Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00096: Binary words —Foata bijection⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0,1,0]=>[2,1]=>0=>0 [1,1,0,0]=>[1,2]=>1=>1 [1,0,1,0,1,0]=>[3,2,1]=>00=>00 [1,0,1,1,0,0]=>[2,3,1]=>00=>00 [1,1,0,0,1,0]=>[3,1,2]=>00=>00 [1,1,0,1,0,0]=>[2,1,3]=>01=>01 [1,1,1,0,0,0]=>[1,2,3]=>11=>11 [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>000=>000 [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>000=>000 [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>000=>000 [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>000=>000 [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>000=>000 [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>000=>000 [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>000=>000 [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>000=>000 [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>001=>001 [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>001=>001 [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>000=>000 [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>001=>001 [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>011=>011 [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>111=>111 [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>0000=>0000 [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>0000=>0000 [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>0000=>0000 [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>0000=>0000 [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>0000=>0000 [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>0000=>0000 [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>0000=>0000 [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>0000=>0000 [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>0000=>0000 [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>0000=>0000 [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>0000=>0000 [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>0000=>0000 [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>0000=>0000 [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>0000=>0000 [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>0000=>0000 [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>0000=>0000 [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>0000=>0000 [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>0000=>0000 [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>0000=>0000 [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>0000=>0000 [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>0000=>0000 [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>0000=>0000 [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>0001=>0001 [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>0001=>0001 [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>0000=>0000 [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>0001=>0001 [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>0001=>0001 [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>0001=>0001 [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>0000=>0000 [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>0000=>0000 [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>0000=>0000 [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>0001=>0001 [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>0001=>0001 [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>0000=>0000 [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>0001=>0001 [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>0011=>0011 [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>0011=>0011 [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>0000=>0000 [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>0001=>0001 [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>0011=>0011 [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>0111=>0111 [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>1111=>1111 [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>00000=>00000 [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>00000=>00000 [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>00000=>00000 [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>00000=>00000 [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>00000=>00000 [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>00000=>00000 [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>00000=>00000 [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>00000=>00000 [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>00000=>00000 [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>00000=>00000 [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>00000=>00000 [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>00000=>00000 [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>00000=>00000 [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>00000=>00000 [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>00000=>00000 [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>00000=>00000 [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>00000=>00000 [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>00000=>00000 [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>00000=>00000 [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>00000=>00000 [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>00000=>00000 [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>00000=>00000 [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>00000=>00000 [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>00000=>00000 [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>00000=>00000 [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>00000=>00000 [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>00000=>00000 [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>00000=>00000 [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>00000=>00000 [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>00000=>00000 [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>00000=>00000 [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>00000=>00000 [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>00000=>00000 [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>00000=>00000 [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>00000=>00000 [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>00000=>00000 [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>00000=>00000 [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>00000=>00000 [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>00000=>00000 [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>00000=>00000 [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>00000=>00000 [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>00000=>00000 [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>00000=>00000 [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>00000=>00000 [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>00000=>00000 [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>00000=>00000 [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>00000=>00000 [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>00000=>00000 [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>00000=>00000 [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>00000=>00000 [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>00000=>00000 [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>00000=>00000 [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>00000=>00000 [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>00000=>00000 [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>00000=>00000 [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>00000=>00000 [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>00000=>00000 [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>00000=>00000 [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>00000=>00000 [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>00000=>00000 [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>00000=>00000 [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>00000=>00000 [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>00000=>00000 [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>00000=>00000 [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>00001=>00001 [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>00001=>00001 [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>00000=>00000 [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>00001=>00001 [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>00001=>00001 [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>00001=>00001 [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>00000=>00000 [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>00000=>00000 [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>00000=>00000 [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>00001=>00001 [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>00001=>00001 [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>00000=>00000 [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>00001=>00001 [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>00001=>00001 [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>00001=>00001 [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>00000=>00000 [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>00001=>00001 [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>00001=>00001 [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>00001=>00001 [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>00001=>00001 [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>00000=>00000 [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>00000=>00000 [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>00000=>00000 [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>00000=>00000 [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>00000=>00000 [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>00000=>00000 [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>00000=>00000 [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>00000=>00000 [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>00001=>00001 [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>00001=>00001 [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>00000=>00000 [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>00001=>00001 [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>00001=>00001 [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>00001=>00001 [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>00000=>00000 [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>00000=>00000 [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>00000=>00000 [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>00001=>00001 [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>00001=>00001 [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>00000=>00000 [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>00001=>00001 [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>00011=>00011 [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>00011=>00011 [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>00000=>00000 [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>00001=>00001 [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>00011=>00011 [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>00011=>00011 [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>00011=>00011 [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>00000=>00000 [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>00000=>00000 [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>00000=>00000 [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>00001=>00001 [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>00001=>00001 [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>00000=>00000 [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>00001=>00001 [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>00011=>00011 [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>00011=>00011 [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>00000=>00000 [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>00001=>00001 [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>00011=>00011 [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>00111=>00111 [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>00111=>00111 [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>00000=>00000 [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>00001=>00001 [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>00011=>00011 [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>00111=>00111 [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>01111=>01111 [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>11111=>11111 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>000000=>000000 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>000000=>000000 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>000000=>000000 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>000000=>000000 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>000000=>000000 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>000000=>000000 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>000000=>000000 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>000000=>000000 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>000000=>000000 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>000000=>000000 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>000000=>000000 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>000000=>000000 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>000000=>000000 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>000000=>000000 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>000000=>000000 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>000000=>000000 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>000000=>000000 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>000000=>000000 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>000000=>000000 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>000000=>000000 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>000000=>000000 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>000000=>000000 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>000000=>000000 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>000000=>000000 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>000000=>000000 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>000000=>000000 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>000000=>000000 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>000000=>000000 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>000000=>000000 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>000000=>000000 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>000000=>000000 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>000000=>000000 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>000000=>000000 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>000000=>000000 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>000000=>000000 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>000000=>000000 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>000000=>000000 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>000000=>000000 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>000000=>000000 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>000000=>000000 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>000000=>000000 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>000000=>000000 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>000000=>000000 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>000000=>000000 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>000000=>000000 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>000000=>000000 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>000000=>000000 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>000000=>000000 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>000000=>000000 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>000000=>000000 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>000000=>000000 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>000000=>000000 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>000000=>000000 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>000000=>000000 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>000000=>000000 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>000000=>000000 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>000000=>000000 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>000000=>000000 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>000000=>000000 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>000000=>000000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>000000=>000000 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>000000=>000000 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>000000=>000000 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>000000=>000000 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>000000=>000000 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>000000=>000000 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>000000=>000000 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>000000=>000000 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>000000=>000000 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>000000=>000000 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>000000=>000000 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>000000=>000000 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>000000=>000000 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>000000=>000000 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>000000=>000000 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>000000=>000000 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>000000=>000000 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>000000=>000000 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>000000=>000000 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>000000=>000000 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>000000=>000000 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>000000=>000000 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>000000=>000000 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>000000=>000000 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>000000=>000000 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>000000=>000000 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>000000=>000000 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>000000=>000000 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>000000=>000000 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>000000=>000000 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>000000=>000000 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>000000=>000000 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>000000=>000000 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>000000=>000000 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>000000=>000000 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[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>000001=>000001 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>000001=>000001 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>000001=>000001 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>000001=>000001 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>000000=>000000 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>000001=>000001 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>000001=>000001 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>000001=>000001 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>000001=>000001 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>000001=>000001 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>000000=>000000 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>000000=>000000 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>000000=>000000 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>000000=>000000 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>000000=>000000 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>000000=>000000 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>000000=>000000 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>000000=>000000 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>000000=>000000 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>000000=>000000 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>000001=>000001 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>000001=>000001 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>000000=>000000 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>000001=>000001 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>000001=>000001 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>000001=>000001 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>000000=>000000 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>000000=>000000 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>000000=>000000 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>000001=>000001 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>000001=>000001 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>000000=>000000 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>000001=>000001 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>000001=>000001 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>000001=>000001 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>000000=>000000 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>000001=>000001 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>000001=>000001 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>000001=>000001 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>000001=>000001 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>000000=>000000 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>000000=>000000 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>000000=>000000 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>000000=>000000 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>000000=>000000 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>000000=>000000 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>000000=>000000 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>000000=>000000 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[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>000000=>000000 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>000001=>000001 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>000011=>000011 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>000011=>000011 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>000011=>000011 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>000000=>000000 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>000000=>000000 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>000000=>000000 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>000001=>000001 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>000001=>000001 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>000000=>000000 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>000001=>000001 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>000011=>000011 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>000011=>000011 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>000000=>000000 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>000001=>000001 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>000011=>000011 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>000011=>000011 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>000011=>000011 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>000000=>000000 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>000001=>000001 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>000011=>000011 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>000011=>000011 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>000011=>000011 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>000011=>000011 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>000000=>000000 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>000000=>000000 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>000000=>000000 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>000000=>000000 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>000000=>000000 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>000000=>000000 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>000000=>000000 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>000000=>000000 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>000001=>000001 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>000001=>000001 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>000000=>000000 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>000001=>000001 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>000001=>000001 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>000001=>000001 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>000000=>000000 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>000000=>000000 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>000000=>000000 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>000001=>000001 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>000001=>000001 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>000000=>000000 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>000001=>000001 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>000011=>000011 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>000011=>000011 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>000000=>000000 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>000001=>000001 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>000011=>000011 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>000011=>000011 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>000011=>000011 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>000000=>000000 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>000000=>000000 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>000000=>000000 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>000001=>000001 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>000001=>000001 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>000000=>000000 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>000001=>000001 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>000011=>000011 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>000011=>000011 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>000000=>000000 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>000001=>000001 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>000011=>000011 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>000111=>000111 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>000111=>000111 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>000000=>000000 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>000001=>000001 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>000011=>000011 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>000111=>000111 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>000111=>000111 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>000111=>000111 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>000000=>000000 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>000000=>000000 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>000000=>000000 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>000001=>000001 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>000001=>000001 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>000000=>000000 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>000001=>000001 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>000011=>000011 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>000011=>000011 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>000000=>000000 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>000001=>000001 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>000011=>000011 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>000111=>000111 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>000111=>000111 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>000000=>000000 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>000001=>000001 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>000011=>000011 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>000111=>000111 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>001111=>001111 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>001111=>001111 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>000000=>000000 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>000001=>000001 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>000011=>000011 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>000111=>000111 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>001111=>001111 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>011111=>011111 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>111111=>111111 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>0000000=>0000000 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>0000000=>0000000 [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>0000000=>0000000 [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,2,1]=>0000000=>0000000 [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>0000000=>0000000 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>0000000=>0000000 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>0000000=>0000000 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>0000000=>0000000 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>0000000=>0000000 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>0000000=>0000000 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>0000000=>0000000 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>0000000=>0000000 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>0000000=>0000000 [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>0000000=>0000000 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>0000000=>0000000 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>0000000=>0000000 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>0000000=>0000000 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>0000000=>0000000 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>0000000=>0000000 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>0000000=>0000000 [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>0000000=>0000000 [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>0000000=>0000000 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>0000000=>0000000 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>0000000=>0000000 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>0000000=>0000000 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>0000000=>0000000 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>0000000=>0000000 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>0000000=>0000000 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>0000000=>0000000 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>0000000=>0000000 [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>0000000=>0000000 [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,8,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>0000000=>0000000 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>0000000=>0000000 [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>0000000=>0000000 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,8,1]=>0000000=>0000000 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>0000000=>0000000 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>0000000=>0000000 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>0000000=>0000000 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>0000000=>0000000 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>0000000=>0000000 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>0000000=>0000000 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>0000000=>0000000 [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>0000000=>0000000 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>0000000=>0000000 [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>0000000=>0000000 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>0000000=>0000000 [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>0000000=>0000000 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,5,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,8,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,7,8,1]=>0000000=>0000000 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,8,1]=>0000000=>0000000 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>0000000=>0000000 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>0000000=>0000000 [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>0000000=>0000000 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>0000000=>0000000 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>0000000=>0000000 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>0000000=>0000000 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>0000000=>0000000 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>0000000=>0000000 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>0000000=>0000000 [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>0000000=>0000000 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>0000000=>0000000 [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>0000000=>0000000 [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>0000000=>0000000 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>0000000=>0000000 [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>0000000=>0000000 [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>0000000=>0000000 [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>0000000=>0000000 [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>0000000=>0000000 [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>0000000=>0000000 [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>0000000=>0000000 [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>0000000=>0000000 [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>0000001=>0000001 [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>0000000=>0000000 [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>0000001=>0000001 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>0000000=>0000000 [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>0000000=>0000000 [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>0000000=>0000000 [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>0000000=>0000000 [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>0000001=>0000001 [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>0000000=>0000000 [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>0000000=>0000000 [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>0000001=>0000001 [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>0000001=>0000001 [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>0000001=>0000001 [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>0000000=>0000000 [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>0000000=>0000000 [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>0000000=>0000000 [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>0000000=>0000000 [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>0000000=>0000000 [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>0000001=>0000001 [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>0000000=>0000000 [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>0000000=>0000000 [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>0000000=>0000000 [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>0000000=>0000000 [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>0000001=>0000001 [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>0000001=>0000001 [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>0000001=>0000001 [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,7,1,8]=>0000001=>0000001 [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>0000001=>0000001 [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>0000000=>0000000 [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>0000000=>0000000 [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>0000000=>0000000 [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>0000000=>0000000 [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>0000000=>0000000 [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>0000000=>0000000 [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>0000000=>0000000 [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>0000000=>0000000 [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>0000000=>0000000 [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>0000000=>0000000 [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,1,2,7]=>0000000=>0000000 [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>0000000=>0000000 [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>0000000=>0000000 [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>0000000=>0000000 [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>0000000=>0000000 [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>0000001=>0000001 [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>0000001=>0000001 [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>0000001=>0000001 [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>0000000=>0000000 [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>0000000=>0000000 [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>0000001=>0000001 [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>0000000=>0000000 [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>0000000=>0000000 [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>0000000=>0000000 [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>0000000=>0000000 [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>0000000=>0000000 [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>0000000=>0000000 [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>0000000=>0000000 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>0000000=>0000000 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>0000000=>0000000 [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>0000000=>0000000 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>0000000=>0000000 [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>0000000=>0000000 [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>0000000=>0000000 [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>0000000=>0000000 [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>0000000=>0000000 [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>0000000=>0000000 [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>0000000=>0000000 [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>0000000=>0000000 [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>0000001=>0000001 [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>0000000=>0000000 [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>0000011=>0000011 [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>0000011=>0000011 [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>0000000=>0000000 [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>0000000=>0000000 [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>0000000=>0000000 [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,1,5,8]=>0000001=>0000001 [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,1,6,7]=>0000000=>0000000 [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>0000011=>0000011 [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>0000011=>0000011 [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>0000000=>0000000 [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>0000000=>0000000 [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>0000000=>0000000 [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>0000000=>0000000 [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>0000000=>0000000 [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>0000000=>0000000 [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>0000000=>0000000 [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>0000001=>0000001 [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>0000000=>0000000 [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>0000000=>0000000 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>0000000=>0000000 [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>0000001=>0000001 [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>0000011=>0000011 [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>0000011=>0000011 [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>0000011=>0000011 [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>0000000=>0000000 [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>0000001=>0000001 [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>0000001=>0000001 [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>0000001=>0000001 [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,1,7,8]=>0000011=>0000011 [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>0000011=>0000011 [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>0000011=>0000011 [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>0000001=>0000001 [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>0000000=>0000000 [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>0000000=>0000000 [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>0000000=>0000000 [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>0000000=>0000000 [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>0000001=>0000001 [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>0000001=>0000001 [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>0000000=>0000000 [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>0000001=>0000001 [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>0000000=>0000000 [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>0000000=>0000000 [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>0000000=>0000000 [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>0000001=>0000001 [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>0000000=>0000000 [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>0000011=>0000011 [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>0000011=>0000011 [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>0000000=>0000000 [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>0000000=>0000000 [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>0000011=>0000011 [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,1,2,7,8]=>0000011=>0000011 [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>0000011=>0000011 [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>0000000=>0000000 [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>0000000=>0000000 [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>0000000=>0000000 [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>0000000=>0000000 [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>0000000=>0000000 [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>0000000=>0000000 [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>0000001=>0000001 [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>0000000=>0000000 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>0000000=>0000000 [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>0000000=>0000000 [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>0000011=>0000011 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>0000011=>0000011 [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>0000000=>0000000 [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>0000000=>0000000 [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>0000000=>0000000 [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>0000001=>0000001 [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,1,4,5,8]=>0000001=>0000001 [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>0000001=>0000001 [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>0000011=>0000011 [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>0000000=>0000000 [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>0000001=>0000001 [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>0000011=>0000011 [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,1,5,7,8]=>0000011=>0000011 [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>0000000=>0000000 [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>0000000=>0000000 [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>0000111=>0000111 [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>0000111=>0000111 [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>0000000=>0000000 [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>0000000=>0000000 [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>0000000=>0000000 [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>0000000=>0000000 [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>0000000=>0000000 [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>0000000=>0000000 [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>0000000=>0000000 [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>0000000=>0000000 [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>0000001=>0000001 [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>0000001=>0000001 [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>0000000=>0000000 [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>0000001=>0000001 [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>0000001=>0000001 [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>0000001=>0000001 [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>0000000=>0000000 [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,1,2,3,6,8]=>0000001=>0000001 [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>0000000=>0000000 [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>0000001=>0000001 [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>0000001=>0000001 [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>0000001=>0000001 [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>0000011=>0000011 [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>0000111=>0000111 [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>0000111=>0000111 [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>0000000=>0000000 [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>0000000=>0000000 [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>0000011=>0000011 [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>0000111=>0000111 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>0000000=>0000000 [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>0000111=>0000111 [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>0001111=>0001111 [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>0001111=>0001111 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>0000000=>0000000 [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>0000111=>0000111 [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>0001111=>0001111 [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>0001111=>0001111 [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>0001111=>0001111 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>0000000=>0000000 [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>0000001=>0000001 [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>0000001=>0000001 [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>0000111=>0000111 [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>0000111=>0000111 [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>0000001=>0000001 [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>0000111=>0000111 [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>0001111=>0001111 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>0001111=>0001111 [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>0000111=>0000111 [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>0001111=>0001111 [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>0011111=>0011111 [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>0011111=>0011111 [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>0000001=>0000001 [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>0000111=>0000111 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>0001111=>0001111 [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>0011111=>0011111 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>0111111=>0111111 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>1111111=>1111111 [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>000000000=>000000000 [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>000011111=>000011111 [1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,7,8,9,10,1,2]=>000000000=>000000000
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
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.
Map
Foata bijection
Description
The Foata bijection $\phi$ is a bijection on the set of words of given content (by a slight generalization of Section 2 in [1]).
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$. At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
For instance, to compute $\phi(4154223)$, the sequence of words is
  • 4,
  • |4|1 -- > 41,
  • |4|1|5 -- > 415,
  • |415|4 -- > 5414,
  • |5|4|14|2 -- > 54412,
  • |5441|2|2 -- > 154422,
  • |1|5442|2|3 -- > 1254423.
So $\phi(4154223) = 1254423$.