Identifier
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]=>
[1,0,1,0]=>[1,2]=>[1,2]=>[1,2]=>0
[1,1,0,0]=>[2,1]=>[2,1]=>[2,1]=>1
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>00
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[1,3,2]=>01
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>10
[1,1,0,1,0,0]=>[2,3,1]=>[3,2,1]=>[2,3,1]=>10
[1,1,1,0,0,0]=>[3,1,2]=>[3,1,2]=>[3,2,1]=>11
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>000
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>001
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>010
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[1,3,4,2]=>010
[1,0,1,1,1,0,0,0]=>[1,4,2,3]=>[1,4,2,3]=>[1,4,3,2]=>011
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>100
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>101
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,2,1,4]=>[2,3,1,4]=>100
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[2,3,4,1]=>100
[1,1,0,1,1,0,0,0]=>[2,4,1,3]=>[4,2,1,3]=>[2,4,3,1]=>101
[1,1,1,0,0,0,1,0]=>[3,1,2,4]=>[3,1,2,4]=>[3,2,1,4]=>110
[1,1,1,0,0,1,0,0]=>[3,1,4,2]=>[3,4,1,2]=>[3,1,4,2]=>110
[1,1,1,0,1,0,0,0]=>[3,4,1,2]=>[4,1,3,2]=>[3,4,2,1]=>110
[1,1,1,1,0,0,0,0]=>[4,1,2,3]=>[4,1,2,3]=>[4,3,2,1]=>111
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>0001
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>0010
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[1,2,4,5,3]=>0010
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,3,4]=>[1,2,5,3,4]=>[1,2,5,4,3]=>0011
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>0100
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>0101
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[1,3,4,2,5]=>0100
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[1,3,4,5,2]=>0100
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[1,5,3,2,4]=>[1,3,5,4,2]=>0101
[1,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,5]=>[1,4,2,3,5]=>[1,4,3,2,5]=>0110
[1,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3]=>[1,4,5,2,3]=>[1,4,2,5,3]=>0110
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,2,3]=>[1,5,2,4,3]=>[1,4,5,3,2]=>0110
[1,0,1,1,1,1,0,0,0,0]=>[1,5,2,3,4]=>[1,5,2,3,4]=>[1,5,4,3,2]=>0111
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]=>1001
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]=>1010
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[2,1,4,5,3]=>1010
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,4]=>[2,1,5,3,4]=>[2,1,5,4,3]=>1011
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>1000
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[2,3,1,5,4]=>1001
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[2,3,4,1,5]=>1000
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[2,3,4,5,1]=>1000
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[5,2,3,1,4]=>[2,3,5,4,1]=>1001
[1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[2,4,3,1,5]=>1010
[1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[2,4,1,5,3]=>1010
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,3]=>[5,2,1,4,3]=>[2,4,5,3,1]=>1010
[1,1,0,1,1,1,0,0,0,0]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[2,5,4,3,1]=>1011
[1,1,1,0,0,0,1,0,1,0]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,2,1,4,5]=>1100
[1,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4]=>[3,1,2,5,4]=>[3,2,1,5,4]=>1101
[1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,5]=>[3,4,1,2,5]=>[3,1,4,2,5]=>1100
[1,1,1,0,0,1,0,1,0,0]=>[3,1,4,5,2]=>[3,5,1,4,2]=>[3,1,4,5,2]=>1100
[1,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4]=>[3,5,1,2,4]=>[3,1,5,4,2]=>1101
[1,1,1,0,1,0,0,0,1,0]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[3,4,2,1,5]=>1100
[1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,2]=>[4,5,3,1,2]=>[3,4,1,5,2]=>1100
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[3,4,5,2,1]=>1100
[1,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[3,5,4,2,1]=>1101
[1,1,1,1,0,0,0,0,1,0]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[4,3,2,1,5]=>1110
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,3]=>[4,1,5,2,3]=>[4,2,1,5,3]=>1110
[1,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,3]=>[4,5,2,1,3]=>[4,1,5,3,2]=>1110
[1,1,1,1,0,1,0,0,0,0]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[4,5,3,2,1]=>1110
[1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[5,4,3,2,1]=>1111
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>00001
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>00010
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>00010
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>00011
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>00100
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>00101
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>00100
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>00100
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>[1,2,4,6,5,3]=>00101
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[1,2,5,4,3,6]=>00110
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[1,2,5,3,6,4]=>00110
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>00110
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[1,2,6,5,4,3]=>00111
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>01000
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>01001
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>01010
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>01010
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[1,3,2,6,5,4]=>01011
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>01000
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>01001
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>01000
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>01000
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>[1,3,4,6,5,2]=>01001
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>[1,3,5,4,2,6]=>01010
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[1,3,5,2,6,4]=>01010
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>[1,3,5,6,4,2]=>01010
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[1,3,6,5,4,2]=>01011
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[1,4,3,2,5,6]=>01100
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[1,4,3,2,6,5]=>01101
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[1,4,2,5,3,6]=>01100
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[1,4,2,5,6,3]=>01100
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5]=>[1,4,6,2,3,5]=>[1,4,2,6,5,3]=>01101
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>01100
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[1,4,5,2,6,3]=>01100
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,2,3]=>[1,6,2,4,5,3]=>[1,4,5,6,3,2]=>01100
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>[1,4,6,5,3,2]=>01101
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[1,5,4,3,2,6]=>01110
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,4]=>[1,5,2,6,3,4]=>[1,5,3,2,6,4]=>01110
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,2,6,3,4]=>[1,5,6,3,2,4]=>[1,5,2,6,4,3]=>01110
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,2,3,4]=>[1,6,2,3,5,4]=>[1,5,6,4,3,2]=>01110
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[1,6,5,4,3,2]=>01111
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>10001
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>10010
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>10010
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[2,1,3,6,5,4]=>10011
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>10100
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>10101
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>10100
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>10100
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>[2,1,4,6,5,3]=>10101
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[2,1,5,4,3,6]=>10110
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[2,1,5,3,6,4]=>10110
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[2,1,5,6,4,3]=>10110
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[2,1,6,5,4,3]=>10111
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>10000
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>10001
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>10010
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>10010
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[2,3,1,6,5,4]=>10011
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>10000
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>10001
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>10000
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>10000
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[2,3,4,6,5,1]=>10001
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[2,3,5,4,1,6]=>10010
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[2,3,5,1,6,4]=>10010
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[2,3,5,6,4,1]=>10010
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[2,3,6,5,4,1]=>10011
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[2,4,3,1,5,6]=>10100
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>[2,4,3,1,6,5]=>10101
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[2,4,1,5,3,6]=>10100
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[2,4,1,5,6,3]=>10100
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5]=>[4,2,6,1,3,5]=>[2,4,1,6,5,3]=>10101
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>[2,4,5,3,1,6]=>10100
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[2,4,5,1,6,3]=>10100
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,1,3]=>[6,2,1,4,5,3]=>[2,4,5,6,3,1]=>10100
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[2,4,6,5,3,1]=>10101
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[2,5,4,3,1,6]=>10110
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,1,3,6,4]=>[5,2,1,6,3,4]=>[2,5,3,1,6,4]=>10110
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,1,6,3,4]=>[5,2,6,3,1,4]=>[2,5,1,6,4,3]=>10110
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[2,5,6,4,3,1]=>10110
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[2,6,5,4,3,1]=>10111
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>11000
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,2,1,4,6,5]=>11001
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,2,1,5,4,6]=>11010
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[3,2,1,5,6,4]=>11010
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,2,1,6,5,4]=>11011
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[3,1,4,2,5,6]=>11000
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[3,1,4,2,6,5]=>11001
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[3,1,4,5,2,6]=>11000
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[3,1,4,5,6,2]=>11000
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,4,6,2,5]=>[3,6,1,4,2,5]=>[3,1,4,6,5,2]=>11001
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,6]=>[3,5,1,2,4,6]=>[3,1,5,4,2,6]=>11010
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[3,1,5,2,6,4]=>11010
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,6,2,4]=>[3,6,1,2,5,4]=>[3,1,5,6,4,2]=>11010
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,2,4,5]=>[3,6,1,2,4,5]=>[3,1,6,5,4,2]=>11011
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[3,4,2,1,5,6]=>11000
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[3,4,2,1,6,5]=>11001
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[3,4,1,5,2,6]=>11000
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[3,4,1,5,6,2]=>11000
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5]=>[4,6,3,1,2,5]=>[3,4,1,6,5,2]=>11001
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[3,4,5,2,1,6]=>11000
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[3,4,5,1,6,2]=>11000
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[3,4,5,6,2,1]=>11000
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[3,4,6,5,2,1]=>11001
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[3,5,4,2,1,6]=>11010
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,6,4]=>[5,1,3,6,2,4]=>[3,5,2,1,6,4]=>11010
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,6,2,4]=>[5,6,3,2,1,4]=>[3,5,1,6,4,2]=>11010
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[3,5,6,4,2,1]=>11010
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[3,6,5,4,2,1]=>11011
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,3,2,1,5,6]=>11100
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[4,3,2,1,6,5]=>11101
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[4,1,5,2,3,6]=>[4,2,1,5,3,6]=>11100
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,6,3]=>[4,1,6,2,5,3]=>[4,2,1,5,6,3]=>11100
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5]=>[4,1,6,2,3,5]=>[4,2,1,6,5,3]=>11101
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,5,2,3,6]=>[4,5,2,1,3,6]=>[4,1,5,3,2,6]=>11100
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>11100
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,5,6,2,3]=>[4,6,2,1,5,3]=>[4,1,5,6,3,2]=>11100
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5]=>[4,6,2,1,3,5]=>[4,1,6,5,3,2]=>11101
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[4,5,3,2,1,6]=>11100
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,1,2,6,3]=>[5,1,6,4,2,3]=>[4,5,2,1,6,3]=>11100
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,1,6,2,3]=>[5,6,2,4,1,3]=>[4,5,1,6,3,2]=>11100
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[4,5,6,3,2,1]=>11100
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[4,6,5,3,2,1]=>11101
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,4,3,2,1,6]=>11110
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,6,4]=>[5,1,2,6,3,4]=>[5,3,2,1,6,4]=>11110
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1,2,6,3,4]=>[5,1,6,3,2,4]=>[5,2,1,6,4,3]=>11110
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1,6,2,3,4]=>[5,6,2,3,1,4]=>[5,1,6,4,3,2]=>11110
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[5,6,4,3,2,1]=>11110
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,5,4,3,2,1]=>11111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>000001
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>000010
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>000010
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,6,5]=>000011
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>000100
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>000101
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>000100
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[1,2,3,5,6,7,4]=>000100
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>[1,2,3,5,7,6,4]=>000101
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]=>000110
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[1,2,3,6,4,7,5]=>000110
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>000110
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[1,2,3,7,6,5,4]=>000111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>001001
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>001010
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>001010
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,6,5]=>001011
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>001000
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>001001
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[1,2,4,5,6,3,7]=>001000
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[1,2,4,5,6,7,3]=>001000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6]=>[1,2,7,4,5,3,6]=>[1,2,4,5,7,6,3]=>001001
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>[1,2,4,6,5,3,7]=>001010
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[1,2,4,6,3,7,5]=>001010
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>[1,2,4,6,7,5,3]=>001010
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>[1,2,4,7,6,5,3]=>001011
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[1,2,5,4,3,6,7]=>001100
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[1,2,5,4,3,7,6]=>001101
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[1,2,5,3,6,4,7]=>001100
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[1,2,5,3,6,7,4]=>001100
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6]=>[1,2,5,7,3,4,6]=>[1,2,5,3,7,6,4]=>001101
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>001100
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[1,2,5,6,3,7,4]=>001100
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,3,4]=>[1,2,7,3,5,6,4]=>[1,2,5,6,7,4,3]=>001100
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>[1,2,5,7,6,4,3]=>001101
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[1,2,6,5,4,3,7]=>001110
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,7,5]=>[1,2,6,3,7,4,5]=>[1,2,6,4,3,7,5]=>001110
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[1,2,6,7,4,3,5]=>[1,2,6,3,7,5,4]=>001110
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,7,3,4,6,5]=>[1,2,6,7,5,4,3]=>001110
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[1,2,7,6,5,4,3]=>001111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>010001
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>010010
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>010010
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,6,5]=>010011
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>010100
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>010101
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>010100
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[1,3,2,5,6,7,4]=>010100
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>[1,3,2,5,7,6,4]=>010101
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[1,3,2,6,5,4,7]=>010110
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[1,3,2,6,4,7,5]=>010110
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>010110
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[1,3,2,7,6,5,4]=>010111
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>010000
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>010001
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>010010
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>010010
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>[1,3,4,2,7,6,5]=>010011
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[1,3,4,5,2,6,7]=>010000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[1,3,4,5,2,7,6]=>010001
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[1,3,4,5,6,2,7]=>010000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[1,3,4,5,6,7,2]=>010000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6]=>[1,7,3,4,5,2,6]=>[1,3,4,5,7,6,2]=>010001
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,7]=>[1,6,3,4,2,5,7]=>[1,3,4,6,5,2,7]=>010010
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[1,3,4,6,2,7,5]=>010010
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,2,5]=>[1,7,3,4,2,6,5]=>[1,3,4,6,7,5,2]=>010010
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[1,7,3,4,2,5,6]=>[1,3,4,7,6,5,2]=>010011
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>[1,3,5,4,2,6,7]=>010100
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>[1,3,5,4,2,7,6]=>010101
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[1,3,5,2,6,4,7]=>010100
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[1,3,5,2,6,7,4]=>010100
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6]=>[1,5,3,7,2,4,6]=>[1,3,5,2,7,6,4]=>010101
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>[1,3,5,6,4,2,7]=>010100
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[1,3,5,6,2,7,4]=>010100
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,2,4]=>[1,7,3,2,5,6,4]=>[1,3,5,6,7,4,2]=>010100
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>[1,3,5,7,6,4,2]=>010101
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>[1,3,6,5,4,2,7]=>010110
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,7,5]=>[1,6,3,2,7,4,5]=>[1,3,6,4,2,7,5]=>010110
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[1,6,3,7,4,2,5]=>[1,3,6,2,7,5,4]=>010110
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[1,7,3,2,4,6,5]=>[1,3,6,7,5,4,2]=>010110
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>[1,3,7,6,5,4,2]=>010111
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[1,4,3,2,5,6,7]=>011000
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[1,4,3,2,5,7,6]=>011001
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[1,4,3,2,6,5,7]=>011010
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>[1,4,3,2,6,7,5]=>011010
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[1,4,3,2,7,6,5]=>011011
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[1,4,2,5,3,6,7]=>011000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[1,4,2,5,3,7,6]=>011001
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[1,4,2,5,6,3,7]=>011000
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[1,4,2,5,6,7,3]=>011000
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6]=>[1,4,7,2,5,3,6]=>[1,4,2,5,7,6,3]=>011001
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,7]=>[1,4,6,2,3,5,7]=>[1,4,2,6,5,3,7]=>011010
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[1,4,2,6,3,7,5]=>011010
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,7,3,5]=>[1,4,7,2,3,6,5]=>[1,4,2,6,7,5,3]=>011010
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,7,3,5,6]=>[1,4,7,2,3,5,6]=>[1,4,2,7,6,5,3]=>011011
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>011000
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>011001
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[1,4,5,2,6,3,7]=>011000
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[1,4,5,2,6,7,3]=>011000
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6]=>[1,5,7,4,2,3,6]=>[1,4,5,2,7,6,3]=>011001
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,2,3,7]=>[1,6,2,4,5,3,7]=>[1,4,5,6,3,2,7]=>011000
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[1,4,5,6,2,7,3]=>011000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,2,3]=>[1,7,2,4,5,6,3]=>[1,4,5,6,7,3,2]=>011000
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[1,7,2,4,5,3,6]=>[1,4,5,7,6,3,2]=>011001
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>[1,4,6,5,3,2,7]=>011010
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,7,5]=>[1,6,2,4,7,3,5]=>[1,4,6,3,2,7,5]=>011010
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[1,6,7,4,3,2,5]=>[1,4,6,2,7,5,3]=>011010
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[1,7,2,4,3,6,5]=>[1,4,6,7,5,3,2]=>011010
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>[1,4,7,6,5,3,2]=>011011
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[1,5,4,3,2,6,7]=>011100
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[1,5,4,3,2,7,6]=>011101
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,6,4,7]=>[1,5,2,6,3,4,7]=>[1,5,3,2,6,4,7]=>011100
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,6,7,4]=>[1,5,2,7,3,6,4]=>[1,5,3,2,6,7,4]=>011100
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6]=>[1,5,2,7,3,4,6]=>[1,5,3,2,7,6,4]=>011101
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,6,3,4,7]=>[1,5,6,3,2,4,7]=>[1,5,2,6,4,3,7]=>011100
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[1,5,2,6,3,7,4]=>011100
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,6,7,3,4]=>[1,5,7,3,2,6,4]=>[1,5,2,6,7,4,3]=>011100
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6]=>[1,5,7,3,2,4,6]=>[1,5,2,7,6,4,3]=>011101
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,7]=>[1,6,2,3,5,4,7]=>[1,5,6,4,3,2,7]=>011100
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,2,3,7,4]=>[1,6,2,7,5,3,4]=>[1,5,6,3,2,7,4]=>011100
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[1,6,7,3,5,2,4]=>[1,5,6,2,7,4,3]=>011100
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[1,7,2,3,5,6,4]=>[1,5,6,7,4,3,2]=>011100
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,2,3,4,6]=>[1,7,2,3,5,4,6]=>[1,5,7,6,4,3,2]=>011101
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[1,6,5,4,3,2,7]=>011110
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[1,6,2,3,7,4,5]=>[1,6,4,3,2,7,5]=>011110
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,7,4,5]=>[1,6,2,7,4,3,5]=>[1,6,3,2,7,5,4]=>011110
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,7,3,4,5]=>[1,6,7,3,4,2,5]=>[1,6,2,7,5,4,3]=>011110
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,2,3,4,5]=>[1,7,2,3,4,6,5]=>[1,6,7,5,4,3,2]=>011110
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>011111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>100001
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>100010
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>100010
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]=>100011
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>100100
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>100101
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>100100
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[2,1,3,5,6,7,4]=>100100
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>[2,1,3,5,7,6,4]=>100101
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>[2,1,3,6,5,4,7]=>100110
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[2,1,3,6,4,7,5]=>100110
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>[2,1,3,6,7,5,4]=>100110
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>[2,1,3,7,6,5,4]=>100111
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>101000
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>101001
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>101010
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>101010
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]=>101011
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>101000
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>101001
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[2,1,4,5,6,3,7]=>101000
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[2,1,4,5,6,7,3]=>101000
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,3,6]=>[2,1,7,4,5,3,6]=>[2,1,4,5,7,6,3]=>101001
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>[2,1,4,6,5,3,7]=>101010
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[2,1,4,6,3,7,5]=>101010
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>[2,1,4,6,7,5,3]=>101010
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>[2,1,4,7,6,5,3]=>101011
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>[2,1,5,4,3,6,7]=>101100
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]=>101101
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[2,1,5,3,6,4,7]=>101100
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[2,1,5,3,6,7,4]=>101100
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6]=>[2,1,5,7,3,4,6]=>[2,1,5,3,7,6,4]=>101101
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>[2,1,5,6,4,3,7]=>101100
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[2,1,5,6,3,7,4]=>101100
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,3,4]=>[2,1,7,3,5,6,4]=>[2,1,5,6,7,4,3]=>101100
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>[2,1,5,7,6,4,3]=>101101
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>[2,1,6,5,4,3,7]=>101110
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,7,5]=>[2,1,6,3,7,4,5]=>[2,1,6,4,3,7,5]=>101110
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,7,4,5]=>[2,1,6,7,4,3,5]=>[2,1,6,3,7,5,4]=>101110
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,3,4,5]=>[2,1,7,3,4,6,5]=>[2,1,6,7,5,4,3]=>101110
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>[2,1,7,6,5,4,3]=>101111
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>100000
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>100001
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>100010
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>100010
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>[2,3,1,4,7,6,5]=>100011
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>100100
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>100101
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>100100
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[2,3,1,5,6,7,4]=>100100
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>[2,3,1,5,7,6,4]=>100101
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>[2,3,1,6,5,4,7]=>100110
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[2,3,1,6,4,7,5]=>100110
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>[2,3,1,6,7,5,4]=>100110
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>[2,3,1,7,6,5,4]=>100111
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,3,4,1,5,6,7]=>100000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[2,3,4,1,5,7,6]=>100001
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[2,3,4,1,6,5,7]=>100010
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[2,3,4,1,6,7,5]=>100010
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,7,5,6]=>[2,3,4,1,7,6,5]=>100011
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,3,4,5,1,6,7]=>100000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[2,3,4,5,1,7,6]=>100001
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,3,4,5,6,1,7]=>100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,7,1]=>100000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[2,3,4,5,7,6,1]=>100001
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>[2,3,4,6,5,1,7]=>100010
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[2,3,4,6,1,7,5]=>100010
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,1,5]=>[7,2,3,4,1,6,5]=>[2,3,4,6,7,5,1]=>100010
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[2,3,4,7,6,5,1]=>100011
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>[2,3,5,4,1,6,7]=>100100
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6]=>[5,2,3,1,4,7,6]=>[2,3,5,4,1,7,6]=>100101
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[2,3,5,1,6,4,7]=>100100
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[2,3,5,1,6,7,4]=>100100
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,7,4,6]=>[5,2,3,7,1,4,6]=>[2,3,5,1,7,6,4]=>100101
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,1,4,7]=>[6,2,3,1,5,4,7]=>[2,3,5,6,4,1,7]=>100100
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[2,3,5,6,1,7,4]=>100100
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,1,4]=>[7,2,3,1,5,6,4]=>[2,3,5,6,7,4,1]=>100100
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[7,2,3,1,5,4,6]=>[2,3,5,7,6,4,1]=>100101
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>[2,3,6,5,4,1,7]=>100110
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,7,5]=>[6,2,3,1,7,4,5]=>[2,3,6,4,1,7,5]=>100110
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[6,2,3,7,4,1,5]=>[2,3,6,1,7,5,4]=>100110
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[7,2,3,1,4,6,5]=>[2,3,6,7,5,4,1]=>100110
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[2,3,7,6,5,4,1]=>100111
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,3,1,5,6,7]=>101000
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>[2,4,3,1,5,7,6]=>101001
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>[2,4,3,1,6,5,7]=>101010
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>[2,4,3,1,6,7,5]=>101010
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>[2,4,3,1,7,6,5]=>101011
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[2,4,1,5,3,6,7]=>101000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[2,4,1,5,3,7,6]=>101001
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[2,4,1,5,6,3,7]=>101000
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[2,4,1,5,6,7,3]=>101000
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,1,5,7,3,6]=>[4,2,7,1,5,3,6]=>[2,4,1,5,7,6,3]=>101001
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,7]=>[4,2,6,1,3,5,7]=>[2,4,1,6,5,3,7]=>101010
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[2,4,1,6,3,7,5]=>101010
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,7,3,5]=>[4,2,7,1,3,6,5]=>[2,4,1,6,7,5,3]=>101010
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,7,3,5,6]=>[4,2,7,1,3,5,6]=>[2,4,1,7,6,5,3]=>101011
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>[2,4,5,3,1,6,7]=>101000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>[2,4,5,3,1,7,6]=>101001
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[2,4,5,1,6,3,7]=>101000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[2,4,5,1,6,7,3]=>101000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6]=>[5,2,7,4,1,3,6]=>[2,4,5,1,7,6,3]=>101001
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,1,3,7]=>[6,2,1,4,5,3,7]=>[2,4,5,6,3,1,7]=>101000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[2,4,5,6,1,7,3]=>101000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,1,3]=>[7,2,1,4,5,6,3]=>[2,4,5,6,7,3,1]=>101000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[7,2,1,4,5,3,6]=>[2,4,5,7,6,3,1]=>101001
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[2,4,6,5,3,1,7]=>101010
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,7,5]=>[6,2,1,4,7,3,5]=>[2,4,6,3,1,7,5]=>101010
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[6,2,7,4,3,1,5]=>[2,4,6,1,7,5,3]=>101010
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[7,2,1,4,3,6,5]=>[2,4,6,7,5,3,1]=>101010
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[2,4,7,6,5,3,1]=>101011
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[2,5,4,3,1,6,7]=>101100
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>[2,5,4,3,1,7,6]=>101101
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,6,4,7]=>[5,2,1,6,3,4,7]=>[2,5,3,1,6,4,7]=>101100
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,6,7,4]=>[5,2,1,7,3,6,4]=>[2,5,3,1,6,7,4]=>101100
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,1,3,7,4,6]=>[5,2,1,7,3,4,6]=>[2,5,3,1,7,6,4]=>101101
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,6,3,4,7]=>[5,2,6,3,1,4,7]=>[2,5,1,6,4,3,7]=>101100
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[2,5,1,6,3,7,4]=>101100
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,6,7,3,4]=>[5,2,7,3,1,6,4]=>[2,5,1,6,7,4,3]=>101100
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,1,7,3,4,6]=>[5,2,7,3,1,4,6]=>[2,5,1,7,6,4,3]=>101101
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[2,5,6,4,3,1,7]=>101100
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,1,3,7,4]=>[6,2,1,7,5,3,4]=>[2,5,6,3,1,7,4]=>101100
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[6,2,7,3,5,1,4]=>[2,5,6,1,7,4,3]=>101100
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[7,2,1,3,5,6,4]=>[2,5,6,7,4,3,1]=>101100
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[2,5,7,6,4,3,1]=>101101
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[2,6,5,4,3,1,7]=>101110
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,7,5]=>[6,2,1,3,7,4,5]=>[2,6,4,3,1,7,5]=>101110
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,7,4,5]=>[6,2,1,7,4,3,5]=>[2,6,3,1,7,5,4]=>101110
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,1,7,3,4,5]=>[6,2,7,3,4,1,5]=>[2,6,1,7,5,4,3]=>101110
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[2,6,7,5,4,3,1]=>101110
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[2,7,6,5,4,3,1]=>101111
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>[3,2,1,4,5,7,6]=>110001
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>[3,2,1,4,6,5,7]=>110010
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>[3,2,1,4,6,7,5]=>110010
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]=>110011
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,2,1,5,4,6,7]=>110100
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,2,1,5,4,7,6]=>110101
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>[3,2,1,5,6,4,7]=>110100
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,4]=>[3,1,2,7,5,6,4]=>[3,2,1,5,6,7,4]=>110100
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>[3,2,1,5,7,6,4]=>110101
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>[3,2,1,6,5,4,7]=>110110
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,6,4,7,5]=>[3,1,2,6,7,4,5]=>[3,2,1,6,4,7,5]=>110110
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>[3,2,1,6,7,5,4]=>110110
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>[3,2,1,7,6,5,4]=>110111
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>110000
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[3,1,4,2,5,7,6]=>110001
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[3,1,4,2,6,5,7]=>110010
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[3,1,4,2,6,7,5]=>110010
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,7,5,6]=>[3,4,1,2,7,5,6]=>[3,1,4,2,7,6,5]=>110011
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[3,1,4,5,2,6,7]=>110000
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[3,1,4,5,2,7,6]=>110001
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[3,1,4,5,6,2,7]=>110000
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[3,1,4,5,6,7,2]=>110000
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,4,5,7,2,6]=>[3,7,1,4,5,2,6]=>[3,1,4,5,7,6,2]=>110001
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,7]=>[3,6,1,4,2,5,7]=>[3,1,4,6,5,2,7]=>110010
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[3,1,4,6,2,7,5]=>110010
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,7,2,5]=>[3,7,1,4,2,6,5]=>[3,1,4,6,7,5,2]=>110010
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,4,7,2,5,6]=>[3,7,1,4,2,5,6]=>[3,1,4,7,6,5,2]=>110011
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[3,5,1,2,4,6,7]=>[3,1,5,4,2,6,7]=>110100
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6]=>[3,5,1,2,4,7,6]=>[3,1,5,4,2,7,6]=>110101
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[3,1,5,2,6,4,7]=>110100
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[3,1,5,2,6,7,4]=>110100
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6]=>[3,5,1,7,2,4,6]=>[3,1,5,2,7,6,4]=>110101
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,2,4,7]=>[3,6,1,2,5,4,7]=>[3,1,5,6,4,2,7]=>110100
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[3,1,5,6,2,7,4]=>110100
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,2,4]=>[3,7,1,2,5,6,4]=>[3,1,5,6,7,4,2]=>110100
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6]=>[3,7,1,2,5,4,6]=>[3,1,5,7,6,4,2]=>110101
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,7]=>[3,6,1,2,4,5,7]=>[3,1,6,5,4,2,7]=>110110
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,7,5]=>[3,6,1,2,7,4,5]=>[3,1,6,4,2,7,5]=>110110
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,7,4,5]=>[3,6,1,7,4,2,5]=>[3,1,6,2,7,5,4]=>110110
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,6,7,2,4,5]=>[3,7,1,2,4,6,5]=>[3,1,6,7,5,4,2]=>110110
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6]=>[3,7,1,2,4,5,6]=>[3,1,7,6,5,4,2]=>110111
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>110000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>[3,4,2,1,5,7,6]=>110001
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>[3,4,2,1,6,5,7]=>110010
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>[3,4,2,1,6,7,5]=>110010
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>[3,4,2,1,7,6,5]=>110011
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[3,4,1,5,2,6,7]=>110000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[3,4,1,5,2,7,6]=>110001
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[3,4,1,5,6,2,7]=>110000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[3,4,1,5,6,7,2]=>110000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6]=>[4,7,3,1,5,2,6]=>[3,4,1,5,7,6,2]=>110001
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,7]=>[4,6,3,1,2,5,7]=>[3,4,1,6,5,2,7]=>110010
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[3,4,1,6,2,7,5]=>110010
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,7,2,5]=>[4,7,3,1,2,6,5]=>[3,4,1,6,7,5,2]=>110010
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,1,7,2,5,6]=>[4,7,3,1,2,5,6]=>[3,4,1,7,6,5,2]=>110011
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[3,4,5,2,1,6,7]=>110000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,1,2,7,6]=>[5,1,3,4,2,7,6]=>[3,4,5,2,1,7,6]=>110001
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[3,4,5,1,6,2,7]=>110000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[3,4,5,1,6,7,2]=>110000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6]=>[5,7,3,4,1,2,6]=>[3,4,5,1,7,6,2]=>110001
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[3,4,5,6,2,1,7]=>110000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[3,4,5,6,1,7,2]=>110000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[3,4,5,6,7,2,1]=>110000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[7,1,3,4,5,2,6]=>[3,4,5,7,6,2,1]=>110001
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[3,4,6,5,2,1,7]=>110010
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,1,2,7,5]=>[6,1,3,4,7,2,5]=>[3,4,6,2,1,7,5]=>110010
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[6,7,3,4,2,1,5]=>[3,4,6,1,7,5,2]=>110010
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[7,1,3,4,2,6,5]=>[3,4,6,7,5,2,1]=>110010
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[3,4,7,6,5,2,1]=>110011
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[3,5,4,2,1,6,7]=>110100
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>[3,5,4,2,1,7,6]=>110101
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,6,4,7]=>[5,1,3,6,2,4,7]=>[3,5,2,1,6,4,7]=>110100
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,6,7,4]=>[5,1,3,7,2,6,4]=>[3,5,2,1,6,7,4]=>110100
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6]=>[5,1,3,7,2,4,6]=>[3,5,2,1,7,6,4]=>110101
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,6,2,4,7]=>[5,6,3,2,1,4,7]=>[3,5,1,6,4,2,7]=>110100
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[3,5,1,6,2,7,4]=>110100
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,6,7,2,4]=>[5,7,3,2,1,6,4]=>[3,5,1,6,7,4,2]=>110100
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6]=>[5,7,3,2,1,4,6]=>[3,5,1,7,6,4,2]=>110101
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[3,5,6,4,2,1,7]=>110100
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,1,2,7,4]=>[6,1,3,7,5,2,4]=>[3,5,6,2,1,7,4]=>110100
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[6,7,3,2,5,1,4]=>[3,5,6,1,7,4,2]=>110100
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[7,1,3,2,5,6,4]=>[3,5,6,7,4,2,1]=>110100
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[3,5,7,6,4,2,1]=>110101
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[3,6,5,4,2,1,7]=>110110
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,7,5]=>[6,1,3,2,7,4,5]=>[3,6,4,2,1,7,5]=>110110
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,7,4,5]=>[6,1,3,7,4,2,5]=>[3,6,2,1,7,5,4]=>110110
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,1,7,2,4,5]=>[6,7,3,2,4,1,5]=>[3,6,1,7,5,4,2]=>110110
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[3,6,7,5,4,2,1]=>110110
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[3,7,6,5,4,2,1]=>110111
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>[4,3,2,1,5,7,6]=>111001
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>[4,3,2,1,6,5,7]=>111010
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>[4,3,2,1,6,7,5]=>111010
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>[4,3,2,1,7,6,5]=>111011
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,5,3,6,7]=>[4,1,5,2,3,6,7]=>[4,2,1,5,3,6,7]=>111000
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6]=>[4,1,5,2,3,7,6]=>[4,2,1,5,3,7,6]=>111001
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,6,3,7]=>[4,1,6,2,5,3,7]=>[4,2,1,5,6,3,7]=>111000
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,3]=>[4,1,7,2,5,6,3]=>[4,2,1,5,6,7,3]=>111000
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6]=>[4,1,7,2,5,3,6]=>[4,2,1,5,7,6,3]=>111001
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,7]=>[4,1,6,2,3,5,7]=>[4,2,1,6,5,3,7]=>111010
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,7,5]=>[4,1,6,2,7,3,5]=>[4,2,1,6,3,7,5]=>111010
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,6,7,3,5]=>[4,1,7,2,3,6,5]=>[4,2,1,6,7,5,3]=>111010
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,7,3,5,6]=>[4,1,7,2,3,5,6]=>[4,2,1,7,6,5,3]=>111011
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[4,5,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>111000
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6]=>[4,5,2,1,3,7,6]=>[4,1,5,3,2,7,6]=>111001
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[4,1,5,2,6,3,7]=>111000
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[4,1,5,2,6,7,3]=>111000
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6]=>[4,5,7,1,2,3,6]=>[4,1,5,2,7,6,3]=>111001
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,5,6,2,3,7]=>[4,6,2,1,5,3,7]=>[4,1,5,6,3,2,7]=>111000
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[4,1,5,6,2,7,3]=>111000
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,5,6,7,2,3]=>[4,7,2,1,5,6,3]=>[4,1,5,6,7,3,2]=>111000
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6]=>[4,7,2,1,5,3,6]=>[4,1,5,7,6,3,2]=>111001
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,7]=>[4,6,2,1,3,5,7]=>[4,1,6,5,3,2,7]=>111010
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,7,5]=>[4,6,2,1,7,3,5]=>[4,1,6,3,2,7,5]=>111010
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,7,3,5]=>[4,6,7,1,3,2,5]=>[4,1,6,2,7,5,3]=>111010
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,7,2,3,5]=>[4,7,2,1,3,6,5]=>[4,1,6,7,5,3,2]=>111010
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6]=>[4,7,2,1,3,5,6]=>[4,1,7,6,5,3,2]=>111011
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[4,5,3,2,1,6,7]=>111000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[5,1,2,4,3,7,6]=>[4,5,3,2,1,7,6]=>111001
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,6,3,7]=>[5,1,6,4,2,3,7]=>[4,5,2,1,6,3,7]=>111000
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,6,7,3]=>[5,1,7,4,2,6,3]=>[4,5,2,1,6,7,3]=>111000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6]=>[5,1,7,4,2,3,6]=>[4,5,2,1,7,6,3]=>111001
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,1,6,2,3,7]=>[5,6,2,4,1,3,7]=>[4,5,1,6,3,2,7]=>111000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[4,5,1,6,2,7,3]=>111000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,1,6,7,2,3]=>[5,7,2,4,1,6,3]=>[4,5,1,6,7,3,2]=>111000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6]=>[5,7,2,4,1,3,6]=>[4,5,1,7,6,3,2]=>111001
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[4,5,6,3,2,1,7]=>111000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,1,2,7,3]=>[6,1,7,4,5,2,3]=>[4,5,6,2,1,7,3]=>111000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[6,7,2,4,5,1,3]=>[4,5,6,1,7,3,2]=>111000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[4,5,6,7,3,2,1]=>111000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[4,5,7,6,3,2,1]=>111001
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[4,6,5,3,2,1,7]=>111010
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,7,5]=>[6,1,2,4,7,3,5]=>[4,6,3,2,1,7,5]=>111010
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,7,3,5]=>[6,1,7,4,3,2,5]=>[4,6,2,1,7,5,3]=>111010
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,7,2,3,5]=>[6,7,2,4,3,1,5]=>[4,6,1,7,5,3,2]=>111010
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[4,6,7,5,3,2,1]=>111010
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[4,7,6,5,3,2,1]=>111011
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,4,3,2,1,6,7]=>111100
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>[5,4,3,2,1,7,6]=>111101
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,6,4,7]=>[5,1,2,6,3,4,7]=>[5,3,2,1,6,4,7]=>111100
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,6,7,4]=>[5,1,2,7,3,6,4]=>[5,3,2,1,6,7,4]=>111100
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,1,2,3,7,4,6]=>[5,1,2,7,3,4,6]=>[5,3,2,1,7,6,4]=>111101
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,6,3,4,7]=>[5,1,6,3,2,4,7]=>[5,2,1,6,4,3,7]=>111100
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,6,3,7,4]=>[5,1,6,7,2,3,4]=>[5,2,1,6,3,7,4]=>111100
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,6,7,3,4]=>[5,1,7,3,2,6,4]=>[5,2,1,6,7,4,3]=>111100
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6]=>[5,1,7,3,2,4,6]=>[5,2,1,7,6,4,3]=>111101
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,7]=>[5,6,2,3,1,4,7]=>[5,1,6,4,3,2,7]=>111100
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,6,2,3,7,4]=>[5,6,2,7,1,3,4]=>[5,1,6,3,2,7,4]=>111100
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,6,2,7,3,4]=>[5,6,7,3,1,2,4]=>[5,1,6,2,7,4,3]=>111100
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,6,7,2,3,4]=>[5,7,2,3,1,6,4]=>[5,1,6,7,4,3,2]=>111100
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,1,7,2,3,4,6]=>[5,7,2,3,1,4,6]=>[5,1,7,6,4,3,2]=>111101
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[5,6,4,3,2,1,7]=>111100
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,7,4]=>[6,1,2,7,5,3,4]=>[5,6,3,2,1,7,4]=>111100
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,1,2,7,3,4]=>[6,1,7,3,5,2,4]=>[5,6,2,1,7,4,3]=>111100
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,1,7,2,3,4]=>[6,7,2,3,5,1,4]=>[5,6,1,7,4,3,2]=>111100
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[5,6,7,4,3,2,1]=>111100
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[5,7,6,4,3,2,1]=>111101
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,5,4,3,2,1,7]=>111110
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,7,5]=>[6,1,2,3,7,4,5]=>[6,4,3,2,1,7,5]=>111110
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,7,4,5]=>[6,1,2,7,4,3,5]=>[6,3,2,1,7,5,4]=>111110
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,7,3,4,5]=>[6,1,7,3,4,2,5]=>[6,2,1,7,5,4,3]=>111110
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1,7,2,3,4,5]=>[6,7,2,3,4,1,5]=>[6,1,7,5,4,3,2]=>111110
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[6,7,5,4,3,2,1]=>111110
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,6,5,4,3,2,1]=>111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>0000001
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>0000010
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>0000010
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]=>0000011
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>0000101
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>0000100
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[1,2,3,4,6,7,8,5]=>0000100
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,6,5,7]=>[1,2,3,4,6,8,7,5]=>0000101
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,6,5,8]=>0000110
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,7,5,8,6]=>0000110
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,6,5]=>0000110
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,7,6,5]=>0000111
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>0001010
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>0001010
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,7,6]=>0001011
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>0001000
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>0001001
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[1,2,3,5,6,7,4,8]=>0001000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[1,2,3,5,6,7,8,4]=>0001000
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,4,7]=>[1,2,3,8,5,6,4,7]=>[1,2,3,5,6,8,7,4]=>0001001
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,4,6,8]=>[1,2,3,7,5,4,6,8]=>[1,2,3,5,7,6,4,8]=>0001010
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>[1,2,3,5,7,4,8,6]=>0001010
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,4,7,6]=>[1,2,3,5,7,8,6,4]=>0001010
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>[1,2,3,8,5,4,6,7]=>[1,2,3,5,8,7,6,4]=>0001011
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,5,4,8,7]=>0001101
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>[1,2,3,6,4,7,5,8]=>0001100
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>[1,2,3,6,4,7,8,5]=>0001100
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,8,4,5,7]=>[1,2,3,6,4,8,7,5]=>0001101
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,5,4,8]=>0001100
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,4,8,5]=>[1,2,3,7,8,6,4,5]=>[1,2,3,6,7,4,8,5]=>0001100
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,4,5]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,7,8,5,4]=>0001100
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,4,5,7]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,8,7,5,4]=>0001101
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,6,5,4,8]=>0001110
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,4,5,8,6]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,5,4,8,6]=>0001110
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,8,5,4,6]=>[1,2,3,7,4,8,6,5]=>0001110
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,5,7,6]=>[1,2,3,7,8,6,5,4]=>0001110
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,7,6,5,4]=>0001111
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>0010001
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>0010100
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>0010101
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,6,7,5,8]=>0010100
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[1,2,4,3,6,7,8,5]=>0010100
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,8,6,5,7]=>[1,2,4,3,6,8,7,5]=>0010101
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,7,5,8,6]=>0010110
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,7,8,6,5]=>0010110
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,7,6,5]=>0010111
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>0010010
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[1,2,4,5,3,8,7,6]=>0010011
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[1,2,4,5,6,3,7,8]=>0010000
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,4,5,7,3,8,6]=>[1,2,7,4,5,8,3,6]=>[1,2,4,5,7,3,8,6]=>0010010
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,7,8,3,6]=>[1,2,8,4,5,3,7,6]=>[1,2,4,5,7,8,6,3]=>0010010
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,8,3,5,7]=>[1,2,4,6,3,8,7,5]=>0010101
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,4,6,7,3,8,5]=>[1,2,7,4,8,6,3,5]=>[1,2,4,6,7,3,8,5]=>0010100
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,3,5]=>[1,2,8,4,3,6,7,5]=>[1,2,4,6,7,8,5,3]=>0010100
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,3,8,5,6]=>[1,2,7,4,8,5,3,6]=>[1,2,4,7,3,8,6,5]=>0010110
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>[1,2,8,4,3,5,7,6]=>[1,2,4,7,8,6,5,3]=>0010110
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]=>[1,2,4,8,7,6,5,3]=>0010111
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,3,4,6,8,7]=>[1,2,5,3,4,6,8,7]=>[1,2,5,4,3,6,8,7]=>0011001
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,3,4,7,8,6]=>[1,2,5,3,4,8,7,6]=>[1,2,5,4,3,7,8,6]=>0011010
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,8,7]=>[1,2,5,6,3,4,8,7]=>[1,2,5,3,6,4,8,7]=>0011001
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>[1,2,5,3,6,7,8,4]=>0011000
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>[1,2,5,3,7,4,8,6]=>0011010
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,8,4,6,7]=>[1,2,5,8,3,4,6,7]=>[1,2,5,3,8,7,6,4]=>0011011
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>[1,2,5,6,3,7,4,8]=>0011000
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,3,7,8,4]=>[1,2,6,8,5,3,7,4]=>[1,2,5,6,3,7,8,4]=>0011000
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,5,6,3,8,4,7]=>[1,2,6,8,5,3,4,7]=>[1,2,5,6,3,8,7,4]=>0011001
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,3,4]=>[1,2,8,3,5,6,7,4]=>[1,2,5,6,7,8,4,3]=>0011000
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,3,4,8,6]=>[1,2,7,3,5,8,4,6]=>[1,2,5,7,4,3,8,6]=>0011010
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,3,8,4,6]=>[1,2,7,8,5,4,3,6]=>[1,2,5,7,3,8,6,4]=>0011010
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]=>[1,2,6,5,4,3,7,8]=>0011100
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>[1,2,6,3,7,4,8,5]=>0011100
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>[1,2,6,8,4,3,7,5]=>[1,2,6,3,7,8,5,4]=>0011100
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,3,8,4,5,7]=>[1,2,6,8,4,3,5,7]=>[1,2,6,3,8,7,5,4]=>0011101
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,6,7,3,4,8,5]=>[1,2,7,3,8,6,4,5]=>[1,2,6,7,4,3,8,5]=>0011100
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,6,7,3,8,4,5]=>[1,2,7,8,4,6,3,5]=>[1,2,6,7,3,8,5,4]=>0011100
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,3,4,5]=>[1,2,8,3,4,6,7,5]=>[1,2,6,7,8,5,4,3]=>0011100
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,3,4,5,8,6]=>[1,2,7,3,4,8,5,6]=>[1,2,7,5,4,3,8,6]=>0011110
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>[1,2,7,3,8,5,4,6]=>[1,2,7,4,3,8,6,5]=>0011110
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,3,8,4,5,6]=>[1,2,7,8,4,5,3,6]=>[1,2,7,3,8,6,5,4]=>0011110
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]=>[1,2,8,7,6,5,4,3]=>0011111
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>0100010
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>0100010
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>0100100
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>0100101
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>[1,3,2,4,6,7,8,5]=>0100100
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,5,7]=>[1,3,2,4,8,6,5,7]=>[1,3,2,4,6,8,7,5]=>0100101
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,5,6,8]=>[1,3,2,4,7,5,6,8]=>[1,3,2,4,7,6,5,8]=>0100110
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,7,5,8,6]=>0100110
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,7,6,5]=>0100111
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>0101000
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>0101010
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>0101010
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,7,6]=>0101011
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>0101000
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,5,6,7,4,8]=>[1,3,2,7,5,6,4,8]=>[1,3,2,5,6,7,4,8]=>0101000
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,4,6,8]=>[1,3,2,7,5,4,6,8]=>[1,3,2,5,7,6,4,8]=>0101010
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]=>[1,3,2,7,5,8,4,6]=>[1,3,2,5,7,4,8,6]=>0101010
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,4,6]=>[1,3,2,8,5,4,7,6]=>[1,3,2,5,7,8,6,4]=>0101010
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>[1,3,2,6,4,7,5,8]=>0101100
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]=>[1,3,2,6,8,4,7,5]=>[1,3,2,6,4,7,8,5]=>0101100
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,4,5,8,6]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,5,4,8,6]=>0101110
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,8,5,4,6]=>[1,3,2,7,4,8,6,5]=>0101110
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,7,6,5,4]=>0101111
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>0100000
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>0100001
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>0100010
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>0100010
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,6,7]=>[1,3,4,2,5,8,7,6]=>0100011
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>0100100
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[1,3,4,2,6,7,8,5]=>0100100
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,5,7]=>[1,4,3,2,8,6,5,7]=>[1,3,4,2,6,8,7,5]=>0100101
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,5,6]=>[1,4,3,2,8,5,7,6]=>[1,3,4,2,7,8,6,5]=>0100110
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,7,6,5]=>0100111
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>0100000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]=>[1,3,4,5,2,7,6,8]=>0100010
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[1,3,4,5,2,7,8,6]=>0100010
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,2,8,5]=>[1,7,3,4,8,6,2,5]=>[1,3,4,6,7,2,8,5]=>0100100
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,2,5]=>[1,8,3,4,2,6,7,5]=>[1,3,4,6,7,8,5,2]=>0100100
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[1,8,3,4,2,5,6,7]=>[1,3,4,8,7,6,5,2]=>0100111
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,2,4,6,7,8]=>[1,5,3,2,4,6,7,8]=>[1,3,5,4,2,6,7,8]=>0101000
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,2,4,6,8,7]=>[1,5,3,2,4,6,8,7]=>[1,3,5,4,2,6,8,7]=>0101001
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,2,4,7,6,8]=>[1,5,3,2,4,7,6,8]=>[1,3,5,4,2,7,6,8]=>0101010
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,2,4,7,8,6]=>[1,5,3,2,4,8,7,6]=>[1,3,5,4,2,7,8,6]=>0101010
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>[1,3,5,2,6,4,7,8]=>0101000
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>[1,3,5,2,6,7,4,8]=>0101000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,2,7,4,6,8]=>[1,5,3,7,2,4,6,8]=>[1,3,5,2,7,6,4,8]=>0101010
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,8,6]=>[1,5,3,7,2,8,4,6]=>[1,3,5,2,7,4,8,6]=>0101010
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,8,4,6]=>[1,5,3,8,2,4,7,6]=>[1,3,5,2,7,8,6,4]=>0101010
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,2,8,4,6,7]=>[1,5,3,8,2,4,6,7]=>[1,3,5,2,8,7,6,4]=>0101011
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,2,4,7,8]=>[1,6,3,2,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>0101000
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,2,7,8,4]=>[1,6,3,8,5,2,7,4]=>[1,3,5,6,2,7,8,4]=>0101000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,2,4,8]=>[1,7,3,2,5,6,4,8]=>[1,3,5,6,7,4,2,8]=>0101000
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,2,4]=>[1,8,3,2,5,6,7,4]=>[1,3,5,6,7,8,4,2]=>0101000
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,2,4,6,8]=>[1,7,3,2,5,4,6,8]=>[1,3,5,7,6,4,2,8]=>0101010
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,2,4,8,6]=>[1,7,3,2,5,8,4,6]=>[1,3,5,7,4,2,8,6]=>0101010
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,2,8,4,6]=>[1,7,3,8,5,4,2,6]=>[1,3,5,7,2,8,6,4]=>0101010
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>[1,8,3,2,5,4,7,6]=>[1,3,5,7,8,6,4,2]=>0101010
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[1,8,3,2,5,4,6,7]=>[1,3,5,8,7,6,4,2]=>0101011
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,2,4,7,5,8]=>[1,6,3,2,7,4,5,8]=>[1,3,6,4,2,7,5,8]=>0101100
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>[1,6,3,2,8,4,5,7]=>[1,3,6,4,2,8,7,5]=>0101101
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,8,5]=>[1,6,3,7,8,2,4,5]=>[1,3,6,2,7,4,8,5]=>0101100
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]=>[1,6,3,8,4,2,7,5]=>[1,3,6,2,7,8,5,4]=>0101100
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,6,2,8,4,5,7]=>[1,6,3,8,4,2,5,7]=>[1,3,6,2,8,7,5,4]=>0101101
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,6,7,2,4,8,5]=>[1,7,3,2,8,6,4,5]=>[1,3,6,7,4,2,8,5]=>0101100
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,2,4,5]=>[1,8,3,2,4,6,7,5]=>[1,3,6,7,8,5,4,2]=>0101100
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,7,2,4,5,8,6]=>[1,7,3,2,4,8,5,6]=>[1,3,7,5,4,2,8,6]=>0101110
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>[1,7,3,2,8,5,4,6]=>[1,3,7,4,2,8,6,5]=>0101110
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,7,2,8,4,5,6]=>[1,7,3,8,4,5,2,6]=>[1,3,7,2,8,6,5,4]=>0101110
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]=>[1,3,8,7,6,5,4,2]=>0101111
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>0110001
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>0110010
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>[1,4,3,2,5,7,8,6]=>0110010
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>[1,4,3,2,5,8,7,6]=>0110011
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,2,3,6,7,8,5]=>[1,4,2,3,8,6,7,5]=>[1,4,3,2,6,7,8,5]=>0110100
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[1,4,3,2,7,6,5,8]=>0110110
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,3,7,5,8,6]=>[1,4,2,3,7,8,5,6]=>[1,4,3,2,7,5,8,6]=>0110110
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[1,4,3,2,8,7,6,5]=>0110111
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>0110000
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>0110010
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,3,7,8,6]=>[1,4,5,2,3,8,7,6]=>[1,4,2,5,3,7,8,6]=>0110010
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>[1,4,2,5,6,7,3,8]=>0110000
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,2,5,6,8,3,7]=>[1,4,8,2,5,6,3,7]=>[1,4,2,5,6,8,7,3]=>0110001
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,2,5,7,3,6,8]=>[1,4,7,2,5,3,6,8]=>[1,4,2,5,7,6,3,8]=>0110010
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>[1,4,7,2,5,8,3,6]=>[1,4,2,5,7,3,8,6]=>0110010
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,2,5,8,3,6,7]=>[1,4,8,2,5,3,6,7]=>[1,4,2,5,8,7,6,3]=>0110011
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>[1,4,2,6,3,7,5,8]=>0110100
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,2,6,7,8,3,5]=>[1,4,8,2,3,6,7,5]=>[1,4,2,6,7,8,5,3]=>0110100
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,2,6,8,3,5,7]=>[1,4,8,2,3,6,5,7]=>[1,4,2,6,8,7,5,3]=>0110101
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,8,5,3,6]=>[1,4,2,7,3,8,6,5]=>0110110
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,2,7,8,3,5,6]=>[1,4,8,2,3,5,7,6]=>[1,4,2,7,8,6,5,3]=>0110110
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>[1,4,8,2,3,5,6,7]=>[1,4,2,8,7,6,5,3]=>0110111
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>[1,4,5,2,6,3,7,8]=>0110000
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,2,6,7,8,3]=>[1,5,8,4,2,6,7,3]=>[1,4,5,2,6,7,8,3]=>0110000
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>[1,5,8,4,2,6,3,7]=>[1,4,5,2,6,8,7,3]=>0110001
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,8,6]=>[1,5,7,4,2,8,3,6]=>[1,4,5,2,7,3,8,6]=>0110010
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,2,8,3,6,7]=>[1,5,8,4,2,3,6,7]=>[1,4,5,2,8,7,6,3]=>0110011
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,2,8,3]=>[1,7,8,4,5,6,2,3]=>[1,4,5,6,7,2,8,3]=>0110000
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,5,7,2,3,8,6]=>[1,7,2,4,5,8,3,6]=>[1,4,5,7,3,2,8,6]=>0110010
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,7,8,2,3,6]=>[1,8,2,4,5,3,7,6]=>[1,4,5,7,8,6,3,2]=>0110010
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,6,2,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>[1,4,6,5,3,2,7,8]=>0110100
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>[1,6,2,4,8,3,5,7]=>[1,4,6,3,2,8,7,5]=>0110101
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,8,5]=>[1,6,7,4,8,2,3,5]=>[1,4,6,2,7,3,8,5]=>0110100
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>[1,6,8,4,3,2,7,5]=>[1,4,6,2,7,8,5,3]=>0110100
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,2,8,3,5,7]=>[1,6,8,4,3,2,5,7]=>[1,4,6,2,8,7,5,3]=>0110101
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,2,8,3,5]=>[1,7,8,4,3,6,2,5]=>[1,4,6,7,2,8,5,3]=>0110100
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[1,8,2,4,3,6,5,7]=>[1,4,6,8,7,5,3,2]=>0110101
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>[1,4,8,7,6,5,3,2]=>0110111
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,2,3,6,4,7,8]=>[1,5,2,6,3,4,7,8]=>[1,5,3,2,6,4,7,8]=>0111000
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,2,3,6,8,4,7]=>[1,5,2,8,3,6,4,7]=>[1,5,3,2,6,8,7,4]=>0111001
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,2,3,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,5,3,2,8,7,6,4]=>0111011
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,6,3,4,7,8]=>[1,5,6,3,2,4,7,8]=>[1,5,2,6,4,3,7,8]=>0111000
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>[1,5,2,6,3,7,4,8]=>0111000
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>[1,5,6,8,2,3,7,4]=>[1,5,2,6,3,7,8,4]=>0111000
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,8,4,7]=>[1,5,6,8,2,3,4,7]=>[1,5,2,6,3,8,7,4]=>0111001
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,2,6,7,3,4,8]=>[1,5,7,3,2,6,4,8]=>[1,5,2,6,7,4,3,8]=>0111000
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>[1,5,7,3,2,8,4,6]=>[1,5,2,7,4,3,8,6]=>0111010
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,8,4,6]=>[1,5,7,8,2,4,3,6]=>[1,5,2,7,3,8,6,4]=>0111010
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,2,7,8,3,4,6]=>[1,5,8,3,2,4,7,6]=>[1,5,2,7,8,6,4,3]=>0111010
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>[1,5,8,3,2,4,6,7]=>[1,5,2,8,7,6,4,3]=>0111011
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,6,2,3,4,7,8]=>[1,6,2,3,5,4,7,8]=>[1,5,6,4,3,2,7,8]=>0111000
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,6,2,3,7,8,4]=>[1,6,2,8,5,3,7,4]=>[1,5,6,3,2,7,8,4]=>0111000
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>[1,6,2,8,5,3,4,7]=>[1,5,6,3,2,8,7,4]=>0111001
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,5,6,7,2,8,3,4]=>[1,7,8,3,5,6,2,4]=>[1,5,6,7,2,8,4,3]=>0111000
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>[1,8,2,3,5,6,7,4]=>[1,5,6,7,8,4,3,2]=>0111000
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,2,8,3,4,6]=>[1,7,8,3,5,4,2,6]=>[1,5,7,2,8,6,4,3]=>0111010
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,3,4,7,8,5]=>[1,6,2,3,8,4,7,5]=>[1,6,4,3,2,7,8,5]=>0111100
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>[1,6,2,7,8,3,4,5]=>[1,6,3,2,7,4,8,5]=>0111100
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,7,3,4,8,5]=>[1,6,7,3,8,2,4,5]=>[1,6,2,7,4,3,8,5]=>0111100
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,8,4,5]=>[1,6,7,8,4,2,3,5]=>[1,6,2,7,3,8,5,4]=>0111100
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,2,3,4,8,5]=>[1,7,2,3,8,6,4,5]=>[1,6,7,4,3,2,8,5]=>0111100
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,2,8,3,4,5]=>[1,7,8,3,4,6,2,5]=>[1,6,7,2,8,5,4,3]=>0111100
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[1,8,2,3,4,6,7,5]=>[1,6,7,8,5,4,3,2]=>0111100
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,2,3,8,4,5,6]=>[1,7,2,8,4,5,3,6]=>[1,7,3,2,8,6,5,4]=>0111110
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>[1,8,2,3,4,5,7,6]=>[1,7,8,6,5,4,3,2]=>0111110
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>0111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>1000001
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>1000100
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>1000101
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[2,1,3,4,6,7,8,5]=>1000100
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,7,6,5]=>1000111
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>1001001
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,6,7,4,8,5]=>[2,1,3,7,8,6,4,5]=>[2,1,3,6,7,4,8,5]=>1001100
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,7,4,5,8,6]=>[2,1,3,7,4,8,5,6]=>[2,1,3,7,5,4,8,6]=>1001110
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,7,6,5,4]=>1001111
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>1010000
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>1010001
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>1010100
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>1010101
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,4,3,6,7,8,5]=>1010100
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,7,5]=>1010101
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,7,5,8,6]=>1010110
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,7,8,6,5]=>1010110
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,7,6,5]=>1010111
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>1010001
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,4,5,6,3,8,7]=>1010001
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[2,1,4,5,6,7,8,3]=>1010000
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,3,7]=>[2,1,8,4,5,6,3,7]=>[2,1,4,5,6,8,7,3]=>1010001
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[2,1,4,5,7,3,8,6]=>1010010
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,3,6]=>[2,1,8,4,5,3,7,6]=>[2,1,4,5,7,8,6,3]=>1010010
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,3,6,7]=>[2,1,8,4,5,3,6,7]=>[2,1,4,5,8,7,6,3]=>1010011
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>[2,1,4,6,5,3,8,7]=>1010101
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,4,6,3,7,8,5]=>[2,1,6,4,8,3,7,5]=>[2,1,4,6,3,7,8,5]=>1010100
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,3,8,5,7]=>[2,1,6,4,8,3,5,7]=>[2,1,4,6,3,8,7,5]=>1010101
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,3,5,7]=>[2,1,8,4,3,6,5,7]=>[2,1,4,6,8,7,5,3]=>1010101
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,3,5,6]=>[2,1,8,4,3,5,7,6]=>[2,1,4,7,8,6,5,3]=>1010110
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>[2,1,8,4,3,5,6,7]=>[2,1,4,8,7,6,5,3]=>1010111
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>1011001
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,3,6,7,8,4]=>[2,1,5,8,3,6,7,4]=>[2,1,5,3,6,7,8,4]=>1011000
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[2,1,5,3,7,4,8,6]=>1011010
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>[2,1,5,6,4,3,8,7]=>1011001
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,7,8,4]=>[2,1,6,8,5,3,7,4]=>[2,1,5,6,3,7,8,4]=>1011000
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,3,4]=>[2,1,8,3,5,6,7,4]=>[2,1,5,6,7,8,4,3]=>1011000
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,3,8,4,6]=>[2,1,7,8,5,4,3,6]=>[2,1,5,7,3,8,6,4]=>1011010
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]=>[2,1,5,7,8,6,4,3]=>1011010
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>[2,1,6,5,4,3,8,7]=>1011101
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,6,3,4,7,8,5]=>[2,1,6,3,8,4,7,5]=>[2,1,6,4,3,7,8,5]=>1011100
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[2,1,6,3,7,4,8,5]=>1011100
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,3,4,8,5]=>[2,1,7,3,8,6,4,5]=>[2,1,6,7,4,3,8,5]=>1011100
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,3,8,4,5]=>[2,1,7,8,4,6,3,5]=>[2,1,6,7,3,8,5,4]=>1011100
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,3,4,5]=>[2,1,8,3,4,6,7,5]=>[2,1,6,7,8,5,4,3]=>1011100
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,3,4,5,6]=>[2,1,8,3,4,5,7,6]=>[2,1,7,8,6,5,4,3]=>1011110
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>[2,1,8,7,6,5,4,3]=>1011111
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>1000000
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>1000010
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>1000100
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[2,3,1,4,6,7,8,5]=>1000100
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,5,7,6]=>[2,3,1,4,7,8,6,5]=>1000110
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,7,6,5]=>1000111
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>1001010
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[2,3,1,5,6,7,4,8]=>1001000
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[2,3,1,5,6,7,8,4]=>1001000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5,8]=>[3,2,1,6,7,4,5,8]=>[2,3,1,6,4,7,5,8]=>1001100
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,4,5]=>[3,2,1,8,4,6,7,5]=>[2,3,1,6,7,8,5,4]=>1001100
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]=>[2,3,1,6,8,7,5,4]=>1001101
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>[3,2,1,7,4,8,5,6]=>[2,3,1,7,5,4,8,6]=>1001110
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,8,5,6]=>[3,2,1,7,8,5,4,6]=>[2,3,1,7,4,8,6,5]=>1001110
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>[3,2,1,8,4,5,6,7]=>[2,3,1,8,7,6,5,4]=>1001111
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>1000000
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[4,2,3,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>1000001
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>1000010
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>1000010
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,8,6,7]=>[2,3,4,1,5,8,7,6]=>1000011
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>1000100
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>1000101
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>1000100
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[2,3,4,1,6,7,8,5]=>1000100
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,5,7]=>[4,2,3,1,8,6,5,7]=>[2,3,4,1,6,8,7,5]=>1000101
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,5,6,8]=>[4,2,3,1,7,5,6,8]=>[2,3,4,1,7,6,5,8]=>1000110
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,8,6]=>[4,2,3,1,7,8,5,6]=>[2,3,4,1,7,5,8,6]=>1000110
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>[2,3,4,1,7,8,6,5]=>1000110
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>[2,3,4,1,8,7,6,5]=>1000111
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>1000000
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,6,7]=>[5,2,3,4,1,8,6,7]=>[2,3,4,5,1,8,7,6]=>1000011
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[2,3,4,5,6,1,8,7]=>1000001
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,1,8,5,7]=>[6,2,3,4,8,1,5,7]=>[2,3,4,6,1,8,7,5]=>1000101
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,1,5]=>[8,2,3,4,1,6,7,5]=>[2,3,4,6,7,8,5,1]=>1000100
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,1,5,6,8]=>[7,2,3,4,1,5,6,8]=>[2,3,4,7,6,5,1,8]=>1000110
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,1,5,8,6]=>[7,2,3,4,1,8,5,6]=>[2,3,4,7,5,1,8,6]=>1000110
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>[2,3,4,8,7,6,5,1]=>1000111
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]=>[5,2,3,1,4,8,6,7]=>[2,3,5,4,1,8,7,6]=>1001011
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,8,7]=>[5,2,3,6,1,4,8,7]=>[2,3,5,1,6,4,8,7]=>1001001
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[2,3,5,1,6,7,8,4]=>1001000
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,8,6]=>[5,2,3,7,1,8,4,6]=>[2,3,5,1,7,4,8,6]=>1001010
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,1,8,4,6,7]=>[5,2,3,8,1,4,6,7]=>[2,3,5,1,8,7,6,4]=>1001011
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,1,4,8,7]=>[6,2,3,1,5,4,8,7]=>[2,3,5,6,4,1,8,7]=>1001001
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,1,7,4,8]=>[6,2,3,7,5,1,4,8]=>[2,3,5,6,1,7,4,8]=>1001000
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,1,7,8,4]=>[6,2,3,8,5,1,7,4]=>[2,3,5,6,1,7,8,4]=>1001000
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,1,8,4]=>[7,2,3,8,5,6,1,4]=>[2,3,5,6,7,1,8,4]=>1001000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,1,4]=>[8,2,3,1,5,6,7,4]=>[2,3,5,6,7,8,4,1]=>1001000
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,1,4,6]=>[8,2,3,1,5,4,7,6]=>[2,3,5,7,8,6,4,1]=>1001010
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,1,4,5,8,7]=>[6,2,3,1,4,5,8,7]=>[2,3,6,5,4,1,8,7]=>1001101
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,1,4,7,8,5]=>[6,2,3,1,8,4,7,5]=>[2,3,6,4,1,7,8,5]=>1001100
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,8,5,7]=>[6,2,3,1,8,4,5,7]=>[2,3,6,4,1,8,7,5]=>1001101
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>[6,2,3,8,4,1,7,5]=>[2,3,6,1,7,8,5,4]=>1001100
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,1,8,4,5,7]=>[6,2,3,8,4,1,5,7]=>[2,3,6,1,8,7,5,4]=>1001101
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,6,7,1,4,8,5]=>[7,2,3,1,8,6,4,5]=>[2,3,6,7,4,1,8,5]=>1001100
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,1,4,8,5,6]=>[7,2,3,1,8,5,4,6]=>[2,3,7,4,1,8,6,5]=>1001110
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>[2,3,8,7,6,5,4,1]=>1001111
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>1010000
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>1010101
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,3,6,7,8,5]=>[4,2,1,3,8,6,7,5]=>[2,4,3,1,6,7,8,5]=>1010100
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>[2,4,3,1,6,8,7,5]=>1010101
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>[2,4,3,1,8,7,6,5]=>1010111
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,8]=>[4,2,5,1,3,7,6,8]=>[2,4,1,5,3,7,6,8]=>1010010
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]=>[4,2,5,1,3,8,7,6]=>[2,4,1,5,3,7,8,6]=>1010010
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,8,6,7]=>[4,2,5,1,3,8,6,7]=>[2,4,1,5,3,8,7,6]=>1010011
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3,7,8]=>[4,2,6,1,5,3,7,8]=>[2,4,1,5,6,3,7,8]=>1010000
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,6,3,8,7]=>[4,2,6,1,5,3,8,7]=>[2,4,1,5,6,3,8,7]=>1010001
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>[4,2,8,1,5,6,7,3]=>[2,4,1,5,6,7,8,3]=>1010000
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>[4,2,7,1,5,8,3,6]=>[2,4,1,5,7,3,8,6]=>1010010
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,6,3,5,8,7]=>[4,2,6,1,3,5,8,7]=>[2,4,1,6,5,3,8,7]=>1010101
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5,8]=>[4,2,6,1,7,3,5,8]=>[2,4,1,6,3,7,5,8]=>1010100
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>[4,2,6,1,8,3,7,5]=>[2,4,1,6,3,7,8,5]=>1010100
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,8,5,7]=>[4,2,6,1,8,3,5,7]=>[2,4,1,6,3,8,7,5]=>1010101
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>[4,2,7,1,8,6,3,5]=>[2,4,1,6,7,3,8,5]=>1010100
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,1,6,8,3,5,7]=>[4,2,8,1,3,6,5,7]=>[2,4,1,6,8,7,5,3]=>1010101
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>[4,2,7,1,3,8,5,6]=>[2,4,1,7,5,3,8,6]=>1010110
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,8,5,6]=>[4,2,7,1,8,5,3,6]=>[2,4,1,7,3,8,6,5]=>1010110
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>[4,2,8,1,3,5,6,7]=>[2,4,1,8,7,6,5,3]=>1010111
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,3,7,8]=>[5,2,6,4,1,3,7,8]=>[2,4,5,1,6,3,7,8]=>1010000
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>[5,2,8,4,1,6,3,7]=>[2,4,5,1,6,8,7,3]=>1010001
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,4,5,1,7,3,6,8]=>[5,2,7,4,1,3,6,8]=>[2,4,5,1,7,6,3,8]=>1010010
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,8,6]=>[5,2,7,4,1,8,3,6]=>[2,4,5,1,7,3,8,6]=>1010010
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,1,3,7,8]=>[6,2,1,4,5,3,7,8]=>[2,4,5,6,3,1,7,8]=>1010000
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,1,8,3]=>[7,2,8,4,5,6,1,3]=>[2,4,5,6,7,1,8,3]=>1010000
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,4,5,7,1,3,8,6]=>[7,2,1,4,5,8,3,6]=>[2,4,5,7,3,1,8,6]=>1010010
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,1,3,5,8,7]=>[6,2,1,4,3,5,8,7]=>[2,4,6,5,3,1,8,7]=>1010101
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,1,3,7,8,5]=>[6,2,1,4,8,3,7,5]=>[2,4,6,3,1,7,8,5]=>1010100
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,1,3,8,5,7]=>[6,2,1,4,8,3,5,7]=>[2,4,6,3,1,8,7,5]=>1010101
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,8,5]=>[6,2,7,4,8,1,3,5]=>[2,4,6,1,7,3,8,5]=>1010100
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,1,8,3,5,7]=>[6,2,8,4,3,1,5,7]=>[2,4,6,1,8,7,5,3]=>1010101
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,1,3,5,8]=>[7,2,1,4,3,6,5,8]=>[2,4,6,7,5,3,1,8]=>1010100
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,1,8,3,5]=>[7,2,8,4,3,6,1,5]=>[2,4,6,7,1,8,5,3]=>1010100
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[8,2,1,4,3,6,5,7]=>[2,4,6,8,7,5,3,1]=>1010101
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,1,3,8,5,6]=>[7,2,1,4,8,5,3,6]=>[2,4,7,3,1,8,6,5]=>1010110
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>[2,5,4,3,1,6,7,8]=>1011000
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,4,7,8,6]=>[5,2,1,3,4,8,7,6]=>[2,5,4,3,1,7,8,6]=>1011010
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,5,1,3,6,4,7,8]=>[5,2,1,6,3,4,7,8]=>[2,5,3,1,6,4,7,8]=>1011000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4,8]=>[5,2,6,7,1,3,4,8]=>[2,5,1,6,3,7,4,8]=>1011000
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>[5,2,6,8,1,3,7,4]=>[2,5,1,6,3,7,8,4]=>1011000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,1,6,7,3,4,8]=>[5,2,7,3,1,6,4,8]=>[2,5,1,6,7,4,3,8]=>1011000
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>[5,2,7,8,1,6,3,4]=>[2,5,1,6,7,3,8,4]=>1011000
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,1,6,7,8,3,4]=>[5,2,8,3,1,6,7,4]=>[2,5,1,6,7,8,4,3]=>1011000
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>[5,2,7,3,1,8,4,6]=>[2,5,1,7,4,3,8,6]=>1011010
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,8,4,6]=>[5,2,7,8,1,4,3,6]=>[2,5,1,7,3,8,6,4]=>1011010
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,1,7,8,3,4,6]=>[5,2,8,3,1,4,7,6]=>[2,5,1,7,8,6,4,3]=>1011010
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,1,3,7,8,4]=>[6,2,1,8,5,3,7,4]=>[2,5,6,3,1,7,8,4]=>1011000
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]=>[6,2,8,3,5,1,7,4]=>[2,5,6,1,7,8,4,3]=>1011000
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>[8,2,1,3,5,6,7,4]=>[2,5,6,7,8,4,3,1]=>1011000
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,5,7,1,3,8,4,6]=>[7,2,1,8,5,4,3,6]=>[2,5,7,3,1,8,6,4]=>1011010
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,5,7,1,8,3,4,6]=>[7,2,8,3,5,4,1,6]=>[2,5,7,1,8,6,4,3]=>1011010
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,1,7,3,4,8,5]=>[6,2,7,3,8,1,4,5]=>[2,6,1,7,4,3,8,5]=>1011100
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>[3,2,1,4,5,8,7,6]=>1100011
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,4,6,7,8,5]=>[3,1,2,4,8,6,7,5]=>[3,2,1,4,6,7,8,5]=>1100100
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,4,6,8,5,7]=>[3,1,2,4,8,6,5,7]=>[3,2,1,4,6,8,7,5]=>1100101
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,2,4,7,5,8,6]=>[3,1,2,4,7,8,5,6]=>[3,2,1,4,7,5,8,6]=>1100110
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,5,7,6]=>[3,2,1,4,7,8,6,5]=>1100110
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>[3,2,1,4,8,7,6,5]=>1100111
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>1101010
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,8,4]=>[3,1,2,8,5,6,7,4]=>[3,2,1,5,6,7,8,4]=>1101000
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,1,2,5,6,8,4,7]=>[3,1,2,8,5,6,4,7]=>[3,2,1,5,6,8,7,4]=>1101001
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>[3,1,2,7,5,4,6,8]=>[3,2,1,5,7,6,4,8]=>1101010
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,2,5,7,4,8,6]=>[3,1,2,7,5,8,4,6]=>[3,2,1,5,7,4,8,6]=>1101010
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,2,5,7,8,4,6]=>[3,1,2,8,5,4,7,6]=>[3,2,1,5,7,8,6,4]=>1101010
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,2,6,4,7,8,5]=>[3,1,2,6,8,4,7,5]=>[3,2,1,6,4,7,8,5]=>1101100
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,2,6,7,4,8,5]=>[3,1,2,7,8,6,4,5]=>[3,2,1,6,7,4,8,5]=>1101100
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,2,7,4,5,8,6]=>[3,1,2,7,4,8,5,6]=>[3,2,1,7,5,4,8,6]=>1101110
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,2,7,8,4,5,6]=>[3,1,2,8,4,5,7,6]=>[3,2,1,7,8,6,5,4]=>1101110
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]=>[3,2,1,8,7,6,5,4]=>1101111
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>1100000
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[3,1,4,2,5,7,8,6]=>1100010
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,2,5,8,6,7]=>[3,4,1,2,5,8,6,7]=>[3,1,4,2,5,8,7,6]=>1100011
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>[3,4,1,2,6,5,7,8]=>[3,1,4,2,6,5,7,8]=>1100100
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>1100101
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,2,6,7,5,8]=>[3,4,1,2,7,6,5,8]=>[3,1,4,2,6,7,5,8]=>1100100
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,2,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[3,1,4,2,6,7,8,5]=>1100100
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,2,6,8,5,7]=>[3,4,1,2,8,6,5,7]=>[3,1,4,2,6,8,7,5]=>1100101
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[3,1,4,2,7,5,8,6]=>1100110
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,8,5,6,7]=>[3,4,1,2,8,5,6,7]=>[3,1,4,2,8,7,6,5]=>1100111
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[3,1,4,5,2,7,6,8]=>1100010
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,5,2,7,8,6]=>[3,5,1,4,2,8,7,6]=>[3,1,4,5,2,7,8,6]=>1100010
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,6,2,8,7]=>[3,6,1,4,5,2,8,7]=>[3,1,4,5,6,2,8,7]=>1100001
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,8,2]=>[3,8,1,4,5,6,7,2]=>[3,1,4,5,6,7,8,2]=>1100000
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,4,5,6,8,2,7]=>[3,8,1,4,5,6,2,7]=>[3,1,4,5,6,8,7,2]=>1100001
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,4,6,2,5,7,8]=>[3,6,1,4,2,5,7,8]=>[3,1,4,6,5,2,7,8]=>1100100
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,4,6,2,8,5,7]=>[3,6,1,4,8,2,5,7]=>[3,1,4,6,2,8,7,5]=>1100101
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4,8,2,5,6,7]=>[3,8,1,4,2,5,6,7]=>[3,1,4,8,7,6,5,2]=>1100111
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>1101001
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,2,6,7,8,4]=>[3,5,1,8,2,6,7,4]=>[3,1,5,2,6,7,8,4]=>1101000
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[3,1,5,2,7,4,8,6]=>1101010
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,2,7,8,4,6]=>[3,5,1,8,2,4,7,6]=>[3,1,5,2,7,8,6,4]=>1101010
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,8,4,6,7]=>[3,5,1,8,2,4,6,7]=>[3,1,5,2,8,7,6,4]=>1101011
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,7,8,4]=>[3,6,1,8,5,2,7,4]=>[3,1,5,6,2,7,8,4]=>1101000
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,5,6,2,8,4,7]=>[3,6,1,8,5,2,4,7]=>[3,1,5,6,2,8,7,4]=>1101001
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,5,6,7,2,8,4]=>[3,7,1,8,5,6,2,4]=>[3,1,5,6,7,2,8,4]=>1101000
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,8,2,4]=>[3,8,1,2,5,6,7,4]=>[3,1,5,6,7,8,4,2]=>1101000
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>[3,7,1,2,5,4,6,8]=>[3,1,5,7,6,4,2,8]=>1101010
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,5,7,2,8,4,6]=>[3,7,1,8,5,4,2,6]=>[3,1,5,7,2,8,6,4]=>1101010
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,1,5,7,8,2,4,6]=>[3,8,1,2,5,4,7,6]=>[3,1,5,7,8,6,4,2]=>1101010
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,6,2,4,5,8,7]=>[3,6,1,2,4,5,8,7]=>[3,1,6,5,4,2,8,7]=>1101101
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[3,1,6,2,7,4,8,5]=>1101100
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,8,4,5,7]=>[3,6,1,8,4,2,5,7]=>[3,1,6,2,8,7,5,4]=>1101101
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>[3,8,1,2,4,6,5,7]=>[3,1,6,8,7,5,4,2]=>1101101
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,7,2,4,5,8,6]=>[3,7,1,2,4,8,5,6]=>[3,1,7,5,4,2,8,6]=>1101110
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,7,2,4,8,5,6]=>[3,7,1,2,8,5,4,6]=>[3,1,7,4,2,8,6,5]=>1101110
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>1100000
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,1,2,5,8,6,7]=>[4,1,3,2,5,8,6,7]=>[3,4,2,1,5,8,7,6]=>1100011
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>1100101
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[3,4,2,1,6,7,8,5]=>1100100
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,1,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>[3,4,2,1,6,8,7,5]=>1100101
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>[3,4,2,1,7,8,6,5]=>1100110
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[3,4,2,1,8,7,6,5]=>1100111
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6,8]=>[4,5,3,1,2,7,6,8]=>[3,4,1,5,2,7,6,8]=>1100010
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2,7,8]=>[4,6,3,1,5,2,7,8]=>[3,4,1,5,6,2,7,8]=>1100000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,7,2,8]=>[4,7,3,1,5,6,2,8]=>[3,4,1,5,6,7,2,8]=>1100000
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,8,6]=>[4,7,3,1,5,8,2,6]=>[3,4,1,5,7,2,8,6]=>1100010
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5,8]=>[4,6,3,1,7,2,5,8]=>[3,4,1,6,2,7,5,8]=>1100100
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,8,5,6]=>[4,7,3,1,8,5,2,6]=>[3,4,1,7,2,8,6,5]=>1100110
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>[4,8,3,1,2,5,6,7]=>[3,4,1,8,7,6,5,2]=>1100111
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,1,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>[3,4,5,2,1,6,7,8]=>1100000
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,5,1,2,7,8,6]=>[5,1,3,4,2,8,7,6]=>[3,4,5,2,1,7,8,6]=>1100010
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>[5,1,3,4,2,8,6,7]=>[3,4,5,2,1,8,7,6]=>1100011
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,2,7,8]=>[5,6,3,4,1,2,7,8]=>[3,4,5,1,6,2,7,8]=>1100000
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,8,7]=>[5,6,3,4,1,2,8,7]=>[3,4,5,1,6,2,8,7]=>1100001
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,1,6,8,2,7]=>[5,8,3,4,1,6,2,7]=>[3,4,5,1,6,8,7,2]=>1100001
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,8,2,6,7]=>[5,8,3,4,1,2,6,7]=>[3,4,5,1,8,7,6,2]=>1100011
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,1,7,2,8]=>[6,7,3,4,5,1,2,8]=>[3,4,5,6,1,7,2,8]=>1100000
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,1,7,8,2]=>[6,8,3,4,5,1,7,2]=>[3,4,5,6,1,7,8,2]=>1100000
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,1,2,8,6]=>[7,1,3,4,5,8,2,6]=>[3,4,5,7,2,1,8,6]=>1100010
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,1,2,6]=>[8,1,3,4,5,2,7,6]=>[3,4,5,7,8,6,2,1]=>1100010
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,1,2,7,5,8]=>[6,1,3,4,7,2,5,8]=>[3,4,6,2,1,7,5,8]=>1100100
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,1,2,7,8,5]=>[6,1,3,4,8,2,7,5]=>[3,4,6,2,1,7,8,5]=>1100100
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,8,5]=>[6,7,3,4,8,1,2,5]=>[3,4,6,1,7,2,8,5]=>1100100
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>[6,8,3,4,2,1,7,5]=>[3,4,6,1,7,8,5,2]=>1100100
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,1,8,2,5]=>[7,8,3,4,2,6,1,5]=>[3,4,6,7,1,8,5,2]=>1100100
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,4,7,1,8,2,5,6]=>[7,8,3,4,2,5,1,6]=>[3,4,7,1,8,6,5,2]=>1100110
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,4,6,7,8]=>[5,1,3,2,4,6,7,8]=>[3,5,4,2,1,6,7,8]=>1101000
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>[5,1,3,2,4,6,8,7]=>[3,5,4,2,1,6,8,7]=>1101001
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,1,2,4,7,6,8]=>[5,1,3,2,4,7,6,8]=>[3,5,4,2,1,7,6,8]=>1101010
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,4,7,8,6]=>[5,1,3,2,4,8,7,6]=>[3,5,4,2,1,7,8,6]=>1101010
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[3,5,4,2,1,8,7,6]=>1101011
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,1,2,6,7,8,4]=>[5,1,3,8,2,6,7,4]=>[3,5,2,1,6,7,8,4]=>1101000
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,1,2,7,8,4,6]=>[5,1,3,8,2,4,7,6]=>[3,5,2,1,7,8,6,4]=>1101010
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,5,1,6,2,4,7,8]=>[5,6,3,2,1,4,7,8]=>[3,5,1,6,4,2,7,8]=>1101000
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,5,1,6,2,4,8,7]=>[5,6,3,2,1,4,8,7]=>[3,5,1,6,4,2,8,7]=>1101001
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4,8]=>[5,6,3,7,1,2,4,8]=>[3,5,1,6,2,7,4,8]=>1101000
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>[5,6,3,8,1,2,7,4]=>[3,5,1,6,2,7,8,4]=>1101000
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,8,4,7]=>[5,6,3,8,1,2,4,7]=>[3,5,1,6,2,8,7,4]=>1101001
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>[5,7,3,8,1,6,2,4]=>[3,5,1,6,7,2,8,4]=>1101000
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,8,4,6]=>[5,7,3,8,1,4,2,6]=>[3,5,1,7,2,8,6,4]=>1101010
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,1,7,8,2,4,6]=>[5,8,3,2,1,4,7,6]=>[3,5,1,7,8,6,4,2]=>1101010
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>[3,5,6,4,2,1,8,7]=>1101001
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,1,2,7,8,4]=>[6,1,3,8,5,2,7,4]=>[3,5,6,2,1,7,8,4]=>1101000
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]=>[6,1,3,8,5,2,4,7]=>[3,5,6,2,1,8,7,4]=>1101001
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,1,7,2,4,8]=>[6,7,3,2,5,1,4,8]=>[3,5,6,1,7,4,2,8]=>1101000
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,8,4]=>[6,7,3,8,5,1,2,4]=>[3,5,6,1,7,2,8,4]=>1101000
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>[6,8,3,2,5,1,7,4]=>[3,5,6,1,7,8,4,2]=>1101000
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,5,6,1,8,2,4,7]=>[6,8,3,2,5,1,4,7]=>[3,5,6,1,8,7,4,2]=>1101001
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>[8,1,3,2,5,6,7,4]=>[3,5,6,7,8,4,2,1]=>1101000
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[8,1,3,2,5,6,4,7]=>[3,5,6,8,7,4,2,1]=>1101001
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>[3,5,7,6,4,2,1,8]=>1101010
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,1,2,4,8,6]=>[7,1,3,2,5,8,4,6]=>[3,5,7,4,2,1,8,6]=>1101010
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]=>[3,5,7,8,6,4,2,1]=>1101010
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,1,2,4,6,7]=>[8,1,3,2,5,4,6,7]=>[3,5,8,7,6,4,2,1]=>1101011
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,1,2,4,7,8,5]=>[6,1,3,2,8,4,7,5]=>[3,6,4,2,1,7,8,5]=>1101100
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,1,2,7,4,8,5]=>[6,1,3,7,8,2,4,5]=>[3,6,2,1,7,4,8,5]=>1101100
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,6,1,7,2,4,5,8]=>[6,7,3,2,4,1,5,8]=>[3,6,1,7,5,4,2,8]=>1101100
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,1,7,8,2,4,5]=>[6,8,3,2,4,1,7,5]=>[3,6,1,7,8,5,4,2]=>1101100
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,6,1,8,2,4,5,7]=>[6,8,3,2,4,1,5,7]=>[3,6,1,8,7,5,4,2]=>1101101
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>[7,1,3,8,4,6,2,5]=>[3,6,7,2,1,8,5,4]=>1101100
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,1,8,2,4,5]=>[7,8,3,2,4,6,1,5]=>[3,6,7,1,8,5,4,2]=>1101100
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,7,1,2,4,5,8,6]=>[7,1,3,2,4,8,5,6]=>[3,7,5,4,2,1,8,6]=>1101110
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,1,2,4,8,5,6]=>[7,1,3,2,8,5,4,6]=>[3,7,4,2,1,8,6,5]=>1101110
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>1110001
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>1110010
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>1110010
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>[4,3,2,1,5,8,7,6]=>1110011
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>1110100
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>1110101
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>1110100
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>[4,3,2,1,6,7,8,5]=>1110100
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>[4,3,2,1,6,8,7,5]=>1110101
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>[4,3,2,1,7,6,5,8]=>1110110
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,3,7,5,8,6]=>[4,1,2,3,7,8,5,6]=>[4,3,2,1,7,5,8,6]=>1110110
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]=>[4,3,2,1,7,8,6,5]=>1110110
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>[4,3,2,1,8,7,6,5]=>1110111
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6,8]=>[4,1,5,2,3,7,6,8]=>[4,2,1,5,3,7,6,8]=>1110010
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,5,3,7,8,6]=>[4,1,5,2,3,8,7,6]=>[4,2,1,5,3,7,8,6]=>1110010
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,2,5,6,3,7,8]=>[4,1,6,2,5,3,7,8]=>[4,2,1,5,6,3,7,8]=>1110000
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,2,5,6,3,8,7]=>[4,1,6,2,5,3,8,7]=>[4,2,1,5,6,3,8,7]=>1110001
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6,8]=>[4,1,7,2,5,3,6,8]=>[4,2,1,5,7,6,3,8]=>1110010
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,5,7,3,8,6]=>[4,1,7,2,5,8,3,6]=>[4,2,1,5,7,3,8,6]=>1110010
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,5,7,8,3,6]=>[4,1,8,2,5,3,7,6]=>[4,2,1,5,7,8,6,3]=>1110010
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,2,6,3,5,8,7]=>[4,1,6,2,3,5,8,7]=>[4,2,1,6,5,3,8,7]=>1110101
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]=>[4,1,6,2,7,3,5,8]=>[4,2,1,6,3,7,5,8]=>1110100
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,2,6,3,7,8,5]=>[4,1,6,2,8,3,7,5]=>[4,2,1,6,3,7,8,5]=>1110100
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,2,6,3,8,5,7]=>[4,1,6,2,8,3,5,7]=>[4,2,1,6,3,8,7,5]=>1110101
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]=>[4,1,7,2,3,6,5,8]=>[4,2,1,6,7,5,3,8]=>1110100
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,2,7,8,3,5,6]=>[4,1,8,2,3,5,7,6]=>[4,2,1,7,8,6,5,3]=>1110110
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>[4,1,8,2,3,5,6,7]=>[4,2,1,8,7,6,5,3]=>1110111
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,2,3,7,6,8]=>[4,5,2,1,3,7,6,8]=>[4,1,5,3,2,7,6,8]=>1110010
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,5,2,3,7,8,6]=>[4,5,2,1,3,8,7,6]=>[4,1,5,3,2,7,8,6]=>1110010
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,5,2,3,8,6,7]=>[4,5,2,1,3,8,6,7]=>[4,1,5,3,2,8,7,6]=>1110011
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[4,1,5,2,6,3,8,7]=>1110001
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,2,6,7,8,3]=>[4,5,8,1,2,6,7,3]=>[4,1,5,2,6,7,8,3]=>1110000
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,2,6,8,3,7]=>[4,5,8,1,2,6,3,7]=>[4,1,5,2,6,8,7,3]=>1110001
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[4,1,5,2,7,3,8,6]=>1110010
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,8,3,6,7]=>[4,5,8,1,2,3,6,7]=>[4,1,5,2,8,7,6,3]=>1110011
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,5,6,2,3,7,8]=>[4,6,2,1,5,3,7,8]=>[4,1,5,6,3,2,7,8]=>1110000
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,5,6,2,3,8,7]=>[4,6,2,1,5,3,8,7]=>[4,1,5,6,3,2,8,7]=>1110001
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,5,7,2,3,6,8]=>[4,7,2,1,5,3,6,8]=>[4,1,5,7,6,3,2,8]=>1110010
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,6,2,3,7,5,8]=>[4,6,2,1,7,3,5,8]=>[4,1,6,3,2,7,5,8]=>1110100
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,6,2,3,7,8,5]=>[4,6,2,1,8,3,7,5]=>[4,1,6,3,2,7,8,5]=>1110100
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,7,3,5,8]=>[4,6,7,1,3,2,5,8]=>[4,1,6,2,7,5,3,8]=>1110100
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[4,1,6,2,7,3,8,5]=>1110100
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,8,3,5,7]=>[4,6,8,1,3,2,5,7]=>[4,1,6,2,8,7,5,3]=>1110101
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>[4,8,2,1,3,6,5,7]=>[4,1,6,8,7,5,3,2]=>1110101
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,8,2,3,5,6,7]=>[4,8,2,1,3,5,6,7]=>[4,1,8,7,6,5,3,2]=>1110111
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[4,5,3,2,1,6,7,8]=>1110000
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,3,6,8,7]=>[5,1,2,4,3,6,8,7]=>[4,5,3,2,1,6,8,7]=>1110001
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,3,7,6,8]=>[5,1,2,4,3,7,6,8]=>[4,5,3,2,1,7,6,8]=>1110010
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,1,2,3,8,6,7]=>[5,1,2,4,3,8,6,7]=>[4,5,3,2,1,8,7,6]=>1110011
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]=>[5,1,6,4,2,3,8,7]=>[4,5,2,1,6,3,8,7]=>1110001
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,5,1,2,6,7,3,8]=>[5,1,7,4,2,6,3,8]=>[4,5,2,1,6,7,3,8]=>1110000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,1,2,7,3,6,8]=>[5,1,7,4,2,3,6,8]=>[4,5,2,1,7,6,3,8]=>1110010
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,5,1,2,7,3,8,6]=>[5,1,7,4,2,8,3,6]=>[4,5,2,1,7,3,8,6]=>1110010
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,1,2,8,3,6,7]=>[5,1,8,4,2,3,6,7]=>[4,5,2,1,8,7,6,3]=>1110011
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,5,1,6,2,3,7,8]=>[5,6,2,4,1,3,7,8]=>[4,5,1,6,3,2,7,8]=>1110000
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,1,6,2,3,8,7]=>[5,6,2,4,1,3,8,7]=>[4,5,1,6,3,2,8,7]=>1110001
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[4,5,1,6,2,7,3,8]=>1110000
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,8,3,7]=>[5,6,8,4,1,2,3,7]=>[4,5,1,6,2,8,7,3]=>1110001
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,5,1,6,7,2,3,8]=>[5,7,2,4,1,6,3,8]=>[4,5,1,6,7,3,2,8]=>1110000
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>[5,7,8,4,1,6,2,3]=>[4,5,1,6,7,2,8,3]=>1110000
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,1,6,7,8,2,3]=>[5,8,2,4,1,6,7,3]=>[4,5,1,6,7,8,3,2]=>1110000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,1,7,2,3,6,8]=>[5,7,2,4,1,3,6,8]=>[4,5,1,7,6,3,2,8]=>1110010
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,8,3,6]=>[5,7,8,4,1,3,2,6]=>[4,5,1,7,2,8,6,3]=>1110010
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,1,2,3,8,7]=>[6,1,2,4,5,3,8,7]=>[4,5,6,3,2,1,8,7]=>1110001
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,1,2,7,8,3]=>[6,1,8,4,5,2,7,3]=>[4,5,6,2,1,7,8,3]=>1110000
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,1,2,8,3,7]=>[6,1,8,4,5,2,3,7]=>[4,5,6,2,1,8,7,3]=>1110001
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,6,1,7,2,3,8]=>[6,7,2,4,5,1,3,8]=>[4,5,6,1,7,3,2,8]=>1110000
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,1,8,2,3,7]=>[6,8,2,4,5,1,3,7]=>[4,5,6,1,8,7,3,2]=>1110001
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]=>[4,5,6,7,3,2,1,8]=>1110000
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,1,2,8,3]=>[7,1,8,4,5,6,2,3]=>[4,5,6,7,2,1,8,3]=>1110000
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,1,8,2,3]=>[7,8,2,4,5,6,1,3]=>[4,5,6,7,1,8,3,2]=>1110000
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[4,5,6,7,8,3,2,1]=>1110000
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[4,5,6,8,7,3,2,1]=>1110001
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>[7,1,8,4,5,3,2,6]=>[4,5,7,2,1,8,6,3]=>1110010
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[8,1,2,4,5,3,7,6]=>[4,5,7,8,6,3,2,1]=>1110010
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>[8,1,2,4,5,3,6,7]=>[4,5,8,7,6,3,2,1]=>1110011
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,8,7]=>[6,1,2,4,3,5,8,7]=>[4,6,5,3,2,1,8,7]=>1110101
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,6,1,2,3,7,5,8]=>[6,1,2,4,7,3,5,8]=>[4,6,3,2,1,7,5,8]=>1110100
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,6,1,2,7,3,5,8]=>[6,1,7,4,3,2,5,8]=>[4,6,2,1,7,5,3,8]=>1110100
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,6,1,2,7,8,3,5]=>[6,1,8,4,3,2,7,5]=>[4,6,2,1,7,8,5,3]=>1110100
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,1,7,2,3,5,8]=>[6,7,2,4,3,1,5,8]=>[4,6,1,7,5,3,2,8]=>1110100
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,1,7,2,3,8,5]=>[6,7,2,4,8,1,3,5]=>[4,6,1,7,3,2,8,5]=>1110100
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,1,8,2,3,5]=>[7,8,2,4,3,6,1,5]=>[4,6,7,1,8,5,3,2]=>1110100
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]=>[4,6,8,7,5,3,2,1]=>1110101
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,1,2,3,5,6,8]=>[7,1,2,4,3,5,6,8]=>[4,7,6,5,3,2,1,8]=>1110110
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>[7,8,2,4,3,5,1,6]=>[4,7,1,8,6,5,3,2]=>1110110
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>[4,8,7,6,5,3,2,1]=>1110111
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,3,4,7,8,6]=>[5,1,2,3,4,8,7,6]=>[5,4,3,2,1,7,8,6]=>1111010
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,2,3,6,4,7,8]=>[5,1,2,6,3,4,7,8]=>[5,3,2,1,6,4,7,8]=>1111000
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,3,6,7,4,8]=>[5,1,2,7,3,6,4,8]=>[5,3,2,1,6,7,4,8]=>1111000
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,2,3,6,7,8,4]=>[5,1,2,8,3,6,7,4]=>[5,3,2,1,6,7,8,4]=>1111000
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,3,7,4,8,6]=>[5,1,2,7,3,8,4,6]=>[5,3,2,1,7,4,8,6]=>1111010
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,2,6,3,4,7,8]=>[5,1,6,3,2,4,7,8]=>[5,2,1,6,4,3,7,8]=>1111000
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,2,6,7,8,3,4]=>[5,1,8,3,2,6,7,4]=>[5,2,1,6,7,8,4,3]=>1111000
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>[5,1,7,3,2,4,6,8]=>[5,2,1,7,6,4,3,8]=>1111010
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,1,2,7,3,4,8,6]=>[5,1,7,3,2,8,4,6]=>[5,2,1,7,4,3,8,6]=>1111010
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7,8]=>[5,6,2,3,1,4,7,8]=>[5,1,6,4,3,2,7,8]=>1111000
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,6,2,3,4,8,7]=>[5,6,2,3,1,4,8,7]=>[5,1,6,4,3,2,8,7]=>1111001
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,6,2,3,7,4,8]=>[5,6,2,7,1,3,4,8]=>[5,1,6,3,2,7,4,8]=>1111000
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,6,2,3,7,8,4]=>[5,6,2,8,1,3,7,4]=>[5,1,6,3,2,7,8,4]=>1111000
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,6,2,3,8,4,7]=>[5,6,2,8,1,3,4,7]=>[5,1,6,3,2,8,7,4]=>1111001
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,7,3,4,8]=>[5,6,7,3,1,2,4,8]=>[5,1,6,2,7,4,3,8]=>1111000
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[5,1,6,2,7,3,8,4]=>1111000
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,8,3,4,7]=>[5,6,8,3,1,2,4,7]=>[5,1,6,2,8,7,4,3]=>1111001
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,6,7,2,3,8,4]=>[5,7,2,8,1,6,3,4]=>[5,1,6,7,3,2,8,4]=>1111000
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,6,7,2,8,3,4]=>[5,7,8,3,1,6,2,4]=>[5,1,6,7,2,8,4,3]=>1111000
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,6,7,8,2,3,4]=>[5,8,2,3,1,6,7,4]=>[5,1,6,7,8,4,3,2]=>1111000
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,1,7,2,3,4,6,8]=>[5,7,2,3,1,4,6,8]=>[5,1,7,6,4,3,2,8]=>1111010
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,8,3,4,6]=>[5,7,8,3,1,4,2,6]=>[5,1,7,2,8,6,4,3]=>1111010
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>[5,6,4,3,2,1,7,8]=>1111000
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,6,1,2,3,7,8,4]=>[6,1,2,8,5,3,7,4]=>[5,6,3,2,1,7,8,4]=>1111000
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,8,4,7]=>[6,1,2,8,5,3,4,7]=>[5,6,3,2,1,8,7,4]=>1111001
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,6,1,2,7,3,8,4]=>[6,1,7,8,5,2,3,4]=>[5,6,2,1,7,3,8,4]=>1111000
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>[6,7,2,8,5,1,3,4]=>[5,6,1,7,3,2,8,4]=>1111000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,8,3,4]=>[6,7,8,3,5,1,2,4]=>[5,6,1,7,2,8,4,3]=>1111000
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,1,7,8,2,3,4]=>[6,8,2,3,5,1,7,4]=>[5,6,1,7,8,4,3,2]=>1111000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[5,6,7,4,3,2,1,8]=>1111000
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,1,2,3,8,4]=>[7,1,2,8,5,6,3,4]=>[5,6,7,3,2,1,8,4]=>1111000
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>[7,1,8,3,5,6,2,4]=>[5,6,7,2,1,8,4,3]=>1111000
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,1,8,2,3,4]=>[7,8,2,3,5,6,1,4]=>[5,6,7,1,8,4,3,2]=>1111000
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[5,6,7,8,4,3,2,1]=>1111000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>[8,1,2,3,5,6,4,7]=>[5,6,8,7,4,3,2,1]=>1111001
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,6,8]=>[7,1,2,3,5,4,6,8]=>[5,7,6,4,3,2,1,8]=>1111010
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>[8,1,2,3,5,4,7,6]=>[5,7,8,6,4,3,2,1]=>1111010
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>[6,5,4,3,2,1,8,7]=>1111101
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,2,3,4,7,5,8]=>[6,1,2,3,7,4,5,8]=>[6,4,3,2,1,7,5,8]=>1111100
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,2,3,4,7,8,5]=>[6,1,2,3,8,4,7,5]=>[6,4,3,2,1,7,8,5]=>1111100
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,1,2,3,4,8,5,7]=>[6,1,2,3,8,4,5,7]=>[6,4,3,2,1,8,7,5]=>1111101
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,2,3,7,8,4,5]=>[6,1,2,8,4,3,7,5]=>[6,3,2,1,7,8,5,4]=>1111100
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,2,7,3,4,8,5]=>[6,1,7,3,8,2,4,5]=>[6,2,1,7,4,3,8,5]=>1111100
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,2,7,3,8,4,5]=>[6,1,7,8,4,2,3,5]=>[6,2,1,7,3,8,5,4]=>1111100
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>[6,1,8,3,4,2,5,7]=>[6,2,1,8,7,5,4,3]=>1111101
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,7,2,3,8,4,5]=>[6,7,2,8,4,1,3,5]=>[6,1,7,3,2,8,5,4]=>1111100
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,8,3,4,5]=>[6,7,8,3,4,1,2,5]=>[6,1,7,2,8,5,4,3]=>1111100
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>[6,8,2,3,4,1,7,5]=>[6,1,7,8,5,4,3,2]=>1111100
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>[6,8,2,3,4,1,5,7]=>[6,1,8,7,5,4,3,2]=>1111101
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>[7,8,2,3,4,6,1,5]=>[6,7,1,8,5,4,3,2]=>1111100
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[6,7,8,5,4,3,2,1]=>1111100
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,6,5,4,3,2,1,8]=>1111110
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,8,4,5,6]=>[7,1,2,8,4,5,3,6]=>[7,3,2,1,8,6,5,4]=>1111110
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1,8,2,3,4,5,6]=>[7,8,2,3,4,5,1,6]=>[7,1,8,6,5,4,3,2]=>1111110
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[8,7,6,5,4,3,2,1]=>1111111
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
searching the database
Sorry, this map was not found in the database.