Identifier
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0,1,0]=>[1,2]=>[1]=> [1,1,0,0]=>[2,1]=>[1]=> [1,0,1,0,1,0]=>[1,2,3]=>[1,2]=>1 [1,0,1,1,0,0]=>[1,3,2]=>[1,2]=>1 [1,1,0,0,1,0]=>[2,1,3]=>[2,1]=>0 [1,1,0,1,0,0]=>[2,3,1]=>[2,1]=>0 [1,1,1,0,0,0]=>[3,2,1]=>[2,1]=>0 [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3]=>11 [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,3]=>11 [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2]=>10 [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,3,2]=>10 [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,3,2]=>10 [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3]=>01 [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,3]=>01 [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[2,3,1]=>00 [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[2,3,1]=>00 [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[2,3,1]=>00 [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1]=>00 [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[3,2,1]=>00 [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[3,2,1]=>00 [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[3,2,1]=>00 [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4]=>111 [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,4]=>111 [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3]=>110 [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,4,3]=>110 [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,4,3]=>110 [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4]=>101 [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,4]=>101 [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,3,4,2]=>100 [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,3,4,2]=>100 [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,3,4,2]=>100 [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,4,3,2]=>100 [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,4,3,2]=>100 [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[1,4,3,2]=>100 [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,4,3,2]=>100 [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4]=>011 [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,4]=>011 [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3]=>010 [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,4,3]=>010 [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,4,3]=>010 [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[2,3,1,4]=>001 [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[2,3,1,4]=>001 [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[2,3,4,1]=>000 [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[2,3,4,1]=>000 [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[2,3,4,1]=>000 [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[2,4,3,1]=>000 [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[2,4,3,1]=>000 [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[2,4,3,1]=>000 [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[2,4,3,1]=>000 [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4]=>001 [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[3,2,1,4]=>001 [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[3,2,4,1]=>000 [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[3,2,4,1]=>000 [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[3,2,4,1]=>000 [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[3,4,2,1]=>000 [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[3,4,2,1]=>000 [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[3,4,2,1]=>000 [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[3,4,2,1]=>000 [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1]=>000 [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[4,3,2,1]=>000 [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[4,3,2,1]=>000 [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[4,3,2,1]=>000 [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1]=>000 [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5]=>1111 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,5]=>1111 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4]=>1110 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,5,4]=>1110 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,5,4]=>1110 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5]=>1101 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,5]=>1101 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,4,5,3]=>1100 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,4,5,3]=>1100 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,4,5,3]=>1100 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,5,4,3]=>1100 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,5,4,3]=>1100 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[1,2,5,4,3]=>1100 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,5,4,3]=>1100 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5]=>1011 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,5]=>1011 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4]=>1010 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,5,4]=>1010 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,5,4]=>1010 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,3,4,2,5]=>1001 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,3,4,2,5]=>1001 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,3,4,5,2]=>1000 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,3,4,5,2]=>1000 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,3,4,5,2]=>1000 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,3,5,4,2]=>1000 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,3,5,4,2]=>1000 [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[1,3,5,4,2]=>1000 [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,3,5,4,2]=>1000 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,4,3,2,5]=>1001 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,4,3,2,5]=>1001 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,4,3,5,2]=>1000 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,4,3,5,2]=>1000 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,4,3,5,2]=>1000 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[1,4,5,3,2]=>1000 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[1,4,5,3,2]=>1000 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[1,4,5,3,2]=>1000 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[1,4,5,3,2]=>1000 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,5,4,3,2]=>1000 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,5,4,3,2]=>1000 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[1,5,4,3,2]=>1000 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[1,5,4,3,2]=>1000 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,5,4,3,2]=>1000 [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5]=>0111 [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,5]=>0111 [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4]=>0110 [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,5,4]=>0110 [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,5,4]=>0110 [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5]=>0101 [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,5]=>0101 [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,4,5,3]=>0100 [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,4,5,3]=>0100 [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,4,5,3]=>0100 [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,5,4,3]=>0100 [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,5,4,3]=>0100 [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[2,1,5,4,3]=>0100 [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,5,4,3]=>0100 [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[2,3,1,4,5]=>0011 [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[2,3,1,4,5]=>0011 [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[2,3,1,5,4]=>0010 [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[2,3,1,5,4]=>0010 [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[2,3,1,5,4]=>0010 [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[2,3,4,1,5]=>0001 [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[2,3,4,1,5]=>0001 [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[2,3,4,5,1]=>0000 [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[2,3,4,5,1]=>0000 [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[2,3,4,5,1]=>0000 [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[2,3,5,4,1]=>0000 [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[2,3,5,4,1]=>0000 [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[2,3,5,4,1]=>0000 [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[2,3,5,4,1]=>0000 [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[2,4,3,1,5]=>0001 [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[2,4,3,1,5]=>0001 [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[2,4,3,5,1]=>0000 [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[2,4,3,5,1]=>0000 [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[2,4,3,5,1]=>0000 [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[2,4,5,3,1]=>0000 [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[2,4,5,3,1]=>0000 [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[2,4,5,3,1]=>0000 [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[2,4,5,3,1]=>0000 [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[2,5,4,3,1]=>0000 [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[2,5,4,3,1]=>0000 [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[2,5,4,3,1]=>0000 [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[2,5,4,3,1]=>0000 [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[2,5,4,3,1]=>0000 [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5]=>0011 [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[3,2,1,4,5]=>0011 [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[3,2,1,5,4]=>0010 [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[3,2,1,5,4]=>0010 [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[3,2,1,5,4]=>0010 [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[3,2,4,1,5]=>0001 [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[3,2,4,1,5]=>0001 [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[3,2,4,5,1]=>0000 [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[3,2,4,5,1]=>0000 [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[3,2,4,5,1]=>0000 [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[3,2,5,4,1]=>0000 [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[3,2,5,4,1]=>0000 [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[3,2,5,4,1]=>0000 [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[3,2,5,4,1]=>0000 [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[3,4,2,1,5]=>0001 [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[3,4,2,1,5]=>0001 [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[3,4,2,5,1]=>0000 [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[3,4,2,5,1]=>0000 [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[3,4,2,5,1]=>0000 [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[3,4,5,2,1]=>0000 [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[3,4,5,2,1]=>0000 [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[3,4,5,2,1]=>0000 [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[3,4,5,2,1]=>0000 [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[3,5,4,2,1]=>0000 [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[3,5,4,2,1]=>0000 [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[3,5,4,2,1]=>0000 [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[3,5,4,2,1]=>0000 [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[3,5,4,2,1]=>0000 [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5]=>0001 [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[4,3,2,1,5]=>0001 [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[4,3,2,5,1]=>0000 [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[4,3,2,5,1]=>0000 [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[4,3,2,5,1]=>0000 [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[4,3,5,2,1]=>0000 [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[4,3,5,2,1]=>0000 [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[4,3,5,2,1]=>0000 [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[4,3,5,2,1]=>0000 [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[4,5,3,2,1]=>0000 [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[4,5,3,2,1]=>0000 [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[4,5,3,2,1]=>0000 [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[4,5,3,2,1]=>0000 [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[4,5,3,2,1]=>0000 [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1]=>0000 [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[5,4,3,2,1]=>0000 [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[5,4,3,2,1]=>0000 [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[5,4,3,2,1]=>0000 [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[5,4,3,2,1]=>0000 [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1]=>0000 [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]=>11111 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,6]=>11111 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5]=>11110 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,6,5]=>11110 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,5]=>11110 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6]=>11101 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,6]=>11101 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,5,6,4]=>11100 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,5,6,4]=>11100 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,2,3,5,6,4]=>11100 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4]=>11100 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,6,5,4]=>11100 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[1,2,3,6,5,4]=>11100 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,6,5,4]=>11100 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6]=>11011 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,6]=>11011 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5]=>11010 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,6,5]=>11010 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,5]=>11010 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,4,5,3,6]=>11001 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,4,5,3,6]=>11001 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,4,5,6,3]=>11000 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,4,5,6,3]=>11000 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,4,5,6,3]=>11000 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,4,6,5,3]=>11000 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,4,6,5,3]=>11000 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[1,2,4,6,5,3]=>11000 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,4,6,5,3]=>11000 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6]=>11001 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,6]=>11001 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,5,4,6,3]=>11000 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,5,4,6,3]=>11000 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,5,4,6,3]=>11000 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[1,2,5,6,4,3]=>11000 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[1,2,5,6,4,3]=>11000 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[1,2,5,6,4,3]=>11000 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[1,2,5,6,4,3]=>11000 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3]=>11000 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,6,5,4,3]=>11000 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[1,2,6,5,4,3]=>11000 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[1,2,6,5,4,3]=>11000 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,6,5,4,3]=>11000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6]=>10111 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,6]=>10111 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5]=>10110 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,6,5]=>10110 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,5]=>10110 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6]=>10101 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,6]=>10101 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,5,6,4]=>10100 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,5,6,4]=>10100 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,5,6,4]=>10100 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4]=>10100 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,6,5,4]=>10100 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[1,3,2,6,5,4]=>10100 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,6,5,4]=>10100 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,3,4,2,5,6]=>10011 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,3,4,2,5,6]=>10011 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,3,4,2,6,5]=>10010 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,3,4,2,6,5]=>10010 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,3,4,2,6,5]=>10010 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,3,4,5,2,6]=>10001 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,3,4,5,2,6]=>10001 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,3,4,5,6,2]=>10000 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,3,4,5,6,2]=>10000 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,3,4,5,6,2]=>10000 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,3,4,6,5,2]=>10000 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,3,4,6,5,2]=>10000 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[1,3,4,6,5,2]=>10000 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,3,4,6,5,2]=>10000 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,3,5,4,2,6]=>10001 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,3,5,4,2,6]=>10001 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,3,5,4,6,2]=>10000 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,3,5,4,6,2]=>10000 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,3,5,4,6,2]=>10000 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[1,3,5,6,4,2]=>10000 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[1,3,5,6,4,2]=>10000 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[1,3,5,6,4,2]=>10000 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[1,3,5,6,4,2]=>10000 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,3,6,5,4,2]=>10000 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,3,6,5,4,2]=>10000 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[1,3,6,5,4,2]=>10000 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[1,3,6,5,4,2]=>10000 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,3,6,5,4,2]=>10000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6]=>10011 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,6]=>10011 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5]=>10010 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,4,3,2,6,5]=>10010 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,4,3,2,6,5]=>10010 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,4,3,5,2,6]=>10001 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,4,3,5,2,6]=>10001 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,4,3,5,6,2]=>10000 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,4,3,5,6,2]=>10000 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,4,3,5,6,2]=>10000 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,4,3,6,5,2]=>10000 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,4,3,6,5,2]=>10000 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[1,4,3,6,5,2]=>10000 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,4,3,6,5,2]=>10000 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[1,4,5,3,2,6]=>10001 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[1,4,5,3,2,6]=>10001 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[1,4,5,3,6,2]=>10000 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[1,4,5,3,6,2]=>10000 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[1,4,5,3,6,2]=>10000 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[1,4,5,6,3,2]=>10000 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[1,4,5,6,3,2]=>10000 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[1,4,5,6,3,2]=>10000 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[1,4,5,6,3,2]=>10000 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[1,4,6,5,3,2]=>10000 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[1,4,6,5,3,2]=>10000 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[1,4,6,5,3,2]=>10000 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[1,4,6,5,3,2]=>10000 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[1,4,6,5,3,2]=>10000 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6]=>10001 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,6]=>10001 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,5,4,3,6,2]=>10000 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,5,4,3,6,2]=>10000 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,5,4,3,6,2]=>10000 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[1,5,4,6,3,2]=>10000 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[1,5,4,6,3,2]=>10000 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[1,5,4,6,3,2]=>10000 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[1,5,4,6,3,2]=>10000 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[1,5,6,4,3,2]=>10000 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[1,5,6,4,3,2]=>10000 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[1,5,6,4,3,2]=>10000 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[1,5,6,4,3,2]=>10000 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[1,5,6,4,3,2]=>10000 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2]=>10000 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,6,5,4,3,2]=>10000 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[1,6,5,4,3,2]=>10000 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[1,6,5,4,3,2]=>10000 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[1,6,5,4,3,2]=>10000 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,6,5,4,3,2]=>10000 [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]=>01111 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,6]=>01111 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5]=>01110 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,6,5]=>01110 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,5]=>01110 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6]=>01101 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,6]=>01101 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,5,6,4]=>01100 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,5,6,4]=>01100 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,5,6,4]=>01100 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4]=>01100 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,6,5,4]=>01100 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[2,1,3,6,5,4]=>01100 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,6,5,4]=>01100 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6]=>01011 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,6]=>01011 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5]=>01010 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,6,5]=>01010 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,5]=>01010 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,4,5,3,6]=>01001 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,4,5,3,6]=>01001 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,4,5,6,3]=>01000 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,4,5,6,3]=>01000 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,4,5,6,3]=>01000 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,4,6,5,3]=>01000 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,4,6,5,3]=>01000 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[2,1,4,6,5,3]=>01000 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,4,6,5,3]=>01000 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6]=>01001 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,6]=>01001 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,5,4,6,3]=>01000 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,5,4,6,3]=>01000 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,5,4,6,3]=>01000 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[2,1,5,6,4,3]=>01000 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[2,1,5,6,4,3]=>01000 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[2,1,5,6,4,3]=>01000 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[2,1,5,6,4,3]=>01000 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3]=>01000 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,6,5,4,3]=>01000 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[2,1,6,5,4,3]=>01000 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[2,1,6,5,4,3]=>01000 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,6,5,4,3]=>01000 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6]=>00111 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[2,3,1,4,5,6]=>00111 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[2,3,1,4,6,5]=>00110 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[2,3,1,4,6,5]=>00110 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[2,3,1,4,6,5]=>00110 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[2,3,1,5,4,6]=>00101 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[2,3,1,5,4,6]=>00101 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[2,3,1,5,6,4]=>00100 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[2,3,1,5,6,4]=>00100 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[2,3,1,5,6,4]=>00100 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[2,3,1,6,5,4]=>00100 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[2,3,1,6,5,4]=>00100 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[2,3,1,6,5,4]=>00100 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[2,3,1,6,5,4]=>00100 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6]=>00011 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[2,3,4,1,5,6]=>00011 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[2,3,4,1,6,5]=>00010 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[2,3,4,1,6,5]=>00010 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[2,3,4,1,6,5]=>00010 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6]=>00001 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[2,3,4,5,1,6]=>00001 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1]=>00000 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,1]=>00000 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[2,3,4,5,6,1]=>00000 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[2,3,4,6,5,1]=>00000 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[2,3,4,6,5,1]=>00000 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[2,3,4,6,5,1]=>00000 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[2,3,4,6,5,1]=>00000 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[2,3,5,4,1,6]=>00001 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[2,3,5,4,1,6]=>00001 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[2,3,5,4,6,1]=>00000 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[2,3,5,4,6,1]=>00000 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[2,3,5,4,6,1]=>00000 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[2,3,5,6,4,1]=>00000 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[2,3,5,6,4,1]=>00000 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[2,3,5,6,4,1]=>00000 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[2,3,5,6,4,1]=>00000 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[2,3,6,5,4,1]=>00000 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[2,3,6,5,4,1]=>00000 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[2,3,6,5,4,1]=>00000 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[2,3,6,5,4,1]=>00000 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[2,3,6,5,4,1]=>00000 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[2,4,3,1,5,6]=>00011 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[2,4,3,1,5,6]=>00011 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[2,4,3,1,6,5]=>00010 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[2,4,3,1,6,5]=>00010 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[2,4,3,1,6,5]=>00010 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[2,4,3,5,1,6]=>00001 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[2,4,3,5,1,6]=>00001 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[2,4,3,5,6,1]=>00000 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[2,4,3,5,6,1]=>00000 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[2,4,3,5,6,1]=>00000 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[2,4,3,6,5,1]=>00000 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[2,4,3,6,5,1]=>00000 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[2,4,3,6,5,1]=>00000 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[2,4,3,6,5,1]=>00000 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[2,4,5,3,1,6]=>00001 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[2,4,5,3,1,6]=>00001 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[2,4,5,3,6,1]=>00000 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[2,4,5,3,6,1]=>00000 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[2,4,5,3,6,1]=>00000 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[2,4,5,6,3,1]=>00000 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[2,4,5,6,3,1]=>00000 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[2,4,5,6,3,1]=>00000 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[2,4,5,6,3,1]=>00000 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[2,4,6,5,3,1]=>00000 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[2,4,6,5,3,1]=>00000 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[2,4,6,5,3,1]=>00000 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[2,4,6,5,3,1]=>00000 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[2,4,6,5,3,1]=>00000 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[2,5,4,3,1,6]=>00001 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[2,5,4,3,1,6]=>00001 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[2,5,4,3,6,1]=>00000 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[2,5,4,3,6,1]=>00000 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[2,5,4,3,6,1]=>00000 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[2,5,4,6,3,1]=>00000 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[2,5,4,6,3,1]=>00000 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[2,5,4,6,3,1]=>00000 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[2,5,4,6,3,1]=>00000 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[2,5,6,4,3,1]=>00000 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[2,5,6,4,3,1]=>00000 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[2,5,6,4,3,1]=>00000 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[2,5,6,4,3,1]=>00000 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[2,5,6,4,3,1]=>00000 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[2,6,5,4,3,1]=>00000 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[2,6,5,4,3,1]=>00000 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[2,6,5,4,3,1]=>00000 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[2,6,5,4,3,1]=>00000 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[2,6,5,4,3,1]=>00000 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[2,6,5,4,3,1]=>00000 [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]=>00111 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,6]=>00111 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5]=>00110 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[3,2,1,4,6,5]=>00110 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[3,2,1,4,6,5]=>00110 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6]=>00101 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,6]=>00101 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[3,2,1,5,6,4]=>00100 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[3,2,1,5,6,4]=>00100 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[3,2,1,5,6,4]=>00100 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4]=>00100 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[3,2,1,6,5,4]=>00100 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[3,2,1,6,5,4]=>00100 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[3,2,1,6,5,4]=>00100 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6]=>00011 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[3,2,4,1,5,6]=>00011 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[3,2,4,1,6,5]=>00010 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[3,2,4,1,6,5]=>00010 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[3,2,4,1,6,5]=>00010 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6]=>00001 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[3,2,4,5,1,6]=>00001 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1]=>00000 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,1]=>00000 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[3,2,4,5,6,1]=>00000 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[3,2,4,6,5,1]=>00000 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[3,2,4,6,5,1]=>00000 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[3,2,4,6,5,1]=>00000 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[3,2,4,6,5,1]=>00000 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[3,2,5,4,1,6]=>00001 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[3,2,5,4,1,6]=>00001 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[3,2,5,4,6,1]=>00000 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[3,2,5,4,6,1]=>00000 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[3,2,5,4,6,1]=>00000 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[3,2,5,6,4,1]=>00000 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[3,2,5,6,4,1]=>00000 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[3,2,5,6,4,1]=>00000 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[3,2,5,6,4,1]=>00000 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[3,2,6,5,4,1]=>00000 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[3,2,6,5,4,1]=>00000 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[3,2,6,5,4,1]=>00000 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[3,2,6,5,4,1]=>00000 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[3,2,6,5,4,1]=>00000 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6]=>00011 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[3,4,2,1,5,6]=>00011 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[3,4,2,1,6,5]=>00010 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[3,4,2,1,6,5]=>00010 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[3,4,2,1,6,5]=>00010 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6]=>00001 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[3,4,2,5,1,6]=>00001 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1]=>00000 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,1]=>00000 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[3,4,2,5,6,1]=>00000 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[3,4,2,6,5,1]=>00000 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[3,4,2,6,5,1]=>00000 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[3,4,2,6,5,1]=>00000 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[3,4,2,6,5,1]=>00000 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6]=>00001 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[3,4,5,2,1,6]=>00001 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1]=>00000 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,1]=>00000 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[3,4,5,2,6,1]=>00000 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1]=>00000 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,1]=>00000 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[3,4,5,6,2,1]=>00000 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[3,4,5,6,2,1]=>00000 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[3,4,6,5,2,1]=>00000 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[3,4,6,5,2,1]=>00000 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[3,4,6,5,2,1]=>00000 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[3,4,6,5,2,1]=>00000 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[3,4,6,5,2,1]=>00000 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[3,5,4,2,1,6]=>00001 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[3,5,4,2,1,6]=>00001 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[3,5,4,2,6,1]=>00000 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[3,5,4,2,6,1]=>00000 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[3,5,4,2,6,1]=>00000 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[3,5,4,6,2,1]=>00000 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[3,5,4,6,2,1]=>00000 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[3,5,4,6,2,1]=>00000 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[3,5,4,6,2,1]=>00000 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[3,5,6,4,2,1]=>00000 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[3,5,6,4,2,1]=>00000 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[3,5,6,4,2,1]=>00000 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[3,5,6,4,2,1]=>00000 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[3,5,6,4,2,1]=>00000 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[3,6,5,4,2,1]=>00000 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[3,6,5,4,2,1]=>00000 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[3,6,5,4,2,1]=>00000 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[3,6,5,4,2,1]=>00000 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[3,6,5,4,2,1]=>00000 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[3,6,5,4,2,1]=>00000 [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]=>00011 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,6]=>00011 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5]=>00010 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[4,3,2,1,6,5]=>00010 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[4,3,2,1,6,5]=>00010 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6]=>00001 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[4,3,2,5,1,6]=>00001 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1]=>00000 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,1]=>00000 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[4,3,2,5,6,1]=>00000 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[4,3,2,6,5,1]=>00000 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[4,3,2,6,5,1]=>00000 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[4,3,2,6,5,1]=>00000 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[4,3,2,6,5,1]=>00000 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6]=>00001 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[4,3,5,2,1,6]=>00001 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1]=>00000 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,1]=>00000 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[4,3,5,2,6,1]=>00000 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1]=>00000 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,1]=>00000 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[4,3,5,6,2,1]=>00000 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[4,3,5,6,2,1]=>00000 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[4,3,6,5,2,1]=>00000 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[4,3,6,5,2,1]=>00000 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[4,3,6,5,2,1]=>00000 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[4,3,6,5,2,1]=>00000 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[4,3,6,5,2,1]=>00000 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6]=>00001 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[4,5,3,2,1,6]=>00001 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1]=>00000 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,1]=>00000 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[4,5,3,2,6,1]=>00000 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1]=>00000 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,1]=>00000 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[4,5,3,6,2,1]=>00000 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[4,5,3,6,2,1]=>00000 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1]=>00000 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,1]=>00000 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[4,5,6,3,2,1]=>00000 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,5,6,3,2,1]=>00000 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[4,5,6,3,2,1]=>00000 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[4,6,5,3,2,1]=>00000 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[4,6,5,3,2,1]=>00000 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[4,6,5,3,2,1]=>00000 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[4,6,5,3,2,1]=>00000 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[4,6,5,3,2,1]=>00000 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[4,6,5,3,2,1]=>00000 [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]=>00001 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,6]=>00001 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1]=>00000 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,1]=>00000 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[5,4,3,2,6,1]=>00000 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1]=>00000 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,1]=>00000 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[5,4,3,6,2,1]=>00000 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[5,4,3,6,2,1]=>00000 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1]=>00000 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,1]=>00000 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[5,4,6,3,2,1]=>00000 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[5,4,6,3,2,1]=>00000 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[5,4,6,3,2,1]=>00000 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1]=>00000 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,1]=>00000 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[5,6,4,3,2,1]=>00000 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[5,6,4,3,2,1]=>00000 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[5,6,4,3,2,1]=>00000 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[5,6,4,3,2,1]=>00000 [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]=>00000 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,1]=>00000 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[6,5,4,3,2,1]=>00000 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[6,5,4,3,2,1]=>00000 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[6,5,4,3,2,1]=>00000 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000 [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]=>111111 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6]=>111110 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,6,7,5]=>111100 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,7,6,5]=>111100 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,7,6,5]=>111100 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7]=>111011 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6]=>111010 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,5,6,7,4]=>111000 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[1,2,3,5,6,7,4]=>111000 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[1,2,3,5,7,6,4]=>111000 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[1,2,3,5,7,6,4]=>111000 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[1,2,3,5,7,6,4]=>111000 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[1,2,3,6,5,7,4]=>111000 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[1,2,3,6,5,7,4]=>111000 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>[1,2,3,6,7,5,4]=>111000 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[1,2,3,6,7,5,4]=>111000 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[1,2,3,6,7,5,4]=>111000 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[1,2,3,7,6,5,4]=>111000 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[1,2,3,7,6,5,4]=>111000 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[1,2,3,7,6,5,4]=>111000 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[1,2,3,7,6,5,4]=>111000 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,6,7,5]=>110100 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,7,6,5]=>110100 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,7,6,5]=>110100 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[1,2,4,7,6,5,3]=>110000 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[1,2,5,6,7,4,3]=>110000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7]=>101111 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6]=>101110 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,6,7,5]=>101100 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,7,6,5]=>101100 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,7,6,5]=>101100 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7]=>101011 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6]=>101010 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[1,3,2,7,6,5,4]=>101000 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,3,4,2,6,7,5]=>100100 [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[1,3,4,2,7,6,5]=>100100 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[1,3,4,2,7,6,5]=>100100 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[1,3,4,7,6,5,2]=>100000 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[1,3,5,6,7,4,2]=>100000 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[1,3,5,7,6,4,2]=>100000 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>[1,3,6,5,7,4,2]=>100000 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[1,4,3,2,6,7,5]=>100100 [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>[1,4,3,2,7,6,5]=>100100 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,7,6,5]=>100100 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[1,4,3,6,5,7,2]=>100000 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>[1,4,3,7,6,5,2]=>100000 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,4,3,7,6,5,2]=>100000 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[1,4,7,6,5,3,2]=>100000 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[1,5,4,3,6,7,2]=>100000 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,4,3,8,7,2]=>[1,5,6,4,3,7,2]=>100000 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[1,5,6,7,4,3,2]=>100000 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[1,6,7,5,4,3,2]=>100000 [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[1,7,6,5,4,3,2]=>100000 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,6,7,5]=>011100 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,7,6,5]=>011100 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,7,6,5]=>011100 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[2,1,3,7,6,5,4]=>011000 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,7]=>010101 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,6,7,5]=>010100 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,6,7,5]=>010100 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,7,6,5]=>010100 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,7,6,5]=>010100 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,6,5]=>010100 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[2,1,4,5,7,6,3]=>010000 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[2,1,4,6,5,3,7]=>010001 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[2,1,4,6,5,7,3]=>010000 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[2,1,4,7,6,5,3]=>010000 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,7]=>010011 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[2,1,5,6,4,3,7]=>010001 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[2,1,5,6,7,4,3]=>010000 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,7]=>010001 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[2,1,6,7,5,4,3]=>010000 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[2,1,6,7,5,4,3]=>010000 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[2,1,7,6,5,4,3]=>010000 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>010000 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[2,3,1,4,6,7,5]=>001100 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[2,3,1,4,7,6,5]=>001100 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[2,3,1,4,7,6,5]=>001100 [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[2,3,1,7,6,5,4]=>001000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7]=>000111 [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[2,3,4,1,5,6,7]=>000111 [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[2,3,4,1,5,7,6]=>000110 [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[2,3,4,1,5,7,6]=>000110 [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[2,3,4,1,5,7,6]=>000110 [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[2,3,4,1,6,5,7]=>000101 [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[2,3,4,1,6,5,7]=>000101 [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[2,3,4,1,6,7,5]=>000100 [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[2,3,4,1,6,7,5]=>000100 [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[2,3,4,1,6,7,5]=>000100 [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[2,3,4,1,7,6,5]=>000100 [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[2,3,4,1,7,6,5]=>000100 [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[2,3,4,1,7,6,5]=>000100 [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[2,3,4,1,7,6,5]=>000100 [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[2,3,4,5,1,7,6]=>000010 [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[2,3,4,7,6,5,1]=>000000 [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[2,3,5,4,1,7,6]=>000010 [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[2,3,5,6,7,4,1]=>000000 [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[2,3,6,5,4,1,7]=>000001 [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[2,4,3,1,6,5,7]=>000101 [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[2,4,3,1,6,7,5]=>000100 [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[2,4,3,1,6,7,5]=>000100 [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[2,4,3,1,7,6,5]=>000100 [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[2,4,3,1,7,6,5]=>000100 [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>[2,4,3,5,1,7,6]=>000010 [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[2,4,3,6,5,1,7]=>000001 [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[2,4,3,6,5,7,1]=>000000 [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[2,4,3,7,6,5,1]=>000000 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[2,4,5,3,1,7,6]=>000010 [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[2,4,7,6,5,3,1]=>000000 [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>[2,5,4,3,1,7,6]=>000010 [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[2,5,4,3,6,7,1]=>000000 [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[2,5,4,3,6,7,1]=>000000 [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>[2,5,4,3,7,6,1]=>000000 [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>[2,5,4,3,7,6,1]=>000000 [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[2,5,4,3,7,6,1]=>000000 [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[2,5,6,7,4,3,1]=>000000 [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[2,7,6,5,4,3,1]=>000000 [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[3,2,1,4,6,7,5]=>001100 [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5]=>001100 [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[3,2,1,4,7,6,5]=>001100 [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>[3,2,1,4,7,6,5]=>001100 [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,7,6,5]=>001100 [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6]=>001010 [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[3,2,1,5,6,7,4]=>001000 [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[3,2,1,5,6,7,4]=>001000 [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[3,2,1,5,7,6,4]=>001000 [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[3,2,1,5,7,6,4]=>001000 [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[3,2,1,5,7,6,4]=>001000 [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[3,2,1,6,5,7,4]=>001000 [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[3,2,1,6,5,7,4]=>001000 [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[3,2,1,6,7,5,4]=>001000 [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,6,7,8,5,4]=>[3,2,1,6,7,5,4]=>001000 [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[3,2,1,6,7,5,4]=>001000 [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[3,2,1,7,6,5,4]=>001000 [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[3,2,1,7,6,5,4]=>001000 [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[3,2,1,7,6,5,4]=>001000 [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[3,2,1,7,6,5,4]=>001000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7]=>000111 [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[3,2,4,1,5,6,7]=>000111 [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>[3,2,4,1,5,7,6]=>000110 [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>[3,2,4,1,5,7,6]=>000110 [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>[3,2,4,1,5,7,6]=>000110 [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>[3,2,4,1,6,5,7]=>000101 [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[3,2,4,1,6,5,7]=>000101 [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>[3,2,4,1,6,7,5]=>000100 [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[3,2,4,1,6,7,5]=>000100 [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[3,2,4,1,6,7,5]=>000100 [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>[3,2,4,1,7,6,5]=>000100 [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[3,2,4,1,7,6,5]=>000100 [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[3,2,4,1,7,6,5]=>000100 [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[3,2,4,1,7,6,5]=>000100 [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>[3,2,4,5,1,7,6]=>000010 [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[3,2,4,7,6,5,1]=>000000 [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[3,2,5,4,1,7,6]=>000010 [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[3,2,5,4,7,6,1]=>000000 [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[3,2,6,7,5,4,1]=>000000 [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[3,4,2,1,6,5,7]=>000101 [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[3,4,2,1,6,7,5]=>000100 [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[3,4,2,1,7,6,5]=>000100 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[3,4,2,1,7,6,5]=>000100 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[3,4,2,1,7,6,5]=>000100 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[3,4,2,5,1,7,6]=>000010 [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[3,4,2,7,6,5,1]=>000000 [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[3,4,5,2,1,7,6]=>000010 [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[3,4,7,6,5,2,1]=>000000 [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[3,5,4,2,1,7,6]=>000010 [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>[3,5,4,2,6,7,1]=>000000 [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,4,2,7,6,1,8]=>[3,5,4,2,7,6,1]=>000000 [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[3,5,6,7,4,2,1]=>000000 [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]=>000111 [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,7]=>000111 [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6]=>000110 [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,7,6]=>000110 [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,7,6]=>000110 [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7]=>000101 [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,7]=>000101 [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,6,7,5]=>000100 [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,6,7,5]=>000100 [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,6,7,5]=>000100 [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5]=>000100 [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,7,6,5]=>000100 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,7,6,5]=>000100 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,7,6,5]=>000100 [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[4,3,2,5,1,7,6]=>000010 [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[4,3,2,7,6,5,1]=>000000 [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>[4,3,5,2,1,7,6]=>000010 [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>[4,5,3,2,1,7,6]=>000010 [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,5,3,2,6,1,7,8]=>[4,5,3,2,6,1,7]=>000001 [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,3,2,6,1,8,7]=>[4,5,3,2,6,1,7]=>000001 [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>[4,5,3,2,7,6,1]=>000000 [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[4,5,3,6,2,1,7]=>000001 [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[4,5,6,3,2,1,7]=>000001 [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,3,2,1]=>000000 [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[4,7,6,5,3,2,1]=>000000 [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[4,7,6,5,3,2,1]=>000000 [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]=>000011 [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,7]=>000011 [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6]=>000010 [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[5,4,3,2,1,7,6]=>000010 [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,7,6]=>000010 [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7]=>000001 [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[5,4,3,2,6,1,7]=>000001 [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,6,7,1]=>000000 [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,1]=>000000 [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>[5,4,3,2,6,7,1]=>000000 [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[5,4,3,2,7,6,1]=>000000 [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[5,4,3,2,7,6,1]=>000000 [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[5,4,3,2,7,6,1]=>000000 [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[5,4,3,2,7,6,1]=>000000 [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,4,3,6,2,1,8,7]=>[5,4,3,6,2,1,7]=>000001 [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,1]=>000000 [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,2,1]=>000000 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1]=>000000 [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[5,6,7,4,3,2,1]=>000000 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[5,7,6,4,3,2,1]=>000000 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,7]=>000001 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
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
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.