Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00130: Permutations —descent tops⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>=>
[1,0,1,0]=>[1,2]=>0=>0
[1,1,0,0]=>[2,1]=>1=>1
[1,0,1,0,1,0]=>[1,2,3]=>00=>00
[1,0,1,1,0,0]=>[1,3,2]=>01=>10
[1,1,0,0,1,0]=>[2,1,3]=>10=>01
[1,1,0,1,0,0]=>[2,3,1]=>01=>10
[1,1,1,0,0,0]=>[3,2,1]=>11=>11
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>000=>000
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>001=>100
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>010=>010
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>001=>100
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>011=>110
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>100=>001
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>101=>101
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>010=>010
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>001=>100
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>011=>110
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>110=>011
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>011=>110
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>101=>101
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>111=>111
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>0000=>0000
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>0001=>1000
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>0010=>0100
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>0001=>1000
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>0011=>1100
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>0100=>0010
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>0101=>1010
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>0010=>0100
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>0001=>1000
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>0011=>1100
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>0110=>0110
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>0011=>1100
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>0101=>1010
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>0111=>1110
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>1000=>0001
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>1001=>1001
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>1010=>0101
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>1001=>1001
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>1011=>1101
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>0100=>0010
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>0101=>1010
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>0010=>0100
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>0001=>1000
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>0011=>1100
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>0110=>0110
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>0011=>1100
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>0101=>1010
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>0111=>1110
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>1100=>0011
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>1101=>1011
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>0110=>0110
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>0101=>1010
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>0111=>1110
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>1010=>0101
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>0011=>1100
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>1001=>1001
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>1011=>1101
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>1110=>0111
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>0111=>1110
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>1011=>1101
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>1101=>1011
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>1111=>1111
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>00000=>00000
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>00001=>10000
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>00010=>01000
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>00001=>10000
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>00011=>11000
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>00100=>00100
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>00101=>10100
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>00010=>01000
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>00001=>10000
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>00011=>11000
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>00110=>01100
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>00011=>11000
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>00101=>10100
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>00111=>11100
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>01000=>00010
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>01001=>10010
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>01010=>01010
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>01001=>10010
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>01011=>11010
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>00100=>00100
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>00101=>10100
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>00010=>01000
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>00001=>10000
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>00011=>11000
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>00110=>01100
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>00011=>11000
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>00101=>10100
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>00111=>11100
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>01100=>00110
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>01101=>10110
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>00110=>01100
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>00101=>10100
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>00111=>11100
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>01010=>01010
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>00011=>11000
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>01001=>10010
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>01011=>11010
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>01110=>01110
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>00111=>11100
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>01011=>11010
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>01101=>10110
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>01111=>11110
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>10000=>00001
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>10001=>10001
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>10010=>01001
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>10001=>10001
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>10011=>11001
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>10100=>00101
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>10101=>10101
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>10010=>01001
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>10001=>10001
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>10011=>11001
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>10110=>01101
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>10011=>11001
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>10101=>10101
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>10111=>11101
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>01000=>00010
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>01001=>10010
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>01010=>01010
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>01001=>10010
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>01011=>11010
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>00100=>00100
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>00101=>10100
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>00010=>01000
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>00001=>10000
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>00011=>11000
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>00110=>01100
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>00011=>11000
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>00101=>10100
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>00111=>11100
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>01100=>00110
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>01101=>10110
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>00110=>01100
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>00101=>10100
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>00111=>11100
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>01010=>01010
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>00011=>11000
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>01001=>10010
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>01011=>11010
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>01110=>01110
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>00111=>11100
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>01011=>11010
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>01101=>10110
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>01111=>11110
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>11000=>00011
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>11001=>10011
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>11010=>01011
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>11001=>10011
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>11011=>11011
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>01100=>00110
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>01101=>10110
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>01010=>01010
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>01001=>10010
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>01011=>11010
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>01110=>01110
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>01011=>11010
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>01101=>10110
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>01111=>11110
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>10100=>00101
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>10101=>10101
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>00110=>01100
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>00101=>10100
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>00111=>11100
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>10010=>01001
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>00011=>11000
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>10001=>10001
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>10011=>11001
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>10110=>01101
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>00111=>11100
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>10011=>11001
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>10101=>10101
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>10111=>11101
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>11100=>00111
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>11101=>10111
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>01110=>01110
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>01101=>10110
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>01111=>11110
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>10110=>01101
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>00111=>11100
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>10101=>10101
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>10111=>11101
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>11010=>01011
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>01011=>11010
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>10011=>11001
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>11001=>10011
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>11011=>11011
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>11110=>01111
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>01111=>11110
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>10111=>11101
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>11011=>11011
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>11101=>10111
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>11111=>11111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>000000=>000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>000001=>100000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>000010=>010000
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>000001=>100000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>000011=>110000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>000100=>001000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>000101=>101000
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>000010=>010000
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>000001=>100000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>000011=>110000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>000110=>011000
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>000011=>110000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>000101=>101000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>000111=>111000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>001000=>000100
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>001001=>100100
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>001010=>010100
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>001001=>100100
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>001011=>110100
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>000100=>001000
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>000101=>101000
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>000010=>010000
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>000001=>100000
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>000011=>110000
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>000110=>011000
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>000011=>110000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>000101=>101000
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>000111=>111000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>001100=>001100
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>001101=>101100
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>000110=>011000
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>000101=>101000
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>000111=>111000
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>001010=>010100
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>000011=>110000
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>001001=>100100
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>001011=>110100
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>001110=>011100
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>000111=>111000
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>001011=>110100
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>001101=>101100
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>001111=>111100
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>010000=>000010
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>010001=>100010
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>010010=>010010
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>010001=>100010
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>010011=>110010
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>010100=>001010
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>010101=>101010
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>010010=>010010
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>010001=>100010
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>010011=>110010
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>010110=>011010
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>010011=>110010
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>010101=>101010
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>010111=>111010
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>001000=>000100
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>001001=>100100
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>001010=>010100
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>001001=>100100
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>001011=>110100
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>000100=>001000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>000101=>101000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>000010=>010000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>000001=>100000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>000011=>110000
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>000110=>011000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>000011=>110000
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>000101=>101000
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>000111=>111000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>001100=>001100
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>001101=>101100
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>000110=>011000
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>000101=>101000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>000111=>111000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>001010=>010100
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>000011=>110000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>001001=>100100
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>001011=>110100
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>001110=>011100
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>000111=>111000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>001011=>110100
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>001101=>101100
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>001111=>111100
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>011000=>000110
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>011001=>100110
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>011010=>010110
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>011001=>100110
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>011011=>110110
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>001100=>001100
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>001101=>101100
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>001010=>010100
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>001001=>100100
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>001011=>110100
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>001110=>011100
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>001011=>110100
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>001101=>101100
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>001111=>111100
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>010100=>001010
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>010101=>101010
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>000110=>011000
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>000101=>101000
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>000111=>111000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>010010=>010010
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>000011=>110000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>010001=>100010
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>010011=>110010
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>010110=>011010
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>000111=>111000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>010011=>110010
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>010101=>101010
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>010111=>111010
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>011100=>001110
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>011101=>101110
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>001110=>011100
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>001101=>101100
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>001111=>111100
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>010110=>011010
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>000111=>111000
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>010101=>101010
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>010111=>111010
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>011010=>010110
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>001011=>110100
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>010011=>110010
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>011001=>100110
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>011011=>110110
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>011110=>011110
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>001111=>111100
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>010111=>111010
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>011011=>110110
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>011101=>101110
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>011111=>111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>100000=>000001
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>100001=>100001
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>100010=>010001
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>100001=>100001
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>100011=>110001
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>100100=>001001
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>100101=>101001
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>100010=>010001
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>100001=>100001
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>100011=>110001
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>100110=>011001
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>100011=>110001
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>100101=>101001
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>100111=>111001
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>101000=>000101
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>101001=>100101
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>101010=>010101
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>101001=>100101
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>101011=>110101
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>100100=>001001
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>100101=>101001
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>100010=>010001
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>100001=>100001
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>100011=>110001
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>100110=>011001
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>100011=>110001
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>100101=>101001
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>100111=>111001
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>101100=>001101
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>101101=>101101
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>100110=>011001
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>100101=>101001
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>100111=>111001
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>101010=>010101
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>100011=>110001
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>101001=>100101
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>101011=>110101
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>101110=>011101
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>100111=>111001
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>101011=>110101
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>101101=>101101
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>101111=>111101
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>010000=>000010
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>010001=>100010
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>010010=>010010
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>010001=>100010
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>010011=>110010
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>010100=>001010
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>010101=>101010
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>010010=>010010
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>010001=>100010
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>010011=>110010
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>010110=>011010
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>010011=>110010
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>010101=>101010
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>010111=>111010
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>001000=>000100
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>001001=>100100
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>001010=>010100
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>001001=>100100
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>001011=>110100
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>000100=>001000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>000101=>101000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>000010=>010000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>000001=>100000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>000011=>110000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>000110=>011000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>000011=>110000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>000101=>101000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>000111=>111000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>001100=>001100
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>001101=>101100
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>000110=>011000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>000101=>101000
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>000111=>111000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>001010=>010100
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>000011=>110000
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>001001=>100100
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>001011=>110100
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>001110=>011100
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>000111=>111000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>001011=>110100
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>001101=>101100
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>001111=>111100
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>011000=>000110
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>011001=>100110
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>011010=>010110
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>011001=>100110
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>011011=>110110
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>001100=>001100
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>001101=>101100
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>001010=>010100
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>001001=>100100
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>001011=>110100
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>001110=>011100
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>001011=>110100
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>001101=>101100
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>001111=>111100
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>010100=>001010
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>010101=>101010
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>000110=>011000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>000101=>101000
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>000111=>111000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>010010=>010010
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>000011=>110000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>010001=>100010
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>010011=>110010
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>010110=>011010
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>000111=>111000
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>010011=>110010
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>010101=>101010
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>010111=>111010
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>011100=>001110
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>011101=>101110
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>001110=>011100
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>001101=>101100
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>001111=>111100
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>010110=>011010
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>000111=>111000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>010101=>101010
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>010111=>111010
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>011010=>010110
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>001011=>110100
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>010011=>110010
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>011001=>100110
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>011011=>110110
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>011110=>011110
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>001111=>111100
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>010111=>111010
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>011011=>110110
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>011101=>101110
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>011111=>111110
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>110000=>000011
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>110001=>100011
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>110010=>010011
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>110001=>100011
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>110011=>110011
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>110100=>001011
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>110101=>101011
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>110010=>010011
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>110001=>100011
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>110011=>110011
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>110110=>011011
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>110011=>110011
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>110101=>101011
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>110111=>111011
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>011000=>000110
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>011001=>100110
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>011010=>010110
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>011001=>100110
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>011011=>110110
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>010100=>001010
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>010101=>101010
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>010010=>010010
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>010001=>100010
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>010011=>110010
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>010110=>011010
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>010011=>110010
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>010101=>101010
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>010111=>111010
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>011100=>001110
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>011101=>101110
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>010110=>011010
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>010101=>101010
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>010111=>111010
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>011010=>010110
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>010011=>110010
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>011001=>100110
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>011011=>110110
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>011110=>011110
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>010111=>111010
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>011011=>110110
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>011101=>101110
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>011111=>111110
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>101000=>000101
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>101001=>100101
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>101010=>010101
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>101001=>100101
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>101011=>110101
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>001100=>001100
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>001101=>101100
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>001010=>010100
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>001001=>100100
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>001011=>110100
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>001110=>011100
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>001011=>110100
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>001101=>101100
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>001111=>111100
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>100100=>001001
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>100101=>101001
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>000110=>011000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>000101=>101000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>000111=>111000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>100010=>010001
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>000011=>110000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>100001=>100001
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>100011=>110001
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>100110=>011001
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>000111=>111000
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>100011=>110001
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>100101=>101001
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>100111=>111001
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>101100=>001101
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>101101=>101101
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>001110=>011100
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>001101=>101100
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>001111=>111100
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>100110=>011001
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>000111=>111000
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>100101=>101001
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>100111=>111001
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>101010=>010101
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>001011=>110100
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>100011=>110001
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>101001=>100101
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>101011=>110101
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>101110=>011101
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>001111=>111100
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>100111=>111001
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>101011=>110101
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>101101=>101101
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>101111=>111101
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>111000=>000111
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>111001=>100111
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>111010=>010111
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>111001=>100111
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>111011=>110111
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>011100=>001110
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>011101=>101110
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>011010=>010110
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>011001=>100110
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>011011=>110110
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>011110=>011110
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>011011=>110110
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>011101=>101110
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>011111=>111110
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>101100=>001101
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>101101=>101101
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>001110=>011100
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>001101=>101100
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>001111=>111100
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>101010=>010101
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>001011=>110100
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>101001=>100101
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>101011=>110101
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>101110=>011101
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>001111=>111100
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>101011=>110101
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>101101=>101101
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>101111=>111101
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>110100=>001011
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>110101=>101011
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>010110=>011010
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>010101=>101010
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>010111=>111010
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>100110=>011001
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>000111=>111000
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>100101=>101001
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>100111=>111001
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>110010=>010011
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>010011=>110010
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>100011=>110001
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>110001=>100011
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>110011=>110011
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>110110=>011011
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>010111=>111010
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>100111=>111001
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>110011=>110011
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>110101=>101011
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>110111=>111011
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>111100=>001111
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>111101=>101111
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>011110=>011110
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>011101=>101110
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>011111=>111110
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>101110=>011101
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>001111=>111100
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>101101=>101101
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>101111=>111101
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>110110=>011011
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>010111=>111010
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>100111=>111001
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>110101=>101011
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>110111=>111011
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>111010=>010111
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>011011=>110110
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>101011=>110101
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>110011=>110011
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>111001=>100111
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>111011=>110111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>111110=>011111
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>011111=>111110
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>101111=>111101
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>110111=>111011
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>111011=>110111
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>111101=>101111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>111111=>111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>0000000=>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=>1000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>0000010=>0100000
[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=>1000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>0000011=>1100000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>0000100=>0010000
[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=>1010000
[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=>0100000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>0000001=>1000000
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>0000011=>1100000
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>0000110=>0110000
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>0000011=>1100000
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>0000101=>1010000
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>0000111=>1110000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>0001000=>0001000
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>0001001=>1001000
[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=>0101000
[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=>1001000
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>0001011=>1101000
[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=>0010000
[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=>1010000
[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=>0100000
[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=>1000000
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>0000011=>1100000
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>0000110=>0110000
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>0000011=>1100000
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>0000101=>1010000
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>0000111=>1110000
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,5,4,7,8]=>0001100=>0011000
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>0001101=>1011000
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>0000110=>0110000
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>0000101=>1010000
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>0000111=>1110000
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,5,4,8]=>0001010=>0101000
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>0000011=>1100000
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>0001001=>1001000
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>0001011=>1101000
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>0001110=>0111000
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>0000111=>1110000
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>0001011=>1101000
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>0001101=>1011000
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>0001111=>1111000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>0010000=>0000100
[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=>1000100
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>0010010=>0100100
[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=>1000100
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,7,6]=>0010011=>1100100
[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=>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=>1010100
[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=>0100100
[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=>1000100
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>0010011=>1100100
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>0010011=>1100100
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,6,5]=>0010101=>1010100
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>0010111=>1110100
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6,8]=>0001010=>0101000
[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=>1001000
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>0001011=>1101000
[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=>0010000
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,6,3,8,7]=>0000101=>1010000
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,7,3,8]=>0000010=>0100000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>0000001=>1000000
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,7,3]=>0000011=>1100000
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,7,8,6,3]=>0000101=>1010000
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,7,6,3]=>0000111=>1110000
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,5,3,7,8]=>0001100=>0011000
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,4,6,5,7,8,3]=>0000101=>1010000
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,4,6,5,8,7,3]=>0000111=>1110000
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,4,6,7,5,3,8]=>0001010=>0101000
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>0001001=>1001000
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,7,5,3]=>0001011=>1101000
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>0000111=>1110000
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,6,8,5,3]=>0001011=>1101000
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>0001101=>1011000
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>0001111=>1111000
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,4,3,6,7,8]=>0011000=>0001100
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>0011001=>1001100
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>0011001=>1001100
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,4,3,8,7,6]=>0011011=>1101100
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>0001010=>0101000
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>0001001=>1001000
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>0001011=>1101000
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,4,7,6,8,3]=>0001011=>1101000
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,4,7,8,6,3]=>0001101=>1011000
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>0001111=>1111000
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,4,3,7,8]=>0010100=>0010100
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,4,7,3,8]=>0000110=>0110000
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,4,7,8,3]=>0000101=>1010000
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,5,6,7,4,3,8]=>0010010=>0100100
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,4,8,3]=>0000011=>1100000
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>0010001=>1000100
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,7,4,3]=>0010011=>1100100
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,5,7,6,4,3,8]=>0010110=>0110100
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,6,4,8,3]=>0000111=>1110000
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,6,8,4,3]=>0010011=>1100100
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,8,7,6,4,3]=>0010111=>1110100
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>0011100=>0011100
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>0001101=>1011000
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>0001111=>1111000
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,5,7,8,4,3]=>0010101=>1010100
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,5,8,7,4,3]=>0010111=>1110100
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,6,7,5,4,3,8]=>0011010=>0101100
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>0011001=>1001100
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>0011110=>0111100
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,6,5,4,8,3]=>0001111=>1111000
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,6,5,8,4,3]=>0010111=>1110100
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,6,8,5,4,3]=>0011011=>1101100
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,6,5,4,3]=>0011101=>1011100
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>0011111=>1111100
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>0100000=>0000010
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>0100001=>1000010
[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=>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=>1000010
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,7,6]=>0100011=>1100010
[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=>0010010
[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=>1010010
[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=>1000010
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>0100011=>1100010
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>0100110=>0110010
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>0100011=>1100010
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>0100111=>1110010
[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=>0001010
[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=>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=>1001010
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>0101011=>1101010
[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=>0010010
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2,5,6,4,8,7]=>0100101=>1010010
[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=>0100010
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>0100001=>1000010
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,2,5,6,8,7,4]=>0100011=>1100010
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>0100110=>0110010
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,6,8,4]=>0100011=>1100010
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>0100101=>1010010
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,7,6,4]=>0100111=>1110010
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,5,4,7,8]=>0101100=>0011010
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,6,5,4,8,7]=>0101101=>1011010
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>0100110=>0110010
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>0100101=>1010010
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>0100111=>1110010
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,2,6,7,5,4,8]=>0101010=>0101010
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,5,8,4]=>0100011=>1100010
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,2,6,7,8,5,4]=>0101001=>1001010
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,6,8,7,5,4]=>0101011=>1101010
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,6,5,4,8]=>0101110=>0111010
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,6,5,8,4]=>0100111=>1110010
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,6,8,5,4]=>0101011=>1101010
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>0101111=>1111010
[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=>0000100
[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=>1000100
[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=>0100100
[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=>1000100
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,7,6]=>0010011=>1100100
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7]=>0010101=>1010100
[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=>0100100
[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=>1000100
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>0010011=>1100100
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>0010011=>1100100
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,6,5]=>0010101=>1010100
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>0010111=>1110100
[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=>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=>1001000
[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=>0101000
[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=>1001000
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,5,2,8,7,6]=>0001011=>1101000
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>0000100=>0010000
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,2,8,7]=>0000101=>1010000
[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=>0100000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>0000001=>1000000
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>0000011=>1100000
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,5,7,6,2,8]=>0000110=>0110000
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,7,6,8,2]=>0000011=>1100000
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,6,2]=>0000101=>1010000
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,7,6,2]=>0000111=>1110000
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,4,6,5,7,2,8]=>0000110=>0110000
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,4,6,5,7,8,2]=>0000101=>1010000
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,4,6,7,5,2,8]=>0001010=>0101000
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,5,8,2]=>0000011=>1100000
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,5,2]=>0001001=>1001000
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>0000111=>1110000
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,7,6,8,5,2]=>0001011=>1101000
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>0001111=>1111000
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,4,2,6,7,8]=>0011000=>0001100
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>0011001=>1001100
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,4,2,7,6,8]=>0011010=>0101100
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,4,2,7,8,6]=>0011001=>1001100
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,5,4,6,2,7,8]=>0001100=>0011000
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,4,6,7,2,8]=>0001010=>0101000
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,5,4,6,7,8,2]=>0001001=>1001000
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>0001110=>0111000
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,4,7,6,8,2]=>0001011=>1101000
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,4,7,8,6,2]=>0001101=>1011000
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,4,8,7,6,2]=>0001111=>1111000
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>0010100=>0010100
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,4,7,2,8]=>0000110=>0110000
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,4,7,8,2]=>0000101=>1010000
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,4,2,8]=>0010010=>0100100
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,5,6,7,4,8,2]=>0000011=>1100000
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>0010001=>1000100
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,8,7,4,2]=>0010011=>1100100
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,6,4,2,8]=>0010110=>0110100
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,6,4,8,2]=>0000111=>1110000
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,6,8,4,2]=>0010011=>1100100
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>0010101=>1010100
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,7,6,4,2]=>0010111=>1110100
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,6,5,4,2,8,7]=>0011101=>1011100
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,5,4,7,2,8]=>0001110=>0111000
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>0001111=>1111000
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,6,5,7,4,2,8]=>0010110=>0110100
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,5,7,4,8,2]=>0000111=>1110000
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>0010101=>1010100
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,6,7,5,4,2,8]=>0011010=>0101100
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,5,8,4,2]=>0010011=>1100100
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,5,4,2]=>0011001=>1001100
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,6,8,7,5,4,2]=>0011011=>1101100
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,7,6,5,4,2,8]=>0011110=>0111100
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,7,8,6,5,4,2]=>0011101=>1011100
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>0011111=>1111100
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>0110000=>0000110
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>0110001=>1000110
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>0110010=>0100110
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,3,2,5,7,8,6]=>0110001=>1000110
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>0110011=>1100110
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,4,3,2,6,7,5,8]=>0110010=>0100110
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>0110001=>1000110
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,3,2,6,8,7,5]=>0110011=>1100110
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>0110110=>0110110
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>0110011=>1100110
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>0110111=>1110110
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>0011010=>0101100
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3,5,2,7,8,6]=>0011001=>1001100
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3,5,2,8,7,6]=>0011011=>1101100
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,3,5,6,2,7,8]=>0010100=>0010100
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>0010001=>1000100
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,3,5,7,6,2,8]=>0010110=>0110100
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,3,5,7,8,6,2]=>0010101=>1010100
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>0010111=>1110100
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>0011100=>0011100
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>0010110=>0110100
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,3,6,5,7,8,2]=>0010101=>1010100
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>0010111=>1110100
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,3,6,7,5,8,2]=>0010011=>1100100
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,6,7,8,5,2]=>0011001=>1001100
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,6,8,7,5,2]=>0011011=>1101100
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,7,6,8,5,2]=>0011011=>1101100
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>0011101=>1011100
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>0011111=>1111100
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,3,2,6,7,8]=>0101000=>0001010
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,5,3,2,6,8,7]=>0101001=>1001010
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,3,2,7,6,8]=>0101010=>0101010
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,5,3,2,7,8,6]=>0101001=>1001010
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,5,3,2,8,7,6]=>0101011=>1101010
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,3,6,2,7,8]=>0001100=>0011000
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,3,6,7,2,8]=>0001010=>0101000
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>0001001=>1001000
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,3,6,8,7,2]=>0001011=>1101000
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,3,7,8,6,2]=>0001101=>1011000
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,3,8,7,6,2]=>0001111=>1111000
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,6,3,2,7,8]=>0100100=>0010010
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,6,3,7,2,8]=>0000110=>0110000
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,6,3,8,7,2]=>0000111=>1110000
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,3,2,8]=>0100010=>0100010
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,3,8,2]=>0000011=>1100000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,3,2]=>0100001=>1000010
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,7,8,6,3,2]=>0100101=>1010010
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,8,7,6,3,2]=>0100111=>1110010
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,6,5,3,2,7,8]=>0101100=>0011010
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,5,3,8,7,2]=>0001111=>1111000
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,5,7,3,2,8]=>0100110=>0110010
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,6,5,7,3,8,2]=>0000111=>1110000
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,5,8,7,3,2]=>0100111=>1110010
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,4,6,7,5,3,2,8]=>0101010=>0101010
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,5,3,8,2]=>0001011=>1101000
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,5,8,3,2]=>0100011=>1100010
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,4,6,7,8,5,3,2]=>0101001=>1001010
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,7,5,3,2]=>0101011=>1101010
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,4,7,6,5,3,2,8]=>0101110=>0111010
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,4,7,6,5,8,3,2]=>0100111=>1110010
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,4,7,8,6,5,3,2]=>0101101=>1011010
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>0101111=>1111010
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>0111000=>0001110
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>0111010=>0101110
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,4,3,2,7,8,6]=>0111001=>1001110
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>0111011=>1101110
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>0011100=>0011100
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,5,4,3,6,7,2,8]=>0011010=>0101100
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>0011001=>1001100
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>0011011=>1101100
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,4,3,8,7,6,2]=>0011111=>1111100
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,4,6,3,2,7,8]=>0101100=>0011010
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,4,6,3,2,8,7]=>0101101=>1011010
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>0001110=>0111000
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,4,6,3,7,8,2]=>0001101=>1011000
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,4,6,7,3,2,8]=>0101010=>0101010
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,4,6,7,3,8,2]=>0001011=>1101000
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,3,2]=>0101001=>1001010
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,4,6,8,7,3,2]=>0101011=>1101010
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,4,7,6,3,2,8]=>0101110=>0111010
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,4,7,8,6,3,2]=>0101101=>1011010
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,6,4,3,2,7,8]=>0110100=>0010110
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,6,4,3,2,8,7]=>0110101=>1010110
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,4,3,8,7,2]=>0010111=>1110100
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,5,6,4,7,3,2,8]=>0100110=>0110010
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,4,7,3,8,2]=>0000111=>1110000
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,5,6,4,7,8,3,2]=>0100101=>1010010
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,5,6,7,4,3,2,8]=>0110010=>0100110
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,4,3,8,2]=>0010011=>1100100
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>0110001=>1000110
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,6,8,4,3,2]=>0110011=>1100110
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>0110111=>1110110
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,5,4,3,2,7,8]=>0111100=>0011110
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,5,4,3,2,8,7]=>0111101=>1011110
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,5,4,3,7,8,2]=>0011101=>1011100
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>0011111=>1111100
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,6,5,4,7,8,3,2]=>0101101=>1011010
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,6,5,4,8,7,3,2]=>0101111=>1111010
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,5,7,4,3,2,8]=>0110110=>0110110
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,5,7,4,3,8,2]=>0010111=>1110100
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,4,3,2]=>0110101=>1010110
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,5,8,7,4,3,2]=>0110111=>1110110
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,5,4,3,2,8]=>0111010=>0101110
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,5,4,3,8,2]=>0011011=>1101100
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,5,8,4,3,2]=>0110011=>1100110
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>0111001=>1001110
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>0111011=>1101110
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>0111110=>0111110
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,6,5,4,3,8,2]=>0011111=>1111100
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,6,5,4,8,3,2]=>0101111=>1111010
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>0110111=>1110110
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>0111011=>1101110
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>0111101=>1011110
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>0111111=>1111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>1000000=>0000001
[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=>1000001
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>1000010=>0100001
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>1000001=>1000001
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,7,6]=>1000011=>1100001
[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=>0010001
[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=>1010001
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,4,6,7,5,8]=>1000010=>0100001
[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=>1000001
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>1000011=>1100001
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,6,5]=>1000101=>1010001
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>1000111=>1110001
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>1001000=>0001001
[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=>1001001
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,5,4,7,8,6]=>1001001=>1001001
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>1001011=>1101001
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,5,6,4,8,7]=>1000101=>1010001
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>1000001=>1000001
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,3,5,7,6,8,4]=>1000011=>1100001
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>1001101=>1011001
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,6,5,8,7,4]=>1000111=>1110001
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,5,4,8]=>1001010=>0101001
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,5,4]=>1001001=>1001001
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,6,8,7,5,4]=>1001011=>1101001
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,6,5,4]=>1001101=>1011001
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>1001111=>1111001
[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=>0000101
[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=>1000101
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,3,5,7,8,6]=>1010001=>1000101
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,7,6]=>1010011=>1100101
[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=>0010101
[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=>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=>0100101
[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=>1000101
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>1010011=>1100101
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>1010011=>1100101
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>1010101=>1010101
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>1010111=>1110101
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>1001000=>0001001
[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=>1001001
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,4,5,3,8,7,6]=>1001011=>1101001
[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=>1010001
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,7,3,8]=>1000010=>0100001
[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=>1000001
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>1000011=>1100001
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>1000101=>1010001
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>1000111=>1110001
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>1001100=>0011001
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>1001101=>1011001
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>1000111=>1110001
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,5,3,8]=>1001010=>0101001
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,5,8,3]=>1000011=>1100001
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,6,7,8,5,3]=>1001001=>1001001
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>1001011=>1101001
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>1000111=>1110001
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,7,6,8,5,3]=>1001011=>1101001
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>1001101=>1011001
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>1001111=>1111001
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,4,3,6,7,8]=>1011000=>0001101
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>1011001=>1001101
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,4,3,7,6,8]=>1011010=>0101101
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,5,4,3,8,7,6]=>1011011=>1101101
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>1001101=>1011001
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,4,6,7,3,8]=>1001010=>0101001
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,4,6,7,8,3]=>1001001=>1001001
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,4,6,8,7,3]=>1001011=>1101001
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>1001011=>1101001
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,4,7,8,6,3]=>1001101=>1011001
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,4,8,7,6,3]=>1001111=>1111001
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,4,3,7,8]=>1010100=>0010101
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>1010101=>1010101
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,4,7,8,3]=>1000101=>1010001
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,5,6,4,8,7,3]=>1000111=>1110001
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,4,3,8]=>1010010=>0100101
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,4,8,3]=>1000011=>1100001
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>1010001=>1000101
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,5,6,8,7,4,3]=>1010011=>1100101
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,6,4,8,3]=>1000111=>1110001
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,6,8,4,3]=>1010011=>1100101
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>1010101=>1010101
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,5,8,7,6,4,3]=>1010111=>1110101
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>1011101=>1011101
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,5,4,8,7,3]=>1001111=>1111001
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>1000111=>1110001
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>1010101=>1010101
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>1010111=>1110101
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,6,7,5,4,3,8]=>1011010=>0101101
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,5,4,8,3]=>1001011=>1101001
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>1010011=>1100101
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>1011001=>1001101
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,6,8,7,5,4,3]=>1011011=>1101101
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>1011110=>0111101
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,6,5,4,8,3]=>1001111=>1111001
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>1010111=>1110101
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>1011011=>1101101
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,6,5,4,3]=>1011101=>1011101
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>1011111=>1111101
[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=>0000010
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,8,7]=>0100001=>1000010
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,5,7,6,8]=>0100010=>0100010
[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=>1000010
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,4,6,5,8,7]=>0100101=>1010010
[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=>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=>1000010
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>0100011=>1100010
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,6,5]=>0100101=>1010010
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>0100111=>1110010
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8]=>0101000=>0001010
[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=>0101010
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,5,6,4,7,8]=>0100100=>0010010
[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=>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=>1000010
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,6,8,4]=>0100011=>1100010
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,7,8,6,4]=>0100101=>1010010
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,5,4,7,8]=>0101100=>0011010
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>0101101=>1011010
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>0100110=>0110010
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>0100111=>1110010
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,6,7,5,4,8]=>0101010=>0101010
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,5,8,4]=>0100011=>1100010
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,5,4]=>0101001=>1001010
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,7,5,4]=>0101011=>1101010
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,6,5,8,4]=>0100111=>1110010
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,6,8,5,4]=>0101011=>1101010
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,6,5,4]=>0101101=>1011010
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>0101111=>1111010
[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=>0000100
[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=>1000100
[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=>0100100
[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=>1000100
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>0010011=>1100100
[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=>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=>1010100
[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=>0100100
[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=>1000100
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>0010011=>1100100
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>0010110=>0110100
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>0010011=>1100100
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>0010101=>1010100
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>0010111=>1110100
[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=>0001000
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,8,7]=>0001001=>1001000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,8]=>0001010=>0101000
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>0001001=>1001000
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>0001011=>1101000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>0000100=>0010000
[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=>1010000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>0000010=>0100000
[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=>1000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>0000011=>1100000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,6,1,8]=>0000110=>0110000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>0000011=>1100000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]=>0000101=>1010000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>0000111=>1110000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,6,5,1,7,8]=>0001100=>0011000
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,6,5,7,1,8]=>0000110=>0110000
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>0000101=>1010000
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]=>0000111=>1110000
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,4,6,7,5,1,8]=>0001010=>0101000
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,5,8,1]=>0000011=>1100000
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>0001001=>1001000
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,8,7,5,1]=>0001011=>1101000
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>0001110=>0111000
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>0000111=>1110000
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,6,8,5,1]=>0001011=>1101000
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,6,5,1]=>0001101=>1011000
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>0001111=>1111000
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>0011000=>0001100
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,5,4,1,6,8,7]=>0011001=>1001100
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,4,1,7,6,8]=>0011010=>0101100
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>0011011=>1101100
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,5,4,6,1,7,8]=>0001100=>0011000
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,5,4,6,7,1,8]=>0001010=>0101000
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>0001001=>1001000
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>0001011=>1101000
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,4,7,8,6,1]=>0001101=>1011000
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>0001111=>1111000
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,5,6,4,1,7,8]=>0010100=>0010100
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,4,1,8,7]=>0010101=>1010100
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,4,7,1,8]=>0000110=>0110000
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>0000101=>1010000
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,6,4,8,7,1]=>0000111=>1110000
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,5,6,7,4,1,8]=>0010010=>0100100
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,4,8,1]=>0000011=>1100000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>0010001=>1000100
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>0010011=>1100100
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,5,7,6,4,1,8]=>0010110=>0110100
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,5,7,6,4,8,1]=>0000111=>1110000
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,6,8,4,1]=>0010011=>1100100
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>0010101=>1010100
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,7,6,4,1]=>0010111=>1110100
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,5,4,1,7,8]=>0011100=>0011100
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>0011101=>1011100
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>0001101=>1011000
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,6,5,7,4,1,8]=>0010110=>0110100
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,5,8,7,4,1]=>0010111=>1110100
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,6,7,5,4,1,8]=>0011010=>0101100
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,5,4,1]=>0011001=>1001100
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>0011110=>0111100
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>0001111=>1111000
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,6,5,8,4,1]=>0010111=>1110100
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>0011111=>1111100
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>0110000=>0000110
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,4,3,1,5,8,7,6]=>0110011=>1100110
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,4,3,1,6,5,7,8]=>0110100=>0010110
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>0110101=>1010110
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>0110001=>1000110
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>0110011=>1100110
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>0110011=>1100110
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,7,8,6,5]=>0110101=>1010110
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>0110111=>1110110
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>0011000=>0001100
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,4,3,5,1,6,8,7]=>0011001=>1001100
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>0011010=>0101100
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,3,5,1,7,8,6]=>0011001=>1001100
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3,5,1,8,7,6]=>0011011=>1101100
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,4,3,5,6,1,8,7]=>0010101=>1010100
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>0010001=>1000100
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>0010011=>1100100
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]=>0010011=>1100100
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,3,5,8,7,6,1]=>0010111=>1110100
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,6,5,1,7,8]=>0011100=>0011100
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>0011101=>1011100
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>0010110=>0110100
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>0010101=>1010100
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>0010111=>1110100
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,3,6,7,5,8,1]=>0010011=>1100100
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,3,6,7,8,5,1]=>0011001=>1001100
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]=>0011011=>1101100
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>0010111=>1110100
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>0011111=>1111100
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,3,1,6,7,8]=>0101000=>0001010
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,3,1,6,8,7]=>0101001=>1001010
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,4,5,3,1,7,6,8]=>0101010=>0101010
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,3,1,7,8,6]=>0101001=>1001010
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>0101011=>1101010
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,5,3,6,1,8,7]=>0001101=>1011000
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,4,5,3,6,7,1,8]=>0001010=>0101000
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>0001001=>1001000
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,3,6,8,7,1]=>0001011=>1101000
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,7,8,6,1]=>0001101=>1011000
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,3,8,7,6,1]=>0001111=>1111000
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,3,1,7,8]=>0100100=>0010010
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,1]=>0000101=>1010000
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,3,8,7,1]=>0000111=>1110000
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,3,1,8]=>0100010=>0100010
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,3,8,1]=>0000011=>1100000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]=>0100001=>1000010
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,8,7,3,1]=>0100011=>1100010
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,6,3,1]=>0100101=>1010010
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,5,3,1,7,8]=>0101100=>0011010
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,5,3,1,8,7]=>0101101=>1011010
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,5,3,7,8,1]=>0001101=>1011000
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,5,3,8,7,1]=>0001111=>1111000
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>0000111=>1110000
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,5,7,8,3,1]=>0100101=>1010010
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]=>0100111=>1110010
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,5,3,1,8]=>0101010=>0101010
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,5,3,8,1]=>0001011=>1101000
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,5,8,3,1]=>0100011=>1100010
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]=>0101001=>1001010
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>0101011=>1101010
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,6,5,8,3,1]=>0100111=>1110010
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>0101101=>1011010
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>0101111=>1111010
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>0111000=>0001110
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,5,4,3,1,6,8,7]=>0111001=>1001110
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,5,4,3,1,7,6,8]=>0111010=>0101110
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>0111001=>1001110
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>0111011=>1101110
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,4,3,6,1,8,7]=>0011101=>1011100
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>0011010=>0101100
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>0011001=>1001100
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>0011011=>1101100
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>0011011=>1101100
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>0011101=>1011100
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>0011111=>1111100
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,4,6,3,7,1,8]=>0001110=>0111000
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]=>0001101=>1011000
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,4,6,7,3,1,8]=>0101010=>0101010
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>0001011=>1101000
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,3,1]=>0101001=>1001010
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,5,4,7,6,3,1,8]=>0101110=>0111010
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>0001111=>1111000
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,4,7,6,8,3,1]=>0101011=>1101010
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]=>0101101=>1011010
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,4,8,7,6,3,1]=>0101111=>1111010
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,5,6,4,3,1,8,7]=>0110101=>1010110
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,4,3,7,8,1]=>0010101=>1010100
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,5,6,4,7,3,1,8]=>0100110=>0110010
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,4,7,8,3,1]=>0100101=>1010010
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,4,8,7,3,1]=>0100111=>1110010
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,5,6,7,4,3,1,8]=>0110010=>0100110
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,4,3,8,1]=>0010011=>1100100
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,4,8,3,1]=>0100011=>1100010
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>0110001=>1000110
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,5,7,6,4,3,1,8]=>0110110=>0110110
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,5,8,7,6,4,3,1]=>0110111=>1110110
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,6,5,4,3,1,8,7]=>0111101=>1011110
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>0011101=>1011100
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,6,5,4,3,8,7,1]=>0011111=>1111100
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]=>0101101=>1011010
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,6,5,4,8,7,3,1]=>0101111=>1111010
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,5,7,4,3,8,1]=>0010111=>1110100
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,6,5,7,8,4,3,1]=>0110101=>1010110
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,6,7,5,4,3,1,8]=>0111010=>0101110
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,6,7,5,4,8,3,1]=>0101011=>1101010
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,5,8,4,3,1]=>0110011=>1100110
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,5,4,3,1]=>0111001=>1001110
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>0111011=>1101110
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,6,5,4,3,1,8]=>0111110=>0111110
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]=>0011111=>1111100
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>0101111=>1111010
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,6,8,5,4,3,1]=>0111011=>1101110
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>0111101=>1011110
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>0111111=>1111110
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>1100000=>0000011
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>1100001=>1000011
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,5,7,6,8]=>1100010=>0100011
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>1100001=>1000011
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>1100011=>1100011
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>1100001=>1000011
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>1100011=>1100011
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>1100110=>0110011
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>1100011=>1100011
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>1100101=>1010011
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>1100111=>1110011
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8]=>1101000=>0001011
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>1101010=>0101011
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>1100100=>0010011
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,5,6,7,4,8]=>1100010=>0100011
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>1100001=>1000011
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>1100011=>1100011
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>1100110=>0110011
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>1100011=>1100011
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>1100101=>1010011
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>1100111=>1110011
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,2,1,6,5,4,7,8]=>1101100=>0011011
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7]=>1101101=>1011011
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,2,1,6,5,7,4,8]=>1100110=>0110011
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>1100101=>1010011
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>1100111=>1110011
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,2,1,6,7,5,4,8]=>1101010=>0101011
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>1100011=>1100011
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,6,7,8,5,4]=>1101001=>1001011
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>1101011=>1101011
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>1101110=>0111011
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>1100111=>1110011
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>1101011=>1101011
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>1101101=>1011011
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>1101111=>1111011
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>0110000=>0000110
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>0110001=>1000110
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>0110010=>0100110
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>0110001=>1000110
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>0110011=>1100110
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>0110100=>0010110
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>0110101=>1010110
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>0110010=>0100110
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>0110001=>1000110
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>0110011=>1100110
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>0110110=>0110110
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>0110011=>1100110
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>0110101=>1010110
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>0110111=>1110110
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>0101000=>0001010
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,5,1,8,7,6]=>0101011=>1101010
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,6,1,7,8]=>0100100=>0010010
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,1,8]=>0100010=>0100010
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>0100001=>1000010
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,8,7,1]=>0100011=>1100010
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>0100011=>1100010
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,7,8,6,1]=>0100101=>1010010
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,2,4,6,5,8,7,1]=>0100111=>1110010
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,2,4,6,7,5,1,8]=>0101010=>0101010
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>0100111=>1110010
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,7,8,6,5,1]=>0101101=>1011010
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>0101111=>1111010
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>0111000=>0001110
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,5,4,1,6,8,7]=>0111001=>1001110
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,5,4,1,7,6,8]=>0111010=>0101110
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>0111001=>1001110
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>0111011=>1101110
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>0101101=>1011010
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,1]=>0101001=>1001010
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,5,4,6,8,7,1]=>0101011=>1101010
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>0101110=>0111010
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>0101011=>1101010
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,4,7,8,6,1]=>0101101=>1011010
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,5,6,4,1,8,7]=>0110101=>1010110
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,5,6,4,7,8,1]=>0100101=>1010010
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,5,6,7,4,1,8]=>0110010=>0100110
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,5,6,7,4,8,1]=>0100011=>1100010
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>0110001=>1000110
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,5,7,6,4,1,8]=>0110110=>0110110
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,5,7,6,4,8,1]=>0100111=>1110010
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,5,7,6,8,4,1]=>0110011=>1100110
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,5,7,8,6,4,1]=>0110101=>1010110
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,2,6,5,4,1,8,7]=>0111101=>1011110
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>0101110=>0111010
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>0101111=>1111010
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,2,6,5,7,4,1,8]=>0110110=>0110110
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>0100111=>1110010
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,2,6,5,8,7,4,1]=>0110111=>1110110
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>0111010=>0101110
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>0101011=>1101010
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]=>0111011=>1101110
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>0111110=>0111110
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,2,7,6,5,4,8,1]=>0101111=>1111010
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]=>0111101=>1011110
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>0111111=>1111110
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8]=>1010000=>0000101
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,4,2,1,5,6,8,7]=>1010001=>1000101
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,2,1,5,8,7,6]=>1010011=>1100101
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>1010101=>1010101
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>1010001=>1000101
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>1010011=>1100101
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>1010011=>1100101
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>1010101=>1010101
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>1010111=>1110101
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8]=>0011000=>0001100
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,2,5,1,7,6,8]=>0011010=>0101100
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,2,5,1,7,8,6]=>0011001=>1001100
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>0011011=>1101100
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,2,5,6,1,7,8]=>0010100=>0010100
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,2,5,6,1,8,7]=>0010101=>1010100
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,7,1,8]=>0010010=>0100100
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>0010001=>1000100
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,8,7,1]=>0010011=>1100100
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,4,2,5,7,6,1,8]=>0010110=>0110100
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,2,5,7,6,8,1]=>0010011=>1100100
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>0010101=>1010100
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,2,5,8,7,6,1]=>0010111=>1110100
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,4,2,6,5,1,8,7]=>0011101=>1011100
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,2,6,5,7,1,8]=>0010110=>0110100
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,1]=>0010101=>1010100
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,8,7,1]=>0010111=>1110100
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,4,2,6,7,5,1,8]=>0011010=>0101100
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>0010011=>1100100
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,4,2,7,6,5,1,8]=>0011110=>0111100
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,2,7,6,5,8,1]=>0010111=>1110100
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,2,7,8,6,5,1]=>0011101=>1011100
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>0011111=>1111100
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8]=>1001000=>0001001
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,5,2,1,6,8,7]=>1001001=>1001001
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,5,2,1,7,6,8]=>1001010=>0101001
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,5,2,1,7,8,6]=>1001001=>1001001
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>1001011=>1101001
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,2,6,1,7,8]=>0001100=>0011000
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,2,6,1,8,7]=>0001101=>1011000
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,5,2,6,7,1,8]=>0001010=>0101000
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>0001001=>1001000
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,5,2,7,6,1,8]=>0001110=>0111000
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]=>0001011=>1101000
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,2,7,8,6,1]=>0001101=>1011000
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,2,1,7,8]=>1000100=>0010001
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,2,1,8,7]=>1000101=>1010001
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>0000110=>0110000
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>0000101=>1010000
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,2,8,7,1]=>0000111=>1110000
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,2,1,8]=>1000010=>0100001
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]=>0000011=>1100000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]=>1000001=>1000001
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,7,2,1]=>1000011=>1100001
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,6,2,8,1]=>0000111=>1110000
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]=>1000011=>1100001
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>1000101=>1010001
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>1000111=>1110001
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,4,6,5,2,1,8,7]=>1001101=>1011001
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,5,2,7,1,8]=>0001110=>0111000
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,5,2,7,8,1]=>0001101=>1011000
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]=>0000111=>1110000
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,2,1]=>1000101=>1010001
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,6,7,5,2,8,1]=>0001011=>1101000
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,5,8,2,1]=>1000011=>1100001
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]=>1001001=>1001001
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>1001110=>0111001
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,6,5,2,8,1]=>0001111=>1111000
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,6,5,8,2,1]=>1000111=>1110001
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>1001111=>1111001
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>1011000=>0001101
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,4,2,1,6,8,7]=>1011001=>1001101
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,4,2,1,7,6,8]=>1011010=>0101101
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,4,2,1,7,8,6]=>1011001=>1001101
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>1011011=>1101101
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,5,4,2,6,1,7,8]=>0011100=>0011100
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,5,4,2,6,1,8,7]=>0011101=>1011100
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>0011010=>0101100
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,4,2,6,7,8,1]=>0011001=>1001100
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,4,2,7,6,1,8]=>0011110=>0111100
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,5,4,2,7,6,8,1]=>0011011=>1101100
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,4,2,7,8,6,1]=>0011101=>1011100
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,4,6,2,7,1,8]=>0001110=>0111000
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,4,6,2,7,8,1]=>0001101=>1011000
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,5,4,6,2,8,7,1]=>0001111=>1111000
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,4,6,7,2,8,1]=>0001011=>1101000
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,4,6,7,8,2,1]=>1001001=>1001001
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,5,4,7,6,2,1,8]=>1001110=>0111001
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,2,8,1]=>0001111=>1111000
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]=>1001011=>1101001
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,4,7,8,6,2,1]=>1001101=>1011001
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,4,2,1,8,7]=>1010101=>1010101
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,4,2,7,1,8]=>0010110=>0110100
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,4,2,7,8,1]=>0010101=>1010100
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,4,2,8,7,1]=>0010111=>1110100
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,4,7,2,1,8]=>1000110=>0110001
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>0000111=>1110000
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,4,7,8,2,1]=>1000101=>1010001
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,5,6,7,4,2,1,8]=>1010010=>0100101
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>0010011=>1100100
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,4,8,2,1]=>1000011=>1100001
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>1010001=>1000101
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]=>1010011=>1100101
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>1010110=>0110101
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]=>0010111=>1110100
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,5,7,6,4,8,2,1]=>1000111=>1110001
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,5,7,6,8,4,2,1]=>1010011=>1100101
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>1010101=>1010101
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>1010111=>1110101
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,6,5,4,2,1,7,8]=>1011100=>0011101
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>1011101=>1011101
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,6,5,4,2,7,1,8]=>0011110=>0111100
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,5,4,2,7,8,1]=>0011101=>1011100
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,6,5,4,2,8,7,1]=>0011111=>1111100
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,6,5,4,7,2,1,8]=>1001110=>0111001
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>0001111=>1111000
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,6,5,4,7,8,2,1]=>1001101=>1011001
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,6,5,4,8,7,2,1]=>1001111=>1111001
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,5,8,4,2,1]=>1010011=>1100101
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,7,5,4,2,1]=>1011011=>1101101
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,6,5,4,8,2,1]=>1001111=>1111001
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]=>1010111=>1110101
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>1011011=>1101101
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]=>1011101=>1011101
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>1011111=>1111101
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>1110000=>0000111
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>1110001=>1000111
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>1110010=>0100111
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>1110001=>1000111
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>1110011=>1100111
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>1110100=>0010111
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>1110101=>1010111
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>1110010=>0100111
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>1110001=>1000111
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>1110011=>1100111
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>1110110=>0110111
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>1110011=>1100111
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>1110101=>1010111
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>1110111=>1110111
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>0111000=>0001110
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,3,2,5,1,7,8,6]=>0111001=>1001110
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>0111011=>1101110
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,3,2,5,6,1,7,8]=>0110100=>0010110
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,3,2,5,6,1,8,7]=>0110101=>1010110
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,7,1,8]=>0110010=>0100110
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>0110001=>1000110
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>0110011=>1100110
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,3,2,5,7,6,1,8]=>0110110=>0110110
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,3,2,5,7,6,8,1]=>0110011=>1100110
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,2,5,7,8,6,1]=>0110101=>1010110
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]=>0110111=>1110110
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>0111100=>0011110
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,3,2,6,5,1,8,7]=>0111101=>1011110
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,3,2,6,5,7,1,8]=>0110110=>0110110
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>0110101=>1010110
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>0110111=>1110110
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,3,2,6,7,5,1,8]=>0111010=>0101110
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,6,7,5,8,1]=>0110011=>1100110
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,3,2,6,8,7,5,1]=>0111011=>1101110
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>0110111=>1110110
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,7,8,6,5,1]=>0111101=>1011110
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>0111111=>1111110
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,3,5,2,1,6,7,8]=>1011000=>0001101
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,3,5,2,1,6,8,7]=>1011001=>1001101
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>1011011=>1101101
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,3,5,2,6,1,7,8]=>0011100=>0011100
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>0011101=>1011100
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>0011001=>1001100
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,3,5,2,7,6,1,8]=>0011110=>0111100
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>0011011=>1101100
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,3,5,2,8,7,6,1]=>0011111=>1111100
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,3,5,6,2,1,8,7]=>1010101=>1010101
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,3,5,6,2,7,1,8]=>0010110=>0110100
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]=>0010101=>1010100
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,7,2,8,1]=>0010011=>1100100
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]=>1010001=>1000101
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,8,7,2,1]=>1010011=>1100101
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,3,5,7,6,2,1,8]=>1010110=>0110101
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,3,5,7,6,8,2,1]=>1010011=>1100101
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]=>1010101=>1010101
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,3,6,5,2,1,7,8]=>1011100=>0011101
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>1011101=>1011101
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>0011111=>1111100
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,3,6,5,7,2,1,8]=>1010110=>0110101
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>0010111=>1110100
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]=>1010101=>1010101
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>1010111=>1110101
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,6,7,5,2,8,1]=>0011011=>1101100
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]=>1011001=>1001101
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,7,6,5,2,1,8]=>1011110=>0111101
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,7,6,5,2,8,1]=>0011111=>1111100
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,7,6,5,8,2,1]=>1010111=>1110101
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]=>1011101=>1011101
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,3,8,7,6,5,2,1]=>1011111=>1111101
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>1101000=>0001011
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>1101001=>1001011
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,5,3,2,1,7,6,8]=>1101010=>0101011
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>1101011=>1101011
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,5,3,2,6,1,7,8]=>0101100=>0011010
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,3,2,6,1,8,7]=>0101101=>1011010
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,1]=>0101001=>1001010
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,8,7,1]=>0101011=>1101010
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>0101110=>0111010
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,3,2,8,7,6,1]=>0101111=>1111010
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>1001101=>1011001
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>0001110=>0111000
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]=>0001111=>1111000
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,3,6,7,2,8,1]=>0001011=>1101000
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]=>1001011=>1101001
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,3,7,6,2,1,8]=>1001110=>0111001
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,5,3,7,6,2,8,1]=>0001111=>1111000
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]=>1001011=>1101001
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]=>1001101=>1011001
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,3,2,1,7,8]=>1100100=>0010011
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>1100101=>1010011
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,3,2,7,8,1]=>0100101=>1010010
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]=>0100111=>1110010
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>0000111=>1110000
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,2,1]=>1000101=>1010001
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]=>1000111=>1110001
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>1100010=>0100011
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>0100011=>1100010
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>1000011=>1100001
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>1100001=>1000011
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]=>1100011=>1100011
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,5,7,6,3,2,1,8]=>1100110=>0110011
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]=>1100011=>1100011
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]=>1100101=>1010011
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>1100111=>1110011
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,6,5,3,2,1,8,7]=>1101101=>1011011
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,5,3,2,8,7,1]=>0101111=>1111010
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,3,7,2,8,1]=>0001111=>1111000
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,5,7,3,2,1,8]=>1100110=>0110011
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,5,7,3,2,8,1]=>0100111=>1110010
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]=>1100101=>1010011
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>1100111=>1110011
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,6,7,5,3,2,1,8]=>1101010=>0101011
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,5,3,2,8,1]=>0101011=>1101010
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]=>1100011=>1100011
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]=>1101001=>1001011
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>1101011=>1101011
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>1101110=>0111011
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]=>0101111=>1111010
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]=>1001111=>1111001
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>1100111=>1110011
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,6,8,5,3,2,1]=>1101011=>1101011
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]=>1101101=>1011011
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>1101111=>1111011
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>1111000=>0001111
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>1111001=>1001111
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>1111010=>0101111
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>1111001=>1001111
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>1111011=>1101111
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>0111100=>0011110
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>0111101=>1011110
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>0111010=>0101110
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>0111001=>1001110
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>0111011=>1101110
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>0111110=>0111110
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>0111011=>1101110
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>0111101=>1011110
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>0111111=>1111110
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,4,3,6,2,1,7,8]=>1011100=>0011101
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,4,3,6,2,1,8,7]=>1011101=>1011101
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,4,3,6,2,7,1,8]=>0011110=>0111100
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,1]=>0011101=>1011100
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,4,3,6,2,8,7,1]=>0011111=>1111100
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,4,3,6,7,2,1,8]=>1011010=>0101101
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,4,3,6,7,2,8,1]=>0011011=>1101100
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,2,1]=>1011001=>1001101
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,4,3,6,8,7,2,1]=>1011011=>1101101
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,4,3,7,6,2,1,8]=>1011110=>0111101
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,4,3,7,6,2,8,1]=>0011111=>1111100
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,3,7,8,6,2,1]=>1011101=>1011101
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,4,3,8,7,6,2,1]=>1011111=>1111101
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,4,6,3,2,1,7,8]=>1101100=>0011011
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,4,6,3,2,1,8,7]=>1101101=>1011011
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,4,6,3,2,7,1,8]=>0101110=>0111010
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,1]=>0101101=>1011010
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,4,6,3,2,8,7,1]=>0101111=>1111010
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,4,6,3,7,2,1,8]=>1001110=>0111001
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>0001111=>1111000
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,4,6,7,3,2,1,8]=>1101010=>0101011
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>1001011=>1101001
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>1101001=>1001011
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,4,7,6,3,2,1,8]=>1101110=>0111011
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,4,7,6,3,8,2,1]=>1001111=>1111001
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]=>1101011=>1101011
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,4,7,8,6,3,2,1]=>1101101=>1011011
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>1110100=>0010111
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,4,3,2,1,8,7]=>1110101=>1010111
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,6,4,3,2,7,1,8]=>0110110=>0110110
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,6,4,3,7,2,1,8]=>1010110=>0110101
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,4,3,8,7,2,1]=>1010111=>1110101
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,4,7,3,2,1,8]=>1100110=>0110011
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>1100101=>1010011
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,4,8,7,3,2,1]=>1100111=>1110011
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>1110010=>0100111
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,4,3,2,8,1]=>0110011=>1100110
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,4,3,8,2,1]=>1010011=>1100101
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>1100011=>1100011
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>1110001=>1000111
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>1110011=>1100111
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>1110110=>0110111
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,6,4,3,2,8,1]=>0110111=>1110110
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>1010111=>1110101
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,6,4,8,3,2,1]=>1100111=>1110011
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>1110011=>1100111
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>1110101=>1010111
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>1110111=>1110111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>1111100=>0011111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>1111101=>1011111
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,5,4,3,2,7,1,8]=>0111110=>0111110
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>0111101=>1011110
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>0111111=>1111110
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,5,4,3,7,2,1,8]=>1011110=>0111101
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>0011111=>1111100
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>1011101=>1011101
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,5,4,3,8,7,2,1]=>1011111=>1111101
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>1101110=>0111011
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,5,4,7,3,2,8,1]=>0101111=>1111010
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>1001111=>1111001
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>1101101=>1011011
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,5,4,8,7,3,2,1]=>1101111=>1111011
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>1110110=>0110111
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>0110111=>1110110
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>1010111=>1110101
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>1100111=>1110011
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>1110101=>1010111
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>1110111=>1110111
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>1111010=>0101111
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>0111011=>1101110
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>1011011=>1101101
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]=>1101011=>1101011
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>1110011=>1100111
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>1111001=>1001111
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>1111011=>1101111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>1111110=>0111111
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>0111111=>1111110
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>1011111=>1111101
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>1101111=>1111011
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>1110111=>1110111
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>1111011=>1101111
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>1111101=>1011111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>1111111=>1111111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>11111110=>01111111
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>01111111=>11111110
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>111111110=>011111111
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,6,5,4,3,2,1,9]=>11111010=>01011111
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,7,6,5,4,3,2]=>01111101=>10111110
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>011111111=>111111110
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110=>0111111111
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,7,6,5,4,3,2,1,10]=>111111010=>010111111
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,6,8,5,4,3,2,1,9]=>11110110=>01101111
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,8,7,5,4,3,2,1,9]=>11110110=>01101111
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,7,9,6,5,4,3,2]=>01111011=>11011110
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,7,9,8,6,5,4,3,2]=>01111011=>11011110
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9,10,8,7,6,5,4,3,2]=>011111101=>101111110
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111=>1111111110
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>11111111110=>01111111111
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[8,7,9,6,5,4,3,2,1,10]=>111110110=>011011111
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[7,6,5,8,4,3,2,1,9]=>11101110=>01110111
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,8,5,4,3,2,1,9]=>11110010=>01001111
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,7,8,9,6,5,4,3,2]=>01111001=>10011110
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,8,10,7,6,5,4,3,2]=>011111011=>110111110
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,6,9,8,7,5,4,3,2]=>01110111=>11101110
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,8,10,9,7,6,5,4,3,2]=>011111011=>110111110
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,8,10,7,6,5,4,3,2,1,11]=>1111110110=>0110111111
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[8,7,6,9,5,4,3,2,1,10]=>111101110=>011101111
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,9,6,5,4,3,2,1,10]=>111110010=>010011111
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[6,7,5,8,4,3,2,1,9]=>11100110=>01100111
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,5,8,7,4,3,2,1,9]=>11101110=>01110111
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,8,7,6,5,3,2,1,9]=>11011110=>01111011
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,7,6,9,8,5,4,3,2]=>01110111=>11101110
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,10,7,6,5,4,3,2]=>011111001=>100111110
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,7,10,9,8,6,5,4,3,2]=>011110111=>111011110
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,9,11,10,8,7,6,5,4,3,2]=>0111111011=>1101111110
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[5,9,8,7,6,4,3,2,1,10]=>111011110=>011110111
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[7,6,5,4,3,8,2,1,9]=>10111110=>01111101
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[6,5,7,8,4,3,2,1,9]=>11101010=>01010111
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,6,8,9,5,4,3,2]=>01110101=>10101110
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,9,8,7,6,5,3,2]=>01011111=>11111010
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,8,11,10,9,7,6,5,4,3,2]=>0111110111=>1110111110
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[8,7,6,5,4,9,3,2,1,10]=>110111110=>011111011
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,6,8,9,5,4,3,2,1,10]=>111101010=>010101111
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,6,5,4,3,2,8,1,9]=>01111110=>01111110
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,8,7,6,5,4,3,1,9]=>01111110=>01111110
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,6,5,4,3,2,1,9,8]=>11111101=>10111111
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,9,5,4,3,2]=>01110001=>10001110
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,8,7,6,5,4,3]=>10111111=>11111101
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,9,8,7,6,5,4,2]=>00111111=>11111100
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,5,10,9,8,7,6,4,3,2]=>011011111=>111110110
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[8,7,6,5,4,3,9,2,1,10]=>101111110=>011111101
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>11111100=>00111111
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,7,6,5,4,3,2,9]=>01111110=>01111110
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,7,5,4,3,2,1,9,8]=>11110101=>10101111
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,7,8,9,10,6,5,4,3,2]=>011110001=>100011110
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,8,9,7,6,5,4,3]=>10111101=>10111101
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,8,7,6,5,4,3]=>00111111=>11111100
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,4,10,9,8,7,6,5,3,2]=>010111111=>111111010
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,6,11,10,9,8,7,5,4,3,2]=>0111011111=>1111101110
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[8,7,6,5,4,3,2,9,1,10]=>011111110=>011111110
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>111111101=>101111111
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9]=>11110100=>00101111
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,7,8,6,5,4,3,2,9]=>01111010=>01011110
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>101111111=>111111101
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,10,9,8,7,6,5,4,2]=>001111111=>111111100
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,5,11,10,9,8,7,6,4,3,2]=>0110111111=>1111110110
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>111111100=>001111111
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,8,7,6,5,4,3,2,10]=>011111110=>011111110
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[6,5,4,3,7,8,2,1,9]=>10111010=>01011101
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,9,4,3,2]=>01101001=>10010110
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,9,8,7,6,5,4,3]=>001111111=>111111100
[]=>[]=>=>
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>00000001=>10000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,8,1]=>00000011=>11000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,8,7,9,1]=>00000011=>11000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,7,1]=>00000101=>10100000
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,9,8,7,1]=>00000111=>11100000
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,1]=>00000101=>10100000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,5,7,8,6,9,1]=>00000011=>11000000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,6,1]=>00001001=>10010000
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,5,7,9,8,6,1]=>00001011=>11010000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,5,8,7,6,9,1]=>00000111=>11100000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,8,7,9,6,1]=>00001011=>11010000
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,8,9,7,6,1]=>00001101=>10110000
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,1]=>00001001=>10010000
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,4,6,7,5,8,9,1]=>00000101=>10100000
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,7,8,9,6,5,1]=>00011001=>10011000
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,9,1]=>00001001=>10010000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,4,1]=>00100001=>10000100
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,6,5,7,8,9,4,1]=>00101001=>10010100
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,9,5,4,1]=>00110001=>10001100
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,8,7,6,5,4,1]=>00111111=>11111100
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,9,1]=>00100001=>10000100
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,3,1]=>01000001=>10000010
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,9,4,3,1]=>01100001=>10000110
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,8,7,6,5,4,3,9,1]=>00111111=>11111100
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,8,7,9,6,5,4,3,1]=>01111011=>11011110
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,8,9,7,6,5,4,3,1]=>01111101=>10111110
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,9,8,7,6,5,4,3,1]=>01111111=>11111110
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>01000001=>10000010
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,9,8,1]=>01010111=>11101010
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,9,8,7,6,5,4,1]=>01111111=>11111110
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,1]=>00100001=>10000100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,2,9,1]=>00000011=>11000000
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>10000001=>10000001
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,9,4,2,1]=>10100001=>10000101
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,7,9,8,4,2,1]=>10100011=>11000101
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,8,7,6,5,4,9,2,1]=>10011111=>11111001
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,9,8,7,6,5,4,2,1]=>10111111=>11111101
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,1]=>01100001=>10000110
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,9,5,2,1]=>10110001=>10001101
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,9,2,1]=>10001001=>10010001
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,7,3,9,8,2,1]=>10000111=>11100001
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>11000001=>10000011
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,7,9,8,3,2,1]=>11000011=>11000011
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,8,7,6,5,9,3,2,1]=>11001111=>11110011
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,9,8,7,6,5,3,2,1]=>11011111=>11111011
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,1]=>01110001=>10001110
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,9,8,7,6,1]=>01111111=>11111110
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,8,3,9,2,1]=>10010011=>11001001
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]=>11010001=>10001011
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,9,8,3,2,1]=>11010111=>11101011
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,6,4,7,3,8,2,9,1]=>00001111=>11110000
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>11100001=>10000111
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,9,8,4,3,2,1]=>11100011=>11000111
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[5,7,9,8,6,4,3,2,1]=>11101011=>11010111
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,8,7,6,9,4,3,2,1]=>11100111=>11100111
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,9,8,7,6,4,3,2,1]=>11101111=>11110111
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,1]=>01111001=>10011110
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,5,4,9,8,7,3,2,1]=>11011111=>11111011
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]=>11101001=>10010111
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[6,5,8,9,7,4,3,2,1]=>11101101=>10110111
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[6,7,5,9,8,4,3,2,1]=>11100111=>11100111
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>11110001=>10001111
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,9,8,5,4,3,2,1]=>11110011=>11001111
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[6,8,7,5,4,3,2,9,1]=>01110111=>11101110
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,8,7,9,5,4,3,2,1]=>11110011=>11001111
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,9,8,7,5,4,3,2,1]=>11110111=>11101111
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,1]=>01111101=>10111110
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,6,5,4,3,2,9,8,1]=>01111111=>11111110
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,6,8,5,4,3,2,9,1]=>01110111=>11101110
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,6,8,5,9,4,3,2,1]=>11100111=>11100111
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>11110101=>10101111
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,6,9,8,5,4,3,2,1]=>11110111=>11101111
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,8,6,5,4,3,2,9,1]=>01111011=>11011110
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>11111001=>10011111
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,9,8,6,5,4,3,2,1]=>11111011=>11011111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>01111111=>11111110
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]=>10111111=>11111101
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,7,6,5,4,9,3,2,1]=>11011111=>11111011
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]=>11101111=>11110111
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,7,6,9,5,4,3,2,1]=>11110111=>11101111
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]=>11111011=>11011111
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]=>11111101=>10111111
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>11111111=>11111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9]=>00000000=>00000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>00000001=>10000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,7]=>00000001=>10000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,6]=>00000001=>10000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,5]=>00000001=>10000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,4]=>00000001=>10000000
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,3]=>00000001=>10000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,2]=>00000001=>10000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>000000000=>000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>000000001=>100000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,8,7]=>00000011=>11000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>000000001=>100000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,5,8,7,9,6]=>00000011=>11000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>000000001=>100000000
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,4,7,6,8,9,5]=>00000101=>10100000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>000000001=>100000000
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,9,4]=>00001001=>10010000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>000000001=>100000000
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,9,3]=>00010001=>10001000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>000000001=>100000000
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,9,2]=>00100001=>10000100
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>000000001=>100000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>000000001=>100000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>000000001=>100000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000=>0000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001=>1000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,10,9,8]=>000000011=>110000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>0000000001=>1000000000
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,5,8,9,7,6]=>00000101=>10100000
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,8,7,6]=>00000111=>11100000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>010000001=>100000010
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,2]=>0000000001=>1000000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001=>1000000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,8,11,10,9]=>0000000011=>1100000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,6,10,9,8,7]=>000000111=>111000000
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,7,4,8,9,3]=>00000101=>10100000
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,10,1]=>011000001=>100000110
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,11,1]=>0100000001=>1000000010
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>00000000001=>10000000000
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,8,7,6,5]=>00001111=>11110000
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,9,8,7,6]=>000001111=>111100000
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,8,3,9,2]=>00000011=>11000000
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,9,10,1]=>000010001=>100010000
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,10,1]=>011100001=>100001110
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,9,3,2]=>01000001=>10000010
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,8,7,6,5,4]=>00011111=>11111000
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,9,4,3,2]=>01100001=>10000110
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,10,9,8,7,6,5]=>000011111=>111110000
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,10,1]=>011110001=>100011110
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,9,10,3,2]=>010000001=>100000010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,2,10,1]=>000000011=>110000000
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,9,10,4,3,2]=>011000001=>100000110
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,9]=>00000010=>01000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9]=>00000100=>00100000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,9,8]=>00000101=>10100000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9]=>00001000=>00010000
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,9]=>00001010=>01010000
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,9,8,7]=>00001011=>11010000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9]=>00010000=>00001000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8]=>00010101=>10101000
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,9,8,7,6]=>00010111=>11101000
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,3,6,5,4,9,8,7]=>00011011=>11011000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9]=>00100000=>00000100
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,9]=>00101010=>01010100
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,9,8,7,6,5]=>00101111=>11110100
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9]=>01000000=>00000010
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>01000001=>10000010
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,6,9,8,7]=>01000011=>11000010
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8,9]=>01010000=>00001010
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>01010101=>10101010
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,9,8,7,6,5,4]=>01011111=>11111010
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8,9]=>01100000=>00000110
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2,9,8,7,6]=>01110111=>11101110
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,7,6,5,4,3,2,9,8]=>01111101=>10111110
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>10000000=>00000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,9,8]=>10000001=>10000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,6,8,7,9]=>10000010=>01000001
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>10100000=>00000101
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>10101010=>01010101
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,9,8,7]=>10101011=>11010101
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,9,8,7,6,5]=>10101111=>11110101
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,8,7,6,5,4,3,9]=>10111110=>01111101
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>11000000=>00000011
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8,9]=>11010000=>00001011
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6,9,8]=>11010101=>10101011
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,6,5,4,7,8,9]=>11011000=>00011011
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4,9,8,7]=>11011011=>11011011
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,1,9,8,7,6,5,4]=>11011111=>11111011
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>11100000=>00000111
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,3,2,1,6,5,7,8,9]=>11101000=>00010111
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,8,7,9]=>11101010=>01010111
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,3,2,1,7,6,5,8,9]=>11101100=>00110111
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2,1,7,6,5,9,8]=>11101101=>10110111
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,8,7,6,5,9]=>11101110=>01110111
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,3,2,1,9,8,7,6,5]=>11101111=>11110111
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>11110000=>00001111
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,4,3,2,1,7,6,8,9]=>11110100=>00101111
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,4,3,2,1,8,7,6,9]=>11110110=>01101111
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4,3,2,1,9,8,7,6]=>11110111=>11101111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>11111000=>00011111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,5,4,3,2,1,8,7,9]=>11111010=>01011111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,5,4,3,2,1,9,8,7]=>11111011=>11011111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,9,8,10]=>000000010=>010000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,7,9,10]=>000000100=>001000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>000000101=>101000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9,10]=>000001000=>000100000
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9,10]=>000010000=>000010000
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9,10]=>000100000=>000001000
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8,10]=>000101010=>010101000
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,9,8,7,6,5,4]=>000111111=>111111000
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9,10]=>001000000=>000000100
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>001010101=>101010100
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3,10,9,8,7]=>001110111=>111011100
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10]=>010000000=>000000010
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>010101010=>010101010
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,7,6,10,9,8]=>010101011=>110101010
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,10,9,8,7,6,5,4]=>010111111=>111111010
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>100000000=>000000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,8,10,9]=>100000001=>100000001
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9,10]=>101000000=>000000101
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>101010101=>101010101
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5,10,9,8]=>101011011=>110110101
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>101110111=>111011101
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,7,6,5,4,3,10,9]=>101111101=>101111101
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>110000000=>000000011
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8,9,10]=>110100000=>000001011
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,9,8,10]=>110101010=>010101011
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7,10,9]=>110110101=>101011011
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,6,5,4,10,9,8,7]=>110110111=>111011011
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,1,10,9,8,7,6,5,4]=>110111111=>111111011
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>111000000=>000000111
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>111010101=>101010111
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,6,5,10,9,8,7]=>111010111=>111010111
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5,10,9,8]=>111011011=>110110111
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,8,7,6,5,9,10]=>111011100=>001110111
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,8,7,6,5,10,9]=>111011101=>101110111
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>111011111=>111110111
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9,10]=>111100000=>000001111
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,9,8,10]=>111101010=>010101111
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,3,2,1,9,8,7,6,10]=>111101110=>011101111
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1,10,9,8,7,6]=>111101111=>111101111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>111110000=>000011111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[6,5,4,3,2,1,9,8,7,10]=>111110110=>011011111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>111110111=>111011111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>111111000=>000111111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,6,5,4,3,2,1,9,8,10]=>111111010=>010111111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,6,5,4,3,2,1,10,9,8]=>111111011=>110111111
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>111111111=>111111111
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9]=>01000000=>00000010
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9]=>00100000=>00000100
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9]=>00010000=>00001000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9]=>00001000=>00010000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>00000100=>00100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>00000010=>01000000
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10]=>010000000=>000000010
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9]=>01100000=>00000110
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9,10]=>001000000=>000000100
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8,9]=>00110000=>00001100
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9,10]=>000100000=>000001000
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,4,6,5,1,7,8,9]=>00011000=>00011000
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9,10]=>000010000=>000010000
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,5,7,6,1,8,9]=>00001100=>00110000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9,10]=>000001000=>000100000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,6,8,7,1,9]=>00000110=>01100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,1,9,10]=>000000100=>001000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>000000010=>010000000
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,8,10,9,4,3,2,1]=>111000011=>110000111
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,4,3,2,1]=>111010001=>100010111
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,11,10,4,3,2,1]=>1110000011=>1100000111
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,7,8,10,9,3,2,1]=>110000011=>110000011
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,9,10,3,2,1]=>110100001=>100001011
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,11,4,3,2,1]=>1110100001=>1000010111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000=>0000000001
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,6,8,9,7]=>10000001=>10000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,9,1]=>000000011=>110000000
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,10,9,7,6,5,4,3,2,1]=>111111011=>110111111
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>111111011=>110111111
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[9,11,10,8,7,6,5,4,3,2,1]=>1111111011=>1101111111
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,8,10,9,6,5,4,3,2,1]=>111110011=>110011111
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[8,7,9,10,6,5,4,3,2,1]=>111110101=>101011111
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[10,9,11,8,7,6,5,4,3,2,1]=>1111111011=>1101111111
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,6,7,9,10,8]=>100000001=>100000001
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,6,8,9,7]=>01000001=>10000010
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,6,8,9,7]=>01000001=>10000010
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,7,9,8]=>01000001=>10000010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,8,2,1,9]=>10000010=>01000001
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,7,2,1,8,9]=>10000100=>00100001
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,6,2,1,7,8,9]=>10001000=>00010001
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8,9]=>10010000=>00001001
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9]=>10100000=>00000101
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,9,8,7,6,5,4,3,1]=>011111111=>111111110
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>011111111=>111111110
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>0111111111=>1111111110
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,9,7,6,5,4,3,2,10,1]=>011111011=>110111110
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[6,5,4,3,2,7,1,8,9]=>01111100=>00111110
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,2,6,1,7,8,9]=>01111000=>00011110
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8,9]=>01110000=>00001110
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9]=>01100000=>00000110
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>111111101=>101111111
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,10,9,8,6,5,4,3,2,1]=>111110111=>111011111
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,10,9,8,7,5,4,3,2,1]=>111101111=>111101111
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,10,9,8,7,6,4,3,2,1]=>111011111=>111110111
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,10,9,8,7,6,5,3,2,1]=>110111111=>111111011
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,10,9,8,7,6,5,4,2,1]=>101111111=>111111101
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,7,2,1,9,8]=>10000101=>10100001
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,9,4,3]=>10100001=>10000101
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,8,3,1,9]=>01000010=>01000010
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,10,3,1]=>010000001=>100000010
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>1111111101=>1011111111
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,9,8,7,6,5,4]=>01011111=>11111010
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,2,1,9,8,7,6,5]=>10101111=>11110101
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,3,2,1,9,8,7,6]=>11010111=>11101011
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,6,4,3,2,1,9,8,7]=>11101011=>11010111
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8,9]=>00010000=>00001000
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8,9]=>00010000=>00001000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6,9,10]=>000000100=>001000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,4,5,7,8,9,6,10]=>000000010=>010000000
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,7,9,8]=>00010001=>10001000
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8,9]=>10010000=>00001001
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,9,10,1]=>000010001=>100010000
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,9,10,1]=>000010001=>100010000
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,10,1]=>000010001=>100010000
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,9,10,5,4,3,2]=>011100001=>100001110
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,9,3,2]=>01010001=>10001010
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,8,1,9]=>01000010=>01000010
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,7,9,8,2]=>00000011=>11000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8]=>00000101=>10100000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,3]=>10000001=>10000001
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,9,8,7]=>00001011=>11010000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,10,9,8,1]=>000000111=>111000000
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,9,8,7,6]=>00010111=>11101000
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,6,9,10,8,7,1]=>000001101=>101100000
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,1,8,9,7,6,5]=>00101101=>10110100
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,8,9,10,7,6,1]=>000011001=>100110000
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,7,8,9,6,5,4]=>01011001=>10011010
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,7,8,9,10,6,5,1]=>000110001=>100011000
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,9,5,4,3]=>10110001=>10001101
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,9,10,5,4,1]=>001100001=>100001100
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,9,10,4,3,1]=>011000001=>100000110
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>110000001=>100000011
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,9,8,7,6,5,3]=>10011111=>11111001
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,7,6,5,4,2,1,9,8]=>10111101=>10111101
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,1,6,9,8,7,5,4]=>11010111=>11101011
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[4,6,5,3,2,1,9,8,7]=>11011011=>11011011
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,2,1,8,9,7,6,5]=>11101101=>10110111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,4,3,2,1,8,9,7]=>11111001=>10011111
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>101111111=>111111101
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,3,2,1,8,9,7,6]=>11110101=>10101111
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>110111111=>111111011
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>111011111=>111110111
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,1,8,9,7,6,5,4]=>11011101=>10111011
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>111101111=>111101111
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>111110111=>111011111
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,5,7,8,9,6]=>00100001=>10000100
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,10,1]=>000001001=>100100000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7,9]=>00001010=>01010000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,6,8,9]=>00010100=>00101000
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,5,7,8,9]=>00101000=>00010100
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8,9]=>01010000=>00001010
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,8,7,1,9]=>00101110=>01110100
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>01010101=>10101010
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7,10,9]=>011010101=>101010110
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,10,9,1]=>001010111=>111010100
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8,10]=>010101010=>010101010
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,9,10,8,1]=>000000101=>101000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,10,7,1]=>000001001=>100100000
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,10,5,1]=>000100001=>100001000
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,10,4,1]=>001000001=>100000100
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>100000001=>100000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,11,10,1]=>0000000011=>1100000000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,8,10,11,9,1]=>0000000101=>1010000000
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,6,9,8,10,7,1]=>000001011=>110100000
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,7,9,10,11,8,1]=>0000001001=>1001000000
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,10,11,6,1]=>0000100001=>1000010000
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,10,11,5,1]=>0001000001=>1000001000
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,10,11,3,1]=>0100000001=>1000000010
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>1000000001=>1000000001
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[8,7,10,9,6,5,4,3,2,1]=>111110111=>111011111
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,10,9,8,4,3,2,1]=>111011111=>111110111
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,10,9,8,7,2,1]=>101111111=>111111101
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,5,7,9,10,8,6,4,2]=>001010101=>101010100
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,7,5,8,4,9,3,10,2]=>000001111=>111100000
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,6,4,7,3,8,2,9,1,10]=>000011110=>011110000
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>1111111111=>1111111111
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,11,10,9,8,7,6,5,4,3]=>1011111111=>1111111101
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,11,10,9,8,7,6,5,4,3,1]=>0111111111=>1111111110
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10,11]=>0100000000=>0000000010
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,9,8,7,6,5,3]=>00011111=>11111000
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,9,8,7,6,4]=>00001111=>11110000
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,4,6,9,8,7,5]=>00000111=>11100000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,9,8,6]=>00000011=>11000000
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,9,4]=>11000001=>10000011
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,9,5]=>11100001=>10000111
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,8,7,6,5,4,3,2,1,11,10]=>1111111101=>1011111111
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>111000001=>100000111
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,6,4,3,2,1,7,8,9]=>11101000=>00010111
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8,9]=>11010000=>00001011
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9]=>00100000=>00000100
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,10,3]=>100000001=>100000001
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,9,4]=>01000001=>10000010
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>111111001=>100111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>0000000010=>0100000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,1,8,9,10,7]=>000010001=>100010000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,5,7,8,6,9]=>00000010=>01000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,7,9,8,4]=>00000011=>11000000
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,5,6,8,9,7,10]=>000000010=>010000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,6,7,2,9,8]=>00000101=>10100000
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8,9]=>00110000=>00001100
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>111100001=>100001111
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>111110001=>100011111
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>0000000010=>0100000000
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,8,2,9]=>00000010=>01000000
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,7,6,5,4,3,2,10,9,1]=>011111111=>111111110
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,2,10,9,8,7,6,5,4,1]=>011111111=>111111110
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,5,7,6,8,1,9]=>00000110=>01100000
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,5,8,7,6,1,9]=>00001110=>01110000
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,9,4]=>10000001=>10000001
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,4,6,8,9,7,5]=>00000101=>10100000
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8,9,10]=>100100000=>000001001
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9,10]=>101000000=>000000101
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,10,9]=>000000101=>101000000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,1,8,9,7]=>00001001=>10010000
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,6,4,3,2,1,7,8,9,10]=>111010000=>000010111
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,6,4,3,2,7,1,8,9]=>01101100=>00110110
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9,10]=>111101000=>000101111
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9,10,11]=>1111010000=>0000101111
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>0101010101=>1010101010
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7,10,9]=>101010101=>101010101
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1,10,11]=>1111111100=>0011111111
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9,10]=>001000000=>000000100
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,8,9,2,10]=>000000010=>010000000
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,3,7,8,9,10]=>000010000=>000010000
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,9,5]=>00100001=>10000100
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,6,8,10,9,7]=>000000011=>110000000
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,7,8,4,9,10]=>000000100=>001000000
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,6,5,4,3,9,8,2]=>00111111=>11111100
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,3,4,6,7,10,9,8,5]=>000000111=>111000000
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,8,7,9]=>01101010=>01010110
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,5,4,6,1,8,7,9]=>01011010=>01011010
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7,10,9]=>011010101=>101010110
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7,10,9]=>010110101=>101011010
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,7,6,8,1,10,9]=>010101101=>101101010
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,10,1]=>010101011=>110101010
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,9,8,1,10]=>010101110=>011101010
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,2,1,7,8,9,6]=>11110001=>10001111
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,6,8,7,9,2]=>00000011=>11000000
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,2,8,7,6,5,4,1,9]=>01111110=>01111110
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,7,8,10,9,2]=>000000011=>110000000
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,7,8,3,9]=>10000010=>01000001
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>011111101=>101111110
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,10,1]=>011111001=>100111110
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,9,8,10,7]=>101010011=>110010101
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,9,8,10,5]=>101001011=>110100101
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,9,8,10,3]=>100101011=>110101001
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>010101001=>100101010
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9,10]=>011000000=>000000110
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,9,5]=>10100001=>10000101
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9,10]=>011000000=>000000110
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,7,2,8,9]=>00000100=>00100000
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,7,9,8,6,4,2]=>00101011=>11010100
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,6,7,9,8,1,10]=>000000110=>011000000
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,4,6,7,9,8,5]=>00000011=>11000000
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,9,8,3]=>00010111=>11101000
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,10,9,2]=>001010111=>111010100
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,4,5,7,8,9,10,6]=>100000001=>100000001
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7,10,9]=>001110101=>101011100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7,10,9]=>100110101=>101011001
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,6,5,7,4,8,3,10,9]=>100011101=>101110001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,6,5,7,4,8,1,10,9]=>010011101=>101110010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,6,5,7,2,8,1,10,9]=>001011101=>101110100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,8,1,10,9]=>000111101=>101111000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,7,6,8,5,10,9]=>101001101=>101100101
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,8,5,10,9]=>011001101=>101100110
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,7,6,8,1,10,9]=>001101101=>101101100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,7,6,8,3,10,9]=>100101101=>101101001
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,8,7,9,6,10,5]=>101000111=>111000101
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,8,7,9,6,10,5]=>011000111=>111000110
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,8,7,9,6,10,1]=>001100111=>111001100
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,8,7,9,6,10,3]=>100100111=>111001001
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,8,7,9,6,10,1]=>010100111=>111001010
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,8,7,9,2,10,1]=>001010111=>111010100
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,8,7,9,2,10,1]=>000110111=>111011000
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,7,6,8,5,9,2,10,1]=>001001111=>111100100
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,8,3,9,2,10,1]=>000101111=>111101000
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,8,7,9,4,10,3]=>100010111=>111010001
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,8,7,9,4,10,1]=>010010111=>111010010
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>000011111=>111110000
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,8,5,9,4,10,3]=>100001111=>111100001
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,7,6,8,5,9,4,10,1]=>010001111=>111100010
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,6,5,9,8,10,7]=>011010011=>110010110
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,9,8,10,7]=>001110011=>110011100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,9,8,10,7]=>100110011=>110011001
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,5,4,6,1,9,8,10,7]=>010110011=>110011010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,6,5,7,4,9,8,10,3]=>100011011=>110110001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,9,8,10,1]=>010011011=>110110010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,6,5,7,2,9,8,10,1]=>001011011=>110110100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,4,6,3,7,2,9,8,10,1]=>000111011=>110111000
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,9,8,10,5]=>011001011=>110100110
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,9,8,10,1]=>001101011=>110101100
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101=>10101010101
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7,10,9,12,11]=>01101010101=>10101010110
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7,10,9,12,11]=>00111010101=>10101011100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7,10,9,12,11]=>10011010101=>10101011001
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7,10,9,12,11]=>01011010101=>10101011010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,6,5,7,4,8,3,10,9,12,11]=>10001110101=>10101110001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,6,5,7,4,8,1,10,9,12,11]=>01001110101=>10101110010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,6,5,7,2,8,1,10,9,12,11]=>00101110101=>10101110100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,8,1,10,9,12,11]=>00011110101=>10101111000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,7,6,8,5,10,9,12,11]=>10100110101=>10101100101
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,8,5,10,9,12,11]=>01100110101=>10101100110
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,7,6,8,1,10,9,12,11]=>00110110101=>10101101100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,5,4,7,6,8,3,10,9,12,11]=>10010110101=>10101101001
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,5,4,7,6,8,1,10,9,12,11]=>01010110101=>10101101010
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,8,7,9,6,10,5,12,11]=>10100011101=>10111000101
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,8,7,9,6,10,5,12,11]=>01100011101=>10111000110
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,8,7,9,6,10,1,12,11]=>00110011101=>10111001100
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,8,7,9,6,10,3,12,11]=>10010011101=>10111001001
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,8,7,9,6,10,1,12,11]=>01010011101=>10111001010
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,6,5,8,7,9,2,10,1,12,11]=>00101011101=>10111010100
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,8,7,9,2,10,1,12,11]=>00011011101=>10111011000
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,7,6,8,5,9,2,10,1,12,11]=>00100111101=>10111100100
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,7,6,8,3,9,2,10,1,12,11]=>00010111101=>10111101000
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,6,5,8,7,9,4,10,3,12,11]=>10001011101=>10111010001
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,6,5,8,7,9,4,10,1,12,11]=>01001011101=>10111010010
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,5,7,4,8,3,9,2,10,1,12,11]=>00001111101=>10111110000
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,7,6,8,5,9,4,10,3,12,11]=>10000111101=>10111100001
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,7,6,8,5,9,4,10,1,12,11]=>01000111101=>10111100010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,9,8,10,7,12,11]=>10101001101=>10110010101
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,9,8,10,7,12,11]=>01101001101=>10110010110
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,9,8,10,7,12,11]=>00111001101=>10110011100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,9,8,10,7,12,11]=>10011001101=>10110011001
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,9,8,10,7,12,11]=>01011001101=>10110011010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,6,5,7,4,9,8,10,3,12,11]=>10001101101=>10110110001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,6,5,7,4,9,8,10,1,12,11]=>01001101101=>10110110010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,6,5,7,2,9,8,10,1,12,11]=>00101101101=>10110110100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,9,8,10,1,12,11]=>00011101101=>10110111000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,7,6,9,8,10,5,12,11]=>10100101101=>10110100101
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,9,8,10,5,12,11]=>01100101101=>10110100110
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,7,6,9,8,10,1,12,11]=>00110101101=>10110101100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,7,6,9,8,10,3,12,11]=>10010101101=>10110101001
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,7,6,9,8,10,1,12,11]=>01010101101=>10110101010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,6,5,10,9,11,8,12,7]=>10101000111=>11100010101
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,6,5,10,9,11,8,12,7]=>01101000111=>11100010110
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1,10,9,11,8,12,7]=>00111000111=>11100011100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,6,3,10,9,11,8,12,7]=>10011000111=>11100011001
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,6,1,10,9,11,8,12,7]=>01011000111=>11100011010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,10,9,11,8,12,3]=>10001100111=>11100110001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,10,9,11,8,12,1]=>01001100111=>11100110010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,10,9,11,8,12,1]=>00101100111=>11100110100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,10,9,11,8,12,1]=>00011100111=>11100111000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,7,6,10,9,11,8,12,5]=>10100100111=>11100100101
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,7,6,10,9,11,8,12,5]=>01100100111=>11100100110
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,7,6,10,9,11,8,12,1]=>00110100111=>11100101100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,7,6,10,9,11,8,12,3]=>10010100111=>11100101001
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,7,6,10,9,11,8,12,1]=>01010100111=>11100101010
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,8,7,10,9,11,4,12,3]=>10001010111=>11101010001
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,8,7,10,9,11,4,12,1]=>01001010111=>11101010010
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,10,9,11,2,12,1]=>00001110111=>11101110000
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,8,5,10,9,11,4,12,3]=>10000110111=>11101100001
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,7,6,8,5,10,9,11,4,12,1]=>01000110111=>11101100010
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,9,8,10,7,11,4,12,3]=>10001001111=>11110010001
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,9,8,10,7,11,4,12,1]=>01001001111=>11110010010
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,9,8,10,3,11,2,12,1]=>00001101111=>11110110000
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,9,8,10,5,11,4,12,3]=>10000101111=>11110100001
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,7,6,9,8,10,5,11,4,12,1]=>01000101111=>11110100010
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,8,7,10,9,11,2,12,1]=>00101010111=>11101010100
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,7,6,8,5,10,9,11,2,12,1]=>00100110111=>11101100100
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,8,7,10,9,11,2,12,1]=>00011010111=>11101011000
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,8,3,10,9,11,2,12,1]=>00010110111=>11101101000
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,8,7,9,4,10,3,11,2,12,1]=>00001011111=>11111010000
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>00000111111=>11111100000
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,9,8,10,7,11,2,12,1]=>00101001111=>11110010100
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,7,6,9,8,10,5,11,2,12,1]=>00100101111=>11110100100
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,9,8,10,7,11,2,12,1]=>00011001111=>11110011000
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,9,8,10,3,11,2,12,1]=>00010101111=>11110101000
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,8,7,10,9,11,6,12,5]=>10100010111=>11101000101
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,8,7,10,9,11,6,12,5]=>01100010111=>11101000110
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,8,7,10,9,11,6,12,1]=>00110010111=>11101001100
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,8,7,10,9,11,6,12,3]=>10010010111=>11101001001
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,8,7,10,9,11,6,12,1]=>01010010111=>11101001010
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,8,7,9,6,10,5,11,4,12,3]=>10000011111=>11111000001
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,8,7,9,6,10,5,11,4,12,1]=>01000011111=>11111000010
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,8,7,9,6,10,5,11,2,12,1]=>00100011111=>11111000100
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,8,7,9,6,10,3,11,2,12,1]=>00010011111=>11111001000
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,9,8,10,7,11,6,12,5]=>10100001111=>11110000101
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,9,8,10,7,11,6,12,5]=>01100001111=>11110000110
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,9,8,10,7,11,6,12,1]=>00110001111=>11110001100
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,9,8,10,7,11,6,12,3]=>10010001111=>11110001001
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,9,8,10,7,11,6,12,1]=>01010001111=>11110001010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,8,7,11,10,12,9]=>10101010011=>11001010101
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,6,5,8,7,11,10,12,9]=>01101010011=>11001010110
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,8,7,11,10,12,9]=>00111010011=>11001011100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,8,7,11,10,12,9]=>10011010011=>11001011001
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,5,4,6,1,8,7,11,10,12,9]=>01011010011=>11001011010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3,11,10,12,9]=>10001110011=>11001110001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1,11,10,12,9]=>01001110011=>11001110010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1,11,10,12,9]=>00101110011=>11001110100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1,11,10,12,9]=>00011110011=>11001111000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5,11,10,12,9]=>10100110011=>11001100101
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5,11,10,12,9]=>01100110011=>11001100110
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1,11,10,12,9]=>00110110011=>11001101100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3,11,10,12,9]=>10010110011=>11001101001
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1,11,10,12,9]=>01010110011=>11001101010
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,8,7,9,6,11,10,12,5]=>10100011011=>11011000101
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,8,7,9,6,11,10,12,5]=>01100011011=>11011000110
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,8,7,9,6,11,10,12,1]=>00110011011=>11011001100
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,8,7,9,6,11,10,12,3]=>10010011011=>11011001001
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,8,7,9,6,11,10,12,1]=>01010011011=>11011001010
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,6,5,8,7,9,2,11,10,12,1]=>00101011011=>11011010100
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,4,6,3,8,7,9,2,11,10,12,1]=>00011011011=>11011011000
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,7,6,8,5,9,2,11,10,12,1]=>00100111011=>11011100100
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,4,7,6,8,3,9,2,11,10,12,1]=>00010111011=>11011101000
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,6,5,8,7,9,4,11,10,12,3]=>10001011011=>11011010001
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,8,7,9,4,11,10,12,1]=>01001011011=>11011010010
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,11,10,12,1]=>00001111011=>11011110000
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,7,6,8,5,9,4,11,10,12,3]=>10000111011=>11011100001
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,7,6,8,5,9,4,11,10,12,1]=>01000111011=>11011100010
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,9,8,11,10,12,7]=>10101001011=>11010010101
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,6,5,9,8,11,10,12,7]=>01101001011=>11010010110
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,9,8,11,10,12,7]=>00111001011=>11010011100
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,9,8,11,10,12,7]=>10011001011=>11010011001
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1,9,8,11,10,12,7]=>01011001011=>11010011010
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,6,5,7,4,9,8,11,10,12,3]=>10001101011=>11010110001
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,9,8,11,10,12,1]=>01001101011=>11010110010
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,6,5,7,2,9,8,11,10,12,1]=>00101101011=>11010110100
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,4,6,3,7,2,9,8,11,10,12,1]=>00011101011=>11010111000
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,9,8,11,10,12,5]=>10100101011=>11010100101
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>01100101011=>11010100110
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,9,8,11,10,12,1]=>00110101011=>11010101100
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,9,8,11,10,12,3]=>10010101011=>11010101001
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>01010101011=>11010101010
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8,10]=>000001010=>010100000
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,10,9,2,1]=>101010111=>111010101
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>11111111101=>10111111111
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,11,10,9,8,7,6,5,4,3]=>0011111111=>1111111100
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7,10,9]=>001010101=>101010100
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,11,10]=>0000000101=>1010000000
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,1,7,8,9,6]=>00010001=>10001000
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,7,8,10,9,1]=>010000011=>110000010
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,5,4,3,2,1,9,10,8]=>111111001=>100111111
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,8,9,10,7]=>111110001=>100011111
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,7,8,9,10,6]=>111100001=>100001111
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,9,10,5]=>111000001=>100000111
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,9,10,4]=>110000001=>100000011
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,6,9,8,7,2]=>00000111=>11100000
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7,10,9]=>100110101=>101011001
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,3,6,8,7,5,10,9]=>101001101=>101100101
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,5,8,10,9,7]=>101010011=>110010101
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,5,8,9,7,10,4,3,1]=>011010011=>110010110
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,11,10,9,8,7,6,5,4,2]=>0011111111=>1111111100
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7,9]=>00101010=>01010100
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,10,9,8,1]=>011011111=>111110110
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,1,9,10,8]=>000001001=>100100000
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,5,8,9,10,7]=>001010001=>100010100
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,3,4,6,7,8,10,9,5]=>000000011=>110000000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,8,10,9,6]=>000000011=>110000000
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,4,6,3,7,2,8,1,9]=>00011110=>01111000
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,5,7,4,8,3,9,2]=>00001111=>11110000
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,7,4,8,3,9,2]=>00000111=>11100000
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,9,10,5]=>101000001=>100000101
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,5,8,9,10,7]=>101010001=>100010101
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,1,7,8,9,10,6,5,4,3]=>101110001=>100011101
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,6,5,9,10,8,7]=>101010101=>101010101
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7,9]=>00101010=>01010100
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6,9,8,10]=>000101010=>010101000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6,9,8]=>00010101=>10101000
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6,9,8]=>00010101=>10101000
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6,9,8,10]=>000101010=>010101000
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,8,7,9]=>01001010=>01010010
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,3,6,2,7,1,8,9]=>00011100=>00111000
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,4,5,7,9,10,8,6]=>000000101=>101000000
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,6,8,9,7,4]=>00000101=>10100000
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,10,9,8,7,6,5,3]=>000111111=>111111000
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7,10,9]=>000010101=>101010000
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7,10,9]=>001010101=>101010100
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,12,10]=>01010101001=>10010101010
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,9,8,7,6,4,2]=>00101111=>11110100
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,5,10,9,8,7,6,4,2]=>001011111=>111110100
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,5,7,10,9,8,6,4,2]=>001010111=>111010100
Map
to 312-avoiding permutation
Description
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.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Map
reverse
Description
Return the reversal of a binary word.
searching the database
Sorry, this map was not found in the database.