6,4,5,1,3,7]=>100100
[1,4,2,6,7,5,3]=>[6,2,4,3,5,7,1]=>[2,6,4,5,3,1,7]=>101100
[1,4,2,7,3,5,6]=>[2,4,3,7,6,5,1]=>[6,4,5,1,2,3,7]=>100100
[1,4,2,7,3,6,5]=>[2,4,3,7,5,6,1]=>[6,4,5,1,3,2,7]=>110100
[1,4,2,7,5,3,6]=>[2,4,3,5,7,6,1]=>[6,4,5,3,1,2,7]=>101100
[1,4,2,7,5,6,3]=>[5,7,2,4,3,6,1]=>[3,1,6,4,5,2,7]=>110100
[1,4,2,7,6,3,5]=>[2,4,3,6,7,5,1]=>[6,4,5,2,1,3,7]=>110100
[1,4,2,7,6,5,3]=>[2,4,3,5,6,7,1]=>[6,4,5,3,2,1,7]=>111100
[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>000110
[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>[2,1,3,6,5,4,7]=>100110
[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>[1,3,2,6,5,4,7]=>010110
[1,4,3,2,6,7,5]=>[6,5,7,2,3,4,1]=>[2,3,1,6,5,4,7]=>100110
[1,4,3,2,7,5,6]=>[5,7,6,2,3,4,1]=>[3,1,2,6,5,4,7]=>100110
[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>[3,2,1,6,5,4,7]=>110110
[1,4,3,5,2,6,7]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>001100
[1,4,3,5,2,7,6]=>[6,7,3,4,2,5,1]=>[2,1,5,4,6,3,7]=>101100
[1,4,3,5,6,2,7]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>010100
[1,4,3,5,6,7,2]=>[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>100100
[1,4,3,5,7,2,6]=>[5,3,4,2,7,6,1]=>[3,5,4,6,1,2,7]=>100100
[1,4,3,5,7,6,2]=>[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>110100
[1,4,3,6,2,5,7]=>[7,3,4,2,6,5,1]=>[1,5,4,6,2,3,7]=>010100
[1,4,3,6,2,7,5]=>[3,4,2,6,5,7,1]=>[5,4,6,2,3,1,7]=>110100
[1,4,3,6,5,2,7]=>[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>011100
[1,4,3,6,5,7,2]=>[5,6,3,4,2,7,1]=>[3,2,5,4,6,1,7]=>110100
[1,4,3,6,7,2,5]=>[6,3,4,2,7,5,1]=>[2,5,4,6,1,3,7]=>100100
[1,4,3,6,7,5,2]=>[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>101100
[1,4,3,7,2,5,6]=>[3,4,2,7,6,5,1]=>[5,4,6,1,2,3,7]=>100100
[1,4,3,7,2,6,5]=>[3,4,2,7,5,6,1]=>[5,4,6,1,3,2,7]=>110100
[1,4,3,7,5,2,6]=>[3,4,2,5,7,6,1]=>[5,4,6,3,1,2,7]=>101100
[1,4,3,7,5,6,2]=>[5,7,3,4,2,6,1]=>[3,1,5,4,6,2,7]=>110100
[1,4,3,7,6,2,5]=>[3,4,2,6,7,5,1]=>[5,4,6,2,1,3,7]=>110100
[1,4,3,7,6,5,2]=>[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>111100
[1,4,5,2,3,6,7]=>[7,6,4,2,5,3,1]=>[1,2,4,6,3,5,7]=>001000
[1,4,5,2,3,7,6]=>[6,7,4,2,5,3,1]=>[2,1,4,6,3,5,7]=>101000
[1,4,5,2,6,3,7]=>[7,4,2,5,3,6,1]=>[1,4,6,3,5,2,7]=>011000
[1,4,5,2,6,7,3]=>[6,4,2,5,3,7,1]=>[2,4,6,3,5,1,7]=>101000
[1,4,5,2,7,3,6]=>[4,2,5,3,7,6,1]=>[4,6,3,5,1,2,7]=>101000
[1,4,5,2,7,6,3]=>[4,2,5,3,6,7,1]=>[4,6,3,5,2,1,7]=>111000
[1,4,5,3,2,6,7]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>001010
[1,4,5,3,2,7,6]=>[6,7,4,2,3,5,1]=>[2,1,4,6,5,3,7]=>101010
[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>011000
[1,4,5,3,6,7,2]=>[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>101000
[1,4,5,3,7,2,6]=>[4,3,5,2,7,6,1]=>[4,5,3,6,1,2,7]=>101000
[1,4,5,3,7,6,2]=>[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>111000
[1,4,5,6,2,3,7]=>[7,5,4,2,6,3,1]=>[1,3,4,6,2,5,7]=>010000
[1,4,5,6,2,7,3]=>[5,4,2,6,3,7,1]=>[3,4,6,2,5,1,7]=>110000
[1,4,5,6,3,2,7]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>010010
[1,4,5,6,3,7,2]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>110000
[1,4,5,6,7,2,3]=>[6,5,4,2,7,3,1]=>[2,3,4,6,1,5,7]=>100000
[1,4,5,6,7,3,2]=>[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>100010
[1,4,5,7,2,3,6]=>[5,4,2,7,6,3,1]=>[3,4,6,1,2,5,7]=>100000
[1,4,5,7,2,6,3]=>[5,4,2,7,3,6,1]=>[3,4,6,1,5,2,7]=>110000
[1,4,5,7,3,2,6]=>[5,4,2,3,7,6,1]=>[3,4,6,5,1,2,7]=>100010
[1,4,5,7,3,6,2]=>[5,4,3,7,2,6,1]=>[3,4,5,1,6,2,7]=>110000
[1,4,5,7,6,2,3]=>[5,4,2,6,7,3,1]=>[3,4,6,2,1,5,7]=>110000
[1,4,5,7,6,3,2]=>[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>110010
[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[1,4,6,2,3,5,7]=>010000
[1,4,6,2,3,7,5]=>[4,2,6,5,7,3,1]=>[4,6,2,3,1,5,7]=>110000
[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[1,4,6,2,5,3,7]=>011000
[1,4,6,2,5,7,3]=>[4,2,6,5,3,7,1]=>[4,6,2,3,5,1,7]=>110000
[1,4,6,2,7,3,5]=>[4,2,6,3,7,5,1]=>[4,6,2,5,1,3,7]=>110000
[1,4,6,2,7,5,3]=>[4,2,6,3,5,7,1]=>[4,6,2,5,3,1,7]=>111000
[1,4,6,3,2,5,7]=>[7,4,2,3,6,5,1]=>[1,4,6,5,2,3,7]=>010010
[1,4,6,3,2,7,5]=>[4,2,3,6,5,7,1]=>[4,6,5,2,3,1,7]=>110010
[1,4,6,3,5,2,7]=>[7,4,3,6,2,5,1]=>[1,4,5,2,6,3,7]=>011000
[1,4,6,3,5,7,2]=>[4,3,6,5,2,7,1]=>[4,5,2,3,6,1,7]=>110000
[1,4,6,3,7,2,5]=>[4,3,6,2,7,5,1]=>[4,5,2,6,1,3,7]=>110000
[1,4,6,3,7,5,2]=>[4,3,6,2,5,7,1]=>[4,5,2,6,3,1,7]=>111000
[1,4,6,5,2,3,7]=>[7,4,2,5,6,3,1]=>[1,4,6,3,2,5,7]=>011000
[1,4,6,5,2,7,3]=>[4,2,5,6,3,7,1]=>[4,6,3,2,5,1,7]=>111000
[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>011010
[1,4,6,5,3,7,2]=>[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>111000
[1,4,6,5,7,2,3]=>[5,6,4,2,7,3,1]=>[3,2,4,6,1,5,7]=>110000
[1,4,6,5,7,3,2]=>[5,6,4,2,3,7,1]=>[3,2,4,6,5,1,7]=>110010
[1,4,6,7,2,3,5]=>[6,4,2,7,5,3,1]=>[2,4,6,1,3,5,7]=>100000
[1,4,6,7,2,5,3]=>[6,4,2,7,3,5,1]=>[2,4,6,1,5,3,7]=>101000
[1,4,6,7,3,2,5]=>[6,4,2,3,7,5,1]=>[2,4,6,5,1,3,7]=>100010
[1,4,6,7,3,5,2]=>[6,4,3,7,2,5,1]=>[2,4,5,1,6,3,7]=>101000
[1,4,6,7,5,2,3]=>[6,4,2,5,7,3,1]=>[2,4,6,3,1,5,7]=>101000
[1,4,6,7,5,3,2]=>[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>101010
[1,4,7,2,3,5,6]=>[4,2,7,6,5,3,1]=>[4,6,1,2,3,5,7]=>100000
[1,4,7,2,3,6,5]=>[4,2,7,5,6,3,1]=>[4,6,1,3,2,5,7]=>110000
[1,4,7,2,5,3,6]=>[4,2,7,6,3,5,1]=>[4,6,1,2,5,3,7]=>101000
[1,4,7,2,5,6,3]=>[4,2,7,5,3,6,1]=>[4,6,1,3,5,2,7]=>110000
[1,4,7,2,6,3,5]=>[4,2,7,3,6,5,1]=>[4,6,1,5,2,3,7]=>110000
[1,4,7,2,6,5,3]=>[4,2,7,3,5,6,1]=>[4,6,1,5,3,2,7]=>111000
[1,4,7,3,2,5,6]=>[4,2,3,7,6,5,1]=>[4,6,5,1,2,3,7]=>100010
[1,4,7,3,2,6,5]=>[4,2,3,7,5,6,1]=>[4,6,5,1,3,2,7]=>110010
[1,4,7,3,5,2,6]=>[4,3,7,6,2,5,1]=>[4,5,1,2,6,3,7]=>101000
[1,4,7,3,5,6,2]=>[4,3,7,5,2,6,1]=>[4,5,1,3,6,2,7]=>110000
[1,4,7,3,6,2,5]=>[4,3,7,2,6,5,1]=>[4,5,1,6,2,3,7]=>110000
[1,4,7,3,6,5,2]=>[4,3,7,2,5,6,1]=>[4,5,1,6,3,2,7]=>111000
[1,4,7,5,2,3,6]=>[4,2,5,7,6,3,1]=>[4,6,3,1,2,5,7]=>101000
[1,4,7,5,2,6,3]=>[4,2,5,7,3,6,1]=>[4,6,3,1,5,2,7]=>111000
[1,4,7,5,3,2,6]=>[4,2,3,5,7,6,1]=>[4,6,5,3,1,2,7]=>101010
[1,4,7,5,3,6,2]=>[4,3,5,7,2,6,1]=>[4,5,3,1,6,2,7]=>111000
[1,4,7,5,6,2,3]=>[5,7,4,2,6,3,1]=>[3,1,4,6,2,5,7]=>110000
[1,4,7,5,6,3,2]=>[5,7,4,2,3,6,1]=>[3,1,4,6,5,2,7]=>110010
[1,4,7,6,2,3,5]=>[4,2,6,7,5,3,1]=>[4,6,2,1,3,5,7]=>110000
[1,4,7,6,2,5,3]=>[4,2,6,7,3,5,1]=>[4,6,2,1,5,3,7]=>111000
[1,4,7,6,3,2,5]=>[4,2,3,6,7,5,1]=>[4,6,5,2,1,3,7]=>110010
[1,4,7,6,3,5,2]=>[4,3,6,7,2,5,1]=>[4,5,2,1,6,3,7]=>111000
[1,4,7,6,5,2,3]=>[4,2,5,6,7,3,1]=>[4,6,3,2,1,5,7]=>111000
[1,4,7,6,5,3,2]=>[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>111010
[1,5,2,3,4,6,7]=>[7,6,2,5,4,3,1]=>[1,2,6,3,4,5,7]=>001000
[1,5,2,3,4,7,6]=>[6,7,2,5,4,3,1]=>[2,1,6,3,4,5,7]=>101000
[1,5,2,3,6,4,7]=>[7,2,5,4,6,3,1]=>[1,6,3,4,2,5,7]=>011000
[1,5,2,3,6,7,4]=>[6,2,5,4,7,3,1]=>[2,6,3,4,1,5,7]=>101000
[1,5,2,3,7,4,6]=>[2,5,4,7,6,3,1]=>[6,3,4,1,2,5,7]=>101000
[1,5,2,3,7,6,4]=>[2,5,4,6,7,3,1]=>[6,3,4,2,1,5,7]=>111000
[1,5,2,4,3,6,7]=>[7,6,2,5,3,4,1]=>[1,2,6,3,5,4,7]=>001100
[1,5,2,4,3,7,6]=>[6,7,2,5,3,4,1]=>[2,1,6,3,5,4,7]=>101100
[1,5,2,4,6,3,7]=>[7,2,5,4,3,6,1]=>[1,6,3,4,5,2,7]=>011000
[1,5,2,4,6,7,3]=>[6,2,5,4,3,7,1]=>[2,6,3,4,5,1,7]=>101000
[1,5,2,4,7,3,6]=>[2,5,4,3,7,6,1]=>[6,3,4,5,1,2,7]=>101000
[1,5,2,4,7,6,3]=>[2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>111000
[1,5,2,6,3,4,7]=>[7,2,5,3,6,4,1]=>[1,6,3,5,2,4,7]=>011000
[1,5,2,6,3,7,4]=>[2,5,3,6,4,7,1]=>[6,3,5,2,4,1,7]=>111000
[1,5,2,6,4,3,7]=>[7,2,5,3,4,6,1]=>[1,6,3,5,4,2,7]=>011100
[1,5,2,6,4,7,3]=>[2,5,4,6,3,7,1]=>[6,3,4,2,5,1,7]=>111000
[1,5,2,6,7,3,4]=>[6,2,5,3,7,4,1]=>[2,6,3,5,1,4,7]=>101000
[1,5,2,6,7,4,3]=>[6,2,5,3,4,7,1]=>[2,6,3,5,4,1,7]=>101100
[1,5,2,7,3,4,6]=>[2,5,3,7,6,4,1]=>[6,3,5,1,2,4,7]=>101000
[1,5,2,7,3,6,4]=>[2,5,3,7,4,6,1]=>[6,3,5,1,4,2,7]=>111000
[1,5,2,7,4,3,6]=>[2,5,3,4,7,6,1]=>[6,3,5,4,1,2,7]=>101100
[1,5,2,7,4,6,3]=>[2,5,4,7,3,6,1]=>[6,3,4,1,5,2,7]=>111000
[1,5,2,7,6,3,4]=>[2,5,3,6,7,4,1]=>[6,3,5,2,1,4,7]=>111000
[1,5,2,7,6,4,3]=>[2,5,3,4,6,7,1]=>[6,3,5,4,2,1,7]=>111100
[1,5,3,2,4,6,7]=>[7,6,2,3,5,4,1]=>[1,2,6,5,3,4,7]=>001010
[1,5,3,2,4,7,6]=>[6,7,2,3,5,4,1]=>[2,1,6,5,3,4,7]=>101010
[1,5,3,2,6,4,7]=>[7,2,3,5,4,6,1]=>[1,6,5,3,4,2,7]=>011010
[1,5,3,2,6,7,4]=>[6,2,3,5,4,7,1]=>[2,6,5,3,4,1,7]=>101010
[1,5,3,2,7,4,6]=>[2,3,5,4,7,6,1]=>[6,5,3,4,1,2,7]=>101010
[1,5,3,2,7,6,4]=>[2,3,5,4,6,7,1]=>[6,5,3,4,2,1,7]=>111010
[1,5,3,4,2,6,7]=>[7,6,3,5,2,4,1]=>[1,2,5,3,6,4,7]=>001100
[1,5,3,4,2,7,6]=>[6,7,3,5,2,4,1]=>[2,1,5,3,6,4,7]=>101100
[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>[1,5,3,4,6,2,7]=>011000
[1,5,3,4,6,7,2]=>[6,3,5,4,2,7,1]=>[2,5,3,4,6,1,7]=>101000
[1,5,3,4,7,2,6]=>[3,5,4,2,7,6,1]=>[5,3,4,6,1,2,7]=>101000
[1,5,3,4,7,6,2]=>[3,5,4,2,6,7,1]=>[5,3,4,6,2,1,7]=>111000
[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[1,5,3,6,2,4,7]=>011000
[1,5,3,6,2,7,4]=>[3,5,2,6,4,7,1]=>[5,3,6,2,4,1,7]=>111000
[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>[1,5,3,6,4,2,7]=>011100
[1,5,3,6,4,7,2]=>[3,5,4,6,2,7,1]=>[5,3,4,2,6,1,7]=>111000
[1,5,3,6,7,2,4]=>[6,3,5,2,7,4,1]=>[2,5,3,6,1,4,7]=>101000
[1,5,3,6,7,4,2]=>[6,3,5,2,4,7,1]=>[2,5,3,6,4,1,7]=>101100
[1,5,3,7,2,4,6]=>[3,5,2,7,6,4,1]=>[5,3,6,1,2,4,7]=>101000
[1,5,3,7,2,6,4]=>[3,5,2,7,4,6,1]=>[5,3,6,1,4,2,7]=>111000
[1,5,3,7,4,2,6]=>[3,5,2,4,7,6,1]=>[5,3,6,4,1,2,7]=>101100
[1,5,3,7,4,6,2]=>[3,5,4,7,2,6,1]=>[5,3,4,1,6,2,7]=>111000
[1,5,3,7,6,2,4]=>[3,5,2,6,7,4,1]=>[5,3,6,2,1,4,7]=>111000
[1,5,3,7,6,4,2]=>[3,5,2,4,6,7,1]=>[5,3,6,4,2,1,7]=>111100
[1,5,4,2,3,6,7]=>[7,6,2,4,5,3,1]=>[1,2,6,4,3,5,7]=>001100
[1,5,4,2,3,7,6]=>[6,7,2,4,5,3,1]=>[2,1,6,4,3,5,7]=>101100
[1,5,4,2,6,3,7]=>[7,2,4,5,3,6,1]=>[1,6,4,3,5,2,7]=>011100
[1,5,4,2,6,7,3]=>[6,2,4,5,3,7,1]=>[2,6,4,3,5,1,7]=>101100
[1,5,4,2,7,3,6]=>[2,4,5,3,7,6,1]=>[6,4,3,5,1,2,7]=>101100
[1,5,4,2,7,6,3]=>[2,4,5,3,6,7,1]=>[6,4,3,5,2,1,7]=>111100
[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>001110
[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>[2,1,6,5,4,3,7]=>101110
[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>011100
[1,5,4,3,6,7,2]=>[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>101100
[1,5,4,3,7,2,6]=>[3,4,5,2,7,6,1]=>[5,4,3,6,1,2,7]=>101100
[1,5,4,3,7,6,2]=>[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>111100
[1,5,4,6,2,3,7]=>[7,4,5,2,6,3,1]=>[1,4,3,6,2,5,7]=>011000
[1,5,4,6,2,7,3]=>[4,5,2,6,3,7,1]=>[4,3,6,2,5,1,7]=>111000
[1,5,4,6,3,2,7]=>[7,4,5,2,3,6,1]=>[1,4,3,6,5,2,7]=>011010
[1,5,4,6,3,7,2]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>111000
[1,5,4,6,7,2,3]=>[6,4,5,2,7,3,1]=>[2,4,3,6,1,5,7]=>101000
[1,5,4,6,7,3,2]=>[6,4,5,2,3,7,1]=>[2,4,3,6,5,1,7]=>101010
[1,5,4,7,2,3,6]=>[4,5,2,7,6,3,1]=>[4,3,6,1,2,5,7]=>101000
[1,5,4,7,2,6,3]=>[4,5,2,7,3,6,1]=>[4,3,6,1,5,2,7]=>111000
[1,5,4,7,3,2,6]=>[4,5,2,3,7,6,1]=>[4,3,6,5,1,2,7]=>101010
[1,5,4,7,3,6,2]=>[4,5,3,7,2,6,1]=>[4,3,5,1,6,2,7]=>111000
[1,5,4,7,6,2,3]=>[4,5,2,6,7,3,1]=>[4,3,6,2,1,5,7]=>111000
[1,5,4,7,6,3,2]=>[4,5,2,3,6,7,1]=>[4,3,6,5,2,1,7]=>111010
[1,5,6,2,3,4,7]=>[7,5,2,6,4,3,1]=>[1,3,6,2,4,5,7]=>010000
[1,5,6,2,3,7,4]=>[5,2,6,4,7,3,1]=>[3,6,2,4,1,5,7]=>110000
[1,5,6,2,4,3,7]=>[7,5,2,6,3,4,1]=>[1,3,6,2,5,4,7]=>010100
[1,5,6,2,4,7,3]=>[5,2,6,4,3,7,1]=>[3,6,2,4,5,1,7]=>110000
[1,5,6,2,7,3,4]=>[5,2,6,3,7,4,1]=>[3,6,2,5,1,4,7]=>110000
[1,5,6,2,7,4,3]=>[5,2,6,3,4,7,1]=>[3,6,2,5,4,1,7]=>110100
[1,5,6,3,2,4,7]=>[7,5,2,3,6,4,1]=>[1,3,6,5,2,4,7]=>010010
[1,5,6,3,2,7,4]=>[5,2,3,6,4,7,1]=>[3,6,5,2,4,1,7]=>110010
[1,5,6,3,4,2,7]=>[7,5,3,6,2,4,1]=>[1,3,5,2,6,4,7]=>010100
[1,5,6,3,4,7,2]=>[5,3,6,4,2,7,1]=>[3,5,2,4,6,1,7]=>110000
[1,5,6,3,7,2,4]=>[5,3,6,2,7,4,1]=>[3,5,2,6,1,4,7]=>110000
[1,5,6,3,7,4,2]=>[5,3,6,2,4,7,1]=>[3,5,2,6,4,1,7]=>110100
[1,5,6,4,2,3,7]=>[7,5,2,4,6,3,1]=>[1,3,6,4,2,5,7]=>010100
[1,5,6,4,2,7,3]=>[5,2,4,6,3,7,1]=>[3,6,4,2,5,1,7]=>110100
[1,5,6,4,3,2,7]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>010110
[1,5,6,4,3,7,2]=>[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>110100
[1,5,6,4,7,2,3]=>[5,4,6,2,7,3,1]=>[3,4,2,6,1,5,7]=>110000
[1,5,6,4,7,3,2]=>[5,4,6,2,3,7,1]=>[3,4,2,6,5,1,7]=>110010
[1,5,6,7,2,3,4]=>[6,5,2,7,4,3,1]=>[2,3,6,1,4,5,7]=>100000
[1,5,6,7,2,4,3]=>[6,5,2,7,3,4,1]=>[2,3,6,1,5,4,7]=>100100
[1,5,6,7,3,2,4]=>[6,5,2,3,7,4,1]=>[2,3,6,5,1,4,7]=>100010
[1,5,6,7,3,4,2]=>[6,5,3,7,2,4,1]=>[2,3,5,1,6,4,7]=>100100
[1,5,6,7,4,2,3]=>[6,5,2,4,7,3,1]=>[2,3,6,4,1,5,7]=>100100
[1,5,6,7,4,3,2]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>100110
[1,5,7,2,3,4,6]=>[5,2,7,6,4,3,1]=>[3,6,1,2,4,5,7]=>100000
[1,5,7,2,3,6,4]=>[5,2,7,4,6,3,1]=>[3,6,1,4,2,5,7]=>110000
[1,5,7,2,4,3,6]=>[5,2,7,6,3,4,1]=>[3,6,1,2,5,4,7]=>100100
[1,5,7,2,4,6,3]=>[5,2,7,4,3,6,1]=>[3,6,1,4,5,2,7]=>110000
[1,5,7,2,6,3,4]=>[5,2,7,3,6,4,1]=>[3,6,1,5,2,4,7]=>110000
[1,5,7,2,6,4,3]=>[5,2,7,3,4,6,1]=>[3,6,1,5,4,2,7]=>110100
[1,5,7,3,2,4,6]=>[5,2,3,7,6,4,1]=>[3,6,5,1,2,4,7]=>100010
[1,5,7,3,2,6,4]=>[5,2,3,7,4,6,1]=>[3,6,5,1,4,2,7]=>110010
[1,5,7,3,4,2,6]=>[5,3,7,6,2,4,1]=>[3,5,1,2,6,4,7]=>100100
[1,5,7,3,4,6,2]=>[5,3,7,4,2,6,1]=>[3,5,1,4,6,2,7]=>110000
[1,5,7,3,6,2,4]=>[5,3,7,2,6,4,1]=>[3,5,1,6,2,4,7]=>110000
[1,5,7,3,6,4,2]=>[5,3,7,2,4,6,1]=>[3,5,1,6,4,2,7]=>110100
[1,5,7,4,2,3,6]=>[5,2,4,7,6,3,1]=>[3,6,4,1,2,5,7]=>100100
[1,5,7,4,2,6,3]=>[5,2,4,7,3,6,1]=>[3,6,4,1,5,2,7]=>110100
[1,5,7,4,3,2,6]=>[5,2,3,4,7,6,1]=>[3,6,5,4,1,2,7]=>100110
[1,5,7,4,3,6,2]=>[5,3,4,7,2,6,1]=>[3,5,4,1,6,2,7]=>110100
[1,5,7,4,6,2,3]=>[5,4,7,2,6,3,1]=>[3,4,1,6,2,5,7]=>110000
[1,5,7,4,6,3,2]=>[5,4,7,2,3,6,1]=>[3,4,1,6,5,2,7]=>110010
[1,5,7,6,2,3,4]=>[5,2,6,7,4,3,1]=>[3,6,2,1,4,5,7]=>110000
[1,5,7,6,2,4,3]=>[5,2,6,7,3,4,1]=>[3,6,2,1,5,4,7]=>110100
[1,5,7,6,3,2,4]=>[5,2,3,6,7,4,1]=>[3,6,5,2,1,4,7]=>110010
[1,5,7,6,3,4,2]=>[5,3,6,7,2,4,1]=>[3,5,2,1,6,4,7]=>110100
[1,5,7,6,4,2,3]=>[5,2,4,6,7,3,1]=>[3,6,4,2,1,5,7]=>110100
[1,5,7,6,4,3,2]=>[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>110110
[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[1,6,2,3,4,5,7]=>010000
[1,6,2,3,4,7,5]=>[2,6,5,7,4,3,1]=>[6,2,3,1,4,5,7]=>110000
[1,6,2,3,5,4,7]=>[7,2,6,4,5,3,1]=>[1,6,2,4,3,5,7]=>011000
[1,6,2,3,5,7,4]=>[2,6,5,4,7,3,1]=>[6,2,3,4,1,5,7]=>110000
[1,6,2,3,7,4,5]=>[2,6,4,7,5,3,1]=>[6,2,4,1,3,5,7]=>110000
[1,6,2,3,7,5,4]=>[2,6,4,5,7,3,1]=>[6,2,4,3,1,5,7]=>111000
[1,6,2,4,3,5,7]=>[7,2,6,5,3,4,1]=>[1,6,2,3,5,4,7]=>010100
[1,6,2,4,3,7,5]=>[2,6,5,7,3,4,1]=>[6,2,3,1,5,4,7]=>110100
[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[1,6,2,4,5,3,7]=>011000
[1,6,2,4,5,7,3]=>[2,6,5,4,3,7,1]=>[6,2,3,4,5,1,7]=>110000
[1,6,2,4,7,3,5]=>[2,6,4,3,7,5,1]=>[6,2,4,5,1,3,7]=>110000
[1,6,2,4,7,5,3]=>[2,6,4,3,5,7,1]=>[6,2,4,5,3,1,7]=>111000
[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[1,6,2,5,3,4,7]=>011000
[1,6,2,5,3,7,4]=>[2,6,3,5,4,7,1]=>[6,2,5,3,4,1,7]=>111000
[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[1,6,2,5,4,3,7]=>011100
[1,6,2,5,4,7,3]=>[2,6,4,5,3,7,1]=>[6,2,4,3,5,1,7]=>111000
[1,6,2,5,7,3,4]=>[2,6,5,3,7,4,1]=>[6,2,3,5,1,4,7]=>110000
[1,6,2,5,7,4,3]=>[2,6,5,3,4,7,1]=>[6,2,3,5,4,1,7]=>110100
[1,6,2,7,3,4,5]=>[2,6,3,7,5,4,1]=>[6,2,5,1,3,4,7]=>110000
[1,6,2,7,3,5,4]=>[2,6,3,7,4,5,1]=>[6,2,5,1,4,3,7]=>111000
[1,6,2,7,4,3,5]=>[2,6,3,4,7,5,1]=>[6,2,5,4,1,3,7]=>110100
[1,6,2,7,4,5,3]=>[2,6,4,7,3,5,1]=>[6,2,4,1,5,3,7]=>111000
[1,6,2,7,5,3,4]=>[2,6,3,5,7,4,1]=>[6,2,5,3,1,4,7]=>111000
[1,6,2,7,5,4,3]=>[2,6,3,4,5,7,1]=>[6,2,5,4,3,1,7]=>111100
[1,6,3,2,4,5,7]=>[7,2,3,6,5,4,1]=>[1,6,5,2,3,4,7]=>010010
[1,6,3,2,4,7,5]=>[2,3,6,5,7,4,1]=>[6,5,2,3,1,4,7]=>110010
[1,6,3,2,5,4,7]=>[7,2,3,6,4,5,1]=>[1,6,5,2,4,3,7]=>011010
[1,6,3,2,5,7,4]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,1,7]=>110010
[1,6,3,2,7,4,5]=>[2,3,6,4,7,5,1]=>[6,5,2,4,1,3,7]=>110010
[1,6,3,2,7,5,4]=>[2,3,6,4,5,7,1]=>[6,5,2,4,3,1,7]=>111010
[1,6,3,4,2,5,7]=>[7,3,6,5,2,4,1]=>[1,5,2,3,6,4,7]=>010100
[1,6,3,4,2,7,5]=>[3,6,5,7,2,4,1]=>[5,2,3,1,6,4,7]=>110100
[1,6,3,4,5,2,7]=>[7,3,6,4,2,5,1]=>[1,5,2,4,6,3,7]=>011000
[1,6,3,4,5,7,2]=>[3,6,5,4,2,7,1]=>[5,2,3,4,6,1,7]=>110000
[1,6,3,4,7,2,5]=>[3,6,4,2,7,5,1]=>[5,2,4,6,1,3,7]=>110000
[1,6,3,4,7,5,2]=>[3,6,4,2,5,7,1]=>[5,2,4,6,3,1,7]=>111000
[1,6,3,5,2,4,7]=>[7,3,6,2,5,4,1]=>[1,5,2,6,3,4,7]=>011000
[1,6,3,5,2,7,4]=>[3,6,2,5,4,7,1]=>[5,2,6,3,4,1,7]=>111000
[1,6,3,5,4,2,7]=>[7,3,6,2,4,5,1]=>[1,5,2,6,4,3,7]=>011100
[1,6,3,5,4,7,2]=>[3,6,4,5,2,7,1]=>[5,2,4,3,6,1,7]=>111000
[1,6,3,5,7,2,4]=>[3,6,5,2,7,4,1]=>[5,2,3,6,1,4,7]=>110000
[1,6,3,5,7,4,2]=>[3,6,5,2,4,7,1]=>[5,2,3,6,4,1,7]=>110100
[1,6,3,7,2,4,5]=>[3,6,2,7,5,4,1]=>[5,2,6,1,3,4,7]=>110000
[1,6,3,7,2,5,4]=>[3,6,2,7,4,5,1]=>[5,2,6,1,4,3,7]=>111000
[1,6,3,7,4,2,5]=>[3,6,2,4,7,5,1]=>[5,2,6,4,1,3,7]=>110100
[1,6,3,7,4,5,2]=>[3,6,4,7,2,5,1]=>[5,2,4,1,6,3,7]=>111000
[1,6,3,7,5,2,4]=>[3,6,2,5,7,4,1]=>[5,2,6,3,1,4,7]=>111000
[1,6,3,7,5,4,2]=>[3,6,2,4,5,7,1]=>[5,2,6,4,3,1,7]=>111100
[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[1,6,4,2,3,5,7]=>010100
[1,6,4,2,3,7,5]=>[2,4,6,5,7,3,1]=>[6,4,2,3,1,5,7]=>110100
[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[1,6,4,2,5,3,7]=>011100
[1,6,4,2,5,7,3]=>[2,4,6,5,3,7,1]=>[6,4,2,3,5,1,7]=>110100
[1,6,4,2,7,3,5]=>[2,4,6,3,7,5,1]=>[6,4,2,5,1,3,7]=>110100
[1,6,4,2,7,5,3]=>[2,4,6,3,5,7,1]=>[6,4,2,5,3,1,7]=>111100
[1,6,4,3,2,5,7]=>[7,2,3,4,6,5,1]=>[1,6,5,4,2,3,7]=>010110
[1,6,4,3,2,7,5]=>[2,3,4,6,5,7,1]=>[6,5,4,2,3,1,7]=>110110
[1,6,4,3,5,2,7]=>[7,3,4,6,2,5,1]=>[1,5,4,2,6,3,7]=>011100
[1,6,4,3,5,7,2]=>[3,4,6,5,2,7,1]=>[5,4,2,3,6,1,7]=>110100
[1,6,4,3,7,2,5]=>[3,4,6,2,7,5,1]=>[5,4,2,6,1,3,7]=>110100
[1,6,4,3,7,5,2]=>[3,4,6,2,5,7,1]=>[5,4,2,6,3,1,7]=>111100
[1,6,4,5,2,3,7]=>[7,4,6,2,5,3,1]=>[1,4,2,6,3,5,7]=>011000
[1,6,4,5,2,7,3]=>[4,6,2,5,3,7,1]=>[4,2,6,3,5,1,7]=>111000
[1,6,4,5,3,2,7]=>[7,4,6,2,3,5,1]=>[1,4,2,6,5,3,7]=>011010
[1,6,4,5,3,7,2]=>[4,6,3,5,2,7,1]=>[4,2,5,3,6,1,7]=>111000
[1,6,4,5,7,2,3]=>[4,6,5,2,7,3,1]=>[4,2,3,6,1,5,7]=>110000
[1,6,4,5,7,3,2]=>[4,6,5,2,3,7,1]=>[4,2,3,6,5,1,7]=>110010
[1,6,4,7,2,3,5]=>[4,6,2,7,5,3,1]=>[4,2,6,1,3,5,7]=>110000
[1,6,4,7,2,5,3]=>[4,6,2,7,3,5,1]=>[4,2,6,1,5,3,7]=>111000
[1,6,4,7,3,2,5]=>[4,6,2,3,7,5,1]=>[4,2,6,5,1,3,7]=>110010
[1,6,4,7,3,5,2]=>[4,6,3,7,2,5,1]=>[4,2,5,1,6,3,7]=>111000
[1,6,4,7,5,2,3]=>[4,6,2,5,7,3,1]=>[4,2,6,3,1,5,7]=>111000
[1,6,4,7,5,3,2]=>[4,6,2,3,5,7,1]=>[4,2,6,5,3,1,7]=>111010
[1,6,5,2,3,4,7]=>[7,2,5,6,4,3,1]=>[1,6,3,2,4,5,7]=>011000
[1,6,5,2,3,7,4]=>[2,5,6,4,7,3,1]=>[6,3,2,4,1,5,7]=>111000
[1,6,5,2,4,3,7]=>[7,2,5,6,3,4,1]=>[1,6,3,2,5,4,7]=>011100
[1,6,5,2,4,7,3]=>[2,5,6,4,3,7,1]=>[6,3,2,4,5,1,7]=>111000
[1,6,5,2,7,3,4]=>[2,5,6,3,7,4,1]=>[6,3,2,5,1,4,7]=>111000
[1,6,5,2,7,4,3]=>[2,5,6,3,4,7,1]=>[6,3,2,5,4,1,7]=>111100
[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[1,6,5,3,2,4,7]=>011010
[1,6,5,3,2,7,4]=>[2,3,5,6,4,7,1]=>[6,5,3,2,4,1,7]=>111010
[1,6,5,3,4,2,7]=>[7,3,5,6,2,4,1]=>[1,5,3,2,6,4,7]=>011100
[1,6,5,3,4,7,2]=>[3,5,6,4,2,7,1]=>[5,3,2,4,6,1,7]=>111000
[1,6,5,3,7,2,4]=>[3,5,6,2,7,4,1]=>[5,3,2,6,1,4,7]=>111000
[1,6,5,3,7,4,2]=>[3,5,6,2,4,7,1]=>[5,3,2,6,4,1,7]=>111100
[1,6,5,4,2,3,7]=>[7,2,4,5,6,3,1]=>[1,6,4,3,2,5,7]=>011100
[1,6,5,4,2,7,3]=>[2,4,5,6,3,7,1]=>[6,4,3,2,5,1,7]=>111100
[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110
[1,6,5,4,3,7,2]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>111100
[1,6,5,4,7,2,3]=>[4,5,6,2,7,3,1]=>[4,3,2,6,1,5,7]=>111000
[1,6,5,4,7,3,2]=>[4,5,6,2,3,7,1]=>[4,3,2,6,5,1,7]=>111010
[1,6,5,7,2,3,4]=>[5,6,2,7,4,3,1]=>[3,2,6,1,4,5,7]=>110000
[1,6,5,7,2,4,3]=>[5,6,2,7,3,4,1]=>[3,2,6,1,5,4,7]=>110100
[1,6,5,7,3,2,4]=>[5,6,2,3,7,4,1]=>[3,2,6,5,1,4,7]=>110010
[1,6,5,7,3,4,2]=>[5,6,3,7,2,4,1]=>[3,2,5,1,6,4,7]=>110100
[1,6,5,7,4,2,3]=>[5,6,2,4,7,3,1]=>[3,2,6,4,1,5,7]=>110100
[1,6,5,7,4,3,2]=>[5,6,2,3,4,7,1]=>[3,2,6,5,4,1,7]=>110110
[1,6,7,2,3,4,5]=>[6,2,7,5,4,3,1]=>[2,6,1,3,4,5,7]=>100000
[1,6,7,2,3,5,4]=>[6,2,7,4,5,3,1]=>[2,6,1,4,3,5,7]=>101000
[1,6,7,2,4,3,5]=>[6,2,7,5,3,4,1]=>[2,6,1,3,5,4,7]=>100100
[1,6,7,2,4,5,3]=>[6,2,7,4,3,5,1]=>[2,6,1,4,5,3,7]=>101000
[1,6,7,2,5,3,4]=>[6,2,7,3,5,4,1]=>[2,6,1,5,3,4,7]=>101000
[1,6,7,2,5,4,3]=>[6,2,7,3,4,5,1]=>[2,6,1,5,4,3,7]=>101100
[1,6,7,3,2,4,5]=>[6,2,3,7,5,4,1]=>[2,6,5,1,3,4,7]=>100010
[1,6,7,3,2,5,4]=>[6,2,3,7,4,5,1]=>[2,6,5,1,4,3,7]=>101010
[1,6,7,3,4,2,5]=>[6,3,7,5,2,4,1]=>[2,5,1,3,6,4,7]=>100100
[1,6,7,3,4,5,2]=>[6,3,7,4,2,5,1]=>[2,5,1,4,6,3,7]=>101000
[1,6,7,3,5,2,4]=>[6,3,7,2,5,4,1]=>[2,5,1,6,3,4,7]=>101000
[1,6,7,3,5,4,2]=>[6,3,7,2,4,5,1]=>[2,5,1,6,4,3,7]=>101100
[1,6,7,4,2,3,5]=>[6,2,4,7,5,3,1]=>[2,6,4,1,3,5,7]=>100100
[1,6,7,4,2,5,3]=>[6,2,4,7,3,5,1]=>[2,6,4,1,5,3,7]=>101100
[1,6,7,4,3,2,5]=>[6,2,3,4,7,5,1]=>[2,6,5,4,1,3,7]=>100110
[1,6,7,4,3,5,2]=>[6,3,4,7,2,5,1]=>[2,5,4,1,6,3,7]=>101100
[1,6,7,4,5,2,3]=>[6,4,7,2,5,3,1]=>[2,4,1,6,3,5,7]=>101000
[1,6,7,4,5,3,2]=>[6,4,7,2,3,5,1]=>[2,4,1,6,5,3,7]=>101010
[1,6,7,5,2,3,4]=>[6,2,5,7,4,3,1]=>[2,6,3,1,4,5,7]=>101000
[1,6,7,5,2,4,3]=>[6,2,5,7,3,4,1]=>[2,6,3,1,5,4,7]=>101100
[1,6,7,5,3,2,4]=>[6,2,3,5,7,4,1]=>[2,6,5,3,1,4,7]=>101010
[1,6,7,5,3,4,2]=>[6,3,5,7,2,4,1]=>[2,5,3,1,6,4,7]=>101100
[1,6,7,5,4,2,3]=>[6,2,4,5,7,3,1]=>[2,6,4,3,1,5,7]=>101100
[1,6,7,5,4,3,2]=>[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>101110
[1,7,2,3,4,5,6]=>[2,7,6,5,4,3,1]=>[6,1,2,3,4,5,7]=>100000
[1,7,2,3,4,6,5]=>[2,7,5,6,4,3,1]=>[6,1,3,2,4,5,7]=>110000
[1,7,2,3,5,4,6]=>[2,7,6,4,5,3,1]=>[6,1,2,4,3,5,7]=>101000
[1,7,2,3,5,6,4]=>[2,7,5,4,6,3,1]=>[6,1,3,4,2,5,7]=>110000
[1,7,2,3,6,4,5]=>[2,7,4,6,5,3,1]=>[6,1,4,2,3,5,7]=>110000
[1,7,2,3,6,5,4]=>[2,7,4,5,6,3,1]=>[6,1,4,3,2,5,7]=>111000
[1,7,2,4,3,5,6]=>[2,7,6,5,3,4,1]=>[6,1,2,3,5,4,7]=>100100
[1,7,2,4,3,6,5]=>[2,7,5,6,3,4,1]=>[6,1,3,2,5,4,7]=>110100
[1,7,2,4,5,3,6]=>[2,7,6,4,3,5,1]=>[6,1,2,4,5,3,7]=>101000
[1,7,2,4,5,6,3]=>[2,7,5,4,3,6,1]=>[6,1,3,4,5,2,7]=>110000
[1,7,2,4,6,3,5]=>[2,7,4,3,6,5,1]=>[6,1,4,5,2,3,7]=>110000
[1,7,2,4,6,5,3]=>[2,7,4,3,5,6,1]=>[6,1,4,5,3,2,7]=>111000
[1,7,2,5,3,4,6]=>[2,7,6,3,5,4,1]=>[6,1,2,5,3,4,7]=>101000
[1,7,2,5,3,6,4]=>[2,7,3,5,4,6,1]=>[6,1,5,3,4,2,7]=>111000
[1,7,2,5,4,3,6]=>[2,7,6,3,4,5,1]=>[6,1,2,5,4,3,7]=>101100
[1,7,2,5,4,6,3]=>[2,7,4,5,3,6,1]=>[6,1,4,3,5,2,7]=>111000
[1,7,2,5,6,3,4]=>[2,7,5,3,6,4,1]=>[6,1,3,5,2,4,7]=>110000
[1,7,2,5,6,4,3]=>[2,7,5,3,4,6,1]=>[6,1,3,5,4,2,7]=>110100
[1,7,2,6,3,4,5]=>[2,7,3,6,5,4,1]=>[6,1,5,2,3,4,7]=>110000
[1,7,2,6,3,5,4]=>[2,7,3,6,4,5,1]=>[6,1,5,2,4,3,7]=>111000
[1,7,2,6,4,3,5]=>[2,7,3,4,6,5,1]=>[6,1,5,4,2,3,7]=>110100
[1,7,2,6,4,5,3]=>[2,7,4,6,3,5,1]=>[6,1,4,2,5,3,7]=>111000
[1,7,2,6,5,3,4]=>[2,7,3,5,6,4,1]=>[6,1,5,3,2,4,7]=>111000
[1,7,2,6,5,4,3]=>[2,7,3,4,5,6,1]=>[6,1,5,4,3,2,7]=>111100
[1,7,3,2,4,5,6]=>[2,3,7,6,5,4,1]=>[6,5,1,2,3,4,7]=>100010
[1,7,3,2,4,6,5]=>[2,3,7,5,6,4,1]=>[6,5,1,3,2,4,7]=>110010
[1,7,3,2,5,4,6]=>[2,3,7,6,4,5,1]=>[6,5,1,2,4,3,7]=>101010
[1,7,3,2,5,6,4]=>[2,3,7,5,4,6,1]=>[6,5,1,3,4,2,7]=>110010
[1,7,3,2,6,4,5]=>[2,3,7,4,6,5,1]=>[6,5,1,4,2,3,7]=>110010
[1,7,3,2,6,5,4]=>[2,3,7,4,5,6,1]=>[6,5,1,4,3,2,7]=>111010
[1,7,3,4,2,5,6]=>[3,7,6,5,2,4,1]=>[5,1,2,3,6,4,7]=>100100
[1,7,3,4,2,6,5]=>[3,7,5,6,2,4,1]=>[5,1,3,2,6,4,7]=>110100
[1,7,3,4,5,2,6]=>[3,7,6,4,2,5,1]=>[5,1,2,4,6,3,7]=>101000
[1,7,3,4,5,6,2]=>[3,7,5,4,2,6,1]=>[5,1,3,4,6,2,7]=>110000
[1,7,3,4,6,2,5]=>[3,7,4,2,6,5,1]=>[5,1,4,6,2,3,7]=>110000
[1,7,3,4,6,5,2]=>[3,7,4,2,5,6,1]=>[5,1,4,6,3,2,7]=>111000
[1,7,3,5,2,4,6]=>[3,7,6,2,5,4,1]=>[5,1,2,6,3,4,7]=>101000
[1,7,3,5,2,6,4]=>[3,7,2,5,4,6,1]=>[5,1,6,3,4,2,7]=>111000
[1,7,3,5,4,2,6]=>[3,7,6,2,4,5,1]=>[5,1,2,6,4,3,7]=>101100
[1,7,3,5,4,6,2]=>[3,7,4,5,2,6,1]=>[5,1,4,3,6,2,7]=>111000
[1,7,3,5,6,2,4]=>[3,7,5,2,6,4,1]=>[5,1,3,6,2,4,7]=>110000
[1,7,3,5,6,4,2]=>[3,7,5,2,4,6,1]=>[5,1,3,6,4,2,7]=>110100
[1,7,3,6,2,4,5]=>[3,7,2,6,5,4,1]=>[5,1,6,2,3,4,7]=>110000
[1,7,3,6,2,5,4]=>[3,7,2,6,4,5,1]=>[5,1,6,2,4,3,7]=>111000
[1,7,3,6,4,2,5]=>[3,7,2,4,6,5,1]=>[5,1,6,4,2,3,7]=>110100
[1,7,3,6,4,5,2]=>[3,7,4,6,2,5,1]=>[5,1,4,2,6,3,7]=>111000
[1,7,3,6,5,2,4]=>[3,7,2,5,6,4,1]=>[5,1,6,3,2,4,7]=>111000
[1,7,3,6,5,4,2]=>[3,7,2,4,5,6,1]=>[5,1,6,4,3,2,7]=>111100
[1,7,4,2,3,5,6]=>[2,4,7,6,5,3,1]=>[6,4,1,2,3,5,7]=>100100
[1,7,4,2,3,6,5]=>[2,4,7,5,6,3,1]=>[6,4,1,3,2,5,7]=>110100
[1,7,4,2,5,3,6]=>[2,4,7,6,3,5,1]=>[6,4,1,2,5,3,7]=>101100
[1,7,4,2,5,6,3]=>[2,4,7,5,3,6,1]=>[6,4,1,3,5,2,7]=>110100
[1,7,4,2,6,3,5]=>[2,4,7,3,6,5,1]=>[6,4,1,5,2,3,7]=>110100
[1,7,4,2,6,5,3]=>[2,4,7,3,5,6,1]=>[6,4,1,5,3,2,7]=>111100
[1,7,4,3,2,5,6]=>[2,3,4,7,6,5,1]=>[6,5,4,1,2,3,7]=>100110
[1,7,4,3,2,6,5]=>[2,3,4,7,5,6,1]=>[6,5,4,1,3,2,7]=>110110
[1,7,4,3,5,2,6]=>[3,4,7,6,2,5,1]=>[5,4,1,2,6,3,7]=>101100
[1,7,4,3,5,6,2]=>[3,4,7,5,2,6,1]=>[5,4,1,3,6,2,7]=>110100
[1,7,4,3,6,2,5]=>[3,4,7,2,6,5,1]=>[5,4,1,6,2,3,7]=>110100
[1,7,4,3,6,5,2]=>[3,4,7,2,5,6,1]=>[5,4,1,6,3,2,7]=>111100
[1,7,4,5,2,3,6]=>[4,7,6,2,5,3,1]=>[4,1,2,6,3,5,7]=>101000
[1,7,4,5,2,6,3]=>[4,7,2,5,3,6,1]=>[4,1,6,3,5,2,7]=>111000
[1,7,4,5,3,2,6]=>[4,7,6,2,3,5,1]=>[4,1,2,6,5,3,7]=>101010
[1,7,4,5,3,6,2]=>[4,7,3,5,2,6,1]=>[4,1,5,3,6,2,7]=>111000
[1,7,4,5,6,2,3]=>[4,7,5,2,6,3,1]=>[4,1,3,6,2,5,7]=>110000
[1,7,4,5,6,3,2]=>[4,7,5,2,3,6,1]=>[4,1,3,6,5,2,7]=>110010
[1,7,4,6,2,3,5]=>[4,7,2,6,5,3,1]=>[4,1,6,2,3,5,7]=>110000
[1,7,4,6,2,5,3]=>[4,7,2,6,3,5,1]=>[4,1,6,2,5,3,7]=>111000
[1,7,4,6,3,2,5]=>[4,7,2,3,6,5,1]=>[4,1,6,5,2,3,7]=>110010
[1,7,4,6,3,5,2]=>[4,7,3,6,2,5,1]=>[4,1,5,2,6,3,7]=>111000
[1,7,4,6,5,2,3]=>[4,7,2,5,6,3,1]=>[4,1,6,3,2,5,7]=>111000
[1,7,4,6,5,3,2]=>[4,7,2,3,5,6,1]=>[4,1,6,5,3,2,7]=>111010
[1,7,5,2,3,4,6]=>[2,5,7,6,4,3,1]=>[6,3,1,2,4,5,7]=>101000
[1,7,5,2,3,6,4]=>[2,5,7,4,6,3,1]=>[6,3,1,4,2,5,7]=>111000
[1,7,5,2,4,3,6]=>[2,5,7,6,3,4,1]=>[6,3,1,2,5,4,7]=>101100
[1,7,5,2,4,6,3]=>[2,5,7,4,3,6,1]=>[6,3,1,4,5,2,7]=>111000
[1,7,5,2,6,3,4]=>[2,5,7,3,6,4,1]=>[6,3,1,5,2,4,7]=>111000
[1,7,5,2,6,4,3]=>[2,5,7,3,4,6,1]=>[6,3,1,5,4,2,7]=>111100
[1,7,5,3,2,4,6]=>[2,3,5,7,6,4,1]=>[6,5,3,1,2,4,7]=>101010
[1,7,5,3,2,6,4]=>[2,3,5,7,4,6,1]=>[6,5,3,1,4,2,7]=>111010
[1,7,5,3,4,2,6]=>[3,5,7,6,2,4,1]=>[5,3,1,2,6,4,7]=>101100
[1,7,5,3,4,6,2]=>[3,5,7,4,2,6,1]=>[5,3,1,4,6,2,7]=>111000
[1,7,5,3,6,2,4]=>[3,5,7,2,6,4,1]=>[5,3,1,6,2,4,7]=>111000
[1,7,5,3,6,4,2]=>[3,5,7,2,4,6,1]=>[5,3,1,6,4,2,7]=>111100
[1,7,5,4,2,3,6]=>[2,4,5,7,6,3,1]=>[6,4,3,1,2,5,7]=>101100
[1,7,5,4,2,6,3]=>[2,4,5,7,3,6,1]=>[6,4,3,1,5,2,7]=>111100
[1,7,5,4,3,2,6]=>[2,3,4,5,7,6,1]=>[6,5,4,3,1,2,7]=>101110
[1,7,5,4,3,6,2]=>[3,4,5,7,2,6,1]=>[5,4,3,1,6,2,7]=>111100
[1,7,5,4,6,2,3]=>[4,5,7,2,6,3,1]=>[4,3,1,6,2,5,7]=>111000
[1,7,5,4,6,3,2]=>[4,5,7,2,3,6,1]=>[4,3,1,6,5,2,7]=>111010
[1,7,5,6,2,3,4]=>[5,7,2,6,4,3,1]=>[3,1,6,2,4,5,7]=>110000
[1,7,5,6,2,4,3]=>[5,7,2,6,3,4,1]=>[3,1,6,2,5,4,7]=>110100
[1,7,5,6,3,2,4]=>[5,7,2,3,6,4,1]=>[3,1,6,5,2,4,7]=>110010
[1,7,5,6,3,4,2]=>[5,7,3,6,2,4,1]=>[3,1,5,2,6,4,7]=>110100
[1,7,5,6,4,2,3]=>[5,7,2,4,6,3,1]=>[3,1,6,4,2,5,7]=>110100
[1,7,5,6,4,3,2]=>[5,7,2,3,4,6,1]=>[3,1,6,5,4,2,7]=>110110
[1,7,6,2,3,4,5]=>[2,6,7,5,4,3,1]=>[6,2,1,3,4,5,7]=>110000
[1,7,6,2,3,5,4]=>[2,6,7,4,5,3,1]=>[6,2,1,4,3,5,7]=>111000
[1,7,6,2,4,3,5]=>[2,6,7,5,3,4,1]=>[6,2,1,3,5,4,7]=>110100
[1,7,6,2,4,5,3]=>[2,6,7,4,3,5,1]=>[6,2,1,4,5,3,7]=>111000
[1,7,6,2,5,3,4]=>[2,6,7,3,5,4,1]=>[6,2,1,5,3,4,7]=>111000
[1,7,6,2,5,4,3]=>[2,6,7,3,4,5,1]=>[6,2,1,5,4,3,7]=>111100
[1,7,6,3,2,4,5]=>[2,3,6,7,5,4,1]=>[6,5,2,1,3,4,7]=>110010
[1,7,6,3,2,5,4]=>[2,3,6,7,4,5,1]=>[6,5,2,1,4,3,7]=>111010
[1,7,6,3,4,2,5]=>[3,6,7,5,2,4,1]=>[5,2,1,3,6,4,7]=>110100
[1,7,6,3,4,5,2]=>[3,6,7,4,2,5,1]=>[5,2,1,4,6,3,7]=>111000
[1,7,6,3,5,2,4]=>[3,6,7,2,5,4,1]=>[5,2,1,6,3,4,7]=>111000
[1,7,6,3,5,4,2]=>[3,6,7,2,4,5,1]=>[5,2,1,6,4,3,7]=>111100
[1,7,6,4,2,3,5]=>[2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>110100
[1,7,6,4,2,5,3]=>[2,4,6,7,3,5,1]=>[6,4,2,1,5,3,7]=>111100
[1,7,6,4,3,2,5]=>[2,3,4,6,7,5,1]=>[6,5,4,2,1,3,7]=>110110
[1,7,6,4,3,5,2]=>[3,4,6,7,2,5,1]=>[5,4,2,1,6,3,7]=>111100
[1,7,6,4,5,2,3]=>[4,6,7,2,5,3,1]=>[4,2,1,6,3,5,7]=>111000
[1,7,6,4,5,3,2]=>[4,6,7,2,3,5,1]=>[4,2,1,6,5,3,7]=>111010
[1,7,6,5,2,3,4]=>[2,5,6,7,4,3,1]=>[6,3,2,1,4,5,7]=>111000
[1,7,6,5,2,4,3]=>[2,5,6,7,3,4,1]=>[6,3,2,1,5,4,7]=>111100
[1,7,6,5,3,2,4]=>[2,3,5,6,7,4,1]=>[6,5,3,2,1,4,7]=>111010
[1,7,6,5,3,4,2]=>[3,5,6,7,2,4,1]=>[5,3,2,1,6,4,7]=>111100
[1,7,6,5,4,2,3]=>[2,4,5,6,7,3,1]=>[6,4,3,2,1,5,7]=>111100
[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>111110
[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>000001
[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001
[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>010001
[2,1,3,4,6,7,5]=>[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>100001
[2,1,3,4,7,5,6]=>[5,7,6,4,3,1,2]=>[3,1,2,4,5,7,6]=>100001
[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>110001
[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>001001
[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>101001
[2,1,3,5,6,4,7]=>[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>010001
[2,1,3,5,6,7,4]=>[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>100001
[2,1,3,5,7,4,6]=>[5,4,7,6,3,1,2]=>[3,4,1,2,5,7,6]=>100001
[2,1,3,5,7,6,4]=>[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>110001
[2,1,3,6,4,5,7]=>[7,4,6,5,3,1,2]=>[1,4,2,3,5,7,6]=>010001
[2,1,3,6,4,7,5]=>[4,6,5,7,3,1,2]=>[4,2,3,1,5,7,6]=>110001
[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>011001
[2,1,3,6,5,7,4]=>[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>110001
[2,1,3,6,7,4,5]=>[6,4,7,5,3,1,2]=>[2,4,1,3,5,7,6]=>100001
[2,1,3,6,7,5,4]=>[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>101001
[2,1,3,7,4,5,6]=>[4,7,6,5,3,1,2]=>[4,1,2,3,5,7,6]=>100001
[2,1,3,7,4,6,5]=>[4,7,5,6,3,1,2]=>[4,1,3,2,5,7,6]=>110001
[2,1,3,7,5,4,6]=>[4,5,7,6,3,1,2]=>[4,3,1,2,5,7,6]=>101001
[2,1,3,7,5,6,4]=>[5,7,4,6,3,1,2]=>[3,1,4,2,5,7,6]=>110001
[2,1,3,7,6,4,5]=>[4,6,7,5,3,1,2]=>[4,2,1,3,5,7,6]=>110001
[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>111001
[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>000101
[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>100101
[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>010101
[2,1,4,3,6,7,5]=>[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>100101
[2,1,4,3,7,5,6]=>[5,7,6,3,4,1,2]=>[3,1,2,5,4,7,6]=>100101
[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>110101
[2,1,4,5,3,6,7]=>[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>001001
[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>101001
[2,1,4,5,6,3,7]=>[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>010001
[2,1,4,5,6,7,3]=>[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>100001
[2,1,4,5,7,3,6]=>[5,4,3,7,6,1,2]=>[3,4,5,1,2,7,6]=>100001
[2,1,4,5,7,6,3]=>[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>110001
[2,1,4,6,3,5,7]=>[7,4,3,6,5,1,2]=>[1,4,5,2,3,7,6]=>010001
[2,1,4,6,3,7,5]=>[4,3,6,5,7,1,2]=>[4,5,2,3,1,7,6]=>110001
[2,1,4,6,5,3,7]=>[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>011001
[2,1,4,6,5,7,3]=>[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>110001
[2,1,4,6,7,3,5]=>[6,4,3,7,5,1,2]=>[2,4,5,1,3,7,6]=>100001
[2,1,4,6,7,5,3]=>[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>101001
[2,1,4,7,3,5,6]=>[4,3,7,6,5,1,2]=>[4,5,1,2,3,7,6]=>100001
[2,1,4,7,3,6,5]=>[4,3,7,5,6,1,2]=>[4,5,1,3,2,7,6]=>110001
[2,1,4,7,5,3,6]=>[4,3,5,7,6,1,2]=>[4,5,3,1,2,7,6]=>101001
[2,1,4,7,5,6,3]=>[5,7,4,3,6,1,2]=>[3,1,4,5,2,7,6]=>110001
[2,1,4,7,6,3,5]=>[4,3,6,7,5,1,2]=>[4,5,2,1,3,7,6]=>110001
[2,1,4,7,6,5,3]=>[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>111001
[2,1,5,3,4,6,7]=>[7,6,3,5,4,1,2]=>[1,2,5,3,4,7,6]=>001001
[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>[2,1,5,3,4,7,6]=>101001
[2,1,5,3,6,4,7]=>[7,3,5,4,6,1,2]=>[1,5,3,4,2,7,6]=>011001
[2,1,5,3,6,7,4]=>[6,3,5,4,7,1,2]=>[2,5,3,4,1,7,6]=>101001
[2,1,5,3,7,4,6]=>[3,5,4,7,6,1,2]=>[5,3,4,1,2,7,6]=>101001
[2,1,5,3,7,6,4]=>[3,5,4,6,7,1,2]=>[5,3,4,2,1,7,6]=>111001
[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>001101
[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[2,1,5,4,6,3,7]=>[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>011001
[2,1,5,4,6,7,3]=>[6,4,5,3,7,1,2]=>[2,4,3,5,1,7,6]=>101001
[2,1,5,4,7,3,6]=>[4,5,3,7,6,1,2]=>[4,3,5,1,2,7,6]=>101001
[2,1,5,4,7,6,3]=>[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>111001
[2,1,5,6,3,4,7]=>[7,5,3,6,4,1,2]=>[1,3,5,2,4,7,6]=>010001
[2,1,5,6,3,7,4]=>[5,3,6,4,7,1,2]=>[3,5,2,4,1,7,6]=>110001
[2,1,5,6,4,3,7]=>[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>010101
[2,1,5,6,4,7,3]=>[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>110001
[2,1,5,6,7,3,4]=>[6,5,3,7,4,1,2]=>[2,3,5,1,4,7,6]=>100001
[2,1,5,6,7,4,3]=>[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>100101
[2,1,5,7,3,4,6]=>[5,3,7,6,4,1,2]=>[3,5,1,2,4,7,6]=>100001
[2,1,5,7,3,6,4]=>[5,3,7,4,6,1,2]=>[3,5,1,4,2,7,6]=>110001
[2,1,5,7,4,3,6]=>[5,3,4,7,6,1,2]=>[3,5,4,1,2,7,6]=>100101
[2,1,5,7,4,6,3]=>[5,4,7,3,6,1,2]=>[3,4,1,5,2,7,6]=>110001
[2,1,5,7,6,3,4]=>[5,3,6,7,4,1,2]=>[3,5,2,1,4,7,6]=>110001
[2,1,5,7,6,4,3]=>[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>110101
[2,1,6,3,4,5,7]=>[7,3,6,5,4,1,2]=>[1,5,2,3,4,7,6]=>010001
[2,1,6,3,4,7,5]=>[3,6,5,7,4,1,2]=>[5,2,3,1,4,7,6]=>110001
[2,1,6,3,5,4,7]=>[7,3,6,4,5,1,2]=>[1,5,2,4,3,7,6]=>011001
[2,1,6,3,5,7,4]=>[3,6,5,4,7,1,2]=>[5,2,3,4,1,7,6]=>110001
[2,1,6,3,7,4,5]=>[3,6,4,7,5,1,2]=>[5,2,4,1,3,7,6]=>110001
[2,1,6,3,7,5,4]=>[3,6,4,5,7,1,2]=>[5,2,4,3,1,7,6]=>111001
[2,1,6,4,3,5,7]=>[7,3,4,6,5,1,2]=>[1,5,4,2,3,7,6]=>010101
[2,1,6,4,3,7,5]=>[3,4,6,5,7,1,2]=>[5,4,2,3,1,7,6]=>110101
[2,1,6,4,5,3,7]=>[7,4,6,3,5,1,2]=>[1,4,2,5,3,7,6]=>011001
[2,1,6,4,5,7,3]=>[4,6,5,3,7,1,2]=>[4,2,3,5,1,7,6]=>110001
[2,1,6,4,7,3,5]=>[4,6,3,7,5,1,2]=>[4,2,5,1,3,7,6]=>110001
[2,1,6,4,7,5,3]=>[4,6,3,5,7,1,2]=>[4,2,5,3,1,7,6]=>111001
[2,1,6,5,3,4,7]=>[7,3,5,6,4,1,2]=>[1,5,3,2,4,7,6]=>011001
[2,1,6,5,3,7,4]=>[3,5,6,4,7,1,2]=>[5,3,2,4,1,7,6]=>111001
[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>011101
[2,1,6,5,4,7,3]=>[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>111001
[2,1,6,5,7,3,4]=>[5,6,3,7,4,1,2]=>[3,2,5,1,4,7,6]=>110001
[2,1,6,5,7,4,3]=>[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>110101
[2,1,6,7,3,4,5]=>[6,3,7,5,4,1,2]=>[2,5,1,3,4,7,6]=>100001
[2,1,6,7,3,5,4]=>[6,3,7,4,5,1,2]=>[2,5,1,4,3,7,6]=>101001
[2,1,6,7,4,3,5]=>[6,3,4,7,5,1,2]=>[2,5,4,1,3,7,6]=>100101
[2,1,6,7,4,5,3]=>[6,4,7,3,5,1,2]=>[2,4,1,5,3,7,6]=>101001
[2,1,6,7,5,3,4]=>[6,3,5,7,4,1,2]=>[2,5,3,1,4,7,6]=>101001
[2,1,6,7,5,4,3]=>[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>101101
[2,1,7,3,4,5,6]=>[3,7,6,5,4,1,2]=>[5,1,2,3,4,7,6]=>100001
[2,1,7,3,4,6,5]=>[3,7,5,6,4,1,2]=>[5,1,3,2,4,7,6]=>110001
[2,1,7,3,5,4,6]=>[3,7,6,4,5,1,2]=>[5,1,2,4,3,7,6]=>101001
[2,1,7,3,5,6,4]=>[3,7,5,4,6,1,2]=>[5,1,3,4,2,7,6]=>110001
[2,1,7,3,6,4,5]=>[3,7,4,6,5,1,2]=>[5,1,4,2,3,7,6]=>110001
[2,1,7,3,6,5,4]=>[3,7,4,5,6,1,2]=>[5,1,4,3,2,7,6]=>111001
[2,1,7,4,3,5,6]=>[3,4,7,6,5,1,2]=>[5,4,1,2,3,7,6]=>100101
[2,1,7,4,3,6,5]=>[3,4,7,5,6,1,2]=>[5,4,1,3,2,7,6]=>110101
[2,1,7,4,5,3,6]=>[4,7,6,3,5,1,2]=>[4,1,2,5,3,7,6]=>101001
[2,1,7,4,5,6,3]=>[4,7,5,3,6,1,2]=>[4,1,3,5,2,7,6]=>110001
[2,1,7,4,6,3,5]=>[4,7,3,6,5,1,2]=>[4,1,5,2,3,7,6]=>110001
[2,1,7,4,6,5,3]=>[4,7,3,5,6,1,2]=>[4,1,5,3,2,7,6]=>111001
[2,1,7,5,3,4,6]=>[3,5,7,6,4,1,2]=>[5,3,1,2,4,7,6]=>101001
[2,1,7,5,3,6,4]=>[3,5,7,4,6,1,2]=>[5,3,1,4,2,7,6]=>111001
[2,1,7,5,4,3,6]=>[3,4,5,7,6,1,2]=>[5,4,3,1,2,7,6]=>101101
[2,1,7,5,4,6,3]=>[4,5,7,3,6,1,2]=>[4,3,1,5,2,7,6]=>111001
[2,1,7,5,6,3,4]=>[5,7,3,6,4,1,2]=>[3,1,5,2,4,7,6]=>110001
[2,1,7,5,6,4,3]=>[5,7,3,4,6,1,2]=>[3,1,5,4,2,7,6]=>110101
[2,1,7,6,3,4,5]=>[3,6,7,5,4,1,2]=>[5,2,1,3,4,7,6]=>110001
[2,1,7,6,3,5,4]=>[3,6,7,4,5,1,2]=>[5,2,1,4,3,7,6]=>111001
[2,1,7,6,4,3,5]=>[3,4,6,7,5,1,2]=>[5,4,2,1,3,7,6]=>110101
[2,1,7,6,4,5,3]=>[4,6,7,3,5,1,2]=>[4,2,1,5,3,7,6]=>111001
[2,1,7,6,5,3,4]=>[3,5,6,7,4,1,2]=>[5,3,2,1,4,7,6]=>111001
[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>111101
[2,3,1,4,5,6,7]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>000010
[2,3,1,4,5,7,6]=>[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>100010
[2,3,1,4,6,5,7]=>[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>010010
[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>100010
[2,3,1,4,7,5,6]=>[5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5]=>100010
[2,3,1,4,7,6,5]=>[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>110010
[2,3,1,5,4,6,7]=>[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>001010
[2,3,1,5,4,7,6]=>[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>101010
[2,3,1,5,6,4,7]=>[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>010010
[2,3,1,5,6,7,4]=>[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>100010
[2,3,1,5,7,4,6]=>[5,4,7,6,2,1,3]=>[3,4,1,2,6,7,5]=>100010
[2,3,1,5,7,6,4]=>[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>110010
[2,3,1,6,4,5,7]=>[7,4,6,5,2,1,3]=>[1,4,2,3,6,7,5]=>010010
[2,3,1,6,4,7,5]=>[4,6,5,7,2,1,3]=>[4,2,3,1,6,7,5]=>110010
[2,3,1,6,5,4,7]=>[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>011010
[2,3,1,6,5,7,4]=>[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>110010
[2,3,1,6,7,4,5]=>[6,4,7,5,2,1,3]=>[2,4,1,3,6,7,5]=>100010
[2,3,1,6,7,5,4]=>[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>101010
[2,3,1,7,4,5,6]=>[4,7,6,5,2,1,3]=>[4,1,2,3,6,7,5]=>100010
[2,3,1,7,4,6,5]=>[4,7,5,6,2,1,3]=>[4,1,3,2,6,7,5]=>110010
[2,3,1,7,5,4,6]=>[4,5,7,6,2,1,3]=>[4,3,1,2,6,7,5]=>101010
[2,3,1,7,5,6,4]=>[5,7,4,6,2,1,3]=>[3,1,4,2,6,7,5]=>110010
[2,3,1,7,6,4,5]=>[4,6,7,5,2,1,3]=>[4,2,1,3,6,7,5]=>110010
[2,3,1,7,6,5,4]=>[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>111010
[2,3,4,1,5,6,7]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>000100
[2,3,4,1,5,7,6]=>[6,7,5,3,2,1,4]=>[2,1,3,5,6,7,4]=>100100
[2,3,4,1,6,5,7]=>[7,5,6,3,2,1,4]=>[1,3,2,5,6,7,4]=>010100
[2,3,4,1,6,7,5]=>[6,5,7,3,2,1,4]=>[2,3,1,5,6,7,4]=>100100
[2,3,4,1,7,5,6]=>[5,7,6,3,2,1,4]=>[3,1,2,5,6,7,4]=>100100
[2,3,4,1,7,6,5]=>[5,6,7,3,2,1,4]=>[3,2,1,5,6,7,4]=>110100
[2,3,4,5,1,6,7]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>001000
[2,3,4,5,1,7,6]=>[6,7,4,3,2,1,5]=>[2,1,4,5,6,7,3]=>101000
[2,3,4,5,6,1,7]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>010000
[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>100000
[2,3,4,5,7,1,6]=>[5,4,3,2,1,7,6]=>[3,4,5,6,7,1,2]=>100000
[2,3,4,5,7,6,1]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>110000
[2,3,4,6,1,5,7]=>[7,4,3,2,1,6,5]=>[1,4,5,6,7,2,3]=>010000
[2,3,4,6,1,7,5]=>[4,3,2,1,6,5,7]=>[4,5,6,7,2,3,1]=>110000
[2,3,4,6,5,1,7]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>011000
[2,3,4,6,5,7,1]=>[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>110000
[2,3,4,6,7,1,5]=>[6,4,3,2,1,7,5]=>[2,4,5,6,7,1,3]=>100000
[2,3,4,6,7,5,1]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>101000
[2,3,4,7,1,5,6]=>[4,3,2,1,7,6,5]=>[4,5,6,7,1,2,3]=>100000
[2,3,4,7,1,6,5]=>[4,3,2,1,7,5,6]=>[4,5,6,7,1,3,2]=>110000
[2,3,4,7,5,1,6]=>[4,3,2,1,5,7,6]=>[4,5,6,7,3,1,2]=>101000
[2,3,4,7,5,6,1]=>[5,7,4,3,2,1,6]=>[3,1,4,5,6,7,2]=>110000
[2,3,4,7,6,1,5]=>[4,3,2,1,6,7,5]=>[4,5,6,7,2,1,3]=>110000
[2,3,4,7,6,5,1]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>111000
[2,3,5,1,4,6,7]=>[7,6,3,2,1,5,4]=>[1,2,5,6,7,3,4]=>001000
[2,3,5,1,4,7,6]=>[6,7,3,2,1,5,4]=>[2,1,5,6,7,3,4]=>101000
[2,3,5,1,6,4,7]=>[7,3,2,1,5,4,6]=>[1,5,6,7,3,4,2]=>011000
[2,3,5,1,6,7,4]=>[6,3,2,1,5,4,7]=>[2,5,6,7,3,4,1]=>101000
[2,3,5,1,7,4,6]=>[3,2,1,5,4,7,6]=>[5,6,7,3,4,1,2]=>101000
[2,3,5,1,7,6,4]=>[3,2,1,5,4,6,7]=>[5,6,7,3,4,2,1]=>111000
[2,3,5,4,1,6,7]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>001100
[2,3,5,4,1,7,6]=>[6,7,3,2,1,4,5]=>[2,1,5,6,7,4,3]=>101100
[2,3,5,4,6,1,7]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>011000
[2,3,5,4,6,7,1]=>[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>101000
[2,3,5,4,7,1,6]=>[4,5,3,2,1,7,6]=>[4,3,5,6,7,1,2]=>101000
[2,3,5,4,7,6,1]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>111000
[2,3,5,6,1,4,7]=>[7,5,3,2,1,6,4]=>[1,3,5,6,7,2,4]=>010000
[2,3,5,6,1,7,4]=>[5,3,2,1,6,4,7]=>[3,5,6,7,2,4,1]=>110000
[2,3,5,6,4,1,7]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>010100
[2,3,5,6,4,7,1]=>[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>110000
[2,3,5,6,7,1,4]=>[6,5,3,2,1,7,4]=>[2,3,5,6,7,1,4]=>100000
[2,3,5,6,7,4,1]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>100100
[2,3,5,7,1,4,6]=>[5,3,2,1,7,6,4]=>[3,5,6,7,1,2,4]=>100000
[2,3,5,7,1,6,4]=>[5,3,2,1,7,4,6]=>[3,5,6,7,1,4,2]=>110000
[2,3,5,7,4,1,6]=>[5,3,2,1,4,7,6]=>[3,5,6,7,4,1,2]=>100100
[2,3,5,7,4,6,1]=>[5,4,7,3,2,1,6]=>[3,4,1,5,6,7,2]=>110000
[2,3,5,7,6,1,4]=>[5,3,2,1,6,7,4]=>[3,5,6,7,2,1,4]=>110000
[2,3,5,7,6,4,1]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>110100
[2,3,6,1,4,5,7]=>[7,3,2,1,6,5,4]=>[1,5,6,7,2,3,4]=>010000
[2,3,6,1,4,7,5]=>[3,2,1,6,5,7,4]=>[5,6,7,2,3,1,4]=>110000
[2,3,6,1,5,4,7]=>[7,3,2,1,6,4,5]=>[1,5,6,7,2,4,3]=>011000
[2,3,6,1,5,7,4]=>[3,2,1,6,5,4,7]=>[5,6,7,2,3,4,1]=>110000
[2,3,6,1,7,4,5]=>[3,2,1,6,4,7,5]=>[5,6,7,2,4,1,3]=>110000
[2,3,6,1,7,5,4]=>[3,2,1,6,4,5,7]=>[5,6,7,2,4,3,1]=>111000
[2,3,6,4,1,5,7]=>[7,3,2,1,4,6,5]=>[1,5,6,7,4,2,3]=>010100
[2,3,6,4,1,7,5]=>[3,2,1,4,6,5,7]=>[5,6,7,4,2,3,1]=>110100
[2,3,6,4,5,1,7]=>[7,4,6,3,2,1,5]=>[1,4,2,5,6,7,3]=>011000
[2,3,6,4,5,7,1]=>[4,6,5,3,2,1,7]=>[4,2,3,5,6,7,1]=>110000
[2,3,6,4,7,1,5]=>[4,6,3,2,1,7,5]=>[4,2,5,6,7,1,3]=>110000
[2,3,6,4,7,5,1]=>[4,6,3,2,1,5,7]=>[4,2,5,6,7,3,1]=>111000
[2,3,6,5,1,4,7]=>[7,3,2,1,5,6,4]=>[1,5,6,7,3,2,4]=>011000
[2,3,6,5,1,7,4]=>[3,2,1,5,6,4,7]=>[5,6,7,3,2,4,1]=>111000
[2,3,6,5,4,1,7]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>011100
[2,3,6,5,4,7,1]=>[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>111000
[2,3,6,5,7,1,4]=>[5,6,3,2,1,7,4]=>[3,2,5,6,7,1,4]=>110000
[2,3,6,5,7,4,1]=>[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>110100
[2,3,6,7,1,4,5]=>[6,3,2,1,7,5,4]=>[2,5,6,7,1,3,4]=>100000
[2,3,6,7,1,5,4]=>[6,3,2,1,7,4,5]=>[2,5,6,7,1,4,3]=>101000
[2,3,6,7,4,1,5]=>[6,3,2,1,4,7,5]=>[2,5,6,7,4,1,3]=>100100
[2,3,6,7,4,5,1]=>[6,4,7,3,2,1,5]=>[2,4,1,5,6,7,3]=>101000
[2,3,6,7,5,1,4]=>[6,3,2,1,5,7,4]=>[2,5,6,7,3,1,4]=>101000
[2,3,6,7,5,4,1]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>101100
[2,3,7,1,4,5,6]=>[3,2,1,7,6,5,4]=>[5,6,7,1,2,3,4]=>100000
[2,3,7,1,4,6,5]=>[3,2,1,7,5,6,4]=>[5,6,7,1,3,2,4]=>110000
[2,3,7,1,5,4,6]=>[3,2,1,7,6,4,5]=>[5,6,7,1,2,4,3]=>101000
[2,3,7,1,5,6,4]=>[3,2,1,7,5,4,6]=>[5,6,7,1,3,4,2]=>110000
[2,3,7,1,6,4,5]=>[3,2,1,7,4,6,5]=>[5,6,7,1,4,2,3]=>110000
[2,3,7,1,6,5,4]=>[3,2,1,7,4,5,6]=>[5,6,7,1,4,3,2]=>111000
[2,3,7,4,1,5,6]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>100100
[2,3,7,4,1,6,5]=>[3,2,1,4,7,5,6]=>[5,6,7,4,1,3,2]=>110100
[2,3,7,4,5,1,6]=>[4,7,6,3,2,1,5]=>[4,1,2,5,6,7,3]=>101000
[2,3,7,4,5,6,1]=>[4,7,5,3,2,1,6]=>[4,1,3,5,6,7,2]=>110000
[2,3,7,4,6,1,5]=>[4,7,3,2,1,6,5]=>[4,1,5,6,7,2,3]=>110000
[2,3,7,4,6,5,1]=>[4,7,3,2,1,5,6]=>[4,1,5,6,7,3,2]=>111000
[2,3,7,5,1,4,6]=>[3,2,1,5,7,6,4]=>[5,6,7,3,1,2,4]=>101000
[2,3,7,5,1,6,4]=>[3,2,1,5,7,4,6]=>[5,6,7,3,1,4,2]=>111000
[2,3,7,5,4,1,6]=>[3,2,1,4,5,7,6]=>[5,6,7,4,3,1,2]=>101100
[2,3,7,5,4,6,1]=>[4,5,7,3,2,1,6]=>[4,3,1,5,6,7,2]=>111000
[2,3,7,5,6,1,4]=>[5,7,3,2,1,6,4]=>[3,1,5,6,7,2,4]=>110000
[2,3,7,5,6,4,1]=>[5,7,3,2,1,4,6]=>[3,1,5,6,7,4,2]=>110100
[2,3,7,6,1,4,5]=>[3,2,1,6,7,5,4]=>[5,6,7,2,1,3,4]=>110000
[2,3,7,6,1,5,4]=>[3,2,1,6,7,4,5]=>[5,6,7,2,1,4,3]=>111000
[2,3,7,6,4,1,5]=>[3,2,1,4,6,7,5]=>[5,6,7,4,2,1,3]=>110100
[2,3,7,6,4,5,1]=>[4,6,7,3,2,1,5]=>[4,2,1,5,6,7,3]=>111000
[2,3,7,6,5,1,4]=>[3,2,1,5,6,7,4]=>[5,6,7,3,2,1,4]=>111000
[2,3,7,6,5,4,1]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>111100
[2,4,1,3,5,6,7]=>[7,6,5,2,1,4,3]=>[1,2,3,6,7,4,5]=>000100
[2,4,1,3,5,7,6]=>[6,7,5,2,1,4,3]=>[2,1,3,6,7,4,5]=>100100
[2,4,1,3,6,5,7]=>[7,5,6,2,1,4,3]=>[1,3,2,6,7,4,5]=>010100
[2,4,1,3,6,7,5]=>[6,5,7,2,1,4,3]=>[2,3,1,6,7,4,5]=>100100
[2,4,1,3,7,5,6]=>[5,7,6,2,1,4,3]=>[3,1,2,6,7,4,5]=>100100
[2,4,1,3,7,6,5]=>[5,6,7,2,1,4,3]=>[3,2,1,6,7,4,5]=>110100
[2,4,1,5,3,6,7]=>[7,6,2,1,4,3,5]=>[1,2,6,7,4,5,3]=>001100
[2,4,1,5,3,7,6]=>[6,7,2,1,4,3,5]=>[2,1,6,7,4,5,3]=>101100
[2,4,1,5,6,3,7]=>[7,5,2,1,4,3,6]=>[1,3,6,7,4,5,2]=>010100
[2,4,1,5,6,7,3]=>[6,5,2,1,4,3,7]=>[2,3,6,7,4,5,1]=>100100
[2,4,1,5,7,3,6]=>[5,2,1,4,3,7,6]=>[3,6,7,4,5,1,2]=>100100
[2,4,1,5,7,6,3]=>[5,2,1,4,3,6,7]=>[3,6,7,4,5,2,1]=>110100
[2,4,1,6,3,5,7]=>[7,2,1,4,3,6,5]=>[1,6,7,4,5,2,3]=>010100
[2,4,1,6,3,7,5]=>[2,1,4,3,6,5,7]=>[6,7,4,5,2,3,1]=>110100
[2,4,1,6,5,3,7]=>[7,2,1,4,3,5,6]=>[1,6,7,4,5,3,2]=>011100
[2,4,1,6,5,7,3]=>[5,6,2,1,4,3,7]=>[3,2,6,7,4,5,1]=>110100
[2,4,1,6,7,3,5]=>[6,2,1,4,3,7,5]=>[2,6,7,4,5,1,3]=>100100
[2,4,1,6,7,5,3]=>[6,2,1,4,3,5,7]=>[2,6,7,4,5,3,1]=>101100
[2,4,1,7,3,5,6]=>[2,1,4,3,7,6,5]=>[6,7,4,5,1,2,3]=>100100
[2,4,1,7,3,6,5]=>[2,1,4,3,7,5,6]=>[6,7,4,5,1,3,2]=>110100
[2,4,1,7,5,3,6]=>[2,1,4,3,5,7,6]=>[6,7,4,5,3,1,2]=>101100
[2,4,1,7,5,6,3]=>[5,7,2,1,4,3,6]=>[3,1,6,7,4,5,2]=>110100
[2,4,1,7,6,3,5]=>[2,1,4,3,6,7,5]=>[6,7,4,5,2,1,3]=>110100
[2,4,1,7,6,5,3]=>[2,1,4,3,5,6,7]=>[6,7,4,5,3,2,1]=>111100
[2,4,3,1,5,6,7]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>000110
[2,4,3,1,5,7,6]=>[6,7,5,2,1,3,4]=>[2,1,3,6,7,5,4]=>100110
[2,4,3,1,6,5,7]=>[7,5,6,2,1,3,4]=>[1,3,2,6,7,5,4]=>010110
[2,4,3,1,6,7,5]=>[6,5,7,2,1,3,4]=>[2,3,1,6,7,5,4]=>100110
[2,4,3,1,7,5,6]=>[5,7,6,2,1,3,4]=>[3,1,2,6,7,5,4]=>100110
[2,4,3,1,7,6,5]=>[5,6,7,2,1,3,4]=>[3,2,1,6,7,5,4]=>110110
[2,4,3,5,1,6,7]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>001100
[2,4,3,5,1,7,6]=>[6,7,3,4,2,1,5]=>[2,1,5,4,6,7,3]=>101100
[2,4,3,5,6,1,7]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>010100
[2,4,3,5,6,7,1]=>[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>100100
[2,4,3,5,7,1,6]=>[5,3,4,2,1,7,6]=>[3,5,4,6,7,1,2]=>100100
[2,4,3,5,7,6,1]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>110100
[2,4,3,6,1,5,7]=>[7,3,4,2,1,6,5]=>[1,5,4,6,7,2,3]=>010100
[2,4,3,6,1,7,5]=>[3,4,2,1,6,5,7]=>[5,4,6,7,2,3,1]=>110100
[2,4,3,6,5,1,7]=>[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>011100
[2,4,3,6,5,7,1]=>[5,6,3,4,2,1,7]=>[3,2,5,4,6,7,1]=>110100
[2,4,3,6,7,1,5]=>[6,3,4,2,1,7,5]=>[2,5,4,6,7,1,3]=>100100
[2,4,3,6,7,5,1]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>101100
[2,4,3,7,1,5,6]=>[3,4,2,1,7,6,5]=>[5,4,6,7,1,2,3]=>100100
[2,4,3,7,1,6,5]=>[3,4,2,1,7,5,6]=>[5,4,6,7,1,3,2]=>110100
[2,4,3,7,5,1,6]=>[3,4,2,1,5,7,6]=>[5,4,6,7,3,1,2]=>101100
[2,4,3,7,5,6,1]=>[5,7,3,4,2,1,6]=>[3,1,5,4,6,7,2]=>110100
[2,4,3,7,6,1,5]=>[3,4,2,1,6,7,5]=>[5,4,6,7,2,1,3]=>110100
[2,4,3,7,6,5,1]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>111100
[2,4,5,1,3,6,7]=>[7,6,4,2,1,5,3]=>[1,2,4,6,7,3,5]=>001000
[2,4,5,1,3,7,6]=>[6,7,4,2,1,5,3]=>[2,1,4,6,7,3,5]=>101000
[2,4,5,1,6,3,7]=>[7,4,2,1,5,3,6]=>[1,4,6,7,3,5,2]=>011000
[2,4,5,1,6,7,3]=>[6,4,2,1,5,3,7]=>[2,4,6,7,3,5,1]=>101000
[2,4,5,1,7,3,6]=>[4,2,1,5,3,7,6]=>[4,6,7,3,5,1,2]=>101000
[2,4,5,1,7,6,3]=>[4,2,1,5,3,6,7]=>[4,6,7,3,5,2,1]=>111000
[2,4,5,3,1,6,7]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>001010
[2,4,5,3,1,7,6]=>[6,7,4,2,1,3,5]=>[2,1,4,6,7,5,3]=>101010
[2,4,5,3,6,1,7]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>011000
[2,4,5,3,6,7,1]=>[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>101000
[2,4,5,3,7,1,6]=>[4,3,5,2,1,7,6]=>[4,5,3,6,7,1,2]=>101000
[2,4,5,3,7,6,1]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>111000
[2,4,5,6,1,3,7]=>[7,5,4,2,1,6,3]=>[1,3,4,6,7,2,5]=>010000
[2,4,5,6,1,7,3]=>[5,4,2,1,6,3,7]=>[3,4,6,7,2,5,1]=>110000
[2,4,5,6,3,1,7]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>010010
[2,4,5,6,3,7,1]=>[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>110000
[2,4,5,6,7,1,3]=>[6,5,4,2,1,7,3]=>[2,3,4,6,7,1,5]=>100000
[2,4,5,6,7,3,1]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>100010
[2,4,5,7,1,3,6]=>[5,4,2,1,7,6,3]=>[3,4,6,7,1,2,5]=>100000
[2,4,5,7,1,6,3]=>[5,4,2,1,7,3,6]=>[3,4,6,7,1,5,2]=>110000
[2,4,5,7,3,1,6]=>[5,4,2,1,3,7,6]=>[3,4,6,7,5,1,2]=>100010
[2,4,5,7,3,6,1]=>[5,4,3,7,2,1,6]=>[3,4,5,1,6,7,2]=>110000
[2,4,5,7,6,1,3]=>[5,4,2,1,6,7,3]=>[3,4,6,7,2,1,5]=>110000
[2,4,5,7,6,3,1]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>110010
[2,4,6,1,3,5,7]=>[7,4,2,1,6,5,3]=>[1,4,6,7,2,3,5]=>010000
[2,4,6,1,3,7,5]=>[4,2,1,6,5,7,3]=>[4,6,7,2,3,1,5]=>110000
[2,4,6,1,5,3,7]=>[7,4,2,1,6,3,5]=>[1,4,6,7,2,5,3]=>011000
[2,4,6,1,5,7,3]=>[4,2,1,6,5,3,7]=>[4,6,7,2,3,5,1]=>110000
[2,4,6,1,7,3,5]=>[4,2,1,6,3,7,5]=>[4,6,7,2,5,1,3]=>110000
[2,4,6,1,7,5,3]=>[4,2,1,6,3,5,7]=>[4,6,7,2,5,3,1]=>111000
[2,4,6,3,1,5,7]=>[7,4,2,1,3,6,5]=>[1,4,6,7,5,2,3]=>010010
[2,4,6,3,1,7,5]=>[4,2,1,3,6,5,7]=>[4,6,7,5,2,3,1]=>110010
[2,4,6,3,5,1,7]=>[7,4,3,6,2,1,5]=>[1,4,5,2,6,7,3]=>011000
[2,4,6,3,5,7,1]=>[4,3,6,5,2,1,7]=>[4,5,2,3,6,7,1]=>110000
[2,4,6,3,7,1,5]=>[4,3,6,2,1,7,5]=>[4,5,2,6,7,1,3]=>110000
[2,4,6,3,7,5,1]=>[4,3,6,2,1,5,7]=>[4,5,2,6,7,3,1]=>111000
[2,4,6,5,1,3,7]=>[7,4,2,1,5,6,3]=>[1,4,6,7,3,2,5]=>011000
[2,4,6,5,1,7,3]=>[4,2,1,5,6,3,7]=>[4,6,7,3,2,5,1]=>111000
[2,4,6,5,3,1,7]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>011010
[2,4,6,5,3,7,1]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>111000
[2,4,6,5,7,1,3]=>[5,6,4,2,1,7,3]=>[3,2,4,6,7,1,5]=>110000
[2,4,6,5,7,3,1]=>[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>110010
[2,4,6,7,1,3,5]=>[6,4,2,1,7,5,3]=>[2,4,6,7,1,3,5]=>100000
[2,4,6,7,1,5,3]=>[6,4,2,1,7,3,5]=>[2,4,6,7,1,5,3]=>101000
[2,4,6,7,3,1,5]=>[6,4,2,1,3,7,5]=>[2,4,6,7,5,1,3]=>100010
[2,4,6,7,3,5,1]=>[6,4,3,7,2,1,5]=>[2,4,5,1,6,7,3]=>101000
[2,4,6,7,5,1,3]=>[6,4,2,1,5,7,3]=>[2,4,6,7,3,1,5]=>101000
[2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>101010
[2,4,7,1,3,5,6]=>[4,2,1,7,6,5,3]=>[4,6,7,1,2,3,5]=>100000
[2,4,7,1,3,6,5]=>[4,2,1,7,5,6,3]=>[4,6,7,1,3,2,5]=>110000
[2,4,7,1,5,3,6]=>[4,2,1,7,6,3,5]=>[4,6,7,1,2,5,3]=>101000
[2,4,7,1,5,6,3]=>[4,2,1,7,5,3,6]=>[4,6,7,1,3,5,2]=>110000
[2,4,7,1,6,3,5]=>[4,2,1,7,3,6,5]=>[4,6,7,1,5,2,3]=>110000
[2,4,7,1,6,5,3]=>[4,2,1,7,3,5,6]=>[4,6,7,1,5,3,2]=>111000
[2,4,7,3,1,5,6]=>[4,2,1,3,7,6,5]=>[4,6,7,5,1,2,3]=>100010
[2,4,7,3,1,6,5]=>[4,2,1,3,7,5,6]=>[4,6,7,5,1,3,2]=>110010
[2,4,7,3,5,1,6]=>[4,3,7,6,2,1,5]=>[4,5,1,2,6,7,3]=>101000
[2,4,7,3,5,6,1]=>[4,3,7,5,2,1,6]=>[4,5,1,3,6,7,2]=>110000
[2,4,7,3,6,1,5]=>[4,3,7,2,1,6,5]=>[4,5,1,6,7,2,3]=>110000
[2,4,7,3,6,5,1]=>[4,3,7,2,1,5,6]=>[4,5,1,6,7,3,2]=>111000
[2,4,7,5,1,3,6]=>[4,2,1,5,7,6,3]=>[4,6,7,3,1,2,5]=>101000
[2,4,7,5,1,6,3]=>[4,2,1,5,7,3,6]=>[4,6,7,3,1,5,2]=>111000
[2,4,7,5,3,1,6]=>[4,2,1,3,5,7,6]=>[4,6,7,5,3,1,2]=>101010
[2,4,7,5,3,6,1]=>[4,3,5,7,2,1,6]=>[4,5,3,1,6,7,2]=>111000
[2,4,7,5,6,1,3]=>[5,7,4,2,1,6,3]=>[3,1,4,6,7,2,5]=>110000
[2,4,7,5,6,3,1]=>[5,7,4,2,1,3,6]=>[3,1,4,6,7,5,2]=>110010
[2,4,7,6,1,3,5]=>[4,2,1,6,7,5,3]=>[4,6,7,2,1,3,5]=>110000
[2,4,7,6,1,5,3]=>[4,2,1,6,7,3,5]=>[4,6,7,2,1,5,3]=>111000
[2,4,7,6,3,1,5]=>[4,2,1,3,6,7,5]=>[4,6,7,5,2,1,3]=>110010
[2,4,7,6,3,5,1]=>[4,3,6,7,2,1,5]=>[4,5,2,1,6,7,3]=>111000
[2,4,7,6,5,1,3]=>[4,2,1,5,6,7,3]=>[4,6,7,3,2,1,5]=>111000
[2,4,7,6,5,3,1]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>111010
[2,5,1,3,4,6,7]=>[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>001000
[2,5,1,3,4,7,6]=>[6,7,2,1,5,4,3]=>[2,1,6,7,3,4,5]=>101000
[2,5,1,3,6,4,7]=>[7,2,1,5,4,6,3]=>[1,6,7,3,4,2,5]=>011000
[2,5,1,3,6,7,4]=>[6,2,1,5,4,7,3]=>[2,6,7,3,4,1,5]=>101000
[2,5,1,3,7,4,6]=>[2,1,5,4,7,6,3]=>[6,7,3,4,1,2,5]=>101000
[2,5,1,3,7,6,4]=>[2,1,5,4,6,7,3]=>[6,7,3,4,2,1,5]=>111000
[2,5,1,4,3,6,7]=>[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>001100
[2,5,1,4,3,7,6]=>[6,7,2,1,5,3,4]=>[2,1,6,7,3,5,4]=>101100
[2,5,1,4,6,3,7]=>[7,2,1,5,4,3,6]=>[1,6,7,3,4,5,2]=>011000
[2,5,1,4,6,7,3]=>[6,2,1,5,4,3,7]=>[2,6,7,3,4,5,1]=>101000
[2,5,1,4,7,3,6]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>101000
[2,5,1,4,7,6,3]=>[2,1,5,4,3,6,7]=>[6,7,3,4,5,2,1]=>111000
[2,5,1,6,3,4,7]=>[7,2,1,5,3,6,4]=>[1,6,7,3,5,2,4]=>011000
[2,5,1,6,3,7,4]=>[2,1,5,3,6,4,7]=>[6,7,3,5,2,4,1]=>111000
[2,5,1,6,4,3,7]=>[7,2,1,5,3,4,6]=>[1,6,7,3,5,4,2]=>011100
[2,5,1,6,4,7,3]=>[2,1,5,4,6,3,7]=>[6,7,3,4,2,5,1]=>111000
[2,5,1,6,7,3,4]=>[6,2,1,5,3,7,4]=>[2,6,7,3,5,1,4]=>101000
[2,5,1,6,7,4,3]=>[6,2,1,5,3,4,7]=>[2,6,7,3,5,4,1]=>101100
[2,5,1,7,3,4,6]=>[2,1,5,3,7,6,4]=>[6,7,3,5,1,2,4]=>101000
[2,5,1,7,3,6,4]=>[2,1,5,3,7,4,6]=>[6,7,3,5,1,4,2]=>111000
[2,5,1,7,4,3,6]=>[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>101100
[2,5,1,7,4,6,3]=>[2,1,5,4,7,3,6]=>[6,7,3,4,1,5,2]=>111000
[2,5,1,7,6,3,4]=>[2,1,5,3,6,7,4]=>[6,7,3,5,2,1,4]=>111000
[2,5,1,7,6,4,3]=>[2,1,5,3,4,6,7]=>[6,7,3,5,4,2,1]=>111100
[2,5,3,1,4,6,7]=>[7,6,2,1,3,5,4]=>[1,2,6,7,5,3,4]=>001010
[2,5,3,1,4,7,6]=>[6,7,2,1,3,5,4]=>[2,1,6,7,5,3,4]=>101010
[2,5,3,1,6,4,7]=>[7,2,1,3,5,4,6]=>[1,6,7,5,3,4,2]=>011010
[2,5,3,1,6,7,4]=>[6,2,1,3,5,4,7]=>[2,6,7,5,3,4,1]=>101010
[2,5,3,1,7,4,6]=>[2,1,3,5,4,7,6]=>[6,7,5,3,4,1,2]=>101010
[2,5,3,1,7,6,4]=>[2,1,3,5,4,6,7]=>[6,7,5,3,4,2,1]=>111010
[2,5,3,4,1,6,7]=>[7,6,3,5,2,1,4]=>[1,2,5,3,6,7,4]=>001100
[2,5,3,4,1,7,6]=>[6,7,3,5,2,1,4]=>[2,1,5,3,6,7,4]=>101100
[2,5,3,4,6,1,7]=>[7,3,5,4,2,1,6]=>[1,5,3,4,6,7,2]=>011000
[2,5,3,4,6,7,1]=>[6,3,5,4,2,1,7]=>[2,5,3,4,6,7,1]=>101000
[2,5,3,4,7,1,6]=>[3,5,4,2,1,7,6]=>[5,3,4,6,7,1,2]=>101000
[2,5,3,4,7,6,1]=>[3,5,4,2,1,6,7]=>[5,3,4,6,7,2,1]=>111000
[2,5,3,6,1,4,7]=>[7,3,5,2,1,6,4]=>[1,5,3,6,7,2,4]=>011000
[2,5,3,6,1,7,4]=>[3,5,2,1,6,4,7]=>[5,3,6,7,2,4,1]=>111000
[2,5,3,6,4,1,7]=>[7,3,5,2,1,4,6]=>[1,5,3,6,7,4,2]=>011100
[2,5,3,6,4,7,1]=>[3,5,4,6,2,1,7]=>[5,3,4,2,6,7,1]=>111000
[2,5,3,6,7,1,4]=>[6,3,5,2,1,7,4]=>[2,5,3,6,7,1,4]=>101000
[2,5,3,6,7,4,1]=>[6,3,5,2,1,4,7]=>[2,5,3,6,7,4,1]=>101100
[2,5,3,7,1,4,6]=>[3,5,2,1,7,6,4]=>[5,3,6,7,1,2,4]=>101000
[2,5,3,7,1,6,4]=>[3,5,2,1,7,4,6]=>[5,3,6,7,1,4,2]=>111000
[2,5,3,7,4,1,6]=>[3,5,2,1,4,7,6]=>[5,3,6,7,4,1,2]=>101100
[2,5,3,7,4,6,1]=>[3,5,4,7,2,1,6]=>[5,3,4,1,6,7,2]=>111000
[2,5,3,7,6,1,4]=>[3,5,2,1,6,7,4]=>[5,3,6,7,2,1,4]=>111000
[2,5,3,7,6,4,1]=>[3,5,2,1,4,6,7]=>[5,3,6,7,4,2,1]=>111100
[2,5,4,1,3,6,7]=>[7,6,2,1,4,5,3]=>[1,2,6,7,4,3,5]=>001100
[2,5,4,1,3,7,6]=>[6,7,2,1,4,5,3]=>[2,1,6,7,4,3,5]=>101100
[2,5,4,1,6,3,7]=>[7,2,1,4,5,3,6]=>[1,6,7,4,3,5,2]=>011100
[2,5,4,1,6,7,3]=>[6,2,1,4,5,3,7]=>[2,6,7,4,3,5,1]=>101100
[2,5,4,1,7,3,6]=>[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]=>101100
[2,5,4,1,7,6,3]=>[2,1,4,5,3,6,7]=>[6,7,4,3,5,2,1]=>111100
[2,5,4,3,1,6,7]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>001110
[2,5,4,3,1,7,6]=>[6,7,2,1,3,4,5]=>[2,1,6,7,5,4,3]=>101110
[2,5,4,3,6,1,7]=>[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>011100
[2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>101100
[2,5,4,3,7,1,6]=>[3,4,5,2,1,7,6]=>[5,4,3,6,7,1,2]=>101100
[2,5,4,3,7,6,1]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>111100
[2,5,4,6,1,3,7]=>[7,4,5,2,1,6,3]=>[1,4,3,6,7,2,5]=>011000
[2,5,4,6,1,7,3]=>[4,5,2,1,6,3,7]=>[4,3,6,7,2,5,1]=>111000
[2,5,4,6,3,1,7]=>[7,4,5,2,1,3,6]=>[1,4,3,6,7,5,2]=>011010
[2,5,4,6,3,7,1]=>[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>111000
[2,5,4,6,7,1,3]=>[6,4,5,2,1,7,3]=>[2,4,3,6,7,1,5]=>101000
[2,5,4,6,7,3,1]=>[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>101010
[2,5,4,7,1,3,6]=>[4,5,2,1,7,6,3]=>[4,3,6,7,1,2,5]=>101000
[2,5,4,7,1,6,3]=>[4,5,2,1,7,3,6]=>[4,3,6,7,1,5,2]=>111000
[2,5,4,7,3,1,6]=>[4,5,2,1,3,7,6]=>[4,3,6,7,5,1,2]=>101010
[2,5,4,7,3,6,1]=>[4,5,3,7,2,1,6]=>[4,3,5,1,6,7,2]=>111000
[2,5,4,7,6,1,3]=>[4,5,2,1,6,7,3]=>[4,3,6,7,2,1,5]=>111000
[2,5,4,7,6,3,1]=>[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>111010
[2,5,6,1,3,4,7]=>[7,5,2,1,6,4,3]=>[1,3,6,7,2,4,5]=>010000
[2,5,6,1,3,7,4]=>[5,2,1,6,4,7,3]=>[3,6,7,2,4,1,5]=>110000
[2,5,6,1,4,3,7]=>[7,5,2,1,6,3,4]=>[1,3,6,7,2,5,4]=>010100
[2,5,6,1,4,7,3]=>[5,2,1,6,4,3,7]=>[3,6,7,2,4,5,1]=>110000
[2,5,6,1,7,3,4]=>[5,2,1,6,3,7,4]=>[3,6,7,2,5,1,4]=>110000
[2,5,6,1,7,4,3]=>[5,2,1,6,3,4,7]=>[3,6,7,2,5,4,1]=>110100
[2,5,6,3,1,4,7]=>[7,5,2,1,3,6,4]=>[1,3,6,7,5,2,4]=>010010
[2,5,6,3,1,7,4]=>[5,2,1,3,6,4,7]=>[3,6,7,5,2,4,1]=>110010
[2,5,6,3,4,1,7]=>[7,5,3,6,2,1,4]=>[1,3,5,2,6,7,4]=>010100
[2,5,6,3,4,7,1]=>[5,3,6,4,2,1,7]=>[3,5,2,4,6,7,1]=>110000
[2,5,6,3,7,1,4]=>[5,3,6,2,1,7,4]=>[3,5,2,6,7,1,4]=>110000
[2,5,6,3,7,4,1]=>[5,3,6,2,1,4,7]=>[3,5,2,6,7,4,1]=>110100
[2,5,6,4,1,3,7]=>[7,5,2,1,4,6,3]=>[1,3,6,7,4,2,5]=>010100
[2,5,6,4,1,7,3]=>[5,2,1,4,6,3,7]=>[3,6,7,4,2,5,1]=>110100
[2,5,6,4,3,1,7]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>010110
[2,5,6,4,3,7,1]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>110100
[2,5,6,4,7,1,3]=>[5,4,6,2,1,7,3]=>[3,4,2,6,7,1,5]=>110000
[2,5,6,4,7,3,1]=>[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>110010
[2,5,6,7,1,3,4]=>[6,5,2,1,7,4,3]=>[2,3,6,7,1,4,5]=>100000
[2,5,6,7,1,4,3]=>[6,5,2,1,7,3,4]=>[2,3,6,7,1,5,4]=>100100
[2,5,6,7,3,1,4]=>[6,5,2,1,3,7,4]=>[2,3,6,7,5,1,4]=>100010
[2,5,6,7,3,4,1]=>[6,5,3,7,2,1,4]=>[2,3,5,1,6,7,4]=>100100
[2,5,6,7,4,1,3]=>[6,5,2,1,4,7,3]=>[2,3,6,7,4,1,5]=>100100
[2,5,6,7,4,3,1]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>100110
[2,5,7,1,3,4,6]=>[5,2,1,7,6,4,3]=>[3,6,7,1,2,4,5]=>100000
[2,5,7,1,3,6,4]=>[5,2,1,7,4,6,3]=>[3,6,7,1,4,2,5]=>110000
[2,5,7,1,4,3,6]=>[5,2,1,7,6,3,4]=>[3,6,7,1,2,5,4]=>100100
[2,5,7,1,4,6,3]=>[5,2,1,7,4,3,6]=>[3,6,7,1,4,5,2]=>110000
[2,5,7,1,6,3,4]=>[5,2,1,7,3,6,4]=>[3,6,7,1,5,2,4]=>110000
[2,5,7,1,6,4,3]=>[5,2,1,7,3,4,6]=>[3,6,7,1,5,4,2]=>110100
[2,5,7,3,1,4,6]=>[5,2,1,3,7,6,4]=>[3,6,7,5,1,2,4]=>100010
[2,5,7,3,1,6,4]=>[5,2,1,3,7,4,6]=>[3,6,7,5,1,4,2]=>110010
[2,5,7,3,4,1,6]=>[5,3,7,6,2,1,4]=>[3,5,1,2,6,7,4]=>100100
[2,5,7,3,4,6,1]=>[5,3,7,4,2,1,6]=>[3,5,1,4,6,7,2]=>110000
[2,5,7,3,6,1,4]=>[5,3,7,2,1,6,4]=>[3,5,1,6,7,2,4]=>110000
[2,5,7,3,6,4,1]=>[5,3,7,2,1,4,6]=>[3,5,1,6,7,4,2]=>110100
[2,5,7,4,1,3,6]=>[5,2,1,4,7,6,3]=>[3,6,7,4,1,2,5]=>100100
[2,5,7,4,1,6,3]=>[5,2,1,4,7,3,6]=>[3,6,7,4,1,5,2]=>110100
[2,5,7,4,3,1,6]=>[5,2,1,3,4,7,6]=>[3,6,7,5,4,1,2]=>100110
[2,5,7,4,3,6,1]=>[5,3,4,7,2,1,6]=>[3,5,4,1,6,7,2]=>110100
[2,5,7,4,6,1,3]=>[5,4,7,2,1,6,3]=>[3,4,1,6,7,2,5]=>110000
[2,5,7,4,6,3,1]=>[5,4,7,2,1,3,6]=>[3,4,1,6,7,5,2]=>110010
[2,5,7,6,1,3,4]=>[5,2,1,6,7,4,3]=>[3,6,7,2,1,4,5]=>110000
[2,5,7,6,1,4,3]=>[5,2,1,6,7,3,4]=>[3,6,7,2,1,5,4]=>110100
[2,5,7,6,3,1,4]=>[5,2,1,3,6,7,4]=>[3,6,7,5,2,1,4]=>110010
[2,5,7,6,3,4,1]=>[5,3,6,7,2,1,4]=>[3,5,2,1,6,7,4]=>110100
[2,5,7,6,4,1,3]=>[5,2,1,4,6,7,3]=>[3,6,7,4,2,1,5]=>110100
[2,5,7,6,4,3,1]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>110110
[2,6,1,3,4,5,7]=>[7,2,1,6,5,4,3]=>[1,6,7,2,3,4,5]=>010000
[2,6,1,3,4,7,5]=>[2,1,6,5,7,4,3]=>[6,7,2,3,1,4,5]=>110000
[2,6,1,3,5,4,7]=>[7,2,1,6,4,5,3]=>[1,6,7,2,4,3,5]=>011000
[2,6,1,3,5,7,4]=>[2,1,6,5,4,7,3]=>[6,7,2,3,4,1,5]=>110000
[2,6,1,3,7,4,5]=>[2,1,6,4,7,5,3]=>[6,7,2,4,1,3,5]=>110000
[2,6,1,3,7,5,4]=>[2,1,6,4,5,7,3]=>[6,7,2,4,3,1,5]=>111000
[2,6,1,4,3,5,7]=>[7,2,1,6,5,3,4]=>[1,6,7,2,3,5,4]=>010100
[2,6,1,4,3,7,5]=>[2,1,6,5,7,3,4]=>[6,7,2,3,1,5,4]=>110100
[2,6,1,4,5,3,7]=>[7,2,1,6,4,3,5]=>[1,6,7,2,4,5,3]=>011000
[2,6,1,4,5,7,3]=>[2,1,6,5,4,3,7]=>[6,7,2,3,4,5,1]=>110000
[2,6,1,4,7,3,5]=>[2,1,6,4,3,7,5]=>[6,7,2,4,5,1,3]=>110000
[2,6,1,4,7,5,3]=>[2,1,6,4,3,5,7]=>[6,7,2,4,5,3,1]=>111000
[2,6,1,5,3,4,7]=>[7,2,1,6,3,5,4]=>[1,6,7,2,5,3,4]=>011000
[2,6,1,5,3,7,4]=>[2,1,6,3,5,4,7]=>[6,7,2,5,3,4,1]=>111000
[2,6,1,5,4,3,7]=>[7,2,1,6,3,4,5]=>[1,6,7,2,5,4,3]=>011100
[2,6,1,5,4,7,3]=>[2,1,6,4,5,3,7]=>[6,7,2,4,3,5,1]=>111000
[2,6,1,5,7,3,4]=>[2,1,6,5,3,7,4]=>[6,7,2,3,5,1,4]=>110000
[2,6,1,5,7,4,3]=>[2,1,6,5,3,4,7]=>[6,7,2,3,5,4,1]=>110100
[2,6,1,7,3,4,5]=>[2,1,6,3,7,5,4]=>[6,7,2,5,1,3,4]=>110000
[2,6,1,7,3,5,4]=>[2,1,6,3,7,4,5]=>[6,7,2,5,1,4,3]=>111000
[2,6,1,7,4,3,5]=>[2,1,6,3,4,7,5]=>[6,7,2,5,4,1,3]=>110100
[2,6,1,7,4,5,3]=>[2,1,6,4,7,3,5]=>[6,7,2,4,1,5,3]=>111000
[2,6,1,7,5,3,4]=>[2,1,6,3,5,7,4]=>[6,7,2,5,3,1,4]=>111000
[2,6,1,7,5,4,3]=>[2,1,6,3,4,5,7]=>[6,7,2,5,4,3,1]=>111100
[2,6,3,1,4,5,7]=>[7,2,1,3,6,5,4]=>[1,6,7,5,2,3,4]=>010010
[2,6,3,1,4,7,5]=>[2,1,3,6,5,7,4]=>[6,7,5,2,3,1,4]=>110010
[2,6,3,1,5,4,7]=>[7,2,1,3,6,4,5]=>[1,6,7,5,2,4,3]=>011010
[2,6,3,1,5,7,4]=>[2,1,3,6,5,4,7]=>[6,7,5,2,3,4,1]=>110010
[2,6,3,1,7,4,5]=>[2,1,3,6,4,7,5]=>[6,7,5,2,4,1,3]=>110010
[2,6,3,1,7,5,4]=>[2,1,3,6,4,5,7]=>[6,7,5,2,4,3,1]=>111010
[2,6,3,4,1,5,7]=>[7,3,6,5,2,1,4]=>[1,5,2,3,6,7,4]=>010100
[2,6,3,4,1,7,5]=>[3,6,5,7,2,1,4]=>[5,2,3,1,6,7,4]=>110100
[2,6,3,4,5,1,7]=>[7,3,6,4,2,1,5]=>[1,5,2,4,6,7,3]=>011000
[2,6,3,4,5,7,1]=>[3,6,5,4,2,1,7]=>[5,2,3,4,6,7,1]=>110000
[2,6,3,4,7,1,5]=>[3,6,4,2,1,7,5]=>[5,2,4,6,7,1,3]=>110000
[2,6,3,4,7,5,1]=>[3,6,4,2,1,5,7]=>[5,2,4,6,7,3,1]=>111000
[2,6,3,5,1,4,7]=>[7,3,6,2,1,5,4]=>[1,5,2,6,7,3,4]=>011000
[2,6,3,5,1,7,4]=>[3,6,2,1,5,4,7]=>[5,2,6,7,3,4,1]=>111000
[2,6,3,5,4,1,7]=>[7,3,6,2,1,4,5]=>[1,5,2,6,7,4,3]=>011100
[2,6,3,5,4,7,1]=>[3,6,4,5,2,1,7]=>[5,2,4,3,6,7,1]=>111000
[2,6,3,5,7,1,4]=>[3,6,5,2,1,7,4]=>[5,2,3,6,7,1,4]=>110000
[2,6,3,5,7,4,1]=>[3,6,5,2,1,4,7]=>[5,2,3,6,7,4,1]=>110100
[2,6,3,7,1,4,5]=>[3,6,2,1,7,5,4]=>[5,2,6,7,1,3,4]=>110000
[2,6,3,7,1,5,4]=>[3,6,2,1,7,4,5]=>[5,2,6,7,1,4,3]=>111000
[2,6,3,7,4,1,5]=>[3,6,2,1,4,7,5]=>[5,2,6,7,4,1,3]=>110100
[2,6,3,7,4,5,1]=>[3,6,4,7,2,1,5]=>[5,2,4,1,6,7,3]=>111000
[2,6,3,7,5,1,4]=>[3,6,2,1,5,7,4]=>[5,2,6,7,3,1,4]=>111000
[2,6,3,7,5,4,1]=>[3,6,2,1,4,5,7]=>[5,2,6,7,4,3,1]=>111100
[2,6,4,1,3,5,7]=>[7,2,1,4,6,5,3]=>[1,6,7,4,2,3,5]=>010100
[2,6,4,1,3,7,5]=>[2,1,4,6,5,7,3]=>[6,7,4,2,3,1,5]=>110100
[2,6,4,1,5,3,7]=>[7,2,1,4,6,3,5]=>[1,6,7,4,2,5,3]=>011100
[2,6,4,1,5,7,3]=>[2,1,4,6,5,3,7]=>[6,7,4,2,3,5,1]=>110100
[2,6,4,1,7,3,5]=>[2,1,4,6,3,7,5]=>[6,7,4,2,5,1,3]=>110100
[2,6,4,1,7,5,3]=>[2,1,4,6,3,5,7]=>[6,7,4,2,5,3,1]=>111100
[2,6,4,3,1,5,7]=>[7,2,1,3,4,6,5]=>[1,6,7,5,4,2,3]=>010110
[2,6,4,3,1,7,5]=>[2,1,3,4,6,5,7]=>[6,7,5,4,2,3,1]=>110110
[2,6,4,3,5,1,7]=>[7,3,4,6,2,1,5]=>[1,5,4,2,6,7,3]=>011100
[2,6,4,3,5,7,1]=>[3,4,6,5,2,1,7]=>[5,4,2,3,6,7,1]=>110100
[2,6,4,3,7,1,5]=>[3,4,6,2,1,7,5]=>[5,4,2,6,7,1,3]=>110100
[2,6,4,3,7,5,1]=>[3,4,6,2,1,5,7]=>[5,4,2,6,7,3,1]=>111100
[2,6,4,5,1,3,7]=>[7,4,6,2,1,5,3]=>[1,4,2,6,7,3,5]=>011000
[2,6,4,5,1,7,3]=>[4,6,2,1,5,3,7]=>[4,2,6,7,3,5,1]=>111000
[2,6,4,5,3,1,7]=>[7,4,6,2,1,3,5]=>[1,4,2,6,7,5,3]=>011010
[2,6,4,5,3,7,1]=>[4,6,3,5,2,1,7]=>[4,2,5,3,6,7,1]=>111000
[2,6,4,5,7,1,3]=>[4,6,5,2,1,7,3]=>[4,2,3,6,7,1,5]=>110000
[2,6,4,5,7,3,1]=>[4,6,5,2,1,3,7]=>[4,2,3,6,7,5,1]=>110010
[2,6,4,7,1,3,5]=>[4,6,2,1,7,5,3]=>[4,2,6,7,1,3,5]=>110000
[2,6,4,7,1,5,3]=>[4,6,2,1,7,3,5]=>[4,2,6,7,1,5,3]=>111000
[2,6,4,7,3,1,5]=>[4,6,2,1,3,7,5]=>[4,2,6,7,5,1,3]=>110010
[2,6,4,7,3,5,1]=>[4,6,3,7,2,1,5]=>[4,2,5,1,6,7,3]=>111000
[2,6,4,7,5,1,3]=>[4,6,2,1,5,7,3]=>[4,2,6,7,3,1,5]=>111000
[2,6,4,7,5,3,1]=>[4,6,2,1,3,5,7]=>[4,2,6,7,5,3,1]=>111010
[2,6,5,1,3,4,7]=>[7,2,1,5,6,4,3]=>[1,6,7,3,2,4,5]=>011000
[2,6,5,1,3,7,4]=>[2,1,5,6,4,7,3]=>[6,7,3,2,4,1,5]=>111000
[2,6,5,1,4,3,7]=>[7,2,1,5,6,3,4]=>[1,6,7,3,2,5,4]=>011100
[2,6,5,1,4,7,3]=>[2,1,5,6,4,3,7]=>[6,7,3,2,4,5,1]=>111000
[2,6,5,1,7,3,4]=>[2,1,5,6,3,7,4]=>[6,7,3,2,5,1,4]=>111000
[2,6,5,1,7,4,3]=>[2,1,5,6,3,4,7]=>[6,7,3,2,5,4,1]=>111100
[2,6,5,3,1,4,7]=>[7,2,1,3,5,6,4]=>[1,6,7,5,3,2,4]=>011010
[2,6,5,3,1,7,4]=>[2,1,3,5,6,4,7]=>[6,7,5,3,2,4,1]=>111010
[2,6,5,3,4,1,7]=>[7,3,5,6,2,1,4]=>[1,5,3,2,6,7,4]=>011100
[2,6,5,3,4,7,1]=>[3,5,6,4,2,1,7]=>[5,3,2,4,6,7,1]=>111000
[2,6,5,3,7,1,4]=>[3,5,6,2,1,7,4]=>[5,3,2,6,7,1,4]=>111000
[2,6,5,3,7,4,1]=>[3,5,6,2,1,4,7]=>[5,3,2,6,7,4,1]=>111100
[2,6,5,4,1,3,7]=>[7,2,1,4,5,6,3]=>[1,6,7,4,3,2,5]=>011100
[2,6,5,4,1,7,3]=>[2,1,4,5,6,3,7]=>[6,7,4,3,2,5,1]=>111100
[2,6,5,4,3,1,7]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>011110
[2,6,5,4,3,7,1]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>111100
[2,6,5,4,7,1,3]=>[4,5,6,2,1,7,3]=>[4,3,2,6,7,1,5]=>111000
[2,6,5,4,7,3,1]=>[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>111010
[2,6,5,7,1,3,4]=>[5,6,2,1,7,4,3]=>[3,2,6,7,1,4,5]=>110000
[2,6,5,7,1,4,3]=>[5,6,2,1,7,3,4]=>[3,2,6,7,1,5,4]=>110100
[2,6,5,7,3,1,4]=>[5,6,2,1,3,7,4]=>[3,2,6,7,5,1,4]=>110010
[2,6,5,7,3,4,1]=>[5,6,3,7,2,1,4]=>[3,2,5,1,6,7,4]=>110100
[2,6,5,7,4,1,3]=>[5,6,2,1,4,7,3]=>[3,2,6,7,4,1,5]=>110100
[2,6,5,7,4,3,1]=>[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>110110
[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>[2,6,7,1,3,4,5]=>100000
[2,6,7,1,3,5,4]=>[6,2,1,7,4,5,3]=>[2,6,7,1,4,3,5]=>101000
[2,6,7,1,4,3,5]=>[6,2,1,7,5,3,4]=>[2,6,7,1,3,5,4]=>100100
[2,6,7,1,4,5,3]=>[6,2,1,7,4,3,5]=>[2,6,7,1,4,5,3]=>101000
[2,6,7,1,5,3,4]=>[6,2,1,7,3,5,4]=>[2,6,7,1,5,3,4]=>101000
[2,6,7,1,5,4,3]=>[6,2,1,7,3,4,5]=>[2,6,7,1,5,4,3]=>101100
[2,6,7,3,1,4,5]=>[6,2,1,3,7,5,4]=>[2,6,7,5,1,3,4]=>100010
[2,6,7,3,1,5,4]=>[6,2,1,3,7,4,5]=>[2,6,7,5,1,4,3]=>101010
[2,6,7,3,4,1,5]=>[6,3,7,5,2,1,4]=>[2,5,1,3,6,7,4]=>100100
[2,6,7,3,4,5,1]=>[6,3,7,4,2,1,5]=>[2,5,1,4,6,7,3]=>101000
[2,6,7,3,5,1,4]=>[6,3,7,2,1,5,4]=>[2,5,1,6,7,3,4]=>101000
[2,6,7,3,5,4,1]=>[6,3,7,2,1,4,5]=>[2,5,1,6,7,4,3]=>101100
[2,6,7,4,1,3,5]=>[6,2,1,4,7,5,3]=>[2,6,7,4,1,3,5]=>100100
[2,6,7,4,1,5,3]=>[6,2,1,4,7,3,5]=>[2,6,7,4,1,5,3]=>101100
[2,6,7,4,3,1,5]=>[6,2,1,3,4,7,5]=>[2,6,7,5,4,1,3]=>100110
[2,6,7,4,3,5,1]=>[6,3,4,7,2,1,5]=>[2,5,4,1,6,7,3]=>101100
[2,6,7,4,5,1,3]=>[6,4,7,2,1,5,3]=>[2,4,1,6,7,3,5]=>101000
[2,6,7,4,5,3,1]=>[6,4,7,2,1,3,5]=>[2,4,1,6,7,5,3]=>101010
[2,6,7,5,1,3,4]=>[6,2,1,5,7,4,3]=>[2,6,7,3,1,4,5]=>101000
[2,6,7,5,1,4,3]=>[6,2,1,5,7,3,4]=>[2,6,7,3,1,5,4]=>101100
[2,6,7,5,3,1,4]=>[6,2,1,3,5,7,4]=>[2,6,7,5,3,1,4]=>101010
[2,6,7,5,3,4,1]=>[6,3,5,7,2,1,4]=>[2,5,3,1,6,7,4]=>101100
[2,6,7,5,4,1,3]=>[6,2,1,4,5,7,3]=>[2,6,7,4,3,1,5]=>101100
[2,6,7,5,4,3,1]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>101110
[2,7,1,3,4,5,6]=>[2,1,7,6,5,4,3]=>[6,7,1,2,3,4,5]=>100000
[2,7,1,3,4,6,5]=>[2,1,7,5,6,4,3]=>[6,7,1,3,2,4,5]=>110000
[2,7,1,3,5,4,6]=>[2,1,7,6,4,5,3]=>[6,7,1,2,4,3,5]=>101000
[2,7,1,3,5,6,4]=>[2,1,7,5,4,6,3]=>[6,7,1,3,4,2,5]=>110000
[2,7,1,3,6,4,5]=>[2,1,7,4,6,5,3]=>[6,7,1,4,2,3,5]=>110000
[2,7,1,3,6,5,4]=>[2,1,7,4,5,6,3]=>[6,7,1,4,3,2,5]=>111000
[2,7,1,4,3,5,6]=>[2,1,7,6,5,3,4]=>[6,7,1,2,3,5,4]=>100100
[2,7,1,4,3,6,5]=>[2,1,7,5,6,3,4]=>[6,7,1,3,2,5,4]=>110100
[2,7,1,4,5,3,6]=>[2,1,7,6,4,3,5]=>[6,7,1,2,4,5,3]=>101000
[2,7,1,4,5,6,3]=>[2,1,7,5,4,3,6]=>[6,7,1,3,4,5,2]=>110000
[2,7,1,4,6,3,5]=>[2,1,7,4,3,6,5]=>[6,7,1,4,5,2,3]=>110000
[2,7,1,4,6,5,3]=>[2,1,7,4,3,5,6]=>[6,7,1,4,5,3,2]=>111000
[2,7,1,5,3,4,6]=>[2,1,7,6,3,5,4]=>[6,7,1,2,5,3,4]=>101000
[2,7,1,5,3,6,4]=>[2,1,7,3,5,4,6]=>[6,7,1,5,3,4,2]=>111000
[2,7,1,5,4,3,6]=>[2,1,7,6,3,4,5]=>[6,7,1,2,5,4,3]=>101100
[2,7,1,5,4,6,3]=>[2,1,7,4,5,3,6]=>[6,7,1,4,3,5,2]=>111000
[2,7,1,5,6,3,4]=>[2,1,7,5,3,6,4]=>[6,7,1,3,5,2,4]=>110000
[2,7,1,5,6,4,3]=>[2,1,7,5,3,4,6]=>[6,7,1,3,5,4,2]=>110100
[2,7,1,6,3,4,5]=>[2,1,7,3,6,5,4]=>[6,7,1,5,2,3,4]=>110000
[2,7,1,6,3,5,4]=>[2,1,7,3,6,4,5]=>[6,7,1,5,2,4,3]=>111000
[2,7,1,6,4,3,5]=>[2,1,7,3,4,6,5]=>[6,7,1,5,4,2,3]=>110100
[2,7,1,6,4,5,3]=>[2,1,7,4,6,3,5]=>[6,7,1,4,2,5,3]=>111000
[2,7,1,6,5,3,4]=>[2,1,7,3,5,6,4]=>[6,7,1,5,3,2,4]=>111000
[2,7,1,6,5,4,3]=>[2,1,7,3,4,5,6]=>[6,7,1,5,4,3,2]=>111100
[2,7,3,1,4,5,6]=>[2,1,3,7,6,5,4]=>[6,7,5,1,2,3,4]=>100010
[2,7,3,1,4,6,5]=>[2,1,3,7,5,6,4]=>[6,7,5,1,3,2,4]=>110010
[2,7,3,1,5,4,6]=>[2,1,3,7,6,4,5]=>[6,7,5,1,2,4,3]=>101010
[2,7,3,1,5,6,4]=>[2,1,3,7,5,4,6]=>[6,7,5,1,3,4,2]=>110010
[2,7,3,1,6,4,5]=>[2,1,3,7,4,6,5]=>[6,7,5,1,4,2,3]=>110010
[2,7,3,1,6,5,4]=>[2,1,3,7,4,5,6]=>[6,7,5,1,4,3,2]=>111010
[2,7,3,4,1,5,6]=>[3,7,6,5,2,1,4]=>[5,1,2,3,6,7,4]=>100100
[2,7,3,4,1,6,5]=>[3,7,5,6,2,1,4]=>[5,1,3,2,6,7,4]=>110100
[2,7,3,4,5,1,6]=>[3,7,6,4,2,1,5]=>[5,1,2,4,6,7,3]=>101000
[2,7,3,4,5,6,1]=>[3,7,5,4,2,1,6]=>[5,1,3,4,6,7,2]=>110000
[2,7,3,4,6,1,5]=>[3,7,4,2,1,6,5]=>[5,1,4,6,7,2,3]=>110000
[2,7,3,4,6,5,1]=>[3,7,4,2,1,5,6]=>[5,1,4,6,7,3,2]=>111000
[2,7,3,5,1,4,6]=>[3,7,6,2,1,5,4]=>[5,1,2,6,7,3,4]=>101000
[2,7,3,5,1,6,4]=>[3,7,2,1,5,4,6]=>[5,1,6,7,3,4,2]=>111000
[2,7,3,5,4,1,6]=>[3,7,6,2,1,4,5]=>[5,1,2,6,7,4,3]=>101100
[2,7,3,5,4,6,1]=>[3,7,4,5,2,1,6]=>[5,1,4,3,6,7,2]=>111000
[2,7,3,5,6,1,4]=>[3,7,5,2,1,6,4]=>[5,1,3,6,7,2,4]=>110000
[2,7,3,5,6,4,1]=>[3,7,5,2,1,4,6]=>[5,1,3,6,7,4,2]=>110100
[2,7,3,6,1,4,5]=>[3,7,2,1,6,5,4]=>[5,1,6,7,2,3,4]=>110000
[2,7,3,6,1,5,4]=>[3,7,2,1,6,4,5]=>[5,1,6,7,2,4,3]=>111000
[2,7,3,6,4,1,5]=>[3,7,2,1,4,6,5]=>[5,1,6,7,4,2,3]=>110100
[2,7,3,6,4,5,1]=>[3,7,4,6,2,1,5]=>[5,1,4,2,6,7,3]=>111000
[2,7,3,6,5,1,4]=>[3,7,2,1,5,6,4]=>[5,1,6,7,3,2,4]=>111000
[2,7,3,6,5,4,1]=>[3,7,2,1,4,5,6]=>[5,1,6,7,4,3,2]=>111100
[2,7,4,1,3,5,6]=>[2,1,4,7,6,5,3]=>[6,7,4,1,2,3,5]=>100100
[2,7,4,1,3,6,5]=>[2,1,4,7,5,6,3]=>[6,7,4,1,3,2,5]=>110100
[2,7,4,1,5,3,6]=>[2,1,4,7,6,3,5]=>[6,7,4,1,2,5,3]=>101100
[2,7,4,1,5,6,3]=>[2,1,4,7,5,3,6]=>[6,7,4,1,3,5,2]=>110100
[2,7,4,1,6,3,5]=>[2,1,4,7,3,6,5]=>[6,7,4,1,5,2,3]=>110100
[2,7,4,1,6,5,3]=>[2,1,4,7,3,5,6]=>[6,7,4,1,5,3,2]=>111100
[2,7,4,3,1,5,6]=>[2,1,3,4,7,6,5]=>[6,7,5,4,1,2,3]=>100110
[2,7,4,3,1,6,5]=>[2,1,3,4,7,5,6]=>[6,7,5,4,1,3,2]=>110110
[2,7,4,3,5,1,6]=>[3,4,7,6,2,1,5]=>[5,4,1,2,6,7,3]=>101100
[2,7,4,3,5,6,1]=>[3,4,7,5,2,1,6]=>[5,4,1,3,6,7,2]=>110100
[2,7,4,3,6,1,5]=>[3,4,7,2,1,6,5]=>[5,4,1,6,7,2,3]=>110100
[2,7,4,3,6,5,1]=>[3,4,7,2,1,5,6]=>[5,4,1,6,7,3,2]=>111100
[2,7,4,5,1,3,6]=>[4,7,6,2,1,5,3]=>[4,1,2,6,7,3,5]=>101000
[2,7,4,5,1,6,3]=>[4,7,2,1,5,3,6]=>[4,1,6,7,3,5,2]=>111000
[2,7,4,5,3,1,6]=>[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>101010
[2,7,4,5,3,6,1]=>[4,7,3,5,2,1,6]=>[4,1,5,3,6,7,2]=>111000
[2,7,4,5,6,1,3]=>[4,7,5,2,1,6,3]=>[4,1,3,6,7,2,5]=>110000
[2,7,4,5,6,3,1]=>[4,7,5,2,1,3,6]=>[4,1,3,6,7,5,2]=>110010
[2,7,4,6,1,3,5]=>[4,7,2,1,6,5,3]=>[4,1,6,7,2,3,5]=>110000
[2,7,4,6,1,5,3]=>[4,7,2,1,6,3,5]=>[4,1,6,7,2,5,3]=>111000
[2,7,4,6,3,1,5]=>[4,7,2,1,3,6,5]=>[4,1,6,7,5,2,3]=>110010
[2,7,4,6,3,5,1]=>[4,7,3,6,2,1,5]=>[4,1,5,2,6,7,3]=>111000
[2,7,4,6,5,1,3]=>[4,7,2,1,5,6,3]=>[4,1,6,7,3,2,5]=>111000
[2,7,4,6,5,3,1]=>[4,7,2,1,3,5,6]=>[4,1,6,7,5,3,2]=>111010
[2,7,5,1,3,4,6]=>[2,1,5,7,6,4,3]=>[6,7,3,1,2,4,5]=>101000
[2,7,5,1,3,6,4]=>[2,1,5,7,4,6,3]=>[6,7,3,1,4,2,5]=>111000
[2,7,5,1,4,3,6]=>[2,1,5,7,6,3,4]=>[6,7,3,1,2,5,4]=>101100
[2,7,5,1,4,6,3]=>[2,1,5,7,4,3,6]=>[6,7,3,1,4,5,2]=>111000
[2,7,5,1,6,3,4]=>[2,1,5,7,3,6,4]=>[6,7,3,1,5,2,4]=>111000
[2,7,5,1,6,4,3]=>[2,1,5,7,3,4,6]=>[6,7,3,1,5,4,2]=>111100
[2,7,5,3,1,4,6]=>[2,1,3,5,7,6,4]=>[6,7,5,3,1,2,4]=>101010
[2,7,5,3,1,6,4]=>[2,1,3,5,7,4,6]=>[6,7,5,3,1,4,2]=>111010
[2,7,5,3,4,1,6]=>[3,5,7,6,2,1,4]=>[5,3,1,2,6,7,4]=>101100
[2,7,5,3,4,6,1]=>[3,5,7,4,2,1,6]=>[5,3,1,4,6,7,2]=>111000
[2,7,5,3,6,1,4]=>[3,5,7,2,1,6,4]=>[5,3,1,6,7,2,4]=>111000
[2,7,5,3,6,4,1]=>[3,5,7,2,1,4,6]=>[5,3,1,6,7,4,2]=>111100
[2,7,5,4,1,3,6]=>[2,1,4,5,7,6,3]=>[6,7,4,3,1,2,5]=>101100
[2,7,5,4,1,6,3]=>[2,1,4,5,7,3,6]=>[6,7,4,3,1,5,2]=>111100
[2,7,5,4,3,1,6]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>101110
[2,7,5,4,3,6,1]=>[3,4,5,7,2,1,6]=>[5,4,3,1,6,7,2]=>111100
[2,7,5,4,6,1,3]=>[4,5,7,2,1,6,3]=>[4,3,1,6,7,2,5]=>111000
[2,7,5,4,6,3,1]=>[4,5,7,2,1,3,6]=>[4,3,1,6,7,5,2]=>111010
[2,7,5,6,1,3,4]=>[5,7,2,1,6,4,3]=>[3,1,6,7,2,4,5]=>110000
[2,7,5,6,1,4,3]=>[5,7,2,1,6,3,4]=>[3,1,6,7,2,5,4]=>110100
[2,7,5,6,3,1,4]=>[5,7,2,1,3,6,4]=>[3,1,6,7,5,2,4]=>110010
[2,7,5,6,3,4,1]=>[5,7,3,6,2,1,4]=>[3,1,5,2,6,7,4]=>110100
[2,7,5,6,4,1,3]=>[5,7,2,1,4,6,3]=>[3,1,6,7,4,2,5]=>110100
[2,7,5,6,4,3,1]=>[5,7,2,1,3,4,6]=>[3,1,6,7,5,4,2]=>110110
[2,7,6,1,3,4,5]=>[2,1,6,7,5,4,3]=>[6,7,2,1,3,4,5]=>110000
[2,7,6,1,3,5,4]=>[2,1,6,7,4,5,3]=>[6,7,2,1,4,3,5]=>111000
[2,7,6,1,4,3,5]=>[2,1,6,7,5,3,4]=>[6,7,2,1,3,5,4]=>110100
[2,7,6,1,4,5,3]=>[2,1,6,7,4,3,5]=>[6,7,2,1,4,5,3]=>111000
[2,7,6,1,5,3,4]=>[2,1,6,7,3,5,4]=>[6,7,2,1,5,3,4]=>111000
[2,7,6,1,5,4,3]=>[2,1,6,7,3,4,5]=>[6,7,2,1,5,4,3]=>111100
[2,7,6,3,1,4,5]=>[2,1,3,6,7,5,4]=>[6,7,5,2,1,3,4]=>110010
[2,7,6,3,1,5,4]=>[2,1,3,6,7,4,5]=>[6,7,5,2,1,4,3]=>111010
[2,7,6,3,4,1,5]=>[3,6,7,5,2,1,4]=>[5,2,1,3,6,7,4]=>110100
[2,7,6,3,4,5,1]=>[3,6,7,4,2,1,5]=>[5,2,1,4,6,7,3]=>111000
[2,7,6,3,5,1,4]=>[3,6,7,2,1,5,4]=>[5,2,1,6,7,3,4]=>111000
[2,7,6,3,5,4,1]=>[3,6,7,2,1,4,5]=>[5,2,1,6,7,4,3]=>111100
[2,7,6,4,1,3,5]=>[2,1,4,6,7,5,3]=>[6,7,4,2,1,3,5]=>110100
[2,7,6,4,1,5,3]=>[2,1,4,6,7,3,5]=>[6,7,4,2,1,5,3]=>111100
[2,7,6,4,3,1,5]=>[2,1,3,4,6,7,5]=>[6,7,5,4,2,1,3]=>110110
[2,7,6,4,3,5,1]=>[3,4,6,7,2,1,5]=>[5,4,2,1,6,7,3]=>111100
[2,7,6,4,5,1,3]=>[4,6,7,2,1,5,3]=>[4,2,1,6,7,3,5]=>111000
[2,7,6,4,5,3,1]=>[4,6,7,2,1,3,5]=>[4,2,1,6,7,5,3]=>111010
[2,7,6,5,1,3,4]=>[2,1,5,6,7,4,3]=>[6,7,3,2,1,4,5]=>111000
[2,7,6,5,1,4,3]=>[2,1,5,6,7,3,4]=>[6,7,3,2,1,5,4]=>111100
[2,7,6,5,3,1,4]=>[2,1,3,5,6,7,4]=>[6,7,5,3,2,1,4]=>111010
[2,7,6,5,3,4,1]=>[3,5,6,7,2,1,4]=>[5,3,2,1,6,7,4]=>111100
[2,7,6,5,4,1,3]=>[2,1,4,5,6,7,3]=>[6,7,4,3,2,1,5]=>111100
[2,7,6,5,4,3,1]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>111110
[3,1,2,4,5,6,7]=>[7,6,5,4,1,3,2]=>[1,2,3,4,7,5,6]=>000010
[3,1,2,4,5,7,6]=>[6,7,5,4,1,3,2]=>[2,1,3,4,7,5,6]=>100010
[3,1,2,4,6,5,7]=>[7,5,6,4,1,3,2]=>[1,3,2,4,7,5,6]=>010010
[3,1,2,4,6,7,5]=>[6,5,7,4,1,3,2]=>[2,3,1,4,7,5,6]=>100010
[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>[3,1,2,4,7,5,6]=>100010
[3,1,2,4,7,6,5]=>[5,6,7,4,1,3,2]=>[3,2,1,4,7,5,6]=>110010
[3,1,2,5,4,6,7]=>[7,6,4,5,1,3,2]=>[1,2,4,3,7,5,6]=>001010
[3,1,2,5,4,7,6]=>[6,7,4,5,1,3,2]=>[2,1,4,3,7,5,6]=>101010
[3,1,2,5,6,4,7]=>[7,5,4,6,1,3,2]=>[1,3,4,2,7,5,6]=>010010
[3,1,2,5,6,7,4]=>[6,5,4,7,1,3,2]=>[2,3,4,1,7,5,6]=>100010
[3,1,2,5,7,4,6]=>[5,4,7,6,1,3,2]=>[3,4,1,2,7,5,6]=>100010
[3,1,2,5,7,6,4]=>[5,4,6,7,1,3,2]=>[3,4,2,1,7,5,6]=>110010
[3,1,2,6,4,5,7]=>[7,4,6,5,1,3,2]=>[1,4,2,3,7,5,6]=>010010
[3,1,2,6,4,7,5]=>[4,6,5,7,1,3,2]=>[4,2,3,1,7,5,6]=>110010
[3,1,2,6,5,4,7]=>[7,4,5,6,1,3,2]=>[1,4,3,2,7,5,6]=>011010
[3,1,2,6,5,7,4]=>[5,6,4,7,1,3,2]=>[3,2,4,1,7,5,6]=>110010
[3,1,2,6,7,4,5]=>[6,4,7,5,1,3,2]=>[2,4,1,3,7,5,6]=>100010
[3,1,2,6,7,5,4]=>[6,4,5,7,1,3,2]=>[2,4,3,1,7,5,6]=>101010
[3,1,2,7,4,5,6]=>[4,7,6,5,1,3,2]=>[4,1,2,3,7,5,6]=>100010
[3,1,2,7,4,6,5]=>[4,7,5,6,1,3,2]=>[4,1,3,2,7,5,6]=>110010
[3,1,2,7,5,4,6]=>[4,5,7,6,1,3,2]=>[4,3,1,2,7,5,6]=>101010
[3,1,2,7,5,6,4]=>[5,7,4,6,1,3,2]=>[3,1,4,2,7,5,6]=>110010
[3,1,2,7,6,4,5]=>[4,6,7,5,1,3,2]=>[4,2,1,3,7,5,6]=>110010
[3,1,2,7,6,5,4]=>[4,5,6,7,1,3,2]=>[4,3,2,1,7,5,6]=>111010
[3,1,4,2,5,6,7]=>[7,6,5,1,3,2,4]=>[1,2,3,7,5,6,4]=>000110
[3,1,4,2,5,7,6]=>[6,7,5,1,3,2,4]=>[2,1,3,7,5,6,4]=>100110
[3,1,4,2,6,5,7]=>[7,5,6,1,3,2,4]=>[1,3,2,7,5,6,4]=>010110
[3,1,4,2,6,7,5]=>[6,5,7,1,3,2,4]=>[2,3,1,7,5,6,4]=>100110
[3,1,4,2,7,5,6]=>[5,7,6,1,3,2,4]=>[3,1,2,7,5,6,4]=>100110
[3,1,4,2,7,6,5]=>[5,6,7,1,3,2,4]=>[3,2,1,7,5,6,4]=>110110
[3,1,4,5,2,6,7]=>[7,6,4,1,3,2,5]=>[1,2,4,7,5,6,3]=>001010
[3,1,4,5,2,7,6]=>[6,7,4,1,3,2,5]=>[2,1,4,7,5,6,3]=>101010
[3,1,4,5,6,2,7]=>[7,5,4,1,3,2,6]=>[1,3,4,7,5,6,2]=>010010
[3,1,4,5,6,7,2]=>[6,5,4,1,3,2,7]=>[2,3,4,7,5,6,1]=>100010
[3,1,4,5,7,2,6]=>[5,4,1,3,2,7,6]=>[3,4,7,5,6,1,2]=>100010
[3,1,4,5,7,6,2]=>[5,4,1,3,2,6,7]=>[3,4,7,5,6,2,1]=>110010
[3,1,4,6,2,5,7]=>[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>010010
[3,1,4,6,2,7,5]=>[4,1,3,2,6,5,7]=>[4,7,5,6,2,3,1]=>110010
[3,1,4,6,5,2,7]=>[7,4,1,3,2,5,6]=>[1,4,7,5,6,3,2]=>011010
[3,1,4,6,5,7,2]=>[5,6,4,1,3,2,7]=>[3,2,4,7,5,6,1]=>110010
[3,1,4,6,7,2,5]=>[6,4,1,3,2,7,5]=>[2,4,7,5,6,1,3]=>100010
[3,1,4,6,7,5,2]=>[6,4,1,3,2,5,7]=>[2,4,7,5,6,3,1]=>101010
[3,1,4,7,2,5,6]=>[4,1,3,2,7,6,5]=>[4,7,5,6,1,2,3]=>100010
[3,1,4,7,2,6,5]=>[4,1,3,2,7,5,6]=>[4,7,5,6,1,3,2]=>110010
[3,1,4,7,5,2,6]=>[4,1,3,2,5,7,6]=>[4,7,5,6,3,1,2]=>101010
[3,1,4,7,5,6,2]=>[5,7,4,1,3,2,6]=>[3,1,4,7,5,6,2]=>110010
[3,1,4,7,6,2,5]=>[4,1,3,2,6,7,5]=>[4,7,5,6,2,1,3]=>110010
[3,1,4,7,6,5,2]=>[4,1,3,2,5,6,7]=>[4,7,5,6,3,2,1]=>111010
[3,1,5,2,4,6,7]=>[7,6,1,3,2,5,4]=>[1,2,7,5,6,3,4]=>001010
[3,1,5,2,4,7,6]=>[6,7,1,3,2,5,4]=>[2,1,7,5,6,3,4]=>101010
[3,1,5,2,6,4,7]=>[7,1,3,2,5,4,6]=>[1,7,5,6,3,4,2]=>011010
[3,1,5,2,6,7,4]=>[6,1,3,2,5,4,7]=>[2,7,5,6,3,4,1]=>101010
[3,1,5,2,7,4,6]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>101010
[3,1,5,2,7,6,4]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>111010
[3,1,5,4,2,6,7]=>[7,6,1,3,2,4,5]=>[1,2,7,5,6,4,3]=>001110
[3,1,5,4,2,7,6]=>[6,7,1,3,2,4,5]=>[2,1,7,5,6,4,3]=>101110
[3,1,5,4,6,2,7]=>[7,4,5,1,3,2,6]=>[1,4,3,7,5,6,2]=>011010
[3,1,5,4,6,7,2]=>[6,4,5,1,3,2,7]=>[2,4,3,7,5,6,1]=>101010
[3,1,5,4,7,2,6]=>[4,5,1,3,2,7,6]=>[4,3,7,5,6,1,2]=>101010
[3,1,5,4,7,6,2]=>[4,5,1,3,2,6,7]=>[4,3,7,5,6,2,1]=>111010
[3,1,5,6,2,4,7]=>[7,5,1,3,2,6,4]=>[1,3,7,5,6,2,4]=>010010
[3,1,5,6,2,7,4]=>[5,1,3,2,6,4,7]=>[3,7,5,6,2,4,1]=>110010
[3,1,5,6,4,2,7]=>[7,5,1,3,2,4,6]=>[1,3,7,5,6,4,2]=>010110
[3,1,5,6,4,7,2]=>[5,4,6,1,3,2,7]=>[3,4,2,7,5,6,1]=>110010
[3,1,5,6,7,2,4]=>[6,5,1,3,2,7,4]=>[2,3,7,5,6,1,4]=>100010
[3,1,5,6,7,4,2]=>[6,5,1,3,2,4,7]=>[2,3,7,5,6,4,1]=>100110
[3,1,5,7,2,4,6]=>[5,1,3,2,7,6,4]=>[3,7,5,6,1,2,4]=>100010
[3,1,5,7,2,6,4]=>[5,1,3,2,7,4,6]=>[3,7,5,6,1,4,2]=>110010
[3,1,5,7,4,2,6]=>[5,1,3,2,4,7,6]=>[3,7,5,6,4,1,2]=>100110
[3,1,5,7,4,6,2]=>[5,4,7,1,3,2,6]=>[3,4,1,7,5,6,2]=>110010
[3,1,5,7,6,2,4]=>[5,1,3,2,6,7,4]=>[3,7,5,6,2,1,4]=>110010
[3,1,5,7,6,4,2]=>[5,1,3,2,4,6,7]=>[3,7,5,6,4,2,1]=>110110
[3,1,6,2,4,5,7]=>[7,1,3,2,6,5,4]=>[1,7,5,6,2,3,4]=>010010
[3,1,6,2,4,7,5]=>[1,3,2,6,5,7,4]=>[7,5,6,2,3,1,4]=>110010
[3,1,6,2,5,4,7]=>[7,1,3,2,6,4,5]=>[1,7,5,6,2,4,3]=>011010
[3,1,6,2,5,7,4]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>110010
[3,1,6,2,7,4,5]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>110010
[3,1,6,2,7,5,4]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>111010
[3,1,6,4,2,5,7]=>[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>010110
[3,1,6,4,2,7,5]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>110110
[3,1,6,4,5,2,7]=>[7,4,6,1,3,2,5]=>[1,4,2,7,5,6,3]=>011010
[3,1,6,4,5,7,2]=>[4,6,5,1,3,2,7]=>[4,2,3,7,5,6,1]=>110010
[3,1,6,4,7,2,5]=>[4,6,1,3,2,7,5]=>[4,2,7,5,6,1,3]=>110010
[3,1,6,4,7,5,2]=>[4,6,1,3,2,5,7]=>[4,2,7,5,6,3,1]=>111010
[3,1,6,5,2,4,7]=>[7,1,3,2,5,6,4]=>[1,7,5,6,3,2,4]=>011010
[3,1,6,5,2,7,4]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>111010
[3,1,6,5,4,2,7]=>[7,1,3,2,4,5,6]=>[1,7,5,6,4,3,2]=>011110
[3,1,6,5,4,7,2]=>[4,5,6,1,3,2,7]=>[4,3,2,7,5,6,1]=>111010
[3,1,6,5,7,2,4]=>[5,6,1,3,2,7,4]=>[3,2,7,5,6,1,4]=>110010
[3,1,6,5,7,4,2]=>[5,6,1,3,2,4,7]=>[3,2,7,5,6,4,1]=>110110
[3,1,6,7,2,4,5]=>[6,1,3,2,7,5,4]=>[2,7,5,6,1,3,4]=>100010
[3,1,6,7,2,5,4]=>[6,1,3,2,7,4,5]=>[2,7,5,6,1,4,3]=>101010
[3,1,6,7,4,2,5]=>[6,1,3,2,4,7,5]=>[2,7,5,6,4,1,3]=>100110
[3,1,6,7,4,5,2]=>[6,4,7,1,3,2,5]=>[2,4,1,7,5,6,3]=>101010
[3,1,6,7,5,2,4]=>[6,1,3,2,5,7,4]=>[2,7,5,6,3,1,4]=>101010
[3,1,6,7,5,4,2]=>[6,1,3,2,4,5,7]=>[2,7,5,6,4,3,1]=>101110
[3,1,7,2,4,5,6]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>100010
[3,1,7,2,4,6,5]=>[1,3,2,7,5,6,4]=>[7,5,6,1,3,2,4]=>110010
[3,1,7,2,5,4,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>101010
[3,1,7,2,5,6,4]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>110010
[3,1,7,2,6,4,5]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>110010
[3,1,7,2,6,5,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>111010
[3,1,7,4,2,5,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>100110
[3,1,7,4,2,6,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>110110
[3,1,7,4,5,2,6]=>[4,7,6,1,3,2,5]=>[4,1,2,7,5,6,3]=>101010
[3,1,7,4,5,6,2]=>[4,7,5,1,3,2,6]=>[4,1,3,7,5,6,2]=>110010
[3,1,7,4,6,2,5]=>[4,7,1,3,2,6,5]=>[4,1,7,5,6,2,3]=>110010
[3,1,7,4,6,5,2]=>[4,7,1,3,2,5,6]=>[4,1,7,5,6,3,2]=>111010
[3,1,7,5,2,4,6]=>[1,3,2,5,7,6,4]=>[7,5,6,3,1,2,4]=>101010
[3,1,7,5,2,6,4]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>111010
[3,1,7,5,4,2,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>101110
[3,1,7,5,4,6,2]=>[4,5,7,1,3,2,6]=>[4,3,1,7,5,6,2]=>111010
[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]=>[3,1,7,5,6,2,4]=>110010
[3,1,7,5,6,4,2]=>[5,7,1,3,2,4,6]=>[3,1,7,5,6,4,2]=>110110
[3,1,7,6,2,4,5]=>[1,3,2,6,7,5,4]=>[7,5,6,2,1,3,4]=>110010
[3,1,7,6,2,5,4]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>111010
[3,1,7,6,4,2,5]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>110110
[3,1,7,6,4,5,2]=>[4,6,7,1,3,2,5]=>[4,2,1,7,5,6,3]=>111010
[3,1,7,6,5,2,4]=>[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]=>111010
[3,1,7,6,5,4,2]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>111110
[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>000011
[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>[2,1,3,4,7,6,5]=>100011
[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>010011
[3,2,1,4,6,7,5]=>[6,5,7,4,1,2,3]=>[2,3,1,4,7,6,5]=>100011
[3,2,1,4,7,5,6]=>[5,7,6,4,1,2,3]=>[3,1,2,4,7,6,5]=>100011
[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>001011
[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>101011
[3,2,1,5,6,4,7]=>[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>010011
[3,2,1,5,6,7,4]=>[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>100011
[3,2,1,5,7,4,6]=>[5,4,7,6,1,2,3]=>[3,4,1,2,7,6,5]=>100011
[3,2,1,5,7,6,4]=>[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>110011
[3,2,1,6,4,5,7]=>[7,4,6,5,1,2,3]=>[1,4,2,3,7,6,5]=>010011
[3,2,1,6,4,7,5]=>[4,6,5,7,1,2,3]=>[4,2,3,1,7,6,5]=>110011
[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>011011
[3,2,1,6,5,7,4]=>[5,6,4,7,1,2,3]=>[3,2,4,1,7,6,5]=>110011
[3,2,1,6,7,4,5]=>[6,4,7,5,1,2,3]=>[2,4,1,3,7,6,5]=>100011
[3,2,1,6,7,5,4]=>[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>101011
[3,2,1,7,4,5,6]=>[4,7,6,5,1,2,3]=>[4,1,2,3,7,6,5]=>100011
[3,2,1,7,4,6,5]=>[4,7,5,6,1,2,3]=>[4,1,3,2,7,6,5]=>110011
[3,2,1,7,5,4,6]=>[4,5,7,6,1,2,3]=>[4,3,1,2,7,6,5]=>101011
[3,2,1,7,5,6,4]=>[5,7,4,6,1,2,3]=>[3,1,4,2,7,6,5]=>110011
[3,2,1,7,6,4,5]=>[4,6,7,5,1,2,3]=>[4,2,1,3,7,6,5]=>110011
[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]=>111011
[3,2,4,1,5,6,7]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>000110
[3,2,4,1,5,7,6]=>[6,7,5,2,3,1,4]=>[2,1,3,6,5,7,4]=>100110
[3,2,4,1,6,5,7]=>[7,5,6,2,3,1,4]=>[1,3,2,6,5,7,4]=>010110
[3,2,4,1,6,7,5]=>[6,5,7,2,3,1,4]=>[2,3,1,6,5,7,4]=>100110
[3,2,4,1,7,5,6]=>[5,7,6,2,3,1,4]=>[3,1,2,6,5,7,4]=>100110
[3,2,4,1,7,6,5]=>[5,6,7,2,3,1,4]=>[3,2,1,6,5,7,4]=>110110
[3,2,4,5,1,6,7]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>001010
[3,2,4,5,1,7,6]=>[6,7,4,2,3,1,5]=>[2,1,4,6,5,7,3]=>101010
[3,2,4,5,6,1,7]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>010010
[3,2,4,5,6,7,1]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>100010
[3,2,4,5,7,1,6]=>[5,4,2,3,1,7,6]=>[3,4,6,5,7,1,2]=>100010
[3,2,4,5,7,6,1]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>110010
[3,2,4,6,1,5,7]=>[7,4,2,3,1,6,5]=>[1,4,6,5,7,2,3]=>010010
[3,2,4,6,1,7,5]=>[4,2,3,1,6,5,7]=>[4,6,5,7,2,3,1]=>110010
[3,2,4,6,5,1,7]=>[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>011010
[3,2,4,6,5,7,1]=>[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>110010
[3,2,4,6,7,1,5]=>[6,4,2,3,1,7,5]=>[2,4,6,5,7,1,3]=>100010
[3,2,4,6,7,5,1]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>101010
[3,2,4,7,1,5,6]=>[4,2,3,1,7,6,5]=>[4,6,5,7,1,2,3]=>100010
[3,2,4,7,1,6,5]=>[4,2,3,1,7,5,6]=>[4,6,5,7,1,3,2]=>110010
[3,2,4,7,5,1,6]=>[4,2,3,1,5,7,6]=>[4,6,5,7,3,1,2]=>101010
[3,2,4,7,5,6,1]=>[5,7,4,2,3,1,6]=>[3,1,4,6,5,7,2]=>110010
[3,2,4,7,6,1,5]=>[4,2,3,1,6,7,5]=>[4,6,5,7,2,1,3]=>110010
[3,2,4,7,6,5,1]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>111010
[3,2,5,1,4,6,7]=>[7,6,2,3,1,5,4]=>[1,2,6,5,7,3,4]=>001010
[3,2,5,1,4,7,6]=>[6,7,2,3,1,5,4]=>[2,1,6,5,7,3,4]=>101010
[3,2,5,1,6,4,7]=>[7,2,3,1,5,4,6]=>[1,6,5,7,3,4,2]=>011010
[3,2,5,1,6,7,4]=>[6,2,3,1,5,4,7]=>[2,6,5,7,3,4,1]=>101010
[3,2,5,1,7,4,6]=>[2,3,1,5,4,7,6]=>[6,5,7,3,4,1,2]=>101010
[3,2,5,1,7,6,4]=>[2,3,1,5,4,6,7]=>[6,5,7,3,4,2,1]=>111010
[3,2,5,4,1,6,7]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>001110
[3,2,5,4,1,7,6]=>[6,7,2,3,1,4,5]=>[2,1,6,5,7,4,3]=>101110
[3,2,5,4,6,1,7]=>[7,4,5,2,3,1,6]=>[1,4,3,6,5,7,2]=>011010
[3,2,5,4,6,7,1]=>[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>101010
[3,2,5,4,7,1,6]=>[4,5,2,3,1,7,6]=>[4,3,6,5,7,1,2]=>101010
[3,2,5,4,7,6,1]=>[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>111010
[3,2,5,6,1,4,7]=>[7,5,2,3,1,6,4]=>[1,3,6,5,7,2,4]=>010010
[3,2,5,6,1,7,4]=>[5,2,3,1,6,4,7]=>[3,6,5,7,2,4,1]=>110010
[3,2,5,6,4,1,7]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>010110
[3,2,5,6,4,7,1]=>[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>110010
[3,2,5,6,7,1,4]=>[6,5,2,3,1,7,4]=>[2,3,6,5,7,1,4]=>100010
[3,2,5,6,7,4,1]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>100110
[3,2,5,7,1,4,6]=>[5,2,3,1,7,6,4]=>[3,6,5,7,1,2,4]=>100010
[3,2,5,7,1,6,4]=>[5,2,3,1,7,4,6]=>[3,6,5,7,1,4,2]=>110010
[3,2,5,7,4,1,6]=>[5,2,3,1,4,7,6]=>[3,6,5,7,4,1,2]=>100110
[3,2,5,7,4,6,1]=>[5,4,7,2,3,1,6]=>[3,4,1,6,5,7,2]=>110010
[3,2,5,7,6,1,4]=>[5,2,3,1,6,7,4]=>[3,6,5,7,2,1,4]=>110010
[3,2,5,7,6,4,1]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>110110
[3,2,6,1,4,5,7]=>[7,2,3,1,6,5,4]=>[1,6,5,7,2,3,4]=>010010
[3,2,6,1,4,7,5]=>[2,3,1,6,5,7,4]=>[6,5,7,2,3,1,4]=>110010
[3,2,6,1,5,4,7]=>[7,2,3,1,6,4,5]=>[1,6,5,7,2,4,3]=>011010
[3,2,6,1,5,7,4]=>[2,3,1,6,5,4,7]=>[6,5,7,2,3,4,1]=>110010
[3,2,6,1,7,4,5]=>[2,3,1,6,4,7,5]=>[6,5,7,2,4,1,3]=>110010
[3,2,6,1,7,5,4]=>[2,3,1,6,4,5,7]=>[6,5,7,2,4,3,1]=>111010
[3,2,6,4,1,5,7]=>[7,2,3,1,4,6,5]=>[1,6,5,7,4,2,3]=>010110
[3,2,6,4,1,7,5]=>[2,3,1,4,6,5,7]=>[6,5,7,4,2,3,1]=>110110
[3,2,6,4,5,1,7]=>[7,4,6,2,3,1,5]=>[1,4,2,6,5,7,3]=>011010
[3,2,6,4,5,7,1]=>[4,6,5,2,3,1,7]=>[4,2,3,6,5,7,1]=>110010
[3,2,6,4,7,1,5]=>[4,6,2,3,1,7,5]=>[4,2,6,5,7,1,3]=>110010
[3,2,6,4,7,5,1]=>[4,6,2,3,1,5,7]=>[4,2,6,5,7,3,1]=>111010
[3,2,6,5,1,4,7]=>[7,2,3,1,5,6,4]=>[1,6,5,7,3,2,4]=>011010
[3,2,6,5,1,7,4]=>[2,3,1,5,6,4,7]=>[6,5,7,3,2,4,1]=>111010
[3,2,6,5,4,1,7]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>011110
[3,2,6,5,4,7,1]=>[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>111010
[3,2,6,5,7,1,4]=>[5,6,2,3,1,7,4]=>[3,2,6,5,7,1,4]=>110010
[3,2,6,5,7,4,1]=>[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>110110
[3,2,6,7,1,4,5]=>[6,2,3,1,7,5,4]=>[2,6,5,7,1,3,4]=>100010
[3,2,6,7,1,5,4]=>[6,2,3,1,7,4,5]=>[2,6,5,7,1,4,3]=>101010
[3,2,6,7,4,1,5]=>[6,2,3,1,4,7,5]=>[2,6,5,7,4,1,3]=>100110
[3,2,6,7,4,5,1]=>[6,4,7,2,3,1,5]=>[2,4,1,6,5,7,3]=>101010
[3,2,6,7,5,1,4]=>[6,2,3,1,5,7,4]=>[2,6,5,7,3,1,4]=>101010
[3,2,6,7,5,4,1]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>101110
[3,2,7,1,4,5,6]=>[2,3,1,7,6,5,4]=>[6,5,7,1,2,3,4]=>100010
[3,2,7,1,4,6,5]=>[2,3,1,7,5,6,4]=>[6,5,7,1,3,2,4]=>110010
[3,2,7,1,5,4,6]=>[2,3,1,7,6,4,5]=>[6,5,7,1,2,4,3]=>101010
[3,2,7,1,5,6,4]=>[2,3,1,7,5,4,6]=>[6,5,7,1,3,4,2]=>110010
[3,2,7,1,6,4,5]=>[2,3,1,7,4,6,5]=>[6,5,7,1,4,2,3]=>110010
[3,2,7,1,6,5,4]=>[2,3,1,7,4,5,6]=>[6,5,7,1,4,3,2]=>111010
[3,2,7,4,1,5,6]=>[2,3,1,4,7,6,5]=>[6,5,7,4,1,2,3]=>100110
[3,2,7,4,1,6,5]=>[2,3,1,4,7,5,6]=>[6,5,7,4,1,3,2]=>110110
[3,2,7,4,5,1,6]=>[4,7,6,2,3,1,5]=>[4,1,2,6,5,7,3]=>101010
[3,2,7,4,5,6,1]=>[4,7,5,2,3,1,6]=>[4,1,3,6,5,7,2]=>110010
[3,2,7,4,6,1,5]=>[4,7,2,3,1,6,5]=>[4,1,6,5,7,2,3]=>110010
[3,2,7,4,6,5,1]=>[4,7,2,3,1,5,6]=>[4,1,6,5,7,3,2]=>111010
[3,2,7,5,1,4,6]=>[2,3,1,5,7,6,4]=>[6,5,7,3,1,2,4]=>101010
[3,2,7,5,1,6,4]=>[2,3,1,5,7,4,6]=>[6,5,7,3,1,4,2]=>111010
[3,2,7,5,4,1,6]=>[2,3,1,4,5,7,6]=>[6,5,7,4,3,1,2]=>101110
[3,2,7,5,4,6,1]=>[4,5,7,2,3,1,6]=>[4,3,1,6,5,7,2]=>111010
[3,2,7,5,6,1,4]=>[5,7,2,3,1,6,4]=>[3,1,6,5,7,2,4]=>110010
[3,2,7,5,6,4,1]=>[5,7,2,3,1,4,6]=>[3,1,6,5,7,4,2]=>110110
[3,2,7,6,1,4,5]=>[2,3,1,6,7,5,4]=>[6,5,7,2,1,3,4]=>110010
[3,2,7,6,1,5,4]=>[2,3,1,6,7,4,5]=>[6,5,7,2,1,4,3]=>111010
[3,2,7,6,4,1,5]=>[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]=>110110
[3,2,7,6,4,5,1]=>[4,6,7,2,3,1,5]=>[4,2,1,6,5,7,3]=>111010
[3,2,7,6,5,1,4]=>[2,3,1,5,6,7,4]=>[6,5,7,3,2,1,4]=>111010
[3,2,7,6,5,4,1]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>111110
[3,4,1,2,5,6,7]=>[7,6,5,3,1,4,2]=>[1,2,3,5,7,4,6]=>000100
[3,4,1,2,5,7,6]=>[6,7,5,3,1,4,2]=>[2,1,3,5,7,4,6]=>100100
[3,4,1,2,6,5,7]=>[7,5,6,3,1,4,2]=>[1,3,2,5,7,4,6]=>010100
[3,4,1,2,6,7,5]=>[6,5,7,3,1,4,2]=>[2,3,1,5,7,4,6]=>100100
[3,4,1,2,7,5,6]=>[5,7,6,3,1,4,2]=>[3,1,2,5,7,4,6]=>100100
[3,4,1,2,7,6,5]=>[5,6,7,3,1,4,2]=>[3,2,1,5,7,4,6]=>110100
[3,4,1,5,2,6,7]=>[7,6,3,1,4,2,5]=>[1,2,5,7,4,6,3]=>001100
[3,4,1,5,2,7,6]=>[6,7,3,1,4,2,5]=>[2,1,5,7,4,6,3]=>101100
[3,4,1,5,6,2,7]=>[7,5,3,1,4,2,6]=>[1,3,5,7,4,6,2]=>010100
[3,4,1,5,6,7,2]=>[6,5,3,1,4,2,7]=>[2,3,5,7,4,6,1]=>100100
[3,4,1,5,7,2,6]=>[5,3,1,4,2,7,6]=>[3,5,7,4,6,1,2]=>100100
[3,4,1,5,7,6,2]=>[5,3,1,4,2,6,7]=>[3,5,7,4,6,2,1]=>110100
[3,4,1,6,2,5,7]=>[7,3,1,4,2,6,5]=>[1,5,7,4,6,2,3]=>010100
[3,4,1,6,2,7,5]=>[3,1,4,2,6,5,7]=>[5,7,4,6,2,3,1]=>110100
[3,4,1,6,5,2,7]=>[7,3,1,4,2,5,6]=>[1,5,7,4,6,3,2]=>011100
[3,4,1,6,5,7,2]=>[5,6,3,1,4,2,7]=>[3,2,5,7,4,6,1]=>110100
[3,4,1,6,7,2,5]=>[6,3,1,4,2,7,5]=>[2,5,7,4,6,1,3]=>100100
[3,4,1,6,7,5,2]=>[6,3,1,4,2,5,7]=>[2,5,7,4,6,3,1]=>101100
[3,4,1,7,2,5,6]=>[3,1,4,2,7,6,5]=>[5,7,4,6,1,2,3]=>100100
[3,4,1,7,2,6,5]=>[3,1,4,2,7,5,6]=>[5,7,4,6,1,3,2]=>110100
[3,4,1,7,5,2,6]=>[3,1,4,2,5,7,6]=>[5,7,4,6,3,1,2]=>101100
[3,4,1,7,5,6,2]=>[5,7,3,1,4,2,6]=>[3,1,5,7,4,6,2]=>110100
[3,4,1,7,6,2,5]=>[3,1,4,2,6,7,5]=>[5,7,4,6,2,1,3]=>110100
[3,4,1,7,6,5,2]=>[3,1,4,2,5,6,7]=>[5,7,4,6,3,2,1]=>111100
[3,4,2,1,5,6,7]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>000101
[3,4,2,1,5,7,6]=>[6,7,5,3,1,2,4]=>[2,1,3,5,7,6,4]=>100101
[3,4,2,1,6,5,7]=>[7,5,6,3,1,2,4]=>[1,3,2,5,7,6,4]=>010101
[3,4,2,1,6,7,5]=>[6,5,7,3,1,2,4]=>[2,3,1,5,7,6,4]=>100101
[3,4,2,1,7,5,6]=>[5,7,6,3,1,2,4]=>[3,1,2,5,7,6,4]=>100101
[3,4,2,1,7,6,5]=>[5,6,7,3,1,2,4]=>[3,2,1,5,7,6,4]=>110101
[3,4,2,5,1,6,7]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>001100
[3,4,2,5,1,7,6]=>[6,7,3,2,4,1,5]=>[2,1,5,6,4,7,3]=>101100
[3,4,2,5,6,1,7]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>010100
[3,4,2,5,6,7,1]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>100100
[3,4,2,5,7,1,6]=>[5,3,2,4,1,7,6]=>[3,5,6,4,7,1,2]=>100100
[3,4,2,5,7,6,1]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>110100
[3,4,2,6,1,5,7]=>[7,3,2,4,1,6,5]=>[1,5,6,4,7,2,3]=>010100
[3,4,2,6,1,7,5]=>[3,2,4,1,6,5,7]=>[5,6,4,7,2,3,1]=>110100
[3,4,2,6,5,1,7]=>[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>011100
[3,4,2,6,5,7,1]=>[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>110100
[3,4,2,6,7,1,5]=>[6,3,2,4,1,7,5]=>[2,5,6,4,7,1,3]=>100100
[3,4,2,6,7,5,1]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>101100
[3,4,2,7,1,5,6]=>[3,2,4,1,7,6,5]=>[5,6,4,7,1,2,3]=>100100
[3,4,2,7,1,6,5]=>[3,2,4,1,7,5,6]=>[5,6,4,7,1,3,2]=>110100
[3,4,2,7,5,1,6]=>[3,2,4,1,5,7,6]=>[5,6,4,7,3,1,2]=>101100
[3,4,2,7,5,6,1]=>[5,7,3,2,4,1,6]=>[3,1,5,6,4,7,2]=>110100
[3,4,2,7,6,1,5]=>[3,2,4,1,6,7,5]=>[5,6,4,7,2,1,3]=>110100
[3,4,2,7,6,5,1]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>111100
[3,4,5,1,2,6,7]=>[7,6,4,3,1,5,2]=>[1,2,4,5,7,3,6]=>001000
[3,4,5,1,2,7,6]=>[6,7,4,3,1,5,2]=>[2,1,4,5,7,3,6]=>101000
[3,4,5,1,6,2,7]=>[7,4,3,1,5,2,6]=>[1,4,5,7,3,6,2]=>011000
[3,4,5,1,6,7,2]=>[6,4,3,1,5,2,7]=>[2,4,5,7,3,6,1]=>101000
[3,4,5,1,7,2,6]=>[4,3,1,5,2,7,6]=>[4,5,7,3,6,1,2]=>101000
[3,4,5,1,7,6,2]=>[4,3,1,5,2,6,7]=>[4,5,7,3,6,2,1]=>111000
[3,4,5,2,1,6,7]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>001001
[3,4,5,2,1,7,6]=>[6,7,4,3,1,2,5]=>[2,1,4,5,7,6,3]=>101001
[3,4,5,2,6,1,7]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>011000
[3,4,5,2,6,7,1]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>101000
[3,4,5,2,7,1,6]=>[4,3,2,5,1,7,6]=>[4,5,6,3,7,1,2]=>101000
[3,4,5,2,7,6,1]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>111000
[3,4,5,6,1,2,7]=>[7,5,4,3,1,6,2]=>[1,3,4,5,7,2,6]=>010000
[3,4,5,6,1,7,2]=>[5,4,3,1,6,2,7]=>[3,4,5,7,2,6,1]=>110000
[3,4,5,6,2,1,7]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>010001
[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>110000
[3,4,5,6,7,1,2]=>[6,5,4,3,1,7,2]=>[2,3,4,5,7,1,6]=>100000
[3,4,5,6,7,2,1]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>100001
[3,4,5,7,1,2,6]=>[5,4,3,1,7,6,2]=>[3,4,5,7,1,2,6]=>100000
[3,4,5,7,1,6,2]=>[5,4,3,1,7,2,6]=>[3,4,5,7,1,6,2]=>110000
[3,4,5,7,2,1,6]=>[5,4,3,1,2,7,6]=>[3,4,5,7,6,1,2]=>100001
[3,4,5,7,2,6,1]=>[5,4,3,2,7,1,6]=>[3,4,5,6,1,7,2]=>110000
[3,4,5,7,6,1,2]=>[5,4,3,1,6,7,2]=>[3,4,5,7,2,1,6]=>110000
[3,4,5,7,6,2,1]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>110001
[3,4,6,1,2,5,7]=>[7,4,3,1,6,5,2]=>[1,4,5,7,2,3,6]=>010000
[3,4,6,1,2,7,5]=>[4,3,1,6,5,7,2]=>[4,5,7,2,3,1,6]=>110000
[3,4,6,1,5,2,7]=>[7,4,3,1,6,2,5]=>[1,4,5,7,2,6,3]=>011000
[3,4,6,1,5,7,2]=>[4,3,1,6,5,2,7]=>[4,5,7,2,3,6,1]=>110000
[3,4,6,1,7,2,5]=>[4,3,1,6,2,7,5]=>[4,5,7,2,6,1,3]=>110000
[3,4,6,1,7,5,2]=>[4,3,1,6,2,5,7]=>[4,5,7,2,6,3,1]=>111000
[3,4,6,2,1,5,7]=>[7,4,3,1,2,6,5]=>[1,4,5,7,6,2,3]=>010001
[3,4,6,2,1,7,5]=>[4,3,1,2,6,5,7]=>[4,5,7,6,2,3,1]=>110001
[3,4,6,2,5,1,7]=>[7,4,3,2,6,1,5]=>[1,4,5,6,2,7,3]=>011000
[3,4,6,2,5,7,1]=>[4,3,2,6,5,1,7]=>[4,5,6,2,3,7,1]=>110000
[3,4,6,2,7,1,5]=>[4,3,2,6,1,7,5]=>[4,5,6,2,7,1,3]=>110000
[3,4,6,2,7,5,1]=>[4,3,2,6,1,5,7]=>[4,5,6,2,7,3,1]=>111000
[3,4,6,5,1,2,7]=>[7,4,3,1,5,6,2]=>[1,4,5,7,3,2,6]=>011000
[3,4,6,5,1,7,2]=>[4,3,1,5,6,2,7]=>[4,5,7,3,2,6,1]=>111000
[3,4,6,5,2,1,7]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>011001
[3,4,6,5,2,7,1]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>111000
[3,4,6,5,7,1,2]=>[5,6,4,3,1,7,2]=>[3,2,4,5,7,1,6]=>110000
[3,4,6,5,7,2,1]=>[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>110001
[3,4,6,7,1,2,5]=>[6,4,3,1,7,5,2]=>[2,4,5,7,1,3,6]=>100000
[3,4,6,7,1,5,2]=>[6,4,3,1,7,2,5]=>[2,4,5,7,1,6,3]=>101000
[3,4,6,7,2,1,5]=>[6,4,3,1,2,7,5]=>[2,4,5,7,6,1,3]=>100001
[3,4,6,7,2,5,1]=>[6,4,3,2,7,1,5]=>[2,4,5,6,1,7,3]=>101000
[3,4,6,7,5,1,2]=>[6,4,3,1,5,7,2]=>[2,4,5,7,3,1,6]=>101000
[3,4,6,7,5,2,1]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>101001
[3,4,7,1,2,5,6]=>[4,3,1,7,6,5,2]=>[4,5,7,1,2,3,6]=>100000
[3,4,7,1,2,6,5]=>[4,3,1,7,5,6,2]=>[4,5,7,1,3,2,6]=>110000
[3,4,7,1,5,2,6]=>[4,3,1,7,6,2,5]=>[4,5,7,1,2,6,3]=>101000
[3,4,7,1,5,6,2]=>[4,3,1,7,5,2,6]=>[4,5,7,1,3,6,2]=>110000
[3,4,7,1,6,2,5]=>[4,3,1,7,2,6,5]=>[4,5,7,1,6,2,3]=>110000
[3,4,7,1,6,5,2]=>[4,3,1,7,2,5,6]=>[4,5,7,1,6,3,2]=>111000
[3,4,7,2,1,5,6]=>[4,3,1,2,7,6,5]=>[4,5,7,6,1,2,3]=>100001
[3,4,7,2,1,6,5]=>[4,3,1,2,7,5,6]=>[4,5,7,6,1,3,2]=>110001
[3,4,7,2,5,1,6]=>[4,3,2,7,6,1,5]=>[4,5,6,1,2,7,3]=>101000
[3,4,7,2,5,6,1]=>[4,3,2,7,5,1,6]=>[4,5,6,1,3,7,2]=>110000
[3,4,7,2,6,1,5]=>[4,3,2,7,1,6,5]=>[4,5,6,1,7,2,3]=>110000
[3,4,7,2,6,5,1]=>[4,3,2,7,1,5,6]=>[4,5,6,1,7,3,2]=>111000
[3,4,7,5,1,2,6]=>[4,3,1,5,7,6,2]=>[4,5,7,3,1,2,6]=>101000
[3,4,7,5,1,6,2]=>[4,3,1,5,7,2,6]=>[4,5,7,3,1,6,2]=>111000
[3,4,7,5,2,1,6]=>[4,3,1,2,5,7,6]=>[4,5,7,6,3,1,2]=>101001
[3,4,7,5,2,6,1]=>[4,3,2,5,7,1,6]=>[4,5,6,3,1,7,2]=>111000
[3,4,7,5,6,1,2]=>[5,7,4,3,1,6,2]=>[3,1,4,5,7,2,6]=>110000
[3,4,7,5,6,2,1]=>[5,7,4,3,1,2,6]=>[3,1,4,5,7,6,2]=>110001
[3,4,7,6,1,2,5]=>[4,3,1,6,7,5,2]=>[4,5,7,2,1,3,6]=>110000
[3,4,7,6,1,5,2]=>[4,3,1,6,7,2,5]=>[4,5,7,2,1,6,3]=>111000
[3,4,7,6,2,1,5]=>[4,3,1,2,6,7,5]=>[4,5,7,6,2,1,3]=>110001
[3,4,7,6,2,5,1]=>[4,3,2,6,7,1,5]=>[4,5,6,2,1,7,3]=>111000
[3,4,7,6,5,1,2]=>[4,3,1,5,6,7,2]=>[4,5,7,3,2,1,6]=>111000
[3,4,7,6,5,2,1]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>111001
[3,5,1,2,4,6,7]=>[7,6,3,1,5,4,2]=>[1,2,5,7,3,4,6]=>001000
[3,5,1,2,4,7,6]=>[6,7,3,1,5,4,2]=>[2,1,5,7,3,4,6]=>101000
[3,5,1,2,6,4,7]=>[7,3,1,5,4,6,2]=>[1,5,7,3,4,2,6]=>011000
[3,5,1,2,6,7,4]=>[6,3,1,5,4,7,2]=>[2,5,7,3,4,1,6]=>101000
[3,5,1,2,7,4,6]=>[3,1,5,4,7,6,2]=>[5,7,3,4,1,2,6]=>101000
[3,5,1,2,7,6,4]=>[3,1,5,4,6,7,2]=>[5,7,3,4,2,1,6]=>111000
[3,5,1,4,2,6,7]=>[7,6,3,1,5,2,4]=>[1,2,5,7,3,6,4]=>001100
[3,5,1,4,2,7,6]=>[6,7,3,1,5,2,4]=>[2,1,5,7,3,6,4]=>101100
[3,5,1,4,6,2,7]=>[7,3,1,5,4,2,6]=>[1,5,7,3,4,6,2]=>011000
[3,5,1,4,6,7,2]=>[6,3,1,5,4,2,7]=>[2,5,7,3,4,6,1]=>101000
[3,5,1,4,7,2,6]=>[3,1,5,4,2,7,6]=>[5,7,3,4,6,1,2]=>101000
[3,5,1,4,7,6,2]=>[3,1,5,4,2,6,7]=>[5,7,3,4,6,2,1]=>111000
[3,5,1,6,2,4,7]=>[7,3,1,5,2,6,4]=>[1,5,7,3,6,2,4]=>011000
[3,5,1,6,2,7,4]=>[3,1,5,2,6,4,7]=>[5,7,3,6,2,4,1]=>111000
[3,5,1,6,4,2,7]=>[7,3,1,5,2,4,6]=>[1,5,7,3,6,4,2]=>011100
[3,5,1,6,4,7,2]=>[3,1,5,4,6,2,7]=>[5,7,3,4,2,6,1]=>111000
[3,5,1,6,7,2,4]=>[6,3,1,5,2,7,4]=>[2,5,7,3,6,1,4]=>101000
[3,5,1,6,7,4,2]=>[6,3,1,5,2,4,7]=>[2,5,7,3,6,4,1]=>101100
[3,5,1,7,2,4,6]=>[3,1,5,2,7,6,4]=>[5,7,3,6,1,2,4]=>101000
[3,5,1,7,2,6,4]=>[3,1,5,2,7,4,6]=>[5,7,3,6,1,4,2]=>111000
[3,5,1,7,4,2,6]=>[3,1,5,2,4,7,6]=>[5,7,3,6,4,1,2]=>101100
[3,5,1,7,4,6,2]=>[3,1,5,4,7,2,6]=>[5,7,3,4,1,6,2]=>111000
[3,5,1,7,6,2,4]=>[3,1,5,2,6,7,4]=>[5,7,3,6,2,1,4]=>111000
[3,5,1,7,6,4,2]=>[3,1,5,2,4,6,7]=>[5,7,3,6,4,2,1]=>111100
[3,5,2,1,4,6,7]=>[7,6,3,1,2,5,4]=>[1,2,5,7,6,3,4]=>001001
[3,5,2,1,4,7,6]=>[6,7,3,1,2,5,4]=>[2,1,5,7,6,3,4]=>101001
[3,5,2,1,6,4,7]=>[7,3,1,2,5,4,6]=>[1,5,7,6,3,4,2]=>011001
[3,5,2,1,6,7,4]=>[6,3,1,2,5,4,7]=>[2,5,7,6,3,4,1]=>101001
[3,5,2,1,7,4,6]=>[3,1,2,5,4,7,6]=>[5,7,6,3,4,1,2]=>101001
[3,5,2,1,7,6,4]=>[3,1,2,5,4,6,7]=>[5,7,6,3,4,2,1]=>111001
[3,5,2,4,1,6,7]=>[7,6,3,2,5,1,4]=>[1,2,5,6,3,7,4]=>001100
[3,5,2,4,1,7,6]=>[6,7,3,2,5,1,4]=>[2,1,5,6,3,7,4]=>101100
[3,5,2,4,6,1,7]=>[7,3,2,5,4,1,6]=>[1,5,6,3,4,7,2]=>011000
[3,5,2,4,6,7,1]=>[6,3,2,5,4,1,7]=>[2,5,6,3,4,7,1]=>101000
[3,5,2,4,7,1,6]=>[3,2,5,4,1,7,6]=>[5,6,3,4,7,1,2]=>101000
[3,5,2,4,7,6,1]=>[3,2,5,4,1,6,7]=>[5,6,3,4,7,2,1]=>111000
[3,5,2,6,1,4,7]=>[7,3,2,5,1,6,4]=>[1,5,6,3,7,2,4]=>011000
[3,5,2,6,1,7,4]=>[3,2,5,1,6,4,7]=>[5,6,3,7,2,4,1]=>111000
[3,5,2,6,4,1,7]=>[7,3,2,5,1,4,6]=>[1,5,6,3,7,4,2]=>011100
[3,5,2,6,4,7,1]=>[3,2,5,4,6,1,7]=>[5,6,3,4,2,7,1]=>111000
[3,5,2,6,7,1,4]=>[6,3,2,5,1,7,4]=>[2,5,6,3,7,1,4]=>101000
[3,5,2,6,7,4,1]=>[6,3,2,5,1,4,7]=>[2,5,6,3,7,4,1]=>101100
[3,5,2,7,1,4,6]=>[3,2,5,1,7,6,4]=>[5,6,3,7,1,2,4]=>101000
[3,5,2,7,1,6,4]=>[3,2,5,1,7,4,6]=>[5,6,3,7,1,4,2]=>111000
[3,5,2,7,4,1,6]=>[3,2,5,1,4,7,6]=>[5,6,3,7,4,1,2]=>101100
[3,5,2,7,4,6,1]=>[3,2,5,4,7,1,6]=>[5,6,3,4,1,7,2]=>111000
[3,5,2,7,6,1,4]=>[3,2,5,1,6,7,4]=>[5,6,3,7,2,1,4]=>111000
[3,5,2,7,6,4,1]=>[3,2,5,1,4,6,7]=>[5,6,3,7,4,2,1]=>111100
[3,5,4,1,2,6,7]=>[7,6,3,1,4,5,2]=>[1,2,5,7,4,3,6]=>001100
[3,5,4,1,2,7,6]=>[6,7,3,1,4,5,2]=>[2,1,5,7,4,3,6]=>101100
[3,5,4,1,6,2,7]=>[7,3,1,4,5,2,6]=>[1,5,7,4,3,6,2]=>011100
[3,5,4,1,6,7,2]=>[6,3,1,4,5,2,7]=>[2,5,7,4,3,6,1]=>101100
[3,5,4,1,7,2,6]=>[3,1,4,5,2,7,6]=>[5,7,4,3,6,1,2]=>101100
[3,5,4,1,7,6,2]=>[3,1,4,5,2,6,7]=>[5,7,4,3,6,2,1]=>111100
[3,5,4,2,1,6,7]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>001101
[3,5,4,2,1,7,6]=>[6,7,3,1,2,4,5]=>[2,1,5,7,6,4,3]=>101101
[3,5,4,2,6,1,7]=>[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>011100
[3,5,4,2,6,7,1]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>101100
[3,5,4,2,7,1,6]=>[3,2,4,5,1,7,6]=>[5,6,4,3,7,1,2]=>101100
[3,5,4,2,7,6,1]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>111100
[3,5,4,6,1,2,7]=>[7,4,5,3,1,6,2]=>[1,4,3,5,7,2,6]=>011000
[3,5,4,6,1,7,2]=>[4,5,3,1,6,2,7]=>[4,3,5,7,2,6,1]=>111000
[3,5,4,6,2,1,7]=>[7,4,5,3,1,2,6]=>[1,4,3,5,7,6,2]=>011001
[3,5,4,6,2,7,1]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>111000
[3,5,4,6,7,1,2]=>[6,4,5,3,1,7,2]=>[2,4,3,5,7,1,6]=>101000
[3,5,4,6,7,2,1]=>[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>101001
[3,5,4,7,1,2,6]=>[4,5,3,1,7,6,2]=>[4,3,5,7,1,2,6]=>101000
[3,5,4,7,1,6,2]=>[4,5,3,1,7,2,6]=>[4,3,5,7,1,6,2]=>111000
[3,5,4,7,2,1,6]=>[4,5,3,1,2,7,6]=>[4,3,5,7,6,1,2]=>101001
[3,5,4,7,2,6,1]=>[4,5,3,2,7,1,6]=>[4,3,5,6,1,7,2]=>111000
[3,5,4,7,6,1,2]=>[4,5,3,1,6,7,2]=>[4,3,5,7,2,1,6]=>111000
[3,5,4,7,6,2,1]=>[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>111001
[3,5,6,1,2,4,7]=>[7,5,3,1,6,4,2]=>[1,3,5,7,2,4,6]=>010000
[3,5,6,1,2,7,4]=>[5,3,1,6,4,7,2]=>[3,5,7,2,4,1,6]=>110000
[3,5,6,1,4,2,7]=>[7,5,3,1,6,2,4]=>[1,3,5,7,2,6,4]=>010100
[3,5,6,1,4,7,2]=>[5,3,1,6,4,2,7]=>[3,5,7,2,4,6,1]=>110000
[3,5,6,1,7,2,4]=>[5,3,1,6,2,7,4]=>[3,5,7,2,6,1,4]=>110000
[3,5,6,1,7,4,2]=>[5,3,1,6,2,4,7]=>[3,5,7,2,6,4,1]=>110100
[3,5,6,2,1,4,7]=>[7,5,3,1,2,6,4]=>[1,3,5,7,6,2,4]=>010001
[3,5,6,2,1,7,4]=>[5,3,1,2,6,4,7]=>[3,5,7,6,2,4,1]=>110001
[3,5,6,2,4,1,7]=>[7,5,3,2,6,1,4]=>[1,3,5,6,2,7,4]=>010100
[3,5,6,2,4,7,1]=>[5,3,2,6,4,1,7]=>[3,5,6,2,4,7,1]=>110000
[3,5,6,2,7,1,4]=>[5,3,2,6,1,7,4]=>[3,5,6,2,7,1,4]=>110000
[3,5,6,2,7,4,1]=>[5,3,2,6,1,4,7]=>[3,5,6,2,7,4,1]=>110100
[3,5,6,4,1,2,7]=>[7,5,3,1,4,6,2]=>[1,3,5,7,4,2,6]=>010100
[3,5,6,4,1,7,2]=>[5,3,1,4,6,2,7]=>[3,5,7,4,2,6,1]=>110100
[3,5,6,4,2,1,7]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>010101
[3,5,6,4,2,7,1]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>110100
[3,5,6,4,7,1,2]=>[5,4,6,3,1,7,2]=>[3,4,2,5,7,1,6]=>110000
[3,5,6,4,7,2,1]=>[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>110001
[3,5,6,7,1,2,4]=>[6,5,3,1,7,4,2]=>[2,3,5,7,1,4,6]=>100000
[3,5,6,7,1,4,2]=>[6,5,3,1,7,2,4]=>[2,3,5,7,1,6,4]=>100100
[3,5,6,7,2,1,4]=>[6,5,3,1,2,7,4]=>[2,3,5,7,6,1,4]=>100001
[3,5,6,7,2,4,1]=>[6,5,3,2,7,1,4]=>[2,3,5,6,1,7,4]=>100100
[3,5,6,7,4,1,2]=>[6,5,3,1,4,7,2]=>[2,3,5,7,4,1,6]=>100100
[3,5,6,7,4,2,1]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>100101
[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]=>[3,5,7,1,2,4,6]=>100000
[3,5,7,1,2,6,4]=>[5,3,1,7,4,6,2]=>[3,5,7,1,4,2,6]=>110000
[3,5,7,1,4,2,6]=>[5,3,1,7,6,2,4]=>[3,5,7,1,2,6,4]=>100100
[3,5,7,1,4,6,2]=>[5,3,1,7,4,2,6]=>[3,5,7,1,4,6,2]=>110000
[3,5,7,1,6,2,4]=>[5,3,1,7,2,6,4]=>[3,5,7,1,6,2,4]=>110000
[3,5,7,1,6,4,2]=>[5,3,1,7,2,4,6]=>[3,5,7,1,6,4,2]=>110100
[3,5,7,2,1,4,6]=>[5,3,1,2,7,6,4]=>[3,5,7,6,1,2,4]=>100001
[3,5,7,2,1,6,4]=>[5,3,1,2,7,4,6]=>[3,5,7,6,1,4,2]=>110001
[3,5,7,2,4,1,6]=>[5,3,2,7,6,1,4]=>[3,5,6,1,2,7,4]=>100100
[3,5,7,2,4,6,1]=>[5,3,2,7,4,1,6]=>[3,5,6,1,4,7,2]=>110000
[3,5,7,2,6,1,4]=>[5,3,2,7,1,6,4]=>[3,5,6,1,7,2,4]=>110000
[3,5,7,2,6,4,1]=>[5,3,2,7,1,4,6]=>[3,5,6,1,7,4,2]=>110100
[3,5,7,4,1,2,6]=>[5,3,1,4,7,6,2]=>[3,5,7,4,1,2,6]=>100100
[3,5,7,4,1,6,2]=>[5,3,1,4,7,2,6]=>[3,5,7,4,1,6,2]=>110100
[3,5,7,4,2,1,6]=>[5,3,1,2,4,7,6]=>[3,5,7,6,4,1,2]=>100101
[3,5,7,4,2,6,1]=>[5,3,2,4,7,1,6]=>[3,5,6,4,1,7,2]=>110100
[3,5,7,4,6,1,2]=>[5,4,7,3,1,6,2]=>[3,4,1,5,7,2,6]=>110000
[3,5,7,4,6,2,1]=>[5,4,7,3,1,2,6]=>[3,4,1,5,7,6,2]=>110001
[3,5,7,6,1,2,4]=>[5,3,1,6,7,4,2]=>[3,5,7,2,1,4,6]=>110000
[3,5,7,6,1,4,2]=>[5,3,1,6,7,2,4]=>[3,5,7,2,1,6,4]=>110100
[3,5,7,6,2,1,4]=>[5,3,1,2,6,7,4]=>[3,5,7,6,2,1,4]=>110001
[3,5,7,6,2,4,1]=>[5,3,2,6,7,1,4]=>[3,5,6,2,1,7,4]=>110100
[3,5,7,6,4,1,2]=>[5,3,1,4,6,7,2]=>[3,5,7,4,2,1,6]=>110100
[3,5,7,6,4,2,1]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>110101
[3,6,1,2,4,5,7]=>[7,3,1,6,5,4,2]=>[1,5,7,2,3,4,6]=>010000
[3,6,1,2,4,7,5]=>[3,1,6,5,7,4,2]=>[5,7,2,3,1,4,6]=>110000
[3,6,1,2,5,4,7]=>[7,3,1,6,4,5,2]=>[1,5,7,2,4,3,6]=>011000
[3,6,1,2,5,7,4]=>[3,1,6,5,4,7,2]=>[5,7,2,3,4,1,6]=>110000
[3,6,1,2,7,4,5]=>[3,1,6,4,7,5,2]=>[5,7,2,4,1,3,6]=>110000
[3,6,1,2,7,5,4]=>[3,1,6,4,5,7,2]=>[5,7,2,4,3,1,6]=>111000
[3,6,1,4,2,5,7]=>[7,3,1,6,5,2,4]=>[1,5,7,2,3,6,4]=>010100
[3,6,1,4,2,7,5]=>[3,1,6,5,7,2,4]=>[5,7,2,3,1,6,4]=>110100
[3,6,1,4,5,2,7]=>[7,3,1,6,4,2,5]=>[1,5,7,2,4,6,3]=>011000
[3,6,1,4,5,7,2]=>[3,1,6,5,4,2,7]=>[5,7,2,3,4,6,1]=>110000
[3,6,1,4,7,2,5]=>[3,1,6,4,2,7,5]=>[5,7,2,4,6,1,3]=>110000
[3,6,1,4,7,5,2]=>[3,1,6,4,2,5,7]=>[5,7,2,4,6,3,1]=>111000
[3,6,1,5,2,4,7]=>[7,3,1,6,2,5,4]=>[1,5,7,2,6,3,4]=>011000
[3,6,1,5,2,7,4]=>[3,1,6,2,5,4,7]=>[5,7,2,6,3,4,1]=>111000
[3,6,1,5,4,2,7]=>[7,3,1,6,2,4,5]=>[1,5,7,2,6,4,3]=>011100
[3,6,1,5,4,7,2]=>[3,1,6,4,5,2,7]=>[5,7,2,4,3,6,1]=>111000
[3,6,1,5,7,2,4]=>[3,1,6,5,2,7,4]=>[5,7,2,3,6,1,4]=>110000
[3,6,1,5,7,4,2]=>[3,1,6,5,2,4,7]=>[5,7,2,3,6,4,1]=>110100
[3,6,1,7,2,4,5]=>[3,1,6,2,7,5,4]=>[5,7,2,6,1,3,4]=>110000
[3,6,1,7,2,5,4]=>[3,1,6,2,7,4,5]=>[5,7,2,6,1,4,3]=>111000
[3,6,1,7,4,2,5]=>[3,1,6,2,4,7,5]=>[5,7,2,6,4,1,3]=>110100
[3,6,1,7,4,5,2]=>[3,1,6,4,7,2,5]=>[5,7,2,4,1,6,3]=>111000
[3,6,1,7,5,2,4]=>[3,1,6,2,5,7,4]=>[5,7,2,6,3,1,4]=>111000
[3,6,1,7,5,4,2]=>[3,1,6,2,4,5,7]=>[5,7,2,6,4,3,1]=>111100
[3,6,2,1,4,5,7]=>[7,3,1,2,6,5,4]=>[1,5,7,6,2,3,4]=>010001
[3,6,2,1,4,7,5]=>[3,1,2,6,5,7,4]=>[5,7,6,2,3,1,4]=>110001
[3,6,2,1,5,4,7]=>[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>011001
[3,6,2,1,5,7,4]=>[3,1,2,6,5,4,7]=>[5,7,6,2,3,4,1]=>110001
[3,6,2,1,7,4,5]=>[3,1,2,6,4,7,5]=>[5,7,6,2,4,1,3]=>110001
[3,6,2,1,7,5,4]=>[3,1,2,6,4,5,7]=>[5,7,6,2,4,3,1]=>111001
[3,6,2,4,1,5,7]=>[7,3,2,6,5,1,4]=>[1,5,6,2,3,7,4]=>010100
[3,6,2,4,1,7,5]=>[3,2,6,5,7,1,4]=>[5,6,2,3,1,7,4]=>110100
[3,6,2,4,5,1,7]=>[7,3,2,6,4,1,5]=>[1,5,6,2,4,7,3]=>011000
[3,6,2,4,5,7,1]=>[3,2,6,5,4,1,7]=>[5,6,2,3,4,7,1]=>110000
[3,6,2,4,7,1,5]=>[3,2,6,4,1,7,5]=>[5,6,2,4,7,1,3]=>110000
[3,6,2,4,7,5,1]=>[3,2,6,4,1,5,7]=>[5,6,2,4,7,3,1]=>111000
[3,6,2,5,1,4,7]=>[7,3,2,6,1,5,4]=>[1,5,6,2,7,3,4]=>011000
[3,6,2,5,1,7,4]=>[3,2,6,1,5,4,7]=>[5,6,2,7,3,4,1]=>111000
[3,6,2,5,4,1,7]=>[7,3,2,6,1,4,5]=>[1,5,6,2,7,4,3]=>011100
[3,6,2,5,4,7,1]=>[3,2,6,4,5,1,7]=>[5,6,2,4,3,7,1]=>111000
[3,6,2,5,7,1,4]=>[3,2,6,5,1,7,4]=>[5,6,2,3,7,1,4]=>110000
[3,6,2,5,7,4,1]=>[3,2,6,5,1,4,7]=>[5,6,2,3,7,4,1]=>110100
[3,6,2,7,1,4,5]=>[3,2,6,1,7,5,4]=>[5,6,2,7,1,3,4]=>110000
[3,6,2,7,1,5,4]=>[3,2,6,1,7,4,5]=>[5,6,2,7,1,4,3]=>111000
[3,6,2,7,4,1,5]=>[3,2,6,1,4,7,5]=>[5,6,2,7,4,1,3]=>110100
[3,6,2,7,4,5,1]=>[3,2,6,4,7,1,5]=>[5,6,2,4,1,7,3]=>111000
[3,6,2,7,5,1,4]=>[3,2,6,1,5,7,4]=>[5,6,2,7,3,1,4]=>111000
[3,6,2,7,5,4,1]=>[3,2,6,1,4,5,7]=>[5,6,2,7,4,3,1]=>111100
[3,6,4,1,2,5,7]=>[7,3,1,4,6,5,2]=>[1,5,7,4,2,3,6]=>010100
[3,6,4,1,2,7,5]=>[3,1,4,6,5,7,2]=>[5,7,4,2,3,1,6]=>110100
[3,6,4,1,5,2,7]=>[7,3,1,4,6,2,5]=>[1,5,7,4,2,6,3]=>011100
[3,6,4,1,5,7,2]=>[3,1,4,6,5,2,7]=>[5,7,4,2,3,6,1]=>110100
[3,6,4,1,7,2,5]=>[3,1,4,6,2,7,5]=>[5,7,4,2,6,1,3]=>110100
[3,6,4,1,7,5,2]=>[3,1,4,6,2,5,7]=>[5,7,4,2,6,3,1]=>111100
[3,6,4,2,1,5,7]=>[7,3,1,2,4,6,5]=>[1,5,7,6,4,2,3]=>010101
[3,6,4,2,1,7,5]=>[3,1,2,4,6,5,7]=>[5,7,6,4,2,3,1]=>110101
[3,6,4,2,5,1,7]=>[7,3,2,4,6,1,5]=>[1,5,6,4,2,7,3]=>011100
[3,6,4,2,5,7,1]=>[3,2,4,6,5,1,7]=>[5,6,4,2,3,7,1]=>110100
[3,6,4,2,7,1,5]=>[3,2,4,6,1,7,5]=>[5,6,4,2,7,1,3]=>110100
[3,6,4,2,7,5,1]=>[3,2,4,6,1,5,7]=>[5,6,4,2,7,3,1]=>111100
[3,6,4,5,1,2,7]=>[7,4,6,3,1,5,2]=>[1,4,2,5,7,3,6]=>011000
[3,6,4,5,1,7,2]=>[4,6,3,1,5,2,7]=>[4,2,5,7,3,6,1]=>111000
[3,6,4,5,2,1,7]=>[7,4,6,3,1,2,5]=>[1,4,2,5,7,6,3]=>011001
[3,6,4,5,2,7,1]=>[4,6,3,2,5,1,7]=>[4,2,5,6,3,7,1]=>111000
[3,6,4,5,7,1,2]=>[4,6,5,3,1,7,2]=>[4,2,3,5,7,1,6]=>110000
[3,6,4,5,7,2,1]=>[4,6,5,3,1,2,7]=>[4,2,3,5,7,6,1]=>110001
[3,6,4,7,1,2,5]=>[4,6,3,1,7,5,2]=>[4,2,5,7,1,3,6]=>110000
[3,6,4,7,1,5,2]=>[4,6,3,1,7,2,5]=>[4,2,5,7,1,6,3]=>111000
[3,6,4,7,2,1,5]=>[4,6,3,1,2,7,5]=>[4,2,5,7,6,1,3]=>110001
[3,6,4,7,2,5,1]=>[4,6,3,2,7,1,5]=>[4,2,5,6,1,7,3]=>111000
[3,6,4,7,5,1,2]=>[4,6,3,1,5,7,2]=>[4,2,5,7,3,1,6]=>111000
[3,6,4,7,5,2,1]=>[4,6,3,1,2,5,7]=>[4,2,5,7,6,3,1]=>111001
[3,6,5,1,2,4,7]=>[7,3,1,5,6,4,2]=>[1,5,7,3,2,4,6]=>011000
[3,6,5,1,2,7,4]=>[3,1,5,6,4,7,2]=>[5,7,3,2,4,1,6]=>111000
[3,6,5,1,4,2,7]=>[7,3,1,5,6,2,4]=>[1,5,7,3,2,6,4]=>011100
[3,6,5,1,4,7,2]=>[3,1,5,6,4,2,7]=>[5,7,3,2,4,6,1]=>111000
[3,6,5,1,7,2,4]=>[3,1,5,6,2,7,4]=>[5,7,3,2,6,1,4]=>111000
[3,6,5,1,7,4,2]=>[3,1,5,6,2,4,7]=>[5,7,3,2,6,4,1]=>111100
[3,6,5,2,1,4,7]=>[7,3,1,2,5,6,4]=>[1,5,7,6,3,2,4]=>011001
[3,6,5,2,1,7,4]=>[3,1,2,5,6,4,7]=>[5,7,6,3,2,4,1]=>111001
[3,6,5,2,4,1,7]=>[7,3,2,5,6,1,4]=>[1,5,6,3,2,7,4]=>011100
[3,6,5,2,4,7,1]=>[3,2,5,6,4,1,7]=>[5,6,3,2,4,7,1]=>111000
[3,6,5,2,7,1,4]=>[3,2,5,6,1,7,4]=>[5,6,3,2,7,1,4]=>111000
[3,6,5,2,7,4,1]=>[3,2,5,6,1,4,7]=>[5,6,3,2,7,4,1]=>111100
[3,6,5,4,1,2,7]=>[7,3,1,4,5,6,2]=>[1,5,7,4,3,2,6]=>011100
[3,6,5,4,1,7,2]=>[3,1,4,5,6,2,7]=>[5,7,4,3,2,6,1]=>111100
[3,6,5,4,2,1,7]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>011101
[3,6,5,4,2,7,1]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>111100
[3,6,5,4,7,1,2]=>[4,5,6,3,1,7,2]=>[4,3,2,5,7,1,6]=>111000
[3,6,5,4,7,2,1]=>[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>111001
[3,6,5,7,1,2,4]=>[5,6,3,1,7,4,2]=>[3,2,5,7,1,4,6]=>110000
[3,6,5,7,1,4,2]=>[5,6,3,1,7,2,4]=>[3,2,5,7,1,6,4]=>110100
[3,6,5,7,2,1,4]=>[5,6,3,1,2,7,4]=>[3,2,5,7,6,1,4]=>110001
[3,6,5,7,2,4,1]=>[5,6,3,2,7,1,4]=>[3,2,5,6,1,7,4]=>110100
[3,6,5,7,4,1,2]=>[5,6,3,1,4,7,2]=>[3,2,5,7,4,1,6]=>110100
[3,6,5,7,4,2,1]=>[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>110101
[3,6,7,1,2,4,5]=>[6,3,1,7,5,4,2]=>[2,5,7,1,3,4,6]=>100000
[3,6,7,1,2,5,4]=>[6,3,1,7,4,5,2]=>[2,5,7,1,4,3,6]=>101000
[3,6,7,1,4,2,5]=>[6,3,1,7,5,2,4]=>[2,5,7,1,3,6,4]=>100100
[3,6,7,1,4,5,2]=>[6,3,1,7,4,2,5]=>[2,5,7,1,4,6,3]=>101000
[3,6,7,1,5,2,4]=>[6,3,1,7,2,5,4]=>[2,5,7,1,6,3,4]=>101000
[3,6,7,1,5,4,2]=>[6,3,1,7,2,4,5]=>[2,5,7,1,6,4,3]=>101100
[3,6,7,2,1,4,5]=>[6,3,1,2,7,5,4]=>[2,5,7,6,1,3,4]=>100001
[3,6,7,2,1,5,4]=>[6,3,1,2,7,4,5]=>[2,5,7,6,1,4,3]=>101001
[3,6,7,2,4,1,5]=>[6,3,2,7,5,1,4]=>[2,5,6,1,3,7,4]=>100100
[3,6,7,2,4,5,1]=>[6,3,2,7,4,1,5]=>[2,5,6,1,4,7,3]=>101000
[3,6,7,2,5,1,4]=>[6,3,2,7,1,5,4]=>[2,5,6,1,7,3,4]=>101000
[3,6,7,2,5,4,1]=>[6,3,2,7,1,4,5]=>[2,5,6,1,7,4,3]=>101100
[3,6,7,4,1,2,5]=>[6,3,1,4,7,5,2]=>[2,5,7,4,1,3,6]=>100100
[3,6,7,4,1,5,2]=>[6,3,1,4,7,2,5]=>[2,5,7,4,1,6,3]=>101100
[3,6,7,4,2,1,5]=>[6,3,1,2,4,7,5]=>[2,5,7,6,4,1,3]=>100101
[3,6,7,4,2,5,1]=>[6,3,2,4,7,1,5]=>[2,5,6,4,1,7,3]=>101100
[3,6,7,4,5,1,2]=>[6,4,7,3,1,5,2]=>[2,4,1,5,7,3,6]=>101000
[3,6,7,4,5,2,1]=>[6,4,7,3,1,2,5]=>[2,4,1,5,7,6,3]=>101001
[3,6,7,5,1,2,4]=>[6,3,1,5,7,4,2]=>[2,5,7,3,1,4,6]=>101000
[3,6,7,5,1,4,2]=>[6,3,1,5,7,2,4]=>[2,5,7,3,1,6,4]=>101100
[3,6,7,5,2,1,4]=>[6,3,1,2,5,7,4]=>[2,5,7,6,3,1,4]=>101001
[3,6,7,5,2,4,1]=>[6,3,2,5,7,1,4]=>[2,5,6,3,1,7,4]=>101100
[3,6,7,5,4,1,2]=>[6,3,1,4,5,7,2]=>[2,5,7,4,3,1,6]=>101100
[3,6,7,5,4,2,1]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>101101
[3,7,1,2,4,5,6]=>[3,1,7,6,5,4,2]=>[5,7,1,2,3,4,6]=>100000
[3,7,1,2,4,6,5]=>[3,1,7,5,6,4,2]=>[5,7,1,3,2,4,6]=>110000
[3,7,1,2,5,4,6]=>[3,1,7,6,4,5,2]=>[5,7,1,2,4,3,6]=>101000
[3,7,1,2,5,6,4]=>[3,1,7,5,4,6,2]=>[5,7,1,3,4,2,6]=>110000
[3,7,1,2,6,4,5]=>[3,1,7,4,6,5,2]=>[5,7,1,4,2,3,6]=>110000
[3,7,1,2,6,5,4]=>[3,1,7,4,5,6,2]=>[5,7,1,4,3,2,6]=>111000
[3,7,1,4,2,5,6]=>[3,1,7,6,5,2,4]=>[5,7,1,2,3,6,4]=>100100
[3,7,1,4,2,6,5]=>[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]=>110100
[3,7,1,4,5,2,6]=>[3,1,7,6,4,2,5]=>[5,7,1,2,4,6,3]=>101000
[3,7,1,4,5,6,2]=>[3,1,7,5,4,2,6]=>[5,7,1,3,4,6,2]=>110000
[3,7,1,4,6,2,5]=>[3,1,7,4,2,6,5]=>[5,7,1,4,6,2,3]=>110000
[3,7,1,4,6,5,2]=>[3,1,7,4,2,5,6]=>[5,7,1,4,6,3,2]=>111000
[3,7,1,5,2,4,6]=>[3,1,7,6,2,5,4]=>[5,7,1,2,6,3,4]=>101000
[3,7,1,5,2,6,4]=>[3,1,7,2,5,4,6]=>[5,7,1,6,3,4,2]=>111000
[3,7,1,5,4,2,6]=>[3,1,7,6,2,4,5]=>[5,7,1,2,6,4,3]=>101100
[3,7,1,5,4,6,2]=>[3,1,7,4,5,2,6]=>[5,7,1,4,3,6,2]=>111000
[3,7,1,5,6,2,4]=>[3,1,7,5,2,6,4]=>[5,7,1,3,6,2,4]=>110000
[3,7,1,5,6,4,2]=>[3,1,7,5,2,4,6]=>[5,7,1,3,6,4,2]=>110100
[3,7,1,6,2,4,5]=>[3,1,7,2,6,5,4]=>[5,7,1,6,2,3,4]=>110000
[3,7,1,6,2,5,4]=>[3,1,7,2,6,4,5]=>[5,7,1,6,2,4,3]=>111000
[3,7,1,6,4,2,5]=>[3,1,7,2,4,6,5]=>[5,7,1,6,4,2,3]=>110100
[3,7,1,6,4,5,2]=>[3,1,7,4,6,2,5]=>[5,7,1,4,2,6,3]=>111000
[3,7,1,6,5,2,4]=>[3,1,7,2,5,6,4]=>[5,7,1,6,3,2,4]=>111000
[3,7,1,6,5,4,2]=>[3,1,7,2,4,5,6]=>[5,7,1,6,4,3,2]=>111100
[3,7,2,1,4,5,6]=>[3,1,2,7,6,5,4]=>[5,7,6,1,2,3,4]=>100001
[3,7,2,1,4,6,5]=>[3,1,2,7,5,6,4]=>[5,7,6,1,3,2,4]=>110001
[3,7,2,1,5,4,6]=>[3,1,2,7,6,4,5]=>[5,7,6,1,2,4,3]=>101001
[3,7,2,1,5,6,4]=>[3,1,2,7,5,4,6]=>[5,7,6,1,3,4,2]=>110001
[3,7,2,1,6,4,5]=>[3,1,2,7,4,6,5]=>[5,7,6,1,4,2,3]=>110001
[3,7,2,1,6,5,4]=>[3,1,2,7,4,5,6]=>[5,7,6,1,4,3,2]=>111001
[3,7,2,4,1,5,6]=>[3,2,7,6,5,1,4]=>[5,6,1,2,3,7,4]=>100100
[3,7,2,4,1,6,5]=>[3,2,7,5,6,1,4]=>[5,6,1,3,2,7,4]=>110100
[3,7,2,4,5,1,6]=>[3,2,7,6,4,1,5]=>[5,6,1,2,4,7,3]=>101000
[3,7,2,4,5,6,1]=>[3,2,7,5,4,1,6]=>[5,6,1,3,4,7,2]=>110000
[3,7,2,4,6,1,5]=>[3,2,7,4,1,6,5]=>[5,6,1,4,7,2,3]=>110000
[3,7,2,4,6,5,1]=>[3,2,7,4,1,5,6]=>[5,6,1,4,7,3,2]=>111000
[3,7,2,5,1,4,6]=>[3,2,7,6,1,5,4]=>[5,6,1,2,7,3,4]=>101000
[3,7,2,5,1,6,4]=>[3,2,7,1,5,4,6]=>[5,6,1,7,3,4,2]=>111000
[3,7,2,5,4,1,6]=>[3,2,7,6,1,4,5]=>[5,6,1,2,7,4,3]=>101100
[3,7,2,5,4,6,1]=>[3,2,7,4,5,1,6]=>[5,6,1,4,3,7,2]=>111000
[3,7,2,5,6,1,4]=>[3,2,7,5,1,6,4]=>[5,6,1,3,7,2,4]=>110000
[3,7,2,5,6,4,1]=>[3,2,7,5,1,4,6]=>[5,6,1,3,7,4,2]=>110100
[3,7,2,6,1,4,5]=>[3,2,7,1,6,5,4]=>[5,6,1,7,2,3,4]=>110000
[3,7,2,6,1,5,4]=>[3,2,7,1,6,4,5]=>[5,6,1,7,2,4,3]=>111000
[3,7,2,6,4,1,5]=>[3,2,7,1,4,6,5]=>[5,6,1,7,4,2,3]=>110100
[3,7,2,6,4,5,1]=>[3,2,7,4,6,1,5]=>[5,6,1,4,2,7,3]=>111000
[3,7,2,6,5,1,4]=>[3,2,7,1,5,6,4]=>[5,6,1,7,3,2,4]=>111000
[3,7,2,6,5,4,1]=>[3,2,7,1,4,5,6]=>[5,6,1,7,4,3,2]=>111100
[3,7,4,1,2,5,6]=>[3,1,4,7,6,5,2]=>[5,7,4,1,2,3,6]=>100100
[3,7,4,1,2,6,5]=>[3,1,4,7,5,6,2]=>[5,7,4,1,3,2,6]=>110100
[3,7,4,1,5,2,6]=>[3,1,4,7,6,2,5]=>[5,7,4,1,2,6,3]=>101100
[3,7,4,1,5,6,2]=>[3,1,4,7,5,2,6]=>[5,7,4,1,3,6,2]=>110100
[3,7,4,1,6,2,5]=>[3,1,4,7,2,6,5]=>[5,7,4,1,6,2,3]=>110100
[3,7,4,1,6,5,2]=>[3,1,4,7,2,5,6]=>[5,7,4,1,6,3,2]=>111100
[3,7,4,2,1,5,6]=>[3,1,2,4,7,6,5]=>[5,7,6,4,1,2,3]=>100101
[3,7,4,2,1,6,5]=>[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>110101
[3,7,4,2,5,1,6]=>[3,2,4,7,6,1,5]=>[5,6,4,1,2,7,3]=>101100
[3,7,4,2,5,6,1]=>[3,2,4,7,5,1,6]=>[5,6,4,1,3,7,2]=>110100
[3,7,4,2,6,1,5]=>[3,2,4,7,1,6,5]=>[5,6,4,1,7,2,3]=>110100
[3,7,4,2,6,5,1]=>[3,2,4,7,1,5,6]=>[5,6,4,1,7,3,2]=>111100
[3,7,4,5,1,2,6]=>[4,7,6,3,1,5,2]=>[4,1,2,5,7,3,6]=>101000
[3,7,4,5,1,6,2]=>[4,7,3,1,5,2,6]=>[4,1,5,7,3,6,2]=>111000
[3,7,4,5,2,1,6]=>[4,7,6,3,1,2,5]=>[4,1,2,5,7,6,3]=>101001
[3,7,4,5,2,6,1]=>[4,7,3,2,5,1,6]=>[4,1,5,6,3,7,2]=>111000
[3,7,4,5,6,1,2]=>[4,7,5,3,1,6,2]=>[4,1,3,5,7,2,6]=>110000
[3,7,4,5,6,2,1]=>[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>110001
[3,7,4,6,1,2,5]=>[4,7,3,1,6,5,2]=>[4,1,5,7,2,3,6]=>110000
[3,7,4,6,1,5,2]=>[4,7,3,1,6,2,5]=>[4,1,5,7,2,6,3]=>111000
[3,7,4,6,2,1,5]=>[4,7,3,1,2,6,5]=>[4,1,5,7,6,2,3]=>110001
[3,7,4,6,2,5,1]=>[4,7,3,2,6,1,5]=>[4,1,5,6,2,7,3]=>111000
[3,7,4,6,5,1,2]=>[4,7,3,1,5,6,2]=>[4,1,5,7,3,2,6]=>111000
[3,7,4,6,5,2,1]=>[4,7,3,1,2,5,6]=>[4,1,5,7,6,3,2]=>111001
[3,7,5,1,2,4,6]=>[3,1,5,7,6,4,2]=>[5,7,3,1,2,4,6]=>101000
[3,7,5,1,2,6,4]=>[3,1,5,7,4,6,2]=>[5,7,3,1,4,2,6]=>111000
[3,7,5,1,4,2,6]=>[3,1,5,7,6,2,4]=>[5,7,3,1,2,6,4]=>101100
[3,7,5,1,4,6,2]=>[3,1,5,7,4,2,6]=>[5,7,3,1,4,6,2]=>111000
[3,7,5,1,6,2,4]=>[3,1,5,7,2,6,4]=>[5,7,3,1,6,2,4]=>111000
[3,7,5,1,6,4,2]=>[3,1,5,7,2,4,6]=>[5,7,3,1,6,4,2]=>111100
[3,7,5,2,1,4,6]=>[3,1,2,5,7,6,4]=>[5,7,6,3,1,2,4]=>101001
[3,7,5,2,1,6,4]=>[3,1,2,5,7,4,6]=>[5,7,6,3,1,4,2]=>111001
[3,7,5,2,4,1,6]=>[3,2,5,7,6,1,4]=>[5,6,3,1,2,7,4]=>101100
[3,7,5,2,4,6,1]=>[3,2,5,7,4,1,6]=>[5,6,3,1,4,7,2]=>111000
[3,7,5,2,6,1,4]=>[3,2,5,7,1,6,4]=>[5,6,3,1,7,2,4]=>111000
[3,7,5,2,6,4,1]=>[3,2,5,7,1,4,6]=>[5,6,3,1,7,4,2]=>111100
[3,7,5,4,1,2,6]=>[3,1,4,5,7,6,2]=>[5,7,4,3,1,2,6]=>101100
[3,7,5,4,1,6,2]=>[3,1,4,5,7,2,6]=>[5,7,4,3,1,6,2]=>111100
[3,7,5,4,2,1,6]=>[3,1,2,4,5,7,6]=>[5,7,6,4,3,1,2]=>101101
[3,7,5,4,2,6,1]=>[3,2,4,5,7,1,6]=>[5,6,4,3,1,7,2]=>111100
[3,7,5,4,6,1,2]=>[4,5,7,3,1,6,2]=>[4,3,1,5,7,2,6]=>111000
[3,7,5,4,6,2,1]=>[4,5,7,3,1,2,6]=>[4,3,1,5,7,6,2]=>111001
[3,7,5,6,1,2,4]=>[5,7,3,1,6,4,2]=>[3,1,5,7,2,4,6]=>110000
[3,7,5,6,1,4,2]=>[5,7,3,1,6,2,4]=>[3,1,5,7,2,6,4]=>110100
[3,7,5,6,2,1,4]=>[5,7,3,1,2,6,4]=>[3,1,5,7,6,2,4]=>110001
[3,7,5,6,2,4,1]=>[5,7,3,2,6,1,4]=>[3,1,5,6,2,7,4]=>110100
[3,7,5,6,4,1,2]=>[5,7,3,1,4,6,2]=>[3,1,5,7,4,2,6]=>110100
[3,7,5,6,4,2,1]=>[5,7,3,1,2,4,6]=>[3,1,5,7,6,4,2]=>110101
[3,7,6,1,2,4,5]=>[3,1,6,7,5,4,2]=>[5,7,2,1,3,4,6]=>110000
[3,7,6,1,2,5,4]=>[3,1,6,7,4,5,2]=>[5,7,2,1,4,3,6]=>111000
[3,7,6,1,4,2,5]=>[3,1,6,7,5,2,4]=>[5,7,2,1,3,6,4]=>110100
[3,7,6,1,4,5,2]=>[3,1,6,7,4,2,5]=>[5,7,2,1,4,6,3]=>111000
[3,7,6,1,5,2,4]=>[3,1,6,7,2,5,4]=>[5,7,2,1,6,3,4]=>111000
[3,7,6,1,5,4,2]=>[3,1,6,7,2,4,5]=>[5,7,2,1,6,4,3]=>111100
[3,7,6,2,1,4,5]=>[3,1,2,6,7,5,4]=>[5,7,6,2,1,3,4]=>110001
[3,7,6,2,1,5,4]=>[3,1,2,6,7,4,5]=>[5,7,6,2,1,4,3]=>111001
[3,7,6,2,4,1,5]=>[3,2,6,7,5,1,4]=>[5,6,2,1,3,7,4]=>110100
[3,7,6,2,4,5,1]=>[3,2,6,7,4,1,5]=>[5,6,2,1,4,7,3]=>111000
[3,7,6,2,5,1,4]=>[3,2,6,7,1,5,4]=>[5,6,2,1,7,3,4]=>111000
[3,7,6,2,5,4,1]=>[3,2,6,7,1,4,5]=>[5,6,2,1,7,4,3]=>111100
[3,7,6,4,1,2,5]=>[3,1,4,6,7,5,2]=>[5,7,4,2,1,3,6]=>110100
[3,7,6,4,1,5,2]=>[3,1,4,6,7,2,5]=>[5,7,4,2,1,6,3]=>111100
[3,7,6,4,2,1,5]=>[3,1,2,4,6,7,5]=>[5,7,6,4,2,1,3]=>110101
[3,7,6,4,2,5,1]=>[3,2,4,6,7,1,5]=>[5,6,4,2,1,7,3]=>111100
[3,7,6,4,5,1,2]=>[4,6,7,3,1,5,2]=>[4,2,1,5,7,3,6]=>111000
[3,7,6,4,5,2,1]=>[4,6,7,3,1,2,5]=>[4,2,1,5,7,6,3]=>111001
[3,7,6,5,1,2,4]=>[3,1,5,6,7,4,2]=>[5,7,3,2,1,4,6]=>111000
[3,7,6,5,1,4,2]=>[3,1,5,6,7,2,4]=>[5,7,3,2,1,6,4]=>111100
[3,7,6,5,2,1,4]=>[3,1,2,5,6,7,4]=>[5,7,6,3,2,1,4]=>111001
[3,7,6,5,2,4,1]=>[3,2,5,6,7,1,4]=>[5,6,3,2,1,7,4]=>111100
[3,7,6,5,4,1,2]=>[3,1,4,5,6,7,2]=>[5,7,4,3,2,1,6]=>111100
[3,7,6,5,4,2,1]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>111101
[4,1,2,3,5,6,7]=>[7,6,5,1,4,3,2]=>[1,2,3,7,4,5,6]=>000100
[4,1,2,3,5,7,6]=>[6,7,5,1,4,3,2]=>[2,1,3,7,4,5,6]=>100100
[4,1,2,3,6,5,7]=>[7,5,6,1,4,3,2]=>[1,3,2,7,4,5,6]=>010100
[4,1,2,3,6,7,5]=>[6,5,7,1,4,3,2]=>[2,3,1,7,4,5,6]=>100100
[4,1,2,3,7,5,6]=>[5,7,6,1,4,3,2]=>[3,1,2,7,4,5,6]=>100100
[4,1,2,3,7,6,5]=>[5,6,7,1,4,3,2]=>[3,2,1,7,4,5,6]=>110100
[4,1,2,5,3,6,7]=>[7,6,1,4,3,5,2]=>[1,2,7,4,5,3,6]=>001100
[4,1,2,5,3,7,6]=>[6,7,1,4,3,5,2]=>[2,1,7,4,5,3,6]=>101100
[4,1,2,5,6,3,7]=>[7,5,1,4,3,6,2]=>[1,3,7,4,5,2,6]=>010100
[4,1,2,5,6,7,3]=>[6,5,1,4,3,7,2]=>[2,3,7,4,5,1,6]=>100100
[4,1,2,5,7,3,6]=>[5,1,4,3,7,6,2]=>[3,7,4,5,1,2,6]=>100100
[4,1,2,5,7,6,3]=>[5,1,4,3,6,7,2]=>[3,7,4,5,2,1,6]=>110100
[4,1,2,6,3,5,7]=>[7,1,4,3,6,5,2]=>[1,7,4,5,2,3,6]=>010100
[4,1,2,6,3,7,5]=>[1,4,3,6,5,7,2]=>[7,4,5,2,3,1,6]=>110100
[4,1,2,6,5,3,7]=>[7,1,4,3,5,6,2]=>[1,7,4,5,3,2,6]=>011100
[4,1,2,6,5,7,3]=>[5,6,1,4,3,7,2]=>[3,2,7,4,5,1,6]=>110100
[4,1,2,6,7,3,5]=>[6,1,4,3,7,5,2]=>[2,7,4,5,1,3,6]=>100100
[4,1,2,6,7,5,3]=>[6,1,4,3,5,7,2]=>[2,7,4,5,3,1,6]=>101100
[4,1,2,7,3,5,6]=>[1,4,3,7,6,5,2]=>[7,4,5,1,2,3,6]=>100100
[4,1,2,7,3,6,5]=>[1,4,3,7,5,6,2]=>[7,4,5,1,3,2,6]=>110100
[4,1,2,7,5,3,6]=>[1,4,3,5,7,6,2]=>[7,4,5,3,1,2,6]=>101100
[4,1,2,7,5,6,3]=>[5,7,1,4,3,6,2]=>[3,1,7,4,5,2,6]=>110100
[4,1,2,7,6,3,5]=>[1,4,3,6,7,5,2]=>[7,4,5,2,1,3,6]=>110100
[4,1,2,7,6,5,3]=>[1,4,3,5,6,7,2]=>[7,4,5,3,2,1,6]=>111100
[4,1,3,2,5,6,7]=>[7,6,5,1,4,2,3]=>[1,2,3,7,4,6,5]=>000110
[4,1,3,2,5,7,6]=>[6,7,5,1,4,2,3]=>[2,1,3,7,4,6,5]=>100110
[4,1,3,2,6,5,7]=>[7,5,6,1,4,2,3]=>[1,3,2,7,4,6,5]=>010110
[4,1,3,2,6,7,5]=>[6,5,7,1,4,2,3]=>[2,3,1,7,4,6,5]=>100110
[4,1,3,2,7,5,6]=>[5,7,6,1,4,2,3]=>[3,1,2,7,4,6,5]=>100110
[4,1,3,2,7,6,5]=>[5,6,7,1,4,2,3]=>[3,2,1,7,4,6,5]=>110110
[4,1,3,5,2,6,7]=>[7,6,1,4,3,2,5]=>[1,2,7,4,5,6,3]=>001100
[4,1,3,5,2,7,6]=>[6,7,1,4,3,2,5]=>[2,1,7,4,5,6,3]=>101100
[4,1,3,5,6,2,7]=>[7,5,1,4,3,2,6]=>[1,3,7,4,5,6,2]=>010100
[4,1,3,5,6,7,2]=>[6,5,1,4,3,2,7]=>[2,3,7,4,5,6,1]=>100100
[4,1,3,5,7,2,6]=>[5,1,4,3,2,7,6]=>[3,7,4,5,6,1,2]=>100100
[4,1,3,5,7,6,2]=>[5,1,4,3,2,6,7]=>[3,7,4,5,6,2,1]=>110100
[4,1,3,6,2,5,7]=>[7,1,4,3,2,6,5]=>[1,7,4,5,6,2,3]=>010100
[4,1,3,6,2,7,5]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>110100
[4,1,3,6,5,2,7]=>[7,1,4,3,2,5,6]=>[1,7,4,5,6,3,2]=>011100
[4,1,3,6,5,7,2]=>[5,6,1,4,3,2,7]=>[3,2,7,4,5,6,1]=>110100
[4,1,3,6,7,2,5]=>[6,1,4,3,2,7,5]=>[2,7,4,5,6,1,3]=>100100
[4,1,3,6,7,5,2]=>[6,1,4,3,2,5,7]=>[2,7,4,5,6,3,1]=>101100
[4,1,3,7,2,5,6]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>100100
[4,1,3,7,2,6,5]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>110100
[4,1,3,7,5,2,6]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>101100
[4,1,3,7,5,6,2]=>[5,7,1,4,3,2,6]=>[3,1,7,4,5,6,2]=>110100
[4,1,3,7,6,2,5]=>[1,4,3,2,6,7,5]=>[7,4,5,6,2,1,3]=>110100
[4,1,3,7,6,5,2]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>111100
[4,1,5,2,3,6,7]=>[7,6,1,4,2,5,3]=>[1,2,7,4,6,3,5]=>001100
[4,1,5,2,3,7,6]=>[6,7,1,4,2,5,3]=>[2,1,7,4,6,3,5]=>101100
[4,1,5,2,6,3,7]=>[7,1,4,2,5,3,6]=>[1,7,4,6,3,5,2]=>011100
[4,1,5,2,6,7,3]=>[6,1,4,2,5,3,7]=>[2,7,4,6,3,5,1]=>101100
[4,1,5,2,7,3,6]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>101100
[4,1,5,2,7,6,3]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>111100
[4,1,5,3,2,6,7]=>[7,6,1,4,2,3,5]=>[1,2,7,4,6,5,3]=>001110
[4,1,5,3,2,7,6]=>[6,7,1,4,2,3,5]=>[2,1,7,4,6,5,3]=>101110
[4,1,5,3,6,2,7]=>[7,1,4,3,5,2,6]=>[1,7,4,5,3,6,2]=>011100
[4,1,5,3,6,7,2]=>[6,1,4,3,5,2,7]=>[2,7,4,5,3,6,1]=>101100
[4,1,5,3,7,2,6]=>[1,4,3,5,2,7,6]=>[7,4,5,3,6,1,2]=>101100
[4,1,5,3,7,6,2]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>111100
[4,1,5,6,2,3,7]=>[7,5,1,4,2,6,3]=>[1,3,7,4,6,2,5]=>010100
[4,1,5,6,2,7,3]=>[5,1,4,2,6,3,7]=>[3,7,4,6,2,5,1]=>110100
[4,1,5,6,3,2,7]=>[7,5,1,4,2,3,6]=>[1,3,7,4,6,5,2]=>010110
[4,1,5,6,3,7,2]=>[5,1,4,3,6,2,7]=>[3,7,4,5,2,6,1]=>110100
[4,1,5,6,7,2,3]=>[6,5,1,4,2,7,3]=>[2,3,7,4,6,1,5]=>100100
[4,1,5,6,7,3,2]=>[6,5,1,4,2,3,7]=>[2,3,7,4,6,5,1]=>100110
[4,1,5,7,2,3,6]=>[5,1,4,2,7,6,3]=>[3,7,4,6,1,2,5]=>100100
[4,1,5,7,2,6,3]=>[5,1,4,2,7,3,6]=>[3,7,4,6,1,5,2]=>110100
[4,1,5,7,3,2,6]=>[5,1,4,2,3,7,6]=>[3,7,4,6,5,1,2]=>100110
[4,1,5,7,3,6,2]=>[5,1,4,3,7,2,6]=>[3,7,4,5,1,6,2]=>110100
[4,1,5,7,6,2,3]=>[5,1,4,2,6,7,3]=>[3,7,4,6,2,1,5]=>110100
[4,1,5,7,6,3,2]=>[5,1,4,2,3,6,7]=>[3,7,4,6,5,2,1]=>110110
[4,1,6,2,3,5,7]=>[7,1,4,2,6,5,3]=>[1,7,4,6,2,3,5]=>010100
[4,1,6,2,3,7,5]=>[1,4,2,6,5,7,3]=>[7,4,6,2,3,1,5]=>110100
[4,1,6,2,5,3,7]=>[7,1,4,2,6,3,5]=>[1,7,4,6,2,5,3]=>011100
[4,1,6,2,5,7,3]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>110100
[4,1,6,2,7,3,5]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>110100
[4,1,6,2,7,5,3]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>111100
[4,1,6,3,2,5,7]=>[7,1,4,2,3,6,5]=>[1,7,4,6,5,2,3]=>010110
[4,1,6,3,2,7,5]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>110110
[4,1,6,3,5,2,7]=>[7,1,4,3,6,2,5]=>[1,7,4,5,2,6,3]=>011100
[4,1,6,3,5,7,2]=>[1,4,3,6,5,2,7]=>[7,4,5,2,3,6,1]=>110100
[4,1,6,3,7,2,5]=>[1,4,3,6,2,7,5]=>[7,4,5,2,6,1,3]=>110100
[4,1,6,3,7,5,2]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>111100
[4,1,6,5,2,3,7]=>[7,1,4,2,5,6,3]=>[1,7,4,6,3,2,5]=>011100
[4,1,6,5,2,7,3]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>111100
[4,1,6,5,3,2,7]=>[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>011110
[4,1,6,5,3,7,2]=>[1,4,3,5,6,2,7]=>[7,4,5,3,2,6,1]=>111100
[4,1,6,5,7,2,3]=>[5,6,1,4,2,7,3]=>[3,2,7,4,6,1,5]=>110100
[4,1,6,5,7,3,2]=>[5,6,1,4,2,3,7]=>[3,2,7,4,6,5,1]=>110110
[4,1,6,7,2,3,5]=>[6,1,4,2,7,5,3]=>[2,7,4,6,1,3,5]=>100100
[4,1,6,7,2,5,3]=>[6,1,4,2,7,3,5]=>[2,7,4,6,1,5,3]=>101100
[4,1,6,7,3,2,5]=>[6,1,4,2,3,7,5]=>[2,7,4,6,5,1,3]=>100110
[4,1,6,7,3,5,2]=>[6,1,4,3,7,2,5]=>[2,7,4,5,1,6,3]=>101100
[4,1,6,7,5,2,3]=>[6,1,4,2,5,7,3]=>[2,7,4,6,3,1,5]=>101100
[4,1,6,7,5,3,2]=>[6,1,4,2,3,5,7]=>[2,7,4,6,5,3,1]=>101110
[4,1,7,2,3,5,6]=>[1,4,2,7,6,5,3]=>[7,4,6,1,2,3,5]=>100100
[4,1,7,2,3,6,5]=>[1,4,2,7,5,6,3]=>[7,4,6,1,3,2,5]=>110100
[4,1,7,2,5,3,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>101100
[4,1,7,2,5,6,3]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>110100
[4,1,7,2,6,3,5]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>110100
[4,1,7,2,6,5,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>111100
[4,1,7,3,2,5,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>100110
[4,1,7,3,2,6,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>110110
[4,1,7,3,5,2,6]=>[1,4,3,7,6,2,5]=>[7,4,5,1,2,6,3]=>101100
[4,1,7,3,5,6,2]=>[1,4,3,7,5,2,6]=>[7,4,5,1,3,6,2]=>110100
[4,1,7,3,6,2,5]=>[1,4,3,7,2,6,5]=>[7,4,5,1,6,2,3]=>110100
[4,1,7,3,6,5,2]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>111100
[4,1,7,5,2,3,6]=>[1,4,2,5,7,6,3]=>[7,4,6,3,1,2,5]=>101100
[4,1,7,5,2,6,3]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>111100
[4,1,7,5,3,2,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>101110
[4,1,7,5,3,6,2]=>[1,4,3,5,7,2,6]=>[7,4,5,3,1,6,2]=>111100
[4,1,7,5,6,2,3]=>[5,7,1,4,2,6,3]=>[3,1,7,4,6,2,5]=>110100
[4,1,7,5,6,3,2]=>[5,7,1,4,2,3,6]=>[3,1,7,4,6,5,2]=>110110
[4,1,7,6,2,3,5]=>[1,4,2,6,7,5,3]=>[7,4,6,2,1,3,5]=>110100
[4,1,7,6,2,5,3]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>111100
[4,1,7,6,3,2,5]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>110110
[4,1,7,6,3,5,2]=>[1,4,3,6,7,2,5]=>[7,4,5,2,1,6,3]=>111100
[4,1,7,6,5,2,3]=>[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]=>111100
[4,1,7,6,5,3,2]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>111110
[4,2,1,3,5,6,7]=>[7,6,5,1,2,4,3]=>[1,2,3,7,6,4,5]=>000101
[4,2,1,3,5,7,6]=>[6,7,5,1,2,4,3]=>[2,1,3,7,6,4,5]=>100101
[4,2,1,3,6,5,7]=>[7,5,6,1,2,4,3]=>[1,3,2,7,6,4,5]=>010101
[4,2,1,3,6,7,5]=>[6,5,7,1,2,4,3]=>[2,3,1,7,6,4,5]=>100101
[4,2,1,3,7,5,6]=>[5,7,6,1,2,4,3]=>[3,1,2,7,6,4,5]=>100101
[4,2,1,3,7,6,5]=>[5,6,7,1,2,4,3]=>[3,2,1,7,6,4,5]=>110101
[4,2,1,5,3,6,7]=>[7,6,1,2,4,3,5]=>[1,2,7,6,4,5,3]=>001101
[4,2,1,5,3,7,6]=>[6,7,1,2,4,3,5]=>[2,1,7,6,4,5,3]=>101101
[4,2,1,5,6,3,7]=>[7,5,1,2,4,3,6]=>[1,3,7,6,4,5,2]=>010101
[4,2,1,5,6,7,3]=>[6,5,1,2,4,3,7]=>[2,3,7,6,4,5,1]=>100101
[4,2,1,5,7,3,6]=>[5,1,2,4,3,7,6]=>[3,7,6,4,5,1,2]=>100101
[4,2,1,5,7,6,3]=>[5,1,2,4,3,6,7]=>[3,7,6,4,5,2,1]=>110101
[4,2,1,6,3,5,7]=>[7,1,2,4,3,6,5]=>[1,7,6,4,5,2,3]=>010101
[4,2,1,6,3,7,5]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>110101
[4,2,1,6,5,3,7]=>[7,1,2,4,3,5,6]=>[1,7,6,4,5,3,2]=>011101
[4,2,1,6,5,7,3]=>[5,6,1,2,4,3,7]=>[3,2,7,6,4,5,1]=>110101
[4,2,1,6,7,3,5]=>[6,1,2,4,3,7,5]=>[2,7,6,4,5,1,3]=>100101
[4,2,1,6,7,5,3]=>[6,1,2,4,3,5,7]=>[2,7,6,4,5,3,1]=>101101
[4,2,1,7,3,5,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>100101
[4,2,1,7,3,6,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>110101
[4,2,1,7,5,3,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>101101
[4,2,1,7,5,6,3]=>[5,7,1,2,4,3,6]=>[3,1,7,6,4,5,2]=>110101
[4,2,1,7,6,3,5]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>110101
[4,2,1,7,6,5,3]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>111101
[4,2,3,1,5,6,7]=>[7,6,5,2,4,1,3]=>[1,2,3,6,4,7,5]=>000110
[4,2,3,1,5,7,6]=>[6,7,5,2,4,1,3]=>[2,1,3,6,4,7,5]=>100110
[4,2,3,1,6,5,7]=>[7,5,6,2,4,1,3]=>[1,3,2,6,4,7,5]=>010110
[4,2,3,1,6,7,5]=>[6,5,7,2,4,1,3]=>[2,3,1,6,4,7,5]=>100110
[4,2,3,1,7,5,6]=>[5,7,6,2,4,1,3]=>[3,1,2,6,4,7,5]=>100110
[4,2,3,1,7,6,5]=>[5,6,7,2,4,1,3]=>[3,2,1,6,4,7,5]=>110110
[4,2,3,5,1,6,7]=>[7,6,2,4,3,1,5]=>[1,2,6,4,5,7,3]=>001100
[4,2,3,5,1,7,6]=>[6,7,2,4,3,1,5]=>[2,1,6,4,5,7,3]=>101100
[4,2,3,5,6,1,7]=>[7,5,2,4,3,1,6]=>[1,3,6,4,5,7,2]=>010100
[4,2,3,5,6,7,1]=>[6,5,2,4,3,1,7]=>[2,3,6,4,5,7,1]=>100100
[4,2,3,5,7,1,6]=>[5,2,4,3,1,7,6]=>[3,6,4,5,7,1,2]=>100100
[4,2,3,5,7,6,1]=>[5,2,4,3,1,6,7]=>[3,6,4,5,7,2,1]=>110100
[4,2,3,6,1,5,7]=>[7,2,4,3,1,6,5]=>[1,6,4,5,7,2,3]=>010100
[4,2,3,6,1,7,5]=>[2,4,3,1,6,5,7]=>[6,4,5,7,2,3,1]=>110100
[4,2,3,6,5,1,7]=>[7,2,4,3,1,5,6]=>[1,6,4,5,7,3,2]=>011100
[4,2,3,6,5,7,1]=>[5,6,2,4,3,1,7]=>[3,2,6,4,5,7,1]=>110100
[4,2,3,6,7,1,5]=>[6,2,4,3,1,7,5]=>[2,6,4,5,7,1,3]=>100100
[4,2,3,6,7,5,1]=>[6,2,4,3,1,5,7]=>[2,6,4,5,7,3,1]=>101100
[4,2,3,7,1,5,6]=>[2,4,3,1,7,6,5]=>[6,4,5,7,1,2,3]=>100100
[4,2,3,7,1,6,5]=>[2,4,3,1,7,5,6]=>[6,4,5,7,1,3,2]=>110100
[4,2,3,7,5,1,6]=>[2,4,3,1,5,7,6]=>[6,4,5,7,3,1,2]=>101100
[4,2,3,7,5,6,1]=>[5,7,2,4,3,1,6]=>[3,1,6,4,5,7,2]=>110100
[4,2,3,7,6,1,5]=>[2,4,3,1,6,7,5]=>[6,4,5,7,2,1,3]=>110100
[4,2,3,7,6,5,1]=>[2,4,3,1,5,6,7]=>[6,4,5,7,3,2,1]=>111100
[4,2,5,1,3,6,7]=>[7,6,2,4,1,5,3]=>[1,2,6,4,7,3,5]=>001100
[4,2,5,1,3,7,6]=>[6,7,2,4,1,5,3]=>[2,1,6,4,7,3,5]=>101100
[4,2,5,1,6,3,7]=>[7,2,4,1,5,3,6]=>[1,6,4,7,3,5,2]=>011100
[4,2,5,1,6,7,3]=>[6,2,4,1,5,3,7]=>[2,6,4,7,3,5,1]=>101100
[4,2,5,1,7,3,6]=>[2,4,1,5,3,7,6]=>[6,4,7,3,5,1,2]=>101100
[4,2,5,1,7,6,3]=>[2,4,1,5,3,6,7]=>[6,4,7,3,5,2,1]=>111100
[4,2,5,3,1,6,7]=>[7,6,2,4,1,3,5]=>[1,2,6,4,7,5,3]=>001110
[4,2,5,3,1,7,6]=>[6,7,2,4,1,3,5]=>[2,1,6,4,7,5,3]=>101110
[4,2,5,3,6,1,7]=>[7,2,4,3,5,1,6]=>[1,6,4,5,3,7,2]=>011100
[4,2,5,3,6,7,1]=>[6,2,4,3,5,1,7]=>[2,6,4,5,3,7,1]=>101100
[4,2,5,3,7,1,6]=>[2,4,3,5,1,7,6]=>[6,4,5,3,7,1,2]=>101100
[4,2,5,3,7,6,1]=>[2,4,3,5,1,6,7]=>[6,4,5,3,7,2,1]=>111100
[4,2,5,6,1,3,7]=>[7,5,2,4,1,6,3]=>[1,3,6,4,7,2,5]=>010100
[4,2,5,6,1,7,3]=>[5,2,4,1,6,3,7]=>[3,6,4,7,2,5,1]=>110100
[4,2,5,6,3,1,7]=>[7,5,2,4,1,3,6]=>[1,3,6,4,7,5,2]=>010110
[4,2,5,6,3,7,1]=>[5,2,4,3,6,1,7]=>[3,6,4,5,2,7,1]=>110100
[4,2,5,6,7,1,3]=>[6,5,2,4,1,7,3]=>[2,3,6,4,7,1,5]=>100100
[4,2,5,6,7,3,1]=>[6,5,2,4,1,3,7]=>[2,3,6,4,7,5,1]=>100110
[4,2,5,7,1,3,6]=>[5,2,4,1,7,6,3]=>[3,6,4,7,1,2,5]=>100100
[4,2,5,7,1,6,3]=>[5,2,4,1,7,3,6]=>[3,6,4,7,1,5,2]=>110100
[4,2,5,7,3,1,6]=>[5,2,4,1,3,7,6]=>[3,6,4,7,5,1,2]=>100110
[4,2,5,7,3,6,1]=>[5,2,4,3,7,1,6]=>[3,6,4,5,1,7,2]=>110100
[4,2,5,7,6,1,3]=>[5,2,4,1,6,7,3]=>[3,6,4,7,2,1,5]=>110100
[4,2,5,7,6,3,1]=>[5,2,4,1,3,6,7]=>[3,6,4,7,5,2,1]=>110110
[4,2,6,1,3,5,7]=>[7,2,4,1,6,5,3]=>[1,6,4,7,2,3,5]=>010100
[4,2,6,1,3,7,5]=>[2,4,1,6,5,7,3]=>[6,4,7,2,3,1,5]=>110100
[4,2,6,1,5,3,7]=>[7,2,4,1,6,3,5]=>[1,6,4,7,2,5,3]=>011100
[4,2,6,1,5,7,3]=>[2,4,1,6,5,3,7]=>[6,4,7,2,3,5,1]=>110100
[4,2,6,1,7,3,5]=>[2,4,1,6,3,7,5]=>[6,4,7,2,5,1,3]=>110100
[4,2,6,1,7,5,3]=>[2,4,1,6,3,5,7]=>[6,4,7,2,5,3,1]=>111100
[4,2,6,3,1,5,7]=>[7,2,4,1,3,6,5]=>[1,6,4,7,5,2,3]=>010110
[4,2,6,3,1,7,5]=>[2,4,1,3,6,5,7]=>[6,4,7,5,2,3,1]=>110110
[4,2,6,3,5,1,7]=>[7,2,4,3,6,1,5]=>[1,6,4,5,2,7,3]=>011100
[4,2,6,3,5,7,1]=>[2,4,3,6,5,1,7]=>[6,4,5,2,3,7,1]=>110100
[4,2,6,3,7,1,5]=>[2,4,3,6,1,7,5]=>[6,4,5,2,7,1,3]=>110100
[4,2,6,3,7,5,1]=>[2,4,3,6,1,5,7]=>[6,4,5,2,7,3,1]=>111100
[4,2,6,5,1,3,7]=>[7,2,4,1,5,6,3]=>[1,6,4,7,3,2,5]=>011100
[4,2,6,5,1,7,3]=>[2,4,1,5,6,3,7]=>[6,4,7,3,2,5,1]=>111100
[4,2,6,5,3,1,7]=>[7,2,4,1,3,5,6]=>[1,6,4,7,5,3,2]=>011110
[4,2,6,5,3,7,1]=>[2,4,3,5,6,1,7]=>[6,4,5,3,2,7,1]=>111100
[4,2,6,5,7,1,3]=>[5,6,2,4,1,7,3]=>[3,2,6,4,7,1,5]=>110100
[4,2,6,5,7,3,1]=>[5,6,2,4,1,3,7]=>[3,2,6,4,7,5,1]=>110110
[4,2,6,7,1,3,5]=>[6,2,4,1,7,5,3]=>[2,6,4,7,1,3,5]=>100100
[4,2,6,7,1,5,3]=>[6,2,4,1,7,3,5]=>[2,6,4,7,1,5,3]=>101100
[4,2,6,7,3,1,5]=>[6,2,4,1,3,7,5]=>[2,6,4,7,5,1,3]=>100110
[4,2,6,7,3,5,1]=>[6,2,4,3,7,1,5]=>[2,6,4,5,1,7,3]=>101100
[4,2,6,7,5,1,3]=>[6,2,4,1,5,7,3]=>[2,6,4,7,3,1,5]=>101100
[4,2,6,7,5,3,1]=>[6,2,4,1,3,5,7]=>[2,6,4,7,5,3,1]=>101110
[4,2,7,1,3,5,6]=>[2,4,1,7,6,5,3]=>[6,4,7,1,2,3,5]=>100100
[4,2,7,1,3,6,5]=>[2,4,1,7,5,6,3]=>[6,4,7,1,3,2,5]=>110100
[4,2,7,1,5,3,6]=>[2,4,1,7,6,3,5]=>[6,4,7,1,2,5,3]=>101100
[4,2,7,1,5,6,3]=>[2,4,1,7,5,3,6]=>[6,4,7,1,3,5,2]=>110100
[4,2,7,1,6,3,5]=>[2,4,1,7,3,6,5]=>[6,4,7,1,5,2,3]=>110100
[4,2,7,1,6,5,3]=>[2,4,1,7,3,5,6]=>[6,4,7,1,5,3,2]=>111100
[4,2,7,3,1,5,6]=>[2,4,1,3,7,6,5]=>[6,4,7,5,1,2,3]=>100110
[4,2,7,3,1,6,5]=>[2,4,1,3,7,5,6]=>[6,4,7,5,1,3,2]=>110110
[4,2,7,3,5,1,6]=>[2,4,3,7,6,1,5]=>[6,4,5,1,2,7,3]=>101100
[4,2,7,3,5,6,1]=>[2,4,3,7,5,1,6]=>[6,4,5,1,3,7,2]=>110100
[4,2,7,3,6,1,5]=>[2,4,3,7,1,6,5]=>[6,4,5,1,7,2,3]=>110100
[4,2,7,3,6,5,1]=>[2,4,3,7,1,5,6]=>[6,4,5,1,7,3,2]=>111100
[4,2,7,5,1,3,6]=>[2,4,1,5,7,6,3]=>[6,4,7,3,1,2,5]=>101100
[4,2,7,5,1,6,3]=>[2,4,1,5,7,3,6]=>[6,4,7,3,1,5,2]=>111100
[4,2,7,5,3,1,6]=>[2,4,1,3,5,7,6]=>[6,4,7,5,3,1,2]=>101110
[4,2,7,5,3,6,1]=>[2,4,3,5,7,1,6]=>[6,4,5,3,1,7,2]=>111100
[4,2,7,5,6,1,3]=>[5,7,2,4,1,6,3]=>[3,1,6,4,7,2,5]=>110100
[4,2,7,5,6,3,1]=>[5,7,2,4,1,3,6]=>[3,1,6,4,7,5,2]=>110110
[4,2,7,6,1,3,5]=>[2,4,1,6,7,5,3]=>[6,4,7,2,1,3,5]=>110100
[4,2,7,6,1,5,3]=>[2,4,1,6,7,3,5]=>[6,4,7,2,1,5,3]=>111100
[4,2,7,6,3,1,5]=>[2,4,1,3,6,7,5]=>[6,4,7,5,2,1,3]=>110110
[4,2,7,6,3,5,1]=>[2,4,3,6,7,1,5]=>[6,4,5,2,1,7,3]=>111100
[4,2,7,6,5,1,3]=>[2,4,1,5,6,7,3]=>[6,4,7,3,2,1,5]=>111100
[4,2,7,6,5,3,1]=>[2,4,1,3,5,6,7]=>[6,4,7,5,3,2,1]=>111110
[4,3,1,2,5,6,7]=>[7,6,5,1,3,4,2]=>[1,2,3,7,5,4,6]=>000110
[4,3,1,2,5,7,6]=>[6,7,5,1,3,4,2]=>[2,1,3,7,5,4,6]=>100110
[4,3,1,2,6,5,7]=>[7,5,6,1,3,4,2]=>[1,3,2,7,5,4,6]=>010110
[4,3,1,2,6,7,5]=>[6,5,7,1,3,4,2]=>[2,3,1,7,5,4,6]=>100110
[4,3,1,2,7,5,6]=>[5,7,6,1,3,4,2]=>[3,1,2,7,5,4,6]=>100110
[4,3,1,2,7,6,5]=>[5,6,7,1,3,4,2]=>[3,2,1,7,5,4,6]=>110110
[4,3,1,5,2,6,7]=>[7,6,1,3,4,2,5]=>[1,2,7,5,4,6,3]=>001110
[4,3,1,5,2,7,6]=>[6,7,1,3,4,2,5]=>[2,1,7,5,4,6,3]=>101110
[4,3,1,5,6,2,7]=>[7,5,1,3,4,2,6]=>[1,3,7,5,4,6,2]=>010110
[4,3,1,5,6,7,2]=>[6,5,1,3,4,2,7]=>[2,3,7,5,4,6,1]=>100110
[4,3,1,5,7,2,6]=>[5,1,3,4,2,7,6]=>[3,7,5,4,6,1,2]=>100110
[4,3,1,5,7,6,2]=>[5,1,3,4,2,6,7]=>[3,7,5,4,6,2,1]=>110110
[4,3,1,6,2,5,7]=>[7,1,3,4,2,6,5]=>[1,7,5,4,6,2,3]=>010110
[4,3,1,6,2,7,5]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>110110
[4,3,1,6,5,2,7]=>[7,1,3,4,2,5,6]=>[1,7,5,4,6,3,2]=>011110
[4,3,1,6,5,7,2]=>[5,6,1,3,4,2,7]=>[3,2,7,5,4,6,1]=>110110
[4,3,1,6,7,2,5]=>[6,1,3,4,2,7,5]=>[2,7,5,4,6,1,3]=>100110
[4,3,1,6,7,5,2]=>[6,1,3,4,2,5,7]=>[2,7,5,4,6,3,1]=>101110
[4,3,1,7,2,5,6]=>[1,3,4,2,7,6,5]=>[7,5,4,6,1,2,3]=>100110
[4,3,1,7,2,6,5]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>110110
[4,3,1,7,5,2,6]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>101110
[4,3,1,7,5,6,2]=>[5,7,1,3,4,2,6]=>[3,1,7,5,4,6,2]=>110110
[4,3,1,7,6,2,5]=>[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]=>110110
[4,3,1,7,6,5,2]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>111110
[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>000111
[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>100111
[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>010111
[4,3,2,1,6,7,5]=>[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>100111
[4,3,2,1,7,5,6]=>[5,7,6,1,2,3,4]=>[3,1,2,7,6,5,4]=>100111
[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>110111
[4,3,2,5,1,6,7]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>001110
[4,3,2,5,1,7,6]=>[6,7,2,3,4,1,5]=>[2,1,6,5,4,7,3]=>101110
[4,3,2,5,6,1,7]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>010110
[4,3,2,5,6,7,1]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>100110
[4,3,2,5,7,1,6]=>[5,2,3,4,1,7,6]=>[3,6,5,4,7,1,2]=>100110
[4,3,2,5,7,6,1]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>110110
[4,3,2,6,1,5,7]=>[7,2,3,4,1,6,5]=>[1,6,5,4,7,2,3]=>010110
[4,3,2,6,1,7,5]=>[2,3,4,1,6,5,7]=>[6,5,4,7,2,3,1]=>110110
[4,3,2,6,5,1,7]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>011110
[4,3,2,6,5,7,1]=>[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>110110
[4,3,2,6,7,1,5]=>[6,2,3,4,1,7,5]=>[2,6,5,4,7,1,3]=>100110
[4,3,2,6,7,5,1]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>101110
[4,3,2,7,1,5,6]=>[2,3,4,1,7,6,5]=>[6,5,4,7,1,2,3]=>100110
[4,3,2,7,1,6,5]=>[2,3,4,1,7,5,6]=>[6,5,4,7,1,3,2]=>110110
[4,3,2,7,5,1,6]=>[2,3,4,1,5,7,6]=>[6,5,4,7,3,1,2]=>101110
[4,3,2,7,5,6,1]=>[5,7,2,3,4,1,6]=>[3,1,6,5,4,7,2]=>110110
[4,3,2,7,6,1,5]=>[2,3,4,1,6,7,5]=>[6,5,4,7,2,1,3]=>110110
[4,3,2,7,6,5,1]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>111110
[4,3,5,1,2,6,7]=>[7,6,3,4,1,5,2]=>[1,2,5,4,7,3,6]=>001100
[4,3,5,1,2,7,6]=>[6,7,3,4,1,5,2]=>[2,1,5,4,7,3,6]=>101100
[4,3,5,1,6,2,7]=>[7,3,4,1,5,2,6]=>[1,5,4,7,3,6,2]=>011100
[4,3,5,1,6,7,2]=>[6,3,4,1,5,2,7]=>[2,5,4,7,3,6,1]=>101100
[4,3,5,1,7,2,6]=>[3,4,1,5,2,7,6]=>[5,4,7,3,6,1,2]=>101100
[4,3,5,1,7,6,2]=>[3,4,1,5,2,6,7]=>[5,4,7,3,6,2,1]=>111100
[4,3,5,2,1,6,7]=>[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>001101
[4,3,5,2,1,7,6]=>[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>101101
[4,3,5,2,6,1,7]=>[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>011100
[4,3,5,2,6,7,1]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>101100
[4,3,5,2,7,1,6]=>[3,4,2,5,1,7,6]=>[5,4,6,3,7,1,2]=>101100
[4,3,5,2,7,6,1]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>111100
[4,3,5,6,1,2,7]=>[7,5,3,4,1,6,2]=>[1,3,5,4,7,2,6]=>010100
[4,3,5,6,1,7,2]=>[5,3,4,1,6,2,7]=>[3,5,4,7,2,6,1]=>110100
[4,3,5,6,2,1,7]=>[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>010101
[4,3,5,6,2,7,1]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>110100
[4,3,5,6,7,1,2]=>[6,5,3,4,1,7,2]=>[2,3,5,4,7,1,6]=>100100
[4,3,5,6,7,2,1]=>[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>100101
[4,3,5,7,1,2,6]=>[5,3,4,1,7,6,2]=>[3,5,4,7,1,2,6]=>100100
[4,3,5,7,1,6,2]=>[5,3,4,1,7,2,6]=>[3,5,4,7,1,6,2]=>110100
[4,3,5,7,2,1,6]=>[5,3,4,1,2,7,6]=>[3,5,4,7,6,1,2]=>100101
[4,3,5,7,2,6,1]=>[5,3,4,2,7,1,6]=>[3,5,4,6,1,7,2]=>110100
[4,3,5,7,6,1,2]=>[5,3,4,1,6,7,2]=>[3,5,4,7,2,1,6]=>110100
[4,3,5,7,6,2,1]=>[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>110101
[4,3,6,1,2,5,7]=>[7,3,4,1,6,5,2]=>[1,5,4,7,2,3,6]=>010100
[4,3,6,1,2,7,5]=>[3,4,1,6,5,7,2]=>[5,4,7,2,3,1,6]=>110100
[4,3,6,1,5,2,7]=>[7,3,4,1,6,2,5]=>[1,5,4,7,2,6,3]=>011100
[4,3,6,1,5,7,2]=>[3,4,1,6,5,2,7]=>[5,4,7,2,3,6,1]=>110100
[4,3,6,1,7,2,5]=>[3,4,1,6,2,7,5]=>[5,4,7,2,6,1,3]=>110100
[4,3,6,1,7,5,2]=>[3,4,1,6,2,5,7]=>[5,4,7,2,6,3,1]=>111100
[4,3,6,2,1,5,7]=>[7,3,4,1,2,6,5]=>[1,5,4,7,6,2,3]=>010101
[4,3,6,2,1,7,5]=>[3,4,1,2,6,5,7]=>[5,4,7,6,2,3,1]=>110101
[4,3,6,2,5,1,7]=>[7,3,4,2,6,1,5]=>[1,5,4,6,2,7,3]=>011100
[4,3,6,2,5,7,1]=>[3,4,2,6,5,1,7]=>[5,4,6,2,3,7,1]=>110100
[4,3,6,2,7,1,5]=>[3,4,2,6,1,7,5]=>[5,4,6,2,7,1,3]=>110100
[4,3,6,2,7,5,1]=>[3,4,2,6,1,5,7]=>[5,4,6,2,7,3,1]=>111100
[4,3,6,5,1,2,7]=>[7,3,4,1,5,6,2]=>[1,5,4,7,3,2,6]=>011100
[4,3,6,5,1,7,2]=>[3,4,1,5,6,2,7]=>[5,4,7,3,2,6,1]=>111100
[4,3,6,5,2,1,7]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>011101
[4,3,6,5,2,7,1]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>111100
[4,3,6,5,7,1,2]=>[5,6,3,4,1,7,2]=>[3,2,5,4,7,1,6]=>110100
[4,3,6,5,7,2,1]=>[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>110101
[4,3,6,7,1,2,5]=>[6,3,4,1,7,5,2]=>[2,5,4,7,1,3,6]=>100100
[4,3,6,7,1,5,2]=>[6,3,4,1,7,2,5]=>[2,5,4,7,1,6,3]=>101100
[4,3,6,7,2,1,5]=>[6,3,4,1,2,7,5]=>[2,5,4,7,6,1,3]=>100101
[4,3,6,7,2,5,1]=>[6,3,4,2,7,1,5]=>[2,5,4,6,1,7,3]=>101100
[4,3,6,7,5,1,2]=>[6,3,4,1,5,7,2]=>[2,5,4,7,3,1,6]=>101100
[4,3,6,7,5,2,1]=>[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>101101
[4,3,7,1,2,5,6]=>[3,4,1,7,6,5,2]=>[5,4,7,1,2,3,6]=>100100
[4,3,7,1,2,6,5]=>[3,4,1,7,5,6,2]=>[5,4,7,1,3,2,6]=>110100
[4,3,7,1,5,2,6]=>[3,4,1,7,6,2,5]=>[5,4,7,1,2,6,3]=>101100
[4,3,7,1,5,6,2]=>[3,4,1,7,5,2,6]=>[5,4,7,1,3,6,2]=>110100
[4,3,7,1,6,2,5]=>[3,4,1,7,2,6,5]=>[5,4,7,1,6,2,3]=>110100
[4,3,7,1,6,5,2]=>[3,4,1,7,2,5,6]=>[5,4,7,1,6,3,2]=>111100
[4,3,7,2,1,5,6]=>[3,4,1,2,7,6,5]=>[5,4,7,6,1,2,3]=>100101
[4,3,7,2,1,6,5]=>[3,4,1,2,7,5,6]=>[5,4,7,6,1,3,2]=>110101
[4,3,7,2,5,1,6]=>[3,4,2,7,6,1,5]=>[5,4,6,1,2,7,3]=>101100
[4,3,7,2,5,6,1]=>[3,4,2,7,5,1,6]=>[5,4,6,1,3,7,2]=>110100
[4,3,7,2,6,1,5]=>[3,4,2,7,1,6,5]=>[5,4,6,1,7,2,3]=>110100
[4,3,7,2,6,5,1]=>[3,4,2,7,1,5,6]=>[5,4,6,1,7,3,2]=>111100
[4,3,7,5,1,2,6]=>[3,4,1,5,7,6,2]=>[5,4,7,3,1,2,6]=>101100
[4,3,7,5,1,6,2]=>[3,4,1,5,7,2,6]=>[5,4,7,3,1,6,2]=>111100
[4,3,7,5,2,1,6]=>[3,4,1,2,5,7,6]=>[5,4,7,6,3,1,2]=>101101
[4,3,7,5,2,6,1]=>[3,4,2,5,7,1,6]=>[5,4,6,3,1,7,2]=>111100
[4,3,7,5,6,1,2]=>[5,7,3,4,1,6,2]=>[3,1,5,4,7,2,6]=>110100
[4,3,7,5,6,2,1]=>[5,7,3,4,1,2,6]=>[3,1,5,4,7,6,2]=>110101
[4,3,7,6,1,2,5]=>[3,4,1,6,7,5,2]=>[5,4,7,2,1,3,6]=>110100
[4,3,7,6,1,5,2]=>[3,4,1,6,7,2,5]=>[5,4,7,2,1,6,3]=>111100
[4,3,7,6,2,1,5]=>[3,4,1,2,6,7,5]=>[5,4,7,6,2,1,3]=>110101
[4,3,7,6,2,5,1]=>[3,4,2,6,7,1,5]=>[5,4,6,2,1,7,3]=>111100
[4,3,7,6,5,1,2]=>[3,4,1,5,6,7,2]=>[5,4,7,3,2,1,6]=>111100
[4,3,7,6,5,2,1]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>111101
[4,5,1,2,3,6,7]=>[7,6,4,1,5,3,2]=>[1,2,4,7,3,5,6]=>001000
[4,5,1,2,3,7,6]=>[6,7,4,1,5,3,2]=>[2,1,4,7,3,5,6]=>101000
[4,5,1,2,6,3,7]=>[7,4,1,5,3,6,2]=>[1,4,7,3,5,2,6]=>011000
[4,5,1,2,6,7,3]=>[6,4,1,5,3,7,2]=>[2,4,7,3,5,1,6]=>101000
[4,5,1,2,7,3,6]=>[4,1,5,3,7,6,2]=>[4,7,3,5,1,2,6]=>101000
[4,5,1,2,7,6,3]=>[4,1,5,3,6,7,2]=>[4,7,3,5,2,1,6]=>111000
[4,5,1,3,2,6,7]=>[7,6,4,1,5,2,3]=>[1,2,4,7,3,6,5]=>001010
[4,5,1,3,2,7,6]=>[6,7,4,1,5,2,3]=>[2,1,4,7,3,6,5]=>101010
[4,5,1,3,6,2,7]=>[7,4,1,5,3,2,6]=>[1,4,7,3,5,6,2]=>011000
[4,5,1,3,6,7,2]=>[6,4,1,5,3,2,7]=>[2,4,7,3,5,6,1]=>101000
[4,5,1,3,7,2,6]=>[4,1,5,3,2,7,6]=>[4,7,3,5,6,1,2]=>101000
[4,5,1,3,7,6,2]=>[4,1,5,3,2,6,7]=>[4,7,3,5,6,2,1]=>111000
[4,5,1,6,2,3,7]=>[7,4,1,5,2,6,3]=>[1,4,7,3,6,2,5]=>011000
[4,5,1,6,2,7,3]=>[4,1,5,2,6,3,7]=>[4,7,3,6,2,5,1]=>111000
[4,5,1,6,3,2,7]=>[7,4,1,5,2,3,6]=>[1,4,7,3,6,5,2]=>011010
[4,5,1,6,3,7,2]=>[4,1,5,3,6,2,7]=>[4,7,3,5,2,6,1]=>111000
[4,5,1,6,7,2,3]=>[6,4,1,5,2,7,3]=>[2,4,7,3,6,1,5]=>101000
[4,5,1,6,7,3,2]=>[6,4,1,5,2,3,7]=>[2,4,7,3,6,5,1]=>101010
[4,5,1,7,2,3,6]=>[4,1,5,2,7,6,3]=>[4,7,3,6,1,2,5]=>101000
[4,5,1,7,2,6,3]=>[4,1,5,2,7,3,6]=>[4,7,3,6,1,5,2]=>111000
[4,5,1,7,3,2,6]=>[4,1,5,2,3,7,6]=>[4,7,3,6,5,1,2]=>101010
[4,5,1,7,3,6,2]=>[4,1,5,3,7,2,6]=>[4,7,3,5,1,6,2]=>111000
[4,5,1,7,6,2,3]=>[4,1,5,2,6,7,3]=>[4,7,3,6,2,1,5]=>111000
[4,5,1,7,6,3,2]=>[4,1,5,2,3,6,7]=>[4,7,3,6,5,2,1]=>111010
[4,5,2,1,3,6,7]=>[7,6,4,1,2,5,3]=>[1,2,4,7,6,3,5]=>001001
[4,5,2,1,3,7,6]=>[6,7,4,1,2,5,3]=>[2,1,4,7,6,3,5]=>101001
[4,5,2,1,6,3,7]=>[7,4,1,2,5,3,6]=>[1,4,7,6,3,5,2]=>011001
[4,5,2,1,6,7,3]=>[6,4,1,2,5,3,7]=>[2,4,7,6,3,5,1]=>101001
[4,5,2,1,7,3,6]=>[4,1,2,5,3,7,6]=>[4,7,6,3,5,1,2]=>101001
[4,5,2,1,7,6,3]=>[4,1,2,5,3,6,7]=>[4,7,6,3,5,2,1]=>111001
[4,5,2,3,1,6,7]=>[7,6,4,2,5,1,3]=>[1,2,4,6,3,7,5]=>001010
[4,5,2,3,1,7,6]=>[6,7,4,2,5,1,3]=>[2,1,4,6,3,7,5]=>101010
[4,5,2,3,6,1,7]=>[7,4,2,5,3,1,6]=>[1,4,6,3,5,7,2]=>011000
[4,5,2,3,6,7,1]=>[6,4,2,5,3,1,7]=>[2,4,6,3,5,7,1]=>101000
[4,5,2,3,7,1,6]=>[4,2,5,3,1,7,6]=>[4,6,3,5,7,1,2]=>101000
[4,5,2,3,7,6,1]=>[4,2,5,3,1,6,7]=>[4,6,3,5,7,2,1]=>111000
[4,5,2,6,1,3,7]=>[7,4,2,5,1,6,3]=>[1,4,6,3,7,2,5]=>011000
[4,5,2,6,1,7,3]=>[4,2,5,1,6,3,7]=>[4,6,3,7,2,5,1]=>111000
[4,5,2,6,3,1,7]=>[7,4,2,5,1,3,6]=>[1,4,6,3,7,5,2]=>011010
[4,5,2,6,3,7,1]=>[4,2,5,3,6,1,7]=>[4,6,3,5,2,7,1]=>111000
[4,5,2,6,7,1,3]=>[6,4,2,5,1,7,3]=>[2,4,6,3,7,1,5]=>101000
[4,5,2,6,7,3,1]=>[6,4,2,5,1,3,7]=>[2,4,6,3,7,5,1]=>101010
[4,5,2,7,1,3,6]=>[4,2,5,1,7,6,3]=>[4,6,3,7,1,2,5]=>101000
[4,5,2,7,1,6,3]=>[4,2,5,1,7,3,6]=>[4,6,3,7,1,5,2]=>111000
[4,5,2,7,3,1,6]=>[4,2,5,1,3,7,6]=>[4,6,3,7,5,1,2]=>101010
[4,5,2,7,3,6,1]=>[4,2,5,3,7,1,6]=>[4,6,3,5,1,7,2]=>111000
[4,5,2,7,6,1,3]=>[4,2,5,1,6,7,3]=>[4,6,3,7,2,1,5]=>111000
[4,5,2,7,6,3,1]=>[4,2,5,1,3,6,7]=>[4,6,3,7,5,2,1]=>111010
[4,5,3,1,2,6,7]=>[7,6,4,1,3,5,2]=>[1,2,4,7,5,3,6]=>001010
[4,5,3,1,2,7,6]=>[6,7,4,1,3,5,2]=>[2,1,4,7,5,3,6]=>101010
[4,5,3,1,6,2,7]=>[7,4,1,3,5,2,6]=>[1,4,7,5,3,6,2]=>011010
[4,5,3,1,6,7,2]=>[6,4,1,3,5,2,7]=>[2,4,7,5,3,6,1]=>101010
[4,5,3,1,7,2,6]=>[4,1,3,5,2,7,6]=>[4,7,5,3,6,1,2]=>101010
[4,5,3,1,7,6,2]=>[4,1,3,5,2,6,7]=>[4,7,5,3,6,2,1]=>111010
[4,5,3,2,1,6,7]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>001011
[4,5,3,2,1,7,6]=>[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>101011
[4,5,3,2,6,1,7]=>[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>011010
[4,5,3,2,6,7,1]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>101010
[4,5,3,2,7,1,6]=>[4,2,3,5,1,7,6]=>[4,6,5,3,7,1,2]=>101010
[4,5,3,2,7,6,1]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>111010
[4,5,3,6,1,2,7]=>[7,4,3,5,1,6,2]=>[1,4,5,3,7,2,6]=>011000
[4,5,3,6,1,7,2]=>[4,3,5,1,6,2,7]=>[4,5,3,7,2,6,1]=>111000
[4,5,3,6,2,1,7]=>[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>011001
[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>111000
[4,5,3,6,7,1,2]=>[6,4,3,5,1,7,2]=>[2,4,5,3,7,1,6]=>101000
[4,5,3,6,7,2,1]=>[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>101001
[4,5,3,7,1,2,6]=>[4,3,5,1,7,6,2]=>[4,5,3,7,1,2,6]=>101000
[4,5,3,7,1,6,2]=>[4,3,5,1,7,2,6]=>[4,5,3,7,1,6,2]=>111000
[4,5,3,7,2,1,6]=>[4,3,5,1,2,7,6]=>[4,5,3,7,6,1,2]=>101001
[4,5,3,7,2,6,1]=>[4,3,5,2,7,1,6]=>[4,5,3,6,1,7,2]=>111000
[4,5,3,7,6,1,2]=>[4,3,5,1,6,7,2]=>[4,5,3,7,2,1,6]=>111000
[4,5,3,7,6,2,1]=>[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>111001
[4,5,6,1,2,3,7]=>[7,5,4,1,6,3,2]=>[1,3,4,7,2,5,6]=>010000
[4,5,6,1,2,7,3]=>[5,4,1,6,3,7,2]=>[3,4,7,2,5,1,6]=>110000
[4,5,6,1,3,2,7]=>[7,5,4,1,6,2,3]=>[1,3,4,7,2,6,5]=>010010
[4,5,6,1,3,7,2]=>[5,4,1,6,3,2,7]=>[3,4,7,2,5,6,1]=>110000
[4,5,6,1,7,2,3]=>[5,4,1,6,2,7,3]=>[3,4,7,2,6,1,5]=>110000
[4,5,6,1,7,3,2]=>[5,4,1,6,2,3,7]=>[3,4,7,2,6,5,1]=>110010
[4,5,6,2,1,3,7]=>[7,5,4,1,2,6,3]=>[1,3,4,7,6,2,5]=>010001
[4,5,6,2,1,7,3]=>[5,4,1,2,6,3,7]=>[3,4,7,6,2,5,1]=>110001
[4,5,6,2,3,1,7]=>[7,5,4,2,6,1,3]=>[1,3,4,6,2,7,5]=>010010
[4,5,6,2,3,7,1]=>[5,4,2,6,3,1,7]=>[3,4,6,2,5,7,1]=>110000
[4,5,6,2,7,1,3]=>[5,4,2,6,1,7,3]=>[3,4,6,2,7,1,5]=>110000
[4,5,6,2,7,3,1]=>[5,4,2,6,1,3,7]=>[3,4,6,2,7,5,1]=>110010
[4,5,6,3,1,2,7]=>[7,5,4,1,3,6,2]=>[1,3,4,7,5,2,6]=>010010
[4,5,6,3,1,7,2]=>[5,4,1,3,6,2,7]=>[3,4,7,5,2,6,1]=>110010
[4,5,6,3,2,1,7]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>010011
[4,5,6,3,2,7,1]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>110010
[4,5,6,3,7,1,2]=>[5,4,3,6,1,7,2]=>[3,4,5,2,7,1,6]=>110000
[4,5,6,3,7,2,1]=>[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>110001
[4,5,6,7,1,2,3]=>[6,5,4,1,7,3,2]=>[2,3,4,7,1,5,6]=>100000
[4,5,6,7,1,3,2]=>[6,5,4,1,7,2,3]=>[2,3,4,7,1,6,5]=>100010
[4,5,6,7,2,1,3]=>[6,5,4,1,2,7,3]=>[2,3,4,7,6,1,5]=>100001
[4,5,6,7,2,3,1]=>[6,5,4,2,7,1,3]=>[2,3,4,6,1,7,5]=>100010
[4,5,6,7,3,1,2]=>[6,5,4,1,3,7,2]=>[2,3,4,7,5,1,6]=>100010
[4,5,6,7,3,2,1]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>100011
[4,5,7,1,2,3,6]=>[5,4,1,7,6,3,2]=>[3,4,7,1,2,5,6]=>100000
[4,5,7,1,2,6,3]=>[5,4,1,7,3,6,2]=>[3,4,7,1,5,2,6]=>110000
[4,5,7,1,3,2,6]=>[5,4,1,7,6,2,3]=>[3,4,7,1,2,6,5]=>100010
[4,5,7,1,3,6,2]=>[5,4,1,7,3,2,6]=>[3,4,7,1,5,6,2]=>110000
[4,5,7,1,6,2,3]=>[5,4,1,7,2,6,3]=>[3,4,7,1,6,2,5]=>110000
[4,5,7,1,6,3,2]=>[5,4,1,7,2,3,6]=>[3,4,7,1,6,5,2]=>110010
[4,5,7,2,1,3,6]=>[5,4,1,2,7,6,3]=>[3,4,7,6,1,2,5]=>100001
[4,5,7,2,1,6,3]=>[5,4,1,2,7,3,6]=>[3,4,7,6,1,5,2]=>110001
[4,5,7,2,3,1,6]=>[5,4,2,7,6,1,3]=>[3,4,6,1,2,7,5]=>100010
[4,5,7,2,3,6,1]=>[5,4,2,7,3,1,6]=>[3,4,6,1,5,7,2]=>110000
[4,5,7,2,6,1,3]=>[5,4,2,7,1,6,3]=>[3,4,6,1,7,2,5]=>110000
[4,5,7,2,6,3,1]=>[5,4,2,7,1,3,6]=>[3,4,6,1,7,5,2]=>110010
[4,5,7,3,1,2,6]=>[5,4,1,3,7,6,2]=>[3,4,7,5,1,2,6]=>100010
[4,5,7,3,1,6,2]=>[5,4,1,3,7,2,6]=>[3,4,7,5,1,6,2]=>110010
[4,5,7,3,2,1,6]=>[5,4,1,2,3,7,6]=>[3,4,7,6,5,1,2]=>100011
[4,5,7,3,2,6,1]=>[5,4,2,3,7,1,6]=>[3,4,6,5,1,7,2]=>110010
[4,5,7,3,6,1,2]=>[5,4,3,7,1,6,2]=>[3,4,5,1,7,2,6]=>110000
[4,5,7,3,6,2,1]=>[5,4,3,7,1,2,6]=>[3,4,5,1,7,6,2]=>110001
[4,5,7,6,1,2,3]=>[5,4,1,6,7,3,2]=>[3,4,7,2,1,5,6]=>110000
[4,5,7,6,1,3,2]=>[5,4,1,6,7,2,3]=>[3,4,7,2,1,6,5]=>110010
[4,5,7,6,2,1,3]=>[5,4,1,2,6,7,3]=>[3,4,7,6,2,1,5]=>110001
[4,5,7,6,2,3,1]=>[5,4,2,6,7,1,3]=>[3,4,6,2,1,7,5]=>110010
[4,5,7,6,3,1,2]=>[5,4,1,3,6,7,2]=>[3,4,7,5,2,1,6]=>110010
[4,5,7,6,3,2,1]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>110011
[4,6,1,2,3,5,7]=>[7,4,1,6,5,3,2]=>[1,4,7,2,3,5,6]=>010000
[4,6,1,2,3,7,5]=>[4,1,6,5,7,3,2]=>[4,7,2,3,1,5,6]=>110000
[4,6,1,2,5,3,7]=>[7,4,1,6,3,5,2]=>[1,4,7,2,5,3,6]=>011000
[4,6,1,2,5,7,3]=>[4,1,6,5,3,7,2]=>[4,7,2,3,5,1,6]=>110000
[4,6,1,2,7,3,5]=>[4,1,6,3,7,5,2]=>[4,7,2,5,1,3,6]=>110000
[4,6,1,2,7,5,3]=>[4,1,6,3,5,7,2]=>[4,7,2,5,3,1,6]=>111000
[4,6,1,3,2,5,7]=>[7,4,1,6,5,2,3]=>[1,4,7,2,3,6,5]=>010010
[4,6,1,3,2,7,5]=>[4,1,6,5,7,2,3]=>[4,7,2,3,1,6,5]=>110010
[4,6,1,3,5,2,7]=>[7,4,1,6,3,2,5]=>[1,4,7,2,5,6,3]=>011000
[4,6,1,3,5,7,2]=>[4,1,6,5,3,2,7]=>[4,7,2,3,5,6,1]=>110000
[4,6,1,3,7,2,5]=>[4,1,6,3,2,7,5]=>[4,7,2,5,6,1,3]=>110000
[4,6,1,3,7,5,2]=>[4,1,6,3,2,5,7]=>[4,7,2,5,6,3,1]=>111000
[4,6,1,5,2,3,7]=>[7,4,1,6,2,5,3]=>[1,4,7,2,6,3,5]=>011000
[4,6,1,5,2,7,3]=>[4,1,6,2,5,3,7]=>[4,7,2,6,3,5,1]=>111000
[4,6,1,5,3,2,7]=>[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]=>011010
[4,6,1,5,3,7,2]=>[4,1,6,3,5,2,7]=>[4,7,2,5,3,6,1]=>111000
[4,6,1,5,7,2,3]=>[4,1,6,5,2,7,3]=>[4,7,2,3,6,1,5]=>110000
[4,6,1,5,7,3,2]=>[4,1,6,5,2,3,7]=>[4,7,2,3,6,5,1]=>110010
[4,6,1,7,2,3,5]=>[4,1,6,2,7,5,3]=>[4,7,2,6,1,3,5]=>110000
[4,6,1,7,2,5,3]=>[4,1,6,2,7,3,5]=>[4,7,2,6,1,5,3]=>111000
[4,6,1,7,3,2,5]=>[4,1,6,2,3,7,5]=>[4,7,2,6,5,1,3]=>110010
[4,6,1,7,3,5,2]=>[4,1,6,3,7,2,5]=>[4,7,2,5,1,6,3]=>111000
[4,6,1,7,5,2,3]=>[4,1,6,2,5,7,3]=>[4,7,2,6,3,1,5]=>111000
[4,6,1,7,5,3,2]=>[4,1,6,2,3,5,7]=>[4,7,2,6,5,3,1]=>111010
[4,6,2,1,3,5,7]=>[7,4,1,2,6,5,3]=>[1,4,7,6,2,3,5]=>010001
[4,6,2,1,3,7,5]=>[4,1,2,6,5,7,3]=>[4,7,6,2,3,1,5]=>110001
[4,6,2,1,5,3,7]=>[7,4,1,2,6,3,5]=>[1,4,7,6,2,5,3]=>011001
[4,6,2,1,5,7,3]=>[4,1,2,6,5,3,7]=>[4,7,6,2,3,5,1]=>110001
[4,6,2,1,7,3,5]=>[4,1,2,6,3,7,5]=>[4,7,6,2,5,1,3]=>110001
[4,6,2,1,7,5,3]=>[4,1,2,6,3,5,7]=>[4,7,6,2,5,3,1]=>111001
[4,6,2,3,1,5,7]=>[7,4,2,6,5,1,3]=>[1,4,6,2,3,7,5]=>010010
[4,6,2,3,1,7,5]=>[4,2,6,5,7,1,3]=>[4,6,2,3,1,7,5]=>110010
[4,6,2,3,5,1,7]=>[7,4,2,6,3,1,5]=>[1,4,6,2,5,7,3]=>011000
[4,6,2,3,5,7,1]=>[4,2,6,5,3,1,7]=>[4,6,2,3,5,7,1]=>110000
[4,6,2,3,7,1,5]=>[4,2,6,3,1,7,5]=>[4,6,2,5,7,1,3]=>110000
[4,6,2,3,7,5,1]=>[4,2,6,3,1,5,7]=>[4,6,2,5,7,3,1]=>111000
[4,6,2,5,1,3,7]=>[7,4,2,6,1,5,3]=>[1,4,6,2,7,3,5]=>011000
[4,6,2,5,1,7,3]=>[4,2,6,1,5,3,7]=>[4,6,2,7,3,5,1]=>111000
[4,6,2,5,3,1,7]=>[7,4,2,6,1,3,5]=>[1,4,6,2,7,5,3]=>011010
[4,6,2,5,3,7,1]=>[4,2,6,3,5,1,7]=>[4,6,2,5,3,7,1]=>111000
[4,6,2,5,7,1,3]=>[4,2,6,5,1,7,3]=>[4,6,2,3,7,1,5]=>110000
[4,6,2,5,7,3,1]=>[4,2,6,5,1,3,7]=>[4,6,2,3,7,5,1]=>110010
[4,6,2,7,1,3,5]=>[4,2,6,1,7,5,3]=>[4,6,2,7,1,3,5]=>110000
[4,6,2,7,1,5,3]=>[4,2,6,1,7,3,5]=>[4,6,2,7,1,5,3]=>111000
[4,6,2,7,3,1,5]=>[4,2,6,1,3,7,5]=>[4,6,2,7,5,1,3]=>110010
[4,6,2,7,3,5,1]=>[4,2,6,3,7,1,5]=>[4,6,2,5,1,7,3]=>111000
[4,6,2,7,5,1,3]=>[4,2,6,1,5,7,3]=>[4,6,2,7,3,1,5]=>111000
[4,6,2,7,5,3,1]=>[4,2,6,1,3,5,7]=>[4,6,2,7,5,3,1]=>111010
[4,6,3,1,2,5,7]=>[7,4,1,3,6,5,2]=>[1,4,7,5,2,3,6]=>010010
[4,6,3,1,2,7,5]=>[4,1,3,6,5,7,2]=>[4,7,5,2,3,1,6]=>110010
[4,6,3,1,5,2,7]=>[7,4,1,3,6,2,5]=>[1,4,7,5,2,6,3]=>011010
[4,6,3,1,5,7,2]=>[4,1,3,6,5,2,7]=>[4,7,5,2,3,6,1]=>110010
[4,6,3,1,7,2,5]=>[4,1,3,6,2,7,5]=>[4,7,5,2,6,1,3]=>110010
[4,6,3,1,7,5,2]=>[4,1,3,6,2,5,7]=>[4,7,5,2,6,3,1]=>111010
[4,6,3,2,1,5,7]=>[7,4,1,2,3,6,5]=>[1,4,7,6,5,2,3]=>010011
[4,6,3,2,1,7,5]=>[4,1,2,3,6,5,7]=>[4,7,6,5,2,3,1]=>110011
[4,6,3,2,5,1,7]=>[7,4,2,3,6,1,5]=>[1,4,6,5,2,7,3]=>011010
[4,6,3,2,5,7,1]=>[4,2,3,6,5,1,7]=>[4,6,5,2,3,7,1]=>110010
[4,6,3,2,7,1,5]=>[4,2,3,6,1,7,5]=>[4,6,5,2,7,1,3]=>110010
[4,6,3,2,7,5,1]=>[4,2,3,6,1,5,7]=>[4,6,5,2,7,3,1]=>111010
[4,6,3,5,1,2,7]=>[7,4,3,6,1,5,2]=>[1,4,5,2,7,3,6]=>011000
[4,6,3,5,1,7,2]=>[4,3,6,1,5,2,7]=>[4,5,2,7,3,6,1]=>111000
[4,6,3,5,2,1,7]=>[7,4,3,6,1,2,5]=>[1,4,5,2,7,6,3]=>011001
[4,6,3,5,2,7,1]=>[4,3,6,2,5,1,7]=>[4,5,2,6,3,7,1]=>111000
[4,6,3,5,7,1,2]=>[4,3,6,5,1,7,2]=>[4,5,2,3,7,1,6]=>110000
[4,6,3,5,7,2,1]=>[4,3,6,5,1,2,7]=>[4,5,2,3,7,6,1]=>110001
[4,6,3,7,1,2,5]=>[4,3,6,1,7,5,2]=>[4,5,2,7,1,3,6]=>110000
[4,6,3,7,1,5,2]=>[4,3,6,1,7,2,5]=>[4,5,2,7,1,6,3]=>111000
[4,6,3,7,2,1,5]=>[4,3,6,1,2,7,5]=>[4,5,2,7,6,1,3]=>110001
[4,6,3,7,2,5,1]=>[4,3,6,2,7,1,5]=>[4,5,2,6,1,7,3]=>111000
[4,6,3,7,5,1,2]=>[4,3,6,1,5,7,2]=>[4,5,2,7,3,1,6]=>111000
[4,6,3,7,5,2,1]=>[4,3,6,1,2,5,7]=>[4,5,2,7,6,3,1]=>111001
[4,6,5,1,2,3,7]=>[7,4,1,5,6,3,2]=>[1,4,7,3,2,5,6]=>011000
[4,6,5,1,2,7,3]=>[4,1,5,6,3,7,2]=>[4,7,3,2,5,1,6]=>111000
[4,6,5,1,3,2,7]=>[7,4,1,5,6,2,3]=>[1,4,7,3,2,6,5]=>011010
[4,6,5,1,3,7,2]=>[4,1,5,6,3,2,7]=>[4,7,3,2,5,6,1]=>111000
[4,6,5,1,7,2,3]=>[4,1,5,6,2,7,3]=>[4,7,3,2,6,1,5]=>111000
[4,6,5,1,7,3,2]=>[4,1,5,6,2,3,7]=>[4,7,3,2,6,5,1]=>111010
[4,6,5,2,1,3,7]=>[7,4,1,2,5,6,3]=>[1,4,7,6,3,2,5]=>011001
[4,6,5,2,1,7,3]=>[4,1,2,5,6,3,7]=>[4,7,6,3,2,5,1]=>111001
[4,6,5,2,3,1,7]=>[7,4,2,5,6,1,3]=>[1,4,6,3,2,7,5]=>011010
[4,6,5,2,3,7,1]=>[4,2,5,6,3,1,7]=>[4,6,3,2,5,7,1]=>111000
[4,6,5,2,7,1,3]=>[4,2,5,6,1,7,3]=>[4,6,3,2,7,1,5]=>111000
[4,6,5,2,7,3,1]=>[4,2,5,6,1,3,7]=>[4,6,3,2,7,5,1]=>111010
[4,6,5,3,1,2,7]=>[7,4,1,3,5,6,2]=>[1,4,7,5,3,2,6]=>011010
[4,6,5,3,1,7,2]=>[4,1,3,5,6,2,7]=>[4,7,5,3,2,6,1]=>111010
[4,6,5,3,2,1,7]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>011011
[4,6,5,3,2,7,1]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>111010
[4,6,5,3,7,1,2]=>[4,3,5,6,1,7,2]=>[4,5,3,2,7,1,6]=>111000
[4,6,5,3,7,2,1]=>[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>111001
[4,6,5,7,1,2,3]=>[5,6,4,1,7,3,2]=>[3,2,4,7,1,5,6]=>110000
[4,6,5,7,1,3,2]=>[5,6,4,1,7,2,3]=>[3,2,4,7,1,6,5]=>110010
[4,6,5,7,2,1,3]=>[5,6,4,1,2,7,3]=>[3,2,4,7,6,1,5]=>110001
[4,6,5,7,2,3,1]=>[5,6,4,2,7,1,3]=>[3,2,4,6,1,7,5]=>110010
[4,6,5,7,3,1,2]=>[5,6,4,1,3,7,2]=>[3,2,4,7,5,1,6]=>110010
[4,6,5,7,3,2,1]=>[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>110011
[4,6,7,1,2,3,5]=>[6,4,1,7,5,3,2]=>[2,4,7,1,3,5,6]=>100000
[4,6,7,1,2,5,3]=>[6,4,1,7,3,5,2]=>[2,4,7,1,5,3,6]=>101000
[4,6,7,1,3,2,5]=>[6,4,1,7,5,2,3]=>[2,4,7,1,3,6,5]=>100010
[4,6,7,1,3,5,2]=>[6,4,1,7,3,2,5]=>[2,4,7,1,5,6,3]=>101000
[4,6,7,1,5,2,3]=>[6,4,1,7,2,5,3]=>[2,4,7,1,6,3,5]=>101000
[4,6,7,1,5,3,2]=>[6,4,1,7,2,3,5]=>[2,4,7,1,6,5,3]=>101010
[4,6,7,2,1,3,5]=>[6,4,1,2,7,5,3]=>[2,4,7,6,1,3,5]=>100001
[4,6,7,2,1,5,3]=>[6,4,1,2,7,3,5]=>[2,4,7,6,1,5,3]=>101001
[4,6,7,2,3,1,5]=>[6,4,2,7,5,1,3]=>[2,4,6,1,3,7,5]=>100010
[4,6,7,2,3,5,1]=>[6,4,2,7,3,1,5]=>[2,4,6,1,5,7,3]=>101000
[4,6,7,2,5,1,3]=>[6,4,2,7,1,5,3]=>[2,4,6,1,7,3,5]=>101000
[4,6,7,2,5,3,1]=>[6,4,2,7,1,3,5]=>[2,4,6,1,7,5,3]=>101010
[4,6,7,3,1,2,5]=>[6,4,1,3,7,5,2]=>[2,4,7,5,1,3,6]=>100010
[4,6,7,3,1,5,2]=>[6,4,1,3,7,2,5]=>[2,4,7,5,1,6,3]=>101010
[4,6,7,3,2,1,5]=>[6,4,1,2,3,7,5]=>[2,4,7,6,5,1,3]=>100011
[4,6,7,3,2,5,1]=>[6,4,2,3,7,1,5]=>[2,4,6,5,1,7,3]=>101010
[4,6,7,3,5,1,2]=>[6,4,3,7,1,5,2]=>[2,4,5,1,7,3,6]=>101000
[4,6,7,3,5,2,1]=>[6,4,3,7,1,2,5]=>[2,4,5,1,7,6,3]=>101001
[4,6,7,5,1,2,3]=>[6,4,1,5,7,3,2]=>[2,4,7,3,1,5,6]=>101000
[4,6,7,5,1,3,2]=>[6,4,1,5,7,2,3]=>[2,4,7,3,1,6,5]=>101010
[4,6,7,5,2,1,3]=>[6,4,1,2,5,7,3]=>[2,4,7,6,3,1,5]=>101001
[4,6,7,5,2,3,1]=>[6,4,2,5,7,1,3]=>[2,4,6,3,1,7,5]=>101010
[4,6,7,5,3,1,2]=>[6,4,1,3,5,7,2]=>[2,4,7,5,3,1,6]=>101010
[4,6,7,5,3,2,1]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>101011
[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]=>[4,7,1,2,3,5,6]=>100000
[4,7,1,2,3,6,5]=>[4,1,7,5,6,3,2]=>[4,7,1,3,2,5,6]=>110000
[4,7,1,2,5,3,6]=>[4,1,7,6,3,5,2]=>[4,7,1,2,5,3,6]=>101000
[4,7,1,2,5,6,3]=>[4,1,7,5,3,6,2]=>[4,7,1,3,5,2,6]=>110000
[4,7,1,2,6,3,5]=>[4,1,7,3,6,5,2]=>[4,7,1,5,2,3,6]=>110000
[4,7,1,2,6,5,3]=>[4,1,7,3,5,6,2]=>[4,7,1,5,3,2,6]=>111000
[4,7,1,3,2,5,6]=>[4,1,7,6,5,2,3]=>[4,7,1,2,3,6,5]=>100010
[4,7,1,3,2,6,5]=>[4,1,7,5,6,2,3]=>[4,7,1,3,2,6,5]=>110010
[4,7,1,3,5,2,6]=>[4,1,7,6,3,2,5]=>[4,7,1,2,5,6,3]=>101000
[4,7,1,3,5,6,2]=>[4,1,7,5,3,2,6]=>[4,7,1,3,5,6,2]=>110000
[4,7,1,3,6,2,5]=>[4,1,7,3,2,6,5]=>[4,7,1,5,6,2,3]=>110000
[4,7,1,3,6,5,2]=>[4,1,7,3,2,5,6]=>[4,7,1,5,6,3,2]=>111000
[4,7,1,5,2,3,6]=>[4,1,7,6,2,5,3]=>[4,7,1,2,6,3,5]=>101000
[4,7,1,5,2,6,3]=>[4,1,7,2,5,3,6]=>[4,7,1,6,3,5,2]=>111000
[4,7,1,5,3,2,6]=>[4,1,7,6,2,3,5]=>[4,7,1,2,6,5,3]=>101010
[4,7,1,5,3,6,2]=>[4,1,7,3,5,2,6]=>[4,7,1,5,3,6,2]=>111000
[4,7,1,5,6,2,3]=>[4,1,7,5,2,6,3]=>[4,7,1,3,6,2,5]=>110000
[4,7,1,5,6,3,2]=>[4,1,7,5,2,3,6]=>[4,7,1,3,6,5,2]=>110010
[4,7,1,6,2,3,5]=>[4,1,7,2,6,5,3]=>[4,7,1,6,2,3,5]=>110000
[4,7,1,6,2,5,3]=>[4,1,7,2,6,3,5]=>[4,7,1,6,2,5,3]=>111000
[4,7,1,6,3,2,5]=>[4,1,7,2,3,6,5]=>[4,7,1,6,5,2,3]=>110010
[4,7,1,6,3,5,2]=>[4,1,7,3,6,2,5]=>[4,7,1,5,2,6,3]=>111000
[4,7,1,6,5,2,3]=>[4,1,7,2,5,6,3]=>[4,7,1,6,3,2,5]=>111000
[4,7,1,6,5,3,2]=>[4,1,7,2,3,5,6]=>[4,7,1,6,5,3,2]=>111010
[4,7,2,1,3,5,6]=>[4,1,2,7,6,5,3]=>[4,7,6,1,2,3,5]=>100001
[4,7,2,1,3,6,5]=>[4,1,2,7,5,6,3]=>[4,7,6,1,3,2,5]=>110001
[4,7,2,1,5,3,6]=>[4,1,2,7,6,3,5]=>[4,7,6,1,2,5,3]=>101001
[4,7,2,1,5,6,3]=>[4,1,2,7,5,3,6]=>[4,7,6,1,3,5,2]=>110001
[4,7,2,1,6,3,5]=>[4,1,2,7,3,6,5]=>[4,7,6,1,5,2,3]=>110001
[4,7,2,1,6,5,3]=>[4,1,2,7,3,5,6]=>[4,7,6,1,5,3,2]=>111001
[4,7,2,3,1,5,6]=>[4,2,7,6,5,1,3]=>[4,6,1,2,3,7,5]=>100010
[4,7,2,3,1,6,5]=>[4,2,7,5,6,1,3]=>[4,6,1,3,2,7,5]=>110010
[4,7,2,3,5,1,6]=>[4,2,7,6,3,1,5]=>[4,6,1,2,5,7,3]=>101000
[4,7,2,3,5,6,1]=>[4,2,7,5,3,1,6]=>[4,6,1,3,5,7,2]=>110000
[4,7,2,3,6,1,5]=>[4,2,7,3,1,6,5]=>[4,6,1,5,7,2,3]=>110000
[4,7,2,3,6,5,1]=>[4,2,7,3,1,5,6]=>[4,6,1,5,7,3,2]=>111000
[4,7,2,5,1,3,6]=>[4,2,7,6,1,5,3]=>[4,6,1,2,7,3,5]=>101000
[4,7,2,5,1,6,3]=>[4,2,7,1,5,3,6]=>[4,6,1,7,3,5,2]=>111000
[4,7,2,5,3,1,6]=>[4,2,7,6,1,3,5]=>[4,6,1,2,7,5,3]=>101010
[4,7,2,5,3,6,1]=>[4,2,7,3,5,1,6]=>[4,6,1,5,3,7,2]=>111000
[4,7,2,5,6,1,3]=>[4,2,7,5,1,6,3]=>[4,6,1,3,7,2,5]=>110000
[4,7,2,5,6,3,1]=>[4,2,7,5,1,3,6]=>[4,6,1,3,7,5,2]=>110010
[4,7,2,6,1,3,5]=>[4,2,7,1,6,5,3]=>[4,6,1,7,2,3,5]=>110000
[4,7,2,6,1,5,3]=>[4,2,7,1,6,3,5]=>[4,6,1,7,2,5,3]=>111000
[4,7,2,6,3,1,5]=>[4,2,7,1,3,6,5]=>[4,6,1,7,5,2,3]=>110010
[4,7,2,6,3,5,1]=>[4,2,7,3,6,1,5]=>[4,6,1,5,2,7,3]=>111000
[4,7,2,6,5,1,3]=>[4,2,7,1,5,6,3]=>[4,6,1,7,3,2,5]=>111000
[4,7,2,6,5,3,1]=>[4,2,7,1,3,5,6]=>[4,6,1,7,5,3,2]=>111010
[4,7,3,1,2,5,6]=>[4,1,3,7,6,5,2]=>[4,7,5,1,2,3,6]=>100010
[4,7,3,1,2,6,5]=>[4,1,3,7,5,6,2]=>[4,7,5,1,3,2,6]=>110010
[4,7,3,1,5,2,6]=>[4,1,3,7,6,2,5]=>[4,7,5,1,2,6,3]=>101010
[4,7,3,1,5,6,2]=>[4,1,3,7,5,2,6]=>[4,7,5,1,3,6,2]=>110010
[4,7,3,1,6,2,5]=>[4,1,3,7,2,6,5]=>[4,7,5,1,6,2,3]=>110010
[4,7,3,1,6,5,2]=>[4,1,3,7,2,5,6]=>[4,7,5,1,6,3,2]=>111010
[4,7,3,2,1,5,6]=>[4,1,2,3,7,6,5]=>[4,7,6,5,1,2,3]=>100011
[4,7,3,2,1,6,5]=>[4,1,2,3,7,5,6]=>[4,7,6,5,1,3,2]=>110011
[4,7,3,2,5,1,6]=>[4,2,3,7,6,1,5]=>[4,6,5,1,2,7,3]=>101010
[4,7,3,2,5,6,1]=>[4,2,3,7,5,1,6]=>[4,6,5,1,3,7,2]=>110010
[4,7,3,2,6,1,5]=>[4,2,3,7,1,6,5]=>[4,6,5,1,7,2,3]=>110010
[4,7,3,2,6,5,1]=>[4,2,3,7,1,5,6]=>[4,6,5,1,7,3,2]=>111010
[4,7,3,5,1,2,6]=>[4,3,7,6,1,5,2]=>[4,5,1,2,7,3,6]=>101000
[4,7,3,5,1,6,2]=>[4,3,7,1,5,2,6]=>[4,5,1,7,3,6,2]=>111000
[4,7,3,5,2,1,6]=>[4,3,7,6,1,2,5]=>[4,5,1,2,7,6,3]=>101001
[4,7,3,5,2,6,1]=>[4,3,7,2,5,1,6]=>[4,5,1,6,3,7,2]=>111000
[4,7,3,5,6,1,2]=>[4,3,7,5,1,6,2]=>[4,5,1,3,7,2,6]=>110000
[4,7,3,5,6,2,1]=>[4,3,7,5,1,2,6]=>[4,5,1,3,7,6,2]=>110001
[4,7,3,6,1,2,5]=>[4,3,7,1,6,5,2]=>[4,5,1,7,2,3,6]=>110000
[4,7,3,6,1,5,2]=>[4,3,7,1,6,2,5]=>[4,5,1,7,2,6,3]=>111000
[4,7,3,6,2,1,5]=>[4,3,7,1,2,6,5]=>[4,5,1,7,6,2,3]=>110001
[4,7,3,6,2,5,1]=>[4,3,7,2,6,1,5]=>[4,5,1,6,2,7,3]=>111000
[4,7,3,6,5,1,2]=>[4,3,7,1,5,6,2]=>[4,5,1,7,3,2,6]=>111000
[4,7,3,6,5,2,1]=>[4,3,7,1,2,5,6]=>[4,5,1,7,6,3,2]=>111001
[4,7,5,1,2,3,6]=>[4,1,5,7,6,3,2]=>[4,7,3,1,2,5,6]=>101000
[4,7,5,1,2,6,3]=>[4,1,5,7,3,6,2]=>[4,7,3,1,5,2,6]=>111000
[4,7,5,1,3,2,6]=>[4,1,5,7,6,2,3]=>[4,7,3,1,2,6,5]=>101010
[4,7,5,1,3,6,2]=>[4,1,5,7,3,2,6]=>[4,7,3,1,5,6,2]=>111000
[4,7,5,1,6,2,3]=>[4,1,5,7,2,6,3]=>[4,7,3,1,6,2,5]=>111000
[4,7,5,1,6,3,2]=>[4,1,5,7,2,3,6]=>[4,7,3,1,6,5,2]=>111010
[4,7,5,2,1,3,6]=>[4,1,2,5,7,6,3]=>[4,7,6,3,1,2,5]=>101001
[4,7,5,2,1,6,3]=>[4,1,2,5,7,3,6]=>[4,7,6,3,1,5,2]=>111001
[4,7,5,2,3,1,6]=>[4,2,5,7,6,1,3]=>[4,6,3,1,2,7,5]=>101010
[4,7,5,2,3,6,1]=>[4,2,5,7,3,1,6]=>[4,6,3,1,5,7,2]=>111000
[4,7,5,2,6,1,3]=>[4,2,5,7,1,6,3]=>[4,6,3,1,7,2,5]=>111000
[4,7,5,2,6,3,1]=>[4,2,5,7,1,3,6]=>[4,6,3,1,7,5,2]=>111010
[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>[4,7,5,3,1,2,6]=>101010
[4,7,5,3,1,6,2]=>[4,1,3,5,7,2,6]=>[4,7,5,3,1,6,2]=>111010
[4,7,5,3,2,1,6]=>[4,1,2,3,5,7,6]=>[4,7,6,5,3,1,2]=>101011
[4,7,5,3,2,6,1]=>[4,2,3,5,7,1,6]=>[4,6,5,3,1,7,2]=>111010
[4,7,5,3,6,1,2]=>[4,3,5,7,1,6,2]=>[4,5,3,1,7,2,6]=>111000
[4,7,5,3,6,2,1]=>[4,3,5,7,1,2,6]=>[4,5,3,1,7,6,2]=>111001
[4,7,5,6,1,2,3]=>[5,7,4,1,6,3,2]=>[3,1,4,7,2,5,6]=>110000
[4,7,5,6,1,3,2]=>[5,7,4,1,6,2,3]=>[3,1,4,7,2,6,5]=>110010
[4,7,5,6,2,1,3]=>[5,7,4,1,2,6,3]=>[3,1,4,7,6,2,5]=>110001
[4,7,5,6,2,3,1]=>[5,7,4,2,6,1,3]=>[3,1,4,6,2,7,5]=>110010
[4,7,5,6,3,1,2]=>[5,7,4,1,3,6,2]=>[3,1,4,7,5,2,6]=>110010
[4,7,5,6,3,2,1]=>[5,7,4,1,2,3,6]=>[3,1,4,7,6,5,2]=>110011
[4,7,6,1,2,3,5]=>[4,1,6,7,5,3,2]=>[4,7,2,1,3,5,6]=>110000
[4,7,6,1,2,5,3]=>[4,1,6,7,3,5,2]=>[4,7,2,1,5,3,6]=>111000
[4,7,6,1,3,2,5]=>[4,1,6,7,5,2,3]=>[4,7,2,1,3,6,5]=>110010
[4,7,6,1,3,5,2]=>[4,1,6,7,3,2,5]=>[4,7,2,1,5,6,3]=>111000
[4,7,6,1,5,2,3]=>[4,1,6,7,2,5,3]=>[4,7,2,1,6,3,5]=>111000
[4,7,6,1,5,3,2]=>[4,1,6,7,2,3,5]=>[4,7,2,1,6,5,3]=>111010
[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>[4,7,6,2,1,3,5]=>110001
[4,7,6,2,1,5,3]=>[4,1,2,6,7,3,5]=>[4,7,6,2,1,5,3]=>111001
[4,7,6,2,3,1,5]=>[4,2,6,7,5,1,3]=>[4,6,2,1,3,7,5]=>110010
[4,7,6,2,3,5,1]=>[4,2,6,7,3,1,5]=>[4,6,2,1,5,7,3]=>111000
[4,7,6,2,5,1,3]=>[4,2,6,7,1,5,3]=>[4,6,2,1,7,3,5]=>111000
[4,7,6,2,5,3,1]=>[4,2,6,7,1,3,5]=>[4,6,2,1,7,5,3]=>111010
[4,7,6,3,1,2,5]=>[4,1,3,6,7,5,2]=>[4,7,5,2,1,3,6]=>110010
[4,7,6,3,1,5,2]=>[4,1,3,6,7,2,5]=>[4,7,5,2,1,6,3]=>111010
[4,7,6,3,2,1,5]=>[4,1,2,3,6,7,5]=>[4,7,6,5,2,1,3]=>110011
[4,7,6,3,2,5,1]=>[4,2,3,6,7,1,5]=>[4,6,5,2,1,7,3]=>111010
[4,7,6,3,5,1,2]=>[4,3,6,7,1,5,2]=>[4,5,2,1,7,3,6]=>111000
[4,7,6,3,5,2,1]=>[4,3,6,7,1,2,5]=>[4,5,2,1,7,6,3]=>111001
[4,7,6,5,1,2,3]=>[4,1,5,6,7,3,2]=>[4,7,3,2,1,5,6]=>111000
[4,7,6,5,1,3,2]=>[4,1,5,6,7,2,3]=>[4,7,3,2,1,6,5]=>111010
[4,7,6,5,2,1,3]=>[4,1,2,5,6,7,3]=>[4,7,6,3,2,1,5]=>111001
[4,7,6,5,2,3,1]=>[4,2,5,6,7,1,3]=>[4,6,3,2,1,7,5]=>111010
[4,7,6,5,3,1,2]=>[4,1,3,5,6,7,2]=>[4,7,5,3,2,1,6]=>111010
[4,7,6,5,3,2,1]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>111011
[5,1,2,3,4,6,7]=>[7,6,1,5,4,3,2]=>[1,2,7,3,4,5,6]=>001000
[5,1,2,3,4,7,6]=>[6,7,1,5,4,3,2]=>[2,1,7,3,4,5,6]=>101000
[5,1,2,3,6,4,7]=>[7,1,5,4,6,3,2]=>[1,7,3,4,2,5,6]=>011000
[5,1,2,3,6,7,4]=>[6,1,5,4,7,3,2]=>[2,7,3,4,1,5,6]=>101000
[5,1,2,3,7,4,6]=>[1,5,4,7,6,3,2]=>[7,3,4,1,2,5,6]=>101000
[5,1,2,3,7,6,4]=>[1,5,4,6,7,3,2]=>[7,3,4,2,1,5,6]=>111000
[5,1,2,4,3,6,7]=>[7,6,1,5,3,4,2]=>[1,2,7,3,5,4,6]=>001100
[5,1,2,4,3,7,6]=>[6,7,1,5,3,4,2]=>[2,1,7,3,5,4,6]=>101100
[5,1,2,4,6,3,7]=>[7,1,5,4,3,6,2]=>[1,7,3,4,5,2,6]=>011000
[5,1,2,4,6,7,3]=>[6,1,5,4,3,7,2]=>[2,7,3,4,5,1,6]=>101000
[5,1,2,4,7,3,6]=>[1,5,4,3,7,6,2]=>[7,3,4,5,1,2,6]=>101000
[5,1,2,4,7,6,3]=>[1,5,4,3,6,7,2]=>[7,3,4,5,2,1,6]=>111000
[5,1,2,6,3,4,7]=>[7,1,5,3,6,4,2]=>[1,7,3,5,2,4,6]=>011000
[5,1,2,6,3,7,4]=>[1,5,3,6,4,7,2]=>[7,3,5,2,4,1,6]=>111000
[5,1,2,6,4,3,7]=>[7,1,5,3,4,6,2]=>[1,7,3,5,4,2,6]=>011100
[5,1,2,6,4,7,3]=>[1,5,4,6,3,7,2]=>[7,3,4,2,5,1,6]=>111000
[5,1,2,6,7,3,4]=>[6,1,5,3,7,4,2]=>[2,7,3,5,1,4,6]=>101000
[5,1,2,6,7,4,3]=>[6,1,5,3,4,7,2]=>[2,7,3,5,4,1,6]=>101100
[5,1,2,7,3,4,6]=>[1,5,3,7,6,4,2]=>[7,3,5,1,2,4,6]=>101000
[5,1,2,7,3,6,4]=>[1,5,3,7,4,6,2]=>[7,3,5,1,4,2,6]=>111000
[5,1,2,7,4,3,6]=>[1,5,3,4,7,6,2]=>[7,3,5,4,1,2,6]=>101100
[5,1,2,7,4,6,3]=>[1,5,4,7,3,6,2]=>[7,3,4,1,5,2,6]=>111000
[5,1,2,7,6,3,4]=>[1,5,3,6,7,4,2]=>[7,3,5,2,1,4,6]=>111000
[5,1,2,7,6,4,3]=>[1,5,3,4,6,7,2]=>[7,3,5,4,2,1,6]=>111100
[5,1,3,2,4,6,7]=>[7,6,1,5,4,2,3]=>[1,2,7,3,4,6,5]=>001010
[5,1,3,2,4,7,6]=>[6,7,1,5,4,2,3]=>[2,1,7,3,4,6,5]=>101010
[5,1,3,2,6,4,7]=>[7,1,5,4,6,2,3]=>[1,7,3,4,2,6,5]=>011010
[5,1,3,2,6,7,4]=>[6,1,5,4,7,2,3]=>[2,7,3,4,1,6,5]=>101010
[5,1,3,2,7,4,6]=>[1,5,4,7,6,2,3]=>[7,3,4,1,2,6,5]=>101010
[5,1,3,2,7,6,4]=>[1,5,4,6,7,2,3]=>[7,3,4,2,1,6,5]=>111010
[5,1,3,4,2,6,7]=>[7,6,1,5,3,2,4]=>[1,2,7,3,5,6,4]=>001100
[5,1,3,4,2,7,6]=>[6,7,1,5,3,2,4]=>[2,1,7,3,5,6,4]=>101100
[5,1,3,4,6,2,7]=>[7,1,5,4,3,2,6]=>[1,7,3,4,5,6,2]=>011000
[5,1,3,4,6,7,2]=>[6,1,5,4,3,2,7]=>[2,7,3,4,5,6,1]=>101000
[5,1,3,4,7,2,6]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>101000
[5,1,3,4,7,6,2]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>111000
[5,1,3,6,2,4,7]=>[7,1,5,3,2,6,4]=>[1,7,3,5,6,2,4]=>011000
[5,1,3,6,2,7,4]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>111000
[5,1,3,6,4,2,7]=>[7,1,5,3,2,4,6]=>[1,7,3,5,6,4,2]=>011100
[5,1,3,6,4,7,2]=>[1,5,4,6,3,2,7]=>[7,3,4,2,5,6,1]=>111000
[5,1,3,6,7,2,4]=>[6,1,5,3,2,7,4]=>[2,7,3,5,6,1,4]=>101000
[5,1,3,6,7,4,2]=>[6,1,5,3,2,4,7]=>[2,7,3,5,6,4,1]=>101100
[5,1,3,7,2,4,6]=>[1,5,3,2,7,6,4]=>[7,3,5,6,1,2,4]=>101000
[5,1,3,7,2,6,4]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>111000
[5,1,3,7,4,2,6]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>101100
[5,1,3,7,4,6,2]=>[1,5,4,7,3,2,6]=>[7,3,4,1,5,6,2]=>111000
[5,1,3,7,6,2,4]=>[1,5,3,2,6,7,4]=>[7,3,5,6,2,1,4]=>111000
[5,1,3,7,6,4,2]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>111100
[5,1,4,2,3,6,7]=>[7,6,1,5,2,4,3]=>[1,2,7,3,6,4,5]=>001100
[5,1,4,2,3,7,6]=>[6,7,1,5,2,4,3]=>[2,1,7,3,6,4,5]=>101100
[5,1,4,2,6,3,7]=>[7,1,5,2,4,3,6]=>[1,7,3,6,4,5,2]=>011100
[5,1,4,2,6,7,3]=>[6,1,5,2,4,3,7]=>[2,7,3,6,4,5,1]=>101100
[5,1,4,2,7,3,6]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>101100
[5,1,4,2,7,6,3]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>111100
[5,1,4,3,2,6,7]=>[7,6,1,5,2,3,4]=>[1,2,7,3,6,5,4]=>001110
[5,1,4,3,2,7,6]=>[6,7,1,5,2,3,4]=>[2,1,7,3,6,5,4]=>101110
[5,1,4,3,6,2,7]=>[7,1,5,3,4,2,6]=>[1,7,3,5,4,6,2]=>011100
[5,1,4,3,6,7,2]=>[6,1,5,3,4,2,7]=>[2,7,3,5,4,6,1]=>101100
[5,1,4,3,7,2,6]=>[1,5,3,4,2,7,6]=>[7,3,5,4,6,1,2]=>101100
[5,1,4,3,7,6,2]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>111100
[5,1,4,6,2,3,7]=>[7,1,5,4,2,6,3]=>[1,7,3,4,6,2,5]=>011000
[5,1,4,6,2,7,3]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>111000
[5,1,4,6,3,2,7]=>[7,1,5,4,2,3,6]=>[1,7,3,4,6,5,2]=>011010
[5,1,4,6,3,7,2]=>[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>111000
[5,1,4,6,7,2,3]=>[6,1,5,4,2,7,3]=>[2,7,3,4,6,1,5]=>101000
[5,1,4,6,7,3,2]=>[6,1,5,4,2,3,7]=>[2,7,3,4,6,5,1]=>101010
[5,1,4,7,2,3,6]=>[1,5,4,2,7,6,3]=>[7,3,4,6,1,2,5]=>101000
[5,1,4,7,2,6,3]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>111000
[5,1,4,7,3,2,6]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>101010
[5,1,4,7,3,6,2]=>[1,5,4,3,7,2,6]=>[7,3,4,5,1,6,2]=>111000
[5,1,4,7,6,2,3]=>[1,5,4,2,6,7,3]=>[7,3,4,6,2,1,5]=>111000
[5,1,4,7,6,3,2]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>111010
[5,1,6,2,3,4,7]=>[7,1,5,2,6,4,3]=>[1,7,3,6,2,4,5]=>011000
[5,1,6,2,3,7,4]=>[1,5,2,6,4,7,3]=>[7,3,6,2,4,1,5]=>111000
[5,1,6,2,4,3,7]=>[7,1,5,2,6,3,4]=>[1,7,3,6,2,5,4]=>011100
[5,1,6,2,4,7,3]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>111000
[5,1,6,2,7,3,4]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>111000
[5,1,6,2,7,4,3]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>111100
[5,1,6,3,2,4,7]=>[7,1,5,2,3,6,4]=>[1,7,3,6,5,2,4]=>011010
[5,1,6,3,2,7,4]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>111010
[5,1,6,3,4,2,7]=>[7,1,5,3,6,2,4]=>[1,7,3,5,2,6,4]=>011100
[5,1,6,3,4,7,2]=>[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>111000
[5,1,6,3,7,2,4]=>[1,5,3,6,2,7,4]=>[7,3,5,2,6,1,4]=>111000
[5,1,6,3,7,4,2]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>111100
[5,1,6,4,2,3,7]=>[7,1,5,2,4,6,3]=>[1,7,3,6,4,2,5]=>011100
[5,1,6,4,2,7,3]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>111100
[5,1,6,4,3,2,7]=>[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>011110
[5,1,6,4,3,7,2]=>[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>111100
[5,1,6,4,7,2,3]=>[1,5,4,6,2,7,3]=>[7,3,4,2,6,1,5]=>111000
[5,1,6,4,7,3,2]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>111010
[5,1,6,7,2,3,4]=>[6,1,5,2,7,4,3]=>[2,7,3,6,1,4,5]=>101000
[5,1,6,7,2,4,3]=>[6,1,5,2,7,3,4]=>[2,7,3,6,1,5,4]=>101100
[5,1,6,7,3,2,4]=>[6,1,5,2,3,7,4]=>[2,7,3,6,5,1,4]=>101010
[5,1,6,7,3,4,2]=>[6,1,5,3,7,2,4]=>[2,7,3,5,1,6,4]=>101100
[5,1,6,7,4,2,3]=>[6,1,5,2,4,7,3]=>[2,7,3,6,4,1,5]=>101100
[5,1,6,7,4,3,2]=>[6,1,5,2,3,4,7]=>[2,7,3,6,5,4,1]=>101110
[5,1,7,2,3,4,6]=>[1,5,2,7,6,4,3]=>[7,3,6,1,2,4,5]=>101000
[5,1,7,2,3,6,4]=>[1,5,2,7,4,6,3]=>[7,3,6,1,4,2,5]=>111000
[5,1,7,2,4,3,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>101100
[5,1,7,2,4,6,3]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>111000
[5,1,7,2,6,3,4]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>111000
[5,1,7,2,6,4,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>111100
[5,1,7,3,2,4,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>101010
[5,1,7,3,2,6,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>111010
[5,1,7,3,4,2,6]=>[1,5,3,7,6,2,4]=>[7,3,5,1,2,6,4]=>101100
[5,1,7,3,4,6,2]=>[1,5,3,7,4,2,6]=>[7,3,5,1,4,6,2]=>111000
[5,1,7,3,6,2,4]=>[1,5,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>111000
[5,1,7,3,6,4,2]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>111100
[5,1,7,4,2,3,6]=>[1,5,2,4,7,6,3]=>[7,3,6,4,1,2,5]=>101100
[5,1,7,4,2,6,3]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>111100
[5,1,7,4,3,2,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>101110
[5,1,7,4,3,6,2]=>[1,5,3,4,7,2,6]=>[7,3,5,4,1,6,2]=>111100
[5,1,7,4,6,2,3]=>[1,5,4,7,2,6,3]=>[7,3,4,1,6,2,5]=>111000
[5,1,7,4,6,3,2]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>111010
[5,1,7,6,2,3,4]=>[1,5,2,6,7,4,3]=>[7,3,6,2,1,4,5]=>111000
[5,1,7,6,2,4,3]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>111100
[5,1,7,6,3,2,4]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>111010
[5,1,7,6,3,4,2]=>[1,5,3,6,7,2,4]=>[7,3,5,2,1,6,4]=>111100
[5,1,7,6,4,2,3]=>[1,5,2,4,6,7,3]=>[7,3,6,4,2,1,5]=>111100
[5,1,7,6,4,3,2]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>111110
[5,2,1,3,4,6,7]=>[7,6,1,2,5,4,3]=>[1,2,7,6,3,4,5]=>001001
[5,2,1,3,4,7,6]=>[6,7,1,2,5,4,3]=>[2,1,7,6,3,4,5]=>101001
[5,2,1,3,6,4,7]=>[7,1,2,5,4,6,3]=>[1,7,6,3,4,2,5]=>011001
[5,2,1,3,6,7,4]=>[6,1,2,5,4,7,3]=>[2,7,6,3,4,1,5]=>101001
[5,2,1,3,7,4,6]=>[1,2,5,4,7,6,3]=>[7,6,3,4,1,2,5]=>101001
[5,2,1,3,7,6,4]=>[1,2,5,4,6,7,3]=>[7,6,3,4,2,1,5]=>111001
[5,2,1,4,3,6,7]=>[7,6,1,2,5,3,4]=>[1,2,7,6,3,5,4]=>001101
[5,2,1,4,3,7,6]=>[6,7,1,2,5,3,4]=>[2,1,7,6,3,5,4]=>101101
[5,2,1,4,6,3,7]=>[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>011001
[5,2,1,4,6,7,3]=>[6,1,2,5,4,3,7]=>[2,7,6,3,4,5,1]=>101001
[5,2,1,4,7,3,6]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>101001
[5,2,1,4,7,6,3]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>111001
[5,2,1,6,3,4,7]=>[7,1,2,5,3,6,4]=>[1,7,6,3,5,2,4]=>011001
[5,2,1,6,3,7,4]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>111001
[5,2,1,6,4,3,7]=>[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>011101
[5,2,1,6,4,7,3]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>111001
[5,2,1,6,7,3,4]=>[6,1,2,5,3,7,4]=>[2,7,6,3,5,1,4]=>101001
[5,2,1,6,7,4,3]=>[6,1,2,5,3,4,7]=>[2,7,6,3,5,4,1]=>101101
[5,2,1,7,3,4,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>101001
[5,2,1,7,3,6,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>111001
[5,2,1,7,4,3,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>101101
[5,2,1,7,4,6,3]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>111001
[5,2,1,7,6,3,4]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>111001
[5,2,1,7,6,4,3]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>111101
[5,2,3,1,4,6,7]=>[7,6,2,5,4,1,3]=>[1,2,6,3,4,7,5]=>001010
[5,2,3,1,4,7,6]=>[6,7,2,5,4,1,3]=>[2,1,6,3,4,7,5]=>101010
[5,2,3,1,6,4,7]=>[7,2,5,4,6,1,3]=>[1,6,3,4,2,7,5]=>011010
[5,2,3,1,6,7,4]=>[6,2,5,4,7,1,3]=>[2,6,3,4,1,7,5]=>101010
[5,2,3,1,7,4,6]=>[2,5,4,7,6,1,3]=>[6,3,4,1,2,7,5]=>101010
[5,2,3,1,7,6,4]=>[2,5,4,6,7,1,3]=>[6,3,4,2,1,7,5]=>111010
[5,2,3,4,1,6,7]=>[7,6,2,5,3,1,4]=>[1,2,6,3,5,7,4]=>001100
[5,2,3,4,1,7,6]=>[6,7,2,5,3,1,4]=>[2,1,6,3,5,7,4]=>101100
[5,2,3,4,6,1,7]=>[7,2,5,4,3,1,6]=>[1,6,3,4,5,7,2]=>011000
[5,2,3,4,6,7,1]=>[6,2,5,4,3,1,7]=>[2,6,3,4,5,7,1]=>101000
[5,2,3,4,7,1,6]=>[2,5,4,3,1,7,6]=>[6,3,4,5,7,1,2]=>101000
[5,2,3,4,7,6,1]=>[2,5,4,3,1,6,7]=>[6,3,4,5,7,2,1]=>111000
[5,2,3,6,1,4,7]=>[7,2,5,3,1,6,4]=>[1,6,3,5,7,2,4]=>011000
[5,2,3,6,1,7,4]=>[2,5,3,1,6,4,7]=>[6,3,5,7,2,4,1]=>111000
[5,2,3,6,4,1,7]=>[7,2,5,3,1,4,6]=>[1,6,3,5,7,4,2]=>011100
[5,2,3,6,4,7,1]=>[2,5,4,6,3,1,7]=>[6,3,4,2,5,7,1]=>111000
[5,2,3,6,7,1,4]=>[6,2,5,3,1,7,4]=>[2,6,3,5,7,1,4]=>101000
[5,2,3,6,7,4,1]=>[6,2,5,3,1,4,7]=>[2,6,3,5,7,4,1]=>101100
[5,2,3,7,1,4,6]=>[2,5,3,1,7,6,4]=>[6,3,5,7,1,2,4]=>101000
[5,2,3,7,1,6,4]=>[2,5,3,1,7,4,6]=>[6,3,5,7,1,4,2]=>111000
[5,2,3,7,4,1,6]=>[2,5,3,1,4,7,6]=>[6,3,5,7,4,1,2]=>101100
[5,2,3,7,4,6,1]=>[2,5,4,7,3,1,6]=>[6,3,4,1,5,7,2]=>111000
[5,2,3,7,6,1,4]=>[2,5,3,1,6,7,4]=>[6,3,5,7,2,1,4]=>111000
[5,2,3,7,6,4,1]=>[2,5,3,1,4,6,7]=>[6,3,5,7,4,2,1]=>111100
[5,2,4,1,3,6,7]=>[7,6,2,5,1,4,3]=>[1,2,6,3,7,4,5]=>001100
[5,2,4,1,3,7,6]=>[6,7,2,5,1,4,3]=>[2,1,6,3,7,4,5]=>101100
[5,2,4,1,6,3,7]=>[7,2,5,1,4,3,6]=>[1,6,3,7,4,5,2]=>011100
[5,2,4,1,6,7,3]=>[6,2,5,1,4,3,7]=>[2,6,3,7,4,5,1]=>101100
[5,2,4,1,7,3,6]=>[2,5,1,4,3,7,6]=>[6,3,7,4,5,1,2]=>101100
[5,2,4,1,7,6,3]=>[2,5,1,4,3,6,7]=>[6,3,7,4,5,2,1]=>111100
[5,2,4,3,1,6,7]=>[7,6,2,5,1,3,4]=>[1,2,6,3,7,5,4]=>001110
[5,2,4,3,1,7,6]=>[6,7,2,5,1,3,4]=>[2,1,6,3,7,5,4]=>101110
[5,2,4,3,6,1,7]=>[7,2,5,3,4,1,6]=>[1,6,3,5,4,7,2]=>011100
[5,2,4,3,6,7,1]=>[6,2,5,3,4,1,7]=>[2,6,3,5,4,7,1]=>101100
[5,2,4,3,7,1,6]=>[2,5,3,4,1,7,6]=>[6,3,5,4,7,1,2]=>101100
[5,2,4,3,7,6,1]=>[2,5,3,4,1,6,7]=>[6,3,5,4,7,2,1]=>111100
[5,2,4,6,1,3,7]=>[7,2,5,4,1,6,3]=>[1,6,3,4,7,2,5]=>011000
[5,2,4,6,1,7,3]=>[2,5,4,1,6,3,7]=>[6,3,4,7,2,5,1]=>111000
[5,2,4,6,3,1,7]=>[7,2,5,4,1,3,6]=>[1,6,3,4,7,5,2]=>011010
[5,2,4,6,3,7,1]=>[2,5,4,3,6,1,7]=>[6,3,4,5,2,7,1]=>111000
[5,2,4,6,7,1,3]=>[6,2,5,4,1,7,3]=>[2,6,3,4,7,1,5]=>101000
[5,2,4,6,7,3,1]=>[6,2,5,4,1,3,7]=>[2,6,3,4,7,5,1]=>101010
[5,2,4,7,1,3,6]=>[2,5,4,1,7,6,3]=>[6,3,4,7,1,2,5]=>101000
[5,2,4,7,1,6,3]=>[2,5,4,1,7,3,6]=>[6,3,4,7,1,5,2]=>111000
[5,2,4,7,3,1,6]=>[2,5,4,1,3,7,6]=>[6,3,4,7,5,1,2]=>101010
[5,2,4,7,3,6,1]=>[2,5,4,3,7,1,6]=>[6,3,4,5,1,7,2]=>111000
[5,2,4,7,6,1,3]=>[2,5,4,1,6,7,3]=>[6,3,4,7,2,1,5]=>111000
[5,2,4,7,6,3,1]=>[2,5,4,1,3,6,7]=>[6,3,4,7,5,2,1]=>111010
[5,2,6,1,3,4,7]=>[7,2,5,1,6,4,3]=>[1,6,3,7,2,4,5]=>011000
[5,2,6,1,3,7,4]=>[2,5,1,6,4,7,3]=>[6,3,7,2,4,1,5]=>111000
[5,2,6,1,4,3,7]=>[7,2,5,1,6,3,4]=>[1,6,3,7,2,5,4]=>011100
[5,2,6,1,4,7,3]=>[2,5,1,6,4,3,7]=>[6,3,7,2,4,5,1]=>111000
[5,2,6,1,7,3,4]=>[2,5,1,6,3,7,4]=>[6,3,7,2,5,1,4]=>111000
[5,2,6,1,7,4,3]=>[2,5,1,6,3,4,7]=>[6,3,7,2,5,4,1]=>111100
[5,2,6,3,1,4,7]=>[7,2,5,1,3,6,4]=>[1,6,3,7,5,2,4]=>011010
[5,2,6,3,1,7,4]=>[2,5,1,3,6,4,7]=>[6,3,7,5,2,4,1]=>111010
[5,2,6,3,4,1,7]=>[7,2,5,3,6,1,4]=>[1,6,3,5,2,7,4]=>011100
[5,2,6,3,4,7,1]=>[2,5,3,6,4,1,7]=>[6,3,5,2,4,7,1]=>111000
[5,2,6,3,7,1,4]=>[2,5,3,6,1,7,4]=>[6,3,5,2,7,1,4]=>111000
[5,2,6,3,7,4,1]=>[2,5,3,6,1,4,7]=>[6,3,5,2,7,4,1]=>111100
[5,2,6,4,1,3,7]=>[7,2,5,1,4,6,3]=>[1,6,3,7,4,2,5]=>011100
[5,2,6,4,1,7,3]=>[2,5,1,4,6,3,7]=>[6,3,7,4,2,5,1]=>111100
[5,2,6,4,3,1,7]=>[7,2,5,1,3,4,6]=>[1,6,3,7,5,4,2]=>011110
[5,2,6,4,3,7,1]=>[2,5,3,4,6,1,7]=>[6,3,5,4,2,7,1]=>111100
[5,2,6,4,7,1,3]=>[2,5,4,6,1,7,3]=>[6,3,4,2,7,1,5]=>111000
[5,2,6,4,7,3,1]=>[2,5,4,6,1,3,7]=>[6,3,4,2,7,5,1]=>111010
[5,2,6,7,1,3,4]=>[6,2,5,1,7,4,3]=>[2,6,3,7,1,4,5]=>101000
[5,2,6,7,1,4,3]=>[6,2,5,1,7,3,4]=>[2,6,3,7,1,5,4]=>101100
[5,2,6,7,3,1,4]=>[6,2,5,1,3,7,4]=>[2,6,3,7,5,1,4]=>101010
[5,2,6,7,3,4,1]=>[6,2,5,3,7,1,4]=>[2,6,3,5,1,7,4]=>101100
[5,2,6,7,4,1,3]=>[6,2,5,1,4,7,3]=>[2,6,3,7,4,1,5]=>101100
[5,2,6,7,4,3,1]=>[6,2,5,1,3,4,7]=>[2,6,3,7,5,4,1]=>101110
[5,2,7,1,3,4,6]=>[2,5,1,7,6,4,3]=>[6,3,7,1,2,4,5]=>101000
[5,2,7,1,3,6,4]=>[2,5,1,7,4,6,3]=>[6,3,7,1,4,2,5]=>111000
[5,2,7,1,4,3,6]=>[2,5,1,7,6,3,4]=>[6,3,7,1,2,5,4]=>101100
[5,2,7,1,4,6,3]=>[2,5,1,7,4,3,6]=>[6,3,7,1,4,5,2]=>111000
[5,2,7,1,6,3,4]=>[2,5,1,7,3,6,4]=>[6,3,7,1,5,2,4]=>111000
[5,2,7,1,6,4,3]=>[2,5,1,7,3,4,6]=>[6,3,7,1,5,4,2]=>111100
[5,2,7,3,1,4,6]=>[2,5,1,3,7,6,4]=>[6,3,7,5,1,2,4]=>101010
[5,2,7,3,1,6,4]=>[2,5,1,3,7,4,6]=>[6,3,7,5,1,4,2]=>111010
[5,2,7,3,4,1,6]=>[2,5,3,7,6,1,4]=>[6,3,5,1,2,7,4]=>101100
[5,2,7,3,4,6,1]=>[2,5,3,7,4,1,6]=>[6,3,5,1,4,7,2]=>111000
[5,2,7,3,6,1,4]=>[2,5,3,7,1,6,4]=>[6,3,5,1,7,2,4]=>111000
[5,2,7,3,6,4,1]=>[2,5,3,7,1,4,6]=>[6,3,5,1,7,4,2]=>111100
[5,2,7,4,1,3,6]=>[2,5,1,4,7,6,3]=>[6,3,7,4,1,2,5]=>101100
[5,2,7,4,1,6,3]=>[2,5,1,4,7,3,6]=>[6,3,7,4,1,5,2]=>111100
[5,2,7,4,3,1,6]=>[2,5,1,3,4,7,6]=>[6,3,7,5,4,1,2]=>101110
[5,2,7,4,3,6,1]=>[2,5,3,4,7,1,6]=>[6,3,5,4,1,7,2]=>111100
[5,2,7,4,6,1,3]=>[2,5,4,7,1,6,3]=>[6,3,4,1,7,2,5]=>111000
[5,2,7,4,6,3,1]=>[2,5,4,7,1,3,6]=>[6,3,4,1,7,5,2]=>111010
[5,2,7,6,1,3,4]=>[2,5,1,6,7,4,3]=>[6,3,7,2,1,4,5]=>111000
[5,2,7,6,1,4,3]=>[2,5,1,6,7,3,4]=>[6,3,7,2,1,5,4]=>111100
[5,2,7,6,3,1,4]=>[2,5,1,3,6,7,4]=>[6,3,7,5,2,1,4]=>111010
[5,2,7,6,3,4,1]=>[2,5,3,6,7,1,4]=>[6,3,5,2,1,7,4]=>111100
[5,2,7,6,4,1,3]=>[2,5,1,4,6,7,3]=>[6,3,7,4,2,1,5]=>111100
[5,2,7,6,4,3,1]=>[2,5,1,3,4,6,7]=>[6,3,7,5,4,2,1]=>111110
[5,3,1,2,4,6,7]=>[7,6,1,3,5,4,2]=>[1,2,7,5,3,4,6]=>001010
[5,3,1,2,4,7,6]=>[6,7,1,3,5,4,2]=>[2,1,7,5,3,4,6]=>101010
[5,3,1,2,6,4,7]=>[7,1,3,5,4,6,2]=>[1,7,5,3,4,2,6]=>011010
[5,3,1,2,6,7,4]=>[6,1,3,5,4,7,2]=>[2,7,5,3,4,1,6]=>101010
[5,3,1,2,7,4,6]=>[1,3,5,4,7,6,2]=>[7,5,3,4,1,2,6]=>101010
[5,3,1,2,7,6,4]=>[1,3,5,4,6,7,2]=>[7,5,3,4,2,1,6]=>111010
[5,3,1,4,2,6,7]=>[7,6,1,3,5,2,4]=>[1,2,7,5,3,6,4]=>001110
[5,3,1,4,2,7,6]=>[6,7,1,3,5,2,4]=>[2,1,7,5,3,6,4]=>101110
[5,3,1,4,6,2,7]=>[7,1,3,5,4,2,6]=>[1,7,5,3,4,6,2]=>011010
[5,3,1,4,6,7,2]=>[6,1,3,5,4,2,7]=>[2,7,5,3,4,6,1]=>101010
[5,3,1,4,7,2,6]=>[1,3,5,4,2,7,6]=>[7,5,3,4,6,1,2]=>101010
[5,3,1,4,7,6,2]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>111010
[5,3,1,6,2,4,7]=>[7,1,3,5,2,6,4]=>[1,7,5,3,6,2,4]=>011010
[5,3,1,6,2,7,4]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>111010
[5,3,1,6,4,2,7]=>[7,1,3,5,2,4,6]=>[1,7,5,3,6,4,2]=>011110
[5,3,1,6,4,7,2]=>[1,3,5,4,6,2,7]=>[7,5,3,4,2,6,1]=>111010
[5,3,1,6,7,2,4]=>[6,1,3,5,2,7,4]=>[2,7,5,3,6,1,4]=>101010
[5,3,1,6,7,4,2]=>[6,1,3,5,2,4,7]=>[2,7,5,3,6,4,1]=>101110
[5,3,1,7,2,4,6]=>[1,3,5,2,7,6,4]=>[7,5,3,6,1,2,4]=>101010
[5,3,1,7,2,6,4]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>111010
[5,3,1,7,4,2,6]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>101110
[5,3,1,7,4,6,2]=>[1,3,5,4,7,2,6]=>[7,5,3,4,1,6,2]=>111010
[5,3,1,7,6,2,4]=>[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]=>111010
[5,3,1,7,6,4,2]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>111110
[5,3,2,1,4,6,7]=>[7,6,1,2,3,5,4]=>[1,2,7,6,5,3,4]=>001011
[5,3,2,1,4,7,6]=>[6,7,1,2,3,5,4]=>[2,1,7,6,5,3,4]=>101011
[5,3,2,1,6,4,7]=>[7,1,2,3,5,4,6]=>[1,7,6,5,3,4,2]=>011011
[5,3,2,1,6,7,4]=>[6,1,2,3,5,4,7]=>[2,7,6,5,3,4,1]=>101011
[5,3,2,1,7,4,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>101011
[5,3,2,1,7,6,4]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>111011
[5,3,2,4,1,6,7]=>[7,6,2,3,5,1,4]=>[1,2,6,5,3,7,4]=>001110
[5,3,2,4,1,7,6]=>[6,7,2,3,5,1,4]=>[2,1,6,5,3,7,4]=>101110
[5,3,2,4,6,1,7]=>[7,2,3,5,4,1,6]=>[1,6,5,3,4,7,2]=>011010
[5,3,2,4,6,7,1]=>[6,2,3,5,4,1,7]=>[2,6,5,3,4,7,1]=>101010
[5,3,2,4,7,1,6]=>[2,3,5,4,1,7,6]=>[6,5,3,4,7,1,2]=>101010
[5,3,2,4,7,6,1]=>[2,3,5,4,1,6,7]=>[6,5,3,4,7,2,1]=>111010
[5,3,2,6,1,4,7]=>[7,2,3,5,1,6,4]=>[1,6,5,3,7,2,4]=>011010
[5,3,2,6,1,7,4]=>[2,3,5,1,6,4,7]=>[6,5,3,7,2,4,1]=>111010
[5,3,2,6,4,1,7]=>[7,2,3,5,1,4,6]=>[1,6,5,3,7,4,2]=>011110
[5,3,2,6,4,7,1]=>[2,3,5,4,6,1,7]=>[6,5,3,4,2,7,1]=>111010
[5,3,2,6,7,1,4]=>[6,2,3,5,1,7,4]=>[2,6,5,3,7,1,4]=>101010
[5,3,2,6,7,4,1]=>[6,2,3,5,1,4,7]=>[2,6,5,3,7,4,1]=>101110
[5,3,2,7,1,4,6]=>[2,3,5,1,7,6,4]=>[6,5,3,7,1,2,4]=>101010
[5,3,2,7,1,6,4]=>[2,3,5,1,7,4,6]=>[6,5,3,7,1,4,2]=>111010
[5,3,2,7,4,1,6]=>[2,3,5,1,4,7,6]=>[6,5,3,7,4,1,2]=>101110
[5,3,2,7,4,6,1]=>[2,3,5,4,7,1,6]=>[6,5,3,4,1,7,2]=>111010
[5,3,2,7,6,1,4]=>[2,3,5,1,6,7,4]=>[6,5,3,7,2,1,4]=>111010
[5,3,2,7,6,4,1]=>[2,3,5,1,4,6,7]=>[6,5,3,7,4,2,1]=>111110
[5,3,4,1,2,6,7]=>[7,6,3,5,1,4,2]=>[1,2,5,3,7,4,6]=>001100
[5,3,4,1,2,7,6]=>[6,7,3,5,1,4,2]=>[2,1,5,3,7,4,6]=>101100
[5,3,4,1,6,2,7]=>[7,3,5,1,4,2,6]=>[1,5,3,7,4,6,2]=>011100
[5,3,4,1,6,7,2]=>[6,3,5,1,4,2,7]=>[2,5,3,7,4,6,1]=>101100
[5,3,4,1,7,2,6]=>[3,5,1,4,2,7,6]=>[5,3,7,4,6,1,2]=>101100
[5,3,4,1,7,6,2]=>[3,5,1,4,2,6,7]=>[5,3,7,4,6,2,1]=>111100
[5,3,4,2,1,6,7]=>[7,6,3,5,1,2,4]=>[1,2,5,3,7,6,4]=>001101
[5,3,4,2,1,7,6]=>[6,7,3,5,1,2,4]=>[2,1,5,3,7,6,4]=>101101
[5,3,4,2,6,1,7]=>[7,3,5,2,4,1,6]=>[1,5,3,6,4,7,2]=>011100
[5,3,4,2,6,7,1]=>[6,3,5,2,4,1,7]=>[2,5,3,6,4,7,1]=>101100
[5,3,4,2,7,1,6]=>[3,5,2,4,1,7,6]=>[5,3,6,4,7,1,2]=>101100
[5,3,4,2,7,6,1]=>[3,5,2,4,1,6,7]=>[5,3,6,4,7,2,1]=>111100
[5,3,4,6,1,2,7]=>[7,3,5,4,1,6,2]=>[1,5,3,4,7,2,6]=>011000
[5,3,4,6,1,7,2]=>[3,5,4,1,6,2,7]=>[5,3,4,7,2,6,1]=>111000
[5,3,4,6,2,1,7]=>[7,3,5,4,1,2,6]=>[1,5,3,4,7,6,2]=>011001
[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>[5,3,4,6,2,7,1]=>111000
[5,3,4,6,7,1,2]=>[6,3,5,4,1,7,2]=>[2,5,3,4,7,1,6]=>101000
[5,3,4,6,7,2,1]=>[6,3,5,4,1,2,7]=>[2,5,3,4,7,6,1]=>101001
[5,3,4,7,1,2,6]=>[3,5,4,1,7,6,2]=>[5,3,4,7,1,2,6]=>101000
[5,3,4,7,1,6,2]=>[3,5,4,1,7,2,6]=>[5,3,4,7,1,6,2]=>111000
[5,3,4,7,2,1,6]=>[3,5,4,1,2,7,6]=>[5,3,4,7,6,1,2]=>101001
[5,3,4,7,2,6,1]=>[3,5,4,2,7,1,6]=>[5,3,4,6,1,7,2]=>111000
[5,3,4,7,6,1,2]=>[3,5,4,1,6,7,2]=>[5,3,4,7,2,1,6]=>111000
[5,3,4,7,6,2,1]=>[3,5,4,1,2,6,7]=>[5,3,4,7,6,2,1]=>111001
[5,3,6,1,2,4,7]=>[7,3,5,1,6,4,2]=>[1,5,3,7,2,4,6]=>011000
[5,3,6,1,2,7,4]=>[3,5,1,6,4,7,2]=>[5,3,7,2,4,1,6]=>111000
[5,3,6,1,4,2,7]=>[7,3,5,1,6,2,4]=>[1,5,3,7,2,6,4]=>011100
[5,3,6,1,4,7,2]=>[3,5,1,6,4,2,7]=>[5,3,7,2,4,6,1]=>111000
[5,3,6,1,7,2,4]=>[3,5,1,6,2,7,4]=>[5,3,7,2,6,1,4]=>111000
[5,3,6,1,7,4,2]=>[3,5,1,6,2,4,7]=>[5,3,7,2,6,4,1]=>111100
[5,3,6,2,1,4,7]=>[7,3,5,1,2,6,4]=>[1,5,3,7,6,2,4]=>011001
[5,3,6,2,1,7,4]=>[3,5,1,2,6,4,7]=>[5,3,7,6,2,4,1]=>111001
[5,3,6,2,4,1,7]=>[7,3,5,2,6,1,4]=>[1,5,3,6,2,7,4]=>011100
[5,3,6,2,4,7,1]=>[3,5,2,6,4,1,7]=>[5,3,6,2,4,7,1]=>111000
[5,3,6,2,7,1,4]=>[3,5,2,6,1,7,4]=>[5,3,6,2,7,1,4]=>111000
[5,3,6,2,7,4,1]=>[3,5,2,6,1,4,7]=>[5,3,6,2,7,4,1]=>111100
[5,3,6,4,1,2,7]=>[7,3,5,1,4,6,2]=>[1,5,3,7,4,2,6]=>011100
[5,3,6,4,1,7,2]=>[3,5,1,4,6,2,7]=>[5,3,7,4,2,6,1]=>111100
[5,3,6,4,2,1,7]=>[7,3,5,1,2,4,6]=>[1,5,3,7,6,4,2]=>011101
[5,3,6,4,2,7,1]=>[3,5,2,4,6,1,7]=>[5,3,6,4,2,7,1]=>111100
[5,3,6,4,7,1,2]=>[3,5,4,6,1,7,2]=>[5,3,4,2,7,1,6]=>111000
[5,3,6,4,7,2,1]=>[3,5,4,6,1,2,7]=>[5,3,4,2,7,6,1]=>111001
[5,3,6,7,1,2,4]=>[6,3,5,1,7,4,2]=>[2,5,3,7,1,4,6]=>101000
[5,3,6,7,1,4,2]=>[6,3,5,1,7,2,4]=>[2,5,3,7,1,6,4]=>101100
[5,3,6,7,2,1,4]=>[6,3,5,1,2,7,4]=>[2,5,3,7,6,1,4]=>101001
[5,3,6,7,2,4,1]=>[6,3,5,2,7,1,4]=>[2,5,3,6,1,7,4]=>101100
[5,3,6,7,4,1,2]=>[6,3,5,1,4,7,2]=>[2,5,3,7,4,1,6]=>101100
[5,3,6,7,4,2,1]=>[6,3,5,1,2,4,7]=>[2,5,3,7,6,4,1]=>101101
[5,3,7,1,2,4,6]=>[3,5,1,7,6,4,2]=>[5,3,7,1,2,4,6]=>101000
[5,3,7,1,2,6,4]=>[3,5,1,7,4,6,2]=>[5,3,7,1,4,2,6]=>111000
[5,3,7,1,4,2,6]=>[3,5,1,7,6,2,4]=>[5,3,7,1,2,6,4]=>101100
[5,3,7,1,4,6,2]=>[3,5,1,7,4,2,6]=>[5,3,7,1,4,6,2]=>111000
[5,3,7,1,6,2,4]=>[3,5,1,7,2,6,4]=>[5,3,7,1,6,2,4]=>111000
[5,3,7,1,6,4,2]=>[3,5,1,7,2,4,6]=>[5,3,7,1,6,4,2]=>111100
[5,3,7,2,1,4,6]=>[3,5,1,2,7,6,4]=>[5,3,7,6,1,2,4]=>101001
[5,3,7,2,1,6,4]=>[3,5,1,2,7,4,6]=>[5,3,7,6,1,4,2]=>111001
[5,3,7,2,4,1,6]=>[3,5,2,7,6,1,4]=>[5,3,6,1,2,7,4]=>101100
[5,3,7,2,4,6,1]=>[3,5,2,7,4,1,6]=>[5,3,6,1,4,7,2]=>111000
[5,3,7,2,6,1,4]=>[3,5,2,7,1,6,4]=>[5,3,6,1,7,2,4]=>111000
[5,3,7,2,6,4,1]=>[3,5,2,7,1,4,6]=>[5,3,6,1,7,4,2]=>111100
[5,3,7,4,1,2,6]=>[3,5,1,4,7,6,2]=>[5,3,7,4,1,2,6]=>101100
[5,3,7,4,1,6,2]=>[3,5,1,4,7,2,6]=>[5,3,7,4,1,6,2]=>111100
[5,3,7,4,2,1,6]=>[3,5,1,2,4,7,6]=>[5,3,7,6,4,1,2]=>101101
[5,3,7,4,2,6,1]=>[3,5,2,4,7,1,6]=>[5,3,6,4,1,7,2]=>111100
[5,3,7,4,6,1,2]=>[3,5,4,7,1,6,2]=>[5,3,4,1,7,2,6]=>111000
[5,3,7,4,6,2,1]=>[3,5,4,7,1,2,6]=>[5,3,4,1,7,6,2]=>111001
[5,3,7,6,1,2,4]=>[3,5,1,6,7,4,2]=>[5,3,7,2,1,4,6]=>111000
[5,3,7,6,1,4,2]=>[3,5,1,6,7,2,4]=>[5,3,7,2,1,6,4]=>111100
[5,3,7,6,2,1,4]=>[3,5,1,2,6,7,4]=>[5,3,7,6,2,1,4]=>111001
[5,3,7,6,2,4,1]=>[3,5,2,6,7,1,4]=>[5,3,6,2,1,7,4]=>111100
[5,3,7,6,4,1,2]=>[3,5,1,4,6,7,2]=>[5,3,7,4,2,1,6]=>111100
[5,3,7,6,4,2,1]=>[3,5,1,2,4,6,7]=>[5,3,7,6,4,2,1]=>111101
[5,4,1,2,3,6,7]=>[7,6,1,4,5,3,2]=>[1,2,7,4,3,5,6]=>001100
[5,4,1,2,3,7,6]=>[6,7,1,4,5,3,2]=>[2,1,7,4,3,5,6]=>101100
[5,4,1,2,6,3,7]=>[7,1,4,5,3,6,2]=>[1,7,4,3,5,2,6]=>011100
[5,4,1,2,6,7,3]=>[6,1,4,5,3,7,2]=>[2,7,4,3,5,1,6]=>101100
[5,4,1,2,7,3,6]=>[1,4,5,3,7,6,2]=>[7,4,3,5,1,2,6]=>101100
[5,4,1,2,7,6,3]=>[1,4,5,3,6,7,2]=>[7,4,3,5,2,1,6]=>111100
[5,4,1,3,2,6,7]=>[7,6,1,4,5,2,3]=>[1,2,7,4,3,6,5]=>001110
[5,4,1,3,2,7,6]=>[6,7,1,4,5,2,3]=>[2,1,7,4,3,6,5]=>101110
[5,4,1,3,6,2,7]=>[7,1,4,5,3,2,6]=>[1,7,4,3,5,6,2]=>011100
[5,4,1,3,6,7,2]=>[6,1,4,5,3,2,7]=>[2,7,4,3,5,6,1]=>101100
[5,4,1,3,7,2,6]=>[1,4,5,3,2,7,6]=>[7,4,3,5,6,1,2]=>101100
[5,4,1,3,7,6,2]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>111100
[5,4,1,6,2,3,7]=>[7,1,4,5,2,6,3]=>[1,7,4,3,6,2,5]=>011100
[5,4,1,6,2,7,3]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>111100
[5,4,1,6,3,2,7]=>[7,1,4,5,2,3,6]=>[1,7,4,3,6,5,2]=>011110
[5,4,1,6,3,7,2]=>[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>111100
[5,4,1,6,7,2,3]=>[6,1,4,5,2,7,3]=>[2,7,4,3,6,1,5]=>101100
[5,4,1,6,7,3,2]=>[6,1,4,5,2,3,7]=>[2,7,4,3,6,5,1]=>101110
[5,4,1,7,2,3,6]=>[1,4,5,2,7,6,3]=>[7,4,3,6,1,2,5]=>101100
[5,4,1,7,2,6,3]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>111100
[5,4,1,7,3,2,6]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>101110
[5,4,1,7,3,6,2]=>[1,4,5,3,7,2,6]=>[7,4,3,5,1,6,2]=>111100
[5,4,1,7,6,2,3]=>[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]=>111100
[5,4,1,7,6,3,2]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>111110
[5,4,2,1,3,6,7]=>[7,6,1,2,4,5,3]=>[1,2,7,6,4,3,5]=>001101
[5,4,2,1,3,7,6]=>[6,7,1,2,4,5,3]=>[2,1,7,6,4,3,5]=>101101
[5,4,2,1,6,3,7]=>[7,1,2,4,5,3,6]=>[1,7,6,4,3,5,2]=>011101
[5,4,2,1,6,7,3]=>[6,1,2,4,5,3,7]=>[2,7,6,4,3,5,1]=>101101
[5,4,2,1,7,3,6]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>101101
[5,4,2,1,7,6,3]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>111101
[5,4,2,3,1,6,7]=>[7,6,2,4,5,1,3]=>[1,2,6,4,3,7,5]=>001110
[5,4,2,3,1,7,6]=>[6,7,2,4,5,1,3]=>[2,1,6,4,3,7,5]=>101110
[5,4,2,3,6,1,7]=>[7,2,4,5,3,1,6]=>[1,6,4,3,5,7,2]=>011100
[5,4,2,3,6,7,1]=>[6,2,4,5,3,1,7]=>[2,6,4,3,5,7,1]=>101100
[5,4,2,3,7,1,6]=>[2,4,5,3,1,7,6]=>[6,4,3,5,7,1,2]=>101100
[5,4,2,3,7,6,1]=>[2,4,5,3,1,6,7]=>[6,4,3,5,7,2,1]=>111100
[5,4,2,6,1,3,7]=>[7,2,4,5,1,6,3]=>[1,6,4,3,7,2,5]=>011100
[5,4,2,6,1,7,3]=>[2,4,5,1,6,3,7]=>[6,4,3,7,2,5,1]=>111100
[5,4,2,6,3,1,7]=>[7,2,4,5,1,3,6]=>[1,6,4,3,7,5,2]=>011110
[5,4,2,6,3,7,1]=>[2,4,5,3,6,1,7]=>[6,4,3,5,2,7,1]=>111100
[5,4,2,6,7,1,3]=>[6,2,4,5,1,7,3]=>[2,6,4,3,7,1,5]=>101100
[5,4,2,6,7,3,1]=>[6,2,4,5,1,3,7]=>[2,6,4,3,7,5,1]=>101110
[5,4,2,7,1,3,6]=>[2,4,5,1,7,6,3]=>[6,4,3,7,1,2,5]=>101100
[5,4,2,7,1,6,3]=>[2,4,5,1,7,3,6]=>[6,4,3,7,1,5,2]=>111100
[5,4,2,7,3,1,6]=>[2,4,5,1,3,7,6]=>[6,4,3,7,5,1,2]=>101110
[5,4,2,7,3,6,1]=>[2,4,5,3,7,1,6]=>[6,4,3,5,1,7,2]=>111100
[5,4,2,7,6,1,3]=>[2,4,5,1,6,7,3]=>[6,4,3,7,2,1,5]=>111100
[5,4,2,7,6,3,1]=>[2,4,5,1,3,6,7]=>[6,4,3,7,5,2,1]=>111110
[5,4,3,1,2,6,7]=>[7,6,1,3,4,5,2]=>[1,2,7,5,4,3,6]=>001110
[5,4,3,1,2,7,6]=>[6,7,1,3,4,5,2]=>[2,1,7,5,4,3,6]=>101110
[5,4,3,1,6,2,7]=>[7,1,3,4,5,2,6]=>[1,7,5,4,3,6,2]=>011110
[5,4,3,1,6,7,2]=>[6,1,3,4,5,2,7]=>[2,7,5,4,3,6,1]=>101110
[5,4,3,1,7,2,6]=>[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]=>101110
[5,4,3,1,7,6,2]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>111110
[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>001111
[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>101111
[5,4,3,2,6,1,7]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>011110
[5,4,3,2,6,7,1]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>101110
[5,4,3,2,7,1,6]=>[2,3,4,5,1,7,6]=>[6,5,4,3,7,1,2]=>101110
[5,4,3,2,7,6,1]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>111110
[5,4,3,6,1,2,7]=>[7,3,4,5,1,6,2]=>[1,5,4,3,7,2,6]=>011100
[5,4,3,6,1,7,2]=>[3,4,5,1,6,2,7]=>[5,4,3,7,2,6,1]=>111100
[5,4,3,6,2,1,7]=>[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>011101
[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>111100
[5,4,3,6,7,1,2]=>[6,3,4,5,1,7,2]=>[2,5,4,3,7,1,6]=>101100
[5,4,3,6,7,2,1]=>[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>101101
[5,4,3,7,1,2,6]=>[3,4,5,1,7,6,2]=>[5,4,3,7,1,2,6]=>101100
[5,4,3,7,1,6,2]=>[3,4,5,1,7,2,6]=>[5,4,3,7,1,6,2]=>111100
[5,4,3,7,2,1,6]=>[3,4,5,1,2,7,6]=>[5,4,3,7,6,1,2]=>101101
[5,4,3,7,2,6,1]=>[3,4,5,2,7,1,6]=>[5,4,3,6,1,7,2]=>111100
[5,4,3,7,6,1,2]=>[3,4,5,1,6,7,2]=>[5,4,3,7,2,1,6]=>111100
[5,4,3,7,6,2,1]=>[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>111101
[5,4,6,1,2,3,7]=>[7,4,5,1,6,3,2]=>[1,4,3,7,2,5,6]=>011000
[5,4,6,1,2,7,3]=>[4,5,1,6,3,7,2]=>[4,3,7,2,5,1,6]=>111000
[5,4,6,1,3,2,7]=>[7,4,5,1,6,2,3]=>[1,4,3,7,2,6,5]=>011010
[5,4,6,1,3,7,2]=>[4,5,1,6,3,2,7]=>[4,3,7,2,5,6,1]=>111000
[5,4,6,1,7,2,3]=>[4,5,1,6,2,7,3]=>[4,3,7,2,6,1,5]=>111000
[5,4,6,1,7,3,2]=>[4,5,1,6,2,3,7]=>[4,3,7,2,6,5,1]=>111010
[5,4,6,2,1,3,7]=>[7,4,5,1,2,6,3]=>[1,4,3,7,6,2,5]=>011001
[5,4,6,2,1,7,3]=>[4,5,1,2,6,3,7]=>[4,3,7,6,2,5,1]=>111001
[5,4,6,2,3,1,7]=>[7,4,5,2,6,1,3]=>[1,4,3,6,2,7,5]=>011010
[5,4,6,2,3,7,1]=>[4,5,2,6,3,1,7]=>[4,3,6,2,5,7,1]=>111000
[5,4,6,2,7,1,3]=>[4,5,2,6,1,7,3]=>[4,3,6,2,7,1,5]=>111000
[5,4,6,2,7,3,1]=>[4,5,2,6,1,3,7]=>[4,3,6,2,7,5,1]=>111010
[5,4,6,3,1,2,7]=>[7,4,5,1,3,6,2]=>[1,4,3,7,5,2,6]=>011010
[5,4,6,3,1,7,2]=>[4,5,1,3,6,2,7]=>[4,3,7,5,2,6,1]=>111010
[5,4,6,3,2,1,7]=>[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>011011
[5,4,6,3,2,7,1]=>[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>111010
[5,4,6,3,7,1,2]=>[4,5,3,6,1,7,2]=>[4,3,5,2,7,1,6]=>111000
[5,4,6,3,7,2,1]=>[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>111001
[5,4,6,7,1,2,3]=>[6,4,5,1,7,3,2]=>[2,4,3,7,1,5,6]=>101000
[5,4,6,7,1,3,2]=>[6,4,5,1,7,2,3]=>[2,4,3,7,1,6,5]=>101010
[5,4,6,7,2,1,3]=>[6,4,5,1,2,7,3]=>[2,4,3,7,6,1,5]=>101001
[5,4,6,7,2,3,1]=>[6,4,5,2,7,1,3]=>[2,4,3,6,1,7,5]=>101010
[5,4,6,7,3,1,2]=>[6,4,5,1,3,7,2]=>[2,4,3,7,5,1,6]=>101010
[5,4,6,7,3,2,1]=>[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>101011
[5,4,7,1,2,3,6]=>[4,5,1,7,6,3,2]=>[4,3,7,1,2,5,6]=>101000
[5,4,7,1,2,6,3]=>[4,5,1,7,3,6,2]=>[4,3,7,1,5,2,6]=>111000
[5,4,7,1,3,2,6]=>[4,5,1,7,6,2,3]=>[4,3,7,1,2,6,5]=>101010
[5,4,7,1,3,6,2]=>[4,5,1,7,3,2,6]=>[4,3,7,1,5,6,2]=>111000
[5,4,7,1,6,2,3]=>[4,5,1,7,2,6,3]=>[4,3,7,1,6,2,5]=>111000
[5,4,7,1,6,3,2]=>[4,5,1,7,2,3,6]=>[4,3,7,1,6,5,2]=>111010
[5,4,7,2,1,3,6]=>[4,5,1,2,7,6,3]=>[4,3,7,6,1,2,5]=>101001
[5,4,7,2,1,6,3]=>[4,5,1,2,7,3,6]=>[4,3,7,6,1,5,2]=>111001
[5,4,7,2,3,1,6]=>[4,5,2,7,6,1,3]=>[4,3,6,1,2,7,5]=>101010
[5,4,7,2,3,6,1]=>[4,5,2,7,3,1,6]=>[4,3,6,1,5,7,2]=>111000
[5,4,7,2,6,1,3]=>[4,5,2,7,1,6,3]=>[4,3,6,1,7,2,5]=>111000
[5,4,7,2,6,3,1]=>[4,5,2,7,1,3,6]=>[4,3,6,1,7,5,2]=>111010
[5,4,7,3,1,2,6]=>[4,5,1,3,7,6,2]=>[4,3,7,5,1,2,6]=>101010
[5,4,7,3,1,6,2]=>[4,5,1,3,7,2,6]=>[4,3,7,5,1,6,2]=>111010
[5,4,7,3,2,1,6]=>[4,5,1,2,3,7,6]=>[4,3,7,6,5,1,2]=>101011
[5,4,7,3,2,6,1]=>[4,5,2,3,7,1,6]=>[4,3,6,5,1,7,2]=>111010
[5,4,7,3,6,1,2]=>[4,5,3,7,1,6,2]=>[4,3,5,1,7,2,6]=>111000
[5,4,7,3,6,2,1]=>[4,5,3,7,1,2,6]=>[4,3,5,1,7,6,2]=>111001
[5,4,7,6,1,2,3]=>[4,5,1,6,7,3,2]=>[4,3,7,2,1,5,6]=>111000
[5,4,7,6,1,3,2]=>[4,5,1,6,7,2,3]=>[4,3,7,2,1,6,5]=>111010
[5,4,7,6,2,1,3]=>[4,5,1,2,6,7,3]=>[4,3,7,6,2,1,5]=>111001
[5,4,7,6,2,3,1]=>[4,5,2,6,7,1,3]=>[4,3,6,2,1,7,5]=>111010
[5,4,7,6,3,1,2]=>[4,5,1,3,6,7,2]=>[4,3,7,5,2,1,6]=>111010
[5,4,7,6,3,2,1]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>111011
[5,6,1,2,3,4,7]=>[7,5,1,6,4,3,2]=>[1,3,7,2,4,5,6]=>010000
[5,6,1,2,3,7,4]=>[5,1,6,4,7,3,2]=>[3,7,2,4,1,5,6]=>110000
[5,6,1,2,4,3,7]=>[7,5,1,6,3,4,2]=>[1,3,7,2,5,4,6]=>010100
[5,6,1,2,4,7,3]=>[5,1,6,4,3,7,2]=>[3,7,2,4,5,1,6]=>110000
[5,6,1,2,7,3,4]=>[5,1,6,3,7,4,2]=>[3,7,2,5,1,4,6]=>110000
[5,6,1,2,7,4,3]=>[5,1,6,3,4,7,2]=>[3,7,2,5,4,1,6]=>110100
[5,6,1,3,2,4,7]=>[7,5,1,6,4,2,3]=>[1,3,7,2,4,6,5]=>010010
[5,6,1,3,2,7,4]=>[5,1,6,4,7,2,3]=>[3,7,2,4,1,6,5]=>110010
[5,6,1,3,4,2,7]=>[7,5,1,6,3,2,4]=>[1,3,7,2,5,6,4]=>010100
[5,6,1,3,4,7,2]=>[5,1,6,4,3,2,7]=>[3,7,2,4,5,6,1]=>110000
[5,6,1,3,7,2,4]=>[5,1,6,3,2,7,4]=>[3,7,2,5,6,1,4]=>110000
[5,6,1,3,7,4,2]=>[5,1,6,3,2,4,7]=>[3,7,2,5,6,4,1]=>110100
[5,6,1,4,2,3,7]=>[7,5,1,6,2,4,3]=>[1,3,7,2,6,4,5]=>010100
[5,6,1,4,2,7,3]=>[5,1,6,2,4,3,7]=>[3,7,2,6,4,5,1]=>110100
[5,6,1,4,3,2,7]=>[7,5,1,6,2,3,4]=>[1,3,7,2,6,5,4]=>010110
[5,6,1,4,3,7,2]=>[5,1,6,3,4,2,7]=>[3,7,2,5,4,6,1]=>110100
[5,6,1,4,7,2,3]=>[5,1,6,4,2,7,3]=>[3,7,2,4,6,1,5]=>110000
[5,6,1,4,7,3,2]=>[5,1,6,4,2,3,7]=>[3,7,2,4,6,5,1]=>110010
[5,6,1,7,2,3,4]=>[5,1,6,2,7,4,3]=>[3,7,2,6,1,4,5]=>110000
[5,6,1,7,2,4,3]=>[5,1,6,2,7,3,4]=>[3,7,2,6,1,5,4]=>110100
[5,6,1,7,3,2,4]=>[5,1,6,2,3,7,4]=>[3,7,2,6,5,1,4]=>110010
[5,6,1,7,3,4,2]=>[5,1,6,3,7,2,4]=>[3,7,2,5,1,6,4]=>110100
[5,6,1,7,4,2,3]=>[5,1,6,2,4,7,3]=>[3,7,2,6,4,1,5]=>110100
[5,6,1,7,4,3,2]=>[5,1,6,2,3,4,7]=>[3,7,2,6,5,4,1]=>110110
[5,6,2,1,3,4,7]=>[7,5,1,2,6,4,3]=>[1,3,7,6,2,4,5]=>010001
[5,6,2,1,3,7,4]=>[5,1,2,6,4,7,3]=>[3,7,6,2,4,1,5]=>110001
[5,6,2,1,4,3,7]=>[7,5,1,2,6,3,4]=>[1,3,7,6,2,5,4]=>010101
[5,6,2,1,4,7,3]=>[5,1,2,6,4,3,7]=>[3,7,6,2,4,5,1]=>110001
[5,6,2,1,7,3,4]=>[5,1,2,6,3,7,4]=>[3,7,6,2,5,1,4]=>110001
[5,6,2,1,7,4,3]=>[5,1,2,6,3,4,7]=>[3,7,6,2,5,4,1]=>110101
[5,6,2,3,1,4,7]=>[7,5,2,6,4,1,3]=>[1,3,6,2,4,7,5]=>010010
[5,6,2,3,1,7,4]=>[5,2,6,4,7,1,3]=>[3,6,2,4,1,7,5]=>110010
[5,6,2,3,4,1,7]=>[7,5,2,6,3,1,4]=>[1,3,6,2,5,7,4]=>010100
[5,6,2,3,4,7,1]=>[5,2,6,4,3,1,7]=>[3,6,2,4,5,7,1]=>110000
[5,6,2,3,7,1,4]=>[5,2,6,3,1,7,4]=>[3,6,2,5,7,1,4]=>110000
[5,6,2,3,7,4,1]=>[5,2,6,3,1,4,7]=>[3,6,2,5,7,4,1]=>110100
[5,6,2,4,1,3,7]=>[7,5,2,6,1,4,3]=>[1,3,6,2,7,4,5]=>010100
[5,6,2,4,1,7,3]=>[5,2,6,1,4,3,7]=>[3,6,2,7,4,5,1]=>110100
[5,6,2,4,3,1,7]=>[7,5,2,6,1,3,4]=>[1,3,6,2,7,5,4]=>010110
[5,6,2,4,3,7,1]=>[5,2,6,3,4,1,7]=>[3,6,2,5,4,7,1]=>110100
[5,6,2,4,7,1,3]=>[5,2,6,4,1,7,3]=>[3,6,2,4,7,1,5]=>110000
[5,6,2,4,7,3,1]=>[5,2,6,4,1,3,7]=>[3,6,2,4,7,5,1]=>110010
[5,6,2,7,1,3,4]=>[5,2,6,1,7,4,3]=>[3,6,2,7,1,4,5]=>110000
[5,6,2,7,1,4,3]=>[5,2,6,1,7,3,4]=>[3,6,2,7,1,5,4]=>110100
[5,6,2,7,3,1,4]=>[5,2,6,1,3,7,4]=>[3,6,2,7,5,1,4]=>110010
[5,6,2,7,3,4,1]=>[5,2,6,3,7,1,4]=>[3,6,2,5,1,7,4]=>110100
[5,6,2,7,4,1,3]=>[5,2,6,1,4,7,3]=>[3,6,2,7,4,1,5]=>110100
[5,6,2,7,4,3,1]=>[5,2,6,1,3,4,7]=>[3,6,2,7,5,4,1]=>110110
[5,6,3,1,2,4,7]=>[7,5,1,3,6,4,2]=>[1,3,7,5,2,4,6]=>010010
[5,6,3,1,2,7,4]=>[5,1,3,6,4,7,2]=>[3,7,5,2,4,1,6]=>110010
[5,6,3,1,4,2,7]=>[7,5,1,3,6,2,4]=>[1,3,7,5,2,6,4]=>010110
[5,6,3,1,4,7,2]=>[5,1,3,6,4,2,7]=>[3,7,5,2,4,6,1]=>110010
[5,6,3,1,7,2,4]=>[5,1,3,6,2,7,4]=>[3,7,5,2,6,1,4]=>110010
[5,6,3,1,7,4,2]=>[5,1,3,6,2,4,7]=>[3,7,5,2,6,4,1]=>110110
[5,6,3,2,1,4,7]=>[7,5,1,2,3,6,4]=>[1,3,7,6,5,2,4]=>010011
[5,6,3,2,1,7,4]=>[5,1,2,3,6,4,7]=>[3,7,6,5,2,4,1]=>110011
[5,6,3,2,4,1,7]=>[7,5,2,3,6,1,4]=>[1,3,6,5,2,7,4]=>010110
[5,6,3,2,4,7,1]=>[5,2,3,6,4,1,7]=>[3,6,5,2,4,7,1]=>110010
[5,6,3,2,7,1,4]=>[5,2,3,6,1,7,4]=>[3,6,5,2,7,1,4]=>110010
[5,6,3,2,7,4,1]=>[5,2,3,6,1,4,7]=>[3,6,5,2,7,4,1]=>110110
[5,6,3,4,1,2,7]=>[7,5,3,6,1,4,2]=>[1,3,5,2,7,4,6]=>010100
[5,6,3,4,1,7,2]=>[5,3,6,1,4,2,7]=>[3,5,2,7,4,6,1]=>110100
[5,6,3,4,2,1,7]=>[7,5,3,6,1,2,4]=>[1,3,5,2,7,6,4]=>010101
[5,6,3,4,2,7,1]=>[5,3,6,2,4,1,7]=>[3,5,2,6,4,7,1]=>110100
[5,6,3,4,7,1,2]=>[5,3,6,4,1,7,2]=>[3,5,2,4,7,1,6]=>110000
[5,6,3,4,7,2,1]=>[5,3,6,4,1,2,7]=>[3,5,2,4,7,6,1]=>110001
[5,6,3,7,1,2,4]=>[5,3,6,1,7,4,2]=>[3,5,2,7,1,4,6]=>110000
[5,6,3,7,1,4,2]=>[5,3,6,1,7,2,4]=>[3,5,2,7,1,6,4]=>110100
[5,6,3,7,2,1,4]=>[5,3,6,1,2,7,4]=>[3,5,2,7,6,1,4]=>110001
[5,6,3,7,2,4,1]=>[5,3,6,2,7,1,4]=>[3,5,2,6,1,7,4]=>110100
[5,6,3,7,4,1,2]=>[5,3,6,1,4,7,2]=>[3,5,2,7,4,1,6]=>110100
[5,6,3,7,4,2,1]=>[5,3,6,1,2,4,7]=>[3,5,2,7,6,4,1]=>110101
[5,6,4,1,2,3,7]=>[7,5,1,4,6,3,2]=>[1,3,7,4,2,5,6]=>010100
[5,6,4,1,2,7,3]=>[5,1,4,6,3,7,2]=>[3,7,4,2,5,1,6]=>110100
[5,6,4,1,3,2,7]=>[7,5,1,4,6,2,3]=>[1,3,7,4,2,6,5]=>010110
[5,6,4,1,3,7,2]=>[5,1,4,6,3,2,7]=>[3,7,4,2,5,6,1]=>110100
[5,6,4,1,7,2,3]=>[5,1,4,6,2,7,3]=>[3,7,4,2,6,1,5]=>110100
[5,6,4,1,7,3,2]=>[5,1,4,6,2,3,7]=>[3,7,4,2,6,5,1]=>110110
[5,6,4,2,1,3,7]=>[7,5,1,2,4,6,3]=>[1,3,7,6,4,2,5]=>010101
[5,6,4,2,1,7,3]=>[5,1,2,4,6,3,7]=>[3,7,6,4,2,5,1]=>110101
[5,6,4,2,3,1,7]=>[7,5,2,4,6,1,3]=>[1,3,6,4,2,7,5]=>010110
[5,6,4,2,3,7,1]=>[5,2,4,6,3,1,7]=>[3,6,4,2,5,7,1]=>110100
[5,6,4,2,7,1,3]=>[5,2,4,6,1,7,3]=>[3,6,4,2,7,1,5]=>110100
[5,6,4,2,7,3,1]=>[5,2,4,6,1,3,7]=>[3,6,4,2,7,5,1]=>110110
[5,6,4,3,1,2,7]=>[7,5,1,3,4,6,2]=>[1,3,7,5,4,2,6]=>010110
[5,6,4,3,1,7,2]=>[5,1,3,4,6,2,7]=>[3,7,5,4,2,6,1]=>110110
[5,6,4,3,2,1,7]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>010111
[5,6,4,3,2,7,1]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>110110
[5,6,4,3,7,1,2]=>[5,3,4,6,1,7,2]=>[3,5,4,2,7,1,6]=>110100
[5,6,4,3,7,2,1]=>[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>110101
[5,6,4,7,1,2,3]=>[5,4,6,1,7,3,2]=>[3,4,2,7,1,5,6]=>110000
[5,6,4,7,1,3,2]=>[5,4,6,1,7,2,3]=>[3,4,2,7,1,6,5]=>110010
[5,6,4,7,2,1,3]=>[5,4,6,1,2,7,3]=>[3,4,2,7,6,1,5]=>110001
[5,6,4,7,2,3,1]=>[5,4,6,2,7,1,3]=>[3,4,2,6,1,7,5]=>110010
[5,6,4,7,3,1,2]=>[5,4,6,1,3,7,2]=>[3,4,2,7,5,1,6]=>110010
[5,6,4,7,3,2,1]=>[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>110011
[5,6,7,1,2,3,4]=>[6,5,1,7,4,3,2]=>[2,3,7,1,4,5,6]=>100000
[5,6,7,1,2,4,3]=>[6,5,1,7,3,4,2]=>[2,3,7,1,5,4,6]=>100100
[5,6,7,1,3,2,4]=>[6,5,1,7,4,2,3]=>[2,3,7,1,4,6,5]=>100010
[5,6,7,1,3,4,2]=>[6,5,1,7,3,2,4]=>[2,3,7,1,5,6,4]=>100100
[5,6,7,1,4,2,3]=>[6,5,1,7,2,4,3]=>[2,3,7,1,6,4,5]=>100100
[5,6,7,1,4,3,2]=>[6,5,1,7,2,3,4]=>[2,3,7,1,6,5,4]=>100110
[5,6,7,2,1,3,4]=>[6,5,1,2,7,4,3]=>[2,3,7,6,1,4,5]=>100001
[5,6,7,2,1,4,3]=>[6,5,1,2,7,3,4]=>[2,3,7,6,1,5,4]=>100101
[5,6,7,2,3,1,4]=>[6,5,2,7,4,1,3]=>[2,3,6,1,4,7,5]=>100010
[5,6,7,2,3,4,1]=>[6,5,2,7,3,1,4]=>[2,3,6,1,5,7,4]=>100100
[5,6,7,2,4,1,3]=>[6,5,2,7,1,4,3]=>[2,3,6,1,7,4,5]=>100100
[5,6,7,2,4,3,1]=>[6,5,2,7,1,3,4]=>[2,3,6,1,7,5,4]=>100110
[5,6,7,3,1,2,4]=>[6,5,1,3,7,4,2]=>[2,3,7,5,1,4,6]=>100010
[5,6,7,3,1,4,2]=>[6,5,1,3,7,2,4]=>[2,3,7,5,1,6,4]=>100110
[5,6,7,3,2,1,4]=>[6,5,1,2,3,7,4]=>[2,3,7,6,5,1,4]=>100011
[5,6,7,3,2,4,1]=>[6,5,2,3,7,1,4]=>[2,3,6,5,1,7,4]=>100110
[5,6,7,3,4,1,2]=>[6,5,3,7,1,4,2]=>[2,3,5,1,7,4,6]=>100100
[5,6,7,3,4,2,1]=>[6,5,3,7,1,2,4]=>[2,3,5,1,7,6,4]=>100101
[5,6,7,4,1,2,3]=>[6,5,1,4,7,3,2]=>[2,3,7,4,1,5,6]=>100100
[5,6,7,4,1,3,2]=>[6,5,1,4,7,2,3]=>[2,3,7,4,1,6,5]=>100110
[5,6,7,4,2,1,3]=>[6,5,1,2,4,7,3]=>[2,3,7,6,4,1,5]=>100101
[5,6,7,4,2,3,1]=>[6,5,2,4,7,1,3]=>[2,3,6,4,1,7,5]=>100110
[5,6,7,4,3,1,2]=>[6,5,1,3,4,7,2]=>[2,3,7,5,4,1,6]=>100110
[5,6,7,4,3,2,1]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>100111
[5,7,1,2,3,4,6]=>[5,1,7,6,4,3,2]=>[3,7,1,2,4,5,6]=>100000
[5,7,1,2,3,6,4]=>[5,1,7,4,6,3,2]=>[3,7,1,4,2,5,6]=>110000
[5,7,1,2,4,3,6]=>[5,1,7,6,3,4,2]=>[3,7,1,2,5,4,6]=>100100
[5,7,1,2,4,6,3]=>[5,1,7,4,3,6,2]=>[3,7,1,4,5,2,6]=>110000
[5,7,1,2,6,3,4]=>[5,1,7,3,6,4,2]=>[3,7,1,5,2,4,6]=>110000
[5,7,1,2,6,4,3]=>[5,1,7,3,4,6,2]=>[3,7,1,5,4,2,6]=>110100
[5,7,1,3,2,4,6]=>[5,1,7,6,4,2,3]=>[3,7,1,2,4,6,5]=>100010
[5,7,1,3,2,6,4]=>[5,1,7,4,6,2,3]=>[3,7,1,4,2,6,5]=>110010
[5,7,1,3,4,2,6]=>[5,1,7,6,3,2,4]=>[3,7,1,2,5,6,4]=>100100
[5,7,1,3,4,6,2]=>[5,1,7,4,3,2,6]=>[3,7,1,4,5,6,2]=>110000
[5,7,1,3,6,2,4]=>[5,1,7,3,2,6,4]=>[3,7,1,5,6,2,4]=>110000
[5,7,1,3,6,4,2]=>[5,1,7,3,2,4,6]=>[3,7,1,5,6,4,2]=>110100
[5,7,1,4,2,3,6]=>[5,1,7,6,2,4,3]=>[3,7,1,2,6,4,5]=>100100
[5,7,1,4,2,6,3]=>[5,1,7,2,4,3,6]=>[3,7,1,6,4,5,2]=>110100
[5,7,1,4,3,2,6]=>[5,1,7,6,2,3,4]=>[3,7,1,2,6,5,4]=>100110
[5,7,1,4,3,6,2]=>[5,1,7,3,4,2,6]=>[3,7,1,5,4,6,2]=>110100
[5,7,1,4,6,2,3]=>[5,1,7,4,2,6,3]=>[3,7,1,4,6,2,5]=>110000
[5,7,1,4,6,3,2]=>[5,1,7,4,2,3,6]=>[3,7,1,4,6,5,2]=>110010
[5,7,1,6,2,3,4]=>[5,1,7,2,6,4,3]=>[3,7,1,6,2,4,5]=>110000
[5,7,1,6,2,4,3]=>[5,1,7,2,6,3,4]=>[3,7,1,6,2,5,4]=>110100
[5,7,1,6,3,2,4]=>[5,1,7,2,3,6,4]=>[3,7,1,6,5,2,4]=>110010
[5,7,1,6,3,4,2]=>[5,1,7,3,6,2,4]=>[3,7,1,5,2,6,4]=>110100
[5,7,1,6,4,2,3]=>[5,1,7,2,4,6,3]=>[3,7,1,6,4,2,5]=>110100
[5,7,1,6,4,3,2]=>[5,1,7,2,3,4,6]=>[3,7,1,6,5,4,2]=>110110
[5,7,2,1,3,4,6]=>[5,1,2,7,6,4,3]=>[3,7,6,1,2,4,5]=>100001
[5,7,2,1,3,6,4]=>[5,1,2,7,4,6,3]=>[3,7,6,1,4,2,5]=>110001
[5,7,2,1,4,3,6]=>[5,1,2,7,6,3,4]=>[3,7,6,1,2,5,4]=>100101
[5,7,2,1,4,6,3]=>[5,1,2,7,4,3,6]=>[3,7,6,1,4,5,2]=>110001
[5,7,2,1,6,3,4]=>[5,1,2,7,3,6,4]=>[3,7,6,1,5,2,4]=>110001
[5,7,2,1,6,4,3]=>[5,1,2,7,3,4,6]=>[3,7,6,1,5,4,2]=>110101
[5,7,2,3,1,4,6]=>[5,2,7,6,4,1,3]=>[3,6,1,2,4,7,5]=>100010
[5,7,2,3,1,6,4]=>[5,2,7,4,6,1,3]=>[3,6,1,4,2,7,5]=>110010
[5,7,2,3,4,1,6]=>[5,2,7,6,3,1,4]=>[3,6,1,2,5,7,4]=>100100
[5,7,2,3,4,6,1]=>[5,2,7,4,3,1,6]=>[3,6,1,4,5,7,2]=>110000
[5,7,2,3,6,1,4]=>[5,2,7,3,1,6,4]=>[3,6,1,5,7,2,4]=>110000
[5,7,2,3,6,4,1]=>[5,2,7,3,1,4,6]=>[3,6,1,5,7,4,2]=>110100
[5,7,2,4,1,3,6]=>[5,2,7,6,1,4,3]=>[3,6,1,2,7,4,5]=>100100
[5,7,2,4,1,6,3]=>[5,2,7,1,4,3,6]=>[3,6,1,7,4,5,2]=>110100
[5,7,2,4,3,1,6]=>[5,2,7,6,1,3,4]=>[3,6,1,2,7,5,4]=>100110
[5,7,2,4,3,6,1]=>[5,2,7,3,4,1,6]=>[3,6,1,5,4,7,2]=>110100
[5,7,2,4,6,1,3]=>[5,2,7,4,1,6,3]=>[3,6,1,4,7,2,5]=>110000
[5,7,2,4,6,3,1]=>[5,2,7,4,1,3,6]=>[3,6,1,4,7,5,2]=>110010
[5,7,2,6,1,3,4]=>[5,2,7,1,6,4,3]=>[3,6,1,7,2,4,5]=>110000
[5,7,2,6,1,4,3]=>[5,2,7,1,6,3,4]=>[3,6,1,7,2,5,4]=>110100
[5,7,2,6,3,1,4]=>[5,2,7,1,3,6,4]=>[3,6,1,7,5,2,4]=>110010
[5,7,2,6,3,4,1]=>[5,2,7,3,6,1,4]=>[3,6,1,5,2,7,4]=>110100
[5,7,2,6,4,1,3]=>[5,2,7,1,4,6,3]=>[3,6,1,7,4,2,5]=>110100
[5,7,2,6,4,3,1]=>[5,2,7,1,3,4,6]=>[3,6,1,7,5,4,2]=>110110
[5,7,3,1,2,4,6]=>[5,1,3,7,6,4,2]=>[3,7,5,1,2,4,6]=>100010
[5,7,3,1,2,6,4]=>[5,1,3,7,4,6,2]=>[3,7,5,1,4,2,6]=>110010
[5,7,3,1,4,2,6]=>[5,1,3,7,6,2,4]=>[3,7,5,1,2,6,4]=>100110
[5,7,3,1,4,6,2]=>[5,1,3,7,4,2,6]=>[3,7,5,1,4,6,2]=>110010
[5,7,3,1,6,2,4]=>[5,1,3,7,2,6,4]=>[3,7,5,1,6,2,4]=>110010
[5,7,3,1,6,4,2]=>[5,1,3,7,2,4,6]=>[3,7,5,1,6,4,2]=>110110
[5,7,3,2,1,4,6]=>[5,1,2,3,7,6,4]=>[3,7,6,5,1,2,4]=>100011
[5,7,3,2,1,6,4]=>[5,1,2,3,7,4,6]=>[3,7,6,5,1,4,2]=>110011
[5,7,3,2,4,1,6]=>[5,2,3,7,6,1,4]=>[3,6,5,1,2,7,4]=>100110
[5,7,3,2,4,6,1]=>[5,2,3,7,4,1,6]=>[3,6,5,1,4,7,2]=>110010
[5,7,3,2,6,1,4]=>[5,2,3,7,1,6,4]=>[3,6,5,1,7,2,4]=>110010
[5,7,3,2,6,4,1]=>[5,2,3,7,1,4,6]=>[3,6,5,1,7,4,2]=>110110
[5,7,3,4,1,2,6]=>[5,3,7,6,1,4,2]=>[3,5,1,2,7,4,6]=>100100
[5,7,3,4,1,6,2]=>[5,3,7,1,4,2,6]=>[3,5,1,7,4,6,2]=>110100
[5,7,3,4,2,1,6]=>[5,3,7,6,1,2,4]=>[3,5,1,2,7,6,4]=>100101
[5,7,3,4,2,6,1]=>[5,3,7,2,4,1,6]=>[3,5,1,6,4,7,2]=>110100
[5,7,3,4,6,1,2]=>[5,3,7,4,1,6,2]=>[3,5,1,4,7,2,6]=>110000
[5,7,3,4,6,2,1]=>[5,3,7,4,1,2,6]=>[3,5,1,4,7,6,2]=>110001
[5,7,3,6,1,2,4]=>[5,3,7,1,6,4,2]=>[3,5,1,7,2,4,6]=>110000
[5,7,3,6,1,4,2]=>[5,3,7,1,6,2,4]=>[3,5,1,7,2,6,4]=>110100
[5,7,3,6,2,1,4]=>[5,3,7,1,2,6,4]=>[3,5,1,7,6,2,4]=>110001
[5,7,3,6,2,4,1]=>[5,3,7,2,6,1,4]=>[3,5,1,6,2,7,4]=>110100
[5,7,3,6,4,1,2]=>[5,3,7,1,4,6,2]=>[3,5,1,7,4,2,6]=>110100
[5,7,3,6,4,2,1]=>[5,3,7,1,2,4,6]=>[3,5,1,7,6,4,2]=>110101
[5,7,4,1,2,3,6]=>[5,1,4,7,6,3,2]=>[3,7,4,1,2,5,6]=>100100
[5,7,4,1,2,6,3]=>[5,1,4,7,3,6,2]=>[3,7,4,1,5,2,6]=>110100
[5,7,4,1,3,2,6]=>[5,1,4,7,6,2,3]=>[3,7,4,1,2,6,5]=>100110
[5,7,4,1,3,6,2]=>[5,1,4,7,3,2,6]=>[3,7,4,1,5,6,2]=>110100
[5,7,4,1,6,2,3]=>[5,1,4,7,2,6,3]=>[3,7,4,1,6,2,5]=>110100
[5,7,4,1,6,3,2]=>[5,1,4,7,2,3,6]=>[3,7,4,1,6,5,2]=>110110
[5,7,4,2,1,3,6]=>[5,1,2,4,7,6,3]=>[3,7,6,4,1,2,5]=>100101
[5,7,4,2,1,6,3]=>[5,1,2,4,7,3,6]=>[3,7,6,4,1,5,2]=>110101
[5,7,4,2,3,1,6]=>[5,2,4,7,6,1,3]=>[3,6,4,1,2,7,5]=>100110
[5,7,4,2,3,6,1]=>[5,2,4,7,3,1,6]=>[3,6,4,1,5,7,2]=>110100
[5,7,4,2,6,1,3]=>[5,2,4,7,1,6,3]=>[3,6,4,1,7,2,5]=>110100
[5,7,4,2,6,3,1]=>[5,2,4,7,1,3,6]=>[3,6,4,1,7,5,2]=>110110
[5,7,4,3,1,2,6]=>[5,1,3,4,7,6,2]=>[3,7,5,4,1,2,6]=>100110
[5,7,4,3,1,6,2]=>[5,1,3,4,7,2,6]=>[3,7,5,4,1,6,2]=>110110
[5,7,4,3,2,1,6]=>[5,1,2,3,4,7,6]=>[3,7,6,5,4,1,2]=>100111
[5,7,4,3,2,6,1]=>[5,2,3,4,7,1,6]=>[3,6,5,4,1,7,2]=>110110
[5,7,4,3,6,1,2]=>[5,3,4,7,1,6,2]=>[3,5,4,1,7,2,6]=>110100
[5,7,4,3,6,2,1]=>[5,3,4,7,1,2,6]=>[3,5,4,1,7,6,2]=>110101
[5,7,4,6,1,2,3]=>[5,4,7,1,6,3,2]=>[3,4,1,7,2,5,6]=>110000
[5,7,4,6,1,3,2]=>[5,4,7,1,6,2,3]=>[3,4,1,7,2,6,5]=>110010
[5,7,4,6,2,1,3]=>[5,4,7,1,2,6,3]=>[3,4,1,7,6,2,5]=>110001
[5,7,4,6,2,3,1]=>[5,4,7,2,6,1,3]=>[3,4,1,6,2,7,5]=>110010
[5,7,4,6,3,1,2]=>[5,4,7,1,3,6,2]=>[3,4,1,7,5,2,6]=>110010
[5,7,4,6,3,2,1]=>[5,4,7,1,2,3,6]=>[3,4,1,7,6,5,2]=>110011
[5,7,6,1,2,3,4]=>[5,1,6,7,4,3,2]=>[3,7,2,1,4,5,6]=>110000
[5,7,6,1,2,4,3]=>[5,1,6,7,3,4,2]=>[3,7,2,1,5,4,6]=>110100
[5,7,6,1,3,2,4]=>[5,1,6,7,4,2,3]=>[3,7,2,1,4,6,5]=>110010
[5,7,6,1,3,4,2]=>[5,1,6,7,3,2,4]=>[3,7,2,1,5,6,4]=>110100
[5,7,6,1,4,2,3]=>[5,1,6,7,2,4,3]=>[3,7,2,1,6,4,5]=>110100
[5,7,6,1,4,3,2]=>[5,1,6,7,2,3,4]=>[3,7,2,1,6,5,4]=>110110
[5,7,6,2,1,3,4]=>[5,1,2,6,7,4,3]=>[3,7,6,2,1,4,5]=>110001
[5,7,6,2,1,4,3]=>[5,1,2,6,7,3,4]=>[3,7,6,2,1,5,4]=>110101
[5,7,6,2,3,1,4]=>[5,2,6,7,4,1,3]=>[3,6,2,1,4,7,5]=>110010
[5,7,6,2,3,4,1]=>[5,2,6,7,3,1,4]=>[3,6,2,1,5,7,4]=>110100
[5,7,6,2,4,1,3]=>[5,2,6,7,1,4,3]=>[3,6,2,1,7,4,5]=>110100
[5,7,6,2,4,3,1]=>[5,2,6,7,1,3,4]=>[3,6,2,1,7,5,4]=>110110
[5,7,6,3,1,2,4]=>[5,1,3,6,7,4,2]=>[3,7,5,2,1,4,6]=>110010
[5,7,6,3,1,4,2]=>[5,1,3,6,7,2,4]=>[3,7,5,2,1,6,4]=>110110
[5,7,6,3,2,1,4]=>[5,1,2,3,6,7,4]=>[3,7,6,5,2,1,4]=>110011
[5,7,6,3,2,4,1]=>[5,2,3,6,7,1,4]=>[3,6,5,2,1,7,4]=>110110
[5,7,6,3,4,1,2]=>[5,3,6,7,1,4,2]=>[3,5,2,1,7,4,6]=>110100
[5,7,6,3,4,2,1]=>[5,3,6,7,1,2,4]=>[3,5,2,1,7,6,4]=>110101
[5,7,6,4,1,2,3]=>[5,1,4,6,7,3,2]=>[3,7,4,2,1,5,6]=>110100
[5,7,6,4,1,3,2]=>[5,1,4,6,7,2,3]=>[3,7,4,2,1,6,5]=>110110
[5,7,6,4,2,1,3]=>[5,1,2,4,6,7,3]=>[3,7,6,4,2,1,5]=>110101
[5,7,6,4,2,3,1]=>[5,2,4,6,7,1,3]=>[3,6,4,2,1,7,5]=>110110
[5,7,6,4,3,1,2]=>[5,1,3,4,6,7,2]=>[3,7,5,4,2,1,6]=>110110
[5,7,6,4,3,2,1]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>110111
[6,1,2,3,4,5,7]=>[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>010000
[6,1,2,3,4,7,5]=>[1,6,5,7,4,3,2]=>[7,2,3,1,4,5,6]=>110000
[6,1,2,3,5,4,7]=>[7,1,6,4,5,3,2]=>[1,7,2,4,3,5,6]=>011000
[6,1,2,3,5,7,4]=>[1,6,5,4,7,3,2]=>[7,2,3,4,1,5,6]=>110000
[6,1,2,3,7,4,5]=>[1,6,4,7,5,3,2]=>[7,2,4,1,3,5,6]=>110000
[6,1,2,3,7,5,4]=>[1,6,4,5,7,3,2]=>[7,2,4,3,1,5,6]=>111000
[6,1,2,4,3,5,7]=>[7,1,6,5,3,4,2]=>[1,7,2,3,5,4,6]=>010100
[6,1,2,4,3,7,5]=>[1,6,5,7,3,4,2]=>[7,2,3,1,5,4,6]=>110100
[6,1,2,4,5,3,7]=>[7,1,6,4,3,5,2]=>[1,7,2,4,5,3,6]=>011000
[6,1,2,4,5,7,3]=>[1,6,5,4,3,7,2]=>[7,2,3,4,5,1,6]=>110000
[6,1,2,4,7,3,5]=>[1,6,4,3,7,5,2]=>[7,2,4,5,1,3,6]=>110000
[6,1,2,4,7,5,3]=>[1,6,4,3,5,7,2]=>[7,2,4,5,3,1,6]=>111000
[6,1,2,5,3,4,7]=>[7,1,6,3,5,4,2]=>[1,7,2,5,3,4,6]=>011000
[6,1,2,5,3,7,4]=>[1,6,3,5,4,7,2]=>[7,2,5,3,4,1,6]=>111000
[6,1,2,5,4,3,7]=>[7,1,6,3,4,5,2]=>[1,7,2,5,4,3,6]=>011100
[6,1,2,5,4,7,3]=>[1,6,4,5,3,7,2]=>[7,2,4,3,5,1,6]=>111000
[6,1,2,5,7,3,4]=>[1,6,5,3,7,4,2]=>[7,2,3,5,1,4,6]=>110000
[6,1,2,5,7,4,3]=>[1,6,5,3,4,7,2]=>[7,2,3,5,4,1,6]=>110100
[6,1,2,7,3,4,5]=>[1,6,3,7,5,4,2]=>[7,2,5,1,3,4,6]=>110000
[6,1,2,7,3,5,4]=>[1,6,3,7,4,5,2]=>[7,2,5,1,4,3,6]=>111000
[6,1,2,7,4,3,5]=>[1,6,3,4,7,5,2]=>[7,2,5,4,1,3,6]=>110100
[6,1,2,7,4,5,3]=>[1,6,4,7,3,5,2]=>[7,2,4,1,5,3,6]=>111000
[6,1,2,7,5,3,4]=>[1,6,3,5,7,4,2]=>[7,2,5,3,1,4,6]=>111000
[6,1,2,7,5,4,3]=>[1,6,3,4,5,7,2]=>[7,2,5,4,3,1,6]=>111100
[6,1,3,2,4,5,7]=>[7,1,6,5,4,2,3]=>[1,7,2,3,4,6,5]=>010010
[6,1,3,2,4,7,5]=>[1,6,5,7,4,2,3]=>[7,2,3,1,4,6,5]=>110010
[6,1,3,2,5,4,7]=>[7,1,6,4,5,2,3]=>[1,7,2,4,3,6,5]=>011010
[6,1,3,2,5,7,4]=>[1,6,5,4,7,2,3]=>[7,2,3,4,1,6,5]=>110010
[6,1,3,2,7,4,5]=>[1,6,4,7,5,2,3]=>[7,2,4,1,3,6,5]=>110010
[6,1,3,2,7,5,4]=>[1,6,4,5,7,2,3]=>[7,2,4,3,1,6,5]=>111010
[6,1,3,4,2,5,7]=>[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>010100
[6,1,3,4,2,7,5]=>[1,6,5,7,3,2,4]=>[7,2,3,1,5,6,4]=>110100
[6,1,3,4,5,2,7]=>[7,1,6,4,3,2,5]=>[1,7,2,4,5,6,3]=>011000
[6,1,3,4,5,7,2]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>110000
[6,1,3,4,7,2,5]=>[1,6,4,3,2,7,5]=>[7,2,4,5,6,1,3]=>110000
[6,1,3,4,7,5,2]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>111000
[6,1,3,5,2,4,7]=>[7,1,6,3,2,5,4]=>[1,7,2,5,6,3,4]=>011000
[6,1,3,5,2,7,4]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>111000
[6,1,3,5,4,2,7]=>[7,1,6,3,2,4,5]=>[1,7,2,5,6,4,3]=>011100
[6,1,3,5,4,7,2]=>[1,6,4,5,3,2,7]=>[7,2,4,3,5,6,1]=>111000
[6,1,3,5,7,2,4]=>[1,6,5,3,2,7,4]=>[7,2,3,5,6,1,4]=>110000
[6,1,3,5,7,4,2]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>110100
[6,1,3,7,2,4,5]=>[1,6,3,2,7,5,4]=>[7,2,5,6,1,3,4]=>110000
[6,1,3,7,2,5,4]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>111000
[6,1,3,7,4,2,5]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>110100
[6,1,3,7,4,5,2]=>[1,6,4,7,3,2,5]=>[7,2,4,1,5,6,3]=>111000
[6,1,3,7,5,2,4]=>[1,6,3,2,5,7,4]=>[7,2,5,6,3,1,4]=>111000
[6,1,3,7,5,4,2]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>111100
[6,1,4,2,3,5,7]=>[7,1,6,5,2,4,3]=>[1,7,2,3,6,4,5]=>010100
[6,1,4,2,3,7,5]=>[1,6,5,7,2,4,3]=>[7,2,3,1,6,4,5]=>110100
[6,1,4,2,5,3,7]=>[7,1,6,2,4,3,5]=>[1,7,2,6,4,5,3]=>011100
[6,1,4,2,5,7,3]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>110100
[6,1,4,2,7,3,5]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>110100
[6,1,4,2,7,5,3]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>111100
[6,1,4,3,2,5,7]=>[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>010110
[6,1,4,3,2,7,5]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>110110
[6,1,4,3,5,2,7]=>[7,1,6,3,4,2,5]=>[1,7,2,5,4,6,3]=>011100
[6,1,4,3,5,7,2]=>[1,6,5,3,4,2,7]=>[7,2,3,5,4,6,1]=>110100
[6,1,4,3,7,2,5]=>[1,6,3,4,2,7,5]=>[7,2,5,4,6,1,3]=>110100
[6,1,4,3,7,5,2]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>111100
[6,1,4,5,2,3,7]=>[7,1,6,4,2,5,3]=>[1,7,2,4,6,3,5]=>011000
[6,1,4,5,2,7,3]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>111000
[6,1,4,5,3,2,7]=>[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>011010
[6,1,4,5,3,7,2]=>[1,6,4,3,5,2,7]=>[7,2,4,5,3,6,1]=>111000
[6,1,4,5,7,2,3]=>[1,6,5,4,2,7,3]=>[7,2,3,4,6,1,5]=>110000
[6,1,4,5,7,3,2]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>110010
[6,1,4,7,2,3,5]=>[1,6,4,2,7,5,3]=>[7,2,4,6,1,3,5]=>110000
[6,1,4,7,2,5,3]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>111000
[6,1,4,7,3,2,5]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>110010
[6,1,4,7,3,5,2]=>[1,6,4,3,7,2,5]=>[7,2,4,5,1,6,3]=>111000
[6,1,4,7,5,2,3]=>[1,6,4,2,5,7,3]=>[7,2,4,6,3,1,5]=>111000
[6,1,4,7,5,3,2]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>111010
[6,1,5,2,3,4,7]=>[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>011000
[6,1,5,2,3,7,4]=>[1,6,2,5,4,7,3]=>[7,2,6,3,4,1,5]=>111000
[6,1,5,2,4,3,7]=>[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>011100
[6,1,5,2,4,7,3]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>111000
[6,1,5,2,7,3,4]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>111000
[6,1,5,2,7,4,3]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>111100
[6,1,5,3,2,4,7]=>[7,1,6,2,3,5,4]=>[1,7,2,6,5,3,4]=>011010
[6,1,5,3,2,7,4]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>111010
[6,1,5,3,4,2,7]=>[7,1,6,3,5,2,4]=>[1,7,2,5,3,6,4]=>011100
[6,1,5,3,4,7,2]=>[1,6,3,5,4,2,7]=>[7,2,5,3,4,6,1]=>111000
[6,1,5,3,7,2,4]=>[1,6,3,5,2,7,4]=>[7,2,5,3,6,1,4]=>111000
[6,1,5,3,7,4,2]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>111100
[6,1,5,4,2,3,7]=>[7,1,6,2,4,5,3]=>[1,7,2,6,4,3,5]=>011100
[6,1,5,4,2,7,3]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>111100
[6,1,5,4,3,2,7]=>[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>011110
[6,1,5,4,3,7,2]=>[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>111100
[6,1,5,4,7,2,3]=>[1,6,4,5,2,7,3]=>[7,2,4,3,6,1,5]=>111000
[6,1,5,4,7,3,2]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>111010
[6,1,5,7,2,3,4]=>[1,6,5,2,7,4,3]=>[7,2,3,6,1,4,5]=>110000
[6,1,5,7,2,4,3]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>110100
[6,1,5,7,3,2,4]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>110010
[6,1,5,7,3,4,2]=>[1,6,5,3,7,2,4]=>[7,2,3,5,1,6,4]=>110100
[6,1,5,7,4,2,3]=>[1,6,5,2,4,7,3]=>[7,2,3,6,4,1,5]=>110100
[6,1,5,7,4,3,2]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>110110
[6,1,7,2,3,4,5]=>[1,6,2,7,5,4,3]=>[7,2,6,1,3,4,5]=>110000
[6,1,7,2,3,5,4]=>[1,6,2,7,4,5,3]=>[7,2,6,1,4,3,5]=>111000
[6,1,7,2,4,3,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>110100
[6,1,7,2,4,5,3]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>111000
[6,1,7,2,5,3,4]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>111000
[6,1,7,2,5,4,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>111100
[6,1,7,3,2,4,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>110010
[6,1,7,3,2,5,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>111010
[6,1,7,3,4,2,5]=>[1,6,3,7,5,2,4]=>[7,2,5,1,3,6,4]=>110100
[6,1,7,3,4,5,2]=>[1,6,3,7,4,2,5]=>[7,2,5,1,4,6,3]=>111000
[6,1,7,3,5,2,4]=>[1,6,3,7,2,5,4]=>[7,2,5,1,6,3,4]=>111000
[6,1,7,3,5,4,2]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>111100
[6,1,7,4,2,3,5]=>[1,6,2,4,7,5,3]=>[7,2,6,4,1,3,5]=>110100
[6,1,7,4,2,5,3]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>111100
[6,1,7,4,3,2,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>110110
[6,1,7,4,3,5,2]=>[1,6,3,4,7,2,5]=>[7,2,5,4,1,6,3]=>111100
[6,1,7,4,5,2,3]=>[1,6,4,7,2,5,3]=>[7,2,4,1,6,3,5]=>111000
[6,1,7,4,5,3,2]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>111010
[6,1,7,5,2,3,4]=>[1,6,2,5,7,4,3]=>[7,2,6,3,1,4,5]=>111000
[6,1,7,5,2,4,3]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>111100
[6,1,7,5,3,2,4]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>111010
[6,1,7,5,3,4,2]=>[1,6,3,5,7,2,4]=>[7,2,5,3,1,6,4]=>111100
[6,1,7,5,4,2,3]=>[1,6,2,4,5,7,3]=>[7,2,6,4,3,1,5]=>111100
[6,1,7,5,4,3,2]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>111110
[6,2,1,3,4,5,7]=>[7,1,2,6,5,4,3]=>[1,7,6,2,3,4,5]=>010001
[6,2,1,3,4,7,5]=>[1,2,6,5,7,4,3]=>[7,6,2,3,1,4,5]=>110001
[6,2,1,3,5,4,7]=>[7,1,2,6,4,5,3]=>[1,7,6,2,4,3,5]=>011001
[6,2,1,3,5,7,4]=>[1,2,6,5,4,7,3]=>[7,6,2,3,4,1,5]=>110001
[6,2,1,3,7,4,5]=>[1,2,6,4,7,5,3]=>[7,6,2,4,1,3,5]=>110001
[6,2,1,3,7,5,4]=>[1,2,6,4,5,7,3]=>[7,6,2,4,3,1,5]=>111001
[6,2,1,4,3,5,7]=>[7,1,2,6,5,3,4]=>[1,7,6,2,3,5,4]=>010101
[6,2,1,4,3,7,5]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>110101
[6,2,1,4,5,3,7]=>[7,1,2,6,4,3,5]=>[1,7,6,2,4,5,3]=>011001
[6,2,1,4,5,7,3]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>110001
[6,2,1,4,7,3,5]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>110001
[6,2,1,4,7,5,3]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>111001
[6,2,1,5,3,4,7]=>[7,1,2,6,3,5,4]=>[1,7,6,2,5,3,4]=>011001
[6,2,1,5,3,7,4]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>111001
[6,2,1,5,4,3,7]=>[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>011101
[6,2,1,5,4,7,3]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>111001
[6,2,1,5,7,3,4]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>110001
[6,2,1,5,7,4,3]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>110101
[6,2,1,7,3,4,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>110001
[6,2,1,7,3,5,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>111001
[6,2,1,7,4,3,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>110101
[6,2,1,7,4,5,3]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>111001
[6,2,1,7,5,3,4]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>111001
[6,2,1,7,5,4,3]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>111101
[6,2,3,1,4,5,7]=>[7,2,6,5,4,1,3]=>[1,6,2,3,4,7,5]=>010010
[6,2,3,1,4,7,5]=>[2,6,5,7,4,1,3]=>[6,2,3,1,4,7,5]=>110010
[6,2,3,1,5,4,7]=>[7,2,6,4,5,1,3]=>[1,6,2,4,3,7,5]=>011010
[6,2,3,1,5,7,4]=>[2,6,5,4,7,1,3]=>[6,2,3,4,1,7,5]=>110010
[6,2,3,1,7,4,5]=>[2,6,4,7,5,1,3]=>[6,2,4,1,3,7,5]=>110010
[6,2,3,1,7,5,4]=>[2,6,4,5,7,1,3]=>[6,2,4,3,1,7,5]=>111010
[6,2,3,4,1,5,7]=>[7,2,6,5,3,1,4]=>[1,6,2,3,5,7,4]=>010100
[6,2,3,4,1,7,5]=>[2,6,5,7,3,1,4]=>[6,2,3,1,5,7,4]=>110100
[6,2,3,4,5,1,7]=>[7,2,6,4,3,1,5]=>[1,6,2,4,5,7,3]=>011000
[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>[6,2,3,4,5,7,1]=>110000
[6,2,3,4,7,1,5]=>[2,6,4,3,1,7,5]=>[6,2,4,5,7,1,3]=>110000
[6,2,3,4,7,5,1]=>[2,6,4,3,1,5,7]=>[6,2,4,5,7,3,1]=>111000
[6,2,3,5,1,4,7]=>[7,2,6,3,1,5,4]=>[1,6,2,5,7,3,4]=>011000
[6,2,3,5,1,7,4]=>[2,6,3,1,5,4,7]=>[6,2,5,7,3,4,1]=>111000
[6,2,3,5,4,1,7]=>[7,2,6,3,1,4,5]=>[1,6,2,5,7,4,3]=>011100
[6,2,3,5,4,7,1]=>[2,6,4,5,3,1,7]=>[6,2,4,3,5,7,1]=>111000
[6,2,3,5,7,1,4]=>[2,6,5,3,1,7,4]=>[6,2,3,5,7,1,4]=>110000
[6,2,3,5,7,4,1]=>[2,6,5,3,1,4,7]=>[6,2,3,5,7,4,1]=>110100
[6,2,3,7,1,4,5]=>[2,6,3,1,7,5,4]=>[6,2,5,7,1,3,4]=>110000
[6,2,3,7,1,5,4]=>[2,6,3,1,7,4,5]=>[6,2,5,7,1,4,3]=>111000
[6,2,3,7,4,1,5]=>[2,6,3,1,4,7,5]=>[6,2,5,7,4,1,3]=>110100
[6,2,3,7,4,5,1]=>[2,6,4,7,3,1,5]=>[6,2,4,1,5,7,3]=>111000
[6,2,3,7,5,1,4]=>[2,6,3,1,5,7,4]=>[6,2,5,7,3,1,4]=>111000
[6,2,3,7,5,4,1]=>[2,6,3,1,4,5,7]=>[6,2,5,7,4,3,1]=>111100
[6,2,4,1,3,5,7]=>[7,2,6,5,1,4,3]=>[1,6,2,3,7,4,5]=>010100
[6,2,4,1,3,7,5]=>[2,6,5,7,1,4,3]=>[6,2,3,1,7,4,5]=>110100
[6,2,4,1,5,3,7]=>[7,2,6,1,4,3,5]=>[1,6,2,7,4,5,3]=>011100
[6,2,4,1,5,7,3]=>[2,6,5,1,4,3,7]=>[6,2,3,7,4,5,1]=>110100
[6,2,4,1,7,3,5]=>[2,6,1,4,3,7,5]=>[6,2,7,4,5,1,3]=>110100
[6,2,4,1,7,5,3]=>[2,6,1,4,3,5,7]=>[6,2,7,4,5,3,1]=>111100
[6,2,4,3,1,5,7]=>[7,2,6,5,1,3,4]=>[1,6,2,3,7,5,4]=>010110
[6,2,4,3,1,7,5]=>[2,6,5,7,1,3,4]=>[6,2,3,1,7,5,4]=>110110
[6,2,4,3,5,1,7]=>[7,2,6,3,4,1,5]=>[1,6,2,5,4,7,3]=>011100
[6,2,4,3,5,7,1]=>[2,6,5,3,4,1,7]=>[6,2,3,5,4,7,1]=>110100
[6,2,4,3,7,1,5]=>[2,6,3,4,1,7,5]=>[6,2,5,4,7,1,3]=>110100
[6,2,4,3,7,5,1]=>[2,6,3,4,1,5,7]=>[6,2,5,4,7,3,1]=>111100
[6,2,4,5,1,3,7]=>[7,2,6,4,1,5,3]=>[1,6,2,4,7,3,5]=>011000
[6,2,4,5,1,7,3]=>[2,6,4,1,5,3,7]=>[6,2,4,7,3,5,1]=>111000
[6,2,4,5,3,1,7]=>[7,2,6,4,1,3,5]=>[1,6,2,4,7,5,3]=>011010
[6,2,4,5,3,7,1]=>[2,6,4,3,5,1,7]=>[6,2,4,5,3,7,1]=>111000
[6,2,4,5,7,1,3]=>[2,6,5,4,1,7,3]=>[6,2,3,4,7,1,5]=>110000
[6,2,4,5,7,3,1]=>[2,6,5,4,1,3,7]=>[6,2,3,4,7,5,1]=>110010
[6,2,4,7,1,3,5]=>[2,6,4,1,7,5,3]=>[6,2,4,7,1,3,5]=>110000
[6,2,4,7,1,5,3]=>[2,6,4,1,7,3,5]=>[6,2,4,7,1,5,3]=>111000
[6,2,4,7,3,1,5]=>[2,6,4,1,3,7,5]=>[6,2,4,7,5,1,3]=>110010
[6,2,4,7,3,5,1]=>[2,6,4,3,7,1,5]=>[6,2,4,5,1,7,3]=>111000
[6,2,4,7,5,1,3]=>[2,6,4,1,5,7,3]=>[6,2,4,7,3,1,5]=>111000
[6,2,4,7,5,3,1]=>[2,6,4,1,3,5,7]=>[6,2,4,7,5,3,1]=>111010
[6,2,5,1,3,4,7]=>[7,2,6,1,5,4,3]=>[1,6,2,7,3,4,5]=>011000
[6,2,5,1,3,7,4]=>[2,6,1,5,4,7,3]=>[6,2,7,3,4,1,5]=>111000
[6,2,5,1,4,3,7]=>[7,2,6,1,5,3,4]=>[1,6,2,7,3,5,4]=>011100
[6,2,5,1,4,7,3]=>[2,6,1,5,4,3,7]=>[6,2,7,3,4,5,1]=>111000
[6,2,5,1,7,3,4]=>[2,6,1,5,3,7,4]=>[6,2,7,3,5,1,4]=>111000
[6,2,5,1,7,4,3]=>[2,6,1,5,3,4,7]=>[6,2,7,3,5,4,1]=>111100
[6,2,5,3,1,4,7]=>[7,2,6,1,3,5,4]=>[1,6,2,7,5,3,4]=>011010
[6,2,5,3,1,7,4]=>[2,6,1,3,5,4,7]=>[6,2,7,5,3,4,1]=>111010
[6,2,5,3,4,1,7]=>[7,2,6,3,5,1,4]=>[1,6,2,5,3,7,4]=>011100
[6,2,5,3,4,7,1]=>[2,6,3,5,4,1,7]=>[6,2,5,3,4,7,1]=>111000
[6,2,5,3,7,1,4]=>[2,6,3,5,1,7,4]=>[6,2,5,3,7,1,4]=>111000
[6,2,5,3,7,4,1]=>[2,6,3,5,1,4,7]=>[6,2,5,3,7,4,1]=>111100
[6,2,5,4,1,3,7]=>[7,2,6,1,4,5,3]=>[1,6,2,7,4,3,5]=>011100
[6,2,5,4,1,7,3]=>[2,6,1,4,5,3,7]=>[6,2,7,4,3,5,1]=>111100
[6,2,5,4,3,1,7]=>[7,2,6,1,3,4,5]=>[1,6,2,7,5,4,3]=>011110
[6,2,5,4,3,7,1]=>[2,6,3,4,5,1,7]=>[6,2,5,4,3,7,1]=>111100
[6,2,5,4,7,1,3]=>[2,6,4,5,1,7,3]=>[6,2,4,3,7,1,5]=>111000
[6,2,5,4,7,3,1]=>[2,6,4,5,1,3,7]=>[6,2,4,3,7,5,1]=>111010
[6,2,5,7,1,3,4]=>[2,6,5,1,7,4,3]=>[6,2,3,7,1,4,5]=>110000
[6,2,5,7,1,4,3]=>[2,6,5,1,7,3,4]=>[6,2,3,7,1,5,4]=>110100
[6,2,5,7,3,1,4]=>[2,6,5,1,3,7,4]=>[6,2,3,7,5,1,4]=>110010
[6,2,5,7,3,4,1]=>[2,6,5,3,7,1,4]=>[6,2,3,5,1,7,4]=>110100
[6,2,5,7,4,1,3]=>[2,6,5,1,4,7,3]=>[6,2,3,7,4,1,5]=>110100
[6,2,5,7,4,3,1]=>[2,6,5,1,3,4,7]=>[6,2,3,7,5,4,1]=>110110
[6,2,7,1,3,4,5]=>[2,6,1,7,5,4,3]=>[6,2,7,1,3,4,5]=>110000
[6,2,7,1,3,5,4]=>[2,6,1,7,4,5,3]=>[6,2,7,1,4,3,5]=>111000
[6,2,7,1,4,3,5]=>[2,6,1,7,5,3,4]=>[6,2,7,1,3,5,4]=>110100
[6,2,7,1,4,5,3]=>[2,6,1,7,4,3,5]=>[6,2,7,1,4,5,3]=>111000
[6,2,7,1,5,3,4]=>[2,6,1,7,3,5,4]=>[6,2,7,1,5,3,4]=>111000
[6,2,7,1,5,4,3]=>[2,6,1,7,3,4,5]=>[6,2,7,1,5,4,3]=>111100
[6,2,7,3,1,4,5]=>[2,6,1,3,7,5,4]=>[6,2,7,5,1,3,4]=>110010
[6,2,7,3,1,5,4]=>[2,6,1,3,7,4,5]=>[6,2,7,5,1,4,3]=>111010
[6,2,7,3,4,1,5]=>[2,6,3,7,5,1,4]=>[6,2,5,1,3,7,4]=>110100
[6,2,7,3,4,5,1]=>[2,6,3,7,4,1,5]=>[6,2,5,1,4,7,3]=>111000
[6,2,7,3,5,1,4]=>[2,6,3,7,1,5,4]=>[6,2,5,1,7,3,4]=>111000
[6,2,7,3,5,4,1]=>[2,6,3,7,1,4,5]=>[6,2,5,1,7,4,3]=>111100
[6,2,7,4,1,3,5]=>[2,6,1,4,7,5,3]=>[6,2,7,4,1,3,5]=>110100
[6,2,7,4,1,5,3]=>[2,6,1,4,7,3,5]=>[6,2,7,4,1,5,3]=>111100
[6,2,7,4,3,1,5]=>[2,6,1,3,4,7,5]=>[6,2,7,5,4,1,3]=>110110
[6,2,7,4,3,5,1]=>[2,6,3,4,7,1,5]=>[6,2,5,4,1,7,3]=>111100
[6,2,7,4,5,1,3]=>[2,6,4,7,1,5,3]=>[6,2,4,1,7,3,5]=>111000
[6,2,7,4,5,3,1]=>[2,6,4,7,1,3,5]=>[6,2,4,1,7,5,3]=>111010
[6,2,7,5,1,3,4]=>[2,6,1,5,7,4,3]=>[6,2,7,3,1,4,5]=>111000
[6,2,7,5,1,4,3]=>[2,6,1,5,7,3,4]=>[6,2,7,3,1,5,4]=>111100
[6,2,7,5,3,1,4]=>[2,6,1,3,5,7,4]=>[6,2,7,5,3,1,4]=>111010
[6,2,7,5,3,4,1]=>[2,6,3,5,7,1,4]=>[6,2,5,3,1,7,4]=>111100
[6,2,7,5,4,1,3]=>[2,6,1,4,5,7,3]=>[6,2,7,4,3,1,5]=>111100
[6,2,7,5,4,3,1]=>[2,6,1,3,4,5,7]=>[6,2,7,5,4,3,1]=>111110
[6,3,1,2,4,5,7]=>[7,1,3,6,5,4,2]=>[1,7,5,2,3,4,6]=>010010
[6,3,1,2,4,7,5]=>[1,3,6,5,7,4,2]=>[7,5,2,3,1,4,6]=>110010
[6,3,1,2,5,4,7]=>[7,1,3,6,4,5,2]=>[1,7,5,2,4,3,6]=>011010
[6,3,1,2,5,7,4]=>[1,3,6,5,4,7,2]=>[7,5,2,3,4,1,6]=>110010
[6,3,1,2,7,4,5]=>[1,3,6,4,7,5,2]=>[7,5,2,4,1,3,6]=>110010
[6,3,1,2,7,5,4]=>[1,3,6,4,5,7,2]=>[7,5,2,4,3,1,6]=>111010
[6,3,1,4,2,5,7]=>[7,1,3,6,5,2,4]=>[1,7,5,2,3,6,4]=>010110
[6,3,1,4,2,7,5]=>[1,3,6,5,7,2,4]=>[7,5,2,3,1,6,4]=>110110
[6,3,1,4,5,2,7]=>[7,1,3,6,4,2,5]=>[1,7,5,2,4,6,3]=>011010
[6,3,1,4,5,7,2]=>[1,3,6,5,4,2,7]=>[7,5,2,3,4,6,1]=>110010
[6,3,1,4,7,2,5]=>[1,3,6,4,2,7,5]=>[7,5,2,4,6,1,3]=>110010
[6,3,1,4,7,5,2]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>111010
[6,3,1,5,2,4,7]=>[7,1,3,6,2,5,4]=>[1,7,5,2,6,3,4]=>011010
[6,3,1,5,2,7,4]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>111010
[6,3,1,5,4,2,7]=>[7,1,3,6,2,4,5]=>[1,7,5,2,6,4,3]=>011110
[6,3,1,5,4,7,2]=>[1,3,6,4,5,2,7]=>[7,5,2,4,3,6,1]=>111010
[6,3,1,5,7,2,4]=>[1,3,6,5,2,7,4]=>[7,5,2,3,6,1,4]=>110010
[6,3,1,5,7,4,2]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>110110
[6,3,1,7,2,4,5]=>[1,3,6,2,7,5,4]=>[7,5,2,6,1,3,4]=>110010
[6,3,1,7,2,5,4]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>111010
[6,3,1,7,4,2,5]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>110110
[6,3,1,7,4,5,2]=>[1,3,6,4,7,2,5]=>[7,5,2,4,1,6,3]=>111010
[6,3,1,7,5,2,4]=>[1,3,6,2,5,7,4]=>[7,5,2,6,3,1,4]=>111010
[6,3,1,7,5,4,2]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>111110
[6,3,2,1,4,5,7]=>[7,1,2,3,6,5,4]=>[1,7,6,5,2,3,4]=>010011
[6,3,2,1,4,7,5]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>110011
[6,3,2,1,5,4,7]=>[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>011011
[6,3,2,1,5,7,4]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>110011
[6,3,2,1,7,4,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>110011
[6,3,2,1,7,5,4]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>111011
[6,3,2,4,1,5,7]=>[7,2,3,6,5,1,4]=>[1,6,5,2,3,7,4]=>010110
[6,3,2,4,1,7,5]=>[2,3,6,5,7,1,4]=>[6,5,2,3,1,7,4]=>110110
[6,3,2,4,5,1,7]=>[7,2,3,6,4,1,5]=>[1,6,5,2,4,7,3]=>011010
[6,3,2,4,5,7,1]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,7,1]=>110010
[6,3,2,4,7,1,5]=>[2,3,6,4,1,7,5]=>[6,5,2,4,7,1,3]=>110010
[6,3,2,4,7,5,1]=>[2,3,6,4,1,5,7]=>[6,5,2,4,7,3,1]=>111010
[6,3,2,5,1,4,7]=>[7,2,3,6,1,5,4]=>[1,6,5,2,7,3,4]=>011010
[6,3,2,5,1,7,4]=>[2,3,6,1,5,4,7]=>[6,5,2,7,3,4,1]=>111010
[6,3,2,5,4,1,7]=>[7,2,3,6,1,4,5]=>[1,6,5,2,7,4,3]=>011110
[6,3,2,5,4,7,1]=>[2,3,6,4,5,1,7]=>[6,5,2,4,3,7,1]=>111010
[6,3,2,5,7,1,4]=>[2,3,6,5,1,7,4]=>[6,5,2,3,7,1,4]=>110010
[6,3,2,5,7,4,1]=>[2,3,6,5,1,4,7]=>[6,5,2,3,7,4,1]=>110110
[6,3,2,7,1,4,5]=>[2,3,6,1,7,5,4]=>[6,5,2,7,1,3,4]=>110010
[6,3,2,7,1,5,4]=>[2,3,6,1,7,4,5]=>[6,5,2,7,1,4,3]=>111010
[6,3,2,7,4,1,5]=>[2,3,6,1,4,7,5]=>[6,5,2,7,4,1,3]=>110110
[6,3,2,7,4,5,1]=>[2,3,6,4,7,1,5]=>[6,5,2,4,1,7,3]=>111010
[6,3,2,7,5,1,4]=>[2,3,6,1,5,7,4]=>[6,5,2,7,3,1,4]=>111010
[6,3,2,7,5,4,1]=>[2,3,6,1,4,5,7]=>[6,5,2,7,4,3,1]=>111110
[6,3,4,1,2,5,7]=>[7,3,6,5,1,4,2]=>[1,5,2,3,7,4,6]=>010100
[6,3,4,1,2,7,5]=>[3,6,5,7,1,4,2]=>[5,2,3,1,7,4,6]=>110100
[6,3,4,1,5,2,7]=>[7,3,6,1,4,2,5]=>[1,5,2,7,4,6,3]=>011100
[6,3,4,1,5,7,2]=>[3,6,5,1,4,2,7]=>[5,2,3,7,4,6,1]=>110100
[6,3,4,1,7,2,5]=>[3,6,1,4,2,7,5]=>[5,2,7,4,6,1,3]=>110100
[6,3,4,1,7,5,2]=>[3,6,1,4,2,5,7]=>[5,2,7,4,6,3,1]=>111100
[6,3,4,2,1,5,7]=>[7,3,6,5,1,2,4]=>[1,5,2,3,7,6,4]=>010101
[6,3,4,2,1,7,5]=>[3,6,5,7,1,2,4]=>[5,2,3,1,7,6,4]=>110101
[6,3,4,2,5,1,7]=>[7,3,6,2,4,1,5]=>[1,5,2,6,4,7,3]=>011100
[6,3,4,2,5,7,1]=>[3,6,5,2,4,1,7]=>[5,2,3,6,4,7,1]=>110100
[6,3,4,2,7,1,5]=>[3,6,2,4,1,7,5]=>[5,2,6,4,7,1,3]=>110100
[6,3,4,2,7,5,1]=>[3,6,2,4,1,5,7]=>[5,2,6,4,7,3,1]=>111100
[6,3,4,5,1,2,7]=>[7,3,6,4,1,5,2]=>[1,5,2,4,7,3,6]=>011000
[6,3,4,5,1,7,2]=>[3,6,4,1,5,2,7]=>[5,2,4,7,3,6,1]=>111000
[6,3,4,5,2,1,7]=>[7,3,6,4,1,2,5]=>[1,5,2,4,7,6,3]=>011001
[6,3,4,5,2,7,1]=>[3,6,4,2,5,1,7]=>[5,2,4,6,3,7,1]=>111000
[6,3,4,5,7,1,2]=>[3,6,5,4,1,7,2]=>[5,2,3,4,7,1,6]=>110000
[6,3,4,5,7,2,1]=>[3,6,5,4,1,2,7]=>[5,2,3,4,7,6,1]=>110001
[6,3,4,7,1,2,5]=>[3,6,4,1,7,5,2]=>[5,2,4,7,1,3,6]=>110000
[6,3,4,7,1,5,2]=>[3,6,4,1,7,2,5]=>[5,2,4,7,1,6,3]=>111000
[6,3,4,7,2,1,5]=>[3,6,4,1,2,7,5]=>[5,2,4,7,6,1,3]=>110001
[6,3,4,7,2,5,1]=>[3,6,4,2,7,1,5]=>[5,2,4,6,1,7,3]=>111000
[6,3,4,7,5,1,2]=>[3,6,4,1,5,7,2]=>[5,2,4,7,3,1,6]=>111000
[6,3,4,7,5,2,1]=>[3,6,4,1,2,5,7]=>[5,2,4,7,6,3,1]=>111001
[6,3,5,1,2,4,7]=>[7,3,6,1,5,4,2]=>[1,5,2,7,3,4,6]=>011000
[6,3,5,1,2,7,4]=>[3,6,1,5,4,7,2]=>[5,2,7,3,4,1,6]=>111000
[6,3,5,1,4,2,7]=>[7,3,6,1,5,2,4]=>[1,5,2,7,3,6,4]=>011100
[6,3,5,1,4,7,2]=>[3,6,1,5,4,2,7]=>[5,2,7,3,4,6,1]=>111000
[6,3,5,1,7,2,4]=>[3,6,1,5,2,7,4]=>[5,2,7,3,6,1,4]=>111000
[6,3,5,1,7,4,2]=>[3,6,1,5,2,4,7]=>[5,2,7,3,6,4,1]=>111100
[6,3,5,2,1,4,7]=>[7,3,6,1,2,5,4]=>[1,5,2,7,6,3,4]=>011001
[6,3,5,2,1,7,4]=>[3,6,1,2,5,4,7]=>[5,2,7,6,3,4,1]=>111001
[6,3,5,2,4,1,7]=>[7,3,6,2,5,1,4]=>[1,5,2,6,3,7,4]=>011100
[6,3,5,2,4,7,1]=>[3,6,2,5,4,1,7]=>[5,2,6,3,4,7,1]=>111000
[6,3,5,2,7,1,4]=>[3,6,2,5,1,7,4]=>[5,2,6,3,7,1,4]=>111000
[6,3,5,2,7,4,1]=>[3,6,2,5,1,4,7]=>[5,2,6,3,7,4,1]=>111100
[6,3,5,4,1,2,7]=>[7,3,6,1,4,5,2]=>[1,5,2,7,4,3,6]=>011100
[6,3,5,4,1,7,2]=>[3,6,1,4,5,2,7]=>[5,2,7,4,3,6,1]=>111100
[6,3,5,4,2,1,7]=>[7,3,6,1,2,4,5]=>[1,5,2,7,6,4,3]=>011101
[6,3,5,4,2,7,1]=>[3,6,2,4,5,1,7]=>[5,2,6,4,3,7,1]=>111100
[6,3,5,4,7,1,2]=>[3,6,4,5,1,7,2]=>[5,2,4,3,7,1,6]=>111000
[6,3,5,4,7,2,1]=>[3,6,4,5,1,2,7]=>[5,2,4,3,7,6,1]=>111001
[6,3,5,7,1,2,4]=>[3,6,5,1,7,4,2]=>[5,2,3,7,1,4,6]=>110000
[6,3,5,7,1,4,2]=>[3,6,5,1,7,2,4]=>[5,2,3,7,1,6,4]=>110100
[6,3,5,7,2,1,4]=>[3,6,5,1,2,7,4]=>[5,2,3,7,6,1,4]=>110001
[6,3,5,7,2,4,1]=>[3,6,5,2,7,1,4]=>[5,2,3,6,1,7,4]=>110100
[6,3,5,7,4,1,2]=>[3,6,5,1,4,7,2]=>[5,2,3,7,4,1,6]=>110100
[6,3,5,7,4,2,1]=>[3,6,5,1,2,4,7]=>[5,2,3,7,6,4,1]=>110101
[6,3,7,1,2,4,5]=>[3,6,1,7,5,4,2]=>[5,2,7,1,3,4,6]=>110000
[6,3,7,1,2,5,4]=>[3,6,1,7,4,5,2]=>[5,2,7,1,4,3,6]=>111000
[6,3,7,1,4,2,5]=>[3,6,1,7,5,2,4]=>[5,2,7,1,3,6,4]=>110100
[6,3,7,1,4,5,2]=>[3,6,1,7,4,2,5]=>[5,2,7,1,4,6,3]=>111000
[6,3,7,1,5,2,4]=>[3,6,1,7,2,5,4]=>[5,2,7,1,6,3,4]=>111000
[6,3,7,1,5,4,2]=>[3,6,1,7,2,4,5]=>[5,2,7,1,6,4,3]=>111100
[6,3,7,2,1,4,5]=>[3,6,1,2,7,5,4]=>[5,2,7,6,1,3,4]=>110001
[6,3,7,2,1,5,4]=>[3,6,1,2,7,4,5]=>[5,2,7,6,1,4,3]=>111001
[6,3,7,2,4,1,5]=>[3,6,2,7,5,1,4]=>[5,2,6,1,3,7,4]=>110100
[6,3,7,2,4,5,1]=>[3,6,2,7,4,1,5]=>[5,2,6,1,4,7,3]=>111000
[6,3,7,2,5,1,4]=>[3,6,2,7,1,5,4]=>[5,2,6,1,7,3,4]=>111000
[6,3,7,2,5,4,1]=>[3,6,2,7,1,4,5]=>[5,2,6,1,7,4,3]=>111100
[6,3,7,4,1,2,5]=>[3,6,1,4,7,5,2]=>[5,2,7,4,1,3,6]=>110100
[6,3,7,4,1,5,2]=>[3,6,1,4,7,2,5]=>[5,2,7,4,1,6,3]=>111100
[6,3,7,4,2,1,5]=>[3,6,1,2,4,7,5]=>[5,2,7,6,4,1,3]=>110101
[6,3,7,4,2,5,1]=>[3,6,2,4,7,1,5]=>[5,2,6,4,1,7,3]=>111100
[6,3,7,4,5,1,2]=>[3,6,4,7,1,5,2]=>[5,2,4,1,7,3,6]=>111000
[6,3,7,4,5,2,1]=>[3,6,4,7,1,2,5]=>[5,2,4,1,7,6,3]=>111001
[6,3,7,5,1,2,4]=>[3,6,1,5,7,4,2]=>[5,2,7,3,1,4,6]=>111000
[6,3,7,5,1,4,2]=>[3,6,1,5,7,2,4]=>[5,2,7,3,1,6,4]=>111100
[6,3,7,5,2,1,4]=>[3,6,1,2,5,7,4]=>[5,2,7,6,3,1,4]=>111001
[6,3,7,5,2,4,1]=>[3,6,2,5,7,1,4]=>[5,2,6,3,1,7,4]=>111100
[6,3,7,5,4,1,2]=>[3,6,1,4,5,7,2]=>[5,2,7,4,3,1,6]=>111100
[6,3,7,5,4,2,1]=>[3,6,1,2,4,5,7]=>[5,2,7,6,4,3,1]=>111101
[6,4,1,2,3,5,7]=>[7,1,4,6,5,3,2]=>[1,7,4,2,3,5,6]=>010100
[6,4,1,2,3,7,5]=>[1,4,6,5,7,3,2]=>[7,4,2,3,1,5,6]=>110100
[6,4,1,2,5,3,7]=>[7,1,4,6,3,5,2]=>[1,7,4,2,5,3,6]=>011100
[6,4,1,2,5,7,3]=>[1,4,6,5,3,7,2]=>[7,4,2,3,5,1,6]=>110100
[6,4,1,2,7,3,5]=>[1,4,6,3,7,5,2]=>[7,4,2,5,1,3,6]=>110100
[6,4,1,2,7,5,3]=>[1,4,6,3,5,7,2]=>[7,4,2,5,3,1,6]=>111100
[6,4,1,3,2,5,7]=>[7,1,4,6,5,2,3]=>[1,7,4,2,3,6,5]=>010110
[6,4,1,3,2,7,5]=>[1,4,6,5,7,2,3]=>[7,4,2,3,1,6,5]=>110110
[6,4,1,3,5,2,7]=>[7,1,4,6,3,2,5]=>[1,7,4,2,5,6,3]=>011100
[6,4,1,3,5,7,2]=>[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>110100
[6,4,1,3,7,2,5]=>[1,4,6,3,2,7,5]=>[7,4,2,5,6,1,3]=>110100
[6,4,1,3,7,5,2]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>111100
[6,4,1,5,2,3,7]=>[7,1,4,6,2,5,3]=>[1,7,4,2,6,3,5]=>011100
[6,4,1,5,2,7,3]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>111100
[6,4,1,5,3,2,7]=>[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]=>011110
[6,4,1,5,3,7,2]=>[1,4,6,3,5,2,7]=>[7,4,2,5,3,6,1]=>111100
[6,4,1,5,7,2,3]=>[1,4,6,5,2,7,3]=>[7,4,2,3,6,1,5]=>110100
[6,4,1,5,7,3,2]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>110110
[6,4,1,7,2,3,5]=>[1,4,6,2,7,5,3]=>[7,4,2,6,1,3,5]=>110100
[6,4,1,7,2,5,3]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>111100
[6,4,1,7,3,2,5]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>110110
[6,4,1,7,3,5,2]=>[1,4,6,3,7,2,5]=>[7,4,2,5,1,6,3]=>111100
[6,4,1,7,5,2,3]=>[1,4,6,2,5,7,3]=>[7,4,2,6,3,1,5]=>111100
[6,4,1,7,5,3,2]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>111110
[6,4,2,1,3,5,7]=>[7,1,2,4,6,5,3]=>[1,7,6,4,2,3,5]=>010101
[6,4,2,1,3,7,5]=>[1,2,4,6,5,7,3]=>[7,6,4,2,3,1,5]=>110101
[6,4,2,1,5,3,7]=>[7,1,2,4,6,3,5]=>[1,7,6,4,2,5,3]=>011101
[6,4,2,1,5,7,3]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>110101
[6,4,2,1,7,3,5]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>110101
[6,4,2,1,7,5,3]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>111101
[6,4,2,3,1,5,7]=>[7,2,4,6,5,1,3]=>[1,6,4,2,3,7,5]=>010110
[6,4,2,3,1,7,5]=>[2,4,6,5,7,1,3]=>[6,4,2,3,1,7,5]=>110110
[6,4,2,3,5,1,7]=>[7,2,4,6,3,1,5]=>[1,6,4,2,5,7,3]=>011100
[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>[6,4,2,3,5,7,1]=>110100
[6,4,2,3,7,1,5]=>[2,4,6,3,1,7,5]=>[6,4,2,5,7,1,3]=>110100
[6,4,2,3,7,5,1]=>[2,4,6,3,1,5,7]=>[6,4,2,5,7,3,1]=>111100
[6,4,2,5,1,3,7]=>[7,2,4,6,1,5,3]=>[1,6,4,2,7,3,5]=>011100
[6,4,2,5,1,7,3]=>[2,4,6,1,5,3,7]=>[6,4,2,7,3,5,1]=>111100
[6,4,2,5,3,1,7]=>[7,2,4,6,1,3,5]=>[1,6,4,2,7,5,3]=>011110
[6,4,2,5,3,7,1]=>[2,4,6,3,5,1,7]=>[6,4,2,5,3,7,1]=>111100
[6,4,2,5,7,1,3]=>[2,4,6,5,1,7,3]=>[6,4,2,3,7,1,5]=>110100
[6,4,2,5,7,3,1]=>[2,4,6,5,1,3,7]=>[6,4,2,3,7,5,1]=>110110
[6,4,2,7,1,3,5]=>[2,4,6,1,7,5,3]=>[6,4,2,7,1,3,5]=>110100
[6,4,2,7,1,5,3]=>[2,4,6,1,7,3,5]=>[6,4,2,7,1,5,3]=>111100
[6,4,2,7,3,1,5]=>[2,4,6,1,3,7,5]=>[6,4,2,7,5,1,3]=>110110
[6,4,2,7,3,5,1]=>[2,4,6,3,7,1,5]=>[6,4,2,5,1,7,3]=>111100
[6,4,2,7,5,1,3]=>[2,4,6,1,5,7,3]=>[6,4,2,7,3,1,5]=>111100
[6,4,2,7,5,3,1]=>[2,4,6,1,3,5,7]=>[6,4,2,7,5,3,1]=>111110
[6,4,3,1,2,5,7]=>[7,1,3,4,6,5,2]=>[1,7,5,4,2,3,6]=>010110
[6,4,3,1,2,7,5]=>[1,3,4,6,5,7,2]=>[7,5,4,2,3,1,6]=>110110
[6,4,3,1,5,2,7]=>[7,1,3,4,6,2,5]=>[1,7,5,4,2,6,3]=>011110
[6,4,3,1,5,7,2]=>[1,3,4,6,5,2,7]=>[7,5,4,2,3,6,1]=>110110
[6,4,3,1,7,2,5]=>[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]=>110110
[6,4,3,1,7,5,2]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>111110
[6,4,3,2,1,5,7]=>[7,1,2,3,4,6,5]=>[1,7,6,5,4,2,3]=>010111
[6,4,3,2,1,7,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>110111
[6,4,3,2,5,1,7]=>[7,2,3,4,6,1,5]=>[1,6,5,4,2,7,3]=>011110
[6,4,3,2,5,7,1]=>[2,3,4,6,5,1,7]=>[6,5,4,2,3,7,1]=>110110
[6,4,3,2,7,1,5]=>[2,3,4,6,1,7,5]=>[6,5,4,2,7,1,3]=>110110
[6,4,3,2,7,5,1]=>[2,3,4,6,1,5,7]=>[6,5,4,2,7,3,1]=>111110
[6,4,3,5,1,2,7]=>[7,3,4,6,1,5,2]=>[1,5,4,2,7,3,6]=>011100
[6,4,3,5,1,7,2]=>[3,4,6,1,5,2,7]=>[5,4,2,7,3,6,1]=>111100
[6,4,3,5,2,1,7]=>[7,3,4,6,1,2,5]=>[1,5,4,2,7,6,3]=>011101
[6,4,3,5,2,7,1]=>[3,4,6,2,5,1,7]=>[5,4,2,6,3,7,1]=>111100
[6,4,3,5,7,1,2]=>[3,4,6,5,1,7,2]=>[5,4,2,3,7,1,6]=>110100
[6,4,3,5,7,2,1]=>[3,4,6,5,1,2,7]=>[5,4,2,3,7,6,1]=>110101
[6,4,3,7,1,2,5]=>[3,4,6,1,7,5,2]=>[5,4,2,7,1,3,6]=>110100
[6,4,3,7,1,5,2]=>[3,4,6,1,7,2,5]=>[5,4,2,7,1,6,3]=>111100
[6,4,3,7,2,1,5]=>[3,4,6,1,2,7,5]=>[5,4,2,7,6,1,3]=>110101
[6,4,3,7,2,5,1]=>[3,4,6,2,7,1,5]=>[5,4,2,6,1,7,3]=>111100
[6,4,3,7,5,1,2]=>[3,4,6,1,5,7,2]=>[5,4,2,7,3,1,6]=>111100
[6,4,3,7,5,2,1]=>[3,4,6,1,2,5,7]=>[5,4,2,7,6,3,1]=>111101
[6,4,5,1,2,3,7]=>[7,4,6,1,5,3,2]=>[1,4,2,7,3,5,6]=>011000
[6,4,5,1,2,7,3]=>[4,6,1,5,3,7,2]=>[4,2,7,3,5,1,6]=>111000
[6,4,5,1,3,2,7]=>[7,4,6,1,5,2,3]=>[1,4,2,7,3,6,5]=>011010
[6,4,5,1,3,7,2]=>[4,6,1,5,3,2,7]=>[4,2,7,3,5,6,1]=>111000
[6,4,5,1,7,2,3]=>[4,6,1,5,2,7,3]=>[4,2,7,3,6,1,5]=>111000
[6,4,5,1,7,3,2]=>[4,6,1,5,2,3,7]=>[4,2,7,3,6,5,1]=>111010
[6,4,5,2,1,3,7]=>[7,4,6,1,2,5,3]=>[1,4,2,7,6,3,5]=>011001
[6,4,5,2,1,7,3]=>[4,6,1,2,5,3,7]=>[4,2,7,6,3,5,1]=>111001
[6,4,5,2,3,1,7]=>[7,4,6,2,5,1,3]=>[1,4,2,6,3,7,5]=>011010
[6,4,5,2,3,7,1]=>[4,6,2,5,3,1,7]=>[4,2,6,3,5,7,1]=>111000
[6,4,5,2,7,1,3]=>[4,6,2,5,1,7,3]=>[4,2,6,3,7,1,5]=>111000
[6,4,5,2,7,3,1]=>[4,6,2,5,1,3,7]=>[4,2,6,3,7,5,1]=>111010
[6,4,5,3,1,2,7]=>[7,4,6,1,3,5,2]=>[1,4,2,7,5,3,6]=>011010
[6,4,5,3,1,7,2]=>[4,6,1,3,5,2,7]=>[4,2,7,5,3,6,1]=>111010
[6,4,5,3,2,1,7]=>[7,4,6,1,2,3,5]=>[1,4,2,7,6,5,3]=>011011
[6,4,5,3,2,7,1]=>[4,6,2,3,5,1,7]=>[4,2,6,5,3,7,1]=>111010
[6,4,5,3,7,1,2]=>[4,6,3,5,1,7,2]=>[4,2,5,3,7,1,6]=>111000
[6,4,5,3,7,2,1]=>[4,6,3,5,1,2,7]=>[4,2,5,3,7,6,1]=>111001
[6,4,5,7,1,2,3]=>[4,6,5,1,7,3,2]=>[4,2,3,7,1,5,6]=>110000
[6,4,5,7,1,3,2]=>[4,6,5,1,7,2,3]=>[4,2,3,7,1,6,5]=>110010
[6,4,5,7,2,1,3]=>[4,6,5,1,2,7,3]=>[4,2,3,7,6,1,5]=>110001
[6,4,5,7,2,3,1]=>[4,6,5,2,7,1,3]=>[4,2,3,6,1,7,5]=>110010
[6,4,5,7,3,1,2]=>[4,6,5,1,3,7,2]=>[4,2,3,7,5,1,6]=>110010
[6,4,5,7,3,2,1]=>[4,6,5,1,2,3,7]=>[4,2,3,7,6,5,1]=>110011
[6,4,7,1,2,3,5]=>[4,6,1,7,5,3,2]=>[4,2,7,1,3,5,6]=>110000
[6,4,7,1,2,5,3]=>[4,6,1,7,3,5,2]=>[4,2,7,1,5,3,6]=>111000
[6,4,7,1,3,2,5]=>[4,6,1,7,5,2,3]=>[4,2,7,1,3,6,5]=>110010
[6,4,7,1,3,5,2]=>[4,6,1,7,3,2,5]=>[4,2,7,1,5,6,3]=>111000
[6,4,7,1,5,2,3]=>[4,6,1,7,2,5,3]=>[4,2,7,1,6,3,5]=>111000
[6,4,7,1,5,3,2]=>[4,6,1,7,2,3,5]=>[4,2,7,1,6,5,3]=>111010
[6,4,7,2,1,3,5]=>[4,6,1,2,7,5,3]=>[4,2,7,6,1,3,5]=>110001
[6,4,7,2,1,5,3]=>[4,6,1,2,7,3,5]=>[4,2,7,6,1,5,3]=>111001
[6,4,7,2,3,1,5]=>[4,6,2,7,5,1,3]=>[4,2,6,1,3,7,5]=>110010
[6,4,7,2,3,5,1]=>[4,6,2,7,3,1,5]=>[4,2,6,1,5,7,3]=>111000
[6,4,7,2,5,1,3]=>[4,6,2,7,1,5,3]=>[4,2,6,1,7,3,5]=>111000
[6,4,7,2,5,3,1]=>[4,6,2,7,1,3,5]=>[4,2,6,1,7,5,3]=>111010
[6,4,7,3,1,2,5]=>[4,6,1,3,7,5,2]=>[4,2,7,5,1,3,6]=>110010
[6,4,7,3,1,5,2]=>[4,6,1,3,7,2,5]=>[4,2,7,5,1,6,3]=>111010
[6,4,7,3,2,1,5]=>[4,6,1,2,3,7,5]=>[4,2,7,6,5,1,3]=>110011
[6,4,7,3,2,5,1]=>[4,6,2,3,7,1,5]=>[4,2,6,5,1,7,3]=>111010
[6,4,7,3,5,1,2]=>[4,6,3,7,1,5,2]=>[4,2,5,1,7,3,6]=>111000
[6,4,7,3,5,2,1]=>[4,6,3,7,1,2,5]=>[4,2,5,1,7,6,3]=>111001
[6,4,7,5,1,2,3]=>[4,6,1,5,7,3,2]=>[4,2,7,3,1,5,6]=>111000
[6,4,7,5,1,3,2]=>[4,6,1,5,7,2,3]=>[4,2,7,3,1,6,5]=>111010
[6,4,7,5,2,1,3]=>[4,6,1,2,5,7,3]=>[4,2,7,6,3,1,5]=>111001
[6,4,7,5,2,3,1]=>[4,6,2,5,7,1,3]=>[4,2,6,3,1,7,5]=>111010
[6,4,7,5,3,1,2]=>[4,6,1,3,5,7,2]=>[4,2,7,5,3,1,6]=>111010
[6,4,7,5,3,2,1]=>[4,6,1,2,3,5,7]=>[4,2,7,6,5,3,1]=>111011
[6,5,1,2,3,4,7]=>[7,1,5,6,4,3,2]=>[1,7,3,2,4,5,6]=>011000
[6,5,1,2,3,7,4]=>[1,5,6,4,7,3,2]=>[7,3,2,4,1,5,6]=>111000
[6,5,1,2,4,3,7]=>[7,1,5,6,3,4,2]=>[1,7,3,2,5,4,6]=>011100
[6,5,1,2,4,7,3]=>[1,5,6,4,3,7,2]=>[7,3,2,4,5,1,6]=>111000
[6,5,1,2,7,3,4]=>[1,5,6,3,7,4,2]=>[7,3,2,5,1,4,6]=>111000
[6,5,1,2,7,4,3]=>[1,5,6,3,4,7,2]=>[7,3,2,5,4,1,6]=>111100
[6,5,1,3,2,4,7]=>[7,1,5,6,4,2,3]=>[1,7,3,2,4,6,5]=>011010
[6,5,1,3,2,7,4]=>[1,5,6,4,7,2,3]=>[7,3,2,4,1,6,5]=>111010
[6,5,1,3,4,2,7]=>[7,1,5,6,3,2,4]=>[1,7,3,2,5,6,4]=>011100
[6,5,1,3,4,7,2]=>[1,5,6,4,3,2,7]=>[7,3,2,4,5,6,1]=>111000
[6,5,1,3,7,2,4]=>[1,5,6,3,2,7,4]=>[7,3,2,5,6,1,4]=>111000
[6,5,1,3,7,4,2]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>111100
[6,5,1,4,2,3,7]=>[7,1,5,6,2,4,3]=>[1,7,3,2,6,4,5]=>011100
[6,5,1,4,2,7,3]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>111100
[6,5,1,4,3,2,7]=>[7,1,5,6,2,3,4]=>[1,7,3,2,6,5,4]=>011110
[6,5,1,4,3,7,2]=>[1,5,6,3,4,2,7]=>[7,3,2,5,4,6,1]=>111100
[6,5,1,4,7,2,3]=>[1,5,6,4,2,7,3]=>[7,3,2,4,6,1,5]=>111000
[6,5,1,4,7,3,2]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>111010
[6,5,1,7,2,3,4]=>[1,5,6,2,7,4,3]=>[7,3,2,6,1,4,5]=>111000
[6,5,1,7,2,4,3]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>111100
[6,5,1,7,3,2,4]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>111010
[6,5,1,7,3,4,2]=>[1,5,6,3,7,2,4]=>[7,3,2,5,1,6,4]=>111100
[6,5,1,7,4,2,3]=>[1,5,6,2,4,7,3]=>[7,3,2,6,4,1,5]=>111100
[6,5,1,7,4,3,2]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>111110
[6,5,2,1,3,4,7]=>[7,1,2,5,6,4,3]=>[1,7,6,3,2,4,5]=>011001
[6,5,2,1,3,7,4]=>[1,2,5,6,4,7,3]=>[7,6,3,2,4,1,5]=>111001
[6,5,2,1,4,3,7]=>[7,1,2,5,6,3,4]=>[1,7,6,3,2,5,4]=>011101
[6,5,2,1,4,7,3]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>111001
[6,5,2,1,7,3,4]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>111001
[6,5,2,1,7,4,3]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>111101
[6,5,2,3,1,4,7]=>[7,2,5,6,4,1,3]=>[1,6,3,2,4,7,5]=>011010
[6,5,2,3,1,7,4]=>[2,5,6,4,7,1,3]=>[6,3,2,4,1,7,5]=>111010
[6,5,2,3,4,1,7]=>[7,2,5,6,3,1,4]=>[1,6,3,2,5,7,4]=>011100
[6,5,2,3,4,7,1]=>[2,5,6,4,3,1,7]=>[6,3,2,4,5,7,1]=>111000
[6,5,2,3,7,1,4]=>[2,5,6,3,1,7,4]=>[6,3,2,5,7,1,4]=>111000
[6,5,2,3,7,4,1]=>[2,5,6,3,1,4,7]=>[6,3,2,5,7,4,1]=>111100
[6,5,2,4,1,3,7]=>[7,2,5,6,1,4,3]=>[1,6,3,2,7,4,5]=>011100
[6,5,2,4,1,7,3]=>[2,5,6,1,4,3,7]=>[6,3,2,7,4,5,1]=>111100
[6,5,2,4,3,1,7]=>[7,2,5,6,1,3,4]=>[1,6,3,2,7,5,4]=>011110
[6,5,2,4,3,7,1]=>[2,5,6,3,4,1,7]=>[6,3,2,5,4,7,1]=>111100
[6,5,2,4,7,1,3]=>[2,5,6,4,1,7,3]=>[6,3,2,4,7,1,5]=>111000
[6,5,2,4,7,3,1]=>[2,5,6,4,1,3,7]=>[6,3,2,4,7,5,1]=>111010
[6,5,2,7,1,3,4]=>[2,5,6,1,7,4,3]=>[6,3,2,7,1,4,5]=>111000
[6,5,2,7,1,4,3]=>[2,5,6,1,7,3,4]=>[6,3,2,7,1,5,4]=>111100
[6,5,2,7,3,1,4]=>[2,5,6,1,3,7,4]=>[6,3,2,7,5,1,4]=>111010
[6,5,2,7,3,4,1]=>[2,5,6,3,7,1,4]=>[6,3,2,5,1,7,4]=>111100
[6,5,2,7,4,1,3]=>[2,5,6,1,4,7,3]=>[6,3,2,7,4,1,5]=>111100
[6,5,2,7,4,3,1]=>[2,5,6,1,3,4,7]=>[6,3,2,7,5,4,1]=>111110
[6,5,3,1,2,4,7]=>[7,1,3,5,6,4,2]=>[1,7,5,3,2,4,6]=>011010
[6,5,3,1,2,7,4]=>[1,3,5,6,4,7,2]=>[7,5,3,2,4,1,6]=>111010
[6,5,3,1,4,2,7]=>[7,1,3,5,6,2,4]=>[1,7,5,3,2,6,4]=>011110
[6,5,3,1,4,7,2]=>[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>111010
[6,5,3,1,7,2,4]=>[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]=>111010
[6,5,3,1,7,4,2]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>111110
[6,5,3,2,1,4,7]=>[7,1,2,3,5,6,4]=>[1,7,6,5,3,2,4]=>011011
[6,5,3,2,1,7,4]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>111011
[6,5,3,2,4,1,7]=>[7,2,3,5,6,1,4]=>[1,6,5,3,2,7,4]=>011110
[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>[6,5,3,2,4,7,1]=>111010
[6,5,3,2,7,1,4]=>[2,3,5,6,1,7,4]=>[6,5,3,2,7,1,4]=>111010
[6,5,3,2,7,4,1]=>[2,3,5,6,1,4,7]=>[6,5,3,2,7,4,1]=>111110
[6,5,3,4,1,2,7]=>[7,3,5,6,1,4,2]=>[1,5,3,2,7,4,6]=>011100
[6,5,3,4,1,7,2]=>[3,5,6,1,4,2,7]=>[5,3,2,7,4,6,1]=>111100
[6,5,3,4,2,1,7]=>[7,3,5,6,1,2,4]=>[1,5,3,2,7,6,4]=>011101
[6,5,3,4,2,7,1]=>[3,5,6,2,4,1,7]=>[5,3,2,6,4,7,1]=>111100
[6,5,3,4,7,1,2]=>[3,5,6,4,1,7,2]=>[5,3,2,4,7,1,6]=>111000
[6,5,3,4,7,2,1]=>[3,5,6,4,1,2,7]=>[5,3,2,4,7,6,1]=>111001
[6,5,3,7,1,2,4]=>[3,5,6,1,7,4,2]=>[5,3,2,7,1,4,6]=>111000
[6,5,3,7,1,4,2]=>[3,5,6,1,7,2,4]=>[5,3,2,7,1,6,4]=>111100
[6,5,3,7,2,1,4]=>[3,5,6,1,2,7,4]=>[5,3,2,7,6,1,4]=>111001
[6,5,3,7,2,4,1]=>[3,5,6,2,7,1,4]=>[5,3,2,6,1,7,4]=>111100
[6,5,3,7,4,1,2]=>[3,5,6,1,4,7,2]=>[5,3,2,7,4,1,6]=>111100
[6,5,3,7,4,2,1]=>[3,5,6,1,2,4,7]=>[5,3,2,7,6,4,1]=>111101
[6,5,4,1,2,3,7]=>[7,1,4,5,6,3,2]=>[1,7,4,3,2,5,6]=>011100
[6,5,4,1,2,7,3]=>[1,4,5,6,3,7,2]=>[7,4,3,2,5,1,6]=>111100
[6,5,4,1,3,2,7]=>[7,1,4,5,6,2,3]=>[1,7,4,3,2,6,5]=>011110
[6,5,4,1,3,7,2]=>[1,4,5,6,3,2,7]=>[7,4,3,2,5,6,1]=>111100
[6,5,4,1,7,2,3]=>[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]=>111100
[6,5,4,1,7,3,2]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>111110
[6,5,4,2,1,3,7]=>[7,1,2,4,5,6,3]=>[1,7,6,4,3,2,5]=>011101
[6,5,4,2,1,7,3]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>111101
[6,5,4,2,3,1,7]=>[7,2,4,5,6,1,3]=>[1,6,4,3,2,7,5]=>011110
[6,5,4,2,3,7,1]=>[2,4,5,6,3,1,7]=>[6,4,3,2,5,7,1]=>111100
[6,5,4,2,7,1,3]=>[2,4,5,6,1,7,3]=>[6,4,3,2,7,1,5]=>111100
[6,5,4,2,7,3,1]=>[2,4,5,6,1,3,7]=>[6,4,3,2,7,5,1]=>111110
[6,5,4,3,1,2,7]=>[7,1,3,4,5,6,2]=>[1,7,5,4,3,2,6]=>011110
[6,5,4,3,1,7,2]=>[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>111110
[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>011111
[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>111110
[6,5,4,3,7,1,2]=>[3,4,5,6,1,7,2]=>[5,4,3,2,7,1,6]=>111100
[6,5,4,3,7,2,1]=>[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>111101
[6,5,4,7,1,2,3]=>[4,5,6,1,7,3,2]=>[4,3,2,7,1,5,6]=>111000
[6,5,4,7,1,3,2]=>[4,5,6,1,7,2,3]=>[4,3,2,7,1,6,5]=>111010
[6,5,4,7,2,1,3]=>[4,5,6,1,2,7,3]=>[4,3,2,7,6,1,5]=>111001
[6,5,4,7,2,3,1]=>[4,5,6,2,7,1,3]=>[4,3,2,6,1,7,5]=>111010
[6,5,4,7,3,1,2]=>[4,5,6,1,3,7,2]=>[4,3,2,7,5,1,6]=>111010
[6,5,4,7,3,2,1]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>111011
[6,5,7,1,2,3,4]=>[5,6,1,7,4,3,2]=>[3,2,7,1,4,5,6]=>110000
[6,5,7,1,2,4,3]=>[5,6,1,7,3,4,2]=>[3,2,7,1,5,4,6]=>110100
[6,5,7,1,3,2,4]=>[5,6,1,7,4,2,3]=>[3,2,7,1,4,6,5]=>110010
[6,5,7,1,3,4,2]=>[5,6,1,7,3,2,4]=>[3,2,7,1,5,6,4]=>110100
[6,5,7,1,4,2,3]=>[5,6,1,7,2,4,3]=>[3,2,7,1,6,4,5]=>110100
[6,5,7,1,4,3,2]=>[5,6,1,7,2,3,4]=>[3,2,7,1,6,5,4]=>110110
[6,5,7,2,1,3,4]=>[5,6,1,2,7,4,3]=>[3,2,7,6,1,4,5]=>110001
[6,5,7,2,1,4,3]=>[5,6,1,2,7,3,4]=>[3,2,7,6,1,5,4]=>110101
[6,5,7,2,3,1,4]=>[5,6,2,7,4,1,3]=>[3,2,6,1,4,7,5]=>110010
[6,5,7,2,3,4,1]=>[5,6,2,7,3,1,4]=>[3,2,6,1,5,7,4]=>110100
[6,5,7,2,4,1,3]=>[5,6,2,7,1,4,3]=>[3,2,6,1,7,4,5]=>110100
[6,5,7,2,4,3,1]=>[5,6,2,7,1,3,4]=>[3,2,6,1,7,5,4]=>110110
[6,5,7,3,1,2,4]=>[5,6,1,3,7,4,2]=>[3,2,7,5,1,4,6]=>110010
[6,5,7,3,1,4,2]=>[5,6,1,3,7,2,4]=>[3,2,7,5,1,6,4]=>110110
[6,5,7,3,2,1,4]=>[5,6,1,2,3,7,4]=>[3,2,7,6,5,1,4]=>110011
[6,5,7,3,2,4,1]=>[5,6,2,3,7,1,4]=>[3,2,6,5,1,7,4]=>110110
[6,5,7,3,4,1,2]=>[5,6,3,7,1,4,2]=>[3,2,5,1,7,4,6]=>110100
[6,5,7,3,4,2,1]=>[5,6,3,7,1,2,4]=>[3,2,5,1,7,6,4]=>110101
[6,5,7,4,1,2,3]=>[5,6,1,4,7,3,2]=>[3,2,7,4,1,5,6]=>110100
[6,5,7,4,1,3,2]=>[5,6,1,4,7,2,3]=>[3,2,7,4,1,6,5]=>110110
[6,5,7,4,2,1,3]=>[5,6,1,2,4,7,3]=>[3,2,7,6,4,1,5]=>110101
[6,5,7,4,2,3,1]=>[5,6,2,4,7,1,3]=>[3,2,6,4,1,7,5]=>110110
[6,5,7,4,3,1,2]=>[5,6,1,3,4,7,2]=>[3,2,7,5,4,1,6]=>110110
[6,5,7,4,3,2,1]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>110111
[6,7,1,2,3,4,5]=>[6,1,7,5,4,3,2]=>[2,7,1,3,4,5,6]=>100000
[6,7,1,2,3,5,4]=>[6,1,7,4,5,3,2]=>[2,7,1,4,3,5,6]=>101000
[6,7,1,2,4,3,5]=>[6,1,7,5,3,4,2]=>[2,7,1,3,5,4,6]=>100100
[6,7,1,2,4,5,3]=>[6,1,7,4,3,5,2]=>[2,7,1,4,5,3,6]=>101000
[6,7,1,2,5,3,4]=>[6,1,7,3,5,4,2]=>[2,7,1,5,3,4,6]=>101000
[6,7,1,2,5,4,3]=>[6,1,7,3,4,5,2]=>[2,7,1,5,4,3,6]=>101100
[6,7,1,3,2,4,5]=>[6,1,7,5,4,2,3]=>[2,7,1,3,4,6,5]=>100010
[6,7,1,3,2,5,4]=>[6,1,7,4,5,2,3]=>[2,7,1,4,3,6,5]=>101010
[6,7,1,3,4,2,5]=>[6,1,7,5,3,2,4]=>[2,7,1,3,5,6,4]=>100100
[6,7,1,3,4,5,2]=>[6,1,7,4,3,2,5]=>[2,7,1,4,5,6,3]=>101000
[6,7,1,3,5,2,4]=>[6,1,7,3,2,5,4]=>[2,7,1,5,6,3,4]=>101000
[6,7,1,3,5,4,2]=>[6,1,7,3,2,4,5]=>[2,7,1,5,6,4,3]=>101100
[6,7,1,4,2,3,5]=>[6,1,7,5,2,4,3]=>[2,7,1,3,6,4,5]=>100100
[6,7,1,4,2,5,3]=>[6,1,7,2,4,3,5]=>[2,7,1,6,4,5,3]=>101100
[6,7,1,4,3,2,5]=>[6,1,7,5,2,3,4]=>[2,7,1,3,6,5,4]=>100110
[6,7,1,4,3,5,2]=>[6,1,7,3,4,2,5]=>[2,7,1,5,4,6,3]=>101100
[6,7,1,4,5,2,3]=>[6,1,7,4,2,5,3]=>[2,7,1,4,6,3,5]=>101000
[6,7,1,4,5,3,2]=>[6,1,7,4,2,3,5]=>[2,7,1,4,6,5,3]=>101010
[6,7,1,5,2,3,4]=>[6,1,7,2,5,4,3]=>[2,7,1,6,3,4,5]=>101000
[6,7,1,5,2,4,3]=>[6,1,7,2,5,3,4]=>[2,7,1,6,3,5,4]=>101100
[6,7,1,5,3,2,4]=>[6,1,7,2,3,5,4]=>[2,7,1,6,5,3,4]=>101010
[6,7,1,5,3,4,2]=>[6,1,7,3,5,2,4]=>[2,7,1,5,3,6,4]=>101100
[6,7,1,5,4,2,3]=>[6,1,7,2,4,5,3]=>[2,7,1,6,4,3,5]=>101100
[6,7,1,5,4,3,2]=>[6,1,7,2,3,4,5]=>[2,7,1,6,5,4,3]=>101110
[6,7,2,1,3,4,5]=>[6,1,2,7,5,4,3]=>[2,7,6,1,3,4,5]=>100001
[6,7,2,1,3,5,4]=>[6,1,2,7,4,5,3]=>[2,7,6,1,4,3,5]=>101001
[6,7,2,1,4,3,5]=>[6,1,2,7,5,3,4]=>[2,7,6,1,3,5,4]=>100101
[6,7,2,1,4,5,3]=>[6,1,2,7,4,3,5]=>[2,7,6,1,4,5,3]=>101001
[6,7,2,1,5,3,4]=>[6,1,2,7,3,5,4]=>[2,7,6,1,5,3,4]=>101001
[6,7,2,1,5,4,3]=>[6,1,2,7,3,4,5]=>[2,7,6,1,5,4,3]=>101101
[6,7,2,3,1,4,5]=>[6,2,7,5,4,1,3]=>[2,6,1,3,4,7,5]=>100010
[6,7,2,3,1,5,4]=>[6,2,7,4,5,1,3]=>[2,6,1,4,3,7,5]=>101010
[6,7,2,3,4,1,5]=>[6,2,7,5,3,1,4]=>[2,6,1,3,5,7,4]=>100100
[6,7,2,3,4,5,1]=>[6,2,7,4,3,1,5]=>[2,6,1,4,5,7,3]=>101000
[6,7,2,3,5,1,4]=>[6,2,7,3,1,5,4]=>[2,6,1,5,7,3,4]=>101000
[6,7,2,3,5,4,1]=>[6,2,7,3,1,4,5]=>[2,6,1,5,7,4,3]=>101100
[6,7,2,4,1,3,5]=>[6,2,7,5,1,4,3]=>[2,6,1,3,7,4,5]=>100100
[6,7,2,4,1,5,3]=>[6,2,7,1,4,3,5]=>[2,6,1,7,4,5,3]=>101100
[6,7,2,4,3,1,5]=>[6,2,7,5,1,3,4]=>[2,6,1,3,7,5,4]=>100110
[6,7,2,4,3,5,1]=>[6,2,7,3,4,1,5]=>[2,6,1,5,4,7,3]=>101100
[6,7,2,4,5,1,3]=>[6,2,7,4,1,5,3]=>[2,6,1,4,7,3,5]=>101000
[6,7,2,4,5,3,1]=>[6,2,7,4,1,3,5]=>[2,6,1,4,7,5,3]=>101010
[6,7,2,5,1,3,4]=>[6,2,7,1,5,4,3]=>[2,6,1,7,3,4,5]=>101000
[6,7,2,5,1,4,3]=>[6,2,7,1,5,3,4]=>[2,6,1,7,3,5,4]=>101100
[6,7,2,5,3,1,4]=>[6,2,7,1,3,5,4]=>[2,6,1,7,5,3,4]=>101010
[6,7,2,5,3,4,1]=>[6,2,7,3,5,1,4]=>[2,6,1,5,3,7,4]=>101100
[6,7,2,5,4,1,3]=>[6,2,7,1,4,5,3]=>[2,6,1,7,4,3,5]=>101100
[6,7,2,5,4,3,1]=>[6,2,7,1,3,4,5]=>[2,6,1,7,5,4,3]=>101110
[6,7,3,1,2,4,5]=>[6,1,3,7,5,4,2]=>[2,7,5,1,3,4,6]=>100010
[6,7,3,1,2,5,4]=>[6,1,3,7,4,5,2]=>[2,7,5,1,4,3,6]=>101010
[6,7,3,1,4,2,5]=>[6,1,3,7,5,2,4]=>[2,7,5,1,3,6,4]=>100110
[6,7,3,1,4,5,2]=>[6,1,3,7,4,2,5]=>[2,7,5,1,4,6,3]=>101010
[6,7,3,1,5,2,4]=>[6,1,3,7,2,5,4]=>[2,7,5,1,6,3,4]=>101010
[6,7,3,1,5,4,2]=>[6,1,3,7,2,4,5]=>[2,7,5,1,6,4,3]=>101110
[6,7,3,2,1,4,5]=>[6,1,2,3,7,5,4]=>[2,7,6,5,1,3,4]=>100011
[6,7,3,2,1,5,4]=>[6,1,2,3,7,4,5]=>[2,7,6,5,1,4,3]=>101011
[6,7,3,2,4,1,5]=>[6,2,3,7,5,1,4]=>[2,6,5,1,3,7,4]=>100110
[6,7,3,2,4,5,1]=>[6,2,3,7,4,1,5]=>[2,6,5,1,4,7,3]=>101010
[6,7,3,2,5,1,4]=>[6,2,3,7,1,5,4]=>[2,6,5,1,7,3,4]=>101010
[6,7,3,2,5,4,1]=>[6,2,3,7,1,4,5]=>[2,6,5,1,7,4,3]=>101110
[6,7,3,4,1,2,5]=>[6,3,7,5,1,4,2]=>[2,5,1,3,7,4,6]=>100100
[6,7,3,4,1,5,2]=>[6,3,7,1,4,2,5]=>[2,5,1,7,4,6,3]=>101100
[6,7,3,4,2,1,5]=>[6,3,7,5,1,2,4]=>[2,5,1,3,7,6,4]=>100101
[6,7,3,4,2,5,1]=>[6,3,7,2,4,1,5]=>[2,5,1,6,4,7,3]=>101100
[6,7,3,4,5,1,2]=>[6,3,7,4,1,5,2]=>[2,5,1,4,7,3,6]=>101000
[6,7,3,4,5,2,1]=>[6,3,7,4,1,2,5]=>[2,5,1,4,7,6,3]=>101001
[6,7,3,5,1,2,4]=>[6,3,7,1,5,4,2]=>[2,5,1,7,3,4,6]=>101000
[6,7,3,5,1,4,2]=>[6,3,7,1,5,2,4]=>[2,5,1,7,3,6,4]=>101100
[6,7,3,5,2,1,4]=>[6,3,7,1,2,5,4]=>[2,5,1,7,6,3,4]=>101001
[6,7,3,5,2,4,1]=>[6,3,7,2,5,1,4]=>[2,5,1,6,3,7,4]=>101100
[6,7,3,5,4,1,2]=>[6,3,7,1,4,5,2]=>[2,5,1,7,4,3,6]=>101100
[6,7,3,5,4,2,1]=>[6,3,7,1,2,4,5]=>[2,5,1,7,6,4,3]=>101101
[6,7,4,1,2,3,5]=>[6,1,4,7,5,3,2]=>[2,7,4,1,3,5,6]=>100100
[6,7,4,1,2,5,3]=>[6,1,4,7,3,5,2]=>[2,7,4,1,5,3,6]=>101100
[6,7,4,1,3,2,5]=>[6,1,4,7,5,2,3]=>[2,7,4,1,3,6,5]=>100110
[6,7,4,1,3,5,2]=>[6,1,4,7,3,2,5]=>[2,7,4,1,5,6,3]=>101100
[6,7,4,1,5,2,3]=>[6,1,4,7,2,5,3]=>[2,7,4,1,6,3,5]=>101100
[6,7,4,1,5,3,2]=>[6,1,4,7,2,3,5]=>[2,7,4,1,6,5,3]=>101110
[6,7,4,2,1,3,5]=>[6,1,2,4,7,5,3]=>[2,7,6,4,1,3,5]=>100101
[6,7,4,2,1,5,3]=>[6,1,2,4,7,3,5]=>[2,7,6,4,1,5,3]=>101101
[6,7,4,2,3,1,5]=>[6,2,4,7,5,1,3]=>[2,6,4,1,3,7,5]=>100110
[6,7,4,2,3,5,1]=>[6,2,4,7,3,1,5]=>[2,6,4,1,5,7,3]=>101100
[6,7,4,2,5,1,3]=>[6,2,4,7,1,5,3]=>[2,6,4,1,7,3,5]=>101100
[6,7,4,2,5,3,1]=>[6,2,4,7,1,3,5]=>[2,6,4,1,7,5,3]=>101110
[6,7,4,3,1,2,5]=>[6,1,3,4,7,5,2]=>[2,7,5,4,1,3,6]=>100110
[6,7,4,3,1,5,2]=>[6,1,3,4,7,2,5]=>[2,7,5,4,1,6,3]=>101110
[6,7,4,3,2,1,5]=>[6,1,2,3,4,7,5]=>[2,7,6,5,4,1,3]=>100111
[6,7,4,3,2,5,1]=>[6,2,3,4,7,1,5]=>[2,6,5,4,1,7,3]=>101110
[6,7,4,3,5,1,2]=>[6,3,4,7,1,5,2]=>[2,5,4,1,7,3,6]=>101100
[6,7,4,3,5,2,1]=>[6,3,4,7,1,2,5]=>[2,5,4,1,7,6,3]=>101101
[6,7,4,5,1,2,3]=>[6,4,7,1,5,3,2]=>[2,4,1,7,3,5,6]=>101000
[6,7,4,5,1,3,2]=>[6,4,7,1,5,2,3]=>[2,4,1,7,3,6,5]=>101010
[6,7,4,5,2,1,3]=>[6,4,7,1,2,5,3]=>[2,4,1,7,6,3,5]=>101001
[6,7,4,5,2,3,1]=>[6,4,7,2,5,1,3]=>[2,4,1,6,3,7,5]=>101010
[6,7,4,5,3,1,2]=>[6,4,7,1,3,5,2]=>[2,4,1,7,5,3,6]=>101010
[6,7,4,5,3,2,1]=>[6,4,7,1,2,3,5]=>[2,4,1,7,6,5,3]=>101011
[6,7,5,1,2,3,4]=>[6,1,5,7,4,3,2]=>[2,7,3,1,4,5,6]=>101000
[6,7,5,1,2,4,3]=>[6,1,5,7,3,4,2]=>[2,7,3,1,5,4,6]=>101100
[6,7,5,1,3,2,4]=>[6,1,5,7,4,2,3]=>[2,7,3,1,4,6,5]=>101010
[6,7,5,1,3,4,2]=>[6,1,5,7,3,2,4]=>[2,7,3,1,5,6,4]=>101100
[6,7,5,1,4,2,3]=>[6,1,5,7,2,4,3]=>[2,7,3,1,6,4,5]=>101100
[6,7,5,1,4,3,2]=>[6,1,5,7,2,3,4]=>[2,7,3,1,6,5,4]=>101110
[6,7,5,2,1,3,4]=>[6,1,2,5,7,4,3]=>[2,7,6,3,1,4,5]=>101001
[6,7,5,2,1,4,3]=>[6,1,2,5,7,3,4]=>[2,7,6,3,1,5,4]=>101101
[6,7,5,2,3,1,4]=>[6,2,5,7,4,1,3]=>[2,6,3,1,4,7,5]=>101010
[6,7,5,2,3,4,1]=>[6,2,5,7,3,1,4]=>[2,6,3,1,5,7,4]=>101100
[6,7,5,2,4,1,3]=>[6,2,5,7,1,4,3]=>[2,6,3,1,7,4,5]=>101100
[6,7,5,2,4,3,1]=>[6,2,5,7,1,3,4]=>[2,6,3,1,7,5,4]=>101110
[6,7,5,3,1,2,4]=>[6,1,3,5,7,4,2]=>[2,7,5,3,1,4,6]=>101010
[6,7,5,3,1,4,2]=>[6,1,3,5,7,2,4]=>[2,7,5,3,1,6,4]=>101110
[6,7,5,3,2,1,4]=>[6,1,2,3,5,7,4]=>[2,7,6,5,3,1,4]=>101011
[6,7,5,3,2,4,1]=>[6,2,3,5,7,1,4]=>[2,6,5,3,1,7,4]=>101110
[6,7,5,3,4,1,2]=>[6,3,5,7,1,4,2]=>[2,5,3,1,7,4,6]=>101100
[6,7,5,3,4,2,1]=>[6,3,5,7,1,2,4]=>[2,5,3,1,7,6,4]=>101101
[6,7,5,4,1,2,3]=>[6,1,4,5,7,3,2]=>[2,7,4,3,1,5,6]=>101100
[6,7,5,4,1,3,2]=>[6,1,4,5,7,2,3]=>[2,7,4,3,1,6,5]=>101110
[6,7,5,4,2,1,3]=>[6,1,2,4,5,7,3]=>[2,7,6,4,3,1,5]=>101101
[6,7,5,4,2,3,1]=>[6,2,4,5,7,1,3]=>[2,6,4,3,1,7,5]=>101110
[6,7,5,4,3,1,2]=>[6,1,3,4,5,7,2]=>[2,7,5,4,3,1,6]=>101110
[6,7,5,4,3,2,1]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>101111
[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>100000
[7,1,2,3,4,6,5]=>[1,7,5,6,4,3,2]=>[7,1,3,2,4,5,6]=>110000
[7,1,2,3,5,4,6]=>[1,7,6,4,5,3,2]=>[7,1,2,4,3,5,6]=>101000
[7,1,2,3,5,6,4]=>[1,7,5,4,6,3,2]=>[7,1,3,4,2,5,6]=>110000
[7,1,2,3,6,4,5]=>[1,7,4,6,5,3,2]=>[7,1,4,2,3,5,6]=>110000
[7,1,2,3,6,5,4]=>[1,7,4,5,6,3,2]=>[7,1,4,3,2,5,6]=>111000
[7,1,2,4,3,5,6]=>[1,7,6,5,3,4,2]=>[7,1,2,3,5,4,6]=>100100
[7,1,2,4,3,6,5]=>[1,7,5,6,3,4,2]=>[7,1,3,2,5,4,6]=>110100
[7,1,2,4,5,3,6]=>[1,7,6,4,3,5,2]=>[7,1,2,4,5,3,6]=>101000
[7,1,2,4,5,6,3]=>[1,7,5,4,3,6,2]=>[7,1,3,4,5,2,6]=>110000
[7,1,2,4,6,3,5]=>[1,7,4,3,6,5,2]=>[7,1,4,5,2,3,6]=>110000
[7,1,2,4,6,5,3]=>[1,7,4,3,5,6,2]=>[7,1,4,5,3,2,6]=>111000
[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>[7,1,2,5,3,4,6]=>101000
[7,1,2,5,3,6,4]=>[1,7,3,5,4,6,2]=>[7,1,5,3,4,2,6]=>111000
[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>[7,1,2,5,4,3,6]=>101100
[7,1,2,5,4,6,3]=>[1,7,4,5,3,6,2]=>[7,1,4,3,5,2,6]=>111000
[7,1,2,5,6,3,4]=>[1,7,5,3,6,4,2]=>[7,1,3,5,2,4,6]=>110000
[7,1,2,5,6,4,3]=>[1,7,5,3,4,6,2]=>[7,1,3,5,4,2,6]=>110100
[7,1,2,6,3,4,5]=>[1,7,3,6,5,4,2]=>[7,1,5,2,3,4,6]=>110000
[7,1,2,6,3,5,4]=>[1,7,3,6,4,5,2]=>[7,1,5,2,4,3,6]=>111000
[7,1,2,6,4,3,5]=>[1,7,3,4,6,5,2]=>[7,1,5,4,2,3,6]=>110100
[7,1,2,6,4,5,3]=>[1,7,4,6,3,5,2]=>[7,1,4,2,5,3,6]=>111000
[7,1,2,6,5,3,4]=>[1,7,3,5,6,4,2]=>[7,1,5,3,2,4,6]=>111000
[7,1,2,6,5,4,3]=>[1,7,3,4,5,6,2]=>[7,1,5,4,3,2,6]=>111100
[7,1,3,2,4,5,6]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>100010
[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>[7,1,3,2,4,6,5]=>110010
[7,1,3,2,5,4,6]=>[1,7,6,4,5,2,3]=>[7,1,2,4,3,6,5]=>101010
[7,1,3,2,5,6,4]=>[1,7,5,4,6,2,3]=>[7,1,3,4,2,6,5]=>110010
[7,1,3,2,6,4,5]=>[1,7,4,6,5,2,3]=>[7,1,4,2,3,6,5]=>110010
[7,1,3,2,6,5,4]=>[1,7,4,5,6,2,3]=>[7,1,4,3,2,6,5]=>111010
[7,1,3,4,2,5,6]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>100100
[7,1,3,4,2,6,5]=>[1,7,5,6,3,2,4]=>[7,1,3,2,5,6,4]=>110100
[7,1,3,4,5,2,6]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>101000
[7,1,3,4,5,6,2]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>110000
[7,1,3,4,6,2,5]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>110000
[7,1,3,4,6,5,2]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>111000
[7,1,3,5,2,4,6]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>101000
[7,1,3,5,2,6,4]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>111000
[7,1,3,5,4,2,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>101100
[7,1,3,5,4,6,2]=>[1,7,4,5,3,2,6]=>[7,1,4,3,5,6,2]=>111000
[7,1,3,5,6,2,4]=>[1,7,5,3,2,6,4]=>[7,1,3,5,6,2,4]=>110000
[7,1,3,5,6,4,2]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>110100
[7,1,3,6,2,4,5]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>110000
[7,1,3,6,2,5,4]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>111000
[7,1,3,6,4,2,5]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>110100
[7,1,3,6,4,5,2]=>[1,7,4,6,3,2,5]=>[7,1,4,2,5,6,3]=>111000
[7,1,3,6,5,2,4]=>[1,7,3,2,5,6,4]=>[7,1,5,6,3,2,4]=>111000
[7,1,3,6,5,4,2]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>111100
[7,1,4,2,3,5,6]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>100100
[7,1,4,2,3,6,5]=>[1,7,5,6,2,4,3]=>[7,1,3,2,6,4,5]=>110100
[7,1,4,2,5,3,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>101100
[7,1,4,2,5,6,3]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>110100
[7,1,4,2,6,3,5]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>110100
[7,1,4,2,6,5,3]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>111100
[7,1,4,3,2,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>100110
[7,1,4,3,2,6,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>110110
[7,1,4,3,5,2,6]=>[1,7,6,3,4,2,5]=>[7,1,2,5,4,6,3]=>101100
[7,1,4,3,5,6,2]=>[1,7,5,3,4,2,6]=>[7,1,3,5,4,6,2]=>110100
[7,1,4,3,6,2,5]=>[1,7,3,4,2,6,5]=>[7,1,5,4,6,2,3]=>110100
[7,1,4,3,6,5,2]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>111100
[7,1,4,5,2,3,6]=>[1,7,6,4,2,5,3]=>[7,1,2,4,6,3,5]=>101000
[7,1,4,5,2,6,3]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>111000
[7,1,4,5,3,2,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>101010
[7,1,4,5,3,6,2]=>[1,7,4,3,5,2,6]=>[7,1,4,5,3,6,2]=>111000
[7,1,4,5,6,2,3]=>[1,7,5,4,2,6,3]=>[7,1,3,4,6,2,5]=>110000
[7,1,4,5,6,3,2]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>110010
[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]=>[7,1,4,6,2,3,5]=>110000
[7,1,4,6,2,5,3]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>111000
[7,1,4,6,3,2,5]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>110010
[7,1,4,6,3,5,2]=>[1,7,4,3,6,2,5]=>[7,1,4,5,2,6,3]=>111000
[7,1,4,6,5,2,3]=>[1,7,4,2,5,6,3]=>[7,1,4,6,3,2,5]=>111000
[7,1,4,6,5,3,2]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>111010
[7,1,5,2,3,4,6]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>101000
[7,1,5,2,3,6,4]=>[1,7,2,5,4,6,3]=>[7,1,6,3,4,2,5]=>111000
[7,1,5,2,4,3,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>101100
[7,1,5,2,4,6,3]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>111000
[7,1,5,2,6,3,4]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>111000
[7,1,5,2,6,4,3]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>111100
[7,1,5,3,2,4,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>101010
[7,1,5,3,2,6,4]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>111010
[7,1,5,3,4,2,6]=>[1,7,6,3,5,2,4]=>[7,1,2,5,3,6,4]=>101100
[7,1,5,3,4,6,2]=>[1,7,3,5,4,2,6]=>[7,1,5,3,4,6,2]=>111000
[7,1,5,3,6,2,4]=>[1,7,3,5,2,6,4]=>[7,1,5,3,6,2,4]=>111000
[7,1,5,3,6,4,2]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>111100
[7,1,5,4,2,3,6]=>[1,7,6,2,4,5,3]=>[7,1,2,6,4,3,5]=>101100
[7,1,5,4,2,6,3]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>111100
[7,1,5,4,3,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>101110
[7,1,5,4,3,6,2]=>[1,7,3,4,5,2,6]=>[7,1,5,4,3,6,2]=>111100
[7,1,5,4,6,2,3]=>[1,7,4,5,2,6,3]=>[7,1,4,3,6,2,5]=>111000
[7,1,5,4,6,3,2]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>111010
[7,1,5,6,2,3,4]=>[1,7,5,2,6,4,3]=>[7,1,3,6,2,4,5]=>110000
[7,1,5,6,2,4,3]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>110100
[7,1,5,6,3,2,4]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>110010
[7,1,5,6,3,4,2]=>[1,7,5,3,6,2,4]=>[7,1,3,5,2,6,4]=>110100
[7,1,5,6,4,2,3]=>[1,7,5,2,4,6,3]=>[7,1,3,6,4,2,5]=>110100
[7,1,5,6,4,3,2]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>110110
[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>110000
[7,1,6,2,3,5,4]=>[1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>111000
[7,1,6,2,4,3,5]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>110100
[7,1,6,2,4,5,3]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>111000
[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>111000
[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>111100
[7,1,6,3,2,4,5]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>110010
[7,1,6,3,2,5,4]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>111010
[7,1,6,3,4,2,5]=>[1,7,3,6,5,2,4]=>[7,1,5,2,3,6,4]=>110100
[7,1,6,3,4,5,2]=>[1,7,3,6,4,2,5]=>[7,1,5,2,4,6,3]=>111000
[7,1,6,3,5,2,4]=>[1,7,3,6,2,5,4]=>[7,1,5,2,6,3,4]=>111000
[7,1,6,3,5,4,2]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>111100
[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>[7,1,6,4,2,3,5]=>110100
[7,1,6,4,2,5,3]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>111100
[7,1,6,4,3,2,5]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>110110
[7,1,6,4,3,5,2]=>[1,7,3,4,6,2,5]=>[7,1,5,4,2,6,3]=>111100
[7,1,6,4,5,2,3]=>[1,7,4,6,2,5,3]=>[7,1,4,2,6,3,5]=>111000
[7,1,6,4,5,3,2]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>111010
[7,1,6,5,2,3,4]=>[1,7,2,5,6,4,3]=>[7,1,6,3,2,4,5]=>111000
[7,1,6,5,2,4,3]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>111100
[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>111010
[7,1,6,5,3,4,2]=>[1,7,3,5,6,2,4]=>[7,1,5,3,2,6,4]=>111100
[7,1,6,5,4,2,3]=>[1,7,2,4,5,6,3]=>[7,1,6,4,3,2,5]=>111100
[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>111110
[7,2,1,3,4,5,6]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>100001
[7,2,1,3,4,6,5]=>[1,2,7,5,6,4,3]=>[7,6,1,3,2,4,5]=>110001
[7,2,1,3,5,4,6]=>[1,2,7,6,4,5,3]=>[7,6,1,2,4,3,5]=>101001
[7,2,1,3,5,6,4]=>[1,2,7,5,4,6,3]=>[7,6,1,3,4,2,5]=>110001
[7,2,1,3,6,4,5]=>[1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>110001
[7,2,1,3,6,5,4]=>[1,2,7,4,5,6,3]=>[7,6,1,4,3,2,5]=>111001
[7,2,1,4,3,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>100101
[7,2,1,4,3,6,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>110101
[7,2,1,4,5,3,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>101001
[7,2,1,4,5,6,3]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>110001
[7,2,1,4,6,3,5]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>110001
[7,2,1,4,6,5,3]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>111001
[7,2,1,5,3,4,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>101001
[7,2,1,5,3,6,4]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>111001
[7,2,1,5,4,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>101101
[7,2,1,5,4,6,3]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>111001
[7,2,1,5,6,3,4]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>110001
[7,2,1,5,6,4,3]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>110101
[7,2,1,6,3,4,5]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>110001
[7,2,1,6,3,5,4]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>111001
[7,2,1,6,4,3,5]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>110101
[7,2,1,6,4,5,3]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>111001
[7,2,1,6,5,3,4]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>111001
[7,2,1,6,5,4,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>111101
[7,2,3,1,4,5,6]=>[2,7,6,5,4,1,3]=>[6,1,2,3,4,7,5]=>100010
[7,2,3,1,4,6,5]=>[2,7,5,6,4,1,3]=>[6,1,3,2,4,7,5]=>110010
[7,2,3,1,5,4,6]=>[2,7,6,4,5,1,3]=>[6,1,2,4,3,7,5]=>101010
[7,2,3,1,5,6,4]=>[2,7,5,4,6,1,3]=>[6,1,3,4,2,7,5]=>110010
[7,2,3,1,6,4,5]=>[2,7,4,6,5,1,3]=>[6,1,4,2,3,7,5]=>110010
[7,2,3,1,6,5,4]=>[2,7,4,5,6,1,3]=>[6,1,4,3,2,7,5]=>111010
[7,2,3,4,1,5,6]=>[2,7,6,5,3,1,4]=>[6,1,2,3,5,7,4]=>100100
[7,2,3,4,1,6,5]=>[2,7,5,6,3,1,4]=>[6,1,3,2,5,7,4]=>110100
[7,2,3,4,5,1,6]=>[2,7,6,4,3,1,5]=>[6,1,2,4,5,7,3]=>101000
[7,2,3,4,5,6,1]=>[2,7,5,4,3,1,6]=>[6,1,3,4,5,7,2]=>110000
[7,2,3,4,6,1,5]=>[2,7,4,3,1,6,5]=>[6,1,4,5,7,2,3]=>110000
[7,2,3,4,6,5,1]=>[2,7,4,3,1,5,6]=>[6,1,4,5,7,3,2]=>111000
[7,2,3,5,1,4,6]=>[2,7,6,3,1,5,4]=>[6,1,2,5,7,3,4]=>101000
[7,2,3,5,1,6,4]=>[2,7,3,1,5,4,6]=>[6,1,5,7,3,4,2]=>111000
[7,2,3,5,4,1,6]=>[2,7,6,3,1,4,5]=>[6,1,2,5,7,4,3]=>101100
[7,2,3,5,4,6,1]=>[2,7,4,5,3,1,6]=>[6,1,4,3,5,7,2]=>111000
[7,2,3,5,6,1,4]=>[2,7,5,3,1,6,4]=>[6,1,3,5,7,2,4]=>110000
[7,2,3,5,6,4,1]=>[2,7,5,3,1,4,6]=>[6,1,3,5,7,4,2]=>110100
[7,2,3,6,1,4,5]=>[2,7,3,1,6,5,4]=>[6,1,5,7,2,3,4]=>110000
[7,2,3,6,1,5,4]=>[2,7,3,1,6,4,5]=>[6,1,5,7,2,4,3]=>111000
[7,2,3,6,4,1,5]=>[2,7,3,1,4,6,5]=>[6,1,5,7,4,2,3]=>110100
[7,2,3,6,4,5,1]=>[2,7,4,6,3,1,5]=>[6,1,4,2,5,7,3]=>111000
[7,2,3,6,5,1,4]=>[2,7,3,1,5,6,4]=>[6,1,5,7,3,2,4]=>111000
[7,2,3,6,5,4,1]=>[2,7,3,1,4,5,6]=>[6,1,5,7,4,3,2]=>111100
[7,2,4,1,3,5,6]=>[2,7,6,5,1,4,3]=>[6,1,2,3,7,4,5]=>100100
[7,2,4,1,3,6,5]=>[2,7,5,6,1,4,3]=>[6,1,3,2,7,4,5]=>110100
[7,2,4,1,5,3,6]=>[2,7,6,1,4,3,5]=>[6,1,2,7,4,5,3]=>101100
[7,2,4,1,5,6,3]=>[2,7,5,1,4,3,6]=>[6,1,3,7,4,5,2]=>110100
[7,2,4,1,6,3,5]=>[2,7,1,4,3,6,5]=>[6,1,7,4,5,2,3]=>110100
[7,2,4,1,6,5,3]=>[2,7,1,4,3,5,6]=>[6,1,7,4,5,3,2]=>111100
[7,2,4,3,1,5,6]=>[2,7,6,5,1,3,4]=>[6,1,2,3,7,5,4]=>100110
[7,2,4,3,1,6,5]=>[2,7,5,6,1,3,4]=>[6,1,3,2,7,5,4]=>110110
[7,2,4,3,5,1,6]=>[2,7,6,3,4,1,5]=>[6,1,2,5,4,7,3]=>101100
[7,2,4,3,5,6,1]=>[2,7,5,3,4,1,6]=>[6,1,3,5,4,7,2]=>110100
[7,2,4,3,6,1,5]=>[2,7,3,4,1,6,5]=>[6,1,5,4,7,2,3]=>110100
[7,2,4,3,6,5,1]=>[2,7,3,4,1,5,6]=>[6,1,5,4,7,3,2]=>111100
[7,2,4,5,1,3,6]=>[2,7,6,4,1,5,3]=>[6,1,2,4,7,3,5]=>101000
[7,2,4,5,1,6,3]=>[2,7,4,1,5,3,6]=>[6,1,4,7,3,5,2]=>111000
[7,2,4,5,3,1,6]=>[2,7,6,4,1,3,5]=>[6,1,2,4,7,5,3]=>101010
[7,2,4,5,3,6,1]=>[2,7,4,3,5,1,6]=>[6,1,4,5,3,7,2]=>111000
[7,2,4,5,6,1,3]=>[2,7,5,4,1,6,3]=>[6,1,3,4,7,2,5]=>110000
[7,2,4,5,6,3,1]=>[2,7,5,4,1,3,6]=>[6,1,3,4,7,5,2]=>110010
[7,2,4,6,1,3,5]=>[2,7,4,1,6,5,3]=>[6,1,4,7,2,3,5]=>110000
[7,2,4,6,1,5,3]=>[2,7,4,1,6,3,5]=>[6,1,4,7,2,5,3]=>111000
[7,2,4,6,3,1,5]=>[2,7,4,1,3,6,5]=>[6,1,4,7,5,2,3]=>110010
[7,2,4,6,3,5,1]=>[2,7,4,3,6,1,5]=>[6,1,4,5,2,7,3]=>111000
[7,2,4,6,5,1,3]=>[2,7,4,1,5,6,3]=>[6,1,4,7,3,2,5]=>111000
[7,2,4,6,5,3,1]=>[2,7,4,1,3,5,6]=>[6,1,4,7,5,3,2]=>111010
[7,2,5,1,3,4,6]=>[2,7,6,1,5,4,3]=>[6,1,2,7,3,4,5]=>101000
[7,2,5,1,3,6,4]=>[2,7,1,5,4,6,3]=>[6,1,7,3,4,2,5]=>111000
[7,2,5,1,4,3,6]=>[2,7,6,1,5,3,4]=>[6,1,2,7,3,5,4]=>101100
[7,2,5,1,4,6,3]=>[2,7,1,5,4,3,6]=>[6,1,7,3,4,5,2]=>111000
[7,2,5,1,6,3,4]=>[2,7,1,5,3,6,4]=>[6,1,7,3,5,2,4]=>111000
[7,2,5,1,6,4,3]=>[2,7,1,5,3,4,6]=>[6,1,7,3,5,4,2]=>111100
[7,2,5,3,1,4,6]=>[2,7,6,1,3,5,4]=>[6,1,2,7,5,3,4]=>101010
[7,2,5,3,1,6,4]=>[2,7,1,3,5,4,6]=>[6,1,7,5,3,4,2]=>111010
[7,2,5,3,4,1,6]=>[2,7,6,3,5,1,4]=>[6,1,2,5,3,7,4]=>101100
[7,2,5,3,4,6,1]=>[2,7,3,5,4,1,6]=>[6,1,5,3,4,7,2]=>111000
[7,2,5,3,6,1,4]=>[2,7,3,5,1,6,4]=>[6,1,5,3,7,2,4]=>111000
[7,2,5,3,6,4,1]=>[2,7,3,5,1,4,6]=>[6,1,5,3,7,4,2]=>111100
[7,2,5,4,1,3,6]=>[2,7,6,1,4,5,3]=>[6,1,2,7,4,3,5]=>101100
[7,2,5,4,1,6,3]=>[2,7,1,4,5,3,6]=>[6,1,7,4,3,5,2]=>111100
[7,2,5,4,3,1,6]=>[2,7,6,1,3,4,5]=>[6,1,2,7,5,4,3]=>101110
[7,2,5,4,3,6,1]=>[2,7,3,4,5,1,6]=>[6,1,5,4,3,7,2]=>111100
[7,2,5,4,6,1,3]=>[2,7,4,5,1,6,3]=>[6,1,4,3,7,2,5]=>111000
[7,2,5,4,6,3,1]=>[2,7,4,5,1,3,6]=>[6,1,4,3,7,5,2]=>111010
[7,2,5,6,1,3,4]=>[2,7,5,1,6,4,3]=>[6,1,3,7,2,4,5]=>110000
[7,2,5,6,1,4,3]=>[2,7,5,1,6,3,4]=>[6,1,3,7,2,5,4]=>110100
[7,2,5,6,3,1,4]=>[2,7,5,1,3,6,4]=>[6,1,3,7,5,2,4]=>110010
[7,2,5,6,3,4,1]=>[2,7,5,3,6,1,4]=>[6,1,3,5,2,7,4]=>110100
[7,2,5,6,4,1,3]=>[2,7,5,1,4,6,3]=>[6,1,3,7,4,2,5]=>110100
[7,2,5,6,4,3,1]=>[2,7,5,1,3,4,6]=>[6,1,3,7,5,4,2]=>110110
[7,2,6,1,3,4,5]=>[2,7,1,6,5,4,3]=>[6,1,7,2,3,4,5]=>110000
[7,2,6,1,3,5,4]=>[2,7,1,6,4,5,3]=>[6,1,7,2,4,3,5]=>111000
[7,2,6,1,4,3,5]=>[2,7,1,6,5,3,4]=>[6,1,7,2,3,5,4]=>110100
[7,2,6,1,4,5,3]=>[2,7,1,6,4,3,5]=>[6,1,7,2,4,5,3]=>111000
[7,2,6,1,5,3,4]=>[2,7,1,6,3,5,4]=>[6,1,7,2,5,3,4]=>111000
[7,2,6,1,5,4,3]=>[2,7,1,6,3,4,5]=>[6,1,7,2,5,4,3]=>111100
[7,2,6,3,1,4,5]=>[2,7,1,3,6,5,4]=>[6,1,7,5,2,3,4]=>110010
[7,2,6,3,1,5,4]=>[2,7,1,3,6,4,5]=>[6,1,7,5,2,4,3]=>111010
[7,2,6,3,4,1,5]=>[2,7,3,6,5,1,4]=>[6,1,5,2,3,7,4]=>110100
[7,2,6,3,4,5,1]=>[2,7,3,6,4,1,5]=>[6,1,5,2,4,7,3]=>111000
[7,2,6,3,5,1,4]=>[2,7,3,6,1,5,4]=>[6,1,5,2,7,3,4]=>111000
[7,2,6,3,5,4,1]=>[2,7,3,6,1,4,5]=>[6,1,5,2,7,4,3]=>111100
[7,2,6,4,1,3,5]=>[2,7,1,4,6,5,3]=>[6,1,7,4,2,3,5]=>110100
[7,2,6,4,1,5,3]=>[2,7,1,4,6,3,5]=>[6,1,7,4,2,5,3]=>111100
[7,2,6,4,3,1,5]=>[2,7,1,3,4,6,5]=>[6,1,7,5,4,2,3]=>110110
[7,2,6,4,3,5,1]=>[2,7,3,4,6,1,5]=>[6,1,5,4,2,7,3]=>111100
[7,2,6,4,5,1,3]=>[2,7,4,6,1,5,3]=>[6,1,4,2,7,3,5]=>111000
[7,2,6,4,5,3,1]=>[2,7,4,6,1,3,5]=>[6,1,4,2,7,5,3]=>111010
[7,2,6,5,1,3,4]=>[2,7,1,5,6,4,3]=>[6,1,7,3,2,4,5]=>111000
[7,2,6,5,1,4,3]=>[2,7,1,5,6,3,4]=>[6,1,7,3,2,5,4]=>111100
[7,2,6,5,3,1,4]=>[2,7,1,3,5,6,4]=>[6,1,7,5,3,2,4]=>111010
[7,2,6,5,3,4,1]=>[2,7,3,5,6,1,4]=>[6,1,5,3,2,7,4]=>111100
[7,2,6,5,4,1,3]=>[2,7,1,4,5,6,3]=>[6,1,7,4,3,2,5]=>111100
[7,2,6,5,4,3,1]=>[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]=>111110
[7,3,1,2,4,5,6]=>[1,3,7,6,5,4,2]=>[7,5,1,2,3,4,6]=>100010
[7,3,1,2,4,6,5]=>[1,3,7,5,6,4,2]=>[7,5,1,3,2,4,6]=>110010
[7,3,1,2,5,4,6]=>[1,3,7,6,4,5,2]=>[7,5,1,2,4,3,6]=>101010
[7,3,1,2,5,6,4]=>[1,3,7,5,4,6,2]=>[7,5,1,3,4,2,6]=>110010
[7,3,1,2,6,4,5]=>[1,3,7,4,6,5,2]=>[7,5,1,4,2,3,6]=>110010
[7,3,1,2,6,5,4]=>[1,3,7,4,5,6,2]=>[7,5,1,4,3,2,6]=>111010
[7,3,1,4,2,5,6]=>[1,3,7,6,5,2,4]=>[7,5,1,2,3,6,4]=>100110
[7,3,1,4,2,6,5]=>[1,3,7,5,6,2,4]=>[7,5,1,3,2,6,4]=>110110
[7,3,1,4,5,2,6]=>[1,3,7,6,4,2,5]=>[7,5,1,2,4,6,3]=>101010
[7,3,1,4,5,6,2]=>[1,3,7,5,4,2,6]=>[7,5,1,3,4,6,2]=>110010
[7,3,1,4,6,2,5]=>[1,3,7,4,2,6,5]=>[7,5,1,4,6,2,3]=>110010
[7,3,1,4,6,5,2]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>111010
[7,3,1,5,2,4,6]=>[1,3,7,6,2,5,4]=>[7,5,1,2,6,3,4]=>101010
[7,3,1,5,2,6,4]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>111010
[7,3,1,5,4,2,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>101110
[7,3,1,5,4,6,2]=>[1,3,7,4,5,2,6]=>[7,5,1,4,3,6,2]=>111010
[7,3,1,5,6,2,4]=>[1,3,7,5,2,6,4]=>[7,5,1,3,6,2,4]=>110010
[7,3,1,5,6,4,2]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>110110
[7,3,1,6,2,4,5]=>[1,3,7,2,6,5,4]=>[7,5,1,6,2,3,4]=>110010
[7,3,1,6,2,5,4]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>111010
[7,3,1,6,4,2,5]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>110110
[7,3,1,6,4,5,2]=>[1,3,7,4,6,2,5]=>[7,5,1,4,2,6,3]=>111010
[7,3,1,6,5,2,4]=>[1,3,7,2,5,6,4]=>[7,5,1,6,3,2,4]=>111010
[7,3,1,6,5,4,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>111110
[7,3,2,1,4,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>100011
[7,3,2,1,4,6,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>110011
[7,3,2,1,5,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>101011
[7,3,2,1,5,6,4]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>110011
[7,3,2,1,6,4,5]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>110011
[7,3,2,1,6,5,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>111011
[7,3,2,4,1,5,6]=>[2,3,7,6,5,1,4]=>[6,5,1,2,3,7,4]=>100110
[7,3,2,4,1,6,5]=>[2,3,7,5,6,1,4]=>[6,5,1,3,2,7,4]=>110110
[7,3,2,4,5,1,6]=>[2,3,7,6,4,1,5]=>[6,5,1,2,4,7,3]=>101010
[7,3,2,4,5,6,1]=>[2,3,7,5,4,1,6]=>[6,5,1,3,4,7,2]=>110010
[7,3,2,4,6,1,5]=>[2,3,7,4,1,6,5]=>[6,5,1,4,7,2,3]=>110010
[7,3,2,4,6,5,1]=>[2,3,7,4,1,5,6]=>[6,5,1,4,7,3,2]=>111010
[7,3,2,5,1,4,6]=>[2,3,7,6,1,5,4]=>[6,5,1,2,7,3,4]=>101010
[7,3,2,5,1,6,4]=>[2,3,7,1,5,4,6]=>[6,5,1,7,3,4,2]=>111010
[7,3,2,5,4,1,6]=>[2,3,7,6,1,4,5]=>[6,5,1,2,7,4,3]=>101110
[7,3,2,5,4,6,1]=>[2,3,7,4,5,1,6]=>[6,5,1,4,3,7,2]=>111010
[7,3,2,5,6,1,4]=>[2,3,7,5,1,6,4]=>[6,5,1,3,7,2,4]=>110010
[7,3,2,5,6,4,1]=>[2,3,7,5,1,4,6]=>[6,5,1,3,7,4,2]=>110110
[7,3,2,6,1,4,5]=>[2,3,7,1,6,5,4]=>[6,5,1,7,2,3,4]=>110010
[7,3,2,6,1,5,4]=>[2,3,7,1,6,4,5]=>[6,5,1,7,2,4,3]=>111010
[7,3,2,6,4,1,5]=>[2,3,7,1,4,6,5]=>[6,5,1,7,4,2,3]=>110110
[7,3,2,6,4,5,1]=>[2,3,7,4,6,1,5]=>[6,5,1,4,2,7,3]=>111010
[7,3,2,6,5,1,4]=>[2,3,7,1,5,6,4]=>[6,5,1,7,3,2,4]=>111010
[7,3,2,6,5,4,1]=>[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]=>111110
[7,3,4,1,2,5,6]=>[3,7,6,5,1,4,2]=>[5,1,2,3,7,4,6]=>100100
[7,3,4,1,2,6,5]=>[3,7,5,6,1,4,2]=>[5,1,3,2,7,4,6]=>110100
[7,3,4,1,5,2,6]=>[3,7,6,1,4,2,5]=>[5,1,2,7,4,6,3]=>101100
[7,3,4,1,5,6,2]=>[3,7,5,1,4,2,6]=>[5,1,3,7,4,6,2]=>110100
[7,3,4,1,6,2,5]=>[3,7,1,4,2,6,5]=>[5,1,7,4,6,2,3]=>110100
[7,3,4,1,6,5,2]=>[3,7,1,4,2,5,6]=>[5,1,7,4,6,3,2]=>111100
[7,3,4,2,1,5,6]=>[3,7,6,5,1,2,4]=>[5,1,2,3,7,6,4]=>100101
[7,3,4,2,1,6,5]=>[3,7,5,6,1,2,4]=>[5,1,3,2,7,6,4]=>110101
[7,3,4,2,5,1,6]=>[3,7,6,2,4,1,5]=>[5,1,2,6,4,7,3]=>101100
[7,3,4,2,5,6,1]=>[3,7,5,2,4,1,6]=>[5,1,3,6,4,7,2]=>110100
[7,3,4,2,6,1,5]=>[3,7,2,4,1,6,5]=>[5,1,6,4,7,2,3]=>110100
[7,3,4,2,6,5,1]=>[3,7,2,4,1,5,6]=>[5,1,6,4,7,3,2]=>111100
[7,3,4,5,1,2,6]=>[3,7,6,4,1,5,2]=>[5,1,2,4,7,3,6]=>101000
[7,3,4,5,1,6,2]=>[3,7,4,1,5,2,6]=>[5,1,4,7,3,6,2]=>111000
[7,3,4,5,2,1,6]=>[3,7,6,4,1,2,5]=>[5,1,2,4,7,6,3]=>101001
[7,3,4,5,2,6,1]=>[3,7,4,2,5,1,6]=>[5,1,4,6,3,7,2]=>111000
[7,3,4,5,6,1,2]=>[3,7,5,4,1,6,2]=>[5,1,3,4,7,2,6]=>110000
[7,3,4,5,6,2,1]=>[3,7,5,4,1,2,6]=>[5,1,3,4,7,6,2]=>110001
[7,3,4,6,1,2,5]=>[3,7,4,1,6,5,2]=>[5,1,4,7,2,3,6]=>110000
[7,3,4,6,1,5,2]=>[3,7,4,1,6,2,5]=>[5,1,4,7,2,6,3]=>111000
[7,3,4,6,2,1,5]=>[3,7,4,1,2,6,5]=>[5,1,4,7,6,2,3]=>110001
[7,3,4,6,2,5,1]=>[3,7,4,2,6,1,5]=>[5,1,4,6,2,7,3]=>111000
[7,3,4,6,5,1,2]=>[3,7,4,1,5,6,2]=>[5,1,4,7,3,2,6]=>111000
[7,3,4,6,5,2,1]=>[3,7,4,1,2,5,6]=>[5,1,4,7,6,3,2]=>111001
[7,3,5,1,2,4,6]=>[3,7,6,1,5,4,2]=>[5,1,2,7,3,4,6]=>101000
[7,3,5,1,2,6,4]=>[3,7,1,5,4,6,2]=>[5,1,7,3,4,2,6]=>111000
[7,3,5,1,4,2,6]=>[3,7,6,1,5,2,4]=>[5,1,2,7,3,6,4]=>101100
[7,3,5,1,4,6,2]=>[3,7,1,5,4,2,6]=>[5,1,7,3,4,6,2]=>111000
[7,3,5,1,6,2,4]=>[3,7,1,5,2,6,4]=>[5,1,7,3,6,2,4]=>111000
[7,3,5,1,6,4,2]=>[3,7,1,5,2,4,6]=>[5,1,7,3,6,4,2]=>111100
[7,3,5,2,1,4,6]=>[3,7,6,1,2,5,4]=>[5,1,2,7,6,3,4]=>101001
[7,3,5,2,1,6,4]=>[3,7,1,2,5,4,6]=>[5,1,7,6,3,4,2]=>111001
[7,3,5,2,4,1,6]=>[3,7,6,2,5,1,4]=>[5,1,2,6,3,7,4]=>101100
[7,3,5,2,4,6,1]=>[3,7,2,5,4,1,6]=>[5,1,6,3,4,7,2]=>111000
[7,3,5,2,6,1,4]=>[3,7,2,5,1,6,4]=>[5,1,6,3,7,2,4]=>111000
[7,3,5,2,6,4,1]=>[3,7,2,5,1,4,6]=>[5,1,6,3,7,4,2]=>111100
[7,3,5,4,1,2,6]=>[3,7,6,1,4,5,2]=>[5,1,2,7,4,3,6]=>101100
[7,3,5,4,1,6,2]=>[3,7,1,4,5,2,6]=>[5,1,7,4,3,6,2]=>111100
[7,3,5,4,2,1,6]=>[3,7,6,1,2,4,5]=>[5,1,2,7,6,4,3]=>101101
[7,3,5,4,2,6,1]=>[3,7,2,4,5,1,6]=>[5,1,6,4,3,7,2]=>111100
[7,3,5,4,6,1,2]=>[3,7,4,5,1,6,2]=>[5,1,4,3,7,2,6]=>111000
[7,3,5,4,6,2,1]=>[3,7,4,5,1,2,6]=>[5,1,4,3,7,6,2]=>111001
[7,3,5,6,1,2,4]=>[3,7,5,1,6,4,2]=>[5,1,3,7,2,4,6]=>110000
[7,3,5,6,1,4,2]=>[3,7,5,1,6,2,4]=>[5,1,3,7,2,6,4]=>110100
[7,3,5,6,2,1,4]=>[3,7,5,1,2,6,4]=>[5,1,3,7,6,2,4]=>110001
[7,3,5,6,2,4,1]=>[3,7,5,2,6,1,4]=>[5,1,3,6,2,7,4]=>110100
[7,3,5,6,4,1,2]=>[3,7,5,1,4,6,2]=>[5,1,3,7,4,2,6]=>110100
[7,3,5,6,4,2,1]=>[3,7,5,1,2,4,6]=>[5,1,3,7,6,4,2]=>110101
[7,3,6,1,2,4,5]=>[3,7,1,6,5,4,2]=>[5,1,7,2,3,4,6]=>110000
[7,3,6,1,2,5,4]=>[3,7,1,6,4,5,2]=>[5,1,7,2,4,3,6]=>111000
[7,3,6,1,4,2,5]=>[3,7,1,6,5,2,4]=>[5,1,7,2,3,6,4]=>110100
[7,3,6,1,4,5,2]=>[3,7,1,6,4,2,5]=>[5,1,7,2,4,6,3]=>111000
[7,3,6,1,5,2,4]=>[3,7,1,6,2,5,4]=>[5,1,7,2,6,3,4]=>111000
[7,3,6,1,5,4,2]=>[3,7,1,6,2,4,5]=>[5,1,7,2,6,4,3]=>111100
[7,3,6,2,1,4,5]=>[3,7,1,2,6,5,4]=>[5,1,7,6,2,3,4]=>110001
[7,3,6,2,1,5,4]=>[3,7,1,2,6,4,5]=>[5,1,7,6,2,4,3]=>111001
[7,3,6,2,4,1,5]=>[3,7,2,6,5,1,4]=>[5,1,6,2,3,7,4]=>110100
[7,3,6,2,4,5,1]=>[3,7,2,6,4,1,5]=>[5,1,6,2,4,7,3]=>111000
[7,3,6,2,5,1,4]=>[3,7,2,6,1,5,4]=>[5,1,6,2,7,3,4]=>111000
[7,3,6,2,5,4,1]=>[3,7,2,6,1,4,5]=>[5,1,6,2,7,4,3]=>111100
[7,3,6,4,1,2,5]=>[3,7,1,4,6,5,2]=>[5,1,7,4,2,3,6]=>110100
[7,3,6,4,1,5,2]=>[3,7,1,4,6,2,5]=>[5,1,7,4,2,6,3]=>111100
[7,3,6,4,2,1,5]=>[3,7,1,2,4,6,5]=>[5,1,7,6,4,2,3]=>110101
[7,3,6,4,2,5,1]=>[3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3]=>111100
[7,3,6,4,5,1,2]=>[3,7,4,6,1,5,2]=>[5,1,4,2,7,3,6]=>111000
[7,3,6,4,5,2,1]=>[3,7,4,6,1,2,5]=>[5,1,4,2,7,6,3]=>111001
[7,3,6,5,1,2,4]=>[3,7,1,5,6,4,2]=>[5,1,7,3,2,4,6]=>111000
[7,3,6,5,1,4,2]=>[3,7,1,5,6,2,4]=>[5,1,7,3,2,6,4]=>111100
[7,3,6,5,2,1,4]=>[3,7,1,2,5,6,4]=>[5,1,7,6,3,2,4]=>111001
[7,3,6,5,2,4,1]=>[3,7,2,5,6,1,4]=>[5,1,6,3,2,7,4]=>111100
[7,3,6,5,4,1,2]=>[3,7,1,4,5,6,2]=>[5,1,7,4,3,2,6]=>111100
[7,3,6,5,4,2,1]=>[3,7,1,2,4,5,6]=>[5,1,7,6,4,3,2]=>111101
[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[7,4,1,2,3,5,6]=>100100
[7,4,1,2,3,6,5]=>[1,4,7,5,6,3,2]=>[7,4,1,3,2,5,6]=>110100
[7,4,1,2,5,3,6]=>[1,4,7,6,3,5,2]=>[7,4,1,2,5,3,6]=>101100
[7,4,1,2,5,6,3]=>[1,4,7,5,3,6,2]=>[7,4,1,3,5,2,6]=>110100
[7,4,1,2,6,3,5]=>[1,4,7,3,6,5,2]=>[7,4,1,5,2,3,6]=>110100
[7,4,1,2,6,5,3]=>[1,4,7,3,5,6,2]=>[7,4,1,5,3,2,6]=>111100
[7,4,1,3,2,5,6]=>[1,4,7,6,5,2,3]=>[7,4,1,2,3,6,5]=>100110
[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>[7,4,1,3,2,6,5]=>110110
[7,4,1,3,5,2,6]=>[1,4,7,6,3,2,5]=>[7,4,1,2,5,6,3]=>101100
[7,4,1,3,5,6,2]=>[1,4,7,5,3,2,6]=>[7,4,1,3,5,6,2]=>110100
[7,4,1,3,6,2,5]=>[1,4,7,3,2,6,5]=>[7,4,1,5,6,2,3]=>110100
[7,4,1,3,6,5,2]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>111100
[7,4,1,5,2,3,6]=>[1,4,7,6,2,5,3]=>[7,4,1,2,6,3,5]=>101100
[7,4,1,5,2,6,3]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>111100
[7,4,1,5,3,2,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>101110
[7,4,1,5,3,6,2]=>[1,4,7,3,5,2,6]=>[7,4,1,5,3,6,2]=>111100
[7,4,1,5,6,2,3]=>[1,4,7,5,2,6,3]=>[7,4,1,3,6,2,5]=>110100
[7,4,1,5,6,3,2]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>110110
[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]=>[7,4,1,6,2,3,5]=>110100
[7,4,1,6,2,5,3]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>111100
[7,4,1,6,3,2,5]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>110110
[7,4,1,6,3,5,2]=>[1,4,7,3,6,2,5]=>[7,4,1,5,2,6,3]=>111100
[7,4,1,6,5,2,3]=>[1,4,7,2,5,6,3]=>[7,4,1,6,3,2,5]=>111100
[7,4,1,6,5,3,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>111110
[7,4,2,1,3,5,6]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>100101
[7,4,2,1,3,6,5]=>[1,2,4,7,5,6,3]=>[7,6,4,1,3,2,5]=>110101
[7,4,2,1,5,3,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>101101
[7,4,2,1,5,6,3]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>110101
[7,4,2,1,6,3,5]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>110101
[7,4,2,1,6,5,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>111101
[7,4,2,3,1,5,6]=>[2,4,7,6,5,1,3]=>[6,4,1,2,3,7,5]=>100110
[7,4,2,3,1,6,5]=>[2,4,7,5,6,1,3]=>[6,4,1,3,2,7,5]=>110110
[7,4,2,3,5,1,6]=>[2,4,7,6,3,1,5]=>[6,4,1,2,5,7,3]=>101100
[7,4,2,3,5,6,1]=>[2,4,7,5,3,1,6]=>[6,4,1,3,5,7,2]=>110100
[7,4,2,3,6,1,5]=>[2,4,7,3,1,6,5]=>[6,4,1,5,7,2,3]=>110100
[7,4,2,3,6,5,1]=>[2,4,7,3,1,5,6]=>[6,4,1,5,7,3,2]=>111100
[7,4,2,5,1,3,6]=>[2,4,7,6,1,5,3]=>[6,4,1,2,7,3,5]=>101100
[7,4,2,5,1,6,3]=>[2,4,7,1,5,3,6]=>[6,4,1,7,3,5,2]=>111100
[7,4,2,5,3,1,6]=>[2,4,7,6,1,3,5]=>[6,4,1,2,7,5,3]=>101110
[7,4,2,5,3,6,1]=>[2,4,7,3,5,1,6]=>[6,4,1,5,3,7,2]=>111100
[7,4,2,5,6,1,3]=>[2,4,7,5,1,6,3]=>[6,4,1,3,7,2,5]=>110100
[7,4,2,5,6,3,1]=>[2,4,7,5,1,3,6]=>[6,4,1,3,7,5,2]=>110110
[7,4,2,6,1,3,5]=>[2,4,7,1,6,5,3]=>[6,4,1,7,2,3,5]=>110100
[7,4,2,6,1,5,3]=>[2,4,7,1,6,3,5]=>[6,4,1,7,2,5,3]=>111100
[7,4,2,6,3,1,5]=>[2,4,7,1,3,6,5]=>[6,4,1,7,5,2,3]=>110110
[7,4,2,6,3,5,1]=>[2,4,7,3,6,1,5]=>[6,4,1,5,2,7,3]=>111100
[7,4,2,6,5,1,3]=>[2,4,7,1,5,6,3]=>[6,4,1,7,3,2,5]=>111100
[7,4,2,6,5,3,1]=>[2,4,7,1,3,5,6]=>[6,4,1,7,5,3,2]=>111110
[7,4,3,1,2,5,6]=>[1,3,4,7,6,5,2]=>[7,5,4,1,2,3,6]=>100110
[7,4,3,1,2,6,5]=>[1,3,4,7,5,6,2]=>[7,5,4,1,3,2,6]=>110110
[7,4,3,1,5,2,6]=>[1,3,4,7,6,2,5]=>[7,5,4,1,2,6,3]=>101110
[7,4,3,1,5,6,2]=>[1,3,4,7,5,2,6]=>[7,5,4,1,3,6,2]=>110110
[7,4,3,1,6,2,5]=>[1,3,4,7,2,6,5]=>[7,5,4,1,6,2,3]=>110110
[7,4,3,1,6,5,2]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>111110
[7,4,3,2,1,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>100111
[7,4,3,2,1,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>110111
[7,4,3,2,5,1,6]=>[2,3,4,7,6,1,5]=>[6,5,4,1,2,7,3]=>101110
[7,4,3,2,5,6,1]=>[2,3,4,7,5,1,6]=>[6,5,4,1,3,7,2]=>110110
[7,4,3,2,6,1,5]=>[2,3,4,7,1,6,5]=>[6,5,4,1,7,2,3]=>110110
[7,4,3,2,6,5,1]=>[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]=>111110
[7,4,3,5,1,2,6]=>[3,4,7,6,1,5,2]=>[5,4,1,2,7,3,6]=>101100
[7,4,3,5,1,6,2]=>[3,4,7,1,5,2,6]=>[5,4,1,7,3,6,2]=>111100
[7,4,3,5,2,1,6]=>[3,4,7,6,1,2,5]=>[5,4,1,2,7,6,3]=>101101
[7,4,3,5,2,6,1]=>[3,4,7,2,5,1,6]=>[5,4,1,6,3,7,2]=>111100
[7,4,3,5,6,1,2]=>[3,4,7,5,1,6,2]=>[5,4,1,3,7,2,6]=>110100
[7,4,3,5,6,2,1]=>[3,4,7,5,1,2,6]=>[5,4,1,3,7,6,2]=>110101
[7,4,3,6,1,2,5]=>[3,4,7,1,6,5,2]=>[5,4,1,7,2,3,6]=>110100
[7,4,3,6,1,5,2]=>[3,4,7,1,6,2,5]=>[5,4,1,7,2,6,3]=>111100
[7,4,3,6,2,1,5]=>[3,4,7,1,2,6,5]=>[5,4,1,7,6,2,3]=>110101
[7,4,3,6,2,5,1]=>[3,4,7,2,6,1,5]=>[5,4,1,6,2,7,3]=>111100
[7,4,3,6,5,1,2]=>[3,4,7,1,5,6,2]=>[5,4,1,7,3,2,6]=>111100
[7,4,3,6,5,2,1]=>[3,4,7,1,2,5,6]=>[5,4,1,7,6,3,2]=>111101
[7,4,5,1,2,3,6]=>[4,7,6,1,5,3,2]=>[4,1,2,7,3,5,6]=>101000
[7,4,5,1,2,6,3]=>[4,7,1,5,3,6,2]=>[4,1,7,3,5,2,6]=>111000
[7,4,5,1,3,2,6]=>[4,7,6,1,5,2,3]=>[4,1,2,7,3,6,5]=>101010
[7,4,5,1,3,6,2]=>[4,7,1,5,3,2,6]=>[4,1,7,3,5,6,2]=>111000
[7,4,5,1,6,2,3]=>[4,7,1,5,2,6,3]=>[4,1,7,3,6,2,5]=>111000
[7,4,5,1,6,3,2]=>[4,7,1,5,2,3,6]=>[4,1,7,3,6,5,2]=>111010
[7,4,5,2,1,3,6]=>[4,7,6,1,2,5,3]=>[4,1,2,7,6,3,5]=>101001
[7,4,5,2,1,6,3]=>[4,7,1,2,5,3,6]=>[4,1,7,6,3,5,2]=>111001
[7,4,5,2,3,1,6]=>[4,7,6,2,5,1,3]=>[4,1,2,6,3,7,5]=>101010
[7,4,5,2,3,6,1]=>[4,7,2,5,3,1,6]=>[4,1,6,3,5,7,2]=>111000
[7,4,5,2,6,1,3]=>[4,7,2,5,1,6,3]=>[4,1,6,3,7,2,5]=>111000
[7,4,5,2,6,3,1]=>[4,7,2,5,1,3,6]=>[4,1,6,3,7,5,2]=>111010
[7,4,5,3,1,2,6]=>[4,7,6,1,3,5,2]=>[4,1,2,7,5,3,6]=>101010
[7,4,5,3,1,6,2]=>[4,7,1,3,5,2,6]=>[4,1,7,5,3,6,2]=>111010
[7,4,5,3,2,1,6]=>[4,7,6,1,2,3,5]=>[4,1,2,7,6,5,3]=>101011
[7,4,5,3,2,6,1]=>[4,7,2,3,5,1,6]=>[4,1,6,5,3,7,2]=>111010
[7,4,5,3,6,1,2]=>[4,7,3,5,1,6,2]=>[4,1,5,3,7,2,6]=>111000
[7,4,5,3,6,2,1]=>[4,7,3,5,1,2,6]=>[4,1,5,3,7,6,2]=>111001
[7,4,5,6,1,2,3]=>[4,7,5,1,6,3,2]=>[4,1,3,7,2,5,6]=>110000
[7,4,5,6,1,3,2]=>[4,7,5,1,6,2,3]=>[4,1,3,7,2,6,5]=>110010
[7,4,5,6,2,1,3]=>[4,7,5,1,2,6,3]=>[4,1,3,7,6,2,5]=>110001
[7,4,5,6,2,3,1]=>[4,7,5,2,6,1,3]=>[4,1,3,6,2,7,5]=>110010
[7,4,5,6,3,1,2]=>[4,7,5,1,3,6,2]=>[4,1,3,7,5,2,6]=>110010
[7,4,5,6,3,2,1]=>[4,7,5,1,2,3,6]=>[4,1,3,7,6,5,2]=>110011
[7,4,6,1,2,3,5]=>[4,7,1,6,5,3,2]=>[4,1,7,2,3,5,6]=>110000
[7,4,6,1,2,5,3]=>[4,7,1,6,3,5,2]=>[4,1,7,2,5,3,6]=>111000
[7,4,6,1,3,2,5]=>[4,7,1,6,5,2,3]=>[4,1,7,2,3,6,5]=>110010
[7,4,6,1,3,5,2]=>[4,7,1,6,3,2,5]=>[4,1,7,2,5,6,3]=>111000
[7,4,6,1,5,2,3]=>[4,7,1,6,2,5,3]=>[4,1,7,2,6,3,5]=>111000
[7,4,6,1,5,3,2]=>[4,7,1,6,2,3,5]=>[4,1,7,2,6,5,3]=>111010
[7,4,6,2,1,3,5]=>[4,7,1,2,6,5,3]=>[4,1,7,6,2,3,5]=>110001
[7,4,6,2,1,5,3]=>[4,7,1,2,6,3,5]=>[4,1,7,6,2,5,3]=>111001
[7,4,6,2,3,1,5]=>[4,7,2,6,5,1,3]=>[4,1,6,2,3,7,5]=>110010
[7,4,6,2,3,5,1]=>[4,7,2,6,3,1,5]=>[4,1,6,2,5,7,3]=>111000
[7,4,6,2,5,1,3]=>[4,7,2,6,1,5,3]=>[4,1,6,2,7,3,5]=>111000
[7,4,6,2,5,3,1]=>[4,7,2,6,1,3,5]=>[4,1,6,2,7,5,3]=>111010
[7,4,6,3,1,2,5]=>[4,7,1,3,6,5,2]=>[4,1,7,5,2,3,6]=>110010
[7,4,6,3,1,5,2]=>[4,7,1,3,6,2,5]=>[4,1,7,5,2,6,3]=>111010
[7,4,6,3,2,1,5]=>[4,7,1,2,3,6,5]=>[4,1,7,6,5,2,3]=>110011
[7,4,6,3,2,5,1]=>[4,7,2,3,6,1,5]=>[4,1,6,5,2,7,3]=>111010
[7,4,6,3,5,1,2]=>[4,7,3,6,1,5,2]=>[4,1,5,2,7,3,6]=>111000
[7,4,6,3,5,2,1]=>[4,7,3,6,1,2,5]=>[4,1,5,2,7,6,3]=>111001
[7,4,6,5,1,2,3]=>[4,7,1,5,6,3,2]=>[4,1,7,3,2,5,6]=>111000
[7,4,6,5,1,3,2]=>[4,7,1,5,6,2,3]=>[4,1,7,3,2,6,5]=>111010
[7,4,6,5,2,1,3]=>[4,7,1,2,5,6,3]=>[4,1,7,6,3,2,5]=>111001
[7,4,6,5,2,3,1]=>[4,7,2,5,6,1,3]=>[4,1,6,3,2,7,5]=>111010
[7,4,6,5,3,1,2]=>[4,7,1,3,5,6,2]=>[4,1,7,5,3,2,6]=>111010
[7,4,6,5,3,2,1]=>[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]=>111011
[7,5,1,2,3,4,6]=>[1,5,7,6,4,3,2]=>[7,3,1,2,4,5,6]=>101000
[7,5,1,2,3,6,4]=>[1,5,7,4,6,3,2]=>[7,3,1,4,2,5,6]=>111000
[7,5,1,2,4,3,6]=>[1,5,7,6,3,4,2]=>[7,3,1,2,5,4,6]=>101100
[7,5,1,2,4,6,3]=>[1,5,7,4,3,6,2]=>[7,3,1,4,5,2,6]=>111000
[7,5,1,2,6,3,4]=>[1,5,7,3,6,4,2]=>[7,3,1,5,2,4,6]=>111000
[7,5,1,2,6,4,3]=>[1,5,7,3,4,6,2]=>[7,3,1,5,4,2,6]=>111100
[7,5,1,3,2,4,6]=>[1,5,7,6,4,2,3]=>[7,3,1,2,4,6,5]=>101010
[7,5,1,3,2,6,4]=>[1,5,7,4,6,2,3]=>[7,3,1,4,2,6,5]=>111010
[7,5,1,3,4,2,6]=>[1,5,7,6,3,2,4]=>[7,3,1,2,5,6,4]=>101100
[7,5,1,3,4,6,2]=>[1,5,7,4,3,2,6]=>[7,3,1,4,5,6,2]=>111000
[7,5,1,3,6,2,4]=>[1,5,7,3,2,6,4]=>[7,3,1,5,6,2,4]=>111000
[7,5,1,3,6,4,2]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>111100
[7,5,1,4,2,3,6]=>[1,5,7,6,2,4,3]=>[7,3,1,2,6,4,5]=>101100
[7,5,1,4,2,6,3]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>111100
[7,5,1,4,3,2,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>101110
[7,5,1,4,3,6,2]=>[1,5,7,3,4,2,6]=>[7,3,1,5,4,6,2]=>111100
[7,5,1,4,6,2,3]=>[1,5,7,4,2,6,3]=>[7,3,1,4,6,2,5]=>111000
[7,5,1,4,6,3,2]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>111010
[7,5,1,6,2,3,4]=>[1,5,7,2,6,4,3]=>[7,3,1,6,2,4,5]=>111000
[7,5,1,6,2,4,3]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>111100
[7,5,1,6,3,2,4]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>111010
[7,5,1,6,3,4,2]=>[1,5,7,3,6,2,4]=>[7,3,1,5,2,6,4]=>111100
[7,5,1,6,4,2,3]=>[1,5,7,2,4,6,3]=>[7,3,1,6,4,2,5]=>111100
[7,5,1,6,4,3,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>111110
[7,5,2,1,3,4,6]=>[1,2,5,7,6,4,3]=>[7,6,3,1,2,4,5]=>101001
[7,5,2,1,3,6,4]=>[1,2,5,7,4,6,3]=>[7,6,3,1,4,2,5]=>111001
[7,5,2,1,4,3,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>101101
[7,5,2,1,4,6,3]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>111001
[7,5,2,1,6,3,4]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>111001
[7,5,2,1,6,4,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>111101
[7,5,2,3,1,4,6]=>[2,5,7,6,4,1,3]=>[6,3,1,2,4,7,5]=>101010
[7,5,2,3,1,6,4]=>[2,5,7,4,6,1,3]=>[6,3,1,4,2,7,5]=>111010
[7,5,2,3,4,1,6]=>[2,5,7,6,3,1,4]=>[6,3,1,2,5,7,4]=>101100
[7,5,2,3,4,6,1]=>[2,5,7,4,3,1,6]=>[6,3,1,4,5,7,2]=>111000
[7,5,2,3,6,1,4]=>[2,5,7,3,1,6,4]=>[6,3,1,5,7,2,4]=>111000
[7,5,2,3,6,4,1]=>[2,5,7,3,1,4,6]=>[6,3,1,5,7,4,2]=>111100
[7,5,2,4,1,3,6]=>[2,5,7,6,1,4,3]=>[6,3,1,2,7,4,5]=>101100
[7,5,2,4,1,6,3]=>[2,5,7,1,4,3,6]=>[6,3,1,7,4,5,2]=>111100
[7,5,2,4,3,1,6]=>[2,5,7,6,1,3,4]=>[6,3,1,2,7,5,4]=>101110
[7,5,2,4,3,6,1]=>[2,5,7,3,4,1,6]=>[6,3,1,5,4,7,2]=>111100
[7,5,2,4,6,1,3]=>[2,5,7,4,1,6,3]=>[6,3,1,4,7,2,5]=>111000
[7,5,2,4,6,3,1]=>[2,5,7,4,1,3,6]=>[6,3,1,4,7,5,2]=>111010
[7,5,2,6,1,3,4]=>[2,5,7,1,6,4,3]=>[6,3,1,7,2,4,5]=>111000
[7,5,2,6,1,4,3]=>[2,5,7,1,6,3,4]=>[6,3,1,7,2,5,4]=>111100
[7,5,2,6,3,1,4]=>[2,5,7,1,3,6,4]=>[6,3,1,7,5,2,4]=>111010
[7,5,2,6,3,4,1]=>[2,5,7,3,6,1,4]=>[6,3,1,5,2,7,4]=>111100
[7,5,2,6,4,1,3]=>[2,5,7,1,4,6,3]=>[6,3,1,7,4,2,5]=>111100
[7,5,2,6,4,3,1]=>[2,5,7,1,3,4,6]=>[6,3,1,7,5,4,2]=>111110
[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[7,5,3,1,2,4,6]=>101010
[7,5,3,1,2,6,4]=>[1,3,5,7,4,6,2]=>[7,5,3,1,4,2,6]=>111010
[7,5,3,1,4,2,6]=>[1,3,5,7,6,2,4]=>[7,5,3,1,2,6,4]=>101110
[7,5,3,1,4,6,2]=>[1,3,5,7,4,2,6]=>[7,5,3,1,4,6,2]=>111010
[7,5,3,1,6,2,4]=>[1,3,5,7,2,6,4]=>[7,5,3,1,6,2,4]=>111010
[7,5,3,1,6,4,2]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>111110
[7,5,3,2,1,4,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>101011
[7,5,3,2,1,6,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>111011
[7,5,3,2,4,1,6]=>[2,3,5,7,6,1,4]=>[6,5,3,1,2,7,4]=>101110
[7,5,3,2,4,6,1]=>[2,3,5,7,4,1,6]=>[6,5,3,1,4,7,2]=>111010
[7,5,3,2,6,1,4]=>[2,3,5,7,1,6,4]=>[6,5,3,1,7,2,4]=>111010
[7,5,3,2,6,4,1]=>[2,3,5,7,1,4,6]=>[6,5,3,1,7,4,2]=>111110
[7,5,3,4,1,2,6]=>[3,5,7,6,1,4,2]=>[5,3,1,2,7,4,6]=>101100
[7,5,3,4,1,6,2]=>[3,5,7,1,4,2,6]=>[5,3,1,7,4,6,2]=>111100
[7,5,3,4,2,1,6]=>[3,5,7,6,1,2,4]=>[5,3,1,2,7,6,4]=>101101
[7,5,3,4,2,6,1]=>[3,5,7,2,4,1,6]=>[5,3,1,6,4,7,2]=>111100
[7,5,3,4,6,1,2]=>[3,5,7,4,1,6,2]=>[5,3,1,4,7,2,6]=>111000
[7,5,3,4,6,2,1]=>[3,5,7,4,1,2,6]=>[5,3,1,4,7,6,2]=>111001
[7,5,3,6,1,2,4]=>[3,5,7,1,6,4,2]=>[5,3,1,7,2,4,6]=>111000
[7,5,3,6,1,4,2]=>[3,5,7,1,6,2,4]=>[5,3,1,7,2,6,4]=>111100
[7,5,3,6,2,1,4]=>[3,5,7,1,2,6,4]=>[5,3,1,7,6,2,4]=>111001
[7,5,3,6,2,4,1]=>[3,5,7,2,6,1,4]=>[5,3,1,6,2,7,4]=>111100
[7,5,3,6,4,1,2]=>[3,5,7,1,4,6,2]=>[5,3,1,7,4,2,6]=>111100
[7,5,3,6,4,2,1]=>[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]=>111101
[7,5,4,1,2,3,6]=>[1,4,5,7,6,3,2]=>[7,4,3,1,2,5,6]=>101100
[7,5,4,1,2,6,3]=>[1,4,5,7,3,6,2]=>[7,4,3,1,5,2,6]=>111100
[7,5,4,1,3,2,6]=>[1,4,5,7,6,2,3]=>[7,4,3,1,2,6,5]=>101110
[7,5,4,1,3,6,2]=>[1,4,5,7,3,2,6]=>[7,4,3,1,5,6,2]=>111100
[7,5,4,1,6,2,3]=>[1,4,5,7,2,6,3]=>[7,4,3,1,6,2,5]=>111100
[7,5,4,1,6,3,2]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>111110
[7,5,4,2,1,3,6]=>[1,2,4,5,7,6,3]=>[7,6,4,3,1,2,5]=>101101
[7,5,4,2,1,6,3]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>111101
[7,5,4,2,3,1,6]=>[2,4,5,7,6,1,3]=>[6,4,3,1,2,7,5]=>101110
[7,5,4,2,3,6,1]=>[2,4,5,7,3,1,6]=>[6,4,3,1,5,7,2]=>111100
[7,5,4,2,6,1,3]=>[2,4,5,7,1,6,3]=>[6,4,3,1,7,2,5]=>111100
[7,5,4,2,6,3,1]=>[2,4,5,7,1,3,6]=>[6,4,3,1,7,5,2]=>111110
[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[7,5,4,3,1,2,6]=>101110
[7,5,4,3,1,6,2]=>[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]=>111110
[7,5,4,3,2,1,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>101111
[7,5,4,3,2,6,1]=>[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]=>111110
[7,5,4,3,6,1,2]=>[3,4,5,7,1,6,2]=>[5,4,3,1,7,2,6]=>111100
[7,5,4,3,6,2,1]=>[3,4,5,7,1,2,6]=>[5,4,3,1,7,6,2]=>111101
[7,5,4,6,1,2,3]=>[4,5,7,1,6,3,2]=>[4,3,1,7,2,5,6]=>111000
[7,5,4,6,1,3,2]=>[4,5,7,1,6,2,3]=>[4,3,1,7,2,6,5]=>111010
[7,5,4,6,2,1,3]=>[4,5,7,1,2,6,3]=>[4,3,1,7,6,2,5]=>111001
[7,5,4,6,2,3,1]=>[4,5,7,2,6,1,3]=>[4,3,1,6,2,7,5]=>111010
[7,5,4,6,3,1,2]=>[4,5,7,1,3,6,2]=>[4,3,1,7,5,2,6]=>111010
[7,5,4,6,3,2,1]=>[4,5,7,1,2,3,6]=>[4,3,1,7,6,5,2]=>111011
[7,5,6,1,2,3,4]=>[5,7,1,6,4,3,2]=>[3,1,7,2,4,5,6]=>110000
[7,5,6,1,2,4,3]=>[5,7,1,6,3,4,2]=>[3,1,7,2,5,4,6]=>110100
[7,5,6,1,3,2,4]=>[5,7,1,6,4,2,3]=>[3,1,7,2,4,6,5]=>110010
[7,5,6,1,3,4,2]=>[5,7,1,6,3,2,4]=>[3,1,7,2,5,6,4]=>110100
[7,5,6,1,4,2,3]=>[5,7,1,6,2,4,3]=>[3,1,7,2,6,4,5]=>110100
[7,5,6,1,4,3,2]=>[5,7,1,6,2,3,4]=>[3,1,7,2,6,5,4]=>110110
[7,5,6,2,1,3,4]=>[5,7,1,2,6,4,3]=>[3,1,7,6,2,4,5]=>110001
[7,5,6,2,1,4,3]=>[5,7,1,2,6,3,4]=>[3,1,7,6,2,5,4]=>110101
[7,5,6,2,3,1,4]=>[5,7,2,6,4,1,3]=>[3,1,6,2,4,7,5]=>110010
[7,5,6,2,3,4,1]=>[5,7,2,6,3,1,4]=>[3,1,6,2,5,7,4]=>110100
[7,5,6,2,4,1,3]=>[5,7,2,6,1,4,3]=>[3,1,6,2,7,4,5]=>110100
[7,5,6,2,4,3,1]=>[5,7,2,6,1,3,4]=>[3,1,6,2,7,5,4]=>110110
[7,5,6,3,1,2,4]=>[5,7,1,3,6,4,2]=>[3,1,7,5,2,4,6]=>110010
[7,5,6,3,1,4,2]=>[5,7,1,3,6,2,4]=>[3,1,7,5,2,6,4]=>110110
[7,5,6,3,2,1,4]=>[5,7,1,2,3,6,4]=>[3,1,7,6,5,2,4]=>110011
[7,5,6,3,2,4,1]=>[5,7,2,3,6,1,4]=>[3,1,6,5,2,7,4]=>110110
[7,5,6,3,4,1,2]=>[5,7,3,6,1,4,2]=>[3,1,5,2,7,4,6]=>110100
[7,5,6,3,4,2,1]=>[5,7,3,6,1,2,4]=>[3,1,5,2,7,6,4]=>110101
[7,5,6,4,1,2,3]=>[5,7,1,4,6,3,2]=>[3,1,7,4,2,5,6]=>110100
[7,5,6,4,1,3,2]=>[5,7,1,4,6,2,3]=>[3,1,7,4,2,6,5]=>110110
[7,5,6,4,2,1,3]=>[5,7,1,2,4,6,3]=>[3,1,7,6,4,2,5]=>110101
[7,5,6,4,2,3,1]=>[5,7,2,4,6,1,3]=>[3,1,6,4,2,7,5]=>110110
[7,5,6,4,3,1,2]=>[5,7,1,3,4,6,2]=>[3,1,7,5,4,2,6]=>110110
[7,5,6,4,3,2,1]=>[5,7,1,2,3,4,6]=>[3,1,7,6,5,4,2]=>110111
[7,6,1,2,3,4,5]=>[1,6,7,5,4,3,2]=>[7,2,1,3,4,5,6]=>110000
[7,6,1,2,3,5,4]=>[1,6,7,4,5,3,2]=>[7,2,1,4,3,5,6]=>111000
[7,6,1,2,4,3,5]=>[1,6,7,5,3,4,2]=>[7,2,1,3,5,4,6]=>110100
[7,6,1,2,4,5,3]=>[1,6,7,4,3,5,2]=>[7,2,1,4,5,3,6]=>111000
[7,6,1,2,5,3,4]=>[1,6,7,3,5,4,2]=>[7,2,1,5,3,4,6]=>111000
[7,6,1,2,5,4,3]=>[1,6,7,3,4,5,2]=>[7,2,1,5,4,3,6]=>111100
[7,6,1,3,2,4,5]=>[1,6,7,5,4,2,3]=>[7,2,1,3,4,6,5]=>110010
[7,6,1,3,2,5,4]=>[1,6,7,4,5,2,3]=>[7,2,1,4,3,6,5]=>111010
[7,6,1,3,4,2,5]=>[1,6,7,5,3,2,4]=>[7,2,1,3,5,6,4]=>110100
[7,6,1,3,4,5,2]=>[1,6,7,4,3,2,5]=>[7,2,1,4,5,6,3]=>111000
[7,6,1,3,5,2,4]=>[1,6,7,3,2,5,4]=>[7,2,1,5,6,3,4]=>111000
[7,6,1,3,5,4,2]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>111100
[7,6,1,4,2,3,5]=>[1,6,7,5,2,4,3]=>[7,2,1,3,6,4,5]=>110100
[7,6,1,4,2,5,3]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>111100
[7,6,1,4,3,2,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>110110
[7,6,1,4,3,5,2]=>[1,6,7,3,4,2,5]=>[7,2,1,5,4,6,3]=>111100
[7,6,1,4,5,2,3]=>[1,6,7,4,2,5,3]=>[7,2,1,4,6,3,5]=>111000
[7,6,1,4,5,3,2]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>111010
[7,6,1,5,2,3,4]=>[1,6,7,2,5,4,3]=>[7,2,1,6,3,4,5]=>111000
[7,6,1,5,2,4,3]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>111100
[7,6,1,5,3,2,4]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>111010
[7,6,1,5,3,4,2]=>[1,6,7,3,5,2,4]=>[7,2,1,5,3,6,4]=>111100
[7,6,1,5,4,2,3]=>[1,6,7,2,4,5,3]=>[7,2,1,6,4,3,5]=>111100
[7,6,1,5,4,3,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>111110
[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[7,6,2,1,3,4,5]=>110001
[7,6,2,1,3,5,4]=>[1,2,6,7,4,5,3]=>[7,6,2,1,4,3,5]=>111001
[7,6,2,1,4,3,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>110101
[7,6,2,1,4,5,3]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>111001
[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>111001
[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>111101
[7,6,2,3,1,4,5]=>[2,6,7,5,4,1,3]=>[6,2,1,3,4,7,5]=>110010
[7,6,2,3,1,5,4]=>[2,6,7,4,5,1,3]=>[6,2,1,4,3,7,5]=>111010
[7,6,2,3,4,1,5]=>[2,6,7,5,3,1,4]=>[6,2,1,3,5,7,4]=>110100
[7,6,2,3,4,5,1]=>[2,6,7,4,3,1,5]=>[6,2,1,4,5,7,3]=>111000
[7,6,2,3,5,1,4]=>[2,6,7,3,1,5,4]=>[6,2,1,5,7,3,4]=>111000
[7,6,2,3,5,4,1]=>[2,6,7,3,1,4,5]=>[6,2,1,5,7,4,3]=>111100
[7,6,2,4,1,3,5]=>[2,6,7,5,1,4,3]=>[6,2,1,3,7,4,5]=>110100
[7,6,2,4,1,5,3]=>[2,6,7,1,4,3,5]=>[6,2,1,7,4,5,3]=>111100
[7,6,2,4,3,1,5]=>[2,6,7,5,1,3,4]=>[6,2,1,3,7,5,4]=>110110
[7,6,2,4,3,5,1]=>[2,6,7,3,4,1,5]=>[6,2,1,5,4,7,3]=>111100
[7,6,2,4,5,1,3]=>[2,6,7,4,1,5,3]=>[6,2,1,4,7,3,5]=>111000
[7,6,2,4,5,3,1]=>[2,6,7,4,1,3,5]=>[6,2,1,4,7,5,3]=>111010
[7,6,2,5,1,3,4]=>[2,6,7,1,5,4,3]=>[6,2,1,7,3,4,5]=>111000
[7,6,2,5,1,4,3]=>[2,6,7,1,5,3,4]=>[6,2,1,7,3,5,4]=>111100
[7,6,2,5,3,1,4]=>[2,6,7,1,3,5,4]=>[6,2,1,7,5,3,4]=>111010
[7,6,2,5,3,4,1]=>[2,6,7,3,5,1,4]=>[6,2,1,5,3,7,4]=>111100
[7,6,2,5,4,1,3]=>[2,6,7,1,4,5,3]=>[6,2,1,7,4,3,5]=>111100
[7,6,2,5,4,3,1]=>[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>111110
[7,6,3,1,2,4,5]=>[1,3,6,7,5,4,2]=>[7,5,2,1,3,4,6]=>110010
[7,6,3,1,2,5,4]=>[1,3,6,7,4,5,2]=>[7,5,2,1,4,3,6]=>111010
[7,6,3,1,4,2,5]=>[1,3,6,7,5,2,4]=>[7,5,2,1,3,6,4]=>110110
[7,6,3,1,4,5,2]=>[1,3,6,7,4,2,5]=>[7,5,2,1,4,6,3]=>111010
[7,6,3,1,5,2,4]=>[1,3,6,7,2,5,4]=>[7,5,2,1,6,3,4]=>111010
[7,6,3,1,5,4,2]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>111110
[7,6,3,2,1,4,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>110011
[7,6,3,2,1,5,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>111011
[7,6,3,2,4,1,5]=>[2,3,6,7,5,1,4]=>[6,5,2,1,3,7,4]=>110110
[7,6,3,2,4,5,1]=>[2,3,6,7,4,1,5]=>[6,5,2,1,4,7,3]=>111010
[7,6,3,2,5,1,4]=>[2,3,6,7,1,5,4]=>[6,5,2,1,7,3,4]=>111010
[7,6,3,2,5,4,1]=>[2,3,6,7,1,4,5]=>[6,5,2,1,7,4,3]=>111110
[7,6,3,4,1,2,5]=>[3,6,7,5,1,4,2]=>[5,2,1,3,7,4,6]=>110100
[7,6,3,4,1,5,2]=>[3,6,7,1,4,2,5]=>[5,2,1,7,4,6,3]=>111100
[7,6,3,4,2,1,5]=>[3,6,7,5,1,2,4]=>[5,2,1,3,7,6,4]=>110101
[7,6,3,4,2,5,1]=>[3,6,7,2,4,1,5]=>[5,2,1,6,4,7,3]=>111100
[7,6,3,4,5,1,2]=>[3,6,7,4,1,5,2]=>[5,2,1,4,7,3,6]=>111000
[7,6,3,4,5,2,1]=>[3,6,7,4,1,2,5]=>[5,2,1,4,7,6,3]=>111001
[7,6,3,5,1,2,4]=>[3,6,7,1,5,4,2]=>[5,2,1,7,3,4,6]=>111000
[7,6,3,5,1,4,2]=>[3,6,7,1,5,2,4]=>[5,2,1,7,3,6,4]=>111100
[7,6,3,5,2,1,4]=>[3,6,7,1,2,5,4]=>[5,2,1,7,6,3,4]=>111001
[7,6,3,5,2,4,1]=>[3,6,7,2,5,1,4]=>[5,2,1,6,3,7,4]=>111100
[7,6,3,5,4,1,2]=>[3,6,7,1,4,5,2]=>[5,2,1,7,4,3,6]=>111100
[7,6,3,5,4,2,1]=>[3,6,7,1,2,4,5]=>[5,2,1,7,6,4,3]=>111101
[7,6,4,1,2,3,5]=>[1,4,6,7,5,3,2]=>[7,4,2,1,3,5,6]=>110100
[7,6,4,1,2,5,3]=>[1,4,6,7,3,5,2]=>[7,4,2,1,5,3,6]=>111100
[7,6,4,1,3,2,5]=>[1,4,6,7,5,2,3]=>[7,4,2,1,3,6,5]=>110110
[7,6,4,1,3,5,2]=>[1,4,6,7,3,2,5]=>[7,4,2,1,5,6,3]=>111100
[7,6,4,1,5,2,3]=>[1,4,6,7,2,5,3]=>[7,4,2,1,6,3,5]=>111100
[7,6,4,1,5,3,2]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>111110
[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[7,6,4,2,1,3,5]=>110101
[7,6,4,2,1,5,3]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>111101
[7,6,4,2,3,1,5]=>[2,4,6,7,5,1,3]=>[6,4,2,1,3,7,5]=>110110
[7,6,4,2,3,5,1]=>[2,4,6,7,3,1,5]=>[6,4,2,1,5,7,3]=>111100
[7,6,4,2,5,1,3]=>[2,4,6,7,1,5,3]=>[6,4,2,1,7,3,5]=>111100
[7,6,4,2,5,3,1]=>[2,4,6,7,1,3,5]=>[6,4,2,1,7,5,3]=>111110
[7,6,4,3,1,2,5]=>[1,3,4,6,7,5,2]=>[7,5,4,2,1,3,6]=>110110
[7,6,4,3,1,5,2]=>[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]=>111110
[7,6,4,3,2,1,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>110111
[7,6,4,3,2,5,1]=>[2,3,4,6,7,1,5]=>[6,5,4,2,1,7,3]=>111110
[7,6,4,3,5,1,2]=>[3,4,6,7,1,5,2]=>[5,4,2,1,7,3,6]=>111100
[7,6,4,3,5,2,1]=>[3,4,6,7,1,2,5]=>[5,4,2,1,7,6,3]=>111101
[7,6,4,5,1,2,3]=>[4,6,7,1,5,3,2]=>[4,2,1,7,3,5,6]=>111000
[7,6,4,5,1,3,2]=>[4,6,7,1,5,2,3]=>[4,2,1,7,3,6,5]=>111010
[7,6,4,5,2,1,3]=>[4,6,7,1,2,5,3]=>[4,2,1,7,6,3,5]=>111001
[7,6,4,5,2,3,1]=>[4,6,7,2,5,1,3]=>[4,2,1,6,3,7,5]=>111010
[7,6,4,5,3,1,2]=>[4,6,7,1,3,5,2]=>[4,2,1,7,5,3,6]=>111010
[7,6,4,5,3,2,1]=>[4,6,7,1,2,3,5]=>[4,2,1,7,6,5,3]=>111011
[7,6,5,1,2,3,4]=>[1,5,6,7,4,3,2]=>[7,3,2,1,4,5,6]=>111000
[7,6,5,1,2,4,3]=>[1,5,6,7,3,4,2]=>[7,3,2,1,5,4,6]=>111100
[7,6,5,1,3,2,4]=>[1,5,6,7,4,2,3]=>[7,3,2,1,4,6,5]=>111010
[7,6,5,1,3,4,2]=>[1,5,6,7,3,2,4]=>[7,3,2,1,5,6,4]=>111100
[7,6,5,1,4,2,3]=>[1,5,6,7,2,4,3]=>[7,3,2,1,6,4,5]=>111100
[7,6,5,1,4,3,2]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>111110
[7,6,5,2,1,3,4]=>[1,2,5,6,7,4,3]=>[7,6,3,2,1,4,5]=>111001
[7,6,5,2,1,4,3]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>111101
[7,6,5,2,3,1,4]=>[2,5,6,7,4,1,3]=>[6,3,2,1,4,7,5]=>111010
[7,6,5,2,3,4,1]=>[2,5,6,7,3,1,4]=>[6,3,2,1,5,7,4]=>111100
[7,6,5,2,4,1,3]=>[2,5,6,7,1,4,3]=>[6,3,2,1,7,4,5]=>111100
[7,6,5,2,4,3,1]=>[2,5,6,7,1,3,4]=>[6,3,2,1,7,5,4]=>111110
[7,6,5,3,1,2,4]=>[1,3,5,6,7,4,2]=>[7,5,3,2,1,4,6]=>111010
[7,6,5,3,1,4,2]=>[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]=>111110
[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>111011
[7,6,5,3,2,4,1]=>[2,3,5,6,7,1,4]=>[6,5,3,2,1,7,4]=>111110
[7,6,5,3,4,1,2]=>[3,5,6,7,1,4,2]=>[5,3,2,1,7,4,6]=>111100
[7,6,5,3,4,2,1]=>[3,5,6,7,1,2,4]=>[5,3,2,1,7,6,4]=>111101
[7,6,5,4,1,2,3]=>[1,4,5,6,7,3,2]=>[7,4,3,2,1,5,6]=>111100
[7,6,5,4,1,3,2]=>[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]=>111110
[7,6,5,4,2,1,3]=>[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]=>111101
[7,6,5,4,2,3,1]=>[2,4,5,6,7,1,3]=>[6,4,3,2,1,7,5]=>111110
[7,6,5,4,3,1,2]=>[1,3,4,5,6,7,2]=>[7,5,4,3,2,1,6]=>111110
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>111111
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
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
searching the database
Sorry, this map was not found in the database.