Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>=>
[1,0,1,0]=>[2,1]=>0=>0
[1,1,0,0]=>[1,2]=>1=>1
[1,0,1,0,1,0]=>[2,3,1]=>00=>00
[1,0,1,1,0,0]=>[2,1,3]=>01=>10
[1,1,0,0,1,0]=>[1,3,2]=>10=>01
[1,1,0,1,0,0]=>[3,1,2]=>00=>00
[1,1,1,0,0,0]=>[1,2,3]=>11=>11
[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>000=>000
[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>001=>100
[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>010=>010
[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>000=>000
[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>011=>110
[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>100=>001
[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>101=>101
[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>000=>000
[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>000=>000
[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>001=>100
[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>110=>011
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>100=>001
[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>000=>000
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>111=>111
[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>0000=>0000
[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>0001=>1000
[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>0010=>0100
[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>0000=>0000
[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>0011=>1100
[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>0100=>0010
[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>0101=>1010
[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>0000=>0000
[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>0000=>0000
[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>0001=>1000
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>0110=>0110
[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>0100=>0010
[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>0000=>0000
[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>0111=>1110
[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>1000=>0001
[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>1001=>1001
[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>1010=>0101
[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>1000=>0001
[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>1011=>1101
[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>0000=>0000
[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>0001=>1000
[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>0000=>0000
[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>0000=>0000
[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>0001=>1000
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>0010=>0100
[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>0000=>0000
[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>0000=>0000
[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>0011=>1100
[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>1100=>0011
[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>1101=>1011
[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>1000=>0001
[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>1000=>0001
[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>1001=>1001
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>0000=>0000
[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>0000=>0000
[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>0000=>0000
[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>0001=>1000
[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>1110=>0111
[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>1100=>0011
[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>1000=>0001
[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>0000=>0000
[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]=>[2,3,4,5,6,1]=>00000=>00000
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>00001=>10000
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>00010=>01000
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>00000=>00000
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>00011=>11000
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>00100=>00100
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>00101=>10100
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>00000=>00000
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>00000=>00000
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>00001=>10000
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>00110=>01100
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>00100=>00100
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>00000=>00000
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>00111=>11100
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>01000=>00010
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>01001=>10010
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>01010=>01010
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>01000=>00010
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>01011=>11010
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>00000=>00000
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>00001=>10000
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>00000=>00000
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>00000=>00000
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>00001=>10000
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>00010=>01000
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>00000=>00000
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>00000=>00000
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>00011=>11000
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>01100=>00110
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>01101=>10110
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>01000=>00010
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>01000=>00010
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>01001=>10010
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>00000=>00000
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>00000=>00000
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>00000=>00000
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>00001=>10000
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>01110=>01110
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>01100=>00110
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>01000=>00010
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>00000=>00000
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>01111=>11110
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>10000=>00001
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>10001=>10001
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>10010=>01001
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>10000=>00001
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>10011=>11001
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>10100=>00101
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>10101=>10101
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>10000=>00001
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>10000=>00001
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>10001=>10001
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>10110=>01101
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>10100=>00101
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>10000=>00001
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>10111=>11101
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>00000=>00000
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>00001=>10000
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>00010=>01000
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>00000=>00000
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>00011=>11000
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>00000=>00000
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>00001=>10000
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>00000=>00000
[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>00000=>00000
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>00001=>10000
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>00010=>01000
[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>00000=>00000
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>00000=>00000
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>00011=>11000
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>00100=>00100
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>00101=>10100
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>00000=>00000
[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>00000=>00000
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>00001=>10000
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>00000=>00000
[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>00000=>00000
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>00000=>00000
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>00001=>10000
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>00110=>01100
[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>00100=>00100
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>00000=>00000
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>00000=>00000
[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>00111=>11100
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>11000=>00011
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>11001=>10011
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>11010=>01011
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>11000=>00011
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>11011=>11011
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>10000=>00001
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>10001=>10001
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>10000=>00001
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>10000=>00001
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>10001=>10001
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>10010=>01001
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>10000=>00001
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>10000=>00001
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>10011=>11001
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>00000=>00000
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>00001=>10000
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>00000=>00000
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>00000=>00000
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>00001=>10000
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>00000=>00000
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>00000=>00000
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>00000=>00000
[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>00001=>10000
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>00010=>01000
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>00000=>00000
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>00000=>00000
[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>00000=>00000
[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>00011=>11000
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>11100=>00111
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>11101=>10111
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>11000=>00011
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>11000=>00011
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>11001=>10011
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>10000=>00001
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>10000=>00001
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>10000=>00001
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>10001=>10001
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>00000=>00000
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>00000=>00000
[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>00000=>00000
[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>00000=>00000
[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>00001=>10000
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>11110=>01111
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>11100=>00111
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>11000=>00011
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>10000=>00001
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>00000=>00000
[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]=>[2,3,4,5,6,7,1]=>000000=>000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>000001=>100000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>000010=>010000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>000000=>000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>000011=>110000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>000100=>001000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>000101=>101000
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>000000=>000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>000000=>000000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]=>000001=>100000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>000110=>011000
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]=>000100=>001000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>000000=>000000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>000111=>111000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>001000=>000100
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>001001=>100100
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>001010=>010100
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]=>001000=>000100
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>001011=>110100
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]=>000000=>000000
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]=>000001=>100000
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]=>000000=>000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>000000=>000000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]=>000001=>100000
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]=>000010=>010000
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]=>000000=>000000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]=>000000=>000000
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]=>000011=>110000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>001100=>001100
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>001101=>101100
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]=>001000=>000100
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]=>001000=>000100
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]=>001001=>100100
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]=>000000=>000000
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]=>000000=>000000
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]=>000000=>000000
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]=>000001=>100000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>001110=>011100
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>001100=>001100
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]=>001000=>000100
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]=>000000=>000000
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>001111=>111100
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>010000=>000010
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>010001=>100010
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>010010=>010010
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]=>010000=>000010
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>010011=>110010
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>010100=>001010
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]=>010101=>101010
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>010000=>000010
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]=>010000=>000010
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]=>010001=>100010
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>010110=>011010
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]=>010100=>001010
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]=>010000=>000010
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>010111=>111010
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]=>000000=>000000
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]=>000001=>100000
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]=>000010=>010000
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]=>000000=>000000
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]=>000011=>110000
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]=>000000=>000000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]=>000001=>100000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]=>000000=>000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]=>000000=>000000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]=>000001=>100000
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]=>000010=>010000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]=>000000=>000000
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]=>000000=>000000
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]=>000011=>110000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]=>000100=>001000
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>000101=>101000
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]=>000000=>000000
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]=>000000=>000000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]=>000001=>100000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]=>000000=>000000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]=>000000=>000000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]=>000000=>000000
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5,7]=>000001=>100000
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]=>000110=>011000
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]=>000100=>001000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]=>000000=>000000
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]=>000000=>000000
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>000111=>111000
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>011000=>000110
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>011001=>100110
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>011010=>010110
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]=>011000=>000110
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>011011=>110110
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>010000=>000010
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]=>010001=>100010
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>010000=>000010
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]=>010000=>000010
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]=>010001=>100010
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]=>010010=>010010
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]=>010000=>000010
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]=>010000=>000010
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]=>010011=>110010
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]=>000000=>000000
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>000001=>100000
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]=>000000=>000000
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]=>000000=>000000
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]=>000001=>100000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]=>000000=>000000
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]=>000000=>000000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]=>000000=>000000
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]=>000001=>100000
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]=>000010=>010000
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]=>000000=>000000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]=>000000=>000000
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>000000=>000000
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>000011=>110000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>011100=>001110
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>011101=>101110
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>011000=>000110
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]=>011000=>000110
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]=>011001=>100110
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]=>010000=>000010
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]=>010000=>000010
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]=>010000=>000010
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>010001=>100010
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]=>000000=>000000
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]=>000000=>000000
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>000000=>000000
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>000000=>000000
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>000001=>100000
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>011110=>011110
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>011100=>001110
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>011000=>000110
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>010000=>000010
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>000000=>000000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>011111=>111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>100000=>000001
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>100001=>100001
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>100010=>010001
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]=>100000=>000001
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>100011=>110001
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>100100=>001001
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>100101=>101001
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]=>100000=>000001
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]=>100000=>000001
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]=>100001=>100001
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>100110=>011001
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]=>100100=>001001
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]=>100000=>000001
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>100111=>111001
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>101000=>000101
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>101001=>100101
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]=>101010=>010101
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]=>101000=>000101
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>101011=>110101
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]=>100000=>000001
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]=>100001=>100001
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]=>100000=>000001
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]=>100000=>000001
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]=>100001=>100001
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,7,6]=>100010=>010001
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]=>100000=>000001
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]=>100000=>000001
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]=>100011=>110001
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>101100=>001101
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>101101=>101101
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]=>101000=>000101
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]=>101000=>000101
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]=>101001=>100101
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]=>100000=>000001
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]=>100000=>000001
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]=>100000=>000001
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]=>100001=>100001
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>101110=>011101
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>101100=>001101
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]=>101000=>000101
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>100000=>000001
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>101111=>111101
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]=>000000=>000000
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]=>000001=>100000
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>000010=>010000
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]=>000000=>000000
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]=>000011=>110000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>000100=>001000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]=>000101=>101000
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>000000=>000000
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]=>000000=>000000
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]=>000001=>100000
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]=>000110=>011000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]=>000100=>001000
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]=>000000=>000000
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]=>000111=>111000
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]=>000000=>000000
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]=>000001=>100000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]=>000010=>010000
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]=>000000=>000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]=>000011=>110000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]=>000000=>000000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]=>000001=>100000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]=>000000=>000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>000000=>000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]=>000001=>100000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]=>000010=>010000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]=>000000=>000000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]=>000000=>000000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]=>000011=>110000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]=>000100=>001000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>000101=>101000
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]=>000000=>000000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]=>000000=>000000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]=>000001=>100000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]=>000000=>000000
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]=>000000=>000000
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]=>000000=>000000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]=>000001=>100000
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]=>000110=>011000
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]=>000100=>001000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]=>000000=>000000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,7,1,2,5,6]=>000000=>000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>000111=>111000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]=>001000=>000100
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]=>001001=>100100
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>001010=>010100
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]=>001000=>000100
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]=>001011=>110100
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>000000=>000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]=>000001=>100000
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>000000=>000000
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]=>000000=>000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]=>000001=>100000
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]=>000010=>010000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]=>000000=>000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]=>000000=>000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]=>000011=>110000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]=>000000=>000000
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>000001=>100000
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]=>000000=>000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]=>000000=>000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]=>000001=>100000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]=>000000=>000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]=>000000=>000000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]=>000000=>000000
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>000001=>100000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]=>000010=>010000
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]=>000000=>000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]=>000000=>000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]=>000000=>000000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]=>000011=>110000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]=>001100=>001100
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]=>001101=>101100
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>001000=>000100
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]=>001000=>000100
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]=>001001=>100100
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]=>000000=>000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]=>000000=>000000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]=>000000=>000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]=>000001=>100000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]=>000000=>000000
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]=>000000=>000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]=>000000=>000000
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]=>000000=>000000
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>000001=>100000
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>001110=>011100
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]=>001100=>001100
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]=>001000=>000100
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]=>000000=>000000
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>000000=>000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>001111=>111100
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>110000=>000011
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]=>110001=>100011
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>110010=>010011
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]=>110000=>000011
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>110011=>110011
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>110100=>001011
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>110101=>101011
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]=>110000=>000011
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]=>110000=>000011
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]=>110001=>100011
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>110110=>011011
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]=>110100=>001011
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]=>110000=>000011
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>110111=>111011
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]=>100000=>000001
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]=>100001=>100001
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]=>100010=>010001
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]=>100000=>000001
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]=>100011=>110001
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]=>100000=>000001
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]=>100001=>100001
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]=>100000=>000001
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]=>100000=>000001
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]=>100001=>100001
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]=>100010=>010001
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]=>100000=>000001
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]=>100000=>000001
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]=>100011=>110001
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]=>100100=>001001
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]=>100101=>101001
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5]=>100000=>000001
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]=>100000=>000001
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]=>100001=>100001
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]=>100000=>000001
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]=>100000=>000001
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>100000=>000001
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]=>100001=>100001
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]=>100110=>011001
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>100100=>001001
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]=>100000=>000001
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>100000=>000001
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]=>100111=>111001
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]=>000000=>000000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]=>000001=>100000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>000010=>010000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]=>000000=>000000
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]=>000011=>110000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>000000=>000000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]=>000001=>100000
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>000000=>000000
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]=>000000=>000000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]=>000001=>100000
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]=>000010=>010000
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]=>000000=>000000
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]=>000000=>000000
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]=>000011=>110000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]=>000000=>000000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>000001=>100000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]=>000000=>000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]=>000000=>000000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>000001=>100000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]=>000000=>000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]=>000000=>000000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,1,2,3]=>000000=>000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>000001=>100000
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]=>000010=>010000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]=>000000=>000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]=>000000=>000000
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]=>000000=>000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]=>000011=>110000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]=>000100=>001000
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]=>000101=>101000
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>000000=>000000
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,6,7,3,5]=>000000=>000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]=>000001=>100000
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]=>000000=>000000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,5]=>000000=>000000
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]=>000000=>000000
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>000001=>100000
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>000000=>000000
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]=>000000=>000000
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]=>000000=>000000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]=>000000=>000000
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>000001=>100000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>000110=>011000
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]=>000100=>001000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]=>000000=>000000
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]=>000000=>000000
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>000000=>000000
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>000111=>111000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]=>111000=>000111
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]=>111001=>100111
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>111010=>010111
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]=>111000=>000111
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>111011=>110111
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,7,4]=>110000=>000011
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]=>110001=>100011
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]=>110000=>000011
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]=>110000=>000011
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]=>110001=>100011
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]=>110010=>010011
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]=>110000=>000011
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]=>110000=>000011
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]=>110011=>110011
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]=>100000=>000001
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]=>100001=>100001
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4]=>100000=>000001
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]=>100000=>000001
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]=>100001=>100001
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,6,2,3,7,4]=>100000=>000001
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>100000=>000001
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>100000=>000001
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]=>100001=>100001
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>100010=>010001
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>100000=>000001
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>100000=>000001
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>100000=>000001
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]=>100011=>110001
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>000000=>000000
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>000001=>100000
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>000000=>000000
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,2,6,7,3,4]=>000000=>000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>000001=>100000
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>000000=>000000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,4]=>000000=>000000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]=>000000=>000000
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>000001=>100000
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>000000=>000000
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]=>000000=>000000
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,3,4]=>000000=>000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]=>000000=>000000
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>000001=>100000
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>000010=>010000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>000000=>000000
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]=>000000=>000000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]=>000000=>000000
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>000000=>000000
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>000011=>110000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>111100=>001111
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>111101=>101111
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>111000=>000111
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]=>111000=>000111
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]=>111001=>100111
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>110000=>000011
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]=>110000=>000011
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]=>110000=>000011
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]=>110001=>100011
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]=>100000=>000001
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>100000=>000001
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>100000=>000001
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>100000=>000001
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]=>100001=>100001
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>000000=>000000
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>000000=>000000
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>000000=>000000
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]=>000000=>000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>000000=>000000
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>000001=>100000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>111110=>011111
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,3,4,7,5,6]=>111100=>001111
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]=>111000=>000111
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]=>110000=>000011
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>100000=>000001
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>000000=>000000
[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]=>[2,3,4,5,6,7,8,1]=>0000000=>0000000
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>0000111=>1110000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>0001000=>0001000
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,8,5,7]=>0001000=>0001000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,1,5]=>0000000=>0000000
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>0000000=>0000000
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>0001111=>1111000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]=>0010000=>0000100
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>0010101=>1010100
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,1,7,8,4]=>0000000=>0000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,1,4]=>0000000=>0000000
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,6,1,8,4,7]=>0000000=>0000000
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,8,1,4,7]=>0000000=>0000000
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]=>0000011=>1100000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,7,1,4,8,6]=>0000000=>0000000
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,6,4,7,5,8]=>0010001=>1000100
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>0010000=>0000100
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,7,8,5]=>0000000=>0000000
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,6,1,4,7,5,8]=>0000001=>1000000
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,7,8,1,4,5]=>0000000=>0000000
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,8,7]=>0000010=>0100000
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>0011100=>0011100
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,7,1,4,5,8,6]=>0000000=>0000000
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>0010000=>0000100
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>0011111=>1111100
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>0100010=>0100010
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,6,8,3,7]=>0100000=>0000010
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>0100000=>0000010
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4,5,8,3,6,7]=>0100000=>0000010
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,7,5,8]=>0101001=>1001010
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>0101010=>0101010
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>0101011=>1101010
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,8,5,7]=>0100000=>0000010
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,3,7,5,8,6]=>0101000=>0001010
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>0101000=>0001010
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>0101110=>0111010
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>0100000=>0000010
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>0101111=>1111010
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,4,1,5,6,3,8,7]=>0000010=>0100000
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,5,6,3,7,8]=>0000011=>1100000
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,5,3,7,8,6]=>0000100=>0010000
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,8]=>0000101=>1010000
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,7,3,8,6]=>0000000=>0000000
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>0000100=>0010000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,1,8,3]=>0000000=>0000000
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,1,3,8]=>0000001=>1000000
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>0000011=>1100000
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,7,8,6]=>0000100=>0010000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,5,1,7,3,8,6]=>0000000=>0000000
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,6,5,7,8]=>0001011=>1101000
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,6,3,7,8,5]=>0000000=>0000000
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5,8]=>0000001=>1000000
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,6,7,3,8,5]=>0000000=>0000000
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>0000000=>0000000
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>0000000=>0000000
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,6,1,3,7,5,8]=>0000001=>1000000
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,6,1,7,3,8,5]=>0000000=>0000000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,6,7,1,3,8,5]=>0000000=>0000000
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,1,3,5]=>0000000=>0000000
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,8,7]=>0000010=>0100000
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,8,5,7]=>0000000=>0000000
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>0000000=>0000000
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>0000000=>0000000
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,3,5,7,8,6]=>0001100=>0011000
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,3,7,5,8,6]=>0001000=>0001000
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,3,7,8,5,6]=>0001000=>0001000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,7,3,5,8,6]=>0000000=>0000000
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>0000000=>0000000
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,7,8,3,5,6]=>0000000=>0000000
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,7,1,3,5,8,6]=>0000000=>0000000
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,3,8,5,6,7]=>0001000=>0001000
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>0000000=>0000000
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8]=>0001111=>1111000
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>0110110=>0110110
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,1,5,3,6,7,4,8]=>0100001=>1000010
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7]=>0100010=>0100010
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,1,5,3,6,8,4,7]=>0100000=>0000010
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,6,3,7,8,4]=>0100000=>0000010
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,1,5,6,3,7,4,8]=>0100001=>1000010
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,3,4]=>0100000=>0000010
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,1,5,6,7,3,4,8]=>0100001=>1000010
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>0100010=>0100010
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,1,5,6,3,4,7,8]=>0100011=>1100010
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,7,4,8,6]=>0100000=>0000010
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,7,8,4,6]=>0100000=>0000010
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,5,7,3,4,8,6]=>0100000=>0000010
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>0100000=>0000010
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,5,7,8,3,4,6]=>0100000=>0000010
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6,8]=>0100001=>1000010
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,4]=>0000000=>0000000
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,6,8,4,7]=>0000000=>0000000
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,6,3,7,4,8]=>0000001=>1000000
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,5,1,6,3,4,7,8]=>0000011=>1100000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,5,6,1,3,7,8,4]=>0000000=>0000000
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,5,6,1,3,7,4,8]=>0000001=>1000000
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,7,8,4,6]=>0000000=>0000000
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,5,1,3,7,4,6,8]=>0000001=>1000000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]=>0000000=>0000000
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,7,8,3,4,6]=>0000000=>0000000
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,5,7,1,3,4,8,6]=>0000000=>0000000
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,4,6,7,8]=>0000111=>1110000
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>0111000=>0001110
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>0111010=>0101110
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>0111011=>1101110
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>0110000=>0000110
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>0100000=>0000010
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,6,3,7,4,8,5]=>0100000=>0000010
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,6,3,7,8,4,5]=>0100000=>0000010
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>0100000=>0000010
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,8,5,7]=>0100000=>0000010
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,6,1,3,7,4,8,5]=>0000000=>0000000
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,6,1,7,3,8,4,5]=>0000000=>0000000
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,6,1,7,8,3,4,5]=>0000000=>0000000
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,6,1,7,3,4,5,8]=>0000001=>1000000
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,6,7,1,3,4,8,5]=>0000000=>0000000
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>0000000=>0000000
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,6,7,1,3,4,5,8]=>0000001=>1000000
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,6,1,8,3,4,5,7]=>0000000=>0000000
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,1,3,4,7,8,5,6]=>0111000=>0001110
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,1,3,7,4,8,5,6]=>0110000=>0000110
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,1,7,3,4,8,5,6]=>0100000=>0000010
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,7,8,3,4,5,6]=>0100000=>0000010
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,7,1,8,3,4,5,6]=>0000000=>0000000
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>0000000=>0000000
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>0111110=>0111110
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,1,3,4,8,5,6,7]=>0111000=>0001110
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>0110000=>0000110
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>0111111=>1111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]=>1000001=>1000001
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,7,8,2,6]=>1000000=>0000001
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,5,2,8,6,7]=>1000100=>0010001
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>1001001=>1001001
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,8,7]=>1000010=>0100001
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,8,2,5,7]=>1000000=>0000001
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>1001100=>0011001
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,4,7,2,5,8,6]=>1000000=>0000001
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,4,2,5,8,6,7]=>1001100=>0011001
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>1001000=>0001001
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>1000000=>0000001
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>1001111=>1111001
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>1010100=>0010101
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>1010101=>1010101
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>1010100=>0010101
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,5,8,4,6,7]=>1010000=>0000101
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>1010111=>1110101
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,5,2,6,7,4,8]=>1000001=>1000001
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,5,2,6,4,8,7]=>1000010=>0100001
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,6,8,4,7]=>1000000=>0000001
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,5,6,2,7,4,8]=>1000001=>1000001
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,2,4]=>1000000=>0000001
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,7,2,4,8]=>1000001=>1000001
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,5,6,2,4,8,7]=>1000010=>0100001
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>1000011=>1100001
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,7,4,8,6]=>1000000=>0000001
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,7,8,4,6]=>1000000=>0000001
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,7,2,4,8,6]=>1000000=>0000001
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>1000001=>1000001
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,5,2,4,6,8,7]=>1000110=>0110001
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,5,2,4,8,6,7]=>1000100=>0010001
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>1000000=>0000001
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>1000000=>0000001
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>1011000=>0001101
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>1011010=>0101101
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>1011000=>0001101
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>1011011=>1101101
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,6,4,7,5,8]=>1010001=>1000101
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>1010000=>0000101
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,2,6,4,5,7,8]=>1010011=>1100101
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,6,2,4,7,8,5]=>1000000=>0000001
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,6,2,4,7,5,8]=>1000001=>1000001
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,2,7,4,8,5]=>1000000=>0000001
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,6,2,7,8,4,5]=>1000000=>0000001
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,6,7,2,4,8,5]=>1000000=>0000001
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,8,5,7]=>1000000=>0000001
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,6,2,4,5,7,8]=>1000011=>1100001
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>1011101=>1011101
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,4,7,5,8,6]=>1011000=>0001101
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>1010000=>0000101
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,7,4,5,6,8]=>1010001=>1000101
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,7,2,4,5,8,6]=>1000000=>0000001
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,7,2,4,8,5,6]=>1000000=>0000001
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>1000000=>0000001
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>1011100=>0011101
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,2,4,8,5,6,7]=>1011000=>0001101
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>1010000=>0000101
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>1000000=>0000001
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>1011111=>1111101
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,5,2,7,8,6]=>0000100=>0010000
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4,5,7,8,2,6]=>0000000=>0000000
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>0001000=>0001000
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,6,7,5,8]=>0001001=>1001000
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7]=>0001010=>0101000
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,8,5,7]=>0001000=>0001000
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,6,5,7,8]=>0001011=>1101000
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,4,6,7,8,2,5]=>0000000=>0000000
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,8,2,5,7]=>0000000=>0000000
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>0001100=>0011000
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,7,5,8,6]=>0001000=>0001000
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,4,2,7,8,5,6]=>0001000=>0001000
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,4,2,7,5,6,8]=>0001001=>1001000
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,2,5,8,6,7]=>0001100=>0011000
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,2,5,6,7,8]=>0001111=>1111000
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,5,6,7,2,8]=>0000001=>1000000
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6,8]=>0000101=>1010000
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>0000000=>0000000
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,2,8,6,7]=>0000100=>0010000
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,5,8,2,6,7]=>0000000=>0000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,2]=>0000000=>0000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,1,7,8,2]=>0000000=>0000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,6,1,7,2,8]=>0000001=>1000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,2]=>0000000=>0000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,1,2,8]=>0000001=>1000000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,6,1,2,8,7]=>0000010=>0100000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,6,1,8,2,7]=>0000000=>0000000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,6,8,1,2,7]=>0000000=>0000000
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,5,1,7,8,2,6]=>0000000=>0000000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,6,7,8,5]=>0001000=>0001000
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>0001010=>0101000
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,6,5,7,8]=>0001011=>1101000
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,6,2,7,5,8]=>0000001=>1000000
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,6,1,7,2,8,5]=>0000000=>0000000
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,6,1,7,8,2,5]=>0000000=>0000000
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,6,7,1,8,2,5]=>0000000=>0000000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,6,7,8,1,2,5]=>0000000=>0000000
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,8,7]=>0000010=>0100000
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,4,1,2,7,5,8,6]=>0001000=>0001000
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>0001000=>0001000
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,4,7,1,2,5,8,6]=>0000000=>0000000
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>0000000=>0000000
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1,2,5,6,8,7]=>0001110=>0111000
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>0000000=>0000000
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>0001111=>1111000
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,4]=>0010000=>0000100
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,5,6,7,4,8]=>0010001=>1000100
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,5,6,8,4,7]=>0010000=>0000100
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>0010000=>0000100
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,5,4,6,8,7]=>0010110=>0110100
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,5,8,4,6,7]=>0010000=>0000100
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]=>0000000=>0000000
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7]=>0000010=>0100000
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>0000000=>0000000
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,5,6,2,4,8,7]=>0000010=>0100000
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]=>0000000=>0000000
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,5,6,8,2,4,7]=>0000000=>0000000
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,5,6,2,4,7,8]=>0000011=>1100000
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,7,4,8,6]=>0000000=>0000000
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,7,8,4,6]=>0000000=>0000000
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6,8]=>0000001=>1000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>0000000=>0000000
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,7,2,8,4,6]=>0000000=>0000000
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,7,8,2,4,6]=>0000000=>0000000
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6,8]=>0000001=>1000000
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,5,2,4,8,6,7]=>0000100=>0010000
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,5,2,8,4,6,7]=>0000000=>0000000
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,5,8,2,4,6,7]=>0000000=>0000000
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,6,7,8,4]=>0000000=>0000000
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,6,8,4,7]=>0000000=>0000000
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,5,1,6,2,7,8,4]=>0000000=>0000000
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,6,2,7,4,8]=>0000001=>1000000
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>0000000=>0000000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>0000010=>0100000
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,5,1,6,2,4,7,8]=>0000011=>1100000
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,5,6,1,2,7,4,8]=>0000001=>1000000
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,5,6,1,7,8,2,4]=>0000000=>0000000
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,5,6,1,2,8,4,7]=>0000000=>0000000
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>0000000=>0000000
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,7,8,6]=>0000100=>0010000
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,7,4,8,6]=>0000000=>0000000
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,7,8,4,6]=>0000000=>0000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,7,2,4,8,6]=>0000000=>0000000
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>0000000=>0000000
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,7,8,2,4,6]=>0000000=>0000000
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6,8]=>0000001=>1000000
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,7,1,2,4,8,6]=>0000000=>0000000
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6,8]=>0000001=>1000000
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,5,1,2,4,6,8,7]=>0000110=>0110000
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,5,1,2,4,8,6,7]=>0000100=>0010000
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,5,1,2,8,4,6,7]=>0000000=>0000000
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,5,1,8,2,4,6,7]=>0000000=>0000000
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,5,1,2,4,6,7,8]=>0000111=>1110000
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,6,7,8,5]=>0011000=>0001100
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,7,5,8]=>0011001=>1001100
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,1,2,4,6,8,5,7]=>0011000=>0001100
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,2,6,4,7,8,5]=>0010000=>0000100
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,1,2,6,4,7,5,8]=>0010001=>1000100
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>0010000=>0000100
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,8,7]=>0010010=>0100100
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]=>0000000=>0000000
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,1,6,2,4,7,5,8]=>0000001=>1000000
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,6,2,7,4,8,5]=>0000000=>0000000
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,1,6,7,2,8,4,5]=>0000000=>0000000
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,1,6,7,2,4,5,8]=>0000001=>1000000
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,8,7]=>0000010=>0100000
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,8,5,7]=>0000000=>0000000
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,1,6,2,8,4,5,7]=>0000000=>0000000
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>0000000=>0000000
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,6,2,4,5,7,8]=>0000011=>1100000
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,6,1,2,4,7,8,5]=>0000000=>0000000
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,6,1,2,7,4,8,5]=>0000000=>0000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,6,1,7,2,4,8,5]=>0000000=>0000000
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>0000000=>0000000
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>0000000=>0000000
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,6,7,1,2,4,8,5]=>0000000=>0000000
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]=>0000000=>0000000
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>0000000=>0000000
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,6,7,1,2,4,5,8]=>0000001=>1000000
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,6,1,8,2,4,5,7]=>0000000=>0000000
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>0011000=>0001100
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,1,2,7,4,8,5,6]=>0010000=>0000100
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,7,8,2,4,5,6]=>0000000=>0000000
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,7,1,2,4,8,5,6]=>0000000=>0000000
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,7,1,2,8,4,5,6]=>0000000=>0000000
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6,8]=>0000001=>1000000
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,8,6,7]=>0011100=>0011100
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,2,4,8,5,6,7]=>0011000=>0001100
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>0010000=>0000100
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>0011111=>1111100
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>1100011=>1100011
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,7,3,8,6]=>1100000=>0000011
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>1101000=>0001011
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,6,7,5,8]=>1101001=>1001011
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>1101010=>0101011
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,8,5,7]=>1101000=>0001011
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>1101011=>1101011
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,8,5,7]=>1100000=>0000011
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,8,3,5,7]=>1100000=>0000011
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]=>1100011=>1100011
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>1101100=>0011011
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,3,7,5,8,6]=>1101000=>0001011
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,4,3,7,8,5,6]=>1101000=>0001011
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,4,7,3,8,5,6]=>1100000=>0000011
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>1101110=>0111011
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,3,5,8,6,7]=>1101100=>0011011
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>1101000=>0001011
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>1100000=>0000011
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>1101111=>1111011
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,5,6,7,3,8]=>1000001=>1000001
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,8]=>1000101=>1010001
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,4,2,5,7,3,8,6]=>1000000=>0000001
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,4,2,5,7,8,3,6]=>1000000=>0000001
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6,8]=>1000001=>1000001
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,5,3,6,8,7]=>1000110=>0110001
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>1000100=>0010001
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,4,2,5,8,3,6,7]=>1000000=>0000001
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,5,3,6,7,8]=>1000111=>1110001
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,5,2,6,7,8,3]=>1000000=>0000001
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,4,5,2,6,3,8,7]=>1000010=>0100001
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,5,2,6,8,3,7]=>1000000=>0000001
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>1000011=>1100001
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,2,8,3]=>1000000=>0000001
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,2,3,8]=>1000001=>1000001
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,6,8,2,3,7]=>1000000=>0000001
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,7,8,6]=>1000100=>0010001
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,4,5,2,7,3,8,6]=>1000000=>0000001
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,7,8,3,6]=>1000000=>0000001
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6,8]=>1000001=>1000001
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,7,8,2,3,6]=>1000000=>0000001
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>1000001=>1000001
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,5,2,3,8,6,7]=>1000100=>0010001
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,2,3,6,7,8]=>1000111=>1110001
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,6,7,8,5]=>1001000=>0001001
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7]=>1001010=>0101001
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,6,5,7,8]=>1001011=>1101001
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,6,3,7,5,8]=>1000001=>1000001
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>1000000=>0000001
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,6,7,3,5,8]=>1000001=>1000001
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,8,7]=>1000010=>0100001
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>1000000=>0000001
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,8,3,5,7]=>1000000=>0000001
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,6,3,5,7,8]=>1000011=>1100001
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,6,2,3,7,8,5]=>1000000=>0000001
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,6,2,7,3,8,5]=>1000000=>0000001
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,6,2,7,8,3,5]=>1000000=>0000001
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>1000001=>1000001
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,6,7,2,8,3,5]=>1000000=>0000001
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,8,5,7]=>1000000=>0000001
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>1000000=>0000001
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,2,3,5,7,8,6]=>1001100=>0011001
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2,3,5,7,6,8]=>1001101=>1011001
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>1001000=>0001001
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2,3,7,5,6,8]=>1001001=>1001001
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,2,7,3,5,8,6]=>1000000=>0000001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>1000000=>0000001
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,2,7,8,3,5,6]=>1000000=>0000001
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2,7,3,5,6,8]=>1000001=>1000001
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,7,2,3,5,8,6]=>1000000=>0000001
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,7,2,3,8,5,6]=>1000000=>0000001
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,4,2,3,5,6,8,7]=>1001110=>0111001
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>1001100=>0011001
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,2,3,8,5,6,7]=>1001000=>0001001
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>1000000=>0000001
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]=>1000000=>0000001
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8]=>1001111=>1111001
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,5,6,7,3,8]=>0000001=>1000000
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>0000010=>0100000
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,5,6,8,3,7]=>0000000=>0000000
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3,7,8]=>0000011=>1100000
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,5,3,7,8,6]=>0000100=>0010000
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,5,7,3,8,6]=>0000000=>0000000
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6,8]=>0000001=>1000000
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,5,3,8,6,7]=>0000100=>0010000
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,5,8,3,6,7]=>0000000=>0000000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>0000000=>0000000
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,2,6,3,8,7]=>0000010=>0100000
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,5,2,6,8,3,7]=>0000000=>0000000
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,5,6,7,2,3,8]=>0000001=>1000000
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>0000010=>0100000
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,5,6,8,2,3,7]=>0000000=>0000000
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>0000100=>0010000
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,5,2,7,3,8,6]=>0000000=>0000000
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,5,2,7,8,3,6]=>0000000=>0000000
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6,8]=>0000001=>1000000
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,5,7,2,8,3,6]=>0000000=>0000000
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[4,1,5,2,3,8,6,7]=>0000100=>0010000
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,8,3,6,7]=>0000000=>0000000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,6,7,8,3]=>0000000=>0000000
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,6,3,8,7]=>0000010=>0100000
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,2,6,8,3,7]=>0000000=>0000000
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,1,6,2,7,8,3]=>0000000=>0000000
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,6,2,7,3,8]=>0000001=>1000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,5,1,6,7,2,8,3]=>0000000=>0000000
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>0000000=>0000000
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,5,1,6,7,2,3,8]=>0000001=>1000000
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>0000000=>0000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,1,7,2,8,3]=>0000000=>0000000
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>0000010=>0100000
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>0000000=>0000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,7,3,8,6]=>0000000=>0000000
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,7,8,3,6]=>0000000=>0000000
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6,8]=>0000001=>1000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,5,1,7,2,3,8,6]=>0000000=>0000000
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>0000000=>0000000
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,5,1,7,8,2,3,6]=>0000000=>0000000
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>0000000=>0000000
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,5,1,2,3,8,6,7]=>0000100=>0010000
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,5,1,2,8,3,6,7]=>0000000=>0000000
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,5,1,8,2,3,6,7]=>0000000=>0000000
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>0000000=>0000000
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>0000111=>1110000
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,6,7,8,5]=>0001000=>0001000
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,6,3,7,8,5]=>0000000=>0000000
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5,8]=>0000001=>1000000
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,6,7,3,5,8]=>0000001=>1000000
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,8,5,7]=>0000000=>0000000
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>0000000=>0000000
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,7,3,8,5]=>0000000=>0000000
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,6,2,7,3,5,8]=>0000001=>1000000
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,6,7,2,3,5,8]=>0000001=>1000000
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,8,3,5,7]=>0000000=>0000000
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>0000000=>0000000
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>0000001=>1000000
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,6,1,2,7,3,5,8]=>0000001=>1000000
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,6,1,7,2,3,5,8]=>0000001=>1000000
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,6,7,1,2,3,8,5]=>0000000=>0000000
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>0000000=>0000000
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>0000000=>0000000
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,8,5,7]=>0000000=>0000000
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,8,3,5,7]=>0000000=>0000000
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>0000000=>0000000
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,7,8,6]=>0001100=>0011000
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>0001000=>0001000
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>0000000=>0000000
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,1,2,7,8,3,5,6]=>0000000=>0000000
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,7,2,3,5,8,6]=>0000000=>0000000
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[4,1,7,2,3,8,5,6]=>0000000=>0000000
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,1,7,2,8,3,5,6]=>0000000=>0000000
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>0000000=>0000000
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]=>0001000=>0001000
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>0000000=>0000000
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>0001111=>1111000
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>1110000=>0000111
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]=>1110001=>1000111
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]=>1110010=>0100111
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,8,4,7]=>1110000=>0000111
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>1110011=>1100111
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>1110100=>0010111
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>1110101=>1010111
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,7,4,8,6]=>1110000=>0000111
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,7,8,4,6]=>1110000=>0000111
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6,8]=>1110001=>1000111
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,5,4,8,6,7]=>1110100=>0010111
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,5,8,4,6,7]=>1110000=>0000111
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>1110111=>1110111
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,4]=>1100000=>0000011
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,5,3,6,4,8,7]=>1100010=>0100011
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,2,5,6,3,7,8,4]=>1100000=>0000011
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,2,5,6,3,7,4,8]=>1100001=>1000011
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,2,5,6,3,4,8,7]=>1100010=>0100011
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,5,6,3,8,4,7]=>1100000=>0000011
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,2,5,6,8,3,4,7]=>1100000=>0000011
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>1100011=>1100011
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,7,4,8,6]=>1100000=>0000011
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,7,8,4,6]=>1100000=>0000011
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,2,5,7,3,4,8,6]=>1100000=>0000011
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,2,5,7,3,8,4,6]=>1100000=>0000011
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,2,5,7,8,3,4,6]=>1100000=>0000011
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>1100001=>1000011
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4,8,6,7]=>1100100=>0010011
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>1100000=>0000011
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>1100000=>0000011
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,6,7,8,4]=>1000000=>0000001
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,6,4,8,7]=>1000010=>0100001
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,5,2,3,6,8,4,7]=>1000000=>0000001
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,2,6,3,7,8,4]=>1000000=>0000001
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2,6,3,7,4,8]=>1000001=>1000001
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,2,6,7,3,4,8]=>1000001=>1000001
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,5,2,6,3,4,8,7]=>1000010=>0100001
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>1000000=>0000001
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,2,6,8,3,4,7]=>1000000=>0000001
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,2,6,3,4,7,8]=>1000011=>1100001
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,6,2,3,7,8,4]=>1000000=>0000001
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,5,6,7,2,3,8,4]=>1000000=>0000001
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,2,3,4]=>1000000=>0000001
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,8,7]=>1000010=>0100001
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,6,2,3,8,4,7]=>1000000=>0000001
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]=>1000000=>0000001
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,7,8,6]=>1000100=>0010001
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6,8]=>1000101=>1010001
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,7,4,8,6]=>1000000=>0000001
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,7,8,4,6]=>1000000=>0000001
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,7,3,4,8,6]=>1000000=>0000001
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>1000000=>0000001
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,7,8,3,4,6]=>1000000=>0000001
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6,8]=>1000001=>1000001
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,5,7,2,3,4,8,6]=>1000000=>0000001
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,7,2,3,8,4,6]=>1000000=>0000001
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>1000000=>0000001
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,5,2,3,4,6,8,7]=>1000110=>0110001
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>1000100=>0010001
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,5,2,3,8,4,6,7]=>1000000=>0000001
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>1000000=>0000001
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8]=>1000111=>1110001
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,4]=>0000000=>0000000
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,3,6,8,4,7]=>0000000=>0000000
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,1,2,6,7,3,4,8]=>0000001=>1000000
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,6,3,8,4,7]=>0000000=>0000000
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,1,2,6,8,3,4,7]=>0000000=>0000000
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,6,3,4,7,8]=>0000011=>1100000
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4]=>0000000=>0000000
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[5,1,6,7,2,8,3,4]=>0000000=>0000000
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,2,3,4]=>0000000=>0000000
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[5,1,6,2,3,8,4,7]=>0000000=>0000000
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,1,6,2,8,3,4,7]=>0000000=>0000000
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,6,1,7,8,2,3,4]=>0000000=>0000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,7,1,2,3,8,4]=>0000000=>0000000
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,7,1,2,8,3,4]=>0000000=>0000000
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>0000000=>0000000
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>0000000=>0000000
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>0000001=>1000000
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,8,4,7]=>0000000=>0000000
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>0000000=>0000000
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>0000000=>0000000
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,7,8,4,6]=>0000000=>0000000
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>0000000=>0000000
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,7,3,8,4,6]=>0000000=>0000000
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,7,8,3,4,6]=>0000000=>0000000
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,7,2,8,3,4,6]=>0000000=>0000000
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,7,1,2,8,3,4,6]=>0000000=>0000000
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>0000000=>0000000
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6,8]=>0000001=>1000000
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>0000000=>0000000
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>0000111=>1110000
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]=>1111000=>0001111
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]=>1111001=>1001111
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>1111010=>0101111
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,6,8,5,7]=>1111000=>0001111
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>1111011=>1101111
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,6,4,7,8,5]=>1110000=>0000111
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,6,4,7,5,8]=>1110001=>1000111
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,2,3,6,7,4,8,5]=>1110000=>0000111
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,7,8,4,5]=>1110000=>0000111
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,8,7]=>1110010=>0100111
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,2,3,6,4,8,5,7]=>1110000=>0000111
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>1110011=>1100111
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,2,6,3,4,7,8,5]=>1100000=>0000011
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,2,6,3,4,7,5,8]=>1100001=>1000011
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,2,6,3,7,4,8,5]=>1100000=>0000011
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,2,6,7,3,4,8,5]=>1100000=>0000011
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,2,6,7,3,8,4,5]=>1100000=>0000011
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,7,8,3,4,5]=>1100000=>0000011
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,8,7]=>1100010=>0100011
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,8,5,7]=>1100000=>0000011
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>1100000=>0000011
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,3,4,5,7,8]=>1100011=>1100011
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,7,5,8]=>1000001=>1000001
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,6,2,3,7,4,8,5]=>1000000=>0000001
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,6,2,7,3,4,8,5]=>1000000=>0000001
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>1000000=>0000001
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,6,2,7,3,4,5,8]=>1000001=>1000001
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,6,7,2,3,4,8,5]=>1000000=>0000001
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,7,2,3,8,4,5]=>1000000=>0000001
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]=>1000000=>0000001
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>1000000=>0000001
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,6,7,2,3,4,5,8]=>1000001=>1000001
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,8,7]=>1000010=>0100001
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>1000000=>0000001
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,8,4,5,7]=>1000000=>0000001
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>1000000=>0000001
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>1000000=>0000001
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,6,2,3,4,5,7,8]=>1000011=>1100001
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,7,3,4,8,5]=>0000000=>0000000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,7,2,8,3,4,5]=>0000000=>0000000
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>0000000=>0000000
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,7,2,3,4,5,8]=>0000001=>1000000
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,7,1,2,3,8,4,5]=>0000000=>0000000
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>0000000=>0000000
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>0000000=>0000000
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5,8]=>0000001=>1000000
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>0000000=>0000000
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>0000000=>0000000
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6]=>1111100=>0011111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>1111101=>1011111
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,7,5,8,6]=>1111000=>0001111
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,7,8,5,6]=>1111000=>0001111
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,7,5,6,8]=>1111001=>1001111
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,7,4,5,8,6]=>1110000=>0000111
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,7,4,8,5,6]=>1110000=>0000111
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,7,8,4,5,6]=>1110000=>0000111
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>1110001=>1000111
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,2,7,3,4,5,8,6]=>1100000=>0000011
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,2,7,3,4,8,5,6]=>1100000=>0000011
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>1100000=>0000011
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6,8]=>1100001=>1000011
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>1000000=>0000001
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>1000000=>0000001
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[7,1,2,8,3,4,5,6]=>0000000=>0000000
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>0000000=>0000000
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8]=>0000001=>1000000
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]=>1111110=>0111111
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,8,6,7]=>1111100=>0011111
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,8,5,6,7]=>1111000=>0001111
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>1110000=>0000111
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>1100000=>0000011
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>1000000=>0000001
[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
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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.
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
reverse
Description
Return the reversal of a binary word.
searching the database
Sorry, this map was not found in the database.