Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=> [1,0,1,0]=>[1,2]=>[1,2]=>0 [1,1,0,0]=>[2,1]=>[2,1]=>1 [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>00 [1,0,1,1,0,0]=>[1,3,2]=>[3,1,2]=>10 [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>10 [1,1,0,1,0,0]=>[2,3,1]=>[1,3,2]=>01 [1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>11 [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>000 [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[4,1,2,3]=>100 [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[3,1,2,4]=>100 [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,1,3]=>010 [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[4,3,1,2]=>110 [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>100 [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[1,4,2,3]=>010 [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[1,3,2,4]=>010 [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[1,2,4,3]=>001 [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,1,3,2]=>101 [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>110 [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[2,1,4,3]=>101 [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[1,4,3,2]=>011 [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[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]=>0000 [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[5,1,2,3,4]=>1000 [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[4,1,2,3,5]=>1000 [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[3,5,1,2,4]=>0100 [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[5,4,1,2,3]=>1100 [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[3,1,2,4,5]=>1000 [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[2,5,1,3,4]=>0100 [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[2,4,1,3,5]=>0100 [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,3,5,1,4]=>0010 [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[5,2,4,1,3]=>1010 [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[4,3,1,2,5]=>1100 [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[3,2,5,1,4]=>1010 [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[2,5,4,1,3]=>0110 [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[5,4,3,1,2]=>1110 [1,1,0,0,1,0,1,0,1,0]=>[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]=>[1,5,2,3,4]=>0100 [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[1,4,2,3,5]=>0100 [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[1,3,5,2,4]=>0010 [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[5,1,4,2,3]=>1010 [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[1,3,2,4,5]=>0100 [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[1,2,5,3,4]=>0010 [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[1,2,4,3,5]=>0010 [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[1,2,3,5,4]=>0001 [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,1,2,4,3]=>1001 [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,1,3,2,5]=>1010 [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[3,1,2,5,4]=>1001 [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[2,5,1,4,3]=>0101 [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,4,1,3,2]=>1101 [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>1100 [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[2,1,5,3,4]=>1010 [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[2,1,4,3,5]=>1010 [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[2,1,3,5,4]=>1001 [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[1,5,2,4,3]=>0101 [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[1,4,3,2,5]=>0110 [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[1,3,2,5,4]=>0101 [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>0011 [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,1,4,3,2]=>1011 [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>1110 [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[3,2,1,5,4]=>1101 [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[2,1,5,4,3]=>1011 [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[1,5,4,3,2]=>0111 [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[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]=>00000 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>10000 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>10000 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[4,6,1,2,3,5]=>01000 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>11000 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>10000 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[3,6,1,2,4,5]=>01000 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[3,5,1,2,4,6]=>01000 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[3,4,6,1,2,5]=>00100 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[6,3,5,1,2,4]=>10100 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>11000 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[4,3,6,1,2,5]=>10100 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[3,6,5,1,2,4]=>01100 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>11100 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>10000 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[2,6,1,3,4,5]=>01000 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[2,5,1,3,4,6]=>01000 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[2,4,6,1,3,5]=>00100 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[6,2,5,1,3,4]=>10100 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>01000 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[2,3,6,1,4,5]=>00100 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[2,3,5,1,4,6]=>00100 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,3,4,6,1,5]=>00010 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[6,2,3,5,1,4]=>10010 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[5,2,4,1,3,6]=>10100 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[4,2,3,6,1,5]=>10010 [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>01010 [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[6,5,2,4,1,3]=>11010 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>11000 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[3,2,6,1,4,5]=>10100 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[3,2,5,1,4,6]=>10100 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[3,2,4,6,1,5]=>10010 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[2,6,3,5,1,4]=>01010 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[2,5,4,1,3,6]=>01100 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[2,4,3,6,1,5]=>01010 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[2,3,6,5,1,4]=>00110 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[6,2,5,4,1,3]=>10110 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>11100 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[4,3,2,6,1,5]=>11010 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[3,2,6,5,1,4]=>10110 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[2,6,5,4,1,3]=>01110 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>11110 [1,1,0,0,1,0,1,0,1,0,1,0]=>[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]=>[1,6,2,3,4,5]=>01000 [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[1,5,2,3,4,6]=>01000 [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[1,4,6,2,3,5]=>00100 [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[6,1,5,2,3,4]=>10100 [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[1,4,2,3,5,6]=>01000 [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[1,3,6,2,4,5]=>00100 [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[1,3,5,2,4,6]=>00100 [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[1,3,4,6,2,5]=>00010 [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[6,1,3,5,2,4]=>10010 [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[5,1,4,2,3,6]=>10100 [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[4,1,3,6,2,5]=>10010 [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[3,6,1,5,2,4]=>01010 [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[6,5,1,4,2,3]=>11010 [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[1,3,2,4,5,6]=>01000 [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[1,2,6,3,4,5]=>00100 [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[1,2,5,3,4,6]=>00100 [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[1,2,4,6,3,5]=>00010 [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[6,1,2,5,3,4]=>10010 [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[1,2,4,3,5,6]=>00100 [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[1,2,3,6,4,5]=>00010 [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[1,2,3,5,4,6]=>00010 [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[1,2,3,4,6,5]=>00001 [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,1,2,3,5,4]=>10001 [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,1,2,4,3,6]=>10010 [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[4,1,2,3,6,5]=>10001 [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[3,6,1,2,5,4]=>01001 [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,5,1,2,4,3]=>11001 [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,1,3,2,5,6]=>10100 [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[3,1,2,6,4,5]=>10010 [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[3,1,2,5,4,6]=>10010 [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[3,1,2,4,6,5]=>10001 [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[2,6,1,3,5,4]=>01001 [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[2,5,1,4,3,6]=>01010 [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[2,4,1,3,6,5]=>01001 [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[2,3,6,1,5,4]=>00101 [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,2,5,1,4,3]=>10101 [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,4,1,3,2,6]=>11010 [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[4,3,1,2,6,5]=>11001 [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[3,2,6,1,5,4]=>10101 [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[2,6,5,1,4,3]=>01101 [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,5,4,1,3,2]=>11101 [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000 [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[2,1,6,3,4,5]=>10100 [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[2,1,5,3,4,6]=>10100 [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[2,1,4,6,3,5]=>10010 [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[1,6,2,5,3,4]=>01010 [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[2,1,4,3,5,6]=>10100 [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[2,1,3,6,4,5]=>10010 [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[2,1,3,5,4,6]=>10010 [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[2,1,3,4,6,5]=>10001 [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[1,6,2,3,5,4]=>01001 [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[1,5,2,4,3,6]=>01010 [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[1,4,2,3,6,5]=>01001 [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[1,3,6,2,5,4]=>00101 [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,1,5,2,4,3]=>10101 [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[1,4,3,2,5,6]=>01100 [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[1,3,2,6,4,5]=>01010 [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[1,3,2,5,4,6]=>01010 [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[1,3,2,4,6,5]=>01001 [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[1,2,6,3,5,4]=>00101 [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[1,2,5,4,3,6]=>00110 [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[1,2,4,3,6,5]=>00101 [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[1,2,3,6,5,4]=>00011 [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,1,2,5,4,3]=>10011 [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,1,4,3,2,6]=>10110 [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[4,1,3,2,6,5]=>10101 [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[3,1,2,6,5,4]=>10011 [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[2,6,1,5,4,3]=>01011 [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,1,4,3,2]=>11011 [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100 [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[3,2,1,6,4,5]=>11010 [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[3,2,1,5,4,6]=>11010 [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[3,2,1,4,6,5]=>11001 [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[2,1,6,3,5,4]=>10101 [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[2,1,5,4,3,6]=>10110 [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[2,1,4,3,6,5]=>10101 [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[2,1,3,6,5,4]=>10011 [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[1,6,2,5,4,3]=>01011 [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[1,5,4,3,2,6]=>01110 [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[1,4,3,2,6,5]=>01101 [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[1,3,2,6,5,4]=>01011 [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[1,2,6,5,4,3]=>00111 [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,1,5,4,3,2]=>10111 [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110 [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[4,3,2,1,6,5]=>11101 [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[3,2,1,6,5,4]=>11011 [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[2,1,6,5,4,3]=>10111 [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[1,6,5,4,3,2]=>01111 [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[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]=>000000 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>100000 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>100000 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[5,7,1,2,3,4,6]=>010000 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>110000 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>100000 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[4,7,1,2,3,5,6]=>010000 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[4,6,1,2,3,5,7]=>010000 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[4,5,7,1,2,3,6]=>001000 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[7,4,6,1,2,3,5]=>101000 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>110000 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[5,4,7,1,2,3,6]=>101000 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[4,7,6,1,2,3,5]=>011000 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>111000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>100000 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[3,7,1,2,4,5,6]=>010000 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[3,6,1,2,4,5,7]=>010000 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[3,5,7,1,2,4,6]=>001000 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[7,3,6,1,2,4,5]=>101000 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[3,5,1,2,4,6,7]=>010000 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[3,4,7,1,2,5,6]=>001000 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[3,4,6,1,2,5,7]=>001000 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[3,4,5,7,1,2,6]=>000100 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[7,3,4,6,1,2,5]=>100100 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[6,3,5,1,2,4,7]=>101000 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[5,3,4,7,1,2,6]=>100100 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[4,7,3,6,1,2,5]=>010100 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[7,6,3,5,1,2,4]=>110100 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>110000 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[4,3,7,1,2,5,6]=>101000 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[4,3,6,1,2,5,7]=>101000 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[4,3,5,7,1,2,6]=>100100 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[3,7,4,6,1,2,5]=>010100 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[3,6,5,1,2,4,7]=>011000 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[3,5,4,7,1,2,6]=>010100 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>001100 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[7,3,6,5,1,2,4]=>101100 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>111000 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[5,4,3,7,1,2,6]=>110100 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[4,3,7,6,1,2,5]=>101100 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[3,7,6,5,1,2,4]=>011100 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>111100 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>100000 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[2,7,1,3,4,5,6]=>010000 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[2,6,1,3,4,5,7]=>010000 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[2,5,7,1,3,4,6]=>001000 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[7,2,6,1,3,4,5]=>101000 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[2,5,1,3,4,6,7]=>010000 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[2,4,7,1,3,5,6]=>001000 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[2,4,6,1,3,5,7]=>001000 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[2,4,5,7,1,3,6]=>000100 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[7,2,4,6,1,3,5]=>100100 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[6,2,5,1,3,4,7]=>101000 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[5,2,4,7,1,3,6]=>100100 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[4,7,2,6,1,3,5]=>010100 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[7,6,2,5,1,3,4]=>110100 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>010000 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[2,3,7,1,4,5,6]=>001000 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[2,3,6,1,4,5,7]=>001000 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[2,3,5,7,1,4,6]=>000100 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[7,2,3,6,1,4,5]=>100100 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[2,3,5,1,4,6,7]=>001000 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[2,3,4,7,1,5,6]=>000100 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[2,3,4,6,1,5,7]=>000100 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,3,4,5,7,1,6]=>000010 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[7,2,3,4,6,1,5]=>100010 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[6,2,3,5,1,4,7]=>100100 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[5,2,3,4,7,1,6]=>100010 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[4,7,2,3,6,1,5]=>010010 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[7,6,2,3,5,1,4]=>110010 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[5,2,4,1,3,6,7]=>101000 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[4,2,3,7,1,5,6]=>100100 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[4,2,3,6,1,5,7]=>100100 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[4,2,3,5,7,1,6]=>100010 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[3,7,2,4,6,1,5]=>010010 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>010100 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[3,5,2,4,7,1,6]=>010010 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[3,4,7,2,6,1,5]=>001010 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[7,3,6,2,5,1,4]=>101010 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[6,5,2,4,1,3,7]=>110100 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[5,4,2,3,7,1,6]=>110010 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[4,3,7,2,6,1,5]=>101010 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[3,7,6,2,5,1,4]=>011010 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[7,6,5,2,4,1,3]=>111010 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>110000 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[3,2,7,1,4,5,6]=>101000 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[3,2,6,1,4,5,7]=>101000 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[3,2,5,7,1,4,6]=>100100 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[2,7,3,6,1,4,5]=>010100 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[3,2,5,1,4,6,7]=>101000 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[3,2,4,7,1,5,6]=>100100 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[3,2,4,6,1,5,7]=>100100 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[3,2,4,5,7,1,6]=>100010 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[2,7,3,4,6,1,5]=>010010 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[2,6,3,5,1,4,7]=>010100 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[2,5,3,4,7,1,6]=>010010 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[2,4,7,3,6,1,5]=>001010 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[7,2,6,3,5,1,4]=>101010 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[2,5,4,1,3,6,7]=>011000 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[2,4,3,7,1,5,6]=>010100 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[2,4,3,6,1,5,7]=>010100 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[2,4,3,5,7,1,6]=>010010 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[2,3,7,4,6,1,5]=>001010 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[2,3,6,5,1,4,7]=>001100 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[2,3,5,4,7,1,6]=>001010 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[2,3,4,7,6,1,5]=>000110 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[7,2,3,6,5,1,4]=>100110 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[6,2,5,4,1,3,7]=>101100 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[5,2,4,3,7,1,6]=>101010 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[4,2,3,7,6,1,5]=>100110 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[3,7,2,6,5,1,4]=>010110 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[7,6,2,5,4,1,3]=>110110 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>111000 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[4,3,2,7,1,5,6]=>110100 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[4,3,2,6,1,5,7]=>110100 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[4,3,2,5,7,1,6]=>110010 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[3,2,7,4,6,1,5]=>101010 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[3,2,6,5,1,4,7]=>101100 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[3,2,5,4,7,1,6]=>101010 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[3,2,4,7,6,1,5]=>100110 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[2,7,3,6,5,1,4]=>010110 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[2,6,5,4,1,3,7]=>011100 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[2,5,4,3,7,1,6]=>011010 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[2,4,3,7,6,1,5]=>010110 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[2,3,7,6,5,1,4]=>001110 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[7,2,6,5,4,1,3]=>101110 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>111100 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[5,4,3,2,7,1,6]=>111010 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[4,3,2,7,6,1,5]=>110110 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[3,2,7,6,5,1,4]=>101110 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[2,7,6,5,4,1,3]=>011110 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>111110 [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]=>100000 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[1,7,2,3,4,5,6]=>010000 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[1,6,2,3,4,5,7]=>010000 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[1,5,7,2,3,4,6]=>001000 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[7,1,6,2,3,4,5]=>101000 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[1,5,2,3,4,6,7]=>010000 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[1,4,7,2,3,5,6]=>001000 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[1,4,6,2,3,5,7]=>001000 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[1,4,5,7,2,3,6]=>000100 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[7,1,4,6,2,3,5]=>100100 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[6,1,5,2,3,4,7]=>101000 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[5,1,4,7,2,3,6]=>100100 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[4,7,1,6,2,3,5]=>010100 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[7,6,1,5,2,3,4]=>110100 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[1,4,2,3,5,6,7]=>010000 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[1,3,7,2,4,5,6]=>001000 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[1,3,6,2,4,5,7]=>001000 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[1,3,5,7,2,4,6]=>000100 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[7,1,3,6,2,4,5]=>100100 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[1,3,5,2,4,6,7]=>001000 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[1,3,4,7,2,5,6]=>000100 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[1,3,4,6,2,5,7]=>000100 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[1,3,4,5,7,2,6]=>000010 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[7,1,3,4,6,2,5]=>100010 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[6,1,3,5,2,4,7]=>100100 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[5,1,3,4,7,2,6]=>100010 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[4,7,1,3,6,2,5]=>010010 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[7,6,1,3,5,2,4]=>110010 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[5,1,4,2,3,6,7]=>101000 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[4,1,3,7,2,5,6]=>100100 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[4,1,3,6,2,5,7]=>100100 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[4,1,3,5,7,2,6]=>100010 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[3,7,1,4,6,2,5]=>010010 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[3,6,1,5,2,4,7]=>010100 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[3,5,1,4,7,2,6]=>010010 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[3,4,7,1,6,2,5]=>001010 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[7,3,6,1,5,2,4]=>101010 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[6,5,1,4,2,3,7]=>110100 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[5,4,1,3,7,2,6]=>110010 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[4,3,7,1,6,2,5]=>101010 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[3,7,6,1,5,2,4]=>011010 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[7,6,5,1,4,2,3]=>111010 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[1,2,7,3,4,5,6]=>001000 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[1,2,6,3,4,5,7]=>001000 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[1,2,5,7,3,4,6]=>000100 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[7,1,2,6,3,4,5]=>100100 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[1,2,5,3,4,6,7]=>001000 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[1,2,4,7,3,5,6]=>000100 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[1,2,4,6,3,5,7]=>000100 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[1,2,4,5,7,3,6]=>000010 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[7,1,2,4,6,3,5]=>100010 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[6,1,2,5,3,4,7]=>100100 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[5,1,2,4,7,3,6]=>100010 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[4,7,1,2,6,3,5]=>010010 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[7,6,1,2,5,3,4]=>110010 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[1,2,4,3,5,6,7]=>001000 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[1,2,3,7,4,5,6]=>000100 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[1,2,3,6,4,5,7]=>000100 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[1,2,3,5,7,4,6]=>000010 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[7,1,2,3,6,4,5]=>100010 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[1,2,3,5,4,6,7]=>000100 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[1,2,3,4,7,5,6]=>000010 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[1,2,3,4,6,5,7]=>000010 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,7,6]=>000001 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,1,2,3,4,6,5]=>100001 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,1,2,3,5,4,7]=>100010 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[5,1,2,3,4,7,6]=>100001 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[4,7,1,2,3,6,5]=>010001 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,6,1,2,3,5,4]=>110001 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,1,2,4,3,6,7]=>100100 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[4,1,2,3,7,5,6]=>100010 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[4,1,2,3,6,5,7]=>100010 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[4,1,2,3,5,7,6]=>100001 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[3,7,1,2,4,6,5]=>010001 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[3,6,1,2,5,4,7]=>010010 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[3,5,1,2,4,7,6]=>010001 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[3,4,7,1,2,6,5]=>001001 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,3,6,1,2,5,4]=>101001 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,5,1,2,4,3,7]=>110010 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[5,4,1,2,3,7,6]=>110001 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[4,3,7,1,2,6,5]=>101001 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[3,7,6,1,2,5,4]=>011001 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,6,5,1,2,4,3]=>111001 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>101000 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[3,1,2,7,4,5,6]=>100100 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[3,1,2,6,4,5,7]=>100100 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[3,1,2,5,7,4,6]=>100010 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[2,7,1,3,6,4,5]=>010010 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[3,1,2,5,4,6,7]=>100100 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[3,1,2,4,7,5,6]=>100010 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[3,1,2,4,6,5,7]=>100010 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[3,1,2,4,5,7,6]=>100001 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[2,7,1,3,4,6,5]=>010001 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[2,6,1,3,5,4,7]=>010010 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[2,5,1,3,4,7,6]=>010001 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[2,4,7,1,3,6,5]=>001001 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,2,6,1,3,5,4]=>101001 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[2,5,1,4,3,6,7]=>010100 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[2,4,1,3,7,5,6]=>010010 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[2,4,1,3,6,5,7]=>010010 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[2,4,1,3,5,7,6]=>010001 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[2,3,7,1,4,6,5]=>001001 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[2,3,6,1,5,4,7]=>001010 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[2,3,5,1,4,7,6]=>001001 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[2,3,4,7,1,6,5]=>000101 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,2,3,6,1,5,4]=>100101 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,2,5,1,4,3,7]=>101010 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[5,2,4,1,3,7,6]=>101001 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[4,2,3,7,1,6,5]=>100101 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[3,7,2,6,1,5,4]=>010101 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,6,2,5,1,4,3]=>110101 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,4,1,3,2,6,7]=>110100 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[4,3,1,2,7,5,6]=>110010 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[4,3,1,2,6,5,7]=>110010 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[4,3,1,2,5,7,6]=>110001 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[3,2,7,1,4,6,5]=>101001 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[3,2,6,1,5,4,7]=>101010 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[3,2,5,1,4,7,6]=>101001 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[3,2,4,7,1,6,5]=>100101 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[2,7,3,6,1,5,4]=>010101 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[2,6,5,1,4,3,7]=>011010 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[2,5,4,1,3,7,6]=>011001 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[2,4,3,7,1,6,5]=>010101 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[2,3,7,6,1,5,4]=>001101 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,2,6,5,1,4,3]=>101101 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,5,4,1,3,2,7]=>111010 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[5,4,3,1,2,7,6]=>111001 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[4,3,2,7,1,6,5]=>110101 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[3,2,7,6,1,5,4]=>101101 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[2,7,6,5,1,4,3]=>011101 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,6,5,4,1,3,2]=>111101 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[2,1,7,3,4,5,6]=>101000 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[2,1,6,3,4,5,7]=>101000 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[2,1,5,7,3,4,6]=>100100 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[1,7,2,6,3,4,5]=>010100 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[2,1,5,3,4,6,7]=>101000 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[2,1,4,7,3,5,6]=>100100 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[2,1,4,6,3,5,7]=>100100 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[2,1,4,5,7,3,6]=>100010 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[1,7,2,4,6,3,5]=>010010 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[1,6,2,5,3,4,7]=>010100 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[1,5,2,4,7,3,6]=>010010 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[1,4,7,2,6,3,5]=>001010 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[7,1,6,2,5,3,4]=>101010 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[2,1,4,3,5,6,7]=>101000 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[2,1,3,7,4,5,6]=>100100 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[2,1,3,6,4,5,7]=>100100 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[2,1,3,5,7,4,6]=>100010 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[1,7,2,3,6,4,5]=>010010 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[2,1,3,5,4,6,7]=>100100 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[2,1,3,4,7,5,6]=>100010 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[2,1,3,4,6,5,7]=>100010 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[2,1,3,4,5,7,6]=>100001 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[1,7,2,3,4,6,5]=>010001 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[1,6,2,3,5,4,7]=>010010 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[1,5,2,3,4,7,6]=>010001 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[1,4,7,2,3,6,5]=>001001 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,1,6,2,3,5,4]=>101001 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[1,5,2,4,3,6,7]=>010100 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[1,4,2,3,7,5,6]=>010010 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[1,4,2,3,6,5,7]=>010010 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[1,4,2,3,5,7,6]=>010001 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[1,3,7,2,4,6,5]=>001001 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[1,3,6,2,5,4,7]=>001010 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[1,3,5,2,4,7,6]=>001001 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[1,3,4,7,2,6,5]=>000101 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,1,3,6,2,5,4]=>100101 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,1,5,2,4,3,7]=>101010 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[5,1,4,2,3,7,6]=>101001 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[4,1,3,7,2,6,5]=>100101 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[3,7,1,6,2,5,4]=>010101 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,6,1,5,2,4,3]=>110101 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[1,4,3,2,5,6,7]=>011000 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[1,3,2,7,4,5,6]=>010100 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[1,3,2,6,4,5,7]=>010100 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[1,3,2,5,7,4,6]=>010010 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[1,2,7,3,6,4,5]=>001010 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[1,3,2,5,4,6,7]=>010100 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[1,3,2,4,7,5,6]=>010010 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[1,3,2,4,6,5,7]=>010010 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[1,3,2,4,5,7,6]=>010001 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[1,2,7,3,4,6,5]=>001001 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[1,2,6,3,5,4,7]=>001010 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[1,2,5,3,4,7,6]=>001001 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[1,2,4,7,3,6,5]=>000101 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,1,2,6,3,5,4]=>100101 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[1,2,5,4,3,6,7]=>001100 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[1,2,4,3,7,5,6]=>001010 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[1,2,4,3,6,5,7]=>001010 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[1,2,4,3,5,7,6]=>001001 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[1,2,3,7,4,6,5]=>000101 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[1,2,3,6,5,4,7]=>000110 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[1,2,3,5,4,7,6]=>000101 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,3,4,7,6,5]=>000011 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,1,2,3,6,5,4]=>100011 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,1,2,5,4,3,7]=>100110 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[5,1,2,4,3,7,6]=>100101 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[4,1,2,3,7,6,5]=>100011 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[3,7,1,2,6,5,4]=>010011 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,1,2,5,4,3]=>110011 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,1,4,3,2,6,7]=>101100 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[4,1,3,2,7,5,6]=>101010 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[4,1,3,2,6,5,7]=>101010 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[4,1,3,2,5,7,6]=>101001 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[3,1,2,7,4,6,5]=>100101 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[3,1,2,6,5,4,7]=>100110 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[3,1,2,5,4,7,6]=>100101 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[3,1,2,4,7,6,5]=>100011 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[2,7,1,3,6,5,4]=>010011 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[2,6,1,5,4,3,7]=>010110 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[2,5,1,4,3,7,6]=>010101 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[2,4,1,3,7,6,5]=>010011 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[2,3,7,1,6,5,4]=>001011 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,2,6,1,5,4,3]=>101011 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,1,4,3,2,7]=>110110 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[5,4,1,3,2,7,6]=>110101 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[4,3,1,2,7,6,5]=>110011 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[3,2,7,1,6,5,4]=>101011 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[2,7,6,1,5,4,3]=>011011 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,5,1,4,3,2]=>111011 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[3,2,1,7,4,5,6]=>110100 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[3,2,1,6,4,5,7]=>110100 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[3,2,1,5,7,4,6]=>110010 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[2,1,7,3,6,4,5]=>101010 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[3,2,1,5,4,6,7]=>110100 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[3,2,1,4,7,5,6]=>110010 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[3,2,1,4,6,5,7]=>110010 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[3,2,1,4,5,7,6]=>110001 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[2,1,7,3,4,6,5]=>101001 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[2,1,6,3,5,4,7]=>101010 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[2,1,5,3,4,7,6]=>101001 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[2,1,4,7,3,6,5]=>100101 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[1,7,2,6,3,5,4]=>010101 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[2,1,5,4,3,6,7]=>101100 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[2,1,4,3,7,5,6]=>101010 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[2,1,4,3,6,5,7]=>101010 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[2,1,4,3,5,7,6]=>101001 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[2,1,3,7,4,6,5]=>100101 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[2,1,3,6,5,4,7]=>100110 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[2,1,3,5,4,7,6]=>100101 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[2,1,3,4,7,6,5]=>100011 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[1,7,2,3,6,5,4]=>010011 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[1,6,2,5,4,3,7]=>010110 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[1,5,2,4,3,7,6]=>010101 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[1,4,2,3,7,6,5]=>010011 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[1,3,7,2,6,5,4]=>001011 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,1,6,2,5,4,3]=>101011 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[1,5,4,3,2,6,7]=>011100 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[1,4,3,2,7,5,6]=>011010 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[1,4,3,2,6,5,7]=>011010 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[1,4,3,2,5,7,6]=>011001 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[1,3,2,7,4,6,5]=>010101 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[1,3,2,6,5,4,7]=>010110 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[1,3,2,5,4,7,6]=>010101 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[1,3,2,4,7,6,5]=>010011 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[1,2,7,3,6,5,4]=>001011 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[1,2,6,5,4,3,7]=>001110 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[1,2,5,4,3,7,6]=>001101 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,4,3,7,6,5]=>001011 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>000111 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,1,2,6,5,4,3]=>100111 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,1,5,4,3,2,7]=>101110 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[5,1,4,3,2,7,6]=>101101 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[4,1,3,2,7,6,5]=>101011 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[3,1,2,7,6,5,4]=>100111 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[2,7,1,6,5,4,3]=>010111 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,1,5,4,3,2]=>110111 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>111100 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[4,3,2,1,7,5,6]=>111010 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[4,3,2,1,6,5,7]=>111010 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[4,3,2,1,5,7,6]=>111001 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[3,2,1,7,4,6,5]=>110101 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[3,2,1,6,5,4,7]=>110110 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[3,2,1,5,4,7,6]=>110101 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[3,2,1,4,7,6,5]=>110011 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[2,1,7,3,6,5,4]=>101011 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[2,1,6,5,4,3,7]=>101110 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[2,1,5,4,3,7,6]=>101101 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[2,1,4,3,7,6,5]=>101011 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[2,1,3,7,6,5,4]=>100111 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[1,7,2,6,5,4,3]=>010111 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[1,6,5,4,3,2,7]=>011110 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[1,5,4,3,2,7,6]=>011101 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,4,3,2,7,6,5]=>011011 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[1,3,2,7,6,5,4]=>010111 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,7,6,5,4,3]=>001111 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,1,6,5,4,3,2]=>101111 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[5,4,3,2,1,7,6]=>111101 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[4,3,2,1,7,6,5]=>111011 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[3,2,1,7,6,5,4]=>110111 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[2,1,7,6,5,4,3]=>101111 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[1,7,6,5,4,3,2]=>011111 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[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]=>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]=>[8,1,2,3,4,5,6,7]=>1000000 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[7,1,2,3,4,5,6,8]=>1000000 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[6,8,1,2,3,4,5,7]=>0100000 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]=>1100000 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[6,1,2,3,4,5,7,8]=>1000000 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[5,8,1,2,3,4,6,7]=>0100000 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[5,7,1,2,3,4,6,8]=>0100000 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[5,6,8,1,2,3,4,7]=>0010000 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>[8,5,7,1,2,3,4,6]=>1010000 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]=>1100000 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[6,5,8,1,2,3,4,7]=>1010000 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[5,8,7,1,2,3,4,6]=>0110000 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>1110000 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>1000000 [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[4,8,1,2,3,5,6,7]=>0100000 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[4,7,1,2,3,5,6,8]=>0100000 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[4,6,8,1,2,3,5,7]=>0010000 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[8,4,7,1,2,3,5,6]=>1010000 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[4,6,1,2,3,5,7,8]=>0100000 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[4,5,8,1,2,3,6,7]=>0010000 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[4,5,6,8,1,2,3,7]=>0001000 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>[7,4,6,1,2,3,5,8]=>1010000 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[6,4,5,8,1,2,3,7]=>1001000 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[5,8,4,7,1,2,3,6]=>0101000 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>1101000 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[5,4,8,1,2,3,6,7]=>1010000 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>[5,4,7,1,2,3,6,8]=>1010000 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[4,8,5,7,1,2,3,6]=>0101000 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,5,4,8]=>[4,7,6,1,2,3,5,8]=>0110000 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[4,5,8,7,1,2,3,6]=>0011000 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[8,4,7,6,1,2,3,5]=>1011000 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>1110000 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[6,5,4,8,1,2,3,7]=>1101000 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[5,4,8,7,1,2,3,6]=>1011000 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[4,8,7,6,1,2,3,5]=>0111000 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>1111000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>1000000 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[3,8,1,2,4,5,6,7]=>0100000 [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[3,7,1,2,4,5,6,8]=>0100000 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>[3,6,8,1,2,4,5,7]=>0010000 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,7,6]=>[8,3,7,1,2,4,5,6]=>1010000 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[3,6,1,2,4,5,7,8]=>0100000 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>[3,5,7,1,2,4,6,8]=>0010000 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[3,5,6,8,1,2,4,7]=>0001000 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>[8,3,5,7,1,2,4,6]=>1001000 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[6,3,5,8,1,2,4,7]=>1001000 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,6,5]=>[5,8,3,7,1,2,4,6]=>0101000 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[8,7,3,6,1,2,4,5]=>1101000 [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8]=>[3,5,1,2,4,6,7,8]=>0100000 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>[3,4,6,8,1,2,5,7]=>0001000 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,6,3,8,7]=>[3,4,5,8,1,2,6,7]=>0001000 [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,7,3,8]=>[3,4,5,7,1,2,6,8]=>0001000 [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[3,4,5,6,8,1,2,7]=>0000100 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,7,3]=>[8,3,4,5,7,1,2,6]=>1000100 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,7,6,3]=>[8,7,3,4,6,1,2,5]=>1100100 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,5,3,7,8]=>[6,3,5,1,2,4,7,8]=>1010000 [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,4,6,5,7,3,8]=>[5,3,4,7,1,2,6,8]=>1001000 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>[4,8,3,5,7,1,2,6]=>0100100 [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,4,6,7,5,3,8]=>[4,7,3,6,1,2,5,8]=>0101000 [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>[4,5,8,3,7,1,2,6]=>0010100 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,7,5,3]=>[8,4,7,3,6,1,2,5]=>1010100 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,6,8,5,3]=>[5,4,8,3,7,1,2,6]=>1010100 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>[4,8,7,3,6,1,2,5]=>0110100 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[8,7,6,3,5,1,2,4]=>1110100 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>1100000 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>[4,3,6,8,1,2,5,7]=>1001000 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,4,3,8,7,6]=>[3,8,4,7,1,2,5,6]=>0101000 [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>[4,3,5,7,1,2,6,8]=>1001000 [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>[3,8,4,5,7,1,2,6]=>0100100 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>[8,3,7,4,6,1,2,5]=>1010100 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,4,7,3,8]=>[3,5,4,7,1,2,6,8]=>0101000 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,4,7,8,3]=>[3,5,4,6,8,1,2,7]=>0100100 [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,5,6,7,4,3,8]=>[3,4,7,6,1,2,5,8]=>0011000 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[3,4,5,8,7,1,2,6]=>0001100 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,7,4,3]=>[8,3,4,7,6,1,2,5]=>1001100 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,6,4,8,3]=>[6,3,5,4,8,1,2,7]=>1010100 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,6,8,4,3]=>[5,3,4,8,7,1,2,6]=>1001100 [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,8,7,6,4,3]=>[8,7,3,6,5,1,2,4]=>1101100 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[6,5,4,1,2,3,7,8]=>1110000 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[5,4,3,6,8,1,2,7]=>1100100 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,5,7,8,4,3]=>[4,3,5,8,7,1,2,6]=>1001100 [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,6,7,5,4,3,8]=>[3,7,6,5,1,2,4,8]=>0111000 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[3,4,8,7,6,1,2,5]=>0011100 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[7,6,5,4,1,2,3,8]=>1111000 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,6,5,4,8,3]=>[6,5,4,3,8,1,2,7]=>1110100 [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,6,8,5,4,3]=>[4,3,8,7,6,1,2,5]=>1011100 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,6,5,4,3]=>[3,8,7,6,5,1,2,4]=>0111100 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]=>1111100 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>1000000 [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[2,8,1,3,4,5,6,7]=>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]=>[2,7,1,3,4,5,6,8]=>0100000 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[2,6,8,1,3,4,5,7]=>0010000 [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[2,6,1,3,4,5,7,8]=>0100000 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[2,5,8,1,3,4,6,7]=>0010000 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[2,5,6,8,1,3,4,7]=>0001000 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>[8,2,5,7,1,3,4,6]=>1001000 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[6,2,5,8,1,3,4,7]=>1001000 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[8,7,2,6,1,3,4,5]=>1101000 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>0100000 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[2,4,6,8,1,3,5,7]=>0001000 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[8,2,4,7,1,3,5,6]=>1001000 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>[2,4,6,1,3,5,7,8]=>0010000 [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2,5,6,4,8,7]=>[2,4,5,8,1,3,6,7]=>0001000 [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>[2,4,5,6,8,1,3,7]=>0000100 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>[7,2,4,6,1,3,5,8]=>1001000 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,6,8,4]=>[6,2,4,5,8,1,3,7]=>1000100 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>[5,8,2,4,7,1,3,6]=>0100100 [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,6,5,4,8,7]=>[5,2,4,8,1,3,6,7]=>1001000 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>[5,2,4,7,1,3,6,8]=>1001000 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>[5,2,4,6,8,1,3,7]=>1000100 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>[4,8,2,5,7,1,3,6]=>0100100 [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,6,8,7,5,4]=>[8,4,7,2,6,1,3,5]=>1010100 [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,6,5,8,4]=>[6,5,2,4,8,1,3,7]=>1100100 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,6,8,5,4]=>[5,4,8,2,7,1,3,6]=>1010100 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[8,7,6,2,5,1,3,4]=>1110100 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>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]=>[2,3,8,1,4,5,6,7]=>0010000 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>[2,3,7,1,4,5,6,8]=>0010000 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[2,3,6,8,1,4,5,7]=>0001000 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,7,6]=>[8,2,3,7,1,4,5,6]=>1001000 [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7]=>[2,3,5,8,1,4,6,7]=>0001000 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[2,3,5,7,1,4,6,8]=>0001000 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[2,3,5,6,8,1,4,7]=>0000100 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>[8,2,3,5,7,1,4,6]=>1000100 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[6,2,3,5,8,1,4,7]=>1000100 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[8,7,2,3,6,1,4,5]=>1100100 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>[2,3,5,1,4,6,7,8]=>0010000 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,5,2,6,8,7]=>[2,3,4,8,1,5,6,7]=>0001000 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,8]=>[2,3,4,7,1,5,6,8]=>0001000 [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>[2,3,4,6,8,1,5,7]=>0000100 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,5,2,8,7,6]=>[8,2,3,4,7,1,5,6]=>1000100 [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>[2,3,4,6,1,5,7,8]=>0001000 [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,2,8,7]=>[2,3,4,5,8,1,6,7]=>0000100 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[2,3,4,5,7,1,6,8]=>0000100 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[2,3,4,5,6,8,1,7]=>0000010 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[8,2,3,4,5,7,1,6]=>1000010 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,7,6,8,2]=>[6,2,3,4,5,8,1,7]=>1000010 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,6,2]=>[5,8,2,3,4,7,1,6]=>0100010 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,7,6,2]=>[8,7,2,3,4,6,1,5]=>1100010 [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,4,6,5,7,2,8]=>[5,2,3,4,7,1,6,8]=>1000100 [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,4,6,5,7,8,2]=>[5,2,3,4,6,8,1,7]=>1000010 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,5,8,2]=>[4,6,2,3,5,8,1,7]=>0100010 [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,5,2]=>[4,5,8,2,3,7,1,6]=>0010010 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>[6,5,2,3,4,8,1,7]=>1100010 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,4,2,6,7,8]=>[5,2,4,1,3,6,7,8]=>1010000 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>[4,2,3,8,1,5,6,7]=>1001000 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,4,2,7,8,6]=>[4,2,3,6,8,1,5,7]=>1000100 [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,5,4,6,7,8,2]=>[4,2,3,5,6,8,1,7]=>1000010 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,4,7,8,6,2]=>[3,5,8,2,4,7,1,6]=>0010010 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,4,8,7,6,2]=>[8,3,7,2,4,6,1,5]=>1010010 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>[3,6,2,5,1,4,7,8]=>0101000 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,4,7,2,8]=>[3,5,2,4,7,1,6,8]=>0100100 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,4,7,8,2]=>[3,5,2,4,6,8,1,7]=>0100010 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[3,4,5,8,2,7,1,6]=>0001010 [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,8,7,4,2]=>[8,3,4,7,2,6,1,5]=>1001010 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,6,4,2,8]=>[7,3,6,2,5,1,4,8]=>1010100 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,6,4,8,2]=>[6,3,5,2,4,8,1,7]=>1010010 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[4,8,3,7,2,6,1,5]=>0101010 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,7,6,4,2]=>[8,7,3,6,2,5,1,4]=>1101010 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>[4,3,8,2,5,7,1,6]=>1010010 [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,6,5,7,4,2,8]=>[4,3,7,2,6,1,5,8]=>1010100 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,5,4,2]=>[3,4,8,7,2,6,1,5]=>0011010 [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,6,8,7,5,4,2]=>[8,3,7,6,2,5,1,4]=>1011010 [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,7,8,6,5,4,2]=>[3,8,7,6,2,5,1,4]=>0111010 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>[8,7,6,5,2,4,1,3]=>1111010 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>1100000 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>[3,2,8,1,4,5,6,7]=>1010000 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,3,2,5,7,8,6]=>[3,2,6,8,1,4,5,7]=>1001000 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>[2,8,3,7,1,4,5,6]=>0101000 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>[3,2,5,7,1,4,6,8]=>1001000 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[3,2,5,6,8,1,4,7]=>1000100 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[2,7,3,6,1,4,5,8]=>0101000 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[8,2,7,3,6,1,4,5]=>1010100 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,3,5,2,6,7,8]=>[3,2,5,1,4,6,7,8]=>1010000 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3,5,2,7,8,6]=>[3,2,4,6,8,1,5,7]=>1000100 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3,5,2,8,7,6]=>[2,8,3,4,7,1,5,6]=>0100100 [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,3,5,6,2,7,8]=>[3,2,4,6,1,5,7,8]=>1001000 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>[3,2,4,5,6,8,1,7]=>1000010 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>[8,2,7,3,4,6,1,5]=>1010010 [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,3,6,5,7,8,2]=>[2,5,3,4,6,8,1,7]=>0100010 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[2,4,8,3,5,7,1,6]=>0010010 [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,3,6,7,5,8,2]=>[2,4,6,3,5,8,1,7]=>0010010 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,6,7,8,5,2]=>[2,4,5,8,3,7,1,6]=>0001010 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,6,8,7,5,2]=>[8,2,4,7,3,6,1,5]=>1001010 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>[4,8,2,7,3,6,1,5]=>0101010 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[8,7,2,6,3,5,1,4]=>1101010 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,3,2,6,7,8]=>[2,5,4,1,3,6,7,8]=>0110000 [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,5,3,2,6,8,7]=>[2,4,3,8,1,5,6,7]=>0101000 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,5,3,2,7,8,6]=>[2,4,3,6,8,1,5,7]=>0100100 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>[2,4,3,5,6,8,1,7]=>0100010 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,3,6,8,7,2]=>[2,3,8,4,5,7,1,6]=>0010010 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,3,8,7,6,2]=>[8,2,3,7,4,6,1,5]=>1001010 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,6,3,8,7,2]=>[2,3,4,8,5,7,1,6]=>0001010 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,3,2,8]=>[2,3,4,7,6,1,5,8]=>0001100 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,3,8,2]=>[2,3,4,6,5,8,1,7]=>0001010 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,3,2]=>[2,3,4,5,8,7,1,6]=>0000110 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,7,8,6,3,2]=>[4,8,2,3,7,6,1,5]=>0100110 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,5,3,8,7,2]=>[4,2,3,8,5,7,1,6]=>1001010 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,5,7,3,2,8]=>[4,2,3,7,6,1,5,8]=>1001100 [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,5,3,8,2]=>[3,6,2,5,4,8,1,7]=>0101010 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,5,8,3,2]=>[3,5,2,4,8,7,1,6]=>0100110 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,4,6,7,8,5,3,2]=>[3,4,8,2,7,6,1,5]=>0010110 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,7,5,3,2]=>[8,3,7,2,6,5,1,4]=>1010110 [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,4,7,8,6,5,3,2]=>[3,8,7,2,6,5,1,4]=>0110110 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[8,7,6,2,5,4,1,3]=>1110110 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>[5,4,3,1,2,6,7,8]=>1110000 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>[4,3,2,7,1,5,6,8]=>1101000 [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>[4,3,2,6,1,5,7,8]=>1101000 [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,5,4,3,6,7,2,8]=>[4,3,2,5,7,1,6,8]=>1100100 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[4,3,2,5,6,8,1,7]=>1100010 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>[3,2,8,4,5,7,1,6]=>1010010 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,4,3,8,7,6,2]=>[2,8,3,7,4,6,1,5]=>0101010 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>[3,2,5,4,7,1,6,8]=>1010100 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,4,6,7,3,2,8]=>[3,2,4,7,6,1,5,8]=>1001100 [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,3,2]=>[3,2,4,5,8,7,1,6]=>1000110 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,4,6,8,7,3,2]=>[2,8,3,4,7,6,1,5]=>0100110 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,4,7,8,6,3,2]=>[2,4,8,3,7,6,1,5]=>0010110 [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,6,4,3,2,7,8]=>[2,6,5,4,1,3,7,8]=>0111000 [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,6,4,3,2,8,7]=>[2,5,4,3,8,1,6,7]=>0110100 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,4,3,8,7,2]=>[2,4,3,8,5,7,1,6]=>0101010 [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,4,7,3,8,2]=>[2,4,3,6,5,8,1,7]=>0101010 [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,5,6,7,4,3,2,8]=>[2,3,7,6,5,1,4,8]=>0011100 [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,4,3,8,2]=>[2,3,6,5,4,8,1,7]=>0011010 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[2,3,4,8,7,6,1,5]=>0001110 [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>[8,7,2,6,5,4,1,3]=>1101110 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,5,4,3,2,7,8]=>[6,5,4,3,1,2,7,8]=>1111000 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,5,4,3,2,8,7]=>[5,4,3,2,8,1,6,7]=>1110100 [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,5,4,3,7,8,2]=>[5,4,3,2,6,8,1,7]=>1110010 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[4,3,2,8,5,7,1,6]=>1101010 [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,6,5,4,8,7,3,2]=>[3,2,8,4,7,6,1,5]=>1010110 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,5,7,4,3,2,8]=>[3,2,7,6,5,1,4,8]=>1011100 [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,4,3,2]=>[3,2,4,8,7,6,1,5]=>1001110 [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,5,4,3,2,8]=>[2,7,6,5,4,1,3,8]=>0111100 [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,5,4,3,8,2]=>[2,6,5,4,3,8,1,7]=>0111010 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[2,3,8,7,6,5,1,4]=>0011110 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>[8,2,7,6,5,4,1,3]=>1011110 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>[7,6,5,4,3,1,2,8]=>1111100 [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,6,5,4,3,8,2]=>[6,5,4,3,2,8,1,7]=>1111010 [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,6,5,4,8,3,2]=>[5,4,3,2,8,7,1,6]=>1110110 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[4,3,2,8,7,6,1,5]=>1101110 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>[3,2,8,7,6,5,1,4]=>1011110 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>[2,8,7,6,5,4,1,3]=>0111110 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]=>1111110 [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]=>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]=>[1,8,2,3,4,5,6,7]=>0100000 [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[1,7,2,3,4,5,6,8]=>0100000 [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>[1,6,8,2,3,4,5,7]=>0010000 [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,7,6]=>[8,1,7,2,3,4,5,6]=>1010000 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[1,6,2,3,4,5,7,8]=>0100000 [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[1,5,8,2,3,4,6,7]=>0010000 [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,4,6,7,5,8]=>[1,5,7,2,3,4,6,8]=>0010000 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[1,5,6,8,2,3,4,7]=>0001000 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[6,1,5,8,2,3,4,7]=>1001000 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[8,7,1,6,2,3,4,5]=>1101000 [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>0100000 [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[1,4,8,2,3,5,6,7]=>0010000 [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,5,4,7,8,6]=>[1,4,6,8,2,3,5,7]=>0001000 [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[8,1,4,7,2,3,5,6]=>1001000 [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,5,6,4,8,7]=>[1,4,5,8,2,3,6,7]=>0001000 [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>[1,4,5,6,8,2,3,7]=>0000100 [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,6,5,8,7,4]=>[4,8,1,5,7,2,3,6]=>0100100 [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,5,4]=>[4,5,8,1,7,2,3,6]=>0010100 [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,6,8,7,5,4]=>[8,4,7,1,6,2,3,5]=>1010100 [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,6,5,4]=>[4,8,7,1,6,2,3,5]=>0110100 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[8,7,6,1,5,2,3,4]=>1110100 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0100000 [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[1,3,8,2,4,5,6,7]=>0010000 [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,7,6]=>[8,1,3,7,2,4,5,6]=>1001000 [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[1,3,6,2,4,5,7,8]=>0010000 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[1,3,5,8,2,4,6,7]=>0001000 [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,3,6,7,5,8]=>[1,3,5,7,2,4,6,8]=>0001000 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[1,3,5,6,8,2,4,7]=>0000100 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[8,1,3,5,7,2,4,6]=>1000100 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[6,1,3,5,8,2,4,7]=>1000100 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[5,8,1,3,7,2,4,6]=>0100100 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[8,7,1,3,6,2,4,5]=>1100100 [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>[1,3,5,2,4,6,7,8]=>0010000 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[1,3,4,8,2,5,6,7]=>0001000 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[1,3,4,5,8,2,6,7]=>0000100 [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,7,3,8]=>[1,3,4,5,7,2,6,8]=>0000100 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[1,3,4,5,6,8,2,7]=>0000010 [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>[5,8,1,3,4,7,2,6]=>0100010 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[8,7,1,3,4,6,2,5]=>1100010 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[5,1,3,4,8,2,6,7]=>1000100 [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,5,8,3]=>[4,6,1,3,5,8,2,7]=>0100010 [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,6,7,8,5,3]=>[4,5,8,1,3,7,2,6]=>0010010 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>[8,4,7,1,3,6,2,5]=>1010010 [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>[6,5,1,3,4,8,2,7]=>1100010 [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,7,6,8,5,3]=>[5,4,8,1,3,7,2,6]=>1010010 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[8,7,6,1,3,5,2,4]=>1110010 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,4,3,6,7,8]=>[5,1,4,2,3,6,7,8]=>1010000 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[4,1,3,8,2,5,6,7]=>1001000 [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,5,4,3,8,7,6]=>[3,8,1,4,7,2,5,6]=>0100100 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[4,1,3,5,8,2,6,7]=>1000100 [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,4,6,8,7,3]=>[3,8,1,4,5,7,2,6]=>0100010 [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[3,6,1,4,5,8,2,7]=>0100010 [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,4,8,7,6,3]=>[8,3,7,1,4,6,2,5]=>1010010 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[3,5,1,4,8,2,6,7]=>0100100 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,4,7,8,3]=>[3,5,1,4,6,8,2,7]=>0100010 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,4,3,8]=>[3,4,7,1,6,2,5,8]=>0010100 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,4,8,3]=>[3,4,6,1,5,8,2,7]=>0010010 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[3,4,5,8,1,7,2,6]=>0001010 [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,5,6,8,7,4,3]=>[8,3,4,7,1,6,2,5]=>1001010 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,6,4,8,3]=>[6,3,5,1,4,8,2,7]=>1010010 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,6,8,4,3]=>[5,3,4,8,1,7,2,6]=>1001010 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>[4,8,3,7,1,6,2,5]=>0101010 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,5,8,7,6,4,3]=>[8,7,3,6,1,5,2,4]=>1101010 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[5,4,1,3,8,2,6,7]=>1100100 [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,5,4,8,7,3]=>[4,3,8,1,5,7,2,6]=>1010010 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[4,3,6,1,5,8,2,7]=>1010010 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>[4,3,5,8,1,7,2,6]=>1001010 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>[3,8,4,7,1,6,2,5]=>0101010 [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,6,7,5,4,3,8]=>[3,7,6,1,5,2,4,8]=>0110100 [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,5,4,8,3]=>[3,6,5,1,4,8,2,7]=>0110010 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[3,5,4,8,1,7,2,6]=>0101010 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[3,4,8,7,1,6,2,5]=>0011010 [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>[7,6,5,1,4,2,3,8]=>1110100 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,6,5,4,8,3]=>[6,5,4,1,3,8,2,7]=>1110010 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[5,4,3,8,1,7,2,6]=>1101010 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>[4,3,8,7,1,6,2,5]=>1011010 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,1,4,2,3]=>1111010 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000 [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,8,7]=>[1,2,8,3,4,5,6,7]=>0010000 [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,5,7,6,8]=>[1,2,7,3,4,5,6,8]=>0010000 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[1,2,6,8,3,4,5,7]=>0001000 [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,4,6,5,8,7]=>[1,2,5,8,3,4,6,7]=>0001000 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[1,2,5,7,3,4,6,8]=>0001000 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[6,1,2,5,8,3,4,7]=>1000100 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[8,7,1,2,6,3,4,5]=>1100100 [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8]=>[1,2,5,3,4,6,7,8]=>0010000 [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[1,2,4,7,3,5,6,8]=>0001000 [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,5,6,4,7,8]=>[1,2,4,6,3,5,7,8]=>0001000 [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[1,2,4,5,7,3,6,8]=>0000100 [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[1,2,4,5,6,8,3,7]=>0000010 [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,7,8,6,4]=>[5,8,1,2,4,7,3,6]=>0100010 [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,5,4,7,8]=>[6,1,2,5,3,4,7,8]=>1001000 [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>[5,1,2,4,8,3,6,7]=>1000100 [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>[4,8,1,2,5,7,3,6]=>0100010 [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,5,8,4]=>[4,6,1,2,5,8,3,7]=>0100010 [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,5,4]=>[4,5,8,1,2,7,3,6]=>0010010 [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,6,5,8,4]=>[6,5,1,2,4,8,3,7]=>1100010 [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,6,8,5,4]=>[5,4,8,1,2,7,3,6]=>1010010 [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[8,7,6,1,2,5,3,4]=>1110010 [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000 [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[1,2,3,8,4,5,6,7]=>0001000 [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[1,2,3,7,4,5,6,8]=>0001000 [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[1,2,3,6,8,4,5,7]=>0000100 [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[8,1,2,3,7,4,5,6]=>1000100 [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[1,2,3,6,4,5,7,8]=>0001000 [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[1,2,3,5,8,4,6,7]=>0000100 [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[1,2,3,5,7,4,6,8]=>0000100 [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[1,2,3,5,6,8,4,7]=>0000010 [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[8,1,2,3,5,7,4,6]=>1000010 [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[7,1,2,3,6,4,5,8]=>1000100 [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[6,1,2,3,5,8,4,7]=>1000010 [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[5,8,1,2,3,7,4,6]=>0100010 [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[8,7,1,2,3,6,4,5]=>1100010 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000 [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,8,7]=>[1,2,3,4,8,5,6,7]=>0000100 [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,8]=>[1,2,3,4,7,5,6,8]=>0000100 [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>[1,2,3,4,6,8,5,7]=>0000010 [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[8,1,2,3,4,7,5,6]=>1000010 [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[1,2,3,4,6,5,7,8]=>0000100 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[1,2,3,4,5,8,6,7]=>0000010 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[1,2,3,4,5,7,6,8]=>0000010 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,8,7]=>0000001 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[8,1,2,3,4,5,7,6]=>1000001 [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,6,1,8]=>[7,1,2,3,4,6,5,8]=>1000010 [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>[6,1,2,3,4,5,8,7]=>1000001 [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]=>[5,8,1,2,3,4,7,6]=>0100001 [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[8,7,1,2,3,4,6,5]=>1100001 [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,6,5,1,7,8]=>[6,1,2,3,5,4,7,8]=>1000100 [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>[5,1,2,3,4,6,8,7]=>1000001 [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>[4,8,1,2,3,5,7,6]=>0100001 [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,5,8,1]=>[4,6,1,2,3,5,8,7]=>0100001 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>[4,5,8,1,2,3,7,6]=>0010001 [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,8,7,5,1]=>[8,4,7,1,2,3,6,5]=>1010001 [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>[7,6,1,2,3,5,4,8]=>1100010 [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[6,5,1,2,3,4,8,7]=>1100001 [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,6,8,5,1]=>[5,4,8,1,2,3,7,6]=>1010001 [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,6,5,1]=>[4,8,7,1,2,3,6,5]=>0110001 [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[8,7,6,1,2,3,5,4]=>1110001 [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>1001000 [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,4,1,7,6,8]=>[4,1,2,3,7,5,6,8]=>1000100 [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,5,4,6,1,7,8]=>[4,1,2,3,6,5,7,8]=>1000100 [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,5,4,6,7,1,8]=>[4,1,2,3,5,7,6,8]=>1000010 [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[4,1,2,3,5,6,8,7]=>1000001 [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[3,6,1,2,4,5,8,7]=>0100001 [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,4,7,8,6,1]=>[3,5,8,1,2,4,7,6]=>0010001 [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>[8,3,7,1,2,4,6,5]=>1010001 [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,4,1,8,7]=>[3,5,1,2,4,8,6,7]=>0100010 [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,4,7,1,8]=>[3,5,1,2,4,7,6,8]=>0100010 [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>[3,5,1,2,4,6,8,7]=>0100001 [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,6,4,8,7,1]=>[3,4,8,1,2,5,7,6]=>0010001 [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,4,8,1]=>[3,4,6,1,2,5,8,7]=>0010001 [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[3,4,5,8,1,2,7,6]=>0001001 [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[8,3,4,7,1,2,6,5]=>1001001 [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,5,7,6,4,1,8]=>[7,3,6,1,2,5,4,8]=>1010010 [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,5,7,6,4,8,1]=>[6,3,5,1,2,4,8,7]=>1010001 [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,6,8,4,1]=>[5,3,4,8,1,2,7,6]=>1001001 [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>[4,8,3,7,1,2,6,5]=>0101001 [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,7,6,4,1]=>[8,7,3,6,1,2,5,4]=>1101001 [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[5,4,1,2,3,8,6,7]=>1100010 [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,5,4,1]=>[3,4,8,7,1,2,6,5]=>0011001 [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>[7,6,5,1,2,4,3,8]=>1110010 [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[6,5,4,1,2,3,8,7]=>1110001 [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,6,5,8,4,1]=>[5,4,3,8,1,2,7,6]=>1101001 [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[8,7,6,5,1,2,4,3]=>1111001 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>1010000 [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,4,3,1,5,8,7,6]=>[2,8,1,3,7,4,5,6]=>0100100 [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[3,1,2,5,8,4,6,7]=>1000100 [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[3,1,2,5,6,8,4,7]=>1000010 [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[2,8,1,3,5,7,4,6]=>0100010 [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[2,6,1,3,5,8,4,7]=>0100010 [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[8,2,7,1,3,6,4,5]=>1010010 [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,4,3,5,1,6,8,7]=>[3,1,2,4,8,5,6,7]=>1000100 [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>[3,1,2,4,7,5,6,8]=>1000100 [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,3,5,1,7,8,6]=>[3,1,2,4,6,8,5,7]=>1000010 [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>[2,8,1,3,4,7,5,6]=>0100010 [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,7,1,8]=>[3,1,2,4,5,7,6,8]=>1000010 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>[3,1,2,4,5,6,8,7]=>1000001 [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[2,8,1,3,4,5,7,6]=>0100001 [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>[2,6,1,3,4,5,8,7]=>0100001 [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,3,5,8,7,6,1]=>[8,2,7,1,3,4,6,5]=>1010001 [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,6,5,1,7,8]=>[2,6,1,3,5,4,7,8]=>0100100 [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[2,4,8,1,3,5,7,6]=>0010001 [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,3,6,7,5,8,1]=>[2,4,6,1,3,5,8,7]=>0010001 [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,3,6,7,8,5,1]=>[2,4,5,8,1,3,7,6]=>0001001 [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]=>[8,2,4,7,1,3,6,5]=>1001001 [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[6,2,5,1,3,4,8,7]=>1010001 [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,3,1,6,8,7]=>[2,4,1,3,8,5,6,7]=>0100100 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,3,1,7,8,6]=>[2,4,1,3,6,8,5,7]=>0100010 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[2,3,8,1,4,7,5,6]=>0010010 [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,3,6,8,7,1]=>[2,3,8,1,4,5,7,6]=>0010001 [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,7,8,6,1]=>[2,3,5,8,1,4,7,6]=>0001001 [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,3,1,7,8]=>[2,3,6,1,5,4,7,8]=>0010100 [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,6,3,7,1,8]=>[2,3,5,1,4,7,6,8]=>0010010 [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,3,8,7,1]=>[2,3,4,8,1,5,7,6]=>0001001 [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,3,1,8]=>[2,3,4,7,1,6,5,8]=>0001010 [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]=>[2,3,4,5,8,1,7,6]=>0000101 [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,6,3,1]=>[4,8,2,3,7,1,6,5]=>0100101 [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>[4,2,3,6,1,5,8,7]=>1001001 [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,5,7,8,3,1]=>[4,2,3,5,8,1,7,6]=>1000101 [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]=>[3,8,2,4,7,1,6,5]=>0100101 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,5,3,1,8]=>[3,7,2,6,1,5,4,8]=>0101010 [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,5,3,8,1]=>[3,6,2,5,1,4,8,7]=>0101001 [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,5,8,3,1]=>[3,5,2,4,8,1,7,6]=>0100101 [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]=>[3,4,8,2,7,1,6,5]=>0010101 [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>[8,3,7,2,6,1,5,4]=>1010101 [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,6,5,8,3,1]=>[5,4,2,3,8,1,7,6]=>1100101 [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>[3,8,7,2,6,1,5,4]=>0110101 [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[8,7,6,2,5,1,4,3]=>1110101 [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>1101000 [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,4,3,1,6,8,7]=>[4,3,1,2,8,5,6,7]=>1100100 [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>[4,3,1,2,6,8,5,7]=>1100010 [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>[4,3,1,2,5,7,6,8]=>1100010 [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[4,3,1,2,5,6,8,7]=>1100001 [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[3,2,8,1,4,5,7,6]=>1010001 [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>[3,2,6,1,4,5,8,7]=>1010001 [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[2,8,3,7,1,4,6,5]=>0101001 [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,4,6,3,7,1,8]=>[3,2,5,1,4,7,6,8]=>1010010 [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]=>[3,2,5,1,4,6,8,7]=>1010001 [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>[3,2,4,6,1,5,8,7]=>1001001 [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,3,1]=>[3,2,4,5,8,1,7,6]=>1000101 [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,4,7,6,8,3,1]=>[2,5,3,4,8,1,7,6]=>0100101 [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]=>[2,4,8,3,7,1,6,5]=>0010101 [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,4,8,7,6,3,1]=>[8,2,7,3,6,1,5,4]=>1010101 [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,5,6,4,3,1,8,7]=>[2,5,4,1,3,8,6,7]=>0110010 [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,5,6,4,7,3,1,8]=>[2,4,3,7,1,6,5,8]=>0101010 [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,4,8,7,3,1]=>[2,3,8,4,7,1,6,5]=>0010101 [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,4,3,8,1]=>[2,3,6,5,1,4,8,7]=>0011001 [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[2,3,4,8,7,1,6,5]=>0001101 [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,5,8,7,6,4,3,1]=>[8,7,2,6,5,1,4,3]=>1101101 [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,5,4,3,1,8,7]=>[5,4,3,1,2,8,6,7]=>1110010 [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]=>[4,3,2,5,8,1,7,6]=>1100101 [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,5,7,4,3,8,1]=>[3,2,6,5,1,4,8,7]=>1011001 [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,6,5,7,8,4,3,1]=>[3,2,4,8,7,1,6,5]=>1001101 [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,6,7,5,4,3,1,8]=>[2,7,6,5,1,4,3,8]=>0111010 [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,5,8,4,3,1]=>[2,4,3,8,7,1,6,5]=>0101101 [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[8,2,7,6,5,1,4,3]=>1011101 [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,6,5,4,3,1,8]=>[7,6,5,4,1,3,2,8]=>1111010 [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]=>[6,5,4,3,1,2,8,7]=>1111001 [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[5,4,3,2,8,1,7,6]=>1110101 [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,6,8,5,4,3,1]=>[3,2,8,7,6,1,5,4]=>1011101 [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[2,8,7,6,5,1,4,3]=>0111101 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[8,7,6,5,4,1,3,2]=>1111101 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000 [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[2,1,8,3,4,5,6,7]=>1010000 [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,5,7,6,8]=>[2,1,7,3,4,5,6,8]=>1010000 [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>[2,1,6,8,3,4,5,7]=>1001000 [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[1,8,2,7,3,4,5,6]=>0101000 [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[2,1,5,6,8,3,4,7]=>1000100 [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>[1,8,2,5,7,3,4,6]=>0100100 [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[1,7,2,6,3,4,5,8]=>0101000 [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[1,6,2,5,8,3,4,7]=>0100100 [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>[1,5,8,2,7,3,4,6]=>0010100 [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[8,1,7,2,6,3,4,5]=>1010100 [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8]=>[2,1,5,3,4,6,7,8]=>1010000 [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>[2,1,4,6,3,5,7,8]=>1001000 [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[2,1,4,5,6,8,3,7]=>1000010 [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>[1,7,2,4,6,3,5,8]=>0100100 [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[1,6,2,4,5,8,3,7]=>0100010 [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[1,5,8,2,4,7,3,6]=>0010010 [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[8,1,7,2,4,6,3,5]=>1010010 [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,2,1,6,5,4,7,8]=>[1,6,2,5,3,4,7,8]=>0101000 [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7]=>[1,5,2,4,8,3,6,7]=>0100100 [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[1,5,2,4,6,8,3,7]=>0100010 [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[1,4,8,2,5,7,3,6]=>0010010 [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,2,1,6,7,5,4,8]=>[1,4,7,2,6,3,5,8]=>0010100 [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[1,4,6,2,5,8,3,7]=>0010010 [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[8,1,4,7,2,6,3,5]=>1001010 [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>[7,1,6,2,5,3,4,8]=>1010100 [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[6,1,5,2,4,8,3,7]=>1010010 [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[5,1,4,8,2,7,3,6]=>1001010 [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[4,8,1,7,2,6,3,5]=>0101010 [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[8,7,1,6,2,5,3,4]=>1101010 [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>1010000 [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[2,1,3,8,4,5,6,7]=>1001000 [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>[2,1,3,6,4,5,7,8]=>1001000 [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[2,1,3,5,8,4,6,7]=>1000100 [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[1,8,2,3,5,7,4,6]=>0100010 [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>[1,7,2,3,6,4,5,8]=>0100100 [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[1,6,2,3,5,8,4,7]=>0100010 [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[1,5,8,2,3,7,4,6]=>0010010 [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[8,1,7,2,3,6,4,5]=>1010010 [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>[1,8,2,3,4,7,5,6]=>0100010 [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,6,1,7,8]=>[2,1,3,4,6,5,7,8]=>1000100 [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,1,8]=>[2,1,3,4,5,7,6,8]=>1000010 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[2,1,3,4,5,6,8,7]=>1000001 [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,8,7,1]=>[1,8,2,3,4,5,7,6]=>0100001 [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>[1,6,2,3,4,5,8,7]=>0100001 [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,7,8,6,1]=>[1,5,8,2,3,4,7,6]=>0010001 [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,2,4,6,5,8,7,1]=>[1,4,8,2,3,5,7,6]=>0010001 [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,2,4,6,7,5,1,8]=>[1,4,7,2,3,6,5,8]=>0010010 [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[6,1,5,2,3,4,8,7]=>1010001 [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[8,7,1,6,2,3,5,4]=>1101001 [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[1,5,2,4,3,6,7,8]=>0101000 [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>[1,4,2,3,8,5,6,7]=>0100100 [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>[1,4,2,3,7,5,6,8]=>0100100 [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[1,3,8,2,4,7,5,6]=>0010010 [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>[1,4,2,3,5,8,6,7]=>0100010 [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,1]=>[1,4,2,3,5,6,8,7]=>0100001 [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,5,4,6,8,7,1]=>[1,3,8,2,4,5,7,6]=>0010001 [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[1,3,7,2,4,6,5,8]=>0010010 [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[1,3,6,2,4,5,8,7]=>0010001 [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,4,7,8,6,1]=>[1,3,5,8,2,4,7,6]=>0001001 [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,5,6,4,1,8,7]=>[1,3,5,2,4,8,6,7]=>0010010 [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,5,6,4,7,8,1]=>[1,3,5,2,4,6,8,7]=>0010001 [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,5,6,7,4,8,1]=>[1,3,4,6,2,5,8,7]=>0001001 [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>[1,3,4,5,8,2,7,6]=>0000101 [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,5,7,6,4,1,8]=>[7,1,3,6,2,5,4,8]=>1001010 [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,5,7,6,8,4,1]=>[5,1,3,4,8,2,7,6]=>1000101 [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,5,7,8,6,4,1]=>[4,8,1,3,7,2,6,5]=>0100101 [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,2,6,5,4,1,8,7]=>[5,1,4,2,3,8,6,7]=>1010010 [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[4,1,3,6,2,5,8,7]=>1001001 [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[3,7,1,6,2,5,4,8]=>0101010 [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>[3,6,1,5,2,4,8,7]=>0101001 [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,2,6,7,5,8,4,1]=>[3,5,1,4,8,2,7,6]=>0100101 [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]=>[8,3,7,1,6,2,5,4]=>1010101 [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[7,6,1,5,2,4,3,8]=>1101010 [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,2,7,6,5,4,8,1]=>[6,5,1,4,2,3,8,7]=>1101001 [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]=>[3,8,7,1,6,2,5,4]=>0110101 [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[8,7,6,1,5,2,4,3]=>1110101 [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000 [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,4,2,1,5,6,8,7]=>[1,3,2,8,4,5,6,7]=>0101000 [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,2,1,5,8,7,6]=>[1,2,8,3,7,4,5,6]=>0010100 [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[1,3,2,5,8,4,6,7]=>0100100 [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>[1,2,8,3,5,7,4,6]=>0010010 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[1,2,5,8,3,7,4,6]=>0001010 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[8,1,2,7,3,6,4,5]=>1001010 [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8]=>[1,3,2,5,4,6,7,8]=>0101000 [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,2,5,1,7,8,6]=>[1,3,2,4,6,8,5,7]=>0100010 [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,2,5,6,1,7,8]=>[1,3,2,4,6,5,7,8]=>0100100 [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,2,5,6,1,8,7]=>[1,3,2,4,5,8,6,7]=>0100010 [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,7,1,8]=>[1,3,2,4,5,7,6,8]=>0100010 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[1,3,2,4,5,6,8,7]=>0100001 [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,8,7,1]=>[1,2,8,3,4,5,7,6]=>0010001 [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,4,2,5,7,6,1,8]=>[1,2,7,3,4,6,5,8]=>0010010 [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,2,5,7,6,8,1]=>[1,2,6,3,4,5,8,7]=>0010001 [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[1,2,5,8,3,4,7,6]=>0001001 [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,2,5,8,7,6,1]=>[8,1,2,7,3,4,6,5]=>1001001 [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,4,2,6,5,1,8,7]=>[1,2,5,3,4,8,6,7]=>0010010 [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,2,6,5,7,1,8]=>[1,2,5,3,4,7,6,8]=>0010010 [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,1]=>[1,2,5,3,4,6,8,7]=>0010001 [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,8,7,1]=>[1,2,4,8,3,5,7,6]=>0001001 [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[1,2,4,6,3,5,8,7]=>0001001 [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,4,2,7,6,5,1,8]=>[7,1,2,6,3,5,4,8]=>1001010 [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8]=>[1,2,5,4,3,6,7,8]=>0011000 [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,5,2,1,6,8,7]=>[1,2,4,3,8,5,6,7]=>0010100 [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,5,2,1,7,6,8]=>[1,2,4,3,7,5,6,8]=>0010100 [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,5,2,1,7,8,6]=>[1,2,4,3,6,8,5,7]=>0010010 [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[1,2,3,8,4,7,5,6]=>0001010 [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,2,6,1,7,8]=>[1,2,4,3,6,5,7,8]=>0010100 [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,2,6,1,8,7]=>[1,2,4,3,5,8,6,7]=>0010010 [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,5,2,6,7,1,8]=>[1,2,4,3,5,7,6,8]=>0010010 [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[1,2,4,3,5,6,8,7]=>0010001 [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,5,2,7,6,1,8]=>[1,2,3,7,4,6,5,8]=>0001010 [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]=>[1,2,3,6,4,5,8,7]=>0001001 [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,2,7,8,6,1]=>[1,2,3,5,8,4,7,6]=>0000101 [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,2,1,7,8]=>[1,2,3,6,5,4,7,8]=>0001100 [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,2,1,8,7]=>[1,2,3,5,4,8,6,7]=>0001010 [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>[1,2,3,5,4,7,6,8]=>0001010 [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>[1,2,3,5,4,6,8,7]=>0001001 [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,2,8,7,1]=>[1,2,3,4,8,5,7,6]=>0000101 [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,2,1,8]=>[1,2,3,4,7,6,5,8]=>0000110 [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]=>[1,2,3,4,6,5,8,7]=>0000101 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]=>[1,2,3,4,5,8,7,6]=>0000011 [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,7,2,1]=>[8,1,2,3,4,7,6,5]=>1000011 [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]=>[5,1,2,3,4,8,7,6]=>1000011 [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>[4,8,1,2,3,7,6,5]=>0100011 [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[8,7,1,2,3,6,5,4]=>1100011 [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,5,2,7,1,8]=>[5,1,2,4,3,7,6,8]=>1001010 [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,5,2,7,8,1]=>[5,1,2,4,3,6,8,7]=>1001001 [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]=>[4,1,2,3,6,5,8,7]=>1000101 [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,2,1]=>[4,1,2,3,5,8,7,6]=>1000011 [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,5,8,2,1]=>[3,5,1,2,4,8,7,6]=>0100011 [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]=>[3,4,8,1,2,7,6,5]=>0010011 [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>1100110 [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,6,5,2,8,1]=>[6,5,1,2,4,3,8,7]=>1100101 [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,6,5,8,2,1]=>[5,4,1,2,3,8,7,6]=>1100011 [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[8,7,6,1,2,5,4,3]=>1110011 [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>1011000 [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,4,2,1,6,8,7]=>[4,1,3,2,8,5,6,7]=>1010100 [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[3,1,2,8,4,7,5,6]=>1001010 [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>[4,1,3,2,5,7,6,8]=>1010010 [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,5,4,2,7,6,8,1]=>[3,1,2,6,4,5,8,7]=>1001001 [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,4,6,2,7,1,8]=>[3,1,2,5,4,7,6,8]=>1001010 [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,4,6,2,7,8,1]=>[3,1,2,5,4,6,8,7]=>1001001 [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,5,4,6,2,8,7,1]=>[3,1,2,4,8,5,7,6]=>1000101 [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,4,6,7,2,8,1]=>[3,1,2,4,6,5,8,7]=>1000101 [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,5,4,7,6,2,1,8]=>[2,7,1,3,6,5,4,8]=>0100110 [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,2,8,1]=>[2,6,1,3,5,4,8,7]=>0100101 [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,4,7,8,6,2,1]=>[2,4,8,1,3,7,6,5]=>0010011 [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,4,2,1,8,7]=>[2,5,1,4,3,8,6,7]=>0101010 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,4,2,7,1,8]=>[2,5,1,4,3,7,6,8]=>0101010 [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,4,2,8,7,1]=>[2,4,1,3,8,5,7,6]=>0100101 [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>[2,4,1,3,6,5,8,7]=>0100101 [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,4,7,8,2,1]=>[2,4,1,3,5,8,7,6]=>0100011 [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,5,6,7,4,2,1,8]=>[2,3,7,1,6,5,4,8]=>0010110 [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>[2,3,6,1,5,4,8,7]=>0010101 [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,4,8,2,1]=>[2,3,5,1,4,8,7,6]=>0010011 [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[2,3,4,8,1,7,6,5]=>0001011 [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]=>[8,2,3,7,1,6,5,4]=>1001011 [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>[7,2,6,1,5,4,3,8]=>1010110 [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]=>[6,2,5,1,4,3,8,7]=>1010101 [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,5,7,6,4,8,2,1]=>[5,2,4,1,3,8,7,6]=>1010011 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>[3,8,2,7,1,6,5,4]=>0101011 [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[8,7,2,6,1,5,4,3]=>1101011 [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,6,5,4,2,1,7,8]=>[6,5,1,4,3,2,7,8]=>1101100 [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>[5,4,1,3,2,8,6,7]=>1101010 [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,6,5,4,2,8,7,1]=>[4,3,1,2,8,5,7,6]=>1100101 [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>[4,3,1,2,6,5,8,7]=>1100101 [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,6,5,4,7,8,2,1]=>[4,3,1,2,5,8,7,6]=>1100011 [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,6,5,4,8,7,2,1]=>[3,2,8,1,4,7,6,5]=>1010011 [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,7,5,4,2,1]=>[8,2,7,6,1,5,4,3]=>1011011 [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,6,5,4,8,2,1]=>[5,4,3,1,2,8,7,6]=>1110011 [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]=>[4,3,2,8,1,7,6,5]=>1101011 [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>[3,2,8,7,1,6,5,4]=>1011011 [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]=>[2,8,7,6,1,5,4,3]=>0111011 [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>[8,7,6,5,1,4,3,2]=>1111011 [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[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]=>[4,3,2,1,5,6,8,7]=>[3,2,1,8,4,5,6,7]=>1101000 [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[3,2,1,6,8,4,5,7]=>1100100 [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[2,1,8,3,7,4,5,6]=>1010100 [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[3,2,1,5,8,4,6,7]=>1100100 [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[3,2,1,5,7,4,6,8]=>1100100 [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[3,2,1,5,6,8,4,7]=>1100010 [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[2,1,8,3,5,7,4,6]=>1010010 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[2,1,5,8,3,7,4,6]=>1001010 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[1,8,2,7,3,6,4,5]=>0101010 [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>[3,2,1,5,4,6,7,8]=>1101000 [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,3,2,5,1,7,8,6]=>[3,2,1,4,6,8,5,7]=>1100010 [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[2,1,8,3,4,7,5,6]=>1010010 [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,3,2,5,6,1,8,7]=>[3,2,1,4,5,8,6,7]=>1100010 [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[3,2,1,4,5,6,8,7]=>1100001 [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,3,2,5,7,6,8,1]=>[2,1,6,3,4,5,8,7]=>1010001 [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>[1,8,2,7,3,4,6,5]=>0101001 [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>[2,1,5,3,4,6,8,7]=>1010001 [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>[2,1,4,8,3,5,7,6]=>1001001 [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,6,7,5,8,1]=>[2,1,4,6,3,5,8,7]=>1001001 [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,3,2,6,8,7,5,1]=>[1,8,2,4,7,3,6,5]=>0100101 [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[1,6,2,5,3,4,8,7]=>0101001 [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[8,1,7,2,6,3,5,4]=>1010101 [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,3,5,2,1,6,7,8]=>[2,1,5,4,3,6,7,8]=>1011000 [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>[2,1,3,8,4,7,5,6]=>1001010 [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,3,5,2,6,1,7,8]=>[2,1,4,3,6,5,7,8]=>1010100 [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>[2,1,4,3,5,8,6,7]=>1010010 [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>[2,1,4,3,5,6,8,7]=>1010001 [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[2,1,3,6,4,5,8,7]=>1001001 [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]=>[2,1,3,5,4,6,8,7]=>1001001 [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,7,2,8,1]=>[2,1,3,4,6,5,8,7]=>1000101 [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]=>[2,1,3,4,5,8,7,6]=>1000011 [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,8,7,2,1]=>[1,8,2,3,4,7,6,5]=>0100011 [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,3,5,7,6,8,2,1]=>[1,5,2,3,4,8,7,6]=>0100011 [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]=>[1,4,8,2,3,7,6,5]=>0010011 [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>[1,5,2,4,3,8,6,7]=>0101010 [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>[1,4,2,3,8,5,7,6]=>0100101 [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[1,4,2,3,6,5,8,7]=>0100101 [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]=>[1,4,2,3,5,8,7,6]=>0100011 [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[1,3,8,2,4,7,6,5]=>0010011 [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,6,7,5,2,8,1]=>[1,3,6,2,5,4,8,7]=>0010101 [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]=>[1,3,4,8,2,7,6,5]=>0001011 [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,7,6,5,2,1,8]=>[7,1,6,2,5,4,3,8]=>1010110 [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,7,6,5,2,8,1]=>[6,1,5,2,4,3,8,7]=>1010101 [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,7,6,5,8,2,1]=>[5,1,4,2,3,8,7,6]=>1010011 [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]=>[3,8,1,7,2,6,5,4]=>0101011 [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,3,8,7,6,5,2,1]=>[8,7,1,6,2,5,4,3]=>1101011 [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000 [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>[1,4,3,2,8,5,6,7]=>0110100 [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>[1,3,2,8,4,7,5,6]=>0101010 [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,3,2,6,1,8,7]=>[1,4,3,2,5,8,6,7]=>0110010 [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,1]=>[1,4,3,2,5,6,8,7]=>0110001 [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,8,7,1]=>[1,3,2,8,4,5,7,6]=>0101001 [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>[1,3,2,7,4,6,5,8]=>0101010 [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,3,2,8,7,6,1]=>[1,2,8,3,7,4,6,5]=>0010101 [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[1,3,2,5,4,8,6,7]=>0101010 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[1,3,2,5,4,7,6,8]=>0101010 [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]=>[1,3,2,4,8,5,7,6]=>0100101 [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,3,6,7,2,8,1]=>[1,3,2,4,6,5,8,7]=>0100101 [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]=>[1,2,8,3,4,7,6,5]=>0010011 [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]=>[1,2,5,3,4,8,7,6]=>0010011 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]=>[1,2,4,8,3,7,6,5]=>0001011 [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,3,2,1,7,8]=>[1,2,6,5,4,3,7,8]=>0011100 [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[1,2,5,4,3,8,6,7]=>0011010 [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,3,2,7,8,1]=>[1,2,5,4,3,6,8,7]=>0011001 [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]=>[1,2,4,3,8,5,7,6]=>0010101 [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>[1,2,4,3,6,5,8,7]=>0010101 [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,2,1]=>[1,2,4,3,5,8,7,6]=>0010011 [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]=>[1,2,3,8,4,7,6,5]=>0001011 [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>[1,2,3,7,6,5,4,8]=>0001110 [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[1,2,3,6,5,4,8,7]=>0001101 [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[1,2,3,5,4,8,7,6]=>0001011 [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[1,2,3,4,8,7,6,5]=>0000111 [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]=>[8,1,2,3,7,6,5,4]=>1000111 [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,5,7,6,3,2,1,8]=>[7,1,2,6,5,4,3,8]=>1001110 [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]=>[4,1,2,3,8,7,6,5]=>1000111 [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]=>[3,8,1,2,7,6,5,4]=>0100111 [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>[8,7,1,2,6,5,4,3]=>1100111 [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]=>[3,1,2,4,8,7,6,5]=>1000111 [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>[2,8,1,3,7,6,5,4]=>0100111 [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]=>[2,4,1,3,8,7,6,5]=>0100111 [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]=>[2,3,8,1,7,6,5,4]=>0010111 [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>[8,2,7,1,6,5,4,3]=>1010111 [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]=>[6,5,1,4,3,2,8,7]=>1101101 [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]=>[5,4,1,3,2,8,7,6]=>1101011 [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[4,3,1,2,8,7,6,5]=>1100111 [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,6,8,5,3,2,1]=>[3,2,8,1,7,6,5,4]=>1010111 [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]=>[2,8,7,1,6,5,4,3]=>0110111 [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>1110111 [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000 [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[4,3,2,1,8,5,6,7]=>1110100 [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[4,3,2,1,7,5,6,8]=>1110100 [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[4,3,2,1,6,8,5,7]=>1110010 [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[3,2,1,8,4,7,5,6]=>1101010 [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[4,3,2,1,6,5,7,8]=>1110100 [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[4,3,2,1,5,8,6,7]=>1110010 [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>[4,3,2,1,5,7,6,8]=>1110010 [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[4,3,2,1,5,6,8,7]=>1110001 [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>[3,2,1,8,4,5,7,6]=>1101001 [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[3,2,1,7,4,6,5,8]=>1101010 [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[2,1,8,3,7,4,6,5]=>1010101 [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,4,3,6,2,1,7,8]=>[3,2,1,6,5,4,7,8]=>1101100 [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,4,3,6,2,7,1,8]=>[3,2,1,5,4,7,6,8]=>1101010 [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,4,3,6,2,8,7,1]=>[3,2,1,4,8,5,7,6]=>1100101 [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,4,3,6,7,2,1,8]=>[3,2,1,4,7,6,5,8]=>1100110 [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,2,1]=>[3,2,1,4,5,8,7,6]=>1100011 [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,4,3,6,8,7,2,1]=>[2,1,8,3,4,7,6,5]=>1010011 [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,3,7,8,6,2,1]=>[2,1,4,8,3,7,6,5]=>1001011 [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,4,3,8,7,6,2,1]=>[1,8,2,7,3,6,5,4]=>0101011 [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,4,6,3,2,7,1,8]=>[2,1,5,4,3,7,6,8]=>1011010 [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[2,1,4,3,6,5,8,7]=>1010101 [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[2,1,3,5,4,8,7,6]=>1001011 [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[2,1,3,4,8,7,6,5]=>1000111 [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,4,7,6,3,2,1,8]=>[1,7,2,6,5,4,3,8]=>0101110 [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,4,7,6,3,8,2,1]=>[1,5,2,4,3,8,7,6]=>0101011 [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]=>[1,4,2,3,8,7,6,5]=>0100111 [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,4,7,8,6,3,2,1]=>[1,3,8,2,7,6,5,4]=>0010111 [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>[1,6,5,4,3,2,7,8]=>0111100 [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,6,4,3,2,7,1,8]=>[1,5,4,3,2,7,6,8]=>0111010 [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,6,4,3,7,2,1,8]=>[1,4,3,2,7,6,5,8]=>0110110 [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,4,7,3,2,1,8]=>[1,3,2,7,6,5,4,8]=>0101110 [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[1,3,2,4,8,7,6,5]=>0100111 [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,4,8,7,3,2,1]=>[1,2,8,3,7,6,5,4]=>0010111 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[1,2,7,6,5,4,3,8]=>0011110 [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,4,3,8,2,1]=>[1,2,5,4,3,8,7,6]=>0011011 [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[1,2,4,3,8,7,6,5]=>0010111 [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[1,2,3,8,7,6,5,4]=>0001111 [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>[8,1,2,7,6,5,4,3]=>1001111 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[7,1,6,5,4,3,2,8]=>1011110 [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,6,4,3,2,8,1]=>[6,1,5,4,3,2,8,7]=>1011101 [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>[5,1,4,3,2,8,7,6]=>1011011 [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,6,4,8,3,2,1]=>[4,1,3,2,8,7,6,5]=>1010111 [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>[3,1,2,8,7,6,5,4]=>1001111 [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>[2,8,1,7,6,5,4,3]=>0101111 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[8,7,1,6,5,4,3,2]=>1101111 [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[5,4,3,2,1,8,6,7]=>1111010 [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,5,4,3,2,7,1,8]=>[5,4,3,2,1,7,6,8]=>1111010 [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>[5,4,3,2,1,6,8,7]=>1111001 [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[4,3,2,1,8,5,7,6]=>1110101 [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,5,4,3,7,2,1,8]=>[4,3,2,1,7,6,5,8]=>1110110 [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[4,3,2,1,6,5,8,7]=>1110101 [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[4,3,2,1,5,8,7,6]=>1110011 [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,5,4,3,8,7,2,1]=>[3,2,1,8,4,7,6,5]=>1101011 [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>[3,2,1,7,6,5,4,8]=>1101110 [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,5,4,7,3,2,8,1]=>[3,2,1,6,5,4,8,7]=>1101101 [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>[3,2,1,4,8,7,6,5]=>1100111 [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,5,4,8,7,3,2,1]=>[2,1,8,3,7,6,5,4]=>1010111 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[2,1,7,6,5,4,3,8]=>1011110 [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[2,1,6,5,4,3,8,7]=>1011101 [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[2,1,5,4,3,8,7,6]=>1011011 [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[2,1,4,3,8,7,6,5]=>1010111 [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[2,1,3,8,7,6,5,4]=>1001111 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[1,8,2,7,6,5,4,3]=>0101111 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[1,7,6,5,4,3,2,8]=>0111110 [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>[1,6,5,4,3,2,8,7]=>0111101 [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[1,5,4,3,2,8,7,6]=>0111011 [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]=>[1,4,3,2,8,7,6,5]=>0110111 [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>[1,3,2,8,7,6,5,4]=>0101111 [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[1,2,8,7,6,5,4,3]=>0011111 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>[8,1,7,6,5,4,3,2]=>1011111 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>1111110 [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[6,5,4,3,2,1,8,7]=>1111101 [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[5,4,3,2,1,8,7,6]=>1111011 [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[4,3,2,1,8,7,6,5]=>1110111 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[3,2,1,8,7,6,5,4]=>1101111 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[2,1,8,7,6,5,4,3]=>1011111 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[1,8,7,6,5,4,3,2]=>0111111 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]=>11111110 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,6,5,4,3,2,1,9]=>[1,8,7,6,5,4,3,2,9]=>01111110 [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,7,6,5,4,3,2]=>[2,9,8,7,6,5,4,1,3]=>01111110 [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]=>111111110 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,7,6,5,4,3,2,1,10]=>[1,9,8,7,6,5,4,3,2,10]=>011111110 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,6,8,5,4,3,2,1,9]=>[2,1,8,7,6,5,4,3,9]=>10111110 [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,7,9,8,6,5,4,3,2]=>[9,2,8,7,6,5,4,1,3]=>10111110 [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9,10,8,7,6,5,4,3,2]=>[2,10,9,8,7,6,5,4,1,3]=>011111110 [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,10,9,8,7,6,5,4,3,1,2]=>1111111110 [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>11111111110 [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,7,8,9,6,5,4,3,2]=>[2,3,9,8,7,6,5,1,4]=>00111110 [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,8,10,7,6,5,4,3,2]=>[3,2,10,9,8,7,6,5,1,4]=>101111110 [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[7,6,5,4,3,8,2,1,9]=>[5,4,3,2,1,8,7,6,9]=>11110110 [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[8,7,6,5,4,9,3,2,1,10]=>[5,4,3,2,1,9,8,7,6,10]=>111101110 [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,6,5,4,3,2,8,1,9]=>[6,5,4,3,2,1,8,7,9]=>11111010 [1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,9,8,7,6,5,4,2]=>[9,8,7,6,5,2,4,1,3]=>11111010 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[8,7,6,5,4,3,9,2,1,10]=>[6,5,4,3,2,1,9,8,7,10]=>111110110 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,7,6,5,4,3,2,9]=>[8,7,6,5,4,3,1,2,9]=>11111100 [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]=>11111100 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[8,7,6,5,4,3,2,9,1,10]=>[7,6,5,4,3,2,1,9,8,10]=>111111010 [1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,10,9,8,7,6,5,4,2]=>[10,9,8,7,6,5,2,4,1,3]=>111111010 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100 [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,8,7,6,5,4,3,2,10]=>[9,8,7,6,5,4,3,1,2,10]=>111111100 [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,1,2,3]=>111111100 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>[1,2,3,4,5,6,7,9,8]=>00000001 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,8,1]=>[9,1,2,3,4,5,6,8,7]=>10000001 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,8,7,9,1]=>[7,1,2,3,4,5,6,9,8]=>10000001 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,9,1]=>[3,1,2,4,5,6,7,9,8]=>10000001 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,8,7,6,5,4,3,9,1]=>[7,6,5,4,3,1,2,9,8]=>11111001 [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,8,9,7,6,5,4,3,1]=>[2,9,8,7,6,5,1,4,3]=>01111101 [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,9,8,7,6,5,4,3,1]=>[9,8,7,6,5,4,1,3,2]=>11111101 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>[2,1,3,4,5,6,7,9,8]=>10000001 [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,1]=>[1,3,2,4,5,6,7,9,8]=>01000001 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,2,9,1]=>[1,2,3,4,5,7,6,9,8]=>00000101 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[1,2,3,4,5,6,9,8,7]=>00000011 [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,9,8,7,6,5,4,2,1]=>[9,8,7,6,5,1,4,3,2]=>11111011 [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[1,2,3,4,5,9,8,7,6]=>00000111 [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,9,8,7,6,5,3,2,1]=>[9,8,7,6,1,5,4,3,2]=>11110111 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,6,4,7,3,8,2,9,1]=>[1,3,2,5,4,7,6,9,8]=>01010101 [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[1,2,3,4,9,8,7,6,5]=>00001111 [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[5,7,9,8,6,4,3,2,1]=>[9,2,8,1,7,6,5,4,3]=>10101111 [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,9,8,7,6,4,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>11101111 [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[1,2,3,9,8,7,6,5,4]=>00011111 [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,9,8,7,5,4,3,2,1]=>[9,8,1,7,6,5,4,3,2]=>11011111 [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,6,8,5,9,4,3,2,1]=>[2,1,4,3,9,8,7,6,5]=>10101111 [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,6,9,8,5,4,3,2,1]=>[1,9,2,8,7,6,5,4,3]=>01011111 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,8,6,5,4,3,2,9,1]=>[1,7,6,5,4,3,2,9,8]=>01111101 [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[1,2,9,8,7,6,5,4,3]=>00111111 [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,9,8,6,5,4,3,2,1]=>[9,1,8,7,6,5,4,3,2]=>10111111 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[7,6,5,4,3,2,1,9,8]=>11111101 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]=>[6,5,4,3,2,1,9,8,7]=>11111011 [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,7,6,5,4,9,3,2,1]=>[5,4,3,2,1,9,8,7,6]=>11110111 [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]=>[4,3,2,1,9,8,7,6,5]=>11101111 [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,7,6,9,5,4,3,2,1]=>[3,2,1,9,8,7,6,5,4]=>11011111 [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]=>[2,1,9,8,7,6,5,4,3]=>10111111 [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]=>[1,9,8,7,6,5,4,3,2]=>01111111 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>[9,1,2,3,4,5,6,7,8]=>10000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,7]=>[7,9,1,2,3,4,5,6,8]=>01000000 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,6]=>[6,7,9,1,2,3,4,5,8]=>00100000 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,5]=>[5,6,7,9,1,2,3,4,8]=>00010000 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,4]=>[4,5,6,7,9,1,2,3,8]=>00001000 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,2]=>[2,3,4,5,6,7,9,1,8]=>00000010 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[10,1,2,3,4,5,6,7,8,9]=>100000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]=>11000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[8,10,1,2,3,4,5,6,7,9]=>010000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[7,8,10,1,2,3,4,5,6,9]=>001000000 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[5,6,7,8,10,1,2,3,4,9]=>000010000 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[4,5,6,7,8,10,1,2,3,9]=>000001000 [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,9,2]=>[3,2,4,5,6,7,9,1,8]=>10000010 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[2,3,4,5,6,7,8,10,1,9]=>000000010 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[1,2,3,4,5,6,7,8,10,9]=>000000001 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,1,2,3,4,5,6,7,8]=>110000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[9,11,1,2,3,4,5,6,7,8,10]=>0100000000 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,5,8,9,7,6]=>[6,9,8,1,2,3,4,5,7]=>01100000 [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]=>11100000 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[2,1,3,4,5,6,7,8,10,9]=>100000001 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,2]=>[2,3,4,5,6,7,8,9,11,1,10]=>0000000010 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,8,11,10,9]=>[11,10,1,2,3,4,5,6,7,8,9]=>1100000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]=>111000000 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>00000000010 [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>11110000 [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,1,2,3,4,5,6]=>111100000 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,9,3,2]=>[2,3,4,5,6,9,8,1,7]=>00000110 [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,6,5,1,2,3,4]=>11111000 [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,6,1,2,3,4,5]=>111110000 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,9,10,3,2]=>[2,3,4,5,6,7,10,9,1,8]=>000000110 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,2,10,1]=>[1,2,3,4,5,6,8,7,10,9]=>000000101 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,9]=>[8,1,2,3,4,5,6,7,9]=>10000000 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>10000000 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>10000000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>10000000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>10000000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[2,9,1,3,4,5,6,7,8]=>01000000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>11000000 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,7,6,5,4,3,2,9,8]=>[6,5,4,3,2,9,1,7,8]=>11110100 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,9,8]=>[1,9,2,3,4,5,6,7,8]=>01000000 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,6,8,7,9]=>[1,8,2,3,4,5,6,7,9]=>01000000 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>01000000 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000 [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000 [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,3,2,1,9,8,7,6,5]=>[9,1,8,2,7,3,6,4,5]=>10101010 [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000 [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,9,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>100000000 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>100000000 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>100000000 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>100000000 [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,9,8,7,6,5,4]=>[10,9,8,7,6,5,1,2,3,4]=>111111000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>100000000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>100000000 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,8,10,9]=>[1,10,2,3,4,5,6,7,8,9]=>010000000 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000 [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000 [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000 [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>01000000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>00100000 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>00010000 [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>00001000 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>[1,2,3,4,5,7,6,8,9]=>00000100 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>[1,2,3,4,5,6,8,7,9]=>00000010 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>010000000 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>10100000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>001000000 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>000100000 [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>000010000 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>000001000 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,6,8,7,1,9]=>[8,1,2,3,4,5,7,6,9]=>10000010 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,1,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>000000100 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>[1,2,3,4,5,6,7,9,8,10]=>000000010 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,6,8,9,7]=>[1,7,9,2,3,4,5,6,8]=>00100000 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,9,1]=>[10,1,2,3,4,5,6,7,9,8]=>100000001 [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,10,9,7,6,5,4,3,2,1]=>[10,1,9,8,7,6,5,4,3,2]=>101111111 [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[2,1,10,9,8,7,6,5,4,3]=>101111111 [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[9,11,10,8,7,6,5,4,3,2,1]=>[11,1,10,9,8,7,6,5,4,3,2]=>1011111111 [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[10,9,11,8,7,6,5,4,3,2,1]=>[2,1,11,10,9,8,7,6,5,4,3]=>1011111111 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,7,9,8]=>[1,2,9,3,4,5,6,7,8]=>00100000 [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>01100000 [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,9,8,7,6,5,4,3,1]=>[10,9,8,7,6,5,4,1,3,2]=>111111101 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[8,7,6,5,4,3,2,1,10,9]=>111111101 [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[9,8,7,6,5,4,3,2,1,11,10]=>1111111101 [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[6,5,4,3,2,7,1,8,9]=>[5,4,3,2,1,7,6,8,9]=>11110100 [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,2,6,1,7,8,9]=>[4,3,2,1,6,5,7,8,9]=>11101000 [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>11010000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>10100000 [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,4,3,2]=>011111111 [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,10,9,8,6,5,4,3,2,1]=>[10,9,1,8,7,6,5,4,3,2]=>110111111 [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,10,9,8,7,5,4,3,2,1]=>[10,9,8,1,7,6,5,4,3,2]=>111011111 [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,10,9,8,7,6,4,3,2,1]=>[10,9,8,7,1,6,5,4,3,2]=>111101111 [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,10,9,8,7,6,5,3,2,1]=>[10,9,8,7,6,1,5,4,3,2]=>111110111 [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,10,9,8,7,6,5,4,2,1]=>[10,9,8,7,6,5,1,4,3,2]=>111111011 [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8,9]=>[2,3,5,1,4,6,7,8,9]=>00100000 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,7,9,8]=>[1,2,3,4,9,5,6,7,8]=>00001000 [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8,9]=>[1,3,5,2,4,6,7,8,9]=>00100000 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,8,1,9]=>[2,1,3,4,5,6,8,7,9]=>10000010 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8]=>[1,2,3,4,5,6,9,7,8]=>00000010 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,3]=>[1,3,4,5,6,7,9,2,8]=>00000010 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,9,8,7]=>[9,1,2,3,4,5,8,6,7]=>10000010 [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[1,2,3,4,5,6,10,9,8,7]=>000000111 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[7,6,5,4,3,2,1,10,9,8]=>111111011 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[6,5,4,3,2,1,10,9,8,7]=>111110111 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[5,4,3,2,1,10,9,8,7,6]=>111101111 [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[4,3,2,1,10,9,8,7,6,5]=>111011111 [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[3,2,1,10,9,8,7,6,5,4]=>110111111 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[1,2,3,4,5,6,7,10,9,8]=>000000011 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[1,2,3,4,5,6,7,8,11,10,9]=>0000000011 [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,5,7,9,10,8,6,4,2]=>[5,10,4,9,3,8,2,7,1,6]=>010101010 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,6,4,7,3,8,2,9,1,10]=>[1,3,2,5,4,7,6,9,8,10]=>010101010 [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>1111111111 [1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,9,8,7,6,5,3]=>[9,8,7,6,3,5,1,2,4]=>11110100 [1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,9,8,7,6,4]=>[9,8,7,4,6,1,2,3,5]=>11101000 [1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,4,6,9,8,7,5]=>[9,8,5,7,1,2,3,4,6]=>11010000 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,9,8,6]=>[9,6,8,1,2,3,4,5,7]=>10100000 [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,9,4]=>[2,1,4,5,6,7,9,3,8]=>10000010 [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[1,2,3,4,5,10,9,8,7,6]=>000001111 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>01000000 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,10,3]=>[1,3,4,5,6,7,8,10,2,9]=>000000010 [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[1,2,10,9,8,7,6,5,4,3]=>001111111 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>1000000000 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,5,7,8,6,9]=>[6,8,1,2,3,4,5,7,9]=>01000000 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,7,2,9,8]=>[2,3,4,5,6,9,1,7,8]=>00000100 [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>01010000 [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,10,9,8,7,6,5]=>000011111 [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[1,2,3,10,9,8,7,6,5,4]=>000111111 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>0000000010 [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,8,2,9]=>[2,3,4,5,6,8,1,7,9]=>00000100 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,4,6,8,9,7,5]=>[6,9,5,8,1,2,3,4,7]=>01010000 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,10,9]=>[1,2,3,4,5,6,7,10,8,9]=>000000010 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,1,8,9,7]=>[1,2,3,4,5,7,9,6,8]=>00000010 [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1,10,11]=>[9,8,7,6,5,4,3,2,1,10,11]=>1111111100 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9,10]=>[2,4,1,3,5,6,7,8,9,10]=>010000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,6,8,10,9,7]=>[10,7,9,1,2,3,4,5,6,8]=>101000000 [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,6,8,7,9,2]=>[7,2,3,4,5,6,9,1,8]=>10000010 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[2,4,6,8,10,1,3,5,7,9]=>000010000 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9,10]=>[4,1,3,2,5,6,7,8,9,10]=>101000000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>101000000 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,7,2,8,9]=>[2,3,4,5,7,1,6,8,9]=>00001000 [1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,7,9,8,6,4,2]=>[9,4,8,3,7,2,6,1,5]=>10101010 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,6,7,9,8,1,10]=>[9,1,2,3,4,5,6,8,7,10]=>100000010 [1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,8,3,9,2,10,1]=>[1,4,2,3,6,5,8,7,10,9]=>010010101 [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[2,1,4,3,6,5,8,7,10,9]=>101010101 [1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,11,10]=>[1,2,3,4,5,6,7,8,11,9,10]=>0000000010 [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,1,7,8,9,6]=>[1,2,3,4,6,7,9,5,8]=>00000010 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,7,8,10,9,1]=>[1,10,2,3,4,5,6,7,9,8]=>010000001 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,1,9,10,8]=>[1,2,3,4,5,6,8,10,7,9]=>000000010 [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,4,6,3,7,2,8,1,9]=>[2,1,4,3,6,5,8,7,9]=>10101010 [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,9,8]=>[1,2,3,4,6,9,5,7,8]=>00000100 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,4,5,7,9,10,8,6]=>[7,10,6,9,1,2,3,4,5,8]=>010100000 [1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,10,9,8,7,6,5,3]=>[10,9,8,7,6,3,5,1,2,4]=>111110100 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,12,10]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>00000100000 [1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,9,8,7,6,4,2]=>[9,8,7,3,6,2,5,1,4]=>11101010 [1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5,10,9,8,7,6,4,2]=>[10,9,8,7,3,6,2,5,1,4]=>111101010 [1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,5,7,10,9,8,6,4,2]=>[10,9,4,8,3,7,2,6,1,5]=>110101010
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
Lehmer-code to major-code bijection
Description
Sends a permutation to the unique permutation such that the Lehmer code is sent to the major code.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.