Identifier
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=> [1,0,1,0]=>[1,2]=>0 [1,1,0,0]=>[2,1]=>1 [1,0,1,0,1,0]=>[1,2,3]=>00 [1,0,1,1,0,0]=>[1,3,2]=>01 [1,1,0,0,1,0]=>[2,1,3]=>10 [1,1,0,1,0,0]=>[2,3,1]=>01 [1,1,1,0,0,0]=>[3,1,2]=>01 [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>000 [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>001 [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>010 [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>001 [1,0,1,1,1,0,0,0]=>[1,4,2,3]=>001 [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>100 [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>101 [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>010 [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>001 [1,1,0,1,1,0,0,0]=>[2,4,1,3]=>001 [1,1,1,0,0,0,1,0]=>[3,1,2,4]=>010 [1,1,1,0,0,1,0,0]=>[3,1,4,2]=>011 [1,1,1,0,1,0,0,0]=>[3,4,1,2]=>001 [1,1,1,1,0,0,0,0]=>[4,1,2,3]=>001 [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>0000 [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>0001 [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>0010 [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>0001 [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,3,4]=>0001 [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>0100 [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>0101 [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>0010 [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>0001 [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>0001 [1,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,5]=>0010 [1,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3]=>0011 [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,2,3]=>0001 [1,0,1,1,1,1,0,0,0,0]=>[1,5,2,3,4]=>0001 [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>1000 [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>1001 [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>1010 [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>1001 [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,4]=>1001 [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>0100 [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>0101 [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>0010 [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>0001 [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>0001 [1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,5]=>0010 [1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,3]=>0011 [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,3]=>0001 [1,1,0,1,1,1,0,0,0,0]=>[2,5,1,3,4]=>0001 [1,1,1,0,0,0,1,0,1,0]=>[3,1,2,4,5]=>0100 [1,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4]=>0101 [1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,5]=>0110 [1,1,1,0,0,1,0,1,0,0]=>[3,1,4,5,2]=>0101 [1,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4]=>0101 [1,1,1,0,1,0,0,0,1,0]=>[3,4,1,2,5]=>0010 [1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,2]=>0011 [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,2]=>0001 [1,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4]=>0001 [1,1,1,1,0,0,0,0,1,0]=>[4,1,2,3,5]=>0010 [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,3]=>0011 [1,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,3]=>0011 [1,1,1,1,0,1,0,0,0,0]=>[4,5,1,2,3]=>0001 [1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4]=>0001 [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>00000 [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>00001 [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>00010 [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>00001 [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,4,5]=>00001 [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>00100 [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>00101 [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>00010 [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>00001 [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5]=>00001 [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,3,4,6]=>00010 [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,3,6,4]=>00011 [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,3,4]=>00001 [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,3,4,5]=>00001 [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>01000 [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>01001 [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>01010 [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>01001 [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,4,5]=>01001 [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>00100 [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>00101 [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>00010 [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>00001 [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,2,5]=>00001 [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,6]=>00010 [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,6,4]=>00011 [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,2,4]=>00001 [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,2,4,5]=>00001 [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,5,6]=>00100 [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5]=>00101 [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3,6]=>00110 [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,6,3]=>00101 [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5]=>00101 [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,2,3,6]=>00010 [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,2,6,3]=>00011 [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,2,3]=>00001 [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5]=>00001 [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,6]=>00010 [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,4]=>00011 [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,2,6,3,4]=>00011 [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,2,3,4]=>00001 [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,2,3,4,5]=>00001 [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>10000 [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>10001 [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>10010 [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>10001 [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,4,5]=>10001 [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>10100 [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>10101 [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>10010 [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>10001 [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5]=>10001 [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,3,4,6]=>10010 [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,6,4]=>10011 [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,3,4]=>10001 [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5]=>10001 [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>01000 [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>01001 [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>01010 [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>01001 [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,4,5]=>01001 [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>00100 [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>00101 [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>00010 [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>00001 [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,1,5]=>00001 [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,6]=>00010 [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,6,4]=>00011 [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,1,4]=>00001 [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,1,4,5]=>00001 [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,5,6]=>00100 [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5]=>00101 [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,5,3,6]=>00110 [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,6,3]=>00101 [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5]=>00101 [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,1,3,6]=>00010 [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,1,6,3]=>00011 [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,1,3]=>00001 [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5]=>00001 [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,6]=>00010 [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,1,3,6,4]=>00011 [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,1,6,3,4]=>00011 [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,1,3,4]=>00001 [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,3,4,5]=>00001 [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,5,6]=>01000 [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,5]=>01001 [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,6]=>01010 [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,6,4]=>01001 [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,6,4,5]=>01001 [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>01100 [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,4,2,6,5]=>01101 [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>01010 [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,2]=>01001 [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,4,6,2,5]=>01001 [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,6]=>01010 [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,6,4]=>01011 [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,6,2,4]=>01001 [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,2,4,5]=>01001 [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,1,2,5,6]=>00100 [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5]=>00101 [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,1,5,2,6]=>00110 [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,6,2]=>00101 [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5]=>00101 [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,1,2,6]=>00010 [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,1,6,2]=>00011 [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,1,2]=>00001 [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5]=>00001 [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,6]=>00010 [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,6,4]=>00011 [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,6,2,4]=>00011 [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,1,2,4]=>00001 [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,1,2,4,5]=>00001 [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,6]=>00100 [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5]=>00101 [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>00110 [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,6,3]=>00101 [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5]=>00101 [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,5,2,3,6]=>00110 [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,5,2,6,3]=>00111 [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,5,6,2,3]=>00101 [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5]=>00101 [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,1,2,3,6]=>00010 [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,1,2,6,3]=>00011 [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,1,6,2,3]=>00011 [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,1,2,3]=>00001 [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5]=>00001 [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>00010 [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,6,4]=>00011 [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1,2,6,3,4]=>00011 [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1,6,2,3,4]=>00011 [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,1,2,3,4]=>00001 [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5]=>00001 [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>000000 [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>000001 [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>000010 [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>000001 [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,5,6]=>000001 [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>000100 [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>000101 [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>000010 [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>000001 [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6]=>000001 [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,7]=>000010 [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,4,7,5]=>000011 [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,4,5]=>000001 [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>000001 [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>001000 [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>001001 [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>001010 [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>001001 [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,5,6]=>001001 [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>000100 [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>000101 [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>000010 [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>000001 [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6]=>000001 [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,7]=>000010 [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,7,5]=>000011 [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,3,5]=>000001 [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>000001 [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,6,7]=>000100 [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6]=>000101 [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,6,4,7]=>000110 [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,6,7,4]=>000101 [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6]=>000101 [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,3,4,7]=>000010 [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,3,7,4]=>000011 [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,3,4]=>000001 [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>000001 [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,7]=>000010 [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,7,5]=>000011 [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>000011 [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>000001 [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6]=>000001 [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>010000 [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>010001 [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>010010 [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>010001 [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,5,6]=>010001 [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>010100 [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>010101 [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>010010 [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>010001 [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6]=>010001 [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,7]=>010010 [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,7,5]=>010011 [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,4,5]=>010001 [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,4,5,6]=>010001 [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>001000 [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>001001 [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>001010 [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>001001 [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,5,6]=>001001 [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>000100 [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>000101 [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>000010 [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>000001 [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6]=>000001 [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,7]=>000010 [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,7,5]=>000011 [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,2,5]=>000001 [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>000001 [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,6,7]=>000100 [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6]=>000101 [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,6,4,7]=>000110 [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,6,7,4]=>000101 [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6]=>000101 [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,2,4,7]=>000010 [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,2,7,4]=>000011 [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,2,4]=>000001 [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>000001 [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,7]=>000010 [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,7,5]=>000011 [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>000011 [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>000001 [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6]=>000001 [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7]=>001000 [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,5,7,6]=>001001 [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,7]=>001010 [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,7,5]=>001001 [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,7,5,6]=>001001 [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,3,6,7]=>001100 [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6]=>001101 [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,3,7]=>001010 [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,3]=>001001 [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6]=>001001 [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,7]=>001010 [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,7,5]=>001011 [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,7,3,5]=>001001 [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,7,3,5,6]=>001001 [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,6,7]=>000100 [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6]=>000101 [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,2,6,3,7]=>000110 [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,2,6,7,3]=>000101 [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6]=>000101 [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,2,3,7]=>000010 [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,2,7,3]=>000011 [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,2,3]=>000001 [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>000001 [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,7]=>000010 [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,7,5]=>000011 [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>000011 [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>000001 [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,2,3,5,6]=>000001 [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,6,7]=>000100 [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6]=>000101 [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,6,4,7]=>000110 [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,6,7,4]=>000101 [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6]=>000101 [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,6,3,4,7]=>000110 [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,7,4]=>000111 [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,6,7,3,4]=>000101 [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6]=>000101 [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,7]=>000010 [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,2,3,7,4]=>000011 [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>000011 [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>000001 [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,2,3,4,6]=>000001 [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,7]=>000010 [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>000011 [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,7,4,5]=>000011 [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,7,3,4,5]=>000011 [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,2,3,4,5]=>000001 [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>000001 [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>100000 [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>100001 [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>100010 [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>100001 [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,5,6]=>100001 [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>100100 [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>100101 [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>100010 [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>100001 [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,4,6]=>100001 [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,7]=>100010 [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,4,7,5]=>100011 [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,4,5]=>100001 [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,4,5,6]=>100001 [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>101000 [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>101001 [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>101010 [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>101001 [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,5,6]=>101001 [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>100100 [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>100101 [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>100010 [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>100001 [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,3,6]=>100001 [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,7]=>100010 [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,7,5]=>100011 [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,3,5]=>100001 [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,3,5,6]=>100001 [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>100100 [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,3,4,7,6]=>100101 [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4,7]=>100110 [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,6,7,4]=>100101 [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6]=>100101 [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,3,4,7]=>100010 [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,3,7,4]=>100011 [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,3,4]=>100001 [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6]=>100001 [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,7]=>100010 [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,7,5]=>100011 [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,7,4,5]=>100011 [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,3,4,5]=>100001 [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6]=>100001 [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>010000 [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>010001 [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>010010 [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>010001 [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,5,6]=>010001 [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>010100 [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>010101 [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>010010 [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>010001 [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,4,6]=>010001 [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,4,5,7]=>010010 [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,7,5]=>010011 [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,4,5]=>010001 [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,4,5,6]=>010001 [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>001000 [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>001001 [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>001010 [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>001001 [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,5,6]=>001001 [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>000100 [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>000101 [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>000010 [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>000001 [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6]=>000001 [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,7]=>000010 [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,7,5]=>000011 [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,1,5]=>000001 [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>000001 [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,6,7]=>000100 [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6]=>000101 [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,6,4,7]=>000110 [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,1,6,7,4]=>000101 [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,7,4,6]=>000101 [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,1,4,7]=>000010 [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,1,7,4]=>000011 [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,1,4]=>000001 [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>000001 [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,7]=>000010 [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,7,5]=>000011 [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>000011 [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>000001 [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6]=>000001 [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7]=>001000 [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>001001 [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,7]=>001010 [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,7,5]=>001001 [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,7,5,6]=>001001 [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,5,3,6,7]=>001100 [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6]=>001101 [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,5,6,3,7]=>001010 [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,3]=>001001 [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,1,5,7,3,6]=>001001 [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,7]=>001010 [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,7,5]=>001011 [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,7,3,5]=>001001 [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,7,3,5,6]=>001001 [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,6,7]=>000100 [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6]=>000101 [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,1,6,3,7]=>000110 [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,1,6,7,3]=>000101 [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6]=>000101 [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,1,3,7]=>000010 [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,1,7,3]=>000011 [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,1,3]=>000001 [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>000001 [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,7]=>000010 [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,7,5]=>000011 [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>000011 [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>000001 [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,1,3,5,6]=>000001 [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,6,7]=>000100 [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>000101 [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,6,4,7]=>000110 [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,6,7,4]=>000101 [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,1,3,7,4,6]=>000101 [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,6,3,4,7]=>000110 [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,1,6,3,7,4]=>000111 [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,6,7,3,4]=>000101 [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,1,7,3,4,6]=>000101 [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,7]=>000010 [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,1,3,7,4]=>000011 [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>000011 [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>000001 [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,1,3,4,6]=>000001 [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,7]=>000010 [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,7,5]=>000011 [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,7,4,5]=>000011 [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,1,7,3,4,5]=>000011 [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,1,3,4,5]=>000001 [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>000001 [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7]=>010000 [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,7,6]=>010001 [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,7]=>010010 [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,4,6,7,5]=>010001 [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,7,5,6]=>010001 [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,5,4,6,7]=>010100 [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6]=>010101 [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,6,4,7]=>010010 [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,4]=>010001 [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6]=>010001 [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,7]=>010010 [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,6,4,7,5]=>010011 [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,6,7,4,5]=>010001 [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,7,4,5,6]=>010001 [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>011000 [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,5,7,6]=>011001 [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,7]=>011010 [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,7,5]=>011001 [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,7,5,6]=>011001 [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2,6,7]=>010100 [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6]=>010101 [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,6,2,7]=>010010 [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,2]=>010001 [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,4,5,7,2,6]=>010001 [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,7]=>010010 [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,7,5]=>010011 [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,7,2,5]=>010001 [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,4,7,2,5,6]=>010001 [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>010100 [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6]=>010101 [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4,7]=>010110 [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,6,7,4]=>010101 [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6]=>010101 [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,2,4,7]=>010010 [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,6,2,7,4]=>010011 [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,2,4]=>010001 [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6]=>010001 [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,7]=>010010 [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,7,5]=>010011 [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,7,4,5]=>010011 [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,6,7,2,4,5]=>010001 [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6]=>010001 [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7]=>001000 [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>001001 [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,7]=>001010 [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,7,5]=>001001 [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,7,5,6]=>001001 [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,5,2,6,7]=>001100 [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6]=>001101 [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,2,7]=>001010 [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,6,7,2]=>001001 [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6]=>001001 [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,7]=>001010 [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,7,5]=>001011 [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,7,2,5]=>001001 [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,1,7,2,5,6]=>001001 [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,6,7]=>000100 [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,1,2,7,6]=>000101 [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,1,6,2,7]=>000110 [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,1,6,7,2]=>000101 [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6]=>000101 [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,1,2,7]=>000010 [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,1,7,2]=>000011 [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,1,2]=>000001 [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>000001 [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,7]=>000010 [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,1,2,7,5]=>000011 [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>000011 [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>000001 [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6]=>000001 [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,6,7]=>000100 [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>000101 [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,6,4,7]=>000110 [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,6,7,4]=>000101 [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6]=>000101 [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,6,2,4,7]=>000110 [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,2,7,4]=>000111 [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,6,7,2,4]=>000101 [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6]=>000101 [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,7]=>000010 [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,1,2,7,4]=>000011 [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>000011 [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>000001 [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6]=>000001 [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,7]=>000010 [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,7,5]=>000011 [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,7,4,5]=>000011 [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,1,7,2,4,5]=>000011 [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,1,2,4,5]=>000001 [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>000001 [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7]=>001000 [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,5,7,6]=>001001 [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,7]=>001010 [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,7,5]=>001001 [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,7,5,6]=>001001 [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,5,3,6,7]=>001100 [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6]=>001101 [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,6,3,7]=>001010 [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,3]=>001001 [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6]=>001001 [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,7]=>001010 [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,7,5]=>001011 [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,6,7,3,5]=>001001 [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,7,3,5,6]=>001001 [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>001100 [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6]=>001101 [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3,7]=>001110 [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,5,2,6,7,3]=>001101 [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6]=>001101 [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,5,6,2,3,7]=>001010 [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,5,6,2,7,3]=>001011 [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,5,6,7,2,3]=>001001 [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6]=>001001 [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,7]=>001010 [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,7,5]=>001011 [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,7,3,5]=>001011 [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,7,2,3,5]=>001001 [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6]=>001001 [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,6,7]=>000100 [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>000101 [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,6,3,7]=>000110 [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,6,7,3]=>000101 [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6]=>000101 [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,1,6,2,3,7]=>000110 [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,1,6,2,7,3]=>000111 [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,1,6,7,2,3]=>000101 [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6]=>000101 [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,7]=>000010 [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,1,2,7,3]=>000011 [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>000011 [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>000001 [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,1,2,3,6]=>000001 [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,7]=>000010 [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,7,5]=>000011 [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,7,3,5]=>000011 [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,7,2,3,5]=>000011 [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,1,2,3,5]=>000001 [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>000001 [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,6,7]=>000100 [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6]=>000101 [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,6,4,7]=>000110 [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,6,7,4]=>000101 [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,1,2,3,7,4,6]=>000101 [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,6,3,4,7]=>000110 [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,6,3,7,4]=>000111 [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,6,7,3,4]=>000101 [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6]=>000101 [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,7]=>000110 [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,6,2,3,7,4]=>000111 [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,6,2,7,3,4]=>000111 [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,6,7,2,3,4]=>000101 [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,1,7,2,3,4,6]=>000101 [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,7]=>000010 [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,7,4]=>000011 [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,1,2,7,3,4]=>000011 [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,1,7,2,3,4]=>000011 [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,1,2,3,4]=>000001 [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>000001 [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>000010 [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,7,5]=>000011 [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,7,4,5]=>000011 [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,7,3,4,5]=>000011 [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1,7,2,3,4,5]=>000011 [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>000001 [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>000001 [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>0000000 [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>0000001 [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>0000010 [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>0000001 [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,6,7]=>0000001 [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>0000100 [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>0000101 [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>0000010 [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>0000001 [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,5,7]=>0000001 [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,5,6,8]=>0000010 [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,5,8,6]=>0000011 [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,5,6]=>0000001 [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>0000001 [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>0001000 [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>0001010 [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>0001001 [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,6,7]=>0001001 [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>0000100 [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>0000101 [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>0000010 [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>0000001 [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,4,7]=>0000001 [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,4,6,8]=>0000010 [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,4,8,6]=>0000011 [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,4,6]=>0000001 [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>0000001 [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,4,5,7,8]=>0000100 [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,4,5,8,7]=>0000101 [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5,8]=>0000110 [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,4,7,8,5]=>0000101 [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,4,8,5,7]=>0000101 [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,4,5,8]=>0000010 [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,4,8,5]=>0000011 [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,4,5]=>0000001 [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,4,5,6,8]=>0000010 [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,4,5,8,6]=>0000011 [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,4,8,5,6]=>0000011 [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>0000001 [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>0000001 [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>0010000 [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>0010001 [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>0010001 [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>0010001 [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>0010100 [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>0010101 [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>0010010 [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>0010001 [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,5,7]=>0010001 [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,8,6]=>0010011 [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]=>0010001 [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,5,6,7]=>0010001 [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>0001001 [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,6,7]=>0001001 [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>0000100 [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,3,7]=>0000001 [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,4,5,7,3,8,6]=>0000011 [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,3,6,7]=>0000001 [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,3,5,7,8]=>0000100 [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,3,8,5,7]=>0000101 [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,4,6,7,3,8,5]=>0000011 [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,3,5,7]=>0000001 [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,3,8,5,6]=>0000011 [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>0000001 [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>0000001 [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,3,4,7,8,6]=>0001001 [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>0001001 [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,8,7]=>0001101 [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,3,6,7,8,4]=>0001001 [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,8,6]=>0001011 [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,3,7,8,4,6]=>0001001 [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,8,4,6,7]=>0001001 [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,3,4,7,8]=>0000100 [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,5,6,3,4,8,7]=>0000101 [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,3,7,4,8]=>0000110 [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,3,7,8,4]=>0000101 [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,5,6,3,8,4,7]=>0000101 [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,3,4]=>0000001 [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,3,4,7]=>0000001 [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,5,7,3,4,6,8]=>0000010 [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,3,4,8,6]=>0000011 [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,3,8,4,6]=>0000011 [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,8,3,4,6]=>0000001 [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>0000001 [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,3,4,5,7,8]=>0000100 [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,6,3,4,5,8,7]=>0000101 [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,6,3,4,7,5,8]=>0000110 [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,3,4,7,8,5]=>0000101 [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,3,4,8,5,7]=>0000101 [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,8,5]=>0000111 [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>0000101 [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,3,8,4,5,7]=>0000101 [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,6,7,3,4,8,5]=>0000011 [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,6,7,3,8,4,5]=>0000011 [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,3,4,5]=>0000001 [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>0000001 [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,3,4,5,6,8]=>0000010 [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,3,4,5,8,6]=>0000011 [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>0000011 [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>0000001 [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>0000001 [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>0100000 [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>0100010 [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>0100001 [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,6,7]=>0100001 [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>0100100 [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>0100101 [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>0100001 [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,5,7]=>0100001 [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>0100011 [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,2,4,7,8,5,6]=>0100001 [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,5,6,7]=>0100001 [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>0101000 [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>0101010 [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>0101001 [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,6,7]=>0101001 [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>0100100 [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,5,6,7,4,8]=>0100010 [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,4,6,8]=>0100010 [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]=>0100011 [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,4,6]=>0100001 [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,4,6,7]=>0100001 [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,4,5,7,8]=>0100100 [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5,8]=>0100110 [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]=>0100101 [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,8,5,7]=>0100101 [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,2,6,7,4,5,8]=>0100010 [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,4,5,6,8]=>0100010 [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,8,5,6]=>0100011 [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>0100001 [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>0010000 [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>0010001 [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>0010010 [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>0010001 [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>0010001 [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>0010010 [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>0010001 [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,5,6]=>0010001 [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,5,6,7]=>0010001 [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>0001000 [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,5,2,6,8,7]=>0001001 [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,8]=>0001010 [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>0001001 [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,5,2,8,6,7]=>0001001 [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>0000010 [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,5,7,2,6,8]=>0000010 [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,7,2,8,6]=>0000011 [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,2,6]=>0000001 [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,2,6,7]=>0000001 [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,4,6,2,5,8,7]=>0000101 [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,2,8,5]=>0000011 [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,8,2,5,7]=>0000001 [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,2,5,8,6]=>0000011 [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>0000001 [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,2,4,6,7,8]=>0001000 [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,2,4,6,8,7]=>0001001 [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,2,4,7,6,8]=>0001010 [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,2,4,7,8,6]=>0001001 [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]=>0001001 [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,4,7,8]=>0001100 [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,8,7]=>0001101 [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,2,6,7,4,8]=>0001010 [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,2,6,8,4,7]=>0001001 [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,2,7,4,6,8]=>0001010 [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,8,6]=>0001011 [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,8,4,6]=>0001001 [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,2,8,4,6,7]=>0001001 [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,2,4,7,8]=>0000100 [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,5,6,2,4,8,7]=>0000101 [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,2,7,4,8]=>0000110 [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,2,7,8,4]=>0000101 [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,2,4,8]=>0000010 [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,2,4]=>0000001 [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,2,4,6,8]=>0000010 [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,2,4,8,6]=>0000011 [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,2,8,4,6]=>0000011 [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>0000001 [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>0000001 [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,6,2,4,5,7,8]=>0000100 [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,2,4,7,5,8]=>0000110 [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,6,2,4,7,8,5]=>0000101 [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>0000101 [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,8,5]=>0000111 [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]=>0000101 [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,6,7,2,4,8,5]=>0000011 [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,7,2,4,5,8,6]=>0000011 [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>0000011 [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,7,2,8,4,5,6]=>0000011 [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>0000001 [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7,8]=>0010000 [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,3,5,6,8,7]=>0010001 [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,2,3,5,7,6,8]=>0010010 [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>0010001 [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,3,5,8,6,7]=>0010001 [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,3,6,5,7,8]=>0010100 [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7]=>0010101 [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,2,3,6,7,8,5]=>0010001 [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,7,5,6,8]=>0010010 [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,4,2,3,7,8,5,6]=>0010001 [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,3,8,5,6,7]=>0010001 [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,3,6,7,8]=>0011000 [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,3,6,8,7]=>0011001 [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6,8]=>0011010 [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,3,7,8,6]=>0011001 [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,8,6,7]=>0011001 [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,7,3,8]=>0010010 [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,2,5,7,3,6,8]=>0010010 [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>0010011 [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,2,5,7,8,3,6]=>0010001 [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,2,5,8,3,6,7]=>0010001 [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,6,3,5,7,8]=>0010100 [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,6,3,5,8,7]=>0010101 [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5,8]=>0010110 [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,8,5,7]=>0010101 [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,2,6,7,3,5,8]=>0010010 [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,2,6,7,8,3,5]=>0010001 [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,2,6,8,3,5,7]=>0010001 [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,7,3,5,6,8]=>0010010 [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>0010011 [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,8,5,6]=>0010011 [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,2,7,8,3,5,6]=>0010001 [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>0010001 [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,2,3,6,7,8]=>0001000 [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,2,3,7,6,8]=>0001010 [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,5,2,3,7,8,6]=>0001001 [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>0001001 [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,3,7,8]=>0001100 [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,8,7]=>0001101 [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,2,6,7,8,3]=>0001001 [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>0001001 [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,4,5,2,7,3,6,8]=>0001010 [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,8,6]=>0001011 [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,8,3,6]=>0001001 [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,2,8,3,6,7]=>0001001 [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,6,2,8,3,7]=>0000101 [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,2,3,8]=>0000010 [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,2,8,3]=>0000011 [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,6,8,2,3,7]=>0000001 [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,4,5,7,2,3,6,8]=>0000010 [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,5,7,2,3,8,6]=>0000011 [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,7,8,2,3,6]=>0000001 [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,8,2,3,6,7]=>0000001 [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,6,2,3,7,8,5]=>0000101 [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>0000101 [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,2,7,3,5,8]=>0000110 [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,8,5]=>0000111 [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>0000101 [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,2,8,3,5,7]=>0000101 [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,2,8,3,5]=>0000011 [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>0000001 [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,7,2,3,5,8,6]=>0000011 [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,4,7,2,3,8,5,6]=>0000011 [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,4,7,2,8,3,5,6]=>0000011 [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]=>0000001 [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,4,6,7,8]=>0001000 [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,4,6,8,7]=>0001001 [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,4,7,6,8]=>0001010 [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>0001001 [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,4,8,6,7]=>0001001 [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,5,2,3,6,4,8,7]=>0001101 [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,3,6,7,8,4]=>0001001 [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,2,3,6,8,4,7]=>0001001 [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]=>0001011 [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,2,3,7,8,4,6]=>0001001 [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,2,3,8,4,6,7]=>0001001 [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,6,3,4,7,8]=>0001100 [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,6,3,4,8,7]=>0001101 [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4,8]=>0001110 [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>0001101 [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,8,4,7]=>0001101 [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,2,6,7,3,4,8]=>0001010 [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,2,6,8,3,4,7]=>0001001 [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,7,3,4,6,8]=>0001010 [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>0001011 [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,8,4,6]=>0001011 [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,2,7,8,3,4,6]=>0001001 [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>0001001 [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,6,2,3,4,8,7]=>0000101 [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,6,2,3,7,8,4]=>0000101 [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>0000101 [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,5,6,2,8,3,4,7]=>0000101 [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,5,6,7,2,3,4,8]=>0000010 [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,2,3,8,4]=>0000011 [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>0000001 [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>0000001 [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,7,2,3,4,8,6]=>0000011 [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,5,7,2,3,8,4,6]=>0000011 [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,2,8,3,4,6]=>0000011 [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,5,7,8,2,3,4,6]=>0000001 [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,2,3,4,5,7,8]=>0000100 [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,5,8,7]=>0000101 [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,6,2,3,4,7,5,8]=>0000110 [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,3,4,7,8,5]=>0000101 [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,2,3,4,8,5,7]=>0000101 [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>0000111 [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,6,2,3,8,4,5,7]=>0000101 [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,7,3,4,5,8]=>0000110 [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,7,3,4,8,5]=>0000111 [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,8,4,5]=>0000111 [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>0000101 [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,2,3,4,5,8]=>0000010 [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,2,3,4,8,5]=>0000011 [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,6,7,2,3,8,4,5]=>0000011 [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,2,8,3,4,5]=>0000011 [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>0000001 [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>0000001 [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,6,8]=>0000010 [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>0000011 [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>0000001 [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>0000001 [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>1000000 [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>1000001 [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>1000100 [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>1000101 [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>1000001 [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,5,6]=>1000001 [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,5,6,7]=>1000001 [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>1001001 [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,6,7,4,8,5]=>1000011 [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,3,7,4,8,5,6]=>1000011 [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>1000001 [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>1010000 [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>1010001 [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>1010100 [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>1010101 [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,3,6,7,5,8]=>1010010 [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>1010001 [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,5,7]=>1010001 [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,8,6]=>1010011 [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,5,6]=>1010001 [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,5,6,7]=>1010001 [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>1001001 [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>1000101 [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>1000001 [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,3,7]=>1000001 [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,4,5,7,3,8,6]=>1000011 [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,3,6,7]=>1000001 [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,3,5,8,7]=>1000101 [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,4,6,3,7,8,5]=>1000101 [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,3,8,5,7]=>1000101 [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,3,5,7]=>1000001 [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>1000001 [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,3,4,6,8,7]=>1001001 [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,8,7]=>1001101 [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,3,6,7,4,8]=>1001010 [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,3,6,7,8,4]=>1001001 [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,3,6,8,4,7]=>1001001 [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,8,6]=>1001011 [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,3,7,8,4,6]=>1001001 [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,8,4,6,7]=>1001001 [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,3,4,7,8]=>1000100 [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,3,4,8,7]=>1000101 [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,4,8]=>1000110 [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,7,8,4]=>1000101 [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,3,4,8]=>1000010 [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,3,8,4]=>1000011 [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,3,4]=>1000001 [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,5,7,3,4,6,8]=>1000010 [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,3,4,8,6]=>1000011 [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,3,8,4,6]=>1000011 [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,3,4,6]=>1000001 [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,5,8,3,4,6,7]=>1000001 [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,3,4,5,8,7]=>1000101 [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,6,3,4,7,8,5]=>1000101 [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,3,4,8,5,7]=>1000101 [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,8,5]=>1000111 [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,3,7,8,4,5]=>1000101 [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,3,8,4,5]=>1000011 [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,3,4,5]=>1000001 [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,3,4,5,8,6]=>1000011 [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,3,4,8,5,6]=>1000011 [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,3,4,5,6]=>1000001 [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>1000001 [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>0100000 [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>0100001 [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>0100010 [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>0100001 [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,5,6]=>0100001 [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,5,6,7]=>0100001 [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>0101010 [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>0100010 [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>0100001 [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5,8]=>0100110 [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,8,5,7]=>0100101 [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,4,5]=>0100001 [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,4,5,7]=>0100001 [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>0100011 [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,4,5,6]=>0100001 [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>0100001 [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>0010000 [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>0010001 [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>0010010 [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>0010001 [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>0010001 [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>0010100 [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>0010101 [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>0010010 [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>0010001 [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,5,7]=>0010001 [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,5,6,8]=>0010010 [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,8,6]=>0010011 [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>0010001 [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,5,6,7]=>0010001 [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>0001000 [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>0000101 [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>0000001 [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,1,6,7]=>0000001 [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,1,8,5,7]=>0000101 [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,1,5]=>0000001 [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,1,5,6,8]=>0000010 [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,1,5,8,6]=>0000011 [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,1,5,6]=>0000001 [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>0000001 [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]=>0001001 [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,8,7]=>0001101 [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,1,6,7,8,4]=>0001001 [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,8,6]=>0001011 [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,5,6,1,4,7,8]=>0000100 [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,1,4,8,7]=>0000101 [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,1,7,4,8]=>0000110 [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,1,7,8,4]=>0000101 [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,6,1,8,4,7]=>0000101 [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,1,8,4]=>0000011 [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,1,4]=>0000001 [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,1,4,7]=>0000001 [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,5,7,1,4,6,8]=>0000010 [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,5,7,1,4,8,6]=>0000011 [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,1,8,4,6]=>0000011 [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,1,4,6,7]=>0000001 [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,1,4,5,7,8]=>0000100 [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,1,4,5,8,7]=>0000101 [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,6,1,4,7,5,8]=>0000110 [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,1,4,7,8,5]=>0000101 [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,8,5,7]=>0000101 [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>0000101 [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,1,8,4,5,7]=>0000101 [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,6,7,1,4,5,8]=>0000010 [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,6,7,1,4,8,5]=>0000011 [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,7,1,8,4,5]=>0000011 [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,1,4,5]=>0000001 [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,6,8,1,4,5,7]=>0000001 [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,1,4,5,8,6]=>0000011 [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>0000001 [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>0000001 [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7,8]=>0010000 [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,3,5,7,8,6]=>0010001 [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,3,6,5,7,8]=>0010100 [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>0010101 [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,3,6,7,8,5]=>0010001 [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,6,8,5,7]=>0010001 [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,3,7,5,8,6]=>0010011 [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,3,7,8,5,6]=>0010001 [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,3,8,5,6,7]=>0010001 [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,8]=>0011010 [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]=>0011001 [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,8,6,7]=>0011001 [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3,7,8]=>0010100 [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,6,3,8,7]=>0010101 [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>0010001 [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>0010011 [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,1,5,8,3,6,7]=>0010001 [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,6,3,5,8,7]=>0010101 [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5,8]=>0010110 [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>0010101 [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,8,5,7]=>0010101 [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>0010011 [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,1,6,7,8,3,5]=>0010001 [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,1,6,8,3,5,7]=>0010001 [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>0010011 [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,8,5,6]=>0010011 [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,4,1,7,8,3,5,6]=>0010001 [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>0010001 [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,1,3,7,8,6]=>0001001 [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,3,7,8]=>0001100 [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>0001001 [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,4,5,1,7,3,6,8]=>0001010 [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,8,6]=>0001011 [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,1,3,7,8]=>0000100 [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,1,8,3,7]=>0000101 [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,1,3,8]=>0000010 [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,1,8,3]=>0000011 [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,8,1,3,7]=>0000001 [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,4,5,7,1,3,8,6]=>0000011 [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,1,3,6]=>0000001 [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,4,5,8,1,3,6,7]=>0000001 [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,1,3,5,8,7]=>0000101 [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,4,6,1,3,7,5,8]=>0000110 [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,1,3,7,8,5]=>0000101 [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,1,3,8,5,7]=>0000101 [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,8,5]=>0000111 [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,1,7,8,3,5]=>0000101 [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,1,8,3,5,7]=>0000101 [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,1,3,5,8]=>0000010 [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,1,3,8,5]=>0000011 [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,1,8,3,5]=>0000011 [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,1,3,5]=>0000001 [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>0000001 [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,4,7,1,3,5,8,6]=>0000011 [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,1,3,8,5,6]=>0000011 [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,4,7,1,8,3,5,6]=>0000011 [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,4,6,7,8]=>0001000 [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,1,3,6,7,8,4]=>0001001 [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,1,3,6,8,4,7]=>0001001 [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,5,1,3,7,4,6,8]=>0001010 [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,1,3,7,4,8,6]=>0001011 [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,1,3,7,8,4,6]=>0001001 [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,5,1,6,3,4,7,8]=>0001100 [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4,8]=>0001110 [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>0001101 [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,8,4,7]=>0001101 [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,1,6,7,3,4,8]=>0001010 [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>0001011 [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,1,6,7,8,3,4]=>0001001 [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,5,1,6,8,3,4,7]=>0001001 [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>0001011 [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,8,4,6]=>0001011 [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,1,7,8,3,4,6]=>0001001 [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,1,8,3,4,6,7]=>0001001 [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,5,6,1,3,7,4,8]=>0000110 [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,1,3,7,8,4]=>0000101 [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]=>0000101 [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>0000001 [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,5,7,1,3,4,8,6]=>0000011 [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,5,7,1,3,8,4,6]=>0000011 [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,8,7]=>0000101 [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,6,1,3,7,4,8,5]=>0000111 [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,6,1,7,3,4,5,8]=>0000110 [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,8,4,5]=>0000111 [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,6,1,7,8,3,4,5]=>0000101 [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,6,1,8,3,4,5,7]=>0000101 [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,6,7,1,3,4,5,8]=>0000010 [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,6,7,1,3,4,8,5]=>0000011 [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>0000001 [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,1,3,4,5,7]=>0000001 [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,7,1,3,8,4,5,6]=>0000011 [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,1,8,3,4,5,6]=>0000011 [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>0000001 [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]=>0000001 [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8]=>0100000 [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,5,8,6,7]=>0100001 [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,4,6,7,5,8]=>0100010 [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,4,6,7,8,5]=>0100001 [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,4,6,8,5,7]=>0100001 [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>0100010 [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,2,4,7,5,8,6]=>0100011 [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,2,4,7,8,5,6]=>0100001 [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,2,4,8,5,6,7]=>0100001 [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,5,4,6,8,7]=>0101001 [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>0101010 [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,6,7,4,8]=>0100010 [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,8,4]=>0100001 [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,1,2,5,6,8,4,7]=>0100001 [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>0100010 [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,2,5,7,4,8,6]=>0100011 [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,2,5,8,4,6,7]=>0100001 [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,2,6,4,5,8,7]=>0100101 [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5,8]=>0100110 [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,2,6,4,7,8,5]=>0100101 [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,2,6,7,4,8,5]=>0100011 [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,2,7,4,8,5,6]=>0100011 [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,2,7,8,4,5,6]=>0100001 [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>0100001 [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>0110000 [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,2,5,7,8,6]=>0110001 [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,2,5,8,6,7]=>0110001 [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>0110100 [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7]=>0110101 [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,2,6,7,5,8]=>0110010 [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,2,6,7,8,5]=>0110001 [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,2,6,8,5,7]=>0110001 [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,7,5,6,8]=>0110010 [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,8,6]=>0110011 [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,2,7,8,5,6]=>0110001 [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,8,5,6,7]=>0110001 [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>0101010 [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,5,2,7,8,6]=>0101001 [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,6,2,8,7]=>0100101 [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,8,2]=>0100001 [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,4,5,7,8,2,6]=>0100001 [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,4,6,2,8,5,7]=>0100101 [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,4,6,7,8,2,5]=>0100001 [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,4,6,8,2,5,7]=>0100001 [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4,8,2,5,6,7]=>0100001 [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,2,4,7,6,8]=>0101010 [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,5,2,4,8,6,7]=>0101001 [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7]=>0101101 [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,2,6,7,8,4]=>0101001 [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,7,4,6,8]=>0101010 [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,8,6]=>0101011 [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,2,7,8,4,6]=>0101001 [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,8,4,6,7]=>0101001 [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,5,6,2,4,7,8]=>0100100 [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,5,6,2,4,8,7]=>0100101 [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,7,8,4]=>0100101 [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,5,6,2,8,4,7]=>0100101 [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,5,6,7,2,8,4]=>0100011 [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,8,2,4]=>0100001 [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,5,6,8,2,4,7]=>0100001 [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>0100010 [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,1,5,7,2,4,8,6]=>0100011 [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,5,7,2,8,4,6]=>0100011 [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,1,5,7,8,2,4,6]=>0100001 [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,1,5,8,2,4,6,7]=>0100001 [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>0100100 [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,6,2,4,5,8,7]=>0100101 [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,6,2,4,7,5,8]=>0100110 [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,6,2,4,7,8,5]=>0100101 [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,6,2,4,8,5,7]=>0100101 [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,8,5]=>0100111 [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,8,4,5,7]=>0100101 [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>0100010 [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,1,6,7,2,8,4,5]=>0100011 [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>0100001 [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,7,8,2,4,5,6]=>0100001 [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]=>0100001 [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7,8]=>0010000 [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,5,6,8,7]=>0010001 [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,2,5,7,6,8]=>0010010 [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,2,5,7,8,6]=>0010001 [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,1,2,5,8,6,7]=>0010001 [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,4,1,2,6,5,7,8]=>0010100 [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>0010101 [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,4,1,2,6,7,5,8]=>0010010 [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,2,6,7,8,5]=>0010001 [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,1,2,6,8,5,7]=>0010001 [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,4,1,2,7,5,6,8]=>0010010 [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,2,7,5,8,6]=>0010011 [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,2,7,8,5,6]=>0010001 [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,1,2,8,5,6,7]=>0010001 [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6,8]=>0011010 [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,8,6,7]=>0011001 [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2,7,8]=>0010100 [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,7,2,8]=>0010010 [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,1,5,6,8,2,7]=>0010001 [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,5,7,2,6,8]=>0010010 [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,8,6]=>0010011 [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,1,5,7,8,2,6]=>0010001 [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,5,8,2,6,7]=>0010001 [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5,8]=>0010110 [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,4,1,6,8,2,5,7]=>0010001 [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>0010001 [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>0001001 [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,2,7,8]=>0001100 [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,8,7]=>0001101 [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,1,6,7,8,2]=>0001001 [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,8,2,6]=>0001001 [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,1,2,8,7]=>0000101 [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,1,7,2,8]=>0000110 [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,1,7,8,2]=>0000101 [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,1,8,2,7]=>0000101 [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,1,2,8]=>0000010 [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,1,2]=>0000001 [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,1,2,7]=>0000001 [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,1,2,8,6]=>0000011 [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>0000001 [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,4,6,1,2,5,8,7]=>0000101 [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,1,2,7,5,8]=>0000110 [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,1,2,7,8,5]=>0000101 [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,8,5]=>0000111 [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>0000101 [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,1,8,2,5]=>0000011 [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,1,2,5]=>0000001 [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,1,2,5,8,6]=>0000011 [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,4,7,1,8,2,5,6]=>0000011 [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,1,2,5,6,7]=>0000001 [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,4,6,7,8]=>0001000 [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>0001001 [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,1,2,4,7,6,8]=>0001010 [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,4,7,8,6]=>0001001 [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,1,2,4,8,6,7]=>0001001 [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,1,2,6,7,8,4]=>0001001 [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,5,1,2,6,8,4,7]=>0001001 [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,1,2,7,4,6,8]=>0001010 [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,5,1,2,7,4,8,6]=>0001011 [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,1,2,7,8,4,6]=>0001001 [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,5,1,2,8,4,6,7]=>0001001 [1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,5,1,6,2,4,7,8]=>0001100 [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,5,1,6,2,4,8,7]=>0001101 [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4,8]=>0001110 [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>0001101 [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>0001011 [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,1,6,7,8,2,4]=>0001001 [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,5,1,6,8,2,4,7]=>0001001 [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,5,1,7,2,4,6,8]=>0001010 [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,1,7,2,4,8,6]=>0001011 [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,8,4,6]=>0001011 [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,1,7,8,2,4,6]=>0001001 [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,5,1,8,2,4,6,7]=>0001001 [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,5,6,1,2,4,7,8]=>0000100 [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,1,2,4,8,7]=>0000101 [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,1,2,7,4,8]=>0000110 [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,1,2,7,8,4]=>0000101 [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]=>0000101 [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,1,7,2,4,8]=>0000110 [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,8,4]=>0000111 [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>0000101 [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,5,6,1,8,2,4,7]=>0000101 [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>0000001 [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,1,2,4,6,8]=>0000010 [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,1,2,4,8,6]=>0000011 [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>0000001 [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,6,1,2,4,7,5,8]=>0000110 [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,1,2,4,7,8,5]=>0000101 [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,6,1,2,4,8,5,7]=>0000101 [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,1,2,7,4,8,5]=>0000111 [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,6,1,7,2,4,8,5]=>0000111 [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,8,4,5]=>0000111 [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,1,7,8,2,4,5]=>0000101 [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,6,1,8,2,4,5,7]=>0000101 [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,6,7,1,2,4,5,8]=>0000010 [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,6,7,1,2,4,8,5]=>0000011 [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>0000011 [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>0000001 [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]=>0000001 [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,6,8]=>0000010 [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,7,1,2,4,5,8,6]=>0000011 [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,1,2,4,8,5,6]=>0000011 [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,1,2,8,4,5,6]=>0000011 [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7,8]=>0010000 [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,3,5,6,8,7]=>0010001 [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>0010010 [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,3,5,7,8,6]=>0010001 [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,3,5,8,6,7]=>0010001 [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,3,6,5,7,8]=>0010100 [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7]=>0010101 [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>0010010 [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,3,6,7,8,5]=>0010001 [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,3,6,8,5,7]=>0010001 [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>0010010 [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,3,7,5,8,6]=>0010011 [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,3,7,8,5,6]=>0010001 [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,8,5,6,7]=>0010001 [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,5,3,7,8,6]=>0011001 [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,8,6,7]=>0011001 [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,2,5,6,3,7,8]=>0010100 [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,2,5,6,3,8,7]=>0010101 [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,6,7,3,8]=>0010010 [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,8,3]=>0010001 [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,2,5,6,8,3,7]=>0010001 [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6,8]=>0010010 [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,5,7,3,8,6]=>0010011 [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,5,7,8,3,6]=>0010001 [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,2,5,8,3,6,7]=>0010001 [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,2,6,3,5,8,7]=>0010101 [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]=>0010110 [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,2,6,3,7,8,5]=>0010101 [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,2,6,3,8,5,7]=>0010101 [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]=>0010010 [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,2,6,7,3,8,5]=>0010011 [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,1,2,7,3,5,8,6]=>0010011 [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,2,7,8,3,5,6]=>0010001 [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>0010001 [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,5,2,3,7,8,6]=>0011001 [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,5,2,3,8,6,7]=>0011001 [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,8,7]=>0011101 [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,2,6,7,8,3]=>0011001 [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,2,6,8,3,7]=>0011001 [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,7,3,6,8]=>0011010 [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,8,6]=>0011011 [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,2,7,8,3,6]=>0011001 [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,8,3,6,7]=>0011001 [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,5,6,2,3,7,8]=>0010100 [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,5,6,2,3,8,7]=>0010101 [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,6,2,8,3,7]=>0010101 [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,5,6,7,2,3,8]=>0010010 [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,5,6,7,2,8,3]=>0010011 [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,5,6,8,2,3,7]=>0010001 [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,5,7,2,3,6,8]=>0010010 [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,5,7,2,8,3,6]=>0010011 [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,5,8,2,3,6,7]=>0010001 [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,6,2,3,7,5,8]=>0010110 [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,6,2,3,7,8,5]=>0010101 [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,7,3,5,8]=>0010110 [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,8,5]=>0010111 [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,8,3,5,7]=>0010101 [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,6,7,2,3,5,8]=>0010010 [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,1,6,7,2,3,8,5]=>0010011 [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>0010001 [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,7,2,3,5,8,6]=>0010011 [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,7,2,3,8,5,6]=>0010011 [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,8,3,5,6]=>0010011 [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,3,6,7,8]=>0001000 [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,3,7,6,8]=>0001010 [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,1,2,3,8,6,7]=>0001001 [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]=>0001101 [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,1,2,6,7,8,3]=>0001001 [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,1,2,6,8,3,7]=>0001001 [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,1,2,7,3,6,8]=>0001010 [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,5,1,2,7,3,8,6]=>0001011 [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,5,1,2,7,8,3,6]=>0001001 [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,1,2,8,3,6,7]=>0001001 [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,5,1,6,2,3,7,8]=>0001100 [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,1,6,2,3,8,7]=>0001101 [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3,8]=>0001110 [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]=>0001101 [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,8,3,7]=>0001101 [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,5,1,6,7,2,3,8]=>0001010 [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>0001011 [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,1,6,7,8,2,3]=>0001001 [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,1,7,2,3,6,8]=>0001010 [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,5,1,7,2,3,8,6]=>0001011 [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,8,3,6]=>0001011 [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,1,7,8,2,3,6]=>0001001 [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,1,8,2,3,6,7]=>0001001 [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,1,2,3,8,7]=>0000101 [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,8,3]=>0000111 [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,1,2,3,8]=>0000010 [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,1,2,8,3]=>0000011 [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,1,8,2,3]=>0000011 [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>0000001 [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>0000001 [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>0000011 [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>0000001 [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,6,1,2,3,7,5,8]=>0000110 [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,1,2,3,8,5,7]=>0000101 [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,6,1,2,7,3,5,8]=>0000110 [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,6,1,2,7,8,3,5]=>0000101 [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,6,1,2,8,3,5,7]=>0000101 [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,1,7,2,3,5,8]=>0000110 [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>0000101 [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,1,2,3,8,5]=>0000011 [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,1,8,2,3,5]=>0000011 [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>0000001 [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>0000001 [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,1,2,8,3,5,6]=>0000011 [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>0000011 [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>0000001 [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,4,6,7,8]=>0001000 [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,3,6,7,4,8]=>0001010 [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,2,3,6,7,8,4]=>0001001 [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2,3,6,8,4,7]=>0001001 [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,3,7,4,8,6]=>0001011 [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,1,2,3,7,8,4,6]=>0001001 [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,2,6,3,4,7,8]=>0001100 [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2,6,3,4,8,7]=>0001101 [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4,8]=>0001110 [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,2,6,3,7,8,4]=>0001101 [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2,6,3,8,4,7]=>0001101 [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,6,7,3,4,8]=>0001010 [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,2,6,7,3,8,4]=>0001011 [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,2,6,7,8,3,4]=>0001001 [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2,6,8,3,4,7]=>0001001 [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>0001010 [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,1,2,7,3,4,8,6]=>0001011 [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,1,2,7,3,8,4,6]=>0001011 [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,1,2,7,8,3,4,6]=>0001001 [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>0001001 [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7,8]=>0001100 [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,6,2,3,7,4,8]=>0001110 [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,6,2,3,7,8,4]=>0001101 [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,6,2,3,8,4,7]=>0001101 [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,7,3,4,8]=>0001110 [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,8,4]=>0001111 [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,8,3,4,7]=>0001101 [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,6,7,2,3,8,4]=>0001011 [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,6,7,2,8,3,4]=>0001011 [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,6,7,8,2,3,4]=>0001001 [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,1,7,2,3,4,8,6]=>0001011 [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,8,3,4,6]=>0001011 [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,6,1,2,3,7,8,4]=>0000101 [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,8,4,7]=>0000101 [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,6,1,2,7,3,8,4]=>0000111 [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,1,2,8,3,4,7]=>0000101 [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>0000111 [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,1,7,8,2,3,4]=>0000101 [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,1,2,3,4,8]=>0000010 [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,1,2,3,8,4]=>0000011 [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>0000011 [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,1,8,2,3,4]=>0000011 [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>0000001 [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>0000001 [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,6,8]=>0000010 [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,1,2,8,3,4,6]=>0000011 [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>0000001 [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,5,8,7]=>0000101 [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,2,3,4,7,8,5]=>0000101 [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,2,3,7,8,4,5]=>0000101 [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,2,7,3,4,8,5]=>0000111 [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>0000101 [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,7,2,3,4,5,8]=>0000110 [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,7,2,3,4,8,5]=>0000111 [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,7,2,3,8,4,5]=>0000111 [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,8,3,4,5]=>0000111 [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>0000101 [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>0000101 [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,5,8]=>0000010 [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,1,2,3,4,8,5]=>0000011 [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,1,2,3,8,4,5]=>0000011 [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>0000011 [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>0000001 [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>0000010 [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,8,4,5,6]=>0000011 [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1,2,8,3,4,5,6]=>0000011 [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>0000001 [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>0000001
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.